/* Group 240.169 downloaded from the LMFDB on 15 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([6, -2, -2, -2, -2, -3, -5, 2234, 1484, 50, 1065, 69, 2650, 118]); a,b,c := Explode([GPC.1, GPC.2, GPC.3]); AssignNames(~GPC, ["a", "b", "c", "c2", "c4", "c12"]);
GPerm := PermutationGroup< 12 | (2,3), (9,10)(11,12), (10,12), (4,5,6,7,8), (9,11)(10,12), (1,2,3) >;
GLZN := MatrixGroup< 2, Integers(22) | [[21, 0, 0, 1], [5, 0, 0, 5], [1, 11, 11, 12], [1, 11, 0, 1], [21, 0, 0, 21], [0, 13, 5, 0]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_240_169 := 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^30>,< 2, 2, a>,< 2, 2, a*c^45>,< 2, 3, b>,< 2, 3, b*c^50>,< 2, 6, a*b>,< 2, 6, a*b*c^25>,< 3, 2, c^40>,< 4, 2, c^15>,< 4, 6, b*c^25>,< 5, 1, c^24>,< 5, 1, c^36>,< 5, 1, c^48>,< 5, 1, c^12>,< 6, 2, c^10>,< 6, 4, a*c^20>,< 6, 4, a*c^5>,< 10, 1, c^42>,< 10, 1, c^18>,< 10, 1, c^6>,< 10, 1, c^54>,< 10, 2, a*c^12>,< 10, 2, a*c^48>,< 10, 2, a*c^36>,< 10, 2, a*c^24>,< 10, 2, a*c^33>,< 10, 2, a*c^57>,< 10, 2, a*c^9>,< 10, 2, a*c^21>,< 10, 3, b*c^12>,< 10, 3, b*c^8>,< 10, 3, b*c^36>,< 10, 3, b*c^4>,< 10, 3, b*c^2>,< 10, 3, b*c^38>,< 10, 3, b*c^6>,< 10, 3, b*c^14>,< 10, 6, a*b*c^12>,< 10, 6, a*b*c^8>,< 10, 6, a*b*c^36>,< 10, 6, a*b*c^4>,< 10, 6, a*b*c>,< 10, 6, a*b*c^9>,< 10, 6, a*b*c^13>,< 10, 6, a*b*c^37>,< 12, 4, c^5>,< 15, 2, c^8>,< 15, 2, c^52>,< 15, 2, c^16>,< 15, 2, c^44>,< 20, 2, c^3>,< 20, 2, c^57>,< 20, 2, c^9>,< 20, 2, c^51>,< 20, 6, b*c>,< 20, 6, b*c^9>,< 20, 6, b*c^13>,< 20, 6, b*c^37>,< 30, 2, c^2>,< 30, 2, c^58>,< 30, 2, c^14>,< 30, 2, c^46>,< 30, 4, a*c^4>,< 30, 4, a*c^16>,< 30, 4, a*c^8>,< 30, 4, a*c^2>,< 30, 4, a*c>,< 30, 4, a*c^49>,< 30, 4, a*c^37>,< 30, 4, a*c^13>,< 60, 4, c>,< 60, 4, c^49>,< 60, 4, c^37>,< 60, 4, c^13>]); 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,1,1,1,K.1^-2,K.1^2,K.1,K.1^-1,1,1,1,K.1^-2,K.1^2,K.1,K.1^-1,K.1^-1,K.1^2,K.1^-1,K.1,K.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,K.1^-2,K.1^-1,K.1^2,K.1^-2,K.1^2,K.1^-2,K.1^-1,K.1,K.1,K.1^-1,1,K.1^-2,K.1^2,K.1^-1,K.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,K.1^-1,K.1^2,K.1,K.1^-1,K.1^2,K.1^-2,K.1,K.1^-1,K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,1,1,1,K.1^2,K.1^-2,K.1^-1,K.1,1,1,1,K.1^2,K.1^-2,K.1^-1,K.1,K.1,K.1^-2,K.1,K.1^-1,K.1^-1,K.1^2,K.1^-2,K.1^2,K.1^2,K.1^-1,K.1,K.1^-2,K.1^-2,K.1^-1,K.1^2,K.1,K.1^-2,K.1^2,K.1^-2,K.1^2,K.1,K.1^-1,K.1^-1,K.1,1,K.1^2,K.1^-2,K.1,K.1^-1,K.1^-1,K.1,K.1^2,K.1^-2,K.1^-2,K.1^2,K.1^-1,K.1,K.1^-1,K.1,K.1^-2,K.1^2,K.1^2,K.1^2,K.1^-1,K.1,K.1^-2,K.1^-1,K.1,K.1^-2,K.1^2,K.1^-1,K.1,K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,1,1,1,K.1^-1,K.1,K.1^-2,K.1^2,1,1,1,K.1^-1,K.1,K.1^-2,K.1^2,K.1^2,K.1,K.1^2,K.1^-2,K.1^-2,K.1^-1,K.1,K.1^-1,K.1^-1,K.1^-2,K.1^2,K.1,K.1,K.1^-2,K.1^-1,K.1^2,K.1,K.1^-1,K.1,K.1^-1,K.1^2,K.1^-2,K.1^-2,K.1^2,1,K.1^-1,K.1,K.1^2,K.1^-2,K.1^-2,K.1^2,K.1^-1,K.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^-1,K.1^-1,K.1^-2,K.1^2,K.1,K.1^-2,K.1^2,K.1,K.1^-1,K.1^-2,K.1^2,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,1,1,1,K.1,K.1^-1,K.1^2,K.1^-2,1,1,1,K.1,K.1^-1,K.1^2,K.1^-2,K.1^-2,K.1^-1,K.1^-2,K.1^2,K.1^2,K.1,K.1^-1,K.1,K.1,K.1^2,K.1^-2,K.1^-1,K.1^-1,K.1^2,K.1,K.1^-2,K.1^-1,K.1,K.1^-1,K.1,K.1^-2,K.1^2,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^-1,K.1,K.1^2,K.1^-2,K.1^2,K.1^-2,K.1^-1,K.1,K.1,K.1,K.1^2,K.1^-2,K.1^-1,K.1^2,K.1^-2,K.1^-1,K.1,K.1^2,K.1^-2,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,-1,-1,-1,-1,1,1,1,1,-1,K.1^-2,K.1^2,K.1,K.1^-1,1,-1,-1,K.1^-2,K.1^2,K.1,K.1^-1,-1*K.1^-1,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-2,-1*K.1^2,-1*K.1^-2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