/* Group 9000.w downloaded from the LMFDB on 11 November 2025. */
 
/* Various presentations of this group are stored in this file: 
	 GPC is polycyclic presentation GPerm is permutation group 
	 GLZ, GLFp, GLZA, GLZq, GLFq if they exist are matrix groups 
 
 Many characteristics of the group are stored as booleans in a record: 
	 Agroup, Zgroup, abelian, almost_simple,cyclic, metabelian, 
	 metacyclic, monomial, nilpotent, perfect, quasisimple, rational, 
	 solvable, supersolvable 
 
 The character table is stored as chartbl_n_i where n is the order of 
 the group and i is which group of that order it is. Conjugacy classes 
 are stored in the variable 'C' with elements from the group 'G'. 
*/
 
/* Constructions */
GPC := PCGroup([8, -2, -3, -2, 2, -3, -5, 5, 5, 24768, 97985, 55881, 44210, 2242, 96387, 134507, 1235, 91, 10564, 112812, 660, 156, 172813, 2325, 201606, 6062, 13462, 6750, 69127, 34575, 38431]); a,b,c,d,e,f := Explode([GPC.1, GPC.2, GPC.3, GPC.4, GPC.7, GPC.8]); AssignNames(~GPC, ["a", "b", "c", "d", "d2", "d6", "e", "f"]);
GPerm := PermutationGroup< 18 | (1,2,5,10,14,7,13,11,6,9)(3,8,12,15,4)(17,18), (1,3,9)(2,6,8)(4,11,5)(7,14,15)(10,13,12)(16,17,18), (2,4,10,15)(3,7,12,9)(5,6)(8,11)(13,14)(17,18) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_9000_w := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false>; 

 
/* Character Table */
G:= GPerm;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 75, G!(4,8)(7,11)(9,10)(12,15)>,< 2, 90, G!(1,2)(5,9)(6,10)(7,13)(11,14)(17,18)>,< 3, 2, G!(16,18,17)>,< 3, 200, G!(1,9,15)(2,12,5)(3,13,7)(4,6,11)(8,14,10)(16,18,17)>,< 3, 200, G!(1,9,8)(2,3,5)(4,14,10)(6,11,12)(7,15,13)>,< 3, 200, G!(1,4,11)(2,14,12)(3,7,6)(5,15,9)(8,10,13)(16,18,17)>,< 4, 2250, G!(1,15,5,12)(2,7)(3,13)(4,14,8,6)(9,11)(16,17)>,< 5, 4, G!(1,13,5,6,14)(2,7,9,10,11)(3,12,4,8,15)>,< 5, 4, G!(1,14,6,5,13)(2,11,10,9,7)(3,15,8,4,12)>,< 5, 4, G!(1,5,14,13,6)(2,9,11,7,10)(3,4,15,12,8)>,< 5, 4, G!(1,6,13,14,5)(2,10,7,11,9)(3,8,12,15,4)>,< 5, 6, G!(3,15,8,4,12)>,< 5, 6, G!(3,8,12,15,4)>,< 5, 12, G!(2,10,7,11,9)(3,8,12,15,4)>,< 5, 12, G!(2,7,9,10,11)(3,12,4,8,15)>,< 5, 12, G!(1,13,5,6,14)(2,10,7,11,9)(3,12,4,8,15)>,< 5, 12, G!(1,14,6,5,13)(2,9,11,7,10)(3,15,8,4,12)>,< 5, 12, G!(1,5,14,13,6)(2,7,9,10,11)(3,4,15,12,8)>,< 5, 12, G!(1,6,13,14,5)(2,11,10,9,7)(3,8,12,15,4)>,< 5, 24, G!(2,10,7,11,9)(3,12,4,8,15)>,< 6, 150, G!(4,8)(7,11)(9,10)(12,15)(16,17,18)>,< 10, 90, G!(1,2)(3,4,15,12,8)(5,9)(6,10)(7,13)(11,14)(17,18)>,< 10, 90, G!(1,2)(3,4,15,12,8)(5,10)(6,9)(7,14)(11,13)(17,18)>,< 10, 90, G!(1,2)(3,12,4,8,15)(5,9)(6,10)(7,13)(11,14)(17,18)>,< 10, 90, G!(1,2)(3,12,4,8,15)(5,10)(6,9)(7,14)(11,13)(17,18)>,< 10, 150, G!(1,5,14,13,6)(4,8)(7,11)(9,10)(12,15)>,< 10, 150, G!(1,13,5,6,14)(4,8)(7,11)(9,10)(12,15)>,< 10, 180, G!(1,8,14,4,6,12,5,3,13,15)(17,18)>,< 10, 180, G!(1,4,5,15,14,12,13,8,6,3)(17,18)>,< 10, 180, G!(1,14,6,5,13)(2,15,7,3,9,12,10,4,11,8)(17,18)>,< 10, 180, G!(1,13,5,6,14)(2,8,11,4,10,12,9,3,7,15)(17,18)>,< 10, 180, G!(1,5,14,13,6)(2,3,10,8,7,12,11,15,9,4)(17,18)>,< 10, 180, G!(1,6,13,14,5)(2,4,9,15,11,12,7,8,10,3)(17,18)>,< 10, 180, G!(1,9,13,7,5,2,6,11,14,10)(3,4,15,12,8)(16,17)>,< 10, 180, G!(1,10,14,11,6,2,5,7,13,9)(3,8,12,15,4)(16,17)>,< 10, 180, G!(1,7,6,10,13,2,14,9,5,11)(3,12,4,8,15)(16,17)>,< 10, 180, G!(1,11,5,9,14,2,13,10,6,7)(3,15,8,4,12)(16,17)>,< 15, 8, G!(1,5,14,13,6)(2,9,11,7,10)(3,4,15,12,8)(16,17,18)>,< 15, 8, G!(1,5,14,13,6)(2,9,11,7,10)(3,8,12,15,4)(16,17,18)>,< 15, 8, G!(1,13,5,6,14)(2,7,9,10,11)(3,15,8,4,12)(16,17,18)>,< 15, 8, G!(1,13,5,6,14)(2,7,9,10,11)(3,12,4,8,15)(16,17,18)>,< 15, 12, G!(1,6,13,14,5)(16,17,18)>,< 15, 12, G!(1,13,5,6,14)(16,18,17)>,< 15, 24, G!(2,7,9,10,11)(3,4,15,12,8)(16,17,18)>,< 15, 24, G!(2,7,9,10,11)(3,4,15,12,8)(16,18,17)>,< 15, 24, G!(2,7,9,10,11)(3,12,4,8,15)(16,17,18)>,< 15, 24, G!(2,9,11,7,10)(3,4,15,12,8)(16,17,18)>,< 15, 24, G!(1,5,14,13,6)(2,7,9,10,11)(3,4,15,12,8)(16,17,18)>,< 15, 24, G!(1,5,14,13,6)(2,7,9,10,11)(3,8,12,15,4)(16,17,18)>,< 15, 24, G!(1,5,14,13,6)(2,7,9,10,11)(3,12,4,8,15)(16,17,18)>,< 15, 24, G!(1,5,14,13,6)(2,7,9,10,11)(3,15,8,4,12)(16,17,18)>,< 15, 200, G!(1,3,2,6,8,9,13,12,11,14,15,7,5,4,10)(16,17,18)>,< 15, 200, G!(1,10,4,5,7,15,14,11,12,13,9,8,6,2,3)(16,18,17)>,< 15, 200, G!(1,2,8,13,11,15,5,10,3,6,9,12,14,7,4)(16,18,17)>,< 15, 200, G!(1,4,7,14,12,9,6,3,10,5,15,11,13,8,2)(16,17,18)>,< 15, 200, G!(1,15,2,6,4,9,13,3,11,14,8,7,5,12,10)>,< 15, 200, G!(1,10,12,5,7,8,14,11,3,13,9,4,6,2,15)>,< 15, 200, G!(1,2,4,13,11,8,5,10,15,6,9,3,14,7,12)>,< 15, 200, G!(1,12,7,14,3,9,6,15,10,5,8,11,13,4,2)>,< 15, 200, G!(1,10,15,6,2,4,13,9,3,14,11,8,5,7,12)(16,17,18)>,< 15, 200, G!(1,12,7,5,8,11,14,3,9,13,4,2,6,15,10)(16,18,17)>,< 15, 200, G!(1,15,2,13,3,11,5,12,10,6,4,9,14,8,7)(16,18,17)>,< 15, 200, G!(1,7,8,14,9,4,6,10,12,5,11,3,13,2,15)(16,17,18)>,< 30, 300, G!(1,14,6,5,13)(4,8)(7,11)(9,10)(12,15)(16,18,17)>,< 30, 300, G!(1,6,13,14,5)(4,8)(7,11)(9,10)(12,15)(16,18,17)>]); 
CR := CharacterRing(G);
