/* Group 1728.34797 downloaded from the LMFDB on 11 November 2025. */
 
/* Various presentations of this group are stored in this file: 
	 GPC is polycyclic presentation GPerm is permutation group 
	 GLZ, GLFp, GLZA, GLZq, GLFq if they exist are matrix groups 
 
 Many characteristics of the group are stored as booleans in a record: 
	 Agroup, Zgroup, abelian, almost_simple,cyclic, metabelian, 
	 metacyclic, monomial, nilpotent, perfect, quasisimple, rational, 
	 solvable, supersolvable 
 
 The character table is stored as chartbl_n_i where n is the order of 
 the group and i is which group of that order it is. Conjugacy classes 
 are stored in the variable 'C' with elements from the group 'G'. 
*/
 
/* Constructions */
GPC := PCGroup([9, 2, 2, 3, 2, 2, 3, 2, 2, 3, 648, 181, 46, 218, 31539, 1092, 102, 2713, 130, 2606, 13614, 34035, 3813, 186, 8674, 214, 7811]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.4, GPC.7]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "c4", "d", "d2", "d4"]);
GPerm := PermutationGroup< 25 | (13,14)(15,16)(18,21), (15,17,16,20)(18,22,21,19)(24,25), (1,2,4,6)(3,7,8,5)(10,11)(15,18,16,21)(17,19,20,22), (1,3,4,8)(2,5,6,7)(15,19)(16,22)(17,18)(20,21), (1,4)(2,6)(3,8)(5,7)(15,16)(17,20)(18,21)(19,22), (15,16)(17,20)(18,21)(19,22), (23,24,25), (12,13,14), (9,10,11) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_1728_34797 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>; 

 
/* Character Table */
G:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, c^6*d^6>,< 2, 1, c^6>,< 2, 1, d^6>,< 2, 6, b^3>,< 2, 6, b^3*c^2>,< 2, 18, b^3*c*d>,< 2, 18, b^3*c*d^3>,< 3, 2, d^4>,< 3, 2, b^2>,< 3, 2, c^4>,< 3, 4, c^4*d^4>,< 3, 4, b^4*d^4>,< 3, 4, b^2*c^4>,< 3, 8, b^4*c^4*d^8>,< 4, 4, d^9>,< 4, 6, c^3*d^7>,< 4, 6, c^3*d^9>,< 4, 6, c^9>,< 4, 6, c^3>,< 4, 12, a*c^6>,< 4, 12, b^3*c^6*d^3>,< 4, 12, a*d^3>,< 4, 18, a*b*c^6>,< 4, 18, a*b>,< 4, 36, b^3*c^7>,< 4, 36, a*b*c^4*d^3>,< 4, 36, a*b^2*c^3*d^11>,< 4, 36, a*b^4*c^3*d^2>,< 4, 54, a*b*c*d^10>,< 4, 54, a*b*c^3*d^8>,< 4, 108, a*b^3*c^7*d^11>,< 6, 2, c^6*d^2>,< 6, 2, c^8*d^6>,< 6, 2, b^4*d^6>,< 6, 2, b^4*c^6>,< 6, 2, d^2>,< 6, 2, c^2*d^6>,< 6, 2, b^4*c^6*d^6>,< 6, 2, c^2>,< 6, 2, c^6*d^8>,< 6, 4, c^2*d^2>,< 6, 4, b^2*c^6*d^2>,< 6, 4, b^4*c^8*d^6>,< 6, 4, c^8*d^2>,< 6, 4, b^4*d^2>,< 6, 4, b^4*c^2*d^6>,< 6, 4, b^4*c^2>,< 6, 4, b^2*c^6*d^8>,< 6, 4, c^2*d^8>,< 6, 8, b^2*c^2*d^4>,< 6, 8, b^2*c^2*d^2>,< 6, 8, b^4*c^8*d^2>,< 6, 12, b>,< 6, 12, b*c^2>,< 6, 12, b^3*d^4>,< 6, 12, b^3*d^2>,< 6, 24, b*d^4>,< 6, 24, b*d^2>,< 6, 36, b*c*d>,< 6, 36, b*c*d^3>,< 12, 4, c^4*d^3>,< 12, 4, c^2*d^3>,< 12, 4, b^2*d^3>,< 12, 4, b^2*d^9>,< 12, 4, b^2*c^4*d^3>,< 12, 4, b^2*c^2*d^3>,< 12, 4, b^2*c^8*d^3>,< 12, 4, b^4*c^4*d^3>,< 12, 6, b^2*c^3>,< 12, 6, b^4*c^9>,< 12, 6, b^4*c^3>,< 12, 6, b^2*c^9>,< 12, 8, d>,< 12, 8, c^4*d>,< 12, 8, c^2*d>,< 12, 8, b^2*d>,< 12, 8, b^4*d>,< 12, 8, b^2*c^4*d>,< 12, 8, b^2*c^2*d>,< 12, 8, b^2*c^8*d>,< 12, 8, b^4*c^4*d>,< 12, 12, c*d>,< 12, 12, c*d^3>,< 12, 12, b^2*c^3*d>,< 12, 12, b^2*c^9*d>,< 12, 12, c>,< 12, 12, c^7>,< 12, 12, a*d^4>,< 12, 12, a*d^8>,< 12, 12, b^2*c*d>,< 12, 12, b^4*c*d>,< 12, 12, b*d^3>,< 12, 12, b*d^9>,< 12, 12, b^2*c*d^3>,< 12, 12, b^4*c*d^3>,< 12, 12, b^2*c>,< 12, 12, b^4*c^7>,< 12, 12, b^4*c>,< 12, 12, b^2*c^7>,< 12, 24, a*d>,< 12, 24, a*c^4>,< 12, 24, b^3*d>,< 12, 24, a*c^4*d^3>,< 12, 24, b*d>,< 12, 24, b*c^2*d>,< 12, 24, a*c^4*d^4>,< 12, 24, a*c^4*d^8>,< 12, 24, a*c^4*d>,< 12, 24, a*c^2*d>,< 12, 36, b*c>,< 12, 36, b*c*d^2>,< 12, 36, a*b*d^4>,< 12, 36, a*b*c^2*d^4>,< 12, 72, a*b*c^10*d^11>,< 12, 72, a*b^2*c*d^11>,< 12, 72, a*b^4*c^11*d^8>]); 
CR := CharacterRing(G);
x := CR!\[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, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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, -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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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, -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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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, -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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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, -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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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, -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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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, -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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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, -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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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, -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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[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, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, 