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lfunc_lfunctions • Show schema
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{'Lhash': '598255051657041490029385426096', 'a10': [-0.763473852459645, 0.4047682190568396], 'a2': [0.09355081141188024, 0.037274050068094804], 'a3': [1.7218974515240826, 0.18726763317474265], 'a4': [-2.896619568185181, -2.7438238001567385], 'a5': [-5.5552353135874855, 6.540128610769586], 'a6': [0.15410468062303767, 0.08170113085491301], 'a7': [5.526842437680387, 3.3253907605699706], 'a8': [-0.33784417840886877, -0.7302382244822596], 'a9': [2.92986166713026, 0.6449113206330722], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.8229006791772555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.7218974515240826, -0.18726763317474265]]], [59, [[1.0, 0], [-41.84164971481138, 41.59659059518009]]]], 'bad_primes': [3, 59], 'central_character': '177.10', 'coefficient_field': 'CDF', 'conductor': 177, 'conductor_radical': 177, 'conjugate': '3034175227029160523098918524350', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[6095.088888186651, -1341.6305173570013]], [[1.0, 0], [-40.99952899642627, -121.68226583166785], [-5484.2851296461795, 4169.045168469848]], [[1.0, 0], [33.23574337248955, -13.242330492060313], [5750.6102915231195, -5447.267413577966]], [[1.0, 0], [43.65827716225131, -57.431481442736484], [-2517.1741372214387, -9066.041879613369]], [[1.0, 0], [-74.99669966866512, -124.64548447344116], [-4778.234503578559, 9012.70636539388]], [[1.0, 0], [-16.555492593510397, -17.477421037228286], [-574.3596811826945, 10593.440987546574]], [[1.0, 0], [2.138680339331201, -39.44563782624681], [-11381.885471460264, -1237.8546419357092]], [[1.0, 0], [21.17992261512536, -96.22135849922128], [-10782.903561110641, -4988.702415637504]], [[1.0, 0], [-82.34313160548477, -69.9428864094377], [2065.794313982253, 12600.787866332748]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-177-59.10-c2-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/177/3/g/a/10/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8463172298158471, 0.6366699084528221, 0.41734791789614517, 0.18697069609010133, -0.05551892374411293, -0.31040718926624267, -0.576816013340006, -0.852392421559085, -1.1331014886727098, -1.413137960407901, -1.6849687312473225, -1.9395161003512982, -2.166488401045192, -2.354858840389708, -2.493484609414359, -2.5718466887852465, -2.5808770453416607, -2.5138253286515275, -2.3671033174517246, -2.1410340430914974, -1.840425624267736, -1.4748891875742816, -1.058827328512988, -0.6110353724873488, -0.15388246475317705, 0.2879274441979617, 0.6889751057318325, 1.025043160750547, 1.2752051970534253, 1.423922689499052, 1.4629574952925333, 1.392893967494047, 1.2240700545334458, 0.976743805261673, 0.6803713825636815, 0.37194346056786015, 0.09341449604284092, 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'root_analytic_conductor': 2.1961103522312477, 'root_angle': -0.6858647827942187, 'root_number': '-0.5512915065324806 - 0.8343126960709323*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.342932391397', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.47194002160321692851053913859', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.04268706414867168382599763682', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.55009671767371279583566686442', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.8229006791772555, 'bad_primes': [3, 59], 'central_character': '59.10', 'conductor': 177, 'conductor_radical': 177, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/177/3/g/a/10/10'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-177-59.10-c2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-177-59.10-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1961103522312477, 'root_angle': -0.34293239139710935, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.47194002160321692851053913859', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '598255051657041490029385426096', 'Lhash_array': ['598255051657041490029385426096'], 'label': '2-177-59.10-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/177/3/g/a/10/10'}