/* Group 1000.183 downloaded from the LMFDB on 08 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, -5, -2, -5, -5, 217, 31, 290, 2169, 69, 2410, 1463]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.4, GPC.6]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "d"]);
GPerm := PermutationGroup< 15 | (1,2)(3,5)(4,6)(7,9)(8,10), (12,13)(14,15), (1,2)(3,6)(4,5)(7,10)(8,9), (1,3,7,8,4)(2,5,9,10,6), (11,12,14,15,13), (1,4,8,7,3)(2,5,9,10,6) >;
GLFp := MatrixGroup< 4, GF(5) | [[4, 0, 0, 0, 3, 2, 2, 2, 1, 1, 3, 4, 0, 0, 0, 4], [1, 0, 0, 0, 2, 3, 3, 3, 1, 2, 3, 4, 3, 2, 4, 3], [2, 3, 0, 4, 0, 1, 0, 0, 0, 0, 1, 0, 1, 3, 0, 0], [4, 1, 1, 2, 0, 1, 0, 0, 0, 0, 1, 0, 3, 1, 1, 3], [2, 2, 4, 4, 3, 2, 2, 2, 4, 3, 2, 1, 0, 0, 0, 1], [3, 2, 1, 1, 0, 4, 0, 0, 3, 2, 3, 2, 1, 0, 2, 3]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_1000_183 := rec< RF |  
Agroup := true,
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, 5, c^5>,< 2, 5, b^5>,< 2, 5, a>,< 2, 25, a*b*c^6>,< 2, 25, a*b^2*c^5*d^4>,< 2, 25, b^5*c*d>,< 2, 125, a*b*c^5*d>,< 5, 2, c^2>,< 5, 2, c^4>,< 5, 2, b^2>,< 5, 2, b^4>,< 5, 2, d^2>,< 5, 2, d^4>,< 5, 4, b^4*c^2>,< 5, 4, b^8*c^4>,< 5, 4, b^2*d^2>,< 5, 4, b^4*d^4>,< 5, 4, b^8*c^2>,< 5, 4, b^6*c^4>,< 5, 4, b^2*d^4>,< 5, 4, b^4*d^3>,< 5, 4, c^4*d^2>,< 5, 4, c^8*d^4>,< 5, 4, c^4*d^4>,< 5, 4, c^8*d^3>,< 5, 8, b^2*c^2*d>,< 5, 8, b^4*c^4*d^2>,< 5, 8, b^2*c^2*d^2>,< 5, 8, b^4*c^4*d>,< 5, 8, b^2*c^4*d>,< 5, 8, b^4*c^2*d^2>,< 5, 8, b^4*c^2*d>,< 5, 8, b^2*c^4*d^2>,< 10, 10, c>,< 10, 10, c^3>,< 10, 10, b>,< 10, 10, b^3>,< 10, 10, a*d>,< 10, 10, a*d^2>,< 10, 10, a*c^2>,< 10, 10, a*c^4>,< 10, 10, b^2*c^5>,< 10, 10, b^4*c^5>,< 10, 10, b^5*d>,< 10, 10, b^5*d^2>,< 10, 20, b^2*c>,< 10, 20, b^4*c^3>,< 10, 20, b*d>,< 10, 20, b^3*d^2>,< 10, 20, b^4*c>,< 10, 20, b^2*c^3>,< 10, 20, b*d^2>,< 10, 20, b^3*d>,< 10, 20, a*c^2*d>,< 10, 20, a*c^4*d^2>,< 10, 20, a*c^2*d^2>,< 10, 20, a*c^4*d>,< 10, 50, a*b*c^6*d>,< 10, 50, a*b*c^6*d^3>,< 10, 50, a*b^2*c^3*d^4>,< 10, 50, a*b^2*c^9*d^4>,< 10, 50, b^7*c*d>,< 10, 50, b*c*d>]); 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,0,2,2,2,0,0,0,K.1^2+K.1^-2,2,2,2,K.1+K.1^-1,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,2,K.1+K.1^-1,2,K.1^2+K.1^-2,2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,2,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^-1,0,2,2,2,0,2,0,0,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,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,0,K.1^2+K.1^-2,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,0,K.1+K.1^-1,0,0,0,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 |2,0,2,2,2,0,0,0,K.1+K.1^-1,2,2,2,K.1^2+K.1^-2,2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,2,K.1^2+K.1^-2,2,K.1+K.1^-1,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-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,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,0,2,2,2,0,2,0,0,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,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,0,K.1+K.1^-1,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,0,K.1^2+K.1^-2,0,0,0,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,0,2,0,2,0,0,2,K.1^2+K.1^-2,2,2,2,K.1+K.1^-1,K.1^2+K.1^-2,2,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-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+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.1^2+K.1^-2,0,0,2,K.1+K.1^-1,2,K.1^2+K.1^-2,0,0,2,2,0,0,0,0,K.1+K.1^-1,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^-2,0,0,K.1+K.1^-1,K.1^2+K.1^-2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,0,2,0,2,0,0,2,K.1+K.1^-1,2,2,2,K.1^2