# Group 240.165 downloaded from the LMFDB on 22 October 2025. ## Various presentations of this group are stored in this file: # GPC is polycyclic presentation GPerm is permutation group # GLZ, GLFp, GLZA, GLZq, GLFq if they exist are matrix groups # Many characteristics of the group are stored as booleans in a record: # Agroup, Zgroup, abelian, almost_simple,cyclic, metabelian, # metacyclic, monomial, nilpotent, perfect, quasisimple, rational, # solvable, supersolvable # The character table is stored as a record chartbl_n_i where n is the order # of the group and i is which group of that order it is. The record is # converted to a character table using ConvertToLibraryCharacterTableNC # Constructions GPC := PcGroupCode(6604223689737096648581127,240); a := GPC.1; b := GPC.2; c := GPC.3; GPerm := Group( (1,2,3,5)(4,8,7,6)(10,11), (1,3)(2,5)(4,7)(6,8)(17,18), (1,4,3,7)(2,6,5,8), (12,13,14,15,16), (1,3)(2,5)(4,7)(6,8), (9,10,11) ); GLFp := Group([[[ Z(11), Z(11)^0, Z(11)^9 ], [ Z(11), 0*Z(11), Z(11)^3 ], [ Z(11)^2, Z(11), Z(11)^7 ]], [[ Z(11)^4, Z(11)^5, Z(11)^4 ], [ Z(11)^5, Z(11)^6, Z(11)^8 ], [ Z(11)^4, Z(11)^4, 0*Z(11) ]], [[ Z(11)^0, 0*Z(11), 0*Z(11) ], [ Z(11)^5, Z(11)^5, 0*Z(11) ], [ Z(11), Z(11)^2, Z(11)^0 ]], [[ Z(11), 0*Z(11), 0*Z(11) ], [ Z(11)^8, Z(11)^3, 0*Z(11) ], [ Z(11)^4, Z(11)^5, Z(11) ]], [[ Z(11)^3, Z(11)^7, Z(11)^6 ], [ Z(11)^0, Z(11)^0, Z(11)^0 ], [ Z(11)^8, Z(11)^2, Z(11)^0 ]], [[ Z(11)^5, 0*Z(11), 0*Z(11) ], [ 0*Z(11), Z(11)^5, 0*Z(11) ], [ 0*Z(11), 0*Z(11), Z(11)^5 ]]]); # Booleans booleans_240_165 := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := true, metacyclic := false, monomial := true, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := true); # Character Table chartbl_240_165:=rec(); chartbl_240_165.IsFinite:= true; chartbl_240_165.UnderlyingCharacteristic:= 0; chartbl_240_165.UnderlyingGroup:= GPC; chartbl_240_165.Size:= 240; chartbl_240_165.InfoText:= "Character table for group 240.165 downloaded from the LMFDB."; chartbl_240_165.Identifier:= " C30:Q8 "; chartbl_240_165.NrConjugacyClasses:= 90; chartbl_240_165.ConjugacyClasses:= [ of ..., f4*f5*f6^2, f1, f1*f4*f5*f6^2, f5*f6^3, f3*f4*f6, f1*f3*f4*f6, f2, f2*f3*f6^2, f1*f2, f1*f2*f3*f6^2, f6^4, f6, f6^3, f6^2, f1*f5^2*f6, f1*f4*f5^2, f4*f5^2, f4*f5*f6^4, f4*f5, f4*f5*f6^3, f4*f5*f6, f1*f6, f1*f6^4, f1*f6^3, f1*f6^2, f1*f4*f5, f1*f4*f5*f6^4, f1*f4*f5*f6, f1*f4*f5*f6^3, f3*f5, f3*f6^2, f1*f3*f5, f1*f3*f6^2, f5^2, f5*f6^4, f5*f6, f5^2*f6^3, f3*f4, f3*f5^2*f6^4, f3*f5^2, f3*f4*f6^4, f1*f3*f4, f1*f3*f5^2*f6^4, f1*f3*f5^2, f1*f3*f4*f6^4, f2*f6, f2*f5^2, f2*f6^3, f2*f5, f2*f3, f2*f3*f5^2, f2*f3*f6, f2*f3*f6^3, f1*f2*f6, f1*f2*f5^2, f1*f2*f6^3, f1*f2*f5, f1*f2*f3, f1*f2*f3*f5^2, f1*f2*f3*f6, f1*f2*f3*f6^3, f1*f5, f1*f5*f6, f1*f5^2, f1*f5^2*f6^2, f1*f4, f1*f4*f6^3, f1*f4*f6, f1*f4*f6^2, f4, f4*f5^2*f6^4, f4*f6, f4*f5^2*f6^3, f3, f3*f6^4, f3*f5*f6, f3*f5*f6^4, f3*f6, f3*f6^3, f3*f5*f6^2, f3*f5*f6^3, f1*f3, f1*f3*f6^4, f1*f3*f5*f6, f1*f3*f5*f6^4, f1*f3*f6, f1*f3*f6^3, f1*f3*f5*f6^2, f1*f3*f5*f6^3]; chartbl_240_165.