Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,2,Mod(293,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.293");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.w (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.79102412128\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 293.13 | ||
Character | \(\chi\) | \(=\) | 600.293 |
Dual form | 600.2.w.j.557.13 |
$q$-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 \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.11940 | + | 0.864261i | 0.791534 | + | 0.611125i | ||||
\(3\) | 1.72368 | + | 0.170116i | 0.995165 | + | 0.0982164i | ||||
\(4\) | 0.506107 | + | 1.93490i | 0.253054 | + | 0.967452i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.78246 | + | 1.68013i | 0.727685 | + | 0.685911i | ||||
\(7\) | −2.06963 | + | 2.06963i | −0.782246 | + | 0.782246i | −0.980209 | − | 0.197964i | \(-0.936567\pi\) |
0.197964 | + | 0.980209i | \(0.436567\pi\) | |||||||
\(8\) | −1.10573 | + | 2.60334i | −0.390933 | + | 0.920419i | ||||
\(9\) | 2.94212 | + | 0.586449i | 0.980707 | + | 0.195483i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.510276 | 0.153854 | 0.0769270 | − | 0.997037i | \(-0.475489\pi\) | ||||
0.0769270 | + | 0.997037i | \(0.475489\pi\) | |||||||
\(12\) | 0.543207 | + | 3.42125i | 0.156810 | + | 0.987629i | ||||
\(13\) | −0.750647 | + | 0.750647i | −0.208192 | + | 0.208192i | −0.803499 | − | 0.595307i | \(-0.797031\pi\) |
0.595307 | + | 0.803499i | \(0.297031\pi\) | |||||||
\(14\) | −4.10544 | + | 0.528041i | −1.09722 | + | 0.141125i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.48771 | + | 1.95854i | −0.871928 | + | 0.489635i | ||||
\(17\) | −3.14698 | − | 3.14698i | −0.763254 | − | 0.763254i | 0.213656 | − | 0.976909i | \(-0.431463\pi\) |
−0.976909 | + | 0.213656i | \(0.931463\pi\) | |||||||
\(18\) | 2.78656 | + | 3.19923i | 0.656799 | + | 0.754066i | ||||
\(19\) | 6.01198 | 1.37924 | 0.689622 | − | 0.724170i | \(-0.257777\pi\) | ||||
0.689622 | + | 0.724170i | \(0.257777\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.91945 | + | 3.21529i | −0.855293 | + | 0.701634i | ||||
\(22\) | 0.571203 | + | 0.441012i | 0.121781 | + | 0.0940240i | ||||
\(23\) | 2.54575 | − | 2.54575i | 0.530825 | − | 0.530825i | −0.389993 | − | 0.920818i | \(-0.627522\pi\) |
0.920818 | + | 0.389993i | \(0.127522\pi\) | |||||||
\(24\) | −2.34878 | + | 4.29921i | −0.479443 | + | 0.877573i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.48903 | + | 0.191519i | −0.292023 | + | 0.0375599i | ||||
\(27\) | 4.97150 | + | 1.51135i | 0.956766 | + | 0.290859i | ||||
\(28\) | −5.05199 | − | 2.95708i | −0.954736 | − | 0.558835i | ||||
\(29\) | − | 5.10739i | − | 0.948418i | −0.880412 | − | 0.474209i | \(-0.842734\pi\) | ||
0.880412 | − | 0.474209i | \(-0.157266\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.56672 | −0.820207 | −0.410104 | − | 0.912039i | \(-0.634507\pi\) | ||||
−0.410104 | + | 0.912039i | \(0.634507\pi\) | |||||||
\(32\) | −5.59683 | − | 0.821906i | −0.989389 | − | 0.145294i | ||||
\(33\) | 0.879551 | + | 0.0868061i | 0.153110 | + | 0.0151110i | ||||
\(34\) | −0.802913 | − | 6.24253i | −0.137699 | − | 1.07058i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.354305 | + | 5.98953i | 0.0590509 | + | 0.998255i | ||||
\(37\) | 6.76263 | + | 6.76263i | 1.11177 | + | 1.11177i | 0.992911 | + | 0.118858i | \(0.0379234\pi\) |
0.118858 | + | 0.992911i | \(0.462077\pi\) | |||||||
\(38\) | 6.72981 | + | 5.19592i | 1.09172 | + | 0.842890i | ||||
\(39\) | −1.42157 | + | 1.16618i | −0.227633 | + | 0.186738i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.24355i | − | 0.662732i | −0.943502 | − | 0.331366i | \(-0.892491\pi\) | ||
0.943502 | − | 0.331366i | \(-0.107509\pi\) | |||||||
\(42\) | −7.16627 | + | 0.211772i | −1.10578 | + | 0.0326771i | ||||
\(43\) | 5.95972 | − | 5.95972i | 0.908848 | − | 0.908848i | −0.0873310 | − | 0.996179i | \(-0.527834\pi\) |
0.996179 | + | 0.0873310i | \(0.0278338\pi\) | |||||||
\(44\) | 0.258254 | + | 0.987336i | 0.0389333 | + | 0.148846i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.04990 | − | 0.649518i | 0.744567 | − | 0.0957661i | ||||
\(47\) | 3.33849 | + | 3.33849i | 0.486969 | + | 0.486969i | 0.907349 | − | 0.420379i | \(-0.138103\pi\) |
−0.420379 | + | 0.907349i | \(0.638103\pi\) | |||||||
\(48\) | −6.34486 | + | 2.78257i | −0.915802 | + | 0.401630i | ||||
\(49\) | − | 1.56672i | − | 0.223817i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.88902 | − | 5.95972i | −0.684599 | − | 0.834527i | ||||
\(52\) | −1.83234 | − | 1.07252i | −0.254100 | − | 0.148732i | ||||
\(53\) | −5.75871 | − | 5.75871i | −0.791019 | − | 0.791019i | 0.190641 | − | 0.981660i | \(-0.438943\pi\) |
−0.981660 | + | 0.190641i | \(0.938943\pi\) | |||||||
\(54\) | 4.25889 | + | 5.98848i | 0.579562 | + | 0.814928i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.09950 | − | 7.67638i | −0.414188 | − | 1.02580i | ||||
\(57\) | 10.3627 | + | 1.02273i | 1.37257 | + | 0.135464i | ||||
\(58\) | 4.41411 | − | 5.71720i | 0.579602 | − | 0.750706i | ||||
\(59\) | − | 1.16514i | − | 0.151689i | −0.997120 | − | 0.0758444i | \(-0.975835\pi\) | ||
0.997120 | − | 0.0758444i | \(-0.0241652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.92929i | − | 0.631131i | −0.948904 | − | 0.315565i | \(-0.897806\pi\) | ||
0.948904 | − | 0.315565i | \(-0.102194\pi\) | |||||||
\(62\) | −5.11198 | − | 3.94684i | −0.649222 | − | 0.501249i | ||||
\(63\) | −7.30283 | + | 4.87536i | −0.920070 | + | 0.614238i | ||||
\(64\) | −5.55474 | − | 5.75716i | −0.694342 | − | 0.719645i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.909545 | + | 0.857332i | 0.111957 | + | 0.105530i | ||||
\(67\) | −7.98415 | − | 7.98415i | −0.975419 | − | 0.975419i | 0.0242864 | − | 0.999705i | \(-0.492269\pi\) |
−0.999705 | + | 0.0242864i | \(0.992269\pi\) | |||||||
\(68\) | 4.49639 | − | 7.68180i | 0.545267 | − | 0.931555i | ||||
\(69\) | 4.82112 | − | 3.95497i | 0.580395 | − | 0.476123i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.09150i | − | 0.604250i | −0.953268 | − | 0.302125i | \(-0.902304\pi\) | ||
0.953268 | − | 0.302125i | \(-0.0976959\pi\) | |||||||
\(72\) | −4.77991 | + | 7.01088i | −0.563317 | + | 0.826241i | ||||
\(73\) | 3.20654 | + | 3.20654i | 0.375297 | + | 0.375297i | 0.869402 | − | 0.494105i | \(-0.164504\pi\) |
−0.494105 | + | 0.869402i | \(0.664504\pi\) | |||||||
\(74\) | 1.72540 | + | 13.4148i | 0.200574 | + | 1.55943i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.04271 | + | 11.6326i | 0.349023 | + | 1.33435i | ||||
\(77\) | −1.05608 | + | 1.05608i | −0.120352 | + | 0.120352i | ||||
\(78\) | −2.59918 | + | 0.0768090i | −0.294300 | + | 0.00869691i | ||||
\(79\) | 7.31215i | 0.822682i | 0.911482 | + | 0.411341i | \(0.134939\pi\) | ||||
−0.911482 | + | 0.411341i | \(0.865061\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.31215 | + | 3.45081i | 0.923573 | + | 0.383423i | ||||
\(82\) | 3.66754 | − | 4.75023i | 0.405012 | − | 0.524575i | ||||
\(83\) | 4.77995 | + | 4.77995i | 0.524668 | + | 0.524668i | 0.918978 | − | 0.394310i | \(-0.129016\pi\) |
−0.394310 | + | 0.918978i | \(0.629016\pi\) | |||||||
\(84\) | −8.20494 | − | 5.95647i | −0.895233 | − | 0.649904i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.8220 | − | 1.52055i | 1.27480 | − | 0.163965i | ||||
\(87\) | 0.868848 | − | 8.80349i | 0.0931502 | − | 0.943833i | ||||
\(88\) | −0.564226 | + | 1.32842i | −0.0601467 | + | 0.141610i | ||||
\(89\) | −12.6431 | −1.34017 | −0.670083 | − | 0.742286i | \(-0.733741\pi\) | ||||
−0.670083 | + | 0.742286i | \(0.733741\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.10712i | − | 0.325715i | ||||||
\(92\) | 6.21420 | + | 3.63736i | 0.647875 | + | 0.379221i | ||||
\(93\) | −7.87155 | − | 0.776871i | −0.816241 | − | 0.0805578i | ||||
\(94\) | 0.851777 | + | 6.62243i | 0.0878541 | + | 0.683052i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.50730 | − | 2.36881i | −0.970335 | − | 0.241766i | ||||
\(97\) | −10.8789 | + | 10.8789i | −1.10458 | + | 1.10458i | −0.110732 | + | 0.993850i | \(0.535320\pi\) |
−0.993850 | + | 0.110732i | \(0.964680\pi\) | |||||||
\(98\) | 1.35405 | − | 1.75378i | 0.136780 | − | 0.177159i | ||||
\(99\) | 1.50129 | + | 0.299251i | 0.150886 | + | 0.0300759i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.41002 | −0.637821 | −0.318911 | − | 0.947785i | \(-0.603317\pi\) | ||||
−0.318911 | + | 0.947785i | \(0.603317\pi\) | |||||||
\(102\) | −0.322010 | − | 10.8967i | −0.0318838 | − | 1.07893i | ||||
\(103\) | 1.86309 | + | 1.86309i | 0.183575 | + | 0.183575i | 0.792912 | − | 0.609336i | \(-0.208564\pi\) |
−0.609336 | + | 0.792912i | \(0.708564\pi\) | |||||||
\(104\) | −1.12418 | − | 2.78420i | −0.110235 | − | 0.273013i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.46927 | − | 11.4233i | −0.142708 | − | 1.10953i | ||||
\(107\) | 10.0319 | − | 10.0319i | 0.969824 | − | 0.969824i | −0.0297341 | − | 0.999558i | \(-0.509466\pi\) |
0.999558 | + | 0.0297341i | \(0.00946607\pi\) | |||||||
\(108\) | −0.408206 | + | 10.3843i | −0.0392797 | + | 0.999228i | ||||
\(109\) | −12.6448 | −1.21115 | −0.605577 | − | 0.795786i | \(-0.707058\pi\) | ||||
−0.605577 | + | 0.795786i | \(0.707058\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.5062 | + | 12.8070i | 0.997200 | + | 1.21559i | ||||
\(112\) | 3.16482 | − | 11.2717i | 0.299047 | − | 1.06508i | ||||
\(113\) | 1.88933 | − | 1.88933i | 0.177733 | − | 0.177733i | −0.612634 | − | 0.790367i | \(-0.709890\pi\) |
0.790367 | + | 0.612634i | \(0.209890\pi\) | |||||||