x := CR!\[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, -1, -1, -1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, -1, -1, 2, -1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, -1, 2, -1, -1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 0, 2, -1, -1, -1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -1, 1, 3, 0, 0, 0, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, -1, -1, 3, 0, 0, 0, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,2,4,1,1,1,0,K.1+3*K.1^-2,-1-K.1+2*K.1^2-K.1^-2,3*K.1+K.1^2,-3-3*K.1-3*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^-2,1+2*K.1+K.1^-2,-1-2*K.1-K.1^2-2*K.1^-2,-1*K.1-K.1^2+K.1^-2,1+K.1+2*K.1^2,-1,0,2*K.1^-2,2*K.1^2,2*K.1,2*K.1^-1,0,0,1+K.1^-2,K.1+K.1^2,1+K.1^-1,1+K.1^2,-1-K.1-K.1^-2,-1-K.1-K.1^2,1+K.1,K.1^2+K.1^-2,K.1+K.1^-2,K.1+K.1^-1,-3-3*K.1-3*K.1^2-2*K.1^-2,3*K.1+K.1^2,K.1+3*K.1^-2,-1-K.1+2*K.1^2-K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,1+K.1+2*K.1^2,-1,1-K.1^2-K.1^-2,1+2*K.1+K.1^-2,-1*K.1-K.1^2+K.1^-2,2+K.1^2+K.1^-2,-1-2*K.1-K.1^2-2*K.1^-2,-1,K.1,K.1^-2,K.1^-2,K.1^-2,K.1^2,K.1^-1,K.1^2,K.1,K.1^2,K.1^-1,K.1^-1,K.1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,2,4,1,1,1,0,-1-K.1+2*K.1^2-K.1^-2,K.1+3*K.1^-2,-3-3*K.1-3*K.1^2-2*K.1^-2,3*K.1+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^-2,-1-2*K.1-K.1^2-2*K.1^-2,1+2*K.1+K.1^-2,1+K.1+2*K.1^2,-1*K.1-K.1^2+K.1^-2,-1,0,2*K.1^2,2*K.1^-2,2*K.1^-1,2*K.1,0,0,1+K.1^2,-1-K.1-K.1^2,1+K.1,1+K.1^-2,K.1+K.1^-2,K.1+K.1^2,1+K.1^-1,K.1^2+K.1^-2,-1-K.1-K.1^-2,K.1+K.1^-1,3*K.1+K.1^2,-3-3*K.1-3*K.1^2-2*K.1^-2,-1-K.1+2*K.1^2-K.1^-2,K.1+3*K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-1*K.1-K.1^2+K.1^-2,-1,1-K.1^2-K.1^-2,-1-2*K.1-K.1^2-2*K.1^-2,1+K.1+2*K.1^2,2+K.1^2+K.1^-2,1+2*K.1+K.1^-2,-1,K.1^-1,K.1^2,K.1^2,K.1^2,K.1^-2,K.1,K.1^-2,K.1^-1,K.1^-2,K.1,K.1,K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,2,4,1,1,1,0,-3-3*K.1-3*K.1^2-2*K.1^-2,3*K.1+K.1^2,K.1+3*K.1^-2,-1-K.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^-2,1-K.1^2-K.1^-2,-1*K.1-K.1^2+K.1^-2,1+K.1+2*K.1^2,-1-2*K.1-K.1^2-2*K.1^-2,1+2*K.1+K.1^-2,-1,0,2*K.1^-1,2*K.1,2*K.1^-2,2*K.1^2,0,0,1+K.1^-1,K.1+K.1^-2,1+K.1^2,1+K.1,K.1+K.1^2,-1-K.1-K.1^-2,1+K.1^-2,K.1+K.1^-1,-1-K.1-K.1^2,K.1^2+K.1^-2,-1-K.1+2*K.1^2-K.1^-2,K.1+3*K.1^-2,-3-3*K.1-3*K.1^2-2*K.1^-2,3*K.1+K.1^2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,1+2*K.1+K.1^-2,-1,2+K.1^2+K.1^-2,-1*K.1-K.1^2+K.1^-2,-1-2*K.1-K.1^2-2*K.1^-2,1-K.1^2-K.1^-2,1+K.1+2*K.1^2,-1,K.1^-2,K.1^-1,K.1^-1,K.1^-1,K.1,K.1^2,K.1,K.1^-2,K.1,K.1^2,K.1^2,K.1^-2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,2,4,1,1,1,0,3*K.1+K.1^2,-3-3*K.1-3*K.1^2-2*K.1^-2,-1-K.1+2*K.1^2-K.1^-2,K.1+3*K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2+K.1^2+K.1^-2,1-K.1^2-K.1^-2,1+K.1+2*K.1^2,-1*K.1-K.1^2+K.1^-2,1+2*K.1+K.1^-2,-1-2*K.1-K.1^2-2*K.1^-2,-1,0,2*K.1,2*K.1^-1,2*K.1^2,2*K.1^-2,0,0,1+K.1,-1-K.1-K.1^-2,1+K.1^-2,1+K.1^-1,-1-K.1-K.1^2,K.1+K.1^-2,1+K.1^2,K.1+K.1^-1,K.1+K.1^2,K.1^2+K.1^-2,K.1+3*K.1^-2,-1-K.1+2*K.1^2-K.1^-2,3*K.1+K.1^2,-3-3*K.1-3*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-1-2*K.1-K.1^2-2*K.1^-2,-1,2+K.1^2+K.1^-2,1+K.1+2*K.1^2,1+2*K.1+K.1^-2,1-K.1^2-K.1^-2,-1*K.1-K.1^2+K.1^-2,-1,K.1^2,K.1,K.1,K.1,K.1^-1,K.1^-2,K.1^-1,K.1^2,K.1^-1,K.1^-2,K.1^-2,K.1^2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,-2,4,1,1,1,0,K.1+3*K.1^-2,-1-K.1+2*K.1^2-K.1^-2,3*K.1+K.1^2,-3-3*K.1-3*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^-2,1+2*K.1+K.1^-2,-1-2*K.1-K.1^2-2*K.1^-2,-1*K.1-K.1^2+K.1^-2,1+K.1+2*K.1^2,-1,0,-2*K.1^-2,-2*K.1^2,-2*K.1,-2*K.1^-1,0,0,-1-K.1^-2,-1*K.1-K.1^2,-1-K.1^-1,-1-K.1^2,1+K.1+K.1^-2,1+K.1+K.1^2,-1-K.1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-2,-1*K.1-K.1^-1,-3-3*K.1-3*K.1^2-2*K.1^-2,3*K.1+K.1^2,K.1+3*K.1^-2,-1-K.1+2*K.1^2-K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,1+K.1+2*K.1^2,-1,1-K.1^2-K.1^-2,1+2*K.1+K.1^-2,-1*K.1-K.1^2+K.1^-2,2+K.1^2+K.1^-2,-1-2*K.1-K.1^2-2*K.1^-2,-1,K.1,K.1^-2,K.1^-2,K.1^-2,K.1^2,K.1^-1,K.1^2,K.1,K.1^2,K.1^-1,K.1^-1,K.1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,-2,4,1,1,1,0,-1-K.1+2*K.1^2-K.1^-2,K.1+3*K.1^-2,-3-3*K.1-3*K.1^2-2*K.1^-2,3*K.1+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^-2,-1-2*K.1-K.1^2-2*K.1^-2,1+2*K.1+K.1^-2,1+K.1+2*K.1^2,-1*K.1-K.1^2+K.1^-2,-1,0,-2*K.1^2,-2*K.1^-2,-2*K.1^-1,-2*K.1,0,0,-1-K.1^2,1+K.1+K.1^2,-1-K.1,-1-K.1^-2,-1*K.1-K.1^-2,-1*K.1-K.1^2,-1-K.1^-1,-1*K.1^2-K.1^-2,1+K.1+K.1^-2,-1*K.1-K.1^-1,3*K.1+K.1^2,-3-3*K.1-3*K.1^2-2*K.1^-2,-1-K.1+2*K.1^2-K.1^-2,K.1+3*K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-1*K.1-K.1^2+K.1^-2,-1,1-K.1^2-K.1^-2,-1-2*K.1-K.1^2-2*K.1^-2,1+K.1+2*K.1^2,2+K.1^2+K.1^-2,1+2*K.1+K.1^-2,-1,K.1^-1,K.1^2,K.1^2,K.1^2,K.1^-2,K.1,K.1^-2,K.1^-1,K.1^-2,K.1,K.1,K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,-2,4,1,1,1,0,-3-3*K.1-3*K.1^2-2*K.1^-2,3*K.1+K.1^2,K.1+3*K.1^-2,-1-K.