Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,2,Mod(110,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.110");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.d (of order \(8\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.30767661842\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 134.2 | ||
Character | \(\chi\) | \(=\) | 289.134 |
Dual form | 289.2.d.f.110.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.08335 | − | 1.08335i | −0.766044 | − | 0.766044i | 0.211363 | − | 0.977408i | \(-0.432210\pi\) |
−0.977408 | + | 0.211363i | \(0.932210\pi\) | |||||||
\(3\) | 0.515588 | + | 1.24474i | 0.297675 | + | 0.718651i | 0.999977 | + | 0.00677177i | \(0.00215554\pi\) |
−0.702302 | + | 0.711879i | \(0.747844\pi\) | |||||||
\(4\) | 0.347296i | 0.173648i | ||||||||
\(5\) | 3.26322 | − | 1.35167i | 1.45936 | − | 0.604486i | 0.494954 | − | 0.868919i | \(-0.335185\pi\) |
0.964404 | + | 0.264433i | \(0.0851848\pi\) | |||||||
\(6\) | 0.789927 | − | 1.90705i | 0.322486 | − | 0.778551i | ||||
\(7\) | −0.320860 | − | 0.132905i | −0.121274 | − | 0.0502332i | 0.321221 | − | 0.947004i | \(-0.395907\pi\) |
−0.442495 | + | 0.896771i | \(0.645907\pi\) | |||||||
\(8\) | −1.79046 | + | 1.79046i | −0.633022 | + | 0.633022i | ||||
\(9\) | 0.837775 | − | 0.837775i | 0.279258 | − | 0.279258i | ||||
\(10\) | −4.99955 | − | 2.07088i | −1.58100 | − | 0.654870i | ||||
\(11\) | 0.673052 | − | 1.62489i | 0.202933 | − | 0.489923i | −0.789346 | − | 0.613948i | \(-0.789580\pi\) |
0.992279 | + | 0.124025i | \(0.0395803\pi\) | |||||||
\(12\) | −0.432294 | + | 0.179062i | −0.124792 | + | 0.0516907i | ||||
\(13\) | 3.29086i | 0.912720i | 0.889795 | + | 0.456360i | \(0.150847\pi\) | ||||
−0.889795 | + | 0.456360i | \(0.849153\pi\) | |||||||
\(14\) | 0.203622 | + | 0.491586i | 0.0544202 | + | 0.131382i | ||||
\(15\) | 3.36496 | + | 3.36496i | 0.868829 | + | 0.868829i | ||||
\(16\) | 4.57398 | 1.14349 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −1.81521 | −0.427849 | ||||||||
\(19\) | −1.08335 | − | 1.08335i | −0.248538 | − | 0.248538i | 0.571833 | − | 0.820370i | \(-0.306233\pi\) |
−0.820370 | + | 0.571833i | \(0.806233\pi\) | |||||||
\(20\) | 0.469431 | + | 1.13331i | 0.104968 | + | 0.253415i | ||||
\(21\) | − | 0.467911i | − | 0.102107i | ||||||
\(22\) | −2.48948 | + | 1.03118i | −0.530759 | + | 0.219847i | ||||
\(23\) | 1.07733 | − | 2.60091i | 0.224640 | − | 0.542328i | −0.770870 | − | 0.636993i | \(-0.780178\pi\) |
0.995509 | + | 0.0946652i | \(0.0301780\pi\) | |||||||
\(24\) | −3.15179 | − | 1.30551i | −0.643357 | − | 0.266487i | ||||
\(25\) | 5.28608 | − | 5.28608i | 1.05722 | − | 1.05722i | ||||
\(26\) | 3.56515 | − | 3.56515i | 0.699184 | − | 0.699184i | ||||
\(27\) | 5.20898 | + | 2.15763i | 1.00247 | + | 0.415236i | ||||
\(28\) | 0.0461573 | − | 0.111434i | 0.00872290 | − | 0.0210590i | ||||
\(29\) | 1.09461 | − | 0.453400i | 0.203263 | − | 0.0841944i | −0.278729 | − | 0.960370i | \(-0.589913\pi\) |
0.481993 | + | 0.876175i | \(0.339913\pi\) | |||||||
\(30\) | − | 7.29086i | − | 1.33112i | ||||||
\(31\) | −2.71937 | − | 6.56515i | −0.488414 | − | 1.17914i | −0.955518 | − | 0.294933i | \(-0.904703\pi\) |
0.467104 | − | 0.884202i | \(-0.345297\pi\) | |||||||
\(32\) | −1.37431 | − | 1.37431i | −0.242945 | − | 0.242945i | ||||
\(33\) | 2.36959 | 0.412492 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.22668 | −0.207347 | ||||||||
\(36\) | 0.290956 | + | 0.290956i | 0.0484927 | + | 0.0484927i | ||||
\(37\) | −1.50061 | − | 3.62279i | −0.246698 | − | 0.595582i | 0.751222 | − | 0.660050i | \(-0.229465\pi\) |
−0.997920 | + | 0.0644679i | \(0.979465\pi\) | |||||||
\(38\) | 2.34730i | 0.380782i | ||||||||
\(39\) | −4.09626 | + | 1.69673i | −0.655927 | + | 0.271694i | ||||
\(40\) | −3.42255 | + | 8.26277i | −0.541153 | + | 1.30646i | ||||
\(41\) | 4.54666 | + | 1.88329i | 0.710070 | + | 0.294121i | 0.708333 | − | 0.705878i | \(-0.249447\pi\) |
0.00173627 | + | 0.999998i | \(0.499447\pi\) | |||||||
\(42\) | −0.506912 | + | 0.506912i | −0.0782182 | + | 0.0782182i | ||||
\(43\) | −7.76789 | + | 7.76789i | −1.18459 | + | 1.18459i | −0.206050 | + | 0.978541i | \(0.566061\pi\) |
−0.978541 | + | 0.206050i | \(0.933939\pi\) | |||||||
\(44\) | 0.564319 | + | 0.233749i | 0.0850743 | + | 0.0352389i | ||||
\(45\) | 1.60145 | − | 3.86624i | 0.238730 | − | 0.576346i | ||||
\(46\) | −3.98483 | + | 1.65057i | −0.587531 | + | 0.243363i | ||||
\(47\) | 5.12061i | 0.746918i | 0.927647 | + | 0.373459i | \(0.121828\pi\) | ||||
−0.927647 | + | 0.373459i | \(0.878172\pi\) | |||||||
\(48\) | 2.35829 | + | 5.69341i | 0.340390 | + | 0.821773i | ||||
\(49\) | −4.86446 | − | 4.86446i | −0.694923 | − | 0.694923i | ||||
\(50\) | −11.4534 | −1.61975 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.14290 | −0.158492 | ||||||||
\(53\) | 5.91819 | + | 5.91819i | 0.812926 | + | 0.812926i | 0.985072 | − | 0.172146i | \(-0.0550699\pi\) |
−0.172146 | + | 0.985072i | \(0.555070\pi\) | |||||||
\(54\) | −3.30568 | − | 7.98062i | −0.449846 | − | 1.08602i | ||||
\(55\) | − | 6.21213i | − | 0.837644i | ||||||
\(56\) | 0.812446 | − | 0.336526i | 0.108568 | − | 0.0449702i | ||||
\(57\) | 0.789927 | − | 1.90705i | 0.104628 | − | 0.252595i | ||||
\(58\) | −1.67703 | − | 0.694650i | −0.220205 | − | 0.0912120i | ||||
\(59\) | −7.68260 | + | 7.68260i | −1.00019 | + | 1.00019i | −0.000189365 | 1.00000i | \(0.500060\pi\) | |
−1.00000 | 0.000189365i | \(0.999940\pi\) | ||||||||
\(60\) | −1.16864 | + | 1.16864i | −0.150871 | + | 0.150871i | ||||
\(61\) | 4.07567 | + | 1.68820i | 0.521836 | + | 0.216152i | 0.628023 | − | 0.778195i | \(-0.283864\pi\) |
−0.106187 | + | 0.994346i | \(0.533864\pi\) | |||||||
\(62\) | −4.16632 | + | 10.0584i | −0.529124 | + | 1.27742i | ||||
\(63\) | −0.380153 | + | 0.157464i | −0.0478947 | + | 0.0198386i | ||||
\(64\) | − | 6.17024i | − | 0.771281i | ||||||
\(65\) | 4.44816 | + | 10.7388i | 0.551727 | + | 1.33199i | ||||
\(66\) | −2.56709 | − | 2.56709i | −0.315987 | − | 0.315987i | ||||
\(67\) | −8.07192 | −0.986142 | −0.493071 | − | 0.869989i | \(-0.664126\pi\) | ||||
−0.493071 | + | 0.869989i | \(0.664126\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.79292 | 0.456614 | ||||||||
\(70\) | 1.32893 | + | 1.32893i | 0.158837 | + | 0.158837i | ||||
\(71\) | 4.30479 | + | 10.3927i | 0.510885 | + | 1.23339i | 0.943369 | + | 0.331744i | \(0.107637\pi\) |
−0.432484 | + | 0.901642i | \(0.642363\pi\) | |||||||
\(72\) | 3.00000i | 0.353553i | ||||||||
\(73\) | 1.57275 | − | 0.651455i | 0.184077 | − | 0.0762470i | −0.288741 | − | 0.957407i | \(-0.593237\pi\) |
0.472818 | + | 0.881160i | \(0.343237\pi\) | |||||||
\(74\) | −2.29906 | + | 5.55043i | −0.267261 | + | 0.645224i | ||||
\(75\) | 9.30524 | + | 3.85436i | 1.07448 | + | 0.445063i | ||||
\(76\) | 0.376244 | − | 0.376244i | 0.0431581 | − | 0.0431581i | ||||
\(77\) | −0.431911 | + | 0.431911i | −0.0492208 | + | 0.0492208i | ||||
\(78\) | 6.27584 | + | 2.59954i | 0.710599 | + | 0.294340i | ||||
\(79\) | −4.43213 | + | 10.7001i | −0.498654 | + | 1.20386i | 0.451555 | + | 0.892243i | \(0.350869\pi\) |
−0.950209 | + | 0.311614i | \(0.899131\pi\) | |||||||
\(80\) | 14.9259 | − | 6.18252i | 1.66877 | − | 0.691226i | ||||
\(81\) | 4.04189i | 0.449099i | ||||||||
\(82\) | −2.88537 | − | 6.96589i | −0.318636 | − | 0.769254i | ||||
\(83\) | −1.51883 | − | 1.51883i | −0.166714 | − | 0.166714i | 0.618820 | − | 0.785533i | \(-0.287611\pi\) |
−0.785533 | + | 0.618820i | \(0.787611\pi\) | |||||||
\(84\) | 0.162504 | 0.0177306 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 16.8307 | 1.81490 | ||||||||
\(87\) | 1.12873 | + | 1.12873i | 0.121013 | + | 0.121013i | ||||
\(88\) | 1.70423 | + | 4.11437i | 0.181671 | + | 0.438593i | ||||
\(89\) | 6.41921i | 0.680435i | 0.940347 | + | 0.340218i | \(0.110501\pi\) | ||||
−0.940347 | + | 0.340218i | \(0.889499\pi\) | |||||||
\(90\) | −5.92343 | + | 2.45356i | −0.624384 | + | 0.258628i | ||||
\(91\) | 0.437370 | − | 1.05591i | 0.0458489 | − | 0.110689i | ||||
\(92\) | 0.903287 | + | 0.374154i | 0.0941742 | + | 0.0390082i | ||||
\(93\) | 6.76982 | − | 6.76982i | 0.701998 | − | 0.701998i | ||||
\(94\) | 5.54742 | − | 5.54742i | 0.572173 | − | 0.572173i | ||||
\(95\) | −4.99955 | − | 2.07088i | −0.512943 | − | 0.212468i | ||||
\(96\) | 1.00208 | − | 2.41923i | 0.102274 | − | 0.246912i | ||||
\(97\) | −3.77292 | + | 1.56279i | −0.383082 | + | 0.158678i | −0.565910 | − | 0.824467i | \(-0.691475\pi\) |
0.182828 | + | 0.983145i | \(0.441475\pi\) | |||||||
\(98\) | 10.5398i | 1.06468i | ||||||||
\(99\) | −0.797427 | − | 1.92516i | −0.0801445 | − | 0.193486i | ||||
\(100\) | 1.83584 | + | 1.83584i | 0.183584 | + | 0.183584i | ||||
\(101\) | −5.26857 | −0.524242 | −0.262121 | − | 0.965035i | \(-0.584422\pi\) | ||||
−0.262121 | + | 0.965035i | \(0.584422\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.4388 | −1.81683 | −0.908415 | − | 0.418069i | \(-0.862707\pi\) | ||||
−0.908415 | + | 0.418069i | \(0.862707\pi\) | |||||||
\(104\) | −5.89214 | − | 5.89214i | −0.577772 | − | 0.577772i | ||||
\(105\) | −0.632462 | − | 1.52690i | −0.0617220 | − | 0.149010i | ||||
\(106\) | − | 12.8229i | − | 1.24547i | ||||||
\(107\) | 4.95370 | − | 2.05189i | 0.478892 | − | 0.198364i | −0.130161 | − | 0.991493i | \(-0.541550\pi\) |
0.609053 | + | 0.793129i | \(0.291550\pi\) | |||||||
\(108\) | −0.749337 | + | 1.80906i | −0.0721049 | + | 0.174077i | ||||
\(109\) | −14.3363 | − | 5.93831i | −1.37317 | − | 0.568787i | −0.430525 | − | 0.902578i | \(-0.641672\pi\) |
−0.942647 | + | 0.333792i | \(0.891672\pi\) | |||||||
\(110\) | −6.72992 | + | 6.72992i | −0.641672 | + | 0.641672i | ||||
\(111\) | 3.73573 | − | 3.73573i | 0.354580 | − | 0.354580i | ||||
\(112\) | −1.46761 | − | 0.607903i | −0.138676 | − | 0.0574414i | ||||
\(113\) | 2.68925 | − | 6.49242i | 0.252983 | − | 0.610755i | −0.745459 | − | 0.666551i | \(-0.767770\pi\) |
