{
    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1)
    ( 0  1  0  0  1  0)
    ( 0  0  1  2  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  1  0 -1 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 1 0 0)
    (0 0 1 0 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  2  0 -1)
    ( 0  0  1  0  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  0  2  2  1)
    ( 0  0  1  0  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  0  1  0  0  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 0)
    (0 1 0 1 0 1)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 1 0)
    (0 1 1 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0 -1)
    ( 0  0  1  0 -1  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -1)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (  1   0   0   0   0   0)
    (  0   1   0 1/2   1 1/2)
    (  0   0   1   1   0   0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0)
    (0 1 0 2 1 1)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 1 0 0)
    (0 0 1 0 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 1 0 0)
    (0 1 1 2 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  1  0  1  1  1)
    ( 0  0  1  0  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  1  2  2  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  1  0  2  2  1)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  1  1)
    ( 0  0  1  0  0 -1)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 0 1 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1)
    ( 0  1  0  0 -1 -1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  0  1  0  0)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0)
    ( 0  1  1  0 -2 -1)
    ( 0  0  0  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 2 0 0 0)
    (0 0 0 1 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 0 0 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 2 1 0)
    (0 1 0 0 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  0  1  1  0)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1)
    ( 0  1  0  1  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1)
    ( 0  1  0  2  1  0)
    ( 0  0  1 -1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  2  0  0  1)
    ( 0  0  0  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 1 0 0)
    (0 0 1 1 0 0)
    (0 0 0 0 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 3 2 1)
    (0 1 0 0 0 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0)
    ( 0  1  0  1  1  0)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0)
    (0 0 1 1 0 1)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 1 0 0)
    (0 1 1 2 2 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 1)
    (0 1 1 0 0 1)
    (0 0 0 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0)
    (0 1 1 1 0 0)
    (0 0 0 0 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -2 -1)
    ( 0  1  1  0 -2 -1)
    ( 0  0  0  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 1)
    (0 1 1 0 0 0)
    (0 0 0 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  1  2  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -3 -2 -1)
    ( 0  1  0  0  0  0)
    ( 0  0  1  3  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 1 1 0 1)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0 -1 -2)
    ( 0  0  1  0  0  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1)
    ( 0  1  1  0  0 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -2 -1  0)
    ( 0  1  0  1  1  1)
    ( 0  0  1  2  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  2  0 -1 -2)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 2 0 1)
    (0 1 0 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 1 0)
    (0 1 1 2 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -2)
    ( 0  1  1  0  0  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 1 2 0 0)
    (0 0 0 0 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1)
    ( 0  1  1  1  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  1  0 -1 -2)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0)
    ( 0  1  0  1  2  1)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1)
    ( 0  1  0  0 -1 -1)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0 -1 -1)
    ( 0  0  1  0  0  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  0 -1  0)
    ( 0  1  0  0  0 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 0 1 0 0 1)
    (0 0 0 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  1)
    ( 0  1  1  0 -1  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  1  0  0  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0 -1)
    ( 0  0  1  1  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 1)
    (0 0 0 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 1 0 1)
    (0 1 0 0 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1)
    ( 0  0  1  0  0  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 1)
    (0 0 1 0 1 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 0)
    (0 1 0 0 0 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  0  1  0 -1  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  1)
    ( 0  0  1  0  0  1)
    ( 0  0  0  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1)
    ( 0  1  0  0  0 -1)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  1)
    ( 0  1  1  0  0  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  1  1)
    ( 0  0  1  0  0  1)
    ( 0  0  0  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 0 1 0 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  1  1  0)
    ( 0  0  1  0 -1  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0)
    ( 0  1  0  1  0 -1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 1 1 0)
    (0 0 1 1 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 2 2 3 0 0)
    (0 0 0 0 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0  2  1  2)
    ( 0  0  1  0  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 1 0 0)
    (0 0 1 0 0 0)
    (0 0 0 0 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0)
    ( 0  1  1  0 -2 -1)
    ( 0  0  0  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0)
    ( 0  1  1  0 -1  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0)
    ( 0  1  1  0 -1  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0)
    ( 0  1  0  0 -1 -1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 2 1)
    (0 1 0 1 0 0)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 1 0 0)
    (0 1 1 2 0 0)
    (0 0 0 0 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0)
    ( 0  1  0  0 -1 -1)
    ( 0  0  1  2  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  1)
    ( 0  1  0  0 -1  0)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  2 -1)
    ( 0  1  0  1  1  0)
    ( 0  0  1  0 -1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0)
    ( 0  0  1  0 -1  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 1 1 2 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0)
    ( 0  1  1  0  1  2)
    ( 0  0  0  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  1)
    ( 0  0  1  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1)
    ( 0  1  1  0  1  1)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 2 0 0 0)
    (0 0 0 1 0 0)
    (0 0 0 0 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  2  1)
