Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [180,3,Mod(19,180)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(180, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("180.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 180.f (of order \(2\), degree \(1\), 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: | \(4.90464475849\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.389136420864.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 24x^{4} + 80x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.7 | ||
Root | \(1.52274 - 1.29664i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 180.19 |
Dual form | 180.3.f.h.19.8 |
$q$-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 \(\left(\mathbb{Z}/180\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(91\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.52274 | − | 1.29664i | 0.761369 | − | 0.648319i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.637459 | − | 3.94888i | 0.159365 | − | 0.987220i | ||||
\(5\) | −4.27492 | − | 2.59328i | −0.854983 | − | 0.518655i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.837253 | 0.119608 | 0.0598038 | − | 0.998210i | \(-0.480952\pi\) | ||||
0.0598038 | + | 0.998210i | \(0.480952\pi\) | |||||||
\(8\) | −4.14959 | − | 6.83966i | −0.518698 | − | 0.854957i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −9.87212 | + | 1.59414i | −0.987212 | + | 0.159414i | ||||
\(11\) | − | 15.7955i | − | 1.43596i | −0.696066 | − | 0.717978i | \(-0.745068\pi\) | ||
0.696066 | − | 0.717978i | \(-0.254932\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.18655i | − | 0.398966i | −0.979901 | − | 0.199483i | \(-0.936074\pi\) | ||
0.979901 | − | 0.199483i | \(-0.0639262\pi\) | |||||||
\(14\) | 1.27492 | − | 1.08561i | 0.0910655 | − | 0.0775439i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −15.1873 | − | 5.03449i | −0.949206 | − | 0.314656i | ||||
\(17\) | 27.3586i | 1.60933i | 0.593728 | + | 0.804666i | \(0.297656\pi\) | ||||
−0.593728 | + | 0.804666i | \(0.702344\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 17.9667i | − | 0.945618i | −0.881165 | − | 0.472809i | \(-0.843240\pi\) | ||
0.881165 | − | 0.472809i | \(-0.156760\pi\) | |||||||
\(20\) | −12.9656 | + | 15.2280i | −0.648281 | + | 0.761401i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −20.4811 | − | 24.0524i | −0.930958 | − | 1.09329i | ||||
\(23\) | 19.1101 | 0.830874 | 0.415437 | − | 0.909622i | \(-0.363629\pi\) | ||||
0.415437 | + | 0.909622i | \(0.363629\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.5498 | + | 22.1721i | 0.461993 | + | 0.886883i | ||||
\(26\) | −6.72508 | − | 7.89776i | −0.258657 | − | 0.303760i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.533714 | − | 3.30621i | 0.0190612 | − | 0.118079i | ||||
\(29\) | 45.6495 | 1.57412 | 0.787060 | − | 0.616876i | \(-0.211602\pi\) | ||||
0.787060 | + | 0.616876i | \(0.211602\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 13.6243i | − | 0.439493i | −0.975557 | − | 0.219747i | \(-0.929477\pi\) | ||
0.975557 | − | 0.219747i | \(-0.0705230\pi\) | |||||||
\(32\) | −29.6542 | + | 12.0262i | −0.926693 | + | 0.375819i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 35.4743 | + | 41.6600i | 1.04336 | + | 1.22529i | ||||
\(35\) | −3.57919 | − | 2.17123i | −0.102263 | − | 0.0620351i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 15.5597i | 0.420531i | 0.977644 | + | 0.210266i | \(0.0674329\pi\) | ||||
−0.977644 | + | 0.210266i | \(0.932567\pi\) | |||||||
\(38\) | −23.2964 | − | 27.3586i | −0.613062 | − | 0.719964i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.00200734 | + | 40.0000i | 5.01834e−5 | + | 1.00000i | ||||
\(41\) | −13.2990 | −0.324366 | −0.162183 | − | 0.986761i | \(-0.551853\pi\) | ||||
−0.162183 | + | 0.986761i | \(0.551853\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.9430 | 0.649837 | 0.324918 | − | 0.945742i | \(-0.394663\pi\) | ||||
0.324918 | + | 0.945742i | \(0.394663\pi\) | |||||||
\(44\) | −62.3746 | − | 10.0690i | −1.41760 | − | 0.228841i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 29.0997 | − | 24.7789i | 0.632601 | − | 0.538672i | ||||
\(47\) | 55.6558 | 1.18417 | 0.592083 | − | 0.805877i | \(-0.298306\pi\) | ||||
0.592083 | + | 0.805877i | \(0.298306\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.2990 | −0.985694 | ||||||||
\(50\) | 46.3365 | + | 18.7863i | 0.926731 | + | 0.375726i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −20.4811 | − | 3.30621i | −0.393867 | − | 0.0635810i | ||||
\(53\) | − | 15.5597i | − | 0.293578i | −0.989168 | − | 0.146789i | \(-0.953106\pi\) | ||
0.989168 | − | 0.146789i | \(-0.0468939\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −40.9621 | + | 67.5245i | −0.744766 | + | 1.22772i | ||||
\(56\) | −3.47425 | − | 5.72653i | −0.0620403 | − | 0.102259i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 69.5122 | − | 59.1909i | 1.19849 | − | 1.02053i | ||||
\(59\) | 87.6625i | 1.48581i | 0.669400 | + | 0.742903i | \(0.266551\pi\) | ||||
−0.669400 | + | 0.742903i | \(0.733449\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 38.0000 | 0.622951 | 0.311475 | − | 0.950254i | \(-0.399177\pi\) | ||||
0.311475 | + | 0.950254i | \(0.399177\pi\) | |||||||
\(62\) | −17.6658 | − | 20.7462i | −0.284932 | − | 0.334616i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −29.5619 | + | 56.7635i | −0.461904 | + | 0.886930i | ||||
\(65\) | −13.4502 | + | 22.1721i | −0.206926 | + | 0.341109i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 92.2015 | 1.37614 | 0.688071 | − | 0.725643i | \(-0.258458\pi\) | ||||
0.688071 | + | 0.725643i | \(0.258458\pi\) | |||||||
\(68\) | 108.036 | + | 17.4400i | 1.58876 | + | 0.256471i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.26547 | + | 1.33470i | −0.118078 | + | 0.0190672i | ||||
\(71\) | − | 130.707i | − | 1.84094i | −0.390816 | − | 0.920469i | \(-0.627807\pi\) | ||
0.390816 | − | 0.920469i | \(-0.372193\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 54.7173i | − | 0.749552i | −0.927115 | − | 0.374776i | \(-0.877720\pi\) | ||
0.927115 | − | 0.374776i | \(-0.122280\pi\) | |||||||
\(74\) | 20.1752 | + | 23.6933i | 0.272638 | + | 0.320179i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −70.9485 | − | 11.4531i | −0.933533 | − | 0.150698i | ||||
\(77\) | − | 13.2249i | − | 0.171751i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6243i | 0.172459i | 0.996275 | + | 0.0862297i | \(0.0274819\pi\) | ||||
−0.996275 | + | 0.0862297i | \(0.972518\pi\) | |||||||
\(80\) | 51.8686 | + | 60.9069i | 0.648357 | + | 0.761336i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −20.2509 | + | 17.2440i | −0.246962 | + | 0.210293i | ||||
\(83\) | −59.0048 | −0.710901 | −0.355451 | − | 0.934695i | \(-0.615673\pi\) | ||||
−0.355451 | + | 0.934695i | \(0.615673\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 70.9485 | − | 116.956i | 0.834688 | − | 1.37595i | ||||
\(86\) | 42.5498 | − | 36.2319i | 0.494766 | − | 0.421302i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −108.036 | + | 65.5448i | −1.22768 | + | 0.744828i | ||||
\(89\) | −39.8007 | −0.447198 | −0.223599 | − | 0.974681i | \(-0.571781\pi\) | ||||
−0.223599 | + | 0.974681i | \(0.571781\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 4.34246i | − | 0.0477193i | ||||||
\(92\) | 12.1819 | − | 75.4635i | 0.132412 | − | 0.820255i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 84.7492 | − | 72.1654i | 0.901587 | − | 0.767717i | ||||
\(95\) | −46.5927 | + | 76.8064i | −0.490450 | + | 0.808488i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 168.821i | 1.74043i | 0.492675 | + | 0.870214i | \(0.336019\pi\) | ||||
−0.492675 | + | 0.870214i | \(0.663981\pi\) | |||||||
\(98\) | −73.5467 | + | 62.6263i | −0.750477 | + | 0.639044i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 94.9174 | − | 31.4751i | 0.949174 | − | 0.314751i | ||||
\(101\) | −44.5498 | −0.441087 | −0.220544 | − | 0.975377i | \(-0.570783\pi\) | ||||
−0.220544 | + | 0.975377i | \(0.570783\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −126.466 | −1.22782 | −0.613911 | − | 0.789375i | \(-0.710405\pi\) | ||||
−0.613911 | + | 0.789375i | \(0.710405\pi\) | |||||||
\(104\) | −35.4743 | + | 21.5220i | −0.341099 | + | 0.206943i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.1752 | − | 23.6933i | −0.190333 | − | 0.223521i | ||||
\(107\) | −104.383 | −0.975546 | −0.487773 | − | 0.872971i | \(-0.662191\pi\) | ||||
−0.487773 | + | 0.872971i | \(0.662191\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.501656 | −0.00460235 | −0.00230117 | − | 0.999997i | \(-0.500732\pi\) | ||||
