# Group 56862.a downloaded from the LMFDB on 30 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(186445302978692415188475583949178425077044221886321410364186939215732448238420238236242408541,56862); a := GPC.1; b := GPC.3; c := GPC.4; d := GPC.5; e := GPC.6; f := GPC.7; g := GPC.8; h := GPC.9; GPerm := Group( (1,29,18,6,32,19,7,36,22,12,38,27,14)(2,28,16,5,33,21,8,35,23,11,39,26,15,3,30,17,4,31,20,9,34,24,10,37,25,13), (1,38,36,31,29,26,22,20,16,13,12,9,6,3,37,35,33,28,25,24,19,18,15,11,8,5,2,39,34,32,30,27,23,21,17,14,10,7,4) ); # Booleans booleans_56862_a := rec( Agroup := true, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := true, metacyclic := false, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := false); # Character Table chartbl_56862_a:=rec(); chartbl_56862_a.IsFinite:= true; chartbl_56862_a.UnderlyingCharacteristic:= 0; chartbl_56862_a.UnderlyingGroup:= GPC; chartbl_56862_a.Size:= 56862; chartbl_56862_a.InfoText:= "Character table for group 56862.a downloaded from the LMFDB."; chartbl_56862_a.Identifier:= " C3^7:C26 "; chartbl_56862_a.NrConjugacyClasses:= 123; chartbl_56862_a.ConjugacyClasses:= [ of ..., f1*f2^6*f3*f6*f8*f9^2, f3^2*f5*f7*f8^2, f9, f8, f7, f6, f5, f4, f3, f8*f9, f6*f9, f6*f8, f6*f7, f5*f9, f5*f7, f5*f6, f4*f8, f4*f7, f4*f5, f3*f9, f3*f7, f3*f6, f3*f4, f8*f9^2, f7*f8^2, f6*f9^2, f6*f8^2, f6*f7^2, f5*f9^2, f5*f8^2, f5*f7^2, f4*f9^2, f4*f8^2, f3*f9^2, f3*f7^2, f6*f8*f9, f6*f7*f9, f5*f8*f9, f5*f7*f9, f5*f7*f8, f5*f6*f9, f4*f8*f9, f4*f7*f9, f4*f6*f9, f4*f6*f8, f4*f5*f9, f4*f5*f6, f3*f8*f9, f3*f7*f9, f3*f5*f6, f3*f4*f8, f3*f4*f7, f3*f4*f5, f7^2*f8*f9, f6*f7*f8^2, f6^2*f7*f9, f6^2*f7*f8, f5*f8*f9^2, f5*f8^2*f9, f5*f7^2*f8, f5*f6*f8^2, f5*f6^2*f9, f5^2*f8*f9, f5^2*f7*f9, f5^2*f6*f8, f4*f7^2*f9, f4*f6*f8^2, f4*f5^2*f8, f4^2*f8*f9, f4^2*f7*f9, f4^2*f6*f7, f4^2*f5*f8, f3*f8*f9^2, f3*f7*f9^2, f3*f5*f9^2, f3*f4^2*f9, f3*f4^2*f7, f3*f4^2*f5, f3^2*f7*f9, f3^2*f6*f8, f5*f6^2*f8*f9, f4*f5*f6^2*f9, f4^2*f5*f7*f9, f3*f5^2*f6*f9, f4*f7^2*f8*f9^2, f4*f5^2*f7^2*f8, f2^3*f3^2*f4*f6^2*f7*f8^2*f9, f2^10*f3*f4^2*f5*f8*f9, f2^6*f3*f4^2*f5*f8^2*f9^2, f2^7*f3^2*f5*f7^2, f2^9*f3*f4*f5^2*f6*f8^2, f2^4*f3*f4^2*f5*f6^2*f9, f2^12*f5^2*f7*f9^2, f2*f3*f6*f7*f8*f9, f2^2*f3^2*f4^2*f5*f6*f8*f9, f2^11*f3*f5^2*f6*f8, f2^5*f3*f5*f6^2, f2^8*f4^2*f5*f6*f7^2*f9, f1*f2*f3*f4*f5^2*f7*f8*f9, f1*f2^11*f5^2*f6^2*f8*f9^2, f1*f2^4*f5*f9^2, f1*f2^8*f3^2*f4*f5^2*f9, f1*f2^7*f7^2*f9, f1*f2^5*f3*f5*f6*f7^2*f8, f1*f2^10*f4*f5^2*f6^2*f8*f9, f1*f2^2*f4^2*f5*f8^2*f9^2, f1*f3^2*f5^2*f6*f7*f8*f9^2, f1*f2^12*f4*f5^2*f6*f8^2, f1*f2^3*f4*f5^2*f6*f9, f1*f2^9*f3^2*f4^2*f6^2*f7^2*f8^2*f9, f2*f3*f4*f5^2*f6^2*f8^2, f2^12*f4*f5^2*f6*f9^2, f2^2*f4^2*f5^2*f7*f9^2, f2^11*f3*f4^2*f6*f7^2*f9^2, f2^4*f3^2*f4*f5*f6*f9^2, f2^9*f3*f4*f5^2*f6^2*f7*f8^2*f9, f2^5*f3*f4^2*f6^2*f7^2*f8, f2^8*f3*f4*f6^2*f7*f8, f2^7*f3*f4^2*f5*f6^2*f7*f9^2, f2^6*f3*f5^2*f6^2*f8*f9, f2^10*f3*f4^2*f5*f6^2*f7^2*f8, f2^3*f3*f5*f6*f8*f9]; chartbl_56862_a.