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 | 167.1 | ||
Character | \(\chi\) | \(=\) | 210.167 |
Dual form | 210.3.k.b.83.1 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||
\(3\) | −2.99999 | + | 0.00829838i | −0.999996 | + | 0.00276613i | ||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | −3.67015 | + | 3.39558i | −0.734030 | + | 0.679117i | ||||
\(6\) | −2.99169 | + | 3.00829i | −0.498615 | + | 0.501381i | ||||
\(7\) | 6.84640 | + | 1.45834i | 0.978058 | + | 0.208334i | ||||
\(8\) | −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 | \(0.910779\pi\) | |||||||
\(12\) | 0.0165968 | + | 5.99998i | 0.00138306 | + | 0.499998i | ||||
\(13\) | 4.00045 | + | 4.00045i | 0.307727 | + | 0.307727i | 0.844027 | − | 0.536300i | \(-0.180179\pi\) |
−0.536300 | + | 0.844027i | \(0.680179\pi\) | |||||||
\(14\) | 8.30474 | − | 5.38806i | 0.593196 | − | 0.384862i | ||||
\(15\) | 10.9822 | − | 10.2172i | 0.732149 | − | 0.681144i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 14.8174 | + | 14.8174i | 0.871610 | + | 0.871610i | 0.992648 | − | 0.121037i | \(-0.0386221\pi\) |
−0.121037 | + | 0.992648i | \(0.538622\pi\) | |||||||
\(18\) | 8.95007 | − | 9.04965i | 0.497226 | − | 0.502758i | ||||
\(19\) | 20.4190 | 1.07468 | 0.537341 | − | 0.843365i | \(-0.319429\pi\) | ||||
0.537341 | + | 0.843365i | \(0.319429\pi\) | |||||||
\(20\) | 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 | \(-0.0313303\pi\) |
−0.0982681 | + | 0.995160i | \(0.531330\pi\) | |||||||
\(24\) | 6.01657 | + | 5.98338i | 0.250691 | + | 0.249308i | ||||
\(25\) | 1.94003 | − | 24.9246i | 0.0776012 | − | 0.996984i | ||||
\(26\) | 8.00089 | 0.307727 | ||||||||
\(27\) | −26.9991 | + | 0.224054i | −0.999966 | + | 0.00829830i | ||||
\(28\) | 2.91668 | − | 13.6928i | 0.104167 | − | 0.489029i | ||||
\(29\) | −19.5317 | −0.673508 | −0.336754 | − | 0.941593i | \(-0.609329\pi\) | ||||
−0.336754 | + | 0.941593i | \(0.609329\pi\) | |||||||
\(30\) | 0.765069 | − | 21.1994i | 0.0255023 | − | 0.706647i | ||||
\(31\) | − | 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 | ||||
\(33\) | −0.0505048 | − | 18.2582i | −0.00153045 | − | 0.553280i | ||||
\(34\) | 29.6348 | 0.871610 | ||||||||
\(35\) | −30.0793 | + | 17.8952i | −0.859407 | + | 0.511292i | ||||
\(36\) | −0.0995802 | − | 17.9997i | −0.00276612 | − | 0.499992i | ||||
\(37\) | −1.64351 | − | 1.64351i | −0.0444191 | − | 0.0444191i | 0.684548 | − | 0.728967i | \(-0.259999\pi\) |
−0.728967 | + | 0.684548i | \(0.759999\pi\) | |||||||
\(38\) | 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 | \(0.672386\pi\) | |||||||
\(42\) | −24.8694 | + | 16.2330i | −0.592129 | + | 0.386501i | ||||
\(43\) | −45.0034 | + | 45.0034i | −1.04659 | + | 1.04659i | −0.0477300 | + | 0.998860i | \(0.515199\pi\) |
−0.998860 | + | 0.0477300i | \(0.984801\pi\) | |||||||
\(44\) | 12.1722 | 0.276641 | ||||||||
\(45\) | −32.8618 | + | 30.7425i | −0.730262 | + | 0.683167i | ||||
\(46\) | 41.2570 | 0.896892 | ||||||||
\(47\) | 36.6983 | + | 36.6983i | 0.780815 | + | 0.780815i | 0.979968 | − | 0.199153i | \(-0.0638191\pi\) |
−0.199153 | + | 0.979968i | \(0.563819\pi\) | |||||||
\(48\) | 12.0000 | − | 0.0331935i | 0.249999 | − | 0.000691532i | ||||
\(49\) | 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 | \(-0.252772\pi\) |
−0.713239 | + | 0.700921i | \(0.752772\pi\) | |||||||
\(54\) | −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 | ||||
\(57\) | −61.2567 | + | 0.169444i | −1.07468 | + | 0.00297271i | ||||
\(58\) | −19.5317 | + | 19.5317i | −0.336754 | + | 0.336754i | ||||
\(59\) | − | 4.02656i | − | 0.0682467i | −0.999418 | − | 0.0341234i | \(-0.989136\pi\) | ||
0.999418 | − | 0.0341234i | \(-0.0108639\pi\) | |||||||
\(60\) | −20.4343 | − | 21.9645i | −0.340572 | − | 0.366075i | ||||
\(61\) | − | 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 | ||||
\(63\) | 61.6893 | + | 12.7840i | 0.979195 | + | 0.202920i | ||||
\(64\) | 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 | 0.994647 | − | 0.103327i | \(-0.0329489\pi\) |
−0.103327 | + | 0.994647i | \(0.532949\pi\) | |||||||
\(68\) | 29.6348 | − | 29.6348i | 0.435805 | − | 0.435805i | ||||
\(69\) | −62.0565 | − | 61.7141i | −0.899369 | − | 0.894408i | ||||
\(70\) | −12.1841 | + | 47.9745i | −0.174058 | + | 0.685349i | ||||
\(71\) | − | 122.856i | − | 1.73037i | −0.501451 | − | 0.865186i | \(-0.667200\pi\) | ||
0.501451 | − | 0.865186i | \(-0.332800\pi\) | |||||||
\(72\) | −18.0993 | − | 17.9001i | −0.251379 | − | 0.248613i | ||||
\(73\) | −13.1414 | − | 13.1414i | −0.180019 | − | 0.180019i | 0.611345 | − | 0.791364i | \(-0.290629\pi\) |
−0.791364 | + | 0.611345i | \(0.790629\pi\) | |||||||
\(74\) | −3.28701 | −0.0444191 | ||||||||
\(75\) | −5.61323 | + | 74.7896i | −0.0748431 | + | 0.997195i | ||||
\(76\) | − | 40.8379i | − | 0.537341i | ||||||
\(77\) | −8.87561 | + | 41.6679i | −0.115268 | + | 0.541142i | ||||
\(78\) | −24.0026 | + | 0.0663945i | −0.307725 | + | 0.000851211i | ||||
\(79\) | 126.052i | 1.59559i | 0.602926 | + | 0.797797i | \(0.294001\pi\) | ||||
−0.602926 | + | 0.797797i | \(0.705999\pi\) | |||||||
\(80\) | 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 | −0.629750 | − | 0.776798i | \(-0.716843\pi\) |
0.776798 | + | 0.629750i | \(0.216843\pi\) | |||||||
\(84\) | −8.63638 | + | 41.1025i | −0.102814 | + | 0.489315i | ||||
\(85\) | −104.696 | − | 4.06839i | −1.23171 | − | 0.0478634i | ||||
\(86\) | 90.0068i | 1.04659i | ||||||||
\(87\) | 58.5950 | − | 0.162082i | 0.673506 | − | 0.00186301i | ||||
\(88\) | 12.1722 | − | 12.1722i | 0.138321 | − | 0.138321i | ||||
\(89\) | − | 97.2971i | − | 1.09323i | −0.837385 | − | 0.546613i | \(-0.815917\pi\) | ||
0.837385 | − | 0.546613i | \(-0.184083\pi\) | |||||||
\(90\) | −2.11928 | + | 63.6043i | −0.0235475 | + | 0.706715i | ||||
\(91\) | 21.5547 | + | 33.2227i | 0.236864 | + | 0.365084i | ||||
\(92\) | 41.2570 | − | 41.2570i | 0.448446 | − | 0.448446i | ||||
\(93\) | 0.0362004 | + | 13.0870i | 0.000389252 | + | 0.140720i | ||||
\(94\) | 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 | \(-0.604298\pi\) |
0.946797 | + | 0.321831i | \(0.104298\pi\) | |||||||
\(98\) | 64.7153 | − | 24.7777i | 0.660360 | − | 0.252834i | ||||
\(99\) | 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 | \(0.658198\pi\) | |||||||
\(102\) | −88.9039 | + | 0.245921i | −0.871607 | + | 0.00241099i | ||||
\(103\) | 113.602 | + | 113.602i | 1.10293 | + | 1.10293i | 0.994055 | + | 0.108878i | \(0.0347258\pi\) |
0.108878 | + | 0.994055i | \(0.465274\pi\) | |||||||
\(104\) | − | 16.0018i | − | 0.153863i | ||||||
\(105\) | 90.0889 | − | 53.9350i | 0.857990 | − | 0.513667i | ||||
\(106\) | −1.30566 | −0.0123176 | ||||||||
\(107\) | 80.0368 | − | 80.0368i | 0.748008 | − | 0.748008i | −0.226097 | − | 0.974105i | \(-0.572597\pi\) |
0.974105 | + | 0.226097i | \(0.0725966\pi\) | |||||||
\(108\) | 0.448108 | + | 53.9981i | 0.00414915 | + | 0.499983i | ||||
\(109\) | − | 193.662i | − | 1.77672i | −0.459150 | − | 0.888359i | \(-0.651846\pi\) | ||
0.459150 | − | 0.888359i | \(-0.348154\pi\) | |||||||
\(110\) | −43.0028 | − | 1.67105i | −0.390934 | − | 0.0151914i | ||||
\(111\) | 4.94414 | + | 4.91686i | 0.0445418 | + | 0.0442960i | ||||
\(112\) | −27.3856 | − | 5.83336i | −0.244514 | − | 0.0520836i | ||||
\(113\) | −130.246 | − | 130.246i | −1.15262 | − | 1.15262i | −0.986025 | − | 0.166596i | \(-0.946722\pi\) |
