Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [471,2,Mod(169,471)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(471, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("471.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 471 = 3 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 471.e (of order \(3\), 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: | \(3.76095393520\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 169.11 | ||
Character | \(\chi\) | \(=\) | 471.169 |
Dual form | 471.2.e.b.301.11 |
$q$-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 \(\left(\mathbb{Z}/471\mathbb{Z}\right)^\times\).
\(n\) | \(158\) | \(319\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.74840 | 1.94341 | 0.971706 | − | 0.236192i | \(-0.0758994\pi\) | ||||
0.971706 | + | 0.236192i | \(0.0758994\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 5.55371 | 2.77685 | ||||||||
\(5\) | 0.277926 | + | 0.481381i | 0.124292 | + | 0.215280i | 0.921456 | − | 0.388483i | \(-0.127001\pi\) |
−0.797164 | + | 0.603763i | \(0.793667\pi\) | |||||||
\(6\) | 1.37420 | + | 2.38018i | 0.561015 | + | 0.971706i | ||||
\(7\) | −4.42840 | −1.67378 | −0.836890 | − | 0.547372i | \(-0.815628\pi\) | ||||
−0.836890 | + | 0.547372i | \(0.815628\pi\) | |||||||
\(8\) | 9.76701 | 3.45316 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.763851 | + | 1.32303i | 0.241551 | + | 0.418378i | ||||
\(11\) | −1.93821 | − | 3.35708i | −0.584392 | − | 1.01220i | −0.994951 | − | 0.100363i | \(-0.968000\pi\) |
0.410558 | − | 0.911834i | \(-0.365334\pi\) | |||||||
\(12\) | 2.77685 | + | 4.80965i | 0.801609 | + | 1.38843i | ||||
\(13\) | 0.286084 | − | 0.495513i | 0.0793455 | − | 0.137430i | −0.823622 | − | 0.567139i | \(-0.808050\pi\) |
0.902968 | + | 0.429708i | \(0.141384\pi\) | |||||||
\(14\) | −12.1710 | −3.25284 | ||||||||
\(15\) | −0.277926 | + | 0.481381i | −0.0717601 | + | 0.124292i | ||||
\(16\) | 15.7362 | 3.93406 | ||||||||
\(17\) | 2.88539 | + | 4.99764i | 0.699809 | + | 1.21210i | 0.968532 | + | 0.248887i | \(0.0800649\pi\) |
−0.268723 | + | 0.963217i | \(0.586602\pi\) | |||||||
\(18\) | −1.37420 | + | 2.38018i | −0.323902 | + | 0.561015i | ||||
\(19\) | −2.35250 | − | 4.07464i | −0.539699 | − | 0.934787i | −0.998920 | − | 0.0464645i | \(-0.985205\pi\) |
0.459221 | − | 0.888322i | \(-0.348129\pi\) | |||||||
\(20\) | 1.54352 | + | 2.67345i | 0.345141 | + | 0.597802i | ||||
\(21\) | −2.21420 | − | 3.83511i | −0.483178 | − | 0.836890i | ||||
\(22\) | −5.32698 | − | 9.22660i | −1.13572 | − | 1.96712i | ||||
\(23\) | −1.19495 | −0.249163 | −0.124582 | − | 0.992209i | \(-0.539759\pi\) | ||||
−0.124582 | + | 0.992209i | \(0.539759\pi\) | |||||||
\(24\) | 4.88351 | + | 8.45848i | 0.996841 | + | 1.72658i | ||||
\(25\) | 2.34551 | − | 4.06255i | 0.469103 | − | 0.812510i | ||||
\(26\) | 0.786274 | − | 1.36187i | 0.154201 | − | 0.267084i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −24.5941 | −4.64784 | ||||||||
\(29\) | −10.3284 | −1.91793 | −0.958964 | − | 0.283527i | \(-0.908495\pi\) | ||||
−0.958964 | + | 0.283527i | \(0.908495\pi\) | |||||||
\(30\) | −0.763851 | + | 1.32303i | −0.139459 | + | 0.241551i | ||||
\(31\) | −1.89212 | + | 3.27726i | −0.339836 | + | 0.588613i | −0.984402 | − | 0.175936i | \(-0.943705\pi\) |
0.644566 | + | 0.764549i | \(0.277038\pi\) | |||||||
\(32\) | 23.7155 | 4.19235 | ||||||||
\(33\) | 1.93821 | − | 3.35708i | 0.337399 | − | 0.584392i | ||||
\(34\) | 7.93020 | + | 13.7355i | 1.36002 | + | 2.35562i | ||||
\(35\) | −1.23077 | − | 2.13175i | −0.208038 | − | 0.360332i | ||||
\(36\) | −2.77685 | + | 4.80965i | −0.462809 | + | 0.801609i | ||||
\(37\) | 1.26780 | − | 2.19590i | 0.208425 | − | 0.361003i | −0.742793 | − | 0.669521i | \(-0.766499\pi\) |
0.951219 | + | 0.308517i | \(0.0998328\pi\) | |||||||
\(38\) | −6.46560 | − | 11.1987i | −1.04886 | − | 1.81668i | ||||
\(39\) | 0.572169 | 0.0916203 | ||||||||
\(40\) | 2.71450 | + | 4.70166i | 0.429200 | + | 0.743397i | ||||
\(41\) | 8.61324 | 1.34516 | 0.672581 | − | 0.740024i | \(-0.265186\pi\) | ||||
0.672581 | + | 0.740024i | \(0.265186\pi\) | |||||||
\(42\) | −6.08551 | − | 10.5404i | −0.939015 | − | 1.62642i | ||||
\(43\) | −5.04965 | + | 8.74625i | −0.770064 | + | 1.33379i | 0.167463 | + | 0.985878i | \(0.446442\pi\) |
−0.937527 | + | 0.347912i | \(0.886891\pi\) | |||||||
\(44\) | −10.7643 | − | 18.6442i | −1.62277 | − | 2.81072i | ||||
\(45\) | −0.555851 | −0.0828614 | ||||||||
\(46\) | −3.28419 | −0.484227 | ||||||||
\(47\) | 1.70863 | − | 2.95943i | 0.249229 | − | 0.431677i | −0.714083 | − | 0.700061i | \(-0.753156\pi\) |
0.963312 | + | 0.268384i | \(0.0864896\pi\) | |||||||
\(48\) | 7.86812 | + | 13.6280i | 1.13567 | + | 1.96703i | ||||
\(49\) | 12.6108 | 1.80154 | ||||||||
\(50\) | 6.44641 | − | 11.1655i | 0.911661 | − | 1.57904i | ||||
\(51\) | −2.88539 | + | 4.99764i | −0.404035 | + | 0.699809i | ||||
\(52\) | 1.58883 | − | 2.75193i | 0.220331 | − | 0.381624i | ||||
\(53\) | 0.565189 | − | 0.978937i | 0.0776347 | − | 0.134467i | −0.824594 | − | 0.565725i | \(-0.808597\pi\) |
0.902229 | + | 0.431257i | \(0.141930\pi\) | |||||||
\(54\) | −2.74840 | −0.374010 | ||||||||
\(55\) | 1.07736 | − | 1.86604i | 0.145271 | − | 0.251616i | ||||
\(56\) | −43.2523 | −5.77983 | ||||||||
\(57\) | 2.35250 | − | 4.07464i | 0.311596 | − | 0.539699i | ||||
\(58\) | −28.3865 | −3.72733 | ||||||||
\(59\) | 1.90366 | 0.247835 | 0.123918 | − | 0.992293i | \(-0.460454\pi\) | ||||
0.123918 | + | 0.992293i | \(0.460454\pi\) | |||||||
\(60\) | −1.54352 | + | 2.67345i | −0.199267 | + | 0.345141i | ||||
\(61\) | −0.175136 | − | 0.303345i | −0.0224239 | − | 0.0388393i | 0.854596 | − | 0.519294i | \(-0.173805\pi\) |
−0.877020 | + | 0.480455i | \(0.840472\pi\) | |||||||
\(62\) | −5.20032 | + | 9.00721i | −0.660441 | + | 1.14392i | ||||
\(63\) | 2.21420 | − | 3.83511i | 0.278963 | − | 0.483178i | ||||
\(64\) | 33.7072 | 4.21340 | ||||||||
\(65\) | 0.318041 | 0.0394481 | ||||||||
\(66\) | 5.32698 | − | 9.22660i | 0.655706 | − | 1.13572i | ||||
\(67\) | 2.06043 | 0.251722 | 0.125861 | − | 0.992048i | \(-0.459831\pi\) | ||||
0.125861 | + | 0.992048i | \(0.459831\pi\) | |||||||
\(68\) | 16.0246 | + | 27.7554i | 1.94327 | + | 3.36584i | ||||
\(69\) | −0.597473 | − | 1.03485i | −0.0719273 | − | 0.124582i | ||||
\(70\) | −3.38264 | − | 5.85890i | −0.404303 | − | 0.700273i | ||||
\(71\) | 4.68078 | − | 8.10735i | 0.555507 | − | 0.962166i | −0.442357 | − | 0.896839i | \(-0.645858\pi\) |
0.997864 | − | 0.0653270i | \(-0.0208091\pi\) | |||||||
\(72\) | −4.88351 | + | 8.45848i | −0.575527 | + | 0.996841i | ||||
\(73\) | 6.74811 | + | 11.6881i | 0.789807 | + | 1.36799i | 0.926085 | + | 0.377315i | \(0.123153\pi\) |
−0.136278 | + | 0.990671i | \(0.543514\pi\) | |||||||
\(74\) | 3.48443 | − | 6.03521i | 0.405057 | − | 0.701579i | ||||
\(75\) | 4.69103 | 0.541673 | ||||||||
\(76\) | −13.0651 | − | 22.6294i | −1.49867 | − | 2.59577i | ||||
\(77\) | 8.58318 | + | 14.8665i | 0.978144 | + | 1.69419i | ||||
\(78\) | 1.57255 | 0.178056 | ||||||||
\(79\) | −7.07153 | −0.795609 | −0.397805 | − | 0.917470i | \(-0.630228\pi\) | ||||
−0.397805 | + | 0.917470i | \(0.630228\pi\) | |||||||
\(80\) | 4.37351 | + | 7.57513i | 0.488973 | + | 0.846926i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 23.6726 | 2.61420 | ||||||||
\(83\) | −3.41445 | + | 5.91401i | −0.374785 | + | 0.649147i | −0.990295 | − | 0.138982i | \(-0.955617\pi\) |
0.615510 | + | 0.788129i | \(0.288950\pi\) | |||||||
\(84\) | −12.2970 | − | 21.2991i | −1.34172 | − | 2.32392i | ||||
\(85\) | −1.60385 | + | 2.77794i | −0.173961 | + | 0.301310i | ||||
\(86\) | −13.8785 | + | 24.0382i | −1.49655 | + | 2.59210i | ||||
\(87\) | −5.16418 | − | 8.94462i | −0.553658 | − | 0.958964i | ||||
\(88\) | −18.9305 | − | 32.7886i | −2.01800 | − | 3.49528i | ||||
\(89\) | 2.76950 | + | 4.79692i | 0.293567 | + | 0.508473i | 0.974650 | − | 0.223733i | \(-0.0718244\pi\) |
−0.681084 | + | 0.732206i | \(0.738491\pi\) | |||||||
\(90\) | −1.52770 | −0.161034 | ||||||||
\(91\) | −1.26690 | + | 2.19433i | −0.132807 | + | 0.230028i | ||||
\(92\) | −6.63638 | −0.691890 | ||||||||
\(93\) | −3.78425 | −0.392408 | ||||||||
\(94\) | 4.69599 | − | 8.13369i | 0.484354 | − | 0.838926i | ||||
\(95\) | 1.30764 | − | 2.26489i | 0.134161 | − | 0.232373i | ||||
\(96\) | 11.8577 | + | 20.5382i | 1.21023 | + | 2.09617i | ||||
\(97\) | −8.40042 | + | 14.5500i | −0.852934 | + | 1.47732i | 0.0256153 | + | 0.999672i | \(0.491845\pi\) |
−0.878549 | + | 0.477652i | \(0.841488\pi\) | |||||||
\(98\) | 34.6594 | 3.50113 | ||||||||
\(99\) | 3.87642 | 0.389595 | ||||||||
\(100\) | 13.0263 | − | 22.5622i | 1.30263 | − | 2.25622i | ||||
\(101\) | −6.06220 | −0.603211 | −0.301606 | − | 0.953433i | \(-0.597523\pi\) | ||||
−0.301606 | + | 0.953433i | \(0.597523\pi\) | |||||||
\(102\) | −7.93020 | + | 13.7355i | −0.785207 | + | 1.36002i | ||||
\(103\) | 8.39372 | 0.827058 | 0.413529 | − | 0.910491i | \(-0.364296\pi\) | ||||
0.413529 | + | 0.910491i | \(0.364296\pi\) | |||||||
\(104\) | 2.79419 | − | 4.83968i | 0.273993 | − | 0.474569i | ||||
\(105\) | 1.23077 | − | 2.13175i | 0.120111 | − | 0.208038i | ||||
\(106\) | 1.55337 | − | 2.69051i | 0.150876 | − | 0.261325i | ||||
\(107\) | −2.24376 | + | 3.88630i | −0.216912 | + | 0.375703i | −0.953862 | − | 0.300244i | \(-0.902932\pi\) |
0.736950 | + | 0.675947i | \(0.236265\pi\) | |||||||
\(108\) | −5.55371 | −0.534406 | ||||||||
