/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^4 - x^3 - 2*x^2 - 3*x + 9.

Traces:    [ 14, 1 ]
Density:   [ 0.0079365079, 1.0000000 ]
Denom max: [ 6, 324 ], [ [ <2, 1>, <3, 1> ], [ <2, 2>, <3, 4> ] ]
Numer max: [ 9, 57 ]
Numer av:  [ 0.013636936, 9.1087176 ]
Denom LCM: [ 6, 324 ], [ [ <2, 1>, <3, 1> ], [ <2, 2>, <3, 4> ] ]

Character:
( 126, 14, 126*zeta(33)_3, -126*zeta(33)_3 - 126, 9*zeta(33)_3 + 9, 
    -9*zeta(33)_3, -9, 0, 2, 1, 1, 14*zeta(33)_3, -14*zeta(33)_3 - 14, -1, 
    -zeta(33)_3, zeta(33)_3 + 1, 2, -2*zeta(33)_3 - 2, 2*zeta(33)_3, 0, 0, 0, 0,
    0, -1, -zeta(33)_11^9 - zeta(33)_11^5 - zeta(33)_11^4 - zeta(33)_11^3 - 
    zeta(33)_11 - 1, zeta(33)_11^9 + zeta(33)_11^5 + zeta(33)_11^4 + 
    zeta(33)_11^3 + zeta(33)_11, 2*zeta(33)_3, -2*zeta(33)_3 - 2, -zeta(33)_3, 
    -1, zeta(33)_3 + 1, 0, 0, -zeta(33)_3 - 1, zeta(33)_3, zeta(33)_3, 
    zeta(33)_3, 1, -zeta(33)_3 - 1, 1, -zeta(33)_3 - 1, -zeta(33)_3 - 1, 
    zeta(33)_3, 0, 0, 0, 0, 0, 0, -zeta(33)_3, zeta(33)_3 + 1, -zeta(33)_3, 
    -zeta(33)_3, -1, zeta(33)_3 + 1, -1, zeta(33)_3 + 1, 
    zeta(33)_3*zeta(33)_11^9 + zeta(33)_3*zeta(33)_11^5 + 
    zeta(33)_3*zeta(33)_11^4 + zeta(33)_3*zeta(33)_11^3 + zeta(33)_3*zeta(33)_11
    + zeta(33)_3 + zeta(33)_11^9 + zeta(33)_11^5 + zeta(33)_11^4 + zeta(33)_11^3
    + zeta(33)_11 + 1, -zeta(33)_3*zeta(33)_11^9 - zeta(33)_3*zeta(33)_11^5 - 
    zeta(33)_3*zeta(33)_11^4 - zeta(33)_3*zeta(33)_11^3 - zeta(33)_3*zeta(33)_11
    - zeta(33)_11^9 - zeta(33)_11^5 - zeta(33)_11^4 - zeta(33)_11^3 - 
    zeta(33)_11, zeta(33)_3*zeta(33)_11^9 + zeta(33)_3*zeta(33)_11^5 + 
    zeta(33)_3*zeta(33)_11^4 + zeta(33)_3*zeta(33)_11^3 + 
    zeta(33)_3*zeta(33)_11, -zeta(33)_3*zeta(33)_11^9 - zeta(33)_3*zeta(33)_11^5
    - zeta(33)_3*zeta(33)_11^4 - zeta(33)_3*zeta(33)_11^3 - 
    zeta(33)_3*zeta(33)_11 - zeta(33)_3, 0, 0, 0, 0 )
*/

G := PermutationGroup(ATLASGroup("3McL"));
M :=
GModule(G, [
    Matrix(SparseMatrix(K, 126, 126, [
    <1, 17, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <2, 68, 1>, 
    <3, 13, 1>, 
    <4, 94, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <5, 62, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <6, 26, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <7, 30, 1>, 
    <8, 20, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <9, 77, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <10, 10, 1>, 
    <11, 46, 1>, 
    <12, 12, 1>, 
    <13, 3, 1>, 
    <14, 28, 1>, 
    <15, 25, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <16, 84, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <17, 1, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <18, 125, 1>, 
    <19, 76, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <20, 8, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <21, 74, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <22, 61, 1>, 
    <23, 89, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <24, 45, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <25, 15, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <26, 6, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <27, 27, 1>, 
    <28, 14, 1>, 
    <29, 124, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <30, 7, 1>, 
    <31, 91, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <32, 32, 1>, 
    <33, 63, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <34, 66, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <35, 85, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <36, 36, 1>, 
    <37, 67, 1>, 
    <38, 38, 1>, 
