Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(221,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 221.11 | ||
Character | \(\chi\) | \(=\) | 570.221 |
Dual form | 570.2.s.b.521.11 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 1.54313 | + | 0.786608i | 0.890926 | + | 0.454148i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.866025 | + | 0.500000i | −0.387298 | + | 0.223607i | ||||
\(6\) | 0.0903420 | + | 1.72969i | 0.0368820 | + | 0.706144i | ||||
\(7\) | 2.34168 | 0.885071 | 0.442536 | − | 0.896751i | \(-0.354079\pi\) | ||||
0.442536 | + | 0.896751i | \(0.354079\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.76250 | + | 2.42768i | 0.587498 | + | 0.809225i | ||||
\(10\) | −0.866025 | − | 0.500000i | −0.273861 | − | 0.158114i | ||||
\(11\) | 2.39841i | 0.723149i | 0.932343 | + | 0.361575i | \(0.117761\pi\) | ||||
−0.932343 | + | 0.361575i | \(0.882239\pi\) | |||||||
\(12\) | −1.45279 | + | 0.943085i | −0.419384 | + | 0.272245i | ||||
\(13\) | −0.414577 | − | 0.239356i | −0.114983 | − | 0.0663855i | 0.441406 | − | 0.897308i | \(-0.354480\pi\) |
−0.556389 | + | 0.830922i | \(0.687813\pi\) | |||||||
\(14\) | 1.17084 | + | 2.02795i | 0.312920 | + | 0.541993i | ||||
\(15\) | −1.72969 | + | 0.0903420i | −0.446605 | + | 0.0233262i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.40013 | + | 1.38572i | −0.582117 | + | 0.336086i | −0.761974 | − | 0.647607i | \(-0.775770\pi\) |
0.179857 | + | 0.983693i | \(0.442436\pi\) | |||||||
\(18\) | −1.22118 | + | 2.74020i | −0.287835 | + | 0.645872i | ||||
\(19\) | 0.994947 | − | 4.24383i | 0.228256 | − | 0.973601i | ||||
\(20\) | − | 1.00000i | − | 0.223607i | ||||||
\(21\) | 3.61351 | + | 1.84198i | 0.788533 | + | 0.401954i | ||||
\(22\) | −2.07709 | + | 1.19921i | −0.442837 | + | 0.255672i | ||||
\(23\) | 1.80040 | + | 1.03946i | 0.375409 | + | 0.216743i | 0.675819 | − | 0.737068i | \(-0.263790\pi\) |
−0.300410 | + | 0.953810i | \(0.597123\pi\) | |||||||
\(24\) | −1.54313 | − | 0.786608i | −0.314990 | − | 0.160566i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | − | 0.478712i | − | 0.0938832i | ||||||
\(27\) | 0.810128 | + | 5.13261i | 0.155909 | + | 0.987771i | ||||
\(28\) | −1.17084 | + | 2.02795i | −0.221268 | + | 0.383247i | ||||
\(29\) | −0.313727 | + | 0.543392i | −0.0582577 | + | 0.100905i | −0.893683 | − | 0.448698i | \(-0.851888\pi\) |
0.835426 | + | 0.549603i | \(0.185221\pi\) | |||||||
\(30\) | −0.943085 | − | 1.45279i | −0.172183 | − | 0.265241i | ||||
\(31\) | − | 2.05113i | − | 0.368394i | −0.982889 | − | 0.184197i | \(-0.941032\pi\) | ||
0.982889 | − | 0.184197i | \(-0.0589684\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −1.88661 | + | 3.70106i | −0.328417 | + | 0.644272i | ||||
\(34\) | −2.40013 | − | 1.38572i | −0.411619 | − | 0.237648i | ||||
\(35\) | −2.02795 | + | 1.17084i | −0.342787 | + | 0.197908i | ||||
\(36\) | −2.98368 | + | 0.312528i | −0.497279 | + | 0.0520880i | ||||
\(37\) | 5.67577i | 0.933091i | 0.884497 | + | 0.466546i | \(0.154502\pi\) | ||||
−0.884497 | + | 0.466546i | \(0.845498\pi\) | |||||||
\(38\) | 4.17274 | − | 1.26026i | 0.676907 | − | 0.204442i | ||||
\(39\) | −0.451467 | − | 0.695467i | −0.0722925 | − | 0.111364i | ||||
\(40\) | 0.866025 | − | 0.500000i | 0.136931 | − | 0.0790569i | ||||
\(41\) | 1.04624 | + | 1.81214i | 0.163395 | + | 0.283008i | 0.936084 | − | 0.351776i | \(-0.114422\pi\) |
−0.772689 | + | 0.634785i | \(0.781089\pi\) | |||||||
\(42\) | 0.211552 | + | 4.05038i | 0.0326432 | + | 0.624988i | ||||
\(43\) | −3.77271 | − | 6.53452i | −0.575333 | − | 0.996506i | −0.996005 | − | 0.0892931i | \(-0.971539\pi\) |
0.420673 | − | 0.907213i | \(-0.361794\pi\) | |||||||
\(44\) | −2.07709 | − | 1.19921i | −0.313133 | − | 0.180787i | ||||
\(45\) | −2.74020 | − | 1.22118i | −0.408485 | − | 0.182043i | ||||
\(46\) | 2.07892i | 0.306520i | ||||||||
\(47\) | 1.94389 | + | 1.12231i | 0.283546 | + | 0.163705i | 0.635028 | − | 0.772490i | \(-0.280989\pi\) |
−0.351482 | + | 0.936195i | \(0.614322\pi\) | |||||||
\(48\) | −0.0903420 | − | 1.72969i | −0.0130397 | − | 0.249660i | ||||
\(49\) | −1.51654 | −0.216649 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −4.79373 | + | 0.250377i | −0.671256 | + | 0.0350597i | ||||
\(52\) | 0.414577 | − | 0.239356i | 0.0574915 | − | 0.0331927i | ||||
\(53\) | 6.64114 | − | 11.5028i | 0.912231 | − | 1.58003i | 0.101325 | − | 0.994853i | \(-0.467692\pi\) |
0.810906 | − | 0.585176i | \(-0.198975\pi\) | |||||||
\(54\) | −4.03991 | + | 3.26790i | −0.549762 | + | 0.444704i | ||||
\(55\) | −1.19921 | − | 2.07709i | −0.161701 | − | 0.280074i | ||||
\(56\) | −2.34168 | −0.312920 | ||||||||
\(57\) | 4.87356 | − | 5.76614i | 0.645519 | − | 0.763744i | ||||
\(58\) | −0.627455 | −0.0823889 | ||||||||
\(59\) | −3.13769 | − | 5.43465i | −0.408493 | − | 0.707531i | 0.586228 | − | 0.810146i | \(-0.300612\pi\) |
−0.994721 | + | 0.102615i | \(0.967279\pi\) | |||||||
\(60\) | 0.786608 | − | 1.54313i | 0.101551 | − | 0.199217i | ||||
\(61\) | 1.25195 | − | 2.16845i | 0.160296 | − | 0.277641i | −0.774679 | − | 0.632355i | \(-0.782088\pi\) |
0.934975 | + | 0.354714i | \(0.115422\pi\) | |||||||
\(62\) | 1.77633 | − | 1.02556i | 0.225594 | − | 0.130247i | ||||
\(63\) | 4.12720 | + | 5.68484i | 0.519978 | + | 0.716222i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.478712 | 0.0593770 | ||||||||
\(66\) | −4.14852 | + | 0.216677i | −0.510648 | + | 0.0266712i | ||||
\(67\) | 11.3258 | + | 6.53894i | 1.38366 | + | 0.798859i | 0.992591 | − | 0.121501i | \(-0.0387707\pi\) |
0.391073 | + | 0.920360i | \(0.372104\pi\) | |||||||
\(68\) | − | 2.77143i | − | 0.336086i | ||||||
\(69\) | 1.96060 | + | 3.02023i | 0.236028 | + | 0.363593i | ||||
\(70\) | −2.02795 | − | 1.17084i | −0.242387 | − | 0.139942i | ||||
\(71\) | −2.68385 | − | 4.64856i | −0.318514 | − | 0.551682i | 0.661664 | − | 0.749800i | \(-0.269850\pi\) |
−0.980178 | + | 0.198118i | \(0.936517\pi\) | |||||||
\(72\) | −1.76250 | − | 2.42768i | −0.207712 | − | 0.286104i | ||||
\(73\) | −5.81045 | − | 10.0640i | −0.680062 | − | 1.17790i | −0.974962 | − | 0.222373i | \(-0.928620\pi\) |
0.294900 | − | 0.955528i | \(-0.404714\pi\) | |||||||
\(74\) | −4.91536 | + | 2.83789i | −0.571399 | + | 0.329898i | ||||
\(75\) | 1.45279 | − | 0.943085i | 0.167753 | − | 0.108898i | ||||
\(76\) | 3.17779 | + | 2.98356i | 0.364517 | + | 0.342238i | ||||
\(77\) | 5.61632i | 0.640038i | ||||||||
\(78\) | 0.376559 | − | 0.738715i | 0.0426369 | − | 0.0836430i | ||||
\(79\) | 10.1589 | − | 5.86527i | 1.14297 | − | 0.659894i | 0.195806 | − | 0.980643i | \(-0.437268\pi\) |
0.947164 | + | 0.320749i | \(0.103934\pi\) | |||||||
\(80\) | 0.866025 | + | 0.500000i | 0.0968246 | + | 0.0559017i | ||||
\(81\) | −2.78722 | + | 8.55753i | −0.309691 | + | 0.950837i | ||||
\(82\) | −1.04624 | + | 1.81214i | −0.115538 | + | 0.200117i | ||||
\(83\) | − | 11.3081i | − | 1.24123i | −0.784115 | − | 0.620615i | \(-0.786883\pi\) | ||
0.784115 | − | 0.620615i | \(-0.213117\pi\) | |||||||
\(84\) | −3.40196 | + | 2.20840i | −0.371184 | + | 0.240956i | ||||
\(85\) | 1.38572 | − | 2.40013i | 0.150302 | − | 0.260331i | ||||
\(86\) | 3.77271 | − | 6.53452i | 0.406822 | − | 0.704636i | ||||
\(87\) | −0.911558 | + | 0.591743i | −0.0977293 | + | 0.0634415i | ||||
\(88\) | − | 2.39841i | − | 0.255672i | ||||||
\(89\) | −4.97362 | + | 8.61457i | −0.527203 | + | 0.913142i | 0.472294 | + | 0.881441i | \(0.343426\pi\) |
−0.999497 | + | 0.0317016i | \(0.989907\pi\) | |||||||
\(90\) | −0.312528 | − | 2.98368i | −0.0329433 | − | 0.314507i | ||||
\(91\) | −0.970806 | − | 0.560495i | −0.101768 | − | 0.0587559i | ||||
\(92\) | −1.80040 | + | 1.03946i | −0.187705 | + | 0.108371i | ||||
\(93\) | 1.61344 | − | 3.16516i | 0.167305 | − | 0.328212i | ||||
\(94\) | 2.24461i | 0.231514i | ||||||||
\(95\) | 1.26026 | + | 4.17274i | 0.129300 | + | 0.428114i | ||||
\(96\) | 1.45279 | − | 0.943085i | 0.148274 | − | 0.0962532i | ||||
\(97\) | 7.49209 | − | 4.32556i | 0.760706 | − | 0.439194i | −0.0688431 | − | 0.997627i | \(-0.521931\pi\) |
0.829549 | + | 0.558434i | \(0.188597\pi\) | |||||||
\(98\) | −0.758271 | − | 1.31336i | −0.0765970 | − | 0.132670i | ||||
\(99\) | −5.82257 | + | 4.22719i | −0.585191 | + | 0.424849i | ||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | 3.96069 | + | 2.28671i | 0.394103 | + | 0.227536i | 0.683937 | − | 0.729542i | \(-0.260267\pi\) |
−0.289833 | + | 0.957077i | \(0.593600\pi\) | |||||||
\(102\) | −2.61370 | − | 4.02630i | −0.258794 | − | 0.398663i | ||||
\(103\) | 2.29913i | 0.226540i | 0.993564 | + | 0.113270i | \(0.0361325\pi\) | ||||
−0.993564 | + | 0.113270i | \(0.963867\pi\) | |||||||
\(104\) | 0.414577 | + | 0.239356i | 0.0406526 | + | 0.0234708i | ||||
\(105\) | −4.05038 | + | 0.211552i | −0.395277 | + | 0.0206453i | ||||
