Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [140,3,Mod(11,140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(140, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("140.11");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 140 = 2^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 140.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.81472370104\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.26 | ||
Character | \(\chi\) | \(=\) | 140.11 |
Dual form | 140.3.t.a.51.26 |
$q$-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 \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(101\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.68963 | + | 1.07012i | 0.844813 | + | 0.535062i | ||||
\(3\) | −4.93310 | − | 2.84813i | −1.64437 | − | 0.949376i | −0.979255 | − | 0.202633i | \(-0.935050\pi\) |
−0.665113 | − | 0.746743i | \(-0.731616\pi\) | |||||||
\(4\) | 1.70967 | + | 3.61622i | 0.427417 | + | 0.904055i | ||||
\(5\) | 1.11803 | + | 1.93649i | 0.223607 | + | 0.387298i | ||||
\(6\) | −5.28724 | − | 10.0913i | −0.881207 | − | 1.68188i | ||||
\(7\) | 6.48796 | + | 2.62800i | 0.926852 | + | 0.375428i | ||||
\(8\) | −0.981105 | + | 7.93961i | −0.122638 | + | 0.992451i | ||||
\(9\) | 11.7237 | + | 20.3060i | 1.30263 | + | 2.25622i | ||||
\(10\) | −0.183228 | + | 4.46838i | −0.0183228 | + | 0.446838i | ||||
\(11\) | 5.26172 | + | 3.03786i | 0.478339 | + | 0.276169i | 0.719724 | − | 0.694260i | \(-0.244268\pi\) |
−0.241385 | + | 0.970429i | \(0.577602\pi\) | |||||||
\(12\) | 1.86549 | − | 22.7085i | 0.155457 | − | 1.89238i | ||||
\(13\) | 11.5457 | 0.888134 | 0.444067 | − | 0.895993i | \(-0.353535\pi\) | ||||
0.444067 | + | 0.895993i | \(0.353535\pi\) | |||||||
\(14\) | 8.14994 | + | 11.3833i | 0.582139 | + | 0.813089i | ||||
\(15\) | − | 12.7372i | − | 0.849148i | ||||||
\(16\) | −10.1541 | + | 12.3651i | −0.634629 | + | 0.772817i | ||||
\(17\) | 2.84067 | − | 4.92019i | 0.167098 | − | 0.289423i | −0.770300 | − | 0.637682i | \(-0.779894\pi\) |
0.937398 | + | 0.348259i | \(0.113227\pi\) | |||||||
\(18\) | −1.92132 | + | 46.8553i | −0.106740 | + | 2.60307i | ||||
\(19\) | −29.1569 | + | 16.8338i | −1.53458 | + | 0.885988i | −0.535434 | + | 0.844577i | \(0.679852\pi\) |
−0.999142 | + | 0.0414103i | \(0.986815\pi\) | |||||||
\(20\) | −5.09131 | + | 7.35381i | −0.254566 | + | 0.367691i | ||||
\(21\) | −24.5209 | − | 31.4427i | −1.16766 | − | 1.49727i | ||||
\(22\) | 5.63946 | + | 10.7635i | 0.256339 | + | 0.489252i | ||||
\(23\) | 17.6580 | − | 10.1948i | 0.767738 | − | 0.443254i | −0.0643288 | − | 0.997929i | \(-0.520491\pi\) |
0.832067 | + | 0.554675i | \(0.187157\pi\) | |||||||
\(24\) | 27.4529 | − | 36.3726i | 1.14387 | − | 1.51553i | ||||
\(25\) | −2.50000 | + | 4.33013i | −0.100000 | + | 0.173205i | ||||
\(26\) | 19.5080 | + | 12.3554i | 0.750307 | + | 0.475207i | ||||
\(27\) | − | 82.2957i | − | 3.04799i | ||||||
\(28\) | 1.58886 | + | 27.9549i | 0.0567448 | + | 0.998389i | ||||
\(29\) | −10.7706 | −0.371399 | −0.185699 | − | 0.982607i | \(-0.559455\pi\) | ||||
−0.185699 | + | 0.982607i | \(0.559455\pi\) | |||||||
\(30\) | 13.6304 | − | 21.5211i | 0.454347 | − | 0.717371i | ||||
\(31\) | 14.2872 | + | 8.24874i | 0.460879 | + | 0.266088i | 0.712414 | − | 0.701760i | \(-0.247602\pi\) |
−0.251535 | + | 0.967848i | \(0.580935\pi\) | |||||||
\(32\) | −30.3887 | + | 10.0262i | −0.949648 | + | 0.313319i | ||||
\(33\) | −17.3044 | − | 29.9721i | −0.524376 | − | 0.908246i | ||||
\(34\) | 10.0649 | − | 5.27340i | 0.296026 | − | 0.155100i | ||||
\(35\) | 2.16467 | + | 15.5021i | 0.0618477 | + | 0.442916i | ||||
\(36\) | −53.3873 | + | 77.1118i | −1.48298 | + | 2.14200i | ||||
\(37\) | −20.3664 | − | 35.2756i | −0.550443 | − | 0.953396i | −0.998242 | − | 0.0592617i | \(-0.981125\pi\) |
0.447799 | − | 0.894134i | \(-0.352208\pi\) | |||||||
\(38\) | −67.2785 | − | 2.75879i | −1.77049 | − | 0.0725997i | ||||
\(39\) | −56.9564 | − | 32.8838i | −1.46042 | − | 0.843173i | ||||
\(40\) | −16.4719 | + | 6.97685i | −0.411798 | + | 0.174421i | ||||
\(41\) | 41.1307 | 1.00319 | 0.501594 | − | 0.865103i | \(-0.332747\pi\) | ||||
0.501594 | + | 0.865103i | \(0.332747\pi\) | |||||||
\(42\) | −7.78354 | − | 79.3668i | −0.185322 | − | 1.88969i | ||||
\(43\) | − | 6.10425i | − | 0.141959i | −0.997478 | − | 0.0709796i | \(-0.977387\pi\) | ||
0.997478 | − | 0.0709796i | \(-0.0226125\pi\) | |||||||
\(44\) | −1.98976 | + | 24.2213i | −0.0452217 | + | 0.550484i | ||||
\(45\) | −26.2149 | + | 45.4056i | −0.582554 | + | 1.00901i | ||||
\(46\) | 40.7451 | + | 1.67077i | 0.885764 | + | 0.0363212i | ||||
\(47\) | −12.6485 | + | 7.30261i | −0.269117 | + | 0.155375i | −0.628486 | − | 0.777821i | \(-0.716325\pi\) |
0.359369 | + | 0.933195i | \(0.382992\pi\) | |||||||
\(48\) | 85.3084 | − | 32.0780i | 1.77726 | − | 0.668292i | ||||
\(49\) | 35.1873 | + | 34.1007i | 0.718108 | + | 0.695932i | ||||
\(50\) | −8.85784 | + | 4.64098i | −0.177157 | + | 0.0928196i | ||||
\(51\) | −28.0267 | + | 16.1812i | −0.549542 | + | 0.317278i | ||||
\(52\) | 19.7394 | + | 41.7519i | 0.379604 | + | 0.802922i | ||||
\(53\) | 15.0792 | − | 26.1180i | 0.284513 | − | 0.492792i | −0.687978 | − | 0.725732i | \(-0.741501\pi\) |
0.972491 | + | 0.232940i | \(0.0748346\pi\) | |||||||
\(54\) | 88.0666 | − | 139.049i | 1.63086 | − | 2.57498i | ||||
\(55\) | 13.5857i | 0.247013i | ||||||||
\(56\) | −27.2306 | + | 48.9336i | −0.486261 | + | 0.873813i | ||||
\(57\) | 191.779 | 3.36454 | ||||||||
\(58\) | −18.1982 | − | 11.5258i | −0.313762 | − | 0.198721i | ||||
\(59\) | 29.1952 | + | 16.8558i | 0.494833 | + | 0.285692i | 0.726577 | − | 0.687085i | \(-0.241110\pi\) |
−0.231744 | + | 0.972777i | \(0.574443\pi\) | |||||||
\(60\) | 46.0606 | − | 21.7764i | 0.767676 | − | 0.362940i | ||||
\(61\) | −40.4936 | − | 70.1370i | −0.663830 | − | 1.14979i | −0.979601 | − | 0.200952i | \(-0.935596\pi\) |
0.315771 | − | 0.948835i | \(-0.397737\pi\) | |||||||
\(62\) | 15.3129 | + | 29.2264i | 0.246982 | + | 0.471394i | ||||
\(63\) | 22.6987 | + | 162.554i | 0.360296 | + | 2.58022i | ||||
\(64\) | −62.0749 | − | 15.5792i | −0.969920 | − | 0.243425i | ||||
\(65\) | 12.9085 | + | 22.3582i | 0.198593 | + | 0.343973i | ||||
\(66\) | 2.83592 | − | 69.1596i | 0.0429685 | − | 1.04787i | ||||
\(67\) | 7.33783 | + | 4.23650i | 0.109520 | + | 0.0632313i | 0.553759 | − | 0.832677i | \(-0.313193\pi\) |
−0.444240 | + | 0.895908i | \(0.646526\pi\) | |||||||
\(68\) | 22.6491 | + | 1.86060i | 0.333075 | + | 0.0273618i | ||||
\(69\) | −116.145 | −1.68326 | ||||||||
\(70\) | −12.9317 | + | 28.5092i | −0.184738 | + | 0.407274i | ||||
\(71\) | − | 21.6625i | − | 0.305105i | −0.988295 | − | 0.152553i | \(-0.951251\pi\) | ||
0.988295 | − | 0.152553i | \(-0.0487494\pi\) | |||||||
\(72\) | −172.724 | + | 73.1590i | −2.39894 | + | 1.01610i | ||||
\(73\) | −13.0220 | + | 22.5548i | −0.178384 | + | 0.308971i | −0.941327 | − | 0.337495i | \(-0.890420\pi\) |
0.762943 | + | 0.646466i | \(0.223754\pi\) | |||||||
\(74\) | 3.33773 | − | 81.3972i | 0.0451045 | − | 1.09996i | ||||
\(75\) | 24.6655 | − | 14.2406i | 0.328873 | − | 0.189875i | ||||
\(76\) | −110.723 | − | 76.6577i | −1.45688 | − | 1.00865i | ||||
\(77\) | 26.1544 | + | 33.5373i | 0.339667 | + | 0.435549i | ||||
\(78\) | −61.0452 | − | 116.512i | −0.782631 | − | 1.49374i | ||||
\(79\) | −7.65825 | + | 4.42149i | −0.0969398 | + | 0.0559682i | −0.547686 | − | 0.836684i | \(-0.684491\pi\) |
0.450746 | + | 0.892652i | \(0.351158\pi\) | |||||||
\(80\) | −35.2974 | − | 5.83871i | −0.441218 | − | 0.0729839i | ||||
\(81\) | −128.876 | + | 223.219i | −1.59106 | + | 2.75579i | ||||
\(82\) | 69.4956 | + | 44.0150i | 0.847507 | + | 0.536768i | ||||
\(83\) | − | 102.748i | − | 1.23793i | −0.785420 | − | 0.618963i | \(-0.787553\pi\) | ||
0.785420 | − | 0.618963i | \(-0.212447\pi\) | |||||||
\(84\) | 71.7811 | − | 142.430i | 0.854537 | − | 1.69559i | ||||
\(85\) | 12.7039 | 0.149457 | ||||||||
\(86\) | 6.53231 | − | 10.3139i | 0.0759570 | − | 0.119929i | ||||
\(87\) | 53.1323 | + | 30.6760i | 0.610716 | + | 0.352597i | ||||
\(88\) | −29.2817 | + | 38.7956i | −0.332747 | + | 0.440859i | ||||
\(89\) | −26.6044 | − | 46.0801i | −0.298926 | − | 0.517754i | 0.676965 | − | 0.736015i | \(-0.263295\pi\) |
−0.975890 | + | 0.218261i | \(0.929962\pi\) | |||||||
\(90\) | −92.8830 | + | 48.6652i | −1.03203 | + | 0.540724i | ||||
\(91\) | 74.9084 | + | 30.3422i | 0.823169 | + | 0.333430i | ||||
\(92\) | 67.0561 | + | 46.4253i | 0.728870 | + | 0.504623i | ||||
\(93\) | −46.9870 | − | 81.3838i | −0.505236 | − | 0.875094i | ||||
\(94\) | −29.1859 | − | 1.19678i | −0.310489 | − | 0.0127317i | ||||
\(95\) | −65.1969 | − | 37.6414i | −0.686283 | − | 0.396226i | ||||
\(96\) | 178.467 | + | 37.0907i | 1.85903 | + | 0.386361i | ||||
\(97\) | −176.818 | −1.82286 | −0.911431 | − | 0.411454i | \(-0.865021\pi\) | ||||
−0.911431 | + | 0.411454i | \(0.865021\pi\) | |||||||
\(98\) | 22.9614 | + | 95.2721i | 0.234300 | + | 0.972164i | ||||
\(99\) | 142.459i | 1.43898i | ||||||||
\(100\) | −19.9329 | − | 1.63747i | −0.199329 | − | 0.0163747i | ||||
\(101\) | −26.1028 | + | 45.2114i | −0.258444 | + | 0.447638i | −0.965825 | − | 0.259194i | \(-0.916543\pi\) |
0.707381 | + | 0.706832i | \(0.249876\pi\) | |||||||
\(102\) | −64.6704 | − | 2.65184i | −0.634024 | − | 0.0259985i | ||||
\(103\) | 9.94014 | − | 5.73894i | 0.0965062 | − | 0.0557179i | −0.450970 | − | 0.892539i | \(-0.648922\pi\) |
0.547476 | + | 0.836821i | \(0.315589\pi\) | |||||||
\(104\) | −11.3276 | + | 91.6688i | −0.108919 | + | 0.881430i | ||||
\(105\) | 33.4733 | − | 82.6386i | 0.318794 | − | 0.787034i | ||||
\(106\) | 53.4277 | − | 27.9929i | 0.504035 | − | 0.264084i | ||||
\(107\) | 130.099 | − | 75.1125i | 1.21588 | − | 0.701986i | 0.251842 | − | 0.967768i | \(-0.418964\pi\) |
0.964033 | + | 0.265783i | \(0.0856303\pi\) | |||||||
\(108\) | 297.599 | − | 140.698i | 2.75555 | − | 1.30276i | ||||
\(109\) | 74.0903 | − | 128.328i | 0.679727 | − | 1.17732i | −0.295335 | − | 0.955394i | \(-0.595431\pi\) |
0.975063 | − | 0.221929i | \(-0.0712353\pi\) | |||||||
\(110\) | −14.5384 | + | 22.9548i | −0.132167 | + | 0.208680i | ||||
\(111\) | 232.024i | 2.09031i | ||||||||