0, 0, -1, 2, 2, -1, 2, -1, -1, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, -1, 2, 2, 2, -1, 2, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, 0, -1, -1, -1, -1, 2, 0, 2, -1, -1, -1, 0, -1, 2, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 0, 0, 2, -1, 2, -1, -1, 2, -1, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, -1, 2, 2, 2, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, -1, 2, 0, 0, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, 0, 0, -1, -1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, 2, 2, -1, 2, -1, -1, -1, -1, 0, -1, -1, -1, 2, -1, 0, -1, -1, -1, 0, 0, 2, 0, 0, 0, 0, -1, -1, 0, -1, -1, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -1, 2, -1, -1, -1, -2, 2, 2, -2, -2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, -2, 1, -2, 2, -1, 2, -1, -1, -1, 1, 0, -1, 1, -1, -2, 1, 0, -1, -1, 1, 0, 0, 2, 0, 0, 0, 0, -1, -1, 0, -1, -1, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -1, 2, -1, -1, -1, 2, 2, 2, 2, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, 1, -2, -2, 1, 1, 1, 1, 1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, 2, 2, -1, 2, -1, -1, -1, -1, 0, 1, -1, -1, 2, -1, 0, 1, -1, -1, 0, 0, -2, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, -2, 0, 0, 2, -1, 2, -1, -1, 2, -1, -2, 0, 0, 0, 0, -2, 2, 2, 2, 2, 0, -2, 0, 0, 0, 0, 0, -1, 2, 2, 2, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -2, 1, 1, -2, 1, 1, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 0, -1, 2, -1, 1, -1, -2, 1, -1, -1, -1, 0, 0, -1, -1, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, -2, 0, 0, 2, -1, 2, -1, -1, 2, -1, -2, 0, 0, 0, 0, 2, 2, -2, -2, -2, 0, 2, 0, 0, 0, 0, 0, -1, 2, 2, 2, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -2, 1, 1, -2, 1, 1, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, -1, 2, 0, 0, 1, -2, -1, -1, 1, 2, -1, -1, -1, 1, 0, 0, 1, 1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, -2, 0, 0, 2, -1, 2, -1, -1, 2, -1, 2, 0, 0, 0, 0, -2, -2, -2, 2, 2, 0, 2, 0, 0, 0, 0, 0, -1, 2, 2, 2, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -2, 1, 1, -2, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 1, -2, 0, 0, 1, -2, 1, 1, 1, -2, 1, 1, 1, 1, 0, 0, -1, -1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, -2, 0, 0, 2, -1, 2, -1, -1, 2, -1, 2, 0, 0, 0, 0, 2, -2, 2, -2, -2, 0, -2, 0, 0, 0, 0, 0, -1, 2, 2, 2, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -2, 1, 1, -2, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, -1, -2, 0, 0, -1, 2, 1, -1, -1, 2, -1, 1, 1, -1, 0, 0, 1, 1, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, -2, 2, 2, 2, 2, -1, 2, -1, -1, -1, -2, -2, -2, 2, 2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, 1, -2, -2, 1, 1, 1, -1, -1, 1, 1, -2, -2, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -2, -2, 1, -2, 1, 2, -2, 1, -2, 1, 1, 1, -1, 0, -1, -1, 1, 2, -1, 0, -1, 1, -1, 0, 0, 2, 0, 0, 0, 0, -1, -1, 0, 1, 1, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -2, -2, 2, 2, 2, 2, -1, 2, -1, -1, -1, 2, -2, -2, -2, -2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, 1, -2, -2, 1, 1, 1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -2, -2, 1, -2, 1, 1, 1, 1, 0, 1, 1, 1, -2, 1, 0, 1, 1, 1, 0, 0, -2, 0, 0, 0, 0, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, 0, 0, -1, 2, 2, -1, 2, -1, -1, -2, -2, -2, 2, 2, -2, 0, 2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 2, -1, 2, 2, 2, -1, 2, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 1, 1, 1, -2, 2, 2, 2, 2, 1, 1, 1, -2, 1, -2, 1, 1, -2, -1, 1, -2, 1, 1, 1, 1, -1, -2, 0, -1, 1, -1, -1, -2, 0, -2, -1, -1, -1, 0, 1, 2, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, 0, 0, -1, 2, 2, -1, 2, -1, -1, -2, -2, -2, 2, 2, 2, 0, -2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 2, -1, 2, 2, 2, -1, 2, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 1, 1, 1, -2, 2, 2, 2, 2, 1, 1, 1, -2, 1, -2, 1, 1, -2, -1, 1, -2, 1, 1, 1, 1, -1, 2, 0, -1, 1, -1, -1, 2, 0, -2, -1, 1, 1, 0, -1, -2, -1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, 0, 0, -1, 2, 2, -1, 2, -1, -1, -2, 2, 2, -2, -2, -2, 0, 2, 0, 0, 0, 0, -2, 2, 0, 0, 0, 2, -1, 2, 2, 2, -1, 2, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, 1, 1, 1, -2, 1, -2, 1, 1, -2, 1, -1, 2, -1, -1, -1, -1, 1, -2, 0, 1, -1, 1, 1, -2, 0, 2, 1, -1, -1, 0, 1, 2, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, 0, 0, -1, 2, 2, -1, 2, -1, -1, -2, 2, 2, -2, -2, 2, 0, -2, 0, 0, 0, 0, 2, -2, 0, 0, 0, 2, -1, 2, 2, 2, -1, 2, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, 1, 1, 1, -2, 1, -2, 1, 1, -2, 1, -1, 2, -1, -1, -1, -1, 1, 2, 0, 1, -1, 1, 1, 2, 0, 2, 1, 1, 1, 0, -1, -2, -1, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, 