\(106\) | 13.2823 | 1.29009 | ||||||||
\(107\) | −12.1841 | −1.17788 | −0.588939 | − | 0.808177i | \(-0.700454\pi\) | ||||
−0.588939 | + | 0.808177i | \(0.700454\pi\) | |||||||
\(108\) | −4.85004 | − | 1.86471i | −0.466695 | − | 0.179432i | ||||
\(109\) | −0.624429 | + | 0.360514i | −0.0598095 | + | 0.0345310i | −0.529607 | − | 0.848243i | \(-0.677660\pi\) |
0.469797 | + | 0.882774i | \(0.344327\pi\) | |||||||
\(110\) | 1.19921 | − | 2.07709i | 0.114340 | − | 0.198043i | ||||
\(111\) | −4.46461 | + | 8.75845i | −0.423762 | + | 0.831315i | ||||
\(112\) | −1.17084 | − | 2.02795i | −0.110634 | − | 0.191624i | ||||
\(113\) | 9.99505 | 0.940255 | 0.470128 | − | 0.882598i | \(-0.344208\pi\) | ||||
0.470128 | + | 0.882598i | \(0.344208\pi\) | |||||||
\(114\) | 7.43041 | + | 1.33756i | 0.695921 | + | 0.125274i | ||||
\(115\) | −2.07892 | −0.193860 | ||||||||
\(116\) | −0.313727 | − | 0.543392i | −0.0291289 | − | 0.0504527i | ||||
\(117\) | −0.149611 | − | 1.42832i | −0.0138315 | − | 0.132049i | ||||
\(118\) | 3.13769 | − | 5.43465i | 0.288848 | − | 0.500300i | ||||
\(119\) | −5.62033 | + | 3.24490i | −0.515215 | + | 0.297460i | ||||
\(120\) | 1.72969 | − | 0.0903420i | 0.157899 | − | 0.00824706i | ||||
\(121\) | 5.24761 | 0.477055 | ||||||||
\(122\) | 2.50391 | 0.226693 | ||||||||
\(123\) | 0.189038 | + | 3.61934i | 0.0170450 | + | 0.326345i | ||||
\(124\) | 1.77633 | + | 1.02556i | 0.159519 | + | 0.0920984i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −2.85961 | + | 6.41668i | −0.254755 | + | 0.571643i | ||||
\(127\) | 9.58763 | + | 5.53542i | 0.850764 | + | 0.491189i | 0.860909 | − | 0.508760i | \(-0.169896\pi\) |
−0.0101444 | + | 0.999949i | \(0.503229\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −0.681668 | − | 13.0513i | −0.0600175 | − | 1.14910i | ||||
\(130\) | 0.239356 | + | 0.414577i | 0.0209929 | + | 0.0363608i | ||||
\(131\) | −13.3817 | + | 7.72594i | −1.16917 | + | 0.675018i | −0.953484 | − | 0.301445i | \(-0.902531\pi\) |
−0.215683 | + | 0.976464i | \(0.569198\pi\) | |||||||
\(132\) | −2.26191 | − | 3.48439i | −0.196874 | − | 0.303277i | ||||
\(133\) | 2.32985 | − | 9.93768i | 0.202023 | − | 0.861706i | ||||
\(134\) | 13.0779i | 1.12976i | ||||||||
\(135\) | −3.26790 | − | 4.03991i | −0.281256 | − | 0.347700i | ||||
\(136\) | 2.40013 | − | 1.38572i | 0.205810 | − | 0.118824i | ||||
\(137\) | −7.57874 | − | 4.37559i | −0.647496 | − | 0.373832i | 0.140000 | − | 0.990151i | \(-0.455290\pi\) |
−0.787496 | + | 0.616320i | \(0.788623\pi\) | |||||||
\(138\) | −1.63530 | + | 3.20804i | −0.139206 | + | 0.273087i | ||||
\(139\) | 3.74921 | − | 6.49383i | 0.318004 | − | 0.550799i | −0.662067 | − | 0.749444i | \(-0.730321\pi\) |
0.980071 | + | 0.198645i | \(0.0636541\pi\) | |||||||
\(140\) | − | 2.34168i | − | 0.197908i | ||||||
\(141\) | 2.11686 | + | 3.26094i | 0.178272 | + | 0.274621i | ||||
\(142\) | 2.68385 | − | 4.64856i | 0.225223 | − | 0.390098i | ||||
\(143\) | 0.574075 | − | 0.994328i | 0.0480066 | − | 0.0831499i | ||||
\(144\) | 1.22118 | − | 2.74020i | 0.101765 | − | 0.228350i | ||||
\(145\) | − | 0.627455i | − | 0.0521073i | ||||||
\(146\) | 5.81045 | − | 10.0640i | 0.480876 | − | 0.832902i | ||||
\(147\) | −2.34022 | − | 1.19293i | −0.193018 | − | 0.0983908i | ||||
\(148\) | −4.91536 | − | 2.83789i | −0.404040 | − | 0.233273i | ||||
\(149\) | 10.5955 | − | 6.11734i | 0.868020 | − | 0.501152i | 0.00133030 | − | 0.999999i | \(-0.499577\pi\) |
0.866690 | + | 0.498847i | \(0.166243\pi\) | |||||||
\(150\) | 1.54313 | + | 0.786608i | 0.125996 | + | 0.0642263i | ||||
\(151\) | 16.0545i | 1.30650i | 0.757143 | + | 0.653250i | \(0.226595\pi\) | ||||
−0.757143 | + | 0.653250i | \(0.773405\pi\) | |||||||
\(152\) | −0.994947 | + | 4.24383i | −0.0807009 | + | 0.344220i | ||||
\(153\) | −7.59429 | − | 3.38442i | −0.613962 | − | 0.273614i | ||||
\(154\) | −4.86387 | + | 2.80816i | −0.391942 | + | 0.226288i | ||||
\(155\) | 1.02556 | + | 1.77633i | 0.0823753 | + | 0.142678i | ||||
\(156\) | 0.828026 | − | 0.0432478i | 0.0662951 | − | 0.00346260i | ||||
\(157\) | −0.836254 | − | 1.44843i | −0.0667404 | − | 0.115598i | 0.830724 | − | 0.556684i | \(-0.187927\pi\) |
−0.897465 | + | 0.441086i | \(0.854593\pi\) | |||||||
\(158\) | 10.1589 | + | 5.86527i | 0.808202 | + | 0.466616i | ||||
\(159\) | 19.2963 | − | 12.5263i | 1.53030 | − | 0.993402i | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | 4.21595 | + | 2.43408i | 0.332264 | + | 0.191833i | ||||
\(162\) | −8.80465 | + | 1.86496i | −0.691759 | + | 0.146525i | ||||
\(163\) | 12.4272 | 0.973371 | 0.486686 | − | 0.873577i | \(-0.338206\pi\) | ||||
0.486686 | + | 0.873577i | \(0.338206\pi\) | |||||||
\(164\) | −2.09248 | −0.163395 | ||||||||
\(165\) | −0.216677 | − | 4.14852i | −0.0168683 | − | 0.322962i | ||||
\(166\) | 9.79314 | − | 5.65407i | 0.760095 | − | 0.438841i | ||||
\(167\) | 0.136815 | − | 0.236971i | 0.0105871 | − | 0.0183374i | −0.860683 | − | 0.509141i | \(-0.829963\pi\) |
0.871270 | + | 0.490803i | \(0.163297\pi\) | |||||||
\(168\) | −3.61351 | − | 1.84198i | −0.278789 | − | 0.142112i | ||||
\(169\) | −6.38542 | − | 11.0599i | −0.491186 | − | 0.850759i | ||||
\(170\) | 2.77143 | 0.212559 | ||||||||
\(171\) | 12.0562 | − | 5.06432i | 0.921963 | − | 0.387278i | ||||
\(172\) | 7.54542 | 0.575333 | ||||||||
\(173\) | −12.1946 | − | 21.1216i | −0.927137 | − | 1.60585i | −0.788088 | − | 0.615563i | \(-0.788929\pi\) |
−0.139049 | − | 0.990286i | \(-0.544404\pi\) | |||||||
\(174\) | −0.968244 | − | 0.493561i | −0.0734024 | − | 0.0374168i | ||||
\(175\) | 1.17084 | − | 2.02795i | 0.0885071 | − | 0.153299i | ||||
\(176\) | 2.07709 | − | 1.19921i | 0.156566 | − | 0.0903936i | ||||
\(177\) | −0.566931 | − | 10.8545i | −0.0426131 | − | 0.815874i | ||||
\(178\) | −9.94725 | −0.745578 | ||||||||
\(179\) | −20.0769 | −1.50062 | −0.750309 | − | 0.661087i | \(-0.770095\pi\) | ||||
−0.750309 | + | 0.661087i | \(0.770095\pi\) | |||||||
\(180\) | 2.42768 | − | 1.76250i | 0.180948 | − | 0.131369i | ||||
\(181\) | 10.2054 | + | 5.89207i | 0.758559 | + | 0.437954i | 0.828778 | − | 0.559578i | \(-0.189037\pi\) |
−0.0702194 | + | 0.997532i | \(0.522370\pi\) | |||||||
\(182\) | − | 1.12099i | − | 0.0830933i | ||||||
\(183\) | 3.63765 | − | 2.36140i | 0.268902 | − | 0.174560i | ||||
\(184\) | −1.80040 | − | 1.03946i | −0.132727 | − | 0.0766301i | ||||
\(185\) | −2.83789 | − | 4.91536i | −0.208646 | − | 0.361385i | ||||
\(186\) | 3.54782 | − | 0.185303i | 0.260139 | − | 0.0135871i | ||||
\(187\) | −3.32352 | − | 5.75651i | −0.243040 | − | 0.420958i | ||||
\(188\) | −1.94389 | + | 1.12231i | −0.141773 | + | 0.0818526i | ||||
\(189\) | 1.89706 | + | 12.0189i | 0.137991 | + | 0.874248i | ||||
\(190\) | −2.98356 | + | 3.17779i | −0.216450 | + | 0.230541i | ||||
\(191\) | 7.36887i | 0.533193i | 0.963808 | + | 0.266596i | \(0.0858991\pi\) | ||||
−0.963808 | + | 0.266596i | \(0.914101\pi\) | |||||||
\(192\) | 1.54313 | + | 0.786608i | 0.111366 | + | 0.0567686i | ||||
\(193\) | −6.47095 | + | 3.73601i | −0.465789 | + | 0.268924i | −0.714475 | − | 0.699661i | \(-0.753335\pi\) |
0.248686 | + | 0.968584i | \(0.420001\pi\) | |||||||
\(194\) | 7.49209 | + | 4.32556i | 0.537900 | + | 0.310557i | ||||
\(195\) | 0.738715 | + | 0.376559i | 0.0529005 | + | 0.0269660i | ||||
\(196\) | 0.758271 | − | 1.31336i | 0.0541622 | − | 0.0938118i | ||||
\(197\) | − | 20.2370i | − | 1.44183i | −0.693025 | − | 0.720913i | \(-0.743723\pi\) | ||
0.693025 | − | 0.720913i | \(-0.256277\pi\) | |||||||
\(198\) | −6.57214 | − | 2.92890i | −0.467062 | − | 0.208148i | ||||
\(199\) | −5.62306 | + | 9.73942i | −0.398608 | + | 0.690409i | −0.993554 | − | 0.113356i | \(-0.963840\pi\) |
0.594946 | + | 0.803765i | \(0.297173\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | 12.3336 | + | 18.9994i | 0.869942 | + | 1.34011i | ||||
\(202\) | 4.57341i | 0.321784i | ||||||||
\(203\) | −0.734649 | + | 1.27245i | −0.0515622 | + | 0.0893084i | ||||
\(204\) | 2.18003 | − | 4.27668i | 0.152633 | − | 0.299427i | ||||
\(205\) | −1.81214 | − | 1.04624i | −0.126565 | − | 0.0730725i | ||||
\(206\) | −1.99110 | + | 1.14956i | −0.138727 | + | 0.0800940i | ||||
\(207\) | 0.649721 | + | 6.20283i | 0.0451587 | + | 0.431126i | ||||
\(208\) | 0.478712i | 0.0331927i | ||||||||
\(209\) | 10.1785 | + | 2.38630i | 0.704059 | + | 0.165063i | ||||
\(210\) | −2.20840 | − | 3.40196i | −0.152394 | − | 0.234758i | ||||
\(211\) | −22.9716 | + | 13.2627i | −1.58143 | + | 0.913040i | −0.586781 | + | 0.809745i | \(0.699605\pi\) |
−0.994651 | + | 0.103295i | \(0.967061\pi\) | |||||||
\(212\) | 6.64114 | + | 11.5028i | 0.456115 | + | 0.790015i | ||||
\(213\) | −0.484928 | − | 9.28446i | −0.0332267 | − | 0.636161i | ||||
\(214\) | −6.09204 | − | 10.5517i | −0.416443 | − | 0.721301i | ||||
