/* Group 38880.bf downloaded from the LMFDB on 25 September 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 */ GPerm := PermutationGroup< 15 | (7,9,8)(10,11,12), (10,12,11)(13,14,15), (7,14,10)(8,15,11)(9,13,12), (5,6)(7,8,9)(10,13,12,15,11,14), (7,10)(8,11)(9,12), (1,2,3,4,5)(7,8,9)(10,13,12,15,11,14) >; /* Booleans */ RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable : BoolElt >; booleans_38880_bf := rec< RF | Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, monomial := false, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := false, supersolvable := false>; /* Character Table */ G:= GPerm; C := SequenceToConjugacyClasses([car |< 1, 1, Id(G)>,< 2, 9, G!(7,12)(8,10)(9,11)>,< 2, 15, G!(5,6)>,< 2, 15, G!(1,2)(3,4)(5,6)>,< 2, 45, G!(3,5)(4,6)>,< 2, 135, G!(5,6)(10,15)(11,13)(12,14)>,< 2, 135, G!(1,2)(3,4)(5,6)(10,15)(11,13)(12,14)>,< 2, 405, G!(1,3)(2,6)(7,10)(8,11)(9,12)>,< 3, 1, G!(7,9,8)(10,12,11)(13,15,14)>,< 3, 1, G!(7,8,9)(10,11,12)(13,14,15)>,< 3, 6, G!(10,12,11)(13,14,15)>,< 3, 6, G!(7,13,10)(8,14,11)(9,15,12)>,< 3, 6, G!(7,14,10)(8,15,11)(9,13,12)>,< 3, 6, G!(7,15,10)(8,13,11)(9,14,12)>,< 3, 40, G!(4,6,5)>,< 3, 40, G!(1,3,5)(2,4,6)>,< 3, 40, G!(4,6,5)(7,9,8)(10,12,11)(13,15,14)>,< 3, 40, G!(4,5,6)(7,8,9)(10,11,12)(13,14,15)>,< 3, 40, G!(1,3,5)(2,4,6)(7,9,8)(10,12,11)(13,15,14)>,< 3, 40, G!(1,5,3)(2,6,4)(7,8,9)(10,11,12)(13,14,15)>,< 3, 240, G!(1,3,5)(2,4,6)(7,10,14)(8,11,15)(9,12,13)>,< 3, 240, G!(1,5,2)(3,6,4)(7,8,9)(13,15,14)>,< 3, 240, G!(2,6,4)(7,13,11)(8,14,12)(9,15,10)>,< 3, 240, G!(1,4,5)(7,15,11)(8,13,12)(9,14,10)>,< 3, 240, G!(1,6,4)(7,12,13)(8,10,14)(9,11,15)>,< 3, 240, G!(1,5,2)(3,6,4)(7,11,14)(8,12,15)(9,10,13)>,< 3, 240, G!(1,5,6)(7,8,9)(10,12,11)>,< 3, 240, G!(1,6,3)(2,4,5)(7,11,15)(8,12,13)(9,10,14)>,< 4, 90, G!(3,6,5,4)>,< 4, 90, G!(1,2)(3,6,5,4)>,< 4, 810, G!(1,4,2,3)(5,6)(7,10)(8,11)(9,12)>,< 4, 810, G!(1,3,6,5)(7,11)(8,12)(9,10)>,< 5, 144, G!(1,4,2,6,3)>,< 6, 9, G!(7,10,9,12,8,11)(13,14,15)>,< 6, 9, G!(7,11,8,12,9,10)(13,15,14)>,< 6, 15, G!(5,6)(7,8,9)(10,11,12)(13,14,15)>,< 6, 15, G!(5,6)(7,9,8)(10,12,11)(13,15,14)>,< 6, 15, G!(1,2)(3,4)(5,6)(7,8,9)(10,11,12)(13,14,15)>,< 6, 15, G!(1,2)(3,4)(5,6)(7,9,8)(10,12,11)(13,15,14)>,< 6, 45, G!(3,5)(4,6)(7,9,8)(10,12,11)(13,15,14)>,< 6, 45, G!(3,5)(4,6)(7,8,9)(10,11,12)(13,14,15)>,< 6, 90, G!(5,6)(10,11,12)(13,15,14)>,< 6, 90, G!(5,6)(7,10,13)(8,11,14)(9,12,15)>,< 6, 90, G!(5,6)(7,10,14)(8,11,15)(9,12,13)>,< 6, 90, G!(5,6)(7,10,15)(8,11,13)(9,12,14)>,< 6, 90, G!(1,2)(3,4)(5,6)(10,11,12)(13,15,14)>,< 6, 90, G!(1,2)(3,4)(5,6)(7,10,13)(8,11,14)(9,12,15)>,< 6, 90, G!(1,2)(3,4)(5,6)(7,10,14)(8,11,15)(9,12,13)>,< 6, 90, G!(1,2)(3,4)(5,6)(7,10,15)(8,11,13)(9,12,14)>,< 6, 120, G!(2,3)(4,5,6)>,< 6, 120, G!(1,2,3,4,5,6)>,< 6, 120, G!(2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)>,< 6, 120, G!(2,3)(4,5,6)(7,9,8)(10,12,11)(13,15,14)>,< 6, 120, G!(1,2,3,4,5,6)(7,8,9)(10,11,12)(13,14,15)>,< 6, 120, G!(1,2,3,4,5,6)(7,9,8)(10,12,11)(13,15,14)>,< 6, 135, G!(5,6)(7,8,9)(10,13,12,15,11,14)>,< 6, 135, G!(5,6)(7,9,8)(10,13,11,14,12,15)>,< 6, 135, G!(1,2)(3,4)(5,6)(7,8,9)(10,13,12,15,11,14)>,< 6, 135, G!(1,2)(3,4)(5,6)(7,9,8)(10,13,11,14,12,15)>,< 6, 270, G!(1,6)(3,4)(7,11,15)(8,12,13)(9,10,14)>,< 6, 270, G!(1,4)(2,5)(7,12,13)(8,10,14)(9,11,15)>,< 6, 270, G!(2,3)(5,6)(7,8,9)(10,12,11)>,< 6, 270, G!(1,6)(3,4)(7,12,15)(8,10,13)(9,11,14)>,< 6, 360, G!(1,5,2)(3,4,6)(10,15)(11,13)(12,14)>,< 6, 360, G!(4,6,5)(7,11)(8,12)(9,10)>,< 6, 360, G!(1,5,6)(2,3,4)(7,14,8,15,9,13)(10,12,11)>,< 6, 360, G!(1,6,5)(2,4,3)(7,13,9,15,8,14)(10,11,12)>,< 6, 360, G!(2,6,4)(7,8,9)(10,13,12,15,11,14)>,< 6, 360, G!(2,4,6)(7,9,8)(10,14,11,15,12,13)>,< 6, 405, G!(1,3)(2,6)(7,12,8,10,9,11)(13,15,14)>,< 6, 405, G!(1,3)(2,6)(7,11,9,10,8,12)(13,14,15)>,< 6, 720, G!(1,2,3,4,5,6)(7,14,10)(8,15,11)(9,13,12)>,< 6, 720, G!(1,3,5,6,2,4)(7,9,8)(13,14,15)>,< 6, 720, G!(2,4,6)(3,5)(7,11,13)(8,12,14)(9,10,15)>,< 6, 720, G!(1,5,4)(2,3)(7,11,15)(8,12,13)(9,10,14)>,< 6, 720, G!(1,4,6)(2,3)(7,13,12)(8,14,10)(9,15,11)>,< 6, 720, G!(1,4,5,3,2,6)(7,14,11)(8,15,12)(9,13,10)>,< 6, 720, G!(1,6,5)(3,4)(7,9,8)(10,11,12)>,< 6, 720, G!(1,4,6,5,3,2)(7,15,11)(8,13,12)(9,14,10)>,< 6, 1080, G!(1,3)(2,6,5)(10,15)(11,13)(12,14)>,< 6, 1080, G!(1,2,4,5,6,3)(7,10)(8,11)(9,12)>,< 6, 1080, G!(1,6)(2,3,4)(7,11,9,10,8,12)(13,14,15)>,< 6, 1080, G!(1,6)(2,4,3)(7,12,8,10,9,11)(13,15,14)>,< 6, 1080, G!(1,6,4,3,5,2)(7,13,8,14,9,15)(10,12,11)>,< 6, 1080, G!(1,2,5,3,4,6)(7,15,9,14,8,13)(10,11,12)>,< 10, 1296, G!(1,5,4,3,2)(7,12)(8,10)(9,11)>,< 12, 90, G!(3,4,5,6)(7,8,9)(10,11,12)(13,14,15)>,< 12, 90, G!(3,4,5,6)(7,9,8)(10,12,11)(13,15,14)>,< 12, 90, G!(1,2)(3,4,5,6)(7,8,9)(10,11,12)(13,14,15)>,< 12, 90, G!(1,2)(3,4,5,6)(7,9,8)(10,12,11)(13,15,14)>,< 12, 540, G!(1,4,6,3)(2,5)(7,15,11)(8,13,12)(9,14,10)>,< 12, 540, G!(1,5,4,2)(3,6)(7,13,12)(8,14,10)(9,15,11)>,< 12, 540, G!(1,4)(2,6,3,5)(7,9,8)(10,11,12)>,< 12, 540, G!(1,4,6,3)(7,8,9)(13,15,14)>,< 12, 540, G!(1,3,6,4)(2,5)(7,15,12)(8,13,10)(9,14,11)>,< 12, 540, G!(1,6,4,5)(7,14,12)(8,15,10)(9,13,11)>,< 12, 540, G!(1,2,5,3)(7,14,10)(8,15,11)(9,13,12)>,< 12, 540, G!(1,3,2,4)(7,13,12)(8,14,10)(9,15,11)>,< 12, 810, G!(1,3,2,4)(5,6)(7,11,9,10,8,12)(13,14,15)>,< 12, 810, G!(1,4,2,3)(5,6)(7,12,8,10,9,11)(13,15,14)>,< 12, 810, G!(1,5,6,3)(7,10,8,11,9,12)(13,15,14)>,< 12, 810, G!(1,3,6,5)(7,12,9,11,8,10)(13,14,15)>,< 15, 144, G!(1,2,3,4,5)(7,8,9)(10,11,12)(13,14,15)>,< 15, 144, G!(1,5,4,3,2)(7,9,8)(10,12,11)(13,15,14)>,< 15, 864, G!(1,2,3,4,6)(7,11,15)(8,12,13)(9,10,14)>,< 15, 864, G!(1,5,2,3,6)(7,13,12)(8,14,10)(9,15,11)>,< 15, 864, G!(1,4,2,6,3)(10,12,11)(13,14,15)>,< 15, 864, G!(1,3,5,2,6)(7,15,12)(8,13,10)(9,14,11)>,< 30, 1296, G!(1,4,2,5,3)(7,11,8,12,9,10)(13,15,14)>,< 30, 1296, G!(1,3,5,2,4)(7,10,9,12,8,11)(13,14,15)>]); CR := CharacterRing(G); x := CR!