\(112\) | −98.3746 | + | 53.5392i | −0.878344 | + | 0.478029i | ||||
\(113\) | 81.3417 | 0.719838 | 0.359919 | − | 0.932984i | \(-0.382804\pi\) | ||||
0.359919 | + | 0.932984i | \(0.382804\pi\) | |||||||
\(114\) | 324.034 | + | 205.227i | 2.84241 | + | 1.80024i | ||||
\(115\) | 39.4845 | + | 22.7964i | 0.343343 | + | 0.198229i | ||||
\(116\) | −18.4141 | − | 38.9487i | −0.158742 | − | 0.335765i | ||||
\(117\) | 135.358 | + | 234.448i | 1.15691 | + | 2.00383i | ||||
\(118\) | 31.2910 | + | 59.7225i | 0.265178 | + | 0.506123i | ||||
\(119\) | 31.3604 | − | 24.4567i | 0.263533 | − | 0.205519i | ||||
\(120\) | 101.129 | + | 12.4965i | 0.842738 | + | 0.104138i | ||||
\(121\) | −42.0428 | − | 72.8203i | −0.347461 | − | 0.601821i | ||||
\(122\) | 6.63627 | − | 161.839i | 0.0543957 | − | 1.32655i | ||||
\(123\) | −202.902 | − | 117.146i | −1.64961 | − | 0.952404i | ||||
\(124\) | −5.40282 | + | 65.7684i | −0.0435711 | + | 0.530390i | ||||
\(125\) | −11.1803 | −0.0894427 | ||||||||
\(126\) | −135.601 | + | 298.946i | −1.07620 | + | 2.37259i | ||||
\(127\) | − | 14.5887i | − | 0.114872i | −0.998349 | − | 0.0574358i | \(-0.981708\pi\) | ||
0.998349 | − | 0.0574358i | \(-0.0182924\pi\) | |||||||
\(128\) | −88.2116 | − | 92.7508i | −0.689153 | − | 0.724616i | ||||
\(129\) | −17.3857 | + | 30.1129i | −0.134773 | + | 0.233433i | ||||
\(130\) | −2.11551 | + | 51.5908i | −0.0162731 | + | 0.396852i | ||||
\(131\) | 69.7591 | − | 40.2755i | 0.532513 | − | 0.307446i | −0.209526 | − | 0.977803i | \(-0.567192\pi\) |
0.742039 | + | 0.670357i | \(0.233859\pi\) | |||||||
\(132\) | 78.8010 | − | 113.819i | 0.596977 | − | 0.862265i | ||||
\(133\) | −233.408 | + | 32.5925i | −1.75495 | + | 0.245057i | ||||
\(134\) | 7.86461 | + | 15.0105i | 0.0586911 | + | 0.112019i | ||||
\(135\) | 159.365 | − | 92.0094i | 1.18048 | − | 0.681551i | ||||
\(136\) | 36.2774 | + | 27.3811i | 0.266745 | + | 0.201331i | ||||
\(137\) | 59.2761 | − | 102.669i | 0.432673 | − | 0.749411i | −0.564430 | − | 0.825481i | \(-0.690904\pi\) |
0.997102 | + | 0.0760701i | \(0.0242373\pi\) | |||||||
\(138\) | −196.241 | − | 124.289i | −1.42204 | − | 0.900648i | ||||
\(139\) | 168.165i | 1.20982i | 0.796293 | + | 0.604911i | \(0.206791\pi\) | ||||
−0.796293 | + | 0.604911i | \(0.793209\pi\) | |||||||
\(140\) | −52.3580 | + | 34.3313i | −0.373986 | + | 0.245224i | ||||
\(141\) | 83.1951 | 0.590036 | ||||||||
\(142\) | 23.1815 | − | 36.6015i | 0.163250 | − | 0.257757i | ||||
\(143\) | 60.7505 | + | 35.0743i | 0.424829 | + | 0.245275i | ||||
\(144\) | −370.128 | − | 61.2245i | −2.57033 | − | 0.425170i | ||||
\(145\) | −12.0419 | − | 20.8571i | −0.0830473 | − | 0.143842i | ||||
\(146\) | −46.1389 | + | 24.1740i | −0.316020 | + | 0.165576i | ||||
\(147\) | −76.4594 | − | 268.440i | −0.520132 | − | 1.82612i | ||||
\(148\) | 92.7447 | − | 133.959i | 0.626653 | − | 0.905128i | ||||
\(149\) | −25.1743 | − | 43.6032i | −0.168955 | − | 0.292639i | 0.769098 | − | 0.639131i | \(-0.220706\pi\) |
−0.938053 | + | 0.346492i | \(0.887373\pi\) | |||||||
\(150\) | 56.9147 | + | 2.33382i | 0.379432 | + | 0.0155588i | ||||
\(151\) | 116.615 | + | 67.3276i | 0.772283 | + | 0.445878i | 0.833689 | − | 0.552235i | \(-0.186225\pi\) |
−0.0614052 | + | 0.998113i | \(0.519558\pi\) | |||||||
\(152\) | −105.048 | − | 248.010i | −0.691102 | − | 1.63165i | ||||
\(153\) | 133.212 | 0.870669 | ||||||||
\(154\) | 8.30205 | + | 84.6539i | 0.0539094 | + | 0.549701i | ||||
\(155\) | 36.8895i | 0.237997i | ||||||||
\(156\) | 21.5384 | − | 262.187i | 0.138067 | − | 1.68069i | ||||
\(157\) | −67.8521 | + | 117.523i | −0.432179 | + | 0.748556i | −0.997061 | − | 0.0766160i | \(-0.975588\pi\) |
0.564882 | + | 0.825172i | \(0.308922\pi\) | |||||||
\(158\) | −17.6711 | − | 0.724613i | −0.111842 | − | 0.00458616i | ||||
\(159\) | −148.775 | + | 85.8950i | −0.935689 | + | 0.540220i | ||||
\(160\) | −53.3913 | − | 47.6379i | −0.333696 | − | 0.297737i | ||||
\(161\) | 141.356 | − | 19.7386i | 0.877989 | − | 0.122600i | ||||
\(162\) | −456.624 | + | 239.244i | −2.81867 | + | 1.47681i | ||||
\(163\) | −211.132 | + | 121.897i | −1.29529 | + | 0.747836i | −0.979587 | − | 0.201023i | \(-0.935574\pi\) |
−0.315703 | + | 0.948858i | \(0.602240\pi\) | |||||||
\(164\) | 70.3199 | + | 148.738i | 0.428780 | + | 0.906938i | ||||
\(165\) | 38.6939 | − | 67.0197i | 0.234508 | − | 0.406180i | ||||
\(166\) | 109.953 | − | 173.605i | 0.662368 | − | 1.04582i | ||||
\(167\) | − | 258.678i | − | 1.54897i | −0.632592 | − | 0.774485i | \(-0.718009\pi\) | ||
0.632592 | − | 0.774485i | \(-0.281991\pi\) | |||||||
\(168\) | 273.701 | − | 163.838i | 1.62917 | − | 0.975226i | ||||
\(169\) | −35.6957 | −0.211217 | ||||||||
\(170\) | 21.4648 | + | 13.5947i | 0.126263 | + | 0.0799690i | ||||
\(171\) | −683.652 | − | 394.707i | −3.99797 | − | 2.30823i | ||||
\(172\) | 22.0743 | − | 10.4362i | 0.128339 | − | 0.0606758i | ||||
\(173\) | 134.127 | + | 232.314i | 0.775298 | + | 1.34286i | 0.934627 | + | 0.355630i | \(0.115734\pi\) |
−0.159329 | + | 0.987226i | \(0.550933\pi\) | |||||||
\(174\) | 56.9466 | + | 108.689i | 0.327279 | + | 0.624650i | ||||
\(175\) | −27.5995 | + | 21.5237i | −0.157711 | + | 0.122993i | ||||
\(176\) | −90.9912 | + | 34.2149i | −0.516996 | + | 0.194403i | ||||
\(177\) | −96.0151 | − | 166.303i | −0.542458 | − | 0.939566i | ||||
\(178\) | 4.36004 | − | 106.328i | 0.0244946 | − | 0.597349i | ||||
\(179\) | −92.2843 | − | 53.2804i | −0.515555 | − | 0.297656i | 0.219559 | − | 0.975599i | \(-0.429538\pi\) |
−0.735114 | + | 0.677943i | \(0.762871\pi\) | |||||||
\(180\) | −209.015 | − | 17.1704i | −1.16120 | − | 0.0953912i | ||||
\(181\) | 196.840 | 1.08751 | 0.543757 | − | 0.839243i | \(-0.317001\pi\) | ||||
0.543757 | + | 0.839243i | \(0.317001\pi\) | |||||||
\(182\) | 94.0972 | + | 131.428i | 0.517017 | + | 0.722133i | ||||
\(183\) | 461.324i | 2.52090i | ||||||||
\(184\) | 63.6187 | + | 150.200i | 0.345754 | + | 0.816303i | ||||
\(185\) | 45.5407 | − | 78.8787i | 0.246166 | − | 0.426372i | ||||
\(186\) | 7.70042 | − | 187.790i | 0.0414001 | − | 1.00962i | ||||
\(187\) | 29.8937 | − | 17.2591i | 0.159859 | − | 0.0922947i | ||||
\(188\) | −48.0326 | − | 33.2547i | −0.255492 | − | 0.176887i | ||||
\(189\) | 216.273 | − | 533.931i | 1.14430 | − | 2.82503i | ||||
\(190\) | −69.8773 | − | 133.369i | −0.367775 | − | 0.701941i | ||||
\(191\) | 195.258 | − | 112.732i | 1.02229 | − | 0.590222i | 0.107527 | − | 0.994202i | \(-0.465707\pi\) |
0.914768 | + | 0.403980i | \(0.132374\pi\) | |||||||
\(192\) | 261.850 | + | 253.651i | 1.36380 | + | 1.32110i | ||||
\(193\) | −92.9293 | + | 160.958i | −0.481499 | + | 0.833980i | −0.999775 | − | 0.0212332i | \(-0.993241\pi\) |
0.518276 | + | 0.855214i | \(0.326574\pi\) | |||||||
\(194\) | −298.755 | − | 189.217i | −1.53998 | − | 0.975344i | ||||
\(195\) | − | 147.061i | − | 0.754157i | ||||||
\(196\) | −63.1569 | + | 185.546i | −0.322229 | + | 0.946662i | ||||
\(197\) | 12.5230 | 0.0635684 | 0.0317842 | − | 0.999495i | \(-0.489881\pi\) | ||||
0.0317842 | + | 0.999495i | \(0.489881\pi\) | |||||||
\(198\) | −152.449 | + | 240.703i | −0.769945 | + | 1.21567i | ||||
\(199\) | 125.106 | + | 72.2299i | 0.628672 | + | 0.362964i | 0.780238 | − | 0.625483i | \(-0.215098\pi\) |
−0.151565 | + | 0.988447i | \(0.548431\pi\) | |||||||
\(200\) | −31.9268 | − | 24.0973i | −0.159634 | − | 0.120487i | ||||
\(201\) | −24.1322 | − | 41.7982i | −0.120061 | − | 0.207951i | ||||
\(202\) | −92.4858 | + | 48.4571i | −0.457851 | + | 0.239887i | ||||
\(203\) | −69.8790 | − | 28.3050i | −0.344232 | − | 0.139433i | ||||
\(204\) | −106.431 | − | 73.6860i | −0.521721 | − | 0.361206i | ||||
\(205\) | 45.9856 | + | 79.6494i | 0.224320 | + | 0.388533i | ||||
\(206\) | 22.9365 | + | 0.940523i | 0.111342 | + | 0.00456564i | ||||
\(207\) | 414.033 | + | 239.042i | 2.00016 | + | 1.15479i | ||||
\(208\) | −117.236 | + | 142.764i | −0.563636 | + | 0.686365i | ||||
\(209\) | −204.554 | −0.978729 | ||||||||
\(210\) | 144.991 | − | 103.808i | 0.690433 | − | 0.494322i | ||||
\(211\) | − | 66.6431i | − | 0.315844i | −0.987452 | − | 0.157922i | \(-0.949521\pi\) | ||
0.987452 | − | 0.157922i | \(-0.0504794\pi\) | |||||||
\(212\) | 120.229 | + | 9.87668i | 0.567116 | + | 0.0465881i | ||||
\(213\) | −61.6975 | + | 106.863i | −0.289660 | + | 0.501705i | ||||
\(214\) | 300.198 | + | 12.3098i | 1.40279 | + | 0.0575222i | ||||
\(215\) | 11.8208 | − | 6.82476i | 0.0549806 | − | 0.0317431i | ||||
\(216\) | 653.396 | + | 80.7407i | 3.02498 | + | 0.373800i | ||||
\(217\) | 71.0174 | + | 91.0643i | 0.327269 | + | 0.419651i | ||||
\(218\) | 262.512 | − | 137.541i | 1.20418 | − | 0.630921i | ||||
\(219\) | 128.478 | − | 74.1769i | 0.586658 | − | 0.338707i | ||||
\(220\) | −49.1289 | + | 23.2271i | −0.223313 | + | 0.105578i | ||||
\(221\) | 32.7977 | − | 56.8073i | 0.148406 | − | 0.257046i | ||||
\(222\) | −248.295 | + | 392.034i | −1.11845 | + | 1.76592i | ||||
\(223\) | − | 185.958i | − | 0.833890i | −0.908932 | − | 0.416945i | \(-0.863101\pi\) | ||
0.908932 | − | 0.416945i | \(-0.136899\pi\) | |||||||
\(224\) | −223.510 | − | 14.8118i | −0.997811 | − | 0.0661240i | ||||
\(225\) | −117.237 | −0.521052 | ||||||||
\(226\) | 137.437 | + | 87.0458i | 0.608128 | + | 0.385158i | ||||
\(227\) | −48.2438 | − | 27.8535i | −0.212528 | − | 0.122703i | 0.389958 | − | 0.920833i | \(-0.372490\pi\) |
−0.602485 | + | 0.798130i | \(0.705823\pi\) | |||||||
\(228\) | 327.878 | + | 693.514i | 1.43806 | + | 3.04173i | ||||
\(229\) | 1.35922 | + | 2.35423i | 0.00593544 | + | 0.0102805i | 0.868978 | − | 0.494851i | \(-0.164777\pi\) |
−0.863042 | + | 0.505131i | \(0.831444\pi\) | |||||||
\(230\) | 42.3190 | + | 80.7706i | 0.183996 | + | 0.351176i | ||||
\(231\) | −33.5038 | − | 239.934i | −0.145038 | − | 1.03868i | ||||
\(232\) | 10.5671 | − | 85.5141i | 0.0455477 | − | 0.368595i | ||||
\(233\) | −31.2928 | − | 54.2008i | −0.134304 | − | 0.232621i | 0.791027 | − | 0.611781i | \(-0.209547\pi\) |
−0.925331 | + | 0.379159i | \(0.876213\pi\) | |||||||
\(234\) | −22.1831 | + | 540.979i | −0.0947997 | + | 2.31188i | ||||
\(235\) | −28.2829 | − | 16.3291i | −0.120353 | − | 0.0694857i | ||||
\(236\) | −11.0403 | + | 134.394i | −0.0467811 | + | 0.569466i | ||||
