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lfunc_lfunctions • Show schema
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{'Lhash': '405684186897871652743632774413', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.8399081983895975, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.36998814595924, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '4680.1', 'coefficient_field': 'CDF', 'conductor': 4680, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.8399081983895975, 0], [7.0, 0]], [[1.0, 0], [2.2551050279403553, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [6.329698142508887, 0], [17.0, 0]], [[1.0, 0], [2.5848031704492422, 0], [19.0, 0]], [[1.0, 0], [4.8399081983895975, 0], [23.0, 0]], [[1.0, 0], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-4680-1.1-c1-0-0', 'leading_term': '0.39564083236272541679617676706732', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4680/2/a/bh/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.3956408323627254, 0.3857314034247179, 0.35597835770085323, 0.30631489967417697, 0.2366541204815382, 0.14692385739454697, 0.03711215292288753, -0.09267962992812581, -0.2421793335212022, -0.4108855804222494, -0.598011711268451, -0.8024351551658712, -1.0226549612308067, -1.2567598280172878, -1.5024085560137868, -1.756824434084551, -2.01680465895924, -2.2787454753449543, -2.5386833072054427, -2.792351722434112, -3.035253630074166, -3.2627476516264187, -3.4701471402597748, -3.65282985246367, -3.806355818077966, 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'5.57686208155334947777720405416589', '6.13484908617887122548345975936169', '6.89977806415916137912556072150794', '7.45059995352314743278744328709820', '8.307570557854964803566252735020317'], 'prelabel': '2-4680-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.113099716670687, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.32002839491010516913047561627', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.19200091241778254745470924294', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.83528862120194662445192562441', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 37.36998814595924, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 4680, 'conductor_radical': 390, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4680/2/a/bh/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': '2-4680-1.1-c1-0-0', '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': '2-4680-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.113099716670687, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.32002839491010516913047561627', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '405684186897871652743632774413', 'Lhash_array': ['405684186897871652743632774413'], 'label': '2-4680-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4680/2/a/bh/1/1'}