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lfunc_lfunctions • Show schema
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{'Lhash': '2224356086245999098896492216767', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.5615528128088303, 0.0], 'a4': [0.0, 0.0], 'a5': [2.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.5615528128088303, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.5615528128088303, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.701974435916174, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 11, 19], 'central_character': '3344.1', 'coefficient_field': 'CDF', 'conductor': 3344, 'conductor_radical': 418, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5615528128088303, 0], [3.0, 0]], [[1.0, 0], [-2.0, 0], [5.0, 0]], [[1.0, 0], [3.5615528128088303, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.5615528128088303, 0], [13.0, 0]], [[1.0, 0], [-3.5615528128088303, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [5.56155281280883, 0], 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'2-3344-1.1-c1-0-84', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/3344/2/a/k/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.1036128656831868e-60, 0.2210002394552052, 0.44162595691265594, 0.6614447714761816, 0.8799121368321934, 1.0963238498658836, 1.309778104225063, 1.5191491228033294, 1.723073639001639, 1.9199507522239139, 2.1079550240848137, 2.2850621446021284, 2.449086090444786, 2.5977264072322193, 2.728624050230817, 2.8394240846988565, 2.9278434538809677, 2.9917419512244106, 3.0291944735544094, 3.0385625806971235, 3.018563347099566, 2.9683334690126775, 2.8874865956023554, 2.7761618934451153, 2.6350619402658437, 2.465478183118101, 2.2693023941065795, 2.049022816362029, 1.8077040147137848, 1.5489498268736435, 1.2768492464994432, 0.9959055508845663, 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'8.168938202621253209161008188640008'], 'prelabel': '2-3344-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.167395324137313, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.75470755572988585628446622639', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78701955004407696067589368274', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10985526071700341300503710576', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.701974435916174, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 3344, 'conductor_radical': 418, 'degree': 2, 'index': 84, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3344/2/a/k/1/2'], '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': '2-3344-1.1-c1-0-84', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-3344-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.167395324137313, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.75470755572988585628446622639', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2224356086245999098896492216767', 'Lhash_array': ['2224356086245999098896492216767'], 'label': '2-3344-1.1-c1-0-84', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3344/2/a/k/1/2'}