/* Group 416.66 downloaded from the LMFDB on 26 October 2026. */
 
/* Various presentations of this group are stored in this file: 
	 GPC is polycyclic presentation, GPerm is permutation group 
	 GLZ, GLFp, GLZN, 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, -2, -13, 12, 4106, 908, 50, 963, 2409, 69, 2404, 6010, 88, 5765, 6923]); a,b := Explode([GPC.1, GPC.3]); AssignNames(~GPC, ["a", "a2", "b", "b2", "b4", "b8"]);
GPerm := PermutationGroup< 21 | (2,3,4,6)(5,8,9,13)(7,11,12,10)(14,15,17,19)(16,18,20,21), (14,16,15,18,17,20,19,21), (2,4)(3,6)(5,9)(7,12)(8,13)(10,11)(14,17)(15,19)(16,20)(18,21), (14,15,17,19)(16,18,20,21), (14,17)(15,19)(16,20)(18,21), (1,2,5,8,12,6,10,11,3,7,13,9,4) >;
F:=GF(169); al:=F.1; GLFq := MatrixGroup< 2, F | [[1, 0], [al^16, al^84]],[[al^84, 0], [0, al^84]],[[al^155, al^107], [al^27, al^159]],[[al^21, 0], [0, al^21]],[[al^42, 0], [al^114, al^84]],[[al^42, 0], [0, al^42]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable : BoolElt >; 
booleans_416_66 := rec< RF | 
Agroup := true,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := true,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>; 

 
/* Character Table */
G:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, b^52>,< 2, 13, a^2>,< 2, 13, a^2*b^12>,< 4, 1, b^26>,< 4, 1, b^78>,< 4, 13, a>,< 4, 13, a^3>,< 4, 13, a*b^4>,< 4, 13, a^3*b^4>,< 4, 13, a*b^2>,< 4, 13, a^3*b^6>,< 4, 13, a*b^6>,< 4, 13, a^3*b^2>,< 4, 13, a^2*b^58>,< 4, 13, a^2*b^6>,< 8, 1, b^13>,< 8, 1, b^91>,< 8, 1, b^39>,< 8, 1, b^65>,< 8, 13, a^2*b>,< 8, 13, a^2*b^7>,< 8, 13, a^2*b^3>,< 8, 13, a^2*b^5>,< 8, 13, a*b>,< 8, 13, a^3*b^7>,< 8, 13, a^3*b^3>,< 8, 13, a*b^5>,< 8, 13, a*b^3>,< 8, 13, a^3*b^5>,< 8, 13, a^3*b>,< 8, 13, a*b^7>,< 13, 4, b^8>,< 13, 4, b^16>,< 13, 4, b^32>,< 26, 4, b^4>,< 26, 4, b^12>,< 26, 4, b^28>,< 52, 4, b^2>,< 52, 4, b^102>,< 52, 4, b^6>,< 52, 4, b^98>,< 52, 4, b^14>,< 52, 4, b^90>,< 104, 4, b>,< 104, 4, b^31>,< 104, 4, b^3>,< 104, 4, b^29>,< 104, 4, b^5>,< 104, 4, b^27>,< 104, 4, b^7>,< 104, 4, b^9>,< 104, 4, b^15>,< 104, 4, b^41>,< 104, 4, b^19>,< 104, 4, b^45>]); 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,-1,-1,-1,-1*K.1,1,K.1,K.1,-1*K.1,-1*K.1,1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1,1,1,-1,-1,1,1,-1,-1*K.1,K.1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1,K.1,K.1,K.1,-1*K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,-1,-1,-1,K.1,1,-1*K.1,-1*K.1,K.1,K.1,1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,-1,1,1,-1,-1,1,1,-1,K.1,-1*K.1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1*K.1,K.1,K.1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,-1,-1,-1,-1*K.1,1,K.1,K.1,-1*K.1,-1*K.1,1,K.1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,1,-1,-1,1,1,-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,K.1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,-1,-1,-1,K.1,1,-1*K.1,-1*K.1,K.1,K.1,1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,1,-1,-1,1,1,-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,-1*K.1,-1*K.1,-1*K.1,K.1,K.1,K.1,K.1,K.1,-1*K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,-1,1,1,-1*K.1,-1,K.1,-1*K.1,-1*K.1,K.1,-1,-1*K.1,K.1,K.1,-1,-1,-1,-1,1,1,-1*K.1,K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,-1*K.1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,-1,1,1,K.1,-1,-1*K.1,K.1,K.1,-1*K.1,-1,K.1,-1*K.1,-1*K.1,-1,-1,-1,-1,1,1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,-1,1,1,-1*K.1,-1,K.1,-1*K.1,-1*K.1,K.1,-1,-1*K.1,K.1,K.1,1,1,1,1,-1,-1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,-1,1,1,K.1,-1,-1*K.1,K.1,K.1,-1*K.1,-1,K.1,-1*K.1,-1*K.1,1,1,1,1,-1,-1,-1*K.1,K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,-1*K.1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-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,K.1,-1*K.1,K.1,-1*K.1,K.1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1*K.1,K.1,K.1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1,K.1,K.1,K.1,-1*K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,-1*K.1,K.1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1*K.1,K.1,K.1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.