−0.00230117 | + | 0.999997i | \(0.500732\pi\) | |||||||
\(110\) | 25.1803 | + | 155.935i | 0.228912 | + | 1.41759i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.7156 | − | 4.21515i | −0.113532 | − | 0.0376352i | ||||
\(113\) | − | 16.9855i | − | 0.150314i | −0.997172 | − | 0.0751572i | \(-0.976054\pi\) | ||
0.997172 | − | 0.0751572i | \(-0.0239459\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −81.6941 | − | 49.5578i | −0.710384 | − | 0.430937i | ||||
\(116\) | 29.0997 | − | 180.264i | 0.250859 | − | 1.55400i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 113.667 | + | 133.487i | 0.963276 | + | 1.13125i | ||||
\(119\) | 22.9061i | 0.192488i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −128.498 | −1.06197 | ||||||||
\(122\) | 57.8640 | − | 49.2723i | 0.474295 | − | 0.403871i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −53.8007 | − | 8.68492i | −0.433876 | − | 0.0700397i | ||||
\(125\) | 8.12376 | − | 124.736i | 0.0649901 | − | 0.997886i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.45598 | 0.0665825 | 0.0332913 | − | 0.999446i | \(-0.489401\pi\) | ||||
0.0332913 | + | 0.999446i | \(0.489401\pi\) | |||||||
\(128\) | 28.5867 | + | 124.767i | 0.223334 | + | 0.974742i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.26810 | + | 51.2023i | 0.0636008 | + | 0.393864i | ||||
\(131\) | 51.7290i | 0.394878i | 0.980315 | + | 0.197439i | \(0.0632624\pi\) | ||||
−0.980315 | + | 0.197439i | \(0.936738\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 15.0427i | − | 0.113103i | ||||||
\(134\) | 140.399 | − | 119.552i | 1.04775 | − | 0.892179i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 187.124 | − | 113.527i | 1.37591 | − | 0.834757i | ||||
\(137\) | − | 53.8083i | − | 0.392762i | −0.980528 | − | 0.196381i | \(-0.937081\pi\) | ||
0.980528 | − | 0.196381i | \(-0.0629189\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 13.6243i | − | 0.0980165i | −0.998798 | − | 0.0490082i | \(-0.984394\pi\) | ||
0.998798 | − | 0.0490082i | \(-0.0156061\pi\) | |||||||
\(140\) | −10.8555 | + | 12.7497i | −0.0775393 | + | 0.0910694i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −169.479 | − | 199.032i | −1.19352 | − | 1.40163i | ||||
\(143\) | −81.9243 | −0.572897 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −195.148 | − | 118.382i | −1.34585 | − | 0.816426i | ||||
\(146\) | −70.9485 | − | 83.3200i | −0.485949 | − | 0.570685i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 61.4432 | + | 9.91864i | 0.415157 | + | 0.0670178i | ||||
\(149\) | 33.6495 | 0.225836 | 0.112918 | − | 0.993604i | \(-0.463980\pi\) | ||||
0.112918 | + | 0.993604i | \(0.463980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 139.988i | − | 0.927076i | −0.886077 | − | 0.463538i | \(-0.846580\pi\) | ||
0.886077 | − | 0.463538i | \(-0.153420\pi\) | |||||||
\(152\) | −122.886 | + | 74.5546i | −0.808463 | + | 0.490490i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −17.1478 | − | 20.1380i | −0.111350 | − | 0.130766i | ||||
\(155\) | −35.3315 | + | 58.2427i | −0.227945 | + | 0.375759i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 21.2631i | − | 0.135434i | −0.997705 | − | 0.0677170i | \(-0.978428\pi\) | ||
0.997705 | − | 0.0677170i | \(-0.0215715\pi\) | |||||||
\(158\) | 17.6658 | + | 20.7462i | 0.111809 | + | 0.131305i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 157.956 | + | 25.4904i | 0.987228 | + | 0.159315i | ||||
\(161\) | 16.0000 | 0.0993789 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −210.211 | −1.28964 | −0.644819 | − | 0.764335i | \(-0.723067\pi\) | ||||
−0.644819 | + | 0.764335i | \(0.723067\pi\) | |||||||
\(164\) | −8.47757 | + | 52.5162i | −0.0516925 | + | 0.320221i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −89.8488 | + | 76.5079i | −0.541258 | + | 0.460891i | ||||
\(167\) | 238.384 | 1.42745 | 0.713725 | − | 0.700426i | \(-0.247006\pi\) | ||||
0.713725 | + | 0.700426i | \(0.247006\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 142.100 | 0.840826 | ||||||||
\(170\) | −43.6136 | − | 270.088i | −0.256550 | − | 1.58875i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 17.8125 | − | 110.343i | 0.103561 | − | 0.641532i | ||||
\(173\) | − | 2.33481i | − | 0.0134960i | −0.999977 | − | 0.00674800i | \(-0.997852\pi\) | ||
0.999977 | − | 0.00674800i | \(-0.00214797\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.67014 | + | 18.5637i | 0.0552579 | + | 0.106078i | ||||
\(176\) | −79.5224 | + | 239.891i | −0.451832 | + | 1.36302i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −60.6060 | + | 51.6071i | −0.340483 | + | 0.289927i | ||||
\(179\) | − | 227.054i | − | 1.26846i | −0.773145 | − | 0.634229i | \(-0.781318\pi\) | ||
0.773145 | − | 0.634229i | \(-0.218682\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 114.096 | 0.630367 | 0.315183 | − | 0.949031i | \(-0.397934\pi\) | ||||
0.315183 | + | 0.949031i | \(0.397934\pi\) | |||||||
\(182\) | −5.63060 | − | 6.61243i | −0.0309374 | − | 0.0363320i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −79.2990 | − | 130.707i | −0.430973 | − | 0.710362i | ||||
\(185\) | 40.3505 | − | 66.5163i | 0.218111 | − | 0.359547i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 432.144 | 2.31093 | ||||||||
\(188\) | 35.4783 | − | 219.778i | 0.188714 | − | 1.16903i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 28.6415 | + | 177.370i | 0.150745 | + | 0.933525i | ||||
\(191\) | 139.392i | 0.729798i | 0.931047 | + | 0.364899i | \(0.118897\pi\) | ||||
−0.931047 | + | 0.364899i | \(0.881103\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 182.046i | 0.943245i | 0.881801 | + | 0.471623i | \(0.156331\pi\) | ||||
−0.881801 | + | 0.471623i | \(0.843669\pi\) | |||||||
\(194\) | 218.900 | + | 257.071i | 1.12835 | + | 1.32511i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −30.7886 | + | 190.727i | −0.157085 | + | 0.973097i | ||||
\(197\) | 258.027i | 1.30978i | 0.755724 | + | 0.654890i | \(0.227285\pi\) | ||||
−0.755724 | + | 0.654890i | \(0.772715\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 256.474i | 1.28881i | 0.764683 | + | 0.644407i | \(0.222896\pi\) | ||||
−0.764683 | + | 0.644407i | \(0.777104\pi\) | |||||||
\(200\) | 103.722 | − | 171.002i | 0.518612 | − | 0.855009i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −67.8377 | + | 57.7650i | −0.335830 | + | 0.285965i | ||||
\(203\) | 38.2202 | 0.188277 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 56.8522 | + | 34.4880i | 0.277328 | + | 0.168234i | ||||
\(206\) | −192.574 | + | 163.980i | −0.934825 | + | 0.796020i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −26.1117 | + | 78.7697i | −0.125537 | + | 0.378700i | ||||
\(209\) | −283.794 | −1.35787 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 211.855i | 1.00405i | 0.864852 | + | 0.502027i | \(0.167412\pi\) | ||||
−0.864852 | + | 0.502027i | \(0.832588\pi\) | |||||||
\(212\) | −61.4432 | − | 9.91864i | −0.289826 | − | 0.0467860i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −158.949 | + | 135.348i | −0.742750 | + | 0.632465i | ||||
\(215\) | −119.454 | − | 72.4639i | −0.555600 | − | 0.337041i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 11.4070i | − | 0.0525667i | ||||||
\(218\) | −0.763890 | + | 0.650466i | −0.00350408 | + | 0.00298379i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 240.535 | + | 204.799i | 1.09334 | + | 0.930903i | ||||
\(221\) | 141.897 | 0.642068 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 349.843 | 1.56880 | 0.784401 | − | 0.620255i | \(-0.212971\pi\) | ||||
0.784401 | + | 0.620255i | \(0.212971\pi\) | |||||||
\(224\) | −24.8281 | + | 10.0690i | −0.110840 | + | 0.0449508i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −22.0241 | − | 25.8645i | −0.0974517 | − | 0.114445i | ||||
\(227\) | 185.554 | 0.817418 | 0.408709 | − | 0.912665i | \(-0.365979\pi\) | ||||
0.408709 | + | 0.912665i | \(0.365979\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 263.897 | 1.15239 | 0.576194 | − | 0.817313i | \(-0.304537\pi\) | ||||
0.576194 | + | 0.817313i | \(0.304537\pi\) | |||||||
\(230\) | −188.657 | + | 30.4642i | −0.820249 | + | 0.132453i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −189.427 | − | 312.227i | −0.816494 | − | 1.34581i | ||||
\(233\) | 58.4780i | 0.250978i | 0.992095 | + | 0.125489i | \(0.0400500\pi\) | ||||
−0.992095 | + | 0.125489i | \(0.959950\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −237.924 | − | 144.331i | −1.01244 | − | 0.614174i | ||||