−0.166596 | − | 0.986025i | \(-0.553278\pi\) | |||||||
\(114\) | −61.0872 | + | 61.4261i | −0.535853 | + | 0.538826i | ||||
\(115\) | −145.756 | − | 5.66394i | −1.26744 | − | 0.0492517i | ||||
\(116\) | 39.0635i | 0.336754i | ||||||||
\(117\) | 36.2026 | + | 35.8043i | 0.309424 | + | 0.306020i | ||||
\(118\) | −4.02656 | − | 4.02656i | −0.0341234 | − | 0.0341234i | ||||
\(119\) | 79.8370 | + | 123.055i | 0.670899 | + | 1.03407i | ||||
\(120\) | −42.3988 | − | 1.53014i | −0.353323 | − | 0.0127511i | ||||
\(121\) | 83.9594 | 0.693879 | ||||||||
\(122\) | −65.2074 | − | 65.2074i | −0.534487 | − | 0.534487i | ||||
\(123\) | 126.807 | − | 0.350767i | 1.03096 | − | 0.00285176i | ||||
\(124\) | −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 | 0.464353 | − | 0.885650i | \(-0.346287\pi\) |
−0.885650 | + | 0.464353i | \(0.846287\pi\) | |||||||
\(128\) | 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 | \(0.835532\pi\) | |||||||
\(132\) | −36.5165 | + | 0.101010i | −0.276640 | + | 0.000765224i | ||||
\(133\) | 139.797 | + | 29.7778i | 1.05110 | + | 0.223893i | ||||
\(134\) | 119.437 | 0.891320 | ||||||||
\(135\) | 98.3299 | − | 92.4999i | 0.728370 | − | 0.685184i | ||||
\(136\) | − | 59.2695i | − | 0.435805i | ||||||
\(137\) | −16.8334 | + | 16.8334i | −0.122872 | + | 0.122872i | −0.765869 | − | 0.642997i | \(-0.777691\pi\) |
0.642997 | + | 0.765869i | \(0.277691\pi\) | |||||||
\(138\) | −123.771 | + | 0.342367i | −0.896888 | + | 0.00248092i | ||||
\(139\) | −30.0414 | −0.216125 | −0.108063 | − | 0.994144i | \(-0.534465\pi\) | ||||
−0.108063 | + | 0.994144i | \(0.534465\pi\) | |||||||
\(140\) | 35.7904 | + | 60.1585i | 0.255646 | + | 0.429704i | ||||
\(141\) | −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 | ||||||||
\(147\) | −134.405 | − | 59.5348i | −0.914317 | − | 0.404998i | ||||
\(148\) | −3.28701 | + | 3.28701i | −0.0222095 | + | 0.0222095i | ||||
\(149\) | −7.65497 | −0.0513756 | −0.0256878 | − | 0.999670i | \(-0.508178\pi\) | ||||
−0.0256878 | + | 0.999670i | \(0.508178\pi\) | |||||||
\(150\) | 69.1764 | + | 80.4029i | 0.461176 | + | 0.536019i | ||||
\(151\) | 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 | ||||
\(153\) | 134.092 | + | 132.617i | 0.876419 | + | 0.866775i | ||||
\(154\) | 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 | \(-0.895216\pi\) |
0.323275 | + | 0.946305i | \(0.395216\pi\) | |||||||
\(158\) | 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 | ||||
\(162\) | 80.0988 | − | 81.8913i | 0.494437 | − | 0.505502i | ||||
\(163\) | 0.909159 | − | 0.909159i | 0.00557766 | − | 0.00557766i | −0.704312 | − | 0.709890i | \(-0.748745\pi\) |
0.709890 | + | 0.704312i | \(0.248745\pi\) | |||||||
\(164\) | 84.5387i | 0.515480i | ||||||||
\(165\) | 62.1827 | + | 66.8390i | 0.376865 | + | 0.405085i | ||||
\(166\) | − | 24.4100i | − | 0.147048i | ||||||
\(167\) | 144.965 | + | 144.965i | 0.868051 | + | 0.868051i | 0.992257 | − | 0.124205i | \(-0.0396381\pi\) |
−0.124205 | + | 0.992257i | \(0.539638\pi\) | |||||||
\(168\) | 32.4661 | + | 49.7388i | 0.193251 | + | 0.296065i | ||||
\(169\) | − | 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 | −0.553831 | − | 0.832629i | \(-0.686834\pi\) |
0.832629 | + | 0.553831i | \(0.186834\pi\) | |||||||
\(174\) | 58.4329 | − | 58.7571i | 0.335821 | − | 0.337684i | ||||
\(175\) | 49.6308 | − | 167.815i | 0.283605 | − | 0.958941i | ||||
\(176\) | − | 24.3444i | − | 0.138321i | ||||||
\(177\) | 0.0334139 | + | 12.0796i | 0.000188779 | + | 0.0682465i | ||||
\(178\) | −97.2971 | − | 97.2971i | −0.546613 | − | 0.546613i | ||||
\(179\) | 277.037 | 1.54769 | 0.773847 | − | 0.633372i | \(-0.218330\pi\) | ||||
0.773847 | + | 0.633372i | \(0.218330\pi\) | |||||||
\(180\) | 61.4850 | + | 65.7236i | 0.341584 | + | 0.365131i | ||||
\(181\) | 271.177i | 1.49822i | 0.662448 | + | 0.749108i | \(0.269518\pi\) | ||||
−0.662448 | + | 0.749108i | \(0.730482\pi\) | |||||||
\(182\) | 54.7773 | + | 11.6680i | 0.300974 | + | 0.0641100i | ||||
\(183\) | 0.541116 | + | 195.621i | 0.00295692 | + | 1.06897i | ||||
\(184\) | − | 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 | \(-0.156433\pi\) | |||||||
\(192\) | −0.0663871 | − | 23.9999i | −0.000345766 | − | 0.125000i | ||||
\(193\) | −194.407 | + | 194.407i | −1.00729 | + | 1.00729i | −0.00731625 | + | 0.999973i | \(0.502329\pi\) |
−0.999973 | + | 0.00731625i | \(0.997671\pi\) | |||||||
\(194\) | − | 121.243i | − | 0.624966i | ||||||
\(195\) | 84.8071 | + | 3.06062i | 0.434908 | + | 0.0156955i | ||||
\(196\) | 39.9375 | − | 89.4930i | 0.203763 | − | 0.456597i | ||||
\(197\) | −78.6926 | + | 78.6926i | −0.399455 | + | 0.399455i | −0.878041 | − | 0.478586i | \(-0.841149\pi\) |
0.478586 | + | 0.878041i | \(0.341149\pi\) | |||||||
\(198\) | 55.0771 | + | 54.4711i | 0.278167 | + | 0.275106i | ||||
\(199\) | −203.776 | −1.02400 | −0.511999 | − | 0.858986i | \(-0.671095\pi\) | ||||
−0.511999 | + | 0.858986i | \(0.671095\pi\) | |||||||
\(200\) | −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 | ||||
\(203\) | −133.722 | − | 28.4839i | −0.658730 | − | 0.140315i | ||||
\(204\) | −88.6580 | + | 89.1499i | −0.434598 | + | 0.437009i | ||||
\(205\) | 155.135 | − | 143.529i | 0.756755 | − | 0.700142i | ||||
\(206\) | 227.204 | 1.10293 | ||||||||
\(207\) | 186.681 | + | 184.627i | 0.901840 | + | 0.891916i | ||||
\(208\) | −16.0018 | − | 16.0018i | −0.0769317 | − | 0.0769317i | ||||
\(209\) | 124.272i | 0.594603i | ||||||||
\(210\) | 36.1539 | − | 144.024i | 0.172161 | − | 0.685828i | ||||
\(211\) | −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 | ||||
\(213\) | 1.01951 | + | 368.568i | 0.00478643 | + | 1.73037i | ||||
\(214\) | − | 160.074i | − | 0.748008i | ||||||
\(215\) | 12.3565 | − | 317.982i | 0.0574722 | − | 1.47899i | ||||
\(216\) | 54.4462 | + | 53.5500i | 0.252066 | + | 0.247917i | ||||
\(217\) | 6.36179 | − | 29.8664i | 0.0293170 | − | 0.137633i | ||||
\(218\) | −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 | ||||||||
\(222\) | 9.86100 | − | 0.0272769i | 0.0444189 | − | 0.000122869i | ||||
\(223\) | −270.204 | − | 270.204i | −1.21168 | − | 1.21168i | −0.970475 | − | 0.241204i | \(-0.922458\pi\) |
−0.241204 | − | 0.970475i | \(-0.577542\pi\) | |||||||
\(224\) | −33.2190 | + | 21.5523i | −0.148299 | + | 0.0962154i | ||||
\(225\) | 16.2190 | − | 224.415i | 0.0720844 | − | 0.997399i | ||||
\(226\) | −260.492 | −1.15262 | ||||||||
\(227\) | −43.7703 | − | 43.7703i | −0.192821 | − | 0.192821i | 0.604093 | − | 0.796914i | \(-0.293535\pi\) |
−0.796914 | + | 0.604093i | \(0.793535\pi\) | |||||||
\(228\) | 0.338889 | + | 122.513i | 0.00148635 | + | 0.537339i | ||||
\(229\) | 74.6694 | 0.326067 | 0.163034 | − | 0.986621i | \(-0.447872\pi\) | ||||
0.163034 | + | 0.986621i | \(0.447872\pi\) | |||||||
\(230\) | −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 | −0.999595 | − | 0.0284664i | \(-0.990938\pi\) |
−0.0284664 | − | 0.999595i | \(-0.509062\pi\) | |||||||
\(234\) | 72.0069 | − | 0.398365i | 0.307722 | − | 0.00170242i | ||||
\(235\) | −259.301 | − | 10.0762i | −1.10341 | − | 0.0428775i | ||||
\(236\) | −8.05312 | −0.0341234 | ||||||||
\(237\) | −1.04603 | − | 378.154i | −0.00441362 | − | 1.59559i | ||||
\(238\) | 202.892 | + | 43.2176i | 0.852485 | + | 0.181586i | ||||
\(239\) | −34.0240 | −0.142360 | −0.0711799 | − | 0.997463i | \(-0.522676\pi\) | ||||
