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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1183.16', 'a10': [-0.8451900855437947, -0.5344658261278011], 'a2': [-0.3546048870425356, -0.9350162426854148], 'a3': [-0.99675730813421, -0.08046656871672588], 'a4': [-0.7485107481711011, 0.6631226582407952], 'a5': [0.7994427634035012, -0.6007422642379789], 'a6': [0.27821746391645263, 0.9605181116313724], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.8854560256532099, 0.46472317204376856], 'a9': [0.9870502626379128, 0.16041128085776024], 'algebraic': True, 'analytic_conductor': 5.493828903459774, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [13, [1]]], 'bad_primes': [7, 13], 'central_character': '1183.16', 'coeff_info': ['x^39 - 1', '0.987050262637913 + 0.160411280857760*I', '\\\\zeta_{39}'], 'conductor': 1183, 'conductor_radical': 91, 'conjugate': 'dirichlet_L_1183.74', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^27', 'a^20', 'a^15', 'a^35', 'a^8', 0, 'a^3', 'a^1', 'a^23', 'a^38', 'a^35', 0, 0, 'a^16', 'a^30', 'a^3', 'a^28', 'a^13', 'a^11', 0, 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False, 'root_analytic_conductor': 5.493828903459774, 'root_angle': -0.13241845443949637, 'root_number': '0.673391386881680784188323068131-0.739286169269766951099000795157*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.132418454439', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(39)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.762197106168035087652023162579-0.338103378534259833351459269720*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.12173816434', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.4011584498', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.75313514065', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 5.493828903459774, 'bad_primes': [7, 13], 'central_character': '1183.16', 'conductor': 1183, 'conductor_radical': 91, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1183/16'], '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': '1-1183-1183.16-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': '1-1183-1183.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.493828903459774, 'root_angle': -0.13241845443949637, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12173816434', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1183.16', 'Lhash_array': ['dirichlet_L_1183.16'], 'factors': ['1-1183-1183.16-r0-0-0'], 'label': '1-1183-1183.16-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1183/16'}
Lfunction data - 1-1183-1183.16-r0-0-0