Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [65,3,Mod(12,65)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(65, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("65.12");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 65 = 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 65.h (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: | \(1.77112171834\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 38.2 | ||
Character | \(\chi\) | \(=\) | 65.38 |
Dual form | 65.3.h.a.12.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.14254 | − | 2.14254i | −1.07127 | − | 1.07127i | −0.997257 | − | 0.0740139i | \(-0.976419\pi\) |
−0.0740139 | − | 0.997257i | \(-0.523581\pi\) | |||||||
\(3\) | 1.85789 | + | 1.85789i | 0.619297 | + | 0.619297i | 0.945351 | − | 0.326054i | \(-0.105719\pi\) |
−0.326054 | + | 0.945351i | \(0.605719\pi\) | |||||||
\(4\) | 5.18097i | 1.29524i | ||||||||
\(5\) | 1.93662 | + | 4.60972i | 0.387325 | + | 0.921943i | ||||
\(6\) | − | 7.96121i | − | 1.32687i | ||||||
\(7\) | 5.84982 | + | 5.84982i | 0.835688 | + | 0.835688i | 0.988288 | − | 0.152600i | \(-0.0487645\pi\) |
−0.152600 | + | 0.988288i | \(0.548765\pi\) | |||||||
\(8\) | 2.53029 | − | 2.53029i | 0.316286 | − | 0.316286i | ||||
\(9\) | − | 2.09649i | − | 0.232944i | ||||||
\(10\) | 5.72722 | − | 14.0258i | 0.572722 | − | 1.40258i | ||||
\(11\) | − | 8.13517i | − | 0.739561i | −0.929119 | − | 0.369780i | \(-0.879433\pi\) | ||
0.929119 | − | 0.369780i | \(-0.120567\pi\) | |||||||
\(12\) | −9.62568 | + | 9.62568i | −0.802140 | + | 0.802140i | ||||
\(13\) | 12.9699 | − | 0.884166i | 0.997684 | − | 0.0680128i | ||||
\(14\) | − | 25.0670i | − | 1.79050i | ||||||
\(15\) | −4.96631 | + | 12.1624i | −0.331088 | + | 0.810825i | ||||
\(16\) | 9.88140 | 0.617588 | ||||||||
\(17\) | −15.0817 | + | 15.0817i | −0.887161 | + | 0.887161i | −0.994249 | − | 0.107089i | \(-0.965847\pi\) |
0.107089 | + | 0.994249i | \(0.465847\pi\) | |||||||
\(18\) | −4.49182 | + | 4.49182i | −0.249546 | + | 0.249546i | ||||
\(19\) | −7.91139 | −0.416389 | −0.208194 | − | 0.978087i | \(-0.566759\pi\) | ||||
−0.208194 | + | 0.978087i | \(0.566759\pi\) | |||||||
\(20\) | −23.8828 | + | 10.0336i | −1.19414 | + | 0.501680i | ||||
\(21\) | 21.7366i | 1.03508i | ||||||||
\(22\) | −17.4299 | + | 17.4299i | −0.792270 | + | 0.792270i | ||||
\(23\) | −0.359560 | − | 0.359560i | −0.0156330 | − | 0.0156330i | 0.699247 | − | 0.714880i | \(-0.253519\pi\) |
−0.714880 | + | 0.699247i | \(0.753519\pi\) | |||||||
\(24\) | 9.40199 | 0.391749 | ||||||||
\(25\) | −17.4990 | + | 17.8546i | −0.699959 | + | 0.714183i | ||||
\(26\) | −29.6829 | − | 25.8942i | −1.14165 | − | 0.995930i | ||||
\(27\) | 20.6161 | − | 20.6161i | 0.763558 | − | 0.763558i | ||||
\(28\) | −30.3078 | + | 30.3078i | −1.08242 | + | 1.08242i | ||||
\(29\) | − | 39.6950i | − | 1.36879i | −0.729109 | − | 0.684397i | \(-0.760065\pi\) | ||
0.729109 | − | 0.684397i | \(-0.239935\pi\) | |||||||
\(30\) | 36.6989 | − | 15.4179i | 1.22330 | − | 0.513929i | ||||
\(31\) | 10.3309i | 0.333256i | 0.986020 | + | 0.166628i | \(0.0532879\pi\) | ||||
−0.986020 | + | 0.166628i | \(0.946712\pi\) | |||||||
\(32\) | −31.2925 | − | 31.2925i | −0.977890 | − | 0.977890i | ||||
\(33\) | 15.1142 | − | 15.1142i | 0.458007 | − | 0.458007i | ||||
\(34\) | 64.6265 | 1.90078 | ||||||||
\(35\) | −15.6371 | + | 38.2949i | −0.446775 | + | 1.09414i | ||||
\(36\) | 10.8619 | 0.301719 | ||||||||
\(37\) | 14.3950 | + | 14.3950i | 0.389053 | + | 0.389053i | 0.874350 | − | 0.485297i | \(-0.161288\pi\) |
−0.485297 | + | 0.874350i | \(0.661288\pi\) | |||||||
\(38\) | 16.9505 | + | 16.9505i | 0.446065 | + | 0.446065i | ||||
\(39\) | 25.7393 | + | 22.4540i | 0.659983 | + | 0.575743i | ||||
\(40\) | 16.5641 | + | 6.76370i | 0.414103 | + | 0.169092i | ||||
\(41\) | − | 38.9872i | − | 0.950908i | −0.879741 | − | 0.475454i | \(-0.842284\pi\) | ||
0.879741 | − | 0.475454i | \(-0.157716\pi\) | |||||||
\(42\) | 46.5717 | − | 46.5717i | 1.10885 | − | 1.10885i | ||||
\(43\) | −37.8080 | − | 37.8080i | −0.879256 | − | 0.879256i | 0.114201 | − | 0.993458i | \(-0.463569\pi\) |
−0.993458 | + | 0.114201i | \(0.963569\pi\) | |||||||
\(44\) | 42.1481 | 0.957911 | ||||||||
\(45\) | 9.66423 | − | 4.06011i | 0.214761 | − | 0.0902247i | ||||
\(46\) | 1.54074i | 0.0334944i | ||||||||
\(47\) | −56.8456 | − | 56.8456i | −1.20948 | − | 1.20948i | −0.971195 | − | 0.238285i | \(-0.923415\pi\) |
−0.238285 | − | 0.971195i | \(-0.576585\pi\) | |||||||
\(48\) | 18.3586 | + | 18.3586i | 0.382470 | + | 0.382470i | ||||
\(49\) | 19.4408i | 0.396750i | ||||||||
\(50\) | 75.7465 | − | 0.761848i | 1.51493 | − | 0.0152370i | ||||
\(51\) | −56.0404 | −1.09883 | ||||||||
\(52\) | 4.58084 | + | 67.1967i | 0.0880931 | + | 1.29224i | ||||
\(53\) | 49.5278 | + | 49.5278i | 0.934486 | + | 0.934486i | 0.997982 | − | 0.0634958i | \(-0.0202250\pi\) |
−0.0634958 | + | 0.997982i | \(0.520225\pi\) | |||||||
\(54\) | −88.3415 | −1.63595 | ||||||||
\(55\) | 37.5008 | − | 15.7548i | 0.681833 | − | 0.286450i | ||||
\(56\) | 29.6034 | 0.528633 | ||||||||
\(57\) | −14.6985 | − | 14.6985i | −0.257868 | − | 0.257868i | ||||
\(58\) | −85.0483 | + | 85.0483i | −1.46635 | + | 1.46635i | ||||
\(59\) | −37.9923 | −0.643937 | −0.321969 | − | 0.946750i | \(-0.604345\pi\) | ||||
−0.321969 | + | 0.946750i | \(0.604345\pi\) | |||||||
\(60\) | −63.0130 | − | 25.7303i | −1.05022 | − | 0.428839i | ||||
\(61\) | −27.8752 | −0.456971 | −0.228486 | − | 0.973547i | \(-0.573377\pi\) | ||||
−0.228486 | + | 0.973547i | \(0.573377\pi\) | |||||||
\(62\) | 22.1345 | − | 22.1345i | 0.357007 | − | 0.357007i | ||||
\(63\) | 12.2641 | − | 12.2641i | 0.194668 | − | 0.194668i | ||||
\(64\) | 94.5653i | 1.47758i | ||||||||
\(65\) | 29.1936 | + | 58.0753i | 0.449132 | + | 0.893466i | ||||
\(66\) | −64.7658 | −0.981300 | ||||||||
\(67\) | 17.5028 | + | 17.5028i | 0.261235 | + | 0.261235i | 0.825556 | − | 0.564320i | \(-0.190862\pi\) |
−0.564320 | + | 0.825556i | \(0.690862\pi\) | |||||||
\(68\) | −78.1381 | − | 78.1381i | −1.14909 | − | 1.14909i | ||||
\(69\) | − | 1.33605i | − | 0.0193630i | ||||||
\(70\) | 115.552 | − | 48.5453i | 1.65074 | − | 0.693504i | ||||
\(71\) | 106.949i | 1.50633i | 0.657831 | + | 0.753165i | \(0.271474\pi\) | ||||
−0.657831 | + | 0.753165i | \(0.728526\pi\) | |||||||
\(72\) | −5.30472 | − | 5.30472i | −0.0736767 | − | 0.0736767i | ||||
\(73\) | 67.9236 | − | 67.9236i | 0.930460 | − | 0.930460i | −0.0672743 | − | 0.997735i | \(-0.521430\pi\) |
0.997735 | + | 0.0672743i | \(0.0214303\pi\) | |||||||
\(74\) | − | 61.6836i | − | 0.833562i | ||||||
\(75\) | −65.6830 | + | 0.660631i | −0.875773 | + | 0.00880841i | ||||
\(76\) | − | 40.9887i | − | 0.539325i | ||||||
\(77\) | 47.5893 | − | 47.5893i | 0.618042 | − | 0.618042i | ||||
\(78\) | −7.03903 | − | 103.256i | −0.0902440 | − | 1.32380i | ||||
\(79\) | − | 106.988i | − | 1.35428i | −0.735853 | − | 0.677141i | \(-0.763219\pi\) | ||
0.735853 | − | 0.677141i | \(-0.236781\pi\) | |||||||
\(80\) | 19.1366 | + | 45.5505i | 0.239207 | + | 0.569381i | ||||
\(81\) | 57.7363 | 0.712794 | ||||||||
\(82\) | −83.5318 | + | 83.5318i | −1.01868 | + | 1.01868i | ||||
\(83\) | −8.61976 | + | 8.61976i | −0.103853 | + | 0.103853i | −0.757124 | − | 0.653271i | \(-0.773396\pi\) |
0.653271 | + | 0.757124i | \(0.273396\pi\) | |||||||
\(84\) | −112.617 | −1.34068 | ||||||||
\(85\) | −98.7301 | − | 40.3149i | −1.16153 | − | 0.474293i | ||||
\(86\) | 162.011i | 1.88384i | ||||||||
\(87\) | 73.7490 | − | 73.7490i | 0.847690 | − | 0.847690i | ||||
\(88\) | −20.5843 | − | 20.5843i | −0.233913 | − | 0.233913i | ||||
\(89\) | 70.4135 | 0.791163 | 0.395581 | − | 0.918431i | \(-0.370543\pi\) | ||||
0.395581 | + | 0.918431i | \(0.370543\pi\) | |||||||
\(90\) | −29.4050 | − | 12.0071i | −0.326722 | − | 0.133412i | ||||
\(91\) | 81.0438 | + | 70.6993i | 0.890591 | + | 0.776916i | ||||
\(92\) | 1.86287 | − | 1.86287i | 0.0202486 | − | 0.0202486i | ||||
\(93\) | −19.1937 | + | 19.1937i | −0.206384 | + | 0.206384i | ||||
\(94\) | 243.588i | 2.59136i | ||||||||
\(95\) | −15.3214 | − | 36.4693i | −0.161278 | − | 0.383887i | ||||
\(96\) | − | 116.276i | − | 1.21121i | ||||||
\(97\) | −33.7421 | − | 33.7421i | −0.347856 | − | 0.347856i | 0.511454 | − | 0.859310i | \(-0.329107\pi\) |
−0.859310 | + | 0.511454i | \(0.829107\pi\) | |||||||
\(98\) | 41.6527 | − | 41.6527i | 0.425027 | − | 0.425027i | ||||
\(99\) | −17.0553 | −0.172276 | ||||||||
\(100\) | −92.5040 | − | 90.6618i | −0.925040 | − | 0.906618i | ||||
\(101\) | 129.417 | 1.28136 | 0.640681 | − | 0.767807i | \(-0.278652\pi\) | ||||
0.640681 | + | 0.767807i | \(0.278652\pi\) | |||||||
\(102\) | 120.069 | + | 120.069i | 1.17715 | + | 1.17715i | ||||
\(103\) | −91.5406 | − | 91.5406i | −0.888744 | − | 0.888744i | 0.105659 | − | 0.994402i | \(-0.466305\pi\) |
−0.994402 | + | 0.105659i | \(0.966305\pi\) | |||||||
\(104\) | 30.5804 | − | 35.0548i | 0.294042 | − | 0.337065i | ||||
\(105\) | −100.200 | + | 42.0957i | −0.954283 | + | 0.400911i | ||||
\(106\) | − | 212.231i | − | 2.00218i | ||||||
\(107\) | −113.834 | + | 113.834i | −1.06387 | + | 1.06387i | −0.0660525 | + | 0.997816i | \(0.521040\pi\) |
−0.997816 | + | 0.0660525i | \(0.978960\pi\) | |||||||
\(108\) | 106.811 | + | 106.811i | 0.988993 | + | 0.988993i | ||||
\(109\) | 1.96303 | 0.0180095 | 0.00900474 | − | 0.999959i | \(-0.497134\pi\) | ||||
0.00900474 | + | 0.999959i | \(0.497134\pi\) | |||||||
\(110\) | −114.102 | − | 46.5919i | −1.03729 | − | 0.423563i | ||||
