/* Group 744.7 downloaded from the LMFDB on 05 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([5, -2, -3, -2, -2, -31, 10, 1866, 8912, 232, 42, 8883, 608, 58, 3604, 1509]); a,b := Explode([GPC.1, GPC.3]); AssignNames(~GPC, ["a", "a2", "b", "b2", "b4"]);
GPerm := PermutationGroup< 39 | (2,3)(4,6)(5,9)(7,8)(10,14)(11,17)(12,20)(13,19)(15,22)(16,23)(18,24)(21,27)(25,30)(26,31)(28,29)(32,33,35,37)(34,38,39,36), (32,34,35,39)(33,36,37,38), (2,4,7)(3,6,8)(5,10,15)(9,14,22)(11,18,25)(12,16,19)(13,20,23)(17,24,30)(21,26,28)(27,31,29), (32,35)(33,37)(34,39)(36,38), (1,2,5,11,19,7,6,12,21,28,15,23,14,18,26,25,30,31,24,10,16,22,29,27,20,4,8,13,17,9,3) >;
GLZN := MatrixGroup< 2, Integers(93) | [[32, 0, 0, 32], [1, 27, 0, 25], [63, 92, 31, 30], [1, 3, 0, 1], [1, 62, 62, 32]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_744_7 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := true,
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, b^62>,< 3, 31, a^4*b^96>,< 3, 31, a^2*b^78>,< 4, 2, b^31>,< 4, 62, a^3*b^85>,< 4, 62, a^3*b^16>,< 6, 31, a^2*b^16>,< 6, 31, a^4*b^34>,< 12, 62, a*b^113>,< 12, 62, a^5*b^7>,< 12, 62, a^4*b^67>,< 12, 62, a^2*b^99>,< 12, 62, a*b^84>,< 12, 62, a^5*b^110>,< 31, 6, b^4>,< 31, 6, b^8>,< 31, 6, b^12>,< 31, 6, b^16>,< 31, 6, b^32>,< 62, 6, b^2>,< 62, 6, b^6>,< 62, 6, b^14>,< 62, 6, b^18>,< 62, 6, b^38>,< 124, 6, b>,< 124, 6, b^3>,< 124, 6, b^73>,< 124, 6, b^9>,< 124, 6, b^69>,< 124, 6, b^13>,< 124, 6, b^17>,< 124, 6, b^21>,< 124, 6, b^33>,< 124, 6, b^37>]); 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,K.1^-1,K.1,1,1,1,K.1,K.1^-1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,K.1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,K.1,K.1^-1,1,1,1,K.1^-1,K.1,K.1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,K.1^-1,K.1,-1,-1,1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,K.1^-1,K.1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,K.1,K.1^-1,-1,-1,1,K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,K.1,K.1^-1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,K.1^-1,K.1,-1,1,-1,K.1,K.1^-1,K.1^-1,K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,K.1,K.1^-1,-1,1,-1,K.1^-1,K.1,K.1,K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,K.1^-1,K.1,1,-1,-1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,K.1^-1,K.1,-1*K.1^-1,-1*K.1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,K.1,K.1^-1,1,-1,-1,K.1^-1,K.1,-1*K.1,-1*K.1^-1,K.1,K.1^-1,-1*K.1,-1*K.1^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, -2, 2, 2, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 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 |2,-2,2*K.1^-1,2*K.1,0,0,0,-2*K.1,-2*K.1^-1,0,0,0,0,0,0,2,2,2,2,2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,-2,2*K.1,2*K.1^-1,0,0,0,-2*K.1^-1,-2*K.1,0,0,0,0,0,0,2,2,2,2,2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(31: Sparse := true);
