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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2912.731', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9659258262890683, -0.25881904510252074], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [2.9010907910729803e-30, -1.0], 'algebraic': True, 'analytic_conductor': 13.523271146977907, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]], [13, [1]]], 'bad_primes': [2, 7, 13], 'central_character': '2912.731', 'coeff_info': ['x^24 - 1', '0.965925826289068 + 0.258819045102521*I', '\\\\zeta_{24}'], 'conductor': 2912, 'conductor_radical': 182, 'conjugate': 'dirichlet_L_2912.243', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^33', 0, 'a^23', 0, 0, 0, 'a^18', 0, 'a^3', 0, 0, 0, 'a^8', 0, 'a^32', 0, 'a^21', 0, 0, 0, 'a^22', 0, 'a^22', 0, 'a^27', 0, 'a^17', 0, 'a^16', 0, 'a^12', 0, 0, 0, 'a^19', 0, 0, 0, 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'191.36197197109051499909536925534', '192.37051529853443804094966945762', '192.586376237561758635037935136474', '192.96002121305878887633438272850', '193.46463995532254276772300656807', '194.07688735040093314752625415449', '194.70374119222041867692588941771', '195.04085897272582404393220418887', '195.79407065895415082440845699602', '196.26273152874846611546926713478', '197.0273457746754325581641439229', '197.53361993702127436008341489612', '197.90331844488949279791344094074', '198.592406805880334851569209018196', '199.13453636455895645330681047545', '199.67923752780902511248738767614'], 'prelabel': '1-2912-2912.731-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.523271146977907, 'root_angle': -0.07255657124977054, 'root_number': '0.897871143692117215981543732436-0.440258343844849122144348147264*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(24)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.06640582092086179626239990159+0.0582020422403377029786783775445*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.592072970524', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.66971040522', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.52377869682', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 13.523271146977907, 'bad_primes': [2, 7, 13], 'central_character': '2912.731', 'conductor': 2912, 'conductor_radical': 182, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2912/731'], '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': '1-2912-2912.731-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': '1-2912-2912.731-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.523271146977907, 'root_angle': -0.07255657124977054, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.592072970524', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2912.731', 'Lhash_array': ['dirichlet_L_2912.731'], 'factors': ['1-2912-2912.731-r0-0-0'], 'label': '1-2912-2912.731-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2912/731'}
Lfunction data - 1-2912-2912.731-r0-0-0