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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': -1, 'A4': 1, 'A5': 0, 'A6': -1, 'A7': 1, 'A8': 1, 'A9': 1, 'Lhash': '742077321009134002', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [-0.4082482904638631, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2784.5911295273036, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [7, [1, -1]], [19, [1]], [23, [1, -1]]], 'bad_primes': [2, 3, 7, 19, 23], 'central_character': '348726.1', 'coefficient_field': '1.1.1.1', 'conductor': 348726, 'conductor_radical': 18354, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1, 0, 5], [1, -1], [1, -6, 11], [1, 2, 13], [1, 6, 17], [1], [1, -1], [1, -6, 29], [1, 8, 31], [1, 8, 37], [1, 6, 41], [1, -2, 43], [1, 0, 47], [1, -12, 53], [1, 0, 59], [1, -8, 61], [1, -10, 67], [1, 0, 71], [1, -14, 73], [1, 8, 79], [1, -6, 83], [1, 6, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 54, 'label': '2-348726-1.1-c1-0-54', 'leading_term': '11.7536070635', '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': 1, 'origin': 'EllipticCurve/Q/348726/cb', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.560431246873472, 3.120021185597389, 1.116572049382581, -1.600191309254028, -2.192156509415378, -0.1932983100765729, 1.546720776602797, 0.6825720792473311, -0.8434981719423963, 0.6949375923487406, 4.77346636446165, 6.521392879140599, 3.763187350182044, 0.3551870506528237, 0.06077615082598489, 1.029739492257994, 0.1300890854539878, -1.150379155934533, -0.189681570282929, 1.087228782536724, 0.001461916459314217, -1.075508537134239, 0.711719216037868, 2.506749196910421, 1.159540417557211, -0.4118251103394134, 0.383023779375632, 0.2199131293115396, -1.669344747709936, 0.5975935923586602, 6.855618508077384, 7.145576589770965, -0.4458626797311204, -4.340314319186549, -0.5523252550502258, 0.3478185186230819, -4.712752957681199, -5.13372870265619, 0.7989411702837133, 2.011471231431583, -2.597191845613116, -2.802788468586486, 1.578327317565484, 2.222465294611316, 0.09300343703489489, 0.5611357930624157, 1.153244111842833, -0.145717298195853, 0.5071176170907886, 1.869297928691797, -0.463524626671826, -2.221428090501386, 0.8100562377068099, 2.437045164351402, -0.2588997669369269, -0.8693553291664482, 0.6165782384403109, -1.283004268409361, -2.906328509386694, -0.290235830835644, 0.4573187879215471, -1.631454701643721, 0.4357609415167267, 3.328486984268397, 0.13908184321384, -2.462013673617435, 0.4929359362454469, 1.226292794877281, -1.065328240980568, -0.1098013689708994, -0.8479083897090262, -5.685047105377198, -3.365295695449062, 4.159674831921077, 1.225982432670055, -7.125591069376107, -5.447731774404016, -0.04896194300247574, -0.2677248786367271, 0.9720175209929833, 3.651028437137247, -0.3912623852328475, -3.988405306315845, 0.3366620292852584, 3.101464721280572, 0.3811389330737062, -0.2840942636614939, 0.3810609511974733, -0.677113488059292, 0.1512262062588647, 0.9483110717668379, -1.083083548692472, -0.261599046144394, 2.551569689350094, 0.8143003018577852, -0.9073443953305619, 0.7930482039054898, 0.03921203424290431, -0.9562770856883233, 0.762811108201833, -2.07895251491796, -5.148431599292669, 0.7693907746946735, 2.145502739624404, -8.457243340618103, -11.11089809206902, -2.359363295332687, -0.2320959230880297, -2.195806221296848, 0.3533294103830129, -0.989290811257772, -3.865842606440567, 1.30077974670766, 4.279178823820089, -0.4659623519658264, -1.404082691076944, 0.4499881566910467, -1.126975417844176, -0.1766310361840625, 1.601140837365118], 'positive_zeros': ['0.8452288909584823', '1.519549511606236', '2.088392180450595', '2.443003064121195', '3.554678328946221', '3.734734455007229', '4.268897060457913', '4.776267402879175', '5.250198448125307', '5.680807674742855', '6.390063063916570', '6.669301290213011', '7.030421220529667', '7.470916299946809', '8.236072191700119', '8.784125263382987', '9.024371603455341', '9.714975934515406', '10.11541571256490', '10.65672036180699', '11.27384857229584', '11.38249476929670', '11.96625810533349', '12.17573466763581', '12.71620849798359', '13.19802312364067', '13.72727045985381', '14.11825049706291', '14.38794924537083', '15.02570053368816', '15.30474155779027', '15.72344402058679', '16.25722430735589', '16.71482840247783', '17.11982244674059', '17.51644117076808', '17.68072365873879', '18.35049765579112', '18.78334415259159', '19.50508808493177', '19.69600485920793', '19.91754275204878'], 'prelabel': '2-348726-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 52.76922521249771, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 742077321009134002, 'z1': {'__RealLiteral__': 0, 'data': '0.8452288909584823', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.519549511606236', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.088392180450595', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2784.5911295273036, 'bad_primes': [2, 3, 7, 19, 23], 'central_character': '1.1', 'conductor': 348726, 'conductor_radical': 18354, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, 0, -1, 1, 1, 1, 0, 6, -1, -2, 1, 0, 1, -6, 1, 0, 0, -1, 6, 1, -1, -5, -2, -1, 1, 6, 0, -8, 1, -6, -6, 0, 1, -8, 0, 2, 0, -6, -1, 2, 6, 0, 1, 0, -1, 1, -5, 6, -2, 12, -1, 0, 1, 0, 6, 0, 0, 8, -8, 1, 1, 0, -6, 10, -6, -1, 0, 0, 1, 14, -8, 5, 0, 6, 2, -8, 0, 1, -6, 6, -1, 0, 2, -6, 6, -6, 0, -2, 1, 8, 0, 0, -1, 10, 1, 6, -5], 'euler11': [1, -6, 11], 'euler13': [1, 2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 0, 0], 'euler2': [1, -1, 0], 'euler23': [1, -1, 0], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, 8, 37], 'euler41': [1, 6, 41], 'euler43': [1, -2, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 5], 'euler53': [1, -12, 53], 'euler59': [1, 0, 59], 'euler61': [1, -8, 61], 'euler67': [1, -10, 67], 'euler7': [1, -1, 0], 'euler71': [1, 0, 71], 'euler73': [1, -14, 73], 'euler79': [1, 8, 79], 'euler83': [1, -6, 83], 'euler89': [1, 6, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, 0, 5], [1, -1, 0], [1, -6, 11], [1, 2, 13], [1, 6, 17], [1, 0, 0], [1, -1, 0], [1, -6, 29], [1, 8, 31], [1, 8, 37], [1, 6, 41], [1, -2, 43], [1, 0, 47], [1, -12, 53], [1, 0, 59], [1, -8, 61], [1, -10, 67], [1, 0, 71], [1, -14, 73], [1, 8, 79], [1, -6, 83], [1, 6, 89], [1, -10, 97]], 'index': 54, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/348726/cb'], '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': '2-348726-1.1-c1-0-54', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-348726-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 52.76922521249771, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 742077321009134002, 'z1': {'__RealLiteral__': 0, 'data': '0.8452288909584823', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '742077321009134002', 'Lhash_array': ['742077321009134002'], 'factors': ['2-348726-1.1-c1-0-54'], 'label': '2-348726-1.1-c1-0-54', 'type': 'ECQ', 'url': 'EllipticCurve/Q/348726/cb'}