Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(178,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("735.178");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.v (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 178.2 | ||
Character | \(\chi\) | \(=\) | 735.178 |
Dual form | 735.2.v.a.607.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.03317 | − | 0.544785i | −1.43766 | − | 0.385221i | −0.545950 | − | 0.837818i | \(-0.683831\pi\) |
−0.891715 | + | 0.452597i | \(0.850498\pi\) | |||||||
\(3\) | 0.258819 | + | 0.965926i | 0.149429 | + | 0.557678i | ||||
\(4\) | 2.10492 | + | 1.21528i | 1.05246 | + | 0.607638i | ||||
\(5\) | 2.22675 | + | 0.203934i | 0.995832 | + | 0.0912019i | ||||
\(6\) | − | 2.10489i | − | 0.859317i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.640825 | − | 0.640825i | −0.226566 | − | 0.226566i | ||||
\(9\) | −0.866025 | + | 0.500000i | −0.288675 | + | 0.166667i | ||||
\(10\) | −4.41625 | − | 1.62773i | −1.39654 | − | 0.514733i | ||||
\(11\) | 1.33594 | − | 2.31391i | 0.402800 | − | 0.697670i | −0.591263 | − | 0.806479i | \(-0.701370\pi\) |
0.994063 | + | 0.108809i | \(0.0347038\pi\) | |||||||
\(12\) | −0.629073 | + | 2.34773i | −0.181598 | + | 0.677732i | ||||
\(13\) | 1.22714 | − | 1.22714i | 0.340348 | − | 0.340348i | −0.516150 | − | 0.856498i | \(-0.672635\pi\) |
0.856498 | + | 0.516150i | \(0.172635\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.379340 | + | 2.20366i | 0.0979452 | + | 0.568982i | ||||
\(16\) | −1.47676 | − | 2.55782i | −0.369190 | − | 0.639456i | ||||
\(17\) | 6.48349 | − | 1.73725i | 1.57248 | − | 0.421344i | 0.635890 | − | 0.771780i | \(-0.280633\pi\) |
0.936587 | + | 0.350436i | \(0.113966\pi\) | |||||||
\(18\) | 2.03317 | − | 0.544785i | 0.479222 | − | 0.128407i | ||||
\(19\) | −3.00865 | − | 5.21113i | −0.690231 | − | 1.19551i | −0.971762 | − | 0.235963i | \(-0.924176\pi\) |
0.281531 | − | 0.959552i | \(-0.409158\pi\) | |||||||
\(20\) | 4.43929 | + | 3.13538i | 0.992656 | + | 0.701092i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.97676 | + | 3.97676i | −0.847848 | + | 0.847848i | ||||
\(23\) | −0.0643048 | + | 0.239989i | −0.0134085 | + | 0.0500411i | −0.972306 | − | 0.233712i | \(-0.924913\pi\) |
0.958897 | + | 0.283753i | \(0.0915795\pi\) | |||||||
\(24\) | 0.453132 | − | 0.784847i | 0.0924951 | − | 0.160206i | ||||
\(25\) | 4.91682 | + | 0.908218i | 0.983364 | + | 0.181644i | ||||
\(26\) | −3.16351 | + | 1.82645i | −0.620416 | + | 0.358197i | ||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.304889i | 0.0566165i | 0.999599 | + | 0.0283083i | \(0.00901200\pi\) | ||||
−0.999599 | + | 0.0283083i | \(0.990988\pi\) | |||||||
\(30\) | 0.429257 | − | 4.68706i | 0.0783713 | − | 0.855736i | ||||
\(31\) | −6.28197 | − | 3.62690i | −1.12827 | − | 0.651410i | −0.184774 | − | 0.982781i | \(-0.559155\pi\) |
−0.943500 | + | 0.331371i | \(0.892489\pi\) | |||||||
\(32\) | 2.07815 | + | 7.75576i | 0.367369 | + | 1.37104i | ||||
\(33\) | 2.58083 | + | 0.691531i | 0.449265 | + | 0.120380i | ||||
\(34\) | −14.1284 | −2.42301 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.43055 | −0.405092 | ||||||||
\(37\) | 1.00463 | + | 0.269190i | 0.165160 | + | 0.0442546i | 0.340452 | − | 0.940262i | \(-0.389420\pi\) |
−0.175291 | + | 0.984517i | \(0.556087\pi\) | |||||||
\(38\) | 3.27813 | + | 12.2341i | 0.531783 | + | 1.98464i | ||||
\(39\) | 1.50294 | + | 0.867721i | 0.240662 | + | 0.138947i | ||||
\(40\) | −1.29627 | − | 1.55764i | −0.204958 | − | 0.246285i | ||||
\(41\) | 7.05736i | 1.10217i | 0.834447 | + | 0.551087i | \(0.185787\pi\) | ||||
−0.834447 | + | 0.551087i | \(0.814213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.304889 | + | 0.304889i | 0.0464952 | + | 0.0464952i | 0.729972 | − | 0.683477i | \(-0.239533\pi\) |
−0.683477 | + | 0.729972i | \(0.739533\pi\) | |||||||
\(44\) | 5.62407 | − | 3.24706i | 0.847861 | − | 0.489513i | ||||
\(45\) | −2.03039 | + | 0.936763i | −0.302672 | + | 0.139644i | ||||
\(46\) | 0.261485 | − | 0.452905i | 0.0385538 | − | 0.0667772i | ||||
\(47\) | 0.203827 | − | 0.760694i | 0.0297313 | − | 0.110959i | −0.949466 | − | 0.313871i | \(-0.898374\pi\) |
0.979197 | + | 0.202912i | \(0.0650407\pi\) | |||||||
\(48\) | 2.08845 | − | 2.08845i | 0.301442 | − | 0.301442i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −9.50193 | − | 4.52517i | −1.34378 | − | 0.639955i | ||||
\(51\) | 3.35610 | + | 5.81294i | 0.469948 | + | 0.813974i | ||||
\(52\) | 4.07435 | − | 1.09172i | 0.565011 | − | 0.151394i | ||||
\(53\) | 6.81689 | − | 1.82658i | 0.936372 | − | 0.250900i | 0.241802 | − | 0.970326i | \(-0.422262\pi\) |
0.694570 | + | 0.719426i | \(0.255595\pi\) | |||||||
\(54\) | 1.05244 | + | 1.82289i | 0.143219 | + | 0.248063i | ||||
\(55\) | 3.44668 | − | 4.88005i | 0.464750 | − | 0.658026i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.25487 | − | 4.25487i | 0.563571 | − | 0.563571i | ||||
\(58\) | 0.166099 | − | 0.619890i | 0.0218099 | − | 0.0813956i | ||||
\(59\) | 3.99419 | − | 6.91813i | 0.519999 | − | 0.900664i | −0.479731 | − | 0.877416i | \(-0.659266\pi\) |
0.999730 | − | 0.0232486i | \(-0.00740092\pi\) | |||||||
\(60\) | −1.87957 | + | 5.09952i | −0.242651 | + | 0.658346i | ||||
\(61\) | −4.79266 | + | 2.76704i | −0.613637 | + | 0.354284i | −0.774388 | − | 0.632711i | \(-0.781942\pi\) |
0.160750 | + | 0.986995i | \(0.448609\pi\) | |||||||
\(62\) | 10.7964 | + | 10.7964i | 1.37114 | + | 1.37114i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 10.9939i | − | 1.37423i | ||||||
\(65\) | 2.98279 | − | 2.48228i | 0.369970 | − | 0.307889i | ||||
\(66\) | −4.87052 | − | 2.81199i | −0.599519 | − | 0.346133i | ||||
\(67\) | −1.25567 | − | 4.68622i | −0.153404 | − | 0.572513i | −0.999237 | − | 0.0390641i | \(-0.987562\pi\) |
0.845832 | − | 0.533449i | \(-0.179104\pi\) | |||||||
\(68\) | 15.7585 | + | 4.22247i | 1.91099 | + | 0.512049i | ||||
\(69\) | −0.248455 | −0.0299104 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.3087 | 1.81681 | 0.908407 | − | 0.418087i | \(-0.137299\pi\) | ||||
0.908407 | + | 0.418087i | \(0.137299\pi\) | |||||||
\(72\) | 0.875383 | + | 0.234558i | 0.103165 | + | 0.0276430i | ||||
\(73\) | 3.66788 | + | 13.6887i | 0.429293 | + | 1.60214i | 0.754366 | + | 0.656454i | \(0.227944\pi\) |
−0.325073 | + | 0.945689i | \(0.605389\pi\) | |||||||
\(74\) | −1.89593 | − | 1.09462i | −0.220397 | − | 0.127247i | ||||
\(75\) | 0.395296 | + | 4.98435i | 0.0456449 | + | 0.575543i | ||||
\(76\) | − | 14.6253i | − | 1.67764i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.58300 | − | 2.58300i | −0.292467 | − | 0.292467i | ||||
\(79\) | 9.78372 | − | 5.64863i | 1.10075 | − | 0.635521i | 0.164335 | − | 0.986405i | \(-0.447452\pi\) |
0.936419 | + | 0.350884i | \(0.114119\pi\) | |||||||
\(80\) | −2.76675 | − | 5.99679i | −0.309332 | − | 0.670462i | ||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 3.84475 | − | 14.3488i | 0.424581 | − | 1.58456i | ||||
\(83\) | −4.88941 | + | 4.88941i | −0.536682 | + | 0.536682i | −0.922553 | − | 0.385871i | \(-0.873901\pi\) |
0.385871 | + | 0.922553i | \(0.373901\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.7914 | − | 2.54621i | 1.60435 | − | 0.276175i | ||||
\(86\) | −0.453791 | − | 0.785990i | −0.0489336 | − | 0.0847554i | ||||
\(87\) | −0.294500 | + | 0.0789112i | −0.0315738 | + | 0.00846017i | ||||
\(88\) | −2.33891 | + | 0.626709i | −0.249329 | + | 0.0668074i | ||||
\(89\) | −3.45626 | − | 5.98641i | −0.366363 | − | 0.634559i | 0.622631 | − | 0.782515i | \(-0.286064\pi\) |
−0.988994 | + | 0.147957i | \(0.952730\pi\) | |||||||
\(90\) | 4.63845 | − | 0.798469i | 0.488935 | − | 0.0841660i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.427009 | + | 0.427009i | −0.0445188 | + | 0.0445188i | ||||
\(93\) | 1.87742 | − | 7.00662i | 0.194679 | − | 0.726553i | ||||
\(94\) | −0.828829 | + | 1.43557i | −0.0854872 | + | 0.148068i | ||||
\(95\) | −5.63678 | − | 12.2174i | −0.578321 | − | 1.25348i | ||||
\(96\) | −6.95363 | + | 4.01468i | −0.709702 | + | 0.409746i | ||||
\(97\) | −8.84137 | − | 8.84137i | −0.897705 | − | 0.897705i | 0.0975276 | − | 0.995233i | \(-0.468907\pi\) |
−0.995233 | + | 0.0975276i | \(0.968907\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.67187i | 0.268533i | ||||||||
\(100\) | 9.24578 | + | 7.88702i | 0.924578 | + | 0.788702i | ||||
\(101\) | −6.26104 | − | 3.61481i | −0.622996 | − | 0.359687i | 0.155038 | − | 0.987908i | \(-0.450450\pi\) |
−0.778035 | + | 0.628221i | \(0.783783\pi\) | |||||||
\(102\) | −3.65671 | − | 13.6470i | −0.362068 | − | 1.35126i | ||||
\(103\) | 9.48757 | + | 2.54219i | 0.934838 | + | 0.250489i | 0.693916 | − | 0.720056i | \(-0.255884\pi\) |
0.240921 | + | 0.970545i | \(0.422550\pi\) | |||||||
\(104\) | −1.57277 | −0.154222 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.8550 | −1.44284 | ||||||||
\(107\) | 10.2082 | + | 2.73529i | 0.986867 | + | 0.264430i | 0.715934 | − | 0.698168i | \(-0.246001\pi\) |
0.270933 | + | 0.962598i | \(0.412668\pi\) | |||||||
\(108\) | −0.629073 | − | 2.34773i | −0.0605326 | − | 0.225911i | ||||
\(109\) | −5.15590 | − | 2.97676i | −0.493846 | − | 0.285122i | 0.232323 | − | 0.972639i | \(-0.425367\pi\) |
−0.726168 | + | 0.687517i | \(0.758701\pi\) | |||||||
\(110\) | −9.66624 | + | 8.04425i | −0.921640 | + | 0.766989i | ||||
\(111\) | 1.04007i | 0.0987192i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.99031 | + | 6.99031i | 0.657593 | + | 0.657593i | 0.954810 | − | 0.297217i | \(-0.0960585\pi\) |
−0.297217 | + | 0.954810i | \(0.596058\pi\) | |||||||
\(114\) | −10.9688 | + | 6.33286i | −1.02733 | + | 0.593127i | ||||
\(115\) | −0.192132 | + | 0.521281i | −0.0179164 | + | 0.0486097i | ||||
\(116\) | −0.370525 | + | 0.641768i | −0.0344024 | + | 0.0595866i | ||||
\(117\) | −0.449165 | + | 1.67631i | −0.0415253 | + | 0.154975i | ||||