    <39, 41, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <40, 106, 1>, 
    <41, 39, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <42, 42, 1>, 
    <43, 57, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <44, 95, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <45, 24, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <46, 11, 1>, 
    <47, 54, 1>, 
    <48, 48, 1>, 
    <49, 55, 1>, 
    <50, 103, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <51, 90, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <52, 105, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <53, 122, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <54, 47, 1>, 
    <55, 49, 1>, 
    <56, 65, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <57, 43, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <58, 69, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <59, 73, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <60, 81, 1>, 
    <61, 22, 1>, 
    <62, 5, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <63, 33, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <64, 87, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <65, 56, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <66, 34, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <67, 37, 1>, 
    <68, 2, 1>, 
    <69, 58, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <70, 88, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <71, 83, 1>, 
    <72, 92, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <73, 59, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <74, 21, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <75, 93, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <76, 19, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <77, 9, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <78, 118, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <79, 110, 1>, 
    <80, 80, 1>, 
    <81, 60, 1>, 
    <82, 82, 1>, 
    <83, 71, 1>, 
    <84, 16, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <85, 35, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <86, 109, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <87, 64, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <88, 70, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <89, 23, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <90, 51, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <91, 31, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <92, 72, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <93, 75, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <94, 4, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <95, 44, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <96, 98, 1>, 
    <97, 117, 1>, 
    <98, 96, 1>, 
    <99, 99, 1>, 
    <100, 101, 1>, 
    <101, 100, 1>, 
    <102, 113, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <103, 50, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <104, 112, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <105, 52, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <106, 40, 1>, 
    <107, 111, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <108, 108, 1>, 
    <109, 86, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <110, 79, 1>, 
    <111, 107, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <112, 104, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <113, 102, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <114, 120, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <115, 123, 1>, 
    <116, 126, 1>, 
    <117, 97, 1>, 
