/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^4 - 5*x^3 + 11*x^2 - 10*x + 4.

Traces:    [ 2, 3 ]
Density:   [ 0.055555556, 0.97222222 ]
Numer max: [ 1, 29 ]
Numer av:  [ 0.013888889, 4.4645061 ]
Denom max: [ 1, 16 ], [ [], [ <2, 4> ] ]
Denom LCM: [ 1, 16 ], [ [], [ <2, 4> ] ]

Character:
( 18, 2, -18*zeta(15)_3 - 18, 18*zeta(15)_3, 3*zeta(15)_3, 3, -3*zeta(15)_3 - 3,
    0, -2, -zeta(15)_5^3 - zeta(15)_5^2, zeta(15)_5^3 + zeta(15)_5^2 + 1, 
    2*zeta(15)_3, -2*zeta(15)_3 - 2, -1, -zeta(15)_3, zeta(15)_3 +
    1, 0, 0, 0, 0, -zeta(15)_5^3 - zeta(15)_5^2 - 1, zeta(15)_5^3
    + zeta(15)_5^2, -2*zeta(15)_3, 2*zeta(15)_3 + 2, zeta(15)_3,
    -zeta(15)_3 - 1, 1, zeta(15)_3*zeta(15)_5^3 + zeta(15)_3*zeta(15)_5^2
    + zeta(15)_5^3 + zeta(15)_5^2, -zeta(15)_3*zeta(15)_5^3 -
    zeta(15)_3*zeta(15)_5^2 - zeta(15)_3 - zeta(15)_5^3 - zeta(15)_5^2
    - 1, -zeta(15)_3*zeta(15)_5^3 - zeta(15)_3*zeta(15)_5^2,
    zeta(15)_3*zeta(15)_5^3 + zeta(15)_3*zeta(15)_5^2 +
    zeta(15)_3, zeta(15)_3*zeta(15)_5^3 + zeta(15)_3*zeta(15)_5^2
    + zeta(15)_5^3 + zeta(15)_5^2, -zeta(15)_5^3 - zeta(15)_5^2,
    -zeta(15)_3*zeta(15)_5^3 - zeta(15)_3*zeta(15)_5^2, zeta(15)_5^3 +
    zeta(15)_5^2 + 1, zeta(15)_3*zeta(15)_5^3 + zeta(15)_3*zeta(15)_5^2
    + zeta(15)_3, -zeta(15)_3*zeta(15)_5^3 - zeta(15)_3*zeta(15)_5^2 -
    zeta(15)_3 - zeta(15)_5^3 - zeta(15)_5^2 - 1, 1, 1, -1, -1, 0, 0,
    zeta(15)_3*zeta(15)_5^3 + zeta(15)_3*zeta(15)_5^2 + zeta(15)_3
    + zeta(15)_5^3 + zeta(15)_5^2 + 1, -zeta(15)_3*zeta(15)_5^3 -
    zeta(15)_3*zeta(15)_5^2 - zeta(15)_3, zeta(15)_3*zeta(15)_5^3
    + zeta(15)_3*zeta(15)_5^2, -zeta(15)_3*zeta(15)_5^3 -
    zeta(15)_3*zeta(15)_5^2 - zeta(15)_5^3 - zeta(15)_5^2, zeta(15)_3,
    -zeta(15)_3 - 1, -zeta(15)_3 - 1, zeta(15)_3, -zeta(15)_3, zeta(15)_3
    + 1, -zeta(15)_3, zeta(15)_3 + 1 )
*/


G := c9Group("3j3p");
M :=
GModule(G, [
    Matrix(SparseMatrix(K, 18, 18, [
    <1, 1, 1>,  <2, 2, 1>,  <3, 3, 1>,  <4, 4, -1>,  <5, 5, 1>,  <6, 6, -1>,  