−0.0711799 | + | 0.997463i | \(0.522676\pi\) | |||||||
\(240\) | −43.9289 | + | 40.8687i | −0.183037 | + | 0.170286i | ||||
\(241\) | − | 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 | ||||
\(243\) | −242.977 | + | 3.36074i | −0.999904 | + | 0.0138302i | ||||
\(244\) | −130.415 | −0.534487 | ||||||||
\(245\) | −232.032 | + | 78.6520i | −0.947070 | + | 0.321029i | ||||
\(246\) | 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 | \(0.488728\pi\) | |||||||
\(252\) | 25.5680 | − | 123.379i | 0.101460 | − | 0.489598i | ||||
\(253\) | −125.547 | + | 125.547i | −0.496234 | + | 0.496234i | ||||
\(254\) | −107.010 | −0.421297 | ||||||||
\(255\) | 314.120 | + | 11.3363i | 1.23184 | + | 0.0444561i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 155.524 | + | 155.524i | 0.605151 | + | 0.605151i | 0.941675 | − | 0.336524i | \(-0.109251\pi\) |
−0.336524 | + | 0.941675i | \(0.609251\pi\) | |||||||
\(258\) | −0.746911 | − | 270.019i | −0.00289500 | − | 1.04659i | ||||
\(259\) | −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 | \(-0.459523\pi\) |
−0.991926 | + | 0.126821i | \(0.959523\pi\) | |||||||
\(264\) | −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 | ||||
\(267\) | 0.807409 | + | 291.890i | 0.00302400 | + | 1.09322i | ||||
\(268\) | 119.437 | − | 119.437i | 0.445660 | − | 0.445660i | ||||
\(269\) | − | 89.7378i | − | 0.333598i | −0.985991 | − | 0.166799i | \(-0.946657\pi\) | ||
0.985991 | − | 0.166799i | \(-0.0533431\pi\) | |||||||
\(270\) | 5.82999 | − | 190.830i | 0.0215926 | − | 0.706777i | ||||
\(271\) | 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 | ||||
\(273\) | −64.9394 | − | 99.4888i | −0.237873 | − | 0.364428i | ||||
\(274\) | 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 | 0.815270 | − | 0.579080i | \(-0.196588\pi\) |
−0.579080 | + | 0.815270i | \(0.696588\pi\) | |||||||
\(278\) | −30.0414 | + | 30.0414i | −0.108063 | + | 0.108063i | ||||
\(279\) | −0.217202 | − | 39.2605i | −0.000778501 | − | 0.140719i | ||||
\(280\) | 95.9489 | + | 24.3681i | 0.342675 | + | 0.0870290i | ||||
\(281\) | 431.212i | 1.53456i | 0.641311 | + | 0.767281i | \(0.278391\pi\) | ||||
−0.641311 | + | 0.767281i | \(0.721609\pi\) | |||||||
\(282\) | −220.189 | + | 0.609073i | −0.780812 | + | 0.00215984i | ||||
\(283\) | −168.146 | − | 168.146i | −0.594155 | − | 0.594155i | 0.344596 | − | 0.938751i | \(-0.388016\pi\) |
−0.938751 | + | 0.344596i | \(0.888016\pi\) | |||||||
\(284\) | −245.713 | −0.865186 | ||||||||
\(285\) | 224.246 | − | 208.624i | 0.786828 | − | 0.732014i | ||||
\(286\) | 48.6943i | 0.170260i | ||||||||
\(287\) | −289.393 | − | 61.6431i | −1.00834 | − | 0.214784i | ||||
\(288\) | −35.8003 | + | 36.1986i | −0.124307 | + | 0.125690i | ||||
\(289\) | 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 | −0.0978068 | − | 0.995205i | \(-0.531183\pi\) |
0.995205 | + | 0.0978068i | \(0.0311827\pi\) | |||||||
\(294\) | −193.939 | + | 74.8699i | −0.659658 | + | 0.254659i | ||||
\(295\) | 13.6725 | + | 14.7781i | 0.0463475 | + | 0.0500952i | ||||
\(296\) | 6.57402i | 0.0222095i | ||||||||
\(297\) | −1.36362 | − | 164.319i | −0.00459130 | − | 0.553263i | ||||
\(298\) | −7.65497 | + | 7.65497i | −0.0256878 | + | 0.0256878i | ||||
\(299\) | 165.047i | 0.551995i | ||||||||
\(300\) | 149.579 | + | 11.2265i | 0.498598 | + | 0.0374215i | ||||
\(301\) | −373.742 | + | 242.481i | −1.24167 | + | 0.805585i | ||||
\(302\) | 236.474 | − | 236.474i | 0.783027 | − | 0.783027i | ||||
\(303\) | 288.931 | − | 0.799223i | 0.953568 | − | 0.00263770i | ||||
\(304\) | −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 | 0.218358 | − | 0.975869i | \(-0.429930\pi\) |
0.975869 | − | 0.218358i | \(-0.0700701\pi\) | |||||||
\(308\) | 83.3358 | + | 17.7512i | 0.270571 | + | 0.0576338i | ||||
\(309\) | −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 | \(0.441454\pi\) | |||||||
\(312\) | 0.132789 | + | 48.0052i | 0.000425606 | + | 0.153863i | ||||
\(313\) | −267.661 | − | 267.661i | −0.855146 | − | 0.855146i | 0.135615 | − | 0.990762i | \(-0.456699\pi\) |
−0.990762 | + | 0.135615i | \(0.956699\pi\) | |||||||
\(314\) | 195.631i | 0.623030i | ||||||||
\(315\) | −269.818 | + | 162.552i | −0.856566 | + | 0.516038i | ||||
\(316\) | 252.104 | 0.797797 | ||||||||
\(317\) | 215.640 | − | 215.640i | 0.680253 | − | 0.680253i | −0.279804 | − | 0.960057i | \(-0.590270\pi\) |
0.960057 | + | 0.279804i | \(0.0902696\pi\) | |||||||
\(318\) | 3.91697 | − | 0.0108349i | 0.0123175 | − | 3.40719e-5i | ||||
\(319\) | − | 118.872i | − | 0.372640i | ||||||
\(320\) | −27.1647 | − | 29.3612i | −0.0848896 | − | 0.0917538i | ||||
\(321\) | −239.445 | + | 240.774i | −0.745936 | + | 0.750074i | ||||
\(322\) | 282.462 | + | 60.1668i | 0.877212 | + | 0.186853i | ||||
\(323\) | 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 | ||||||
\(327\) | 1.60708 | + | 580.984i | 0.00491463 | + | 1.77671i | ||||
\(328\) | 84.5387 | + | 84.5387i | 0.257740 | + | 0.257740i | ||||
\(329\) | 197.733 | + | 304.770i | 0.601012 | + | 0.926353i | ||||
\(330\) | 129.022 | + | 4.65629i | 0.390975 | + | 0.0141100i | ||||
\(331\) | 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 | ||||
\(333\) | −14.8732 | − | 14.7095i | −0.0446641 | − | 0.0441727i | ||||
\(334\) | 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 | 0.647156 | − | 0.762357i | \(-0.275958\pi\) |
−0.762357 | + | 0.647156i | \(0.775958\pi\) | |||||||
\(338\) | −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 | ||||||||
\(342\) | 182.751 | − | 184.785i | 0.534360 | − | 0.540306i | ||||
\(343\) | 277.231 | + | 201.970i | 0.808254 | + | 0.588833i | ||||
\(344\) | 180.014 | 0.523295 | ||||||||
\(345\) | 437.312 | + | 15.7822i | 1.26757 | + | 0.0457456i | ||||
\(346\) | − | 96.4644i | − | 0.278799i | ||||||
\(347\) | 137.429 | − | 137.429i | 0.396050 | − | 0.396050i | −0.480788 | − | 0.876837i | \(-0.659649\pi\) |
0.876837 | + | 0.480788i | \(0.159649\pi\) | |||||||
\(348\) | −0.324164 | − | 117.190i | −0.000931505 | − | 0.336753i | ||||
\(349\) | −508.928 | −1.45825 | −0.729123 | − | 0.684383i | \(-0.760072\pi\) | ||||
−0.729123 | + | 0.684383i | \(0.760072\pi\) | |||||||
\(350\) | −118.184 | − | 217.446i | −0.337668 | − | 0.621273i | ||||
\(351\) | −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 | −0.935794 | − | 0.352546i | \(-0.885316\pi\) |
0.352546 | + | 0.935794i | \(0.385316\pi\) | |||||||
\(354\) | 12.1130 | + | 12.0462i | 0.0342176 | + | 0.0340288i | ||||
\(355\) | 417.169 | + | 450.902i | 1.17512 | + | 1.27015i | ||||
\(356\) | −194.594 | −0.546613 | ||||||||
\(357\) | −240.531 | − | 368.500i | −0.673757 | − | 1.03221i | ||||
\(358\) | 277.037 | − | 277.037i | 0.773847 | − | 0.773847i | ||||
\(359\) | 51.9892 | 0.144817 | 0.0724084 | − | 0.997375i | \(-0.476932\pi\) | ||||
0.0724084 | + | 0.997375i | \(0.476932\pi\) | |||||||
\(360\) | 127.209 | + | 4.23855i | 0.353357 | + | 0.0117738i | ||||
\(361\) | 55.9344 | 0.154943 | ||||||||
\(362\) | 271.177 | + | 271.177i | 0.749108 | + | 0.749108i | ||||
\(363\) | −251.877 | + | 0.696727i | −0.693876 | + | 0.00191936i | ||||
\(364\) | 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 | \(-0.522538\pi\) |
0.997494 | + | 0.0707450i | \(0.0225377\pi\) | |||||||
\(368\) | −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 | ||||
\(372\) | 26.1740 | − | 0.0724009i | 0.0703602 | − | 0.000194626i | ||||