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90]; chartbl_240_165.ComputedPowerMaps:= [ , [1, 1, 1, 1, 5, 2, 2, 2, 2, 2, 2, 14, 15, 13, 12, 5, 5, 5, 12, 13, 15, 14, 15, 14, 13, 12, 13, 12, 14, 15, 18, 18, 18, 18, 37, 38, 36, 35, 20, 19, 22, 21, 20, 19, 22, 21, 19, 20, 21, 22, 21, 22, 20, 19, 19, 20, 21, 22, 21, 22, 20, 19, 35, 36, 37, 38, 38, 37, 35, 36, 38, 37, 35, 36, 71, 72, 73, 74, 74, 73, 72, 71, 71, 72, 73, 74, 74, 73, 72, 71], [1, 2, 3, 4, 1, 6, 7, 8, 9, 10, 11, 15, 14, 12, 13, 3, 4, 2, 21, 22, 20, 19, 25, 26, 24, 23, 29, 30, 28, 27, 6, 6, 7, 7, 15, 14, 12, 13, 41, 42, 40, 39, 45, 46, 44, 43, 49, 50, 48, 47, 53, 54, 52, 51, 57, 58, 56, 55, 61, 62, 60, 59, 23, 24, 26, 25, 27, 28, 30, 29, 20, 19, 21, 22, 39, 40, 42, 41, 41, 42, 40, 39, 43, 44, 46, 45, 45, 46, 44, 43], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 1, 1, 1, 16, 17, 18, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 32, 31, 34, 33, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 31, 31, 32, 32, 31, 31, 32, 32, 33, 33, 34, 34, 33, 33, 34, 34]]; chartbl_240_165.SizesCentralizers:= [240, 240, 240, 240, 120, 120, 120, 40, 40, 40, 40, 240, 240, 240, 240, 120, 120, 120, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120]; chartbl_240_165.ClassNames:= ["1A", "2A", "2B", "2C", "3A", "4A", "4B", "4C", "4D", "4E", "4F", "5A1", "5A-1", "5A2", "5A-2", "6A", "6B", "6C", "10A1", "10A-1", "10A3", "10A-3", "10B1", "10B-1", "10B3", "10B-3", "10C1", "10C-1", "10C3", "10C-3", "12A1", "12A5", "12B1", "12B5", "15A1", "15A-1", "15A2", "15A-2", "20A1", "20A-1", "20A3", "20A-3", "20B1", "20B-1", "20B3", "20B-3", "20C1", "20C-1", "20C3", "20C-3", "20D1", "20D-1", "20D3", "20D-3", "20E1", "20E-1", "20E3", "20E-3", "20F1", "20F-1", "20F3", "20F-3", "30A1", "30A-1", "30A7", "30A-7", "30B1", "30B-1", "30B7", "30B-7", "30C1", "30C-1", "30C7", "30C-7", "60A1", "60A-1", "60A7", "60A-7", "60A13", "60A-13", "60A19", "60A-19", "60B1", "60B-1", "60B7", "60B-7", "60B13", "60B-13", "60B19", "60B-19"]; chartbl_240_165.OrderClassRepresentatives:= [1, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 15, 15, 15, 15, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60]; chartbl_240_165.Irr:= [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1], [1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1], [1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1], [1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1], [1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, E(5)^-2, E(5), E(5)^-1, E(5)^2, 1, 1, 1, E(5)^-2, E(5)^2, E(5)^2, E(5)^-1, E(5), E(5)^2, E(5), E(5)^-1, E(5)^-2, E(5)^-1, E(5)^-2, E(5), 1, 1, 1, 