\[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -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, 0, 2, 2, 2, 0, 0, 0, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, -1, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 0, 0, 0, 0, 2, 2, -1, -1, 2, -1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[2, 0, 2, 2, 2, 0, 0, 0, 2, 2, -1, -1, 2, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, -1, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 2, 2, -1, -1, -1, 2, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[2, 0, 2, 2, 2, 0, 0, 0, 2, 2, -1, 2, -1, -1, 2, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 2, -1, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, 2, -1, -1, -1, -1, 2, -1, 0, 0, 0, 0, 2, 2, -1, 2, -1, -1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, 2, -1, 2, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[2, 0, -2, -2, 2, 0, 0, 0, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -2, 2, 0, 0, 2, 0, 0, -2, -2, -2, -2, 2, 2, -2, 1, 1, -2, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 1, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, -1, -1, 1, -2, -1, 1, 1, 0, 0, 0, 0, 2, 2, -1, -1, 2, -1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[2, 0, -2, -2, 2, 0, 0, 0, 2, 2, -1, -1, 2, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, -2, 2, 0, 0, 2, 0, 0, -2, -2, -2, -2, 2, 2, 1, 1, 1, 1, -2, -2, 1, 1, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, -1, -1, 2, -2, 1, -1, 1, 1, 0, 0, 0, 0, 2, 2, -1, -1, -1, 2, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[2, 0, -2, -2, 2, 0, 0, 0, 2, 2, -1, 2, -1, -1, 2, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, -2, 2, 0, 0, 2, 0, 0, -2, -2, -2, -2, 2, 2, 1, -2, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 1, 1, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, -1, 2, -1, 1, 1, -1, -2, 1, 0, 0, 0, 0, 2, 2, -1, 2, -1, -1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[2, 0, -2, -2, 2, 0, 0, 0, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, -2, 2, 0, 0, 2, 0, 0, -2, -2, -2, -2, 2, 2, 1, 1, -2, 1, 1, 1, -2, 1, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -2, 1, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, -1, -1, -1, 1, 1, 2, 1, -2, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |3,1,3,3,3,1,1,1,3*K.1^-1,3*K.1,0,0,0,0,3,3*K.1,3,3*K.1,3*K.1^-1,3*K.1^-1,0,0,0,0,0,0,0,0,3,3,1,1,3,K.1,K.1^-1,3*K.1^-1,3*K.1,3*K.1,3*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,3,3*K.1,3*K.1^-1,3*K.1^-1,3,3*K.1,K.1,K.1^-1,K.1,K.1^-1,0,0,0,0,1,1,K.1^-1,K.1,K.1,K.1^-1,K.1^-1,K.1,0,0,0,0,0,0,0,0,1,1,K.1,K.1^-1,K.1^-1,K.1,1,3*K.1,3*K.1^-1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,K.1,K.1,K.1^-1,K.1^-1,3*K.1,3*K.1^-1,0,0,0,0,K.1^-1,K.1]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |3,1,3,3,3,1,1,1,3*K.1,3*K.1^-1,0,0,0,0,3,3*K.1^-1,3,3*K.1^-1,3*K.1,3*K.1,0,0,0,0,0,0,0,0,3,3,1,1,3,K.1^-1,K.1,3*K.1,3*K.1^-1,3*K.1^-1,3*K.1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,3,3*K.1^-1,3*K.1,3*K.1,3,3*K.1^-1,K.1^-1,K.1,K.1^-1,K.1,0,0,0,0,1,1,K.1,K.1^-1,K.1^-1,K.1,K.1,K.1^-1,0,0,0,0,0,0,0,0,1,1,K.1^-1,K.1,K.1,K.1^-1,1,3*K.1^-1,3*K.1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,K.1^-1,K.1^-1,K.1,K.1,3*K.1^-1,3*K.1,0,0,0,0,K.1,K.1^-1]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |3,-1,3,3,3,-1,-1,-1,3*K.1^-1,3*K.1,0,0,0,0,3,3*K.1,3,3*K.1,3*K.1^-1,3*K.1^-1,0,0,0,0,0,0,0,0,3,3,-1,-1,3,-1*K.1,-1*K.1^-1,3*K.1^-1,3*K.1,3*K.1,3*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,3,3*K.1,3*K.1^-1,3*K.1^-1,3,3*K.1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,0,0,0,0,-1,-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,0,0,0,0,0,0,0,0,-1,-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1,3*K.1,3*K.1^-1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,3*K.1,3*K.1^-1,0,0,0,0,-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 |3,-1,3,3,3,-1,-1,-1,3*K.1,3*K.1^-1,0,0,0,0,3,3*K.1^-1,3,3*K.1^-1,3*K.1,3*K.1,0,0,0,0,0,0,0,0,3,3,-1,-1,3,-1*K.1^-1,-1*K.1,3*K.1,3*K.1^-1,3*K.1^-1,3*K.1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,3,3*K.1^-1,3*K.1,3*K.1,3,3*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,0,0,0,0,-1,-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,0,-1,-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,-1,3*K.1^-1,3*K.1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,3*K.1^-1,3*K.1,0,0,0,0,-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 |3,-1,-3,-3,3,1,1,-1,3*K.1^-1,3*K.1,0,0,0,0,3,3*K.1,3,3*K.1,3*K.1^-1,3*K.1^-1,0,0,0,0,0,0,0,0,-3,3,-1,1,3,-1*K.1,-1*K.1^-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,-3,-3*K.1,-3*K.1^-1,-3*K.1^-1,-3,-3*K.1,K.1,K.1^-1,K.1,K.1^-1,0,0,0,0,-1,-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,0,0,0,0,0,0,0,0,1,1,K.1,K.1^-1,K.1^-1,K.1,-1,-3*K.1,-3*K.1^-1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,-1*K.1,K.1,-1*K.1^-1,K.1^-1,3*K.1,3*K.1^-1,0,0,0,0,-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 |3,-1,-3,-3,3,1,1,-1,3*K.1,3*K.1^-1,0,0,0,0,3,3*K.1^-1,3,3*K.1^-1,3*K.1,3*K.1,0,0,0,0,0,0,0,0,-3,3,-1,1,3,-1*K.1^-1,-1*K.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,-3,-3*K.1^-1,-3*K.1,-3*K.1,-3,-3*K.1^-1,K.1^-1,K.1,K.1^-1,K.1,0,0,0,0,-1,-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,0,1,1,K.1^-1,K.1,K.1,K.1^-1,-1,-3*K.1^-1,-3*K.1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,-1*K.1^-1,K.1^-1,-1*K.1,K.1,3*K.1^-1,3*K.1,0,0,0,0,-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 |3,1,-3,-3,3,-1,-1,1,3*K.1^-1,3*K.1,0,0,0,0,3,3*K.1,3,3*K.1,3*K.1^-1,3*K.1^-1,0,0,0,0,0,0,0,0,-3,3,1,-1,3,K.1,K.1^-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,-3,-3*K.1,-3*K.1^-1,-3*K.1^-1,-3,-3*K.1,-1*K.1,-1*K.1^-1,-1*K.1,-1*K.1^-1,0,0,0,0,1,1,K.1^-1,K.1,K.1,K.1^-1,K.1^-1,K.1,0,0,0,0,0,0,0,0,-1,-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,1,-3*K.1,-3*K.1^-1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,K.1,-1*K.1,K.1^-1,-1*K.1^-1,3*K.1,3*K.1^-1,0,0,0,0,K.1^-1,K.1]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |3,1,-3,-3,3,-1,-1,1,3*K.1,3*K.1^-1,0,0,0,0,3,3*K.1^-1,3,3*K.1^-1,3*K.1,3*K.1,0,0,0,0,0,0,0,0,-3,3,1,-1,3,K.1^-1,K.