/* Group 135.3 downloaded from the LMFDB on 23 October 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([4, -3, -3, -3, -5, 745, 46]); a,b,c := Explode([GPC.1, GPC.2, GPC.3]); AssignNames(~GPC, ["a", "b", "c", "c3"]);
GPerm := PermutationGroup< 14 | (1,4,8)(2,5,9)(3,6,7), (1,7,4)(2,8,5)(3,9,6), (10,14,13,12,11), (1,3,2)(4,6,5)(7,9,8) >;
GLZN := MatrixGroup< 2, Integers(45) | [[1, 0, 0, 16], [31, 20, 30, 1], [1, 15, 0, 1], [1, 9, 0, 1]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_135_3 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := true,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>; 

 
/* Character Table */
G:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 3, 1, c^5>,< 3, 1, c^10>,< 3, 3, b^2>,< 3, 3, b>,< 3, 3, a^2>,< 3, 3, a>,< 3, 3, a^2*b^2*c^10>,< 3, 3, a*b>,< 3, 3, a^2*b*c^5>,< 3, 3, a*b^2>,< 5, 1, c^3>,< 5, 1, c^12>,< 5, 1, c^6>,< 5, 1, c^9>,< 15, 1, c>,< 15, 1, c^14>,< 15, 1, c^2>,< 15, 1, c^13>,< 15, 1, c^4>,< 15, 1, c^11>,< 15, 1, c^7>,< 15, 1, c^8>,< 15, 3, b*c^3>,< 15, 3, b^2*c^2>,< 15, 3, b^2*c>,< 15, 3, b*c^9>,< 15, 3, b*c^2>,< 15, 3, b^2*c^3>,< 15, 3, b*c>,< 15, 3, b^2*c^9>,< 15, 3, a*c^3>,< 15, 3, a^2*c^2>,< 15, 3, a^2*c>,< 15, 3, a*c^9>,< 15, 3, a*c^2>,< 15, 3, a^2*c^3>,< 15, 3, a*c>,< 15, 3, a^2*c^9>,< 15, 3, a*b*c^3>,< 15, 3, a^2*b^2*c^2>,< 15, 3, a^2*b^2*c>,< 15, 3, a*b*c^9>,< 15, 3, a*b*c^2>,< 15, 3, a^2*b^2*c^3>,< 15, 3, a*b*c>,< 15, 3, a^2*b^2*c^9>,< 15, 3, a*b^2*c^3>,< 15, 3, a^2*b*c^2>,< 15, 3, a^2*b*c>,< 15, 3, a*b^2*c^9>,< 15, 3, a*b^2*c^2>,< 15, 3, a^2*b*c^3>,< 15, 3, a*b^2*c>,< 15, 3, a^2*b*c^9>]); 
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; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,K.1^-1,K.1,K.1,K.1,1,1,K.1^-1,K.1^-1,1,1,1,1,1,1,1,1,1,1,1,1,K.1,K.1^-1,K.1,K.1^-1,1,K.1^-1,K.1,K.1,1,K.1^-1,K.1^-1,K.1^-1,K.1,1,K.1,K.1^-1,K.1,K.1,1,K.1^-1,1,K.1^-1,K.1,K.1,1,K.1^-1,1,K.1,K.1^-1,K.1^-1,1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,K.1,K.1^-1,K.1^-1,K.1^-1,1,1,K.1,K.1,1,1,1,1,1,1,1,1,1,1,1,1,K.1^-1,K.1,K.1^-1,K.1,1,K.1,K.1^-1,K.1^-1,1,K.1,K.1,K.1,K.1^-1,1,K.1^-1,K.1,K.1^-1,K.1^-1,1,K.1,1,K.1,K.1^-1,K.1^-1,1,K.1,1,K.1^-1,K.1,K.1,1,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,K.1^-1,K.1^-1,K.1,1,K.1,K.1^-1,K.1,1,1,1,1,1,1,1,1,1,1,1,1,1,K.1^-1,K.1,1,K.1^-1,K.1,K.1^-1,K.1^-1,1,K.1,K.1,1,1,1,K.1^-1,K.1