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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_5600.4381', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.8910065241883679, 0.4539904997395468], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.5877852522924731, -0.8090169943749475], 'algebraic': True, 'analytic_conductor': 601.8035788499001, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '5600.4381', 'coeff_info': ['x^40 - 1', '0.987688340595138 + 0.156434465040231*I', '\\\\zeta_{40}'], 'conductor': 5600, 'conductor_radical': 70, 'conjugate': 'dirichlet_L_5600.2421', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^17', 0, 0, 0, 0, 0, 'a^34', 0, 'a^51', 0, 'a^29', 0, 0, 0, 'a^48', 0, 'a^53', 0, 0, 0, 'a^26', 0, 0, 0, 'a^51', 0, 'a^37', 0, 'a^28', 0, 'a^28', 0, 0, 0, 'a^39', 0, 'a^46', 0, 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{'__RealLiteral__': 0, 'data': '1.81448307772', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.67280715162', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 601.8035788499001, 'bad_primes': [2, 5, 7], 'central_character': '5600.4381', 'conductor': 5600, 'conductor_radical': 70, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5600/4381'], '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': '1-5600-5600.4381-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': '1-5600-5600.4381-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 601.8035788499001, 'root_angle': -0.44625000000000004, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.836643987646', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_5600.4381', 'Lhash_array': ['dirichlet_L_5600.4381'], 'factors': ['1-5600-5600.4381-r1-0-0'], 'label': '1-5600-5600.4381-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5600/4381'}
Lfunction data - 1-5600-5600.4381-r1-0-0