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lfunc_lfunctions • Show schema
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{'Lhash': '784996490565573266932440914566', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.7269218729004554, -0.133194763027618], 'a4': [0.0, 0.0], 'a5': [-4.222962936514775, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.3780237962028683, -1.159742568285264], 'a8': [0.0, 0.0], 'a9': [2.9645183102040336, 0.4600338992563729], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.024460261872533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.7269218729004554, 0.133194763027618]]], [7, [[1.0, 0], [2.3780237962028683, 1.159742568285264]]]], 'bad_primes': [2, 3, 7], 'central_character': '504.457', 'coefficient_field': 'CDF', 'conductor': 504, 'conductor_radical': 42, 'conjugate': '1057379841560219175410781956307', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.7269218729004554, 0.133194763027618]], [[1.0, 0], [4.222962936514775, 0], [5.0, 0]], [[1.0, 0], [2.3780237962028683, 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'7.913213547258601945339693870054218', '9.264181684218671813758245851407578', '9.993835846361120890222544113163977', '11.24752251620071133239241736319735'], 'prelabel': '2-504-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': -0.10451232865576386, 'root_number': '0.9465805107434639 - 0.322467574618973*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0522561643279', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61925304214287558081790021112', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21775095225591091225620571640', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.09596258707585516849540996857', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.024460261872533, 'bad_primes': [2, 3, 7], 'central_character': '63.16', 'conductor': 504, 'conductor_radical': 42, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/504/2/t/c/457/1'], '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': '2-504-63.16-c1-0-6', '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': '2-504-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': -0.05225616432788193, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61925304214287558081790021112', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '784996490565573266932440914566', 'Lhash_array': ['784996490565573266932440914566'], 'label': '2-504-63.16-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/504/2/t/c/457/1'}