^2,-1*K.1,-1*K.1^-2,-1*K.1^-1,K.1^2,K.1^-2,K.1^2,K.1^-2,K.1^-1,K.1,K.1,K.1^-1,1,K.1^-2,K.1^2,K.1^-1,K.1,K.1,K.1^-1,K.1^-2,K.1^2,-1*K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-1,K.1,K.1^-1,K.1^2,K.1^-2,-1*K.1^-2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1,-1*K.1^-1,-1*K.1^2,K.1^-2,K.1,K.1^-1,K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,-1,-1,-1,-1,1,1,1,1,-1,K.1^2,K.1^-2,K.1^-1,K.1,1,-1,-1,K.1^2,K.1^-2,K.1^-1,K.1,-1*K.1,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1^2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,-1*K.1,K.1^-2,K.1^2,K.1^-2,K.1^2,K.1,K.1^-1,K.1^-1,K.1,1,K.1^2,K.1^-2,K.1,K.1^-1,K.1^-1,K.1,K.1^2,K.1^-2,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1,K.1^-1,K.1,K.1^-2,K.1^2,-1*K.1^2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1^-2,K.1^2,K.1^-1,K.1,K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,-1,-1,-1,-1,1,1,1,1,-1,K.1^-1,K.1,K.1^-2,K.1^2,1,-1,-1,K.1^-1,K.1,K.1^-2,K.1^2,-1*K.1^2,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,K.1,K.1^-1,K.1,K.1^-1,K.1^2,K.1^-2,K.1^-2,K.1^2,1,K.1^-1,K.1,K.1^2,K.1^-2,K.1^-2,K.1^2,K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,K.1^-2,K.1^2,K.1,K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-2,-1*K.1^2,-1*K.1,K.1^-1,K.1^-2,K.1^2,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,-1,-1,-1,-1,1,1,1,1,-1,K.1,K.1^-1,K.1^2,K.1^-2,1,-1,-1,K.1,K.1^-1,K.1^2,K.1^-2,-1*K.1^-2,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1^2,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1^-1,-1*K.1^2,-1*K.1,-1*K.1^-2,K.1^-1,K.1,K.1^-1,K.1,K.1^-2,K.1^2,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,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,K.1^2,K.1^-2,K.1^-1,K.1,-1*K.1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,K.1,K.1^2,K.1^-2,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,-1,-1,1,1,-1,-1,1,1,1,K.1^-2,K.1^2,K.1,K.1^-1,1,-1,-1,K.1^-2,K.1^2,K.1,K.1^-1,-1*K.1^-1,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-2,-1*K.1^2,-1*K.1^-2,K.1^-2,K.1,K.1^-1,K.1^2,K.1^2,K.1,K.1^-2,K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,1,K.1^-2,K.1^2,K.1^-1,K.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,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1,-1*K.1^-1,-1*K.1^2,K.1^-2,K.1,K.1^-1,K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,-1,-1,1,1,-1,-1,1,1,1,K.1^2,K.1^-2,K.1^-1,K.1,1,-1,-1,K.1^2,K.1^-2,K.1^-1,K.1,-1*K.1,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1^2,K.1^2,K.1^-1,K.1,K.1^-2,K.1^-2,K.1^-1,K.1^2,K.1,-1*K.1^-2,-1*K.1^2,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,1,K.1^2,K.1^-2,K.1,K.1^-1,K.1^-1,K.1,K.1^2,K.1^-2,K.1^-2,K.1^2,K.1^-1,K.1,K.1^-1,K.1,K.1^-2,K.1^2,-1*K.1^2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1^-2,K.1^2,K.1^-1,K.1,K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,-1,-1,1,1,-1,-1,1,1,1,K.1^-1,K.1,K.1^-2,K.1^2,1,-1,-1,K.1^-1,K.1,K.1^-2,K.1^2,-1*K.1^2,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1^-1,K.1^-1,K.1^-2,K.1^2,K.1,K.1,K.1^-2,K.1^-1,K.1^2,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1^-2,-1*K.1^2,1,K.1^-1,K.1,K.1^2,K.1^-2,K.1^-2,K.1^2,K.1^-1,K.