1, E(5)^-1, E(5)^2, E(5)^-2, E(5), E(5)^-1, E(5)^-2, E(5)^2, E(5), E(5)^2, E(5)^-2, E(5), E(5)^-1, E(5)^-2, E(5)^2, E(5)^-1, E(5), E(5)^-1, E(5)^-2, E(5), E(5)^2, E(5)^-2, E(5)^2, E(5)^-1, E(5), E(5)^-1, E(5)^-2, E(5), E(5)^2, E(5)^-2, E(5)^-1, E(5)^-2, E(5), E(5)^2, E(5), E(5), E(5)^-1, E(5)^-1, E(5)^2, E(5)^-2, E(5)^2, E(5)^2, E(5)^2, E(5)^-2, E(5), E(5)^-1, E(5)^2, E(5), E(5)^-2, E(5)^-1, E(5), E(5)^2, E(5)^-2, E(5), E(5)^-1, E(5)^-1, E(5)^-2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, E(5)^2, E(5)^-1, E(5), E(5)^-2, 1, 1, 1, E(5)^2, E(5)^-2, E(5)^-2, E(5), E(5)^-1, E(5)^-2, E(5)^-1, E(5), E(5)^2, E(5), E(5)^2, E(5)^-1, 1, 1, 1, 1, E(5), E(5)^-2, E(5)^2, E(5)^-1, E(5), E(5)^2, E(5)^-2, E(5)^-1, E(5)^-2, E(5)^2, E(5)^-1, E(5), E(5)^2, E(5)^-2, E(5), E(5)^-1, E(5), E(5)^2, E(5)^-1, E(5)^-2, E(5)^2, E(5)^-2, E(5), E(5)^-1, E(5), E(5)^2, E(5)^-1, E(5)^-2, E(5)^2, E(5), E(5)^2, E(5)^-1, E(5)^-2, E(5)^-1, E(5)^-1, E(5), E(5), E(5)^-2, E(5)^2, E(5)^-2, E(5)^-2, E(5)^-2, E(5)^2, E(5)^-1, E(5), E(5)^-2, E(5)^-1, E(5)^2, E(5), E(5)^-1, E(5)^-2, E(5)^2, E(5)^-1, E(5), E(5), E(5)^2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, E(5)^-1, E(5)^-2, E(5)^2, E(5), 1, 1, 1, E(5)^-1, E(5), E(5), E(5)^2, E(5)^-2, E(5), E(5)^-2, E(5)^2, E(5)^-1, E(5)^2, E(5)^-1, E(5)^-2, 1, 1, 1, 1, E(5)^2, E(5), E(5)^-1, E(5)^-2, E(5)^2, E(5)^-1, E(5), E(5)^-2, E(5), E(5)^-1, E(5)^-2, E(5)^2, E(5)^-1, E(5), E(5)^2, E(5)^-2, E(5)^2, E(5)^-1, E(5)^-2, E(5), E(5)^-1, E(5), E(5)^2, E(5)^-2, E(5)^2, E(5)^-1, E(5)^-2, E(5), E(5)^-1, E(5)^2, E(5)^-1, E(5)^-2, E(5), E(5)^-2, E(5)^-2, E(5)^2, E(5)^2, E(5), E(5)^-1, E(5), E(5), E(5), E(5)^-1, E(5)^-2, E(5)^2, E(5), E(5)^-2, E(5)^-1, E(5)^2, E(5)^-2, E(5), E(5)^-1, E(5)^-2, E(5)^2, E(5)^2, 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E(5)^2, -1, -1, -1, -1, E(5)^-2, E(5)^-1, E(5), E(5)^2, -1*E(5)^-2, -1*E(5), -1*E(5)^-1, -1*E(5)^2, -1*E(5)^-1, -1*E(5), -1*E(5)^2, -1*E(5)^-2, E(5), E(5)^-1, E(5)^-2, E(5)^2, -1*E(5)^-2, -1*E(5), -1*E(5)^2, -1*E(5)^-1, E(5), E(5)^-1, E(5)^-2, E(5)^2, -1*E(5)^-2, -1*E(5), -1*E(5)^2, -1*E(5)^-1, E(5), E(5)^-2, E(5), E(5)^2, E(5)^-1, E(5)^2, E(5)^2, E(5)^-2, E(5)^-2, E(5)^-1, E(5), E(5)^-1, -1*E(5)^-1, -1*E(5)^-1, -1*E(5), -1*E(5)^2, -1*E(5)^-2, -1*E(5)^-1, -1*E(5)^2, -1*E(5), -1*E(5)^-2, -1*E(5)^2, -1*E(5)^-1, -1*E(5), -1*E(5)^2, -1*E(5)^-2, -1*E(5)^-2, -1*E(5)], [1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, E(5)^-2, E(5), E(5)^-1, E(5)^2, 1, 1, 1, E(5)^-2, E(5)^2, E(5)^2, E(5)^-1, E(5), E(5)^2, E(5), E(5)^-1, E(5)^-2, E(5)^-1, E(5)^-2, E(5), 1, 1, 1, 1, E(5)^-1, E(5)^2, E(5)^-2, E(5), E(5)^-1, E(5)^-2, E(5)^2, E(5), E(5)^2, E(5)^-2, E(5), E(5)^-1, -1*E(5)^-2, -1*E(5)^2, -1*E(5)^-1, -1*E(5), -1*E(5)^-1, -1*E(5)^-2, -1*E(5), -1*E(5)^2, -1*E(5)^-2, -1*E(5)^2, -1*E(5)^-1, -1*E(5), -1*E(5)^-1, 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-1*E(5), -1*E(5)^-1, -1*E(5)^-2, -1*E(5)^2, -1*E(5)^-2, -1*E(5), -1*E(5)^2, -1*E(5)^-1, E(5), E(5)^-2, E(5), E(5)^2, E(5)^-1, E(5)^2, E(5)^2, E(5)^-2, E(5)^-2, E(5)^-1, E(5), E(5)^-1, E(5)^-1, E(5)^-1, E(5), E(5)^2, E(5)^-2, E(5)^-1, E(5)^2, E(5), E(5)^-2, E(5)^2, E(5)^-1, E(5), E(5)^2, E(5)^-2, E(5)^-2, E(5)], [2, 2, 2, 2, -1, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 