Table lfunc_lfunctions
L-functions
{'Lhash': '3327981958329994492107237401816', 'a10': [-22.52332176794024, 0.0], 'a2': [4.504664353588048, 0.0], 'a3': [5.08998471379805, 0.0], 'a4': [12.292000938486824, 0.0], 'a5': [-5.0, 0.0], 'a6': [22.92867270055414, 0.0], 'a7': [-0.61669586447877, 0.0], 'a8': [19.33402363316804, 0.0], 'a9': [-1.0920556133021757, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.015162350487954, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[5, [[1.0, 0], [5.0, 0]]], [17, [[1.0, 0], [17.0, 0]]]], 'bad_primes': [5, 17], 'central_character': '85.1', 'coefficient_field': 'CDF', 'conductor': 85, 'conductor_radical': 85, 'conjugate': '3327981958329994492107237401816', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.504664353588048, 0], [8.0, 0]], [[1.0, 0], [-5.08998471379805, 0], [27.0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [0.61669586447877, 0], [343.0, 0]], [[1.0, 0], [8.63535327883096, 0], [1331.0, 0]], [[1.0, 0], [-6.440115819623149, 0], [2197.0, 0]], [[1.0, 0], [17.0, 0]], [[1.0, 0], [-7.968058428762647, 0], [6859.0, 0]], [[1.0, 0], [-66.12088117587581, 0], [12167.0, 0]], [[1.0, 0], [-219.81335113144453, 0], [24389.0, 0]], [[1.0, 0], [0.6086856405390302, 0], [29791.0, 0]], [[1.0, 0], [216.12382313498438, 0], [50653.0, 0]], [[1.0, 0], [-355.50815306085013, 0], [68921.0, 0]], [[1.0, 0], [-209.94686337245935, 0], [79507.0, 0]], [[1.0, 0], [324.6257951158812, 0], [103823.0, 0]], [[1.0, 0], [-189.59059429315542, 0], [148877.0, 0]], [[1.0, 0], [257.61869203894935, 0], [205379.0, 0]], [[1.0, 0], [-240.33495009899096, 0], [226981.0, 0]], [[1.0, 0], [66.94280859822868, 0], [300763.0, 0]], [[1.0, 0], [131.6640873477827, 0], [357911.0, 0]], [[1.0, 0], [-1172.7603261281695, 0], [389017.0, 0]], [[1.0, 0], [-707.8248114250163, 0], [493039.0, 0]], [[1.0, 0], [-1007.3012426208853, 0], [571787.0, 0]], [[1.0, 0], [-1013.0058962179612, 0], [704969.0, 0]], [[1.0, 0], [-973.1474432824037, 0], [912673.0, 0]], [[1.0, 0], [1451.1068789517283, 0], [1030301.0, 0]], [[1.0, 0], [341.60494734685955, 0], [1092727.0, 0]], [[1.0, 0], [-996.5212463995917, 0], [1225043.0, 0]], [[1.0, 0], [1891.8240836082366, 0], [1295029.0, 0]], [[1.0, 0], [1365.331341821823, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 9967208, 'index': 9, 'label': '2-85-1.1-c3-0-9', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/85/4/a/f/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [3.946676989289549, 3.9402360783293933, 3.92057364543689, 3.8866982682248454, 3.8370481550084063, 3.769621371353036, 3.6821476361958485, 3.572292654089612, 3.4378848912188325, 3.2771540466076994, 3.088969923020023, 2.873069769777224, 2.6302614206394472, 2.3625888161210433, 2.073446033569053, 1.7676260620372464, 1.4512915647735651, 1.1318570333920162, 0.8177752308256364, 0.5182257052658528, 0.24270935733863, 0.0005603288896940284, -0.19960553229536762, -0.3504782300571925, -0.4466421605212073, -0.4851242394964148, -0.46585596121446204, -0.39200237082296413, -0.2701131677788445, -0.1100575028831329, 0.07528527211647619, 0.270591711044077, 0.4589114061233194, 0.6227079513205875, 0.745073868620076, 0.8110474652953904, 0.8089400364601395, 0.7315671253952313, 0.5772698884150289, 0.3506138801460755, 0.06266415037378824, -0.2692419645706331, -0.6222699131425576, -0.9694142340801034, -1.2813307350694743, -1.5285775538541195, -1.6841181106373915, -1.7258956740014066, -1.639257898319128, -1.4189950606900994, -1.0707616796546349, -0.6116800691333254, -0.06997650373325173, 0.5164259592328837, 1.102343824481311, 1.6386844548609873, 2.0764969938593083, 2.371415564170507, 2.48811501411694, 2.4043566365004034, 2.114196001347845, 1.6299623805703058, 0.9827003261542373, 0.22088535684503227, -0.592620794471384, -1.385236980370941, -2.0806369613148012, -2.605555854502855, -2.8968265314683923, -2.9079682168186065, -2.614638444926756, -2.018320363277876, -1.1477502759406573, -0.05778732915448556, 1.1743276638255753, 2.455107109123055, 3.6828609213957924, 4.756932002328376, 5.587233139351939, 6.103110696683301, 6.260578545698733, 6.047092118804244, 5.483260269927958, 4.621202130281289, 3.5396163896159445, 2.336002014832858, 