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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_119.39', 'a10': [-0.7933533402912352, -0.6087614290087207], 'a2': [-0.25881904510252074, -0.9659258262890683], 'a3': [0.9914448613738104, -0.1305261922200516], 'a4': [-0.8660254037844386, 0.5], 'a5': [0.7933533402912352, -0.6087614290087207], 'a6': [-0.3826834323650898, -0.9238795325112867], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0.9659258262890683, -0.25881904510252074], 'algebraic': True, 'analytic_conductor': 12.788326050560377, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [17, [1]]], 'bad_primes': [7, 17], 'central_character': '119.39', 'coeff_info': ['x^48 - 1', '0.991444861373810 + 0.130526192220052*I', '\\\\zeta_{48}'], 'conductor': 119, 'conductor_radical': 119, 'conjugate': 'dirichlet_L_119.58', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^34', 'a^47', 'a^20', 'a^43', 'a^33', 0, 'a^6', 'a^46', 'a^29', 'a^41', 'a^19', 'a^12', 0, 'a^42', 'a^40', 0, 'a^32', 'a^34', 'a^15', 0, 'a^27', 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'197.403307888916255703999027200680', '198.13893673090531737126119864045', '199.100277013040793686484361732167', '199.86816295677093650164276648435'], 'prelabel': '1-119-119.39-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.788326050560377, 'root_angle': -0.2862735297679508, 'root_number': '-0.225945288037812638089907111121-0.974139993437036687806452410830*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.286273529768', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(48)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.21408101328960966367865426222-0.843210493108923373200007656945*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.12447605245', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.25906778263', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.60834682497', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 12.788326050560377, 'bad_primes': [7, 17], 'central_character': '119.39', 'conductor': 119, 'conductor_radical': 119, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/119/39'], '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': '1-119-119.39-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': '1-119-119.39-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.788326050560377, 'root_angle': -0.2862735297679508, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12447605245', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_119.39', 'Lhash_array': ['dirichlet_L_119.39'], 'factors': ['1-119-119.39-r1-0-0'], 'label': '1-119-119.39-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/119/39'}
Lfunction data - 1-119-119.39-r1-0-0