/*
Generated by Allan Steel in Magma, 2011.

Field defining polynomial: x^2 + x + 18 [optimized Q(sqrt(-71)]].

Traces:    [ 0, 0 ]
Density:   [ 0.99074074, 0.98919753 ]
Numer max: [ 140260, 191025 ]
Numer av:  [ 10662.322, 9768.7018 ]
Denom max: [ 71, 71 ], [ [ <71, 1> ], [ <71, 1> ] ]
Denom LCM: [ 71, 71 ], [ [ <71, 1> ], [ <71, 1> ] ]

Character:
( 36, -36, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, -1, -1, -1, 0, 
0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, 
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -zeta(71)_71^64 - zeta(71)_71^60 - 
    zeta(71)_71^58 - zeta(71)_71^57 - zeta(71)_71^54 - zeta(71)_71^50 - 
    zeta(71)_71^49 - zeta(71)_71^48 - zeta(71)_71^45 - zeta(71)_71^43 - 
    zeta(71)_71^40 - zeta(71)_71^38 - zeta(71)_71^37 - zeta(71)_71^36 - 
    zeta(71)_71^32 - zeta(71)_71^30 - zeta(71)_71^29 - zeta(71)_71^27 - 
    zeta(71)_71^25 - zeta(71)_71^24 - zeta(71)_71^20 - zeta(71)_71^19 - 
    zeta(71)_71^18 - zeta(71)_71^16 - zeta(71)_71^15 - zeta(71)_71^12 - 
    zeta(71)_71^10 - zeta(71)_71^9 - zeta(71)_71^8 - zeta(71)_71^6 - 
    zeta(71)_71^5 - zeta(71)_71^4 - zeta(71)_71^3 - zeta(71)_71^2 - zeta(71)_71,
    zeta(71)_71^64 + zeta(71)_71^60 + zeta(71)_71^58 + zeta(71)_71^57 + 
    zeta(71)_71^54 + zeta(71)_71^50 + zeta(71)_71^49 + zeta(71)_71^48 + 
    zeta(71)_71^45 + zeta(71)_71^43 + zeta(71)_71^40 + zeta(71)_71^38 + 
    zeta(71)_71^37 + zeta(71)_71^36 + zeta(71)_71^32 + zeta(71)_71^30 + 
    zeta(71)_71^29 + zeta(71)_71^27 + zeta(71)_71^25 + zeta(71)_71^24 + 
    zeta(71)_71^20 + zeta(71)_71^19 + zeta(71)_71^18 + zeta(71)_71^16 + 
    zeta(71)_71^15 + zeta(71)_71^12 + zeta(71)_71^10 + zeta(71)_71^9 + 
    zeta(71)_71^8 + zeta(71)_71^6 + zeta(71)_71^5 + zeta(71)_71^4 + 
    zeta(71)_71^3 + zeta(71)_71^2 + zeta(71)_71 + 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, 0, 0, -zeta(71)_71^64 - zeta(71)_71^60 - zeta(71)_71^58 - zeta(71)_71^57
    - zeta(71)_71^54 - zeta(71)_71^50 - zeta(71)_71^49 - zeta(71)_71^48 - 
    zeta(71)_71^45 - zeta(71)_71^43 - zeta(71)_71^40 - zeta(71)_71^38 - 
    zeta(71)_71^37 - zeta(71)_71^36 - zeta(71)_71^32 - zeta(71)_71^30 - 
    zeta(71)_71^29 - zeta(71)_71^27 - zeta(71)_71^25 - zeta(71)_71^24 - 
    zeta(71)_71^20 - zeta(71)_71^19 - zeta(71)_71^18 - zeta(71)_71^16 - 
    zeta(71)_71^15 - zeta(71)_71^12 - zeta(71)_71^10 - zeta(71)_71^9 - 
    zeta(71)_71^8 - zeta(71)_71^6 - zeta(71)_71^5 - zeta(71)_71^4 - 
    zeta(71)_71^3 - zeta(71)_71^2 - zeta(71)_71 - 1, zeta(71)_71^64 + 
    zeta(71)_71^60 + zeta(71)_71^58 + zeta(71)_71^57 + zeta(71)_71^54 + 
    zeta(71)_71^50 + zeta(71)_71^49 + zeta(71)_71^48 + zeta(71)_71^45 + 
    zeta(71)_71^43 + zeta(71)_71^40 + zeta(71)_71^38 + zeta(71)_71^37 + 
    zeta(71)_71^36 + zeta(71)_71^32 + zeta(71)_71^30 + zeta(71)_71^29 + 
    zeta(71)_71^27 + zeta(71)_71^25 + zeta(71)_71^24 + zeta(71)_71^20 + 
    zeta(71)_71^19 + zeta(71)_71^18 + zeta(71)_71^16 + zeta(71)_71^15 + 
    zeta(71)_71^12 + zeta(71)_71^10 + zeta(71)_71^9 + zeta(71)_71^8 + 
    zeta(71)_71^6 + zeta(71)_71^5 + zeta(71)_71^4 + zeta(71)_71^3 + 
    zeta(71)_71^2 + zeta(71)_71 )
*/

G := c9Group("sl271p");
M :=
GModule(G, [
    Matrix(K, 36, 36,
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]: Check := false) where w := K.1 where K := ext<K|Polynomial(K, [18, 1, 1])> where K is 
RationalField();
K<w>:=BaseRing(M);
M;
K;
