/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^2 + x + 1 [Q(zeta_3)].

Traces:    [ 0, 3 ]
Density:   [ 0.88888889, 0.86805555 ]
Numer max: [ 3, 3 ]
Numer av:  [ 0.86458334, 0.81250000 ]
Denom max: [ 1, 1 ], [ [], [] ]
Denom LCM: [ 1, 1 ], [ [], [] ]

Character:
( 12, -12, -4, 4, 12*zeta(3)_3, -12*zeta(3)_3 - 12, -6, -6*zeta(3)_3, 
    6*zeta(3)_3 + 6, -3*zeta(3)_3 - 3, 3*zeta(3)_3, 3, 0, 0, 4, -4,
    0, 0, -3, 2, 12*zeta(3)_3 + 12, -12*zeta(3)_3, -6*zeta(3)_3 - 6,
    6*zeta(3)_3, 6, -4*zeta(3)_3 - 4, 4*zeta(3)_3, 4*zeta(3)_3 + 4,
    -4*zeta(3)_3, 3*zeta(3)_3 + 3, -3*zeta(3)_3, -3, 2, 2*zeta(3)_3 +
    2, -2*zeta(3)_3, -2, -2*zeta(3)_3 - 2, 2*zeta(3)_3, -3*zeta(3)_3 -
    2, -3*zeta(3)_3 - 1, zeta(3)_3 - 2, 2*zeta(3)_3 + 3, 3*zeta(3)_3 +
    1, -zeta(3)_3 + 2, -2*zeta(3)_3 - 3, -2*zeta(3)_3 + 1, -zeta(3)_3 -
    3, 3*zeta(3)_3 + 2, 2*zeta(3)_3 - 1, zeta(3)_3 + 3, 0, zeta(3)_3 +
    1, zeta(3)_3, 1, -zeta(3)_3 - 1, -zeta(3)_3, -1, -2, 0, 0, 2, -2,
    0, -zeta(3)_3 + 1, -2*zeta(3)_3 - 1, zeta(3)_3 - 1, zeta(3)_3
    + 2, -zeta(3)_3 - 2, 2*zeta(3)_3 + 1, 3, -2, -1, 1, 1, 0, 0,
    -4*zeta(3)_3, 4*zeta(3)_3, -4*zeta(3)_3 - 4, 4*zeta(3)_3 + 4,
    0, 0, 0, 0, 2*zeta(3)_3 + 2, 2*zeta(3)_3, 2, -2*zeta(3)_3 - 2,
    -2*zeta(3)_3, -2, zeta(3)_3 + 1, zeta(3)_3, 1, -zeta(3)_3 - 1,
    -zeta(3)_3, -1, -zeta(3)_3 - 2, 0, 0, 0, -2*zeta(3)_3 - 1, zeta(3)_3
    - 1, zeta(3)_3 + 2, 2*zeta(3)_3 + 1, -zeta(3)_3 + 1, 0, -1, -1,
    2, -3*zeta(3)_3, 3*zeta(3)_3 + 3, 2*zeta(3)_3, -2*zeta(3)_3 - 2,
    -zeta(3)_3, 0, 0, -1, zeta(3)_3 + 1, zeta(3)_3 + 2, -2*zeta(3)_3 -
    1, -zeta(3)_3 - 2, 2*zeta(3)_3 + 1, -zeta(3)_3 + 1, zeta(3)_3 -
    1, -1, zeta(3)_3 + 1, -zeta(3)_3, -1, -zeta(3)_3 - 1, zeta(3)_3,
    1, -zeta(3)_3 - 1, zeta(3)_3, 1, zeta(3)_3 + 1, -zeta(3)_3, 1,
    -1, 0, 2*zeta(3)_3 + 2, -2*zeta(3)_3, -zeta(3)_3 - 1, -zeta(3)_3
    - 1, zeta(3)_3, 1, zeta(3)_3, 1, -1, 0, 0, 0, 0, 2*zeta(3)_3,
    -2*zeta(3)_3 - 2, -2*zeta(3)_3, 2*zeta(3)_3 + 2, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 1, 1, 0, 3*zeta(3)_3, -3*zeta(3)_3 - 3, 2*zeta(3)_3 +
