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lfunc_lfunctions • Show schema
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{'Lhash': '627093001665510155840264818454', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.224744871391589, -1.224744871391589], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [4.775255128608411, 4.775255128608411], 'a8': [0, 0], 'a9': [0, -3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.69763172323563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.224744871391589, 1.224744871391589]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1200.1057', 'coefficient_field': 'CDF', 'conductor': 1200, 'conductor_radical': 30, 'conjugate': '1682271474483199271578213499927', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.224744871391589, 1.224744871391589]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.775255128608411, -4.775255128608411], [0, 49.0]], [[1.0, 0], [20.69693845669907, 0], [121.0, 0]], [[1.0, 0], [-8.325765385825234, 8.325765385825234], [0, -169.0]], 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{'__RealLiteral__': 0, 'data': '-0.19708054137514797', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49468915295161580528199684779', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16099170220949301263563291237', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.03964902260561882728975641963', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.69763172323563, 'bad_primes': [2, 3, 5], 'central_character': '5.2', 'conductor': 1200, 'conductor_radical': 30, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1200/3/bg/p/1057/2'], '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': '2-1200-5.2-c2-0-10', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1200-5.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.718184303013993, 'root_angle': -0.19708054137514794, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.49468915295161580528199684779', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '627093001665510155840264818454', 'Lhash_array': ['627093001665510155840264818454'], 'label': '2-1200-5.2-c2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1200/3/bg/p/1057/2'}