\(236\) | 346.169 | + | 55.8812i | 1.46682 | + | 0.236785i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 29.7009 | + | 34.8800i | 0.124794 | + | 0.146555i | ||||
\(239\) | − | 113.337i | − | 0.474212i | −0.971484 | − | 0.237106i | \(-0.923801\pi\) | ||
0.971484 | − | 0.237106i | \(-0.0761989\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −77.7940 | −0.322797 | −0.161398 | − | 0.986889i | \(-0.551600\pi\) | ||||
−0.161398 | + | 0.986889i | \(0.551600\pi\) | |||||||
\(242\) | −195.669 | + | 166.616i | −0.808551 | + | 0.688495i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 24.2234 | − | 150.057i | 0.0992763 | − | 0.614989i | ||||
\(245\) | 206.474 | + | 125.253i | 0.842752 | + | 0.511235i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −93.1855 | −0.377269 | ||||||||
\(248\) | −93.1855 | + | 56.5351i | −0.375748 | + | 0.227964i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −149.367 | − | 200.473i | −0.597467 | − | 0.801893i | ||||
\(251\) | 106.226i | 0.423212i | 0.977355 | + | 0.211606i | \(0.0678693\pi\) | ||||
−0.977355 | + | 0.211606i | \(0.932131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 301.854i | − | 1.19310i | ||||||
\(254\) | 12.8762 | − | 10.9644i | 0.0506939 | − | 0.0431667i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 205.308 | + | 152.921i | 0.801983 | + | 0.597346i | ||||
\(257\) | 381.078i | 1.48279i | 0.671067 | + | 0.741397i | \(0.265836\pi\) | ||||
−0.671067 | + | 0.741397i | \(0.734164\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.0274i | 0.0502988i | ||||||||
\(260\) | 78.9810 | + | 67.2469i | 0.303773 | + | 0.258642i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 67.0738 | + | 78.7697i | 0.256007 | + | 0.300648i | ||||
\(263\) | 11.4914 | 0.0436934 | 0.0218467 | − | 0.999761i | \(-0.493045\pi\) | ||||
0.0218467 | + | 0.999761i | \(0.493045\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −40.3505 | + | 66.5163i | −0.152266 | + | 0.251005i | ||||
\(266\) | −19.5050 | − | 22.9061i | −0.0733269 | − | 0.0861132i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 58.7746 | − | 364.093i | 0.219308 | − | 1.35855i | ||||
\(269\) | 77.9518 | 0.289784 | 0.144892 | − | 0.989447i | \(-0.453717\pi\) | ||||
0.144892 | + | 0.989447i | \(0.453717\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 86.6851i | 0.319871i | 0.987127 | + | 0.159936i | \(0.0511287\pi\) | ||||
−0.987127 | + | 0.159936i | \(0.948871\pi\) | |||||||
\(272\) | 137.737 | − | 415.504i | 0.506386 | − | 1.52759i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −69.7700 | − | 81.9360i | −0.254635 | − | 0.299036i | ||||
\(275\) | 350.220 | − | 182.436i | 1.27353 | − | 0.663402i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 287.328i | 1.03729i | 0.854991 | + | 0.518643i | \(0.173563\pi\) | ||||
−0.854991 | + | 0.518643i | \(0.826437\pi\) | |||||||
\(278\) | −17.6658 | − | 20.7462i | −0.0635459 | − | 0.0746267i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.00168065 | + | 33.4901i | 6.00232e−6 | + | 0.119608i | ||||
\(281\) | 224.598 | 0.799281 | 0.399641 | − | 0.916672i | \(-0.369135\pi\) | ||||
0.399641 | + | 0.916672i | \(0.369135\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −84.1224 | −0.297252 | −0.148626 | − | 0.988893i | \(-0.547485\pi\) | ||||
−0.148626 | + | 0.988893i | \(0.547485\pi\) | |||||||
\(284\) | −516.145 | − | 83.3200i | −1.81741 | − | 0.293380i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −124.749 | + | 106.226i | −0.436186 | + | 0.371420i | ||||
\(287\) | −11.1346 | −0.0387967 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −459.495 | −1.58995 | ||||||||
\(290\) | −450.657 | + | 72.7718i | −1.55399 | + | 0.250937i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −216.072 | − | 34.8800i | −0.739972 | − | 0.119452i | ||||
\(293\) | − | 246.620i | − | 0.841706i | −0.907129 | − | 0.420853i | \(-0.861731\pi\) | ||
0.907129 | − | 0.420853i | \(-0.138269\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 227.333 | − | 374.750i | 0.770621 | − | 1.27034i | ||||
\(296\) | 106.423 | − | 64.5661i | 0.359536 | − | 0.218129i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 51.2394 | − | 43.6312i | 0.171944 | − | 0.146414i | ||||
\(299\) | − | 99.1156i | − | 0.331490i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.3954 | 0.0777255 | ||||||||
\(302\) | −181.514 | − | 213.166i | −0.601041 | − | 0.705846i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −90.4535 | + | 272.866i | −0.297544 | + | 0.897586i | ||||
\(305\) | −162.447 | − | 98.5445i | −0.532613 | − | 0.323097i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −115.811 | −0.377236 | −0.188618 | − | 0.982051i | \(-0.560401\pi\) | ||||
−0.188618 | + | 0.982051i | \(0.560401\pi\) | |||||||
\(308\) | −52.2233 | − | 8.43030i | −0.169556 | − | 0.0273711i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 21.7190 | + | 134.501i | 0.0700614 | + | 0.433873i | ||||
\(311\) | 203.767i | 0.655201i | 0.944816 | + | 0.327600i | \(0.106240\pi\) | ||||
−0.944816 | + | 0.327600i | \(0.893760\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 99.0614i | 0.316490i | 0.987400 | + | 0.158245i | \(0.0505836\pi\) | ||||
−0.987400 | + | 0.158245i | \(0.949416\pi\) | |||||||
\(314\) | −27.5706 | − | 32.3782i | −0.0878045 | − | 0.103115i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 53.8007 | + | 8.68492i | 0.170255 | + | 0.0274839i | ||||
\(317\) | − | 471.192i | − | 1.48641i | −0.669063 | − | 0.743206i | \(-0.733304\pi\) | ||
0.669063 | − | 0.743206i | \(-0.266696\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 721.057i | − | 2.26037i | ||||||
\(320\) | 273.578 | − | 165.997i | 0.854931 | − | 0.518741i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 24.3638 | − | 20.7462i | 0.0756640 | − | 0.0644292i | ||||
\(323\) | 491.546 | 1.52181 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 114.997 | − | 59.9038i | 0.353836 | − | 0.184319i | ||||
\(326\) | −320.096 | + | 272.568i | −0.981891 | + | 0.836098i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 55.1854 | + | 90.9607i | 0.168248 | + | 0.277319i | ||||
\(329\) | 46.5980 | 0.141635 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 270.695i | − | 0.817810i | −0.912577 | − | 0.408905i | \(-0.865911\pi\) | ||
0.912577 | − | 0.408905i | \(-0.134089\pi\) | |||||||
\(332\) | −37.6131 | + | 233.003i | −0.113293 | + | 0.701816i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 362.997 | − | 309.098i | 1.08682 | − | 0.925444i | ||||
\(335\) | −394.154 | − | 239.104i | −1.17658 | − | 0.713743i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 377.317i | 1.11964i | 0.828615 | + | 0.559818i | \(0.189129\pi\) | ||||
−0.828615 | + | 0.559818i | \(0.810871\pi\) | |||||||
\(338\) | 216.380 | − | 184.252i | 0.640179 | − | 0.545124i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −416.618 | − | 354.722i | −1.22535 | − | 1.04330i | ||||
\(341\) | −215.203 | −0.631093 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −81.4639 | −0.237504 | ||||||||
\(344\) | −115.952 | − | 191.121i | −0.337069 | − | 0.555583i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.02740 | − | 3.55530i | −0.00874971 | − | 0.0102754i | ||||
\(347\) | −462.222 | −1.33205 | −0.666025 | − | 0.745929i | \(-0.732006\pi\) | ||||
−0.666025 | + | 0.745929i | \(0.732006\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 200.598 | 0.574779 | 0.287390 | − | 0.957814i | \(-0.407213\pi\) | ||||
0.287390 | + | 0.957814i | \(0.407213\pi\) | |||||||
\(350\) | 38.7954 | + | 15.7289i | 0.110844 | + | 0.0449397i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 189.960 | + | 468.403i | 0.539660 | + | 1.33069i | ||||
\(353\) | 250.897i | 0.710757i | 0.934722 | + | 0.355379i | \(0.115648\pi\) | ||||
−0.934722 | + | 0.355379i | \(0.884352\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −338.958 | + | 558.760i | −0.954812 | + | 1.57397i | ||||
\(356\) | −25.3713 | + | 157.168i | −0.0712676 | + | 0.441483i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −294.407 | − | 345.744i | −0.822366 | − | 0.965764i | ||||
\(359\) | 215.601i | 0.600560i | 0.953851 | + | 0.300280i | \(0.0970801\pi\) | ||||
−0.953851 | + | 0.300280i | \(0.902920\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.1960 | 0.105806 | ||||||||
\(362\) | 173.739 | − | 147.942i | 0.479941 | − | 0.408679i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −17.1478 | − | 2.76814i | −0.0471095 | − | 0.00760478i | ||||