\(237\) | 50.3719 | 0.212540 | ||||||||
\(238\) | 79.1591 | − | 7.76317i | 0.332601 | − | 0.0326183i | ||||
\(239\) | − | 53.3613i | − | 0.223269i | −0.993749 | − | 0.111634i | \(-0.964391\pi\) | ||
0.993749 | − | 0.111634i | \(-0.0356086\pi\) | |||||||
\(240\) | 157.496 | + | 129.335i | 0.656235 | + | 0.538894i | ||||
\(241\) | 13.4004 | − | 23.2102i | 0.0556033 | − | 0.0963077i | −0.836884 | − | 0.547380i | \(-0.815625\pi\) |
0.892487 | + | 0.451073i | \(0.148958\pi\) | |||||||
\(242\) | 6.89016 | − | 168.030i | 0.0284717 | − | 0.694339i | ||||
\(243\) | 630.082 | − | 363.778i | 2.59293 | − | 1.49703i | ||||
\(244\) | 184.400 | − | 266.345i | 0.755738 | − | 1.09158i | ||||
\(245\) | −26.6951 | + | 106.266i | −0.108959 | + | 0.433737i | ||||
\(246\) | −217.468 | − | 415.063i | −0.884017 | − | 1.68725i | ||||
\(247\) | −336.639 | + | 194.358i | −1.36291 | + | 0.786876i | ||||
\(248\) | −79.5091 | + | 105.342i | −0.320601 | + | 0.424767i | ||||
\(249\) | −292.639 | + | 506.866i | −1.17526 | + | 2.03561i | ||||
\(250\) | −18.8906 | − | 11.9644i | −0.0755623 | − | 0.0478574i | ||||
\(251\) | 36.4631i | 0.145271i | 0.997359 | + | 0.0726356i | \(0.0231410\pi\) | ||||
−0.997359 | + | 0.0726356i | \(0.976859\pi\) | |||||||
\(252\) | −549.024 | + | 359.997i | −2.17867 | + | 1.42856i | ||||
\(253\) | 123.882 | 0.489652 | ||||||||
\(254\) | 15.6117 | − | 24.6494i | 0.0614634 | − | 0.0970449i | ||||
\(255\) | −62.6695 | − | 36.1823i | −0.245763 | − | 0.141891i | ||||
\(256\) | −49.7897 | − | 251.112i | −0.194491 | − | 0.980904i | ||||
\(257\) | −153.385 | − | 265.671i | −0.596829 | − | 1.03374i | −0.993286 | − | 0.115684i | \(-0.963094\pi\) |
0.396457 | − | 0.918053i | \(-0.370239\pi\) | |||||||
\(258\) | −61.5998 | + | 32.2747i | −0.238759 | + | 0.125096i | ||||
\(259\) | −39.4322 | − | 282.390i | −0.152248 | − | 1.09031i | ||||
\(260\) | −58.7830 | + | 84.9053i | −0.226088 | + | 0.326559i | ||||
\(261\) | −126.271 | − | 218.707i | −0.483795 | − | 0.837958i | ||||
\(262\) | 160.967 | + | 6.60052i | 0.614376 | + | 0.0251928i | ||||
\(263\) | −398.549 | − | 230.102i | −1.51539 | − | 0.874914i | −0.999837 | − | 0.0180589i | \(-0.994251\pi\) |
−0.515558 | − | 0.856855i | \(-0.672415\pi\) | |||||||
\(264\) | 254.945 | − | 107.985i | 0.965699 | − | 0.409032i | ||||
\(265\) | 67.4363 | 0.254477 | ||||||||
\(266\) | −429.250 | − | 194.707i | −1.61372 | − | 0.731980i | ||||
\(267\) | 303.091i | 1.13517i | ||||||||
\(268\) | −2.77485 | + | 33.7782i | −0.0103539 | + | 0.126038i | ||||
\(269\) | −127.202 | + | 220.320i | −0.472870 | + | 0.819035i | −0.999518 | − | 0.0310488i | \(-0.990115\pi\) |
0.526648 | + | 0.850083i | \(0.323449\pi\) | |||||||
\(270\) | 367.728 | + | 15.0789i | 1.36196 | + | 0.0558477i | ||||
\(271\) | −399.058 | + | 230.396i | −1.47254 | + | 0.850171i | −0.999523 | − | 0.0308829i | \(-0.990168\pi\) |
−0.473016 | + | 0.881054i | \(0.656835\pi\) | |||||||
\(272\) | 31.9941 | + | 85.0850i | 0.117625 | + | 0.312813i | ||||
\(273\) | −283.112 | − | 363.030i | −1.03704 | − | 1.32978i | ||||
\(274\) | 210.023 | − | 110.040i | 0.766509 | − | 0.401605i | ||||
\(275\) | −26.3086 | + | 15.1893i | −0.0956677 | + | 0.0552338i | ||||
\(276\) | −198.569 | − | 420.005i | −0.719453 | − | 1.52176i | ||||
\(277\) | −264.219 | + | 457.641i | −0.953860 | + | 1.65213i | −0.216903 | + | 0.976193i | \(0.569596\pi\) |
−0.736956 | + | 0.675940i | \(0.763738\pi\) | |||||||
\(278\) | −179.958 | + | 284.136i | −0.647330 | + | 1.02207i | ||||
\(279\) | 386.822i | 1.38646i | ||||||||
\(280\) | −125.204 | + | 1.97749i | −0.447158 | + | 0.00706245i | ||||
\(281\) | 495.355 | 1.76283 | 0.881415 | − | 0.472344i | \(-0.156592\pi\) | ||||
0.881415 | + | 0.472344i | \(0.156592\pi\) | |||||||
\(282\) | 140.569 | + | 89.0291i | 0.498470 | + | 0.315706i | ||||
\(283\) | 37.3080 | + | 21.5398i | 0.131830 | + | 0.0761123i | 0.564465 | − | 0.825457i | \(-0.309083\pi\) |
−0.432634 | + | 0.901569i | \(0.642416\pi\) | |||||||
\(284\) | 78.3362 | − | 37.0356i | 0.275832 | − | 0.130407i | ||||
\(285\) | 214.415 | + | 371.378i | 0.752334 | + | 1.30308i | ||||
\(286\) | 65.1118 | + | 124.273i | 0.227663 | + | 0.434521i | ||||
\(287\) | 266.855 | + | 108.091i | 0.929807 | + | 0.376625i | ||||
\(288\) | −559.859 | − | 499.529i | −1.94396 | − | 1.73448i | ||||
\(289\) | 128.361 | + | 222.328i | 0.444156 | + | 0.769301i | ||||
\(290\) | 1.97347 | − | 48.1270i | 0.00680508 | − | 0.165955i | ||||
\(291\) | 872.259 | + | 503.599i | 2.99745 | + | 1.73058i | ||||
\(292\) | −103.827 | − | 8.52927i | −0.355571 | − | 0.0292098i | ||||
\(293\) | 138.208 | 0.471700 | 0.235850 | − | 0.971789i | \(-0.424213\pi\) | ||||
0.235850 | + | 0.971789i | \(0.424213\pi\) | |||||||
\(294\) | 158.076 | − | 535.384i | 0.537674 | − | 1.82103i | ||||
\(295\) | 75.3816i | 0.255531i | ||||||||
\(296\) | 300.057 | − | 127.092i | 1.01370 | − | 0.429366i | ||||
\(297\) | 250.003 | − | 433.017i | 0.841760 | − | 1.45797i | ||||
\(298\) | 4.12568 | − | 100.613i | 0.0138446 | − | 0.337627i | ||||
\(299\) | 203.875 | − | 117.707i | 0.681855 | − | 0.393669i | ||||
\(300\) | 93.6671 | + | 64.8491i | 0.312224 | + | 0.216164i | ||||
\(301\) | 16.0419 | − | 39.6041i | 0.0532955 | − | 0.131575i | ||||
\(302\) | 124.986 | + | 238.551i | 0.413862 | + | 0.789903i | ||||
\(303\) | 257.536 | − | 148.688i | 0.849953 | − | 0.490721i | ||||
\(304\) | 87.9110 | − | 531.459i | 0.289181 | − | 1.74822i | ||||
\(305\) | 90.5465 | − | 156.831i | 0.296874 | − | 0.514201i | ||||
\(306\) | 225.079 | + | 142.554i | 0.735552 | + | 0.465862i | ||||
\(307\) | − | 51.7152i | − | 0.168453i | −0.996447 | − | 0.0842267i | \(-0.973158\pi\) | ||
0.996447 | − | 0.0842267i | \(-0.0268420\pi\) | |||||||
\(308\) | −76.5629 | + | 151.918i | −0.248581 | + | 0.493239i | ||||
\(309\) | −65.3810 | −0.211589 | ||||||||
\(310\) | −39.4764 | + | 62.3294i | −0.127343 | + | 0.201063i | ||||
\(311\) | 367.714 | + | 212.300i | 1.18236 | + | 0.682637i | 0.956560 | − | 0.291537i | \(-0.0941665\pi\) |
0.225802 | + | 0.974173i | \(0.427500\pi\) | |||||||
\(312\) | 316.964 | − | 419.949i | 1.01591 | − | 1.34599i | ||||
\(313\) | −9.08660 | − | 15.7385i | −0.0290307 | − | 0.0502826i | 0.851145 | − | 0.524931i | \(-0.175909\pi\) |
−0.880176 | + | 0.474648i | \(0.842575\pi\) | |||||||
\(314\) | −240.409 | + | 125.960i | −0.765634 | + | 0.401147i | ||||
\(315\) | −289.407 | + | 225.697i | −0.918752 | + | 0.716498i | ||||
\(316\) | −29.0821 | − | 20.1346i | −0.0920321 | − | 0.0637171i | ||||
\(317\) | 253.390 | + | 438.884i | 0.799337 | + | 1.38449i | 0.920048 | + | 0.391805i | \(0.128149\pi\) |
−0.120711 | + | 0.992688i | \(0.538518\pi\) | |||||||
\(318\) | −343.292 | − | 14.0768i | −1.07953 | − | 0.0442668i | ||||
\(319\) | −56.6718 | − | 32.7195i | −0.177654 | − | 0.102569i | ||||
\(320\) | −39.2328 | − | 137.626i | −0.122603 | − | 0.430080i | ||||
\(321\) | −855.720 | −2.66579 | ||||||||
\(322\) | 259.962 | + | 117.918i | 0.807335 | + | 0.366205i | ||||
\(323\) | 191.277i | 0.592188i | ||||||||
\(324\) | −1027.54 | − | 84.4118i | −3.17143 | − | 0.260530i | ||||
\(325\) | −28.8644 | + | 49.9946i | −0.0888134 | + | 0.153829i | ||||
\(326\) | −487.179 | − | 19.9770i | −1.49442 | − | 0.0612793i | ||||
\(327\) | −730.990 | + | 422.037i | −2.23544 | + | 1.29063i | ||||
\(328\) | −40.3536 | + | 326.562i | −0.123029 | + | 0.995616i | ||||
\(329\) | −101.254 | + | 14.1389i | −0.307764 | + | 0.0429753i | ||||
\(330\) | 137.098 | − | 71.8310i | 0.415447 | − | 0.217670i | ||||
\(331\) | −403.045 | + | 232.698i | −1.21766 | + | 0.703015i | −0.964416 | − | 0.264388i | \(-0.914830\pi\) |
−0.253241 | + | 0.967403i | \(0.581497\pi\) | |||||||
\(332\) | 371.559 | − | 175.665i | 1.11915 | − | 0.529111i | ||||
\(333\) | 477.538 | − | 827.120i | 1.43405 | − | 2.48384i | ||||
\(334\) | 276.818 | − | 437.069i | 0.828796 | − | 1.30859i | ||||
\(335\) | 18.9462i | 0.0565558i | ||||||||
\(336\) | 637.778 | + | 16.0689i | 1.89815 | + | 0.0478240i | ||||
\(337\) | −370.888 | −1.10056 | −0.550278 | − | 0.834981i | \(-0.685478\pi\) | ||||
−0.550278 | + | 0.834981i | \(0.685478\pi\) | |||||||
\(338\) | −60.3124 | − | 38.1989i | −0.178439 | − | 0.113014i | ||||
\(339\) | −401.267 | − | 231.672i | −1.18368 | − | 0.683397i | ||||
\(340\) | 21.7194 | + | 45.9400i | 0.0638806 | + | 0.135118i | ||||
\(341\) | 50.1170 | + | 86.8052i | 0.146971 | + | 0.254561i | ||||
\(342\) | −732.731 | − | 1398.50i | −2.14249 | − | 4.08918i | ||||
\(343\) | 138.677 | + | 313.716i | 0.404307 | + | 0.914623i | ||||
\(344\) | 48.4654 | + | 5.98891i | 0.140888 | + | 0.0174096i | ||||
\(345\) | −129.854 | − | 224.914i | −0.376388 | − | 0.651923i | ||||
\(346\) | −21.9812 | + | 536.056i | −0.0635296 | + | 1.54929i | ||||
\(347\) | 52.3973 | + | 30.2516i | 0.151001 | + | 0.0871804i | 0.573597 | − | 0.819138i | \(-0.305548\pi\) |
−0.422596 | + | 0.906318i | \(0.638881\pi\) | |||||||
\(348\) | −20.0923 | + | 244.584i | −0.0577366 | + | 0.702827i | ||||
\(349\) | 419.084 | 1.20081 | 0.600406 | − | 0.799695i | \(-0.295006\pi\) | ||||
0.600406 | + | 0.799695i | \(0.295006\pi\) | |||||||
\(350\) | −69.6658 | + | 6.83216i | −0.199045 | + | 0.0195204i | ||||
\(351\) | − | 950.165i | − | 2.70702i | ||||||
\(352\) | −190.355 | − | 39.5615i | −0.540782 | − | 0.112391i | ||||
\(353\) | −279.568 | + | 484.226i | −0.791977 | + | 1.37174i | 0.132764 | + | 0.991148i | \(0.457615\pi\) |
−0.924741 | + | 0.380597i | \(0.875719\pi\) | |||||||
\(354\) | 15.7354 | − | 383.738i | 0.0444502 | − | 1.08401i | ||||
\(355\) | 41.9492 | − | 24.2194i | 0.118167 | − | 0.0682236i | ||||
\(356\) | 121.151 | − | 174.989i | 0.340312 | − | 0.491542i | ||||
\(357\) | −224.360 | + | 31.3291i | −0.628459 | + | 0.0877565i | ||||
\(358\) | −98.9093 | − | 188.780i | −0.276283 | − | 0.527317i | ||||
\(359\) | −559.064 | + | 322.776i | −1.55728 | + | 0.899097i | −0.559765 | + | 0.828651i | \(0.689109\pi\) |
−0.997516 | + | 0.0704454i | \(0.977558\pi\) | |||||||
\(360\) | −334.783 | − | 252.684i | −0.929953 | − | 0.701900i | ||||
\(361\) | 386.251 | − | 669.007i | 1.06995 | − | 1.85321i | ||||
\(362\) | 332.586 | + | 210.643i | 0.918746 | + | 0.581888i | ||||
