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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4024.1269', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.731021655560995, 0.6823542621694849], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.8832086139858775, -0.4689803238741955], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.4185176499477741, 0.9082086636242755], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.06878532179827576, -0.997631484820476], 'algebraic': True, 'analytic_conductor': 18.68737743662057, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [503, [1]]], 'bad_primes': [2, 503], 'central_character': '4024.1269', 'coeff_info': ['x^502 - 1', '0.999921672072223 + 0.0125159785989932*I', '\\\\zeta_{502}'], 'conductor': 4024, 'conductor_radical': 1006, 'conjugate': 'dirichlet_L_4024.853', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^693', 0, 'a^463', 0, 'a^160', 0, 'a^382', 0, 'a^621', 0, 'a^435', 0, 'a^152', 0, 'a^356', 0, 'a^295', 0, 'a^351', 0, 'a^420', 0, 'a^424', 0, 'a^573', 0, 'a^261', 0, 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'196.35015134891317421761895664397', '196.6136606603226844015596491921', '197.49164220908389831421123003405', '197.78793414475390435496323750038', '198.532879342062475024187805564811', '199.09638908145724823550166918386', '199.46325546529730850152904434720', '199.964757837339671977998895523735'], 'prelabel': '1-4024-4024.1269-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.68737743662057, 'root_angle': -0.1676258128091682, 'root_number': '0.864514851224198909107882862655-0.502607274134389370107033662319*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(502)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.928497258852272950769043129193+0.0855040724243919681066108248002*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.463741572109', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.57647498071', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.55916178217', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 18.68737743662057, 'bad_primes': [2, 503], 'central_character': '4024.1269', 'conductor': 4024, 'conductor_radical': 1006, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4024/1269'], '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': '1-4024-4024.1269-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': '1-4024-4024.1269-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.68737743662057, 'root_angle': -0.0838129064045841, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.463741572109', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4024.1269', 'Lhash_array': ['dirichlet_L_4024.1269'], 'label': '1-4024-4024.1269-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4024/1269'}
Lfunction data - 1-4024-4024.1269-r0-0-0