S := [ K |6,6,0,0,6,0,0,0,0,0,0,0,0,0,0,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(31: Sparse := true);
S := [ K |6,6,0,0,6,0,0,0,0,0,0,0,0,0,0,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(31: Sparse := true);
S := [ K |6,6,0,0,6,0,0,0,0,0,0,0,0,0,0,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(31: Sparse := true);
S := [ K |6,6,0,0,6,0,0,0,0,0,0,0,0,0,0,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(31: Sparse := true);
S := [ K |6,6,0,0,6,0,0,0,0,0,0,0,0,0,0,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(31: Sparse := true);
S := [ K |6,6,0,0,-6,0,0,0,0,0,0,0,0,0,0,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,-1*K.1-K.1^5-K.1^6-K.1^-6-K.1^-5-K.1^-1,-1*K.1^4-K.1^7-K.1^11-K.1^-11-K.1^-7-K.1^-4,-1*K.1^8-K.1^9-K.1^14-K.1^-14-K.1^-9-K.1^-8,-1*K.1^2-K.1^10-K.1^12-K.1^-12-K.1^-10-K.1^-2,-1*K.1^3-K.1^13-K.1^15-K.1^-15-K.1^-13-K.1^-3,-1*K.1-K.1^5-K.1^6-K.1^-6-K.1^-5-K.1^-1,-1*K.1^8-K.1^9-K.1^14-K.1^-14-K.1^-9-K.1^-8,-1*K.1^3-K.1^13-K.1^15-K.1^-15-K.1^-13-K.1^-3,-1*K.1^4-K.1^7-K.1^11-K.1^-11-K.1^-7-K.1^-4,-1*K.1^2-K.1^10-K.1^12-K.1^-12-K.1^-10-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(31: Sparse := true);
S := [ K |6,6,0,0,-6,0,0,0,0,0,0,0,0,0,0,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,-1*K.1^2-K.1^10-K.1^12-K.1^-12-K.1^-10-K.1^-2,-1*K.1^8-K.1^9-K.1^14-K.1^-14-K.1^-9-K.1^-8,-1*K.1^3-K.1^13-K.1^15-K.1^-15-K.1^-13-K.1^-3,-1*K.1^4-K.1^7-K.1^11-K.1^-11-K.1^-7-K.1^-4,-1*K.1-K.1^5-K.1^6-K.1^-6-K.1^-5-K.1^-1,-1*K.1^2-K.1^10-K.1^12-K.1^-12-K.1^-10-K.1^-2,-1*K.1^3-K.1^13-K.1^15-K.1^-15-K.1^-13-K.1^-3,-1*K.1-K.1^5-K.1^6-K.1^-6-K.1^-5-K.1^-1,-1*K.1^8-K.1^9-K.1^14-K.1^-14-K.1^-9-K.1^-8,-1*K.1^4-K.1^7-K.1^11-K.1^-11-K.1^-7-K.1^-4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(31: Sparse := true);
S := [ K |6,6,0,0,-6,0,0,0,0,0,0,0,0,0,0,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,-1*K.1^8-K.1^9-K.1^14-K.1^-14-K.1^-9-K.1^-8,-1*K.1-K.1^5-K.1^6-K.1^-6-K.1^-5-K.1^-1,-1*K.1^2-K.1^10-K.1^12-K.1^-12-K.1^-10-K.1^-2,-1*K.1^3-K.1^13-K.1^15-K.1^-15-K.1^-13-K.1^-3,-1*K.1^4-K.1^7-K.1^11-K.1^-11-K.1^-7-K.1^-4,-1*K.1^8-K.1^9-K.1^14-K.1^-14-K.1^-9-K.1^-8,-1*K.1^2-K.1^10-K.1^12-K.1^-12-K.1^-10-K.1^-2,-1*K.1^4-K.1^7-K.1^11-K.1^-11-K.1^-7-K.1^-4,-1*K.1-K.1^5-K.1^6-K.1^-6-K.1^-5-K.1^-1,-1*K.1^3-K.1^13-K.1^15-K.1^-15-K.1^-13-K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(31: Sparse := true);
S := [ K |6,6,0,0,-6,0,0,0,0,0,0,0,0,0,0,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,-1*K.1^3-K.1^13-K.1^15-K.1^-15-K.1^-13-K.1^-3,-1*K.1^2-K.1^10-K.1^12-K.1^-12-K.1^-10-K.1^-2,-1*K.1^4-K.1^7-K.1^11-K.1^-11-K.1^-7-K.1^-4,-1*K.1-K.1^5-K.1^6-K.1^-6-K.1^-5-K.1^-1,-1*K.1^8-K.1^9-K.1^14-K.1^-14-K.1^-9-K.1^-8,-1*K.1^3-K.1^13-K.1^15-K.1^-15-K.1^-13-K.1^-3,-1*K.1^4-K.1^7-K.1^11-K.1^-11-K.1^-7-K.1^-4,-1*K.1^8-K.1^9-K.1^14-K.1^-14-K.1^-9-K.1^-8,-1*K.1^2-K.1^10-K.1^12-K.1^-12-K.1^-10-K.1^-2,-1*K.1-K.1^5-K.1^6-K.1^-6-K.1^-5-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(31: Sparse := true);
