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lfunc_lfunctions • Show schema
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{'Lhash': '3928045244579042356279287974807', 'a10': [0.3339325736260828, 0.9174722056580306], 'a2': [1.2812060638360745, -1.0750595356269448], 'a3': [0.6584375905694375, -1.6020174591199416], 'a4': [0.1384396175340445, -0.7851300860356556], 'a5': [-0.19966124078180236, 0.5485647505882943], 'a6': [-0.8786699119725645, -2.7603740933526337], 'a7': [-1.2576328403963226, -2.1782839768335913], 'a8': [1.005803826627858, 1.7421033301666482], 'a9': [-2.1329198786502275, -2.1096570316662135], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.6584375905694375, 1.6020174591199416]]], [19, [[1.0, 0], [3.470081813666067, -2.6379029941345493]]]], 'bad_primes': [3, 19], 'central_character': '171.110', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '2390853432861775543532654197625', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[-83.63264324994584, -30.439792755984517]], [[1.0, 0], [2.3559015906001255, 2.8076541843961134], [-16.843873233692243, 95.52635204218419]], [[1.0, 0], [-5.712845691653982, 6.808304376964987], [-17.538465944359967, -99.46558305423301]], [[1.0, 0], [0.24025275588929954, 0.13870999328623654], [51.5, 89.20061658979718]], [[1.0, 0], [-2.990558772424835, 5.179799736860625], [-53.5, -92.66471820493493]], [[1.0, 0], [-5.963227029017488, -7.106697235286489], [-18.927651365695407, 107.34404507833068]], [[1.0, 0], [10.043487383946161, 17.395830434171778], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-171-171.110-c1-0-16', '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/171/2/x/a/110/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.09868132738771406845118059381', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.26975440490490606662714995763', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.53466843670101034658905479857', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '171.110', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/x/a/110/14'], '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': '2-171-171.110-c1-0-16', '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': '2-171-171.110-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.23428642212334044, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.09868132738771406845118059381', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3928045244579042356279287974807', 'Lhash_array': ['3928045244579042356279287974807'], 'label': '2-171-171.110-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/x/a/110/14'}