Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(83,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.83");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 83.8 | ||
Character | \(\chi\) | \(=\) | 210.83 |
Dual form | 210.3.k.a.167.8 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | −0.00829838 | − | 2.99999i | −0.00276613 | − | 0.999996i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | −3.67015 | − | 3.39558i | −0.734030 | − | 0.679117i | ||||
\(6\) | −2.99169 | + | 3.00829i | −0.498615 | + | 0.501381i | ||||
\(7\) | 1.45834 | − | 6.84640i | 0.208334 | − | 0.978058i | ||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | −8.99986 | + | 0.0497901i | −0.999985 | + | 0.00553223i | ||||
\(10\) | 0.274569 | + | 7.06574i | 0.0274569 | + | 0.706574i | ||||
\(11\) | 6.08610i | 0.553282i | 0.960973 | + | 0.276641i | \(0.0892213\pi\) | ||||
−0.960973 | + | 0.276641i | \(0.910779\pi\) | |||||||
\(12\) | 5.99998 | − | 0.0165968i | 0.499998 | − | 0.00138306i | ||||
\(13\) | −4.00045 | + | 4.00045i | −0.307727 | + | 0.307727i | −0.844027 | − | 0.536300i | \(-0.819821\pi\) |
0.536300 | + | 0.844027i | \(0.319821\pi\) | |||||||
\(14\) | −8.30474 | + | 5.38806i | −0.593196 | + | 0.384862i | ||||
\(15\) | −10.1563 | + | 11.0386i | −0.677084 | + | 0.735906i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 14.8174 | − | 14.8174i | 0.871610 | − | 0.871610i | −0.121037 | − | 0.992648i | \(-0.538622\pi\) |
0.992648 | + | 0.121037i | \(0.0386221\pi\) | |||||||
\(18\) | 9.04965 | + | 8.95007i | 0.502758 | + | 0.497226i | ||||
\(19\) | −20.4190 | −1.07468 | −0.537341 | − | 0.843365i | \(-0.680571\pi\) | ||||
−0.537341 | + | 0.843365i | \(0.680571\pi\) | |||||||
\(20\) | 6.79117 | − | 7.34030i | 0.339558 | − | 0.367015i | ||||
\(21\) | −20.5512 | − | 4.31819i | −0.978630 | − | 0.205628i | ||||
\(22\) | 6.08610 | − | 6.08610i | 0.276641 | − | 0.276641i | ||||
\(23\) | −20.6285 | + | 20.6285i | −0.896892 | + | 0.896892i | −0.995160 | − | 0.0982681i | \(-0.968670\pi\) |
0.0982681 | + | 0.995160i | \(0.468670\pi\) | |||||||
\(24\) | −6.01657 | − | 5.98338i | −0.250691 | − | 0.249308i | ||||
\(25\) | 1.94003 | + | 24.9246i | 0.0776012 | + | 0.996984i | ||||
\(26\) | 8.00089 | 0.307727 | ||||||||
\(27\) | 0.224054 | + | 26.9991i | 0.00829830 | + | 0.999966i | ||||
\(28\) | 13.6928 | + | 2.91668i | 0.489029 | + | 0.104167i | ||||
\(29\) | 19.5317 | 0.673508 | 0.336754 | − | 0.941593i | \(-0.390671\pi\) | ||||
0.336754 | + | 0.941593i | \(0.390671\pi\) | |||||||
\(30\) | 21.1948 | − | 0.882337i | 0.706495 | − | 0.0294112i | ||||
\(31\) | − | 4.36235i | − | 0.140721i | −0.997522 | − | 0.0703605i | \(-0.977585\pi\) | ||
0.997522 | − | 0.0703605i | \(-0.0224150\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | 18.2582 | − | 0.0505048i | 0.553280 | − | 0.00153045i | ||||
\(34\) | −29.6348 | −0.871610 | ||||||||
\(35\) | −28.5999 | + | 20.1754i | −0.817139 | + | 0.576441i | ||||
\(36\) | −0.0995802 | − | 17.9997i | −0.00276612 | − | 0.499992i | ||||
\(37\) | −1.64351 | + | 1.64351i | −0.0444191 | + | 0.0444191i | −0.728967 | − | 0.684548i | \(-0.759999\pi\) |
0.684548 | + | 0.728967i | \(0.259999\pi\) | |||||||
\(38\) | 20.4190 | + | 20.4190i | 0.537341 | + | 0.537341i | ||||
\(39\) | 12.0345 | + | 11.9681i | 0.308577 | + | 0.306874i | ||||
\(40\) | −14.1315 | + | 0.549137i | −0.353287 | + | 0.0137284i | ||||
\(41\) | −42.2693 | −1.03096 | −0.515480 | − | 0.856902i | \(-0.672386\pi\) | ||||
−0.515480 | + | 0.856902i | \(0.672386\pi\) | |||||||
\(42\) | 16.2330 | + | 24.8694i | 0.386501 | + | 0.592129i | ||||
\(43\) | −45.0034 | − | 45.0034i | −1.04659 | − | 1.04659i | −0.998860 | − | 0.0477300i | \(-0.984801\pi\) |
−0.0477300 | − | 0.998860i | \(-0.515199\pi\) | |||||||
\(44\) | −12.1722 | −0.276641 | ||||||||
\(45\) | 33.1999 | + | 30.3770i | 0.737776 | + | 0.675045i | ||||
\(46\) | 41.2570 | 0.896892 | ||||||||
\(47\) | 36.6983 | − | 36.6983i | 0.780815 | − | 0.780815i | −0.199153 | − | 0.979968i | \(-0.563819\pi\) |
0.979968 | + | 0.199153i | \(0.0638191\pi\) | |||||||
\(48\) | 0.0331935 | + | 12.0000i | 0.000691532 | + | 0.249999i | ||||
\(49\) | −44.7465 | − | 19.9688i | −0.913194 | − | 0.407526i | ||||
\(50\) | 22.9846 | − | 26.8646i | 0.459692 | − | 0.537293i | ||||
\(51\) | −44.5749 | − | 44.3290i | −0.874018 | − | 0.869196i | ||||
\(52\) | −8.00089 | − | 8.00089i | −0.153863 | − | 0.153863i | ||||
\(53\) | 0.652830 | − | 0.652830i | 0.0123176 | − | 0.0123176i | −0.700921 | − | 0.713239i | \(-0.747228\pi\) |
0.713239 | + | 0.700921i | \(0.247228\pi\) | |||||||
\(54\) | 26.7750 | − | 27.2231i | 0.495834 | − | 0.504132i | ||||
\(55\) | 20.6659 | − | 22.3369i | 0.375743 | − | 0.406126i | ||||
\(56\) | −10.7761 | − | 16.6095i | −0.192431 | − | 0.296598i | ||||
\(57\) | 0.169444 | + | 61.2567i | 0.00297271 | + | 1.07468i | ||||
\(58\) | −19.5317 | − | 19.5317i | −0.336754 | − | 0.336754i | ||||
\(59\) | 4.02656i | 0.0682467i | 0.999418 | + | 0.0341234i | \(0.0108639\pi\) | ||||
−0.999418 | + | 0.0341234i | \(0.989136\pi\) | |||||||
\(60\) | −22.0772 | − | 20.3125i | −0.367953 | − | 0.338542i | ||||
\(61\) | − | 65.2074i | − | 1.06897i | −0.845177 | − | 0.534487i | \(-0.820505\pi\) | ||
0.845177 | − | 0.534487i | \(-0.179495\pi\) | |||||||
\(62\) | −4.36235 | + | 4.36235i | −0.0703605 | + | 0.0703605i | ||||
\(63\) | −12.7840 | + | 61.6893i | −0.202920 | + | 0.979195i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 28.2661 | − | 1.09840i | 0.434863 | − | 0.0168984i | ||||
\(66\) | −18.3087 | − | 18.2077i | −0.277405 | − | 0.275875i | ||||
\(67\) | 59.7184 | − | 59.7184i | 0.891320 | − | 0.891320i | −0.103327 | − | 0.994647i | \(-0.532949\pi\) |
0.994647 | + | 0.103327i | \(0.0329489\pi\) | |||||||
\(68\) | 29.6348 | + | 29.6348i | 0.435805 | + | 0.435805i | ||||
\(69\) | 62.0565 | + | 61.7141i | 0.899369 | + | 0.894408i | ||||
\(70\) | 48.7753 | + | 8.42444i | 0.696790 | + | 0.120349i | ||||
\(71\) | − | 122.856i | − | 1.73037i | −0.501451 | − | 0.865186i | \(-0.667200\pi\) | ||
0.501451 | − | 0.865186i | \(-0.332800\pi\) | |||||||
\(72\) | −17.9001 | + | 18.0993i | −0.248613 | + | 0.251379i | ||||
\(73\) | 13.1414 | − | 13.1414i | 0.180019 | − | 0.180019i | −0.611345 | − | 0.791364i | \(-0.709371\pi\) |
0.791364 | + | 0.611345i | \(0.209371\pi\) | |||||||
\(74\) | 3.28701 | 0.0444191 | ||||||||
\(75\) | 74.7575 | − | 6.02690i | 0.996766 | − | 0.0803587i | ||||
\(76\) | − | 40.8379i | − | 0.537341i | ||||||
\(77\) | 41.6679 | + | 8.87561i | 0.541142 | + | 0.115268i | ||||
\(78\) | −0.0663945 | − | 24.0026i | −0.000851211 | − | 0.307725i | ||||
\(79\) | − | 126.052i | − | 1.59559i | −0.602926 | − | 0.797797i | \(-0.705999\pi\) | ||
0.602926 | − | 0.797797i | \(-0.294001\pi\) | |||||||
\(80\) | 14.6806 | + | 13.5823i | 0.183508 | + | 0.169779i | ||||
\(81\) | 80.9950 | − | 0.896208i | 0.999939 | − | 0.0110643i | ||||
\(82\) | 42.2693 | + | 42.2693i | 0.515480 | + | 0.515480i | ||||
\(83\) | 12.2050 | + | 12.2050i | 0.147048 | + | 0.147048i | 0.776798 | − | 0.629750i | \(-0.216843\pi\) |
−0.629750 | + | 0.776798i | \(0.716843\pi\) | |||||||
\(84\) | 8.63638 | − | 41.1025i | 0.102814 | − | 0.489315i | ||||
\(85\) | −104.696 | + | 4.06839i | −1.23171 | + | 0.0478634i | ||||
\(86\) | 90.0068i | 1.04659i | ||||||||
\(87\) | −0.162082 | − | 58.5950i | −0.00186301 | − | 0.673506i | ||||
\(88\) | 12.1722 | + | 12.1722i | 0.138321 | + | 0.138321i | ||||
\(89\) | 97.2971i | 1.09323i | 0.837385 | + | 0.546613i | \(0.184083\pi\) | ||||
−0.837385 | + | 0.546613i | \(0.815917\pi\) | |||||||
\(90\) | −2.82288 | − | 63.5770i | −0.0313654 | − | 0.706411i | ||||
\(91\) | 21.5547 | + | 33.2227i | 0.236864 | + | 0.365084i | ||||
\(92\) | −41.2570 | − | 41.2570i | −0.448446 | − | 0.448446i | ||||
\(93\) | −13.0870 | + | 0.0362004i | −0.140720 | + | 0.000389252i | ||||
\(94\) | −73.3967 | −0.780815 | ||||||||
\(95\) | 74.9407 | + | 69.3343i | 0.788850 | + | 0.729835i | ||||
\(96\) | 11.9668 | − | 12.0331i | 0.124654 | − | 0.125345i | ||||
\(97\) | −60.6217 | − | 60.6217i | −0.624966 | − | 0.624966i | 0.321831 | − | 0.946797i | \(-0.395702\pi\) |
−0.946797 | + | 0.321831i | \(0.895702\pi\) | |||||||
\(98\) | 24.7777 | + | 64.7153i | 0.252834 | + | 0.660360i | ||||
\(99\) | −0.303028 | − | 54.7741i | −0.00306089 | − | 0.553274i | ||||
\(100\) | −49.8492 | + | 3.88006i | −0.498492 | + | 0.0388006i | ||||
\(101\) | −96.3108 | −0.953572 | −0.476786 | − | 0.879019i | \(-0.658198\pi\) | ||||
−0.476786 | + | 0.879019i | \(0.658198\pi\) | |||||||
\(102\) | 0.245921 | + | 88.9039i | 0.00241099 | + | 0.871607i | ||||
\(103\) | −113.602 | + | 113.602i | −1.10293 | + | 1.10293i | −0.108878 | + | 0.994055i | \(0.534726\pi\) |
−0.994055 | + | 0.108878i | \(0.965274\pi\) | |||||||
\(104\) | 16.0018i | 0.153863i | ||||||||
\(105\) | 60.7634 | + | 85.6318i | 0.578699 | + | 0.815541i | ||||
\(106\) | −1.30566 | −0.0123176 | ||||||||
\(107\) | −80.0368 | − | 80.0368i | −0.748008 | − | 0.748008i | 0.226097 | − | 0.974105i | \(-0.427403\pi\) |
−0.974105 | + | 0.226097i | \(0.927403\pi\) | |||||||
\(108\) | −53.9981 | + | 0.448108i | −0.499983 | + | 0.00414915i | ||||
\(109\) | 193.662i | 1.77672i | 0.459150 | + | 0.888359i | \(0.348154\pi\) | ||||
−0.459150 | + | 0.888359i | \(0.651846\pi\) | |||||||
\(110\) | −43.0028 | + | 1.67105i | −0.390934 | + | 0.0151914i | ||||
\(111\) | 4.94414 | + | 4.91686i | 0.0445418 | + | 0.0442960i | ||||
\(112\) | −5.83336 | + | 27.3856i | −0.0520836 | + | 0.244514i | ||||
\(113\) | 130.246 | − | 130.246i | 1.15262 | − | 1.15262i | 0.166596 | − | 0.986025i | \(-0.446722\pi\) |
0.986025 | − | 0.166596i | \(-0.0532776\pi\) | |||||||
\(114\) | 61.0872 | − | 61.4261i | 0.535853 | − | 0.538826i | ||||
\(115\) | 145.756 | − | 5.66394i | 1.26744 | − | 0.0492517i | ||||
\(116\) | 39.0635i | 0.336754i | ||||||||
\(117\) | 35.8043 | − | 36.2026i | 0.306020 | − | 0.309424i | ||||
\(118\) | 4.02656 | − | 4.02656i | 0.0341234 | − | 0.0341234i | ||||
