-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1577720466434883261562120778015', 'a10': [-26141124731.01554, 12196865396.398571], 'a2': [1855.92635238102, -865.9338164881207], 'a3': [0, 0], 'a4': [2694621.2509246357, -3214218.7788763465], 'a5': [-14085216.634527743, 0], 'a6': [0, 0], 'a7': [0, 781740827.7741289], 'a8': [2217717855.056759, -8298716997.837717], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 110.41467654306618, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '11.0', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [-1855.92635238102, 865.9338164881207]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '36.19', 'coefficient_field': 'CDF', 'conductor': 36, 'conductor_radical': 6, 'conjugate': '487493359093919122948118561887', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1855.92635238102, 865.9338164881207]], [[1.0, 0], [0, 0]], [[1.0, 0], [14085216.634527743, 0], [2384185791015625.0, 0]], [[1.0, 0], [0, -781740827.7741289], [-3909821048582988300, 0]], [[1.0, 0], [0, -454625189225.5526], [-81402749386839760000000, 0]], [[1.0, 0], [1515683886597.747, 0], [3211838877954855300000000, 0]], [[1.0, 0], [-33423294532642.004, 0], [1174562876521148400000000000, 0]], [[1.0, 0], [0, 116923962296699.17], [-13569980418174090000000000000, 0]], [[1.0, 0], [0, 1023672664874491.0], [-907846434775996200000000000000, 0]], [[1.0, 0], [-20432479600629744, 0], [148852438543083300000000000000000, 0]], [[1.0, 0], [0, 31190670947779030], [-645590698195138100000000000000000, 0]], [[1.0, 0], [7541937194366796.0, 0], [31654680139659126000000000000000000, 0]], [[1.0, 0], [527932019814111940, 0], [302862043149743570000000000000000000, 0]], [[1.0, 0], [0, 497530583040503200], [-863586854220408700000000000000000000, 0]], [[1.0, 0], [0, 1077982568576252000], [-6111571184724800000000000000000000000, 0]], [[1.0, 0], [5009541159660160000, 0], [85915027059992620000000000000000000000, 0]], [[1.0, 0], [0, -16364548734878431000], [-909377607891473300000000000000000000000, 0]], [[1.0, 0], [65286058419456690000, 0], [1893461025894826200000000000000000000000, 0]], [[1.0, 0], [0, 163628810000716000000], [-14915769363385152000000000000000000000000, 0]], [[1.0, 0], [0, 391076266628919460000], [-53417513915589150000000000000000000000000, 0]], [[1.0, 0], [-253546545452478900000, 0], [98424433237708430000000000000000000000000, 0]], [[1.0, 0], [0, 485910866325694640000], [-559494740587480900000000000000000000000000, 0]], [[1.0, 0], [0, -1584684209074411700000], [-1658509762573818300000000000000000000000000, 0]], [[1.0, 0], [-337182129614150500000, 0], [7701585589361325000000000000000000000000000, 0]], [[1.0, 0], [-416329544897152350000, 0], [51165609725977650000000000000000000000000000, 0]], [[1.0, 0], [5835952988022475000000, 0], [124471585975092090000000000000000000000000000, 0]], [[1.0, 0], [0, -2510800659892248000000], [-191610340886078100000000000000000000000000000, 0]], [[1.0, 0], [0, 19992640097146750000000], [-443040174110042700000000000000000000000000000, 0]], [[1.0, 0], [-17817564204077437000000, 0], [665860043319738800000000000000000000000000000, 0]], [[1.0, 0], [37531208083451167000000, 0], [1471383076677527800000000000000000000000000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 43, 'label': '2-6e2-4.3-c22-0-43', 'leading_term': '2.602325627522896416832012428176297152078993982639170259', 'load_key': 'CMFs-workshop', 'motivic_weight': 22, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [22], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/36/23/d/c/19/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.07421875', 'prec': 