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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2001.50', 'a10': [-0.9981278731933669, -0.061161660821842705], 'a2': [-0.983192890799503, 0.18256982083936169], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9333365210373668, -0.3590026998475987], 'a5': [0.9701859555740645, 0.24236173709321235], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.061161660821842705, -0.9981278731933669], 'a8': [-0.8521067736154565, 0.523367983696612], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 9.292604933071013, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]], [29, [1]]], 'bad_primes': [3, 23, 29], 'central_character': '2001.50', 'coeff_info': ['x^308 - 1', '0.999791928189206 + 0.0203985373914054*I', '\\\\zeta_{308}'], 'conductor': 2001, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_2001.1961', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^145', 0, 'a^290', 'a^12', 0, 'a^228', 'a^127', 0, 'a^157', 'a^97', 0, 'a^146', 'a^65', 0, 'a^272', 'a^161', 0, 'a^59', 'a^302', 0, 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'191.58040714746391764858217065432', '192.10988729952002259159236685834', '192.91951990611056530595328889090', '193.403859666483228385191499771056', '193.65741773521415352079569727811', '194.37543164424989651055305239769', '195.362798689880475010455005302304', '195.7146577678264638373578739680', '196.4978182094597119230086726715', '196.96090326051287277162458788338', '197.525341691863846429054196414246', '198.09518763529047228229450954427', '198.31386268943719943278826236486', '198.94345462181334003280620197317', '199.909420778246377012514526230106'], 'prelabel': '1-2001-2001.50-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.292604933071013, 'root_angle': 0.12544029640369944, 'root_number': '0.923349308887392635160461407697+0.383961005542456594933199185372*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0627201482018', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(308)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.772940174608091654765340096136+0.0631157210709868554173039221026*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.774764367767', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.0614815719', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.31591490346', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 9.292604933071013, 'bad_primes': [3, 23, 29], 'central_character': '2001.50', 'conductor': 2001, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2001/50'], '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': '1-2001-2001.50-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': '1-2001-2001.50-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.292604933071013, 'root_angle': 0.06272014820184972, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.774764367767', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2001.50', 'Lhash_array': ['dirichlet_L_2001.50'], 'label': '1-2001-2001.50-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2001/50'}
Lfunction data - 1-2001-2001.50-r0-0-0