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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_967.121', 'a10': [-0.9320569735915272, 0.3623117414318825], 'a2': [-0.7997432346737522, -0.6003422012432275], 'a3': [-0.14582564136906345, -0.9893103063848578], 'a4': [0.27917848281287244, 0.9602392278668388], 'a5': [0.5278952305728325, -0.8493094992630519], 'a6': [-0.477301656920828, 0.878739511061516], 'a7': [0.42507292640888433, 0.9051591060328494], 'a8': [0.3532010288815979, -0.9355474510664762], 'a9': [-0.9574697646386026, 0.2885336198831931], 'algebraic': True, 'analytic_conductor': 4.490729120579545, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.121', 'coeff_info': ['x^161 - 1', '0.999238582475670 + 0.0390160901682098*I', '\\\\zeta_{161}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.8', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^97', 'a^117', 'a^33', 'a^135', 'a^53', 'a^29', 'a^130', 'a^73', 'a^71', 'a^96', 'a^150', 'a^65', 'a^126', 'a^91', 'a^66', 'a^93', 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'186.80550020694822629375136331026', '188.00699711141653803108397284210', '188.63934638787669182589491808670', '188.913039551082392122273588715309', '189.304628140194728705044316715132', '190.10253307512986537060035425469', '190.51734536035962049858482216519', '191.25860452943986283653800398999', '191.83484644577383634246457554598', '192.26140289550015856049564162293', '193.01583824317842448979105953385', '193.591133534558962691615838620511', '194.02312134789569544727047278783', '194.94755146507789964804311973022', '195.79301078499570367103195820384', '195.90934517042465002560667453650', '196.86744338964289501105062931093', '197.15168633649615108262748770861', '197.97693300262275642454992270722', '198.67457390518427387851553419312', '199.62750546738439458930744612578', '199.66413484808547355491336671654'], 'prelabel': '1-967-967.121-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': 0.23017538045826144, 'root_number': '0.749746590175683649909331083897+0.661725056590677594610899587664*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.115087690229', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(161)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.515322136188426333293288812690-0.265423759795741123591349879835*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.17080152207', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.27690302904', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.47059732988', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.490729120579545, 'bad_primes': [967], 'central_character': '967.121', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/121'], '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': '1-967-967.121-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': '1-967-967.121-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': 0.11508769022913072, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17080152207', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_967.121', 'Lhash_array': ['dirichlet_L_967.121'], 'label': '1-967-967.121-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/121'}
Lfunction data - 1-967-967.121-r0-0-0