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lfunc_lfunctions • Show schema
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{'Lhash': '569113272300419218017253722122', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.618033988749895, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.6180339887498949, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.38196601125010515, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 60.81406617940717, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 7, 17], 'central_character': '7616.1', 'coefficient_field': 'CDF', 'conductor': 7616, 'conductor_radical': 238, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.618033988749895, 0], [3.0, 0]], [[1.0, 0], [0.6180339887498949, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.7639320225002103, 0], [11.0, 0]], [[1.0, 0], [1.2360679774997898, 0], [13.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [8.47213595499958, 0], [19.0, 0]], [[1.0, 0], 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'4.98042881469667387876819810877821', '5.80776637951241252556581362967164', '6.43328215411556502267113282877537', '7.07108608951389518664019393259714', '7.85321447766400466279884035026078'], 'prelabel': '2-7616-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.798337398407892, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44895121116020088799937542157', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.69010823860617216346377122733', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.66819410727380007603645683899', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 60.81406617940717, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 7616, 'conductor_radical': 238, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7616/2/a/p/1/1'], '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': '2-7616-1.1-c1-0-21', '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': '2-7616-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.798337398407892, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44895121116020088799937542157', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '569113272300419218017253722122', 'Lhash_array': ['569113272300419218017253722122'], 'label': '2-7616-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7616/2/a/p/1/1'}