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lfunc_lfunctions • Show schema
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{'Lhash': '1786577406199099314040221856005', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.5244586697611526, -0.3479477433504717], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.7818314824680298, 0.6234898018587335], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.46313233172342627, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [-0.7818314824680298, 0.6234898018587335]]]], 'bad_primes': [2, 29], 'central_character': '928.193', 'coefficient_field': 'CDF', 'conductor': 928, 'conductor_radical': 58, 'conjugate': '1365747966741215000009471980900', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.7818314824680298, -0.6234898018587335]], [[1.0, 0], [1.5244586697611526, 0.3479477433504717], [0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [0, 0], [0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [0, 0], 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'9.505775998147763574491798699711796', '10.42195329414409723608940135567815'], 'prelabel': '2-928-29.19-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6805382661712905, 'root_angle': 0.14938507905322299, 'root_number': '0.89188189401752942051164772744748 + 0.45226837953111913135132485052091*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.07469253952661148', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40936106990162879311051470072', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.41997989777306363497619921353', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83332625637441541170774250405', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.46313233172342627, 'bad_primes': [2, 29], 'central_character': '29.19', 'conductor': 928, 'conductor_radical': 58, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/928/1/bs/a/193/1'], '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': '2-928-29.19-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-928-29.19-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6805382661712905, 'root_angle': 0.07469253952661149, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40936106990162879311051470072', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1786577406199099314040221856005', 'Lhash_array': ['1786577406199099314040221856005'], 'label': '2-928-29.19-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/928/1/bs/a/193/1'}