\(114\) | 10.7161 | + | 10.1009i | 1.00365 | + | 0.946039i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.88231 | − | 2.58489i | 0.917549 | − | 0.240001i | ||||
\(117\) | −2.64871 | + | 1.76828i | −0.244874 | + | 0.163477i | ||||
\(118\) | 1.00699 | − | 1.30426i | 0.0927008 | − | 0.120067i | ||||
\(119\) | 13.0261 | 1.19410 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7396 | −0.976329 | ||||||||
\(122\) | 4.26019 | − | 5.51784i | 0.385700 | − | 0.499562i | ||||
\(123\) | 0.721896 | − | 7.31452i | 0.0650912 | − | 0.659528i | ||||
\(124\) | −2.31125 | − | 8.83617i | −0.207556 | − | 0.793511i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −12.3884 | − | 0.854070i | −1.10364 | − | 0.0760866i | ||||
\(127\) | −0.964015 | + | 0.964015i | −0.0855425 | + | 0.0855425i | −0.748583 | − | 0.663041i | \(-0.769266\pi\) |
0.663041 | + | 0.748583i | \(0.269266\pi\) | |||||||
\(128\) | −1.24228 | − | 11.2453i | −0.109803 | − | 0.993953i | ||||
\(129\) | 11.2865 | − | 9.25878i | 0.993718 | − | 0.815190i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.59234 | 0.663346 | 0.331673 | − | 0.943395i | \(-0.392387\pi\) | ||||
0.331673 | + | 0.943395i | \(0.392387\pi\) | |||||||
\(132\) | 0.277186 | + | 1.74578i | 0.0241259 | + | 0.151951i | ||||
\(133\) | −12.4426 | + | 12.4426i | −1.07891 | + | 1.07891i | ||||
\(134\) | −2.03706 | − | 15.8378i | −0.175975 | − | 1.36818i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.6723 | − | 4.71295i | 1.00089 | − | 0.404132i | ||||
\(137\) | 0.713542 | + | 0.713542i | 0.0609620 | + | 0.0609620i | 0.736931 | − | 0.675968i | \(-0.236274\pi\) |
−0.675968 | + | 0.736931i | \(0.736274\pi\) | |||||||
\(138\) | 8.81488 | − | 0.260491i | 0.750373 | − | 0.0221744i | ||||
\(139\) | 9.01457 | 0.764606 | 0.382303 | − | 0.924037i | \(-0.375131\pi\) | ||||
0.382303 | + | 0.924037i | \(0.375131\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.18655 | + | 6.32241i | 0.436787 | + | 0.532443i | ||||
\(142\) | 4.40038 | − | 5.69942i | 0.369272 | − | 0.478284i | ||||
\(143\) | −0.383038 | + | 0.383038i | −0.0320312 | + | 0.0320312i | ||||
\(144\) | −11.4099 | + | 3.71689i | −0.950821 | + | 0.309741i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.818111 | + | 6.36069i | 0.0677073 | + | 0.526414i | ||||
\(147\) | 0.266524 | − | 2.70052i | 0.0219825 | − | 0.222735i | ||||
\(148\) | −9.66243 | + | 16.5077i | −0.794247 | + | 1.35692i | ||||
\(149\) | − | 13.1573i | − | 1.07789i | −0.842341 | − | 0.538944i | \(-0.818823\pi\) | ||
0.842341 | − | 0.538944i | \(-0.181177\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.75982 | 0.224591 | 0.112295 | − | 0.993675i | \(-0.464180\pi\) | ||||
0.112295 | + | 0.993675i | \(0.464180\pi\) | |||||||
\(152\) | −6.64761 | + | 15.6512i | −0.539192 | + | 1.26948i | ||||
\(153\) | −7.41324 | − | 11.1043i | −0.599325 | − | 0.897731i | ||||
\(154\) | −2.09491 | + | 0.269447i | −0.168812 | + | 0.0217126i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.97591 | − | 2.16039i | −0.238263 | − | 0.172970i | ||||
\(157\) | −4.38090 | − | 4.38090i | −0.349634 | − | 0.349634i | 0.510339 | − | 0.859973i | \(-0.329520\pi\) |
−0.859973 | + | 0.510339i | \(0.829520\pi\) | |||||||
\(158\) | −6.31961 | + | 8.18522i | −0.502761 | + | 0.651181i | ||||
\(159\) | −8.94650 | − | 10.9058i | −0.709504 | − | 0.864886i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.5375i | 0.830472i | ||||||||
\(162\) | 6.32222 | + | 11.0467i | 0.496720 | + | 0.867911i | ||||
\(163\) | −0.470868 | + | 0.470868i | −0.0368812 | + | 0.0368812i | −0.725307 | − | 0.688426i | \(-0.758302\pi\) |
0.688426 | + | 0.725307i | \(0.258302\pi\) | |||||||
\(164\) | 8.21087 | − | 2.14769i | 0.641162 | − | 0.167707i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.21955 | + | 9.48180i | 0.0946553 | + | 0.735930i | ||||
\(167\) | −0.495354 | − | 0.495354i | −0.0383316 | − | 0.0383316i | 0.687681 | − | 0.726013i | \(-0.258629\pi\) |
−0.726013 | + | 0.687681i | \(0.758629\pi\) | |||||||
\(168\) | −4.03666 | − | 13.7589i | −0.311435 | − | 1.06152i | ||||
\(169\) | 11.8731i | 0.913312i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.6880 | + | 3.52572i | 1.35263 | + | 0.269619i | ||||
\(172\) | 14.5477 | + | 8.51523i | 1.10925 | + | 0.649280i | ||||
\(173\) | 2.32674 | + | 2.32674i | 0.176899 | + | 0.176899i | 0.790002 | − | 0.613104i | \(-0.210079\pi\) |
−0.613104 | + | 0.790002i | \(0.710079\pi\) | |||||||
\(174\) | 8.58109 | − | 9.10370i | 0.650531 | − | 0.690150i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.77970 | + | 0.999395i | −0.134150 | + | 0.0753323i | ||||
\(177\) | 0.198209 | − | 2.00833i | 0.0148983 | − | 0.150955i | ||||
\(178\) | −14.1527 | − | 10.9269i | −1.06079 | − | 0.819008i | ||||
\(179\) | 13.9141i | 1.03999i | 0.854169 | + | 0.519996i | \(0.174066\pi\) | ||||
−0.854169 | + | 0.519996i | \(0.825934\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.80972i | 0.431833i | 0.976412 | + | 0.215917i | \(0.0692740\pi\) | ||||
−0.976412 | + | 0.215917i | \(0.930726\pi\) | |||||||
\(182\) | 2.68536 | − | 3.47811i | 0.199052 | − | 0.257814i | ||||
\(183\) | 0.838550 | − | 8.49650i | 0.0619874 | − | 0.628079i | ||||
\(184\) | 3.81254 | + | 9.44235i | 0.281064 | + | 0.696099i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −8.13998 | − | 7.67270i | −0.596852 | − | 0.562589i | ||||
\(187\) | −1.60583 | − | 1.60583i | −0.117430 | − | 0.117430i | ||||
\(188\) | −4.77003 | + | 8.14930i | −0.347890 | + | 0.594349i | ||||
\(189\) | −13.4171 | + | 7.16122i | −0.975950 | + | 0.520902i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 13.8456i | − | 1.00183i | −0.865497 | − | 0.500914i | \(-0.832997\pi\) | ||
0.865497 | − | 0.500914i | \(-0.167003\pi\) | |||||||
\(192\) | −8.59519 | − | 10.8684i | −0.620304 | − | 0.784361i | ||||
\(193\) | −4.57254 | − | 4.57254i | −0.329138 | − | 0.329138i | 0.523120 | − | 0.852259i | \(-0.324768\pi\) |
−0.852259 | + | 0.523120i | \(0.824768\pi\) | |||||||
\(194\) | −21.5800 | + | 2.77562i | −1.54935 | + | 0.199278i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.03145 | − | 0.792928i | 0.216532 | − | 0.0566377i | ||||
\(197\) | 3.85757 | − | 3.85757i | 0.274840 | − | 0.274840i | −0.556205 | − | 0.831045i | \(-0.687743\pi\) |
0.831045 | + | 0.556205i | \(0.187743\pi\) | |||||||
\(198\) | 1.42192 | + | 1.63249i | 0.101051 | + | 0.116016i | ||||
\(199\) | − | 5.91833i | − | 0.419540i | −0.977751 | − | 0.209770i | \(-0.932729\pi\) | ||
0.977751 | − | 0.209770i | \(-0.0672714\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.4039 | − | 15.1203i | −0.874900 | − | 1.06650i | ||||
\(202\) | −7.17537 | − | 5.53993i | −0.504858 | − | 0.389788i | ||||
\(203\) | 10.5704 | + | 10.5704i | 0.741896 | + | 0.741896i | ||||
\(204\) | 9.05712 | − | 12.4760i | 0.634125 | − | 0.873497i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.475344 | + | 3.69573i | 0.0331188 | + | 0.257494i | ||||
\(207\) | 8.98285 | − | 5.99695i | 0.624351 | − | 0.416817i | ||||
\(208\) | 1.14787 | − | 4.08821i | 0.0795904 | − | 0.283467i | ||||
\(209\) | 3.06777 | 0.212202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 6.95372i | − | 0.478714i | −0.970932 | − | 0.239357i | \(-0.923063\pi\) | ||
0.970932 | − | 0.239357i | \(-0.0769366\pi\) | |||||||
\(212\) | 8.22802 | − | 14.0571i | 0.565103 | − | 0.965444i | ||||
\(213\) | 0.866144 | − | 8.77609i | 0.0593472 | − | 0.601328i | ||||
\(214\) | 19.8999 | − | 2.55953i | 1.36033 | − | 0.174966i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −9.43167 | + | 11.2714i | −0.641744 | + | 0.766919i | ||||
\(217\) | 9.45141 | − | 9.45141i | 0.641604 | − | 0.641604i | ||||
\(218\) | −14.1546 | − | 10.9284i | −0.958671 | − | 0.740166i | ||||
\(219\) | 4.98156 | + | 6.07252i | 0.336622 | + | 0.410343i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.72454 | 0.317807 | ||||||||
\(222\) | 0.691978 | + | 23.4162i | 0.0464425 | + | 1.57159i | ||||
\(223\) | 16.7218 | + | 16.7218i | 1.11977 | + | 1.11977i | 0.991774 | + | 0.127998i | \(0.0408550\pi\) |
0.127998 | + | 0.991774i | \(0.459145\pi\) | |||||||
\(224\) | 13.2844 | − | 9.88231i | 0.887601 | − | 0.660290i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.74778 | − | 0.482039i | 0.249298 | − | 0.0320647i | ||||
\(227\) | −12.4814 | + | 12.4814i | −0.828416 | + | 0.828416i | −0.987298 | − | 0.158881i | \(-0.949211\pi\) |
0.158881 | + | 0.987298i | \(0.449211\pi\) | |||||||
\(228\) | 3.26575 | + | 20.5685i | 0.216280 | + | 1.36218i | ||||
\(229\) | −1.09678 | −0.0724770 | −0.0362385 | − | 0.999343i | \(-0.511538\pi\) | ||||
−0.0362385 | + | 0.999343i | \(0.511538\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.00000 | + | 1.64069i | −0.131590 | + | 0.107949i | ||||
\(232\) | 13.2963 | + | 5.64737i | 0.872942 | + | 0.370768i | ||||
\(233\) | −6.98082 | + | 6.98082i | −0.457329 | + | 0.457329i | −0.897778 | − | 0.440449i | \(-0.854819\pi\) |
0.440449 | + | 0.897778i | \(0.354819\pi\) | |||||||
\(234\) | −4.49322 | − | 0.309768i | −0.293731 | − | 0.0202502i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.25444 | − | 0.589688i | 0.146752 | − | 0.0383854i | ||||
\(237\) | −1.24391 | + | 12.6038i | −0.0808008 | + | 0.818704i | ||||
\(238\) | 14.5814 | + | 11.2580i | 0.945174 | + | 0.729746i | ||||
\(239\) | −12.3210 | −0.796976 | −0.398488 | − | 0.917173i | \(-0.630465\pi\) | ||||
−0.398488 | + | 0.917173i | \(0.630465\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.03833 | −0.453379 | −0.226689 | − | 0.973967i | \(-0.572790\pi\) | ||||
−0.226689 | + | 0.973967i | \(0.572790\pi\) | |||||||
