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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.292', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9945218953682733, 0.10452846326765347], 'a3': [-0.20791169081775934, 0.9781476007338057], 'a4': [0.9781476007338057, -0.20791169081775934], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.10452846326765347, -0.9945218953682733], 'a7': [-0.9510565162951535, -0.30901699437494745], 'a8': [-0.9510565162951535, 0.30901699437494745], 'a9': [-0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.292', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.68', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^29', 'a^17', 'a^58', 0, 'a^46', 'a^33', 'a^27', 'a^34', 0, 0, 'a^15', 'a^19', 'a^2', 0, 'a^56', 'a^41', 'a^3', 0, 0, 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'187.26008486439367359221540396063', '188.09941104447852455655146928530', '188.51548543302446155389702246965', '188.82180869172254615419783331770', '189.83956540022706222536985051526', '190.45133939360443860901661296652', '190.74260990985488916607327293389', '191.66257716324004946248679831036', '191.99227418561800723254938414019', '192.771967820880572409348569733874', '193.22506955320126460373071442476', '193.93224865303234890055174660733', '194.08609759814268360771835397841', '195.30585110276436595611396339699', '195.77965177127634368923651424720', '196.63060190118821900257462824280', '197.33267712589020554555866544089', '197.747949118618132383321149277435', '198.077944095842173158197105079050', '198.85781134258368294047654065152', '199.453583422233098229237640391855', '199.95795506666488666274882238088'], 'prelabel': '1-1045-1045.292-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.025606748948858553, 'root_number': '0.987084787012159953883747858815-0.160198699274241362428622640355*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0256067489489', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.478711585551303483108012634580+0.130687646915179079228865969455*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.359913742067', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.01473868894', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.08274295431', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.292', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/292'], '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': '1-1045-1045.292-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': '1-1045-1045.292-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.025606748948858553, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.359913742067', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.292', 'Lhash_array': ['dirichlet_L_1045.292'], 'factors': ['1-1045-1045.292-r0-0-0'], 'label': '1-1045-1045.292-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/292'}
Lfunction data - 1-1045-1045.292-r0-0-0