0.998442 | + | 0.0557962i | \(0.0177697\pi\) | |||||||
\(114\) | −2.92177 | + | 1.21024i | −0.273649 | + | 0.113349i | ||||
\(115\) | − | 9.94356i | − | 0.927242i | ||||||
\(116\) | 0.157464 | + | 0.380153i | 0.0146202 | + | 0.0352963i | ||||
\(117\) | 2.75700 | + | 2.75700i | 0.254885 | + | 0.254885i | ||||
\(118\) | 16.6459 | 1.53238 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −12.0496 | −1.09998 | ||||||||
\(121\) | 5.59090 | + | 5.59090i | 0.508264 | + | 0.508264i | ||||
\(122\) | −2.58647 | − | 6.24429i | −0.234168 | − | 0.565331i | ||||
\(123\) | 6.63041i | 0.597844i | ||||||||
\(124\) | 2.28005 | − | 0.944429i | 0.204755 | − | 0.0848122i | ||||
\(125\) | 3.34627 | − | 8.07861i | 0.299299 | − | 0.722573i | ||||
\(126\) | 0.582427 | + | 0.241249i | 0.0518868 | + | 0.0214922i | ||||
\(127\) | 5.47599 | − | 5.47599i | 0.485916 | − | 0.485916i | −0.421099 | − | 0.907015i | \(-0.638355\pi\) |
0.907015 | + | 0.421099i | \(0.138355\pi\) | |||||||
\(128\) | −9.43315 | + | 9.43315i | −0.833781 | + | 0.833781i | ||||
\(129\) | −13.6740 | − | 5.66397i | −1.20393 | − | 0.498685i | ||||
\(130\) | 6.81498 | − | 16.4528i | 0.597713 | − | 1.44301i | ||||
\(131\) | −17.2013 | + | 7.12501i | −1.50288 | + | 0.622515i | −0.974075 | − | 0.226225i | \(-0.927361\pi\) |
−0.528810 | + | 0.848740i | \(0.677361\pi\) | |||||||
\(132\) | 0.822948i | 0.0716285i | ||||||||
\(133\) | 0.203622 | + | 0.491586i | 0.0176562 | + | 0.0426259i | ||||
\(134\) | 8.74472 | + | 8.74472i | 0.755428 | + | 0.755428i | ||||
\(135\) | 19.9145 | 1.71396 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0719 | 0.860502 | 0.430251 | − | 0.902709i | \(-0.358425\pi\) | ||||
0.430251 | + | 0.902709i | \(0.358425\pi\) | |||||||
\(138\) | −4.10906 | − | 4.10906i | −0.349786 | − | 0.349786i | ||||
\(139\) | −3.27362 | − | 7.90321i | −0.277665 | − | 0.670342i | 0.722105 | − | 0.691783i | \(-0.243175\pi\) |
−0.999770 | + | 0.0214411i | \(0.993175\pi\) | |||||||
\(140\) | − | 0.426022i | − | 0.0360054i | ||||||
\(141\) | −6.37383 | + | 2.64013i | −0.536773 | + | 0.222339i | ||||
\(142\) | 6.59533 | − | 15.9225i | 0.553468 | − | 1.33619i | ||||
\(143\) | 5.34729 | + | 2.21492i | 0.447163 | + | 0.185221i | ||||
\(144\) | 3.83196 | − | 3.83196i | 0.319330 | − | 0.319330i | ||||
\(145\) | 2.95910 | − | 2.95910i | 0.245739 | − | 0.245739i | ||||
\(146\) | −2.40959 | − | 0.998087i | −0.199419 | − | 0.0826022i | ||||
\(147\) | 3.54693 | − | 8.56304i | 0.292546 | − | 0.706268i | ||||
\(148\) | 1.25818 | − | 0.521155i | 0.103422 | − | 0.0428387i | ||||
\(149\) | − | 11.8794i | − | 0.973197i | −0.873626 | − | 0.486599i | \(-0.838237\pi\) | ||
0.873626 | − | 0.486599i | \(-0.161763\pi\) | |||||||
\(150\) | −5.90522 | − | 14.2565i | −0.482159 | − | 1.16403i | ||||
\(151\) | 4.63822 | + | 4.63822i | 0.377453 | + | 0.377453i | 0.870182 | − | 0.492730i | \(-0.164001\pi\) |
−0.492730 | + | 0.870182i | \(0.664001\pi\) | |||||||
\(152\) | 3.87939 | 0.314660 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.935822 | 0.0754107 | ||||||||
\(155\) | −17.7479 | − | 17.7479i | −1.42554 | − | 1.42554i | ||||
\(156\) | −0.589267 | − | 1.42262i | −0.0471791 | − | 0.113901i | ||||
\(157\) | 8.88444i | 0.709055i | 0.935046 | + | 0.354528i | \(0.115358\pi\) | ||||
−0.935046 | + | 0.354528i | \(0.884642\pi\) | |||||||
\(158\) | 16.3935 | − | 6.79042i | 1.30420 | − | 0.540217i | ||||
\(159\) | −4.31526 | + | 10.4180i | −0.342222 | + | 0.826197i | ||||
\(160\) | −6.34228 | − | 2.62706i | −0.501401 | − | 0.207687i | ||||
\(161\) | −0.691346 | + | 0.691346i | −0.0544857 | + | 0.0544857i | ||||
\(162\) | 4.37878 | − | 4.37878i | 0.344030 | − | 0.344030i | ||||
\(163\) | 8.94320 | + | 3.70439i | 0.700485 | + | 0.290150i | 0.704361 | − | 0.709842i | \(-0.251234\pi\) |
−0.00387577 | + | 0.999992i | \(0.501234\pi\) | |||||||
\(164\) | −0.654060 | + | 1.57904i | −0.0510735 | + | 0.123302i | ||||
\(165\) | 7.73249 | − | 3.20290i | 0.601973 | − | 0.249346i | ||||
\(166\) | 3.29086i | 0.255420i | ||||||||
\(167\) | −0.703179 | − | 1.69763i | −0.0544137 | − | 0.131366i | 0.894335 | − | 0.447398i | \(-0.147649\pi\) |
−0.948749 | + | 0.316032i | \(0.897649\pi\) | |||||||
\(168\) | 0.837775 | + | 0.837775i | 0.0646357 | + | 0.0646357i | ||||
\(169\) | 2.17024 | 0.166942 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.81521 | −0.138812 | ||||||||
\(172\) | −2.69776 | − | 2.69776i | −0.205702 | − | 0.205702i | ||||
\(173\) | 8.70976 | + | 21.0272i | 0.662191 | + | 1.59867i | 0.794363 | + | 0.607443i | \(0.207805\pi\) |
−0.132172 | + | 0.991227i | \(0.542195\pi\) | |||||||
\(174\) | − | 2.44562i | − | 0.185402i | ||||||
\(175\) | −2.39864 | + | 0.993548i | −0.181320 | + | 0.0751052i | ||||
\(176\) | 3.07853 | − | 7.43222i | 0.232053 | − | 0.560225i | ||||
\(177\) | −13.5239 | − | 5.60178i | −1.01652 | − | 0.421056i | ||||
\(178\) | 6.95426 | − | 6.95426i | 0.521244 | − | 0.521244i | ||||
\(179\) | 12.3922 | − | 12.3922i | 0.926240 | − | 0.926240i | −0.0712207 | − | 0.997461i | \(-0.522689\pi\) |
0.997461 | + | 0.0712207i | \(0.0226895\pi\) | |||||||
\(180\) | 1.34273 | + | 0.556178i | 0.100081 | + | 0.0414551i | ||||
\(181\) | 1.74585 | − | 4.21485i | 0.129768 | − | 0.313287i | −0.845619 | − | 0.533786i | \(-0.820769\pi\) |
0.975387 | + | 0.220499i | \(0.0707686\pi\) | |||||||
\(182\) | −1.61774 | + | 0.670090i | −0.119915 | + | 0.0496704i | ||||
\(183\) | 5.94356i | 0.439361i | ||||||||
\(184\) | 2.72790 | + | 6.58574i | 0.201104 | + | 0.485507i | ||||
\(185\) | −9.79363 | − | 9.79363i | −0.720042 | − | 0.720042i | ||||
\(186\) | −14.6682 | −1.07552 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.77837 | −0.129701 | ||||||||
\(189\) | −1.38459 | − | 1.38459i | −0.100714 | − | 0.100714i | ||||
\(190\) | 3.17277 | + | 7.65976i | 0.230177 | + | 0.555697i | ||||
\(191\) | − | 9.72462i | − | 0.703649i | −0.936066 | − | 0.351824i | \(-0.885561\pi\) | ||
0.936066 | − | 0.351824i | \(-0.114439\pi\) | |||||||
\(192\) | 7.68035 | − | 3.18130i | 0.554281 | − | 0.229591i | ||||
\(193\) | −0.323101 | + | 0.780035i | −0.0232573 | + | 0.0561481i | −0.935082 | − | 0.354433i | \(-0.884674\pi\) |
0.911824 | + | 0.410581i | \(0.134674\pi\) | |||||||
\(194\) | 5.78045 | + | 2.39434i | 0.415012 | + | 0.171904i | ||||
\(195\) | −11.0736 | + | 11.0736i | −0.792997 | + | 0.792997i | ||||
\(196\) | 1.68941 | − | 1.68941i | 0.120672 | − | 0.120672i | ||||
\(197\) | −15.7068 | − | 6.50598i | −1.11906 | − | 0.463532i | −0.255014 | − | 0.966937i | \(-0.582080\pi\) |
−0.864050 | + | 0.503406i | \(0.832080\pi\) | |||||||
\(198\) | −1.22173 | + | 2.94952i | −0.0868245 | + | 0.209613i | ||||
\(199\) | 11.7291 | − | 4.85837i | 0.831456 | − | 0.344401i | 0.0739773 | − | 0.997260i | \(-0.476431\pi\) |
0.757479 | + | 0.652859i | \(0.226431\pi\) | |||||||
\(200\) | 18.9290i | 1.33848i | ||||||||
\(201\) | −4.16178 | − | 10.0474i | −0.293550 | − | 0.708691i | ||||
\(202\) | 5.70771 | + | 5.70771i | 0.401593 | + | 0.401593i | ||||
\(203\) | −0.411474 | −0.0288798 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.3824 | 1.21404 | ||||||||
\(206\) | 19.9757 | + | 19.9757i | 1.39177 | + | 1.39177i | ||||
\(207\) | −1.27642 | − | 3.08154i | −0.0887171 | − | 0.214182i | ||||
\(208\) | 15.0523i | 1.04369i | ||||||||
\(209\) | −2.48948 | + | 1.03118i | −0.172201 | + | 0.0713279i | ||||
\(210\) | −0.968988 | + | 2.33935i | −0.0668666 | + | 0.161430i | ||||
\(211\) | 21.7392 | + | 9.00467i | 1.49659 | + | 0.619907i | 0.972739 | − | 0.231904i | \(-0.0744955\pi\) |
0.523849 | + | 0.851811i | \(0.324496\pi\) | |||||||
\(212\) | −2.05537 | + | 2.05537i | −0.141163 | + | 0.141163i | ||||
\(213\) | −10.7167 | + | 10.7167i | −0.734296 | + | 0.734296i | ||||
\(214\) | −7.58951 | − | 3.14368i | −0.518808 | − | 0.214897i | ||||
\(215\) | −14.8487 | + | 35.8480i | −1.01267 | + | 2.44481i | ||||
\(216\) | −13.1896 | + | 5.46331i | −0.897438 | + | 0.371731i | ||||
\(217\) | 2.46791i | 0.167533i | ||||||||
\(218\) | 9.09801 | + | 21.9645i | 0.616195 | + | 1.48763i | ||||
\(219\) | 1.62178 | + | 1.62178i | 0.109590 | + | 0.109590i | ||||
\(220\) | 2.15745 | 0.145455 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −8.09421 | −0.543248 | ||||||||
\(223\) | −3.51496 | − | 3.51496i | −0.235379 | − | 0.235379i | 0.579554 | − | 0.814934i | \(-0.303227\pi\) |
−0.814934 | + | 0.579554i | \(0.803227\pi\) | |||||||
\(224\) | 0.258308 | + | 0.623612i | 0.0172590 | + | 0.0416668i | ||||
\(225\) | − | 8.85710i | − | 0.590473i | ||||||
\(226\) | −9.94696 | + | 4.12017i | −0.661662 | + | 0.274069i | ||||
\(227\) | −2.01166 | + | 4.85657i | −0.133518 | + | 0.322342i | −0.976472 | − | 0.215645i | \(-0.930815\pi\) |
0.842954 | + | 0.537986i | \(0.180815\pi\) | |||||||
\(228\) | 0.662312 | + | 0.274339i | 0.0438627 | + | 0.0181685i | ||||
\(229\) | −17.1158 | + | 17.1158i | −1.13104 | + | 1.13104i | −0.141036 | + | 0.990004i | \(0.545043\pi\) |
−0.990004 | + | 0.141036i | \(0.954957\pi\) | |||||||
\(230\) | −10.7724 | + | 10.7724i | −0.710309 | + | 0.710309i | ||||
\(231\) | −0.760305 | − | 0.314929i | −0.0500244 | − | 0.0207208i | ||||
\(232\) | −1.14805 | + | 2.77164i | −0.0753732 | + | 0.181967i | ||||
\(233\) | 26.5356 | − | 10.9914i | 1.73841 | − | 0.720071i | 0.739507 | − | 0.673149i | \(-0.235059\pi\) |
0.998899 | − | 0.0469221i | \(-0.0149412\pi\) | |||||||
\(234\) | − | 5.97359i | − | 0.390506i | ||||||
\(235\) | 6.92139 | + | 16.7097i | 0.451502 | + | 1.09002i | ||||
\(236\) | −2.66814 | − | 2.66814i | −0.173681 | − | 0.173681i | ||||
\(237\) | −15.6040 | −1.01359 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.63310 | −0.170321 | −0.0851606 | − | 0.996367i | \(-0.527140\pi\) | ||||
−0.0851606 | + | 0.996367i | \(0.527140\pi\) | |||||||
\(240\) | 15.3912 | + | 15.3912i | 0.993501 | + | 0.993501i | ||||
