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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1573.1200', 'a10': [-0.32706796331742166, 0.9450008187146685], 'a2': [-0.5800569095711982, 0.8145759520503357], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.32706796331742166, -0.9450008187146685], 'a5': [0.9594929736144974, -0.28173255684142967], 'a6': [0.9954719225730846, 0.09505604330418266], 'a7': [0.7860530947427875, 0.6181589862206052], 'a8': [0.9594929736144974, 0.28173255684142967], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 7.304981289215744, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '1573.1200', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 1573, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_1573.738', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^23', 'a^44', 'a^46', 'a^63', 'a^1', 'a^7', 'a^3', 'a^22', 'a^20', 0, 'a^24', 0, 'a^30', 'a^41', 'a^26', 'a^16', 'a^45', 'a^61', 'a^43', 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'195.681007480751591551039175932752', '196.07066695773178305472416445521', '196.537858391072857245927623462139', '197.17615628125447765143606416536', '197.469359717815868779668590685719', '198.46799382180306665606710493701', '198.85347327326416343012191011047', '199.63872508772422774193800529412', '199.920294777121952997862299030360'], 'prelabel': '1-1573-1573.1200-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.304981289215744, 'root_angle': 0.11292249409229121, 'root_number': '0.758679257934318908470552276297+0.651464337918992461841792129928*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.112922494092', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.878690071720159834968266833611+0.148161661774697503722950274628*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.04712713808', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.7029063926', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.53179944886', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 7.304981289215744, 'bad_primes': [11, 13], 'central_character': '1573.1200', 'conductor': 1573, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1573/1200'], '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': '1-1573-1573.1200-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': '1-1573-1573.1200-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.304981289215744, 'root_angle': 0.11292249409229121, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04712713808', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1573.1200', 'Lhash_array': ['dirichlet_L_1573.1200'], 'factors': ['1-1573-1573.1200-r0-0-0'], 'label': '1-1573-1573.1200-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1573/1200'}
Lfunction data - 1-1573-1573.1200-r0-0-0