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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2496.1805', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.3826834323650898, -0.9238795325112867], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.25881904510252074, -0.9659258262890683], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 11.591375268838206, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1]]], 'bad_primes': [2, 3, 13], 'central_character': '2496.1805', 'coeff_info': ['x^48 - 1', '0.991444861373810 + 0.130526192220052*I', '\\\\zeta_{48}'], 'conductor': 2496, 'conductor_radical': 78, 'conjugate': 'dirichlet_L_2496.773', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^81', 0, 'a^38', 0, 0, 0, 'a^61', 0, 0, 0, 0, 0, 'a^44', 0, 'a^71', 0, 0, 0, 'a^22', 0, 'a^66', 0, 0, 0, 'a^55', 0, 'a^36', 0, 0, 0, 'a^23', 0, 'a^25', 0, 0, 0, 'a^10', 0, 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'192.311934842478574672120472846603', '193.118990717044457748270581044903', '193.64425679592978990515941862060', '194.35388837317081201574653192903', '194.66636318651242831473742129475', '195.50733189320727560957906857533', '195.93437139344373642057154991238', '196.24792289778841668600048286611', '196.96586979117479456040445314249', '197.60000468871136540732216703696', '198.25739484287407019668788996842', '198.72938904335432901597213313201', '198.981490681994676667776634965633'], 'prelabel': '1-2496-2496.1805-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.591375268838206, 'root_angle': 0.3238539028156997, 'root_number': '-0.447562520477928767219930196535+0.894252643419880304295837522930*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.323853902816', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(48)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.800337086086896216878495605149-0.139769355646437371941206410432*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.1825469682', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '1.86744202786', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.16616132367', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 11.591375268838206, 'bad_primes': [2, 3, 13], 'central_character': '2496.1805', 'conductor': 2496, 'conductor_radical': 78, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2496/1805'], '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': '1-2496-2496.1805-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': '1-2496-2496.1805-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.591375268838206, 'root_angle': 0.3238539028156997, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.1825469682', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2496.1805', 'Lhash_array': ['dirichlet_L_2496.1805'], 'factors': ['1-2496-2496.1805-r0-0-0'], 'label': '1-2496-2496.1805-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2496/1805'}
Lfunction data - 1-2496-2496.1805-r0-0-0