\(118\) | −11.8897 | + | 11.8897i | −1.09454 | + | 1.09454i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.16907 | − | 1.65525i | 0.106721 | − | 0.151103i | ||||
\(121\) | 1.93055 | + | 3.34381i | 0.175505 | + | 0.303983i | ||||
\(122\) | 11.2517 | − | 3.01489i | 1.01868 | − | 0.272955i | ||||
\(123\) | −6.81689 | + | 1.82658i | −0.614658 | + | 0.164697i | ||||
\(124\) | −8.81536 | − | 15.2686i | −0.791643 | − | 1.37117i | ||||
\(125\) | 10.7633 | + | 3.02508i | 0.962700 | + | 0.270571i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.86110 | − | 2.86110i | 0.253882 | − | 0.253882i | −0.568678 | − | 0.822560i | \(-0.692545\pi\) |
0.822560 | + | 0.568678i | \(0.192545\pi\) | |||||||
\(128\) | −1.83298 | + | 6.84079i | −0.162014 | + | 0.604646i | ||||
\(129\) | −0.215589 | + | 0.373412i | −0.0189816 | + | 0.0328771i | ||||
\(130\) | −7.41682 | + | 3.42191i | −0.650498 | + | 0.300121i | ||||
\(131\) | −8.09529 | + | 4.67382i | −0.707289 | + | 0.408353i | −0.810056 | − | 0.586352i | \(-0.800564\pi\) |
0.102767 | + | 0.994705i | \(0.467230\pi\) | |||||||
\(132\) | 4.59204 | + | 4.59204i | 0.399686 | + | 0.399686i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 10.2119i | 0.882177i | ||||||||
\(135\) | −1.43035 | − | 1.71875i | −0.123105 | − | 0.147927i | ||||
\(136\) | −5.26805 | − | 3.04151i | −0.451732 | − | 0.260807i | ||||
\(137\) | 2.75230 | + | 10.2717i | 0.235145 | + | 0.877573i | 0.978083 | + | 0.208213i | \(0.0667648\pi\) |
−0.742938 | + | 0.669360i | \(0.766569\pi\) | |||||||
\(138\) | 0.505150 | + | 0.135354i | 0.0430012 | + | 0.0115221i | ||||
\(139\) | 7.78902 | 0.660656 | 0.330328 | − | 0.943866i | \(-0.392841\pi\) | ||||
0.330328 | + | 0.943866i | \(0.392841\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.787528 | 0.0663218 | ||||||||
\(142\) | −31.1252 | − | 8.33998i | −2.61197 | − | 0.699875i | ||||
\(143\) | −1.20011 | − | 4.47888i | −0.100358 | − | 0.374543i | ||||
\(144\) | 2.55782 | + | 1.47676i | 0.213152 | + | 0.123063i | ||||
\(145\) | −0.0621772 | + | 0.678912i | −0.00516353 | + | 0.0563806i | ||||
\(146\) | − | 29.8296i | − | 2.46872i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.78753 | + | 1.78753i | 0.146934 | + | 0.146934i | ||||
\(149\) | −12.3716 | + | 7.14275i | −1.01352 | + | 0.585157i | −0.912221 | − | 0.409699i | \(-0.865634\pi\) |
−0.101301 | + | 0.994856i | \(0.532301\pi\) | |||||||
\(150\) | 1.91170 | − | 10.3494i | 0.156089 | − | 0.845022i | ||||
\(151\) | −4.88995 | + | 8.46964i | −0.397939 | + | 0.689250i | −0.993471 | − | 0.114081i | \(-0.963608\pi\) |
0.595533 | + | 0.803331i | \(0.296941\pi\) | |||||||
\(152\) | −1.41141 | + | 5.26744i | −0.114480 | + | 0.427245i | ||||
\(153\) | −4.74624 | + | 4.74624i | −0.383711 | + | 0.383711i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.2487 | − | 9.35729i | −1.06416 | − | 0.751596i | ||||
\(156\) | 2.10904 | + | 3.65296i | 0.168858 | + | 0.292471i | ||||
\(157\) | −2.97426 | + | 0.796951i | −0.237372 | + | 0.0636036i | −0.375544 | − | 0.926805i | \(-0.622544\pi\) |
0.138172 | + | 0.990408i | \(0.455877\pi\) | |||||||
\(158\) | −22.9692 | + | 6.15458i | −1.82733 | + | 0.489632i | ||||
\(159\) | 3.52868 | + | 6.11186i | 0.279843 | + | 0.484702i | ||||
\(160\) | 3.04586 | + | 17.6939i | 0.240796 | + | 1.39883i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.48838 | + | 1.48838i | −0.116938 | + | 0.116938i | ||||
\(163\) | −5.00566 | + | 18.6814i | −0.392074 | + | 1.46324i | 0.434633 | + | 0.900607i | \(0.356878\pi\) |
−0.826707 | + | 0.562632i | \(0.809789\pi\) | |||||||
\(164\) | −8.57664 | + | 14.8552i | −0.669723 | + | 1.15999i | ||||
\(165\) | 5.60583 | + | 2.06618i | 0.436414 | + | 0.160852i | ||||
\(166\) | 12.6047 | − | 7.27730i | 0.978311 | − | 0.564828i | ||||
\(167\) | −6.23288 | − | 6.23288i | −0.482315 | − | 0.482315i | 0.423555 | − | 0.905870i | \(-0.360782\pi\) |
−0.905870 | + | 0.423555i | \(0.860782\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.98824i | 0.768326i | ||||||||
\(170\) | −31.4605 | − | 2.88126i | −2.41291 | − | 0.220983i | ||||
\(171\) | 5.21113 | + | 3.00865i | 0.398505 | + | 0.230077i | ||||
\(172\) | 0.271243 | + | 1.01229i | 0.0206821 | + | 0.0771866i | ||||
\(173\) | −9.24710 | − | 2.47775i | −0.703044 | − | 0.188380i | −0.110450 | − | 0.993882i | \(-0.535229\pi\) |
−0.592594 | + | 0.805501i | \(0.701896\pi\) | |||||||
\(174\) | 0.641758 | 0.0486515 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.89143 | −0.594839 | ||||||||
\(177\) | 7.71617 | + | 2.06754i | 0.579983 | + | 0.155406i | ||||
\(178\) | 3.76583 | + | 14.0543i | 0.282261 | + | 1.05341i | ||||
\(179\) | 1.12673 | + | 0.650516i | 0.0842155 | + | 0.0486218i | 0.541516 | − | 0.840690i | \(-0.317850\pi\) |
−0.457301 | + | 0.889312i | \(0.651184\pi\) | |||||||
\(180\) | −5.41223 | − | 0.495671i | −0.403404 | − | 0.0369452i | ||||
\(181\) | − | 8.48528i | − | 0.630706i | −0.948974 | − | 0.315353i | \(-0.897877\pi\) | ||
0.948974 | − | 0.315353i | \(-0.102123\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.91319 | − | 3.91319i | −0.289271 | − | 0.289271i | ||||
\(184\) | 0.194999 | − | 0.112583i | 0.0143755 | − | 0.00829971i | ||||
\(185\) | 2.18217 | + | 0.804297i | 0.160436 | + | 0.0591331i | ||||
\(186\) | −7.63421 | + | 13.2228i | −0.559767 | + | 0.969545i | ||||
\(187\) | 4.64170 | − | 17.3230i | 0.339434 | − | 1.26679i | ||||
\(188\) | 1.35349 | − | 1.35349i | 0.0987136 | − | 0.0987136i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.80462 | + | 27.9109i | 0.348564 | + | 2.02487i | ||||
\(191\) | −0.968954 | − | 1.67828i | −0.0701110 | − | 0.121436i | 0.828839 | − | 0.559488i | \(-0.189002\pi\) |
−0.898950 | + | 0.438052i | \(0.855669\pi\) | |||||||
\(192\) | 10.6192 | − | 2.84542i | 0.766378 | − | 0.205350i | ||||
\(193\) | 10.6931 | − | 2.86520i | 0.769703 | − | 0.206241i | 0.147463 | − | 0.989068i | \(-0.452889\pi\) |
0.622240 | + | 0.782826i | \(0.286223\pi\) | |||||||
\(194\) | 13.1593 | + | 22.7926i | 0.944784 | + | 1.63641i | ||||
\(195\) | 3.16970 | + | 2.23870i | 0.226987 | + | 0.160316i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.50767 | + | 8.50767i | −0.606146 | + | 0.606146i | −0.941937 | − | 0.335790i | \(-0.890997\pi\) |
0.335790 | + | 0.941937i | \(0.390997\pi\) | |||||||
\(198\) | 1.45560 | − | 5.43236i | 0.103445 | − | 0.386061i | ||||
\(199\) | 1.62730 | − | 2.81856i | 0.115356 | − | 0.199803i | −0.802566 | − | 0.596563i | \(-0.796532\pi\) |
0.917922 | + | 0.396761i | \(0.129866\pi\) | |||||||
\(200\) | −2.56881 | − | 3.73283i | −0.181643 | − | 0.263951i | ||||
\(201\) | 4.20155 | − | 2.42577i | 0.296355 | − | 0.171100i | ||||
\(202\) | 10.7604 | + | 10.7604i | 0.757101 | + | 0.757101i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 16.3144i | 1.14223i | ||||||||
\(205\) | −1.43923 | + | 15.7150i | −0.100520 | + | 1.09758i | ||||
\(206\) | −17.9048 | − | 10.3374i | −1.24749 | − | 0.720238i | ||||
\(207\) | −0.0643048 | − | 0.239989i | −0.00446949 | − | 0.0166804i | ||||
\(208\) | −4.95101 | − | 1.32662i | −0.343291 | − | 0.0919845i | ||||
\(209\) | −16.0774 | −1.11210 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.2508 | −1.18759 | −0.593797 | − | 0.804615i | \(-0.702372\pi\) | ||||
−0.593797 | + | 0.804615i | \(0.702372\pi\) | |||||||
\(212\) | 16.5688 | + | 4.43960i | 1.13795 | + | 0.304913i | ||||
\(213\) | 3.96220 | + | 14.7871i | 0.271485 | + | 1.01320i | ||||
\(214\) | −19.2649 | − | 11.1226i | −1.31692 | − | 0.760324i | ||||
\(215\) | 0.616735 | + | 0.741089i | 0.0420610 | + | 0.0505419i | ||||
\(216\) | 0.906263i | 0.0616634i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.86110 | + | 8.86110i | 0.600150 | + | 0.600150i | ||||
\(219\) | −12.2730 | + | 7.08580i | −0.829330 | + | 0.478814i | ||||
\(220\) | 13.1856 | − | 6.08345i | 0.888972 | − | 0.410146i | ||||
\(221\) | 5.82432 | − | 10.0880i | 0.391786 | − | 0.678593i | ||||
\(222\) | 0.566615 | − | 2.11464i | 0.0380287 | − | 0.141925i | ||||
\(223\) | −4.58392 | + | 4.58392i | −0.306962 | + | 0.306962i | −0.843730 | − | 0.536768i | \(-0.819645\pi\) |
0.536768 | + | 0.843730i | \(0.319645\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.71220 | + | 1.67187i | −0.314147 | + | 0.111458i | ||||
\(226\) | −10.4042 | − | 18.0207i | −0.692080 | − | 1.19872i | ||||
\(227\) | −19.3447 | + | 5.18339i | −1.28395 | + | 0.344034i | −0.835360 | − | 0.549703i | \(-0.814741\pi\) |
−0.448592 | + | 0.893737i | \(0.648074\pi\) | |||||||
\(228\) | 14.1270 | − | 3.78532i | 0.935583 | − | 0.250689i | ||||
\(229\) | 14.4654 | + | 25.0547i | 0.955898 | + | 1.65566i | 0.732300 | + | 0.680982i | \(0.238447\pi\) |
0.223598 | + | 0.974681i | \(0.428220\pi\) | |||||||
\(230\) | 0.674623 | − | 0.955180i | 0.0444833 | − | 0.0629827i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.195381 | − | 0.195381i | 0.0128274 | − | 0.0128274i | ||||
\(233\) | −1.75160 | + | 6.53706i | −0.114751 | + | 0.428257i | −0.999268 | − | 0.0382507i | \(-0.987821\pi\) |
0.884517 | + | 0.466508i | \(0.154488\pi\) | |||||||
\(234\) | 1.82645 | − | 3.16351i | 0.119399 | − | 0.206805i | ||||
\(235\) | 0.609003 | − | 1.65231i | 0.0397270 | − | 0.107785i | ||||
\(236\) | 16.8149 | − | 9.70808i | 1.09456 | − | 0.631942i | ||||
\(237\) | 7.98837 | + | 7.98837i | 0.518901 | + | 0.518901i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 16.1769i | − | 1.04640i | −0.852210 | − | 0.523200i | \(-0.824738\pi\) | ||
0.852210 | − | 0.523200i | \(-0.175262\pi\) | |||||||
\(240\) | 5.07637 | − | 4.22456i | 0.327678 | − | 0.272694i | ||||
\(241\) | −9.84735 | − | 5.68537i | −0.634324 | − | 0.366227i | 0.148101 | − | 0.988972i | \(-0.452684\pi\) |
−0.782425 | + | 0.622745i | \(0.786017\pi\) | |||||||
\(242\) | −2.10347 | − | 7.85026i | −0.135216 | − | 0.504634i | ||||
\(243\) | 0.965926 | + | 0.258819i | 0.0619642 | + | 0.0166032i | ||||
