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lfunc_lfunctions • Show schema
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{'Lhash': '2981564994987449068240383457074', 'a10': [-21410135.679049175, 0], 'a2': [0, -185.17226149077203], 'a3': [0, 0], 'a4': [-17904.766425606857, 0], 'a5': [0, -115622.80174515305], 'a6': [0, 0], 'a7': [-369097.53192447964, 0], 'a8': [0, 281603.7582288595], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.56882140101463, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '7.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '27.26', 'coefficient_field': 'CDF', 'conductor': 27, 'conductor_radical': 3, 'conjugate': '617226426872507932315098460713', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 185.17226149077203], [-16384.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 115622.80174515305], [-6103515625.0, 0]], [[1.0, 0], [369097.53192447964, 0], [678223072849.0, 0]], [[1.0, 0], [0, 36928508.02732468], [-379749833583241.0, 0]], [[1.0, 0], [-61196594.24359078, 0], [3937376385699289.0, 0]], [[1.0, 0], [0, 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1.00000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'c14-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.35204006092108059810810320010', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.24138880662367272586306045439', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.17385784515120228842873929778', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.56882140101463, 'bad_primes': [3], 'central_character': '3.2', 'conductor': 27, 'conductor_radical': 3, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/27/15/b/d/26/2'], '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': '2-3e3-3.2-c14-0-18', 'motivic_weight': 14, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [14], 'order_of_vanishing': 0, 'prelabel': '2-3e3-3.2-c14-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.793860664618595, 'root_angle': -0.25, 'self_dual': False, 'spectral_label': 'c14-0', 'z1': {'__RealLiteral__': 0, 'data': '2.35204006092108059810810320010', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2981564994987449068240383457074', 'Lhash_array': ['2981564994987449068240383457074'], 'factors': ['2-3e3-3.2-c14-0-18'], 'label': '2-3e3-3.2-c14-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/27/15/b/d/26/2'}