S := [ K |6,6,0,0,-6,0,0,0,0,0,0,0,0,0,0,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^3+K.1^13+K.1^15+K.1^-15+K.1^-13+K.1^-3,K.1^8+K.1^9+K.1^14+K.1^-14+K.1^-9+K.1^-8,K.1^2+K.1^10+K.1^12+K.1^-12+K.1^-10+K.1^-2,K.1^4+K.1^7+K.1^11+K.1^-11+K.1^-7+K.1^-4,K.1+K.1^5+K.1^6+K.1^-6+K.1^-5+K.1^-1,-1*K.1^4-K.1^7-K.1^11-K.1^-11-K.1^-7-K.1^-4,-1*K.1^3-K.1^13-K.1^15-K.1^-15-K.1^-13-K.1^-3,-1*K.1-K.1^5-K.1^6-K.1^-6-K.1^-5-K.1^-1,-1*K.1^8-K.1^9-K.1^14-K.1^-14-K.1^-9-K.1^-8,-1*K.1^2-K.1^10-K.1^12-K.1^-12-K.1^-10-K.1^-2,-1*K.1^4-K.1^7-K.1^11-K.1^-11-K.1^-7-K.1^-4,-1*K.1-K.1^5-K.1^6-K.1^-6-K.1^-5-K.1^-1,-1*K.1^2-K.1^10-K.1^12-K.1^-12-K.1^-10-K.1^-2,-1*K.1^3-K.1^13-K.1^15-K.1^-15-K.1^-13-K.1^-3,-1*K.1^8-K.1^9-K.1^14-K.1^-14-K.1^-9-K.1^-8]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(124: Sparse := true);
S := [ K |6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1^6-K.1^26-K.1^30+K.1^32+K.1^36+K.1^56,-1-K.1^4+K.1^6-K.1^8+K.1^14-K.1^16+K.1^18-K.1^20+K.1^22-K.1^24+K.1^26-K.1^28+K.1^30-K.1^32+K.1^34-K.1^36+K.1^38-K.1^40+K.1^42-K.1^44+K.1^46-K.1^48+K.1^54-K.1^56+K.1^58,K.1^16-K.1^18+K.1^28-K.1^34+K.1^44-K.1^46,K.1^4+K.1^20+K.1^24-K.1^38-K.1^42-K.1^58,K.1^8-K.1^14-K.1^22+K.1^40+K.1^48-K.1^54,-1*K.1^16+K.1^18-K.1^28+K.1^34-K.1^44+K.1^46,-1*K.1^8+K.1^14+K.1^22-K.1^40-K.1^48+K.1^54,1+K.1^4-K.1^6+K.1^8-K.1^14+K.1^16-K.1^18+K.1^20-K.1^22+K.1^24-K.1^26+K.1^28-K.1^30+K.1^32-K.1^34+K.1^36-K.1^38+K.1^40-K.1^42+K.1^44-K.1^46+K.1^48-K.1^54+K.1^56-K.1^58,-1*K.1^4-K.1^20-K.1^24+K.1^38+K.1^42+K.1^58,K.1^6+K.1^26+K.1^30-K.1^32-K.1^36-K.1^56,K.1^7-K.1^11-K.1^27+K.1^35+K.1^51-K.1^55,-1*K.1^3+K.1^13-K.1^15+K.1^47-K.1^49+K.1^59,2*K.1-K.1^3+2*K.1^5-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19+K.1^21-K.1^23+2*K.1^25-K.1^27+K.1^29-K.1^31+K.1^33-K.1^35-K.1^39+K.1^41-K.1^43+K.1^45-K.1^47+K.1^49-K.1^51+K.1^53-K.1^55-K.1^59,-1*K.1^9+K.1^17-K.1^23+K.1^39-K.1^45+K.1^53,K.1^19+K.1^21+K.1^29-K.1^33-K.1^41-K.1^43,-1*K.1^7+K.1^11+K.1^27-K.1^35-K.1^51+K.1^55,-2*K.1+K.1^3-2*K.1^5+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19-K.1^21+K.1^23-2*K.1^25+K.1^27-K.1^29+K.1^31-K.1^33+K.1^35+K.1^39-K.1^41+K.1^43-K.1^45+K.1^47-K.1^49+K.1^51-K.1^53+K.1^55+K.1^59,-1*K.1^19-K.1^21-K.1^29+K.1^33+K.1^41+K.1^43,K.1^3-K.1^13+K.1^15-K.1^47+K.1^49-K.1^59,K.1^9-K.1^17+K.1^23-K.1^39+K.1^45-K.1^53]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(124: Sparse := true);
