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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_117.103', 'a10': [1.0, 0.0], 'a2': [0.5, -0.8660254037844386], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.5, 0.8660254037844386], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, -0.8660254037844386], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.5433457157267909, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '117.103', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 117, 'conductor_radical': 39, 'conjugate': 'dirichlet_L_117.25', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 0, 'a^4', 'a^1', 0, 'a^5', 'a^3', 0, 'a^0', 'a^5', 0, 0, 'a^4', 0, 'a^2', 'a^0', 0, 'a^3', 'a^5', 0, 'a^4', 'a^4', 0, 'a^2', 0, 0, 'a^3', 'a^2', 0, 'a^1', 'a^1', 0, 'a^5', 'a^0', 0, 'a^3', 'a^2', 0, 'a^4', 'a^1', 0, 'a^2', 'a^3', 0, 'a^3', 'a^5', 0, 'a^4', 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-0.4444444444444444, 'root_number': '0.173648177666930348851716626769-0.984807753012208059366743024589*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.222222222222', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.19187176402917498534765422073-0.645189393855817251446886474544*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.43953985585', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.98920976045', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.12974155348', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.5433457157267909, 'bad_primes': [3, 13], 'central_character': '117.103', 'conductor': 117, 'conductor_radical': 39, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/117/103'], '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': '1-117-117.103-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': '1-117-117.103-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5433457157267909, 'root_angle': -0.2222222222222222, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43953985585', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_117.103', 'Lhash_array': ['dirichlet_L_117.103'], 'label': '1-117-117.103-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/117/103'}
Lfunction data - 1-117-117.103-r0-0-0