Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(37,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.y (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 181.4 | ||
Character | \(\chi\) | \(=\) | 432.181 |
Dual form | 432.2.y.e.253.4 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.24122 | − | 0.677764i | −0.877677 | − | 0.479252i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.08127 | + | 1.68251i | 0.540636 | + | 0.841257i | ||||
\(5\) | −1.10094 | + | 4.10876i | −0.492355 | + | 1.83750i | 0.0520092 | + | 0.998647i | \(0.483437\pi\) |
−0.544365 | + | 0.838849i | \(0.683229\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.63313 | + | 0.942891i | 0.617267 | + | 0.356379i | 0.775804 | − | 0.630974i | \(-0.217344\pi\) |
−0.158537 | + | 0.987353i | \(0.550678\pi\) | |||||||
\(8\) | −0.201751 | − | 2.82122i | −0.0713297 | − | 0.997453i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.15129 | − | 4.35372i | 1.31275 | − | 1.37677i | ||||
\(11\) | 1.18389 | − | 0.317223i | 0.356957 | − | 0.0956464i | −0.0758838 | − | 0.997117i | \(-0.524178\pi\) |
0.432841 | + | 0.901470i | \(0.357511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.31428 | − | 0.620109i | −0.641865 | − | 0.171987i | −0.0768171 | − | 0.997045i | \(-0.524476\pi\) |
−0.565048 | + | 0.825058i | \(0.691142\pi\) | |||||||
\(14\) | −1.38803 | − | 2.27722i | −0.370966 | − | 0.608612i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.66171 | + | 3.63851i | −0.415426 | + | 0.909627i | ||||
\(17\) | −3.44622 | −0.835831 | −0.417915 | − | 0.908486i | \(-0.637239\pi\) | ||||
−0.417915 | + | 0.908486i | \(0.637239\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.17726 | + | 4.17726i | −0.958328 | + | 0.958328i | −0.999166 | − | 0.0408377i | \(-0.986997\pi\) |
0.0408377 | + | 0.999166i | \(0.486997\pi\) | |||||||
\(20\) | −8.10347 | + | 2.59034i | −1.81199 | + | 0.579218i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.68448 | − | 0.408656i | −0.359132 | − | 0.0871257i | ||||
\(23\) | 1.34867 | − | 0.778655i | 0.281217 | − | 0.162361i | −0.352757 | − | 0.935715i | \(-0.614756\pi\) |
0.633974 | + | 0.773354i | \(0.281422\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.3397 | − | 6.54701i | −2.26795 | − | 1.30940i | ||||
\(26\) | 2.45225 | + | 2.33823i | 0.480925 | + | 0.458564i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.179434 | + | 3.76729i | 0.0339099 | + | 0.711951i | ||||
\(29\) | 0.343336 | + | 1.28135i | 0.0637558 | + | 0.237940i | 0.990449 | − | 0.137878i | \(-0.0440283\pi\) |
−0.926693 | + | 0.375818i | \(0.877362\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.25840 | + | 2.17961i | 0.226015 | + | 0.391469i | 0.956623 | − | 0.291327i | \(-0.0940969\pi\) |
−0.730609 | + | 0.682796i | \(0.760764\pi\) | |||||||
\(32\) | 4.52860 | − | 3.38996i | 0.800551 | − | 0.599265i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.27753 | + | 2.33572i | 0.733590 | + | 0.400573i | ||||
\(35\) | −5.67210 | + | 5.67210i | −0.958760 | + | 0.958760i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.77154 | + | 5.77154i | 0.948836 | + | 0.948836i | 0.998753 | − | 0.0499178i | \(-0.0158959\pi\) |
−0.0499178 | + | 0.998753i | \(0.515896\pi\) | |||||||
\(38\) | 8.01610 | − | 2.35371i | 1.30038 | − | 0.381823i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 11.8139 | + | 2.27705i | 1.86793 | + | 0.360033i | ||||
\(41\) | 3.43245 | − | 1.98173i | 0.536058 | − | 0.309493i | −0.207422 | − | 0.978252i | \(-0.566507\pi\) |
0.743480 | + | 0.668758i | \(0.233174\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.96053 | + | 0.793272i | −0.451477 | + | 0.120973i | −0.477390 | − | 0.878691i | \(-0.658417\pi\) |
0.0259136 | + | 0.999664i | \(0.491751\pi\) | |||||||
\(44\) | 1.81384 | + | 1.64891i | 0.273447 | + | 0.248583i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.20175 | + | 0.0524044i | −0.324630 | + | 0.00772660i | ||||
\(47\) | −0.230692 | + | 0.399570i | −0.0336498 | + | 0.0582832i | −0.882360 | − | 0.470575i | \(-0.844046\pi\) |
0.848710 | + | 0.528858i | \(0.177380\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.72191 | − | 2.98244i | −0.245988 | − | 0.426063i | ||||
\(50\) | 9.63783 | + | 15.8120i | 1.36300 | + | 2.23615i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.45902 | − | 4.56431i | −0.202330 | − | 0.632956i | ||||
\(53\) | −5.61507 | − | 5.61507i | −0.771289 | − | 0.771289i | 0.207043 | − | 0.978332i | \(-0.433616\pi\) |
−0.978332 | + | 0.207043i | \(0.933616\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.21358i | 0.702999i | ||||||||
\(56\) | 2.33062 | − | 4.79766i | 0.311442 | − | 0.641115i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.442294 | − | 1.82314i | 0.0580761 | − | 0.239390i | ||||
\(59\) | −2.92766 | + | 10.9262i | −0.381148 | + | 1.42247i | 0.463001 | + | 0.886358i | \(0.346773\pi\) |
−0.844150 | + | 0.536108i | \(0.819894\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.27078 | + | 4.74261i | 0.162707 | + | 0.607229i | 0.998322 | + | 0.0579138i | \(0.0184448\pi\) |
−0.835615 | + | 0.549316i | \(0.814888\pi\) | |||||||
\(62\) | −0.0846915 | − | 3.55828i | −0.0107558 | − | 0.451902i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.91859 | + | 1.13837i | −0.989824 | + | 0.142296i | ||||
\(65\) | 5.09576 | − | 8.82612i | 0.632052 | − | 1.09475i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.286572 | + | 0.0767867i | 0.0350103 | + | 0.00938099i | 0.276282 | − | 0.961077i | \(-0.410898\pi\) |
−0.241271 | + | 0.970458i | \(0.577564\pi\) | |||||||
\(68\) | −3.72630 | − | 5.79831i | −0.451880 | − | 0.703148i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 10.8847 | − | 3.19600i | 1.30097 | − | 0.381995i | ||||
\(71\) | 13.9935i | 1.66073i | 0.557221 | + | 0.830364i | \(0.311867\pi\) | ||||
−0.557221 | + | 0.830364i | \(0.688133\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.0279090i | 0.00326650i | 0.999999 | + | 0.00163325i | \(0.000519880\pi\) | ||||
−0.999999 | + | 0.00163325i | \(0.999480\pi\) | |||||||
\(74\) | −3.25203 | − | 11.0755i | −0.378040 | − | 1.28750i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.5450 | − | 2.51154i | −1.32431 | − | 0.288094i | ||||
\(77\) | 2.23256 | + | 0.598214i | 0.254424 | + | 0.0681728i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.19067 | − | 3.79435i | 0.246470 | − | 0.426898i | −0.716074 | − | 0.698024i | \(-0.754063\pi\) |
0.962544 | + | 0.271126i | \(0.0873960\pi\) | |||||||
\(80\) | −13.1203 | − | 10.8333i | −1.46690 | − | 1.21120i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.60358 | + | 0.133372i | −0.618812 | + | 0.0147285i | ||||
\(83\) | 0.915902 | + | 3.41819i | 0.100533 | + | 0.375195i | 0.997800 | − | 0.0662931i | \(-0.0211172\pi\) |
−0.897267 | + | 0.441489i | \(0.854451\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.79408 | − | 14.1597i | 0.411526 | − | 1.53584i | ||||
\(86\) | 4.21233 | + | 1.02191i | 0.454227 | + | 0.110196i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.13381 | − | 3.27603i | −0.120864 | − | 0.349226i | ||||
\(89\) | 4.74894i | 0.503386i | 0.967807 | + | 0.251693i | \(0.0809874\pi\) | ||||
−0.967807 | + | 0.251693i | \(0.919013\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.19483 | − | 3.19483i | −0.334909 | − | 0.334909i | ||||
\(92\) | 2.76838 | + | 1.42722i | 0.288623 | + | 0.148798i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.557154 | − | 0.339601i | 0.0574660 | − | 0.0350271i | ||||
\(95\) | −12.5645 | − | 21.7623i | −1.28909 | − | 2.23276i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.17352 | − | 7.22875i | 0.423757 | − | 0.733968i | −0.572547 | − | 0.819872i | \(-0.694045\pi\) |
0.996303 | + | 0.0859041i | \(0.0273779\pi\) | |||||||
\(98\) | 0.115887 | + | 4.86893i | 0.0117063 | + | 0.491836i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.24591 | − | 26.1584i | −0.124591 | − | 2.61584i | ||||
\(101\) | 7.20785 | − | 1.93134i | 0.717208 | − | 0.192175i | 0.118282 | − | 0.992980i | \(-0.462261\pi\) |
0.598926 | + | 0.800805i | \(0.295594\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.2204 | − | 7.05547i | 1.20411 | − | 0.695196i | 0.242647 | − | 0.970115i | \(-0.421984\pi\) |
0.961468 | + | 0.274919i | \(0.0886509\pi\) | |||||||
\(104\) | −1.28256 | + | 6.65420i | −0.125765 | + | 0.652498i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.16386 | + | 10.7753i | 0.307302 | + | 1.04659i | ||||
\(107\) | 3.84992 | + | 3.84992i | 0.372186 | + | 0.372186i | 0.868273 | − | 0.496087i | \(-0.165230\pi\) |
−0.496087 | + | 0.868273i | \(0.665230\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.08616 | − | 2.08616i | 0.199818 | − | 0.199818i | −0.600104 | − | 0.799922i | \(-0.704874\pi\) |
0.799922 | + | 0.600104i | \(0.204874\pi\) | |||||||
\(110\) | 3.53358 | − | 6.47122i | 0.336914 | − | 0.617007i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.14450 | + | 4.37536i | −0.580601 | + | 0.413433i | ||||
\(113\) | 2.04799 | + | 3.54722i | 0.192658 | + | 0.333694i | 0.946130 | − | 0.323786i | \(-0.104956\pi\) |