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, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123]; chartbl_56862_a.ComputedPowerMaps:= [ , [1, 1, 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, 90, 91, 94, 95, 98, 99, 97, 96, 93, 92, 89, 88, 88, 89, 92, 93, 96, 97, 99, 98, 95, 94, 91, 90, 114, 115, 116, 117, 119, 118, 122, 123, 112, 113, 120, 121], [1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 92, 93, 98, 99, 95, 94, 89, 88, 90, 91, 96, 97, 102, 103, 108, 109, 111, 110, 105, 104, 100, 101, 106, 107, 88, 89, 90, 91, 94, 95, 96, 97, 99, 98, 93, 92], [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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]]; chartbl_56862_a.SizesCentralizers:= [56862, 26, 28431, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 2187, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39]; chartbl_56862_a.ClassNames:= ["1A", "2A", "3A", "3B", "3C", "3D", "3E", "3F", "3G", "3H", "3I", "3J", "3K", "3L", "3M", "3N", "3O", "3P", "3Q", "3R", "3S", "3T", "3U", "3V", "3W", "3X", "3Y", "3Z", "3AA", "3AB", "3AC", "3AD", "3AE", "3AF", "3AG", "3AH", "3AI", "3AJ", "3AK", "3AL", "3AM", "3AN", "3AO", "3AP", "3AQ", "3AR", "3AS", "3AT", "3AU", "3AV", "3AW", "3AX", "3AY", "3AZ", "3BA", "3BB", "3BC", "3BD", "3BE", "3BF", "3BG", "3BH", "3BI", "3BJ", "3BK", "3BL", "3BM", "3BN", "3BO", "3BP", "3BQ", "3BR", "3BS", "3BT", "3BU", "3BV", "3BW", "3BX", "3BY", "3BZ", "3CA", "3CB", "3CC", "3CD", "3CE", "3CF", "3CG", "13A1", "13A-1", "13A2", "13A-2", "13A3", "13A-3", "13A4", "13A-4", "13A5", "13A-5", "13A6", "13A-6", "26A1", "26A-1", "26A3", "26A-3", "26A5", "26A-5", "26A7", "26A-7", "26A9", "26A-9", "26A11", "26A-11", "39A1", "39A-1", "39A2", "39A-2", "39A4", "39A-4", "39A5", "39A-5", "39A7", "39A-7", "39A10", "39A-10"]; chartbl_56862_a.OrderClassRepresentatives:= [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39]; chartbl_56862_a.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, E(13)^-6, E(13)^3, E(13)^-4, E(13)^2, E(13)^-5, E(13), E(13)^-3, E(13)^4, E(13)^6, E(13)^5, E(13)^-1, E(13)^-2, E(13), E(13)^2, E(13)^-4, E(13)^-3, E(13)^3, E(13)^4, E(13)^5, E(13)^-5, E(13)^-1, E(13)^6, E(13)^-2, E(13)^-6, E(13)^-2, E(13)^-5, E(13)^2, E(13)^-4, E(13)^6, E(13)^-1, E(13)^4, E(13)^3, E(13)^5, E(13)^-6, E(13)^-3, E(13)], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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(13)^6, E(13)^-3, E(13)^4, E(13)^-2, E(13)^5, E(13)^-1, E(13)^3, E(13)^-4, E(13)^-6, E(13)^-5, E(13), E(13)^2, E(13)^-1, E(13)^-2, E(13)^4, E(13)^3, E(13)^-3, E(13)^-4, E(13)^-5, E(13)^5, E(13), E(13)^-6, E(13)^2, E(13)^6, E(13)^2, E(13)^5, E(13)^-2, E(13)^4, E(13)^-6, E(13), E(13)^-4, E(13)^-3, E(13)^-5, E(13)^6, E(13)^3, E(13)^-1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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(13)^-5, E(13)^-4, E(13), E(13)^6, E(13)^-2, E(13)^3, E(13)^4, E(13)^-1, E(13)^5, E(13)^2, E(13)^-3, E(13)^-6, E(13)^3, E(13)^6, E(13), E(13)^4, E(13)^-4, E(13)^-1, E(13)^2, E(13)^-2, E(13)^-3, E(13)^5, E(13)^-6, E(13)^-5, E(13)^-6, E(13)^-2, E(13)^6, E(13), E(13)^5, E(13)^-3, E(13)^-1, E(13)^-4, E(13)^2, E(13)^-5, E(13)^4, E(13)^3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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(13)^5, E(13)^4, E(13)^-1, E(13)^-6