\(109\) | −0.345821 | − | 0.598979i | −0.0331236 | − | 0.0573718i | 0.848988 | − | 0.528412i | \(-0.177212\pi\) |
−0.882112 | + | 0.471040i | \(0.843879\pi\) | |||||||
\(110\) | 2.96101 | − | 5.12862i | 0.282321 | − | 0.488994i | ||||
\(111\) | 2.53560 | 0.240669 | ||||||||
\(112\) | −69.6864 | −6.58475 | ||||||||
\(113\) | −8.28854 | − | 14.3562i | −0.779720 | − | 1.35051i | −0.932103 | − | 0.362193i | \(-0.882028\pi\) |
0.152383 | − | 0.988321i | \(-0.451305\pi\) | |||||||
\(114\) | 6.46560 | − | 11.1987i | 0.605559 | − | 1.04886i | ||||
\(115\) | −0.332106 | − | 0.575225i | −0.0309690 | − | 0.0536400i | ||||
\(116\) | −57.3607 | −5.32581 | ||||||||
\(117\) | 0.286084 | + | 0.495513i | 0.0264485 | + | 0.0458102i | ||||
\(118\) | 5.23202 | 0.481646 | ||||||||
\(119\) | −12.7777 | − | 22.1315i | −1.17133 | − | 2.02880i | ||||
\(120\) | −2.71450 | + | 4.70166i | −0.247799 | + | 0.429200i | ||||
\(121\) | −2.01332 | + | 3.48717i | −0.183029 | + | 0.317015i | ||||
\(122\) | −0.481345 | − | 0.833713i | −0.0435789 | − | 0.0754808i | ||||
\(123\) | 4.30662 | + | 7.45928i | 0.388315 | + | 0.672581i | ||||
\(124\) | −10.5083 | + | 18.2009i | −0.943674 | + | 1.63449i | ||||
\(125\) | 5.38677 | 0.481807 | ||||||||
\(126\) | 6.08551 | − | 10.5404i | 0.542141 | − | 0.939015i | ||||
\(127\) | 0.762895 | − | 1.32137i | 0.0676960 | − | 0.117253i | −0.830191 | − | 0.557479i | \(-0.811769\pi\) |
0.897887 | + | 0.440227i | \(0.145102\pi\) | |||||||
\(128\) | 45.2098 | 3.99602 | ||||||||
\(129\) | −10.0993 | −0.889193 | ||||||||
\(130\) | 0.874103 | 0.0766639 | ||||||||
\(131\) | 9.47219 | − | 16.4063i | 0.827589 | − | 1.43343i | −0.0723352 | − | 0.997380i | \(-0.523045\pi\) |
0.899924 | − | 0.436046i | \(-0.143622\pi\) | |||||||
\(132\) | 10.7643 | − | 18.6442i | 0.936908 | − | 1.62277i | ||||
\(133\) | 10.4178 | + | 18.0442i | 0.903338 | + | 1.56463i | ||||
\(134\) | 5.66289 | 0.489199 | ||||||||
\(135\) | −0.277926 | − | 0.481381i | −0.0239200 | − | 0.0414307i | ||||
\(136\) | 28.1816 | + | 48.8120i | 2.41655 | + | 4.18559i | ||||
\(137\) | −5.66096 | − | 9.80506i | −0.483648 | − | 0.837703i | 0.516176 | − | 0.856483i | \(-0.327355\pi\) |
−0.999824 | + | 0.0187797i | \(0.994022\pi\) | |||||||
\(138\) | −1.64210 | − | 2.84419i | −0.139784 | − | 0.242114i | ||||
\(139\) | −1.21676 | + | 2.10749i | −0.103204 | + | 0.178755i | −0.913003 | − | 0.407953i | \(-0.866243\pi\) |
0.809799 | + | 0.586707i | \(0.199576\pi\) | |||||||
\(140\) | −6.83532 | − | 11.8391i | −0.577690 | − | 1.00059i | ||||
\(141\) | 3.41725 | 0.287785 | ||||||||
\(142\) | 12.8647 | − | 22.2823i | 1.07958 | − | 1.86989i | ||||
\(143\) | −2.21797 | −0.185476 | ||||||||
\(144\) | −7.86812 | + | 13.6280i | −0.655677 | + | 1.13567i | ||||
\(145\) | −2.87052 | − | 4.97188i | −0.238383 | − | 0.412892i | ||||
\(146\) | 18.5465 | + | 32.1235i | 1.53492 | + | 2.65856i | ||||
\(147\) | 6.30538 | + | 10.9212i | 0.520059 | + | 0.900768i | ||||
\(148\) | 7.04100 | − | 12.1954i | 0.578767 | − | 1.00245i | ||||
\(149\) | 9.57621 | 0.784514 | 0.392257 | − | 0.919856i | \(-0.371694\pi\) | ||||
0.392257 | + | 0.919856i | \(0.371694\pi\) | |||||||
\(150\) | 12.8928 | 1.05270 | ||||||||
\(151\) | 8.01468 | + | 13.8818i | 0.652225 | + | 1.12969i | 0.982582 | + | 0.185831i | \(0.0594978\pi\) |
−0.330356 | + | 0.943856i | \(0.607169\pi\) | |||||||
\(152\) | −22.9768 | − | 39.7971i | −1.86367 | − | 3.22797i | ||||
\(153\) | −5.77077 | −0.466539 | ||||||||
\(154\) | 23.5900 | + | 40.8591i | 1.90094 | + | 3.29252i | ||||
\(155\) | −2.10348 | −0.168956 | ||||||||
\(156\) | 3.17766 | 0.254416 | ||||||||
\(157\) | −5.13171 | + | 11.4309i | −0.409555 | + | 0.912286i | ||||
\(158\) | −19.4354 | −1.54620 | ||||||||
\(159\) | 1.13038 | 0.0896448 | ||||||||
\(160\) | 6.59114 | + | 11.4162i | 0.521075 | + | 0.902529i | ||||
\(161\) | 5.29170 | 0.417045 | ||||||||
\(162\) | −1.37420 | − | 2.38018i | −0.107967 | − | 0.187005i | ||||
\(163\) | 7.24553 | + | 12.5496i | 0.567514 | + | 0.982962i | 0.996811 | + | 0.0797993i | \(0.0254279\pi\) |
−0.429297 | + | 0.903163i | \(0.641239\pi\) | |||||||
\(164\) | 47.8354 | 3.73532 | ||||||||
\(165\) | 2.15471 | 0.167744 | ||||||||
\(166\) | −9.38429 | + | 16.2541i | −0.728362 | + | 1.26156i | ||||
\(167\) | −1.53417 | − | 2.65725i | −0.118717 | − | 0.205625i | 0.800542 | − | 0.599276i | \(-0.204545\pi\) |
−0.919260 | + | 0.393652i | \(0.871212\pi\) | |||||||
\(168\) | −21.6261 | − | 37.4576i | −1.66849 | − | 2.88991i | ||||
\(169\) | 6.33631 | + | 10.9748i | 0.487409 | + | 0.844216i | ||||
\(170\) | −4.40801 | + | 7.63490i | −0.338079 | + | 0.585570i | ||||
\(171\) | 4.70499 | 0.359800 | ||||||||
\(172\) | −28.0443 | + | 48.5741i | −2.13835 | + | 3.70374i | ||||
\(173\) | −5.45837 | −0.414992 | −0.207496 | − | 0.978236i | \(-0.566531\pi\) | ||||
−0.207496 | + | 0.978236i | \(0.566531\pi\) | |||||||
\(174\) | −14.1932 | − | 24.5834i | −1.07599 | − | 1.86366i | ||||
\(175\) | −10.3869 | + | 17.9906i | −0.785175 | + | 1.35996i | ||||
\(176\) | −30.5002 | − | 52.8278i | −2.29904 | − | 3.98205i | ||||
\(177\) | 0.951830 | + | 1.64862i | 0.0715439 | + | 0.123918i | ||||
\(178\) | 7.61171 | + | 13.1839i | 0.570521 | + | 0.988172i | ||||
\(179\) | −5.02532 | − | 8.70410i | −0.375610 | − | 0.650575i | 0.614808 | − | 0.788677i | \(-0.289233\pi\) |
−0.990418 | + | 0.138101i | \(0.955900\pi\) | |||||||
\(180\) | −3.08703 | −0.230094 | ||||||||
\(181\) | −7.94327 | − | 13.7582i | −0.590419 | − | 1.02264i | −0.994176 | − | 0.107769i | \(-0.965629\pi\) |
0.403757 | − | 0.914866i | \(-0.367704\pi\) | |||||||
\(182\) | −3.48194 | + | 6.03090i | −0.258099 | + | 0.447040i | ||||
\(183\) | 0.175136 | − | 0.303345i | 0.0129464 | − | 0.0224239i | ||||
\(184\) | −11.6710 | −0.860401 | ||||||||
\(185\) | 1.40942 | 0.103623 | ||||||||
\(186\) | −10.4006 | −0.762611 | ||||||||
\(187\) | 11.1850 | − | 19.3729i | 0.817926 | − | 1.41669i | ||||
\(188\) | 9.48921 | − | 16.4358i | 0.692072 | − | 1.19870i | ||||
\(189\) | 4.42840 | 0.322119 | ||||||||
\(190\) | 3.59391 | − | 6.22484i | 0.260730 | − | 0.451597i | ||||
\(191\) | 1.29645 | + | 2.24552i | 0.0938081 | + | 0.162480i | 0.909111 | − | 0.416555i | \(-0.136763\pi\) |
−0.815302 | + | 0.579035i | \(0.803429\pi\) | |||||||
\(192\) | 16.8536 | + | 29.1913i | 1.21630 | + | 2.10670i | ||||
\(193\) | 7.55176 | − | 13.0800i | 0.543587 | − | 0.941521i | −0.455107 | − | 0.890437i | \(-0.650399\pi\) |
0.998694 | − | 0.0510843i | \(-0.0162677\pi\) | |||||||
\(194\) | −23.0877 | + | 39.9891i | −1.65760 | + | 2.87105i | ||||
\(195\) | 0.159020 | + | 0.275431i | 0.0113877 | + | 0.0197240i | ||||
\(196\) | 70.0364 | 5.00260 | ||||||||
\(197\) | 5.59983 | + | 9.69919i | 0.398971 | + | 0.691039i | 0.993599 | − | 0.112962i | \(-0.0360339\pi\) |
−0.594628 | + | 0.804001i | \(0.702701\pi\) | |||||||
\(198\) | 10.6540 | 0.757144 | ||||||||
\(199\) | 2.13021 | + | 3.68964i | 0.151007 | + | 0.261552i | 0.931598 | − | 0.363491i | \(-0.118415\pi\) |
−0.780591 | + | 0.625042i | \(0.785082\pi\) | |||||||
\(200\) | 22.9087 | − | 39.6790i | 1.61989 | − | 2.80573i | ||||
\(201\) | 1.03022 | + | 1.78439i | 0.0726658 | + | 0.125861i | ||||
\(202\) | −16.6613 | −1.17229 | ||||||||
\(203\) | 45.7381 | 3.21019 | ||||||||
\(204\) | −16.0246 | + | 27.7554i | −1.12195 | + | 1.94327i | ||||
\(205\) | 2.39384 | + | 4.14625i | 0.167193 | + | 0.289587i | ||||
\(206\) | 23.0693 | 1.60732 | ||||||||
\(207\) | 0.597473 | − | 1.03485i | 0.0415272 | − | 0.0719273i | ||||
\(208\) | 4.50189 | − | 7.79751i | 0.312150 | − | 0.540660i | ||||
\(209\) | −9.11926 | + | 15.7950i | −0.630792 | + | 1.09256i | ||||
\(210\) | 3.38264 | − | 5.85890i | 0.233424 | − | 0.404303i | ||||
\(211\) | −17.2752 | −1.18928 | −0.594638 | − | 0.803994i | \(-0.702704\pi\) | ||||
−0.594638 | + | 0.803994i | \(0.702704\pi\) | |||||||
\(212\) | 3.13890 | − | 5.43673i | 0.215580 | − | 0.373396i | ||||
\(213\) | 9.36157 | 0.641444 | ||||||||
\(214\) | −6.16675 | + | 10.6811i | −0.421550 | + | 0.730146i | ||||
\(215\) | −5.61370 | −0.382851 | ||||||||
\(216\) | −9.76701 | −0.664561 | ||||||||
\(217\) | 8.37909 | − | 14.5130i | 0.568810 | − | 0.985207i | ||||
\(218\) | −0.950454 | − | 1.64623i | −0.0643728 | − | 0.111497i | ||||
\(219\) | −6.74811 | + | 11.6881i | −0.455995 | + | 0.789807i | ||||
\(220\) | 5.98332 | − | 10.3634i | 0.403395 | − | 0.698701i | ||||
\(221\) | 3.30186 | 0.222107 | ||||||||
\(222\) | 6.96886 | 0.467719 | ||||||||
\(223\) | 13.7028 | − | 23.7340i | 0.917610 | − | 1.58935i | 0.114575 | − | 0.993415i | \(-0.463449\pi\) |
0.803035 | − | 0.595932i | \(-0.203217\pi\) | |||||||
\(224\) | −105.022 | −7.01706 | ||||||||
\(225\) | 2.34551 | + | 4.06255i | 0.156368 | + | 0.270837i | ||||
\(226\) | −22.7802 | − | 39.4565i | −1.51532 | − | 2.62461i | ||||
\(227\) | −1.85385 | − | 3.21097i | −0.123045 | − | 0.213119i | 0.797922 | − | 0.602760i | \(-0.205932\pi\) |
−0.920967 | + | 0.389641i | \(0.872599\pi\) | |||||||
\(228\) | 13.0651 | − | 22.6294i | 0.865255 | − | 1.49867i | ||||
\(229\) | −2.67308 | + | 4.62991i | −0.176642 | + | 0.305953i | −0.940728 | − | 0.339161i | \(-0.889857\pi\) |
0.764086 | + | 0.645114i | \(0.223190\pi\) | |||||||
\(230\) | −0.912760 | − | 1.58095i | −0.0601856 | − | 0.104245i | ||||
\(231\) | −8.58318 | + | 14.8665i | −0.564732 | + | 0.978144i | ||||
\(232\) | −100.877 | −6.62291 | ||||||||
\(233\) | 6.47919 | + | 11.2223i | 0.424466 | + | 0.735196i | 0.996370 | − | 0.0851239i | \(-0.0271286\pi\) |
−0.571905 | + | 0.820320i | \(0.693795\pi\) | |||||||
