Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,6,Mod(68,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.68");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.c (of order \(2\), degree \(1\), 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: | \(11.0664835671\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 68.31 | ||
Character | \(\chi\) | \(=\) | 69.68 |
Dual form | 69.6.c.b.68.1 |
$q$-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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 9.90483i | 1.75094i | 0.483270 | + | 0.875471i | \(0.339449\pi\) | ||||
−0.483270 | + | 0.875471i | \(0.660551\pi\) | |||||||
\(3\) | 13.3502 | + | 8.04819i | 0.856413 | + | 0.516292i | ||||
\(4\) | −66.1056 | −2.06580 | ||||||||
\(5\) | −91.0951 | −1.62956 | −0.814779 | − | 0.579772i | \(-0.803142\pi\) | ||||
−0.814779 | + | 0.579772i | \(0.803142\pi\) | |||||||
\(6\) | −79.7159 | + | 132.231i | −0.903997 | + | 1.49953i | ||||
\(7\) | − | 106.321i | − | 0.820117i | −0.912059 | − | 0.410059i | \(-0.865508\pi\) | ||
0.912059 | − | 0.410059i | \(-0.134492\pi\) | |||||||
\(8\) | − | 337.810i | − | 1.86616i | ||||||
\(9\) | 113.453 | + | 214.889i | 0.466886 | + | 0.884317i | ||||
\(10\) | − | 902.281i | − | 2.85326i | ||||||
\(11\) | 429.596 | 1.07048 | 0.535240 | − | 0.844700i | \(-0.320221\pi\) | ||||
0.535240 | + | 0.844700i | \(0.320221\pi\) | |||||||
\(12\) | −882.520 | − | 532.031i | −1.76918 | − | 1.06656i | ||||
\(13\) | −363.595 | −0.596705 | −0.298353 | − | 0.954456i | \(-0.596437\pi\) | ||||
−0.298353 | + | 0.954456i | \(0.596437\pi\) | |||||||
\(14\) | 1053.10 | 1.43598 | ||||||||
\(15\) | −1216.13 | − | 733.150i | −1.39557 | − | 0.841327i | ||||
\(16\) | 1230.57 | 1.20173 | ||||||||
\(17\) | −1775.89 | −1.49037 | −0.745184 | − | 0.666859i | \(-0.767638\pi\) | ||||
−0.745184 | + | 0.666859i | \(0.767638\pi\) | |||||||
\(18\) | −2128.44 | + | 1123.74i | −1.54839 | + | 0.817491i | ||||
\(19\) | 1106.92i | 0.703452i | 0.936103 | + | 0.351726i | \(0.114405\pi\) | ||||
−0.936103 | + | 0.351726i | \(0.885595\pi\) | |||||||
\(20\) | 6021.90 | 3.36634 | ||||||||
\(21\) | 855.695 | − | 1419.41i | 0.423420 | − | 0.702359i | ||||
\(22\) | 4255.07i | 1.87435i | ||||||||
\(23\) | −2031.78 | − | 1519.28i | −0.800861 | − | 0.598850i | ||||
\(24\) | 2718.76 | − | 4509.82i | 0.963481 | − | 1.59820i | ||||
\(25\) | 5173.31 | 1.65546 | ||||||||
\(26\) | − | 3601.35i | − | 1.04480i | ||||||
\(27\) | −214.848 | + | 3781.90i | −0.0567182 | + | 0.998390i | ||||
\(28\) | 7028.45i | 1.69420i | ||||||||
\(29\) | − | 3057.54i | − | 0.675113i | −0.941305 | − | 0.337557i | \(-0.890400\pi\) | ||
0.941305 | − | 0.337557i | \(-0.109600\pi\) | |||||||
\(30\) | 7261.73 | − | 12045.6i | 1.47312 | − | 2.44357i | ||||
\(31\) | −6824.43 | −1.27545 | −0.637723 | − | 0.770266i | \(-0.720123\pi\) | ||||
−0.637723 | + | 0.770266i | \(0.720123\pi\) | |||||||
\(32\) | 1378.69i | 0.238009i | ||||||||
\(33\) | 5735.17 | + | 3457.47i | 0.916772 | + | 0.552679i | ||||
\(34\) | − | 17589.9i | − | 2.60955i | ||||||
\(35\) | 9685.36i | 1.33643i | ||||||||
\(36\) | −7499.90 | − | 14205.4i | −0.964494 | − | 1.82682i | ||||
\(37\) | − | 3538.10i | − | 0.424879i | −0.977174 | − | 0.212440i | \(-0.931859\pi\) | ||
0.977174 | − | 0.212440i | \(-0.0681409\pi\) | |||||||
\(38\) | −10963.9 | −1.23170 | ||||||||
\(39\) | −4854.06 | − | 2926.28i | −0.511026 | − | 0.308074i | ||||
\(40\) | 30772.9i | 3.04101i | ||||||||
\(41\) | 15552.1i | 1.44488i | 0.691436 | + | 0.722438i | \(0.256978\pi\) | ||||
−0.691436 | + | 0.722438i | \(0.743022\pi\) | |||||||
\(42\) | 14059.0 | + | 8475.52i | 1.22979 | + | 0.741383i | ||||
\(43\) | 15844.9i | 1.30683i | 0.757000 | + | 0.653415i | \(0.226664\pi\) | ||||
−0.757000 | + | 0.653415i | \(0.773336\pi\) | |||||||
\(44\) | −28398.7 | −2.21140 | ||||||||
\(45\) | −10335.0 | − | 19575.3i | −0.760818 | − | 1.44105i | ||||
\(46\) | 15048.2 | − | 20124.4i | 1.04855 | − | 1.40226i | ||||
\(47\) | − | 1848.69i | − | 0.122073i | −0.998136 | − | 0.0610365i | \(-0.980559\pi\) | ||
0.998136 | − | 0.0610365i | \(-0.0194406\pi\) | |||||||
\(48\) | 16428.4 | + | 9903.89i | 1.02918 | + | 0.620444i | ||||
\(49\) | 5502.74 | 0.327408 | ||||||||
\(50\) | 51240.8i | 2.89862i | ||||||||
\(51\) | −23708.4 | − | 14292.7i | −1.27637 | − | 0.769465i | ||||
\(52\) | 24035.7 | 1.23267 | ||||||||
\(53\) | −29357.1 | −1.43557 | −0.717784 | − | 0.696266i | \(-0.754843\pi\) | ||||
−0.717784 | + | 0.696266i | \(0.754843\pi\) | |||||||
\(54\) | −37459.0 | − | 2128.04i | −1.74812 | − | 0.0993104i | ||||
\(55\) | −39134.0 | −1.74441 | ||||||||
\(56\) | −35916.5 | −1.53047 | ||||||||
\(57\) | −8908.74 | + | 14777.6i | −0.363186 | + | 0.602445i | ||||
\(58\) | 30284.4 | 1.18208 | ||||||||
\(59\) | − | 17358.4i | − | 0.649200i | −0.945851 | − | 0.324600i | \(-0.894770\pi\) | ||
0.945851 | − | 0.324600i | \(-0.105230\pi\) | |||||||
\(60\) | 80393.3 | + | 48465.4i | 2.88298 | + | 1.73801i | ||||
\(61\) | − | 25278.1i | − | 0.869802i | −0.900478 | − | 0.434901i | \(-0.856783\pi\) | ||
0.900478 | − | 0.434901i | \(-0.143217\pi\) | |||||||
\(62\) | − | 67594.8i | − | 2.23323i | ||||||
\(63\) | 22847.3 | − | 12062.5i | 0.725244 | − | 0.382901i | ||||
\(64\) | 25722.7 | 0.784993 | ||||||||
\(65\) | 33121.8 | 0.972366 | ||||||||
\(66\) | −34245.6 | + | 56805.9i | −0.967710 | + | 1.60522i | ||||
\(67\) | 12342.5i | 0.335904i | 0.985795 | + | 0.167952i | \(0.0537153\pi\) | ||||
−0.985795 | + | 0.167952i | \(0.946285\pi\) | |||||||
\(68\) | 117396. | 3.07880 | ||||||||
\(69\) | −14897.2 | − | 36634.8i | −0.376687 | − | 0.926341i | ||||
\(70\) | −95931.9 | −2.34001 | ||||||||
\(71\) | 84587.6i | 1.99141i | 0.0925811 | + | 0.995705i | \(0.470488\pi\) | ||||
−0.0925811 | + | 0.995705i | \(0.529512\pi\) | |||||||
\(72\) | 72591.8 | − | 38325.7i | 1.65027 | − | 0.871283i | ||||
\(73\) | −8013.84 | −0.176008 | −0.0880042 | − | 0.996120i | \(-0.528049\pi\) | ||||
−0.0880042 | + | 0.996120i | \(0.528049\pi\) | |||||||
\(74\) | 35044.3 | 0.743940 | ||||||||
\(75\) | 69064.5 | + | 41635.8i | 1.41776 | + | 0.854700i | ||||
\(76\) | − | 73174.0i | − | 1.45319i | ||||||
\(77\) | − | 45675.2i | − | 0.877918i | ||||||
\(78\) | 28984.3 | − | 48078.6i | 0.539420 | − | 0.894778i | ||||
\(79\) | 66223.2i | 1.19383i | 0.802305 | + | 0.596915i | \(0.203607\pi\) | ||||
−0.802305 | + | 0.596915i | \(0.796393\pi\) | |||||||
\(80\) | −112099. | −1.95829 | ||||||||
\(81\) | −33305.7 | + | 48759.8i | −0.564035 | + | 0.825751i | ||||
\(82\) | −154041. | −2.52989 | ||||||||
\(83\) | −45004.7 | −0.717072 | −0.358536 | − | 0.933516i | \(-0.616724\pi\) | ||||
−0.358536 | + | 0.933516i | \(0.616724\pi\) | |||||||
\(84\) | −56566.3 | + | 93830.9i | −0.874701 | + | 1.45093i | ||||
\(85\) | 161775. | 2.42864 | ||||||||
\(86\) | −156941. | −2.28818 | ||||||||
\(87\) | 24607.6 | − | 40818.6i | 0.348555 | − | 0.578175i | ||||
\(88\) | − | 145122.i | − | 1.99768i | ||||||
\(89\) | 23975.3 | 0.320841 | 0.160420 | − | 0.987049i | \(-0.448715\pi\) | ||||
0.160420 | + | 0.987049i | \(0.448715\pi\) | |||||||
\(90\) | 193890. | − | 102367.i | 2.52319 | − | 1.33215i | ||||
\(91\) | 38658.0i | 0.489368i | ||||||||
\(92\) | 134312. | + | 100433.i | 1.65442 | + | 1.23710i | ||||
\(93\) | −91107.1 | − | 54924.3i | −1.09231 | − | 0.658502i | ||||
\(94\) | 18311.0 | 0.213743 | ||||||||
\(95\) | − | 100835.i | − | 1.14632i | ||||||
\(96\) | −11096.0 | + | 18405.8i | −0.122882 | + | 0.203834i | ||||
\(97\) | − | 96721.1i | − | 1.04374i | −0.853025 | − | 0.521869i | \(-0.825235\pi\) | ||
0.853025 | − | 0.521869i | \(-0.174765\pi\) | |||||||
\(98\) | 54503.7i | 0.573272i | ||||||||
\(99\) | 48739.1 | + | 92315.4i | 0.499792 | + | 0.946643i | ||||
\(100\) | −341985. | −3.41985 | ||||||||
\(101\) | − | 12371.5i | − | 0.120676i | −0.998178 | − | 0.0603378i | \(-0.980782\pi\) | ||
0.998178 | − | 0.0603378i | \(-0.0192178\pi\) | |||||||
\(102\) | 141567. | − | 234828.i | 1.34729 | − | 2.23485i | ||||
\(103\) | 177600.i | 1.64950i | 0.565501 | + | 0.824748i | \(0.308683\pi\) | ||||
−0.565501 | + | 0.824748i | \(0.691317\pi\) | |||||||
\(104\) | 122826.i | 1.11355i | ||||||||
\(105\) | −77949.6 | + | 129301.i | −0.689987 | + | 1.14453i | ||||
\(106\) | − | 290777.i | − | 2.51360i | ||||||
\(107\) | −77063.6 | −0.650713 | −0.325357 | − | 0.945591i | \(-0.605484\pi\) | ||||
−0.325357 | + | 0.945591i | \(0.605484\pi\) | |||||||
\(108\) | 14202.7 | − | 250005.i | 0.117169 | − | 2.06248i | ||||
\(109\) | 104977.i | 0.846304i | 0.906059 | + | 0.423152i | \(0.139076\pi\) | ||||
−0.906059 | + | 0.423152i | \(0.860924\pi\) | |||||||
\(110\) | − | 387616.i | − | 3.05436i | ||||||
\(111\) | 28475.3 | − | 47234.2i | 0.219362 | − | 0.363872i | ||||
\(112\) | − | 130836.i | − | 0.985562i | ||||||
\(113\) | 11275.6 | 0.0830702 | 0.0415351 | − | 0.999137i | \(-0.486775\pi\) | ||||
