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lfunc_lfunctions • Show schema
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{'Lhash': '700541029809108434032381882085', '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': [-4.778457118258388, 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], [4.778457118258388, 0], [7.0, 0]], [[1.0, 0], [3.307773698387228, 0], [11.0, 0]], [[1.0, 0], [-3.1905073778718704, 0], [13.0, 0]], [[1.0, 0], [-2.4120502596134816, 0], [17.0, 0]], [[1.0, 0], [-2.2491405381295495, 0], [19.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-8280-1.1-c1-0-16', 'leading_term': '1.3337003139517683899413750442750', '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/bm/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.3337003139517685, 1.323779799946863, 1.2940220433557061, 1.244444755859255, 1.1750981974540806, 1.086094773597488, 0.9776475844414095, 0.850115343755816, 0.7040507278302994, 0.5402490625036708, 0.359794290208188, 0.16409934484654654, -0.045061638812765356, -0.26553148013821254, -0.4947602517507196, -0.7298090605114708, -0.9673681971301252, -1.2037900882108914, -1.4351370326940032, -1.6572432550815446, -1.865790361956212, -2.056394849031879, -2.224705878511359, -2.3665111385701136, -2.477848218373533, 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'5.79985145912396292439848601502479', '6.32620635415832967358459785261554', '7.12426793746826750400411119482011', '7.62523578504340344127715946882456'], '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': '0.55262943091967309427702018438', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.79015294388898879380917452127', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.94778673171720573651073140046', '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': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8280/2/a/bm/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-c1-0-16', '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': '0.55262943091967309427702018438', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '700541029809108434032381882085', 'Lhash_array': ['700541029809108434032381882085'], 'label': '2-8280-1.1-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8280/2/a/bm/1/1'}