,K.1,K.1,K.1,K.1,K.1^-1,K.1,K.1^-1,1,K.1,K.1^-1,K.1,K.1^-1,K.1^-1,1,1,K.1^-1,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,K.1,K.1,K.1^-1,1,K.1^-1,K.1,K.1^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,K.1,K.1^-1,1,K.1,K.1^-1,K.1,K.1,1,K.1^-1,K.1^-1,1,1,1,K.1,K.1^-1,K.1^-1,K.1^-1,K.1^-1,K.1^-1,K.1,K.1^-1,K.1,1,K.1^-1,K.1,K.1^-1,K.1,K.1,1,1,K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,K.1^-1,1,K.1,K.1^-1,K.1^-1,K.1,1,K.1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,K.1^-1,K.1^-1,K.1^-1,K.1^-1,1,K.1^-1,K.1^-1,1,K.1,K.1,K.1^-1,K.1,K.1,1,K.1,K.1,K.1^-1,K.1^-1,K.1^-1,K.1^-1,K.1^-1,K.1,K.1,1,K.1,1,K.1,K.1,K.1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,K.1,1,K.1^-1,K.1,K.1,K.1^-1,1,K.1^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,K.1,K.1,K.1,K.1,1,K.1,K.1,1,K.1^-1,K.1^-1,K.1,K.1^-1,K.1^-1,1,K.1^-1,K.1^-1,K.1,K.1,K.1,K.1,K.1,K.1^-1,K.1^-1,1,K.1^-1,1,K.1^-1,K.1^-1,K.1^-1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,K.1^-1,1,K.1,K.1^-1,K.1,K.1,K.1^-1,1,1,1,1,1,1,1,1,1,1,1,1,K.1^-1,K.1,K.1,1,K.1^-1,1,K.1^-1,K.1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,K.1,1,K.1,1,1,K.1^-1,1,K.1^-1,1,K.1,1,K.1,K.1,K.1,K.1^-1,K.1^-1,K.1^-1,K.1,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |1,1,1,1,K.1,1,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,1,1,1,1,1,1,1,1,1,1,1,1,K.1,K.1^-1,K.1^-1,1,K.1,1,K.1,K.1^-1,K.1,K.1^-1,K.1,K.1,K.1^-1,K.1^-1,1,K.1^-1,1,1,K.1,1,K.1,1,K.1^-1,1,K.1^-1,K.1^-1,K.1^-1,K.1,K.1,K.1,K.1^-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^-2,K.1^2,K.1,K.1^-1,K.1,K.1^2,K.1^2,K.1^-2,K.1^-1,K.1^-1,K.1^-2,K.1,K.1^-2,K.1^2,K.1^2,K.1^-2,K.1,K.1^2,K.1^2,K.1^-2,K.1^2,K.1^-2,K.1,K.1^-1,K.1,K.1,K.1^-1,K.1,K.1^-2,K.1^2,K.1^-2,K.1^-1,K.1^-1,K.1,K.1^-1,K.1,K.1^2,K.1^-1,K.1^-1,K.1,K.1^2,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^-1,K.1,K.1^-1,K.1^-2,K.1^-2,K.1^2,K.1,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^-2,K.1^-2,K.1^2,K.1^-2,K.1^2,K.1^-1,K.1,K.1^-1,K.1^-1,K.1,K.1^-1,K.1^2,K.1^-2,K.1^2,K.1,K.1,K.1^-1,K.1,K.1^-1,K.1^-2,K.1,K.1,K.1^-1,K.1^-2,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^-1,K.1,K.1^-2,K.1^2,K.1^-2,K.1,K.1,K.1^-1,K.1^2,K.1^2,K.1^-1,K.1^-2,K.1^-1,K.1,K.1,K.1^-1,K.1^-2,K.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^-1,K.1,K.1^-1,K.1^2,K.1^2,K.1^-2,K.1^2,K.1^-2,K.1,K.1^2,K.1^2,K.1^-2,K.1,K.