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^-1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-2,-1*K.1^2,-1*K.1,K.1^-1,K.1^-2,K.1^2,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,-1,-1,1,1,-1,-1,1,1,1,K.1,K.1^-1,K.1^2,K.1^-2,1,-1,-1,K.1,K.1^-1,K.1^2,K.1^-2,-1*K.1^-2,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1^2,-1*K.1,-1*K.1^-1,-1*K.1,K.1,K.1^2,K.1^-2,K.1^-1,K.1^-1,K.1^2,K.1,K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,-1*K.1^2,-1*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^-1,K.1,K.1^2,K.1^-2,K.1^2,K.1^-2,K.1^-1,K.1,-1*K.1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,K.1,K.1^2,K.1^-2,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,-1,1,-1,-1,1,-1,1,-1,1,K.1^-2,K.1^2,K.1,K.1^-1,1,-1,1,K.1^-2,K.1^2,K.1,K.1^-1,-1*K.1^-1,K.1^2,K.1^-1,-1*K.1,K.1,K.1^-2,-1*K.1^2,-1*K.1^-2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^2,-1*K.1,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,K.1^2,K.1^-2,K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1,K.1^-2,K.1^2,K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*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,-1*K.1^-2,K.1,-1*K.1^-1,K.1^2,-1*K.1,K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,-1,1,-1,-1,1,-1,1,-1,1,K.1^2,K.1^-2,K.1^-1,K.1,1,-1,1,K.1^2,K.1^-2,K.1^-1,K.1,-1*K.1,K.1^-2,K.1,-1*K.1^-1,K.1^-1,K.1^2,-1*K.1^-2,-1*K.1^2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,-1*K.1,-1*K.1^-2,-1*K.1^2,K.1^-2,K.1^2,K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1,K.1^2,K.1^-2,K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,K.1^-2,K.1^2,K.1^-1,K.1,K.1^-1,K.1,K.1^-2,K.1^2,K.1^2,-1*K.1^2,K.1^-1,-1*K.1,K.1^-2,-1*K.1^-1,K.1,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,-1,1,-1,-1,1,-1,1,-1,1,K.1^-1,K.1,K.1^-2,K.1^2,1,-1,1,K.1^-1,K.1,K.1^-2,K.1^2,-1*K.1^2,K.1,K.1^2,-1*K.1^-2,K.1^-2,K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,-1*K.1,-1*K.1^-1,K.1,K.1^-1,K.1^2,K.1^-2,-1*K.1^-2,-1*K.1^2,-1,K.1^-1,K.1,K.1^2,K.1^-2,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.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^-1,-1*K.1^-1,K.1^-2,-1*K.1^2,K.1,-1*K.1^-2,K.1^2,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,-1,1,-1,-1,1,-1,1,-1,1,K.1,K.1^-1,K.1^2,K.1^-2,1,-1,1,K.1,K.1^-1,K.1^2,K.1^-2,-1*K.1^-2,K.1^-1,K.1^-2,-1*K.1^2,K.1^2,K.1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1^-1,-1*K.1^2,-1*K.1,-1*K.1^-2,-1*K.1^-1,-1*K.1,K.1^-1,K.1,K.1^-2,K.1^2,-1*K.1^2,-1*K.1^-2,-1,K.1,K.1^-1,K.1^-2,K.1^2,-1*K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-1,K.1^-1,K.1,K.1^2,K.1^-2,K.1^2,K.1^-2,K.1^-1,K.1,K.1,-1*K.1,K.1^2,-1*K.1^-2,K.1^-1,-1*K.1^2,K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,-1,1,1,1,-1,1,1,-1,-1,K.1^-2,K.1^2,K.1,K.1^-1,1,-1,1,K.1^-2,K.1^2,K.1,K.1^-1,-1*K.1^-1,K.1^2,K.1^-1,-1*K.1,K.1,K.1^-2,-1*K.1^2,-1*K.1^-2,K.1^-2,K.1,K.1^-1,K.1^2,K.1^2,K.1,K.1^-2,K.1^-1,K.1^2,K.1^-2,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1,K.1,K.1^-1,-1,K.1^-2,K.1^2,K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-1,K.1,K.1^-1,K.1^2,K.1^-2,K.1^-2,-1*K.1^-2,K.1,-1*K.1^-1,K.1^2,-1*K.1,K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,-1,1,1,1,-1,1,1,-1,-1,K.1^2,K.1^-2,K.1^-1,K.1,1,-1,1,K.1^2,K.1^-2,K.1^-1,K.1,-1*K.1,K.1^-2,K.1,-1*K.1^-1,K.1^-1,K.1^2,-1*K.1^-2,-1*K.1^2,K.1^2,K.1^-1,K.1,K.1^-2,K.1^-2,K.1^-1,K.1^2,K.1,K.1^-2,K.1^2,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,K.1^-1,K.1,-1,K.1^2,K.1^-2,K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1,K.1^-1,K.1,K.1^-2,K.1^2,K.1^2,-1*K.1^2,K.1^-1,-1*K.1,K.1^-2,-1*K.1^-1,K.1,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,-1,1,1,1,-1,1,1,-1,-1,K.1^-1,K.1,K.1^-2,K.1^2,1,-1,1,K.1^-1,K.1,K.1^-2,K.1^2,-1*K.1^2,K.1,K.1^2,-1*K.1^-2,K.1^-2,K.1^-1,-1*K.1,-1*K.1^-1,K.1^-1,K.1^-2,K.1^2,K.1,K.1,K.1^-2,K.1^-1,K.1^2,K.1,K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,K.1^-2,K.1^2,-1,K.1^-1,K.1,K.1^2,K.1^-2,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,K.1^-2,K.1^2,K.1,K.1^-1,K.1^-1,-1*K.1^-1,K.1^-2,-1*K.1^2,K.1,-1*K.1^-2,K.1^2,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,-1,1,1,1,-1,1,1,-1