+K.1^-2,K.1+K.1^-1,2,2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+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+K.1^-1,0,0,2,K.1^2+K.1^-2,2,K.1+K.1^-1,0,0,2,2,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,0,0,K.1^2+K.1^-2,K.1+K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,0,0,0,2,0,2,2,K.1^2+K.1^-2,K.1+K.1^-1,2,2,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,2,2,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^-1,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^-2,2,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,0,K.1^2+K.1^-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^-1,0,K.1^2+K.1^-2,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,0,0,K.1+K.1^-1,0,0,0,K.1^2+K.1^-2,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,0,0,0,2,0,2,2,K.1+K.1^-1,K.1^2+K.1^-2,2,2,2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,2,2,K.1+K.1^-1,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,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,2,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,0,K.1+K.1^-1,2,2,2,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,0,K.1+K.1^-1,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,0,0,K.1^2+K.1^-2,0,0,0,K.1+K.1^-1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,-2,0,0,0,2,0,2,2,K.1^2+K.1^-2,K.1+K.1^-1,2,2,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,2,2,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^-1,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,-2,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,-1*K.1^2-K.1^-2,-2,-2,-2,0,0,-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^-1,0,-1*K.1^2-K.1^-2,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,K.1+K.1^-1,0,0,0,K.1^2+K.1^-2,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,-2,0,0,0,2,0,2,2,K.1+K.1^-1,K.1^2+K.1^-2,2,2,2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,2,2,K.1+K.1^-1,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,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,-2,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,-1*K.1-K.1^-1,-2,-2,-2,0,0,-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^-2,0,-1*K.1-K.1^-1,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,K.1^2+K.1^-2,0,0,0,K.1+K.1^-1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,0,-2,0,2,0,0,2,K.1^2+K.1^-2,2,2,2,K.1+K.1^-1,K.1^2+K.1^-2,2,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-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+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,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,-2,-1*K.1-K.1^-1,-2,-1*K.1^2-K.1^-2,0,0,-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-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^-2,0,0,K.1+K.1^-1,K.1^2+K.1^-2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,0,-2,0,2,0,0,2,K.1+K.1^-1,2,2,2,K.1^2+K.1^-2,K.1+K.1^-1,2,2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,-2,-1*K.1^2-K.1^-2,-2,-1*K.1-K.1^-1,0,0,-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.1^2-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^-1,0,0,K.1^2+K.1^-2,K.1+K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,0,2,0,-2,0,0,2,K.1^2+K.1^-2,2,2,2,K.1+K.1^-1,K.1^2+K.1^-2,2,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-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+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,-1*K.1-K.1^-1,K.1^2+K.1^-2,0,0,-2,K.1+K.1^-1,-2,-1*K.1^2-K.1^-2,0,0,2,2,0,0,0,0,K.1+K.1^-1,-1*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,K.1^2+K.1^-2,K.1^2+K.1^-2,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