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,K.1^-1,K.1^2,K.1^-2,K.1^2,K.1^-1,K.1^-1,K.1,K.1^-2,K.1^-2,K.1,K.1^2,K.1,K.1^-1,K.1^-1,K.1,K.1^2,K.1^-1,K.1^-1,K.1,K.1^-1,K.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^-2,K.1^-2,K.1^2,K.1^-2,K.1^2,K.1^-1,K.1^-2,K.1^-2,K.1^2,K.1^-1,K.1,K.1,K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^-5,K.1^5,K.1^5,K.1^5,1,1,K.1^-5,K.1^-5,K.1^-6,K.1^6,K.1^3,K.1^-3,K.1^3,K.1^6,K.1^6,K.1^-6,K.1^-3,K.1^-3,K.1^-6,K.1^3,K.1^-1,K.1,K.1^-4,K.1^4,K.1^3,K.1,K.1^-4,K.1^-1,K.1^6,K.1^4,K.1^-2,K.1^7,K.1^-7,K.1^3,K.1^2,K.1^-2,K.1^-1,K.1^-4,K.1^-6,K.1^7,K.1^-3,K.1^-2,K.1^2,K.1^-7,K.1^6,K.1^7,K.1^-3,K.1^-7,K.1,K.1^4,K.1^-6,K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^5,K.1^-5,K.1^-5,K.1^-5,1,1,K.1^5,K.1^5,K.1^6,K.1^-6,K.1^-3,K.1^3,K.1^-3,K.1^-6,K.1^-6,K.1^6,K.1^3,K.1^3,K.1^6,K.1^-3,K.1,K.1^-1,K.1^4,K.1^-4,K.1^-3,K.1^-1,K.1^4,K.1,K.1^-6,K.1^-4,K.1^2,K.1^-7,K.1^7,K.1^-3,K.1^-2,K.1^2,K.1,K.1^4,K.1^6,K.1^-7,K.1^3,K.1^2,K.1^-2,K.1^7,K.1^-6,K.1^-7,K.1^3,K.1^7,K.1^-1,K.1^-4,K.1^6,K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^-5,K.1^5,K.1^5,K.1^5,1,1,K.1^-5,K.1^-5,K.1^6,K.1^-6,K.1^-3,K.1^3,K.1^-3,K.1^-6,K.1^-6,K.1^6,K.1^3,K.1^3,K.1^6,K.1^-3,K.1^-4,K.1^4,K.1^-1,K.1,K.1^-3,K.1^4,K.1^-1,K.1^-4,K.1^-6,K.1,K.1^7,K.1^-2,K.1^2,K.1^-3,K.1^-7,K.1^7,K.1^-4,K.1^-1,K.1^6,K.1^-2,K.1^3,K.1^7,K.1^-7,K.1^2,K.1^-6,K.1^-2,K.1^3,K.1^2,K.1^4,K.1,K.1^6,K.1^-7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^5,K.1^-5,K.1^-5,K.1^-5,1,1,K.1^5,K.1^5,K.1^-6,K.1^6,K.1^3,K.1^-3,K.1^3,K.1^6,K.1^6,K.1^-6,K.1^-3,K.1^-3,K.1^-6,K.1^3,K.1^4,K.1^-4,K.1,K.1^-1,K.1^3,K.1^-4,K.1,K.1^4,K.1^6,K.1^-1,K.1^-7,K.1^2,K.1^-2,K.1^3,K.1^7,K.1^-7,K.1^4,K.1,K.1^-6,K.1^2,K.1^-3,K.1^-7,K.1^7,K.1^-2,K.1^6,K.1^2,K.1^-3,K.1^-2,K.1^-4,K.1^-1,K.1^-6,K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^-5,K.1^5,K.1^5,K.1^5,1,1,K.1^-5,K.1^-5,K.1^-3,K.1^3,K.1^-6,K.1^6,K.1^-6,K.1^3,K.1^3,K.1^-3,K.1^6,K.1^6,K.1^-3,K.1^-6,K.1^2,K.1^-2,K.1^-7,K.1^7,K.1^-6,K.1^-2,K.1^-7,K.1^2,K.1^3,K.1^7,K.1^4,K.1,K.1^-1,K.1^-6,K.1^-4,K.1^4,K.1^2,K.1^-7,K.1^-3,K.1,K.1^6,K.1^4,K.1^-4,K.1^-1,K.1^3,K.1,K.1^6,K.1^-1,K.1^-2,K.1^7,K.1^-3,K.1^-4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^5,K.1^-5,K.1^-5,K.1^-5,1,1,K.1^5,K.1^5,K.1^3,K.1^-3,K.1^6,K.1^-6,K.1^6,K.1^-3,K.1^-3,K.1^3,K.1^-6,K.1^-6,K.1^3,K.1^6,