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lfunc_lfunctions • Show schema
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{'Lhash': '1941373902804309272484969482025', 'a10': [-0.5894079398726905, 1.285534239300934], 'a2': [1.3257843292263527, -0.492235626888008], 'a3': [0.0, 0.0], 'a4': [1.5154081752443396, -1.3051965608300617], 'a5': [-0.7071067811865476, 0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [0.0, 2.0544636061476074], 'a8': [1.3666401637881904, -2.4763470400412353], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.749228945532191, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.3257843292263527, 0.492235626888008]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 3, 5], 'central_character': '720.541', 'coefficient_field': 'CDF', 'conductor': 720, 'conductor_radical': 30, 'conjugate': '1750719871014443680040571667714', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3257843292263527, 0.492235626888008]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53147397433865600183037867026', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.23994398858375432615666458560', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.09001784943550083066879856404', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.749228945532191, 'bad_primes': [2, 3, 5], 'central_character': '16.13', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/2/t/e/541/15'], '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': '2-720-16.13-c1-0-23', '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': '2-720-16.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.397754980295566, 'root_angle': 0.08617895140413574, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53147397433865600183037867026', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1941373902804309272484969482025', 'Lhash_array': ['1941373902804309272484969482025'], 'label': '2-720-16.13-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/2/t/e/541/15'}