0, 0, -1, 2, 2, -1, 2, -1, -1, 2, -2, -2, -2, -2, -2, 0, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, -1, 2, 2, 2, -1, 2, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, -1, -1, -1, -1, 2, -2, -2, -2, -2, -1, -1, -1, 2, -1, 2, -1, -1, 2, 1, 1, -2, 1, 1, 1, 1, 1, -2, 0, 1, 1, 1, 1, -2, 0, -2, 1, 1, 1, 0, 1, -2, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, 0, 0, -1, 2, 2, -1, 2, -1, -1, 2, -2, -2, -2, -2, 2, 0, 2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 2, -1, 2, 2, 2, -1, 2, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, -1, -1, -1, -1, 2, -2, -2, -2, -2, -1, -1, -1, 2, -1, 2, -1, -1, 2, 1, 1, -2, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 2, 0, -2, 1, -1, -1, 0, -1, 2, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, 0, 0, -1, 2, 2, -1, 2, -1, -1, 2, 2, 2, 2, 2, -2, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 2, -1, 2, 2, 2, -1, 2, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -2, 0, -1, -1, -1, -1, -2, 0, 2, -1, 1, 1, 0, 1, -2, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -1, 2, -1, -1, -1, -2, -2, -2, 2, 2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -2, -2, 1, -2, 1, 2, -2, 1, -2, 1, 1, 1, -1, 0, 1, -1, 1, 2, -1, 0, 1, 1, -1, 0, 0, -2, 0, 0, 0, 0, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -1, 2, -1, -1, -1, 2, -2, -2, -2, -2, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 1, 1, -1, -1, 2, 2, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -2, -2, 1, -2, 1, 1, 1, 1, 0, -1, 1, 1, -2, 1, 0, -1, 1, 1, 0, 0, 2, 0, 0, 0, 0, -1, -1, 0, 1, 1, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 0, 0, 2, -1, 2, -1, -1, 2, -1, -2, 0, 0, 0, 0, -2, -2, 2, -2, -2, 0, 2, 0, 0, 0, 0, 0, -1, 2, 2, 2, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 1, -2, 0, 0, -1, 2, 1, 1, -1, -2, 1, 1, 1, -1, 0, 0, 1, 1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 0, 0, 2, -1, 2, -1, -1, 2, -1, -2, 0, 0, 0, 0, 2, -2, -2, 2, 2, 0, -2, 0, 0, 0, 0, 0, -1, 2, 2, 2, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, -1, -2, 0, 0, 1, -2, 1, -1, 1, 2, -1, 1, 1, 1, 0, 0, -1, -1, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 0, 0, 2, -1, 2, -1, -1, 2, -1, 2, 0, 0, 0, 0, -2, 2, -2, -2, -2, 0, -2, 0, 0, 0, 0, 0, -1, 2, 2, 2, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 0, 1, -2, -1, 1, 1, -2, 1, -1, -1, 1, 0, 0, 1, 1, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, -2, 2, 2, -2, -2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, -2, 1, -2, 2, -1, 2, -1, -1, -1, 1, 0, 1, 1, -1, -2, 1, 0, 1, -1, 1, 0, 0, -2, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, -2, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 2, -2, -2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 2, -2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 2, -2, 2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, -2, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,-2,-2,0,0,0,0,2,2,2,2,2,2,2,0,0,0,-2*K.1,2*K.1,0,0,0,2*K.1,-2*K.1,0,0,0,0,-2,2,0,-2,-2,2,-2,-2,2,-2,-2,2,2,2,-2,-2,-2,-2,-2,2,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1,-2*K.1,2*K.1,2*K.1,0,0,0,0,0,0,0,0,0,-2*K.1,0,0,0,0,0,0,-2*K.1,0,0,2*K.1,0,2*K.1,-2*K.1,0,0,0,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1,-2*K.1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,-2,-2,0,0,0,0,2,2,2,2,2,2,2,0,0,0,2*K.1,-2*K.1,0,0,0,-2*K.1,2*K.1,0,0,0,0,-2,2,0,-2,-2,2,-2,-2,2,-2,-2,2,2,2,-2,-2,-2,-2,-2,2,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1,2*K.1,-2*K.1,-2*K.1,0,0,0,0,0,0,0,0,0,2*K.1,0,0,0,0,0,0,2*K.1,0,0,-2*K.1,0,-2*K.1,2*K.1,0,0,0,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1,2*K.1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,-2,-2,0,0,0,0,2,2,2,2,2,2,2,0,0,0,-2*K.1,2*K.1,0,0,0,-2*K.1,2*K.1,0,0,0,0,2,-2,0,-2,-2,2,-2,-2,2,-2,-2,2,2,2,-2,-2,-2,-2,-2,2,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1,-2*K.1,2*K.1,2*K.1,0,0,0,0,0,0,0,0,0,-2*K.1,0,0,0,0,0,0,-2*K.1,0,0,2*K.1,0,2*K.1,-2*K.1,0,0,0,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1,2*K.1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,-2,-2,0,0,0,0,2,2,2,2,2,2,2,0,0,0,2*K.1,-2*K.1,0,0,0,2*K.1,-2*K.1,0,0,0,0,2,-2,0,-2,-2,2,-2,-2,2,-2,-2,2,2,2,-2,-2,-2,-2,-2,2,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1,2*K.1,-2*K.1,-2*K.1,0,0,0,0,0,0,0,0,0,2*K.1,0,0,0,0,0,0,2*K.1,0,0,-2*K.1,0,-2*K.1,2*K.1,0,0,0,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1,-2*K.1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,-2,2,-2,2,2,2,-1,2,-1,-1,-1,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,1,1,-2,-2,-1,-2,-2,1,1,-1,1,2,-1,-2,-2,1,1,-1,1,-1,2,-2,1,1,-1,1,-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,K.1+K.1^-1,0,-1*K.1-K.1^-1,0,-2,1,2,-1,1,-1,K.1+K.1^-1,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,1,0,-1*K.1-K.1^-1,0,K.1+K.1^-1,-1,K.1+K.1^-1,0,0,0,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,0,