\(234\) | 0.786274 | + | 1.36187i | 0.0514004 | + | 0.0890281i | ||||
\(235\) | 1.89948 | 0.123909 | ||||||||
\(236\) | 10.5724 | 0.688202 | ||||||||
\(237\) | −3.53577 | − | 6.12412i | −0.229673 | − | 0.397805i | ||||
\(238\) | −35.1181 | − | 60.8264i | −2.27637 | − | 3.94279i | ||||
\(239\) | −26.9233 | −1.74153 | −0.870763 | − | 0.491703i | \(-0.836375\pi\) | ||||
−0.870763 | + | 0.491703i | \(0.836375\pi\) | |||||||
\(240\) | −4.37351 | + | 7.57513i | −0.282309 | + | 0.488973i | ||||
\(241\) | 6.63584 | + | 11.4936i | 0.427452 | + | 0.740369i | 0.996646 | − | 0.0818345i | \(-0.0260779\pi\) |
−0.569194 | + | 0.822203i | \(0.692745\pi\) | |||||||
\(242\) | −5.53341 | + | 9.58414i | −0.355701 | + | 0.616092i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −0.972655 | − | 1.68469i | −0.0622679 | − | 0.107851i | ||||
\(245\) | 3.50485 | + | 6.07058i | 0.223917 | + | 0.387835i | ||||
\(246\) | 11.8363 | + | 20.5011i | 0.754656 | + | 1.30710i | ||||
\(247\) | −2.69205 | −0.171291 | ||||||||
\(248\) | −18.4804 | + | 32.0090i | −1.17351 | + | 2.03257i | ||||
\(249\) | −6.82891 | −0.432765 | ||||||||
\(250\) | 14.8050 | 0.936351 | ||||||||
\(251\) | 6.15031 | − | 10.6526i | 0.388204 | − | 0.672389i | −0.604004 | − | 0.796981i | \(-0.706429\pi\) |
0.992208 | + | 0.124592i | \(0.0397623\pi\) | |||||||
\(252\) | 12.2970 | − | 21.2991i | 0.774640 | − | 1.34172i | ||||
\(253\) | 2.31606 | + | 4.01153i | 0.145609 | + | 0.252203i | ||||
\(254\) | 2.09674 | − | 3.63166i | 0.131561 | − | 0.227871i | ||||
\(255\) | −3.20769 | −0.200873 | ||||||||
\(256\) | 56.8404 | 3.55253 | ||||||||
\(257\) | 13.9682 | − | 24.1936i | 0.871312 | − | 1.50916i | 0.0106718 | − | 0.999943i | \(-0.496603\pi\) |
0.860640 | − | 0.509214i | \(-0.170064\pi\) | |||||||
\(258\) | −27.7569 | −1.72807 | ||||||||
\(259\) | −5.61434 | + | 9.72432i | −0.348858 | + | 0.604240i | ||||
\(260\) | 1.76630 | 0.109542 | ||||||||
\(261\) | 5.16418 | − | 8.94462i | 0.319655 | − | 0.553658i | ||||
\(262\) | 26.0334 | − | 45.0911i | 1.60835 | − | 2.78574i | ||||
\(263\) | 12.0428 | − | 20.8587i | 0.742591 | − | 1.28621i | −0.208721 | − | 0.977975i | \(-0.566930\pi\) |
0.951312 | − | 0.308230i | \(-0.0997367\pi\) | |||||||
\(264\) | 18.9305 | − | 32.7886i | 1.16509 | − | 2.01800i | ||||
\(265\) | 0.628322 | 0.0385975 | ||||||||
\(266\) | 28.6323 | + | 49.5926i | 1.75556 | + | 3.04072i | ||||
\(267\) | −2.76950 | + | 4.79692i | −0.169491 | + | 0.293567i | ||||
\(268\) | 11.4430 | 0.698994 | ||||||||
\(269\) | −5.31204 | −0.323881 | −0.161940 | − | 0.986801i | \(-0.551775\pi\) | ||||
−0.161940 | + | 0.986801i | \(0.551775\pi\) | |||||||
\(270\) | −0.763851 | − | 1.32303i | −0.0464865 | − | 0.0805170i | ||||
\(271\) | −10.2479 | + | 17.7499i | −0.622517 | + | 1.07823i | 0.366498 | + | 0.930419i | \(0.380557\pi\) |
−0.989015 | + | 0.147813i | \(0.952777\pi\) | |||||||
\(272\) | 45.4051 | + | 78.6440i | 2.75309 | + | 4.76849i | ||||
\(273\) | −2.53379 | −0.153352 | ||||||||
\(274\) | −15.5586 | − | 26.9482i | −0.939928 | − | 1.62800i | ||||
\(275\) | −18.1844 | −1.09656 | ||||||||
\(276\) | −3.31819 | − | 5.74727i | −0.199732 | − | 0.345945i | ||||
\(277\) | −4.35788 | + | 7.54807i | −0.261840 | + | 0.453520i | −0.966731 | − | 0.255796i | \(-0.917663\pi\) |
0.704891 | + | 0.709316i | \(0.250996\pi\) | |||||||
\(278\) | −3.34414 | + | 5.79222i | −0.200568 | + | 0.347394i | ||||
\(279\) | −1.89212 | − | 3.27726i | −0.113279 | − | 0.196204i | ||||
\(280\) | −12.0209 | − | 20.8208i | −0.718387 | − | 1.24428i | ||||
\(281\) | 5.63715 | − | 9.76382i | 0.336284 | − | 0.582461i | −0.647447 | − | 0.762111i | \(-0.724163\pi\) |
0.983731 | + | 0.179650i | \(0.0574965\pi\) | |||||||
\(282\) | 9.39198 | 0.559284 | ||||||||
\(283\) | −2.43965 | + | 4.22560i | −0.145022 | + | 0.251186i | −0.929381 | − | 0.369121i | \(-0.879659\pi\) |
0.784359 | + | 0.620307i | \(0.212992\pi\) | |||||||
\(284\) | 25.9957 | − | 45.0259i | 1.54256 | − | 2.67179i | ||||
\(285\) | 2.61527 | 0.154915 | ||||||||
\(286\) | −6.09586 | −0.360456 | ||||||||
\(287\) | −38.1429 | −2.25150 | ||||||||
\(288\) | −11.8577 | + | 20.5382i | −0.698724 | + | 1.21023i | ||||
\(289\) | −8.15091 | + | 14.1178i | −0.479465 | + | 0.830458i | ||||
\(290\) | −7.88933 | − | 13.6647i | −0.463277 | − | 0.802420i | ||||
\(291\) | −16.8008 | −0.984883 | ||||||||
\(292\) | 37.4771 | + | 64.9122i | 2.19318 | + | 3.79870i | ||||
\(293\) | 3.23932 | + | 5.61067i | 0.189243 | + | 0.327779i | 0.944998 | − | 0.327076i | \(-0.106063\pi\) |
−0.755755 | + | 0.654854i | \(0.772730\pi\) | |||||||
\(294\) | 17.3297 | + | 30.0159i | 1.01069 | + | 1.75056i | ||||
\(295\) | 0.529076 | + | 0.916386i | 0.0308040 | + | 0.0533540i | ||||
\(296\) | 12.3826 | − | 21.4474i | 0.719726 | − | 1.24660i | ||||
\(297\) | 1.93821 | + | 3.35708i | 0.112466 | + | 0.194797i | ||||
\(298\) | 26.3193 | 1.52463 | ||||||||
\(299\) | −0.341855 | + | 0.592111i | −0.0197700 | + | 0.0342427i | ||||
\(300\) | 26.0526 | 1.50415 | ||||||||
\(301\) | 22.3619 | − | 38.7319i | 1.28892 | − | 2.23247i | ||||
\(302\) | 22.0276 | + | 38.1528i | 1.26754 | + | 2.19545i | ||||
\(303\) | −3.03110 | − | 5.25002i | −0.174132 | − | 0.301606i | ||||
\(304\) | −37.0194 | − | 64.1195i | −2.12321 | − | 3.67751i | ||||
\(305\) | 0.0973497 | − | 0.168615i | 0.00557423 | − | 0.00965484i | ||||
\(306\) | −15.8604 | −0.906678 | ||||||||
\(307\) | 8.81502 | 0.503100 | 0.251550 | − | 0.967844i | \(-0.419060\pi\) | ||||
0.251550 | + | 0.967844i | \(0.419060\pi\) | |||||||
\(308\) | 47.6684 | + | 82.5642i | 2.71616 | + | 4.70453i | ||||
\(309\) | 4.19686 | + | 7.26918i | 0.238751 | + | 0.413529i | ||||
\(310\) | −5.78120 | −0.328350 | ||||||||
\(311\) | 3.01535 | + | 5.22275i | 0.170985 | + | 0.296155i | 0.938765 | − | 0.344559i | \(-0.111972\pi\) |
−0.767779 | + | 0.640714i | \(0.778638\pi\) | |||||||
\(312\) | 5.58838 | 0.316380 | ||||||||
\(313\) | −1.80118 | −0.101809 | −0.0509044 | − | 0.998704i | \(-0.516210\pi\) | ||||
−0.0509044 | + | 0.998704i | \(0.516210\pi\) | |||||||
\(314\) | −14.1040 | + | 31.4167i | −0.795934 | + | 1.77295i | ||||
\(315\) | 2.46153 | 0.138692 | ||||||||
\(316\) | −39.2732 | −2.20929 | ||||||||
\(317\) | −9.54975 | − | 16.5406i | −0.536367 | − | 0.929015i | −0.999096 | − | 0.0425153i | \(-0.986463\pi\) |
0.462729 | − | 0.886500i | \(-0.346870\pi\) | |||||||
\(318\) | 3.10673 | 0.174217 | ||||||||
\(319\) | 20.0185 | + | 34.6731i | 1.12082 | + | 1.94132i | ||||
\(320\) | 9.36809 | + | 16.2260i | 0.523692 | + | 0.907061i | ||||
\(321\) | −4.48752 | −0.250469 | ||||||||
\(322\) | 14.5437 | 0.810490 | ||||||||
\(323\) | 13.5757 | − | 23.5138i | 0.755373 | − | 1.30834i | ||||
\(324\) | −2.77685 | − | 4.80965i | −0.154270 | − | 0.267203i | ||||
\(325\) | −1.34203 | − | 2.32446i | −0.0744424 | − | 0.128938i | ||||
\(326\) | 19.9136 | + | 34.4914i | 1.10291 | + | 1.91030i | ||||
\(327\) | 0.345821 | − | 0.598979i | 0.0191239 | − | 0.0331236i | ||||
\(328\) | 84.1256 | 4.64506 | ||||||||
\(329\) | −7.56649 | + | 13.1055i | −0.417154 | + | 0.722532i | ||||
\(330\) | 5.92201 | 0.325996 | ||||||||
\(331\) | −3.27008 | − | 5.66394i | −0.179740 | − | 0.311318i | 0.762052 | − | 0.647516i | \(-0.224192\pi\) |
−0.941791 | + | 0.336198i | \(0.890859\pi\) | |||||||
\(332\) | −18.9629 | + | 32.8447i | −1.04072 | + | 1.80259i | ||||
\(333\) | 1.26780 | + | 2.19590i | 0.0694751 | + | 0.120334i | ||||
\(334\) | −4.21650 | − | 7.30320i | −0.230717 | − | 0.399613i | ||||
\(335\) | 0.572646 | + | 0.991853i | 0.0312870 | + | 0.0541907i | ||||
\(336\) | −34.8432 | − | 60.3502i | −1.90085 | − | 3.29237i | ||||
\(337\) | 13.5462 | 0.737906 | 0.368953 | − | 0.929448i | \(-0.379716\pi\) | ||||
0.368953 | + | 0.929448i | \(0.379716\pi\) | |||||||
\(338\) | 17.4147 | + | 30.1632i | 0.947236 | + | 1.64066i | ||||
\(339\) | 8.28854 | − | 14.3562i | 0.450172 | − | 0.779720i | ||||
\(340\) | −8.90729 | + | 15.4279i | −0.483065 | + | 0.836694i | ||||
\(341\) | 14.6693 | 0.794389 | ||||||||
\(342\) | 12.9312 | 0.699239 | ||||||||
\(343\) | −24.8467 | −1.34159 | ||||||||
\(344\) | −49.3200 | + | 85.4247i | −2.65915 | + | 4.60579i | ||||
\(345\) | 0.332106 | − | 0.575225i | 0.0178800 | − | 0.0309690i | ||||
\(346\) | −15.0018 | −0.806501 | ||||||||
\(347\) | 13.5077 | − | 23.3961i | 0.725134 | − | 1.25597i | −0.233786 | − | 0.972288i | \(-0.575111\pi\) |
0.958919 | − | 0.283680i | \(-0.0915553\pi\) | |||||||
\(348\) | −28.6803 | − | 49.6758i | −1.53743 | − | 2.66290i | ||||
\(349\) | −13.8261 | − | 23.9476i | −0.740096 | − | 1.28188i | −0.952451 | − | 0.304691i | \(-0.901447\pi\) |
0.212355 | − | 0.977193i | \(-0.431887\pi\) | |||||||
\(350\) | −28.5473 | + | 49.4454i | −1.52592 | + | 2.64297i | ||||
\(351\) | −0.286084 | + | 0.495513i | −0.0152701 | + | 0.0264485i | ||||
\(352\) | −45.9656 | − | 79.6148i | −2.44997 | − | 4.24348i | ||||
\(353\) | −14.5495 | −0.774392 | −0.387196 | − | 0.921997i | \(-0.626556\pi\) | ||||
−0.387196 | + | 0.921997i | \(0.626556\pi\) | |||||||
\(354\) | 2.61601 | + | 4.53106i | 0.139039 | + | 0.240823i | ||||
\(355\) | 5.20364 | 0.276180 | ||||||||
\(356\) | 15.3810 | + | 26.6407i | 0.815192 | + | 1.41195i | ||||
\(357\) | 12.7777 | − | 22.1315i | 0.676265 | − | 1.17133i | ||||
\(358\) | −13.8116 | − | 23.9224i | −0.729965 | − | 1.26434i | ||||
\(359\) | 3.69915 | 0.195233 | 0.0976167 | − | 0.995224i | \(-0.468878\pi\) | ||||
0.0976167 | + | 0.995224i | \(0.468878\pi\) | |||||||
\(360\) | −5.42900 | −0.286134 | ||||||||