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^-2,1-K.1^2-K.1^-2,-1*K.1-K.1^2+K.1^-2,1+K.1+2*K.1^2,-1-2*K.1-K.1^2-2*K.1^-2,1+2*K.1+K.1^-2,-1,0,-2*K.1^-1,-2*K.1,-2*K.1^-2,-2*K.1^2,0,0,-1-K.1^-1,-1*K.1-K.1^-2,-1-K.1^2,-1-K.1,-1*K.1-K.1^2,1+K.1+K.1^-2,-1-K.1^-2,-1*K.1-K.1^-1,1+K.1+K.1^2,-1*K.1^2-K.1^-2,-1-K.1+2*K.1^2-K.1^-2,K.1+3*K.1^-2,-3-3*K.1-3*K.1^2-2*K.1^-2,3*K.1+K.1^2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,1+2*K.1+K.1^-2,-1,2+K.1^2+K.1^-2,-1*K.1-K.1^2+K.1^-2,-1-2*K.1-K.1^2-2*K.1^-2,1-K.1^2-K.1^-2,1+K.1+2*K.1^2,-1,K.1^-2,K.1^-1,K.1^-1,K.1^-1,K.1,K.1^2,K.1,K.1^-2,K.1,K.1^2,K.1^2,K.1^-2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,0,-2,4,1,1,1,0,3*K.1+K.1^2,-3-3*K.1-3*K.1^2-2*K.1^-2,-1-K.1+2*K.1^2-K.1^-2,K.1+3*K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2+K.1^2+K.1^-2,1-K.1^2-K.1^-2,1+K.1+2*K.1^2,-1*K.1-K.1^2+K.1^-2,1+2*K.1+K.1^-2,-1-2*K.1-K.1^2-2*K.1^-2,-1,0,-2*K.1,-2*K.1^-1,-2*K.1^2,-2*K.1^-2,0,0,-1-K.1,1+K.1+K.1^-2,-1-K.1^-2,-1-K.1^-1,1+K.1+K.1^2,-1*K.1-K.1^-2,-1-K.1^2,-1*K.1-K.1^-1,-1*K.1-K.1^2,-1*K.1^2-K.1^-2,K.1+3*K.1^-2,-1-K.1+2*K.1^2-K.1^-2,3*K.1+K.1^2,-3-3*K.1-3*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-1-2*K.1-K.1^2-2*K.1^-2,-1,2+K.1^2+K.1^-2,1+K.1+2*K.1^2,1+2*K.1+K.1^-2,1-K.1^2-K.1^-2,-1*K.1-K.1^2+K.1^-2,-1,K.1^2,K.1,K.1,K.1,K.1^-1,K.1^-2,K.1^-1,K.1^2,K.1^-1,K.1^-2,K.1^-2,K.1^2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[6, -2, 0, -3, 0, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,2,2,6,0,0,0,0,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,4+K.1^2+K.1^-2,3-K.1^2-K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,-1+K.1^2+K.1^-2,-1+K.1^2+K.1^-2,-2-K.1^2-K.1^-2,-2-K.1^2-K.1^-2,1,2,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,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,2,K.1^2+K.1^-2,2,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3-K.1^2-K.1^-2,4+K.1^2+K.1^-2,-2-K.1^2-K.1^-2,1,-2*K.1-2*K.1^-1,-1+K.1^2+K.1^-2,-2-K.1^2-K.1^-2,-2*K.1^2-2*K.1^-2,-1+K.1^2+K.1^-2,1,0,0,0,0,0,0,0,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,2,2,6,0,0,0,0,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3-K.1^2-K.1^-2,4+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^-2,-2-K.1^2-K.1^-2,-1+K.1^2+K.1^-2,-1+K.1^2+K.1^-2,1,2,K.1+K.1^-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,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,2,K.1+K.1^-1,2,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,4+K.1^2+K.1^-2,3-K.1^2-K.1^-2,-1+K.1^2+K.1^-2,1,-2*K.1^2-2*K.1^-2,-2-K.1^2-K.1^-2,-1+K.1^2+K.1^-2,-2*K.1-2*K.1^-1,-2-K.1^2-K.1^-2,1,0,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,2,-2,6,0,0,0,0,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,4+K.1^2+K.1^-2,3-K.1^2-K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,-1+K.1^2+K.1^-2,-1+K.1^2+K.1^-2,-2-K.1^2-K.1^-2,-2-K.1^2-K.1^-2,1,2,-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,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-2,-1*K.1^2-K.1^-2,-2,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3-K.1^2-K.1^-2,4+K.1^2+K.1^-2,-2-K.1^2-K.1^-2,1,-2*K.1-2*K.1^-1,-1+K.1^2+K.1^-2,-2-K.1^2-K.1^-2,-2*K.1^2-2*K.1^-2,-1+K.1^2+K.1^-2,1,0,0,0,0,0,0,0,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,2,-2,6,0,0,0,0,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3-K.1^2-K.1^-2,4+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^-2,-2-K.1^2-K.1^-2,-1+K.1^2+K.1^-2,-1+K.1^2+K.1^-2,1,2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-2,-1*K.1-K.1^-1,-2,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,4+K.1^2+K.1^-2,3-K.1^2-K.1^-2,-1+K.1^2+K.1^-2,1,-2*K.1^2-2*K.1^-2,-2-K.1^2-K.1^-2,-1+K.1^2+K.1^-2,-2*K.1-2*K.1^-1,-2-K.1^2-K.1^-2,1,0,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,-2,0,6,0,0,0,0,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,4+K.1^2+K.1^-2,3-K.1^2-K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,-1+K.1^2+K.1^-2,-1+K.1^2+K.1^-2,-2-K.1^2-K.1^-2,-2-K.1^2-K.1^-2,1,-2,-1*K.1^2+K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,0,K.1^2-K.1^-2,0,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3-K.1^2-K.1^-2,4+K.1^2+K.1^-2,-2-K.1^2-K.1^-2,1,-2*K.1-2*K.1^-1,-1+K.1^2+K.1^-2,-2-K.1^2-K.1^-2,-2*K.1^2-2*K.1^-2,-1+K.1^2+K.1^-2,1,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,-2,0,6,0,0,0,0,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,4+K.1^2+K.1^-2,3-K.1^2-K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,-1+K.1^2+K.1^-2,-1+K.1^2+K.1^-2,-2-K.1^2-K.1^-2,-2-K.1^2-K.1^-2,1,-2,K.1^2-K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,0,-1*K.1^2+K.1^-2,0,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3-K.1^2-K.1^-2,4+K.1^2+K.1^-2,-2-K.1^2-K.1^-2,1,-2*K.1-2*K.1^-1,-1+K.1^2+K.1^-2,-2-K.1^2-K.1^-2,-2*K.1^2-2*K.1^-2,-1+K.1^2+K.1^-2,1,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,-2,0,6,0,0,0,0,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3-K.1^2-K.1^-2,4+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^-2,-2-K.1^2-K.1^-2,-1+K.1^2+K.1^-2,-1+K.1^2+K.1^-2,1,-2,-1-2*K.1-K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2-K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,0,1+2*K.1+K.1^2+K.1^-2,0,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,4+K.1^2+K.1^-2,3-K.1^2-K.1^-2,-1+K.1^2+K.1^-2,1,-2*K.1^2-2*K.1^-2,-2-K.1^2-K.1^-2,-1+K.1^2+K.1^-2,-2*K.1-2*K.1^-1,-2-K.1^2-K.1^-2,1,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |6,-2,0,6,0,0,0,0,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3-K.1^2-K.1^-2,4+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^-2,-2-K.1^2-K.1^-2,-1+K.1^2+K.1^-2,-1+K.1^2+K.1^-2,1,-2,1+2*K.1+K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,-1*K.1^2+K.1^-2,-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,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,0,-1-2*K.1-K.1^2-K.1^-2,0,3*K.