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lfunc_lfunctions • Show schema
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{'Lhash': '2332054988497679607228666781258', 'a10': [38.0, -4.9400473305118605e-60], 'a2': [1.618033988749895, -1.1755705045849463], 'a3': [-2.163118960624632, -6.657395614066075], 'a4': [1.2360679774997898, -3.804226065180614], 'a5': [15.371322893124, 11.16791979355699], 'a6': [-11.326237921249264, -8.228993532094623], 'a7': [4.326237921249264, -13.31479122813215], 'a8': [-2.4721359549995796, -7.608452130361228], 'a9': [-17.798373876248842, 12.931275550434409], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.278462221389235, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.618033988749895, 1.1755705045849463]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 11], 'central_character': '242.3', 'coefficient_field': 'CDF', 'conductor': 242, 'conductor_radical': 22, 'conjugate': '1396001428529105498408795716003', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.618033988749895, 1.1755705045849463]], [[1.0, 0], 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'data': '3.78545497740369775409294383016', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.94434783191715792275016143541', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.278462221389235, 'bad_primes': [2, 11], 'central_character': '11.3', 'conductor': 242, 'conductor_radical': 22, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/242/4/c/l/3/1'], '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': '2-242-11.3-c3-0-20', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-242-11.3-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7786852503733668, 'root_angle': 0.31456573986078645, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.83966700925145580868575068189', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2332054988497679607228666781258', 'Lhash_array': ['2332054988497679607228666781258'], 'label': '2-242-11.3-c3-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/242/4/c/l/3/1'}