{
    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  1  0  1 -1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  1  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0 0 0)
    (0 1 0 0 0 1 0 0)
    (0 0 1 0 0 0 0 1)
    (0 0 0 0 1 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0 -1  1 -1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1 -1 -1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0 -1  1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  0 -1  1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0 -1 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1 -1  0  0  0  1)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  0 -1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1 -1  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  1  0  0 -1 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  1  0  1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  0  1  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1 -1 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0 -1 -1 -1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1 -1 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0 -1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  0  1  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  1  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  0  1 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  1  0  0 -1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0 0 0)
    (0 1 0 0 0 0 1 0)
    (0 0 0 1 0 1 0 0)
    (0 0 0 0 1 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1  0  1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 1)
    (0 0 0 1 0 1 0 0)
    (0 0 0 0 1 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0 0 0)
    (0 1 0 0 0 0 1 0)
    (0 0 1 0 1 0 0 0)
    (0 0 0 0 0 1 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1 -1  0  0  0  1)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  1 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0 -1 -1  0 -1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  1  1  0  1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  1  0 -1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  1  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  1  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1 -1  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  1 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1  0  1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  1  0  0  1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0 -1  0 -1  1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  1  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  1 -1  1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0 -1  0  0  1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  0 -1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0 -1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  0 -1  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0 -1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  1  0 -1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  1 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  0 -1  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  1  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  0  1  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  1  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  1  0  1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  1  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  1  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  1  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0 0 0)
    (0 0 1 0 0 1 0 0)
    (0 0 0 1 0 0 1 0)
    (0 0 0 0 1 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  1  1  0 -1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1 -1  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  1  0  0  1 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0 0 0)
    (0 1 0 1 0 0 0 0)
    (0 0 0 0 1 0 1 0)
    (0 0 0 0 0 1 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0 -1  0 -1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 1 0)
    (0 1 0 0 0 0 0 1)
    (0 0 1 0 0 1 0 0)
    (0 0 0 1 1 0 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  0  1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1 -1  0  0  0  1  1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0 -1 -1  0 -1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  0  1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  0 -1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  1 -1  1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  1  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1 0 0)
    (0 1 0 0 1 0 0 0)
    (0 0 1 0 0 0 1 0)
    (0 0 0 1 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0 -1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0 -1  1  1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  1 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0 -1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0 -1  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1 -1  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1 -1  0  1  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1 -1  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1 -1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  1  0 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0  1  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  0  1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1 -1  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1 -1  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0 -1  1  1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  1  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  1  0  0  0 -1 -1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  1 -1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0 -1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0 -1 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0 -1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0 -1 -1  1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  1  1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0 -1  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1 -1  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0 -1  0 -1  1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1 -1  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 1)
    (0 1 0 0 1 0 0 0)
    (0 0 1 1 0 0 0 0)
    (0 0 0 0 0 1 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  0 -1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1 -1  0  0  0 -1 -1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1 0 0)
    (0 1 0 0 0 0 0 1)
    (0 0 1 0 1 0 0 0)
    (0 0 0 1 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  1  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0 0 0)
    (0 1 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 1)
    (0 0 0 0 0 1 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0 -1 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  1  0  0  1  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  1  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1 -1  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  1  1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  1  0  1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  1  0  1 -1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  0 -1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  1  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0 -1  1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1 -1  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0 -1  1  0 -1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  1  0  0  0  1  1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  1 -1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1 -1  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  0  1 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  1  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0 -1 -1  0  1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  0 -1 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0 -1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  1  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1 -1 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0 -1  0 -1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  0  1 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  1  0  0  0 -1  1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1 -1  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1 -1  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0 -1  0  0 -1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  1 -1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0 -1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0 0 0)
    (0 1 0 0 1 0 0 0)
    (0 0 1 0 0 0 1 0)
    (0 0 0 0 0 1 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1 -1  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  1 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  1  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  0 -1 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  1  0  0  0 -1 -1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  0 -1  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1 -1  0  0  1 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 1 0)
    (0 1 0 1 0 0 0 0)
    (0 0 1 0 0 1 0 0)
    (0 0 0 0 1 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0 -1  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0 -1 -1  1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0 -1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  1  1  1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1 -1  0  0  0 -1  1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  0 -1  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  1  1  0  1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1 -1  0  1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  0 -1  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  1  0  1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0 0 0)
    (0 1 0 0 0 0 1 0)
    (0 0 1 1 0 0 0 0)
    (0 0 0 0 0 1 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  1 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1  0 -1  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0 -1  1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  1  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  1  1  0 -1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0 -1  1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  0 -1  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0 0 0)
    (0 1 0 0 0 0 0 1)
    (0 0 0 1 0 1 0 0)
    (0 0 0 0 1 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1 -1  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  1  0  0 -1  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1  0 -1  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0 -1 -1  0  1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0 0 0)
    (0 1 0 0 0 0 0 1)
    (0 0 1 0 1 0 0 0)
    (0 0 0 0 0 1 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  1  1  1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  1  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  1 -1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1 -1  0  0 -1 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0 -1  0  0 -1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  1 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  1  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  1 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 1 0 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1 -1  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0 -1  1 -1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  0  1  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  0  1  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1 0 0)
    (0 1 0 1 0 0 0 0)
    (0 0 1 0 1 0 0 0)