    2, -2*zeta(3)_3, -zeta(3)_3, zeta(3)_3, -zeta(3)_3 - 1, zeta(3)_3 +
    1, 1, 0, zeta(3)_3, 0, -zeta(3)_3 - 1, zeta(3)_3, -zeta(3)_3 - 1,
    -zeta(3)_3, -zeta(3)_3, zeta(3)_3 + 1, zeta(3)_3 + 1, 2*zeta(3)_3,
    -2*zeta(3)_3 - 2, -zeta(3)_3, -1, -zeta(3)_3, -1, zeta(3)_3 + 1,
    zeta(3)_3 + 1, -zeta(3)_3, -zeta(3)_3 - 1, zeta(3)_3, zeta(3)_3 +
    1, 0, 0, -zeta(3)_3, zeta(3)_3 + 1, zeta(3)_3, -zeta(3)_3 - 1,
    zeta(3)_3, -zeta(3)_3 - 1, 0, 0 )
*/

G:=c9Group("6suzp");
M:=
GModule(G, [
    Matrix(K, 12, 12,
        [ [ 1, 0 ], [ 0, 0 ], [ 0, 2 ], [ -1, -3 ], [ -1, -1 ], [ -2, 0 ], [ 1, 
        1 ], [ -1, -1 ], [ -1, 1 ], [ -1, -2 ], [ -2, -1 ], [ 0, 1 ], [ -2, -1 
        ], [ 0, 1 ], [ 1, 2 ], [ -1, 0 ], [ 0, 2 ], [ 0, 0 ], [ -1, -2 ], [ -2, 
        -1 ], [ -1, 0 ], [ 0, -1 ], [ -1, -1 ], [ 1, 1 ], [ 1, 1 ], [ 0, 0 ], [ 
        -1, -2 ], [ 2, 2 ], [ 1, 0 ], [ 1, 0 ], [ 0, 0 ], [ 1, 0 ], [ 0, -1 ], [
        1, 1 ], [ 2, 1 ], [ -1, -2 ], [ -2, -2 ], [ -1, 0 ], [ 0, 1 ], [ -1, 0 
        ], [ -1, 0 ], [ 1, 1 ], [ 0, -1 ], [ 0, 0 ], [ 1, 0 ], [ 0, 0 ], [ 0, -1
        ], [ 0, 1 ], [ -2, -2 ], [ -1, 0 ], [ 2, 2 ], [ -3, -1 ], [ -1, 1 ], [ 
        0, 2 ], [ 0, -1 ], [ -1, 1 ], [ 0, 2 ], [ -1, -1 ], [ -2, 1 ], [ 2, 2 ],
        [ 0, 2 ], [ 1, 1 ], [ 2, 2 ], [ 0, 1 ], [ 1, 1 ], [ 0, 1 ], [ -1, 0 ], [
        0, 1 ], [ 1, 2 ], [ -1, -1 ], [ -1, 1 ], [ 1, 0 ], [ -1, -1 ], [ -1, 0 
        ], [ -2, 0 ], [ 1, 1 ], [ -1, 0 ], [ 1, 0 ], [ 0, -1 ], [ 0, -1 ], [ 0, 
        -1 ], [ 2, 0 ], [ 1, -1 ], [ -1, 0 ], [ 1, 1 ], [ 1, 0 ], [ 1, 2 ], [ 0,
        -1 ], [ 1, 1 ], [ -2, -1 ], [ 0, 0 ], [ -2, -1 ], [ -2, 0 ], [ -1, -2 ],
        [ -2, -1 ], [ 0, 0 ], [ 0, -1 ], [ 0, 0 ], [ 1, 0 ], [ -1, -1 ], [ -1, 
        -1 ], [ 1, 1 ], [ 0, 0 ], [ 0, 0 ], [ 1, 0 ], [ -1, 0 ], [ 0, 0 ], [ 0, 
        1 ], [ -1, 0 ], [ 0, 1 ], [ 1, 0 ], [ 0, 1 ], [ 0, 1 ], [ 1, 1 ], [ -1, 
        -1 ], [ 0, 0 ], [ 0, 0 ], [ 0, 0 ], [ 0, 1 ], [ 1, 0 ], [ -1, 0 ], [ -1,
        0 ], [ -2, -2 ], [ 1, 1 ], [ 1, 1 ], [ 0, -1 ], [ 0, 0 ], [ 1, 0 ], [ 