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, -1, -1, -1], [2, 2, -2, -2, -1, -2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 1, 1, -1, -2, -2, -2, 2, -2, 2, -2, -2, -2, -2, 2, 2, 1, 1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 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, 1, -1, -1], [2, 2, -2, -2, -1, 2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 1, 1, -1, -2, -2, -2, 2, -2, 2, -2, -2, -2, -2, 2, 2, -1, -1, 1, 1, -1, -1, -1, -1, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 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, -1, 1, 1], [2, 2, 2, 2, -1, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 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, 1, 1, 1], [2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, 2, -2, 2, 2, -2, -2, 2, -2, -2, -2, -2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 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, 2, 2, -2, -2, 2, -2, 2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 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, -2, -2, -2, -2, -2, 2, -2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, -2, 2, -1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, -1, 1, 2, 2, -2, -2, 2, -2, -2, -2, -2, 2, -2, -2, -1*E(12)-E(12)^-1, E(12)+E(12)^-1, E(12)+E(12)^-1, -1*E(12)-E(12)^-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, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1*E(12)-E(12)^-1, E(12)+E(12)^-1, -1*E(12)-E(12)^-1, E(12)+E(12)^-1, -1*E(12)-E(12)^-1, -1*E(12)-E(12)^-1, -1*E(12)-E(12)^-1, E(12)+E(12)^-1, -1*E(12)-E(12)^-1, E(12)+E(12)^-1, E(12)+E(12)^-1, E(12)+E(12)^-1, -1*E(12)-E(12)^-1, E(12)+E(12)^-1, E(12)+E(12)^-1, -1*E(12)-E(12)^-1], [2, -2, -2, 2, -1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, -1, 1, 2, 2, -2, -2, 2, -2, -2, -2, -2, 2, -2, -2, E(12)+E(12)^-1, -1*E(12)-E(12)^-1, -1*E(12)-E(12)^-1, E(12)+E(12)^-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, -1, -1, 1, 1, -1, 1, -1, 1, 1, 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-2*E(5), -2*E(5)^-1, 2*E(5)^-1, -2*E(5)^-2, -2*E(5)^2, -2*E(5)^-1, 2*E(5)^2, 2*E(5)^-2, 2*E(5), -2*E(5)^-2, -2*E(5), -2*E(5)^2, 0, 0, 0, 0, 2*E(5)^-2, 2*E(5)^-1, 2*E(5), 2*E(5)^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, -2*E(5), -2*E(5)^-2, -2*E(5), -2*E(5)^2, -2*E(5)^-1, 2*E(5)^2, -2*E(5)^2, 2*E(5)^-2, -2*E(5)^-2, -2*E(5)^-1, 2*E(5), 2*E(5)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, -2, 2, -1, 0, 0, 0, 0, 0, 0, -2*E(60)^6, 2*E(60)^12, -2*E(60)^18, 2*E(60)^24, 1, -1, 1, -2*E(60)^6, 2*E(60)^24, -2*E(60)^24, 2*E(60)^18, 2*E(60)^12, -2*E(60)^24, -2*E(60)^12, 2*E(60)^18, 2*E(60)^6, -2*E(60)^18, 2*E(60)^6, -2*E(60)^12, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, E(60)^18, -1*E(60)^24, E(60)^6, -1*E(60)^12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(60)^6, E(60)^18, -1*E(60)^6, E(60)^12, -1*E(60)^24, E(60)^12, -1*E(60)^12, -1*E(60)^18, -1*E(60)^18, E(60)^24, -1*E(60)^6, 