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lfunc_lfunctions • Show schema
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{'Lhash': '467174326127290054017891581528', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-8.0, 0.0], 'a5': [5.196152422706632, 0.0], 'a6': [0.0, 0.0], 'a7': [-10.392304845413264, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.196152422706632, 0], [125.0, 0]], [[1.0, 0], [10.392304845413264, 0], [343.0, 0]], [[1.0, 0], [51.96152422706632, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [117.0, 0], [4913.0, 0]], [[1.0, 0], [24.24871130596428, 0], [6859.0, 0]], [[1.0, 0], [-18.0, 0], [12167.0, 0]], [[1.0, 0], [-99.0, 0], [24389.0, 0]], 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'label': '2-39e2-1.1-c3-0-21', 'leading_term': '0.62354367053717385612736088532476', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1521/4/a/m/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.6235436705371739, 0.6069405472361791, 0.5573945363313915, 0.4756944492739183, 0.36315061018649625, 0.22158782182254247, 0.05333456817185399, -0.13879241972700335, -0.3515092531907761, -0.5810927228968037, -0.8234159706341742, -1.0739929940992925, -1.328032810055693, -1.5805038473500814, -1.8262088134875023, -2.0598698869033423, -2.27622364483366, -2.470124659380008, -2.636656199634671, -2.771245984783037, -2.8697844621909754, -2.928742656387047, -2.945286270261135, -2.9173824387230662, -2.843895356128019, -2.72466693853466, -2.5605787540670324, -2.353591669520515, 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'6.56612766689132293110780450779556', '7.64271061413475533377782181774570', '8.393941427481593426623831459224333', '9.196855160486392250069417837271735'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36853556180479021846945288883', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.00637084948877784728035379564', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01002074647692909532497695576', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/m/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': '2-39e2-1.1-c3-0-21', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.36853556180479021846945288883', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '467174326127290054017891581528', 'Lhash_array': ['467174326127290054017891581528'], 'label': '2-39e2-1.1-c3-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/m/1/2'}