0.0415351 | + | 0.999137i | \(0.486775\pi\) | |||||||
\(114\) | −146370. | − | 88239.5i | −1.05485 | − | 0.635918i | ||||
\(115\) | 185085. | + | 138399.i | 1.30505 | + | 0.975860i | ||||
\(116\) | 202120.i | 1.39465i | ||||||||
\(117\) | −41251.1 | − | 78132.7i | −0.278594 | − | 0.527677i | ||||
\(118\) | 171931. | 1.13671 | ||||||||
\(119\) | 188815.i | 1.22228i | ||||||||
\(120\) | −247666. | + | 410823.i | −1.57005 | + | 2.60436i | ||||
\(121\) | 23501.4 | 0.145925 | ||||||||
\(122\) | 250376. | 1.52297 | ||||||||
\(123\) | −125167. | + | 207623.i | −0.745977 | + | 1.23741i | ||||
\(124\) | 451133. | 2.63482 | ||||||||
\(125\) | −186591. | −1.06811 | ||||||||
\(126\) | 119477. | + | 226299.i | 0.670438 | + | 1.26986i | ||||
\(127\) | 125559. | 0.690780 | 0.345390 | − | 0.938459i | \(-0.387747\pi\) | ||||
0.345390 | + | 0.938459i | \(0.387747\pi\) | |||||||
\(128\) | 298897.i | 1.61249i | ||||||||
\(129\) | −127523. | + | 211532.i | −0.674705 | + | 1.11919i | ||||
\(130\) | 328065.i | 1.70256i | ||||||||
\(131\) | − | 193572.i | − | 0.985518i | −0.870166 | − | 0.492759i | \(-0.835988\pi\) | ||
0.870166 | − | 0.492759i | \(-0.164012\pi\) | |||||||
\(132\) | −379127. | − | 228558.i | −1.89387 | − | 1.14173i | ||||
\(133\) | 117690. | 0.576913 | ||||||||
\(134\) | −122250. | −0.588148 | ||||||||
\(135\) | 19571.6 | − | 344512.i | 0.0924257 | − | 1.62693i | ||||
\(136\) | 599914.i | 2.78126i | ||||||||
\(137\) | 408836. | 1.86100 | 0.930502 | − | 0.366287i | \(-0.119371\pi\) | ||||
0.930502 | + | 0.366287i | \(0.119371\pi\) | |||||||
\(138\) | 362861. | − | 147554.i | 1.62197 | − | 0.659558i | ||||
\(139\) | 56526.6 | 0.248151 | 0.124076 | − | 0.992273i | \(-0.460403\pi\) | ||||
0.124076 | + | 0.992273i | \(0.460403\pi\) | |||||||
\(140\) | − | 640257.i | − | 2.76080i | ||||||
\(141\) | 14878.6 | − | 24680.3i | 0.0630253 | − | 0.104545i | ||||
\(142\) | −837826. | −3.48685 | ||||||||
\(143\) | −156199. | −0.638761 | ||||||||
\(144\) | 139613. | + | 264437.i | 0.561072 | + | 1.06271i | ||||
\(145\) | 278526.i | 1.10014i | ||||||||
\(146\) | − | 79375.7i | − | 0.308181i | ||||||
\(147\) | 73462.5 | + | 44287.1i | 0.280396 | + | 0.169038i | ||||
\(148\) | 233888.i | 0.877716i | ||||||||
\(149\) | −22027.5 | −0.0812831 | −0.0406416 | − | 0.999174i | \(-0.512940\pi\) | ||||
−0.0406416 | + | 0.999174i | \(0.512940\pi\) | |||||||
\(150\) | −412395. | + | 684072.i | −1.49653 | + | 2.48241i | ||||
\(151\) | 188664. | 0.673359 | 0.336679 | − | 0.941619i | \(-0.390696\pi\) | ||||
0.336679 | + | 0.941619i | \(0.390696\pi\) | |||||||
\(152\) | 373931. | 1.31275 | ||||||||
\(153\) | −201481. | − | 381619.i | −0.695832 | − | 1.31796i | ||||
\(154\) | 452405. | 1.53718 | ||||||||
\(155\) | 621672. | 2.07841 | ||||||||
\(156\) | 320880. | + | 193444.i | 1.05568 | + | 0.636420i | ||||
\(157\) | − | 347055.i | − | 1.12370i | −0.827240 | − | 0.561848i | \(-0.810091\pi\) | ||
0.827240 | − | 0.561848i | \(-0.189909\pi\) | |||||||
\(158\) | −655929. | −2.09033 | ||||||||
\(159\) | −391922. | − | 236272.i | −1.22944 | − | 0.741171i | ||||
\(160\) | − | 125592.i | − | 0.387849i | ||||||
\(161\) | −161532. | + | 216022.i | −0.491127 | + | 0.656800i | ||||
\(162\) | −482957. | − | 329887.i | −1.44584 | − | 0.987592i | ||||
\(163\) | −313519. | −0.924262 | −0.462131 | − | 0.886812i | \(-0.652915\pi\) | ||||
−0.462131 | + | 0.886812i | \(0.652915\pi\) | |||||||
\(164\) | − | 1.02808e6i | − | 2.98483i | ||||||
\(165\) | −522446. | − | 314958.i | −1.49393 | − | 0.900623i | ||||
\(166\) | − | 445764.i | − | 1.25555i | ||||||
\(167\) | − | 521073.i | − | 1.44580i | −0.690954 | − | 0.722899i | \(-0.742809\pi\) | ||
0.690954 | − | 0.722899i | \(-0.257191\pi\) | |||||||
\(168\) | −479491. | − | 289063.i | −1.31071 | − | 0.790167i | ||||
\(169\) | −239091. | −0.643943 | ||||||||
\(170\) | 1.60235e6i | 4.25241i | ||||||||
\(171\) | −237866. | + | 125584.i | −0.622074 | + | 0.328432i | ||||
\(172\) | − | 1.04744e6i | − | 2.69965i | ||||||
\(173\) | 246126.i | 0.625234i | 0.949879 | + | 0.312617i | \(0.101206\pi\) | ||||
−0.949879 | + | 0.312617i | \(0.898794\pi\) | |||||||
\(174\) | 404301. | + | 243734.i | 1.01235 | + | 0.610300i | ||||
\(175\) | − | 550034.i | − | 1.35767i | ||||||
\(176\) | 528649. | 1.28643 | ||||||||
\(177\) | 139703. | − | 231737.i | 0.335176 | − | 0.555983i | ||||
\(178\) | 237472.i | 0.561774i | ||||||||
\(179\) | − | 109168.i | − | 0.254661i | −0.991860 | − | 0.127330i | \(-0.959359\pi\) | ||
0.991860 | − | 0.127330i | \(-0.0406409\pi\) | |||||||
\(180\) | 683204. | + | 1.29404e6i | 1.57170 | + | 2.97692i | ||||
\(181\) | 578258.i | 1.31197i | 0.754773 | + | 0.655986i | \(0.227747\pi\) | ||||
−0.754773 | + | 0.655986i | \(0.772253\pi\) | |||||||
\(182\) | −382901. | −0.856856 | ||||||||
\(183\) | 203443. | − | 337467.i | 0.449072 | − | 0.744910i | ||||
\(184\) | −513228. | + | 686357.i | −1.11755 | + | 1.49453i | ||||
\(185\) | 322303.i | 0.692366i | ||||||||
\(186\) | 544015. | − | 902401.i | 1.15300 | − | 1.91257i | ||||
\(187\) | −762914. | −1.59541 | ||||||||
\(188\) | 122209.i | 0.252179i | ||||||||
\(189\) | 402097. | + | 22843.0i | 0.818797 | + | 0.0465156i | ||||
\(190\) | 998757. | 2.00713 | ||||||||
\(191\) | 432293. | 0.857422 | 0.428711 | − | 0.903442i | \(-0.358968\pi\) | ||||
0.428711 | + | 0.903442i | \(0.358968\pi\) | |||||||
\(192\) | 343401. | + | 207021.i | 0.672278 | + | 0.405285i | ||||
\(193\) | 59028.8 | 0.114070 | 0.0570349 | − | 0.998372i | \(-0.481835\pi\) | ||||
0.0570349 | + | 0.998372i | \(0.481835\pi\) | |||||||
\(194\) | 958006. | 1.82753 | ||||||||
\(195\) | 442181. | + | 266570.i | 0.832747 | + | 0.502024i | ||||
\(196\) | −363762. | −0.676359 | ||||||||
\(197\) | 102969.i | 0.189035i | 0.995523 | + | 0.0945173i | \(0.0301308\pi\) | ||||
−0.995523 | + | 0.0945173i | \(0.969869\pi\) | |||||||
\(198\) | −914369. | + | 482752.i | −1.65752 | + | 0.875107i | ||||
\(199\) | − | 441031.i | − | 0.789471i | −0.918795 | − | 0.394735i | \(-0.870836\pi\) | ||
0.918795 | − | 0.394735i | \(-0.129164\pi\) | |||||||
\(200\) | − | 1.74760e6i | − | 3.08935i | ||||||
\(201\) | −99334.5 | + | 164774.i | −0.173424 | + | 0.287672i | ||||
\(202\) | 122538. | 0.211296 | ||||||||
\(203\) | −325082. | −0.553672 | ||||||||
\(204\) | 1.56726e6 | + | 944827.i | 2.63673 | + | 1.58956i | ||||
\(205\) | − | 1.41672e6i | − | 2.35451i | ||||||
\(206\) | −1.75910e6 | −2.88817 | ||||||||
\(207\) | 95964.0 | − | 608975.i | 0.155662 | − | 0.987810i | ||||
\(208\) | −447431. | −0.717080 | ||||||||
\(209\) | 475530.i | 0.753030i | ||||||||
\(210\) | −1.28071e6 | − | 772078.i | −2.00402 | − | 1.20813i | ||||
\(211\) | −108642. | −0.167993 | −0.0839967 | − | 0.996466i | \(-0.526769\pi\) | ||||
−0.0839967 | + | 0.996466i | \(0.526769\pi\) | |||||||
\(212\) | 1.94067e6 | 2.96560 | ||||||||
\(213\) | −680777. | + | 1.12926e6i | −1.02815 | + | 1.70547i | ||||
\(214\) | − | 763301.i | − | 1.13936i | ||||||
\(215\) | − | 1.44339e6i | − | 2.12956i | ||||||
\(216\) | 1.27756e6 | + | 72578.0i | 1.86315 | + | 0.105845i | ||||
\(217\) | 725583.i | 1.04601i | ||||||||
\(218\) | −1.03978e6 | −1.48183 | ||||||||
\(219\) | −106986. | − | 64496.9i | −0.150736 | − | 0.0908716i | ||||
\(220\) | 2.58698e6 | 3.60360 | ||||||||
\(221\) | 645705. | 0.889311 | ||||||||
\(222\) | 467846. | + | 282043.i | 0.637119 | + | 0.384090i | ||||
\(223\) | −210918. | −0.284021 | −0.142011 | − | 0.989865i | \(-0.545357\pi\) | ||||
−0.142011 | + | 0.989865i | \(0.545357\pi\) | |||||||
\(224\) | 146585. | 0.195195 | ||||||||
\(225\) | 586930. | + | 1.11169e6i | 0.772911 | + | 1.46395i | ||||
\(226\) | 111683.i | 0.145451i | ||||||||
\(227\) | 146307. | 0.188452 | 0.0942260 | − | 0.995551i | \(-0.469962\pi\) | ||||
0.0942260 | + | 0.995551i | \(0.469962\pi\) | |||||||
\(228\) | 588918. | − | 976884.i | 0.750270 | − | 1.24453i | ||||
\(229\) | 1.11197e6i | 1.40122i | 0.713547 | + | 0.700608i | \(0.247088\pi\) | ||||
−0.713547 | + | 0.700608i | \(0.752912\pi\) | |||||||
\(230\) | −1.37082e6 | + | 1.83324e6i | −1.70868 | + | 2.28507i | ||||
\(231\) | 367603. | − | 609772.i | 0.453262 | − | 0.751861i | ||||
\(232\) | −1.03287e6 | −1.25987 | ||||||||
\(233\) | − | 1.34569e6i | − | 1.62389i | −0.583734 | − | 0.811945i | \(-0.698409\pi\) | ||
0.583734 | − | 0.811945i | \(-0.301591\pi\) | |||||||
\(234\) | 773891. | − | 408585.i | 0.923932 | − | 0.487801i | ||||
\(235\) | 168407.i | 0.198925i | ||||||||
\(236\) | 1.14748e6i | 1.34112i | ||||||||
\(237\) | −532976. | + | 884089.i | −0.616364 | + | 1.02241i | ||||
\(238\) | −1.87018e6 | −2.14014 | ||||||||
\(239\) | − | 95336.4i | − | 0.107960i | −0.998542 | − | 0.0539802i | \(-0.982809\pi\) | ||
0.998542 | − | 0.0539802i | \(-0.0171908\pi\) | |||||||
\(240\) | −1.49654e6 | − | 902196.i | −1.67711 | − | 1.01105i | ||||