\(242\) | −12.0219 | − | 9.28183i | −0.772798 | − | 0.596659i | ||||
\(243\) | 13.7404 | + | 7.36211i | 0.881449 | + | 0.472279i | ||||
\(244\) | 9.53771 | − | 2.49475i | 0.610589 | − | 0.159710i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.12974 | − | 7.56395i | 0.454575 | − | 0.482260i | ||||
\(247\) | −4.51288 | + | 4.51288i | −0.287148 | + | 0.287148i | ||||
\(248\) | 5.04954 | − | 11.8887i | 0.320646 | − | 0.754934i | ||||
\(249\) | 7.42595 | + | 9.05224i | 0.470600 | + | 0.573662i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.92262 | −0.626311 | −0.313155 | − | 0.949702i | \(-0.601386\pi\) | ||||
−0.313155 | + | 0.949702i | \(0.601386\pi\) | |||||||
\(252\) | −13.1294 | − | 11.6628i | −0.827073 | − | 0.734688i | ||||
\(253\) | 1.29904 | − | 1.29904i | 0.0816696 | − | 0.0816696i | ||||
\(254\) | −1.91228 | + | 0.245957i | −0.119987 | + | 0.0154327i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.32826 | − | 13.6616i | 0.520516 | − | 0.853852i | ||||
\(257\) | −14.5324 | − | 14.5324i | −0.906508 | − | 0.906508i | 0.0894809 | − | 0.995989i | \(-0.471479\pi\) |
−0.995989 | + | 0.0894809i | \(0.971479\pi\) | |||||||
\(258\) | 20.6361 | − | 0.609821i | 1.28474 | − | 0.0379658i | ||||
\(259\) | −27.9923 | −1.73935 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.99522 | − | 15.0266i | 0.185400 | − | 0.930120i | ||||
\(262\) | 8.49885 | + | 6.56176i | 0.525061 | + | 0.405387i | ||||
\(263\) | 10.8634 | − | 10.8634i | 0.669867 | − | 0.669867i | −0.287818 | − | 0.957685i | \(-0.592930\pi\) |
0.957685 | + | 0.287818i | \(0.0929298\pi\) | |||||||
\(264\) | −1.19853 | + | 2.19379i | −0.0737643 | + | 0.135018i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −24.6818 | + | 3.17457i | −1.51334 | + | 0.194646i | ||||
\(267\) | −21.7926 | − | 2.15079i | −1.33369 | − | 0.131626i | ||||
\(268\) | 11.4077 | − | 19.4894i | 0.696838 | − | 1.19050i | ||||
\(269\) | 32.3280i | 1.97108i | 0.169455 | + | 0.985538i | \(0.445799\pi\) | ||||
−0.169455 | + | 0.985538i | \(0.554201\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.306338 | 0.0186087 | 0.00930434 | − | 0.999957i | \(-0.497038\pi\) | ||||
0.00930434 | + | 0.999957i | \(0.497038\pi\) | |||||||
\(272\) | 17.1392 | + | 4.81227i | 1.03922 | + | 0.291787i | ||||
\(273\) | 0.528571 | − | 5.35567i | 0.0319905 | − | 0.324140i | ||||
\(274\) | 0.182052 | + | 1.41543i | 0.0109982 | + | 0.0855090i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 10.0925 | + | 7.32676i | 0.607497 | + | 0.441019i | ||||
\(277\) | −6.97897 | − | 6.97897i | −0.419326 | − | 0.419326i | 0.465645 | − | 0.884971i | \(-0.345822\pi\) |
−0.884971 | + | 0.465645i | \(0.845822\pi\) | |||||||
\(278\) | 10.0909 | + | 7.79094i | 0.605212 | + | 0.467270i | ||||
\(279\) | −13.4358 | − | 2.67815i | −0.804383 | − | 0.160337i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.4596i | 0.922240i | 0.887338 | + | 0.461120i | \(0.152552\pi\) | ||||
−0.887338 | + | 0.461120i | \(0.847448\pi\) | |||||||
\(282\) | 0.341607 | + | 11.5598i | 0.0203424 | + | 0.688378i | ||||
\(283\) | −8.86458 | + | 8.86458i | −0.526945 | + | 0.526945i | −0.919660 | − | 0.392715i | \(-0.871536\pi\) |
0.392715 | + | 0.919660i | \(0.371536\pi\) | |||||||
\(284\) | 9.85156 | − | 2.57684i | 0.584583 | − | 0.152908i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.759816 | + | 0.0977275i | −0.0449289 | + | 0.00577875i | ||||
\(287\) | 8.78258 | + | 8.78258i | 0.518419 | + | 0.518419i | ||||
\(288\) | −15.9845 | − | 5.70040i | −0.941898 | − | 0.335899i | ||||
\(289\) | 2.80690i | 0.165112i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.6023 | + | 16.9010i | −1.20773 | + | 0.990754i | ||||
\(292\) | −4.58150 | + | 7.82720i | −0.268112 | + | 0.458053i | ||||
\(293\) | 1.49638 | + | 1.49638i | 0.0874192 | + | 0.0874192i | 0.749464 | − | 0.662045i | \(-0.230311\pi\) |
−0.662045 | + | 0.749464i | \(0.730311\pi\) | |||||||
\(294\) | 2.63230 | − | 2.79261i | 0.153519 | − | 0.162868i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −25.0830 | + | 10.1278i | −1.45792 | + | 0.588666i | ||||
\(297\) | 2.53684 | + | 0.771206i | 0.147202 | + | 0.0447499i | ||||
\(298\) | 11.3713 | − | 14.7283i | 0.658724 | − | 0.853186i | ||||
\(299\) | 3.82192i | 0.221027i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.6688i | 1.42189i | ||||||||
\(302\) | 3.08933 | + | 2.38520i | 0.177771 | + | 0.137253i | ||||
\(303\) | −11.0488 | − | 1.09045i | −0.634738 | − | 0.0626445i | ||||
\(304\) | −20.9681 | + | 11.7747i | −1.20260 | + | 0.675325i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.29866 | − | 18.8371i | 0.0742393 | − | 1.07685i | ||||
\(307\) | 12.4948 | + | 12.4948i | 0.713118 | + | 0.713118i | 0.967186 | − | 0.254068i | \(-0.0817688\pi\) |
−0.254068 | + | 0.967186i | \(0.581769\pi\) | |||||||
\(308\) | −2.57791 | − | 1.50893i | −0.146890 | − | 0.0859791i | ||||
\(309\) | 2.89442 | + | 3.52830i | 0.164658 | + | 0.200718i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.224632i | 0.0127377i | 0.999980 | + | 0.00636886i | \(0.00202728\pi\) | ||||
−0.999980 | + | 0.00636886i | \(0.997973\pi\) | |||||||
\(312\) | −1.46408 | − | 4.99030i | −0.0828874 | − | 0.282520i | ||||
\(313\) | 12.0383 | + | 12.0383i | 0.680447 | + | 0.680447i | 0.960101 | − | 0.279654i | \(-0.0902198\pi\) |
−0.279654 | + | 0.960101i | \(0.590220\pi\) | |||||||
\(314\) | −1.11774 | − | 8.69022i | −0.0630775 | − | 0.490417i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.1483 | + | 3.70073i | −0.795905 | + | 0.208183i | ||||
\(317\) | −20.2257 | + | 20.2257i | −1.13599 | + | 1.13599i | −0.146829 | + | 0.989162i | \(0.546907\pi\) |
−0.989162 | + | 0.146829i | \(0.953093\pi\) | |||||||
\(318\) | −0.589252 | − | 19.9400i | −0.0330436 | − | 1.11818i | ||||
\(319\) | − | 2.60618i | − | 0.145918i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.9984 | − | 15.5852i | 1.06039 | − | 0.869882i | ||||
\(322\) | −9.10715 | + | 11.7957i | −0.507522 | + | 0.657347i | ||||
\(323\) | −18.9196 | − | 18.9196i | −1.05271 | − | 1.05271i | ||||
\(324\) | −2.47015 | + | 17.8297i | −0.137230 | + | 0.990539i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.934042 | + | 0.120136i | −0.0517318 | + | 0.00665374i | ||||
\(327\) | −21.7956 | − | 2.15109i | −1.20530 | − | 0.118955i | ||||
\(328\) | 11.0474 | + | 4.69221i | 0.609991 | + | 0.259084i | ||||
\(329\) | −13.8189 | −0.761860 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.3308i | 0.677760i | 0.940830 | + | 0.338880i | \(0.110048\pi\) | ||||
−0.940830 | + | 0.338880i | \(0.889952\pi\) | |||||||
\(332\) | −6.82959 | + | 11.6679i | −0.374822 | + | 0.640361i | ||||
\(333\) | 15.9305 | + | 23.8624i | 0.872988 | + | 1.30765i | ||||
\(334\) | −0.126384 | − | 0.982613i | −0.00691540 | − | 0.0537662i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.37262 | − | 18.8904i | 0.402209 | − | 1.03056i | ||||
\(337\) | −10.6723 | + | 10.6723i | −0.581359 | + | 0.581359i | −0.935277 | − | 0.353918i | \(-0.884849\pi\) |
0.353918 | + | 0.935277i | \(0.384849\pi\) | |||||||
\(338\) | −10.2614 | + | 13.2907i | −0.558147 | + | 0.722918i | ||||
\(339\) | 3.57799 | − | 2.93518i | 0.194330 | − | 0.159417i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.33029 | −0.126192 | ||||||||
\(342\) | 16.7528 | + | 19.2337i | 0.905886 | + | 1.04004i | ||||
\(343\) | −11.2449 | − | 11.2449i | −0.607166 | − | 0.607166i | ||||
\(344\) | 8.92534 | + | 22.1050i | 0.481222 | + | 1.19182i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.593640 | + | 4.61546i | 0.0319143 | + | 0.248129i | ||||
\(347\) | −8.00457 | + | 8.00457i | −0.429708 | + | 0.429708i | −0.888529 | − | 0.458821i | \(-0.848272\pi\) |
0.458821 | + | 0.888529i | \(0.348272\pi\) | |||||||
\(348\) | 17.4736 | − | 2.77437i | 0.936685 | − | 0.148722i | ||||
\(349\) | 13.9579 | 0.747152 | 0.373576 | − | 0.927600i | \(-0.378132\pi\) | ||||
0.373576 | + | 0.927600i | \(0.378132\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.86633 | + | 2.59735i | −0.259746 | + | 0.138636i | ||||
\(352\) | −2.85593 | − | 0.419399i | −0.152221 | − | 0.0223541i | ||||
\(353\) | −11.8744 | + | 11.8744i | −0.632008 | + | 0.632008i | −0.948571 | − | 0.316563i | \(-0.897471\pi\) |
0.316563 | + | 0.948571i | \(0.397471\pi\) | |||||||
\(354\) | 1.95760 | − | 2.07682i | 0.104045 | − | 0.110382i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.39876 | − | 24.4632i | −0.339134 | − | 1.29655i | ||||
\(357\) | 22.4528 | + | 2.21595i | 1.18833 | + | 0.117281i | ||||
\(358\) | −12.0254 | + | 15.5755i | −0.635564 | + | 0.823189i | ||||
\(359\) | 33.8765 | 1.78793 | 0.893967 | − | 0.448133i | \(-0.147911\pi\) | ||||
0.893967 | + | 0.448133i | \(0.147911\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.1439 | 0.902313 | ||||||||
\(362\) | −5.02112 | + | 6.50340i | −0.263904 | + | 0.341811i | ||||
\(363\) | −18.5116 | − | 1.82698i | −0.971608 | − | 0.0958915i | ||||
\(364\) | 6.01198 | − | 1.57254i | 0.315114 | − | 0.0824233i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.28186 | − | 8.78625i | 0.432900 | − | 0.459265i | ||||
\(367\) | −10.7900 | + | 10.7900i | −0.563233 | + | 0.563233i | −0.930224 | − | 0.366992i | \(-0.880388\pi\) |
0.366992 | + | 0.930224i | \(0.380388\pi\) | |||||||
\(368\) | −3.89289 | + | 13.8648i | −0.202931 | + | 0.722752i | ||||
\(369\) | 2.48863 | − | 12.4851i | 0.129553 | − | 0.649946i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.8368 | 1.23754 | ||||||||
\(372\) | −2.48067 | − | 15.6239i | −0.128617 | − | 0.810060i | ||||
