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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_51.20', 'a10': [0.3826834323650898, 0.9238795325112867], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [2.9010907910729803e-30, -1.0], 'a5': [0.3826834323650898, -0.9238795325112867], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.3826834323650898, -0.9238795325112867], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.23684300429116525, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [17, [1]]], 'bad_primes': [3, 17], 'central_character': '51.20', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 51, 'conductor_radical': 51, 'conjugate': 'dirichlet_L_51.23', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^6', 0, 'a^12', 'a^13', 0, 'a^11', 'a^2', 0, 'a^3', 'a^15', 0, 'a^4', 'a^1', 0, 'a^8', 0, 0, 'a^14', 'a^9', 0, 'a^5', 'a^7', 0, 'a^10', 'a^10', 0, 'a^7', 'a^5', 0, 'a^9', 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'199.98669073039325626910708206809'], 'prelabel': '1-51-51.20-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.23684300429116525, 'root_angle': -0.032859417681573896, 'root_number': '0.978762361965820185943964942344-0.204998143404004483865064729148*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0328594176816', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(16)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.762057514523243069012559419685+0.0114499288834923522649931546912*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.31456830312', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.35697644224', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.01360098703', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.23684300429116525, 'bad_primes': [3, 17], 'central_character': '51.20', 'conductor': 51, 'conductor_radical': 51, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/51/20'], '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': '1-51-51.20-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': '1-51-51.20-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.23684300429116525, 'root_angle': -0.032859417681573896, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31456830312', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_51.20', 'Lhash_array': ['dirichlet_L_51.20'], 'factors': ['1-51-51.20-r0-0-0'], 'label': '1-51-51.20-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/51/20'}
Lfunction data - 1-51-51.20-r0-0-0