\(241\) | −9.69478 | − | 23.4053i | −0.624496 | − | 1.50767i | −0.846373 | − | 0.532591i | \(-0.821218\pi\) |
0.221877 | − | 0.975075i | \(-0.428782\pi\) | |||||||
\(242\) | − | 12.1138i | − | 0.778705i | ||||||
\(243\) | 10.5958 | − | 4.38894i | 0.679723 | − | 0.281550i | ||||
\(244\) | −0.586305 | + | 1.41547i | −0.0375343 | + | 0.0906159i | ||||
\(245\) | −22.4490 | − | 9.29867i | −1.43421 | − | 0.594070i | ||||
\(246\) | 7.18306 | − | 7.18306i | 0.457975 | − | 0.457975i | ||||
\(247\) | 3.56515 | − | 3.56515i | 0.226845 | − | 0.226845i | ||||
\(248\) | 16.6235 | + | 6.88570i | 1.05560 | + | 0.437242i | ||||
\(249\) | 1.10746 | − | 2.67365i | 0.0701824 | − | 0.169435i | ||||
\(250\) | −12.3771 | + | 5.12678i | −0.782799 | + | 0.324246i | ||||
\(251\) | − | 10.6851i | − | 0.674437i | −0.941426 | − | 0.337219i | \(-0.890514\pi\) | ||
0.941426 | − | 0.337219i | \(-0.109486\pi\) | |||||||
\(252\) | −0.0546868 | − | 0.132026i | −0.00344494 | − | 0.00831683i | ||||
\(253\) | −3.50110 | − | 3.50110i | −0.220112 | − | 0.220112i | ||||
\(254\) | −11.8648 | −0.744466 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.09833 | 0.506145 | ||||||||
\(257\) | 2.64209 | + | 2.64209i | 0.164809 | + | 0.164809i | 0.784693 | − | 0.619884i | \(-0.212820\pi\) |
−0.619884 | + | 0.784693i | \(0.712820\pi\) | |||||||
\(258\) | 8.67770 | + | 20.9498i | 0.540250 | + | 1.30428i | ||||
\(259\) | 1.36184i | 0.0846209i | ||||||||
\(260\) | −3.72955 | + | 1.54483i | −0.231297 | + | 0.0958063i | ||||
\(261\) | 0.537185 | − | 1.29688i | 0.0332509 | − | 0.0802749i | ||||
\(262\) | 26.3539 | + | 10.9162i | 1.62815 | + | 0.674402i | ||||
\(263\) | 7.21917 | − | 7.21917i | 0.445153 | − | 0.445153i | −0.448586 | − | 0.893739i | \(-0.648072\pi\) |
0.893739 | + | 0.448586i | \(0.148072\pi\) | |||||||
\(264\) | −4.24264 | + | 4.24264i | −0.261116 | + | 0.261116i | ||||
\(265\) | 27.3118 | + | 11.3129i | 1.67775 | + | 0.694948i | ||||
\(266\) | 0.311966 | − | 0.753153i | 0.0191279 | − | 0.0461788i | ||||
\(267\) | −7.99025 | + | 3.30967i | −0.488995 | + | 0.202549i | ||||
\(268\) | − | 2.80335i | − | 0.171242i | ||||||
\(269\) | −4.49239 | − | 10.8456i | −0.273906 | − | 0.661267i | 0.725738 | − | 0.687971i | \(-0.241499\pi\) |
−0.999643 | + | 0.0267048i | \(0.991499\pi\) | |||||||
\(270\) | −21.5743 | − | 21.5743i | −1.31297 | − | 1.31297i | ||||
\(271\) | −17.0000 | −1.03268 | −0.516338 | − | 0.856385i | \(-0.672705\pi\) | ||||
−0.516338 | + | 0.856385i | \(0.672705\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.53983 | 0.0931947 | ||||||||
\(274\) | −10.9114 | − | 10.9114i | −0.659183 | − | 0.659183i | ||||
\(275\) | −5.03150 | − | 12.1471i | −0.303411 | − | 0.732499i | ||||
\(276\) | 1.31727i | 0.0792901i | ||||||||
\(277\) | −22.4902 | + | 9.31573i | −1.35130 | + | 0.559728i | −0.936655 | − | 0.350254i | \(-0.886095\pi\) |
−0.414648 | + | 0.909982i | \(0.636095\pi\) | |||||||
\(278\) | −5.01547 | + | 12.1084i | −0.300808 | + | 0.726215i | ||||
\(279\) | −7.77834 | − | 3.22189i | −0.465677 | − | 0.192890i | ||||
\(280\) | 2.19632 | − | 2.19632i | 0.131255 | − | 0.131255i | ||||
\(281\) | 4.09687 | − | 4.09687i | 0.244399 | − | 0.244399i | −0.574268 | − | 0.818667i | \(-0.694713\pi\) |
0.818667 | + | 0.574268i | \(0.194713\pi\) | |||||||
\(282\) | 9.76528 | + | 4.04491i | 0.581514 | + | 0.240871i | ||||
\(283\) | 5.86269 | − | 14.1538i | 0.348501 | − | 0.841356i | −0.648297 | − | 0.761388i | \(-0.724518\pi\) |
0.996797 | − | 0.0799677i | \(-0.0254817\pi\) | |||||||
\(284\) | −3.60934 | + | 1.49504i | −0.214175 | + | 0.0887143i | ||||
\(285\) | − | 7.29086i | − | 0.431873i | ||||||
\(286\) | −3.39346 | − | 8.19253i | −0.200659 | − | 0.484434i | ||||
\(287\) | −1.20854 | − | 1.20854i | −0.0713382 | − | 0.0713382i | ||||
\(288\) | −2.30272 | −0.135689 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −6.41147 | −0.376495 | ||||||||
\(291\) | −3.89054 | − | 3.89054i | −0.228068 | − | 0.228068i | ||||
\(292\) | 0.226248 | + | 0.546211i | 0.0132402 | + | 0.0319646i | ||||
\(293\) | 2.98040i | 0.174117i | 0.996203 | + | 0.0870584i | \(0.0277467\pi\) | ||||
−0.996203 | + | 0.0870584i | \(0.972253\pi\) | |||||||
\(294\) | −13.1193 | + | 5.43421i | −0.765136 | + | 0.316930i | ||||
\(295\) | −14.6857 | + | 35.4544i | −0.855034 | + | 2.06424i | ||||
\(296\) | 9.17321 | + | 3.79967i | 0.533182 | + | 0.220851i | ||||
\(297\) | 7.01183 | − | 7.01183i | 0.406868 | − | 0.406868i | ||||
\(298\) | −12.8695 | + | 12.8695i | −0.745512 | + | 0.745512i | ||||
\(299\) | 8.55924 | + | 3.54535i | 0.494993 | + | 0.205033i | ||||
\(300\) | −1.33860 | + | 3.23168i | −0.0772843 | + | 0.186581i | ||||
\(301\) | 3.52479 | − | 1.46002i | 0.203166 | − | 0.0841540i | ||||
\(302\) | − | 10.0496i | − | 0.578291i | ||||||
\(303\) | −2.71641 | − | 6.55800i | −0.156054 | − | 0.376747i | ||||
\(304\) | −4.95522 | − | 4.95522i | −0.284201 | − | 0.284201i | ||||
\(305\) | 15.5817 | 0.892207 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.26857 | −0.186547 | −0.0932736 | − | 0.995641i | \(-0.529733\pi\) | ||||
−0.0932736 | + | 0.995641i | \(0.529733\pi\) | |||||||
\(308\) | −0.150001 | − | 0.150001i | −0.00854711 | − | 0.00854711i | ||||
\(309\) | −9.50683 | − | 22.9515i | −0.540825 | − | 1.30567i | ||||
\(310\) | 38.4543i | 2.18406i | ||||||||
\(311\) | 3.26322 | − | 1.35167i | 0.185040 | − | 0.0766463i | −0.288239 | − | 0.957558i | \(-0.593070\pi\) |
0.473280 | + | 0.880912i | \(0.343070\pi\) | |||||||
\(312\) | 4.29627 | − | 10.3721i | 0.243228 | − | 0.587205i | ||||
\(313\) | 1.36961 | + | 0.567313i | 0.0774151 | + | 0.0320664i | 0.421055 | − | 0.907035i | \(-0.361660\pi\) |
−0.343640 | + | 0.939102i | \(0.611660\pi\) | |||||||
\(314\) | 9.62496 | − | 9.62496i | 0.543168 | − | 0.543168i | ||||
\(315\) | −1.02768 | + | 1.02768i | −0.0579034 | + | 0.0579034i | ||||
\(316\) | −3.71611 | − | 1.53926i | −0.209048 | − | 0.0865903i | ||||
\(317\) | 5.53505 | − | 13.3628i | 0.310880 | − | 0.750530i | −0.688793 | − | 0.724958i | \(-0.741859\pi\) |
0.999673 | − | 0.0255720i | \(-0.00814071\pi\) | |||||||
\(318\) | 15.9612 | − | 6.61136i | 0.895061 | − | 0.370747i | ||||
\(319\) | − | 2.08378i | − | 0.116669i | ||||||
\(320\) | −8.34015 | − | 20.1349i | −0.466228 | − | 1.12557i | ||||
\(321\) | 5.10813 | + | 5.10813i | 0.285108 | + | 0.285108i | ||||
\(322\) | 1.49794 | 0.0834770 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.40373 | −0.0779852 | ||||||||
\(325\) | 17.3958 | + | 17.3958i | 0.964943 | + | 0.964943i | ||||
\(326\) | −5.67546 | − | 13.7018i | −0.314335 | − | 0.758871i | ||||
\(327\) | − | 20.9067i | − | 1.15614i | ||||||
\(328\) | −11.5126 | + | 4.76866i | −0.635675 | + | 0.263305i | ||||
\(329\) | 0.680553 | − | 1.64300i | 0.0375201 | − | 0.0905815i | ||||
\(330\) | −11.8469 | − | 4.90713i | −0.652148 | − | 0.270129i | ||||
\(331\) | −6.38877 | + | 6.38877i | −0.351158 | + | 0.351158i | −0.860540 | − | 0.509382i | \(-0.829874\pi\) |
0.509382 | + | 0.860540i | \(0.329874\pi\) | |||||||
\(332\) | 0.527486 | − | 0.527486i | 0.0289495 | − | 0.0289495i | ||||
\(333\) | −4.29225 | − | 1.77791i | −0.235214 | − | 0.0974287i | ||||
\(334\) | −1.07733 | + | 2.60091i | −0.0589491 | + | 0.142316i | ||||
\(335\) | −26.3405 | + | 10.9106i | −1.43913 | + | 0.596109i | ||||
\(336\) | − | 2.14022i | − | 0.116758i | ||||||
\(337\) | 6.87523 | + | 16.5983i | 0.374518 | + | 0.904166i | 0.992972 | + | 0.118346i | \(0.0377591\pi\) |
−0.618455 | + | 0.785821i | \(0.712241\pi\) | |||||||
\(338\) | −2.35114 | − | 2.35114i | −0.127885 | − | 0.127885i | ||||
\(339\) | 9.46791 | 0.514226 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.4979 | −0.676801 | ||||||||
\(342\) | 1.96651 | + | 1.96651i | 0.106336 | + | 0.106336i | ||||
\(343\) | 1.84463 | + | 4.45334i | 0.0996009 | + | 0.240458i | ||||
\(344\) | − | 27.8161i | − | 1.49975i | ||||||
\(345\) | 12.3771 | − | 5.12678i | 0.666363 | − | 0.276017i | ||||
\(346\) | 13.3441 | − | 32.2156i | 0.717385 | − | 1.73192i | ||||
\(347\) | −7.19125 | − | 2.97871i | −0.386046 | − | 0.159906i | 0.181215 | − | 0.983444i | \(-0.441997\pi\) |
−0.567261 | + | 0.823538i | \(0.691997\pi\) | |||||||
\(348\) | −0.392004 | + | 0.392004i | −0.0210136 | + | 0.0210136i | ||||
\(349\) | 4.70227 | − | 4.70227i | 0.251707 | − | 0.251707i | −0.569963 | − | 0.821670i | \(-0.693043\pi\) |
0.821670 | + | 0.569963i | \(0.193043\pi\) | |||||||
\(350\) | 3.67493 | + | 1.52220i | 0.196433 | + | 0.0813652i | ||||
\(351\) | −7.10045 | + | 17.1420i | −0.378994 | + | 0.914973i | ||||
\(352\) | −3.15808 | + | 1.30812i | −0.168326 | + | 0.0697230i | ||||
\(353\) | − | 4.14559i | − | 0.220648i | −0.993896 | − | 0.110324i | \(-0.964811\pi\) | ||
0.993896 | − | 0.110324i | \(-0.0351888\pi\) | |||||||
\(354\) | 8.58242 | + | 20.7198i | 0.456151 | + | 1.10125i | ||||
\(355\) | 28.0950 | + | 28.0950i | 1.49113 | + | 1.49113i | ||||
\(356\) | −2.22937 | −0.118156 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −26.8503 | −1.41908 | ||||||||
\(359\) | 12.0752 | + | 12.0752i | 0.637307 | + | 0.637307i | 0.949890 | − | 0.312583i | \(-0.101194\pi\) |
−0.312583 | + | 0.949890i | \(0.601194\pi\) | |||||||
\(360\) | 4.05502 | + | 9.78967i | 0.213718 | + | 0.515961i | ||||
\(361\) | − | 16.6527i | − | 0.876458i | ||||||
\(362\) | −6.45752 | + | 2.67479i | −0.339400 | + | 0.140584i | ||||
\(363\) | −4.07661 | + | 9.84181i | −0.213967 | + | 0.516561i | ||||
\(364\) | 0.366712 | + | 0.151897i | 0.0192209 | + | 0.00796157i | ||||
\(365\) | 4.25169 | − | 4.25169i | 0.222543 | − | 0.222543i | ||||
\(366\) | 6.43896 | − | 6.43896i | 0.336570 | − | 0.336570i | ||||
\(367\) | −17.3973 | − | 7.20619i | −0.908131 | − | 0.376160i | −0.120790 | − | 0.992678i | \(-0.538543\pi\) |
−0.787341 | + | 0.616518i | \(0.788543\pi\) | |||||||
\(368\) | 4.92770 | − | 11.8965i | 0.256874 | − | 0.620149i | ||||
\(369\) | 5.38685 | − | 2.23131i | 0.280428 | − | 0.116157i | ||||
