/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^3 + x^2 - 4*x + 1.

Traces:    [ 3, -1 ]
Density:   [ 0.092244898, 0.99918368 ]
Numer max: [ 29, 560 ]
Numer av:  [ 0.30857143, 28.544490 ]
Denom max: [ 1, 13 ]
Denom LCM: [ 1, 13 ]

Character:
( 35, 3, -1, -1, 0, 0, 0, 0, -zeta(13)_13^11 - zeta(13)_13^10 - zeta(13)_13^3 - 
    zeta(13)_13^2, -zeta(13)_13^9 - zeta(13)_13^7 - zeta(13)_13^6 - 
    zeta(13)_13^4, zeta(13)_13^11 + zeta(13)_13^10 + zeta(13)_13^9 + 
    zeta(13)_13^7 + zeta(13)_13^6 + zeta(13)_13^4 + zeta(13)_13^3 + 
    zeta(13)_13^2 + 1 )
*/

G:=PermutationGroup(ATLASGroup("Sz8"));
M:=
GModule(G, [
    Matrix(SparseMatrix(K, 35, 35, [
    <1, 1, 1>, 
    <2, 2, 1>, 
    <3, 3, 1>, 
    <4, 4, -w - 2>, <4, 5, w^2 + 2*w - 1>, <4, 6, -w^2 - 2*w + 2>, <4, 7, w^2 + 
    2*w - 1>, 
    <5, 4, -w - 3>, <5, 5, w^2 + 2*w>, <5, 6, -2*w^2 - 3*w + 4>, <5, 7, w^2 + 
    2*w - 1>, 
    <6, 6, -1>, 
    <7, 4, -4*w^2 - 5*w + 16>, <7, 5, -w^2 - w + 2>, <7, 6, 5*w^2 + 6*w - 17>, 
    <7, 7, -w^2 - w + 3>, 
    <8, 8, -w - 2>, <8, 9, w^2 + 2*w - 1>, <8, 10, -w^2 - 2*w + 2>, <8, 11, w^2 
    + 2*w - 1>, 
    <9, 8, -w - 3>, <9, 9, w^2 + 2*w>, <9, 10, -2*w^2 - 3*w + 4>, <9, 11, w^2 + 
    2*w - 1>, 
    <10, 10, -1>, 
    <11, 8, -4*w^2 - 5*w + 16>, <11, 9, -w^2 - w + 2>, <11, 10, 5*w^2 + 6*w - 
    17>, <11, 11, -w^2 - w + 3>, 
    <12, 12, -w - 2>, <12, 13, w^2 + 2*w - 1>, <12, 14, -w^2 - 2*w + 2>, <12, 
    15, w^2 + 2*w - 1>, 
    <13, 12, -w - 3>, <13, 13, w^2 + 2*w>, <13, 14, -2*w^2 - 3*w + 4>, <13, 15, 
    w^2 + 2*w - 1>, 
    <14, 14, -1>, 
    <15, 12, -4*w^2 - 5*w + 16>, <15, 13, -w^2 - w + 2>, <15, 14, 5*w^2 + 6*w - 
    17>, <15, 15, -w^2 - w + 3>, 
    <16, 16, -1>, 
    <17, 16, -6*w^2 - 14*w + 5>, <17, 17, -5*w^2 - 12*w + 5>, <17, 18, -3*w^2 - 
    6*w + 3>, <17, 19, 2*w^2 + 5*w - 2>, 
    <18, 16, 12*w^2 + 29*w - 6>, <18, 17, 11*w^2 + 25*w - 9>, <18, 18, 6*w^2 + 
    15*w - 8>, <18, 19, -5*w^2 - 10*w + 5>, 
    <19, 16, -w^2 + w + 7>, <19, 17, 2*w^2 + 5*w - 3>, <19, 18, 3*w^2 + 3*w - 
    6>, <19, 19, -w^2 - 3*w + 4>, 
    <20, 20, -1>, 
    <21, 20, -6*w^2 - 14*w + 5>, <21, 21, -5*w^2 - 12*w + 5>, <21, 22, -3*w^2 - 
    6*w + 3>, <21, 23, 2*w^2 + 5*w - 2>, 
    <22, 20, 12*w^2 + 29*w - 6>, <22, 21, 11*w^2 + 25*w - 9>, <22, 22, 6*w^2 + 
    15*w - 8>, <22, 23, -5*w^2 - 10*w + 5>, 
    <23, 20, -w^2 + w + 7>, <23, 21, 2*w^2 + 5*w - 3>, <23, 22, 3*w^2 + 3*w - 
    6>, <23, 23, -w^2 - 3*w + 4>, 
    <24, 24, -w^2 - 2*w + 3>, <24, 25, -2*w^2 - 4*w + 3>, <24, 26, -4*w^2 - 6*w 
    + 13>, <24, 27, -w^2 - 2*w + 2>, 
    <25, 24, -w^2 - w + 4>, <25, 25, w + 2>, <25, 26, -5*w^2 - 6*w + 19>, <25, 
    27, -w^2 - w + 4>, 
    <26, 24, -1>, <26, 25, -w^2 - 3*w>, <26, 26, w^2 + w - 6>, <26, 27, -1>, 
    <27, 25, w + 1>, <27, 26, -w^2 - w + 5>, <27, 27, 1>, 
    <28, 28, -w^2 - 2*w + 3>, <28, 29, -2*w^2 - 4*w + 3>, <28, 30, -4*w^2 - 6*w 
    + 13>, <28, 31, -w^2 - 2*w + 2>, 
    <29, 28, -w^2 - w + 4>, <29, 29, w + 2>, <29, 30, -5*w^2 - 6*w + 19>, <29, 
    31, -w^2 - w + 4>, 
    <30, 28, -1>, <30, 29, -w^2 - 3*w>, <30, 30, w^2 + w - 6>, <30, 31, -1>, 
    <31, 29, w + 1>, <31, 30, -w^2 - w + 5>, <31, 31, 1>, 
    <32, 32, -w^2 - 2*w + 3>, <32, 33, -2*w^2 - 4*w + 3>, <32, 34, -4*w^2 - 6*w 
    + 13>, <32, 35, -w^2 - 2*w + 2>, 
    <33, 32, -w^2 - w + 4>, <33, 33, w + 2>, <33, 34, -5*w^2 - 6*w + 19>, <33, 
    35, -w^2 - w + 4>, 
    <34, 32, -1>, <34, 33, -w^2 - 3*w>, <34, 34, w^2 + w - 6>, <34, 35, -1>, 
    <35, 33, w + 1>, <35, 34, -w^2 - w + 5>, <35, 35, 1>
    ])),
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]: Check := false) where w := K.1 where K := ext<K|Polynomial(K, [1, -4, 1, 1])> where K is 
RationalField();
K<w> := BaseRing(M);
K;
M;