\(241\) | − | 171943.i | − | 0.190696i | −0.995444 | − | 0.0953481i | \(-0.969604\pi\) | ||
0.995444 | − | 0.0953481i | \(-0.0303964\pi\) | |||||||
\(242\) | 232778.i | 0.255507i | ||||||||
\(243\) | −837064. | + | 382900.i | −0.909375 | + | 0.415978i | ||||
\(244\) | 1.67103e6i | 1.79684i | ||||||||
\(245\) | −501273. | −0.533530 | ||||||||
\(246\) | −2.05647e6 | − | 1.23975e6i | −2.16663 | − | 1.30616i | ||||
\(247\) | − | 402473.i | − | 0.419753i | ||||||
\(248\) | 2.30536e6i | 2.38018i | ||||||||
\(249\) | −600820. | − | 362206.i | −0.614110 | − | 0.370218i | ||||
\(250\) | − | 1.84815e6i | − | 1.87020i | ||||||
\(251\) | 510614. | 0.511574 | 0.255787 | − | 0.966733i | \(-0.417665\pi\) | ||||
0.255787 | + | 0.966733i | \(0.417665\pi\) | |||||||
\(252\) | −1.51034e6 | + | 797401.i | −1.49821 | + | 0.790998i | ||||
\(253\) | −872844. | − | 652675.i | −0.857305 | − | 0.641056i | ||||
\(254\) | 1.24364e6i | 1.20952i | ||||||||
\(255\) | 2.15972e6 | + | 1.30199e6i | 2.07992 | + | 1.25389i | ||||
\(256\) | −2.13740e6 | −2.03838 | ||||||||
\(257\) | − | 1.06311e6i | − | 1.00403i | −0.864860 | − | 0.502013i | \(-0.832593\pi\) | ||
0.864860 | − | 0.502013i | \(-0.167407\pi\) | |||||||
\(258\) | −2.09519e6 | − | 1.26309e6i | −1.95963 | − | 1.18137i | ||||
\(259\) | −376176. | −0.348451 | ||||||||
\(260\) | −2.18953e6 | −2.00872 | ||||||||
\(261\) | 657031. | − | 346888.i | 0.597014 | − | 0.315201i | ||||
\(262\) | 1.91730e6 | 1.72559 | ||||||||
\(263\) | 868216. | 0.773995 | 0.386998 | − | 0.922081i | \(-0.373512\pi\) | ||||
0.386998 | + | 0.922081i | \(0.373512\pi\) | |||||||
\(264\) | 1.16797e6 | − | 1.93740e6i | 1.03139 | − | 1.71084i | ||||
\(265\) | 2.67429e6 | 2.33934 | ||||||||
\(266\) | 1.16570e6i | 1.01014i | ||||||||
\(267\) | 320074. | + | 192958.i | 0.274772 | + | 0.165647i | ||||
\(268\) | − | 815907.i | − | 0.693911i | ||||||
\(269\) | − | 169298.i | − | 0.142650i | −0.997453 | − | 0.0713251i | \(-0.977277\pi\) | ||
0.997453 | − | 0.0713251i | \(-0.0227228\pi\) | |||||||
\(270\) | 3.41233e6 | + | 193854.i | 2.84867 | + | 0.161832i | ||||
\(271\) | −2.33325e6 | −1.92992 | −0.964959 | − | 0.262400i | \(-0.915486\pi\) | ||||
−0.964959 | + | 0.262400i | \(0.915486\pi\) | |||||||
\(272\) | −2.18536e6 | −1.79102 | ||||||||
\(273\) | −311127. | + | 516090.i | −0.252657 | + | 0.419101i | ||||
\(274\) | 4.04945e6i | 3.25851i | ||||||||
\(275\) | 2.22243e6 | 1.77214 | ||||||||
\(276\) | 984786. | + | 2.42176e6i | 0.778161 | + | 1.91364i | ||||
\(277\) | 942252. | 0.737849 | 0.368925 | − | 0.929459i | \(-0.379726\pi\) | ||||
0.368925 | + | 0.929459i | \(0.379726\pi\) | |||||||
\(278\) | 559887.i | 0.434498i | ||||||||
\(279\) | −774254. | − | 1.46649e6i | −0.595488 | − | 1.12790i | ||||
\(280\) | 3.27182e6 | 2.49399 | ||||||||
\(281\) | −1.20393e6 | −0.909567 | −0.454783 | − | 0.890602i | \(-0.650283\pi\) | ||||
−0.454783 | + | 0.890602i | \(0.650283\pi\) | |||||||
\(282\) | 244454. | + | 147370.i | 0.183052 | + | 0.110354i | ||||
\(283\) | 1.82107e6i | 1.35164i | 0.737067 | + | 0.675820i | \(0.236210\pi\) | ||||
−0.737067 | + | 0.675820i | \(0.763790\pi\) | |||||||
\(284\) | − | 5.59172e6i | − | 4.11386i | ||||||
\(285\) | 811542. | − | 1.34617e6i | 0.591833 | − | 0.981719i | ||||
\(286\) | − | 1.54712e6i | − | 1.11843i | ||||||
\(287\) | 1.65353e6 | 1.18497 | ||||||||
\(288\) | −296266. | + | 156417.i | −0.210475 | + | 0.111123i | ||||
\(289\) | 1.73393e6 | 1.22120 | ||||||||
\(290\) | −2.75876e6 | −1.92628 | ||||||||
\(291\) | 778429. | − | 1.29124e6i | 0.538873 | − | 0.893871i | ||||
\(292\) | 529760. | 0.363598 | ||||||||
\(293\) | −1.56595e6 | −1.06563 | −0.532816 | − | 0.846231i | \(-0.678866\pi\) | ||||
−0.532816 | + | 0.846231i | \(0.678866\pi\) | |||||||
\(294\) | −438656. | + | 727633.i | −0.295976 | + | 0.490958i | ||||
\(295\) | 1.58126e6i | 1.05791i | ||||||||
\(296\) | −1.19521e6 | −0.792891 | ||||||||
\(297\) | −92297.9 | + | 1.62469e6i | −0.0607157 | + | 1.06876i | ||||
\(298\) | − | 218179.i | − | 0.142322i | ||||||
\(299\) | 738746. | + | 552403.i | 0.477878 | + | 0.357337i | ||||
\(300\) | −4.56555e6 | − | 2.75236e6i | −2.92880 | − | 1.76564i | ||||
\(301\) | 1.68466e6 | 1.07175 | ||||||||
\(302\) | 1.86868e6i | 1.17901i | ||||||||
\(303\) | 99568.3 | − | 165162.i | 0.0623038 | − | 0.103348i | ||||
\(304\) | 1.36215e6i | 0.845361i | ||||||||
\(305\) | 2.30271e6i | 1.41739i | ||||||||
\(306\) | 3.77987e6 | − | 1.99563e6i | 2.30767 | − | 1.21836i | ||||
\(307\) | 118971. | 0.0720435 | 0.0360218 | − | 0.999351i | \(-0.488531\pi\) | ||||
0.0360218 | + | 0.999351i | \(0.488531\pi\) | |||||||
\(308\) | 3.01939e6i | 1.81360i | ||||||||
\(309\) | −1.42936e6 | + | 2.37099e6i | −0.851620 | + | 1.41265i | ||||
\(310\) | 6.15755e6i | 3.63918i | ||||||||
\(311\) | 1.39044e6i | 0.815175i | 0.913166 | + | 0.407587i | \(0.133630\pi\) | ||||
−0.913166 | + | 0.407587i | \(0.866370\pi\) | |||||||
\(312\) | −988529. | + | 1.63975e6i | −0.574914 | + | 0.953655i | ||||
\(313\) | − | 2.09007e6i | − | 1.20587i | −0.797792 | − | 0.602933i | \(-0.793999\pi\) | ||
0.797792 | − | 0.602933i | \(-0.206001\pi\) | |||||||
\(314\) | 3.43752e6 | 1.96753 | ||||||||
\(315\) | −2.08128e6 | + | 1.09884e6i | −1.18183 | + | 0.623960i | ||||
\(316\) | − | 4.37772e6i | − | 2.46621i | ||||||
\(317\) | 204837.i | 0.114488i | 0.998360 | + | 0.0572440i | \(0.0182313\pi\) | ||||
−0.998360 | + | 0.0572440i | \(0.981769\pi\) | |||||||
\(318\) | 2.34023e6 | − | 3.88192e6i | 1.29775 | − | 2.15268i | ||||
\(319\) | − | 1.31350e6i | − | 0.722694i | ||||||
\(320\) | −2.34321e6 | −1.27919 | ||||||||
\(321\) | −1.02881e6 | − | 620222.i | −0.557279 | − | 0.335958i | ||||
\(322\) | −2.13966e6 | − | 1.59995e6i | −1.15002 | − | 0.859935i | ||||
\(323\) | − | 1.96578e6i | − | 1.04840i | ||||||
\(324\) | 2.20169e6 | − | 3.22330e6i | 1.16518 | − | 1.70584i | ||||
\(325\) | −1.88099e6 | −0.987822 | ||||||||
\(326\) | − | 3.10535e6i | − | 1.61833i | ||||||
\(327\) | −844871. | + | 1.40145e6i | −0.436939 | + | 0.724786i | ||||
\(328\) | 5.25367e6 | 2.69636 | ||||||||
\(329\) | −196556. | −0.100114 | ||||||||
\(330\) | 3.11961e6 | − | 5.17473e6i | 1.57694 | − | 2.61579i | ||||
\(331\) | −3.31167e6 | −1.66141 | −0.830706 | − | 0.556711i | \(-0.812063\pi\) | ||||
−0.830706 | + | 0.556711i | \(0.812063\pi\) | |||||||
\(332\) | 2.97507e6 | 1.48133 | ||||||||
\(333\) | 760299. | − | 401409.i | 0.375728 | − | 0.198370i | ||||
\(334\) | 5.16114e6 | 2.53151 | ||||||||
\(335\) | − | 1.12434e6i | − | 0.547375i | ||||||
\(336\) | 1.05300e6 | − | 1.74669e6i | 0.508837 | − | 0.844048i | ||||
\(337\) | 2.72902e6i | 1.30898i | 0.756072 | + | 0.654489i | \(0.227116\pi\) | ||||
−0.756072 | + | 0.654489i | \(0.772884\pi\) | |||||||
\(338\) | − | 2.36816e6i | − | 1.12751i | ||||||
\(339\) | 150532. | + | 90748.5i | 0.0711424 | + | 0.0428885i | ||||
\(340\) | −1.06942e7 | −5.01709 | ||||||||
\(341\) | −2.93174e6 | −1.36534 | ||||||||
\(342\) | −1.24389e6 | − | 2.35602e6i | −0.575065 | − | 1.08922i | ||||
\(343\) | − | 2.37200e6i | − | 1.08863i | ||||||
\(344\) | 5.35258e6 | 2.43875 | ||||||||
\(345\) | 1.35706e6 | + | 3.33725e6i | 0.613834 | + | 1.50953i | ||||
\(346\) | −2.43784e6 | −1.09475 | ||||||||
\(347\) | − | 366434.i | − | 0.163370i | −0.996658 | − | 0.0816849i | \(-0.973970\pi\) | ||
0.996658 | − | 0.0816849i | \(-0.0260301\pi\) | |||||||
\(348\) | −1.62670e6 | + | 2.69834e6i | −0.720045 | + | 1.19440i | ||||
\(349\) | −1.55226e6 | −0.682184 | −0.341092 | − | 0.940030i | \(-0.610797\pi\) | ||||
−0.341092 | + | 0.940030i | \(0.610797\pi\) | |||||||
\(350\) | 5.44799e6 | 2.37720 | ||||||||
\(351\) | 78117.9 | − | 1.37508e6i | 0.0338441 | − | 0.595745i | ||||
\(352\) | 592281.i | 0.254783i | ||||||||
\(353\) | 1.97096e6i | 0.841860i | 0.907093 | + | 0.420930i | \(0.138296\pi\) | ||||
−0.907093 | + | 0.420930i | \(0.861704\pi\) | |||||||
\(354\) | 2.29531e6 | + | 1.38374e6i | 0.973495 | + | 0.586875i | ||||
\(355\) | − | 7.70551e6i | − | 3.24512i | ||||||
\(356\) | −1.58490e6 | −0.662793 | ||||||||
\(357\) | −1.51962e6 | + | 2.52071e6i | −0.631051 | + | 1.04677i | ||||
\(358\) | 1.08129e6 | 0.445897 | ||||||||
\(359\) | 988239. | 0.404693 | 0.202347 | − | 0.979314i | \(-0.435143\pi\) | ||||
0.202347 | + | 0.979314i | \(0.435143\pi\) | |||||||
\(360\) | −6.61275e6 | + | 3.49128e6i | −2.68922 | + | 1.41981i | ||||
\(361\) | 1.25082e6 | 0.505156 | ||||||||
\(362\) | −5.72754e6 | −2.29719 | ||||||||
\(363\) | 313748. | + | 189144.i | 0.124972 | + | 0.0753400i | ||||
\(364\) | − | 2.55551e6i | − | 1.01094i | ||||||
\(365\) | 730021. | 0.286816 | ||||||||
\(366\) | 3.34255e6 | + | 2.01507e6i | 1.30429 | + | 0.786299i | ||||
\(367\) | − | 1.66563e6i | − | 0.645526i | −0.946480 | − | 0.322763i | \(-0.895388\pi\) | ||
0.946480 | − | 0.322763i | \(-0.104612\pi\) | |||||||
