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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_43.29', 'a10': [0.07473009358642425, -0.9972037971811801], 'a2': [-0.6234898018587335, 0.7818314824680298], 'a3': [0.9888308262251285, -0.14904226617617444], 'a4': [-0.2225209339563144, -0.9749279121818236], 'a5': [-0.8262387743159949, 0.5633200580636221], 'a6': [-0.5, 0.8660254037844386], 'a7': [0.5, 0.8660254037844386], 'a8': [0.9009688679024191, 0.4338837391175581], 'a9': [0.9555728057861407, -0.2947551744109042], 'algebraic': True, 'analytic_conductor': 4.620991766168876, 'analytic_normalization': 0, 'bad_lfactors': [[43, [1]]], 'bad_primes': [43], 'central_character': '43.29', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 43, 'conductor_radical': 43, 'conjugate': 'dirichlet_L_43.3', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^15', 'a^41', 'a^30', 'a^17', 'a^14', 'a^7', 'a^3', 'a^40', 'a^32', 'a^12', 'a^29', 'a^10', 'a^22', 'a^16', 'a^18', 'a^4', 'a^13', 'a^23', 'a^5', 'a^6', 'a^27', 'a^26', 'a^2', 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'primitive': True, 'rational': False, 'root_analytic_conductor': 4.620991766168876, 'root_angle': 0.5848219779581741, 'root_number': '-0.263333558056469874198380403501+0.964704844603425742644941413520*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.292410988979', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.859007043222306648455846668407+0.528496212162938334662679796773*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.1180772592', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '4.4141717624', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '6.6591675056', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.620991766168876, 'bad_primes': [43], 'central_character': '43.29', 'conductor': 43, 'conductor_radical': 43, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/43/29'], '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': '1-43-43.29-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-43-43.29-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.620991766168876, 'root_angle': 0.29241098897908707, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.1180772592', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_43.29', 'Lhash_array': ['dirichlet_L_43.29'], 'label': '1-43-43.29-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/43/29'}
Lfunction data - 1-43-43.29-r1-0-0