\(244\) | −13.4509 | −0.861105 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.8550 | 0.947117 | ||||||||
\(247\) | −10.0868 | − | 2.70276i | −0.641810 | − | 0.171972i | ||||
\(248\) | 1.70144 | + | 6.34985i | 0.108041 | + | 0.403216i | ||||
\(249\) | −5.98828 | − | 3.45733i | −0.379492 | − | 0.219100i | ||||
\(250\) | −20.2356 | − | 12.0142i | −1.27981 | − | 0.759843i | ||||
\(251\) | − | 6.95039i | − | 0.438705i | −0.975646 | − | 0.219352i | \(-0.929606\pi\) | ||
0.975646 | − | 0.219352i | \(-0.0703944\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.469405 | + | 0.469405i | 0.0295112 | + | 0.0295112i | ||||
\(254\) | −7.37578 | + | 4.25841i | −0.462798 | + | 0.267196i | ||||
\(255\) | 6.28774 | + | 13.6284i | 0.393754 | + | 0.853442i | ||||
\(256\) | −3.54033 | + | 6.13203i | −0.221271 | + | 0.383252i | ||||
\(257\) | 3.69280 | − | 13.7817i | 0.230350 | − | 0.859679i | −0.749840 | − | 0.661620i | \(-0.769869\pi\) |
0.980190 | − | 0.198060i | \(-0.0634640\pi\) | |||||||
\(258\) | 0.641758 | − | 0.641758i | 0.0399541 | − | 0.0399541i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 9.29520 | − | 1.60009i | 0.576464 | − | 0.0992332i | ||||
\(261\) | −0.152445 | − | 0.264042i | −0.00943609 | − | 0.0163438i | ||||
\(262\) | 19.0053 | − | 5.09245i | 1.17415 | − | 0.314613i | ||||
\(263\) | −24.8595 | + | 6.66107i | −1.53290 | + | 0.410739i | −0.923964 | − | 0.382480i | \(-0.875070\pi\) |
−0.608936 | + | 0.793219i | \(0.708403\pi\) | |||||||
\(264\) | −1.21071 | − | 2.09701i | −0.0745140 | − | 0.129062i | ||||
\(265\) | 15.5520 | − | 2.67714i | 0.955352 | − | 0.164456i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.88789 | − | 4.88789i | 0.299134 | − | 0.299134i | ||||
\(268\) | 3.05197 | − | 11.3901i | 0.186429 | − | 0.695761i | ||||
\(269\) | 7.75593 | − | 13.4337i | 0.472888 | − | 0.819065i | −0.526631 | − | 0.850094i | \(-0.676545\pi\) |
0.999518 | + | 0.0310287i | \(0.00987831\pi\) | |||||||
\(270\) | 1.97178 | + | 4.27374i | 0.119999 | + | 0.260091i | ||||
\(271\) | −11.5544 | + | 6.67091i | −0.701877 | + | 0.405229i | −0.808046 | − | 0.589119i | \(-0.799475\pi\) |
0.106169 | + | 0.994348i | \(0.466142\pi\) | |||||||
\(272\) | −14.0181 | − | 14.0181i | −0.849974 | − | 0.849974i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 22.3835i | − | 1.35224i | ||||||
\(275\) | 8.67009 | − | 10.1638i | 0.522826 | − | 0.612898i | ||||
\(276\) | −0.522977 | − | 0.301941i | −0.0314795 | − | 0.0181747i | ||||
\(277\) | −0.734104 | − | 2.73971i | −0.0441080 | − | 0.164613i | 0.940359 | − | 0.340184i | \(-0.110489\pi\) |
−0.984467 | + | 0.175571i | \(0.943823\pi\) | |||||||
\(278\) | −15.8364 | − | 4.24334i | −0.949802 | − | 0.254499i | ||||
\(279\) | 7.25379 | 0.434273 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.5557 | 0.808664 | 0.404332 | − | 0.914612i | \(-0.367504\pi\) | ||||
0.404332 | + | 0.914612i | \(0.367504\pi\) | |||||||
\(282\) | −1.60117 | − | 0.429034i | −0.0953486 | − | 0.0255486i | ||||
\(283\) | −5.94585 | − | 22.1902i | −0.353444 | − | 1.31907i | −0.882431 | − | 0.470441i | \(-0.844095\pi\) |
0.528987 | − | 0.848630i | \(-0.322572\pi\) | |||||||
\(284\) | 32.2237 | + | 18.6044i | 1.91212 | + | 1.10397i | ||||
\(285\) | 10.3422 | − | 8.60681i | 0.612621 | − | 0.509824i | ||||
\(286\) | 9.76010i | 0.577127i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.67761 | − | 5.67761i | −0.334557 | − | 0.334557i | ||||
\(289\) | 24.2952 | − | 14.0268i | 1.42913 | − | 0.825107i | ||||
\(290\) | 0.496278 | − | 1.34647i | 0.0291424 | − | 0.0790673i | ||||
\(291\) | 6.25179 | − | 10.8284i | 0.366487 | − | 0.634773i | ||||
\(292\) | −8.91497 | + | 33.2711i | −0.521709 | + | 1.94705i | ||||
\(293\) | −2.41765 | + | 2.41765i | −0.141240 | + | 0.141240i | −0.774192 | − | 0.632951i | \(-0.781843\pi\) |
0.632951 | + | 0.774192i | \(0.281843\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.3049 | − | 14.5904i | 0.599974 | − | 0.849486i | ||||
\(296\) | −0.471289 | − | 0.816297i | −0.0273931 | − | 0.0474463i | ||||
\(297\) | −2.58083 | + | 0.691531i | −0.149755 | + | 0.0401267i | ||||
\(298\) | 29.0448 | − | 7.78253i | 1.68252 | − | 0.450830i | ||||
\(299\) | 0.215589 | + | 0.373412i | 0.0124679 | + | 0.0215950i | ||||
\(300\) | −5.22529 | + | 10.9720i | −0.301682 | + | 0.633472i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 14.5562 | − | 14.5562i | 0.837616 | − | 0.837616i | ||||
\(303\) | 1.87116 | − | 6.98328i | 0.107496 | − | 0.401179i | ||||
\(304\) | −8.88610 | + | 15.3912i | −0.509653 | + | 0.882744i | ||||
\(305\) | −11.2363 | + | 5.18413i | −0.643391 | + | 0.296842i | ||||
\(306\) | 12.2356 | − | 7.06422i | 0.699462 | − | 0.403834i | ||||
\(307\) | 7.21300 | + | 7.21300i | 0.411667 | + | 0.411667i | 0.882319 | − | 0.470652i | \(-0.155981\pi\) |
−0.470652 | + | 0.882319i | \(0.655981\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.82225i | 0.558768i | ||||||||
\(310\) | 21.8391 | + | 26.2426i | 1.24038 | + | 1.49048i | ||||
\(311\) | 8.88036 | + | 5.12708i | 0.503559 | + | 0.290730i | 0.730182 | − | 0.683253i | \(-0.239435\pi\) |
−0.226623 | + | 0.973983i | \(0.572769\pi\) | |||||||
\(312\) | −0.407062 | − | 1.51918i | −0.0230453 | − | 0.0860064i | ||||
\(313\) | −30.1760 | − | 8.08564i | −1.70565 | − | 0.457027i | −0.731298 | − | 0.682059i | \(-0.761085\pi\) |
−0.974352 | + | 0.225031i | \(0.927752\pi\) | |||||||
\(314\) | 6.48134 | 0.365763 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 27.4586 | 1.54467 | ||||||||
\(317\) | 16.7425 | + | 4.48613i | 0.940351 | + | 0.251966i | 0.696263 | − | 0.717787i | \(-0.254845\pi\) |
0.244088 | + | 0.969753i | \(0.421511\pi\) | |||||||
\(318\) | −3.84475 | − | 14.3488i | −0.215603 | − | 0.804640i | ||||
\(319\) | 0.705486 | + | 0.407313i | 0.0394996 | + | 0.0228051i | ||||
\(320\) | 2.24202 | − | 24.4805i | 0.125332 | − | 1.36850i | ||||
\(321\) | 10.5683i | 0.589867i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.5595 | − | 28.5595i | −1.58909 | − | 1.58909i | ||||
\(324\) | 2.10492 | − | 1.21528i | 0.116940 | − | 0.0675153i | ||||
\(325\) | 7.14815 | − | 4.91913i | 0.396508 | − | 0.272864i | ||||
\(326\) | 20.3547 | − | 35.2553i | 1.12734 | − | 1.95261i | ||||
\(327\) | 1.54088 | − | 5.75066i | 0.0852111 | − | 0.318012i | ||||
\(328\) | 4.52253 | − | 4.52253i | 0.249715 | − | 0.249715i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −10.2720 | − | 7.25487i | −0.565453 | − | 0.399367i | ||||
\(331\) | −0.631541 | − | 1.09386i | −0.0347126 | − | 0.0601240i | 0.848147 | − | 0.529761i | \(-0.177718\pi\) |
−0.882860 | + | 0.469637i | \(0.844385\pi\) | |||||||
\(332\) | −16.2338 | + | 4.34983i | −0.890945 | + | 0.238728i | ||||
\(333\) | −1.00463 | + | 0.269190i | −0.0550535 | + | 0.0147515i | ||||
\(334\) | 9.27690 | + | 16.0681i | 0.507609 | + | 0.879205i | ||||
\(335\) | −1.84038 | − | 10.6911i | −0.100551 | − | 0.584118i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.55621 | + | 9.55621i | −0.520560 | + | 0.520560i | −0.917741 | − | 0.397180i | \(-0.869989\pi\) |
0.397180 | + | 0.917741i | \(0.369989\pi\) | |||||||
\(338\) | 5.44145 | − | 20.3078i | 0.295976 | − | 1.10460i | ||||
\(339\) | −4.94289 | + | 8.56135i | −0.268461 | + | 0.464988i | ||||
\(340\) | 34.2290 | + | 12.6161i | 1.85633 | + | 0.684201i | ||||
\(341\) | −16.7846 | + | 9.69060i | −0.908938 | + | 0.524775i | ||||
\(342\) | −8.95602 | − | 8.95602i | −0.484286 | − | 0.484286i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 0.390761i | − | 0.0210684i | ||||||
\(345\) | −0.553246 | − | 0.0506683i | −0.0297858 | − | 0.00272789i | ||||
\(346\) | 17.4510 | + | 10.0754i | 0.938174 | + | 0.541655i | ||||
\(347\) | 2.39738 | + | 8.94713i | 0.128698 | + | 0.480307i | 0.999944 | − | 0.0105386i | \(-0.00335460\pi\) |
−0.871247 | + | 0.490846i | \(0.836688\pi\) | |||||||
\(348\) | −0.715799 | − | 0.191798i | −0.0383708 | − | 0.0102814i | ||||
\(349\) | −2.77139 | −0.148349 | −0.0741746 | − | 0.997245i | \(-0.523632\pi\) | ||||
−0.0741746 | + | 0.997245i | \(0.523632\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.73544 | −0.0926310 | ||||||||
\(352\) | 20.7224 | + | 5.55255i | 1.10451 | + | 0.295952i | ||||
\(353\) | −0.355252 | − | 1.32582i | −0.0189082 | − | 0.0705663i | 0.955827 | − | 0.293929i | \(-0.0949631\pi\) |
−0.974735 | + | 0.223363i | \(0.928296\pi\) | |||||||
\(354\) | −14.5619 | − | 8.40731i | −0.773956 | − | 0.446844i | ||||
\(355\) | 34.0887 | + | 3.12197i | 1.80924 | + | 0.165697i | ||||
\(356\) | − | 16.8012i | − | 0.890463i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.93643 | − | 1.93643i | −0.102344 | − | 0.102344i | ||||
\(359\) | 8.07840 | − | 4.66406i | 0.426361 | − | 0.246160i | −0.271434 | − | 0.962457i | \(-0.587498\pi\) |
0.697795 | + | 0.716297i | \(0.254164\pi\) | |||||||
\(360\) | 1.90142 | + | 0.700822i | 0.100214 | + | 0.0369366i | ||||
\(361\) | −8.60390 | + | 14.9024i | −0.452837 | + | 0.784336i | ||||
\(362\) | −4.62265 | + | 17.2520i | −0.242961 | + | 0.906744i | ||||
\(363\) | −2.73021 | + | 2.73021i | −0.143299 | + | 0.143299i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.37586 | + | 31.2293i | 0.281385 | + | 1.63462i | ||||
\(366\) | 5.82432 | + | 10.0880i | 0.304442 | + | 0.527309i | ||||
\(367\) | −17.7631 | + | 4.75960i | −0.927225 | + | 0.248449i | −0.690671 | − | 0.723169i | \(-0.742685\pi\) |
−0.236554 | + | 0.971618i | \(0.576018\pi\) | |||||||
\(368\) | 0.708812 | − | 0.189926i | 0.0369494 | − | 0.00990056i | ||||
\(369\) | −3.52868 | − | 6.11186i | −0.183696 | − | 0.318170i | ||||
\(370\) | −3.99853 | − | 2.82408i | −0.207874 | − | 0.146817i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 12.4668 | − | 12.4668i | 0.646373 | − | 0.646373i | ||||
\(373\) | 7.56784 | − | 28.2436i | 0.391848 | − | 1.46240i | −0.435235 | − | 0.900317i | \(-0.643335\pi\) |
0.827083 | − | 0.562080i | \(-0.189999\pi\) | |||||||