K.1^-2,K.1^2,K.1^7,K.1^-7,K.1^6,K.1^2,K.1^7,K.1^-2,K.1^-3,K.1^-7,K.1^-4,K.1^-1,K.1,K.1^6,K.1^4,K.1^-4,K.1^-2,K.1^7,K.1^3,K.1^-1,K.1^-6,K.1^-4,K.1^4,K.1,K.1^-3,K.1^-1,K.1^-6,K.1,K.1^2,K.1^-7,K.1^3,K.1^4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^-5,K.1^5,K.1^5,K.1^5,1,1,K.1^-5,K.1^-5,K.1^3,K.1^-3,K.1^6,K.1^-6,K.1^6,K.1^-3,K.1^-3,K.1^3,K.1^-6,K.1^-6,K.1^3,K.1^6,K.1^-7,K.1^7,K.1^2,K.1^-2,K.1^6,K.1^7,K.1^2,K.1^-7,K.1^-3,K.1^-2,K.1,K.1^4,K.1^-4,K.1^6,K.1^-1,K.1,K.1^-7,K.1^2,K.1^3,K.1^4,K.1^-6,K.1,K.1^-1,K.1^-4,K.1^-3,K.1^4,K.1^-6,K.1^-4,K.1^7,K.1^-2,K.1^3,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^5,K.1^-5,K.1^-5,K.1^-5,1,1,K.1^5,K.1^5,K.1^-3,K.1^3,K.1^-6,K.1^6,K.1^-6,K.1^3,K.1^3,K.1^-3,K.1^6,K.1^6,K.1^-3,K.1^-6,K.1^7,K.1^-7,K.1^-2,K.1^2,K.1^-6,K.1^-7,K.1^-2,K.1^7,K.1^3,K.1^2,K.1^-1,K.1^-4,K.1^4,K.1^-6,K.1,K.1^-1,K.1^7,K.1^-2,K.1^-3,K.1^-4,K.1^6,K.1^-1,K.1,K.1^4,K.1^3,K.1^-4,K.1^6,K.1^4,K.1^-7,K.1^2,K.1^-3,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^-5,K.1^-5,K.1^5,1,K.1^5,K.1^-5,K.1^5,1,K.1^-6,K.1^6,K.1^3,K.1^-3,K.1^3,K.1^6,K.1^6,K.1^-6,K.1^-3,K.1^-3,K.1^-6,K.1^3,K.1^4,K.1^-4,K.1^6,K.1^4,K.1^-7,K.1,K.1,K.1^-6,K.1^-4,K.1^-1,K.1^3,K.1^-3,K.1^3,K.1^-2,K.1^2,K.1^-7,K.1^-1,K.1^-4,K.1^-1,K.1^7,K.1^2,K.1^-2,K.1^-3,K.1^-7,K.1,K.1^2,K.1^7,K.1^-2,K.1^6,K.1^-6,K.1^4,K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^5,K.1^5,K.1^-5,1,K.1^-5,K.1^5,K.1^-5,1,K.1^6,K.1^-6,K.1^-3,K.1^3,K.1^-3,K.1^-6,K.1^-6,K.1^6,K.1^3,K.1^3,K.1^6,K.1^-3,K.1^-4,K.1^4,K.1^-6,K.1^-4,K.1^7,K.1^-1,K.1^-1,K.1^6,K.1^4,K.1,K.1^-3,K.1^3,K.1^-3,K.1^2,K.1^-2,K.1^7,K.1,K.1^4,K.1,K.1^-7,K.1^-2,K.1^2,K.1^3,K.1^7,K.1^-1,K.1^-2,K.1^-7,K.1^2,K.1^-6,K.1^6,K.1^-4,K.1^-7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^-5,K.1^-5,K.1^5,1,K.1^5,K.1^-5,K.1^5,1,K.1^6,K.1^-6,K.1^-3,K.1^3,K.1^-3,K.1^-6,K.1^-6,K.1^6,K.1^3,K.1^3,K.1^6,K.1^-3,K.1,K.1^-1,K.1^-6,K.1,K.1^2,K.1^4,K.1^4,K.1^6,K.1^-1,K.1^-4,K.1^-3,K.1^3,K.1^-3,K.1^7,K.1^-7,K.1^2,K.1^-4,K.1^-1,K.1^-4,K.1^-2,K.1^-7,K.1^7,K.1^3,K.1^2,K.1^4,K.1^-7,K.1^-2,K.1^7,K.1^-6,K.1^6,K.1,K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^5,K.1^5,K.1^-5,1,K.1^-5,K.1^5,K.1^-5,1,K.1^-6,K.1^6,K.1^3,K.1^-3,K.1^3,K.1^6,K.1^6,K.1^-6,K.1^-3,K.1^-3,K.1^-6,K.1^3,K.1^-1,K.1,K.1^6,K.1^-1,K.1^-2,K.1^-4,K.1^-4,K.1^-6,K.1,K.1^4,K.1^3,K.1^-3,K.1^3,K.1^-7,K.1^7,K.1^-2,K.1^4,K.1,K.1^4,K.1^2,