    <7, 7, -1>,  <8, 8, 1>,  <9, 9, -1>,  <10, 10, 1>,  <11, 11, 1>,  <12, 12, 
    1>,  <13, 13, -1>,  <14, 14, -1>,  <15, 15, 1>,  <16, 16, 1>,  <17, 17, -1>,
    <18, 18, -1> ])),
    Matrix(K, 18, 18,
        [ [ -3/4, 11/8, -5/8, 1/8 ], [ 3/4, -11/8, 5/8, -1/8 ], [ 0, -3/4, 3/4, 
        -1/4 ], [ 1/4, -9/16, 5/16, -1/16 ], [ -1/4, -3/16, 3/16, -1/16 ], [ 
        1/4, -7/16, 5/16, -1/16 ], [ -7/8, 5/4, -5/8, 1/8 ], [ 1/4, -9/16, 5/16,
        -1/16 ], [ -1/8, 1/4, -1/8, 0 ], [ 0, 1/2, -3/8, 1/8 ], [ 5/8, -23/16, 
        13/16, -3/16 ], [ -1/4, 9/16, -5/16, 1/16 ], [ 0, 1/2, -3/8, 1/8 ], [ 
        1/2, -1, 1/2, -1/8 ], [ 5/4, -29/16, 15/16, -3/16 ], [ -1/4, 7/16, 
        -5/16, 1/16 ], [ 1/4, -3/16, 3/16, -1/16 ], [ -1/8, 0, 0, 0 ], [ 0, 
        -5/8, 3/8, -1/8 ], [ 0, 5/8, -3/8, 1/8 ], [ 1/2, -1/2, 0, 0 ], [ -7/8, 
        2, -9/8, 1/4 ], [ -1/8, 0, 0, 0 ], [ 7/8, -5/4, 5/8, -1/8 ], [ -3/8, 
        9/16, -5/16, 1/16 ], [ 1/8, -1/4, 1/8, 0 ], [ -5/8, 23/16, -13/16, 3/16 
        ], [ 1/2, -1, 1/2, -1/8 ], [ 1/4, -9/16, 5/16, -1/16 ], [ -1/8, 1/4, 
        -1/8, 0 ], [ 1/2, -1, 1/2, -1/8 ], [ -1/2, 1/2, -1/8, 0 ], [ 5/8, -1, 
        5/8, -1/8 ], [ -7/8, 5/4, -5/8, 1/8 ], [ -1/8, 0, 0, 0 ], [ -1/8, 3/16, 
        -3/16, 1/16 ], [ 1/2, -17/8, 11/8, -3/8 ], [ -1/2, 17/8, -11/8, 3/8 ], [
        3/2, -2, 1, -1/4 ], [ 3/8, 3/8, -3/8, 1/8 ], [ 7/8, -5/4, 5/8, -1/8 ], [
        3/8, -7/8, 1/2, -1/8 ], [ 5/8, -23/16, 13/16, -3/16 ], [ -1/8, 0, 0, 0 
        ], [ 1/8, 3/16, -3/16, 1/16 ], [ -5/4, 13/8, -3/4, 1/8 ], [ 1/4, 3/16, 
        -3/16, 1/16 ], [ 1/8, 0, 0, 0 ], [ -5/4, 13/8, -3/4, 1/8 ], [ 1/4, 1/2, 
        -3/8, 1/8 ], [ -9/8, 21/8, -3/2, 3/8 ], [ -3/8, 7/8, -1/2, 1/8 ], [ 1/8,
        -1/8, 0, 0 ], [ -3/8, 9/16, -5/16, 1/16 ], [ -3/4, -3/8, 3/8, -1/8 ], [ 
        1/4, 3/8, -3/8, 1/8 ], [ 1, -19/8, 11/8, -3/8 ], [ 0, 0, 0, 0 ], [ -3/8,
        1, -1/2, 1/8 ], [ -3/4, 23/16, -13/16, 3/16 ], [ -1/4, 5/16, -3/16, 1/16