1.1168087368582151, -0.013439987698659941, -0.9628557066547052, -1.661512518875848, -2.0683089476986725, -2.1745449862471533, -2.0037709814030658, -1.6079090942244942, -1.0601068704593, -0.4451975122692197, 0.15104314671726649, 0.6524828502595273, 1.0017059375926372, 1.1664008486542283, 1.14223629147217, 0.9518679874889224, 0.640246736689033, 0.2669167153097794, -0.10357334616456311, -0.41173949247294755, -0.6122184928026111, -0.6804464933505701, -0.6159332781594173, -0.44160705721908294, -0.19930333548809087, 0.05792012578927714, 0.27543494811898594, 0.4070963044523044, 0.4240114923801152, 0.32047517002729364, 0.11592060537804093, -0.14765845707506137, -0.41263174346431797, -0.616075415533212, -0.7019686090223265, -0.6332540546886705, -0.4016469411042778, -0.03328855857593782, 0.41111816285005925, 0.8422493994661975, 1.1537778910570469, 1.238300362651262, 1.0053869309180457, 0.3990321583370448, -0.5883494396748701, -1.9079313963305864, -3.4542969202128435, -5.07380521533616, -6.58096130259575, -7.780971441710368, -8.49558686995718, -8.588639600227982, -7.987489131732227, -6.6969877738368, -4.8035064227245385, -2.4679249827068417, 0.0919095965310718, 2.6271590070070974, 4.888962659995336, 6.660094297619758, 7.782766679571408, 8.178504049753716, 7.857105684374652, 6.913317528188968, 5.511673415627125, 3.8617744667011347, 2.1877538063034514, 0.6965780066831628, -0.4499912082882969, -1.1555519330183623, -1.3983964980591108, -1.2288553491436325, -0.7554398599617161, -0.12239810179970183, 0.5173224472220911, 1.0290140544380937, 1.3184675280977072, 1.3458681696605157, 1.1291822952947939, 0.7367906686998585, 0.27105729226555103, -0.15386381431208765, -0.4356785582067524, -0.5045484912422551, -0.3367538774427451, 0.04109715782178718, 0.5580031061515902, 1.1133737156197983, 1.5977091776057297, 1.9150095823074393, 2.002423129033638, 1.8431730872214445, 1.470121973345576, 0.9591896277417891, 0.4138814862259618, -0.05599783696861497, -0.3571404797646015, -0.43235426179247305, -0.27288252581137984, 0.07927727266666605, 0.5397484840557268, 0.9993292420308248, 1.3472534501780828, 1.4953884588170654, 1.3982500926638894, 1.0644219220738929, 0.5566203910454509, -0.02005564611040283, -0.539664529532006, -0.8825549759900629, -0.9625128867470778, -0.7480664265570414, -0.273036928324778, 0.3665536623330972, 1.0293732192992233, 1.556709470550173, 1.806187814573853, 1.6844906036109255, 1.172084836724905, 0.33419934327695594, -0.6852106826141805, -1.6864616395863694, -2.45056113459765, -2.7825448172571225, -2.5534217838657804, -1.732201311148365, -0.40096410169358687, 1.2510777096208288, 2.9546465213272355, 4.404553284372973, 5.313360061583992, 5.46477384988664, 4.756630940138132, 3.224941589095204, 1.043797239700966, -1.4996087023293074, -4.050878162428337, -6.247194497841898, -7.778380628429352, -8.439038434032875, -8.162165341410963, -7.028107208606351, -5.24738042799399, -3.1208624891350962, -0.9851228148824527, 0.8466083899024716, 2.136698849055393, 2.7590361604962204, 2.712490871974136, 2.1103935512913004, 1.1492917088600052, 0.06425379527728452, -0.9196181388316866, -1.6294861759573391, -1.9726808796495245, -1.9454543243457105, -1.6221561230138453, -1.128661502497227, -0.6071253147501366, -0.1806765708556151, 0.07379762821181288, 0.13894625205746647, 0.05408472860600281, -0.10207890283657108, -0.23790114022244296, -0.2771178805368731, -0.18143448059156506, 0.038552669931001995, 0.32692136144265455, 0.5994545403081296, 0.7695171800828408], 'positive_zeros': ['2.62531486020739504467690275917730', '3.70063376827350616544234187634761', '5.02466628915192005655822693514154', '6.51524584481201277119234762981032', '7.909279614510233861968010838681288', '9.131126785841765477617157557679301', '10.87340721492894986045430752164811', '11.96700065379150229602644614103589', '12.96371228446560967973435590436129', '13.84607403568569026553937743450832'], 'prelabel': '2-85-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.239455815703439, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.62531486020739504467690275918', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.70063376827350616544234187635', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.02466628915192005655822693514', 'prec': 100}}