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lfunc_lfunctions • Show schema
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{'Lhash': '3228273893851701411803967033021', 'a10': [-0.8019377358048383, 0.0], 'a2': [0.8019377358048383, 0.0], 'a3': [1.6920214716300959, 0.0], 'a4': [-1.3568958678922094, 0.0], 'a5': [-1.0, 0.0], 'a6': [1.3568958678922094, 0.0], 'a7': [-1.0, 0.0], 'a8': [-2.692021471630096, 0.0], 'a9': [-0.13706333954272468, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.427957362713074, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 7, 23], 'central_character': '805.1', 'coefficient_field': 'CDF', 'conductor': 805, 'conductor_radical': 805, 'conjugate': '3228273893851701411803967033021', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8019377358048383, 0], [2.0, 0]], [[1.0, 0], [-1.6920214716300959, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.801937735804838, 0], [11.0, 0]], [[1.0, 0], [4.542876546957239, 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'4.30294272305617922110948871446375', '5.15398351663416817176671487953396', '6.16210499881621762735684485021915', '7.59960726974466287279060004096329', '8.048140721938519622070096694678501', '8.984847345582920926673361043673937', '9.692231273254223181823404317904514'], 'prelabel': '2-805-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.535341665873275, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.54665906620521375314917062626', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.20990569499169791234434488287', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.30294272305617922110948871446', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.427957362713074, 'bad_primes': [5, 7, 23], 'central_character': '1.1', 'conductor': 805, 'conductor_radical': 805, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/805/2/a/f/1/3'], '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': '2-805-1.1-c1-0-41', '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': '2-805-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.535341665873275, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.54665906620521375314917062626', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3228273893851701411803967033021', 'Lhash_array': ['3228273893851701411803967033021'], 'label': '2-805-1.1-c1-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/805/2/a/f/1/3'}