\(368\) | −2.50026e6 | − | 1.86958e6i | −0.962421 | − | 0.719657i | ||||
\(369\) | −3.34199e6 | + | 1.76444e6i | −1.27773 | + | 0.674592i | ||||
\(370\) | −3.19236e6 | −1.21229 | ||||||||
\(371\) | 3.12129e6i | 1.17733i | ||||||||
\(372\) | 6.02270e6 | + | 3.63080e6i | 2.25649 | + | 1.36033i | ||||
\(373\) | − | 749868.i | − | 0.279070i | −0.990217 | − | 0.139535i | \(-0.955439\pi\) | ||
0.990217 | − | 0.139535i | \(-0.0445607\pi\) | |||||||
\(374\) | − | 7.55654e6i | − | 2.79347i | ||||||
\(375\) | −2.49102e6 | − | 1.50172e6i | −0.914743 | − | 0.551456i | ||||
\(376\) | −624507. | −0.227807 | ||||||||
\(377\) | 1.11171e6i | 0.402844i | ||||||||
\(378\) | −226256. | + | 3.98270e6i | −0.0814462 | + | 1.43367i | ||||
\(379\) | − | 1.95458e6i | − | 0.698966i | −0.936943 | − | 0.349483i | \(-0.886357\pi\) | ||
0.936943 | − | 0.349483i | \(-0.113643\pi\) | |||||||
\(380\) | 6.66579e6i | 2.36806i | ||||||||
\(381\) | 1.67624e6 | + | 1.01053e6i | 0.591593 | + | 0.356644i | ||||
\(382\) | 4.28179e6i | 1.50130i | ||||||||
\(383\) | −1.10006e6 | −0.383195 | −0.191597 | − | 0.981474i | \(-0.561367\pi\) | ||||
−0.191597 | + | 0.981474i | \(0.561367\pi\) | |||||||
\(384\) | −2.40558e6 | + | 3.99032e6i | −0.832513 | + | 1.38095i | ||||
\(385\) | 4.16079e6i | 1.43062i | ||||||||
\(386\) | 584670.i | 0.199730i | ||||||||
\(387\) | −3.40490e6 | + | 1.79766e6i | −1.15565 | + | 0.610141i | ||||
\(388\) | 6.39381e6i | 2.15616i | ||||||||
\(389\) | 4.15611e6 | 1.39256 | 0.696278 | − | 0.717772i | \(-0.254838\pi\) | ||||
0.696278 | + | 0.717772i | \(0.254838\pi\) | |||||||
\(390\) | −2.64033e6 | + | 4.37972e6i | −0.879016 | + | 1.45809i | ||||
\(391\) | 3.60822e6 | + | 2.69807e6i | 1.19358 | + | 0.892507i | ||||
\(392\) | − | 1.85888e6i | − | 0.610994i | ||||||
\(393\) | 1.55790e6 | − | 2.58422e6i | 0.508814 | − | 0.844010i | ||||
\(394\) | −1.01989e6 | −0.330989 | ||||||||
\(395\) | − | 6.03260e6i | − | 1.94541i | ||||||
\(396\) | −3.22193e6 | − | 6.10257e6i | −1.03247 | − | 1.95558i | ||||
\(397\) | −2.25716e6 | −0.718763 | −0.359382 | − | 0.933191i | \(-0.617012\pi\) | ||||
−0.359382 | + | 0.933191i | \(0.617012\pi\) | |||||||
\(398\) | 4.36833e6 | 1.38232 | ||||||||
\(399\) | 1.57118e6 | + | 947190.i | 0.494076 | + | 0.297855i | ||||
\(400\) | 6.36614e6 | 1.98942 | ||||||||
\(401\) | −3.44745e6 | −1.07063 | −0.535313 | − | 0.844654i | \(-0.679806\pi\) | ||||
−0.535313 | + | 0.844654i | \(0.679806\pi\) | |||||||
\(402\) | −1.63206e6 | − | 983891.i | −0.503698 | − | 0.303656i | ||||
\(403\) | 2.48133e6 | 0.761065 | ||||||||
\(404\) | 817827.i | 0.249292i | ||||||||
\(405\) | 3.03398e6 | − | 4.44178e6i | 0.919127 | − | 1.34561i | ||||
\(406\) | − | 3.21988e6i | − | 0.969448i | ||||||
\(407\) | − | 1.51995e6i | − | 0.454824i | ||||||
\(408\) | −4.82822e6 | + | 8.00895e6i | −1.43594 | + | 2.38191i | ||||
\(409\) | −3.68766e6 | −1.09004 | −0.545021 | − | 0.838422i | \(-0.683478\pi\) | ||||
−0.545021 | + | 0.838422i | \(0.683478\pi\) | |||||||
\(410\) | 1.40324e7 | 4.12261 | ||||||||
\(411\) | 5.45802e6 | + | 3.29039e6i | 1.59379 | + | 0.960821i | ||||
\(412\) | − | 1.17404e7i | − | 3.40753i | ||||||
\(413\) | −1.84557e6 | −0.532420 | ||||||||
\(414\) | 6.03179e6 | + | 950507.i | 1.72960 | + | 0.272555i | ||||
\(415\) | 4.09971e6 | 1.16851 | ||||||||
\(416\) | − | 501287.i | − | 0.142021i | ||||||
\(417\) | 754639. | + | 454937.i | 0.212520 | + | 0.128118i | ||||
\(418\) | −4.71004e6 | −1.31851 | ||||||||
\(419\) | −4.00739e6 | −1.11513 | −0.557566 | − | 0.830132i | \(-0.688265\pi\) | ||||
−0.557566 | + | 0.830132i | \(0.688265\pi\) | |||||||
\(420\) | 5.15291e6 | − | 8.54753e6i | 1.42538 | − | 2.36438i | ||||
\(421\) | − | 735310.i | − | 0.202192i | −0.994877 | − | 0.101096i | \(-0.967765\pi\) | ||
0.994877 | − | 0.101096i | \(-0.0322350\pi\) | |||||||
\(422\) | − | 1.07608e6i | − | 0.294147i | ||||||
\(423\) | 397264. | − | 209740.i | 0.107951 | − | 0.0569942i | ||||
\(424\) | 9.91714e6i | 2.67899i | ||||||||
\(425\) | −9.18723e6 | −2.46725 | ||||||||
\(426\) | −1.11851e7 | − | 6.74298e6i | −2.98618 | − | 1.80023i | ||||
\(427\) | −2.68761e6 | −0.713340 | ||||||||
\(428\) | 5.09434e6 | 1.34424 | ||||||||
\(429\) | −2.08528e6 | − | 1.25712e6i | −0.547043 | − | 0.329787i | ||||
\(430\) | 1.42966e7 | 3.72873 | ||||||||
\(431\) | 5.54306e6 | 1.43733 | 0.718664 | − | 0.695357i | \(-0.244754\pi\) | ||||
0.718664 | + | 0.695357i | \(0.244754\pi\) | |||||||
\(432\) | −264387. | + | 4.65391e6i | −0.0681602 | + | 1.19980i | ||||
\(433\) | 2.50040e6i | 0.640898i | 0.947266 | + | 0.320449i | \(0.103834\pi\) | ||||
−0.947266 | + | 0.320449i | \(0.896166\pi\) | |||||||
\(434\) | −7.18678e6 | −1.83151 | ||||||||
\(435\) | −2.24163e6 | + | 3.71837e6i | −0.567991 | + | 0.942171i | ||||
\(436\) | − | 6.93954e6i | − | 1.74830i | ||||||
\(437\) | 1.68173e6 | − | 2.24903e6i | 0.421262 | − | 0.563367i | ||||
\(438\) | 638830. | − | 1.05968e6i | 0.159111 | − | 0.263930i | ||||
\(439\) | −2.72593e6 | −0.675076 | −0.337538 | − | 0.941312i | \(-0.609594\pi\) | ||||
−0.337538 | + | 0.941312i | \(0.609594\pi\) | |||||||
\(440\) | 1.32199e7i | 3.25534i | ||||||||
\(441\) | 624304. | + | 1.18248e6i | 0.152862 | + | 0.289532i | ||||
\(442\) | 6.39560e6i | 1.55713i | ||||||||
\(443\) | 3.79610e6i | 0.919027i | 0.888171 | + | 0.459513i | \(0.151976\pi\) | ||||
−0.888171 | + | 0.459513i | \(0.848024\pi\) | |||||||
\(444\) | −1.88238e6 | + | 3.12244e6i | −0.453157 | + | 0.751688i | ||||
\(445\) | −2.18403e6 | −0.522829 | ||||||||
\(446\) | − | 2.08910e6i | − | 0.497305i | ||||||
\(447\) | −294071. | − | 177282.i | −0.0696119 | − | 0.0419658i | ||||
\(448\) | − | 2.73487e6i | − | 0.643786i | ||||||
\(449\) | − | 926346.i | − | 0.216849i | −0.994105 | − | 0.108424i | \(-0.965419\pi\) | ||
0.994105 | − | 0.108424i | \(-0.0345806\pi\) | |||||||
\(450\) | −1.10111e7 | + | 5.81344e6i | −2.56330 | + | 1.35332i | ||||
\(451\) | 6.68113e6i | 1.54671i | ||||||||
\(452\) | −745384. | −0.171607 | ||||||||
\(453\) | 2.51869e6 | + | 1.51840e6i | 0.576673 | + | 0.347649i | ||||
\(454\) | 1.44915e6i | 0.329969i | ||||||||
\(455\) | − | 3.52155e6i | − | 0.797454i | ||||||
\(456\) | 4.99203e6 | + | 3.00947e6i | 1.12426 | + | 0.677762i | ||||
\(457\) | − | 4.48757e6i | − | 1.00513i | −0.864541 | − | 0.502563i | \(-0.832391\pi\) | ||
0.864541 | − | 0.502563i | \(-0.167609\pi\) | |||||||
\(458\) | −1.10139e7 | −2.45345 | ||||||||
\(459\) | 381547. | − | 6.71623e6i | 0.0845311 | − | 1.48797i | ||||
\(460\) | −1.22352e7 | − | 9.14894e6i | −2.69597 | − | 2.01593i | ||||
\(461\) | 1.17047e6i | 0.256512i | 0.991741 | + | 0.128256i | \(0.0409380\pi\) | ||||
−0.991741 | + | 0.128256i | \(0.959062\pi\) | |||||||
\(462\) | 6.03968e6 | + | 3.64104e6i | 1.31646 | + | 0.793635i | ||||
\(463\) | −710023. | −0.153929 | −0.0769644 | − | 0.997034i | \(-0.524523\pi\) | ||||
−0.0769644 | + | 0.997034i | \(0.524523\pi\) | |||||||
\(464\) | − | 3.76252e6i | − | 0.811305i | ||||||
\(465\) | 8.29941e6 | + | 5.00333e6i | 1.77998 | + | 1.07307i | ||||
\(466\) | 1.33289e7 | 2.84334 | ||||||||
\(467\) | −1.07076e6 | −0.227195 | −0.113597 | − | 0.993527i | \(-0.536237\pi\) | ||||
−0.113597 | + | 0.993527i | \(0.536237\pi\) | |||||||
\(468\) | 2.72693e6 | + | 5.16501e6i | 0.575519 | + | 1.09008i | ||||
\(469\) | 1.31227e6 | 0.275481 | ||||||||
\(470\) | −1.66804e6 | −0.348307 | ||||||||
\(471\) | 2.79316e6 | − | 4.63324e6i | 0.580155 | − | 0.962348i | ||||
\(472\) | −5.86383e6 | −1.21151 | ||||||||
\(473\) | 6.80691e6i | 1.39893i | ||||||||
\(474\) | −8.75675e6 | − | 5.27904e6i | −1.79018 | − | 1.07922i | ||||
\(475\) | 5.72647e6i | 1.16454i | ||||||||
\(476\) | − | 1.24817e7i | − | 2.52498i | ||||||
\(477\) | −3.33066e6 | − | 6.30852e6i | −0.670247 | − | 1.26950i | ||||
\(478\) | 944291. | 0.189032 | ||||||||
\(479\) | 318202. | 0.0633671 | 0.0316835 | − | 0.999498i | \(-0.489913\pi\) | ||||
0.0316835 | + | 0.999498i | \(0.489913\pi\) | |||||||
\(480\) | 1.01079e6 | − | 1.67668e6i | 0.200243 | − | 0.332159i | ||||
\(481\) | 1.28644e6i | 0.253528i | ||||||||
\(482\) | 1.70307e6 | 0.333898 | ||||||||
\(483\) | −3.89506e6 | + | 1.58389e6i | −0.759708 | + | 0.308928i | ||||
\(484\) | −1.55358e6 | −0.301453 | ||||||||
\(485\) | 8.81081e6i | 1.70083i | ||||||||
\(486\) | −3.79256e6 | − | 8.29097e6i | −0.728353 | − | 1.59226i | ||||
\(487\) | −1.94918e6 | −0.372417 | −0.186209 | − | 0.982510i | \(-0.559620\pi\) | ||||
−0.186209 | + | 0.982510i | \(0.559620\pi\) | |||||||
\(488\) | −8.53922e6 | −1.62319 | ||||||||
\(489\) | −4.18553e6 | − | 2.52326e6i | −0.791550 | − | 0.477189i | ||||
\(490\) | − | 4.96502e6i | − | 0.934180i | ||||||
\(491\) | 9.83002e6i | 1.84014i | 0.391754 | + | 0.920070i | \(0.371868\pi\) | ||||
−0.391754 | + | 0.920070i | \(0.628132\pi\) | |||||||
\(492\) | 8.27421e6 | − | 1.37251e7i | 1.54104 | − | 2.55624i | ||||