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,-3,-3*K.1^-1,-3*K.1,-3*K.1,-3,-3*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1^-1,-1*K.1,0,0,0,0,1,1,K.1,K.1^-1,K.1^-1,K.1,K.1,K.1^-1,0,0,0,0,0,0,0,0,-1,-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,1,-3*K.1^-1,-3*K.1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,K.1^-1,-1*K.1^-1,K.1,-1*K.1,3*K.1^-1,3*K.1,0,0,0,0,K.1,K.1^-1]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; x := CR!\[5, 5, -1, 3, 1, -1, 3, 1, 5, 5, 5, 5, 5, 5, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, 2, 2, 1, -1, -1, 1, 0, 5, 5, -1, 3, -1, 3, 1, 1, 3, -1, -1, -1, 3, -1, 3, 3, -1, -1, -1, 0, 0, 0, -1, -1, 3, 3, 1, 1, 1, 1, 2, -1, 2, 2, -1, -1, 1, 1, 0, 0, 0, -1, -1, -1, 0, -1, -1, 0, -1, -1, 0, 0, 0, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[5, 5, 3, -1, 1, 3, -1, 1, 5, 5, 5, 5, 5, 5, 2, 2, -1, -1, 2, -1, 2, 2, 2, 2, -1, -1, -1, -1, 1, -1, -1, 1, 0, 5, 5, 3, -1, 3, -1, 1, 1, -1, 3, 3, 3, -1, 3, -1, -1, 0, 0, 0, -1, -1, -1, 3, 3, -1, -1, 1, 1, 1, 1, -1, 2, -1, -1, 2, 2, 1, 1, -1, -1, -1, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, -1, 0, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[5, 5, -3, 1, 1, -3, 1, 1, 5, 5, 5, 5, 5, 5, 2, 2, -1, -1, 2, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 0, 5, 5, -3, 1, -3, 1, 1, 1, 1, -3, -3, -3, 1, -3, 1, 1, 0, 0, 0, 1, 1, 1, -3, -3, 1, 1, 1, 1, 1, 1, -1, 2, -1, -1, 2, 2, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[5, 5, 1, -3, 1, 1, -3, 1, 5, 5, 5, 5, 5, 5, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 0, 5, 5, 1, -3, 1, -3, 1, 1, -3, 1, 1, 1, -3, 1, -3, -3, 1, 1, 1, 0, 0, 0, 1, 1, -3, -3, 1, 1, 1, 1, 2, -1, 2, 2, -1, -1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[5, -5, -3, 1, 1, 3, -1, -1, 5, 5, 5, 5, 5, 5, 2, 2, -1, -1, 2, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 1, 1, 0, -5, -5, -3, 1, -3, 1, 1, 1, 1, -3, -3, -3, 1, -3, 1, 1, 0, 0, 0, 1, 1, 1, 3, 3, -1, -1, 1, 1, 1, 1, 1, -2, 1, 1, -2, -2, -1, -1, 1, 1, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[5, -5, -1, 3, 1, 1, -3, -1, 5, 5, 5, 5, 5, 5, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, 2, 2, 1, -1, 1, -1, 0, -5, -5, -1, 3, -1, 3, 1, 1, 3, -1, -1, -1, 3, -1, 3, 3, -1, -1, -1, 0, 0, 0, 1, 1, -3, -3, 1, 1, 1, 1, -2, 1, -2, -2, 1, 1, -1, -1, 0, 0, 0, -1, -1, -1, 0, -1, 1, 0, 1, 1, 0, 0, 0, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[5, -5, 1, -3, 1, -1, 3, -1, 5, 5, 5, 5, 5, 5, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, 1, 1, 0, -5, -5, 1, -3, 1, -3, 1, 1, -3, 1, 1, 1, -3, 1, -3, -3, 1, 1, 1, 0, 0, 0, -1, -1, 3, 3, 1, 1, 1, 1, -2, 1, -2, -2, 1, 1, -1, -1, 0, 0, 0, 1, 1, 1, 0, 1, -1, 0, -1, -1, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[5, -5, 3, -1, 1, -3, 1, -1, 5, 5, 5, 5, 5, 5, 2, 2, -1, -1, 2, -1, 2, 2, 2, 2, -1, -1, -1, -1, 1, -1, 1, -1, 0, -5, -5, 3, -1, 3, -1, 1, 1, -1, 3, 3, 3, -1, 3, -1, -1, 0, 0, 0, -1, -1, -1, -3, -3, 1, 1, 1, 1, 1, 1, 1, -2, 1, 1, -2, -2, -1, -1, -1, -1, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[9, 9, 3, 3, 1, 3, 3, 1, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, -1, 9, 9, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 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, -1, -1, -1, -1, -1, -1, -1, -1]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[9, 9, -3, -3, 1, -3, -3, 1, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, 9, 9, -3, -3, -3, -3, 1, 1, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 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, -1, -1, -1, -1, -1, -1, -1, -1]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[9, -9, -3, -3, 1, 3, 3, -1, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1, -9, -9, -3, -3, -3, -3, 1, 1, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 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, -1, -1, -1, -1, -1, -1, 1, 1]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[9, -9, 3, 3, 1, -3, -3, -1, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, -9, -9, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 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, -1, -1, -1, -1, -1, -1, 1, 1]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 0, -2, 6, 2, 0, 0, 0, 10, 10, -5, -5, -5, 10, -2, -2, 4, 4, -2, 4, 1, 1, -2, 1, -2, 4, -2, -2, 2, -2, 0, 0, 0, 0, 0, -2, 6, -2, 6, 2, 2, 6, 1, 1, -2, -3, 1, -3, -3, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, -2, 1, 1, -1, 2, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 0, -2, 6, 2, 0, 0, 0, 10, 10, -5, -5, 10, -5, -2, -2, 4, 4, -2, 4, -2, 1, 1, 1, 4, -2, -2, -2, 2, -2, 0, 0, 0, 0, 0, -2, 6, -2, 6, 2, 2, -3, 1, 1, 1, 6, -2, -3, -3, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 1, 1, -2, 2, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 0, -2, 6, 2, 0, 0, 0, 10, 10, -5, 10, -5, -5, -2, -2, 4, 4, -2, 4, 1, -2, 1, 1, -2, -2, -2, 4, 2, -2, 0, 0, 0, 0, 0, -2, 6, -2, 6, 2, 2, -3, -2, 1, 1, -3, 1, -3, 6, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 1, -2, 1, -1, -1, 1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 0, -2, 6, 2, 0, 0, 0, 10, 10, 10, -5, -5, -5, -2, -2, 4, 4, -2, 4, 1, 1, 1, -2, -2, -2, 4, -2, 2, -2, 0, 0, 0, 0, 0, -2, 6, -2, 6, 2, 2, -3, 1, -2, 1, -3, 1, 6, -3, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 1, 1, 1, -1, -1, -2, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 0, 6, -2, 2, 0, 0, 0, 