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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_273.2', 'a10': [0.5, 0.8660254037844386], 'a2': [-7.040766286173228e-31, 1.0], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [0.8660254037844386, -0.5], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [2.9010907910729803e-30, -1.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 1.2678066700291788, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [13, [1]]], 'bad_primes': [3, 7, 13], 'central_character': '273.2', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 273, 'conductor_radical': 273, 'conjugate': 'dirichlet_L_273.137', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 0, 'a^6', 'a^11', 0, 0, 'a^9', 0, 'a^2', 'a^5', 0, 0, 0, 0, 'a^0', 'a^0', 0, 'a^1', 'a^5', 0, 'a^8', 'a^0', 0, 'a^10', 0, 0, 0, 'a^10', 0, 'a^1', 'a^3', 0, 'a^3', 0, 0, 'a^3', 'a^4', 0, 'a^8', 'a^7', 0, 'a^2', 'a^11', 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'183.077015268660747248473180464177', '184.123385603141739884418999295981', '184.96116333678602620761872741833', '185.45794396901361271448837274640', '185.95913007097611724462755173459', '186.81268944574076386067743520771', '187.60009517583415868870801702545', '188.08869210875042139196268576063', '189.03126783215375303243763015824', '189.24514372651946904394126154799', '189.91454338641653699772475516751', '191.00156546111164229439384325168', '191.293928537761989871323881285', '192.27689017640534154193543768807', '193.34704850558983739075039139875', '193.56521474198153324378001570176', '194.52241293719729595692872108290', '195.23594795944875579355430603111', '196.14001706674063708236097568073', '196.38612762127144068021394354847', '197.12335985041559279690537698382', '197.76383353434467491570676345498', '198.47621866546022590206942691655', '199.12994093215867112512395748509', '199.93293915879555374136240590608'], 'prelabel': '1-273-273.2-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2678066700291788, 'root_angle': 0.3452970502076801, 'root_number': '0.467104871037747568521902775259+0.884201922330419508316463463066*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.172648525104', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.02224672095803801546115098764+0.452112411706561805279765884228*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.23908350651', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.03331695775', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.70354882181', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.2678066700291788, 'bad_primes': [3, 7, 13], 'central_character': '273.2', 'conductor': 273, 'conductor_radical': 273, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/273/2'], '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': '1-273-273.2-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': '1-273-273.2-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2678066700291788, 'root_angle': 0.17264852510384004, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23908350651', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_273.2', 'Lhash_array': ['dirichlet_L_273.2'], 'label': '1-273-273.2-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/273/2'}
Lfunction data - 1-273-273.2-r0-0-0