Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,8,Mod(11,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.11");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.k (of order \(4\), degree \(2\), 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: | \(14.9944812232\) |
Analytic rank: | \(0\) |
Dimension: | \(108\) |
Relative dimension: | \(54\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 11.18 | ||
Character | \(\chi\) | \(=\) | 48.11 |
Dual form | 48.8.k.a.35.18 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.30926 | − | 9.39113i | −0.557665 | − | 0.830066i | ||||
\(3\) | −45.6917 | − | 9.96321i | −0.977042 | − | 0.213047i | ||||
\(4\) | −48.3865 | + | 118.502i | −0.378019 | + | 0.925798i | ||||
\(5\) | −316.866 | + | 316.866i | −1.13365 | + | 1.13365i | −0.144088 | + | 0.989565i | \(0.546025\pi\) |
−0.989565 | + | 0.144088i | \(0.953975\pi\) | |||||||
\(6\) | 194.715 | + | 491.957i | 0.368019 | + | 0.929818i | ||||
\(7\) | −1511.21 | −1.66525 | −0.832627 | − | 0.553834i | \(-0.813164\pi\) | ||||
−0.832627 | + | 0.553834i | \(0.813164\pi\) | |||||||
\(8\) | 1418.15 | − | 293.257i | 0.979281 | − | 0.202504i | ||||
\(9\) | 1988.47 | + | 910.472i | 0.909222 | + | 0.416311i | ||||
\(10\) | 4974.91 | + | 976.537i | 1.57321 | + | 0.308808i | ||||
\(11\) | −997.776 | − | 997.776i | −0.226026 | − | 0.226026i | 0.585004 | − | 0.811030i | \(-0.301093\pi\) |
−0.811030 | + | 0.585004i | \(0.801093\pi\) | |||||||
\(12\) | 3391.52 | − | 4932.48i | 0.566579 | − | 0.824008i | ||||
\(13\) | −8214.45 | + | 8214.45i | −1.03700 | + | 1.03700i | −0.0377070 | + | 0.999289i | \(0.512005\pi\) |
−0.999289 | + | 0.0377070i | \(0.987995\pi\) | |||||||
\(14\) | 9534.59 | + | 14191.9i | 0.928654 | + | 1.38227i | ||||
\(15\) | 17635.1 | − | 11321.1i | 1.34915 | − | 0.866106i | ||||
\(16\) | −11701.5 | − | 11467.8i | −0.714203 | − | 0.699939i | ||||
\(17\) | − | 2084.84i | − | 0.102920i | −0.998675 | − | 0.0514602i | \(-0.983612\pi\) | ||
0.998675 | − | 0.0514602i | \(-0.0163875\pi\) | |||||||
\(18\) | −3995.41 | − | 24418.4i | −0.161476 | − | 0.986877i | ||||
\(19\) | −31568.8 | − | 31568.8i | −1.05590 | − | 1.05590i | −0.998342 | − | 0.0575527i | \(-0.981670\pi\) |
−0.0575527 | − | 0.998342i | \(-0.518330\pi\) | |||||||
\(20\) | −22217.2 | − | 52881.2i | −0.620991 | − | 1.47808i | ||||
\(21\) | 69049.6 | + | 15056.5i | 1.62702 | + | 0.354777i | ||||
\(22\) | −3075.01 | + | 15665.5i | −0.0615698 | + | 0.313664i | ||||
\(23\) | 61890.6i | 1.06066i | 0.847791 | + | 0.530331i | \(0.177932\pi\) | ||||
−0.847791 | + | 0.530331i | \(0.822068\pi\) | |||||||
\(24\) | −67719.6 | − | 729.896i | −0.999942 | − | 0.0107776i | ||||
\(25\) | − | 122683.i | − | 1.57034i | ||||||
\(26\) | 128970. | + | 25315.8i | 1.43907 | + | 0.282479i | ||||
\(27\) | −81785.4 | − | 61412.6i | −0.799655 | − | 0.600460i | ||||
\(28\) | 73121.9 | − | 179081.i | 0.629498 | − | 1.54169i | ||||
\(29\) | −7310.95 | − | 7310.95i | −0.0556648 | − | 0.0556648i | 0.678726 | − | 0.734391i | \(-0.262532\pi\) |
−0.734391 | + | 0.678726i | \(0.762532\pi\) | |||||||
\(30\) | −217583. | − | 94185.7i | −1.47130 | − | 0.636885i | ||||
\(31\) | − | 32731.1i | − | 0.197331i | −0.995121 | − | 0.0986655i | \(-0.968543\pi\) | ||
0.995121 | − | 0.0986655i | \(-0.0314574\pi\) | |||||||
\(32\) | −33867.7 | + | 182244.i | −0.182709 | + | 0.983167i | ||||
\(33\) | 35649.1 | + | 55531.2i | 0.172683 | + | 0.268991i | ||||
\(34\) | −19579.0 | + | 13153.8i | −0.0854308 | + | 0.0573952i | ||||
\(35\) | 478849. | − | 478849.i | 1.88782 | − | 1.88782i | ||||
\(36\) | −204108. | + | 191583.i | −0.729123 | + | 0.684382i | ||||
\(37\) | 122355. | + | 122355.i | 0.397114 | + | 0.397114i | 0.877214 | − | 0.480100i | \(-0.159400\pi\) |
−0.480100 | + | 0.877214i | \(0.659400\pi\) | |||||||
\(38\) | −97290.8 | + | 495643.i | −0.287627 | + | 1.46530i | ||||
\(39\) | 457175. | − | 293490.i | 1.23412 | − | 0.792260i | ||||
\(40\) | −356440. | + | 542286.i | −0.880596 | + | 1.33973i | ||||
\(41\) | −83043.4 | −0.188175 | −0.0940874 | − | 0.995564i | \(-0.529993\pi\) | ||||
−0.0940874 | + | 0.995564i | \(0.529993\pi\) | |||||||
\(42\) | −294255. | − | 743449.i | −0.612846 | − | 1.54838i | ||||
\(43\) | −159561. | + | 159561.i | −0.306047 | + | 0.306047i | −0.843374 | − | 0.537327i | \(-0.819434\pi\) |
0.537327 | + | 0.843374i | \(0.319434\pi\) | |||||||
\(44\) | 166517. | − | 69959.7i | 0.294697 | − | 0.123812i | ||||
\(45\) | −918575. | + | 341580.i | −1.50269 | + | 0.558790i | ||||
\(46\) | 581222. | − | 390484.i | 0.880419 | − | 0.591494i | ||||
\(47\) | 991040. | 1.39235 | 0.696176 | − | 0.717872i | \(-0.254884\pi\) | ||||
0.696176 | + | 0.717872i | \(0.254884\pi\) | |||||||
\(48\) | 420406. | + | 640568.i | 0.548687 | + | 0.836028i | ||||
\(49\) | 1.46020e6 | 1.77307 | ||||||||
\(50\) | −1.15213e6 | + | 774036.i | −1.30348 | + | 0.875722i | ||||
\(51\) | −20771.7 | + | 95260.0i | −0.0219269 | + | 0.100558i | ||||
\(52\) | −575962. | − | 1.37090e6i | −0.568044 | − | 1.35205i | ||||
\(53\) | −1.01135e6 | + | 1.01135e6i | −0.933117 | + | 0.933117i | −0.997899 | − | 0.0647822i | \(-0.979365\pi\) |
0.0647822 | + | 0.997899i | \(0.479365\pi\) | |||||||
\(54\) | −60728.0 | + | 1.15552e6i | −0.0524821 | + | 0.998622i | ||||
\(55\) | 632322. | 0.512470 | ||||||||
\(56\) | −2.14312e6 | + | 443172.i | −1.63075 | + | 0.337221i | ||||
\(57\) | 1.12791e6 | + | 1.75696e6i | 0.806699 | + | 1.25661i | ||||
\(58\) | −22531.3 | + | 114785.i | −0.0151631 | + | 0.0772478i | ||||
\(59\) | 692364. | + | 692364.i | 0.438887 | + | 0.438887i | 0.891637 | − | 0.452751i | \(-0.149557\pi\) |
−0.452751 | + | 0.891637i | \(0.649557\pi\) | |||||||
\(60\) | 488277. | + | 2.63759e6i | 0.291835 | + | 1.57644i | ||||
\(61\) | −528329. | + | 528329.i | −0.298023 | + | 0.298023i | −0.840239 | − | 0.542216i | \(-0.817586\pi\) |
0.542216 | + | 0.840239i | \(0.317586\pi\) | |||||||
\(62\) | −307382. | + | 206509.i | −0.163798 | + | 0.110045i | ||||
\(63\) | −3.00499e6 | − | 1.37591e6i | −1.51409 | − | 0.693264i | ||||
\(64\) | 1.92515e6 | − | 831766.i | 0.917984 | − | 0.396617i | ||||
\(65\) | − | 5.20576e6i | − | 2.35119i | ||||||
\(66\) | 296581. | − | 685146.i | 0.126981 | − | 0.293345i | ||||
\(67\) | 559587. | + | 559587.i | 0.227303 | + | 0.227303i | 0.811565 | − | 0.584262i | \(-0.198616\pi\) |
−0.584262 | + | 0.811565i | \(0.698616\pi\) | |||||||
\(68\) | 247058. | + | 100878.i | 0.0952836 | + | 0.0389059i | ||||
\(69\) | 616628. | − | 2.82789e6i | 0.225970 | − | 1.03631i | ||||
\(70\) | −7.51812e6 | − | 1.47575e6i | −2.61979 | − | 0.514244i | ||||
\(71\) | − | 1.71256e6i | − | 0.567861i | −0.958845 | − | 0.283931i | \(-0.908361\pi\) | ||
0.958845 | − | 0.283931i | \(-0.0916386\pi\) | |||||||
\(72\) | 3.08695e6 | + | 708054.i | 0.974689 | + | 0.223564i | ||||
\(73\) | 1.46382e6i | 0.440410i | 0.975454 | + | 0.220205i | \(0.0706727\pi\) | ||||
−0.975454 | + | 0.220205i | \(0.929327\pi\) | |||||||
\(74\) | 377081. | − | 1.92102e6i | 0.108174 | − | 0.551087i | ||||
\(75\) | −1.22231e6 | + | 5.60558e6i | −0.334555 | + | 1.53429i | ||||
\(76\) | 5.26848e6 | − | 2.21347e6i | 1.37669 | − | 0.578397i | ||||
\(77\) | 1.50785e6 | + | 1.50785e6i | 0.376391 | + | 0.376391i | ||||
\(78\) | −5.64064e6 | − | 2.44168e6i | −1.34585 | − | 0.582583i | ||||
\(79\) | − | 7.53603e6i | − | 1.71968i | −0.510563 | − | 0.859840i | \(-0.670563\pi\) | ||
0.510563 | − | 0.859840i | \(-0.329437\pi\) | |||||||
\(80\) | 7.34155e6 | − | 74052.3i | 1.60315 | − | 0.0161705i | ||||
\(81\) | 3.12505e6 | + | 3.62089e6i | 0.653370 | + | 0.757039i | ||||
\(82\) | 523942. | + | 779871.i | 0.104939 | + | 0.156198i | ||||
\(83\) | −1.84269e6 | + | 1.84269e6i | −0.353736 | + | 0.353736i | −0.861498 | − | 0.507762i | \(-0.830473\pi\) |
0.507762 | + | 0.861498i | \(0.330473\pi\) | |||||||
\(84\) | −5.12529e6 | + | 7.45400e6i | −0.943498 | + | 1.37218i | ||||
\(85\) | 660615. | + | 660615.i | 0.116676 | + | 0.116676i | ||||
\(86\) | 2.50517e6 | + | 491746.i | 0.424711 | + | 0.0833675i | ||||
\(87\) | 261209. | + | 406890.i | 0.0425276 | + | 0.0662460i | ||||
\(88\) | −1.70760e6 | − | 1.12239e6i | −0.267114 | − | 0.175572i | ||||
\(89\) | −5.79970e6 | −0.872049 | −0.436024 | − | 0.899935i | \(-0.643614\pi\) | ||||
−0.436024 | + | 0.899935i | \(0.643614\pi\) | |||||||
\(90\) | 9.00335e6 | + | 6.47133e6i | 1.30183 | + | 0.935718i | ||||
\(91\) | 1.24137e7 | − | 1.24137e7i | 1.72686 | − | 1.72686i | ||||
\(92\) | −7.33416e6 | − | 2.99467e6i | −0.981958 | − | 0.400951i | ||||
\(93\) | −326107. | + | 1.49554e6i | −0.0420407 | + | 0.192801i | ||||
\(94\) | −6.25273e6 | − | 9.30698e6i | −0.776466 | − | 1.15574i | ||||
\(95\) | 2.00061e7 | 2.39404 | ||||||||
\(96\) | 3.36320e6 | − | 7.98959e6i | 0.387975 | − | 0.921670i | ||||
\(97\) | −5.91455e6 | −0.657992 | −0.328996 | − | 0.944331i | \(-0.606710\pi\) | ||||
−0.328996 | + | 0.944331i | \(0.606710\pi\) | |||||||
\(98\) | −9.21278e6 | − | 1.37129e7i | −0.988780 | − | 1.47177i | ||||
\(99\) | −1.07560e6 | − | 2.89249e6i | −0.111411 | − | 0.299605i | ||||
\(100\) | 1.45381e7 | + | 5.93618e6i | 1.45381 | + | 0.593618i | ||||
\(101\) | −5.25028e6 | + | 5.25028e6i | −0.507058 | + | 0.507058i | −0.913622 | − | 0.406564i | \(-0.866727\pi\) |
0.406564 | + | 0.913622i | \(0.366727\pi\) | |||||||
\(102\) | 1.02565e6 | − | 405951.i | 0.0956973 | − | 0.0378767i | ||||
\(103\) | −1.49130e7 | −1.34473 | −0.672365 | − | 0.740219i | \(-0.734722\pi\) | ||||
−0.672365 | + | 0.740219i | \(0.734722\pi\) | |||||||
\(104\) | −9.24039e6 | + | 1.40583e7i | −0.805515 | + | 1.22551i | ||||
\(105\) | −2.66503e7 | + | 1.71086e7i | −2.24667 | + | 1.44229i | ||||
\(106\) | 1.58786e7 | + | 3.11685e6i | 1.29492 | + | 0.254182i | ||||
\(107\) | −2.88012e6 | − | 2.88012e6i | −0.227283 | − | 0.227283i | 0.584273 | − | 0.811557i | \(-0.301380\pi\) |
−0.811557 | + | 0.584273i | \(0.801380\pi\) | |||||||
\(108\) | 1.12348e7 | − | 6.72020e6i | 0.858190 | − | 0.513333i | ||||
\(109\) | −1.11967e7 | + | 1.11967e7i | −0.828129 | + | 0.828129i | −0.987258 | − | 0.159129i | \(-0.949131\pi\) |
0.159129 | + | 0.987258i | \(0.449131\pi\) | |||||||
\(110\) | −3.98948e6 | − | 5.93821e6i | −0.285787 | − | 0.425384i | ||||
\(111\) | −4.37156e6 | − | 6.80965e6i | −0.303393 | − | 0.472601i | ||||
\(112\) | 1.76834e7 | + | 1.73302e7i | 1.18933 | + | 1.16558i | ||||
\(113\) | 6.48206e6i | 0.422609i | 0.977420 | + | 0.211304i | \(0.0677711\pi\) | ||||
−0.977420 | + | 0.211304i | \(0.932229\pi\) | |||||||
\(114\) | 9.38358e6 | − | 2.16774e7i | 0.593200 | − | 1.37038i | ||||