\(215\) | 6.53452 | + | 3.77271i | 0.445651 | + | 0.257297i | ||||
\(216\) | −0.810128 | − | 5.13261i | −0.0551222 | − | 0.349230i | ||||
\(217\) | − | 4.80309i | − | 0.326055i | ||||||
\(218\) | −0.624429 | − | 0.360514i | −0.0422917 | − | 0.0244171i | ||||
\(219\) | −1.04985 | − | 20.1006i | −0.0709426 | − | 1.35827i | ||||
\(220\) | 2.39841 | 0.161701 | ||||||||
\(221\) | 1.32672 | 0.0892448 | ||||||||
\(222\) | −9.81735 | + | 0.512760i | −0.658897 | + | 0.0344142i | ||||
\(223\) | −13.2112 | + | 7.62747i | −0.884685 | + | 0.510773i | −0.872200 | − | 0.489149i | \(-0.837307\pi\) |
−0.0124845 | + | 0.999922i | \(0.503974\pi\) | |||||||
\(224\) | 1.17084 | − | 2.02795i | 0.0782300 | − | 0.135498i | ||||
\(225\) | 2.98368 | − | 0.312528i | 0.198912 | − | 0.0208352i | ||||
\(226\) | 4.99753 | + | 8.65597i | 0.332430 | + | 0.575786i | ||||
\(227\) | 1.74109 | 0.115560 | 0.0577800 | − | 0.998329i | \(-0.481598\pi\) | ||||
0.0577800 | + | 0.998329i | \(0.481598\pi\) | |||||||
\(228\) | 2.55684 | + | 7.10370i | 0.169331 | + | 0.470454i | ||||
\(229\) | −16.6454 | −1.09996 | −0.549979 | − | 0.835179i | \(-0.685364\pi\) | ||||
−0.549979 | + | 0.835179i | \(0.685364\pi\) | |||||||
\(230\) | −1.03946 | − | 1.80040i | −0.0685400 | − | 0.118715i | ||||
\(231\) | −4.41784 | + | 8.66670i | −0.290672 | + | 0.570227i | ||||
\(232\) | 0.313727 | − | 0.543392i | 0.0205972 | − | 0.0356754i | ||||
\(233\) | 7.51278 | − | 4.33751i | 0.492179 | − | 0.284160i | −0.233299 | − | 0.972405i | \(-0.574952\pi\) |
0.725478 | + | 0.688245i | \(0.241619\pi\) | |||||||
\(234\) | 1.16216 | − | 0.843728i | 0.0759727 | − | 0.0551563i | ||||
\(235\) | −2.24461 | −0.146422 | ||||||||
\(236\) | 6.27539 | 0.408493 | ||||||||
\(237\) | 20.2902 | − | 1.05976i | 1.31799 | − | 0.0688388i | ||||
\(238\) | −5.62033 | − | 3.24490i | −0.364312 | − | 0.210336i | ||||
\(239\) | 19.1483i | 1.23860i | 0.785153 | + | 0.619302i | \(0.212584\pi\) | ||||
−0.785153 | + | 0.619302i | \(0.787416\pi\) | |||||||
\(240\) | 0.943085 | + | 1.45279i | 0.0608759 | + | 0.0937770i | ||||
\(241\) | −16.6382 | − | 9.60606i | −1.07176 | − | 0.618781i | −0.143098 | − | 0.989709i | \(-0.545706\pi\) |
−0.928662 | + | 0.370928i | \(0.879040\pi\) | |||||||
\(242\) | 2.62380 | + | 4.54456i | 0.168665 | + | 0.292135i | ||||
\(243\) | −11.0325 | + | 11.0129i | −0.707733 | + | 0.706480i | ||||
\(244\) | 1.25195 | + | 2.16845i | 0.0801481 | + | 0.138821i | ||||
\(245\) | 1.31336 | − | 0.758271i | 0.0839078 | − | 0.0484442i | ||||
\(246\) | −3.03992 | + | 1.97338i | −0.193818 | + | 0.125818i | ||||
\(247\) | −1.42827 | + | 1.52125i | −0.0908786 | + | 0.0967947i | ||||
\(248\) | 2.05113i | 0.130247i | ||||||||
\(249\) | 8.89508 | − | 17.4499i | 0.563703 | − | 1.10584i | ||||
\(250\) | −0.866025 | + | 0.500000i | −0.0547723 | + | 0.0316228i | ||||
\(251\) | −10.8299 | − | 6.25262i | −0.683574 | − | 0.394662i | 0.117626 | − | 0.993058i | \(-0.462472\pi\) |
−0.801200 | + | 0.598396i | \(0.795805\pi\) | |||||||
\(252\) | −6.98681 | + | 0.731839i | −0.440128 | + | 0.0461016i | ||||
\(253\) | −2.49306 | + | 4.31810i | −0.156737 | + | 0.271477i | ||||
\(254\) | 11.0708i | 0.694646i | ||||||||
\(255\) | 4.02630 | − | 2.61370i | 0.252137 | − | 0.163676i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −0.733753 | + | 1.27090i | −0.0457702 | + | 0.0792764i | −0.888003 | − | 0.459838i | \(-0.847908\pi\) |
0.842233 | + | 0.539114i | \(0.181241\pi\) | |||||||
\(258\) | 10.9619 | − | 7.11597i | 0.682457 | − | 0.443021i | ||||
\(259\) | 13.2908i | 0.825852i | ||||||||
\(260\) | −0.239356 | + | 0.414577i | −0.0148442 | + | 0.0257110i | ||||
\(261\) | −1.87212 | + | 0.196097i | −0.115881 | + | 0.0121381i | ||||
\(262\) | −13.3817 | − | 7.72594i | −0.826725 | − | 0.477310i | ||||
\(263\) | −12.2015 | + | 7.04453i | −0.752376 | + | 0.434384i | −0.826552 | − | 0.562861i | \(-0.809701\pi\) |
0.0741759 | + | 0.997245i | \(0.476367\pi\) | |||||||
\(264\) | 1.88661 | − | 3.70106i | 0.116113 | − | 0.227785i | ||||
\(265\) | 13.2823i | 0.815924i | ||||||||
\(266\) | 9.77121 | − | 2.95113i | 0.599111 | − | 0.180946i | ||||
\(267\) | −14.4512 | + | 9.38110i | −0.884401 | + | 0.574114i | ||||
\(268\) | −11.3258 | + | 6.53894i | −0.691832 | + | 0.399429i | ||||
\(269\) | 9.48574 | + | 16.4298i | 0.578356 | + | 1.00174i | 0.995668 | + | 0.0929788i | \(0.0296389\pi\) |
−0.417312 | + | 0.908763i | \(0.637028\pi\) | |||||||
\(270\) | 1.86471 | − | 4.85004i | 0.113483 | − | 0.295164i | ||||
\(271\) | 12.6913 | + | 21.9819i | 0.770940 | + | 1.33531i | 0.937048 | + | 0.349200i | \(0.113547\pi\) |
−0.166108 | + | 0.986108i | \(0.553120\pi\) | |||||||
\(272\) | 2.40013 | + | 1.38572i | 0.145529 | + | 0.0840214i | ||||
\(273\) | −1.05719 | − | 1.62856i | −0.0639840 | − | 0.0985650i | ||||
\(274\) | − | 8.75118i | − | 0.528678i | ||||||
\(275\) | 2.07709 | + | 1.19921i | 0.125253 | + | 0.0723149i | ||||
\(276\) | −3.59590 | + | 0.187814i | −0.216448 | + | 0.0113051i | ||||
\(277\) | 8.10858 | 0.487198 | 0.243599 | − | 0.969876i | \(-0.421672\pi\) | ||||
0.243599 | + | 0.969876i | \(0.421672\pi\) | |||||||
\(278\) | 7.49842 | 0.449726 | ||||||||
\(279\) | 4.97948 | − | 3.61511i | 0.298114 | − | 0.216431i | ||||
\(280\) | 2.02795 | − | 1.17084i | 0.121193 | − | 0.0699710i | ||||
\(281\) | −12.6467 | + | 21.9047i | −0.754438 | + | 1.30672i | 0.191216 | + | 0.981548i | \(0.438757\pi\) |
−0.945653 | + | 0.325176i | \(0.894576\pi\) | |||||||
\(282\) | −1.76563 | + | 3.46373i | −0.105142 | + | 0.206262i | ||||
\(283\) | 0.496185 | + | 0.859418i | 0.0294952 | + | 0.0510871i | 0.880396 | − | 0.474239i | \(-0.157277\pi\) |
−0.850901 | + | 0.525326i | \(0.823943\pi\) | |||||||
\(284\) | 5.36769 | 0.318514 | ||||||||
\(285\) | −1.33756 | + | 7.43041i | −0.0792301 | + | 0.440139i | ||||
\(286\) | 1.14815 | 0.0678916 | ||||||||
\(287\) | 2.44995 | + | 4.24344i | 0.144616 | + | 0.250483i | ||||
\(288\) | 2.98368 | − | 0.312528i | 0.175815 | − | 0.0184159i | ||||
\(289\) | −4.65958 | + | 8.07063i | −0.274093 | + | 0.474743i | ||||
\(290\) | 0.543392 | − | 0.313727i | 0.0319091 | − | 0.0184227i | ||||
\(291\) | 14.9638 | − | 0.781559i | 0.877192 | − | 0.0458158i | ||||
\(292\) | 11.6209 | 0.680062 | ||||||||
\(293\) | −23.3348 | −1.36323 | −0.681617 | − | 0.731709i | \(-0.738723\pi\) | ||||
−0.681617 | + | 0.731709i | \(0.738723\pi\) | |||||||
\(294\) | −0.137007 | − | 2.62315i | −0.00799044 | − | 0.152985i | ||||
\(295\) | 5.43465 | + | 3.13769i | 0.316417 | + | 0.182684i | ||||
\(296\) | − | 5.67577i | − | 0.329898i | ||||||
\(297\) | −12.3101 | + | 1.94302i | −0.714306 | + | 0.112746i | ||||
\(298\) | 10.5955 | + | 6.11734i | 0.613783 | + | 0.354368i | ||||
\(299\) | −0.497603 | − | 0.861873i | −0.0287771 | − | 0.0498434i | ||||
\(300\) | 0.0903420 | + | 1.72969i | 0.00521590 | + | 0.0998639i | ||||
\(301\) | −8.83447 | − | 15.3018i | −0.509210 | − | 0.881978i | ||||
\(302\) | −13.9036 | + | 8.02727i | −0.800064 | + | 0.461917i | ||||
\(303\) | 4.31311 | + | 6.64419i | 0.247782 | + | 0.381699i | ||||
\(304\) | −4.17274 | + | 1.26026i | −0.239323 | + | 0.0722811i | ||||
\(305\) | 2.50391i | 0.143373i | ||||||||
\(306\) | −0.866149 | − | 8.26906i | −0.0495145 | − | 0.472711i | ||||
\(307\) | −21.4512 | + | 12.3849i | −1.22429 | + | 0.706842i | −0.965829 | − | 0.259180i | \(-0.916548\pi\) |
−0.258458 | + | 0.966023i | \(0.583214\pi\) | |||||||
\(308\) | −4.86387 | − | 2.80816i | −0.277145 | − | 0.160010i | ||||
\(309\) | −1.80851 | + | 3.54785i | −0.102883 | + | 0.201830i | ||||
\(310\) | −1.02556 | + | 1.77633i | −0.0582482 | + | 0.100889i | ||||
\(311\) | 11.2512i | 0.637999i | 0.947755 | + | 0.318999i | \(0.103347\pi\) | ||||
−0.947755 | + | 0.318999i | \(0.896653\pi\) | |||||||
\(312\) | 0.451467 | + | 0.695467i | 0.0255593 | + | 0.0393731i | ||||
\(313\) | 5.46644 | − | 9.46816i | 0.308982 | − | 0.535172i | −0.669158 | − | 0.743120i | \(-0.733345\pi\) |
0.978140 | + | 0.207948i | \(0.0666785\pi\) | |||||||
\(314\) | 0.836254 | − | 1.44843i | 0.0471926 | − | 0.0817399i | ||||
\(315\) | −6.41668 | − | 2.85961i | −0.361539 | − | 0.161121i | ||||
\(316\) | 11.7305i | 0.659894i | ||||||||
\(317\) | 8.95027 | − | 15.5023i | 0.502697 | − | 0.870697i | −0.497298 | − | 0.867580i | \(-0.665674\pi\) |
0.999995 | − | 0.00311703i | \(-0.000992183\pi\) | |||||||
\(318\) | 20.4963 | + | 10.4479i | 1.14937 | + | 0.585892i | ||||
\(319\) | −1.30328 | − | 0.752448i | −0.0729696 | − | 0.0421290i | ||||
\(320\) | −0.866025 | + | 0.500000i | −0.0484123 | + | 0.0279508i | ||||
\(321\) | −18.8016 | − | 9.58409i | −1.04940 | − | 0.534932i | ||||
\(322\) | 4.86817i | 0.271292i | ||||||||
\(323\) | 3.49274 | + | 11.5645i | 0.194341 | + | 0.643464i | ||||
\(324\) | −6.01743 | − | 6.69257i | −0.334302 | − | 0.371810i | ||||