\(119\) | −79.8370 | − | 123.055i | −0.670899 | − | 1.03407i | ||||
\(120\) | 1.76467 | + | 42.3897i | 0.0147056 | + | 0.353247i | ||||
\(121\) | 83.9594 | 0.693879 | ||||||||
\(122\) | −65.2074 | + | 65.2074i | −0.534487 | + | 0.534487i | ||||
\(123\) | 0.350767 | + | 126.807i | 0.00285176 | + | 1.03096i | ||||
\(124\) | 8.72470 | 0.0703605 | ||||||||
\(125\) | 77.5134 | − | 98.0646i | 0.620107 | − | 0.784517i | ||||
\(126\) | 74.4733 | − | 48.9053i | 0.591058 | − | 0.388137i | ||||
\(127\) | −53.5048 | + | 53.5048i | −0.421297 | + | 0.421297i | −0.885650 | − | 0.464353i | \(-0.846287\pi\) |
0.464353 | + | 0.885650i | \(0.346287\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −134.636 | + | 135.383i | −1.04369 | + | 1.04948i | ||||
\(130\) | −29.3645 | − | 27.1677i | −0.225881 | − | 0.208982i | ||||
\(131\) | −227.798 | −1.73892 | −0.869459 | − | 0.494005i | \(-0.835532\pi\) | ||||
−0.869459 | + | 0.494005i | \(0.835532\pi\) | |||||||
\(132\) | 0.101010 | + | 36.5165i | 0.000765224 | + | 0.276640i | ||||
\(133\) | −29.7778 | + | 139.797i | −0.223893 | + | 1.05110i | ||||
\(134\) | −119.437 | −0.891320 | ||||||||
\(135\) | 90.8553 | − | 99.8515i | 0.673002 | − | 0.739641i | ||||
\(136\) | − | 59.2695i | − | 0.435805i | ||||||
\(137\) | 16.8334 | + | 16.8334i | 0.122872 | + | 0.122872i | 0.765869 | − | 0.642997i | \(-0.222309\pi\) |
−0.642997 | + | 0.765869i | \(0.722309\pi\) | |||||||
\(138\) | −0.342367 | − | 123.771i | −0.00248092 | − | 0.896888i | ||||
\(139\) | 30.0414 | 0.216125 | 0.108063 | − | 0.994144i | \(-0.465535\pi\) | ||||
0.108063 | + | 0.994144i | \(0.465535\pi\) | |||||||
\(140\) | −40.3509 | − | 57.1997i | −0.288220 | − | 0.408569i | ||||
\(141\) | −110.399 | − | 109.790i | −0.782972 | − | 0.778653i | ||||
\(142\) | −122.856 | + | 122.856i | −0.865186 | + | 0.865186i | ||||
\(143\) | −24.3471 | − | 24.3471i | −0.170260 | − | 0.170260i | ||||
\(144\) | 35.9994 | − | 0.199160i | 0.249996 | − | 0.00138306i | ||||
\(145\) | −71.6845 | − | 66.3217i | −0.494376 | − | 0.457391i | ||||
\(146\) | −26.2828 | −0.180019 | ||||||||
\(147\) | −59.5348 | + | 134.405i | −0.404998 | + | 0.914317i | ||||
\(148\) | −3.28701 | − | 3.28701i | −0.0222095 | − | 0.0222095i | ||||
\(149\) | 7.65497 | 0.0513756 | 0.0256878 | − | 0.999670i | \(-0.491822\pi\) | ||||
0.0256878 | + | 0.999670i | \(0.491822\pi\) | |||||||
\(150\) | −80.7844 | − | 68.7306i | −0.538562 | − | 0.458204i | ||||
\(151\) | 236.474 | 1.56605 | 0.783027 | − | 0.621987i | \(-0.213674\pi\) | ||||
0.783027 | + | 0.621987i | \(0.213674\pi\) | |||||||
\(152\) | −40.8379 | + | 40.8379i | −0.268671 | + | 0.268671i | ||||
\(153\) | −132.617 | + | 134.092i | −0.866775 | + | 0.876419i | ||||
\(154\) | −32.7923 | − | 50.5435i | −0.212937 | − | 0.328205i | ||||
\(155\) | −14.8127 | + | 16.0105i | −0.0955659 | + | 0.103293i | ||||
\(156\) | −23.9362 | + | 24.0690i | −0.153437 | + | 0.154288i | ||||
\(157\) | 97.8157 | + | 97.8157i | 0.623030 | + | 0.623030i | 0.946305 | − | 0.323275i | \(-0.104784\pi\) |
−0.323275 | + | 0.946305i | \(0.604784\pi\) | |||||||
\(158\) | −126.052 | + | 126.052i | −0.797797 | + | 0.797797i | ||||
\(159\) | −1.96390 | − | 1.95307i | −0.0123516 | − | 0.0122834i | ||||
\(160\) | −1.09827 | − | 28.2629i | −0.00686422 | − | 0.176643i | ||||
\(161\) | 111.148 | + | 171.315i | 0.690359 | + | 1.06407i | ||||
\(162\) | −81.8913 | − | 80.0988i | −0.505502 | − | 0.494437i | ||||
\(163\) | 0.909159 | + | 0.909159i | 0.00557766 | + | 0.00557766i | 0.709890 | − | 0.704312i | \(-0.248745\pi\) |
−0.704312 | + | 0.709890i | \(0.748745\pi\) | |||||||
\(164\) | − | 84.5387i | − | 0.515480i | ||||||
\(165\) | −67.1820 | − | 61.8120i | −0.407164 | − | 0.374618i | ||||
\(166\) | − | 24.4100i | − | 0.147048i | ||||||
\(167\) | 144.965 | − | 144.965i | 0.868051 | − | 0.868051i | −0.124205 | − | 0.992257i | \(-0.539638\pi\) |
0.992257 | + | 0.124205i | \(0.0396381\pi\) | |||||||
\(168\) | −49.7388 | + | 32.4661i | −0.296065 | + | 0.193251i | ||||
\(169\) | 136.993i | 0.810609i | ||||||||
\(170\) | 108.764 | + | 100.627i | 0.639789 | + | 0.591925i | ||||
\(171\) | 183.768 | − | 1.01666i | 1.07467 | − | 0.00594540i | ||||
\(172\) | 90.0068 | − | 90.0068i | 0.523295 | − | 0.523295i | ||||
\(173\) | 48.2322 | + | 48.2322i | 0.278799 | + | 0.278799i | 0.832629 | − | 0.553831i | \(-0.186834\pi\) |
−0.553831 | + | 0.832629i | \(0.686834\pi\) | |||||||
\(174\) | −58.4329 | + | 58.7571i | −0.335821 | + | 0.337684i | ||||
\(175\) | 173.473 | + | 23.0663i | 0.991275 | + | 0.131808i | ||||
\(176\) | − | 24.3444i | − | 0.138321i | ||||||
\(177\) | 12.0796 | − | 0.0334139i | 0.0682465 | − | 0.000188779i | ||||
\(178\) | 97.2971 | − | 97.2971i | 0.546613 | − | 0.546613i | ||||
\(179\) | −277.037 | −1.54769 | −0.773847 | − | 0.633372i | \(-0.781670\pi\) | ||||
−0.773847 | + | 0.633372i | \(0.781670\pi\) | |||||||
\(180\) | −60.7541 | + | 66.3999i | −0.337523 | + | 0.368888i | ||||
\(181\) | 271.177i | 1.49822i | 0.662448 | + | 0.749108i | \(0.269518\pi\) | ||||
−0.662448 | + | 0.749108i | \(0.730482\pi\) | |||||||
\(182\) | 11.6680 | − | 54.7773i | 0.0641100 | − | 0.300974i | ||||
\(183\) | −195.621 | + | 0.541116i | −1.06897 | + | 0.00295692i | ||||
\(184\) | 82.5141i | 0.448446i | ||||||||
\(185\) | 11.6126 | − | 0.451255i | 0.0627707 | − | 0.00243922i | ||||
\(186\) | 13.1232 | + | 13.0508i | 0.0705548 | + | 0.0701656i | ||||
\(187\) | 90.1801 | + | 90.1801i | 0.482246 | + | 0.482246i | ||||
\(188\) | 73.3967 | + | 73.3967i | 0.390408 | + | 0.390408i | ||||
\(189\) | 185.173 | + | 37.8399i | 0.979753 | + | 0.200211i | ||||
\(190\) | −5.60641 | − | 144.275i | −0.0295074 | − | 0.759342i | ||||
\(191\) | − | 180.267i | − | 0.943807i | −0.881650 | − | 0.471904i | \(-0.843567\pi\) | ||
0.881650 | − | 0.471904i | \(-0.156433\pi\) | |||||||
\(192\) | −23.9999 | + | 0.0663871i | −0.125000 | + | 0.000345766i | ||||
\(193\) | −194.407 | − | 194.407i | −1.00729 | − | 1.00729i | −0.999973 | − | 0.00731625i | \(-0.997671\pi\) |
−0.00731625 | − | 0.999973i | \(-0.502329\pi\) | |||||||
\(194\) | 121.243i | 0.624966i | ||||||||
\(195\) | −3.52974 | − | 84.7888i | −0.0181012 | − | 0.434815i | ||||
\(196\) | 39.9375 | − | 89.4930i | 0.203763 | − | 0.456597i | ||||
\(197\) | 78.6926 | + | 78.6926i | 0.399455 | + | 0.399455i | 0.878041 | − | 0.478586i | \(-0.158851\pi\) |
−0.478586 | + | 0.878041i | \(0.658851\pi\) | |||||||
\(198\) | −54.4711 | + | 55.0771i | −0.275106 | + | 0.278167i | ||||
\(199\) | 203.776 | 1.02400 | 0.511999 | − | 0.858986i | \(-0.328905\pi\) | ||||
0.511999 | + | 0.858986i | \(0.328905\pi\) | |||||||
\(200\) | 53.7293 | + | 45.9692i | 0.268646 | + | 0.229846i | ||||
\(201\) | −179.650 | − | 178.659i | −0.893782 | − | 0.888851i | ||||
\(202\) | 96.3108 | + | 96.3108i | 0.476786 | + | 0.476786i | ||||
\(203\) | 28.4839 | − | 133.722i | 0.140315 | − | 0.658730i | ||||
\(204\) | 88.6580 | − | 89.1499i | 0.434598 | − | 0.437009i | ||||
\(205\) | 155.135 | + | 143.529i | 0.756755 | + | 0.700142i | ||||
\(206\) | 227.204 | 1.10293 | ||||||||
\(207\) | 184.627 | − | 186.681i | 0.891916 | − | 0.901840i | ||||
\(208\) | 16.0018 | − | 16.0018i | 0.0769317 | − | 0.0769317i | ||||
\(209\) | − | 124.272i | − | 0.594603i | ||||||
\(210\) | 24.8685 | − | 146.395i | 0.118421 | − | 0.697120i | ||||
\(211\) | −267.545 | −1.26798 | −0.633992 | − | 0.773340i | \(-0.718585\pi\) | ||||
−0.633992 | + | 0.773340i | \(0.718585\pi\) | |||||||
\(212\) | 1.30566 | + | 1.30566i | 0.00615878 | + | 0.00615878i | ||||
\(213\) | −368.568 | + | 1.01951i | −1.73037 | + | 0.00478643i | ||||
\(214\) | 160.074i | 0.748008i | ||||||||
\(215\) | 12.3565 | + | 317.982i | 0.0574722 | + | 1.47899i | ||||
\(216\) | 54.4462 | + | 53.5500i | 0.252066 | + | 0.247917i | ||||
\(217\) | −29.8664 | − | 6.36179i | −0.137633 | − | 0.0293170i | ||||
\(218\) | 193.662 | − | 193.662i | 0.888359 | − | 0.888359i | ||||
\(219\) | −39.5331 | − | 39.3150i | −0.180516 | − | 0.179520i | ||||
\(220\) | 44.6738 | + | 41.3317i | 0.203063 | + | 0.187872i | ||||
\(221\) | 118.552i | 0.536436i | ||||||||
\(222\) | −0.0272769 | − | 9.86100i | −0.000122869 | − | 0.0444189i | ||||
\(223\) | 270.204 | − | 270.204i | 1.21168 | − | 1.21168i | 0.241204 | − | 0.970475i | \(-0.422458\pi\) |
0.970475 | − | 0.241204i | \(-0.0775422\pi\) | |||||||
\(224\) | 33.2190 | − | 21.5523i | 0.148299 | − | 0.0962154i | ||||
\(225\) | −18.7010 | − | 224.221i | −0.0831155 | − | 0.996540i | ||||
\(226\) | −260.492 | −1.15262 | ||||||||
\(227\) | −43.7703 | + | 43.7703i | −0.192821 | + | 0.192821i | −0.796914 | − | 0.604093i | \(-0.793535\pi\) |
0.604093 | + | 0.796914i | \(0.293535\pi\) | |||||||
\(228\) | −122.513 | + | 0.338889i | −0.537339 | + | 0.00148635i | ||||
\(229\) | −74.6694 | −0.326067 | −0.163034 | − | 0.986621i | \(-0.552128\pi\) | ||||
−0.163034 | + | 0.986621i | \(0.552128\pi\) | |||||||
\(230\) | −151.420 | − | 140.092i | −0.658346 | − | 0.609094i | ||||
\(231\) | 26.2809 | − | 125.077i | 0.113770 | − | 0.541459i | ||||
\(232\) | 39.0635 | − | 39.0635i | 0.168377 | − | 0.168377i | ||||
\(233\) | 239.538 | − | 239.538i | 1.02806 | − | 1.02806i | 0.0284664 | − | 0.999595i | \(-0.490938\pi\) |
0.999595 | − | 0.0284664i | \(-0.00906237\pi\) | |||||||
\(234\) | −72.0069 | + | 0.398365i | −0.307722 | + | 0.00170242i | ||||
\(235\) | −259.301 | + | 10.0762i | −1.10341 | + | 0.0428775i | ||||
\(236\) | −8.05312 | −0.0341234 | ||||||||
\(237\) | −378.154 | + | 1.04603i | −1.59559 | + | 0.00441362i | ||||
\(238\) | −43.2176 | + | 202.892i | −0.181586 | + | 0.852485i | ||||
\(239\) | 34.0240 | 0.142360 | 0.0711799 | − | 0.997463i | \(-0.477324\pi\) | ||||
0.0711799 | + | 0.997463i | \(0.477324\pi\) | |||||||
\(240\) | 40.6250 | − | 44.1544i | 0.169271 | − | 0.183977i | ||||
\(241\) | − | 268.995i | − | 1.11616i | −0.829786 | − | 0.558081i | \(-0.811538\pi\) | ||
0.829786 | − | 0.558081i | \(-0.188462\pi\) | |||||||
\(242\) | −83.9594 | − | 83.9594i | −0.346939 | − | 0.346939i | ||||