\(361\) | −1.56847 | + | 2.71666i | −0.0825509 | + | 0.142982i | ||||
\(362\) | −21.8313 | − | 37.8129i | −1.14743 | − | 1.98740i | ||||
\(363\) | −4.02664 | −0.211344 | ||||||||
\(364\) | −7.03597 | + | 12.1867i | −0.368785 | + | 0.638755i | ||||
\(365\) | −3.75095 | + | 6.49683i | −0.196334 | + | 0.340060i | ||||
\(366\) | 0.481345 | − | 0.833713i | 0.0251603 | − | 0.0435789i | ||||
\(367\) | 9.61899 | − | 16.6606i | 0.502107 | − | 0.869675i | −0.497890 | − | 0.867240i | \(-0.665892\pi\) |
0.999997 | − | 0.00243470i | \(-0.000774989\pi\) | |||||||
\(368\) | −18.8040 | −0.980224 | ||||||||
\(369\) | −4.30662 | + | 7.45928i | −0.224194 | + | 0.388315i | ||||
\(370\) | 3.87365 | 0.201381 | ||||||||
\(371\) | −2.50289 | + | 4.33513i | −0.129943 | + | 0.225069i | ||||
\(372\) | −21.0166 | −1.08966 | ||||||||
\(373\) | −11.2613 | −0.583085 | −0.291543 | − | 0.956558i | \(-0.594169\pi\) | ||||
−0.291543 | + | 0.956558i | \(0.594169\pi\) | |||||||
\(374\) | 30.7408 | − | 53.2446i | 1.58957 | − | 2.75321i | ||||
\(375\) | 2.69339 | + | 4.66508i | 0.139086 | + | 0.240904i | ||||
\(376\) | 16.6882 | − | 28.9048i | 0.860627 | − | 1.49065i | ||||
\(377\) | −2.95478 | + | 5.11783i | −0.152179 | + | 0.263582i | ||||
\(378\) | 12.1710 | 0.626010 | ||||||||
\(379\) | 17.6749 | 0.907899 | 0.453949 | − | 0.891028i | \(-0.350015\pi\) | ||||
0.453949 | + | 0.891028i | \(0.350015\pi\) | |||||||
\(380\) | 7.26223 | − | 12.5786i | 0.372545 | − | 0.645266i | ||||
\(381\) | 1.52579 | 0.0781686 | ||||||||
\(382\) | 3.56317 | + | 6.17160i | 0.182308 | + | 0.315766i | ||||
\(383\) | 6.36056 | + | 11.0168i | 0.325009 | + | 0.562933i | 0.981514 | − | 0.191389i | \(-0.0612992\pi\) |
−0.656505 | + | 0.754322i | \(0.727966\pi\) | |||||||
\(384\) | 22.6049 | + | 39.1529i | 1.15355 | + | 1.99801i | ||||
\(385\) | −4.77097 | + | 8.26356i | −0.243151 | + | 0.421150i | ||||
\(386\) | 20.7553 | − | 35.9492i | 1.05641 | − | 1.82976i | ||||
\(387\) | −5.04965 | − | 8.74625i | −0.256688 | − | 0.444597i | ||||
\(388\) | −46.6535 | + | 80.8062i | −2.36847 | + | 4.10231i | ||||
\(389\) | −23.2925 | −1.18098 | −0.590489 | − | 0.807046i | \(-0.701065\pi\) | ||||
−0.590489 | + | 0.807046i | \(0.701065\pi\) | |||||||
\(390\) | 0.437052 | + | 0.756996i | 0.0221310 | + | 0.0383320i | ||||
\(391\) | −3.44788 | − | 5.97190i | −0.174367 | − | 0.302012i | ||||
\(392\) | 123.169 | 6.22099 | ||||||||
\(393\) | 18.9444 | 0.955618 | ||||||||
\(394\) | 15.3906 | + | 26.6573i | 0.775366 | + | 1.34297i | ||||
\(395\) | −1.96536 | − | 3.40410i | −0.0988880 | − | 0.171279i | ||||
\(396\) | 21.5285 | 1.08185 | ||||||||
\(397\) | −2.83255 | + | 4.90613i | −0.142162 | + | 0.246232i | −0.928310 | − | 0.371806i | \(-0.878739\pi\) |
0.786149 | + | 0.618037i | \(0.212072\pi\) | |||||||
\(398\) | 5.85468 | + | 10.1406i | 0.293469 | + | 0.508303i | ||||
\(399\) | −10.4178 | + | 18.0442i | −0.521542 | + | 0.903338i | ||||
\(400\) | 36.9096 | − | 63.9293i | 1.84548 | − | 3.19646i | ||||
\(401\) | −3.42273 | − | 5.92835i | −0.170923 | − | 0.296048i | 0.767820 | − | 0.640666i | \(-0.221342\pi\) |
−0.938743 | + | 0.344618i | \(0.888008\pi\) | |||||||
\(402\) | 2.83144 | + | 4.90421i | 0.141220 | + | 0.244600i | ||||
\(403\) | 1.08261 | + | 1.87514i | 0.0539289 | + | 0.0934075i | ||||
\(404\) | −33.6677 | −1.67503 | ||||||||
\(405\) | 0.277926 | − | 0.481381i | 0.0138102 | − | 0.0239200i | ||||
\(406\) | 125.707 | 6.23872 | ||||||||
\(407\) | −9.82907 | −0.487209 | ||||||||
\(408\) | −28.1816 | + | 48.8120i | −1.39520 | + | 2.41655i | ||||
\(409\) | −11.3065 | + | 19.5834i | −0.559069 | + | 0.968336i | 0.438506 | + | 0.898728i | \(0.355508\pi\) |
−0.997574 | + | 0.0696071i | \(0.977825\pi\) | |||||||
\(410\) | 6.57923 | + | 11.3956i | 0.324925 | + | 0.562787i | ||||
\(411\) | 5.66096 | − | 9.80506i | 0.279234 | − | 0.483648i | ||||
\(412\) | 46.6163 | 2.29662 | ||||||||
\(413\) | −8.43017 | −0.414822 | ||||||||
\(414\) | 1.64210 | − | 2.84419i | 0.0807046 | − | 0.139784i | ||||
\(415\) | −3.79586 | −0.186331 | ||||||||
\(416\) | 6.78463 | − | 11.7513i | 0.332644 | − | 0.576156i | ||||
\(417\) | −2.43352 | −0.119170 | ||||||||
\(418\) | −25.0634 | + | 43.4111i | −1.22589 | + | 2.12330i | ||||
\(419\) | −14.0041 | + | 24.2558i | −0.684146 | + | 1.18498i | 0.289559 | + | 0.957160i | \(0.406491\pi\) |
−0.973704 | + | 0.227815i | \(0.926842\pi\) | |||||||
\(420\) | 6.83532 | − | 11.8391i | 0.333529 | − | 0.577690i | ||||
\(421\) | 5.64983 | − | 9.78580i | 0.275356 | − | 0.476931i | −0.694869 | − | 0.719136i | \(-0.744538\pi\) |
0.970225 | + | 0.242206i | \(0.0778709\pi\) | |||||||
\(422\) | −47.4792 | −2.31125 | ||||||||
\(423\) | 1.70863 | + | 2.95943i | 0.0830762 | + | 0.143892i | ||||
\(424\) | 5.52021 | − | 9.56128i | 0.268085 | − | 0.464337i | ||||
\(425\) | 27.0709 | 1.31313 | ||||||||
\(426\) | 25.7293 | 1.24659 | ||||||||
\(427\) | 0.775574 | + | 1.34333i | 0.0375326 | + | 0.0650084i | ||||
\(428\) | −12.4612 | + | 21.5834i | −0.602334 | + | 1.04327i | ||||
\(429\) | −1.10898 | − | 1.92082i | −0.0535422 | − | 0.0927378i | ||||
\(430\) | −15.4287 | −0.744038 | ||||||||
\(431\) | −17.4011 | − | 30.1397i | −0.838184 | − | 1.45178i | −0.891412 | − | 0.453194i | \(-0.850284\pi\) |
0.0532284 | − | 0.998582i | \(-0.483049\pi\) | |||||||
\(432\) | −15.7362 | −0.757110 | ||||||||
\(433\) | −14.0184 | − | 24.2806i | −0.673681 | − | 1.16685i | −0.976852 | − | 0.213914i | \(-0.931379\pi\) |
0.303171 | − | 0.952936i | \(-0.401955\pi\) | |||||||
\(434\) | 23.0291 | − | 39.8876i | 1.10543 | − | 1.91466i | ||||
\(435\) | 2.87052 | − | 4.97188i | 0.137631 | − | 0.238383i | ||||
\(436\) | −1.92059 | − | 3.32655i | −0.0919794 | − | 0.159313i | ||||
\(437\) | 2.81110 | + | 4.86898i | 0.134473 | + | 0.232915i | ||||
\(438\) | −18.5465 | + | 32.1235i | −0.886187 | + | 1.53492i | ||||
\(439\) | −25.4068 | −1.21260 | −0.606301 | − | 0.795235i | \(-0.707347\pi\) | ||||
−0.606301 | + | 0.795235i | \(0.707347\pi\) | |||||||
\(440\) | 10.5226 | − | 18.2256i | 0.501643 | − | 0.868871i | ||||
\(441\) | −6.30538 | + | 10.9212i | −0.300256 | + | 0.520059i | ||||
\(442\) | 9.07482 | 0.431645 | ||||||||
\(443\) | −10.5502 | −0.501256 | −0.250628 | − | 0.968083i | \(-0.580637\pi\) | ||||
−0.250628 | + | 0.968083i | \(0.580637\pi\) | |||||||
\(444\) | 14.0820 | 0.668302 | ||||||||
\(445\) | −1.53943 | + | 2.66637i | −0.0729761 | + | 0.126398i | ||||
\(446\) | 37.6609 | − | 65.2306i | 1.78329 | − | 3.08876i | ||||
\(447\) | 4.78810 | + | 8.29324i | 0.226470 | + | 0.392257i | ||||
\(448\) | −149.269 | −7.05229 | ||||||||
\(449\) | 1.16703 | + | 2.02135i | 0.0550755 | + | 0.0953935i | 0.892249 | − | 0.451544i | \(-0.149127\pi\) |
−0.837173 | + | 0.546938i | \(0.815793\pi\) | |||||||
\(450\) | 6.44641 | + | 11.1655i | 0.303887 | + | 0.526348i | ||||
\(451\) | −16.6943 | − | 28.9153i | −0.786102 | − | 1.36157i | ||||
\(452\) | −46.0321 | − | 79.7299i | −2.16517 | − | 3.75018i | ||||
\(453\) | −8.01468 | + | 13.8818i | −0.376562 | + | 0.652225i | ||||
\(454\) | −5.09513 | − | 8.82503i | −0.239126 | − | 0.414179i | ||||
\(455\) | −1.40841 | −0.0660274 | ||||||||
\(456\) | 22.9768 | − | 39.7971i | 1.07599 | − | 1.86367i | ||||
\(457\) | 37.2626 | 1.74307 | 0.871535 | − | 0.490333i | \(-0.163125\pi\) | ||||
0.871535 | + | 0.490333i | \(0.163125\pi\) | |||||||
\(458\) | −7.34670 | + | 12.7249i | −0.343289 | + | 0.594594i | ||||
\(459\) | −2.88539 | − | 4.99764i | −0.134678 | − | 0.233270i | ||||
\(460\) | −1.84442 | − | 3.19463i | −0.0859965 | − | 0.148950i | ||||
\(461\) | 5.18045 | + | 8.97280i | 0.241278 | + | 0.417905i | 0.961078 | − | 0.276276i | \(-0.0891002\pi\) |
−0.719801 | + | 0.694181i | \(0.755767\pi\) | |||||||
\(462\) | −23.5900 | + | 40.8591i | −1.09751 | + | 1.90094i | ||||
\(463\) | −9.61981 | −0.447071 | −0.223535 | − | 0.974696i | \(-0.571760\pi\) | ||||
−0.223535 | + | 0.974696i | \(0.571760\pi\) | |||||||
\(464\) | −162.530 | −7.54525 | ||||||||
\(465\) | −1.05174 | − | 1.82167i | −0.0487733 | − | 0.0844778i | ||||
\(466\) | 17.8074 | + | 30.8433i | 0.824912 | + | 1.42879i | ||||
\(467\) | −37.6168 | −1.74070 | −0.870348 | − | 0.492437i | \(-0.836106\pi\) | ||||
−0.870348 | + | 0.492437i | \(0.836106\pi\) | |||||||
\(468\) | 1.58883 | + | 2.75193i | 0.0734436 | + | 0.127208i | ||||
\(469\) | −9.12442 | −0.421326 | ||||||||
\(470\) | 5.22054 | 0.240806 | ||||||||
\(471\) | −12.4653 | + | 1.27126i | −0.574371 | + | 0.0585767i | ||||
\(472\) | 18.5931 | 0.855815 | ||||||||
\(473\) | 39.1491 | 1.80008 | ||||||||
\(474\) | −9.71770 | − | 16.8315i | −0.446349 | − | 0.773099i | ||||
\(475\) | −22.0712 | −1.01270 | ||||||||
\(476\) | −70.9633 | − | 122.912i | −3.25260 | − | 5.63367i | ||||
\(477\) | 0.565189 | + | 0.978937i | 0.0258782 | + | 0.0448224i | ||||
\(478\) | −73.9961 | −3.38450 | ||||||||
\(479\) | −19.9238 | −0.910343 | −0.455172 | − | 0.890404i | \(-0.650422\pi\) | ||||
−0.455172 | + | 0.890404i | \(0.650422\pi\) | |||||||
\(480\) | −6.59114 | + | 11.4162i | −0.300843 | + | 0.521075i | ||||
\(481\) | −0.725397 | − | 1.25642i | −0.0330752 | − | 0.0572880i | ||||
\(482\) | 18.2380 | + | 31.5891i | 0.830716 | + | 1.43884i | ||||
\(483\) | 2.64585 | + | 4.58275i | 0.120390 | + | 0.208522i | ||||
\(484\) | −11.1814 | + | 19.3667i | −0.508245 | + | 0.880305i | ||||
\(485\) | −9.33877 | −0.424052 | ||||||||
\(486\) | 1.37420 | − | 2.38018i | 0.0623350 | − | 0.107967i | ||||
\(487\) | −32.7100 | −1.48223 | −0.741117 | − | 0.671376i | \(-0.765704\pi\) | ||||