\(325\) | −0.414577 | + | 0.239356i | −0.0229966 | + | 0.0132771i | ||||
\(326\) | 6.21359 | + | 10.7622i | 0.344139 | + | 0.596066i | ||||
\(327\) | −1.24716 | + | 0.0651391i | −0.0689680 | + | 0.00360220i | ||||
\(328\) | −1.04624 | − | 1.81214i | −0.0577688 | − | 0.100059i | ||||
\(329\) | 4.55197 | + | 2.62808i | 0.250958 | + | 0.144891i | ||||
\(330\) | 3.48439 | − | 2.26191i | 0.191809 | − | 0.124514i | ||||
\(331\) | − | 10.3625i | − | 0.569572i | −0.958591 | − | 0.284786i | \(-0.908077\pi\) | ||
0.958591 | − | 0.284786i | \(-0.0919226\pi\) | |||||||
\(332\) | 9.79314 | + | 5.65407i | 0.537468 | + | 0.310308i | ||||
\(333\) | −13.7789 | + | 10.0035i | −0.755081 | + | 0.548190i | ||||
\(334\) | 0.273631 | 0.0149724 | ||||||||
\(335\) | −13.0779 | −0.714521 | ||||||||
\(336\) | −0.211552 | − | 4.05038i | −0.0115411 | − | 0.220967i | ||||
\(337\) | −23.7499 | + | 13.7120i | −1.29374 | + | 0.746939i | −0.979315 | − | 0.202344i | \(-0.935144\pi\) |
−0.314422 | + | 0.949283i | \(0.601811\pi\) | |||||||
\(338\) | 6.38542 | − | 11.0599i | 0.347321 | − | 0.601577i | ||||
\(339\) | 15.4237 | + | 7.86219i | 0.837698 | + | 0.427015i | ||||
\(340\) | 1.38572 | + | 2.40013i | 0.0751510 | + | 0.130165i | ||||
\(341\) | 4.91946 | 0.266404 | ||||||||
\(342\) | 10.4139 | + | 7.90884i | 0.563122 | + | 0.427661i | ||||
\(343\) | −19.9430 | −1.07682 | ||||||||
\(344\) | 3.77271 | + | 6.53452i | 0.203411 | + | 0.352318i | ||||
\(345\) | −3.20804 | − | 1.63530i | −0.172715 | − | 0.0880414i | ||||
\(346\) | 12.1946 | − | 21.1216i | 0.655585 | − | 1.13551i | ||||
\(347\) | 22.5112 | − | 12.9969i | 1.20847 | − | 0.697709i | 0.246042 | − | 0.969259i | \(-0.420870\pi\) |
0.962424 | + | 0.271551i | \(0.0875364\pi\) | |||||||
\(348\) | −0.0566855 | − | 1.08530i | −0.00303866 | − | 0.0581784i | ||||
\(349\) | 8.16697 | 0.437168 | 0.218584 | − | 0.975818i | \(-0.429856\pi\) | ||||
0.218584 | + | 0.975818i | \(0.429856\pi\) | |||||||
\(350\) | 2.34168 | 0.125168 | ||||||||
\(351\) | 0.892662 | − | 2.32177i | 0.0476468 | − | 0.123927i | ||||
\(352\) | 2.07709 | + | 1.19921i | 0.110709 | + | 0.0639180i | ||||
\(353\) | − | 23.1015i | − | 1.22957i | −0.788696 | − | 0.614783i | \(-0.789243\pi\) | ||
0.788696 | − | 0.614783i | \(-0.210757\pi\) | |||||||
\(354\) | 9.11681 | − | 5.91823i | 0.484553 | − | 0.314550i | ||||
\(355\) | 4.64856 | + | 2.68385i | 0.246720 | + | 0.142444i | ||||
\(356\) | −4.97362 | − | 8.61457i | −0.263602 | − | 0.456571i | ||||
\(357\) | −11.2254 | + | 0.586301i | −0.594109 | + | 0.0310304i | ||||
\(358\) | −10.0385 | − | 17.3871i | −0.530549 | − | 0.918937i | ||||
\(359\) | −17.3948 | + | 10.0429i | −0.918063 | + | 0.530044i | −0.883017 | − | 0.469342i | \(-0.844491\pi\) |
−0.0350462 | + | 0.999386i | \(0.511158\pi\) | |||||||
\(360\) | 2.74020 | + | 1.22118i | 0.144421 | + | 0.0643619i | ||||
\(361\) | −17.0202 | − | 8.44477i | −0.895798 | − | 0.444462i | ||||
\(362\) | 11.7841i | 0.619361i | ||||||||
\(363\) | 8.09774 | + | 4.12781i | 0.425021 | + | 0.216654i | ||||
\(364\) | 0.970806 | − | 0.560495i | 0.0508841 | − | 0.0293779i | ||||
\(365\) | 10.0640 | + | 5.81045i | 0.526773 | + | 0.304133i | ||||
\(366\) | 3.86385 | + | 1.96959i | 0.201967 | + | 0.102952i | ||||
\(367\) | 4.83084 | − | 8.36726i | 0.252168 | − | 0.436768i | −0.711955 | − | 0.702226i | \(-0.752190\pi\) |
0.964122 | + | 0.265458i | \(0.0855231\pi\) | |||||||
\(368\) | − | 2.07892i | − | 0.108371i | ||||||
\(369\) | −2.55529 | + | 5.73381i | −0.133023 | + | 0.298490i | ||||
\(370\) | 2.83789 | − | 4.91536i | 0.147535 | − | 0.255538i | ||||
\(371\) | 15.5514 | − | 26.9358i | 0.807389 | − | 1.39844i | ||||
\(372\) | 1.93439 | + | 2.97985i | 0.100293 | + | 0.154498i | ||||
\(373\) | − | 16.8317i | − | 0.871515i | −0.900064 | − | 0.435757i | \(-0.856481\pi\) | ||
0.900064 | − | 0.435757i | \(-0.143519\pi\) | |||||||
\(374\) | 3.32352 | − | 5.75651i | 0.171855 | − | 0.297662i | ||||
\(375\) | −0.786608 | + | 1.54313i | −0.0406203 | + | 0.0796868i | ||||
\(376\) | −1.94389 | − | 1.12231i | −0.100249 | − | 0.0578785i | ||||
\(377\) | 0.260128 | − | 0.150185i | 0.0133973 | − | 0.00773493i | ||||
\(378\) | −9.46016 | + | 7.65236i | −0.486578 | + | 0.393595i | ||||
\(379\) | 31.6110i | 1.62375i | 0.583834 | + | 0.811873i | \(0.301552\pi\) | ||||
−0.583834 | + | 0.811873i | \(0.698448\pi\) | |||||||
\(380\) | −4.24383 | − | 0.994947i | −0.217704 | − | 0.0510397i | ||||
\(381\) | 10.4407 | + | 16.0836i | 0.534895 | + | 0.823986i | ||||
\(382\) | −6.38163 | + | 3.68444i | −0.326513 | + | 0.188512i | ||||
\(383\) | 14.8637 | + | 25.7447i | 0.759500 | + | 1.31549i | 0.943106 | + | 0.332493i | \(0.107890\pi\) |
−0.183605 | + | 0.983000i | \(0.558777\pi\) | |||||||
\(384\) | 0.0903420 | + | 1.72969i | 0.00461024 | + | 0.0882680i | ||||
\(385\) | −2.80816 | − | 4.86387i | −0.143117 | − | 0.247886i | ||||
\(386\) | −6.47095 | − | 3.73601i | −0.329363 | − | 0.190158i | ||||
\(387\) | 9.21432 | − | 20.6760i | 0.468390 | − | 1.05102i | ||||
\(388\) | 8.65112i | 0.439194i | ||||||||
\(389\) | 6.06103 | + | 3.49934i | 0.307307 | + | 0.177424i | 0.645721 | − | 0.763574i | \(-0.276557\pi\) |
−0.338414 | + | 0.940997i | \(0.609890\pi\) | |||||||
\(390\) | 0.0432478 | + | 0.828026i | 0.00218994 | + | 0.0419287i | ||||
\(391\) | −5.76159 | −0.291376 | ||||||||
\(392\) | 1.51654 | 0.0765970 | ||||||||
\(393\) | −26.7270 | + | 1.39595i | −1.34820 | + | 0.0704165i | ||||
\(394\) | 17.5258 | − | 10.1185i | 0.882935 | − | 0.509763i | ||||
\(395\) | −5.86527 | + | 10.1589i | −0.295114 | + | 0.511152i | ||||
\(396\) | −0.749571 | − | 7.15609i | −0.0376674 | − | 0.359607i | ||||
\(397\) | 14.8564 | + | 25.7320i | 0.745621 | + | 1.29145i | 0.949904 | + | 0.312542i | \(0.101180\pi\) |
−0.204283 | + | 0.978912i | \(0.565486\pi\) | |||||||
\(398\) | −11.2461 | −0.563717 | ||||||||
\(399\) | 11.4123 | − | 13.5024i | 0.571330 | − | 0.675968i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | −14.8000 | − | 25.6344i | −0.739079 | − | 1.28012i | −0.952910 | − | 0.303252i | \(-0.901928\pi\) |
0.213831 | − | 0.976871i | \(-0.431406\pi\) | |||||||
\(402\) | −10.2872 | + | 20.1809i | −0.513077 | + | 1.00653i | ||||
\(403\) | −0.490951 | + | 0.850351i | −0.0244560 | + | 0.0423590i | ||||
\(404\) | −3.96069 | + | 2.28671i | −0.197052 | + | 0.113768i | ||||
\(405\) | −1.86496 | − | 8.80465i | −0.0926708 | − | 0.437507i | ||||
\(406\) | −1.46930 | −0.0729200 | ||||||||
\(407\) | −13.6129 | −0.674764 | ||||||||
\(408\) | 4.79373 | − | 0.250377i | 0.237325 | − | 0.0123955i | ||||
\(409\) | −1.05270 | − | 0.607777i | −0.0520527 | − | 0.0300526i | 0.473748 | − | 0.880661i | \(-0.342901\pi\) |
−0.525800 | + | 0.850608i | \(0.676234\pi\) | |||||||
\(410\) | − | 2.09248i | − | 0.103340i | ||||||
\(411\) | −8.25310 | − | 12.7136i | −0.407096 | − | 0.627116i | ||||
\(412\) | −1.99110 | − | 1.14956i | −0.0980947 | − | 0.0566350i | ||||
\(413\) | −7.34747 | − | 12.7262i | −0.361545 | − | 0.626215i | ||||
\(414\) | −5.04695 | + | 3.66409i | −0.248044 | + | 0.180080i | ||||
\(415\) | 5.65407 | + | 9.79314i | 0.277547 | + | 0.480726i | ||||
\(416\) | −0.414577 | + | 0.239356i | −0.0203263 | + | 0.0117354i | ||||
\(417\) | 10.8936 | − | 7.07165i | 0.533463 | − | 0.346300i | ||||
\(418\) | 3.02264 | + | 10.0080i | 0.147842 | + | 0.489505i | ||||
\(419\) | − | 3.26405i | − | 0.159459i | −0.996817 | − | 0.0797297i | \(-0.974594\pi\) | ||
0.996817 | − | 0.0797297i | \(-0.0254057\pi\) | |||||||
\(420\) | 1.84198 | − | 3.61351i | 0.0898796 | − | 0.176321i | ||||
\(421\) | −18.4508 | + | 10.6526i | −0.899236 | + | 0.519174i | −0.876952 | − | 0.480578i | \(-0.840427\pi\) |
−0.0222837 | + | 0.999752i | \(0.507094\pi\) | |||||||
\(422\) | −22.9716 | − | 13.2627i | −1.11824 | − | 0.645617i | ||||
\(423\) | 0.701504 | + | 6.69720i | 0.0341083 | + | 0.325629i | ||||
\(424\) | −6.64114 | + | 11.5028i | −0.322522 | + | 0.558625i | ||||
\(425\) | 2.77143i | 0.134434i | ||||||||
\(426\) | 7.79812 | − | 5.06219i | 0.377820 | − | 0.245264i | ||||
\(427\) | 2.93167 | − | 5.07781i | 0.141874 | − | 0.245732i | ||||
\(428\) | 6.09204 | − | 10.5517i | 0.294470 | − | 0.510037i | ||||
\(429\) | 1.66802 | − | 1.08280i | 0.0805327 | − | 0.0522783i | ||||
\(430\) | 7.54542i | 0.363872i | ||||||||
\(431\) | −2.14280 | + | 3.71143i | −0.103215 | + | 0.178774i | −0.913007 | − | 0.407943i | \(-0.866246\pi\) |
0.809793 | + | 0.586716i | \(0.199580\pi\) | |||||||
\(432\) | 4.03991 | − | 3.26790i | 0.194370 | − | 0.157227i | ||||
\(433\) | 18.0367 | + | 10.4135i | 0.866789 | + | 0.500441i | 0.866280 | − | 0.499559i | \(-0.166505\pi\) |
0.000509428 | 1.00000i | \(0.499838\pi\) | ||||||||
\(434\) | 4.15959 | − | 2.40154i | 0.199667 | − | 0.115278i | ||||
\(435\) | 0.493561 | − | 0.968244i | 0.0236644 | − | 0.0464237i | ||||