\(373\) | 25.8380 | − | 25.8380i | 1.33784 | − | 1.33784i | 0.439697 | − | 0.898146i | \(-0.355086\pi\) |
0.898146 | − | 0.439697i | \(-0.144914\pi\) | |||||||
\(374\) | −0.409708 | − | 3.18541i | −0.0211855 | − | 0.164714i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.3827 | + | 4.99977i | −0.638588 | + | 0.257843i | ||||
\(377\) | 3.83385 | + | 3.83385i | 0.197453 | + | 0.197453i | ||||
\(378\) | −21.2082 | − | 3.57960i | −1.09083 | − | 0.184115i | ||||
\(379\) | −12.2262 | −0.628019 | −0.314010 | − | 0.949420i | \(-0.601672\pi\) | ||||
−0.314010 | + | 0.949420i | \(0.601672\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.82564 | + | 1.49766i | −0.0935306 | + | 0.0767272i | ||||
\(382\) | 11.9662 | − | 15.4987i | 0.612242 | − | 0.792982i | ||||
\(383\) | −21.6256 | + | 21.6256i | −1.10501 | + | 1.10501i | −0.111219 | + | 0.993796i | \(0.535475\pi\) |
−0.993796 | + | 0.111219i | \(0.964525\pi\) | |||||||
\(384\) | −0.228292 | − | 19.5946i | −0.0116500 | − | 0.999932i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.16663 | − | 9.07035i | −0.0593798 | − | 0.461669i | ||||
\(387\) | 21.0293 | − | 14.0391i | 1.06898 | − | 0.713649i | ||||
\(388\) | −26.5555 | − | 15.5437i | −1.34815 | − | 0.789112i | ||||
\(389\) | − | 6.63941i | − | 0.336632i | −0.985733 | − | 0.168316i | \(-0.946167\pi\) | ||
0.985733 | − | 0.168316i | \(-0.0538328\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0228 | −0.810309 | ||||||||
\(392\) | 4.07870 | + | 1.73236i | 0.206006 | + | 0.0874975i | ||||
\(393\) | 13.0867 | + | 1.29158i | 0.660138 | + | 0.0651514i | ||||
\(394\) | 7.65210 | − | 0.984213i | 0.385507 | − | 0.0495839i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.180794 | + | 3.05631i | 0.00908522 | + | 0.153586i | ||||
\(397\) | −14.0596 | − | 14.0596i | −0.705629 | − | 0.705629i | 0.259984 | − | 0.965613i | \(-0.416283\pi\) |
−0.965613 | + | 0.259984i | \(0.916283\pi\) | |||||||
\(398\) | 5.11498 | − | 6.62498i | 0.256391 | − | 0.332080i | ||||
\(399\) | −23.5636 | + | 19.3303i | −1.17966 | + | 0.967725i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.1176i | 0.904751i | 0.891827 | + | 0.452376i | \(0.149423\pi\) | ||||
−0.891827 | + | 0.452376i | \(0.850577\pi\) | |||||||
\(402\) | −0.816968 | − | 27.6458i | −0.0407466 | − | 1.37885i | ||||
\(403\) | 3.42800 | − | 3.42800i | 0.170761 | − | 0.170761i | ||||
\(404\) | −3.24416 | − | 12.4028i | −0.161403 | − | 0.617062i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.69691 | + | 20.9681i | 0.133845 | + | 1.04063i | ||||
\(407\) | 3.45081 | + | 3.45081i | 0.171050 | + | 0.171050i | ||||
\(408\) | 20.9211 | − | 6.13795i | 1.03575 | − | 0.303874i | ||||
\(409\) | − | 26.3245i | − | 1.30166i | −0.759223 | − | 0.650831i | \(-0.774421\pi\) | ||
0.759223 | − | 0.650831i | \(-0.225579\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.10853 | + | 1.35130i | 0.0546798 | + | 0.0666548i | ||||
\(412\) | −2.66197 | + | 4.54782i | −0.131146 | + | 0.224055i | ||||
\(413\) | 2.41142 | + | 2.41142i | 0.118658 | + | 0.118658i | ||||
\(414\) | 15.2383 | + | 1.05055i | 0.748923 | + | 0.0516317i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.81820 | − | 3.58428i | 0.236232 | − | 0.175734i | ||||
\(417\) | 15.5382 | + | 1.53352i | 0.760909 | + | 0.0750969i | ||||
\(418\) | 3.43406 | + | 2.65135i | 0.167965 | + | 0.129682i | ||||
\(419\) | − | 12.7809i | − | 0.624385i | −0.950019 | − | 0.312193i | \(-0.898937\pi\) | ||
0.950019 | − | 0.312193i | \(-0.101063\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 26.3792i | − | 1.28564i | −0.766017 | − | 0.642821i | \(-0.777764\pi\) | ||
0.766017 | − | 0.642821i | \(-0.222236\pi\) | |||||||
\(422\) | 6.00983 | − | 7.78398i | 0.292554 | − | 0.378918i | ||||
\(423\) | 7.86440 | + | 11.7801i | 0.382380 | + | 0.572769i | ||||
\(424\) | 21.3594 | − | 8.62431i | 1.03730 | − | 0.418833i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.55439 | − | 9.07537i | 0.414462 | − | 0.439703i | ||||
\(427\) | 10.2018 | + | 10.2018i | 0.493700 | + | 0.493700i | ||||
\(428\) | 24.4881 | + | 14.3336i | 1.18368 | + | 0.692841i | ||||
\(429\) | −0.725393 | + | 0.595072i | −0.0350223 | + | 0.0287303i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.6818i | 1.38155i | 0.723068 | + | 0.690777i | \(0.242731\pi\) | ||||
−0.723068 | + | 0.690777i | \(0.757269\pi\) | |||||||
\(432\) | −20.2992 | + | 4.46572i | −0.976646 | + | 0.214857i | ||||
\(433\) | 2.25457 | + | 2.25457i | 0.108347 | + | 0.108347i | 0.759202 | − | 0.650855i | \(-0.225589\pi\) |
−0.650855 | + | 0.759202i | \(0.725589\pi\) | |||||||
\(434\) | 18.7484 | − | 2.41142i | 0.899951 | − | 0.115752i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.39964 | − | 24.4665i | −0.306487 | − | 1.17173i | ||||
\(437\) | 15.3050 | − | 15.3050i | 0.732137 | − | 0.732137i | ||||
\(438\) | 0.328105 | + | 11.1029i | 0.0156775 | + | 0.530519i | ||||
\(439\) | 11.8510i | 0.565620i | 0.959176 | + | 0.282810i | \(0.0912665\pi\) | ||||
−0.959176 | + | 0.282810i | \(0.908733\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.918802 | − | 4.60948i | 0.0437525 | − | 0.219499i | ||||
\(442\) | 5.28864 | + | 4.08323i | 0.251555 | + | 0.194219i | ||||
\(443\) | 1.66807 | + | 1.66807i | 0.0792526 | + | 0.0792526i | 0.745622 | − | 0.666369i | \(-0.232153\pi\) |
−0.666369 | + | 0.745622i | \(0.732153\pi\) | |||||||
\(444\) | −19.4631 | + | 26.8101i | −0.923679 | + | 1.27235i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.26636 | + | 33.1703i | 0.202018 | + | 1.57066i | ||||
\(447\) | 2.23827 | − | 22.6789i | 0.105866 | − | 1.07268i | ||||
\(448\) | 23.4114 | + | 0.418930i | 1.10609 | + | 0.0197926i | ||||
\(449\) | −34.3414 | −1.62067 | −0.810336 | − | 0.585966i | \(-0.800715\pi\) | ||||
−0.810336 | + | 0.585966i | \(0.800715\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.16539i | − | 0.101964i | ||||||
\(452\) | 4.61186 | + | 2.69946i | 0.216924 | + | 0.126972i | ||||
\(453\) | 4.75703 | + | 0.469488i | 0.223505 | + | 0.0220585i | ||||
\(454\) | −24.7588 | + | 3.18447i | −1.16199 | + | 0.149455i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −14.1208 | + | 25.8468i | −0.661269 | + | 1.21039i | ||||
\(457\) | 4.61474 | − | 4.61474i | 0.215869 | − | 0.215869i | −0.590886 | − | 0.806755i | \(-0.701222\pi\) |
0.806755 | + | 0.590886i | \(0.201222\pi\) | |||||||
\(458\) | −1.22773 | − | 0.947900i | −0.0573680 | − | 0.0442925i | ||||
\(459\) | −10.8890 | − | 20.4014i | −0.508255 | − | 0.952254i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.6452 | 0.961543 | 0.480772 | − | 0.876846i | \(-0.340357\pi\) | ||||
0.480772 | + | 0.876846i | \(0.340357\pi\) | |||||||
\(462\) | −3.65678 | + | 0.108062i | −0.170129 | + | 0.00502751i | ||||
\(463\) | −27.1817 | − | 27.1817i | −1.26324 | − | 1.26324i | −0.949512 | − | 0.313730i | \(-0.898421\pi\) |
−0.313730 | − | 0.949512i | \(-0.601579\pi\) | |||||||
\(464\) | 10.0030 | + | 17.8131i | 0.464378 | + | 0.826952i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.8476 | + | 1.78107i | −0.641476 | + | 0.0825067i | ||||
\(467\) | −6.39901 | + | 6.39901i | −0.296111 | + | 0.296111i | −0.839488 | − | 0.543378i | \(-0.817145\pi\) |
0.543378 | + | 0.839488i | \(0.317145\pi\) | |||||||
\(468\) | −4.76198 | − | 4.23007i | −0.220123 | − | 0.195535i | ||||
\(469\) | 33.0484 | 1.52603 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.80600 | − | 8.29652i | −0.313604 | − | 0.382283i | ||||
\(472\) | 3.03326 | + | 1.28833i | 0.139617 | + | 0.0593002i | ||||
\(473\) | 3.04110 | − | 3.04110i | 0.139830 | − | 0.139830i | ||||
\(474\) | −12.2854 | + | 13.0336i | −0.564287 | + | 0.598653i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.59262 | + | 25.2043i | 0.302172 | + | 1.15524i | ||||
\(477\) | −13.5656 | − | 20.3200i | −0.621127 | − | 0.930389i | ||||
\(478\) | −13.7921 | − | 10.6485i | −0.630834 | − | 0.487052i | ||||
\(479\) | 35.9113 | 1.64083 | 0.820414 | − | 0.571770i | \(-0.193743\pi\) | ||||
0.820414 | + | 0.571770i | \(0.193743\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.1527 | −0.462923 | ||||||||
\(482\) | −7.87870 | − | 6.08295i | −0.358865 | − | 0.277071i | ||||
\(483\) | −1.79260 | + | 18.1632i | −0.0815660 | + | 0.826456i | ||||
\(484\) | −5.43540 | − | 20.7801i | −0.247064 | − | 0.944552i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9.01824 | + | 20.1164i | 0.409076 | + | 0.912501i | ||||
\(487\) | 23.9090 | − | 23.9090i | 1.08342 | − | 1.08342i | 0.0872343 | − | 0.996188i | \(-0.472197\pi\) |
0.996188 | − | 0.0872343i | \(-0.0278029\pi\) | |||||||
\(488\) | 12.8326 | + | 5.45044i | 0.580905 | + | 0.246730i | ||||
\(489\) | −0.891726 | + | 0.731522i | −0.0403252 | + | 0.0330806i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.9507 | −1.39678 | −0.698392 | − | 0.715715i | \(-0.746101\pi\) | ||||
−0.698392 | + | 0.715715i | \(0.746101\pi\) | |||||||
\(492\) | 14.5182 | − | 2.30513i | 0.654533 | − | 0.103923i | ||||
\(493\) | −16.0728 | + | 16.0728i | −0.723884 | + | 0.723884i | ||||
\(494\) | −8.95201 | + | 1.15141i | −0.402770 | + | 0.0518043i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.9274 | − | 8.94409i | 0.715161 | − | 0.401602i | ||||
\(497\) | 10.5375 | + | 10.5375i | 0.472672 | + | 0.472672i | ||||
\(498\) | 0.489103 | + | 16.5510i | 0.0219172 | + | 0.741669i | ||||
\(499\) | 19.9194 | 0.891716 | 0.445858 | − | 0.895104i | \(-0.352899\pi\) | ||||
0.445858 | + | 0.895104i | \(0.352899\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.769562 | − | 0.938097i | −0.0343815 | − | 0.0419111i | ||||
\(502\) | −11.1074 | − | 8.57573i | −0.495746 | − | 0.382754i | ||||
