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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': 1, 'A8': 0, 'A9': 1, 'Lhash': '1190324319331424492', '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': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 912.2109926911075, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [7, [1, -1]], [17, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 17], 'central_character': '114240.1', 'coefficient_field': '1.1.1.1', 'conductor': 114240, 'conductor_radical': 3570, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, -1], [1, 2, 11], [1, 3, 13], [1, -1], [1, 2, 19], [1, -3, 23], [1, 4, 29], [1, -5, 31], [1, -1, 37], [1, -11, 41], [1, -4, 43], [1, -9, 47], [1, 0, 53], [1, 12, 59], [1, -5, 61], [1, 12, 67], [1, -2, 71], [1, 4, 73], [1, -10, 79], [1, 5, 83], [1, 14, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 18, 'label': '2-114240-1.1-c1-0-18', 'leading_term': '1.34371793243', '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/114240/bq', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.343717932428402, 0.8027639138042496, -0.4206489111489116, -1.232678136549162, -0.5409093770311985, 1.486235591504409, 3.012903486744519, 2.161828225891962, -0.6164621359082902, -2.494791277316809, -1.450575132128565, 0.8755011783285365, 0.848718542950893, -2.349204705031063, -5.187521298062898, -4.301108725696623, -1.12454237966078, 0.2322030752650853, -1.006226262597188, -1.550790874050535, 0.225434344363497, 1.522121090255536, 0.134817039443792, -1.290460415514406, 0.3330036824386126, 2.677382980919631, 1.465340019375774, -2.021508597888319, -2.751785330684721, -0.4569484012534535, 0.3475674785322632, -0.9495465917659831, 0.03685973260777377, 3.580838125332954, 4.001714900417763, -0.03793777604483598, -2.069409146926471, 1.012153239106297, 3.209623037150024, 0.3074780019630985, -2.582913903837675, -0.7853179675111178, 1.730783443098064, 0.8635590931233319, -0.06883270858007824, 1.706016398112785, 2.364992727905219, -0.01106057314432889, -0.8950731897174281, 1.16199459412774, 1.499934927611392, -0.04714042863830199, 1.811686154684638, 5.540961307686727, 4.012913958247772, -0.7799555803675948, -0.2233376718253482, 4.243768068585487, 4.005376276299659, 0.2051194149501674, 0.2511070505323748, 2.363091379857568, 0.8177375988788304, -0.9935815184457136, 1.41571840476783, 3.051847197337079, 0.2168355503969794, -1.527132009327868, 0.1233193101214751, -0.2362895517332636, -2.470580094742453, -1.11243971214661, 1.246209201288083, -0.8158928032821083, -2.820905696790292, -0.1426680731393035, 1.428027306942492, -0.855940517063767, -0.2100894776084197, 3.120181125928714, 0.7797764819704216, -4.665984916813806, -3.799600200062958, 0.1642600271317344, -0.3868330568110364, -1.025542846502447, 2.433987181141074, 3.172781590274642, -0.5786736885514724, -1.084891667114418, 1.302042299208761, 0.008867194973796276, -2.014989832672711, -0.2680745699180633, 0.4021361956497753, -1.510594378188085, -0.4173720950612741, 1.611029121460559, -0.3523298481984744, -0.6756204485503753, 3.224254146062809, 2.064204901533991, -4.025394859582976, -3.099673473243119, 2.926969236563092, 2.459578475448966, -1.21919601052331, -0.2019661140009346, 0.321985513713776, -2.623016407373076, -2.209532639118735, 0.6345210135212795, 0.05932236026546926, 0.1818702388350425, 3.34181416705411, 2.57406217768895, -0.952245114876238, 0.03421884219913725, 1.289421983050613, -1.58390352190804, -1.60948551373321], 'positive_zeros': ['0.4178150229750929', '1.077017046312325', '1.947713285983290', '2.646463144603246', '3.085676301062236', '4.132325372025140', '4.330600632260190', '4.974655308374570', '5.515604611884502', '5.969778755321974', '6.603360406172408', '7.307119178799569', '7.576943174649977', '7.996840426160851', '8.747805008299409', '9.187507024661447', '9.768226303818282', '10.30913314966844', '10.89315252132489', '11.02297085673368', '11.74891010300284', '12.12337483924051', '12.73260348952368', '12.82513322877940', '13.69817048409241', '14.01370670298383', '14.77106003757600', '14.97066673729783', '15.57072946810036', '15.89203726384790', '16.51567992870864', '16.98111555022936', '17.22145139768617', '17.83726088495274', '18.18975871830334', '18.76021087421134', '19.16317809828628', '19.51549172362114'], 'prelabel': '2-114240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 30.20283087214024, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1190324319331424492, 'z1': {'__RealLiteral__': 0, 'data': '0.4178150229750929', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.077017046312325', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.947713285983290', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 912.2109926911075, 'bad_primes': [2, 3, 5, 7, 17], 'central_character': '1.1', 'conductor': 114240, 'conductor_radical': 3570, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -2, 0, -3, 0, 1, 0, 1, 0, -2, 0, -1, 0, 3, 0, 1, 0, -1, 0, -4, 0, 5, 0, 2, 0, -1, 0, 1, 0, 3, 0, 11, 0, 4, 0, -1, 0, 9, 0, 1, 0, -1, 0, 0, 0, 2, 0, 2, 0, -12, 0, 5, 0, 1, 0, 3, 0, -12, 0, -3, 0, 2, 0, -4, 0, -1, 0, -2, 0, 10, 0, 1, 0, -5, 0, -1, 0, 4, 0, -14, 0, -3, 0, -5, 0, 2, 0, -2, 0, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, 3, 13], 'euler17': [1, -1, 0], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -3, 23], 'euler29': [1, 4, 29], 'euler3': [1, 1, 0], 'euler31': [1, -5, 31], 'euler37': [1, -1, 37], 'euler41': [1, -11, 41], 'euler43': [1, -4, 43], 'euler47': [1, -9, 47], 'euler5': [1, 1, 0], 'euler53': [1, 0, 53], 'euler59': [1, 12, 59], 'euler61': [1, -5, 61], 'euler67': [1, 12, 67], 'euler7': [1, -1, 0], 'euler71': [1, -2, 71], 'euler73': [1, 4, 73], 'euler79': [1, -10, 79], 'euler83': [1, 5, 83], 'euler89': [1, 14, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, -1, 0], [1, 2, 11], [1, 3, 13], [1, -1, 0], [1, 2, 19], [1, -3, 23], [1, 4, 29], [1, -5, 31], [1, -1, 37], [1, -11, 41], [1, -4, 43], [1, -9, 47], [1, 0, 53], [1, 12, 59], [1, -5, 61], [1, 12, 67], [1, -2, 71], [1, 4, 73], [1, -10, 79], [1, 5, 83], [1, 14, 89], [1, 2, 97]], 'index': 18, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/114240/bq'], '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': '2-114240-1.1-c1-0-18', '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': '2-114240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 30.20283087214024, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1190324319331424492, 'z1': {'__RealLiteral__': 0, 'data': '0.4178150229750929', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1190324319331424492', 'Lhash_array': ['1190324319331424492'], 'label': '2-114240-1.1-c1-0-18', 'type': 'ECQ', 'url': 'EllipticCurve/Q/114240/bq'}