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lfunc_lfunctions • Show schema
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{'Lhash': '1974586021942785188958784913341', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.16178199655276473, -0.9868265225415261], 'a4': [0.907575419670957, -0.4198891015602646], 'a5': [-0.2675283385292208, 0.9635499925192229], 'a6': [0.0, 0.0], 'a7': [0.7259954919231308, -0.6876994588534233], 'a8': [0.0, 0.0], 'a9': [6.5311334497095925e-80, -6.78413926823097e-80], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7372453089754814, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[59, [[1.0, 0], [0, 0]]]], 'bad_primes': [59], 'central_character': '3481.2076', 'coefficient_field': 'CDF', 'conductor': 3481, 'conductor_radical': 59, 'conjugate': '1392467180880533379086149926326', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.907575419670957, 0.4198891015602646]], [[1.0, 0], [-0.16178199655276473, 0.9868265225415261], [-0.9476531711828025, -0.31930153013597995]], [[1.0, 0], [0.2675283385292208, -0.9635499925192229], 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[0.8568571761675893, 0.5155538571770217]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-59e2-59.11-c0-0-2', 'leading_term': '1.7679760687886695838945730269820', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3481/1/d/a/2076/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.7679760687886696, 1.8206584571887532, 1.8856027950743561, 1.962457021210723, 2.049952922295476, 2.1460538550136303, 2.2481402477422803, 2.3531941466195856, 2.4579594521693453, 2.5590700909142163, 2.653148789747777, 2.736883754454456, 2.807091148987413, 2.8607698529980534, 2.895152947179455, 2.9077584602314586, 2.896440369496046, 2.8594397082846315, 2.795434836798104, 2.703589403862566, 2.5835961982808393, 2.4357149139974372, 2.2608018008377417, 2.0603292221737926, 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'5.80912298649199108411996619202956', '6.67269363381142436995715299714741', '7.57786434503199466295932654659391', '8.325095609531724886487425194392769', '8.934264483514245658674134973190146'], 'prelabel': '2-59e2-59.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.318046019293515, 'root_angle': 0.38093708236588775, 'root_number': '0.36538576353051349578634761141825 + 0.93085618857545534064173979995795*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.19046854118294387', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55767371670654220403296110562', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44190168001201087730604213643', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56915405655178696872502074147', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7372453089754814, 'bad_primes': [59], 'central_character': '59.11', 'conductor': 3481, 'conductor_radical': 59, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3481/1/d/a/2076/1'], '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': '2-59e2-59.11-c0-0-2', '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': '2-59e2-59.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.318046019293515, 'root_angle': 0.19046854118294387, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55767371670654220403296110562', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1974586021942785188958784913341', 'Lhash_array': ['1974586021942785188958784913341'], 'label': '2-59e2-59.11-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3481/1/d/a/2076/1'}