    ( 0  1  0  1  2  1)
    ( 0  0  1  0 -2 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 2 0 1)
    (0 1 0 0 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0  1)
    ( 0  0  1  0 -1 -1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -1)
    ( 0  1  0  0 -1  0)
    ( 0  0  1  2  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 1 0)
    (0 0 1 0 1 1)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  1)
    ( 0  1  0  0  0 -1)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0)
    ( 0  1  0  1  1  0)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (  1   0   0   0   0   0)
    (  0   1   0   1   1   0)
    (  0   0   1 1/2   0 1/2),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -2 -1  0)
    ( 0  1  0  0  0  0)
    ( 0  0  1  2  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 1)
    (0 1 0 0 1 0)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1)
    ( 0  1  0  1  1  1)
    ( 0  0  1  0  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1)
    ( 0  1  0  0  0  0)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0)
    (0 1 1 0 1 1)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0)
    ( 0  1  0  1  0  1)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  0  1  0  0  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 1 0)
    (0 0 1 0 0 1)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 2 1)
    (0 1 0 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 1)
    (0 1 0 0 0 0)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -2 -3)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  0  1  0  0)
    ( 0  0  1  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0)
    (0 1 1 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1 -1)
    ( 0  0  1  0  1  1)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -1)
    ( 0  1  0  0  0  0)
    ( 0  0  1  2  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  1  0  1  0  0)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  1  0  1  0  1)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0)
    ( 0  1  1  2  2  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  1  1  0  1  1)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  1  1  0  0 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  0 -1 -1)
    ( 0  1  0  0  0  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0)
    ( 0  1  1  0 -1 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  2  0  0 -2)
    ( 0  0  0  1  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  0  1  0  0  1)
    ( 0  0  0  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 0 1 0 1 1)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 0 1 0 1 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1)
    ( 0  1  1  0 -1  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1)
    ( 0  0  0  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  0  0 -1 -1)
    ( 0  0  1  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  1)
    ( 0  0  1  0 -1 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0)
    ( 0  1  0  2  2  1)
    ( 0  0  1  0 -1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0  1)
    ( 0  0  1  0 -1  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 1 1 0)
    (0 0 1 1 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1)
    ( 0  1  0  0  1  1)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  1  0  0  0  0)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 1)
    (0 1 0 1 1 1)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 1 1)
    (0 1 1 0 1 1)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 0)
    (0 1 1 1 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 1 0 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 0 1 0 0 0)
    (0 0 0 0 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0)
    ( 0  1  0  1  2  1)
    ( 0  0  1  0 -1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1)
    ( 0  1  0  0  1  1)
    ( 0  0  1  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 1 1 0)
    (0 0 1 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -2  1)
    ( 0  1  0  1  1  0)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  1  1  0  2  1)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 2 1)
    (0 1 0 0 0 0)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1)
    (0 1 1 0 0 0)
    (0 0 0 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  1  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1)
    ( 0  1  1  2  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 1 1 1)
    (0 0 1 1 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  2  0 -2)
    ( 0  0  1  0  0  1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 0)
    (0 1 1 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1)
    ( 0  1  1  0  0 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 1 1)
    (0 1 1 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0 -1)
    ( 0  1  1  2  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0)
    ( 0  1  0  0  0  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 2 1 0)
    (0 1 0 1 1 1)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0 -1)
    ( 0  0  1  0  1  0)
    ( 0  0  0  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  1  0  0  0 -1)
    ( 0  0  1  2  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  0  1  1  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0 -1)
    ( 0  0  1  0  1  0)
    ( 0  0  0  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0)
    (0 1 1 2 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 1)
    (0 1 0 2 1 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0)
    ( 0  1  0  0  1  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  1  0 -1)
    ( 0  0  1  0  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  1  0 -1)
    ( 0  0  1  0  0  1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  1  0  0  0  0)
    ( 0  0  1  2  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 2 0 0)
    (0 0 1 0 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  1  0  0  0  1)
    ( 0  0  1  2  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0 -1 -1)
    ( 0  0  1  0 -1  0)
    ( 0  0  0  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 2 0 1 0 0)
    (0 0 1 1 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0)
    ( 0  1  0  0  0 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  2  0  2)
    ( 0  0  1  0  0 -1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1 -1)
    ( 0  0  1  0 -1  0)
    ( 0  0  0  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  2  0 -1)
    ( 0  1  1  1  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0)
    ( 0  1  0  1  1  0)
    ( 0  0  1  0 -1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 0)
    (0 1 0 2 1 1)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0)
    ( 0  1  0  0  0  0)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 1 1 0)
    (0 0 1 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  1  0 -1  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1)
    ( 0  1  0  1  1  0)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 1)
    (0 0 1 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1)
    ( 0  1  0  0  1  1)
    ( 0  0  0  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  0)