\(111\) | 53.4885i | 0.481878i | ||||||||
\(112\) | 57.8044 | + | 57.8044i | 0.516111 | + | 0.516111i | ||||
\(113\) | 152.551 | + | 152.551i | 1.35001 | + | 1.35001i | 0.885646 | + | 0.464361i | \(0.153716\pi\) |
0.464361 | + | 0.885646i | \(0.346284\pi\) | |||||||
\(114\) | 62.9843i | 0.552494i | ||||||||
\(115\) | 0.961137 | − | 2.35380i | 0.00835772 | − | 0.0204678i | ||||
\(116\) | 205.659 | 1.77292 | ||||||||
\(117\) | −1.85365 | − | 27.1913i | −0.0158431 | − | 0.232404i | ||||
\(118\) | 81.4001 | + | 81.4001i | 0.689832 | + | 0.689832i | ||||
\(119\) | −176.451 | −1.48278 | ||||||||
\(120\) | 18.2081 | + | 43.3405i | 0.151734 | + | 0.361171i | ||||
\(121\) | 54.8190 | 0.453050 | ||||||||
\(122\) | 59.7239 | + | 59.7239i | 0.489540 | + | 0.489540i | ||||
\(123\) | 72.4340 | − | 72.4340i | 0.588894 | − | 0.588894i | ||||
\(124\) | −53.5243 | −0.431648 | ||||||||
\(125\) | −116.193 | − | 46.0878i | −0.929547 | − | 0.368702i | ||||
\(126\) | −52.5527 | −0.417085 | ||||||||
\(127\) | −32.1405 | + | 32.1405i | −0.253075 | + | 0.253075i | −0.822230 | − | 0.569155i | \(-0.807270\pi\) |
0.569155 | + | 0.822230i | \(0.307270\pi\) | |||||||
\(128\) | 77.4402 | − | 77.4402i | 0.605001 | − | 0.605001i | ||||
\(129\) | − | 140.486i | − | 1.08904i | ||||||
\(130\) | 61.8803 | − | 186.977i | 0.476002 | − | 1.43829i | ||||
\(131\) | −69.7160 | −0.532184 | −0.266092 | − | 0.963948i | \(-0.585732\pi\) | ||||
−0.266092 | + | 0.963948i | \(0.585732\pi\) | |||||||
\(132\) | 78.3065 | + | 78.3065i | 0.593231 | + | 0.593231i | ||||
\(133\) | −46.2802 | − | 46.2802i | −0.347971 | − | 0.347971i | ||||
\(134\) | − | 75.0008i | − | 0.559708i | ||||||
\(135\) | 134.960 | + | 55.1087i | 0.999702 | + | 0.408212i | ||||
\(136\) | 76.3222i | 0.561193i | ||||||||
\(137\) | 66.6819 | + | 66.6819i | 0.486729 | + | 0.486729i | 0.907273 | − | 0.420543i | \(-0.138160\pi\) |
−0.420543 | + | 0.907273i | \(0.638160\pi\) | |||||||
\(138\) | −2.86253 | + | 2.86253i | −0.0207430 | + | 0.0207430i | ||||
\(139\) | 2.94331i | 0.0211749i | 0.999944 | + | 0.0105875i | \(0.00337015\pi\) | ||||
−0.999944 | + | 0.0105875i | \(0.996630\pi\) | |||||||
\(140\) | −198.405 | − | 81.0155i | −1.41718 | − | 0.578682i | ||||
\(141\) | − | 211.226i | − | 1.49805i | ||||||
\(142\) | 229.144 | − | 229.144i | 1.61369 | − | 1.61369i | ||||
\(143\) | −7.19284 | − | 105.512i | −0.0502996 | − | 0.737848i | ||||
\(144\) | − | 20.7163i | − | 0.143863i | ||||||
\(145\) | 182.983 | − | 76.8743i | 1.26195 | − | 0.530168i | ||||
\(146\) | −291.058 | −1.99355 | ||||||||
\(147\) | −36.1188 | + | 36.1188i | −0.245706 | + | 0.245706i | ||||
\(148\) | −74.5799 | + | 74.5799i | −0.503918 | + | 0.503918i | ||||
\(149\) | 143.091 | 0.960343 | 0.480171 | − | 0.877175i | \(-0.340574\pi\) | ||||
0.480171 | + | 0.877175i | \(0.340574\pi\) | |||||||
\(150\) | 142.144 | + | 139.313i | 0.947627 | + | 0.928754i | ||||
\(151\) | 116.794i | 0.773468i | 0.922191 | + | 0.386734i | \(0.126397\pi\) | ||||
−0.922191 | + | 0.386734i | \(0.873603\pi\) | |||||||
\(152\) | −20.0181 | + | 20.0181i | −0.131698 | + | 0.131698i | ||||
\(153\) | 31.6187 | + | 31.6187i | 0.206658 | + | 0.206658i | ||||
\(154\) | −203.924 | −1.32418 | ||||||||
\(155\) | −47.6227 | + | 20.0071i | −0.307243 | + | 0.129078i | ||||
\(156\) | −116.333 | + | 133.355i | −0.745727 | + | 0.854838i | ||||
\(157\) | −151.195 | + | 151.195i | −0.963027 | + | 0.963027i | −0.999340 | − | 0.0363137i | \(-0.988438\pi\) |
0.0363137 | + | 0.999340i | \(0.488438\pi\) | |||||||
\(158\) | −229.227 | + | 229.227i | −1.45080 | + | 1.45080i | ||||
\(159\) | 184.034i | 1.15745i | ||||||||
\(160\) | 83.6477 | − | 204.851i | 0.522798 | − | 1.28032i | ||||
\(161\) | − | 4.20672i | − | 0.0261287i | ||||||
\(162\) | −123.702 | − | 123.702i | −0.763595 | − | 0.763595i | ||||
\(163\) | −170.294 | + | 170.294i | −1.04475 | + | 1.04475i | −0.0457966 | + | 0.998951i | \(0.514583\pi\) |
−0.998951 | + | 0.0457966i | \(0.985417\pi\) | |||||||
\(164\) | 201.992 | 1.23166 | ||||||||
\(165\) | 98.9430 | + | 40.4018i | 0.599655 | + | 0.244859i | ||||
\(166\) | 36.9364 | 0.222508 | ||||||||
\(167\) | −115.052 | − | 115.052i | −0.688931 | − | 0.688931i | 0.273064 | − | 0.961996i | \(-0.411963\pi\) |
−0.961996 | + | 0.273064i | \(0.911963\pi\) | |||||||
\(168\) | 54.9999 | + | 54.9999i | 0.327381 | + | 0.327381i | ||||
\(169\) | 167.437 | − | 22.9351i | 0.990749 | − | 0.135711i | ||||
\(170\) | 125.157 | + | 297.910i | 0.736218 | + | 1.75241i | ||||
\(171\) | 16.5862i | 0.0969951i | ||||||||
\(172\) | 195.882 | − | 195.882i | 1.13885 | − | 1.13885i | ||||
\(173\) | −178.343 | − | 178.343i | −1.03088 | − | 1.03088i | −0.999508 | − | 0.0313760i | \(-0.990011\pi\) |
−0.0313760 | − | 0.999508i | \(-0.509989\pi\) | |||||||
\(174\) | −316.021 | −1.81621 | ||||||||
\(175\) | −206.812 | + | 2.08009i | −1.18178 | + | 0.0118862i | ||||
\(176\) | − | 80.3869i | − | 0.456744i | ||||||
\(177\) | −70.5855 | − | 70.5855i | −0.398788 | − | 0.398788i | ||||
\(178\) | −150.864 | − | 150.864i | −0.847550 | − | 0.847550i | ||||
\(179\) | 109.444i | 0.611417i | 0.952125 | + | 0.305709i | \(0.0988934\pi\) | ||||
−0.952125 | + | 0.305709i | \(0.901107\pi\) | |||||||
\(180\) | 21.0353 | + | 50.0701i | 0.116863 | + | 0.278167i | ||||
\(181\) | −176.025 | −0.972516 | −0.486258 | − | 0.873815i | \(-0.661639\pi\) | ||||
−0.486258 | + | 0.873815i | \(0.661639\pi\) | |||||||
\(182\) | −22.1634 | − | 325.116i | −0.121777 | − | 1.78635i | ||||
\(183\) | −51.7891 | − | 51.7891i | −0.283001 | − | 0.283001i | ||||
\(184\) | −1.81958 | −0.00988902 | ||||||||
\(185\) | −38.4791 | + | 94.2343i | −0.207995 | + | 0.509375i | ||||
\(186\) | 82.2468 | 0.442187 | ||||||||
\(187\) | 122.692 | + | 122.692i | 0.656109 | + | 0.656109i | ||||
\(188\) | 294.515 | − | 294.515i | 1.56657 | − | 1.56657i | ||||
\(189\) | 241.200 | 1.27619 | ||||||||
\(190\) | −45.3103 | + | 110.964i | −0.238475 | + | 0.584019i | ||||
\(191\) | 268.857 | 1.40763 | 0.703815 | − | 0.710384i | \(-0.251479\pi\) | ||||
0.703815 | + | 0.710384i | \(0.251479\pi\) | |||||||
\(192\) | −175.692 | + | 175.692i | −0.915062 | + | 0.915062i | ||||
\(193\) | −185.483 | + | 185.483i | −0.961053 | + | 0.961053i | −0.999269 | − | 0.0382165i | \(-0.987832\pi\) |
0.0382165 | + | 0.999269i | \(0.487832\pi\) | |||||||
\(194\) | 144.588i | 0.745297i | ||||||||
\(195\) | −53.6590 | + | 162.136i | −0.275175 | + | 0.831466i | ||||
\(196\) | −100.722 | −0.513888 | ||||||||
\(197\) | −21.7152 | − | 21.7152i | −0.110229 | − | 0.110229i | 0.649841 | − | 0.760070i | \(-0.274835\pi\) |
−0.760070 | + | 0.649841i | \(0.774835\pi\) | |||||||
\(198\) | 36.5417 | + | 36.5417i | 0.184554 | + | 0.184554i | ||||
\(199\) | − | 66.5114i | − | 0.334228i | −0.985938 | − | 0.167114i | \(-0.946555\pi\) | ||
0.985938 | − | 0.167114i | \(-0.0534448\pi\) | |||||||
\(200\) | 0.899723 | + | 89.4546i | 0.00449861 | + | 0.447273i | ||||
\(201\) | 65.0364i | 0.323564i | ||||||||
\(202\) | −277.282 | − | 277.282i | −1.37269 | − | 1.37269i | ||||
\(203\) | 232.209 | − | 232.209i | 1.14389 | − | 1.14389i | ||||
\(204\) | − | 290.344i | − | 1.42325i | ||||||
\(205\) | 179.720 | − | 75.5035i | 0.876683 | − | 0.368310i | ||||
\(206\) | 392.259i | 1.90417i | ||||||||
\(207\) | −0.753814 | + | 0.753814i | −0.00364161 | + | 0.00364161i | ||||
\(208\) | 128.161 | − | 8.73680i | 0.616158 | − | 0.0420038i | ||||
\(209\) | 64.3605i | 0.307945i | ||||||||
\(210\) | 304.874 | + | 124.490i | 1.45178 | + | 0.592812i | ||||
\(211\) | 21.9873 | 0.104205 | 0.0521027 | − | 0.998642i | \(-0.483408\pi\) | ||||
0.0521027 | + | 0.998642i | \(0.483408\pi\) | |||||||
\(212\) | −256.602 | + | 256.602i | −1.21039 | + | 1.21039i | ||||
\(213\) | −198.700 | + | 198.700i | −0.932866 | + | 0.932866i | ||||
\(214\) | 487.788 | 2.27938 | ||||||||
\(215\) | 101.064 | − | 247.504i | 0.470067 | − | 1.15118i | ||||
\(216\) | − | 104.329i | − | 0.483005i | ||||||
\(217\) | −60.4341 | + | 60.4341i | −0.278498 | + | 0.278498i | ||||
\(218\) | −4.20588 | − | 4.20588i | −0.0192930 | − | 0.0192930i | ||||
\(219\) | 252.389 | 1.15246 | ||||||||
\(220\) | 81.6250 | + | 194.291i | 0.371023 | + | 0.883140i | ||||
\(221\) | −182.274 | + | 208.943i | −0.824768 | + | 0.945445i | ||||
\(222\) | 114.601 | − | 114.601i | 0.516222 | − | 0.516222i | ||||
\(223\) | 57.1409 | − | 57.1409i | 0.256237 | − | 0.256237i | −0.567285 | − | 0.823522i | \(-0.692006\pi\) |
0.823522 | + | 0.567285i | \(0.192006\pi\) | |||||||
\(224\) | − | 366.111i | − | 1.63442i | ||||||
\(225\) | 37.4319 | + | 36.6865i | 0.166364 | + | 0.163051i | ||||
\(226\) | − | 653.693i | − | 2.89245i | ||||||
\(227\) | 176.929 | + | 176.929i | 0.779424 | + | 0.779424i | 0.979733 | − | 0.200309i | \(-0.0641945\pi\) |
−0.200309 | + | 0.979733i | \(0.564195\pi\) | |||||||
\(228\) | 76.1525 | − | 76.1525i | 0.334002 | − | 0.334002i | ||||
\(229\) | −110.421 | −0.482189 | −0.241094 | − | 0.970502i | \(-0.577506\pi\) | ||||
−0.241094 | + | 0.970502i | \(0.577506\pi\) | |||||||
\(230\) | −7.10240 | + | 2.98384i | −0.0308800 | + | 0.0129732i | ||||
\(231\) | 176.831 | 0.765503 | ||||||||
\(232\) | −100.440 | − | 100.440i | −0.432930 | − | 0.432930i | ||||
\(233\) | −5.66668 | − | 5.66668i | −0.0243205 | − | 0.0243205i | 0.694842 | − | 0.719162i | \(-0.255474\pi\) |
−0.719162 | + | 0.694842i | \(0.755474\pi\) | |||||||
\(234\) | −54.2870 | + | 62.2300i | −0.231996 | + | 0.265940i | ||||
\(235\) | 151.954 | − | 372.130i | 0.646611 | − | 1.58353i | ||||