K.1^7,K.1^-7,K.1^-3,K.1^-2,K.1^-4,K.1^7,K.1^2,K.1^-7,K.1^6,K.1^-6,K.1^-1,K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^-5,K.1^-5,K.1^5,1,K.1^5,K.1^-5,K.1^5,1,K.1^-3,K.1^3,K.1^-6,K.1^6,K.1^-6,K.1^3,K.1^3,K.1^-3,K.1^6,K.1^6,K.1^-3,K.1^-6,K.1^7,K.1^-7,K.1^3,K.1^7,K.1^-1,K.1^-2,K.1^-2,K.1^-3,K.1^-7,K.1^2,K.1^-6,K.1^6,K.1^-6,K.1^4,K.1^-4,K.1^-1,K.1^2,K.1^-7,K.1^2,K.1,K.1^-4,K.1^4,K.1^6,K.1^-1,K.1^-2,K.1^-4,K.1,K.1^4,K.1^3,K.1^-3,K.1^7,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^5,K.1^5,K.1^-5,1,K.1^-5,K.1^5,K.1^-5,1,K.1^3,K.1^-3,K.1^6,K.1^-6,K.1^6,K.1^-3,K.1^-3,K.1^3,K.1^-6,K.1^-6,K.1^3,K.1^6,K.1^-7,K.1^7,K.1^-3,K.1^-7,K.1,K.1^2,K.1^2,K.1^3,K.1^7,K.1^-2,K.1^6,K.1^-6,K.1^6,K.1^-4,K.1^4,K.1,K.1^-2,K.1^7,K.1^-2,K.1^-1,K.1^4,K.1^-4,K.1^-6,K.1,K.1^2,K.1^4,K.1^-1,K.1^-4,K.1^-3,K.1^3,K.1^-7,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^-5,K.1^-5,K.1^5,1,K.1^5,K.1^-5,K.1^5,1,K.1^3,K.1^-3,K.1^6,K.1^-6,K.1^6,K.1^-3,K.1^-3,K.1^3,K.1^-6,K.1^-6,K.1^3,K.1^6,K.1^-2,K.1^2,K.1^-3,K.1^-2,K.1^-4,K.1^7,K.1^7,K.1^3,K.1^2,K.1^-7,K.1^6,K.1^-6,K.1^6,K.1,K.1^-1,K.1^-4,K.1^-7,K.1^2,K.1^-7,K.1^4,K.1^-1,K.1,K.1^-6,K.1^-4,K.1^7,K.1^-1,K.1^4,K.1,K.1^-3,K.1^3,K.1^-2,K.1^4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^5,K.1^5,K.1^-5,1,K.1^-5,K.1^5,K.1^-5,1,K.1^-3,K.1^3,K.1^-6,K.1^6,K.1^-6,K.1^3,K.1^3,K.1^-3,K.1^6,K.1^6,K.1^-3,K.1^-6,K.1^2,K.1^-2,K.1^3,K.1^2,K.1^4,K.1^-7,K.1^-7,K.1^-3,K.1^-2,K.1^7,K.1^-6,K.1^6,K.1^-6,K.1^-1,K.1,K.1^4,K.1^7,K.1^-2,K.1^7,K.1^-4,K.1,K.1^-1,K.1^6,K.1^4,K.1^-7,K.1,K.1^-4,K.1^-1,K.1^3,K.1^-3,K.1^2,K.1^-4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^-5,1,K.1^5,K.1^-5,K.1^-5,K.1^5,1,K.1^5,K.1^-6,K.1^6,K.1^3,K.1^-3,K.1^3,K.1^6,K.1^6,K.1^-6,K.1^-3,K.1^-3,K.1^-6,K.1^3,K.1^-6,K.1^6,K.1,K.1^4,K.1^-2,K.1,K.1^6,K.1^4,K.1,K.1^-6,K.1^-7,K.1^2,K.1^-2,K.1^-7,K.1^2,K.1^3,K.1^-1,K.1^-4,K.1^4,K.1^7,K.1^7,K.1^-2,K.1^7,K.1^-7,K.1^-4,K.1^-3,K.1^2,K.1^3,K.1^-4,K.1^-1,K.1^-1,K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^5,1,K.1^-5,K.1^5,K.1^5,K.1^-5,1,K.1^-5,K.1^6,K.1^-6,K.1^-3,K.1^3,K.1^-3,K.1^-6,K.1^-6,K.1^6,K.1^3,K.1^3,K.1^6,K.1^-3,K.1^6,K.1^-6,K.1^-1,K.1^-4,K.1^2,K.1^-1,K.1^-6,K.1^-4,K.1^-1,K.1^6,K.1^7,K.1^-2,K.1^2,K.1^7,K.1^-2,K.1^-3,K.1,K.1^4,K.1^-4,K.1^-7,K.1^-7,K.1^2,K.1^-7,K.1^7,K.1^4,K.1^3,K.1^-2,K.1^-3,K.1^4,K.1,K.1,K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