Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(19,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.w (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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 19.4 | ||
Character | \(\chi\) | \(=\) | 784.19 |
Dual form | 784.2.w.e.619.4 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.830359 | − | 1.14477i | −0.587153 | − | 0.809476i | ||||
\(3\) | 0.472168 | − | 1.76215i | 0.272606 | − | 1.01738i | −0.684822 | − | 0.728710i | \(-0.740120\pi\) |
0.957429 | − | 0.288670i | \(-0.0932131\pi\) | |||||||
\(4\) | −0.621007 | + | 1.90114i | −0.310504 | + | 0.950572i | ||||
\(5\) | −0.818676 | + | 0.219363i | −0.366123 | + | 0.0981023i | −0.437190 | − | 0.899369i | \(-0.644026\pi\) |
0.0710670 | + | 0.997472i | \(0.477360\pi\) | |||||||
\(6\) | −2.40933 | + | 0.922696i | −0.983606 | + | 0.376689i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.69204 | − | 0.867721i | 0.951779 | − | 0.306786i | ||||
\(9\) | −0.284168 | − | 0.164064i | −0.0947226 | − | 0.0546881i | ||||
\(10\) | 0.930916 | + | 0.755047i | 0.294381 | + | 0.238767i | ||||
\(11\) | −0.732051 | + | 2.73205i | −0.220722 | + | 0.823744i | 0.763352 | + | 0.645983i | \(0.223552\pi\) |
−0.984074 | + | 0.177762i | \(0.943114\pi\) | |||||||
\(12\) | 3.05689 | + | 1.99197i | 0.882448 | + | 0.575032i | ||||
\(13\) | −1.00197 | + | 1.00197i | −0.277897 | + | 0.277897i | −0.832269 | − | 0.554372i | \(-0.812959\pi\) |
0.554372 | + | 0.832269i | \(0.312959\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.54621i | 0.399229i | ||||||||
\(16\) | −3.22870 | − | 2.36125i | −0.807175 | − | 0.590312i | ||||
\(17\) | −5.61300 | + | 3.24067i | −1.36135 | + | 0.785977i | −0.989804 | − | 0.142436i | \(-0.954506\pi\) |
−0.371549 | + | 0.928413i | \(0.621173\pi\) | |||||||
\(18\) | 0.0481450 | + | 0.461540i | 0.0113479 | + | 0.108786i | ||||
\(19\) | −5.37031 | + | 1.43897i | −1.23203 | + | 0.330123i | −0.815371 | − | 0.578938i | \(-0.803467\pi\) |
−0.416663 | + | 0.909061i | \(0.636800\pi\) | |||||||
\(20\) | 0.0913619 | − | 1.69265i | 0.0204292 | − | 0.378487i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.73544 | − | 1.43055i | 0.796399 | − | 0.304995i | ||||
\(23\) | −2.20366 | + | 3.81684i | −0.459494 | + | 0.795867i | −0.998934 | − | 0.0461569i | \(-0.985303\pi\) |
0.539440 | + | 0.842024i | \(0.318636\pi\) | |||||||
\(24\) | −0.257965 | − | 5.15349i | −0.0526568 | − | 1.05195i | ||||
\(25\) | −3.70802 | + | 2.14082i | −0.741604 | + | 0.428165i | ||||
\(26\) | 1.97903 | + | 0.315033i | 0.388119 | + | 0.0617831i | ||||
\(27\) | 3.44668 | − | 3.44668i | 0.663313 | − | 0.663313i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.241319 | + | 0.241319i | 0.0448119 | + | 0.0448119i | 0.729158 | − | 0.684346i | \(-0.239912\pi\) |
−0.684346 | + | 0.729158i | \(0.739912\pi\) | |||||||
\(30\) | 1.77006 | − | 1.28391i | 0.323167 | − | 0.234409i | ||||
\(31\) | 1.69265 | + | 2.93175i | 0.304008 | + | 0.526558i | 0.977040 | − | 0.213056i | \(-0.0683416\pi\) |
−0.673032 | + | 0.739614i | \(0.735008\pi\) | |||||||
\(32\) | −0.0221123 | + | 5.65681i | −0.00390894 | + | 0.999992i | ||||
\(33\) | 4.46864 | + | 2.57997i | 0.777891 | + | 0.449116i | ||||
\(34\) | 8.37063 | + | 3.73469i | 1.43555 | + | 0.640494i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.488380 | − | 0.438359i | 0.0813967 | − | 0.0730598i | ||||
\(37\) | 1.00124 | + | 3.73668i | 0.164603 | + | 0.614307i | 0.998091 | + | 0.0617685i | \(0.0196740\pi\) |
−0.833488 | + | 0.552538i | \(0.813659\pi\) | |||||||
\(38\) | 6.10658 | + | 4.95292i | 0.990619 | + | 0.803470i | ||||
\(39\) | 1.29253 | + | 2.23873i | 0.206971 | + | 0.358484i | ||||
\(40\) | −2.01356 | + | 1.30092i | −0.318372 | + | 0.205693i | ||||
\(41\) | −4.88941 | −0.763597 | −0.381799 | − | 0.924246i | \(-0.624695\pi\) | ||||
−0.381799 | + | 0.924246i | \(0.624695\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.40731 | + | 4.40731i | 0.672109 | + | 0.672109i | 0.958202 | − | 0.286093i | \(-0.0923566\pi\) |
−0.286093 | + | 0.958202i | \(0.592357\pi\) | |||||||
\(44\) | −4.73941 | − | 3.08836i | −0.714494 | − | 0.465587i | ||||
\(45\) | 0.268631 | + | 0.0719794i | 0.0400451 | + | 0.0107301i | ||||
\(46\) | 6.19924 | − | 0.646667i | 0.914029 | − | 0.0953459i | ||||
\(47\) | 4.72731 | − | 8.18793i | 0.689548 | − | 1.19433i | −0.282436 | − | 0.959286i | \(-0.591142\pi\) |
0.971984 | − | 0.235047i | \(-0.0755243\pi\) | |||||||
\(48\) | −5.68537 | + | 4.57456i | −0.820613 | + | 0.660281i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.52974 | + | 2.46718i | 0.782024 | + | 0.348912i | ||||
\(51\) | 3.06028 | + | 11.4211i | 0.428525 | + | 1.59928i | ||||
\(52\) | −1.28266 | − | 2.52713i | −0.177873 | − | 0.350449i | ||||
\(53\) | −4.39598 | − | 1.17790i | −0.603834 | − | 0.161797i | −0.0560660 | − | 0.998427i | \(-0.517856\pi\) |
−0.547768 | + | 0.836630i | \(0.684522\pi\) | |||||||
\(54\) | −6.80764 | − | 1.08368i | −0.926403 | − | 0.147470i | ||||
\(55\) | − | 2.39725i | − | 0.323245i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.1428i | 1.34344i | ||||||||
\(58\) | 0.0758740 | − | 0.476638i | 0.00996274 | − | 0.0625856i | ||||
\(59\) | 1.84601 | + | 0.494636i | 0.240329 | + | 0.0643961i | 0.376973 | − | 0.926224i | \(-0.376965\pi\) |
−0.136644 | + | 0.990620i | \(0.543632\pi\) | |||||||
\(60\) | −2.93957 | − | 0.960207i | −0.379496 | − | 0.123962i | ||||
\(61\) | −3.60291 | − | 13.4463i | −0.461306 | − | 1.72162i | −0.668855 | − | 0.743392i | \(-0.733216\pi\) |
0.207550 | − | 0.978224i | \(-0.433451\pi\) | |||||||
\(62\) | 1.95068 | − | 4.37210i | 0.247737 | − | 0.555257i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.49412 | − | 4.67187i | 0.811765 | − | 0.583984i | ||||
\(65\) | 0.600494 | − | 1.04009i | 0.0744822 | − | 0.129007i | ||||
\(66\) | −0.757098 | − | 7.25788i | −0.0931923 | − | 0.893384i | ||||
\(67\) | 11.9011 | + | 3.18889i | 1.45395 | + | 0.389585i | 0.897396 | − | 0.441227i | \(-0.145457\pi\) |
0.556554 | + | 0.830812i | \(0.312123\pi\) | |||||||
\(68\) | −2.67526 | − | 12.6836i | −0.324423 | − | 1.53811i | ||||
\(69\) | 5.68537 | + | 5.68537i | 0.684438 | + | 0.684438i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.2855 | −1.45802 | −0.729011 | − | 0.684502i | \(-0.760020\pi\) | ||||
−0.729011 | + | 0.684502i | \(0.760020\pi\) | |||||||
\(72\) | −0.907352 | − | 0.195089i | −0.106932 | − | 0.0229915i | ||||
\(73\) | −0.402661 | − | 0.697429i | −0.0471279 | − | 0.0816278i | 0.841499 | − | 0.540258i | \(-0.181673\pi\) |
−0.888627 | + | 0.458631i | \(0.848340\pi\) | |||||||
\(74\) | 3.44626 | − | 4.24898i | 0.400620 | − | 0.493934i | ||||
\(75\) | 2.02166 | + | 7.54493i | 0.233441 | + | 0.871213i | ||||
\(76\) | 0.599312 | − | 11.1034i | 0.0687458 | − | 1.27364i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.48957 | − | 3.33860i | 0.168661 | − | 0.378022i | ||||
\(79\) | 9.32549 | + | 5.38407i | 1.04920 | + | 0.605756i | 0.922425 | − | 0.386176i | \(-0.126204\pi\) |
0.126774 | + | 0.991932i | \(0.459538\pi\) | |||||||
\(80\) | 3.16123 | + | 1.22484i | 0.353436 | + | 0.136941i | ||||
\(81\) | −4.93836 | − | 8.55349i | −0.548707 | − | 0.950388i | ||||
\(82\) | 4.05997 | + | 5.59726i | 0.448348 | + | 0.618114i | ||||
\(83\) | −5.76738 | − | 5.76738i | −0.633052 | − | 0.633052i | 0.315780 | − | 0.948832i | \(-0.397734\pi\) |
−0.948832 | + | 0.315780i | \(0.897734\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.88434 | − | 3.88434i | 0.421316 | − | 0.421316i | ||||
\(86\) | 1.38572 | − | 8.70502i | 0.149426 | − | 0.938687i | ||||
\(87\) | 0.539185 | − | 0.311299i | 0.0578067 | − | 0.0333747i | ||||
\(88\) | 0.399949 | + | 7.99000i | 0.0426347 | + | 0.851736i | ||||
\(89\) | −6.66406 | + | 11.5425i | −0.706389 | + | 1.22350i | 0.259799 | + | 0.965663i | \(0.416344\pi\) |
−0.966188 | + | 0.257839i | \(0.916990\pi\) | |||||||
\(90\) | −0.140660 | − | 0.367290i | −0.0148269 | − | 0.0387158i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.88789 | − | 6.55976i | −0.613855 | − | 0.683902i | ||||
\(93\) | 5.96541 | − | 1.59843i | 0.618584 | − | 0.165749i | ||||
\(94\) | −13.2987 | + | 1.38724i | −1.37165 | + | 0.143083i | ||||
\(95\) | 4.08089 | − | 2.35610i | 0.418690 | − | 0.241731i | ||||
\(96\) | 9.95773 | + | 2.70993i | 1.01631 | + | 0.276581i | ||||
\(97\) | 10.8360i | 1.10022i | 0.835091 | + | 0.550112i | \(0.185415\pi\) | ||||
−0.835091 | + | 0.550112i | \(0.814585\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.656257 | − | 0.656257i | 0.0659564 | − | 0.0659564i | ||||
\(100\) | −1.76731 | − | 8.37894i | −0.176731 | − | 0.837894i | ||||
\(101\) | 2.00559 | − | 7.48495i | 0.199563 | − | 0.744780i | −0.791475 | − | 0.611202i | \(-0.790686\pi\) |
0.991038 | − | 0.133579i | \(-0.0426469\pi\) | |||||||
\(102\) | 10.5334 | − | 12.9869i | 1.04297 | − | 1.28590i | ||||
\(103\) | 10.0056 | + | 5.77673i | 0.985881 | + | 0.569199i | 0.904040 | − | 0.427447i | \(-0.140587\pi\) |
0.0818403 | + | 0.996645i | \(0.473920\pi\) | |||||||
\(104\) | −1.82791 | + | 3.56678i | −0.179242 | + | 0.349752i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.30182 | + | 6.01047i | 0.223572 | + | 0.583789i | ||||
\(107\) | −6.64039 | + | 1.77929i | −0.641951 | + | 0.172010i | −0.565087 | − | 0.825031i | \(-0.691157\pi\) |
−0.0768639 | + | 0.997042i | \(0.524491\pi\) | |||||||
\(108\) | 4.41222 | + | 8.69304i | 0.424566 | + | 0.836488i | ||||
\(109\) | 3.68924 | − | 13.7684i | 0.353365 | − | 1.31878i | −0.529165 | − | 0.848519i | \(-0.677495\pi\) |
0.882530 | − | 0.470257i | \(-0.155839\pi\) | |||||||
\(110\) | −2.74430 | + | 1.99058i | −0.261659 | + | 0.189794i | ||||
\(111\) | 7.05736 | 0.669855 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.05034 | −0.286952 | −0.143476 | − | 0.989654i | \(-0.545828\pi\) | ||||
−0.143476 | + | 0.989654i | \(0.545828\pi\) | |||||||
\(114\) | 11.6111 | − | 8.42213i | 1.08748 | − | 0.788805i | ||||
\(115\) | 0.966803 | − | 3.60816i | 0.0901549 | − | 0.336463i | ||||