\(370\) | 21.2199i | 1.10317i | ||||||||
\(371\) | −1.11236 | − | 2.68547i | −0.0577506 | − | 0.139422i | ||||
\(372\) | 2.35114 | + | 2.35114i | 0.121901 | + | 0.121901i | ||||
\(373\) | 11.7314 | 0.607430 | 0.303715 | − | 0.952763i | \(-0.401773\pi\) | ||||
0.303715 | + | 0.952763i | \(0.401773\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.7811 | 0.608371 | ||||||||
\(376\) | −9.16824 | − | 9.16824i | −0.472816 | − | 0.472816i | ||||
\(377\) | 1.49208 | + | 3.60219i | 0.0768459 | + | 0.185522i | ||||
\(378\) | 3.00000i | 0.154303i | ||||||||
\(379\) | 7.54365 | − | 3.12468i | 0.387491 | − | 0.160504i | −0.180428 | − | 0.983588i | \(-0.557748\pi\) |
0.567920 | + | 0.823084i | \(0.307748\pi\) | |||||||
\(380\) | 0.719210 | − | 1.73633i | 0.0368947 | − | 0.0890716i | ||||
\(381\) | 9.63954 | + | 3.99283i | 0.493849 | + | 0.204559i | ||||
\(382\) | −10.5352 | + | 10.5352i | −0.539026 | + | 0.539026i | ||||
\(383\) | −11.4933 | + | 11.4933i | −0.587282 | + | 0.587282i | −0.936894 | − | 0.349613i | \(-0.886313\pi\) |
0.349613 | + | 0.936894i | \(0.386313\pi\) | |||||||
\(384\) | −16.6054 | − | 6.87820i | −0.847393 | − | 0.351001i | ||||
\(385\) | −0.825621 | + | 1.99323i | −0.0420775 | + | 0.101584i | ||||
\(386\) | 1.19508 | − | 0.495019i | 0.0608281 | − | 0.0251958i | ||||
\(387\) | 13.0155i | 0.661614i | ||||||||
\(388\) | −0.542753 | − | 1.31032i | −0.0275541 | − | 0.0665215i | ||||
\(389\) | −4.10650 | − | 4.10650i | −0.208208 | − | 0.208208i | 0.595298 | − | 0.803505i | \(-0.297034\pi\) |
−0.803505 | + | 0.595298i | \(0.797034\pi\) | |||||||
\(390\) | 23.9932 | 1.21494 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 17.4192 | 0.879803 | ||||||||
\(393\) | −17.7376 | − | 17.7376i | −0.894742 | − | 0.894742i | ||||
\(394\) | 9.96773 | + | 24.0642i | 0.502167 | + | 1.21234i | ||||
\(395\) | 40.9077i | 2.05829i | ||||||||
\(396\) | 0.668601 | − | 0.276944i | 0.0335985 | − | 0.0139169i | ||||
\(397\) | 3.92314 | − | 9.47130i | 0.196897 | − | 0.475351i | −0.794336 | − | 0.607479i | \(-0.792181\pi\) |
0.991233 | + | 0.132128i | \(0.0421810\pi\) | |||||||
\(398\) | −17.9701 | − | 7.44345i | −0.900759 | − | 0.373106i | ||||
\(399\) | −0.506912 | + | 0.506912i | −0.0253773 | + | 0.0253773i | ||||
\(400\) | 24.1784 | − | 24.1784i | 1.20892 | − | 1.20892i | ||||
\(401\) | −28.2357 | − | 11.6956i | −1.41002 | − | 0.584051i | −0.457691 | − | 0.889111i | \(-0.651323\pi\) |
−0.952333 | + | 0.305060i | \(0.901323\pi\) | |||||||
\(402\) | −6.37622 | + | 15.3936i | −0.318017 | + | 0.767761i | ||||
\(403\) | 21.6050 | − | 8.94908i | 1.07622 | − | 0.445785i | ||||
\(404\) | − | 1.82976i | − | 0.0910337i | ||||||
\(405\) | 5.46331 | + | 13.1896i | 0.271474 | + | 0.655396i | ||||
\(406\) | 0.445771 | + | 0.445771i | 0.0221232 | + | 0.0221232i | ||||
\(407\) | −6.89662 | −0.341853 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.9736 | 0.987631 | 0.493815 | − | 0.869567i | \(-0.335602\pi\) | ||||
0.493815 | + | 0.869567i | \(0.335602\pi\) | |||||||
\(410\) | −18.8312 | − | 18.8312i | −0.930007 | − | 0.930007i | ||||
\(411\) | 5.19296 | + | 12.5369i | 0.256150 | + | 0.618400i | ||||
\(412\) | − | 6.40373i | − | 0.315489i | ||||||
\(413\) | 3.48609 | − | 1.44399i | 0.171539 | − | 0.0710539i | ||||
\(414\) | −1.95558 | + | 4.72120i | −0.0961117 | + | 0.232034i | ||||
\(415\) | −7.00926 | − | 2.90333i | −0.344071 | − | 0.142519i | ||||
\(416\) | 4.52265 | − | 4.52265i | 0.221741 | − | 0.221741i | ||||
\(417\) | 8.14960 | − | 8.14960i | 0.399088 | − | 0.399088i | ||||
\(418\) | 3.81410 | + | 1.57985i | 0.186554 | + | 0.0772731i | ||||
\(419\) | 6.47845 | − | 15.6404i | 0.316493 | − | 0.764082i | −0.682942 | − | 0.730473i | \(-0.739300\pi\) |
0.999435 | − | 0.0336094i | \(-0.0107002\pi\) | |||||||
\(420\) | 0.530286 | − | 0.219652i | 0.0258753 | − | 0.0107179i | ||||
\(421\) | 23.7297i | 1.15651i | 0.815855 | + | 0.578257i | \(0.196267\pi\) | ||||
−0.815855 | + | 0.578257i | \(0.803733\pi\) | |||||||
\(422\) | −13.7960 | − | 33.3064i | −0.671577 | − | 1.62133i | ||||
\(423\) | 4.28992 | + | 4.28992i | 0.208583 | + | 0.208583i | ||||
\(424\) | −21.1925 | −1.02920 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 23.2199 | 1.12501 | ||||||||
\(427\) | −1.08335 | − | 1.08335i | −0.0524270 | − | 0.0524270i | ||||
\(428\) | 0.712614 | + | 1.72040i | 0.0344455 | + | 0.0831587i | ||||
\(429\) | 7.79797i | 0.376490i | ||||||||
\(430\) | 54.9223 | − | 22.7496i | 2.64859 | − | 1.09708i | ||||
\(431\) | 9.02832 | − | 21.7963i | 0.434879 | − | 1.04989i | −0.542814 | − | 0.839853i | \(-0.682641\pi\) |
0.977693 | − | 0.210038i | \(-0.0673588\pi\) | |||||||
\(432\) | 23.8257 | + | 9.86895i | 1.14632 | + | 0.474820i | ||||
\(433\) | −8.97643 | + | 8.97643i | −0.431380 | + | 0.431380i | −0.889098 | − | 0.457718i | \(-0.848667\pi\) |
0.457718 | + | 0.889098i | \(0.348667\pi\) | |||||||
\(434\) | 2.67361 | − | 2.67361i | 0.128338 | − | 0.128338i | ||||
\(435\) | 5.20898 | + | 2.15763i | 0.249751 | + | 0.103450i | ||||
\(436\) | 2.06235 | − | 4.97896i | 0.0987687 | − | 0.238449i | ||||
\(437\) | −3.98483 | + | 1.65057i | −0.190620 | + | 0.0789575i | ||||
\(438\) | − | 3.51392i | − | 0.167902i | ||||||
\(439\) | −8.98181 | − | 21.6840i | −0.428678 | − | 1.03492i | −0.979707 | − | 0.200435i | \(-0.935765\pi\) |
0.551029 | − | 0.834486i | \(-0.314235\pi\) | |||||||
\(440\) | 11.1226 | + | 11.1226i | 0.530247 | + | 0.530247i | ||||
\(441\) | −8.15064 | −0.388126 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.4124 | −0.922311 | −0.461156 | − | 0.887319i | \(-0.652565\pi\) | ||||
−0.461156 | + | 0.887319i | \(0.652565\pi\) | |||||||
\(444\) | 1.29741 | + | 1.29741i | 0.0615721 | + | 0.0615721i | ||||
\(445\) | 8.67667 | + | 20.9473i | 0.411314 | + | 0.992999i | ||||
\(446\) | 7.61587i | 0.360622i | ||||||||
\(447\) | 14.7867 | − | 6.12487i | 0.699389 | − | 0.289696i | ||||
\(448\) | −0.820054 | + | 1.97978i | −0.0387439 | + | 0.0935360i | ||||
\(449\) | 16.2846 | + | 6.74529i | 0.768517 | + | 0.318330i | 0.732271 | − | 0.681013i | \(-0.238460\pi\) |
0.0362452 | + | 0.999343i | \(0.488460\pi\) | |||||||
\(450\) | −9.59534 | + | 9.59534i | −0.452329 | + | 0.452329i | ||||
\(451\) | 6.12029 | − | 6.12029i | 0.288193 | − | 0.288193i | ||||
\(452\) | 2.25479 | + | 0.933966i | 0.106057 | + | 0.0439301i | ||||
\(453\) | −3.38196 | + | 8.16478i | −0.158899 | + | 0.383615i | ||||
\(454\) | 7.44069 | − | 3.08204i | 0.349209 | − | 0.144647i | ||||
\(455\) | − | 4.03684i | − | 0.189250i | ||||||
\(456\) | 2.00016 | + | 4.82882i | 0.0936663 | + | 0.226130i | ||||
\(457\) | −26.2489 | − | 26.2489i | −1.22787 | − | 1.22787i | −0.964767 | − | 0.263104i | \(-0.915254\pi\) |
−0.263104 | − | 0.964767i | \(-0.584746\pi\) | |||||||
\(458\) | 37.0847 | 1.73285 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.45336 | 0.161014 | ||||||||
\(461\) | −20.7941 | − | 20.7941i | −0.968480 | − | 0.968480i | 0.0310385 | − | 0.999518i | \(-0.490119\pi\) |
−0.999518 | + | 0.0310385i | \(0.990119\pi\) | |||||||
\(462\) | 0.482499 | + | 1.16485i | 0.0224479 | + | 0.0541940i | ||||
\(463\) | − | 9.72462i | − | 0.451942i | −0.974134 | − | 0.225971i | \(-0.927445\pi\) | ||
0.974134 | − | 0.225971i | \(-0.0725554\pi\) | |||||||
\(464\) | 5.00670 | − | 2.07384i | 0.232430 | − | 0.0962758i | ||||
\(465\) | 12.9409 | − | 31.2420i | 0.600119 | − | 1.44881i | ||||
\(466\) | −40.6549 | − | 16.8398i | −1.88330 | − | 0.780089i | ||||
\(467\) | −3.26872 | + | 3.26872i | −0.151259 | + | 0.151259i | −0.778680 | − | 0.627421i | \(-0.784110\pi\) |
0.627421 | + | 0.778680i | \(0.284110\pi\) | |||||||
\(468\) | −0.957496 | + | 0.957496i | −0.0442603 | + | 0.0442603i | ||||
\(469\) | 2.58996 | + | 1.07279i | 0.119593 | + | 0.0495371i | ||||
\(470\) | 10.6042 | − | 25.6008i | 0.489135 | − | 1.18088i | ||||
\(471\) | −11.0588 | + | 4.58071i | −0.509563 | + | 0.211068i | ||||
\(472\) | − | 27.5107i | − | 1.26628i | ||||||
\(473\) | 7.39378 | + | 17.8502i | 0.339967 | + | 0.820752i | ||||
\(474\) | 16.9046 | + | 16.9046i | 0.776454 | + | 0.776454i | ||||
\(475\) | −11.4534 | −0.525516 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.91622 | 0.454033 | ||||||||
\(478\) | 2.85257 | + | 2.85257i | 0.130474 | + | 0.130474i | ||||
\(479\) | 2.61624 | + | 6.31616i | 0.119539 | + | 0.288593i | 0.972311 | − | 0.233691i | \(-0.0750803\pi\) |
−0.852772 | + | 0.522283i | \(0.825080\pi\) | |||||||
\(480\) | − | 9.24897i | − | 0.422156i | ||||||
\(481\) | 11.9221 | − | 4.93829i | 0.543600 | − | 0.225166i | ||||
\(482\) | −14.8533 | + | 35.8590i | −0.676548 | + | 1.63333i | ||||
\(483\) | −1.21700 | − | 0.504096i | −0.0553752 | − | 0.0229372i | ||||
\(484\) | −1.94170 | + | 1.94170i | −0.0882591 | + | 0.0882591i | ||||
\(485\) | −10.1995 | + | 10.1995i | −0.463135 | + | 0.463135i | ||||
\(486\) | −16.2338 | − | 6.72424i | −0.736378 | − | 0.305018i | ||||
\(487\) | 2.93243 | − | 7.07951i | 0.132881 | − | 0.320803i | −0.843408 | − | 0.537273i | \(-0.819454\pi\) |
0.976289 | + | 0.216470i | \(0.0694544\pi\) | |||||||
\(488\) | −10.3200 | + | 4.27467i | −0.467163 | + | 0.193505i | ||||
\(489\) | 13.0419i | 0.589775i | ||||||||
\(490\) | 14.2464 | + | 34.3938i | 0.643586 | + | 1.55375i | ||||
\(491\) | 6.38139 | + | 6.38139i | 0.287988 | + | 0.287988i | 0.836284 | − | 0.548296i | \(-0.184723\pi\) |
−0.548296 | + | 0.836284i | \(0.684723\pi\) | |||||||
\(492\) | −2.30272 | −0.103815 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −7.72462 | −0.347547 | ||||||||
\(495\) | −5.20437 | − | 5.20437i | −0.233919 | − | 0.233919i | ||||
\(496\) | −12.4384 | − | 30.0289i | −0.558499 | − | 1.34834i | ||||
\(497\) | − | 3.90673i | − | 0.175241i | ||||||
\(498\) | −4.09626 | + | 1.69673i | −0.183558 | + | 0.0760322i | ||||
\(499\) | 10.2149 | − | 24.6610i | 0.457282 | − | 1.10398i | −0.512211 | − | 0.858859i | \(-0.671174\pi\) |