\(243\) | −3.36074 | − | 242.977i | −0.0138302 | − | 0.999904i | ||||
\(244\) | 130.415 | 0.534487 | ||||||||
\(245\) | 96.4208 | + | 225.229i | 0.393554 | + | 0.919301i | ||||
\(246\) | 126.457 | − | 127.158i | 0.514052 | − | 0.516904i | ||||
\(247\) | 81.6850 | − | 81.6850i | 0.330709 | − | 0.330709i | ||||
\(248\) | −8.72470 | − | 8.72470i | −0.0351802 | − | 0.0351802i | ||||
\(249\) | 36.5136 | − | 36.7162i | 0.146641 | − | 0.147455i | ||||
\(250\) | −175.578 | + | 20.5513i | −0.702312 | + | 0.0822050i | ||||
\(251\) | 17.7724 | 0.0708064 | 0.0354032 | − | 0.999373i | \(-0.488728\pi\) | ||||
0.0354032 | + | 0.999373i | \(0.488728\pi\) | |||||||
\(252\) | −123.379 | − | 25.5680i | −0.489598 | − | 0.101460i | ||||
\(253\) | −125.547 | − | 125.547i | −0.496234 | − | 0.496234i | ||||
\(254\) | 107.010 | 0.421297 | ||||||||
\(255\) | 13.0739 | + | 314.052i | 0.0512703 | + | 1.23158i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 155.524 | − | 155.524i | 0.605151 | − | 0.605151i | −0.336524 | − | 0.941675i | \(-0.609251\pi\) |
0.941675 | + | 0.336524i | \(0.109251\pi\) | |||||||
\(258\) | 270.019 | − | 0.746911i | 1.04659 | − | 0.00289500i | ||||
\(259\) | 8.85531 | + | 13.6489i | 0.0341904 | + | 0.0526984i | ||||
\(260\) | 2.19679 | + | 56.5322i | 0.00844921 | + | 0.217431i | ||||
\(261\) | −175.783 | + | 0.972488i | −0.673498 | + | 0.00372601i | ||||
\(262\) | 227.798 | + | 227.798i | 0.869459 | + | 0.869459i | ||||
\(263\) | 227.523 | − | 227.523i | 0.865105 | − | 0.865105i | −0.126821 | − | 0.991926i | \(-0.540477\pi\) |
0.991926 | + | 0.126821i | \(0.0404772\pi\) | |||||||
\(264\) | 36.4155 | − | 36.6175i | 0.137937 | − | 0.138703i | ||||
\(265\) | −4.61273 | + | 0.179247i | −0.0174065 | + | 0.000676403i | ||||
\(266\) | 169.574 | − | 110.019i | 0.637497 | − | 0.413604i | ||||
\(267\) | 291.890 | − | 0.807409i | 1.09322 | − | 0.00302400i | ||||
\(268\) | 119.437 | + | 119.437i | 0.445660 | + | 0.445660i | ||||
\(269\) | 89.7378i | 0.333598i | 0.985991 | + | 0.166799i | \(0.0533431\pi\) | ||||
−0.985991 | + | 0.166799i | \(0.946657\pi\) | |||||||
\(270\) | −190.707 | + | 8.99621i | −0.706321 | + | 0.0333193i | ||||
\(271\) | 318.345i | 1.17470i | 0.809332 | + | 0.587352i | \(0.199830\pi\) | ||||
−0.809332 | + | 0.587352i | \(0.800170\pi\) | |||||||
\(272\) | −59.2695 | + | 59.2695i | −0.217903 | + | 0.217903i | ||||
\(273\) | 99.4888 | − | 64.9394i | 0.364428 | − | 0.237873i | ||||
\(274\) | − | 33.6668i | − | 0.122872i | ||||||
\(275\) | −151.694 | + | 11.8072i | −0.551614 | + | 0.0429353i | ||||
\(276\) | −123.428 | + | 124.113i | −0.447204 | + | 0.449685i | ||||
\(277\) | 65.4246 | − | 65.4246i | 0.236190 | − | 0.236190i | −0.579080 | − | 0.815270i | \(-0.696588\pi\) |
0.815270 | + | 0.579080i | \(0.196588\pi\) | |||||||
\(278\) | −30.0414 | − | 30.0414i | −0.108063 | − | 0.108063i | ||||
\(279\) | 0.217202 | + | 39.2605i | 0.000778501 | + | 0.140719i | ||||
\(280\) | −16.8489 | + | 97.5506i | −0.0601746 | + | 0.348395i | ||||
\(281\) | 431.212i | 1.53456i | 0.641311 | + | 0.767281i | \(0.278391\pi\) | ||||
−0.641311 | + | 0.767281i | \(0.721609\pi\) | |||||||
\(282\) | 0.609073 | + | 220.189i | 0.00215984 | + | 0.780812i | ||||
\(283\) | 168.146 | − | 168.146i | 0.594155 | − | 0.594155i | −0.344596 | − | 0.938751i | \(-0.611984\pi\) |
0.938751 | + | 0.344596i | \(0.111984\pi\) | |||||||
\(284\) | 245.713 | 0.865186 | ||||||||
\(285\) | 207.380 | − | 225.397i | 0.727650 | − | 0.790866i | ||||
\(286\) | 48.6943i | 0.170260i | ||||||||
\(287\) | −61.6431 | + | 289.393i | −0.214784 | + | 1.00834i | ||||
\(288\) | −36.1986 | − | 35.8003i | −0.125690 | − | 0.124307i | ||||
\(289\) | − | 150.109i | − | 0.519410i | ||||||
\(290\) | 5.36281 | + | 138.006i | 0.0184924 | + | 0.475883i | ||||
\(291\) | −181.361 | + | 182.367i | −0.623235 | + | 0.626692i | ||||
\(292\) | 26.2828 | + | 26.2828i | 0.0900095 | + | 0.0900095i | ||||
\(293\) | 262.938 | + | 262.938i | 0.897399 | + | 0.897399i | 0.995205 | − | 0.0978068i | \(-0.0311827\pi\) |
−0.0978068 | + | 0.995205i | \(0.531183\pi\) | |||||||
\(294\) | 193.939 | − | 74.8699i | 0.659658 | − | 0.254659i | ||||
\(295\) | 13.6725 | − | 14.7781i | 0.0463475 | − | 0.0500952i | ||||
\(296\) | 6.57402i | 0.0222095i | ||||||||
\(297\) | −164.319 | + | 1.36362i | −0.553263 | + | 0.00459130i | ||||
\(298\) | −7.65497 | − | 7.65497i | −0.0256878 | − | 0.0256878i | ||||
\(299\) | − | 165.047i | − | 0.551995i | ||||||
\(300\) | 12.0538 | + | 149.515i | 0.0401793 | + | 0.498383i | ||||
\(301\) | −373.742 | + | 242.481i | −1.24167 | + | 0.805585i | ||||
\(302\) | −236.474 | − | 236.474i | −0.783027 | − | 0.783027i | ||||
\(303\) | 0.799223 | + | 288.931i | 0.00263770 | + | 0.953568i | ||||
\(304\) | 81.6759 | 0.268671 | ||||||||
\(305\) | −221.417 | + | 239.321i | −0.725958 | + | 0.784659i | ||||
\(306\) | 266.709 | − | 1.47552i | 0.871597 | − | 0.00482195i | ||||
\(307\) | −366.628 | − | 366.628i | −1.19423 | − | 1.19423i | −0.975869 | − | 0.218358i | \(-0.929930\pi\) |
−0.218358 | − | 0.975869i | \(-0.570070\pi\) | |||||||
\(308\) | −17.7512 | + | 83.3358i | −0.0576338 | + | 0.270571i | ||||
\(309\) | 341.748 | + | 339.862i | 1.10598 | + | 1.09988i | ||||
\(310\) | 30.8232 | − | 1.19776i | 0.0994297 | − | 0.00386376i | ||||
\(311\) | 113.759 | 0.365785 | 0.182893 | − | 0.983133i | \(-0.441454\pi\) | ||||
0.182893 | + | 0.983133i | \(0.441454\pi\) | |||||||
\(312\) | 48.0052 | − | 0.132789i | 0.153863 | − | 0.000425606i | ||||
\(313\) | 267.661 | − | 267.661i | 0.855146 | − | 0.855146i | −0.135615 | − | 0.990762i | \(-0.543301\pi\) |
0.990762 | + | 0.135615i | \(0.0433012\pi\) | |||||||
\(314\) | − | 195.631i | − | 0.623030i | ||||||
\(315\) | 256.390 | − | 183.000i | 0.813937 | − | 0.580953i | ||||
\(316\) | 252.104 | 0.797797 | ||||||||
\(317\) | −215.640 | − | 215.640i | −0.680253 | − | 0.680253i | 0.279804 | − | 0.960057i | \(-0.409730\pi\) |
−0.960057 | + | 0.279804i | \(0.909730\pi\) | |||||||
\(318\) | 0.0108349 | + | 3.91697i | 3.40719e−5 | + | 0.0123175i | ||||
\(319\) | 118.872i | 0.372640i | ||||||||
\(320\) | −27.1647 | + | 29.3612i | −0.0848896 | + | 0.0917538i | ||||
\(321\) | −239.445 | + | 240.774i | −0.745936 | + | 0.750074i | ||||
\(322\) | 60.1668 | − | 282.462i | 0.186853 | − | 0.877212i | ||||
\(323\) | −302.556 | + | 302.556i | −0.936705 | + | 0.936705i | ||||
\(324\) | 1.79242 | + | 161.990i | 0.00553215 | + | 0.499969i | ||||
\(325\) | −107.471 | − | 91.9486i | −0.330679 | − | 0.282919i | ||||
\(326\) | − | 1.81832i | − | 0.00557766i | ||||||
\(327\) | 580.984 | − | 1.60708i | 1.77671 | − | 0.00491463i | ||||
\(328\) | −84.5387 | + | 84.5387i | −0.257740 | + | 0.257740i | ||||
\(329\) | −197.733 | − | 304.770i | −0.601012 | − | 0.926353i | ||||
\(330\) | 5.36999 | + | 128.994i | 0.0162727 | + | 0.390891i | ||||
\(331\) | 70.4637 | 0.212881 | 0.106441 | − | 0.994319i | \(-0.466055\pi\) | ||||
0.106441 | + | 0.994319i | \(0.466055\pi\) | |||||||
\(332\) | −24.4100 | + | 24.4100i | −0.0735242 | + | 0.0735242i | ||||
\(333\) | 14.7095 | − | 14.8732i | 0.0441727 | − | 0.0446641i | ||||
\(334\) | −289.929 | −0.868051 | ||||||||
\(335\) | −421.955 | + | 16.3968i | −1.25957 | + | 0.0489457i | ||||
\(336\) | 82.2049 | + | 17.2728i | 0.244658 | + | 0.0514070i | ||||
\(337\) | −38.8228 | + | 38.8228i | −0.115201 | + | 0.115201i | −0.762357 | − | 0.647156i | \(-0.775958\pi\) |
0.647156 | + | 0.762357i | \(0.275958\pi\) | |||||||
\(338\) | 136.993 | − | 136.993i | 0.405304 | − | 0.405304i | ||||
\(339\) | −391.818 | − | 389.656i | −1.15581 | − | 1.14943i | ||||
\(340\) | −8.13678 | − | 209.391i | −0.0239317 | − | 0.615857i | ||||
\(341\) | 26.5497 | 0.0778584 | ||||||||
\(342\) | −184.785 | − | 182.751i | −0.540306 | − | 0.534360i | ||||
\(343\) | −201.970 | + | 277.231i | −0.588833 | + | 0.808254i | ||||
\(344\) | −180.014 | −0.523295 | ||||||||
\(345\) | −18.2013 | − | 437.218i | −0.0527574 | − | 1.26730i | ||||
\(346\) | − | 96.4644i | − | 0.278799i | ||||||
\(347\) | −137.429 | − | 137.429i | −0.396050 | − | 0.396050i | 0.480788 | − | 0.876837i | \(-0.340351\pi\) |
−0.876837 | + | 0.480788i | \(0.840351\pi\) | |||||||
\(348\) | 117.190 | − | 0.324164i | 0.336753 | − | 0.000931505i | ||||
\(349\) | 508.928 | 1.45825 | 0.729123 | − | 0.684383i | \(-0.239928\pi\) | ||||
0.729123 | + | 0.684383i | \(0.239928\pi\) | |||||||
\(350\) | −150.407 | − | 196.540i | −0.429734 | − | 0.561541i | ||||
\(351\) | −108.905 | − | 107.112i | −0.310270 | − | 0.305162i | ||||
\(352\) | −24.3444 | + | 24.3444i | −0.0691603 | + | 0.0691603i | ||||
\(353\) | −205.887 | − | 205.887i | −0.583248 | − | 0.583248i | 0.352546 | − | 0.935794i | \(-0.385316\pi\) |
−0.935794 | + | 0.352546i | \(0.885316\pi\) | |||||||
\(354\) | −12.1130 | − | 12.0462i | −0.0342176 | − | 0.0340288i | ||||
\(355\) | −417.169 | + | 450.902i | −1.17512 | + | 1.27015i | ||||
\(356\) | −194.594 | −0.546613 | ||||||||
\(357\) | −368.500 | + | 240.531i | −1.03221 | + | 0.673757i | ||||
\(358\) | 277.037 | + | 277.037i | 0.773847 | + | 0.773847i | ||||
\(359\) | −51.9892 | −0.144817 | −0.0724084 | − | 0.997375i | \(-0.523068\pi\) | ||||
−0.0724084 | + | 0.997375i | \(0.523068\pi\) | |||||||
\(360\) | 127.154 | − | 5.64577i | 0.353205 | − | 0.0156827i | ||||
\(361\) | 55.9344 | 0.154943 | ||||||||
\(362\) | 271.177 | − | 271.177i | 0.749108 | − | 0.749108i | ||||
\(363\) | −0.696727 | − | 251.877i | −0.00191936 | − | 0.693876i | ||||
\(364\) | −66.4454 | + | 43.1093i | −0.182542 | + | 0.118432i | ||||
\(365\) | −92.8536 | + | 3.60821i | −0.254393 | + | 0.00988552i | ||||
\(366\) | 196.163 | + | 195.080i | 0.535963 | + | 0.533006i | ||||
\(367\) | −340.117 | − | 340.117i | −0.926749 | − | 0.926749i | 0.0707450 | − | 0.997494i | \(-0.477462\pi\) |
−0.997494 | + | 0.0707450i | \(0.977462\pi\) | |||||||
\(368\) | 82.5141 | − | 82.5141i | 0.224223 | − | 0.224223i | ||||
\(369\) | 380.418 | − | 2.10459i | 1.03094 | − | 0.00570351i | ||||
