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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_925.471', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.10452846326765347, -0.9945218953682733], 'a3': [-0.9781476007338057, -0.20791169081775934], 'a4': [-0.9781476007338057, -0.20791169081775934], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.30901699437494745, 0.9510565162951535], 'a7': [-0.5, 0.8660254037844386], 'a8': [-0.30901699437494745, 0.9510565162951535], 'a9': [0.9135454576426009, 0.4067366430758002], 'algebraic': True, 'analytic_conductor': 4.295681940575056, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [37, [1]]], 'bad_primes': [5, 37], 'central_character': '925.471', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 925, 'conductor_radical': 185, 'conjugate': 'dirichlet_L_925.381', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^23', 'a^16', 'a^16', 0, 'a^9', 'a^10', 'a^9', 'a^2', 0, 'a^18', 'a^2', 'a^7', 'a^3', 0, 'a^2', 'a^29', 'a^25', 'a^19', 0, 'a^26', 'a^11', 'a^3', 'a^25', 0, 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'190.90291196723592387818956170594', '191.77653012825293413837076540562', '192.28900204070467613139746998588', '192.99695249842581996497078210955', '193.59938938338538899559559656001', '193.92133242914452645047764417603', '194.48097318697628721144431794855', '195.309478387718884925061845877435', '195.58255643347723783312213806448', '196.47254126787099454319222876787', '196.72466635678499236699143051053', '197.90836960697765923178346298390', '198.80136240470584718737092055962', '199.0900378011602299019838797007', '199.82449157258873029569106248166'], 'prelabel': '1-925-925.471-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.295681940575056, 'root_angle': 0.3931759332480522, 'root_number': '-0.783078775228003701930357508127+0.621922528766573671338530554697*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.393175933248', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.508742549096276536871667847704-0.261172286039778722881741586278*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0793865744038', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.44855919616', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.48479908557', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.295681940575056, 'bad_primes': [5, 37], 'central_character': '925.471', 'conductor': 925, 'conductor_radical': 185, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/925/471'], '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': '1-925-925.471-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': '1-925-925.471-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.295681940575056, 'root_angle': 0.3931759332480522, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0793865744038', 'prec': 50}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_925.471', 'Lhash_array': ['dirichlet_L_925.471'], 'factors': ['1-925-925.471-r0-0-0'], 'label': '1-925-925.471-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/925/471'}
Lfunction data - 1-925-925.471-r0-0-0