\(436\) | − | 0.721029i | − | 0.0345310i | ||||||
\(437\) | 6.20259 | − | 6.60638i | 0.296710 | − | 0.316026i | ||||
\(438\) | 16.8827 | − | 10.9595i | 0.806686 | − | 0.523665i | ||||
\(439\) | 14.9323 | − | 8.62117i | 0.712680 | − | 0.411466i | −0.0993728 | − | 0.995050i | \(-0.531684\pi\) |
0.812052 | + | 0.583584i | \(0.198350\pi\) | |||||||
\(440\) | 1.19921 | + | 2.07709i | 0.0571700 | + | 0.0990213i | ||||
\(441\) | −2.67290 | − | 3.68167i | −0.127281 | − | 0.175318i | ||||
\(442\) | 0.663360 | + | 1.14897i | 0.0315528 | + | 0.0546510i | ||||
\(443\) | 19.6711 | + | 11.3571i | 0.934602 | + | 0.539592i | 0.888264 | − | 0.459333i | \(-0.151912\pi\) |
0.0463376 | + | 0.998926i | \(0.485245\pi\) | |||||||
\(444\) | −5.35274 | − | 8.24569i | −0.254030 | − | 0.391323i | ||||
\(445\) | − | 9.94725i | − | 0.471545i | ||||||
\(446\) | −13.2112 | − | 7.62747i | −0.625566 | − | 0.361171i | ||||
\(447\) | 21.1622 | − | 1.10530i | 1.00094 | − | 0.0522791i | ||||
\(448\) | 2.34168 | 0.110634 | ||||||||
\(449\) | 24.4007 | 1.15154 | 0.575770 | − | 0.817612i | \(-0.304702\pi\) | ||||
0.575770 | + | 0.817612i | \(0.304702\pi\) | |||||||
\(450\) | 1.76250 | + | 2.42768i | 0.0830848 | + | 0.114442i | ||||
\(451\) | −4.34626 | + | 2.50931i | −0.204657 | + | 0.118159i | ||||
\(452\) | −4.99753 | + | 8.65597i | −0.235064 | + | 0.407142i | ||||
\(453\) | −12.6286 | + | 24.7742i | −0.593345 | + | 1.16399i | ||||
\(454\) | 0.870543 | + | 1.50782i | 0.0408566 | + | 0.0707657i | ||||
\(455\) | 1.12099 | 0.0525528 | ||||||||
\(456\) | −4.87356 | + | 5.76614i | −0.228225 | + | 0.270024i | ||||
\(457\) | 5.57921 | 0.260984 | 0.130492 | − | 0.991449i | \(-0.458344\pi\) | ||||
0.130492 | + | 0.991449i | \(0.458344\pi\) | |||||||
\(458\) | −8.32269 | − | 14.4153i | −0.388894 | − | 0.673584i | ||||
\(459\) | −9.05675 | − | 11.1963i | −0.422733 | − | 0.522600i | ||||
\(460\) | 1.03946 | − | 1.80040i | 0.0484651 | − | 0.0839440i | ||||
\(461\) | 13.2971 | − | 7.67711i | 0.619310 | − | 0.357559i | −0.157291 | − | 0.987552i | \(-0.550276\pi\) |
0.776600 | + | 0.629994i | \(0.216943\pi\) | |||||||
\(462\) | −9.71450 | + | 0.507389i | −0.451960 | + | 0.0236059i | ||||
\(463\) | 29.0927 | 1.35205 | 0.676027 | − | 0.736877i | \(-0.263700\pi\) | ||||
0.676027 | + | 0.736877i | \(0.263700\pi\) | |||||||
\(464\) | 0.627455 | 0.0291289 | ||||||||
\(465\) | 0.185303 | + | 3.54782i | 0.00859322 | + | 0.164526i | ||||
\(466\) | 7.51278 | + | 4.33751i | 0.348023 | + | 0.200931i | ||||
\(467\) | − | 30.7109i | − | 1.42113i | −0.703630 | − | 0.710567i | \(-0.748439\pi\) | ||
0.703630 | − | 0.710567i | \(-0.251561\pi\) | |||||||
\(468\) | 1.31177 | + | 0.584595i | 0.0606366 | + | 0.0270229i | ||||
\(469\) | 26.5213 | + | 15.3121i | 1.22464 | + | 0.707047i | ||||
\(470\) | −1.12231 | − | 1.94389i | −0.0517681 | − | 0.0896650i | ||||
\(471\) | −0.151098 | − | 2.89293i | −0.00696221 | − | 0.133299i | ||||
\(472\) | 3.13769 | + | 5.43465i | 0.144424 | + | 0.250150i | ||||
\(473\) | 15.6725 | − | 9.04852i | 0.720622 | − | 0.416051i | ||||
\(474\) | 11.0629 | + | 17.0420i | 0.508135 | + | 0.782764i | ||||
\(475\) | −3.17779 | − | 2.98356i | −0.145807 | − | 0.136895i | ||||
\(476\) | − | 6.48980i | − | 0.297460i | ||||||
\(477\) | 39.6300 | − | 4.15108i | 1.81453 | − | 0.190065i | ||||
\(478\) | −16.5830 | + | 9.57417i | −0.758487 | + | 0.437912i | ||||
\(479\) | −22.3097 | − | 12.8805i | −1.01935 | − | 0.588525i | −0.105438 | − | 0.994426i | \(-0.533624\pi\) |
−0.913917 | + | 0.405901i | \(0.866958\pi\) | |||||||
\(480\) | −0.786608 | + | 1.54313i | −0.0359036 | + | 0.0704339i | ||||
\(481\) | 1.35853 | − | 2.35305i | 0.0619437 | − | 0.107290i | ||||
\(482\) | − | 19.2121i | − | 0.875088i | ||||||
\(483\) | 4.59109 | + | 7.07241i | 0.208902 | + | 0.321806i | ||||
\(484\) | −2.62380 | + | 4.54456i | −0.119264 | + | 0.206571i | ||||
\(485\) | −4.32556 | + | 7.49209i | −0.196413 | + | 0.340198i | ||||
\(486\) | −15.0537 | − | 4.04793i | −0.682850 | − | 0.183618i | ||||
\(487\) | 19.2342i | 0.871583i | 0.900048 | + | 0.435791i | \(0.143531\pi\) | ||||
−0.900048 | + | 0.435791i | \(0.856469\pi\) | |||||||
\(488\) | −1.25195 | + | 2.16845i | −0.0566733 | + | 0.0981610i | ||||
\(489\) | 19.1767 | + | 9.77532i | 0.867202 | + | 0.442055i | ||||
\(490\) | 1.31336 | + | 0.758271i | 0.0593318 | + | 0.0342552i | ||||
\(491\) | −18.7155 | + | 10.8054i | −0.844619 | + | 0.487641i | −0.858832 | − | 0.512258i | \(-0.828809\pi\) |
0.0142124 | + | 0.999899i | \(0.495476\pi\) | |||||||
\(492\) | −3.22896 | − | 1.64596i | −0.145573 | − | 0.0742056i | ||||
\(493\) | − | 1.73895i | − | 0.0783183i | ||||||
\(494\) | −2.03157 | − | 0.476294i | −0.0914048 | − | 0.0214295i | ||||
\(495\) | 2.92890 | − | 6.57214i | 0.131644 | − | 0.295396i | ||||
\(496\) | −1.77633 | + | 1.02556i | −0.0797596 | + | 0.0460492i | ||||
\(497\) | −6.28470 | − | 10.8854i | −0.281908 | − | 0.488278i | ||||
\(498\) | 19.5596 | − | 1.02160i | 0.876488 | − | 0.0457790i | ||||
\(499\) | −9.49912 | − | 16.4530i | −0.425239 | − | 0.736535i | 0.571204 | − | 0.820808i | \(-0.306477\pi\) |
−0.996443 | + | 0.0842728i | \(0.973143\pi\) | |||||||
\(500\) | −0.866025 | − | 0.500000i | −0.0387298 | − | 0.0223607i | ||||
\(501\) | 0.397527 | − | 0.258057i | 0.0177602 | − | 0.0115291i | ||||
\(502\) | − | 12.5052i | − | 0.558136i | ||||||
\(503\) | −17.2526 | − | 9.96081i | −0.769256 | − | 0.444130i | 0.0633529 | − | 0.997991i | \(-0.479821\pi\) |
−0.832609 | + | 0.553861i | \(0.813154\pi\) | |||||||
\(504\) | −4.12720 | − | 5.68484i | −0.183840 | − | 0.253223i | ||||
\(505\) | −4.57341 | −0.203514 | ||||||||
\(506\) | −4.98612 | −0.221660 | ||||||||
\(507\) | −1.15374 | − | 22.0896i | −0.0512395 | − | 0.981035i | ||||
\(508\) | −9.58763 | + | 5.53542i | −0.425382 | + | 0.245594i | ||||
\(509\) | −15.7560 | + | 27.2902i | −0.698372 | + | 1.20962i | 0.270658 | + | 0.962675i | \(0.412759\pi\) |
−0.969031 | + | 0.246941i | \(0.920575\pi\) | |||||||
\(510\) | 4.27668 | + | 2.18003i | 0.189374 | + | 0.0965334i | ||||
\(511\) | −13.6062 | − | 23.5666i | −0.601903 | − | 1.04253i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 22.5880 | + | 1.66863i | 0.997283 | + | 0.0736718i | ||||
\(514\) | −1.46751 | −0.0647289 | ||||||||
\(515\) | −1.14956 | − | 1.99110i | −0.0506559 | − | 0.0877385i | ||||
\(516\) | 11.6436 | + | 5.93529i | 0.512579 | + | 0.261286i | ||||
\(517\) | −2.69176 | + | 4.66226i | −0.118383 | + | 0.205046i | ||||
\(518\) | −11.5102 | + | 6.64542i | −0.505729 | + | 0.291983i | ||||
\(519\) | −2.20336 | − | 42.1858i | −0.0967170 | − | 1.85175i | ||||
\(520\) | −0.478712 | −0.0209929 | ||||||||
\(521\) | 11.3505 | 0.497273 | 0.248637 | − | 0.968597i | \(-0.420018\pi\) | ||||
0.248637 | + | 0.968597i | \(0.420018\pi\) | |||||||
\(522\) | −1.10589 | − | 1.52326i | −0.0484033 | − | 0.0666712i | ||||
\(523\) | 31.9970 | + | 18.4735i | 1.39913 | + | 0.807788i | 0.994301 | − | 0.106605i | \(-0.0339980\pi\) |
0.404828 | + | 0.914393i | \(0.367331\pi\) | |||||||
\(524\) | − | 15.4519i | − | 0.675018i | ||||||
\(525\) | 3.40196 | − | 2.20840i | 0.148474 | − | 0.0963825i | ||||
\(526\) | −12.2015 | − | 7.04453i | −0.532010 | − | 0.307156i | ||||
\(527\) | 2.84228 | + | 4.92298i | 0.123812 | + | 0.214448i | ||||
\(528\) | 4.14852 | − | 0.216677i | 0.180541 | − | 0.00942968i | ||||
\(529\) | −9.33904 | − | 16.1757i | −0.406045 | − | 0.703291i | ||||
\(530\) | −11.5028 | + | 6.64114i | −0.499649 | + | 0.288473i | ||||
\(531\) | 7.66339 | − | 17.1958i | 0.332563 | − | 0.746236i | ||||
\(532\) | 7.44136 | + | 6.98655i | 0.322624 | + | 0.302905i | ||||
\(533\) | − | 1.00169i | − | 0.0433882i | ||||||
\(534\) | −15.3499 | − | 7.82459i | −0.664255 | − | 0.338603i | ||||
\(535\) | 10.5517 | − | 6.09204i | 0.456191 | − | 0.263382i | ||||
\(536\) | −11.3258 | − | 6.53894i | −0.489199 | − | 0.282439i | ||||
\(537\) | −30.9813 | − | 15.7927i | −1.33694 | − | 0.681503i | ||||
\(538\) | −9.48574 | + | 16.4298i | −0.408959 | + | 0.708339i | ||||
\(539\) | − | 3.63730i | − | 0.156670i | ||||||
\(540\) | 5.13261 | − | 0.810128i | 0.220872 | − | 0.0348624i | ||||
\(541\) | 15.2223 | − | 26.3657i | 0.654456 | − | 1.13355i | −0.327574 | − | 0.944826i | \(-0.606231\pi\) |
0.982030 | − | 0.188725i | \(-0.0604356\pi\) | |||||||
\(542\) | −12.6913 | + | 21.9819i | −0.545137 | + | 0.944205i | ||||
\(543\) | 11.1134 | + | 17.1198i | 0.476924 | + | 0.734683i | ||||
\(544\) | 2.77143i | 0.118824i | ||||||||
\(545\) | 0.360514 | − | 0.624429i | 0.0154427 | − | 0.0267476i | ||||
\(546\) | 0.881780 | − | 1.72983i | 0.0377367 | − | 0.0740300i | ||||
\(547\) | −7.08775 | − | 4.09212i | −0.303050 | − | 0.174966i | 0.340762 | − | 0.940150i | \(-0.389315\pi\) |
−0.643812 | + | 0.765183i | \(0.722648\pi\) | |||||||
