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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_847.164', 'a10': [0.23575893550942723, 0.9718115683235417], 'a2': [-0.9283679330160726, -0.3716624556603275], 'a3': [0.5, 0.8660254037844386], 'a4': [0.7237340381050702, 0.690079011482112], 'a5': [-0.5800569095711982, -0.8145759520503357], 'a6': [-0.14231483827328514, -0.9898214418809327], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.41541501300188644, -0.9096319953545183], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.164', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.439', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^37', 'a^11', 'a^8', 'a^43', 'a^48', 0, 'a^45', 'a^22', 'a^14', 0, 'a^19', 'a^30', 0, 'a^54', 'a^16', 'a^20', 'a^59', 'a^46', 'a^51', 0, 0, 'a^16', 'a^56', 'a^20', 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'192.18655130342737414489623058579', '192.690321065243602626308294065879', '193.03797560763912802750343139838', '193.94048196327426475348788517559', '194.36158206295969398760470427383', '195.29953093946298553877453185630', '196.12115005174056277635959590986', '196.75085373725130407395356908465', '197.1538860786763704291564906853', '198.042690272927350227437871201248', '198.498255192678210748205632213691', '199.00302458995947485014531231972', '199.469252041686505840026972857410'], 'prelabel': '1-847-847.164-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': -0.7241169038094631, 'root_number': '-0.647335935724697140962875284019-0.762204819139469080673250823988*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.362058451905', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.577059009767818733909778484715+0.0111318222262228870790843350001*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.147814297416', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.78921131732', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.73912364452', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.933451463423862, 'bad_primes': [7, 11], 'central_character': '847.164', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/164'], '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': '1-847-847.164-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': '1-847-847.164-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': -0.36205845190473157, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.147814297416', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_847.164', 'Lhash_array': ['dirichlet_L_847.164'], 'label': '1-847-847.164-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/164'}
Lfunction data - 1-847-847.164-r0-0-0