\(374\) | −18.8747 | + | 32.6919i | −0.975986 | + | 1.69046i | ||||
\(375\) | −0.136251 | + | 11.1795i | −0.00703599 | + | 0.577307i | ||||
\(376\) | −0.618089 | + | 0.356854i | −0.0318755 | + | 0.0184033i | ||||
\(377\) | 0.374143 | + | 0.374143i | 0.0192693 | + | 0.0192693i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 22.0077i | − | 1.13046i | −0.824933 | − | 0.565230i | \(-0.808787\pi\) | ||
0.824933 | − | 0.565230i | \(-0.191213\pi\) | |||||||
\(380\) | 2.98260 | − | 32.5670i | 0.153004 | − | 1.67065i | ||||
\(381\) | 3.50412 | + | 2.02311i | 0.179522 | + | 0.103647i | ||||
\(382\) | 1.05574 | + | 3.94009i | 0.0540165 | + | 0.201592i | ||||
\(383\) | 0.533272 | + | 0.142890i | 0.0272489 | + | 0.00730133i | 0.272418 | − | 0.962179i | \(-0.412177\pi\) |
−0.245169 | + | 0.969480i | \(0.578843\pi\) | |||||||
\(384\) | −7.08211 | −0.361407 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.3017 | −1.18602 | ||||||||
\(387\) | −0.416487 | − | 0.111597i | −0.0211712 | − | 0.00567281i | ||||
\(388\) | −7.86567 | − | 29.3551i | −0.399319 | − | 1.49028i | ||||
\(389\) | 22.4560 | + | 12.9650i | 1.13857 | + | 0.657352i | 0.946075 | − | 0.323947i | \(-0.105010\pi\) |
0.192491 | + | 0.981299i | \(0.438343\pi\) | |||||||
\(390\) | −5.22493 | − | 6.27844i | −0.264574 | − | 0.317921i | ||||
\(391\) | 1.66768i | 0.0843381i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.60978 | − | 6.60978i | −0.333419 | − | 0.333419i | ||||
\(394\) | 21.9324 | − | 12.6626i | 1.10494 | − | 0.637935i | ||||
\(395\) | 22.9378 | − | 10.5829i | 1.15413 | − | 0.532481i | ||||
\(396\) | −3.24706 | + | 5.62407i | −0.163171 | + | 0.282620i | ||||
\(397\) | −6.28213 | + | 23.4452i | −0.315291 | + | 1.17668i | 0.608427 | + | 0.793609i | \(0.291801\pi\) |
−0.923718 | + | 0.383072i | \(0.874866\pi\) | |||||||
\(398\) | −4.84408 | + | 4.84408i | −0.242812 | + | 0.242812i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.93791 | − | 13.9176i | −0.246895 | − | 0.695879i | ||||
\(401\) | 6.47088 | + | 11.2079i | 0.323140 | + | 0.559696i | 0.981134 | − | 0.193328i | \(-0.0619280\pi\) |
−0.657994 | + | 0.753023i | \(0.728595\pi\) | |||||||
\(402\) | −9.86397 | + | 2.64304i | −0.491970 | + | 0.131823i | ||||
\(403\) | −12.1596 | + | 3.25815i | −0.605712 | + | 0.162300i | ||||
\(404\) | −8.78598 | − | 15.2178i | −0.437119 | − | 0.757112i | ||||
\(405\) | 1.28999 | − | 1.82645i | 0.0640999 | − | 0.0907572i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.96500 | − | 1.96500i | 0.0974016 | − | 0.0974016i | ||||
\(408\) | 1.57440 | − | 5.87575i | 0.0779445 | − | 0.290893i | ||||
\(409\) | 1.32139 | − | 2.28872i | 0.0653386 | − | 0.113170i | −0.831506 | − | 0.555516i | \(-0.812521\pi\) |
0.896844 | + | 0.442347i | \(0.145854\pi\) | |||||||
\(410\) | 11.4875 | − | 31.1671i | 0.567326 | − | 1.53923i | ||||
\(411\) | −9.20938 | + | 5.31704i | −0.454265 | + | 0.262270i | ||||
\(412\) | 16.8811 | + | 16.8811i | 0.831672 | + | 0.831672i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.522969i | 0.0257025i | ||||||||
\(415\) | −11.8846 | + | 9.89037i | −0.583392 | + | 0.485499i | ||||
\(416\) | 12.0676 | + | 6.96724i | 0.591663 | + | 0.341597i | ||||
\(417\) | 2.01595 | + | 7.52362i | 0.0987214 | + | 0.368433i | ||||
\(418\) | 32.6881 | + | 8.75874i | 1.59883 | + | 0.428404i | ||||
\(419\) | 10.0302 | 0.490007 | 0.245003 | − | 0.969522i | \(-0.421211\pi\) | ||||
0.245003 | + | 0.969522i | \(0.421211\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.6440 | −1.29855 | −0.649274 | − | 0.760555i | \(-0.724927\pi\) | ||||
−0.649274 | + | 0.760555i | \(0.724927\pi\) | |||||||
\(422\) | 35.0737 | + | 9.39797i | 1.70736 | + | 0.457486i | ||||
\(423\) | 0.203827 | + | 0.760694i | 0.00991042 | + | 0.0369862i | ||||
\(424\) | −5.53895 | − | 3.19791i | −0.268995 | − | 0.155304i | ||||
\(425\) | 33.4560 | − | 2.65331i | 1.62285 | − | 0.128704i | ||||
\(426\) | − | 32.2232i | − | 1.56122i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 18.1634 | + | 18.1634i | 0.877960 | + | 0.877960i | ||||
\(429\) | 4.01565 | − | 2.31844i | 0.193878 | − | 0.111935i | ||||
\(430\) | −0.850190 | − | 1.84274i | −0.0409998 | − | 0.0888650i | ||||
\(431\) | −11.1873 | + | 19.3771i | −0.538876 | + | 0.933360i | 0.460089 | + | 0.887873i | \(0.347817\pi\) |
−0.998965 | + | 0.0454873i | \(0.985516\pi\) | |||||||
\(432\) | −0.764428 | + | 2.85288i | −0.0367785 | + | 0.137259i | ||||
\(433\) | 13.4723 | − | 13.4723i | 0.647438 | − | 0.647438i | −0.304935 | − | 0.952373i | \(-0.598635\pi\) |
0.952373 | + | 0.304935i | \(0.0986349\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.671871 | + | 0.115657i | −0.0322138 | + | 0.00554532i | ||||
\(436\) | −7.23517 | − | 12.5317i | −0.346502 | − | 0.600159i | ||||
\(437\) | 1.44408 | − | 0.386941i | 0.0690799 | − | 0.0185099i | ||||
\(438\) | 28.8132 | − | 7.72048i | 1.37675 | − | 0.368899i | ||||
\(439\) | −12.8395 | − | 22.2386i | −0.612795 | − | 1.06139i | −0.990767 | − | 0.135576i | \(-0.956712\pi\) |
0.377972 | − | 0.925817i | \(-0.376622\pi\) | |||||||
\(440\) | −5.33598 | + | 0.918542i | −0.254383 | + | 0.0437898i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.3376 | + | 17.3376i | −0.824665 | + | 0.824665i | ||||
\(443\) | −5.72284 | + | 21.3579i | −0.271900 | + | 1.01475i | 0.685990 | + | 0.727611i | \(0.259369\pi\) |
−0.957890 | + | 0.287135i | \(0.907297\pi\) | |||||||
\(444\) | −1.26397 | + | 2.18927i | −0.0599855 | + | 0.103898i | ||||
\(445\) | −6.47539 | − | 14.0351i | −0.306963 | − | 0.665327i | ||||
\(446\) | 11.8171 | − | 6.82261i | 0.559556 | − | 0.323060i | ||||
\(447\) | −10.1014 | − | 10.1014i | −0.477779 | − | 0.477779i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.01947i | 0.331269i | 0.986187 | + | 0.165635i | \(0.0529673\pi\) | ||||
−0.986187 | + | 0.165635i | \(0.947033\pi\) | |||||||
\(450\) | 10.4915 | − | 0.832054i | 0.494574 | − | 0.0392234i | ||||
\(451\) | 16.3301 | + | 9.42818i | 0.768954 | + | 0.443956i | ||||
\(452\) | 6.21888 | + | 23.2092i | 0.292512 | + | 1.09167i | ||||
\(453\) | −9.44666 | − | 2.53123i | −0.443843 | − | 0.118927i | ||||
\(454\) | 42.1548 | 1.97842 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.45325 | −0.255372 | ||||||||
\(457\) | −15.3158 | − | 4.10385i | −0.716442 | − | 0.191970i | −0.117858 | − | 0.993030i | \(-0.537603\pi\) |
−0.598584 | + | 0.801060i | \(0.704270\pi\) | |||||||
\(458\) | −15.7610 | − | 58.8209i | −0.736464 | − | 2.74852i | ||||
\(459\) | −5.81294 | − | 3.35610i | −0.271325 | − | 0.156649i | ||||
\(460\) | −1.03792 | + | 0.863761i | −0.0483934 | + | 0.0402731i | ||||
\(461\) | 29.9845i | 1.39652i | 0.715846 | + | 0.698259i | \(0.246041\pi\) | ||||
−0.715846 | + | 0.698259i | \(0.753959\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.70220 | + | 7.70220i | 0.357951 | + | 0.357951i | 0.863057 | − | 0.505106i | \(-0.168547\pi\) |
−0.505106 | + | 0.863057i | \(0.668547\pi\) | |||||||
\(464\) | 0.779853 | − | 0.450249i | 0.0362038 | − | 0.0209023i | ||||
\(465\) | 5.60943 | − | 15.2191i | 0.260131 | − | 0.705770i | ||||
\(466\) | 7.12259 | − | 12.3367i | 0.329948 | − | 0.571486i | ||||
\(467\) | 0.662362 | − | 2.47197i | 0.0306504 | − | 0.114389i | −0.948906 | − | 0.315559i | \(-0.897808\pi\) |
0.979556 | + | 0.201170i | \(0.0644745\pi\) | |||||||
\(468\) | −2.98263 | + | 2.98263i | −0.137872 | + | 0.137872i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.13836 | + | 3.02764i | −0.0986350 | + | 0.139654i | ||||
\(471\) | −1.53959 | − | 2.66665i | −0.0709407 | − | 0.122873i | ||||
\(472\) | −6.99289 | + | 1.87374i | −0.321874 | + | 0.0862458i | ||||
\(473\) | 1.11280 | − | 0.298173i | 0.0511665 | − | 0.0137100i | ||||
\(474\) | −11.8897 | − | 20.5936i | −0.546114 | − | 0.945897i | ||||
\(475\) | −10.0601 | − | 28.3547i | −0.461591 | − | 1.30100i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.99031 | + | 4.99031i | −0.228491 | + | 0.228491i | ||||
\(478\) | −8.81295 | + | 32.8904i | −0.403095 | + | 1.50437i | ||||
\(479\) | −2.04728 | + | 3.54599i | −0.0935425 | + | 0.162020i | −0.908999 | − | 0.416798i | \(-0.863152\pi\) |
0.815457 | + | 0.578818i | \(0.196486\pi\) | |||||||
\(480\) | −16.3027 | + | 7.52160i | −0.744114 | + | 0.343313i | ||||
\(481\) | 1.56316 | − | 0.902491i | 0.0712740 | − | 0.0411500i | ||||
\(482\) | 16.9240 | + | 16.9240i | 0.770867 | + | 0.770867i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.38461i | 0.426573i | ||||||||
\(485\) | −17.8845 | − | 21.4906i | −0.812092 | − | 0.975836i | ||||
\(486\) | −1.82289 | − | 1.05244i | −0.0826878 | − | 0.0477398i | ||||
\(487\) | −3.77185 | − | 14.0767i | −0.170919 | − | 0.637878i | −0.997211 | − | 0.0746360i | \(-0.976221\pi\) |
0.826292 | − | 0.563242i | \(-0.190446\pi\) | |||||||
\(488\) | 4.84445 | + | 1.29807i | 0.219298 | + | 0.0587607i | ||||
\(489\) | −19.3404 | −0.874603 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.55953 | −0.386286 | −0.193143 | − | 0.981171i | \(-0.561868\pi\) | ||||
−0.193143 | + | 0.981171i | \(0.561868\pi\) | |||||||
\(492\) | −16.5688 | − | 4.43960i | −0.746979 | − | 0.200153i | ||||
\(493\) | 0.529668 | + | 1.97675i | 0.0238550 | + | 0.0890282i | ||||
\(494\) | 19.0358 | + | 10.9903i | 0.856460 | + | 0.494477i | ||||
\(495\) | −0.544884 | + | 5.94959i | −0.0244907 | + | 0.267414i | ||||
\(496\) | 21.4242i | 0.961976i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 10.2917 | + | 10.2917i | 0.461180 | + | 0.461180i | ||||
\(499\) | −20.5736 | + | 11.8782i | −0.921002 | + | 0.531741i | −0.883955 | − | 0.467572i | \(-0.845129\pi\) |
−0.0370477 | + | 0.999313i | \(0.511795\pi\) | |||||||
\(500\) | 18.9796 | + | 19.4479i | 0.848794 | + | 0.869738i | ||||
\(501\) | 4.40731 | − | 7.63369i | 0.196904 | − | 0.341048i | ||||
\(502\) | −3.78647 | + | 14.1313i | −0.168998 | + | 0.630710i | ||||
\(503\) | −17.9504 | + | 17.9504i | −0.800367 | + | 0.800367i | −0.983153 | − | 0.182786i | \(-0.941489\pi\) |
