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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2808.2245', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9396926207859084, 0.3420201433256687], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.766044443118978, 0.6427876096865394], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 13.040297177442982, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1]]], 'bad_primes': [2, 3, 13], 'central_character': '2808.2245', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 2808, 'conductor_radical': 78, 'conjugate': 'dirichlet_L_2808.2005', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^19', 0, 'a^2', 0, 0, 0, 'a^11', 0, 0, 0, 0, 0, 'a^0', 0, 'a^21', 0, 0, 0, 'a^16', 0, 'a^2', 0, 0, 0, 'a^23', 0, 'a^4', 0, 0, 0, 'a^21', 0, 'a^15', 0, 0, 0, 'a^10', 0, 'a^23', 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'192.759614257399957221111019082308', '193.23846738397009659928753797602', '193.77548176942325960886211110657', '194.08014534856215233752479246644', '195.05418208312958443985667057584', '195.25733551120824537286394045804', '196.13992208810670377885480564844', '196.48794837427527922156929658592', '197.08532074801653555249607736915', '197.56763298631623223200077138449', '198.1913553063905519495528675038', '198.70681730004674277679175175422', '199.33897609570387292644773683778', '199.669749312534891066384145396580'], 'prelabel': '1-2808-2808.2245-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.040297177442982, 'root_angle': 0.13323878356297592, 'root_number': '0.669571971073750233244502660479+0.742747181450332385523586997674*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.38799686339799616004956325605+0.244194619438159819056096597044*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.13424818616', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.87951221674', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.84808273154', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 13.040297177442982, 'bad_primes': [2, 3, 13], 'central_character': '2808.2245', 'conductor': 2808, 'conductor_radical': 78, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2808/2245'], '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': '1-2808-2808.2245-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': '1-2808-2808.2245-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.040297177442982, 'root_angle': 0.13323878356297592, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13424818616', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2808.2245', 'Lhash_array': ['dirichlet_L_2808.2245'], 'factors': ['1-2808-2808.2245-r0-0-0'], 'label': '1-2808-2808.2245-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2808/2245'}
Lfunction data - 1-2808-2808.2245-r0-0-0