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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '26323438588445324', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2075.4716493371207, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1]], [19, [1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '259920.1', 'coefficient_field': '1.1.1.1', 'conductor': 259920, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[1], [1], [1, 1], [1, 0, 7], [1, 0, 11], [1, 2, 13], [1, 0, 17], [1], [1, -6, 23], [1, -6, 29], [1, 2, 31], [1, 2, 37], [1, -6, 41], [1, 4, 43], [1, -10, 47], [1, -2, 53], [1, 8, 59], [1, -6, 61], [1, 4, 67], [1, -16, 71], [1, 10, 73], [1, 14, 79], [1, -12, 83], [1, -2, 89], [1, 8, 97]], 'gamma_factors': [[], [0]], 'index': 112, 'label': '2-259920-1.1-c1-0-112', 'leading_term': '7.1961395648', '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/259920/bt', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.54231890202438, 1.745279680395683, 0.3369032448436478, -1.199686931004433, -0.7495497458205267, 1.800623013090246, 3.730962991226182, 2.568889246557674, -0.3518091967155765, -1.294856084838395, 0.599487531353953, 1.913437739787662, 0.2987481918366134, -1.520105449389574, -0.1240344549091592, 2.5814609374618, 2.283890541704162, -0.2864103635712936, -0.6495927476765515, 1.122605825565616, 0.3996555291260953, -2.903173748587678, -3.215023704092337, 0.5118059437289488, 2.193710448740287, -0.5286993897762564, -2.124846256404844, 0.1303600786838256, 1.388406816734014, -0.3980233572873091, -0.3406831004186628, 2.618695253480212, 2.768167929062571, -0.557807200049713, -1.252370412942723, 0.7678563844327226, -0.5753285437486301, -3.965443970907469, -2.724275466442217, 0.922554668166222, 0.1282592207518255, -2.249027184469596, -0.1805886511559185, 2.384351287933683, 0.5930082356804466, -0.5328814332835754, 2.177833267176637, 2.670776898797125, -0.3941601107345595, -0.6302004861637661, 1.010503902774564, -1.360063759511629, -3.604867426002585, 0.005325979284117119, 2.97189839442002, 0.141899988396949, -1.271523147340975, 1.63338877969546, 1.613035862039754, -1.070102715978873, 0.2350182883953983, 2.235089652353256, 0.05752647969092189, -0.4478686967046566, 2.741049806846586, 1.995232816781687, -1.700663463352391, -0.798527802867812, 0.7980349923512897, -2.020983733104891, -2.157571536414184, 2.263508538330596, 2.099421616289573, -1.473118199361094, 0.05573966946652513, 2.60182578849539, 0.650562973535209, 0.1929015566258904, 2.018003749448717, -0.2147538163342027, -2.1352209363878, 1.328079371852524, 2.263676756409134, -1.160218537652149, -0.08885646630680409, 2.705917219151062, -0.06065384052681586, -1.500672610354463, 1.935788364517684, 1.330370878617538, -2.201206241157728, -0.8296282654839742, 0.4838862827811808, -1.585755731491275, 0.09314371239986859, 2.832354698087692, -0.2903503491779864, -2.215624228635798, 0.4385877847401008, -0.4493622037422106, -1.959874301760766, 2.31463695597831, 3.670345911975405, -0.619205347542448, -0.03656471604090252, 3.108488496401319, 0.8422141741937381, -0.5902621627216885, 1.162589789513604, -0.3442347336586833, -0.536680394454017, 3.61685712655839, 2.478513965541168, -2.098254354346105, -0.5738535955127921, 0.9955732303587727, -1.058303664141135, 1.584496841307313, 4.607513913981787, 0.6499284897568991], 'positive_zeros': ['0.7953891136586241', '1.337674626729268', '2.216529329517179', '2.686527574865745', '3.279809338385207', '3.760782865451362', '4.468001857599859', '4.843921128005130', '5.284247094493156', '5.967824488106377', '6.460922675458417', '6.988372842314857', '7.449698214971081', '7.785373355125114', '8.456415432351417', '8.894460913072334', '9.205854348136056', '9.918597060908297', '10.26069099687374', '10.76214762556946', '11.30691951107962', '11.57018178920738', '12.21476359608504', '12.57452289772409', '12.90587891835188', '13.49973807902200', '14.00961746069122', '14.37194084201923', '14.88275608306885', '15.23071510979412', '15.75527336153238', '16.04257209530603', '16.62040127001089', '17.07022333610290', '17.34988282128591', '17.87358130579448', '18.37900469995921', '18.74627211191057', '19.33149379727506', '19.46900409794198', '19.98577471787370'], 'prelabel': '2-259920-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 45.557344625615755, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 26323438588445324, 'z1': {'__RealLiteral__': 0, 'data': '0.7953891136586241', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.337674626729268', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.216529329517179', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2075.4716493371207, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 259920, 'conductor_radical': 570, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 1, 0, 0, 0, 6, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 6, 0, -4, 0, 0, 0, 10, 0, -7, 0, 0, 0, 2, 0, 0, 0, 0, 0, -8, 0, 6, 0, 0, 0, 2, 0, -4, 0, 0, 0, 16, 0, -10, 0, 0, 0, 0, 0, -14, 0, 0, 0, 12, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 2, 13], 'euler17': [1, 0, 17], 'euler19': [1, 0, 0], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 2, 31], 'euler37': [1, 2, 37], 'euler41': [1, -6, 41], 'euler43': [1, 4, 43], 'euler47': [1, -10, 47], 'euler5': [1, 1, 0], 'euler53': [1, -2, 53], 'euler59': [1, 8, 59], 'euler61': [1, -6, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 7], 'euler71': [1, -16, 71], 'euler73': [1, 10, 73], 'euler79': [1, 14, 79], 'euler83': [1, -12, 83], 'euler89': [1, -2, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 0], [1, 0, 7], [1, 0, 11], [1, 2, 13], [1, 0, 17], [1, 0, 0], [1, -6, 23], [1, -6, 29], [1, 2, 31], [1, 2, 37], [1, -6, 41], [1, 4, 43], [1, -10, 47], [1, -2, 53], [1, 8, 59], [1, -6, 61], [1, 4, 67], [1, -16, 71], [1, 10, 73], [1, 14, 79], [1, -12, 83], [1, -2, 89], [1, 8, 97]], 'index': 112, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/259920/bt'], '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': '2-259920-1.1-c1-0-112', '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': '2-259920-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 45.557344625615755, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 26323438588445324, 'z1': {'__RealLiteral__': 0, 'data': '0.7953891136586241', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '26323438588445324', 'Lhash_array': ['26323438588445324'], 'label': '2-259920-1.1-c1-0-112', 'type': 'ECQ', 'url': 'EllipticCurve/Q/259920/bt'}