\(370\) | −12.0638 | − | 11.1613i | −0.0326050 | − | 0.0301657i | ||||
\(371\) | −3.51749 | − | 5.42159i | −0.00948111 | − | 0.0146134i | ||||
\(372\) | −0.0724009 | − | 26.1740i | −0.000194626 | − | 0.0703602i | ||||
\(373\) | 185.919 | + | 185.919i | 0.498441 | + | 0.498441i | 0.910952 | − | 0.412511i | \(-0.135348\pi\) |
−0.412511 | + | 0.910952i | \(0.635348\pi\) | |||||||
\(374\) | − | 180.360i | − | 0.482246i | ||||||
\(375\) | −294.836 | − | 231.726i | −0.786229 | − | 0.617935i | ||||
\(376\) | − | 146.793i | − | 0.390408i | ||||||
\(377\) | −78.1357 | + | 78.1357i | −0.207257 | + | 0.207257i | ||||
\(378\) | −147.333 | − | 223.013i | −0.389771 | − | 0.589982i | ||||
\(379\) | − | 123.430i | − | 0.325672i | −0.986653 | − | 0.162836i | \(-0.947936\pi\) | ||
0.986653 | − | 0.162836i | \(-0.0520641\pi\) | |||||||
\(380\) | −138.669 | + | 149.881i | −0.364917 | + | 0.394425i | ||||
\(381\) | 160.958 | + | 160.070i | 0.422461 | + | 0.420130i | ||||
\(382\) | −180.267 | + | 180.267i | −0.471904 | + | 0.471904i | ||||
\(383\) | 44.1167 | + | 44.1167i | 0.115187 | + | 0.115187i | 0.762351 | − | 0.647164i | \(-0.224045\pi\) |
−0.647164 | + | 0.762351i | \(0.724045\pi\) | |||||||
\(384\) | 24.0663 | + | 23.9335i | 0.0626726 | + | 0.0623269i | ||||
\(385\) | −122.790 | − | 174.062i | −0.318934 | − | 0.452108i | ||||
\(386\) | 388.814i | 1.00729i | ||||||||
\(387\) | 407.265 | + | 402.784i | 1.05236 | + | 1.04078i | ||||
\(388\) | 121.243 | − | 121.243i | 0.312483 | − | 0.312483i | ||||
\(389\) | −116.363 | −0.299133 | −0.149566 | − | 0.988752i | \(-0.547788\pi\) | ||||
−0.149566 | + | 0.988752i | \(0.547788\pi\) | |||||||
\(390\) | −81.2591 | + | 88.3186i | −0.208357 | + | 0.226458i | ||||
\(391\) | 611.321i | 1.56348i | ||||||||
\(392\) | −129.431 | + | 49.5554i | −0.330180 | + | 0.126417i | ||||
\(393\) | 1.89036 | + | 683.392i | 0.00481007 | + | 1.73891i | ||||
\(394\) | − | 157.385i | − | 0.399455i | ||||||
\(395\) | −428.020 | + | 462.630i | −1.08359 | + | 1.17121i | ||||
\(396\) | 109.548 | − | 0.606055i | 0.276637 | − | 0.00153044i | ||||
\(397\) | 8.73597 | + | 8.73597i | 0.0220050 | + | 0.0220050i | 0.718024 | − | 0.696019i | \(-0.245047\pi\) |
−0.696019 | + | 0.718024i | \(0.745047\pi\) | |||||||
\(398\) | −203.776 | − | 203.776i | −0.511999 | − | 0.511999i | ||||
\(399\) | 419.635 | + | 88.1730i | 1.05172 | + | 0.220985i | ||||
\(400\) | −7.76012 | − | 99.6984i | −0.0194003 | − | 0.249246i | ||||
\(401\) | 27.9968i | 0.0698174i | 0.999391 | + | 0.0349087i | \(0.0111140\pi\) | ||||
−0.999391 | + | 0.0349087i | \(0.988886\pi\) | |||||||
\(402\) | 0.991133 | + | 358.309i | 0.00246551 | + | 0.891317i | ||||
\(403\) | 17.4513 | + | 17.4513i | 0.0433036 | + | 0.0433036i | ||||
\(404\) | − | 192.622i | − | 0.476786i | ||||||
\(405\) | −300.307 | − | 271.736i | −0.741499 | − | 0.670954i | ||||
\(406\) | −162.206 | + | 105.238i | −0.399523 | + | 0.259208i | ||||
\(407\) | −10.0025 | − | 10.0025i | −0.0245763 | − | 0.0245763i | ||||
\(408\) | −177.808 | + | 0.491841i | −0.435804 | + | 0.00120549i | ||||
\(409\) | 234.500 | 0.573349 | 0.286675 | − | 0.958028i | \(-0.407450\pi\) | ||||
0.286675 | + | 0.958028i | \(0.407450\pi\) | |||||||
\(410\) | −11.6058 | − | 298.664i | −0.0283069 | − | 0.728448i | ||||
\(411\) | 50.3604 | − | 50.6397i | 0.122531 | − | 0.123211i | ||||
\(412\) | −227.204 | − | 227.204i | −0.551467 | − | 0.551467i | ||||
\(413\) | 27.5674 | + | 5.87209i | 0.0667492 | + | 0.0142181i | ||||
\(414\) | −371.308 | + | 2.05419i | −0.896878 | + | 0.00496182i | ||||
\(415\) | −3.35112 | − | 86.2375i | −0.00807498 | − | 0.207801i | ||||
\(416\) | −32.0036 | −0.0769317 | ||||||||
\(417\) | −0.249295 | − | 90.1239i | −0.000597830 | − | 0.216125i | ||||
\(418\) | −124.272 | + | 124.272i | −0.297301 | + | 0.297301i | ||||
\(419\) | 339.624i | 0.810559i | 0.914193 | + | 0.405279i | \(0.132826\pi\) | ||||
−0.914193 | + | 0.405279i | \(0.867174\pi\) | |||||||
\(420\) | −171.264 | + | 121.527i | −0.407771 | + | 0.289349i | ||||
\(421\) | 699.038 | 1.66042 | 0.830211 | − | 0.557449i | \(-0.188220\pi\) | ||||
0.830211 | + | 0.557449i | \(0.188220\pi\) | |||||||
\(422\) | 267.545 | + | 267.545i | 0.633992 | + | 0.633992i | ||||
\(423\) | −328.453 | + | 332.107i | −0.776484 | + | 0.785123i | ||||
\(424\) | − | 2.61132i | − | 0.00615878i | ||||||
\(425\) | 398.064 | + | 340.571i | 0.936620 | + | 0.801344i | ||||
\(426\) | 369.587 | + | 367.548i | 0.867576 | + | 0.862789i | ||||
\(427\) | −446.436 | − | 95.0946i | −1.04552 | − | 0.222704i | ||||
\(428\) | 160.074 | − | 160.074i | 0.374004 | − | 0.374004i | ||||
\(429\) | −72.8391 | + | 73.2431i | −0.169788 | + | 0.170730i | ||||
\(430\) | 305.625 | − | 330.338i | 0.710757 | − | 0.768229i | ||||
\(431\) | − | 590.362i | − | 1.36975i | −0.728661 | − | 0.684875i | \(-0.759857\pi\) | ||
0.728661 | − | 0.684875i | \(-0.240143\pi\) | |||||||
\(432\) | −0.896216 | − | 107.996i | −0.00207457 | − | 0.249991i | ||||
\(433\) | −340.107 | + | 340.107i | −0.785466 | + | 0.785466i | −0.980747 | − | 0.195281i | \(-0.937438\pi\) |
0.195281 | + | 0.980747i | \(0.437438\pi\) | |||||||
\(434\) | 23.5046 | + | 36.2282i | 0.0541581 | + | 0.0834751i | ||||
\(435\) | −198.369 | + | 215.603i | −0.456022 | + | 0.495639i | ||||
\(436\) | −387.324 | −0.888359 | ||||||||
\(437\) | 421.213 | − | 421.213i | 0.963874 | − | 0.963874i | ||||
\(438\) | 0.218105 | + | 78.8480i | 0.000497956 | + | 0.180018i | ||||
\(439\) | −732.833 | −1.66932 | −0.834661 | − | 0.550764i | \(-0.814337\pi\) | ||||
−0.834661 | + | 0.550764i | \(0.814337\pi\) | |||||||
\(440\) | −3.34211 | − | 86.0056i | −0.00759570 | − | 0.195467i | ||||
\(441\) | 403.706 | + | 177.488i | 0.915434 | + | 0.402468i | ||||
\(442\) | 118.552 | − | 118.552i | 0.268218 | − | 0.268218i | ||||
\(443\) | −110.990 | + | 110.990i | −0.250541 | + | 0.250541i | −0.821192 | − | 0.570651i | \(-0.806691\pi\) |
0.570651 | + | 0.821192i | \(0.306691\pi\) | |||||||
\(444\) | −9.83372 | + | 9.88827i | −0.0221480 | + | 0.0222709i | ||||
\(445\) | 330.380 | − | 357.095i | 0.742428 | − | 0.802461i | ||||
\(446\) | −540.408 | −1.21168 | ||||||||
\(447\) | −0.0635238 | − | 22.9648i | −0.000142111 | − | 0.0513754i | ||||
\(448\) | −54.7712 | − | 11.6667i | −0.122257 | − | 0.0260418i | ||||
\(449\) | 196.292 | 0.437175 | 0.218588 | − | 0.975817i | \(-0.429855\pi\) | ||||
0.218588 | + | 0.975817i | \(0.429855\pi\) | |||||||
\(450\) | −205.520 | + | 242.922i | −0.456712 | + | 0.539828i | ||||
\(451\) | − | 257.255i | − | 0.570411i | ||||||
\(452\) | 260.492 | + | 260.492i | 0.576311 | + | 0.576311i | ||||
\(453\) | −1.96235 | − | 709.420i | −0.00433191 | − | 1.56605i | ||||
\(454\) | 87.5405 | 0.192821 | ||||||||
\(455\) | 33.7015 | − | 195.123i | 0.0740693 | − | 0.428842i | ||||
\(456\) | 122.852 | + | 122.174i | 0.269413 | + | 0.267926i | ||||
\(457\) | 52.4299 | − | 52.4299i | 0.114726 | − | 0.114726i | −0.647413 | − | 0.762139i | \(-0.724149\pi\) |
0.762139 | + | 0.647413i | \(0.224149\pi\) | |||||||
\(458\) | 74.6694 | + | 74.6694i | 0.163034 | + | 0.163034i | ||||
\(459\) | 403.375 | + | 396.736i | 0.878813 | + | 0.864348i | ||||
\(460\) | 11.3279 | + | 291.511i | 0.0246258 | + | 0.633720i | ||||
\(461\) | 549.751 | 1.19252 | 0.596259 | − | 0.802792i | \(-0.296653\pi\) | ||||
0.596259 | + | 0.802792i | \(0.296653\pi\) | |||||||
\(462\) | −151.358 | + | 98.7960i | −0.327614 | + | 0.213844i | ||||
\(463\) | 333.035 | + | 333.035i | 0.719298 | + | 0.719298i | 0.968461 | − | 0.249164i | \(-0.0801558\pi\) |
−0.249164 | + | 0.968461i | \(0.580156\pi\) | |||||||
\(464\) | −78.1270 | −0.168377 | ||||||||
\(465\) | 48.1542 | + | 44.3051i | 0.103557 | + | 0.0952798i | ||||
\(466\) | −479.077 | −1.02806 | ||||||||
\(467\) | −9.53974 | + | 9.53974i | −0.0204277 | + | 0.0204277i | −0.717247 | − | 0.696819i | \(-0.754598\pi\) |
0.696819 | + | 0.717247i | \(0.254598\pi\) | |||||||
\(468\) | 72.4053 | + | 71.6086i | 0.154712 | + | 0.153010i | ||||
\(469\) | −321.767 | − | 495.946i | −0.686070 | − | 1.05746i | ||||
\(470\) | 269.377 | + | 249.224i | 0.573142 | + | 0.530265i | ||||
\(471\) | 292.634 | − | 294.258i | 0.621304 | − | 0.624751i | ||||
\(472\) | 8.05312 | + | 8.05312i | 0.0170617 | + | 0.0170617i | ||||
\(473\) | 273.895 | − | 273.895i | 0.579060 | − | 0.579060i | ||||
\(474\) | 379.200 | + | 377.108i | 0.800001 | + | 0.795587i | ||||
\(475\) | −39.6134 | − | 508.935i | −0.0833966 | − | 1.07144i | ||||
\(476\) | 246.109 | − | 159.674i | 0.517036 | − | 0.335449i | ||||
\(477\) | −5.84288 | + | 5.90789i | −0.0122492 | + | 0.0123855i | ||||
\(478\) | −34.0240 | − | 34.0240i | −0.0711799 | − | 0.0711799i | ||||
\(479\) | 30.2411i | 0.0631339i | 0.999502 | + | 0.0315670i | \(0.0100497\pi\) | ||||
−0.999502 | + | 0.0315670i | \(0.989950\pi\) | |||||||
\(480\) | −84.7794 | + | 3.52935i | −0.176624 | + | 0.00735281i | ||||
\(481\) | − | 13.1495i | − | 0.0273379i | ||||||
\(482\) | −268.995 | + | 268.995i | −0.558081 | + | 0.558081i | ||||
\(483\) | 513.019 | − | 334.864i | 1.06215 | − | 0.693299i | ||||
\(484\) | 167.919i | 0.346939i | ||||||||
\(485\) | 16.6448 | + | 428.337i | 0.0343192 | + | 0.883169i | ||||
\(486\) | −239.616 | + | 246.338i | −0.493037 | + | 0.506867i | ||||
\(487\) | −249.687 | + | 249.687i | −0.512704 | + | 0.512704i | −0.915354 | − | 0.402650i | \(-0.868089\pi\) |
0.402650 | + | 0.915354i | \(0.368089\pi\) | |||||||
\(488\) | −130.415 | − | 130.415i | −0.267243 | − | 0.267243i | ||||
\(489\) | 2.71992 | − | 2.73501i | 0.00556221 | − | 0.00559307i | ||||
\(490\) | 128.808 | − | 321.650i | 0.262874 | − | 0.656428i | ||||
\(491\) | 775.321i | 1.57907i | 0.613708 | + | 0.789533i | \(0.289677\pi\) | ||||
−0.613708 | + | 0.789533i | \(0.710323\pi\) | |||||||
\(492\) | −253.615 | + | 0.701534i | −0.515478 | + | 0.00142588i | ||||
\(493\) | 289.409 | − | 289.409i | 0.587037 | − | 0.587037i | ||||
\(494\) | −163.370 | −0.330709 | ||||||||