    (0 0 0 0 0 0 1 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  1  0 -1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  1  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  1  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0 -1  0 -1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  1 -1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1 -1  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0 0 0)
    (0 1 0 0 0 1 0 0)
    (0 0 0 1 0 0 1 0)
    (0 0 0 0 1 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0 -1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 1)
    (0 1 0 0 0 0 1 0)
    (0 0 1 1 0 0 0 0)
    (0 0 0 0 1 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0 -1  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0 -1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0 -1  1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0 0 0)
    (0 0 1 1 0 0 0 0)
    (0 0 0 0 1 0 0 1)
    (0 0 0 0 0 1 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  1 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0 -1  0  0 -1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  0  1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0 -1  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  0  1 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1 -1 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1  1  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  1  0  0  1  1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  1  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  1  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  1  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  1  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1 -1  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  1 -1 -1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 0 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  0 -1  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0 -1 -1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0 -1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  0 -1 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1 -1  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0  0 -1  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0 -1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  0  1  0  1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  1  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  1  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  1  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0 -1  0  0 -1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0 -1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 0 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  0 -1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  1  0 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  1 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1 -1 -1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  1  0  1  1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0 -1  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  1 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  0  1  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  1  0  0  1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0 -1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0 -1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0 -1  0  0 -1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0 -1  1 -1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  0  1  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  0  1 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0 -1  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  0 -1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1 -1 -1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  1  1  0  1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  0  1  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0 -1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  1  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  1  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0 -1 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0 -1  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  1  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  0 -1 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1 -1  1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 1)
    (0 1 0 0 1 0 0 0)
    (0 0 1 0 0 1 0 0)
    (0 0 0 1 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  1  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  1 -1  0  1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0 -1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0 -1  0 -1 -1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  1 -1 -1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 1 0)
    (0 1 1 0 0 0 0 0)
    (0 0 0 1 0 1 0 0)
    (0 0 0 0 1 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  1 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  1 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1 -1  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0 -1  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0 -1 -1  1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0 -1  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1 -1  0  0  0  1 -1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  1  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  1  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1 -1  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 0 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  0  1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1 -1  1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  1  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  1  1  0 -1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1  0 -1  0  1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1  0 -1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  0  1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1 -1  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1 -1  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  1  0  0 -1 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0 -1  0 -1 -1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1 -1  0  0  0  1)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0 -1 -1  0 -1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  1  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0 0 0)
    (0 1 0 0 0 0 0 1)
    (0 0 1 1 0 0 0 0)
    (0 0 0 0 0 1 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 0 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 0 1 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1 -1  0  0  1  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  1 -1 -1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  1  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  1  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  1  0 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0 -1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0 -1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0 -1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  1 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  0 -1  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1 0 0)
    (0 1 1 0 0 0 0 0)
    (0 0 0 1 1 0 0 0)
    (0 0 0 0 0 0 1 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  1  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0  0  1  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0 0 0)
    (0 1 0 0 0 0 1 0)
    (0 0 1 0 0 1 0 0)
    (0 0 0 1 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  0  1  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1 -1 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  1  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  1 -1 -1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1 -1 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  1  0  0  1  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1 0 0)
    (0 1 0 0 0 0 0 1)
    (0 0 1 0 0 0 1 0)
    (0 0 0 1 1 0 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  1  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  1  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0 -1  0  1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  0  1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  0  1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0 -1  0  0  1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  1  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1 -1  0  0 -1  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0 -1  0 -1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  0  1  1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 1)
    (0 1 0 0 0 1 0 0)
    (0 0 1 0 1 0 0 0)
    (0 0 0 1 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1 -1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  1  1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1 -1 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1 -1  0  0  1  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  1  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0 -1  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  1  1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  1 -1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0 0 0)
    (0 0 1 0 0 1 0 0)
    (0 0 0 1 0 0 0 1)
    (0 0 0 0 1 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0 -1  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  1 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0 0 0)
    (0 1 0 1 0 0 0 0)
    (0 0 0 0 1 0 0 1)
    (0 0 0 0 0 1 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  1  0  0  1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1 -1  0 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  0  1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  1  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1 -1  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  1  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1 -1  1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  0  1 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0 -1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  1 -1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  0  1  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  1 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1 0 0)
    (0 1 0 0 1 0 0 0)
    (0 0 1 0 0 0 0 1)
    (0 0 0 1 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  1  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  0  1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  1 -1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 1)
    (0 1 0 0 0 0 1 0)
    (0 0 1 0 0 1 0 0)
    (0 0 0 1 1 0 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1 -1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0 -1  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1 -1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0 -1  0  1  1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  0  0  1  1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0 -1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1 -1  0  0  0  1 -1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1  1  0  0  1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1 -1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0 -1  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 1 0)
    (0 0 0 1 1 0 0 0)
    (0 0 0 0 0 1 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  0  1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1 -1  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0 -1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0 -1 -1 -1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0 0 0)
    (0 1 0 0 0 0 0 1)
    (0 0 1 0 0 0 1 0)
