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lfunc_lfunctions • Show schema
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{'Lhash': '2857334535824029343194366199023', 'a10': [-1.704558895796801, -0.6357675979873152], 'a2': [0.28173255684142967, -0.9594929736144974], 'a3': [0.0, 0.0], 'a4': [-0.8412535328311812, -0.5406408174555976], 'a5': [0.1297848071209585, -1.8146287145670172], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.7557495743542583, 0.6548607339452851], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5990043004761398, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.28173255684142967, 0.9594929736144974]]], [3, [[1.0, 0], [0, 0]]], [89, [[1.0, 0], [-0.9974521146102535, 0.07133918319923234]]]], 'bad_primes': [2, 3, 89], 'central_character': '3204.2555', 'coefficient_field': 'CDF', 'conductor': 3204, 'conductor_radical': 534, 'conjugate': '449496961494405111509381634420', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.28173255684142967, 0.9594929736144974]], [[1.0, 0], [0, 0]], [[1.0, 0], 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['2.25403950844940337284661544714283', '3.13519161703217269899774248016713', '3.79754156636927992258651305856009', '4.91577054204361984163322998927177', '5.71003239349443295588580246692586', '6.58837400802465096669523903351547', '6.85076131601468152980701088157414', '7.71098128783134700229167069995284', '8.265857250132607772993146751511430', '9.261367312934358856303284147640405'], 'prelabel': '2-3204-1068.419-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2645174180200682, 'root_angle': -0.6998107161437438, 'root_number': '-0.58730406419838478547750142700699 - 0.80936637944509377950645357054103*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3499053580718719', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.25403950844940337284661544714', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.13519161703217269899774248017', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79754156636927992258651305856', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5990043004761398, 'bad_primes': [2, 3, 89], 'central_character': '1068.419', 'conductor': 3204, 'conductor_radical': 534, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3204/1/cd/b/2555/1'], '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': '2-3204-1068.419-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3204-1068.419-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2645174180200682, 'root_angle': -0.3499053580718719, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.25403950844940337284661544714', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2857334535824029343194366199023', 'Lhash_array': ['2857334535824029343194366199023'], 'label': '2-3204-1068.419-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3204/1/cd/b/2555/1'}