        -1, -1 ], [ 2, 1 ], [ 1, 0 ], [ 0, -1 ], [ -3, 0 ], [ 0, 2 ], [ 2, 2 ], 
        [ -2, 0 ], [ 1, 2 ], [ 1, 2 ], [ -1, -1 ], [ 0, 1 ], [ 2, 3 ], [ -2, -2 
        ], [ -1, 1 ], [ 2, 1 ] ])    ,
    Matrix(K, 12, 12,
        [ [ 3, 2 ], [ 1, 0 ], [ 0, 0 ], [ 2, 0 ], [ 1, 0 ], [ -2, -2 ], [ 0, 1 
        ], [ -1, -2 ], [ -3, -2 ], [ 1, 0 ], [ -1, -1 ], [ -1, -1 ], [ 1, -1 ], 
        [ 0, -1 ], [ 0, 0 ], [ -1, -2 ], [ -1, -1 ], [ -1, 0 ], [ 2, 1 ], [ -1, 
        -1 ], [ -1, 0 ], [ 0, 0 ], [ -1, 0 ], [ 0, 1 ], [ -2, -1 ], [ 0, 0 ], [ 
        0, 0 ], [ -1, 1 ], [ 0, 1 ], [ 1, 1 ], [ 0, -1 ], [ 0, 1 ], [ 1, 1 ], [ 
        -1, 0 ], [ 1, 1 ], [ 1, 0 ], [ -1, -1 ], [ -1, 0 ], [ 1, 1 ], [ -1, -1 
        ], [ -1, 0 ], [ 1, 1 ], [ 1, 0 ], [ 0, 0 ], [ 1, 1 ], [ 0, 0 ], [ -1, 0 
        ], [ 0, 1 ], [ 2, -1 ], [ 1, -1 ], [ 0, 0 ], [ -2, -3 ], [ 0, -1 ], [ 
        -2, 0 ], [ 2, 1 ], [ -3, -2 ], [ -2, 1 ], [ -1, -1 ], [ -1, 0 ], [ -1, 0
        ], [ 1, -1 ], [ 0, -1 ], [ 0, -1 ], [ 0, 0 ], [ 0, 0 ], [ -1, -1 ], [ 0,
        -1 ], [ -2, -1 ], [ -2, -1 ], [ 1, 1 ], [ 0, 0 ], [ 0, 0 ], [ 1, 2 ], [ 
        1, 0 ], [ 0, 0 ], [ 2, 1 ], [ 1, 0 ], [ 0, -1 ], [ 0, 1 ], [ 1, 0 ], [ 
        0, -1 ], [ 0, 0 ], [ 0, -1 ], [ -1, -1 ], [ 3, -1 ], [ 0, -2 ], [ -1, -1
        ], [ 0, -3 ], [ -1, -2 ], [ -3, -1 ], [ 2, 2 ], [ -1, -2 ], [ -3, -1 ], 
        [ 0, 0 ], [ -1, -1 ], [ -1, 0 ], [ -1, 1 ], [ 0, 1 ], [ 1, 1 ], [ 0, 1 
        ], [ 1, 1 ], [ 1, 1 ], [ -1, -1 ], [ 0, 1 ], [ 2, 2 ], [ 0, -1 ], [ 0, 1
        ], [ 0, 0 ], [ -1, 0 ], [ 1, 0 ], [ 1, 0 ], [ -2, 1 ], [ 1, 1 ], [ 0, 1 
        ], [ 0, -1 ], [ -1, 1 ], [ 1, 2 ], [ -1, 0 ], [ 0, 2 ], [ 1, 0 ], [ -2, 
        0 ], [ 0, 1 ], [ -1, 0 ], [ 0, 1 ], [ 0, 1 ], [ 1, 0 ], [ 0, 0 ], [ 1, 0
        ], [ 0, -1 ], [ 0, 0 ], [ 1, 0 ], [ 1, 0 ], [ -1, -1 ], [ -1, -1 ], [ 1,
        1 ], [ -2, 0 ], [ 0, 1 ], [ 0, 1 ], [ 1, -1 ], [ -2, 0 ], [ 0, 2 ], [ 0,
        0 ], [ -1, 1 ], [ 1, 1 ] ])
]: Check := false) where w := K.1 where K := CyclotomicField(3);
K<w> := BaseRing(M);
K;
M;