        ], [ 3/8, -1, 1/2, -1/8 ], [ 1/4, -5/16, 3/16, -1/16 ], [ -3/8, 17/16, 
        -11/16, 3/16 ], [ -5/8, 11/16, -5/16, 1/16 ], [ 1/8, -7/16, 5/16, -1/16 
        ], [ -1/4, -1/16, 3/16, -1/16 ], [ -1/4, -1/16, 3/16, -1/16 ], [ 0, 0, 
        0, 0 ], [ 3/8, -1, 1/2, -1/8 ], [ 0, 0, 0, 0 ], [ 1/8, -3/4, 1/2, -1/8 
        ], [ 1/2, -9/8, 5/8, -1/8 ], [ 1/2, -9/8, 5/8, -1/8 ], [ 1/4, -1/4, 0, 0
        ], [ -3/4, 5/4, -5/8, 1/8 ], [ 7/8, -23/16, 13/16, -3/16 ], [ -5/8, 5/4,
        -5/8, 1/8 ], [ 5/8, -7/8, 1/2, -1/8 ], [ 5/8, -9/16, 5/16, -1/16 ], [ 
        7/8, -9/8, 5/8, -1/8 ], [ -1/4, 7/16, -5/16, 1/16 ], [ 1/4, -9/16, 5/16,
        -1/16 ], [ 0, 3/16, -3/16, 1/16 ], [ 1/8, 0, 0, 0 ], [ -7/8, 5/4, -5/8, 
        1/8 ], [ 1/4, -1/4, 1/8, 0 ], [ 1/8, 3/16, -3/16, 1/16 ], [ 3/4, -1, 
        1/2, -1/8 ], [ -5/8, 15/16, -7/16, 1/16 ], [ -7/4, 5/2, -5/4, 1/4 ], [ 
        1/4, -1/4, 0, 0 ], [ -1/4, -3/8, 3/8, -1/8 ], [ 1/4, -1/4, 1/8, 0 ], [ 
        0, 3/16, -3/16, 1/16 ], [ 7/8, -23/16, 13/16, -3/16 ], [ 5/8, -15/16, 
        7/16, -1/16 ], [ 0, 9/16, -5/16, 1/16 ], [ 3/8, -9/16, 5/16, -1/16 ], [ 
        1/8, -1/4, 1/8, 0 ], [ 3/8, -9/8, 5/8, -1/8 ], [ -5/8, 5/4, -5/8, 1/8 ],
        [ -3/8, 9/16, -5/16, 1/16 ], [ 5/8, -23/16, 13/16, -3/16 ], [ -3/4, 1, 
        -1/2, 1/8 ], [ 0, -7/16, 5/16, -1/16 ], [ 3/4, -5/4, 5/8, -1/8 ], [ 1/2,
        -11/16, 5/16, -1/16 ], [ -3/4, 9/8, -5/8, 1/8 ], [ -3/4, 9/8, -5/8, 1/8 
        ], [ 0, -3/8, 3/8, -1/8 ], [ 0, 5/8, -1/2, 1/8 ], [ -3/8, 7/8, -1/2, 1/8
        ], [ 1/4, -11/16, 5/16, -1/16 ], [ 0, 9/16, -5/16, 1/16 ], [ 3/8, -1/8, 
        0, 0 ], [ 0, 3/16, -3/16, 1/16 ], [ -3/8, 9/16, -5/16, 1/16 ], [ 1/8, 
        5/16, -3/16, 1/16 ], [ 5/8, -21/16, 13/16, -3/16 ], [ 1/4, 3/16, -3/16, 
        1/16 ], [ -1/4, 7/16, -5/16, 1/16 ], [ 1/2, -3/8, 1/8, 0 ], [ 3/8, -9/8,
        5/8, -1/8 ], [ 0, 1/8, 0, 0 ], [ -1/8, 0, 0, 0 ], [ -1/4, -3/8, 3/8, 