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*K.1,K.1,K.1,K.1,K.1,K.1,-1*K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,-1,1,-1*K.1^2,K.1^2,-1,K.1^2,1,K.1^2,1,-1*K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1,-1*K.1,K.1^3,-1*K.1^3,K.1,K.1^3,K.1,K.1,-1*K.1,K.1^3,-1*K.1^3,K.1^3,K.1,-1*K.1^3,-1*K.1,-1*K.1,-1*K.1^3,1,1,1,-1,-1,-1,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,K.1,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1^3,-1*K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,-1,1,K.1^2,-1*K.1^2,-1,-1*K.1^2,1,-1*K.1^2,1,K.1^2,K.1^2,K.1^2,-1*K.1^2,-1,K.1^3,-1*K.1,K.1,-1*K.1^3,-1*K.1,-1*K.1^3,-1*K.1^3,K.1^3,-1*K.1,K.1,-1*K.1,-1*K.1^3,K.1,K.1^3,K.1^3,K.1,1,1,1,-1,-1,-1,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^3,-1*K.1,K.1,-1*K.1,K.1,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,-1*K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,-1,1,-1*K.1^2,K.1^2,-1,K.1^2,1,K.1^2,1,-1*K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1,K.1,-1*K.1^3,K.1^3,-1*K.1,-1*K.1^3,-1*K.1,-1*K.1,K.1,-1*K.1^3,K.1^3,-1*K.1^3,-1*K.1,K.1^3,K.1,K.1,K.1^3,1,1,1,-1,-1,-1,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,-1*K.1,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1^3,K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,-1,1,K.1^2,-1*K.1^2,-1,-1*K.1^2,1,-1*K.1^2,1,K.1^2,K.1^2,K.1^2,-1*K.1^2,-1,-1*K.1^3,K.1,-1*K.1,K.1^3,K.1,K.1^3,K.1^3,-1*K.1^3,K.1,-1*K.1,K.1,K.1^3,-1*K.1,-1*K.1^3,-1*K.1^3,-1*K.1,1,1,1,-1,-1,-1,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,K.1^3,K.1,-1*K.1,K.1,-1*K.1,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,-1,1,-1*K.1^2,K.1^2,1,K.1^2,-1,-1*K.1^2,-1,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,1,-1*K.1,K.1^3,-1*K.1^3,K.1,K.1^3,K.1,-1*K.1,K.1,-1*K.1^3,K.1^3,-1*K.1^3,-1*K.1,K.1^3,K.1,-1*K.1,-1*K.1^3,1,1,1,-1,-1,-1,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,K.1,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1^3,-1*K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,-1,1,K.1^2,-1*K.1^2,1,-1*K.1^2,-1,K.1^2,-1,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,1,K.1^3,-1*K.1,K.1,-1*K.1^3,-1*K.1,-1*K.1^3,K.1^3,-1*K.1^3,K.1,-1*K.1,K.1,K.1^3,-1*K.1,-1*K.1^3,K.1^3,K.1,1,1,1,-1,-1,-1,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^3,-1*K.1,K.1,-1*K.1,K.1,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,-1*K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,-1,1,-1*K.1^2,K.1^2,1,K.1^2,-1,-1*K.1^2,-1,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,1,K.1,-1*K.1^3,K.1^3,-1*K.1,-1*K.1^3,-1*K.1,K.1,-1*K.1,K.1^3,-1*K.1^3,K.1^3,K.1,-1*K.1^3,-1*K.1,K.1,K.1^3,1,1,1,-1,-1,-1,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,-1*K.1,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1^3,K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,-1,1,K.1^2,-1*K.1^2,1,-1*K.1^2,-1,K.1^2,-1,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,1,-1*K.1^3,K.1,-1*K.1,K.1^3,K.1,K.1^3,-1*K.1^3,K.1^3,-1*K.1,K.1,-1*K.1,-1*K.1^3,K.1,K.1^3,-1*K.1^3,-1*K.1,1,1,1,-1,-1,-1,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,K.1^3,K.1,-1*K.1,K.1,-1*K.1,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,-1*K.1^2,K.1^2,-1*K.1^2,-1*K.1^2,-1*K.1^2,-1,K.1^2,-1,K.1^2,1,1,K.1^2,-1*K.1,K.1^3,-1*K.1^3,K.1,-1*K.1^3,-1*K.1,-1*K.1^3,-1*K.1^3,K.1,K.1,-1*K.1,K.1^3,-1*K.1,K.1^3,K.1,K.1^3,1,1,1,-1,-1,-1,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,K.1,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1^3,-1*K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,K.1^2,-1*K.1^2,K.1^2,K.1^2,K.1^2,-1,-1*K.1^2,-1,-1*K.1^2,1,1,-1*K.1^2,K.1^3,-1*K.1,K.1,-1*K.1^3,K.1,K.1^3,K.1,K.1,-1*K.1^3,-1*K.1^3,K.1^3,-1*K.1,K.1^3,-1*K.1,-1*K.1^3,-1*K.1,1,1,1,-1,-1,-1,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^3,-1*K.1,K.1,-1*K.1,K.1,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,-1*K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,-1*K.1^2,K.1^2,-1*K.1^2,-1*K.1^2,-1*K.1^2,-1,K.1^2,-1,K.1^2,1,1,K.1^2,K.1,-1*K.1^3,K.1^3,-1*K.1,K.1^3,K.1,K.1^3,K.1^3,-1*K.1,-1*K.1,K.1,-1*K.1^3,K.1,-1*K.1^3,-1*K.1,-1*K.1^3,1,1,1,-1,-1,-1,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