\(236\) | − | 196.837i | − | 0.834056i | ||||||
\(237\) | 198.772 | − | 198.772i | 0.838702 | − | 0.838702i | ||||
\(238\) | 378.053 | + | 378.053i | 1.58846 | + | 1.58846i | ||||
\(239\) | −215.554 | −0.901901 | −0.450950 | − | 0.892549i | \(-0.648915\pi\) | ||||
−0.450950 | + | 0.892549i | \(0.648915\pi\) | |||||||
\(240\) | −49.0742 | + | 120.181i | −0.204476 | + | 0.500756i | ||||
\(241\) | 72.6956i | 0.301642i | 0.988561 | + | 0.150821i | \(0.0481917\pi\) | ||||
−0.988561 | + | 0.150821i | \(0.951808\pi\) | |||||||
\(242\) | −117.452 | − | 117.452i | −0.485339 | − | 0.485339i | ||||
\(243\) | −78.2768 | − | 78.2768i | −0.322127 | − | 0.322127i | ||||
\(244\) | − | 144.421i | − | 0.591889i | ||||||
\(245\) | −89.6164 | + | 37.6494i | −0.365781 | + | 0.153671i | ||||
\(246\) | −310.386 | −1.26173 | ||||||||
\(247\) | −102.610 | + | 6.99498i | −0.415425 | + | 0.0283198i | ||||
\(248\) | 26.1402 | + | 26.1402i | 0.105404 | + | 0.105404i | ||||
\(249\) | −32.0291 | −0.128631 | ||||||||
\(250\) | 150.204 | + | 347.694i | 0.600817 | + | 1.39078i | ||||
\(251\) | 1.33457 | 0.00531702 | 0.00265851 | − | 0.999996i | \(-0.499154\pi\) | ||||
0.00265851 | + | 0.999996i | \(0.499154\pi\) | |||||||
\(252\) | 63.5400 | + | 63.5400i | 0.252143 | + | 0.252143i | ||||
\(253\) | −2.92508 | + | 2.92508i | −0.0115616 | + | 0.0115616i | ||||
\(254\) | 137.725 | 0.542224 | ||||||||
\(255\) | −108.529 | − | 258.330i | −0.425604 | − | 1.01306i | ||||
\(256\) | 46.4233 | 0.181341 | ||||||||
\(257\) | −17.9322 | + | 17.9322i | −0.0697753 | + | 0.0697753i | −0.741133 | − | 0.671358i | \(-0.765711\pi\) |
0.671358 | + | 0.741133i | \(0.265711\pi\) | |||||||
\(258\) | −300.998 | + | 300.998i | −1.16666 | + | 1.16666i | ||||
\(259\) | 168.416i | 0.650254i | ||||||||
\(260\) | −300.886 | + | 151.251i | −1.15726 | + | 0.581735i | ||||
\(261\) | −83.2203 | −0.318852 | ||||||||
\(262\) | 149.370 | + | 149.370i | 0.570113 | + | 0.570113i | ||||
\(263\) | −131.362 | − | 131.362i | −0.499473 | − | 0.499473i | 0.411801 | − | 0.911274i | \(-0.364900\pi\) |
−0.911274 | + | 0.411801i | \(0.864900\pi\) | |||||||
\(264\) | − | 76.4868i | − | 0.289723i | ||||||
\(265\) | −132.392 | + | 324.226i | −0.499594 | + | 1.22349i | ||||
\(266\) | 198.315i | 0.745543i | ||||||||
\(267\) | 130.820 | + | 130.820i | 0.489964 | + | 0.489964i | ||||
\(268\) | −90.6814 | + | 90.6814i | −0.338363 | + | 0.338363i | ||||
\(269\) | 299.295i | 1.11262i | 0.830975 | + | 0.556310i | \(0.187783\pi\) | ||||
−0.830975 | + | 0.556310i | \(0.812217\pi\) | |||||||
\(270\) | −171.084 | − | 407.230i | −0.633645 | − | 1.50826i | ||||
\(271\) | − | 388.157i | − | 1.43231i | −0.697940 | − | 0.716156i | \(-0.745900\pi\) | ||
0.697940 | − | 0.716156i | \(-0.254100\pi\) | |||||||
\(272\) | −149.029 | + | 149.029i | −0.547900 | + | 0.547900i | ||||
\(273\) | 19.2188 | + | 281.922i | 0.0703985 | + | 1.03268i | ||||
\(274\) | − | 285.738i | − | 1.04284i | ||||||
\(275\) | 145.250 | + | 142.357i | 0.528181 | + | 0.517663i | ||||
\(276\) | 6.92202 | 0.0250798 | ||||||||
\(277\) | −136.515 | + | 136.515i | −0.492833 | + | 0.492833i | −0.909198 | − | 0.416365i | \(-0.863304\pi\) |
0.416365 | + | 0.909198i | \(0.363304\pi\) | |||||||
\(278\) | 6.30617 | − | 6.30617i | 0.0226841 | − | 0.0226841i | ||||
\(279\) | 21.6587 | 0.0776298 | ||||||||
\(280\) | 57.3307 | + | 136.463i | 0.204752 | + | 0.487370i | ||||
\(281\) | 16.8095i | 0.0598205i | 0.999553 | + | 0.0299102i | \(0.00952214\pi\) | ||||
−0.999553 | + | 0.0299102i | \(0.990478\pi\) | |||||||
\(282\) | −452.560 | + | 452.560i | −1.60482 | + | 1.60482i | ||||
\(283\) | 172.741 | + | 172.741i | 0.610391 | + | 0.610391i | 0.943048 | − | 0.332657i | \(-0.107945\pi\) |
−0.332657 | + | 0.943048i | \(0.607945\pi\) | |||||||
\(284\) | −554.103 | −1.95107 | ||||||||
\(285\) | 39.2905 | − | 96.2213i | 0.137861 | − | 0.337619i | ||||
\(286\) | −210.654 | + | 241.476i | −0.736551 | + | 0.844320i | ||||
\(287\) | 228.068 | − | 228.068i | 0.794663 | − | 0.794663i | ||||
\(288\) | −65.6044 | + | 65.6044i | −0.227793 | + | 0.227793i | ||||
\(289\) | − | 165.917i | − | 0.574108i | ||||||
\(290\) | −556.755 | − | 227.342i | −1.91984 | − | 0.783938i | ||||
\(291\) | − | 125.378i | − | 0.430852i | ||||||
\(292\) | 351.910 | + | 351.910i | 1.20517 | + | 1.20517i | ||||
\(293\) | 41.8279 | − | 41.8279i | 0.142757 | − | 0.142757i | −0.632116 | − | 0.774874i | \(-0.717814\pi\) |
0.774874 | + | 0.632116i | \(0.217814\pi\) | |||||||
\(294\) | 154.772 | 0.526436 | ||||||||
\(295\) | −73.5768 | − | 175.134i | −0.249413 | − | 0.593674i | ||||
\(296\) | 72.8468 | 0.246104 | ||||||||
\(297\) | −167.715 | − | 167.715i | −0.564697 | − | 0.564697i | ||||
\(298\) | −306.579 | − | 306.579i | −1.02879 | − | 1.02879i | ||||
\(299\) | −4.98137 | − | 4.34554i | −0.0166601 | − | 0.0145336i | ||||
\(300\) | −3.42271 | − | 340.302i | −0.0114090 | − | 1.13434i | ||||
\(301\) | − | 442.340i | − | 1.46957i | ||||||
\(302\) | 250.235 | − | 250.235i | 0.828593 | − | 0.828593i | ||||
\(303\) | 240.443 | + | 240.443i | 0.793543 | + | 0.793543i | ||||
\(304\) | −78.1756 | −0.257157 | ||||||||
\(305\) | −53.9838 | − | 128.497i | −0.176996 | − | 0.421302i | ||||
\(306\) | − | 135.489i | − | 0.442774i | ||||||
\(307\) | 74.7402 | + | 74.7402i | 0.243453 | + | 0.243453i | 0.818277 | − | 0.574824i | \(-0.194929\pi\) |
−0.574824 | + | 0.818277i | \(0.694929\pi\) | |||||||
\(308\) | 246.559 | + | 246.559i | 0.800515 | + | 0.800515i | ||||
\(309\) | − | 340.145i | − | 1.10079i | ||||||
\(310\) | 144.900 | + | 59.1675i | 0.467418 | + | 0.190863i | ||||
\(311\) | 86.8500 | 0.279260 | 0.139630 | − | 0.990204i | \(-0.455409\pi\) | ||||
0.139630 | + | 0.990204i | \(0.455409\pi\) | |||||||
\(312\) | 121.943 | − | 8.31292i | 0.390842 | − | 0.0266440i | ||||
\(313\) | −219.953 | − | 219.953i | −0.702726 | − | 0.702726i | 0.262269 | − | 0.964995i | \(-0.415529\pi\) |
−0.964995 | + | 0.262269i | \(0.915529\pi\) | |||||||
\(314\) | 647.884 | 2.06333 | ||||||||
\(315\) | 80.2849 | + | 32.7831i | 0.254873 | + | 0.104073i | ||||
\(316\) | 554.303 | 1.75412 | ||||||||
\(317\) | 180.080 | + | 180.080i | 0.568076 | + | 0.568076i | 0.931589 | − | 0.363513i | \(-0.118423\pi\) |
−0.363513 | + | 0.931589i | \(0.618423\pi\) | |||||||
\(318\) | 394.301 | − | 394.301i | 1.23994 | − | 1.23994i | ||||
\(319\) | −322.926 | −1.01231 | ||||||||
\(320\) | −435.919 | + | 183.137i | −1.36225 | + | 0.572304i | ||||
\(321\) | −422.982 | −1.31770 | ||||||||
\(322\) | −9.01308 | + | 9.01308i | −0.0279909 | + | 0.0279909i | ||||
\(323\) | 119.317 | − | 119.317i | 0.369404 | − | 0.369404i | ||||
\(324\) | 299.130i | 0.923242i | ||||||||
\(325\) | −211.174 | + | 247.044i | −0.649765 | + | 0.760135i | ||||
\(326\) | 729.723 | 2.23842 | ||||||||
\(327\) | 3.64710 | + | 3.64710i | 0.0111532 | + | 0.0111532i | ||||
\(328\) | −98.6489 | − | 98.6489i | −0.300759 | − | 0.300759i | ||||
\(329\) | − | 665.072i | − | 2.02150i | ||||||
\(330\) | −125.427 | − | 298.552i | −0.380082 | − | 0.904703i | ||||
\(331\) | − | 163.850i | − | 0.495015i | −0.968886 | − | 0.247508i | \(-0.920388\pi\) | ||
0.968886 | − | 0.247508i | \(-0.0796115\pi\) | |||||||
\(332\) | −44.6588 | − | 44.6588i | −0.134514 | − | 0.134514i | ||||
\(333\) | 30.1789 | − | 30.1789i | 0.0906274 | − | 0.0906274i | ||||
\(334\) | 493.006i | 1.47606i | ||||||||
\(335\) | −46.7866 | + | 114.579i | −0.139661 | + | 0.342027i | ||||
\(336\) | 214.788i | 0.639251i | ||||||||
\(337\) | −79.9086 | + | 79.9086i | −0.237117 | + | 0.237117i | −0.815655 | − | 0.578538i | \(-0.803623\pi\) |
0.578538 | + | 0.815655i | \(0.303623\pi\) | |||||||
\(338\) | −407.879 | − | 309.600i | −1.20674 | − | 0.915977i | ||||
\(339\) | 566.845i | 1.67211i | ||||||||
\(340\) | 208.870 | − | 511.518i | 0.614325 | − | 1.50447i | ||||
\(341\) | 84.0439 | 0.246463 | ||||||||
\(342\) | 35.5366 | − | 35.5366i | 0.103908 | − | 0.103908i | ||||
\(343\) | 172.916 | − | 172.916i | 0.504129 | − | 0.504129i | ||||
\(344\) | −191.330 | −0.556193 | ||||||||
\(345\) | 6.15879 | − | 2.58742i | 0.0178516 | − | 0.00749975i | ||||
\(346\) | 764.214i | 2.20871i | ||||||||
\(347\) | −96.4247 | + | 96.4247i | −0.277881 | + | 0.277881i | −0.832263 | − | 0.554382i | \(-0.812955\pi\) |
0.554382 | + | 0.832263i | \(0.312955\pi\) | |||||||
\(348\) | 382.092 | + | 382.092i | 1.09796 | + | 1.09796i | ||||
\(349\) | −207.740 | −0.595243 | −0.297622 | − | 0.954684i | \(-0.596193\pi\) | ||||
−0.297622 | + | 0.954684i | \(0.596193\pi\) | |||||||
\(350\) | 447.560 | + | 438.646i | 1.27874 | + | 1.25328i | ||||
\(351\) | 249.160 | − | 285.616i | 0.709858 | − | 0.813721i | ||||
\(352\) | −254.570 | + | 254.570i | −0.723209 | + | 0.723209i | ||||
\(353\) | 147.867 | − | 147.867i | 0.418886 | − | 0.418886i | −0.465934 | − | 0.884820i | \(-0.654281\pi\) |
0.884820 | + | 0.465934i | \(0.154281\pi\) | |||||||
\(354\) | 302.465i | 0.854421i | ||||||||
\(355\) | −493.007 | + | 207.121i | −1.38875 | + | 0.583439i | ||||
\(356\) | 364.810i | 1.02475i | ||||||||
\(357\) | −327.826 | − | 327.826i | −0.918280 | − | 0.918280i | ||||
\(358\) | 234.488 | − | 234.488i | 0.654994 | − | 0.654994i | ||||
\(359\) | 17.3232 | 0.0482541 | 0.0241270 | − | 0.999709i | \(-0.492319\pi\) | ||||
0.0241270 | + | 0.999709i | \(0.492319\pi\) | |||||||
\(360\) | 14.1800 | − | 34.7265i | 0.0393890 | − | 0.0964626i | ||||
\(361\) | −298.410 | −0.826620 | ||||||||
\(362\) | 377.142 | + | 377.142i | 1.04183 | + | 1.04183i | ||||
\(363\) | 101.848 | + | 101.848i | 0.280572 | + | 0.280572i | ||||