\(363\) | 478.973i | 1.31949i | ||||||||
\(364\) | 18.3445 | + | 322.760i | 0.0503970 | + | 0.886703i | ||||
\(365\) | −58.2364 | −0.159552 | ||||||||
\(366\) | −493.674 | + | 779.465i | −1.34884 | + | 2.12969i | ||||
\(367\) | 167.226 | + | 96.5482i | 0.455658 | + | 0.263074i | 0.710217 | − | 0.703983i | \(-0.248597\pi\) |
−0.254559 | + | 0.967057i | \(0.581930\pi\) | |||||||
\(368\) | −53.2405 | + | 321.861i | −0.144675 | + | 0.874623i | ||||
\(369\) | 482.203 | + | 835.200i | 1.30678 | + | 2.26342i | ||||
\(370\) | 161.357 | − | 84.5414i | 0.436099 | − | 0.228490i | ||||
\(371\) | 166.471 | − | 129.824i | 0.448709 | − | 0.349931i | ||||
\(372\) | 213.969 | − | 309.054i | 0.575187 | − | 0.830791i | ||||
\(373\) | −157.421 | − | 272.661i | −0.422040 | − | 0.730995i | 0.574099 | − | 0.818786i | \(-0.305352\pi\) |
−0.996139 | + | 0.0877913i | \(0.972019\pi\) | |||||||
\(374\) | 68.9785 | + | 2.82850i | 0.184435 | + | 0.00756283i | ||||
\(375\) | 55.1538 | + | 31.8430i | 0.147077 | + | 0.0849148i | ||||
\(376\) | −45.5704 | − | 107.589i | −0.121198 | − | 0.286140i | ||||
\(377\) | −124.354 | −0.329852 | ||||||||
\(378\) | 936.793 | − | 670.705i | 2.47829 | − | 1.77435i | ||||
\(379\) | − | 660.417i | − | 1.74252i | −0.490818 | − | 0.871262i | \(-0.663302\pi\) | ||
0.490818 | − | 0.871262i | \(-0.336698\pi\) | |||||||
\(380\) | 24.6546 | − | 300.121i | 0.0648807 | − | 0.789791i | ||||
\(381\) | −41.5504 | + | 71.9675i | −0.109056 | + | 0.188891i | ||||
\(382\) | 450.551 | + | 18.4751i | 1.17945 | + | 0.0483641i | ||||
\(383\) | 314.240 | − | 181.427i | 0.820471 | − | 0.473699i | −0.0301079 | − | 0.999547i | \(-0.509585\pi\) |
0.850579 | + | 0.525848i | \(0.176252\pi\) | |||||||
\(384\) | 170.991 | + | 708.787i | 0.445288 | + | 1.84580i | ||||
\(385\) | −35.7032 | + | 88.1436i | −0.0927356 | + | 0.228944i | ||||
\(386\) | −329.261 | + | 172.513i | −0.853008 | + | 0.446925i | ||||
\(387\) | 123.953 | − | 71.5642i | 0.320291 | − | 0.184920i | ||||
\(388\) | −302.299 | − | 639.411i | −0.779122 | − | 1.64797i | ||||
\(389\) | −122.135 | + | 211.545i | −0.313973 | + | 0.543817i | −0.979219 | − | 0.202808i | \(-0.934993\pi\) |
0.665246 | + | 0.746624i | \(0.268327\pi\) | |||||||
\(390\) | 157.373 | − | 248.477i | 0.403521 | − | 0.637122i | ||||
\(391\) | − | 115.841i | − | 0.296268i | ||||||
\(392\) | −305.268 | + | 245.917i | −0.778746 | + | 0.627339i | ||||
\(393\) | −458.839 | −1.16753 | ||||||||
\(394\) | 21.1591 | + | 13.4011i | 0.0537034 | + | 0.0340130i | ||||
\(395\) | −17.1244 | − | 9.88675i | −0.0433528 | − | 0.0250298i | ||||
\(396\) | −515.164 | + | 243.558i | −1.30092 | + | 0.615046i | ||||
\(397\) | −263.260 | − | 455.979i | −0.663123 | − | 1.14856i | −0.979791 | − | 0.200026i | \(-0.935897\pi\) |
0.316668 | − | 0.948536i | \(-0.397436\pi\) | |||||||
\(398\) | 134.087 | + | 255.920i | 0.336902 | + | 0.643015i | ||||
\(399\) | 1244.25 | + | 503.994i | 3.11843 | + | 1.26314i | ||||
\(400\) | −28.1571 | − | 74.8811i | −0.0703928 | − | 0.187203i | ||||
\(401\) | 128.106 | + | 221.885i | 0.319465 | + | 0.553330i | 0.980377 | − | 0.197134i | \(-0.0631633\pi\) |
−0.660911 | + | 0.750464i | \(0.729830\pi\) | |||||||
\(402\) | 3.95489 | − | 96.4477i | 0.00983803 | − | 0.239920i | ||||
\(403\) | 164.957 | + | 95.2379i | 0.409322 | + | 0.236322i | ||||
\(404\) | −208.122 | − | 17.0970i | −0.515152 | − | 0.0423193i | ||||
\(405\) | −576.349 | −1.42309 | ||||||||
\(406\) | −87.7795 | − | 122.604i | −0.216206 | − | 0.301981i | ||||
\(407\) | − | 247.481i | − | 0.608061i | ||||||
\(408\) | −100.975 | − | 238.396i | −0.247489 | − | 0.584304i | ||||
\(409\) | 161.101 | − | 279.035i | 0.393890 | − | 0.682237i | −0.599069 | − | 0.800697i | \(-0.704463\pi\) |
0.992959 | + | 0.118460i | \(0.0377959\pi\) | |||||||
\(410\) | −7.53631 | + | 183.788i | −0.0183813 | + | 0.448263i | ||||
\(411\) | −584.831 | + | 337.652i | −1.42295 | + | 0.821538i | ||||
\(412\) | 37.7476 | + | 26.1340i | 0.0916204 | + | 0.0634321i | ||||
\(413\) | 145.120 | + | 186.085i | 0.351380 | + | 0.450568i | ||||
\(414\) | 443.755 | + | 846.957i | 1.07187 | + | 2.04579i | ||||
\(415\) | 198.970 | − | 114.876i | 0.479447 | − | 0.276809i | ||||
\(416\) | −350.861 | + | 115.760i | −0.843415 | + | 0.278269i | ||||
\(417\) | 478.956 | − | 829.576i | 1.14858 | − | 1.98939i | ||||
\(418\) | −345.620 | − | 218.899i | −0.826843 | − | 0.523681i | ||||
\(419\) | − | 492.233i | − | 1.17478i | −0.809304 | − | 0.587391i | \(-0.800155\pi\) | ||
0.809304 | − | 0.587391i | \(-0.199845\pi\) | |||||||
\(420\) | 356.067 | − | 20.2376i | 0.847779 | − | 0.0481847i | ||||
\(421\) | 137.943 | 0.327656 | 0.163828 | − | 0.986489i | \(-0.447616\pi\) | ||||
0.163828 | + | 0.986489i | \(0.447616\pi\) | |||||||
\(422\) | 71.3164 | − | 112.602i | 0.168996 | − | 0.266829i | ||||
\(423\) | −296.574 | − | 171.227i | −0.701119 | − | 0.404791i | ||||
\(424\) | 192.572 | + | 145.348i | 0.454180 | + | 0.342801i | ||||
\(425\) | 14.2034 | + | 24.6009i | 0.0334197 | + | 0.0578846i | ||||
\(426\) | −218.603 | + | 114.535i | −0.513152 | + | 0.268861i | ||||
\(427\) | −78.4014 | − | 561.463i | −0.183610 | − | 1.31490i | ||||
\(428\) | 494.049 | + | 342.048i | 1.15432 | + | 0.799177i | ||||
\(429\) | −199.792 | − | 346.051i | −0.465717 | − | 0.806645i | ||||
\(430\) | 27.2761 | + | 1.11847i | 0.0634328 | + | 0.00260109i | ||||
\(431\) | −140.916 | − | 81.3578i | −0.326951 | − | 0.188765i | 0.327536 | − | 0.944839i | \(-0.393782\pi\) |
−0.654487 | + | 0.756074i | \(0.727115\pi\) | |||||||
\(432\) | 1017.59 | + | 835.636i | 2.35554 | + | 1.93434i | ||||
\(433\) | 816.898 | 1.88660 | 0.943300 | − | 0.331940i | \(-0.107703\pi\) | ||||
0.943300 | + | 0.331940i | \(0.107703\pi\) | |||||||
\(434\) | 22.5427 | + | 229.862i | 0.0519417 | + | 0.529636i | ||||
\(435\) | 137.187i | 0.315373i | ||||||||
\(436\) | 590.732 | + | 48.5282i | 1.35489 | + | 0.111303i | ||||
\(437\) | −343.235 | + | 594.501i | −0.785435 | + | 1.36041i | ||||
\(438\) | 296.459 | + | 12.1564i | 0.676846 | + | 0.0277544i | ||||
\(439\) | −306.378 | + | 176.888i | −0.697901 | + | 0.402933i | −0.806565 | − | 0.591145i | \(-0.798676\pi\) |
0.108664 | + | 0.994078i | \(0.465343\pi\) | |||||||
\(440\) | −107.865 | − | 13.3290i | −0.245148 | − | 0.0302932i | ||||
\(441\) | −279.923 | + | 1114.30i | −0.634747 | + | 2.52675i | ||||
\(442\) | 116.207 | − | 60.8854i | 0.262911 | − | 0.137750i | ||||
\(443\) | 29.0873 | − | 16.7936i | 0.0656599 | − | 0.0379087i | −0.466811 | − | 0.884357i | \(-0.654597\pi\) |
0.532471 | + | 0.846449i | \(0.321264\pi\) | |||||||
\(444\) | −839.051 | + | 396.685i | −1.88976 | + | 0.893434i | ||||
\(445\) | 59.4892 | − | 103.038i | 0.133684 | − | 0.231547i | ||||
\(446\) | 198.998 | − | 314.199i | 0.446183 | − | 0.704481i | ||||
\(447\) | 286.799i | 0.641609i | ||||||||
\(448\) | −361.797 | − | 264.210i | −0.807583 | − | 0.589754i | ||||
\(449\) | −447.816 | −0.997362 | −0.498681 | − | 0.866785i | \(-0.666182\pi\) | ||||
−0.498681 | + | 0.866785i | \(0.666182\pi\) | |||||||
\(450\) | −198.086 | − | 125.458i | −0.440191 | − | 0.278795i | ||||
\(451\) | 216.419 | + | 124.949i | 0.479864 | + | 0.277050i | ||||
\(452\) | 139.067 | + | 294.149i | 0.307671 | + | 0.650773i | ||||
\(453\) | −383.515 | − | 664.268i | −0.846612 | − | 1.46637i | ||||
\(454\) | −51.7071 | − | 98.6889i | −0.113892 | − | 0.217376i | ||||
\(455\) | 24.9927 | + | 178.983i | 0.0549291 | + | 0.393369i | ||||
\(456\) | −188.155 | + | 1522.65i | −0.412621 | + | 3.33914i | ||||
\(457\) | −182.498 | − | 316.096i | −0.399340 | − | 0.691676i | 0.594305 | − | 0.804240i | \(-0.297427\pi\) |
−0.993645 | + | 0.112563i | \(0.964094\pi\) | |||||||
\(458\) | −0.222754 | + | 5.43230i | −0.000486363 | + | 0.0118609i | ||||
\(459\) | −404.910 | − | 233.775i | −0.882157 | − | 0.509314i | ||||
\(460\) | −14.9313 | + | 181.759i | −0.0324594 | + | 0.395127i | ||||
\(461\) | −41.1257 | −0.0892098 | −0.0446049 | − | 0.999005i | \(-0.514203\pi\) | ||||
−0.0446049 | + | 0.999005i | \(0.514203\pi\) | |||||||
\(462\) | 200.150 | − | 441.252i | 0.433226 | − | 0.955090i | ||||
\(463\) | − | 71.6681i | − | 0.154791i | −0.997000 | − | 0.0773953i | \(-0.975340\pi\) | ||
0.997000 | − | 0.0773953i | \(-0.0246604\pi\) | |||||||
\(464\) | 109.365 | − | 133.179i | 0.235701 | − | 0.287023i | ||||
\(465\) | 105.066 | − | 181.980i | 0.225948 | − | 0.391354i | ||||
\(466\) | 5.12840 | − | 125.066i | 0.0110052 | − | 0.268383i | ||||
\(467\) | −474.607 | + | 274.014i | −1.01629 | + | 0.586755i | −0.913027 | − | 0.407900i | \(-0.866261\pi\) |
−0.103262 | + | 0.994654i | \(0.532928\pi\) | |||||||
\(468\) | −616.396 | + | 890.314i | −1.31709 | + | 1.90238i | ||||
\(469\) | 36.4741 | + | 46.7700i | 0.0777699 | + | 0.0997229i | ||||
\(470\) | −30.3133 | − | 57.8564i | −0.0644964 | − | 0.123099i | ||||
\(471\) | 669.443 | − | 386.503i | 1.42132 | − | 0.820601i | ||||
\(472\) | −162.472 | + | 215.261i | −0.344221 | + | 0.456061i | ||||
\(473\) | 18.5438 | − | 32.1189i | 0.0392047 | − | 0.0679046i | ||||
\(474\) | 85.1096 | + | 53.9042i | 0.179556 | + | 0.113722i | ||||
\(475\) | − | 168.338i | − | 0.354395i | ||||||
\(476\) | 142.057 | + | 71.5932i | 0.298438 | + | 0.150406i | ||||
\(477\) | 707.134 | 1.48246 | ||||||||
\(478\) | 57.1032 | − | 90.1606i | 0.119463 | − | 0.188620i | ||||
\(479\) | 446.814 | + | 257.968i | 0.932805 | + | 0.538555i | 0.887698 | − | 0.460427i | \(-0.152304\pi\) |
0.0451075 | + | 0.998982i | \(0.485637\pi\) | |||||||
\(480\) | 127.706 | + | 387.068i | 0.266054 | + | 0.806391i | ||||
\(481\) | −235.145 | − | 407.284i | −0.488868 | − | 0.846744i | ||||
\(482\) | 47.4794 | − | 24.8764i | 0.0985050 | − | 0.0516108i | ||||
\(483\) | −753.543 | − | 305.228i | −1.56013 | − | 0.631942i | ||||
\(484\) | 191.455 | − | 276.535i | 0.395568 | − | 0.571353i | ||||
\(485\) | −197.688 | − | 342.406i | −0.407604 | − | 0.705991i | ||||
\(486\) | 1453.89 | + | 59.6175i | 2.99154 | + | 0.122670i | ||||
\(487\) | −239.379 | − | 138.206i | −0.491538 | − | 0.283790i | 0.233674 | − | 0.972315i | \(-0.424925\pi\) |
−0.725212 | + | 0.688525i | \(0.758258\pi\) | |||||||
\(488\) | 596.589 | − | 252.692i | 1.22252 | − | 0.517811i | ||||