0.182786 | + | 0.983153i | \(0.441489\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.2046 | − | 9.32611i | −0.587596 | − | 0.415007i | ||||
\(506\) | −0.698653 | − | 1.21010i | −0.0310589 | − | 0.0537956i | ||||
\(507\) | −9.64790 | + | 2.58515i | −0.428478 | + | 0.114810i | ||||
\(508\) | 9.49942 | − | 2.54536i | 0.421469 | − | 0.112932i | ||||
\(509\) | −8.44887 | − | 14.6339i | −0.374489 | − | 0.648635i | 0.615761 | − | 0.787933i | \(-0.288849\pi\) |
−0.990250 | + | 0.139298i | \(0.955515\pi\) | |||||||
\(510\) | −5.35948 | − | 31.1342i | −0.237322 | − | 1.37865i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 20.5543 | − | 20.5543i | 0.908382 | − | 0.908382i | ||||
\(513\) | −1.55739 | + | 5.81226i | −0.0687604 | + | 0.256617i | ||||
\(514\) | −15.0161 | + | 26.0087i | −0.662333 | + | 1.14720i | ||||
\(515\) | 20.6080 | + | 7.59564i | 0.908097 | + | 0.334704i | ||||
\(516\) | −0.907596 | + | 0.524001i | −0.0399547 | + | 0.0230679i | ||||
\(517\) | −1.48788 | − | 1.48788i | −0.0654367 | − | 0.0654367i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 9.57331i | − | 0.420221i | ||||||
\(520\) | −3.50216 | − | 0.320740i | −0.153580 | − | 0.0140654i | ||||
\(521\) | −6.82841 | − | 3.94238i | −0.299158 | − | 0.172719i | 0.342907 | − | 0.939370i | \(-0.388589\pi\) |
−0.642065 | + | 0.766651i | \(0.721922\pi\) | |||||||
\(522\) | 0.166099 | + | 0.619890i | 0.00726996 | + | 0.0271319i | ||||
\(523\) | 1.68225 | + | 0.450757i | 0.0735595 | + | 0.0197102i | 0.295411 | − | 0.955370i | \(-0.404543\pi\) |
−0.221852 | + | 0.975080i | \(0.571210\pi\) | |||||||
\(524\) | −22.7199 | −0.992524 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 54.1722 | 2.36202 | ||||||||
\(527\) | −47.0299 | − | 12.6016i | −2.04865 | − | 0.548935i | ||||
\(528\) | −2.04245 | − | 7.62253i | −0.0888863 | − | 0.331728i | ||||
\(529\) | 19.8651 | + | 11.4691i | 0.863701 | + | 0.498658i | ||||
\(530\) | −33.0783 | − | 3.02942i | −1.43683 | − | 0.131590i | ||||
\(531\) | 7.98837i | 0.346666i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.66039 | + | 8.66039i | 0.375123 | + | 0.375123i | ||||
\(534\) | −12.6007 | + | 7.27503i | −0.545287 | + | 0.314821i | ||||
\(535\) | 22.1734 | + | 8.17260i | 0.958638 | + | 0.353332i | ||||
\(536\) | −2.19838 | + | 3.80771i | −0.0949557 | + | 0.164468i | ||||
\(537\) | −0.336732 | + | 1.25670i | −0.0145310 | + | 0.0542306i | ||||
\(538\) | −23.0876 | + | 23.0876i | −0.995375 | + | 0.995375i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.922006 | − | 5.35610i | −0.0396768 | − | 0.230490i | ||||
\(541\) | −17.4747 | − | 30.2671i | −0.751298 | − | 1.30129i | −0.947194 | − | 0.320661i | \(-0.896095\pi\) |
0.195896 | − | 0.980625i | \(-0.437238\pi\) | |||||||
\(542\) | 27.1261 | − | 7.26843i | 1.16517 | − | 0.312206i | ||||
\(543\) | 8.19615 | − | 2.19615i | 0.351731 | − | 0.0942459i | ||||
\(544\) | 26.9473 | + | 46.6741i | 1.15536 | + | 2.00114i | ||||
\(545\) | −10.8738 | − | 7.67996i | −0.465784 | − | 0.328973i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.83548 | − | 3.83548i | 0.163993 | − | 0.163993i | −0.620340 | − | 0.784333i | \(-0.713005\pi\) |
0.784333 | + | 0.620340i | \(0.213005\pi\) | |||||||
\(548\) | −6.68961 | + | 24.9660i | −0.285766 | + | 1.06649i | ||||
\(549\) | 2.76704 | − | 4.79266i | 0.118095 | − | 0.204546i | ||||
\(550\) | −23.1648 | + | 15.9413i | −0.987750 | + | 0.679738i | ||||
\(551\) | 1.58882 | − | 0.917304i | 0.0676859 | − | 0.0390785i | ||||
\(552\) | 0.159216 | + | 0.159216i | 0.00677668 | + | 0.00677668i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.97022i | 0.253650i | ||||||||
\(555\) | −0.212105 | + | 2.31598i | −0.00900337 | + | 0.0983077i | ||||
\(556\) | 16.3953 | + | 9.46581i | 0.695314 | + | 0.401440i | ||||
\(557\) | −5.97158 | − | 22.2863i | −0.253024 | − | 0.944299i | −0.969179 | − | 0.246358i | \(-0.920766\pi\) |
0.716155 | − | 0.697941i | \(-0.245900\pi\) | |||||||
\(558\) | −14.7482 | − | 3.95176i | −0.624339 | − | 0.167291i | ||||
\(559\) | 0.748285 | 0.0316491 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.9341 | 0.757180 | ||||||||
\(562\) | −27.5609 | − | 7.38493i | −1.16259 | − | 0.311514i | ||||
\(563\) | 8.69386 | + | 32.4459i | 0.366402 | + | 1.36743i | 0.865510 | + | 0.500892i | \(0.166995\pi\) |
−0.499107 | + | 0.866540i | \(0.666339\pi\) | |||||||
\(564\) | 1.65768 | + | 0.957064i | 0.0698011 | + | 0.0402997i | ||||
\(565\) | 14.1401 | + | 16.9912i | 0.594879 | + | 0.714826i | ||||
\(566\) | 48.3556i | 2.03254i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.81023 | − | 9.81023i | −0.411628 | − | 0.411628i | ||||
\(569\) | 0.240575 | − | 0.138896i | 0.0100854 | − | 0.00582283i | −0.494949 | − | 0.868922i | \(-0.664813\pi\) |
0.505034 | + | 0.863099i | \(0.331480\pi\) | |||||||
\(570\) | −25.7163 | + | 11.8648i | −1.07714 | + | 0.496961i | ||||
\(571\) | 1.55769 | − | 2.69800i | 0.0651874 | − | 0.112908i | −0.831590 | − | 0.555390i | \(-0.812569\pi\) |
0.896777 | + | 0.442483i | \(0.145902\pi\) | |||||||
\(572\) | 2.91693 | − | 10.8861i | 0.121963 | − | 0.455173i | ||||
\(573\) | 1.37031 | − | 1.37031i | 0.0572454 | − | 0.0572454i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.534138 | + | 1.12158i | −0.0222751 | + | 0.0467731i | ||||
\(576\) | 5.49693 | + | 9.52095i | 0.229039 | + | 0.396706i | ||||
\(577\) | −40.4214 | + | 10.8309i | −1.68277 | + | 0.450896i | −0.968507 | − | 0.248986i | \(-0.919903\pi\) |
−0.714259 | + | 0.699882i | \(0.753236\pi\) | |||||||
\(578\) | −57.0377 | + | 15.2832i | −2.37246 | + | 0.635698i | ||||
\(579\) | 5.53513 | + | 9.58713i | 0.230032 | + | 0.398428i | ||||
\(580\) | −0.955943 | + | 1.35349i | −0.0396934 | + | 0.0562007i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −18.6101 | + | 18.6101i | −0.771413 | + | 0.771413i | ||||
\(583\) | 4.88039 | − | 18.2139i | 0.202125 | − | 0.754341i | ||||
\(584\) | 6.42160 | − | 11.1225i | 0.265728 | − | 0.460254i | ||||
\(585\) | −1.34203 | + | 3.64112i | −0.0554863 | + | 0.150542i | ||||
\(586\) | 6.23257 | − | 3.59838i | 0.257465 | − | 0.148648i | ||||
\(587\) | 26.6462 | + | 26.6462i | 1.09981 | + | 1.09981i | 0.994433 | + | 0.105375i | \(0.0336041\pi\) |
0.105375 | + | 0.994433i | \(0.466396\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 43.6482i | 1.79849i | ||||||||
\(590\) | −28.9002 | + | 24.0507i | −1.18980 | + | 0.990153i | ||||
\(591\) | −10.4197 | − | 6.01583i | −0.428610 | − | 0.247458i | ||||
\(592\) | −0.795059 | − | 2.96720i | −0.0326767 | − | 0.121951i | ||||
\(593\) | −20.7484 | − | 5.55952i | −0.852036 | − | 0.228302i | −0.193732 | − | 0.981055i | \(-0.562059\pi\) |
−0.658304 | + | 0.752752i | \(0.728726\pi\) | |||||||
\(594\) | 5.62399 | 0.230755 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −34.7217 | −1.42225 | ||||||||
\(597\) | 3.14370 | + | 0.842351i | 0.128663 | + | 0.0344751i | ||||
\(598\) | −0.234900 | − | 0.876657i | −0.00960576 | − | 0.0358492i | ||||
\(599\) | −19.2930 | − | 11.1388i | −0.788290 | − | 0.455119i | 0.0510705 | − | 0.998695i | \(-0.483737\pi\) |
−0.839360 | + | 0.543576i | \(0.817070\pi\) | |||||||
\(600\) | 2.94078 | − | 3.44741i | 0.120057 | − | 0.140740i | ||||
\(601\) | − | 22.3458i | − | 0.911503i | −0.890107 | − | 0.455752i | \(-0.849371\pi\) | ||
0.890107 | − | 0.455752i | \(-0.150629\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.43055 | + | 3.43055i | 0.139703 | + | 0.139703i | ||||
\(604\) | −20.5859 | + | 11.8853i | −0.837629 | + | 0.483605i | ||||
\(605\) | 3.61694 | + | 7.83954i | 0.147049 | + | 0.318723i | ||||
\(606\) | −7.60877 | + | 13.1788i | −0.309085 | + | 0.535351i | ||||
\(607\) | −0.210840 | + | 0.786867i | −0.00855775 | + | 0.0319380i | −0.970073 | − | 0.242815i | \(-0.921929\pi\) |
0.961515 | + | 0.274753i | \(0.0885960\pi\) | |||||||
\(608\) | 34.1639 | − | 34.1639i | 1.38553 | − | 1.38553i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 25.6696 | − | 4.41880i | 1.03933 | − | 0.178912i | ||||
\(611\) | −0.683354 | − | 1.18360i | −0.0276456 | − | 0.0478835i | ||||
\(612\) | −15.7585 | + | 4.22247i | −0.636998 | + | 0.170683i | ||||
\(613\) | 22.4996 | − | 6.02876i | 0.908752 | − | 0.243499i | 0.225981 | − | 0.974132i | \(-0.427441\pi\) |
0.682771 | + | 0.730632i | \(0.260775\pi\) | |||||||
\(614\) | −10.7357 | − | 18.5947i | −0.433257 | − | 0.750423i | ||||
\(615\) | −15.5520 | + | 2.67714i | −0.627117 | + | 0.107953i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.70013 | + | 3.70013i | −0.148962 | + | 0.148962i | −0.777654 | − | 0.628692i | \(-0.783590\pi\) |
0.628692 | + | 0.777654i | \(0.283590\pi\) | |||||||
\(618\) | 5.35101 | − | 19.9703i | 0.215249 | − | 0.803322i | ||||
\(619\) | 19.9420 | − | 34.5405i | 0.801536 | − | 1.38830i | −0.117068 | − | 0.993124i | \(-0.537350\pi\) |
0.918605 | − | 0.395178i | \(-0.129317\pi\) | |||||||
\(620\) | −16.5158 | − | 35.7972i | −0.663290 | − | 1.43765i | ||||
\(621\) | 0.215168 | − | 0.124227i | 0.00863440 | − | 0.00498507i | ||||
\(622\) | −15.2621 | − | 15.2621i | −0.611954 | − | 0.611954i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 5.12566i | − | 0.205191i | ||||||
\(625\) | 23.3503 | + | 8.93109i | 0.934011 | + | 0.357244i | ||||
\(626\) | 56.9479 | + | 32.8789i | 2.27610 | + | 1.31410i | ||||
\(627\) | −4.16114 | − | 15.5296i | −0.166180 | − | 0.620193i | ||||
\(628\) | −7.22910 | − | 1.93703i | −0.288473 | − | 0.0772960i | ||||
\(629\) | 6.98117 | 0.278357 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.9725 | −1.35242 | −0.676211 | − | 0.736708i | \(-0.736379\pi\) | ||||
−0.676211 | + | 0.736708i | \(0.736379\pi\) | |||||||
\(632\) | −9.88943 | − | 2.64987i | −0.393381 | − | 0.105406i | ||||
\(633\) | −4.46483 | − | 16.6630i | −0.177461 | − | 0.662294i | ||||
\(634\) | −31.5962 | − | 18.2421i | −1.25485 | − | 0.724486i | ||||