−0.741117 | + | 0.671376i | \(0.765704\pi\) | |||||||
\(488\) | −1.71056 | − | 2.96277i | −0.0774333 | − | 0.134118i | ||||
\(489\) | −7.24553 | + | 12.5496i | −0.327654 | + | 0.567514i | ||||
\(490\) | 9.63274 | + | 16.6844i | 0.435163 | + | 0.753724i | ||||
\(491\) | 1.19785 | + | 2.07473i | 0.0540581 | + | 0.0936313i | 0.891788 | − | 0.452453i | \(-0.149451\pi\) |
−0.837730 | + | 0.546085i | \(0.816118\pi\) | |||||||
\(492\) | 23.9177 | + | 41.4267i | 1.07829 | + | 1.86766i | ||||
\(493\) | −29.8013 | − | 51.6174i | −1.34218 | − | 2.32473i | ||||
\(494\) | −7.39883 | −0.332889 | ||||||||
\(495\) | 1.07736 | + | 1.86604i | 0.0484236 | + | 0.0838721i | ||||
\(496\) | −29.7749 | + | 51.5717i | −1.33693 | + | 2.31564i | ||||
\(497\) | −20.7284 | + | 35.9026i | −0.929796 | + | 1.61045i | ||||
\(498\) | −18.7686 | −0.841040 | ||||||||
\(499\) | 7.19526 | 0.322104 | 0.161052 | − | 0.986946i | \(-0.448511\pi\) | ||||
0.161052 | + | 0.986946i | \(0.448511\pi\) | |||||||
\(500\) | 29.9165 | 1.33791 | ||||||||
\(501\) | 1.53417 | − | 2.65725i | 0.0685415 | − | 0.118717i | ||||
\(502\) | 16.9035 | − | 29.2777i | 0.754440 | − | 1.30673i | ||||
\(503\) | 27.3124 | 1.21780 | 0.608899 | − | 0.793248i | \(-0.291611\pi\) | ||||
0.608899 | + | 0.793248i | \(0.291611\pi\) | |||||||
\(504\) | 21.6261 | − | 37.4576i | 0.963304 | − | 1.66849i | ||||
\(505\) | −1.68484 | − | 2.91823i | −0.0749744 | − | 0.129859i | ||||
\(506\) | 6.36545 | + | 11.0253i | 0.282979 | + | 0.490134i | ||||
\(507\) | −6.33631 | + | 10.9748i | −0.281405 | + | 0.487409i | ||||
\(508\) | 4.23689 | − | 7.33852i | 0.187982 | − | 0.325594i | ||||
\(509\) | 17.6495 | + | 30.5698i | 0.782299 | + | 1.35498i | 0.930599 | + | 0.366040i | \(0.119287\pi\) |
−0.148300 | + | 0.988942i | \(0.547380\pi\) | |||||||
\(510\) | −8.81602 | −0.390380 | ||||||||
\(511\) | −29.8834 | − | 51.7595i | −1.32196 | − | 2.28971i | ||||
\(512\) | 65.8006 | 2.90800 | ||||||||
\(513\) | 2.35250 | + | 4.07464i | 0.103865 | + | 0.179900i | ||||
\(514\) | 38.3902 | − | 66.4938i | 1.69332 | − | 2.93291i | ||||
\(515\) | 2.33283 | + | 4.04058i | 0.102797 | + | 0.178049i | ||||
\(516\) | −56.0885 | −2.46916 | ||||||||
\(517\) | −13.2467 | −0.582590 | ||||||||
\(518\) | −15.4305 | + | 26.7263i | −0.677975 | + | 1.17429i | ||||
\(519\) | −2.72918 | − | 4.72709i | −0.119798 | − | 0.207496i | ||||
\(520\) | 3.10631 | 0.136221 | ||||||||
\(521\) | 4.61151 | − | 7.98737i | 0.202034 | − | 0.349933i | −0.747150 | − | 0.664656i | \(-0.768578\pi\) |
0.949184 | + | 0.314723i | \(0.101912\pi\) | |||||||
\(522\) | 14.1932 | − | 24.5834i | 0.621221 | − | 1.07599i | ||||
\(523\) | −5.97535 | + | 10.3496i | −0.261284 | + | 0.452557i | −0.966583 | − | 0.256353i | \(-0.917479\pi\) |
0.705300 | + | 0.708909i | \(0.250813\pi\) | |||||||
\(524\) | 52.6058 | − | 91.1159i | 2.29809 | − | 3.98042i | ||||
\(525\) | −20.7738 | −0.906642 | ||||||||
\(526\) | 33.0985 | − | 57.3282i | 1.44316 | − | 2.49963i | ||||
\(527\) | −21.8380 | −0.951280 | ||||||||
\(528\) | 30.5002 | − | 52.8278i | 1.32735 | − | 2.29904i | ||||
\(529\) | −21.5721 | −0.937918 | ||||||||
\(530\) | 1.72688 | 0.0750109 | ||||||||
\(531\) | −0.951830 | + | 1.64862i | −0.0413059 | + | 0.0715439i | ||||
\(532\) | 57.8574 | + | 100.212i | 2.50844 | + | 4.34474i | ||||
\(533\) | 2.46411 | − | 4.26797i | 0.106733 | − | 0.184866i | ||||
\(534\) | −7.61171 | + | 13.1839i | −0.329391 | + | 0.570521i | ||||
\(535\) | −2.49439 | −0.107842 | ||||||||
\(536\) | 20.1242 | 0.869235 | ||||||||
\(537\) | 5.02532 | − | 8.70410i | 0.216858 | − | 0.375610i | ||||
\(538\) | −14.5996 | −0.629434 | ||||||||
\(539\) | −24.4423 | − | 42.3353i | −1.05280 | − | 1.82351i | ||||
\(540\) | −1.54352 | − | 2.67345i | −0.0664224 | − | 0.115047i | ||||
\(541\) | −8.17072 | − | 14.1521i | −0.351287 | − | 0.608446i | 0.635189 | − | 0.772357i | \(-0.280922\pi\) |
−0.986475 | + | 0.163911i | \(0.947589\pi\) | |||||||
\(542\) | −28.1654 | + | 48.7839i | −1.20981 | + | 2.09545i | ||||
\(543\) | 7.94327 | − | 13.7582i | 0.340878 | − | 0.590419i | ||||
\(544\) | 68.4283 | + | 118.521i | 2.93384 | + | 5.08156i | ||||
\(545\) | 0.192225 | − | 0.332943i | 0.00823400 | − | 0.0142617i | ||||
\(546\) | −6.96388 | −0.298027 | ||||||||
\(547\) | 11.8974 | + | 20.6069i | 0.508697 | + | 0.881089i | 0.999949 | + | 0.0100715i | \(0.00320592\pi\) |
−0.491252 | + | 0.871017i | \(0.663461\pi\) | |||||||
\(548\) | −31.4393 | − | 54.4544i | −1.34302 | − | 2.32618i | ||||
\(549\) | 0.350272 | 0.0149493 | ||||||||
\(550\) | −49.9780 | −2.13107 | ||||||||
\(551\) | 24.2974 | + | 42.0844i | 1.03510 | + | 1.79285i | ||||
\(552\) | −5.83552 | − | 10.1074i | −0.248376 | − | 0.430201i | ||||
\(553\) | 31.3156 | 1.33167 | ||||||||
\(554\) | −11.9772 | + | 20.7451i | −0.508863 | + | 0.881376i | ||||
\(555\) | 0.704709 | + | 1.22059i | 0.0299132 | + | 0.0518113i | ||||
\(556\) | −6.75752 | + | 11.7044i | −0.286583 | + | 0.496376i | ||||
\(557\) | −9.97395 | + | 17.2754i | −0.422610 | + | 0.731982i | −0.996194 | − | 0.0871650i | \(-0.972219\pi\) |
0.573584 | + | 0.819147i | \(0.305553\pi\) | |||||||
\(558\) | −5.20032 | − | 9.00721i | −0.220147 | − | 0.381306i | ||||
\(559\) | 2.88925 | + | 5.00433i | 0.122202 | + | 0.211661i | ||||
\(560\) | −19.3676 | − | 33.5457i | −0.818432 | − | 1.41757i | ||||
\(561\) | 22.3699 | 0.944460 | ||||||||
\(562\) | 15.4931 | − | 26.8349i | 0.653539 | − | 1.13196i | ||||
\(563\) | −18.5052 | −0.779900 | −0.389950 | − | 0.920836i | \(-0.627508\pi\) | ||||
−0.389950 | + | 0.920836i | \(0.627508\pi\) | |||||||
\(564\) | 18.9784 | 0.799135 | ||||||||
\(565\) | 4.60719 | − | 7.97989i | 0.193826 | − | 0.335717i | ||||
\(566\) | −6.70514 | + | 11.6136i | −0.281838 | + | 0.488158i | ||||
\(567\) | 2.21420 | + | 3.83511i | 0.0929877 | + | 0.161059i | ||||
\(568\) | 45.7173 | − | 79.1846i | 1.91825 | − | 3.32251i | ||||
\(569\) | 21.2740 | 0.891852 | 0.445926 | − | 0.895070i | \(-0.352874\pi\) | ||||
0.445926 | + | 0.895070i | \(0.352874\pi\) | |||||||
\(570\) | 7.18782 | 0.301065 | ||||||||
\(571\) | −10.4991 | + | 18.1849i | −0.439372 | + | 0.761014i | −0.997641 | − | 0.0686458i | \(-0.978132\pi\) |
0.558270 | + | 0.829660i | \(0.311466\pi\) | |||||||
\(572\) | −12.3179 | −0.515039 | ||||||||
\(573\) | −1.29645 | + | 2.24552i | −0.0541601 | + | 0.0938081i | ||||
\(574\) | −104.832 | −4.37560 | ||||||||
\(575\) | −2.80276 | + | 4.85453i | −0.116883 | + | 0.202448i | ||||
\(576\) | −16.8536 | + | 29.1913i | −0.702233 | + | 1.21630i | ||||
\(577\) | −17.3629 | + | 30.0734i | −0.722827 | + | 1.25197i | 0.237036 | + | 0.971501i | \(0.423824\pi\) |
−0.959862 | + | 0.280471i | \(0.909509\pi\) | |||||||
\(578\) | −22.4020 | + | 38.8013i | −0.931799 | + | 1.61392i | ||||
\(579\) | 15.1035 | 0.627681 | ||||||||
\(580\) | −15.9420 | − | 27.6124i | −0.661956 | − | 1.14654i | ||||
\(581\) | 15.1206 | − | 26.1896i | 0.627307 | − | 1.08653i | ||||
\(582\) | −46.1754 | −1.91403 | ||||||||
\(583\) | −4.38182 | −0.181477 | ||||||||
\(584\) | 65.9089 | + | 114.158i | 2.72733 | + | 4.72387i | ||||
\(585\) | −0.159020 | + | 0.275431i | −0.00657468 | + | 0.0113877i | ||||
\(586\) | 8.90295 | + | 15.4204i | 0.367777 | + | 0.637009i | ||||
\(587\) | 11.4699 | 0.473413 | 0.236706 | − | 0.971581i | \(-0.423932\pi\) | ||||
0.236706 | + | 0.971581i | \(0.423932\pi\) | |||||||
\(588\) | 35.0182 | + | 60.6533i | 1.44413 | + | 2.50130i | ||||
\(589\) | 17.8049 | 0.733636 | ||||||||
\(590\) | 1.45411 | + | 2.51860i | 0.0598648 | + | 0.103689i | ||||
\(591\) | −5.59983 | + | 9.69919i | −0.230346 | + | 0.398971i | ||||
\(592\) | 19.9504 | − | 34.5552i | 0.819958 | − | 1.42021i | ||||
\(593\) | −2.03686 | − | 3.52795i | −0.0836440 | − | 0.144876i | 0.821169 | − | 0.570686i | \(-0.193323\pi\) |
−0.904813 | + | 0.425810i | \(0.859989\pi\) | |||||||
\(594\) | 5.32698 | + | 9.22660i | 0.218569 | + | 0.378572i | ||||
\(595\) | 7.10247 | − | 12.3018i | 0.291173 | − | 0.504326i | ||||
\(596\) | 53.1835 | 2.17848 | ||||||||
\(597\) | −2.13021 | + | 3.68964i | −0.0871839 | + | 0.151007i | ||||
\(598\) | −0.939555 | + | 1.62736i | −0.0384213 | + | 0.0665476i | ||||
\(599\) | −30.6585 | −1.25267 | −0.626336 | − | 0.779553i | \(-0.715446\pi\) | ||||
−0.626336 | + | 0.779553i | \(0.715446\pi\) | |||||||
\(600\) | 45.8173 | 1.87048 | ||||||||
\(601\) | 22.7170 | 0.926646 | 0.463323 | − | 0.886189i | \(-0.346657\pi\) | ||||
0.463323 | + | 0.886189i | \(0.346657\pi\) | |||||||
\(602\) | 61.4594 | − | 106.451i | 2.50490 | − | 4.33861i | ||||
\(603\) | −1.03022 | + | 1.78439i | −0.0419536 | + | 0.0726658i | ||||
\(604\) | 44.5112 | + | 77.0956i | 1.81113 | + | 3.13698i | ||||
\(605\) | −2.23821 | −0.0909962 | ||||||||
\(606\) | −8.33067 | − | 14.4292i | −0.338411 | − | 0.586144i | ||||
\(607\) | 9.68733 | + | 16.7790i | 0.393197 | + | 0.681037i | 0.992869 | − | 0.119209i | \(-0.0380358\pi\) |
−0.599673 | + | 0.800246i | \(0.704702\pi\) | |||||||
\(608\) | −55.7906 | − | 96.6321i | −2.26261 | − | 3.91895i | ||||
\(609\) | 22.8691 | + | 39.6104i | 0.926702 | + | 1.60509i | ||||
\(610\) | 0.267556 | − | 0.463420i | 0.0108330 | − | 0.0187633i | ||||
\(611\) | −0.977622 | − | 1.69329i | −0.0395504 | − | 0.0685032i | ||||
\(612\) | −32.0492 | −1.29551 | ||||||||
\(613\) | 14.6408 | − | 25.3586i | 0.591336 | − | 1.02422i | −0.402717 | − | 0.915325i | \(-0.631934\pi\) |
0.994053 | − | 0.108899i | \(-0.0347325\pi\) | |||||||
\(614\) | 24.2272 | 0.977730 | ||||||||
\(615\) | −2.39384 | + | 4.14625i | −0.0965289 | + | 0.167193i | ||||
