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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': 0, 'A8': 0, 'A9': 1, 'Lhash': '1607763225960657065', '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': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 553.842388419601, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, -1]], [17, [1]]], 'bad_primes': [2, 3, 5, 17], 'central_character': '69360.1', 'coefficient_field': '1.1.1.1', 'conductor': 69360, 'conductor_radical': 510, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -1], [1, 0, 7], [1, 4, 11], [1, -6, 13], [1], [1, 4, 19], [1, 8, 23], [1, -6, 29], [1, -4, 31], [1, 2, 37], [1, 6, 41], [1, -4, 43], [1, 4, 47], [1, -10, 53], [1, 12, 59], [1, 6, 61], [1, -4, 67], [1, 0, 71], [1, 14, 73], [1, 4, 79], [1, 16, 83], [1, -10, 89], [1, 6, 97]], 'gamma_factors': [[], [0]], 'index': 13, 'label': '2-69360-1.1-c1-0-13', 'leading_term': '1.26741659616', '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/69360/bp', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.267416596156481, 0.7120313826944406, -0.665297769764303, -1.992343938573944, -2.180652119990756, -0.896080644516813, 0.7553351199789605, 0.9911373722056538, -0.7180026912477026, -2.636431659854822, -2.37384350852531, 0.1860307453480204, 2.23205681152948, 1.134966651133499, -2.098459202089665, -3.724562976275411, -1.956456667282804, 0.62935001549427, 0.585540847980137, -1.611307874442253, -2.378459525995109, -0.3940403303611767, 1.55657824154262, 1.109918754993098, -0.04995332949917971, 0.5221247549589758, 1.381622608289902, -0.4265390257730279, -3.456489889847355, -3.034390657112708, 1.191961498453086, 3.882836807442615, 2.145042678960665, -0.002002921776669818, 1.210858189999287, 2.549355863083385, -0.4806144585774449, -5.062091429551506, -5.045138795968342, -1.026548035318002, 1.012402427712851, -0.221557362675922, -0.5967554832824823, 0.5992573651311759, -0.3397791730437817, -3.158109085200825, -3.138752602444636, -0.3121060437936971, -0.1245084320293656, -3.205155944488341, -3.907686543104135, -1.003384229891365, 0.1926604921421124, -1.563538019651098, -1.444081799004647, 0.8010184221061462, -0.111272014188034, -3.217769193064344, -1.282550872970512, 5.173760040680077, 7.174445251193469, 2.782423831626374, -0.428957141454784, 0.1426048844133583, -0.5675896022268517, -2.90246188918042, -2.009867498122404, 0.5932268185144058, -0.7216937997307821, -3.860397431468879, -3.021985941185349, -0.2123569281876227, -0.01228242099546142, 0.04969864471548783, 2.281053841725393, 2.157581753473157, -0.9428046479240048, 0.3366598690258306, 6.211107788775709, 6.800679300455929, 0.7246767528196788, -1.839403498644591, 1.435120806737338, 2.36513927101644, -0.2489220590725792, -0.4483051357829075, 0.506053558095277, -1.606894850650291, -2.475454619480202, 1.512449577856211, 3.916513695894375, 1.047037307579664, -0.9423461397956631, 0.1243941288112527, -0.594917100600302, -1.810333317506421, 0.8844647159314093, 2.858528719260608, -0.06545629528795464, -0.721079700520962, 4.495354771944167, 6.66150539011746, 2.410172466519948, -0.2433272178147631, 0.03757288958172337, -2.198898750827034, -3.100448816731279, 2.529793816601022, 6.636134476660293, 2.722347098926658, -1.058968578101647, 0.6048054113005668, 1.233006275255945, -0.7363965815336038, -0.05188970835690018, 1.191115220078586, -0.6520114244633749, -0.82770496156654, 1.679174485183877, 0.2414949680741223, -3.327497552615695], 'positive_zeros': ['0.3897631740076203', '1.374999391891432', '1.916838154163154', '2.734072227865354', '3.342962788976036', '4.173021535118584', '4.575768327038694', '5.288109146698472', '5.977068625558145', '6.123417084339866', '6.714679114718276', '7.435682678320041', '8.249096432406123', '8.317122054565853', '8.975077399595546', '9.823820060905659', '10.21463752500358', '10.62079494269614', '10.96387677603017', '11.78711115946839', '11.98442917951755', '12.85731663887896', '13.04253222031639', '13.65074548645903', '13.99080584900570', '14.55409850895983', '15.42841407480224', '15.71049266366325', '15.92309151784737', '16.67096356610112', '16.94049323519258', '17.78542790763505', '17.99590270463845', '18.24101959948143', '18.91658310503692', '19.23169529550867'], 'prelabel': '2-69360-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.533856216514984, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1607763225960657065, 'z1': {'__RealLiteral__': 0, 'data': '0.3897631740076203', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.374999391891432', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.916838154163154', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 553.842388419601, 'bad_primes': [2, 3, 5, 17], 'central_character': '1.1', 'conductor': 69360, 'conductor_radical': 510, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, 0, 0, 1, 0, -4, 0, 6, 0, -1, 0, 0, 0, -4, 0, 0, 0, -8, 0, 1, 0, -1, 0, 6, 0, 4, 0, 4, 0, 0, 0, -2, 0, -6, 0, -6, 0, 4, 0, 1, 0, -4, 0, -7, 0, 0, 0, 10, 0, -4, 0, 4, 0, -12, 0, -6, 0, 0, 0, 6, 0, 4, 0, 8, 0, 0, 0, -14, 0, -1, 0, 0, 0, -4, 0, 1, 0, -16, 0, 0, 0, -6, 0, 10, 0, 0, 0, -4, 0, -4, 0, -6, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, -6, 13], 'euler17': [1, 0, 0], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 4, 47], 'euler5': [1, -1, 0], 'euler53': [1, -10, 53], 'euler59': [1, 12, 59], 'euler61': [1, 6, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, 14, 73], 'euler79': [1, 4, 79], 'euler83': [1, 16, 83], 'euler89': [1, -10, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, 0, 7], [1, 4, 11], [1, -6, 13], [1, 0, 0], [1, 4, 19], [1, 8, 23], [1, -6, 29], [1, -4, 31], [1, 2, 37], [1, 6, 41], [1, -4, 43], [1, 4, 47], [1, -10, 53], [1, 12, 59], [1, 6, 61], [1, -4, 67], [1, 0, 71], [1, 14, 73], [1, 4, 79], [1, 16, 83], [1, -10, 89], [1, 6, 97]], 'index': 13, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/69360/bp'], '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': '2-69360-1.1-c1-0-13', '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': '2-69360-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.533856216514984, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1607763225960657065, 'z1': {'__RealLiteral__': 0, 'data': '0.3897631740076203', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1607763225960657065', 'Lhash_array': ['1607763225960657065'], 'label': '2-69360-1.1-c1-0-13', 'type': 'ECQ', 'url': 'EllipticCurve/Q/69360/bp'}