\(503\) | 14.6687 | − | 14.6687i | 0.654047 | − | 0.654047i | −0.299918 | − | 0.953965i | \(-0.596959\pi\) |
0.953965 | + | 0.299918i | \(0.0969593\pi\) | |||||||
\(504\) | −4.61729 | − | 24.4025i | −0.205671 | − | 1.08698i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.57684 | − | 0.331433i | 0.114555 | − | 0.0147340i | ||||
\(507\) | −2.01979 | + | 20.4653i | −0.0897022 | + | 0.908896i | ||||
\(508\) | −2.35317 | − | 1.37738i | −0.104405 | − | 0.0611114i | ||||
\(509\) | 4.85493i | 0.215191i | 0.994195 | + | 0.107595i | \(0.0343151\pi\) | ||||
−0.994195 | + | 0.107595i | \(0.965685\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.2727 | −0.587149 | ||||||||
\(512\) | 21.1298 | − | 8.09503i | 0.933816 | − | 0.357753i | ||||
\(513\) | 29.8886 | + | 9.08621i | 1.31961 | + | 0.401166i | ||||
\(514\) | −3.70778 | − | 28.8274i | −0.163543 | − | 1.27152i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 23.6270 | + | 17.1523i | 1.04012 | + | 0.755088i | ||||
\(517\) | 1.70355 | + | 1.70355i | 0.0749222 | + | 0.0749222i | ||||
\(518\) | −31.3345 | − | 24.1926i | −1.37676 | − | 1.06296i | ||||
\(519\) | 3.61473 | + | 4.40636i | 0.158669 | + | 0.193418i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 15.0499i | − | 0.659346i | −0.944095 | − | 0.329673i | \(-0.893061\pi\) | ||
0.944095 | − | 0.329673i | \(-0.106939\pi\) | |||||||
\(522\) | 16.3397 | − | 14.2321i | 0.715170 | − | 0.622920i | ||||
\(523\) | −15.6997 | + | 15.6997i | −0.686499 | + | 0.686499i | −0.961456 | − | 0.274957i | \(-0.911336\pi\) |
0.274957 | + | 0.961456i | \(0.411336\pi\) | |||||||
\(524\) | 3.84254 | + | 14.6904i | 0.167862 | + | 0.641755i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.5493 | − | 2.77167i | 0.939596 | − | 0.120851i | ||||
\(527\) | 14.3714 | + | 14.3714i | 0.626026 | + | 0.626026i | ||||
\(528\) | −3.23763 | + | 1.41988i | −0.140900 | + | 0.0617923i | ||||
\(529\) | 10.0383i | 0.436449i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.683298 | − | 3.42800i | 0.0296526 | − | 0.148762i | ||||
\(532\) | −30.3725 | − | 17.7779i | −1.31681 | − | 0.770770i | ||||
\(533\) | 3.18541 | + | 3.18541i | 0.137976 | + | 0.137976i | ||||
\(534\) | −22.5358 | − | 21.2421i | −0.975218 | − | 0.919235i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 29.6137 | − | 11.9572i | 1.27912 | − | 0.516470i | ||||
\(537\) | −2.36701 | + | 23.9835i | −0.102144 | + | 1.03496i | ||||
\(538\) | −27.9399 | + | 36.1880i | −1.20457 | + | 1.56017i | ||||
\(539\) | − | 0.799460i | − | 0.0344352i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.45079i | 0.0623742i | 0.999514 | + | 0.0311871i | \(0.00992877\pi\) | ||||
−0.999514 | + | 0.0311871i | \(0.990071\pi\) | |||||||
\(542\) | 0.342914 | + | 0.264756i | 0.0147294 | + | 0.0113722i | ||||
\(543\) | −0.988326 | + | 10.0141i | −0.0424131 | + | 0.429745i | ||||
\(544\) | 15.0266 | + | 20.1996i | 0.644258 | + | 0.866050i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.22038 | − | 5.53831i | 0.223412 | − | 0.237018i | ||||
\(547\) | 1.86763 | + | 1.86763i | 0.0798541 | + | 0.0798541i | 0.745906 | − | 0.666052i | \(-0.232017\pi\) |
−0.666052 | + | 0.745906i | \(0.732017\pi\) | |||||||
\(548\) | −1.01951 | + | 1.74177i | −0.0435512 | + | 0.0744045i | ||||
\(549\) | 2.89078 | − | 14.5026i | 0.123375 | − | 0.618955i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 30.7055i | − | 1.30810i | ||||||
\(552\) | 4.96530 | + | 16.9241i | 0.211337 | + | 0.720339i | ||||
\(553\) | −15.1334 | − | 15.1334i | −0.643539 | − | 0.643539i | ||||
\(554\) | −1.78060 | − | 13.8439i | −0.0756505 | − | 0.588171i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.56234 | + | 17.4423i | 0.193486 | + | 0.739720i | ||||
\(557\) | 22.6188 | − | 22.6188i | 0.958389 | − | 0.958389i | −0.0407789 | − | 0.999168i | \(-0.512984\pi\) |
0.999168 | + | 0.0407789i | \(0.0129839\pi\) | |||||||
\(558\) | −12.7254 | − | 14.6100i | −0.538711 | − | 0.618490i | ||||
\(559\) | 8.94729i | 0.378430i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.49475 | − | 3.04110i | −0.105328 | − | 0.128395i | ||||
\(562\) | −13.3611 | + | 17.3054i | −0.563604 | + | 0.729985i | ||||
\(563\) | −26.6638 | − | 26.6638i | −1.12375 | − | 1.12375i | −0.991173 | − | 0.132574i | \(-0.957676\pi\) |
−0.132574 | − | 0.991173i | \(-0.542324\pi\) | |||||||
\(564\) | −9.60832 | + | 13.2353i | −0.404583 | + | 0.557307i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −17.5843 | + | 2.26169i | −0.739123 | + | 0.0950660i | ||||
\(567\) | −24.3450 | + | 10.0612i | −1.02239 | + | 0.422530i | ||||
\(568\) | 13.2549 | + | 5.62980i | 0.556163 | + | 0.236221i | ||||
\(569\) | 29.3180 | 1.22907 | 0.614537 | − | 0.788888i | \(-0.289343\pi\) | ||||
0.614537 | + | 0.788888i | \(0.289343\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 28.4036i | − | 1.18865i | −0.804224 | − | 0.594326i | \(-0.797419\pi\) | ||
0.804224 | − | 0.594326i | \(-0.202581\pi\) | |||||||
\(572\) | −0.934999 | − | 0.547283i | −0.0390943 | − | 0.0228831i | ||||
\(573\) | 2.35535 | − | 23.8652i | 0.0983960 | − | 0.996985i | ||||
\(574\) | 2.24077 | + | 17.4216i | 0.0935280 | + | 0.727165i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12.9664 | − | 20.1958i | −0.540268 | − | 0.841493i | ||||
\(577\) | 18.9787 | − | 18.9787i | 0.790092 | − | 0.790092i | −0.191417 | − | 0.981509i | \(-0.561308\pi\) |
0.981509 | + | 0.191417i | \(0.0613081\pi\) | |||||||
\(578\) | −2.42590 | + | 3.14204i | −0.100904 | + | 0.130692i | ||||
\(579\) | −7.10371 | − | 8.65943i | −0.295220 | − | 0.359874i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.7855 | −0.820839 | ||||||||
\(582\) | −37.6691 | + | 1.11317i | −1.56143 | + | 0.0461423i | ||||
\(583\) | −2.93853 | − | 2.93853i | −0.121702 | − | 0.121702i | ||||
\(584\) | −11.8933 | + | 4.80216i | −0.492147 | + | 0.198715i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.381782 | + | 2.96830i | 0.0157713 | + | 0.122619i | ||||
\(587\) | 11.2326 | − | 11.2326i | 0.463619 | − | 0.463619i | −0.436220 | − | 0.899840i | \(-0.643683\pi\) |
0.899840 | + | 0.436220i | \(0.143683\pi\) | |||||||
\(588\) | 5.36013 | − | 0.851053i | 0.221048 | − | 0.0350968i | ||||
\(589\) | −27.4550 | −1.13127 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.30543 | − | 5.99297i | 0.300505 | − | 0.246518i | ||||
\(592\) | −36.8310 | − | 10.3412i | −1.51374 | − | 0.425022i | ||||
\(593\) | 0.161070 | − | 0.161070i | 0.00661435 | − | 0.00661435i | −0.703792 | − | 0.710406i | \(-0.748511\pi\) |
0.710406 | + | 0.703792i | \(0.248511\pi\) | |||||||
\(594\) | 2.17321 | + | 3.05578i | 0.0891679 | + | 0.125380i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 25.4581 | − | 6.65901i | 1.04281 | − | 0.272764i | ||||
\(597\) | 1.00680 | − | 10.2013i | 0.0412057 | − | 0.417511i | ||||
\(598\) | −3.30313 | + | 4.27825i | −0.135075 | + | 0.174951i | ||||
\(599\) | −15.6557 | −0.639673 | −0.319837 | − | 0.947473i | \(-0.603628\pi\) | ||||
−0.319837 | + | 0.947473i | \(0.603628\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.1506 | 1.18908 | 0.594540 | − | 0.804066i | \(-0.297334\pi\) | ||||
0.594540 | + | 0.804066i | \(0.297334\pi\) | |||||||
\(602\) | −21.3203 | + | 27.6142i | −0.868949 | + | 1.12547i | ||||
\(603\) | −18.8080 | − | 28.1726i | −0.765922 | − | 1.14728i | ||||
\(604\) | 1.39676 | + | 5.33998i | 0.0568335 | + | 0.217281i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.4256 | − | 10.7697i | −0.464133 | − | 0.437489i | ||||
\(607\) | −18.7872 | + | 18.7872i | −0.762550 | + | 0.762550i | −0.976783 | − | 0.214232i | \(-0.931275\pi\) |
0.214232 | + | 0.976783i | \(0.431275\pi\) | |||||||
\(608\) | −33.6480 | − | 4.94129i | −1.36461 | − | 0.200396i | ||||
\(609\) | 16.4217 | + | 20.0181i | 0.665443 | + | 0.811176i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.01206 | −0.202766 | ||||||||
\(612\) | 17.7339 | − | 19.9639i | 0.716851 | − | 0.806992i | ||||
\(613\) | 29.5115 | − | 29.5115i | 1.19196 | − | 1.19196i | 0.215443 | − | 0.976516i | \(-0.430880\pi\) |
0.976516 | − | 0.215443i | \(-0.0691195\pi\) | |||||||
\(614\) | 3.18791 | + | 24.7855i | 0.128654 | + | 1.00026i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.58160 | − | 3.91708i | −0.0637245 | − | 0.157823i | ||||
\(617\) | −29.7517 | − | 29.7517i | −1.19776 | − | 1.19776i | −0.974836 | − | 0.222923i | \(-0.928440\pi\) |
−0.222923 | − | 0.974836i | \(-0.571560\pi\) | |||||||
\(618\) | 0.190638 | + | 6.45111i | 0.00766859 | + | 0.259502i | ||||
\(619\) | −12.4498 | −0.500402 | −0.250201 | − | 0.968194i | \(-0.580497\pi\) | ||||
−0.250201 | + | 0.968194i | \(0.580497\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.5037 | − | 8.80867i | 0.662271 | − | 0.353480i | ||||
\(622\) | −0.194141 | + | 0.251453i | −0.00778433 | + | 0.0100823i | ||||
\(623\) | 26.1665 | − | 26.1665i | 1.04834 | − | 1.04834i | ||||
\(624\) | 2.67403 | − | 6.85148i | 0.107047 | − | 0.274279i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.07144 | + | 23.8799i | 0.122759 | + | 0.954434i | ||||
\(627\) | 5.28785 | + | 0.521877i | 0.211176 | + | 0.0208417i | ||||
\(628\) | 6.25942 | − | 10.6938i | 0.249778 | − | 0.426730i | ||||
\(629\) | − | 42.5637i | − | 1.69712i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.7481 | 1.74158 | 0.870791 | − | 0.491653i | \(-0.163607\pi\) | ||||
0.870791 | + | 0.491653i | \(0.163607\pi\) | |||||||
\(632\) | −19.0360 | − | 8.08524i | −0.757212 | − | 0.321614i | ||||
\(633\) | 1.18294 | − | 11.9860i | 0.0470176 | − | 0.476399i | ||||