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-2*E(60)^18, 2*E(60)^6, -2*E(60)^12, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, E(60)^18, -1*E(60)^24, E(60)^6, -1*E(60)^12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(60)^6, E(60)^18, -1*E(60)^6, E(60)^12, -1*E(60)^24, E(60)^12, -1*E(60)^12, -1*E(60)^18, -1*E(60)^18, E(60)^24, -1*E(60)^6, E(60)^24, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, -1*E(60)-E(60)^11, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, E(60)^3-2*E(60)^13, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, E(60)+E(60)^11, E(60)^3-2*E(60)^13, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, E(60)+E(60)^11, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, -1*E(60)^3+2*E(60)^13, -1*E(60)^3+2*E(60)^13, -1*E(60)-E(60)^11], [2, -2, -2, 2, -1, 0, 0, 0, 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E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15], [2, -2, -2, 2, -1, 0, 0, 0, 0, 0, 0, -2*E(60)^18, -2*E(60)^6, 2*E(60)^24, 2*E(60)^12, 1, -1, 1, -2*E(60)^18, 2*E(60)^12, -2*E(60)^12, -2*E(60)^24, -2*E(60)^6, -2*E(60)^12, 2*E(60)^6, -2*E(60)^24, 2*E(60)^18, 2*E(60)^24, 2*E(60)^18, 2*E(60)^6, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, -1*E(60)^24, -1*E(60)^12, E(60)^18, E(60)^6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(60)^18, -1*E(60)^24, -1*E(60)^18, -1*E(60)^6, -1*E(60)^12, -1*E(60)^6, E(60)^6, E(60)^24, E(60)^24, E(60)^12, -1*E(60)^18, E(60)^12, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, -1*E(60)^3+2*E(60)^13, -1*E(60)-E(60)^11, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, E(60)+E(60)^11, E(60)^3-2*E(60)^13, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, -1*E(60)-E(60)^11, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, E(60)^3-2*E(60)^13, E(60)+E(60)^11, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, -1*E(60)^3+2*E(60)^13], [2, -2, -2, 2, -1, 0, 0, 0, 0, 0, 0, 2*E(60)^12, 2*E(60)^24, -2*E(60)^6, -2*E(60)^18, 1, -1, 1, 2*E(60)^12, -2*E(60)^18, 2*E(60)^18, 2*E(60)^6, 2*E(60)^24, 2*E(60)^18, -2*E(60)^24, 2*E(60)^6, -2*E(60)^12, -2*E(60)^6, -2*E(60)^12, -2*E(60)^24, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, E(60)^6, E(60)^18, -1*E(60)^12, -1*E(60)^24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(60)^12, E(60)^6, E(60)^12, E(60)^24, E(60)^18, E(60)^24, -1*E(60)^24, -1*E(60)^6, -1*E(60)^6, -1*E(60)^18, E(60)^12, -1*E(60)^18, -1*E(60)^3+2*E(60)^13, E(60)^3-2*E(60)^13, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, E(60)+E(60)^11, -1*E(60)^3+2*E(60)^13, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, E(60)+E(60)^11, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, E(60)^3-2*E(60)^13, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, -1*E(60)-E(60)^11, -1*E(60)-E(60)^11, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15], [2, -2, -2, 2, -1, 0, 0, 0, 0, 0, 0, -2*E(60)^18, -2*E(60)^6, 2*E(60)^24, 2*E(60)^12, 1, -1, 1, -2*E(60)^18, 