,-1*K.1,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1^3,K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,K.1^2,-1*K.1^2,K.1^2,K.1^2,K.1^2,-1,-1*K.1^2,-1,-1*K.1^2,1,1,-1*K.1^2,-1*K.1^3,K.1,-1*K.1,K.1^3,-1*K.1,-1*K.1^3,-1*K.1,-1*K.1,K.1^3,K.1^3,-1*K.1^3,K.1,-1*K.1^3,K.1,K.1^3,K.1,1,1,1,-1,-1,-1,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,K.1^3,K.1,-1*K.1,K.1,-1*K.1,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,K.1^2,1,-1*K.1^2,1,K.1^2,-1,-1,-1*K.1^2,-1*K.1,K.1^3,-1*K.1^3,K.1,-1*K.1^3,-1*K.1,K.1^3,K.1^3,-1*K.1,-1*K.1,K.1,-1*K.1^3,K.1,-1*K.1^3,K.1,K.1^3,1,1,1,-1,-1,-1,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,K.1,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1^3,-1*K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,1,K.1^2,1,-1*K.1^2,-1,-1,K.1^2,K.1^3,-1*K.1,K.1,-1*K.1^3,K.1,K.1^3,-1*K.1,-1*K.1,K.1^3,K.1^3,-1*K.1^3,K.1,-1*K.1^3,K.1,-1*K.1^3,-1*K.1,1,1,1,-1,-1,-1,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^3,-1*K.1,K.1,-1*K.1,K.1,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,-1*K.1,K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,K.1^2,1,-1*K.1^2,1,K.1^2,-1,-1,-1*K.1^2,K.1,-1*K.1^3,K.1^3,-1*K.1,K.1^3,K.1,-1*K.1^3,-1*K.1^3,K.1,K.1,-1*K.1,K.1^3,-1*K.1,K.1^3,-1*K.1,-1*K.1^3,1,1,1,-1,-1,-1,-1*K.1^2,K.1^2,K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,-1*K.1,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1^3,K.1^3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |1,-1,1,-1,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,1,K.1^2,1,-1*K.1^2,-1,-1,K.1^2,-1*K.1^3,K.1,-1*K.1,K.1^3,-1*K.1,-1*K.1^3,K.1,K.1,-1*K.1^3,-1*K.1^3,K.1^3,-1*K.1,K.1^3,-1*K.1,K.1^3,K.1,1,1,1,-1,-1,-1,K.1^2,-1*K.1^2,-1*K.1^2,K.1^2,-1*K.1^2,K.1^2,K.1^3,K.1,-1*K.1,K.1,-1*K.1,-1*K.1^3,K.1^3,-1*K.1^3,K.1^3,-1*K.1^3,K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(13: Sparse := true);
S := [ K |4,4,0,0,4,4,0,0,0,0,0,0,0,0,0,0,4,4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1,K.1+K.1^5+K.1^-5+K.1^-1,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1+K.1^5+K.1^-5+K.1^-1,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(13: Sparse := true);
S := [ K |4,4,0,0,4,4,0,0,0,0,0,0,0,0,0,0,4,4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1+K.1^5+K.1^-5+K.1^-1,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1+K.1^5+K.1^-5+K.1^-1,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(13: Sparse := true);
S := [ K |4,4,0,0,4,4,0,0,0,0,0,0,0,0,0,0,4,4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1+K.1^5+K.1^-5+K.1^-1,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1+K.1^5+K.1^-5+K.1^-1,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(13: Sparse := true);
S := [ K |4,4,0,0,4,4,0,0,0,0,0,0,0,0,0,0,-4,-4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1,K.1+K.1^5+K.1^-5+K.1^-1,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^4+K.1^6+K.1^-6+K.1^-4,-1*K.1-K.1^5-K.1^-5-K.1^-1,-1*K.1-K.1^5-K.1^-5-K.1^-1,-1*K.1^2-K.1^3-K.1^-3-K.1^-2,-1*K.1^4-K.1^6-K.1^-6-K.1^-4,-1*K.1-K.1^5-K.1^-5-K.1^-1,-1*K.1^4-K.1^6-K.1^-6-K.1^-4,-1*K.1^2-K.1^3-K.1^-3-K.1^-2,-1*K.1-K.1^5-K.1^-5-K.1^-1,-1*K.1^4-K.1^6-K.1^-6-K.1^-4,-1*K.1^2-K.1^3-K.1^-3-K.1^-2,-1*K.1^2-K.1^3-K.1^-3-K.1^-2,-1*K.1^4-K.1^6-K.1^-6-K.1^-4]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(13: Sparse := true);
S := [ K |4,4,0,0,4,4,0,0,0,0,0,0,0,0,0,0,-4,-4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1,K.1+K.1^5+K.1^-5+K.1^-1,-1*K.1^2-K.1^3-K.1^-3-K.1^-2,-1*K.1^2-K.1^3-K.1^-3-K.1^-2,-1*K.1^4-K.1^6-K.1^-6-K.1^-4,-1*K.1-K.1^5-K.1^-5-K.1^-1,-1*K.1^2-K.1^3-K.1^-3-K.1^-2,-1*K.1-K.1^5-K.1^-5-K.1^-1,-1*K.1^4-K.1^6-K.1^-6-K.1^-4,-1*K.1^2-K.1^3-K.1^-3-K.1^-2,-1*K.1-K.1^5-K.1^-5-K.1^-1,-1*K.1^4-K.1^6-K.1^-6-K.1^-4,-1*K.1^4-K.1^6-K.1^-6-K.1^-4,-1*K.1-K.1^5-K.1^-5-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(13: Sparse := true);