\(548\) | 7.57874 | − | 4.37559i | 0.323748 | − | 0.186916i | ||||
\(549\) | 7.47085 | − | 0.782541i | 0.318848 | − | 0.0333980i | ||||
\(550\) | 2.39841i | 0.102269i | ||||||||
\(551\) | 1.99392 | + | 1.87205i | 0.0849438 | + | 0.0797521i | ||||
\(552\) | −1.96060 | − | 3.02023i | −0.0834487 | − | 0.128550i | ||||
\(553\) | 23.7890 | − | 13.7346i | 1.01161 | − | 0.584053i | ||||
\(554\) | 4.05429 | + | 7.02224i | 0.172250 | + | 0.298346i | ||||
\(555\) | −0.512760 | − | 9.81735i | −0.0217655 | − | 0.416723i | ||||
\(556\) | 3.74921 | + | 6.49383i | 0.159002 | + | 0.275400i | ||||
\(557\) | 1.37346 | + | 0.792970i | 0.0581956 | + | 0.0335992i | 0.528815 | − | 0.848737i | \(-0.322636\pi\) |
−0.470620 | + | 0.882336i | \(0.655970\pi\) | |||||||
\(558\) | 5.62051 | + | 2.50480i | 0.237935 | + | 0.106037i | ||||
\(559\) | 3.61209i | 0.152775i | ||||||||
\(560\) | 2.02795 | + | 1.17084i | 0.0856966 | + | 0.0494770i | ||||
\(561\) | −0.600507 | − | 11.4973i | −0.0253534 | − | 0.485418i | ||||
\(562\) | −25.2934 | −1.06694 | ||||||||
\(563\) | 12.2083 | 0.514519 | 0.257260 | − | 0.966342i | \(-0.417180\pi\) | ||||
0.257260 | + | 0.966342i | \(0.417180\pi\) | |||||||
\(564\) | −3.88249 | + | 0.202783i | −0.163482 | + | 0.00853869i | ||||
\(565\) | −8.65597 | + | 4.99753i | −0.364159 | + | 0.210247i | ||||
\(566\) | −0.496185 | + | 0.859418i | −0.0208562 | + | 0.0361240i | ||||
\(567\) | −6.52677 | + | 20.0390i | −0.274099 | + | 0.841559i | ||||
\(568\) | 2.68385 | + | 4.64856i | 0.112612 | + | 0.195049i | ||||
\(569\) | 30.1807 | 1.26524 | 0.632620 | − | 0.774462i | \(-0.281979\pi\) | ||||
0.632620 | + | 0.774462i | \(0.281979\pi\) | |||||||
\(570\) | −7.10370 | + | 2.55684i | −0.297541 | + | 0.107094i | ||||
\(571\) | −35.1445 | −1.47075 | −0.735375 | − | 0.677660i | \(-0.762994\pi\) | ||||
−0.735375 | + | 0.677660i | \(0.762994\pi\) | |||||||
\(572\) | 0.574075 | + | 0.994328i | 0.0240033 | + | 0.0415749i | ||||
\(573\) | −5.79641 | + | 11.3711i | −0.242149 | + | 0.475035i | ||||
\(574\) | −2.44995 | + | 4.24344i | −0.102259 | + | 0.177118i | ||||
\(575\) | 1.80040 | − | 1.03946i | 0.0750818 | − | 0.0433485i | ||||
\(576\) | 1.76250 | + | 2.42768i | 0.0734373 | + | 0.101153i | ||||
\(577\) | 3.33452 | 0.138818 | 0.0694088 | − | 0.997588i | \(-0.477889\pi\) | ||||
0.0694088 | + | 0.997588i | \(0.477889\pi\) | |||||||
\(578\) | −9.31916 | −0.387626 | ||||||||
\(579\) | −12.9243 | + | 0.675036i | −0.537115 | + | 0.0280536i | ||||
\(580\) | 0.543392 | + | 0.313727i | 0.0225631 | + | 0.0130268i | ||||
\(581\) | − | 26.4800i | − | 1.09858i | ||||||
\(582\) | 8.15874 | + | 12.5682i | 0.338191 | + | 0.520970i | ||||
\(583\) | 27.5885 | + | 15.9282i | 1.14260 | + | 0.659679i | ||||
\(584\) | 5.81045 | + | 10.0640i | 0.240438 | + | 0.416451i | ||||
\(585\) | 0.843728 | + | 1.16216i | 0.0348839 | + | 0.0480493i | ||||
\(586\) | −11.6674 | − | 20.2085i | −0.481976 | − | 0.834807i | ||||
\(587\) | 6.62612 | − | 3.82559i | 0.273489 | − | 0.157899i | −0.356983 | − | 0.934111i | \(-0.616195\pi\) |
0.630472 | + | 0.776212i | \(0.282861\pi\) | |||||||
\(588\) | 2.20321 | − | 1.43023i | 0.0908590 | − | 0.0589816i | ||||
\(589\) | −8.70464 | − | 2.04077i | −0.358668 | − | 0.0840883i | ||||
\(590\) | 6.27539i | 0.258354i | ||||||||
\(591\) | 15.9186 | − | 31.2283i | 0.654803 | − | 1.28456i | ||||
\(592\) | 4.91536 | − | 2.83789i | 0.202020 | − | 0.116636i | ||||
\(593\) | −16.7538 | − | 9.67281i | −0.687996 | − | 0.397215i | 0.114865 | − | 0.993381i | \(-0.463357\pi\) |
−0.802861 | + | 0.596166i | \(0.796690\pi\) | |||||||
\(594\) | −7.83777 | − | 9.68937i | −0.321588 | − | 0.397560i | ||||
\(595\) | 3.24490 | − | 5.62033i | 0.133028 | − | 0.230411i | ||||
\(596\) | 12.2347i | 0.501152i | ||||||||
\(597\) | −16.3382 | + | 10.6060i | −0.668678 | + | 0.434076i | ||||
\(598\) | 0.497603 | − | 0.861873i | 0.0203485 | − | 0.0352446i | ||||
\(599\) | −0.00576144 | + | 0.00997910i | −0.000235406 | + | 0.000407735i | −0.866143 | − | 0.499796i | \(-0.833408\pi\) |
0.865908 | + | 0.500204i | \(0.166742\pi\) | |||||||
\(600\) | −1.45279 | + | 0.943085i | −0.0593098 | + | 0.0385013i | ||||
\(601\) | − | 19.6294i | − | 0.800698i | −0.916363 | − | 0.400349i | \(-0.868889\pi\) | ||
0.916363 | − | 0.400349i | \(-0.131111\pi\) | |||||||
\(602\) | 8.83447 | − | 15.3018i | 0.360066 | − | 0.623653i | ||||
\(603\) | 4.08720 | + | 39.0202i | 0.166444 | + | 1.58902i | ||||
\(604\) | −13.9036 | − | 8.02727i | −0.565731 | − | 0.326625i | ||||
\(605\) | −4.54456 | + | 2.62380i | −0.184763 | + | 0.106673i | ||||
\(606\) | −3.59748 | + | 7.05736i | −0.146138 | + | 0.286686i | ||||
\(607\) | − | 48.4715i | − | 1.96740i | −0.179821 | − | 0.983699i | \(-0.557552\pi\) | ||
0.179821 | − | 0.983699i | \(-0.442448\pi\) | |||||||
\(608\) | −3.17779 | − | 2.98356i | −0.128876 | − | 0.120999i | ||||
\(609\) | −2.13458 | + | 1.38567i | −0.0864974 | + | 0.0561503i | ||||
\(610\) | −2.16845 | + | 1.25195i | −0.0877979 | + | 0.0506901i | ||||
\(611\) | −0.537262 | − | 0.930565i | −0.0217353 | − | 0.0376466i | ||||
\(612\) | 6.72814 | − | 4.88464i | 0.271969 | − | 0.197450i | ||||
\(613\) | 17.8645 | + | 30.9422i | 0.721539 | + | 1.24974i | 0.960383 | + | 0.278685i | \(0.0898985\pi\) |
−0.238843 | + | 0.971058i | \(0.576768\pi\) | |||||||
\(614\) | −21.4512 | − | 12.3849i | −0.865702 | − | 0.499813i | ||||
\(615\) | −1.97338 | − | 3.03992i | −0.0795745 | − | 0.122582i | ||||
\(616\) | − | 5.61632i | − | 0.226288i | ||||||
\(617\) | 28.5725 | + | 16.4963i | 1.15028 | + | 0.664117i | 0.948957 | − | 0.315407i | \(-0.102141\pi\) |
0.201328 | + | 0.979524i | \(0.435474\pi\) | |||||||
\(618\) | −3.97679 | + | 0.207708i | −0.159970 | + | 0.00835524i | ||||
\(619\) | −33.4945 | −1.34626 | −0.673129 | − | 0.739525i | \(-0.735050\pi\) | ||||
−0.673129 | + | 0.739525i | \(0.735050\pi\) | |||||||
\(620\) | −2.05113 | −0.0823753 | ||||||||
\(621\) | −3.87659 | + | 10.0828i | −0.155562 | + | 0.404611i | ||||
\(622\) | −9.74385 | + | 5.62562i | −0.390693 | + | 0.225567i | ||||
\(623\) | −11.6466 | + | 20.1725i | −0.466612 | + | 0.808196i | ||||
\(624\) | −0.376559 | + | 0.738715i | −0.0150744 | + | 0.0295723i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 10.9329 | 0.436966 | ||||||||
\(627\) | 13.8296 | + | 11.6888i | 0.552301 | + | 0.466807i | ||||
\(628\) | 1.67251 | 0.0667404 | ||||||||
\(629\) | −7.86501 | − | 13.6226i | −0.313598 | − | 0.543169i | ||||
\(630\) | −0.731839 | − | 6.98681i | −0.0291572 | − | 0.278361i | ||||
\(631\) | −11.0092 | + | 19.0686i | −0.438271 | + | 0.759108i | −0.997556 | − | 0.0698675i | \(-0.977742\pi\) |
0.559285 | + | 0.828975i | \(0.311076\pi\) | |||||||
\(632\) | −10.1589 | + | 5.86527i | −0.404101 | + | 0.233308i | ||||
\(633\) | −45.8807 | + | 2.39635i | −1.82359 | + | 0.0952465i | ||||
\(634\) | 17.9005 | 0.710921 | ||||||||
\(635\) | −11.0708 | −0.439333 | ||||||||
\(636\) | 1.19995 | + | 22.9743i | 0.0475810 | + | 0.910989i | ||||
\(637\) | 0.628724 | + | 0.362994i | 0.0249110 | + | 0.0143823i | ||||
\(638\) | − | 1.50490i | − | 0.0595794i | ||||||
\(639\) | 6.55493 | − | 14.7086i | 0.259309 | − | 0.581862i | ||||
\(640\) | −0.866025 | − | 0.500000i | −0.0342327 | − | 0.0197642i | ||||
\(641\) | 7.33431 | + | 12.7034i | 0.289688 | + | 0.501754i | 0.973735 | − | 0.227684i | \(-0.0731152\pi\) |
−0.684047 | + | 0.729438i | \(0.739782\pi\) | |||||||
\(642\) | −1.10073 | − | 21.0747i | −0.0434425 | − | 0.831752i | ||||
\(643\) | −15.3180 | − | 26.5315i | −0.604082 | − | 1.04630i | −0.992196 | − | 0.124690i | \(-0.960207\pi\) |
0.388114 | − | 0.921612i | \(-0.373127\pi\) | |||||||
\(644\) | −4.21595 | + | 2.43408i | −0.166132 | + | 0.0959163i | ||||
\(645\) | 7.11597 | + | 10.9619i | 0.280191 | + | 0.431624i | ||||
\(646\) | −8.26874 | + | 8.80703i | −0.325329 | + | 0.346508i | ||||
\(647\) | 9.82606i | 0.386302i | 0.981169 | + | 0.193151i | \(0.0618707\pi\) | ||||
−0.981169 | + | 0.193151i | \(0.938129\pi\) | |||||||
\(648\) | 2.78722 | − | 8.55753i | 0.109492 | − | 0.336172i | ||||
\(649\) | 13.0345 | − | 7.52549i | 0.511650 | − | 0.295401i | ||||
\(650\) | −0.414577 | − | 0.239356i | −0.0162611 | − | 0.00938832i | ||||
\(651\) | 3.77815 | − | 7.41178i | 0.148077 | − | 0.290491i | ||||
\(652\) | −6.21359 | + | 10.7622i | −0.243343 | + | 0.421482i | ||||
\(653\) | − | 31.4026i | − | 1.22888i | −0.788964 | − | 0.614440i | \(-0.789382\pi\) | ||
0.788964 | − | 0.614440i | \(-0.210618\pi\) | |||||||
\(654\) | −0.679991 | − | 1.04750i | −0.0265898 | − | 0.0409605i | ||||
\(655\) | 7.72594 | − | 13.3817i | 0.301877 | − | 0.522867i | ||||
\(656\) | 1.04624 | − | 1.81214i | 0.0408487 | − | 0.0707521i | ||||
\(657\) | 14.1912 | − | 31.8436i | 0.553652 | − | 1.24234i | ||||
\(658\) | 5.25616i | 0.204906i | ||||||||