\(116\) | −0.608644 | + | 0.308922i | −0.0565112 | + | 0.0286827i | ||||
\(117\) | 0.449116 | − | 0.120340i | 0.0415208 | − | 0.0111255i | ||||
\(118\) | −0.966602 | − | 2.52398i | −0.0889829 | − | 0.232351i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.34168 | + | 4.16245i | 0.122478 | + | 0.379978i | ||||
\(121\) | 2.59808 | + | 1.50000i | 0.236189 | + | 0.136364i | ||||
\(122\) | −12.4012 | + | 15.2897i | −1.12275 | + | 1.38427i | ||||
\(123\) | −2.30862 | + | 8.61589i | −0.208161 | + | 0.776869i | ||||
\(124\) | −6.62483 | + | 1.39733i | −0.594927 | + | 0.125484i | ||||
\(125\) | 5.56261 | − | 5.56261i | 0.497535 | − | 0.497535i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.01709i | 0.800137i | 0.916485 | + | 0.400069i | \(0.131014\pi\) | ||||
−0.916485 | + | 0.400069i | \(0.868986\pi\) | |||||||
\(128\) | −10.7407 | − | 3.55496i | −0.949351 | − | 0.314217i | ||||
\(129\) | 9.84735 | − | 5.68537i | 0.867011 | − | 0.500569i | ||||
\(130\) | −1.68929 | + | 0.176216i | −0.148160 | + | 0.0154552i | ||||
\(131\) | −0.662065 | + | 0.177400i | −0.0578449 | + | 0.0154995i | −0.287625 | − | 0.957743i | \(-0.592866\pi\) |
0.229781 | + | 0.973242i | \(0.426199\pi\) | |||||||
\(132\) | −7.67996 | + | 6.89335i | −0.668455 | + | 0.599989i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.23163 | − | 16.2720i | −0.538331 | − | 1.40568i | ||||
\(135\) | −2.06564 | + | 3.57779i | −0.177782 | + | 0.307927i | ||||
\(136\) | −12.2984 | + | 13.5945i | −1.05458 | + | 1.16572i | ||||
\(137\) | −14.8494 | + | 8.57331i | −1.26867 | + | 0.732467i | −0.974736 | − | 0.223359i | \(-0.928298\pi\) |
−0.293934 | + | 0.955826i | \(0.594964\pi\) | |||||||
\(138\) | 1.78756 | − | 11.2294i | 0.152167 | − | 0.955906i | ||||
\(139\) | −7.13391 | + | 7.13391i | −0.605090 | + | 0.605090i | −0.941659 | − | 0.336568i | \(-0.890734\pi\) |
0.336568 | + | 0.941659i | \(0.390734\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.1963 | − | 12.1963i | −1.02712 | − | 1.02712i | ||||
\(142\) | 10.2014 | + | 14.0641i | 0.856081 | + | 1.18023i | ||||
\(143\) | −2.00395 | − | 3.47094i | −0.167578 | − | 0.290254i | ||||
\(144\) | 0.530096 | + | 1.20071i | 0.0441746 | + | 0.100059i | ||||
\(145\) | −0.250499 | − | 0.144626i | −0.0208028 | − | 0.0120105i | ||||
\(146\) | −0.464044 | + | 1.04007i | −0.0384046 | + | 0.0860769i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.72575 | − | 0.417003i | −0.635053 | − | 0.0342775i | ||||
\(149\) | −3.23973 | − | 12.0908i | −0.265409 | − | 0.990519i | −0.962000 | − | 0.273050i | \(-0.911967\pi\) |
0.696591 | − | 0.717468i | \(-0.254699\pi\) | |||||||
\(150\) | 6.95852 | − | 8.57934i | 0.568161 | − | 0.700500i | ||||
\(151\) | −3.36965 | − | 5.83640i | −0.274218 | − | 0.474960i | 0.695719 | − | 0.718314i | \(-0.255086\pi\) |
−0.969938 | + | 0.243354i | \(0.921752\pi\) | |||||||
\(152\) | −13.2085 | + | 8.53369i | −1.07135 | + | 0.692174i | ||||
\(153\) | 2.12671 | 0.171935 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.02885 | − | 2.02885i | −0.162961 | − | 0.162961i | ||||
\(156\) | −5.05882 | + | 1.06702i | −0.405030 | + | 0.0854300i | ||||
\(157\) | 6.94769 | + | 1.86163i | 0.554486 | + | 0.148574i | 0.525172 | − | 0.850996i | \(-0.324001\pi\) |
0.0293140 | + | 0.999570i | \(0.490668\pi\) | |||||||
\(158\) | −1.57997 | − | 15.1463i | −0.125695 | − | 1.20497i | ||||
\(159\) | −4.15128 | + | 7.19023i | −0.329218 | + | 0.570222i | ||||
\(160\) | −1.22279 | − | 4.63594i | −0.0966704 | − | 0.366504i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.69119 | + | 12.7558i | −0.447142 | + | 1.00219i | ||||
\(163\) | 2.30775 | + | 8.61264i | 0.180757 | + | 0.674594i | 0.995499 | + | 0.0947706i | \(0.0302118\pi\) |
−0.814742 | + | 0.579823i | \(0.803122\pi\) | |||||||
\(164\) | 3.03636 | − | 9.29547i | 0.237100 | − | 0.725854i | ||||
\(165\) | −4.22432 | − | 1.13190i | −0.328863 | − | 0.0881186i | ||||
\(166\) | −1.81334 | + | 11.3913i | −0.140742 | + | 0.884138i | ||||
\(167\) | 16.3480i | 1.26504i | 0.774543 | + | 0.632522i | \(0.217980\pi\) | ||||
−0.774543 | + | 0.632522i | \(0.782020\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.9921i | 0.845546i | ||||||||
\(170\) | −7.67209 | − | 1.22129i | −0.588422 | − | 0.0936686i | ||||
\(171\) | 1.76215 | + | 0.472168i | 0.134755 | + | 0.0361076i | ||||
\(172\) | −11.1159 | + | 5.64196i | −0.847580 | + | 0.430196i | ||||
\(173\) | 4.18902 | + | 15.6337i | 0.318486 | + | 1.18860i | 0.920700 | + | 0.390270i | \(0.127618\pi\) |
−0.602215 | + | 0.798334i | \(0.705715\pi\) | |||||||
\(174\) | −0.804083 | − | 0.358754i | −0.0609574 | − | 0.0271971i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.81463 | − | 7.09242i | 0.664427 | − | 0.534611i | ||||
\(177\) | 1.74325 | − | 3.01939i | 0.131031 | − | 0.226952i | ||||
\(178\) | 18.7471 | − | 1.95558i | 1.40515 | − | 0.146577i | ||||
\(179\) | 12.0804 | + | 3.23694i | 0.902932 | + | 0.241940i | 0.680275 | − | 0.732957i | \(-0.261860\pi\) |
0.222657 | + | 0.974897i | \(0.428527\pi\) | |||||||
\(180\) | −0.303665 | + | 0.466006i | −0.0226339 | + | 0.0347341i | ||||
\(181\) | −17.5233 | − | 17.5233i | −1.30250 | − | 1.30250i | −0.926703 | − | 0.375794i | \(-0.877370\pi\) |
−0.375794 | − | 0.926703i | \(-0.622630\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −25.3956 | −1.87729 | ||||||||
\(184\) | −2.62037 | + | 12.1872i | −0.193176 | + | 0.898455i | ||||
\(185\) | −1.63938 | − | 2.83949i | −0.120530 | − | 0.208764i | ||||
\(186\) | −6.78327 | − | 5.50177i | −0.497373 | − | 0.403409i | ||||
\(187\) | −4.74467 | − | 17.7073i | −0.346964 | − | 1.29489i | ||||
\(188\) | 12.6308 | + | 14.0721i | 0.921192 | + | 1.02631i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.08580 | − | 2.71528i | −0.441510 | − | 0.196987i | ||||
\(191\) | −3.90555 | − | 2.25487i | −0.282595 | − | 0.163157i | 0.352002 | − | 0.935999i | \(-0.385501\pi\) |
−0.634598 | + | 0.772843i | \(0.718834\pi\) | |||||||
\(192\) | −5.16624 | − | 13.6495i | −0.372841 | − | 0.985071i | ||||
\(193\) | −6.96133 | − | 12.0574i | −0.501087 | − | 0.867909i | −0.999999 | − | 0.00125604i | \(-0.999600\pi\) |
0.498912 | − | 0.866653i | \(-0.333733\pi\) | |||||||
\(194\) | 12.4047 | − | 8.99774i | 0.890606 | − | 0.646000i | ||||
\(195\) | −1.54926 | − | 1.54926i | −0.110945 | − | 0.110945i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.1598 | − | 10.1598i | 0.723859 | − | 0.723859i | −0.245530 | − | 0.969389i | \(-0.578962\pi\) |
0.969389 | + | 0.245530i | \(0.0789620\pi\) | |||||||
\(198\) | −1.29619 | − | 0.206336i | −0.0921165 | − | 0.0146637i | ||||
\(199\) | −8.58508 | + | 4.95660i | −0.608580 | + | 0.351364i | −0.772410 | − | 0.635125i | \(-0.780949\pi\) |
0.163829 | + | 0.986489i | \(0.447615\pi\) | |||||||
\(200\) | −8.12448 | + | 8.98070i | −0.574488 | + | 0.635032i | ||||
\(201\) | 11.2386 | − | 19.4659i | 0.792711 | − | 1.37302i | ||||
\(202\) | −10.2339 | + | 3.91926i | −0.720056 | + | 0.275758i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −23.6136 | − | 1.27456i | −1.65329 | − | 0.0892374i | ||||
\(205\) | 4.00284 | − | 1.07256i | 0.279570 | − | 0.0749107i | ||||
\(206\) | −1.69519 | − | 16.2509i | −0.118110 | − | 1.13225i | ||||
\(207\) | 1.25242 | − | 0.723083i | 0.0870490 | − | 0.0502577i | ||||
\(208\) | 5.60098 | − | 0.869162i | 0.388358 | − | 0.0602655i | ||||
\(209\) | − | 15.7254i | − | 1.08775i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.53445 | − | 6.53445i | 0.449850 | − | 0.449850i | −0.445454 | − | 0.895305i | \(-0.646958\pi\) |
0.895305 | + | 0.445454i | \(0.146958\pi\) | |||||||
\(212\) | 4.96929 | − | 7.62591i | 0.341292 | − | 0.523749i | ||||
\(213\) | −5.80082 | + | 21.6490i | −0.397466 | + | 1.48336i | ||||
\(214\) | 7.55079 | + | 6.12429i | 0.516161 | + | 0.418648i | ||||
\(215\) | −4.57496 | − | 2.64136i | −0.312010 | − | 0.180139i | ||||
\(216\) | 6.28783 | − | 12.2693i | 0.427833 | − | 0.834822i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −18.8251 | + | 7.20940i | −1.27500 | + | 0.488282i | ||||
\(219\) | −1.41910 | + | 0.380247i | −0.0958939 | + | 0.0256947i | ||||
\(220\) | 4.55752 | + | 1.48871i | 0.307268 | + | 0.100369i | ||||
\(221\) | 2.37701 | − | 8.87114i | 0.159895 | − | 0.596737i | ||||
\(222\) | −5.86015 | − | 8.07907i | −0.393307 | − | 0.542232i | ||||
\(223\) | 2.27448 | 0.152311 | 0.0761553 | − | 0.997096i | \(-0.475736\pi\) | ||||
0.0761553 | + | 0.997096i | \(0.475736\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.40493 | 0.0936622 | ||||||||
\(226\) | 2.53287 | + | 3.49194i | 0.168484 | + | 0.232280i | ||||
\(227\) | −3.26076 | + | 12.1693i | −0.216424 | + | 0.807706i | 0.769236 | + | 0.638965i | \(0.220637\pi\) |
−0.985660 | + | 0.168742i | \(0.946030\pi\) | |||||||
\(228\) | −19.2828 | − | 6.29872i | −1.27704 | − | 0.417143i | ||||
\(229\) | 8.24963 | − | 2.21048i | 0.545151 | − | 0.146073i | 0.0242754 | − | 0.999705i | \(-0.492272\pi\) |
0.520876 | + | 0.853633i | \(0.325605\pi\) | |||||||
\(230\) | −4.93331 | + | 1.88930i | −0.325293 | + | 0.124577i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.859038 | + | 0.440243i | 0.0563986 | + | 0.0289034i | ||||
\(233\) | −22.6834 | − | 13.0963i | −1.48604 | − | 0.857966i | −0.486166 | − | 0.873866i | \(-0.661605\pi\) |
−0.999874 | + | 0.0159008i | \(0.994938\pi\) | |||||||
\(234\) | −0.510690 | − | 0.414210i | −0.0333849 | − | 0.0270778i | ||||
\(235\) | −2.07400 | + | 7.74026i | −0.135293 | + | 0.504919i | ||||
\(236\) | −2.08676 | + | 3.20235i | −0.135836 | + | 0.208455i | ||||
\(237\) | 13.8908 | − | 13.8908i | 0.902302 | − | 0.902302i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 20.6122i | − | 1.33329i | −0.745375 | − | 0.666645i | \(-0.767730\pi\) | ||
0.745375 | − | 0.666645i | \(-0.232270\pi\) | |||||||
\(240\) | 3.65098 | − | 4.99224i | 0.235670 | − | 0.322248i | ||||
\(241\) | 0.615233 | − | 0.355205i | 0.0396306 | − | 0.0228808i | −0.480054 | − | 0.877239i | \(-0.659383\pi\) |
0.519684 | + | 0.854358i | \(0.326050\pi\) | |||||||
\(242\) | −0.440178 | − | 4.21974i | −0.0282957 | − | 0.271255i | ||||