S := [ K |4,4,0,0,4,4,0,0,0,0,0,0,0,0,0,0,-4,-4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1^4+K.1^6+K.1^-6+K.1^-4,K.1+K.1^5+K.1^-5+K.1^-1,K.1+K.1^5+K.1^-5+K.1^-1,K.1^2+K.1^3+K.1^-3+K.1^-2,K.1^2+K.1^3+K.1^-3+K.1^-2,-1*K.1^4-K.1^6-K.1^-6-K.1^-4,-1*K.1^4-K.1^6-K.1^-6-K.1^-4,-1*K.1-K.1^5-K.1^-5-K.1^-1,-1*K.1^2-K.1^3-K.1^-3-K.1^-2,-1*K.1^4-K.1^6-K.1^-6-K.1^-4,-1*K.1^2-K.1^3-K.1^-3-K.1^-2,-1*K.1-K.1^5-K.1^-5-K.1^-1,-1*K.1^4-K.1^6-K.1^-6-K.1^-4,-1*K.1^2-K.1^3-K.1^-3-K.1^-2,-1*K.1-K.1^5-K.1^-5-K.1^-1,-1*K.1-K.1^5-K.1^-5-K.1^-1,-1*K.1^2-K.1^3-K.1^-3-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(52: Sparse := true);
S := [ K |4,4,0,0,-4,-4,0,0,0,0,0,0,0,0,0,0,-4*K.1^13,4*K.1^13,4*K.1^13,-4*K.1^13,0,0,0,0,0,0,0,0,0,0,0,0,-1-K.1^4+K.1^6-K.1^8-K.1^12+K.1^14+K.1^18-K.1^20+K.1^22,K.1^4-K.1^6+K.1^20-K.1^22,K.1^8+K.1^12-K.1^14-K.1^18,K.1^8+K.1^12-K.1^14-K.1^18,-1-K.1^4+K.1^6-K.1^8-K.1^12+K.1^14+K.1^18-K.1^20+K.1^22,K.1^4-K.1^6+K.1^20-K.1^22,-1*K.1^4+K.1^6-K.1^20+K.1^22,-1*K.1^4+K.1^6-K.1^20+K.1^22,-1*K.1^8-K.1^12+K.1^14+K.1^18,-1*K.1^8-K.1^12+K.1^14+K.1^18,1+K.1^4-K.1^6+K.1^8+K.1^12-K.1^14-K.1^18+K.1^20-K.1^22,1+K.1^4-K.1^6+K.1^8+K.1^12-K.1^14-K.1^18+K.1^20-K.1^22,K.1^7-K.1^9-K.1^17+K.1^19,-1*K.1^7+K.1^9+K.1^17-K.1^19,K.1^3+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19+K.1^23,-1*K.1^3-K.1^11-K.1^15-K.1^23,-1*K.1^7+K.1^9+K.1^17-K.1^19,K.1^3+K.1^11+K.1^15+K.1^23,-1*K.1^3-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19-K.1^23,K.1^7-K.1^9-K.1^17+K.1^19,K.1^3+K.1^11+K.1^15+K.1^23,-1*K.1^3-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19-K.1^23,K.1^3+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19+K.1^23,-1*K.1^3-K.1^11-K.1^15-K.1^23]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(52: Sparse := true);
S := [ K |4,4,0,0,-4,-4,0,0,0,0,0,0,0,0,0,0,4*K.1^13,-4*K.1^13,-4*K.1^13,4*K.1^13,0,0,0,0,0,0,0,0,0,0,0,0,-1-K.1^4+K.1^6-K.1^8-K.1^12+K.1^14+K.1^18-K.1^20+K.1^22,K.1^4-K.1^6+K.1^20-K.1^22,K.1^8+K.1^12-K.1^14-K.1^18,K.1^8+K.1^12-K.1^14-K.1^18,-1-K.1^4+K.1^6-K.1^8-K.1^12+K.1^14+K.1^18-K.1^20+K.1^22,K.1^4-K.1^6+K.1^20-K.1^22,-1*K.1^4+K.1^6-K.1^20+K.1^22,-1*K.1^4+K.1^6-K.1^20+K.1^22,-1*K.1^8-K.1^12+K.1^14+K.1^18,-1*K.1^8-K.1^12+K.1^14+K.1^18,1+K.1^4-K.1^6+K.1^8+K.1^12-K.1^14-K.1^18+K.1^20-K.1^22,1+K.1^4-K.1^6+K.1^8+K.1^12-K.1^14-K.1^18+K.1^20-K.1^22,-1*K.1^7+K.1^9+K.1^17-K.1^19,K.1^7-K.1^9-K.1^17+K.1^19,-1*K.1^3-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19-K.1^23,K.1^3+K.1^11+K.1^15+K.1^23,K.1^7-K.1^9-K.1^17+K.1^19,-1*K.1^3-K.1^11-K.1^15-K.1^23,K.1^3+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19+K.1^23,-1*K.1^7+K.1^9+K.1^17-K.1^19,-1*K.1^3-K.1^11-K.1^15-K.1^23,K.1^3+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19+K.1^23,-1*K.1^3-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19-K.1^23,K.1^3+K.1^11+K.1^15+K.1^23]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(52: Sparse := true);
S := [ K |4,4,0,0,-4,-4,0,0,0,0,0,0,0,0,0,0,-4*K.1^13,4*K.1^13,4*K.1^13,-4*K.1^13,0,0,0,0,0,0,0,0,0,0,0,0,K.1^4-K.1^6+K.1^20-K.1^22,K.1^8+K.1^12-K.1^14-K.1^18,-1-K.1^4+K.1^6-K.1^8-K.1^12+K.1^14+K.1^18-K.1^20+K.1^22,-1-K.1^4+K.1^6-K.1^8-K.1^12+K.1^14+K.1^18-K.1^20+K.1^22,K.1^4-K.1^6+K.1^20-K.1^22,K.1^8+K.1^12-K.1^14-K.1^18,-1*K.1^8-K.1^12+K.1^14+K.1^18,-1*K.1^8-K.1^12+K.1^14+K.1^18,1+K.1^4-K.1^6+K.1^8+K.1^12-K.1^14-K.1^18+K.1^20-K.1^22,1+K.1^4-K.1^6+K.1^8+K.1^12-K.1^14-K.1^18+K.1^20-K.1^22,-1*K.1^4+K.1^6-K.1^20+K.1^22,-1*K.1^4+K.1^6-K.1^20+K.1^22,-1*K.1^3-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19-K.1^23,K.1^3+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19+K.1^23,-1*K.1^3-K.1^11-K.1^15-K.1^23,-1*K.1^7+K.1^9+K.1^17-K.1^19,K.1^3+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19+K.1^23,K.1^7-K.1^9-K.1^17+K.1^19,K.1^3+K.1^11+K.1^15+K.1^23,-1*K.1^3-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19-K.1^23,K.1^7-K.1^9-K.1^17+K.1^19,K.1^3+K.1^11+K.1^15+K.1^23,-1*K.1^3-K.1^11-K.1^15-K.1^23,-1*K.1^7+K.1^9+K.1^17-K.1^19]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(52: Sparse := true);