\(365\) | −141.897 | + | 233.912i | −0.388759 | + | 0.640854i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −67.0637 | −0.182735 | −0.0913675 | − | 0.995817i | \(-0.529124\pi\) | ||||
−0.0913675 | + | 0.995817i | \(0.529124\pi\) | |||||||
\(368\) | −290.231 | − | 96.2097i | −0.788670 | − | 0.261439i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −24.8043 | − | 153.607i | −0.0670387 | − | 0.415153i | ||||
\(371\) | − | 13.0274i | − | 0.0351142i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 567.402i | − | 1.52119i | −0.649230 | − | 0.760593i | \(-0.724909\pi\) | ||
0.649230 | − | 0.760593i | \(-0.275091\pi\) | |||||||
\(374\) | 658.042 | − | 560.334i | 1.75947 | − | 1.49822i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −230.949 | − | 380.667i | −0.614225 | − | 1.01241i | ||||
\(377\) | − | 236.764i | − | 0.628020i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 240.298i | 0.634031i | 0.948420 | + | 0.317016i | \(0.102681\pi\) | ||||
−0.948420 | + | 0.317016i | \(0.897319\pi\) | |||||||
\(380\) | 273.598 | + | 232.950i | 0.719995 | + | 0.613026i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 180.740 | + | 212.257i | 0.473142 | + | 0.555646i | ||||
\(383\) | −670.068 | −1.74952 | −0.874762 | − | 0.484553i | \(-0.838982\pi\) | ||||
−0.874762 | + | 0.484553i | \(0.838982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −34.2957 | + | 56.5351i | −0.0890797 | + | 0.146845i | ||||
\(386\) | 236.048 | + | 277.209i | 0.611524 | + | 0.718157i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 666.655 | + | 107.617i | 1.71818 | + | 0.277363i | ||||
\(389\) | 474.640 | 1.22015 | 0.610077 | − | 0.792342i | \(-0.291139\pi\) | ||||
0.610077 | + | 0.792342i | \(0.291139\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 522.826i | 1.33715i | ||||||||
\(392\) | 200.421 | + | 330.349i | 0.511278 | + | 0.842726i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 334.567 | + | 392.907i | 0.849156 | + | 0.997226i | ||||
\(395\) | 35.3315 | − | 58.2427i | 0.0894469 | − | 0.147450i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 499.460i | − | 1.25809i | −0.777371 | − | 0.629043i | \(-0.783447\pi\) | ||
0.777371 | − | 0.629043i | \(-0.216553\pi\) | |||||||
\(398\) | 332.554 | + | 390.542i | 0.835562 | + | 0.981262i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −63.7855 | − | 394.882i | −0.159464 | − | 0.987204i | ||||
\(401\) | −344.694 | −0.859587 | −0.429793 | − | 0.902927i | \(-0.641414\pi\) | ||||
−0.429793 | + | 0.902927i | \(0.641414\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −70.6631 | −0.175343 | ||||||||
\(404\) | −28.3987 | + | 175.922i | −0.0702938 | + | 0.435450i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 58.1993 | − | 49.5578i | 0.143348 | − | 0.122063i | ||||
\(407\) | 245.773 | 0.603864 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −501.890 | −1.22712 | −0.613558 | − | 0.789650i | \(-0.710262\pi\) | ||||
−0.613558 | + | 0.789650i | \(0.710262\pi\) | |||||||
\(410\) | 131.289 | − | 21.2005i | 0.320218 | − | 0.0517085i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −80.6166 | + | 499.397i | −0.195671 | + | 1.21213i | ||||
\(413\) | 73.3957i | 0.177714i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 252.241 | + | 153.016i | 0.607809 | + | 0.368713i | ||||
\(416\) | 62.3746 | + | 153.803i | 0.149939 | + | 0.369719i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −432.144 | + | 367.978i | −1.03384 | + | 0.880331i | ||||
\(419\) | 218.369i | 0.521167i | 0.965451 | + | 0.260584i | \(0.0839150\pi\) | ||||
−0.965451 | + | 0.260584i | \(0.916085\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 281.698 | 0.669116 | 0.334558 | − | 0.942375i | \(-0.391413\pi\) | ||||
0.334558 | + | 0.942375i | \(0.391413\pi\) | |||||||
\(422\) | 274.700 | + | 322.600i | 0.650947 | + | 0.764455i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −106.423 | + | 64.5661i | −0.250997 | + | 0.152279i | ||||
\(425\) | −606.598 | + | 315.988i | −1.42729 | + | 0.743501i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.8156 | 0.0745097 | ||||||||
\(428\) | −66.5401 | + | 412.197i | −0.155468 | + | 0.963078i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −275.856 | + | 44.5451i | −0.641527 | + | 0.103593i | ||||
\(431\) | 441.081i | 1.02339i | 0.859167 | + | 0.511694i | \(0.170982\pi\) | ||||
−0.859167 | + | 0.511694i | \(0.829018\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 123.443i | 0.285089i | 0.989788 | + | 0.142544i | \(0.0455283\pi\) | ||||
−0.989788 | + | 0.142544i | \(0.954472\pi\) | |||||||
\(434\) | −14.7907 | − | 17.3698i | −0.0340800 | − | 0.0400227i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.319785 | + | 1.98098i | −0.000733451 | + | 0.00454353i | ||||
\(437\) | − | 343.346i | − | 0.785690i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 330.728i | 0.753368i | 0.926342 | + | 0.376684i | \(0.122936\pi\) | ||||
−0.926342 | + | 0.376684i | \(0.877064\pi\) | |||||||
\(440\) | 631.821 | − | 0.0317069i | 1.43596 | − | 7.20612e-5i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 216.072 | − | 183.989i | 0.488850 | − | 0.416265i | ||||
\(443\) | −154.952 | −0.349780 | −0.174890 | − | 0.984588i | \(-0.555957\pi\) | ||||
−0.174890 | + | 0.984588i | \(0.555957\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 170.145 | + | 103.214i | 0.382347 | + | 0.231942i | ||||
\(446\) | 532.718 | − | 453.619i | 1.19444 | − | 1.01708i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −24.7508 | + | 47.5254i | −0.0552473 | + | 0.106084i | ||||
\(449\) | 95.8970 | 0.213579 | 0.106790 | − | 0.994282i | \(-0.465943\pi\) | ||||
0.106790 | + | 0.994282i | \(0.465943\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 210.065i | 0.465775i | ||||||||
\(452\) | −67.0738 | − | 10.8276i | −0.148393 | − | 0.0239548i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 282.550 | − | 240.596i | 0.622356 | − | 0.529948i | ||||
\(455\) | −11.2612 | + | 18.5637i | −0.0247499 | + | 0.0407992i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 485.718i | − | 1.06284i | −0.847108 | − | 0.531420i | \(-0.821659\pi\) | ||
0.847108 | − | 0.531420i | \(-0.178341\pi\) | |||||||
\(458\) | 401.846 | − | 342.179i | 0.877393 | − | 0.747116i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −247.774 | + | 291.009i | −0.538640 | + | 0.632629i | ||||
\(461\) | −353.650 | −0.767136 | −0.383568 | − | 0.923513i | \(-0.625305\pi\) | ||||
−0.383568 | + | 0.923513i | \(0.625305\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 421.720 | 0.910842 | 0.455421 | − | 0.890276i | \(-0.349489\pi\) | ||||
0.455421 | + | 0.890276i | \(0.349489\pi\) | |||||||
\(464\) | −693.292 | − | 229.822i | −1.49416 | − | 0.495306i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 75.8248 | + | 89.0466i | 0.162714 | + | 0.191087i | ||||
\(467\) | −640.974 | −1.37254 | −0.686268 | − | 0.727349i | \(-0.740752\pi\) | ||||
−0.686268 | + | 0.727349i | \(0.740752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 77.1960 | 0.164597 | ||||||||
\(470\) | −549.441 | + | 88.7232i | −1.16902 | + | 0.188773i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 599.582 | − | 363.763i | 1.27030 | − | 0.770684i | ||||
\(473\) | − | 441.374i | − | 0.933137i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 398.360 | − | 207.513i | 0.838653 | − | 0.436869i | ||||
\(476\) | 90.4535 | + | 14.6017i | 0.190028 | + | 0.0306758i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −146.957 | − | 172.582i | −0.307441 | − | 0.361050i | ||||
\(479\) | 221.137i | 0.461664i | 0.972994 | + | 0.230832i | \(0.0741448\pi\) | ||||
−0.972994 | + | 0.230832i | \(0.925855\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 80.7010 | 0.167778 | ||||||||
\(482\) | −118.460 | + | 100.871i | −0.245767 | + | 0.209275i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −81.9124 | + | 507.424i | −0.169240 | + | 1.04840i | ||||
\(485\) | 437.801 | − | 721.698i | 0.902682 | − | 1.48804i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −889.949 | −1.82741 | −0.913705 | − | 0.406377i | \(-0.866792\pi\) | ||||
−0.913705 | + | 0.406377i | \(0.866792\pi\) | |||||||
\(488\) | −157.684 | − | 259.907i | −0.323123 | − | 0.532596i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 476.813 | − | 76.9955i | 0.973089 | − | 0.157134i | ||||
\(491\) | − | 552.843i | − | 1.12595i | −0.826473 | − | 0.562977i | \(-0.809656\pi\) | ||
0.826473 | − | 0.562977i | \(-0.190344\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1248.91i | 2.53328i | ||||||||