\(364\) | −366.291 | + | 419.886i | −1.00630 | + | 1.15353i | ||||
\(365\) | 444.651 | + | 181.566i | 1.21822 | + | 0.497442i | ||||
\(366\) | 221.921i | 0.606341i | ||||||||
\(367\) | 375.328 | − | 375.328i | 1.02269 | − | 1.02269i | 0.0229563 | − | 0.999736i | \(-0.492692\pi\) |
0.999736 | − | 0.0229563i | \(-0.00730785\pi\) | |||||||
\(368\) | −3.55296 | − | 3.55296i | −0.00965477 | − | 0.00965477i | ||||
\(369\) | −81.7364 | −0.221508 | ||||||||
\(370\) | 284.344 | − | 119.458i | 0.768497 | − | 0.322859i | ||||
\(371\) | 579.457i | 1.56188i | ||||||||
\(372\) | −99.4423 | − | 99.4423i | −0.267318 | − | 0.267318i | ||||
\(373\) | −20.6902 | − | 20.6902i | −0.0554698 | − | 0.0554698i | 0.678828 | − | 0.734298i | \(-0.262488\pi\) |
−0.734298 | + | 0.678828i | \(0.762488\pi\) | |||||||
\(374\) | − | 525.747i | − | 1.40574i | ||||||
\(375\) | −130.249 | − | 301.501i | −0.347329 | − | 0.804002i | ||||
\(376\) | −287.671 | −0.765083 | ||||||||
\(377\) | −35.0970 | − | 514.841i | −0.0930955 | − | 1.36562i | ||||
\(378\) | −516.782 | − | 516.782i | −1.36715 | − | 1.36715i | ||||
\(379\) | −550.791 | −1.45327 | −0.726637 | − | 0.687021i | \(-0.758918\pi\) | ||||
−0.726637 | + | 0.687021i | \(0.758918\pi\) | |||||||
\(380\) | 188.946 | − | 79.3797i | 0.497227 | − | 0.208894i | ||||
\(381\) | −119.427 | −0.313457 | ||||||||
\(382\) | −576.038 | − | 576.038i | −1.50795 | − | 1.50795i | ||||
\(383\) | −265.558 | + | 265.558i | −0.693363 | + | 0.693363i | −0.962970 | − | 0.269607i | \(-0.913106\pi\) |
0.269607 | + | 0.962970i | \(0.413106\pi\) | |||||||
\(384\) | 287.751 | 0.749351 | ||||||||
\(385\) | 311.536 | + | 127.211i | 0.809183 | + | 0.330417i | ||||
\(386\) | 794.811 | 2.05910 | ||||||||
\(387\) | −79.2642 | + | 79.2642i | −0.204817 | + | 0.204817i | ||||
\(388\) | 174.817 | − | 174.817i | 0.450559 | − | 0.450559i | ||||
\(389\) | 262.682i | 0.675275i | 0.941276 | + | 0.337638i | \(0.109628\pi\) | ||||
−0.941276 | + | 0.337638i | \(0.890372\pi\) | |||||||
\(390\) | 462.350 | − | 232.416i | 1.18551 | − | 0.595939i | ||||
\(391\) | 10.8456 | 0.0277380 | ||||||||
\(392\) | 49.1907 | + | 49.1907i | 0.125487 | + | 0.125487i | ||||
\(393\) | −129.525 | − | 129.525i | −0.329579 | − | 0.329579i | ||||
\(394\) | 93.0513i | 0.236171i | ||||||||
\(395\) | 493.186 | − | 207.196i | 1.24857 | − | 0.524547i | ||||
\(396\) | − | 88.3631i | − | 0.223139i | ||||||
\(397\) | 546.439 | + | 546.439i | 1.37642 | + | 1.37642i | 0.850588 | + | 0.525833i | \(0.176246\pi\) |
0.525833 | + | 0.850588i | \(0.323754\pi\) | |||||||
\(398\) | −142.503 | + | 142.503i | −0.358049 | + | 0.358049i | ||||
\(399\) | − | 171.967i | − | 0.430995i | ||||||
\(400\) | −172.915 | + | 176.428i | −0.432286 | + | 0.441070i | ||||
\(401\) | − | 318.719i | − | 0.794810i | −0.917643 | − | 0.397405i | \(-0.869911\pi\) | ||
0.917643 | − | 0.397405i | \(-0.130089\pi\) | |||||||
\(402\) | 139.343 | − | 139.343i | 0.346625 | − | 0.346625i | ||||
\(403\) | 9.13426 | + | 133.991i | 0.0226657 | + | 0.332484i | ||||
\(404\) | 670.509i | 1.65967i | ||||||||
\(405\) | 111.813 | + | 266.148i | 0.276083 | + | 0.657156i | ||||
\(406\) | −995.034 | −2.45082 | ||||||||
\(407\) | 117.105 | − | 117.105i | 0.287728 | − | 0.287728i | ||||
\(408\) | −141.798 | + | 141.798i | −0.347545 | + | 0.347545i | ||||
\(409\) | 213.233 | 0.521352 | 0.260676 | − | 0.965426i | \(-0.416055\pi\) | ||||
0.260676 | + | 0.965426i | \(0.416055\pi\) | |||||||
\(410\) | −546.827 | − | 223.288i | −1.33373 | − | 0.544606i | ||||
\(411\) | 247.775i | 0.602860i | ||||||||
\(412\) | 474.270 | − | 474.270i | 1.15114 | − | 1.15114i | ||||
\(413\) | −222.248 | − | 222.248i | −0.538131 | − | 0.538131i | ||||
\(414\) | 3.23016 | 0.00780231 | ||||||||
\(415\) | −56.4279 | − | 23.0414i | −0.135971 | − | 0.0555215i | ||||
\(416\) | −433.528 | − | 378.192i | −1.04213 | − | 0.909116i | ||||
\(417\) | −5.46835 | + | 5.46835i | −0.0131135 | + | 0.0131135i | ||||
\(418\) | 137.895 | − | 137.895i | 0.329893 | − | 0.329893i | ||||
\(419\) | 246.659i | 0.588685i | 0.955700 | + | 0.294343i | \(0.0951007\pi\) | ||||
−0.955700 | + | 0.294343i | \(0.904899\pi\) | |||||||
\(420\) | −218.097 | − | 519.132i | −0.519278 | − | 1.23603i | ||||
\(421\) | 587.204i | 1.39478i | 0.716690 | + | 0.697392i | \(0.245656\pi\) | ||||
−0.716690 | + | 0.697392i | \(0.754344\pi\) | |||||||
\(422\) | −47.1088 | − | 47.1088i | −0.111632 | − | 0.111632i | ||||
\(423\) | −119.176 | + | 119.176i | −0.281741 | + | 0.281741i | ||||
\(424\) | 250.639 | 0.591130 | ||||||||
\(425\) | −5.36278 | − | 533.193i | −0.0126183 | − | 1.25457i | ||||
\(426\) | 851.448 | 1.99870 | ||||||||
\(427\) | −163.065 | − | 163.065i | −0.381885 | − | 0.381885i | ||||
\(428\) | −589.771 | − | 589.771i | −1.37797 | − | 1.37797i | ||||
\(429\) | 182.667 | − | 209.394i | 0.425797 | − | 0.488097i | ||||
\(430\) | −746.823 | + | 313.753i | −1.73680 | + | 0.729659i | ||||
\(431\) | 159.391i | 0.369817i | 0.982756 | + | 0.184909i | \(0.0591989\pi\) | ||||
−0.982756 | + | 0.184909i | \(0.940801\pi\) | |||||||
\(432\) | 203.716 | − | 203.716i | 0.471564 | − | 0.471564i | ||||
\(433\) | 535.308 | + | 535.308i | 1.23628 | + | 1.23628i | 0.961511 | + | 0.274767i | \(0.0886009\pi\) |
0.274767 | + | 0.961511i | \(0.411399\pi\) | |||||||
\(434\) | 258.965 | 0.596694 | ||||||||
\(435\) | 482.786 | + | 197.138i | 1.10985 | + | 0.453191i | ||||
\(436\) | 10.1704i | 0.0233267i | ||||||||
\(437\) | 2.84462 | + | 2.84462i | 0.00650942 | + | 0.00650942i | ||||
\(438\) | −540.754 | − | 540.754i | −1.23460 | − | 1.23460i | ||||
\(439\) | 48.6760i | 0.110879i | 0.998462 | + | 0.0554396i | \(0.0176560\pi\) | ||||
−0.998462 | + | 0.0554396i | \(0.982344\pi\) | |||||||
\(440\) | 55.0238 | − | 134.752i | 0.125054 | − | 0.306254i | ||||
\(441\) | 40.7574 | 0.0924204 | ||||||||
\(442\) | 838.199 | − | 57.1405i | 1.89638 | − | 0.129277i | ||||
\(443\) | 51.4871 | + | 51.4871i | 0.116224 | + | 0.116224i | 0.762827 | − | 0.646603i | \(-0.223811\pi\) |
−0.646603 | + | 0.762827i | \(0.723811\pi\) | |||||||
\(444\) | −277.123 | −0.624150 | ||||||||
\(445\) | 136.364 | + | 324.586i | 0.306437 | + | 0.729407i | ||||
\(446\) | −244.853 | −0.548999 | ||||||||
\(447\) | 265.847 | + | 265.847i | 0.594737 | + | 0.594737i | ||||
\(448\) | −553.190 | + | 553.190i | −1.23480 | + | 1.23480i | ||||
\(449\) | −208.122 | −0.463524 | −0.231762 | − | 0.972773i | \(-0.574449\pi\) | ||||
−0.231762 | + | 0.972773i | \(0.574449\pi\) | |||||||
\(450\) | −1.59721 | − | 158.802i | −0.00354935 | − | 0.352893i | ||||
\(451\) | −317.168 | −0.703254 | ||||||||
\(452\) | −790.362 | + | 790.362i | −1.74859 | + | 1.74859i | ||||
\(453\) | −216.990 | + | 216.990i | −0.479006 | + | 0.479006i | ||||
\(454\) | − | 758.157i | − | 1.66995i | ||||||
\(455\) | −168.953 | + | 510.507i | −0.371325 | + | 1.12199i | ||||
\(456\) | −74.3828 | −0.163120 | ||||||||
\(457\) | −132.896 | − | 132.896i | −0.290800 | − | 0.290800i | 0.546596 | − | 0.837396i | \(-0.315923\pi\) |
−0.837396 | + | 0.546596i | \(0.815923\pi\) | |||||||
\(458\) | 236.582 | + | 236.582i | 0.516555 | + | 0.516555i | ||||
\(459\) | 621.852i | 1.35480i | ||||||||
\(460\) | 12.1950 | + | 4.97963i | 0.0265108 | + | 0.0108253i | ||||
\(461\) | − | 493.512i | − | 1.07052i | −0.844686 | − | 0.535262i | \(-0.820213\pi\) | ||
0.844686 | − | 0.535262i | \(-0.179787\pi\) | |||||||
\(462\) | −378.868 | − | 378.868i | −0.820061 | − | 0.820061i | ||||
\(463\) | 255.494 | − | 255.494i | 0.551823 | − | 0.551823i | −0.375144 | − | 0.926967i | \(-0.622407\pi\) |
0.926967 | + | 0.375144i | \(0.122407\pi\) | |||||||
\(464\) | − | 392.243i | − | 0.845351i | ||||||
\(465\) | −125.649 | − | 51.3067i | −0.270212 | − | 0.110337i | ||||
\(466\) | 24.2822i | 0.0521077i | ||||||||
\(467\) | 399.519 | − | 399.519i | 0.855502 | − | 0.855502i | −0.135302 | − | 0.990804i | \(-0.543201\pi\) |
0.990804 | + | 0.135302i | \(0.0432006\pi\) | |||||||
\(468\) | 140.877 | − | 9.60369i | 0.301020 | − | 0.0205207i | ||||
\(469\) | 204.776i | 0.436623i | ||||||||
\(470\) | −1122.87 | + | 471.738i | −2.38909 | + | 1.00370i | ||||
\(471\) | −561.808 | −1.19280 | ||||||||
\(472\) | −96.1314 | + | 96.1314i | −0.203668 | + | 0.203668i | ||||
\(473\) | −307.575 | + | 307.575i | −0.650263 | + | 0.650263i | ||||
\(474\) | −851.757 | −1.79695 | ||||||||
\(475\) | 138.441 | − | 141.254i | 0.291455 | − | 0.297378i | ||||
\(476\) | − | 914.187i | − | 1.92056i | ||||||
\(477\) | 103.835 | − | 103.835i | 0.217683 | − | 0.217683i | ||||
\(478\) | 461.834 | + | 461.834i | 0.966180 | + | 0.966180i | ||||
\(479\) | 52.5979 | 0.109808 | 0.0549039 | − | 0.998492i | \(-0.482515\pi\) | ||||
0.0549039 | + | 0.998492i | \(0.482515\pi\) | |||||||
\(480\) | 535.999 | − | 225.183i | 1.11666 | − | 0.469130i | ||||
\(481\) | 199.429 | + | 173.974i | 0.414613 | + | 0.361692i | ||||
\(482\) | 155.753 | − | 155.753i | 0.323140 | − | 0.323140i | ||||
\(483\) | 7.81562 | − | 7.81562i | 0.0161814 | − | 0.0161814i | ||||
\(484\) | 284.016i | 0.586810i | ||||||||
\(485\) | 90.1957 | − | 220.887i | 0.185971 | − | 0.455437i | ||||
\(486\) | 335.423i | 0.690171i | ||||||||
\(487\) | −96.3440 | − | 96.3440i | −0.197832 | − | 0.197832i | 0.601238 | − | 0.799070i | \(-0.294674\pi\) |
−0.799070 | + | 0.601238i | \(0.794674\pi\) | |||||||
\(488\) | −70.5323 | + | 70.5323i | −0.144533 | + | 0.144533i | ||||
\(489\) | −632.774 | −1.29402 | ||||||||
\(490\) | 272.672 | + | 111.341i | 0.556474 | + | 0.227228i | ||||