S := [ K |4,4,0,0,-4,-4,0,0,0,0,0,0,0,0,0,0,4*K.1^13,-4*K.1^13,-4*K.1^13,4*K.1^13,0,0,0,0,0,0,0,0,0,0,0,0,K.1^4-K.1^6+K.1^20-K.1^22,K.1^8+K.1^12-K.1^14-K.1^18,-1-K.1^4+K.1^6-K.1^8-K.1^12+K.1^14+K.1^18-K.1^20+K.1^22,-1-K.1^4+K.1^6-K.1^8-K.1^12+K.1^14+K.1^18-K.1^20+K.1^22,K.1^4-K.1^6+K.1^20-K.1^22,K.1^8+K.1^12-K.1^14-K.1^18,-1*K.1^8-K.1^12+K.1^14+K.1^18,-1*K.1^8-K.1^12+K.1^14+K.1^18,1+K.1^4-K.1^6+K.1^8+K.1^12-K.1^14-K.1^18+K.1^20-K.1^22,1+K.1^4-K.1^6+K.1^8+K.1^12-K.1^14-K.1^18+K.1^20-K.1^22,-1*K.1^4+K.1^6-K.1^20+K.1^22,-1*K.1^4+K.1^6-K.1^20+K.1^22,K.1^3+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19+K.1^23,-1*K.1^3-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19-K.1^23,K.1^3+K.1^11+K.1^15+K.1^23,K.1^7-K.1^9-K.1^17+K.1^19,-1*K.1^3-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19-K.1^23,-1*K.1^7+K.1^9+K.1^17-K.1^19,-1*K.1^3-K.1^11-K.1^15-K.1^23,K.1^3+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19+K.1^23,-1*K.1^7+K.1^9+K.1^17-K.1^19,-1*K.1^3-K.1^11-K.1^15-K.1^23,K.1^3+K.1^11+K.1^15+K.1^23,K.1^7-K.1^9-K.1^17+K.1^19]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(52: Sparse := true);
S := [ K |4,4,0,0,-4,-4,0,0,0,0,0,0,0,0,0,0,-4*K.1^13,4*K.1^13,4*K.1^13,-4*K.1^13,0,0,0,0,0,0,0,0,0,0,0,0,K.1^8+K.1^12-K.1^14-K.1^18,-1-K.1^4+K.1^6-K.1^8-K.1^12+K.1^14+K.1^18-K.1^20+K.1^22,K.1^4-K.1^6+K.1^20-K.1^22,K.1^4-K.1^6+K.1^20-K.1^22,K.1^8+K.1^12-K.1^14-K.1^18,-1-K.1^4+K.1^6-K.1^8-K.1^12+K.1^14+K.1^18-K.1^20+K.1^22,1+K.1^4-K.1^6+K.1^8+K.1^12-K.1^14-K.1^18+K.1^20-K.1^22,1+K.1^4-K.1^6+K.1^8+K.1^12-K.1^14-K.1^18+K.1^20-K.1^22,-1*K.1^4+K.1^6-K.1^20+K.1^22,-1*K.1^4+K.1^6-K.1^20+K.1^22,-1*K.1^8-K.1^12+K.1^14+K.1^18,-1*K.1^8-K.1^12+K.1^14+K.1^18,K.1^3+K.1^11+K.1^15+K.1^23,-1*K.1^3-K.1^11-K.1^15-K.1^23,-1*K.1^7+K.1^9+K.1^17-K.1^19,K.1^3+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19+K.1^23,-1*K.1^3-K.1^11-K.1^15-K.1^23,-1*K.1^3-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19-K.1^23,K.1^7-K.1^9-K.1^17+K.1^19,K.1^3+K.1^11+K.1^15+K.1^23,-1*K.1^3-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19-K.1^23,K.1^7-K.1^9-K.1^17+K.1^19,-1*K.1^7+K.1^9+K.1^17-K.1^19,K.1^3+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19+K.1^23]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(52: Sparse := true);
S := [ K |4,4,0,0,-4,-4,0,0,0,0,0,0,0,0,0,0,4*K.1^13,-4*K.1^13,-4*K.1^13,4*K.1^13,0,0,0,0,0,0,0,0,0,0,0,0,K.1^8+K.1^12-K.1^14-K.1^18,-1-K.1^4+K.1^6-K.1^8-K.1^12+K.1^14+K.1^18-K.1^20+K.1^22,K.1^4-K.1^6+K.1^20-K.1^22,K.1^4-K.1^6+K.1^20-K.1^22,K.1^8+K.1^12-K.1^14-K.1^18,-1-K.1^4+K.1^6-K.1^8-K.1^12+K.1^14+K.1^18-K.1^20+K.1^22,1+K.1^4-K.1^6+K.1^8+K.1^12-K.1^14-K.1^18+K.1^20-K.1^22,1+K.1^4-K.1^6+K.1^8+K.1^12-K.1^14-K.1^18+K.1^20-K.1^22,-1*K.1^4+K.1^6-K.1^20+K.1^22,-1*K.1^4+K.1^6-K.1^20+K.1^22,-1*K.1^8-K.1^12+K.1^14+K.1^18,-1*K.1^8-K.1^12+K.1^14+K.1^18,-1*K.1^3-K.1^11-K.1^15-K.1^23,K.1^3+K.1^11+K.1^15+K.1^23,K.1^7-K.1^9-K.1^17+K.1^19,-1*K.1^3-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19-K.1^23,K.1^3+K.1^11+K.1^15+K.1^23,K.1^3+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19+K.1^23,-1*K.1^7+K.1^9+K.1^17-K.1^19,-1*K.1^3-K.1^11-K.1^15-K.1^23,K.1^3+K.1^7-K.1^9+K.1^11-K.1^13+K.1^15-K.1^17+K.1^19+K.1^23,-1*K.1^7+K.1^9+K.1^17-K.1^19,K.1^7-K.1^9-K.1^17+K.1^19,-1*K.1^3-K.1^7+K.1^9-K.1^11+K.1^13-K.1^15+K.1^17-K.1^19-K.1^23]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(104: Sparse := true);
S := [ K |4,-4,0,0,-4*K.1^26,4*K.1^26,0,0,0,0,0,0,0,0,0,0,-4*K.1^13,4*K.1^39,-4*K.1^39,4*K.1^13,0,0,0,0,0,0,0,0,0,0,0,0,-1-K.1^8+K.1^12-K.1^16-K.1^24+K.1^28+K.1^36-K.1^40+K.1^44,K.1^8-K.1^12+K.1^40-K.1^44,K.1^16+K.1^24-K.1^28-K.1^36,-1*K.1^16-K.1^24+K.1^28+K.1^36,1+K.1^8-K.1^12+K.1^16+K.1^24-K.1^28-K.1^36+K.1^40-K.1^44,-1*K.1^8+K.1^12-K.1^40+K.1^44,K.1^14-K.1^18-K.1^34+K.1^38,-1*K.1^14+K.1^18+K.1^34-K.1^38,K.1^6+K.1^14-K.1^18+K.1^22-K.1^26+K.1^30-K.1^34+K.1^38+K.1^46,-1*K.1^6-K.1^14+K.1^18-K.1^22+K.1^26-K.1^30+K.1^34-K.1^38-K.1^46,-1*K.1^6-K.1^22-K.1^30-K.1^46,K.1^6+K.1^22+K.1^30+K.1^46,-1*K.1+K.1^5+K.1^21-K.1^25,K.1^3-K.1^7+K.1^11-K.1^15+K.1^19-K.1^23+K.1^35-K.1^39+K.1^43,K.1^3+K.1^11-K.1^15-K.1^23,K.1^7-K.1^19-K.1^35-K.1^43,-1*K.1^3+K.1^7-K.1^11+K.1^15-K.1^19+K.1^23-K.1^35+K.1^39-K.1^43,K.1^9+K.1^17+K.1^33-K.1^45,K.1-K.1^5+K.1^9-K.1^13+K.1^17-K.1^21+K.1^25+K.1^33-K.1^45,K.1-K.1^5-K.1^21+K.1^25,-1*K.1^9-K.1^17-K.1^33+K.1^45,-1*K.1+K.1^5-K.1^9+K.1^13-K.1^17+K.1^21-K.1^25-K.1^33+K.1^45,-1*K.1^3-K.1^11+K.1^15+K.1^23,-1*K.1^7+K.1^19+K.1^35+K.1^43]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(104: Sparse := true);
