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lfunc_lfunctions • Show schema
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{'Lhash': '1629640730691740697958648582299', 'a10': [-1.9628954182006662, -3.399834594267713], 'a2': [-2.2586098703892405, 1.3040090166635738], 'a3': [-0.5, -0.8660254037844386], 'a4': [2.400879031079801, -4.158444464656953], 'a5': [0.0, 1.5052774889723641], 'a6': [2.2586098703892405, 1.3040090166635738], 'a7': [-0.8660254037844386, -0.5], 'a8': [0.0, 7.307035551131967], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [0.8660254037844386, 0.5]]], [13, [[1.0, 0], [1.3033153797328796, 3.36175088621268]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.127', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '966670176185300862805946362827', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.2586098703892405, -1.3040090166635738], [1.0, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-273-13.10-c1-0-6', '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/273/2/bd/a/127/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.49185652909854866, 0.5205223821263715, 0.5406253484910696, 0.5508181155387358, 0.5482442310728654, 0.5290153511785044, 0.48879084497165876, 0.42339061522162436, 0.3294088682892753, 0.20481475169603316, 0.04952367708460911, -0.1340901832757751, -0.3407852391105503, -0.5622045635222375, -0.7868507521592014, -1.0003423092174666, -1.185997706642967, -1.3257711398827963, -1.401532974407447, -1.3966495852781204, -1.2977745523280375, -1.096719978788009, -0.7922380497371891, -0.39151447509349585, 0.08883711133976882, 0.622482309526702, 1.1739441150253995, 1.700162388718486, 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'9.753931775434619153373476844398804', '10.84357067047201607727327422666145', '11.74967548827776552999295846883351'], 'prelabel': '2-273-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.053021975664646, 'root_number': '0.9861586916911234 + 0.16580420622545125*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0265109878323', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28555986199851768307966132343', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.97811001665262521775832877720', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.37738897376545960411673567704', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '13.10', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/1'], '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': '2-273-13.10-c1-0-6', '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': '2-273-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.026510987832323, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28555986199851768307966132343', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1629640730691740697958648582299', 'Lhash_array': ['1629640730691740697958648582299'], 'label': '2-273-13.10-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/1'}