10, 10, -5, -5, -5, 10, 4, 4, -2, -2, 4, -2, -2, -2, 4, -2, 1, -2, 1, 1, 2, -2, 0, 0, 0, 0, 0, 6, -2, 6, -2, 2, 2, -2, -3, -3, 6, 1, -3, 1, 1, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, -2, 1, 1, -1, 2, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 0, 6, -2, 2, 0, 0, 0, 10, 10, -5, -5, 10, -5, 4, 4, -2, -2, 4, -2, 4, -2, -2, -2, -2, 1, 1, 1, 2, -2, 0, 0, 0, 0, 0, 6, -2, 6, -2, 2, 2, 1, -3, -3, -3, -2, 6, 1, 1, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 1, 1, -2, 2, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 0, 6, -2, 2, 0, 0, 0, 10, 10, -5, 10, -5, -5, 4, 4, -2, -2, 4, -2, -2, 4, -2, -2, 1, 1, 1, -2, 2, -2, 0, 0, 0, 0, 0, 6, -2, 6, -2, 2, 2, 1, 6, -3, -3, 1, -3, 1, -2, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 1, -2, 1, -1, -1, 1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 0, 6, -2, 2, 0, 0, 0, 10, 10, 10, -5, -5, -5, 4, 4, -2, -2, 4, -2, -2, -2, -2, 4, 1, 1, -2, 1, 2, -2, 0, 0, 0, 0, 0, 6, -2, 6, -2, 2, 2, 1, -3, 6, -3, 1, -3, -2, 1, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 1, 1, 1, -1, -1, -2, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 10, -2, 2, -2, -2, 2, -2, 10, 10, 10, 10, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 10, 10, -2, 2, -2, 2, -2, -2, 2, -2, -2, -2, 2, -2, 2, 2, 1, 1, 1, -1, -1, -1, -2, -2, 2, 2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, -2, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -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]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 10, 2, -2, -2, 2, -2, -2, 10, 10, 10, 10, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 10, 10, 2, -2, 2, -2, -2, -2, -2, 2, 2, 2, -2, 2, -2, -2, -1, -1, -1, 1, 1, 1, 2, 2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 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]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, -10, -2, 2, -2, 2, -2, 2, 10, 10, 10, 10, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, -10, -10, -2, 2, -2, 2, -2, -2, 2, -2, -2, -2, 2, -2, 2, 2, 1, 1, 1, -1, -1, -1, 2, 2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 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]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, -10, 2, -2, -2, -2, 2, 2, 10, 10, 10, 10, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, -10, -10, 2, -2, 2, -2, -2, -2, -2, 2, 2, 2, -2, 2, -2, -2, -1, -1, -1, 1, 1, 1, -2, -2, 2, 2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, 2, 2, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -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]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 0, -6, 2, 2, 0, 0, 0, 10, 10, -5, -5, -5, 10, 4, 4, -2, -2, 4, -2, -2, -2, 4, -2, 1, -2, 1, 1, -2, -2, 0, 0, 0, 0, 0, -6, 2, -6, 2, 2, 2, 2, 3, 3, -6, -1, 3, -1, -1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 1, 1, 1, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 0, -6, 2, 2, 0, 0, 0, 10, 10, -5, -5, 10, -5, 4, 4, -2, -2, 4, -2, 4, -2, -2, -2, -2, 1, 1, 1, -2, -2, 0, 0, 0, 0, 0, -6, 2, -6, 2, 2, 2, -1, 3, 3, 3, 2, -6, -1, -1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 0, -6, 2, 2, 0, 0, 0, 10, 10, -5, 10, -5, -5, 4, 4, -2, -2, 4, -2, -2, 4, -2, -2, 1, 1, 1, -2, -2, -2, 0, 0, 0, 0, 0, -6, 2, -6, 2, 2, 2, -1, -6, 3, 3, -1, 3, -1, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, -2, 1, 1, 1, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 0, -6, 2, 2, 0, 0, 0, 10, 10, 10, -5, -5, -5, 4, 4, -2, -2, 4, -2, -2, -2, -2, 4, 1, 1, -2, 1, -2, -2, 0, 0, 0, 0, 0, -6, 2, -6, 2, 2, 2, -1, 3, -6, 3, -1, 3, 2, -1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, 1, -2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 0, 2, -6, 2, 0, 0, 0, 10, 10, -5, -5, -5, 10, -2, -2, 4, 4, -2, 4, 1, 1, -2, 1, -2, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 2, -6, 2, -6, 2, 2, -6, -1, -1, 2, 3, -1, 3, 3, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 1, 1, 1, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 0, 2, -6, 2, 0, 0, 0, 10, 10, -5, -5, 10, -5, -2, -2, 4, 4, -2, 4, -2, 1, 1, 1, 4, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 2, -6, 2, -6, 2, 2, 3, -1, -1, -1, -6, 2, 3, 3, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 0, 2, -6, 2, 0, 0, 0, 10, 10, -5, 10, -5, -5, -2, -2, 4, 4, -2, 4, 1, -2, 1, 1, -2, -2, -2, 4, -2, -2, 0, 0, 0, 0, 0, 2, -6, 2, -6, 2, 2, 3, 2, -1, -1, 3, -1, 3, -6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, -2, 1, 1, 1, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[10, 0, 2, -6, 2, 0, 0, 0, 10, 10, 10, -5, -5, -5, -2, -2, 4, 4, -2, 4, 1, 1, 1, -2, -2, -2, 4, -2, -2, -2, 0, 0, 0, 0, 0, 2, -6, 2, -6, 2, 2, 3, -1, 2, -1, 3, -1, -6, 3, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, 1, -2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |15,5,-3,9,3,-1,3,1,15*K.1^-1,15*K.1,0,0,0,0,-3,-3*K.1,6,6*K.1,-3*K.1^-1,6*K.1^-1,0,0,0,0,0,0,0,0,3,-3,-1,1,0,5*K.1,5*K.1^-1,-3*K.1^-1,9*K.1,-3*K.1,9*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,-3,-3*K.1,-3*K.1^-1,0,0,0,-1*K.1,-1*K.1^-1,3*K.1,3*K.1^-1,0,0,0,0,2,-1,2*K.1^-1,2*K.1,-1*K.1,-1*K.1^-1,K.1^-1,K.1,0,0,0,0,0,0,0,0,-1,0,-1*K.1,-1*K.1^-1,0,0,0,3*K.1,3*K.1^-1,-3*K.1,-3*K.1^-1,0,0,0,0,0,0,0,0,-1*K.1,K.1,-1*K.1^-1,K.1^-1,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |15,5,-3,9,3,-1,3,1,15*K.1,15*K.1^-1,0,0,0,0,-3,-3*K.1^-1,6,6*K.1^-1,-3*K.1,6*K.1,0,0,0,0,0,0,0,0,3,-3,-1,1,0,5*K.1^-1,5*K.1,-3*K.1,9*K.1^-1,-3*K.1^-1,9*K.1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,-3,-3*K.1^-1,-3*K.1,0,0,0,-1*K.1^-1,-1*K.1,3*K.1^-1,3*K.1,0,0,0,0,2,-1,2*K.1,2*K.1^-1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,0,0,0,0,0,0,0,0,-1,0,-1*K.1^-1,-1*K.1,0,0,0,3*K.1^-1,3*K.1,-3*K.1^-1,-3*K.1,0,0,0,0,0,0,0,0,-1*K.1^-1,K.1^-1,-1*K.1,K.1,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |15,5,9,-3,3,3,-1,1,15*K.1^-1,15*K.1,0,0,0,0,6,6*K.1,-3,-3*K.1,6*K.1^-1,-3*K.1^-1,0,0,0,0,0,0,0,0,3,-3,-1,1,0,5*K.1,5*K.1^-1,9*K.1^-1,-3*K.1,9*K.1,-3*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,0,0,0,-3*K.1^-1,-3,-3*K.1,3*K.1,3*K.1^-1,-1*K.1,-1*K.1^-1,0,0,0,0,-1,2,-1*K.1^-1,-1*K.1,2*K.1,2*K.1^-1,K.1^-1,K.1,0,0,0,0,0,0,0,0,0,-1,0,0,-1*K.1^-1,-1*K.1,0,3*K.1,3*K.1^-1,-3*K.1,-3*K.1^-1,0,0,0,0,0,0,0,0,-1*K.1,K.1,-1*K.1^-1,K.1^-1,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |15,5,9,-3,3,3,-1,1,15*K.1,15*K.1^-1,0,0,0,0,6,6*K.1^-1,-3,-3*K.1^-1,6*K.1,-3*K.1,0,0,0,0,0,0,0,0,3,-3,-1,1,0,5*K.1^-1,5*K.1,9*K.1,-3*K.1^-1,9*K.1^-1,-3*K.1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,-3*K.1,-3,-3*K.1^-1,3*K.1^-1,3*K.1,-1*K.1^-1,-1*K.1,0,0,0,0,-1,2,-1*K.1,-1*K.1^-1,2*K.1^-1,2*K.1,K.1,K.1^-1,0,0,0,0,0,0,0,0,0,-1,0,0,-1*K.1,-1*K.1^-1,0,3*K.1^-1,3*K.1,-3*K.1^-1,-3*K.1,0,0,0,0,0,0,0,0,-1*K.1^-1,K.1^-1,-1*K.1,K.1,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |15,-5,-9,3,3,3,-1,-1,15*K.1^-1,15*K.1,0,0,0,0,6,6*K.1,-3,-3*K.1,6*K.1^-1,-3*K.1^-1,0,0,0,0,0,0,0,0,-3,-3,1,1,0,-5*K.1,-5*K.1^-1,-9*K.1^-1,3*K.1,-9*K.1,3*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,0,0,0,3*K.1^-1,3,3*K.1,3*K.1,3*K.1^-1,-1*K.1,-1*K.1^-1,0,0,0,0,1,-2,K.1^-1,K.1,-2*K.1,-2*K.1^-1,-1*K.1^-1,-1*K.1,0,0,0,0,0,0,0,0,0,-1,0,0,-1*K.1^-1,-1*K.1,0,-3*K.1,-3*K.1^-1,-3*K.1,-3*K.1^-1,0,0,0,0,0,0,0,0,K.1,K.1,K.1^-1,K.1^-1,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |15,-5,-9,3,3,3,-1,-1,15*K.1,15*K.1^-1,0,0,0,0,6,6*K.1^-1,-3,-3*K.1^-1,6*K.1,-3*K.1,0,0,0,0,0,0,0,0,-3,-3,1,1,0,-5*K.1^-1,-5*K.1,-9*K.1,3*K.1^-1,-9*K.1^-1,3*K.1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,3*K.1,3,3*K.1^-1,3*K.1^-1,3*K.1,-1*K.1^-1,-1*K.1,0,0,0,0,1,-2,K.1,K.1^-1,-2*K.1^-1,-2*K.1,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,0,0,-1,0,0,-1*K.1,-1*K.1^-1,0,-3*K.1^-1,-3*K.1,-3*K.1^-1,-3*K.1,0,0,0,0,0,0,0,0,K.1^-1,K.1^-1,K.1,K.1,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |15,-5,-3,9,3,1,-3,-1,15*K.1^-1,15*K.1,0,0,0,0,-3,-3*K.1,6,6*K.1,-3*K.1^-1,6*K.1^-1,0,0,0,0,0,0,0,0,3,-3,1,-1,0,-5*K.1,-5*K.1^-1,-3*K.1^-1,9*K.1,-3*K.1,9*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,-3,-3*K.1,-3*K.1^-1,0,0,0,K.1,K.1^-1,-3*K.1,-3*K.1^-1,0,0,0,0,-2,1,-2*K.1^-1,-2*K.1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,0,0,0,0,0,0,0,0,1,0,K.1,K.1^-1,0,0,0,3*K.1,3*K.1^-1,-3*K.1,-3*K.1^-1,0,0,0,0,0,0,0,0,K.1,-1*K.1,K.1^-1,-1*K.1^-1,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |15,-5,-3,9,3,1,-3,-1,15*K.1,15*K.1^-1,0,0,0,0,-3,-3*K.1^-1,6,6*K.1^-1,-3*K.1,6*K.1,0,0,0,0,0,0,0,0,3,-3,1,-1,0,-5*K.1^-1,-5*K.1,-3*K.1,9*K.1^-1,-3*K.1^-1,9*K.1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,-3,-3*K.1^-1,-3*K.1,0,0,0,K.1^-1,K.1,-3*K.1^-1,-3*K.1,0,0,0,0,-2,1,-2*K.1,-2*K.1^-1,K.1^-1,K.1,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,0,1,0,K.1^-1,K.1,0,0,0,3*K.1^-1,3*K.1,-3*K.1^-1,-3*K.1,0,0,0,0,0,0,0,0,K.1^-1,-1*K.1^-1,K.1,-1*K.1,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |15,-5,3,-9,3,-1,3,-1,15*K.1^-1,15*K.1,0,0,0,0,-3,-3*K.1,6,6*K.1,-3*K.1^-1,6*K.1^-1,0,0,0,0,0,0,0,0,-3,-3,1,1,0,-5*K.1,-5*K.1^-1,3*K.1^-1,-9*K.1,3*K.1,-9*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,3,3*K.1,3*K.1^-1,0,0,0,-1*K.1,-1*K.1^-1,3*K.1,3*K.1^-1,0,0,0,0,-2,1,-2*K.1^-1,-2*K.1,K.1,K.1^-1,-1*K.1^-1,-1*K.1,0,0,0,0,0,0,0,0,-1,0,-1*K.1,-1*K.1^-1,0,0,0,-3*K.1,-3*K.1^-1,-3*K.1,-3*K.1^-1,0,0,0,0,0,0,0,0,K.1,K.1,K.1^-1,K.1^-1,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |15,-5,3,-9,3,-1,3,-1,15*K.1,15*K.1^-1,0,0,0,0,-3,-3*K.1^-1,6,6*K.1^-1,-3*K.1,6*K.1,0,0,0,0,0,0,0,0,-3,-3,1,1,0,-5*K.1^-1,-5*K.1,3*K.1,-9*K.1^-1,3*K.1^-1,-9*K.1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,3,3*K.1^-1,3*K.1,0,0,0,-1*K.1^-1,-1*K.1,3*K.1^-1,3*K.1,0,0,0,0,-2,1,-2*K.1,-2*K.1^-1,K.1^-1,K.1,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,0,-1,0,-1*K.1^-1,-1*K.1,0,0,0,-3*K.1^-1,-3*K.1,-3*K.1^-1,-3*K.1,0,0,0,0,0,0,0,0,K.1^-1,K.1^-1,K.1,K.1,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |15,-5,9,-3,3,-3,1,-1,15*K.1^-1,15*K.1,0,0,0,0,6,6*K.1,-3,-3*K.1,6*K.1^-1,-3*K.1^-1,0,0,0,0,0,0,0,0,3,-3,1,-1,0,-5*K.1,-5*K.1^-1,9*K.1^-1,-3*K.1,9*K.1,-3*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,0,0,0,-3*K.1^-1,-3,-3*K.1,-3*K.1,-3*K.1^-1,K.1,K.1^-1,0,0,0,0,1,-2,K.1^-1,K.1,-2*K.1,-2*K.1^-1,-1*K.1^-1,-1*K.1,0,0,0,0,0,0,0,0,0,1,0,0,K.1^-1,K.1,0,3*K.1,3*K.1^-1,-3*K.1,-3*K.1^-1,0,0,0,0,0,0,0,0,K.1,-1*K.1,K.1^-1,-1*K.1^-1,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |15,-5,9,-3,3,-3,1,-1,15*K.1,15*K.1^-1,0,0,0,0,6,6*K.1^-1,-3,-3*K.1^-1,6*K.1,-3*K.1,0,0,0,0,0,0,0,0,3,-3,1,-1,0,-5*K.1^-1,-5*K.1,9*K.1,-3*K.1^-1,9*K.1^-1,-3*K.1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,-3*K.1,-3,-3*K.1^-1,-3*K.1^-1,-3*K.1,K.1^-1,K.1,0,0,0,0,1,-2,K.1,K.1^-1,-2*K.1^-1,-2*K.1,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,0,0,1,0,0,K.1,K.1^-1,0,3*K.1^-1,3*K.1,-3*K.1^-1,-3*K.1,0,0,0,0,0,0,0,0,K.1^-1,-1*K.1^-1,K.1,-1*K.1,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |15,5,-9,3,3,-3,1,1,15*K.1^-1,15*K.1,0,0,0,0,6,6*K.1,-3,-3*K.1,6*K.1^-1,-3*K.1^-1,0,0,0,0,0,0,0,0,-3,-3,-1,-1,0,5*K.1,5*K.1^-1,-9*K.1^-1,3*K.1,-9*K.1,3*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,0,0,0,3*K.1^-1,3,3*K.1,-3*K.1,-3*K.1^-1,K.1,K.1^-1,0,0,0,0,-1,2,-1*K.1^-1,-1*K.1,2*K.1,2*K.1^-1,K.1^-1,K.1,0,0,0,0,0,0,0,0,0,1,0,0,K.1^-1,K.1,0,-3*K.1,-3*K.1^-1,-3*K.1,-3*K.1^-1,0,0,0,0,0,0,0,0,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |15,5,-9,3,3,-3,1,1,15*K.1,15*K.1^-1,0,0,0,0,6,6*K.1^-1,-3,-3*K.1^-1,6*K.1,-3*K.1,0,0,0,0,0,0,0,0,-3,-3,-1,-1,0,5*K.1^-1,5*K.1,-9*K.1,3*K.1^-1,-9*K.1^-1,3*K.1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,3*K.1,3,3*K.1^-1,-3*K.1^-1,-3*K.1,K.1^-1,K.1,0,0,0,0,-1,2,-1*K.1,-1*K.1^-1,2*K.1^-1,2*K.1,