\(495\) | −184.878 | + | 202.058i | −0.373491 | + | 0.408198i | ||||
\(496\) | 17.4494i | 0.0351802i | ||||||||
\(497\) | −841.124 | − | 179.166i | −1.69240 | − | 0.360496i | ||||
\(498\) | −73.2299 | + | 0.202564i | −0.147048 | + | 0.000406755i | ||||
\(499\) | − | 596.688i | − | 1.19577i | −0.801583 | − | 0.597884i | \(-0.796009\pi\) | ||
0.801583 | − | 0.597884i | \(-0.203991\pi\) | |||||||
\(500\) | 196.129 | + | 155.027i | 0.392259 | + | 0.310054i | ||||
\(501\) | −436.095 | − | 433.689i | −0.870449 | − | 0.865647i | ||||
\(502\) | −17.7724 | − | 17.7724i | −0.0354032 | − | 0.0354032i | ||||
\(503\) | 653.010 | + | 653.010i | 1.29823 | + | 1.29823i | 0.929560 | + | 0.368671i | \(0.120187\pi\) |
0.368671 | + | 0.929560i | \(0.379813\pi\) | |||||||
\(504\) | 97.8106 | + | 148.947i | 0.194069 | + | 0.295529i | ||||
\(505\) | 353.475 | + | 327.031i | 0.699951 | + | 0.647586i | ||||
\(506\) | 251.095i | 0.496234i | ||||||||
\(507\) | 410.977 | − | 1.13682i | 0.810606 | − | 0.00224225i | ||||
\(508\) | −107.010 | − | 107.010i | −0.210649 | − | 0.210649i | ||||
\(509\) | 288.101i | 0.566014i | 0.959118 | + | 0.283007i | \(0.0913320\pi\) | ||||
−0.959118 | + | 0.283007i | \(0.908668\pi\) | |||||||
\(510\) | 300.978 | − | 327.126i | 0.590153 | − | 0.641423i | ||||
\(511\) | −70.8066 | − | 109.136i | −0.138565 | − | 0.213573i | ||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −4.57495 | − | 551.293i | −0.00891804 | − | 1.07465i | ||||
\(514\) | −311.048 | −0.605151 | ||||||||
\(515\) | 802.683 | − | 31.1916i | 1.55861 | − | 0.0605662i | ||||
\(516\) | −270.766 | − | 269.272i | −0.524741 | − | 0.521846i | ||||
\(517\) | 223.350 | + | 223.350i | 0.432011 | + | 0.432011i | ||||
\(518\) | 4.79358 | − | 22.5042i | 0.00925402 | − | 0.0434444i | ||||
\(519\) | 144.296 | − | 145.096i | 0.278027 | − | 0.279569i | ||||
\(520\) | 54.3354 | − | 58.7290i | 0.104491 | − | 0.112940i | ||||
\(521\) | 190.167 | 0.365004 | 0.182502 | − | 0.983206i | \(-0.441580\pi\) | ||||
0.182502 | + | 0.983206i | \(0.441580\pi\) | |||||||
\(522\) | 176.756 | + | 174.811i | 0.338612 | + | 0.334886i | ||||
\(523\) | 315.417 | − | 315.417i | 0.603093 | − | 0.603093i | −0.338039 | − | 0.941132i | \(-0.609764\pi\) |
0.941132 | + | 0.338039i | \(0.109764\pi\) | |||||||
\(524\) | − | 455.597i | − | 0.869459i | ||||||
\(525\) | 67.7592 | − | 520.609i | 0.129065 | − | 0.991636i | ||||
\(526\) | −455.045 | −0.865105 | ||||||||
\(527\) | −64.6386 | − | 64.6386i | −0.122654 | − | 0.122654i | ||||
\(528\) | −73.0330 | + | 0.202019i | −0.138320 | + | 0.000382612i | ||||
\(529\) | − | 322.071i | − | 0.608830i | ||||||
\(530\) | 4.79197 | + | 4.43348i | 0.00904146 | + | 0.00836506i | ||||
\(531\) | −0.200483 | − | 36.2385i | −0.000377557 | − | 0.0682457i | ||||
\(532\) | −279.593 | − | 59.5556i | −0.525551 | − | 0.111947i | ||||
\(533\) | 169.096 | − | 169.096i | 0.317254 | − | 0.317254i | ||||
\(534\) | −292.698 | − | 291.083i | −0.548123 | − | 0.545099i | ||||
\(535\) | 21.9756 | + | 565.519i | 0.0410759 | + | 1.05705i | ||||
\(536\) | − | 238.874i | − | 0.445660i | ||||||
\(537\) | 2.29896 | + | 831.109i | 0.00428112 | + | 1.54769i | ||||
\(538\) | 89.7378 | − | 89.7378i | 0.166799 | − | 0.166799i | ||||
\(539\) | 121.532 | − | 272.332i | 0.225477 | − | 0.505254i | ||||
\(540\) | 199.703 | + | 181.711i | 0.369820 | + | 0.336501i | ||||
\(541\) | 219.489 | 0.405710 | 0.202855 | − | 0.979209i | \(-0.434978\pi\) | ||||
0.202855 | + | 0.979209i | \(0.434978\pi\) | |||||||
\(542\) | 318.345 | − | 318.345i | 0.587352 | − | 0.587352i | ||||
\(543\) | 813.528 | − | 2.25033i | 1.49821 | − | 0.00414426i | ||||
\(544\) | 118.539 | 0.217903 | ||||||||
\(545\) | 657.596 | − | 710.770i | 1.20660 | − | 1.30416i | ||||
\(546\) | −164.428 | − | 34.5494i | −0.301151 | − | 0.0632772i | ||||
\(547\) | 44.8504 | − | 44.8504i | 0.0819934 | − | 0.0819934i | −0.664921 | − | 0.746914i | \(-0.731535\pi\) |
0.746914 | + | 0.664921i | \(0.231535\pi\) | |||||||
\(548\) | −33.6668 | + | 33.6668i | −0.0614358 | + | 0.0614358i | ||||
\(549\) | 3.24668 | + | 586.858i | 0.00591381 | + | 1.06896i | ||||
\(550\) | 163.501 | + | 139.887i | 0.297274 | + | 0.254339i | ||||
\(551\) | −398.818 | −0.723808 | ||||||||
\(552\) | 247.541 | − | 0.684733i | 0.448444 | − | 0.00124046i | ||||
\(553\) | −863.002 | − | 183.827i | −1.56058 | − | 0.332417i | ||||
\(554\) | −130.849 | −0.236190 | ||||||||
\(555\) | −1.45013 | − | 34.8339i | −0.00261284 | − | 0.0627637i | ||||
\(556\) | 60.0828i | 0.108063i | ||||||||
\(557\) | −221.625 | − | 221.625i | −0.397890 | − | 0.397890i | 0.479598 | − | 0.877488i | \(-0.340782\pi\) |
−0.877488 | + | 0.479598i | \(0.840782\pi\) | |||||||
\(558\) | 39.0433 | − | 39.4777i | 0.0699701 | − | 0.0707486i | ||||
\(559\) | 360.067 | 0.644127 | ||||||||
\(560\) | 114.399 | − | 80.7017i | 0.204285 | − | 0.144110i | ||||
\(561\) | 269.791 | − | 271.288i | 0.480911 | − | 0.483579i | ||||
\(562\) | 431.212 | − | 431.212i | 0.767281 | − | 0.767281i | ||||
\(563\) | −39.5010 | − | 39.5010i | −0.0701616 | − | 0.0701616i | 0.671155 | − | 0.741317i | \(-0.265798\pi\) |
−0.741317 | + | 0.671155i | \(0.765798\pi\) | |||||||
\(564\) | 219.580 | − | 220.798i | 0.389326 | − | 0.391486i | ||||
\(565\) | −920.285 | + | 35.7615i | −1.62882 | + | 0.0632947i | ||||
\(566\) | −336.292 | −0.594155 | ||||||||
\(567\) | 111.983 | − | 555.832i | 0.197500 | − | 0.980303i | ||||
\(568\) | −245.713 | − | 245.713i | −0.432593 | − | 0.432593i | ||||
\(569\) | −63.0549 | −0.110817 | −0.0554085 | − | 0.998464i | \(-0.517646\pi\) | ||||
−0.0554085 | + | 0.998464i | \(0.517646\pi\) | |||||||
\(570\) | −432.777 | + | 18.0164i | −0.759258 | + | 0.0316077i | ||||
\(571\) | −269.370 | −0.471751 | −0.235875 | − | 0.971783i | \(-0.575796\pi\) | ||||
−0.235875 | + | 0.971783i | \(0.575796\pi\) | |||||||
\(572\) | 48.6943 | − | 48.6943i | 0.0851298 | − | 0.0851298i | ||||
\(573\) | −540.800 | + | 1.49593i | −0.943804 | + | 0.00261069i | ||||
\(574\) | 351.036 | − | 227.750i | 0.611561 | − | 0.396777i | ||||
\(575\) | −554.178 | − | 474.138i | −0.963787 | − | 0.824587i | ||||
\(576\) | 0.398321 | + | 71.9989i | 0.000691529 | + | 0.124998i | ||||
\(577\) | 612.246 | + | 612.246i | 1.06108 | + | 1.06108i | 0.998009 | + | 0.0630759i | \(0.0200910\pi\) |
0.0630759 | + | 0.998009i | \(0.479909\pi\) | |||||||
\(578\) | −150.109 | + | 150.109i | −0.259705 | + | 0.259705i | ||||
\(579\) | −581.605 | + | 584.832i | −1.00450 | + | 1.01007i | ||||
\(580\) | 132.643 | − | 143.369i | 0.228695 | − | 0.247188i | ||||
\(581\) | 101.360 | − | 65.7614i | 0.174457 | − | 0.113187i | ||||
\(582\) | 363.729 | − | 1.00612i | 0.624964 | − | 0.00172874i | ||||
\(583\) | 3.97319 | + | 3.97319i | 0.00681508 | + | 0.00681508i | ||||
\(584\) | − | 52.5656i | − | 0.0900095i | ||||||
\(585\) | −254.336 | + | 11.2928i | −0.434763 | + | 0.0193039i | ||||
\(586\) | − | 525.876i | − | 0.897399i | ||||||
\(587\) | −228.676 | + | 228.676i | −0.389567 | + | 0.389567i | −0.874533 | − | 0.484966i | \(-0.838832\pi\) |
0.484966 | + | 0.874533i | \(0.338832\pi\) | |||||||
\(588\) | −268.809 | − | 119.070i | −0.457159 | − | 0.202499i | ||||
\(589\) | 89.0747i | 0.151230i | ||||||||
\(590\) | −28.4506 | + | 1.10557i | −0.0482213 | + | 0.00187384i | ||||
\(591\) | 235.424 | − | 236.730i | 0.398348 | − | 0.400558i | ||||
\(592\) | 6.57402 | − | 6.57402i | 0.0111048 | − | 0.0111048i | ||||
\(593\) | −576.695 | − | 576.695i | −0.972503 | − | 0.972503i | 0.0271286 | − | 0.999632i | \(-0.491364\pi\) |
−0.999632 | + | 0.0271286i | \(0.991364\pi\) | |||||||
\(594\) | 165.683 | + | 162.956i | 0.278927 | + | 0.274336i | ||||
\(595\) | −124.828 | + | 722.722i | −0.209795 | + | 1.21466i | ||||
\(596\) | 15.3099i | 0.0256878i | ||||||||
\(597\) | −1.69101 | − | 611.325i | −0.00283251 | − | 1.02399i | ||||
\(598\) | −165.047 | + | 165.047i | −0.275998 | + | 0.275998i | ||||
\(599\) | 456.495 | 0.762095 | 0.381048 | − | 0.924555i | \(-0.375563\pi\) | ||||
0.381048 | + | 0.924555i | \(0.375563\pi\) | |||||||
\(600\) | 137.461 | − | 161.569i | 0.229102 | − | 0.269281i | ||||
\(601\) | − | 631.907i | − | 1.05143i | −0.850662 | − | 0.525713i | \(-0.823798\pi\) | ||
0.850662 | − | 0.525713i | \(-0.176202\pi\) | |||||||
\(602\) | 616.223 | + | 131.260i | 1.02363 | + | 0.218041i | ||||
\(603\) | −534.484 | + | 540.431i | −0.886376 | + | 0.896237i | ||||
\(604\) | 472.948i | 0.783027i | ||||||||
\(605\) | −308.144 | − | 285.091i | −0.509328 | − | 0.471225i | ||||
\(606\) | 288.132 | − | 289.730i | 0.475465 | − | 0.478103i | ||||
\(607\) | 463.511 | + | 463.511i | 0.763610 | + | 0.763610i | 0.976973 | − | 0.213363i | \(-0.0684418\pi\) |
−0.213363 | + | 0.976973i | \(0.568442\pi\) | |||||||
\(608\) | −81.6759 | − | 81.6759i | −0.134335 | − | 0.134335i | ||||
\(609\) | −401.401 | − | 84.3418i | −0.659116 | − | 0.138492i | ||||
\(610\) | 460.738 | − | 17.9039i | 0.755309 | − | 0.0293507i | ||||
\(611\) | 293.619i | 0.480555i | ||||||||
\(612\) | −268.184 | − | 265.233i | −0.438210 | − | 0.433388i | ||||
\(613\) | −491.048 | − | 491.048i | −0.801057 | − | 0.801057i | 0.182204 | − | 0.983261i | \(-0.441677\pi\) |
−0.983261 | + | 0.182204i | \(0.941677\pi\) | |||||||
\(614\) | 733.255i | 1.19423i | ||||||||
\(615\) | 429.298 | − | 466.594i | 0.698046 | − | 0.758689i | ||||
\(616\) | 101.087 | − | 65.5846i | 0.164102 | − | 0.106469i | ||||
\(617\) | 392.264 | + | 392.264i | 0.635759 | + | 0.635759i | 0.949507 | − | 0.313747i | \(-0.101584\pi\) |
−0.313747 | + | 0.949507i | \(0.601584\pi\) | |||||||
\(618\) | −1.88543 | − | 681.610i | −0.00305085 | − | 1.10293i | ||||
\(619\) | 1005.88 | 1.62500 | 0.812500 | − | 0.582961i | \(-0.198106\pi\) | ||||
0.812500 | + | 0.582961i | \(0.198106\pi\) | |||||||
\(620\) | −32.0210 | − | 29.6254i | −0.0516467 | − | 0.0477830i | ||||
\(621\) | −561.573 | − | 552.329i | −0.904304 | − | 0.889418i | ||||
\(622\) | −113.759 | − | 113.759i | −0.182893 | − | 0.182893i | ||||
\(623\) | 666.135 | + | 141.892i | 1.06924 | + | 0.227757i | ||||