S := [ K |4,-4,0,0,4*K.1^26,-4*K.1^26,0,0,0,0,0,0,0,0,0,0,4*K.1^39,-4*K.1^13,4*K.1^13,-4*K.1^39,0,0,0,0,0,0,0,0,0,0,0,0,-1-K.1^8+K.1^12-K.1^16-K.1^24+K.1^28+K.1^36-K.1^40+K.1^44,K.1^8-K.1^12+K.1^40-K.1^44,K.1^16+K.1^24-K.1^28-K.1^36,-1*K.1^16-K.1^24+K.1^28+K.1^36,1+K.1^8-K.1^12+K.1^16+K.1^24-K.1^28-K.1^36+K.1^40-K.1^44,-1*K.1^8+K.1^12-K.1^40+K.1^44,-1*K.1^14+K.1^18+K.1^34-K.1^38,K.1^14-K.1^18-K.1^34+K.1^38,-1*K.1^6-K.1^14+K.1^18-K.1^22+K.1^26-K.1^30+K.1^34-K.1^38-K.1^46,K.1^6+K.1^14-K.1^18+K.1^22-K.1^26+K.1^30-K.1^34+K.1^38+K.1^46,K.1^6+K.1^22+K.1^30+K.1^46,-1*K.1^6-K.1^22-K.1^30-K.1^46,-1*K.1^3+K.1^7-K.1^11+K.1^15-K.1^19+K.1^23-K.1^35+K.1^39-K.1^43,K.1-K.1^5-K.1^21+K.1^25,K.1-K.1^5+K.1^9-K.1^13+K.1^17-K.1^21+K.1^25+K.1^33-K.1^45,K.1^9+K.1^17+K.1^33-K.1^45,-1*K.1+K.1^5+K.1^21-K.1^25,K.1^7-K.1^19-K.1^35-K.1^43,K.1^3+K.1^11-K.1^15-K.1^23,K.1^3-K.1^7+K.1^11-K.1^15+K.1^19-K.1^23+K.1^35-K.1^39+K.1^43,-1*K.1^7+K.1^19+K.1^35+K.1^43,-1*K.1^3-K.1^11+K.1^15+K.1^23,-1*K.1+K.1^5-K.1^9+K.1^13-K.1^17+K.1^21-K.1^25-K.1^33+K.1^45,-1*K.1^9-K.1^17-K.1^33+K.1^45]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(104: Sparse := true);
S := [ K |4,-4,0,0,-4*K.1^26,4*K.1^26,0,0,0,0,0,0,0,0,0,0,-4*K.1^13,4*K.1^39,-4*K.1^39,4*K.1^13,0,0,0,0,0,0,0,0,0,0,0,0,K.1^8-K.1^12+K.1^40-K.1^44,K.1^16+K.1^24-K.1^28-K.1^36,-1-K.1^8+K.1^12-K.1^16-K.1^24+K.1^28+K.1^36-K.1^40+K.1^44,1+K.1^8-K.1^12+K.1^16+K.1^24-K.1^28-K.1^36+K.1^40-K.1^44,-1*K.1^8+K.1^12-K.1^40+K.1^44,-1*K.1^16-K.1^24+K.1^28+K.1^36,-1*K.1^6-K.1^14+K.1^18-K.1^22+K.1^26-K.1^30+K.1^34-K.1^38-K.1^46,K.1^6+K.1^14-K.1^18+K.1^22-K.1^26+K.1^30-K.1^34+K.1^38+K.1^46,-1*K.1^6-K.1^22-K.1^30-K.1^46,K.1^6+K.1^22+K.1^30+K.1^46,-1*K.1^14+K.1^18+K.1^34-K.1^38,K.1^14-K.1^18-K.1^34+K.1^38,K.1-K.1^5+K.1^9-K.1^13+K.1^17-K.1^21+K.1^25+K.1^33-K.1^45,-1*K.1^3-K.1^11+K.1^15+K.1^23,-1*K.1^7+K.1^19+K.1^35+K.1^43,K.1^3-K.1^7+K.1^11-K.1^15+K.1^19-K.1^23+K.1^35-K.1^39+K.1^43,K.1^3+K.1^11-K.1^15-K.1^23,K.1-K.1^5-K.1^21+K.1^25,-1*K.1^9-K.1^17-K.1^33+K.1^45,-1*K.1+K.1^5-K.1^9+K.1^13-K.1^17+K.1^21-K.1^25-K.1^33+K.1^45,-1*K.1+K.1^5+K.1^21-K.1^25,K.1^9+K.1^17+K.1^33-K.1^45,K.1^7-K.1^19-K.1^35-K.1^43,-1*K.1^3+K.1^7-K.1^11+K.1^15-K.1^19+K.1^23-K.1^35+K.1^39-K.1^43]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(104: Sparse := true);
S := [ K |4,-4,0,0,4*K.1^26,-4*K.1^26,0,0,0,0,0,0,0,0,0,0,4*K.1^39,-4*K.1^13,4*K.1^13,-4*K.1^39,0,0,0,0,0,0,0,0,0,0,0,0,K.1^8-K.1^12+K.1^40-K.1^44,K.1^16+K.1^24-K.1^28-K.1^36,-1-K.1^8+K.1^12-K.1^16-K.1^24+K.1^28+K.1^36-K.1^40+K.1^44,1+K.1^8-K.1^12+K.1^16+K.1^24-K.1^28-K.1^36+K.1^40-K.1^44,-1*K.1^8+K.1^12-K.1^40+K.1^44,-1*K.1^16-K.1^24+K.1^28+K.1^36,K.1^6+K.1^14-K.1^18+K.1^22-K.1^26+K.1^30-K.1^34+K.1^38+K.1^46,-1*K.1^6-K.1^14+K.1^18-K.1^22+K.1^26-K.1^30+K.1^34-K.1^38-K.1^46,K.1^6+K.1^22+K.1^30+K.1^46,-1*K.1^6-K.1^22-K.1^30-K.1^46,K.1^14-K.1^18-K.1^34+K.1^38,-1*K.1^14+K.1^18+K.1^34-K.1^38,K.1^3+K.1^11-K.1^15-K.1^23,-1*K.1+K.1^5-K.1^9+K.1^13-K.1^17+K.1^21-K.1^25-K.1^33+K.1^45,-1*K.1^9-K.1^17-K.1^33+K.1^45,K.1-K.1^5-K.1^21+K.1^25,K.1-K.1^5+K.1^9-K.1^13+K.1^17-K.1^21+K.1^25+K.1^33-K.1^45,K.1^3-K.1^7+K.1^11-K.1^15+K.1^19-K.1^23+K.1^35-K.1^39+K.1^43,-1*K.1^7+K.1^19+K.1^35+K.1^43,-1*K.1^3-K.1^11+K.1^15+K.1^23,-1*K.1^3+K.1^7-K.1^11+K.1^15-K.1^19+K.1^23-K.1^35+K.1^39-K.1^43,K.1^7-K.1^19-K.1^35-K.1^43,K.1^9+K.1^17+K.1^33-K.1^45,-1*K.1+K.1^5+K.1^21-K.1^25]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(104: Sparse := true);
S := [ K |4,-4,0,0,-4*K.1^26,4*K.1^26,0,0,0,0,0,0,0,0,0,0,-4*K.1^13,4*K.1^39,-4*K.1^39,4*K.1^13,0,0,0,0,0,0,0,0,0,0,0,0,K.1^16+K.1^24-K.1^28-K.1^36,-1-K.1^8+K.1^12-K.1^16-K.1^24+K.1^28+K.1^36-K.1^40+K.1^44,K.1^8-K.1^12+K.1^40-K.1^44,-1*K.1^8+K.1^12-K.1^40+K.1^44,-1*K.1^16-K.1^24+K.1^28+K.1^36,1+K.1^8-K.1^12+K.1^16+K.1^24-K.1^28-K.1^36+K.1^40-K.1^44,K.1^6+K.1^22+K.1^30+K.1^46,-1*K.1^6-K.1^22-K.1^30-K.1^46,-1*K.1^14+K.1^18+K.1^34-K.1^38,K.1^14-K.1^18-K.1^34+K.1^38,K.1^6+K.1^14-K.1^18+K.1^22-K.1^26+K.1^30-K.1^34+K.1^38+K.1^46,-1*K.1^6-K.1^14+K.1^18-K.1^22+K.1^26-K.1^30+K.1^34-K.1^38-K.1^46,-1*K.1^9-K.1^17-K.1^33+K.1^45,K.1^7-K.1^19-K.1^35-K.1^43,-1*K.1^3+K.1^7-K.1^11+K.1^15-K.1^19+K.1^23-K.1^35+K.1^39-K.1^43,-1*K.1^3-K.1^11+K.1^15+K.1^23,-1*K.1^7+K.1^19+K.1^35+K.1^43,-1*K.1+K.1^5-K.1^9+K.1^13-K.1^17+K.1^21-K.1^25-K.1^33+K.1^45,-1*K.1+K.1^5+K.1^21-K.1^25,K.1^9+K.1^17+K.1^33-K.1^45,K.1-K.1^5+K.1^9-K.1^13+K.1^17-K.1^21+K.1^25+K.1^33-K.1^45,K.1-K.1^5-K.1^21+K.1^25,K.1^3-K.1^7+K.1^11-K.1^15+K.1^19-K.1^23+K.1^35-K.1^39+K.1^43,K.1^3+K.1^11-K.1^15-K.1^23]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(104: Sparse := true);
