/*
L2(32) as 33 x 33 monomial matrices over Z[z31].
Representation 33a.
Absolutely irreducible representation.
Schur Index 1 [despite being written over a field of dimension 2 over
the field of character values (which is Q(y31))].

SEED:
Nonzero v such that v.x = v and v.y*x*y*x*y^-1*x*y*x*y^-1*x*y = z31^5*v
where <x,y*x*y*x*y^-1*x*y*x*y^-1*x*y> = 2^5:31.
v has 31 x 33 = 1023 images under G; <v> has 33 images under G.
BASIS:
NSB([x,y,y^2]) with above v.

Possible matrix entries are in {0,1,z31^j:1<=j<=30} (all of norm 1).

Number of nonzero entries for any element of the group:
33  (33 exactly; about 3.030%).

  Entry  Av/Mat             %Av/Mat
      0  1056                 96.970 [96+32/33]
nonzero    33                  3.030  [3+1/33]
      1     1.065  [1+2/31]    0.098 [100/1023]
  z31^j     1.065  [1+2/31]    0.098 [100/1023]  [holds for each j.]
*/


F<z31>:=CyclotomicField(31);
// F<w>:=GF(61^2);z31:=w^120;

G<x,y>:=MatrixGroup<33,F|[
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,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,z31^5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,z31^26,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,z31^26,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,z31^5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
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,z31,0,0,
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,z31^30,0,0,0,
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,z31^30,
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,z31,0]
,[
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,z31^12,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,z31^19,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,z31^19,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,z31^12,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0]
>;

// Forms: B1 (Symmetric); B2 (Hermitian).