    (0 0 0 0 1 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0 -1  1 -1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  1  0  1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1 -1 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  1  0 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  0 -1 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1 -1  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1 -1  0  0  0  1)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1 -1  0  0 -1 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0 -1  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  1  1 -1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1 -1 -1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  0  1  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 1 0)
    (0 1 0 0 0 1 0 0)
    (0 0 1 0 0 0 0 1)
    (0 0 0 1 1 0 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1 -1  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0 -1  0  1  1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1 -1 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  1  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1 -1  0 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  1  1  1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  0 -1 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0 -1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  1 -1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  0 -1  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1 0 0)
    (0 1 0 1 0 0 0 0)
    (0 0 1 0 0 0 1 0)
    (0 0 0 0 1 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  1 -1  0 -1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1 -1  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  1 -1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  1  1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1 -1  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 0 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 0 1 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0 -1 -1  0 -1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  1  1 -1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1 -1  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  1 -1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  0 -1  1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1 -1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  1 -1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1 -1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  1 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  1  0  0  1 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  0 -1  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0 0 0)
    (0 1 0 0 1 0 0 0)
    (0 0 1 0 0 0 0 1)
    (0 0 0 0 0 1 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  0 -1  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  1  0  0  1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  1  1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1 -1 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  0  1  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0  1  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  1  1 -1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  1 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  1  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 1 0 0 0 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  1  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  0 -1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  1  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  0  1  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0 -1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1 -1  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0 -1 -1 -1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  1  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1 -1  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  1  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0 -1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0 -1  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0 -1 -1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  1  0  1 -1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  1  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  1  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 1 0 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1 -1 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0 -1  0 -1  1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1 -1  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  1  0  0  0 -1  1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1 -1  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0 0 0)
    (0 1 0 0 0 0 0 1)
    (0 0 1 0 0 1 0 0)
    (0 0 0 1 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1 0 0)
    (0 1 0 0 0 0 1 0)
    (0 0 1 0 0 0 0 1)
    (0 0 0 1 1 0 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0 -1 -1  1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0 -1  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  1  0  0  0  1 -1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  0  1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0 -1 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1 -1  0  0  0  1  1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  1 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  0  1  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1 -1  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0 -1  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0 -1 -1  1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  1  0 -1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  1  1 -1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  1  1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1 -1  0  0  0  1 -1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0 0 0)
    (0 1 0 0 0 1 0 0)
    (0 0 0 1 0 0 0 1)
    (0 0 0 0 1 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0 -1 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1 -1  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0 -1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1 -1  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0 0 0)
    (0 0 1 0 1 0 0 0)
    (0 0 0 1 0 0 1 0)
    (0 0 0 0 0 1 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0 -1  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0 -1  1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0 -1 -1 -1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1 -1  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  1  0  0  1  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0  0  1  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  1  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0 -1  0 -1  1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  1  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  1  1  1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  0 -1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1 -1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  1 -1  0  1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0 0 0)
    (0 1 0 0 0 1 0 0)
    (0 0 1 0 0 0 1 0)
    (0 0 0 1 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 1 0 0 0 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  0 -1 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  1  1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1 -1  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  1  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  1  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  1 -1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  1  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  1  1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1 -1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0 -1  0  0  1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  1  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  0  1  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  0 -1  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  1  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0 -1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0  0  1  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  1  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0 0 0)
    (0 1 0 0 0 0 1 0)
    (0 0 0 1 1 0 0 0)
    (0 0 0 0 0 1 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 1 0 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  1  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  1  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0 0 0)
    (0 1 0 0 0 0 1 0)
    (0 0 1 0 0 0 0 1)
    (0 0 0 0 1 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0 -1 -1  1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1 -1  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 1)
    (0 0 0 1 1 0 0 0)
    (0 0 0 0 0 1 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  1 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  0 -1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  0  1  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  1  0  0 -1  1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0 -1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1 -1  0  1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1 0 0)
    (0 1 1 0 0 0 0 0)
    (0 0 0 1 0 0 1 0)
    (0 0 0 0 1 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0 -1  0  1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0 -1  0  0  1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  1 -1 -1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  1 -1 -1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0 -1 -1 -1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  1  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0 0 0)
    (0 1 1 0 0 0 0 0)
    (0 0 0 0 1 1 0 0)
    (0 0 0 0 0 0 1 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  1 -1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0 -1  0  1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  0 -1  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  0  1 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1 -1 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1 -1  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1 -1  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  1 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1 -1  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0 0 0)
    (0 1 0 1 0 0 0 0)
    (0 0 1 0 0 1 0 0)
    (0 0 0 0 0 0 1 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  1  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0 -1  0  1 -1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1 -1  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  0  1  1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  1  1  0 -1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  1  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0 -1  0  1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  1 -1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  1 -1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  1  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 1)
    (0 1 0 0 0 1 0 0)
    (0 0 1 0 0 0 1 0)
    (0 0 0 1 1 0 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0 -1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  0  1  1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  1  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  1  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0 -1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0 -1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1 -1  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  0  1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 1 0)
    (0 1 0 0 0 0 0 1)
    (0 0 1 0 1 0 0 0)