−0.753472 | + | 0.657480i | \(0.771622\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.71451 | + | 6.39862i | 0.159878 | + | 0.596674i | ||||
\(116\) | −1.78464 | + | 1.96315i | −0.165700 | + | 0.182274i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.0392 | − | 11.5775i | 1.01624 | − | 1.06580i | ||||
\(119\) | −5.62814 | − | 3.24941i | −0.515931 | − | 0.297873i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.22531 | + | 4.74888i | −0.747755 | + | 0.431717i | ||||
\(122\) | 1.63705 | − | 6.74793i | 0.148212 | − | 0.610929i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.30655 | + | 4.47402i | −0.207134 | + | 0.401779i | ||||
\(125\) | 24.3454 | − | 24.3454i | 2.17752 | − | 2.17752i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.89832 | 0.434656 | 0.217328 | − | 0.976099i | \(-0.430266\pi\) | ||||
0.217328 | + | 0.976099i | \(0.430266\pi\) | |||||||
\(128\) | 10.6003 | + | 3.95397i | 0.936942 | + | 0.349485i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.3070 | + | 7.50146i | −1.07940 | + | 0.657922i | ||||
\(131\) | 17.7751 | + | 4.76283i | 1.55302 | + | 0.416130i | 0.930446 | − | 0.366430i | \(-0.119420\pi\) |
0.622574 | + | 0.782561i | \(0.286087\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.7607 | + | 2.88332i | −0.933072 | + | 0.250016i | ||||
\(134\) | −0.303657 | − | 0.289538i | −0.0262319 | − | 0.0250123i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.695278 | + | 9.72255i | 0.0596196 | + | 0.833702i | ||||
\(137\) | −13.4198 | − | 7.74793i | −1.14653 | − | 0.661950i | −0.198492 | − | 0.980103i | \(-0.563604\pi\) |
−0.948040 | + | 0.318153i | \(0.896938\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.90836 | + | 7.12209i | −0.161865 | + | 0.604088i | 0.836555 | + | 0.547884i | \(0.184566\pi\) |
−0.998419 | + | 0.0562039i | \(0.982100\pi\) | |||||||
\(140\) | −15.6765 | − | 3.41031i | −1.32490 | − | 0.288224i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.48432 | − | 17.3691i | 0.795907 | − | 1.45758i | ||||
\(143\) | −2.93657 | −0.245568 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.64274 | −0.468604 | ||||||||
\(146\) | 0.0189157 | − | 0.0346413i | 0.00156548 | − | 0.00286694i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.47010 | + | 15.9513i | −0.285240 | + | 1.31119i | ||||
\(149\) | 1.99897 | − | 7.46026i | 0.163762 | − | 0.611168i | −0.834433 | − | 0.551110i | \(-0.814205\pi\) |
0.998195 | − | 0.0600585i | \(-0.0191287\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.36540 | + | 1.94301i | 0.273872 | + | 0.158120i | 0.630646 | − | 0.776071i | \(-0.282790\pi\) |
−0.356774 | + | 0.934191i | \(0.616123\pi\) | |||||||
\(152\) | 12.6277 | + | 10.9422i | 1.02424 | + | 0.887530i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.36566 | − | 2.25567i | −0.190631 | − | 0.181767i | ||||
\(155\) | −10.3409 | + | 2.77084i | −0.830602 | + | 0.222559i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.23351 | + | 1.67026i | 0.497488 | + | 0.133302i | 0.498834 | − | 0.866698i | \(-0.333762\pi\) |
−0.00134577 | + | 0.999999i | \(0.500428\pi\) | |||||||
\(158\) | −5.29079 | + | 3.22488i | −0.420913 | + | 0.256558i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.94281 | + | 22.3391i | 0.706991 | + | 1.76606i | ||||
\(161\) | 2.93675 | 0.231448 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.5783 | − | 10.5783i | 0.828556 | − | 0.828556i | −0.158761 | − | 0.987317i | \(-0.550750\pi\) |
0.987317 | + | 0.158761i | \(0.0507499\pi\) | |||||||
\(164\) | 7.04569 | + | 3.63236i | 0.550176 | + | 0.283640i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.17989 | − | 4.86351i | 0.0915773 | − | 0.377481i | ||||
\(167\) | 18.7147 | − | 10.8050i | 1.44819 | − | 0.836112i | 0.449815 | − | 0.893122i | \(-0.351490\pi\) |
0.998374 | + | 0.0570092i | \(0.0181564\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.28698 | − | 3.62979i | −0.483614 | − | 0.279215i | ||||
\(170\) | −14.3062 | + | 15.0039i | −1.09724 | + | 1.15074i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.53583 | − | 4.12339i | −0.345854 | − | 0.314406i | ||||
\(173\) | 5.00981 | + | 18.6969i | 0.380889 | + | 1.42150i | 0.844546 | + | 0.535483i | \(0.179870\pi\) |
−0.463657 | + | 0.886015i | \(0.653463\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.3462 | − | 21.3843i | −0.933287 | − | 1.61650i | ||||
\(176\) | −0.813064 | + | 4.83474i | −0.0612870 | + | 0.364432i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.21866 | − | 5.89449i | 0.241249 | − | 0.441811i | ||||
\(179\) | 2.88152 | − | 2.88152i | 0.215375 | − | 0.215375i | −0.591171 | − | 0.806546i | \(-0.701334\pi\) |
0.806546 | + | 0.591171i | \(0.201334\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.50186 | − | 9.50186i | −0.706268 | − | 0.706268i | 0.259480 | − | 0.965748i | \(-0.416449\pi\) |
−0.965748 | + | 0.259480i | \(0.916449\pi\) | |||||||
\(182\) | 1.80016 | + | 6.13084i | 0.133437 | + | 0.454448i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.46885 | − | 3.64780i | −0.182006 | − | 0.268920i | ||||
\(185\) | −30.0680 | + | 17.3598i | −2.21065 | + | 1.27632i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.07996 | + | 1.09322i | −0.298356 | + | 0.0799442i | ||||
\(188\) | −0.921721 | + | 0.0439012i | −0.0672234 | + | 0.00320182i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.845602 | + | 35.5276i | 0.0613464 | + | 2.57744i | ||||
\(191\) | −2.36417 | + | 4.09487i | −0.171066 | + | 0.296294i | −0.938793 | − | 0.344483i | \(-0.888054\pi\) |
0.767727 | + | 0.640777i | \(0.221388\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.76542 | + | 16.9142i | 0.702931 | + | 1.21751i | 0.967433 | + | 0.253127i | \(0.0814589\pi\) |
−0.264503 | + | 0.964385i | \(0.585208\pi\) | |||||||
\(194\) | −10.0797 | + | 6.14383i | −0.723677 | + | 0.441101i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.15615 | − | 6.12198i | 0.225439 | − | 0.437284i | ||||
\(197\) | −6.89966 | − | 6.89966i | −0.491581 | − | 0.491581i | 0.417223 | − | 0.908804i | \(-0.363003\pi\) |
−0.908804 | + | 0.417223i | \(0.863003\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.4752i | 1.73500i | 0.497438 | + | 0.867500i | \(0.334274\pi\) | ||||
−0.497438 | + | 0.867500i | \(0.665726\pi\) | |||||||
\(200\) | −16.1828 | + | 33.3128i | −1.14429 | + | 2.35557i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.2555 | − | 2.48800i | −0.721578 | − | 0.175055i | ||||
\(203\) | −0.647456 | + | 2.41634i | −0.0454425 | + | 0.169594i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.36352 | + | 16.2849i | 0.304762 | + | 1.13739i | ||||
\(206\) | −19.9502 | + | 0.474841i | −1.39000 | + | 0.0330837i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.10192 | − | 7.39008i | 0.423092 | − | 0.512410i | ||||
\(209\) | −3.62030 | + | 6.27055i | −0.250422 | + | 0.433743i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.1840 | + | 5.67623i | 1.45837 | + | 0.390768i | 0.898925 | − | 0.438102i | \(-0.144349\pi\) |
0.559441 | + | 0.828870i | \(0.311016\pi\) | |||||||
\(212\) | 3.37602 | − | 15.5189i | 0.231866 | − | 1.06584i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.16927 | − | 7.38795i | −0.148288 | − | 0.505030i | ||||
\(215\) | − | 13.0375i | − | 0.889148i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.74612i | 0.322188i | ||||||||
\(218\) | −4.00332 | + | 1.17547i | −0.271139 | + | 0.0796126i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.77193 | + | 5.63730i | −0.591403 | + | 0.380066i | ||||
\(221\) | 7.97551 | + | 2.13703i | 0.536491 | + | 0.143752i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.56986 | + | 2.71908i | −0.105126 | + | 0.182083i | −0.913790 | − | 0.406188i | \(-0.866858\pi\) |
0.808664 | + | 0.588271i | \(0.200191\pi\) | |||||||
\(224\) | 10.5922 | − | 1.26628i | 0.707719 | − | 0.0846068i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.137832 | − | 5.79094i | −0.00916844 | − | 0.385208i | ||||
\(227\) | −3.64479 | − | 13.6026i | −0.241913 | − | 0.902833i | −0.974910 | − | 0.222601i | \(-0.928545\pi\) |
0.732996 | − | 0.680233i | \(-0.238121\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.91218 | + | 18.3325i | −0.324606 | + | 1.21145i | 0.590101 | + | 0.807330i | \(0.299088\pi\) |
−0.914707 | + | 0.404117i | \(0.867579\pi\) | |||||||
\(230\) | 2.20867 | − | 9.10415i | 0.145636 | − | 0.600310i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.54569 | − | 1.22714i | 0.232786 | − | 0.0805656i | ||||
\(233\) | − | 12.6802i | − | 0.830708i | −0.909660 | − | 0.415354i | \(-0.863658\pi\) | ||
0.909660 | − | 0.415354i | \(-0.136342\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.38776 | − | 1.38776i | −0.0905275 | − | 0.0905275i | ||||
\(236\) | −21.5490 | + | 6.88832i | −1.40272 | + | 0.448391i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.78344 | + | 7.84779i | 0.310065 | + | 0.508697i | ||||
\(239\) | 3.69405 | + | 6.39829i | 0.238948 | + | 0.413871i | 0.960413 | − | 0.278581i | \(-0.0898640\pi\) |
−0.721464 | + | 0.692451i | \(0.756531\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.1955 | − | 19.3912i | 0.721167 | − | 1.24910i | −0.239366 | − | 0.970929i | \(-0.576940\pi\) |