\(373\) | 185.919 | − | 185.919i | 0.498441 | − | 0.498441i | −0.412511 | − | 0.910952i | \(-0.635348\pi\) |
0.910952 | + | 0.412511i | \(0.135348\pi\) | |||||||
\(374\) | 180.360i | 0.482246i | ||||||||
\(375\) | −233.353 | − | 293.550i | −0.622275 | − | 0.782799i | ||||
\(376\) | − | 146.793i | − | 0.390408i | ||||||
\(377\) | −78.1357 | − | 78.1357i | −0.207257 | − | 0.207257i | ||||
\(378\) | −223.013 | + | 147.333i | −0.589982 | + | 0.389771i | ||||
\(379\) | 123.430i | 0.325672i | 0.986653 | + | 0.162836i | \(0.0520641\pi\) | ||||
−0.986653 | + | 0.162836i | \(0.947936\pi\) | |||||||
\(380\) | 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 | −0.647164 | − | 0.762351i | \(-0.724045\pi\) |
0.762351 | + | 0.647164i | \(0.224045\pi\) | |||||||
\(384\) | −24.0663 | − | 23.9335i | −0.0626726 | − | 0.0623269i | ||||
\(385\) | −108.912 | − | 183.065i | −0.282888 | − | 0.475495i | ||||
\(386\) | 388.814i | 1.00729i | ||||||||
\(387\) | −402.784 | + | 407.265i | −1.04078 | + | 1.05236i | ||||
\(388\) | −121.243 | − | 121.243i | −0.312483 | − | 0.312483i | ||||
\(389\) | 116.363 | 0.299133 | 0.149566 | − | 0.988752i | \(-0.452212\pi\) | ||||
0.149566 | + | 0.988752i | \(0.452212\pi\) | |||||||
\(390\) | 87.8677 | − | 81.7465i | 0.225302 | − | 0.209606i | ||||
\(391\) | 611.321i | 1.56348i | ||||||||
\(392\) | −49.5554 | − | 129.431i | −0.126417 | − | 0.330180i | ||||
\(393\) | 683.392 | − | 1.89036i | 1.73891 | − | 0.00481007i | ||||
\(394\) | 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 | \(-0.754953\pi\) |
0.696019 | + | 0.718024i | \(0.254953\pi\) | |||||||
\(398\) | −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 | \(0.988886\pi\) | |||||||
\(402\) | −358.309 | + | 0.991133i | −0.891317 | + | 0.00246551i | ||||
\(403\) | 17.4513 | − | 17.4513i | 0.0433036 | − | 0.0433036i | ||||
\(404\) | 192.622i | 0.476786i | ||||||||
\(405\) | −294.221 | + | 278.315i | −0.726471 | + | 0.687197i | ||||
\(406\) | −162.206 | + | 105.238i | −0.399523 | + | 0.259208i | ||||
\(407\) | 10.0025 | − | 10.0025i | 0.0245763 | − | 0.0245763i | ||||
\(408\) | 0.491841 | + | 177.808i | 0.00120549 | + | 0.435804i | ||||
\(409\) | −234.500 | −0.573349 | −0.286675 | − | 0.958028i | \(-0.592550\pi\) | ||||
−0.286675 | + | 0.958028i | \(0.592550\pi\) | |||||||
\(410\) | 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 | ||||
\(413\) | 5.87209 | − | 27.5674i | 0.0142181 | − | 0.0667492i | ||||
\(414\) | 371.308 | − | 2.05419i | 0.896878 | − | 0.00496182i | ||||
\(415\) | −3.35112 | + | 86.2375i | −0.00807498 | + | 0.207801i | ||||
\(416\) | −32.0036 | −0.0769317 | ||||||||
\(417\) | 90.1239 | − | 0.249295i | 0.216125 | − | 0.000597830i | ||||
\(418\) | 124.272 | + | 124.272i | 0.297301 | + | 0.297301i | ||||
\(419\) | − | 339.624i | − | 0.810559i | −0.914193 | − | 0.405279i | \(-0.867174\pi\) | ||
0.914193 | − | 0.405279i | \(-0.132826\pi\) | |||||||
\(420\) | −107.870 | − | 180.178i | −0.256833 | − | 0.428995i | ||||
\(421\) | 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 | ||||
\(423\) | 332.107 | + | 328.453i | 0.785123 | + | 0.776484i | ||||
\(424\) | 2.61132i | 0.00615878i | ||||||||
\(425\) | 398.064 | − | 340.571i | 0.936620 | − | 0.801344i | ||||
\(426\) | 369.587 | + | 367.548i | 0.867576 | + | 0.862789i | ||||
\(427\) | 95.0946 | − | 446.436i | 0.222704 | − | 1.04552i | ||||
\(428\) | −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 | \(-0.240143\pi\) | |||||||
\(432\) | 107.996 | − | 0.896216i | 0.249991 | − | 0.00207457i | ||||
\(433\) | 340.107 | + | 340.107i | 0.785466 | + | 0.785466i | 0.980747 | − | 0.195281i | \(-0.0625619\pi\) |
−0.195281 | + | 0.980747i | \(0.562562\pi\) | |||||||
\(434\) | −23.5046 | − | 36.2282i | −0.0541581 | − | 0.0834751i | ||||
\(435\) | −214.502 | + | 199.559i | −0.493109 | + | 0.458757i | ||||
\(436\) | −387.324 | −0.888359 | ||||||||
\(437\) | 421.213 | + | 421.213i | 0.963874 | + | 0.963874i | ||||
\(438\) | 78.8480 | − | 0.218105i | 0.180018 | − | 0.000497956i | ||||
\(439\) | 732.833 | 1.66932 | 0.834661 | − | 0.550764i | \(-0.185663\pi\) | ||||
0.834661 | + | 0.550764i | \(0.185663\pi\) | |||||||
\(440\) | −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 | \(-0.193309\pi\) |
−0.570651 | + | 0.821192i | \(0.693309\pi\) | |||||||
\(444\) | 9.83372 | − | 9.88827i | 0.0221480 | − | 0.0222709i | ||||
\(445\) | 330.380 | + | 357.095i | 0.742428 | + | 0.802461i | ||||
\(446\) | −540.408 | −1.21168 | ||||||||
\(447\) | 22.9648 | − | 0.0635238i | 0.0513754 | − | 0.000142111i | ||||
\(448\) | −11.6667 | + | 54.7712i | −0.0260418 | + | 0.122257i | ||||
\(449\) | −196.292 | −0.437175 | −0.218588 | − | 0.975817i | \(-0.570145\pi\) | ||||
−0.218588 | + | 0.975817i | \(0.570145\pi\) | |||||||
\(450\) | −208.196 | − | 240.634i | −0.462657 | − | 0.534741i | ||||
\(451\) | − | 257.255i | − | 0.570411i | ||||||
\(452\) | −260.492 | + | 260.492i | −0.576311 | + | 0.576311i | ||||
\(453\) | −709.420 | + | 1.96235i | −1.56605 | + | 0.00433191i | ||||
\(454\) | −87.5405 | −0.192821 | ||||||||
\(455\) | −191.919 | − | 48.7417i | −0.421801 | − | 0.107125i | ||||
\(456\) | 122.852 | + | 122.174i | 0.269413 | + | 0.267926i | ||||
\(457\) | 52.4299 | + | 52.4299i | 0.114726 | + | 0.114726i | 0.762139 | − | 0.647413i | \(-0.224149\pi\) |
−0.647413 | + | 0.762139i | \(0.724149\pi\) | |||||||
\(458\) | 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 | \(0.296653\pi\) | |||||||
\(462\) | −98.7960 | − | 151.358i | −0.213844 | − | 0.327614i | ||||
\(463\) | 333.035 | − | 333.035i | 0.719298 | − | 0.719298i | −0.249164 | − | 0.968461i | \(-0.580156\pi\) |
0.968461 | + | 0.249164i | \(0.0801558\pi\) | |||||||
\(464\) | 78.1270 | 0.168377 | ||||||||
\(465\) | −44.5708 | − | 47.9083i | −0.0958513 | − | 0.103029i | ||||
\(466\) | −479.077 | −1.02806 | ||||||||
\(467\) | −9.53974 | − | 9.53974i | −0.0204277 | − | 0.0204277i | 0.696819 | − | 0.717247i | \(-0.254598\pi\) |
−0.717247 | + | 0.696819i | \(0.754598\pi\) | |||||||
\(468\) | 71.6086 | − | 72.4053i | 0.153010 | − | 0.154712i | ||||
\(469\) | 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 | ||||
\(477\) | −5.90789 | − | 5.84288i | −0.0123855 | − | 0.0122492i | ||||
\(478\) | −34.0240 | + | 34.0240i | −0.0711799 | + | 0.0711799i | ||||
\(479\) | − | 30.2411i | − | 0.0631339i | −0.999502 | − | 0.0315670i | \(-0.989950\pi\) | ||
0.999502 | − | 0.0315670i | \(-0.0100497\pi\) | |||||||
\(480\) | −3.06027 | + | 84.7976i | −0.00637557 | + | 0.176662i | ||||
\(481\) | − | 13.1495i | − | 0.0273379i | ||||||
\(482\) | −268.995 | − | 268.995i | −0.558081 | − | 0.558081i | ||||
\(483\) | −334.864 | − | 513.019i | −0.693299 | − | 1.06215i | ||||
\(484\) | − | 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 | 0.402650 | − | 0.915354i | \(-0.368089\pi\) |
−0.915354 | + | 0.402650i | \(0.868089\pi\) | |||||||
\(488\) | −130.415 | + | 130.415i | −0.267243 | + | 0.267243i | ||||
\(489\) | −2.71992 | + | 2.73501i | −0.00556221 | + | 0.00559307i | ||||
\(490\) | −153.380 | + | 310.684i | −0.313020 | + | 0.634049i | ||||
\(491\) | 775.321i | 1.57907i | 0.613708 | + | 0.789533i | \(0.289677\pi\) | ||||
−0.613708 | + | 0.789533i | \(0.710323\pi\) | |||||||
\(492\) | −0.701534 | − | 253.615i | −0.00142588 | − | 0.515478i | ||||
\(493\) | −289.409 | − | 289.409i | −0.587037 | − | 0.587037i | ||||
