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lfunc_lfunctions • Show schema
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{'Lhash': '1406168202002041924682759251069', 'a10': [82148.23693321265, 0], 'a2': [19.595917942265423, -11.313708498984761], 'a3': [0, 0], 'a4': [256.0, -443.40500673763256], 'a5': [3144.082246181666, 1815.2367311873081], 'a6': [0, 0], 'a7': [11613.264808325792, 20114.76468977191], 'a8': [0, -11585.237502960395], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 102.92787493314336, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-19.595917942265423, 11.313708498984761]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '162.53', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '1226725159166607098458120268887', 'degree': 2, 'euler_factors': [[[1.0, 0], [-19.595917942265423, 11.313708498984761]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3144.082246181666, -1815.2367311873081], [4882812.5, 8457279.33383241]], [[1.0, 0], [-11613.264808325792, 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-1.907743344534327, -2.2354208467698387], 'positive_zeros': ['1.10927112072433337759021881651180', '1.91563874876337797355540455165691', '3.74634646868112316449145125615680', '4.60255662290978280473843182089577', '5.72440080288015595206312718183743', '6.69814110635918449714703541914254', '7.86543918766505767854117264771607', '8.892938262611265020415635695449830', '10.15615750623862710357979264893999', '10.98993465908002490891466796972879'], 'prelabel': '2-162-9.5-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.145337595819242, 'root_angle': 0.1111111111111111, 'root_number': '0.93969262078590838405410927732473146993620813426446463309 + 0.3420201433256687330440996146822595807630833675141606285*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.05555555555555555', 'prec': 64}, 'spectral_label': 'c10-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10927112072433337759021881651', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 102.92787493314336, 'bad_primes': [2, 3], 'central_character': '9.5', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/11/d/d/53/4'], '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': '2-162-9.5-c10-0-28', 'motivic_weight': 10, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [10], 'order_of_vanishing': 0, 'prelabel': '2-162-9.5-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.145337595819242, 'root_angle': 0.05555555555555555, 'self_dual': False, 'spectral_label': 'c10-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10927112072433337759021881651', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1406168202002041924682759251069', 'Lhash_array': ['1406168202002041924682759251069'], 'label': '2-162-9.5-c10-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/11/d/d/53/4'}