\(616\) | 83.8320 | + | 145.201i | 3.37769 | + | 5.85032i | ||||
\(617\) | −1.51295 | − | 2.62050i | −0.0609089 | − | 0.105497i | 0.833963 | − | 0.551820i | \(-0.186067\pi\) |
−0.894872 | + | 0.446323i | \(0.852733\pi\) | |||||||
\(618\) | 11.5347 | + | 19.9786i | 0.463992 | + | 0.803658i | ||||
\(619\) | 13.2838 | − | 23.0083i | 0.533922 | − | 0.924780i | −0.465293 | − | 0.885157i | \(-0.654051\pi\) |
0.999215 | − | 0.0396231i | \(-0.0126157\pi\) | |||||||
\(620\) | −11.6821 | −0.469165 | ||||||||
\(621\) | 1.19495 | 0.0479515 | ||||||||
\(622\) | 8.28740 | + | 14.3542i | 0.332294 | + | 0.575551i | ||||
\(623\) | −12.2645 | − | 21.2427i | −0.491366 | − | 0.851071i | ||||
\(624\) | 9.00379 | 0.360440 | ||||||||
\(625\) | −10.2305 | − | 17.7197i | −0.409218 | − | 0.708787i | ||||
\(626\) | −4.95037 | −0.197857 | ||||||||
\(627\) | −18.2385 | −0.728376 | ||||||||
\(628\) | −28.5000 | + | 63.4839i | −1.13727 | + | 2.53328i | ||||
\(629\) | 14.6324 | 0.583432 | ||||||||
\(630\) | 6.76528 | 0.269535 | ||||||||
\(631\) | −12.2938 | − | 21.2935i | −0.489410 | − | 0.847682i | 0.510516 | − | 0.859868i | \(-0.329454\pi\) |
−0.999926 | + | 0.0121859i | \(0.996121\pi\) | |||||||
\(632\) | −69.0677 | −2.74737 | ||||||||
\(633\) | −8.63761 | − | 14.9608i | −0.343314 | − | 0.594638i | ||||
\(634\) | −26.2465 | − | 45.4603i | −1.04238 | − | 1.80546i | ||||
\(635\) | 0.848112 | 0.0336563 | ||||||||
\(636\) | 6.27779 | 0.248931 | ||||||||
\(637\) | 3.60774 | − | 6.24879i | 0.142944 | − | 0.247586i | ||||
\(638\) | 55.0190 | + | 95.2956i | 2.17822 | + | 3.77279i | ||||
\(639\) | 4.68078 | + | 8.10735i | 0.185169 | + | 0.320722i | ||||
\(640\) | 12.5650 | + | 21.7632i | 0.496674 | + | 0.860265i | ||||
\(641\) | 16.6301 | − | 28.8041i | 0.656848 | − | 1.13769i | −0.324579 | − | 0.945859i | \(-0.605222\pi\) |
0.981427 | − | 0.191836i | \(-0.0614442\pi\) | |||||||
\(642\) | −12.3335 | −0.486764 | ||||||||
\(643\) | 9.12819 | − | 15.8105i | 0.359981 | − | 0.623505i | −0.627976 | − | 0.778232i | \(-0.716117\pi\) |
0.987957 | + | 0.154727i | \(0.0494499\pi\) | |||||||
\(644\) | 29.3886 | 1.15807 | ||||||||
\(645\) | −2.80685 | − | 4.86161i | −0.110520 | − | 0.191426i | ||||
\(646\) | 37.3115 | − | 64.6254i | 1.46800 | − | 2.54265i | ||||
\(647\) | 14.6648 | + | 25.4002i | 0.576534 | + | 0.998586i | 0.995873 | + | 0.0907564i | \(0.0289285\pi\) |
−0.419339 | + | 0.907830i | \(0.637738\pi\) | |||||||
\(648\) | −4.88351 | − | 8.45848i | −0.191842 | − | 0.332280i | ||||
\(649\) | −3.68969 | − | 6.39073i | −0.144833 | − | 0.250858i | ||||
\(650\) | −3.68844 | − | 6.38856i | −0.144672 | − | 0.250580i | ||||
\(651\) | 16.7582 | 0.656805 | ||||||||
\(652\) | 40.2395 | + | 69.6969i | 1.57590 | + | 2.72954i | ||||
\(653\) | 4.58519 | − | 7.94178i | 0.179432 | − | 0.310786i | −0.762254 | − | 0.647278i | \(-0.775907\pi\) |
0.941686 | + | 0.336492i | \(0.109241\pi\) | |||||||
\(654\) | 0.950454 | − | 1.64623i | 0.0371657 | − | 0.0643728i | ||||
\(655\) | 10.5303 | 0.411451 | ||||||||
\(656\) | 135.540 | 5.29195 | ||||||||
\(657\) | −13.4962 | −0.526538 | ||||||||
\(658\) | −20.7957 | + | 36.0193i | −0.810702 | + | 1.40418i | ||||
\(659\) | −9.52136 | + | 16.4915i | −0.370900 | + | 0.642417i | −0.989704 | − | 0.143128i | \(-0.954284\pi\) |
0.618805 | + | 0.785545i | \(0.287617\pi\) | |||||||
\(660\) | 11.9666 | 0.465801 | ||||||||
\(661\) | −2.51320 | + | 4.35300i | −0.0977523 | + | 0.169312i | −0.910754 | − | 0.412949i | \(-0.864499\pi\) |
0.813002 | + | 0.582261i | \(0.197832\pi\) | |||||||
\(662\) | −8.98749 | − | 15.5668i | −0.349309 | − | 0.605020i | ||||
\(663\) | 1.65093 | + | 2.85949i | 0.0641167 | + | 0.111053i | ||||
\(664\) | −33.3490 | + | 57.7622i | −1.29419 | + | 2.24161i | ||||
\(665\) | −5.79074 | + | 10.0299i | −0.224555 | + | 0.388941i | ||||
\(666\) | 3.48443 | + | 6.03521i | 0.135019 | + | 0.233860i | ||||
\(667\) | 12.3418 | 0.477878 | ||||||||
\(668\) | −8.52031 | − | 14.7576i | −0.329661 | − | 0.570989i | ||||
\(669\) | 27.4057 | 1.05956 | ||||||||
\(670\) | 1.57386 | + | 2.72601i | 0.0608036 | + | 0.105315i | ||||
\(671\) | −0.678902 | + | 1.17589i | −0.0262087 | + | 0.0453948i | ||||
\(672\) | −52.5109 | − | 90.9515i | −2.02565 | − | 3.50853i | ||||
\(673\) | 33.4070 | 1.28774 | 0.643872 | − | 0.765133i | \(-0.277327\pi\) | ||||
0.643872 | + | 0.765133i | \(0.277327\pi\) | |||||||
\(674\) | 37.2303 | 1.43406 | ||||||||
\(675\) | −2.34551 | + | 4.06255i | −0.0902789 | + | 0.156368i | ||||
\(676\) | 35.1900 | + | 60.9509i | 1.35346 | + | 2.34427i | ||||
\(677\) | −1.63873 | −0.0629814 | −0.0314907 | − | 0.999504i | \(-0.510025\pi\) | ||||
−0.0314907 | + | 0.999504i | \(0.510025\pi\) | |||||||
\(678\) | 22.7802 | − | 39.4565i | 0.874869 | − | 1.51532i | ||||
\(679\) | 37.2005 | − | 64.4331i | 1.42762 | − | 2.47271i | ||||
\(680\) | −15.6648 | + | 27.1322i | −0.600717 | + | 1.04047i | ||||
\(681\) | 1.85385 | − | 3.21097i | 0.0710398 | − | 0.123045i | ||||
\(682\) | 40.3172 | 1.54383 | ||||||||
\(683\) | 14.2677 | − | 24.7124i | 0.545938 | − | 0.945593i | −0.452609 | − | 0.891709i | \(-0.649507\pi\) |
0.998547 | − | 0.0538837i | \(-0.0171600\pi\) | |||||||
\(684\) | 26.1301 | 0.999111 | ||||||||
\(685\) | 3.14665 | − | 5.45016i | 0.120227 | − | 0.208240i | ||||
\(686\) | −68.2886 | −2.60727 | ||||||||
\(687\) | −5.34617 | −0.203969 | ||||||||
\(688\) | −79.4625 | + | 137.633i | −3.02948 | + | 5.24721i | ||||
\(689\) | −0.323384 | − | 0.560117i | −0.0123199 | − | 0.0213388i | ||||
\(690\) | 0.912760 | − | 1.58095i | 0.0347482 | − | 0.0601856i | ||||
\(691\) | −19.5833 | + | 33.9192i | −0.744983 | + | 1.29035i | 0.205220 | + | 0.978716i | \(0.434209\pi\) |
−0.950203 | + | 0.311632i | \(0.899124\pi\) | |||||||
\(692\) | −30.3142 | −1.15237 | ||||||||
\(693\) | −17.1664 | −0.652096 | ||||||||
\(694\) | 37.1247 | − | 64.3018i | 1.40923 | − | 2.44086i | ||||
\(695\) | −1.35267 | −0.0513098 | ||||||||
\(696\) | −50.4386 | − | 87.3622i | −1.91187 | − | 3.31146i | ||||
\(697\) | 24.8525 | + | 43.0458i | 0.941356 | + | 1.63048i | ||||
\(698\) | −37.9998 | − | 65.8175i | −1.43831 | − | 2.49123i | ||||
\(699\) | −6.47919 | + | 11.2223i | −0.245065 | + | 0.424466i | ||||
\(700\) | −57.6857 | + | 99.9146i | −2.18031 | + | 3.77642i | ||||
\(701\) | 16.1264 | + | 27.9318i | 0.609086 | + | 1.05497i | 0.991391 | + | 0.130932i | \(0.0417971\pi\) |
−0.382305 | + | 0.924036i | \(0.624870\pi\) | |||||||
\(702\) | −0.786274 | + | 1.36187i | −0.0296760 | + | 0.0514004i | ||||
\(703\) | −11.9300 | −0.449948 | ||||||||
\(704\) | −65.3316 | − | 113.158i | −2.46228 | − | 4.26479i | ||||
\(705\) | 0.949742 | + | 1.64500i | 0.0357693 | + | 0.0619543i | ||||
\(706\) | −39.9879 | −1.50496 | ||||||||
\(707\) | 26.8459 | 1.00964 | ||||||||
\(708\) | 5.28618 | + | 9.15594i | 0.198667 | + | 0.344101i | ||||
\(709\) | 18.7819 | + | 32.5312i | 0.705369 | + | 1.22174i | 0.966558 | + | 0.256447i | \(0.0825520\pi\) |
−0.261189 | + | 0.965288i | \(0.584115\pi\) | |||||||
\(710\) | 14.3017 | 0.536733 | ||||||||
\(711\) | 3.53577 | − | 6.12412i | 0.132602 | − | 0.229673i | ||||
\(712\) | 27.0498 | + | 46.8516i | 1.01373 | + | 1.75584i | ||||
\(713\) | 2.26099 | − | 3.91614i | 0.0846746 | − | 0.146661i | ||||
\(714\) | 35.1181 | − | 60.8264i | 1.31426 | − | 2.27637i | ||||
\(715\) | −0.616430 | − | 1.06769i | −0.0230532 | − | 0.0399292i | ||||
\(716\) | −27.9091 | − | 48.3400i | −1.04301 | − | 1.80655i | ||||
\(717\) | −13.4617 | − | 23.3163i | −0.502735 | − | 0.870763i | ||||
\(718\) | 10.1667 | 0.379419 | ||||||||
\(719\) | −2.94846 | + | 5.10689i | −0.109959 | + | 0.190455i | −0.915753 | − | 0.401741i | \(-0.868405\pi\) |
0.805794 | + | 0.592195i | \(0.201739\pi\) | |||||||
\(720\) | −8.74701 | −0.325982 | ||||||||
\(721\) | −37.1708 | −1.38431 | ||||||||
\(722\) | −4.31077 | + | 7.46648i | −0.160430 | + | 0.277874i | ||||
\(723\) | −6.63584 | + | 11.4936i | −0.246790 | + | 0.427452i | ||||
\(724\) | −44.1146 | − | 76.4087i | −1.63951 | − | 2.83971i | ||||
\(725\) | −24.2253 | + | 41.9595i | −0.899706 | + | 1.55834i | ||||
\(726\) | −11.0668 | −0.410728 | ||||||||
\(727\) | −36.0466 | −1.33689 | −0.668447 | − | 0.743760i | \(-0.733041\pi\) | ||||
−0.668447 | + | 0.743760i | \(0.733041\pi\) | |||||||
\(728\) | −12.3738 | + | 21.4320i | −0.458603 | + | 0.794324i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −10.3091 | + | 17.8559i | −0.381557 | + | 0.660876i | ||||
\(731\) | −58.2807 | −2.15559 | ||||||||
\(732\) | 0.972655 | − | 1.68469i | 0.0359504 | − | 0.0622679i | ||||
\(733\) | 11.3298 | − | 19.6238i | 0.418475 | − | 0.724820i | −0.577311 | − | 0.816524i | \(-0.695898\pi\) |
0.995786 | + | 0.0917041i | \(0.0292314\pi\) | |||||||
\(734\) | 26.4368 | − | 45.7899i | 0.975801 | − | 1.69014i | ||||
\(735\) | −3.50485 | + | 6.07058i | −0.129278 | + | 0.223917i | ||||
\(736\) | −28.3387 | −1.04458 | ||||||||
\(737\) | −3.99355 | − | 6.91703i | −0.147104 | − | 0.254792i | ||||
\(738\) | −11.8363 | + | 20.5011i | −0.435701 | + | 0.754656i | ||||
\(739\) | −2.87789 | −0.105865 | −0.0529324 | − | 0.998598i | \(-0.516857\pi\) | ||||
−0.0529324 | + | 0.998598i | \(0.516857\pi\) | |||||||
\(740\) | 7.82750 | 0.287745 | ||||||||
\(741\) | −1.34602 | − | 2.33138i | −0.0494474 | − | 0.0856455i | ||||
\(742\) | −6.87893 | + | 11.9147i | −0.252534 | + | 0.437401i | ||||
\(743\) | 24.0698 | + | 41.6900i | 0.883034 | + | 1.52946i | 0.847951 | + | 0.530075i | \(0.177836\pi\) |