\(115\) | −1.96110e7 | − | 1.96110e7i | −1.20242 | − | 1.20242i | ||||
\(116\) | 1.22011e6 | − | 512612.i | 0.0725767 | − | 0.0304920i | ||||
\(117\) | −2.38132e7 | + | 8.85516e6i | −1.37457 | + | 0.511147i | ||||
\(118\) | 2.13377e6 | − | 1.08704e7i | 0.119553 | − | 0.609057i | ||||
\(119\) | 3.15063e6i | 0.171389i | ||||||||
\(120\) | 2.16893e7 | − | 2.12267e7i | 1.14580 | − | 1.12137i | ||||
\(121\) | − | 1.74961e7i | − | 0.897824i | ||||||
\(122\) | 8.29498e6 | + | 1.62824e6i | 0.413576 | + | 0.0811819i | ||||
\(123\) | 3.79440e6 | + | 827378.i | 0.183855 | + | 0.0400900i | ||||
\(124\) | 3.87871e6 | + | 1.58374e6i | 0.182689 | + | 0.0745949i | ||||
\(125\) | 1.41188e7 | + | 1.41188e7i | 0.646564 | + | 0.646564i | ||||
\(126\) | 6.03789e6 | + | 3.69012e7i | 0.268898 | + | 1.64340i | ||||
\(127\) | 2.82756e7i | 1.22489i | 0.790512 | + | 0.612447i | \(0.209815\pi\) | ||||
−0.790512 | + | 0.612447i | \(0.790185\pi\) | |||||||
\(128\) | −1.99575e7 | − | 1.28315e7i | −0.841146 | − | 0.540808i | ||||
\(129\) | 8.88038e6 | − | 5.70089e6i | 0.364223 | − | 0.233818i | ||||
\(130\) | −4.88879e7 | + | 3.28445e7i | −1.95164 | + | 1.31117i | ||||
\(131\) | −1.00935e7 | + | 1.00935e7i | −0.392278 | + | 0.392278i | −0.875499 | − | 0.483221i | \(-0.839467\pi\) |
0.483221 | + | 0.875499i | \(0.339467\pi\) | |||||||
\(132\) | −8.30549e6 | + | 1.53753e6i | −0.314309 | + | 0.0581856i | ||||
\(133\) | 4.77070e7 | + | 4.77070e7i | 1.75833 | + | 1.75833i | ||||
\(134\) | 1.72457e6 | − | 8.78574e6i | 0.0619177 | − | 0.315436i | ||||
\(135\) | 4.53745e7 | − | 6.45544e6i | 1.58724 | − | 0.225817i | ||||
\(136\) | −611395. | − | 2.95662e6i | −0.0208418 | − | 0.100788i | ||||
\(137\) | 2.74239e7 | 0.911188 | 0.455594 | − | 0.890188i | \(-0.349427\pi\) | ||||
0.455594 | + | 0.890188i | \(0.349427\pi\) | |||||||
\(138\) | −3.04475e7 | + | 1.20510e7i | −0.986223 | + | 0.390344i | ||||
\(139\) | −3.07201e6 | + | 3.07201e6i | −0.0970223 | + | 0.0970223i | −0.753952 | − | 0.656930i | \(-0.771855\pi\) |
0.656930 | + | 0.753952i | \(0.271855\pi\) | |||||||
\(140\) | 3.35748e7 | + | 7.99144e7i | 1.03411 | + | 2.46137i | ||||
\(141\) | −4.52823e7 | − | 9.87394e6i | −1.36039 | − | 0.296636i | ||||
\(142\) | −1.60829e7 | + | 1.08050e7i | −0.471362 | + | 0.316676i | ||||
\(143\) | 1.63924e7 | 0.468776 | ||||||||
\(144\) | −1.28270e7 | − | 3.34573e7i | −0.357977 | − | 0.933730i | ||||
\(145\) | 4.63317e6 | 0.126209 | ||||||||
\(146\) | 1.37469e7 | − | 9.23561e6i | 0.365569 | − | 0.245601i | ||||
\(147\) | −6.67191e7 | − | 1.45483e7i | −1.73236 | − | 0.377747i | ||||
\(148\) | −2.04196e7 | + | 8.57899e6i | −0.517764 | + | 0.217530i | ||||
\(149\) | 2.20595e7 | − | 2.20595e7i | 0.546315 | − | 0.546315i | −0.379058 | − | 0.925373i | \(-0.623752\pi\) |
0.925373 | + | 0.379058i | \(0.123752\pi\) | |||||||
\(150\) | 6.03546e7 | − | 2.38882e7i | 1.46013 | − | 0.577915i | ||||
\(151\) | 2.26818e7 | 0.536115 | 0.268058 | − | 0.963403i | \(-0.413618\pi\) | ||||
0.268058 | + | 0.963403i | \(0.413618\pi\) | |||||||
\(152\) | −5.40271e7 | − | 3.55116e7i | −1.24784 | − | 0.820195i | ||||
\(153\) | 1.89819e6 | − | 4.14564e6i | 0.0428469 | − | 0.0935776i | ||||
\(154\) | 4.64698e6 | − | 2.36738e7i | 0.102529 | − | 0.522330i | ||||
\(155\) | 1.03714e7 | + | 1.03714e7i | 0.223705 | + | 0.223705i | ||||
\(156\) | 1.26581e7 | + | 6.83772e7i | 0.266953 | + | 1.44203i | ||||
\(157\) | −2.39977e6 | + | 2.39977e6i | −0.0494903 | + | 0.0494903i | −0.731419 | − | 0.681929i | \(-0.761142\pi\) |
0.681929 | + | 0.731419i | \(0.261142\pi\) | |||||||
\(158\) | −7.07718e7 | + | 4.75468e7i | −1.42745 | + | 0.959006i | ||||
\(159\) | 5.62867e7 | − | 3.61341e7i | 1.11049 | − | 0.712897i | ||||
\(160\) | −4.70152e7 | − | 6.84782e7i | −0.907441 | − | 1.32170i | ||||
\(161\) | − | 9.35294e7i | − | 1.76627i | ||||||
\(162\) | 1.42875e7 | − | 5.21929e7i | 0.264030 | − | 0.964514i | ||||
\(163\) | 1.43447e6 | + | 1.43447e6i | 0.0259439 | + | 0.0259439i | 0.719960 | − | 0.694016i | \(-0.244160\pi\) |
−0.694016 | + | 0.719960i | \(0.744160\pi\) | |||||||
\(164\) | 4.01818e6 | − | 9.84082e6i | 0.0711337 | − | 0.174212i | ||||
\(165\) | −2.88919e7 | − | 6.29995e6i | −0.500705 | − | 0.109180i | ||||
\(166\) | 2.89310e7 | + | 5.67892e6i | 0.490890 | + | 0.0963580i | ||||
\(167\) | − | 6.17509e7i | − | 1.02597i | −0.858397 | − | 0.512986i | \(-0.828539\pi\) | ||
0.858397 | − | 0.512986i | \(-0.171461\pi\) | |||||||
\(168\) | 1.02338e8 | + | 1.10302e6i | 1.66516 | + | 0.0179474i | ||||
\(169\) | − | 7.22060e7i | − | 1.15072i | ||||||
\(170\) | 2.03593e6 | − | 1.03719e7i | 0.0317827 | − | 0.161915i | ||||
\(171\) | −3.40311e7 | − | 9.15162e7i | −0.520463 | − | 1.39962i | ||||
\(172\) | −1.11877e7 | − | 2.66290e7i | −0.167646 | − | 0.399029i | ||||
\(173\) | 7.54742e7 | + | 7.54742e7i | 1.10825 | + | 1.10825i | 0.993381 | + | 0.114868i | \(0.0366446\pi\) |
0.114868 | + | 0.993381i | \(0.463355\pi\) | |||||||
\(174\) | 2.17312e6 | − | 5.02023e6i | 0.0312724 | − | 0.0722438i | ||||
\(175\) | 1.85399e8i | 2.61501i | ||||||||
\(176\) | 233183. | + | 2.31178e7i | 0.00322405 | + | 0.319633i | ||||
\(177\) | −2.47371e7 | − | 3.85335e7i | −0.335307 | − | 0.522314i | ||||
\(178\) | 3.65918e7 | + | 5.44657e7i | 0.486311 | + | 0.723858i | ||||
\(179\) | 2.70955e7 | − | 2.70955e7i | 0.353111 | − | 0.353111i | −0.508155 | − | 0.861266i | \(-0.669672\pi\) |
0.861266 | + | 0.508155i | \(0.169672\pi\) | |||||||
\(180\) | 3.96863e6 | − | 1.25381e8i | 0.0507208 | − | 1.60242i | ||||
\(181\) | −6.87870e7 | − | 6.87870e7i | −0.862247 | − | 0.862247i | 0.129352 | − | 0.991599i | \(-0.458710\pi\) |
−0.991599 | + | 0.129352i | \(0.958710\pi\) | |||||||
\(182\) | −1.94900e8 | − | 3.82574e7i | −2.39642 | − | 0.470399i | ||||
\(183\) | 2.94041e7 | − | 1.88764e7i | 0.354674 | − | 0.227689i | ||||
\(184\) | 1.81499e7 | + | 8.77702e7i | 0.214788 | + | 1.03869i | ||||
\(185\) | −7.75401e7 | −0.900379 | ||||||||
\(186\) | 1.61023e7 | − | 6.37325e6i | 0.183482 | − | 0.0726216i | ||||
\(187\) | −2.08021e6 | + | 2.08021e6i | −0.0232627 | + | 0.0232627i | ||||
\(188\) | −4.79529e7 | + | 1.17440e8i | −0.526336 | + | 1.28904i | ||||
\(189\) | 1.23595e8 | + | 9.28070e7i | 1.33163 | + | 0.999919i | ||||
\(190\) | −1.26224e8 | − | 1.87880e8i | −1.33507 | − | 1.98721i | ||||
\(191\) | 1.02497e8 | 1.06437 | 0.532187 | − | 0.846627i | \(-0.321370\pi\) | ||||
0.532187 | + | 0.846627i | \(0.321370\pi\) | |||||||
\(192\) | −9.62506e7 | + | 1.88242e7i | −0.981407 | + | 0.191938i | ||||
\(193\) | 1.01174e8 | 1.01302 | 0.506510 | − | 0.862234i | \(-0.330935\pi\) | ||||
0.506510 | + | 0.862234i | \(0.330935\pi\) | |||||||
\(194\) | 3.73164e7 | + | 5.55443e7i | 0.366939 | + | 0.546177i | ||||
\(195\) | −5.18660e7 | + | 2.37860e8i | −0.500912 | + | 2.29721i | ||||
\(196\) | −7.06539e7 | + | 1.73037e8i | −0.670255 | + | 1.64150i | ||||
\(197\) | 1.45920e8 | − | 1.45920e8i | 1.35982 | − | 1.35982i | 0.485690 | − | 0.874131i | \(-0.338568\pi\) |
0.874131 | − | 0.485690i | \(-0.161432\pi\) | |||||||
\(198\) | −2.03775e7 | + | 2.83506e7i | −0.186562 | + | 0.259558i | ||||
\(199\) | −1.37812e8 | −1.23965 | −0.619827 | − | 0.784739i | \(-0.712797\pi\) | ||||
−0.619827 | + | 0.784739i | \(0.712797\pi\) | |||||||
\(200\) | −3.59776e7 | − | 1.73982e8i | −0.318000 | − | 1.53780i | ||||
\(201\) | −1.99932e7 | − | 3.11438e7i | −0.173659 | − | 0.270511i | ||||
\(202\) | 8.24315e7 | + | 1.61807e7i | 0.703661 | + | 0.138123i | ||||
\(203\) | 1.10483e7 | + | 1.10483e7i | 0.0926960 | + | 0.0926960i | ||||
\(204\) | −1.02834e7 | − | 7.07079e6i | −0.0848073 | − | 0.0583126i | ||||
\(205\) | 2.63136e7 | − | 2.63136e7i | 0.213325 | − | 0.213325i | ||||
\(206\) | 9.40901e7 | + | 1.40050e8i | 0.749909 | + | 1.11622i | ||||
\(207\) | −5.63496e7 | + | 1.23067e8i | −0.441565 | + | 0.964377i | ||||
\(208\) | 1.90323e8 | − | 1.91974e6i | 1.46646 | − | 0.0147918i | ||||
\(209\) | 6.29972e7i | 0.477320i | ||||||||
\(210\) | 3.28813e8 | + | 1.42334e8i | 2.45008 | + | 1.06057i | ||||
\(211\) | 2.56400e7 | + | 2.56400e7i | 0.187901 | + | 0.187901i | 0.794788 | − | 0.606887i | \(-0.207582\pi\) |
−0.606887 | + | 0.794788i | \(0.707582\pi\) | |||||||
\(212\) | −7.09115e7 | − | 1.68783e8i | −0.511141 | − | 1.21661i | ||||
\(213\) | −1.70626e7 | + | 7.82500e7i | −0.120981 | + | 0.554824i | ||||
\(214\) | −8.87615e6 | + | 4.52190e7i | −0.0619122 | + | 0.315408i | ||||
\(215\) | − | 1.01119e8i | − | 0.693902i | ||||||
\(216\) | −1.33994e8 | − | 6.31082e7i | −0.904683 | − | 0.426086i | ||||
\(217\) | 4.94635e7i | 0.328606i | ||||||||
\(218\) | 1.75793e8 | + | 3.45068e7i | 1.14922 | + | 0.225583i | ||||
\(219\) | 1.45843e7 | − | 6.68844e7i | 0.0938279 | − | 0.430299i | ||||
\(220\) | −3.05958e7 | + | 7.49315e7i | −0.193724 | + | 0.474444i | ||||
\(221\) | 1.71258e7 | + | 1.71258e7i | 0.106728 | + | 0.106728i | ||||
\(222\) | −3.63690e7 | + | 8.40177e7i | −0.223098 | + | 0.515389i | ||||
\(223\) | − | 1.72177e8i | − | 1.03970i | −0.854258 | − | 0.519849i | \(-0.825988\pi\) | ||
0.854258 | − | 0.519849i | \(-0.174012\pi\) | |||||||
\(224\) | 5.11811e7 | − | 2.75408e8i | 0.304258 | − | 1.63722i | ||||
\(225\) | 1.11699e8 | − | 2.43951e8i | 0.653749 | − | 1.42779i | ||||
\(226\) | 6.08738e7 | − | 4.08970e7i | 0.350793 | − | 0.235674i | ||||
\(227\) | −1.90552e8 | + | 1.90552e8i | −1.08125 | + | 1.08125i | −0.0848515 | + | 0.996394i | \(0.527042\pi\) |
−0.996394 | + | 0.0848515i | \(0.972958\pi\) | |||||||
\(228\) | −2.62779e8 | + | 4.86463e7i | −1.46831 | + | 0.271818i | ||||
\(229\) | −1.55895e8 | − | 1.55895e8i | −0.857844 | − | 0.857844i | 0.133240 | − | 0.991084i | \(-0.457462\pi\) |
−0.991084 | + | 0.133240i | \(0.957462\pi\) | |||||||
\(230\) | −6.04384e7 | + | 3.07900e8i | −0.327541 | + | 1.66864i | ||||
\(231\) | −5.38731e7 | − | 8.39190e7i | −0.287561 | − | 0.447939i | ||||
\(232\) | −1.25120e7 | − | 8.22404e6i | −0.0657838 | − | 0.0432391i | ||||
\(233\) | −1.29313e8 | −0.669725 | −0.334862 | − | 0.942267i | \(-0.608690\pi\) | ||||
−0.334862 | + | 0.942267i | \(0.608690\pi\) | |||||||
\(234\) | 2.33404e8 | + | 1.67763e8i | 1.19084 | + | 0.855937i | ||||
\(235\) | −3.14027e8 | + | 3.14027e8i | −1.57844 | + | 1.57844i | ||||
\(236\) | −1.15548e8 | + | 4.85455e7i | −0.572228 | + | 0.240413i | ||||
\(237\) | −7.50830e7 | + | 3.44334e8i | −0.366372 | + | 1.68020i | ||||
\(238\) | 2.95879e7 | − | 1.98781e7i | 0.142264 | − | 0.0955775i | ||||
\(239\) | −5.31235e7 | −0.251706 | −0.125853 | − | 0.992049i | \(-0.540167\pi\) | ||||
−0.125853 | + | 0.992049i | \(0.540167\pi\) | |||||||
