/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^2 + 1 [Q(zeta_4)].
Schur index 2 (rational character).

Traces:    [ -16, 0 ]
Density:   [ 0.78541667, 0.0041666667 ]
Numer max: [ 3, 1 ]
Numer av:  [ 0.76614583, 0.0020833333 ]
Denom max: [ 32, 1 ], [ [ <2, 5> ], [] ]
Denom LCM: [ 32, 1 ], [ [ <2, 5> ], [] ]

Character:
( 240, -16, 0, 0, 0, 0, 0, 0, 0, 0, -15, -15, -15, -15, -15, -15, -15, -15, 
    -15, -15, -15, -15, -15, -15, -15, -15, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
    2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
        2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 0, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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, 
    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, 
    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, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 )
*/

G := PermutationGroup(ATLASGroup("U316"));
M :=
GModule(G, [
    Matrix(K, 240, 240,
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    38, w>,  <176, 50, w>,  <177, 48, -w>,  <178, 49, 1>,  <179, 56, 1>,  <180, 
    51, 1>,  <181, 57, -w>,  <182, 58, 1>,  <183, 55, w>,  <184, 52, 1>,  <185, 
    54, 1>,  <186, 64, w>,  <187, 172, -w>,  <188, 81, w>,  <189, 63, 1>,  <190,
    66, 1>,  <191, 65, 1>,  <192, 53, 1>,  <193, 61, -1>,  <194, 62, 1>,  <195, 
    60, 1>,  <196, 171, 1>,  <197, 29, 1>,  <198, 170, 1>,  <199, 177, -w>,  
    <200, 174, w>,  <201, 167, -1>,  <202, 164, w>,  <203, 166, -1>,  <204, 239,
    1>,  <205, 168, 1>,  <206, 178, w>,  <207, 162, 1>,  <208, 176, 1>,  <209, 
    175, 1>,  <210, 169, -w>,  <211, 24, w>,  <212, 74, -1>,  <213, 84, 1>,  
    <214, 88, w>,  <215, 77, w>,  <216, 76, w>,  <217, 79, 1>,  <218, 78, -w>,  
    <219, 70, 1>,  <220, 71, w>,  <221, 68, w>,  <222, 69, w>,  <223, 72, 1>,  
    <224, 67, 1>,  <225, 75, w>,  <226, 15, 1>,  <227, 11, 1>,  <228, 1, 1>,  
    <229, 17, -1>,  <230, 13, -w>,  <231, 12, -1>,  <232, 16, -w>,  <233, 19, 
    1>,  <234, 7, -w>,  <235, 3, -w>,  <236, 10, -1>,  <237, 5, w>,  <238, 8, 
    -1>,  <239, 6, w>,  <240, 2, -w> ]))
]: Check := false) where w := K.1 where K := CyclotomicField(4);
K<w> := BaseRing(M);
K;
M;
