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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '117433867426717965', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 156.50678796170962, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '19600.1', 'coefficient_field': '1.1.1.1', 'conductor': 19600, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1], [1], [1, 0, 11], [1, 0, 13], [1, 2, 17], [1, 2, 19], [1, -8, 23], [1, -2, 29], [1, -4, 31], [1, -6, 37], [1, -2, 41], [1, -8, 43], [1, -4, 47], [1, -10, 53], [1, -6, 59], [1, 4, 61], [1, 12, 67], [1, 0, 71], [1, 14, 73], [1, -8, 79], [1, 6, 83], [1, 10, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 21, 'label': '2-140e2-1.1-c1-0-21', 'leading_term': '1.2819558226', 'load_key': 'Cremona', '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': 'EllipticCurve/Q/19600/u', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.281955822600042, 0.9917887157618325, 0.2294716548664243, -0.6123524195886453, -0.8697403644304654, 0.0149709482504562, 1.902445809194323, 3.720107522679748, 4.060250007150521, 2.388268420451798, -0.1619813105587022, -1.412039149316475, 0.002403691398910031, 3.154335329936717, 5.395539709831649, 4.776392122497537, 2.003135171557549, -0.2592400277169891, -0.198550348640016, 1.280120491511632, 1.83542800941921, 0.6279118148816244, -0.7318380982015676, -0.4749978214591196, 0.8176954641254393, 1.007270999030987, -0.4356760441586338, -1.408670997787742, -0.1707334270525469, 1.654704819875773, 0.7894013092266507, -2.97374172075443, -5.684101669041195, -4.09592609053241, -0.2303483272692591, 1.035043795462066, -1.461055292813584, -3.56369432836102, -1.668985906233253, 2.197641870353136, 3.376294210185478, 1.137453412409244, -0.8362480491107324, -0.3002953232745997, 0.6603175774281326, -0.1849731879809499, -1.332001547263227, -0.4708594676037203, 1.052014526414617, 0.3316391992105954, -1.752985286487668, -1.564329544619579, 0.8868606269487209, 1.248904021707992, -1.876535816227258, -3.617686404850295, -0.145122276521985, 4.628966518998438, 4.515130615996165, 0.564535898924242, -0.7916788615572277, 1.95974683275353, 3.536048042776912, 1.028695986293515, -1.613675741347133, -0.7992779141625289, 0.9408714470098152, 0.2195133228993195, -1.272870131588559, -0.7594486359836127, 0.07791270694228693, -1.165740339265227, -2.183974984213473, -0.1928547335440191, 1.812049758481393, -0.2548291387351448, -3.555533808028146, -2.657443075452023, 0.4006089304344551, -0.872501743308358, -5.502153042594363, -5.838578885864312, -0.6468871229262584, 2.631299039257491, 0.5761484440901165, -1.227353451464032, 0.9511604442039726, 2.813634900032358, 0.9524756800794127, -1.047292955693922, -0.1829240753701099, 0.593133938483642, -0.7724053707198153, -1.278764072271084, 0.1356307799844698, -0.2193819516487375, -2.657535289252844, -2.180688317867071, 1.549429906048729, 2.24108591423619, -1.170233800837854, -1.715921841311449, 2.276295978524221, 3.084513661597419, -2.093738750184991, -5.292659549312802, -2.07697786481723, 0.9129914530098999, -1.114579789635909, -3.10327007225518, -1.232288801331373, 0.1471792342405606, -1.637175470371506, -2.437500558083603, -0.5544545086112322, 0.1344193866088403, -0.9078333412120756, -0.171033955253527, 1.030340304762711, -1.173012695825162, -3.527804193356041], 'positive_zeros': ['0.5635329325736111', '1.247481123266087', '2.482486436164423', '2.999772450411071', '4.204446779708564', '4.539733454781880', '5.345202499043781', '5.843726739378018', '6.436078599670725', '7.020168058158480', '7.563653662121162', '8.518256119484362', '8.882095097205039', '9.604735318591604', '10.36002821240915', '10.80610808729591', '11.21878183900450', '11.81498146814740', '12.28972355809745', '12.91073723587234', '13.36900657864091', '14.00675929628737', '14.79230825543658', '15.09693119252884', '15.82405765005163', '16.34307820542899', '16.78045594117067', '17.42174576617656', '17.54838933574426', '18.26638439744295', '18.73280979473083', '19.45280892493704', '19.68679293532573'], 'prelabel': '2-140e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.51026730176896, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 117433867426717965, 'z1': {'__RealLiteral__': 0, 'data': '0.5635329325736111', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.247481123266087', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.482486436164423', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 156.50678796170962, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 19600, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 8, 0, 0, 0, 4, 0, 2, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 8, 0, 0, 0, 4, 0, 0, 0, 4, 0, 10, 0, 0, 0, 4, 0, 6, 0, -4, 0, 0, 0, 0, 0, -12, 0, -16, 0, 0, 0, -14, 0, 0, 0, 0, 0, 8, 0, -11, 0, -6, 0, 0, 0, -4, 0, -10, 0, 0, 0, -8, 0, 0, 0, -2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 0, 13], 'euler17': [1, 2, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, -2, 29], 'euler3': [1, 2, 3], 'euler31': [1, -4, 31], 'euler37': [1, -6, 37], 'euler41': [1, -2, 41], 'euler43': [1, -8, 43], 'euler47': [1, -4, 47], 'euler5': [1, 0, 0], 'euler53': [1, -10, 53], 'euler59': [1, -6, 59], 'euler61': [1, 4, 61], 'euler67': [1, 12, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, 14, 73], 'euler79': [1, -8, 79], 'euler83': [1, 6, 83], 'euler89': [1, 10, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, 0, 0], [1, 0, 0], [1, 0, 11], [1, 0, 13], [1, 2, 17], [1, 2, 19], [1, -8, 23], [1, -2, 29], [1, -4, 31], [1, -6, 37], [1, -2, 41], [1, -8, 43], [1, -4, 47], [1, -10, 53], [1, -6, 59], [1, 4, 61], [1, 12, 67], [1, 0, 71], [1, 14, 73], [1, -8, 79], [1, 6, 83], [1, 10, 89], [1, 2, 97]], 'index': 21, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/19600/u'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-140e2-1.1-c1-0-21', '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': '2-140e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.51026730176896, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 117433867426717965, 'z1': {'__RealLiteral__': 0, 'data': '0.5635329325736111', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '117433867426717965', 'Lhash_array': ['117433867426717965'], 'label': '2-140e2-1.1-c1-0-21', 'type': 'ECQ', 'url': 'EllipticCurve/Q/19600/u'}