S := [ K |6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1^6-K.1^26-K.1^30+K.1^32+K.1^36+K.1^56,-1-K.1^4+K.1^6-K.1^8+K.1^14-K.1^16+K.1^18-K.1^20+K.1^22-K.1^24+K.1^26-K.1^28+K.1^30-K.1^32+K.1^34-K.1^36+K.1^38-K.1^40+K.1^42-K.1^44+K.1^46-K.1^48+K.1^54-K.1^56+K.1^58,K.1^16-K.1^18+K.1^28-K.1^34+K.1^44-K.1^46,K.1^4+K.1^20+K.1^24-K.1^38-K.1^42-K.1^58,K.1^8-K.1^14-K.1^22+K.1^40+K.1^48-K.1^54,-1*K.1^16+K.1^18-K.1^28+K.1^34-K.1^44+K.1^46,-1*K.1^8+K.1^14+K.1^22-K.1^40-K.1^48+K.1^54,1+K.1^4-K.1^6+K.1^8-K.1^14+K.1^16-K.1^18+K.1^20-K.1^22+K.1^24-K.1^26+K.1^28-K.1^30+K.1^32-K.1^34+K.1^36-K.1^38+K.1^40-K.1^42+K.1^44-K.1^46+K.1^48-K.1^54+K.1^56-K.1^58,-1*K.1^4-K.1^20-K.1^24+K.1^38+K.1^42+K.1^58,K.1^6+K.1^26+K.1^30-K.1^32-K.1^36-K.1^56,-1*K.1^7+K.1^11+K.1^27-K.1^35-K.1^51+K.1^55,K.1^3-K.1^13+K.1^15-K.1^47+K.1^49-K.1^59,-2*K.1+K.1^3-2*K.1^5+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19-K.1^21+K.1^23-2*K.1^25+K.1^27-K.1^29+K.1^31-K.1^33+K.1^35+K.1^39-K.1^41+K.1^43-K.1^45+K.1^47-K.1^49+K.1^51-K.1^53+K.1^55+K.1^59,K.1^9-K.1^17+K.1^23-K.1^39+K.1^45-K.1^53,-1*K.1^19-K.1^21-K.1^29+K.1^33+K.1^41+K.1^43,K.1^7-K.1^11-K.1^27+K.1^35+K.1^51-K.1^55,2*K.1-K.1^3+2*K.1^5-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19+K.1^21-K.1^23+2*K.1^25-K.1^27+K.1^29-K.1^31+K.1^33-K.1^35-K.1^39+K.1^41-K.1^43+K.1^45-K.1^47+K.1^49-K.1^51+K.1^53-K.1^55-K.1^59,K.1^19+K.1^21+K.1^29-K.1^33-K.1^41-K.1^43,-1*K.1^3+K.1^13-K.1^15+K.1^47-K.1^49+K.1^59,-1*K.1^9+K.1^17-K.1^23+K.1^39-K.1^45+K.1^53]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(124: Sparse := true);
S := [ K |6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,-1-K.1^4+K.1^6-K.1^8+K.1^14-K.1^16+K.1^18-K.1^20+K.1^22-K.1^24+K.1^26-K.1^28+K.1^30-K.1^32+K.1^34-K.1^36+K.1^38-K.1^40+K.1^42-K.1^44+K.1^46-K.1^48+K.1^54-K.1^56+K.1^58,K.1^4+K.1^20+K.1^24-K.1^38-K.1^42-K.1^58,-1*K.1^6-K.1^26-K.1^30+K.1^32+K.1^36+K.1^56,K.1^8-K.1^14-K.1^22+K.1^40+K.1^48-K.1^54,K.1^16-K.1^18+K.1^28-K.1^34+K.1^44-K.1^46,K.1^6+K.1^26+K.1^30-K.1^32-K.1^36-K.1^56,-1*K.1^16+K.1^18-K.1^28+K.1^34-K.1^44+K.1^46,-1*K.1^4-K.1^20-K.1^24+K.1^38+K.1^42+K.1^58,-1*K.1^8+K.1^14+K.1^22-K.1^40-K.1^48+K.1^54,1+K.1^4-K.1^6+K.1^8-K.1^14+K.1^16-K.1^18+K.1^20-K.1^22+K.1^24-K.1^26+K.1^28-K.1^30+K.1^32-K.1^34+K.1^36-K.1^38+K.1^40-K.1^42+K.1^44-K.1^46+K.1^48-K.1^54+K.1^56-K.1^58,-1*K.1^9+K.1^17-K.1^23+K.1^39-K.1^45+K.1^53,-2*K.1+K.1^3-2*K.1^5+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19-K.1^21+K.1^23-2*K.1^25+K.1^27-K.1^29+K.1^31-K.1^33+K.1^35+K.1^39-K.1^41+K.1^43-K.1^45+K.1^47-K.1^49+K.1^51-K.1^53+K.1^55+K.1^59,-1*K.1^19-K.1^21-K.1^29+K.1^33+K.1^41+K.1^43,-1*K.1^3+K.1^13-K.1^15+K.1^47-K.1^49+K.1^59,K.1^7-K.1^11-K.1^27+K.1^35+K.1^51-K.1^55,K.1^9-K.1^17+K.1^23-K.1^39+K.1^45-K.1^53,K.1^19+K.1^21+K.1^29-K.1^33-K.1^41-K.1^43,-1*K.1^7+K.1^11+K.1^27-K.1^35-K.1^51+K.1^55,2*K.1-K.1^3+2*K.1^5-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19+K.1^21-K.1^23+2*K.1^25-K.1^27+K.1^29-K.1^31+K.1^33-K.1^35-K.1^39+K.1^41-K.1^43+K.1^45-K.1^47+K.1^49-K.1^51+K.1^53-K.1^55-K.1^59,K.1^3-K.1^13+K.1^15-K.1^47+K.1^49-K.1^59]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(124: Sparse := true);