\(493\) | 5.42984e6i | 1.00617i | ||||||||
\(494\) | 3.98642e6 | 0.734964 | ||||||||
\(495\) | −4.43989e6 | − | 8.40948e6i | −0.814440 | − | 1.54261i | ||||
\(496\) | −8.39796e6 | −1.53274 | ||||||||
\(497\) | 8.99348e6 | 1.63319 | ||||||||
\(498\) | 3.58759e6 | − | 5.95102e6i | 0.648231 | − | 1.07527i | ||||
\(499\) | 9.33546e6 | 1.67836 | 0.839178 | − | 0.543856i | \(-0.183036\pi\) | ||||
0.839178 | + | 0.543856i | \(0.183036\pi\) | |||||||
\(500\) | 1.23347e7 | 2.20650 | ||||||||
\(501\) | 4.19369e6 | − | 6.95641e6i | 0.746453 | − | 1.23820i | ||||
\(502\) | 5.05755e6i | 0.895737i | ||||||||
\(503\) | −1.08142e6 | −0.190579 | −0.0952894 | − | 0.995450i | \(-0.530378\pi\) | ||||
−0.0952894 | + | 0.995450i | \(0.530378\pi\) | |||||||
\(504\) | −4.07485e6 | − | 7.71807e6i | −0.714554 | − | 1.35342i | ||||
\(505\) | 1.12698e6i | 0.196648i | ||||||||
\(506\) | 6.46464e6 | − | 8.64538e6i | 1.12245 | − | 1.50109i | ||||
\(507\) | −3.19191e6 | − | 1.92425e6i | −0.551481 | − | 0.332462i | ||||
\(508\) | −8.30018e6 | −1.42701 | ||||||||
\(509\) | − | 2.59686e6i | − | 0.444277i | −0.975015 | − | 0.222139i | \(-0.928696\pi\) | ||
0.975015 | − | 0.222139i | \(-0.0713038\pi\) | |||||||
\(510\) | −1.28960e7 | + | 2.13916e7i | −2.19548 | + | 3.64182i | ||||
\(511\) | 852043.i | 0.144348i | ||||||||
\(512\) | − | 1.16058e7i | − | 1.95660i | ||||||
\(513\) | −4.18628e6 | − | 237821.i | −0.702319 | − | 0.0398985i | ||||
\(514\) | 1.05299e7 | 1.75799 | ||||||||
\(515\) | − | 1.61785e7i | − | 2.68795i | ||||||
\(516\) | 8.42998e6 | − | 1.39835e7i | 1.39381 | − | 2.31202i | ||||
\(517\) | − | 794190.i | − | 0.130677i | ||||||
\(518\) | − | 3.72596e6i | − | 0.610118i | ||||||
\(519\) | −1.98087e6 | + | 3.28582e6i | −0.322803 | + | 0.535458i | ||||
\(520\) | − | 1.11889e7i | − | 1.81459i | ||||||
\(521\) | 2.67623e6 | 0.431946 | 0.215973 | − | 0.976399i | \(-0.430708\pi\) | ||||
0.215973 | + | 0.976399i | \(0.430708\pi\) | |||||||
\(522\) | 3.43586e6 | + | 6.50778e6i | 0.551899 | + | 1.04534i | ||||
\(523\) | 1.30259e6i | 0.208235i | 0.994565 | + | 0.104118i | \(0.0332019\pi\) | ||||
−0.994565 | + | 0.104118i | \(0.966798\pi\) | |||||||
\(524\) | 1.27962e7i | 2.03588i | ||||||||
\(525\) | 4.42678e6 | − | 7.34304e6i | 0.700954 | − | 1.16273i | ||||
\(526\) | 8.59953e6i | 1.35522i | ||||||||
\(527\) | 1.21194e7 | 1.90088 | ||||||||
\(528\) | 7.05755e6 | + | 4.25467e6i | 1.10171 | + | 0.664173i | ||||
\(529\) | 1.81993e6 | + | 6.17368e6i | 0.282758 | + | 0.959191i | ||||
\(530\) | 2.64884e7i | 4.09605i | ||||||||
\(531\) | 3.73012e6 | − | 1.96936e6i | 0.574099 | − | 0.303102i | ||||
\(532\) | −7.77997e6 | −1.19179 | ||||||||
\(533\) | − | 5.65469e6i | − | 0.862165i | ||||||
\(534\) | −1.91122e6 | + | 3.17028e6i | −0.290039 | + | 0.481111i | ||||
\(535\) | 7.02011e6 | 1.06038 | ||||||||
\(536\) | 4.16941e6 | 0.626849 | ||||||||
\(537\) | 878604. | − | 1.45741e6i | 0.131479 | − | 0.218095i | ||||
\(538\) | 1.67687e6 | 0.249772 | ||||||||
\(539\) | 2.36395e6 | 0.350483 | ||||||||
\(540\) | −1.29380e6 | + | 2.27742e7i | −0.190933 | + | 3.36092i | ||||
\(541\) | −9.58678e6 | −1.40825 | −0.704125 | − | 0.710076i | \(-0.748661\pi\) | ||||
−0.704125 | + | 0.710076i | \(0.748661\pi\) | |||||||
\(542\) | − | 2.31105e7i | − | 3.37918i | ||||||
\(543\) | −4.65393e6 | + | 7.71983e6i | −0.677361 | + | 1.12359i | ||||
\(544\) | − | 2.44841e6i | − | 0.354721i | ||||||
\(545\) | − | 9.56285e6i | − | 1.37910i | ||||||
\(546\) | −5.11179e6 | − | 3.08166e6i | −0.733823 | − | 0.442388i | ||||
\(547\) | 1.15831e7 | 1.65522 | 0.827609 | − | 0.561306i | \(-0.189701\pi\) | ||||
0.827609 | + | 0.561306i | \(0.189701\pi\) | |||||||
\(548\) | −2.70263e7 | −3.84446 | ||||||||
\(549\) | 5.43200e6 | − | 2.86789e6i | 0.769181 | − | 0.406099i | ||||
\(550\) | 2.20128e7i | 3.10291i | ||||||||
\(551\) | 3.38446e6 | 0.474909 | ||||||||
\(552\) | −1.23756e7 | + | 5.03242e6i | −1.72870 | + | 0.702957i | ||||
\(553\) | 7.04094e6 | 0.979080 | ||||||||
\(554\) | 9.33284e6i | 1.29193i | ||||||||
\(555\) | −2.59396e6 | + | 4.30280e6i | −0.357463 | + | 0.592951i | ||||
\(556\) | −3.73673e6 | −0.512631 | ||||||||
\(557\) | 1.87141e6 | 0.255583 | 0.127791 | − | 0.991801i | \(-0.459211\pi\) | ||||
0.127791 | + | 0.991801i | \(0.459211\pi\) | |||||||
\(558\) | 1.45254e7 | − | 7.66885e6i | 1.97489 | − | 1.04267i | ||||
\(559\) | − | 5.76114e6i | − | 0.779793i | ||||||
\(560\) | 1.19186e7i | 1.60603i | ||||||||
\(561\) | −1.01850e7 | − | 6.14008e6i | −1.36633 | − | 0.823696i | ||||
\(562\) | − | 1.19247e7i | − | 1.59260i | ||||||
\(563\) | 3.40573e6 | 0.452834 | 0.226417 | − | 0.974030i | \(-0.427299\pi\) | ||||
0.226417 | + | 0.974030i | \(0.427299\pi\) | |||||||
\(564\) | −983560. | + | 1.63151e6i | −0.130198 | + | 0.215969i | ||||
\(565\) | −1.02716e6 | −0.135368 | ||||||||
\(566\) | −1.80374e7 | −2.36664 | ||||||||
\(567\) | 5.18421e6 | + | 3.54111e6i | 0.677213 | + | 0.462575i | ||||
\(568\) | 2.85746e7 | 3.71628 | ||||||||
\(569\) | −1.46985e7 | −1.90324 | −0.951618 | − | 0.307283i | \(-0.900580\pi\) | ||||
−0.951618 | + | 0.307283i | \(0.900580\pi\) | |||||||
\(570\) | 1.33336e7 | + | 8.03819e6i | 1.71893 | + | 1.03627i | ||||
\(571\) | 3.73074e6i | 0.478856i | 0.970914 | + | 0.239428i | \(0.0769598\pi\) | ||||
−0.970914 | + | 0.239428i | \(0.923040\pi\) | |||||||
\(572\) | 1.03256e7 | 1.31955 | ||||||||
\(573\) | 5.77118e6 | + | 3.47918e6i | 0.734308 | + | 0.442680i | ||||
\(574\) | 1.63779e7i | 2.07481i | ||||||||
\(575\) | −1.05110e7 | − | 7.85970e6i | −1.32579 | − | 0.991372i | ||||
\(576\) | 2.91832e6 | + | 5.52752e6i | 0.366502 | + | 0.694183i | ||||
\(577\) | −2.38914e6 | −0.298746 | −0.149373 | − | 0.988781i | \(-0.547725\pi\) | ||||
−0.149373 | + | 0.988781i | \(0.547725\pi\) | |||||||
\(578\) | 1.71742e7i | 2.13825i | ||||||||
\(579\) | 788044. | + | 475075.i | 0.0976908 | + | 0.0588933i | ||||
\(580\) | − | 1.84122e7i | − | 2.27266i | ||||||
\(581\) | 4.78497e6i | 0.588083i | ||||||||
\(582\) | 1.27895e7 | + | 7.71021e6i | 1.56512 | + | 0.943537i | ||||
\(583\) | −1.26117e7 | −1.53674 | ||||||||
\(584\) | 2.70716e6i | 0.328459i | ||||||||
\(585\) | 3.75777e6 | + | 7.11750e6i | 0.453984 | + | 0.859880i | ||||
\(586\) | − | 1.55104e7i | − | 1.86586i | ||||||
\(587\) | − | 88203.1i | − | 0.0105655i | −0.999986 | − | 0.00528273i | \(-0.998318\pi\) | ||
0.999986 | − | 0.00528273i | \(-0.00168155\pi\) | |||||||
\(588\) | −4.85628e6 | − | 2.92763e6i | −0.579243 | − | 0.349199i | ||||
\(589\) | − | 7.55413e6i | − | 0.897214i | ||||||
\(590\) | −1.56621e7 | −1.85234 | ||||||||
\(591\) | −828714. | + | 1.37465e6i | −0.0975969 | + | 0.161892i | ||||
\(592\) | − | 4.35389e6i | − | 0.510591i | ||||||
\(593\) | 1.88014e6i | 0.219560i | 0.993956 | + | 0.109780i | \(0.0350147\pi\) | ||||
−0.993956 | + | 0.109780i | \(0.964985\pi\) | |||||||
\(594\) | −1.60922e7 | − | 914195.i | −1.87133 | − | 0.106310i | ||||
\(595\) | − | 1.72001e7i | − | 1.99177i | ||||||
\(596\) | 1.45614e6 | 0.167915 | ||||||||
\(597\) | 3.54950e6 | − | 5.88783e6i | 0.407597 | − | 0.676113i | ||||
\(598\) | −5.47145e6 | + | 7.31716e6i | −0.625676 | + | 0.836738i | ||||
\(599\) | 1.26695e7i | 1.44276i | 0.692541 | + | 0.721378i | \(0.256491\pi\) | ||||
−0.692541 | + | 0.721378i | \(0.743509\pi\) | |||||||
\(600\) | 1.40650e7 | − | 2.33307e7i | 1.59500 | − | 2.64576i | ||||
\(601\) | 1.09195e7 | 1.23315 | 0.616574 | − | 0.787297i | \(-0.288520\pi\) | ||||
0.616574 | + | 0.787297i | \(0.288520\pi\) | |||||||
\(602\) | 1.66862e7i | 1.87658i | ||||||||
\(603\) | −2.65226e6 | + | 1.40029e6i | −0.297046 | + | 0.156829i | ||||
\(604\) | −1.24718e7 | −1.39103 | ||||||||
\(605\) | −2.14086e6 | −0.237794 | ||||||||
\(606\) | 1.63590e6 | + | 986207.i | 0.180957 | + | 0.109090i | ||||
\(607\) | −5.76812e6 | −0.635423 | −0.317711 | − | 0.948187i | \(-0.602914\pi\) | ||||
−0.317711 | + | 0.948187i | \(0.602914\pi\) | |||||||
\(608\) | −1.52611e6 | −0.167428 | ||||||||
\(609\) | −4.33989e6 | − | 2.61632e6i | −0.474172 | − | 0.285856i | ||||
\(610\) | −2.28080e7 | −2.48178 | ||||||||
\(611\) | 672176.i | 0.0728417i | ||||||||
\(612\) | 1.33190e7 | + | 2.52272e7i | 1.43745 | + | 2.72264i | ||||
\(613\) | − | 224080.i | − | 0.0240853i | −0.999927 | − | 0.0120427i | \(-0.996167\pi\) | ||
0.999927 | − | 0.0120427i | \(-0.00383339\pi\) | |||||||
\(614\) | 1.17839e6i | 0.126144i | ||||||||
\(615\) | 1.14021e7 | − | 1.89135e7i | 1.21561 | − | 2.01643i | ||||
\(616\) | −1.54296e7 | −1.63833 | ||||||||
\(617\) | 3.12193e6 | 0.330149 | 0.165075 | − | 0.986281i | \(-0.447214\pi\) | ||||
0.165075 | + | 0.986281i | \(0.447214\pi\) | |||||||
\(618\) | −2.34843e7 | − | 1.41576e7i | −2.47347 | − | 1.49114i | ||||
\(619\) | − | 8.70665e6i | − | 0.913324i | −0.889640 | − | 0.456662i | \(-0.849045\pi\) | ||
0.889640 | − | 0.456662i | \(-0.150955\pi\) | |||||||
