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lfunc_lfunctions • Show schema
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{'Lhash': '978936546018269276394163394270', 'a10': [0.0, 0.0], 'a2': [-2.700742776162394, 0.0], 'a3': [9.0, 0.0], 'a4': [-24.705988457006647, 0.0], 'a5': [0.0, 0.0], 'a6': [-24.306684985461544, 0.0], 'a7': [-73.49004914935172, 0.0], 'a8': [153.14828869040878, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 132.31665134570906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-9.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.700742776162394, 0], [32.0, 0]], [[1.0, 0], [-9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [73.49004914935172, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [-1058.3042797219694, 0], [371293.0, 0]], [[1.0, 0], [-1854.0857511624379, 0], [1419857.0, 0]], [[1.0, 0], 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-2.235328202947078], 'positive_zeros': ['0.77224476984590258132901426726861', '1.52961194932198781301557134126114', '3.36964060725435515413598707137275', '3.65569328064232813788006389996237', '5.05160025033866913473700757949656', '5.97374694437684774856541383898185', '7.14032208320914009892878391845701', '8.003021698151049031017673215322031', '8.708646009914872151917790068389974', '9.387284255263875154375756798398403'], 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77224476984590258132901426727', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.52961194932198781301557134126', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36964060725435515413598707137', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 132.31665134570906, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 57, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/6/a/t/1/5'], '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': '2-825-1.1-c5-0-57', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77224476984590258132901426727', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '978936546018269276394163394270', 'Lhash_array': ['978936546018269276394163394270'], 'label': '2-825-1.1-c5-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/6/a/t/1/5'}