0.960533 | − | 0.278168i | \(-0.0897271\pi\) | |||||||
\(242\) | 13.4281 | − | 0.319605i | 0.863189 | − | 0.0205450i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.60546 | + | 7.26615i | −0.422871 | + | 0.465168i | ||||
\(245\) | 14.1499 | − | 3.79145i | 0.904003 | − | 0.242227i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.2577 | − | 7.07698i | 0.779938 | − | 0.450297i | ||||
\(248\) | 5.89527 | − | 3.98996i | 0.374350 | − | 0.253362i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −46.7185 | + | 13.7176i | −2.95474 | + | 0.867579i | ||||
\(251\) | 7.52339 | + | 7.52339i | 0.474872 | + | 0.474872i | 0.903487 | − | 0.428615i | \(-0.140998\pi\) |
−0.428615 | + | 0.903487i | \(0.640998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.34967 | − | 1.34967i | 0.0848533 | − | 0.0848533i | ||||
\(254\) | −6.07991 | − | 3.31991i | −0.381487 | − | 0.208309i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.4775 | − | 12.0923i | −0.654842 | − | 0.755766i | ||||
\(257\) | −2.21664 | − | 3.83934i | −0.138270 | − | 0.239491i | 0.788572 | − | 0.614943i | \(-0.210821\pi\) |
−0.926842 | + | 0.375452i | \(0.877488\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.98377 | + | 14.8676i | 0.247539 | + | 0.923830i | ||||
\(260\) | 20.3600 | − | 0.969736i | 1.26267 | − | 0.0601405i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −18.8348 | − | 17.9591i | −1.16362 | − | 1.10952i | ||||
\(263\) | −4.61948 | − | 2.66706i | −0.284850 | − | 0.164458i | 0.350767 | − | 0.936463i | \(-0.385921\pi\) |
−0.635617 | + | 0.772005i | \(0.719254\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 29.2529 | − | 16.8891i | 1.79699 | − | 1.03749i | ||||
\(266\) | 15.3107 | + | 3.71438i | 0.938757 | + | 0.227743i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.180667 | + | 0.565189i | 0.0110360 | + | 0.0345244i | ||||
\(269\) | −20.6406 | + | 20.6406i | −1.25848 | + | 1.25848i | −0.306663 | + | 0.951818i | \(0.599212\pi\) |
−0.951818 | + | 0.306663i | \(0.900788\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.2339 | 1.41136 | 0.705680 | − | 0.708530i | \(-0.250642\pi\) | ||||
0.705680 | + | 0.708530i | \(0.250642\pi\) | |||||||
\(272\) | 5.72660 | − | 12.5391i | 0.347226 | − | 0.760294i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.4057 | + | 18.7124i | 0.689044 | + | 1.13046i | ||||
\(275\) | −15.5019 | − | 4.15373i | −0.934801 | − | 0.250479i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.0092 | − | 5.09351i | 1.14215 | − | 0.306039i | 0.362338 | − | 0.932047i | \(-0.381979\pi\) |
0.779817 | + | 0.626007i | \(0.215312\pi\) | |||||||
\(278\) | 7.19579 | − | 7.54668i | 0.431575 | − | 0.452620i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 17.1466 | + | 14.8579i | 1.02471 | + | 0.887929i | ||||
\(281\) | 16.3011 | + | 9.41146i | 0.972444 | + | 0.561441i | 0.899980 | − | 0.435930i | \(-0.143581\pi\) |
0.0724633 | + | 0.997371i | \(0.476914\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.43848 | + | 12.8326i | −0.204397 | + | 0.762819i | 0.785236 | + | 0.619197i | \(0.212542\pi\) |
−0.989633 | + | 0.143622i | \(0.954125\pi\) | |||||||
\(284\) | −23.5443 | + | 15.1308i | −1.39710 | + | 0.897848i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.64494 | + | 1.99030i | 0.215530 | + | 0.117689i | ||||
\(287\) | 7.47420 | 0.441188 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.12358 | −0.301387 | ||||||||
\(290\) | 7.00390 | + | 3.82445i | 0.411283 | + | 0.224579i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.0469573 | + | 0.0301772i | −0.00274797 | + | 0.00176599i | ||||
\(293\) | −2.20679 | + | 8.23584i | −0.128922 | + | 0.481143i | −0.999949 | − | 0.0100919i | \(-0.996788\pi\) |
0.871027 | + | 0.491235i | \(0.163454\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −41.6699 | − | 24.0581i | −2.42611 | − | 1.40072i | ||||
\(296\) | 15.1184 | − | 17.4472i | 0.878738 | − | 1.01410i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.53746 | + | 7.90502i | −0.436634 | + | 0.457925i | ||||
\(299\) | −3.60405 | + | 0.965702i | −0.208427 | + | 0.0558480i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.58291 | − | 1.49594i | −0.321794 | − | 0.0862244i | ||||
\(302\) | −2.86031 | − | 4.69266i | −0.164592 | − | 0.270032i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.25760 | − | 22.1403i | −0.473606 | − | 1.26984i | ||||
\(305\) | −20.8853 | −1.19589 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.13558 | + | 7.13558i | −0.407249 | + | 0.407249i | −0.880778 | − | 0.473529i | \(-0.842980\pi\) |
0.473529 | + | 0.880778i | \(0.342980\pi\) | |||||||
\(308\) | 1.40750 | + | 4.40315i | 0.0802000 | + | 0.250893i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.7134 | + | 3.56947i | 0.835663 | + | 0.202732i | ||||
\(311\) | −10.0741 | + | 5.81630i | −0.571252 | + | 0.329812i | −0.757649 | − | 0.652662i | \(-0.773652\pi\) |
0.186397 | + | 0.982474i | \(0.440319\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.76956 | + | 3.33106i | 0.326115 | + | 0.188282i | 0.654115 | − | 0.756395i | \(-0.273041\pi\) |
−0.328000 | + | 0.944678i | \(0.606375\pi\) | |||||||
\(314\) | −6.60513 | − | 6.29802i | −0.372749 | − | 0.355418i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.75276 | − | 0.416890i | 0.492381 | − | 0.0234519i | ||||
\(317\) | −0.708583 | − | 2.64447i | −0.0397980 | − | 0.148528i | 0.943168 | − | 0.332317i | \(-0.107830\pi\) |
−0.982966 | + | 0.183789i | \(0.941164\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.812945 | + | 1.40806i | 0.0455162 | + | 0.0788364i | ||||
\(320\) | 4.04061 | − | 33.7889i | 0.225877 | − | 1.88886i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.64516 | − | 1.99042i | −0.203137 | − | 0.110922i | ||||
\(323\) | 14.3957 | − | 14.3957i | 0.801000 | − | 0.801000i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.1835 | + | 22.1835i | 1.23052 | + | 1.23052i | ||||
\(326\) | −20.2996 | + | 5.96044i | −1.12429 | + | 0.330118i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.28339 | − | 9.28389i | −0.346942 | − | 0.512617i | ||||
\(329\) | −0.753501 | + | 0.435034i | −0.0415418 | + | 0.0239842i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.6789 | + | 5.27295i | −1.08165 | + | 0.289827i | −0.755272 | − | 0.655412i | \(-0.772495\pi\) |
−0.326379 | + | 0.945239i | \(0.605829\pi\) | |||||||
\(332\) | −4.76082 | + | 5.23701i | −0.261284 | + | 0.287418i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −30.5524 | + | 0.727186i | −1.67175 | + | 0.0397898i | ||||
\(335\) | −0.630997 | + | 1.09292i | −0.0344751 | + | 0.0597126i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.514533 | − | 0.891197i | −0.0280284 | − | 0.0485466i | 0.851671 | − | 0.524077i | \(-0.175590\pi\) |
−0.879699 | + | 0.475530i | \(0.842256\pi\) | |||||||
\(338\) | 5.34341 | + | 8.76647i | 0.290643 | + | 0.476833i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 27.9263 | − | 8.92688i | 1.51452 | − | 0.484128i | ||||
\(341\) | 2.18123 | + | 2.18123i | 0.118120 | + | 0.118120i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.6948i | − | 1.06342i | ||||||
\(344\) | 2.83529 | + | 8.19227i | 0.152868 | + | 0.441698i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.45378 | − | 26.6025i | 0.346957 | − | 1.43016i | ||||
\(347\) | 8.08026 | − | 30.1559i | 0.433771 | − | 1.61886i | −0.310219 | − | 0.950665i | \(-0.600402\pi\) |
0.743990 | − | 0.668191i | \(-0.232931\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.62320 | + | 17.2540i | 0.247474 | + | 0.923587i | 0.972124 | + | 0.234469i | \(0.0753352\pi\) |
−0.724649 | + | 0.689118i | \(0.757998\pi\) | |||||||
\(350\) | 0.830915 | + | 34.9105i | 0.0444143 | + | 1.86605i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.28601 | − | 5.44992i | 0.228445 | − | 0.290482i | ||||
\(353\) | 1.02827 | − | 1.78101i | 0.0547291 | − | 0.0947935i | −0.837363 | − | 0.546647i | \(-0.815904\pi\) |
0.892092 | + | 0.451854i | \(0.149237\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −57.4962 | − | 15.4061i | −3.05158 | − | 0.817668i | ||||
\(356\) | −7.99015 | + | 5.13489i | −0.423477 | + | 0.272149i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.52961 | + | 1.62362i | −0.292249 | + | 0.0858110i | ||||
\(359\) | − | 4.76579i | − | 0.251529i | −0.992060 | − | 0.125764i | \(-0.959862\pi\) | ||
0.992060 | − | 0.125764i | \(-0.0401383\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 15.8989i | − | 0.836785i | ||||||
\(362\) | 5.35391 | + | 18.2340i | 0.281395 | + | 0.958356i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.92087 | − | 8.82983i | 0.100681 | − | 0.462809i | ||||
\(365\) | −0.114672 | − | 0.0307261i | −0.00600218 | − | 0.00160828i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.61021 | − | 14.9133i | 0.449449 | − | 0.778469i | −0.548901 | − | 0.835887i | \(-0.684954\pi\) |
0.998350 | + | 0.0574187i | \(0.0182870\pi\) | |||||||
\(368\) | 0.592049 | + | 6.20104i | 0.0308627 | + | 0.323252i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 49.0870 | − | 1.16833i | 2.55191 | − | 0.0607387i | ||||
