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lfunc_lfunctions • Show schema
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{'Lhash': '576993309722647664393131936650', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.36602540378443865, 0.36602540378443865], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.868499407297961, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0.8660254037844386, -0.5]]]], 'bad_primes': [2, 3, 13], 'central_character': '3744.2017', 'coefficient_field': 'CDF', 'conductor': 3744, 'conductor_radical': 78, 'conjugate': '1850579437379105403421044352501', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.36602540378443865, -0.36602540378443865], [0, -1.0]], [[1.0, 0], [0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0.8660254037844386, 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103}, 'z3': {'__RealLiteral__': 0, 'data': '2.83876289848417107042140460102', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.868499407297961, 'bad_primes': [2, 3, 13], 'central_character': '13.2', 'conductor': 3744, 'conductor_radical': 78, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3744/1/gs/c/2017/1'], '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': '2-3744-13.2-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': '2-3744-13.2-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3669306519710358, 'root_angle': -0.28756204857686696, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.45516746461427546862159337261', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '576993309722647664393131936650', 'Lhash_array': ['576993309722647664393131936650'], 'label': '2-3744-13.2-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3744/1/gs/c/2017/1'}