    (0 0 0 1 0 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  1  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1 -1  0  0  0  1  1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0  0 -1  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1 -1 -1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  0 -1  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0 -1 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  1  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0 -1  0  1 -1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1 -1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  1  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  1 -1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1 -1  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 1 0 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0 -1  0  0  1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  1  0  0 -1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0 -1 -1 -1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0 -1 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  1 -1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0 -1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 1)
    (0 1 0 1 0 0 0 0)
    (0 0 1 0 0 1 0 0)
    (0 0 0 0 1 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1 -1  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0 -1  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0 -1  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 0 0 1 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1 -1  1  0  0  0)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1 -1  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  0  1 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1 -1 -1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0 -1  0  1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  0  1  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  1  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  1  1 -1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  0  1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  1 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  1 -1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0 -1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  0  1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  1  0 -1 -1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  0 -1  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  1  0 -1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1 -1  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0 -1  0  1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1 -1  0  1  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  1 -1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0 -1 -1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1 -1  0  0 -1  1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  0 -1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  0  1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  1  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1 -1  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1  1  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0 -1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0 -1 -1 -1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  0 -1  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  0  1  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 1 0 0 0 0 0 0)
    (0 0 0 0 0 0 1 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0 -1 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0 0 0)
    (0 1 0 0 1 0 0 0)
    (0 0 0 1 0 0 1 0)
    (0 0 0 0 0 1 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1 -1 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1 -1 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  0  1  0  1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0 -1 -1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0 -1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  0 -1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1  0  1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1 -1 -1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0 -1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 1 0)
    (0 1 0 1 0 0 0 0)
    (0 0 1 0 1 0 0 0)
    (0 0 0 0 0 1 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1 -1  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  0  1  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1 -1  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0 -1  1  1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1 -1 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  0  1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1 -1  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 1 0 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0  0 -1  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1 -1  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  1  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  1  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1 -1  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 1 0 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1  0  1  0  1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  1  1 -1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0 -1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1 -1 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0 -1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0 -1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  1  0 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1 -1 -1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0 0 0)
    (0 1 0 0 0 0 0 1)
    (0 0 0 1 1 0 0 0)
    (0 0 0 0 0 1 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 0 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0 -1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1 -1 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1 -1  0  0  0 -1 -1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0 0 0)
    (0 1 1 0 0 0 0 0)
    (0 0 0 1 0 1 0 0)
    (0 0 0 0 0 0 1 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1 -1  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  0  1  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  1  1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0 -1  1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1 -1  0  0  1  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0 -1  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1 -1  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  1  1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  1  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  1 -1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  1 -1 -1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1 -1 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  1  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1 0 0)
    (0 1 0 1 0 0 0 0)
    (0 0 1 0 0 0 0 1)
    (0 0 0 0 1 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  0 -1  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 1 0 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 1 0 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1 -1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0 -1  1 -1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0 -1  1 -1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  0  1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0 -1 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0 -1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0 -1 -1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  1 -1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  1  1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0 -1  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1 -1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  1  0  0  1 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  1 -1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1 -1 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0 -1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1  1  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0 -1  1  1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  1  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  1  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1 -1  0  0  0 -1 -1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 1)
    (0 1 1 0 0 0 0 0)
    (0 0 0 1 0 1 0 0)
    (0 0 0 0 1 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  1  0  0 -1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1 -1 -1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1 -1  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1 -1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  1  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0 -1  0  0 -1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0 -1  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  1 -1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1 -1  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  1 -1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1 -1  0  1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1 -1 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0 -1 -1 -1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0 -1  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  1  1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 1)
    (0 0 0 1 0 0 1 0)
    (0 0 0 0 1 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0 -1 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  1  0  0  0  1)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0 -1  0 -1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 0 1 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0 -1  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1 -1  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0 -1  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  0 -1  1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0 -1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0 -1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  1  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0 -1  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  1  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  1 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1 -1  0  0  0 -1  1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0 -1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  1  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1 -1  0  0 -1 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  0  1  1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  1  0 -1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  1  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  1  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1 -1 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1 0 0)
    (0 1 0 0 1 0 0 0)
    (0 0 1 1 0 0 0 0)
    (0 0 0 0 0 0 1 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1 -1  0 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  1  0  0  0 -1 -1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1 -1  0  0  0 -1 -1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0 -1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0 -1  1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  1 -1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0 0 0)
    (0 0 1 1 0 0 0 0)
    (0 0 0 0 1 1 0 0)
    (0 0 0 0 0 0 1 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0 -1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1 -1  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1 -1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1 -1  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1 -1  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0 -1  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  0 -1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  1  1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  1  0 -1  1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  1  1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 1 0)
    (0 1 1 0 0 0 0 0)
    (0 0 0 1 1 0 0 0)
