-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2113086017916313720829986080290', 'a10': [104.51448198280593, 181.0243929209619], 'a2': [-2.4447597911651475, 4.234448170599514], 'a3': [0.0, 0.0], 'a4': [4.046299127004287, 7.0083956705930195], 'a5': [21.375204705284233, -37.02294057173762], 'a6': [0.0, 0.0], 'a7': [43.22555254005817, -122.22336768231627], 'a8': [-196.03354426947632, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.104180648217781, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-43.22555254005817, 122.22336768231627]]]], 'bad_primes': [3, 7], 'central_character': '63.37', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'conjugate': '1033490582054842890606291210699', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.4447597911651475, -4.234448170599514], [-16.0, -27.712812921102035]], [[1.0, 0], [0, 0]], [[1.0, 0], [-21.375204705284233, 37.02294057173762], [-1562.5, -2706.329386826371]], [[1.0, 0], [-43.22555254005817, 122.22336768231627]], [[1.0, 0], [355.43901637112657, 615.6384353470971], [-80525.5, 139474.25730488764]], [[1.0, 0], [-885.6235593615269, 0], [371293.0, 0]], [[1.0, 0], [-350.6585953580906, -607.358503270949], [-709928.5, 1229632.2317411618]], [[1.0, 0], [-627.9460841269905, 1087.634522121868], [-1238049.5, -2144364.636285245]], [[1.0, 0], [-523.0919459100394, 906.0218273462591], [-3218171.5, -5574036.5454701455]], [[1.0, 0], [-6150.883048504781, 0], [20511149.0, 0]], [[1.0, 0], [1147.1186734922312, 1986.8678247995583], [-14314575.5, 24793572.054780666]], [[1.0, 0], [202.05429843410903, -349.96831077556146], [-34671978.5, -60053628.36093575]], [[1.0, 0], [17891.39607302714, 0], [115856201.0, 0]], [[1.0, 0], [14604.816967561965, 0], [147008443.0, 0]], [[1.0, 0], [-10568.635021243734, 18305.412823445928], [-114672503.5, -198618602.2931199]], [[1.0, 0], [53.606372463568064, 92.84896071636109], [-209097746.5, 362167920.6861574]], [[1.0, 0], [-22249.38846722607, -38537.07126257258], [-357462149.5, 619142604.7167817]], [[1.0, 0], [-11606.175918061881, 20102.486371665538], [-422298150.5, -731441852.6083683]], [[1.0, 0], [-3335.6595571540984, -5777.5318297436], [-675062553.5, 1169242640.9491835]], [[1.0, 0], [-25110.49298926514, 0], [1804229351.0, 0]], [[1.0, 0], [4737.485702262821, 8205.56593645033], [-1036535796.5, 1795332663.4018745]], [[1.0, 0], [-13238.057874310287, 22928.988831842667], [-1538528199.5, -2664809010.4114656]], [[1.0, 0], [7494.028253441662, 0], [3939040643.0, 0]], [[1.0, 0], [16085.644984838284, -27861.15438625541], [-2792029724.5, -4835937339.076535]], [[1.0, 0], [155070.21115564014, 0], [8587340257.0, 0]], [[1.0, 0], [-55960.90023324993, -96927.12244128191], [-5255050250.5, 9102014030.193556]], [[1.0, 0], [-30342.12763744844, 52554.10667780052], [-5796370371.5, -10039607982.924889]], [[1.0, 0], [56266.396302019704, -97456.25715390372], [-7012758653.5, -12146454289.080307]], [[1.0, 0], [-3811.6731419430057, -6602.011543690983], [-7693119774.5, 13324874318.146824]], [[1.0, 0], [-41498.65374106765, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-63-7.2-c5-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/63/6/e/f/37/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4312871597591643, 1.517587456421843, 1.5650939683762857, 1.5740125385532129, 1.5451373645246569, 1.4798895448640623, 1.3803705742788352, 1.2494243157222196, 1.0906992163764966, 0.9087011651478921, 0.7088265031508245, 0.4973643813979502, 0.2814579907964425, 0.06901523761381284, -0.13143874486267915, -0.3109722443829421, -0.460522375298121, -0.5712327170696648, -0.6348459357665859, -0.6441390005011048, -0.5933833193999174, -0.47880701742058634, -0.29903205667384947, -0.05545539786479124, 0.24745862488137854, 0.6020076550059987, 0.9972331442418977, 1.4190806549170376, 1.8507571536825356, 2.273293690469104, 2.666309355341176, 3.0089580531752187, 3.2810242038110338, 3.464117966819537, 3.5429061982604053, 3.5063033875253695, 3.3485386431688897, 3.0700116656653957, 2.677853625955203, 2.186118690997674, 1.6155488740972646, 0.9928786517632432, 0.34967546491434676, -0.27925375646978373, -0.8578237236661262, -1.3508976125491476, -1.7266455789734734, -1.9588757185371262, -2.0291628185720194, -1.9285972933495568, -1.6589880371379127, -1.2333793910095765, -0.6757835537729112, -0.020083732821156837, 0.691873132232133, 1.4129066897168974, 2.0937011853113967, 2.686354636895658, 3.1480146110483833, 3.4443069511775395, 3.552258358122636, 3.4624348468640065, 3.1800664774394174, 2.7250024698522086, 2.130435240962192, 1.4404398764859572, 0.7064878002938958, -0.016800727296545265, -0.6763122372699711, -1.225090187389445, -1.626541772230517, -1.8577812672327738, -1.9117510402902498, -1.7978634382574188, -1.5410422408953326, -1.1791996216906928, -0.7593485144764082, -0.3327038454253149, 0.05074820890363484, 0.34765181323705296, 0.526066910729235, 0.5690887790611683, 0.476852915310907, 0.2666343201296489, -0.029048806811495208, -0.3661928983697062, -0.694571452800304, -0.9639495810755864, -1.13055490587972, -1.163038808325567, -1.0471784556532528, -0.7886774288085059, -0.4136146781112311, 