2*E(60)^12, -2*E(60)^12, -2*E(60)^24, -2*E(60)^6, -2*E(60)^12, 2*E(60)^6, -2*E(60)^24, 2*E(60)^18, 2*E(60)^24, 2*E(60)^18, 2*E(60)^6, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, -1*E(60)^24, -1*E(60)^12, E(60)^18, E(60)^6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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-1*E(60)^5-E(60)^-5, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, E(60)^6, E(60)^18, -1*E(60)^12, -1*E(60)^24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(60)^12, E(60)^6, E(60)^12, E(60)^24, E(60)^18, E(60)^24, -1*E(60)^24, -1*E(60)^6, -1*E(60)^6, -1*E(60)^18, E(60)^12, -1*E(60)^18, E(60)^3-2*E(60)^13, -1*E(60)^3+2*E(60)^13, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, -1*E(60)-E(60)^11, E(60)^3-2*E(60)^13, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, -1*E(60)-E(60)^11, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, -1*E(60)^3+2*E(60)^13, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, E(60)+E(60)^11, E(60)+E(60)^11, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15], [2, -2, 2, -2, -1, 0, 0, 0, 0, 0, 0, -2*E(60)^6, 2*E(60)^12, -2*E(60)^18, 2*E(60)^24, -1, 1, 1, 2*E(60)^6, -2*E(60)^24, 2*E(60)^24, 2*E(60)^18, -2*E(60)^12, -2*E(60)^24, 2*E(60)^12, -2*E(60)^18, -2*E(60)^6, 2*E(60)^18, 2*E(60)^6, -2*E(60)^12, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, E(60)^18, -1*E(60)^24, E(60)^6, -1*E(60)^12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(60)^6, -1*E(60)^18, -1*E(60)^6, E(60)^12, E(60)^24, -1*E(60)^12, E(60)^12, E(60)^18, -1*E(60)^18, E(60)^24, E(60)^6, -1*E(60)^24, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, E(60)+E(60)^11, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, -1*E(60)^3+2*E(60)^13, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, E(60)+E(60)^11, E(60)^3-2*E(60)^13, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, -1*E(60)-E(60)^11, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, E(60)^3-2*E(60)^13, -1*E(60)^3+2*E(60)^13, -1*E(60)-E(60)^11], [2, -2, 2, -2, -1, 0, 0, 0, 0, 0, 0, 2*E(60)^24, -2*E(60)^18, 2*E(60)^12, -2*E(60)^6, -1, 1, 1, -2*E(60)^24, 2*E(60)^6, -2*E(60)^6, -2*E(60)^12, 2*E(60)^18, 2*E(60)^6, -2*E(60)^18, 2*E(60)^12, 2*E(60)^24, -2*E(60)^12, -2*E(60)^24, 2*E(60)^18, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, -1*E(60)^12, E(60)^6, -1*E(60)^24, E(60)^18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(60)^24, E(60)^12, E(60)^24, -1*E(60)^18, -1*E(60)^6, E(60)^18, -1*E(60)^18, -1*E(60)^12, E(60)^12, -1*E(60)^6, -1*E(60)^24, E(60)^6, -1*E(60)-E(60)^11, -1*E(60)-E(60)^11, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, E(60)^3-2*E(60)^13, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, E(60)+E(60)^11, E(60)^3-2*E(60)^13, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, -1*E(60)^3+2*E(60)^13, E(60)+E(60)^11, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, -1*E(60)^3+2*E(60)^13, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15], [2, -2, 2, -2, -1, 