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lfunc_lfunctions • Show schema
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{'Lhash': '1007781731284069216115181392139', 'a10': [-9.7260290860697, 0.7288651185252327], 'a2': [-2.1635274674864906, 1.7253555814366166], 'a3': [0.581017998162504, -1.6316917864018428], 'a4': [1.258957352261393, -5.515852558874842], 'a5': [2.9121111933220356, 1.9854437936151645], 'a6': [1.5582001327241104, 4.532672644397293], 'a7': [-2.072318882176764, 1.6448387308710986], 'a8': [4.391683862672517, 9.119425507820928], 'a9': [-2.324836171622473, -1.8960845907067971], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.581017998162504, 1.6316917864018428]]], [7, [[1.0, 0], [2.072318882176764, -1.6448387308710986]]]], 'bad_primes': [3, 7], 'central_character': '441.5', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '2040467763000847100584423717924', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.1635274674864906, 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[-65.24161659285454, 60.53537366161183]], [[1.0, 0], [-0.8455082463126353, 0.4881544136106484], [48.5, -84.00446416709055]], [[1.0, 0], [1.3168437638821016, -17.57205884024402], [-99.87191344873798, -15.053268883793619]], [[1.0, 0], [-8.014192518690201, 11.754661509012257], [-37.63012550973869, -95.87999611035303]], [[1.0, 0], [5.586279458879932, -2.1924531257613222], [78.43655028579141, -72.77848294148838]], [[1.0, 0], [-2.782261320261349, 7.089086229478705], [-79.90265402945107, -74.13882841703021]], [[1.0, 0], [-2.9133815318041854, 1.1434179927726176], [82.83486151677037, -76.8595193681139]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-21e2-441.5-c1-0-12', '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/441/2/bn/a/5/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.28380353086', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.794999608805949313799312208780', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.45696845518746486333831320145', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37890503124496108609003615174', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'bad_primes': [3, 7], 'central_character': '441.5', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/bn/a/5/1'], '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': '2-21e2-441.5-c1-0-12', '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': '2-21e2-441.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': -0.2838035308596755, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.794999608805949313799312208780', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1007781731284069216115181392139', 'Lhash_array': ['1007781731284069216115181392139'], 'label': '2-21e2-441.5-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/bn/a/5/1'}