S := [ K |6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,-1-K.1^4+K.1^6-K.1^8+K.1^14-K.1^16+K.1^18-K.1^20+K.1^22-K.1^24+K.1^26-K.1^28+K.1^30-K.1^32+K.1^34-K.1^36+K.1^38-K.1^40+K.1^42-K.1^44+K.1^46-K.1^48+K.1^54-K.1^56+K.1^58,K.1^4+K.1^20+K.1^24-K.1^38-K.1^42-K.1^58,-1*K.1^6-K.1^26-K.1^30+K.1^32+K.1^36+K.1^56,K.1^8-K.1^14-K.1^22+K.1^40+K.1^48-K.1^54,K.1^16-K.1^18+K.1^28-K.1^34+K.1^44-K.1^46,K.1^6+K.1^26+K.1^30-K.1^32-K.1^36-K.1^56,-1*K.1^16+K.1^18-K.1^28+K.1^34-K.1^44+K.1^46,-1*K.1^4-K.1^20-K.1^24+K.1^38+K.1^42+K.1^58,-1*K.1^8+K.1^14+K.1^22-K.1^40-K.1^48+K.1^54,1+K.1^4-K.1^6+K.1^8-K.1^14+K.1^16-K.1^18+K.1^20-K.1^22+K.1^24-K.1^26+K.1^28-K.1^30+K.1^32-K.1^34+K.1^36-K.1^38+K.1^40-K.1^42+K.1^44-K.1^46+K.1^48-K.1^54+K.1^56-K.1^58,K.1^9-K.1^17+K.1^23-K.1^39+K.1^45-K.1^53,2*K.1-K.1^3+2*K.1^5-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19+K.1^21-K.1^23+2*K.1^25-K.1^27+K.1^29-K.1^31+K.1^33-K.1^35-K.1^39+K.1^41-K.1^43+K.1^45-K.1^47+K.1^49-K.1^51+K.1^53-K.1^55-K.1^59,K.1^19+K.1^21+K.1^29-K.1^33-K.1^41-K.1^43,K.1^3-K.1^13+K.1^15-K.1^47+K.1^49-K.1^59,-1*K.1^7+K.1^11+K.1^27-K.1^35-K.1^51+K.1^55,-1*K.1^9+K.1^17-K.1^23+K.1^39-K.1^45+K.1^53,-1*K.1^19-K.1^21-K.1^29+K.1^33+K.1^41+K.1^43,K.1^7-K.1^11-K.1^27+K.1^35+K.1^51-K.1^55,-2*K.1+K.1^3-2*K.1^5+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19-K.1^21+K.1^23-2*K.1^25+K.1^27-K.1^29+K.1^31-K.1^33+K.1^35+K.1^39-K.1^41+K.1^43-K.1^45+K.1^47-K.1^49+K.1^51-K.1^53+K.1^55+K.1^59,-1*K.1^3+K.1^13-K.1^15+K.1^47-K.1^49+K.1^59]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(124: Sparse := true);
S := [ K |6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1^8-K.1^14-K.1^22+K.1^40+K.1^48-K.1^54,K.1^16-K.1^18+K.1^28-K.1^34+K.1^44-K.1^46,K.1^4+K.1^20+K.1^24-K.1^38-K.1^42-K.1^58,-1*K.1^6-K.1^26-K.1^30+K.1^32+K.1^36+K.1^56,-1-K.1^4+K.1^6-K.1^8+K.1^14-K.1^16+K.1^18-K.1^20+K.1^22-K.1^24+K.1^26-K.1^28+K.1^30-K.1^32+K.1^34-K.1^36+K.1^38-K.1^40+K.1^42-K.1^44+K.1^46-K.1^48+K.1^54-K.1^56+K.1^58,-1*K.1^4-K.1^20-K.1^24+K.1^38+K.1^42+K.1^58,1+K.1^4-K.1^6+K.1^8-K.1^14+K.1^16-K.1^18+K.1^20-K.1^22+K.1^24-K.1^26+K.1^28-K.1^30+K.1^32-K.1^34+K.1^36-K.1^38+K.1^40-K.1^42+K.1^44-K.1^46+K.1^48-K.1^54+K.1^56-K.1^58,-1*K.1^16+K.1^18-K.1^28+K.1^34-K.1^44+K.1^46,K.1^6+K.1^26+K.1^30-K.1^32-K.1^36-K.1^56,-1*K.1^8+K.1^14+K.1^22-K.1^40-K.1^48+K.1^54,-2*K.1+K.1^3-2*K.1^5+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19-K.1^21+K.1^23-2*K.1^25+K.1^27-K.1^29+K.1^31-K.1^33+K.1^35+K.1^39-K.1^41+K.1^43-K.1^45+K.1^47-K.1^49+K.1^51-K.1^53+K.1^55+K.1^59,K.1^7-K.1^11-K.1^27+K.1^35+K.1^51-K.1^55,K.1^9-K.1^17+K.1^23-K.1^39+K.1^