\(620\) | −4.10960e7 | −4.29359 | ||||||||
\(621\) | 6.18228e6 | − | 7.35757e6i | 0.643309 | − | 0.765607i | ||||
\(622\) | −1.37721e7 | −1.42732 | ||||||||
\(623\) | − | 2.54909e6i | − | 0.263127i | ||||||
\(624\) | −5.97328e6 | − | 3.60101e6i | −0.614117 | − | 0.370223i | ||||
\(625\) | 830934. | 0.0850876 | ||||||||
\(626\) | 2.07017e7 | 2.11140 | ||||||||
\(627\) | −3.82716e6 | + | 6.34840e6i | −0.388783 | + | 0.644905i | ||||
\(628\) | 2.29423e7i | 2.32133i | ||||||||
\(629\) | 6.28327e6i | 0.633227i | ||||||||
\(630\) | −1.08838e7 | − | 2.06147e7i | −1.09252 | − | 2.06931i | ||||
\(631\) | − | 285663.i | − | 0.0285614i | −0.999898 | − | 0.0142807i | \(-0.995454\pi\) | ||
0.999898 | − | 0.0142807i | \(-0.00454585\pi\) | |||||||
\(632\) | 2.23709e7 | 2.22787 | ||||||||
\(633\) | −1.45039e6 | − | 874373.i | −0.143872 | − | 0.0867336i | ||||
\(634\) | −2.02888e6 | −0.200462 | ||||||||
\(635\) | −1.14378e7 | −1.12567 | ||||||||
\(636\) | 2.59082e7 | + | 1.56189e7i | 2.53978 | + | 1.53111i | ||||
\(637\) | −2.00077e6 | −0.195366 | ||||||||
\(638\) | 1.30100e7 | 1.26540 | ||||||||
\(639\) | −1.81770e7 | + | 9.59674e6i | −1.76104 | + | 0.929762i | ||||
\(640\) | − | 2.72280e7i | − | 2.62764i | ||||||
\(641\) | −1.12266e7 | −1.07920 | −0.539601 | − | 0.841921i | \(-0.681425\pi\) | ||||
−0.539601 | + | 0.841921i | \(0.681425\pi\) | |||||||
\(642\) | 6.14319e6 | − | 1.01902e7i | 0.588243 | − | 0.975764i | ||||
\(643\) | 3.68982e6i | 0.351948i | 0.984395 | + | 0.175974i | \(0.0563074\pi\) | ||||
−0.984395 | + | 0.175974i | \(0.943693\pi\) | |||||||
\(644\) | 1.06782e7 | − | 1.42803e7i | 1.01457 | − | 1.35682i | ||||
\(645\) | 1.16167e7 | − | 1.92695e7i | 1.09947 | − | 1.82378i | ||||
\(646\) | 1.94707e7 | 1.83569 | ||||||||
\(647\) | 1.53881e7i | 1.44519i | 0.691273 | + | 0.722594i | \(0.257050\pi\) | ||||
−0.691273 | + | 0.722594i | \(0.742950\pi\) | |||||||
\(648\) | 1.64716e7 | + | 1.12510e7i | 1.54098 | + | 1.05258i | ||||
\(649\) | − | 7.45707e6i | − | 0.694955i | ||||||
\(650\) | − | 1.86309e7i | − | 1.72962i | ||||||
\(651\) | −5.83963e6 | + | 9.68665e6i | −0.540049 | + | 0.895821i | ||||
\(652\) | 2.07254e7 | 1.90934 | ||||||||
\(653\) | 7.65531e6i | 0.702554i | 0.936272 | + | 0.351277i | \(0.114253\pi\) | ||||
−0.936272 | + | 0.351277i | \(0.885747\pi\) | |||||||
\(654\) | −1.38812e7 | − | 8.36831e6i | −1.26906 | − | 0.765056i | ||||
\(655\) | 1.76335e7i | 1.60596i | ||||||||
\(656\) | 1.91381e7i | 1.73635i | ||||||||
\(657\) | −909197. | − | 1.72209e6i | −0.0821759 | − | 0.155647i | ||||
\(658\) | − | 1.94685e6i | − | 0.175294i | ||||||
\(659\) | 3.28275e6 | 0.294458 | 0.147229 | − | 0.989102i | \(-0.452965\pi\) | ||||
0.147229 | + | 0.989102i | \(0.452965\pi\) | |||||||
\(660\) | 3.45366e7 | + | 2.08205e7i | 3.08617 | + | 1.86051i | ||||
\(661\) | 1.61641e7i | 1.43896i | 0.694512 | + | 0.719481i | \(0.255620\pi\) | ||||
−0.694512 | + | 0.719481i | \(0.744380\pi\) | |||||||
\(662\) | − | 3.28016e7i | − | 2.90904i | ||||||
\(663\) | 8.62027e6 | + | 5.19676e6i | 0.761617 | + | 0.459144i | ||||
\(664\) | 1.52031e7i | 1.33817i | ||||||||
\(665\) | −1.07210e7 | −0.940113 | ||||||||
\(666\) | 3.97589e6 | + | 7.53063e6i | 0.347335 | + | 0.657879i | ||||
\(667\) | −4.64525e6 | + | 6.21224e6i | −0.404291 | + | 0.540672i | ||||
\(668\) | 3.44459e7i | 2.98673i | ||||||||
\(669\) | −2.81578e6 | − | 1.69751e6i | −0.243240 | − | 0.146638i | ||||
\(670\) | 1.11364e7 | 0.958422 | ||||||||
\(671\) | − | 1.08594e7i | − | 0.931105i | ||||||
\(672\) | 1.95693e6 | + | 1.17974e6i | 0.167168 | + | 0.100778i | ||||
\(673\) | 1.47135e7 | 1.25221 | 0.626106 | − | 0.779738i | \(-0.284648\pi\) | ||||
0.626106 | + | 0.779738i | \(0.284648\pi\) | |||||||
\(674\) | −2.70305e7 | −2.29194 | ||||||||
\(675\) | −1.11148e6 | + | 1.95649e7i | −0.0938948 | + | 1.65279i | ||||
\(676\) | 1.58053e7 | 1.33026 | ||||||||
\(677\) | −2.08650e7 | −1.74963 | −0.874816 | − | 0.484455i | \(-0.839018\pi\) | ||||
−0.874816 | + | 0.484455i | \(0.839018\pi\) | |||||||
\(678\) | −898849. | + | 1.49099e6i | −0.0750952 | + | 0.124566i | ||||
\(679\) | −1.02835e7 | −0.855988 | ||||||||
\(680\) | − | 5.46492e7i | − | 4.53223i | ||||||
\(681\) | 1.95322e6 | + | 1.17751e6i | 0.161393 | + | 0.0972962i | ||||
\(682\) | − | 2.90384e7i | − | 2.39063i | ||||||
\(683\) | 5.62315e6i | 0.461241i | 0.973044 | + | 0.230620i | \(0.0740756\pi\) | ||||
−0.973044 | + | 0.230620i | \(0.925924\pi\) | |||||||
\(684\) | 1.57243e7 | − | 8.30183e6i | 1.28508 | − | 0.678475i | ||||
\(685\) | −3.72429e7 | −3.03261 | ||||||||
\(686\) | 2.34943e7 | 1.90613 | ||||||||
\(687\) | −8.94935e6 | + | 1.48450e7i | −0.723436 | + | 1.20002i | ||||
\(688\) | 1.94984e7i | 1.57046i | ||||||||
\(689\) | 1.06741e7 | 0.856611 | ||||||||
\(690\) | −3.30549e7 | + | 1.34414e7i | −2.64309 | + | 1.07479i | ||||
\(691\) | −913111. | −0.0727492 | −0.0363746 | − | 0.999338i | \(-0.511581\pi\) | ||||
−0.0363746 | + | 0.999338i | \(0.511581\pi\) | |||||||
\(692\) | − | 1.62703e7i | − | 1.29161i | ||||||
\(693\) | 9.81511e6 | − | 5.18201e6i | 0.776358 | − | 0.409888i | ||||
\(694\) | 3.62946e6 | 0.286051 | ||||||||
\(695\) | −5.14930e6 | −0.404377 | ||||||||
\(696\) | −1.37889e7 | − | 8.31271e6i | −1.07897 | − | 0.650458i | ||||
\(697\) | − | 2.76189e7i | − | 2.15340i | ||||||
\(698\) | − | 1.53749e7i | − | 1.19447i | ||||||
\(699\) | 1.08304e7 | − | 1.79652e7i | 0.838401 | − | 1.39072i | ||||
\(700\) | 3.63604e7i | 2.80468i | ||||||||
\(701\) | 1.66750e7 | 1.28165 | 0.640826 | − | 0.767686i | \(-0.278592\pi\) | ||||
0.640826 | + | 0.767686i | \(0.278592\pi\) | |||||||
\(702\) | 1.36199e7 | + | 773744.i | 1.04312 | + | 0.0592591i | ||||
\(703\) | 3.91641e6 | 0.298882 | ||||||||
\(704\) | 1.10503e7 | 0.840319 | ||||||||
\(705\) | −1.35537e6 | + | 2.24826e6i | −0.102703 | + | 0.170362i | ||||
\(706\) | −1.95220e7 | −1.47405 | ||||||||
\(707\) | −1.31536e6 | −0.0989682 | ||||||||
\(708\) | −9.23517e6 | + | 1.53191e7i | −0.692408 | + | 1.14855i | ||||
\(709\) | 681530.i | 0.0509178i | 0.999676 | + | 0.0254589i | \(0.00810469\pi\) | ||||
−0.999676 | + | 0.0254589i | \(0.991895\pi\) | |||||||
\(710\) | 7.63218e7 | 5.68202 | ||||||||
\(711\) | −1.42306e7 | + | 7.51324e6i | −1.05572 | + | 0.557382i | ||||
\(712\) | − | 8.09912e6i | − | 0.598739i | ||||||
\(713\) | 1.38657e7 | + | 1.03682e7i | 1.02146 | + | 0.763800i | ||||
\(714\) | −2.49672e7 | − | 1.50516e7i | −1.83284 | − | 1.10493i | ||||
\(715\) | 1.42290e7 | 1.04090 | ||||||||
\(716\) | 7.21661e6i | 0.526079i | ||||||||
\(717\) | 767286. | − | 1.27276e6i | 0.0557390 | − | 0.0924586i | ||||
\(718\) | 9.78834e6i | 0.708594i | ||||||||
\(719\) | 1.36916e7i | 0.987713i | 0.869543 | + | 0.493857i | \(0.164413\pi\) | ||||
−0.869543 | + | 0.493857i | \(0.835587\pi\) | |||||||
\(720\) | −1.27180e7 | − | 2.40889e7i | −0.914300 | − | 1.73175i | ||||
\(721\) | 1.88827e7 | 1.35278 | ||||||||
\(722\) | 1.23891e7i | 0.884499i | ||||||||
\(723\) | 1.38383e6 | − | 2.29547e6i | 0.0984549 | − | 0.163315i | ||||
\(724\) | − | 3.82261e7i | − | 2.71028i | ||||||
\(725\) | − | 1.58176e7i | − | 1.11762i | ||||||
\(726\) | −1.87344e6 | + | 3.10762e6i | −0.131916 | + | 0.218819i | ||||
\(727\) | − | 1.83897e6i | − | 0.129044i | −0.997916 | − | 0.0645221i | \(-0.979448\pi\) | ||
0.997916 | − | 0.0645221i | \(-0.0205523\pi\) | |||||||
\(728\) | 1.30591e7 | 0.913238 | ||||||||
\(729\) | −1.42566e7 | − | 1.62507e6i | −0.993566 | − | 0.113254i | ||||
\(730\) | 7.23073e6i | 0.502198i | ||||||||
\(731\) | − | 2.81388e7i | − | 1.94766i | ||||||
\(732\) | −1.34487e7 | + | 2.23085e7i | −0.927693 | + | 1.53884i | ||||
\(733\) | 2.18827e7i | 1.50432i | 0.658979 | + | 0.752162i | \(0.270989\pi\) | ||||
−0.658979 | + | 0.752162i | \(0.729011\pi\) | |||||||
\(734\) | 1.64978e7 | 1.13028 | ||||||||
\(735\) | −6.69207e6 | − | 4.03434e6i | −0.456922 | − | 0.275457i | ||||
\(736\) | 2.09462e6 | − | 2.80120e6i | 0.142531 | − | 0.190612i | ||||
\(737\) | 5.30227e6i | 0.359578i | ||||||||
\(738\) | −1.74765e7 | − | 3.31018e7i | −1.18117 | − | 2.23723i | ||||
\(739\) | 2.21664e7 | 1.49308 | 0.746541 | − | 0.665340i | \(-0.231713\pi\) | ||||
0.746541 | + | 0.665340i | \(0.231713\pi\) | |||||||
\(740\) | − | 2.13061e7i | − | 1.43029i | ||||||
\(741\) | 3.23918e6 | − | 5.37308e6i | 0.216715 | − | 0.359482i | ||||
\(742\) | −3.09159e7 | −2.06144 | ||||||||
\(743\) | 1.24012e7 | 0.824126 | 0.412063 | − | 0.911155i | \(-0.364808\pi\) | ||||
0.412063 | + | 0.911155i | \(0.364808\pi\) | |||||||
\(744\) | −1.85540e7 | + | 3.07769e7i | −1.22887 | + | 2.03842i | ||||
\(745\) | 2.00660e6 | 0.132456 | ||||||||
\(746\) | 7.42731e6 | 0.488635 | ||||||||
\(747\) | −5.10594e6 | − | 9.67103e6i | −0.334791 | − | 0.634119i | ||||
\(748\) | 5.04329e7 | 3.29580 | ||||||||
\(749\) | 8.19351e6i | 0.533661i | ||||||||