    ( 0  1  0  1  0 -1)
    ( 0  0  1  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  1  0  1  2  1)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (  1   0   0   0   0   0)
    (  0   1   0   1   0   0)
    (  0   0   1 1/2   1 1/2),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1)
    (0 1 1 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 1)
    (0 1 0 0 0 0)
    (0 0 1 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  0  1  1  0)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  1  0  0)
    ( 0  0  1  0  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 2 1 0)
    (0 1 1 1 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0)
    ( 0  1  1  0  1 -1)
    ( 0  0  0  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 1 0 0)
    (0 0 1 1 0 1)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1)
    ( 0  1  0  0  0 -1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 1 0 0)
    (0 0 1 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  2)
    ( 0  1  0  1  0  0)
    ( 0  0  1  0  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  1  0  1  0 -1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  0  1  1  0)
    ( 0  0  1  0  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1 -1)
    ( 0  0  1  0 -1  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0)
    (0 1 1 1 0 1)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (  1   0   1   0   0   0)
    (  0   1 1/2   0   1 1/2)
    (  0   0   0   1   0   0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0)
    (0 1 1 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  1  2  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  1  0  1  0  0)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1)
    ( 0  1  1  0 -1 -2)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  2)
    ( 0  1  0  1  1  1)
    ( 0  0  1  0  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0)
    (0 0 1 2 0 1)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  2)
    ( 0  1  1  0  1  2)
    ( 0  0  0  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 2 2 0 1)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 1 1 0)
    (0 0 1 0 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  1  0  2  2  1)
    ( 0  0  1  0  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  1  1  1  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1)
    ( 0  1  0  0  0  1)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0)
    (0 0 1 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  1  1  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 1)
    (0 1 0 0 0 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 1 2 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 0 1 0 0 1)
    (0 0 0 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0 -1  0)
    ( 0  0  1  1  1  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0 -1)
    ( 0  0  1  1  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 2 0 1)
    (0 1 0 0 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  1  0  0  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1)
    ( 0  1  1  0  1 -1)
    ( 0  0  0  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 2 0 1 0)
    (0 0 0 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 2 1 0)
    (0 1 0 0 0 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (  1   0   0   0   0   0)
    (  0   1   0 3/2   1 1/2)
    (  0   0   1   0   0   0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  2  3  0)
    ( 0  0  1  0 -1  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 1 1 0)
    (0 1 1 2 2 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1 -1)
    ( 0  1  1  0 -2 -1)
    ( 0  0  0  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 1 0 0)
    (0 0 1 1 2 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0  0)
    ( 0  0  1  2  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1 -1)
    ( 0  1  0  0  1  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0)
    ( 0  0  1  0 -1 -1)
    ( 0  0  0  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0 -1  0)
    ( 0  0  1  0 -1 -1)
    ( 0  0  0  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  1)
    ( 0  1  0  1  0  0)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 2 0 0)
    (0 0 1 0 0 0)
    (0 0 0 0 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (   1    0    0    0    0    0)
    (   0    1    0  1/2    0 -1/2)
    (   0    0    1    1    1    1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1)
    ( 0  1  1  2  0  0)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 1)
    (0 1 1 2 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 1 0 0)
    (0 0 1 0 0 1)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 1 0 0)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -2 -1)
    ( 0  1  0  1  2  1)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  1  0  0)
    ( 0  0  1  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 1 0 0)
    (0 0 1 0 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  1)
    ( 0  1  0  1  1  0)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 0 1 1 0 1)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1)
    ( 0  1  0  0 -1  0)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 1 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0)
    (0 0 0 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 1 1)
    (0 0 1 0 1 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0)
    ( 0  1  1  2  1  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 1 0 0)
    (0 0 1 0 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0 -1  0)
    ( 0  0  1  0  0 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 1 0 0)
    (0 1 1 2 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0  1)
    ( 0  0  1  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0  1  1  1)
    ( 0  0  1  0  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1 -1)
    ( 0  1  0  1  0  0)
    ( 0  0  1  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0)
    ( 0  1  0  0  1  1)
    ( 0  0  1  2  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  2  0  0 -1 -2)
    ( 0  0  1  0  0  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 3 2 0)
    (0 1 0 0 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 1)
    (0 1 1 0 1 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 3 0 1)
    (0 1 0 0 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1)
    ( 0  1  0  0  0  0)
    ( 0  0  1  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0 -1)
    ( 0  0  1  0 -1 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1 -1)
    ( 0  1  0  1  1  0)
    ( 0  0  1  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  0  1  0 -1 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 2 0 0 0)
    (0 0 0 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0)
    ( 0  1  0  0  0  0)
    ( 0  0  1  2  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 1 0 0)
    (0 1 0 1 0 0)
    (0 0 0 0 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 1)
    (0 1 1 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  0 -1  0)
    ( 0  1  0  0  0  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1)
    ( 0  0  1  0  1  1)