\(634\) | −40.1210 | + | 5.16036i | −1.59341 | + | 0.204944i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 16.5738 | − | 22.8301i | 0.657193 | − | 0.905273i | ||||
\(637\) | 1.17605 | + | 1.17605i | 0.0465969 | + | 0.0465969i | ||||
\(638\) | 2.25242 | − | 2.91735i | 0.0891741 | − | 0.115499i | ||||
\(639\) | 2.98590 | − | 14.9798i | 0.118121 | − | 0.592592i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 13.3935i | − | 0.529013i | −0.964384 | − | 0.264506i | \(-0.914791\pi\) | ||
0.964384 | − | 0.264506i | \(-0.0852090\pi\) | |||||||
\(642\) | 34.7365 | − | 1.02651i | 1.37094 | − | 0.0405129i | ||||
\(643\) | −12.4335 | + | 12.4335i | −0.490331 | + | 0.490331i | −0.908410 | − | 0.418080i | \(-0.862703\pi\) |
0.418080 | + | 0.908410i | \(0.362703\pi\) | |||||||
\(644\) | −20.3891 | + | 5.33311i | −0.803442 | + | 0.210154i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.82710 | − | 37.5300i | −0.189920 | − | 1.47660i | ||||
\(647\) | 0.352589 | + | 0.352589i | 0.0138617 | + | 0.0138617i | 0.714004 | − | 0.700142i | \(-0.246880\pi\) |
−0.700142 | + | 0.714004i | \(0.746880\pi\) | |||||||
\(648\) | −18.1746 | + | 17.8237i | −0.713965 | + | 0.700181i | ||||
\(649\) | − | 0.594545i | − | 0.0233380i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.8990 | − | 14.6833i | 0.701517 | − | 0.575485i | ||||
\(652\) | −1.14939 | − | 0.672775i | −0.0450138 | − | 0.0263479i | ||||
\(653\) | 10.5497 | + | 10.5497i | 0.412841 | + | 0.412841i | 0.882727 | − | 0.469886i | \(-0.155705\pi\) |
−0.469886 | + | 0.882727i | \(0.655705\pi\) | |||||||
\(654\) | −22.5389 | − | 21.2450i | −0.881339 | − | 0.830745i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.31116 | + | 14.8003i | 0.324496 | + | 0.577854i | ||||
\(657\) | 7.55356 | + | 11.3145i | 0.294692 | + | 0.441421i | ||||
\(658\) | −15.4688 | − | 11.9431i | −0.603038 | − | 0.465591i | ||||
\(659\) | − | 30.8600i | − | 1.20213i | −0.799199 | − | 0.601067i | \(-0.794742\pi\) | ||
0.799199 | − | 0.601067i | \(-0.205258\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 44.1992i | − | 1.71915i | −0.511009 | − | 0.859575i | \(-0.670728\pi\) | ||
0.511009 | − | 0.859575i | \(-0.329272\pi\) | |||||||
\(662\) | −10.6570 | + | 13.8030i | −0.414196 | + | 0.536470i | ||||
\(663\) | 8.14357 | + | 0.803718i | 0.316270 | + | 0.0312138i | ||||
\(664\) | −17.7292 | + | 7.15852i | −0.688025 | + | 0.277804i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.79072 | + | 40.4797i | −0.108138 | + | 1.56856i | ||||
\(667\) | −13.0021 | − | 13.0021i | −0.503444 | − | 0.503444i | ||||
\(668\) | 0.707760 | − | 1.20916i | 0.0273841 | − | 0.0467840i | ||||
\(669\) | 25.9783 | + | 31.6675i | 1.00438 | + | 1.22434i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.51530i | − | 0.0971021i | ||||||
\(672\) | 24.5791 | − | 14.7740i | 0.948160 | − | 0.569920i | ||||
\(673\) | −13.1276 | − | 13.1276i | −0.506033 | − | 0.506033i | 0.407274 | − | 0.913306i | \(-0.366480\pi\) |
−0.913306 | + | 0.407274i | \(0.866480\pi\) | |||||||
\(674\) | −21.1703 | + | 2.72292i | −0.815448 | + | 0.104883i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.9732 | + | 6.00904i | −0.883586 | + | 0.231117i | ||||
\(677\) | 23.1658 | − | 23.1658i | 0.890334 | − | 0.890334i | −0.104220 | − | 0.994554i | \(-0.533235\pi\) |
0.994554 | + | 0.104220i | \(0.0332347\pi\) | |||||||
\(678\) | 6.54196 | − | 0.193323i | 0.251242 | − | 0.00742452i | ||||
\(679\) | − | 45.0304i | − | 1.72811i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.6371 | + | 19.3905i | −0.905775 | + | 0.743047i | ||||
\(682\) | −2.60852 | − | 2.01398i | −0.0998855 | − | 0.0771192i | ||||
\(683\) | 14.8655 | + | 14.8655i | 0.568814 | + | 0.568814i | 0.931796 | − | 0.362982i | \(-0.118241\pi\) |
−0.362982 | + | 0.931796i | \(0.618241\pi\) | |||||||
\(684\) | 2.13008 | + | 36.0090i | 0.0814455 | + | 1.37684i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.86899 | − | 22.3060i | −0.109539 | − | 0.851647i | ||||
\(687\) | −1.89049 | − | 0.186579i | −0.0721266 | − | 0.00711843i | ||||
\(688\) | −9.11344 | + | 32.4581i | −0.347447 | + | 1.23745i | ||||
\(689\) | 8.64552 | 0.329368 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.2699i | 1.79823i | 0.437710 | + | 0.899116i | \(0.355790\pi\) | ||||
−0.437710 | + | 0.899116i | \(0.644210\pi\) | |||||||
\(692\) | −3.32444 | + | 5.67960i | −0.126376 | + | 0.215906i | ||||
\(693\) | −3.72646 | + | 2.48778i | −0.141557 | + | 0.0945031i | ||||
\(694\) | −15.8783 | + | 2.04227i | −0.602733 | + | 0.0775235i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 21.9577 | + | 11.9961i | 0.832306 | + | 0.454713i | ||||
\(697\) | −13.3544 | + | 13.3544i | −0.505833 | + | 0.505833i | ||||
\(698\) | 15.6245 | + | 12.0633i | 0.591396 | + | 0.456603i | ||||
\(699\) | −13.2202 | + | 10.8451i | −0.500035 | + | 0.410201i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.65973 | −0.289304 | −0.144652 | − | 0.989483i | \(-0.546206\pi\) | ||||
−0.144652 | + | 0.989483i | \(0.546206\pi\) | |||||||
\(702\) | −7.69216 | − | 1.29831i | −0.290322 | − | 0.0490015i | ||||
\(703\) | 40.6568 | + | 40.6568i | 1.53340 | + | 1.53340i | ||||
\(704\) | −2.83445 | − | 2.93774i | −0.106827 | − | 0.110720i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.5547 | + | 3.02960i | −0.886492 | + | 0.114021i | ||||
\(707\) | 13.2664 | − | 13.2664i | 0.498933 | − | 0.498933i | ||||
\(708\) | 3.98625 | − | 0.632915i | 0.149812 | − | 0.0237864i | ||||
\(709\) | 43.9829 | 1.65181 | 0.825906 | − | 0.563808i | \(-0.190664\pi\) | ||||
0.825906 | + | 0.563808i | \(0.190664\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.28821 | + | 21.5132i | −0.160820 | + | 0.806810i | ||||
\(712\) | 13.9798 | − | 32.9143i | 0.523915 | − | 1.23351i | ||||
\(713\) | −11.6257 | + | 11.6257i | −0.435387 | + | 0.435387i | ||||
\(714\) | 23.2185 | + | 21.8856i | 0.868931 | + | 0.819050i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −26.9225 | + | 7.04204i | −1.00614 | + | 0.263174i | ||||
\(717\) | −21.2373 | − | 2.09599i | −0.793123 | − | 0.0782762i | ||||
\(718\) | 37.9213 | + | 29.2781i | 1.41521 | + | 1.09265i | ||||
\(719\) | −14.6227 | −0.545333 | −0.272666 | − | 0.962109i | \(-0.587906\pi\) | ||||
−0.272666 | + | 0.962109i | \(0.587906\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.71179 | −0.287202 | ||||||||
\(722\) | 19.1909 | + | 14.8168i | 0.714212 | + | 0.551425i | ||||
\(723\) | −12.1318 | − | 1.19733i | −0.451186 | − | 0.0445292i | ||||
\(724\) | −11.2413 | + | 2.94034i | −0.417778 | + | 0.109277i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −19.1429 | − | 18.0440i | −0.710460 | − | 0.669675i | ||||
\(727\) | 22.1109 | − | 22.1109i | 0.820048 | − | 0.820048i | −0.166067 | − | 0.986115i | \(-0.553107\pi\) |
0.986115 | + | 0.166067i | \(0.0531067\pi\) | |||||||
\(728\) | 8.08889 | + | 3.43563i | 0.299794 | + | 0.127333i | ||||
\(729\) | 22.4316 | + | 15.0274i | 0.830802 | + | 0.556569i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37.5102 | −1.38736 | ||||||||
\(732\) | 16.8643 | − | 2.67763i | 0.623323 | − | 0.0989679i | ||||
\(733\) | 8.64610 | − | 8.64610i | 0.319351 | − | 0.319351i | −0.529167 | − | 0.848518i | \(-0.677495\pi\) |
0.848518 | + | 0.529167i | \(0.177495\pi\) | |||||||
\(734\) | −21.4037 | + | 2.75294i | −0.790023 | + | 0.101613i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.3405 | + | 12.1557i | −0.602318 | + | 0.448067i | ||||
\(737\) | −4.07412 | − | 4.07412i | −0.150072 | − | 0.150072i | ||||
\(738\) | 13.5761 | − | 11.8249i | 0.499743 | − | 0.435282i | ||||
\(739\) | 29.8509 | 1.09808 | 0.549041 | − | 0.835796i | \(-0.314993\pi\) | ||||
0.549041 | + | 0.835796i | \(0.314993\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.54646 | + | 7.01103i | −0.313962 | + | 0.257557i | ||||
\(742\) | 26.6828 | + | 20.6012i | 0.979558 | + | 0.756293i | ||||
\(743\) | −6.78930 | + | 6.78930i | −0.249075 | + | 0.249075i | −0.820591 | − | 0.571516i | \(-0.806356\pi\) |
0.571516 | + | 0.820591i | \(0.306356\pi\) | |||||||
\(744\) | 10.7262 | − | 19.6333i | 0.393243 | − | 0.719791i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 51.2539 | − | 6.59227i | 1.87654 | − | 0.241360i | ||||
\(747\) | 11.2600 | + | 16.8664i | 0.411982 | + | 0.617110i | ||||
\(748\) | 2.29440 | − | 3.91984i | 0.0838916 | − | 0.143324i | ||||
\(749\) | 41.5247i | 1.51728i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.5357 | 0.822339 | 0.411170 | − | 0.911559i | \(-0.365120\pi\) | ||||
0.411170 | + | 0.911559i | \(0.365120\pi\) | |||||||
\(752\) | −18.1823 | − | 5.10513i | −0.663039 | − | 0.186165i | ||||
\(753\) | −17.1034 | − | 1.68800i | −0.623282 | − | 0.0615140i | ||||
\(754\) | 0.978161 | + | 7.60505i | 0.0356225 | + | 0.276959i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −20.6468 | − | 22.3364i | −0.750916 | − | 0.812368i | ||||
\(757\) | 33.9790 | + | 33.9790i | 1.23499 | + | 1.23499i | 0.962025 | + | 0.272963i | \(0.0880035\pi\) |
0.272963 | + | 0.962025i | \(0.411996\pi\) | |||||||
\(758\) | −13.6860 | − | 10.5666i | −0.497099 | − | 0.383798i | ||||
\(759\) | 2.46010 | − | 2.01813i | 0.0892961 | − | 0.0732535i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.4290i | 1.24805i | 0.781404 | + | 0.624025i | \(0.214504\pi\) | ||||
−0.781404 | + | 0.624025i | \(0.785496\pi\) | |||||||
\(762\) | −3.33799 | + | 0.0986416i | −0.120923 | + | 0.00357341i | ||||
\(763\) | 26.1701 | − | 26.1701i | 0.947421 | − | 0.947421i | ||||
\(764\) | 26.7898 | − | 7.00733i | 0.969222 | − | 0.253516i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −42.8977 | + | 5.51751i | −1.54996 | + | 0.199356i | ||||