0.033649267883421936, 0.4950002590149742, 0.9051178403198779, 1.1993516448199155, 1.3220281835719068, 1.234178754052303, 0.9196871221582954, 0.38898943563395083, -0.32028957842096956, -1.1460343596006366, -2.0075380196163786, -2.8140597464247907, -3.475127341003614, -3.911396202583507, -4.064734840820893, -3.9062275016859798, -3.440974542878467, -2.7089168796209298, -1.7813768270903532, -0.7535404532200537, 0.2663597516080014, 1.1699387101098015, 1.8620762873419807, 2.273162250303054, 2.36854470001508, 2.153848345113116, 1.6753102379092226, 1.0148981904126697, 0.2806547851503722, -0.40664098893699663, -0.9288714725274652, -1.186079631646273, -1.1100283716764572, -0.6739684915969578, 0.10278631056370334, 1.1562208749376375, 2.384876581715396, 3.662161914251321, 4.852158818396602, 5.826850638541348, 6.482455600826266, 6.752627589025012, 6.61668276165906, 6.101679401823246, 5.278030725222252, 4.249247407519356, 3.1372557105626884, 2.065391127334017, 1.1415240978887342, 0.4437725711321638, 0.010887255073279705, -0.16129379129808205, -0.1168365470847048, 0.06933640303978199, 0.30508186884291566, 0.49708743303615094, 0.566772695577784, 0.4634829948614963, 0.17283503918263626, -0.2811575442080477, -0.8405458155708908, -1.4237774619361483, -1.9401946740294822, -2.306267547133463, -2.460795733834751, -2.376430820926671, -2.0654419783012083, -1.578585977316633, -0.9971029376445386, -0.4190515156752363, 0.057780528374353914, 0.35348343262811605, 0.42105169472521764, 0.2560701563920578, -0.10086731331369375, -0.5697329852131017, -1.0439844676608279, -1.4088581579781734, -1.5620356109011735, -1.4331304753058616, -0.9984902254588397, -0.28846921741413756, 0.6144807984518038, 1.5870241305678996, 2.4839573093480913, 3.1620934808330947, 3.5050957529994804, 3.4449957351490688, 2.9765174368134586, 2.1614032031153476, 1.1215485567218781, 0.021637340496515705, -0.9561909712765327, -1.6416371959494769, -1.9046640228057956, -1.6781824931213516, -0.9709630949735749, 0.1317184124180087, 1.4801567983811572, 2.8832954441605634, 4.139147356061733, 5.0675440101506295, 5.539681434625525, 5.499372060224312, 4.972252188013342, 4.06122332879458, 2.9287771258581516, 1.7691534458302673, 0.775097347630374, 0.10497825752513838, -0.1439805181807469, 0.04834345172394925, 0.6226398529548987, 1.451841719098033, 2.3646825221233283, 3.176863342149504, 3.7241811041691006, 3.89161873912069, 3.633150692771714, 2.9787421889072516, 2.0274034981956732, 0.9277585408224093, -0.15008837731829763, -1.045995570046927, -1.6385630630852877, -1.865836167357805, -1.7341247573023688, -1.313467162753315, -0.7208875450580736, -0.09498504656167636, 0.4329211173163541, 0.7652229988343912, 0.8566981825072408, 0.7217060760357138, 0.4285589088965867, 0.08237872944993054, -0.1998456269123555, -0.31663812373689204, -0.20594298253985904, 0.1396596964762138, 0.6698497499151789, 1.2864390075042993, 1.8642966946714148, 2.2789675912824756, 2.435058908746765, 2.289137122566788, 1.861875624883049, 1.2363552538147426, 0.5423190145348119, -0.07077347624097012, -0.4665004928745715, -0.5531627010698555, -0.3074445351643603, 0.21549262938841737, 0.8883826621477082, 1.5342148787843959, 1.9606895635176396, 2.0001395888632816, 1.546834300359154, 0.5837643865407237, -0.8071501300057325, -2.4543068992075585, -4.1241018942264995, -5.56219211925174], 'positive_zeros': ['1.66693094890332641188782487929767', '2.89974664570084167583647620331509', '5.31868938362709709086369339041172', '6.62862699214713072443855765288033', '8.372002678532643089343562625063016', '9.732017246765153082062072759508735', '10.48874096009288516450101096681883', '11.61593991443827032408818663062580', '12.57178759089621464448134635304178', '14.09149093873541031598996588206297'], 'prelabel': '2-63-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.08803074228290643, 'root_number': '0.9620013054751293 + 0.27304484661708417*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0440153711415', 'prec': 50}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.66693094890332641188782487930', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.89974664570084167583647620332', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.31868938362709709086369339041', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.104180648217781, 'bad_primes': [3, 7], 'central_character': '7.2', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/6/e/f/37/3'], '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': '2-63-7.2-c5-0-10', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-63-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.044015371141453215, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.66693094890332641188782487930', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2113086017916313720829986080290', 'Lhash_array': ['2113086017916313720829986080290'], 'label': '2-63-7.2-c5-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/6/e/f/37/3'}