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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_469.438', 'a10': [0.9283679330160726, 0.3716624556603275], 'a2': [-0.9594929736144974, -0.28173255684142967], 'a3': [0.9283679330160726, -0.3716624556603275], 'a4': [0.8412535328311812, 0.5406408174555976], 'a5': [-0.9954719225730846, -0.09505604330418266], 'a6': [-0.9954719225730846, 0.09505604330418266], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.6548607339452851, -0.7557495743542583], 'a9': [0.7237340381050702, -0.690079011482112], 'algebraic': True, 'analytic_conductor': 2.178026843383461, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [67, [1]]], 'bad_primes': [7, 67], 'central_character': '469.438', 'coeff_info': ['x^33 - 1', '0.981928697262707 + 0.189251244360410*I', '\\\\zeta_{33}'], 'conductor': 469, 'conductor_radical': 469, 'conjugate': 'dirichlet_L_469.121', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^18', 'a^31', 'a^3', 'a^17', 'a^16', 0, 'a^21', 'a^29', 'a^2', 'a^6', 'a^1', 'a^1', 0, 'a^15', 'a^6', 'a^8', 'a^14', 'a^15', 'a^20', 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'0.991204040425301313998032264658+0.132342548881898290703372023662*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0211249452874', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(33)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.872735501778798111137836289460-0.0730611130591876442645413873346*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.25102620447', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.16336593465', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.59487932227', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.178026843383461, 'bad_primes': [7, 67], 'central_character': '469.438', 'conductor': 469, 'conductor_radical': 469, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/469/438'], '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': '1-469-469.438-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': '1-469-469.438-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.178026843383461, 'root_angle': 0.021124945287435942, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25102620447', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_469.438', 'Lhash_array': ['dirichlet_L_469.438'], 'label': '1-469-469.438-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/469/438'}
Lfunction data - 1-469-469.438-r0-0-0