1^2+3*K.1^-2,3*K.1^2+3*K.1^-2,3*K.1+3*K.1^-1,3*K.1+3*K.1^-1,4+K.1^2+K.1^-2,3-K.1^2-K.1^-2,-1+K.1^2+K.1^-2,1,-2*K.1^2-2*K.1^-2,-2-K.1^2-K.1^-2,-1+K.1^2+K.1^-2,-2*K.1-2*K.1^-1,-2-K.1^2-K.1^-2,1,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,-4,-1,-1,2,0,2*K.1+6*K.1^-2,-2-2*K.1+4*K.1^2-2*K.1^-2,6*K.1+2*K.1^2,-6-6*K.1-6*K.1^2-4*K.1^-2,4*K.1^2+4*K.1^-2,4*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+4*K.1+2*K.1^-2,-2-4*K.1-2*K.1^2-4*K.1^-2,-2*K.1-2*K.1^2+2*K.1^-2,2+2*K.1+4*K.1^2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3+3*K.1+3*K.1^2+2*K.1^-2,-3*K.1-K.1^2,-1*K.1-3*K.1^-2,1+K.1-2*K.1^2+K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,-1-K.1-2*K.1^2,1,-1+K.1^2+K.1^-2,-1-2*K.1-K.1^-2,K.1+K.1^2-K.1^-2,-2-K.1^2-K.1^-2,1+2*K.1+K.1^2+2*K.1^-2,1,-1*K.1,-1*K.1^-2,2*K.1^-2,-1*K.1^-2,-1*K.1^2,2*K.1^-1,2*K.1^2,2*K.1,-1*K.1^2,-1*K.1^-1,-1*K.1^-1,-1*K.1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,-4,-1,-1,2,0,-2-2*K.1+4*K.1^2-2*K.1^-2,2*K.1+6*K.1^-2,-6-6*K.1-6*K.1^2-4*K.1^-2,6*K.1+2*K.1^2,4*K.1^2+4*K.1^-2,4*K.1+4*K.1^-1,2-2*K.1^2-2*K.1^-2,4+2*K.1^2+2*K.1^-2,-2-4*K.1-2*K.1^2-4*K.1^-2,2+4*K.1+2*K.1^-2,2+2*K.1+4*K.1^2,-2*K.1-2*K.1^2+2*K.1^-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3*K.1-K.1^2,3+3*K.1+3*K.1^2+2*K.1^-2,1+K.1-2*K.1^2+K.1^-2,-1*K.1-3*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,K.1+K.1^2-K.1^-2,1,-1+K.1^2+K.1^-2,1+2*K.1+K.1^2+2*K.1^-2,-1-K.1-2*K.1^2,-2-K.1^2-K.1^-2,-1-2*K.1-K.1^-2,1,-1*K.1^-1,-1*K.1^2,2*K.1^2,-1*K.1^2,-1*K.1^-2,2*K.1,2*K.1^-2,2*K.1^-1,-1*K.1^-2,-1*K.1,-1*K.1,-1*K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,-4,-1,-1,2,0,-6-6*K.1-6*K.1^2-4*K.1^-2,6*K.1+2*K.1^2,2*K.1+6*K.1^-2,-2-2*K.1+4*K.1^2-2*K.1^-2,4*K.1+4*K.1^-1,4*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*K.1-2*K.1^2+2*K.1^-2,2+2*K.1+4*K.1^2,-2-4*K.1-2*K.1^2-4*K.1^-2,2+4*K.1+2*K.1^-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1+K.1-2*K.1^2+K.1^-2,-1*K.1-3*K.1^-2,3+3*K.1+3*K.1^2+2*K.1^-2,-3*K.1-K.1^2,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,-1-2*K.1-K.1^-2,1,-2-K.1^2-K.1^-2,K.1+K.1^2-K.1^-2,1+2*K.1+K.1^2+2*K.1^-2,-1+K.1^2+K.1^-2,-1-K.1-2*K.1^2,1,-1*K.1^-2,-1*K.1^-1,2*K.1^-1,-1*K.1^-1,-1*K.1,2*K.1^2,2*K.1,2*K.1^-2,-1*K.1,-1*K.1^2,-1*K.1^2,-1*K.1^-2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,-4,-1,-1,2,0,6*K.1+2*K.1^2,-6-6*K.1-6*K.1^2-4*K.1^-2,-2-2*K.1+4*K.1^2-2*K.1^-2,2*K.1+6*K.1^-2,4*K.1+4*K.1^-1,4*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*K.1+4*K.1^2,-2*K.1-2*K.1^2+2*K.1^-2,2+4*K.1+2*K.1^-2,-2-4*K.1-2*K.1^2-4*K.1^-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1-3*K.1^-2,1+K.1-2*K.1^2+K.1^-2,-3*K.1-K.1^2,3+3*K.1+3*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,1+2*K.1+K.1^2+2*K.1^-2,1,-2-K.1^2-K.1^-2,-1-K.1-2*K.1^2,-1-2*K.1-K.1^-2,-1+K.1^2+K.1^-2,K.1+K.1^2-K.1^-2,1,-1*K.1^2,-1*K.1,2*K.1,-1*K.1,-1*K.1^-1,2*K.1^-2,2*K.1^-1,2*K.1^2,-1*K.1^-1,-1*K.1^-2,-1*K.1^-2,-1*K.1^2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,-4,-1,2,-1,0,2*K.1+6*K.1^-2,-2-2*K.1+4*K.1^2-2*K.1^-2,6*K.1+2*K.1^2,-6-6*K.1-6*K.1^2-4*K.1^-2,4*K.1^2+4*K.1^-2,4*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+4*K.1+2*K.1^-2,-2-4*K.1-2*K.1^2-4*K.1^-2,-2*K.1-2*K.1^2+2*K.1^-2,2+2*K.1+4*K.1^2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3+3*K.1+3*K.1^2+2*K.1^-2,-3*K.1-K.1^2,-1*K.1-3*K.1^-2,1+K.1-2*K.1^2+K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,-1-K.1-2*K.1^2,1,-1+K.1^2+K.1^-2,-1-2*K.1-K.1^-2,K.1+K.1^2-K.1^-2,-2-K.1^2-K.1^-2,1+2*K.1+K.1^2+2*K.1^-2,1,2*K.1,2*K.1^-2,-1*K.1^-2,-1*K.1^-2,2*K.1^2,-1*K.1^-1,-1*K.1^2,-1*K.1,-1*K.1^2,-1*K.1^-1,2*K.1^-1,-1*K.1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,-4,-1,2,-1,0,-2-2*K.1+4*K.1^2-2*K.1^-2,2*K.1+6*K.1^-2,-6-6*K.1-6*K.1^2-4*K.1^-2,6*K.1+2*K.1^2,4*K.1^2+4*K.1^-2,4*K.1+4*K.1^-1,2-2*K.1^2-2*K.1^-2,4+2*K.1^2+2*K.1^-2,-2-4*K.1-2*K.1^2-4*K.1^-2,2+4*K.1+2*K.1^-2,2+2*K.1+4*K.1^2,-2*K.1-2*K.1^2+2*K.1^-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3*K.1-K.1^2,3+3*K.1+3*K.1^2+2*K.1^-2,1+K.1-2*K.1^2+K.1^-2,-1*K.1-3*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,K.1+K.1^2-K.1^-2,1,-1+K.1^2+K.1^-2,1+2*K.1+K.1^2+2*K.1^-2,-1-K.1-2*K.1^2,-2-K.1^2-K.1^-2,-1-2*K.1-K.1^-2,1,2*K.1^-1,2*K.1^2,-1*K.1^2,-1*K.1^2,2*K.1^-2,-1*K.1,-1*K.1^-2,-1*K.1^-1,-1*K.1^-2,-1*K.1,2*K.1,-1*K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,-4,-1,2,-1,0,-6-6*K.1-6*K.1^2-4*K.1^-2,6*K.1+2*K.1^2,2*K.1+6*K.1^-2,-2-2*K.1+4*K.1^2-2*K.1^-2,4*K.1+4*K.1^-1,4*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*K.1-2*K.1^2+2*K.1^-2,2+2*K.1+4*K.1^2,-2-4*K.1-2*K.1^2-4*K.1^-2,2+4*K.1+2*K.1^-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1+K.1-2*K.1^2+K.1^-2,-1*K.1-3*K.1^-2,3+3*K.1+3*K.1^2+2*K.1^-2,-3*K.1-K.1^2,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,-1-2*K.1-K.1^-2,1,-2-K.1^2-K.1^-2,K.1+K.1^2-K.1^-2,1+2*K.1+K.1^2+2*K.1^-2,-1+K.1^2+K.1^-2,-1-K.1-2*K.1^2,1,2*K.1^-2,2*K.1^-1,-1*K.1^-1,-1*K.1^-1,2*K.1,-1*K.1^2,-1*K.1,-1*K.1^-2,-1*K.1,-1*K.1^2,2*K.1^2,-1*K.1^-2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,-4,-1,2,-1,0,6*K.1+2*K.1^2,-6-6*K.1-6*K.1^2-4*K.1^-2,-2-2*K.1+4*K.1^2-2*K.1^-2,2*K.1+6*K.1^-2,4*K.1+4*K.1^-1,4*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*K.1+4*K.1^2,-2*K.1-2*K.1^2+2*K.