        -1/8 ], [ -1/4, 3/8, -3/8, 1/8 ], [ 0, -1/8, 1/8, -1/8 ], [ 3/4, -5/4, 
        5/8, -1/8 ], [ 1/8, 0, 0, 0 ], [ 0, 9/16, -5/16, 1/16 ], [ -1/2, 21/16, 
        -13/16, 3/16 ], [ 3/8, -1/4, 1/8, 0 ], [ -1/2, 11/16, -5/16, 1/16 ], [ 
        -5/8, 23/16, -13/16, 3/16 ], [ 5/8, -21/16, 13/16, -3/16 ], [ 5/8, 
        -9/16, 5/16, -1/16 ], [ 1/4, -7/16, 5/16, -1/16 ], [ -1/4, 9/16, -5/16, 
        1/16 ], [ -1/4, 1/4, -1/8, 0 ], [ -5/8, 5/4, -5/8, 1/8 ], [ -3/4, 1, 
        -1/2, 1/8 ], [ 1/8, -1/8, 0, 0 ], [ 1/2, 3/8, -3/8, 1/8 ], [ 0, -3/8, 
        3/8, -1/8 ], [ -3/4, 7/4, -1, 1/4 ], [ 0, 5/8, -1/2, 1/8 ], [ -7/8, 
        27/16, -15/16, 3/16 ], [ -3/8, 9/8, -5/8, 1/8 ], [ 5/8, -5/4, 5/8, -1/8 
        ], [ -5/8, 21/16, -13/16, 3/16 ], [ 3/8, -1/4, 1/8, 0 ], [ 1/4, 3/16, 
        -3/16, 1/16 ], [ -1/2, 11/16, -5/16, 1/16 ], [ -1/4, 9/16, -5/16, 1/16 
        ], [ 1/8, -1/4, 1/8, 0 ], [ 1/8, 0, 0, 0 ], [ 1/2, -3/8, 1/8, 0 ], [ 
        -1/8, 5/16, -3/16, 1/16 ], [ 0, 1/8, 0, 0 ], [ 7/8, -23/16, 13/16, -3/16
        ], [ 0, 5/8, -3/8, 1/8 ], [ 0, -5/8, 3/8, -1/8 ], [ -1/4, 3/4, -1/4, 0 
        ], [ -1/2, 1, -1/2, 1/8 ], [ -1/8, 3/16, -3/16, 1/16 ], [ -1/8, 1/4, 
        -1/8, 0 ], [ 1/8, 0, 0, 0 ], [ 5/8, -23/16, 13/16, -3/16 ], [ 7/8, -5/4,
        5/8, -1/8 ], [ -1/4, 9/16, -5/16, 1/16 ], [ 1/4, 3/16, -3/16, 1/16 ], [ 
        1/4, -7/16, 5/16, -1/16 ], [ -5/8, 1, -5/8, 1/8 ], [ 7/8, -2, 9/8, -1/4 
        ], [ 0, -1/2, 3/8, -1/8 ], [ -3/8, 9/16, -5/16, 1/16 ], [ -1/2, 1/2, 
        -1/8, 0 ], [ 3/8, -9/16, 5/16, -1/16 ], [ -1/4, 0, 0, 0 ], [ -1/4, 0, 0,
        0 ], [ 1/4, -5/8, 3/8, -1/8 ], [ 1/4, -3/8, 1/8, 0 ], [ -1, 27/16, 
        -15/16, 3/16 ], [ -3/8, 9/16, -5/16, 1/16 ], [ 1/8, -5/16, 3/16, -1/16 
        ], [ 1/2, -11/16, 5/16, -1/16 ], [ -5/8, 21/16, -13/16, 3/16 ], [ 7/8, 
        -5/4, 5/8, -1/8 ], [ 3/8, -1/4, 1/8, 0 ], [ -7/8, 9/8, -5/8, 1/8 ], [ 
        -1/8, 3/16, -3/16, 1/16 ], [ 3/8, -9/16, 5/16, -1/16 ], [ -3/4, 13/8, 