,-1,K.1,K.1^-1,K.1^2,K.1^-2,1,-1,1,K.1,K.1^-1,K.1^2,K.1^-2,-1*K.1^-2,K.1^-1,K.1^-2,-1*K.1^2,K.1^2,K.1,-1*K.1^-1,-1*K.1,K.1,K.1^2,K.1^-2,K.1^-1,K.1^-1,K.1^2,K.1,K.1^-2,K.1^-1,K.1,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,K.1^2,K.1^-2,-1,K.1,K.1^-1,K.1^-2,K.1^2,-1*K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,K.1^2,K.1^-2,K.1^-1,K.1,K.1,-1*K.1,K.1^2,-1*K.1^-2,K.1^-1,-1*K.1^2,K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,-1,-1,-1,-1,1,1,-1,1,K.1^-2,K.1^2,K.1,K.1^-1,1,1,-1,K.1^-2,K.1^2,K.1,K.1^-1,K.1^-1,-1*K.1^2,-1*K.1^-1,K.1,-1*K.1,-1*K.1^-2,K.1^2,K.1^-2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^2,-1*K.1,-1*K.1^-2,-1*K.1^-1,K.1^2,K.1^-2,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1,K.1,K.1^-1,-1,K.1^-2,K.1^2,K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*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,K.1^-1,-1*K.1^2,K.1,-1*K.1^-1,K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,-1,-1,-1,-1,1,1,-1,1,K.1^2,K.1^-2,K.1^-1,K.1,1,1,-1,K.1^2,K.1^-2,K.1^-1,K.1,K.1,-1*K.1^-2,-1*K.1,K.1^-1,-1*K.1^-1,-1*K.1^2,K.1^-2,K.1^2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,-1*K.1,K.1^-2,K.1^2,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,K.1^-1,K.1,-1,K.1^2,K.1^-2,K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,K.1^-2,K.1^2,K.1^-1,K.1,K.1^-1,K.1,K.1^-2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^-1,K.1,-1*K.1^-2,K.1^-1,-1*K.1,K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,-1,-1,-1,-1,1,1,-1,1,K.1^-1,K.1,K.1^-2,K.1^2,1,1,-1,K.1^-1,K.1,K.1^-2,K.1^2,K.1^2,-1*K.1,-1*K.1^2,K.1^-2,-1*K.1^-2,-1*K.1^-1,K.1,K.1^-1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,K.1,K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,K.1^-2,K.1^2,-1,K.1^-1,K.1,K.1^2,K.1^-2,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.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^-1,K.1^-1,-1*K.1^-2,K.1^2,-1*K.1,K.1^-2,-1*K.1^2,K.1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,-1,-1,-1,-1,1,1,-1,1,K.1,K.1^-1,K.1^2,K.1^-2,1,1,-1,K.1,K.1^-1,K.1^2,K.1^-2,K.1^-2,-1*K.1^-1,-1*K.1^-2,K.1^2,-1*K.1^2,-1*K.1,K.1^-1,K.1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1^-1,-1*K.1^2,-1*K.1,-1*K.1^-2,K.1^-1,K.1,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,K.1^2,K.1^-2,-1,K.1,K.1^-1,K.1^-2,K.1^2,-1*K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-1,K.1^-1,K.1,K.1^2,K.1^-2,K.1^2,K.1^-2,K.1^-1,K.1,-1*K.1,K.1,-1*K.1^2,K.1^-2,-1*K.1^-1,K.1^2,-1*K.1^-2,K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,-1,1,1,1,-1,1,-1,-1,K.1^-2,K.1^2,K.1,K.1^-1,1,1,-1,K.1^-2,K.1^2,K.1,K.1^-1,K.1^-1,-1*K.1^2,-1*K.1^-1,K.1,-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,K.1^-2,K.1^-1,-1*K.1^2,-1*K.1^-2,K.1^2,K.1^-2,K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1,K.1^-2,K.1^2,K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1^2,-1*K.1^-2,-1*K.1,-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,-1*K.1^2,K.1,-1*K.1^-1,K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,-1,1,1,1,-1,1,-1,-1,K.1^2,K.1^-2,K.1^-1,K.1,1,1,-1,K.1^2,K.1^-2,K.1^-1,K.1,K.1,-1*K.1^-2,-1*K.1,K.1^-1,-1*K.1^-1,-1*K.1^2,K.1^-2,K.1^2,K.1^2,K.1^-1,K.1,K.1^-2,K.1^-2,K.1^-1,K.1^2,K.1,-1*K.1^-2,-1*K.1^2,K.1^-2,K.1^2,K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1,K.1^2,K.1^-2,K.1,K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1,K.1^-1,K.1,K.1^-2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^-1,K.1,-1*K.1^-2,K.1^-1,-1*K.1,K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,-1,1,1,1,-1,1,-1,-1,K.1^-1,K.1,K.1^-2,K.1^2,1,1,-1,K.1^-1,K.1,K.1^-2,K.1^2,K.1^2,-1*K.1,-1*K.1^2,K.1^-2,-1*K.1^-2,-1*K.1^-1,K.1,K.1^-1,K.1^