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lfunc_lfunctions • Show schema
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{'Lhash': '1104435909743333622260568087667', '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': [2.712309190826646, 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], [-2.712309190826646, 0], [7.0, 0]], [[1.0, 0], [-2.7646551364550116, 0], [11.0, 0]], [[1.0, 0], [1.0111083427484484, 0], [13.0, 0]], [[1.0, 0], [4.504075585165549, 0], [17.0, 0]], [[1.0, 0], [-4.764655136455011, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 44, 'label': '2-8280-1.1-c1-0-44', 'leading_term': '2.84416986908644022639982243808', '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/bu/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [2.84416986908644, 2.835021097744934, 2.807553141281936, 2.761707929126281, 2.697411056244586, 2.6146037294046285, 2.5132844021674683, 2.3935573449821845, 2.255685028947706, 2.100141057834259, 1.9276604397177424, 1.7392842081256947, 1.5363957381387316, 1.3207465132075167, 1.094469549253982, 0.8600791497684117, 0.6204561345988159, 0.37881814903091027, 0.13867511644741748, -0.09622965270211935, -0.32199174083667353, -0.5346299043963448, -0.7301805489853966, -0.9048001920358488, -1.0548733370481584, -1.1771228553006918, 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'5.08055642214788381092113862289924', '5.57381143784980566143549943265499', '6.58358677270305216707555746942490', '7.03464312280223326771081121723761', '7.77613123578000845192872578522189'], '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': '0.871246311518717853347318950590', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.76520432537489537850685469556', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.50225248407168403152636984477', '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': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8280/2/a/bu/1/5'], '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-c1-0-44', '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': '0.871246311518717853347318950590', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1104435909743333622260568087667', 'Lhash_array': ['1104435909743333622260568087667'], 'label': '2-8280-1.1-c1-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8280/2/a/bu/1/5'}