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lfunc_lfunctions • Show schema
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{'Lhash': '402391709225689183369810314371', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.3722813232690143, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.11613287362019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '8280.1', 'coefficient_field': 'CDF', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.3722813232690143, 0], [7.0, 0]], [[1.0, 0], [4.0, 0], [11.0, 0]], [[1.0, 0], [6.744562646538029, 0], [13.0, 0]], [[1.0, 0], [-0.3722813232690143, 0], [17.0, 0]], [[1.0, 0], [-4.0, 0], [19.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.3722813232690143, 0], 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'2-8280-1.1-c1-0-3', 'leading_term': '0.47691757299749966687095578493581', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/8280/2/a/z/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [0.47691757299749965, 0.466430227793087, 0.434983516994537, 0.38262947934793196, 0.30947463457307506, 0.2157082141028963, 0.10163891251535177, -0.03226232499104053, -0.18531631417418823, -0.35658943299201923, -0.5448501809382365, -0.7485312958080249, -0.9656999474882314, -1.1940381727428584, -1.430835312253347, -1.6729937822822152, -1.9170490715328226, -2.1592044063454017, -2.3953800777788476, -2.6212769742672397, -2.8324534155153276, -3.0244139406897856, -3.192708272529233, -3.333038266881503, -3.4413702747529284, -3.514050003385435, -3.547916677507644, -3.54041308554384, 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'6.63659154652459136049439924999409', '7.13185210646970560630039252648375', '7.78528995257728834276143300478663'], 'prelabel': '2-8280-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31743108799320733658050039418', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.88060025084583719953162132411', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.88501937440715585415500182619', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 66.11613287362019, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8280/2/a/z/1/1'], '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': '2-8280-1.1-c1-0-3', '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': '2-8280-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.31743108799320733658050039418', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '402391709225689183369810314371', 'Lhash_array': ['402391709225689183369810314371'], 'label': '2-8280-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8280/2/a/z/1/1'}