\(240\) | −3.36186e8 | − | 6.97618e7i | −1.56979 | − | 0.325746i | ||||
\(241\) | 3.47041e8 | 1.59706 | 0.798529 | − | 0.601956i | \(-0.205612\pi\) | ||||
0.798529 | + | 0.601956i | \(0.205612\pi\) | |||||||
\(242\) | −1.64308e8 | + | 1.10387e8i | −0.745253 | + | 0.500685i | ||||
\(243\) | −1.06713e8 | − | 1.96580e8i | −0.477086 | − | 0.878857i | ||||
\(244\) | −3.70442e7 | − | 8.81722e7i | −0.163251 | − | 0.388568i | ||||
\(245\) | −4.62687e8 | + | 4.62687e8i | −2.01005 | + | 2.01005i | ||||
\(246\) | −1.61698e7 | − | 4.08538e7i | −0.0692520 | − | 0.174968i | ||||
\(247\) | 5.18641e8 | 2.18992 | ||||||||
\(248\) | −9.59864e6 | − | 4.64177e7i | −0.0399603 | − | 0.193243i | ||||
\(249\) | 1.02555e8 | − | 6.58366e7i | 0.420977 | − | 0.270253i | ||||
\(250\) | 4.35121e7 | − | 2.21670e8i | 0.176125 | − | 0.897258i | ||||
\(251\) | −1.85712e7 | − | 1.85712e7i | −0.0741281 | − | 0.0741281i | 0.669071 | − | 0.743199i | \(-0.266692\pi\) |
−0.743199 | + | 0.669071i | \(0.766692\pi\) | |||||||
\(252\) | 3.08449e8 | − | 2.89522e8i | 1.21418 | − | 1.13967i | ||||
\(253\) | 6.17529e7 | − | 6.17529e7i | 0.239737 | − | 0.239737i | ||||
\(254\) | 2.65539e8 | − | 1.78398e8i | 1.01674 | − | 0.683080i | ||||
\(255\) | −2.36028e7 | − | 3.67665e7i | −0.0891400 | − | 0.138855i | ||||
\(256\) | 5.41472e6 | + | 2.68381e8i | 0.0201714 | + | 0.999797i | ||||
\(257\) | − | 2.88995e8i | − | 1.06200i | −0.847372 | − | 0.531000i | \(-0.821816\pi\) | ||
0.847372 | − | 0.531000i | \(-0.178184\pi\) | |||||||
\(258\) | −1.09566e8 | − | 4.74283e7i | −0.397199 | − | 0.171937i | ||||
\(259\) | −1.84903e8 | − | 1.84903e8i | −0.661296 | − | 0.661296i | ||||
\(260\) | 6.16893e8 | + | 2.51888e8i | 2.17672 | + | 0.888794i | ||||
\(261\) | −7.88118e6 | − | 2.11940e7i | −0.0274378 | − | 0.0737855i | ||||
\(262\) | 1.58473e8 | + | 3.11069e7i | 0.544377 | + | 0.106857i | ||||
\(263\) | 1.59344e8i | 0.540120i | 0.962844 | + | 0.270060i | \(0.0870435\pi\) | ||||
−0.962844 | + | 0.270060i | \(0.912956\pi\) | |||||||
\(264\) | 6.68407e7 | + | 6.82972e7i | 0.223577 | + | 0.228449i | ||||
\(265\) | − | 6.40924e8i | − | 2.11566i | ||||||
\(266\) | 1.47026e8 | − | 7.49018e8i | 0.478972 | − | 2.44009i | ||||
\(267\) | 2.64998e8 | + | 5.77836e7i | 0.852028 | + | 0.185787i | ||||
\(268\) | −9.33887e7 | + | 3.92358e7i | −0.296362 | + | 0.124512i | ||||
\(269\) | 4.06306e8 | + | 4.06306e8i | 1.27268 | + | 1.27268i | 0.944675 | + | 0.328007i | \(0.106377\pi\) |
0.328007 | + | 0.944675i | \(0.393623\pi\) | |||||||
\(270\) | −3.46903e8 | − | 3.85389e8i | −1.07259 | − | 1.19159i | ||||
\(271\) | 3.35239e8i | 1.02320i | 0.859223 | + | 0.511601i | \(0.170947\pi\) | ||||
−0.859223 | + | 0.511601i | \(0.829053\pi\) | |||||||
\(272\) | −2.39085e7 | + | 2.43958e7i | −0.0720380 | + | 0.0735061i | ||||
\(273\) | −6.90885e8 | + | 4.43524e8i | −2.05512 | + | 1.31931i | ||||
\(274\) | −1.73025e8 | − | 2.57542e8i | −0.508138 | − | 0.756346i | ||||
\(275\) | −1.22410e8 | + | 1.22410e8i | −0.354937 | + | 0.354937i | ||||
\(276\) | 3.05274e8 | + | 2.09903e8i | 0.873993 | + | 0.600949i | ||||
\(277\) | −3.11994e8 | − | 3.11994e8i | −0.881997 | − | 0.881997i | 0.111740 | − | 0.993737i | \(-0.464358\pi\) |
−0.993737 | + | 0.111740i | \(0.964358\pi\) | |||||||
\(278\) | 4.82318e7 | + | 9.46753e6i | 0.134641 | + | 0.0264290i | ||||
\(279\) | 2.98008e7 | − | 6.50849e7i | 0.0821510 | − | 0.179418i | ||||
\(280\) | 5.38654e8 | − | 8.19506e8i | 1.46642 | − | 2.23100i | ||||
\(281\) | 2.68024e8 | 0.720611 | 0.360306 | − | 0.932834i | \(-0.382672\pi\) | ||||
0.360306 | + | 0.932834i | \(0.382672\pi\) | |||||||
\(282\) | 1.92971e8 | + | 4.87549e8i | 0.512412 | + | 1.29463i | ||||
\(283\) | −2.85261e8 | + | 2.85261e8i | −0.748153 | + | 0.748153i | −0.974132 | − | 0.225979i | \(-0.927442\pi\) |
0.225979 | + | 0.974132i | \(0.427442\pi\) | |||||||
\(284\) | 2.02942e8 | + | 8.28649e7i | 0.525725 | + | 0.214663i | ||||
\(285\) | −9.14116e8 | − | 1.99325e8i | −2.33907 | − | 0.510042i | ||||
\(286\) | −1.03424e8 | − | 1.53943e8i | −0.261420 | − | 0.389115i | ||||
\(287\) | 1.25496e8 | 0.313359 | ||||||||
\(288\) | −2.33273e8 | + | 3.31550e8i | −0.575427 | + | 0.817853i | ||||
\(289\) | 4.05992e8 | 0.989407 | ||||||||
\(290\) | −2.92319e7 | − | 4.35107e7i | −0.0703824 | − | 0.104762i | ||||
\(291\) | 2.70246e8 | + | 5.89279e7i | 0.642886 | + | 0.140183i | ||||
\(292\) | −1.73466e8 | − | 7.08290e7i | −0.407731 | − | 0.166484i | ||||
\(293\) | 4.12499e8 | − | 4.12499e8i | 0.958045 | − | 0.958045i | −0.0411100 | − | 0.999155i | \(-0.513089\pi\) |
0.999155 | + | 0.0411100i | \(0.0130894\pi\) | |||||||
\(294\) | 2.84323e8 | + | 7.18356e8i | 0.652524 | + | 1.64863i | ||||
\(295\) | −4.38773e8 | −0.995090 | ||||||||
\(296\) | 2.09399e8 | + | 1.37636e8i | 0.469304 | + | 0.308469i | ||||
\(297\) | 2.03275e7 | + | 1.42880e8i | 0.0450232 | + | 0.316463i | ||||
\(298\) | −3.46342e8 | − | 6.79843e7i | −0.758138 | − | 0.148817i | ||||
\(299\) | −5.08397e8 | − | 5.08397e8i | −1.09990 | − | 1.09990i | ||||
\(300\) | −6.05130e8 | − | 4.16081e8i | −1.29397 | − | 0.889720i | ||||
\(301\) | 2.41130e8 | − | 2.41130e8i | 0.509646 | − | 0.509646i | ||||
\(302\) | −1.43105e8 | − | 2.13008e8i | −0.298973 | − | 0.445011i | ||||
\(303\) | 2.92204e8 | − | 1.87585e8i | 0.603444 | − | 0.387390i | ||||
\(304\) | 7.37772e6 | + | 7.31427e8i | 0.0150614 | + | 1.49319i | ||||
\(305\) | − | 3.34819e8i | − | 0.675710i | ||||||
\(306\) | −5.09084e7 | + | 8.32980e6i | −0.101570 | + | 0.0166192i | ||||
\(307\) | −2.25856e8 | − | 2.25856e8i | −0.445499 | − | 0.445499i | 0.448356 | − | 0.893855i | \(-0.352010\pi\) |
−0.893855 | + | 0.448356i | \(0.852010\pi\) | |||||||
\(308\) | −2.51642e8 | + | 1.05724e8i | −0.490745 | + | 0.206179i | ||||
\(309\) | 6.81402e8 | + | 1.48581e8i | 1.31386 | + | 0.286490i | ||||
\(310\) | 3.19632e7 | − | 1.62835e8i | 0.0609374 | − | 0.310442i | ||||
\(311\) | 5.16381e8i | 0.973439i | 0.873558 | + | 0.486719i | \(0.161807\pi\) | ||||
−0.873558 | + | 0.486719i | \(0.838193\pi\) | |||||||
\(312\) | 5.62275e8 | − | 5.50284e8i | 1.04811 | − | 1.02576i | ||||
\(313\) | 4.53248e8i | 0.835470i | 0.908569 | + | 0.417735i | \(0.137176\pi\) | ||||
−0.908569 | + | 0.417735i | \(0.862824\pi\) | |||||||
\(314\) | 3.76773e7 | + | 7.39576e6i | 0.0686793 | + | 0.0134812i | ||||
\(315\) | 1.38816e9 | − | 5.16198e8i | 2.50237 | − | 0.930528i | ||||
\(316\) | 8.93036e8 | + | 3.64642e8i | 1.59208 | + | 0.650073i | ||||
\(317\) | −2.20515e8 | − | 2.20515e8i | −0.388803 | − | 0.388803i | 0.485457 | − | 0.874260i | \(-0.338653\pi\) |
−0.874260 | + | 0.485457i | \(0.838653\pi\) | |||||||
\(318\) | −6.94467e8 | − | 3.00616e8i | −1.21103 | − | 0.524224i | ||||
\(319\) | 1.45894e7i | 0.0251634i | ||||||||
\(320\) | −3.46456e8 | + | 8.73573e8i | −0.591049 | + | 1.49030i | ||||
\(321\) | 1.02903e8 | + | 1.60293e8i | 0.173644 | + | 0.270487i | ||||
\(322\) | −8.78346e8 | + | 5.90101e8i | −1.46612 | + | 0.984988i | ||||
\(323\) | −6.58160e7 | + | 6.58160e7i | −0.108673 | + | 0.108673i | ||||
\(324\) | −5.80293e8 | + | 1.95123e8i | −0.947851 | + | 0.318714i | ||||
\(325\) | 1.00777e9 | + | 1.00777e9i | 1.62843 | + | 1.62843i | ||||
\(326\) | 4.42084e6 | − | 2.25217e7i | 0.00706714 | − | 0.0360031i | ||||
\(327\) | 6.23152e8 | − | 4.00042e8i | 0.985546 | − | 0.632686i | ||||
\(328\) | −1.17768e8 | + | 2.43531e7i | −0.184276 | + | 0.0381062i | ||||
\(329\) | −1.49767e9 | −2.31862 | ||||||||
\(330\) | 1.23123e8 | + | 3.11075e8i | 0.188599 | + | 0.476504i | ||||
\(331\) | 5.33443e8 | − | 5.33443e8i | 0.808519 | − | 0.808519i | −0.175890 | − | 0.984410i | \(-0.556280\pi\) |
0.984410 | + | 0.175890i | \(0.0562804\pi\) | |||||||
\(332\) | −1.29201e8 | − | 3.07524e8i | −0.193769 | − | 0.461207i | ||||
\(333\) | 1.31898e8 | + | 3.54700e8i | 0.195742 | + | 0.526388i | ||||
\(334\) | −5.79911e8 | + | 3.89603e8i | −0.851625 | + | 0.572149i | ||||
\(335\) | −3.54628e8 | −0.515366 | ||||||||
\(336\) | −6.35320e8 | − | 9.68030e8i | −0.913703 | − | 1.39220i | ||||
\(337\) | −6.08348e8 | −0.865860 | −0.432930 | − | 0.901428i | \(-0.642520\pi\) | ||||
−0.432930 | + | 0.901428i | \(0.642520\pi\) | |||||||
\(338\) | −6.78096e8 | + | 4.55567e8i | −0.955174 | + | 0.641717i | ||||
\(339\) | 6.45821e7 | − | 2.96177e8i | 0.0900354 | − | 0.412907i | ||||
\(340\) | −1.10249e8 | + | 4.63194e7i | −0.152124 | + | 0.0639127i | ||||
\(341\) | −3.26584e7 | + | 3.26584e7i | −0.0446020 | + | 0.0446020i | ||||
\(342\) | −6.44729e8 | + | 8.96990e8i | −0.871537 | + | 1.21254i | ||||
\(343\) | −9.62120e8 | −1.28736 | ||||||||
\(344\) | −1.79490e8 | + | 2.73075e8i | −0.237730 | + | 0.361682i | ||||
\(345\) | 7.00672e8 | + | 1.09145e9i | 0.918645 | + | 1.43099i | ||||
\(346\) | 2.32601e8 | − | 1.18497e9i | 0.301888 | − | 1.53795i | ||||
\(347\) | −5.33079e8 | − | 5.33079e8i | −0.684917 | − | 0.684917i | 0.276187 | − | 0.961104i | \(-0.410929\pi\) |
−0.961104 | + | 0.276187i | \(0.910929\pi\) | |||||||
\(348\) | −6.08563e7 | + | 1.12659e7i | −0.0774067 | + | 0.0143297i | ||||
\(349\) | 5.92520e8 | − | 5.92520e8i | 0.746130 | − | 0.746130i | −0.227620 | − | 0.973750i | \(-0.573095\pi\) |
0.973750 | + | 0.227620i | \(0.0730945\pi\) | |||||||
\(350\) | 1.74110e9 | − | 1.16973e9i | 2.17063 | − | 1.45830i | ||||
\(351\) | 1.17629e9 | − | 1.67351e8i | 1.45191 | − | 0.206564i | ||||
\(352\) | 2.15631e8 | − | 1.48046e8i | 0.263519 | − | 0.180924i | ||||
\(353\) | 3.01802e8i | 0.365183i | 0.983189 | + | 0.182591i | \(0.0584485\pi\) | ||||
−0.983189 | + | 0.182591i | \(0.941551\pi\) | |||||||
\(354\) | −2.05800e8 | + | 4.75427e8i | −0.246566 | + | 0.569604i | ||||
\(355\) | 5.42652e8 | + | 5.42652e8i | 0.643758 | + | 0.643758i | ||||
\(356\) | 2.80627e8 | − | 6.87277e8i | 0.329651 | − | 0.807341i | ||||
\(357\) | 3.13903e7 | − | 1.43958e8i | 0.0365138 | − | 0.167454i | ||||
\(358\) | −4.25410e8 | − | 8.35046e7i | −0.490023 | − | 0.0961878i | ||||
\(359\) | − | 6.80496e6i | − | 0.00776238i | −0.999992 | − | 0.00388119i | \(-0.998765\pi\) | ||
0.999992 | − | 0.00388119i | \(-0.00123542\pi\) | |||||||
\(360\) | −1.20251e9 | + | 7.53791e8i | −1.35840 | + | 0.851515i | ||||
\(361\) | 1.09931e9i | 1.22983i | ||||||||
\(362\) | −2.11992e8 | + | 1.07998e9i | −0.234877 | + | 1.19657i | ||||
\(363\) | −1.74317e8 | + | 7.99425e8i | −0.191278 | + | 0.877212i | ||||
\(364\) | 8.70397e8 | + | 2.07171e9i | 0.945937 | + | 2.25151i | ||||
\(365\) | −4.63834e8 | − | 4.63834e8i | −0.499272 | − | 0.499272i | ||||
\(366\) | −3.62789e8 | − | 1.57042e8i | −0.386786 | − | 0.167429i | ||||
\(367\) | 2.37968e8i | 0.251297i | 0.992075 | + | 0.125649i | \(0.0401012\pi\) | ||||
