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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_135.14', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9396926207859084, 0.3420201433256687], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.766044443118978, -0.6427876096865394], 'a8': [-0.5, 0.8660254037844386], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 14.507764847274379, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '135.14', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 135, 'conductor_radical': 15, 'conjugate': 'dirichlet_L_135.29', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 0, 'a^16', 0, 0, 'a^11', 'a^6', 0, 0, 'a^5', 0, 'a^1', 'a^1', 0, 'a^14', 'a^12', 0, 'a^6', 0, 0, 'a^13', 'a^16', 0, 0, 'a^9', 0, 'a^9', 'a^17', 0, 'a^16', 'a^4', 0, 'a^2', 0, 0, 'a^3', 'a^14', 0, 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'199.295849887268939102574472513969'], 'prelabel': '1-135-135.14-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.507764847274379, 'root_angle': 0.18518518518518517, 'root_number': '0.835487811412936419653826170020+0.549508978070806035262780374050*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0925925925926', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.712731683934177552495105299139+0.102907123518226149462396860940*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.92919202059', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.60863882497', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.42856376079', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 14.507764847274379, 'bad_primes': [3, 5], 'central_character': '135.14', 'conductor': 135, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/135/14'], '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': '1-135-135.14-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': '1-135-135.14-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.507764847274379, 'root_angle': 0.09259259259259259, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.92919202059', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_135.14', 'Lhash_array': ['dirichlet_L_135.14'], 'label': '1-135-135.14-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/135/14'}
Lfunction data - 1-135-135.14-r1-0-0