    ( 0  0  0  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  0 -1  0)
    ( 0  1  0  0  0  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0  1)
    ( 0  0  1  0  1  1)
    ( 0  0  0  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0)
    (0 1 0 1 1 0)
    (0 0 1 1 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -2 -1)
    ( 0  1  0  0  0  0)
    ( 0  0  0  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0)
    ( 0  1  0  2  1  1)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0)
    ( 0  1  1  2  2  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  0)
    ( 0  1  0  0  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  0  1  0  0  0)
    ( 0  0  0  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  1  0 -1  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  0  2  1  1)
    ( 0  0  1  0  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  1  0  0  0 -1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0)
    ( 0  0  0  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0  0)
    ( 0  0  1  0 -1  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 1 0 0 2 1)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  0  1  0  0  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  1)
    ( 0  1  0  0 -1  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  2  0 -1  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0)
    ( 0  0  1  0 -1  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  1  0  1  0  0)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  2  3)
    ( 0  1  0  1  1  1)
    ( 0  0  1  0 -1 -2),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0  2  0 -1)
    ( 0  0  1  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  0 -1 -1)
    ( 0  1  0  0  0  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1)
    ( 0  1  0  0  0 -1)
    ( 0  0  1  2  1  2),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0)
    ( 0  0  1  1  1  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 0 0 0)
    (0 0 0 1 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -2  0)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1 -1)
    ( 0  1  0  0  0  0)
    ( 0  0  0  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0  0  1  2)
    ( 0  0  1  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -2  0)
    ( 0  1  0  1  1  0)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  3  0 -1)
    ( 0  1  0  0  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  1)
    ( 0  0  1  0  0 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 0 0 1)
    (0 1 0 0 1 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  0  0  1  1)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  1  0  1)
    ( 0  1  0  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0)
    ( 0  1  0  1  0 -1)
    ( 0  0  1  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  1)
    ( 0  1  0  0  0  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0)
    (0 0 0 0 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 2 1 1)
    (0 1 0 1 1 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0)
    ( 0  1  1  0 -1  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0)
    (0 0 1 0 0 0)
    (0 0 0 0 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0 -1 -2 -1)
    ( 0  0  1  2  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 0 1 0 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 1 0 2 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1)
    ( 0  1  1  2  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  0  0 -1 -1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  1  0  0 -1  0)
    ( 0  0  1  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 1 1 0)
    (0 0 1 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 1)
    (0 1 0 2 1 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 0 2 1)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (  1   0   0   0   0   0)
    (  0   1   0   0   0   0)
    (  0   0   1 3/2   1 1/2),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0)
    ( 0  1  0  2  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (   1    0    0    0    0    0)
    (   0    1    0    1    1    1)
    (   0    0    1  1/2    0 -1/2),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  1  0)
    ( 0  0  1  0  0 -1)
    ( 0  0  0  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0)
    ( 0  1  0  1  1  0)
    ( 0  0  1  0 -1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1)
    ( 0  1  0  1  1  0)
    ( 0  0  1  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0)
    ( 0  1  0  0 -1 -1)
    ( 0  0  0  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  1  0  0  0  0)
    ( 0  0  1  2  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  0)
    ( 0  0  1  0  0 -1)
    ( 0  0  0  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (  1   0   1   1   0   0)
    (  0   1 1/2   1   0 1/2)
    (  0   0   0   0   1   0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1)
    ( 0  1  0  1  0  1)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0 -1)
    ( 0  1  1  2  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1)
    ( 0  1  1  0  0  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0)
    ( 0  1  0  0  1  2)
    ( 0  0  0  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0)
    (0 0 1 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0  2  3  1)
    ( 0  0  1  0 -1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1)
    ( 0  1  0  0  1  1)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 1 0 0)
    (0 0 0 0 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0)
    ( 0  0  0  1  1  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 1 0)
    (0 1 0 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 1 2 0)
    (0 0 1 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  0  1  0  1  1)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  0  1  0 -1  0)
    ( 0  0  0  1  1  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1)
    ( 0  0  0  1  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0)
    ( 0  1  0  0  0 -1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 0 1 0)
    (0 1 0 0 1 1)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  2  0 -1)
    ( 0  1  0  0  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  0  1  0  0 -1)
    ( 0  0  0  1  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1)
    ( 0  1  0  1  0 -1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 2 0)
    (0 1 1 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 2 1)
    (0 1 1 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -1)
    ( 0  1  0  0  0  0)
    ( 0  0  1  2  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1)
    ( 0  1  0  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1)
    ( 0  1  0  0 -1 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 0 1 0)
    (0 1 0 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0)
    (0 1 0 1 0 0)
    (0 0 1 1 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  0  1  1  0  0)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -1)
    ( 0  1  0  0  1  0)
    ( 0  0  1  2  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1)
    ( 0  1  0  0 -1  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 1 0 0)