\(635\) | 6.95444 | − | 5.78748i | 0.275978 | − | 0.229669i | ||||
\(636\) | 17.1533i | 0.680172i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.21247 | − | 1.21247i | −0.0480022 | − | 0.0480022i | ||||
\(639\) | −13.2578 | + | 7.65437i | −0.524469 | + | 0.302802i | ||||
\(640\) | −5.47666 | + | 14.8589i | −0.216484 | + | 0.587350i | ||||
\(641\) | 9.05563 | − | 15.6848i | 0.357676 | − | 0.619513i | −0.629896 | − | 0.776679i | \(-0.716903\pi\) |
0.987572 | + | 0.157167i | \(0.0502359\pi\) | |||||||
\(642\) | 5.75748 | − | 21.4872i | 0.227229 | − | 0.848032i | ||||
\(643\) | 32.1062 | − | 32.1062i | 1.26614 | − | 1.26614i | 0.318082 | − | 0.948063i | \(-0.396961\pi\) |
0.948063 | − | 0.318082i | \(-0.103039\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.556214 | + | 0.787528i | −0.0219009 | + | 0.0310089i | ||||
\(646\) | 42.5074 | + | 73.6251i | 1.67243 | + | 2.89674i | ||||
\(647\) | −17.6596 | + | 4.73187i | −0.694270 | + | 0.186029i | −0.588663 | − | 0.808379i | \(-0.700345\pi\) |
−0.105607 | + | 0.994408i | \(0.533679\pi\) | |||||||
\(648\) | −0.875383 | + | 0.234558i | −0.0343883 | + | 0.00921432i | ||||
\(649\) | −10.6720 | − | 18.4844i | −0.418911 | − | 0.725575i | ||||
\(650\) | −17.2132 | + | 6.10719i | −0.675159 | + | 0.239544i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −33.2396 | + | 33.2396i | −1.30176 | + | 1.30176i | ||||
\(653\) | −3.44041 | + | 12.8398i | −0.134634 | + | 0.502459i | 0.865366 | + | 0.501141i | \(0.167086\pi\) |
−0.999999 | + | 0.00131826i | \(0.999580\pi\) | |||||||
\(654\) | −6.26575 | + | 10.8526i | −0.245010 | + | 0.424370i | ||||
\(655\) | −18.9793 | + | 8.75652i | −0.741584 | + | 0.342146i | ||||
\(656\) | 18.0515 | − | 10.4220i | 0.704792 | − | 0.406912i | ||||
\(657\) | −10.0208 | − | 10.0208i | −0.390950 | − | 0.390950i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.13808i | 0.355969i | 0.984033 | + | 0.177985i | \(0.0569577\pi\) | ||||
−0.984033 | + | 0.177985i | \(0.943042\pi\) | |||||||
\(660\) | 9.28884 | + | 11.1618i | 0.361568 | + | 0.434472i | ||||
\(661\) | −24.6676 | − | 14.2418i | −0.959458 | − | 0.553943i | −0.0634519 | − | 0.997985i | \(-0.520211\pi\) |
−0.896006 | + | 0.444042i | \(0.853544\pi\) | |||||||
\(662\) | 0.688108 | + | 2.56805i | 0.0267441 | + | 0.0998102i | ||||
\(663\) | 11.2517 | + | 3.01489i | 0.436980 | + | 0.117089i | ||||
\(664\) | 6.26651 | 0.243188 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.18923 | 0.0848310 | ||||||||
\(667\) | −0.0731700 | − | 0.0196059i | −0.00283316 | − | 0.000759142i | ||||
\(668\) | −5.54504 | − | 20.6944i | −0.214544 | − | 0.800690i | ||||
\(669\) | −5.61413 | − | 3.24132i | −0.217055 | − | 0.125317i | ||||
\(670\) | −2.08256 | + | 22.7394i | −0.0804562 | + | 0.878500i | ||||
\(671\) | 14.7864i | 0.570821i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.8815 | + | 26.8815i | 1.03621 | + | 1.03621i | 0.999319 | + | 0.0368867i | \(0.0117441\pi\) |
0.0368867 | + | 0.999319i | \(0.488256\pi\) | |||||||
\(674\) | 24.6354 | − | 14.2233i | 0.948922 | − | 0.547860i | ||||
\(675\) | −2.83451 | − | 4.11893i | −0.109100 | − | 0.158538i | ||||
\(676\) | −12.1385 | + | 21.0245i | −0.466864 | + | 0.808633i | ||||
\(677\) | −0.438111 | + | 1.63505i | −0.0168380 | + | 0.0628402i | −0.973834 | − | 0.227262i | \(-0.927023\pi\) |
0.956996 | + | 0.290102i | \(0.0936893\pi\) | |||||||
\(678\) | 14.7138 | − | 14.7138i | 0.565081 | − | 0.565081i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −11.1104 | − | 7.84702i | −0.426063 | − | 0.300919i | ||||
\(681\) | −10.0135 | − | 17.3440i | −0.383720 | − | 0.664623i | ||||
\(682\) | 39.4052 | − | 10.5586i | 1.50890 | − | 0.404309i | ||||
\(683\) | −3.29967 | + | 0.884144i | −0.126258 | + | 0.0338308i | −0.321395 | − | 0.946945i | \(-0.604152\pi\) |
0.195137 | + | 0.980776i | \(0.437485\pi\) | |||||||
\(684\) | 7.31267 | + | 12.6659i | 0.279607 | + | 0.484293i | ||||
\(685\) | 4.03393 | + | 23.4338i | 0.154129 | + | 0.895361i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.4571 | + | 20.4571i | −0.780487 | + | 0.780487i | ||||
\(688\) | 0.329605 | − | 1.23010i | 0.0125661 | − | 0.0468972i | ||||
\(689\) | 6.12382 | − | 10.6068i | 0.233299 | − | 0.404086i | ||||
\(690\) | 1.09724 | + | 0.404417i | 0.0417711 | + | 0.0153959i | ||||
\(691\) | −36.0875 | + | 20.8351i | −1.37283 | + | 0.792606i | −0.991284 | − | 0.131743i | \(-0.957943\pi\) |
−0.381549 | + | 0.924348i | \(0.624609\pi\) | |||||||
\(692\) | −16.4533 | − | 16.4533i | −0.625459 | − | 0.625459i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 19.4970i | − | 0.740098i | ||||||
\(695\) | 17.3442 | + | 1.58844i | 0.657903 | + | 0.0602531i | ||||
\(696\) | 0.239292 | + | 0.138155i | 0.00907032 | + | 0.00523675i | ||||
\(697\) | 12.2604 | + | 45.7563i | 0.464395 | + | 1.73314i | ||||
\(698\) | 5.63470 | + | 1.50981i | 0.213276 | + | 0.0571472i | ||||
\(699\) | −6.76767 | −0.255977 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.7870 | 0.520727 | 0.260364 | − | 0.965511i | \(-0.416158\pi\) | ||||
0.260364 | + | 0.965511i | \(0.416158\pi\) | |||||||
\(702\) | 3.52844 | + | 0.945442i | 0.133172 | + | 0.0356834i | ||||
\(703\) | −1.61980 | − | 6.04516i | −0.0610918 | − | 0.227998i | ||||
\(704\) | −25.4388 | − | 14.6871i | −0.958760 | − | 0.553540i | ||||
\(705\) | 1.75363 | + | 0.160603i | 0.0660454 | + | 0.00604868i | ||||
\(706\) | 2.88915i | 0.108735i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 13.7293 | + | 13.7293i | 0.515978 | + | 0.515978i | ||||
\(709\) | −21.3668 | + | 12.3361i | −0.802446 | + | 0.463293i | −0.844326 | − | 0.535830i | \(-0.819999\pi\) |
0.0418795 | + | 0.999123i | \(0.486665\pi\) | |||||||
\(710\) | −67.6072 | − | 24.9185i | −2.53725 | − | 0.935175i | ||||
\(711\) | −5.64863 | + | 9.78372i | −0.211840 | + | 0.366918i | ||||
\(712\) | −1.62139 | + | 6.05110i | −0.0607641 | + | 0.226775i | ||||
\(713\) | 1.27438 | − | 1.27438i | 0.0477257 | − | 0.0477257i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.75895 | − | 10.2181i | −0.0657811 | − | 0.382135i | ||||
\(716\) | 1.58111 | + | 2.73857i | 0.0590890 | + | 0.102345i | ||||
\(717\) | 15.6257 | − | 4.18690i | 0.583553 | − | 0.156363i | ||||
\(718\) | −18.9656 | + | 5.08182i | −0.707791 | + | 0.189652i | ||||
\(719\) | 14.9558 | + | 25.9043i | 0.557758 | + | 0.966066i | 0.997683 | + | 0.0680313i | \(0.0216718\pi\) |
−0.439925 | + | 0.898035i | \(0.644995\pi\) | |||||||
\(720\) | 5.39447 | + | 3.81000i | 0.201040 | + | 0.141990i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 25.6118 | − | 25.6118i | 0.953171 | − | 0.953171i | ||||
\(723\) | 2.94297 | − | 10.9833i | 0.109450 | − | 0.408473i | ||||
\(724\) | 10.3120 | − | 17.8608i | 0.383241 | − | 0.663793i | ||||
\(725\) | −0.276906 | + | 1.49909i | −0.0102840 | + | 0.0556747i | ||||
\(726\) | 7.03835 | − | 4.06359i | 0.261218 | − | 0.150814i | ||||
\(727\) | −29.8488 | − | 29.8488i | −1.10703 | − | 1.10703i | −0.993539 | − | 0.113491i | \(-0.963797\pi\) |
−0.113491 | − | 0.993539i | \(-0.536203\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 6.08326 | − | 66.4231i | 0.225152 | − | 2.45843i | ||||
\(731\) | 2.50641 | + | 1.44708i | 0.0927031 | + | 0.0535222i | ||||
\(732\) | −3.48135 | − | 12.9926i | −0.128674 | − | 0.480219i | ||||
\(733\) | 5.28252 | + | 1.41545i | 0.195114 | + | 0.0522807i | 0.355053 | − | 0.934846i | \(-0.384463\pi\) |
−0.159938 | + | 0.987127i | \(0.551130\pi\) | |||||||
\(734\) | 38.7082 | 1.42875 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.99493 | −0.0735342 | ||||||||
\(737\) | −12.5210 | − | 3.35499i | −0.461216 | − | 0.123583i | ||||
\(738\) | 3.84475 | + | 14.3488i | 0.141527 | + | 0.528186i | ||||
\(739\) | −10.3694 | − | 5.98677i | −0.381444 | − | 0.220227i | 0.297002 | − | 0.954877i | \(-0.404013\pi\) |
−0.678446 | + | 0.734650i | \(0.737346\pi\) | |||||||
\(740\) | 3.61584 | + | 4.34491i | 0.132921 | + | 0.159722i | ||||
\(741\) | − | 10.4427i | − | 0.383621i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.0406 | − | 12.0406i | −0.441728 | − | 0.441728i | 0.450864 | − | 0.892593i | \(-0.351116\pi\) |
−0.892593 | + | 0.450864i | \(0.851116\pi\) | |||||||
\(744\) | −5.69312 | + | 3.28692i | −0.208720 | + | 0.120504i | ||||
\(745\) | −29.0051 | + | 13.3821i | −1.06267 | + | 0.490283i | ||||
\(746\) | −30.7733 | + | 53.3010i | −1.12669 | + | 1.95149i | ||||
\(747\) | 1.78965 | − | 6.67906i | 0.0654798 | − | 0.244374i | ||||
\(748\) | 30.8227 | − | 30.8227i | 1.12699 | − | 1.12699i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 6.36745 | − | 22.6556i | 0.232506 | − | 0.827264i | ||||
\(751\) | 12.0559 | + | 20.8815i | 0.439928 | + | 0.761977i | 0.997683 | − | 0.0680281i | \(-0.0216707\pi\) |
−0.557756 | + | 0.830005i | \(0.688337\pi\) | |||||||
\(752\) | −2.24673 | + | 0.602008i | −0.0819296 | + | 0.0219530i | ||||
\(753\) | 6.71356 | − | 1.79889i | 0.244656 | − | 0.0655553i | ||||
\(754\) | −0.556866 | − | 0.964521i | −0.0202799 | − | 0.0351258i | ||||
\(755\) | −12.6159 | + | 17.8625i | −0.459141 | + | 0.650085i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.2896 | − | 29.2896i | 1.06455 | − | 1.06455i | 0.0667825 | − | 0.997768i | \(-0.478727\pi\) |
0.997768 | − | 0.0667825i | \(-0.0212733\pi\) | |||||||
\(758\) | −11.9895 | + | 44.7453i | −0.435477 | + | 1.62522i | ||||
\(759\) | −0.331920 | + | 0.574902i | −0.0120479 | + | 0.0208676i | ||||
\(760\) | −4.21705 | + | 11.4414i | −0.152969 | + | 0.415024i | ||||
\(761\) | 27.9728 | − | 16.1501i | 1.01401 | − | 0.585440i | 0.101648 | − | 0.994820i | \(-0.467589\pi\) |
0.912364 | + | 0.409381i | \(0.134255\pi\) | |||||||
\(762\) | −6.02230 | − | 6.02230i | −0.218165 | − | 0.218165i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 4.71018i | − | 0.170408i | ||||||
\(765\) | −11.5366 | + | 9.60077i | −0.417107 | + | 0.347117i | ||||