\(491\) | −444.562 | −0.905421 | −0.452710 | − | 0.891658i | \(-0.649543\pi\) | ||||
−0.452710 | + | 0.891658i | \(0.649543\pi\) | |||||||
\(492\) | 375.279 | + | 375.279i | 0.762761 | + | 0.762761i | ||||
\(493\) | 598.670 | + | 598.670i | 1.21434 | + | 1.21434i | ||||
\(494\) | 234.833 | + | 204.859i | 0.475371 | + | 0.414694i | ||||
\(495\) | −33.0297 | − | 78.6202i | −0.0667267 | − | 0.158829i | ||||
\(496\) | 102.084i | 0.205815i | ||||||||
\(497\) | −625.635 | + | 625.635i | −1.25882 | + | 1.25882i | ||||
\(498\) | 68.6238 | + | 68.6238i | 0.137799 | + | 0.137799i | ||||
\(499\) | 604.573 | 1.21157 | 0.605785 | − | 0.795629i | \(-0.292859\pi\) | ||||
0.605785 | + | 0.795629i | \(0.292859\pi\) | |||||||
\(500\) | 238.780 | − | 601.995i | 0.477560 | − | 1.20399i | ||||
\(501\) | − | 427.506i | − | 0.853306i | ||||||
\(502\) | −2.85938 | − | 2.85938i | −0.00569597 | − | 0.00569597i | ||||
\(503\) | 289.710 | + | 289.710i | 0.575964 | + | 0.575964i | 0.933789 | − | 0.357825i | \(-0.116482\pi\) |
−0.357825 | + | 0.933789i | \(0.616482\pi\) | |||||||
\(504\) | − | 62.0634i | − | 0.123142i | ||||||
\(505\) | 250.633 | + | 596.578i | 0.496303 | + | 1.18134i | ||||
\(506\) | 12.5342 | 0.0247712 | ||||||||
\(507\) | 353.689 | + | 268.468i | 0.697612 | + | 0.529522i | ||||
\(508\) | −166.519 | − | 166.519i | −0.327794 | − | 0.327794i | ||||
\(509\) | 725.956 | 1.42624 | 0.713119 | − | 0.701043i | \(-0.247282\pi\) | ||||
0.713119 | + | 0.701043i | \(0.247282\pi\) | |||||||
\(510\) | −320.955 | + | 786.012i | −0.629324 | + | 1.54120i | ||||
\(511\) | 794.682 | 1.55515 | ||||||||
\(512\) | −409.225 | − | 409.225i | −0.799267 | − | 0.799267i | ||||
\(513\) | −163.102 | + | 163.102i | −0.317937 | + | 0.317937i | ||||
\(514\) | 76.8412 | 0.149496 | ||||||||
\(515\) | 244.697 | − | 599.256i | 0.475139 | − | 1.16360i | ||||
\(516\) | 727.856 | 1.41057 | ||||||||
\(517\) | −462.448 | + | 462.448i | −0.894484 | + | 0.894484i | ||||
\(518\) | 360.838 | − | 360.838i | 0.696598 | − | 0.696598i | ||||
\(519\) | − | 662.683i | − | 1.27685i | ||||||
\(520\) | 220.815 | + | 73.0790i | 0.424644 | + | 0.140537i | ||||
\(521\) | −238.823 | −0.458394 | −0.229197 | − | 0.973380i | \(-0.573610\pi\) | ||||
−0.229197 | + | 0.973380i | \(0.573610\pi\) | |||||||
\(522\) | 178.303 | + | 178.303i | 0.341577 | + | 0.341577i | ||||
\(523\) | 192.082 | + | 192.082i | 0.367270 | + | 0.367270i | 0.866481 | − | 0.499211i | \(-0.166377\pi\) |
−0.499211 | + | 0.866481i | \(0.666377\pi\) | |||||||
\(524\) | − | 361.197i | − | 0.689307i | ||||||
\(525\) | −388.098 | − | 380.369i | −0.739235 | − | 0.724513i | ||||
\(526\) | 562.895i | 1.07014i | ||||||||
\(527\) | −155.808 | − | 155.808i | −0.295652 | − | 0.295652i | ||||
\(528\) | 149.350 | − | 149.350i | 0.282860 | − | 0.282860i | ||||
\(529\) | − | 528.741i | − | 0.999511i | ||||||
\(530\) | 978.323 | − | 411.011i | 1.84589 | − | 0.775492i | ||||
\(531\) | 79.6505i | 0.150001i | ||||||||
\(532\) | 239.777 | − | 239.777i | 0.450708 | − | 0.450708i | ||||
\(533\) | −34.4712 | − | 505.660i | −0.0646739 | − | 0.948706i | ||||
\(534\) | − | 560.577i | − | 1.04977i | ||||||
\(535\) | −745.196 | − | 304.289i | −1.39289 | − | 0.568764i | ||||
\(536\) | 88.5740 | 0.165250 | ||||||||
\(537\) | −203.334 | + | 203.334i | −0.378649 | + | 0.378649i | ||||
\(538\) | 641.252 | − | 641.252i | 1.19192 | − | 1.19192i | ||||
\(539\) | 158.154 | 0.293421 | ||||||||
\(540\) | −285.517 | + | 699.223i | −0.528734 | + | 1.29486i | ||||
\(541\) | − | 574.763i | − | 1.06241i | −0.847244 | − | 0.531205i | \(-0.821740\pi\) | ||
0.847244 | − | 0.531205i | \(-0.178260\pi\) | |||||||
\(542\) | −831.642 | + | 831.642i | −1.53439 | + | 1.53439i | ||||
\(543\) | −327.036 | − | 327.036i | −0.602276 | − | 0.602276i | ||||
\(544\) | 943.889 | 1.73509 | ||||||||
\(545\) | 3.80166 | + | 9.04903i | 0.00697552 | + | 0.0166037i | ||||
\(546\) | 562.853 | − | 645.207i | 1.03087 | − | 1.18170i | ||||
\(547\) | −73.3806 | + | 73.3806i | −0.134151 | + | 0.134151i | −0.770994 | − | 0.636843i | \(-0.780240\pi\) |
0.636843 | + | 0.770994i | \(0.280240\pi\) | |||||||
\(548\) | −345.477 | + | 345.477i | −0.630433 | + | 0.630433i | ||||
\(549\) | 58.4402i | 0.106448i | ||||||||
\(550\) | −6.19776 | − | 616.210i | −0.0112687 | − | 1.12038i | ||||
\(551\) | 314.043i | 0.569951i | ||||||||
\(552\) | −3.38058 | − | 3.38058i | −0.00612423 | − | 0.00612423i | ||||
\(553\) | 625.862 | − | 625.862i | 1.13176 | − | 1.13176i | ||||
\(554\) | 584.977 | 1.05592 | ||||||||
\(555\) | −246.567 | + | 103.587i | −0.444265 | + | 0.186643i | ||||
\(556\) | −15.2492 | −0.0274267 | ||||||||
\(557\) | 14.5118 | + | 14.5118i | 0.0260535 | + | 0.0260535i | 0.720014 | − | 0.693960i | \(-0.244136\pi\) |
−0.693960 | + | 0.720014i | \(0.744136\pi\) | |||||||
\(558\) | −46.4047 | − | 46.4047i | −0.0831626 | − | 0.0831626i | ||||
\(559\) | −523.795 | − | 456.938i | −0.937021 | − | 0.817420i | ||||
\(560\) | −154.517 | + | 378.407i | −0.275923 | + | 0.675728i | ||||
\(561\) | 455.898i | 0.812652i | ||||||||
\(562\) | 36.0152 | − | 36.0152i | 0.0640839 | − | 0.0640839i | ||||
\(563\) | −366.360 | − | 366.360i | −0.650729 | − | 0.650729i | 0.302440 | − | 0.953168i | \(-0.402199\pi\) |
−0.953168 | + | 0.302440i | \(0.902199\pi\) | |||||||
\(564\) | 1094.35 | 1.94034 | ||||||||
\(565\) | −407.783 | + | 998.649i | −0.721739 | + | 1.76752i | ||||
\(566\) | − | 740.208i | − | 1.30779i | ||||||
\(567\) | 337.747 | + | 337.747i | 0.595674 | + | 0.595674i | ||||
\(568\) | 270.613 | + | 270.613i | 0.476431 | + | 0.476431i | ||||
\(569\) | 125.290i | 0.220194i | 0.993921 | + | 0.110097i | \(0.0351161\pi\) | ||||
−0.993921 | + | 0.110097i | \(0.964884\pi\) | |||||||
\(570\) | −290.340 | + | 121.977i | −0.509368 | + | 0.213994i | ||||
\(571\) | 74.4532 | 0.130391 | 0.0651955 | − | 0.997873i | \(-0.479233\pi\) | ||||
0.0651955 | + | 0.997873i | \(0.479233\pi\) | |||||||
\(572\) | 546.657 | − | 37.2659i | 0.955693 | − | 0.0651502i | ||||
\(573\) | 499.507 | + | 499.507i | 0.871740 | + | 0.871740i | ||||
\(574\) | −977.292 | −1.70260 | ||||||||
\(575\) | 12.7117 | − | 0.127853i | 0.0221073 | − | 0.000222353i | ||||
\(576\) | 198.255 | 0.344193 | ||||||||
\(577\) | −733.284 | − | 733.284i | −1.27086 | − | 1.27086i | −0.945640 | − | 0.325216i | \(-0.894563\pi\) |
−0.325216 | − | 0.945640i | \(-0.605437\pi\) | |||||||
\(578\) | −355.484 | + | 355.484i | −0.615025 | + | 0.615025i | ||||
\(579\) | −689.215 | −1.19035 | ||||||||
\(580\) | 398.284 | + | 948.030i | 0.686696 | + | 1.63453i | ||||
\(581\) | −100.848 | −0.173577 | ||||||||
\(582\) | −268.628 | + | 268.628i | −0.461560 | + | 0.461560i | ||||
\(583\) | 402.917 | − | 402.917i | 0.691109 | − | 0.691109i | ||||
\(584\) | − | 343.732i | − | 0.588583i | ||||||
\(585\) | 121.754 | − | 61.2040i | 0.208127 | − | 0.104622i | ||||
\(586\) | −179.236 | −0.305863 | ||||||||
\(587\) | −176.214 | − | 176.214i | −0.300195 | − | 0.300195i | 0.540895 | − | 0.841090i | \(-0.318086\pi\) |
−0.841090 | + | 0.540895i | \(0.818086\pi\) | |||||||
\(588\) | −187.131 | − | 187.131i | −0.318249 | − | 0.318249i | ||||
\(589\) | − | 81.7321i | − | 0.138764i | ||||||
\(590\) | −217.590 | + | 532.873i | −0.368797 | + | 0.903174i | ||||
\(591\) | − | 80.6887i | − | 0.136529i | ||||||
\(592\) | 142.242 | + | 142.242i | 0.240274 | + | 0.240274i | ||||
\(593\) | −324.274 | + | 324.274i | −0.546836 | + | 0.546836i | −0.925524 | − | 0.378689i | \(-0.876375\pi\) |
0.378689 | + | 0.925524i | \(0.376375\pi\) | |||||||
\(594\) | 718.673i | 1.20989i | ||||||||
\(595\) | −341.719 | − | 813.388i | −0.574317 | − | 1.36704i | ||||
\(596\) | 741.351i | 1.24388i | ||||||||
\(597\) | 123.571 | − | 123.571i | 0.206986 | − | 0.206986i | ||||
\(598\) | 1.36227 | + | 19.9833i | 0.00227805 | + | 0.0334169i | ||||
\(599\) | 505.327i | 0.843618i | 0.906685 | + | 0.421809i | \(0.138605\pi\) | ||||
−0.906685 | + | 0.421809i | \(0.861395\pi\) | |||||||
\(600\) | −164.525 | + | 167.868i | −0.274209 | + | 0.279781i | ||||
\(601\) | 153.252 | 0.254995 | 0.127497 | − | 0.991839i | \(-0.459306\pi\) | ||||
0.127497 | + | 0.991839i | \(0.459306\pi\) | |||||||
\(602\) | −947.732 | + | 947.732i | −1.57431 | + | 1.57431i | ||||
\(603\) | 36.6944 | − | 36.6944i | 0.0608531 | − | 0.0608531i | ||||
\(604\) | −605.105 | −1.00183 | ||||||||
\(605\) | 106.164 | + | 252.700i | 0.175477 | + | 0.417686i | ||||
\(606\) | − | 1030.32i | − | 1.70020i | ||||||
\(607\) | 85.7922 | − | 85.7922i | 0.141338 | − | 0.141338i | −0.632897 | − | 0.774236i | \(-0.718135\pi\) |
0.774236 | + | 0.632897i | \(0.218135\pi\) | |||||||
\(608\) | 247.567 | + | 247.567i | 0.407182 | + | 0.407182i | ||||
\(609\) | 862.837 | 1.41681 | ||||||||
\(610\) | −159.648 | + | 390.973i | −0.261717 | + | 0.640939i | ||||
\(611\) | −787.542 | − | 687.020i | −1.28894 | − | 1.12442i | ||||
\(612\) | −163.816 | + | 163.816i | −0.267673 | + | 0.267673i | ||||
\(613\) | 196.289 | − | 196.289i | 0.320210 | − | 0.320210i | −0.528637 | − | 0.848848i | \(-0.677297\pi\) |
0.848848 | + | 0.528637i | \(0.177297\pi\) | |||||||
\(614\) | − | 320.268i | − | 0.521609i | ||||||
\(615\) | 474.177 | + | 193.623i | 0.771020 | + | 0.314834i | ||||
\(616\) | − | 240.829i | − | 0.390956i | ||||||
\(617\) | −305.676 | − | 305.676i | −0.495423 | − | 0.495423i | 0.414587 | − | 0.910010i | \(-0.363926\pi\) |
−0.910010 | + | 0.414587i | \(0.863926\pi\) | |||||||
\(618\) | −728.774 | + | 728.774i | −1.17925 | + | 1.17925i | ||||
\(619\) | −782.801 | −1.26462 | −0.632311 | − | 0.774715i | \(-0.717893\pi\) | ||||
