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lfunc_lfunctions • Show schema
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{'A10': 2, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 2, 'A6': 0, 'A7': -2, 'A8': 1, 'A9': 0, 'Lhash': '1870294191162402386', 'a10': [0.6324555320336759, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1193.3961983688444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [19, [1]], [23, [1, -1]]], 'bad_primes': [2, 3, 19, 23], 'central_character': '149454.1', 'coefficient_field': '1.1.1.1', 'conductor': 149454, 'conductor_radical': 2622, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, -2, 5], [1, 2, 7], [1, 4, 11], [1, 0, 13], [1, -2, 17], [1], [1, -1], [1, 6, 29], [1, -2, 31], [1, 2, 37], [1, -2, 41], [1, -4, 43], [1, 12, 47], [1, 2, 53], [1, 0, 59], [1, -8, 61], [1, -4, 67], [1, 8, 71], [1, -2, 73], [1, -8, 79], [1, -16, 83], [1, 8, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 12, 'label': '2-149454-1.1-c1-0-12', 'leading_term': '2.96267866846', '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/149454/ck', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.962678668455411, 1.837036275486755, -0.9390193428688285, -3.607445584442965, -4.09280313180132, -1.860645590574679, 1.124220709648825, 2.145421608175936, 0.7596442348343069, -0.6710057358914312, -0.09289933956495978, 1.436005080486065, 1.421940259661145, -0.06504662556308212, -0.2702450777342977, 1.768116144019152, 3.104530486510524, 1.172791776504255, -1.913171312559861, -2.344584962446541, -0.4659062659630087, 0.2126198080859714, -0.8614412907178765, -0.8372769634858755, 0.6586617285195047, 0.6512156783264855, -0.9075537755394145, -0.1131285347122669, 3.267743528940147, 3.996525489117544, 0.7899150776708262, -0.1735006584953196, 3.633913154953607, 5.013215454615158, -0.6816575891584079, -6.013929463332584, -3.412099243016172, 1.99237890507225, 2.010111692720376, -0.7445779037587448, -0.1471392933098219, 1.077108945808878, -1.520799018935353, -3.605580450457364, -0.8647794505041192, 1.208741891048958, -2.058745652627899, -4.68226349216129, -1.52773968310978, 1.96576655267654, 0.8889430256173495, -0.8021946560731058, -0.1252609640579242, -0.08562943199941488, -0.8534723624497417, 0.6261915372332241, 2.118913367460775, 0.4019583741088375, -0.4774146303149242, 2.36043256663418, 3.324576171027104, 0.1909070848124639, -0.5865306548673705, 1.953911881081965, 1.287040725057302, -1.417248740776179, -0.1441227995364968, 0.987842706825359, -3.347189516756556, -5.758816883255323, -1.178989111896879, 1.27058638333936, -1.971775412628676, -1.003344757459402, 4.727992463348133, 4.254754010010424, -0.7836029948320875, -0.3177548056158129, 1.360728197275052, -3.668139550722787, -7.705945598840449, -3.65966440072608, 0.4898323078963876, -0.2300239151570488, -0.1481816743700468, 0.9834743170102379, -0.8404194778998461, -1.90032602184723, 0.2110954743496522, 0.2199202526463704, -1.557253580184415, -0.02508364357137514, 1.561322140004949, -0.0759056715389128, 0.5677708902450143, 3.514484186122359, 1.979459589457481, -0.7833784909405119, 1.224415322875358, 2.006270661603615, -1.668857790623839, -2.196443507994888, 0.3097482492073697, -0.3635698969011118, -0.1962991256658233, 2.762617982677778, 1.074938303152163, -0.1516002510549107, 9.894626198769501, 18.5966656969257, 10.86655449325471, 0.6057995072165459, 1.688377920632859, 2.888220232340805, -1.979070974992537, -2.955934653153249, -0.09882867352704278, -0.1572273095218467, 0.01898970118374603, 0.7888855016522489, -2.530608541589837], 'positive_zeros': ['0.4234791271007763', '1.397105341735579', '2.103888229702031', '2.515285175459499', '3.238058173638045', '3.549011904276544', '4.337150232879291', '5.077036151519321', '5.316715869997508', '5.890559639513438', '6.352773991383995', '6.760252815914556', '7.569582411378861', '7.769905122073400', '8.477111637496385', '9.141706950056806', '9.664633383052790', '10.01762836881648', '10.39050746251313', '11.05844072842022', '11.37992634284704', '12.08227258183470', '12.59434906398314', '13.03648798396610', '13.22435323156125', '13.68109565902770', '14.29404183388933', '14.56312373565229', '15.26580962270203', '15.56498667871542', '16.10108461221335', '16.51306481105578', '16.83502559360653', '17.55836092855368', '17.86474848545410', '18.29606508205949', '18.94927176516941', '19.27509198218408', '19.60310623917870'], 'prelabel': '2-149454-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 34.545566985777555, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1870294191162402386, 'z1': {'__RealLiteral__': 0, 'data': '0.4234791271007763', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.397105341735579', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.103888229702031', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1193.3961983688444, 'bad_primes': [2, 3, 19, 23], 'central_character': '1.1', 'conductor': 149454, 'conductor_radical': 2622, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 2, 0, -2, 1, 0, 2, -4, 0, 0, -2, 0, 1, 2, 0, 0, 2, 0, -4, 1, 0, -1, 0, 0, -2, -6, 0, 2, 1, 0, 2, -4, 0, -2, 0, 0, 2, 2, 0, 4, -4, 0, 1, -12, 0, -3, -1, 0, 0, -2, 0, -8, -2, 0, -6, 0, 0, 8, 2, 0, 1, 0, 0, 4, 2, 0, -4, -8, 0, 2, -2, 0, 0, 8, 0, 8, 2, 0, 2, 16, 0, 4, 4, 0, -4, -8, 0, 0, 1, 0, -12, 0, 0, -2, -3, 0, -1], 'euler11': [1, 4, 11], 'euler13': [1, 0, 13], 'euler17': [1, -2, 17], 'euler19': [1, 0, 0], 'euler2': [1, -1, 0], 'euler23': [1, -1, 0], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -2, 31], 'euler37': [1, 2, 37], 'euler41': [1, -2, 41], 'euler43': [1, -4, 43], 'euler47': [1, 12, 47], 'euler5': [1, -2, 5], 'euler53': [1, 2, 53], 'euler59': [1, 0, 59], 'euler61': [1, -8, 61], 'euler67': [1, -4, 67], 'euler7': [1, 2, 7], 'euler71': [1, 8, 71], 'euler73': [1, -2, 73], 'euler79': [1, -8, 79], 'euler83': [1, -16, 83], 'euler89': [1, 8, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, -2, 5], [1, 2, 7], [1, 4, 11], [1, 0, 13], [1, -2, 17], [1, 0, 0], [1, -1, 0], [1, 6, 29], [1, -2, 31], [1, 2, 37], [1, -2, 41], [1, -4, 43], [1, 12, 47], [1, 2, 53], [1, 0, 59], [1, -8, 61], [1, -4, 67], [1, 8, 71], [1, -2, 73], [1, -8, 79], [1, -16, 83], [1, 8, 89], [1, 2, 97]], 'index': 12, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/149454/ck'], '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': '2-149454-1.1-c1-0-12', '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': '2-149454-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 34.545566985777555, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1870294191162402386, 'z1': {'__RealLiteral__': 0, 'data': '0.4234791271007763', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1870294191162402386', 'Lhash_array': ['1870294191162402386'], 'factors': ['2-149454-1.1-c1-0-12'], 'label': '2-149454-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/149454/ck'}