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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': 1, 'Lhash': '539058027814223846', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1694.1061292834854, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [13, [1, -1]], [17, [1, 1]]], 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '212160.1', 'coefficient_field': '1.1.1.1', 'conductor': 212160, 'conductor_radical': 6630, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, -2, 7], [1, 0, 11], [1, -1], [1, 1], [1, 6, 19], [1, 0, 23], [1, 6, 29], [1, 4, 31], [1, 2, 37], [1, 10, 41], [1, 2, 43], [1, 0, 47], [1, 14, 53], [1, 6, 59], [1, 10, 61], [1, -8, 67], [1, -4, 71], [1, 6, 73], [1, 2, 79], [1, 0, 83], [1, -6, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 198, 'label': '2-212160-1.1-c1-0-198', 'leading_term': '11.9961060421', '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': 2, 'origin': 'EllipticCurve/Q/212160/bk', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -0.7004842899556976, -2.227043625374978, -3.120930980090986, -2.189873628124904, -0.04821805502182835, 1.077849191204783, 0.01755512732919742, -1.258238114036611, 0.2762050879228453, 4.225388569162789, 6.303812204226004, 3.799826358854005, -0.24487385542968, -0.9437546059733924, 1.492613077918201, 2.438496835457295, 0.3324522043220716, -1.216406293569346, -0.1604183088400537, 0.358040782550103, -1.829123268580655, -3.323370278235387, -1.294032123972107, 0.7663663310370489, -0.8139186385778561, -2.855346390145308, -1.306663659846462, 0.7051182612868017, -1.186496106558076, -3.728357615743647, -2.164195591117257, 0.3039252813596827, -0.9352925542350214, -2.214805717014178, 0.7806436999824798, 3.120507265856169, -0.01059493833832002, -2.66123558308004, 1.019744113286076, 5.081859493575268, 2.979204629093286, -0.6302514071967344, -0.2964797945941973, 0.5725027190978679, -0.534412837212153, 0.1467473249265684, 2.33950044163511, 1.243135978744799, -0.9722662517356876, 0.7877265010251309, 2.642238286701786, 0.1819611402556189, -0.602188353748064, 3.569119088305035, 4.227019935096802, -1.382604191053042, -3.512190393516209, 0.1761797266530841, 0.9630377799789608, -1.420770820584899, -0.1022314033665966, 2.010331967779511, -0.2203538583169916, -1.068391444867708, 2.767205516391744, 3.845338169959, 0.5806018374589502, -0.2807530244268934, 0.10381571480056, -2.643380739189379, -3.434006974459801, 0.294238641301392, 1.380734082526236, -0.4418608877691066, 1.221991867455383, 2.477225477430611, -1.390471962716934, -2.235720847053231, 2.70070272547641, 3.006695781982049, -1.537973497215996, -1.13325950771991, 1.133825930086936, -1.521897555076038, -2.464713313499574, 1.370678130600558, 1.715637084403333, -0.5179071285056628, 1.600179752176506, 2.863009843812425, -0.900823847115904, -1.945461419067999, 0.6822383220047749, 0.2722767663074716, -0.5725827735834295, 0.7728848438463068, -1.105129205474217, -3.33630927429367, 0.03523681563861689, 0.9254413533624691, -4.176805786939032, -3.484148448660624, 2.426330774175604, 1.509311183500996, -1.028335668590954, 3.428621751312287, 5.564536703890314, 1.128302027631301, -0.424261315937246, 0.7200313991237646, -0.2577978194758368, 1.003969474229294, 3.149382789931515, 0.4698271759925597, -0.7272165789969871, 2.162954002853665, 0.06241940997623593, -4.178322042417059, -1.833197693187296, 0.3914046810797248], 'positive_zeros': ['1.255977236038738', '1.752529681293272', '2.227783472474129', '3.230090259466500', '3.610900692144056', '4.282973179637623', '4.776898430204708', '5.064593368263802', '5.865382363695187', '6.172405176067659', '6.870707621570298', '7.150712573109657', '7.941678971402497', '8.143181269249686', '8.702231062392874', '9.249417221209253', '9.703572460036373', '10.43437544598491', '10.79640664222695', '11.14096344000361', '11.48296983689232', '12.10865055787662', '12.43470815322462', '13.01481848535974', '13.30070968177192', '13.94261961479967', '14.48798513381723', '14.84470505460703', '15.25813545089906', '15.73223893300740', '16.08723205986468', '16.80850197764603', '17.06952637677441', '17.26902960351644', '17.98048004463426', '18.41614551948410', '18.63833710051717', '19.17368874295305', '19.62137826056946'], 'prelabel': '2-212160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 41.159520518143616, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 539058027814223846, 'z1': {'__RealLiteral__': 0, 'data': '1.255977236038738', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.752529681293272', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.227783472474129', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1694.1061292834854, 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '1.1', 'conductor': 212160, 'conductor_radical': 6630, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 1, 0, -1, 0, -6, 0, -2, 0, 0, 0, 1, 0, -1, 0, -6, 0, -4, 0, 0, 0, -2, 0, -2, 0, -1, 0, -10, 0, -2, 0, -1, 0, 0, 0, -3, 0, 1, 0, -14, 0, 0, 0, 6, 0, -6, 0, -10, 0, 2, 0, -1, 0, 8, 0, 0, 0, 4, 0, -6, 0, -1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 1, 0, 6, 0, 6, 0, 2, 0, 4, 0, 6, 0, -14, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -1, 0], 'euler17': [1, 1, 0], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 10, 41], 'euler43': [1, 2, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, 14, 53], 'euler59': [1, 6, 59], 'euler61': [1, 10, 61], 'euler67': [1, -8, 67], 'euler7': [1, -2, 7], 'euler71': [1, -4, 71], 'euler73': [1, 6, 73], 'euler79': [1, 2, 79], 'euler83': [1, 0, 83], 'euler89': [1, -6, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, -2, 7], [1, 0, 11], [1, -1, 0], [1, 1, 0], [1, 6, 19], [1, 0, 23], [1, 6, 29], [1, 4, 31], [1, 2, 37], [1, 10, 41], [1, 2, 43], [1, 0, 47], [1, 14, 53], [1, 6, 59], [1, 10, 61], [1, -8, 67], [1, -4, 71], [1, 6, 73], [1, 2, 79], [1, 0, 83], [1, -6, 89], [1, 14, 97]], 'index': 198, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/212160/bk'], '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': '2-212160-1.1-c1-0-198', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'prelabel': '2-212160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 41.159520518143616, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 539058027814223846, 'z1': {'__RealLiteral__': 0, 'data': '1.255977236038738', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '539058027814223846', 'Lhash_array': ['539058027814223846'], 'label': '2-212160-1.1-c1-0-198', 'type': 'ECQ', 'url': 'EllipticCurve/Q/212160/bk'}