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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_847.468', 'a10': [-0.14231483827328514, -0.9898214418809327], 'a2': [-0.9740119169423335, -0.22649676742576438], 'a3': [-0.30901699437494745, -0.9510565162951535], 'a4': [0.8973984286913584, 0.4412211012432213], 'a5': [0.362807705350641, 0.9318640292114523], 'a6': [0.08557500847883974, 0.9963317308626913], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.7741416106390825, -0.6330124538088704], 'a9': [-0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.468', 'coeff_info': ['x^110 - 1', '0.998369103926136 + 0.0570888108627680*I', '\\\\zeta_{110}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.552', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^59', 'a^77', 'a^8', 'a^21', 'a^26', 0, 'a^67', 'a^44', 'a^80', 0, 'a^85', 'a^74', 0, 'a^98', 'a^16', 'a^86', 'a^103', 'a^2', 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'190.84810172571441251590348345209', '191.51281047242659152709929054238', '191.799354748531441514759558433774', '192.9721862109525886370686561215', '193.49902582508738437700177489546', '193.906186458227130785107490250515', '194.64145669040559482670429544070', '195.223140920193928646841401900215', '196.14406390343683398054463313787', '196.605008398033344883537605215048', '197.292427605971585668990813211939', '197.71423039669972636690518837923', '198.59527695314638024375829616495', '198.8521679460826157873050563544', '199.83984641107448793253145788036'], 'prelabel': '1-847-847.468-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': -0.32024793388429756, 'root_number': '-0.427188327095007153973301809381-0.904162669652850231337624386539*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.320247933884', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(110)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.577123346083455137728527785243-0.224791042978867565724724095187*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.449075621877', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.74394940915', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.62082775708', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.933451463423862, 'bad_primes': [7, 11], 'central_character': '847.468', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/468'], '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': '1-847-847.468-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': '1-847-847.468-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': -0.32024793388429756, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.449075621877', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_847.468', 'Lhash_array': ['dirichlet_L_847.468'], 'factors': ['1-847-847.468-r0-0-0'], 'label': '1-847-847.468-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/468'}
Lfunction data - 1-847-847.468-r0-0-0