/* Group 960.5792 downloaded from the LMFDB on 16 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([8, -2, -2, -2, -3, -2, 2, -2, -5, 3840, 353, 41, 482, 66, 515, 28804, 4812, 7460, 1228, 836, 14981, 22477, 9525, 3341, 1093, 141, 24206, 166, 24591]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.5, GPC.6]); AssignNames(~GPC, ["a", "b", "b2", "b4", "c", "d", "d2", "d4"]);
GPerm := PermutationGroup< 25 | (18,19)(20,21)(22,23,24,25), (1,2,5,8)(3,9,11,7)(4,12,14,6)(10,16,13,15)(22,23)(24,25), (22,24)(23,25), (3,4,13)(6,7,16)(9,15,12)(10,11,14), (17,18,20,21,19), (1,3,5,11)(2,6,8,12)(4,13,14,10)(7,16,9,15), (1,4,5,14)(2,7,8,9)(3,10,11,13)(6,15,12,16), (1,5)(2,8)(3,11)(4,14)(6,12)(7,9)(10,13)(15,16) >;
GLZN := MatrixGroup< 2, Integers(77) | [[67, 66, 0, 23], [45, 55, 66, 67], [36, 21, 56, 22], [36, 54, 41, 52], [1, 21, 35, 43], [23, 33, 55, 12], [43, 0, 0, 43], [34, 0, 0, 34]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_960_5792 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false>; 

 
/* Character Table */
G:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, d^10>,< 2, 1, b^6>,< 2, 1, b^6*d^10>,< 3, 8, b^4>,< 4, 6, b^6*d^5>,< 4, 6, c*d^5>,< 4, 10, b^3*d^2>,< 4, 10, b^9*d^8>,< 4, 24, a>,< 4, 60, b^3*d>,< 4, 120, a*b^5*c*d^2>,< 5, 2, d^4>,< 5, 2, d^8>,< 6, 8, b^8*d^10>,< 6, 8, b^10>,< 6, 8, b^10*d^10>,< 8, 12, a*d^15>,< 8, 12, a*c*d^10>,< 8, 60, a*b^5*d^3>,< 8, 60, a*b^5*c*d^13>,< 10, 2, d^2>,< 10, 2, d^6>,< 10, 2, b^6*d^12>,< 10, 2, b^6*d^16>,< 10, 2, b^6*d^6>,< 10, 2, b^6*d^18>,< 12, 40, b^5*d^7>,< 12, 40, b*c*d^7>,< 12, 40, b^7*c*d^18>,< 12, 40, b^11*c*d^3>,< 15, 16, b^8*d^4>,< 15, 16, b^4*d^8>,< 20, 12, b^6*d>,< 20, 12, b^6*d^3>,< 20, 12, c*d^17>,< 20, 12, c*d^11>,< 20, 24, a*d^4>,< 20, 24, a*d^16>,< 20, 24, a*d^2>,< 20, 24, a*d^8>,< 30, 16, b^4*d^2>,< 30, 16, b^4*d>,< 30, 16, b^2*d^4>,< 30, 16, b^2*d^8>,< 30, 16, b^2*d^2>,< 30, 16, b^2*d^6>,< 40, 12, a*d>,< 40, 12, a*d^9>,< 40, 12, a*d^3>,< 40, 12, a*c*d^12>,< 40, 12, a*c*d^2>,< 40, 12, a*d^13>,< 40, 12, a*b^8*d>,< 40, 12, a*c*d^4>]); 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -1, 2, 2, 2, 2, 0, 2, 0, 2, 2, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 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, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, -1, 2, 2, -2, -2, 0, -2, 0, 2, 2, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,2,2,2,2,0,0,2,0,0,K.1^2+K.1^-2,K.1+K.1^-1,2,2,2,2,2,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,2,2,2,2,0,0,2,0,0,K.1+K.1^-1,K.1^2+K.1^-2,2,2,2,2,2,0,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,2,2,2,2,0,0,-2,0,0,K.1^2+K.1^-2,K.1+K.1^-1,2,2,2,-2,-2,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,2,2,2,2,0,0,-2,0,0,K.1+K.1^-1,K.1^2+K.1^-2,2,2,2,-2,-2,0,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,2,-2,-2,-1,-2,2,0,0,0,0,0,2,2,1,1,-1,0,0,0,0,-2,-2,-2,-2,2,2,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1,-1,-2,-2,2,2,0,0,0,0,-1,-1,1,1,1,1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,2,-2,-2,-1,-2,2,0,0,0,0,0,2,2,1,1,-1,0,0,0,0,-2,-2,-2,-2,2,2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1,-1,-2,-2,2,2,0,0,0,0,-1,-1,1,1,1,1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,-1,0,0,-2,2,0,0,0,2,2,-1,1,1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,2,2,-2,-2,-2,-2,-1,1,-1,1,-1,-1,0,0,0,0,0,0,0,0,1,1,-1,-1,1,1,-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,-1,0,0