−0.992075 | + | 0.125649i | \(0.959899\pi\) | |||||||
\(368\) | 7.09748e8 | − | 7.24212e8i | 0.742398 | − | 0.757528i | ||||
\(369\) | −1.65129e8 | − | 7.56087e7i | −0.171093 | − | 0.0783393i | ||||
\(370\) | 4.89221e8 | + | 7.28189e8i | 0.502110 | + | 0.747374i | ||||
\(371\) | 1.52836e9 | − | 1.52836e9i | 1.55388 | − | 1.55388i | ||||
\(372\) | −1.61446e8 | − | 1.11008e8i | −0.162602 | − | 0.111804i | ||||
\(373\) | −5.45034e7 | − | 5.45034e7i | −0.0543804 | − | 0.0543804i | 0.679394 | − | 0.733774i | \(-0.262243\pi\) |
−0.733774 | + | 0.679394i | \(0.762243\pi\) | |||||||
\(374\) | 3.26600e7 | + | 6.41091e6i | 0.0322824 | + | 0.00633679i | ||||
\(375\) | −5.04443e8 | − | 7.85779e8i | −0.493972 | − | 0.769469i | ||||
\(376\) | 1.40544e9 | − | 2.90630e8i | 1.36350 | − | 0.281957i | ||||
\(377\) | 1.20111e8 | 0.115448 | ||||||||
\(378\) | 9.17725e7 | − | 1.74624e9i | 0.0873959 | − | 1.66296i | ||||
\(379\) | −2.63889e8 | + | 2.63889e8i | −0.248991 | + | 0.248991i | −0.820556 | − | 0.571565i | \(-0.806336\pi\) |
0.571565 | + | 0.820556i | \(0.306336\pi\) | |||||||
\(380\) | −9.68027e8 | + | 2.37077e9i | −0.904992 | + | 2.21639i | ||||
\(381\) | 2.81715e8 | − | 1.29196e9i | 0.260959 | − | 1.19677i | ||||
\(382\) | −6.46681e8 | − | 9.62563e8i | −0.593565 | − | 0.883501i | ||||
\(383\) | 9.41312e7 | 0.0856126 | 0.0428063 | − | 0.999083i | \(-0.486370\pi\) | ||||
0.0428063 | + | 0.999083i | \(0.486370\pi\) | |||||||
\(384\) | 7.84050e8 | + | 7.85135e8i | 0.706618 | + | 0.707596i | ||||
\(385\) | −9.55569e8 | −0.853393 | ||||||||
\(386\) | −6.38333e8 | − | 9.50137e8i | −0.564926 | − | 0.840874i | ||||
\(387\) | −4.62559e8 | + | 1.72007e8i | −0.405675 | + | 0.150854i | ||||
\(388\) | 2.86184e8 | − | 7.00887e8i | 0.248734 | − | 0.609168i | ||||
\(389\) | −7.16086e8 | + | 7.16086e8i | −0.616796 | + | 0.616796i | −0.944708 | − | 0.327912i | \(-0.893655\pi\) |
0.327912 | + | 0.944708i | \(0.393655\pi\) | |||||||
\(390\) | 2.56101e9 | − | 1.01364e9i | 2.18618 | − | 0.865282i | ||||
\(391\) | 1.29032e8 | 0.109164 | ||||||||
\(392\) | 2.07078e9 | − | 4.28214e8i | 1.73634 | − | 0.359054i | ||||
\(393\) | 5.61756e8 | − | 3.60627e8i | 0.466846 | − | 0.299699i | ||||
\(394\) | −2.29099e9 | − | 4.49704e8i | −1.88707 | − | 0.370417i | ||||
\(395\) | 2.38791e9 | + | 2.38791e9i | 1.94952 | + | 1.94952i | ||||
\(396\) | 3.94811e8 | + | 1.24968e7i | 0.319489 | + | 0.0101127i | ||||
\(397\) | −1.03641e9 | + | 1.03641e9i | −0.831312 | + | 0.831312i | −0.987696 | − | 0.156385i | \(-0.950016\pi\) |
0.156385 | + | 0.987696i | \(0.450016\pi\) | |||||||
\(398\) | 8.69490e8 | + | 1.29421e9i | 0.691311 | + | 1.02899i | ||||
\(399\) | −1.70450e9 | − | 2.65513e9i | −1.34336 | − | 2.09257i | ||||
\(400\) | −1.40690e9 | + | 1.43557e9i | −1.09914 | + | 1.12154i | ||||
\(401\) | 2.41358e9i | 1.86920i | 0.355699 | + | 0.934601i | \(0.384243\pi\) | ||||
−0.355699 | + | 0.934601i | \(0.615757\pi\) | |||||||
\(402\) | −1.66333e8 | + | 3.84253e8i | −0.127699 | + | 0.295003i | ||||
\(403\) | 2.68868e8 | + | 2.68868e8i | 0.204631 | + | 0.204631i | ||||
\(404\) | −3.68127e8 | − | 8.76212e8i | −0.277756 | − | 0.661111i | ||||
\(405\) | −2.13756e9 | − | 1.57115e8i | −1.59891 | − | 0.117524i | ||||
\(406\) | 3.40495e7 | − | 1.73463e8i | 0.0252505 | − | 0.128637i | ||||
\(407\) | − | 2.44166e8i | − | 0.179516i | ||||||
\(408\) | −1.52172e6 | + | 1.41185e8i | −0.00110923 | + | 0.102915i | ||||
\(409\) | − | 8.38522e8i | − | 0.606014i | −0.952988 | − | 0.303007i | \(-0.902009\pi\) | ||
0.952988 | − | 0.303007i | \(-0.0979906\pi\) | |||||||
\(410\) | −4.13133e8 | − | 8.10949e7i | −0.296038 | − | 0.0581099i | ||||
\(411\) | −1.25305e9 | − | 2.73230e8i | −0.890269 | − | 0.194125i | ||||
\(412\) | 7.21588e8 | − | 1.76722e9i | 0.508334 | − | 1.24495i | ||||
\(413\) | −1.04630e9 | − | 1.04630e9i | −0.730858 | − | 0.730858i | ||||
\(414\) | 1.51127e9 | − | 2.47278e8i | 1.04674 | − | 0.171271i | ||||
\(415\) | − | 1.16777e9i | − | 0.802027i | ||||||
\(416\) | −1.21883e9 | − | 1.77524e9i | −0.830071 | − | 1.20901i | ||||
\(417\) | 1.70973e8 | − | 1.09759e8i | 0.115465 | − | 0.0741246i | ||||
\(418\) | 5.91615e8 | − | 3.97466e8i | 0.396207 | − | 0.266185i | ||||
\(419\) | 1.00640e9 | − | 1.00640e9i | 0.668375 | − | 0.668375i | −0.288964 | − | 0.957340i | \(-0.593311\pi\) |
0.957340 | + | 0.288964i | \(0.0933109\pi\) | |||||||
\(420\) | −7.37887e8 | − | 3.98594e9i | −0.485979 | − | 2.62518i | ||||
\(421\) | 6.80423e8 | + | 6.80423e8i | 0.444418 | + | 0.444418i | 0.893494 | − | 0.449076i | \(-0.148247\pi\) |
−0.449076 | + | 0.893494i | \(0.648247\pi\) | |||||||
\(422\) | 7.90191e7 | − | 4.02558e8i | 0.0511845 | − | 0.260757i | ||||
\(423\) | 1.97065e9 | + | 9.02315e8i | 1.26596 | + | 0.579651i | ||||
\(424\) | −1.13766e9 | + | 1.73083e9i | −0.724824 | + | 1.10274i | ||||
\(425\) | −2.55774e8 | −0.161620 | ||||||||
\(426\) | 8.42508e8 | − | 3.33462e8i | 0.528008 | − | 0.208984i | ||||
\(427\) | 7.98415e8 | − | 7.98415e8i | 0.496285 | − | 0.496285i | ||||
\(428\) | 4.80660e8 | − | 2.01942e8i | 0.296336 | − | 0.124501i | ||||
\(429\) | −7.48996e8 | − | 1.63321e8i | −0.458014 | − | 0.0998712i | ||||
\(430\) | −9.49621e8 | + | 6.37986e8i | −0.575984 | + | 0.386965i | ||||
\(431\) | −1.91227e9 | −1.15048 | −0.575241 | − | 0.817984i | \(-0.695092\pi\) | ||||
−0.575241 | + | 0.817984i | \(0.695092\pi\) | |||||||
\(432\) | 2.52745e8 | + | 1.65652e9i | 0.150830 | + | 0.988560i | ||||
\(433\) | 1.31602e9 | 0.779032 | 0.389516 | − | 0.921020i | \(-0.372642\pi\) | ||||
0.389516 | + | 0.921020i | \(0.372642\pi\) | |||||||
\(434\) | 4.64518e8 | − | 3.12078e8i | 0.272765 | − | 0.183252i | ||||
\(435\) | −2.11698e8 | − | 4.61613e7i | −0.123312 | − | 0.0268884i | ||||
\(436\) | −7.85065e8 | − | 1.86860e9i | −0.453631 | − | 1.07973i | ||||
\(437\) | 1.95381e9 | − | 1.95381e9i | 1.11995 | − | 1.11995i | ||||
\(438\) | −7.20136e8 | + | 2.85028e8i | −0.409501 | + | 0.162079i | ||||
\(439\) | −2.63233e9 | −1.48496 | −0.742480 | − | 0.669868i | \(-0.766351\pi\) | ||||
−0.742480 | + | 0.669868i | \(0.766351\pi\) | |||||||
\(440\) | 8.96728e8 | − | 1.85433e8i | 0.501853 | − | 0.103777i | ||||
\(441\) | 2.90356e9 | + | 1.32947e9i | 1.61212 | + | 0.738149i | ||||
\(442\) | 5.27795e7 | − | 2.68882e8i | 0.0290728 | − | 0.148110i | ||||
\(443\) | −1.88393e9 | − | 1.88393e9i | −1.02956 | − | 1.02956i | −0.999550 | − | 0.0300083i | \(-0.990447\pi\) |
−0.0300083 | − | 0.999550i | \(-0.509553\pi\) | |||||||
\(444\) | 1.01848e9 | − | 1.88544e8i | 0.552221 | − | 0.102229i | ||||
\(445\) | 1.83773e9 | − | 1.83773e9i | 0.988600 | − | 0.988600i | ||||
\(446\) | −1.61693e9 | + | 1.08631e9i | −0.863018 | + | 0.579803i | ||||
\(447\) | −1.22772e9 | + | 7.88153e8i | −0.650163 | + | 0.417382i | ||||
\(448\) | −2.90930e9 | + | 1.25697e9i | −1.52868 | + | 0.660468i | ||||
\(449\) | − | 4.51150e8i | − | 0.235212i | −0.993060 | − | 0.117606i | \(-0.962478\pi\) | ||
0.993060 | − | 0.117606i | \(-0.0375220\pi\) | |||||||
\(450\) | −2.99571e9 | + | 4.90167e8i | −1.54973 | + | 0.253572i | ||||
\(451\) | 8.28587e7 | + | 8.28587e7i | 0.0425324 | + | 0.0425324i | ||||
\(452\) | −7.68138e8 | − | 3.13644e8i | −0.391250 | − | 0.159754i | ||||
\(453\) | −1.03637e9 | − | 2.25983e8i | −0.523807 | − | 0.114218i | ||||
\(454\) | 2.99175e9 | + | 5.87257e8i | 1.50048 | + | 0.294532i | ||||
\(455\) | 7.86697e9i | 3.91532i | ||||||||
\(456\) | 2.11478e9 | + | 2.16087e9i | 1.04445 | + | 1.06721i | ||||
\(457\) | − | 2.65297e9i | − | 1.30025i | −0.759829 | − | 0.650123i | \(-0.774717\pi\) | ||
0.759829 | − | 0.650123i | \(-0.225283\pi\) | |||||||
\(458\) | −4.80448e8 | + | 2.44761e9i | −0.233677 | + | 1.19046i | ||||
\(459\) | −1.28036e8 | + | 1.70510e8i | −0.0617997 | + | 0.0823009i | ||||
\(460\) | 3.27285e9 | − | 1.37504e9i | 1.56774 | − | 0.658661i | ||||
\(461\) | 8.95901e8 | + | 8.95901e8i | 0.425899 | + | 0.425899i | 0.887229 | − | 0.461330i | \(-0.152628\pi\) |
−0.461330 | + | 0.887229i | \(0.652628\pi\) | |||||||
\(462\) | −4.48195e8 | + | 1.03540e9i | −0.211456 | + | 0.488494i | ||||
\(463\) | 1.79839e9i | 0.842074i | 0.907043 | + | 0.421037i | \(0.138334\pi\) | ||||
−0.907043 | + | 0.421037i | \(0.861666\pi\) | |||||||
\(464\) | 1.70859e6 | + | 1.69389e8i | 0.000794007 | + | 0.0787179i | ||||
\(465\) | −3.70554e8 | − | 5.77218e8i | −0.170909 | − | 0.266229i | ||||
\(466\) | 8.15869e8 | + | 1.21439e9i | 0.373482 | + | 0.555916i | ||||
\(467\) | 4.10614e8 | − | 4.10614e8i | 0.186563 | − | 0.186563i | −0.607646 | − | 0.794208i | \(-0.707886\pi\) |
0.794208 | + | 0.607646i | \(0.207886\pi\) | |||||||
\(468\) | 1.02883e8 | − | 3.25039e9i | 0.0463963 | − | 1.46580i | ||||
\(469\) | −8.45652e8 | − | 8.45652e8i | −0.378518 | − | 0.378518i | ||||
\(470\) | 4.93034e9 | + | 9.67787e8i | 2.19045 | + | 0.429969i | ||||
\(471\) | 1.33559e8 | − | 8.57402e7i | 0.0588979 | − | 0.0378104i | ||||
\(472\) | 1.18492e9 | + | 7.78836e8i | 0.518670 | + | 0.340917i | ||||
\(473\) | 3.18413e8 | 0.138349 | ||||||||
\(474\) | 3.70741e9 | − | 1.46738e9i | 1.59899 | − | 0.632876i | ||||
\(475\) | −3.87295e9 | + | 3.87295e9i | −1.65811 | + | 1.65811i | ||||
\(476\) | −3.73356e8 | − | 1.52448e8i | −0.158671 | − | 0.0647883i | ||||
\(477\) | −2.93185e9 | + | 1.09023e9i | −1.23688 | + | 0.459944i | ||||
\(478\) | 3.35170e8 | + | 4.98890e8i | 0.140368 | + | 0.208933i | ||||
\(479\) | −4.12493e9 | −1.71491 | −0.857456 | − | 0.514557i | \(-0.827957\pi\) | ||||
−0.857456 | + | 0.514557i | \(0.827957\pi\) | |||||||
\(480\) | 1.46594e9 | + | 3.59731e9i | 0.605024 | + | 1.48468i | ||||
\(481\) | −2.01016e9 | −0.823611 | ||||||||
\(482\) | −2.18957e9 | − | 3.25910e9i | −0.890624 | − | 1.32566i | ||||
\(483\) | −9.31852e8 | + | 4.27352e9i | −0.376298 | + | 1.72572i | ||||
\(484\) | 2.07332e9 | + | 8.46572e8i | 0.831204 | + | 0.339395i | ||||
\(485\) | 1.87412e9 | − | 1.87412e9i | 0.745935 | − | 0.745935i | ||||
\(486\) | −1.17283e9 | + | 2.24243e9i | −0.463455 | + | 0.886120i | ||||
\(487\) | 1.41285e9 | 0.554299 | 0.277149 | − | 0.960827i | \(-0.410610\pi\) | ||||
0.277149 | + | 0.960827i | \(0.410610\pi\) | |||||||
\(488\) | −5.94314e8 | + | 9.04187e8i | −0.231498 | + | 0.352200i | ||||
\(489\) | −5.12515e7 | − | 7.98353e7i | −0.0198210 | − | 0.0308755i | ||||
\(490\) | 7.26437e9 | + | 1.42594e9i | 2.78940 | + | 0.547539i | ||||
\(491\) | −2.08950e8 | − | 2.08950e8i | −0.0796630 | − | 0.0796630i | 0.666153 | − | 0.745816i | \(-0.267940\pi\) |
−0.745816 | + | 0.666153i | \(0.767940\pi\) | |||||||
\(492\) | −2.81643e8 | + | 4.09610e8i | −0.106616 | + | 0.155057i | ||||