\(494\) | −141.897 | + | 120.828i | −0.287241 | + | 0.244591i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −68.5914 | + | 206.916i | −0.138289 | + | 0.417169i | ||||
\(497\) | − | 109.435i | − | 0.220190i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 533.302i | − | 1.06874i | −0.845250 | − | 0.534371i | \(-0.820549\pi\) | ||
0.845250 | − | 0.534371i | \(-0.179451\pi\) | |||||||
\(500\) | −487.388 | − | 111.594i | −0.974776 | − | 0.223187i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 137.737 | + | 161.755i | 0.274376 | + | 0.322220i | ||||
\(503\) | 574.914 | 1.14297 | 0.571485 | − | 0.820612i | \(-0.306367\pi\) | ||||
0.571485 | + | 0.820612i | \(0.306367\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 190.447 | + | 115.530i | 0.377122 | + | 0.228772i | ||||
\(506\) | −391.395 | − | 459.644i | −0.773509 | − | 0.908388i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.39034 | − | 33.3917i | 0.0106109 | − | 0.0657316i | ||||
\(509\) | −207.547 | −0.407753 | −0.203877 | − | 0.978997i | \(-0.565354\pi\) | ||||
−0.203877 | + | 0.978997i | \(0.565354\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 45.8122i | − | 0.0896521i | ||||||
\(512\) | 510.913 | − | 33.3518i | 0.997876 | − | 0.0651403i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 494.120 | + | 580.282i | 0.961324 | + | 1.12895i | ||||
\(515\) | 540.630 | + | 327.960i | 1.04977 | + | 0.636816i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 879.112i | − | 1.70041i | ||||||
\(518\) | 16.8918 | + | 19.8373i | 0.0326096 | + | 0.0382959i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 207.462 | − | 0.0104112i | 0.398966 | − | 2.00214e-5i | ||||
\(521\) | 712.900 | 1.36833 | 0.684165 | − | 0.729327i | \(-0.260167\pi\) | ||||
0.684165 | + | 0.729327i | \(0.260167\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −139.548 | −0.266822 | −0.133411 | − | 0.991061i | \(-0.542593\pi\) | ||||
−0.133411 | + | 0.991061i | \(0.542593\pi\) | |||||||
\(524\) | 204.272 | + | 32.9751i | 0.389831 | + | 0.0629296i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.4983 | − | 14.9002i | 0.0332668 | − | 0.0283273i | ||||
\(527\) | 372.742 | 0.707290 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −163.804 | −0.309648 | ||||||||
\(530\) | 24.8043 | + | 153.607i | 0.0468006 | + | 0.289824i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −59.4019 | − | 9.58911i | −0.111658 | − | 0.0180246i | ||||
\(533\) | 68.9760i | 0.129411i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 446.230 | + | 270.695i | 0.834075 | + | 0.505972i | ||||
\(536\) | −382.598 | − | 630.627i | −0.713802 | − | 1.17654i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 118.700 | − | 101.075i | 0.220632 | − | 0.187872i | ||||
\(539\) | 762.908i | 1.41541i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −946.688 | −1.74988 | −0.874942 | − | 0.484227i | \(-0.839101\pi\) | ||||
−0.874942 | + | 0.484227i | \(0.839101\pi\) | |||||||
\(542\) | 112.399 | + | 131.999i | 0.207379 | + | 0.243540i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −329.021 | − | 811.298i | −0.604818 | − | 1.49136i | ||||
\(545\) | 2.14454 | + | 1.30093i | 0.00393493 | + | 0.00238703i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −50.3388 | −0.0920271 | −0.0460136 | − | 0.998941i | \(-0.514652\pi\) | ||||
−0.0460136 | + | 0.998941i | \(0.514652\pi\) | |||||||
\(548\) | −212.483 | − | 34.3006i | −0.387742 | − | 0.0625923i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 296.739 | − | 731.910i | 0.539526 | − | 1.33074i | ||||
\(551\) | − | 820.173i | − | 1.48852i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.4070i | 0.0206275i | ||||||||
\(554\) | 372.561 | + | 437.525i | 0.672492 | + | 0.789757i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −53.8007 | − | 8.68492i | −0.0967638 | − | 0.0156204i | ||||
\(557\) | 790.157i | 1.41859i | 0.704910 | + | 0.709297i | \(0.250987\pi\) | ||||
−0.704910 | + | 0.709297i | \(0.749013\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 144.928i | − | 0.259263i | ||||||
\(560\) | 43.4272 | + | 50.9945i | 0.0775485 | + | 0.0910616i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 342.004 | − | 291.222i | 0.608548 | − | 0.518189i | ||||
\(563\) | −354.133 | −0.629010 | −0.314505 | − | 0.949256i | \(-0.601838\pi\) | ||||
−0.314505 | + | 0.949256i | \(0.601838\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −44.0482 | + | 72.6117i | −0.0779614 | + | 0.128516i | ||||
\(566\) | −128.096 | + | 109.076i | −0.226319 | + | 0.192714i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −893.989 | + | 542.378i | −1.57392 | + | 0.954891i | ||||
\(569\) | −55.4983 | −0.0975366 | −0.0487683 | − | 0.998810i | \(-0.515530\pi\) | ||||
−0.0487683 | + | 0.998810i | \(0.515530\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 791.134i | − | 1.38552i | −0.721167 | − | 0.692762i | \(-0.756394\pi\) | ||
0.721167 | − | 0.692762i | \(-0.243606\pi\) | |||||||
\(572\) | −52.2233 | + | 323.509i | −0.0912995 | + | 0.565575i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.9551 | + | 14.4376i | −0.0295386 | + | 0.0251526i | ||||
\(575\) | 220.719 | + | 423.711i | 0.383858 | + | 0.736888i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 201.759i | − | 0.349668i | −0.984598 | − | 0.174834i | \(-0.944061\pi\) | ||
0.984598 | − | 0.174834i | \(-0.0559389\pi\) | |||||||
\(578\) | −699.690 | + | 595.799i | −1.21054 | + | 1.03079i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −591.874 | + | 695.152i | −1.02047 | + | 1.19854i | ||||
\(581\) | −49.4020 | −0.0850292 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −245.773 | −0.421566 | ||||||||
\(584\) | −374.248 | + | 227.054i | −0.640835 | + | 0.388791i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −319.777 | − | 375.537i | −0.545694 | − | 0.640848i | ||||
\(587\) | −444.556 | −0.757335 | −0.378668 | − | 0.925533i | \(-0.623618\pi\) | ||||
−0.378668 | + | 0.925533i | \(0.623618\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −244.784 | −0.415593 | ||||||||
\(590\) | −139.746 | − | 865.415i | −0.236858 | − | 1.46680i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 78.3350 | − | 236.309i | 0.132323 | − | 0.399171i | ||||
\(593\) | 563.908i | 0.950942i | 0.879731 | + | 0.475471i | \(0.157722\pi\) | ||||
−0.879731 | + | 0.475471i | \(0.842278\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 59.4019 | − | 97.9217i | 0.0998351 | − | 0.164574i | ||||
\(596\) | 21.4502 | − | 132.878i | 0.0359902 | − | 0.222949i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −128.517 | − | 150.927i | −0.214911 | − | 0.252386i | ||||
\(599\) | − | 845.034i | − | 1.41074i | −0.708839 | − | 0.705371i | \(-0.750781\pi\) | ||
0.708839 | − | 0.705371i | \(-0.249219\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 672.296 | 1.11863 | 0.559314 | − | 0.828956i | \(-0.311065\pi\) | ||||
0.559314 | + | 0.828956i | \(0.311065\pi\) | |||||||
\(602\) | 35.6250 | − | 30.3353i | 0.0591777 | − | 0.0503909i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −552.797 | − | 89.2368i | −0.915227 | − | 0.147743i | ||||
\(605\) | 549.320 | + | 333.232i | 0.907967 | + | 0.550796i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −882.664 | −1.45414 | −0.727071 | − | 0.686562i | \(-0.759119\pi\) | ||||
−0.727071 | + | 0.686562i | \(0.759119\pi\) | |||||||
\(608\) | 216.072 | + | 532.789i | 0.355381 | + | 0.876298i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −375.140 | + | 60.5774i | −0.614984 | + | 0.0993072i | ||||
\(611\) | − | 288.662i | − | 0.472442i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 469.374i | 0.765701i | 0.923810 | + | 0.382850i | \(0.125057\pi\) | ||||
−0.923810 | + | 0.382850i | \(0.874943\pi\) | |||||||
\(614\) | −176.350 | + | 150.166i | −0.287216 | + | 0.244569i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −90.4535 | + | 54.8777i | −0.146840 | + | 0.0890871i | ||||
\(617\) | 218.994i | 0.354934i | 0.984127 | + | 0.177467i | \(0.0567902\pi\) | ||||
−0.984127 | + | 0.177467i | \(0.943210\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 879.610i | 1.42102i | 0.703689 | + | 0.710509i | \(0.251535\pi\) | ||||
−0.703689 | + | 0.710509i | \(0.748465\pi\) | |||||||
\(620\) | 207.471 | + | 176.647i | 0.334631 | + | 0.284915i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 264.213 | + | 310.284i | 0.424779 | + | 0.498849i | ||||
\(623\) | −33.3232 | −0.0534884 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −358.203 | + | 512.168i | −0.573124 | + | 0.819468i | ||||
\(626\) | 128.447 | + | 150.845i | 0.205187 | + | 0.240966i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −83.9656 | − | 13.5544i | −0.133703 | − | 0.0215834i | ||||
