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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1625.1134', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.985996037070505, 0.16676874671610228], 'a3': [-0.387515586452103, 0.9218631515885005], 'a4': [0.9443763702374811, -0.32886664673858323], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.22835087011065575, -0.9735789028731603], 'a7': [-0.9135454576426009, -0.4067366430758002], 'a8': [-0.8763066800438636, 0.48175367410171527], 'a9': [-0.6996633405133654, -0.7144726796328034], 'algebraic': True, 'analytic_conductor': 7.546468273983207, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [13, [1]]], 'bad_primes': [5, 13], 'central_character': '1625.1134', 'coeff_info': ['x^150 - 1', '0.999122830098858 + 0.0418756537291996*I', '\\\\zeta_{150}'], 'conductor': 1625, 'conductor_radical': 65, 'conjugate': 'dirichlet_L_1625.139', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^71', 'a^47', 'a^142', 0, 'a^118', 'a^85', 'a^63', 'a^94', 0, 'a^146', 'a^39', 0, 'a^6', 0, 'a^134', 'a^133', 'a^15', 'a^28', 0, 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'195.18961025188001858875677338314', '195.97873473556901437346609640189', '196.57705353430485951639671236406', '197.288471944072198500036492539663', '197.736235029800899519281165621048', '198.2088066694088137104329124937', '198.56841622465762019574284135650', '199.50682527847537890270097133830', '199.8624159640576986919827013921'], 'prelabel': '1-1625-1625.1134-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.546468273983207, 'root_angle': -0.17464619097038334, 'root_number': '0.455970126312510494547760001394-0.889995080835030921774607826355*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17464619097', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(150)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.539485623618527139671273203658+0.0782673719907284832436732383332*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.307940835587', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.40064904833', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.91188084217', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 7.546468273983207, 'bad_primes': [5, 13], 'central_character': '1625.1134', 'conductor': 1625, 'conductor_radical': 65, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1625/1134'], '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': '1-1625-1625.1134-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': '1-1625-1625.1134-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.546468273983207, 'root_angle': -0.17464619097038334, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.307940835587', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1625.1134', 'Lhash_array': ['dirichlet_L_1625.1134'], 'factors': ['1-1625-1625.1134-r0-0-0'], 'label': '1-1625-1625.1134-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1625/1134'}
Lfunction data - 1-1625-1625.1134-r0-0-0