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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1225.447', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9195277725514507, -0.3930250316539236], 'a3': [-0.8345732537213026, -0.5508969814521025], 'a4': [0.6910626489868646, 0.7227948638273916], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.5508969814521025, 0.8345732537213026], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.3513748240813427, -0.9362348706397372], 'a9': [0.3930250316539236, 0.9195277725514507], 'algebraic': True, 'analytic_conductor': 5.6888760834642635, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '1225.447', 'coeff_info': ['x^140 - 1', '0.998993066541315 + 0.0448648303505149*I', '\\\\zeta_{140}'], 'conductor': 1225, 'conductor_radical': 35, 'conjugate': 'dirichlet_L_1225.433', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^79', 'a^83', 'a^18', 0, 'a^22', 0, 'a^97', 'a^26', 0, 'a^44', 'a^101', 'a^51', 0, 0, 'a^36', 'a^17', 'a^105', 'a^112', 0, 0, 'a^123', 'a^109', 'a^40', 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5.6888760834642635, 'root_angle': 0.6106122448979592, 'root_number': '-0.340547005260388196689788716423+0.940227492263537853359551022334*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.305306122449', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(140)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.474283306069216571710176544378-0.0398096362137060383074921309534*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.22437124818', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.02099681562', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.98362317914', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 5.6888760834642635, 'bad_primes': [5, 7], 'central_character': '1225.447', 'conductor': 1225, 'conductor_radical': 35, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1225/447'], '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': '1-35e2-1225.447-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': '1-35e2-1225.447-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6888760834642635, 'root_angle': 0.3053061224489796, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22437124818', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1225.447', 'Lhash_array': ['dirichlet_L_1225.447'], 'label': '1-35e2-1225.447-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1225/447'}
Lfunction data - 1-35e2-1225.447-r0-0-0