\(243\) | −3.27955 | + | 0.878753i | −0.210383 | + | 0.0563720i | ||||
\(244\) | 27.8007 | + | 1.50057i | 1.77976 | + | 0.0960639i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.7802 | − | 4.51144i | 0.751079 | − | 0.287639i | ||||
\(247\) | 3.93910 | − | 6.82272i | 0.250639 | − | 0.434119i | ||||
\(248\) | 7.10061 | + | 6.42363i | 0.450889 | + | 0.407901i | ||||
\(249\) | −12.8862 | + | 7.43984i | −0.816628 | + | 0.471480i | ||||
\(250\) | −10.9869 | − | 1.74896i | −0.694871 | − | 0.110614i | ||||
\(251\) | −4.98077 | + | 4.98077i | −0.314383 | + | 0.314383i | −0.846605 | − | 0.532222i | \(-0.821357\pi\) |
0.532222 | + | 0.846605i | \(0.321357\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.81463 | − | 8.81463i | −0.554171 | − | 0.554171i | ||||
\(254\) | 10.3225 | − | 7.48742i | 0.647692 | − | 0.469803i | ||||
\(255\) | −5.01075 | − | 8.67887i | −0.313785 | − | 0.543492i | ||||
\(256\) | 4.84900 | + | 15.2475i | 0.303063 | + | 0.952971i | ||||
\(257\) | −5.37871 | − | 3.10540i | −0.335515 | − | 0.193710i | 0.322772 | − | 0.946477i | \(-0.395385\pi\) |
−0.658287 | + | 0.752767i | \(0.728719\pi\) | |||||||
\(258\) | −14.6853 | − | 6.55208i | −0.914267 | − | 0.407914i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.60444 | + | 1.78753i | 0.0995034 | + | 0.110858i | ||||
\(261\) | −0.0289833 | − | 0.108167i | −0.00179402 | − | 0.00669538i | ||||
\(262\) | 0.752834 | + | 0.610608i | 0.0465102 | + | 0.0377235i | ||||
\(263\) | −0.391699 | − | 0.678442i | −0.0241532 | − | 0.0418345i | 0.853696 | − | 0.520771i | \(-0.174356\pi\) |
−0.877849 | + | 0.478937i | \(0.841022\pi\) | |||||||
\(264\) | 14.2684 | + | 3.06785i | 0.878162 | + | 0.188813i | ||||
\(265\) | 3.85727 | 0.236950 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.1931 | + | 17.1931i | 1.05220 | + | 1.05220i | ||||
\(268\) | −13.4532 | + | 20.6454i | −0.821785 | + | 1.26112i | ||||
\(269\) | −16.8759 | − | 4.52188i | −1.02894 | − | 0.275704i | −0.295417 | − | 0.955368i | \(-0.595459\pi\) |
−0.733523 | + | 0.679664i | \(0.762125\pi\) | |||||||
\(270\) | 5.81097 | − | 0.606165i | 0.353644 | − | 0.0368900i | ||||
\(271\) | −3.21738 | + | 5.57267i | −0.195442 | + | 0.338516i | −0.947045 | − | 0.321100i | \(-0.895947\pi\) |
0.751603 | + | 0.659615i | \(0.229281\pi\) | |||||||
\(272\) | 25.7747 | + | 2.79055i | 1.56282 | + | 0.169202i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.1448 | + | 9.88026i | 1.33782 | + | 0.596888i | ||||
\(275\) | −3.13439 | − | 11.6977i | −0.189011 | − | 0.705397i | ||||
\(276\) | −14.3394 | + | 7.27806i | −0.863129 | + | 0.438087i | ||||
\(277\) | 7.14372 | + | 1.91415i | 0.429224 | + | 0.115010i | 0.466962 | − | 0.884277i | \(-0.345348\pi\) |
−0.0377377 | + | 0.999288i | \(0.512015\pi\) | |||||||
\(278\) | 14.0904 | + | 2.24300i | 0.845087 | + | 0.134526i | ||||
\(279\) | − | 1.11081i | − | 0.0665026i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.8611i | 0.886539i | 0.896388 | + | 0.443270i | \(0.146182\pi\) | ||||
−0.896388 | + | 0.443270i | \(0.853818\pi\) | |||||||
\(282\) | −3.83468 | + | 24.0893i | −0.228352 | + | 1.43450i | ||||
\(283\) | −11.3208 | − | 3.03340i | −0.672951 | − | 0.180317i | −0.0938672 | − | 0.995585i | \(-0.529923\pi\) |
−0.579084 | + | 0.815268i | \(0.696590\pi\) | |||||||
\(284\) | 7.62939 | − | 23.3565i | 0.452721 | − | 1.38595i | ||||
\(285\) | −2.22495 | − | 8.30362i | −0.131795 | − | 0.491864i | ||||
\(286\) | −2.30944 | + | 5.17618i | −0.136560 | + | 0.306074i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.934365 | − | 1.60386i | 0.0550580 | − | 0.0945081i | ||||
\(289\) | 12.5039 | − | 21.6573i | 0.735521 | − | 1.27396i | ||||
\(290\) | 0.0424407 | + | 0.406855i | 0.00249220 | + | 0.0238914i | ||||
\(291\) | 19.0946 | + | 5.11639i | 1.11935 | + | 0.299928i | ||||
\(292\) | 1.57597 | − | 0.332408i | 0.0922265 | − | 0.0194527i | ||||
\(293\) | 8.11929 | + | 8.11929i | 0.474334 | + | 0.474334i | 0.903314 | − | 0.428980i | \(-0.141127\pi\) |
−0.428980 | + | 0.903314i | \(0.641127\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.61978 | −0.0943075 | ||||||||
\(296\) | 5.93777 | + | 9.19049i | 0.345126 | + | 0.534186i | ||||
\(297\) | 6.89335 | + | 11.9396i | 0.399993 | + | 0.692808i | ||||
\(298\) | −11.1511 | + | 13.7485i | −0.645966 | + | 0.796428i | ||||
\(299\) | −1.61637 | − | 6.03238i | −0.0934771 | − | 0.348861i | ||||
\(300\) | −15.5995 | − | 0.841993i | −0.900635 | − | 0.0486125i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.88333 | + | 8.70379i | −0.223461 | + | 0.500847i | ||||
\(303\) | −12.2427 | − | 7.06830i | −0.703322 | − | 0.406063i | ||||
\(304\) | 20.7369 | + | 8.03464i | 1.18934 | + | 0.460818i | ||||
\(305\) | 5.89924 | + | 10.2178i | 0.337789 | + | 0.585068i | ||||
\(306\) | −1.76594 | − | 2.43460i | −0.100952 | − | 0.139177i | ||||
\(307\) | 14.2527 | + | 14.2527i | 0.813442 | + | 0.813442i | 0.985148 | − | 0.171706i | \(-0.0549279\pi\) |
−0.171706 | + | 0.985148i | \(0.554928\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.9038 | − | 14.9038i | 0.847848 | − | 0.847848i | ||||
\(310\) | −0.637896 | + | 4.00724i | −0.0362301 | + | 0.227596i | ||||
\(311\) | 11.0134 | − | 6.35857i | 0.624511 | − | 0.360561i | −0.154112 | − | 0.988053i | \(-0.549252\pi\) |
0.778623 | + | 0.627492i | \(0.215918\pi\) | |||||||
\(312\) | 5.42213 | + | 4.90519i | 0.306968 | + | 0.277701i | ||||
\(313\) | −12.3991 | + | 21.4760i | −0.700841 | + | 1.21389i | 0.267330 | + | 0.963605i | \(0.413859\pi\) |
−0.968172 | + | 0.250288i | \(0.919475\pi\) | |||||||
\(314\) | −3.63794 | − | 9.49934i | −0.205301 | − | 0.536079i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.0271 | + | 14.3856i | −0.901595 | + | 0.809250i | ||||
\(317\) | 1.96459 | − | 0.526409i | 0.110342 | − | 0.0295661i | −0.203225 | − | 0.979132i | \(-0.565142\pi\) |
0.313568 | + | 0.949566i | \(0.398476\pi\) | |||||||
\(318\) | 11.6782 | − | 1.21820i | 0.654882 | − | 0.0683133i | ||||
\(319\) | −0.835955 | + | 0.482639i | −0.0468045 | + | 0.0270226i | ||||
\(320\) | −4.29174 | + | 5.24932i | −0.239916 | + | 0.293446i | ||||
\(321\) | 12.5415i | 0.699999i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.4803 | − | 25.4803i | 1.41776 | − | 1.41776i | ||||
\(324\) | 19.3282 | − | 4.07675i | 1.07379 | − | 0.226486i | ||||
\(325\) | 1.57028 | − | 5.86038i | 0.0871037 | − | 0.325075i | ||||
\(326\) | 7.94325 | − | 9.79343i | 0.439936 | − | 0.542408i | ||||
\(327\) | −22.5201 | − | 13.0020i | −1.24537 | − | 0.719013i | ||||
\(328\) | −13.1625 | + | 4.24264i | −0.726776 | + | 0.234261i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.21193 | + | 5.77577i | 0.121763 | + | 0.317946i | ||||
\(331\) | −1.41585 | + | 0.379375i | −0.0778221 | + | 0.0208524i | −0.297520 | − | 0.954716i | \(-0.596159\pi\) |
0.219698 | + | 0.975568i | \(0.429493\pi\) | |||||||
\(332\) | 14.5462 | − | 7.38303i | 0.798326 | − | 0.405197i | ||||
\(333\) | 0.328536 | − | 1.22611i | 0.0180037 | − | 0.0671906i | ||||
\(334\) | 18.7147 | − | 13.5747i | 1.02402 | − | 0.742774i | ||||
\(335\) | −10.4427 | −0.570543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.9109 | 0.921195 | 0.460598 | − | 0.887609i | \(-0.347635\pi\) | ||||
0.460598 | + | 0.887609i | \(0.347635\pi\) | |||||||
\(338\) | 12.5835 | − | 9.12739i | 0.684450 | − | 0.496465i | ||||
\(339\) | −1.44027 | + | 5.37516i | −0.0782247 | + | 0.291939i | ||||
\(340\) | 4.97249 | + | 9.79690i | 0.269671 | + | 0.531312i | ||||
\(341\) | −9.24879 | + | 2.47821i | −0.500850 | + | 0.134202i | ||||
\(342\) | −0.922696 | − | 2.40933i | −0.0498937 | − | 0.130282i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 15.6890 | + | 8.04033i | 0.845892 | + | 0.433506i | ||||
\(345\) | −5.90164 | − | 3.40731i | −0.317734 | − | 0.183444i | ||||
\(346\) | 14.4186 | − | 17.7770i | 0.775148 | − | 0.955699i | ||||
\(347\) | −0.483878 | + | 1.80586i | −0.0259760 | + | 0.0969436i | −0.977697 | − | 0.210021i | \(-0.932647\pi\) |
0.951721 | + | 0.306965i | \(0.0993134\pi\) | |||||||
\(348\) | 0.256986 | + | 1.21839i | 0.0137759 | + | 0.0653124i | ||||
\(349\) | −17.2528 | + | 17.2528i | −0.923520 | + | 0.923520i | −0.997276 | − | 0.0737567i | \(-0.976501\pi\) |
0.0737567 | + | 0.997276i | \(0.476501\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.90695i | 0.368666i | ||||||||
\(352\) | −15.4385 | − | 4.20149i | −0.822875 | − | 0.223940i | ||||
\(353\) | 2.58900 | − | 1.49476i | 0.137798 | − | 0.0795579i | −0.429516 | − | 0.903059i | \(-0.641316\pi\) |
0.567314 | + | 0.823501i | \(0.307982\pi\) | |||||||
\(354\) | −4.90404 | + | 0.511560i | −0.260647 | + | 0.0271891i | ||||
\(355\) | 10.0578 | − | 2.69499i | 0.533815 | − | 0.143035i | ||||
\(356\) | −17.8055 | − | 19.8373i | −0.943690 | − | 1.05138i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.32552 | − | 16.5171i | −0.334314 | − | 0.872958i | ||||
\(359\) | 4.81343 | − | 8.33711i | 0.254043 | − | 0.440016i | −0.710592 | − | 0.703604i | \(-0.751573\pi\) |
0.964635 | + | 0.263588i | \(0.0849061\pi\) | |||||||
\(360\) | 0.785622 | − | 0.0393253i | 0.0414059 | − | 0.00207263i | ||||
\(361\) | 10.3151 | − | 5.95545i | 0.542902 | − | 0.313445i | ||||
\(362\) | −5.50956 | + | 34.6108i | −0.289576 | + | 1.81910i | ||||
\(363\) | 3.86996 | − | 3.86996i | 0.203120 | − | 0.203120i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.482639 | + | 0.482639i | 0.0252625 | + | 0.0252625i | ||||
\(366\) | 21.0874 | + | 29.0721i | 1.10226 | + | 1.51962i | ||||
\(367\) | 3.69078 | + | 6.39263i | 0.192657 | + | 0.333692i | 0.946130 | − | 0.323787i | \(-0.104956\pi\) |
−0.753473 | + | 0.657479i | \(0.771623\pi\) | |||||||
\(368\) | 16.1275 | − | 7.12006i | 0.840702 | − | 0.371159i | ||||
\(369\) | 1.38941 | + | 0.802178i | 0.0723299 | + | 0.0417597i | ||||
\(370\) | −1.88930 | + | 4.23452i | −0.0982199 | + | 0.220142i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.665723 | + | 12.3337i | −0.0345161 | + | 0.639474i | ||||
\(373\) | 0.900941 | + | 3.36236i | 0.0466490 | + | 0.174096i | 0.985320 | − | 0.170718i | \(-0.0546086\pi\) |
