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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': '431812692512958288', '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': 2967.6322060806847, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [43, [1]], [67, [1, 1]]], 'bad_primes': [3, 43, 67], 'central_character': '371649.1', 'coefficient_field': '1.1.1.1', 'conductor': 371649, 'conductor_radical': 8643, 'degree': 2, 'euler_factors': [[1, -2, 2], [1, -1], [1, 0, 5], [1, 0, 7], [1, 6, 11], [1, -4, 13], [1, 7, 17], [1, -5, 19], [1, 1, 23], [1, 1, 29], [1, 4, 31], [1, 3, 37], [1, 0, 41], [1], [1, -9, 47], [1, -10, 53], [1, -3, 59], [1, 2, 61], [1, 1], [1, -16, 71], [1, -7, 73], [1, -8, 79], [1, 4, 83], [1, -15, 89], [1, -4, 97]], 'gamma_factors': [[], [0]], 'index': 2, 'label': '2-371649-1.1-c1-0-2', 'leading_term': '17.3888795335', '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/371649/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 3.759793861126811, 4.335472696870458, 0.5018657317472872, -5.290824476428607, -8.273385131196527, -6.074661652654316, -1.52919638059081, 0.7439241292722455, 0.001488177608183526, -0.5866460789460405, 0.6301680316101673, 1.553498490569236, 0.6007610169826797, -0.3957991762091858, 0.1342980325476455, 0.420837621143229, -0.947454564412121, -1.803359819610074, -0.5463804159225957, 0.4252092969040885, -0.4909904050269138, -0.6491478395095467, 1.031062462557128, 0.9518571773108955, -1.51742712467623, -1.259314073997982, 2.344929027926038, 2.61739244713836, -1.361730786758233, -1.846210806343562, 1.969614749598307, 1.51000594705388, -3.215213214456743, -2.584375829850535, 2.365144904581742, 1.306958913321424, -2.915853380073269, 1.007738335615416, 8.155834377207187, 5.384744409385976, -2.30236864009181, -1.770933714475678, 2.892472959173508, 1.706316082169523, -0.5260020497878461, 2.293345642257867, 3.454521053135004, -0.5151612358157687, -2.062690887127403, 0.6457305643726124, 1.392292537153568, 0.02650185656906137, 0.07149038346163304, 0.1410151378993132, -0.3391475326043874, 0.3443581445495767, -0.2367600341951686, -2.851356255809077, -2.46697379674302, 0.5089940793381958, 0.7021480857662262, -0.1362878635018473, 0.377047802964669, -0.8951792840405144, 0.2636387419697019, 8.164307781031077, 7.91028212515348, -9.281577356927215, -20.30497022019716, -10.00035735736852, 0.9541119424917193, -0.1998436305900503, -0.01823595268988053, 1.945259384768774, -4.366558409868265, -7.341529027513443, 2.461304257197231, 8.336880881393357, 2.569980413902032, -0.7905907784551419, 1.00181056675108, 0.09179356905442143, -0.6689486694962925, 0.9252918396832777, 0.3556238265068889, -0.006427417559353143, 1.868222879801854, 0.8646990200568845, -1.091069099703287, 0.5813788890567531, 1.003245459616397, -0.8773504434344037, 0.2298328241210457, 1.334291729013091, -0.2081471000779842, 0.2444771219965799, 0.8758540998115696, -0.3334646462729971, 2.42112537514748, 4.968420078005733, 0.06065087809829197, -2.601852934210998, 0.7595968030539003, -0.628688983708041, -2.132014820180411, 3.186546645472344, 2.779454526210824, -1.265001977260923, 5.806442721530558, 8.479242827972298, -5.647254251097404, -10.45577468066873, 1.806062103897883, 5.460349016835978, 5.718510829414341e-05, 0.3424403589897462, -0.8727921149803106, -5.371074390103548, -2.104603391722093, 2.342056106609288], 