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lfunc_lfunctions • Show schema
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{'Lhash': '3975619810604153378176842603618', 'a10': [2.457206913390737, 0.0], 'a2': [-0.6306443807544658, 0.0], 'a3': [2.338062240113569, 0.0], 'a4': [-1.6022876650228164, 0.0], 'a5': [-3.8963431505582897, 0.0], 'a6': [-1.4744858135818208, 0.0], 'a7': [-3.682314943105496, 0.0], 'a8': [2.271762473807765, 0.0], 'a9': [2.46653503864488, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9243946887128582, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[241, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [241], 'central_character': '241.1', 'coefficient_field': 'CDF', 'conductor': 241, 'conductor_radical': 241, 'conjugate': '3975619810604153378176842603618', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6306443807544658, 0], [2.0, 0]], [[1.0, 0], [-2.338062240113569, 0], [3.0, 0]], [[1.0, 0], [3.8963431505582897, 0], [5.0, 0]], [[1.0, 0], [3.682314943105496, 0], [7.0, 0]], [[1.0, 0], [4.964307234345302, 0], [11.0, 0]], [[1.0, 0], 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'5.12427730936274790035134874150087', '7.29897276924746874175733809289259', '7.908998052440644390690202248352153', '8.489925672175542386946953323801056', '9.695344026124302163756742099127947', '10.17434043997518723376568310916784', '11.79063960355224178040041347396943'], 'prelabel': '2-241-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3872255363540775, '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': '3.13621104260777994263964962567', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.63381427959368206018850117794', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.12427730936274790035134874150', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9243946887128582, 'bad_primes': [241], 'central_character': '1.1', 'conductor': 241, 'conductor_radical': 241, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/241/2/a/a/1/4'], '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': '2-241-1.1-c1-0-17', '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': '2-241-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3872255363540775, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.13621104260777994263964962567', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3975619810604153378176842603618', 'Lhash_array': ['3975619810604153378176842603618'], 'label': '2-241-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/241/2/a/a/1/4'}