0.969493 | − | 0.245117i | \(-0.0788264\pi\) | |||||||
\(500\) | 2.80567 | + | 1.16215i | 0.125473 | + | 0.0519728i | ||||
\(501\) | 1.75055 | − | 1.75055i | 0.0782088 | − | 0.0782088i | ||||
\(502\) | −11.5757 | + | 11.5757i | −0.516649 | + | 0.516649i | ||||
\(503\) | −11.9427 | − | 4.94682i | −0.532497 | − | 0.220568i | 0.100199 | − | 0.994967i | \(-0.468052\pi\) |
−0.632697 | + | 0.774400i | \(0.718052\pi\) | |||||||
\(504\) | 0.398714 | − | 0.962580i | 0.0177601 | − | 0.0428767i | ||||
\(505\) | −17.1925 | + | 7.12138i | −0.765058 | + | 0.316897i | ||||
\(506\) | 7.58584i | 0.337232i | ||||||||
\(507\) | 1.11895 | + | 2.70139i | 0.0496944 | + | 0.119973i | ||||
\(508\) | 1.90179 | + | 1.90179i | 0.0843784 | + | 0.0843784i | ||||
\(509\) | 27.8753 | 1.23555 | 0.617775 | − | 0.786355i | \(-0.288034\pi\) | ||||
0.617775 | + | 0.786355i | \(0.288034\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.591214 | −0.0261538 | ||||||||
\(512\) | 10.0930 | + | 10.0930i | 0.446051 | + | 0.446051i | ||||
\(513\) | −3.30568 | − | 7.98062i | −0.145949 | − | 0.352353i | ||||
\(514\) | − | 5.72462i | − | 0.252502i | ||||||
\(515\) | −60.1700 | + | 24.9232i | −2.65141 | + | 1.09825i | ||||
\(516\) | 1.96708 | − | 4.74894i | 0.0865957 | − | 0.209060i | ||||
\(517\) | 8.32045 | + | 3.44644i | 0.365933 | + | 0.151574i | ||||
\(518\) | 1.47535 | − | 1.47535i | 0.0648234 | − | 0.0648234i | ||||
\(519\) | −21.6828 | + | 21.6828i | −0.951768 | + | 0.951768i | ||||
\(520\) | −27.1916 | − | 11.2631i | −1.19243 | − | 0.493921i | ||||
\(521\) | −1.95890 | + | 4.72921i | −0.0858211 | + | 0.207190i | −0.960964 | − | 0.276675i | \(-0.910768\pi\) |
0.875143 | + | 0.483865i | \(0.160768\pi\) | |||||||
\(522\) | −1.98694 | + | 0.823016i | −0.0869658 | + | 0.0360224i | ||||
\(523\) | − | 15.3182i | − | 0.669818i | −0.942250 | − | 0.334909i | \(-0.891294\pi\) | ||
0.942250 | − | 0.334909i | \(-0.108706\pi\) | |||||||
\(524\) | −2.47449 | − | 5.97395i | −0.108099 | − | 0.260973i | ||||
\(525\) | −2.47342 | − | 2.47342i | −0.107949 | − | 0.107949i | ||||
\(526\) | −15.6418 | −0.682014 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 10.8384 | 0.471682 | ||||||||
\(529\) | 10.6594 | + | 10.6594i | 0.463450 | + | 0.463450i | ||||
\(530\) | −17.3324 | − | 41.8442i | −0.752872 | − | 1.81759i | ||||
\(531\) | 12.8726i | 0.558622i | ||||||||
\(532\) | −0.170726 | + | 0.0707170i | −0.00740191 | + | 0.00306597i | ||||
\(533\) | −6.19764 | + | 14.9624i | −0.268450 | + | 0.648095i | ||||
\(534\) | 12.2418 | + | 5.07071i | 0.529753 | + | 0.219431i | ||||
\(535\) | 13.3915 | − | 13.3915i | 0.578967 | − | 0.578967i | ||||
\(536\) | 14.4524 | − | 14.4524i | 0.624250 | − | 0.624250i | ||||
\(537\) | 21.8144 | + | 9.03582i | 0.941361 | + | 0.389925i | ||||
\(538\) | −6.88273 | + | 16.6164i | −0.296736 | + | 0.716383i | ||||
\(539\) | −11.1783 | + | 4.63019i | −0.481482 | + | 0.199436i | ||||
\(540\) | 6.91622i | 0.297627i | ||||||||
\(541\) | −14.3302 | − | 34.5961i | −0.616102 | − | 1.48740i | −0.856195 | − | 0.516653i | \(-0.827178\pi\) |
0.240093 | − | 0.970750i | \(-0.422822\pi\) | |||||||
\(542\) | 18.4170 | + | 18.4170i | 0.791076 | + | 0.791076i | ||||
\(543\) | 6.14653 | 0.263773 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −54.8093 | −2.34777 | ||||||||
\(546\) | −1.66818 | − | 1.66818i | −0.0713913 | − | 0.0713913i | ||||
\(547\) | 10.4828 | + | 25.3077i | 0.448211 | + | 1.08208i | 0.972992 | + | 0.230840i | \(0.0741473\pi\) |
−0.524781 | + | 0.851237i | \(0.675853\pi\) | |||||||
\(548\) | 3.49794i | 0.149425i | ||||||||
\(549\) | 4.82882 | − | 2.00016i | 0.206089 | − | 0.0853649i | ||||
\(550\) | −7.70871 | + | 18.6105i | −0.328701 | + | 0.793553i | ||||
\(551\) | −1.67703 | − | 0.694650i | −0.0714440 | − | 0.0295931i | ||||
\(552\) | −6.79106 | + | 6.79106i | −0.289047 | + | 0.289047i | ||||
\(553\) | 2.84419 | − | 2.84419i | 0.120947 | − | 0.120947i | ||||
\(554\) | 34.4569 | + | 14.2725i | 1.46393 | + | 0.606382i | ||||
\(555\) | 7.14104 | − | 17.2400i | 0.303120 | − | 0.731797i | ||||
\(556\) | 2.74476 | − | 1.13692i | 0.116404 | − | 0.0482160i | ||||
\(557\) | − | 9.07604i | − | 0.384564i | −0.981340 | − | 0.192282i | \(-0.938411\pi\) | ||
0.981340 | − | 0.192282i | \(-0.0615888\pi\) | |||||||
\(558\) | 4.93623 | + | 11.9171i | 0.208967 | + | 0.504491i | ||||
\(559\) | −25.5630 | − | 25.5630i | −1.08120 | − | 1.08120i | ||||
\(560\) | −5.61081 | −0.237100 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.87670 | −0.374441 | ||||||||
\(563\) | 27.2161 | + | 27.2161i | 1.14702 | + | 1.14702i | 0.987135 | + | 0.159886i | \(0.0511128\pi\) |
0.159886 | + | 0.987135i | \(0.448887\pi\) | |||||||
\(564\) | −0.916907 | − | 2.21361i | −0.0386087 | − | 0.0932097i | ||||
\(565\) | − | 24.8212i | − | 1.04424i | ||||||
\(566\) | −21.6849 | + | 8.98217i | −0.911483 | + | 0.377549i | ||||
\(567\) | 0.537185 | − | 1.29688i | 0.0225597 | − | 0.0544639i | ||||
\(568\) | −26.3152 | − | 10.9001i | −1.10416 | − | 0.457359i | ||||
\(569\) | 31.9492 | − | 31.9492i | 1.33938 | − | 1.33938i | 0.442723 | − | 0.896658i | \(-0.354012\pi\) |
0.896658 | − | 0.442723i | \(-0.145988\pi\) | |||||||
\(570\) | −7.89856 | + | 7.89856i | −0.330834 | + | 0.330834i | ||||
\(571\) | 28.1386 | + | 11.6554i | 1.17756 | + | 0.487763i | 0.883686 | − | 0.468081i | \(-0.155054\pi\) |
0.293877 | + | 0.955843i | \(0.405054\pi\) | |||||||
\(572\) | −0.769234 | + | 1.85709i | −0.0321633 | + | 0.0776490i | ||||
\(573\) | 12.1046 | − | 5.01390i | 0.505678 | − | 0.209459i | ||||
\(574\) | 2.61856i | 0.109296i | ||||||||
\(575\) | −8.05377 | − | 19.4435i | −0.335865 | − | 0.810851i | ||||
\(576\) | −5.16928 | − | 5.16928i | −0.215386 | − | 0.215386i | ||||
\(577\) | 9.90167 | 0.412212 | 0.206106 | − | 0.978530i | \(-0.433921\pi\) | ||||
0.206106 | + | 0.978530i | \(0.433921\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.13753 | −0.0472740 | ||||||||
\(580\) | 1.02768 | + | 1.02768i | 0.0426722 | + | 0.0426722i | ||||
\(581\) | 0.285473 | + | 0.689193i | 0.0118434 | + | 0.0285925i | ||||
\(582\) | 8.42964i | 0.349420i | ||||||||
\(583\) | 13.5997 | − | 5.63317i | 0.563241 | − | 0.233302i | ||||
\(584\) | −1.64954 | + | 3.98235i | −0.0682585 | + | 0.164791i | ||||
\(585\) | 12.7233 | + | 5.27015i | 0.526042 | + | 0.217894i | ||||
\(586\) | 3.22882 | − | 3.22882i | 0.133381 | − | 0.133381i | ||||
\(587\) | 25.5508 | − | 25.5508i | 1.05460 | − | 1.05460i | 0.0561750 | − | 0.998421i | \(-0.482110\pi\) |
0.998421 | − | 0.0561750i | \(-0.0178905\pi\) | |||||||
\(588\) | 2.97391 | + | 1.23184i | 0.122642 | + | 0.0508000i | ||||
\(589\) | −4.16632 | + | 10.0584i | −0.171670 | + | 0.414449i | ||||
\(590\) | 54.3193 | − | 22.4998i | 2.23629 | − | 0.926302i | ||||
\(591\) | − | 22.9053i | − | 0.942198i | ||||||
\(592\) | −6.86374 | − | 16.5705i | −0.282098 | − | 0.681045i | ||||
\(593\) | −5.24428 | − | 5.24428i | −0.215357 | − | 0.215357i | 0.591182 | − | 0.806538i | \(-0.298662\pi\) |
−0.806538 | + | 0.591182i | \(0.798662\pi\) | |||||||
\(594\) | −15.1925 | −0.623357 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.12567 | 0.168994 | ||||||||
\(597\) | 12.0948 | + | 12.0948i | 0.495007 | + | 0.495007i | ||||
\(598\) | −5.43179 | − | 13.1135i | −0.222123 | − | 0.536251i | ||||
\(599\) | 7.61350i | 0.311079i | 0.987830 | + | 0.155540i | \(0.0497116\pi\) | ||||
−0.987830 | + | 0.155540i | \(0.950288\pi\) | |||||||
\(600\) | −23.5617 | + | 9.75957i | −0.961902 | + | 0.398433i | ||||
\(601\) | −12.4652 | + | 30.0937i | −0.508466 | + | 1.22755i | 0.436300 | + | 0.899801i | \(0.356289\pi\) |
−0.944766 | + | 0.327745i | \(0.893711\pi\) | |||||||
\(602\) | −5.40029 | − | 2.23688i | −0.220100 | − | 0.0911682i | ||||
\(603\) | −6.76245 | + | 6.76245i | −0.275388 | + | 0.275388i | ||||
\(604\) | −1.61084 | + | 1.61084i | −0.0655440 | + | 0.0655440i | ||||
\(605\) | 25.8014 | + | 10.6873i | 1.04898 | + | 0.434501i | ||||
\(606\) | −4.16178 | + | 10.0474i | −0.169061 | + | 0.408149i | ||||
\(607\) | 2.78508 | − | 1.15362i | 0.113043 | − | 0.0468239i | −0.325445 | − | 0.945561i | \(-0.605514\pi\) |
0.438488 | + | 0.898737i | \(0.355514\pi\) | |||||||
\(608\) | 2.97771i | 0.120762i | ||||||||
\(609\) | −0.212151 | − | 0.512178i | −0.00859680 | − | 0.0207545i | ||||
\(610\) | −16.8805 | − | 16.8805i | −0.683470 | − | 0.683470i | ||||
\(611\) | −16.8512 | −0.681728 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.26857 | 0.293575 | 0.146787 | − | 0.989168i | \(-0.453107\pi\) | ||||
0.146787 | + | 0.989168i | \(0.453107\pi\) | |||||||
\(614\) | 3.54101 | + | 3.54101i | 0.142903 | + | 0.142903i | ||||
\(615\) | 8.96215 | + | 21.6365i | 0.361389 | + | 0.872469i | ||||
\(616\) | − | 1.54664i | − | 0.0623158i | ||||||
\(617\) | −31.6381 | + | 13.1049i | −1.27370 | + | 0.527585i | −0.914088 | − | 0.405516i | \(-0.867092\pi\) |
−0.359615 | + | 0.933101i | \(0.617092\pi\) | |||||||
\(618\) | −14.5653 | + | 35.1638i | −0.585903 | + | 1.41449i | ||||
\(619\) | 18.8745 | + | 7.81809i | 0.758631 | + | 0.314235i | 0.728258 | − | 0.685303i | \(-0.240330\pi\) |
0.0303735 | + | 0.999539i | \(0.490330\pi\) | |||||||
\(620\) | 6.16377 | − | 6.16377i | 0.247543 | − | 0.247543i | ||||
\(621\) | 11.2236 | − | 11.2236i | 0.450388 | − | 0.450388i | ||||
\(622\) | −4.99955 | − | 2.07088i | −0.200464 | − | 0.0830348i | ||||
\(623\) | 0.853143 | − | 2.05967i | 0.0341805 | − | 0.0825189i | ||||
\(624\) | −18.7362 | + | 7.76079i | −0.750049 | + | 0.310680i | ||||
\(625\) | 6.49289i | 0.259716i | ||||||||
\(626\) | −0.869173 | − | 2.09837i | −0.0347391 | − | 0.0838677i | ||||
\(627\) | −2.56709 | − | 2.56709i | −0.102520 | − | 0.102520i | ||||
\(628\) | −3.08553 | −0.123126 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 2.22668 | 0.0887131 | ||||||||
\(631\) | −10.9658 | − | 10.9658i | −0.436543 | − | 0.436543i | 0.454304 | − | 0.890847i | \(-0.349888\pi\) |