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,-2,2,-2,2,2,2,-1,2,-1,-1,-1,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,1,1,-2,-2,-1,-2,-2,1,1,-1,1,2,-1,-2,-2,1,1,-1,1,-1,2,-2,1,1,-1,1,-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,-1*K.1-K.1^-1,0,K.1+K.1^-1,0,-2,1,2,-1,1,-1,-1*K.1-K.1^-1,0,K.1+K.1^-1,K.1+K.1^-1,1,0,K.1+K.1^-1,0,-1*K.1-K.1^-1,-1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,0,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,-2,2,2,-2,2,2,-1,2,-1,-1,-1,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,1,1,-2,-2,-1,-2,-2,1,1,-1,1,2,-1,-2,-2,1,1,-1,1,-1,2,-2,1,1,-1,-1,1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,K.1+K.1^-1,0,-1*K.1-K.1^-1,0,2,-1,-2,1,-1,1,-1*K.1-K.1^-1,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1,0,K.1+K.1^-1,0,K.1+K.1^-1,1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,0,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,-2,2,2,-2,2,2,-1,2,-1,-1,-1,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,1,1,-2,-2,-1,-2,-2,1,1,-1,1,2,-1,-2,-2,1,1,-1,1,-1,2,-2,1,1,-1,-1,1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,-1*K.1-K.1^-1,0,K.1+K.1^-1,0,2,-1,-2,1,-1,1,K.1+K.1^-1,0,K.1+K.1^-1,-1*K.1-K.1^-1,-1,0,-1*K.1-K.1^-1,0,-1*K.1-K.1^-1,1,K.1+K.1^-1,0,0,0,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,0,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,-2,2,2,2,-1,2,-1,-1,-1,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,1,1,-2,-2,-1,-2,-2,1,1,-1,1,2,-1,-2,-2,1,1,-1,1,1,-2,2,-1,-1,1,1,-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,K.1+K.1^-1,0,-1*K.1-K.1^-1,0,2,-1,-2,1,-1,1,-1*K.1-K.1^-1,0,K.1+K.1^-1,K.1+K.1^-1,-1,0,K.1+K.1^-1,0,-1*K.1-K.1^-1,1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,0,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,-2,2,2,2,-1,2,-1,-1,-1,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,1,1,-2,-2,-1,-2,-2,1,1,-1,1,2,-1,-2,-2,1,1,-1,1,1,-2,2,-1,-1,1,1,-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,-1*K.1-K.1^-1,0,K.1+K.1^-1,0,2,-1,-2,1,-1,1,K.1+K.1^-1,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1,0,-1*K.1-K.1^-1,0,K.1+K.1^-1,1,K.1+K.1^-1,0,0,0,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,0,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,2,-2,2,2,-1,2,-1,-1,-1,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,1,1,-2,-2,-1,-2,-2,1,1,-1,1,2,-1,-2,-2,1,1,-1,1,1,-2,2,-1,-1,1,-1,1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,K.1+K.1^-1,0,-1*K.1-K.1^-1,0,-2,1,2,-1,1,-1,K.1+K.1^-1,0,K.1+K.1^-1,-1*K.1-K.1^-1,1,0,-1*K.1-K.1^-1,0,-1*K.1-K.1^-1,-1,K.1+K.1^-1,0,0,0,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,0,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,2,-2,2,2,-1,2,-1,-1,-1,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,1,1,-2,-2,-1,-2,-2,1,1,-1,1,2,-1,-2,-2,1,1,-1,1,1,-2,2,-1,-1,1,-1,1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,-1*K.1-K.1^-1,0,K.1+K.1^-1,0,-2,1,2,-1,1,-1,-1*K.1-K.1^-1,0,-1*K.1-K.1^-1,K.1+K.1^-1,1,0,K.1+K.1^-1,0,K.1+K.1^-1,-1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,0,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 0, 0, 0, 0, -2, -2, 4, 1, -2, -2, 1, 4, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, 4, -2, -2, 4, -2, -2, -2, -2, -2, -2, 1, -2, 1, 1, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, -2, -2, -2, -2, 4, 0, 0, 0, 0, 1, 1, 1, -2, 1, -2, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, -2, 0, 1, -2, -2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 0, 0, 0, 0, -2, 4, -2, -2, -2, 1, 1, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, 4, -2, -2, -2, 4, -2, 1, -2, -2, -2, 1, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2, -2, 1, 1, 1, -2, -2, -2, -2, -2, 1, 1, 1, -2, -2, 4, 1, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 1, 1, -2, 1, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 4, 4, 0, 0, 4, -2, -2, -2, 1, -2, 1, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, -2, -2, 4, -2, 4, -2, 1, -2, 1, 1, -2, -2, -2, -2, -2, 1, 1, 1, -2, -2, -2, -2, 1, 1, 0, 0, -2, -2, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, -2, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 4, 4, -4, -4, 4, -4, -4, -4, -4, 4, -4, -4, 4, -4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, -4, -4, 0, 0, 4, -2, -2, -2, 1, -2, 1, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, -2, -2, 4, -2, 4, -2, 1, -2, 1, 1, -2, -2, -2, -2, -2, 1, 1, 1, 2, 2, 2, 2, -1, -1, 0, 0, 2, 2, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, 2, 2, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, -4, -4, 0, 0, 4, -2, -2, -2, 1, -2, 1, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, -2, -2, 4, -2, 4, -2, 1, -2, 1, 1, -2, -2, -2, -2, -2, 1, 1, 1, 2, 2, 2, 2, -1, -1, 0, 0, -2, -2, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, -2, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 0, 0, 0, 0, -2, -2, 4, 1, -2, -2, 