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lfunc_lfunctions • Show schema
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{'Lhash': '1631508434603577125673499029550', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.5, 0.8660254037844386], 'a4': [0, 0], 'a5': [4.1447446659354386, 0], 'a6': [0, 0], 'a7': [-1.206346929183281, -2.089454172900137], 'a8': [0, 0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.19366152991567, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.5, -0.8660254037844386]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '2028.529', 'coefficient_field': 'CDF', 'conductor': 2028, 'conductor_radical': 78, 'conjugate': '1162721699271856299667706353766', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-4.1447446659354386, 0], [5.0, 0]], [[1.0, 0], [1.206346929183281, 2.089454172900137], [-3.5, 6.06217782649107]], [[1.0, 0], [-1.7320508075688772, 3.0], [-5.5, -9.526279441628825]], 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'root_number': '0.94519171983407171464172511119902426210969658547441650942 + 0.3265158690739390124954051518189353466474175641445689053*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.052937329935116094', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28703322059709379227229484600', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.20809680650128159447433353229', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.90996562213687026031525663194', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.19366152991567, 'bad_primes': [2, 3, 13], 'central_character': '13.9', 'conductor': 2028, 'conductor_radical': 78, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2028/2/i/n/529/4'], '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': '2-2028-13.9-c1-0-15', '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': '2-2028-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.024134879687269, 'root_angle': 0.0529373299351161, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28703322059709379227229484600', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1631508434603577125673499029550', 'Lhash_array': ['1631508434603577125673499029550'], 'label': '2-2028-13.9-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2028/2/i/n/529/4'}