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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4851.2428', 'a10': [-0.9009688679024191, 0.4338837391175581], 'a2': [0.4473131483156326, -0.8943774076663368], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5998218946879137, -0.8001335480112063], 'a5': [-0.7910710346563412, -0.6117242991150064], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9839295885986297, 0.17855689479863665], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 22.527949290518485, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [11, [1]]], 'bad_primes': [3, 7, 11], 'central_character': '4851.2428', 'coeff_info': ['x^210 - 1', '0.999552432283503 + 0.0299154661693985*I', '\\\\zeta_{210}'], 'conductor': 4851, 'conductor_radical': 231, 'conjugate': 'dirichlet_L_4851.2911', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^173', 0, 'a^136', 'a^127', 0, 0, 'a^99', 0, 'a^90', 0, 0, 'a^208', 0, 0, 'a^62', 'a^102', 0, 'a^84', 'a^53', 0, 0, 'a^10', 0, 'a^44', 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'0.826465619099468976876828269993-0.615053991569880360588867869770*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.483664585906', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.38173867863', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.13732995529', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 22.527949290518485, 'bad_primes': [3, 7, 11], 'central_character': '4851.2428', 'conductor': 4851, 'conductor_radical': 231, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4851/2428'], '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': '1-4851-4851.2428-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': '1-4851-4851.2428-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 22.527949290518485, 'root_angle': -0.3673914428540564, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.483664585906', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4851.2428', 'Lhash_array': ['dirichlet_L_4851.2428'], 'factors': ['1-4851-4851.2428-r0-0-0'], 'label': '1-4851-4851.2428-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4851/2428'}
Lfunction data - 1-4851-4851.2428-r0-0-0