−0.890847 | + | 0.454304i | \(0.849888\pi\) | |||||||
\(632\) | −11.2226 | − | 27.0936i | −0.446409 | − | 1.07773i | ||||
\(633\) | 31.7023i | 1.26005i | ||||||||
\(634\) | −20.4730 | + | 8.48019i | −0.813087 | + | 0.336792i | ||||
\(635\) | 10.4676 | − | 25.2711i | 0.415396 | − | 1.00285i | ||||
\(636\) | −3.61812 | − | 1.49867i | −0.143468 | − | 0.0594263i | ||||
\(637\) | 16.0083 | − | 16.0083i | 0.634270 | − | 0.634270i | ||||
\(638\) | −2.25746 | + | 2.25746i | −0.0893738 | + | 0.0893738i | ||||
\(639\) | 12.3132 | + | 5.10029i | 0.487102 | + | 0.201764i | ||||
\(640\) | −18.0320 | + | 43.5330i | −0.712776 | + | 1.72079i | ||||
\(641\) | −30.1134 | + | 12.4734i | −1.18941 | + | 0.492669i | −0.887562 | − | 0.460688i | \(-0.847603\pi\) |
−0.301846 | + | 0.953357i | \(0.597603\pi\) | |||||||
\(642\) | − | 11.0678i | − | 0.436811i | ||||||
\(643\) | 15.7696 | + | 38.0712i | 0.621893 | + | 1.50138i | 0.849478 | + | 0.527625i | \(0.176917\pi\) |
−0.227584 | + | 0.973758i | \(0.573083\pi\) | |||||||
\(644\) | −0.240102 | − | 0.240102i | −0.00946135 | − | 0.00946135i | ||||
\(645\) | −52.2772 | −2.05841 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.5131 | 1.04234 | 0.521169 | − | 0.853454i | \(-0.325496\pi\) | ||||
0.521169 | + | 0.853454i | \(0.325496\pi\) | |||||||
\(648\) | −7.23683 | − | 7.23683i | −0.284290 | − | 0.284290i | ||||
\(649\) | 7.31260 | + | 17.6542i | 0.287045 | + | 0.692987i | ||||
\(650\) | − | 37.6914i | − | 1.47838i | ||||||
\(651\) | −3.07191 | + | 1.27243i | −0.120398 | + | 0.0498703i | ||||
\(652\) | −1.28652 | + | 3.10594i | −0.0503841 | + | 0.121638i | ||||
\(653\) | 13.1075 | + | 5.42931i | 0.512937 | + | 0.212465i | 0.624111 | − | 0.781335i | \(-0.285461\pi\) |
−0.111174 | + | 0.993801i | \(0.535461\pi\) | |||||||
\(654\) | −22.6493 | + | 22.6493i | −0.885658 | + | 0.885658i | ||||
\(655\) | −46.5010 | + | 46.5010i | −1.81695 | + | 1.81695i | ||||
\(656\) | 20.7963 | + | 8.61413i | 0.811961 | + | 0.336325i | ||||
\(657\) | 0.771839 | − | 1.86338i | 0.0301123 | − | 0.0726975i | ||||
\(658\) | −2.51722 | + | 1.04267i | −0.0981316 | + | 0.0406474i | ||||
\(659\) | 28.3628i | 1.10486i | 0.833560 | + | 0.552428i | \(0.186299\pi\) | ||||
−0.833560 | + | 0.552428i | \(0.813701\pi\) | |||||||
\(660\) | 1.11236 | + | 2.68547i | 0.0432984 | + | 0.104532i | ||||
\(661\) | 20.6236 | + | 20.6236i | 0.802164 | + | 0.802164i | 0.983433 | − | 0.181270i | \(-0.0580207\pi\) |
−0.181270 | + | 0.983433i | \(0.558021\pi\) | |||||||
\(662\) | 13.8425 | 0.538006 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.43882 | 0.211067 | ||||||||
\(665\) | 1.32893 | + | 1.32893i | 0.0515335 | + | 0.0515335i | ||||
\(666\) | 2.72391 | + | 6.57611i | 0.105549 | + | 0.254819i | ||||
\(667\) | − | 3.33544i | − | 0.129149i | ||||||
\(668\) | 0.589579 | − | 0.244212i | 0.0228115 | − | 0.00944883i | ||||
\(669\) | 2.56294 | − | 6.18748i | 0.0990889 | − | 0.239222i | ||||
\(670\) | 40.3560 | + | 16.7160i | 1.55909 | + | 0.645795i | ||||
\(671\) | 5.48628 | − | 5.48628i | 0.211795 | − | 0.211795i | ||||
\(672\) | −0.643053 | + | 0.643053i | −0.0248063 | + | 0.0248063i | ||||
\(673\) | −27.1323 | − | 11.2386i | −1.04587 | − | 0.433216i | −0.207457 | − | 0.978244i | \(-0.566519\pi\) |
−0.838417 | + | 0.545029i | \(0.816519\pi\) | |||||||
\(674\) | 10.5335 | − | 25.4300i | 0.405734 | − | 0.979529i | ||||
\(675\) | 38.9405 | − | 16.1297i | 1.49882 | − | 0.620832i | ||||
\(676\) | 0.753718i | 0.0289892i | ||||||||
\(677\) | 15.0694 | + | 36.3808i | 0.579164 | + | 1.39823i | 0.893564 | + | 0.448936i | \(0.148197\pi\) |
−0.314400 | + | 0.949291i | \(0.601803\pi\) | |||||||
\(678\) | −10.2571 | − | 10.2571i | −0.393920 | − | 0.393920i | ||||
\(679\) | 1.41828 | 0.0544286 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.08235 | −0.271396 | ||||||||
\(682\) | 13.5396 | + | 13.5396i | 0.518460 | + | 0.518460i | ||||
\(683\) | −10.3950 | − | 25.0957i | −0.397754 | − | 0.960262i | −0.988198 | − | 0.153184i | \(-0.951047\pi\) |
0.590444 | − | 0.807078i | \(-0.298953\pi\) | |||||||
\(684\) | − | 0.630415i | − | 0.0241045i | ||||||
\(685\) | 32.8669 | − | 13.6139i | 1.25578 | − | 0.520161i | ||||
\(686\) | 2.82614 | − | 6.82291i | 0.107903 | − | 0.260500i | ||||
\(687\) | −30.1293 | − | 12.4800i | −1.14951 | − | 0.476141i | ||||
\(688\) | −35.5301 | + | 35.5301i | −1.35457 | + | 1.35457i | ||||
\(689\) | −19.4759 | + | 19.4759i | −0.741974 | + | 0.741974i | ||||
\(690\) | −18.9629 | − | 7.85469i | −0.721905 | − | 0.299023i | ||||
\(691\) | −12.9539 | + | 31.2736i | −0.492791 | + | 1.18970i | 0.460502 | + | 0.887658i | \(0.347669\pi\) |
−0.953294 | + | 0.302045i | \(0.902331\pi\) | |||||||
\(692\) | −7.30268 | + | 3.02487i | −0.277606 | + | 0.114988i | ||||
\(693\) | 0.723689i | 0.0274907i | ||||||||
\(694\) | 4.56365 | + | 11.0176i | 0.173234 | + | 0.418223i | ||||
\(695\) | −21.3651 | − | 21.3651i | −0.810425 | − | 0.810425i | ||||
\(696\) | −4.04189 | −0.153207 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −10.1884 | −0.385637 | ||||||||
\(699\) | 27.3629 | + | 27.3629i | 1.03496 | + | 1.03496i | ||||
\(700\) | −0.345056 | − | 0.833038i | −0.0130419 | − | 0.0314859i | ||||
\(701\) | 20.9540i | 0.791421i | 0.918375 | + | 0.395711i | \(0.129502\pi\) | ||||
−0.918375 | + | 0.395711i | \(0.870498\pi\) | |||||||
\(702\) | 26.2631 | − | 10.8785i | 0.991236 | − | 0.410583i | ||||
\(703\) | −2.29906 | + | 5.55043i | −0.0867108 | + | 0.209338i | ||||
\(704\) | −10.0260 | − | 4.15290i | −0.377868 | − | 0.156518i | ||||
\(705\) | −17.2307 | + | 17.2307i | −0.648944 | + | 0.648944i | ||||
\(706\) | −4.49113 | + | 4.49113i | −0.169026 | + | 0.169026i | ||||
\(707\) | 1.69047 | + | 0.700217i | 0.0635768 | + | 0.0263344i | ||||
\(708\) | 1.94548 | − | 4.69680i | 0.0731155 | − | 0.176516i | ||||
\(709\) | −28.9392 | + | 11.9870i | −1.08683 | + | 0.450182i | −0.852902 | − | 0.522071i | \(-0.825160\pi\) |
−0.233933 | + | 0.972253i | \(0.575160\pi\) | |||||||
\(710\) | − | 60.8735i | − | 2.28454i | ||||||
\(711\) | 5.25116 | + | 12.6774i | 0.196934 | + | 0.475440i | ||||
\(712\) | −11.4933 | − | 11.4933i | −0.430731 | − | 0.430731i | ||||
\(713\) | −20.0051 | −0.749195 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.4433 | 0.764535 | ||||||||
\(716\) | 4.30378 | + | 4.30378i | 0.160840 | + | 0.160840i | ||||
\(717\) | −1.35760 | − | 3.27753i | −0.0507004 | − | 0.122402i | ||||
\(718\) | − | 26.1634i | − | 0.976411i | ||||||
\(719\) | 41.0292 | − | 16.9949i | 1.53013 | − | 0.633801i | 0.550542 | − | 0.834807i | \(-0.314421\pi\) |
0.979590 | + | 0.201006i | \(0.0644211\pi\) | |||||||
\(720\) | 7.32500 | − | 17.6841i | 0.272987 | − | 0.659048i | ||||
\(721\) | 5.91628 | + | 2.45060i | 0.220334 | + | 0.0912652i | ||||
\(722\) | −18.0407 | + | 18.0407i | −0.671406 | + | 0.671406i | ||||
\(723\) | 24.1350 | − | 24.1350i | 0.897589 | − | 0.897589i | ||||
\(724\) | 1.46380 | + | 0.606326i | 0.0544017 | + | 0.0225339i | ||||
\(725\) | 3.38946 | − | 8.18289i | 0.125882 | − | 0.303905i | ||||
\(726\) | 15.0785 | − | 6.24573i | 0.559617 | − | 0.231801i | ||||
\(727\) | 39.5354i | 1.46629i | 0.680074 | + | 0.733143i | \(0.261947\pi\) | ||||
−0.680074 | + | 0.733143i | \(0.738053\pi\) | |||||||
\(728\) | 1.10746 | + | 2.67365i | 0.0410452 | + | 0.0990919i | ||||
\(729\) | 19.5003 | + | 19.5003i | 0.722234 | + | 0.722234i | ||||
\(730\) | −9.21213 | −0.340956 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −2.06418 | −0.0762942 | ||||||||
\(733\) | −9.82807 | − | 9.82807i | −0.363008 | − | 0.363008i | 0.501911 | − | 0.864919i | \(-0.332630\pi\) |
−0.864919 | + | 0.501911i | \(0.832630\pi\) | |||||||
\(734\) | 11.0405 | + | 26.6542i | 0.407513 | + | 0.983824i | ||||
\(735\) | − | 32.7374i | − | 1.20754i | ||||||
\(736\) | −5.05504 | + | 2.09387i | −0.186331 | + | 0.0771809i | ||||
\(737\) | −5.43282 | + | 13.1160i | −0.200121 | + | 0.483134i | ||||
\(738\) | −8.25314 | − | 3.41856i | −0.303802 | − | 0.125839i | ||||
\(739\) | 8.06366 | − | 8.06366i | 0.296626 | − | 0.296626i | −0.543065 | − | 0.839691i | \(-0.682736\pi\) |
0.839691 | + | 0.543065i | \(0.182736\pi\) | |||||||
\(740\) | 3.40129 | − | 3.40129i | 0.125034 | − | 0.125034i | ||||
\(741\) | 6.27584 | + | 2.59954i | 0.230549 | + | 0.0954964i | ||||
\(742\) | −1.70423 | + | 4.11437i | −0.0625642 | + | 0.151043i | ||||
\(743\) | −13.5080 | + | 5.59518i | −0.495559 | + | 0.205267i | −0.616443 | − | 0.787399i | \(-0.711427\pi\) |
0.120884 | + | 0.992667i | \(0.461427\pi\) | |||||||
\(744\) | 24.2422i | 0.888761i | ||||||||
\(745\) | −16.0570 | − | 38.7651i | −0.588284 | − | 1.42024i | ||||
\(746\) | −12.7092 | − | 12.7092i | −0.465319 | − | 0.465319i | ||||
\(747\) | −2.54488 | −0.0931124 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.86215 | −0.0680414 | ||||||||
\(750\) | −12.7630 | − | 12.7630i | −0.466039 | − | 0.466039i | ||||
\(751\) | −10.7226 | − | 25.8867i | −0.391275 | − | 0.944620i | −0.989663 | − | 0.143414i | \(-0.954192\pi\) |
0.598388 | − | 0.801206i | \(-0.295808\pi\) | |||||||
\(752\) | 23.4216i | 0.854097i | ||||||||
\(753\) | 13.3002 | − | 5.50911i | 0.484685 | − | 0.200763i | ||||
\(754\) | 2.28599 | − | 5.51888i | 0.0832510 | − | 0.200986i | ||||
\(755\) | 21.4049 | + | 8.86620i | 0.779004 | + | 0.322674i | ||||
\(756\) | 0.480864 | − | 0.480864i | 0.0174889 | − | 0.0174889i | ||||
\(757\) | −11.0440 | + | 11.0440i | −0.401401 | + | 0.401401i | −0.878726 | − | 0.477326i | \(-0.841606\pi\) |
0.477326 | + | 0.878726i | \(0.341606\pi\) | |||||||
\(758\) | −11.5575 | − | 4.78729i | −0.419789 | − | 0.173882i | ||||
\(759\) | 2.55283 | − | 6.16308i | 0.0926620 | − | 0.223706i | ||||
\(760\) | 12.6593 | − | 5.24366i | 0.459201 | − | 0.190207i | ||||
\(761\) | − | 20.5868i | − | 0.746270i | −0.927777 | − | 0.373135i | \(-0.878283\pi\) | ||
0.927777 | − | 0.373135i | \(-0.121717\pi\) | |||||||