\(493\) | −1.52422e7 | + | 1.52422e7i | −0.00572905 | + | 0.00572905i | ||||
\(494\) | −3.27224e9 | − | 4.87063e9i | −1.22124 | − | 1.81778i | ||||
\(495\) | 1.25735e9 | + | 5.75712e8i | 0.465950 | + | 0.213347i | ||||
\(496\) | −3.75354e8 | + | 3.83003e8i | −0.138120 | + | 0.140934i | ||||
\(497\) | 2.58804e9i | 0.945633i | ||||||||
\(498\) | −1.26533e9 | − | 5.47725e8i | −0.459092 | − | 0.198728i | ||||
\(499\) | 2.83335e9 | + | 2.83335e9i | 1.02082 | + | 1.02082i | 0.999779 | + | 0.0210380i | \(0.00669711\pi\) |
0.0210380 | + | 0.999779i | \(0.493303\pi\) | |||||||
\(500\) | −2.35626e9 | + | 9.89947e8i | −0.843002 | + | 0.354174i | ||||
\(501\) | −6.15237e8 | + | 2.82151e9i | −0.218580 | + | 1.00242i | ||||
\(502\) | −5.72340e7 | + | 2.91575e8i | −0.0201926 | + | 0.102870i | ||||
\(503\) | − | 4.30020e9i | − | 1.50661i | −0.657671 | − | 0.753305i | \(-0.728458\pi\) | ||
0.657671 | − | 0.753305i | \(-0.271542\pi\) | |||||||
\(504\) | −4.66502e9 | − | 1.07002e9i | −1.62310 | − | 0.372292i | ||||
\(505\) | − | 3.32727e9i | − | 1.14966i | ||||||
\(506\) | −9.69545e8 | − | 1.90314e8i | −0.332691 | − | 0.0653047i | ||||
\(507\) | −7.19403e8 | + | 3.29922e9i | −0.245157 | + | 1.12430i | ||||
\(508\) | −3.35071e9 | − | 1.36816e9i | −1.13400 | − | 0.463033i | ||||
\(509\) | 1.79218e9 | + | 1.79218e9i | 0.602380 | + | 0.602380i | 0.940943 | − | 0.338564i | \(-0.109941\pi\) |
−0.338564 | + | 0.940943i | \(0.609941\pi\) | |||||||
\(510\) | −1.96362e8 | + | 4.53626e8i | −0.0655485 | + | 0.151427i | ||||
\(511\) | − | 2.21213e9i | − | 0.733395i | ||||||
\(512\) | 2.48624e9 | − | 1.74413e9i | 0.818648 | − | 0.574295i | ||||
\(513\) | 6.43145e8 | + | 4.52059e9i | 0.210329 | + | 1.47837i | ||||
\(514\) | −2.71399e9 | + | 1.82335e9i | −0.881530 | + | 0.592240i | ||||
\(515\) | 4.72542e9 | − | 4.72542e9i | 1.52446 | − | 1.52446i | ||||
\(516\) | 2.45878e8 | + | 1.32819e9i | 0.0787853 | + | 0.425585i | ||||
\(517\) | −9.88836e8 | − | 9.88836e8i | −0.314708 | − | 0.314708i | ||||
\(518\) | −5.69847e8 | + | 2.90305e9i | −0.180138 | + | 0.917700i | ||||
\(519\) | −2.69658e9 | − | 4.20051e9i | −0.846697 | − | 1.31891i | ||||
\(520\) | −1.52663e9 | − | 7.38255e9i | −0.476125 | − | 2.30247i | ||||
\(521\) | 1.42418e9 | 0.441197 | 0.220598 | − | 0.975365i | \(-0.429199\pi\) | ||||
0.220598 | + | 0.975365i | \(0.429199\pi\) | |||||||
\(522\) | −1.49311e8 | + | 2.07732e8i | −0.0459458 | + | 0.0639228i | ||||
\(523\) | 3.21371e9 | − | 3.21371e9i | 0.982314 | − | 0.982314i | −0.0175319 | − | 0.999846i | \(-0.505581\pi\) |
0.999846 | + | 0.0175319i | \(0.00558085\pi\) | |||||||
\(524\) | −7.07715e8 | − | 1.68450e9i | −0.214882 | − | 0.511459i | ||||
\(525\) | 1.84716e9 | − | 8.47119e9i | 0.557119 | − | 2.55498i | ||||
\(526\) | 1.49642e9 | − | 1.00534e9i | 0.448335 | − | 0.301206i | ||||
\(527\) | −6.82392e7 | −0.0203094 | ||||||||
\(528\) | 2.19673e8 | − | 1.05861e9i | 0.0649467 | − | 0.312982i | ||||
\(529\) | −4.25615e8 | −0.125004 | ||||||||
\(530\) | −6.01900e9 | + | 4.04376e9i | −1.75614 | + | 1.17983i | ||||
\(531\) | 7.46366e8 | + | 2.00712e9i | 0.216332 | + | 0.581759i | ||||
\(532\) | −7.96175e9 | + | 3.34501e9i | −2.29255 | + | 0.963177i | ||||
\(533\) | 6.82156e8 | − | 6.82156e8i | 0.195136 | − | 0.195136i | ||||
\(534\) | −1.12929e9 | − | 2.85321e9i | −0.320931 | − | 0.810847i | ||||
\(535\) | 1.82522e9 | 0.515321 | ||||||||
\(536\) | 9.57682e8 | + | 6.29476e8i | 0.268624 | + | 0.176564i | ||||
\(537\) | −1.50800e9 | + | 9.68082e8i | −0.420233 | + | 0.269775i | ||||
\(538\) | 1.25218e9 | − | 6.37916e9i | 0.346680 | − | 1.76614i | ||||
\(539\) | −1.45695e9 | − | 1.45695e9i | −0.400760 | − | 0.400760i | ||||
\(540\) | −1.43053e9 | + | 5.68933e9i | −0.390948 | + | 1.55483i | ||||
\(541\) | 2.40850e9 | − | 2.40850e9i | 0.653969 | − | 0.653969i | −0.299978 | − | 0.953946i | \(-0.596979\pi\) |
0.953946 | + | 0.299978i | \(0.0969792\pi\) | |||||||
\(542\) | 3.14827e9 | − | 2.11511e9i | 0.849326 | − | 0.570604i | ||||
\(543\) | 2.45766e9 | + | 3.82834e9i | 0.658752 | + | 1.02615i | ||||
\(544\) | 3.79949e8 | + | 7.06088e7i | 0.101188 | + | 0.0188045i | ||||
\(545\) | − | 7.09570e9i | − | 1.87762i | ||||||
\(546\) | 8.52417e9 | + | 3.68988e9i | 2.24119 | + | 0.970148i | ||||
\(547\) | −9.78391e8 | − | 9.78391e8i | −0.255598 | − | 0.255598i | 0.567663 | − | 0.823261i | \(-0.307848\pi\) |
−0.823261 | + | 0.567663i | \(0.807848\pi\) | |||||||
\(548\) | −1.32695e9 | + | 3.24979e9i | −0.344447 | + | 0.843576i | ||||
\(549\) | −1.53160e9 | + | 5.69537e8i | −0.395040 | + | 0.146899i | ||||
\(550\) | 1.92188e9 | + | 3.77250e8i | 0.492558 | + | 0.0966853i | ||||
\(551\) | 4.61596e8i | 0.117552i | ||||||||
\(552\) | 4.51737e7 | − | 4.19120e9i | 0.0114314 | − | 1.06060i | ||||
\(553\) | 1.13885e10i | 2.86371i | ||||||||
\(554\) | −9.61524e8 | + | 4.89843e9i | −0.240257 | + | 1.22398i | ||||
\(555\) | 3.54294e9 | + | 7.72548e8i | 0.879708 | + | 0.191823i | ||||
\(556\) | −2.15396e8 | − | 5.12684e8i | −0.0531467 | − | 0.126499i | ||||
\(557\) | 4.61818e9 | + | 4.61818e9i | 1.13234 | + | 1.13234i | 0.989787 | + | 0.142556i | \(0.0455322\pi\) |
0.142556 | + | 0.989787i | \(0.454468\pi\) | |||||||
\(558\) | −7.99241e8 | + | 1.30774e8i | −0.194741 | + | 0.0318642i | ||||
\(559\) | − | 2.62142e9i | − | 0.634739i | ||||||
\(560\) | −1.10946e10 | + | 1.11908e8i | −2.66964 | + | 0.0269280i | ||||
\(561\) | 1.15774e8 | − | 7.43227e7i | 0.0276847 | − | 0.0177726i | ||||
\(562\) | −1.69103e9 | − | 2.51704e9i | −0.401860 | − | 0.598155i | ||||
\(563\) | 7.41388e8 | − | 7.41388e8i | 0.175092 | − | 0.175092i | −0.614120 | − | 0.789212i | \(-0.710489\pi\) |
0.789212 | + | 0.614120i | \(0.210489\pi\) | |||||||
\(564\) | 3.36114e9 | − | 4.88829e9i | 0.788877 | − | 1.14731i | ||||
\(565\) | −2.05394e9 | − | 2.05394e9i | −0.479092 | − | 0.479092i | ||||
\(566\) | 4.47872e9 | + | 8.79137e8i | 1.03824 | + | 0.203798i | ||||
\(567\) | −4.72259e9 | − | 5.47191e9i | −1.08803 | − | 1.26066i | ||||
\(568\) | −5.02222e8 | − | 2.42867e9i | −0.114994 | − | 0.556096i | ||||
\(569\) | −1.77637e9 | −0.404240 | −0.202120 | − | 0.979361i | \(-0.564783\pi\) | ||||
−0.202120 | + | 0.979361i | \(0.564783\pi\) | |||||||
\(570\) | 3.89550e9 | + | 9.84217e9i | 0.881052 | + | 2.22602i | ||||
\(571\) | 2.91820e9 | − | 2.91820e9i | 0.655977 | − | 0.655977i | −0.298448 | − | 0.954426i | \(-0.596469\pi\) |
0.954426 | + | 0.298448i | \(0.0964691\pi\) | |||||||
\(572\) | −7.93169e8 | + | 1.94253e9i | −0.177207 | + | 0.433992i | ||||
\(573\) | −4.68327e9 | − | 1.02120e9i | −1.03994 | − | 0.226761i | ||||
\(574\) | −7.91785e8 | − | 1.17855e9i | −0.174749 | − | 0.260109i | ||||
\(575\) | 7.59289e9 | 1.66560 | ||||||||
\(576\) | 4.58541e9 | + | 9.88564e7i | 0.999768 | + | 0.0215539i | ||||
\(577\) | 1.27582e9 | 0.276487 | 0.138243 | − | 0.990398i | \(-0.455854\pi\) | ||||
0.138243 | + | 0.990398i | \(0.455854\pi\) | |||||||
\(578\) | −2.56151e9 | − | 3.81272e9i | −0.551758 | − | 0.821273i | ||||
\(579\) | −4.62281e9 | − | 1.00802e9i | −0.989764 | − | 0.215821i | ||||
\(580\) | −2.24183e8 | + | 5.49041e8i | −0.0477095 | + | 0.116844i | ||||
\(581\) | 2.78468e9 | − | 2.78468e9i | 0.589060 | − | 0.589060i | ||||
\(582\) | −1.15165e9 | − | 2.90971e9i | −0.242154 | − | 0.611813i | ||||
\(583\) | 2.01820e9 | 0.421818 | ||||||||
\(584\) | 4.29276e8 | + | 2.07592e9i | 0.0891849 | + | 0.431285i | ||||
\(585\) | 4.73970e9 | − | 1.03515e10i | 0.978825 | − | 2.13775i | ||||
\(586\) | −6.47639e9 | − | 1.27126e9i | −1.32951 | − | 0.260972i | ||||
\(587\) | −8.28532e8 | − | 8.28532e8i | −0.169074 | − | 0.169074i | 0.617499 | − | 0.786572i | \(-0.288146\pi\) |
−0.786572 | + | 0.617499i | \(0.788146\pi\) | |||||||
\(588\) | 4.95230e9 | − | 7.20241e9i | 1.00458 | − | 1.46102i | ||||
\(589\) | −1.03328e9 | + | 1.03328e9i | −0.208361 | + | 0.208361i | ||||
\(590\) | 2.76833e9 | + | 4.12057e9i | 0.554927 | + | 0.825990i | ||||
\(591\) | −8.12115e9 | + | 5.21349e9i | −1.61831 | + | 1.03890i | ||||
\(592\) | −2.85946e7 | − | 2.83488e9i | −0.00566446 | − | 0.561575i | ||||
\(593\) | − | 6.23217e9i | − | 1.22729i | −0.789582 | − | 0.613646i | \(-0.789702\pi\) | ||
0.789582 | − | 0.613646i | \(-0.210298\pi\) | |||||||
\(594\) | 1.21355e9 | − | 1.09236e9i | 0.237577 | − | 0.213852i | ||||
\(595\) | −9.98325e8 | − | 9.98325e8i | −0.194295 | − | 0.194295i | ||||
\(596\) | 1.54671e9 | + | 3.68147e9i | 0.299260 | + | 0.712295i | ||||
\(597\) | 6.29685e9 | + | 1.37305e9i | 1.21119 | + | 0.264104i | ||||
\(598\) | −1.56681e9 | + | 7.98203e9i | −0.299614 | + | 1.52637i | ||||
\(599\) | 2.86565e9i | 0.544790i | 0.962185 | + | 0.272395i | \(0.0878158\pi\) | ||||
−0.962185 | + | 0.272395i | \(0.912184\pi\) | |||||||
\(600\) | −8.95455e7 | + | 8.30801e9i | −0.0169244 | + | 1.57025i | ||||
\(601\) | 1.10087e9i | 0.206859i | 0.994637 | + | 0.103430i | \(0.0329816\pi\) | ||||
−0.994637 | + | 0.103430i | \(0.967018\pi\) | |||||||
\(602\) | −3.78583e9 | − | 7.43130e8i | −0.707251 | − | 0.138828i | ||||
\(603\) | 6.03233e8 | + | 1.62221e9i | 0.112040 | + | 0.301298i | ||||
\(604\) | −1.09749e9 | + | 2.68784e9i | −0.202662 | + | 0.496334i | ||||
\(605\) | 5.54390e9 | + | 5.54390e9i | 1.01782 | + | 1.01782i | ||||
\(606\) | −3.60523e9 | − | 1.56060e9i | −0.658079 | − | 0.284865i | ||||
\(607\) | 6.43120e9i | 1.16716i | 0.812054 | + | 0.583582i | \(0.198349\pi\) | ||||
−0.812054 | + | 0.583582i | \(0.801651\pi\) | |||||||
\(608\) | 6.82238e9 | − | 4.68405e9i | 1.23104 | − | 0.845199i | ||||
\(609\) | −3.94741e8 | − | 6.14895e8i | −0.0708193 | − | 0.110316i | ||||
\(610\) | −3.14433e9 | + | 2.11246e9i | −0.560884 | + | 0.376820i | ||||
\(611\) | −8.14085e9 | + | 8.14085e9i | −1.44386 | + | 1.44386i | ||||
\(612\) | 3.99421e8 | + | 4.25533e8i | 0.0704370 | + | 0.0750417i | ||||
\(613\) | 1.97742e9 | + | 1.97742e9i | 0.346726 | + | 0.346726i | 0.858888 | − | 0.512163i | \(-0.171156\pi\) |
−0.512163 | + | 0.858888i | \(0.671156\pi\) | |||||||
\(614\) | −6.96057e8 | + | 3.54602e9i | −0.121354 | + | 0.618233i | ||||
\(615\) | −1.46448e9 | + | 9.40146e8i | −0.253876 | + | 0.162979i | ||||
\(616\) | 2.58054e9 | + | 1.69617e9i | 0.444813 | + | 0.292372i | ||||
\(617\) | −1.14463e8 | −0.0196186 | −0.00980931 | − | 0.999952i | \(-0.503122\pi\) | ||||
−0.00980931 | + | 0.999952i | \(0.503122\pi\) | |||||||
\(618\) | −2.90379e9 | − | 7.33657e9i | −0.494887 | − | 1.25035i | ||||
\(619\) | −3.05207e8 | + | 3.05207e8i | −0.0517223 | + | 0.0517223i | −0.732495 | − | 0.680773i | \(-0.761644\pi\) |
0.680773 | + | 0.732495i | \(0.261644\pi\) | |||||||
