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lfunc_lfunctions • Show schema
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{'Lhash': '1475665185290757188573130866391', 'a10': [0.0, 0.0], 'a2': [0.5996764100727928, -1.2807764064044151], 'a3': [0.0, 0.9364263849242712], 'a4': [-1.2807764064044151, -1.536102794997064], 'a5': [0.0, 0.0], 'a6': [1.1993528201455856, 0.5615528128088303], 'a7': [-0.4682131924621356, 2.6039923975319925], 'a8': [-2.7354556151426497, 0.7192235935955849], 'a9': [2.1231056256176606, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.589528141489629, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5996764100727928, 1.2807764064044151]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.4682131924621356, -2.6039923975319925]]]], 'bad_primes': [2, 5, 7], 'central_character': '700.699', 'coefficient_field': 'CDF', 'conductor': 700, 'conductor_radical': 70, 'conjugate': '1619063724496509592630502317983', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5996764100727928, 1.2807764064044151]], [[1.0, 0], [0, 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['1.16409457387159883069739887958543', '3.17476491606323765463608195784224', '4.21530023195643504068210216894762', '5.08292083633555256138750149163593', '6.39351272821206985877217851980355', '6.94772378170229437301420233569069', '7.70851546191513258179037631320310', '8.413728558438311504483106777557247', '9.753173803121566206999763606031416', '10.24508598978273084359893787904676'], 'prelabel': '2-700-140.139-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.364218293958836, 'root_angle': 0.18781876149091256, 'root_number': '0.8309128370274858 + 0.5564026035731096*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0939093807455', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16409457387159883069739887959', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.17476491606323765463608195784', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.21530023195643504068210216895', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.589528141489629, 'bad_primes': [2, 5, 7], 'central_character': '140.139', 'conductor': 700, 'conductor_radical': 70, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/700/2/c/j/699/5'], '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': '2-700-140.139-c1-0-28', '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': '2-700-140.139-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.364218293958836, 'root_angle': 0.09390938074545628, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16409457387159883069739887959', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1475665185290757188573130866391', 'Lhash_array': ['1475665185290757188573130866391'], 'label': '2-700-140.139-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/700/2/c/j/699/5'}