1^-2,2+4*K.1+2*K.1^-2,-2-4*K.1-2*K.1^2-4*K.1^-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1-3*K.1^-2,1+K.1-2*K.1^2+K.1^-2,-3*K.1-K.1^2,3+3*K.1+3*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,1+2*K.1+K.1^2+2*K.1^-2,1,-2-K.1^2-K.1^-2,-1-K.1-2*K.1^2,-1-2*K.1-K.1^-2,-1+K.1^2+K.1^-2,K.1+K.1^2-K.1^-2,1,2*K.1^2,2*K.1,-1*K.1,-1*K.1,2*K.1^-1,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,-1*K.1^-1,-1*K.1^-2,2*K.1^-2,-1*K.1^2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,-4,2,-1,-1,0,2*K.1+6*K.1^-2,-2-2*K.1+4*K.1^2-2*K.1^-2,6*K.1+2*K.1^2,-6-6*K.1-6*K.1^2-4*K.1^-2,4*K.1^2+4*K.1^-2,4*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+4*K.1+2*K.1^-2,-2-4*K.1-2*K.1^2-4*K.1^-2,-2*K.1-2*K.1^2+2*K.1^-2,2+2*K.1+4*K.1^2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3+3*K.1+3*K.1^2+2*K.1^-2,-3*K.1-K.1^2,-1*K.1-3*K.1^-2,1+K.1-2*K.1^2+K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,-1-K.1-2*K.1^2,1,-1+K.1^2+K.1^-2,-1-2*K.1-K.1^-2,K.1+K.1^2-K.1^-2,-2-K.1^2-K.1^-2,1+2*K.1+K.1^2+2*K.1^-2,1,-1*K.1,-1*K.1^-2,-1*K.1^-2,2*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1^2,-1*K.1,2*K.1^2,2*K.1^-1,-1*K.1^-1,2*K.1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,-4,2,-1,-1,0,-2-2*K.1+4*K.1^2-2*K.1^-2,2*K.1+6*K.1^-2,-6-6*K.1-6*K.1^2-4*K.1^-2,6*K.1+2*K.1^2,4*K.1^2+4*K.1^-2,4*K.1+4*K.1^-1,2-2*K.1^2-2*K.1^-2,4+2*K.1^2+2*K.1^-2,-2-4*K.1-2*K.1^2-4*K.1^-2,2+4*K.1+2*K.1^-2,2+2*K.1+4*K.1^2,-2*K.1-2*K.1^2+2*K.1^-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3*K.1-K.1^2,3+3*K.1+3*K.1^2+2*K.1^-2,1+K.1-2*K.1^2+K.1^-2,-1*K.1-3*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,K.1+K.1^2-K.1^-2,1,-1+K.1^2+K.1^-2,1+2*K.1+K.1^2+2*K.1^-2,-1-K.1-2*K.1^2,-2-K.1^2-K.1^-2,-1-2*K.1-K.1^-2,1,-1*K.1^-1,-1*K.1^2,-1*K.1^2,2*K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-2,-1*K.1^-1,2*K.1^-2,2*K.1,-1*K.1,2*K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,-4,2,-1,-1,0,-6-6*K.1-6*K.1^2-4*K.1^-2,6*K.1+2*K.1^2,2*K.1+6*K.1^-2,-2-2*K.1+4*K.1^2-2*K.1^-2,4*K.1+4*K.1^-1,4*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*K.1-2*K.1^2+2*K.1^-2,2+2*K.1+4*K.1^2,-2-4*K.1-2*K.1^2-4*K.1^-2,2+4*K.1+2*K.1^-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1+K.1-2*K.1^2+K.1^-2,-1*K.1-3*K.1^-2,3+3*K.1+3*K.1^2+2*K.1^-2,-3*K.1-K.1^2,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,-1-2*K.1-K.1^-2,1,-2-K.1^2-K.1^-2,K.1+K.1^2-K.1^-2,1+2*K.1+K.1^2+2*K.1^-2,-1+K.1^2+K.1^-2,-1-K.1-2*K.1^2,1,-1*K.1^-2,-1*K.1^-1,-1*K.1^-1,2*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1,-1*K.1^-2,2*K.1,2*K.1^2,-1*K.1^2,2*K.1^-2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,-4,2,-1,-1,0,6*K.1+2*K.1^2,-6-6*K.1-6*K.1^2-4*K.1^-2,-2-2*K.1+4*K.1^2-2*K.1^-2,2*K.1+6*K.1^-2,4*K.1+4*K.1^-1,4*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*K.1+4*K.1^2,-2*K.1-2*K.1^2+2*K.1^-2,2+4*K.1+2*K.1^-2,-2-4*K.1-2*K.1^2-4*K.1^-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1-3*K.1^-2,1+K.1-2*K.1^2+K.1^-2,-3*K.1-K.1^2,3+3*K.1+3*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,1+2*K.1+K.1^2+2*K.1^-2,1,-2-K.1^2-K.1^-2,-1-K.1-2*K.1^2,-1-2*K.1-K.1^-2,-1+K.1^2+K.1^-2,K.1+K.1^2-K.1^-2,1,-1*K.1^2,-1*K.1,-1*K.1,2*K.1,-1*K.1^-1,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,2*K.1^-1,2*K.1^-2,-1*K.1^-2,2*K.1^2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,8,-1,-1,-1,0,2*K.1+6*K.1^-2,-2-2*K.1+4*K.1^2-2*K.1^-2,6*K.1+2*K.1^2,-6-6*K.1-6*K.1^2-4*K.1^-2,4*K.1^2+4*K.1^-2,4*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+4*K.1+2*K.1^-2,-2-4*K.1-2*K.1^2-4*K.1^-2,-2*K.1-2*K.1^2+2*K.1^-2,2+2*K.1+4*K.1^2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6-6*K.1-6*K.1^2-4*K.1^-2,6*K.1+2*K.1^2,2*K.1+6*K.1^-2,-2-2*K.1+4*K.1^2-2*K.1^-2,4*K.1+4*K.1^-1,4*K.1^2+4*K.1^-2,2+2*K.1+4*K.1^2,-2,2-2*K.1^2-2*K.1^-2,2+4*K.1+2*K.1^-2,-2*K.1-2*K.1^2+2*K.1^-2,4+2*K.1^2+2*K.1^-2,-2-4*K.1-2*K.1^2-4*K.1^-2,-2,-1*K.1,-1*K.1^-2,-1*K.1^-2,-1*K.1^-2,-1*K.1^2,-1*K.1^-1,-1*K.1^2,-1*K.1,-1*K.1^2,-1*K.1^-1,-1*K.1^-1,-1*K.1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,8,-1,-1,-1,0,-2-2*K.1+4*K.1^2-2*K.1^-2,2*K.1+6*K.1^-2,-6-6*K.1-6*K.1^2-4*K.1^-2,6*K.1+2*K.1^2,4*K.1^2+4*K.1^-2,4*K.1+4*K.1^-1,2-2*K.1^2-2*K.1^-2,4+2*K.1^2+2*K.1^-2,-2-4*K.1-2*K.1^2-4*K.1^-2,2+4*K.1+2*K.1^-2,2+2*K.1+4*K.1^2,-2*K.1-2*K.1^2+2*K.1^-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6*K.1+2*K.1^2,-6-6*K.1-6*K.1^2-4*K.1^-2,-2-2*K.1+4*K.1^2-2*K.1^-2,2*K.1+6*K.1^-2,4*K.1+4*K.1^-1,4*K.1^2+4*K.1^-2,-2*K.1-2*K.1^2+2*K.1^-2,-2,2-2*K.1^2-2*K.1^-2,-2-4*K.1-2*K.1^2-4*K.1^-2,2+2*K.1+4*K.1^2,4+2*K.1^2+2*K.1^-2,2+4*K.1+2*K.1^-2,-2,-1*K.1^-1,-1*K.1^2,-1*K.1^2,-1*K.1^2,-1*K.1^-2,-1*K.1,-1*K.1^-2,-1*K.1^-1,-1*K.1^-2,-1*K.1,-1*K.1,-1*K.1^-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,8,-1,-1,-1,0,-6-6*K.1-6*K.1^2-4*K.1^-2,6*K.1+2*K.1^2,2*K.1+6*K.1^-2,-2-2*K.1+4*K.1^2-2*K.1^-2,4*K.1+4*K.1^-1,4*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*K.1-2*K.1^2+2*K.1^-2,2+2*K.1+4*K.1^2,-2-4*K.1-2*K.1^2-4*K.1^-2,2+4*K.1+2*K.1^-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2-2*K.1+4*K.1^2-2*K.1^-2,2*K.1+6*K.1^-2,-6-6*K.1-6*K.1^2-4*K.1^-2,6*K.1+2*K.1^2,4*K.1^2+4*K.1^-2,4*K.1+4*K.1^-1,2+4*K.1+2*K.1^-2,-2,4+2*K.1^2+2*K.1^-2,-2*K.1-2*K.1^2+2*K.1^-2,-2-4*K.1-2*K.1^2-4*K.1^-2,2-2*K.1^