,0,2,0,-2,0,0,2,K.1+K.1^-1,2,2,2,K.1^2+K.1^-2,K.1+K.1^-1,2,2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1^2-K.1^-2,K.1+K.1^-1,0,0,-2,K.1^2+K.1^-2,-2,-1*K.1-K.1^-1,0,0,2,2,0,0,0,0,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*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,2,0,0,0,-2,0,2,2,K.1^2+K.1^-2,K.1+K.1^-1,2,2,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,2,2,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^-1,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,-2,0,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1-K.1^-1,0,-1*K.1^2-K.1^-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^-1,0,-1*K.1^2-K.1^-2,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,-1*K.1-K.1^-1,0,0,0,-1*K.1^2-K.1^-2,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,2,0,0,0,-2,0,2,2,K.1+K.1^-1,K.1^2+K.1^-2,2,2,2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,2,2,K.1+K.1^-1,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,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,-2,0,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1^2-K.1^-2,0,-1*K.1-K.1^-1,-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^-2,0,-1*K.1-K.1^-1,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,-1*K.1^2-K.1^-2,0,0,0,-1*K.1-K.1^-1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,0,-2,-2,2,0,0,0,K.1^2+K.1^-2,2,2,2,K.1+K.1^-1,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,2,K.1+K.1^-1,2,K.1^2+K.1^-2,2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,2,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^-1,0,-2,-2,-2,0,-2,0,0,-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,-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,-1*K.1^2-K.1^-2,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,K.1+K.1^-1,0,0,0,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 |2,0,-2,-2,2,0,0,0,K.1+K.1^-1,2,2,2,K.1^2+K.1^-2,2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,2,K.1^2+K.1^-2,2,K.1+K.1^-1,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-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,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,0,-2,-2,-2,0,-2,0,0,-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,-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,-1*K.1-K.1^-1,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,K.1^2+K.1^-2,0,0,0,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,0,-2,2,-2,0,0,0,K.1^2+K.1^-2,2,2,2,K.1+K.1^-1,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,2,K.1+K.1^-1,2,K.1^2+K.1^-2,2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,2,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^-1,0,2,-2,-2,0,2,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,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,K.1+K.1^-1,0,K.1^2+K.1^-2,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,0,-1*K.1-K.1^-1,0,0,0,-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 |2,0,-2,2,-2,0,0,0,K.1+K.1^-1,2,2,2,K.1^2+K.1^-2,2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,2,K.1^2+K.1^-2,2,K.1+K.1^-1,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-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,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,0,2,-2,-2,0,2,0,0,-1*K.1-K.1^-1,-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^-2,0,K.1+K.1^-1,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,0,-1*K.1^2-K.1^-2,0,0,0,-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 |2,0,2,-2,-2,0,0,0,K.1^2+K.1^-2,2,2,2,K.1+K.1^-1,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,2,K.1+K.1^-1,2,K.1^2+K.1^-2,2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,2,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^-1,0,-2,2,2,0,-2,0,0,K.1^2+K.1^-2,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,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,0,-1*K.1^2-K.1^-2,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,-1*K.1-K.1^-1,0,0,0,-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 |2,0,2,-2,-2,0,0,0,K.1+K.1^-1,2,2,2,K.1^2+K.1^-2,2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,2,K.1^2+K.1^-2,2,K.1+K.1^-1,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-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,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,0,-2,2,2,0,-2,0,0,K.1+K.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,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,0,-1*K.1-K.1^-1,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,-1*K.1^2-K.1^-2,0,0,0,-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,-2,0,0,0,-2,0,2,2,K.1^2+K.1^-2,K.1+K.1^-1,2,2,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,2,2,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^-1,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^-2,2,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1+K.1^-1,0,K.1^2+K.1^-2,2,-2,-2,0,0,-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^-1,0,K.1^2+K.1^-2,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,0,0,-1*K.1-K.1^-1,0,0,0,-1*K.1^2-K.1^-2,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,-2,0,0,0,-2,0,2,2,K.1+K.1^-1,K.1^2+K.1^-2,2,2,2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,2,2,K.1+K.1^-1,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,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,2,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2+K.1^-2,0,K.1+K.1^-1,2,-2,-2,0,0,-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^-2,0,K.1+K.1^-1,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,0,0,-1*K.1^2-K.1^-2,0,0,0,-1*K.1-K.1^-1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,0,-2,0,-2,0,0,2,K.1^2+K.1^-2,2,2,2,K.1+K.1^-1,K.1^2+K.1^-2,2,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-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+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,-1*K.1^2-K.1^-2,0,0,2,-1*K.1-K.1^-1,2,K.1^2+K.1^-2,0,0,-2,-2,0,0,0,0,-1*K.1-K.1^-1,K.1^2+K.1^-2,-1*K.1-K.1^-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.1^2-K.1^-2,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,0,-2,0,-2,0,0,2,K.1+K.1^-1,2,2,2,K.1^2+K.1^-2,K.1+K.1^-1,2,2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+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,-1*K.1-K.1^-1,0,0,2,-1*K.1^2-K.1^-2,2,K.1+K.1^-1,0,0,-2,-2,0,0,0,0,-1*K.1^2-K.1^-2,K.1+K.1^-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,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,0,4,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,4,4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2+K.1^2+K.1^-2,1-K.1^2-K.1^-2,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2+K.1^2+K.1^-2,-1,-1,1-K.1^2-K.1^-2,1-K.1^2-K.1^-2,-1,-1,2+K.1^2+K.1^-2,0,2*K.1+2*K.1^-1,0,0,0,2*K.1^2+2*K.1^-2,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,0,0,-1,0,1-K.1^2-K.1^-2,0,0,0,2+K.1^2+K.1^-2,-1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,0,4,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,4,4,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,1-K.1^2-K.1^-2,2+K.1^2+K.1^-2,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,1-K.1^2-K.1^-2,-1,-1,2+K.1^2+K.1^-2,2+K.1^2+K.1^-2,-1,-1,1-K.1^2-K.1^-2,0,2*K.1^2+2*K.1^-2,0,0,0,2*K.1+2*K.