\(629\) | −425.691 | −0.676774 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 635.566i | − | 1.00724i | −0.863926 | − | 0.503618i | \(-0.832002\pi\) | ||
0.863926 | − | 0.503618i | \(-0.167998\pi\) | |||||||
\(632\) | 93.1855 | − | 56.5351i | 0.147445 | − | 0.0894543i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −610.966 | − | 717.502i | −0.963669 | − | 1.13171i | ||||
\(635\) | −36.1486 | − | 21.9287i | −0.0569270 | − | 0.0345334i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 250.505i | 0.393258i | ||||||||
\(638\) | −934.951 | − | 1097.98i | −1.46544 | − | 1.72097i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 201.349 | − | 607.502i | 0.314608 | − | 0.949222i | ||||
\(641\) | 296.309 | 0.462260 | 0.231130 | − | 0.972923i | \(-0.425758\pi\) | ||||
0.231130 | + | 0.972923i | \(0.425758\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 591.032 | 0.919179 | 0.459590 | − | 0.888131i | \(-0.347997\pi\) | ||||
0.459590 | + | 0.888131i | \(0.347997\pi\) | |||||||
\(644\) | 10.1993 | − | 63.1821i | 0.0158375 | − | 0.0981088i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 748.495 | − | 637.357i | 1.15866 | − | 0.986621i | ||||
\(647\) | 166.507 | 0.257352 | 0.128676 | − | 0.991687i | \(-0.458927\pi\) | ||||
0.128676 | + | 0.991687i | \(0.458927\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1384.67 | 2.13355 | ||||||||
\(650\) | 97.4362 | − | 240.327i | 0.149902 | − | 0.369734i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −134.001 | + | 830.098i | −0.205523 | + | 1.27316i | ||||
\(653\) | 621.335i | 0.951509i | 0.879578 | + | 0.475754i | \(0.157825\pi\) | ||||
−0.879578 | + | 0.475754i | \(0.842175\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 134.148 | − | 221.137i | 0.204806 | − | 0.337614i | ||||
\(656\) | 201.976 | + | 66.9538i | 0.307890 | + | 0.102064i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 70.9565 | − | 60.4208i | 0.107837 | − | 0.0918249i | ||||
\(659\) | − | 702.113i | − | 1.06542i | −0.846297 | − | 0.532711i | \(-0.821173\pi\) | ||
0.846297 | − | 0.532711i | \(-0.178827\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 358.193 | 0.541895 | 0.270948 | − | 0.962594i | \(-0.412663\pi\) | ||||
0.270948 | + | 0.962594i | \(0.412663\pi\) | |||||||
\(662\) | −350.994 | − | 412.197i | −0.530202 | − | 0.622655i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 244.846 | + | 403.573i | 0.368743 | + | 0.607790i | ||||
\(665\) | −39.0099 | + | 64.3064i | −0.0586616 | + | 0.0967013i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 872.367 | 1.30790 | ||||||||
\(668\) | 151.960 | − | 941.351i | 0.227485 | − | 1.40921i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −910.224 | + | 146.982i | −1.35854 | + | 0.219377i | ||||
\(671\) | − | 600.230i | − | 0.894530i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 714.176i | − | 1.06118i | −0.847628 | − | 0.530592i | \(-0.821970\pi\) | ||
0.847628 | − | 0.530592i | \(-0.178030\pi\) | |||||||
\(674\) | 489.244 | + | 574.555i | 0.725882 | + | 0.852456i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 90.5827 | − | 561.134i | 0.133998 | − | 0.830081i | ||||
\(677\) | − | 509.833i | − | 0.753077i | −0.926401 | − | 0.376538i | \(-0.877114\pi\) | ||
0.926401 | − | 0.376538i | \(-0.122886\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 141.346i | 0.208168i | ||||||||
\(680\) | −1094.35 | + | 0.0549180i | −1.60933 | + | 8.07617e-5i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −327.697 | + | 279.040i | −0.480494 | + | 0.409150i | ||||
\(683\) | 1263.93 | 1.85055 | 0.925275 | − | 0.379298i | \(-0.123834\pi\) | ||||
0.925275 | + | 0.379298i | \(0.123834\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −139.540 | + | 230.026i | −0.203708 | + | 0.335805i | ||||
\(686\) | −124.048 | + | 105.629i | −0.180828 | + | 0.153978i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −424.378 | − | 140.679i | −0.616829 | − | 0.204475i | ||||
\(689\) | −80.7010 | −0.117128 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 512.351i | − | 0.741463i | −0.928740 | − | 0.370731i | \(-0.879107\pi\) | ||
0.928740 | − | 0.370731i | \(-0.120893\pi\) | |||||||
\(692\) | −9.21987 | − | 1.48834i | −0.0133235 | − | 0.00215078i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −703.842 | + | 599.334i | −1.01418 | + | 0.863594i | ||||
\(695\) | −35.3315 | + | 58.2427i | −0.0508368 | + | 0.0838024i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 363.843i | − | 0.522012i | ||||||
\(698\) | 305.458 | − | 260.103i | 0.437619 | − | 0.372640i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 79.4699 | − | 26.3526i | 0.113528 | − | 0.0376466i | ||||
\(701\) | −1092.03 | −1.55781 | −0.778907 | − | 0.627139i | \(-0.784226\pi\) | ||||
−0.778907 | + | 0.627139i | \(0.784226\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 279.556 | 0.397662 | ||||||||
\(704\) | 896.609 | + | 466.945i | 1.27359 | + | 0.663274i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 325.323 | + | 382.051i | 0.460798 | + | 0.541148i | ||||
\(707\) | −37.2995 | −0.0527574 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 416.887 | 0.587993 | 0.293997 | − | 0.955806i | \(-0.405015\pi\) | ||||
0.293997 | + | 0.955806i | \(0.405015\pi\) | |||||||
\(710\) | 208.365 | + | 1290.35i | 0.293472 | + | 1.81740i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 165.156 | + | 272.223i | 0.231961 | + | 0.382336i | ||||
\(713\) | − | 260.362i | − | 0.365163i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 350.220 | + | 212.452i | 0.489818 | + | 0.297136i | ||||
\(716\) | −896.609 | − | 144.738i | −1.25225 | − | 0.202147i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 279.556 | + | 328.304i | 0.389354 | + | 0.457247i | ||||
\(719\) | − | 395.268i | − | 0.549747i | −0.961480 | − | 0.274874i | \(-0.911364\pi\) | ||
0.961480 | − | 0.274874i | \(-0.0886361\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −105.884 | −0.146857 | ||||||||
\(722\) | 58.1625 | − | 49.5264i | 0.0805575 | − | 0.0685962i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 72.7317 | − | 450.553i | 0.100458 | − | 0.622310i | ||||
\(725\) | 527.244 | + | 1012.14i | 0.727233 | + | 1.39606i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −597.583 | −0.821985 | −0.410993 | − | 0.911639i | \(-0.634818\pi\) | ||||
−0.410993 | + | 0.911639i | \(0.634818\pi\) | |||||||
\(728\) | −29.7009 | + | 18.0194i | −0.0407980 | + | 0.0247519i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 87.2271 | + | 540.175i | 0.119489 | + | 0.739966i | ||||
\(731\) | 764.482i | 1.04580i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.8650i | 0.0325580i | 0.999867 | + | 0.0162790i | \(0.00518200\pi\) | ||||
−0.999867 | + | 0.0162790i | \(0.994818\pi\) | |||||||
\(734\) | −102.120 | + | 86.9574i | −0.139129 | + | 0.118471i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −566.694 | + | 229.822i | −0.769965 | + | 0.312258i | ||||
\(737\) | − | 1456.37i | − | 1.97608i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 125.767i | − | 0.170186i | −0.996373 | − | 0.0850928i | \(-0.972881\pi\) | ||
0.996373 | − | 0.0850928i | \(-0.0271187\pi\) | |||||||
\(740\) | −236.943 | − | 201.741i | −0.320193 | − | 0.272622i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −16.8918 | − | 19.8373i | −0.0227652 | − | 0.0267349i | ||||
\(743\) | 148.841 | 0.200325 | 0.100162 | − | 0.994971i | \(-0.468064\pi\) | ||||
0.100162 | + | 0.994971i | \(0.468064\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −143.849 | − | 87.2625i | −0.193086 | − | 0.117131i | ||||
\(746\) | −735.715 | − | 864.004i | −0.986213 | − | 1.15818i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 275.474 | − | 1706.48i | 0.368280 | − | 2.28140i | ||||
\(749\) | −87.3954 | −0.116683 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 463.390i | 0.617030i | 0.951219 | + | 0.308515i | \(0.0998321\pi\) | ||||
−0.951219 | + | 0.308515i | \(0.900168\pi\) | |||||||
\(752\) | −845.261 | − | 280.199i | −1.12402 | − | 0.372605i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −306.997 | − | 360.529i | −0.407157 | − | 0.478155i | ||||
\(755\) | −363.029 | + | 598.439i | −0.480833 | + | 0.792634i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 719.363i | 0.950281i | 0.879910 | + | 0.475141i | \(0.157603\pi\) | ||||
−0.879910 | + | 0.475141i | \(0.842397\pi\) | |||||||
\(758\) | 311.579 | + | 365.910i | 0.411054 | + | 0.482731i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 718.670 | − | 0.0360653i | 0.945618 | − | 4.74543e-5i | ||||