0.0350825 | + | 0.999384i | \(0.488831\pi\) | |||||||
\(744\) | −36.9608 | −1.35505 | ||||||||
\(745\) | 2.66147 | + | 4.60981i | 0.0975088 | + | 0.168890i | ||||
\(746\) | −30.9504 | −1.13318 | ||||||||
\(747\) | −3.41445 | − | 5.91401i | −0.124928 | − | 0.216382i | ||||
\(748\) | 62.1180 | − | 107.592i | 2.27126 | − | 3.93394i | ||||
\(749\) | 9.93627 | − | 17.2101i | 0.363063 | − | 0.628844i | ||||
\(750\) | 7.40250 | + | 12.8215i | 0.270301 | + | 0.468175i | ||||
\(751\) | −11.4410 | − | 19.8164i | −0.417489 | − | 0.723112i | 0.578197 | − | 0.815897i | \(-0.303756\pi\) |
−0.995686 | + | 0.0927849i | \(0.970423\pi\) | |||||||
\(752\) | 26.8874 | − | 46.5703i | 0.980481 | − | 1.69824i | ||||
\(753\) | 12.3006 | 0.448259 | ||||||||
\(754\) | −8.12093 | + | 14.0659i | −0.295747 | + | 0.512248i | ||||
\(755\) | −4.45497 | + | 7.71623i | −0.162133 | + | 0.280822i | ||||
\(756\) | 24.5941 | 0.894477 | ||||||||
\(757\) | −34.5432 | −1.25549 | −0.627747 | − | 0.778417i | \(-0.716023\pi\) | ||||
−0.627747 | + | 0.778417i | \(0.716023\pi\) | |||||||
\(758\) | 48.5777 | 1.76442 | ||||||||
\(759\) | −2.31606 | + | 4.01153i | −0.0840675 | + | 0.145609i | ||||
\(760\) | 12.7717 | − | 22.1212i | 0.463278 | − | 0.802422i | ||||
\(761\) | 4.10100 | + | 7.10314i | 0.148661 | + | 0.257489i | 0.930733 | − | 0.365700i | \(-0.119170\pi\) |
−0.782072 | + | 0.623188i | \(0.785837\pi\) | |||||||
\(762\) | 4.19348 | 0.151914 | ||||||||
\(763\) | 1.53143 | + | 2.65252i | 0.0554416 | + | 0.0960277i | ||||
\(764\) | 7.20012 | + | 12.4710i | 0.260491 | + | 0.451184i | ||||
\(765\) | −1.60385 | − | 2.77794i | −0.0579872 | − | 0.100437i | ||||
\(766\) | 17.4814 | + | 30.2786i | 0.631627 | + | 1.09401i | ||||
\(767\) | 0.544607 | − | 0.943287i | 0.0196646 | − | 0.0340601i | ||||
\(768\) | 28.4202 | + | 49.2253i | 1.02553 | + | 1.77626i | ||||
\(769\) | 1.23692 | 0.0446045 | 0.0223022 | − | 0.999751i | \(-0.492900\pi\) | ||||
0.0223022 | + | 0.999751i | \(0.492900\pi\) | |||||||
\(770\) | −13.1125 | + | 22.7116i | −0.472543 | + | 0.818468i | ||||
\(771\) | 27.9364 | 1.00610 | ||||||||
\(772\) | 41.9403 | − | 72.6426i | 1.50946 | − | 2.61447i | ||||
\(773\) | −12.8471 | − | 22.2518i | −0.462078 | − | 0.800343i | 0.536986 | − | 0.843591i | \(-0.319563\pi\) |
−0.999064 | + | 0.0432479i | \(0.986229\pi\) | |||||||
\(774\) | −13.8785 | − | 24.0382i | −0.498851 | − | 0.864035i | ||||
\(775\) | 8.87601 | + | 15.3737i | 0.318836 | + | 0.552240i | ||||
\(776\) | −82.0470 | + | 142.110i | −2.94532 | + | 5.10144i | ||||
\(777\) | −11.2287 | −0.402827 | ||||||||
\(778\) | −64.0171 | −2.29513 | ||||||||
\(779\) | −20.2626 | − | 35.0959i | −0.725983 | − | 1.25744i | ||||
\(780\) | 0.883152 | + | 1.52966i | 0.0316219 | + | 0.0547708i | ||||
\(781\) | −36.2894 | −1.29854 | ||||||||
\(782\) | −9.47616 | − | 16.4132i | −0.338867 | − | 0.586934i | ||||
\(783\) | 10.3284 | 0.369105 | ||||||||
\(784\) | 198.446 | 7.08735 | ||||||||
\(785\) | −6.92886 | + | 0.706633i | −0.247301 | + | 0.0252208i | ||||
\(786\) | 52.0668 | 1.85716 | ||||||||
\(787\) | 16.2761 | 0.580180 | 0.290090 | − | 0.956999i | \(-0.406315\pi\) | ||||
0.290090 | + | 0.956999i | \(0.406315\pi\) | |||||||
\(788\) | 31.0998 | + | 53.8665i | 1.10789 | + | 1.91891i | ||||
\(789\) | 24.0856 | 0.857470 | ||||||||
\(790\) | −5.40159 | − | 9.35584i | −0.192180 | − | 0.332866i | ||||
\(791\) | 36.7050 | + | 63.5749i | 1.30508 | + | 2.26046i | ||||
\(792\) | 37.8610 | 1.34533 | ||||||||
\(793\) | −0.200415 | −0.00711694 | ||||||||
\(794\) | −7.78500 | + | 13.4840i | −0.276279 | + | 0.478530i | ||||
\(795\) | 0.314161 | + | 0.544143i | 0.0111421 | + | 0.0192988i | ||||
\(796\) | 11.8306 | + | 20.4912i | 0.419324 | + | 0.726290i | ||||
\(797\) | 0.574141 | + | 0.994441i | 0.0203371 | + | 0.0352249i | 0.876015 | − | 0.482284i | \(-0.160193\pi\) |
−0.855678 | + | 0.517509i | \(0.826859\pi\) | |||||||
\(798\) | −28.6323 | + | 49.5926i | −1.01357 | + | 1.75556i | ||||
\(799\) | 19.7202 | 0.697650 | ||||||||
\(800\) | 55.6250 | − | 96.3454i | 1.96664 | − | 3.40632i | ||||
\(801\) | −5.53901 | −0.195711 | ||||||||
\(802\) | −9.40704 | − | 16.2935i | −0.332174 | − | 0.575343i | ||||
\(803\) | 26.1585 | − | 45.3079i | 0.923115 | − | 1.59888i | ||||
\(804\) | 5.72151 | + | 9.90995i | 0.201782 | + | 0.349497i | ||||
\(805\) | 1.47070 | + | 2.54733i | 0.0518353 | + | 0.0897814i | ||||
\(806\) | 2.97546 | + | 5.15365i | 0.104806 | + | 0.181529i | ||||
\(807\) | −2.65602 | − | 4.60036i | −0.0934963 | − | 0.161940i | ||||
\(808\) | −59.2095 | −2.08298 | ||||||||
\(809\) | −23.7265 | − | 41.0954i | −0.834178 | − | 1.44484i | −0.894698 | − | 0.446671i | \(-0.852609\pi\) |
0.0605206 | − | 0.998167i | \(-0.480724\pi\) | |||||||
\(810\) | 0.763851 | − | 1.32303i | 0.0268390 | − | 0.0464865i | ||||
\(811\) | −11.2672 | + | 19.5154i | −0.395646 | + | 0.685279i | −0.993183 | − | 0.116562i | \(-0.962813\pi\) |
0.597537 | + | 0.801841i | \(0.296146\pi\) | |||||||
\(812\) | 254.016 | 8.91422 | ||||||||
\(813\) | −20.4959 | −0.718821 | ||||||||
\(814\) | −27.0142 | −0.946848 | ||||||||
\(815\) | −4.02744 | + | 6.97572i | −0.141075 | + | 0.244349i | ||||
\(816\) | −45.4051 | + | 78.6440i | −1.58950 | + | 2.75309i | ||||
\(817\) | 47.5171 | 1.66241 | ||||||||
\(818\) | −31.0747 | + | 53.8230i | −1.08650 | + | 1.88188i | ||||
\(819\) | −1.26690 | − | 2.19433i | −0.0442690 | − | 0.0766761i | ||||
\(820\) | 13.2947 | + | 23.0271i | 0.464270 | + | 0.804140i | ||||
\(821\) | −15.4423 | + | 26.7469i | −0.538941 | + | 0.933474i | 0.460020 | + | 0.887908i | \(0.347842\pi\) |
−0.998961 | + | 0.0455651i | \(0.985491\pi\) | |||||||
\(822\) | 15.5586 | − | 26.9482i | 0.542668 | − | 0.939928i | ||||
\(823\) | 5.83220 | + | 10.1017i | 0.203298 | + | 0.352122i | 0.949589 | − | 0.313498i | \(-0.101501\pi\) |
−0.746291 | + | 0.665619i | \(0.768167\pi\) | |||||||
\(824\) | 81.9816 | 2.85596 | ||||||||
\(825\) | −9.09220 | − | 15.7482i | −0.316550 | − | 0.548280i | ||||
\(826\) | −23.1695 | −0.806170 | ||||||||
\(827\) | 15.8961 | + | 27.5329i | 0.552762 | + | 0.957411i | 0.998074 | + | 0.0620358i | \(0.0197593\pi\) |
−0.445312 | + | 0.895375i | \(0.646907\pi\) | |||||||
\(828\) | 3.31819 | − | 5.74727i | 0.115315 | − | 0.199732i | ||||
\(829\) | −18.2199 | − | 31.5578i | −0.632803 | − | 1.09605i | −0.986976 | − | 0.160867i | \(-0.948571\pi\) |
0.354173 | − | 0.935180i | \(-0.384762\pi\) | |||||||
\(830\) | −10.4325 | −0.362119 | ||||||||
\(831\) | −8.71576 | −0.302346 | ||||||||
\(832\) | 9.64309 | − | 16.7023i | 0.334314 | − | 0.579049i | ||||
\(833\) | 36.3869 | + | 63.0240i | 1.26073 | + | 2.18365i | ||||
\(834\) | −6.68828 | −0.231596 | ||||||||
\(835\) | 0.852768 | − | 1.47704i | 0.0295113 | − | 0.0511150i | ||||
\(836\) | −50.6457 | + | 87.7209i | −1.75162 | + | 3.03389i | ||||
\(837\) | 1.89212 | − | 3.27726i | 0.0654014 | − | 0.113279i | ||||
\(838\) | −38.4889 | + | 66.6648i | −1.32958 | + | 2.30290i | ||||
\(839\) | 13.3836 | 0.462052 | 0.231026 | − | 0.972948i | \(-0.425792\pi\) | ||||
0.231026 | + | 0.972948i | \(0.425792\pi\) | |||||||
\(840\) | 12.0209 | − | 20.8208i | 0.414761 | − | 0.718387i | ||||
\(841\) | 77.6750 | 2.67845 | ||||||||
\(842\) | 15.5280 | − | 26.8953i | 0.535130 | − | 0.926873i | ||||
\(843\) | 11.2743 | 0.388307 | ||||||||
\(844\) | −95.9415 | −3.30244 | ||||||||
\(845\) | −3.52205 | + | 6.10036i | −0.121162 | + | 0.209859i | ||||
\(846\) | 4.69599 | + | 8.13369i | 0.161451 | + | 0.279642i | ||||
\(847\) | 8.91579 | − | 15.4426i | 0.306350 | − | 0.530614i | ||||
\(848\) | 8.89396 | − | 15.4048i | 0.305420 | − | 0.529002i | ||||
\(849\) | −4.87931 | −0.167457 | ||||||||
\(850\) | 74.4016 | 2.55195 | ||||||||
\(851\) | −1.51496 | + | 2.62398i | −0.0519320 | + | 0.0899489i | ||||
\(852\) | 51.9914 | 1.78120 | ||||||||
\(853\) | 17.7724 | + | 30.7827i | 0.608516 | + | 1.05398i | 0.991485 | + | 0.130219i | \(0.0415681\pi\) |
−0.382969 | + | 0.923761i | \(0.625099\pi\) | |||||||
\(854\) | 2.13159 | + | 3.69202i | 0.0729414 | + | 0.126338i | ||||
\(855\) | 1.30764 | + | 2.26489i | 0.0447202 | + | 0.0774577i | ||||
\(856\) | −21.9148 | + | 37.9576i | −0.749033 | + | 1.29736i | ||||
\(857\) | 23.0527 | − | 39.9284i | 0.787464 | − | 1.36393i | −0.140052 | − | 0.990144i | \(-0.544727\pi\) |
0.927516 | − | 0.373784i | \(-0.121940\pi\) | |||||||
\(858\) | −3.04793 | − | 5.27917i | −0.104055 | − | 0.180228i | ||||
\(859\) | −8.85858 | + | 15.3435i | −0.302251 | + | 0.523514i | −0.976645 | − | 0.214857i | \(-0.931071\pi\) |
0.674395 | + | 0.738371i | \(0.264405\pi\) | |||||||
\(860\) | −31.1769 | −1.06312 | ||||||||
\(861\) | −19.0714 | − | 33.0327i | −0.649953 | − | 1.12575i | ||||
\(862\) | −47.8253 | − | 82.8359i | −1.62894 | − | 2.82140i | ||||
\(863\) | 31.5711 | 1.07469 | 0.537346 | − | 0.843362i | \(-0.319427\pi\) | ||||
0.537346 | + | 0.843362i | \(0.319427\pi\) | |||||||
\(864\) | −23.7155 | −0.806817 | ||||||||
\(865\) | −1.51702 | − | 2.62756i | −0.0515802 | − | 0.0893396i | ||||
\(866\) | −38.5282 | − | 66.7328i | −1.30924 | − | 2.26767i | ||||
\(867\) | −16.3018 | −0.553639 | ||||||||
\(868\) | 46.5350 | − | 80.6010i | 1.57950 | − | 2.73578i | ||||
\(869\) | 13.7061 | + | 23.7397i | 0.464948 | + | 0.805314i | ||||
\(870\) | 7.88933 | − | 13.6647i | 0.267473 | − | 0.463277i | ||||
\(871\) | 0.589457 | − | 1.02097i | 0.0199730 | − | 0.0345942i | ||||
\(872\) | −3.37763 | − | 5.85023i | −0.114381 | − | 0.198114i | ||||
\(873\) | −8.40042 | − | 14.5500i | −0.284311 | − | 0.492441i | ||||
