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lfunc_lfunctions • Show schema
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{'Lhash': '1835711132138954501320525137281', 'a10': [5.794550024544673, 4.862204788433734], 'a2': [-1.8225366559053315, -1.931775997188624], 'a3': [0.0, 0.0], 'a4': [-0.29382898337456204, 5.044848815206147], 'a5': [-2.8289158351965047, 0.3306528393341602], 'a6': [0.0, 0.0], 'a7': [1.7094162628648777, 0.8585011141910003], 'a8': [6.212074303454833, -5.212549256874809], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.109', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '33161926640919549124546181996', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.8225366559053315, 1.931775997188624], [-0.11628965782095166, 1.9966163165425364]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.8289158351965047, -0.3306528393341602], [4.865224352899119, -1.1530793537122008]], 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.44812074542342406519397171073', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.78566536414404686306820919691', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.91353870057884672784692227481', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '81.22', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/g/b/109/1'], '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': '2-3e6-81.22-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': '2-3e6-81.22-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.348522097480238, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44812074542342406519397171073', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1835711132138954501320525137281', 'Lhash_array': ['1835711132138954501320525137281'], 'label': '2-3e6-81.22-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/g/b/109/1'}