\(761\) | 1107.49 | 1.45530 | 0.727651 | − | 0.685947i | \(-0.240612\pi\) | ||||
0.727651 | + | 0.685947i | \(0.240612\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.420013 | −0.000550476 | ||||||||
\(764\) | 550.440 | + | 88.8563i | 0.720472 | + | 0.116304i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1020.34 | + | 868.835i | −1.33203 | + | 1.13425i | ||||
\(767\) | 454.666 | 0.592785 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −231.691 | −0.301289 | −0.150644 | − | 0.988588i | \(-0.548135\pi\) | ||||
−0.150644 | + | 0.988588i | \(0.548135\pi\) | |||||||
\(770\) | 21.0823 | + | 130.557i | 0.0273796 | + | 0.169555i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 718.879 | + | 116.047i | 0.931190 | + | 0.150320i | ||||
\(773\) | 519.956i | 0.672647i | 0.941746 | + | 0.336324i | \(0.109184\pi\) | ||||
−0.941746 | + | 0.336324i | \(0.890816\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 302.079 | − | 157.358i | 0.389779 | − | 0.203043i | ||||
\(776\) | 1154.68 | − | 700.539i | 1.48799 | − | 0.902756i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 722.751 | − | 615.436i | 0.928986 | − | 0.791049i | ||||
\(779\) | 238.940i | 0.306726i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2064.58 | −2.64351 | ||||||||
\(782\) | 677.917 | + | 796.127i | 0.866901 | + | 1.01807i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 733.531 | + | 243.161i | 0.935626 | + | 0.310154i | ||||
\(785\) | −55.1412 | + | 90.8982i | −0.0702436 | + | 0.115794i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −46.0288 | −0.0584864 | −0.0292432 | − | 0.999572i | \(-0.509310\pi\) | ||||
−0.0292432 | + | 0.999572i | \(0.509310\pi\) | |||||||
\(788\) | 1018.92 | + | 164.481i | 1.29304 | + | 0.208733i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −21.7190 | − | 134.501i | −0.0274925 | − | 0.170254i | ||||
\(791\) | − | 14.2212i | − | 0.0179788i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 197.089i | − | 0.248536i | ||||||
\(794\) | −647.619 | − | 760.546i | −0.815641 | − | 0.957867i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1012.78 | + | 163.491i | 1.27234 | + | 0.205391i | ||||
\(797\) | 15.3098i | 0.0192093i | 0.999954 | + | 0.00960463i | \(0.00305730\pi\) | ||||
−0.999954 | + | 0.00960463i | \(0.996943\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1522.67i | 1.90572i | ||||||||
\(800\) | −609.147 | − | 518.594i | −0.761434 | − | 0.648243i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −524.879 | + | 446.944i | −0.654463 | + | 0.557287i | ||||
\(803\) | −864.288 | −1.07632 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −68.3987 | − | 41.4924i | −0.0849673 | − | 0.0515434i | ||||
\(806\) | −107.601 | + | 91.6245i | −0.133500 | + | 0.113678i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 184.863 | + | 304.706i | 0.228791 | + | 0.377111i | ||||
\(809\) | 313.093 | 0.387012 | 0.193506 | − | 0.981099i | \(-0.438014\pi\) | ||||
0.193506 | + | 0.981099i | \(0.438014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1056.89i | 1.30319i | 0.758566 | + | 0.651596i | \(0.225900\pi\) | ||||
−0.758566 | + | 0.651596i | \(0.774100\pi\) | |||||||
\(812\) | 24.3638 | − | 150.927i | 0.0300047 | − | 0.185871i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 374.248 | − | 318.678i | 0.459764 | − | 0.391497i | ||||
\(815\) | 898.635 | + | 545.136i | 1.10262 | + | 0.668878i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 502.045i | − | 0.614498i | ||||||
\(818\) | −764.247 | + | 650.770i | −0.934288 | + | 0.795563i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 172.430 | − | 202.518i | 0.210280 | − | 0.246973i | ||||
\(821\) | −308.659 | −0.375955 | −0.187978 | − | 0.982173i | \(-0.560193\pi\) | ||||
−0.187978 | + | 0.982173i | \(0.560193\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −109.680 | −0.133269 | −0.0666344 | − | 0.997777i | \(-0.521226\pi\) | ||||
−0.0666344 | + | 0.997777i | \(0.521226\pi\) | |||||||
\(824\) | 524.780 | + | 864.982i | 0.636869 | + | 1.04974i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 95.1677 | + | 111.762i | 0.115215 | + | 0.135306i | ||||
\(827\) | −711.971 | −0.860908 | −0.430454 | − | 0.902613i | \(-0.641646\pi\) | ||||
−0.430454 | + | 0.902613i | \(0.641646\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −118.688 | −0.143170 | −0.0715849 | − | 0.997435i | \(-0.522806\pi\) | ||||
−0.0715849 | + | 0.997435i | \(0.522806\pi\) | |||||||
\(830\) | 582.502 | − | 94.0621i | 0.701810 | − | 0.113328i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 294.407 | + | 153.324i | 0.353854 | + | 0.184284i | ||||
\(833\) | − | 1321.40i | − | 1.58631i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1019.07 | − | 618.196i | −1.22045 | − | 0.740355i | ||||
\(836\) | −180.907 | + | 1120.67i | −0.216396 | + | 1.34051i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 283.146 | + | 332.519i | 0.337883 | + | 0.396800i | ||||
\(839\) | 1413.67i | 1.68495i | 0.538736 | + | 0.842475i | \(0.318902\pi\) | ||||
−0.538736 | + | 0.842475i | \(0.681098\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1242.88 | 1.47786 | ||||||||
\(842\) | 428.952 | − | 365.260i | 0.509444 | − | 0.433800i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 836.591 | + | 135.049i | 0.991222 | + | 0.160011i | ||||
\(845\) | −607.464 | − | 368.504i | −0.718893 | − | 0.436099i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −107.586 | −0.127020 | ||||||||
\(848\) | −78.3350 | + | 236.309i | −0.0923762 | + | 0.278666i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −513.968 | + | 1267.70i | −0.604668 | + | 1.49142i | ||||
\(851\) | 297.347i | 0.349409i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1308.03i | − | 1.53344i | −0.641979 | − | 0.766722i | \(-0.721886\pi\) | ||
0.641979 | − | 0.766722i | \(-0.278114\pi\) | |||||||
\(854\) | 48.4469 | − | 41.2534i | 0.0567293 | − | 0.0483060i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 433.148 | + | 713.947i | 0.506014 | + | 0.834050i | ||||
\(857\) | 719.755i | 0.839854i | 0.907558 | + | 0.419927i | \(0.137944\pi\) | ||||
−0.907558 | + | 0.419927i | \(0.862056\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1402.44i | − | 1.63264i | −0.577601 | − | 0.816319i | \(-0.696011\pi\) | ||
0.577601 | − | 0.816319i | \(-0.303989\pi\) | |||||||
\(860\) | −362.298 | + | 425.517i | −0.421277 | + | 0.494787i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 571.922 | + | 671.650i | 0.663483 | + | 0.779176i | ||||
\(863\) | 72.4412 | 0.0839411 | 0.0419706 | − | 0.999119i | \(-0.486636\pi\) | ||||
0.0419706 | + | 0.999119i | \(0.486636\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.05480 | + | 9.98111i | −0.00699977 | + | 0.0115389i | ||||
\(866\) | 160.061 | + | 187.972i | 0.184828 | + | 0.217058i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −45.0448 | − | 7.27148i | −0.0518949 | − | 0.00837728i | ||||
\(869\) | 215.203 | 0.247644 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 478.208i | − | 0.549033i | ||||||
\(872\) | 2.08166 | + | 3.43115i | 0.00238723 | + | 0.00393481i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −445.196 | − | 522.826i | −0.509378 | − | 0.598200i | ||||
\(875\) | 6.80164 | − | 104.435i | 0.00777331 | − | 0.119355i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1382.21i | 1.57606i | 0.615635 | + | 0.788032i | \(0.288900\pi\) | ||||
−0.615635 | + | 0.788032i | \(0.711100\pi\) | |||||||
\(878\) | 428.835 | + | 503.613i | 0.488423 | + | 0.573591i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 962.056 | − | 819.291i | 1.09325 | − | 0.931013i | ||||
\(881\) | 1131.38 | 1.28419 | 0.642097 | − | 0.766623i | \(-0.278064\pi\) | ||||
0.642097 | + | 0.766623i | \(0.278064\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1077.39 | 1.22014 | 0.610072 | − | 0.792346i | \(-0.291140\pi\) | ||||
0.610072 | + | 0.792346i | \(0.291140\pi\) | |||||||
\(884\) | 90.4535 | − | 560.334i | 0.102323 | − | 0.633862i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −235.952 | + | 200.917i | −0.266311 | + | 0.226769i | ||||
\(887\) | −766.896 | −0.864595 | −0.432297 | − | 0.901731i | \(-0.642297\pi\) | ||||
−0.432297 | + | 0.901731i | \(0.642297\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.07980 | 0.00796378 | ||||||||
\(890\) | 392.917 | − | 63.4479i | 0.441480 | − | 0.0712898i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 223.010 | − | 1381.49i | 0.250011 | − | 1.54875i | ||||
