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  • lfunc_lfunctions • Show schema
    {'Lhash': '3627058072186252587828233725974', 'a10': [-1.464144513576055, 1.464144513576055], 'a2': [0.0, -2.070613028373415], 'a3': [1.7843574765522912, 1.7843574765522912], 'a4': [-2.287438313269725, 0.0], 'a5': [-0.7071067811865476, -0.7071067811865476], 'a6': [3.6947138382246845, -3.6947138382246845], 'a7': [-0.2608949330902091, 0.2608949330902091], 'a8': [0.0, 0.5951735163099721], 'a9': [0.0, 3.3678632082561197], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6787284171808836, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [17, [[1.0, 0], [-3.845583426242639, 1.4871072966695862]]]], 'bad_primes': [5, 17], 'central_character': '85.81', 'coefficient_field': 'CDF', 'conductor': 85, 'conductor_radical': 85, 'conjugate': '3176819511663511075789429920813', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.070613028373415], [-2.0, 0]], [[1.0, 0], [-1.7843574765522912, 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.171778139989', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.86124431411402519785983983850', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.19449471782889344578460285821', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.82466121839099380516016418398', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.6787284171808836, 'bad_primes': [5, 17], 'central_character': '17.13', 'conductor': 85, 'conductor_radical': 85, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/85/2/e/a/81/2'], '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': '2-85-17.13-c1-0-3', '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': '2-85-17.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8238497540091176, 'root_angle': 0.1717781399892859, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.86124431411402519785983983850', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '3627058072186252587828233725974', 'Lhash_array': ['3627058072186252587828233725974'], 'factors': ['2-85-17.13-c1-0-3'], 'label': '2-85-17.13-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/85/2/e/a/81/2'}