/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^8 - x^4 + 1 [Q(zeta_24)].

Traces:    [ 0, 0 ]
Density:   [ 0.80555555, 0.0083333333 ]
Numer max: [ 12, 1 ]
Numer av:  [ 1.4247569, 0.0013715278 ]
Denom max: [ 84, 1 ], [ [ <2, 2>, <3, 1>, <7, 1> ], [] ]
Denom LCM: [ 84, 1 ], [ [ <2, 2>, <3, 1>, <7, 1> ], [] ]

Character:
*/

G := PermutationGroup(ATLASGroup("12M22"));
M :=
GModule(G, [
    Matrix(K, 120, 120,
        [ [ 0, 1/12, 0, 1/12, 0, -5/84, 0, -1/42 ], [ 0, -1/12, 0, -1/12, 0, 
        5/84, 0, 1/42 ], [ 0, -5/84, 0, 5/84, 0, 1/12, 0, 1/42 ], [ 0, -1/42, 0,
        -1/12, 0, -5/84, 0, 5/84 ], [ 0, 5/84, 0, -5/84, 0, -1/12, 0, -1/42 ], [
        0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 
        0, 0, 0 ], [ 0, -5/84, 0, 5/84, 0, 1/12, 0, 1/42 ], [ 0, 5/84, 0, -5/84,
        0, -1/12, 0, -1/42 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0,
        0 ], [ 0, -1/12, 0, -1/12, 0, 5/84, 0, 1/42 ], [ 1/14, 0, -1/42, -1/28, 
        -1/14, -1/28, 1/21, 1/28 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -1/12, 0, 
        -1/42, 0, 1/42, 0, 1/12 ], [ 0, 5/84, 0, -5/84, 0, -1/12, 0, -1/42 ], [ 
        0, 5/84, 0, 1/42, 0, 1/42, 0, 5/84 ], [ 0, -1/12, 0, -1/12, 0, 5/84, 0, 
        1/42 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ -1/42, 0, 1/14, 1/28, -1/42, 
        -1/28, 0, -1/28 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/28, -1/21, -1/28, 
        0, -1/28, 1/42, 0 ], [ 0, -1/28, 1/21, 1/28, 0, 1/28, -1/42, 0 ], [ 0, 
        0, 0, 0, 0, 0, 0, 0 ], [ 0, 1/28, -1/21, -1/28, 0, -1/28, 1/42, 0 ], [ 
        0, 1/28, -1/21, -1/28, 0, -1/28, 1/42, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], 
        [ 1/21, 1/28, 0, 0, -1/42, 0, 0, 1/28 ], [ 0, -1/28, 1/21, 1/28, 0, 
        1/28, -1/42, 0 ], [ -1/14, -1/28, 1/21, 1/28, 0, 1/28, -1/42, 0 ], [ 
        -1/42, 0, 1/14, 1/28, -1/42, -1/28, 0, -1/28 ], [ 1/14, 0, -1/42, -1/28,
        -1/14, -1/28, 1/21, 1/28 ], [ -1/14, 0, -1/21, -1/14, 1/14, -1/14, 2/21,
        1/14 ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -1/28, 1/42, 0, -1/14, 0, 1/42,
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        0, 1/12, 0, 5/84, 0, -5/84 ], [ 1/14, 1/28, -1/21, -1/28, 0, -1/28, 
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        -1/28, 1/21, 1/28, 0, 0 ], [ 0, 1/12, 0, 1/42, 0, -1/42, 0, -1/12 ], [ 
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        ], [ 1/42, 0, 0, -1/28, 1/42, 1/28, 0, 1/28 ], [ 1/42, 1/28, 0, 1/28, 
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        ], [ 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -1/42, 0, 2/21, 0, -2/21, 0, 1/42 ],
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    <75, 117, -w^4 + 1>, 
    <76, 73, -w^6 + w^2>, 
    <77, 49, -w^6 + w^2>, 
    <78, 45, 1>, 
    <79, 71, -w^6 + w^2>, 
    <80, 44, -w^4 + 1>, 
    <81, 50, -w^2>, 
    <82, 16, w^6 - w^2>, 
    <83, 31, w^6 - w^2>, 
    <84, 86, -1>, 
    <85, 109, -w^2>, 
    <86, 80, 1>, 
    <87, 17, w^2>, 
    <88, 39, -w^2>, 
    <89, 96, w^4 - 1>, 
    <90, 23, w^6>, 
    <91, 75, -1>, 
    <92, 91, w^6>, 
    <93, 82, w^6>, 
    <94, 27, -1>, 
    <95, 13, -1>, 
    <96, 9, w^4>, 
    <97, 54, -w^2>, 
    <98, 48, w^6 - w^2>, 
    <99, 38, 1>, 
    <100, 83, w^6>, 
    <101, 101, w^6>, 
    <102, 59, -w^2>, 
    <103, 116, -w^6 + w^2>, 
    <104, 11, w^4 - 1>, 
    <105, 32, w^6 - w^2>, 
    <106, 69, 1>, 
    <107, 90, 1>, 
    <108, 68, w^4>, 
    <109, 74, 1>, 
    <110, 89, -w^6>, 
    <111, 72, -1>, 
    <112, 62, w^6>, 
    <113, 76, w^6 - w^2>, 
    <114, 63, w^4>, 
    <115, 24, -1>, 
    <116, 56, 1>, 
    <117, 92, w^6 - w^2>, 
    <118, 78, w^6 - w^2>, 
    <119, 85, w^4 - 1>, 
    <120, 93, w^4 - 1>
    ]))
]: Check := false) where w := K.1 where K := CyclotomicField(24);

K<w> := K;
K;
M;