\(766\) | −1.00639 | − | 0.581037i | −0.0363622 | − | 0.0209937i | ||||
\(767\) | −3.58810 | − | 13.3910i | −0.129559 | − | 0.483520i | ||||
\(768\) | −6.83939 | − | 1.83261i | −0.246795 | − | 0.0661286i | ||||
\(769\) | 18.4310 | 0.664640 | 0.332320 | − | 0.943167i | \(-0.392169\pi\) | ||||
0.332320 | + | 0.943167i | \(0.392169\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.2679 | 0.513845 | ||||||||
\(772\) | 25.9900 | + | 6.96401i | 0.935401 | + | 0.250640i | ||||
\(773\) | 6.51389 | + | 24.3102i | 0.234288 | + | 0.874376i | 0.978468 | + | 0.206397i | \(0.0661738\pi\) |
−0.744180 | + | 0.667979i | \(0.767160\pi\) | |||||||
\(774\) | 0.785990 | + | 0.453791i | 0.0282518 | + | 0.0163112i | ||||
\(775\) | −27.5933 | − | 23.5382i | −0.991181 | − | 0.845517i | ||||
\(776\) | 11.3315i | 0.406779i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −38.5937 | − | 38.5937i | −1.38365 | − | 1.38365i | ||||
\(779\) | 36.7768 | − | 21.2331i | 1.31767 | − | 0.760755i | ||||
\(780\) | 3.95134 | + | 8.56434i | 0.141481 | + | 0.306653i | ||||
\(781\) | 20.4515 | − | 35.4230i | 0.731812 | − | 1.26754i | ||||
\(782\) | 0.908526 | − | 3.39067i | 0.0324888 | − | 0.121250i | ||||
\(783\) | 0.215589 | − | 0.215589i | 0.00770453 | − | 0.00770453i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.78546 | + | 1.16806i | −0.242184 | + | 0.0416898i | ||||
\(786\) | 9.83786 | + | 17.0397i | 0.350905 | + | 0.607785i | ||||
\(787\) | 21.9481 | − | 5.88096i | 0.782364 | − | 0.209634i | 0.154537 | − | 0.987987i | \(-0.450611\pi\) |
0.627827 | + | 0.778353i | \(0.283945\pi\) | |||||||
\(788\) | −28.2471 | + | 7.56880i | −1.00626 | + | 0.269627i | ||||
\(789\) | −12.8682 | − | 22.2884i | −0.458120 | − | 0.793487i | ||||
\(790\) | −52.4018 | + | 9.02051i | −1.86437 | + | 0.320935i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.71220 | − | 1.71220i | 0.0608404 | − | 0.0608404i | ||||
\(793\) | −2.48572 | + | 9.27683i | −0.0882705 | + | 0.329430i | ||||
\(794\) | 25.5452 | − | 44.2456i | 0.906565 | − | 1.57022i | ||||
\(795\) | 6.61108 | + | 14.3292i | 0.234471 | + | 0.508204i | ||||
\(796\) | 6.85066 | − | 3.95523i | 0.242815 | − | 0.140189i | ||||
\(797\) | −25.5337 | − | 25.5337i | −0.904451 | − | 0.904451i | 0.0913664 | − | 0.995817i | \(-0.470877\pi\) |
−0.995817 | + | 0.0913664i | \(0.970877\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.28605i | − | 0.187007i | ||||||
\(800\) | 3.17397 | + | 40.0211i | 0.112217 | + | 1.41496i | ||||
\(801\) | 5.98641 | + | 3.45626i | 0.211520 | + | 0.122121i | ||||
\(802\) | −7.05048 | − | 26.3127i | −0.248961 | − | 0.929135i | ||||
\(803\) | 36.5745 | + | 9.80010i | 1.29069 | + | 0.345838i | ||||
\(804\) | 11.7919 | 0.415868 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26.4974 | 0.933332 | ||||||||
\(807\) | 14.9833 | + | 4.01477i | 0.527438 | + | 0.141326i | ||||
\(808\) | 1.69577 | + | 6.32869i | 0.0596569 | + | 0.222642i | ||||
\(809\) | 23.8507 | + | 13.7702i | 0.838546 | + | 0.484135i | 0.856770 | − | 0.515699i | \(-0.172468\pi\) |
−0.0182236 | + | 0.999834i | \(0.505801\pi\) | |||||||
\(810\) | −3.61778 | + | 3.01072i | −0.127116 | + | 0.105786i | ||||
\(811\) | 34.2545i | 1.20284i | 0.798933 | + | 0.601420i | \(0.205398\pi\) | ||||
−0.798933 | + | 0.601420i | \(0.794602\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.43409 | − | 9.43409i | −0.330868 | − | 0.330868i | ||||
\(814\) | −5.06568 | + | 2.92467i | −0.177552 | + | 0.102510i | ||||
\(815\) | −14.9561 | + | 40.5780i | −0.523890 | + | 1.42138i | ||||
\(816\) | 9.91232 | − | 17.1686i | 0.347000 | − | 0.601022i | ||||
\(817\) | 0.671513 | − | 2.50612i | 0.0234933 | − | 0.0876781i | ||||
\(818\) | −3.93347 | + | 3.93347i | −0.137530 | + | 0.137530i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.1275 | + | 31.3297i | −0.772726 | + | 1.09408i | ||||
\(821\) | −24.8741 | − | 43.0832i | −0.868113 | − | 1.50361i | −0.863923 | − | 0.503624i | \(-0.832000\pi\) |
−0.00418940 | − | 0.999991i | \(-0.501334\pi\) | |||||||
\(822\) | 21.6208 | − | 5.79328i | 0.754113 | − | 0.202064i | ||||
\(823\) | 8.33846 | − | 2.23428i | 0.290660 | − | 0.0778822i | −0.110543 | − | 0.993871i | \(-0.535259\pi\) |
0.401203 | + | 0.915989i | \(0.368592\pi\) | |||||||
\(824\) | −4.45077 | − | 7.70896i | −0.155050 | − | 0.268555i | ||||
\(825\) | 12.0614 | + | 5.74409i | 0.419925 | + | 0.199984i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.96734 | + | 4.96734i | −0.172731 | + | 0.172731i | −0.788178 | − | 0.615447i | \(-0.788976\pi\) |
0.615447 | + | 0.788178i | \(0.288976\pi\) | |||||||
\(828\) | 0.156296 | − | 0.583305i | 0.00543167 | − | 0.0202713i | ||||
\(829\) | 14.1750 | − | 24.5518i | 0.492318 | − | 0.852720i | −0.507643 | − | 0.861568i | \(-0.669483\pi\) |
0.999961 | + | 0.00884765i | \(0.00281633\pi\) | |||||||
\(830\) | 29.5515 | − | 13.6342i | 1.02575 | − | 0.473250i | ||||
\(831\) | 2.45636 | − | 1.41818i | 0.0852101 | − | 0.0491961i | ||||
\(832\) | −13.4910 | − | 13.4910i | −0.467717 | − | 0.467717i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 16.3950i | − | 0.567713i | ||||||
\(835\) | −12.6080 | − | 15.1502i | −0.436317 | − | 0.524293i | ||||
\(836\) | −33.8417 | − | 19.5385i | −1.17044 | − | 0.675754i | ||||
\(837\) | 1.87742 | + | 7.00662i | 0.0648931 | + | 0.242184i | ||||
\(838\) | −20.3930 | − | 5.46430i | −0.704466 | − | 0.188761i | ||||
\(839\) | 32.8100 | 1.13273 | 0.566364 | − | 0.824156i | \(-0.308350\pi\) | ||||
0.566364 | + | 0.824156i | \(0.308350\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9070 | 0.996795 | ||||||||
\(842\) | 54.1716 | + | 14.5152i | 1.86688 | + | 0.500228i | ||||
\(843\) | 3.50847 | + | 13.0938i | 0.120838 | + | 0.450974i | ||||
\(844\) | −36.3115 | − | 20.9645i | −1.24989 | − | 0.721627i | ||||
\(845\) | −2.03694 | + | 22.2413i | −0.0700728 | + | 0.765124i | ||||
\(846\) | − | 1.65766i | − | 0.0569915i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −14.7390 | − | 14.7390i | −0.506139 | − | 0.506139i | ||||
\(849\) | 19.8952 | − | 11.4865i | 0.682801 | − | 0.394216i | ||||
\(850\) | −69.4670 | − | 12.8317i | −2.38270 | − | 0.440123i | ||||
\(851\) | −0.129205 | + | 0.223790i | −0.00442910 | + | 0.00767143i | ||||
\(852\) | −9.63032 | + | 35.9408i | −0.329929 | + | 1.23131i | ||||
\(853\) | −15.4954 | + | 15.4954i | −0.530553 | + | 0.530553i | −0.920737 | − | 0.390184i | \(-0.872411\pi\) |
0.390184 | + | 0.920737i | \(0.372411\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.9903 | + | 7.76222i | 0.375861 | + | 0.265462i | ||||
\(856\) | −4.78885 | − | 8.29453i | −0.163680 | − | 0.283501i | ||||
\(857\) | 24.3625 | − | 6.52792i | 0.832208 | − | 0.222989i | 0.182531 | − | 0.983200i | \(-0.441571\pi\) |
0.649677 | + | 0.760211i | \(0.274904\pi\) | |||||||
\(858\) | −9.42753 | + | 2.52610i | −0.321851 | + | 0.0862396i | ||||
\(859\) | −8.63556 | − | 14.9572i | −0.294641 | − | 0.510334i | 0.680260 | − | 0.732971i | \(-0.261867\pi\) |
−0.974901 | + | 0.222637i | \(0.928534\pi\) | |||||||
\(860\) | 0.397549 | + | 2.30944i | 0.0135563 | + | 0.0787511i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.3021 | − | 33.3021i | 1.13427 | − | 1.13427i | ||||
\(863\) | 1.07752 | − | 4.02135i | 0.0366791 | − | 0.136888i | −0.945158 | − | 0.326613i | \(-0.894093\pi\) |
0.981837 | + | 0.189724i | \(0.0607594\pi\) | |||||||
\(864\) | 4.01468 | − | 6.95363i | 0.136582 | − | 0.236567i | ||||
\(865\) | −20.0857 | − | 7.40313i | −0.682934 | − | 0.251714i | ||||
\(866\) | −34.7309 | + | 20.0519i | −1.18021 | + | 0.681392i | ||||
\(867\) | 19.8369 | + | 19.8369i | 0.673697 | + | 0.673697i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 30.1848i | − | 1.02395i | ||||||
\(870\) | 1.42903 | + | 0.130876i | 0.0484488 | + | 0.00443711i | ||||
\(871\) | −7.29154 | − | 4.20978i | −0.247065 | − | 0.142643i | ||||
\(872\) | 1.39645 | + | 5.21161i | 0.0472897 | + | 0.176487i | ||||
\(873\) | 12.0775 | + | 3.23617i | 0.408763 | + | 0.109528i | ||||
\(874\) | −3.14686 | −0.106444 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −34.4448 | −1.16378 | ||||||||
\(877\) | 11.6076 | + | 3.11025i | 0.391961 | + | 0.105026i | 0.449416 | − | 0.893323i | \(-0.351632\pi\) |
−0.0574555 | + | 0.998348i | \(0.518299\pi\) | |||||||
\(878\) | 13.9895 | + | 52.2096i | 0.472124 | + | 1.76199i | ||||
\(879\) | −2.96100 | − | 1.70953i | −0.0998721 | − | 0.0576612i | ||||
\(880\) | −17.5722 | − | 1.60933i | −0.592360 | − | 0.0542504i | ||||
\(881\) | − | 35.7762i | − | 1.20533i | −0.797994 | − | 0.602665i | \(-0.794106\pi\) | ||
0.797994 | − | 0.602665i | \(-0.205894\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.6278 | + | 24.6278i | 0.828791 | + | 0.828791i | 0.987350 | − | 0.158559i | \(-0.0506848\pi\) |
−0.158559 | + | 0.987350i | \(0.550685\pi\) | |||||||
\(884\) | 24.5194 | − | 14.1563i | 0.824678 | − | 0.476128i | ||||
\(885\) | 16.7603 | + | 6.17749i | 0.563393 | + | 0.207654i | ||||
\(886\) | 23.2710 | − | 40.3065i | 0.781803 | − | 1.35412i | ||||
\(887\) | 0.268110 | − | 1.00060i | 0.00900226 | − | 0.0335969i | −0.961279 | − | 0.275578i | \(-0.911131\pi\) |
0.970281 | + | 0.241981i | \(0.0777973\pi\) | |||||||
\(888\) | 0.666503 | − | 0.666503i | 0.0223664 | − | 0.0223664i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.51943 | + | 32.0633i | 0.185012 | + | 1.07477i | ||||
\(891\) | −1.33594 | − | 2.31391i | −0.0447555 | − | 0.0775188i | ||||
\(892\) | −15.2195 | + | 4.07805i | −0.509587 | + | 0.136543i | ||||
\(893\) | −4.57732 | + | 1.22649i | −0.153174 | + | 0.0410429i | ||||
\(894\) | 15.0347 | + | 26.0409i | 0.502835 | + | 0.870936i | ||||
\(895\) | 2.37628 | + | 1.67831i | 0.0794301 | + | 0.0560998i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.304889 | + | 0.304889i | −0.0101800 | + | 0.0101800i | ||||
\(898\) | 3.82410 | − | 14.2717i | 0.127612 | − | 0.476254i | ||||
