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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_113.106', 'a10': [-0.2225209339563144, 0.9749279121818236], 'a2': [0.6234898018587335, -0.7818314824680298], 'a3': [-0.9009688679024191, -0.4338837391175581], 'a4': [-0.2225209339563144, -0.9749279121818236], 'a5': [-0.9009688679024191, 0.4338837391175581], 'a6': [-0.9009688679024191, 0.4338837391175581], 'a7': [-0.9009688679024191, -0.4338837391175581], 'a8': [-0.9009688679024191, -0.4338837391175581], 'a9': [0.6234898018587335, 0.7818314824680298], 'algebraic': True, 'analytic_conductor': 0.5247697938216015, 'analytic_normalization': 0, 'bad_lfactors': [[113, [1]]], 'bad_primes': [113], 'central_character': '113.106', 'coeff_info': ['x^7 - 1', '0.623489801858734 + 0.781831482468030*I', '\\\\zeta_{7}'], 'conductor': 113, 'conductor_radical': 113, 'conjugate': 'dirichlet_L_113.16', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^6', 'a^4', 'a^5', 'a^3', 'a^3', 'a^4', 'a^4', 'a^1', 'a^2', 'a^2', 'a^2', 'a^4', 'a^3', 'a^0', 'a^3', 'a^6', 'a^0', 'a^4', 'a^1', 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'196.44680363664002141863391908308', '198.12473720702908980574746243255', '198.7211188359794522512611599635', '199.784918384009447489953232186514'], 'prelabel': '1-113-113.106-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5247697938216015, 'root_angle': 0.39274304460243487, 'root_number': '-0.781384301459924915103918329833+0.624050136953742829788378216184*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.392743044602', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(7)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.464549980326114977392269644966-0.397872650959990906898598012576*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.250470632127', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.40883381594', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.93430207967', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.5247697938216015, 'bad_primes': [113], 'central_character': '113.106', 'conductor': 113, 'conductor_radical': 113, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/113/106'], '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': '1-113-113.106-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': '1-113-113.106-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5247697938216015, 'root_angle': 0.39274304460243487, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.250470632127', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_113.106', 'Lhash_array': ['dirichlet_L_113.106'], 'factors': ['1-113-113.106-r0-0-0'], 'label': '1-113-113.106-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/113/106'}
Lfunction data - 1-113-113.106-r0-0-0