2-2*K.1^-2,2+2*K.1+4*K.1^2,-2,-1*K.1^-2,-1*K.1^-1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^2,-1*K.1,-1*K.1^-2,-1*K.1,-1*K.1^2,-1*K.1^2,-1*K.1^-2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |8,0,0,8,-1,-1,-1,0,6*K.1+2*K.1^2,-6-6*K.1-6*K.1^2-4*K.1^-2,-2-2*K.1+4*K.1^2-2*K.1^-2,2*K.1+6*K.1^-2,4*K.1+4*K.1^-1,4*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*K.1+4*K.1^2,-2*K.1-2*K.1^2+2*K.1^-2,2+4*K.1+2*K.1^-2,-2-4*K.1-2*K.1^2-4*K.1^-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1+6*K.1^-2,-2-2*K.1+4*K.1^2-2*K.1^-2,6*K.1+2*K.1^2,-6-6*K.1-6*K.1^2-4*K.1^-2,4*K.1^2+4*K.1^-2,4*K.1+4*K.1^-1,-2-4*K.1-2*K.1^2-4*K.1^-2,-2,4+2*K.1^2+2*K.1^-2,2+2*K.1+4*K.1^2,2+4*K.1+2*K.1^-2,2-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^2+2*K.1^-2,-2,-1*K.1^2,-1*K.1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-2,-1*K.1^-1,-1*K.1^2,-1*K.1^-1,-1*K.1^-2,-1*K.1^-2,-1*K.1^2,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,0,2,12,0,0,0,0,6+3*K.1^2+3*K.1^-2,6+3*K.1^2+3*K.1^-2,3-3*K.1^2-3*K.1^-2,3-3*K.1^2-3*K.1^-2,-4*K.1^2-4*K.1^-2,-4*K.1-4*K.1^-1,-2-3*K.1^2-3*K.1^-2,1+3*K.1^2+3*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,-3,0,2,2,2,2,0,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,3-3*K.1^2-3*K.1^-2,3-3*K.1^2-3*K.1^-2,6+3*K.1^2+3*K.1^-2,6+3*K.1^2+3*K.1^-2,-4*K.1-4*K.1^-1,-4*K.1^2-4*K.1^-2,K.1+K.1^-1,-3,-2-3*K.1^2-3*K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,1+3*K.1^2+3*K.1^-2,K.1^2+K.1^-2,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,0,2,12,0,0,0,0,3-3*K.1^2-3*K.1^-2,3-3*K.1^2-3*K.1^-2,6+3*K.1^2+3*K.1^-2,6+3*K.1^2+3*K.1^-2,-4*K.1-4*K.1^-1,-4*K.1^2-4*K.1^-2,1+3*K.1^2+3*K.1^-2,-2-3*K.1^2-3*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,-3,0,2,2,2,2,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,6+3*K.1^2+3*K.1^-2,6+3*K.1^2+3*K.1^-2,3-3*K.1^2-3*K.1^-2,3-3*K.1^2-3*K.1^-2,-4*K.1^2-4*K.1^-2,-4*K.1-4*K.1^-1,K.1^2+K.1^-2,-3,1+3*K.1^2+3*K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,-2-3*K.1^2-3*K.1^-2,K.1+K.1^-1,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,4,0,-6,0,0,0,0,6*K.1^2+6*K.1^-2,6*K.1^2+6*K.1^-2,6*K.1+6*K.1^-1,6*K.1+6*K.1^-1,8+2*K.1^2+2*K.1^-2,6-2*K.1^2-2*K.1^-2,-4*K.1-4*K.1^-1,-4*K.1^2-4*K.1^-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^-2,2,-2,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,0,0,0,0,0,0,-3*K.1-3*K.1^-1,-3*K.1-3*K.1^-1,-3*K.1^2-3*K.1^-2,-3*K.1^2-3*K.1^-2,-3+K.1^2+K.1^-2,-4-K.1^2-K.1^-2,2+K.1^2+K.1^-2,-1,2*K.1+2*K.1^-1,1-K.1^2-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,-1,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1^2-K.1^-2,-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 |12,4,0,-6,0,0,0,0,6*K.1+6*K.1^-1,6*K.1+6*K.1^-1,6*K.1^2+6*K.1^-2,6*K.1^2+6*K.1^-2,6-2*K.1^2-2*K.1^-2,8+2*K.1^2+2*K.1^-2,-4*K.1^2-4*K.1^-2,-4*K.1-4*K.1^-1,-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,-2,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,0,0,0,0,0,0,0,0,-3*K.1^2-3*K.1^-2,-3*K.1^2-3*K.1^-2,-3*K.1-3*K.1^-1,-3*K.1-3*K.1^-1,-4-K.1^2-K.1^-2,-3+K.1^2+K.1^-2,1-K.1^2-K.1^-2,-1,2*K.1^2+2*K.1^-2,2+K.1^2+K.1^-2,1-K.1^2-K.1^-2,2*K.1+2*K.1^-1,2+K.1^2+K.1^-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^-1,-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 |12,0,-2,12,0,0,0,0,6+3*K.1^2+3*K.1^-2,6+3*K.1^2+3*K.1^-2,3-3*K.1^2-3*K.1^-2,3-3*K.1^2-3*K.1^-2,-4*K.1^2-4*K.1^-2,-4*K.1-4*K.1^-1,-2-3*K.1^2-3*K.1^-2,1+3*K.1^2+3*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,-3,0,-2,-2,-2,-2,0,0,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-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^-2,3-3*K.1^2-3*K.1^-2,3-3*K.1^2-3*K.1^-2,6+3*K.1^2+3*K.1^-2,6+3*K.1^2+3*K.1^-2,-4*K.1-4*K.1^-1,-4*K.1^2-4*K.1^-2,K.1+K.1^-1,-3,-2-3*K.1^2-3*K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,1+3*K.1^2+3*K.1^-2,K.1^2+K.1^-2,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,0,-2,12,0,0,0,0,3-3*K.1^2-3*K.1^-2,3-3*K.1^2-3*K.1^-2,6+3*K.1^2+3*K.1^-2,6+3*K.1^2+3*K.1^-2,-4*K.1-4*K.1^-1,-4*K.1^2-4*K.1^-2,1+3*K.1^2+3*K.1^-2,-2-3*K.1^2-3*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,-3,0,-2,-2,-2,-2,0,0,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-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^-1,6+3*K.1^2+3*K.1^-2,6+3*K.1^2+3*K.1^-2,3-3*K.1^2-3*K.1^-2,3-3*K.1^2-3*K.1^-2,-4*K.1^2-4*K.1^-2,-4*K.1-4*K.1^-1,K.1^2+K.1^-2,-3,1+3*K.1^2+3*K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,-2-3*K.1^2-3*K.1^-2,K.1+K.1^-1,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,-4,0,-6,0,0,0,0,6*K.1^2+6*K.1^-2,6*K.1^2+6*K.1^-2,6*K.1+6*K.1^-1,6*K.1+6*K.1^-1,8+2*K.1^2+2*K.1^-2,6-2*K.1^2-2*K.1^-2,-4*K.1-4*K.1^-1,-4*K.1^2-4*K.1^-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^-2,2,2,0,0,0,0,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,0,0,0,0,0,0,0,0,0,0,-3*K.1-3*K.1^-1,-3*K.1-3*K.1^-1,-3*K.1^2-3*K.1^-2,-3*K.1^2-3*K.1^-2,-3+K.1^2+K.1^-2,-4-K.1^2-K.1^-2,2+K.1^2+K.1^-2,-1,2*K.1+2*K.1^-1,1-K.1^2-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,-1,0,0,0,0,0,0,0,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,-4,0,-6,0,0,0,0,6*K.1+6*K.1^-1,6*K.1+6*K.1^-1,6*K.1^2+6*K.1^-2,6*K.1^2+6*K.1^-2,6-2*K.1^2-2*K.1^-2,8+2*K.1^2+2*K.1^-2,-4*K.1^2-4*K.1^-2,-4*K.1-4*K.1^-1,-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^-2,2,2,0,0,0,0,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,0,0,0,0,0,0,0,0,0,0,-3*K.1^2-3*K.1^-2,-3*K.1^2-3*K.1^-2,-3*K.1-3*K.1^-1,-3*K.1-3*K.1^-1,-4-K.1^2-K.1^-2,-3+K.1^2+K.1^-2,1-K.1^2-K.1^-2,-1,2*K.1^2+2*K.1^-2,2+K.1^2+K.1^-2,1-K.1^2-K.1^-2,2*K.1+2*K.1^-1,2+K.1^2+K.1^-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^-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 |12,0,2,12,0,0,0,0,-3*K.1-3*K.1^2+3*K.1^-2,3+3*K.1+6*K.1^2,3+6*K.1+3*K.1^-2,-3-6*K.1-3*K.1^2-6*K.1^-2,-4-2*K.1^2-2*K.1^-2,-2+2*K.1^2+2*K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,-2-K.1-K.1^2-4*K.1^-2,-1+K.1-3*K.1^2,2+3*K.1+4*K.1^2+3*K.1^-2,-1-3*K.1+K.1^-2,2,0,2*K.1^-2,2*K.1^2,2*K.1,2*K.1^-1,0,0,K.1+K.1^2,1+K.1^-2,K.1+K.1^-2,-1-K.1-K.1^2,1+K.1,1+K.1^2,-1-K.1-K.1^-2,K.1+K.1^-1,1+K.1^-1,K.1^2+K.1^-2,-3-6*K.1-3*K.1^2-6*K.1^-2,3+6*K.1+3*K.1^-2,-3*K.1-3*K.1^2+3*K.1^-2,3+3*K.1+6*K.1^2,-2+2*K.1^2+2*K.1^-2,-4-2*K.1^2-2*K.1^-2,-1-3*K.1+K.1^-2,2,K.1^2+K.1^-2,-2-K.1-K.1^2-4*K.1^-2,2+3*K.1+4*K.1^2+3*K.1^-2,K.1+K.1^-1,-1+K.1-3*K.1^2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,0,2,12,0,0,0,0,3+3*K.1+6*K.1^2,-3*K.1-3*K.1^2+3*K.1^-2,-3-6*K.1-3*K.1^2-6*K.1^-2,3+6*K.1+3*K.1^-2,-4-2*K.1^2-2*K.1^-2,-2+2*K.1^2+2*K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,-1+K.1-3*K.1^2,-2-K.1-K.1^2-4*K.1^-2,-1-3*K.1+K.1^-2,2+3*K.1+4*K.1^2+3*K.1^-2,2,0,2*K.1^2,2*K.1^-2,2*K.1^-1,2*K.1,0,0,-1-K.1-K.1^2,1+K.1^2,-1-K.1-K.1^-2,K.1+K.1^2,1+K.1^-1,1+K.1^-2,K.1+K.1^-2,K.1+K.1^-1,1+K.1,K.1^2+K.1^-2,3+6*K.1+3*K.1^-2,-3-6*K.1-3*K.1^2-6*K.1^-2,3+3*K.1+6*K.1^2,-3*K.1-3*K.1^2+3*K.1^-2,-2+2*K.1^2+2*K.1^-2,-4-2*K.1^2-2*K.1^-2,2+3*K.1+4*K.1^2+3*K.1^-2,2,K.1^2+K.1^-2,-1+K.1-3*K.1^2,-1-3*K.1+K.1^-2,K.1+K.1^-1,-2-K.1-K.1^2-4*K.1^-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,0,2,12,0,0,0,0,-3-6*K.1-3*K.1^2-6*K.1^-2,3+6*K.1+3*K.1^-2,-3*K.1-3*K.1^2+3*K.1^-2,3+3*K.1+6*K.1^2,-2+2*K.1^2+2*K.1^-2,-4-2*K.1^2-2*K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,2+3*K.1+4*K.1^2+3*K.1^-2,-1-3*K.1+K.1^-2,-1+K.1-3*K.1^2,-2-K.1-K.1^2-4*K.1^-2,2,0,2*K.1^-1,2*K.1,2*K.1^-2,2*K.1^2,0,0,K.1+K.1^-2,1+K.1^-1,-1-K.1-K.1^2,-1-K.1-K.1^-2,1+K.1^-2,1+K.1,K.1+K.1^2,K.1^2+K.1^-2,1+K.1^2,K.1+K.1^-1,3+3*K.1+6*K.1^2,-3*K.1-3*K.1^2+3*K.1^-2,-3-6*K.1-3*K.1^2-6*K.1^-2,3+6*K.1+3*K.1^-2,-4-2*K.1^2-2*K.1^-2,-2+2*K.1^2+2*K.1^-2,-2-K.1-K.1^2-4*K.1^-2,2,K.1+K.1^-1,2+3*K.1+4*K.1^2+3*K.1^-2,-1+K.1-3*K.1^2,K.1^2+K.1^-2,-1-3*K.1+K.1^-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,0,2,12,0,0,0,0,3+6*K.1+3*K.1^-2,-3-6*K.1-3*K.1^2-6*K.1^-2,3+3*K.1+6*K.1^2,-3*K.1-3*K.1^2+3*K.1^-2,-2+2*K.1^2+2*K.1^-2,-4-2*K.1^2-2*K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,-1-3*K.1+K.1^-2,2+3*K.1+4*K.1^2+3*K.1^-2,-2-K.1-K.1^2-4*K.1^-2,-1+K.1-3*K.1^2,2,0,2*K.1,2*K.1^-1,2*K.1^2,2*K.1^-2,0,0,-1-K.1-K.1^-2,1+K.1,K.1+K.1^2,K.1+K.1^-2,1+K.1^2,1+K.1^-1,-1-K.1-K.1^2,K.1^2+K.1^-2,1+K.1^-2,K.1+K.1^-1,-3*K.1-3*K.1^2+3*K.1^-2,3+3*K.1+6*K.1^2,3+6*K.1+3*K.1^-2,-3-6*K.1-3*K.1^2-6*K.1^-2,-4-2*K.1^2-2*K.1^-2,-2+2*K.1^2+2*K.1^-2,-1+K.1-3*K.1^2,2,K.1+K.1^-1,-1-3*K.1+K.1^-2,-2-K.1-K.1^2-4*K.1^-2,K.1^2+K.1^-2,2+3*K.1+4*K.1^2+3*K.1^-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,0,-2,12,0,0,0,0,-3*K.1-3*K.1^2+3*K.1^-2,3+3*K.1+6*K.1^2,3+6*K.1+3*K.1^-2,-3-6*K.1-3*K.1^2-6*K.1^-2,-4-2*K.1^2-2*K.1^-2,-2+2*K.1^2+2*K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,-2-K.1-K.1^2-4*K.1^-2,-1+K.1-3*K.1^2,2+3*K.1+4*K.1^2+3*K.1^-2,-1-3*K.1+K.1^-2,2,0,-2*K.1^-2,-2*K.1^2,-2*K.1,-2*K.1^-1,0,0,-1*K.1-K.1^2,-1-K.1^-2,-1*K.1-K.1^-2,1+K.1+K.1^2,-1-K.1,-1-K.1^2,1+K.1+K.1^-2,-1*K.1-K.1^-1,-1-K.1^-1,-1*K.1^2-K.1^-2,-3-6*K.1-3*K.1^2-6*K.1^-2,3+6*K.1+3*K.1^-2,-3*K.1-3*K.1^2+3*K.1^-2,3+3*K.1+6*K.1^2,-2+2*K.1^2+2*K.1^-2,-4-2*K.1^2-2*K.1^-2,-1-3*K.1+K.1^-2,2,K.1^2+K.1^-2,-2-K.1-K.1^2-4*K.1^-2,2+3*K.1+4*K.1^2+3*K.1^-2,K.1+K.1^-1,-1+K.1-3*K.1^2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,0,-2,12,0,0,0,0,3+3*K.1+6*K.1^2,-3*K.1-3*K.1^2+3*K.1^-2,-3-6*K.1-3*K.1^2-6*K.1^-2,3+6*K.1+3*K.1^-2,-4-2*K.1^2-2*K.1^-2,-2+2*K.1^2+2*K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,-1+K.1-3*K.1^2,-2-K.1-K.1^2-4*K.1^-2,-1-3*K.1+K.1^-2,2+3*K.1+4*K.1^2+3*K.1^-2,2,0,-2*K.1^2,-2*K.1^-2,-2*K.1^-1,-2*K.1,0,0,1+K.1+K.1^2,-1-K.1^2,1+K.1+K.1^-2,-1*K.1-K.1^2,-1-K.1^-1,-1-K.1^-2,-1*K.1-K.1^-2,-1*K.1-K.1^-1,-1-K.1,-1*K.1^2-K.1^-2,3+6*K.1+3*K.1^-2,-3-6*K.1-3*K.1^2-6*K.1^-2,3+3*K.1+6*K.1^2,-3*K.1-3*K.1^2+3*K.1^-2,-2+2*K.1^2+2*K.1^-2,-4-2*K.1^2-2*K.1^-2,2+3*K.1+4*K.1^2+3*K.1^-2,2,K.1^2+K.1^-2,-1+K.1-3*K.1^2,-1-3*K.1+K.1^-2,K.1+K.1^-1,-2-K.1-K.1^2-4*K.1^-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,0,-2,12,0,0,0,0,-3-6*K.1-3*K.1^2-6*K.1^-2,3+6*K.1+3*K.1^-2,-3*K.1-3*K.1^2+3*K.1^-2,3+3*K.1+6*K.1^2,-2+2*K.1^2+2*K.1^-2,-4-2*K.1^2-2*K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,2+3*K.1+4*K.1^2+3*K.1^-2,-1-3*K.1+K.1^-2,-1+K.1-3*K.1^2,-2-K.1-K.1^2-4*K.1^-2,2,0,-2*K.1^-1,-2*K.1,-2*K.1^-2,-2*K.1^2,0,0,-1*K.1-K.1^-2,-1-K.1^-1,1+K.1+K.1^2,1+K.1+K.1^-2,-1-K.1^-2,-1-K.1,-1*K.1-K.1^2,-1*K.1^2-K.1^-2,-1-K.1^2,-1*K.1-K.1^-1,3+3*K.1+6*K.1^2,-3*K.1-3*K.1^2+3*K.1^-2,-3-6*K.1-3*K.1^2-6*K.1^-2,3+6*K.1+3*K.1^-2,-4-2*K.1^2-2*K.1^-2,-2+2*K.1^2+2*K.1^-2,-2-K.1-K.1^2-4*K.1^-2,2,K.1+K.1^-1,2+3*K.1+4*K.1^2+3*K.1^-2,-1+K.1-