,-2,2,0,0,0,2,2,-1,1,1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,2,2,-2,-2,-2,-2,-1,1,-1,1,-1,-1,0,0,0,0,0,0,0,0,1,1,-1,-1,1,1,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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,-1,0,0,2,-2,0,0,0,2,2,-1,1,1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,2,2,-2,-2,-2,-2,1,-1,1,-1,-1,-1,0,0,0,0,0,0,0,0,1,1,-1,-1,1,1,-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,-2,2,-2,-1,0,0,2,-2,0,0,0,2,2,-1,1,1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,2,2,-2,-2,-2,-2,1,-1,1,-1,-1,-1,0,0,0,0,0,0,0,0,1,1,-1,-1,1,1,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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,-2,-2,2,-2,2,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,-2,-2,2,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1^2+K.1^-2,K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1^2-K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1*K.1^2+K.1^-2,-1*K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,-2,-2,2,-2,2,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,-2,-2,2,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2-K.1^-2,-1*K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2+K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,K.1^2-K.1^-2,K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,-2,-2,2,-2,2,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,-2,-2,2,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,K.1^2-K.1^-2,-1*K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,1+2*K.1+K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,-1*K.1^2+K.1^-2,K.1^2-K.1^-2,K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,-2,-2,2,-2,2,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,-2,-2,2,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1*K.1^2+K.1^-2,K.1^2-K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1-2*K.1-K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,K.1^2-K.1^-2,-1*K.1^2+K.1^-2,-1*K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 0, -1, -1, 3, 3, 1, -1, 1, 3, 3, 0, 0, 0, -1, -1, -1, -1, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 0, -1, -1, 3, 3, -1, -1, -1, 3, 3, 0, 0, 0, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 0, -1, -1, -3, -3, -1, 1, 1, 3, 3, 0, 0, 0, 1, 1, -1, -1, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 0, -1, -1, -3, -3, 1, 1, -1, 3, 3, 0, 0, 0, -1, -1, 1, 1, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 4, -4, 1, 0, 0, -4, 4, 0, 0, 0, 4, 4, 1, -1, -1, 0, 0, 0, 0, 4, 4, -4, -4, -4, -4, 1, -1, 1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, -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, 1, 0, 0, 4, -4, 0, 0, 0, 4, 4, 1, -1, -1, 0, 0, 0, 0, 4, 4, -4, -4, -4, -4, -1, 1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, -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, -2, 0, 0, 0, 0, 0, 0, 0, 4, 4, 2, -2, 2, 0, 0, 0, 0, -4, -4, 4, 