-1,K.1^-2,K.1^2,K.1,K.1,K.1^-2,K.1^-1,K.1^2,-1*K.1,-1*K.1^-1,K.1,K.1^-1,K.1^2,K.1^-2,-1*K.1^-2,-1*K.1^2,-1,K.1^-1,K.1,K.1^2,K.1^-2,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,K.1^-2,K.1^2,K.1,K.1^-1,-1*K.1^-1,K.1^-1,-1*K.1^-2,K.1^2,-1*K.1,K.1^-2,-1*K.1^2,K.1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,-1,1,1,1,-1,1,-1,-1,K.1,K.1^-1,K.1^2,K.1^-2,1,1,-1,K.1,K.1^-1,K.1^2,K.1^-2,K.1^-2,-1*K.1^-1,-1*K.1^-2,K.1^2,-1*K.1^2,-1*K.1,K.1^-1,K.1,K.1,K.1^2,K.1^-2,K.1^-1,K.1^-1,K.1^2,K.1,K.1^-2,-1*K.1^-1,-1*K.1,K.1^-1,K.1,K.1^-2,K.1^2,-1*K.1^2,-1*K.1^-2,-1,K.1,K.1^-1,K.1^-2,K.1^2,-1*K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,K.1^2,K.1^-2,K.1^-1,K.1,-1*K.1,K.1,-1*K.1^2,K.1^-2,-1*K.1^-1,K.1^2,-1*K.1^-2,K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,1,-1,-1,-1,-1,1,1,-1,K.1^-2,K.1^2,K.1,K.1^-1,1,1,1,K.1^-2,K.1^2,K.1,K.1^-1,K.1^-1,K.1^2,K.1^-1,K.1,K.1,K.1^-2,K.1^2,K.1^-2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^2,-1*K.1,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,1,K.1^-2,K.1^2,K.1^-1,K.1,K.1,K.1^-1,K.1^-2,K.1^2,-1*K.1^2,-1*K.1^-2,-1*K.1,-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,K.1^-1,K.1^2,K.1^-2,K.1,K.1^-1,K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,1,-1,-1,-1,-1,1,1,-1,K.1^2,K.1^-2,K.1^-1,K.1,1,1,1,K.1^2,K.1^-2,K.1^-1,K.1,K.1,K.1^-2,K.1,K.1^-1,K.1^-1,K.1^2,K.1^-2,K.1^2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,-1*K.1,-1*K.1^-2,-1*K.1^2,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,1,K.1^2,K.1^-2,K.1,K.1^-1,K.1^-1,K.1,K.1^2,K.1^-2,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1,K.1^-1,K.1,K.1^-2,K.1^2,K.1^2,K.1^2,K.1^-1,K.1,K.1^-2,K.1^-1,K.1,K.1^-2,K.1^2,K.1^-1,K.1,K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,1,-1,-1,-1,-1,1,1,-1,K.1^-1,K.1,K.1^-2,K.1^2,1,1,1,K.1^-1,K.1,K.1^-2,K.1^2,K.1^2,K.1,K.1^2,K.1^-2,K.1^-2,K.1^-1,K.1,K.1^-1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1^-2,-1*K.1^2,1,K.1^-1,K.1,K.1^2,K.1^-2,K.1^-2,K.1^2,K.1^-1,K.1,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,K.1^-2,K.1^2,K.1,K.1^-1,K.1^-1,K.1^-1,K.1^-2,K.1^2,K.1,K.1^-2,K.1^2,K.1,K.1^-1,K.1^-2,K.1^2,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |1,1,1,1,-1,-1,-1,-1,1,1,-1,K.1,K.1^-1,K.1^2,K.1^-2,1,1,1,K.1,K.1^-1,K.1^2,K.1^-2,K.1^-2,K.1^-1,K.1^-2,K.1^2,K.1^2,K.1,K.1^-1,K.1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1^-1,-1*K.1^2,-1*K.1,-1*K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,-1*K.1^2,-1*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,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,K.1^2,K.1^-2,K.1^-1,K.1,K.1,K.1,K.1^2,K.1^-2,K.1^-1,K.1^2,K.1^-2,K.1^-1,K.1,K.1^2,K.1^-2,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 0, 0, 0, 0, -1, 2, 0, 2, 2, 2, 2, -1, -1, -1, 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, -1, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, -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, 0, 0, -2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, -2, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 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, 0, 0, 2, -2, 0, 0, 2, 0, 0, 2, 2, 2, 2, -2, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 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, 0, 0, 0, 0, -1, 2, 0, 2, 2, 2, 2, -1, 1, 1, 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, -1, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, -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, 0, 2, 2, 2, 2, -1, 1, -1, 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, 1, -1, -1, -1, -1, -2, -2, -2, -2, 0, 0, 0, 0, -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, 0, 2, 2, 2, 2, -1, -1, 1, 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, 1, -1, -1, -1, -1, -2, -2, -2, -2, 0, 0, 0, 0, -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(5: Sparse := true);