3*K.1^2,K.1^2+K.1^-2,-1-3*K.1+K.1^-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |12,0,-2,12,0,0,0,0,3+6*K.1+3*K.1^-2,-3-6*K.1-3*K.1^2-6*K.1^-2,3+3*K.1+6*K.1^2,-3*K.1-3*K.1^2+3*K.1^-2,-2+2*K.1^2+2*K.1^-2,-4-2*K.1^2-2*K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,-1-3*K.1+K.1^-2,2+3*K.1+4*K.1^2+3*K.1^-2,-2-K.1-K.1^2-4*K.1^-2,-1+K.1-3*K.1^2,2,0,-2*K.1,-2*K.1^-1,-2*K.1^2,-2*K.1^-2,0,0,1+K.1+K.1^-2,-1-K.1,-1*K.1-K.1^2,-1*K.1-K.1^-2,-1-K.1^2,-1-K.1^-1,1+K.1+K.1^2,-1*K.1^2-K.1^-2,-1-K.1^-2,-1*K.1-K.1^-1,-3*K.1-3*K.1^2+3*K.1^-2,3+3*K.1+6*K.1^2,3+6*K.1+3*K.1^-2,-3-6*K.1-3*K.1^2-6*K.1^-2,-4-2*K.1^2-2*K.1^-2,-2+2*K.1^2+2*K.1^-2,-1+K.1-3*K.1^2,2,K.1+K.1^-1,-1-3*K.1+K.1^-2,-2-K.1-K.1^2-4*K.1^-2,K.1^2+K.1^-2,2+3*K.1+4*K.1^2+3*K.1^-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[24, 0, 0, 24, 0, 0, 0, 0, -6, -6, -6, -6, 4, 4, -6, -6, 4, 4, 4, 4, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, 4, 4, 4, -1, -6, 4, 4, -6, 4, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |24,0,0,-12,0,0,0,0,-6,-6,-6,-6,4,4,-6,-6,4,4,4,4,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,3,-2,-2,-2,8-10*K.1-5*K.1^2+5*K.1^3-10*K.1^4+5*K.1^5-5*K.1^7,3,-2,-2,3,-2,-7+10*K.1+5*K.1^2-5*K.1^3+10*K.1^4-5*K.1^5+5*K.1^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(15: Sparse := true);
S := [ K |24,0,0,-12,0,0,0,0,-6,-6,-6,-6,4,4,-6,-6,4,4,4,4,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,3,-2,-2,-2,-7+10*K.1+5*K.1^2-5*K.1^3+10*K.1^4-5*K.1^5+5*K.1^7,3,-2,-2,3,-2,8-10*K.1-5*K.1^2+5*K.1^3-10*K.1^4+5*K.1^5-5*K.1^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |24,0,0,-12,0,0,0,0,12+6*K.1^2+6*K.1^-2,12+6*K.1^2+6*K.1^-2,6-6*K.1^2-6*K.1^-2,6-6*K.1^2-6*K.1^-2,-8*K.1^2-8*K.1^-2,-8*K.1-8*K.1^-1,-4-6*K.1^2-6*K.1^-2,2+6*K.1^2+6*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^-1,2*K.1+2*K.1^-1,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3+3*K.1^2+3*K.1^-2,-3+3*K.1^2+3*K.1^-2,-6-3*K.1^2-3*K.1^-2,-6-3*K.1^2-3*K.1^-2,4*K.1+4*K.1^-1,4*K.1^2+4*K.1^-2,-1*K.1-K.1^-1,3,2+3*K.1^2+3*K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1-3*K.1^2-3*K.1^-2,-1*K.1^2-K.1^-2,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |24,0,0,-12,0,0,0,0,6-6*K.1^2-6*K.1^-2,6-6*K.1^2-6*K.1^-2,12+6*K.1^2+6*K.1^-2,12+6*K.1^2+6*K.1^-2,-8*K.1-8*K.1^-1,-8*K.1^2-8*K.1^-2,2+6*K.1^2+6*K.1^-2,-4-6*K.1^2-6*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+2*K.1^-2,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6-3*K.1^2-3*K.1^-2,-6-3*K.1^2-3*K.1^-2,-3+3*K.1^2+3*K.1^-2,-3+3*K.1^2+3*K.1^-2,4*K.1^2+4*K.1^-2,4*K.1+4*K.1^-1,-1*K.1^2-K.1^-2,3,-1-3*K.1^2-3*K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,2+3*K.1^2+3*K.1^-2,-1*K.1-K.1^-1,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |24,0,0,-12,0,0,0,0,-6*K.1-6*K.1^2+6*K.1^-2,6+6*K.1+12*K.1^2,6+12*K.1+6*K.1^-2,-6-12*K.1-6*K.1^2-12*K.1^-2,-8-4*K.1^2-4*K.1^-2,-4+4*K.1^2+4*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-4-2*K.1-2*K.1^2-8*K.1^-2,-2+2*K.1-6*K.1^2,4+6*K.1+8*K.1^2+6*K.1^-2,-2-6*K.1+2*K.1^-2,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3+6*K.1+3*K.1^2+6*K.1^-2,-3-6*K.1-3*K.1^-2,3*K.1+3*K.1^2-3*K.1^-2,-3-3*K.1-6*K.1^2,2-2*K.1^2-2*K.1^-2,4+2*K.1^2+2*K.1^-2,1+3*K.1-K.1^-2,-2,-1*K.1^2-K.1^-2,2+K.1+K.1^2+4*K.1^-2,-2-3*K.1-4*K.1^2-3*K.1^-2,-1*K.1-K.1^-1,1-K.1+3*K.1^2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |24,0,0,-12,0,0,0,0,6+6*K.1+12*K.1^2,-6*K.1-6*K.1^2+6*K.1^-2,-6-12*K.1-6*K.1^2-12*K.1^-2,6+12*K.1+6*K.1^-2,-8-4*K.1^2-4*K.1^-2,-4+4*K.1^2+4*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-2+2*K.1-6*K.1^2,-4-2*K.1-2*K.1^2-8*K.1^-2,-2-6*K.1+2*K.1^-2,4+6*K.1+8*K.1^2+6*K.1^-2,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3-6*K.1-3*K.1^-2,3+6*K.1+3*K.1^2+6*K.1^-2,-3-3*K.1-6*K.1^2,3*K.1+3*K.1^2-3*K.1^-2,2-2*K.1^2-2*K.1^-2,4+2*K.1^2+2*K.1^-2,-2-3*K.1-4*K.1^2-3*K.1^-2,-2,-1*K.1^2-K.1^-2,1-K.1+3*K.1^2,1+3*K.1-K.1^-2,-1*K.1-K.1^-1,2+K.1+K.1^2+4*K.1^-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |24,0,0,-12,0,0,0,0,-6-12*K.1-6*K.1^2-12*K.1^-2,6+12*K.1+6*K.1^-2,-6*K.1-6*K.1^2+6*K.1^-2,6+6*K.1+12*K.1^2,-4+4*K.1^2+4*K.1^-2,-8-4*K.1^2-4*K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,4+6*K.1+8*K.1^2+6*K.1^-2,-2-6*K.1+2*K.1^-2,-2+2*K.1-6*K.1^2,-4-2*K.1-2*K.1^2-8*K.1^-2,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3-3*K.1-6*K.1^2,3*K.1+3*K.1^2-3*K.1^-2,3+6*K.1+3*K.1^2+6*K.1^-2,-3-6*K.1-3*K.1^-2,4+2*K.1^2+2*K.1^-2,2-2*K.1^2-2*K.1^-2,2+K.1+K.1^2+4*K.1^-2,-2,-1*K.1-K.1^-1,-2-3*K.1-4*K.1^2-3*K.1^-2,1-K.1+3*K.1^2,-1*K.1^2-K.1^-2,1+3*K.1-K.1^-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |24,0,0,-12,0,0,0,0,6+12*K.1+6*K.1^-2,-6-12*K.1-6*K.1^2-12*K.1^-2,6+6*K.1+12*K.1^2,-6*K.1-6*K.1^2+6*K.1^-2,-4+4*K.1^2+4*K.1^-2,-8-4*K.1^2-4*K.1^-2,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-2-6*K.1+2*K.1^-2,4+6*K.1+8*K.1^2+6*K.1^-2,-4-2*K.1-2*K.1^2-8*K.1^-2,-2+2*K.1-6*K.1^2,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3*K.1+3*K.1^2-3*K.1^-2,-3-3*K.1-6*K.1^2,-3-6*K.1-3*K.1^-2,3+6*K.1+3*K.1^2+6*K.1^-2,4+2*K.1^2+2*K.1^-2,2-2*K.1^2-2*K.1^-2,1-K.1+3*K.1^2,-2,-1*K.1-K.1^-1,1+3*K.1-K.1^-2,2+K.1+K.1^2+4*K.1^-2,-1*K.1^2-K.1^-2,-2-3*K.1-4*K.1^2-3*K.1^-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_9000_w:= KnownIrreducibles(CR);