4, -4, -4, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,4,4,4,-2,4,4,0,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-2,-2,-2,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,4,4,4,-2,4,4,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-2,-2,-2,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-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,-4,4,1,0,0,0,0,0,0,0,4,4,-1,1,-1,0,0,0,0,-4,-4,4,4,-4,-4,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,1,1,0,0,0,0,0,0,0,0,-1,-1,-1,-1,1,1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,-4,-4,4,1,0,0,0,0,0,0,0,4,4,-1,1,-1,0,0,0,0,-4,-4,4,4,-4,-4,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,1,1,0,0,0,0,0,0,0,0,-1,-1,-1,-1,1,1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,4,-4,-4,-2,-4,4,0,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2,2,-2,0,0,0,0,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,4,-4,-4,-2,-4,4,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2,2,-2,0,0,0,0,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,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(40: Sparse := true);
S := [ K |4,-4,-4,4,-2,0,0,0,0,0,0,0,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,2,-2,2,0,0,0,0,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,2*K.1^8+2*K.1^-8,-2*K.1^4-2*K.1^-4,2*K.1^4+2*K.1^-4,-2*K.1^8-2*K.1^-8,0,0,0,0,K.1^4+K.1^-4,-1*K.1^8-K.1^-8,0,0,0,0,0,0,0,0,K.1^8+K.1^-8,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^8+K.1^-8,-1*K.1^8-K.1^-8,K.1^4+K.1^-4,K.1-K.1^3+K.1^7-K.1^9-2*K.1^11+K.1^15,-1*K.1+K.1^3-K.1^7+K.1^9+2*K.1^11-K.1^15,-1*K.1+K.1^3+K.1^5+K.1^7-K.1^9+2*K.1^13,K.1-K.1^3-K.1^5-K.1^7+K.1^9-2*K.1^13,K.1-K.1^3-K.1^5-K.1^7+K.1^9-2*K.1^13,-1*K.1+K.1^3+K.1^5+K.1^7-K.1^9+2*K.1^13,K.1-K.1^3+K.1^7-K.1^9-2*K.1^11+K.1^15,-1*K.1+K.1^3-K.1^7+K.1^9+2*K.1^11-K.1^15]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |4,-4,-4,4,-2,0,0,0,0,0,0,0,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,2,-2,2,0,0,0,0,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,2*K.1^8+2*K.1^-8,-2*K.1^4-2*K.1^-4,2*K.1^4+2*K.1^-4,-2*K.1^8-2*K.1^-8,0,0,0,0,K.1^4+K.1^-4,-1*K.1^8-K.1^-8,0,0,0,0,0,0,0,0,K.1^8+K.1^-8,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^8+K.1^-8,-1*K.1^8-K.1^-8,K.1^4+K.1^-4,-1*K.1+K.1^3-K.1^7+K.1^9+2*K.1^11-K.1^15,K.1-K.1^3+K.1^7-K.1^9-2*K.1^11+K.1^15,K.1-K.1^3-K.1^5-K.1^7+K.1^9-2*K.1^13,-1*K.1+K.1^3+K.1^5+K.1^7-K.1^9+2*K.1^13,-1*K.1+K.1^3+K.1^5+K.1^7-K.1^9+2*K.1^13,K.1-K.1^3-K.1^5-K.1^7+K.1^9-2*K.1^13,-1*K.1+K.1^3-K.1^7+K.1^9+2*K.1^11-K.1^15,K.1-K.1^3+K.1^7-K.1^9-2*K.1^11+K.1^15]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |4,-4,-4,4,-2,0,0,0,0,0,0,0,2*K.1^8+2*K.1^-8,-2*K.1^4-2*K.1^-4,2,-2,2,0,0,0,0,2*K.1^4+2*K.1^-4,-2*K.1^8-2*K.1^-8,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,0,0,0,0,-1*K.1^8-K.1^-8,K.1^4+K.1^-4,0,0,0,0,0,0,0,0,-1*K.1^4-K.1^-4,K.1^8+K.1^-8,K.1^8+K.1^-8,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^8-K.1^-8,K.1-K.1^3-K.1^5-K.1^7+K.1^9-2*K.1^13,-1*K.1+K.1^3+K.1^5+K.1^7-K.1^9+2*K.1^13,K.1-K.1^3+K.1^7-K.1^9-2*K.1^11+K.1^15,-1*K.1+K.1^3-K.1^7+K.1^9+2*K.1^11-K.1^15,-1*K.1+K.1^3-K.1^7+K.1^9+2*K.1^11-K.1^15,K.1-K.1^3+K.1^7-K.1^9-2*K.1^11+K.1^15,K.1-K.1^3-K.1^5-K.1^7+K.1^9-2*K.1^13,-1*K.1+K.1^3+K.1^5+K.1^7-K.1^9+2*K.1^13]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |4,-4,-4,4,-2,0,0,0,0,0,0,0,2*K.1^8+2*K.1^-8,-2*K.1^4-2*K.1^-4,2,-2,2,0,0,0,0,2*K.1^4+2*K.1^-4,-2*K.1^8-2*K.1^-8,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,0,0,0,0,-1*K.1^8-K.1^-8,K.1^4+K.1^-4,0,0,0,0,0,0,0,0,-1*K.1^4-K.1^-4,K.1^8+K.1^-8,K.1^8+K.1^-8,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^8-K.1^-8,-1*K.1+K.1^3+K.1^5+K.1^7-K.1^9+2*K.1^13,K.1-K.1^3-K.1^5-K.1^7+K.1^9-2*K.1^13,-1*K.1+K.1^3-K.1^7+K.1^9+2*K.1^11-K.1^15,K.1-K.1^3+K.1^7-K.1^9-2*K.1^11+K.1^15,K.1-K.1^3+K.1^7-K.1^9-2*K.1^11+K.1^15,-1*K.1+K.1^3-K.1^7+K.1^9+2*K.1^11-K.1^15,-1*K.1+K.1^3+K.1^5+K.1^7-K.1^9+2*K.1^