34}, 'plot_values': [2.6023256275228963, 3.01268864590011, 3.365419799815162, 3.6510866575513465, 3.861872474939445, 3.9917978641191696, 4.036892571051824, 3.995312342818233, 3.867397417520044, 3.6556708243541385, 3.364776392144529, 3.0013580825728647, 2.5738839404740634, 2.092419539810966, 1.568357254648143, 1.0141089576273072, 0.4427708070046718, -0.13223040390189442, -0.6974993182685293, -1.2400322357266376, -1.7475652474172583, -2.208900387556023, -2.6142005247741062, -2.9552446088350464, -3.2256360266224826, -3.4209581737653827, -3.5388728767206095, -3.5791589610012604, -3.543690006787619, -3.436352112816651, -3.262904251244892, -3.0307854882360266, -2.7488749170511326, -2.4272115552051186, -2.076682652074117, -1.7086898012631813, -1.3348029230834857, -0.9664125545684858, -0.6143909441702005, -0.288772191388243, 0.0015388967091360553, 0.2490204252115969, 0.44774183868327444, 0.5935208664912497, 0.684024276611135, 0.7188094628686075, 0.6993057277077748, 0.6287360067236397, 0.5119816545499771, 0.3553947159940658, 0.16656378461552546, -0.045958950589281636, -0.2729606001529729, -0.5048905424363909, -0.7321929051613615, -0.9456376402805075, -1.1366392601206878, -1.2975526431013937, -1.421936004022609, -1.5047721396031584, -1.5426403764864374, -1.5338332280339528, -1.4784135604868474, -1.3782100232727157, -1.2367505509470074, -1.059135829700831, -0.8518566714226586, -0.6225611846751131, -0.37977940838415336, -0.1326146185294573, 0.109588224957354, 0.3375855018083801, 0.542577486202995, 0.7165383408778921, 0.8525217166450733, 0.9449307911193274, 0.9897426435673008, 0.9846782932291892, 0.9293114851038248, 0.8251113368793151, 0.6754161997414138, 0.4853384618394372, 0.2616024574296429, 0.01232005440716372, -0.25328920588111636, -0.5252244323199294, -0.7930653453536198, -1.0463575477371054, -1.2750076740017506, -1.4696743336407494, -1.6221405909107949, -1.7256540522726993, -1.7752214618933746, -1.767846019802537, -1.702697402261441, -1.5812066288857942, -1.407080419797775, -1.18623243866871, -0.9266317328599865, -0.6380716605744273, -0.33186553256831763, -0.02047798666116452, 0.28289634659523166, 0.56479313673199, 0.8119620982885544, 1.0118574361161237, 1.1531175630637485, 1.226016594476271, 1.2228706837988266, 1.1383834474971104, 0.9699165093860587, 0.7176735258107476, 0.384788864114287, -0.022684691785630394, -0.4958913490819086, -1.0233893164853973, -1.5914642194785833, -2.184530132348455, -2.7856060795668114, -3.376852859399553, -3.9401525217193174, -4.457710894510178, -4.912662285353086, -5.289654948602763, -5.575396143799199, -5.759136626188182, -5.833076187271602, -5.792674354298373, -5.636853486764296, -5.368085173610717, -4.99235491239861, -4.5190043980919015, -3.9604552072609804, -3.3318220684280697, -2.6504280937992846, -1.9352381489720312, -1.2062298032924297, -0.4837238991594197, 0.21230140892272273, 0.8628883504847417, 1.450744152933545, 1.96082867409991, 2.3808629969290855, 2.701739642749808, 2.9178185545691604, 3.0270971577224404, 3.031247472205415, 2.93551825599834, 2.748505311459069, 2.481798187328787, 2.149516354853436, 1.767752331726582, 1.353942989761992, 0.926193250872115, 0.5025784192625712, 0.10045241872896063, -0.2642108549104239, -0.5774170095353929, -0.8276676218949989, -1.0063730622039022, -1.1081451312866057, -1.130957766473195, -1.0761694081466537, -0.948406274127827, -0.7553115335642699, -0.5071709671864609, -0.21643091002121623, 0.10287112894055786, 0.4357389912383598, 0.7668865607702395, 1.081413968207333, 1.3654621835139196, 1.6068176484708352, 1.7954406085297103, 1.9238939732248481, 1.9876537464194006, 1.9852871538892962, 