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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1183.395', 'a10': [-0.20002569377604443, 0.9797906520422677], 'a2': [-0.9605181116313724, -0.27821746391645263], 'a3': [-0.7994427634035012, 0.6007422642379789], 'a4': [0.8451900855437947, 0.5344658261278011], 'a5': [-0.08046656871672588, -0.99675730813421], 'a6': [0.9350162426854148, -0.3546048870425356], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.6631226582407952, -0.7485107481711011], 'a9': [0.27821746391645263, -0.9605181116313724], 'algebraic': True, 'analytic_conductor': 5.493828903459774, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [13, [1]]], 'bad_primes': [7, 13], 'central_character': '1183.395', 'coeff_info': ['x^156 - 1', '0.999188998171570 + 0.0402659401094151*I', '\\\\zeta_{156}'], 'conductor': 1183, 'conductor_radical': 91, 'conjugate': 'dirichlet_L_1183.593', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^85', 'a^62', 'a^14', 'a^115', 'a^147', 0, 'a^99', 'a^124', 'a^44', 'a^71', 'a^76', 0, 0, 'a^21', 'a^28', 'a^8', 'a^53', 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0.2948277854010862, 'root_number': '-0.277951851141753138979224971643+0.960595007506739389597123720940*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.294827785401', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(156)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.436809790423625935609136397240-0.0327775780409937093490368292399*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.932754859722', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.07177479032', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.35640483945', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 5.493828903459774, 'bad_primes': [7, 13], 'central_character': '1183.395', 'conductor': 1183, 'conductor_radical': 91, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1183/395'], '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': '1-1183-1183.395-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': '1-1183-1183.395-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.493828903459774, 'root_angle': 0.2948277854010862, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.932754859722', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1183.395', 'Lhash_array': ['dirichlet_L_1183.395'], 'factors': ['1-1183-1183.395-r0-0-0'], 'label': '1-1183-1183.395-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1183/395'}
Lfunction data - 1-1183-1183.395-r0-0-0