\(899\) | 1.10580 | − | 1.91530i | 0.0368806 | − | 0.0638790i | ||||
\(900\) | −11.9506 | − | 2.20747i | −0.398353 | − | 0.0735824i | ||||
\(901\) | 41.0240 | − | 23.6852i | 1.36671 | − | 0.789069i | ||||
\(902\) | −28.0654 | − | 28.0654i | −0.934477 | − | 0.934477i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 8.95913i | − | 0.297976i | ||||||
\(905\) | 1.73043 | − | 18.8946i | 0.0575216 | − | 0.628077i | ||||
\(906\) | 17.8276 | + | 10.2928i | 0.592284 | + | 0.341955i | ||||
\(907\) | −8.37259 | − | 31.2469i | −0.278007 | − | 1.03754i | −0.953799 | − | 0.300445i | \(-0.902865\pi\) |
0.675792 | − | 0.737092i | \(-0.263802\pi\) | |||||||
\(908\) | −47.0183 | − | 12.5985i | −1.56036 | − | 0.418096i | ||||
\(909\) | 7.22962 | 0.239791 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.7867 | 0.821220 | 0.410610 | − | 0.911811i | \(-0.365316\pi\) | ||||
0.410610 | + | 0.911811i | \(0.365316\pi\) | |||||||
\(912\) | −17.1666 | − | 4.59978i | −0.568444 | − | 0.152314i | ||||
\(913\) | 4.78171 | + | 17.8456i | 0.158251 | + | 0.590602i | ||||
\(914\) | 28.9038 | + | 16.6876i | 0.956053 | + | 0.551977i | ||||
\(915\) | −7.91566 | − | 9.51172i | −0.261684 | − | 0.314448i | ||||
\(916\) | 70.3176i | 2.32336i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 9.99031 | + | 9.99031i | 0.329729 | + | 0.329729i | ||||
\(919\) | −12.6351 | + | 7.29488i | −0.416794 | + | 0.240636i | −0.693705 | − | 0.720260i | \(-0.744023\pi\) |
0.276911 | + | 0.960896i | \(0.410689\pi\) | |||||||
\(920\) | 0.457173 | − | 0.210927i | 0.0150726 | − | 0.00695404i | ||||
\(921\) | −5.10036 | + | 8.83408i | −0.168063 | + | 0.291093i | ||||
\(922\) | 16.3351 | − | 60.9634i | 0.537968 | − | 2.00772i | ||||
\(923\) | 18.7860 | − | 18.7860i | 0.618349 | − | 0.618349i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.69511 | + | 2.23598i | 0.154374 | + | 0.0735187i | ||||
\(926\) | −11.4638 | − | 19.8559i | −0.376724 | − | 0.652505i | ||||
\(927\) | −9.48757 | + | 2.54219i | −0.311613 | + | 0.0834963i | ||||
\(928\) | −2.36465 | + | 0.633606i | −0.0776234 | + | 0.0207991i | ||||
\(929\) | 12.5763 | + | 21.7828i | 0.412615 | + | 0.714669i | 0.995175 | − | 0.0981182i | \(-0.0312823\pi\) |
−0.582560 | + | 0.812788i | \(0.697949\pi\) | |||||||
\(930\) | −19.6960 | + | 27.8871i | −0.645859 | + | 0.914453i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −11.6313 | + | 11.6313i | −0.380996 | + | 0.380996i | ||||
\(933\) | −2.65397 | + | 9.90476i | −0.0868871 | + | 0.324267i | ||||
\(934\) | −2.69338 | + | 4.66507i | −0.0881301 | + | 0.152646i | ||||
\(935\) | 13.8686 | − | 37.6275i | 0.453553 | − | 1.23055i | ||||
\(936\) | 1.36206 | − | 0.786383i | 0.0445202 | − | 0.0257037i | ||||
\(937\) | 28.3540 | + | 28.3540i | 0.926286 | + | 0.926286i | 0.997464 | − | 0.0711778i | \(-0.0226758\pi\) |
−0.0711778 | + | 0.997464i | \(0.522676\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 31.2405i | − | 1.01950i | ||||||
\(940\) | 3.28991 | − | 2.73787i | 0.107305 | − | 0.0892993i | ||||
\(941\) | 0.0926410 | + | 0.0534863i | 0.00302001 | + | 0.00174360i | 0.501509 | − | 0.865152i | \(-0.332778\pi\) |
−0.498489 | + | 0.866896i | \(0.666112\pi\) | |||||||
\(942\) | 1.67749 | + | 6.26049i | 0.0546557 | + | 0.203978i | ||||
\(943\) | −1.69369 | − | 0.453822i | −0.0551541 | − | 0.0147785i | ||||
\(944\) | −23.5938 | −0.767914 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.42494 | −0.0788417 | ||||||||
\(947\) | −24.5435 | − | 6.57640i | −0.797556 | − | 0.213704i | −0.163045 | − | 0.986619i | \(-0.552132\pi\) |
−0.634511 | + | 0.772914i | \(0.718798\pi\) | |||||||
\(948\) | 7.10681 | + | 26.5230i | 0.230818 | + | 0.861426i | ||||
\(949\) | 21.2990 | + | 12.2970i | 0.691395 | + | 0.399177i | ||||
\(950\) | 5.00671 | + | 63.1304i | 0.162439 | + | 2.04822i | ||||
\(951\) | 17.3331i | 0.562064i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.8008 | + | 31.8008i | 1.03013 | + | 1.03013i | 0.999532 | + | 0.0305973i | \(0.00974093\pi\) |
0.0305973 | + | 0.999532i | \(0.490259\pi\) | |||||||
\(954\) | 12.8648 | − | 7.42748i | 0.416512 | − | 0.240473i | ||||
\(955\) | −1.81536 | − | 3.93470i | −0.0587437 | − | 0.127324i | ||||
\(956\) | 19.6594 | − | 34.0512i | 0.635832 | − | 1.10129i | ||||
\(957\) | −0.210840 | + | 0.786867i | −0.00681550 | + | 0.0254358i | ||||
\(958\) | 6.09425 | − | 6.09425i | 0.196896 | − | 0.196896i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 24.2267 | − | 4.17041i | 0.781912 | − | 0.134599i | ||||
\(961\) | 10.8087 | + | 18.7213i | 0.348669 | + | 0.603913i | ||||
\(962\) | −3.66983 | + | 0.983327i | −0.118320 | + | 0.0317037i | ||||
\(963\) | −10.2082 | + | 2.73529i | −0.328956 | + | 0.0881434i | ||||
\(964\) | −13.8186 | − | 23.9345i | −0.445067 | − | 0.770878i | ||||
\(965\) | 24.3951 | − | 4.19940i | 0.785305 | − | 0.135183i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.210995 | − | 0.210995i | 0.00678513 | − | 0.00678513i | −0.703706 | − | 0.710491i | \(-0.748473\pi\) |
0.710491 | + | 0.703706i | \(0.248473\pi\) | |||||||
\(968\) | 0.905654 | − | 3.37995i | 0.0291088 | − | 0.108636i | ||||
\(969\) | 20.1946 | − | 34.9781i | 0.648745 | − | 1.12366i | ||||
\(970\) | 24.6543 | + | 53.4371i | 0.791603 | + | 1.71576i | ||||
\(971\) | −46.8662 | + | 27.0582i | −1.50401 | + | 0.868340i | −0.504020 | + | 0.863692i | \(0.668146\pi\) |
−0.999989 | + | 0.00464820i | \(0.998520\pi\) | |||||||
\(972\) | 1.71866 | + | 1.71866i | 0.0551260 | + | 0.0551260i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 30.6752i | 0.982896i | ||||||||
\(975\) | 6.60159 | + | 5.63142i | 0.211420 | + | 0.180350i | ||||
\(976\) | 14.1552 | + | 8.17252i | 0.453098 | + | 0.261596i | ||||
\(977\) | 9.18653 | + | 34.2846i | 0.293903 | + | 1.09686i | 0.942085 | + | 0.335375i | \(0.108863\pi\) |
−0.648181 | + | 0.761486i | \(0.724470\pi\) | |||||||
\(978\) | 39.3222 | + | 10.5364i | 1.25739 | + | 0.336916i | ||||
\(979\) | −18.4693 | −0.590283 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.95352 | 0.190081 | ||||||||
\(982\) | 17.4029 | + | 4.66310i | 0.555350 | + | 0.148806i | ||||
\(983\) | −0.451521 | − | 1.68510i | −0.0144013 | − | 0.0537463i | 0.958351 | − | 0.285592i | \(-0.0921902\pi\) |
−0.972753 | + | 0.231846i | \(0.925524\pi\) | |||||||
\(984\) | 5.53895 | + | 3.19791i | 0.176575 | + | 0.101946i | ||||
\(985\) | −20.6794 | + | 17.2094i | −0.658902 | + | 0.548339i | ||||
\(986\) | − | 4.30761i | − | 0.137182i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.9474 | − | 17.9474i | −0.570982 | − | 0.570982i | ||||
\(989\) | −0.0927759 | + | 0.0535642i | −0.00295010 | + | 0.00170324i | ||||
\(990\) | 4.34909 | − | 11.7996i | 0.138223 | − | 0.375017i | ||||
\(991\) | −24.4818 | + | 42.4038i | −0.777691 | + | 1.34700i | 0.155579 | + | 0.987823i | \(0.450276\pi\) |
−0.933270 | + | 0.359177i | \(0.883058\pi\) | |||||||
\(992\) | 15.0745 | − | 56.2587i | 0.478615 | − | 1.78622i | ||||
\(993\) | 0.893133 | − | 0.893133i | 0.0283427 | − | 0.0283427i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.19838 | − | 5.94437i | 0.133098 | − | 0.188449i | ||||
\(996\) | −8.40323 | − | 14.5548i | −0.266267 | − | 0.461187i | ||||
\(997\) | −16.3710 | + | 4.38661i | −0.518476 | + | 0.138925i | −0.508562 | − | 0.861026i | \(-0.669823\pi\) |
−0.00991437 | + | 0.999951i | \(0.503156\pi\) | |||||||
\(998\) | 48.3007 | − | 12.9421i | 1.52893 | − | 0.409676i | ||||
\(999\) | −0.520035 | − | 0.900728i | −0.0164532 | − | 0.0284978i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 735.2.v.a.178.2 | 32 | ||
5.2 | odd | 4 | inner | 735.2.v.a.472.8 | 32 | ||
7.2 | even | 3 | inner | 735.2.v.a.313.7 | 32 | ||
7.3 | odd | 6 | 105.2.m.a.13.7 | ✓ | 16 | ||
7.4 | even | 3 | 105.2.m.a.13.8 | yes | 16 | ||
7.5 | odd | 6 | inner | 735.2.v.a.313.8 | 32 | ||
7.6 | odd | 2 | inner | 735.2.v.a.178.1 | 32 | ||
21.11 | odd | 6 | 315.2.p.e.118.2 | 16 | |||
21.17 | even | 6 | 315.2.p.e.118.1 | 16 | |||
28.3 | even | 6 | 1680.2.cz.d.433.8 | 16 | |||
28.11 | odd | 6 | 1680.2.cz.d.433.1 | 16 | |||
35.2 | odd | 12 | inner | 735.2.v.a.607.1 | 32 | ||
35.3 | even | 12 | 525.2.m.b.307.1 | 16 | |||
35.4 | even | 6 | 525.2.m.b.118.1 | 16 | |||
35.12 | even | 12 | inner | 735.2.v.a.607.2 | 32 | ||
35.17 | even | 12 | 105.2.m.a.97.8 | yes | 16 | ||
35.18 | odd | 12 | 525.2.m.b.307.2 | 16 | |||
35.24 | odd | 6 | 525.2.m.b.118.2 | 16 | |||
35.27 | even | 4 | inner | 735.2.v.a.472.7 | 32 | ||
35.32 | odd | 12 | 105.2.m.a.97.7 | yes | 16 | ||
105.17 | odd | 12 | 315.2.p.e.307.2 | 16 | |||
105.32 | even | 12 | 315.2.p.e.307.1 | 16 | |||
140.67 | even | 12 | 1680.2.cz.d.97.8 | 16 | |||
140.87 | odd | 12 | 1680.2.cz.d.97.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.m.a.13.7 | ✓ | 16 | 7.3 | odd | 6 | ||
105.2.m.a.13.8 | yes | 16 | 7.4 | even | 3 | ||
105.2.m.a.97.7 | yes | 16 | 35.32 | odd | 12 | ||
105.2.m.a.97.8 | yes | 16 | 35.17 | even | 12 | ||
315.2.p.e.118.1 | 16 | 21.17 | even | 6 | |||
315.2.p.e.118.2 | 16 | 21.11 | odd | 6 | |||
315.2.p.e.307.1 | 16 | 105.32 | even | 12 | |||
315.2.p.e.307.2 | 16 | 105.17 | odd | 12 | |||
525.2.m.b.118.1 | 16 | 35.4 | even | 6 | |||
525.2.m.b.118.2 | 16 | 35.24 | odd | 6 | |||
525.2.m.b.307.1 | 16 | 35.3 | even | 12 | |||
525.2.m.b.307.2 | 16 | 35.18 | odd | 12 | |||
735.2.v.a.178.1 | 32 | 7.6 | odd | 2 | inner | ||
735.2.v.a.178.2 | 32 | 1.1 | even | 1 | trivial | ||
735.2.v.a.313.7 | 32 | 7.2 | even | 3 | inner | ||
735.2.v.a.313.8 | 32 | 7.5 | odd | 6 | inner | ||
735.2.v.a.472.7 | 32 | 35.27 | even | 4 | inner | ||
735.2.v.a.472.8 | 32 | 5.2 | odd | 4 | inner | ||
735.2.v.a.607.1 | 32 | 35.2 | odd | 12 | inner | ||
735.2.v.a.607.2 | 32 | 35.12 | even | 12 | inner | ||
1680.2.cz.d.97.1 | 16 | 140.87 | odd | 12 | |||
1680.2.cz.d.97.8 | 16 | 140.67 | even | 12 | |||
1680.2.cz.d.433.1 | 16 | 28.11 | odd | 6 | |||
1680.2.cz.d.433.8 | 16 | 28.3 | even | 6 |