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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.312', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.7431448254773942, -0.6691306063588582], 'a3': [-0.9945218953682733, -0.10452846326765347], 'a4': [0.10452846326765347, 0.9945218953682733], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.6691306063588582, 0.7431448254773942], 'a7': [-0.5877852522924731, -0.8090169943749475], 'a8': [0.5877852522924731, -0.8090169943749475], 'a9': [0.9781476007338057, 0.20791169081775934], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.312', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.278', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^37', 'a^31', 'a^14', 0, 'a^8', 'a^39', 'a^51', 'a^2', 0, 0, 'a^45', 'a^47', 'a^16', 0, 'a^28', 'a^43', 'a^39', 0, 0, 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'189.2961278019335326735032131408', '190.23027925746422767611341075653', '190.56144610446198697389883979521', '191.17892463713073543244590838217', '191.84991737140367985226999975338', '192.37398471571334738622760882736', '193.29620991257256089588622391172', '193.75148400889116350820699616513', '193.975407917886220315400117643', '194.88542484851961419487109779979', '195.07634897251082318100552610553', '196.149718511130477334709654556799', '196.73554513535129228444228841206', '197.48596679596945762818008418970', '198.18793097987153843321586880014', '198.5099165208944467046669700096', '199.46103355658169764939180846083', '199.87688676928530258941671756392'], 'prelabel': '1-1045-1045.312-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.9517309107454268, 'root_number': '-0.988524395454033288288730774799-0.151061310706077257850975640680*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.475865455373', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.430683416156159549899903517715-0.274264880994515063230804820142*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.374490608844', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.1387185887', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.52876983375', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.312', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/312'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-1045-1045.312-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1045-1045.312-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.4758654553727134, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.374490608844', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.312', 'Lhash_array': ['dirichlet_L_1045.312'], 'label': '1-1045-1045.312-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/312'}
Lfunction data - 1-1045-1045.312-r0-0-0