\(494\) | 163.370 | 0.330709 | ||||||||
\(495\) | −187.102 | − | 200.000i | −0.377984 | − | 0.404041i | ||||
\(496\) | 17.4494i | 0.0351802i | ||||||||
\(497\) | 179.166 | − | 841.124i | 0.360496 | − | 1.69240i | ||||
\(498\) | 0.202564 | + | 73.2299i | 0.000406755 | + | 0.147048i | ||||
\(499\) | 596.688i | 1.19577i | 0.801583 | + | 0.597884i | \(0.203991\pi\) | ||||
−0.801583 | + | 0.597884i | \(0.796009\pi\) | |||||||
\(500\) | 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 | 0.368671 | − | 0.929560i | \(-0.379813\pi\) |
0.929560 | − | 0.368671i | \(-0.120187\pi\) | |||||||
\(504\) | −97.8106 | − | 148.947i | −0.194069 | − | 0.295529i | ||||
\(505\) | 353.475 | − | 327.031i | 0.699951 | − | 0.647586i | ||||
\(506\) | 251.095i | 0.496234i | ||||||||
\(507\) | 1.13682 | + | 410.977i | 0.00224225 | + | 0.810606i | ||||
\(508\) | −107.010 | + | 107.010i | −0.210649 | + | 0.210649i | ||||
\(509\) | − | 288.101i | − | 0.566014i | −0.959118 | − | 0.283007i | \(-0.908668\pi\) | ||
0.959118 | − | 0.283007i | \(-0.0913320\pi\) | |||||||
\(510\) | 325.456 | − | 302.783i | 0.638149 | − | 0.593693i | ||||
\(511\) | −70.8066 | − | 109.136i | −0.138565 | − | 0.213573i | ||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −551.293 | + | 4.57495i | −1.07465 | + | 0.00891804i | ||||
\(514\) | 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 | ||||
\(518\) | −22.5042 | − | 4.79358i | −0.0434444 | − | 0.00925402i | ||||
\(519\) | −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 | \(0.441580\pi\) | |||||||
\(522\) | −174.811 | + | 176.756i | −0.334886 | + | 0.338612i | ||||
\(523\) | −315.417 | − | 315.417i | −0.603093 | − | 0.603093i | 0.338039 | − | 0.941132i | \(-0.390236\pi\) |
−0.941132 | + | 0.338039i | \(0.890236\pi\) | |||||||
\(524\) | 455.597i | 0.869459i | ||||||||
\(525\) | −147.499 | + | 503.854i | −0.280951 | + | 0.959722i | ||||
\(526\) | −455.045 | −0.865105 | ||||||||
\(527\) | 64.6386 | − | 64.6386i | 0.122654 | − | 0.122654i | ||||
\(528\) | 0.202019 | + | 73.0330i | 0.000382612 | + | 0.138320i | ||||
\(529\) | 322.071i | 0.608830i | ||||||||
\(530\) | 4.79197 | − | 4.43348i | 0.00904146 | − | 0.00836506i | ||||
\(531\) | −0.200483 | − | 36.2385i | −0.000377557 | − | 0.0682457i | ||||
\(532\) | 59.5556 | − | 279.593i | 0.111947 | − | 0.525551i | ||||
\(533\) | −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 | ||||||
\(537\) | −831.109 | + | 2.29896i | −1.54769 | + | 0.00428112i | ||||
\(538\) | −89.7378 | − | 89.7378i | −0.166799 | − | 0.166799i | ||||
\(539\) | −121.532 | + | 272.332i | −0.225477 | + | 0.505254i | ||||
\(540\) | −185.000 | − | 196.660i | −0.342592 | − | 0.364185i | ||||
\(541\) | 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 | ||||
\(543\) | −2.25033 | − | 813.528i | −0.00414426 | − | 1.49821i | ||||
\(544\) | −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 | 0.746914 | − | 0.664921i | \(-0.231535\pi\) |
−0.664921 | + | 0.746914i | \(0.731535\pi\) | |||||||
\(548\) | 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 | ||||||||
\(552\) | 0.684733 | + | 247.541i | 0.00124046 | + | 0.448444i | ||||
\(553\) | −183.827 | + | 863.002i | −0.332417 | + | 1.56058i | ||||
\(554\) | 130.849 | 0.236190 | ||||||||
\(555\) | −34.8413 | − | 1.25739i | −0.0627772 | − | 0.00226558i | ||||
\(556\) | 60.0828i | 0.108063i | ||||||||
\(557\) | 221.625 | − | 221.625i | 0.397890 | − | 0.397890i | −0.479598 | − | 0.877488i | \(-0.659218\pi\) |
0.877488 | + | 0.479598i | \(0.159218\pi\) | |||||||
\(558\) | −39.4777 | − | 39.0433i | −0.0707486 | − | 0.0699701i | ||||
\(559\) | −360.067 | −0.644127 | ||||||||
\(560\) | 120.317 | − | 71.5808i | 0.214852 | − | 0.127823i | ||||
\(561\) | 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 | −0.741317 | − | 0.671155i | \(-0.765798\pi\) |
0.671155 | + | 0.741317i | \(0.265798\pi\) | |||||||
\(564\) | −219.580 | + | 220.798i | −0.389326 | + | 0.391486i | ||||
\(565\) | 920.285 | + | 35.7615i | 1.62882 | + | 0.0632947i | ||||
\(566\) | −336.292 | −0.594155 | ||||||||
\(567\) | 555.832 | + | 111.983i | 0.980303 | + | 0.197500i | ||||
\(568\) | −245.713 | + | 245.713i | −0.432593 | + | 0.432593i | ||||
\(569\) | 63.0549 | 0.110817 | 0.0554085 | − | 0.998464i | \(-0.482354\pi\) | ||||
0.0554085 | + | 0.998464i | \(0.482354\pi\) | |||||||
\(570\) | 15.6219 | − | 432.870i | 0.0274069 | − | 0.759421i | ||||
\(571\) | −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 | ||||
\(573\) | 1.49593 | + | 540.800i | 0.00261069 | + | 0.943804i | ||||
\(574\) | −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 | −0.0630759 | + | 0.998009i | \(0.520091\pi\) |
−0.998009 | + | 0.0630759i | \(0.979909\pi\) | |||||||
\(578\) | 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 | ||||
\(582\) | 1.00612 | + | 363.729i | 0.00172874 | + | 0.624964i | ||||
\(583\) | 3.97319 | − | 3.97319i | 0.00681508 | − | 0.00681508i | ||||
\(584\) | 52.5656i | 0.0900095i | ||||||||
\(585\) | −254.446 | − | 8.47805i | −0.434950 | − | 0.0144924i | ||||
\(586\) | − | 525.876i | − | 0.897399i | ||||||
\(587\) | −228.676 | − | 228.676i | −0.389567 | − | 0.389567i | 0.484966 | − | 0.874533i | \(-0.338832\pi\) |
−0.874533 | + | 0.484966i | \(0.838832\pi\) | |||||||
\(588\) | −119.070 | + | 268.809i | −0.202499 | + | 0.457159i | ||||
\(589\) | − | 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 | −0.999632 | − | 0.0271286i | \(-0.991364\pi\) |
0.0271286 | + | 0.999632i | \(0.491364\pi\) | |||||||
\(594\) | −165.683 | − | 162.956i | −0.278927 | − | 0.274336i | ||||
\(595\) | −710.856 | − | 180.536i | −1.19472 | − | 0.303421i | ||||
\(596\) | 15.3099i | 0.0256878i | ||||||||
\(597\) | 611.325 | − | 1.69101i | 1.02399 | − | 0.00283251i | ||||
\(598\) | 165.047 | + | 165.047i | 0.275998 | + | 0.275998i | ||||
\(599\) | −456.495 | −0.762095 | −0.381048 | − | 0.924555i | \(-0.624437\pi\) | ||||
−0.381048 | + | 0.924555i | \(0.624437\pi\) | |||||||
\(600\) | 160.806 | − | 138.353i | 0.268010 | − | 0.230588i | ||||
\(601\) | − | 631.907i | − | 1.05143i | −0.850662 | − | 0.525713i | \(-0.823798\pi\) | ||
0.850662 | − | 0.525713i | \(-0.176202\pi\) | |||||||
\(602\) | −131.260 | + | 616.223i | −0.218041 | + | 1.02363i | ||||
\(603\) | 540.431 | + | 534.484i | 0.896237 | + | 0.886376i | ||||
\(604\) | − | 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 | \(-0.931558\pi\) |
0.213363 | + | 0.976973i | \(0.431558\pi\) | |||||||
\(608\) | −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 | ||||||||
\(612\) | 265.233 | − | 268.184i | 0.433388 | − | 0.438210i | ||||
\(613\) | −491.048 | + | 491.048i | −0.801057 | + | 0.801057i | −0.983261 | − | 0.182204i | \(-0.941677\pi\) |
0.182204 | + | 0.983261i | \(0.441677\pi\) | |||||||
\(614\) | − | 733.255i | − | 1.19423i | ||||||
\(615\) | −464.212 | + | 431.873i | −0.754816 | + | 0.702232i | ||||
\(616\) | 101.087 | − | 65.5846i | 0.164102 | − | 0.106469i | ||||
\(617\) | −392.264 | + | 392.264i | −0.635759 | + | 0.635759i | −0.949507 | − | 0.313747i | \(-0.898416\pi\) |
0.313747 | + | 0.949507i | \(0.398416\pi\) | |||||||
\(618\) | −681.610 | + | 1.88543i | −1.10293 | + | 0.00305085i | ||||
\(619\) | −1005.88 | −1.62500 | −0.812500 | − | 0.582961i | \(-0.801894\pi\) | ||||
−0.812500 | + | 0.582961i | \(0.801894\pi\) | |||||||
\(620\) | 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 | ||||