−0.938671 | + | 0.344814i | \(0.887942\pi\) | |||||||
\(374\) | −16.3311 | + | 20.1350i | −0.844461 | + | 1.04116i | ||||
\(375\) | −7.17568 | − | 12.4286i | −0.370551 | − | 0.641813i | ||||
\(376\) | 5.62124 | − | 26.1442i | 0.289893 | − | 1.34828i | ||||
\(377\) | −0.483591 | −0.0249062 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.4803 | + | 11.4803i | 0.589706 | + | 0.589706i | 0.937552 | − | 0.347846i | \(-0.113087\pi\) |
−0.347846 | + | 0.937552i | \(0.613087\pi\) | |||||||
\(380\) | 1.94503 | + | 9.22151i | 0.0997778 | + | 0.473054i | ||||
\(381\) | 15.8895 | + | 4.25758i | 0.814044 | + | 0.218122i | ||||
\(382\) | 0.661695 | + | 6.34331i | 0.0338553 | + | 0.324552i | ||||
\(383\) | −0.0820044 | + | 0.142036i | −0.00419023 | + | 0.00725769i | −0.868113 | − | 0.496367i | \(-0.834667\pi\) |
0.863923 | + | 0.503624i | \(0.168000\pi\) | |||||||
\(384\) | −11.3358 | + | 17.2482i | −0.578477 | + | 0.880193i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.02255 | + | 17.9811i | −0.408337 | + | 0.915213i | ||||
\(387\) | −0.529333 | − | 1.97550i | −0.0269075 | − | 0.100420i | ||||
\(388\) | −20.6007 | − | 6.72921i | −1.04584 | − | 0.341624i | ||||
\(389\) | 21.2418 | + | 5.69172i | 1.07700 | + | 0.288582i | 0.753367 | − | 0.657601i | \(-0.228429\pi\) |
0.323634 | + | 0.946182i | \(0.395095\pi\) | |||||||
\(390\) | −0.487107 | + | 3.05999i | −0.0246656 | + | 0.154949i | ||||
\(391\) | − | 28.5653i | − | 1.44461i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.25042i | 0.0630755i | ||||||||
\(394\) | −20.0670 | − | 3.19439i | −1.01096 | − | 0.160931i | ||||
\(395\) | −8.81562 | − | 2.36214i | −0.443562 | − | 0.118852i | ||||
\(396\) | 0.840099 | + | 1.65518i | 0.0422166 | + | 0.0831760i | ||||
\(397\) | 6.69170 | + | 24.9738i | 0.335847 | + | 1.25340i | 0.902948 | + | 0.429749i | \(0.141398\pi\) |
−0.567102 | + | 0.823648i | \(0.691935\pi\) | |||||||
\(398\) | 12.8029 | + | 5.71221i | 0.641750 | + | 0.286327i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.0271 | + | 1.84347i | 0.851355 | + | 0.0921736i | ||||
\(401\) | −7.86891 | + | 13.6294i | −0.392955 | + | 0.680617i | −0.992838 | − | 0.119470i | \(-0.961880\pi\) |
0.599883 | + | 0.800088i | \(0.295214\pi\) | |||||||
\(402\) | −31.6161 | + | 3.29799i | −1.57687 | + | 0.164489i | ||||
\(403\) | −4.63352 | − | 1.24155i | −0.230812 | − | 0.0618459i | ||||
\(404\) | 12.9845 | + | 8.46112i | 0.646002 | + | 0.420956i | ||||
\(405\) | 5.91924 | + | 5.91924i | 0.294129 | + | 0.294129i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.9418 | −0.542363 | ||||||||
\(408\) | 18.1487 | + | 28.0906i | 0.898495 | + | 1.39069i | ||||
\(409\) | −13.9126 | − | 24.0974i | −0.687935 | − | 1.19154i | −0.972505 | − | 0.232883i | \(-0.925184\pi\) |
0.284570 | − | 0.958655i | \(-0.408149\pi\) | |||||||
\(410\) | −4.55163 | − | 3.69173i | −0.224789 | − | 0.182322i | ||||
\(411\) | 8.09608 | + | 30.2150i | 0.399350 | + | 1.49039i | ||||
\(412\) | −17.1960 | + | 15.4347i | −0.847184 | + | 0.760413i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.86772 | − | 0.833313i | −0.0917935 | − | 0.0409551i | ||||
\(415\) | 5.98676 | + | 3.45646i | 0.293879 | + | 0.169671i | ||||
\(416\) | −5.64581 | − | 5.69013i | −0.276809 | − | 0.278981i | ||||
\(417\) | 9.20265 | + | 15.9395i | 0.450656 | + | 0.780558i | ||||
\(418\) | −18.0020 | + | 13.0577i | −0.880505 | + | 0.638673i | ||||
\(419\) | 0.380613 | + | 0.380613i | 0.0185942 | + | 0.0185942i | 0.716343 | − | 0.697749i | \(-0.245815\pi\) |
−0.697749 | + | 0.716343i | \(0.745815\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.48089 | − | 5.48089i | 0.267122 | − | 0.267122i | −0.560817 | − | 0.827940i | \(-0.689513\pi\) |
0.827940 | + | 0.560817i | \(0.189513\pi\) | |||||||
\(422\) | −12.9064 | − | 2.05452i | −0.628274 | − | 0.100012i | ||||
\(423\) | −2.68670 | + | 1.55116i | −0.130632 | + | 0.0754202i | ||||
\(424\) | −12.8562 | + | 0.643534i | −0.624353 | + | 0.0312528i | ||||
\(425\) | 13.8754 | − | 24.0329i | 0.673056 | − | 1.16577i | ||||
\(426\) | 29.5999 | − | 11.3358i | 1.43412 | − | 0.549221i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.741049 | − | 13.7293i | 0.0358200 | − | 0.663630i | ||||
\(429\) | −7.06252 | + | 1.89240i | −0.340982 | + | 0.0913658i | ||||
\(430\) | 0.775111 | + | 7.43056i | 0.0373792 | + | 0.358334i | ||||
\(431\) | 16.0085 | − | 9.24251i | 0.771102 | − | 0.445196i | −0.0621655 | − | 0.998066i | \(-0.519801\pi\) |
0.833268 | + | 0.552870i | \(0.186467\pi\) | |||||||
\(432\) | −19.2667 | + | 2.98982i | −0.926972 | + | 0.143848i | ||||
\(433\) | − | 30.9347i | − | 1.48663i | −0.668944 | − | 0.743313i | \(-0.733254\pi\) | ||
0.668944 | − | 0.743313i | \(-0.266746\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.373130 | + | 0.373130i | −0.0178902 | + | 0.0178902i | ||||
\(436\) | 23.8847 | + | 15.5641i | 1.14387 | + | 0.745383i | ||||
\(437\) | 6.34200 | − | 23.6686i | 0.303379 | − | 1.13222i | ||||
\(438\) | 1.61366 | + | 1.30881i | 0.0771036 | + | 0.0625371i | ||||
\(439\) | 17.3479 | + | 10.0158i | 0.827971 | + | 0.478029i | 0.853157 | − | 0.521654i | \(-0.174685\pi\) |
−0.0251865 | + | 0.999683i | \(0.508018\pi\) | |||||||
\(440\) | −2.08014 | − | 6.45348i | −0.0991669 | − | 0.307658i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.1292 | + | 4.64509i | −0.576927 | + | 0.220944i | ||||
\(443\) | 0.582875 | − | 0.156181i | 0.0276932 | − | 0.00742038i | −0.244946 | − | 0.969537i | \(-0.578770\pi\) |
0.272639 | + | 0.962116i | \(0.412104\pi\) | |||||||
\(444\) | −4.38267 | + | 13.4171i | −0.207993 | + | 0.636746i | ||||
\(445\) | 2.92370 | − | 10.9114i | 0.138597 | − | 0.517250i | ||||
\(446\) | −1.88864 | − | 2.60376i | −0.0894295 | − | 0.123292i | ||||
\(447\) | −22.8356 | −1.08009 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.1266 | 0.619483 | 0.309741 | − | 0.950821i | \(-0.399758\pi\) | ||||
0.309741 | + | 0.950821i | \(0.399758\pi\) | |||||||
\(450\) | −1.16660 | − | 1.60833i | −0.0549940 | − | 0.0758173i | ||||
\(451\) | 3.57930 | − | 13.3581i | 0.168542 | − | 0.629009i | ||||
\(452\) | 1.89428 | − | 5.79913i | 0.0890995 | − | 0.272768i | ||||
\(453\) | −11.8757 | + | 3.18208i | −0.557968 | + | 0.149507i | ||||
\(454\) | 16.6387 | − | 6.37208i | 0.780893 | − | 0.299057i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.80108 | + | 27.3047i | 0.412148 | + | 1.27866i | ||||
\(457\) | 13.5488 | + | 7.82243i | 0.633788 | + | 0.365918i | 0.782218 | − | 0.623005i | \(-0.214088\pi\) |
−0.148429 | + | 0.988923i | \(0.547422\pi\) | |||||||
\(458\) | −9.38066 | − | 7.60846i | −0.438329 | − | 0.355520i | ||||
\(459\) | −8.17667 | + | 30.5157i | −0.381654 | + | 1.42435i | ||||
\(460\) | 6.25924 | + | 4.07873i | 0.291839 | + | 0.190172i | ||||
\(461\) | −28.3593 | + | 28.3593i | −1.32082 | + | 1.32082i | −0.407712 | + | 0.913111i | \(0.633673\pi\) |
−0.913111 | + | 0.407712i | \(0.866327\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.1195i | 0.609716i | 0.952398 | + | 0.304858i | \(0.0986089\pi\) | ||||
−0.952398 | + | 0.304858i | \(0.901391\pi\) | |||||||
\(464\) | −0.209333 | − | 1.34896i | −0.00971802 | − | 0.0626240i | ||||
\(465\) | −4.53310 | + | 2.61719i | −0.210217 | + | 0.121369i | ||||
\(466\) | 3.84313 | + | 36.8420i | 0.178029 | + | 1.70667i | ||||
\(467\) | 38.8600 | − | 10.4125i | 1.79823 | − | 0.481833i | 0.804527 | − | 0.593916i | \(-0.202419\pi\) |
0.993699 | + | 0.112083i | \(0.0357523\pi\) | |||||||
\(468\) | −0.0501202 | + | 0.928567i | −0.00231680 | + | 0.0429230i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10.5830 | − | 4.05294i | 0.488157 | − | 0.186948i | ||||
\(471\) | 6.56095 | − | 11.3639i | 0.302312 | − | 0.523621i | ||||
\(472\) | 5.39872 | − | 0.270240i | 0.248496 | − | 0.0124388i | ||||
\(473\) | −15.2674 | + | 8.81463i | −0.701995 | + | 0.405297i | ||||
\(474\) | −27.4361 | − | 4.36744i | −1.26018 | − | 0.200603i | ||||
\(475\) | 16.8326 | − | 16.8326i | 0.772334 | − | 0.772334i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.05594 | + | 1.05594i | 0.0483484 | + | 0.0483484i | ||||
\(478\) | −23.5962 | + | 17.1155i | −1.07927 | + | 0.782845i | ||||
\(479\) | 16.7806 | + | 29.0649i | 0.766725 | + | 1.32801i | 0.939330 | + | 0.343016i | \(0.111449\pi\) |
−0.172604 | + | 0.984991i | \(0.555218\pi\) | |||||||
\(480\) | −8.74661 | − | 0.0341902i | −0.399226 | − | 0.00156056i | ||||
\(481\) | −4.74727 | − | 2.74084i | −0.216457 | − | 0.124971i | ||||
\(482\) | −0.917493 | − | 0.409354i | −0.0417906 | − | 0.0186456i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.46514 | + | 4.00781i | −0.202961 | + | 0.182173i | ||||
\(485\) | −2.37701 | − | 8.87114i | −0.107935 | − | 0.402818i | ||||
\(486\) | 3.72918 | + | 3.02466i | 0.169159 | + | 0.137201i | ||||
\(487\) | −8.71339 | − | 15.0920i | −0.394841 | − | 0.683886i | 0.598239 | − | 0.801317i | \(-0.295867\pi\) |
−0.993081 | + | 0.117432i | \(0.962534\pi\) | |||||||
\(488\) | −21.3668 | − | 33.0715i | −0.967228 | − | 1.49708i | ||||
\(489\) | 16.2664 | 0.735594 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.00947 | − | 4.00947i | −0.180945 | − | 0.180945i | 0.610823 | − | 0.791767i | \(-0.290839\pi\) |
−0.791767 | + | 0.610823i | \(0.790839\pi\) | |||||||
\(492\) | −14.9464 | − | 9.73955i | −0.673835 | − | 0.439093i | ||||
\(493\) | −2.13656 | − | 0.572490i | −0.0962259 | − | 0.0257837i | ||||
\(494\) | −11.0813 | + | 1.15594i | −0.498572 | + | 0.0520080i | ||||
\(495\) | −0.393303 | + | 0.681221i | −0.0176777 | + | 0.0306186i | ||||
\(496\) | 1.45754 | − | 13.4625i | 0.0654457 | − | 0.604484i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 19.2171 | + | 8.57400i | 0.861138 | + | 0.384210i | ||||
\(499\) | −5.94130 | − | 22.1732i | −0.265969 | − | 0.992611i | −0.961654 | − | 0.274264i | \(-0.911566\pi\) |
0.695685 | − | 0.718347i | \(-0.255101\pi\) | |||||||
\(500\) | 7.12090 | + | 14.0297i | 0.318456 | + | 0.627429i | ||||
\(501\) | 28.8076 | + | 7.71898i | 1.28703 | + | 0.344859i | ||||
