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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -2, 'A3': 1, 'A4': 2, 'A5': 0, 'A6': -2, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '120754364895399596', 'a10': [0.0, 0], 'a2': [-1.414213562373095, 0], 'a3': [0.5773502691896258, 0], 'a4': [1.0, 0], 'a5': [0.0, 0], 'a6': [-0.8164965809277261, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 381.48529565666723, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [5, [1]], [7, [1]], [13, [1, -1]]], 'bad_primes': [3, 5, 7, 13], 'central_character': '47775.1', 'coefficient_field': '1.1.1.1', 'conductor': 47775, 'conductor_radical': 1365, 'degree': 2, 'euler_factors': [[1, 2, 2], [1, -1], [1], [1], [1, 5, 11], [1, -1], [1, -5, 17], [1, 2, 19], [1, -1, 23], [1, -10, 29], [1, -2, 31], [1, -3, 37], [1, -9, 41], [1, -4, 43], [1, -10, 47], [1, 9, 53], [1, 0, 59], [1, -11, 61], [1, -4, 67], [1, -15, 71], [1, -6, 73], [1, 11, 79], [1, -8, 83], [1, -11, 89], [1, 9, 97]], 'gamma_factors': [[], [0]], 'index': 39, 'label': '2-47775-1.1-c1-0-39', 'leading_term': '1.58691348381', '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/47775/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.586913483812912, 1.27432982691921, 0.5092175462082479, -0.1803916850747017, -0.1265816033593027, 0.8711347084984588, 2.084191084097838, 2.308999554132597, 1.140984649978346, -0.2631643370688347, -0.2213970270600152, 1.313169381811758, 2.069270908403714, -0.1587317926396056, -4.269290573777506, -6.07472964827272, -2.895996915488636, 2.507300432643635, 4.293046531012896, 0.4685868613316131, -4.09228687762608, -3.27380012507418, 2.462452305060369, 6.365230877280516, 3.939210347136059, -1.424480444132873, -3.247360567840765, -0.3718245865568755, 2.541737254243615, 2.159209412836703, 0.3333041138914511, -0.05703835104516325, 0.4763455290186926, 0.1176371061620058, -0.4995143041029685, 0.1977257665370729, 1.254816772179543, 0.7017725694676709, -0.6407769633196424, -0.513840465578132, 0.5095206944372096, 0.1744622050359276, -0.7500805610296148, 0.1653217107626437, 1.245898147361741, -1.511011993629163, -6.102585132156435, -5.328668601684416, 1.493893560783803, 5.633129261714885, 2.306437375481065, -1.359827859410876, 1.507685054055045, 5.60153570391515, 2.97346622570167, -2.662305566136567, -2.693362085304686, 0.7400946284998484, -1.141476835695247, -7.389065750281377, -8.685136921425405, -3.560320453945043, 0.1110526457297828, -0.5438564689993992, -0.4659802906408374, 1.69198490489959, 1.450568923487238, -1.303698262680862, -1.57142330491221, 0.875863761330348, 1.403754949374988, -0.2105067611800367, -0.2320681654926004, 0.986554750717813, 0.5280486037894636, -0.5083099235322145, -0.06597712939560967, -0.09650353123699504, -1.538582408718502, -1.081663789616541, 1.422705746135795, 1.305189745731533, -1.166146513777026, -0.7760599219408385, 1.102365819056031, -0.6927552819814689, -1.548279224898743, 5.580516572167446, 12.05806194187511, 4.74682854224036, -8.627968231802019, -9.890844138709944, -1.023665346239411, 1.912887231886952, -1.293910309945516, 1.263568367767828, 7.422921655987414, 5.684199389049353, -1.451321692390978, -3.032243422111066, 0.1466830481496209, 0.686196623669267, -0.5927833086778567, -0.06345661125813323, 0.2217543861857246, -0.8211244498726696, -0.3785568496557986, 0.8208465552901375, 0.07127871237061652, -0.4944959998550514, 0.7690871555567705, 