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lfunc_lfunctions • Show schema
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{'A10': -1, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': 1, 'A6': 0, 'A7': 3, 'A8': -1, 'A9': 0, 'Lhash': '1719096479023713601', 'a10': [-0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [1.1338934190276817, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 189.00590158437075, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1, -1]], [263, [1, -1]]], 'bad_primes': [2, 3, 5, 263], 'central_character': '23670.1', 'coefficient_field': '1.1.1.1', 'conductor': 23670, 'conductor_radical': 7890, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, -1], [1, -3, 7], [1, 1, 11], [1, -2, 13], [1, 8, 17], [1, -4, 19], [1, 6, 23], [1, 2, 29], [1, 7, 31], [1, -10, 37], [1, 10, 41], [1, 4, 43], [1, -13, 47], [1, -9, 53], [1, -14, 59], [1, -15, 61], [1, 12, 67], [1, 8, 71], [1, 9, 73], [1, 4, 79], [1, 14, 83], [1, -17, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 5, 'label': '2-23670-1.1-c1-0-5', 'leading_term': '1.70119759536', '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/23670/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.701197595363745, 1.346005672280355, 0.378437952234628, -0.8302556425986011, -1.639036470530879, -1.509730687659069, -0.5522402786180016, 0.3533379230911412, 0.2444489199541343, -0.8519534617354662, -1.578540157956498, -0.3661082126405248, 2.75347627911913, 5.575919526679124, 5.519758688262916, 2.380777652192235, -0.969531309998413, -1.253863279521625, 1.672982110113647, 4.48465795228589, 4.056629709770502, 1.096547781463796, -0.7435172349904117, 0.572851768250753, 2.892373190051121, 2.711523154100926, -0.1666976897839724, -2.377262202864463, -1.556159113542181, 0.5349463458201222, 0.6679632436703833, -1.262981997327758, -2.360496046362902, -1.215406385207793, 0.1188057487818138, -0.3618775695026292, -1.277549882938513, -0.1803552808655809, 2.132627908960153, 2.526612019324023, 0.5521022522647842, -0.6113097770682419, 0.8058528318585428, 2.290028461194929, 1.313414342210701, -0.339711966845336, 0.1139061323073191, 0.898368037627661, -1.876539550407025, -6.791280437237663, -7.601290388852836, -2.533041923995957, 2.261826907529046, 1.683128384312547, -0.7568028243822377, 0.8079226010594068, 4.719741586007649, 4.755731401547729, 0.8171308539054885, -0.9169517777421357, 1.487686859613065, 2.76707580720473, -0.0634660081112757, -2.65014345050046, -1.297941385811734, 0.5975963060296482, -0.9918777914887809, -3.456010774696794, -2.471742676443589, 0.3720373278375777, 0.9631177629990288, -0.1422546608459413, -0.09111374028805268, 0.2383804902022614, -0.9860217550457129, -1.181885134880029, 2.303516269866342, 5.701571377827583, 4.052156297956391, -0.1357111437101966, -1.149804357848044, 0.2805189627245673, -0.01802073608074629, -0.5615567415910402, 2.409987101189956, 5.787576720931135, 4.157717266417539, 0.2966010510831643, 0.02967329433652323, 0.1398828069766781, -5.980416302956143, -13.74195563339141, -12.54495326226709, -3.668146499803201, 1.484690774368731, -0.1639073877793066, -1.217528384980925, 0.8027038104283731, 0.7415971193449729, -1.769467418670813, -1.422873509504855, 1.34751741969227, 1.154176495886815, -1.146478326877665, -0.3213688845701203, 2.421020061751283, 2.133132053617112, 0.09148544922283113, 0.1389943797235156, 0.1475249992239121, -2.675192641510353, -4.523886607125399, -2.2708703964073, 0.01201744419429544, -0.4808992837459583, -0.1403942651785293, 1.692356646693879, 0.102195728382937, -4.121685130082369, -4.094334678760594, -0.3425310937812324], 'positive_zeros': ['0.5781456593998382', '1.630738283012276', '2.069875270577684', '2.786297017461432', '3.911303304941278', '4.377912257423193', '5.352800944524097', '5.687117921763152', '6.487071180720912', '7.175597127207453', '7.600899416746623', '8.457018404391522', '8.661871434135977', '9.270141072157397', '10.06877153223267', '10.39753659941750', '11.17575458856966', '11.47830047426297', '11.87936996271918', '12.85639307427693', '13.39698879925986', '13.68975759072900', '14.55833709871243', '14.87427407352857', '15.49580051186756', '16.13076842970189', '16.40515783451932', '17.21038439483512', '17.71074971693281', '18.03296771562788', '18.32731608780238', '18.86244874496949', '19.73966285004312'], 'prelabel': '2-23670-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.747941721740412, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1719096479023713601, 'z1': {'__RealLiteral__': 0, 'data': '0.5781456593998382', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.630738283012276', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.069875270577684', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 189.00590158437075, 'bad_primes': [2, 3, 5, 263], 'central_character': '1.1', 'conductor': 23670, 'conductor_radical': 7890, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 1, 0, 3, -1, 0, -1, -1, 0, 2, -3, 0, 1, -8, 0, 4, 1, 0, 1, -6, 0, 1, -2, 0, 3, -2, 0, -7, -1, 0, 8, 3, 0, 10, -4, 0, -1, -10, 0, -4, -1, 0, 6, 13, 0, 2, -1, 0, 2, 9, 0, -1, -3, 0, 2, 14, 0, 15, 7, 0, 1, 2, 0, -12, -8, 0, -3, -8, 0, -9, -10, 0, 4, -3, 0, -4, 1, 0, 10, -14, 0, -8, 4, 0, 1, 17, 0, 6, -6, 0, -13, 4, 0, -2, -2, 0, 1], 'euler11': [1, 1, 11], 'euler13': [1, -2, 13], 'euler17': [1, 8, 17], 'euler19': [1, -4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 6, 23], 'euler29': [1, 2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 7, 31], 'euler37': [1, -10, 37], 'euler41': [1, 10, 41], 'euler43': [1, 4, 43], 'euler47': [1, -13, 47], 'euler5': [1, -1, 0], 'euler53': [1, -9, 53], 'euler59': [1, -14, 59], 'euler61': [1, -15, 61], 'euler67': [1, 12, 67], 'euler7': [1, -3, 7], 'euler71': [1, 8, 71], 'euler73': [1, 9, 73], 'euler79': [1, 4, 79], 'euler83': [1, 14, 83], 'euler89': [1, -17, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, -1, 0], [1, -3, 7], [1, 1, 11], [1, -2, 13], [1, 8, 17], [1, -4, 19], [1, 6, 23], [1, 2, 29], [1, 7, 31], [1, -10, 37], [1, 10, 41], [1, 4, 43], [1, -13, 47], [1, -9, 53], [1, -14, 59], [1, -15, 61], [1, 12, 67], [1, 8, 71], [1, 9, 73], [1, 4, 79], [1, 14, 83], [1, -17, 89], [1, 2, 97]], 'index': 5, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/23670/h'], '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': '2-23670-1.1-c1-0-5', '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': '2-23670-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.747941721740412, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1719096479023713601, 'z1': {'__RealLiteral__': 0, 'data': '0.5781456593998382', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1719096479023713601', 'Lhash_array': ['1719096479023713601'], 'factors': ['2-23670-1.1-c1-0-5'], 'label': '2-23670-1.1-c1-0-5', 'type': 'ECQ', 'url': 'EllipticCurve/Q/23670/h'}