\(620\) | −1.73086e9 | + | 7.27195e8i | −0.291670 | + | 0.122541i | ||||
\(621\) | 3.80086e9 | − | 5.06174e9i | 0.636885 | − | 0.848163i | ||||
\(622\) | 4.84940e9 | − | 3.25798e9i | 0.808018 | − | 0.542853i | ||||
\(623\) | 8.76454e9 | 1.45218 | ||||||||
\(624\) | −8.71532e9 | − | 1.80851e9i | −1.43594 | − | 0.297972i | ||||
\(625\) | 6.37073e8 | 0.104378 | ||||||||
\(626\) | 4.25651e9 | − | 2.85966e9i | 0.693496 | − | 0.465913i | ||||
\(627\) | 6.27655e8 | − | 2.87845e9i | 0.101691 | − | 0.466362i | ||||
\(628\) | −1.68261e8 | − | 4.00494e8i | −0.0271097 | − | 0.0645263i | ||||
\(629\) | 2.55091e8 | − | 2.55091e8i | 0.0408712 | − | 0.0408712i | ||||
\(630\) | −1.36059e10 | − | 9.77952e9i | −2.16788 | − | 1.55821i | ||||
\(631\) | 7.46141e9 | 1.18227 | 0.591137 | − | 0.806571i | \(-0.298679\pi\) | ||||
0.591137 | + | 0.806571i | \(0.298679\pi\) | |||||||
\(632\) | −2.21000e9 | − | 1.06872e10i | −0.348242 | − | 1.68405i | ||||
\(633\) | −9.16080e8 | − | 1.42699e9i | −0.143556 | − | 0.223619i | ||||
\(634\) | −6.79596e8 | + | 3.46216e9i | −0.105910 | + | 0.539554i | ||||
\(635\) | −8.95956e9 | − | 8.95956e9i | −1.38860 | − | 1.38860i | ||||
\(636\) | 1.55845e9 | + | 8.41849e9i | 0.240211 | + | 1.29758i | ||||
\(637\) | −1.19947e10 | + | 1.19947e10i | −1.83867 | + | 1.83867i | ||||
\(638\) | 1.37011e8 | − | 9.20482e7i | 0.0208873 | − | 0.0140327i | ||||
\(639\) | 1.55924e9 | − | 3.40538e9i | 0.236407 | − | 0.516312i | ||||
\(640\) | 1.03897e10 | − | 2.25798e9i | 1.56666 | − | 0.340479i | ||||
\(641\) | 1.30471e10i | 1.95664i | 0.207109 | + | 0.978318i | \(0.433595\pi\) | ||||
−0.207109 | + | 0.978318i | \(0.566405\pi\) | |||||||
\(642\) | 8.56093e8 | − | 1.97770e9i | 0.127688 | − | 0.294977i | ||||
\(643\) | −5.89846e9 | − | 5.89846e9i | −0.874984 | − | 0.874984i | 0.118026 | − | 0.993011i | \(-0.462343\pi\) |
−0.993011 | + | 0.118026i | \(0.962343\pi\) | |||||||
\(644\) | 1.10834e10 | + | 4.52556e9i | 1.63521 | + | 0.667685i | ||||
\(645\) | −1.00747e9 | + | 4.62030e9i | −0.147833 | + | 0.677971i | ||||
\(646\) | 1.03334e9 | + | 2.02836e8i | 0.150809 | + | 0.0296027i | ||||
\(647\) | 1.20673e10i | 1.75164i | 0.482638 | + | 0.875820i | \(0.339679\pi\) | ||||
−0.482638 | + | 0.875820i | \(0.660321\pi\) | |||||||
\(648\) | 5.49364e9 | + | 4.21853e9i | 0.793137 | + | 0.609044i | ||||
\(649\) | − | 1.38165e9i | − | 0.198400i | ||||||
\(650\) | 3.10581e9 | − | 1.58224e10i | 0.443587 | − | 2.25983i | ||||
\(651\) | 4.92815e8 | − | 2.26007e9i | 0.0700084 | − | 0.321062i | ||||
\(652\) | −2.39397e8 | + | 1.00579e8i | −0.0338261 | + | 0.0142115i | ||||
\(653\) | −8.78108e9 | − | 8.78108e9i | −1.23410 | − | 1.23410i | −0.962373 | − | 0.271731i | \(-0.912404\pi\) |
−0.271731 | − | 0.962373i | \(-0.587596\pi\) | |||||||
\(654\) | −7.68847e9 | − | 3.32813e9i | −1.07478 | − | 0.465241i | ||||
\(655\) | − | 6.39659e9i | − | 0.889415i | ||||||
\(656\) | 9.71732e8 | + | 9.52325e8i | 0.134395 | + | 0.131711i | ||||
\(657\) | −1.33277e9 | + | 2.91076e9i | −0.183348 | + | 0.400431i | ||||
\(658\) | 9.44916e9 | + | 1.40648e10i | 1.29301 | + | 1.92461i | ||||
\(659\) | 3.93222e9 | − | 3.93222e9i | 0.535228 | − | 0.535228i | −0.386896 | − | 0.922123i | \(-0.626453\pi\) |
0.922123 | + | 0.386896i | \(0.126453\pi\) | |||||||
\(660\) | 2.14453e9 | − | 3.11892e9i | 0.290355 | − | 0.422280i | ||||
\(661\) | 3.59193e9 | + | 3.59193e9i | 0.483752 | + | 0.483752i | 0.906328 | − | 0.422576i | \(-0.138874\pi\) |
−0.422576 | + | 0.906328i | \(0.638874\pi\) | |||||||
\(662\) | −8.37527e9 | − | 1.64400e9i | −1.12201 | − | 0.220241i | ||||
\(663\) | −6.11881e8 | − | 9.53137e8i | −0.0815398 | − | 0.127016i | ||||
\(664\) | −2.07283e9 | + | 3.15360e9i | −0.274774 | + | 0.418040i | ||||
\(665\) | −3.02334e10 | −3.98668 | ||||||||
\(666\) | 2.49885e9 | − | 3.47656e9i | 0.327778 | − | 0.456027i | ||||
\(667\) | 4.52478e8 | − | 4.52478e8i | 0.0590415 | − | 0.0590415i | ||||
\(668\) | 7.31761e9 | + | 2.98791e9i | 0.949843 | + | 0.387837i | ||||
\(669\) | −1.71543e9 | + | 7.86705e9i | −0.221504 | + | 1.01583i | ||||
\(670\) | 2.23744e9 | + | 3.33036e9i | 0.287402 | + | 0.427788i | ||||
\(671\) | 1.05431e9 | 0.134722 | ||||||||
\(672\) | −5.08249e9 | + | 1.20739e10i | −0.646077 | + | 1.53481i | ||||
\(673\) | −1.26829e10 | −1.60386 | −0.801929 | − | 0.597419i | \(-0.796193\pi\) | ||||
−0.801929 | + | 0.597419i | \(0.796193\pi\) | |||||||
\(674\) | 3.83823e9 | + | 5.71307e9i | 0.482860 | + | 0.718721i | ||||
\(675\) | −7.53426e9 | + | 1.00336e10i | −0.942925 | + | 1.25573i | ||||
\(676\) | 8.55656e9 | + | 3.49379e9i | 1.06533 | + | 0.434995i | ||||
\(677\) | −9.61552e9 | + | 9.61552e9i | −1.19100 | + | 1.19100i | −0.214216 | + | 0.976786i | \(0.568720\pi\) |
−0.976786 | + | 0.214216i | \(0.931280\pi\) | |||||||
\(678\) | −3.18890e9 | + | 1.26216e9i | −0.392949 | + | 0.155528i | ||||
\(679\) | 8.93810e9 | 1.09572 | ||||||||
\(680\) | 1.13058e9 | + | 7.43121e8i | 0.137886 | + | 0.0906314i | ||||
\(681\) | 1.06052e10 | − | 6.80816e9i | 1.28678 | − | 0.826066i | ||||
\(682\) | 5.12749e8 | + | 1.00649e8i | 0.0618955 | + | 0.0121496i | ||||
\(683\) | 8.26144e9 | + | 8.26144e9i | 0.992163 | + | 0.992163i | 0.999970 | − | 0.00780614i | \(-0.00248480\pi\) |
−0.00780614 | + | 0.999970i | \(0.502485\pi\) | |||||||
\(684\) | 1.24915e10 | + | 3.95388e8i | 1.49251 | + | 0.0472419i | ||||
\(685\) | −8.68970e9 | + | 8.68970e9i | −1.03297 | + | 1.03297i | ||||
\(686\) | 6.07026e9 | + | 9.03539e9i | 0.717915 | + | 1.06859i | ||||
\(687\) | 5.56990e9 | + | 8.67633e9i | 0.655389 | + | 1.02091i | ||||
\(688\) | 3.69692e9 | − | 3.72899e7i | 0.432794 | − | 0.00436548i | ||||
\(689\) | − | 1.66154e10i | − | 1.93528i | ||||||
\(690\) | 5.82921e9 | − | 1.34663e10i | 0.675519 | − | 1.56055i | ||||
\(691\) | −9.55815e9 | − | 9.55815e9i | −1.10205 | − | 1.10205i | −0.994163 | − | 0.107885i | \(-0.965592\pi\) |
−0.107885 | − | 0.994163i | \(-0.534408\pi\) | |||||||
\(692\) | −1.25958e10 | + | 5.29192e9i | −1.44495 | + | 0.607075i | ||||
\(693\) | 1.62545e9 | + | 4.37116e9i | 0.185527 | + | 0.498919i | ||||
\(694\) | −1.64288e9 | + | 8.36954e9i | −0.186572 | + | 0.950481i | ||||
\(695\) | − | 1.94683e9i | − | 0.219979i | ||||||
\(696\) | 4.89758e8 | + | 5.00430e8i | 0.0550616 | + | 0.0562615i | ||||
\(697\) | 1.73132e8i | 0.0193670i | ||||||||
\(698\) | −9.30280e9 | − | 1.82607e9i | −1.03543 | − | 0.203246i | ||||
\(699\) | 5.90853e9 | + | 1.28837e9i | 0.654349 | + | 0.142683i | ||||
\(700\) | −2.19701e10 | − | 8.97079e9i | −2.42097 | − | 0.988524i | ||||
\(701\) | 1.23899e10 | + | 1.23899e10i | 1.35848 | + | 1.35848i | 0.875790 | + | 0.482692i | \(0.160341\pi\) |
0.482692 | + | 0.875790i | \(0.339659\pi\) | |||||||
\(702\) | −8.99316e9 | − | 9.99085e9i | −0.981143 | − | 1.08999i | ||||
\(703\) | − | 7.72520e9i | − | 0.838621i | ||||||
\(704\) | −2.75079e9 | − | 1.09095e9i | −0.297134 | − | 0.117843i | ||||
\(705\) | 1.74771e10 | − | 1.12197e10i | 1.87849 | − | 1.20592i | ||||
\(706\) | 2.83426e9 | − | 1.90415e9i | 0.303126 | − | 0.203650i | ||||
\(707\) | 7.93426e9 | − | 7.93426e9i | 0.844381 | − | 0.844381i | ||||
\(708\) | 5.76324e9 | − | 1.06691e9i | 0.610310 | − | 0.112982i | ||||
\(709\) | −5.87439e9 | − | 5.87439e9i | −0.619014 | − | 0.619014i | 0.326264 | − | 0.945279i | \(-0.394210\pi\) |
−0.945279 | + | 0.326264i | \(0.894210\pi\) | |||||||
\(710\) | 1.67238e9 | − | 8.51985e9i | 0.175360 | − | 0.893363i | ||||
\(711\) | 6.86135e9 | − | 1.49852e10i | 0.715922 | − | 1.56357i | ||||
\(712\) | −8.22485e9 | + | 1.70080e9i | −0.853981 | + | 0.176593i | ||||
\(713\) | 2.02575e9 | 0.209301 | ||||||||
\(714\) | −1.54997e9 | + | 6.13475e8i | −0.159360 | + | 0.0630744i | ||||
\(715\) | −5.19418e9 | + | 5.19418e9i | −0.531430 | + | 0.531430i | ||||
\(716\) | 1.89982e9 | + | 4.52193e9i | 0.193427 | + | 0.460392i | ||||
\(717\) | 2.42731e9 | + | 5.29280e8i | 0.245928 | + | 0.0536252i | ||||
\(718\) | −6.39062e7 | + | 4.29343e7i | −0.00644329 | + | 0.00432881i | ||||
\(719\) | −1.07192e10 | −1.07550 | −0.537752 | − | 0.843103i | \(-0.680726\pi\) | ||||
−0.537752 | + | 0.843103i | \(0.680726\pi\) | |||||||
\(720\) | 1.46659e10 | + | 6.53703e9i | 1.46435 | + | 0.652705i | ||||
\(721\) | 2.25366e10 | 2.23932 | ||||||||
\(722\) | 1.03238e10 | − | 6.93583e9i | 1.02084 | − | 0.685833i | ||||
\(723\) | −1.58569e10 | − | 3.45764e9i | −1.56039 | − | 0.340248i | ||||
\(724\) | 1.14798e10 | − | 4.82305e9i | 1.12421 | − | 0.472320i | ||||
\(725\) | −8.96926e8 | + | 8.96926e8i | −0.0874125 | + | 0.0874125i | ||||
\(726\) | 8.60731e9 | − | 3.40675e9i | 0.834813 | − | 0.330417i | ||||
\(727\) | −1.33447e10 | −1.28807 | −0.644035 | − | 0.764996i | \(-0.722741\pi\) | ||||
−0.644035 | + | 0.764996i | \(0.722741\pi\) | |||||||
\(728\) | 1.39641e10 | − | 2.12450e10i | 1.34139 | − | 2.04078i | ||||
\(729\) | 2.91734e9 | + | 1.00453e10i | 0.278895 | + | 0.960322i | ||||
\(730\) | −1.42947e9 | + | 7.28237e9i | −0.136002 | + | 0.692856i | ||||
\(731\) | 3.32660e8 | + | 3.32660e8i | 0.0314985 | + | 0.0314985i | ||||
\(732\) | 8.14135e8 | + | 4.39782e9i | 0.0767198 | + | 0.414427i | ||||
\(733\) | 5.08063e9 | − | 5.08063e9i | 0.476490 | − | 0.476490i | −0.427517 | − | 0.904007i | \(-0.640612\pi\) |
0.904007 | + | 0.427517i | \(0.140612\pi\) | |||||||
\(734\) | 2.23479e9 | − | 1.50140e9i | 0.208593 | − | 0.140140i | ||||
\(735\) | 2.57508e10 | − | 1.65311e10i | 2.39213 | − | 1.53567i | ||||
\(736\) | −1.12792e10 | − | 2.09609e9i | −1.04281 | − | 0.193793i | ||||
\(737\) | − | 1.11669e9i | − | 0.102753i | ||||||
\(738\) | 3.31792e8 | + | 2.02778e9i | 0.0303857 | + | 0.185705i | ||||
\(739\) | 1.47179e10 | + | 1.47179e10i | 1.34150 | + | 1.34150i | 0.894573 | + | 0.446923i | \(0.147480\pi\) |
0.446923 | + | 0.894573i | \(0.352520\pi\) | |||||||
\(740\) | 3.75189e9 | − | 9.18866e9i | 0.340361 | − | 0.833569i | ||||
\(741\) | −2.36976e10 | − | 5.16733e9i | −2.13964 | − | 0.466555i | ||||
\(742\) | −2.39958e10 | − | 4.71020e9i | −2.15636 | − | 0.423278i | ||||
\(743\) | − | 8.51607e9i | − | 0.761690i | −0.924639 | − | 0.380845i | \(-0.875633\pi\) | ||
0.924639 | − | 0.380845i | \(-0.124367\pi\) | |||||||
\(744\) | −2.38903e7 | + | 2.21654e9i | −0.00212675 | + | 0.197319i | ||||
\(745\) | 1.39798e10i | 1.23866i | ||||||||
\(746\) | −1.67972e8 | + | 8.55724e8i | −0.0148133 | + | 0.0754654i | ||||
\(747\) | −5.34185e9 | + | 1.98641e9i | −0.468889 | + | 0.174360i | ||||
\(748\) | −1.45855e8 | − | 3.47163e8i | −0.0127428 | − | 0.0303303i | ||||
\(749\) | 4.35246e9 | + | 4.35246e9i | 0.378485 | + | 0.378485i | ||||
\(750\) | −4.19669e9 | + | 9.69497e9i | −0.363239 | + | 0.839136i | ||||