1^-1,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,-1,0,2+K.1^2+K.1^-2,0,0,0,1-K.1^2-K.1^-2,-1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,0,4,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,4,4,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,1-K.1^2-K.1^-2,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2+K.1^2+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,-1,-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-1,2+K.1^2+K.1^-2,2+K.1^2+K.1^-2,-1,-1,1-K.1^2-K.1^-2,1-K.1^2-K.1^-2,-1,0,2*K.1^2+2*K.1^-2,0,0,0,2*K.1+2*K.1^-1,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,0,0,2+K.1^2+K.1^-2,0,-1,0,0,0,-1,1-K.1^2-K.1^-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,0,4,0,0,0,0,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,4,4,2*K.1^2+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.1^2+2*K.1^-2,2*K.1+2*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,-1,-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-1,1-K.1^2-K.1^-2,1-K.1^2-K.1^-2,-1,-1,2+K.1^2+K.1^-2,2+K.1^2+K.1^-2,-1,0,2*K.1+2*K.1^-1,0,0,0,2*K.1^2+2*K.1^-2,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,1-K.1^2-K.1^-2,0,-1,0,0,0,-1,2+K.1^2+K.1^-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,4,0,0,0,0,0,2*K.1^2+2*K.1^-2,4,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,4,2*K.1^2+2*K.1^-2,-1,2+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,-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,1-K.1^2-K.1^-2,2*K.1^2+2*K.1^-2,2+K.1^2+K.1^-2,-1,2+K.1^2+K.1^-2,-1,1-K.1^2-K.1^-2,-1,1-K.1^2-K.1^-2,-1,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,-1,-1,1-K.1^2-K.1^-2,2+K.1^2+K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,4,0,0,0,0,0,2*K.1+2*K.1^-1,4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,4,2*K.1+2*K.1^-1,-1,1-K.1^2-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,-1,2*K.1^2+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^-2,2*K.1+2*K.1^-1,1-K.1^2-K.1^-2,-1,1-K.1^2-K.1^-2,-1,2+K.1^2+K.1^-2,-1,2+K.1^2+K.1^-2,-1,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,-1,-1,2+K.1^2+K.1^-2,1-K.1^2-K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,4,0,0,0,0,0,2*K.1^2+2*K.1^-2,4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,4,2*K.1^2+2*K.1^-2,2+K.1^2+K.1^-2,-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,1-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+2*K.1^-2,-1,2*K.1+2*K.1^-1,-1,2+K.1^2+K.1^-2,-1,1-K.1^2-K.1^-2,-1,1-K.1^2-K.1^-2,-1,2+K.1^2+K.1^-2,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,2+K.1^2+K.1^-2,1-K.1^2-K.1^-2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,4,0,0,0,0,0,2*K.1+2*K.1^-1,4,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,4,2*K.1+2*K.1^-1,1-K.1^2-K.1^-2,-1,2*K.1^2+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^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-1,2*K.1^2+2*K.1^-2,-1,1-K.1^2-K.1^-2,-1,2+K.1^2+K.1^-2,-1,2+K.1^2+K.1^-2,-1,1-K.1^2-K.1^-2,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,1-K.1^2-K.1^-2,2+K.1^2+K.1^-2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,4,0,0,0,0,0,0,4,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,4,2*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,-1,2*K.1+2*K.1^-1,-1,2*K.1^2+2*K.1^-2,1-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+K.1^-2,1-K.1^2-K.1^-2,2+K.1^2+K.1^-2,-1,-1,2+K.1^2+K.1^-2,1-K.1^2-K.1^-2,-1,-1,2*K.1+2*K.1^-1,0,0,0,2*K.1^2+2*K.1^-2,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,0,0,0,0,0,-1,0,-1,2+K.1^2+K.1^-2,1-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 |4,4,0,0,0,0,0,0,4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,4,2*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,-1,2*K.1^2+2*K.1^-2,-1,2*K.1+2*K.1^-1,2+K.1^2+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^-2,1-K.1^2-K.1^-2,2+K.1^2+K.1^-2,1-K.1^2-K.1^-2,-1,-1,1-K.1^2-K.1^-2,2+K.1^2+K.1^-2,-1,-1,2*K.1^2+2*K.1^-2,0,0,0,2*K.1+2*K.1^-1,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,0,0,0,0,0,0,0,-1,0,-1,1-K.1^2-K.1^-2,2+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 |4,4,0,0,0,0,0,0,4,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,4,2*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^-1,1-K.1^2-K.1^-2,2*K.1+2*K.1^-1,2+K.1^2+K.1^-2,2*K.1+2*K.1^-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,-1,-1,-1,2+K.1^2+K.1^-2,2+K.1^2+K.1^-2,-1,-1,1-K.1^2-K.1^-2,1-K.1^2-K.1^-2,2*K.1+2*K.1^-1,0,0,0,2*K.1+2*K.1^-1,0,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,0,0,0,0,0,0,0,0,0,1-K.1^2-K.1^-2,0,2+K.1^2+K.1^-2,-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 |4,4,0,0,0,0,0,0,4,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,4,2*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^-2,2+K.1^2+K.1^-2,2*K.1^2+2*K.1^-2,1-K.1^2-K.1^-2,2*K.1^2+2*K.1^-2,-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-1,-1,-1,1-K.1^2-K.1^-2,1-K.1^2-K.1^-2,-1,-1,2+K.1^2+K.1^-2,2+K.1^2+K.1^-2,2*K.1^2+2*K.1^-2,0,0,0,2*K.1^2+2*K.1^-2,0,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,0,0,0,0,0,0,0,0,0,2+K.1^2+K.1^-2,0,1-K.1^2-K.1^-2,-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,-4,0,0,0,0,0,0,4,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,4,2*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,-1,2*K.1+2*K.1^-1,-1,2*K.1^2+2*K.1^-2,1-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+K.1^-2,1-K.1^2-K.1^-2,2+K.1^2+K.1^-2,-1,-1,2+K.1^2+K.1^-2,1-K.1^2-K.1^-2,-1,-1,-2*K.1-2*K.1^-1,0,0,0,-2*K.1^2-2*K.1^-2,0,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,0,0,0,0,0,0,0,0,0,1,0,1,-2-K.1^2-K.1^-2,-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,-4,0,0,0,0,0,0,4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,4,2*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,-1,2*K.1^2+2*K.1^-2,-1,2*K.1+2*K.1^-1,2+K.1^2+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^-2,1-K.1^2-K.1^-2,2+K.1^2+K.1^-2,1-K.1^2-K.1^-2,-1,-1,1-K.1^2-K.1^-2,2+K.1^2+K.1^-2,-1,-1,-2*K.1^2-2*K.1^-2,0,0,0,-2*K.1-2*K.1^-1,0,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,0,0,0,0,0,0,0,0,0,1,0,1,-1+K.1^2+K.1^-2,-2-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,-4,0,0,0,0,0,0,4,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,4,2*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^-1,1-K.1^2-K.1^-2,2*K.1+2*K.1^-1,2+K.1^2+K.1^-2,2*K.1+2*K.1^-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,-1,-1,-1,2+K.1^2+K.1^-2,2+K.1^2+K.1^-2,-1,-1,1-K.1^2-K.1^-2,1-K.1^2-K.1^-2,-2*K.1-2*K.1^-1,0,0,0,-2*K.1-2*K.1^-1,0,-2*K.1^2-2*K.1^-2,-2*K.1^2-2*K.1^-2,0,0,0,0,0,0,0,0,0,-1+K.1^2+K.1^-2,0,-2-K.1^2-K.1^-2,1,1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,-4,0,0,0,0,0,0,4,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,4,2*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^-2,2+K.1^2+K.1^-2,2*K.1^2+2*K.1^-2,1-K.1^2-K.1^-2,2*K.1^2+2*K.1^-2,-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-1,-1,-1,1-K.1^2-K.1^-2,1-K.1^2-K.1^-2,-1,-1,2+K.1^2+K.1^-2,2+K.1^2+K.1^-2,-2*K.1^2-2*K.1^-2,0,0,0,-2*K.1^2-2*K.1^-2,0,-2*K.1-2*K.1^-1,-2*K.1-2*K.1^-1,0,0,0,0,0,0,0,0,0,-2-K.1^2-K.1^-2,0,-1+K.1^2+K.1^-2,1,1,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,-4,0,0,0,0,0,2*K.1^2+2*K.1^-2,4,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,4,2*K.1