1, -4, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, 4, -2, -2, 4, -2, -2, -2, -2, -2, -2, 1, -2, 1, 1, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, 2, 2, 2, 2, -4, 0, 0, 0, 0, -1, -1, -1, 2, -1, 2, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, -2, 0, -1, -2, 2, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 0, 0, 0, 0, -2, -2, 4, 1, -2, -2, 1, -4, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, 4, -2, -2, 4, -2, -2, -2, -2, -2, -2, 1, -2, 1, 1, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, 2, 2, 2, 2, -4, 0, 0, 0, 0, -1, -1, -1, 2, -1, 2, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 2, 0, 1, 2, -2, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 0, 0, 0, 0, -2, -2, 4, 1, -2, -2, 1, 4, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, 4, -2, -2, 4, -2, -2, -2, -2, -2, -2, 1, -2, 1, 1, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, -2, -2, -2, -2, 4, 0, 0, 0, 0, 1, 1, 1, -2, 1, -2, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 2, 0, -1, 2, 2, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 0, 0, 0, 0, -2, 4, -2, -2, -2, 1, 1, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, 4, -2, -2, -2, 4, -2, 1, -2, -2, -2, 1, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, -1, -1, -1, 2, -2, -2, -2, -2, -1, -1, -1, 2, 2, -4, -1, 2, 2, -2, 2, 2, 2, -1, -1, -1, 1, 0, 0, 1, -1, -2, 1, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 0, 0, 0, 0, -2, 4, -2, -2, -2, 1, 1, -4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, 4, -2, -2, -2, 4, -2, 1, -2, -2, -2, 1, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, -4, -1, 2, 2, 2, -2, -2, -2, 1, 1, 1, -1, 0, 0, -1, 1, 2, -1, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 0, 0, 0, 0, -2, 4, -2, -2, -2, 1, 1, 4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, 4, -2, -2, -2, 4, -2, 1, -2, -2, -2, 1, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2, -2, 1, 1, 1, -2, 2, 2, 2, 2, 1, 1, 1, -2, -2, 4, 1, -2, -2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, -1, -1, 2, -1, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 4, 4, 0, 0, 4, -2, -2, -2, 1, -2, 1, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, -2, -2, 4, -2, 4, -2, 1, -2, 1, 1, -2, -2, -2, -2, -2, 1, 1, 1, -2, -2, -2, -2, 1, 1, 0, 0, 2, 2, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, 2, 2, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, -4, 4, 0, 0, 4, -2, 4, -2, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -4, -4, 2, -4, 4, -4, 2, 2, -4, -2, 2, -2, 4, 2, 2, -4, 2, -2, 2, 4, -2, 2, -4, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, 0, 0, 0, 0, -2, 4, 4, -2, 4, -2, -2, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -4, -4, -4, 2, 4, 2, -4, -4, 2, 4, -4, -2, -2, 2, 2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 2, 2, -2, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, 0, 0, 0, 0, -2, 4, 4, -2, 4, -2, -2, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -4, -4, -4, 2, 4, 2, -4, -4, 2, 4, -4, -2, -2, 2, 2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, -2, -2, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, 4, -4, 0, 0, 4, -2, 4, -2, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -4, -4, 2, -4, 4, -4, 2, 2, -4, -2, 2, -2, 4, 2, 2, -4, 2, -2, 2, -4, 2, -2, 4, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,4,-2,4,-2,-2,4,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-4,-4,4,-2,-4,-4,4,2,2,-4,2,-2,2,-4,-2,2,4,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2-4*K.1,0,0,0,0,0,2+4*K.1,0,0,0,0,0,0,2+4*K.1,0,0,-2-4*K.1,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,4,-2,4,-2,-2,4,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-4,-4,4,-2,-4,-4,4,2,2,-4,2,-2,2,-4,-2,2,4,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2+4*K.1,0,0,0,0,0,-2-4*K.1,0,0,0,0,0,0,-2-4*K.1,0,0,2+4*K.1,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,4,4,-2,4,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,2,-2,4,-4,2,4,-4,2,2,2,-2,-4,2,4,-4,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2-4*K.1,2+4*K.1,-2-4*K.1,2+4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2-4*K.1,0,0,-2-4*K.1,0,0,2+4*K.1,0,0,0,2+4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,4,4,-2,4,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,2,-2,4,-4,2,4,-4,2,2,2,-2,-4,2,4,-4,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2+4*K.1,-2-4*K.1,2+4*K.1,-2-4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2+4*K.1,0,0,2+4*K.1,0,0,-2-4*K.1,0,0,0,-2-4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,-4,-4,0,0,0,0,-2,4,4,-2,4,-2,-2,0,0,0,-4*K.1,4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,-4,2,4,-4,-4,-2,-4,2,4,4,-2,-4,-4,2,2,2,-2,2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4*K.1,-4*K.1,4*K.1,4*K.1,0,0,0,0,0,0,0,0,0,2*K.1,0,0,0,0,0,0,2*K.1,0,0,-2*K.1,0,-2*K.1,2*K.1,0,0,0,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,-4,-4,0,0,0,0,-2,4,4,