/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^2 + x + 1 [Q(zeta_3)].

Traces:    [ -39, w ]
Density:   [ 0.0082644628, 0.95546752 ]
Numer max: [ 1, 97 ]
Numer av:  [ 0.0041322314, 3.3268220 ]
Denom max: [ 1, 72 ], [ [], [ <2, 3>, <3, 2> ] ]
Denom LCM: [ 1, 72 ], [ [], [ <2, 3>, <3, 2> ] ]
*/

G := PSp(10, 3);
M:= GModule(G, [
    DiagonalMatrix(K, 
        \[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 
        -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 
        -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 
        -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
        -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 
        -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 
        -1, -1, -1, -1 ]
    ),
    Matrix(K, 121, 121,
        [ [ -1/4, -1/4 ], [ 0, 0 ], [ 1/6, 1/12 ], [ -1/4, -1/4 ], [ -1/6, -1/12
        ], [ 0, 0 ], [ 1/6, 1/12 ], [ 0, 0 ], [ -1/6, -1/12 ], [ -1/6, -1/12 ], 
        [ -1/6, -1/12 ], [ 0, 0 ], [ 1/12, 1/6 ], [ 1/3, 1/6 ], [ -1/6, -1/12 ],
        [ 1/4, 1/4 ], [ 1/4, 1/4 ], [ 1/6, 1/12 ], [ -1/6, -1/12 ], [ 0, 0 ], [ 
        -1/72, 1/72 ], [ -1/18, 1/72 ], [ -1/18, 1/72 ], [ 1/36, 1/18 ], [ 1/24,
        0 ], [ 1/36, 1/72 ], [ -1/12, -1/12 ], [ 1/36, -1/36 ], [ 1/18, 1/36 ], 
        [ 0, 1/24 ], [ 1/36, 1/72 ], [ -1/36, 1/36 ], [ -1/18, -1/36 ], [ 1/24, 
        -1/24 ], [ 0, 0 ], [ 1/24, 0 ], [ -1/36, -1/18 ], [ -1/36, 1/9 ], [ 
        1/24, 0 ], [ -1/72, 1/72 ], [ 1/24, 0 ], [ 5/72, 1/18 ], [ -1/72, 1/72 
        ], [ -1/36, 1/36 ], [ 0, 0 ], [ 1/72, 1/36 ], [ 7/72, 1/36 ], [ 1/72, 
        -1/72 ], [ 1/18, -1/72 ], [ 1/72, 1/36 ], [ 0, -1/24 ], [ 1/24, -1/24 ],
        [ 1/8, 1/24 ], [ 1/36, 1/72 ], [ -1/72, 1/72 ], [ 1/18, 1/36 ], [ -1/12,
        -1/12 ], [ 0, 0 ], [ 1/18, -1/72 ], [ 1/24, 0 ], [ -1/6, -1/12 ], [ 0, 0
        ], [ -1/12, -1/6 ], [ -1/12, 1/12 ], [ -1/6, -1/12 ], [ 1/6, 1/12 ], [ 
        -1/6, -1/12 ], [ -1/12, 1/12 ], [ 0, 0 ], [ -1/12, 1/12 ], [ 0, 0 ], [ 
        1/12, -1/12 ], [ 1/12, -1/12 ], [ 1/4, 0 ], [ -1/12, 1/12 ], [ -1/12, 
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        0, 1/24 ], [ 0, -1/24 ], [ 7/24, 1/12 ], [ -1/6, 1/6 ], [ 1/24, 1/6 ], [
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        1/24 ], [ 0, -1/12 ], [ 1/12, -1/8 ], [ 1/12, -1/8 ], [ 1/6, 0 ], [ 0, 
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        1/12 ], [ 0, 0 ], [ -1/6, -1/3 ], [ -1/12, 1/12 ], [ -1/72, 1/18 ], [ 
        -5/72, -7/72 ], [ 1/24, 1/24 ], [ 1/72, 1/36 ], [ -1/24, -1/12 ], [ 
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        -1/18 ], [ -1/36, 1/36 ], [ 1/36, 1/72 ], [ 0, 1/24 ], [ -1/24, -1/24 ],
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]: Check := false) where w := K.1 where K := CyclotomicField(3);
K<w>:=BaseRing(M);
K;
M;