\(762\) | −6.11737 | − | 14.7686i | −0.221609 | − | 0.535011i | ||||
\(763\) | 3.81073 | + | 3.81073i | 0.137958 | + | 0.137958i | ||||
\(764\) | 3.37733 | 0.122187 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.9026 | 0.899768 | ||||||||
\(767\) | −25.2824 | − | 25.2824i | −0.912893 | − | 0.912893i | ||||
\(768\) | 4.17540 | + | 10.0803i | 0.150667 | + | 0.363742i | ||||
\(769\) | 22.2249i | 0.801451i | 0.916198 | + | 0.400726i | \(0.131242\pi\) | ||||
−0.916198 | + | 0.400726i | \(0.868758\pi\) | |||||||
\(770\) | 3.05380 | − | 1.26492i | 0.110051 | − | 0.0455847i | ||||
\(771\) | −1.92649 | + | 4.65095i | −0.0693807 | + | 0.167500i | ||||
\(772\) | −0.270903 | − | 0.112212i | −0.00975002 | − | 0.00403859i | ||||
\(773\) | −19.0980 | + | 19.0980i | −0.686908 | + | 0.686908i | −0.961547 | − | 0.274639i | \(-0.911442\pi\) |
0.274639 | + | 0.961547i | \(0.411442\pi\) | |||||||
\(774\) | 14.1003 | − | 14.1003i | 0.506826 | − | 0.506826i | ||||
\(775\) | −49.0788 | − | 20.3291i | −1.76296 | − | 0.730243i | ||||
\(776\) | 3.95713 | − | 9.55337i | 0.142053 | − | 0.342946i | ||||
\(777\) | −1.69514 | + | 0.702151i | −0.0608129 | + | 0.0251895i | ||||
\(778\) | 8.89756i | 0.318993i | ||||||||
\(779\) | −2.88537 | − | 6.96589i | −0.103379 | − | 0.249579i | ||||
\(780\) | −3.84582 | − | 3.84582i | −0.137703 | − | 0.137703i | ||||
\(781\) | 19.7844 | 0.707940 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.68004 | 0.238725 | ||||||||
\(784\) | −22.2499 | − | 22.2499i | −0.794640 | − | 0.794640i | ||||
\(785\) | 12.0088 | + | 28.9919i | 0.428614 | + | 1.03477i | ||||
\(786\) | 38.4320i | 1.37082i | ||||||||
\(787\) | −19.3839 | + | 8.02908i | −0.690962 | + | 0.286206i | −0.700401 | − | 0.713749i | \(-0.746996\pi\) |
0.00943877 | + | 0.999955i | \(0.496996\pi\) | |||||||
\(788\) | 2.25950 | − | 5.45492i | 0.0804914 | − | 0.194323i | ||||
\(789\) | 12.7081 | + | 5.26387i | 0.452420 | + | 0.187399i | ||||
\(790\) | 44.3173 | − | 44.3173i | 1.57674 | − | 1.57674i | ||||
\(791\) | −1.72574 | + | 1.72574i | −0.0613604 | + | 0.0613604i | ||||
\(792\) | 4.87468 | + | 2.01916i | 0.173214 | + | 0.0717476i | ||||
\(793\) | −5.55562 | + | 13.4125i | −0.197286 | + | 0.476290i | ||||
\(794\) | −14.5109 | + | 6.01060i | −0.514971 | + | 0.213308i | ||||
\(795\) | 39.8289i | 1.41259i | ||||||||
\(796\) | 1.68729 | + | 4.07349i | 0.0598045 | + | 0.144381i | ||||
\(797\) | 24.3490 | + | 24.3490i | 0.862486 | + | 0.862486i | 0.991626 | − | 0.129140i | \(-0.0412217\pi\) |
−0.129140 | + | 0.991626i | \(0.541222\pi\) | |||||||
\(798\) | 1.09833 | 0.0388803 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −14.5294 | −0.513692 | ||||||||
\(801\) | 5.37786 | + | 5.37786i | 0.190017 | + | 0.190017i | ||||
\(802\) | 17.9187 | + | 43.2596i | 0.632732 | + | 1.52755i | ||||
\(803\) | − | 2.99401i | − | 0.105656i | ||||||
\(804\) | 3.48944 | − | 1.44537i | 0.123063 | − | 0.0509744i | ||||
\(805\) | −1.32154 | + | 3.19049i | −0.0465783 | + | 0.112450i | ||||
\(806\) | −33.1008 | − | 13.7108i | −1.16592 | − | 0.482942i | ||||
\(807\) | 11.1837 | − | 11.1837i | 0.393685 | − | 0.393685i | ||||
\(808\) | 9.43315 | − | 9.43315i | 0.331857 | − | 0.331857i | ||||
\(809\) | 26.7228 | + | 11.0690i | 0.939524 | + | 0.389164i | 0.799284 | − | 0.600954i | \(-0.205212\pi\) |
0.140241 | + | 0.990117i | \(0.455212\pi\) | |||||||
\(810\) | 8.37027 | − | 20.2076i | 0.294101 | − | 0.710024i | ||||
\(811\) | 35.6836 | − | 14.7806i | 1.25302 | − | 0.519018i | 0.345259 | − | 0.938507i | \(-0.387791\pi\) |
0.907760 | + | 0.419490i | \(0.137791\pi\) | |||||||
\(812\) | − | 0.142903i | − | 0.00501493i | ||||||
\(813\) | −8.76500 | − | 21.1606i | −0.307402 | − | 0.742134i | ||||
\(814\) | 7.47146 | + | 7.47146i | 0.261874 | + | 0.261874i | ||||
\(815\) | 34.1908 | 1.19765 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.8307 | 0.588831 | ||||||||
\(818\) | −21.6384 | − | 21.6384i | −0.756569 | − | 0.756569i | ||||
\(819\) | −0.518193 | − | 1.25103i | −0.0181071 | − | 0.0437145i | ||||
\(820\) | 6.03684i | 0.210815i | ||||||||
\(821\) | −4.98525 | + | 2.06496i | −0.173986 | + | 0.0720675i | −0.467976 | − | 0.883741i | \(-0.655017\pi\) |
0.293990 | + | 0.955808i | \(0.405017\pi\) | |||||||
\(822\) | 7.95608 | − | 19.2077i | 0.277500 | − | 0.669944i | ||||
\(823\) | −28.3518 | − | 11.7437i | −0.988282 | − | 0.409360i | −0.170795 | − | 0.985307i | \(-0.554634\pi\) |
−0.817487 | + | 0.575947i | \(0.804634\pi\) | |||||||
\(824\) | 33.0139 | − | 33.0139i | 1.15009 | − | 1.15009i | ||||
\(825\) | 12.5258 | − | 12.5258i | 0.436093 | − | 0.436093i | ||||
\(826\) | −5.34100 | − | 2.21232i | −0.185837 | − | 0.0769763i | ||||
\(827\) | 13.5998 | − | 32.8329i | 0.472913 | − | 1.14171i | −0.489957 | − | 0.871746i | \(-0.662988\pi\) |
0.962870 | − | 0.269965i | \(-0.0870123\pi\) | |||||||
\(828\) | 1.07021 | − | 0.443295i | 0.0371923 | − | 0.0154056i | ||||
\(829\) | − | 3.17200i | − | 0.110168i | −0.998482 | − | 0.0550840i | \(-0.982457\pi\) | ||
0.998482 | − | 0.0550840i | \(-0.0175427\pi\) | |||||||
\(830\) | 4.44816 | + | 10.7388i | 0.154398 | + | 0.372750i | ||||
\(831\) | −23.1913 | − | 23.1913i | −0.804498 | − | 0.804498i | ||||
\(832\) | 20.3054 | 0.703963 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −17.6578 | −0.611438 | ||||||||
\(835\) | −4.58926 | − | 4.58926i | −0.158818 | − | 0.158818i | ||||
\(836\) | −0.358124 | − | 0.864587i | −0.0123860 | − | 0.0299024i | ||||
\(837\) | − | 40.0651i | − | 1.38485i | ||||||
\(838\) | −23.9624 | + | 9.92557i | −0.827769 | + | 0.342873i | ||||
\(839\) | 14.0886 | − | 34.0128i | 0.486391 | − | 1.17425i | −0.470132 | − | 0.882596i | \(-0.655794\pi\) |
0.956523 | − | 0.291657i | \(-0.0942064\pi\) | |||||||
\(840\) | 3.86624 | + | 1.60145i | 0.133398 | + | 0.0552553i | ||||
\(841\) | −19.5135 | + | 19.5135i | −0.672880 | + | 0.672880i | ||||
\(842\) | 25.7076 | − | 25.7076i | 0.885941 | − | 0.885941i | ||||
\(843\) | 7.21184 | + | 2.98724i | 0.248389 | + | 0.102886i | ||||
\(844\) | −3.12729 | + | 7.54994i | −0.107646 | + | 0.259880i | ||||
\(845\) | 7.08200 | − | 2.93346i | 0.243628 | − | 0.100914i | ||||
\(846\) | − | 9.29498i | − | 0.319568i | ||||||
\(847\) | −1.05084 | − | 2.53695i | −0.0361073 | − | 0.0871707i | ||||
\(848\) | 27.0697 | + | 27.0697i | 0.929576 | + | 0.929576i | ||||
\(849\) | 20.6405 | 0.708381 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.0392 | −0.378419 | ||||||||
\(852\) | −3.72187 | − | 3.72187i | −0.127509 | − | 0.127509i | ||||
\(853\) | −7.67859 | − | 18.5377i | −0.262910 | − | 0.634720i | 0.736206 | − | 0.676757i | \(-0.236615\pi\) |
−0.999116 | + | 0.0420369i | \(0.986615\pi\) | |||||||
\(854\) | 2.34730i | 0.0803228i | ||||||||
\(855\) | −5.92343 | + | 2.45356i | −0.202577 | + | 0.0839101i | ||||
\(856\) | −5.19557 | + | 12.5432i | −0.177581 | + | 0.428718i | ||||
\(857\) | −18.4129 | − | 7.62686i | −0.628972 | − | 0.260529i | 0.0453444 | − | 0.998971i | \(-0.485561\pi\) |
−0.674316 | + | 0.738443i | \(0.735561\pi\) | |||||||
\(858\) | 8.44794 | − | 8.44794i | 0.288408 | − | 0.288408i | ||||
\(859\) | 16.5128 | − | 16.5128i | 0.563411 | − | 0.563411i | −0.366864 | − | 0.930275i | \(-0.619569\pi\) |
0.930275 | + | 0.366864i | \(0.119569\pi\) | |||||||
\(860\) | −12.4499 | − | 5.15691i | −0.424537 | − | 0.175849i | ||||
\(861\) | 0.881212 | − | 2.12743i | 0.0300316 | − | 0.0725028i | ||||
\(862\) | −33.3939 | + | 13.8322i | −1.13740 | + | 0.471126i | ||||
\(863\) | − | 44.3878i | − | 1.51098i | −0.655162 | − | 0.755488i | \(-0.727400\pi\) | ||
0.655162 | − | 0.755488i | \(-0.272600\pi\) | |||||||
\(864\) | −4.19349 | − | 10.1240i | −0.142665 | − | 0.344425i | ||||
\(865\) | 56.8438 | + | 56.8438i | 1.93275 | + | 1.93275i | ||||
\(866\) | 19.4492 | 0.660912 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.857097 | −0.0290918 | ||||||||
\(869\) | 14.4035 | + | 14.4035i | 0.488604 | + | 0.488604i | ||||
\(870\) | −3.30568 | − | 7.98062i | −0.112073 | − | 0.270568i | ||||
\(871\) | − | 26.5635i | − | 0.900072i | ||||||
\(872\) | 36.3009 | − | 15.0363i | 1.22930 | − | 0.509194i | ||||
\(873\) | −1.85159 | + | 4.47013i | −0.0626667 | + | 0.151291i | ||||
\(874\) | 6.10511 | + | 2.52882i | 0.206509 | + | 0.0855386i | ||||
\(875\) | −2.14737 | + | 2.14737i | −0.0725943 | + | 0.0725943i | ||||
\(876\) | −0.563239 | + | 0.563239i | −0.0190301 | + | 0.0190301i | ||||
\(877\) | −8.45323 | − | 3.50144i | −0.285445 | − | 0.118235i | 0.235367 | − | 0.971907i | \(-0.424371\pi\) |
−0.520812 | + | 0.853671i | \(0.674371\pi\) | |||||||
\(878\) | −13.7609 | + | 33.2218i | −0.464409 | + | 1.12118i | ||||
\(879\) | −3.70982 | + | 1.53666i | −0.125129 | + | 0.0518302i | ||||
\(880\) | − | 28.4142i | − | 0.957841i | ||||||
\(881\) | −2.58998 | − | 6.25276i | −0.0872586 | − | 0.210661i | 0.874226 | − | 0.485519i | \(-0.161369\pi\) |
−0.961485 | + | 0.274858i | \(0.911369\pi\) | |||||||
\(882\) | 8.83000 | + | 8.83000i | 0.297322 | + | 0.297322i | ||||
\(883\) | 47.9760 | 1.61452 | 0.807260 | − | 0.590196i | \(-0.200950\pi\) | ||||
0.807260 | + | 0.590196i | \(0.200950\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −51.7033 | −1.73799 | ||||||||
\(886\) | 21.0304 | + | 21.0304i | 0.706531 | + | 0.706531i | ||||
\(887\) | −15.9572 | − | 38.5241i | −0.535791 | − | 1.29351i | −0.927637 | − | 0.373483i | \(-0.878163\pi\) |
0.391846 | − | 0.920031i | \(-0.371837\pi\) | |||||||
\(888\) | 13.3773i | 0.448914i | ||||||||
\(889\) | −2.48481 | + | 1.02924i | −0.0833379 | + | 0.0345197i | ||||
\(890\) | 13.2934 | − | 32.0932i | 0.445597 | − | 1.07577i | ||||
\(891\) | 6.56763 | + | 2.72040i | 0.220024 | + | 0.0911369i | ||||
\(892\) | 1.22073 | − | 1.22073i | 0.0408732 | − | 0.0408732i | ||||
\(893\) | 5.54742 | − | 5.54742i | 0.185637 | − | 0.185637i | ||||
\(894\) | −22.6546 | − | 9.38384i | −0.757683 | − | 0.313843i | ||||