\(489\) | 1388.72 | 2.83991 | ||||||||
\(490\) | −158.822 | + | 150.982i | −0.324127 | + | 0.308127i | ||||
\(491\) | 733.948i | 1.49480i | 0.664373 | + | 0.747401i | \(0.268699\pi\) | ||||
−0.664373 | + | 0.747401i | \(0.731301\pi\) | |||||||
\(492\) | 76.7288 | − | 934.019i | 0.155953 | − | 1.89841i | ||||
\(493\) | −30.5957 | + | 52.9932i | −0.0620601 | + | 0.107491i | ||||
\(494\) | −776.781 | − | 31.8523i | −1.57243 | − | 0.0644783i | ||||
\(495\) | −275.871 | + | 159.274i | −0.557316 | + | 0.321766i | ||||
\(496\) | −247.070 | + | 92.9044i | −0.498125 | + | 0.187307i | ||||
\(497\) | 56.9289 | − | 140.545i | 0.114545 | − | 0.282787i | ||||
\(498\) | −1036.86 | + | 543.253i | −2.08205 | + | 1.09087i | ||||
\(499\) | 329.770 | − | 190.393i | 0.660861 | − | 0.381548i | −0.131744 | − | 0.991284i | \(-0.542058\pi\) |
0.792605 | + | 0.609736i | \(0.208724\pi\) | |||||||
\(500\) | −19.1147 | − | 40.4306i | −0.0382293 | − | 0.0808611i | ||||
\(501\) | −736.748 | + | 1276.09i | −1.47056 | + | 2.54708i | ||||
\(502\) | −39.0200 | + | 61.6089i | −0.0777291 | + | 0.122727i | ||||
\(503\) | − | 676.248i | − | 1.34443i | −0.740356 | − | 0.672214i | \(-0.765343\pi\) | ||
0.740356 | − | 0.672214i | \(-0.234657\pi\) | |||||||
\(504\) | −1312.89 | + | 20.7359i | −2.60493 | + | 0.0411426i | ||||
\(505\) | −116.735 | −0.231159 | ||||||||
\(506\) | 209.314 | + | 132.569i | 0.413664 | + | 0.261994i | ||||
\(507\) | 176.091 | + | 101.666i | 0.347319 | + | 0.200525i | ||||
\(508\) | 52.7559 | − | 24.9418i | 0.103850 | − | 0.0490980i | ||||
\(509\) | −335.005 | − | 580.245i | −0.658163 | − | 1.13997i | −0.981091 | − | 0.193548i | \(-0.938001\pi\) |
0.322928 | − | 0.946424i | \(-0.395333\pi\) | |||||||
\(510\) | −67.1685 | − | 128.199i | −0.131703 | − | 0.251370i | ||||
\(511\) | −143.761 | + | 112.113i | −0.281332 | + | 0.219399i | ||||
\(512\) | 184.595 | − | 477.566i | 0.360536 | − | 0.932745i | ||||
\(513\) | 1385.35 | + | 2399.49i | 2.70048 | + | 4.67737i | ||||
\(514\) | 25.1374 | − | 613.025i | 0.0489054 | − | 1.19266i | ||||
\(515\) | 22.2268 | + | 12.8327i | 0.0431589 | + | 0.0249178i | ||||
\(516\) | −138.619 | − | 11.3874i | −0.268641 | − | 0.0220686i | ||||
\(517\) | −88.7372 | −0.171639 | ||||||||
\(518\) | 235.567 | − | 519.330i | 0.454762 | − | 1.00257i | ||||
\(519\) | − | 1528.04i | − | 2.94420i | ||||||
\(520\) | −190.180 | + | 80.5530i | −0.365732 | + | 0.154910i | ||||
\(521\) | −50.7341 | + | 87.8740i | −0.0973783 | + | 0.168664i | −0.910599 | − | 0.413292i | \(-0.864379\pi\) |
0.813220 | + | 0.581956i | \(0.197712\pi\) | |||||||
\(522\) | 20.6938 | − | 504.658i | 0.0396432 | − | 0.966778i | ||||
\(523\) | 571.486 | − | 329.948i | 1.09271 | − | 0.630875i | 0.158412 | − | 0.987373i | \(-0.449363\pi\) |
0.934296 | + | 0.356498i | \(0.116029\pi\) | |||||||
\(524\) | 264.910 | + | 183.407i | 0.505553 | + | 0.350013i | ||||
\(525\) | 197.453 | − | 27.5719i | 0.376101 | − | 0.0525179i | ||||
\(526\) | −427.160 | − | 815.283i | −0.812092 | − | 1.54997i | ||||
\(527\) | 81.1707 | − | 46.8639i | 0.154024 | − | 0.0889259i | ||||
\(528\) | 546.318 | + | 90.3689i | 1.03469 | + | 0.171153i | ||||
\(529\) | −56.6304 | + | 98.0868i | −0.107052 | + | 0.185419i | ||||
\(530\) | 113.942 | + | 72.1652i | 0.214985 | + | 0.136161i | ||||
\(531\) | 790.449i | 1.48860i | ||||||||
\(532\) | −516.912 | − | 788.332i | −0.971639 | − | 1.48183i | ||||
\(533\) | 474.885 | 0.890967 | ||||||||
\(534\) | −324.345 | + | 512.110i | −0.607387 | + | 0.959007i | ||||
\(535\) | 290.909 | + | 167.957i | 0.543756 | + | 0.313938i | ||||
\(536\) | −40.8353 | + | 54.1031i | −0.0761853 | + | 0.100939i | ||||
\(537\) | 303.499 | + | 525.675i | 0.565174 | + | 0.978911i | ||||
\(538\) | −450.694 | + | 236.137i | −0.837721 | + | 0.438916i | ||||
\(539\) | 81.5528 | + | 286.322i | 0.151304 | + | 0.531210i | ||||
\(540\) | 605.187 | + | 418.993i | 1.12072 | + | 0.775913i | ||||
\(541\) | 246.462 | + | 426.885i | 0.455568 | + | 0.789067i | 0.998721 | − | 0.0505668i | \(-0.0161028\pi\) |
−0.543152 | + | 0.839634i | \(0.682769\pi\) | |||||||
\(542\) | −920.811 | − | 37.7583i | −1.69891 | − | 0.0696648i | ||||
\(543\) | −971.033 | − | 560.626i | −1.78827 | − | 1.03246i | ||||
\(544\) | −36.9936 | + | 177.999i | −0.0680029 | + | 0.327205i | ||||
\(545\) | 331.342 | 0.607967 | ||||||||
\(546\) | −89.8668 | − | 916.349i | −0.164591 | − | 1.67830i | ||||
\(547\) | 21.0836i | 0.0385441i | 0.999814 | + | 0.0192720i | \(0.00613486\pi\) | ||||
−0.999814 | + | 0.0192720i | \(0.993865\pi\) | |||||||
\(548\) | 472.617 | + | 38.8251i | 0.862440 | + | 0.0708487i | ||||
\(549\) | 949.468 | − | 1644.53i | 1.72945 | − | 2.99549i | ||||
\(550\) | −60.7061 | − | 2.48929i | −0.110375 | − | 0.00452598i | ||||
\(551\) | 314.037 | − | 181.309i | 0.569940 | − | 0.329055i | ||||
\(552\) | 113.950 | − | 922.145i | 0.206432 | − | 1.67055i | ||||
\(553\) | −61.3061 | + | 8.56063i | −0.110861 | + | 0.0154803i | ||||
\(554\) | −936.164 | + | 490.494i | −1.68983 | + | 0.885369i | ||||
\(555\) | −449.314 | + | 259.411i | −0.809574 | + | 0.467408i | ||||
\(556\) | −608.122 | + | 287.507i | −1.09374 | + | 0.517098i | ||||
\(557\) | −167.523 | + | 290.158i | −0.300759 | + | 0.520930i | −0.976308 | − | 0.216385i | \(-0.930573\pi\) |
0.675549 | + | 0.737315i | \(0.263907\pi\) | |||||||
\(558\) | −413.948 | + | 653.584i | −0.741842 | + | 1.17130i | ||||
\(559\) | − | 70.4781i | − | 0.126079i | ||||||
\(560\) | −213.664 | − | 130.643i | −0.381543 | − | 0.233291i | ||||
\(561\) | −196.625 | −0.350490 | ||||||||
\(562\) | 836.964 | + | 530.091i | 1.48926 | + | 0.943223i | ||||
\(563\) | 177.179 | + | 102.294i | 0.314705 | + | 0.181695i | 0.649030 | − | 0.760763i | \(-0.275175\pi\) |
−0.334325 | + | 0.942458i | \(0.608508\pi\) | |||||||
\(564\) | 142.236 | + | 300.852i | 0.252192 | + | 0.533425i | ||||
\(565\) | 90.9428 | + | 157.518i | 0.160961 | + | 0.278792i | ||||
\(566\) | 39.9863 | + | 76.3184i | 0.0706472 | + | 0.134838i | ||||
\(567\) | −1422.76 | + | 1109.55i | −2.50928 | + | 1.95688i | ||||
\(568\) | 171.992 | + | 21.2532i | 0.302802 | + | 0.0374175i | ||||
\(569\) | −266.777 | − | 462.071i | −0.468852 | − | 0.812075i | 0.530514 | − | 0.847676i | \(-0.321999\pi\) |
−0.999366 | + | 0.0356009i | \(0.988665\pi\) | |||||||
\(570\) | −35.1393 | + | 856.941i | −0.0616479 | + | 1.50341i | ||||
\(571\) | −655.774 | − | 378.611i | −1.14847 | − | 0.663067i | −0.199953 | − | 0.979805i | \(-0.564079\pi\) |
−0.948513 | + | 0.316738i | \(0.897412\pi\) | |||||||
\(572\) | −22.9732 | + | 279.653i | −0.0401630 | + | 0.488903i | ||||
\(573\) | −1284.31 | −2.24137 | ||||||||
\(574\) | 335.213 | + | 468.202i | 0.583995 | + | 0.815682i | ||||
\(575\) | 101.948i | 0.177302i | ||||||||
\(576\) | −411.394 | − | 1443.14i | −0.714226 | − | 2.50545i | ||||
\(577\) | 284.714 | − | 493.140i | 0.493439 | − | 0.854662i | −0.506532 | − | 0.862221i | \(-0.669073\pi\) |
0.999971 | + | 0.00755940i | \(0.00240625\pi\) | |||||||
\(578\) | −21.0364 | + | 513.014i | −0.0363951 | + | 0.887567i | ||||
\(579\) | 916.859 | − | 529.349i | 1.58352 | − | 0.914247i | ||||
\(580\) | 54.8363 | − | 79.2047i | 0.0945453 | − | 0.136560i | ||||
\(581\) | 270.021 | − | 666.624i | 0.464752 | − | 1.14737i | ||||
\(582\) | 934.878 | + | 1784.32i | 1.60632 | + | 3.06584i | ||||
\(583\) | 158.685 | − | 91.6170i | 0.272188 | − | 0.157148i | ||||
\(584\) | −166.301 | − | 125.519i | −0.284762 | − | 0.214929i | ||||
\(585\) | −302.671 | + | 524.241i | −0.517386 | + | 0.896139i | ||||
\(586\) | 233.520 | + | 147.900i | 0.398498 | + | 0.252389i | ||||
\(587\) | − | 333.386i | − | 0.567949i | −0.958832 | − | 0.283975i | \(-0.908347\pi\) | ||
0.958832 | − | 0.283975i | \(-0.0916531\pi\) | |||||||
\(588\) | 840.017 | − | 735.437i | 1.42860 | − | 1.25074i | ||||
\(589\) | −555.430 | −0.943005 | ||||||||
\(590\) | −80.6677 | + | 127.367i | −0.136725 | + | 0.215876i | ||||
\(591\) | −61.7771 | − | 35.6670i | −0.104530 | − | 0.0603503i | ||||
\(592\) | 642.988 | + | 106.360i | 1.08613 | + | 0.179661i | ||||
\(593\) | −504.094 | − | 873.117i | −0.850074 | − | 1.47237i | −0.881140 | − | 0.472855i | \(-0.843224\pi\) |
0.0310661 | − | 0.999517i | \(-0.490110\pi\) | |||||||
\(594\) | 885.793 | − | 464.103i | 1.49123 | − | 0.781318i | ||||
\(595\) | 82.4222 | + | 33.3857i | 0.138525 | + | 0.0561104i | ||||
\(596\) | 114.639 | − | 165.583i | 0.192347 | − | 0.277824i | ||||
\(597\) | −411.440 | − | 712.635i | −0.689179 | − | 1.19369i | ||||
\(598\) | 470.433 | + | 19.2903i | 0.786677 | + | 0.0322581i | ||||
\(599\) | 67.5011 | + | 38.9718i | 0.112690 | + | 0.0650614i | 0.555285 | − | 0.831660i | \(-0.312609\pi\) |
−0.442596 | + | 0.896721i | \(0.645942\pi\) | |||||||
\(600\) | 88.8657 | + | 209.806i | 0.148109 | + | 0.349677i | ||||
\(601\) | 412.145 | 0.685765 | 0.342882 | − | 0.939378i | \(-0.388597\pi\) | ||||
0.342882 | + | 0.939378i | \(0.388597\pi\) | |||||||
\(602\) | 69.4862 | − | 49.7493i | 0.115426 | − | 0.0826400i | ||||
\(603\) | 198.669i | 0.329468i | ||||||||
\(604\) | −44.0987 | + | 536.812i | −0.0730110 | + | 0.888762i | ||||
\(605\) | 94.0106 | − | 162.831i | 0.155389 | − | 0.269142i | ||||
\(606\) | 594.254 | + | 24.3677i | 0.980617 | + | 0.0402107i | ||||
\(607\) | −242.872 | + | 140.222i | −0.400119 | + | 0.231009i | −0.686535 | − | 0.727096i | \(-0.740869\pi\) |
0.286416 | + | 0.958105i | \(0.407536\pi\) | |||||||
\(608\) | 717.264 | − | 803.890i | 1.17971 | − | 1.32219i | ||||
\(609\) | 264.104 | + | 338.656i | 0.433669 | + | 0.556085i | ||||
\(610\) | 320.819 | − | 168.090i | 0.525932 | − | 0.275557i | ||||
\(611\) | −146.036 | + | 84.3141i | −0.239012 | + | 0.137994i | ||||
\(612\) | 227.749 | + | 481.725i | 0.372139 | + | 0.787132i | ||||
\(613\) | −32.5499 | + | 56.3782i | −0.0530994 | + | 0.0919709i | −0.891353 | − | 0.453309i | \(-0.850243\pi\) |
0.838254 | + | 0.545280i | \(0.183577\pi\) | |||||||
\(614\) | 55.3417 | − | 87.3793i | 0.0901331 | − | 0.142312i | ||||
\(615\) | − | 523.891i | − | 0.851856i | ||||||
\(616\) | −291.933 | + | 174.752i | −0.473918 | + | 0.283688i | ||||
\(617\) | 144.024 | 0.233426 | 0.116713 | − | 0.993166i | \(-0.462764\pi\) | ||||
