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lfunc_lfunctions • Show schema
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{'Lhash': '3311998325626537857088061550635', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.1705015243094106, 0.11176934382516301], 'a4': [0.0, 0.0], 'a5': [-1.3674943756534763, -3.9511155157867606], 'a6': [0.0, 0.0], 'a7': [-0.9660880798413872, -2.463061879447689], 'a8': [0.0, 0.0], 'a9': [-1.588204659596574, 0.3061013584443988], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.142365890170459, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.9660880798413872, 2.463061879447689]]], [23, [[1.0, 0], [0.23451690666253555, -4.790094134825477]]]], 'bad_primes': [2, 7, 23], 'central_character': '644.233', 'coefficient_field': 'CDF', 'conductor': 644, 'conductor_radical': 322, 'conjugate': '136777895637696226186233700730', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.1705015243094106, -0.11176934382516301], [2.9457860917881202, -0.5677537330812306]], [[1.0, 0], 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'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.61270599724422607542659210605', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.20393371923938140093852392238', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.70921212830919264218889702613', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.142365890170459, 'bad_primes': [2, 7, 23], 'central_character': '161.72', 'conductor': 644, 'conductor_radical': 322, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/644/2/y/a/233/5'], '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': '2-644-161.72-c1-0-15', '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': '2-644-161.72-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2676785244320805, 'root_angle': -0.39684725292774337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.61270599724422607542659210605', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3311998325626537857088061550635', 'Lhash_array': ['3311998325626537857088061550635'], 'label': '2-644-161.72-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/644/2/y/a/233/5'}