0.3347862441077381, -2.046708123501343, -1.825163764241906, -0.03242289204013124, -0.8362715089049302, -1.119296308798683, 1.959949477638407, 2.122317245028251, -2.484236827643203, -2.949291702906958], 'positive_zeros': ['0.6655789494363450', '1.047765564949570', '2.188791230472139', '2.547783530588825', '3.239152322949533', '4.129531595549746', '4.771517578291045', '5.401962248344214', '6.177997012163910', '6.774378158432202', '7.580033103856334', '7.779113903433311', '8.285143286113601', '8.709545231166088', '9.368623699701371', '9.864071112448425', '10.28812877646407', '10.72571358492815', '11.15931454077530', '11.94961917263172', '12.61621622985925', '12.92169388650719', '13.62011807388121', '14.17984118547039', '14.43913844645003', '15.47814053159920', '15.64303942123077', '16.06009948458989', '16.63166989532542', '17.16171217482124', '17.71330519871150', '18.04586403052402', '18.59958972333364', '19.02334294369693', '19.22445524232444', '19.85765224668499'], 'prelabel': '2-47775-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.53164856474402, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 120754364895399596, 'z1': {'__RealLiteral__': 0, 'data': '0.6655789494363450', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.047765564949570', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.188791230472139', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 381.48529565666723, 'bad_primes': [3, 5, 7, 13], 'central_character': '1.1', 'conductor': 47775, 'conductor_radical': 1365, 'degree': 2, 'dirichlet_coefficients': [1, -2, 1, 2, 0, -2, 0, 0, 1, 0, -5, 2, 1, 0, 0, -4, 5, -2, -2, 0, 0, 10, 1, 0, 0, -2, 1, 0, 10, 0, 2, 8, -5, -10, 0, 2, 3, 4, 1, 0, 9, 0, 4, -10, 0, -2, 10, -4, 0, 0, 5, 2, -9, -2, 0, 0, -2, -20, 0, 0, 11, -4, 0, -8, 0, 10, 4, 10, 1, 0, 15, 0, 6, -6, 0, -4, 0, -2, -11, 0, 1, -18, 8, 0, 0, -8, 10, 0, 11, 0, 0, 2, 2, -20, 0, 8, -9, 0, -5, 0], 'euler11': [1, 5, 11], 'euler13': [1, -1, 0], 'euler17': [1, -5, 17], 'euler19': [1, 2, 19], 'euler2': [1, 2, 2], 'euler23': [1, -1, 23], 'euler29': [1, -10, 29], 'euler3': [1, -1, 0], 'euler31': [1, -2, 31], 'euler37': [1, -3, 37], 'euler41': [1, -9, 41], 'euler43': [1, -4, 43], 'euler47': [1, -10, 47], 'euler5': [1, 0, 0], 'euler53': [1, 9, 53], 'euler59': [1, 0, 59], 'euler61': [1, -11, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, -15, 71], 'euler73': [1, -6, 73], 'euler79': [1, 11, 79], 'euler83': [1, -8, 83], 'euler89': [1, -11, 89], 'euler97': [1, 9, 97], 'euler_factors': [[1, 2, 2], [1, -1, 0], [1, 0, 0], [1, 0, 0], [1, 5, 11], [1, -1, 0], [1, -5, 17], [1, 2, 19], [1, -1, 23], [1, -10, 29], [1, -2, 31], [1, -3, 37], [1, -9, 41], [1, -4, 43], [1, -10, 47], [1, 9, 53], [1, 0, 59], [1, -11, 61], [1, -4, 67], [1, -15, 71], [1, -6, 73], [1, 11, 79], [1, -8, 83], [1, -11, 89], [1, 9, 97]], 'index': 39, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/47775/g'], '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': '2-47775-1.1-c1-0-39', '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': '2-47775-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.53164856474402, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 120754364895399596, 'z1': {'__RealLiteral__': 0, 'data': '0.6655789494363450', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '120754364895399596', 'Lhash_array': ['120754364895399596'], 'label': '2-47775-1.1-c1-0-39', 'type': 'ECQ', 'url': 'EllipticCurve/Q/47775/g'}