    (0 0 0 0 0 1 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  0  1  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  1  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  1  1  1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0 -1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0 0 0)
    (0 0 1 0 1 0 0 0)
    (0 0 0 1 0 0 0 1)
    (0 0 0 0 0 1 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1 -1  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  0 -1  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1 -1  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0 -1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0 -1  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0 -1  1  0  1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  1  0  0  1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  1  0  1  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1 -1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 1 0)
    (0 1 0 0 0 1 0 0)
    (0 0 1 1 0 0 0 0)
    (0 0 0 0 1 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  0  1 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0 0 0)
    (0 1 0 0 0 1 0 0)
    (0 0 1 0 0 0 0 1)
    (0 0 0 1 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  1 -1  0 -1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0 -1  0  1  1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  0 -1 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1 -1  1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0 -1  1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  0  1  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 1 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0 -1  0  1  1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  1  0  0  0  1)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0 -1 -1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  1  0  0  0 -1  1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0 -1 -1  1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1 -1  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  1 -1  0  1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0 -1 -1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0 -1  0 -1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  0 -1  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  1  0  1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0 -1  1 -1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  0 -1  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1 -1  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1 -1  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1 0 0)
    (0 1 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 1)
    (0 0 0 0 1 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1 -1  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0 -1 -1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  1  0  0  1  1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1 -1  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  1  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 1 0)
    (0 1 0 0 1 0 0 0)
    (0 0 1 0 0 0 0 1)
    (0 0 0 1 0 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0 -1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  1  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  1  1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 0 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1 -1  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0 -1  0 -1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1 -1 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  1  1  1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0 -1 -1  1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  1 -1  1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1 -1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0  0 -1  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  0 -1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0 -1  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1 -1  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1 -1  0  0  1  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0 -1  1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0 -1  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0 -1 -1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0 -1 -1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  1  0  0  0 -1  1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1 -1  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1 -1  0  0  1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  1 -1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  1  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  1  0 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0 -1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 0 1 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  1 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  1  1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  1  0  1  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  1  1  0  0  0)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0 -1  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0 -1  1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  1  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  1  0  0  1  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0 -1 -1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1 0 0)
    (0 1 0 0 0 0 1 0)
    (0 0 1 1 0 0 0 0)
    (0 0 0 0 1 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1 -1  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  1  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1 -1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1 -1  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 0 1 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0  0  1  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  0  0  1  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  1  1  1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0 -1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0 -1 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  0  1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0 -1  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 1)
    (0 1 0 0 0 0 1 0)
    (0 0 1 0 1 0 0 0)
    (0 0 0 1 0 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1 -1  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1 -1  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  0  1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  1  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1 -1  0  1  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  0 -1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 1 0)
    (0 0 0 1 0 0 0 1)
    (0 0 0 0 1 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  1  0 -1 -1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1 -1  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0 -1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0 0 0)
    (0 1 0 0 0 0 0 1)
    (0 0 0 1 0 0 1 0)
    (0 0 0 0 1 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1 -1  0  0  1 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1 -1  1  0  0  0)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0 -1 -1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0 -1  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  0  1  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1 -1  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0 -1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1 -1  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  1  1  0  0  0)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0 -1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  1  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  1  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1 -1  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1 -1  0  0  1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1 -1 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1 -1  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 1 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  1  1 -1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  1 -1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0 -1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0 0 0)
    (0 1 0 1 0 0 0 0)
    (0 0 0 0 1 1 0 0)
    (0 0 0 0 0 0 1 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  1  1  1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1 -1  0  0  1  1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1  0 -1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1 -1  0 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  1  0 -1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1 -1 -1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1 -1  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0 -1  1  0 -1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 1 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1 -1 -1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0 0 0)
    (0 1 0 0 1 0 0 0)
    (0 0 0 1 0 0 0 1)
    (0 0 0 0 0 1 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  1  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 1 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0 -1  1  1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1 -1  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  0  1  0  1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  1  1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1 -1  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  1  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1 -1  0 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  1 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0 -1  0  0 -1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0 -1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  1  0  0  0  1 -1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  1  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0 -1  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0 -1 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1 -1  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1 -1  1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  1  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1 -1  1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0 -1  0  1 -1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0 -1  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1 -1  0  0  1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  0 -1  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  1  0  1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  1  0  0 -1 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0 -1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1 -1  0  1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  1 -1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  1  0  1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  0 -1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0 -1 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  1 -1  1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1  0  1  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0 -1  1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1 -1  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1  0 -1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  1 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0 -1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0 -1  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1 -1 -1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1 -1 -1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0 -1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  1  1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  1  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  1  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  1  1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  1 -1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  1  0  1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  1  0  0  1 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0 -1  0 -1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  1  1 -1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1 -1  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0 0 0)