\(751\) | 9.07887e8i | 0.0782154i | 0.999235 | + | 0.0391077i | \(0.0124515\pi\) | ||||
−0.999235 | + | 0.0391077i | \(0.987548\pi\) | |||||||
\(752\) | −1.15967e10 | − | 1.13650e10i | −0.994421 | − | 0.974561i | ||||
\(753\) | 6.63523e8 | + | 1.03358e9i | 0.0566335 | + | 0.0882190i | ||||
\(754\) | −7.57811e8 | − | 1.12798e9i | −0.0643815 | − | 0.0958297i | ||||
\(755\) | −7.18708e9 | + | 7.18708e9i | −0.607769 | + | 0.607769i | ||||
\(756\) | −1.69781e10 | + | 1.01556e10i | −1.42910 | + | 0.854830i | ||||
\(757\) | −9.50445e9 | − | 9.50445e9i | −0.796327 | − | 0.796327i | 0.186187 | − | 0.982514i | \(-0.440387\pi\) |
−0.982514 | + | 0.186187i | \(0.940387\pi\) | |||||||
\(758\) | 4.14315e9 | + | 8.13269e8i | 0.345532 | + | 0.0678254i | ||||
\(759\) | −3.43686e9 | + | 2.20634e9i | −0.285309 | + | 0.183158i | ||||
\(760\) | 2.83717e10 | − | 5.86695e9i | 2.34444 | − | 0.484802i | ||||
\(761\) | −5.98321e9 | −0.492139 | −0.246070 | − | 0.969252i | \(-0.579139\pi\) | ||||
−0.246070 | + | 0.969252i | \(0.579139\pi\) | |||||||
\(762\) | −1.39104e10 | + | 5.50569e9i | −1.13893 | + | 0.450785i | ||||
\(763\) | 1.69205e10 | − | 1.69205e10i | 1.37904 | − | 1.37904i | ||||
\(764\) | −4.95947e9 | + | 1.21461e10i | −0.402354 | + | 0.985396i | ||||
\(765\) | 7.12140e8 | + | 1.91508e9i | 0.0575110 | + | 0.154658i | ||||
\(766\) | −5.93898e8 | − | 8.83997e8i | −0.0477432 | − | 0.0710641i | ||||
\(767\) | −1.13748e10 | −0.910247 | ||||||||
\(768\) | 2.42653e9 | − | 1.23167e10i | 0.193295 | − | 0.981141i | ||||
\(769\) | −4.50714e9 | −0.357404 | −0.178702 | − | 0.983903i | \(-0.557190\pi\) | ||||
−0.178702 | + | 0.983903i | \(0.557190\pi\) | |||||||
\(770\) | 6.02893e9 | + | 8.97386e9i | 0.475908 | + | 0.708373i | ||||
\(771\) | −2.87932e9 | + | 1.32047e10i | −0.226256 | + | 1.03762i | ||||
\(772\) | −4.89545e9 | + | 1.19893e10i | −0.382941 | + | 0.937852i | ||||
\(773\) | 7.16450e9 | − | 7.16450e9i | 0.557901 | − | 0.557901i | −0.370808 | − | 0.928709i | \(-0.620919\pi\) |
0.928709 | + | 0.370808i | \(0.120919\pi\) | |||||||
\(774\) | 4.53374e9 | + | 3.25871e9i | 0.351450 | + | 0.252611i | ||||
\(775\) | −4.01554e9 | −0.309876 | ||||||||
\(776\) | −8.38773e9 | + | 1.73449e9i | −0.644359 | + | 0.133246i | ||||
\(777\) | 6.60632e9 | + | 1.02908e10i | 0.505227 | + | 0.787000i | ||||
\(778\) | 1.12428e10 | + | 2.20688e9i | 0.855947 | + | 0.168016i | ||||
\(779\) | 2.62158e9 | + | 2.62158e9i | 0.198693 | + | 0.198693i | ||||
\(780\) | −2.56773e10 | − | 1.76554e10i | −1.93740 | − | 1.33213i | ||||
\(781\) | −1.70875e9 | + | 1.70875e9i | −0.128352 | + | 0.128352i | ||||
\(782\) | −8.14097e8 | − | 1.21176e9i | −0.0608769 | − | 0.0906132i | ||||
\(783\) | 1.48944e8 | + | 1.04691e9i | 0.0110881 | + | 0.0779371i | ||||
\(784\) | −1.70865e10 | − | 1.67453e10i | −1.26633 | − | 1.24104i | ||||
\(785\) | − | 1.52081e9i | − | 0.112210i | ||||||
\(786\) | −6.93096e9 | − | 3.00022e9i | −0.509113 | − | 0.220381i | ||||
\(787\) | −1.38937e10 | − | 1.38937e10i | −1.01603 | − | 1.01603i | −0.999869 | − | 0.0161617i | \(-0.994855\pi\) |
−0.0161617 | − | 0.999869i | \(-0.505145\pi\) | |||||||
\(788\) | 1.02312e10 | + | 2.43523e10i | 0.744881 | + | 1.77296i | ||||
\(789\) | 1.58758e9 | − | 7.28070e9i | 0.115071 | − | 0.527720i | ||||
\(790\) | 7.35921e9 | − | 3.74911e10i | 0.531051 | − | 2.70541i | ||||
\(791\) | − | 9.79573e9i | − | 0.703751i | ||||||
\(792\) | −2.37361e9 | − | 3.78657e9i | −0.169774 | − | 0.270837i | ||||
\(793\) | − | 8.67988e9i | − | 0.618098i | ||||||
\(794\) | 1.62720e10 | + | 3.19407e9i | 1.15364 | + | 0.226450i | ||||
\(795\) | −6.38566e9 | + | 2.92849e10i | −0.450735 | + | 2.06709i | ||||
\(796\) | 6.66822e9 | − | 1.63310e10i | 0.468613 | − | 1.14767i | ||||
\(797\) | −1.90624e9 | − | 1.90624e9i | −0.133375 | − | 0.133375i | 0.637268 | − | 0.770642i | \(-0.280065\pi\) |
−0.770642 | + | 0.637268i | \(0.780065\pi\) | |||||||
\(798\) | −1.41805e10 | + | 3.27591e10i | −0.987829 | + | 2.28203i | ||||
\(799\) | − | 2.06616e9i | − | 0.143301i | ||||||
\(800\) | 2.23581e10 | + | 4.15498e9i | 1.54390 | + | 0.286915i | ||||
\(801\) | −1.15325e10 | − | 5.28047e9i | −0.792886 | − | 0.363043i | ||||
\(802\) | 2.26662e10 | − | 1.52279e10i | 1.55156 | − | 1.04239i | ||||
\(803\) | 1.46056e9 | − | 1.46056e9i | 0.0995442 | − | 0.0995442i | ||||
\(804\) | 4.65801e9 | − | 8.62302e8i | 0.316085 | − | 0.0585144i | ||||
\(805\) | 2.96362e10 | + | 2.96362e10i | 2.00234 | + | 2.00234i | ||||
\(806\) | 8.28616e8 | − | 4.22134e9i | 0.0557418 | − | 0.283973i | ||||
\(807\) | −1.45167e10 | − | 2.26129e10i | −0.972323 | − | 1.51460i | ||||
\(808\) | −5.90601e9 | + | 8.98538e9i | −0.393871 | + | 0.599234i | ||||
\(809\) | −2.64210e10 | −1.75440 | −0.877202 | − | 0.480121i | \(-0.840593\pi\) | ||||
−0.877202 | + | 0.480121i | \(0.840593\pi\) | |||||||
\(810\) | 1.20109e10 | + | 2.10653e10i | 0.794106 | + | 1.39274i | ||||
\(811\) | 1.12769e9 | − | 1.12769e9i | 0.0742361 | − | 0.0742361i | −0.669014 | − | 0.743250i | \(-0.733283\pi\) |
0.743250 | + | 0.669014i | \(0.233283\pi\) | |||||||
\(812\) | −1.84384e9 | + | 7.74662e8i | −0.120859 | + | 0.0507769i | ||||
\(813\) | 3.34005e9 | − | 1.53176e10i | 0.217990 | − | 0.999712i | ||||
\(814\) | −2.29299e9 | + | 1.54050e9i | −0.149010 | + | 0.100110i | ||||
\(815\) | −9.09068e8 | −0.0588227 | ||||||||
\(816\) | 1.33548e9 | − | 8.76480e8i | 0.0860444 | − | 0.0564711i | ||||
\(817\) | 1.00743e10 | 0.646307 | ||||||||
\(818\) | −7.87467e9 | + | 5.29045e9i | −0.503032 | + | 0.337953i | ||||
\(819\) | 3.59867e10 | − | 1.33820e10i | 2.28901 | − | 0.851189i | ||||
\(820\) | 1.84499e9 | + | 4.39144e9i | 0.116855 | + | 0.278137i | ||||
\(821\) | 1.72292e10 | − | 1.72292e10i | 1.08658 | − | 1.08658i | 0.0907063 | − | 0.995878i | \(-0.471088\pi\) |
0.995878 | − | 0.0907063i | \(-0.0289124\pi\) | |||||||
\(822\) | 5.33986e9 | + | 1.34914e10i | 0.335335 | + | 0.847239i | ||||
\(823\) | 1.77668e10 | 1.11099 | 0.555493 | − | 0.831521i | \(-0.312529\pi\) | ||||
0.555493 | + | 0.831521i | \(0.312529\pi\) | |||||||
\(824\) | −2.11489e10 | + | 4.37335e9i | −1.31687 | + | 0.272313i | ||||
\(825\) | 6.81271e9 | − | 4.37352e9i | 0.422407 | − | 0.271171i | ||||
\(826\) | −3.22457e9 | + | 1.64274e10i | −0.199086 | + | 1.01423i | ||||
\(827\) | −1.48933e10 | − | 1.48933e10i | −0.915631 | − | 0.915631i | 0.0810766 | − | 0.996708i | \(-0.474164\pi\) |
−0.996708 | + | 0.0810766i | \(0.974164\pi\) | |||||||
\(828\) | −1.18572e10 | − | 1.26323e10i | −0.725898 | − | 0.773353i | ||||
\(829\) | −8.76714e9 | + | 8.76714e9i | −0.534462 | + | 0.534462i | −0.921897 | − | 0.387435i | \(-0.873361\pi\) |
0.387435 | + | 0.921897i | \(0.373361\pi\) | |||||||
\(830\) | −1.09667e10 | + | 7.36777e9i | −0.665736 | + | 0.447263i | ||||
\(831\) | 1.11471e10 | + | 1.73640e10i | 0.673842 | + | 1.04966i | ||||
\(832\) | −8.98157e9 | + | 2.26466e10i | −0.540656 | + | 1.36324i | ||||
\(833\) | − | 3.04429e9i | − | 0.182485i | ||||||
\(834\) | −2.10947e9 | − | 9.13131e8i | −0.125919 | − | 0.0545070i | ||||
\(835\) | 1.95667e10 | + | 1.95667e10i | 1.16310 | + | 1.16310i | ||||
\(836\) | −7.46531e9 | − | 3.04821e9i | −0.441902 | − | 0.180436i | ||||
\(837\) | −2.01010e9 | + | 2.67693e9i | −0.118489 | + | 0.157797i | ||||
\(838\) | −1.58008e10 | − | 3.10158e9i | −0.927525 | − | 0.182066i | ||||
\(839\) | 3.27205e10i | 1.91273i | 0.292181 | + | 0.956363i | \(0.405619\pi\) | ||||
−0.292181 | + | 0.956363i | \(0.594381\pi\) | |||||||
\(840\) | −3.27770e10 | + | 3.20779e10i | −1.90806 | + | 1.86736i | ||||
\(841\) | − | 1.71430e10i | − | 0.993803i | ||||||
\(842\) | 2.09697e9 | − | 1.06829e10i | 0.121060 | − | 0.616733i | ||||
\(843\) | −1.22465e10 | − | 2.67037e9i | −0.704067 | − | 0.153524i | ||||
\(844\) | −4.27903e9 | + | 1.79777e9i | −0.244989 | + | 0.102928i | ||||
\(845\) | 2.28796e10 | + | 2.28796e10i | 1.30452 | + | 1.30452i | ||||
\(846\) | −3.95961e9 | − | 2.41996e10i | −0.224831 | − | 1.37408i | ||||
\(847\) | 2.64401e10i | 1.49511i | ||||||||
\(848\) | 2.34323e10 | − | 2.36355e8i | 1.31956 | − | 0.0133101i | ||||
\(849\) | 1.58762e10 | − | 1.01920e10i | 0.890369 | − | 0.571586i | ||||
\(850\) | 1.61374e9 | + | 2.40200e9i | 0.0901298 | + | 0.134155i | ||||
\(851\) | −7.57261e9 | + | 7.57261e9i | −0.421204 | + | 0.421204i | ||||
\(852\) | −8.44719e9 | − | 5.80820e9i | −0.467922 | − | 0.321738i | ||||
\(853\) | −1.21022e10 | − | 1.21022e10i | −0.667640 | − | 0.667640i | 0.289529 | − | 0.957169i | \(-0.406501\pi\) |
−0.957169 | + | 0.289529i | \(0.906501\pi\) | |||||||
\(854\) | −1.25354e10 | − | 2.46061e9i | −0.688710 | − | 0.135188i | ||||
\(855\) | 3.97816e10 | + | 1.82150e10i | 2.17671 | + | 0.996664i | ||||
\(856\) | −4.92907e9 | − | 3.23983e9i | −0.268600 | − | 0.176549i | ||||
\(857\) | 3.22325e10 | 1.74929 | 0.874643 | − | 0.484768i | \(-0.161096\pi\) | ||||
0.874643 | + | 0.484768i | \(0.161096\pi\) | |||||||
\(858\) | 3.19185e9 | + | 8.06435e9i | 0.172519 | + | 0.435877i | ||||
\(859\) | 1.39418e10 | − | 1.39418e10i | 0.750485 | − | 0.750485i | −0.224085 | − | 0.974570i | \(-0.571939\pi\) |
0.974570 | + | 0.224085i | \(0.0719393\pi\) | |||||||
\(860\) | 1.19828e10 | + | 4.89279e9i | 0.642413 | + | 0.262308i | ||||
\(861\) | −5.73411e9 | − | 1.25034e9i | −0.306165 | − | 0.0667601i | ||||
\(862\) | 1.20650e10 | + | 1.79584e10i | 0.641583 | + | 0.954975i | ||||
\(863\) | −1.72765e9 | −0.0914995 | −0.0457498 | − | 0.998953i | \(-0.514568\pi\) | ||||
−0.0457498 | + | 0.998953i | \(0.514568\pi\) | |||||||
\(864\) | 1.39619e10 | − | 1.28250e10i | 0.736457 | − | 0.676484i | ||||
\(865\) | −4.78304e10 | −2.51274 | ||||||||
\(866\) | −8.30313e9 | − | 1.23589e10i | −0.434439 | − | 0.646648i | ||||
\(867\) | −1.85505e10 | − | 4.04498e9i | −0.966693 | − | 0.210790i | ||||
\(868\) | −5.86153e9 | − | 2.39336e9i | −0.304223 | − | 0.124219i | ||||
\(869\) | −7.51927e9 | + | 7.51927e9i | −0.388693 | + | 0.388693i | ||||
\(870\) | 9.02150e8 | + | 2.27932e9i | 0.0464474 | + | 0.117351i | ||||
\(871\) | −9.19341e9 | −0.471425 | ||||||||
\(872\) | −1.25951e10 | + | 1.91621e10i | −0.643271 | + | 0.978670i | ||||
\(873\) | −1.17609e10 | − | 5.38503e9i | −0.598261 | − | 0.273929i | ||||
\(874\) | −3.06756e10 | − | 6.02138e9i | −1.55419 | − | 0.305075i | ||||
\(875\) | −2.13364e10 | − | 2.13364e10i | −1.07669 | − | 1.07669i | ||||
\(876\) | 7.22026e9 | + | 4.96457e9i | 0.362901 | + | 0.249527i | ||||
\(877\) | 2.51720e10 | − | 2.51720e10i | 1.26014 | − | 1.26014i | 0.309116 | − | 0.951024i | \(-0.399967\pi\) |
0.951024 | − | 0.309116i | \(-0.100033\pi\) | |||||||