\(502\) | 9.83768 | + | 1.56602i | 0.439077 | + | 0.0698949i | ||||
\(503\) | − | 1.85332i | − | 0.0826356i | −0.999146 | − | 0.0413178i | \(-0.986844\pi\) | ||
0.999146 | − | 0.0413178i | \(-0.0131556\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.56770i | 0.292259i | ||||||||
\(506\) | −2.77143 | + | 17.4100i | −0.123205 | + | 0.773971i | ||||
\(507\) | 19.3698 | + | 5.19012i | 0.860242 | + | 0.230501i | ||||
\(508\) | −17.1428 | − | 5.59968i | −0.760588 | − | 0.248446i | ||||
\(509\) | −2.79659 | − | 10.4370i | −0.123957 | − | 0.462613i | 0.875844 | − | 0.482595i | \(-0.160306\pi\) |
−0.999800 | + | 0.0199820i | \(0.993639\pi\) | |||||||
\(510\) | −5.77461 | + | 12.9427i | −0.255704 | + | 0.573114i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 13.4285 | − | 18.2119i | 0.593463 | − | 0.804861i | ||||
\(513\) | −13.5501 | + | 23.4694i | −0.598250 | + | 1.03620i | ||||
\(514\) | 0.911286 | + | 8.73600i | 0.0401951 | + | 0.385328i | ||||
\(515\) | −9.45854 | − | 2.53441i | −0.416793 | − | 0.111679i | ||||
\(516\) | 4.69343 | + | 22.2519i | 0.206617 | + | 0.979585i | ||||
\(517\) | 18.9092 | + | 18.9092i | 0.831627 | + | 0.831627i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.5268 | 1.29608 | ||||||||
\(520\) | 0.714048 | − | 3.32101i | 0.0313131 | − | 0.145636i | ||||
\(521\) | 16.9527 | + | 29.3630i | 0.742713 | + | 1.28642i | 0.951256 | + | 0.308403i | \(0.0997945\pi\) |
−0.208543 | + | 0.978013i | \(0.566872\pi\) | |||||||
\(522\) | −0.0997602 | + | 0.122997i | −0.00436638 | + | 0.00538342i | ||||
\(523\) | −0.442850 | − | 1.65274i | −0.0193645 | − | 0.0722691i | 0.955567 | − | 0.294772i | \(-0.0952439\pi\) |
−0.974932 | + | 0.222503i | \(0.928577\pi\) | |||||||
\(524\) | 0.0738846 | − | 1.36885i | 0.00322766 | − | 0.0597984i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.451411 | + | 1.01176i | −0.0196825 | + | 0.0441147i | ||||
\(527\) | −19.0017 | − | 10.9706i | −0.827725 | − | 0.477887i | ||||
\(528\) | −8.33595 | − | 18.8815i | −0.362776 | − | 0.821713i | ||||
\(529\) | 1.78780 | + | 3.09656i | 0.0777304 | + | 0.134633i | ||||
\(530\) | −3.20292 | − | 4.41569i | −0.139126 | − | 0.191806i | ||||
\(531\) | −0.443423 | − | 0.443423i | −0.0192429 | − | 0.0192429i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.89905 | − | 4.89905i | 0.212202 | − | 0.212202i | ||||
\(534\) | 5.40573 | − | 33.9586i | 0.233929 | − | 1.46953i | ||||
\(535\) | 5.04602 | − | 2.91332i | 0.218158 | − | 0.125954i | ||||
\(536\) | 34.8052 | − | 1.74222i | 1.50336 | − | 0.0752524i | ||||
\(537\) | 11.4080 | − | 19.7592i | 0.492290 | − | 0.852671i | ||||
\(538\) | 8.83652 | + | 23.0738i | 0.380969 | + | 0.994783i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.51911 | − | 6.14890i | −0.237505 | − | 0.264607i | ||||
\(541\) | 3.27803 | − | 0.878346i | 0.140934 | − | 0.0377631i | −0.187663 | − | 0.982234i | \(-0.560091\pi\) |
0.328596 | + | 0.944470i | \(0.393424\pi\) | |||||||
\(542\) | 9.05102 | − | 0.944147i | 0.388775 | − | 0.0405546i | ||||
\(543\) | −39.1527 | + | 22.6048i | −1.68020 | + | 0.970066i | ||||
\(544\) | −18.2077 | − | 31.8233i | −0.780650 | − | 1.36441i | ||||
\(545\) | 12.0812i | 0.517500i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.2048 | − | 14.2048i | 0.607355 | − | 0.607355i | −0.334899 | − | 0.942254i | \(-0.608702\pi\) |
0.942254 | + | 0.334899i | \(0.108702\pi\) | |||||||
\(548\) | −7.07750 | − | 33.5549i | −0.302336 | − | 1.43340i | ||||
\(549\) | −1.18222 | + | 4.41210i | −0.0504559 | + | 0.188304i | ||||
\(550\) | −10.7885 | + | 13.3014i | −0.460024 | + | 0.567175i | ||||
\(551\) | −1.64321 | − | 0.948709i | −0.0700032 | − | 0.0404164i | ||||
\(552\) | 20.2385 | + | 10.3719i | 0.861410 | + | 0.441458i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.74058 | − | 9.76736i | −0.158922 | − | 0.414975i | ||||
\(555\) | −5.77769 | + | 1.54813i | −0.245249 | + | 0.0657144i | ||||
\(556\) | −9.13238 | − | 17.9928i | −0.387299 | − | 0.763065i | ||||
\(557\) | −8.04752 | + | 30.0337i | −0.340984 | + | 1.27257i | 0.556250 | + | 0.831015i | \(0.312240\pi\) |
−0.897234 | + | 0.441555i | \(0.854427\pi\) | |||||||
\(558\) | −1.27163 | + | 0.922373i | −0.0538323 | + | 0.0390472i | ||||
\(559\) | −8.83201 | −0.373554 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33.4433 | −1.41198 | ||||||||
\(562\) | 17.0126 | − | 12.3401i | 0.717632 | − | 0.520534i | ||||
\(563\) | 7.06109 | − | 26.3524i | 0.297590 | − | 1.11062i | −0.641549 | − | 0.767082i | \(-0.721708\pi\) |
0.939139 | − | 0.343538i | \(-0.111625\pi\) | |||||||
\(564\) | 30.7610 | − | 15.6130i | 1.29527 | − | 0.657424i | ||||
\(565\) | 2.49724 | − | 0.669132i | 0.105060 | − | 0.0281506i | ||||
\(566\) | 5.92777 | + | 15.4785i | 0.249163 | + | 0.650611i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −33.0730 | + | 10.6604i | −1.38771 | + | 0.447300i | ||||
\(569\) | −7.94537 | − | 4.58726i | −0.333087 | − | 0.192308i | 0.324124 | − | 0.946015i | \(-0.394931\pi\) |
−0.657211 | + | 0.753707i | \(0.728264\pi\) | |||||||
\(570\) | −7.65825 | + | 9.44205i | −0.320769 | + | 0.395484i | ||||
\(571\) | 10.8851 | − | 40.6239i | 0.455529 | − | 1.70006i | −0.230999 | − | 0.972954i | \(-0.574199\pi\) |
0.686528 | − | 0.727103i | \(-0.259134\pi\) | |||||||
\(572\) | 7.84321 | − | 1.65431i | 0.327941 | − | 0.0691703i | ||||
\(573\) | −5.81750 | + | 5.81750i | −0.243029 | + | 0.243029i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 18.8706i | − | 0.786957i | ||||||
\(576\) | −2.61191 | + | 0.262141i | −0.108829 | + | 0.0109226i | ||||
\(577\) | −22.0711 | + | 12.7427i | −0.918830 | + | 0.530487i | −0.883262 | − | 0.468880i | \(-0.844658\pi\) |
−0.0355687 | + | 0.999367i | \(0.511324\pi\) | |||||||
\(578\) | −35.1754 | + | 3.66928i | −1.46310 | + | 0.152622i | ||||
\(579\) | −24.5339 | + | 6.57383i | −1.01959 | + | 0.273199i | ||||
\(580\) | 0.430516 | − | 0.386421i | 0.0178762 | − | 0.0160453i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −9.99830 | − | 26.1074i | −0.414443 | − | 1.08219i | ||||
\(583\) | 6.43616 | − | 11.1478i | 0.266559 | − | 0.461693i | ||||
\(584\) | −1.68915 | − | 1.52811i | −0.0698975 | − | 0.0632335i | ||||
\(585\) | −0.341282 | + | 0.197039i | −0.0141103 | + | 0.00814658i | ||||
\(586\) | 2.55281 | − | 16.0367i | 0.105456 | − | 0.662469i | ||||
\(587\) | 18.3219 | − | 18.3219i | 0.756227 | − | 0.756227i | −0.219406 | − | 0.975634i | \(-0.570412\pi\) |
0.975634 | + | 0.219406i | \(0.0704121\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.3087 | − | 13.3087i | −0.548377 | − | 0.548377i | ||||
\(590\) | 1.34500 | + | 1.85428i | 0.0553729 | + | 0.0763397i | ||||
\(591\) | −13.1061 | − | 22.7004i | −0.539111 | − | 0.933768i | ||||
\(592\) | 5.59053 | − | 14.4288i | 0.229769 | − | 0.593020i | ||||
\(593\) | −13.4221 | − | 7.74927i | −0.551181 | − | 0.318225i | 0.198417 | − | 0.980118i | \(-0.436420\pi\) |
−0.749598 | + | 0.661893i | \(0.769753\pi\) | |||||||
\(594\) | 7.94421 | − | 17.8055i | 0.325955 | − | 0.730569i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 24.9983 | + | 1.34930i | 1.02397 | + | 0.0552696i | ||||
\(597\) | 4.68069 | + | 17.4686i | 0.191568 | + | 0.714942i | ||||
\(598\) | −5.56353 | + | 6.85942i | −0.227510 | + | 0.280502i | ||||
\(599\) | −6.73751 | − | 11.6697i | −0.275287 | − | 0.476811i | 0.694920 | − | 0.719087i | \(-0.255440\pi\) |
−0.970208 | + | 0.242275i | \(0.922106\pi\) | |||||||
\(600\) | 11.9893 | + | 18.5570i | 0.489460 | + | 0.757586i | ||||
\(601\) | −0.365448 | −0.0149069 | −0.00745346 | − | 0.999972i | \(-0.502373\pi\) | ||||
−0.00745346 | + | 0.999972i | \(0.502373\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.85872 | − | 2.85872i | −0.116416 | − | 0.116416i | ||||
\(604\) | 13.1884 | − | 2.78174i | 0.536629 | − | 0.113187i | ||||
\(605\) | −2.45603 | − | 0.658090i | −0.0998517 | − | 0.0267552i | ||||
\(606\) | 2.07421 | + | 19.8843i | 0.0842589 | + | 0.807744i | ||||
\(607\) | 3.15743 | − | 5.46882i | 0.128156 | − | 0.221973i | −0.794806 | − | 0.606863i | \(-0.792428\pi\) |
0.922962 | + | 0.384891i | \(0.125761\pi\) | |||||||
\(608\) | −8.02124 | − | 30.4107i | −0.325304 | − | 1.23332i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.79854 | − | 15.2377i | 0.275265 | − | 0.616957i | ||||
\(611\) | 3.46745 | + | 12.9407i | 0.140278 | + | 0.523525i | ||||
\(612\) | −1.32070 | + | 4.04319i | −0.0533863 | + | 0.163436i | ||||
\(613\) | −9.59594 | − | 2.57122i | −0.387576 | − | 0.103851i | 0.0597686 | − | 0.998212i | \(-0.480964\pi\) |
−0.447345 | + | 0.894361i | \(0.647630\pi\) | |||||||
\(614\) | 4.48122 | − | 28.1509i | 0.180847 | − | 1.13608i | ||||
\(615\) | − | 7.56005i | − | 0.304850i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.7832i | 1.36006i | 0.733184 | + | 0.680031i | \(0.238034\pi\) | ||||
−0.733184 | + | 0.680031i | \(0.761966\pi\) | |||||||
\(618\) | −29.4370 | − | 4.68596i | −1.18413 | − | 0.188497i | ||||
\(619\) | 26.0189 | + | 6.97174i | 1.04579 | + | 0.280218i | 0.740510 | − | 0.672045i | \(-0.234584\pi\) |
0.305278 | + | 0.952263i | \(0.401251\pi\) | |||||||
\(620\) | 5.11706 | − | 2.59720i | 0.205506 | − | 0.104306i | ||||
\(621\) | 5.56014 | + | 20.7507i | 0.223121 | + | 0.832698i | ||||
\(622\) | −16.4242 | − | 7.32790i | −0.658549 | − | 0.293822i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.11300 | − | 10.2802i | 0.0445558 | − | 0.411536i | ||||
\(625\) | 7.37039 | − | 12.7659i | 0.294816 | − | 0.510635i | ||||
\(626\) | 34.8808 | − | 3.63855i | 1.39412 | − | 0.145426i | ||||
\(627\) | −27.7105 | − | 7.42501i | −1.10665 | − | 0.296526i | ||||
\(628\) | −7.85379 | + | 12.0525i | −0.313400 | + | 0.480946i | ||||
\(629\) | −17.7293 | − | 17.7293i | −0.706914 | − | 0.706914i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.5097 | −1.29419 | −0.647096 | − | 0.762408i | \(-0.724017\pi\) | ||||
−0.647096 | + | 0.762408i | \(0.724017\pi\) | |||||||
\(632\) | 29.7764 | + | 6.40220i | 1.18444 | + | 0.254666i | ||||
\(633\) | −8.42935 | − | 14.6001i | −0.335037 | − | 0.580301i | ||||