0.116713 | + | 0.993166i | \(0.462764\pi\) | |||||||
\(618\) | −110.469 | − | 69.9658i | −0.178753 | − | 0.113213i | ||||
\(619\) | 588.125 | + | 339.554i | 0.950120 | + | 0.548552i | 0.893118 | − | 0.449822i | \(-0.148513\pi\) |
0.0570020 | + | 0.998374i | \(0.481846\pi\) | |||||||
\(620\) | −133.400 | + | 63.0688i | −0.215162 | + | 0.101724i | ||||
\(621\) | −838.991 | − | 1453.18i | −1.35103 | − | 2.34006i | ||||
\(622\) | 394.112 | + | 752.208i | 0.633621 | + | 1.20934i | ||||
\(623\) | −51.5098 | − | 368.882i | −0.0826803 | − | 0.592106i | ||||
\(624\) | 984.949 | − | 370.365i | 1.57844 | − | 0.593534i | ||||
\(625\) | −12.5000 | − | 21.6506i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 1.48915 | − | 36.3159i | 0.00237884 | − | 0.0580126i | ||||
\(627\) | 1009.09 | + | 582.597i | 1.60939 | + | 0.929182i | ||||
\(628\) | −540.994 | − | 44.4422i | −0.861456 | − | 0.0707679i | ||||
\(629\) | −231.417 | −0.367913 | ||||||||
\(630\) | −730.513 | + | 71.6418i | −1.15954 | + | 0.113717i | ||||
\(631\) | − | 275.380i | − | 0.436418i | −0.975902 | − | 0.218209i | \(-0.929979\pi\) | ||
0.975902 | − | 0.218209i | \(-0.0700215\pi\) | |||||||
\(632\) | −27.5914 | − | 65.1415i | −0.0436572 | − | 0.103072i | ||||
\(633\) | −189.808 | + | 328.757i | −0.299855 | + | 0.519363i | ||||
\(634\) | −41.5266 | + | 1012.71i | −0.0654994 | + | 1.59733i | ||||
\(635\) | 28.2509 | − | 16.3106i | 0.0444895 | − | 0.0256860i | ||||
\(636\) | −564.970 | − | 391.149i | −0.888318 | − | 0.615015i | ||||
\(637\) | 406.264 | + | 393.718i | 0.637776 | + | 0.618081i | ||||
\(638\) | −60.7402 | − | 115.929i | −0.0952040 | − | 0.181708i | ||||
\(639\) | 439.878 | − | 253.964i | 0.688385 | − | 0.397439i | ||||
\(640\) | 80.9876 | − | 274.520i | 0.126543 | − | 0.428937i | ||||
\(641\) | 519.631 | − | 900.027i | 0.810657 | − | 1.40410i | −0.101748 | − | 0.994810i | \(-0.532444\pi\) |
0.912405 | − | 0.409289i | \(-0.134223\pi\) | |||||||
\(642\) | −1445.85 | − | 915.727i | −2.25210 | − | 1.42637i | ||||
\(643\) | 1054.99i | 1.64073i | 0.571839 | + | 0.820366i | \(0.306230\pi\) | ||||
−0.571839 | + | 0.820366i | \(0.693770\pi\) | |||||||
\(644\) | 313.052 | + | 477.429i | 0.486105 | + | 0.741349i | ||||
\(645\) | −77.7511 | −0.120544 | ||||||||
\(646\) | −204.690 | + | 323.186i | −0.316858 | + | 0.500288i | ||||
\(647\) | −377.661 | − | 218.043i | −0.583711 | − | 0.337006i | 0.178896 | − | 0.983868i | \(-0.442748\pi\) |
−0.762607 | + | 0.646862i | \(0.776081\pi\) | |||||||
\(648\) | −1645.83 | − | 1242.22i | −2.53987 | − | 1.91701i | ||||
\(649\) | 102.411 | + | 177.382i | 0.157799 | + | 0.273315i | ||||
\(650\) | −102.270 | + | 53.5836i | −0.157339 | + | 0.0824363i | ||||
\(651\) | −90.9733 | − | 651.496i | −0.139744 | − | 1.00076i | ||||
\(652\) | −801.773 | − | 555.096i | −1.22971 | − | 0.851375i | ||||
\(653\) | −24.3804 | − | 42.2281i | −0.0373360 | − | 0.0646679i | 0.846754 | − | 0.531985i | \(-0.178554\pi\) |
−0.884090 | + | 0.467317i | \(0.845221\pi\) | |||||||
\(654\) | −1686.73 | − | 69.1653i | −2.57910 | − | 0.105757i | ||||
\(655\) | 155.986 | + | 90.0587i | 0.238147 | + | 0.137494i | ||||
\(656\) | −417.645 | + | 508.584i | −0.636653 | + | 0.775281i | ||||
\(657\) | −610.664 | −0.929474 | ||||||||
\(658\) | −186.212 | − | 84.4652i | −0.282997 | − | 0.128367i | ||||
\(659\) | 1163.45i | 1.76548i | 0.469866 | + | 0.882738i | \(0.344302\pi\) | ||||
−0.469866 | + | 0.882738i | \(0.655698\pi\) | |||||||
\(660\) | 308.512 | + | 25.3440i | 0.467442 | + | 0.0383999i | ||||
\(661\) | −159.543 | + | 276.336i | −0.241366 | + | 0.418058i | −0.961104 | − | 0.276188i | \(-0.910929\pi\) |
0.719738 | + | 0.694246i | \(0.244262\pi\) | |||||||
\(662\) | −930.010 | − | 38.1355i | −1.40485 | − | 0.0576065i | ||||
\(663\) | −323.589 | + | 186.824i | −0.488067 | + | 0.281786i | ||||
\(664\) | 815.778 | + | 100.806i | 1.22858 | + | 0.151817i | ||||
\(665\) | −324.073 | − | 415.553i | −0.487328 | − | 0.624892i | ||||
\(666\) | 1691.98 | − | 886.498i | 2.54051 | − | 1.33108i | ||||
\(667\) | −190.187 | + | 109.804i | −0.285137 | + | 0.164624i | ||||
\(668\) | 935.437 | − | 442.254i | 1.40035 | − | 0.662056i | ||||
\(669\) | −529.631 | + | 917.347i | −0.791675 | + | 1.37122i | ||||
\(670\) | −20.2748 | + | 32.0120i | −0.0302609 | + | 0.0477791i | ||||
\(671\) | − | 492.056i | − | 0.733317i | ||||||
\(672\) | 1060.41 | + | 709.652i | 1.57799 | + | 1.05603i | ||||
\(673\) | −678.408 | −1.00804 | −0.504018 | − | 0.863693i | \(-0.668145\pi\) | ||||
−0.504018 | + | 0.863693i | \(0.668145\pi\) | |||||||
\(674\) | −626.661 | − | 396.896i | −0.929764 | − | 0.588866i | ||||
\(675\) | 356.351 | + | 205.739i | 0.527927 | + | 0.304799i | ||||
\(676\) | −61.0278 | − | 129.084i | −0.0902778 | − | 0.190952i | ||||
\(677\) | 77.0733 | + | 133.495i | 0.113845 | + | 0.197186i | 0.917318 | − | 0.398156i | \(-0.130350\pi\) |
−0.803472 | + | 0.595342i | \(0.797017\pi\) | |||||||
\(678\) | −430.074 | − | 820.844i | −0.634327 | − | 1.21068i | ||||
\(679\) | −1147.19 | − | 464.676i | −1.68952 | − | 0.684353i | ||||
\(680\) | −12.4638 | + | 100.864i | −0.0183292 | + | 0.148329i | ||||
\(681\) | 158.661 | + | 274.809i | 0.232982 | + | 0.403537i | ||||
\(682\) | −8.21339 | + | 200.300i | −0.0120431 | + | 0.293695i | ||||
\(683\) | 387.106 | + | 223.496i | 0.566773 | + | 0.327226i | 0.755859 | − | 0.654734i | \(-0.227219\pi\) |
−0.189087 | + | 0.981960i | \(0.560553\pi\) | |||||||
\(684\) | 258.528 | − | 3147.05i | 0.377965 | − | 4.60096i | ||||
\(685\) | 265.091 | 0.386994 | ||||||||
\(686\) | −101.402 | + | 678.464i | −0.147816 | + | 0.989015i | ||||
\(687\) | − | 15.4849i | − | 0.0225399i | ||||||
\(688\) | 75.4794 | + | 61.9830i | 0.109708 | + | 0.0900915i | ||||
\(689\) | 174.101 | − | 301.551i | 0.252686 | − | 0.437665i | ||||
\(690\) | 21.2810 | − | 518.979i | 0.0308420 | − | 0.752144i | ||||
\(691\) | 601.490 | − | 347.271i | 0.870463 | − | 0.502562i | 0.00296125 | − | 0.999996i | \(-0.499057\pi\) |
0.867502 | + | 0.497433i | \(0.165724\pi\) | |||||||
\(692\) | −610.786 | + | 882.211i | −0.882639 | + | 1.27487i | ||||
\(693\) | −374.382 | + | 924.271i | −0.540234 | + | 1.33372i | ||||
\(694\) | 56.1588 | + | 107.185i | 0.0809205 | + | 0.154446i | ||||
\(695\) | −325.651 | + | 188.014i | −0.468562 | + | 0.270524i | ||||
\(696\) | −295.684 | + | 391.754i | −0.424833 | + | 0.562864i | ||||
\(697\) | 116.839 | − | 202.371i | 0.167631 | − | 0.290346i | ||||
\(698\) | 708.094 | + | 448.471i | 1.01446 | + | 0.642509i | ||||
\(699\) | 356.504i | 0.510020i | ||||||||
\(700\) | −125.020 | − | 63.0073i | −0.178600 | − | 0.0900104i | ||||
\(701\) | −1073.69 | −1.53166 | −0.765830 | − | 0.643043i | \(-0.777672\pi\) | ||||
−0.765830 | + | 0.643043i | \(0.777672\pi\) | |||||||
\(702\) | 1016.79 | − | 1605.42i | 1.44843 | − | 2.28693i | ||||
\(703\) | 1187.64 | + | 685.687i | 1.68939 | + | 0.975372i | ||||
\(704\) | −279.294 | − | 270.548i | −0.396724 | − | 0.384301i | ||||
\(705\) | 93.0150 | + | 161.107i | 0.131936 | + | 0.228520i | ||||
\(706\) | −990.547 | + | 518.988i | −1.40304 | + | 0.735110i | ||||
\(707\) | −288.170 | + | 224.732i | −0.407595 | + | 0.317867i | ||||
\(708\) | 437.234 | − | 631.535i | 0.617563 | − | 0.891998i | ||||
\(709\) | 42.5633 | + | 73.7218i | 0.0600328 | + | 0.103980i | 0.894480 | − | 0.447108i | \(-0.147546\pi\) |
−0.834447 | + | 0.551088i | \(0.814213\pi\) | |||||||
\(710\) | 96.7962 | + | 3.96918i | 0.136333 | + | 0.00559039i | ||||
\(711\) | −179.565 | − | 103.672i | −0.252553 | − | 0.145812i | ||||
\(712\) | 391.960 | − | 166.019i | 0.550506 | − | 0.233173i | ||||
\(713\) | 336.379 | 0.471779 | ||||||||
\(714\) | −412.610 | − | 187.159i | −0.577885 | − | 0.262127i | ||||
\(715\) | 156.857i | 0.219381i | ||||||||
\(716\) | 34.8979 | − | 424.812i | 0.0487401 | − | 0.593313i | ||||
\(717\) | −151.980 | + | 263.237i | −0.211966 | + | 0.367136i | ||||
\(718\) | −1290.02 | − | 52.8979i | −1.79668 | − | 0.0736739i | ||||
\(719\) | −701.029 | + | 404.739i | −0.975005 | + | 0.562919i | −0.900758 | − | 0.434321i | \(-0.856989\pi\) |
−0.0742465 | + | 0.997240i | \(0.523655\pi\) | |||||||
\(720\) | −295.255 | − | 785.200i | −0.410076 | − | 1.09056i | ||||
\(721\) | 79.5732 | − | 11.1114i | 0.110365 | − | 0.0154111i | ||||
\(722\) | 1368.54 | − | 717.034i | 1.89549 | − | 0.993122i | ||||
\(723\) | −132.211 | + | 76.3321i | −0.182864 | + | 0.105577i | ||||
\(724\) | 336.531 | + | 711.817i | 0.464822 | + | 0.983173i | ||||
\(725\) | 26.9264 | − | 46.6379i | 0.0371399 | − | 0.0643282i | ||||
\(726\) | −512.561 | + | 809.286i | −0.706007 | + | 1.11472i | ||||
\(727\) | 25.6541i | 0.0352876i | 0.999844 | + | 0.0176438i | \(0.00561648\pi\) | ||||
−0.999844 | + | 0.0176438i | \(0.994384\pi\) | |||||||
\(728\) | −314.398 | + | 564.974i | −0.431865 | + | 0.776064i | ||||
\(729\) | −1824.58 | −2.50286 | ||||||||
\(730\) | −98.3976 | − | 62.3202i | −0.134791 | − | 0.0853701i | ||||
\(731\) | −30.0341 | − | 17.3402i | −0.0410863 | − | 0.0237212i | ||||
\(732\) | −1668.25 | + | 788.711i | −2.27903 | + | 1.07747i | ||||
\(733\) | 481.102 | + | 833.293i | 0.656346 | + | 1.13682i | 0.981555 | + | 0.191183i | \(0.0612322\pi\) |
−0.325208 | + | 0.945642i | \(0.605434\pi\) | |||||||
\(734\) | 179.231 | + | 342.083i | 0.244184 | + | 0.466053i | ||||
\(735\) | 434.347 | − | 448.188i | 0.590949 | − | 0.609780i | ||||
\(736\) | −434.388 | + | 486.851i | −0.590201 | + | 0.661482i | ||||
\(737\) | 25.7398 | + | 44.5826i | 0.0349251 | + | 0.0604920i | ||||
\(738\) | −79.0255 | + | 1927.19i | −0.107081 | + | 2.61137i | ||||
\(739\) | 197.899 | + | 114.257i | 0.267793 | + | 0.154611i | 0.627884 | − | 0.778307i | \(-0.283921\pi\) |
−0.360091 | + | 0.932917i | \(0.617254\pi\) | |||||||
\(740\) | 363.102 | + | 29.8285i | 0.490679 | + | 0.0403088i | ||||
\(741\) | 2214.23 | 2.98817 | ||||||||
\(742\) | 420.202 | − | 41.2094i | 0.566310 | − | 0.0555383i | ||||
\(743\) | 539.269i | 0.725799i | 0.931828 | + | 0.362900i | \(0.118213\pi\) | ||||
−0.931828 | + | 0.362900i | \(0.881787\pi\) | |||||||
\(744\) | 692.255 | − | 293.212i | 0.930450 | − | 0.394102i | ||||
\(745\) | 56.2915 | − | 97.4998i | 0.0755591 | − | 0.130872i | ||||
