/*
Generated by Allan Steel in Magma, 2010.

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

Traces:    [ 0, 0 ]
Density:   [ 0.025000000, 0.96062500 ]
Numer max: [ 1, 9 ]
Numer av:  [ 0.0083333333, 1.3006250 ]
Denom max: [ 1, 8 ], [ [], [ <2, 3> ] ]
Denom LCM: [ 1, 8 ], [ [], [ <2, 3> ] ]

Character:
( 40, -40, 0, 0, 0, 0, zeta(7)_7^5 + zeta(7)_7^4 + zeta(7)_7^3 + zeta(7)_7^2 + 
    1, -zeta(7)_7^4 - zeta(7)_7^3, -zeta(7)_7^5 - zeta(7)_7^2, 0, 1, 1, 1, 
    zeta(7)_7^4 + zeta(7)_7^3, zeta(7)_7^5 + zeta(7)_7^2, -zeta(7)_7^5 - 
    zeta(7)_7^4 - zeta(7)_7^3 - zeta(7)_7^2 - 1, -1, -1, -1 )
*/

G:=PermutationGroup(ATLASGroup("2Sz8"));
M:=
GModule(G, [
    Matrix(SparseMatrix(K, 40, 40, [
    <1, 6, -1>, 
    <2, 8, -1>, 
    <3, 5, 1>, 
    <4, 7, -1>, 
    <5, 3, 1>, 
    <6, 1, -1>, 
    <7, 4, -1>, 
    <8, 2, -1>, 
    <9, 14, -1>, 
    <10, 16, -1>, 
    <11, 13, 1>, 
    <12, 15, -1>, 
    <13, 11, 1>, 
    <14, 9, -1>, 
    <15, 12, -1>, 
    <16, 10, -1>, 
    <17, 22, -1>, 
    <18, 24, -1>, 
    <19, 21, 1>, 
    <20, 23, -1>, 
    <21, 19, 1>, 
    <22, 17, -1>, 
    <23, 20, -1>, 
    <24, 18, -1>, 
    <25, 30, -1>, 
    <26, 32, -1>, 
    <27, 29, 1>, 
    <28, 31, -1>, 
    <29, 27, 1>, 
    <30, 25, -1>, 
    <31, 28, -1>, 
    <32, 26, -1>, 
    <33, 38, -1>, 
    <34, 40, -1>, 
    <35, 37, 1>, 
    <36, 39, -1>, 
    <37, 35, 1>, 
    <38, 33, -1>, 
    <39, 36, -1>, 
    <40, 34, -1>
    ])),
    Matrix(K, 40, 40,
        [ [ -3/8, -1/8, 1/4 ], [ 1/4, -1/8, -1/8 ], [ -1/8, 1/8, 1/8 ], [ 1/4, 
        -1/8, -1/8 ], [ -1/8, 0, 0 ], [ 1/8, 0, -1/8 ], [ -1/2, 0, 1/4 ], [ 0, 
        0, 0 ], [ -1/2, -3/8, 3/8 ], [ 0, 0, 0 ], [ 1/8, 1/8, -1/4 ], [ 5/8, 0, 
        -1/4 ], [ -1/8, 0, 1/8 ], [ 0, 0, 0 ], [ -1/8, -1/8, 3/8 ], [ -1/2, 
        -1/8, 3/8 ], [ 1/8, -1/8, -1/4 ], [ -1/4, 1/8, 1/8 ], [ 1/4, -1/8, -1/8 
        ], [ 1/2, 0, -1/8 ], [ 1/2, 0, -1/8 ], [ 1/8, 0, 0 ], [ 1/4, -1/8, -1/8 
        ], [ -1/4, 0, 1/8 ], [ -1/8, 0, 1/8 ], [ -1/8, 1/8, 1/8 ], [ 0, 0, -1/8 
        ], [ -3/8, 1/8, 1/8 ], [ -3/8, 1/8, 1/4 ], [ 0, -1/8, 0 ], [ -1/2, 0, 
        1/4 ], [ 1/4, 0, 0 ], [ 3/8, 3/8, -1/2 ], [ -1/8, 1/8, 1/8 ], [ 0, -1/4,
        1/4 ], [ -1/8, 0, 1/8 ], [ 1/8, 1/8, -1/8 ], [ 0, 0, -1/8 ], [ 1/2, 1/8,
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        -1/4 ], [ 0, 1/4, 0 ], [ 1/8, -1/8, 0 ], [ -1/8, -1/8, 1/4 ], [ 1/4, 0, 
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]: Check := false) where w := K.1 where K := ext<K|Polynomial(K, [-1, -2, 1, 1])> where K is 
RationalField();
K<w> := BaseRing(M);
K;
M;