// B1 (Symmetric form): Determinant has norm 2^2475.
B1:=MatrixAlgebra(F,33)![
0,1,1,1,1,z31^4,z31^10,z31^10,z31^4,z31^4,z31^10,z31^10,z31^4,z31^20,z31^13,z31^8,z31^13,z31^13,z31^8,z31^13,z31^20,z31^20,z31^13,z31^13,z31^20,z31^12,z31^24,z31^12,z31^24,z31^26,z31^25,z31^6,z31^7,
1,0,1,z31^10,z31^4,1,z31^4,1,z31^10,z31^13,z31^13,z31^8,z31^20,z31^4,z31^20,z31^10,z31^8,z31^10,z31^13,z31^4,z31^13,z31^1,z31^1,z31^24,z31^12,z31^20,z31^13,z31^25,z31^7,z31^12,z31^26,z31^24,z31^6,
1,1,0,z31^4,z31^10,z31^10,1,z31^4,1,z31^20,z31^8,z31^13,z31^13,z31^13,z31^4,z31^13,z31^10,z31^8,z31^10,z31^20,z31^4,z31^12,z31^24,z31^1,z31^1,z31^1,z31^1,z31^26,z31^6,z31^25,z31^12,z31^7,z31^24,
1,z31^10,z31^4,0,1,z31^13,z31^13,z31^8,z31^20,1,z31^4,1,z31^10,z31^1,z31^18,z31^30,z31^1,z31^24,z31^15,z31^15,z31^12,z31^4,z31^8,z31^10,z31^13,z31^25,z31^7,z31^20,z31^13,z31^27,z31^11,z31^5,z31^25,
1,z31^4,z31^10,1,0,z31^20,z31^8,z31^13,z31^13,z31^10,1,z31^4,1,z31^12,z31^15,z31^15,z31^24,z31^1,z31^30,z31^18,z31^1,z31^13,z31^10,z31^8,z31^4,z31^26,z31^6,z31^1,z31^1,z31^13,z31^24,z31^23,z31^8,
z31^4,1,z31^10,z31^13,z31^20,0,z31^13,1,z31^8,z31^18,z31^1,z31^15,z31^12,1,z31^1,z31^4,z31^30,1,z31^24,z31^10,z31^15,z31^29,z31^25,z31^6,z31^26,z31^4,z31^8,z31^11,z31^25,z31^20,z31^27,z31^13,z31^5,
z31^10,z31^4,1,z31^13,z31^8,z31^13,0,z31^20,1,z31^1,z31^30,z31^24,z31^15,z31^18,1,z31^1,z31^4,z31^15,1,z31^12,z31^10,z31^25,z31^7,z31^16,z31^27,z31^29,z31^25,z31^27,z31^5,z31^11,z31^20,z31^25,z31^13,
z31^10,1,z31^4,z31^8,z31^13,1,z31^20,0,z31^13,z31^15,z31^24,z31^30,z31^1,z31^10,z31^12,1,z31^15,z31^4,z31^1,1,z31^18,z31^27,z31^16,z31^7,z31^25,z31^13,z31^10,z31^24,z31^8,z31^1,z31^13,z31^1,z31^23,
z31^4,z31^10,1,z31^20,z31^13,z31^8,1,z31^13,0,z31^12,z31^15,z31^1,z31^18,z31^15,z31^10,z31^24,1,z31^30,z31^4,z31^1,1,z31^26,z31^6,z31^25,z31^29,z31^27,z31^16,z31^13,z31^23,z31^24,z31^1,z31^8,z31^1,
z31^4,z31^13,z31^20,1,z31^10,z31^18,z31^1,z31^15,z31^12,0,z31^13,1,z31^8,z31^29,z31^29,z31^5,z31^25,z31^6,z31^27,z31^9,z31^26,1,z31^30,1,z31^15,z31^11,z31^25,z31^4,z31^8,z31^28,z31^19,z31^4,z31^14,
z31^10,z31^13,z31^8,z31^4,1,z31^1,z31^30,z31^24,z31^15,z31^13,0,z31^20,1,z31^25,z31^5,z31^7,z31^7,z31^16,z31^26,z31^6,z31^27,z31^18,z31^4,z31^15,z31^10,z31^27,z31^5,z31^29,z31^25,z31^21,z31^10,z31^12,z31^26,
z31^10,z31^8,z31^13,1,z31^4,z31^15,z31^24,z31^30,z31^1,1,z31^20,0,z31^13,z31^27,z31^6,z31^26,z31^16,z31^7,z31^7,z31^5,z31^25,z31^10,z31^15,z31^4,z31^18,z31^24,z31^8,z31^13,z31^10,z31^14,1,z31^22,z31^2,
z31^4,z31^20,z31^13,z31^10,1,z31^12,z31^15,z31^1,z31^18,z31^8,1,z31^13,0,z31^26,z31^9,z31^27,z31^6,z31^25,z31^5,z31^29,z31^29,z31^15,1,z31^30,1,z31^13,z31^23,z31^27,z31^16,z31^2,z31^23,1,z31^9,
z31^20,z31^4,z31^13,z31^1,z31^12,1,z31^18,z31^10,z31^15,z31^29,z31^25,z31^27,z31^26,0,z31^29,z31^13,z31^5,1,z31^6,z31^8,z31^9,z31^19,z31^27,z31^23,z31^13,1,z31^30,z31^19,z31^14,z31^4,z31^28,z31^8,z31^4,
z31^13,z31^20,z31^4,z31^18,z31^15,z31^1,1,z31^12,z31^10,z31^29,z31^5,z31^6,z31^9,z31^29,0,z31^25,z31^13,z31^27,1,z31^26,z31^8,z31^11,z31^25,z31^12,z31^18,z31^19,z31^27,z31^28,z31^4,z31^19,z31^4,z31^14,z31^8,
z31^8,z31^10,z31^13,z31^30,z31^15,z31^4,z31^1,1,z31^24,z31^5,z31^7,z31^26,z31^27,z31^13,z31^25,0,z31^7,z31^20,z31^16,1,z31^6,z31^3,z31^22,z31^8,z31^24,z31^18,z31^4,z31^10,z31^26,z31^29,z31^21,z31^25,z31^12,
z31^13,z31^8,z31^10,z31^1,z31^24,z31^30,z31^4,z31^15,1,z31^25,z31^7,z31^16,z31^6,z31^5,z31^13,z31^7,0,z31^26,z31^20,z31^27,1,z31^27,z31^5,z31^30,z31^23,z31^3,z31^22,z31^21,z31^12,z31^10,z31^29,z31^26,z31^25,