\(371\) | −3.87577 | − | 14.4646i | −0.201220 | − | 0.750963i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.29744 | − | 16.0383i | 0.222513 | − | 0.830430i | −0.760872 | − | 0.648901i | \(-0.775229\pi\) |
0.983386 | − | 0.181529i | \(-0.0581046\pi\) | |||||||
\(374\) | 5.80508 | + | 1.40832i | 0.300174 | + | 0.0728224i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.17382 | + | 0.570219i | 0.0605350 | + | 0.0294068i | ||||
\(377\) | − | 3.17830i | − | 0.163691i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.5741 | − | 22.5741i | −1.15955 | − | 1.15955i | −0.984572 | − | 0.174981i | \(-0.944013\pi\) |
−0.174981 | − | 0.984572i | \(-0.555987\pi\) | |||||||
\(380\) | 23.0297 | − | 44.6708i | 1.18140 | − | 2.29156i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.70983 | − | 3.48030i | 0.292140 | − | 0.178067i | ||||
\(383\) | 12.6153 | + | 21.8504i | 0.644614 | + | 1.11650i | 0.984391 | + | 0.175997i | \(0.0563150\pi\) |
−0.339777 | + | 0.940506i | \(0.610352\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.91584 | + | 8.51448i | −0.250534 | + | 0.433938i | ||||
\(386\) | −0.657224 | − | 27.6130i | −0.0334518 | − | 1.40546i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.6752 | − | 0.794231i | 0.846554 | − | 0.0403210i | ||||
\(389\) | −7.09570 | + | 1.90129i | −0.359766 | + | 0.0963991i | −0.434175 | − | 0.900829i | \(-0.642960\pi\) |
0.0744082 | + | 0.997228i | \(0.476293\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.64781 | + | 2.68342i | −0.235050 | + | 0.135706i | ||||
\(392\) | −8.06674 | + | 5.45962i | −0.407432 | + | 0.275752i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.88768 | + | 13.2404i | 0.195858 | + | 0.667040i | ||||
\(395\) | 13.1783 | + | 13.1783i | 0.663073 | + | 0.663073i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.23236 | + | 2.23236i | −0.112039 | + | 0.112039i | −0.760904 | − | 0.648865i | \(-0.775244\pi\) |
0.648865 | + | 0.760904i | \(0.275244\pi\) | |||||||
\(398\) | 16.5884 | − | 30.3792i | 0.831501 | − | 1.52277i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 42.6647 | − | 30.3806i | 2.13323 | − | 1.51903i | ||||
\(401\) | −9.10949 | − | 15.7781i | −0.454906 | − | 0.787921i | 0.543777 | − | 0.839230i | \(-0.316994\pi\) |
−0.998683 | + | 0.0513094i | \(0.983661\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.56069 | − | 5.82456i | −0.0777433 | − | 0.290142i | ||||
\(404\) | 11.0431 | + | 10.0390i | 0.549417 | + | 0.499460i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.44134 | − | 2.56039i | 0.121162 | − | 0.127070i | ||||
\(407\) | 8.66376 | + | 5.00202i | 0.429447 | + | 0.247941i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.6986 | + | 13.1050i | −1.12237 | + | 0.648002i | −0.942006 | − | 0.335597i | \(-0.891062\pi\) |
−0.180368 | + | 0.983599i | \(0.557729\pi\) | |||||||
\(410\) | 5.62121 | − | 23.1706i | 0.277612 | − | 1.14432i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 25.0845 | + | 12.9322i | 1.23583 | + | 0.637122i | ||||
\(413\) | −15.0834 | + | 15.0834i | −0.742207 | + | 0.742207i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.0529 | −0.738918 | ||||||||
\(416\) | −12.5826 | + | 5.03707i | −0.616912 | + | 0.246963i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.74356 | − | 5.32944i | 0.427661 | − | 0.260671i | ||||
\(419\) | −11.2202 | − | 3.00645i | −0.548144 | − | 0.146875i | −0.0258901 | − | 0.999665i | \(-0.508242\pi\) |
−0.522254 | + | 0.852790i | \(0.674909\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.74548 | + | 2.61129i | −0.474966 | + | 0.127267i | −0.488358 | − | 0.872644i | \(-0.662404\pi\) |
0.0133918 | + | 0.999910i | \(0.495737\pi\) | |||||||
\(422\) | −22.4469 | − | 21.4032i | −1.09270 | − | 1.04189i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.7085 | + | 16.9742i | −0.714309 | + | 0.824341i | ||||
\(425\) | 39.0793 | + | 22.5624i | 1.89562 | + | 1.09444i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.39641 | + | 8.94353i | −0.115970 | + | 0.432808i | ||||
\(428\) | −2.31474 | + | 10.6404i | −0.111887 | + | 0.514321i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.83633 | + | 16.1824i | −0.426126 | + | 0.780385i | ||||
\(431\) | 4.07825 | 0.196442 | 0.0982211 | − | 0.995165i | \(-0.468685\pi\) | ||||
0.0982211 | + | 0.995165i | \(0.468685\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.1331 | −1.20782 | −0.603910 | − | 0.797052i | \(-0.706392\pi\) | ||||
−0.603910 | + | 0.797052i | \(0.706392\pi\) | |||||||
\(434\) | 3.21675 | − | 5.89100i | 0.154409 | − | 0.282777i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.76570 | + | 1.25429i | 0.276127 | + | 0.0600696i | ||||
\(437\) | −2.38110 | + | 8.88638i | −0.113903 | + | 0.425093i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.5272 | + | 7.80991i | 0.645616 | + | 0.372747i | 0.786775 | − | 0.617240i | \(-0.211749\pi\) |
−0.141158 | + | 0.989987i | \(0.545083\pi\) | |||||||
\(440\) | 14.7087 | − | 1.05185i | 0.701209 | − | 0.0501448i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.45098 | − | 8.05805i | −0.401972 | − | 0.383282i | ||||
\(443\) | −32.6709 | + | 8.75415i | −1.55224 | + | 0.415922i | −0.930197 | − | 0.367060i | \(-0.880364\pi\) |
−0.622045 | + | 0.782982i | \(0.713698\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.5123 | − | 5.22830i | −0.924970 | − | 0.247845i | ||||
\(446\) | 3.79144 | − | 2.31099i | 0.179530 | − | 0.109428i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −14.0055 | − | 5.60726i | −0.661697 | − | 0.264918i | ||||
\(449\) | 28.0284 | 1.32274 | 0.661370 | − | 0.750060i | \(-0.269975\pi\) | ||||
0.661370 | + | 0.750060i | \(0.269975\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.43500 | − | 3.43500i | 0.161748 | − | 0.161748i | ||||
\(452\) | −3.75381 | + | 7.28127i | −0.176565 | + | 0.342482i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.69532 | + | 19.3541i | −0.220362 | + | 0.908334i | ||||
\(455\) | 16.6441 | − | 9.60949i | 0.780289 | − | 0.450500i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.8363 | + | 8.56574i | 0.694012 | + | 0.400688i | 0.805113 | − | 0.593121i | \(-0.202104\pi\) |
−0.111101 | + | 0.993809i | \(0.535438\pi\) | |||||||
\(458\) | 18.5222 | − | 19.4254i | 0.865488 | − | 0.907692i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.91192 | + | 9.80332i | −0.415521 | + | 0.457082i | ||||
\(461\) | −2.43727 | − | 9.09603i | −0.113515 | − | 0.423644i | 0.885656 | − | 0.464341i | \(-0.153709\pi\) |
−0.999172 | + | 0.0406970i | \(0.987042\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.777204 | − | 1.34616i | −0.0361197 | − | 0.0625612i | 0.847400 | − | 0.530954i | \(-0.178166\pi\) |
−0.883520 | + | 0.468393i | \(0.844833\pi\) | |||||||
\(464\) | −5.23271 | − | 0.879991i | −0.242922 | − | 0.0408526i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.59420 | + | 15.7390i | −0.398118 | + | 0.729094i | ||||
\(467\) | −9.81211 | + | 9.81211i | −0.454050 | + | 0.454050i | −0.896696 | − | 0.442646i | \(-0.854040\pi\) |
0.442646 | + | 0.896696i | \(0.354040\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.395609 | + | 0.395609i | 0.0182675 | + | 0.0182675i | ||||
\(470\) | 0.781946 | + | 2.66309i | 0.0360685 | + | 0.122839i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 31.4158 | + | 6.05521i | 1.44603 | + | 0.278713i | ||||
\(473\) | −3.25331 | + | 1.87830i | −0.149587 | + | 0.0863643i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 74.7175 | − | 20.0205i | 3.42828 | − | 0.918604i | ||||
\(476\) | −0.618370 | − | 12.9829i | −0.0283429 | − | 0.595071i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.248614 | − | 10.4454i | −0.0113713 | − | 0.477761i | ||||
\(479\) | 11.7030 | − | 20.2702i | 0.534724 | − | 0.926169i | −0.464453 | − | 0.885598i | \(-0.653749\pi\) |
0.999177 | − | 0.0405710i | \(-0.0129177\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.77797 | − | 16.9359i | −0.445837 | − | 0.772212i | ||||
\(482\) | −27.0388 | + | 16.4809i | −1.23158 | + | 0.750684i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.8838 | − | 8.70436i | −0.767448 | − | 0.395653i | ||||
\(485\) | 25.1064 | + | 25.1064i | 1.14002 | + | 1.14002i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.0301i | 0.952967i | 0.879183 | + | 0.476483i | \(0.158089\pi\) | ||||
−0.879183 | + | 0.476483i | \(0.841911\pi\) | |||||||
\(488\) | 13.1236 | − | 4.54198i | 0.594077 | − | 0.205606i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −20.1329 | − | 4.88425i | −0.909511 | − | 0.220648i | ||||
\(491\) | 6.82214 | − | 25.4606i | 0.307879 | − | 1.14902i | −0.622560 | − | 0.782572i | \(-0.713907\pi\) |
0.930439 | − | 0.366447i | \(-0.119426\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.18321 | − | 4.41580i | −0.0532891 | − | 0.198877i | ||||
\(494\) | −20.0110 | + | 0.476289i | −0.900339 | + | 0.0214292i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.0216 | + | 0.956819i | −0.449983 | + | 0.0429625i | ||||