    (0 1 0 0 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -2 -2)
    ( 0  1  0  1  1  0)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 0 1 0 0 0)
    (0 0 0 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  0  0  0 -1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -2 -2)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1)
    (0 1 1 2 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 0 0 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1 -1)
    ( 0  0  1  0 -1  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 2 1 0)
    (0 0 1 0 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 1 0 0)
    (0 1 0 0 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1)
    (0 0 1 0 0 0)
    (0 0 0 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1 -1)
    ( 0  1  1  0 -1  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  0  1  0  1  0)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 2 1 1)
    (0 1 0 0 0 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0  2  1 -1)
    ( 0  0  1  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  1  1  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 1 1 1 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0)
    (0 1 0 0 0 0)
    (0 0 1 1 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -2 -1)
    ( 0  1  0  0 -1 -1)
    ( 0  0  1  2  3  2),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 1 1 0)
    (0 1 0 1 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  1  0  1  0  0)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0 -1)
    ( 0  0  1  1  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  2)
    ( 0  0  1  0 -1 -2)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 0 0 1)
    (0 1 0 0 0 0)
    (0 0 0 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0)
    ( 0  1  0  0  0 -1)
    ( 0  0  1  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -2 -1)
    ( 0  0  1  0  1  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0)
    ( 0  1  1  0  1 -1)
    ( 0  0  0  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 1 0 1 0 1)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 1 1 0)
    (0 1 0 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0 -1 -1)
    ( 0  0  1  0  0 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  0  0 -1  0)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1)
    (0 1 0 1 1 0)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1 -2)
    ( 0  1  0  0  0  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 2 0 1)
    (0 1 1 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0)
    ( 0  1  0  1  0  0)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1)
    ( 0  1  1  0 -1 -2)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1)
    ( 0  1  1  0 -1 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  2)
    ( 0  1  0  0  0  0)
    ( 0  0  1  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  1  1  2  0  0)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  1  1  2  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0)
    ( 0  1  0  0 -1 -2)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1)
    ( 0  1  1  2  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (   1    0    1    0    0    0)
    (   0    1  1/2    0 -1/2   -1)
    (   0    0    0    1    1    1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 1 0 1)
    (0 0 1 0 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0)
    ( 0  1  1  0  0 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  1  0)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  0  1  1)
    ( 0  1  0  0 -1  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1)
    (0 0 1 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 0 0 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 1 0 1)
    (0 1 1 2 0 1)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1 -1)
    ( 0  1  0  0  0  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  0  1  0  0)
    ( 0  0  1  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 1 0 1)
    (0 1 1 2 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0  0)
    ( 0  0  1  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -2 -1)
    ( 0  1  0  1  0  0)
    ( 0  0  1  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 2 0 0)
    (0 0 1 0 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 0 1 0 0 0)
    (0 0 0 0 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 0 0 0 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1 -1)
    ( 0  1  1  0  1 -1)
    ( 0  0  0  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 1)
    (0 1 0 0 1 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 2 0 2 0)
    (0 0 0 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0)
    (0 1 0 1 0 0)
    (0 0 1 0 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 1 1 0 0 0)
    (0 0 0 1 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0  0)
    ( 0  0  1  0  1  2)
    ( 0  0  0  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0)
    ( 0  1  0  0  0 -1)
    ( 0  0  0  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0)
    ( 0  0  1  0  1  2)
    ( 0  0  0  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  1  0)
    ( 0  1  0  0 -1  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 1 0 0)
    (0 0 1 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 0)
    (0 0 1 0 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  2)
    ( 0  1  0  0  0  0)
    ( 0  0  0  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  1  0  0  1  0)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 1 0 0)
    (0 1 0 1 0 1)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 1 0 0)
    (0 1 0 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0  0 -1 -2)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  2  1)
    ( 0  1  0  0 -1 -1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0)
    (0 1 0 1 1 0)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  2  0  0 -1  1)
    ( 0  0  1  0  0  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  2  1)
    ( 0  1  0  1  0  0)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  2  1)
    ( 0  1  0  2  2  1)
    ( 0  0  1 -1 -2 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0)
    (0 1 0 1 0 0)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -1)
    ( 0  1  0  1  2  1)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  1)
    ( 0  1  0  1  0  1)
    ( 0  0  1  0  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  0  2  1  0)
    ( 0  0  1  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1)
    ( 0  1  0  0 -1  0)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 1 0)
    (0 0 0 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0 -1  0)
    ( 0  0  0  1  1  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0)
    ( 0  0  1  0  0 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1)
    (0 1 0 0 1 0)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  0  0 -1)
    ( 0  1  0  0  1  1)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0 -1)
    ( 0  0  0  1  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  1)
    ( 0  1  0  1  1  1)
    ( 0  0  1  0  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  1)
    ( 0  1  1  0  1  2)
