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lfunc_lfunctions • Show schema
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{'Lhash': '1432118655148123848848293691596', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-3.0, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.64830368017082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, -3.3166247903554]]]], 'bad_primes': [2, 3, 11], 'central_character': '1584.703', 'coefficient_field': 'CDF', 'conductor': 1584, 'conductor_radical': 66, 'conjugate': '434841680797740104103080735138', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.0, 0], [5.0, 0]], [[1.0, 0], [0, 0], [7.0, 0]], [[1.0, 0], [0, -3.3166247903554]], [[1.0, 0], [0, 0], [-13.0, 0]], [[1.0, 0], [0, 0], [-17.0, 0]], [[1.0, 0], [0, 0], [19.0, 0]], [[1.0, 0], [0, 3.3166247903554], [-23.0, 0]], [[1.0, 0], [0, 0], [-29.0, 0]], [[1.0, 0], [0, 9.9498743710662], [-31.0, 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3.5564453714588136, 'root_angle': 0.5, 'root_number': '0.e-55 + 1.0000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12974241868404701799265172265', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.89569895439985644400896794507', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.63200033997258241259008051521', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.64830368017082, 'bad_primes': [2, 3, 11], 'central_character': '44.43', 'conductor': 1584, 'conductor_radical': 66, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1584/2/o/a/703/2'], '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': '2-1584-44.43-c1-0-16', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1584-44.43-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5564453714588136, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12974241868404701799265172265', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1432118655148123848848293691596', 'Lhash_array': ['1432118655148123848848293691596'], 'label': '2-1584-44.43-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1584/2/o/a/703/2'}