    (0 1 0 0 1 0 0 0)
    (0 0 1 0 0 1 0 0)
    (0 0 0 0 0 0 1 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  0 -1 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0 -1 -1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 1)
    (0 1 0 0 1 0 0 0)
    (0 0 1 0 0 0 1 0)
    (0 0 0 1 0 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 0 1 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1 -1  0  0 -1  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  1  0  0 -1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  1  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0 -1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0 -1  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1 -1  0  0 -1 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0 -1  0  1 -1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1 0 0)
    (0 1 0 0 0 0 0 1)
    (0 0 1 1 0 0 0 0)
    (0 0 0 0 1 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  1  0 -1 -1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  1  0  0  1  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1 -1  0 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1 -1  0  0  1  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  1  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  1  0  0  0  1  1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0 -1 -1  1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  0 -1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  0  1  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1 -1  1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0 -1  1  0  1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0 0 0)
    (0 1 0 0 0 0 1 0)
    (0 0 0 1 0 0 0 1)
    (0 0 0 0 1 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0 -1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1 -1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  1  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0 -1 -1 -1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0 -1 -1 -1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0 -1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1 -1  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1 -1  0  0  0  1  1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  1  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0 -1 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  1  0  0 -1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  1  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  0 -1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1 -1  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1 -1  0  0  1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1  1  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0 -1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1 -1  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 1 0 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  0 -1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0 -1 -1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0 0 0)
    (0 1 0 0 0 1 0 0)
    (0 0 1 0 1 0 0 0)
    (0 0 0 0 0 0 1 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1 -1  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1 -1  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1 -1 -1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0 -1  0  0  1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  1 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1 -1  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  1  0  0  1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  1  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1 -1  0  0  1 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  1 -1 -1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  0 -1  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0 -1 -1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1 -1  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0 -1 -1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  0  1 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  0  1 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  0 -1 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0 -1 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  0 -1  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  0  0  1  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0 0 0)
    (0 1 0 0 0 0 1 0)
    (0 0 1 0 0 1 0 0)
    (0 0 0 0 1 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1  0  1  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  1  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  1  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0 -1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0 -1  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  0  1  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  1 -1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  1 -1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1 -1  0  0  0  1 -1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  1  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  1 -1  0 -1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1 -1  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 1)
    (0 1 0 1 0 0 0 0)
    (0 0 1 0 1 0 0 0)
    (0 0 0 0 0 1 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0 -1 -1 -1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0 -1  1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1 -1 -1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  0 -1  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0 -1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1 -1  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  1  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  0 -1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  1  0  1  1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  1  0 -1  1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  1 -1  1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0 -1 -1  1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  1 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  1  0  1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  1  1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0 -1 -1  1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1 -1  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1 -1  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  0  1 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0 -1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0 -1  1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0 -1  0  0  1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  1  0  0  0  1  1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1 -1  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  0 -1  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  1 -1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0 -1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  1  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  0  1  1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0 -1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  1  0  0  0  1 -1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  1  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  1  1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0 -1  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  1 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0 -1  1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  1 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0 -1 -1 -1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1 -1  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 1 0)
    (0 1 0 1 0 0 0 0)
    (0 0 1 0 0 0 0 1)
    (0 0 0 0 1 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  0 -1  0  1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1  1  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  1  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  1 -1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1 -1 -1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  1  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0 -1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1 -1  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  0 -1  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1 -1 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  1  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  1  0 -1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  0 -1  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  0 -1  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1 -1  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1 -1  0  0 -1  1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0 -1  0  1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1  0 -1  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  1  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  1  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0 -1  1  0  1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  1  1  1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  0  1 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1 -1  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1 -1  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  0  1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  1  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  1  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 1 0 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  1  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0 0 0)
    (0 1 0 0 0 0 0 1)
    (0 0 1 0 0 0 1 0)
    (0 0 0 1 0 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  1  0  0 -1  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  1 -1  0  1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1  0  1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1 -1  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0 0 0)
    (0 1 0 0 0 1 0 0)
    (0 0 1 1 0 0 0 0)
    (0 0 0 0 0 0 1 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1 -1  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0 -1  1 -1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  1  0  0  1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  1  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  1  1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  1  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1 -1  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  1  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  1 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  0 -1 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1 -1 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1 -1 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0 -1  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1 -1  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0 -1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1 -1  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  1  0  0  0  1)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  0 -1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1 -1  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1  0  1  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0 -1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0 -1  1 -1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  0  1  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 1 0)
    (0 1 0 0 1 0 0 0)
    (0 0 1 1 0 0 0 0)
    (0 0 0 0 0 1 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  0 -1 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  1  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 1)