-2,4,-2,-2,0,0,0,4*K.1,-4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,-4,2,4,-4,-4,-2,-4,2,4,4,-2,-4,-4,2,2,2,-2,2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4*K.1,4*K.1,-4*K.1,-4*K.1,0,0,0,0,0,0,0,0,0,-2*K.1,0,0,0,0,0,0,-2*K.1,0,0,2*K.1,0,2*K.1,-2*K.1,0,0,0,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,-4,-4,0,0,0,0,4,-2,4,-2,-2,4,-2,0,0,0,0,0,0,0,0,-4*K.1,4*K.1,0,0,0,0,0,0,0,2,-4,4,-4,2,4,-4,-4,-2,-2,4,2,2,2,-4,2,-2,-4,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1,-2*K.1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,-4,-4,0,0,0,0,4,-2,4,-2,-2,4,-2,0,0,0,0,0,0,0,0,4*K.1,-4*K.1,0,0,0,0,0,0,0,2,-4,4,-4,2,4,-4,-4,-2,-2,4,2,2,2,-4,2,-2,-4,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1,2*K.1,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,-4,-4,0,0,0,0,4,4,-2,4,-2,-2,-2,0,0,0,-4*K.1,4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,-2,2,-4,4,2,-4,4,-2,-2,2,2,-4,2,-4,4,2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1,2*K.1,-2*K.1,-2*K.1,0,0,0,0,0,0,0,0,0,-4*K.1,0,0,0,0,0,0,2*K.1,0,0,-2*K.1,0,4*K.1,2*K.1,0,0,0,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,-4,-4,0,0,0,0,4,4,-2,4,-2,-2,-2,0,0,0,4*K.1,-4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,-2,2,-4,4,2,-4,4,-2,-2,2,2,-4,2,-4,4,2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1,-2*K.1,2*K.1,2*K.1,0,0,0,0,0,0,0,0,0,4*K.1,0,0,0,0,0,0,-2*K.1,0,0,2*K.1,0,-4*K.1,-2*K.1,0,0,0,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,-2,4,4,-2,4,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,2,-4,4,4,2,-4,-2,-4,-4,2,-4,4,2,2,-2,2,-2,-2,2,2,0,0,0,0,0,0,0,0,-2*K.1-2*K.1^-1,0,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,0,0,0,0,0,-2*K.1-2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,0,-2*K.1-2*K.1^-1,0,2*K.1+2*K.1^-1,2*K.1+2*K.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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,-2,4,4,-2,4,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,2,-4,4,4,2,-4,-2,-4,-4,2,-4,4,2,2,-2,2,-2,-2,2,2,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,0,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,-2*K.1-2*K.1^-1,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,0,2*K.1+2*K.1^-1,0,-2*K.1-2*K.1^-1,-2*K.1-2*K.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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,-4,-4,0,0,0,0,-2,4,-2,-2,-2,1,1,0,0,0,-4*K.1,4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,-4,2,-2,2,-4,-2,2,2,4,-2,1,2,2,2,-1,2,-2,-1,-1,-1,1,0,0,0,0,0,0,0,0,-3,0,0,0,3,3,-3,0,2*K.1,2*K.1,-2*K.1,-2*K.1,-3,3,3,0,0,0,-3,0,0,2*K.1,0,0,0,3*K.1,3*K.1,-3*K.1,-1*K.1,0,0,K.1,-3*K.1,-2*K.1,-1*K.1,0,0,0,K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,-4,-4,0,0,0,0,-2,4,-2,-2,-2,1,1,0,0,0,4*K.1,-4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,-4,2,-2,2,-4,-2,2,2,4,-2,1,2,2,2,-1,2,-2,-1,-1,-1,1,0,0,0,0,0,0,0,0,-3,0,0,0,3,3,-3,0,-2*K.1,-2*K.1,2*K.1,2*K.1,-3,3,3,0,0,0,-3,0,0,-2*K.1,0,0,0,-3*K.1,-3*K.1,3*K.1,K.1,0,0,-1*K.1,3*K.1,2*K.1,K.1,0,0,0,-1*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,-4,-4,0,0,0,0,-2,4,-2,-2,-2,1,1,0,0,0,-4*K.1,4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,-4,2,-2,2,-4,-2,2,2,4,-2,1,2,2,2,-1,2,-2,-1,-1,-1,1,0,0,0,0,0,0,0,0,3,0,0,0,-3,-3,3,0,2*K.1,2*K.1,-2*K.1,-2*K.1,3,-3,-3,0,0,0,3,0,0,2*K.1,0,0,0,-3*K.1,-3*K.1,3*K.1,-1*K.1,0,0,K.1,3*K.1,-2*K.1,-1*K.1,0,0,0,K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,-4,-4,0,0,0,0,-2,4,-2,-2,-2,1,1,0,0,0,4*K.1,-4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,-4,2,-2,2,-4,-2,2,2,4,-2,1,2,2,2,-1,2,-2,-1,-1,-1,1,0,0,0,0,0,0,0,0,3,0,0,0,-3,-3,3,0,-2*K.1,-2*K.1,2*K.1,2*K.1,3,-3,-3,0,0,0,3,0,0,-2*K.1,0,0,0,3*K.1,3*K.1,-3*K.1,K.1,0,0,-1*K.1,-3*K.1,2*K.1,K.1,0,0,0,-1*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,4,-4,-4,4,0,0,4,-2,-2,-2,1,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,4,2,2,2,-4,-2,-4,2,-1,2,1,-1,-2,-2,2,2,2,-1,1,-1,-2,-2,2,2,-1,1,0,0,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,0,0,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,-1*K.1-K.1^-1,0,K.1+K.1^-1,0,0,0,0,0,0,0,0,0,-2*K.1-2*K.1^-1,0,0,0,0,0,2*K.1+2*K.1^-1,0,0,0,0,0,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,4,-4,-4,4,0,0,4,-2,-2,-2,1,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,4,2,2,2,-4,-2,-4,2,-1,2,1,-1,-2,-2,2,2,2,-1,1,-1,-2,-2,2,2,-1,1,0,0,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,0,0,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,K.1+K.1^-1,0,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,0,0,0,0,0,-2*K.1-2*K.1^-1,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,4,-4,0,0,0,0,-2,4,-2,-2,-2,1,1,0,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-2,2,2,-4,2,-2,2,-4,2,-1,-2,2,-2,1,2,2,-1,-1,1,-1,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,-2*K.1-2*K.1^-1,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-2*K.1-2*K.1^-1,0,0,K.1+K.1^-1,0,2*K.1+2*K.1^