0, 0, 0, 0, 0, 0, -2*E(60)^6, 2*E(60)^12, -2*E(60)^18, 2*E(60)^24, -1, 1, 1, 2*E(60)^6, -2*E(60)^24, 2*E(60)^24, 2*E(60)^18, -2*E(60)^12, -2*E(60)^24, 2*E(60)^12, -2*E(60)^18, -2*E(60)^6, 2*E(60)^18, 2*E(60)^6, -2*E(60)^12, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, E(60)^18, -1*E(60)^24, E(60)^6, -1*E(60)^12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(60)^6, -1*E(60)^18, -1*E(60)^6, E(60)^12, E(60)^24, -1*E(60)^12, E(60)^12, E(60)^18, -1*E(60)^18, E(60)^24, E(60)^6, -1*E(60)^24, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, -1*E(60)-E(60)^11, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, E(60)^3-2*E(60)^13, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, -1*E(60)-E(60)^11, -1*E(60)^3+2*E(60)^13, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, E(60)+E(60)^11, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, -1*E(60)^3+2*E(60)^13, E(60)^3-2*E(60)^13, E(60)+E(60)^11], [2, -2, 2, -2, -1, 0, 0, 0, 0, 0, 0, 2*E(60)^24, -2*E(60)^18, 2*E(60)^12, -2*E(60)^6, -1, 1, 1, -2*E(60)^24, 2*E(60)^6, -2*E(60)^6, -2*E(60)^12, 2*E(60)^18, 2*E(60)^6, -2*E(60)^18, 2*E(60)^12, 2*E(60)^24, -2*E(60)^12, -2*E(60)^24, 2*E(60)^18, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, -1*E(60)^12, E(60)^6, -1*E(60)^24, E(60)^18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(60)^24, E(60)^12, E(60)^24, -1*E(60)^18, -1*E(60)^6, E(60)^18, -1*E(60)^18, -1*E(60)^12, E(60)^12, -1*E(60)^6, -1*E(60)^24, E(60)^6, E(60)+E(60)^11, E(60)+E(60)^11, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, -1*E(60)^3+2*E(60)^13, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, -1*E(60)-E(60)^11, -1*E(60)^3+2*E(60)^13, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, E(60)^3-2*E(60)^13, -1*E(60)-E(60)^11, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, E(60)^3-2*E(60)^13, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15], [2, -2, 2, -2, -1, 0, 0, 0, 0, 0, 0, -2*E(60)^18, -2*E(60)^6, 2*E(60)^24, 2*E(60)^12, -1, 1, 1, 2*E(60)^18, -2*E(60)^12, 2*E(60)^12, -2*E(60)^24, 2*E(60)^6, -2*E(60)^12, -2*E(60)^6, 2*E(60)^24, -2*E(60)^18, -2*E(60)^24, 2*E(60)^18, 2*E(60)^6, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, -1*E(60)^24, -1*E(60)^12, E(60)^18, E(60)^6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(60)^18, E(60)^24, -1*E(60)^18, -1*E(60)^6, E(60)^12, E(60)^6, -1*E(60)^6, -1*E(60)^24, E(60)^24, E(60)^12, E(60)^18, -1*E(60)^12, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, -1*E(60)^3+2*E(60)^13, -1*E(60)-E(60)^11, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, -1*E(60)-E(60)^11, -1*E(60)^3+2*E(60)^13, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, E(60)+E(60)^11, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, E(60)^3-2*E(60)^13, E(60)+E(60)^11, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, E(60)^3-2*E(60)^13], [2, -2, 2, -2, -1, 0, 0, 0, 0, 0, 0, 2*E(60)^12, 2*E(60)^24, -2*E(60)^6, -2*E(60)^18, -1, 1, 1, -2*E(60)^12, 2*E(60)^18, -2*E(60)^18, 