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lfunc_lfunctions • Show schema
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{'Lhash': '145905807227319460512158707750', 'a10': [-191.20302226704175, -439.58727085831055], 'a2': [0, 8.575230645055953], 'a3': [0, -9.0], 'a4': [-41.53458061590673, 0], 'a5': [-51.26244284889928, 22.297128809856538], 'a6': [77.17707580550358, 0], 'a7': [0, 178.46239721276177], 'a8': [0, -81.76122788527982], 'a9': [-81.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.46333026914181, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 9.0]]], [5, [[1.0, 0], [51.26244284889928, -22.297128809856538]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '165.34', 'coefficient_field': 'CDF', 'conductor': 165, 'conductor_radical': 165, 'conjugate': '2973604548964374182041067458327', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -8.575230645055953], [-32.0, 0]], [[1.0, 0], [0, 9.0]], [[1.0, 0], [51.26244284889928, -22.297128809856538]], [[1.0, 0], [0, -178.46239721276177], [-16807.0, 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.1847024202818331', 'prec': 60}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.11509938716634567621909878965', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.21391557670851474598101385131', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.20594100869549149885628519183', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.46333026914181, 'bad_primes': [3, 5, 11], 'central_character': '5.4', 'conductor': 165, 'conductor_radical': 165, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/165/6/c/b/34/23'], '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': '2-165-5.4-c5-0-0', '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': '2-165-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.144252158394047, 'root_angle': 0.18470242028183312, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.11509938716634567621909878965', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '145905807227319460512158707750', 'Lhash_array': ['145905807227319460512158707750'], 'label': '2-165-5.4-c5-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/165/6/c/b/34/23'}