^-5,1,K.1^5,K.1^-5,K.1^-5,K.1^5,1,K.1^5,K.1^6,K.1^-6,K.1^-3,K.1^3,K.1^-3,K.1^-6,K.1^-6,K.1^6,K.1^3,K.1^3,K.1^6,K.1^-3,K.1^6,K.1^-6,K.1^4,K.1,K.1^7,K.1^4,K.1^-6,K.1,K.1^4,K.1^6,K.1^2,K.1^-7,K.1^7,K.1^2,K.1^-7,K.1^-3,K.1^-4,K.1^-1,K.1,K.1^-2,K.1^-2,K.1^7,K.1^-2,K.1^2,K.1^-1,K.1^3,K.1^-7,K.1^-3,K.1^-1,K.1^-4,K.1^-4,K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^5,1,K.1^-5,K.1^5,K.1^5,K.1^-5,1,K.1^-5,K.1^-6,K.1^6,K.1^3,K.1^-3,K.1^3,K.1^6,K.1^6,K.1^-6,K.1^-3,K.1^-3,K.1^-6,K.1^3,K.1^-6,K.1^6,K.1^-4,K.1^-1,K.1^-7,K.1^-4,K.1^6,K.1^-1,K.1^-4,K.1^-6,K.1^-2,K.1^7,K.1^-7,K.1^-2,K.1^7,K.1^3,K.1^4,K.1,K.1^-1,K.1^2,K.1^2,K.1^-7,K.1^2,K.1^-2,K.1,K.1^-3,K.1^7,K.1^3,K.1,K.1^4,K.1^4,K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^-5,1,K.1^5,K.1^-5,K.1^-5,K.1^5,1,K.1^5,K.1^-3,K.1^3,K.1^-6,K.1^6,K.1^-6,K.1^3,K.1^3,K.1^-3,K.1^6,K.1^6,K.1^-3,K.1^-6,K.1^-3,K.1^3,K.1^-2,K.1^7,K.1^4,K.1^-2,K.1^3,K.1^7,K.1^-2,K.1^-3,K.1^-1,K.1^-4,K.1^4,K.1^-1,K.1^-4,K.1^-6,K.1^2,K.1^-7,K.1^7,K.1,K.1,K.1^4,K.1,K.1^-1,K.1^-7,K.1^6,K.1^-4,K.1^-6,K.1^-7,K.1^2,K.1^2,K.1^6]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^5,1,K.1^-5,K.1^5,K.1^5,K.1^-5,1,K.1^-5,K.1^3,K.1^-3,K.1^6,K.1^-6,K.1^6,K.1^-3,K.1^-3,K.1^3,K.1^-6,K.1^-6,K.1^3,K.1^6,K.1^3,K.1^-3,K.1^2,K.1^-7,K.1^-4,K.1^2,K.1^-3,K.1^-7,K.1^2,K.1^3,K.1,K.1^4,K.1^-4,K.1,K.1^4,K.1^6,K.1^-2,K.1^7,K.1^-7,K.1^-1,K.1^-1,K.1^-4,K.1^-1,K.1,K.1^7,K.1^-6,K.1^4,K.1^6,K.1^7,K.1^-2,K.1^-2,K.1^-6]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^-5,1,K.1^5,K.1^-5,K.1^-5,K.1^5,1,K.1^5,K.1^3,K.1^-3,K.1^6,K.1^-6,K.1^6,K.1^-3,K.1^-3,K.1^3,K.1^-6,K.1^-6,K.1^3,K.1^6,K.1^3,K.1^-3,K.1^7,K.1^-2,K.1,K.1^7,K.1^-3,K.1^-2,K.1^7,K.1^3,K.1^-4,K.1^-1,K.1,K.1^-4,K.1^-1,K.1^6,K.1^-7,K.1^2,K.1^-2,K.1^4,K.1^4,K.1,K.1^4,K.1^-4,K.1^2,K.1^-6,K.1^-1,K.1^6,K.1^2,K.1^-7,K.1^-7,K.1^-6]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,K.1^5,1,K.1^-5,K.1^5,K.1^5,K.1^-5,1,K.1^-5,K.1^-3,K.1^3,K.1^-6,K.1^6,K.1^-6,K.1^3,K.1^3,K.1^-3,K.1^6,K.1^6,K.1^-3,K.1^-6,K.1^-3,K.1^3,K.1^-7,K.1^2,K.1^-1,K.1^-7,K.1^3,K.1^2,K.1^-7,K.1^-3,K.1^4,K.1,K.1^-1,K.1^4,K.1,K.1^-6,K.1^7,K.1^-2,K.1^2,K.1^-4,K.1^-4,K.1^-1,K.1^-4,K.1^4,K.1^-2,K.1^6,K.1,K.1^-6,K.1^-2,K.1^7,K.1^7,K.1^6]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,1,K.1^-5,1,K.1^5,K.1^-5,K.1^5,K.1^5,K.1^-5,K.1^-6,K.1^6,K.1^3,K.1^-3,K.1^3,K.1^6,K.1^6,K.1^-6,K.1^-3