13,K.1-K.1^3-K.1^5-K.1^7+K.1^9-2*K.1^13]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |4,-4,4,-4,-2,0,0,0,0,0,0,0,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,-2,2,2,-2*K.1^5-2*K.1^-5,2*K.1^5+2*K.1^-5,0,0,2*K.1^8+2*K.1^-8,-2*K.1^4-2*K.1^-4,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,2*K.1^4+2*K.1^-4,-2*K.1^8-2*K.1^-8,0,0,0,0,K.1^4+K.1^-4,-1*K.1^8-K.1^-8,0,0,0,0,0,0,0,0,K.1^8+K.1^-8,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^8-K.1^-8,K.1^8+K.1^-8,-1*K.1^4-K.1^-4,K.1+K.1^3-K.1^7+K.1^9-K.1^15,-1*K.1-K.1^3+K.1^7-K.1^9+K.1^15,K.1+K.1^3-K.1^5-K.1^7+K.1^9,-1*K.1-K.1^3+K.1^5+K.1^7-K.1^9,K.1+K.1^3-K.1^5-K.1^7+K.1^9,-1*K.1-K.1^3+K.1^5+K.1^7-K.1^9,-1*K.1-K.1^3+K.1^7-K.1^9+K.1^15,K.1+K.1^3-K.1^7+K.1^9-K.1^15]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |4,-4,4,-4,-2,0,0,0,0,0,0,0,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,-2,2,2,2*K.1^5+2*K.1^-5,-2*K.1^5-2*K.1^-5,0,0,2*K.1^8+2*K.1^-8,-2*K.1^4-2*K.1^-4,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,2*K.1^4+2*K.1^-4,-2*K.1^8-2*K.1^-8,0,0,0,0,K.1^4+K.1^-4,-1*K.1^8-K.1^-8,0,0,0,0,0,0,0,0,K.1^8+K.1^-8,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^8-K.1^-8,K.1^8+K.1^-8,-1*K.1^4-K.1^-4,-1*K.1-K.1^3+K.1^7-K.1^9+K.1^15,K.1+K.1^3-K.1^7+K.1^9-K.1^15,-1*K.1-K.1^3+K.1^5+K.1^7-K.1^9,K.1+K.1^3-K.1^5-K.1^7+K.1^9,-1*K.1-K.1^3+K.1^5+K.1^7-K.1^9,K.1+K.1^3-K.1^5-K.1^7+K.1^9,K.1+K.1^3-K.1^7+K.1^9-K.1^15,-1*K.1-K.1^3+K.1^7-K.1^9+K.1^15]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |4,-4,4,-4,-2,0,0,0,0,0,0,0,2*K.1^8+2*K.1^-8,-2*K.1^4-2*K.1^-4,-2,2,2,-2*K.1^5-2*K.1^-5,2*K.1^5+2*K.1^-5,0,0,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,2*K.1^4+2*K.1^-4,-2*K.1^8-2*K.1^-8,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,0,0,0,0,-1*K.1^8-K.1^-8,K.1^4+K.1^-4,0,0,0,0,0,0,0,0,-1*K.1^4-K.1^-4,K.1^8+K.1^-8,-1*K.1^8-K.1^-8,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,K.1^8+K.1^-8,-1*K.1-K.1^3+K.1^5+K.1^7-K.1^9,K.1+K.1^3-K.1^5-K.1^7+K.1^9,-1*K.1-K.1^3+K.1^7-K.1^9+K.1^15,K.1+K.1^3-K.1^7+K.1^9-K.1^15,-1*K.1-K.1^3+K.1^7-K.1^9+K.1^15,K.1+K.1^3-K.1^7+K.1^9-K.1^15,K.1+K.1^3-K.1^5-K.1^7+K.1^9,-1*K.1-K.1^3+K.1^5+K.1^7-K.1^9]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(40: Sparse := true);
S := [ K |4,-4,4,-4,-2,0,0,0,0,0,0,0,2*K.1^8+2*K.1^-8,-2*K.1^4-2*K.1^-4,-2,2,2,2*K.1^5+2*K.1^-5,-2*K.1^5-2*K.1^-5,0,0,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,2*K.1^4+2*K.1^-4,-2*K.1^8-2*K.1^-8,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,0,0,0,0,-1*K.1^8-K.1^-8,K.1^4+K.1^-4,0,0,0,0,0,0,0,0,-1*K.1^4-K.1^-4,K.1^8+K.1^-8,-1*K.1^8-K.1^-8,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,K.1^8+K.1^-8,K.1+K.1^3-K.1^5-K.1^7+K.1^9,-1*K.1-K.1^3+K.1^5+K.1^7-K.1^9,K.1+K.1^3-K.1^7+K.1^9-K.1^15,-1*K.1-K.1^3+K.1^7-K.1^9+K.1^15,K.1+K.1^3-K.1^7+K.1^9-K.1^15,-1*K.1-K.1^3+K.1^7-K.1^9+K.1^15,-1*K.1-K.1^3+K.1^5+K.1^7-K.1^9,K.1+K.1^3-K.1^5-K.1^7+K.1^9]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -6, 0, 2, -2, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, 6, 6, 0, 0, 0, 0, 0, 0, 2, 2, -2, -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(5: Sparse := true);