z31^13,z31^10,z31^8,z31^24,z31^1,1,z31^15,z31^4,z31^30,z31^6,z31^16,z31^7,z31^25,1,z31^27,z31^20,z31^26,0,z31^7,z31^13,z31^5,z31^23,z31^30,z31^5,z31^27,z31^10,z31^15,1,z31^2,z31^13,z31^14,z31^10,z31^22,
z31^8,z31^13,z31^10,z31^15,z31^30,z31^24,1,z31^1,z31^4,z31^27,z31^26,z31^7,z31^5,z31^6,1,z31^16,z31^20,z31^7,0,z31^25,z31^13,z31^24,z31^8,z31^22,z31^3,z31^23,z31^30,z31^14,z31^22,1,z31^13,z31^2,z31^10,
z31^13,z31^4,z31^20,z31^15,z31^18,z31^10,z31^12,1,z31^1,z31^9,z31^6,z31^5,z31^29,z31^8,z31^26,1,z31^27,z31^13,z31^25,0,z31^29,z31^18,z31^12,z31^25,z31^11,z31^15,1,z31^23,z31^9,z31^27,z31^2,z31^16,1,
z31^20,z31^13,z31^4,z31^12,z31^1,z31^15,z31^10,z31^18,1,z31^26,z31^27,z31^25,z31^29,z31^9,z31^8,z31^6,1,z31^5,z31^13,z31^29,0,z31^13,z31^23,z31^27,z31^19,z31^18,z31^12,z31^2,1,z31^23,z31^27,z31^9,z31^16,
z31^20,z31^1,z31^12,z31^4,z31^13,z31^29,z31^25,z31^27,z31^26,1,z31^18,z31^10,z31^15,z31^19,z31^11,z31^3,z31^27,z31^23,z31^24,z31^18,z31^13,0,z31^5,1,z31^9,z31^19,z31^14,1,z31^30,z31^29,z31^3,z31^3,z31^9,
z31^13,z31^1,z31^24,z31^8,z31^10,z31^25,z31^7,z31^16,z31^6,z31^30,z31^4,z31^15,1,z31^27,z31^25,z31^22,z31^5,z31^30,z31^8,z31^12,z31^23,z31^5,0,z31^26,1,z31^21,z31^12,z31^3,z31^22,z31^30,z31^9,z31^24,z31^27,
z31^13,z31^24,z31^1,z31^10,z31^8,z31^6,z31^16,z31^7,z31^25,1,z31^15,z31^4,z31^30,z31^23,z31^12,z31^8,z31^30,z31^5,z31^22,z31^25,z31^27,1,z31^26,0,z31^5,1,z31^2,z31^10,z31^15,z31^15,z31^12,z31^21,z31^11,
z31^20,z31^12,z31^1,z31^13,z31^4,z31^26,z31^27,z31^25,z31^29,z31^15,z31^10,z31^18,1,z31^13,z31^18,z31^24,z31^23,z31^27,z31^3,z31^11,z31^19,z31^9,1,z31^5,0,z31^2,1,z31^18,z31^12,z31^28,z31^22,z31^15,z31^10,
z31^12,z31^20,z31^1,z31^25,z31^26,z31^4,z31^29,z31^13,z31^27,z31^11,z31^27,z31^24,z31^13,1,z31^19,z31^18,z31^3,z31^10,z31^23,z31^15,z31^18,z31^19,z31^21,1,z31^2,0,z31^5,z31^3,z31^9,1,z31^29,z31^30,z31^3,
z31^24,z31^13,z31^1,z31^7,z31^6,z31^8,z31^25,z31^10,z31^16,z31^25,z31^5,z31^8,z31^23,z31^30,z31^27,z31^4,z31^22,z31^15,z31^30,1,z31^12,z31^14,z31^12,z31^2,1,z31^5,0,z31^9,z31^27,z31^3,z31^30,z31^22,z31^24,
z31^12,z31^25,z31^26,z31^20,z31^1,z31^11,z31^27,z31^24,z31^13,z31^4,z31^29,z31^13,z31^27,z31^19,z31^28,z31^10,z31^21,1,z31^14,z31^23,z31^2,1,z31^3,z31^10,z31^18,z31^3,z31^9,0,z31^5,z31^30,z31^30,z31^2,1,
z31^24,z31^7,z31^6,z31^13,z31^1,z31^25,z31^5,z31^8,z31^23,z31^8,z31^25,z31^10,z31^16,z31^14,z31^4,z31^26,z31^12,z31^2,z31^22,z31^9,1,z31^30,z31^22,z31^15,z31^12,z31^9,z31^27,z31^5,0,1,z31^2,z31^23,z31^23,
z31^26,z31^12,z31^25,z31^27,z31^13,z31^20,z31^11,z31^1,z31^24,z31^28,z31^21,z31^14,z31^2,z31^4,z31^19,z31^29,z31^10,z31^13,1,z31^27,z31^23,z31^29,z31^30,z31^15,z31^28,1,z31^3,z31^30,1,0,z31^30,z31^5,z31^2,
z31^25,z31^26,z31^12,z31^11,z31^24,z31^27,z31^20,z31^13,z31^1,z31^19,z31^10,1,z31^23,z31^28,z31^4,z31^21,z31^29,z31^14,z31^13,z31^2,z31^27,z31^3,z31^9,z31^12,z31^22,z31^29,z31^30,z31^30,z31^2,z31^30,0,1,z31^5,
z31^6,z31^24,z31^7,z31^5,z31^23,z31^13,z31^25,z31^1,z31^8,z31^4,z31^12,z31^22,1,z31^8,z31^14,z31^25,z31^26,z31^10,z31^2,z31^16,z31^9,z31^3,z31^24,z31^21,z31^15,z31^30,z31^22,z31^2,z31^23,z31^5,1,0,z31^23,
z31^7,z31^6,z31^24,z31^25,z31^8,z31^5,z31^13,z31^23,z31^1,z31^14,z31^26,z31^2,z31^9,z31^4,z31^8,z31^12,z31^25,z31^22,z31^10,1,z31^16,z31^9,z31^27,z31^11,z31^10,z31^3,z31^24,1,z31^23,z31^2,z31^5,z31^23,0];

// B2 (Hermitian form): Identity matrix, Determinant 1.
B2:=MatrixAlgebra(F,33)!(x*x);


// Centralising algebra: Scalars only.
C1:=B2;