, E(13)^2, E(13)^-3, E(13)^-4, E(13), E(13)^-5, E(13)^-2, E(13)^3, E(13)^6, E(13)^-3, E(13)^-6, E(13)^-1, E(13)^-4, E(13)^4, E(13), E(13)^-2, E(13)^2, E(13)^3, E(13)^-5, E(13)^6, E(13)^5, E(13)^6, E(13)^2, E(13)^-6, E(13)^-1, E(13)^-5, E(13)^3, E(13), E(13)^4, E(13)^-2, E(13)^5, E(13)^-4, E(13)^-3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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(13)^-4, E(13)^2, E(13)^6, E(13)^-3, E(13), E(13)^5, E(13)^-2, E(13)^-6, E(13)^4, E(13)^-1, E(13)^-5, E(13)^3, E(13)^5, E(13)^-3, E(13)^6, E(13)^-2, E(13)^2, E(13)^-6, E(13)^-1, E(13), E(13)^-5, E(13)^4, E(13)^3, E(13)^-4, E(13)^3, E(13), E(13)^-3, E(13)^6, E(13)^4, E(13)^-5, E(13)^-6, E(13)^2, E(13)^-1, E(13)^-4, E(13)^-2, E(13)^5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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(13)^4, E(13)^-2, E(13)^-6, E(13)^3, E(13)^-1, E(13)^-5, E(13)^2, E(13)^6, E(13)^-4, E(13), E(13)^5, E(13)^-3, E(13)^-5, E(13)^3, E(13)^-6, E(13)^2, E(13)^-2, E(13)^6, E(13), E(13)^-1, E(13)^5, E(13)^-4, E(13)^-3, E(13)^4, E(13)^-3, E(13)^-1, E(13)^3, E(13)^-6, E(13)^-4, E(13)^5, E(13)^6, E(13)^-2, E(13), E(13)^4, E(13)^2, E(13)^-5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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(13)^-3, E(13)^-5, E(13)^-2, E(13), E(13)^4, E(13)^-6, E(13)^5, E(13)^2, E(13)^3, E(13)^-4, E(13)^6, E(13)^-1, E(13)^-6, E(13), E(13)^-2, E(13)^5, E(13)^-5, E(13)^2, E(13)^-4, E(13)^4, E(13)^6, E(13)^3, E(13)^-1, E(13)^-3, 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E(13)^-5, E(13)^4, E(13)^3], [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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(13)^5, E(13)^4, E(13)^-1, E(13)^-6, E(13)^2, E(13)^-3, E(13)^-4, E(13), E(13)^-5, E(13)^-2, E(13)^3, E(13)^6, -1*E(13)^-3, -1*E(13)^-6, -1*E(13)^-1, -1*E(13)^-4, -1*E(13)^4, -1*E(13), -1*E(13)^-2, -1*E(13)^2, -1*E(13)^3, -1*E(13)^-5, -1*E(13)^6, -1*E(13)^5, E(13)^6, E(13)^2, E(13)^-6, E(13)^-1, E(13)^-5, E(13)^3, E(13), E(13)^4, E(13)^-2, E(13)^5, E(13)^-4, E(13)^-3], [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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(13)^-4, E(13)^2, E(13)^6, E(13)^-3, E(13), E(13)^5, E(13)^-2, E(13)^-6, E(13)^4, E(13)^-1, E(13)^-5, E(13)^3, -1*E(13)^5, -1*E(13)^-3, -1*E(13)^6, -1*E(13)^-2, -1*E(13)^2, -1*E(13)^-6, -1*E(13)^-1, -1*E(13), -1*E(13)^-5, -1*E(13)^4, -1*E(13)^3, -1*E(13)^-4, E(13)^3, E(13), E(13)^-3, E(13)^6, E(13)^4, E(13)^-5, E(13)^-6, E(13)^2, E(13)^-1, E(13)^-4, E(13)^-2, E(13)^5], [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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(13)^4, E(13)^-2, E(13)^-6, E(13)^3, E(13)^-1, E(13)^-5, E(13)^2, E(13)^6, E(13)^-4, E(13), E(13)^5, E(13)^-3, -1*E(13)^-5, -1*E(13)^3, -1*E(13)^-6, -1*E(13)^2, -1*E(13)^-2, -1*E(13)^6, -1*E(13), -1*E(13)^-1, -1*E(13)^5, -1*E(13)^-4, -1*E(13)^-3, -1*E(13)^4, E(13)^-3, E(13)^-1, E(13)^3, E(13)^-6, E(13)^-4, E(13)^5, E(13)^6, E(13)^-2, E(13), E(13)^4, E(13)^2, E(13)^-5], [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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