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lfunc_lfunctions • Show schema
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{'Lhash': '3276024437695081896409253631334', 'a10': [2.214515750661193, -0.3097095253192762], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [2.33944940185801, -0.9690316707352127], 'a4': [0.0, -1.0], 'a5': [-1.7848968098882745, -1.3469013987856207], 'a6': [-0.9690316707352127, 2.33944940185801], 'a7': [1.2675785891170788, -3.0602054212202043], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [2.41268078140628, -2.41268078140628], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3574568343617672, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [1.7848968098882745, 1.3469013987856207]]], [17, [[1.0, 0], [4.045023402077742, -0.7986148487496375]]]], 'bad_primes': [2, 5, 17], 'central_character': '170.49', 'coefficient_field': 'CDF', 'conductor': 170, 'conductor_radical': 170, 'conjugate': '1891695625813390793190484999040', 'degree': 2, 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.84217624369133522827559534116', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3574568343617672, 'bad_primes': [2, 5, 17], 'central_character': '85.49', 'conductor': 170, 'conductor_radical': 170, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/170/2/n/b/49/5'], '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': '2-170-85.49-c1-0-7', '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': '2-170-85.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1650994954774323, 'root_angle': 0.08395098402626221, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.58432760344629849439845300110', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3276024437695081896409253631334', 'Lhash_array': ['3276024437695081896409253631334'], 'label': '2-170-85.49-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/170/2/n/b/49/5'}