\(497\) | −13.1944 | + | 22.8533i | −0.591849 | + | 1.02511i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.8466 | + | 3.44223i | 0.575092 | + | 0.154095i | 0.534631 | − | 0.845086i | \(-0.320451\pi\) |
0.0404610 | + | 0.999181i | \(0.487117\pi\) | |||||||
\(500\) | 67.2854 | + | 14.6375i | 3.00909 | + | 0.654608i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.23912 | − | 14.4373i | −0.189201 | − | 0.644368i | ||||
\(503\) | 7.97796i | 0.355720i | 0.984056 | + | 0.177860i | \(0.0569174\pi\) | ||||
−0.984056 | + | 0.177860i | \(0.943083\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.7417i | 1.41249i | ||||||||
\(506\) | −2.59001 | + | 0.760486i | −0.115140 | + | 0.0338077i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.29641 | + | 8.24149i | 0.234990 | + | 0.365657i | ||||
\(509\) | −33.3037 | − | 8.92371i | −1.47616 | − | 0.395536i | −0.571123 | − | 0.820865i | \(-0.693492\pi\) |
−0.905039 | + | 0.425328i | \(0.860159\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0263151 | + | 0.0455792i | −0.00116411 | + | 0.00201630i | ||||
\(512\) | 4.80918 | + | 22.1104i | 0.212538 | + | 0.977153i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.149183 | + | 6.26784i | 0.00658016 | + | 0.276463i | ||||
\(515\) | 15.5353 | + | 57.9785i | 0.684567 | + | 2.55484i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.146362 | + | 0.546229i | −0.00643697 | + | 0.0240231i | ||||
\(518\) | 5.13200 | − | 21.1541i | 0.225487 | − | 0.929458i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −25.9285 | − | 12.5956i | −1.13704 | − | 0.552354i | ||||
\(521\) | 20.0111i | 0.876703i | 0.898804 | + | 0.438352i | \(0.144438\pi\) | ||||
−0.898804 | + | 0.438352i | \(0.855562\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.2432 | − | 11.2432i | −0.491633 | − | 0.491633i | 0.417188 | − | 0.908820i | \(-0.363016\pi\) |
−0.908820 | + | 0.417188i | \(0.863016\pi\) | |||||||
\(524\) | 11.2062 | + | 35.0568i | 0.489545 | + | 1.53146i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.92617 | + | 6.44134i | 0.171189 | + | 0.280856i | ||||
\(527\) | −4.33671 | − | 7.51140i | −0.188910 | − | 0.327202i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.2874 | + | 17.8183i | −0.447278 | + | 0.774708i | ||||
\(530\) | −47.7562 | + | 1.13666i | −2.07440 | + | 0.0493733i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −16.4865 | − | 14.9874i | −0.714780 | − | 0.649786i | ||||
\(533\) | −9.17253 | + | 2.45777i | −0.397306 | + | 0.106458i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.0569 | + | 11.5799i | −0.867137 | + | 0.500642i | ||||
\(536\) | 0.158816 | − | 0.823975i | 0.00685982 | − | 0.0355903i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 39.6091 | − | 11.6301i | 1.70767 | − | 0.501411i | ||||
\(539\) | −2.98466 | − | 2.98466i | −0.128559 | − | 0.128559i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.38252 | − | 9.38252i | 0.403386 | − | 0.403386i | −0.476038 | − | 0.879424i | \(-0.657928\pi\) |
0.879424 | + | 0.476038i | \(0.157928\pi\) | |||||||
\(542\) | −28.8385 | − | 15.7471i | −1.23872 | − | 0.676397i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −15.6065 | + | 11.6825i | −0.669125 | + | 0.500884i | ||||
\(545\) | 6.27481 | + | 10.8683i | 0.268783 | + | 0.465546i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.70067 | − | 36.2034i | −0.414770 | − | 1.54794i | −0.785295 | − | 0.619122i | \(-0.787489\pi\) |
0.370524 | − | 0.928823i | \(-0.379178\pi\) | |||||||
\(548\) | −1.47445 | − | 30.9566i | −0.0629854 | − | 1.32240i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 16.4261 | + | 15.6624i | 0.700411 | + | 0.667845i | ||||
\(551\) | −6.78671 | − | 3.91831i | −0.289123 | − | 0.166926i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.15532 | − | 4.13113i | 0.304275 | − | 0.175673i | ||||
\(554\) | −27.0469 | − | 6.56160i | −1.14911 | − | 0.278776i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.0465 | + | 4.49007i | −0.595703 | + | 0.190421i | ||||
\(557\) | −9.01169 | + | 9.01169i | −0.381838 | + | 0.381838i | −0.871764 | − | 0.489926i | \(-0.837024\pi\) |
0.489926 | + | 0.871764i | \(0.337024\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.34341 | 0.310593 | ||||||||
\(560\) | −11.2126 | − | 30.0633i | −0.473819 | − | 1.27041i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.8546 | − | 22.7300i | −0.584420 | − | 0.958809i | ||||
\(563\) | 16.4015 | + | 4.39477i | 0.691241 | + | 0.185218i | 0.587304 | − | 0.809366i | \(-0.300189\pi\) |
0.103937 | + | 0.994584i | \(0.466856\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.8294 | + | 4.50942i | −0.708018 | + | 0.189713i | ||||
\(566\) | 12.9654 | − | 13.5976i | 0.544976 | − | 0.571551i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 39.4789 | − | 2.82321i | 1.65650 | − | 0.118459i | ||||
\(569\) | −14.1855 | − | 8.19001i | −0.594688 | − | 0.343343i | 0.172261 | − | 0.985051i | \(-0.444893\pi\) |
−0.766949 | + | 0.641708i | \(0.778226\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.58794 | + | 35.7827i | −0.401243 | + | 1.49746i | 0.409638 | + | 0.912248i | \(0.365655\pi\) |
−0.810881 | + | 0.585211i | \(0.801012\pi\) | |||||||
\(572\) | −3.17523 | − | 4.94082i | −0.132763 | − | 0.206586i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.27715 | − | 5.06575i | −0.387221 | − | 0.211440i | ||||
\(575\) | −20.3914 | −0.850382 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.14863 | −0.0894487 | −0.0447243 | − | 0.998999i | \(-0.514241\pi\) | ||||
−0.0447243 | + | 0.998999i | \(0.514241\pi\) | |||||||
\(578\) | 6.35950 | + | 3.47258i | 0.264520 | + | 0.144440i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.10133 | − | 9.49399i | −0.253344 | − | 0.394216i | ||||
\(581\) | −1.72719 | + | 6.44597i | −0.0716560 | + | 0.267424i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.42888 | − | 4.86642i | −0.349088 | − | 0.201546i | ||||
\(584\) | 0.0787375 | − | 0.00563067i | 0.00325818 | − | 0.000232999i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.32107 | − | 8.72684i | 0.343740 | − | 0.360502i | ||||
\(587\) | 21.6014 | − | 5.78807i | 0.891585 | − | 0.238899i | 0.216186 | − | 0.976352i | \(-0.430638\pi\) |
0.675399 | + | 0.737453i | \(0.263972\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.3614 | − | 3.84813i | −0.591752 | − | 0.158559i | ||||
\(590\) | 35.4159 | + | 58.1038i | 1.45805 | + | 2.39210i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −30.5904 | + | 11.4092i | −1.25726 | + | 0.468915i | ||||
\(593\) | −10.7128 | −0.439921 | −0.219960 | − | 0.975509i | \(-0.570593\pi\) | ||||
−0.219960 | + | 0.975509i | \(0.570593\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.5473 | − | 19.5473i | 0.801361 | − | 0.801361i | ||||
\(596\) | 14.7134 | − | 4.70327i | 0.602685 | − | 0.192653i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.12795 | + | 1.24404i | 0.209697 | + | 0.0508727i | ||||
\(599\) | −23.8944 | + | 13.7955i | −0.976300 | + | 0.563667i | −0.901151 | − | 0.433505i | \(-0.857277\pi\) |
−0.0751489 | + | 0.997172i | \(0.523943\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.37490 | − | 5.41260i | −0.382410 | − | 0.220785i | 0.296456 | − | 0.955046i | \(-0.404195\pi\) |
−0.678866 | + | 0.734262i | \(0.737528\pi\) | |||||||
\(602\) | 5.91575 | + | 5.64069i | 0.241108 | + | 0.229897i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.369760 | + | 7.76325i | 0.0150453 | + | 0.315882i | ||||
\(605\) | −10.4565 | − | 39.0241i | −0.425116 | − | 1.58655i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.0270 | + | 32.9557i | 0.772282 | + | 1.33763i | 0.936310 | + | 0.351175i | \(0.114218\pi\) |
−0.164028 | + | 0.986456i | \(0.552449\pi\) | |||||||
\(608\) | −4.75640 | + | 33.0778i | −0.192898 | + | 1.34148i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 25.9234 | + | 14.1553i | 1.04961 | + | 0.573133i | ||||
\(611\) | 0.781661 | − | 0.781661i | 0.0316226 | − | 0.0316226i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.9758 | − | 34.9758i | −1.41266 | − | 1.41266i | −0.739489 | − | 0.673168i | \(-0.764933\pi\) |
−0.673168 | − | 0.739489i | \(-0.735067\pi\) | |||||||
\(614\) | 13.6931 | − | 4.02061i | 0.552608 | − | 0.162259i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.23727 | − | 6.41925i | 0.0498511 | − | 0.258639i | ||||
\(617\) | 11.9478 | − | 6.89807i | 0.481001 | − | 0.277706i | −0.239833 | − | 0.970814i | \(-0.577093\pi\) |
0.720834 | + | 0.693108i | \(0.243759\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.9231 | − | 8.82171i | 1.32329 | − | 0.354574i | 0.473080 | − | 0.881019i | \(-0.343142\pi\) |
0.850209 | + | 0.526445i | \(0.176475\pi\) | |||||||
\(620\) | −15.8433 | − | 14.4027i | −0.636282 | − | 0.578426i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.4463 | − | 0.391444i | 0.659438 | − | 0.0156955i | ||||
\(623\) | −4.47773 | + | 7.75565i | −0.179396 | + | 0.310724i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 40.4916 | + | 70.1335i | 1.61966 | + | 2.80534i | ||||
\(626\) | −4.90364 | − | 8.04499i | −0.195989 | − | 0.321542i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.92987 | + | 12.2940i | 0.156819 | + | 0.490583i | ||||
