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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3381.1067', 'a10': [0.03399337025129776, 0.9994220583812218], 'a2': [0.476262120839475, 0.8793033562164342], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5463487845069707, 0.8375577625858146], 'a5': [0.8949849248217099, 0.4460963845873202], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9966725824941932, -0.08150928354706316], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 15.701297990361368, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [23, [1]]], 'bad_primes': [3, 7, 23], 'central_character': '3381.1067', 'coeff_info': ['x^462 - 1', '0.999907521857918 + 0.0135995489615099*I', '\\\\zeta_{462}'], 'conductor': 3381, 'conductor_radical': 483, 'conjugate': 'dirichlet_L_3381.1559', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^79', 0, 'a^158', 'a^34', 0, 0, 'a^237', 0, 'a^113', 'a^317', 0, 'a^135', 0, 0, 'a^316', 'a^458', 0, 'a^301', 'a^192', 0, 'a^396', 0, 0, 'a^68', 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'199.112593200531371820571425919315'], 'prelabel': '1-3381-3381.1067-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': 0.2660020515582505, 'root_number': '0.670680795878142532285103343321+0.741746095399403710859286569505*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(462)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.29002887168081626987611141755+0.650148990633070538116543111807*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.647643887872', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.14552580161', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.81135522453', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 15.701297990361368, 'bad_primes': [3, 7, 23], 'central_character': '3381.1067', 'conductor': 3381, 'conductor_radical': 483, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3381/1067'], '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': '1-3381-3381.1067-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': '1-3381-3381.1067-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': 0.13300102577912526, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.647643887872', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3381.1067', 'Lhash_array': ['dirichlet_L_3381.1067'], 'label': '1-3381-3381.1067-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3381/1067'}
Lfunction data - 1-3381-3381.1067-r0-0-0