\(623\) | 141.892 | − | 666.135i | 0.227757 | − | 1.06924i | ||||
\(624\) | 48.1380 | + | 47.8724i | 0.0771442 | + | 0.0767186i | ||||
\(625\) | −617.473 | − | 96.7090i | −0.987956 | − | 0.154734i | ||||
\(626\) | −535.321 | −0.855146 | ||||||||
\(627\) | −1.03126 | − | 372.814i | −0.00164475 | − | 0.594600i | ||||
\(628\) | 195.631 | + | 195.631i | 0.311515 | + | 0.311515i | ||||
\(629\) | − | 48.7049i | − | 0.0774323i | ||||||
\(630\) | −107.266 | + | 432.370i | −0.170264 | + | 0.686302i | ||||
\(631\) | 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 | ||||
\(633\) | 802.631 | − | 2.22019i | 1.26798 | − | 0.00350741i | ||||
\(634\) | − | 431.280i | − | 0.680253i | ||||||
\(635\) | 378.050 | + | 14.6907i | 0.595355 | + | 0.0231350i | ||||
\(636\) | 3.90613 | − | 3.92780i | 0.00614172 | − | 0.00617579i | ||||
\(637\) | 99.1219 | + | 258.890i | 0.155607 | + | 0.406421i | ||||
\(638\) | −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 | \(0.968960\pi\) | |||||||
\(642\) | 1.32835 | + | 480.219i | 0.00206909 | + | 0.748005i | ||||
\(643\) | 160.790 | + | 160.790i | 0.250062 | + | 0.250062i | 0.820996 | − | 0.570934i | \(-0.193419\pi\) |
−0.570934 | + | 0.820996i | \(0.693419\pi\) | |||||||
\(644\) | 342.629 | − | 222.295i | 0.532033 | − | 0.345179i | ||||
\(645\) | −34.4307 | + | 954.045i | −0.0533809 | + | 1.47914i | ||||
\(646\) | 605.111 | 0.936705 | ||||||||
\(647\) | −257.644 | − | 257.644i | −0.398213 | − | 0.398213i | 0.479389 | − | 0.877602i | \(-0.340858\pi\) |
−0.877602 | + | 0.479389i | \(0.840858\pi\) | |||||||
\(648\) | −163.783 | − | 160.198i | −0.252751 | − | 0.247219i | ||||
\(649\) | 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 | 0.979835 | + | 0.199809i | \(0.0640321\pi\) |
0.199809 | + | 0.979835i | \(0.435968\pi\) | |||||||
\(654\) | 582.592 | + | 579.377i | 0.890813 | + | 0.885898i | ||||
\(655\) | 836.054 | − | 773.508i | 1.27642 | − | 1.18093i | ||||
\(656\) | 169.077 | 0.257740 | ||||||||
\(657\) | −118.925 | − | 117.616i | −0.181012 | − | 0.179020i | ||||
\(658\) | 502.503 | + | 107.037i | 0.763683 | + | 0.162671i | ||||
\(659\) | 112.781 | 0.171139 | 0.0855695 | − | 0.996332i | \(-0.472729\pi\) | ||||
0.0855695 | + | 0.996332i | \(0.472729\pi\) | |||||||
\(660\) | 133.678 | − | 124.365i | 0.202542 | − | 0.188433i | ||||
\(661\) | − | 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 | ||||
\(663\) | −0.983792 | − | 355.655i | −0.00148385 | − | 0.536433i | ||||
\(664\) | −48.8201 | −0.0735242 | ||||||||
\(665\) | −614.188 | + | 365.402i | −0.923590 | + | 0.549476i | ||||
\(666\) | −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 | ||||||||
\(672\) | 99.4777 | − | 64.9322i | 0.148032 | − | 0.0966253i | ||||
\(673\) | −179.988 | + | 179.988i | −0.267441 | + | 0.267441i | −0.828068 | − | 0.560628i | \(-0.810560\pi\) |
0.560628 | + | 0.828068i | \(0.310560\pi\) | |||||||
\(674\) | −77.6457 | −0.115201 | ||||||||
\(675\) | −46.7945 | + | 673.376i | −0.0693252 | + | 0.997594i | ||||
\(676\) | −273.986 | −0.405304 | ||||||||
\(677\) | 697.081 | + | 697.081i | 1.02966 | + | 1.02966i | 0.999546 | + | 0.0301147i | \(0.00958726\pi\) |
0.0301147 | + | 0.999546i | \(0.490413\pi\) | |||||||
\(678\) | 781.474 | − | 2.16167i | 1.15262 | − | 0.00318830i | ||||
\(679\) | 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 | \(-0.0982875\pi\) |
−0.303896 | + | 0.952705i | \(0.598288\pi\) | |||||||
\(684\) | −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 | ||||
\(687\) | −224.007 | + | 0.619635i | −0.326066 | + | 0.000901944i | ||||
\(688\) | 180.014 | − | 180.014i | 0.261648 | − | 0.261648i | ||||
\(689\) | − | 5.22323i | − | 0.00758088i | ||||||
\(690\) | 453.094 | − | 421.530i | 0.656659 | − | 0.610913i | ||||
\(691\) | − | 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 | ||||
\(693\) | −77.8046 | + | 375.447i | −0.112272 | + | 0.541771i | ||||
\(694\) | − | 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 | ||||
\(700\) | −335.629 | − | 99.2616i | −0.479471 | − | 0.141802i | ||||
\(701\) | − | 664.169i | − | 0.947460i | −0.880670 | − | 0.473730i | \(-0.842907\pi\) | ||
0.880670 | − | 0.473730i | \(-0.157093\pi\) | |||||||
\(702\) | −216.017 | + | 1.79263i | −0.307716 | + | 0.00255361i | ||||
\(703\) | −33.5587 | − | 33.5587i | −0.0477364 | − | 0.0477364i | ||||
\(704\) | −48.6888 | −0.0691603 | ||||||||
\(705\) | 777.983 | + | 28.0767i | 1.10352 | + | 0.0398252i | ||||
\(706\) | 411.773i | 0.583248i | ||||||||
\(707\) | −659.382 | − | 140.454i | −0.932648 | − | 0.198662i | ||||
\(708\) | 24.1593 | − | 0.0668278i | 0.0341232 | − | 9.43896e-5i | ||||
\(709\) | − | 1003.81i | − | 1.41582i | −0.706304 | − | 0.707909i | \(-0.749639\pi\) | ||
0.706304 | − | 0.707909i | \(-0.250361\pi\) | |||||||
\(710\) | 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 | ||||||
\(717\) | 102.072 | − | 0.282344i | 0.142359 | − | 0.000393786i | ||||
\(718\) | 51.9892 | − | 51.9892i | 0.0724084 | − | 0.0724084i | ||||
\(719\) | 227.010i | 0.315731i | 0.987461 | + | 0.157865i | \(0.0504612\pi\) | ||||
−0.987461 | + | 0.157865i | \(0.949539\pi\) | |||||||
\(720\) | 131.447 | − | 122.970i | 0.182566 | − | 0.170792i | ||||
\(721\) | 612.095 | + | 943.437i | 0.848953 | + | 1.30851i | ||||
\(722\) | 55.9344 | − | 55.9344i | 0.0774715 | − | 0.0774715i | ||||
\(723\) | 2.23222 | + | 806.982i | 0.00308745 | + | 1.11616i | ||||
\(724\) | 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 | \(-0.646404\pi\) |
0.896079 | + | 0.443895i | \(0.146404\pi\) | |||||||
\(728\) | 23.3360 | − | 109.555i | 0.0320550 | − | 0.150487i | ||||
\(729\) | 728.900 | − | 12.0985i | 0.999862 | − | 0.0165960i | ||||
\(730\) | 96.4618 | − | 89.2454i | 0.132139 | − | 0.122254i | ||||
\(731\) | −1333.66 | −1.82444 | ||||||||
\(732\) | 391.243 | − | 1.08223i | 0.534485 | − | 0.00147846i | ||||
\(733\) | 320.943 | + | 320.943i | 0.437848 | + | 0.437848i | 0.891287 | − | 0.453439i | \(-0.149803\pi\) |
−0.453439 | + | 0.891287i | \(0.649803\pi\) | |||||||
\(734\) | − | 680.234i | − | 0.926749i | ||||||
\(735\) | 695.441 | − | 237.881i | 0.946178 | − | 0.323647i | ||||
\(736\) | −165.028 | −0.224223 | ||||||||
\(737\) | −363.453 | + | 363.453i | −0.493151 | + | 0.493151i | ||||
\(738\) | −378.314 | + | 382.523i | −0.512620 | + | 0.518323i | ||||
\(739\) | 742.829i | 1.00518i | 0.864524 | + | 0.502591i | \(0.167620\pi\) | ||||
−0.864524 | + | 0.502591i | \(0.832380\pi\) | |||||||
\(740\) | 0.902510 | − | 23.2252i | 0.00121961 | − | 0.0313853i | ||||
\(741\) | −245.732 | − | 244.376i | −0.331622 | − | 0.329792i | ||||
\(742\) | −8.93908 | − | 1.90410i | −0.0120473 | − | 0.00256617i | ||||
\(743\) | 319.664 | + | 319.664i | 0.430234 | + | 0.430234i | 0.888708 | − | 0.458474i | \(-0.151604\pi\) |
−0.458474 | + | 0.888708i | \(0.651604\pi\) | |||||||
\(744\) | 26.1016 | − | 26.2464i | 0.0350828 | − | 0.0352774i | ||||
\(745\) | 28.0949 | − | 25.9931i | 0.0377113 | − | 0.0348900i | ||||
\(746\) | − | 371.837i | − | 0.498441i | ||||||
\(747\) | 109.236 | − | 110.451i | 0.146233 | − | 0.147860i | ||||
\(748\) | 180.360 | + | 180.360i | 0.241123 | + | 0.241123i | ||||
\(749\) | 664.686 | − | 431.244i | 0.887431 | − | 0.575759i | ||||
\(750\) | −526.903 | − | 60.1965i | −0.702537 | − | 0.0802620i | ||||
\(751\) | −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 | ||||
\(753\) | −53.3170 | + | 0.147482i | −0.0708062 | + | 0.000195860i | ||||