^2+2*K.1^-2,-1,2+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,-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,1-K.1^2-K.1^-2,2*K.1^2+2*K.1^-2,2+K.1^2+K.1^-2,-1,2+K.1^2+K.1^-2,-1,1-K.1^2-K.1^-2,-1,1-K.1^2-K.1^-2,-1,0,0,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,0,0,0,0,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,0,0,1,1,-1+K.1^2+K.1^-2,-2-K.1^2-K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,-4,0,0,0,0,0,2*K.1+2*K.1^-1,4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,4,2*K.1+2*K.1^-1,-1,1-K.1^2-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,-1,2*K.1^2+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^-2,2*K.1+2*K.1^-1,1-K.1^2-K.1^-2,-1,1-K.1^2-K.1^-2,-1,2+K.1^2+K.1^-2,-1,2+K.1^2+K.1^-2,-1,0,0,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,0,0,0,0,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,0,0,1,1,-2-K.1^2-K.1^-2,-1+K.1^2+K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,-4,0,0,0,0,0,2*K.1^2+2*K.1^-2,4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,4,2*K.1^2+2*K.1^-2,2+K.1^2+K.1^-2,-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,1-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+2*K.1^-2,-1,2*K.1+2*K.1^-1,-1,2+K.1^2+K.1^-2,-1,1-K.1^2-K.1^-2,-1,1-K.1^2-K.1^-2,-1,2+K.1^2+K.1^-2,0,0,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,0,0,0,0,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,0,0,-2-K.1^2-K.1^-2,-1+K.1^2+K.1^-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,-4,0,0,0,0,0,2*K.1+2*K.1^-1,4,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,4,2*K.1+2*K.1^-1,1-K.1^2-K.1^-2,-1,2*K.1^2+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^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-1,2*K.1^2+2*K.1^-2,-1,1-K.1^2-K.1^-2,-1,2+K.1^2+K.1^-2,-1,2+K.1^2+K.1^-2,-1,1-K.1^2-K.1^-2,0,0,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,0,0,0,0,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,0,0,-1+K.1^2+K.1^-2,-2-K.1^2-K.1^-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,0,-4,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,4,4,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2+K.1^2+K.1^-2,1-K.1^2-K.1^-2,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2+K.1^2+K.1^-2,-1,-1,1-K.1^2-K.1^-2,1-K.1^2-K.1^-2,-1,-1,2+K.1^2+K.1^-2,0,-2*K.1-2*K.1^-1,0,0,0,-2*K.1^2-2*K.1^-2,0,0,0,0,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,0,0,0,0,1,0,-1+K.1^2+K.1^-2,0,0,0,-2-K.1^2-K.1^-2,1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,0,-4,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,4,4,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,1-K.1^2-K.1^-2,2+K.1^2+K.1^-2,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,1-K.1^2-K.1^-2,-1,-1,2+K.1^2+K.1^-2,2+K.1^2+K.1^-2,-1,-1,1-K.1^2-K.1^-2,0,-2*K.1^2-2*K.1^-2,0,0,0,-2*K.1-2*K.1^-1,0,0,0,0,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,0,0,0,0,1,0,-2-K.1^2-K.1^-2,0,0,0,-1+K.1^2+K.1^-2,1,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,0,-4,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,4,4,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,1-K.1^2-K.1^-2,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2+K.1^2+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,-1,-1,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-1,2+K.1^2+K.1^-2,2+K.1^2+K.1^-2,-1,-1,1-K.1^2-K.1^-2,1-K.1^2-K.1^-2,-1,0,-2*K.1^2-2*K.1^-2,0,0,0,-2*K.1-2*K.1^-1,0,0,0,0,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,0,0,0,0,-2-K.1^2-K.1^-2,0,1,0,0,0,1,-1+K.1^2+K.1^-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,0,-4,0,0,0,0,