-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '998508672132053423410834593184', 'a10': [-57.517821739175574, 0.0], 'a2': [-3.2789738409484843, 0.0], 'a3': [0.0, 0.0], 'a4': [2.751669449624455, 0.0], 'a5': [17.541409150900034, 0.0], 'a6': [0.0, 0.0], 'a7': [26.699896838720537, 0.0], 'a8': [17.209138583332173, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [3.2789738409484843, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-17.541409150900034, 0], [125.0, 0]], [[1.0, 0], [-26.699896838720537, 0], [343.0, 0]], [[1.0, 0], [21.402574504689536, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [83.9629750383598, 0], [4913.0, 0]], [[1.0, 0], [-77.11415728743033, 0], [6859.0, 0]], [[1.0, 0], [142.11934553024736, 0], [12167.0, 0]], [[1.0, 0], [134.22305804118787, 0], [24389.0, 0]], [[1.0, 0], [122.55923460430999, 0], [29791.0, 0]], [[1.0, 0], [-222.5873143468058, 0], [50653.0, 0]], [[1.0, 0], [-198.32077032087702, 0], [68921.0, 0]], [[1.0, 0], [-154.65576335966375, 0], [79507.0, 0]], [[1.0, 0], [78.79556488458275, 0], [103823.0, 0]], [[1.0, 0], [-477.08802666575025, 0], [148877.0, 0]], [[1.0, 0], [42.92816310761106, 0], [205379.0, 0]], [[1.0, 0], [-496.5389272106959, 0], [226981.0, 0]], [[1.0, 0], [-484.6587483343133, 0], [300763.0, 0]], [[1.0, 0], [-382.43236557693376, 0], [357911.0, 0]], [[1.0, 0], [193.62195604715103, 0], [389017.0, 0]], [[1.0, 0], [-1049.59899515665, 0], [493039.0, 0]], [[1.0, 0], [-861.8995001957009, 0], [571787.0, 0]], [[1.0, 0], [-967.6452838815062, 0], [704969.0, 0]], [[1.0, 0], [591.4697292385971, 0], [912673.0, 0]], [[1.0, 0], [255.10993969026978, 0], [1030301.0, 0]], [[1.0, 0], [247.3545667994593, 0], [1092727.0, 0]], [[1.0, 0], [683.4836956667759, 0], [1225043.0, 0]], [[1.0, 0], [1697.7631292210588, 0], [1295029.0, 0]], [[1.0, 0], [-380.70873895866737, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 69, 'label': '2-39e2-1.1-c3-0-69', 'leading_term': '1.7311230361548413167784812991603', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1521/4/a/bk/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.7311230361548413, 1.718529697743116, 1.6809626040841634, 1.619058842619759, 1.533874521640056, 1.4268758265939823, 1.2999257541244225, 1.1552658479493945, 0.9954921619517473, 0.8235246409571868, 0.642569145783602, 0.4560714598054248, 0.26766279941822485, 0.08109660673461387, -0.09982327750216528, -0.27132258966751904, -0.42974388294960986, -0.5716397075897137, -0.6938699618130529, -0.793701208102467, -0.8689053445986551, -0.9178546671785617, -0.939610073932361, -0.9339989691968065, -0.9016793362894467, -0.8441864815994147, -0.7639591196624878, -0.6643417774565332, -0.5495609501319311, -0.42467303842555676, -0.29548283323954694, -0.16843217255412557, -0.050459361199641596, 0.051169009734605884, 0.12905111037737965, 0.1758639413716885, 0.1845934932701619, 0.14877504557532423, 0.0627367489325958, -0.07816111437316521, -0.27729934372039805, -0.5365939655403678, -0.856319799641689, -1.2349716630445138, -1.6691708347558212, -2.15362348367888, -2.681136517450775, -3.2426947605120975, -3.8276015468605387, -4.42368276211003, -5.017552149134581, -5.594933372083288, -6.14103199536981, -6.640948265527896, -7.08011947750297, -7.444778857277123, -7.722416391515923, -7.902225967532512, -7.975522628080908, -7.936113755547696, -7.780608620958123, -7.508651985262895, -7.1230693199109325, -6.629913691130781, -6.038407371347864, -5.360774719094135, -4.6119666980759115, -3.8092814570211146, -2.9718895164869337, -2.120276145609736, -1.2756172920927853, -0.45910878319609677, 0.30872871860549883, 1.0087444928718552, 1.623826594320536, 2.1395188627621873, 2.5445610549904862, 2.831328917974671, 2.996153927161128, 3.039506283203228, 2.966029484361377, 2.784420216128844, 2.507153231135477, 2.150057104916978, 1.7317529957992044, 1.2729745440799591, 0.795792547230788, 0.3227727825144634, -0.12390092471195253, -0.5233037779142692, -0.856611491886896, -1.1078708012546832, -1.264665514368391, -1.3186480508912446, -1.2659112511145918, -1.107181367096109, -0.8478203160213373, -0.49763321241989655, -0.07048556788931484, 0.4162570098220913, 0.942445655555582, 1.4859932265495914, 2.0238126574683153, 2.5328089529536366, 2.990881784722343, 3.377894251917901, 3.676563970307801, 