    <118, 78, 1/6*(w^3 + 2*w^2 - 2*w - 9)>, 
    <119, 119, 1>, 
    <120, 114, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <121, 121, 1>, 
    <122, 53, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <123, 115, 1>, 
    <124, 29, 1/6*(-w^3 - 2*w^2 + 2*w + 3)>, 
    <125, 18, 1>, 
    <126, 116, 1>
    ])),
    Matrix(K, 126, 126,
        [ [ -19/54, -13/162, 5/81, 4/81 ], [ -7/54, 1/324, 1/162, 7/324 ], [ 
        7/108, 7/324, 5/324, -5/324 ], [ -2/27, -17/324, 1/162, 7/324 ], [ 
        7/108, -5/324, -1/324, 1/324 ], [ 7/108, 1/81, -1/324, -2/81 ], [ -2/27,
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        -5/324, 2/81, 1/324 ], [ 7/108, 1/81, -1/324, -2/81 ], [ 1/108, 5/162, 
        -7/324, -1/162 ], [ -2/27, -5/324, 2/81, 1/324 ], [ 7/108, -2/81, 
        -7/324, -1/162 ], [ 1/108, 13/324, -1/324, 1/324 ], [ 7/108, 1/81, 
        -1/324, -2/81 ], [ 7/108, 7/324, 5/324, -5/324 ], [ -2/27, -5/324, 2/81,
        1/324 ], [ 1/108, 5/162, -7/324, -1/162 ], [ 7/108, -2/81, -7/324, 
        -1/162 ], [ 1/108, 13/324, -1/324, 1/324 ], [ 7/108, 7/324, 5/324, 
        -5/324 ], [ -7/54, 1/324, 1/162, 7/324 ], [ -2/27, -5/324, 2/81, 1/324 
        ], [ 7/108, 7/324, 5/324, -5/324 ], [ 1/108, 5/162, -7/324, -1/162 ], [ 
        -7/54, 1/324, 1/162, 7/324 ], [ 1/108, 5/162, -7/324, -1/162 ], [ -7/54,
        1/324, 1/162, 7/324 ], [ 7/108, -2/81, -7/324, -1/162 ], [ -2/27, 
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        13/324, -1/324, 1/324 ], [ 7/108, 1/81, -1/324, -2/81 ], [ 1/108, 5/162,
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        -1/324, 1/324 ], [ -19/54, -13/162, 5/81, 4/81 ], [ 4/27, 4/81, -11/162,
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        1/108, 13/324, -1/324, 1/324 ], [ 7/108, 1/81, -1/324, -2/81 ], [ -2/27,
        -17/324, 1/162, 7/324 ], [ 1/108, 5/162, -7/324, -1/162 ], [ 7/108, 
        -2/81, -7/324, -1/162 ], [ 1/108, 13/324, -1/324, 1/324 ], [ -2/27, 
        -17/324, 1/162, 7/324 ], [ 1/108, 13/324, -1/324, 1/324 ], [ 7/108, 
        1/81, -1/324, -2/81 ], [ 4/27, 4/81, -11/162, -7/162 ], [ 1/108, 5/162, 
        -7/324, -1/162 ], [ -2/27, -5/324, 2/81, 1/324 ], [ -2/27, -5/324, 2/81,
        1/324 ], [ 7/108, -2/81, -7/324, -1/162 ], [ 1/108, 5/162, -7/324, 
        -1/162 ], [ 1/108, 5/162, -7/324, -1/162 ], [ -2/27, -5/324, 2/81, 1/324
        ], [ -7/54, 1/324, 1/162, 7/324 ], [ 7/108, 1/81, -1/324, -2/81 ], [ 
        7/108, -2/81, -7/324, -1/162 ], [ -2/27, -5/324, 2/81, 1/324 ], [ -2/27,
        -5/324, 2/81, 1/324 ], [ 1/108, 13/324, -1/324, 1/324 ], [ 7/108, -2/81,
        -7/324, -1/162 ], [ -7/54, 1/324, 1/162, 7/324 ], [ -2/27, -17/324, 
        1/162, 7/324 ], [ 7/108, -2/81, -7/324, -1/162 ], [ 1/108, 13/324, 
        -1/324, 1/324 ], [ 7/108, 1/81, -1/324, -2/81 ], [ -2/27, -5/324, 2/81, 
        1/324 ], [ 1/108, 5/162, -7/324, -1/162 ], [ -2/27, -5/324, 2/81, 1/324 
        ], [ -2/27, -5/324, 2/81, 1/324 ], [ -2/27, -17/324, 1/162, 7/324 ], [ 
        1/108, 5/162, -7/324, -1/162 ], [ -7/54, 1/324, 1/162, 7/324 ], [ 4/27, 
        4/81, -11/162, -7/162 ], [ 7/108, -2/81, -7/324, -1/162 ], [ -2/27, 
        -5/324, 2/81, 1/324 ], [ 7/108, 7/324, 5/324, -5/324 ], [ 7/108, 1/81, 
        -1/324, -2/81 ], [ -7/54, 1/324, 1/162, 7/324 ], [ 1/108, 13/324, 
        -1/324, 1/324 ], [ 7/108, 1/81, -1/324, -2/81 ], [ 7/108, 1/81, -1/324, 
        -2/81 ] ])
]: Check := false) where w := K.1 where K := ext<K|Polynomial(K, [9, -3, -2, -1, 1])> where K is 
RationalField();

K<w> := BaseRing(M);
K;
M;
