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lfunc_lfunctions • Show schema
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{'Lhash': '2644344403244053317777814930475', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, -1.7320508075688772], 'a6': [0.0, 0.0], 'a7': [1.7320508075688772, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6068630553617309, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 19], 'central_character': '1216.417', 'coefficient_field': 'CDF', 'conductor': 1216, 'conductor_radical': 38, 'conjugate': '1345825222469140079856594361868', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-1.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 1.0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], 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'0.25881904510252076234889883762393 + 0.96592582628906828674974319972852*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.20833333333333334', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.08601991965922016682182788152', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68253133036454636010506112612', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05939879201996381022235652347', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6068630553617309, 'bad_primes': [2, 19], 'central_character': '152.37', 'conductor': 1216, 'conductor_radical': 38, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1216/1/g/b/417/2'], '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': '2-1216-152.37-c0-0-4', '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': '2-1216-152.37-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7790141560727448, 'root_angle': 0.20833333333333334, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.08601991965922016682182788152', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2644344403244053317777814930475', 'Lhash_array': ['2644344403244053317777814930475'], 'label': '2-1216-152.37-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/1/g/b/417/2'}