-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '2736906545858293274369407668769', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2853298799574647, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, 0, 5]], [179, [1, -5, 173, 179]]], 'bad_primes': [5, 179], 'central_character': '4475.1', 'coefficient_field': '1.1.1.1', 'conductor': 4475, 'conductor_radical': 895, 'degree': 4, 'euler_factors': [[1, 0, -1, 0, 4], [1, 0, 0, 0, 9], [1, 0, 5], [1, 0, 5, 0, 49], [1, 2, 7, 22, 121], [1, 0, 19, 0, 169], [1, 0, 15, 0, 289], [1, 3, 34, 57, 361], [1, 0, -14, 0, 529], [1, -12, 93, -348, 841], [1, -3, 64, -93, 961], [1, 0, -42, 0, 1369], [1, 9, 100, 369, 1681], [1, 0, 14, 0, 1849], [1, 0, -16, 0, 2209], [1, 0, -30, 0, 2809], [1, -4, 86, -236, 3481], [1, 21, 232, 1281, 3721], [1, 0, 30, 0, 4489], [1, -22, 262, -1562, 5041], [1, 0, 140, 0, 5329], [1, -12, 158, -948, 6241], [1, 0, 44, 0, 6889], [1, -8, 194, -712, 7921], [1, 0, 80, 0, 9409], [1, -4, 202, -404, 10201], [1, 0, -111, 0, 10609], [1, 0, -2, 0, 11449], [1, -21, 286, -2289, 11881], [1, 0, 22, 0, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 1, 'label': '4-4475-1.1-c1e2-0-1', 'leading_term': '0.855031419186', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/2.2.5.1/179.2/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.8550314191861742, 0.8580518483048059, 0.8670874592956823, 0.8820601502281492, 0.9028362128118306, 0.9292211573018075, 0.9609527341778544, 0.9976924232557322, 1.0390157429097893, 1.0844018162434355, 1.1332227163285178, 1.18473319722233, 1.2380614986474252, 1.292201986344461, 1.3460104526301007, 1.3982029472182305, 1.4473590307973487, 1.4919303366084065, 1.5302552815333934, 1.5605806813344922, 1.581090888613451, 1.5899448818184883, 1.5853214858854956, 1.5654725987692455, 1.5287839349318513, 1.4738423819294972, 1.399508608570258, 1.3049930759492707, 1.1899331036978766, 1.0544681551427308, 0.8993100530460829, 0.7258044520387532, 0.5359796072403075, 0.33257832469820836, 0.11906899166387662, -0.1003682054466184, -0.3208833336512073, -0.5370298171960745, -0.7428704418010683, -0.9321169253997161, -1.0983023025622871, -1.2349837475318808, -1.335971684605729, -1.3955791714868702, -1.4088836751316984, -1.3719915894728687, -1.2822942810364928, -1.1387032101405343, -0.9418508819449617, -0.6942441477293078, -0.40035680387866335, -0.06664960409930423, 0.29849224078624265, 0.6849112398345001, 1.0809231099952754, 1.4736549945761181, 1.8494710699483425, 2.1944750812410936, 2.495074116904783, 2.7385828717411878, 2.913843074180216, 3.0118289983759676, 3.0262073747809954, 2.9538188599769266, 2.795048786275029, 2.554057371780948, 2.23884402692068, 1.8611268259385527, 1.436026476454822, 0.9815539363379543, 0.5179117791471365, 0.06663095557601087, -0.3504239094365456, -0.7121368309629128, -0.9992573652050953, -1.1954921968036656, -1.2885076225334975, -1.270778813808365, -1.140225376679585, -0.9005805102658359, -0.5614529145205004, -0.13805615175914668, 0.34940123472666823, 0.8766508370837925, 1.4165891028826738, 1.9407348610500574, 2.4208436354427123, 2.830586956534458, 3.1471939715934045, 3.352947810263336, 3.436431273681909, 3.3934259520083305, 3.227385812131918, 2.949430063282282, 2.5778295736885526, 2.1369946176846555, 1.6560071659566866, 1.1667758407341682, 0.7019234106614195, 0.292542671569466, -0.03402566296135092, -0.2562318428177841, -0.36001547361332703, -0.34002225159633026, -0.20022577680217543, 0.04612038875554992, 0.37722852069526297, 0.7641965368611212, 1.1730245153037204, 1.5670998724659744, 1.9099793338550728, 2.1682629951378205, 2.3143373562398355, 2.3287627200152463, 2.2020970631346297, 1.935983260985044, 