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lfunc_lfunctions • Show schema
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{'Lhash': '2967441408773803938881924802227', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.766044443118978, -0.6427876096865394], 'a4': [0.17364817766693036, -0.984807753012208], 'a5': [-0.6736481776669303, -1.8508331567966467], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.17364817766693036, 0.984807753012208], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.630445396272019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.766044443118978, 0.6427876096865394]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '3267.2300', 'coefficient_field': 'CDF', 'conductor': 3267, 'conductor_radical': 33, 'conjugate': '357509556352508302302937068447', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.17364817766693036, 0.984807753012208]], [[1.0, 0], [0.766044443118978, 0.6427876096865394]], [[1.0, 0], [0.6736481776669303, 1.8508331567966467], [-0.766044443118978, 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'0.41417411194608647548209019679961', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3267/1/q/a/2300/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.4141741119460865, 0.5198693576933293, 0.6394627734664194, 0.7761331040624627, 0.9325313823226923, 1.1105976484080768, 1.311472668038418, 1.5354741574074924, 1.7821056106070736, 2.050076223421981, 2.3373222669609794, 2.641028700266743, 2.957654269050192, 3.282964952754605, 3.6120806225384086, 3.9395389860534404, 4.259379768441958, 4.565250821938671, 4.850536557775246, 5.108507792753758, 5.332490823115686, 5.516052304767998, 5.6531953616168265, 5.738561298837948, 5.767630406131006, 5.736914640417618, 5.644134520733051, 5.488372389693675, 5.270194329290317, 4.991733488410253, 4.656728398578742, 4.27051102247325, 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'prelabel': '2-3267-27.5-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': -0.6296296296296297, 'root_number': '-0.39607976603915682369604339161009 - 0.91821610688027401475896141531460*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3148148148148148', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.34089851591561749872558152667', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.12769073541937506830247325078', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.98175038357704093492069605889', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.630445396272019, 'bad_primes': [3, 11], 'central_character': '27.5', 'conductor': 3267, 'conductor_radical': 33, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3267/1/q/a/2300/1'], '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': '2-3267-27.5-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3267-27.5-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': -0.3148148148148148, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.34089851591561749872558152667', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2967441408773803938881924802227', 'Lhash_array': ['2967441408773803938881924802227'], 'label': '2-3267-27.5-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3267/1/q/a/2300/1'}