-1,0,-2,-2,2,-1,1,-1,-1*K.1-K.1^-1,0,0,K.1+K.1^-1,1,0,K.1+K.1^-1,0,0,2,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,4,-4,0,0,0,0,-2,4,-2,-2,-2,1,1,0,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-2,2,2,-4,2,-2,2,-4,2,-1,-2,2,-2,1,2,2,-1,-1,1,-1,0,0,0,0,0,0,0,0,K.1+K.1^-1,2*K.1+2*K.1^-1,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-2*K.1-2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,2*K.1+2*K.1^-1,0,0,-1*K.1-K.1^-1,0,-2*K.1-2*K.1^-1,0,-2,-2,2,-1,1,-1,K.1+K.1^-1,0,0,-1*K.1-K.1^-1,1,0,-1*K.1-K.1^-1,0,0,2,K.1+K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,4,-4,0,0,0,0,-2,4,-2,-2,-2,1,1,0,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-2,2,2,-4,2,-2,2,-4,2,-1,-2,2,-2,1,2,2,-1,-1,1,-1,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,-2*K.1-2*K.1^-1,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-2*K.1-2*K.1^-1,0,0,K.1+K.1^-1,0,2*K.1+2*K.1^-1,0,2,2,-2,1,-1,1,K.1+K.1^-1,0,0,-1*K.1-K.1^-1,-1,0,-1*K.1-K.1^-1,0,0,-2,K.1+K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,4,-4,0,0,0,0,-2,4,-2,-2,-2,1,1,0,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-2,2,2,-4,2,-2,2,-4,2,-1,-2,2,-2,1,2,2,-1,-1,1,-1,0,0,0,0,0,0,0,0,K.1+K.1^-1,2*K.1+2*K.1^-1,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,2*K.1+2*K.1^-1,0,0,-1*K.1-K.1^-1,0,-2*K.1-2*K.1^-1,0,2,2,-2,1,-1,1,-1*K.1-K.1^-1,0,0,K.1+K.1^-1,-1,0,K.1+K.1^-1,0,0,-2,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,4,-4,4,-4,0,0,4,-2,-2,-2,1,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,4,2,2,2,-4,-2,-4,2,-1,2,1,-1,-2,-2,2,2,2,-1,1,-1,2,2,-2,-2,1,-1,0,0,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,0,0,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,-1*K.1-K.1^-1,0,K.1+K.1^-1,0,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,0,0,0,0,0,-2*K.1-2*K.1^-1,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,4,-4,4,-4,0,0,4,-2,-2,-2,1,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,4,2,2,2,-4,-2,-4,2,-1,2,1,-1,-2,-2,2,2,2,-1,1,-1,2,2,-2,-2,1,-1,0,0,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,0,0,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,K.1+K.1^-1,0,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,-2*K.1-2*K.1^-1,0,0,0,0,0,2*K.1+2*K.1^-1,0,0,0,0,0,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,-2,-2,4,1,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-4,4,-2,2,-4,-2,2,2,2,2,-2,-1,2,1,-1,-2,1,-1,-1,0,0,0,0,0,0,0,0,-2*K.1-2*K.1^-1,0,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,0,0,0,0,0,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,K.1+K.1^-1,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,2-4*K.1^2,0,0,0,0,0,-2+4*K.1^2,0,0,0,-3*K.1^3,0,0,1-2*K.1^2,0,0,-1+2*K.1^2,0,0,3*K.1^3,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,-2,-2,4,1,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-4,4,-2,2,-4,-2,2,2,2,2,-2,-1,2,1,-1,-2,1,-1,-1,0,0,0,0,0,0,0,0,-2*K.1-2*K.1^-1,0,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,0,0,0,0,0,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,K.1+K.1^-1,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,-2+4*K.1^2,0,0,0,0,0,2-4*K.1^2,0,0,0,3*K.1^3,0,0,-1+2*K.1^2,0,0,1-2*K.1^2,0,0,-3*K.1^3,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,-2,-2,4,1,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-4,4,-2,2,-4,-2,2,2,2,2,-2,-1,2,1,-1,-2,1,-1,-1,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,0,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,-2*K.1-2*K.1^-1,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,-1*K.1-K.1^-1,0,K.1+K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,0,0,0,2-4*K.1^2,0,0,0,0,0,-2+4*K.1^2,0,0,0,3*K.1^3,0,0,1-2*K.1^2,0,0,-1+2*K.1^2,0,0,-3*K.1^3,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,-2,-2,4,1,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-4,4,-2,2,-4,-2,2,2,2,2,-2,-1,2,1,-1,-2,1,-1,-1,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,0,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,-2*K.1-2*K.1^-1,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,-1*K.1-K.1^-1,0,K.1+K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,0,0,0,-2+4*K.1^2,0,0,0,0,0,2-4*K.1^2,0,0,0,-3*K.1^3,0,0,-1+2*K.1^2,0,0,1-2*K.1^2,0,0,3*K.1^3,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,-2,4,-2,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,2,2,-2,4,2,2,-2,-4,2,-1,2,-2,2,-1,-2,2,1,1,-1,-1,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,0,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,0,2-4*K.1^2,-2+4*K.1^2,2-4*K.1^2,-2+4*K.1^2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,2*K.1+2*K.1^-1,0,K.1+K.1^-1,-2*K.1-2*K.1^-1,0,0,0,0,0,-3*K.1^3,3*K.1^3,3*K.1^3,-1+2*K.1^2,0,0,-1+2*K.1^2,-3*K.1^3,0,1-2*K.1^2,0,0,0,1-2*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,-2,4,-2,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,2,2,-2,4,2,2,-2,-4,2,-1,2,-2,2,-1,-2,2,1,1,-1,-1,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