\(874\) | 7.72604 | + | 13.3819i | 0.261337 | + | 0.452649i | ||||
\(875\) | −23.8548 | −0.806439 | ||||||||
\(876\) | −37.4771 | + | 64.9122i | −1.26623 | + | 2.19318i | ||||
\(877\) | −51.1839 | −1.72836 | −0.864178 | − | 0.503186i | \(-0.832161\pi\) | ||||
−0.864178 | + | 0.503186i | \(0.832161\pi\) | |||||||
\(878\) | −69.8281 | −2.35659 | ||||||||
\(879\) | −3.23932 | + | 5.61067i | −0.109260 | + | 0.189243i | ||||
\(880\) | 16.9535 | − | 29.3644i | 0.571504 | − | 0.989874i | ||||
\(881\) | −4.55283 | − | 7.88573i | −0.153389 | − | 0.265677i | 0.779082 | − | 0.626921i | \(-0.215685\pi\) |
−0.932471 | + | 0.361244i | \(0.882352\pi\) | |||||||
\(882\) | −17.3297 | + | 30.0159i | −0.583521 | + | 1.01069i | ||||
\(883\) | 21.0563 | 0.708602 | 0.354301 | − | 0.935131i | \(-0.384719\pi\) | ||||
0.354301 | + | 0.935131i | \(0.384719\pi\) | |||||||
\(884\) | 18.3375 | 0.616758 | ||||||||
\(885\) | −0.529076 | + | 0.916386i | −0.0177847 | + | 0.0308040i | ||||
\(886\) | −28.9962 | −0.974148 | ||||||||
\(887\) | 10.5389 | − | 18.2539i | 0.353862 | − | 0.612907i | −0.633061 | − | 0.774102i | \(-0.718202\pi\) |
0.986923 | + | 0.161195i | \(0.0515349\pi\) | |||||||
\(888\) | 24.7653 | 0.831068 | ||||||||
\(889\) | −3.37841 | + | 5.85157i | −0.113308 | + | 0.196255i | ||||
\(890\) | −4.23098 | + | 7.32826i | −0.141823 | + | 0.245644i | ||||
\(891\) | −1.93821 | + | 3.35708i | −0.0649325 | + | 0.112466i | ||||
\(892\) | 76.1015 | − | 131.812i | 2.54807 | − | 4.41338i | ||||
\(893\) | −16.0781 | −0.538034 | ||||||||
\(894\) | 13.1596 | + | 22.7931i | 0.440124 | + | 0.762317i | ||||
\(895\) | 2.79333 | − | 4.83819i | 0.0933707 | − | 0.161723i | ||||
\(896\) | −200.207 | −6.68846 | ||||||||
\(897\) | −0.683711 | −0.0228284 | ||||||||
\(898\) | 3.20746 | + | 5.55549i | 0.107034 | + | 0.185389i | ||||
\(899\) | 19.5425 | − | 33.8487i | 0.651780 | − | 1.12892i | ||||
\(900\) | 13.0263 | + | 22.5622i | 0.434210 | + | 0.752074i | ||||
\(901\) | 6.52316 | 0.217318 | ||||||||
\(902\) | −45.8825 | − | 79.4709i | −1.52772 | − | 2.64609i | ||||
\(903\) | 44.7237 | 1.48831 | ||||||||
\(904\) | −80.9542 | − | 140.217i | −2.69250 | − | 4.66354i | ||||
\(905\) | 4.41528 | − | 7.64748i | 0.146769 | − | 0.254211i | ||||
\(906\) | −22.0276 | + | 38.1528i | −0.731816 | + | 1.26754i | ||||
\(907\) | 6.28390 | + | 10.8840i | 0.208653 | + | 0.361398i | 0.951291 | − | 0.308296i | \(-0.0997586\pi\) |
−0.742637 | + | 0.669694i | \(0.766425\pi\) | |||||||
\(908\) | −10.2958 | − | 17.8328i | −0.341677 | − | 0.591801i | ||||
\(909\) | 3.03110 | − | 5.25002i | 0.100535 | − | 0.174132i | ||||
\(910\) | −3.87088 | −0.128318 | ||||||||
\(911\) | 10.0571 | − | 17.4193i | 0.333205 | − | 0.577128i | −0.649933 | − | 0.759991i | \(-0.725203\pi\) |
0.983138 | + | 0.182863i | \(0.0585365\pi\) | |||||||
\(912\) | 37.0194 | − | 64.1195i | 1.22584 | − | 2.12321i | ||||
\(913\) | 26.4717 | 0.876086 | ||||||||
\(914\) | 102.413 | 3.38750 | ||||||||
\(915\) | 0.194699 | 0.00643656 | ||||||||
\(916\) | −14.8455 | + | 25.7132i | −0.490510 | + | 0.849588i | ||||
\(917\) | −41.9467 | + | 72.6538i | −1.38520 | + | 2.39924i | ||||
\(918\) | −7.93020 | − | 13.7355i | −0.261736 | − | 0.453339i | ||||
\(919\) | 44.3075 | 1.46157 | 0.730785 | − | 0.682608i | \(-0.239154\pi\) | ||||
0.730785 | + | 0.682608i | \(0.239154\pi\) | |||||||
\(920\) | −3.24368 | − | 5.61822i | −0.106941 | − | 0.185227i | ||||
\(921\) | 4.40751 | + | 7.63403i | 0.145232 | + | 0.251550i | ||||
\(922\) | 14.2380 | + | 24.6609i | 0.468902 | + | 0.812162i | ||||
\(923\) | −2.67820 | − | 4.63877i | −0.0881540 | − | 0.152687i | ||||
\(924\) | −47.6684 | + | 82.5642i | −1.56818 | + | 2.71616i | ||||
\(925\) | −5.94730 | − | 10.3010i | −0.195546 | − | 0.338696i | ||||
\(926\) | −26.4391 | −0.868843 | ||||||||
\(927\) | −4.19686 | + | 7.26918i | −0.137843 | + | 0.238751i | ||||
\(928\) | −244.942 | −8.04062 | ||||||||
\(929\) | −12.5366 | + | 21.7140i | −0.411311 | + | 0.712412i | −0.995033 | − | 0.0995413i | \(-0.968262\pi\) |
0.583722 | + | 0.811954i | \(0.301596\pi\) | |||||||
\(930\) | −2.89060 | − | 5.00667i | −0.0947866 | − | 0.164175i | ||||
\(931\) | −29.6667 | − | 51.3843i | −0.972288 | − | 1.68405i | ||||
\(932\) | 35.9835 | + | 62.3253i | 1.17868 | + | 2.04153i | ||||
\(933\) | −3.01535 | + | 5.22275i | −0.0987182 | + | 0.170985i | ||||
\(934\) | −103.386 | −3.38289 | ||||||||
\(935\) | 12.4344 | 0.406647 | ||||||||
\(936\) | 2.79419 | + | 4.83968i | 0.0913309 | + | 0.158190i | ||||
\(937\) | 18.1986 | + | 31.5209i | 0.594523 | + | 1.02974i | 0.993614 | + | 0.112832i | \(0.0359922\pi\) |
−0.399092 | + | 0.916911i | \(0.630674\pi\) | |||||||
\(938\) | −25.0776 | −0.818811 | ||||||||
\(939\) | −0.900591 | − | 1.55987i | −0.0293897 | − | 0.0509044i | ||||
\(940\) | 10.5492 | 0.344076 | ||||||||
\(941\) | −8.00495 | −0.260954 | −0.130477 | − | 0.991451i | \(-0.541651\pi\) | ||||
−0.130477 | + | 0.991451i | \(0.541651\pi\) | |||||||
\(942\) | −34.2597 | + | 3.49394i | −1.11624 | + | 0.113839i | ||||
\(943\) | −10.2924 | −0.335165 | ||||||||
\(944\) | 29.9564 | 0.974999 | ||||||||
\(945\) | 1.23077 | + | 2.13175i | 0.0400368 | + | 0.0693458i | ||||
\(946\) | 107.597 | 3.49829 | ||||||||
\(947\) | 5.66048 | + | 9.80424i | 0.183941 | + | 0.318595i | 0.943219 | − | 0.332171i | \(-0.107781\pi\) |
−0.759278 | + | 0.650766i | \(0.774448\pi\) | |||||||
\(948\) | −19.6366 | − | 34.0116i | −0.637767 | − | 1.10465i | ||||
\(949\) | 7.72212 | 0.250671 | ||||||||
\(950\) | −60.6606 | −1.96809 | ||||||||
\(951\) | 9.54975 | − | 16.5406i | 0.309672 | − | 0.536367i | ||||
\(952\) | −124.799 | − | 216.159i | −4.04477 | − | 7.00575i | ||||
\(953\) | 0.0397597 | + | 0.0688658i | 0.00128794 | + | 0.00223078i | 0.866669 | − | 0.498884i | \(-0.166257\pi\) |
−0.865381 | + | 0.501115i | \(0.832923\pi\) | |||||||
\(954\) | 1.55337 | + | 2.69051i | 0.0502921 | + | 0.0871085i | ||||
\(955\) | −0.720635 | + | 1.24818i | −0.0233192 | + | 0.0403901i | ||||
\(956\) | −149.524 | −4.83596 | ||||||||
\(957\) | −20.0185 | + | 34.6731i | −0.647107 | + | 1.12082i | ||||
\(958\) | −54.7587 | −1.76917 | ||||||||
\(959\) | 25.0690 | + | 43.4208i | 0.809520 | + | 1.40213i | ||||
\(960\) | −9.36809 | + | 16.2260i | −0.302354 | + | 0.523692i | ||||
\(961\) | 8.33973 | + | 14.4448i | 0.269023 | + | 0.465962i | ||||
\(962\) | −1.99368 | − | 3.45316i | −0.0642789 | − | 0.111334i | ||||
\(963\) | −2.24376 | − | 3.88630i | −0.0723041 | − | 0.125234i | ||||
\(964\) | 36.8535 | + | 63.8322i | 1.18697 | + | 2.05590i | ||||
\(965\) | 8.39531 | 0.270255 | ||||||||
\(966\) | 7.27186 | + | 12.5952i | 0.233968 | + | 0.405245i | ||||
\(967\) | −21.3744 | + | 37.0215i | −0.687353 | + | 1.19053i | 0.285338 | + | 0.958427i | \(0.407894\pi\) |
−0.972691 | + | 0.232103i | \(0.925439\pi\) | |||||||
\(968\) | −19.6641 | + | 34.0592i | −0.632028 | + | 1.09470i | ||||
\(969\) | 27.1514 | 0.872230 | ||||||||
\(970\) | −25.6667 | −0.824107 | ||||||||
\(971\) | 21.3792 | 0.686091 | 0.343046 | − | 0.939319i | \(-0.388541\pi\) | ||||
0.343046 | + | 0.939319i | \(0.388541\pi\) | |||||||
\(972\) | 2.77685 | − | 4.80965i | 0.0890676 | − | 0.154270i | ||||
\(973\) | 5.38830 | − | 9.33280i | 0.172741 | − | 0.299196i | ||||
\(974\) | −89.9003 | −2.88059 | ||||||||
\(975\) | 1.34203 | − | 2.32446i | 0.0429794 | − | 0.0744424i | ||||
\(976\) | −2.75599 | − | 4.77351i | −0.0882170 | − | 0.152796i | ||||
\(977\) | 8.08335 | + | 14.0008i | 0.258609 | + | 0.447925i | 0.965870 | − | 0.259029i | \(-0.0834024\pi\) |
−0.707260 | + | 0.706953i | \(0.750069\pi\) | |||||||
\(978\) | −19.9136 | + | 34.4914i | −0.636767 | + | 1.10291i | ||||
\(979\) | 10.7358 | − | 18.5949i | 0.343116 | − | 0.594295i | ||||
\(980\) | 19.4649 | + | 33.7142i | 0.621784 | + | 1.07696i | ||||
\(981\) | 0.691641 | 0.0220824 | ||||||||
\(982\) | 3.29216 | + | 5.70219i | 0.105057 | + | 0.181964i | ||||
\(983\) | 22.6666 | 0.722952 | 0.361476 | − | 0.932381i | \(-0.382273\pi\) | ||||
0.361476 | + | 0.932381i | \(0.382273\pi\) | |||||||
\(984\) | 42.0628 | + | 72.8549i | 1.34091 | + | 2.32253i | ||||
\(985\) | −3.11267 | + | 5.39131i | −0.0991780 | + | 0.171781i | ||||
\(986\) | −81.9059 | − | 141.865i | −2.60842 | − | 4.51791i | ||||
\(987\) | −15.1330 | −0.481688 | ||||||||
\(988\) | −14.9508 | −0.475650 | ||||||||
\(989\) | 6.03406 | − | 10.4513i | 0.191872 | − | 0.332332i | ||||
\(990\) | 2.96101 | + | 5.12862i | 0.0941070 | + | 0.162998i | ||||
\(991\) | 8.70427 | 0.276500 | 0.138250 | − | 0.990397i | \(-0.455852\pi\) | ||||
0.138250 | + | 0.990397i | \(0.455852\pi\) | |||||||
\(992\) | −44.8727 | + | 77.7217i | −1.42471 | + | 2.46767i | ||||
\(993\) | 3.27008 | − | 5.66394i | 0.103773 | − | 0.179740i | ||||
\(994\) | −56.9699 | + | 98.6748i | −1.80698 | + | 3.12978i | ||||
\(995\) | −1.18408 | + | 2.05089i | −0.0375379 | + | 0.0650176i | ||||
\(996\) | −37.9258 | −1.20172 | ||||||||
\(997\) | −28.5071 | + | 49.3757i | −0.902827 | + | 1.56374i | −0.0790202 | + | 0.996873i | \(0.525179\pi\) |
−0.823807 | + | 0.566870i | \(0.808154\pi\) | |||||||
\(998\) | 19.7755 | 0.625982 | ||||||||
\(999\) | −1.26780 | + | 2.19590i | −0.0401115 | + | 0.0694751i |
(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 | 471.2.e.b.169.11 | ✓ | 22 | |
157.144 | even | 3 | inner | 471.2.e.b.301.11 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
471.2.e.b.169.11 | ✓ | 22 | 1.1 | even | 1 | trivial | |
471.2.e.b.301.11 | yes | 22 | 157.144 | even | 3 | inner |