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,4,4,2*K.1^2+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.1^2+2*K.1^-2,2*K.1+2*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,-1,-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-1,1-K.1^2-K.1^-2,1-K.1^2-K.1^-2,-1,-1,2+K.1^2+K.1^-2,2+K.1^2+K.1^-2,-1,0,-2*K.1-2*K.1^-1,0,0,0,-2*K.1^2-2*K.1^-2,0,0,0,0,-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^-2,0,1,0,0,0,1,-2-K.1^2-K.1^-2,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,0,0,0,0,0,4*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,-2,-2,4+2*K.1^2+2*K.1^-2,-2,-2,-2,-2,4+2*K.1^2+2*K.1^-2,4+2*K.1^2+2*K.1^-2,2-2*K.1^2-2*K.1^-2,2-2*K.1^2-2*K.1^-2,2-2*K.1^2-2*K.1^-2,-3-2*K.1^2-2*K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1+2*K.1^2+2*K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,0,0,0,0,0,4*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,-2,-2,2-2*K.1^2-2*K.1^-2,-2,-2,-2,-2,2-2*K.1^2-2*K.1^-2,2-2*K.1^2-2*K.1^-2,4+2*K.1^2+2*K.1^-2,4+2*K.1^2+2*K.1^-2,4+2*K.1^2+2*K.1^-2,-1+2*K.1^2+2*K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-3-2*K.1^2-2*K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,0,0,0,0,0,4*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^-2,4*K.1+4*K.1^-1,4*K.1^2+4*K.1^-2,-2,4+2*K.1^2+2*K.1^-2,-2,4+2*K.1^2+2*K.1^-2,-2,2-2*K.1^2-2*K.1^-2,2-2*K.1^2-2*K.1^-2,-2,4+2*K.1^2+2*K.1^-2,2-2*K.1^2-2*K.1^-2,-2,-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1+2*K.1^2+2*K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-3-2*K.1^2-2*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,0,0,0,0,0,4*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^-1,4*K.1^2+4*K.1^-2,4*K.1+4*K.1^-1,-2,2-2*K.1^2-2*K.1^-2,-2,2-2*K.1^2-2*K.1^-2,-2,4+2*K.1^2+2*K.1^-2,4+2*K.1^2+2*K.1^-2,-2,2-2*K.1^2-2*K.1^-2,4+2*K.1^2+2*K.1^-2,-2,-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-3-2*K.1^2-2*K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1+2*K.1^2+2*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,0,0,0,0,0,4*K.1^2+4*K.1^-2,4*K.1^2+4*K.1^-2,4*K.1^2+4*K.1^-2,4*K.1+4*K.1^-1,4*K.1+4*K.1^-1,4*K.1+4*K.1^-1,2-2*K.1^2-2*K.1^-2,-2,4+2*K.1^2+2*K.1^-2,2-2*K.1^2-2*K.1^-2,4+2*K.1^2+2*K.1^-2,4+2*K.1^2+2*K.1^-2,-2,-2,-2,-2,2-2*K.1^2-2*K.1^-2,-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-3-2*K.1^2-2*K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1+2*K.1^2+2*K.1^-2,-1*K.1^2-K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,0,0,0,0,0,4*K.1+4*K.1^-1,4*K.1+4*K.1^-1,4*K.1+4*K.1^-1,4*K.1^2+4*K.1^-2,4*K.1^2+4*K.1^-2,4*K.1^2+4*K.1^-2,4+2*K.1^2+2*K.1^-2,-2,2-2*K.1^2-2*K.1^-2,4+2*K.1^2+2*K.1^-2,2-2*K.1^2-2*K.1^-2,2-2*K.1^2-2*K.1^-2,-2,-2,-2,-2,4+2*K.1^2+2*K.1^-2,-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1+2*K.1^2+2*K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-3-2*K.1^2-2*K.1^-2,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,0,0,0,0,0,4*K.1^2+4*K.1^-2,4*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^-1,2-2*K.1^2-2*K.1^-2,4+2*K.1^2+2*K.1^-2,-2,-2,4+2*K.1^2+2*K.1^-2,-2,2-2*K.1^2-2*K.1^-2,2-2*K.1^2-2*K.1^-2,-2,-2,-2,4+2*K.1^2+2*K.1^-2,-1*K.1^2-K.1^-2,-3-2*K.1^2-2*K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1+2*K.1^2+2*K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,0,0,0,0,0,4*K.1+4*K.1^-1,4*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+2*K.1^2+2*K.1^-2,2-2*K.1^2-2*K.1^-2,-2,-2,2-2*K.1^2-2*K.1^-2,-2,4+2*K.1^2+2*K.1^-2,4+2*K.1^2+2*K.1^-2,-2,-2,-2,2-2*K.1^2-2*K.1^-2,-1*K.1-K.1^-1,-1+2*K.1^2+2*K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-3-2*K.1^2-2*K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_1000_183:= KnownIrreducibles(CR);