\(634\) | −2.23393 | − | 1.81190i | −0.0887208 | − | 0.0719596i | ||||
\(635\) | −1.97802 | − | 7.38207i | −0.0784953 | − | 0.292949i | ||||
\(636\) | −11.0917 | − | 12.3574i | −0.439814 | − | 0.490001i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.24665 | + | 0.556214i | 0.0493555 | + | 0.0220207i | ||||
\(639\) | 3.49115 | + | 2.01561i | 0.138108 | + | 0.0797365i | ||||
\(640\) | 9.57296 | + | 0.554246i | 0.378405 | + | 0.0219085i | ||||
\(641\) | 7.79534 | + | 13.5019i | 0.307897 | + | 0.533294i | 0.977902 | − | 0.209063i | \(-0.0670414\pi\) |
−0.670005 | + | 0.742357i | \(0.733708\pi\) | |||||||
\(642\) | 14.3572 | − | 10.4140i | 0.566633 | − | 0.411006i | ||||
\(643\) | 12.1182 | + | 12.1182i | 0.477896 | + | 0.477896i | 0.904458 | − | 0.426562i | \(-0.140275\pi\) |
−0.426562 | + | 0.904458i | \(0.640275\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.81463 | + | 6.81463i | −0.268326 | + | 0.268326i | ||||
\(646\) | −50.3270 | − | 8.01136i | −1.98009 | − | 0.315203i | ||||
\(647\) | 20.9126 | − | 12.0739i | 0.822161 | − | 0.474675i | −0.0290002 | − | 0.999579i | \(-0.509232\pi\) |
0.851161 | + | 0.524905i | \(0.175899\pi\) | |||||||
\(648\) | −20.7163 | − | 18.7412i | −0.813812 | − | 0.736223i | ||||
\(649\) | −2.70274 | + | 4.68128i | −0.106092 | + | 0.183756i | ||||
\(650\) | −8.01270 | + | 3.06860i | −0.314284 | + | 0.120361i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.8070 | − | 0.961147i | −0.697376 | − | 0.0376414i | ||||
\(653\) | −10.5351 | + | 2.82286i | −0.412269 | + | 0.110467i | −0.458991 | − | 0.888441i | \(-0.651789\pi\) |
0.0467223 | + | 0.998908i | \(0.485122\pi\) | |||||||
\(654\) | 3.81546 | + | 36.5768i | 0.149196 | + | 1.43026i | ||||
\(655\) | 0.503101 | − | 0.290466i | 0.0196578 | − | 0.0113494i | ||||
\(656\) | 15.7864 | + | 11.5451i | 0.616357 | + | 0.450761i | ||||
\(657\) | 0.264249i | 0.0103093i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.7175 | + | 20.7175i | −0.807041 | + | 0.807041i | −0.984185 | − | 0.177144i | \(-0.943314\pi\) |
0.177144 | + | 0.984185i | \(0.443314\pi\) | |||||||
\(660\) | 4.77525 | − | 7.32812i | 0.185876 | − | 0.285247i | ||||
\(661\) | −0.0890254 | + | 0.332247i | −0.00346269 | + | 0.0129229i | −0.967636 | − | 0.252352i | \(-0.918796\pi\) |
0.964173 | + | 0.265275i | \(0.0854627\pi\) | |||||||
\(662\) | 1.60996 | + | 1.30581i | 0.0625729 | + | 0.0507516i | ||||
\(663\) | −14.5100 | − | 8.37733i | −0.563520 | − | 0.325348i | ||||
\(664\) | −20.5305 | − | 10.5215i | −0.796736 | − | 0.408314i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.67642 | + | 0.642015i | −0.0649601 | + | 0.0248776i | ||||
\(667\) | −1.45286 | + | 0.389294i | −0.0562551 | + | 0.0150735i | ||||
\(668\) | −31.0798 | − | 10.1522i | −1.20252 | − | 0.392801i | ||||
\(669\) | 1.07394 | − | 4.00799i | 0.0415208 | − | 0.154958i | ||||
\(670\) | 8.67116 | + | 11.9545i | 0.334996 | + | 0.461841i | ||||
\(671\) | 39.3734 | 1.51999 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.4244 | −0.594567 | −0.297284 | − | 0.954789i | \(-0.596081\pi\) | ||||
−0.297284 | + | 0.954789i | \(0.596081\pi\) | |||||||
\(674\) | −14.0421 | − | 19.3591i | −0.540882 | − | 0.745686i | ||||
\(675\) | −5.40161 | + | 20.1591i | −0.207908 | + | 0.775923i | ||||
\(676\) | −20.8976 | − | 6.82618i | −0.803753 | − | 0.262545i | ||||
\(677\) | 18.2947 | − | 4.90205i | 0.703122 | − | 0.188401i | 0.110494 | − | 0.993877i | \(-0.464757\pi\) |
0.592629 | + | 0.805476i | \(0.298090\pi\) | |||||||
\(678\) | 7.34928 | − | 2.81453i | 0.282247 | − | 0.108092i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.08627 | − | 13.8273i | 0.271746 | − | 0.530253i | ||||
\(681\) | 19.9046 | + | 11.4919i | 0.762746 | + | 0.440371i | ||||
\(682\) | 10.5168 | + | 8.52996i | 0.402709 | + | 0.326629i | ||||
\(683\) | 2.28082 | − | 8.51213i | 0.0872731 | − | 0.325708i | −0.908462 | − | 0.417968i | \(-0.862742\pi\) |
0.995735 | + | 0.0922601i | \(0.0294091\pi\) | |||||||
\(684\) | −1.99197 | + | 3.05689i | −0.0761649 | + | 0.116883i | ||||
\(685\) | 10.2762 | − | 10.2762i | 0.392632 | − | 0.392632i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 15.5808i | − | 0.594446i | ||||||
\(688\) | −3.82313 | − | 24.6367i | −0.145755 | − | 0.939264i | ||||
\(689\) | 5.58487 | − | 3.22443i | 0.212767 | − | 0.122841i | ||||
\(690\) | 0.999882 | + | 9.58533i | 0.0380649 | + | 0.364907i | ||||
\(691\) | −9.37022 | + | 2.51074i | −0.356460 | + | 0.0955131i | −0.432605 | − | 0.901584i | \(-0.642405\pi\) |
0.0761450 | + | 0.997097i | \(0.475739\pi\) | |||||||
\(692\) | −32.3232 | − | 1.74467i | −1.22875 | − | 0.0663225i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.46909 | − | 0.945581i | 0.0937254 | − | 0.0358938i | ||||
\(695\) | 4.27544 | − | 7.40528i | 0.162177 | − | 0.280898i | ||||
\(696\) | 1.18139 | − | 1.30589i | 0.0447803 | − | 0.0494996i | ||||
\(697\) | 27.4443 | − | 15.8449i | 1.03953 | − | 0.600170i | ||||
\(698\) | 34.0765 | + | 5.42450i | 1.28981 | + | 0.205320i | ||||
\(699\) | −33.7880 | + | 33.7880i | −1.27798 | + | 1.27798i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.666263 | + | 0.666263i | 0.0251644 | + | 0.0251644i | 0.719577 | − | 0.694413i | \(-0.244336\pi\) |
−0.694413 | + | 0.719577i | \(0.744336\pi\) | |||||||
\(702\) | 7.90689 | − | 5.73525i | 0.298426 | − | 0.216463i | ||||
\(703\) | −10.7540 | − | 18.6264i | −0.405593 | − | 0.702508i | ||||
\(704\) | 8.00976 | + | 21.1623i | 0.301879 | + | 0.797585i | ||||
\(705\) | 12.6603 | + | 7.30940i | 0.476813 | + | 0.275288i | ||||
\(706\) | −3.86095 | − | 1.72263i | −0.145309 | − | 0.0648319i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.65773 | + | 5.18923i | 0.175048 | + | 0.195023i | ||||
\(709\) | 10.6349 | + | 39.6900i | 0.399403 | + | 1.49059i | 0.814150 | + | 0.580654i | \(0.197203\pi\) |
−0.414747 | + | 0.909937i | \(0.636130\pi\) | |||||||
\(710\) | −11.4368 | − | 9.27613i | −0.429215 | − | 0.348127i | ||||
\(711\) | −1.76667 | − | 3.05996i | −0.0662553 | − | 0.114757i | ||||
\(712\) | −7.92424 | + | 36.8553i | −0.296973 | + | 1.38121i | ||||
\(713\) | −14.9200 | −0.558760 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.40198 | + | 2.40198i | 0.0898289 | + | 0.0898289i | ||||
\(716\) | −13.6559 | + | 20.9564i | −0.510345 | + | 0.783179i | ||||
\(717\) | −36.3218 | − | 9.73240i | −1.35646 | − | 0.363463i | ||||
\(718\) | −13.5410 | + | 1.41251i | −0.505345 | + | 0.0527145i | ||||
\(719\) | −15.6434 | + | 27.0951i | −0.583399 | + | 1.01048i | 0.411674 | + | 0.911331i | \(0.364944\pi\) |
−0.995073 | + | 0.0991455i | \(0.968389\pi\) | |||||||
\(720\) | −0.697367 | − | 0.866705i | −0.0259893 | − | 0.0323002i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.3829 | − | 6.86333i | −0.572493 | − | 0.255427i | ||||
\(723\) | −0.335432 | − | 1.25185i | −0.0124749 | − | 0.0465568i | ||||
\(724\) | 44.1964 | − | 22.4322i | 1.64255 | − | 0.833687i | ||||
\(725\) | −1.41144 | − | 0.378194i | −0.0524195 | − | 0.0140458i | ||||
\(726\) | −7.64368 | − | 1.21677i | −0.283683 | − | 0.0451584i | ||||
\(727\) | 22.8730i | 0.848313i | 0.905589 | + | 0.424157i | \(0.139429\pi\) | ||||
−0.905589 | + | 0.424157i | \(0.860571\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 23.4362i | − | 0.868006i | ||||||
\(730\) | 0.151748 | − | 0.953275i | 0.00561644 | − | 0.0352823i | ||||
\(731\) | −39.0209 | − | 10.4556i | −1.44324 | − | 0.386715i | ||||
\(732\) | 15.7708 | − | 48.2806i | 0.582907 | − | 1.78450i | ||||
\(733\) | −4.86396 | − | 18.1526i | −0.179655 | − | 0.670480i | −0.995712 | − | 0.0925090i | \(-0.970511\pi\) |
0.816057 | − | 0.577971i | \(-0.196155\pi\) | |||||||
\(734\) | 4.25342 | − | 9.53328i | 0.156997 | − | 0.351880i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −21.5424 | − | 12.5501i | −0.794065 | − | 0.462602i | ||||
\(737\) | −17.4244 | + | 30.1800i | −0.641836 | + | 1.11169i | ||||
\(738\) | −0.235401 | − | 2.25666i | −0.00866522 | − | 0.0830687i | ||||
\(739\) | −26.3976 | − | 7.07321i | −0.971050 | − | 0.260192i | −0.261779 | − | 0.965128i | \(-0.584309\pi\) |
−0.709271 | + | 0.704936i | \(0.750976\pi\) | |||||||
\(740\) | 6.41636 | − | 1.35336i | 0.235870 | − | 0.0497504i | ||||
\(741\) | −10.1628 | − | 10.1628i | −0.373338 | − | 0.373338i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.76335 | 0.0646911 | 0.0323455 | − | 0.999477i | \(-0.489702\pi\) | ||||
0.0323455 | + | 0.999477i | \(0.489702\pi\) | |||||||
\(744\) | 14.6721 | − | 9.47933i | 0.537906 | − | 0.347529i | ||||
\(745\) | 5.30457 | + | 9.18779i | 0.194344 | + | 0.336614i | ||||
\(746\) | 3.10103 | − | 3.82334i | 0.113537 | − | 0.139982i | ||||
\(747\) | 0.692682 | + | 2.58512i | 0.0253439 | + | 0.0945847i | ||||
\(748\) | 36.6107 | + | 1.97609i | 1.33862 | + | 0.0722530i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8.26958 | + | 18.5348i | −0.301962 | + | 0.676794i | ||||
\(751\) | 38.6945 | + | 22.3403i | 1.41198 | + | 0.815208i | 0.995575 | − | 0.0939709i | \(-0.0299561\pi\) |
0.416406 | + | 0.909179i | \(0.363289\pi\) | |||||||
\(752\) | −34.5968 | + | 15.2740i | −1.26162 | + | 0.556987i | ||||
\(753\) | 6.42513 | + | 11.1286i | 0.234145 | + | 0.405550i | ||||
\(754\) | 0.401554 | + | 0.553601i | 0.0146237 | + | 0.0201610i | ||||
\(755\) | 4.03894 | + | 4.03894i | 0.146992 | + | 0.146992i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.5033 | + | 36.5033i | −1.32674 | + | 1.32674i | −0.418535 | + | 0.908201i | \(0.637456\pi\) |
−0.908201 | + | 0.418535i | \(0.862544\pi\) | |||||||
\(758\) | 3.60957 | − | 22.6752i | 0.131106 | − | 0.823600i | ||||
\(759\) | −19.6947 | + | 11.3707i | −0.714873 | + | 0.412732i | ||||
\(760\) | 8.94146 | − | 9.88378i | 0.324341 | − | 0.358522i | ||||
\(761\) | −20.6645 | + | 35.7919i | −0.749087 | + | 1.29746i | 0.199173 | + | 0.979964i | \(0.436174\pi\) |
−0.948261 | + | 0.317493i | \(0.897159\pi\) | |||||||
\(762\) | −8.32003 | − | 21.7252i | −0.301403 | − | 0.787020i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.71220 | − | 6.02472i | 0.242839 | − | 0.217967i | ||||