\(659\) | 1.68244 | − | 2.91407i | 0.0655385 | − | 0.113516i | −0.831394 | − | 0.555683i | \(-0.812457\pi\) |
0.896933 | + | 0.442167i | \(0.145790\pi\) | |||||||
\(660\) | 3.70106 | + | 1.88661i | 0.144064 | + | 0.0734363i | ||||
\(661\) | −6.16334 | − | 3.55840i | −0.239726 | − | 0.138406i | 0.375325 | − | 0.926893i | \(-0.377531\pi\) |
−0.615051 | + | 0.788487i | \(0.710865\pi\) | |||||||
\(662\) | 8.97416 | − | 5.18123i | 0.348790 | − | 0.201374i | ||||
\(663\) | 2.04730 | + | 1.04361i | 0.0795105 | + | 0.0405304i | ||||
\(664\) | 11.3081i | 0.438841i | ||||||||
\(665\) | 2.95113 | + | 9.77121i | 0.114440 | + | 0.378911i | ||||
\(666\) | −15.5528 | − | 6.93115i | −0.602658 | − | 0.268577i | ||||
\(667\) | −1.12967 | + | 0.652215i | −0.0437410 | + | 0.0252539i | ||||
\(668\) | 0.136815 | + | 0.236971i | 0.00529355 | + | 0.00916869i | ||||
\(669\) | −26.3864 | + | 1.37816i | −1.02016 | + | 0.0532828i | ||||
\(670\) | −6.53894 | − | 11.3258i | −0.252621 | − | 0.437553i | ||||
\(671\) | 5.20084 | + | 3.00270i | 0.200776 | + | 0.115918i | ||||
\(672\) | 3.40196 | − | 2.20840i | 0.131233 | − | 0.0851909i | ||||
\(673\) | 26.5117i | 1.02195i | 0.859596 | + | 0.510975i | \(0.170716\pi\) | ||||
−0.859596 | + | 0.510975i | \(0.829284\pi\) | |||||||
\(674\) | −23.7499 | − | 13.7120i | −0.914810 | − | 0.528166i | ||||
\(675\) | 4.85004 | + | 1.86471i | 0.186678 | + | 0.0717729i | ||||
\(676\) | 12.7708 | 0.491186 | ||||||||
\(677\) | 42.3166 | 1.62636 | 0.813179 | − | 0.582013i | \(-0.197735\pi\) | ||||
0.813179 | + | 0.582013i | \(0.197735\pi\) | |||||||
\(678\) | 0.902972 | + | 17.2884i | 0.0346784 | + | 0.663956i | ||||
\(679\) | 17.5441 | − | 10.1291i | 0.673279 | − | 0.388718i | ||||
\(680\) | −1.38572 | + | 2.40013i | −0.0531398 | + | 0.0920408i | ||||
\(681\) | 2.68672 | + | 1.36955i | 0.102955 | + | 0.0524813i | ||||
\(682\) | 2.45973 | + | 4.26038i | 0.0941879 | + | 0.163138i | ||||
\(683\) | −11.0677 | −0.423493 | −0.211746 | − | 0.977325i | \(-0.567915\pi\) | ||||
−0.211746 | + | 0.977325i | \(0.567915\pi\) | |||||||
\(684\) | −1.64229 | + | 12.9732i | −0.0627944 | + | 0.496041i | ||||
\(685\) | 8.75118 | 0.334365 | ||||||||
\(686\) | −9.97150 | − | 17.2711i | −0.380714 | − | 0.659415i | ||||
\(687\) | −25.6860 | − | 13.0934i | −0.979981 | − | 0.499544i | ||||
\(688\) | −3.77271 | + | 6.53452i | −0.143833 | + | 0.249126i | ||||
\(689\) | −5.50653 | + | 3.17920i | −0.209782 | + | 0.121118i | ||||
\(690\) | −0.187814 | − | 3.59590i | −0.00714995 | − | 0.136893i | ||||
\(691\) | 20.2406 | 0.769990 | 0.384995 | − | 0.922919i | \(-0.374203\pi\) | ||||
0.384995 | + | 0.922919i | \(0.374203\pi\) | |||||||
\(692\) | 24.3892 | 0.927137 | ||||||||
\(693\) | −13.6346 | + | 9.89873i | −0.517935 | + | 0.376022i | ||||
\(694\) | 22.5112 | + | 12.9969i | 0.854515 | + | 0.493354i | ||||
\(695\) | 7.49842i | 0.284431i | ||||||||
\(696\) | 0.911558 | − | 0.591743i | 0.0345525 | − | 0.0224300i | ||||
\(697\) | −5.02222 | − | 2.89958i | −0.190230 | − | 0.109829i | ||||
\(698\) | 4.08348 | + | 7.07280i | 0.154562 | + | 0.267710i | ||||
\(699\) | 15.0051 | − | 0.783718i | 0.567545 | − | 0.0296429i | ||||
\(700\) | 1.17084 | + | 2.02795i | 0.0442536 | + | 0.0766494i | ||||
\(701\) | 12.8127 | − | 7.39742i | 0.483929 | − | 0.279397i | −0.238123 | − | 0.971235i | \(-0.576532\pi\) |
0.722053 | + | 0.691838i | \(0.243199\pi\) | |||||||
\(702\) | 2.45704 | − | 0.387819i | 0.0927352 | − | 0.0146373i | ||||
\(703\) | 24.0870 | + | 5.64709i | 0.908459 | + | 0.212984i | ||||
\(704\) | 2.39841i | 0.0903936i | ||||||||
\(705\) | −3.46373 | − | 1.76563i | −0.130452 | − | 0.0664975i | ||||
\(706\) | 20.0065 | − | 11.5507i | 0.752953 | − | 0.434718i | ||||
\(707\) | 9.27466 | + | 5.35473i | 0.348810 | + | 0.201385i | ||||
\(708\) | 9.68374 | + | 4.93627i | 0.363937 | + | 0.185516i | ||||
\(709\) | −0.506440 | + | 0.877179i | −0.0190197 | + | 0.0329432i | −0.875379 | − | 0.483438i | \(-0.839388\pi\) |
0.856359 | + | 0.516381i | \(0.172721\pi\) | |||||||
\(710\) | 5.36769i | 0.201446i | ||||||||
\(711\) | 32.1440 | + | 14.3251i | 1.20550 | + | 0.537234i | ||||
\(712\) | 4.97362 | − | 8.61457i | 0.186394 | − | 0.322845i | ||||
\(713\) | 2.13207 | − | 3.69285i | 0.0798466 | − | 0.138298i | ||||
\(714\) | −6.12044 | − | 9.42830i | −0.229052 | − | 0.352845i | ||||
\(715\) | 1.14815i | 0.0429384i | ||||||||
\(716\) | 10.0385 | − | 17.3871i | 0.375155 | − | 0.649787i | ||||
\(717\) | −15.0622 | + | 29.5484i | −0.562510 | + | 1.10350i | ||||
\(718\) | −17.3948 | − | 10.0429i | −0.649168 | − | 0.374798i | ||||
\(719\) | −2.95761 | + | 1.70758i | −0.110300 | + | 0.0636819i | −0.554135 | − | 0.832427i | \(-0.686951\pi\) |
0.443835 | + | 0.896109i | \(0.353618\pi\) | |||||||
\(720\) | 0.312528 | + | 2.98368i | 0.0116472 | + | 0.111195i | ||||
\(721\) | 5.38382i | 0.200504i | ||||||||
\(722\) | −1.19670 | − | 18.9623i | −0.0445364 | − | 0.705703i | ||||
\(723\) | −18.1187 | − | 27.9111i | −0.673840 | − | 1.03803i | ||||
\(724\) | −10.2054 | + | 5.89207i | −0.379279 | + | 0.218977i | ||||
\(725\) | 0.313727 | + | 0.543392i | 0.0116515 | + | 0.0201811i | ||||
\(726\) | 0.474079 | + | 9.07675i | 0.0175947 | + | 0.336870i | ||||
\(727\) | −20.0624 | − | 34.7491i | −0.744074 | − | 1.28877i | −0.950626 | − | 0.310338i | \(-0.899558\pi\) |
0.206552 | − | 0.978436i | \(-0.433776\pi\) | |||||||
\(728\) | 0.970806 | + | 0.560495i | 0.0359805 | + | 0.0207733i | ||||
\(729\) | −25.6874 | + | 8.31615i | −0.951385 | + | 0.308005i | ||||
\(730\) | 11.6209i | 0.430109i | ||||||||
\(731\) | 18.1100 | + | 10.4558i | 0.669822 | + | 0.386722i | ||||
\(732\) | 0.226208 | + | 4.33099i | 0.00836089 | + | 0.160078i | ||||
\(733\) | 42.4761 | 1.56889 | 0.784446 | − | 0.620197i | \(-0.212947\pi\) | ||||
0.784446 | + | 0.620197i | \(0.212947\pi\) | |||||||
\(734\) | 9.66168 | 0.356619 | ||||||||
\(735\) | 2.62315 | − | 0.137007i | 0.0967565 | − | 0.00505360i | ||||
\(736\) | 1.80040 | − | 1.03946i | 0.0663636 | − | 0.0383150i | ||||
\(737\) | −15.6831 | + | 27.1639i | −0.577694 | + | 1.00060i | ||||
\(738\) | −6.24327 | + | 0.653957i | −0.229818 | + | 0.0240725i | ||||
\(739\) | −25.6660 | − | 44.4548i | −0.944139 | − | 1.63530i | −0.757466 | − | 0.652874i | \(-0.773563\pi\) |
−0.186673 | − | 0.982422i | \(-0.559770\pi\) | |||||||
\(740\) | 5.67577 | 0.208646 | ||||||||
\(741\) | −3.40063 | + | 1.22399i | −0.124925 | + | 0.0449645i | ||||
\(742\) | 31.1028 | 1.14182 | ||||||||
\(743\) | 14.7044 | + | 25.4688i | 0.539454 | + | 0.934361i | 0.998933 | + | 0.0461730i | \(0.0147025\pi\) |
−0.459480 | + | 0.888188i | \(0.651964\pi\) | |||||||
\(744\) | −1.61344 | + | 3.16516i | −0.0591514 | + | 0.116040i | ||||
\(745\) | −6.11734 | + | 10.5955i | −0.224122 | + | 0.388190i | ||||
\(746\) | 14.5767 | − | 8.41587i | 0.533692 | − | 0.308127i | ||||
\(747\) | 27.4525 | − | 19.9306i | 1.00443 | − | 0.729221i | ||||
\(748\) | 6.64704 | 0.243040 | ||||||||
\(749\) | −28.5312 | −1.04251 | ||||||||
\(750\) | −1.72969 | + | 0.0903420i | −0.0631595 | + | 0.00329882i | ||||
\(751\) | 9.26493 | + | 5.34911i | 0.338082 | + | 0.195192i | 0.659424 | − | 0.751772i | \(-0.270800\pi\) |
−0.321342 | + | 0.946963i | \(0.604134\pi\) | |||||||
\(752\) | − | 2.24461i | − | 0.0818526i | ||||||
\(753\) | −11.7935 | − | 18.1675i | −0.429779 | − | 0.662059i | ||||
\(754\) | 0.260128 | + | 0.150185i | 0.00947332 | + | 0.00546942i | ||||
\(755\) | −8.02727 | − | 13.9036i | −0.292142 | − | 0.506005i | ||||
\(756\) | −11.3572 | − | 4.36656i | −0.413058 | − | 0.158810i | ||||
\(757\) | −8.59944 | − | 14.8947i | −0.312552 | − | 0.541356i | 0.666362 | − | 0.745628i | \(-0.267851\pi\) |
−0.978914 | + | 0.204272i | \(0.934517\pi\) | |||||||
\(758\) | −27.3759 | + | 15.8055i | −0.994337 | + | 0.574081i | ||||
\(759\) | −7.24376 | + | 4.70233i | −0.262932 | + | 0.170684i | ||||
\(760\) | −1.26026 | − | 4.17274i | −0.0457146 | − | 0.151361i | ||||
\(761\) | − | 35.2476i | − | 1.27772i | −0.769321 | − | 0.638862i | \(-0.779405\pi\) | ||
0.769321 | − | 0.638862i | \(-0.220595\pi\) | |||||||
\(762\) | −8.70841 | + | 17.0837i | −0.315472 | + | 0.618878i | ||||
\(763\) | −1.46221 | + | 0.844208i | −0.0529356 | + | 0.0305624i | ||||
\(764\) | −6.38163 | − | 3.68444i | −0.230879 | − | 0.133298i | ||||
\(765\) | 8.26906 | − | 0.866149i | 0.298968 | − | 0.0313157i | ||||
\(766\) | −14.8637 | + | 25.7447i | −0.537048 | + | 0.930194i | ||||
\(767\) | 3.00411i | 0.108472i | ||||||||
\(768\) | −1.45279 | + | 0.943085i | −0.0524229 | + | 0.0340306i | ||||
\(769\) | −16.3809 | + | 28.3725i | −0.590710 | + | 1.02314i | 0.403427 | + | 0.915012i | \(0.367819\pi\) |
−0.994137 | + | 0.108128i | \(0.965514\pi\) | |||||||
\(770\) | 2.80816 | − | 4.86387i | 0.101199 | − | 0.175282i | ||||
