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lfunc_lfunctions • Show schema
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{'A10': -4, 'A2': -1, 'A3': -1, 'A4': -1, 'A5': 4, 'A6': 1, 'A7': 0, 'A8': 3, 'A9': 1, 'Lhash': '1918743340051722260', 'a10': [-1.2649110640673518, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [-0.5, 0], 'a5': [1.7888543819998317, 0], 'a6': [0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [1.0606601717798212, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 259.4100010465337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [7, [1]], [13, [1, 1]], [17, [1, 1]]], 'bad_primes': [3, 7, 13, 17], 'central_character': '32487.1', 'coefficient_field': '1.1.1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, 1], [1, -4, 5], [1], [1, 4, 11], [1, 1], [1, 1], [1, 0, 19], [1, 4, 23], [1, 4, 29], [1, 8, 31], [1, -4, 37], [1, 0, 41], [1, 4, 43], [1, 10, 47], [1, -6, 53], [1, -2, 59], [1, 0, 61], [1, -14, 67], [1, 8, 71], [1, -10, 73], [1, 16, 79], [1, 10, 83], [1, -2, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 1, 'label': '2-32487-1.1-c1-0-1', 'leading_term': '0.781427515322', '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/32487/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.7814275153214996, 0.4421867766886402, -0.4336881434724714, -1.380403395846019, -1.72394207104859, -1.085660260753579, 0.08380787430266944, 0.6567657711606403, -0.1083262717745436, -1.464098125762182, -1.432394824618936, 1.253657702488512, 5.240325929603969, 7.082861781493781, 4.438455871747281, -1.121304155191778, -5.116804373209835, -4.530502197445539, -0.8812323472550633, 1.701753956556906, 1.263796493814312, -0.1918377126733656, -0.06936885581240874, 1.020198291281142, 0.4148512093555494, -2.143849257317198, -3.499652153532388, -1.519487389491486, 1.352126739038253, 1.137836896779391, -1.957549370598864, -3.632710804046643, -1.626107580834455, 1.07695587125933, 0.783314877022104, -1.565615521407402, -2.304684174185111, -0.769411313392124, 0.3502649848584849, -0.06603657814814343, -0.1390813218541311, 0.8449323986941006, 0.8479366537562826, -0.5128067628102169, -0.01318051043574183, 3.485258591322025, 5.06601853804024, 0.2887615887156158, -6.875731473414667, -8.526723307271688, -4.00878377295188, -0.08832240255063106, -0.07619728957029458, -0.1592261034588586, 1.876300458740735, 2.253976316277846, -0.7297884192346901, -1.965804185648265, 1.421569384698267, 3.226829253082583, -2.168341248050053, -9.032741088760819, -8.076455899867574, -0.8659163662966055, 3.114759083508934, 1.129968333851178, -0.9401344424040295, -0.02962495198002845, 0.6523935895682564, -0.4467583861644147, -0.8147046993507829, 0.1027206578616681, 0.1993054312959405, -0.2228411417798313, 0.2212430151283802, -0.615997294375843, -4.148380352555795, -5.385824122911054, -0.3218311372223093, 5.088732939680394, 3.47951211649012, -1.023102065229047, 0.09229926369110653, 4.642453529936736, 4.481740729465321, 0.4611106533113147, -0.6959855096488057, 0.3864687365076207, -0.9867619425846098, -2.509494508355361, -0.2550704327788163, 1.354639791644787, -2.083561667793069, -4.566308778841449, -0.5457693465161599, 3.35540724017508, 0.4448053985782971, -3.136044633516011, -0.5321335964268518, 2.709319959103264, 0.1604422665583184, -3.267554470827217, -1.94257799433657, 0.3408225794109544, 0.01079471266545074, 0.3851487399022479, 2.183425485552972, 1.004080758299723, -2.114745994993861, -1.46526803472003, 1.559387532245482, 1.159574798571047, -1.198862702122805, -0.7893015853512967, 0.5478754856919587, -0.1088684189021321, -0.2168128217117605, 0.8761251483984491, -0.1755599221357332, -1.044093210451747, 2.937999917535556], 'positive_zeros': ['0.3888705876474981', '1.480883016501761', '1.979125611878906', '2.659904825900388', '3.700837518835119', '4.561643356929584', '5.204791788076253', '5.516472003061428', '6.049046819337342', '6.867346849919181', '7.353342401113191', '8.130265949084457', '8.587819529830844', '9.374308559823552', '9.724527331279095', '10.04580971769586', '10.65478247852165', '11.00139646078963', '11.75974918619360', '12.76341928959910', '12.97895469555851', '13.27901375138402', '13.94598344407437', '14.41556384660158', '14.92803430802243', '15.78206347170679', '16.34611474538957', '16.75499299337178', '17.16403310245702', '17.71982933545194', '18.08664846805179', '18.40131962168767', '18.66883721974652', '19.51158583952180'], 'prelabel': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1918743340051722260, 'z1': {'__RealLiteral__': 0, 'data': '0.3888705876474981', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.480883016501761', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.979125611878906', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 259.4100010465337, 'bad_primes': [3, 7, 13, 17], 'central_character': '1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, -1, 4, 1, 0, 3, 1, -4, -4, 1, -1, 0, -4, -1, -1, -1, 0, -4, 0, 4, -4, -3, 11, 1, -1, 0, -4, 4, -8, -5, 4, 1, 0, -1, 4, 0, 1, 12, 0, 0, -4, 4, 4, 4, -10, 1, 0, -11, 1, 1, 6, 1, -16, 0, 0, 4, 2, 4, 0, 8, 0, 7, -4, -4, 14, 1, 4, 0, -8, 3, 10, -4, -11, 0, 0, -1, -16, -4, 1, 0, -10, 0, -4, 4, 4, -12, 2, -4, 0, 4, 8, 10, 0, 5, 2, 0, -4, -11], 'euler11': [1, 4, 11], 'euler13': [1, 1, 0], 'euler17': [1, 1, 0], 'euler19': [1, 0, 19], 'euler2': [1, 1, 2], 'euler23': [1, 4, 23], 'euler29': [1, 4, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, -4, 37], 'euler41': [1, 0, 41], 'euler43': [1, 4, 43], 'euler47': [1, 10, 47], 'euler5': [1, -4, 5], 'euler53': [1, -6, 53], 'euler59': [1, -2, 59], 'euler61': [1, 0, 61], 'euler67': [1, -14, 67], 'euler7': [1, 0, 0], 'euler71': [1, 8, 71], 'euler73': [1, -10, 73], 'euler79': [1, 16, 79], 'euler83': [1, 10, 83], 'euler89': [1, -2, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 1, 2], [1, 1, 0], [1, -4, 5], [1, 0, 0], [1, 4, 11], [1, 1, 0], [1, 1, 0], [1, 0, 19], [1, 4, 23], [1, 4, 29], [1, 8, 31], [1, -4, 37], [1, 0, 41], [1, 4, 43], [1, 10, 47], [1, -6, 53], [1, -2, 59], [1, 0, 61], [1, -14, 67], [1, 8, 71], [1, -10, 73], [1, 16, 79], [1, 10, 83], [1, -2, 89], [1, -2, 97]], 'index': 1, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32487/c'], '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': '2-32487-1.1-c1-0-1', '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': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1918743340051722260, 'z1': {'__RealLiteral__': 0, 'data': '0.3888705876474981', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1918743340051722260', 'Lhash_array': ['1918743340051722260'], 'label': '2-32487-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32487/c'}