/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^2 + x - 1 [optimized Q(sqrt5)].

Traces:    [ -2, 1 ]
Density:   [ 0.86183673, 0.064285714 ]
Numer max: [ 25, 1 ]
Numer av:  [ 2.3213265, 0.032142857 ]
Denom max: [ 27, 1 ], [ [ <3, 3> ], [] ]
Denom LCM: [ 27, 1 ], [ [ <3, 3> ], [] ]

Character:
( 70, -10, -2, 7, 1, 2, -5*zeta(5)_5^3 - 5*zeta(5)_5^2, 5*zeta(5)_5^3 + 
    5*zeta(5)_5^2 + 5, 0, 0, -1, 1, 0, 0, zeta(5)_5^3 + zeta(5)_5^2 + 1, 
    -zeta(5)_5^3 - zeta(5)_5^2, 0, 0, -1, -zeta(5)_5^3 - zeta(5)_5^2 - 1, 
    zeta(5)_5^3 + zeta(5)_5^2 )
*/

G := PermutationGroup(ATLASGroup("J2"));
M :=
GModule(G, [
    Matrix(K, 70, 70,
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    <56, 29, 1>, <56, 43, -1>, <56, 51, -1>, <56, 63, -1>,  <57, 25, 1>, <57, 
    33, 1>, <57, 52, 1>, <57, 57, 1>, <57, 63, -1>,  <58, 26, -1>, <58, 33, -1>,
    <58, 37, -1>, <58, 43, 1>, <58, 52, -1>, <58, 63, 1>,  <59, 18, 1>, <59, 28,
    -1>, <59, 29, -1>, <59, 32, -1>, <59, 52, 1>, <59, 63, -1>,  <60, 18, -1>, 
    <60, 23, -1>, <60, 28, 1>, <60, 29, 1>, <60, 35, 1>, <60, 52, -1>, <60, 63, 
    1>,  <61, 26, -1>, <61, 28, -1>, <61, 29, -1>, <61, 33, -1>, <61, 43, 1>, 
    <61, 63, 1>, <61, 64, 1>,  <62, 18, -1>, <62, 28, 1>, <62, 29, 1>, <62, 33, 
    1>, <62, 39, 1>, <62, 46, -1>,  <63, 18, -1>, <63, 25, 1>, <63, 26, -1>, 
    <63, 33, 1>, <63, 39, 1>, <63, 63, -1>,  <64, 33, -1>, <64, 39, -1>, <64, 
    52, -1>, <64, 53, 1>, <64, 63, 1>,  <65, 18, -1>, <65, 28, 1>, <65, 29, 1>, 
    <65, 39, 1>, <65, 52, -1>, <65, 63, 1>, <65, 68, 1>,  <66, 18, -1>, <66, 28,
    1>, <66, 29, 1>, <66, 33, 1>, <66, 39, 1>, <66, 43, -1>, <66, 59, 1>, <66, 
    63, -1>,  <67, 18, -1>, <67, 26, -1>, <67, 29, 1>, <67, 33, 1>, <67, 39, 1>,
    <67, 55, -1>, <67, 63, -1>,  <68, 18, 1>, <68, 28, -1>, <68, 29, -1>, <68, 
    33, -1>, <68, 38, -1>, <68, 43, 1>, <68, 63, 1>,  <69, 18, -1>, <69, 28, 1>,
    <69, 29, 1>, <69, 33, 1>, <69, 39, 1>, <69, 52, -1>,  <70, 18, -1>, <70, 33,
    1>, <70, 39, 1>, <70, 52, 1>, <70, 60, -1>, <70, 63, -1> ]))
]: Check := false) where w := K.1 where K := ext<K|Polynomial(K, [-1, 1, 1])> where K is 
RationalField();
K<w> := BaseRing(M);
K;
M;