\(629\) | −19.8900 | − | 19.8900i | −0.793066 | − | 0.793066i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 7.97657i | − | 0.317542i | −0.987315 | − | 0.158771i | \(-0.949247\pi\) | ||
0.987315 | − | 0.158771i | \(-0.0507532\pi\) | |||||||
\(632\) | −11.1467 | − | 5.41486i | −0.443392 | − | 0.215391i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.912816 | + | 3.76263i | −0.0362526 | + | 0.149433i | ||||
\(635\) | −5.39276 | + | 20.1260i | −0.214005 | + | 0.798677i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.13555 | + | 7.96998i | 0.0846135 | + | 0.315782i | ||||
\(638\) | −0.0547121 | − | 2.29871i | −0.00216607 | − | 0.0910066i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −27.9162 | + | 39.2010i | −1.10349 | + | 1.54956i | ||||
\(641\) | 18.6956 | − | 32.3818i | 0.738434 | − | 1.27900i | −0.214767 | − | 0.976665i | \(-0.568899\pi\) |
0.953200 | − | 0.302339i | \(-0.0977676\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.4765 | + | 3.34308i | 0.492026 | + | 0.131838i | 0.496297 | − | 0.868153i | \(-0.334693\pi\) |
−0.00427070 | + | 0.999991i | \(0.501359\pi\) | |||||||
\(644\) | 3.17542 | + | 4.94112i | 0.125129 | + | 0.194707i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −27.6252 | + | 8.11141i | −1.08690 | + | 0.319139i | ||||
\(647\) | 4.85394i | 0.190828i | 0.995438 | + | 0.0954140i | \(0.0304175\pi\) | ||||
−0.995438 | + | 0.0954140i | \(0.969582\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.8641i | 0.544215i | ||||||||
\(650\) | −12.4995 | − | 42.5698i | −0.490270 | − | 1.66973i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 29.2361 | + | 6.36013i | 1.14498 | + | 0.249082i | ||||
\(653\) | 37.4249 | + | 10.0280i | 1.46455 | + | 0.392425i | 0.901059 | − | 0.433696i | \(-0.142791\pi\) |
0.563492 | + | 0.826121i | \(0.309458\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −39.1387 | + | 67.7902i | −1.52928 | + | 2.64878i | ||||
\(656\) | 1.50680 | + | 15.7820i | 0.0588307 | + | 0.616185i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.23011 | − | 0.0292783i | 0.0479548 | − | 0.00114139i | ||||
\(659\) | −9.85502 | − | 36.7794i | −0.383897 | − | 1.43272i | −0.839898 | − | 0.542744i | \(-0.817385\pi\) |
0.456001 | − | 0.889979i | \(-0.349281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.10339 | − | 11.5820i | 0.120708 | − | 0.450488i | −0.878943 | − | 0.476927i | \(-0.841750\pi\) |
0.999650 | + | 0.0264400i | \(0.00841709\pi\) | |||||||
\(662\) | 27.9997 | + | 6.79276i | 1.08824 | + | 0.264008i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.45870 | − | 3.27359i | 0.367069 | − | 0.127040i | ||||
\(665\) | − | 47.3876i | − | 1.83761i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.46077 | + | 1.46077i | 0.0565613 | + | 0.0565613i | ||||
\(668\) | 38.4152 | + | 19.8047i | 1.48633 | + | 0.766267i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.52395 | − | 0.928890i | 0.0588753 | − | 0.0358861i | ||||
\(671\) | 3.00893 | + | 5.21163i | 0.116159 | + | 0.201193i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.9076 | − | 25.8207i | 0.574645 | − | 0.995314i | −0.421435 | − | 0.906858i | \(-0.638474\pi\) |
0.996080 | − | 0.0884554i | \(-0.0281931\pi\) | |||||||
\(674\) | 0.0346286 | + | 1.45491i | 0.00133385 | + | 0.0560409i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.690758 | − | 14.5027i | −0.0265676 | − | 0.557797i | ||||
\(677\) | −27.4303 | + | 7.34993i | −1.05423 | + | 0.282481i | −0.744000 | − | 0.668180i | \(-0.767074\pi\) |
−0.310233 | + | 0.950661i | \(0.600407\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.6318 | − | 7.87034i | 0.523142 | − | 0.302036i | ||||
\(680\) | −40.7131 | − | 7.84721i | −1.56128 | − | 0.300927i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.22903 | − | 4.18575i | −0.0470621 | − | 0.160281i | ||||
\(683\) | −34.9639 | − | 34.9639i | −1.33786 | − | 1.33786i | −0.898134 | − | 0.439721i | \(-0.855077\pi\) |
−0.439721 | − | 0.898134i | \(-0.644923\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 46.6088 | − | 46.6088i | 1.78083 | − | 1.78083i | ||||
\(686\) | −13.3484 | + | 24.4456i | −0.509645 | + | 0.933338i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.03321 | − | 12.0901i | 0.0775153 | − | 0.460931i | ||||
\(689\) | 9.51288 | + | 16.4768i | 0.362412 | + | 0.627716i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.37585 | − | 12.5989i | −0.128424 | − | 0.479283i | 0.871515 | − | 0.490369i | \(-0.163138\pi\) |
−0.999939 | + | 0.0110856i | \(0.996471\pi\) | |||||||
\(692\) | −26.0408 | + | 28.6455i | −0.989922 | + | 1.08894i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30.4680 | + | 31.9538i | −1.15655 | + | 1.21295i | ||||
\(695\) | −27.1620 | − | 15.6820i | −1.03031 | − | 0.594851i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.8290 | + | 6.82946i | −0.448054 | + | 0.258684i | ||||
\(698\) | 5.95574 | − | 24.5495i | 0.225428 | − | 0.929214i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 22.6297 | − | 43.8949i | 0.855324 | − | 1.65907i | ||||
\(701\) | 1.18582 | − | 1.18582i | 0.0447879 | − | 0.0447879i | −0.684358 | − | 0.729146i | \(-0.739917\pi\) |
0.729146 | + | 0.684358i | \(0.239917\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −48.2184 | −1.81859 | ||||||||
\(704\) | −9.01365 | + | 3.85967i | −0.339715 | + | 0.145467i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.48341 | + | 1.51371i | −0.0934644 | + | 0.0569691i | ||||
\(707\) | 13.5924 | + | 3.64208i | 0.511196 | + | 0.136975i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.3909 | − | 3.58808i | 0.502906 | − | 0.134753i | 0.00155784 | − | 0.999999i | \(-0.499504\pi\) |
0.501349 | + | 0.865245i | \(0.332837\pi\) | |||||||
\(710\) | 60.9239 | + | 58.0912i | 2.28643 | + | 2.18012i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.3978 | − | 0.958103i | 0.502104 | − | 0.0359064i | ||||
\(713\) | 3.39432 | + | 1.95971i | 0.127118 | + | 0.0733919i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.23299 | − | 12.0657i | 0.120907 | − | 0.451231i | ||||
\(716\) | 7.96391 | + | 1.73250i | 0.297625 | + | 0.0647464i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.23008 | + | 5.91541i | −0.120546 | + | 0.220761i | ||||
\(719\) | −22.9314 | −0.855198 | −0.427599 | − | 0.903968i | \(-0.640641\pi\) | ||||
−0.427599 | + | 0.903968i | \(0.640641\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.6101 | 0.991013 | ||||||||
\(722\) | −10.7757 | + | 19.7341i | −0.401031 | + | 0.734428i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.71293 | − | 26.2611i | 0.212319 | − | 0.975986i | ||||
\(725\) | 4.49564 | − | 16.7780i | 0.166964 | − | 0.623118i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.6244 | + | 8.44338i | 0.542387 | + | 0.313147i | 0.746046 | − | 0.665894i | \(-0.231950\pi\) |
−0.203659 | + | 0.979042i | \(0.565283\pi\) | |||||||
\(728\) | −8.36877 | + | 9.65789i | −0.310167 | + | 0.357945i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.121508 | + | 0.115858i | 0.00449721 | + | 0.00428811i | ||||
\(731\) | 10.2026 | − | 2.73379i | 0.377358 | − | 0.101113i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.1181 | − | 10.4817i | −1.44486 | − | 0.387149i | −0.550626 | − | 0.834752i | \(-0.685611\pi\) |
−0.894232 | + | 0.447603i | \(0.852278\pi\) | |||||||
\(734\) | −20.7949 | + | 12.6751i | −0.767554 | + | 0.467845i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.46798 | − | 8.09815i | 0.127831 | − | 0.298502i | ||||
\(737\) | 0.363629 | 0.0133945 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.2719 | − | 20.2719i | 0.745713 | − | 0.745713i | −0.227958 | − | 0.973671i | \(-0.573205\pi\) |
0.973671 | + | 0.227958i | \(0.0732050\pi\) | |||||||
\(740\) | −61.7198 | − | 31.8192i | −2.26886 | − | 1.16970i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.99287 | + | 20.5806i | −0.183294 | + | 0.755538i | ||||
\(743\) | −33.3722 | + | 19.2674i | −1.22431 | + | 0.706853i | −0.965833 | − | 0.259165i | \(-0.916553\pi\) |
−0.258473 | + | 0.966019i | \(0.583219\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.4517 | + | 16.4266i | 1.04239 | + | 0.601824i | ||||
\(746\) | −16.2043 | + | 16.9944i | −0.593280 | + | 0.622210i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.25090 | − | 5.68251i | −0.228555 | − | 0.207773i | ||||
\(749\) | 2.65738 | + | 9.91749i | 0.0970987 | + | 0.362377i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.59701 | − | 4.49815i | −0.0947663 | − | 0.164140i | 0.814745 | − | 0.579820i | \(-0.196877\pi\) |
−0.909511 | + | 0.415680i | \(0.863544\pi\) | |||||||
\(752\) | −1.07050 | − | 1.50334i | −0.0390369 | − | 0.0548212i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.15414 | + | 3.94497i | −0.0784490 | + | 0.143667i | ||||
\(755\) | −11.6885 | + | 11.6885i | −0.425388 | + | 0.425388i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.3310 | + | 16.3310i | 0.593562 | + | 0.593562i | 0.938592 | − | 0.345030i | \(-0.112131\pi\) |
−0.345030 | + | 0.938592i | \(0.612131\pi\) | |||||||