\(750\) | 1.48743e7 | − | 2.46731e7i | 0.965568 | − | 1.60166i | ||||
\(751\) | − | 1.39231e7i | − | 0.900818i | −0.892822 | − | 0.450409i | \(-0.851278\pi\) | ||
0.892822 | − | 0.450409i | \(-0.148722\pi\) | |||||||
\(752\) | − | 2.27495e6i | − | 0.146699i | ||||||
\(753\) | 6.81678e6 | + | 4.10952e6i | 0.438119 | + | 0.264121i | ||||
\(754\) | −1.10113e7 | −0.705356 | ||||||||
\(755\) | −1.71864e7 | −1.09728 | ||||||||
\(756\) | −2.65809e7 | − | 1.51005e6i | −1.69147 | − | 0.0960920i | ||||
\(757\) | − | 2.60434e7i | − | 1.65180i | −0.563817 | − | 0.825900i | \(-0.690668\pi\) | ||
0.563817 | − | 0.825900i | \(-0.309332\pi\) | |||||||
\(758\) | 1.93598e7 | 1.22385 | ||||||||
\(759\) | −6.39976e6 | − | 1.57381e7i | −0.403236 | − | 0.991628i | ||||
\(760\) | −3.40633e7 | −2.13920 | ||||||||
\(761\) | 9.67510e6i | 0.605611i | 0.953052 | + | 0.302805i | \(0.0979232\pi\) | ||||
−0.953052 | + | 0.302805i | \(0.902077\pi\) | |||||||
\(762\) | −1.00091e7 | + | 1.66028e7i | −0.624463 | + | 1.03585i | ||||
\(763\) | 1.11613e7 | 0.694068 | ||||||||
\(764\) | −2.85770e7 | −1.77126 | ||||||||
\(765\) | 1.83539e7 | + | 3.47636e7i | 1.13390 | + | 2.14769i | ||||
\(766\) | − | 1.08959e7i | − | 0.670952i | ||||||
\(767\) | 6.31142e6i | 0.387381i | ||||||||
\(768\) | −2.85346e7 | − | 1.72022e7i | −1.74569 | − | 1.05240i | ||||
\(769\) | − | 205320.i | − | 0.0125203i | −0.999980 | − | 0.00626017i | \(-0.998007\pi\) | ||
0.999980 | − | 0.00626017i | \(-0.00199269\pi\) | |||||||
\(770\) | −4.12119e7 | −2.50493 | ||||||||
\(771\) | 8.55609e6 | − | 1.41927e7i | 0.518370 | − | 0.859860i | ||||
\(772\) | −3.90214e6 | −0.235645 | ||||||||
\(773\) | −8.35486e6 | −0.502910 | −0.251455 | − | 0.967869i | \(-0.580909\pi\) | ||||
−0.251455 | + | 0.967869i | \(0.580909\pi\) | |||||||
\(774\) | −1.78055e7 | − | 3.37250e7i | −1.06832 | − | 2.02348i | ||||
\(775\) | −3.53049e7 | −2.11145 | ||||||||
\(776\) | −3.26734e7 | −1.94778 | ||||||||
\(777\) | −5.02201e6 | − | 3.02753e6i | −0.298418 | − | 0.179902i | ||||
\(778\) | 4.11655e7i | 2.43829i | ||||||||
\(779\) | −1.72150e7 | −1.01640 | ||||||||
\(780\) | −2.92306e7 | − | 1.76218e7i | −1.72029 | − | 1.03708i | ||||
\(781\) | 3.63385e7i | 2.13176i | ||||||||
\(782\) | −2.67239e7 | + | 3.57388e7i | −1.56273 | + | 2.08989i | ||||
\(783\) | 1.15633e7 | + | 656907.i | 0.674026 | + | 0.0382912i | ||||
\(784\) | 6.77153e6 | 0.393457 | ||||||||
\(785\) | 3.16150e7i | 1.83113i | ||||||||
\(786\) | 2.55962e7 | + | 1.54308e7i | 1.47781 | + | 0.890905i | ||||
\(787\) | − | 6.22102e6i | − | 0.358035i | −0.983846 | − | 0.179017i | \(-0.942708\pi\) | ||
0.983846 | − | 0.179017i | \(-0.0572918\pi\) | |||||||
\(788\) | − | 6.80683e6i | − | 0.390508i | ||||||
\(789\) | 1.15908e7 | + | 6.98757e6i | 0.662860 | + | 0.399607i | ||||
\(790\) | 5.97519e7 | 3.40631 | ||||||||
\(791\) | − | 1.19884e6i | − | 0.0681273i | ||||||
\(792\) | 3.11851e7 | − | 1.64646e7i | 1.76658 | − | 0.932690i | ||||
\(793\) | 9.19102e6i | 0.519016i | ||||||||
\(794\) | − | 2.23568e7i | − | 1.25851i | ||||||
\(795\) | 3.57022e7 | + | 2.15232e7i | 2.00344 | + | 1.20778i | ||||
\(796\) | 2.91546e7i | 1.63089i | ||||||||
\(797\) | −2.01459e7 | −1.12342 | −0.561708 | − | 0.827336i | \(-0.689855\pi\) | ||||
−0.561708 | + | 0.827336i | \(0.689855\pi\) | |||||||
\(798\) | −9.38176e6 | + | 1.55623e7i | −0.521527 | + | 0.865098i | ||||
\(799\) | 3.28307e6i | 0.181934i | ||||||||
\(800\) | 7.13241e6i | 0.394014i | ||||||||
\(801\) | 2.72008e6 | + | 5.15204e6i | 0.149796 | + | 0.283725i | ||||
\(802\) | − | 3.41464e7i | − | 1.87460i | ||||||
\(803\) | −3.44271e6 | −0.188413 | ||||||||
\(804\) | 6.56657e6 | − | 1.08925e7i | 0.358260 | − | 0.594274i | ||||
\(805\) | 1.47148e7 | − | 1.96785e7i | 0.800320 | − | 1.07029i | ||||
\(806\) | 2.45771e7i | 1.33258i | ||||||||
\(807\) | 1.36255e6 | − | 2.26016e6i | 0.0736491 | − | 0.122167i | ||||
\(808\) | −4.17923e6 | −0.225200 | ||||||||
\(809\) | − | 2.79244e7i | − | 1.50007i | −0.661397 | − | 0.750036i | \(-0.730036\pi\) | ||
0.661397 | − | 0.750036i | \(-0.269964\pi\) | |||||||
\(810\) | 4.39950e7 | + | 3.00511e7i | 2.35609 | + | 1.60934i | ||||
\(811\) | −1.89999e7 | −1.01438 | −0.507189 | − | 0.861835i | \(-0.669315\pi\) | ||||
−0.507189 | + | 0.861835i | \(0.669315\pi\) | |||||||
\(812\) | 2.14897e7 | 1.14378 | ||||||||
\(813\) | −3.11493e7 | − | 1.87785e7i | −1.65281 | − | 0.996401i | ||||
\(814\) | 1.50549e7 | 0.796372 | ||||||||
\(815\) | 2.85601e7 | 1.50614 | ||||||||
\(816\) | −2.91749e7 | − | 1.75882e7i | −1.53386 | − | 0.924691i | ||||
\(817\) | −1.75391e7 | −0.919291 | ||||||||
\(818\) | − | 3.65257e7i | − | 1.90860i | ||||||
\(819\) | −8.30719e6 | + | 4.38588e6i | −0.432757 | + | 0.228479i | ||||
\(820\) | 9.36534e7i | 4.86395i | ||||||||
\(821\) | − | 2.62417e7i | − | 1.35873i | −0.733800 | − | 0.679365i | \(-0.762255\pi\) | ||
0.733800 | − | 0.679365i | \(-0.237745\pi\) | |||||||
\(822\) | −3.25907e7 | + | 5.40607e7i | −1.68234 | + | 2.79063i | ||||
\(823\) | 4.65495e6 | 0.239561 | 0.119780 | − | 0.992800i | \(-0.461781\pi\) | ||||
0.119780 | + | 0.992800i | \(0.461781\pi\) | |||||||
\(824\) | 5.99953e7 | 3.07822 | ||||||||
\(825\) | 2.96698e7 | + | 1.78866e7i | 1.51768 | + | 0.914938i | ||||
\(826\) | − | 1.82800e7i | − | 0.932237i | ||||||
\(827\) | −3.37577e7 | −1.71636 | −0.858181 | − | 0.513347i | \(-0.828405\pi\) | ||||
−0.858181 | + | 0.513347i | \(0.828405\pi\) | |||||||
\(828\) | −6.34376e6 | + | 4.02567e7i | −0.321567 | + | 2.04062i | ||||
\(829\) | −2.46431e7 | −1.24540 | −0.622701 | − | 0.782460i | \(-0.713964\pi\) | ||||
−0.622701 | + | 0.782460i | \(0.713964\pi\) | |||||||
\(830\) | 4.06069e7i | 2.04600i | ||||||||
\(831\) | 1.25792e7 | + | 7.58342e6i | 0.631903 | + | 0.380945i | ||||
\(832\) | −9.35264e6 | −0.468410 | ||||||||
\(833\) | −9.77226e6 | −0.487958 | ||||||||
\(834\) | −4.50607e6 | + | 7.47457e6i | −0.224328 | + | 0.372110i | ||||
\(835\) | 4.74672e7i | 2.35601i | ||||||||
\(836\) | − | 3.14352e7i | − | 1.55561i | ||||||
\(837\) | 1.46622e6 | − | 2.58093e7i | 0.0723410 | − | 1.27339i | ||||
\(838\) | − | 3.96925e7i | − | 1.95253i | ||||||
\(839\) | 2.10537e7 | 1.03258 | 0.516290 | − | 0.856414i | \(-0.327313\pi\) | ||||
0.516290 | + | 0.856414i | \(0.327313\pi\) | |||||||
\(840\) | 4.36793e7 | + | 2.63322e7i | 2.13588 | + | 1.28762i | ||||
\(841\) | 1.11626e7 | 0.544222 | ||||||||
\(842\) | 7.28312e6 | 0.354027 | ||||||||
\(843\) | −1.60726e7 | − | 9.68944e6i | −0.778965 | − | 0.469602i | ||||
\(844\) | 7.18186e6 | 0.347041 | ||||||||
\(845\) | 2.17800e7 | 1.04934 | ||||||||
\(846\) | 2.07744e6 | + | 3.93483e6i | 0.0997936 | + | 0.189017i | ||||
\(847\) | − | 2.49871e6i | − | 0.119676i | ||||||
\(848\) | −3.61261e7 | −1.72517 | ||||||||
\(849\) | −1.46563e7 | + | 2.43116e7i | −0.697840 | + | 1.15756i | ||||
\(850\) | − | 9.09979e7i | − | 4.32001i | ||||||
\(851\) | −5.37536e6 | + | 7.18864e6i | −0.254439 | + | 0.340270i | ||||
\(852\) | 4.50032e7 | − | 7.46503e7i | 2.12395 | − | 3.52316i | ||||
\(853\) | 1.35687e7 | 0.638509 | 0.319254 | − | 0.947669i | \(-0.396568\pi\) | ||||
0.319254 | + | 0.947669i | \(0.396568\pi\) | |||||||
\(854\) | − | 2.66203e7i | − | 1.24902i | ||||||
\(855\) | 2.16684e7 | − | 1.14401e7i | 1.01371 | − | 0.535199i | ||||
\(856\) | 2.60329e7i | 1.21433i | ||||||||
\(857\) | 1.29010e7i | 0.600029i | 0.953935 | + | 0.300014i | \(0.0969915\pi\) | ||||
−0.953935 | + | 0.300014i | \(0.903009\pi\) | |||||||
\(858\) | 1.24515e7 | − | 2.06544e7i | 0.577438 | − | 0.957841i | ||||
\(859\) | −6.49337e6 | −0.300253 | −0.150126 | − | 0.988667i | \(-0.547968\pi\) | ||||
−0.150126 | + | 0.988667i | \(0.547968\pi\) | |||||||
\(860\) | 9.54165e7i | 4.39924i | ||||||||
\(861\) | 2.20748e7 | + | 1.33079e7i | 1.01482 | + | 0.611789i | ||||
\(862\) | 5.49030e7i | 2.51668i | ||||||||
\(863\) | − | 3.22421e7i | − | 1.47366i | −0.676079 | − | 0.736829i | \(-0.736322\pi\) | ||
0.676079 | − | 0.736829i | \(-0.263678\pi\) | |||||||
\(864\) | −5.21408e6 | − | 296210.i | −0.237626 | − | 0.0134994i | ||||
\(865\) | − | 2.24209e7i | − | 1.01885i | ||||||
\(866\) | −2.47660e7 | −1.12218 | ||||||||
\(867\) | 2.31482e7 | + | 1.39550e7i | 1.04585 | + | 0.630494i | ||||
\(868\) | − | 4.79651e7i | − | 2.16086i | ||||||
\(869\) | 2.84492e7i | 1.27797i | ||||||||
\(870\) | −3.68298e7 | − | 2.22030e7i | −1.64969 | − | 0.994520i | ||||
\(871\) | − | 4.48766e6i | − | 0.200436i | ||||||
\(872\) | 3.54622e7 | 1.57934 | ||||||||
\(873\) | 2.07843e7 | − | 1.09733e7i | 0.922996 | − | 0.487307i | ||||
\(874\) | 2.22763e7 | + | 1.66572e7i | 0.986424 | + | 0.737605i | ||||
\(875\) | 1.98386e7i | 0.875975i | ||||||||
\(876\) | 7.07238e6 | + | 4.26361e6i | 0.311390 | + | 0.187723i | ||||
\(877\) | −3.04161e7 | −1.33538 | −0.667689 | − | 0.744441i | \(-0.732716\pi\) | ||||
−0.667689 | + | 0.744441i | \(0.732716\pi\) | |||||||
