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lfunc_lfunctions • Show schema
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{'Lhash': '1098321605301399652085335713068', 'a10': [10.478876972091154, 13.589196656292044], 'a2': [-1.5838022083590282, 1.2212987205418115], 'a3': [0, 0], 'a4': [1.0168588704058685, -3.868591221320353], 'a5': [0, -8.580109678197609], 'a6': [0, 0], 'a7': [0, 1.974916327456981], 'a8': [3.1142021843595495, 7.368971756963804], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.63765008224431, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.5838022083590282, -1.2212987205418115]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [18.856517368392915, 2.3306120946001303]]]], 'bad_primes': [2, 3, 19], 'central_character': '684.683', 'coefficient_field': 'CDF', 'conductor': 684, 'conductor_radical': 114, 'conjugate': '1292479742631323874086062785172', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5838022083590282, -1.2212987205418115]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 8.580109678197609], [-25.0, 0]], [[1.0, 0], 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{'__RealLiteral__': 0, 'data': '0.866422975781856968221093352743', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.56753606366817702916433636216', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.23544982555357658139777410171', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.63765008224431, 'bad_primes': [2, 3, 19], 'central_character': '228.227', 'conductor': 684, 'conductor_radical': 114, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/684/3/b/a/683/16'], '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': '2-684-228.227-c2-0-36', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-684-228.227-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.317134475811972, 'root_angle': -0.03747630117111829, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.866422975781856968221093352743', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1098321605301399652085335713068', 'Lhash_array': ['1098321605301399652085335713068'], 'label': '2-684-228.227-c2-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/684/3/b/a/683/16'}