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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2349.355', 'a10': [-0.024930691738072875, -0.9996891820008162], 'a2': [0.3026867562368259, -0.953090094166773], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.8167614551976566, -0.5769754980095829], 'a5': [0.9452476663977248, -0.3263538710811556], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.908056166236305, 0.41884842002832484], 'a8': [-0.7971325072229225, 0.6038044103254774], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 10.908710138822494, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [29, [1]]], 'bad_primes': [3, 29], 'central_character': '2349.355', 'coeff_info': ['x^189 - 1', '0.999447456932676 + 0.0332382434976267*I', '\\\\zeta_{189}'], 'conductor': 2349, 'conductor_radical': 87, 'conjugate': 'dirichlet_L_2349.1330', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^151', 0, 'a^113', 'a^179', 0, 'a^13', 'a^75', 0, 'a^141', 'a^100', 0, 'a^128', 'a^164', 0, 'a^37', 'a^42', 0, 'a^120', 'a^103', 0, 'a^62', 'a^122', 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{'__RealLiteral__': 0, 'data': '-0.498853927653', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(189)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.913789965486071046257886300396-0.794543226041957114407114692873*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.425937513839', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.60760033449', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.3403552977', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 10.908710138822494, 'bad_primes': [3, 29], 'central_character': '2349.355', 'conductor': 2349, 'conductor_radical': 87, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2349/355'], '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': '1-2349-2349.355-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': '1-2349-2349.355-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.908710138822494, 'root_angle': 0.49885392765324443, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.425937513839', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2349.355', 'Lhash_array': ['dirichlet_L_2349.355'], 'factors': ['1-2349-2349.355-r0-0-0'], 'label': '1-2349-2349.355-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2349/355'}
Lfunction data - 1-2349-2349.355-r0-0-0