\(758\) | 12.7196 | + | 43.3194i | 0.461996 | + | 1.57343i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −58.8613 | + | 39.8377i | −2.13512 | + | 1.44506i | ||||
\(761\) | 30.2706 | − | 17.4767i | 1.09731 | − | 0.633530i | 0.161794 | − | 0.986824i | \(-0.448272\pi\) |
0.935512 | + | 0.353294i | \(0.114939\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.37400 | − | 1.43996i | 0.194552 | − | 0.0521300i | ||||
\(764\) | −9.44599 | + | 0.449908i | −0.341744 | + | 0.0162771i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.849026 | − | 35.6715i | −0.0306766 | − | 1.28886i | ||||
\(767\) | 13.5508 | − | 23.4707i | 0.489292 | − | 0.847478i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.5439 | − | 19.9946i | −0.416284 | − | 0.721024i | 0.579279 | − | 0.815130i | \(-0.303334\pi\) |
−0.995562 | + | 0.0941052i | \(0.970001\pi\) | |||||||
\(770\) | 11.8725 | − | 7.23659i | 0.427854 | − | 0.260789i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.8993 | + | 34.7193i | −0.644211 | + | 1.24958i | ||||
\(773\) | −14.4736 | − | 14.4736i | −0.520581 | − | 0.520581i | 0.397166 | − | 0.917747i | \(-0.369994\pi\) |
−0.917747 | + | 0.397166i | \(0.869994\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 32.9549i | − | 1.18378i | ||||||
\(776\) | −21.2359 | − | 10.3160i | −0.762325 | − | 0.370323i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.0960 | + | 2.44929i | 0.361958 | + | 0.0878113i | ||||
\(779\) | −6.06004 | + | 22.6164i | −0.217124 | + | 0.810316i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.43908 | + | 16.5669i | 0.158843 | + | 0.592809i | ||||
\(782\) | 7.58770 | − | 0.180597i | 0.271335 | − | 0.00645813i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 13.7130 | − | 1.30925i | 0.489749 | − | 0.0467591i | ||||
\(785\) | −13.7254 | + | 23.7732i | −0.489882 | + | 0.848501i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.2907 | − | 8.92022i | −1.18669 | − | 0.317971i | −0.389110 | − | 0.921191i | \(-0.627218\pi\) |
−0.797575 | + | 0.603220i | \(0.793884\pi\) | |||||||
\(788\) | 4.14837 | − | 19.0692i | 0.147780 | − | 0.679312i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.42544 | − | 25.2890i | −0.264185 | − | 0.899743i | ||||
\(791\) | 7.72411i | 0.274638i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 11.7637i | − | 0.417743i | ||||||
\(794\) | 4.28387 | − | 1.25784i | 0.152029 | − | 0.0446392i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −41.1798 | + | 26.4643i | −1.45958 | + | 0.938002i | ||||
\(797\) | −19.0745 | − | 5.11099i | −0.675652 | − | 0.181040i | −0.0953525 | − | 0.995444i | \(-0.530398\pi\) |
−0.580299 | + | 0.814403i | \(0.697064\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.795014 | − | 1.37700i | 0.0281256 | − | 0.0487149i | ||||
\(800\) | −73.5472 | + | 8.79247i | −2.60029 | + | 0.310861i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.613079 | + | 25.7582i | 0.0216486 | + | 0.909555i | ||||
\(803\) | 0.00885339 | + | 0.0330413i | 0.000312429 | + | 0.00116600i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.23318 | + | 12.0664i | −0.113955 | + | 0.425285i | ||||
\(806\) | −2.01052 | + | 8.28736i | −0.0708175 | + | 0.291910i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.90293 | − | 19.9453i | −0.242844 | − | 0.701673i | ||||
\(809\) | 2.32596i | 0.0817763i | 0.999164 | + | 0.0408882i | \(0.0130187\pi\) | ||||
−0.999164 | + | 0.0408882i | \(0.986981\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.5092 | + | 34.5092i | 1.21178 | + | 1.21178i | 0.970440 | + | 0.241343i | \(0.0775878\pi\) |
0.241343 | + | 0.970440i | \(0.422412\pi\) | |||||||
\(812\) | −4.76560 | + | 1.52336i | −0.167240 | + | 0.0534595i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.36347 | − | 12.0806i | −0.258089 | − | 0.423425i | ||||
\(815\) | 31.8177 | + | 55.1098i | 1.11452 | + | 1.93041i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.05319 | − | 15.6806i | 0.316731 | − | 0.548594i | ||||
\(818\) | 37.0562 | − | 0.881984i | 1.29564 | − | 0.0308378i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.6814 | + | 24.9501i | −0.792069 | + | 0.871294i | ||||
\(821\) | 51.3558 | − | 13.7607i | 1.79233 | − | 0.480253i | 0.799590 | − | 0.600547i | \(-0.205050\pi\) |
0.992738 | + | 0.120294i | \(0.0383836\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.35343 | − | 4.82286i | 0.291182 | − | 0.168114i | −0.347293 | − | 0.937757i | \(-0.612899\pi\) |
0.638475 | + | 0.769643i | \(0.279566\pi\) | |||||||
\(824\) | −22.3705 | − | 33.0531i | −0.779314 | − | 1.15146i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 28.9449 | − | 8.49890i | 1.00712 | − | 0.295714i | ||||
\(827\) | 18.2747 | + | 18.2747i | 0.635475 | + | 0.635475i | 0.949436 | − | 0.313961i | \(-0.101656\pi\) |
−0.313961 | + | 0.949436i | \(0.601656\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.63529 | − | 6.63529i | 0.230453 | − | 0.230453i | −0.582429 | − | 0.812882i | \(-0.697897\pi\) |
0.812882 | + | 0.582429i | \(0.197897\pi\) | |||||||
\(830\) | 18.6840 | + | 10.2023i | 0.648532 | + | 0.354128i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19.0317 | + | 2.27589i | 0.659807 | + | 0.0789022i | ||||
\(833\) | 5.93409 | + | 10.2782i | 0.205604 | + | 0.356117i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.7912 | + | 88.7900i | 0.823329 | + | 3.07271i | ||||
\(836\) | −14.4648 | + | 0.688953i | −0.500276 | + | 0.0238279i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11.8891 | + | 11.3363i | 0.410704 | + | 0.391608i | ||||
\(839\) | 34.7829 | + | 20.0819i | 1.20084 | + | 0.693306i | 0.960742 | − | 0.277443i | \(-0.0894869\pi\) |
0.240099 | + | 0.970749i | \(0.422820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.5908 | − | 13.6201i | 0.813475 | − | 0.469660i | ||||
\(842\) | 13.8662 | + | 3.36394i | 0.477860 | + | 0.115929i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.3553 | + | 41.7799i | 0.459708 | + | 1.43812i | ||||
\(845\) | 21.8355 | − | 21.8355i | 0.751166 | − | 0.751166i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.9107 | −0.615419 | ||||||||
\(848\) | 29.7611 | − | 11.0999i | 1.02200 | − | 0.381171i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −33.2141 | − | 54.4915i | −1.13923 | − | 1.86904i | ||||
\(851\) | 12.2779 | + | 3.28987i | 0.420883 | + | 0.112775i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.70204 | + | 0.724010i | −0.0925162 | + | 0.0247896i | −0.304780 | − | 0.952423i | \(-0.598583\pi\) |
0.212264 | + | 0.977212i | \(0.431916\pi\) | |||||||
\(854\) | 9.03609 | − | 9.47672i | 0.309209 | − | 0.324287i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.0848 | − | 11.6382i | 0.344690 | − | 0.397786i | ||||
\(857\) | −32.4678 | − | 18.7453i | −1.10908 | − | 0.640326i | −0.170488 | − | 0.985360i | \(-0.554534\pi\) |
−0.938590 | + | 0.345033i | \(0.887868\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.4963 | − | 46.6369i | 0.426369 | − | 1.59123i | −0.334547 | − | 0.942379i | \(-0.608583\pi\) |
0.760916 | − | 0.648850i | \(-0.224750\pi\) | |||||||
\(860\) | 21.9357 | − | 14.0970i | 0.748002 | − | 0.480705i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.06202 | − | 2.76409i | −0.172413 | − | 0.0941453i | ||||
\(863\) | 40.4745 | 1.37777 | 0.688883 | − | 0.724872i | \(-0.258101\pi\) | ||||
0.688883 | + | 0.724872i | \(0.258101\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −82.3366 | −2.79953 | ||||||||
\(866\) | 31.1958 | + | 17.0343i | 1.06008 | + | 0.578850i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.98542 | + | 5.13184i | −0.271043 | + | 0.174186i | ||||
\(869\) | 1.38986 | − | 5.18704i | 0.0471479 | − | 0.175958i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.615591 | − | 0.355412i | −0.0208585 | − | 0.0120427i | ||||
\(872\) | −6.30641 | − | 5.46464i | −0.213562 | − | 0.185056i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.97835 | − | 9.41616i | 0.303697 | − | 0.318506i | ||||
\(875\) | 62.7143 | − | 16.8042i | 2.12013 | − | 0.568087i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.1530 | + | 8.34743i | 1.05196 | + | 0.281873i | 0.743063 | − | 0.669222i | \(-0.233372\pi\) |
0.308901 | + | 0.951094i | \(0.400039\pi\) | |||||||
\(878\) | −11.4970 | − | 18.8621i | −0.388003 | − | 0.636564i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −18.9697 | − | 8.66344i | −0.639467 | − | 0.292045i | ||||
\(881\) | 44.0930 | 1.48553 | 0.742765 | − | 0.669552i | \(-0.233514\pi\) | ||||
0.742765 | + | 0.669552i | \(0.233514\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.6867 | + | 28.6867i | −0.965385 | + | 0.965385i | −0.999421 | − | 0.0340356i | \(-0.989164\pi\) |
0.0340356 | + | 0.999421i | \(0.489164\pi\) | |||||||
\(884\) | 5.02810 | + | 15.7296i | 0.169113 | + | 0.529044i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 46.4852 | + | 11.2773i | 1.56170 | + | 0.378869i | ||||
\(887\) | 6.66474 | − | 3.84789i | 0.223780 | − | 0.129199i | −0.383919 | − | 0.923367i | \(-0.625426\pi\) |
0.607699 | + | 0.794167i | \(0.292093\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.99961 | + | 4.61858i | 0.268298 | + | 0.154902i | ||||
