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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1183.9', 'a10': [0.12053668025532305, 0.992708874098054], 'a2': [-0.040265940109415144, 0.9991889981715696], 'a3': [-0.970941817426052, 0.23931566428755777], 'a4': [-0.99675730813421, -0.08046656871672588], 'a5': [0.9870502626379128, -0.16041128085776024], 'a6': [-0.20002569377604443, -0.9797906520422677], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.12053668025532305, -0.992708874098054], 'a9': [0.8854560256532099, -0.46472317204376856], 'algebraic': True, 'analytic_conductor': 5.493828903459774, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [13, [1]]], 'bad_primes': [7, 13], 'central_character': '1183.9', 'coeff_info': ['x^39 - 1', '0.987050262637913 + 0.160411280857760*I', '\\\\zeta_{39}'], 'conductor': 1183, 'conductor_radical': 91, 'conjugate': 'dirichlet_L_1183.263', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^10', 'a^18', 'a^20', 'a^38', 'a^28', 0, 'a^30', 'a^36', 'a^9', 'a^3', 'a^38', 0, 0, 'a^17', 'a^1', 'a^17', 'a^7', 'a^0', 'a^19', 0, 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'root_analytic_conductor': 5.493828903459774, 'root_angle': 0.4649461285963525, 'root_number': '0.109902529464615208466110613789+0.993942369565398588325940258757*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.232473064298', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(39)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.788573315134062703400415298101+0.458184753862330534384081081854*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.887891081104', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.98002748355', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.84424671599', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 5.493828903459774, 'bad_primes': [7, 13], 'central_character': '1183.9', 'conductor': 1183, 'conductor_radical': 91, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1183/9'], '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': '1-1183-1183.9-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': '1-1183-1183.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.493828903459774, 'root_angle': 0.23247306429817624, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.887891081104', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1183.9', 'Lhash_array': ['dirichlet_L_1183.9'], 'label': '1-1183-1183.9-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1183/9'}
Lfunction data - 1-1183-1183.9-r0-0-0