\(765\) | −1.74109 | + | 0.466523i | −0.0629492 | + | 0.0168672i | ||||
\(766\) | 0.230692 | − | 0.0240643i | 0.00833523 | − | 0.000869480i | ||||
\(767\) | −2.34526 | + | 1.35404i | −0.0846824 | + | 0.0488914i | ||||
\(768\) | 29.1580 | − | 1.34530i | 1.05215 | − | 0.0485444i | ||||
\(769\) | 11.7612i | 0.424120i | 0.977257 | + | 0.212060i | \(0.0680171\pi\) | ||||
−0.977257 | + | 0.212060i | \(0.931983\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.01185 | + | 8.01185i | −0.288540 | + | 0.288540i | ||||
\(772\) | 27.2458 | − | 5.74677i | 0.980599 | − | 0.206831i | ||||
\(773\) | −8.35443 | + | 31.1792i | −0.300488 | + | 1.12144i | 0.636272 | + | 0.771465i | \(0.280476\pi\) |
−0.936760 | + | 0.349972i | \(0.886191\pi\) | |||||||
\(774\) | −1.82196 | + | 2.24634i | −0.0654890 | + | 0.0807430i | ||||
\(775\) | −12.5527 | − | 7.24732i | −0.450907 | − | 0.260331i | ||||
\(776\) | 9.40259 | + | 29.1708i | 0.337533 | + | 1.04717i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.1226 | − | 29.0432i | −0.398764 | − | 1.04125i | ||||
\(779\) | 26.2577 | − | 7.03572i | 0.940778 | − | 0.252081i | ||||
\(780\) | 3.90747 | − | 1.98326i | 0.139910 | − | 0.0710122i | ||||
\(781\) | 8.99362 | − | 33.5646i | 0.321817 | − | 1.20104i | ||||
\(782\) | −32.7007 | + | 23.7194i | −1.16938 | + | 0.848205i | ||||
\(783\) | 1.66350 | 0.0594486 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.09628 | −0.217585 | ||||||||
\(786\) | 1.43145 | − | 1.03830i | 0.0510581 | − | 0.0370349i | ||||
\(787\) | −10.3388 | + | 38.5848i | −0.368537 | + | 1.37540i | 0.494024 | + | 0.869448i | \(0.335525\pi\) |
−0.862562 | + | 0.505952i | \(0.831141\pi\) | |||||||
\(788\) | 13.0060 | + | 25.6247i | 0.463319 | + | 0.912841i | ||||
\(789\) | −1.38047 | + | 0.369895i | −0.0491459 | + | 0.0131686i | ||||
\(790\) | 4.61602 | + | 12.0533i | 0.164231 | + | 0.428837i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.19722 | − | 2.33612i | 0.0425414 | − | 0.0830103i | ||||
\(793\) | 17.0828 | + | 9.86276i | 0.606628 | + | 0.350237i | ||||
\(794\) | 23.0327 | − | 28.3977i | 0.817402 | − | 1.00779i | ||||
\(795\) | 1.82128 | − | 6.79710i | 0.0645941 | − | 0.241068i | ||||
\(796\) | −4.09181 | − | 19.3996i | −0.145030 | − | 0.687599i | ||||
\(797\) | 34.7459 | − | 34.7459i | 1.23076 | − | 1.23076i | 0.267092 | − | 0.963671i | \(-0.413937\pi\) |
0.963671 | − | 0.267092i | \(-0.0860628\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 61.2785i | 2.16788i | ||||||||
\(800\) | −12.0282 | − | 21.0229i | −0.425263 | − | 0.743272i | ||||
\(801\) | 3.78742 | − | 2.18667i | 0.133822 | − | 0.0772622i | ||||
\(802\) | 22.1365 | − | 2.30915i | 0.781668 | − | 0.0815388i | ||||
\(803\) | 2.20018 | − | 0.589536i | 0.0776426 | − | 0.0208043i | ||||
\(804\) | 30.0281 | + | 33.4547i | 1.05901 | + | 1.17986i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.42620 | + | 6.33526i | 0.0854591 | + | 0.223150i | ||||
\(807\) | −15.9365 | + | 27.6028i | −0.560991 | + | 0.971665i | ||||
\(808\) | −1.09573 | − | 21.8900i | −0.0385478 | − | 0.770089i | ||||
\(809\) | 0.273987 | − | 0.158186i | 0.00963285 | − | 0.00556153i | −0.495176 | − | 0.868793i | \(-0.664896\pi\) |
0.504809 | + | 0.863231i | \(0.331563\pi\) | |||||||
\(810\) | 1.86109 | − | 11.6913i | 0.0653919 | − | 0.410789i | ||||
\(811\) | −16.0273 | + | 16.0273i | −0.562795 | + | 0.562795i | −0.930100 | − | 0.367305i | \(-0.880280\pi\) |
0.367305 | + | 0.930100i | \(0.380280\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.30076 | + | 8.30076i | 0.291120 | + | 0.291120i | ||||
\(814\) | 9.08559 | + | 12.5258i | 0.318450 | + | 0.439030i | ||||
\(815\) | −3.77860 | − | 6.54472i | −0.132358 | − | 0.229252i | ||||
\(816\) | 17.0874 | − | 44.1014i | 0.598178 | − | 1.54386i | ||||
\(817\) | −30.0106 | − | 17.3267i | −1.04994 | − | 0.606183i | ||||
\(818\) | −16.0335 | + | 35.9362i | −0.560599 | + | 1.25648i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.446706 | + | 8.27604i | −0.0155996 | + | 0.289012i | ||||
\(821\) | 7.66156 | + | 28.5933i | 0.267390 | + | 0.997914i | 0.960771 | + | 0.277342i | \(0.0894536\pi\) |
−0.693381 | + | 0.720571i | \(0.743880\pi\) | |||||||
\(822\) | 27.8666 | − | 34.3574i | 0.971960 | − | 1.19835i | ||||
\(823\) | −21.9691 | − | 38.0517i | −0.765796 | − | 1.32640i | −0.939825 | − | 0.341657i | \(-0.889012\pi\) |
0.174029 | − | 0.984741i | \(-0.444321\pi\) | |||||||
\(824\) | 31.9480 | + | 6.86912i | 1.11296 | + | 0.239297i | ||||
\(825\) | −22.0931 | −0.769182 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.6799 | − | 31.6799i | −1.10162 | − | 1.10162i | −0.994216 | − | 0.107401i | \(-0.965747\pi\) |
−0.107401 | − | 0.994216i | \(-0.534253\pi\) | |||||||
\(828\) | 0.596925 | + | 2.83006i | 0.0207446 | + | 0.0983515i | ||||
\(829\) | 12.0022 | + | 3.21597i | 0.416853 | + | 0.111695i | 0.461148 | − | 0.887323i | \(-0.347438\pi\) |
−0.0442955 | + | 0.999018i | \(0.514104\pi\) | |||||||
\(830\) | −1.01430 | − | 9.72358i | −0.0352070 | − | 0.337510i | ||||
\(831\) | 6.74606 | − | 11.6845i | 0.234018 | − | 0.405332i | ||||
\(832\) | −1.82585 | + | 11.1880i | −0.0632998 | + | 0.387875i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.6055 | − | 23.7704i | 0.367240 | − | 0.823102i | ||||
\(835\) | −3.58615 | − | 13.3837i | −0.124104 | − | 0.463161i | ||||
\(836\) | 29.8962 | + | 9.76557i | 1.03398 | + | 0.337749i | ||||
\(837\) | 15.9388 | + | 4.27079i | 0.550926 | + | 0.147620i | ||||
\(838\) | 0.119670 | − | 0.751761i | 0.00413392 | − | 0.0259692i | ||||
\(839\) | − | 15.1931i | − | 0.524523i | −0.964997 | − | 0.262261i | \(-0.915532\pi\) | ||
0.964997 | − | 0.262261i | \(-0.0844682\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 28.8835i | − | 0.995984i | ||||||
\(842\) | −10.8255 | − | 1.72326i | −0.373071 | − | 0.0593876i | ||||
\(843\) | 26.1876 | + | 7.01693i | 0.901947 | + | 0.241676i | ||||
\(844\) | 8.36499 | + | 16.4809i | 0.287935 | + | 0.567295i | ||||
\(845\) | −2.41127 | − | 8.99896i | −0.0829501 | − | 0.309574i | ||||
\(846\) | 4.00665 | + | 1.78763i | 0.137752 | + | 0.0614600i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11.4120 | + | 14.1831i | 0.391889 | + | 0.487049i | ||||
\(849\) | −10.6906 | + | 18.5167i | −0.366901 | + | 0.635491i | ||||
\(850\) | −39.0338 | + | 4.07176i | −1.33885 | + | 0.139660i | ||||
\(851\) | −16.4687 | − | 4.41278i | −0.564541 | − | 0.151268i | ||||
\(852\) | −37.5554 | − | 24.4724i | −1.28663 | − | 0.838409i | ||||
\(853\) | −1.19631 | − | 1.19631i | −0.0409610 | − | 0.0409610i | 0.686330 | − | 0.727291i | \(-0.259221\pi\) |
−0.727291 | + | 0.686330i | \(0.759221\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.54621 | −0.0528792 | ||||||||
\(856\) | −16.3323 | + | 10.5519i | −0.558225 | + | 0.360657i | ||||
\(857\) | 9.71265 | + | 16.8228i | 0.331778 | + | 0.574656i | 0.982860 | − | 0.184351i | \(-0.0590183\pi\) |
−0.651083 | + | 0.759007i | \(0.725685\pi\) | |||||||
\(858\) | 8.03079 | + | 6.51361i | 0.274167 | + | 0.222371i | ||||
\(859\) | −1.60630 | − | 5.99481i | −0.0548064 | − | 0.204540i | 0.933093 | − | 0.359634i | \(-0.117099\pi\) |
−0.987900 | + | 0.155094i | \(0.950432\pi\) | |||||||
\(860\) | 7.86268 | − | 7.05736i | 0.268115 | − | 0.240654i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.8734 | − | 10.6515i | −0.813130 | − | 0.362791i | ||||
\(863\) | −21.9244 | − | 12.6580i | −0.746315 | − | 0.430885i | 0.0780460 | − | 0.996950i | \(-0.475132\pi\) |
−0.824361 | + | 0.566065i | \(0.808465\pi\) | |||||||
\(864\) | 19.4210 | + | 19.5734i | 0.660715 | + | 0.665901i | ||||
\(865\) | −6.85890 | − | 11.8800i | −0.233210 | − | 0.403931i | ||||
\(866\) | −35.4131 | + | 25.6869i | −1.20339 | + | 0.872876i | ||||
\(867\) | −32.2596 | − | 32.2596i | −1.09559 | − | 1.09559i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.5363 | + | 21.5363i | −0.730569 | + | 0.730569i | ||||
\(870\) | 0.736981 | + | 0.117317i | 0.0249860 | + | 0.00397742i | ||||
\(871\) | −15.1197 | + | 8.72939i | −0.512313 | + | 0.295784i | ||||
\(872\) | −2.01558 | − | 40.2663i | −0.0682562 | − | 1.36359i | ||||
\(873\) | 1.77779 | − | 3.07923i | 0.0601692 | − | 0.104216i | ||||
\(874\) | −32.3613 | + | 12.3933i | −1.09464 | + | 0.419211i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.158368 | − | 2.93405i | 0.00535075 | − | 0.0991324i | ||||
\(877\) | 19.9280 | − | 5.33968i | 0.672920 | − | 0.180308i | 0.0938501 | − | 0.995586i | \(-0.470083\pi\) |
0.579070 | + | 0.815278i | \(0.303416\pi\) | |||||||
\(878\) | −2.93916 | − | 28.1761i | −0.0991920 | − | 0.950899i | ||||
\(879\) | 18.1411 | − | 10.4738i | 0.611884 | − | 0.353272i | ||||
\(880\) | −5.66050 | + | 7.74000i | −0.190815 | + | 0.260915i | ||||
\(881\) | 12.5228i | 0.421904i | 0.977496 | + | 0.210952i | \(0.0676563\pi\) | ||||
−0.977496 | + | 0.210952i | \(0.932344\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.9459 | + | 26.9459i | −0.906802 | + | 0.906802i | −0.996013 | − | 0.0892111i | \(-0.971565\pi\) |
0.0892111 | + | 0.996013i | \(0.471565\pi\) | |||||||
\(884\) | 15.3892 | + | 10.0281i | 0.517594 | + | 0.337281i | ||||
\(885\) | −0.764810 | + | 2.85431i | −0.0257088 | + | 0.0959466i | ||||
\(886\) | −0.662787 | − | 0.537573i | −0.0222668 | − | 0.0180601i | ||||
\(887\) | 16.6823 | + | 9.63153i | 0.560137 | + | 0.323395i | 0.753200 | − | 0.657791i | \(-0.228509\pi\) |
−0.193064 | + | 0.981186i | \(0.561842\pi\) | |||||||
\(888\) | 18.9987 | − | 6.12382i | 0.637554 | − | 0.205502i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −14.9188 | + | 5.71341i | −0.500079 | + | 0.191514i | ||||
\(891\) | 26.9837 | − | 7.23026i | 0.903988 | − | 0.242223i | ||||
\(892\) | −1.41247 | + | 4.32412i | −0.0472930 | + | 0.144782i | ||||
\(893\) | −13.6049 | + | 50.7742i | −0.455271 | + | 1.69909i | ||||
\(894\) | 18.9617 | + | 26.1415i | 0.634175 | + | 0.874304i | ||||
\(895\) | −10.6000 | −0.354319 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.3932 | −0.380407 | ||||||||
\(898\) | −10.8998 | − | 15.0270i | −0.363731 | − | 0.501456i | ||||