2*E(60)^6, -2*E(60)^24, 2*E(60)^18, 2*E(60)^24, -2*E(60)^6, 2*E(60)^12, 2*E(60)^6, -2*E(60)^12, -2*E(60)^24, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, E(60)^6, E(60)^18, -1*E(60)^12, -1*E(60)^24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(60)^12, -1*E(60)^6, E(60)^12, E(60)^24, -1*E(60)^18, -1*E(60)^24, E(60)^24, E(60)^6, -1*E(60)^6, -1*E(60)^18, -1*E(60)^12, E(60)^18, E(60)^3-2*E(60)^13, E(60)^3-2*E(60)^13, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, E(60)+E(60)^11, -1*E(60)^3+2*E(60)^13, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, -1*E(60)-E(60)^11, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, -1*E(60)^3+2*E(60)^13, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, -1*E(60)-E(60)^11, E(60)+E(60)^11, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15], [2, -2, 2, -2, -1, 0, 0, 0, 0, 0, 0, -2*E(60)^18, -2*E(60)^6, 2*E(60)^24, 2*E(60)^12, -1, 1, 1, 2*E(60)^18, -2*E(60)^12, 2*E(60)^12, -2*E(60)^24, 2*E(60)^6, -2*E(60)^12, -2*E(60)^6, 2*E(60)^24, -2*E(60)^18, -2*E(60)^24, 2*E(60)^18, 2*E(60)^6, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, -1*E(60)^24, -1*E(60)^12, E(60)^18, E(60)^6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(60)^18, E(60)^24, -1*E(60)^18, -1*E(60)^6, E(60)^12, E(60)^6, -1*E(60)^6, -1*E(60)^24, E(60)^24, E(60)^12, E(60)^18, -1*E(60)^12, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, E(60)^3-2*E(60)^13, E(60)+E(60)^11, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, E(60)+E(60)^11, E(60)^3-2*E(60)^13, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, -1*E(60)-E(60)^11, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, -1*E(60)^3+2*E(60)^13, -1*E(60)-E(60)^11, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, -1*E(60)^3+2*E(60)^13], [2, -2, 2, -2, -1, 0, 0, 0, 0, 0, 0, 2*E(60)^12, 2*E(60)^24, -2*E(60)^6, -2*E(60)^18, -1, 1, 1, -2*E(60)^12, 2*E(60)^18, -2*E(60)^18, 2*E(60)^6, -2*E(60)^24, 2*E(60)^18, 2*E(60)^24, -2*E(60)^6, 2*E(60)^12, 2*E(60)^6, -2*E(60)^12, -2*E(60)^24, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, E(60)^5+E(60)^-5, -1*E(60)^5-E(60)^-5, E(60)^6, E(60)^18, -1*E(60)^12, -1*E(60)^24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(60)^12, -1*E(60)^6, E(60)^12, E(60)^24, -1*E(60)^18, -1*E(60)^24, E(60)^24, E(60)^6, -1*E(60)^6, -1*E(60)^18, -1*E(60)^12, E(60)^18, -1*E(60)^3+2*E(60)^13, -1*E(60)^3+2*E(60)^13, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, -1*E(60)-E(60)^11, E(60)^3-2*E(60)^13, -2*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-2*E(60)^13-2*E(60)^15, -1*E(60)-E(60)^3+2*E(60)^7+E(60)^9+E(60)^11-E(60)^15, E(60)+E(60)^11, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, E(60)^3-2*E(60)^13, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15, 2*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+2*E(60)^13+2*E(60)^15, E(60)+E(60)^11, -1*E(60)-E(60)^11, E(60)+E(60)^3-2*E(60)^7-E(60)^9-E(60)^11+E(60)^15]]; ConvertToLibraryCharacterTableNC(chartbl_240_165);