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lfunc_lfunctions • Show schema
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{'Lhash': '688264621257668818418230580069', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.17364817766693036, -0.984807753012208], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.4396926207859084, 1.2080455471101075], 'a8': [0.0, 0.0], 'a9': [-0.9396926207859084, 0.3420201433256687], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8863394624362123, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.17364817766693036, 0.984807753012208]]], [37, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 37], 'central_character': '1776.929', 'coefficient_field': 'CDF', 'conductor': 1776, 'conductor_radical': 222, 'conjugate': '1900370162177041154685937021376', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.17364817766693036, 0.984807753012208]], [[1.0, 0], [0, 0], [0.17364817766693036, -0.984807753012208]], [[1.0, 0], [1.4396926207859084, 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'rational': False, 'root_analytic_conductor': 0.9414560331933788, 'root_angle': -0.30752625985560633, 'root_number': '0.56849398279175665006888820793157 - 0.82268742030589351526383185798051*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.15376312992780317', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.54294505215692146883286300459', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75931047402259033012746961469', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60346629829847162360796310563', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8863394624362123, 'bad_primes': [2, 3, 37], 'central_character': '111.41', 'conductor': 1776, 'conductor_radical': 222, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1776/1/dk/a/929/1'], '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': '2-1776-111.41-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1776-111.41-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9414560331933788, 'root_angle': -0.15376312992780317, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.54294505215692146883286300459', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '688264621257668818418230580069', 'Lhash_array': ['688264621257668818418230580069'], 'label': '2-1776-111.41-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1776/1/dk/a/929/1'}