\(624\) | −48.1380 | − | 47.8724i | −0.0771442 | − | 0.0767186i | ||||
\(625\) | −617.473 | + | 96.7090i | −0.987956 | + | 0.154734i | ||||
\(626\) | −535.321 | −0.855146 | ||||||||
\(627\) | −372.814 | + | 1.03126i | −0.594600 | + | 0.00164475i | ||||
\(628\) | −195.631 | + | 195.631i | −0.311515 | + | 0.311515i | ||||
\(629\) | 48.7049i | 0.0774323i | ||||||||
\(630\) | −439.390 | − | 73.3903i | −0.697445 | − | 0.116492i | ||||
\(631\) | 499.042 | 0.790874 | 0.395437 | − | 0.918493i | \(-0.370593\pi\) | ||||
0.395437 | + | 0.918493i | \(0.370593\pi\) | |||||||
\(632\) | −252.104 | − | 252.104i | −0.398898 | − | 0.398898i | ||||
\(633\) | 2.22019 | + | 802.631i | 0.00350741 | + | 1.26798i | ||||
\(634\) | 431.280i | 0.680253i | ||||||||
\(635\) | 378.050 | − | 14.6907i | 0.595355 | − | 0.0231350i | ||||
\(636\) | 3.90613 | − | 3.92780i | 0.00614172 | − | 0.00617579i | ||||
\(637\) | 258.890 | − | 99.1219i | 0.406421 | − | 0.155607i | ||||
\(638\) | 118.872 | − | 118.872i | 0.186320 | − | 0.186320i | ||||
\(639\) | 6.11703 | + | 1105.69i | 0.00957282 | + | 1.73035i | ||||
\(640\) | 56.5259 | − | 2.19655i | 0.0883217 | − | 0.00343211i | ||||
\(641\) | 124.816i | 0.194721i | 0.995249 | + | 0.0973607i | \(0.0310400\pi\) | ||||
−0.995249 | + | 0.0973607i | \(0.968960\pi\) | |||||||
\(642\) | 480.219 | − | 1.32835i | 0.748005 | − | 0.00206909i | ||||
\(643\) | −160.790 | + | 160.790i | −0.250062 | + | 0.250062i | −0.820996 | − | 0.570934i | \(-0.806581\pi\) |
0.570934 | + | 0.820996i | \(0.306581\pi\) | |||||||
\(644\) | −342.629 | + | 222.295i | −0.532033 | + | 0.345179i | ||||
\(645\) | 953.840 | − | 39.7081i | 1.47882 | − | 0.0615630i | ||||
\(646\) | 605.111 | 0.936705 | ||||||||
\(647\) | −257.644 | + | 257.644i | −0.398213 | + | 0.398213i | −0.877602 | − | 0.479389i | \(-0.840858\pi\) |
0.479389 | + | 0.877602i | \(0.340858\pi\) | |||||||
\(648\) | 160.198 | − | 163.783i | 0.247219 | − | 0.252751i | ||||
\(649\) | −24.5060 | −0.0377597 | ||||||||
\(650\) | 15.5220 | + | 199.419i | 0.0238800 | + | 0.306799i | ||||
\(651\) | −18.8374 | + | 89.6516i | −0.0289362 | + | 0.137714i | ||||
\(652\) | −1.81832 | + | 1.81832i | −0.00278883 | + | 0.00278883i | ||||
\(653\) | −770.307 | + | 770.307i | −1.17964 | + | 1.17964i | −0.199809 | + | 0.979835i | \(0.564032\pi\) |
−0.979835 | + | 0.199809i | \(0.935968\pi\) | |||||||
\(654\) | −582.592 | − | 579.377i | −0.890813 | − | 0.885898i | ||||
\(655\) | 836.054 | + | 773.508i | 1.27642 | + | 1.18093i | ||||
\(656\) | 169.077 | 0.257740 | ||||||||
\(657\) | −117.616 | + | 118.925i | −0.179020 | + | 0.181012i | ||||
\(658\) | −107.037 | + | 502.503i | −0.162671 | + | 0.763683i | ||||
\(659\) | −112.781 | −0.171139 | −0.0855695 | − | 0.996332i | \(-0.527271\pi\) | ||||
−0.0855695 | + | 0.996332i | \(0.527271\pi\) | |||||||
\(660\) | 123.624 | − | 134.364i | 0.187309 | − | 0.203582i | ||||
\(661\) | − | 947.097i | − | 1.43282i | −0.697678 | − | 0.716412i | \(-0.745783\pi\) | ||
0.697678 | − | 0.716412i | \(-0.254217\pi\) | |||||||
\(662\) | −70.4637 | − | 70.4637i | −0.106441 | − | 0.106441i | ||||
\(663\) | 355.655 | − | 0.983792i | 0.536433 | − | 0.00148385i | ||||
\(664\) | 48.8201 | 0.0735242 | ||||||||
\(665\) | 583.980 | − | 411.961i | 0.878165 | − | 0.619491i | ||||
\(666\) | −29.5827 | + | 0.163661i | −0.0444184 | + | 0.000245737i | ||||
\(667\) | −402.911 | + | 402.911i | −0.604064 | + | 0.604064i | ||||
\(668\) | 289.929 | + | 289.929i | 0.434026 | + | 0.434026i | ||||
\(669\) | −812.852 | − | 808.367i | −1.21503 | − | 1.20832i | ||||
\(670\) | 438.352 | + | 405.558i | 0.654256 | + | 0.605310i | ||||
\(671\) | 396.859 | 0.591444 | ||||||||
\(672\) | −64.9322 | − | 99.4777i | −0.0966253 | − | 0.148032i | ||||
\(673\) | −179.988 | − | 179.988i | −0.267441 | − | 0.267441i | 0.560628 | − | 0.828068i | \(-0.310560\pi\) |
−0.828068 | + | 0.560628i | \(0.810560\pi\) | |||||||
\(674\) | 77.6457 | 0.115201 | ||||||||
\(675\) | −672.507 | + | 57.9635i | −0.996306 | + | 0.0858718i | ||||
\(676\) | −273.986 | −0.405304 | ||||||||
\(677\) | 697.081 | − | 697.081i | 1.02966 | − | 1.02966i | 0.0301147 | − | 0.999546i | \(-0.490413\pi\) |
0.999546 | − | 0.0301147i | \(-0.00958726\pi\) | |||||||
\(678\) | 2.16167 | + | 781.474i | 0.00318830 | + | 1.15262i | ||||
\(679\) | −503.448 | + | 326.634i | −0.741455 | + | 0.481051i | ||||
\(680\) | −201.255 | + | 217.528i | −0.295963 | + | 0.319894i | ||||
\(681\) | 131.673 | + | 130.947i | 0.193353 | + | 0.192286i | ||||
\(682\) | −26.5497 | − | 26.5497i | −0.0389292 | − | 0.0389292i | ||||
\(683\) | −443.137 | + | 443.137i | −0.648809 | + | 0.648809i | −0.952705 | − | 0.303896i | \(-0.901712\pi\) |
0.303896 | + | 0.952705i | \(0.401712\pi\) | |||||||
\(684\) | 2.03333 | + | 367.536i | 0.00297270 | + | 0.537333i | ||||
\(685\) | −4.62193 | − | 118.940i | −0.00674734 | − | 0.173636i | ||||
\(686\) | 479.201 | − | 75.2614i | 0.698544 | − | 0.109710i | ||||
\(687\) | 0.619635 | + | 224.007i | 0.000901944 | + | 0.326066i | ||||
\(688\) | 180.014 | + | 180.014i | 0.261648 | + | 0.261648i | ||||
\(689\) | 5.22323i | 0.00758088i | ||||||||
\(690\) | −419.017 | + | 455.419i | −0.607271 | + | 0.660028i | ||||
\(691\) | − | 829.239i | − | 1.20006i | −0.799979 | − | 0.600028i | \(-0.795156\pi\) | ||
0.799979 | − | 0.600028i | \(-0.204844\pi\) | |||||||
\(692\) | −96.4644 | + | 96.4644i | −0.139399 | + | 0.139399i | ||||
\(693\) | −375.447 | − | 77.8046i | −0.541771 | − | 0.112272i | ||||
\(694\) | 274.858i | 0.396050i | ||||||||
\(695\) | −110.257 | − | 102.008i | −0.158643 | − | 0.146774i | ||||
\(696\) | −117.514 | − | 116.866i | −0.168842 | − | 0.167911i | ||||
\(697\) | −626.321 | + | 626.321i | −0.898595 | + | 0.898595i | ||||
\(698\) | −508.928 | − | 508.928i | −0.729123 | − | 0.729123i | ||||
\(699\) | −720.600 | − | 716.624i | −1.03090 | − | 1.02521i | ||||
\(700\) | −46.1327 | + | 346.946i | −0.0659038 | + | 0.495638i | ||||
\(701\) | − | 664.169i | − | 0.947460i | −0.880670 | − | 0.473730i | \(-0.842907\pi\) | ||
0.880670 | − | 0.473730i | \(-0.157093\pi\) | |||||||
\(702\) | 1.79263 | + | 216.017i | 0.00255361 | + | 0.307716i | ||||
\(703\) | 33.5587 | − | 33.5587i | 0.0477364 | − | 0.0477364i | ||||
\(704\) | 48.6888 | 0.0691603 | ||||||||
\(705\) | 32.3803 | + | 777.815i | 0.0459295 | + | 1.10328i | ||||
\(706\) | 411.773i | 0.583248i | ||||||||
\(707\) | −140.454 | + | 659.382i | −0.198662 | + | 0.932648i | ||||
\(708\) | 0.0668278 | + | 24.1593i | 9.43896e−5 | + | 0.0341232i | ||||
\(709\) | 1003.81i | 1.41582i | 0.706304 | + | 0.707909i | \(0.250361\pi\) | ||||
−0.706304 | + | 0.707909i | \(0.749639\pi\) | |||||||
\(710\) | 868.071 | − | 33.7325i | 1.22263 | − | 0.0475106i | ||||
\(711\) | 6.27614 | + | 1134.45i | 0.00882720 | + | 1.59557i | ||||
\(712\) | 194.594 | + | 194.594i | 0.273307 | + | 0.273307i | ||||
\(713\) | 89.9888 | + | 89.9888i | 0.126211 | + | 0.126211i | ||||
\(714\) | 609.031 | + | 127.969i | 0.852984 | + | 0.179228i | ||||
\(715\) | 6.68496 | + | 172.030i | 0.00934959 | + | 0.240602i | ||||
\(716\) | − | 554.075i | − | 0.773847i | ||||||
\(717\) | −0.282344 | − | 102.072i | −0.000393786 | − | 0.142359i | ||||
\(718\) | 51.9892 | + | 51.9892i | 0.0724084 | + | 0.0724084i | ||||
\(719\) | − | 227.010i | − | 0.315731i | −0.987461 | − | 0.157865i | \(-0.949539\pi\) | ||
0.987461 | − | 0.157865i | \(-0.0504612\pi\) | |||||||
\(720\) | −132.800 | − | 121.508i | −0.184444 | − | 0.168761i | ||||
\(721\) | 612.095 | + | 943.437i | 0.848953 | + | 1.30851i | ||||
\(722\) | −55.9344 | − | 55.9344i | −0.0774715 | − | 0.0774715i | ||||
\(723\) | −806.982 | + | 2.23222i | −1.11616 | + | 0.00308745i | ||||
\(724\) | −542.354 | −0.749108 | ||||||||
\(725\) | 37.8922 | + | 486.821i | 0.0522651 | + | 0.671478i | ||||
\(726\) | −251.180 | + | 252.574i | −0.345978 | + | 0.347898i | ||||
\(727\) | −328.738 | − | 328.738i | −0.452184 | − | 0.452184i | 0.443895 | − | 0.896079i | \(-0.353596\pi\) |
−0.896079 | + | 0.443895i | \(0.853596\pi\) | |||||||
\(728\) | 109.555 | + | 23.3360i | 0.150487 | + | 0.0320550i | ||||
\(729\) | −728.900 | + | 12.0985i | −0.999862 | + | 0.0165960i | ||||
\(730\) | 96.4618 | + | 89.2454i | 0.132139 | + | 0.122254i | ||||
\(731\) | −1333.66 | −1.82444 | ||||||||
\(732\) | −1.08223 | − | 391.243i | −0.00147846 | − | 0.534485i | ||||
\(733\) | −320.943 | + | 320.943i | −0.437848 | + | 0.437848i | −0.891287 | − | 0.453439i | \(-0.850197\pi\) |
0.453439 | + | 0.891287i | \(0.350197\pi\) | |||||||
\(734\) | 680.234i | 0.926749i | ||||||||
\(735\) | 674.884 | − | 291.130i | 0.918209 | − | 0.396096i | ||||
\(736\) | −165.028 | −0.224223 | ||||||||
\(737\) | 363.453 | + | 363.453i | 0.493151 | + | 0.493151i | ||||
\(738\) | −382.523 | − | 378.314i | −0.518323 | − | 0.512620i | ||||
\(739\) | − | 742.829i | − | 1.00518i | −0.864524 | − | 0.502591i | \(-0.832380\pi\) | ||
0.864524 | − | 0.502591i | \(-0.167620\pi\) | |||||||
\(740\) | 0.902510 | + | 23.2252i | 0.00121961 | + | 0.0313853i | ||||
\(741\) | −245.732 | − | 244.376i | −0.331622 | − | 0.329792i | ||||
\(742\) | −1.90410 | + | 8.93908i | −0.00256617 | + | 0.0120473i | ||||
\(743\) | −319.664 | + | 319.664i | −0.430234 | + | 0.430234i | −0.888708 | − | 0.458474i | \(-0.848396\pi\) |
0.458474 | + | 0.888708i | \(0.348396\pi\) | |||||||
\(744\) | −26.1016 | + | 26.2464i | −0.0350828 | + | 0.0352774i | ||||
\(745\) | −28.0949 | − | 25.9931i | −0.0377113 | − | 0.0348900i | ||||
\(746\) | − | 371.837i | − | 0.498441i | ||||||
\(747\) | −110.451 | − | 109.236i | −0.147860 | − | 0.146233i | ||||
\(748\) | −180.360 | + | 180.360i | −0.241123 | + | 0.241123i | ||||
\(749\) | −664.686 | + | 431.244i | −0.887431 | + | 0.575759i | ||||
\(750\) | 63.1105 | + | 526.562i | 0.0841474 | + | 0.702082i | ||||
\(751\) | −467.775 | −0.622870 | −0.311435 | − | 0.950267i | \(-0.600810\pi\) | ||||
−0.311435 | + | 0.950267i | \(0.600810\pi\) | |||||||