    (0 1 1 0 0 0 0 0)
    (0 0 0 1 1 0 0 0)
    (0 0 0 0 0 1 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0 -1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1 -1  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0 -1  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0 0 0)
    (0 1 0 0 0 0 0 1)
    (0 0 1 0 0 1 0 0)
    (0 0 0 0 1 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1 -1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  1 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  0  1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1 -1  1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 1)
    (0 1 0 0 0 1 0 0)
    (0 0 1 1 0 0 0 0)
    (0 0 0 0 1 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1 -1  1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  1  1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  1  0 -1  1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1 -1  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  1  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  1 -1 -1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0 -1  1  1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0 -1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1 -1 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0 -1  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0 -1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  1  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1 -1  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1 -1  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  1  1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0 -1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0 0 0)
    (0 1 1 0 0 0 0 0)
    (0 0 0 0 1 0 1 0)
    (0 0 0 0 0 1 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  1  0  0  1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0 -1  0  1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1 -1 -1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0 0 0)
    (0 1 0 1 0 0 0 0)
    (0 0 1 0 0 0 1 0)
    (0 0 0 0 0 1 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  1  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  1 -1  1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0 0 0)
    (0 1 0 0 0 1 0 0)
    (0 0 1 0 0 0 1 0)
    (0 0 0 0 1 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0 -1  1 -1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1 -1  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  0  1  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 1 0)
    (0 1 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 1)
    (0 0 0 0 1 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1 -1 -1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  1  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1 -1  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  1  0  0 -1 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  0  1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1 -1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1 -1  0  0  1  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1 -1 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  1  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  0 -1  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1  1  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  0 -1  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  1 -1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0 -1  1  1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  1  0 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  1  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  0  1 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  0 -1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1 -1  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1 -1  1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0 -1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  0 -1  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0 -1  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  1  0 -1 -1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0 -1  1  0 -1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  0  1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1 -1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  1  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1 -1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 1)
    (0 1 0 1 0 0 0 0)
    (0 0 1 0 0 0 1 0)
    (0 0 0 0 1 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  1  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  1  0  0  0  1 -1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  1 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  1  0  1 -1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1 -1  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  1 -1  0 -1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  1 -1  1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0 0 0)
    (0 1 0 0 0 0 1 0)
    (0 0 1 0 0 0 0 1)
    (0 0 0 1 0 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  1  0  0  0 -1 -1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1 -1  0 -1  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0 -1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0  1  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  1 -1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  1 -1  1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  1 -1  1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  1 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  0 -1  1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1 -1 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  1  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0 -1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  1  0 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  1  1 -1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  1  0  0  0  1)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  1  1 -1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  1  1  0  1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0 0 0)
    (0 0 1 0 1 0 0 0)
    (0 0 0 1 0 1 0 0)
    (0 0 0 0 0 0 1 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  1  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1 -1  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  0  1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1 -1 -1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  1 -1 -1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1 -1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  1  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  0 -1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1 -1  0 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1 -1 -1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1 -1 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1 -1  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  1  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  0  1  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0 -1 -1  0  1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0 -1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1 -1  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  1  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  1 -1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1 -1  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1 -1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  0  1 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1 -1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  1 -1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  0  1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0 -1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0 -1 -1  1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  0 -1 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0 -1  0  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  0  1  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1 -1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  1  0  0  1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1 -1 -1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1 -1  0  0  0 -1  1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1  0 -1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0 -1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1 -1  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1 -1  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0 -1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  1  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1  1  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 1 0)
    (0 1 0 0 1 0 0 0)
    (0 0 1 0 0 1 0 0)
    (0 0 0 1 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0 -1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1 -1  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  1  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  1 -1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  1  1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  1  0  1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0 -1  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  1 -1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0 0 0)
    (0 1 1 0 0 0 0 0)
    (0 0 0 1 0 0 1 0)
    (0 0 0 0 0 1 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  0  1  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  1  0  0  1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  1  0  1  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1 -1  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1 -1  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  1  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  1 -1  1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0 -1  1  1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  1  1 -1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  1 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  0  1  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  1  0  1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1  0 -1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  1  0  1  1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  0 -1 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0 -1  0  0  1 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  1  0  0  1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  1  1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0 0 0)
    (0 0 1 0 0 1 0 0)
    (0 0 0 1 1 0 0 0)
    (0 0 0 0 0 0 1 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  1  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0 -1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  1  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1 -1  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1 -1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0 -1  1 -1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1 -1  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1 -1  0 -1  0  1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1 -1  1  0  0  0)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1 -1  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  1  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  0 -1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  1  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0 -1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  0 -1  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1 -1  1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0 -1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 0 0 1 0 0 0)