\(767\) | 0.874612 | + | 0.874612i | 0.0315804 | + | 0.0315804i | ||||
\(768\) | 16.6793 | − | 22.1315i | 0.601862 | − | 0.798600i | ||||
\(769\) | 14.8941i | 0.537094i | 0.963267 | + | 0.268547i | \(0.0865434\pi\) | ||||
−0.963267 | + | 0.268547i | \(0.913457\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.5770 | − | 27.5214i | −0.813091 | − | 0.991159i | ||||
\(772\) | 6.53323 | − | 11.1616i | 0.235136 | − | 0.401715i | ||||
\(773\) | −7.32969 | − | 7.32969i | −0.263631 | − | 0.263631i | 0.562897 | − | 0.826527i | \(-0.309687\pi\) |
−0.826527 | + | 0.562897i | \(0.809687\pi\) | |||||||
\(774\) | 35.6736 | + | 2.45939i | 1.28226 | + | 0.0884008i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16.2923 | − | 40.3504i | −0.584861 | − | 1.44850i | ||||
\(777\) | −48.2496 | − | 4.76193i | −1.73094 | − | 0.170833i | ||||
\(778\) | 5.73818 | − | 7.43215i | 0.205724 | − | 0.266455i | ||||
\(779\) | − | 25.5122i | − | 0.914069i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 2.59807i | − | 0.0929663i | ||||||
\(782\) | −17.9359 | − | 13.8479i | −0.641387 | − | 0.495199i | ||||
\(783\) | 7.71905 | − | 25.3914i | 0.275856 | − | 0.907414i | ||||
\(784\) | 3.06848 | + | 5.46427i | 0.109589 | + | 0.195152i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 13.5330 | + | 12.7561i | 0.482707 | + | 0.454996i | ||||
\(787\) | 4.66068 | + | 4.66068i | 0.166135 | + | 0.166135i | 0.785278 | − | 0.619143i | \(-0.212520\pi\) |
−0.619143 | + | 0.785278i | \(0.712520\pi\) | |||||||
\(788\) | 9.41637 | + | 5.51168i | 0.335444 | + | 0.196346i | ||||
\(789\) | 20.5731 | − | 16.8770i | 0.732421 | − | 0.600837i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.82040i | 0.278061i | ||||||||
\(792\) | −2.43907 | + | 3.57749i | −0.0866687 | + | 0.127120i | ||||
\(793\) | 3.70016 | + | 3.70016i | 0.131396 | + | 0.131396i | ||||
\(794\) | −3.58713 | − | 27.8894i | −0.127303 | − | 0.989757i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.4514 | − | 2.99531i | 0.405884 | − | 0.106166i | ||||
\(797\) | −27.8720 | + | 27.8720i | −0.987276 | + | 0.987276i | −0.999920 | − | 0.0126440i | \(-0.995975\pi\) |
0.0126440 | + | 0.999920i | \(0.495975\pi\) | |||||||
\(798\) | −43.0835 | + | 1.27317i | −1.52514 | + | 0.0450697i | ||||
\(799\) | − | 21.0123i | − | 0.743362i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −37.1975 | − | 7.41454i | −1.31431 | − | 0.261980i | ||||
\(802\) | −15.6584 | + | 20.2809i | −0.552916 | + | 0.716142i | ||||
\(803\) | 1.63622 | + | 1.63622i | 0.0577410 | + | 0.0577410i | ||||
\(804\) | 22.9787 | − | 31.6528i | 0.810396 | − | 1.11631i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.79998 | − | 0.874612i | 0.239519 | − | 0.0308069i | ||||
\(807\) | −5.49951 | + | 55.7231i | −0.193592 | + | 1.96155i | ||||
\(808\) | 7.08773 | − | 16.6875i | 0.249346 | − | 0.587063i | ||||
\(809\) | −18.8285 | −0.661975 | −0.330988 | − | 0.943635i | \(-0.607382\pi\) | ||||
−0.330988 | + | 0.943635i | \(0.607382\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.4113i | 1.31369i | 0.754026 | + | 0.656845i | \(0.228109\pi\) | ||||
−0.754026 | + | 0.656845i | \(0.771891\pi\) | |||||||
\(812\) | −15.1030 | + | 25.8025i | −0.530010 | + | 0.905489i | ||||
\(813\) | 0.528027 | + | 0.0521129i | 0.0185187 | + | 0.00182768i | ||||
\(814\) | 0.880433 | + | 6.84523i | 0.0308592 | + | 0.239925i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 28.7238 | + | 11.2104i | 1.00553 | + | 0.392444i | ||||
\(817\) | 35.8297 | − | 35.8297i | 1.25352 | − | 1.25352i | ||||
\(818\) | 22.7512 | − | 29.4676i | 0.795477 | − | 1.03031i | ||||
\(819\) | 1.82217 | − | 9.14153i | 0.0636717 | − | 0.319431i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.3129 | −0.499523 | −0.249761 | − | 0.968307i | \(-0.580352\pi\) | ||||
−0.249761 | + | 0.968307i | \(0.580352\pi\) | |||||||
\(822\) | 0.0730123 | + | 2.47070i | 0.00254660 | + | 0.0861757i | ||||
\(823\) | −10.8660 | − | 10.8660i | −0.378766 | − | 0.378766i | 0.491891 | − | 0.870657i | \(-0.336306\pi\) |
−0.870657 | + | 0.491891i | \(0.836306\pi\) | |||||||
\(824\) | −6.91031 | + | 2.79018i | −0.240732 | + | 0.0972006i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.615244 | + | 4.78343i | 0.0214071 | + | 0.166437i | ||||
\(827\) | −2.49596 | + | 2.49596i | −0.0867932 | + | 0.0867932i | −0.749170 | − | 0.662377i | \(-0.769548\pi\) |
0.662377 | + | 0.749170i | \(0.269548\pi\) | |||||||
\(828\) | 16.1498 | + | 14.3459i | 0.561245 | + | 0.498553i | ||||
\(829\) | −49.1212 | −1.70605 | −0.853026 | − | 0.521869i | \(-0.825235\pi\) | ||||
−0.853026 | + | 0.521869i | \(0.825235\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.8423 | − | 13.2167i | −0.376114 | − | 0.458483i | ||||
\(832\) | 8.49125 | + | 0.151945i | 0.294381 | + | 0.00526773i | ||||
\(833\) | −4.93043 | + | 4.93043i | −0.170829 | + | 0.170829i | ||||
\(834\) | 16.0681 | + | 15.1457i | 0.556392 | + | 0.524452i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.55262 | + | 5.93585i | 0.0536985 | + | 0.205296i | ||||
\(837\) | −22.7034 | − | 6.90191i | −0.784746 | − | 0.238565i | ||||
\(838\) | 11.0460 | − | 14.3069i | 0.381577 | − | 0.494223i | ||||
\(839\) | −26.9749 | −0.931277 | −0.465638 | − | 0.884975i | \(-0.654175\pi\) | ||||
−0.465638 | + | 0.884975i | \(0.654175\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.91458 | 0.100503 | ||||||||
\(842\) | 22.7985 | − | 29.5288i | 0.785687 | − | 1.01763i | ||||
\(843\) | −2.62992 | + | 26.6473i | −0.0905792 | + | 0.917782i | ||||
\(844\) | 13.4548 | − | 3.51933i | 0.463133 | − | 0.121140i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.37769 | + | 19.9835i | −0.0473660 | + | 0.687048i | ||||
\(847\) | 22.2270 | − | 22.2270i | 0.763729 | − | 0.763729i | ||||
\(848\) | 31.3634 | + | 8.80606i | 1.07702 | + | 0.302401i | ||||
\(849\) | −16.7877 | + | 13.7717i | −0.576151 | + | 0.472642i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.4319 | 1.18031 | ||||||||
\(852\) | 17.4193 | − | 2.76574i | 0.596774 | − | 0.0947526i | ||||
\(853\) | −16.4190 | + | 16.4190i | −0.562174 | + | 0.562174i | −0.929925 | − | 0.367750i | \(-0.880128\pi\) |
0.367750 | + | 0.929925i | \(0.380128\pi\) | |||||||
\(854\) | 2.60287 | + | 20.2369i | 0.0890683 | + | 0.692492i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.0239 | + | 37.2091i | 0.513508 | + | 1.27178i | ||||
\(857\) | 24.4641 | + | 24.4641i | 0.835678 | + | 0.835678i | 0.988287 | − | 0.152608i | \(-0.0487673\pi\) |
−0.152608 | + | 0.988287i | \(0.548767\pi\) | |||||||
\(858\) | −1.32630 | + | 0.0391938i | −0.0452792 | + | 0.00133806i | ||||
\(859\) | 1.68121 | 0.0573622 | 0.0286811 | − | 0.999589i | \(-0.490869\pi\) | ||||
0.0286811 | + | 0.999589i | \(0.490869\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.6443 | + | 16.6324i | 0.464995 | + | 0.566830i | ||||
\(862\) | −24.7886 | + | 32.1064i | −0.844302 | + | 1.09355i | ||||
\(863\) | −23.0950 | + | 23.0950i | −0.786161 | + | 0.786161i | −0.980863 | − | 0.194701i | \(-0.937626\pi\) |
0.194701 | + | 0.980863i | \(0.437626\pi\) | |||||||
\(864\) | −26.5824 | − | 12.5449i | −0.904353 | − | 0.426785i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.575226 | + | 4.47229i | 0.0195470 | + | 0.151975i | ||||
\(867\) | −0.477499 | + | 4.83819i | −0.0162167 | + | 0.164314i | ||||
\(868\) | 23.0710 | + | 13.5042i | 0.783081 | + | 0.458361i | ||||
\(869\) | 3.73122i | 0.126573i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.9866 | 0.406149 | ||||||||
\(872\) | 13.9817 | − | 32.9188i | 0.473481 | − | 1.11477i | ||||
\(873\) | −38.3869 | + | 25.6271i | −1.29920 | + | 0.867345i | ||||
\(874\) | 30.3599 | − | 3.90489i | 1.02694 | − | 0.132085i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.22855 | + | 12.7122i | −0.311804 | + | 0.429505i | ||||
\(877\) | 14.2900 | + | 14.2900i | 0.482539 | + | 0.482539i | 0.905942 | − | 0.423403i | \(-0.139164\pi\) |
−0.423403 | + | 0.905942i | \(0.639164\pi\) | |||||||
\(878\) | −10.2424 | + | 13.2660i | −0.345664 | + | 0.447707i | ||||
\(879\) | 2.32471 | + | 2.83382i | 0.0784105 | + | 0.0955825i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 45.2886i | − | 1.52581i | −0.646509 | − | 0.762906i | \(-0.723772\pi\) | ||
0.646509 | − | 0.762906i | \(-0.276228\pi\) | |||||||
\(882\) | 5.01230 | − | 4.36576i | 0.168773 | − | 0.147003i | ||||
\(883\) | −3.68252 | + | 3.68252i | −0.123927 | + | 0.123927i | −0.766350 | − | 0.642423i | \(-0.777929\pi\) |
0.642423 | + | 0.766350i | \(0.277929\pi\) | |||||||
\(884\) | 2.39112 | + | 9.14153i | 0.0804221 | + | 0.307463i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.425589 | + | 3.30889i | 0.0142980 | + | 0.111164i | ||||
\(887\) | −14.7506 | − | 14.7506i | −0.495277 | − | 0.495277i | 0.414687 | − | 0.909964i | \(-0.363891\pi\) |
−0.909964 | + | 0.414687i | \(0.863891\pi\) | |||||||
\(888\) | −44.9579 | + | 13.1900i | −1.50869 | + | 0.442628i | ||||
\(889\) | − | 3.99030i | − | 0.133830i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.24150 | + | 1.76087i | 0.142095 | + | 0.0589912i | ||||
\(892\) | −23.8920 | + | 40.8180i | −0.799964 | + | 1.36669i | ||||
\(893\) | 20.0710 | + | 20.0710i | 0.671649 | + | 0.671649i | ||||
\(894\) | 22.1060 | − | 23.4523i | 0.739336 | − | 0.784363i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 25.8446 | + | 20.7025i | 0.863409 | + | 0.691623i | ||||
\(897\) | −0.650169 | + | 6.58775i | −0.0217085 | + | 0.219959i | ||||
\(898\) | −38.4417 | − | 29.6799i | −1.28282 | − | 0.990432i | ||||