S := [ K |2,2,2,2,0,0,0,0,-1,2,0,2*K.1^-2,2*K.1^2,2*K.1,2*K.1^-1,-1,-1,-1,2*K.1^-2,2*K.1^2,2*K.1,2*K.1^-1,2*K.1^-1,2*K.1^2,2*K.1^-1,2*K.1,2*K.1,2*K.1^-2,2*K.1^2,2*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1,2*K.1,2*K.1^-1,2*K.1^-2,2*K.1^2,0,0,0,0,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1^-2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,2,0,0,0,0,-1,2,0,2*K.1^2,2*K.1^-2,2*K.1^-1,2*K.1,-1,-1,-1,2*K.1^2,2*K.1^-2,2*K.1^-1,2*K.1,2*K.1,2*K.1^-2,2*K.1,2*K.1^-1,2*K.1^-1,2*K.1^2,2*K.1^-2,2*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1*K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-1,2*K.1^-1,2*K.1,2*K.1^2,2*K.1^-2,0,0,0,0,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,-1*K.1^2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,2,0,0,0,0,-1,2,0,2*K.1^-1,2*K.1,2*K.1^-2,2*K.1^2,-1,-1,-1,2*K.1^-1,2*K.1,2*K.1^-2,2*K.1^2,2*K.1^2,2*K.1,2*K.1^2,2*K.1^-2,2*K.1^-2,2*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,-1,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,2*K.1^-2,2*K.1^2,2*K.1^-1,2*K.1,0,0,0,0,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,2,0,0,0,0,-1,2,0,2*K.1,2*K.1^-1,2*K.1^2,2*K.1^-2,-1,-1,-1,2*K.1,2*K.1^-1,2*K.1^2,2*K.1^-2,2*K.1^-2,2*K.1^-1,2*K.1^-2,2*K.1^2,2*K.1^2,2*K.1,2*K.1^-1,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*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,-1*K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,0,0,-2,2,0,0,2,0,0,2*K.1^-2,2*K.1^2,2*K.1,2*K.1^-1,-2,0,0,-2*K.1^-2,-2*K.1^2,-2*K.1,-2*K.1^-1,0,0,0,0,0,0,0,0,-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^-2,2*K.1^-1,0,0,0,0,0,0,0,0,0,2*K.1^-2,2*K.1^2,2*K.1^-1,2*K.1,0,0,0,0,0,0,0,0,-2*K.1,-2*K.1^-1,-2*K.1^2,-2*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,0,0,-2,2,0,0,2,0,0,2*K.1^2,2*K.1^-2,2*K.1^-1,2*K.1,-2,0,0,-2*K.1^2,-2*K.1^-2,-2*K.1^-1,-2*K.1,0,0,0,0,0,0,0,0,-2*K.1^2,-2*K.1^-1,-2*K.1,-2*K.1^-2,2*K.1^-2,2*K.1^-1,2*K.1^2,2*K.1,0,0,0,0,0,0,0,0,0,2*K.1^2,2*K.1^-2,2*K.1,2*K.1^-1,0,0,0,0,0,0,0,0,-2*K.1^-1,-2*K.1,-2*K.1^-2,-2*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,0,0,-2,2,0,0,2,0,0,2*K.1^-1,2*K.1,2*K.1^-2,2*K.1^2,-2,0,0,-2*K.1^-1,-2*K.1,-2*K.1^-2,-2*K.1^2,0,0,0,0,0,0,0,0,-2*K.1^-1,-2*K.1^-2,-2*K.1^2,-2*K.1,2*K.1,2*K.1^-2,2*K.1^-1,2*K.1^2,0,0,0,0,0,0,0,0,0,2*K.1^-1,2*K.1,2*K.1^2,2*K.1^-2,0,0,0,0,0,0,0,0,-2*K.1^-2,-2*K.1^2,-2*K.1,-2*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,0,0,-2,2,0,0,2,0,0,2*K.1,2*K.1^-1,2*K.1^2,2*K.1^-2,-2,0,0,-2*K.1,-2*K.1^-1,-2*K.1^2,-2*K.1^-2,0,0,0,0,0,0,0,0,-2*K.1,-2*K.1^2,-2*K.1^-2,-2*K.1^-1,2*K.1^-1,2*K.1^2,2*K.1,2*K.1^-2,0,0,0,0,0,0,0,0,0,2*K.1,2*K.1^-1,2*K.1^-2,2*K.1^2,0,0,0,0,0,0,0,0,-2*K.1^2,-2*K.1^-2,-2*K.1^-1,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,0,0,2,-2,0,0,2,0,0,2*K.1^-2,2*K.1^2,2*K.1,2*K.1^-1,-2,0,0,-2*K.1^-2,-2*K.1^2,-2*K.1,-2*K.1^-1,0,0,0,0,0,0,0,0,2*K.1^-2,2*K.1,2*K.1^-1,2*K.1^2,-2*K.1^2,-2*K.1,-2*K.1^-2,-2*K.1^-1,0,0,0,0,0,0,0,0,0,2*K.1^-2,2*K.1^2,2*K.1^-1,2*K.1,0,0,0,0,0,0,0,0,-2*K.1,-2*K.1^-1,-2*K.1^2,-2*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,0,0,2,-2,0,0,2,0,0,2*K.1^2,2*K.1^-2,2*K.1^-1,2*K.1,-2,0,0,-2*K.1^2,-2*K.1^-2,-2*K.1^-1,-2*K.1,0,0,0,0,0,0,0,0,2*K.1^2,2*K.1^-1,2*K.1,2*K.1^-2,-2*K.1^-2,-2*K.1^-1,-2*K.1^2,-2*K.1,0,0,0,0,0,0,0,0,0,2*K.1^2,2*K.1^-2,2*K.1,2*K.1^-1,0,0,0,0,0,0,0,0,-2*K.1^-1,-2*K.1,-2*K.1^-2,-2*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,0,0,2,-2,0,0,2,0,0,2*K.1^-1,2*K.1,2*K.1^-2,2*K.1^2,-2,0,