    (0 0 0 0 0 0 1 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0 -1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0 -1  0  0 -1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  1 -1 -1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  1  0  0 -1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1 -1  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0 -1 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0 -1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  1  1  0  0  0)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1 -1  0  0  1 -1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  0 -1  0  1)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0 -1 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1 -1 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1 -1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  1  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0 -1  0 -1 -1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  0 -1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  1  1 -1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  1 -1  0  0  0)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0 -1  0 -1 -1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 1 0)
    (0 0 0 1 0 1 0 0)
    (0 0 0 0 1 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 1)
    (0 1 1 0 0 0 0 0)
    (0 0 0 1 0 0 1 0)
    (0 0 0 0 1 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  1  1  1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1  0 -1  0  1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  1  0  0 -1  1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0 -1  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1 -1  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1 -1  1)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1 -1  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1 -1  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  0  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1 -1 -1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  1  1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  1  0  0 -1 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  1  0  1  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1 -1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  1  1  1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  0  1  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0 -1 -1  0  1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  1  1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 1 0)
    (0 1 0 0 0 1 0 0)
    (0 0 1 0 1 0 0 0)
    (0 0 0 1 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  1  1  1  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  1 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1 -1  0  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0 -1  1  0 -1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  0  1  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  1  1 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0 -1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0 -1  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1 -1  0  0  1  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 1 0)
    (0 1 0 0 0 0 0 1)
    (0 0 1 1 0 0 0 0)
    (0 0 0 0 1 1 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1 -1  0  0  0 -1  1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  1  0 -1  1)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  0  1  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  1  0  0 -1  1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  1  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  1  1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  0 -1 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  1  0  0  1  1)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1 -1 -1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1 -1  0  0  1  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  1 -1  0  0  1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 0 0 0 1 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0 0 0)
    (0 1 0 0 1 0 0 0)
    (0 0 0 1 0 1 0 0)
    (0 0 0 0 0 0 1 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0 0 0)
    (0 0 0 0 0 1 0 0)
    (0 0 0 0 0 0 1 0)
    (0 0 0 0 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  0 -1 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  1  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1 -1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1 -1  0  0 -1  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  1  0  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0 0 0)
    (0 0 1 1 0 0 0 0)
    (0 0 0 0 1 0 1 0)
    (0 0 0 0 0 1 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  1  0  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  1  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1 -1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1  0  1  0 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0 -1 -1 -1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  1 -1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  1  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0 -1  1  1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  0  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1 -1  1  0  0  0)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0 -1  1  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 0 0 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1 -1  0  0  1  1)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0 -1  1 -1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  1  0  1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  0 -1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  1  0  1  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  1  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0 -1  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  1 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  1  1  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  1 -1  0  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0 -1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  1  0  0  0  1  1)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  1 -1  1)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  0 -1  1  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0 -1  1  1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1 -1  1  0  0  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0 -1  1  1  0)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  1  0  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  0  1  0  1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  1  0  0  0)
    ( 0  0  0  1  0 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1  0  1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1 -1 -1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  0  1  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  1  1  0  0  0)
    ( 0  0  0  0  0  1  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  1  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1  0  0)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1 -1  0 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1 0 0)
    (0 1 0 0 0 0 1 0)
    (0 0 1 0 1 0 0 0)
    (0 0 0 1 0 0 0 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  1  0  1  1)
    ( 0  0  0  1  0  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0 -1 -1  0 -1  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0 -1  1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  1  0  1  1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1 -1  0  0  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0  0  1 -1 -1)
    ( 0  0  1  0 -1  0  0  0)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0 -1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  0  0  1  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1 -1  0  0 -1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0 -1  0)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0 -1  0  0  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  0  1  0  1  0  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  1  1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  1 -1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0 0 0)
    (0 0 1 0 0 0 0 0)
    (0 0 0 1 0 0 0 0)
    (0 0 0 0 1 0 0 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0 -1  0 -1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  1  0  0  0  0  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  1  0  0  0  0)
    ( 0  0  0  0  1 -1  0  0)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0  1  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0 -1  0  0  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  1 -1)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  1  0  0)
    ( 0  0  0  1  0 -1  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0 0 0)
    (0 1 1 0 0 0 0 0)
    (0 0 0 0 1 0 0 1)
    (0 0 0 0 0 1 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  1  0  1  1  0  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1 -1  0  0  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  1  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  1  0 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  1 -1  0  0 -1)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  0  0  1  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1 -1 -1  0  1  0  0)
    ( 0  0  0  0  1  0  0  1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0 -1  0  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1 -1  0  0  1 -1  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  1  0 -1  0  0)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1  1 -1  0  0)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0 -1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1 -1 -1  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0 -1)
    ( 0  1  0  0  0  0  0  1)
    ( 0  0  1 -1  1  0 -1  0)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1  1  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  0  0  0  0  1)
    ( 0  0  0  1  0  0  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0  0  0)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  0  1  1  0  0  0)
    ( 0  0  0  0  0  1  0 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  1  0  0  1  0  0)
    ( 0  0  0  1  0  0  0  1)
    ( 0  0  0  0  1  0  0 -1)
    ( 0  0  0  0  0  0  1 -1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0 -1  1  1)
    ( 0  0  0  1 -1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0 0 0)
    (0 1 0 1 0 0 0 0)
    (0 0 1 0 0 0 0 1)
    (0 0 0 0 0 1 1 0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  0  1)
    ( 0  1  1  0  1  0  1  0)
    ( 0  0  0  1  0  0  0 -1)
    ( 0  0  0  0  0  1  0  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0  0  0)
    ( 0  1  0  0 -1  0  0  0)
    ( 0  0  1  0  0  1 -1  1)
    ( 0  0  0  1  1  0  0  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1  0 -1)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1 -1  0  1  1  0  0  0)
    ( 0  0  1  0  0  0  0 -1)
    ( 0  0  0  0  0  1  0 -1)
    ( 0  0  0  0  0  0  1  1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  1  1  0  0  0 -1)
    ( 0  0  0  0  1  0  1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1  0  0)
    ( 0  1  0  0  0  0  0 -1)
    ( 0  0  1  1  0  0  0  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0  0  1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  1  0  0 -1  0)
    ( 0  0  0  0  0  1 -1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0  1  0)
    ( 0  1  0  0  0  0  1  0)
    ( 0  0  1  0 -1  1  0  1)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0 -1  0)
    ( 0  1  0  1  0 -1  0 -1)
    ( 0  0  1  0  0  0  1  0)
    ( 0  0  0  0  1  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1  0 -1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0  1  0),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0 0 0)
    (0 1 0 0 0 1 0 0)
    (0 0 0 1 1 0 0 0)
    (0 0 0 0 0 0 1 1),

    Vector space of degree 8, dimension 4 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1  0  1)
    ( 0  1  0  0  0  0 -1  0)
    ( 0  0  1  0  0  0 -1  0)
    ( 0  0  0  1  0  0 -1  0)
}