K.1,K.1^-1,0,0,0,0,0,0,0,0,0,1,0,0,K.1,K.1^-1,0,-3*K.1^-1,-3*K.1,-3*K.1^-1,-3*K.1,0,0,0,0,0,0,0,0,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |15,5,3,-9,3,1,-3,1,15*K.1^-1,15*K.1,0,0,0,0,-3,-3*K.1,6,6*K.1,-3*K.1^-1,6*K.1^-1,0,0,0,0,0,0,0,0,-3,-3,-1,-1,0,5*K.1,5*K.1^-1,3*K.1^-1,-9*K.1,3*K.1,-9*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,3,3*K.1,3*K.1^-1,0,0,0,K.1,K.1^-1,-3*K.1,-3*K.1^-1,0,0,0,0,2,-1,2*K.1^-1,2*K.1,-1*K.1,-1*K.1^-1,K.1^-1,K.1,0,0,0,0,0,0,0,0,1,0,K.1,K.1^-1,0,0,0,-3*K.1,-3*K.1^-1,-3*K.1,-3*K.1^-1,0,0,0,0,0,0,0,0,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |15,5,3,-9,3,1,-3,1,15*K.1,15*K.1^-1,0,0,0,0,-3,-3*K.1^-1,6,6*K.1^-1,-3*K.1,6*K.1,0,0,0,0,0,0,0,0,-3,-3,-1,-1,0,5*K.1^-1,5*K.1,3*K.1,-9*K.1^-1,3*K.1^-1,-9*K.1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,3,3*K.1^-1,3*K.1,0,0,0,K.1^-1,K.1,-3*K.1^-1,-3*K.1,0,0,0,0,2,-1,2*K.1,2*K.1^-1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,0,0,0,0,0,0,0,0,1,0,K.1^-1,K.1,0,0,0,-3*K.1^-1,-3*K.1,-3*K.1^-1,-3*K.1,0,0,0,0,0,0,0,0,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; x := CR!\[16, 16, 0, 0, 0, 0, 0, 0, 16, 16, 16, 16, 16, 16, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 1, 16, 16, 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, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[16, -16, 0, 0, 0, 0, 0, 0, 16, 16, 16, 16, 16, 16, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 1, -16, -16, 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, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, -1, -1]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[18, 0, 6, 6, 2, 0, 0, 0, 18, 18, -9, -9, -9, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, 0, 0, 6, 6, 6, 6, 2, 2, 6, -3, -3, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, -1, -1, 1, -2, -1, 1, 1, 0, 0, 0, 0, -2, -2, 1, 1, -2, 1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[18, 0, 6, 6, 2, 0, 0, 0, 18, 18, -9, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, 0, 0, 6, 6, 6, 6, 2, 2, -3, -3, -3, -3, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -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, -2, -2, 2, 2, -1, -1, 2, -2, 1, -1, 1, 1, 0, 0, 0, 0, -2, -2, 1, 1, 1, -2, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[18, 0, 6, 6, 2, 0, 0, 0, 18, 18, -9, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, 0, 0, 6, 6, 6, 6, 2, 2, -3, 6, -3, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -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, -2, -2, 2, 2, -1, 2, -1, 1, 1, -1, -2, 1, 0, 0, 0, 0, -2, -2, 1, -2, 1, 1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[18, 0, 6, 6, 2, 0, 0, 0, 18, 18, 18, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, 0, 0, 6, 6, 6, 6, 2, 2, -3, -3, 6, -3, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -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, -2, -2, 2, 2, -1, -1, -1, 1, 1, 2, 1, -2, 0, 0, 0, 0, -2, -2, -2, 1, 1, 1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[18, 0, -6, -6, 2, 0, 0, 0, 18, 18, -9, -9, -9, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, -6, -6, -6, -6, 2, 2, -6, 3, 3, -6, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 0, 0, 0, 0, -2, -2, 1, 1, -2, 1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[18, 0, -6, -6, 2, 0, 0, 0, 18, 18, -9, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, -6, -6, -6, -6, 2, 2, 3, 3, 3, 3, -6, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -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, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, -2, -2, 1, 1, 1, -2, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[18, 0, -6, -6, 2, 0, 0, 0, 18, 18, -9, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, -6, -6, -6, -6, 2, 2, 3, -6, 3, 3, 3, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -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, 2, 2, 2, 2, -1, 2, -1, -1, -1, -1, 2, -1, 0, 0, 0, 0, -2, -2, 1, -2, 1, 1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[18, 0, -6, -6, 2, 0, 0, 0, 18, 18, 18, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, -6, -6, -6, -6, 2, 2, 3, 3, -6, 3, 3, 3, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -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, 2, 2, 2, 2, -1, -1, -1, -1, -1, 2, -1, 2, 0, 0, 0, 0, -2, -2, -2, 1, 1, 1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[20, 0, -4, 4, -4, 0, 0, 0, 20, 20, -10, -10, -10, 20, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, -4, -4, 4, 2, 2, -4, -2, 2, -2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 2, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, -1, 2, -1, 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]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[20, 0, -4, 4, -4, 0, 0, 0, 20, 20, -10, -10, 20, -10, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, -4, -4, -2, 2, 2, 2, 4, -4, -2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, -1, -1, 2, 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]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[20, 0, -4, 4, -4, 0, 0, 0, 20, 20, -10, 20, -10, -10, 2, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, -4, -4, -2, -4, 2, 2, -2, 2, -2, 4, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, -1, -1, -1, 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]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[20, 0, -4, 4, -4, 0, 0, 0, 20, 20, 20, -10, -10, -10, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, -4, -4, -2, 2, -4, 2, -2, 2, 4, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 2, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, -1, -1, -2, -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]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[20, 0, 4, -4, -4, 0, 0, 0, 20, 20, -10, -10, -10, 20, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -4, -4, -4, -4, -2, -2, 4, 2, -2, 2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 2, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, 1, -2, 1, -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]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[20, 0, 4, -4, -4, 0, 0, 0, 20, 20, -10, -10, 20, -10, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -4, -4, -4, 2, -2, -2, -2, -4, 4, 2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 1, 1, -2, -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]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[20, 0, 4, -4, -4, 0, 0, 0, 20, 20, -10, 20, -10, -10, 2, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -4, -4, -4, 2, 4, -2, -2, 2, -2, 2, -4, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 2, 1, 1, 1, -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]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[20, 0, 4, -4, -4, 0, 0, 0, 20, 20, 20, -10, -10, -10, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -4, -4, -4, 2, -2, 4, -2, 2, -2, -4, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 2, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -2, 1, 1, 2, 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]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |27,9,9,9,3,3,3,1,27*K.1^-1,27*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,3,1,-1,-3,9*K.1,9*K.1^-1,9*K.1^-1,9*K.1,9*K.1,9*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3*K.1,3*K.1^-1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,0,0,K.1^-1,K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-3*K.1,-3*K.1^-1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,K.1,-1*K.1,K.1^-1,-1*K.1^-1,-3*K.1,-3*K.1^-1,0,0,0,0,-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 |27,9,9,9,3,3,3,1,27*K.1,27*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,3,1,-1,-3,9*K.1^-1,9*K.1,9*K.1,9*K.1^-1,9*K.1^-1,9*K.1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3*K.1^-1,3*K.1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,0,0,K.1,K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-3*K.1^-1,-3*K.1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,K.1^-1,-1*K.1^-1,K.1,-1*K.1,-3*K.1^-1,-3*K.1,0,0,0,0,-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 |27,-9,-9,-9,3,3,3,-1,27*K.1^-1,27*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,-1,-1,-3,-9*K.1,-9*K.1^-1,-9*K.1^-1,-9*K.1,-9*K.1,-9*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3*K.1,3*K.1^-1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,0,0,-1*K.1^-1,-1*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3*K.1,3*K.1^-1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,-1*K.1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-3*K.1,-3*K.1^-1,0,0,0,0,K.1^-1,K.1]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |27,-9,-9,-9,3,3,3,-1,27*K.1,27*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,-1,-1,-3,-9*K.1^-1,-9*K.1,-9*K.1,-9*K.1^-1,-9*K.1^-1,-9*K.1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3*K.1^-1,3*K.1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,0,0,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3*K.1^-1,3*K.1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,-1*K.1^-1,-1*K.1^-1,-1*K.1,-1*K.1,-3*K.1^-1,-3*K.1,0,0,0,0,K.1,K.1^-1]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |27,-9,9,9,3,-3,-3,-1,27*K.1^-1,27*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,3,-1,1,-3,-9*K.1,-9*K.1^-1,9*K.1^-1,9*K.1,9*K.1,9*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3*K.1,-3*K.1^-1,-3*K.1,-3*K.1^-1,0,0,0,0,0,0,0,0,0,0,-1*K.1^-1,-1*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-3*K.1,-3*K.1^-1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,-1*K.1,K.1,-1*K.1^-1,K.1^-1,-3*K.1,-3*K.1^-1,0,0,0,0,K.1^-1,K.1]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |27,-9,9,9,3,-3,-3,-1,27*K.1,27*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,3,-1,1,-3,-9*K.1^-1,-9*K.1,9*K.1,9*K.1^-1,9*K.1^-1,9*K.1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3*K.1^-1,-3*K.1,-3*K.1^-1,-3*K.1,0,0,0,0,0,0,0,0,0,0,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-3*K.1^-1,-3*K.1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,-1*K.1^-1,K.1^-1,-1*K.1,K.1,-3*K.1^-1,-3*K.1,0,0,0,0,K.1,K.1^-1]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |27,9,-9,-9,3,-3,-3,1,27*K.1^-1,27*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,1,1,-3,9*K.1,9*K.1^-1,-9*K.1^-1,-9*K.1,-9*K.1,-9*K.1^-1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3*K.1,-3*K.1^-1,-3*K.1,-3*K.1^-1,0,0,0,0,0,0,0,0,0,0,K.1^-1,K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,3*K.1,3*K.1^-1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,K.1,K.1,K.1^-1,K.1^-1,-3*K.1,-3*K.1^-1,0,0,0,0,-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 |27,9,-9,-9,3,-3,-3,1,27*K.1,27*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,1,1,-3,9*K.1^-1,9*K.1,-9*K.1,-9*K.1^-1,-9*K.1^-1,-9*K.1,3*K.1,3*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3*K.1^-1,-3*K.1,-3*K.1^-1,-3*K.1,0,0,0,0,0,0,0,0,0,0,K.1,K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,3*K.1^-1,3*K.1,3*K.1^-1,3*K.1,0,0,0,0,0,0,0,0,K.1^-1,K.1^-1,K.1,K.1,-3*K.1^-1,-3*K.1,0,0,0,0,-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 |30,-10,-6,6,-6,2,-2,2,30*K.1^-1,30*K.1,0,0,0,0,3,3*K.1,3,3*K.1,3*K.1^-1,3*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-10*K.1,-10*K.1^-1,-6*K.1^-1,6*K.1,-6*K.1,6*K.1^-1,-6*K.1^-1,-6*K.1,0,0,0,0,0,0,0,0,3,3*K.1,3*K.1^-1,-3*K.1^-1,-3,-3*K.1,2*K.1,2*K.1^-1,-2*K.1,-2*K.1^-1,0,0,0,0,-1,-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,2*K.1^-1,2*K.1,0,0,0,0,0,0,0,0,-1,1,-1*K.1,-1*K.1^-1,K.1^-1,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]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |30,-10,-6,6,-6,2,-2,2,30*K.1,30*K.1^-1,0,0,0,0,3,3*K.1^-1,3,3*K.1^-1,3*K.1,3*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,-10*K.1^-1,-10*K.1,-6*K.1,6*K.1^-1,-6*K.1^-1,6*K.1,-6*K.1,-6*K.1^-1,0,0,0,0,0,0,0,0,3,3*K.1^-1,3*K.1,-3*K.1,-3,-3*K.1^-1,2*K.1^-1,2*K.1,-2*K.1^-1,-2*K.1,0,0,0,0,-1,-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,2*K.1,2*K.1^-1,0,0,0,0,0,0,0,0,-1,1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |30,-10,6,-6,-6,-2,2,2,30*K.1^-1,30*K.1,0,0,0,0,3,3*K.1,3,3*K.1,3*K.1^-1,3*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-10*K.1,-10*K.1^-1,6*K.1^-1,-6*K.1,6*K.1,-6*K.1^-1,-6*K.1^-1,-6*K.1,0,0,0,0,0,0,0,0,-3,-3*K.1,-3*K.1^-1,3*K.1^-1,3,3*K.1,-2*K.1,-2*K.1^-1,2*K.1,2*K.1^-1,0,0,0,0,-1,-1,-1*K.1^-1,-1*K.1,-1*K.1,-1*K.1^-1,2*K.1^-1,2*K.1,0,0,0,0,0,0,0,0,1,-1,K.1,K.1^-1,-1*K.1^-1,-1*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]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |30,-10,6,-6,-6,-2,2,2,30*K.1,30*K.1^-1,0,0,0,0,3,3*K.1^-1,3,3*K.1^-1,3*K.1,3*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,-10*K.1^-1,-10*K.1,6*K.1,-6*K.1^-1,6*K.1^-1,-6*K.1,-6*K.1,-6*K.1^-1,0,0,0,0,0,0,0,0,-3,-3*K.1^-1,-3*K.1,3*K.1,3,3*K.1^-1,-2*K.1^-1,-2*K.1,2*K.1^-1,2*K.1,0,0,0,0,-1,-1,-1*K.1,-1*K.1^-1,-1*K.1^-1,-1*K.1,2*K.1,2*K.1^-1,0,0,0,0,0,0,0,0,1,-1,K.1^-1,K.1,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |30,10,-6,6,-6,-2,2,-2,30*K.1^-1,30*K.1,0,0,0,0,3,3*K.1,3,3*K.1,3*K.1^-1,3*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,10*K.1,10*K.1^-1,-6*K.1^-1,6*K.1,-6*K.1,6*K.1^-1,-6*K.1^-1,-6*K.1,0,0,0,0,0,0,0,0,3,3*K.1,3*K.1^-1,-3*K.1^-1,-3,-3*K.1,-2*K.1,-2*K.1^-1,2*K.1,2*K.1^-1,0,0,0,0,1,1,K.1^-1,K.1,K.1,K.1^-1,-2*K.1^-1,-2*K.1,0,0,0,0,0,0,0,0,1,-1,K.1,K.1^-1,-1*K.1^-1,-1*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]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |30,10,-6,6,-6,-2,2,-2,30*K.1,30*K.1^-1,0,0,0,0,3,3*K.1^-1,3,3*K.1^-1,3*K.1,3*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,10*K.1^-1,10*K.1,-6*K.1,6*K.1^-1,-6*K.1^-1,6*K.1,-6*K.1,-6*K.1^-1,0,0,0,0,0,0,0,0,3,3*K.1^-1,3*K.1,-3*K.1,-3,-3*K.1^-1,-2*K.1^-1,-2*K.1,2*K.1^-1,2*K.1,0,0,0,0,1,1,K.1,K.1^-1,K.1^-1,K.1,-2*K.1,-2*K.1^-1,0,0,0,0,0,0,0,0,1,-1,K.1^-1,K.1,-1*K.1,-1*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |30,10,6,-6,-6,2,-2,-2,30*K.1^-1,30*K.1,0,0,0,0,3,3*K.1,3,3*K.1,3*K.1^-1,3*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,10*K.1,10*K.1^-1,6*K.1^-1,-6*K.1,6*K.1,-6*K.1^-1,-6*K.1^-1,-6*K.1,0,0,0,0,0,0,0,0,-3,-3*K.1,-3*K.1^-1,3*K.1^-1,3,3*K.1,2*K.1,2*K.1^-1,-2*K.1,-2*K.1^-1,0,0,0,0,1,1,K.1^-1,K.1,K.1,K.1^-1,-2*K.1^-1,-2*K.1,0,0,0,0,0,0,0,0,-1,1,-1*K.1,-1*K.1^-1,K.1^-1,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]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |30,10,6,-6,-6,2,-2,-2,30*K.1,30*K.1^-1,0,0,0,0,3,3*K.1^-1,3,3*K.1^-1,3*K.1,3*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,10*K.1^-1,10*K.1,6*K.1,-6*K.1^-1,6*K.1^-1,-6*K.1,-6*K.1,-6*K.1^-1,0,0,0,0,0,0,0,0,-3,-3*K.1^-1,-3*K.1,3*K.1,3,3*K.1^-1,2*K.1^-1,2*K.1,-2*K.1^-1,-2*K.1,0,0,0,0,1,1,K.1,K.1^-1,K.1^-1,K.1,-2*K.1,-2*K.1^-1,0,0,0,0,0,0,0,0,-1,1,-1*K.1^-1,-1*K.1,K.1,K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; x := CR!\[32, 0, 0, 0, 0, 0, 0, 0, 32, 32, -16, -16, -16, 32, -4, -4, -4, -4, -4, -4, 2, 2, -4, 2, 2, -4, 2, 2, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 2, 2, -1, -1, 2, -1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[32, 0, 0, 0, 0, 0, 0, 0, 32, 32, -16, -16, 32, -16, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, -4, 2, 2, 2, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 2, 2, -1, -1, -1, 2, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[32, 0, 0, 0, 0, 0, 0, 0, 32, 32, -16, 32, -16, -16, -4, -4, -4, -4, -4, -4, 2, -4, 2, 2, 2, 2, 2, -4, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 2, 2, -1, 2, -1, -1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; x := CR!\[32, 0, 0, 0, 0, 0, 0, 0, 32, 32, 32, -16, -16, -16, -4, -4, -4, -4, -4, -4, 2, 2, 2, -4, 2, 2, -4, 2, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, 0, 0]; x`IsCharacter := true; x`Schur := 1; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |48,16,0,0,0,0,0,0,48*K.1^-1,48*K.1,0,0,0,0,-6,-6*K.1,-6,-6*K.1,-6*K.1^-1,-6*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,3,16*K.1,16*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,-2,-2,-2*K.1^-1,-2*K.1,-2*K.1,-2*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3*K.1,3*K.1^-1,0,0,0,0,K.1^-1,K.1]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |48,16,0,0,0,0,0,0,48*K.1,48*K.1^-1,0,0,0,0,-6,-6*K.1^-1,-6,-6*K.1^-1,-6*K.1,-6*K.1,0,0,0,0,0,0,0,0,0,0,0,0,3,16*K.1^-1,16*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,-2,-2,-2*K.1,-2*K.1^-1,-2*K.1^-1,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3*K.1^-1,3*K.1,0,0,0,0,K.1,K.1^-1]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; K := CyclotomicField(3: Sparse := true); S := [ K |48,-16,0,0,0,0,0,0,48*K.1^-1,48*K.1,0,0,0,0,-6,-6*K.1,-6,-6*K.1,-6*K.1^-1,-6*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,3,-16*K.1,-16*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2*K.1^-1,2*K.1,2*K.1,2*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3*K.1,3*K.1^-1,0,0,0,0,-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 |48,-16,0,0,0,0,0,0,48*K.1,48*K.1^-1,0,0,0,0,-6,-6*K.1^-1,-6,-6*K.1^-1,-6*K.1,-6*K.1,0,0,0,0,0,0,0,0,0,0,0,0,3,-16*K.1^-1,-16*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2*K.1,2*K.1^-1,2*K.1^-1,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3*K.1^-1,3*K.1,0,0,0,0,-1*K.1,-1*K.1^-1]; x := CR!S; x`IsCharacter := true; x`Schur := 0; x`IsIrreducible := true; _ := CharacterTable(G : Check := 0); chartbl_38880_bf:= KnownIrreducibles(CR);