45-K.1^53,K.1^19+K.1^21+K.1^29-K.1^33-K.1^41-K.1^43,-1*K.1^3+K.1^13-K.1^15+K.1^47-K.1^49+K.1^59,2*K.1-K.1^3+2*K.1^5-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19+K.1^21-K.1^23+2*K.1^25-K.1^27+K.1^29-K.1^31+K.1^33-K.1^35-K.1^39+K.1^41-K.1^43+K.1^45-K.1^47+K.1^49-K.1^51+K.1^53-K.1^55-K.1^59,-1*K.1^9+K.1^17-K.1^23+K.1^39-K.1^45+K.1^53,K.1^3-K.1^13+K.1^15-K.1^47+K.1^49-K.1^59,-1*K.1^7+K.1^11+K.1^27-K.1^35-K.1^51+K.1^55,-1*K.1^19-K.1^21-K.1^29+K.1^33+K.1^41+K.1^43]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(124: Sparse := true);
S := [ K |6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1^8-K.1^14-K.1^22+K.1^40+K.1^48-K.1^54,K.1^16-K.1^18+K.1^28-K.1^34+K.1^44-K.1^46,K.1^4+K.1^20+K.1^24-K.1^38-K.1^42-K.1^58,-1*K.1^6-K.1^26-K.1^30+K.1^32+K.1^36+K.1^56,-1-K.1^4+K.1^6-K.1^8+K.1^14-K.1^16+K.1^18-K.1^20+K.1^22-K.1^24+K.1^26-K.1^28+K.1^30-K.1^32+K.1^34-K.1^36+K.1^38-K.1^40+K.1^42-K.1^44+K.1^46-K.1^48+K.1^54-K.1^56+K.1^58,-1*K.1^4-K.1^20-K.1^24+K.1^38+K.1^42+K.1^58,1+K.1^4-K.1^6+K.1^8-K.1^14+K.1^16-K.1^18+K.1^20-K.1^22+K.1^24-K.1^26+K.1^28-K.1^30+K.1^32-K.1^34+K.1^36-K.1^38+K.1^40-K.1^42+K.1^44-K.1^46+K.1^48-K.1^54+K.1^56-K.1^58,-1*K.1^16+K.1^18-K.1^28+K.1^34-K.1^44+K.1^46,K.1^6+K.1^26+K.1^30-K.1^32-K.1^36-K.1^56,-1*K.1^8+K.1^14+K.1^22-K.1^40-K.1^48+K.1^54,2*K.1-K.1^3+2*K.1^5-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19+K.1^21-K.1^23+2*K.1^25-K.1^27+K.1^29-K.1^31+K.1^33-K.1^35-K.1^39+K.1^41-K.1^43+K.1^45-K.1^47+K.1^49-K.1^51+K.1^53-K.1^55-K.1^59,-1*K.1^7+K.1^11+K.1^27-K.1^35-K.1^51+K.1^55,-1*K.1^9+K.1^17-K.1^23+K.1^39-K.1^45+K.1^53,-1*K.1^19-K.1^21-K.1^29+K.1^33+K.1^41+K.1^43,K.1^3-K.1^13+K.1^15-K.1^47+K.1^49-K.1^59,-2*K.1+K.1^3-2*K.1^5+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19-K.1^21+K.1^23-2*K.1^25+K.1^27-K.1^29+K.1^31-K.1^33+K.1^35+K.1^39-K.1^41+K.1^43-K.1^45+K.1^47-K.1^49+K.1^51-K.1^53+K.1^55+K.1^59,K.1^9-K.1^17+K.1^23-K.1^39+K.1^45-K.1^53,-1*K.1^3+K.1^13-K.1^15+K.1^47-K.1^49+K.1^59,K.1^7-K.1^11-K.1^27+K.1^35+K.1^51-K.1^55,K.1^19+K.1^21+K.1^29-K.1^33-K.1^41-K.1^43]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(124: Sparse := true);
S := [ K |6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1^16-K.1^18+K.1^28-K.1^34+K.1^44-K.1^46,-1*K.1^6-K.1^26-K.1^30+K.1^32+K.1^36+K.1^56,K.1^8-K.1^14-K.1^22+K.1^40+K.1^48-K.1^54,-1-K.1^4+K.1^6-K.1^8+K.1^14-K.1^16+K.1^18-K.1^20+K.1^22-K.1^24+K.1^26-K.1^28+K.1^30-K.1^32+K.1^34-K.1^36+K.1^38-K.1^40+K.1^42-K.1^44+K.1^46-K.1^48+K.1^54-K.1^56+K.1^58,K.1^4+K.1^20+K.1^24-K.1^38-K.1^42-K.1^58,-1*K.1^8+K.1^14+K.1^22-K.1^40-K.1^48+K.1^54,-1*K.1^4-K.1^20-K.1^24+K.1^38+K.1^42+K.1^58,K.1^6+K.1^26+K.1^30-K.1^32-K.1^36-K.1^56,1+K.1^4-K.1^6+K.1^8-K.1^14+K.1^16-K.1^18+K.1^20-K.1^22+K.1^24-K.1^26+K.1^28-K.1^30+K.1^32-K.1^34+K.1^36-K.1^38+K.1^40-K.1^42+K.1^44-K.1^46+K.1^48-K.1^54+