0,-2*K.1^-1,-2*K.1,-2*K.1^-2,-2*K.1^2,0,0,0,0,0,0,0,0,2*K.1^-1,2*K.1^-2,2*K.1^2,2*K.1,-2*K.1,-2*K.1^-2,-2*K.1^-1,-2*K.1^2,0,0,0,0,0,0,0,0,0,2*K.1^-1,2*K.1,2*K.1^2,2*K.1^-2,0,0,0,0,0,0,0,0,-2*K.1^-2,-2*K.1^2,-2*K.1,-2*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,0,0,2,-2,0,0,2,0,0,2*K.1,2*K.1^-1,2*K.1^2,2*K.1^-2,-2,0,0,-2*K.1,-2*K.1^-1,-2*K.1^2,-2*K.1^-2,0,0,0,0,0,0,0,0,2*K.1,2*K.1^2,2*K.1^-2,2*K.1^-1,-2*K.1^-1,-2*K.1^2,-2*K.1,-2*K.1^-2,0,0,0,0,0,0,0,0,0,2*K.1,2*K.1^-1,2*K.1^-2,2*K.1^2,0,0,0,0,0,0,0,0,-2*K.1^2,-2*K.1^-2,-2*K.1^-1,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,-2,-2,0,0,0,0,-1,2,0,2*K.1^-2,2*K.1^2,2*K.1,2*K.1^-1,-1,1,1,2*K.1^-2,2*K.1^2,2*K.1,2*K.1^-1,-2*K.1^-1,-2*K.1^2,-2*K.1^-1,-2*K.1,-2*K.1,-2*K.1^-2,-2*K.1^2,-2*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1,2*K.1,2*K.1^-1,2*K.1^-2,2*K.1^2,0,0,0,0,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,K.1^-2,K.1^-2,K.1,K.1^-1,K.1^2,K.1,K.1^-1,K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-1*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,-2,0,0,0,0,-1,2,0,2*K.1^2,2*K.1^-2,2*K.1^-1,2*K.1,-1,1,1,2*K.1^2,2*K.1^-2,2*K.1^-1,2*K.1,-2*K.1,-2*K.1^-2,-2*K.1,-2*K.1^-1,-2*K.1^-1,-2*K.1^2,-2*K.1^-2,-2*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1*K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-1,2*K.1^-1,2*K.1,2*K.1^2,2*K.1^-2,0,0,0,0,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,K.1^2,K.1^2,K.1^-1,K.1,K.1^-2,K.1^-1,K.1,K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1,-1*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,-2,0,0,0,0,-1,2,0,2*K.1^-1,2*K.1,2*K.1^-2,2*K.1^2,-1,1,1,2*K.1^-1,2*K.1,2*K.1^-2,2*K.1^2,-2*K.1^2,-2*K.1,-2*K.1^2,-2*K.1^-2,-2*K.1^-2,-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,-1,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,2*K.1^-2,2*K.1^2,2*K.1^-1,2*K.1,0,0,0,0,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,K.1^-1,K.1^-1,K.1^-2,K.1^2,K.1,K.1^-2,K.1^2,K.1,-1*K.1^-1,-1*K.1^-2,-1*K.1^2,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,-2,-2,0,0,0,0,-1,2,0,2*K.1,2*K.1^-1,2*K.1^2,2*K.1^-2,-1,1,1,2*K.1,2*K.1^-1,2*K.1^2,2*K.1^-2,-2*K.1^-2,-2*K.1^-1,-2*K.1^-2,-2*K.1^2,-2*K.1^2,-2*K.1,-2*K.1^-1,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*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,-1*K.1^-2,-1*K.1^-1,-1*K.1,K.1,K.1,K.1^2,K.1^-2,K.1^-1,K.1^2,K.1^-2,K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,-1*K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,-2,2,0,0,0,0,-1,-2,0,2*K.1^-2,2*K.1^2,2*K.1,2*K.1^-1,-1,1,-1,2*K.1^-2,2*K.1^2,2*K.1,2*K.1^-1,-2*K.1^-1,2*K.1^2,2*K.1^-1,-2*K.1,2*K.1,2*K.1^-2,-2*K.1^2,-2*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1,-2*K.1,-2*K.1^-1,-2*K.1^-2,-2*K.1^2,0,0,0,0,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,-1*K.1^-2,K.1^-2,-1*K.1,K.1^-1,-1*K.1^2,K.1,-1*K.1^-1,K.1^2,K.1^-2,K.1,K.1^-1,K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,-2,2,0,0,0,0,-1,-2,0,2*K.1^2,2*K.1^-2,2*K.1^-1,2*K.1,-1,1,-1,2*K.1^2,2*K.1^-2,2*K.1^-1,2*K.1,-2*K.1,2*K.1^-2,2*K.1,-2*K.1^-1,2*K.1^-1,2*K.1^2,-2*K.1^-2,-2*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1*K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-2*K.1^-1,-2*K.1,-2*K.1^2,-2*K.1^-2,0,0,0,0,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,-1*K.1^2,K.1^2,-1*K.1^-1,K.1,-1*K.1^-2,K.1^-1,-1*K.1,K.1^-2,K.1^2,K.1^-1,K.1,K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,-2,2,0,0,0,0,-1,-2,0,2*K.1^-1,2*K.1,2*K.1^-2,2*K.1^2,-1,1,-1,2*K.1^-1,2*K.1,2*K.1^-2,2*K.1^2,-2*K.1^2,2*K.1,2*K.1^2,-2*K.1^-2,2*K.1^-2,2*K.1^-1,-2*K.1,-2*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,-2*K.1^-2,-2*K.1^2,