,0,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,0,-2+4*K.1^2,2-4*K.1^2,-2+4*K.1^2,2-4*K.1^2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,2*K.1+2*K.1^-1,0,K.1+K.1^-1,-2*K.1-2*K.1^-1,0,0,0,0,0,3*K.1^3,-3*K.1^3,-3*K.1^3,1-2*K.1^2,0,0,1-2*K.1^2,3*K.1^3,0,-1+2*K.1^2,0,0,0,-1+2*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,-2,4,-2,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,2,2,-2,4,2,2,-2,-4,2,-1,2,-2,2,-1,-2,2,1,1,-1,-1,0,0,0,0,0,0,0,0,K.1+K.1^-1,0,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,2-4*K.1^2,-2+4*K.1^2,2-4*K.1^2,-2+4*K.1^2,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,-2*K.1-2*K.1^-1,0,-1*K.1-K.1^-1,2*K.1+2*K.1^-1,0,0,0,0,0,3*K.1^3,-3*K.1^3,-3*K.1^3,-1+2*K.1^2,0,0,-1+2*K.1^2,3*K.1^3,0,1-2*K.1^2,0,0,0,1-2*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,-2,4,-2,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,2,2,-2,4,2,2,-2,-4,2,-1,2,-2,2,-1,-2,2,1,1,-1,-1,0,0,0,0,0,0,0,0,K.1+K.1^-1,0,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,-2+4*K.1^2,2-4*K.1^2,-2+4*K.1^2,2-4*K.1^2,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,-2*K.1-2*K.1^-1,0,-1*K.1-K.1^-1,2*K.1+2*K.1^-1,0,0,0,0,0,-3*K.1^3,3*K.1^3,3*K.1^3,1-2*K.1^2,0,0,1-2*K.1^2,-3*K.1^3,0,-1+2*K.1^2,0,0,0,-1+2*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[8, 8, 8, 8, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, -4, -4, 2, 2, 2, -4, 0, 0, 0, 0, -1, -1, -1, 2, 2, -4, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 8, -8, -8, 0, 0, 0, 0, -4, -4, 8, 2, -4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 8, -8, 4, -4, -8, 4, -4, -4, -4, 4, 4, -2, 4, -2, 2, 4, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 8, -8, -8, 0, 0, 0, 0, 8, -4, -4, -4, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -8, -4, 4, 4, 8, 4, -8, -4, 2, -4, -2, -2, 4, 4, 4, -4, 4, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 8, 8, 8, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 4, 4, -2, -2, -2, 4, 0, 0, 0, 0, 1, 1, 1, -2, -2, 4, 1, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 8, -8, -8, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, 4, 4, -4, 4, 4, -4, 2, 2, -2, -2, -2, -2, -2, 2, -2, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 6, 6, -6, 0, 0, 0, 0, 0, 3, -3, -3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, 8, -8, -8, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, 4, 4, -4, 4, 4, -4, 2, 2, -2, -2, -2, -2, -2, 2, -2, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -6, -6, 6, 0, 0, 0, 0, 0, -3, 3, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, -8, -8, 8, 0, 0, 0, 0, 8, -4, -4, -4, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -8, 4, -4, -4, -8, 4, 8, 4, -2, 4, -2, 2, 4, 4, -4, 4, -4, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[8, -8, 8, -8, 0, 0, 0, 0, -4, -4, 8, 2, -4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -8, -8, 4, 4, 8, 4, 4, 4, 4, -4, 4, 2, -4, -2, -2, 4, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |8,-8,-8,8,0,0,0,0,-4,-4,-4,2,2,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,4,4,-4,-4,4,4,-4,4,-2,-2,-2,2,-2,-2,2,-2,2,-1,1,1,0,0,0,0,0,0,0,0,-2*K.1-2*K.1^-1,0,4*K.1+4*K.1^-1,-4*K.1-4*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,0,0,0,0,0,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,-2*K.1-2*K.1^-1,0,-1*K.1-K.1^-1,2*K.1+2*K.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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |8,-8,-8,8,0,0,0,0,-4,-4,-4,2,2,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,4,4,-4,-4,4,4,-4,4,-2,-2,-2,2,-2,-2,2,-2,2,-1,1,1,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,0,-4*K.1-4*K.1^-1,4*K.1+4*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,-2*K.1-2*K.1^-1,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,2*K.1+2*K.1^-1,0,K.1+K.1^-1,-2*K.1-2*K.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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |8,-8,8,-8,0,0,0,0,-4,-4,-4,2,2,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,4,4,4,4,-4,4,4,-2,-2,2,-2,2,2,-2,-2,-2,1,-1,1,0,0,0,0,0,0,0,0,-2*K.1-2*K.1^-1,-4*K.1-4*K.1^-1,0,0,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,4*K.1+4*K.1^-1,0,0,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,2*K.1+2*K.1^-1,0,0,-1*K.1-K.1^-1,0,-2*K.1-2*K.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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |8,-8,8,-8,0,0,0,0,-4,-4,-4,2,2,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,4,4,4,4,-4,4,4,-2,-2,2,-2,2,2,-2,-2,-2,1,-1,1,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,4*K.1+4*K.1^-1,0,0,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,-4*K.1-4*K.1^-1,0,0,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-2*K.1-2*K.1^-1,0,0,K.1+K.1^-1,0,2*K.1+2*K.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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_1728_34797:= KnownIrreducibles(CR);