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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_111.20', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.3420201433256687, 0.9396926207859084], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.766044443118978, 0.6427876096865394], 'a5': [-0.984807753012208, 0.17364817766693036], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.17364817766693036, 0.984807753012208], 'a8': [-0.8660254037844386, -0.5], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.5154818328690067, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [37, [1]]], 'bad_primes': [3, 37], 'central_character': '111.20', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 111, 'conductor_radical': 111, 'conjugate': 'dirichlet_L_111.50', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 0, 'a^14', 'a^17', 0, 'a^8', 'a^21', 0, 'a^24', 'a^12', 0, 'a^23', 'a^15', 0, 'a^28', 'a^13', 0, 'a^11', 'a^31', 0, 'a^19', 'a^33', 0, 'a^34', 'a^30', 0, 'a^22', 'a^3', 0, 'a^9', 'a^35', 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'182.054619471656050094228821068318', '183.02957643919184154522810416765', '183.647024548625743194666451549763', '184.43666070635697308660409406424', '185.63624079116896359034120879824', '186.04501090048152134492900243260', '186.86248452659243215496084587688', '187.46898512903895457886772853256', '188.21756164233735821829671703720', '189.00712531286510430524919370784', '189.73938166677393526421506356695', '190.55601738605576968928959503464', '191.19374998404518868240115344730', '192.07195058764977410820868515521', '193.44622225688032180520128751620', '193.59959396859852529050879369578', '194.833644023633918911345625788580', '195.371291893844210444689512747862', '196.068404918156996289362154905890', '196.59261551321859010005268058070', '197.54738322990615481979715171365', '198.578183404186429988691587666352', '199.01189918467540267746151512164', '199.35644385750632119606053420192'], 'prelabel': '1-111-111.20-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5154818328690067, 'root_angle': 0.9342556929038665, 'root_number': '-0.978745954509767802000163994379+0.205076465082572398931909015765*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.467127846452', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.593362893525876776802214065127+0.622360605318610255868331746433*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.79932319386', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.33228461753', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.41316266626', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.5154818328690067, 'bad_primes': [3, 37], 'central_character': '111.20', 'conductor': 111, 'conductor_radical': 111, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/111/20'], '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': '1-111-111.20-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': '1-111-111.20-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5154818328690067, 'root_angle': 0.4671278464519332, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.79932319386', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_111.20', 'Lhash_array': ['dirichlet_L_111.20'], 'label': '1-111-111.20-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/111/20'}
Lfunction data - 1-111-111.20-r0-0-0