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lfunc_lfunctions • Show schema
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{'Lhash': '2766044627245462170173306481926', 'a10': [-0.9623362248530434, 1.4114880013959283], 'a2': [0.5689075422784095, -0.22327975686121135], 'a3': [0.0, 0.0], 'a4': [-1.192301801822394, 1.1062944001089736], 'a5': [-2.309544221831998, 1.5746205886064262], 'a6': [0.0, 0.0], 'a7': [0.09534665990134551, -2.644032718111797], 'a8': [-0.9616362135600036, 1.9968581731761526], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.09534665990134551, 2.644032718111797]]]], 'bad_primes': [3, 7], 'central_character': '441.278', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '40573911836847038055373597176', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5689075422784095, 0.22327975686121135], [1.4661037436596527, -1.3603454755418387]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.18202446853057146162310991635', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.23446286729220273411691576354', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.51084548037325553814084355476', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'bad_primes': [3, 7], 'central_character': '147.131', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/bg/a/278/11'], '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': '2-21e2-147.131-c1-0-14', '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': '2-21e2-147.131-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.45773467376089305, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.18202446853057146162310991635', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2766044627245462170173306481926', 'Lhash_array': ['2766044627245462170173306481926'], 'label': '2-21e2-147.131-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/bg/a/278/11'}