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lfunc_lfunctions • Show schema
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{'Lhash': '2268572708574445100634173375000', 'a10': [-7.344425315823212, 0.0], 'a2': [2.4873805260159547, 0.0], 'a3': [-1.0, 0.0], 'a4': [4.187061881203408, 0.0], 'a5': [-2.9526746064812213, 0.0], 'a6': [-2.4873805260159547, 0.0], 'a7': [0.0, 0.0], 'a8': [5.440055132497176, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.997420923394913, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7, 23], 'central_character': '3381.1', 'coefficient_field': 'CDF', 'conductor': 3381, 'conductor_radical': 483, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.4873805260159547, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.9526746064812213, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.300318644812547, 0], [11.0, 0]], [[1.0, 0], [3.252993251293768, 0], [13.0, 0]], [[1.0, 0], [-2.4355956338816633, 0], [17.0, 0]], [[1.0, 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'5.14097316226701265655770015583506', '5.62510779053437322607366459755223', '6.66824416332416588297364816012028', '7.30412295599284880828537382501645', '7.72879885669060147781257494042328'], 'prelabel': '2-3381-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.195904245017888, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78958832044571937198890335764', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.06197372247463101654167557982', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.67117293685936556768412915123', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.997420923394913, 'bad_primes': [3, 7, 23], 'central_character': '1.1', 'conductor': 3381, 'conductor_radical': 483, 'degree': 2, 'index': 139, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3381/2/a/y/1/5'], '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': '2-3381-1.1-c1-0-139', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-3381-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.195904245017888, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.78958832044571937198890335764', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2268572708574445100634173375000', 'Lhash_array': ['2268572708574445100634173375000'], 'label': '2-3381-1.1-c1-0-139', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3381/2/a/y/1/5'}