1.5433776965095798, 1.0478626075303914, 0.4820574733442421, -0.11477931410064919, -0.6997945904936693, -1.2300035386971364, -1.6658978061630756, -1.9748983557397013, -2.1343509680730413, -2.1337866423520784, -1.9762190843895187, -1.6783241695050861, -1.269436631171294, -0.7894002346793207, -0.2854109057980275, 0.19191148941052533, 0.5929069092153452, 0.8733428781600837, 0.9985697141620058, 0.946976692402486, 0.7124084368090263, 0.3052802910344733, -0.24776106885435517, -0.905658511554829, -1.6161379514373304, -2.3200337721140176, -2.9563900996021815, -3.4678947769449273, -3.806153874490999, -3.9363102151491867, -3.8405523134447703, -3.520148444787866, -2.9957678366591396, -2.306006580374633, -1.5042058138524836, -0.6538178915961488, 0.17727412700565084, 0.9229630090952002, 1.5250612322793946, 1.9387817442173616, 2.1370030706121748, 2.112871562764054, 1.8804478557041906, 1.4732939906272298, 0.9411040033018083, 0.3446833677528715, -0.2502397422088625, -0.7797554055683792, -1.1883764007095252, -1.4348148778635355, -1.4963105144210354, -1.3710281488870284, -1.0782374145260105, -0.656218210527432, -0.15808016771085537, 0.35408460137177433, 0.8161040375019228, 1.1689419190697636, 1.3654324092990806, 1.375773156140814, 1.1911369351201329, 0.8249574490581516, 0.3116965040043216, -0.2968191954529227, -0.9371239095538934, -1.5412877341162954, -2.044743852446463, -2.3938748150824347, -2.5524682289014744, -2.5062595217610375, -2.264981405609763, -1.8616159761344646, -1.3488662146345638, -0.7931927414518101, -0.2670603703437682, 0.15972919626476648, 0.42860727302469104, 0.4996809300958459, 0.3571230190047373, 0.011802698961423195, -0.49923936222914045, -1.1164981171781765, -1.7645365899978946, -2.360633569430199, -2.824558421873679, -3.088318445918161, -3.1046935394806683, -2.8534865069455657, -2.3446660098996355, -1.6179368220202706, -0.7386980776211355, 0.20920597221171425, 1.1331311651439535, 1.9425447901127921, 2.559886405026129, 2.930033491825948, 3.0271669174149447, 2.858125906068651, 2.4617596940692885, 1.90427413616119, 1.2710761713433063, 0.6560734430237357, 0.1497310847482299, -0.17262451864004258, -0.2607628519089265, -0.0964637768758946, 0.30355345984776194, 0.8891389269859972, 1.5825499361583708, 2.2879499724710275, 2.9034144955390833, 3.3339427010101677, 3.5038155284606973, 3.3666947843705595, 2.912124112991279, 2.1675395161015354, 1.1954701378623591, 0.08623579698917862, -1.0529559545893643, -2.1111239603275194, -2.9871402825108246, -3.6020845109343664, -3.9086922180887904, -3.8966386969309306, -3.592949446245333, -3.0574831315646147, -2.3741030986166676, -1.6387479040177533, -0.9460461719115504, -0.3763331289456784, 0.015118147460376334, 0.20513679723116854, 0.20496792651871135, 0.05752702266893686, -0.17001661463080406, -0.3972626510684088, -0.5436100416006955, -0.5413843349910867, -0.34711089822687646, 0.05077459950921092, 0.6289909287374521], 'positive_zeros': ['2.15903857527108589111778351412610', '3.19927072892018814112145833708695', '4.44707173903413455078484909830334', '5.08092392375524683764994471481035', '6.24250290881522639965665078254406', '6.55242182696352198698522228539677', '7.42552510871024539328538624857837', '8.161520469114403666133450142718506', '8.598744632548457290278597687344714', '9.486285470594352926661943054562003', '10.09824820839617711680801197799470', '10.64410761568902312948617043339734', '11.15784032260619640773533614357153', '11.91174558478368732921328236764601', '12.18918167804562075041683901286642'], 'prelabel': '4-4475-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.7308644088594294, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 