K.1^56-K.1^58,-1*K.1^16+K.1^18-K.1^28+K.1^34-K.1^44+K.1^46,-1*K.1^19-K.1^21-K.1^29+K.1^33+K.1^41+K.1^43,K.1^9-K.1^17+K.1^23-K.1^39+K.1^45-K.1^53,-1*K.1^3+K.1^13-K.1^15+K.1^47-K.1^49+K.1^59,-1*K.1^7+K.1^11+K.1^27-K.1^35-K.1^51+K.1^55,2*K.1-K.1^3+2*K.1^5-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19+K.1^21-K.1^23+2*K.1^25-K.1^27+K.1^29-K.1^31+K.1^33-K.1^35-K.1^39+K.1^41-K.1^43+K.1^45-K.1^47+K.1^49-K.1^51+K.1^53-K.1^55-K.1^59,K.1^19+K.1^21+K.1^29-K.1^33-K.1^41-K.1^43,K.1^3-K.1^13+K.1^15-K.1^47+K.1^49-K.1^59,-2*K.1+K.1^3-2*K.1^5+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19-K.1^21+K.1^23-2*K.1^25+K.1^27-K.1^29+K.1^31-K.1^33+K.1^35+K.1^39-K.1^41+K.1^43-K.1^45+K.1^47-K.1^49+K.1^51-K.1^53+K.1^55+K.1^59,-1*K.1^9+K.1^17-K.1^23+K.1^39-K.1^45+K.1^53,K.1^7-K.1^11-K.1^27+K.1^35+K.1^51-K.1^55]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(124: Sparse := true);
S := [ K |6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1^16-K.1^18+K.1^28-K.1^34+K.1^44-K.1^46,-1*K.1^6-K.1^26-K.1^30+K.1^32+K.1^36+K.1^56,K.1^8-K.1^14-K.1^22+K.1^40+K.1^48-K.1^54,-1-K.1^4+K.1^6-K.1^8+K.1^14-K.1^16+K.1^18-K.1^20+K.1^22-K.1^24+K.1^26-K.1^28+K.1^30-K.1^32+K.1^34-K.1^36+K.1^38-K.1^40+K.1^42-K.1^44+K.1^46-K.1^48+K.1^54-K.1^56+K.1^58,K.1^4+K.1^20+K.1^24-K.1^38-K.1^42-K.1^58,-1*K.1^8+K.1^14+K.1^22-K.1^40-K.1^48+K.1^54,-1*K.1^4-K.1^20-K.1^24+K.1^38+K.1^42+K.1^58,K.1^6+K.1^26+K.1^30-K.1^32-K.1^36-K.1^56,1+K.1^4-K.1^6+K.1^8-K.1^14+K.1^16-K.1^18+K.1^20-K.1^22+K.1^24-K.1^26+K.1^28-K.1^30+K.1^32-K.1^34+K.1^36-K.1^38+K.1^40-K.1^42+K.1^44-K.1^46+K.1^48-K.1^54+K.1^56-K.1^58,-1*K.1^16+K.1^18-K.1^28+K.1^34-K.1^44+K.1^46,K.1^19+K.1^21+K.1^29-K.1^33-K.1^41-K.1^43,-1*K.1^9+K.1^17-K.1^23+K.1^39-K.1^45+K.1^53,K.1^3-K.1^13+K.1^15-K.1^47+K.1^49-K.1^59,K.1^7-K.1^11-K.1^27+K.1^35+K.1^51-K.1^55,-2*K.1+K.1^3-2*K.1^5+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19-K.1^21+K.1^23-2*K.1^25+K.1^27-K.1^29+K.1^31-K.1^33+K.1^35+K.1^39-K.1^41+K.1^43-K.1^45+K.1^47-K.1^49+K.1^51-K.1^53+K.1^55+K.1^59,-1*K.1^19-K.1^21-K.1^29+K.1^33+K.1^41+K.1^43,-1*K.1^3+K.1^13-K.1^15+K.1^47-K.1^49+K.1^59,2*K.1-K.1^3+2*K.1^5-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19+K.1^21-K.1^23+2*K.1^25-K.1^27+K.1^29-K.1^31+K.1^33-K.1^35-K.1^39+K.1^41-K.1^43+K.1^45-K.1^47+K.1^49-K.1^51+K.1^53-K.1^55-K.1^59,K.1^9-K.1^17+K.1^23-K.1^39+K.1^45-K.1^53,-1*K.1^7+K.1^11+K.1^27-K.1^35-K.1^51+K.1^55]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(124: Sparse := true);
