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lfunc_lfunctions • Show schema
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{'Lhash': '518731047881777557429885812960', 'a10': [-22.531723336829646, -35.089274949433864], 'a2': [0.13351135246952034, 2.8252742731922083], 'a3': [2.5908406694016914, 4.5041696932702475], 'a4': [-7.964349437523519, 0.7544123786224656], 'a5': [-12.768133329471562, 7.371685214819439], 'a6': [-12.379608114683611, 7.9211932767014135], 'a7': [-2.3671554014705323, 18.368357991537753], 'a8': [-3.1947529496434197, -22.4007489515584], 'a9': [-13.57508925154839, 23.3391720464222], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.912320880964428, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.13351135246952034, -2.8252742731922083]]], [3, [[1.0, 0], [-2.5908406694016914, -4.5041696932702475]]], [7, [[1.0, 0], [2.3671554014705323, -18.368357991537753]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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['0.40920664399826306237829867114636', '1.71739009078218311042441457135194', '3.69614582392399687463718813538961', '4.29131473859066383319769599992669', '6.39397855576656190005199373337894', '7.890714999483698047369687383472158', '8.382212741934992278474686026820353', '9.650590520749376121558249685124277', '10.81839604856857518340231525950255', '12.05400732391255062305590987902631'], 'prelabel': '2-168-168.101-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.148383852227112, 'root_angle': 0.6225358351653374, 'root_number': '-0.37551991389087364 + 0.9268143256722949*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.311267917583', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40920664399826306237829867115', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.71739009078218311042441457135', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.69614582392399687463718813539', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.912320880964428, 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/4/ba/c/101/46'], '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': '2-168-168.101-c3-0-21', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-168-168.101-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.148383852227112, 'root_angle': 0.3112679175826687, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.40920664399826306237829867115', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '518731047881777557429885812960', 'Lhash_array': ['518731047881777557429885812960'], 'label': '2-168-168.101-c3-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/4/ba/c/101/46'}