436554882796545540, 'z1': {'__RealLiteral__': 0, 'data': '2.15903857527108589111778351412610', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.19927072892018814112145833708695', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.44707173903413455078484909830334', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.2853298799574647, 'bad_primes': [5, 179], 'central_character': '1.1', 'conductor': 4475, 'conductor_radical': 895, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -3, 0, 0, -3, 0, 0, 0, 0, 0, -5, 0, 0, 0, 12, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, -2, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -21, 0, 0, -7, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, -3, 0, 0, 12, 0, -9, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5], 'euler11': [1, 2, 7, 22, 121], 'euler13': [1, 0, 19, 0, 169], 'euler17': [1, 0, 15, 0, 289], 'euler19': [1, 3, 34, 57, 361], 'euler2': [1, 0, -1, 0, 4], 'euler23': [1, 0, -14, 0, 529], 'euler29': [1, -12, 93, -348, 841], 'euler3': [1, 0, 0, 0, 9], 'euler31': [1, -3, 64, -93, 961], 'euler37': [1, 0, -42, 0, 1369], 'euler41': [1, 9, 100, 369, 1681], 'euler43': [1, 0, 14, 0, 1849], 'euler47': [1, 0, -16, 0, 2209], 'euler5': [1, 0, 5, 0, 0], 'euler53': [1, 0, -30, 0, 2809], 'euler59': [1, -4, 86, -236, 3481], 'euler61': [1, 21, 232, 1281, 3721], 'euler67': [1, 0, 30, 0, 4489], 'euler7': [1, 0, 5, 0, 49], 'euler71': [1, -22, 262, -1562, 5041], 'euler73': [1, 0, 140, 0, 5329], 'euler79': [1, -12, 158, -948, 6241], 'euler83': [1, 0, 44, 0, 6889], 'euler89': [1, -8, 194, -712, 7921], 'euler97': [1, 0, 80, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 4], [1, 0, 0, 0, 9], [1, 0, 5, 0, 0], [1, 0, 5, 0, 49], [1, 2, 7, 22, 121], [1, 0, 19, 0, 169], [1, 0, 15, 0, 289], [1, 3, 34, 57, 361], [1, 0, -14, 0, 529], [1, -12, 93, -348, 841], [1, -3, 64, -93, 961], [1, 0, -42, 0, 1369], [1, 9, 100, 369, 1681], [1, 0, 14, 0, 1849], [1, 0, -16, 0, 2209], [1, 0, -30, 0, 2809], [1, -4, 86, -236, 3481], [1, 21, 232, 1281, 3721], [1, 0, 30, 0, 4489], [1, -22, 262, -1562, 5041], [1, 0, 140, 0, 5329], [1, -12, 158, -948, 6241], [1, 0, 44, 0, 6889], [1, -8, 194, -712, 7921], [1, 0, 80, 0, 9409]], 'index': 1, 'instance_types': ['ECNF', 'HMF', 'ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.5.1/179.1/a', 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-179.2-a', 'EllipticCurve/2.2.5.1/179.2/a', 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-179.1-a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-4475-1.1-c1e2-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-4475-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.7308644088594294, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 436554882796545540, 'z1': {'__RealLiteral__': 0, 'data': '2.15903857527108589111778351412610', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9517863
{'Lhash': '2736906545858293274369407668769', 'Lhash_array': ['2736906545858293274369407668769'], 'label': '4-4475-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-179.1-a'}
-
id: 9517698
{'Lhash': '2736906545858293274369407668769', 'Lhash_array': ['2736906545858293274369407668769'], 'label': '4-4475-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/179.2/a'}
-
id: 9517581
{'Lhash': '2736906545858293274369407668769', 'Lhash_array': ['2736906545858293274369407668769'], 'label': '4-4475-1.1-c1e2-0-1', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-179.2-a'}
-
id: 9517310
{'Lhash': '2736906545858293274369407668769', 'Lhash_array': ['2736906545858293274369407668769'], 'label': '4-4475-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/179.1/a'}