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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_83.77', 'a10': [0.8961655569610556, -0.4437198378669597], 'a2': [-0.7714891798219429, 0.6362424423265598], 'a3': [0.8179293607667176, 0.5753186602186205], 'a4': [0.19039110916466837, -0.9817083199968549], 'a5': [-0.9736954238777791, -0.22785350890313757], 'a6': [-0.9970658011837404, 0.07654925283649565], 'a7': [0.720521593600787, 0.6934325007922417], 'a8': [0.4777198185122629, 0.8785122509109424], 'a9': [0.33801687840850275, 0.9411400479795615], 'algebraic': True, 'analytic_conductor': 0.38545037953268074, 'analytic_normalization': 0, 'bad_lfactors': [[83, [1]]], 'bad_primes': [83], 'central_character': '83.77', 'coeff_info': ['x^41 - 1', '0.988280423780349 + 0.152649284218874*I', '\\\\zeta_{41}'], 'conductor': 83, 'conductor_radical': 83, 'conjugate': 'dirichlet_L_83.69', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^16', 'a^4', 'a^32', 'a^22', 'a^20', 'a^5', 'a^7', 'a^8', 'a^38', 'a^15', 'a^36', 'a^2', 'a^21', 'a^26', 'a^23', 'a^35', 'a^24', 'a^14', 'a^13', 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'label': '1-83-83.77-r0-0-0', 'leading_term': '0.540449254245399738313719504509+0.576531056761078680270467527674*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/83/77', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.7902363290968434, 1.0672619979219244, 1.4997311129679227, 1.8577862107621685, 1.9295683130648604, 1.570180029995991, 0.7437752431091864, -0.44068199799315944, -1.7287274468414042, -2.773249044909456, -3.238128322849423, -2.9244824214043184, -1.872053351489434, -0.38625484180731373, 1.0375108133102715, 1.8804972754566058, 1.8022336514763295, 0.7939557993846957, -0.7918232237573635, -2.3653404780897604, -3.338120209966467, -3.376240701270132, -2.549010919623346, -1.292613841400117, -0.1942599376123594, 0.30368015717080277, 0.1284092445841104, -0.3957009711966488, 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0.5205575728945254, 'root_number': '-0.0645386326988522049769318305659+0.997915209268484215416308119354*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.260278786447', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(41)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.735114280351136501057534590788+0.433940943062348527763985628540*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.07848542871', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.1412610838', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '5.47639655605', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.38545037953268074, 'bad_primes': [83], 'central_character': '83.77', 'conductor': 83, 'conductor_radical': 83, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/83/77'], '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': '1-83-83.77-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': '1-83-83.77-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.38545037953268074, 'root_angle': 0.2602787864472627, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.07848542871', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_83.77', 'Lhash_array': ['dirichlet_L_83.77'], 'label': '1-83-83.77-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/83/77'}
Lfunction data - 1-83-83.77-r0-0-0