\(899\) | 23.3240i | 0.777899i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.2450i | 1.20750i | ||||||||
\(902\) | 1.87146 | − | 2.42393i | 0.0623127 | − | 0.0807080i | ||||
\(903\) | −4.19655 | + | 42.5210i | −0.139653 | + | 1.41501i | ||||
\(904\) | 2.82948 | + | 7.00763i | 0.0941070 | + | 0.233070i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.91925 | + | 4.63686i | 0.163431 | + | 0.154049i | ||||
\(907\) | 8.08868 | + | 8.08868i | 0.268580 | + | 0.268580i | 0.828528 | − | 0.559948i | \(-0.189179\pi\) |
−0.559948 | + | 0.828528i | \(0.689179\pi\) | |||||||
\(908\) | −30.4671 | − | 17.8333i | −1.01109 | − | 0.591820i | ||||
\(909\) | −18.8591 | − | 3.75915i | −0.625516 | − | 0.124683i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 38.7011i | − | 1.28222i | −0.767448 | − | 0.641112i | \(-0.778473\pi\) | ||
0.767448 | − | 0.641112i | \(-0.221527\pi\) | |||||||
\(912\) | −38.1452 | + | 16.7288i | −1.26311 | + | 0.553945i | ||||
\(913\) | 2.43910 | + | 2.43910i | 0.0807223 | + | 0.0807223i | ||||
\(914\) | 9.15408 | − | 1.17740i | 0.302790 | − | 0.0389448i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.555086 | − | 2.12216i | −0.0183406 | − | 0.0701180i | ||||
\(917\) | −15.7133 | + | 15.7133i | −0.518899 | + | 0.518899i | ||||
\(918\) | 5.44296 | − | 32.2482i | 0.179644 | − | 1.06435i | ||||
\(919\) | 39.9611i | 1.31819i | 0.752058 | + | 0.659097i | \(0.229061\pi\) | ||||
−0.752058 | + | 0.659097i | \(0.770939\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.4115 | + | 23.6626i | 0.639630 | + | 0.779710i | ||||
\(922\) | 23.1102 | + | 17.8428i | 0.761094 | + | 0.587623i | ||||
\(923\) | 3.82192 | + | 3.82192i | 0.125800 | + | 0.125800i | ||||
\(924\) | −4.18679 | − | 3.03945i | −0.137735 | − | 0.0999904i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.93510 | − | 53.9193i | −0.227901 | − | 1.77190i | ||||
\(927\) | 4.38882 | + | 6.57403i | 0.144148 | + | 0.215920i | ||||
\(928\) | −4.19779 | + | 28.5852i | −0.137799 | + | 0.938354i | ||||
\(929\) | 0.568113 | 0.0186392 | 0.00931959 | − | 0.999957i | \(-0.497033\pi\) | ||||
0.00931959 | + | 0.999957i | \(0.497033\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 9.41909i | − | 0.308698i | ||||||
\(932\) | −17.0403 | − | 9.97418i | −0.558173 | − | 0.326715i | ||||
\(933\) | −0.0382135 | + | 0.387193i | −0.00125105 | + | 0.0126761i | ||||
\(934\) | −12.6935 | + | 1.63263i | −0.415343 | + | 0.0534213i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.67468 | − | 8.85073i | −0.0547386 | − | 0.289295i | ||||
\(937\) | −18.2630 | + | 18.2630i | −0.596626 | + | 0.596626i | −0.939413 | − | 0.342787i | \(-0.888629\pi\) |
0.342787 | + | 0.939413i | \(0.388629\pi\) | |||||||
\(938\) | 36.9944 | + | 28.5624i | 1.20791 | + | 0.932597i | ||||
\(939\) | 18.7023 | + | 22.7981i | 0.610326 | + | 0.743988i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.3971 | 0.730125 | 0.365063 | − | 0.930983i | \(-0.381048\pi\) | ||||
0.365063 | + | 0.930983i | \(0.381048\pi\) | |||||||
\(942\) | −0.448270 | − | 15.1693i | −0.0146054 | − | 0.494242i | ||||
\(943\) | −10.8030 | − | 10.8030i | −0.351795 | − | 0.351795i | ||||
\(944\) | 2.28198 | + | 4.06369i | 0.0742721 | + | 0.132262i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.03251 | − | 0.775901i | 0.196134 | − | 0.0252267i | ||||
\(947\) | −15.7486 | + | 15.7486i | −0.511761 | + | 0.511761i | −0.915066 | − | 0.403305i | \(-0.867861\pi\) |
0.403305 | + | 0.915066i | \(0.367861\pi\) | |||||||
\(948\) | −25.0167 | + | 3.97201i | −0.812504 | + | 0.129005i | ||||
\(949\) | −4.81396 | −0.156268 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −38.3034 | + | 31.4219i | −1.24207 | + | 1.01893i | ||||
\(952\) | −14.4033 | + | 33.9114i | −0.466815 | + | 1.09908i | ||||
\(953\) | 33.3609 | − | 33.3609i | 1.08067 | − | 1.08067i | 0.0842194 | − | 0.996447i | \(-0.473160\pi\) |
0.996447 | − | 0.0842194i | \(-0.0268396\pi\) | |||||||
\(954\) | 2.37644 | − | 34.4704i | 0.0769400 | − | 1.11602i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.23572 | − | 23.8399i | −0.201678 | − | 0.771037i | ||||
\(957\) | 0.443352 | − | 4.49221i | 0.0143315 | − | 0.145213i | ||||
\(958\) | 40.1990 | + | 31.0367i | 1.29877 | + | 1.00275i | ||||
\(959\) | −2.95353 | −0.0953746 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.1451 | −0.327260 | ||||||||
\(962\) | −11.3649 | − | 8.77458i | −0.366420 | − | 0.282904i | ||||
\(963\) | 35.3984 | − | 23.6319i | 1.14070 | − | 0.761529i | ||||
\(964\) | −3.56215 | − | 13.6185i | −0.114729 | − | 0.438622i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −17.7044 | + | 18.7826i | −0.569630 | + | 0.604322i | ||||
\(967\) | 8.01398 | − | 8.01398i | 0.257712 | − | 0.257712i | −0.566411 | − | 0.824123i | \(-0.691668\pi\) |
0.824123 | + | 0.566411i | \(0.191668\pi\) | |||||||
\(968\) | 11.8751 | − | 27.9589i | 0.381679 | − | 0.898632i | ||||
\(969\) | −29.3927 | − | 35.8297i | −0.944229 | − | 1.15102i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.4981 | 1.39592 | 0.697961 | − | 0.716136i | \(-0.254091\pi\) | ||||
0.697961 | + | 0.716136i | \(0.254091\pi\) | |||||||
\(972\) | −7.29085 | + | 30.3124i | −0.233854 | + | 0.972272i | ||||
\(973\) | −18.6568 | + | 18.6568i | −0.598110 | + | 0.598110i | ||||
\(974\) | 47.4274 | − | 6.10011i | 1.51967 | − | 0.195460i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.65420 | + | 17.1919i | 0.309024 | + | 0.550301i | ||||
\(977\) | 39.7367 | + | 39.7367i | 1.27129 | + | 1.27129i | 0.945411 | + | 0.325880i | \(0.105661\pi\) |
0.325880 | + | 0.945411i | \(0.394339\pi\) | |||||||
\(978\) | −1.63042 | + | 0.0481810i | −0.0521352 | + | 0.00154066i | ||||
\(979\) | −6.45147 | −0.206190 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −37.2026 | − | 7.41555i | −1.18779 | − | 0.236760i | ||||
\(982\) | −34.6462 | − | 26.7495i | −1.10560 | − | 0.853609i | ||||
\(983\) | −9.14087 | + | 9.14087i | −0.291548 | + | 0.291548i | −0.837692 | − | 0.546143i | \(-0.816095\pi\) |
0.546143 | + | 0.837692i | \(0.316095\pi\) | |||||||
\(984\) | 18.2439 | + | 9.96719i | 0.581596 | + | 0.317742i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −31.8830 | + | 4.10079i | −1.01536 | + | 0.130596i | ||||
\(987\) | −23.8193 | − | 2.35081i | −0.758176 | − | 0.0748271i | ||||
\(988\) | −11.0160 | − | 6.44799i | −0.350465 | − | 0.205138i | ||||
\(989\) | − | 30.3439i | − | 0.964879i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.1823 | −0.736409 | −0.368205 | − | 0.929745i | \(-0.620027\pi\) | ||||
−0.368205 | + | 0.929745i | \(0.620027\pi\) | |||||||
\(992\) | 25.5591 | + | 3.75342i | 0.811503 | + | 0.119171i | ||||
\(993\) | −2.09766 | + | 21.2542i | −0.0665671 | + | 0.674483i | ||||
\(994\) | 2.68852 | + | 20.9028i | 0.0852747 | + | 0.662997i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13.7569 | + | 18.9499i | −0.435904 | + | 0.600451i | ||||
\(997\) | 3.70273 | + | 3.70273i | 0.117267 | + | 0.117267i | 0.763305 | − | 0.646038i | \(-0.223575\pi\) |
−0.646038 | + | 0.763305i | \(0.723575\pi\) | |||||||
\(998\) | 22.2978 | + | 17.2156i | 0.705824 | + | 0.544949i | ||||
\(999\) | 23.3997 | + | 43.8411i | 0.740334 | + | 1.38707i |
(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 | 600.2.w.j.293.13 | 32 | ||
3.2 | odd | 2 | inner | 600.2.w.j.293.4 | 32 | ||
5.2 | odd | 4 | inner | 600.2.w.j.557.5 | 32 | ||
5.3 | odd | 4 | 120.2.w.c.77.12 | yes | 32 | ||
5.4 | even | 2 | 120.2.w.c.53.4 | ✓ | 32 | ||
8.5 | even | 2 | inner | 600.2.w.j.293.12 | 32 | ||
15.2 | even | 4 | inner | 600.2.w.j.557.12 | 32 | ||
15.8 | even | 4 | 120.2.w.c.77.5 | yes | 32 | ||
15.14 | odd | 2 | 120.2.w.c.53.13 | yes | 32 | ||
20.3 | even | 4 | 480.2.bi.c.17.9 | 32 | |||
20.19 | odd | 2 | 480.2.bi.c.113.16 | 32 | |||
24.5 | odd | 2 | inner | 600.2.w.j.293.5 | 32 | ||
40.3 | even | 4 | 480.2.bi.c.17.8 | 32 | |||
40.13 | odd | 4 | 120.2.w.c.77.13 | yes | 32 | ||
40.19 | odd | 2 | 480.2.bi.c.113.1 | 32 | |||
40.29 | even | 2 | 120.2.w.c.53.5 | yes | 32 | ||
40.37 | odd | 4 | inner | 600.2.w.j.557.4 | 32 | ||
60.23 | odd | 4 | 480.2.bi.c.17.1 | 32 | |||
60.59 | even | 2 | 480.2.bi.c.113.8 | 32 | |||
120.29 | odd | 2 | 120.2.w.c.53.12 | yes | 32 | ||
120.53 | even | 4 | 120.2.w.c.77.4 | yes | 32 | ||
120.59 | even | 2 | 480.2.bi.c.113.9 | 32 | |||
120.77 | even | 4 | inner | 600.2.w.j.557.13 | 32 | ||
120.83 | odd | 4 | 480.2.bi.c.17.16 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.2.w.c.53.4 | ✓ | 32 | 5.4 | even | 2 | ||
120.2.w.c.53.5 | yes | 32 | 40.29 | even | 2 | ||
120.2.w.c.53.12 | yes | 32 | 120.29 | odd | 2 | ||
120.2.w.c.53.13 | yes | 32 | 15.14 | odd | 2 | ||
120.2.w.c.77.4 | yes | 32 | 120.53 | even | 4 | ||
120.2.w.c.77.5 | yes | 32 | 15.8 | even | 4 | ||
120.2.w.c.77.12 | yes | 32 | 5.3 | odd | 4 | ||
120.2.w.c.77.13 | yes | 32 | 40.13 | odd | 4 | ||
480.2.bi.c.17.1 | 32 | 60.23 | odd | 4 | |||
480.2.bi.c.17.8 | 32 | 40.3 | even | 4 | |||
480.2.bi.c.17.9 | 32 | 20.3 | even | 4 | |||
480.2.bi.c.17.16 | 32 | 120.83 | odd | 4 | |||
480.2.bi.c.113.1 | 32 | 40.19 | odd | 2 | |||
480.2.bi.c.113.8 | 32 | 60.59 | even | 2 | |||
480.2.bi.c.113.9 | 32 | 120.59 | even | 2 | |||
480.2.bi.c.113.16 | 32 | 20.19 | odd | 2 | |||
600.2.w.j.293.4 | 32 | 3.2 | odd | 2 | inner | ||
600.2.w.j.293.5 | 32 | 24.5 | odd | 2 | inner | ||
600.2.w.j.293.12 | 32 | 8.5 | even | 2 | inner | ||
600.2.w.j.293.13 | 32 | 1.1 | even | 1 | trivial | ||
600.2.w.j.557.4 | 32 | 40.37 | odd | 4 | inner | ||
600.2.w.j.557.5 | 32 | 5.2 | odd | 4 | inner | ||
600.2.w.j.557.12 | 32 | 15.2 | even | 4 | inner | ||
600.2.w.j.557.13 | 32 | 120.77 | even | 4 | inner |