\(752\) | −146.793 | + | 146.793i | −0.195204 | + | 0.195204i | ||||
\(753\) | −0.147482 | − | 53.3170i | −0.000195860 | − | 0.0708062i | ||||
\(754\) | 156.271 | 0.207257 | ||||||||
\(755\) | −867.896 | − | 802.968i | −1.14953 | − | 1.06353i | ||||
\(756\) | −75.6797 | + | 370.347i | −0.100105 | + | 0.489876i | ||||
\(757\) | −342.526 | + | 342.526i | −0.452478 | + | 0.452478i | −0.896176 | − | 0.443699i | \(-0.853666\pi\) |
0.443699 | + | 0.896176i | \(0.353666\pi\) | |||||||
\(758\) | −123.430 | + | 123.430i | −0.162836 | + | 0.162836i | ||||
\(759\) | −375.598 | + | 377.682i | −0.494860 | + | 0.497605i | ||||
\(760\) | 288.550 | − | 11.2128i | 0.379671 | − | 0.0147537i | ||||
\(761\) | −367.731 | −0.483221 | −0.241611 | − | 0.970373i | \(-0.577676\pi\) | ||||
−0.241611 | + | 0.970373i | \(0.577676\pi\) | |||||||
\(762\) | −0.888006 | − | 321.027i | −0.00116536 | − | 0.421296i | ||||
\(763\) | 1325.89 | + | 282.425i | 1.73773 | + | 0.370151i | ||||
\(764\) | 360.534 | 0.471904 | ||||||||
\(765\) | 942.044 | − | 41.8277i | 1.23143 | − | 0.0546768i | ||||
\(766\) | − | 88.2335i | − | 0.115187i | ||||||
\(767\) | −16.1080 | − | 16.1080i | −0.0210013 | − | 0.0210013i | ||||
\(768\) | −0.132774 | − | 47.9998i | −0.000172883 | − | 0.0624998i | ||||
\(769\) | 217.804 | 0.283230 | 0.141615 | − | 0.989922i | \(-0.454770\pi\) | ||||
0.141615 | + | 0.989922i | \(0.454770\pi\) | |||||||
\(770\) | −51.2720 | + | 296.851i | −0.0665870 | + | 0.385521i | ||||
\(771\) | −467.860 | − | 465.279i | −0.606823 | − | 0.603475i | ||||
\(772\) | 388.814 | − | 388.814i | 0.503645 | − | 0.503645i | ||||
\(773\) | −335.022 | − | 335.022i | −0.433405 | − | 0.433405i | 0.456380 | − | 0.889785i | \(-0.349146\pi\) |
−0.889785 | + | 0.456380i | \(0.849146\pi\) | |||||||
\(774\) | −4.48145 | − | 810.048i | −0.00578998 | − | 1.04657i | ||||
\(775\) | 108.730 | − | 8.46308i | 0.140297 | − | 0.0109201i | ||||
\(776\) | −242.487 | −0.312483 | ||||||||
\(777\) | 40.8730 | − | 26.6791i | 0.0526037 | − | 0.0343360i | ||||
\(778\) | 116.363 | + | 116.363i | 0.149566 | + | 0.149566i | ||||
\(779\) | 863.096 | 1.10795 | ||||||||
\(780\) | 169.578 | − | 7.05948i | 0.217407 | − | 0.00905062i | ||||
\(781\) | 747.717 | 0.957384 | ||||||||
\(782\) | 611.321 | − | 611.321i | 0.781740 | − | 0.781740i | ||||
\(783\) | 4.37617 | + | 527.339i | 0.00558897 | + | 0.673485i | ||||
\(784\) | 178.986 | + | 79.8751i | 0.228298 | + | 0.101881i | ||||
\(785\) | −26.8571 | − | 691.140i | −0.0342129 | − | 0.880433i | ||||
\(786\) | 681.502 | − | 685.283i | 0.867051 | − | 0.871861i | ||||
\(787\) | 264.926 | + | 264.926i | 0.336627 | + | 0.336627i | 0.855096 | − | 0.518469i | \(-0.173498\pi\) |
−0.518469 | + | 0.855096i | \(0.673498\pi\) | |||||||
\(788\) | −157.385 | + | 157.385i | −0.199727 | + | 0.199727i | ||||
\(789\) | −684.453 | − | 680.677i | −0.867495 | − | 0.862709i | ||||
\(790\) | 890.649 | − | 34.6099i | 1.12740 | − | 0.0438100i | ||||
\(791\) | −701.775 | − | 1081.66i | −0.887199 | − | 1.36746i | ||||
\(792\) | −110.154 | − | 108.942i | −0.139084 | − | 0.137553i | ||||
\(793\) | 260.859 | + | 260.859i | 0.328952 | + | 0.328952i | ||||
\(794\) | − | 17.4719i | − | 0.0220050i | ||||||
\(795\) | 0.576016 | + | 13.8366i | 0.000724549 | + | 0.0174046i | ||||
\(796\) | 407.552i | 0.511999i | ||||||||
\(797\) | −708.060 | + | 708.060i | −0.888407 | + | 0.888407i | −0.994370 | − | 0.105963i | \(-0.966207\pi\) |
0.105963 | + | 0.994370i | \(0.466207\pi\) | |||||||
\(798\) | −331.462 | − | 507.808i | −0.415366 | − | 0.636351i | ||||
\(799\) | − | 1087.55i | − | 1.36113i | ||||||
\(800\) | −91.9383 | + | 107.459i | −0.114923 | + | 0.134323i | ||||
\(801\) | −4.84443 | − | 875.661i | −0.00604798 | − | 1.09321i | ||||
\(802\) | 27.9968 | − | 27.9968i | 0.0349087 | − | 0.0349087i | ||||
\(803\) | 79.9799 | + | 79.9799i | 0.0996013 | + | 0.0996013i | ||||
\(804\) | 357.318 | − | 359.300i | 0.444426 | − | 0.446891i | ||||
\(805\) | 173.784 | − | 1006.16i | 0.215880 | − | 1.24989i | ||||
\(806\) | − | 34.9027i | − | 0.0433036i | ||||||
\(807\) | 269.212 | − | 0.744679i | 0.333597 | − | 0.000922774i | ||||
\(808\) | −192.622 | + | 192.622i | −0.238393 | + | 0.238393i | ||||
\(809\) | −1263.12 | −1.56133 | −0.780666 | − | 0.624949i | \(-0.785120\pi\) | ||||
−0.780666 | + | 0.624949i | \(0.785120\pi\) | |||||||
\(810\) | 28.5711 | + | 572.043i | 0.0352729 | + | 0.706226i | ||||
\(811\) | 26.8053i | 0.0330522i | 0.999863 | + | 0.0165261i | \(0.00526066\pi\) | ||||
−0.999863 | + | 0.0165261i | \(0.994739\pi\) | |||||||
\(812\) | 267.444 | + | 56.9679i | 0.329365 | + | 0.0701575i | ||||
\(813\) | 955.031 | − | 2.64175i | 1.17470 | − | 0.00324938i | ||||
\(814\) | 20.0051i | 0.0245763i | ||||||||
\(815\) | −0.249627 | − | 6.42388i | −0.000306290 | − | 0.00788206i | ||||
\(816\) | 178.300 | + | 177.316i | 0.218505 | + | 0.217299i | ||||
\(817\) | 918.923 | + | 918.923i | 1.12475 | + | 1.12475i | ||||
\(818\) | −234.500 | − | 234.500i | −0.286675 | − | 0.286675i | ||||
\(819\) | −195.643 | − | 297.926i | −0.238880 | − | 0.363768i | ||||
\(820\) | −287.058 | + | 310.270i | −0.350071 | + | 0.378378i | ||||
\(821\) | 180.354i | 0.219677i | 0.993949 | + | 0.109838i | \(0.0350333\pi\) | ||||
−0.993949 | + | 0.109838i | \(0.964967\pi\) | |||||||
\(822\) | −101.000 | + | 0.279380i | −0.122871 | + | 0.000339879i | ||||
\(823\) | 138.696 | + | 138.696i | 0.168525 | + | 0.168525i | 0.786331 | − | 0.617806i | \(-0.211978\pi\) |
−0.617806 | + | 0.786331i | \(0.711978\pi\) | |||||||
\(824\) | 454.408i | 0.551467i | ||||||||
\(825\) | 36.6803 | + | 454.982i | 0.0444610 | + | 0.551493i | ||||
\(826\) | −21.6953 | − | 33.4395i | −0.0262656 | − | 0.0404837i | ||||
\(827\) | −219.678 | − | 219.678i | −0.265633 | − | 0.265633i | 0.561705 | − | 0.827338i | \(-0.310146\pi\) |
−0.827338 | + | 0.561705i | \(0.810146\pi\) | |||||||
\(828\) | 373.362 | + | 369.253i | 0.450920 | + | 0.445958i | ||||
\(829\) | 459.488 | 0.554268 | 0.277134 | − | 0.960831i | \(-0.410615\pi\) | ||||
0.277134 | + | 0.960831i | \(0.410615\pi\) | |||||||
\(830\) | −82.8863 | + | 89.5886i | −0.0998631 | + | 0.107938i | ||||
\(831\) | −196.816 | − | 195.730i | −0.236842 | − | 0.235536i | ||||
\(832\) | 32.0036 | + | 32.0036i | 0.0384658 | + | 0.0384658i | ||||
\(833\) | −958.910 | + | 367.141i | −1.15115 | + | 0.440745i | ||||
\(834\) | −89.8746 | + | 90.3732i | −0.107763 | + | 0.108361i | ||||
\(835\) | −1024.28 | + | 39.8027i | −1.22668 | + | 0.0476679i | ||||
\(836\) | 248.544 | 0.297301 | ||||||||
\(837\) | 117.779 | − | 0.977402i | 0.140716 | − | 0.00116774i | ||||
\(838\) | 339.624 | − | 339.624i | 0.405279 | − | 0.405279i | ||||
\(839\) | 122.197i | 0.145646i | 0.997345 | + | 0.0728232i | \(0.0232009\pi\) | ||||
−0.997345 | + | 0.0728232i | \(0.976799\pi\) | |||||||
\(840\) | 292.790 | + | 49.7369i | 0.348560 | + | 0.0592106i | ||||
\(841\) | −459.511 | −0.546386 | ||||||||
\(842\) | −699.038 | − | 699.038i | −0.830211 | − | 0.830211i | ||||
\(843\) | 1293.63 | − | 3.57836i | 1.53456 | − | 0.00424479i | ||||
\(844\) | − | 535.089i | − | 0.633992i | ||||||
\(845\) | 465.171 | − | 502.785i | 0.550498 | − | 0.595011i | ||||
\(846\) | 660.560 | − | 3.65443i | 0.780804 | − | 0.00431965i | ||||
\(847\) | 122.441 | − | 574.820i | 0.144559 | − | 0.678654i | ||||
\(848\) | −2.61132 | + | 2.61132i | −0.00307939 | + | 0.00307939i | ||||
\(849\) | −505.831 | − | 503.040i | −0.595796 | − | 0.592509i | ||||
\(850\) | −57.4923 | − | 738.635i | −0.0676380 | − | 0.868982i | ||||
\(851\) | − | 67.8062i | − | 0.0796782i | ||||||
\(852\) | −2.03902 | − | 737.135i | −0.00239321 | − | 0.865183i | ||||
\(853\) | −80.0867 | + | 80.0867i | −0.0938883 | + | 0.0938883i | −0.752491 | − | 0.658603i | \(-0.771148\pi\) |
0.658603 | + | 0.752491i | \(0.271148\pi\) | |||||||
\(854\) | 351.342 | + | 541.531i | 0.411407 | + | 0.634111i | ||||
\(855\) | −677.908 | − | 620.268i | −0.792875 | − | 0.725460i | ||||
\(856\) | −320.147 | −0.374004 | ||||||||
\(857\) | 93.1855 | − | 93.1855i | 0.108735 | − | 0.108735i | −0.650646 | − | 0.759381i | \(-0.725502\pi\) |
0.759381 | + | 0.650646i | \(0.225502\pi\) | |||||||
\(858\) | 146.082 | − | 0.404084i | 0.170259 | − | 0.000470960i | ||||
\(859\) | −885.439 | −1.03078 | −0.515389 | − | 0.856956i | \(-0.672353\pi\) | ||||
−0.515389 | + | 0.856956i | \(0.672353\pi\) | |||||||
\(860\) | −635.964 | + | 24.7130i | −0.739493 | + | 0.0287361i | ||||
\(861\) | 868.687 | + | 182.527i | 1.00893 | + | 0.211994i | ||||
\(862\) | −590.362 | + | 590.362i | −0.684875 | + | 0.684875i | ||||
\(863\) | 611.055 | − | 611.055i | 0.708060 | − | 0.708060i | −0.258067 | − | 0.966127i | \(-0.583086\pi\) |
0.966127 | + | 0.258067i | \(0.0830857\pi\) | |||||||
\(864\) | −107.100 | + | 108.892i | −0.123958 | + | 0.126033i | ||||
\(865\) | −13.2431 | − | 340.796i | −0.0153099 | − | 0.393984i | ||||
\(866\) | 680.214 | 0.785466 | ||||||||
\(867\) | −450.326 | + | 1.24567i | −0.519408 | + | 0.00143675i | ||||
\(868\) | 12.7236 | − | 59.7328i | 0.0146585 | − | 0.0688166i | ||||
\(869\) | 767.165 | 0.882814 | ||||||||
\(870\) | 413.972 | − | 17.2336i | 0.475830 | − | 0.0198087i | ||||
\(871\) | 477.801i | 0.548566i | ||||||||
\(872\) | 387.324 | + | 387.324i | 0.444179 | + | 0.444179i | ||||
\(873\) | 548.605 | + | 542.569i | 0.628414 | + | 0.621499i | ||||
\(874\) | −842.426 | −0.963874 | ||||||||
\(875\) | −558.349 | − | 673.700i | −0.638113 | − | 0.769942i | ||||
\(876\) | 78.6299 | − | 79.0661i | 0.0897602 | − | 0.0902582i | ||||
\(877\) | −176.159 | + | 176.159i | −0.200866 | + | 0.200866i | −0.800371 | − | 0.599505i | \(-0.795364\pi\) |
0.599505 | + | 0.800371i | \(0.295364\pi\) | |||||||
\(878\) | 732.833 | + | 732.833i | 0.834661 | + | 0.834661i | ||||
\(879\) | 786.628 | − | 790.992i | 0.894913 | − | 0.899877i | ||||
\(880\) | −82.6635 | + | 89.3477i | −0.0939358 | + | 0.101531i | ||||
\(881\) | 796.181 | 0.903724 | 0.451862 | − | 0.892088i | \(-0.350760\pi\) | ||||
