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lfunc_lfunctions • Show schema
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{'Lhash': '2403200975599245216346497232706', 'a10': [-1.1790467921809504, -0.7809280772566772], 'a2': [-0.086780157342344, 1.4115485129075933], 'a3': [0.980170618336407, -1.6977053110448594], 'a4': [-1.984938408583276, -0.24498880409294524], 'a5': [-0.5, 0.8660254037844386], 'a6': [2.3113340466791183, 1.5308855127218775], 'a7': [0.0, -1.9718053936090045], 'a8': [0.5180668495081251, -2.7805766918825894], 'a9': [-0.4214688820999487, -0.730005517606368], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.034315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.086780157342344, -1.4115485129075933]]], [5, [[1.0, 0], [0.5, -0.8660254037844386]]], [19, [[1.0, 0], [4.337146802863116, -0.4349225338083198]]]], 'bad_primes': [2, 5, 19], 'central_character': '380.331', 'coefficient_field': 'CDF', 'conductor': 380, 'conductor_radical': 190, 'conjugate': '1238192388892548289249562356083', 'degree': 2, 'euler_factors': 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[-9.293303355343784, -5.3654911938685865], [54.5, 94.39676901250381]], [[1.0, 0], [0, -10.723255949490978], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-380-76.27-c1-0-28', '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/380/2/n/b/331/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3578008547558509, 1.4426279733677352, 1.5245217240513118, 1.6017618693597893, 1.6696124104465362, 1.7210759438872838, 1.7478370270312804, 1.7412536510236214, 1.6933321367468366, 1.5976636726897517, 1.4503041731493038, 1.2505600429202346, 1.0016185679725156, 0.7109442831608338, 0.3903574510776223, 0.05572010778306284, -0.2738204972076456, -0.5770427919463421, -0.8322778643364114, -1.019357124116802, -1.1217269160678758, -1.1285244130364849, 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'4.85537149675535614283995353103790', '6.67284117914372097642023375517498', '8.273382681856332878007292064986568', '9.039507697869492754888251214431809', '9.492885183936663212840334653216774', '10.41187978899430721187916739449244', '11.39296825818081452903574693588725'], 'prelabel': '2-380-76.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': 0.14278264574098198, 'root_number': '0.9010703892000635 + 0.4336728648495844*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0713913228705', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89579129703923928506843523224', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.22113265916010099444485541581', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.43198576021285730705304010142', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.034315276808656, 'bad_primes': [2, 5, 19], 'central_character': '76.27', 'conductor': 380, 'conductor_radical': 190, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/380/2/n/b/331/9'], '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': '2-380-76.27-c1-0-28', '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': '2-380-76.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': 0.07139132287049099, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89579129703923928506843523224', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2403200975599245216346497232706', 'Lhash_array': ['2403200975599245216346497232706'], 'label': '2-380-76.27-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/380/2/n/b/331/9'}