−0.632311 | + | 0.774715i | \(0.717893\pi\) | |||||||
\(620\) | −103.656 | − | 246.732i | −0.167188 | − | 0.397955i | ||||
\(621\) | −14.8254 | −0.0238735 | ||||||||
\(622\) | −186.080 | − | 186.080i | −0.299164 | − | 0.299164i | ||||
\(623\) | 411.906 | + | 411.906i | 0.661166 | + | 0.661166i | ||||
\(624\) | 254.341 | + | 221.877i | 0.407597 | + | 0.355572i | ||||
\(625\) | −12.5711 | − | 624.874i | −0.0201137 | − | 0.999798i | ||||
\(626\) | 942.518i | 1.50562i | ||||||||
\(627\) | −119.575 | + | 119.575i | −0.190709 | + | 0.190709i | ||||
\(628\) | −783.338 | − | 783.338i | −1.24735 | − | 1.24735i | ||||
\(629\) | −434.202 | −0.690305 | ||||||||
\(630\) | −101.775 | − | 242.253i | −0.161547 | − | 0.384529i | ||||
\(631\) | 109.969i | 0.174278i | 0.996196 | + | 0.0871390i | \(0.0277724\pi\) | ||||
−0.996196 | + | 0.0871390i | \(0.972228\pi\) | |||||||
\(632\) | −270.711 | − | 270.711i | −0.428340 | − | 0.428340i | ||||
\(633\) | 40.8500 | + | 40.8500i | 0.0645340 | + | 0.0645340i | ||||
\(634\) | − | 771.658i | − | 1.21713i | ||||||
\(635\) | −210.403 | − | 85.9146i | −0.331343 | − | 0.135299i | ||||
\(636\) | −953.477 | −1.49918 | ||||||||
\(637\) | 17.1889 | + | 252.145i | 0.0269841 | + | 0.395832i | ||||
\(638\) | 691.882 | + | 691.882i | 1.08445 | + | 1.08445i | ||||
\(639\) | 224.219 | 0.350890 | ||||||||
\(640\) | 506.950 | + | 207.005i | 0.792109 | + | 0.323445i | ||||
\(641\) | 1036.39 | 1.61683 | 0.808413 | − | 0.588616i | \(-0.200327\pi\) | ||||
0.808413 | + | 0.588616i | \(0.200327\pi\) | |||||||
\(642\) | 906.256 | + | 906.256i | 1.41161 | + | 1.41161i | ||||
\(643\) | −510.295 | + | 510.295i | −0.793616 | + | 0.793616i | −0.982080 | − | 0.188464i | \(-0.939649\pi\) |
0.188464 | + | 0.982080i | \(0.439649\pi\) | |||||||
\(644\) | 21.7949 | 0.0338430 | ||||||||
\(645\) | 647.602 | − | 272.069i | 1.00403 | − | 0.421812i | ||||
\(646\) | −511.285 | −0.791463 | ||||||||
\(647\) | 821.330 | − | 821.330i | 1.26944 | − | 1.26944i | 0.323068 | − | 0.946376i | \(-0.395286\pi\) |
0.946376 | − | 0.323068i | \(-0.104714\pi\) | |||||||
\(648\) | 146.089 | − | 146.089i | 0.225447 | − | 0.225447i | ||||
\(649\) | 309.074i | 0.476231i | ||||||||
\(650\) | 981.750 | − | 76.8535i | 1.51039 | − | 0.118236i | ||||
\(651\) | −224.560 | −0.344946 | ||||||||
\(652\) | −882.288 | − | 882.288i | −1.35320 | − | 1.35320i | ||||
\(653\) | −804.144 | − | 804.144i | −1.23146 | − | 1.23146i | −0.963403 | − | 0.268058i | \(-0.913618\pi\) |
−0.268058 | − | 0.963403i | \(-0.586382\pi\) | |||||||
\(654\) | − | 15.6281i | − | 0.0238962i | ||||||
\(655\) | −135.014 | − | 321.371i | −0.206128 | − | 0.490643i | ||||
\(656\) | − | 385.249i | − | 0.587269i | ||||||
\(657\) | −142.401 | − | 142.401i | −0.216745 | − | 0.216745i | ||||
\(658\) | −1424.95 | + | 1424.95i | −2.16557 | + | 2.16557i | ||||
\(659\) | − | 74.8778i | − | 0.113623i | −0.998385 | − | 0.0568117i | \(-0.981907\pi\) | ||
0.998385 | − | 0.0568117i | \(-0.0180935\pi\) | |||||||
\(660\) | −209.321 | + | 512.621i | −0.317153 | + | 0.776699i | ||||
\(661\) | − | 374.898i | − | 0.567168i | −0.958947 | − | 0.283584i | \(-0.908477\pi\) | ||
0.958947 | − | 0.283584i | \(-0.0915234\pi\) | |||||||
\(662\) | −351.056 | + | 351.056i | −0.530295 | + | 0.530295i | ||||
\(663\) | −726.838 | + | 49.5490i | −1.09629 | + | 0.0747345i | ||||
\(664\) | 43.6209i | 0.0656942i | ||||||||
\(665\) | 123.711 | − | 302.966i | 0.186032 | − | 0.455588i | ||||
\(666\) | −129.319 | −0.194173 | ||||||||
\(667\) | −14.2727 | + | 14.2727i | −0.0213984 | + | 0.0213984i | ||||
\(668\) | 596.079 | − | 596.079i | 0.892334 | − | 0.892334i | ||||
\(669\) | 212.323 | 0.317373 | ||||||||
\(670\) | 345.733 | − | 145.248i | 0.516019 | − | 0.216789i | ||||
\(671\) | 226.770i | 0.337958i | ||||||||
\(672\) | 680.193 | − | 680.193i | 1.01219 | − | 1.01219i | ||||
\(673\) | 151.987 | + | 151.987i | 0.225835 | + | 0.225835i | 0.810950 | − | 0.585115i | \(-0.198951\pi\) |
−0.585115 | + | 0.810950i | \(0.698951\pi\) | |||||||
\(674\) | 342.415 | 0.508034 | ||||||||
\(675\) | 7.33069 | + | 728.851i | 0.0108603 | + | 1.07978i | ||||
\(676\) | 118.826 | + | 867.484i | 0.175778 | + | 1.28326i | ||||
\(677\) | 523.082 | − | 523.082i | 0.772646 | − | 0.772646i | −0.205922 | − | 0.978568i | \(-0.566019\pi\) |
0.978568 | + | 0.205922i | \(0.0660193\pi\) | |||||||
\(678\) | 1214.49 | − | 1214.49i | 1.79128 | − | 1.79128i | ||||
\(679\) | − | 394.770i | − | 0.581399i | ||||||
\(680\) | −351.824 | + | 147.807i | −0.517388 | + | 0.217364i | ||||
\(681\) | 657.430i | 0.965389i | ||||||||
\(682\) | −180.068 | − | 180.068i | −0.264029 | − | 0.264029i | ||||
\(683\) | −465.705 | + | 465.705i | −0.681853 | + | 0.681853i | −0.960417 | − | 0.278565i | \(-0.910141\pi\) |
0.278565 | + | 0.960417i | \(0.410141\pi\) | |||||||
\(684\) | −85.9325 | −0.125632 | ||||||||
\(685\) | −178.247 | + | 436.523i | −0.260215 | + | 0.637259i | ||||
\(686\) | −740.960 | −1.08012 | ||||||||
\(687\) | −205.150 | − | 205.150i | −0.298618 | − | 0.298618i | ||||
\(688\) | −373.596 | − | 373.596i | −0.543018 | − | 0.543018i | ||||
\(689\) | 686.161 | + | 598.579i | 0.995879 | + | 0.868765i | ||||
\(690\) | −18.7391 | − | 7.65182i | −0.0271581 | − | 0.0110896i | ||||
\(691\) | 446.872i | 0.646704i | 0.946279 | + | 0.323352i | \(0.104810\pi\) | ||||
−0.946279 | + | 0.323352i | \(0.895190\pi\) | |||||||
\(692\) | 923.990 | − | 923.990i | 1.33525 | − | 1.33525i | ||||
\(693\) | −99.7705 | − | 99.7705i | −0.143969 | − | 0.143969i | ||||
\(694\) | 413.188 | 0.595372 | ||||||||
\(695\) | −13.5678 | + | 5.70008i | −0.0195221 | + | 0.00820156i | ||||
\(696\) | − | 373.212i | − | 0.536224i | ||||||
\(697\) | 587.995 | + | 587.995i | 0.843608 | + | 0.843608i | ||||
\(698\) | 445.091 | + | 445.091i | 0.637667 | + | 0.637667i | ||||
\(699\) | − | 21.0561i | − | 0.0301232i | ||||||
\(700\) | −10.7769 | − | 1071.49i | −0.0153955 | − | 1.53070i | ||||
\(701\) | −605.527 | −0.863804 | −0.431902 | − | 0.901921i | \(-0.642157\pi\) | ||||
−0.431902 | + | 0.901921i | \(0.642157\pi\) | |||||||
\(702\) | −1145.78 | + | 78.1086i | −1.63217 | + | 0.111266i | ||||
\(703\) | −113.884 | − | 113.884i | −0.161997 | − | 0.161997i | ||||
\(704\) | 769.304 | 1.09276 | ||||||||
\(705\) | 973.690 | − | 409.064i | 1.38112 | − | 0.580233i | ||||
\(706\) | −633.622 | −0.897481 | ||||||||
\(707\) | 757.069 | + | 757.069i | 1.07082 | + | 1.07082i | ||||
\(708\) | 365.702 | − | 365.702i | 0.516528 | − | 0.516528i | ||||
\(709\) | 331.454 | 0.467496 | 0.233748 | − | 0.972297i | \(-0.424901\pi\) | ||||
0.233748 | + | 0.972297i | \(0.424901\pi\) | |||||||
\(710\) | 1500.05 | + | 612.523i | 2.11275 | + | 0.862708i | ||||
\(711\) | −224.300 | −0.315471 | ||||||||
\(712\) | 178.166 | − | 178.166i | 0.250234 | − | 0.250234i | ||||
\(713\) | 3.71459 | − | 3.71459i | 0.00520980 | − | 0.00520980i | ||||
\(714\) | 1404.76i | 1.96745i | ||||||||
\(715\) | 472.452 | − | 237.494i | 0.660772 | − | 0.332160i | ||||
\(716\) | −567.025 | −0.791934 | ||||||||
\(717\) | −400.476 | − | 400.476i | −0.558544 | − | 0.558544i | ||||
\(718\) | −37.1157 | − | 37.1157i | −0.0516932 | − | 0.0516932i | ||||
\(719\) | 142.878i | 0.198718i | 0.995052 | + | 0.0993591i | \(0.0316792\pi\) | ||||
−0.995052 | + | 0.0993591i | \(0.968321\pi\) | |||||||
\(720\) | 95.4962 | − | 40.1196i | 0.132634 | − | 0.0557217i | ||||
\(721\) | − | 1070.99i | − | 1.48543i | ||||||
\(722\) | 639.356 | + | 639.356i | 0.885534 | + | 0.885534i | ||||
\(723\) | −135.060 | + | 135.060i | −0.186806 | + | 0.186806i | ||||
\(724\) | − | 911.983i | − | 1.25965i | ||||||
\(725\) | 708.738 | + | 694.623i | 0.977569 | + | 0.958100i | ||||
\(726\) | − | 436.426i | − | 0.601138i | ||||||
\(727\) | −218.258 | + | 218.258i | −0.300218 | + | 0.300218i | −0.841099 | − | 0.540881i | \(-0.818091\pi\) |
0.540881 | + | 0.841099i | \(0.318091\pi\) | |||||||
\(728\) | 383.954 | − | 26.1743i | 0.527409 | − | 0.0359538i | ||||
\(729\) | − | 810.486i | − | 1.11178i | ||||||
\(730\) | −563.670 | − | 1341.70i | −0.772151 | − | 1.83794i | ||||
\(731\) | 1140.42 | 1.56008 | ||||||||
\(732\) | 268.318 | − | 268.318i | 0.366555 | − | 0.366555i | ||||
\(733\) | 541.958 | − | 541.958i | 0.739370 | − | 0.739370i | −0.233086 | − | 0.972456i | \(-0.574882\pi\) |
0.972456 | + | 0.233086i | \(0.0748824\pi\) | |||||||
\(734\) | −1608.31 | −2.19116 | ||||||||
\(735\) | −236.446 | − | 96.5490i | −0.321695 | − | 0.131359i | ||||
\(736\) | 22.5030i | 0.0305748i | ||||||||
\(737\) | 142.388 | − | 142.388i | 0.193199 | − | 0.193199i | ||||
\(738\) | 175.124 | + | 175.124i | 0.237295 | + | 0.237295i | ||||
\(739\) | 192.974 | 0.261128 | 0.130564 | − | 0.991440i | \(-0.458321\pi\) | ||||
0.130564 | + | 0.991440i | \(0.458321\pi\) | |||||||
\(740\) | −488.225 | − | 199.359i | −0.659764 | − | 0.269404i | ||||
\(741\) | −203.634 | − | 177.642i | −0.274809 | − | 0.239733i | ||||
\(742\) | 1241.51 | − | 1241.51i | 1.67320 | − | 1.67320i | ||||
\(743\) | −547.384 | + | 547.384i | −0.736722 | + | 0.736722i | −0.971942 | − | 0.235220i | \(-0.924419\pi\) |
0.235220 | + | 0.971942i | \(0.424419\pi\) | |||||||
\(744\) | 97.1313i | 0.130553i | ||||||||
\(745\) | 277.113 | + | 659.610i | 0.371964 | + | 0.885382i | ||||
\(746\) | 88.6594i | 0.118846i | ||||||||
\(747\) | 18.0713 | + | 18.0713i | 0.0241918 | + | 0.0241918i | ||||
\(748\) | −635.666 | + | 635.666i | −0.849821 | + | 0.849821i | ||||
\(749\) | −1331.82 | −1.77813 | ||||||||