\(746\) | 25.7988 | − | 629.155i | 0.0345829 | − | 0.843371i | ||||
\(747\) | 2086.40 | − | 1204.58i | 2.79303 | − | 1.61256i | ||||
\(748\) | 113.521 | + | 78.5947i | 0.151766 | + | 0.105073i | ||||
\(749\) | 1041.47 | − | 145.428i | 1.39048 | − | 0.194163i | ||||
\(750\) | 59.1132 | + | 112.824i | 0.0788176 | + | 0.150432i | ||||
\(751\) | −864.958 | + | 499.384i | −1.15174 | + | 0.664959i | −0.949311 | − | 0.314338i | \(-0.898218\pi\) |
−0.202431 | + | 0.979297i | \(0.564884\pi\) | |||||||
\(752\) | 38.1365 | − | 230.551i | 0.0507134 | − | 0.306583i | ||||
\(753\) | 103.852 | − | 179.876i | 0.137917 | − | 0.238879i | ||||
\(754\) | −210.112 | − | 133.075i | −0.278663 | − | 0.176491i | ||||
\(755\) | 301.098i | 0.398805i | ||||||||
\(756\) | 2300.57 | − | 130.756i | 3.04308 | − | 0.172958i | ||||
\(757\) | −98.5371 | −0.130168 | −0.0650839 | − | 0.997880i | \(-0.520732\pi\) | ||||
−0.0650839 | + | 0.997880i | \(0.520732\pi\) | |||||||
\(758\) | 706.728 | − | 1115.86i | 0.932359 | − | 1.47211i | ||||
\(759\) | −611.122 | − | 352.832i | −0.805168 | − | 0.464864i | ||||
\(760\) | 362.823 | − | 480.708i | 0.477399 | − | 0.632510i | ||||
\(761\) | 565.509 | + | 979.491i | 0.743113 | + | 1.28711i | 0.951071 | + | 0.308972i | \(0.0999849\pi\) |
−0.207958 | + | 0.978138i | \(0.566682\pi\) | |||||||
\(762\) | −147.219 | + | 77.1339i | −0.193201 | + | 0.101226i | ||||
\(763\) | 817.941 | − | 637.879i | 1.07201 | − | 0.836015i | ||||
\(764\) | 741.492 | + | 513.361i | 0.970539 | + | 0.671939i | ||||
\(765\) | 148.936 | + | 257.965i | 0.194687 | + | 0.337209i | ||||
\(766\) | 725.098 | + | 29.7330i | 0.946603 | + | 0.0388159i | ||||
\(767\) | 337.080 | + | 194.613i | 0.439478 | + | 0.253733i | ||||
\(768\) | −469.580 | + | 1380.57i | −0.611432 | + | 1.79761i | ||||
\(769\) | −699.195 | −0.909226 | −0.454613 | − | 0.890689i | \(-0.650222\pi\) | ||||
−0.454613 | + | 0.890689i | \(0.650222\pi\) | |||||||
\(770\) | −154.650 | + | 110.723i | −0.200844 | + | 0.143796i | ||||
\(771\) | 1747.44i | 2.26646i | ||||||||
\(772\) | −740.938 | − | 60.8674i | −0.959765 | − | 0.0788438i | ||||
\(773\) | 424.994 | − | 736.111i | 0.549798 | − | 0.952278i | −0.448490 | − | 0.893788i | \(-0.648038\pi\) |
0.998288 | − | 0.0584904i | \(-0.0186287\pi\) | |||||||
\(774\) | 286.016 | + | 11.7282i | 0.369530 | + | 0.0151528i | ||||
\(775\) | −71.4362 | + | 41.2437i | −0.0921758 | + | 0.0532177i | ||||
\(776\) | 173.477 | − | 1403.86i | 0.223552 | − | 1.80910i | ||||
\(777\) | −609.759 | + | 1505.37i | −0.784761 | + | 1.93741i | ||||
\(778\) | −432.742 | + | 226.731i | −0.556224 | + | 0.291428i | ||||
\(779\) | −1199.25 | + | 692.385i | −1.53947 | + | 0.888813i | ||||
\(780\) | 531.804 | − | 251.425i | 0.681799 | − | 0.322340i | ||||
\(781\) | 65.8075 | − | 113.982i | 0.0842606 | − | 0.145944i | ||||
\(782\) | 123.964 | − | 195.728i | 0.158522 | − | 0.250291i | ||||
\(783\) | 886.371i | 1.13202i | ||||||||
\(784\) | −778.951 | + | 88.8325i | −0.993560 | + | 0.113307i | ||||
\(785\) | −303.444 | −0.386553 | ||||||||
\(786\) | −775.265 | − | 491.014i | −0.986343 | − | 0.624700i | ||||
\(787\) | −284.056 | − | 164.000i | −0.360936 | − | 0.208386i | 0.308555 | − | 0.951206i | \(-0.400154\pi\) |
−0.669491 | + | 0.742820i | \(0.733488\pi\) | |||||||
\(788\) | 21.4101 | + | 45.2858i | 0.0271702 | + | 0.0574693i | ||||
\(789\) | 1310.72 | + | 2270.24i | 1.66124 | + | 2.87736i | ||||
\(790\) | −18.3537 | − | 35.0301i | −0.0232325 | − | 0.0443419i | ||||
\(791\) | 527.742 | + | 213.766i | 0.667183 | + | 0.270247i | ||||
\(792\) | −1131.07 | − | 139.768i | −1.42812 | − | 0.176474i | ||||
\(793\) | −467.529 | − | 809.785i | −0.589570 | − | 1.02117i | ||||
\(794\) | 43.1441 | − | 1052.15i | 0.0543377 | − | 1.32513i | ||||
\(795\) | −332.670 | − | 192.067i | −0.418453 | − | 0.241594i | ||||
\(796\) | −47.3096 | + | 575.899i | −0.0594342 | + | 0.723491i | ||||
\(797\) | −1404.95 | −1.76280 | −0.881398 | − | 0.472375i | \(-0.843397\pi\) | ||||
−0.881398 | + | 0.472375i | \(0.843397\pi\) | |||||||
\(798\) | 1562.99 | + | 2183.07i | 1.95863 | + | 2.73567i | ||||
\(799\) | 82.9773i | 0.103851i | ||||||||
\(800\) | 32.5571 | − | 156.653i | 0.0406963 | − | 0.195816i | ||||
\(801\) | 623.802 | − | 1080.46i | 0.778778 | − | 1.34888i | ||||
\(802\) | −20.9945 | + | 511.992i | −0.0261777 | + | 0.638394i | ||||
\(803\) | −137.037 | + | 79.1183i | −0.170656 | + | 0.0985284i | ||||
\(804\) | 109.893 | − | 158.728i | 0.136683 | − | 0.197423i | ||||
\(805\) | 196.265 | + | 251.667i | 0.243807 | + | 0.312630i | ||||
\(806\) | 176.799 | + | 337.441i | 0.219354 | + | 0.418661i | ||||
\(807\) | 1255.00 | − | 724.575i | 1.55514 | − | 0.897863i | ||||
\(808\) | −333.352 | − | 251.603i | −0.412564 | − | 0.311390i | ||||
\(809\) | −133.528 | + | 231.278i | −0.165053 | + | 0.285881i | −0.936674 | − | 0.350202i | \(-0.886113\pi\) |
0.771621 | + | 0.636083i | \(0.219446\pi\) | |||||||
\(810\) | −973.815 | − | 616.766i | −1.20224 | − | 0.761439i | ||||
\(811\) | 805.620i | 0.993366i | 0.867932 | + | 0.496683i | \(0.165449\pi\) | ||||
−0.867932 | + | 0.496683i | \(0.834551\pi\) | |||||||
\(812\) | −17.1129 | − | 301.090i | −0.0210750 | − | 0.370800i | ||||
\(813\) | 2624.79 | 3.22853 | ||||||||
\(814\) | 264.835 | − | 418.150i | 0.325351 | − | 0.513698i | ||||
\(815\) | −472.106 | − | 272.570i | −0.579271 | − | 0.334442i | ||||
\(816\) | 84.5031 | − | 510.856i | 0.103558 | − | 0.626049i | ||||
\(817\) | 102.758 | + | 177.981i | 0.125774 | + | 0.217847i | ||||
\(818\) | 570.802 | − | 299.067i | 0.697802 | − | 0.365607i | ||||
\(819\) | 262.073 | + | 1876.81i | 0.319991 | + | 2.29159i | ||||
\(820\) | −209.409 | + | 302.468i | −0.255377 | + | 0.368863i | ||||
\(821\) | 605.903 | + | 1049.46i | 0.738007 | + | 1.27826i | 0.953392 | + | 0.301736i | \(0.0975660\pi\) |
−0.215385 | + | 0.976529i | \(0.569101\pi\) | |||||||
\(822\) | −1349.47 | − | 55.3359i | −1.64170 | − | 0.0673186i | ||||
\(823\) | 700.584 | + | 404.482i | 0.851256 | + | 0.491473i | 0.861075 | − | 0.508479i | \(-0.169792\pi\) |
−0.00981819 | + | 0.999952i | \(0.503125\pi\) | |||||||
\(824\) | 35.8127 | + | 84.5514i | 0.0434620 | + | 0.102611i | ||||
\(825\) | 173.044 | 0.209751 | ||||||||
\(826\) | 46.0647 | + | 469.710i | 0.0557684 | + | 0.568656i | ||||
\(827\) | 689.432i | 0.833654i | 0.908986 | + | 0.416827i | \(0.136858\pi\) | ||||
−0.908986 | + | 0.416827i | \(0.863142\pi\) | |||||||
\(828\) | −156.569 | + | 1905.91i | −0.189093 | + | 2.30183i | ||||
\(829\) | −555.021 | + | 961.325i | −0.669507 | + | 1.15962i | 0.308535 | + | 0.951213i | \(0.400161\pi\) |
−0.978042 | + | 0.208407i | \(0.933172\pi\) | |||||||
\(830\) | 459.117 | + | 18.8263i | 0.553153 | + | 0.0226823i | ||||
\(831\) | 2606.84 | − | 1505.06i | 3.13699 | − | 1.81114i | ||||
\(832\) | −716.701 | − | 179.873i | −0.861419 | − | 0.216194i | ||||
\(833\) | 267.737 | − | 76.2593i | 0.321413 | − | 0.0915477i | ||||
\(834\) | 1697.01 | − | 889.131i | 2.03478 | − | 1.06610i | ||||
\(835\) | 500.928 | − | 289.211i | 0.599914 | − | 0.346360i | ||||
\(836\) | −349.720 | − | 739.713i | −0.418325 | − | 0.884825i | ||||
\(837\) | 678.836 | − | 1175.78i | 0.811035 | − | 1.40475i | ||||
\(838\) | 526.751 | − | 831.690i | 0.628581 | − | 0.992470i | ||||
\(839\) | 125.958i | 0.150129i | 0.997179 | + | 0.0750643i | \(0.0239162\pi\) | ||||
−0.997179 | + | 0.0750643i | \(0.976084\pi\) | |||||||
\(840\) | 623.277 | + | 346.842i | 0.741997 | + | 0.412908i | ||||
\(841\) | −724.995 | −0.862063 | ||||||||
\(842\) | 233.072 | + | 147.616i | 0.276808 | + | 0.175316i | ||||
\(843\) | −2443.64 | − | 1410.83i | −2.89874 | − | 1.67359i | ||||
\(844\) | 240.996 | − | 113.938i | 0.285540 | − | 0.134997i | ||||
\(845\) | −39.9090 | − | 69.1245i | −0.0472296 | − | 0.0818041i | ||||
\(846\) | −317.864 | − | 606.680i | −0.375726 | − | 0.717115i | ||||
\(847\) | −81.4008 | − | 582.944i | −0.0961049 | − | 0.688245i | ||||
\(848\) | 169.835 | + | 451.659i | 0.200277 | + | 0.532617i | ||||
\(849\) | −122.696 | − | 212.516i | −0.144518 | − | 0.250313i | ||||
\(850\) | −2.32771 | + | 56.7657i | −0.00273848 | + | 0.0667832i | ||||
\(851\) | −719.259 | − | 415.265i | −0.845193 | − | 0.487972i | ||||
\(852\) | −491.923 | − | 40.4110i | −0.577374 | − | 0.0474308i | ||||
\(853\) | −861.828 | −1.01035 | −0.505174 | − | 0.863017i | \(-0.668572\pi\) | ||||
−0.505174 | + | 0.863017i | \(0.668572\pi\) | |||||||
\(854\) | 468.367 | − | 1032.56i | 0.548439 | − | 1.20909i | ||||
\(855\) | − | 1765.18i | − | 2.06454i | ||||||
\(856\) | 468.723 | + | 1106.63i | 0.547574 | + | 1.29279i | ||||
\(857\) | 295.395 | − | 511.639i | 0.344685 | − | 0.597012i | −0.640611 | − | 0.767865i | \(-0.721319\pi\) |
0.985297 | + | 0.170853i | \(0.0546523\pi\) | |||||||
\(858\) | 32.7428 | − | 798.499i | 0.0381618 | − | 0.930651i | ||||
\(859\) | 515.282 | − | 297.498i | 0.599863 | − | 0.346331i | −0.169125 | − | 0.985595i | \(-0.554094\pi\) |
0.768988 | + | 0.639264i | \(0.220761\pi\) | |||||||
\(860\) | 44.8895 | + | 31.0786i | 0.0521971 | + | 0.0361379i | ||||
\(861\) | −1008.56 | − | 1293.26i | −1.17139 | − | 1.50205i | ||||
\(862\) | −151.032 | − | 288.262i | −0.175211 | − | 0.334410i | ||||
\(863\) | −1191.72 | + | 688.042i | −1.38091 | + | 0.797268i | −0.992267 | − | 0.124122i | \(-0.960389\pi\) |
−0.388641 | + | 0.921389i | \(0.627055\pi\) | |||||||
\(864\) | 825.114 | + | 2500.86i | 0.954993 | + | 2.89452i | ||||
\(865\) | −299.916 | + | 519.470i | −0.346724 | + | 0.600543i | ||||
\(866\) | 1380.25 | + | 874.183i | 1.59382 | + | 1.00945i | ||||
\(867\) | − | 1462.36i | − | 1.68669i | ||||||
\(868\) | −207.892 | + | 412.504i | −0.239507 | + | 0.475235i | ||||
\(869\) | −53.7275 | −0.0618268 | ||||||||
\(870\) | −146.807 | + | 231.795i | −0.168744 | + | 0.266431i | ||||
\(871\) | 84.7208 | + | 48.9136i | 0.0972684 | + | 0.0561579i | ||||
\(872\) | 946.185 | + | 714.152i | 1.08507 | + | 0.818981i | ||||
\(873\) | −2072.95 | − | 3590.45i | −2.37451 | − | 4.11278i | ||||
\(874\) | −1216.13 | + | 637.179i | −1.39145 | + | 0.729038i | ||||
\(875\) | −72.5376 | − | 29.3819i | −0.0829001 | − | 0.0335793i | ||||
\(876\) | 487.895 | + | 337.787i | 0.556958 | + | 0.385602i | ||||