S := [ K |6,6,6,6,0,-2,-2,0,0,2,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,0,0,-2,-2,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,6,6,0,-2,-2,0,0,2,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,0,0,-2,-2,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,0,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,0,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,6,6,0,-2,-2,0,0,-2,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,0,0,2,2,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,6,6,0,-2,-2,0,0,-2,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,0,0,2,2,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,0,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,0,0,0,0,0,0,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,-6,-6,0,2,-2,0,0,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,0,0,0,0,0,0,-3*K.1-3*K.1^-1,-3*K.1^2-3*K.1^-2,-3*K.1-3*K.1^-1,-3*K.1^2-3*K.1^-2,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2+K.1^-2,K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,0,0,0,0,0,0,-1*K.1^2+K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,K.1^2-K.1^-2,K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,-6,-6,0,2,-2,0,0,0,0,0,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,0,0,0,0,0,0,-3*K.1-3*K.1^-1,-3*K.1^2-3*K.1^-2,-3*K.1-3*K.1^-1,-3*K.1^2-3*K.1^-2,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2-K.1^-2,-1*K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,0,0,0,0,0,0,K.1^2-K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1*K.1^2+K.1^-2,-1*K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,-6,-6,0,2,-2,0,0,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,0,0,0,0,0,0,-3*K.1^2-3*K.1^-2,-3*K.1-3*K.1^-1,-3*K.1^2-3*K.1^-2,-3*K.1-3*K.1^-1,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,K.1^2-K.1^-2,-1*K.1^2+K.1^-2,0,0,0,0,0,0,-1-2*K.1-K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,K.1^2-K.1^-2,-1*K.1^2+K.1^-2,-1*K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,6,-6,-6,0,2,-2,0,0,0,0,0,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,0,0,0,0,0,0,-3*K.1^2-3*K.1^-2,-3*K.1-3*K.1^-1,-3*K.1^2-3*K.1^-2,-3*K.1-3*K.1^-1,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,0,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1*K.1^2+K.1^-2,K.1^2-K.1^-2,0,0,0,0,0,0,1+2*K.1+K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,-1*K.1^2+K.1^-2,K.1^2-K.1^-2,K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,-8,8,-8,2,0,0,0,0,0,0,0,4*K.1^2+4*K.1^-2,4*K.1+4*K.1^-1,2,-2,-2,0,0,0,0,4*K.1+4*K.1^-1,4*K.1^2+4*K.1^-2,-4*K.1-4*K.1^-1,-4*K.1^2-4*K.1^-2,-4*K.1^2-4*K.1^-2,-4*K.1-4*K.1^-1,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,-8,8,-8,2,0,0,0,0,0,0,0,4*K.1+4*K.1^-1,4*K.1^2+4*K.1^-2,2,-2,-2,0,0,0,0,4*K.1^2+4*K.1^-2,4*K.1+4*K.1^-1,-4*K.1^2-4*K.1^-2,-4*K.1-4*K.1^-1,-4*K.1-4*K.1^-1,-4*K.1^2-4*K.1^-2,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,0,0,0,0,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-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(5: Sparse := true);
S := [ K |8,-8,-8,8,2,0,0,0,0,0,0,0,4*K.1^2+4*K.1^-2,4*K.1+4*K.1^-1,-2,2,-2,0,0,0,0,-4*K.1-4*K.1^-1,-4*K.1^2-4*K.1^-2,4*K.1+4*K.1^-1,4*K.1^2+4*K.1^-2,-4*K.1^2-4*K.1^-2,-4*K.1-4*K.1^-1,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,-8,-8,8,2,0,0,0,0,0,0,0,4*K.1+4*K.1^-1,4*K.1^2+4*K.1^-2,-2,2,-2,0,0,0,0,-4*K.1^2-4*K.1^-2,-4*K.1-4*K.1^-1,4*K.1^2+4*K.1^-2,4*K.1+4*K.1^-1,-4*K.1-4*K.1^-1,-4*K.1^2-4*K.1^-2,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,0,0,0,0,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,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; 
_ := CharacterTable(G : Check := 0); 
chartbl_960_5792:= KnownIrreducibles(CR);