1.9184903467970034, 1.7919837329899624, 1.6132693180737392, 1.3922606471400643, 1.14080174815937, 0.8720966239903861, 0.6000750807567652, 0.3387238107799641, 0.10141350888546476, -0.09974671375908645, -0.2544972895532893, -0.3549305376764229, -0.39588305922308864, -0.3751986887969333, -0.2938483191256047, -0.15589945368459335, 0.03166468129688636, 0.25926953457088586, 0.515203311244928, 0.7861805459006651, 1.0579894470122917, 1.3161928766856026, 1.5468497573421816, 1.737222140329344, 1.8764332361495595, 1.9560434240334872, 1.9705145848736303, 1.9175379141666211, 1.7982064755469922, 1.6170208898930343, 1.381724403806277, 1.1029717867813928, 0.7938446850332049, 0.46923381986705215, 0.1451153779080266, -0.16224525376535345, -0.4371249095605107, -0.6651690871382732, -0.8341725078647854, -0.9347740902188965, -0.9610297772324434, -0.910831655306799, -0.7861484538922918, -0.5930705451434707, -0.34165161768567376, -0.04554886825626449, 0.27852661202886386, 0.6115280546684829, 0.9329298826330059, 1.2216857496721683, 1.4572443536386477, 1.620575655171099, 1.6951583457940491, 1.6678799495518575, 1.5298038428053917, 1.2767626570837556, 0.9097447963374943, 0.4350498526561166, -0.13580085091445698, -0.7864009974266315, -1.4960339442709822, -2.240464387597406, -2.9929152369187966, -3.7251883419204663, -4.408879914672553, -5.0166358838107445, -5.523389324289879, -5.907521732729048, -6.151892341163618, -6.244684822662036, -6.180028446398486, -5.958360663714568, -5.58650981054897, -5.077489558467187, -4.450010327041309, -3.727726431486154, -2.938250616168696, -2.111979172700311, -1.2807804702050931, -0.476606928732297], 'positive_zeros': ['1.24460199533753898200705435932887', '2.96832720983697464615237661879514', '3.76963405971642755220313558816451', '5.16135974284923372528643988409505', '6.16368062041010677737974352926662', '7.50100688955575855230853361976888', '8.382895249633662000796387849194798', '10.21912210766330775334527466348633', '11.52348601152684201456064276254065', '12.37112798716303979258740176555826'], 'prelabel': '2-6e2-4.3-c22-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.507838814098081, 'root_angle': 0.722081036872131, 'root_number': '-0.6424477698623265404267062642214071317202169292373606771 + 0.7663294741812578320133143156874103131208735934291762335*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3610405184360655', 'prec': 60}, 'spectral_label': 'c22-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24460199533753898200705435933', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96832720983697464615237661880', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.76963405971642755220313558816', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 110.41467654306618, 'bad_primes': [2, 3], 'central_character': '4.3', 'conductor': 36, 'conductor_radical': 6, 'degree': 2, 'index': 43, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/36/23/d/c/19/9'], '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': '2-6e2-4.3-c22-0-43', 'motivic_weight': 22, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [22], 'order_of_vanishing': 0, 'prelabel': '2-6e2-4.3-c22-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.507838814098081, 'root_angle': 0.3610405184360655, 'self_dual': False, 'spectral_label': 'c22-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24460199533753898200705435933', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1577720466434883261562120778015', 'Lhash_array': ['1577720466434883261562120778015'], 'label': '2-6e2-4.3-c22-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/36/23/d/c/19/9'}