    ( 0  0  0  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0 -1)
    ( 0  1  0  1  0 -1)
    ( 0  0  1  0  1  2),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  1  0  0)
    ( 0  1  0  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0  1  1  1)
    ( 0  0  1  0 -1 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 2 1)
    (0 0 1 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  0  1  1  1)
    ( 0  0  1  0  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 1 1 1 0 0)
    (0 0 0 0 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  2  2  0 -1  0)
    ( 0  0  0  1  1  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 1 0)
    (0 1 0 0 1 1)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  2  0 -1)
    ( 0  1  0  0  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  2)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 0 0 0)
    (0 0 0 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 2 1)
    (0 1 1 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  0  0  1  0)
    ( 0  0  1  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  2)
    ( 0  0  1  0  0 -1)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -1)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 1 0)
    (0 1 0 0 0 1)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1)
    (0 1 0 1 1 1)
    (0 0 1 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  0  0 -1)
    ( 0  1  0  0 -1 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1)
    (0 1 0 1 1 0)
    (0 0 1 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -2 -1)
    ( 0  1  0  0  0  0)
    ( 0  0  1  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 0 0 1 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -2  0)
    ( 0  1  1  2  2  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0)
    (0 0 1 0 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0 -1  0  1)
    ( 0  0  1  2  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0 -1)
    ( 0  1  0  2  1  1)
    ( 0  0  1  0  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 3 2 1)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  1  0  1  0  0)
    ( 0  0  1  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  2  0  0  2)
    ( 0  0  0  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1 -1)
    ( 0  1  1  0  0  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1 -1)
    ( 0  1  0  0  0 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -2 -2 -1)
    ( 0  1  0  0  0  0)
    ( 0  0  1  2  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  0  1  0)
    ( 0  1  0  0 -1 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0)
    ( 0  1  0  0 -2 -1)
    ( 0  0  0  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1)
    ( 0  0  1  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1)
    ( 0  1  0  0 -1  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1)
    ( 0  1  0  2  1  0)
    ( 0  0  1  0  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0  0)
    ( 0  0  1  0 -1 -2)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 1)
    (0 0 1 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -1)
    ( 0  1  0  1  0 -1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0)
    ( 0  0  1  0 -1 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1 -1)
    ( 0  0  1  0  0  1)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0)
    (0 0 1 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1)
    (0 1 0 1 1 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0  1)
    ( 0  0  0  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0)
    (0 0 0 1 0 1)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0)
    (0 1 0 0 1 1)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 0 1 1)
    (0 1 0 0 1 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 1 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1)
    ( 0  1  0  1  1  1)
    ( 0  0  1  0 -1 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0)
    ( 0  1  0  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1)
    ( 0  1  0  0  1  0)
    ( 0  0  0  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0)
    (0 1 0 0 0 1)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 0 1 1)
    (0 1 0 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  1  0  0  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  1  0  0  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0 -1)
    ( 0  1  0  0  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0 -1)
    ( 0  1  0  0  0  1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0)
    (0 1 0 1 0 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 1 1 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1)
    ( 0  0  0  1  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 2 2 1)
    (0 1 0 1 0 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -2 -1 -1)
    ( 0  1  0  0  0  0)
    ( 0  0  1  2  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  0  1  0  0 -1)
    ( 0  0  0  1  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 0 0 0)
    (0 0 1 2 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0 -1  0)
    ( 0  0  1  0  0  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  1)
    ( 0  0  1  2  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1 -1)
    ( 0  1  0  0 -1  0)
    ( 0  0  0  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1)
    ( 0  1  0  0  1  1)
    ( 0  0  1  2  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  1  0 -1)
    ( 0  1  0  1  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0  0 -2 -1)
    ( 0  0  1  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  2)
    ( 0  0  1  0  0  0)
    ( 0  0  0  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  2  0 -1)
    ( 0  1  0  1  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0 -1  0)
    ( 0  0  1  0  1  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  1  2)
    ( 0  0  1  0  0  0)
    ( 0  0  0  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  0  1  1  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0)
    (0 1 0 1 2 1)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1)
    ( 0  0  1  0  0 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -2)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  0  1  1  0)
    ( 0  0  1  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0  1  1  0)
    ( 0  0  1  0 -1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1)
    ( 0  1  1  2  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0)
    (0 0 1 0 0 0)
    (0 0 0 1 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 0 0 0 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 0)
    (0 1 0 1 1 0)
    (0 0 1 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0  0)
    ( 0  0  1  0  1 -1)
    ( 0  0  0  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -1)
    ( 0  1  0  2  1  0)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -2 -1)
    ( 0  1  0  0 -1  0)
    ( 0  0  1  2  3  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 1 0 0 0)
    (0 0 0 1 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0)
    ( 0  0  1  0  1 -1)
    ( 0  0  0  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -1)
    ( 0  1  0  1  0  1)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  2  0 -1)
