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lfunc_lfunctions • Show schema
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{'Lhash': '1577575279404169606924626322622', 'a10': [2.23606797749979, 3.872983346207417], 'a2': [1.118033988749895, -1.9364916731037085], 'a3': [1.618033988749895, 2.802517076888147], 'a4': [-1.5, -2.598076211353316], 'a5': [-1.0, 1.7320508075688772], 'a6': [7.23606797749979, 9.52203041677556e-61], 'a7': [0.0, 0.0], 'a8': [-2.23606797749979, 0.0], 'a9': [-3.73606797749979, 6.471059557560733], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.303936668947014, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [7, 11], 'central_character': '539.177', 'coefficient_field': 'CDF', 'conductor': 539, 'conductor_radical': 77, 'conjugate': '2899799040952815732285013204448', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.118033988749895, 1.9364916731037085], [-1.0, -1.7320508075688772]], [[1.0, 0], [-1.618033988749895, -2.802517076888147], [-1.5, 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'11.14887764763805061681379492241730'], 'prelabel': '2-539-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0745931333509744, 'root_angle': -0.0806918122157845, 'root_number': '0.9680403732843879 - 0.25079440921085727*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0403459061079', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24448746296506385756608264342', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.02569756970455851140797070376', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.20184981005406760522424458129', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.303936668947014, 'bad_primes': [7, 11], 'central_character': '7.2', 'conductor': 539, 'conductor_radical': 77, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/539/2/e/j/177/2'], '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': '2-539-7.2-c1-0-14', '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': '2-539-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0745931333509744, 'root_angle': -0.04034590610789225, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24448746296506385756608264342', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1577575279404169606924626322622', 'Lhash_array': ['1577575279404169606924626322622'], 'label': '2-539-7.2-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/539/2/e/j/177/2'}