0.451862 | + | 0.892088i | \(0.350760\pi\) | |||||||
\(882\) | −226.218 | − | 581.195i | −0.256483 | − | 0.658951i | ||||
\(883\) | −1116.28 | − | 1116.28i | −1.26419 | − | 1.26419i | −0.949043 | − | 0.315146i | \(-0.897946\pi\) |
−0.315146 | − | 0.949043i | \(-0.602054\pi\) | |||||||
\(884\) | −237.105 | −0.268218 | ||||||||
\(885\) | −44.4475 | − | 40.8947i | −0.0502232 | − | 0.0462087i | ||||
\(886\) | 221.979 | 0.250541 | ||||||||
\(887\) | 992.100 | − | 992.100i | 1.11849 | − | 1.11849i | 0.126525 | − | 0.991963i | \(-0.459617\pi\) |
0.991963 | − | 0.126525i | \(-0.0403825\pi\) | |||||||
\(888\) | 19.7220 | − | 0.0545538i | 0.0222095 | − | 6.14344e-5i | ||||
\(889\) | 288.287 | + | 444.343i | 0.324282 | + | 0.499824i | ||||
\(890\) | −687.476 | + | 26.7147i | −0.772445 | + | 0.0300166i | ||||
\(891\) | 5.45442 | + | 492.944i | 0.00612168 | + | 0.553248i | ||||
\(892\) | 540.408 | + | 540.408i | 0.605839 | + | 0.605839i | ||||
\(893\) | −749.342 | + | 749.342i | −0.839129 | + | 0.839129i | ||||
\(894\) | −22.9013 | + | 23.0283i | −0.0256166 | + | 0.0257588i | ||||
\(895\) | 1016.77 | + | 940.703i | 1.13605 | + | 1.05107i | ||||
\(896\) | 43.1045 | + | 66.4380i | 0.0481077 | + | 0.0741495i | ||||
\(897\) | −495.138 | + | 1.36962i | −0.551993 | + | 0.00152689i | ||||
\(898\) | −196.292 | − | 196.292i | −0.218588 | − | 0.218588i | ||||
\(899\) | − | 85.2043i | − | 0.0947767i | ||||||
\(900\) | 448.443 | − | 37.4020i | 0.498270 | − | 0.0415578i | ||||
\(901\) | − | 19.3465i | − | 0.0214722i | ||||||
\(902\) | −257.255 | + | 257.255i | −0.285206 | + | 0.285206i | ||||
\(903\) | 730.542 | + | 1119.21i | 0.809016 | + | 1.23943i | ||||
\(904\) | − | 520.985i | − | 0.576311i | ||||||
\(905\) | 920.805 | − | 995.261i | 1.01746 | − | 1.09974i | ||||
\(906\) | −707.458 | + | 711.382i | −0.780858 | + | 0.785190i | ||||
\(907\) | −718.497 | + | 718.497i | −0.792169 | + | 0.792169i | −0.981846 | − | 0.189678i | \(-0.939256\pi\) |
0.189678 | + | 0.981846i | \(0.439256\pi\) | |||||||
\(908\) | −87.5405 | − | 87.5405i | −0.0964103 | − | 0.0964103i | ||||
\(909\) | 866.784 | − | 4.79532i | 0.953557 | − | 0.00527538i | ||||
\(910\) | −228.824 | + | 161.421i | −0.251455 | + | 0.177386i | ||||
\(911\) | 142.178i | 0.156068i | 0.996951 | + | 0.0780339i | \(0.0248642\pi\) | ||||
−0.996951 | + | 0.0780339i | \(0.975136\pi\) | |||||||
\(912\) | −0.677778 | − | 245.027i | −0.000743177 | − | 0.268670i | ||||
\(913\) | −74.2810 | + | 74.2810i | −0.0813593 | + | 0.0813593i | ||||
\(914\) | −104.860 | −0.114726 | ||||||||
\(915\) | 719.798 | + | 662.263i | 0.786664 | + | 0.723785i | ||||
\(916\) | − | 149.339i | − | 0.163034i | ||||||
\(917\) | −332.207 | + | 1559.60i | −0.362276 | + | 1.70076i | ||||
\(918\) | −6.63979 | − | 800.111i | −0.00723288 | − | 0.871580i | ||||
\(919\) | − | 722.274i | − | 0.785934i | −0.919553 | − | 0.392967i | \(-0.871449\pi\) | ||
0.919553 | − | 0.392967i | \(-0.128551\pi\) | |||||||
\(920\) | 280.183 | − | 302.839i | 0.304547 | − | 0.329173i | ||||
\(921\) | −1096.84 | + | 1102.92i | −1.19092 | + | 1.19753i | ||||
\(922\) | −549.751 | − | 549.751i | −0.596259 | − | 0.596259i | ||||
\(923\) | 491.480 | + | 491.480i | 0.532481 | + | 0.532481i | ||||
\(924\) | 250.154 | + | 52.5619i | 0.270729 | + | 0.0568852i | ||||
\(925\) | −44.1522 | − | 37.7753i | −0.0477321 | − | 0.0408382i | ||||
\(926\) | − | 666.069i | − | 0.719298i | ||||||
\(927\) | 1016.75 | − | 1028.06i | 1.09681 | − | 1.10902i | ||||
\(928\) | 78.1270 | + | 78.1270i | 0.0841886 | + | 0.0841886i | ||||
\(929\) | 274.997i | 0.296014i | 0.988986 | + | 0.148007i | \(0.0472858\pi\) | ||||
−0.988986 | + | 0.148007i | \(0.952714\pi\) | |||||||
\(930\) | −3.84906 | − | 92.4593i | −0.00413878 | − | 0.0994186i | ||||
\(931\) | 913.677 | + | 407.742i | 0.981393 | + | 0.437961i | ||||
\(932\) | 479.077 | + | 479.077i | 0.514031 | + | 0.514031i | ||||
\(933\) | −0.944017 | − | 341.276i | −0.00101181 | − | 0.365784i | ||||
\(934\) | 19.0795 | 0.0204277 | ||||||||
\(935\) | −24.7606 | − | 637.189i | −0.0264820 | − | 0.681485i | ||||
\(936\) | −0.796731 | − | 144.014i | −0.000851208 | − | 0.153861i | ||||
\(937\) | −658.299 | − | 658.299i | −0.702560 | − | 0.702560i | 0.262399 | − | 0.964959i | \(-0.415486\pi\) |
−0.964959 | + | 0.262399i | \(0.915486\pi\) | |||||||
\(938\) | −174.180 | + | 817.713i | −0.185693 | + | 0.871763i | ||||
\(939\) | −805.200 | − | 800.758i | −0.857508 | − | 0.852777i | ||||
\(940\) | −20.1524 | − | 518.601i | −0.0214387 | − | 0.551704i | ||||
\(941\) | 1599.56 | 1.69985 | 0.849923 | − | 0.526907i | \(-0.176648\pi\) | ||||
0.849923 | + | 0.526907i | \(0.176648\pi\) | |||||||
\(942\) | −586.892 | + | 1.62342i | −0.623027 | + | 0.00172338i | ||||
\(943\) | 871.953 | − | 871.953i | 0.924659 | − | 0.924659i | ||||
\(944\) | − | 16.1062i | − | 0.0170617i | ||||||
\(945\) | −551.126 | − | 767.649i | −0.583202 | − | 0.812327i | ||||
\(946\) | −547.790 | −0.579060 | ||||||||
\(947\) | 135.247 | + | 135.247i | 0.142816 | + | 0.142816i | 0.774900 | − | 0.632084i | \(-0.217800\pi\) |
−0.632084 | + | 0.774900i | \(0.717800\pi\) | |||||||
\(948\) | −2.09205 | − | 756.309i | −0.00220681 | − | 0.797794i | ||||
\(949\) | 105.143i | 0.110793i | ||||||||
\(950\) | −469.322 | + | 548.548i | −0.494023 | + | 0.577419i | ||||
\(951\) | −645.128 | + | 648.707i | −0.678368 | + | 0.682132i | ||||
\(952\) | −405.783 | − | 86.4351i | −0.426243 | − | 0.0907932i | ||||
\(953\) | 1333.30 | − | 1333.30i | 1.39905 | − | 1.39905i | 0.596269 | − | 0.802784i | \(-0.296649\pi\) |
0.802784 | − | 0.596269i | \(-0.203351\pi\) | |||||||
\(954\) | 11.7508 | − | 0.0650090i | 0.0123174 | − | 6.81436e-5i | ||||
\(955\) | −612.112 | + | 661.608i | −0.640955 | + | 0.692783i | ||||
\(956\) | 68.0480i | 0.0711799i | ||||||||
\(957\) | 356.615 | − | 0.986447i | 0.372639 | − | 0.00103077i | ||||
\(958\) | 30.2411 | − | 30.2411i | 0.0315670 | − | 0.0315670i | ||||
\(959\) | 139.797 | − | 90.6995i | 0.145774 | − | 0.0945772i | ||||
\(960\) | 88.3087 | + | 81.2500i | 0.0919883 | + | 0.0846355i | ||||
\(961\) | 941.970 | 0.980198 | ||||||||
\(962\) | −13.1495 | + | 13.1495i | −0.0136689 | + | 0.0136689i | ||||
\(963\) | 724.306 | + | 716.336i | 0.752135 | + | 0.743858i | ||||
\(964\) | 537.990 | 0.558081 | ||||||||
\(965\) | 53.3780 | + | 1373.63i | 0.0553140 | + | 1.42345i | ||||
\(966\) | −847.883 | − | 178.156i | −0.877725 | − | 0.184426i | ||||
\(967\) | 546.204 | − | 546.204i | 0.564844 | − | 0.564844i | −0.365835 | − | 0.930680i | \(-0.619217\pi\) |
0.930680 | + | 0.365835i | \(0.119217\pi\) | |||||||
\(968\) | 167.919 | − | 167.919i | 0.173470 | − | 0.173470i | ||||
\(969\) | 910.174 | + | 905.153i | 0.939292 | + | 0.934110i | ||||
\(970\) | 411.692 | − | 444.982i | 0.424425 | − | 0.458744i | ||||
\(971\) | −527.389 | −0.543140 | −0.271570 | − | 0.962419i | \(-0.587543\pi\) | ||||
−0.271570 | + | 0.962419i | \(0.587543\pi\) | |||||||
\(972\) | 485.954 | − | 6.72148i | 0.499952 | − | 0.00691511i | ||||
\(973\) | 43.8106 | − | 205.676i | 0.0450263 | − | 0.211383i | ||||
\(974\) | 499.374 | 0.512704 | ||||||||
\(975\) | −274.953 | + | 323.173i | −0.282003 | + | 0.331460i | ||||
\(976\) | 260.830i | 0.267243i | ||||||||
\(977\) | 1236.41 | + | 1236.41i | 1.26551 | + | 1.26551i | 0.948381 | + | 0.317134i | \(0.102720\pi\) |
0.317134 | + | 0.948381i | \(0.397280\pi\) | |||||||
\(978\) | −5.45493 | + | 0.0150891i | −0.00557764 | + | 1.54285e-5i | ||||
\(979\) | −592.160 | −0.604862 | ||||||||
\(980\) | −450.458 | + | 192.842i | −0.459651 | + | 0.196777i | ||||
\(981\) | −9.64246 | − | 1742.93i | −0.00982922 | − | 1.77669i | ||||
\(982\) | 775.321 | − | 775.321i | 0.789533 | − | 0.789533i | ||||
\(983\) | −668.454 | − | 668.454i | −0.680014 | − | 0.680014i | 0.279989 | − | 0.960003i | \(-0.409669\pi\) |
−0.960003 | + | 0.279989i | \(0.909669\pi\) | |||||||
\(984\) | 254.317 | + | 252.913i | 0.258452 | + | 0.257026i | ||||
\(985\) | −21.6065 | − | 556.021i | −0.0219355 | − | 0.564488i | ||||
\(986\) | −578.819 | −0.587037 | ||||||||
\(987\) | −912.666 | + | 595.726i | −0.924687 | + | 0.603572i | ||||
\(988\) | 163.370 | + | 163.370i | 0.165354 | + | 0.165354i | ||||
\(989\) | 1856.71 | 1.87736 | ||||||||
\(990\) | 386.936 | − | 17.1804i | 0.390844 | − | 0.0173539i | ||||
\(991\) | 486.244 | 0.490660 | 0.245330 | − | 0.969440i | \(-0.421104\pi\) | ||||
0.245330 | + | 0.969440i | \(0.421104\pi\) | |||||||
\(992\) | 17.4494 | − | 17.4494i | 0.0175901 | − | 0.0175901i | ||||
\(993\) | −0.584735 | − | 211.390i | −0.000588857 | − | 0.212880i | ||||
\(994\) | 661.958 | + | 1020.29i | 0.665954 | + | 1.02645i | ||||
\(995\) | −747.888 | − | 691.938i | −0.751646 | − | 0.695415i | ||||
\(996\) | 73.4324 | + | 73.0273i | 0.0737273 | + | 0.0733206i | ||||
\(997\) | −686.852 | − | 686.852i | −0.688918 | − | 0.688918i | 0.273074 | − | 0.961993i | \(-0.411959\pi\) |
−0.961993 | + | 0.273074i | \(0.911959\pi\) | |||||||
\(998\) | −596.688 | + | 596.688i | −0.597884 | + | 0.597884i | ||||
\(999\) | −44.7414 | − | 44.0049i | −0.0447861 | − | 0.0440489i |
(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 | 210.3.k.a.83.8 | ✓ | 32 | |
3.2 | odd | 2 | 210.3.k.b.83.16 | yes | 32 | ||
5.2 | odd | 4 | 210.3.k.b.167.1 | yes | 32 | ||
7.6 | odd | 2 | inner | 210.3.k.a.83.9 | yes | 32 | |
15.2 | even | 4 | inner | 210.3.k.a.167.9 | yes | 32 | |
21.20 | even | 2 | 210.3.k.b.83.1 | yes | 32 | ||
35.27 | even | 4 | 210.3.k.b.167.16 | yes | 32 | ||
105.62 | odd | 4 | inner | 210.3.k.a.167.8 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.k.a.83.8 | ✓ | 32 | 1.1 | even | 1 | trivial | |
210.3.k.a.83.9 | yes | 32 | 7.6 | odd | 2 | inner | |
210.3.k.a.167.8 | yes | 32 | 105.62 | odd | 4 | inner | |
210.3.k.a.167.9 | yes | 32 | 15.2 | even | 4 | inner | |
210.3.k.b.83.1 | yes | 32 | 21.20 | even | 2 | ||
210.3.k.b.83.16 | yes | 32 | 3.2 | odd | 2 | ||
210.3.k.b.167.1 | yes | 32 | 5.2 | odd | 4 | ||
210.3.k.b.167.16 | yes | 32 | 35.27 | even | 4 |