\(890\) | 20.6755 | + | 19.7142i | 0.693045 | + | 0.660822i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.27233 | + | 0.298748i | −0.210013 | + | 0.0100028i | ||||
\(893\) | −0.705446 | − | 2.63276i | −0.0236069 | − | 0.0881020i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.66712 | + | 15.0119i | 0.289710 | + | 0.501792i | ||||
\(896\) | 13.5835 | + | 16.4523i | 0.453794 | + | 0.549632i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −34.7895 | − | 18.9966i | −1.16094 | − | 0.633926i | ||||
\(899\) | −2.36078 | + | 2.36078i | −0.0787364 | + | 0.0787364i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.3508 | + | 19.3508i | 0.644667 | + | 0.644667i | ||||
\(902\) | −6.59173 | + | 1.93548i | −0.219481 | + | 0.0644446i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.59430 | − | 6.49348i | 0.319102 | − | 0.215970i | ||||
\(905\) | 49.5019 | − | 28.5799i | 1.64550 | − | 0.950029i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.2432 | + | 8.10365i | −1.00421 | + | 0.269077i | −0.723208 | − | 0.690630i | \(-0.757333\pi\) |
−0.281002 | + | 0.959707i | \(0.590667\pi\) | |||||||
\(908\) | 18.9455 | − | 20.8405i | 0.628728 | − | 0.691615i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −27.1721 | + | 0.646730i | −0.900745 | + | 0.0214389i | ||||
\(911\) | −11.1615 | + | 19.3322i | −0.369796 | + | 0.640506i | −0.989533 | − | 0.144304i | \(-0.953906\pi\) |
0.619737 | + | 0.784809i | \(0.287239\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.16866 | + | 3.75623i | 0.0717722 | + | 0.124313i | ||||
\(914\) | −12.6096 | − | 20.6875i | −0.417089 | − | 0.684282i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −36.1561 | + | 11.5576i | −1.19463 | + | 0.381874i | ||||
\(917\) | 24.5383 | + | 24.5383i | 0.810327 | + | 0.810327i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 51.8070i | 1.70895i | 0.519489 | + | 0.854477i | \(0.326123\pi\) | ||||
−0.519489 | + | 0.854477i | \(0.673877\pi\) | |||||||
\(920\) | 17.7060 | − | 6.12793i | 0.583750 | − | 0.202032i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.13976 | + | 12.9421i | −0.103403 | + | 0.426225i | ||||
\(923\) | 8.67752 | − | 32.3849i | 0.285624 | − | 1.06596i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27.6615 | − | 103.234i | −0.909505 | − | 3.39432i | ||||
\(926\) | 0.0523067 | + | 2.19764i | 0.00171890 | + | 0.0722190i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.89853 | + | 4.63881i | 0.193629 | + | 0.152276i | ||||
\(929\) | 13.9260 | − | 24.1206i | 0.456899 | − | 0.791372i | −0.541897 | − | 0.840445i | \(-0.682294\pi\) |
0.998795 | + | 0.0490736i | \(0.0156269\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.6513 | + | 5.26555i | 0.644046 | + | 0.172571i | ||||
\(932\) | 21.3346 | − | 13.7107i | 0.698839 | − | 0.449110i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.8293 | − | 5.52872i | 0.616114 | − | 0.180905i | ||||
\(935\) | − | 17.9671i | − | 0.587589i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 35.0104i | − | 1.14374i | −0.820344 | − | 0.571870i | \(-0.806218\pi\) | ||
0.820344 | − | 0.571870i | \(-0.193782\pi\) | |||||||
\(938\) | −0.222910 | − | 0.759169i | −0.00727825 | − | 0.0247877i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.834381 | − | 3.83547i | 0.0272145 | − | 0.125099i | ||||
\(941\) | −25.0151 | − | 6.70277i | −0.815468 | − | 0.218504i | −0.173104 | − | 0.984904i | \(-0.555380\pi\) |
−0.642364 | + | 0.766400i | \(0.722046\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.08616 | − | 5.34539i | 0.100499 | − | 0.174070i | ||||
\(944\) | −34.8900 | − | 28.8084i | −1.13557 | − | 0.937633i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.31113 | − | 0.126412i | 0.172680 | − | 0.00411000i | ||||
\(947\) | −5.18039 | − | 19.3335i | −0.168340 | − | 0.628254i | −0.997591 | − | 0.0693768i | \(-0.977899\pi\) |
0.829250 | − | 0.558877i | \(-0.188768\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.0173066 | − | 0.0645892i | 0.000561797 | − | 0.00209665i | ||||
\(950\) | −106.310 | − | 25.7910i | −3.44916 | − | 0.836770i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.03182 | + | 16.5338i | −0.260313 | + | 0.535864i | ||||
\(953\) | 6.37793i | 0.206601i | 0.994650 | + | 0.103301i | \(0.0329404\pi\) | ||||
−0.994650 | + | 0.103301i | \(0.967060\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.2220 | − | 14.2220i | −0.460215 | − | 0.460215i | ||||
\(956\) | −6.77093 | + | 13.1336i | −0.218988 | + | 0.424770i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −28.2645 | + | 17.2280i | −0.913183 | + | 0.556610i | ||||
\(959\) | −14.6109 | − | 25.3068i | −0.471810 | − | 0.817199i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.3329 | − | 21.3612i | 0.397835 | − | 0.689070i | ||||
\(962\) | 0.658068 | + | 27.6484i | 0.0212170 | + | 0.891421i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 44.7314 | − | 2.13053i | 1.44070 | − | 0.0686199i | ||||
\(965\) | −80.2477 | + | 21.5023i | −2.58326 | + | 0.692183i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.7206 | − | 18.8912i | 1.05222 | − | 0.607501i | 0.128952 | − | 0.991651i | \(-0.458839\pi\) |
0.923271 | + | 0.384149i | \(0.125505\pi\) | |||||||
\(968\) | 15.0571 | + | 22.2473i | 0.483954 | + | 0.715056i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.1464 | − | 48.1789i | −0.454215 | − | 1.54693i | ||||
\(971\) | −39.2528 | − | 39.2528i | −1.25968 | − | 1.25968i | −0.951245 | − | 0.308436i | \(-0.900194\pi\) |
−0.308436 | − | 0.951245i | \(-0.599806\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.83195 | + | 9.83195i | −0.315198 | + | 0.315198i | ||||
\(974\) | 14.2535 | − | 26.1031i | 0.456711 | − | 0.836398i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −19.3677 | − | 3.25709i | −0.619945 | − | 0.104257i | ||||
\(977\) | 13.9657 | + | 24.1893i | 0.446803 | + | 0.773885i | 0.998176 | − | 0.0603737i | \(-0.0192293\pi\) |
−0.551373 | + | 0.834259i | \(0.685896\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.50647 | + | 5.62224i | 0.0481471 | + | 0.179687i | ||||
\(980\) | 21.6790 | + | 19.7078i | 0.692511 | + | 0.629542i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −25.7240 | + | 26.9784i | −0.820887 | + | 0.860916i | ||||
\(983\) | 31.3818 | + | 18.1183i | 1.00092 | + | 0.577883i | 0.908521 | − | 0.417839i | \(-0.137212\pi\) |
0.0924017 | + | 0.995722i | \(0.470546\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.9452 | − | 20.7530i | 1.14531 | − | 0.661245i | ||||
\(986\) | −1.52424 | + | 6.28293i | −0.0485418 | + | 0.200089i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 25.1610 | + | 12.9716i | 0.800478 | + | 0.412681i | ||||
\(989\) | −3.37509 | + | 3.37509i | −0.107322 | + | 0.107322i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.0673 | 1.65397 | 0.826985 | − | 0.562223i | \(-0.190054\pi\) | ||||
0.826985 | + | 0.562223i | \(0.190054\pi\) | |||||||
\(992\) | 13.0875 | + | 5.60466i | 0.415530 | + | 0.177948i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 31.8663 | − | 19.4234i | 1.01074 | − | 0.616073i | ||||
\(995\) | −100.563 | − | 26.9457i | −3.18805 | − | 0.854236i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52.9980 | + | 14.2008i | −1.67846 | + | 0.449743i | −0.967373 | − | 0.253357i | \(-0.918465\pi\) |
−0.711091 | + | 0.703100i | \(0.751798\pi\) | |||||||
\(998\) | −13.6125 | − | 12.9795i | −0.430895 | − | 0.410860i | ||||
\(999\) | 0 | 0 |
(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 | 432.2.y.e.181.4 | 72 | ||
3.2 | odd | 2 | 144.2.x.e.133.15 | yes | 72 | ||
4.3 | odd | 2 | 1728.2.bc.e.1585.1 | 72 | |||
9.4 | even | 3 | inner | 432.2.y.e.37.15 | 72 | ||
9.5 | odd | 6 | 144.2.x.e.85.4 | yes | 72 | ||
12.11 | even | 2 | 576.2.bb.e.241.16 | 72 | |||
16.3 | odd | 4 | 1728.2.bc.e.721.18 | 72 | |||
16.13 | even | 4 | inner | 432.2.y.e.397.15 | 72 | ||
36.23 | even | 6 | 576.2.bb.e.49.6 | 72 | |||
36.31 | odd | 6 | 1728.2.bc.e.1009.18 | 72 | |||
48.29 | odd | 4 | 144.2.x.e.61.4 | yes | 72 | ||
48.35 | even | 4 | 576.2.bb.e.529.6 | 72 | |||
144.13 | even | 12 | inner | 432.2.y.e.253.4 | 72 | ||
144.67 | odd | 12 | 1728.2.bc.e.145.1 | 72 | |||
144.77 | odd | 12 | 144.2.x.e.13.15 | ✓ | 72 | ||
144.131 | even | 12 | 576.2.bb.e.337.16 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.e.13.15 | ✓ | 72 | 144.77 | odd | 12 | ||
144.2.x.e.61.4 | yes | 72 | 48.29 | odd | 4 | ||
144.2.x.e.85.4 | yes | 72 | 9.5 | odd | 6 | ||
144.2.x.e.133.15 | yes | 72 | 3.2 | odd | 2 | ||
432.2.y.e.37.15 | 72 | 9.4 | even | 3 | inner | ||
432.2.y.e.181.4 | 72 | 1.1 | even | 1 | trivial | ||
432.2.y.e.253.4 | 72 | 144.13 | even | 12 | inner | ||
432.2.y.e.397.15 | 72 | 16.13 | even | 4 | inner | ||
576.2.bb.e.49.6 | 72 | 36.23 | even | 6 | |||
576.2.bb.e.241.16 | 72 | 12.11 | even | 2 | |||
576.2.bb.e.337.16 | 72 | 144.131 | even | 12 | |||
576.2.bb.e.529.6 | 72 | 48.35 | even | 4 | |||
1728.2.bc.e.145.1 | 72 | 144.67 | odd | 12 | |||
1728.2.bc.e.721.18 | 72 | 16.3 | odd | 4 | |||
1728.2.bc.e.1009.18 | 72 | 36.31 | odd | 6 | |||
1728.2.bc.e.1585.1 | 72 | 4.3 | odd | 2 |