\(754\) | −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 | 0.443699 | − | 0.896176i | \(-0.353666\pi\) |
−0.896176 | + | 0.443699i | \(0.853666\pi\) | |||||||
\(758\) | 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 | \(0.577676\pi\) | |||||||
\(762\) | 321.027 | − | 0.888006i | 0.421296 | − | 0.00116536i | ||||
\(763\) | 282.425 | − | 1325.89i | 0.370151 | − | 1.73773i | ||||
\(764\) | −360.534 | −0.471904 | ||||||||
\(765\) | −942.449 | − | 31.4021i | −1.23196 | − | 0.0410485i | ||||
\(766\) | − | 88.2335i | − | 0.115187i | ||||||
\(767\) | 16.1080 | − | 16.1080i | 0.0210013 | − | 0.0210013i | ||||
\(768\) | −47.9998 | + | 0.132774i | −0.0624998 | + | 0.000172883i | ||||
\(769\) | −217.804 | −0.283230 | −0.141615 | − | 0.989922i | \(-0.545230\pi\) | ||||
−0.141615 | + | 0.989922i | \(0.545230\pi\) | |||||||
\(770\) | −291.978 | − | 74.1534i | −0.379192 | − | 0.0963031i | ||||
\(771\) | −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 | −0.889785 | − | 0.456380i | \(-0.849146\pi\) |
0.456380 | + | 0.889785i | \(0.349146\pi\) | |||||||
\(774\) | 4.48145 | + | 810.048i | 0.00578998 | + | 1.04657i | ||||
\(775\) | −108.730 | − | 8.46308i | −0.140297 | − | 0.0109201i | ||||
\(776\) | −242.487 | −0.312483 | ||||||||
\(777\) | 26.6791 | + | 40.8730i | 0.0343360 | + | 0.0526037i | ||||
\(778\) | 116.363 | − | 116.363i | 0.149566 | − | 0.149566i | ||||
\(779\) | −863.096 | −1.10795 | ||||||||
\(780\) | 6.12123 | − | 169.614i | 0.00784773 | − | 0.217454i | ||||
\(781\) | 747.717 | 0.957384 | ||||||||
\(782\) | 611.321 | + | 611.321i | 0.781740 | + | 0.781740i | ||||
\(783\) | 527.339 | − | 4.37617i | 0.673485 | − | 0.00558897i | ||||
\(784\) | −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 | \(-0.826502\pi\) |
0.518469 | + | 0.855096i | \(0.326502\pi\) | |||||||
\(788\) | 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 | ||||
\(792\) | 108.942 | − | 110.154i | 0.137553 | − | 0.139084i | ||||
\(793\) | 260.859 | − | 260.859i | 0.328952 | − | 0.328952i | ||||
\(794\) | 17.4719i | 0.0220050i | ||||||||
\(795\) | −13.8396 | − | 0.499460i | −0.0174083 | − | 0.000628252i | ||||
\(796\) | 407.552i | 0.511999i | ||||||||
\(797\) | −708.060 | − | 708.060i | −0.888407 | − | 0.888407i | 0.105963 | − | 0.994370i | \(-0.466207\pi\) |
−0.994370 | + | 0.105963i | \(0.966207\pi\) | |||||||
\(798\) | −507.808 | + | 331.462i | −0.636351 | + | 0.415366i | ||||
\(799\) | 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 | ||||
\(805\) | −989.642 | − | 251.339i | −1.22937 | − | 0.312222i | ||||
\(806\) | − | 34.9027i | − | 0.0433036i | ||||||
\(807\) | 0.744679 | + | 269.212i | 0.000922774 | + | 0.333597i | ||||
\(808\) | 192.622 | + | 192.622i | 0.238393 | + | 0.238393i | ||||
\(809\) | 1263.12 | 1.56133 | 0.780666 | − | 0.624949i | \(-0.214880\pi\) | ||||
0.780666 | + | 0.624949i | \(0.214880\pi\) | |||||||
\(810\) | −15.9063 | + | 572.536i | −0.0196374 | + | 0.706834i | ||||
\(811\) | 26.8053i | 0.0330522i | 0.999863 | + | 0.0165261i | \(0.00526066\pi\) | ||||
−0.999863 | + | 0.0165261i | \(0.994739\pi\) | |||||||
\(812\) | −56.9679 | + | 267.444i | −0.0701575 | + | 0.329365i | ||||
\(813\) | −2.64175 | − | 955.031i | −0.00324938 | − | 1.17470i | ||||
\(814\) | − | 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 | \(0.964967\pi\) | |||||||
\(822\) | −0.279380 | − | 101.000i | −0.000339879 | − | 0.122871i | ||||
\(823\) | 138.696 | − | 138.696i | 0.168525 | − | 0.168525i | −0.617806 | − | 0.786331i | \(-0.711978\pi\) |
0.786331 | + | 0.617806i | \(0.211978\pi\) | |||||||
\(824\) | − | 454.408i | − | 0.551467i | ||||||
\(825\) | −455.178 | − | 34.1627i | −0.551730 | − | 0.0414093i | ||||
\(826\) | −21.6953 | − | 33.4395i | −0.0262656 | − | 0.0404837i | ||||
\(827\) | 219.678 | − | 219.678i | 0.265633 | − | 0.265633i | −0.561705 | − | 0.827338i | \(-0.689854\pi\) |
0.827338 | + | 0.561705i | \(0.189854\pi\) | |||||||
\(828\) | 369.253 | − | 373.362i | 0.445958 | − | 0.450920i | ||||
\(829\) | −459.488 | −0.554268 | −0.277134 | − | 0.960831i | \(-0.589385\pi\) | ||||
−0.277134 | + | 0.960831i | \(0.589385\pi\) | |||||||
\(830\) | 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 | ||||
\(833\) | 367.141 | + | 958.910i | 0.440745 | + | 1.15115i | ||||
\(834\) | 89.8746 | − | 90.3732i | 0.107763 | − | 0.108361i | ||||
\(835\) | −1024.28 | − | 39.8027i | −1.22668 | − | 0.0476679i | ||||
\(836\) | 248.544 | 0.297301 | ||||||||
\(837\) | 0.977402 | + | 117.779i | 0.00116774 | + | 0.140716i | ||||
\(838\) | −339.624 | − | 339.624i | −0.405279 | − | 0.405279i | ||||
\(839\) | − | 122.197i | − | 0.145646i | −0.997345 | − | 0.0728232i | \(-0.976799\pi\) | ||
0.997345 | − | 0.0728232i | \(-0.0232009\pi\) | |||||||
\(840\) | −288.048 | − | 72.3078i | −0.342914 | − | 0.0860807i | ||||
\(841\) | −459.511 | −0.546386 | ||||||||
\(842\) | 699.038 | − | 699.038i | 0.830211 | − | 0.830211i | ||||
\(843\) | −3.57836 | − | 1293.63i | −0.00424479 | − | 1.53456i | ||||
\(844\) | 535.089i | 0.633992i | ||||||||
\(845\) | 465.171 | + | 502.785i | 0.550498 | + | 0.595011i | ||||
\(846\) | 660.560 | − | 3.65443i | 0.780804 | − | 0.00431965i | ||||
\(847\) | 574.820 | + | 122.441i | 0.678654 | + | 0.144559i | ||||
\(848\) | 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 | ||||||
\(852\) | 737.135 | − | 2.03902i | 0.865183 | − | 0.00239321i | ||||
\(853\) | 80.0867 | + | 80.0867i | 0.0938883 | + | 0.0938883i | 0.752491 | − | 0.658603i | \(-0.228852\pi\) |
−0.658603 | + | 0.752491i | \(0.728852\pi\) | |||||||
\(854\) | −351.342 | − | 541.531i | −0.411407 | − | 0.634111i | ||||
\(855\) | −671.004 | + | 627.731i | −0.784800 | + | 0.734188i | ||||
\(856\) | −320.147 | −0.374004 | ||||||||
\(857\) | 93.1855 | + | 93.1855i | 0.108735 | + | 0.108735i | 0.759381 | − | 0.650646i | \(-0.225502\pi\) |
−0.650646 | + | 0.759381i | \(0.725502\pi\) | |||||||
\(858\) | −0.404084 | − | 146.082i | −0.000470960 | − | 0.170259i | ||||
\(859\) | 885.439 | 1.03078 | 0.515389 | − | 0.856956i | \(-0.327647\pi\) | ||||
0.515389 | + | 0.856956i | \(0.327647\pi\) | |||||||
\(860\) | −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 | \(-0.416914\pi\) |
−0.966127 | + | 0.258067i | \(0.916914\pi\) | |||||||
\(864\) | 107.100 | − | 108.892i | 0.123958 | − | 0.126033i | ||||
\(865\) | −13.2431 | + | 340.796i | −0.0153099 | + | 0.393984i | ||||
\(866\) | 680.214 | 0.785466 | ||||||||
\(867\) | −1.24567 | − | 450.326i | −0.00143675 | − | 0.519408i | ||||
\(868\) | −59.7328 | − | 12.7236i | −0.0688166 | − | 0.0146585i | ||||
\(869\) | −767.165 | −0.882814 | ||||||||
\(870\) | −14.9431 | + | 414.061i | −0.0171760 | + | 0.475933i | ||||
\(871\) | 477.801i | 0.548566i | ||||||||
\(872\) | −387.324 | + | 387.324i | −0.444179 | + | 0.444179i | ||||
\(873\) | 542.569 | − | 548.605i | 0.621499 | − | 0.628414i | ||||
\(874\) | 842.426 | 0.963874 | ||||||||
\(875\) | 387.676 | + | 784.431i | 0.443059 | + | 0.896493i | ||||
\(876\) | 78.6299 | − | 79.0661i | 0.0897602 | − | 0.0902582i | ||||
\(877\) | −176.159 | − | 176.159i | −0.200866 | − | 0.200866i | 0.599505 | − | 0.800371i | \(-0.295364\pi\) |
−0.800371 | + | 0.599505i | \(0.795364\pi\) | |||||||
\(878\) | 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 | \(0.350760\pi\) | |||||||
\(882\) | 581.195 | − | 226.218i | 0.658951 | − | 0.256483i | ||||
