-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '720664426620703521786755083211', 'a10': [-3.7853188626880683, -6.556364593024573], 'a2': [1.8827759562723798, 1.5798366104976047], 'a3': [0.0, 0.0], 'a4': [0.7016652303149536, 3.9793412641430694], 'a5': [-2.8945003338173687, -1.0535119645831086], 'a6': [0.0, 0.0], 'a7': [-0.4616727027722975, 2.6182760058463015], 'a8': [-2.507841132270207, 4.34370825840306], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.406', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '3361176223353937695684159643856', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.8827759562723798, -1.5798366104976047], [0.3472963553338607, 1.969615506024416]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.8945003338173687, 1.0535119645831086], [3.83022221559489, 3.2139380484326967]], [[1.0, 0], [0.4616727027722975, -2.6182760058463015], [-6.5778483455013586, -2.3941410032796813]], [[1.0, 0], [3.2272246153170574, -1.174613699266604], [8.426488874308758, -7.070663706551932]], [[1.0, 0], [2.5616190102484464, -2.1494535667161805], [2.2574263096700946, -12.802500789158705]], [[1.0, 0], [-1.2864089518119453, -2.228125663849713], [-8.5, 14.722431864335457]], [[1.0, 0], [-1.0483815613409906, 1.815850129960983], [-9.5, -16.454482671904334]], [[1.0, 0], [0.092805235686555, 0.526324645914496], [-21.612930278075893, 7.866463296490381]], [[1.0, 0], [1.9387771079730998, 1.6268271562351817], [5.03579715234098, 28.559424837354033]], [[1.0, 0], [-1.3396438113788047, -7.597497592235991], [-29.13047124436316, 10.602624443095731]], [[1.0, 0], [-5.147831404849026, -8.916305541997184], [-18.5, 32.04293994002423]], [[1.0, 0], [-3.742132177656214, 3.1400217300879607], [7.119575284344144, -40.37711787350053]], [[1.0, 0], [2.576158130487292, -0.9376448782602417], [32.93991105411605, -27.639867216521193]], [[1.0, 0], [-0.9825007218380509, 5.572038481521415], [-44.16555317693769, -16.07494673630643]], [[1.0, 0], [6.426574211857975, 0], [53.0, 0]], [[1.0, 0], [-1.555144049150873, -0.5660261438871338], [45.196622144019706, 37.92446897150582]], [[1.0, 0], [-2.4957077844907114, 14.153862185260564], [-57.32124986794041, -20.863228742865793]], [[1.0, 0], [4.50356176877388, -3.778937019162261], [11.634427903684333, -65.98211945181794]], [[1.0, 0], [-7.408133900946371, -12.831264305712539], [-35.5, 61.48780366869514]], [[1.0, 0], [0.9406991495700744, -1.6293387216922033], [-36.5, -63.21985447626402]], [[1.0, 0], [-13.170976217679938, -11.051761286499962], [13.718206035687498, 77.79981248796443]], [[1.0, 0], [3.040265507013148, 2.551085665615739], [14.412798746355218, 81.73904350001327]], [[1.0, 0], [-2.549398168735345, 4.4156871569726714], [-44.5, -77.07626093681505]], [[1.0, 0], [-9.99069744419561, 3.636316489246625], [74.30631098254086, -62.35039813959431]], [[1.0, 0], [0.9825168900265222, -5.572130175874747], [-94.90895469937675, -34.544034475892545]], [[1.0, 0], [9.745120011700553, 3.5469336136109066], [78.90257764125474, 66.20712379771355]], [[1.0, 0], [-14.245739156793164, 0], [107.0, 0]], [[1.0, 0], [-5.76063657725292, 0], [109.0, 0]], [[1.0, 0], [10.728181816255184, 3.9047388489128116], [86.56302207244451, 72.63499989457894]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-3e6-27.16-c1-0-4', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/729/2/e/s/406/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.748847248737698, 1.3569762929953557, 0.9767614241509429, 0.5980131090882622, 0.21381257439440438, -0.17783312329429404, -0.5732699771130755, -0.9633179618276753, -1.3340674022864556, -1.6682035306577958, -1.9467446642563664, -2.151083586824122, -2.265193879098173, -2.2778179590633054, -2.1844101969617133, -1.988583255429999, -1.7028113404222138, -1.3481880795599104, -0.9531213752288883, -0.5509684585273847, -0.17676027221991833, 0.13668247023940996, 0.36280136849031996, 0.4849829624985279, 0.49930097041101285, 0.41579595123974844, 0.2579090558400455, 0.05991002295661261, -0.1375531111102261, -0.29333973956236425, -0.37239900810351995, -0.3520864634955699, -0.22715249966519832, -0.012401541562936295, 0.2577386050888494, 0.5330893977475026, 0.7548547986346095, 0.8652475621405165, 0.8182967602489878, 0.5901254914102277, 0.18682779504549463, -0.3517801878541561, -0.9537859396334615, -1.522667144751275, -1.9501563283390684, -2.132979549497186, -1.9910670926161405, -1.484240997281382, -0.624248446195992, 0.5205789392243996, 1.8298015432173658, 3.144841915167266, 4.291157108993456, 5.1056991081276015, 5.465457512483058, 5.31219853549063, 4.668646346904788, 3.6423680724442455, 2.4154340886391803, 1.2202805652152853, 0.3047189746385186, -0.10873818723523665, 0.13741717815252072, 1.1039959103775048, 2.737598571581961, 4.871359375660779, 7.245014821869353, 9.541936194219144, 11.43754153599048, 12.651118629065985, 12.992063452514646, 12.392154847962114, 10.91772426013888, 8.759091553315391, 6.198797723710388, 3.5641785514415574, 1.17288188335056, -0.7186180364942071, -1.9539648187081697, -2.496205947604071, -2.4242033110999706, -1.9075465395619386, -1.165686254215254, -0.42015754938089395, 