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lfunc_lfunctions • Show schema
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{'Lhash': '2140757634150064294498277687770', 'a10': [-1.8676365892166082, -1.229607079769531], 'a2': [0.9396926207859084, -0.3420201433256687], 'a3': [-0.43468605881498174, 1.1942901311458862], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [-1.3344539315395776, -1.7942220332496657], 'a6': [1.9448315616246206e-61, 1.270937011452794], 'a7': [2.396274647637323, -0.4225278735661299], 'a8': [0.5, -0.8660254037844386], 'a9': [1.0607563817325778, 0.8900802886807522], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9396926207859084, 0.3420201433256687]]], [5, [[1.0, 0], [1.3344539315395776, 1.7942220332496657]]], [37, [[1.0, 0], [-5.803617200649803, 1.8215453297466282]]]], 'bad_primes': [2, 5, 37], 'central_character': '370.289', 'coefficient_field': 'CDF', 'conductor': 370, 'conductor_radical': 370, 'conjugate': 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{'__RealLiteral__': 0, 'data': '0.0455810950638', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68876000513441133483854427764', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.38293790656414954238677931827', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.39409280606608460230005167476', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'bad_primes': [2, 5, 37], 'central_character': '185.104', 'conductor': 370, 'conductor_radical': 370, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/370/2/v/b/289/3'], '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': '2-370-185.104-c1-0-11', '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': '2-370-185.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': 0.04558109506378805, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68876000513441133483854427764', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2140757634150064294498277687770', 'Lhash_array': ['2140757634150064294498277687770'], 'label': '2-370-185.104-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/370/2/v/b/289/3'}