    ( 0  0  1  0  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -2 -2 -1)
    ( 0  1  0  1  0  0)
    ( 0  0  1  2  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  0  1  0  0  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 1)
    (0 1 0 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1)
    ( 0  1  1  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 2 1 0)
    (0 1 0 1 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0)
    (0 1 0 1 0 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -1)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0)
    (0 1 0 0 0 1)
    (0 0 1 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0)
    (0 1 0 0 0 0)
    (0 0 1 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0 -1  0 -1)
    ( 0  0  1  2  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1  2)
    ( 0  0  1  0 -1 -1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -2)
    ( 0  1  0  1  0  0)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -2 -1)
    ( 0  0  1  0  1  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 0 0 1 0 0)
    (0 0 0 0 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (   1    0    1    1    0    0)
    (   0    1  1/2    1    0 -1/2)
    (   0    0    0    0    1    1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 0 1 0 1 0)
    (0 0 0 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (   1    0    1    0    0    0)
    (   0    1  1/2    0 -1/2  1/2)
    (   0    0    0    1    1    0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -2)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 1 0)
    (0 0 0 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0)
    ( 0  1  0  1  1  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0 -1)
    ( 0  0  1  2  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 2 3 0 0)
    (0 0 0 0 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0 -1)
    ( 0  1  0  1  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 1 0 2 0 1)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 2 0 1)
    (0 0 1 0 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 2 2 0)
    (0 0 1 0 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  1  1  2  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1)
    ( 0  1  0  1  0  1)
    ( 0  0  1  0  1 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 2 0 1 0 1)
    (0 0 1 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  1  0  2  1)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0)
    (0 1 0 0 0 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 2 2 1)
    (0 1 0 0 0 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  1)
    ( 0  1  0  1  0 -1)
    ( 0  0  1  0  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0  0)
    ( 0  0  1  0 -2 -1)
    ( 0  0  0  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 1 1 2 2 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  0  0)
    ( 0  0  1  0 -2 -1)
    ( 0  0  0  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0)
    ( 0  0  1  0 -1  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 0)
    (0 1 0 0 0 0)
    (0 0 1 1 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  1  0  1)
    ( 0  0  1  0  0 -1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -2 -1 -1)
    ( 0  1  0  1  1  0)
    ( 0  0  1  2  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0)
    ( 0  1  0  0  0  0)
    ( 0  0  1  2  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0 -1 -1)
    ( 0  0  1  0  1  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  2  0  1)
    ( 0  0  1  0  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0)
    (0 1 0 1 0 1)
    (0 0 1 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 1 2 0)
    (0 1 0 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0)
    (0 1 0 1 0 0)
    (0 0 1 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 1 1 0 0 0)
    (0 0 0 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 0 0 0)
    (0 0 1 2 2 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  1  0  1  0)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0  0  1 -1)
    ( 0  0  1  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 1)
    (0 1 0 1 1 1)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -2)
    ( 0  1  0  0  0  0)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -1  0)
    ( 0  0  1  0  1  0)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  1)
    ( 0  1  0  2  1  1)
    ( 0  0  1 -1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  0 -1 -1)
    ( 0  1  0  0  0 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  1  1  0  0  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  0)
    ( 0  1  0  0 -1 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 1)
    (0 1 0 1 0 0)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 2 0 1)
    (0 0 1 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  1)
    ( 0  1  0  0  0  1)
    ( 0  0  1  2  1 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  2  1)
    ( 0  1  0  0 -1  0)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0  0 -1  1)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  0  0  1)
    ( 0  1  0  0 -1  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  0  1  1  0)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  0  1  1  1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 0 1 0 0 0)
    (0 0 0 1 0 1)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 0 0 1 0 1)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  1  0  0  0  1)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 1 0 0)
    (0 1 0 0 0 1)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 2 2 1 0)
    (0 1 0 0 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  2  2)
    ( 0  1  0  1  1  1)
    ( 0  0  1  0 -1 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  1  0  1  0  0)
    ( 0  0  1  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  2  2)
    ( 0  1  0  1  1  0)
    ( 0  0  1  0 -1 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0)
    (0 0 1 0 1 1)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (  1   0   1   1   1   0)
    (  0   1 1/2   1 1/2   0)
    (  0   0   0   0   0   1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0)
    (0 0 1 0 1 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 1 1)
    (0 1 0 0 1 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 1)
    (0 1 0 0 1 0)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1)
    ( 0  0  1  0 -1 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0 -1)
    ( 0  0  0  1  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0 -2 -1)
    ( 0  0  1  0  0  0)
    ( 0  0  0  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0)
    (0 0 1 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1  0)
    ( 0  1  1  0  0  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -2 -1)
    ( 0  0  1  0  0  0)
    ( 0  0  0  1  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  1  0  1  1  0)
    ( 0  0  1  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0)
    ( 0  1  0  0  1 -1)
    ( 0  0  0  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 1 1 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 1 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1  0  0)