0.14996695129831175, 0.44017347303552995, 0.43386147514905726, 0.19497179270035822, -0.15737337448872396, -0.4854230424482996, -0.6713033563012295, -0.6479970469391441, -0.4153559650822445, -0.0375539573835409, 0.3768799850621997, 0.7068546906265682, 0.8536913704278739, 0.7697877369036379, 0.473098283304444, 0.04327935912685111, -0.39974713273233486, -0.729231541136591, -0.8479984028273339, -0.7176645110672225, -0.3721544490869431, 0.08896187091425607, 0.5263230780726225, 0.799385862588852, 0.8074228756020329, 0.5213003833686248, -0.0036243671095211294, -0.6383592414004103, -1.2132953853857007, -1.5653561577012836, -1.5866397809368054, -1.260569773302124, -0.6740888188047667, -0.00039999649899146334, 0.545244662048848, 0.7662769742858495, 0.5460028129948296, -0.10838361919778502, -1.0533320497395544, -2.0348068295117776, -2.749148936433975, -2.9254855309878764, -2.408982752189056, -1.222040640592534, 0.4155978095152648, 2.117488967429441, 3.408816644614103, 3.83642811324189, 3.084962780432902, 1.0698957595696579, -2.017826768664572, -5.730179722952905, -9.442979216374564, -12.483040316513405, -14.272928485560778, -14.459126387871985, -12.992433814705699, -10.140453676663464, -6.428447102871687, -2.5225089552465922, 0.9166695718936514, 3.3740149888339066, 4.580747235639432, 4.552544585553888, 3.5585919209227, 2.032710329612099, 0.4522230887485036, -0.7825328877383646, -1.4369395903619913, -1.4781343131100553, -1.052934553961322, -0.4186251896914429, 0.14983356936966816, 0.44733556976134875, 0.39538550136694195, 0.05328155728982346, -0.41639639959983377, -0.8139927837496014, -0.9774015010134717, -0.8401433864798591, -0.45417512430229834, 0.02922753455938629, 0.4132158248408691, 0.5250972666458379, 0.2782935593592651, -0.2944770527519971, -1.0481146427068557, -1.7700442189964833, -2.2482647424031423, -2.339863663898211, -2.0170529042265724, -1.375233691799782, -0.6003472277590721, 0.09342409174563779, 0.534349449418098, 0.6479527382297254, 0.4769629812076604, 0.15947439573579072, -0.1268931659283058, -0.2346808495709533, -0.10441004299010023, 0.2117010686742578, 0.5706624127623908, 0.7986526865074104, 0.7692404862227895, 0.47057002781161933, 0.033664110307553244, -0.29426008084374977, -0.2289067654694034, 0.4416676010981288, 1.7531043441190397, 3.5045915379163795, 5.27033416580657, 6.4893799612641105, 6.615050172268766, 5.283484413895426, 2.4503171191340574, -1.550411353189726, -6.050822912321936, -10.193110499894443, -13.138019190513072, -14.281383058441602, -13.41666835587408, -10.794686110841955, -7.060290131142854, -3.081648245803384, 0.2802965435421381, 2.396288940608751, 3.022699763169618, 2.3415104449141158, 0.8772211988070484, -0.681410877156183, -1.698671440819608, -1.781472847489654, -0.8846843531650382, 0.6966858282828421, 2.441242637359562, 3.7807163631188843, 4.285728566907061, 3.7985336376665915, 2.4727242605695006, 0.7114533121007781, -0.9710665438550055, -2.1161411675247837, -2.459665359088213, -1.9998605234474154, -0.9757373369234263, 0.2308935998331727, 1.2320321913863004, 1.7599864523644706, 1.7414396407134751, 1.2975816947034855, 0.6761170260175605, 0.14483149067932824, -0.11158940478152111, -0.05353901738232259, 0.21315065403707886, 0.49451482597417906, 0.5975959881225932, 0.4143814767980134, -0.03303174123943576, -0.603125152741246, -1.0956910588616582, -1.3365620393468844, -1.250688498816981, -0.8927762505962831, -0.42216098523098045, -0.03177872482518592, 0.13929891428546945, 0.07233417478020346, -0.11571771951373967, -0.2178792323536172, -0.028378206815006177], 'positive_zeros': ['0.56850399194458961795683669809801', '2.56672551061248547029219776715006', '3.41169542268791910393748498967474', '4.13117443413267270097228363715756', '5.04628112296742258748840746131807', '6.07124496740267976576608218791248', '7.56977392441613195673303595026793', '7.71609267533037867467580444182860', '9.572655116893152668871128055354681', '10.46125411840791470625019045359923'], 'prelabel': '2-3e6-27.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.9629629629629629, 'root_number': '-0.993238357741943 + 0.11609291412523036*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.481481481481', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56850399194458961795683669810', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56672551061248547029219776715', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41169542268791910393748498967', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.16', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/s/406/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-3e6-27.16-c1-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-3e6-27.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.48148148148148145, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56850399194458961795683669810', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '720664426620703521786755083211', 'Lhash_array': ['720664426620703521786755083211'], 'label': '2-3e6-27.16-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/s/406/2'}