        -1, 1/4 ], [ -1/2, 21/16, -13/16, 3/16 ], [ 1/4, -7/8, 1/2, -1/8 ], [ 
        -3/4, 15/16, -7/16, 1/16 ], [ 1/4, 3/8, -3/8, 1/8 ], [ 1/4, -3/8, 3/8, 
        -1/8 ], [ 0, 1/8, -1/8, 1/8 ], [ -3/4, 1, -1/2, 1/8 ], [ -5/8, 5/4, 
        -5/8, 1/8 ], [ 0, 3/16, -3/16, 1/16 ], [ -1/2, 11/16, -5/16, 1/16 ], [ 
        1/8, 0, 0, 0 ], [ 1, -27/16, 15/16, -3/16 ], [ 1/8, -3/16, 3/16, -1/16 
        ], [ 7/8, -27/16, 15/16, -3/16 ], [ 7/8, -23/16, 13/16, -3/16 ], [ 1/4, 
        -9/16, 5/16, -1/16 ], [ 1/4, 3/16, -3/16, 1/16 ], [ -3/4, 5/4, -5/8, 1/8
        ], [ -3/8, 1/4, -1/8, 0 ], [ -1/4, 1/4, -1/8, 0 ], [ -5/8, 7/8, -1/2, 
        1/8 ], [ 0, -5/8, 3/8, -1/8 ], [ 0, 5/8, -3/8, 1/8 ], [ 1/4, -3/4, 1/4, 
        0 ], [ -1/2, 1/2, -1/8, 0 ], [ -3/8, 9/16, -5/16, 1/16 ], [ 1/8, 0, 0, 0
        ], [ 7/8, -5/4, 5/8, -1/8 ], [ -1/8, 3/16, -3/16, 1/16 ], [ 1/8, -1/4, 
        1/8, 0 ], [ -1/4, 3/16, -3/16, 1/16 ], [ 1/4, -7/16, 5/16, -1/16 ], [ 
        1/4, -9/16, 5/16, -1/16 ], [ -7/8, 2, -9/8, 1/4 ], [ 1/8, 0, 0, 0 ], [ 
        1/2, -1, 1/2, -1/8 ], [ -5/8, 23/16, -13/16, 3/16 ], [ 0, -1/2, 3/8, 
        -1/8 ], [ 5/8, -23/16, 13/16, -3/16 ], [ 3/4, -3/4, 1/4, 0 ], [ -3/4, 
        3/4, -1/4, 0 ], [ 3/4, -7/8, 5/8, -1/8 ], [ -1/2, 1/2, -1/8, 0 ], [ 1/4,
        3/16, -3/16, 1/16 ], [ 5/8, -23/16, 13/16, -3/16 ], [ -1/8, 3/16, -3/16,
        1/16 ], [ -1/4, 9/16, -5/16, 1/16 ], [ -3/8, 9/16, -5/16, 1/16 ], [ 
        -7/8, 2, -9/8, 1/4 ], [ -1/8, 0, 0, 0 ], [ -7/8, 5/4, -5/8, 1/8 ], [ 
        -3/8, 9/16, -5/16, 1/16 ], [ -3/8, 13/16, -7/16, 1/16 ], [ 1/2, -1, 1/2,
        -1/8 ], [ 1/4, -7/16, 5/16, -1/16 ], [ 0, -1/2, 3/8, -1/8 ], [ -1/4, 
        7/16, -5/16, 1/16 ], [ 1/4, -1/4, 0, 0 ], [ 5/4, -2, 5/4, -1/4 ], [ 
        -1/4, 9/8, -9/8, 3/8 ], [ 0, 0, 0, 0 ], [ -3/4, 23/16, -13/16, 3/16 ], [
        1/8, -7/16, 5/16, -1/16 ], [ 3/8, -1/16, -1/16, 1/16 ], [ 3/4, -23/16, 
        13/16, -3/16 ], [ -3/8, 1/16, 1/16, -1/16 ], [ 5/8, -1, 1/2, -1/8 ], [ 