    ( 0  1  1  2  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  2  2  0  0 -1)
    ( 0  0  0  1  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1 -2)
    ( 0  1  1  0  0  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  0)
    ( 0  1  0  0 -1 -1)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0)
    (0 0 1 0 2 1)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 2 0 2 1)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1 -1)
    ( 0  1  0  1  1  0)
    ( 0  0  1  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 0)
    (0 1 1 2 0 0)
    (0 0 0 0 1 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  0  1  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  0)
    ( 0  1  0  0 -1  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1)
    ( 0  1  0  2  1  1)
    ( 0  0  1  0  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 1 0 2 1)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  0)
    ( 0  1  0  1  1  0)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1 -1)
    ( 0  1  0  1  0  0)
    ( 0  0  1  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 2 2 0 0 1)
    (0 0 0 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1)
    ( 0  1  1  2  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (  1   0   0   0   0   0)
    (  0   1   0 1/2   0 1/2)
    (  0   0   1   1   1   0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  1  1)
    ( 0  0  1  0 -1  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1 -1)
    ( 0  1  0  0  0  0)
    ( 0  0  1  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  0  2  3  2)
    ( 0  0  1  0 -1 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  2)
    ( 0  1  1  0 -1 -2)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1 -1)
    ( 0  1  1  0  0  1)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0  0)
    ( 0  0  0  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1 -1)
    ( 0  1  0  2  1  0)
    ( 0  0  1  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1)
    ( 0  1  0  0  0  1)
    ( 0  0  1  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 1)
    (0 1 0 0 1 0)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 1)
    (0 0 0 1 0 0)
    (0 0 0 0 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  0  1)
    ( 0  1  1  0  1  2)
    ( 0  0  0  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0 -2 -1)
    ( 0  0  1  0  2  1)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  0  2  1  1)
    ( 0  0  1  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0 -1  0  0)
    ( 0  0  1  2  1  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 0 1)
    (0 1 1 0 1 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  0  0  1 -1)
    ( 0  0  1  0  0  0)
    ( 0  0  0  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  1)
    ( 0  1  0  1  1  0)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -2 -1)
    ( 0  1  1  0  2  1)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0)
    ( 0  1  0  1  0  0)
    ( 0  0  1  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  1)
    ( 0  1  1  0  0  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  1 -1)
    ( 0  0  1  0  0  0)
    ( 0  0  0  1  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 0)
    (0 1 0 0 1 1)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 0 0)
    (0 0 1 2 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 2 2 1 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  1)
    ( 0  1  0  1  1  1)
    ( 0  0  1  0 -1 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  0  0  0  1)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -1  1)
    ( 0  1  0  1  0  0)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0 -1  1)
    ( 0  0  1  0  0  0)
    ( 0  0  0  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -1  0)
    ( 0  1  0  1  1  1)
    ( 0  0  1  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 0)
    (0 1 0 0 0 0)
    (0 0 1 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 1)
    (0 1 0 2 1 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  1  0  1)
    ( 0  1  0  0  0 -1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  1  0  0  1  1)
    ( 0  0  1  1  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1 -2 -1)
    ( 0  1  0  1  0  0)
    ( 0  0  1  0  2  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 1)
    (0 1 0 1 0 0)
    (0 0 1 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  0  1  0  0 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  2  0)
    ( 0  1  0  1  1  0)
    ( 0  0  1  0 -1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  2  0)
    ( 0  1  0  1  1  1)
    ( 0  0  1  0 -1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 0 0 0 0)
    (0 0 1 2 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0 -1 -2 -1)
    ( 0  1  0  2  2  1)
    ( 0  0  1  0  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 2 0 0 2 1)
    (0 0 1 0 0 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0  1  1)
    ( 0  1  0  0  0  1)
    ( 0  0  0  1  0 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  1  2  0  0 -1)
    ( 0  0  0  1  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  1  0)
    ( 0  0  1  0 -1 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  0)
    ( 0  1  2  2  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  1  1)
    ( 0  1  0  1  2  1)
    ( 0  0  1  0 -1 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  2  0  0 -1)
    ( 0  1  0  0  0  0)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (0 1 0 0 1 0)
    (0 0 1 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 1 2 2 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  1  0  0)
    ( 0  1  1  1  0 -1)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0 -1  0)
    ( 0  0  1  1  1  0)
    ( 0  0  0  0  0  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0)
    (0 0 1 0 0 1)
    (0 0 0 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 0)
    (0 1 1 1 0 0)
    (0 0 0 0 0 1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 1 1)
    (0 1 0 1 0 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0 -1)
    ( 0  0  1  1  0  1)
    ( 0  0  0  0  1  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 0  1  0  0  0 -1)
    ( 0  0  1  0  1  1)
    ( 0  0  0  1  0  0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 1 0 0 0 0)
    (0 0 1 0 0 0)
    (0 0 0 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  1  1)
    ( 0  1  0  2  2  1)
    ( 0  0  1  0 -1 -1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  1  0 -1 -1)
    ( 0  1  1  0 -1 -1)
    ( 0  0  0  1  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 1 0)
    (0 1 0 1 1 0)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 1 0 0)
    (0 1 0 2 2 1)
    (0 0 1 0 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 1 0 1 0)
    (0 1 1 0 1 0)
    (0 0 0 1 0 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  2  0  1  0 -1)
    ( 0  0  1  1  0  0)
    ( 0  0  0  0  1  1),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    (1 0 0 0 0 0)
    (0 1 1 0 0 0)
    (0 0 0 1 1 0),

    Vector space of degree 6, dimension 3 over Rational Field
    Echelonized basis:
    ( 1  0  0  0  0  1)
    ( 0  1  1  1  0 -1)
    ( 0  0  0  0  1  1)
}