\(750\) | −366.915 | + | 925.041i | −0.489220 | + | 1.23339i | ||||
\(751\) | 1416.39 | 1.88601 | 0.943004 | − | 0.332780i | \(-0.107987\pi\) | ||||
0.943004 | + | 0.332780i | \(0.107987\pi\) | |||||||
\(752\) | −561.714 | − | 561.714i | −0.746960 | − | 0.746960i | ||||
\(753\) | 2.47949 | + | 2.47949i | 0.00329281 | + | 0.00329281i | ||||
\(754\) | −1027.87 | + | 1178.26i | −1.36322 | + | 1.56268i | ||||
\(755\) | −538.385 | + | 226.185i | −0.713093 | + | 0.299583i | ||||
\(756\) | 1249.65i | 1.65298i | ||||||||
\(757\) | −130.692 | + | 130.692i | −0.172644 | + | 0.172644i | −0.788140 | − | 0.615496i | \(-0.788956\pi\) |
0.615496 | + | 0.788140i | \(0.288956\pi\) | |||||||
\(758\) | 1180.09 | + | 1180.09i | 1.55685 | + | 1.55685i | ||||
\(759\) | −10.8690 | −0.0143201 | ||||||||
\(760\) | −131.045 | − | 53.5102i | −0.172428 | − | 0.0704082i | ||||
\(761\) | 527.493i | 0.693158i | 0.938021 | + | 0.346579i | \(0.112657\pi\) | ||||
−0.938021 | + | 0.346579i | \(0.887343\pi\) | |||||||
\(762\) | 255.877 | + | 255.877i | 0.335797 | + | 0.335797i | ||||
\(763\) | 11.4834 | + | 11.4834i | 0.0150503 | + | 0.0150503i | ||||
\(764\) | 1392.94i | 1.82322i | ||||||||
\(765\) | −84.5198 | + | 206.987i | −0.110483 | + | 0.270571i | ||||
\(766\) | 1137.94 | 1.48556 | ||||||||
\(767\) | −492.756 | + | 33.5915i | −0.642446 | + | 0.0437960i | ||||
\(768\) | 86.2495 | + | 86.2495i | 0.112304 | + | 0.112304i | ||||
\(769\) | 1162.78 | 1.51206 | 0.756032 | − | 0.654535i | \(-0.227136\pi\) | ||||
0.756032 | + | 0.654535i | \(0.227136\pi\) | |||||||
\(770\) | −394.924 | − | 940.032i | −0.512888 | − | 1.22082i | ||||
\(771\) | −66.6323 | −0.0864232 | ||||||||
\(772\) | −960.984 | − | 960.984i | −1.24480 | − | 1.24480i | ||||
\(773\) | −51.0887 | + | 51.0887i | −0.0660915 | + | 0.0660915i | −0.739380 | − | 0.673288i | \(-0.764881\pi\) |
0.673288 | + | 0.739380i | \(0.264881\pi\) | |||||||
\(774\) | 339.654 | 0.438829 | ||||||||
\(775\) | −184.454 | − | 180.781i | −0.238006 | − | 0.233266i | ||||
\(776\) | −170.754 | −0.220044 | ||||||||
\(777\) | −312.898 | + | 312.898i | −0.402700 | + | 0.402700i | ||||
\(778\) | 562.807 | − | 562.807i | 0.723403 | − | 0.723403i | ||||
\(779\) | 308.443i | 0.395948i | ||||||||
\(780\) | −840.022 | − | 278.006i | −1.07695 | − | 0.356418i | ||||
\(781\) | 870.052 | 1.11402 | ||||||||
\(782\) | −23.2371 | − | 23.2371i | −0.0297149 | − | 0.0297149i | ||||
\(783\) | −818.355 | − | 818.355i | −1.04515 | − | 1.04515i | ||||
\(784\) | 192.102i | 0.245028i | ||||||||
\(785\) | −989.775 | − | 404.159i | −1.26086 | − | 0.514852i | ||||
\(786\) | 555.024i | 0.706138i | ||||||||
\(787\) | −42.2712 | − | 42.2712i | −0.0537118 | − | 0.0537118i | 0.679741 | − | 0.733453i | \(-0.262092\pi\) |
−0.733453 | + | 0.679741i | \(0.762092\pi\) | |||||||
\(788\) | 112.506 | − | 112.506i | 0.142774 | − | 0.142774i | ||||
\(789\) | − | 488.110i | − | 0.618644i | ||||||
\(790\) | −1500.60 | − | 612.745i | −1.89949 | − | 0.775627i | ||||
\(791\) | 1784.79i | 2.25637i | ||||||||
\(792\) | −43.1548 | + | 43.1548i | −0.0544884 | + | 0.0544884i | ||||
\(793\) | −361.539 | + | 24.6463i | −0.455913 | + | 0.0310799i | ||||
\(794\) | − | 2341.54i | − | 2.94904i | ||||||
\(795\) | −848.346 | + | 356.405i | −1.06710 | + | 0.448308i | ||||
\(796\) | 344.594 | 0.432907 | ||||||||
\(797\) | 58.3327 | − | 58.3327i | 0.0731903 | − | 0.0731903i | −0.669564 | − | 0.742754i | \(-0.733519\pi\) |
0.742754 | + | 0.669564i | \(0.233519\pi\) | |||||||
\(798\) | −368.447 | + | 368.447i | −0.461713 | + | 0.461713i | ||||
\(799\) | 1714.66 | 2.14601 | ||||||||
\(800\) | 1106.30 | − | 11.1270i | 1.38288 | − | 0.0139088i | ||||
\(801\) | − | 147.621i | − | 0.184296i | ||||||
\(802\) | −682.869 | + | 682.869i | −0.851457 | + | 0.851457i | ||||
\(803\) | −552.570 | − | 552.570i | −0.688132 | − | 0.688132i | ||||
\(804\) | −336.952 | −0.419095 | ||||||||
\(805\) | 19.3918 | − | 8.14683i | 0.0240892 | − | 0.0101203i | ||||
\(806\) | 267.511 | − | 306.652i | 0.331900 | − | 0.380462i | ||||
\(807\) | −556.057 | + | 556.057i | −0.689042 | + | 0.689042i | ||||
\(808\) | 327.463 | − | 327.463i | 0.405276 | − | 0.405276i | ||||
\(809\) | 1297.47i | 1.60380i | 0.597461 | + | 0.801898i | \(0.296176\pi\) | ||||
−0.597461 | + | 0.801898i | \(0.703824\pi\) | |||||||
\(810\) | 330.668 | − | 809.798i | 0.408233 | − | 0.999751i | ||||
\(811\) | − | 1185.64i | − | 1.46195i | −0.682405 | − | 0.730974i | \(-0.739066\pi\) | ||
0.682405 | − | 0.730974i | \(-0.260934\pi\) | |||||||
\(812\) | 1203.07 | + | 1203.07i | 1.48161 | + | 1.48161i | ||||
\(813\) | 721.152 | − | 721.152i | 0.887026 | − | 0.887026i | ||||
\(814\) | −501.807 | −0.616470 | ||||||||
\(815\) | −1114.80 | − | 455.211i | −1.36785 | − | 0.558542i | ||||
\(816\) | −553.758 | −0.678625 | ||||||||
\(817\) | 299.114 | + | 299.114i | 0.366113 | + | 0.366113i | ||||
\(818\) | −456.860 | − | 456.860i | −0.558509 | − | 0.558509i | ||||
\(819\) | 148.221 | − | 169.908i | 0.180978 | − | 0.207457i | ||||
\(820\) | 391.182 | + | 931.125i | 0.477051 | + | 1.13552i | ||||
\(821\) | − | 378.986i | − | 0.461615i | −0.972999 | − | 0.230807i | \(-0.925863\pi\) | ||
0.972999 | − | 0.230807i | \(-0.0741367\pi\) | |||||||
\(822\) | 530.869 | − | 530.869i | 0.645826 | − | 0.645826i | ||||
\(823\) | −879.804 | − | 879.804i | −1.06902 | − | 1.06902i | −0.997434 | − | 0.0715868i | \(-0.977194\pi\) |
−0.0715868 | − | 0.997434i | \(-0.522806\pi\) | |||||||
\(824\) | −463.248 | −0.562194 | ||||||||
\(825\) | 5.37435 | + | 534.342i | 0.00651436 | + | 0.647688i | ||||
\(826\) | 952.352i | 1.15297i | ||||||||
\(827\) | 695.484 | + | 695.484i | 0.840972 | + | 0.840972i | 0.988985 | − | 0.148014i | \(-0.0472880\pi\) |
−0.148014 | + | 0.988985i | \(0.547288\pi\) | |||||||
\(828\) | −3.90549 | − | 3.90549i | −0.00471678 | − | 0.00471678i | ||||
\(829\) | 59.4731i | 0.0717407i | 0.999356 | + | 0.0358704i | \(0.0114203\pi\) | ||||
−0.999356 | + | 0.0358704i | \(0.988580\pi\) | |||||||
\(830\) | 71.5319 | + | 170.266i | 0.0861830 | + | 0.205140i | ||||
\(831\) | −507.259 | −0.610420 | ||||||||
\(832\) | 83.6114 | + | 1226.50i | 0.100494 | + | 1.47416i | ||||
\(833\) | −293.200 | − | 293.200i | −0.351981 | − | 0.351981i | ||||
\(834\) | 23.4323 | 0.0280963 | ||||||||
\(835\) | 307.544 | − | 753.166i | 0.368316 | − | 0.901996i | ||||
\(836\) | −333.450 | −0.398864 | ||||||||
\(837\) | 212.983 | + | 212.983i | 0.254460 | + | 0.254460i | ||||
\(838\) | 528.478 | − | 528.478i | 0.630641 | − | 0.630641i | ||||
\(839\) | −1394.24 | −1.66179 | −0.830893 | − | 0.556432i | \(-0.812170\pi\) | ||||
−0.830893 | + | 0.556432i | \(0.812170\pi\) | |||||||
\(840\) | −147.020 | + | 360.048i | −0.175024 | + | 0.428629i | ||||
\(841\) | −734.696 | −0.873598 | ||||||||
\(842\) | 1258.11 | − | 1258.11i | 1.49419 | − | 1.49419i | ||||
\(843\) | −31.2303 | + | 31.2303i | −0.0370466 | + | 0.0370466i | ||||
\(844\) | 113.916i | 0.134971i | ||||||||
\(845\) | 429.986 | + | 727.418i | 0.508859 | + | 0.860850i | ||||
\(846\) | 510.680 | 0.603641 | ||||||||
\(847\) | 320.681 | + | 320.681i | 0.378608 | + | 0.378608i | ||||
\(848\) | 489.404 | + | 489.404i | 0.577127 | + | 0.577127i | ||||
\(849\) | 641.866i | 0.756026i | ||||||||
\(850\) | −1130.90 | + | 1153.88i | −1.33047 | + | 1.35750i | ||||
\(851\) | − | 10.3517i | − | 0.0121642i | ||||||
\(852\) | −1029.46 | − | 1029.46i | −1.20829 | − | 1.20829i | ||||
\(853\) | −500.786 | + | 500.786i | −0.587088 | + | 0.587088i | −0.936842 | − | 0.349754i | \(-0.886265\pi\) |
0.349754 | + | 0.936842i | \(0.386265\pi\) | |||||||
\(854\) | 698.748i | 0.818206i | ||||||||
\(855\) | −76.4575 | + | 32.1211i | −0.0894240 | + | 0.0375686i | ||||
\(856\) | 576.065i | 0.672973i | ||||||||
\(857\) | 183.439 | − | 183.439i | 0.214048 | − | 0.214048i | −0.591937 | − | 0.805984i | \(-0.701636\pi\) |
0.805984 | + | 0.591937i | \(0.201636\pi\) | |||||||
\(858\) | −840.006 | + | 57.2637i | −0.979028 | + | 0.0667409i | ||||
\(859\) | 76.4724i | 0.0890249i | 0.999009 | + | 0.0445125i | \(0.0141734\pi\) | ||||
−0.999009 | + | 0.0445125i | \(0.985827\pi\) | |||||||
\(860\) | 1282.31 | + | 523.612i | 1.49106 | + | 0.608851i | ||||
\(861\) | 847.451 | 0.984264 | ||||||||
\(862\) | 341.503 | − | 341.503i | 0.396175 | − | 0.396175i | ||||
\(863\) | 1133.00 | − | 1133.00i | 1.31286 | − | 1.31286i | 0.393557 | − | 0.919300i | \(-0.371245\pi\) |
0.919300 | − | 0.393557i | \(-0.128755\pi\) | |||||||
\(864\) | −1290.25 | −1.49335 | ||||||||
\(865\) | 476.727 | − | 1167.49i | 0.551130 | − | 1.34970i | ||||
\(866\) | − | 2293.84i | − | 2.64878i | ||||||
\(867\) | 308.256 | − | 308.256i | 0.355543 | − | 0.355543i | ||||
\(868\) | −313.108 | − | 313.108i | −0.360723 | − | 0.360723i | ||||
\(869\) | −870.368 | −1.00157 | ||||||||
\(870\) | −612.013 | − | 1456.77i | −0.703463 | − | 1.67444i | ||||
\(871\) | 242.484 | + | 211.534i | 0.278398 | + | 0.242863i | ||||
\(872\) | 4.96704 | − | 4.96704i | 0.00569614 | − | 0.00569614i | ||||
\(873\) | −70.7399 | + | 70.7399i | −0.0810308 | + | 0.0810308i | ||||
\(874\) | − | 12.1894i | − | 0.0139467i | ||||||
\(875\) | −410.105 | − | 949.316i | −0.468692 | − | 1.08493i | ||||
\(876\) | 1307.62i | 1.49272i | ||||||||
\(877\) | 125.284 | + | 125.284i | 0.142856 | + | 0.142856i | 0.774918 | − | 0.632062i | \(-0.217791\pi\) |
−0.632062 | + | 0.774918i | \(0.717791\pi\) | |||||||
\(878\) | 104.290 | − | 104.290i | 0.118782 | − | 0.118782i | ||||
\(879\) | 155.423 | 0.176818 | ||||||||
\(880\) | 370.561 | − | 155.679i | 0.421092 | − | 0.176908i | ||||