S := [ K |4,-4,0,0,4*K.1^26,-4*K.1^26,0,0,0,0,0,0,0,0,0,0,4*K.1^39,-4*K.1^13,4*K.1^13,-4*K.1^39,0,0,0,0,0,0,0,0,0,0,0,0,K.1^16+K.1^24-K.1^28-K.1^36,-1-K.1^8+K.1^12-K.1^16-K.1^24+K.1^28+K.1^36-K.1^40+K.1^44,K.1^8-K.1^12+K.1^40-K.1^44,-1*K.1^8+K.1^12-K.1^40+K.1^44,-1*K.1^16-K.1^24+K.1^28+K.1^36,1+K.1^8-K.1^12+K.1^16+K.1^24-K.1^28-K.1^36+K.1^40-K.1^44,-1*K.1^6-K.1^22-K.1^30-K.1^46,K.1^6+K.1^22+K.1^30+K.1^46,K.1^14-K.1^18-K.1^34+K.1^38,-1*K.1^14+K.1^18+K.1^34-K.1^38,-1*K.1^6-K.1^14+K.1^18-K.1^22+K.1^26-K.1^30+K.1^34-K.1^38-K.1^46,K.1^6+K.1^14-K.1^18+K.1^22-K.1^26+K.1^30-K.1^34+K.1^38+K.1^46,-1*K.1^7+K.1^19+K.1^35+K.1^43,K.1^9+K.1^17+K.1^33-K.1^45,-1*K.1+K.1^5+K.1^21-K.1^25,-1*K.1+K.1^5-K.1^9+K.1^13-K.1^17+K.1^21-K.1^25-K.1^33+K.1^45,-1*K.1^9-K.1^17-K.1^33+K.1^45,-1*K.1^3-K.1^11+K.1^15+K.1^23,-1*K.1^3+K.1^7-K.1^11+K.1^15-K.1^19+K.1^23-K.1^35+K.1^39-K.1^43,K.1^7-K.1^19-K.1^35-K.1^43,K.1^3+K.1^11-K.1^15-K.1^23,K.1^3-K.1^7+K.1^11-K.1^15+K.1^19-K.1^23+K.1^35-K.1^39+K.1^43,K.1-K.1^5-K.1^21+K.1^25,K.1-K.1^5+K.1^9-K.1^13+K.1^17-K.1^21+K.1^25+K.1^33-K.1^45]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(104: Sparse := true);
S := [ K |4,-4,0,0,-4*K.1^26,4*K.1^26,0,0,0,0,0,0,0,0,0,0,4*K.1^13,-4*K.1^39,4*K.1^39,-4*K.1^13,0,0,0,0,0,0,0,0,0,0,0,0,-1-K.1^8+K.1^12-K.1^16-K.1^24+K.1^28+K.1^36-K.1^40+K.1^44,K.1^8-K.1^12+K.1^40-K.1^44,K.1^16+K.1^24-K.1^28-K.1^36,-1*K.1^16-K.1^24+K.1^28+K.1^36,1+K.1^8-K.1^12+K.1^16+K.1^24-K.1^28-K.1^36+K.1^40-K.1^44,-1*K.1^8+K.1^12-K.1^40+K.1^44,K.1^14-K.1^18-K.1^34+K.1^38,-1*K.1^14+K.1^18+K.1^34-K.1^38,K.1^6+K.1^14-K.1^18+K.1^22-K.1^26+K.1^30-K.1^34+K.1^38+K.1^46,-1*K.1^6-K.1^14+K.1^18-K.1^22+K.1^26-K.1^30+K.1^34-K.1^38-K.1^46,-1*K.1^6-K.1^22-K.1^30-K.1^46,K.1^6+K.1^22+K.1^30+K.1^46,K.1-K.1^5-K.1^21+K.1^25,-1*K.1^3+K.1^7-K.1^11+K.1^15-K.1^19+K.1^23-K.1^35+K.1^39-K.1^43,-1*K.1^3-K.1^11+K.1^15+K.1^23,-1*K.1^7+K.1^19+K.1^35+K.1^43,K.1^3-K.1^7+K.1^11-K.1^15+K.1^19-K.1^23+K.1^35-K.1^39+K.1^43,-1*K.1^9-K.1^17-K.1^33+K.1^45,-1*K.1+K.1^5-K.1^9+K.1^13-K.1^17+K.1^21-K.1^25-K.1^33+K.1^45,-1*K.1+K.1^5+K.1^21-K.1^25,K.1^9+K.1^17+K.1^33-K.1^45,K.1-K.1^5+K.1^9-K.1^13+K.1^17-K.1^21+K.1^25+K.1^33-K.1^45,K.1^3+K.1^11-K.1^15-K.1^23,K.1^7-K.1^19-K.1^35-K.1^43]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(104: Sparse := true);
S := [ K |4,-4,0,0,4*K.1^26,-4*K.1^26,0,0,0,0,0,0,0,0,0,0,-4*K.1^39,4*K.1^13,-4*K.1^13,4*K.1^39,0,0,0,0,0,0,0,0,0,0,0,0,-1-K.1^8+K.1^12-K.1^16-K.1^24+K.1^28+K.1^36-K.1^40+K.1^44,K.1^8-K.1^12+K.1^40-K.1^44,K.1^16+K.1^24-K.1^28-K.1^36,-1*K.1^16-K.1^24+K.1^28+K.1^36,1+K.1^8-K.1^12+K.1^16+K.1^24-K.1^28-K.1^36+K.1^40-K.1^44,-1*K.1^8+K.1^12-K.1^40+K.1^44,-1*K.1^14+K.1^18+K.1^34-K.1^38,K.1^14-K.1^18-K.1^34+K.1^38,-1*K.1^6-K.1^14+K.1^18-K.1^22+K.1^26-K.1^30+K.1^34-K.1^38-K.1^46,K.1^6+K.1^14-K.1^18+K.1^22-K.1^26+K.1^30-K.1^34+K.1^38+K.1^46,K.1^6+K.1^22+K.1^30+K.1^46,-1*K.1^6-K.1^22-K.1^30-K.1^46,K.1^3-K.1^7+K.1^11-K.1^15+K.1^19-K.1^23+K.1^35-K.1^39+K.1^43,-1*K.1+K.1^5+K.1^21-K.1^25,-1*K.1+K.1^5-K.1^9+K.1^13-K.1^17+K.1^21-K.1^25-K.1^33+K.1^45,-1*K.1^9-K.1^17-K.1^33+K.1^45,K.1-K.1^5-K.1^21+K.1^25,-1*K.1^7+K.1^19+K.1^35+K.1^43,-1*K.1^3-K.1^11+K.1^15+K.1^23,-1*K.1^3+K.1^7-K.1^11+K.1^15-K.1^19+K.1^23-K.1^35+K.1^39-K.1^43,K.1^7-K.1^19-K.1^35-K.1^43,K.1^3+K.1^11-K.1^15-K.1^23,K.1-K.1^5+K.1^9-K.1^13+K.1^17-K.1^21+K.1^25+K.1^33-K.1^45,K.1^9+K.1^17+K.1^33-K.1^45]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(104: Sparse := true);