\(895\) | 23.6884 | − | 57.1889i | 0.791817 | − | 1.91162i | ||||
\(896\) | 4.28043 | − | 1.77301i | 0.142999 | − | 0.0592322i | ||||
\(897\) | 12.4820i | 0.416761i | ||||||||
\(898\) | −10.3344 | − | 24.9494i | −0.344863 | − | 0.832573i | ||||
\(899\) | −5.95328 | − | 5.95328i | −0.198553 | − | 0.198553i | ||||
\(900\) | 3.07604 | 0.102535 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −13.2608 | −0.441537 | ||||||||
\(903\) | 3.63468 | + | 3.63468i | 0.120955 | + | 0.120955i | ||||
\(904\) | 6.80941 | + | 16.4394i | 0.226478 | + | 0.546766i | ||||
\(905\) | − | 16.1138i | − | 0.535641i | ||||||
\(906\) | 12.5092 | − | 5.18147i | 0.415589 | − | 0.172143i | ||||
\(907\) | 12.6037 | − | 30.4280i | 0.418498 | − | 1.01034i | −0.564285 | − | 0.825580i | \(-0.690848\pi\) |
0.982783 | − | 0.184764i | \(-0.0591521\pi\) | |||||||
\(908\) | −1.68667 | − | 0.698641i | −0.0559741 | − | 0.0231852i | ||||
\(909\) | −4.41388 | + | 4.41388i | −0.146399 | + | 0.146399i | ||||
\(910\) | −4.37331 | + | 4.37331i | −0.144974 | + | 0.144974i | ||||
\(911\) | −17.0849 | − | 7.07680i | −0.566048 | − | 0.234465i | 0.0812605 | − | 0.996693i | \(-0.474105\pi\) |
−0.647308 | + | 0.762228i | \(0.724105\pi\) | |||||||
\(912\) | 3.61311 | − | 8.72281i | 0.119642 | − | 0.288841i | ||||
\(913\) | −3.49020 | + | 1.44569i | −0.115509 | + | 0.0478452i | ||||
\(914\) | 56.8735i | 1.88121i | ||||||||
\(915\) | 8.03375 | + | 19.3952i | 0.265587 | + | 0.641185i | ||||
\(916\) | −5.94424 | − | 5.94424i | −0.196403 | − | 0.196403i | ||||
\(917\) | 6.46616 | 0.213531 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.3909 | −0.441726 | −0.220863 | − | 0.975305i | \(-0.570887\pi\) | ||||
−0.220863 | + | 0.975305i | \(0.570887\pi\) | |||||||
\(920\) | 17.8035 | + | 17.8035i | 0.586965 | + | 0.586965i | ||||
\(921\) | −1.68524 | − | 4.06852i | −0.0555304 | − | 0.134062i | ||||
\(922\) | 45.0547i | 1.48380i | ||||||||
\(923\) | −34.2009 | + | 14.1665i | −1.12574 | + | 0.466295i | ||||
\(924\) | 0.109374 | − | 0.264051i | 0.00359813 | − | 0.00868665i | ||||
\(925\) | −27.0827 | − | 11.2180i | −0.890473 | − | 0.368846i | ||||
\(926\) | −10.5352 | + | 10.5352i | −0.346207 | + | 0.346207i | ||||
\(927\) | −15.4476 | + | 15.4476i | −0.507365 | + | 0.507365i | ||||
\(928\) | −2.12743 | − | 0.881212i | −0.0698365 | − | 0.0289272i | ||||
\(929\) | −2.04336 | + | 4.93311i | −0.0670404 | + | 0.161850i | −0.953849 | − | 0.300288i | \(-0.902917\pi\) |
0.886808 | + | 0.462138i | \(0.152917\pi\) | |||||||
\(930\) | −47.8656 | + | 19.8266i | −1.56957 | + | 0.650139i | ||||
\(931\) | 10.5398i | 0.345429i | ||||||||
\(932\) | 3.81728 | + | 9.21572i | 0.125039 | + | 0.301871i | ||||
\(933\) | 3.36496 | + | 3.36496i | 0.110164 | + | 0.110164i | ||||
\(934\) | 7.08235 | 0.231741 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.87258 | −0.322695 | ||||||||
\(937\) | −29.2998 | − | 29.2998i | −0.957182 | − | 0.957182i | 0.0419385 | − | 0.999120i | \(-0.486647\pi\) |
−0.999120 | + | 0.0419385i | \(0.986647\pi\) | |||||||
\(938\) | −1.64362 | − | 3.96804i | −0.0536660 | − | 0.129561i | ||||
\(939\) | 1.99731i | 0.0651798i | ||||||||
\(940\) | −5.80322 | + | 2.40377i | −0.189280 | + | 0.0784025i | ||||
\(941\) | −16.0957 | + | 38.8584i | −0.524704 | + | 1.26675i | 0.410248 | + | 0.911974i | \(0.365442\pi\) |
−0.934952 | + | 0.354774i | \(0.884558\pi\) | |||||||
\(942\) | 16.9431 | + | 7.01805i | 0.552035 | + | 0.228661i | ||||
\(943\) | 9.79655 | − | 9.79655i | 0.319019 | − | 0.319019i | ||||
\(944\) | −35.1400 | + | 35.1400i | −1.14371 | + | 1.14371i | ||||
\(945\) | −6.38976 | − | 2.64672i | −0.207859 | − | 0.0860979i | ||||
\(946\) | 11.3279 | − | 27.3481i | 0.368303 | − | 0.889162i | ||||
\(947\) | 38.2735 | − | 15.8534i | 1.24372 | − | 0.515167i | 0.338846 | − | 0.940842i | \(-0.389963\pi\) |
0.904876 | + | 0.425675i | \(0.139963\pi\) | |||||||
\(948\) | − | 5.41921i | − | 0.176008i | ||||||
\(949\) | 2.14385 | + | 5.17570i | 0.0695922 | + | 0.168010i | ||||
\(950\) | 12.4080 | + | 12.4080i | 0.402569 | + | 0.402569i | ||||
\(951\) | 19.4870 | 0.631910 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.0719 | 0.876945 | 0.438473 | − | 0.898744i | \(-0.355520\pi\) | ||||
0.438473 | + | 0.898744i | \(0.355520\pi\) | |||||||
\(954\) | −10.7427 | − | 10.7427i | −0.347809 | − | 0.347809i | ||||
\(955\) | −13.1445 | − | 31.7336i | −0.425346 | − | 1.02688i | ||||
\(956\) | − | 0.914467i | − | 0.0295760i | ||||||
\(957\) | 2.59376 | − | 1.07437i | 0.0838444 | − | 0.0347295i | ||||
\(958\) | 4.00831 | − | 9.67692i | 0.129503 | − | 0.312647i | ||||
\(959\) | −3.23168 | − | 1.33860i | −0.104356 | − | 0.0432258i | ||||
\(960\) | 20.7626 | − | 20.7626i | 0.670111 | − | 0.670111i | ||||
\(961\) | −13.7859 | + | 13.7859i | −0.444706 | + | 0.444706i | ||||
\(962\) | −18.2657 | − | 7.56589i | −0.588909 | − | 0.243934i | ||||
\(963\) | 2.43106 | − | 5.86910i | 0.0783399 | − | 0.189129i | ||||
\(964\) | 8.12857 | − | 3.36696i | 0.261803 | − | 0.108443i | ||||
\(965\) | 2.98215i | 0.0959989i | ||||||||
\(966\) | 0.772320 | + | 1.86455i | 0.0248490 | + | 0.0599908i | ||||
\(967\) | −30.6628 | − | 30.6628i | −0.986048 | − | 0.986048i | 0.0138557 | − | 0.999904i | \(-0.495589\pi\) |
−0.999904 | + | 0.0138557i | \(0.995589\pi\) | |||||||
\(968\) | −20.0205 | −0.643484 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 22.0993 | 0.709564 | ||||||||
\(971\) | 0.898916 | + | 0.898916i | 0.0288476 | + | 0.0288476i | 0.721383 | − | 0.692536i | \(-0.243507\pi\) |
−0.692536 | + | 0.721383i | \(0.743507\pi\) | |||||||
\(972\) | 1.52426 | + | 3.67989i | 0.0488907 | + | 0.118033i | ||||
\(973\) | 2.97090i | 0.0952428i | ||||||||
\(974\) | −10.8464 | + | 4.49274i | −0.347542 | + | 0.143957i | ||||
\(975\) | −12.6841 | + | 30.6222i | −0.406218 | + | 0.980696i | ||||
\(976\) | 18.6420 | + | 7.72178i | 0.596717 | + | 0.247168i | ||||
\(977\) | −17.5109 | + | 17.5109i | −0.560223 | + | 0.560223i | −0.929371 | − | 0.369148i | \(-0.879650\pi\) |
0.369148 | + | 0.929371i | \(0.379650\pi\) | |||||||
\(978\) | 14.1289 | − | 14.1289i | 0.451794 | − | 0.451794i | ||||
\(979\) | 10.4305 | + | 4.32047i | 0.333361 | + | 0.138083i | ||||
\(980\) | 3.22939 | − | 7.79645i | 0.103159 | − | 0.249048i | ||||
\(981\) | −16.9856 | + | 7.03566i | −0.542308 | + | 0.224631i | ||||
\(982\) | − | 13.8266i | − | 0.441224i | ||||||
\(983\) | −15.1598 | − | 36.5990i | −0.483522 | − | 1.16733i | −0.957925 | − | 0.287018i | \(-0.907336\pi\) |
0.474403 | − | 0.880308i | \(-0.342664\pi\) | |||||||
\(984\) | −11.8715 | − | 11.8715i | −0.378449 | − | 0.378449i | ||||
\(985\) | −60.0488 | −1.91331 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.39599 | 0.0762653 | ||||||||
\(988\) | 1.23816 | + | 1.23816i | 0.0393913 | + | 0.0393913i | ||||
\(989\) | 11.8350 | + | 28.5722i | 0.376331 | + | 0.908543i | ||||
\(990\) | 11.2763i | 0.358385i | ||||||||
\(991\) | 30.7779 | − | 12.7486i | 0.977692 | − | 0.404973i | 0.164122 | − | 0.986440i | \(-0.447521\pi\) |
0.813570 | + | 0.581467i | \(0.197521\pi\) | |||||||
\(992\) | −5.28527 | + | 12.7598i | −0.167808 | + | 0.405123i | ||||
\(993\) | −11.2463 | − | 4.65838i | −0.356891 | − | 0.147829i | ||||
\(994\) | −4.23235 | + | 4.23235i | −0.134242 | + | 0.134242i | ||||
\(995\) | 31.7079 | − | 31.7079i | 1.00521 | − | 1.00521i | ||||
\(996\) | 0.928547 | + | 0.384617i | 0.0294221 | + | 0.0121871i | ||||
\(997\) | −9.90989 | + | 23.9246i | −0.313849 | + | 0.757700i | 0.685706 | + | 0.727879i | \(0.259494\pi\) |
−0.999555 | + | 0.0298209i | \(0.990506\pi\) | |||||||
\(998\) | −37.7828 | + | 15.6501i | −1.19599 | + | 0.495397i | ||||
\(999\) | − | 22.1088i | − | 0.699490i |
(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 | 289.2.d.f.134.2 | 24 | ||
17.2 | even | 8 | inner | 289.2.d.f.179.6 | 24 | ||
17.3 | odd | 16 | 289.2.b.d.288.2 | 6 | |||
17.4 | even | 4 | inner | 289.2.d.f.155.6 | 24 | ||
17.5 | odd | 16 | 289.2.a.d.1.3 | ✓ | 3 | ||
17.6 | odd | 16 | 289.2.c.d.251.2 | 12 | |||
17.7 | odd | 16 | 289.2.c.d.38.6 | 12 | |||
17.8 | even | 8 | inner | 289.2.d.f.110.2 | 24 | ||
17.9 | even | 8 | inner | 289.2.d.f.110.1 | 24 | ||
17.10 | odd | 16 | 289.2.c.d.38.5 | 12 | |||
17.11 | odd | 16 | 289.2.c.d.251.1 | 12 | |||
17.12 | odd | 16 | 289.2.a.e.1.3 | yes | 3 | ||
17.13 | even | 4 | inner | 289.2.d.f.155.5 | 24 | ||
17.14 | odd | 16 | 289.2.b.d.288.1 | 6 | |||
17.15 | even | 8 | inner | 289.2.d.f.179.5 | 24 | ||
17.16 | even | 2 | inner | 289.2.d.f.134.1 | 24 | ||
51.5 | even | 16 | 2601.2.a.x.1.1 | 3 | |||
51.29 | even | 16 | 2601.2.a.w.1.1 | 3 | |||
68.39 | even | 16 | 4624.2.a.bg.1.2 | 3 | |||
68.63 | even | 16 | 4624.2.a.bd.1.2 | 3 | |||
85.29 | odd | 16 | 7225.2.a.s.1.1 | 3 | |||
85.39 | odd | 16 | 7225.2.a.t.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.2.a.d.1.3 | ✓ | 3 | 17.5 | odd | 16 | ||
289.2.a.e.1.3 | yes | 3 | 17.12 | odd | 16 | ||
289.2.b.d.288.1 | 6 | 17.14 | odd | 16 | |||
289.2.b.d.288.2 | 6 | 17.3 | odd | 16 | |||
289.2.c.d.38.5 | 12 | 17.10 | odd | 16 | |||
289.2.c.d.38.6 | 12 | 17.7 | odd | 16 | |||
289.2.c.d.251.1 | 12 | 17.11 | odd | 16 | |||
289.2.c.d.251.2 | 12 | 17.6 | odd | 16 | |||
289.2.d.f.110.1 | 24 | 17.9 | even | 8 | inner | ||
289.2.d.f.110.2 | 24 | 17.8 | even | 8 | inner | ||
289.2.d.f.134.1 | 24 | 17.16 | even | 2 | inner | ||
289.2.d.f.134.2 | 24 | 1.1 | even | 1 | trivial | ||
289.2.d.f.155.5 | 24 | 17.13 | even | 4 | inner | ||
289.2.d.f.155.6 | 24 | 17.4 | even | 4 | inner | ||
289.2.d.f.179.5 | 24 | 17.15 | even | 8 | inner | ||
289.2.d.f.179.6 | 24 | 17.2 | even | 8 | inner | ||
2601.2.a.w.1.1 | 3 | 51.29 | even | 16 | |||
2601.2.a.x.1.1 | 3 | 51.5 | even | 16 | |||
4624.2.a.bd.1.2 | 3 | 68.63 | even | 16 | |||
4624.2.a.bg.1.2 | 3 | 68.39 | even | 16 | |||
7225.2.a.s.1.1 | 3 | 85.29 | odd | 16 | |||
7225.2.a.t.1.1 | 3 | 85.39 | odd | 16 |