\(878\) | 1.66081e10 | + | 2.47206e10i | 0.828111 | + | 1.23262i | ||||
\(879\) | −2.29576e10 | + | 1.47380e10i | −1.14016 | + | 0.731942i | ||||
\(880\) | −7.39911e9 | − | 7.25134e9i | −0.366008 | − | 0.358698i | ||||
\(881\) | 2.74080e10i | 1.35040i | 0.737635 | + | 0.675199i | \(0.235942\pi\) | ||||
−0.737635 | + | 0.675199i | \(0.764058\pi\) | |||||||
\(882\) | −5.83410e9 | − | 3.56557e10i | −0.286308 | − | 1.74980i | ||||
\(883\) | 1.69764e10 | + | 1.69764e10i | 0.829817 | + | 0.829817i | 0.987491 | − | 0.157674i | \(-0.0503995\pi\) |
−0.157674 | + | 0.987491i | \(0.550399\pi\) | |||||||
\(884\) | −2.85811e9 | + | 1.20079e9i | −0.139154 | + | 0.0584634i | ||||
\(885\) | 2.00483e10 | + | 4.37158e9i | 0.972245 | + | 0.212001i | ||||
\(886\) | −5.80601e9 | + | 2.95784e10i | −0.280453 | + | 1.42875i | ||||
\(887\) | − | 2.45295e9i | − | 0.118020i | −0.998257 | − | 0.0590099i | \(-0.981206\pi\) | ||
0.998257 | − | 0.0590099i | \(-0.0187944\pi\) | |||||||
\(888\) | −8.19651e9 | − | 8.37512e9i | −0.392811 | − | 0.401371i | ||||
\(889\) | − | 4.27302e10i | − | 2.03976i | ||||||
\(890\) | −2.88530e10 | − | 5.66362e9i | −1.37191 | − | 0.269296i | ||||
\(891\) | 4.94740e8 | − | 6.73094e9i | 0.0234318 | − | 0.318789i | ||||
\(892\) | 2.04033e10 | + | 8.33102e9i | 0.962550 | + | 0.393026i | ||||
\(893\) | −3.12860e10 | − | 3.12860e10i | −1.47018 | − | 1.47018i | ||||
\(894\) | 1.51476e10 | + | 6.55700e9i | 0.709028 | + | 0.306919i | ||||
\(895\) | 1.71713e10i | 0.800611i | ||||||||
\(896\) | 3.01599e10 | + | 1.93911e10i | 1.40072 | + | 0.900583i | ||||
\(897\) | 1.81643e10 | + | 2.82948e10i | 0.840320 | + | 1.30898i | ||||
\(898\) | −4.23681e9 | + | 2.84642e9i | −0.195241 | + | 0.131169i | ||||
\(899\) | −2.39296e8 | + | 2.39296e8i | −0.0109844 | + | 0.0109844i | ||||
\(900\) | 2.35039e10 | + | 2.50405e10i | 1.07471 | + | 1.14497i | ||||
\(901\) | 2.10851e9 | + | 2.10851e9i | 0.0960369 | + | 0.0960369i | ||||
\(902\) | 2.55359e8 | − | 1.30091e9i | 0.0115859 | − | 0.0590236i | ||||
\(903\) | −1.34201e10 | + | 8.61522e9i | −0.606524 | + | 0.389367i | ||||
\(904\) | 1.90091e9 | + | 9.19254e9i | 0.0855800 | + | 0.413853i | ||||
\(905\) | 4.35925e10 | 1.95498 | ||||||||
\(906\) | 4.41649e9 | + | 1.11585e10i | 0.197301 | + | 0.498490i | ||||
\(907\) | −1.88847e10 | + | 1.88847e10i | −0.840395 | + | 0.840395i | −0.988910 | − | 0.148515i | \(-0.952551\pi\) |
0.148515 | + | 0.988910i | \(0.452551\pi\) | |||||||
\(908\) | −1.33607e10 | − | 3.18010e10i | −0.592283 | − | 1.40975i | ||||
\(909\) | −1.52203e10 | + | 5.65979e9i | −0.672123 | + | 0.249935i | ||||
\(910\) | 7.38797e10 | − | 4.96348e10i | 3.24998 | − | 2.18344i | ||||
\(911\) | 1.63226e10 | 0.715278 | 0.357639 | − | 0.933860i | \(-0.383582\pi\) | ||||
0.357639 | + | 0.933860i | \(0.383582\pi\) | |||||||
\(912\) | 6.95026e9 | − | 3.34937e10i | 0.303403 | − | 1.46211i | ||||
\(913\) | 3.67719e9 | 0.159907 | ||||||||
\(914\) | −2.49144e10 | + | 1.67383e10i | −1.07929 | + | 0.725102i | ||||
\(915\) | −3.33587e9 | + | 1.52985e10i | −0.143958 | + | 0.660197i | ||||
\(916\) | 2.60171e10 | − | 1.09307e10i | 1.11847 | − | 0.469908i | ||||
\(917\) | 1.52534e10 | − | 1.52534e10i | 0.653243 | − | 0.653243i | ||||
\(918\) | 2.40909e9 | + | 1.26608e8i | 0.102779 | + | 0.00540148i | ||||
\(919\) | −2.57371e10 | −1.09384 | −0.546922 | − | 0.837183i | \(-0.684201\pi\) | ||||
−0.546922 | + | 0.837183i | \(0.684201\pi\) | |||||||
\(920\) | −3.35624e10 | − | 2.20603e10i | −1.42101 | − | 0.934014i | ||||
\(921\) | 8.06950e9 | + | 1.25700e10i | 0.340359 | + | 0.530184i | ||||
\(922\) | 2.76104e9 | − | 1.40660e10i | 0.116015 | − | 0.591033i | ||||
\(923\) | 1.40678e10 | + | 1.40678e10i | 0.588870 | + | 0.588870i | ||||
\(924\) | 1.25513e10 | − | 2.32353e9i | 0.523404 | − | 0.0968939i | ||||
\(925\) | 1.50108e10 | − | 1.50108e10i | 0.623603 | − | 0.623603i | ||||
\(926\) | 1.68889e10 | − | 1.13465e10i | 0.698977 | − | 0.469595i | ||||
\(927\) | −2.96541e10 | − | 1.35779e10i | −1.22266 | − | 0.559826i | ||||
\(928\) | 1.57998e9 | − | 1.08477e9i | 0.0648983 | − | 0.0445573i | ||||
\(929\) | − | 1.94199e10i | − | 0.794680i | −0.917671 | − | 0.397340i | \(-0.869933\pi\) | ||
0.917671 | − | 0.397340i | \(-0.130067\pi\) | |||||||
\(930\) | −3.08281e9 | + | 7.12174e9i | −0.125677 | + | 0.290332i | ||||
\(931\) | −4.60968e10 | − | 4.60968e10i | −1.87218 | − | 1.87218i | ||||
\(932\) | 6.25700e9 | − | 1.53239e10i | 0.253169 | − | 0.620030i | ||||
\(933\) | 5.14481e9 | − | 2.35943e10i | 0.207388 | − | 0.951091i | ||||
\(934\) | −6.44680e9 | − | 1.26546e9i | −0.258899 | − | 0.0508199i | ||||
\(935\) | − | 1.31829e9i | − | 0.0527437i | ||||||
\(936\) | −3.11739e10 | + | 1.95413e10i | −1.24258 | + | 0.778913i | ||||
\(937\) | − | 1.61086e10i | − | 0.639689i | −0.947470 | − | 0.319845i | \(-0.896369\pi\) | ||
0.947470 | − | 0.319845i | \(-0.103631\pi\) | |||||||
\(938\) | −2.60618e9 | + | 1.32771e10i | −0.103109 | + | 0.525281i | ||||
\(939\) | 4.51581e9 | − | 2.07097e10i | 0.177994 | − | 0.816290i | ||||
\(940\) | −2.20182e10 | − | 5.24074e10i | −0.864637 | − | 2.05800i | ||||
\(941\) | −5.75312e9 | − | 5.75312e9i | −0.225082 | − | 0.225082i | 0.585553 | − | 0.810634i | \(-0.300878\pi\) |
−0.810634 | + | 0.585553i | \(0.800878\pi\) | |||||||
\(942\) | −1.64785e9 | − | 7.13311e8i | −0.0642304 | − | 0.0278036i | ||||
\(943\) | − | 5.13960e9i | − | 0.199590i | ||||||
\(944\) | −1.61807e8 | − | 1.60416e10i | −0.00626031 | − | 0.620648i | ||||
\(945\) | −6.85702e10 | + | 9.75550e9i | −2.64316 | + | 0.376043i | ||||
\(946\) | −2.00895e9 | − | 2.99026e9i | −0.0771526 | − | 0.114839i | ||||
\(947\) | 9.82385e9 | − | 9.82385e9i | 0.375887 | − | 0.375887i | −0.493729 | − | 0.869616i | \(-0.664367\pi\) |
0.869616 | + | 0.493729i | \(0.164367\pi\) | |||||||
\(948\) | −3.71713e10 | − | 2.55586e10i | −1.41703 | − | 0.974335i | ||||
\(949\) | −1.20245e10 | − | 1.20245e10i | −0.456703 | − | 0.456703i | ||||
\(950\) | 6.08067e10 | + | 1.19359e10i | 2.30101 | + | 0.451671i | ||||
\(951\) | 7.87866e9 | + | 1.22727e10i | 0.297044 | + | 0.462710i | ||||
\(952\) | 9.23944e8 | + | 4.46806e9i | 0.0347069 | + | 0.167838i | ||||
\(953\) | −7.68624e8 | −0.0287666 | −0.0143833 | − | 0.999897i | \(-0.504579\pi\) | ||||
−0.0143833 | + | 0.999897i | \(0.504579\pi\) | |||||||
\(954\) | 2.87363e10 | + | 2.06548e10i | 1.07155 | + | 0.770196i | ||||
\(955\) | −3.24778e10 | + | 3.24778e10i | −1.20663 | + | 1.20663i | ||||
\(956\) | 2.57046e9 | − | 6.29525e9i | 0.0951498 | − | 0.233029i | ||||
\(957\) | 1.45357e8 | − | 6.66614e8i | 0.00536098 | − | 0.0245857i | ||||
\(958\) | 2.60252e10 | + | 3.87377e10i | 0.956347 | + | 1.42349i | ||||
\(959\) | −4.14432e10 | −1.51736 | ||||||||
\(960\) | 2.45338e10 | − | 3.64632e10i | 0.894984 | − | 1.33017i | ||||
\(961\) | 2.64413e10 | 0.961061 | ||||||||
\(962\) | 1.26826e10 | + | 1.88776e10i | 0.459299 | + | 0.683652i | ||||
\(963\) | −3.10476e9 | − | 8.34931e9i | −0.112031 | − | 0.301272i | ||||
\(964\) | −1.67921e10 | + | 4.11250e10i | −0.603719 | + | 1.47855i | ||||
\(965\) | −3.20585e10 | + | 3.20585e10i | −1.14841 | + | 1.14841i | ||||
\(966\) | 4.60124e10 | − | 1.82116e10i | 1.64231 | − | 0.650022i | ||||
\(967\) | −1.34957e10 | −0.479957 | −0.239979 | − | 0.970778i | \(-0.577140\pi\) | ||||
−0.239979 | + | 0.970778i | \(0.577140\pi\) | |||||||
\(968\) | −5.13085e9 | − | 2.48120e10i | −0.181813 | − | 0.879223i | ||||
\(969\) | 3.66299e9 | − | 2.35151e9i | 0.129331 | − | 0.0830259i | ||||
\(970\) | −2.94244e10 | − | 5.77578e9i | −1.03516 | − | 0.203193i | ||||
\(971\) | 2.76593e10 | + | 2.76593e10i | 0.969557 | + | 0.969557i | 0.999550 | − | 0.0299927i | \(-0.00954841\pi\) |
−0.0299927 | + | 0.999550i | \(0.509548\pi\) | |||||||
\(972\) | 2.84587e10 | − | 3.13392e9i | 0.993991 | − | 0.109460i | ||||
\(973\) | 4.64245e9 | − | 4.64245e9i | 0.161567 | − | 0.161567i | ||||
\(974\) | −8.91403e9 | − | 1.32682e10i | −0.309113 | − | 0.460105i | ||||
\(975\) | −3.60062e10 | − | 5.60874e10i | −1.24412 | − | 1.93798i | ||||
\(976\) | 1.22410e10 | − | 1.23472e8i | 0.421447 | − | 0.00425103i | ||||
\(977\) | 2.41000e10i | 0.826773i | 0.910556 | + | 0.413387i | \(0.135654\pi\) | ||||
−0.910556 | + | 0.413387i | \(0.864346\pi\) | |||||||
\(978\) | −4.26385e8 | + | 9.85011e8i | −0.0145752 | + | 0.0336709i | ||||
\(979\) | 5.78681e9 | + | 5.78681e9i | 0.197106 | + | 0.197106i | ||||
\(980\) | −3.24416e10 | − | 7.72172e10i | −1.10106 | − | 2.62073i | ||||
\(981\) | −3.24586e10 | + | 1.20700e10i | −1.09771 | + | 0.408194i | ||||
\(982\) | −6.43955e8 | + | 3.28059e9i | −0.0217003 | + | 0.110551i | ||||
\(983\) | 3.06695e10i | 1.02984i | 0.857239 | + | 0.514919i | \(0.172178\pi\) | ||||
−0.857239 | + | 0.514919i | \(0.827822\pi\) | |||||||
\(984\) | 5.62366e9 | + | 6.06130e7i | 0.188164 | + | 0.00202807i | ||||
\(985\) | 9.24738e10i | 3.08313i | ||||||||
\(986\) | 2.39308e8 | + | 4.69743e7i | 0.00795038 | + | 0.00156060i | ||||
\(987\) | 6.84309e10 | + | 1.49216e10i | 2.26539 | + | 0.493974i | ||||
\(988\) | −2.50952e10 | + | 6.14601e10i | −0.827831 | + | 2.02742i | ||||
\(989\) | −9.87534e9 | − | 9.87534e9i | −0.324612 | − | 0.324612i | ||||
\(990\) | −2.52639e9 | − | 1.54403e10i | −0.0827516 | − | 0.505745i | ||||
\(991\) | − | 7.67545e9i | − | 0.250522i | −0.992124 | − | 0.125261i | \(-0.960023\pi\) | ||
0.992124 | − | 0.125261i | \(-0.0399768\pi\) | |||||||
\(992\) | 5.96504e9 | + | 1.10853e9i | 0.194009 | + | 0.0360542i | ||||
\(993\) | −2.96888e10 | + | 1.90592e10i | −0.962210 | + | 0.617705i | ||||
\(994\) | 2.43046e10 | − | 1.63286e10i | 0.784938 | − | 0.527347i | ||||
\(995\) | 4.36678e10 | − | 4.36678e10i | 1.40534 | − | 1.40534i | ||||
\(996\) | 2.83951e9 | + | 1.53386e10i | 0.0910618 | + | 0.491900i | ||||
\(997\) | 9.39856e9 | + | 9.39856e9i | 0.300350 | + | 0.300350i | 0.841151 | − | 0.540800i | \(-0.181879\pi\) |
−0.540800 | + | 0.841151i | \(0.681879\pi\) | |||||||
\(998\) | 8.73199e9 | − | 4.44846e10i | 0.278071 | − | 1.41662i | ||||
\(999\) | −2.49271e9 | − | 1.75210e10i | −0.0791029 | − | 0.556005i |
(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 | 48.8.k.a.11.18 | ✓ | 108 | |
3.2 | odd | 2 | inner | 48.8.k.a.11.37 | yes | 108 | |
16.3 | odd | 4 | inner | 48.8.k.a.35.37 | yes | 108 | |
48.35 | even | 4 | inner | 48.8.k.a.35.18 | yes | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.8.k.a.11.18 | ✓ | 108 | 1.1 | even | 1 | trivial | |
48.8.k.a.11.37 | yes | 108 | 3.2 | odd | 2 | inner | |
48.8.k.a.35.18 | yes | 108 | 48.35 | even | 4 | inner | |
48.8.k.a.35.37 | yes | 108 | 16.3 | odd | 4 | inner |