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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_128.101', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.5555702330196022, -0.8314696123025452], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.19509032201612828, 0.9807852804032304], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.3826834323650898, -0.9238795325112867], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.3826834323650898, -0.9238795325112867], 'algebraic': True, 'analytic_conductor': 0.5944295009660618, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]]], 'bad_primes': [2], 'central_character': '128.101', 'coeff_info': ['x^32 - 1', '0.980785280403230 + 0.195090322016128*I', '\\\\zeta_{32}'], 'conductor': 128, 'conductor_radical': 2, 'conjugate': 'dirichlet_L_128.109', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^27', 0, 'a^9', 0, 'a^26', 0, 'a^22', 0, 'a^29', 0, 'a^7', 0, 'a^4', 0, 'a^28', 0, 'a^15', 0, 'a^21', 0, 'a^30', 0, 'a^18', 0, 'a^17', 0, 'a^19', 0, 'a^8', 0, 'a^24', 0, 'a^3', 0, 'a^1', 0, 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'198.7763008667718037437802245037'], 'prelabel': '1-2e7-128.101-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5944295009660618, 'root_angle': -0.11718750000000001, 'root_number': '0.740951125354959091175616897495-0.671558954847018400625376850427*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1171875', 'prec': 34}, 'spectral_label': 'r0-0', 'st_group': 'mu(32)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.20209625360282774109483588201-0.285229152342048003591537540016*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.40615458747', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.98818333623', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.13577637136', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.5944295009660618, 'bad_primes': [2], 'central_character': '128.101', 'conductor': 128, 'conductor_radical': 2, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/128/101'], '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': '1-2e7-128.101-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': '1-2e7-128.101-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5944295009660618, 'root_angle': -0.11718750000000001, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40615458747', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_128.101', 'Lhash_array': ['dirichlet_L_128.101'], 'factors': ['1-2e7-128.101-r0-0-0'], 'label': '1-2e7-128.101-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/128/101'}
Lfunction data - 1-2e7-128.101-r0-0-0