S := [ K |6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1^4+K.1^20+K.1^24-K.1^38-K.1^42-K.1^58,K.1^8-K.1^14-K.1^22+K.1^40+K.1^48-K.1^54,-1-K.1^4+K.1^6-K.1^8+K.1^14-K.1^16+K.1^18-K.1^20+K.1^22-K.1^24+K.1^26-K.1^28+K.1^30-K.1^32+K.1^34-K.1^36+K.1^38-K.1^40+K.1^42-K.1^44+K.1^46-K.1^48+K.1^54-K.1^56+K.1^58,K.1^16-K.1^18+K.1^28-K.1^34+K.1^44-K.1^46,-1*K.1^6-K.1^26-K.1^30+K.1^32+K.1^36+K.1^56,1+K.1^4-K.1^6+K.1^8-K.1^14+K.1^16-K.1^18+K.1^20-K.1^22+K.1^24-K.1^26+K.1^28-K.1^30+K.1^32-K.1^34+K.1^36-K.1^38+K.1^40-K.1^42+K.1^44-K.1^46+K.1^48-K.1^54+K.1^56-K.1^58,K.1^6+K.1^26+K.1^30-K.1^32-K.1^36-K.1^56,-1*K.1^8+K.1^14+K.1^22-K.1^40-K.1^48+K.1^54,-1*K.1^16+K.1^18-K.1^28+K.1^34-K.1^44+K.1^46,-1*K.1^4-K.1^20-K.1^24+K.1^38+K.1^42+K.1^58,-1*K.1^3+K.1^13-K.1^15+K.1^47-K.1^49+K.1^59,K.1^19+K.1^21+K.1^29-K.1^33-K.1^41-K.1^43,-1*K.1^7+K.1^11+K.1^27-K.1^35-K.1^51+K.1^55,-2*K.1+K.1^3-2*K.1^5+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19-K.1^21+K.1^23-2*K.1^25+K.1^27-K.1^29+K.1^31-K.1^33+K.1^35+K.1^39-K.1^41+K.1^43-K.1^45+K.1^47-K.1^49+K.1^51-K.1^53+K.1^55+K.1^59,-1*K.1^9+K.1^17-K.1^23+K.1^39-K.1^45+K.1^53,K.1^3-K.1^13+K.1^15-K.1^47+K.1^49-K.1^59,K.1^7-K.1^11-K.1^27+K.1^35+K.1^51-K.1^55,K.1^9-K.1^17+K.1^23-K.1^39+K.1^45-K.1^53,-1*K.1^19-K.1^21-K.1^29+K.1^33+K.1^41+K.1^43,2*K.1-K.1^3+2*K.1^5-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19+K.1^21-K.1^23+2*K.1^25-K.1^27+K.1^29-K.1^31+K.1^33-K.1^35-K.1^39+K.1^41-K.1^43+K.1^45-K.1^47+K.1^49-K.1^51+K.1^53-K.1^55-K.1^59]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(124: Sparse := true);
S := [ K |6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1^4+K.1^20+K.1^24-K.1^38-K.1^42-K.1^58,K.1^8-K.1^14-K.1^22+K.1^40+K.1^48-K.1^54,-1-K.1^4+K.1^6-K.1^8+K.1^14-K.1^16+K.1^18-K.1^20+K.1^22-K.1^24+K.1^26-K.1^28+K.1^30-K.1^32+K.1^34-K.1^36+K.1^38-K.1^40+K.1^42-K.1^44+K.1^46-K.1^48+K.1^54-K.1^56+K.1^58,K.1^16-K.1^18+K.1^28-K.1^34+K.1^44-K.1^46,-1*K.1^6-K.1^26-K.1^30+K.1^32+K.1^36+K.1^56,1+K.1^4-K.1^6+K.1^8-K.1^14+K.1^16-K.1^18+K.1^20-K.1^22+K.1^24-K.1^26+K.1^28-K.1^30+K.1^32-K.1^34+K.1^36-K.1^38+K.1^40-K.1^42+K.1^44-K.1^46+K.1^48-K.1^54+K.1^56-K.1^58,K.1^6+K.1^26+K.1^30-K.1^32-K.1^36-K.1^56,-1*K.1^8+K.1^14+K.1^22-K.1^40-K.1^48+K.1^54,-1*K.1^16+K.1^18-K.1^28+K.1^34-K.1^44+K.1^46,-1*K.1^4-K.1^20-K.1^24+K.1^38+K.1^42+K.1^58,K.1^3-K.1^13+K.1^15-K.1^47+K.1^49-K.1^59,-1*K.1^19-K.1^21-K.1^29+K.1^33+K.1^41+K.1^43,K.1^7-K.1^11-K.1^27+K.1^35+K.1^51-K.1^55,2*K.1-K.1^3+2*K.1^5-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19+K.1^21-K.1^23+2*K.1^25-K.1^27+K.1^29-K.1^31+K.1^33-K.1^35-K.1^39+K.1^41-K.1^43+K.1^45-K.1^47+K.1^49-K.1^51+K.1^53-K.1^55-K.1^59,K.1^9-K.1^17+K.1^23-K.1^39+K.1^45-K.1^53,-1*K.1^3+K.1^13-K.1^15+K.1^47-K.1^49+K.1^59,-1*K.1^7+K.1^11+K.1^27-K.1^35-K.1^51+K.1^55,-1*K.1^9+K.1^17-K.1^23+K.1^39-K.1^45+K.1^53,K.1^19+K.1^21+K.1^29-K.1^33-K.1^41-K.1^43,-2*K.1+K.1^3-2*K.1^5+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19-K.1^21+K.1^23-2*K.1^25+K.1^27-K.1^29+K.1^31-K.1^33+K.1^35+K.1^39-K.1^41+K.1^43-K.1^45+K.1^47-K.1^49+K.1^51-K.1^53+K.1^55+K.1^59]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_744_7:= KnownIrreducibles(CR);