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lfunc_lfunctions • Show schema
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{'Lhash': '1418048260723926724468114674410', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 3.0], 'a4': [0, 0], 'a5': [5.864843853663881, 0], 'a6': [0, 0], 'a7': [18.32972071101699, 2.649780869452201], 'a8': [0, 0], 'a9': [-9.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 79.29856704771542, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -3.0]]], [7, [[1.0, 0], [-18.32972071101699, -2.649780869452201]]]], 'bad_primes': [2, 3, 7], 'central_character': '1344.223', 'coefficient_field': 'CDF', 'conductor': 1344, 'conductor_radical': 42, 'conjugate': '788463649266872654641521487275', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.0]], [[1.0, 0], [-5.864843853663881, 0], [125.0, 0]], [[1.0, 0], [-18.32972071101699, -2.649780869452201]], [[1.0, 0], [34.5205982362997, 0], [1331.0, 0]], [[1.0, 0], [-55.86003109318696, 0], [2197.0, 0]], [[1.0, 0], [0, -2.771036962879953], 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-2.477035760665191], 'positive_zeros': ['1.11864283460175819728115921365090', '1.82456516987459920474647470601167', '3.01063862823282269651508255668487', '4.17406854034897631331054464518732', '5.35513996622629108371618997304312', '5.84865091735134172309418283509842', '6.85891923926160897093153602782164', '8.018970953557332640166702160102349', '8.072614124066005040486237396850276', '9.252183531913923089902263045125251'], 'prelabel': '2-1344-56.27-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.904974286752063, 'root_angle': 0.12903225698699847, 'root_number': '0.91895781295517313872356000955632029261975344774459904076 + 0.3943558520025346597398629348802405117639852890830156501*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.06451612849349923', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11864283460175819728115921365', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.82456516987459920474647470601', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01063862823282269651508255668', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 79.29856704771542, 'bad_primes': [2, 3, 7], 'central_character': '56.27', 'conductor': 1344, 'conductor_radical': 42, 'degree': 2, 'index': 68, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1344/4/p/c/223/18'], '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': '2-1344-56.27-c3-0-68', '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': '2-1344-56.27-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.904974286752063, 'root_angle': 0.06451612849349923, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11864283460175819728115921365', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1418048260723926724468114674410', 'Lhash_array': ['1418048260723926724468114674410'], 'label': '2-1344-56.27-c3-0-68', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1344/4/p/c/223/18'}