\(899\) | −0.299020 | + | 1.11596i | −0.00997286 | + | 0.0372192i | ||||
\(900\) | −0.872473 | + | 2.67098i | −0.0290824 | + | 0.0890326i | ||||
\(901\) | 28.4918 | − | 7.63436i | 0.949200 | − | 0.254337i | ||||
\(902\) | −18.2641 | + | 6.99455i | −0.608128 | + | 0.232893i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.21162 | + | 2.64684i | −0.273114 | + | 0.0880326i | ||||
\(905\) | 18.1899 | + | 10.5019i | 0.604652 | + | 0.349096i | ||||
\(906\) | 13.5038 | + | 10.9527i | 0.448635 | + | 0.363879i | ||||
\(907\) | 1.17521 | − | 4.38593i | 0.0390221 | − | 0.145632i | −0.943666 | − | 0.330899i | \(-0.892648\pi\) |
0.982688 | + | 0.185266i | \(0.0593148\pi\) | |||||||
\(908\) | −21.1107 | − | 13.7564i | −0.700583 | − | 0.456523i | ||||
\(909\) | −1.79794 | + | 1.79794i | −0.0596338 | + | 0.0596338i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 45.2409i | − | 1.49890i | −0.662063 | − | 0.749448i | \(-0.730319\pi\) | ||
0.662063 | − | 0.749448i | \(-0.269681\pi\) | |||||||
\(912\) | 23.9496 | − | 32.7479i | 0.793049 | − | 1.08439i | ||||
\(913\) | 19.9788 | − | 11.5348i | 0.661201 | − | 0.381745i | ||||
\(914\) | −2.29551 | − | 22.0058i | −0.0759286 | − | 0.727886i | ||||
\(915\) | 20.7907 | − | 5.57086i | 0.687320 | − | 0.184167i | ||||
\(916\) | −0.920636 | + | 17.0565i | −0.0304187 | + | 0.563562i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 41.7231 | − | 15.9786i | 1.37707 | − | 0.527372i | ||||
\(919\) | 1.45702 | − | 2.52363i | 0.0480626 | − | 0.0832469i | −0.840993 | − | 0.541046i | \(-0.818029\pi\) |
0.889056 | + | 0.457799i | \(0.151362\pi\) | |||||||
\(920\) | −0.528204 | − | 10.5522i | −0.0174144 | − | 0.347896i | ||||
\(921\) | 31.8450 | − | 18.3857i | 1.04933 | − | 0.605830i | ||||
\(922\) | 56.0133 | + | 8.91653i | 1.84470 | + | 0.293650i | ||||
\(923\) | 12.3097 | − | 12.3097i | 0.405180 | − | 0.405180i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.7122 | − | 11.7122i | −0.385095 | − | 0.385095i | ||||
\(926\) | 15.0189 | − | 10.8939i | 0.493550 | − | 0.357996i | ||||
\(927\) | −1.89551 | − | 3.28312i | −0.0622568 | − | 0.107832i | ||||
\(928\) | −1.37043 | + | 1.35976i | −0.0449867 | + | 0.0446364i | ||||
\(929\) | 24.5497 | + | 14.1738i | 0.805451 | + | 0.465027i | 0.845374 | − | 0.534176i | \(-0.179378\pi\) |
−0.0399228 | + | 0.999203i | \(0.512711\pi\) | |||||||
\(930\) | 6.76018 | + | 3.01616i | 0.221675 | + | 0.0989038i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 38.9845 | − | 34.9916i | 1.27698 | − | 1.14619i | ||||
\(933\) | −6.00462 | − | 22.4096i | −0.196582 | − | 0.733656i | ||||
\(934\) | −44.1877 | − | 35.8397i | −1.44587 | − | 1.17271i | ||||
\(935\) | 7.76869 | + | 13.4558i | 0.254063 | + | 0.440050i | ||||
\(936\) | 1.10462 | − | 0.713668i | 0.0361055 | − | 0.0233270i | ||||
\(937\) | 14.1147 | 0.461108 | 0.230554 | − | 0.973060i | \(-0.425946\pi\) | ||||
0.230554 | + | 0.973060i | \(0.425946\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.9895 | + | 31.9895i | 1.04394 | + | 1.04394i | ||||
\(940\) | −13.4274 | − | 8.74972i | −0.437953 | − | 0.285385i | ||||
\(941\) | 27.5221 | + | 7.37453i | 0.897195 | + | 0.240403i | 0.677811 | − | 0.735236i | \(-0.262929\pi\) |
0.219384 | + | 0.975639i | \(0.429595\pi\) | |||||||
\(942\) | −18.4570 | + | 1.92532i | −0.601362 | + | 0.0627304i | ||||
\(943\) | 10.7746 | − | 18.6621i | 0.350868 | − | 0.607722i | ||||
\(944\) | −4.79224 | − | 5.95591i | −0.155974 | − | 0.193848i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.7681 | + | 10.1584i | 0.740256 | + | 0.330277i | ||||
\(947\) | 7.47414 | + | 27.8939i | 0.242877 | + | 0.906429i | 0.974439 | + | 0.224654i | \(0.0721251\pi\) |
−0.731562 | + | 0.681775i | \(0.761208\pi\) | |||||||
\(948\) | 17.7821 | + | 35.0346i | 0.577535 | + | 1.13787i | ||||
\(949\) | 1.10226 | + | 0.295350i | 0.0357809 | + | 0.00958745i | ||||
\(950\) | −33.2467 | − | 5.29240i | −1.07866 | − | 0.171708i | ||||
\(951\) | − | 3.71046i | − | 0.120320i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 7.38196i | − | 0.239125i | −0.992827 | − | 0.119563i | \(-0.961851\pi\) | ||
0.992827 | − | 0.119563i | \(-0.0381492\pi\) | |||||||
\(954\) | 0.332003 | − | 2.08563i | 0.0107490 | − | 0.0675247i | ||||
\(955\) | 3.69201 | + | 0.989271i | 0.119471 | + | 0.0320121i | ||||
\(956\) | 39.1867 | + | 12.8003i | 1.26739 | + | 0.413991i | ||||
\(957\) | 0.455773 | + | 1.70097i | 0.0147330 | + | 0.0549845i | ||||
\(958\) | 19.3387 | − | 43.3442i | 0.624806 | − | 1.40039i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 7.22369 | + | 10.0413i | 0.233144 | + | 0.324081i | ||||
\(961\) | 9.76989 | − | 16.9220i | 0.315158 | − | 0.545869i | ||||
\(962\) | 0.804304 | + | 7.71042i | 0.0259318 | + | 0.248594i | ||||
\(963\) | 2.17890 | + | 0.583835i | 0.0702142 | + | 0.0188138i | ||||
\(964\) | 0.293232 | + | 1.39023i | 0.00944435 | + | 0.0447763i | ||||
\(965\) | 8.34402 | + | 8.34402i | 0.268603 | + | 0.268603i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.4068 | 1.52450 | 0.762250 | − | 0.647283i | \(-0.224095\pi\) | ||||
0.762250 | + | 0.647283i | \(0.224095\pi\) | |||||||
\(968\) | 8.29570 | + | 1.78365i | 0.266634 | + | 0.0573287i | ||||
\(969\) | −32.8693 | − | 56.9313i | −1.05591 | − | 1.82890i | ||||
\(970\) | −8.18166 | + | 10.0874i | −0.262697 | + | 0.323886i | ||||
\(971\) | −5.24615 | − | 19.5789i | −0.168357 | − | 0.628317i | −0.997588 | − | 0.0694112i | \(-0.977888\pi\) |
0.829231 | − | 0.558906i | \(-0.188779\pi\) | |||||||
\(972\) | 0.365989 | − | 6.78061i | 0.0117391 | − | 0.217488i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10.0417 | + | 22.5067i | −0.321757 | + | 0.721160i | ||||
\(975\) | −9.58546 | − | 5.53417i | −0.306980 | − | 0.177235i | ||||
\(976\) | −20.1172 | + | 51.9213i | −0.643937 | + | 1.66196i | ||||
\(977\) | 3.29726 | + | 5.71103i | 0.105489 | + | 0.182712i | 0.913938 | − | 0.405854i | \(-0.133026\pi\) |
−0.808449 | + | 0.588566i | \(0.799693\pi\) | |||||||
\(978\) | −13.5070 | − | 18.6214i | −0.431906 | − | 0.595446i | ||||
\(979\) | −26.6562 | − | 26.6562i | −0.851937 | − | 0.851937i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.30727 | + | 3.30727i | −0.105593 | + | 0.105593i | ||||
\(982\) | −1.26063 | + | 7.91922i | −0.0402283 | + | 0.252713i | ||||
\(983\) | −32.5034 | + | 18.7658i | −1.03670 | + | 0.598537i | −0.918896 | − | 0.394500i | \(-0.870918\pi\) |
−0.117801 | + | 0.993037i | \(0.537584\pi\) | |||||||
\(984\) | 1.26129 | + | 25.1975i | 0.0402086 | + | 0.803268i | ||||
\(985\) | −6.08892 | + | 10.5463i | −0.194009 | + | 0.336034i | ||||
\(986\) | 1.11874 | + | 2.92125i | 0.0356280 | + | 0.0930315i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.5248 | + | 11.7258i | 0.334837 | + | 0.373046i | ||||
\(989\) | −26.5342 | + | 7.10983i | −0.843739 | + | 0.226079i | ||||
\(990\) | 1.10643 | − | 0.115416i | 0.0351645 | − | 0.00366815i | ||||
\(991\) | −10.2256 | + | 5.90372i | −0.324825 | + | 0.187538i | −0.653541 | − | 0.756891i | \(-0.726717\pi\) |
0.328716 | + | 0.944429i | \(0.393384\pi\) | |||||||
\(992\) | −16.6218 | + | 9.51016i | −0.527742 | + | 0.301948i | ||||
\(993\) | 2.67407i | 0.0848591i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.94110 | − | 5.94110i | 0.188346 | − | 0.188346i | ||||
\(996\) | −6.14179 | − | 29.1187i | −0.194610 | − | 0.922660i | ||||
\(997\) | 6.21823 | − | 23.2067i | 0.196933 | − | 0.734965i | −0.794825 | − | 0.606839i | \(-0.792437\pi\) |
0.991758 | − | 0.128126i | \(-0.0408962\pi\) | |||||||
\(998\) | −20.4499 | + | 25.2132i | −0.647330 | + | 0.798110i | ||||
\(999\) | 16.3301 | + | 9.42818i | 0.516661 | + | 0.298294i |
(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 | 784.2.w.e.19.4 | 32 | ||
7.2 | even | 3 | 112.2.j.d.83.4 | yes | 16 | ||
7.3 | odd | 6 | inner | 784.2.w.e.227.8 | 32 | ||
7.4 | even | 3 | inner | 784.2.w.e.227.7 | 32 | ||
7.5 | odd | 6 | 112.2.j.d.83.3 | yes | 16 | ||
7.6 | odd | 2 | inner | 784.2.w.e.19.3 | 32 | ||
16.11 | odd | 4 | inner | 784.2.w.e.411.8 | 32 | ||
28.19 | even | 6 | 448.2.j.d.111.6 | 16 | |||
28.23 | odd | 6 | 448.2.j.d.111.3 | 16 | |||
56.5 | odd | 6 | 896.2.j.h.223.6 | 16 | |||
56.19 | even | 6 | 896.2.j.g.223.3 | 16 | |||
56.37 | even | 6 | 896.2.j.h.223.3 | 16 | |||
56.51 | odd | 6 | 896.2.j.g.223.6 | 16 | |||
112.5 | odd | 12 | 448.2.j.d.335.3 | 16 | |||
112.11 | odd | 12 | inner | 784.2.w.e.619.3 | 32 | ||
112.19 | even | 12 | 896.2.j.h.671.3 | 16 | |||
112.27 | even | 4 | inner | 784.2.w.e.411.7 | 32 | ||
112.37 | even | 12 | 448.2.j.d.335.6 | 16 | |||
112.51 | odd | 12 | 896.2.j.h.671.6 | 16 | |||
112.59 | even | 12 | inner | 784.2.w.e.619.4 | 32 | ||
112.61 | odd | 12 | 896.2.j.g.671.6 | 16 | |||
112.75 | even | 12 | 112.2.j.d.27.4 | yes | 16 | ||
112.93 | even | 12 | 896.2.j.g.671.3 | 16 | |||
112.107 | odd | 12 | 112.2.j.d.27.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.j.d.27.3 | ✓ | 16 | 112.107 | odd | 12 | ||
112.2.j.d.27.4 | yes | 16 | 112.75 | even | 12 | ||
112.2.j.d.83.3 | yes | 16 | 7.5 | odd | 6 | ||
112.2.j.d.83.4 | yes | 16 | 7.2 | even | 3 | ||
448.2.j.d.111.3 | 16 | 28.23 | odd | 6 | |||
448.2.j.d.111.6 | 16 | 28.19 | even | 6 | |||
448.2.j.d.335.3 | 16 | 112.5 | odd | 12 | |||
448.2.j.d.335.6 | 16 | 112.37 | even | 12 | |||
784.2.w.e.19.3 | 32 | 7.6 | odd | 2 | inner | ||
784.2.w.e.19.4 | 32 | 1.1 | even | 1 | trivial | ||
784.2.w.e.227.7 | 32 | 7.4 | even | 3 | inner | ||
784.2.w.e.227.8 | 32 | 7.3 | odd | 6 | inner | ||
784.2.w.e.411.7 | 32 | 112.27 | even | 4 | inner | ||
784.2.w.e.411.8 | 32 | 16.11 | odd | 4 | inner | ||
784.2.w.e.619.3 | 32 | 112.11 | odd | 12 | inner | ||
784.2.w.e.619.4 | 32 | 112.59 | even | 12 | inner | ||
896.2.j.g.223.3 | 16 | 56.19 | even | 6 | |||
896.2.j.g.223.6 | 16 | 56.51 | odd | 6 | |||
896.2.j.g.671.3 | 16 | 112.93 | even | 12 | |||
896.2.j.g.671.6 | 16 | 112.61 | odd | 12 | |||
896.2.j.h.223.3 | 16 | 56.37 | even | 6 | |||
896.2.j.h.223.6 | 16 | 56.5 | odd | 6 | |||
896.2.j.h.671.3 | 16 | 112.19 | even | 12 | |||
896.2.j.h.671.6 | 16 | 112.51 | odd | 12 |