\(881\) | 508.152 | 0.576790 | 0.288395 | − | 0.957512i | \(-0.406878\pi\) | ||||
0.288395 | + | 0.957512i | \(0.406878\pi\) | |||||||
\(882\) | −87.3244 | − | 87.3244i | −0.0990073 | − | 0.0990073i | ||||
\(883\) | 164.059 | + | 164.059i | 0.185797 | + | 0.185797i | 0.793876 | − | 0.608079i | \(-0.208060\pi\) |
−0.608079 | + | 0.793876i | \(0.708060\pi\) | |||||||
\(884\) | −1082.53 | − | 944.356i | −1.22458 | − | 1.06828i | ||||
\(885\) | 188.682 | − | 462.077i | 0.213200 | − | 0.522121i | ||||
\(886\) | − | 220.627i | − | 0.249014i | ||||||
\(887\) | −999.858 | + | 999.858i | −1.12724 | + | 1.12724i | −0.136611 | + | 0.990625i | \(0.543621\pi\) |
−0.990625 | + | 0.136611i | \(0.956379\pi\) | |||||||
\(888\) | 135.341 | + | 135.341i | 0.152411 | + | 0.152411i | ||||
\(889\) | −376.032 | −0.422983 | ||||||||
\(890\) | 403.273 | − | 987.606i | 0.453116 | − | 1.10967i | ||||
\(891\) | − | 469.695i | − | 0.527154i | ||||||
\(892\) | 296.045 | + | 296.045i | 0.331889 | + | 0.331889i | ||||
\(893\) | 449.727 | + | 449.727i | 0.503614 | + | 0.503614i | ||||
\(894\) | − | 1139.18i | − | 1.27425i | ||||||
\(895\) | −504.505 | + | 211.951i | −0.563692 | + | 0.236817i | ||||
\(896\) | 906.022 | 1.01119 | ||||||||
\(897\) | −1.18129 | − | 17.3284i | −0.00131693 | − | 0.0193181i | ||||
\(898\) | 445.911 | + | 445.911i | 0.496560 | + | 0.496560i | ||||
\(899\) | 410.087 | 0.456159 | ||||||||
\(900\) | −190.072 | + | 193.934i | −0.211191 | + | 0.215482i | ||||
\(901\) | −1493.93 | −1.65808 | ||||||||
\(902\) | 679.545 | + | 679.545i | 0.753376 | + | 0.753376i | ||||
\(903\) | 821.819 | − | 821.819i | 0.910099 | − | 0.910099i | ||||
\(904\) | 771.994 | 0.853976 | ||||||||
\(905\) | −340.895 | − | 811.428i | −0.376679 | − | 0.896605i | ||||
\(906\) | 929.819 | 1.02629 | ||||||||
\(907\) | −781.132 | + | 781.132i | −0.861226 | + | 0.861226i | −0.991481 | − | 0.130255i | \(-0.958420\pi\) |
0.130255 | + | 0.991481i | \(0.458420\pi\) | |||||||
\(908\) | −916.666 | + | 916.666i | −1.00954 | + | 1.00954i | ||||
\(909\) | − | 271.323i | − | 0.298485i | ||||||
\(910\) | 1455.77 | − | 731.794i | 1.59975 | − | 0.804169i | ||||
\(911\) | −484.480 | −0.531811 | −0.265906 | − | 0.963999i | \(-0.585671\pi\) | ||||
−0.265906 | + | 0.963999i | \(0.585671\pi\) | |||||||
\(912\) | −145.242 | − | 145.242i | −0.159256 | − | 0.159256i | ||||
\(913\) | 70.1232 | + | 70.1232i | 0.0768053 | + | 0.0768053i | ||||
\(914\) | 569.469i | 0.623052i | ||||||||
\(915\) | 138.437 | − | 339.029i | 0.151297 | − | 0.370524i | ||||
\(916\) | − | 572.090i | − | 0.624552i | ||||||
\(917\) | −407.826 | − | 407.826i | −0.444740 | − | 0.444740i | ||||
\(918\) | 1332.34 | − | 1332.34i | 1.45135 | − | 1.45135i | ||||
\(919\) | 1462.32i | 1.59121i | 0.605816 | + | 0.795605i | \(0.292847\pi\) | ||||
−0.605816 | + | 0.795605i | \(0.707153\pi\) | |||||||
\(920\) | −3.52384 | − | 8.38774i | −0.00383026 | − | 0.00911711i | ||||
\(921\) | 277.718i | 0.301540i | ||||||||
\(922\) | −1057.37 | + | 1057.37i | −1.14682 | + | 1.14682i | ||||
\(923\) | 94.5611 | + | 1387.12i | 0.102450 | + | 1.50284i | ||||
\(924\) | 916.158i | 0.991513i | ||||||||
\(925\) | −508.913 | + | 5.11858i | −0.550176 | + | 0.00553360i | ||||
\(926\) | −1094.81 | −1.18230 | ||||||||
\(927\) | −191.914 | + | 191.914i | −0.207027 | + | 0.207027i | ||||
\(928\) | −1242.16 | + | 1242.16i | −1.33853 | + | 1.33853i | ||||
\(929\) | −93.0218 | −0.100131 | −0.0500656 | − | 0.998746i | \(-0.515943\pi\) | ||||
−0.0500656 | + | 0.998746i | \(0.515943\pi\) | |||||||
\(930\) | 159.281 | + | 379.134i | 0.171270 | + | 0.407671i | ||||
\(931\) | − | 153.803i | − | 0.165202i | ||||||
\(932\) | 29.3589 | − | 29.3589i | 0.0315010 | − | 0.0315010i | ||||
\(933\) | 161.358 | + | 161.358i | 0.172945 | + | 0.172945i | ||||
\(934\) | −1711.97 | −1.83295 | ||||||||
\(935\) | −327.968 | + | 803.186i | −0.350768 | + | 0.859023i | ||||
\(936\) | −73.4920 | − | 64.1115i | −0.0785171 | − | 0.0684952i | ||||
\(937\) | −714.871 | + | 714.871i | −0.762936 | + | 0.762936i | −0.976852 | − | 0.213916i | \(-0.931378\pi\) |
0.213916 | + | 0.976852i | \(0.431378\pi\) | |||||||
\(938\) | 438.741 | − | 438.741i | 0.467741 | − | 0.467741i | ||||
\(939\) | − | 817.298i | − | 0.870391i | ||||||
\(940\) | 1928.00 | + | 787.267i | 2.05106 | + | 0.837519i | ||||
\(941\) | 891.314i | 0.947199i | 0.880740 | + | 0.473599i | \(0.157046\pi\) | ||||
−0.880740 | + | 0.473599i | \(0.842954\pi\) | |||||||
\(942\) | 1203.70 | + | 1203.70i | 1.27781 | + | 1.27781i | ||||
\(943\) | −14.0182 | + | 14.0182i | −0.0148656 | + | 0.0148656i | ||||
\(944\) | −375.417 | −0.397688 | ||||||||
\(945\) | 467.114 | + | 1111.87i | 0.494301 | + | 1.17658i | ||||
\(946\) | 1317.98 | 1.39322 | ||||||||
\(947\) | 256.254 | + | 256.254i | 0.270596 | + | 0.270596i | 0.829340 | − | 0.558744i | \(-0.188717\pi\) |
−0.558744 | + | 0.829340i | \(0.688717\pi\) | |||||||
\(948\) | 1029.83 | + | 1029.83i | 1.08632 | + | 1.08632i | ||||
\(949\) | 820.906 | − | 941.018i | 0.865023 | − | 0.991589i | ||||
\(950\) | −599.260 | + | 6.02728i | −0.630800 | + | 0.00634450i | ||||
\(951\) | 669.138i | 0.703615i | ||||||||
\(952\) | −446.471 | + | 446.471i | −0.468982 | + | 0.468982i | ||||
\(953\) | 263.391 | + | 263.391i | 0.276381 | + | 0.276381i | 0.831663 | − | 0.555281i | \(-0.187389\pi\) |
−0.555281 | + | 0.831663i | \(0.687389\pi\) | |||||||
\(954\) | −444.940 | −0.466394 | ||||||||
\(955\) | 520.675 | + | 1239.36i | 0.545209 | + | 1.29775i | ||||
\(956\) | − | 1116.78i | − | 1.16818i | ||||||
\(957\) | −599.961 | − | 599.961i | −0.626918 | − | 0.626918i | ||||
\(958\) | −112.693 | − | 112.693i | −0.117634 | − | 0.117634i | ||||
\(959\) | 780.155i | 0.813508i | ||||||||
\(960\) | −1150.14 | − | 469.641i | −1.19806 | − | 0.489209i | ||||
\(961\) | 854.272 | 0.888940 | ||||||||
\(962\) | −54.5385 | − | 800.030i | −0.0566929 | − | 0.831632i | ||||
\(963\) | 238.652 | + | 238.652i | 0.247821 | + | 0.247821i | ||||
\(964\) | −376.634 | −0.390699 | ||||||||
\(965\) | −1214.24 | − | 495.814i | −1.25828 | − | 0.513797i | ||||
\(966\) | −33.4906 | −0.0346694 | ||||||||
\(967\) | −480.135 | − | 480.135i | −0.496521 | − | 0.496521i | 0.413832 | − | 0.910353i | \(-0.364190\pi\) |
−0.910353 | + | 0.413832i | \(0.864190\pi\) | |||||||
\(968\) | 138.708 | − | 138.708i | 0.143293 | − | 0.143293i | ||||
\(969\) | 443.357 | 0.457541 | ||||||||
\(970\) | −666.508 | + | 280.012i | −0.687121 | + | 0.288672i | ||||
\(971\) | −330.493 | −0.340364 | −0.170182 | − | 0.985413i | \(-0.554435\pi\) | ||||
−0.170182 | + | 0.985413i | \(0.554435\pi\) | |||||||
\(972\) | 405.550 | − | 405.550i | 0.417233 | − | 0.417233i | ||||
\(973\) | −17.2178 | + | 17.2178i | −0.0176956 | + | 0.0176956i | ||||
\(974\) | 412.842i | 0.423863i | ||||||||
\(975\) | −851.318 | + | 66.6430i | −0.873146 | + | 0.0683518i | ||||
\(976\) | −275.447 | −0.282220 | ||||||||
\(977\) | 562.631 | + | 562.631i | 0.575876 | + | 0.575876i | 0.933764 | − | 0.357888i | \(-0.116503\pi\) |
−0.357888 | + | 0.933764i | \(0.616503\pi\) | |||||||
\(978\) | 1355.75 | + | 1355.75i | 1.38624 | + | 1.38624i | ||||
\(979\) | − | 572.826i | − | 0.585113i | ||||||
\(980\) | −195.061 | − | 464.300i | −0.199042 | − | 0.473776i | ||||
\(981\) | − | 4.11548i | − | 0.00419519i | ||||||
\(982\) | 952.492 | + | 952.492i | 0.969951 | + | 0.969951i | ||||
\(983\) | 610.708 | − | 610.708i | 0.621270 | − | 0.621270i | −0.324586 | − | 0.945856i | \(-0.605225\pi\) |
0.945856 | + | 0.324586i | \(0.105225\pi\) | |||||||
\(984\) | − | 366.557i | − | 0.372518i | ||||||
\(985\) | 58.0467 | − | 142.155i | 0.0589306 | − | 0.144320i | ||||
\(986\) | − | 2565.35i | − | 2.60178i | ||||||
\(987\) | 1235.63 | − | 1235.63i | 1.25191 | − | 1.25191i | ||||
\(988\) | −36.2408 | − | 531.619i | −0.0366810 | − | 0.538076i | ||||
\(989\) | 27.1885i | 0.0274909i | ||||||||
\(990\) | −97.6795 | + | 239.215i | −0.0986661 | + | 0.241631i | ||||
\(991\) | 5.75936 | 0.00581166 | 0.00290583 | − | 0.999996i | \(-0.499075\pi\) | ||||
0.00290583 | + | 0.999996i | \(0.499075\pi\) | |||||||
\(992\) | 323.281 | − | 323.281i | 0.325888 | − | 0.325888i | ||||
\(993\) | 304.415 | − | 304.415i | 0.306561 | − | 0.306561i | ||||
\(994\) | 2680.90 | 2.69708 | ||||||||
\(995\) | 306.599 | − | 128.808i | 0.308139 | − | 0.129455i | ||||
\(996\) | − | 165.942i | − | 0.166609i | ||||||
\(997\) | 609.083 | − | 609.083i | 0.610916 | − | 0.610916i | −0.332269 | − | 0.943185i | \(-0.607814\pi\) |
0.943185 | + | 0.332269i | \(0.107814\pi\) | |||||||
\(998\) | −1295.32 | − | 1295.32i | −1.29792 | − | 1.29792i | ||||
\(999\) | 593.535 | 0.594129 |
(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 | 65.3.h.a.38.2 | yes | 24 | |
5.2 | odd | 4 | inner | 65.3.h.a.12.11 | yes | 24 | |
5.3 | odd | 4 | 325.3.h.b.207.2 | 24 | |||
5.4 | even | 2 | 325.3.h.b.168.11 | 24 | |||
13.12 | even | 2 | inner | 65.3.h.a.38.11 | yes | 24 | |
65.12 | odd | 4 | inner | 65.3.h.a.12.2 | ✓ | 24 | |
65.38 | odd | 4 | 325.3.h.b.207.11 | 24 | |||
65.64 | even | 2 | 325.3.h.b.168.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.3.h.a.12.2 | ✓ | 24 | 65.12 | odd | 4 | inner | |
65.3.h.a.12.11 | yes | 24 | 5.2 | odd | 4 | inner | |
65.3.h.a.38.2 | yes | 24 | 1.1 | even | 1 | trivial | |
65.3.h.a.38.11 | yes | 24 | 13.12 | even | 2 | inner | |
325.3.h.b.168.2 | 24 | 65.64 | even | 2 | |||
325.3.h.b.168.11 | 24 | 5.4 | even | 2 | |||
325.3.h.b.207.2 | 24 | 5.3 | odd | 4 | |||
325.3.h.b.207.11 | 24 | 65.38 | odd | 4 |