'positive_zeros': ['0.7722893013465825', '1.867591975674871', '2.250294487393313', '2.648613539676754', '3.360815486032203', '3.712238922208798', '4.103124805119255', '4.837576646464523', '5.148191734175272', '5.607240903288553', '6.101649357091048', '6.593824776473997', '7.166115544010178', '7.623516358338530', '8.080965869911054', '8.622336819118775', '9.064208603027857', '9.467533363489391', '10.15965307907732', '10.58330525641611', '11.12985273523012', '11.33552001201244', '11.97019863894752', '12.44364159302050', '13.00790151752050', '13.21732120632309', '13.55650279413874', '13.90252979739512', '14.22016690487161', '14.94817474084563', '15.39839564216693', '15.57724705628078', '15.87335274605182', '16.23694417583675', '16.88244558193132', '17.70531232451984', '17.98350286608308', '18.25138956164766', '18.61178112483367', '19.19801756735127', '19.86546400802723'], 'prelabel': '2-371649-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.47597824803778, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 431812692512958288, 'z1': {'__RealLiteral__': 0, 'data': '0.7722893013465825', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.867591975674871', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.250294487393313', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2967.6322060806847, 'bad_primes': [3, 43, 67], 'central_character': '1.1', 'conductor': 371649, 'conductor_radical': 8643, 'degree': 2, 'dirichlet_coefficients': [1, 2, 1, 2, 0, 2, 0, 0, 1, 0, -6, 2, 4, 0, 0, -4, -7, 2, 5, 0, 0, -12, -1, 0, -5, 8, 1, 0, -1, 0, -4, -8, -6, -14, 0, 2, -3, 10, 4, 0, 0, 0, 0, -12, 0, -2, 9, -4, -7, -10, -7, 8, 10, 2, 0, 0, 5, -2, 3, 0, -2, -8, 0, -8, 0, -12, -1, -14, -1, 0, 16, 0, 7, -6, -5, 10, 0, 8, 8, 0, 1, 0, -4, 0, 0, 0, -1, 0, 15, 0, 0, -2, -4, 18, 0, -8, 4, -14, -6, -10], 'euler11': [1, 6, 11], 'euler13': [1, -4, 13], 'euler17': [1, 7, 17], 'euler19': [1, -5, 19], 'euler2': [1, -2, 2], 'euler23': [1, 1, 23], 'euler29': [1, 1, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 3, 37], 'euler41': [1, 0, 41], 'euler43': [1, 0, 0], 'euler47': [1, -9, 47], 'euler5': [1, 0, 5], 'euler53': [1, -10, 53], 'euler59': [1, -3, 59], 'euler61': [1, 2, 61], 'euler67': [1, 1, 0], 'euler7': [1, 0, 7], 'euler71': [1, -16, 71], 'euler73': [1, -7, 73], 'euler79': [1, -8, 79], 'euler83': [1, 4, 83], 'euler89': [1, -15, 89], 'euler97': [1, -4, 97], 'euler_factors': [[1, -2, 2], [1, -1, 0], [1, 0, 5], [1, 0, 7], [1, 6, 11], [1, -4, 13], [1, 7, 17], [1, -5, 19], [1, 1, 23], [1, 1, 29], [1, 4, 31], [1, 3, 37], [1, 0, 41], [1, 0, 0], [1, -9, 47], [1, -10, 53], [1, -3, 59], [1, 2, 61], [1, 1, 0], [1, -16, 71], [1, -7, 73], [1, -8, 79], [1, 4, 83], [1, -15, 89], [1, -4, 97]], 'index': 2, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/371649/d'], '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': '2-371649-1.1-c1-0-2', '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': '2-371649-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.47597824803778, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 431812692512958288, 'z1': {'__RealLiteral__': 0, 'data': '0.7722893013465825', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '431812692512958288', 'Lhash_array': ['431812692512958288'], 'factors': ['2-371649-1.1-c1-0-2'], 'label': '2-371649-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/371649/d'}