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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_5445.857', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.8145759520503357, 0.5800569095711982], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.32706796331742166, 0.9450008187146685], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.3716624556603275, -0.9283679330160726], 'a8': [-0.28173255684142967, 0.9594929736144974], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 585.1465155067333, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [11, [1]]], 'bad_primes': [3, 5, 11], 'central_character': '5445.857', 'coeff_info': ['x^132 - 1', '0.998867339183008 + 0.0475819158237423*I', '\\\\zeta_{132}'], 'conductor': 5445, 'conductor_radical': 165, 'conjugate': 'dirichlet_L_5445.2408', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 0, 'a^26', 0, 0, 'a^91', 'a^39', 0, 0, 0, 0, 'a^125', 'a^104', 0, 'a^52', 'a^21', 0, 'a^12', 0, 0, 0, 'a^41', 0, 0, 'a^6', 0, 'a^117', 'a^34', 0, 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'0.998814628462', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.75527101525', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.10186351822', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 585.1465155067333, 'bad_primes': [3, 5, 11], 'central_character': '5445.857', 'conductor': 5445, 'conductor_radical': 165, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5445/857'], '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': '1-5445-5445.857-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-5445-5445.857-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 585.1465155067333, 'root_angle': 0.428783618085096, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.998814628462', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_5445.857', 'Lhash_array': ['dirichlet_L_5445.857'], 'label': '1-5445-5445.857-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5445/857'}
Lfunction data - 1-5445-5445.857-r1-0-0