,K.1^-3,K.1^-6,K.1^3,K.1^4,K.1^-4,K.1^-4,K.1^-6,K.1^-2,K.1^6,K.1,K.1^-1,K.1,K.1^-1,K.1^-2,K.1^7,K.1^-7,K.1^-7,K.1^-3,K.1^-7,K.1^-6,K.1^6,K.1^4,K.1^-3,K.1^7,K.1^3,K.1^2,K.1^3,K.1^-4,K.1^2,K.1^2,K.1^-2,K.1,K.1^4,K.1^-1,K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,1,K.1^5,1,K.1^-5,K.1^5,K.1^-5,K.1^-5,K.1^5,K.1^6,K.1^-6,K.1^-3,K.1^3,K.1^-3,K.1^-6,K.1^-6,K.1^6,K.1^3,K.1^3,K.1^6,K.1^-3,K.1^-4,K.1^4,K.1^4,K.1^6,K.1^2,K.1^-6,K.1^-1,K.1,K.1^-1,K.1,K.1^2,K.1^-7,K.1^7,K.1^7,K.1^3,K.1^7,K.1^6,K.1^-6,K.1^-4,K.1^3,K.1^-7,K.1^-3,K.1^-2,K.1^-3,K.1^4,K.1^-2,K.1^-2,K.1^2,K.1^-1,K.1^-4,K.1,K.1^-7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,1,K.1^-5,1,K.1^5,K.1^-5,K.1^5,K.1^5,K.1^-5,K.1^6,K.1^-6,K.1^-3,K.1^3,K.1^-3,K.1^-6,K.1^-6,K.1^6,K.1^3,K.1^3,K.1^6,K.1^-3,K.1,K.1^-1,K.1^-1,K.1^6,K.1^7,K.1^-6,K.1^4,K.1^-4,K.1^4,K.1^-4,K.1^7,K.1^-2,K.1^2,K.1^2,K.1^3,K.1^2,K.1^6,K.1^-6,K.1,K.1^3,K.1^-2,K.1^-3,K.1^-7,K.1^-3,K.1^-1,K.1^-7,K.1^-7,K.1^7,K.1^4,K.1,K.1^-4,K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,1,K.1^5,1,K.1^-5,K.1^5,K.1^-5,K.1^-5,K.1^5,K.1^-6,K.1^6,K.1^3,K.1^-3,K.1^3,K.1^6,K.1^6,K.1^-6,K.1^-3,K.1^-3,K.1^-6,K.1^3,K.1^-1,K.1,K.1,K.1^-6,K.1^-7,K.1^6,K.1^-4,K.1^4,K.1^-4,K.1^4,K.1^-7,K.1^2,K.1^-2,K.1^-2,K.1^-3,K.1^-2,K.1^-6,K.1^6,K.1^-1,K.1^-3,K.1^2,K.1^3,K.1^7,K.1^3,K.1,K.1^7,K.1^7,K.1^-7,K.1^-4,K.1^-1,K.1^4,K.1^2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,1,K.1^-5,1,K.1^5,K.1^-5,K.1^5,K.1^5,K.1^-5,K.1^-3,K.1^3,K.1^-6,K.1^6,K.1^-6,K.1^3,K.1^3,K.1^-3,K.1^6,K.1^6,K.1^-3,K.1^-6,K.1^7,K.1^-7,K.1^-7,K.1^-3,K.1^4,K.1^3,K.1^-2,K.1^2,K.1^-2,K.1^2,K.1^4,K.1,K.1^-1,K.1^-1,K.1^6,K.1^-1,K.1^-3,K.1^3,K.1^7,K.1^6,K.1,K.1^-6,K.1^-4,K.1^-6,K.1^-7,K.1^-4,K.1^-4,K.1^4,K.1^-2,K.1^7,K.1^2,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,1,K.1^5,1,K.1^-5,K.1^5,K.1^-5,K.1^-5,K.1^5,K.1^3,K.1^-3,K.1^6,K.1^-6,K.1^6,K.1^-3,K.1^-3,K.1^3,K.1^-6,K.1^-6,K.1^3,K.1^6,K.1^-7,K.1^7,K.1^7,K.1^3,K.1^-4,K.1^-3,K.1^2,K.1^-2,K.1^2,K.1^-2,K.1^-4,K.1^-1,K.1,K.1,K.1^-6,K.1,K.1^3,K.1^-3,K.1^-7,K.1^-6,K.1^-1,K.1^6,K.1^4,K.1^6,K.1^7,K.1^4,K.1^4,K.1^-4,K.1^2,K.1^-7,K.1^-2,K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,1,K.1^-5,1,K.1^5,K.1^-5,K.1^5,K.1^5,K.1^-5,K.1^3,K.1^-3,K.1^6,K.1^-6,K.1^6,K.1^-3,K.1^-3,K.1^3,K.1^-6,K.1^-6,K.1^3,K.1^6,K.1^-2,K.1^2,K.1^2,K.1^3,K.1,K.1^-3,K.1^7,K.1^-7,K.1^7,K.1^-7,K.1,K.1^4,K.1^-