-2*K.1^-1,-2*K.1,0,0,0,0,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,-1*K.1^-1,K.1^-1,-1*K.1^-2,K.1^2,-1*K.1,K.1^-2,-1*K.1^2,K.1,K.1^-1,K.1^-2,K.1^2,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,-2,2,0,0,0,0,-1,-2,0,2*K.1,2*K.1^-1,2*K.1^2,2*K.1^-2,-1,1,-1,2*K.1,2*K.1^-1,2*K.1^2,2*K.1^-2,-2*K.1^-2,2*K.1^-1,2*K.1^-2,-2*K.1^2,2*K.1^2,2*K.1,-2*K.1^-1,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*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,-1*K.1^-2,-1*K.1^-1,-1*K.1,-1*K.1,K.1,-1*K.1^2,K.1^-2,-1*K.1^-1,K.1^2,-1*K.1^-2,K.1^-1,K.1,K.1^2,K.1^-2,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,-2,0,0,0,0,-1,-2,0,2*K.1^-2,2*K.1^2,2*K.1,2*K.1^-1,-1,-1,1,2*K.1^-2,2*K.1^2,2*K.1,2*K.1^-1,2*K.1^-1,-2*K.1^2,-2*K.1^-1,2*K.1,-2*K.1,-2*K.1^-2,2*K.1^2,2*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1,-2*K.1,-2*K.1^-1,-2*K.1^-2,-2*K.1^2,0,0,0,0,-1*K.1,-1*K.1^-1,-1*K.1^2,-1*K.1^-2,K.1^-2,-1*K.1^-2,K.1,-1*K.1^-1,K.1^2,-1*K.1,K.1^-1,-1*K.1^2,K.1^-2,K.1,K.1^-1,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,-2,0,0,0,0,-1,-2,0,2*K.1^2,2*K.1^-2,2*K.1^-1,2*K.1,-1,-1,1,2*K.1^2,2*K.1^-2,2*K.1^-1,2*K.1,2*K.1,-2*K.1^-2,-2*K.1,2*K.1^-1,-2*K.1^-1,-2*K.1^2,2*K.1^-2,2*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1*K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-1,-2*K.1^-1,-2*K.1,-2*K.1^2,-2*K.1^-2,0,0,0,0,-1*K.1^-1,-1*K.1,-1*K.1^-2,-1*K.1^2,K.1^2,-1*K.1^2,K.1^-1,-1*K.1,K.1^-2,-1*K.1^-1,K.1,-1*K.1^-2,K.1^2,K.1^-1,K.1,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,-2,0,0,0,0,-1,-2,0,2*K.1^-1,2*K.1,2*K.1^-2,2*K.1^2,-1,-1,1,2*K.1^-1,2*K.1,2*K.1^-2,2*K.1^2,2*K.1^2,-2*K.1,-2*K.1^2,2*K.1^-2,-2*K.1^-2,-2*K.1^-1,2*K.1,2*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1^-2,-2*K.1^-2,-2*K.1^2,-2*K.1^-1,-2*K.1,0,0,0,0,-1*K.1^-2,-1*K.1^2,-1*K.1,-1*K.1^-1,K.1^-1,-1*K.1^-1,K.1^-2,-1*K.1^2,K.1,-1*K.1^-2,K.1^2,-1*K.1,K.1^-1,K.1^-2,K.1^2,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,-2,0,0,0,0,-1,-2,0,2*K.1,2*K.1^-1,2*K.1^2,2*K.1^-2,-1,-1,1,2*K.1,2*K.1^-1,2*K.1^2,2*K.1^-2,2*K.1^-2,-2*K.1^-1,-2*K.1^-2,2*K.1^2,-2*K.1^2,-2*K.1,2*K.1^-1,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*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,-1*K.1^-2,-1*K.1^-1,-1*K.1,K.1,-1*K.1,K.1^2,-1*K.1^-2,K.1^-1,-1*K.1^2,K.1^-2,-1*K.1^-1,K.1,K.1^2,K.1^-2,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 4, 4, 4, 2, 0, 0, -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, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 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 |4,-4,0,0,0,0,0,0,-2,0,0,4*K.1^-2,4*K.1^2,4*K.1,4*K.1^-1,2,0,0,-4*K.1^-2,-4*K.1^2,-4*K.1,-4*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,-2*K.1^-2,-2*K.1^2,-2*K.1^-1,-2*K.1,0,0,0,0,0,0,0,0,2*K.1,2*K.1^-1,2*K.1^2,2*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,0,-2,0,0,4*K.1^2,4*K.1^-2,4*K.1^-1,4*K.1,2,0,0,-4*K.1^2,-4*K.1^-2,-4*K.1^-1,-4*K.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,-2*K.1^2,-2*K.1^-2,-2*K.1,-2*K.1^-1,0,0,0,0,0,0,0,0,2*K.1^-1,2*K.1,2*K.1^-2,2*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,0,-2,0,0,4*K.1^-1,4*K.1,4*K.1^-2,4*K.1^2,2,0,0,-4*K.1^-1,-4*K.1,-4*K.1^-2,-4*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1^-1,-2*K.1,-2*K.1^2,-2*K.1^-2,0,0,0,0,0,0,0,0,2*K.1^-2,2*K.1^2,2*K.1,2*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,0,-2,0,0,4*K.1,4*K.1^-1,4*K.1^2,4*K.1^-2,2,0,0,-4*K.1,-4*K.1^-1,-4*K.1^2,-4*K.1^-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,-2*K.1,-2*K.1^-1,-2*K.1^-2,-2*K.1^2,0,0,0,0,0,0,0,0,2*K.1^2,2*K.1^-2,2*K.1^-1,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_240_169:= KnownIrreducibles(CR);