\(877\) | 463.668 | + | 803.097i | 0.528698 | + | 0.915732i | 0.999440 | + | 0.0334607i | \(0.0106529\pi\) |
−0.470742 | + | 0.882271i | \(0.656014\pi\) | |||||||
\(878\) | −706.957 | − | 28.9891i | −0.805190 | − | 0.0330172i | ||||
\(879\) | −681.795 | − | 393.635i | −0.775649 | − | 0.447821i | ||||
\(880\) | −167.988 | − | 137.950i | −0.190896 | − | 0.156762i | ||||
\(881\) | −1043.50 | −1.18445 | −0.592226 | − | 0.805772i | \(-0.701751\pi\) | ||||
−0.592226 | + | 0.805772i | \(0.701751\pi\) | |||||||
\(882\) | −1665.40 | + | 1583.19i | −1.88821 | + | 1.79500i | ||||
\(883\) | − | 1689.98i | − | 1.91391i | −0.290233 | − | 0.956956i | \(-0.593733\pi\) | ||
0.290233 | − | 0.956956i | \(-0.406267\pi\) | |||||||
\(884\) | 261.501 | + | 21.4820i | 0.295815 | + | 0.0243010i | ||||
\(885\) | 214.696 | − | 371.865i | 0.242595 | − | 0.420187i | ||||
\(886\) | 67.1179 | + | 2.75220i | 0.0757538 | + | 0.00310632i | ||||
\(887\) | −89.7890 | + | 51.8397i | −0.101228 | + | 0.0584439i | −0.549759 | − | 0.835323i | \(-0.685281\pi\) |
0.448531 | + | 0.893767i | \(0.351947\pi\) | |||||||
\(888\) | −1842.18 | − | 227.640i | −2.07453 | − | 0.256352i | ||||
\(889\) | 38.3390 | − | 94.6508i | 0.0431260 | − | 0.106469i | ||||
\(890\) | 210.778 | − | 110.435i | 0.236829 | − | 0.124085i | ||||
\(891\) | −1356.22 | + | 783.012i | −1.52213 | + | 0.878801i | ||||
\(892\) | 672.463 | − | 317.926i | 0.753882 | − | 0.356419i | ||||
\(893\) | 245.861 | − | 425.844i | 0.275320 | − | 0.476869i | ||||
\(894\) | −306.911 | + | 484.583i | −0.343300 | + | 0.542039i | ||||
\(895\) | − | 238.277i | − | 0.266231i | ||||||
\(896\) | −328.565 | − | 833.583i | −0.366702 | − | 0.930339i | ||||
\(897\) | −1340.98 | −1.49496 | ||||||||
\(898\) | −756.641 | − | 479.218i | −0.842584 | − | 0.533651i | ||||
\(899\) | −153.882 | − | 88.8436i | −0.171170 | − | 0.0988250i | ||||
\(900\) | −200.436 | − | 423.953i | −0.222706 | − | 0.471059i | ||||
\(901\) | −85.6702 | − | 148.385i | −0.0950834 | − | 0.164689i | ||||
\(902\) | 231.955 | + | 442.713i | 0.257156 | + | 0.490812i | ||||
\(903\) | −191.934 | + | 149.682i | −0.212552 | + | 0.165761i | ||||
\(904\) | −79.8048 | + | 645.822i | −0.0882796 | + | 0.714405i | ||||
\(905\) | 220.074 | + | 381.179i | 0.243176 | + | 0.421193i | ||||
\(906\) | 62.8521 | − | 1532.77i | 0.0693732 | − | 1.69180i | ||||
\(907\) | −172.967 | − | 99.8623i | −0.190702 | − | 0.110102i | 0.401609 | − | 0.915811i | \(-0.368451\pi\) |
−0.592311 | + | 0.805709i | \(0.701784\pi\) | |||||||
\(908\) | 18.2437 | − | 222.080i | 0.0200922 | − | 0.244582i | ||||
\(909\) | −1224.08 | −1.34663 | ||||||||
\(910\) | −149.306 | + | 329.160i | −0.164072 | + | 0.361714i | ||||
\(911\) | − | 137.150i | − | 0.150548i | −0.997163 | − | 0.0752742i | \(-0.976017\pi\) | ||
0.997163 | − | 0.0752742i | \(-0.0239832\pi\) | |||||||
\(912\) | −1947.34 | + | 2371.36i | −2.13524 | + | 2.60017i | ||||
\(913\) | 312.134 | − | 540.631i | 0.341877 | − | 0.592148i | ||||
\(914\) | 29.9086 | − | 729.380i | 0.0327227 | − | 0.798009i | ||||
\(915\) | −893.351 | + | 515.776i | −0.976339 | + | 0.563690i | ||||
\(916\) | −6.18960 | + | 8.94017i | −0.00675721 | + | 0.00976001i | ||||
\(917\) | 558.438 | − | 77.9789i | 0.608984 | − | 0.0850370i | ||||
\(918\) | −433.978 | − | 828.297i | −0.472743 | − | 0.902284i | ||||
\(919\) | −394.412 | + | 227.714i | −0.429175 | + | 0.247784i | −0.698995 | − | 0.715126i | \(-0.746369\pi\) |
0.269820 | + | 0.962911i | \(0.413036\pi\) | |||||||
\(920\) | −219.733 | + | 291.126i | −0.238840 | + | 0.316441i | ||||
\(921\) | −147.292 | + | 255.116i | −0.159926 | + | 0.276999i | ||||
\(922\) | −69.4871 | − | 44.0096i | −0.0753656 | − | 0.0477328i | ||||
\(923\) | − | 250.109i | − | 0.270974i | ||||||
\(924\) | 810.373 | − | 531.364i | 0.877027 | − | 0.575070i | ||||
\(925\) | 203.664 | 0.220177 | ||||||||
\(926\) | 76.6938 | − | 121.092i | 0.0828226 | − | 0.130769i | ||||
\(927\) | 233.070 | + | 134.563i | 0.251424 | + | 0.145160i | ||||
\(928\) | 327.304 | − | 107.988i | 0.352698 | − | 0.116366i | ||||
\(929\) | −151.570 | − | 262.526i | −0.163153 | − | 0.282590i | 0.772845 | − | 0.634595i | \(-0.218833\pi\) |
−0.935998 | + | 0.352005i | \(0.885500\pi\) | |||||||
\(930\) | 372.263 | − | 195.044i | 0.400283 | − | 0.209725i | ||||
\(931\) | −1600.00 | − | 401.936i | −1.71858 | − | 0.431725i | ||||
\(932\) | 142.502 | − | 205.827i | 0.152899 | − | 0.220845i | ||||
\(933\) | −1209.32 | − | 2094.60i | −1.29616 | − | 2.24501i | ||||
\(934\) | −1095.14 | − | 44.9067i | −1.17252 | − | 0.0480799i | ||||
\(935\) | 66.8443 | + | 38.5926i | 0.0714912 | + | 0.0412755i | ||||
\(936\) | −1994.22 | + | 844.676i | −2.13058 | + | 0.902431i | ||||
\(937\) | 471.776 | 0.503496 | 0.251748 | − | 0.967793i | \(-0.418995\pi\) | ||||
0.251748 | + | 0.967793i | \(0.418995\pi\) | |||||||
\(938\) | 11.5778 | + | 118.056i | 0.0123430 | + | 0.125859i | ||||
\(939\) | 103.519i | 0.110244i | ||||||||
\(940\) | 10.6954 | − | 130.195i | 0.0113781 | − | 0.138505i | ||||
\(941\) | −572.998 | + | 992.461i | −0.608924 | + | 1.05469i | 0.382494 | + | 0.923958i | \(0.375065\pi\) |
−0.991418 | + | 0.130730i | \(0.958268\pi\) | |||||||
\(942\) | 1544.71 | + | 63.3417i | 1.63982 | + | 0.0672418i | ||||
\(943\) | 726.286 | − | 419.321i | 0.770187 | − | 0.444668i | ||||
\(944\) | −504.873 | + | 189.845i | −0.534823 | + | 0.201107i | ||||
\(945\) | 1275.75 | − | 178.143i | 1.35000 | − | 0.188511i | ||||
\(946\) | 65.7033 | − | 34.4247i | 0.0694538 | − | 0.0363897i | ||||
\(947\) | 968.169 | − | 558.972i | 1.02235 | − | 0.590256i | 0.107569 | − | 0.994198i | \(-0.465693\pi\) |
0.914785 | + | 0.403942i | \(0.132360\pi\) | |||||||
\(948\) | 86.1192 | + | 182.156i | 0.0908430 | + | 0.192147i | ||||
\(949\) | −150.349 | + | 260.413i | −0.158429 | + | 0.274407i | ||||
\(950\) | 180.142 | − | 284.428i | 0.189623 | − | 0.299397i | ||||
\(951\) | − | 2886.75i | − | 3.03549i | ||||||
\(952\) | 163.409 | + | 272.984i | 0.171648 | + | 0.286748i | ||||
\(953\) | −58.6630 | −0.0615561 | −0.0307781 | − | 0.999526i | \(-0.509799\pi\) | ||||
−0.0307781 | + | 0.999526i | \(0.509799\pi\) | |||||||
\(954\) | 1194.79 | + | 756.722i | 1.25240 | + | 0.793209i | ||||
\(955\) | 436.611 | + | 252.077i | 0.457184 | + | 0.263955i | ||||
\(956\) | 192.966 | − | 91.2301i | 0.201847 | − | 0.0954289i | ||||
\(957\) | 186.378 | + | 322.817i | 0.194753 | + | 0.337322i | ||||
\(958\) | 478.890 | + | 914.015i | 0.499885 | + | 0.954087i | ||||
\(959\) | 654.396 | − | 510.337i | 0.682373 | − | 0.532155i | ||||
\(960\) | −198.435 | + | 790.661i | −0.206704 | + | 0.823605i | ||||
\(961\) | −344.416 | − | 596.547i | −0.358394 | − | 0.620756i | ||||
\(962\) | 38.5366 | − | 939.792i | 0.0400589 | − | 0.976914i | ||||
\(963\) | 3050.47 | + | 1761.19i | 3.16767 | + | 1.82885i | ||||
\(964\) | 106.843 | + | 8.77708i | 0.110833 | + | 0.00910485i | ||||
\(965\) | −415.592 | −0.430666 | ||||||||
\(966\) | −946.574 | − | 1322.11i | −0.979890 | − | 1.36864i | ||||
\(967\) | 1265.41i | 1.30860i | 0.756236 | + | 0.654299i | \(0.227036\pi\) | ||||
−0.756236 | + | 0.654299i | \(0.772964\pi\) | |||||||
\(968\) | 619.414 | − | 262.359i | 0.639890 | − | 0.271032i | ||||
\(969\) | 544.781 | − | 943.588i | 0.562209 | − | 0.973775i | ||||
\(970\) | 32.3980 | − | 790.088i | 0.0334000 | − | 0.814524i | ||||
\(971\) | 20.5601 | − | 11.8704i | 0.0211742 | − | 0.0122249i | −0.489376 | − | 0.872073i | \(-0.662775\pi\) |
0.510550 | + | 0.859848i | \(0.329442\pi\) | |||||||
\(972\) | 2392.73 | + | 1656.57i | 2.46166 | + | 1.70430i | ||||
\(973\) | −441.937 | + | 1091.05i | −0.454201 | + | 1.12133i | ||||
\(974\) | −256.564 | − | 489.681i | −0.263413 | − | 0.502753i | ||||
\(975\) | 284.782 | − | 164.419i | 0.292084 | − | 0.168635i | ||||
\(976\) | 1278.42 | + | 211.470i | 1.30986 | + | 0.216670i | ||||
\(977\) | −13.7669 | + | 23.8449i | −0.0140910 | + | 0.0244063i | −0.872985 | − | 0.487747i | \(-0.837819\pi\) |
0.858894 | + | 0.512153i | \(0.171152\pi\) | |||||||
\(978\) | 2346.41 | + | 1486.10i | 2.39919 | + | 1.51953i | ||||
\(979\) | − | 323.281i | − | 0.330216i | ||||||
\(980\) | −429.919 | + | 85.1437i | −0.438693 | + | 0.0868813i | ||||
\(981\) | 3474.44 | 3.54173 | ||||||||
\(982\) | −785.415 | + | 1240.10i | −0.799812 | + | 1.26283i | ||||
\(983\) | −750.120 | − | 433.082i | −0.763092 | − | 0.440572i | 0.0673126 | − | 0.997732i | \(-0.478558\pi\) |
−0.830405 | + | 0.557160i | \(0.811891\pi\) | |||||||
\(984\) | 1129.16 | − | 1496.03i | 1.14752 | − | 1.52036i | ||||
\(985\) | 14.0011 | + | 24.2506i | 0.0142143 | + | 0.0246199i | ||||
\(986\) | −108.405 | + | 56.7975i | −0.109944 | + | 0.0576040i | ||||
\(987\) | 539.767 | + | 218.636i | 0.546876 | + | 0.221516i | ||||
\(988\) | −1278.38 | − | 885.071i | −1.29391 | − | 0.895820i | ||||
\(989\) | −62.2319 | − | 107.789i | −0.0629240 | − | 0.108988i | ||||
\(990\) | −636.563 | − | 26.1026i | −0.642992 | − | 0.0263662i | ||||
\(991\) | −1334.55 | − | 770.503i | −1.34667 | − | 0.777501i | −0.358894 | − | 0.933378i | \(-0.616846\pi\) |
−0.987776 | + | 0.155877i | \(0.950179\pi\) | |||||||
\(992\) | −516.875 | − | 107.422i | −0.521043 | − | 0.108288i | ||||
\(993\) | 2651.01 | 2.66970 | ||||||||
\(994\) | 246.589 | − | 176.548i | 0.248078 | − | 0.177614i | ||||
\(995\) | 323.022i | 0.324645i | ||||||||
\(996\) | −2333.25 | − | 191.675i | −2.34262 | − | 0.192445i | ||||
\(997\) | 699.010 | − | 1210.72i | 0.701114 | − | 1.21436i | −0.266962 | − | 0.963707i | \(-0.586020\pi\) |
0.968076 | − | 0.250657i | \(-0.0806468\pi\) | |||||||
\(998\) | 760.931 | + | 31.2024i | 0.762456 | + | 0.0312649i | ||||
\(999\) | −2903.03 | + | 1676.07i | −2.90594 | + | 1.67774i |
(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 | 140.3.t.a.11.26 | yes | 64 | |
4.3 | odd | 2 | inner | 140.3.t.a.11.16 | ✓ | 64 | |
7.2 | even | 3 | inner | 140.3.t.a.51.16 | yes | 64 | |
28.23 | odd | 6 | inner | 140.3.t.a.51.26 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.3.t.a.11.16 | ✓ | 64 | 4.3 | odd | 2 | inner | |
140.3.t.a.11.26 | yes | 64 | 1.1 | even | 1 | trivial | |
140.3.t.a.51.16 | yes | 64 | 7.2 | even | 3 | inner | |
140.3.t.a.51.26 | yes | 64 | 28.23 | odd | 6 | inner |