/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^2 + x + 5 [optimized Q(sqrt(-19)]].
Schur index 2 (rational character).

Traces:    [ -19, 0 ]
Density:   [ 0.99785467, 0.99868512 ]
1>, <5, 1>, <19, 1> ] ]
Numer max: [ 1613, 1983 ]
Numer av:  [ 34.789360, 40.926626 ]
Denom max: [ 4560, 9120 ], [ [ <2, 4>, <3, 1>, <5, 1>, <19, 1> ],
	   [ <2, 5>, <3, 1>, <5, 1>, <19, 1> ] ]
Denom LCM: [ 36480, 36480 ], [ [ <2, 7>, <3, 1>, <5, 1>, <19, 1> ],
	   [ <2, 7>, <3, 1>, <5, 1>, <19, 1> ] ]
*/

G := PSU(9, 2);
M :=
GModule(G, [
    Matrix(K, 170, 170,
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]: Check := false) where w := K.1 where K := ext<K|Polynomial(K, [5, 1, 1])> where K is 
RationalField();
K<w> := BaseRing(M);
K;
M;
