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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_143.106', 'a10': [-0.5, 0.8660254037844386], 'a2': [0.20791169081775934, -0.9781476007338057], 'a3': [0.9135454576426009, -0.4067366430758002], 'a4': [-0.9135454576426009, -0.4067366430758002], 'a5': [-0.9510565162951535, -0.30901699437494745], 'a6': [-0.20791169081775934, -0.9781476007338057], 'a7': [0.4067366430758002, -0.9135454576426009], 'a8': [-0.5877852522924731, 0.8090169943749475], 'a9': [0.6691306063588582, -0.7431448254773942], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.106', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.85', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^47', 'a^56', 'a^34', 'a^33', 'a^43', 'a^49', 'a^21', 'a^52', 'a^20', 0, 'a^30', 0, 'a^36', 'a^29', 'a^8', 'a^28', 'a^39', 'a^31', 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'189.78542143863667168433179757405', '190.758497170742980091476551246908', '190.98918130230005378488678440259', '191.75748588268680811601230300720', '192.27774004590297665281588141519', '192.902446966770273827478060187433', '194.06382517265632673309229060382', '194.8166630737341093129335757745', '195.36796802250996762672010335884', '195.913819979768772733017601807208', '196.871834323615113742913029212668', '197.70170930037884500427495321055', '198.72238284207246383271081176127', '199.03211324979184759400040713147'], 'prelabel': '1-143-143.106-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': -0.8303424502447294, 'root_number': '-0.861289175469832409464392569306-0.508115101348598217499187309123*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.415171225122', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.797281460728540458823793752697-0.893427037608305814342504195314*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.999152840173', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.52114318356', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.90723810471', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.106', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/106'], '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': '1-143-143.106-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': '1-143-143.106-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': -0.4151712251223647, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.999152840173', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_143.106', 'Lhash_array': ['dirichlet_L_143.106'], 'label': '1-143-143.106-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/106'}
Lfunction data - 1-143-143.106-r0-0-0