\(893\) | − | 999.954i | − | 1.11977i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −588.814 | + | 970.637i | −0.657893 | + | 1.08451i | ||||
\(896\) | 23.9344 | + | 104.462i | 0.0267124 | + | 0.116587i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 146.026 | − | 124.344i | 0.162612 | − | 0.138467i | ||||
\(899\) | − | 621.942i | − | 0.691815i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 425.691 | 0.472465 | ||||||||
\(902\) | 272.378 | + | 319.873i | 0.301971 | + | 0.354627i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −116.175 | + | 70.4829i | −0.128512 | + | 0.0779678i | ||||
\(905\) | −487.752 | − | 295.883i | −0.538953 | − | 0.326943i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1086.43 | −1.19783 | −0.598913 | − | 0.800814i | \(-0.704400\pi\) | ||||
−0.598913 | + | 0.800814i | \(0.704400\pi\) | |||||||
\(908\) | 118.283 | − | 732.730i | 0.130268 | − | 0.806971i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.92250 | + | 42.8693i | 0.00760714 | + | 0.0471091i | ||||
\(911\) | 237.746i | 0.260973i | 0.991450 | + | 0.130486i | \(0.0416539\pi\) | ||||
−0.991450 | + | 0.130486i | \(0.958346\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 932.012i | 1.02082i | ||||||||
\(914\) | −629.801 | − | 739.621i | −0.689060 | − | 0.809214i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 168.223 | − | 1042.10i | 0.183650 | − | 1.13766i | ||||
\(917\) | 43.3103i | 0.0472304i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 344.517i | − | 0.374882i | −0.982276 | − | 0.187441i | \(-0.939981\pi\) | ||
0.982276 | − | 0.187441i | \(-0.0600194\pi\) | |||||||
\(920\) | 0.0383604 | + | 764.404i | 4.16961e−5 | + | 0.830874i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −538.515 | + | 458.555i | −0.584073 | + | 0.497349i | ||||
\(923\) | −677.917 | −0.734471 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −344.990 | + | 179.711i | −0.372962 | + | 0.194283i | ||||
\(926\) | 642.169 | − | 546.818i | 0.693487 | − | 0.590516i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1353.70 | + | 548.991i | −1.45873 | + | 0.591585i | ||||
\(929\) | −1478.10 | −1.59106 | −0.795531 | − | 0.605913i | \(-0.792808\pi\) | ||||
−0.795531 | + | 0.605913i | \(0.792808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 867.776i | 0.932090i | ||||||||
\(932\) | 230.922 | + | 37.2773i | 0.247771 | + | 0.0399971i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −976.035 | + | 831.111i | −1.04501 | + | 0.889841i | ||||
\(935\) | −1847.38 | − | 1120.67i | −1.97581 | − | 1.19858i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 246.887i | − | 0.263486i | −0.991284 | − | 0.131743i | \(-0.957943\pi\) | ||
0.991284 | − | 0.131743i | \(-0.0420574\pi\) | |||||||
\(938\) | 117.549 | − | 100.095i | 0.125319 | − | 0.106711i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −721.612 | + | 847.528i | −0.767672 | + | 0.901625i | ||||
\(941\) | −1658.64 | −1.76264 | −0.881318 | − | 0.472525i | \(-0.843343\pi\) | ||||
−0.881318 | + | 0.472525i | \(0.843343\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −254.145 | −0.269507 | ||||||||
\(944\) | 441.336 | − | 1331.36i | 0.467517 | − | 1.41033i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −572.302 | − | 672.097i | −0.604971 | − | 0.710462i | ||||
\(947\) | −6.00750 | −0.00634372 | −0.00317186 | − | 0.999995i | \(-0.501010\pi\) | ||||
−0.00317186 | + | 0.999995i | \(0.501010\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −283.794 | −0.299045 | ||||||||
\(950\) | 337.529 | − | 832.517i | 0.355293 | − | 0.876333i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 156.670 | − | 95.0509i | 0.164569 | − | 0.0998434i | ||||
\(953\) | 1089.55i | 1.14329i | 0.820503 | + | 0.571643i | \(0.193694\pi\) | ||||
−0.820503 | + | 0.571643i | \(0.806306\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 361.481 | − | 595.887i | 0.378514 | − | 0.623966i | ||||
\(956\) | −447.553 | − | 72.2475i | −0.468152 | − | 0.0755727i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 286.735 | + | 336.734i | 0.299306 | + | 0.351497i | ||||
\(959\) | − | 45.0512i | − | 0.0469773i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 775.379 | 0.806846 | ||||||||
\(962\) | 122.886 | − | 104.640i | 0.127741 | − | 0.108773i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −49.5905 | + | 307.199i | −0.0514424 | + | 0.318671i | ||||
\(965\) | 472.096 | − | 778.233i | 0.489219 | − | 0.806459i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1699.27 | 1.75726 | 0.878630 | − | 0.477502i | \(-0.158458\pi\) | ||||
0.878630 | + | 0.477502i | \(0.158458\pi\) | |||||||
\(968\) | 533.215 | + | 878.885i | 0.550842 | + | 0.907939i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −269.125 | − | 1666.63i | −0.277449 | − | 1.71817i | ||||
\(971\) | 197.851i | 0.203760i | 0.994797 | + | 0.101880i | \(0.0324857\pi\) | ||||
−0.994797 | + | 0.101880i | \(0.967514\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 11.4070i | − | 0.0117235i | ||||||
\(974\) | −1355.16 | + | 1153.94i | −1.39133 | + | 1.18475i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −577.117 | − | 191.311i | −0.591309 | − | 0.196015i | ||||
\(977\) | 847.868i | 0.867828i | 0.900954 | + | 0.433914i | \(0.142868\pi\) | ||||
−0.900954 | + | 0.433914i | \(0.857132\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 628.672i | 0.642157i | ||||||||
\(980\) | 626.226 | − | 735.498i | 0.639007 | − | 0.750509i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −716.837 | − | 841.835i | −0.729977 | − | 0.857266i | ||||
\(983\) | −96.0512 | −0.0977123 | −0.0488562 | − | 0.998806i | \(-0.515558\pi\) | ||||
−0.0488562 | + | 0.998806i | \(0.515558\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 669.135 | − | 1103.04i | 0.679324 | − | 1.11984i | ||||
\(986\) | 1619.38 | + | 1901.76i | 1.64238 | + | 1.92876i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −59.4019 | + | 367.978i | −0.0601234 | + | 0.372448i | ||||
\(989\) | 533.993 | 0.539933 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1184.45i | − | 1.19520i | −0.801793 | − | 0.597602i | \(-0.796120\pi\) | ||
0.801793 | − | 0.597602i | \(-0.203880\pi\) | |||||||
\(992\) | 163.849 | + | 404.017i | 0.165170 | + | 0.407275i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −141.897 | − | 166.640i | −0.142754 | − | 0.167646i | ||||
\(995\) | 665.108 | − | 1096.40i | 0.668450 | − | 1.10191i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1887.35i | − | 1.89303i | −0.322655 | − | 0.946517i | \(-0.604575\pi\) | ||
0.322655 | − | 0.946517i | \(-0.395425\pi\) | |||||||
\(998\) | −691.500 | − | 812.079i | −0.692886 | − | 0.813706i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 180.3.f.h.19.7 | 8 | ||
3.2 | odd | 2 | 60.3.f.b.19.2 | yes | 8 | ||
4.3 | odd | 2 | inner | 180.3.f.h.19.1 | 8 | ||
5.2 | odd | 4 | 900.3.c.r.451.6 | 8 | |||
5.3 | odd | 4 | 900.3.c.r.451.3 | 8 | |||
5.4 | even | 2 | inner | 180.3.f.h.19.2 | 8 | ||
12.11 | even | 2 | 60.3.f.b.19.8 | yes | 8 | ||
15.2 | even | 4 | 300.3.c.f.151.3 | 8 | |||
15.8 | even | 4 | 300.3.c.f.151.6 | 8 | |||
15.14 | odd | 2 | 60.3.f.b.19.7 | yes | 8 | ||
20.3 | even | 4 | 900.3.c.r.451.4 | 8 | |||
20.7 | even | 4 | 900.3.c.r.451.5 | 8 | |||
20.19 | odd | 2 | inner | 180.3.f.h.19.8 | 8 | ||
24.5 | odd | 2 | 960.3.j.e.319.1 | 8 | |||
24.11 | even | 2 | 960.3.j.e.319.5 | 8 | |||
60.23 | odd | 4 | 300.3.c.f.151.5 | 8 | |||
60.47 | odd | 4 | 300.3.c.f.151.4 | 8 | |||
60.59 | even | 2 | 60.3.f.b.19.1 | ✓ | 8 | ||
120.29 | odd | 2 | 960.3.j.e.319.6 | 8 | |||
120.59 | even | 2 | 960.3.j.e.319.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.f.b.19.1 | ✓ | 8 | 60.59 | even | 2 | ||
60.3.f.b.19.2 | yes | 8 | 3.2 | odd | 2 | ||
60.3.f.b.19.7 | yes | 8 | 15.14 | odd | 2 | ||
60.3.f.b.19.8 | yes | 8 | 12.11 | even | 2 | ||
180.3.f.h.19.1 | 8 | 4.3 | odd | 2 | inner | ||
180.3.f.h.19.2 | 8 | 5.4 | even | 2 | inner | ||
180.3.f.h.19.7 | 8 | 1.1 | even | 1 | trivial | ||
180.3.f.h.19.8 | 8 | 20.19 | odd | 2 | inner | ||
300.3.c.f.151.3 | 8 | 15.2 | even | 4 | |||
300.3.c.f.151.4 | 8 | 60.47 | odd | 4 | |||
300.3.c.f.151.5 | 8 | 60.23 | odd | 4 | |||
300.3.c.f.151.6 | 8 | 15.8 | even | 4 | |||
900.3.c.r.451.3 | 8 | 5.3 | odd | 4 | |||
900.3.c.r.451.4 | 8 | 20.3 | even | 4 | |||
900.3.c.r.451.5 | 8 | 20.7 | even | 4 | |||
900.3.c.r.451.6 | 8 | 5.2 | odd | 4 | |||
960.3.j.e.319.1 | 8 | 24.5 | odd | 2 | |||
960.3.j.e.319.2 | 8 | 120.59 | even | 2 | |||
960.3.j.e.319.5 | 8 | 24.11 | even | 2 | |||
960.3.j.e.319.6 | 8 | 120.29 | odd | 2 |