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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 0, 'Lhash': '555915390019089711', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 546.1767498255581, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [19, [1, 1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '68400.1', 'coefficient_field': '1.1.1.1', 'conductor': 68400, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 4, 7], [1, -2, 11], [1, 6, 13], [1, 2, 17], [1, 1], [1, 6, 23], [1, 8, 29], [1, -8, 31], [1, 10, 37], [1, -4, 41], [1, -4, 43], [1, 6, 47], [1, -12, 53], [1, 8, 59], [1, -2, 61], [1, -4, 67], [1, -12, 71], [1, -10, 73], [1, -8, 79], [1, 2, 83], [1, -12, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 57, 'label': '2-68400-1.1-c1-0-57', 'leading_term': '3.90231938444', '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': 1, 'origin': 'EllipticCurve/Q/68400/m', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.8194899297886684, 0.7586476353248445, -0.662759675276115, -2.945889262131016, -4.564947698723863, -4.089109241570227, -1.727937450105799, 0.482736129009454, 0.600535199478004, -1.000897469011896, -1.899254533127136, -0.5502685935002292, 1.603657836065176, 1.911016937008713, 0.2280613416172007, -0.6036030980936103, 1.253134725661435, 3.586897119030711, 2.926356214627306, -0.2790995675718823, -1.832886007872894, 0.2933509994155329, 2.92641590899799, 2.425460674622975, 0.07196927113391564, -0.3969829168694227, 0.924391075272802, 0.5661234513173471, -1.767587803714711, -2.089595368193646, 0.8455413262825833, 2.393403031193834, -0.7874389965737973, -4.775384934456571, -4.279557812752315, -0.9126128152563818, 0.1279540737008523, -1.177298590292714, -0.9563060640896928, 0.4507199251415418, -0.5842803349396247, -2.741315325209784, -0.9195586103664877, 3.906831350788247, 4.843249152729727, 0.5565082386946026, -2.437818554565887, -1.086471594935829, 0.05537834728480493, -1.299324938174143, -1.13552746537174, 1.598964155904776, 1.956877739108341, -0.9827928072135271, -1.561359958093639, 1.298425112678112, 1.51548255972183, -2.059607846243164, -2.916768686040244, 0.4224314315908042, 1.595971246490883, -0.8278284357622929, -0.9671332116616483, 1.864069129952037, 1.934046104063678, -0.6417219430976391, -0.3503320872966012, 1.758214893518055, 0.7484185910552189, -0.5445335238117895, 2.87678793896604, 6.135145282816295, 2.805372697786632, -2.021154828039287, -1.156799532952817, 1.657604616021, 0.895189855895557, -0.3242616771086367, 0.5029075528386134, -0.4690963433777106, -2.405872322636465, 0.8090343886844508, 6.237491911323112, 4.927483709109083, -0.6581772596368596, -1.120911892721272, 2.019829929891161, 1.523222841942341, -0.6266059079564339, -0.1128352098070097, -0.07700035440374607, -1.102600358833288, 2.559518461848495, 8.59873888932332, 7.687268893060319, 1.582589287639004, -0.4786559617720755, 0.2427362389334622, -1.785522738822562, -2.214689391680163, 2.410464619132083, 4.783761844750969, 1.700447129431866, -0.09273585138948912, 0.3625243638176049, -1.815829652611411, -3.068644546102227, 1.043504903975048, 3.45124811390158, -0.1656841137839848, -1.65300209764851, 1.567793381108934, 1.416754612622498, -1.799427000926279, -0.5039432262903986, 2.506059147138564, 1.187583630327758, -0.3699999860704162, 0.3518646785885017, -1.465767281277411], 'positive_zeros': ['0.6600856253612702', '1.927365343718279', '2.357924156791244', '3.059771332235521', '3.782638105159374', '4.120593115377330', '4.978178065429219', '5.476858239712131', '6.259860874605243', '6.582619187653926', '7.067592933959059', '7.687352728252688', '8.207269491745188', '9.108603662790901', '9.285185901573059', '9.898703151306828', '10.18217143491335', '10.79986723139690', '11.52928441323280', '12.16475377247884', '12.27427675779346', '12.86088593786913', '13.42018279765648', '13.89312677979031', '14.36553725489250', '14.96990615991822', '15.42018830291761', '15.84089329293809', '16.42914609079316', '16.78796759885272', '17.33132892673931', '17.57569785626087', '18.37210893276949', '18.83488145756775', '19.37478662553950', '19.62090518253786', '19.94737789201233'], 'prelabel': '2-68400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.370424682182353, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 555915390019089711, 'z1': {'__RealLiteral__': 0, 'data': '0.6600856253612702', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.927365343718279', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.357924156791244', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 546.1767498255581, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 68400, 'conductor_radical': 570, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, -6, 0, 0, 0, -2, 0, -1, 0, 0, 0, -6, 0, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, -10, 0, 0, 0, 4, 0, 4, 0, 0, 0, -6, 0, 9, 0, 0, 0, 12, 0, 0, 0, 0, 0, -8, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 12, 0, 10, 0, 0, 0, -8, 0, 8, 0, 0, 0, -2, 0, 0, 0, 0, 0, 12, 0, 24, 0, 0, 0, 0, 0, 14, 0, 0, 0], 'euler11': [1, -2, 11], 'euler13': [1, 6, 13], 'euler17': [1, 2, 17], 'euler19': [1, 1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, 8, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, 10, 37], 'euler41': [1, -4, 41], 'euler43': [1, -4, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 0], 'euler53': [1, -12, 53], 'euler59': [1, 8, 59], 'euler61': [1, -2, 61], 'euler67': [1, -4, 67], 'euler7': [1, 4, 7], 'euler71': [1, -12, 71], 'euler73': [1, -10, 73], 'euler79': [1, -8, 79], 'euler83': [1, 2, 83], 'euler89': [1, -12, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 4, 7], [1, -2, 11], [1, 6, 13], [1, 2, 17], [1, 1, 0], [1, 6, 23], [1, 8, 29], [1, -8, 31], [1, 10, 37], [1, -4, 41], [1, -4, 43], [1, 6, 47], [1, -12, 53], [1, 8, 59], [1, -2, 61], [1, -4, 67], [1, -12, 71], [1, -10, 73], [1, -8, 79], [1, 2, 83], [1, -12, 89], [1, -14, 97]], 'index': 57, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/68400/m'], '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': '2-68400-1.1-c1-0-57', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-68400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.370424682182353, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 555915390019089711, 'z1': {'__RealLiteral__': 0, 'data': '0.6600856253612702', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '555915390019089711', 'Lhash_array': ['555915390019089711'], 'label': '2-68400-1.1-c1-0-57', 'type': 'ECQ', 'url': 'EllipticCurve/Q/68400/m'}