        3/8, -3/4, 1/2, -1/8 ], [ -3/8, 1, -1/2, 1/8 ], [ -3/8, 17/16, -11/16, 
        3/16 ], [ -3/8, 17/16, -11/16, 3/16 ], [ 0, 0, 0, 0 ], [ 3/4, -23/16, 
        13/16, -3/16 ], [ 0, 0, 0, 0 ], [ 1/4, -5/16, 3/16, -1/16 ], [ -7/4, 
        5/2, -5/4, 1/4 ], [ 1/4, -1/4, 0, 0 ], [ -1/4, -3/8, 3/8, -1/8 ], [ 
        -3/4, 5/4, -5/8, 1/8 ], [ 0, 7/16, -5/16, 1/16 ], [ -1/8, -3/16, 3/16, 
        -1/16 ], [ -3/8, 9/16, -5/16, 1/16 ], [ 0, -3/16, 3/16, -1/16 ], [ -1/8,
        -5/16, 3/16, -1/16 ], [ 1/8, 0, 0, 0 ], [ 3/8, -1/8, 0, 0 ], [ 3/8, 
        -1/4, 1/8, 0 ], [ 5/8, -23/16, 13/16, -3/16 ], [ 1/8, -3/16, 3/16, -1/16
        ], [ 1/4, -1/4, 1/8, 0 ], [ 0, 9/16, -5/16, 1/16 ], [ 3/4, -1, 1/2, -1/8
        ], [ 1, -27/16, 15/16, -3/16 ], [ 1/2, -9/8, 5/8, -1/8 ], [ 1/2, -9/8, 
        5/8, -1/8 ], [ -1/4, 1/4, 0, 0 ], [ 0, 0, 0, 0 ], [ -1/8, 7/16, -5/16, 
        1/16 ], [ 3/8, -1, 1/2, -1/8 ], [ 1/8, -3/4, 1/2, -1/8 ], [ 1/8, -7/16, 
        5/16, -1/16 ], [ -1/8, 3/4, -1/2, 1/8 ], [ 1/4, 1/16, -3/16, 1/16 ], [ 
        3/4, -17/16, 7/16, -1/16 ], [ 3/4, -23/16, 13/16, -3/16 ], [ -5/8, 1, 
        -1/2, 1/8 ], [ -5/8, 1, -1/2, 1/8 ], [ 0, 0, 0, 0 ], [ 1/8, -7/16, 5/16,
        -1/16 ], [ 0, 0, 0, 0 ], [ 3/8, -1/16, -1/16, 1/16 ], [ -3/4, 7/4, -1, 
        1/4 ], [ -1/4, 1/2, -1/4, 0 ], [ 1/4, -5/8, 5/8, -1/8 ], [ 0, 1/8, 0, 0 
        ], [ -1/4, 11/16, -5/16, 1/16 ], [ -5/8, 21/16, -13/16, 3/16 ], [ -5/8, 
        9/16, -5/16, 1/16 ], [ 3/4, -15/16, 7/16, -1/16 ], [ -7/8, 23/16, 
        -13/16, 3/16 ], [ -1/8, 0, 0, 0 ], [ -1/8, 1/8, 0, 0 ], [ 3/8, -7/8, 
        1/2, -1/8 ], [ -5/8, 23/16, -13/16, 3/16 ], [ -1/8, 3/16, -3/16, 1/16 ],
        [ 0, -5/8, 1/2, -1/8 ], [ -1/4, 9/16, -5/16, 1/16 ], [ 1/2, -3/8, 1/8, 0
        ], [ 0, 9/16, -5/16, 1/16 ] ])
]: Check := false) where w := K.1 where K := ext<K|Polynomial(K, [4, -10, 11, -5, 1])> where K is
RationalField();
K<w> := BaseRing(M);
K;
M;