\(878\) | − | 2.69998e7i | − | 1.18202i | ||||||
\(879\) | −2.09056e7 | − | 1.26030e7i | −0.912622 | − | 0.550177i | ||||
\(880\) | −4.81574e7 | −2.09631 | ||||||||
\(881\) | 3.88903e7 | 1.68811 | 0.844056 | − | 0.536256i | \(-0.180162\pi\) | ||||
0.844056 | + | 0.536256i | \(0.180162\pi\) | |||||||
\(882\) | −1.17123e7 | + | 6.18363e6i | −0.506955 | + | 0.267653i | ||||
\(883\) | −1.71093e7 | −0.738465 | −0.369232 | − | 0.929337i | \(-0.620379\pi\) | ||||
−0.369232 | + | 0.929337i | \(0.620379\pi\) | |||||||
\(884\) | −4.26848e7 | −1.83714 | ||||||||
\(885\) | −1.27263e7 | + | 2.11101e7i | −0.546189 | + | 0.906007i | ||||
\(886\) | −3.75997e7 | −1.60916 | ||||||||
\(887\) | 1.09242e7i | 0.466207i | 0.972452 | + | 0.233103i | \(0.0748881\pi\) | ||||
−0.972452 | + | 0.233103i | \(0.925112\pi\) | |||||||
\(888\) | −1.59562e7 | − | 9.61925e6i | −0.679042 | − | 0.409363i | ||||
\(889\) | − | 1.33497e7i | − | 0.566521i | ||||||
\(890\) | − | 2.16325e7i | − | 0.915443i | ||||||
\(891\) | −1.43080e7 | + | 2.09470e7i | −0.603787 | + | 0.883949i | ||||
\(892\) | 1.39429e7 | 0.586732 | ||||||||
\(893\) | 2.04636e6 | 0.0858725 | ||||||||
\(894\) | 1.75595e6 | − | 2.91272e6i | 0.0734797 | − | 0.121886i | ||||
\(895\) | 9.94466e6i | 0.414985i | ||||||||
\(896\) | 3.17791e7 | 1.32243 | ||||||||
\(897\) | 5.41654e6 | + | 1.33202e7i | 0.224771 | + | 0.552752i | ||||
\(898\) | 9.17530e6 | 0.379690 | ||||||||
\(899\) | 2.08659e7i | 0.861070i | ||||||||
\(900\) | −3.87993e7 | − | 7.34889e7i | −1.59668 | − | 3.02423i | ||||
\(901\) | 5.21350e7 | 2.13952 | ||||||||
\(902\) | −6.61754e7 | −2.70820 | ||||||||
\(903\) | 2.24904e7 | + | 1.35584e7i | 0.917864 | + | 0.553337i | ||||
\(904\) | − | 3.80903e6i | − | 0.155022i | ||||||
\(905\) | − | 5.26764e7i | − | 2.13794i | ||||||
\(906\) | −1.50395e7 | + | 2.49472e7i | −0.608714 | + | 1.00972i | ||||
\(907\) | − | 4.09281e6i | − | 0.165198i | −0.996583 | − | 0.0825988i | \(-0.973678\pi\) | ||
0.996583 | − | 0.0825988i | \(-0.0263220\pi\) | |||||||
\(908\) | −9.67173e6 | −0.389304 | ||||||||
\(909\) | 2.65851e6 | − | 1.40359e6i | 0.106716 | − | 0.0563418i | ||||
\(910\) | 3.48804e7 | 1.39630 | ||||||||
\(911\) | −1.85854e6 | −0.0741951 | −0.0370975 | − | 0.999312i | \(-0.511811\pi\) | ||||
−0.0370975 | + | 0.999312i | \(0.511811\pi\) | |||||||
\(912\) | −1.09629e7 | + | 1.81850e7i | −0.436453 | + | 0.723978i | ||||
\(913\) | −1.93338e7 | −0.767611 | ||||||||
\(914\) | 4.44486e7 | 1.75992 | ||||||||
\(915\) | −1.85327e7 | + | 3.07416e7i | −0.731788 | + | 1.21387i | ||||
\(916\) | − | 7.35076e7i | − | 2.89463i | ||||||
\(917\) | −2.05809e7 | −0.808240 | ||||||||
\(918\) | 6.65231e7 | + | 3.77916e6i | 2.60535 | + | 0.148009i | ||||
\(919\) | 1.45437e7i | 0.568049i | 0.958817 | + | 0.284024i | \(0.0916696\pi\) | ||||
−0.958817 | + | 0.284024i | \(0.908330\pi\) | |||||||
\(920\) | 4.67526e7 | − | 6.25237e7i | 1.82111 | − | 2.43543i | ||||
\(921\) | 1.58828e6 | + | 957501.i | 0.0616990 | + | 0.0371955i | ||||
\(922\) | −1.15933e7 | −0.449139 | ||||||||
\(923\) | − | 3.07557e7i | − | 1.18829i | ||||||
\(924\) | −2.43006e7 | + | 4.03093e7i | −0.936349 | + | 1.55319i | ||||
\(925\) | − | 1.83037e7i | − | 0.703371i | ||||||
\(926\) | − | 7.03266e6i | − | 0.269521i | ||||||
\(927\) | −3.81644e7 | + | 2.01494e7i | −1.45868 | + | 0.770127i | ||||
\(928\) | 4.21540e6 | 0.160683 | ||||||||
\(929\) | − | 2.19276e7i | − | 0.833588i | −0.909001 | − | 0.416794i | \(-0.863154\pi\) | ||
0.909001 | − | 0.416794i | \(-0.136846\pi\) | |||||||
\(930\) | −4.95571e7 | + | 8.22043e7i | −1.87888 | + | 3.11664i | ||||
\(931\) | 6.09112e6i | 0.230315i | ||||||||
\(932\) | 8.89580e7i | 3.35463i | ||||||||
\(933\) | −1.11905e7 | + | 1.85626e7i | −0.420868 | + | 0.698126i | ||||
\(934\) | − | 1.06056e7i | − | 0.397805i | ||||||
\(935\) | 6.94977e7 | 2.59981 | ||||||||
\(936\) | −2.63940e7 | + | 1.39351e7i | −0.984728 | + | 0.519899i | ||||
\(937\) | − | 3.88257e7i | − | 1.44468i | −0.691540 | − | 0.722338i | \(-0.743068\pi\) | ||
0.691540 | − | 0.722338i | \(-0.256932\pi\) | |||||||
\(938\) | 1.29978e7i | 0.482351i | ||||||||
\(939\) | 1.68212e7 | − | 2.79027e7i | 0.622578 | − | 1.03272i | ||||
\(940\) | − | 1.11326e7i | − | 0.410940i | ||||||
\(941\) | −2.45501e7 | −0.903815 | −0.451907 | − | 0.892065i | \(-0.649256\pi\) | ||||
−0.451907 | + | 0.892065i | \(0.649256\pi\) | |||||||
\(942\) | 4.58914e7 | + | 2.76658e7i | 1.68502 | + | 1.01582i | ||||
\(943\) | 2.36280e7 | − | 3.15985e7i | 0.865263 | − | 1.15715i | ||||
\(944\) | − | 2.13607e7i | − | 0.780165i | ||||||
\(945\) | −3.66290e7 | − | 2.08088e6i | −1.33428 | − | 0.0757999i | ||||
\(946\) | −6.74213e7 | −2.44945 | ||||||||
\(947\) | 4.71447e7i | 1.70828i | 0.520047 | + | 0.854138i | \(0.325915\pi\) | ||||
−0.520047 | + | 0.854138i | \(0.674085\pi\) | |||||||
\(948\) | 3.52327e7 | − | 5.84433e7i | 1.27328 | − | 2.11210i | ||||
\(949\) | 2.91379e6 | 0.105025 | ||||||||
\(950\) | −5.67197e7 | −2.03904 | ||||||||
\(951\) | −1.64857e6 | + | 2.73461e6i | −0.0591092 | + | 0.0980491i | ||||
\(952\) | 6.37837e7 | 2.28096 | ||||||||
\(953\) | −1.32970e7 | −0.474264 | −0.237132 | − | 0.971477i | \(-0.576207\pi\) | ||||
−0.237132 | + | 0.971477i | \(0.576207\pi\) | |||||||
\(954\) | 6.24848e7 | − | 3.29896e7i | 2.22282 | − | 1.17356i | ||||
\(955\) | −3.93798e7 | −1.39722 | ||||||||
\(956\) | 6.30228e6i | 0.223025i | ||||||||
\(957\) | 1.05713e7 | − | 1.75355e7i | 0.373121 | − | 0.618925i | ||||
\(958\) | 3.15173e6i | 0.110952i | ||||||||
\(959\) | − | 4.34680e7i | − | 1.52624i | ||||||
\(960\) | −3.12822e7 | − | 1.88586e7i | −1.09552 | − | 0.660436i | ||||
\(961\) | 1.79436e7 | 0.626761 | ||||||||
\(962\) | −1.27419e7 | −0.443913 | ||||||||
\(963\) | −8.74312e6 | − | 1.65601e7i | −0.303809 | − | 0.575437i | ||||
\(964\) | 1.13664e7i | 0.393941i | ||||||||
\(965\) | −5.37723e6 | −0.185883 | ||||||||
\(966\) | −1.56881e7 | − | 3.85799e7i | −0.540915 | − | 1.33021i | ||||
\(967\) | 9.80014e6 | 0.337028 | 0.168514 | − | 0.985699i | \(-0.446103\pi\) | ||||
0.168514 | + | 0.985699i | \(0.446103\pi\) | |||||||
\(968\) | − | 7.93903e6i | − | 0.272320i | ||||||
\(969\) | 1.58209e7 | − | 2.62434e7i | 0.541281 | − | 0.897865i | ||||
\(970\) | −8.72696e7 | −2.97806 | ||||||||
\(971\) | 1.61360e7 | 0.549223 | 0.274612 | − | 0.961555i | \(-0.411451\pi\) | ||||
0.274612 | + | 0.961555i | \(0.411451\pi\) | |||||||
\(972\) | 5.53346e7 | − | 2.53119e7i | 1.87859 | − | 0.859327i | ||||
\(973\) | − | 6.00999e6i | − | 0.203513i | ||||||
\(974\) | − | 1.93063e7i | − | 0.652081i | ||||||
\(975\) | −2.51115e7 | − | 1.51386e7i | −0.845984 | − | 0.510004i | ||||
\(976\) | − | 3.11066e7i | − | 1.04527i | ||||||
\(977\) | 8.04948e6 | 0.269793 | 0.134897 | − | 0.990860i | \(-0.456930\pi\) | ||||
0.134897 | + | 0.990860i | \(0.456930\pi\) | |||||||
\(978\) | 2.49925e7 | − | 4.14570e7i | 0.835530 | − | 1.38596i | ||||
\(979\) | 1.02997e7 | 0.343453 | ||||||||
\(980\) | 3.31369e7 | 1.10217 | ||||||||
\(981\) | −2.25583e7 | + | 1.19099e7i | −0.748401 | + | 0.395128i | ||||
\(982\) | −9.73647e7 | −3.22198 | ||||||||
\(983\) | −4.56565e7 | −1.50702 | −0.753510 | − | 0.657436i | \(-0.771641\pi\) | ||||
−0.753510 | + | 0.657436i | \(0.771641\pi\) | |||||||
\(984\) | 7.01374e7 | + | 4.22826e7i | 2.30920 | + | 1.39211i | ||||
\(985\) | − | 9.37997e6i | − | 0.308043i | ||||||
\(986\) | −5.37817e7 | −1.76174 | ||||||||
\(987\) | −2.62405e6 | − | 1.58192e6i | −0.0857391 | − | 0.0516881i | ||||
\(988\) | 2.66057e7i | 0.867127i | ||||||||
\(989\) | 2.40729e7 | − | 3.21934e7i | 0.782595 | − | 1.04659i | ||||
\(990\) | 8.32945e7 | − | 4.39763e7i | 2.70102 | − | 1.42604i | ||||
\(991\) | 1.58528e7 | 0.512769 | 0.256384 | − | 0.966575i | \(-0.417469\pi\) | ||||
0.256384 | + | 0.966575i | \(0.417469\pi\) | |||||||
\(992\) | − | 9.40879e6i | − | 0.303567i | ||||||
\(993\) | −4.42114e7 | − | 2.66530e7i | −1.42286 | − | 0.857773i | ||||
\(994\) | 8.90789e7i | 2.85962i | ||||||||
\(995\) | 4.01757e7i | 1.28649i | ||||||||
\(996\) | 3.97176e7 | + | 2.39439e7i | 1.26863 | + | 0.764797i | ||||
\(997\) | −2.12213e7 | −0.676136 | −0.338068 | − | 0.941122i | \(-0.609773\pi\) | ||||
−0.338068 | + | 0.941122i | \(0.609773\pi\) | |||||||
\(998\) | 9.24661e7i | 2.93871i | ||||||||
\(999\) | 1.33807e7 | + | 760155.i | 0.424195 | + | 0.0240984i |
(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 | 69.6.c.b.68.31 | yes | 32 | |
3.2 | odd | 2 | inner | 69.6.c.b.68.2 | yes | 32 | |
23.22 | odd | 2 | inner | 69.6.c.b.68.32 | yes | 32 | |
69.68 | even | 2 | inner | 69.6.c.b.68.1 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.6.c.b.68.1 | ✓ | 32 | 69.68 | even | 2 | inner | |
69.6.c.b.68.2 | yes | 32 | 3.2 | odd | 2 | inner | |
69.6.c.b.68.31 | yes | 32 | 1.1 | even | 1 | trivial | |
69.6.c.b.68.32 | yes | 32 | 23.22 | odd | 2 | inner |