4,K.1^-4,K.1^-6,K.1^-4,K.1^3,K.1^-3,K.1^-2,K.1^-6,K.1^4,K.1^6,K.1^-1,K.1^6,K.1^2,K.1^-1,K.1^-1,K.1,K.1^7,K.1^-2,K.1^-7,K.1^4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |1,1,1,1,K.1^5,1,K.1^-5,K.1^5,K.1^-5,K.1^-5,K.1^5,K.1^-3,K.1^3,K.1^-6,K.1^6,K.1^-6,K.1^3,K.1^3,K.1^-3,K.1^6,K.1^6,K.1^-3,K.1^-6,K.1^2,K.1^-2,K.1^-2,K.1^-3,K.1^-1,K.1^3,K.1^-7,K.1^7,K.1^-7,K.1^7,K.1^-1,K.1^-4,K.1^4,K.1^4,K.1^6,K.1^4,K.1^-3,K.1^3,K.1^2,K.1^6,K.1^-4,K.1^-6,K.1,K.1^-6,K.1^-2,K.1,K.1,K.1^-1,K.1^-7,K.1^2,K.1^7,K.1^-4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,3,3,3,3,3*K.1^-1,3*K.1,3*K.1^-1,3*K.1,3*K.1,3*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |3,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,3,3,3,3,3*K.1,3*K.1^-1,3*K.1,3*K.1^-1,3*K.1^-1,3*K.1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |3,3*K.1^-5,3*K.1^5,0,0,0,0,0,0,0,0,3*K.1^-6,3*K.1^6,3*K.1^3,3*K.1^-3,3*K.1^-2,3*K.1^-4,3*K.1,3*K.1^-1,3*K.1^2,3*K.1^7,3*K.1^4,3*K.1^-7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |3,3*K.1^5,3*K.1^-5,0,0,0,0,0,0,0,0,3*K.1^6,3*K.1^-6,3*K.1^-3,3*K.1^3,3*K.1^2,3*K.1^4,3*K.1^-1,3*K.1,3*K.1^-2,3*K.1^-7,3*K.1^-4,3*K.1^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |3,3*K.1^-5,3*K.1^5,0,0,0,0,0,0,0,0,3*K.1^6,3*K.1^-6,3*K.1^-3,3*K.1^3,3*K.1^7,3*K.1^-1,3*K.1^4,3*K.1^-4,3*K.1^-7,3*K.1^-2,3*K.1,3*K.1^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |3,3*K.1^5,3*K.1^-5,0,0,0,0,0,0,0,0,3*K.1^-6,3*K.1^6,3*K.1^3,3*K.1^-3,3*K.1^-7,3*K.1,3*K.1^-4,3*K.1^4,3*K.1^7,3*K.1^2,3*K.1^-1,3*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |3,3*K.1^-5,3*K.1^5,0,0,0,0,0,0,0,0,3*K.1^-3,3*K.1^3,3*K.1^-6,3*K.1^6,3*K.1^4,3*K.1^-7,3*K.1^-2,3*K.1^2,3*K.1^-4,3*K.1,3*K.1^7,3*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |3,3*K.1^5,3*K.1^-5,0,0,0,0,0,0,0,0,3*K.1^3,3*K.1^-3,3*K.1^6,3*K.1^-6,3*K.1^-4,3*K.1^7,3*K.1^2,3*K.1^-2,3*K.1^4,3*K.1^-1,3*K.1^-7,3*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |3,3*K.1^-5,3*K.1^5,0,0,0,0,0,0,0,0,3*K.1^3,3*K.1^-3,3*K.1^6,3*K.1^-6,3*K.1,3*K.1^2,3*K.1^7,3*K.1^-7,3*K.1^-1,3*K.1^4,3*K.1^-2,3*K.1^-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |3,3*K.1^5,3*K.1^-5,0,0,0,0,0,0,0,0,3*K.1^-3,3*K.1^3,3*K.1^-6,3*K.1^6,3*K.1^-1,3*K.1^-2,3*K.1^-7,3*K.1^7,3*K.1,3*K.1^-4,3*K.1^2,3*K.1^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_135_3:= KnownIrreducibles(CR);