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lfunc_lfunctions • Show schema
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{'Lhash': '2974457608670804510347662503654', 'a10': [0.4118440787747781, 2.8644384860288903], 'a2': [0.41541501300188644, -0.9096319953545183], 'a3': [0.0, 0.0], 'a4': [-0.6548607339452851, -0.7557495743542583], 'a5': [-2.434498682277761, 1.5645573020676402], 'a6': [0.0, 0.0], 'a7': [0.3943064548886837, -2.7424616326472004], 'a8': [-0.9594929736144974, 0.28173255684142967], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3058066436810094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.41541501300188644, 0.9096319953545183]]], [3, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-0.9655010956826228, 4.697638516769426]]]], 'bad_primes': [2, 3, 23], 'central_character': '414.397', 'coefficient_field': 'CDF', 'conductor': 414, 'conductor_radical': 138, 'conjugate': '519987835727894043567408083055', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.41541501300188644, 0.9096319953545183]], [[1.0, 0], [0, 0]], 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47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.34643332171757693932392622661', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.08359950865950002198377982291', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.83177775159997837715305187959', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3058066436810094, 'bad_primes': [2, 3, 23], 'central_character': '23.6', 'conductor': 414, 'conductor_radical': 138, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/414/2/i/b/397/1'], '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': '2-414-23.6-c1-0-9', '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': '2-414-23.6-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8181877360935557, 'root_angle': 0.46009155786605516, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.34643332171757693932392622661', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2974457608670804510347662503654', 'Lhash_array': ['2974457608670804510347662503654'], 'factors': ['2-414-23.6-c1-0-9'], 'label': '2-414-23.6-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/414/2/i/b/397/1'}