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lfunc_lfunctions • Show schema
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{'Lhash': '1140186176015068302507467839536', 'a10': [-129.46815848005323, 0.0], 'a2': [-2.8150729063673245, 0.0], 'a3': [0.0, 0.0], 'a4': [-24.075364531836623, 0.0], 'a5': [45.99104988976068, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [157.85623940824453, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 70.72926453752447, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.8150729063673245, 0], [32.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-45.99104988976068, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-551.7808748764079, 0], [161051.0, 0]], [[1.0, 0], [-1094.0979542840346, 0], [371293.0, 0]], [[1.0, 0], [-1180.7142909404147, 0], [1419857.0, 0]], [[1.0, 0], [1166.1261193295124, 0], 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['0.899448298931730680019440020296176', '1.66387198162066838971252768009889', '3.51484784521431073877568077678462', '4.39467154116960977911908823002038', '5.79032646207954608974514372714626', '6.40438565033029593167913416804285', '7.82853761618949846477799265146199', '8.729198854313764510374298329105877', '9.319429788991684450246708417121745', '10.13169690943674373442241027933007'], 'prelabel': '2-21e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.899448298931730680019440020296', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.66387198162066838971252768010', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51484784521431073877568077678', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 70.72926453752447, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/6/a/z/1/2'], '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': '2-21e2-1.1-c5-0-33', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-21e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.899448298931730680019440020296', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1140186176015068302507467839536', 'Lhash_array': ['1140186176015068302507467839536'], 'label': '2-21e2-1.1-c5-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/6/a/z/1/2'}