3.8732353142644214, 3.9584962839292093, 3.927609948519931, 3.7807384705748937, 3.5229470042176536, 3.163984870013365, 2.7178518718113684, 2.2021679360564277, 1.6373739111402479, 1.045799869514625, 0.45064415662493496, -0.1250886569168572, -0.6596401363861272, -1.1334897207469032, -1.5302372899474668, -1.8373328851897097, -2.0466170672890525, -2.1546445358210837, -2.1627743183546895, -2.077021554687997, -1.9076780570964218, -1.6687207962882715, -1.3770386092019273, -1.0515171411288462, -0.7120297737925348, -0.37838759818475554, -0.069304031413726, 0.19857074211400813, 0.4114937388140933, 0.5593060678231707, 0.6359061191098709, 0.6394934152177774, 0.5725700558035548, 0.44170014038045124, 0.25704116613918626, 0.031674398032467486, -0.21922715308898777, -0.47934492295778897, -0.7322199938156653, -0.9622582933456056, -1.1556763202674774, -1.301330936846637, -1.3913831519480173, -1.421755266102867, -1.3923527674040799, -1.307036293959384, -1.1733440243213547, -1.0019801432733884, -0.8060996401864677, -0.6004327303912069, -0.40030281675803714, -0.2205994219974912, -0.07477138476003077, 0.026094505231310034, 0.07404845131043837, 0.0648533082628972, -0.0016802690949598432, -0.12162587509311196, -0.2871506845397427, -0.48699446178030026, -0.7071929496992775, -0.9320037586038439, -1.1449784859566892, -1.3301135824405435, -1.4730052511699185, -1.5619310147180754, -1.5887828301765448, -1.5497837986208072, -1.4459323146180103, -1.2831333427694758, -1.0719955234601986, -0.8272938981563147, -0.5671199334041324, -0.31176184246536076, -0.08237757040635733, 0.10046108842811202, 0.21826308429852337, 0.2560549036194664, 0.20366262619475395, 0.05674809129507584, -0.18248014587268171, -0.5049430048301392, -0.8947941244719849, -1.3299646100281959, -1.783136329925233, -2.223103131590656, -2.6164531329385023, -2.9294822156266545, -3.1302305737444613, -3.1905219895527233, -3.087880410344312, -2.8072009678947865, -2.3420629294151367, -1.695589822273719, -0.8807862773413873, 0.07968931376057817, 1.1543241123815853, 2.30409517432648, 3.4842976679133164, 4.6467642946275305, 5.742356465591836, 6.723587593465234, 7.547226714077104, 8.17672755865732, 8.58433461515801, 8.752733514549098, 8.676137523721513, 8.360733718286777, 7.824449739409084, 7.096042699405157, 6.213553309698164, 5.222208060447767, 4.171887726983523, 3.1143092680274593, 2.1000883366226186, 1.1758596743757868, 0.3816317448499756, -0.2514600902039192, -0.7028601969140709, -0.9636494517279718, -1.0368820347331034, -0.9371766866220259, -0.6895838036311411, -0.327796007158159, 0.1081875717455311, 0.5747969286162259, 1.0278531851529733, 1.425567047082673, 1.7313795521103394, 1.9164592295813594, 1.9616902878707247, 1.8590179862106382, 1.6120580279851104, 1.2359240900499748, 0.7562784568707306, 0.20766185347384894, -0.3687934077319812, -0.9281211540816573, -1.4245716143411062, -1.814754793189534, -2.060669440736471, -2.132415682528123, -2.0104084221944873, -1.6869400157859162, -1.1669824759595429, -0.4681689043627976, 0.3800522695195238, 1.338041923335101, 2.358273503282453, 3.3881690732900056], 'positive_zeros': ['0.78768445496912214744739203244825', '1.90265759062467063737005529845250', '2.25560464040033717588463149437549', '4.19464452831454166136577642030321', '5.13947947755596359639685768273002', '5.75107760180436472336145051407883', '6.90104484342265511047926124290966', '7.80717406097310269301191776174421', '8.327968303696890063457261204583757', '9.356719185524293968437475339887481'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78768445496912214744739203245', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.90265759062467063737005529845', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.25560464040033717588463149438', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 69, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/bk/1/3'], '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': '2-39e2-1.1-c3-0-69', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78768445496912214744739203245', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '998508672132053423410834593184', 'Lhash_array': ['998508672132053423410834593184'], 'label': '2-39e2-1.1-c3-0-69', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/bk/1/3'}