S := [ K |4,-4,0,0,-4*K.1^26,4*K.1^26,0,0,0,0,0,0,0,0,0,0,4*K.1^13,-4*K.1^39,4*K.1^39,-4*K.1^13,0,0,0,0,0,0,0,0,0,0,0,0,K.1^8-K.1^12+K.1^40-K.1^44,K.1^16+K.1^24-K.1^28-K.1^36,-1-K.1^8+K.1^12-K.1^16-K.1^24+K.1^28+K.1^36-K.1^40+K.1^44,1+K.1^8-K.1^12+K.1^16+K.1^24-K.1^28-K.1^36+K.1^40-K.1^44,-1*K.1^8+K.1^12-K.1^40+K.1^44,-1*K.1^16-K.1^24+K.1^28+K.1^36,-1*K.1^6-K.1^14+K.1^18-K.1^22+K.1^26-K.1^30+K.1^34-K.1^38-K.1^46,K.1^6+K.1^14-K.1^18+K.1^22-K.1^26+K.1^30-K.1^34+K.1^38+K.1^46,-1*K.1^6-K.1^22-K.1^30-K.1^46,K.1^6+K.1^22+K.1^30+K.1^46,-1*K.1^14+K.1^18+K.1^34-K.1^38,K.1^14-K.1^18-K.1^34+K.1^38,-1*K.1+K.1^5-K.1^9+K.1^13-K.1^17+K.1^21-K.1^25-K.1^33+K.1^45,K.1^3+K.1^11-K.1^15-K.1^23,K.1^7-K.1^19-K.1^35-K.1^43,-1*K.1^3+K.1^7-K.1^11+K.1^15-K.1^19+K.1^23-K.1^35+K.1^39-K.1^43,-1*K.1^3-K.1^11+K.1^15+K.1^23,-1*K.1+K.1^5+K.1^21-K.1^25,K.1^9+K.1^17+K.1^33-K.1^45,K.1-K.1^5+K.1^9-K.1^13+K.1^17-K.1^21+K.1^25+K.1^33-K.1^45,K.1-K.1^5-K.1^21+K.1^25,-1*K.1^9-K.1^17-K.1^33+K.1^45,-1*K.1^7+K.1^19+K.1^35+K.1^43,K.1^3-K.1^7+K.1^11-K.1^15+K.1^19-K.1^23+K.1^35-K.1^39+K.1^43]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(104: Sparse := true);
S := [ K |4,-4,0,0,4*K.1^26,-4*K.1^26,0,0,0,0,0,0,0,0,0,0,-4*K.1^39,4*K.1^13,-4*K.1^13,4*K.1^39,0,0,0,0,0,0,0,0,0,0,0,0,K.1^8-K.1^12+K.1^40-K.1^44,K.1^16+K.1^24-K.1^28-K.1^36,-1-K.1^8+K.1^12-K.1^16-K.1^24+K.1^28+K.1^36-K.1^40+K.1^44,1+K.1^8-K.1^12+K.1^16+K.1^24-K.1^28-K.1^36+K.1^40-K.1^44,-1*K.1^8+K.1^12-K.1^40+K.1^44,-1*K.1^16-K.1^24+K.1^28+K.1^36,K.1^6+K.1^14-K.1^18+K.1^22-K.1^26+K.1^30-K.1^34+K.1^38+K.1^46,-1*K.1^6-K.1^14+K.1^18-K.1^22+K.1^26-K.1^30+K.1^34-K.1^38-K.1^46,K.1^6+K.1^22+K.1^30+K.1^46,-1*K.1^6-K.1^22-K.1^30-K.1^46,K.1^14-K.1^18-K.1^34+K.1^38,-1*K.1^14+K.1^18+K.1^34-K.1^38,-1*K.1^3-K.1^11+K.1^15+K.1^23,K.1-K.1^5+K.1^9-K.1^13+K.1^17-K.1^21+K.1^25+K.1^33-K.1^45,K.1^9+K.1^17+K.1^33-K.1^45,-1*K.1+K.1^5+K.1^21-K.1^25,-1*K.1+K.1^5-K.1^9+K.1^13-K.1^17+K.1^21-K.1^25-K.1^33+K.1^45,-1*K.1^3+K.1^7-K.1^11+K.1^15-K.1^19+K.1^23-K.1^35+K.1^39-K.1^43,K.1^7-K.1^19-K.1^35-K.1^43,K.1^3+K.1^11-K.1^15-K.1^23,K.1^3-K.1^7+K.1^11-K.1^15+K.1^19-K.1^23+K.1^35-K.1^39+K.1^43,-1*K.1^7+K.1^19+K.1^35+K.1^43,-1*K.1^9-K.1^17-K.1^33+K.1^45,K.1-K.1^5-K.1^21+K.1^25]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(104: Sparse := true);
S := [ K |4,-4,0,0,-4*K.1^26,4*K.1^26,0,0,0,0,0,0,0,0,0,0,4*K.1^13,-4*K.1^39,4*K.1^39,-4*K.1^13,0,0,0,0,0,0,0,0,0,0,0,0,K.1^16+K.1^24-K.1^28-K.1^36,-1-K.1^8+K.1^12-K.1^16-K.1^24+K.1^28+K.1^36-K.1^40+K.1^44,K.1^8-K.1^12+K.1^40-K.1^44,-1*K.1^8+K.1^12-K.1^40+K.1^44,-1*K.1^16-K.1^24+K.1^28+K.1^36,1+K.1^8-K.1^12+K.1^16+K.1^24-K.1^28-K.1^36+K.1^40-K.1^44,K.1^6+K.1^22+K.1^30+K.1^46,-1*K.1^6-K.1^22-K.1^30-K.1^46,-1*K.1^14+K.1^18+K.1^34-K.1^38,K.1^14-K.1^18-K.1^34+K.1^38,K.1^6+K.1^14-K.1^18+K.1^22-K.1^26+K.1^30-K.1^34+K.1^38+K.1^46,-1*K.1^6-K.1^14+K.1^18-K.1^22+K.1^26-K.1^30+K.1^34-K.1^38-K.1^46,K.1^9+K.1^17+K.1^33-K.1^45,-1*K.1^7+K.1^19+K.1^35+K.1^43,K.1^3-K.1^7+K.1^11-K.1^15+K.1^19-K.1^23+K.1^35-K.1^39+K.1^43,K.1^3+K.1^11-K.1^15-K.1^23,K.1^7-K.1^19-K.1^35-K.1^43,K.1-K.1^5+K.1^9-K.1^13+K.1^17-K.1^21+K.1^25+K.1^33-K.1^45,K.1-K.1^5-K.1^21+K.1^25,-1*K.1^9-K.1^17-K.1^33+K.1^45,-1*K.1+K.1^5-K.1^9+K.1^13-K.1^17+K.1^21-K.1^25-K.1^33+K.1^45,-1*K.1+K.1^5+K.1^21-K.1^25,-1*K.1^3+K.1^7-K.1^11+K.1^15-K.1^19+K.1^23-K.1^35+K.1^39-K.1^43,-1*K.1^3-K.1^11+K.1^15+K.1^23]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(104: Sparse := true);
S := [ K |4,-4,0,0,4*K.1^26,-4*K.1^26,0,0,0,0,0,0,0,0,0,0,-4*K.1^39,4*K.1^13,-4*K.1^13,4*K.1^39,0,0,0,0,0,0,0,0,0,0,0,0,K.1^16+K.1^24-K.1^28-K.1^36,-1-K.1^8+K.1^12-K.1^16-K.1^24+K.1^28+K.1^36-K.1^40+K.1^44,K.1^8-K.1^12+K.1^40-K.1^44,-1*K.1^8+K.1^12-K.1^40+K.1^44,-1*K.1^16-K.1^24+K.1^28+K.1^36,1+K.1^8-K.1^12+K.1^16+K.1^24-K.1^28-K.1^36+K.1^40-K.1^44,-1*K.1^6-K.1^22-K.1^30-K.1^46,K.1^6+K.1^22+K.1^30+K.1^46,K.1^14-K.1^18-K.1^34+K.1^38,-1*K.1^14+K.1^18+K.1^34-K.1^38,-1*K.1^6-K.1^14+K.1^18-K.1^22+K.1^26-K.1^30+K.1^34-K.1^38-K.1^46,K.1^6+K.1^14-K.1^18+K.1^22-K.1^26+K.1^30-K.1^34+K.1^38+K.1^46,K.1^7-K.1^19-K.1^35-K.1^43,-1*K.1^9-K.1^17-K.1^33+K.1^45,K.1-K.1^5-K.1^21+K.1^25,K.1-K.1^5+K.1^9-K.1^13+K.1^17-K.1^21+K.1^25+K.1^33-K.1^45,K.1^9+K.1^17+K.1^33-K.1^45,K.1^3+K.1^11-K.1^15-K.1^23,K.1^3-K.1^7+K.1^11-K.1^15+K.1^19-K.1^23+K.1^35-K.1^39+K.1^43,-1*K.1^7+K.1^19+K.1^35+K.1^43,-1*K.1^3-K.1^11+K.1^15+K.1^23,-1*K.1^3+K.1^7-K.1^11+K.1^15-K.1^19+K.1^23-K.1^35+K.1^39-K.1^43,-1*K.1+K.1^5+K.1^21-K.1^25,-1*K.1+K.1^5-K.1^9+K.1^13-K.1^17+K.1^21-K.1^25-K.1^33+K.1^45]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_416_66:= KnownIrreducibles(CR);