\(883\) | −1116.28 | + | 1116.28i | −1.26419 | + | 1.26419i | −0.315146 | + | 0.949043i | \(0.602054\pi\) |
−0.949043 | + | 0.315146i | \(0.897946\pi\) | |||||||
\(884\) | 237.105 | 0.268218 | ||||||||
\(885\) | −41.1400 | − | 44.2206i | −0.0464859 | − | 0.0499668i | ||||
\(886\) | 221.979 | 0.250541 | ||||||||
\(887\) | 992.100 | + | 992.100i | 1.11849 | + | 1.11849i | 0.991963 | + | 0.126525i | \(0.0403825\pi\) |
0.126525 | + | 0.991963i | \(0.459617\pi\) | |||||||
\(888\) | −0.0545538 | − | 19.7220i | −6.14344e−5 | − | 0.0222095i | ||||
\(889\) | −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 | ||||
\(897\) | −1.36962 | − | 495.138i | −0.00152689 | − | 0.551993i | ||||
\(898\) | −196.292 | + | 196.292i | −0.218588 | + | 0.218588i | ||||
\(899\) | 85.2043i | 0.0947767i | ||||||||
\(900\) | −448.829 | − | 32.4380i | −0.498699 | − | 0.0360422i | ||||
\(901\) | − | 19.3465i | − | 0.0214722i | ||||||
\(902\) | −257.255 | − | 257.255i | −0.285206 | − | 0.285206i | ||||
\(903\) | 1119.21 | − | 730.542i | 1.23943 | − | 0.809016i | ||||
\(904\) | 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 | 0.189678 | − | 0.981846i | \(-0.439256\pi\) |
−0.981846 | + | 0.189678i | \(0.939256\pi\) | |||||||
\(908\) | −87.5405 | + | 87.5405i | −0.0964103 | + | 0.0964103i | ||||
\(909\) | −866.784 | + | 4.79532i | −0.953557 | + | 0.00527538i | ||||
\(910\) | −240.661 | + | 143.178i | −0.264463 | + | 0.157338i | ||||
\(911\) | 142.178i | 0.156068i | 0.996951 | + | 0.0780339i | \(0.0248642\pi\) | ||||
−0.996951 | + | 0.0780339i | \(0.975136\pi\) | |||||||
\(912\) | 245.027 | − | 0.677778i | 0.268670 | − | 0.000743177i | ||||
\(913\) | 74.2810 | + | 74.2810i | 0.0813593 | + | 0.0813593i | ||||
\(914\) | 104.860 | 0.114726 | ||||||||
\(915\) | −666.235 | − | 716.123i | −0.728126 | − | 0.782648i | ||||
\(916\) | − | 149.339i | − | 0.163034i | ||||||
\(917\) | −1559.60 | − | 332.207i | −1.70076 | − | 0.362276i | ||||
\(918\) | −800.111 | + | 6.63979i | −0.871580 | + | 0.00723288i | ||||
\(919\) | 722.274i | 0.785934i | 0.919553 | + | 0.392967i | \(0.128551\pi\) | ||||
−0.919553 | + | 0.392967i | \(0.871449\pi\) | |||||||
\(920\) | 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 | ||||||
\(927\) | 1028.06 | + | 1016.75i | 1.10902 | + | 1.09681i | ||||
\(928\) | 78.1270 | − | 78.1270i | 0.0841886 | − | 0.0841886i | ||||
\(929\) | − | 274.997i | − | 0.296014i | −0.988986 | − | 0.148007i | \(-0.952714\pi\) | ||
0.988986 | − | 0.148007i | \(-0.0472858\pi\) | |||||||
\(930\) | −92.4792 | − | 3.33750i | −0.0994400 | − | 0.00358871i | ||||
\(931\) | 913.677 | + | 407.742i | 0.981393 | + | 0.437961i | ||||
\(932\) | −479.077 | + | 479.077i | −0.514031 | + | 0.514031i | ||||
\(933\) | −341.276 | + | 0.944017i | −0.365784 | + | 0.00101181i | ||||
\(934\) | −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 | \(-0.584514\pi\) |
0.964959 | + | 0.262399i | \(0.0845138\pi\) | |||||||
\(938\) | 817.713 | + | 174.180i | 0.871763 | + | 0.185693i | ||||
\(939\) | 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 | \(0.176648\pi\) | |||||||
\(942\) | −1.62342 | − | 586.892i | −0.00172338 | − | 0.623027i | ||||
\(943\) | −871.953 | − | 871.953i | −0.924659 | − | 0.924659i | ||||
\(944\) | 16.1062i | 0.0170617i | ||||||||
\(945\) | 808.102 | − | 489.893i | 0.855135 | − | 0.518406i | ||||
\(946\) | −547.790 | −0.579060 | ||||||||
\(947\) | −135.247 | + | 135.247i | −0.142816 | + | 0.142816i | −0.774900 | − | 0.632084i | \(-0.782200\pi\) |
0.632084 | + | 0.774900i | \(0.282200\pi\) | |||||||
\(948\) | −756.309 | + | 2.09205i | −0.797794 | + | 0.00220681i | ||||
\(949\) | − | 105.143i | − | 0.110793i | ||||||
\(950\) | −469.322 | − | 548.548i | −0.494023 | − | 0.577419i | ||||
\(951\) | −645.128 | + | 648.707i | −0.678368 | + | 0.682132i | ||||
\(952\) | 86.4351 | − | 405.783i | 0.0907932 | − | 0.426243i | ||||
\(953\) | −1333.30 | − | 1333.30i | −1.39905 | − | 1.39905i | −0.802784 | − | 0.596269i | \(-0.796649\pi\) |
−0.596269 | − | 0.802784i | \(-0.703351\pi\) | |||||||
\(954\) | −11.7508 | + | 0.0650090i | −0.0123174 | + | 6.81436e-5i | ||||
\(955\) | 612.112 | + | 661.608i | 0.640955 | + | 0.692783i | ||||
\(956\) | 68.0480i | 0.0711799i | ||||||||
\(957\) | 0.986447 | + | 356.615i | 0.00103077 | + | 0.372639i | ||||
\(958\) | −30.2411 | − | 30.2411i | −0.0315670 | − | 0.0315670i | ||||
\(959\) | −139.797 | + | 90.6995i | −0.145774 | + | 0.0945772i | ||||
\(960\) | 81.7373 | + | 87.8579i | 0.0851431 | + | 0.0915186i | ||||
\(961\) | 941.970 | 0.980198 | ||||||||
\(962\) | −13.1495 | − | 13.1495i | −0.0136689 | − | 0.0136689i | ||||
\(963\) | 716.336 | − | 724.306i | 0.743858 | − | 0.752135i | ||||
\(964\) | −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 | 0.930680 | − | 0.365835i | \(-0.119217\pi\) |
−0.365835 | + | 0.930680i | \(0.619217\pi\) | |||||||
\(968\) | −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 | \(0.587543\pi\) | |||||||
\(972\) | 6.72148 | + | 485.954i | 0.00691511 | + | 0.499952i | ||||
\(973\) | −205.676 | − | 43.8106i | −0.211383 | − | 0.0450263i | ||||
\(974\) | −499.374 | −0.512704 | ||||||||
\(975\) | −321.647 | + | 276.737i | −0.329895 | + | 0.283832i | ||||
\(976\) | 260.830i | 0.267243i | ||||||||
\(977\) | −1236.41 | + | 1236.41i | −1.26551 | + | 1.26551i | −0.317134 | + | 0.948381i | \(0.602720\pi\) |
−0.948381 | + | 0.317134i | \(0.897280\pi\) | |||||||
\(978\) | 0.0150891 | + | 5.45493i | 1.54285e−5 | + | 0.00557764i | ||||
\(979\) | 592.160 | 0.604862 | ||||||||
\(980\) | 157.304 | + | 464.064i | 0.160514 | + | 0.473535i | ||||
\(981\) | −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 | −0.960003 | − | 0.279989i | \(-0.909669\pi\) |
0.279989 | + | 0.960003i | \(0.409669\pi\) | |||||||
\(984\) | −254.317 | − | 252.913i | −0.258452 | − | 0.257026i | ||||
\(985\) | 21.6065 | − | 556.021i | 0.0219355 | − | 0.564488i | ||||
\(986\) | −578.819 | −0.587037 | ||||||||
\(987\) | −595.726 | − | 912.666i | −0.603572 | − | 0.924687i | ||||
\(988\) | 163.370 | − | 163.370i | 0.165354 | − | 0.165354i | ||||
\(989\) | −1856.71 | −1.87736 | ||||||||
\(990\) | −387.102 | − | 12.8981i | −0.391013 | − | 0.0130284i | ||||
\(991\) | 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 | ||||
\(993\) | −211.390 | + | 0.584735i | −0.212880 | + | 0.000588857i | ||||
\(994\) | −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 | \(-0.588041\pi\) |
0.961993 | + | 0.273074i | \(0.0880405\pi\) | |||||||
\(998\) | 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.b.167.1 | yes | 32 | |
3.2 | odd | 2 | 210.3.k.a.167.9 | yes | 32 | ||
5.3 | odd | 4 | 210.3.k.a.83.8 | ✓ | 32 | ||
7.6 | odd | 2 | inner | 210.3.k.b.167.16 | yes | 32 | |
15.8 | even | 4 | inner | 210.3.k.b.83.16 | yes | 32 | |
21.20 | even | 2 | 210.3.k.a.167.8 | yes | 32 | ||
35.13 | even | 4 | 210.3.k.a.83.9 | yes | 32 | ||
105.83 | odd | 4 | inner | 210.3.k.b.83.1 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.k.a.83.8 | ✓ | 32 | 5.3 | odd | 4 | ||
210.3.k.a.83.9 | yes | 32 | 35.13 | even | 4 | ||
210.3.k.a.167.8 | yes | 32 | 21.20 | even | 2 | ||
210.3.k.a.167.9 | yes | 32 | 3.2 | odd | 2 | ||
210.3.k.b.83.1 | yes | 32 | 105.83 | odd | 4 | inner | |
210.3.k.b.83.16 | yes | 32 | 15.8 | even | 4 | inner | |
210.3.k.b.167.1 | yes | 32 | 1.1 | even | 1 | trivial | |
210.3.k.b.167.16 | yes | 32 | 7.6 | odd | 2 | inner |