\(771\) | −2.13197 | + | 1.38398i | −0.0767811 | + | 0.0498429i | ||||
\(772\) | − | 7.47201i | − | 0.268924i | ||||||
\(773\) | −9.83728 | + | 17.0387i | −0.353822 | + | 0.612838i | −0.986916 | − | 0.161237i | \(-0.948452\pi\) |
0.633093 | + | 0.774075i | \(0.281785\pi\) | |||||||
\(774\) | 22.5131 | − | 2.35815i | 0.809216 | − | 0.0847620i | ||||
\(775\) | −1.77633 | − | 1.02556i | −0.0638077 | − | 0.0368394i | ||||
\(776\) | −7.49209 | + | 4.32556i | −0.268950 | + | 0.155278i | ||||
\(777\) | −10.4547 | + | 20.5095i | −0.375059 | + | 0.735773i | ||||
\(778\) | 6.99868i | 0.250915i | ||||||||
\(779\) | 8.73135 | − | 2.63707i | 0.312833 | − | 0.0944830i | ||||
\(780\) | −0.695467 | + | 0.451467i | −0.0249017 | + | 0.0161651i | ||||
\(781\) | 11.1492 | − | 6.43698i | 0.398949 | − | 0.230333i | ||||
\(782\) | −2.88079 | − | 4.98968i | −0.103017 | − | 0.178431i | ||||
\(783\) | −3.04318 | − | 1.17002i | −0.108754 | − | 0.0418132i | ||||
\(784\) | 0.758271 | + | 1.31336i | 0.0270811 | + | 0.0469059i | ||||
\(785\) | 1.44843 | + | 0.836254i | 0.0516969 | + | 0.0298472i | ||||
\(786\) | −14.5724 | − | 22.4483i | −0.519781 | − | 0.800704i | ||||
\(787\) | − | 42.0288i | − | 1.49816i | −0.662478 | − | 0.749082i | \(-0.730495\pi\) | ||
0.662478 | − | 0.749082i | \(-0.269505\pi\) | |||||||
\(788\) | 17.5258 | + | 10.1185i | 0.624329 | + | 0.360457i | ||||
\(789\) | −24.3698 | + | 1.27283i | −0.867586 | + | 0.0453141i | ||||
\(790\) | −11.7305 | −0.417354 | ||||||||
\(791\) | 23.4052 | 0.832193 | ||||||||
\(792\) | 5.82257 | − | 4.22719i | 0.206896 | − | 0.150207i | ||||
\(793\) | −1.03806 | + | 0.599326i | −0.0368627 | + | 0.0212827i | ||||
\(794\) | −14.8564 | + | 25.7320i | −0.527234 | + | 0.913196i | ||||
\(795\) | −10.4479 | + | 20.4963i | −0.370551 | + | 0.726928i | ||||
\(796\) | −5.62306 | − | 9.73942i | −0.199304 | − | 0.345205i | ||||
\(797\) | 31.9447 | 1.13154 | 0.565769 | − | 0.824564i | \(-0.308579\pi\) | ||||
0.565769 | + | 0.824564i | \(0.308579\pi\) | |||||||
\(798\) | 17.3996 | + | 3.13213i | 0.615940 | + | 0.110876i | ||||
\(799\) | −6.22079 | −0.220076 | ||||||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | −29.6794 | + | 3.10879i | −1.04867 | + | 0.109844i | ||||
\(802\) | 14.8000 | − | 25.6344i | 0.522608 | − | 0.905183i | ||||
\(803\) | 24.1376 | − | 13.9359i | 0.851798 | − | 0.491786i | ||||
\(804\) | −22.6207 | + | 1.18148i | −0.797772 | + | 0.0416677i | ||||
\(805\) | −4.86817 | −0.171580 | ||||||||
\(806\) | −0.981901 | −0.0345860 | ||||||||
\(807\) | 1.71392 | + | 32.8149i | 0.0603329 | + | 1.15514i | ||||
\(808\) | −3.96069 | − | 2.28671i | −0.139337 | − | 0.0804460i | ||||
\(809\) | 45.3248i | 1.59354i | 0.604285 | + | 0.796768i | \(0.293459\pi\) | ||||
−0.604285 | + | 0.796768i | \(0.706541\pi\) | |||||||
\(810\) | 6.69257 | − | 6.01743i | 0.235153 | − | 0.211431i | ||||
\(811\) | −22.3241 | − | 12.8888i | −0.783907 | − | 0.452589i | 0.0539064 | − | 0.998546i | \(-0.482833\pi\) |
−0.837813 | + | 0.545957i | \(0.816166\pi\) | |||||||
\(812\) | −0.734649 | − | 1.27245i | −0.0257811 | − | 0.0446542i | ||||
\(813\) | 2.29311 | + | 43.9040i | 0.0804229 | + | 1.53978i | ||||
\(814\) | −6.80643 | − | 11.7891i | −0.238565 | − | 0.413207i | ||||
\(815\) | −10.7622 | + | 6.21359i | −0.376985 | + | 0.217652i | ||||
\(816\) | 2.61370 | + | 4.02630i | 0.0914977 | + | 0.140949i | ||||
\(817\) | −31.4850 | + | 9.50923i | −1.10152 | + | 0.332686i | ||||
\(818\) | − | 1.21555i | − | 0.0425008i | ||||||
\(819\) | −0.350341 | − | 3.34467i | −0.0122419 | − | 0.116872i | ||||
\(820\) | 1.81214 | − | 1.04624i | 0.0632826 | − | 0.0365362i | ||||
\(821\) | −1.49955 | − | 0.865764i | −0.0523345 | − | 0.0302154i | 0.473604 | − | 0.880738i | \(-0.342953\pi\) |
−0.525939 | + | 0.850522i | \(0.676286\pi\) | |||||||
\(822\) | 6.88375 | − | 13.5042i | 0.240098 | − | 0.471013i | ||||
\(823\) | −14.3880 | + | 24.9207i | −0.501534 | + | 0.868682i | 0.498465 | + | 0.866910i | \(0.333897\pi\) |
−0.999998 | + | 0.00177204i | \(0.999436\pi\) | |||||||
\(824\) | − | 2.29913i | − | 0.0800940i | ||||||
\(825\) | 2.26191 | + | 3.48439i | 0.0787496 | + | 0.121311i | ||||
\(826\) | 7.34747 | − | 12.7262i | 0.255651 | − | 0.442801i | ||||
\(827\) | −15.2033 | + | 26.3329i | −0.528671 | + | 0.915684i | 0.470770 | + | 0.882256i | \(0.343976\pi\) |
−0.999441 | + | 0.0334287i | \(0.989357\pi\) | |||||||
\(828\) | −5.69667 | − | 2.53874i | −0.197973 | − | 0.0882273i | ||||
\(829\) | 6.37093i | 0.221272i | 0.993861 | + | 0.110636i | \(0.0352887\pi\) | ||||
−0.993861 | + | 0.110636i | \(0.964711\pi\) | |||||||
\(830\) | −5.65407 | + | 9.79314i | −0.196256 | + | 0.339925i | ||||
\(831\) | 12.5126 | + | 6.37828i | 0.434057 | + | 0.221260i | ||||
\(832\) | −0.414577 | − | 0.239356i | −0.0143729 | − | 0.00829818i | ||||
\(833\) | 3.63990 | − | 2.10150i | 0.126115 | − | 0.0728126i | ||||
\(834\) | 11.5710 | + | 5.89832i | 0.400672 | + | 0.204242i | ||||
\(835\) | 0.273631i | 0.00946938i | ||||||||
\(836\) | −7.15582 | + | 7.62166i | −0.247489 | + | 0.263601i | ||||
\(837\) | 10.5276 | − | 1.66168i | 0.363889 | − | 0.0574360i | ||||
\(838\) | 2.82675 | − | 1.63203i | 0.0976485 | − | 0.0563774i | ||||
\(839\) | 8.20502 | + | 14.2115i | 0.283269 | + | 0.490636i | 0.972188 | − | 0.234202i | \(-0.0752478\pi\) |
−0.688919 | + | 0.724838i | \(0.741914\pi\) | |||||||
\(840\) | 4.05038 | − | 0.211552i | 0.139752 | − | 0.00729923i | ||||
\(841\) | 14.3032 | + | 24.7738i | 0.493212 | + | 0.854268i | ||||
\(842\) | −18.4508 | − | 10.6526i | −0.635856 | − | 0.367112i | ||||
\(843\) | −36.7459 | + | 23.8538i | −1.26560 | + | 0.821568i | ||||
\(844\) | − | 26.5254i | − | 0.913040i | ||||||
\(845\) | 11.0599 | + | 6.38542i | 0.380471 | + | 0.219665i | ||||
\(846\) | −5.44919 | + | 3.95612i | −0.187347 | + | 0.136014i | ||||
\(847\) | 12.2882 | 0.422228 | ||||||||
\(848\) | −13.2823 | −0.456115 | ||||||||
\(849\) | 0.0896527 | + | 1.71650i | 0.00307687 | + | 0.0589100i | ||||
\(850\) | −2.40013 | + | 1.38572i | −0.0823238 | + | 0.0475297i | ||||
\(851\) | −5.89974 | + | 10.2187i | −0.202241 | + | 0.350291i | ||||
\(852\) | 8.28304 | + | 4.22227i | 0.283772 | + | 0.144653i | ||||
\(853\) | −18.9054 | − | 32.7451i | −0.647308 | − | 1.12117i | −0.983763 | − | 0.179470i | \(-0.942562\pi\) |
0.336456 | − | 0.941699i | \(-0.390772\pi\) | |||||||
\(854\) | 5.86335 | 0.200640 | ||||||||
\(855\) | −7.90884 | + | 10.4139i | −0.270477 | + | 0.356149i | ||||
\(856\) | 12.1841 | 0.416443 | ||||||||
\(857\) | −0.203026 | − | 0.351652i | −0.00693525 | − | 0.0120122i | 0.862537 | − | 0.505994i | \(-0.168874\pi\) |
−0.869472 | + | 0.493982i | \(0.835541\pi\) | |||||||
\(858\) | 1.77175 | + | 0.903145i | 0.0604864 | + | 0.0308329i | ||||
\(859\) | 2.87993 | − | 4.98819i | 0.0982621 | − | 0.170195i | −0.812703 | − | 0.582678i | \(-0.802005\pi\) |
0.910965 | + | 0.412483i | \(0.135338\pi\) | |||||||
\(860\) | −6.53452 | + | 3.77271i | −0.222825 | + | 0.128648i | ||||
\(861\) | 0.442667 | + | 8.47534i | 0.0150861 | + | 0.288839i | ||||
\(862\) | −4.28560 | −0.145968 | ||||||||
\(863\) | 26.1179 | 0.889065 | 0.444532 | − | 0.895763i | \(-0.353370\pi\) | ||||
0.444532 | + | 0.895763i | \(0.353370\pi\) | |||||||
\(864\) | 4.85004 | + | 1.86471i | 0.165002 | + | 0.0634388i | ||||
\(865\) | 21.1216 | + | 12.1946i | 0.718157 | + | 0.414628i | ||||
\(866\) | 20.8270i | 0.707731i | ||||||||
\(867\) | −13.5388 | + | 8.78876i | −0.459800 | + | 0.298482i | ||||
\(868\) | 4.15959 | + | 2.40154i | 0.141186 | + | 0.0815137i | ||||
\(869\) | 14.0673 | + | 24.3653i | 0.477202 | + | 0.826538i | ||||
\(870\) | 1.08530 | − | 0.0566855i | 0.0367953 | − | 0.00192182i | ||||
\(871\) | −3.13027 | − | 5.42179i | −0.106065 | − | 0.183710i | ||||
\(872\) | 0.624429 | − | 0.360514i | 0.0211458 | − | 0.0122086i | ||||
\(873\) | 23.7058 | + | 10.5646i | 0.802320 | + | 0.357557i | ||||
\(874\) | 8.82259 | + | 2.06842i | 0.298428 | + | 0.0699652i | ||||
\(875\) | 2.34168i | 0.0791632i | ||||||||
\(876\) | 17.9325 | + | 9.14109i | 0.605885 | + | 0.308849i | ||||
\(877\) | 7.26280 | − | 4.19318i | 0.245247 | − | 0.141594i | −0.372339 | − | 0.928097i | \(-0.621444\pi\) |
0.617586 | + | 0.786503i | \(0.288111\pi\) | |||||||
\(878\) | 14.9323 | + | 8.62117i | 0.503941 | + | 0.290950i | ||||
\(879\) | −36.0086 | − | 18.3554i | −1.21454 | − | 0.619111i | ||||
\(880\) | −1.19921 | + | 2.07709i | −0.0404253 | + | 0.0700186i | ||||
\(881\) | 41.7995i | 1.40826i | 0.710071 | + | 0.704130i | \(0.248663\pi\) | ||||
−0.710071 | + | 0.704130i | \(0.751337\pi\) | |||||||
\(882\) | 1.85197 | − | 4.15564i | 0.0623592 | − | 0.139928i | ||||
\(883\) | 1.58994 | − | 2.75386i | 0.0535057 | − | 0.0926746i | −0.838032 | − | 0.545621i | \(-0.816294\pi\) |
0.891538 | + | 0.452946i | \(0.149627\pi\) | |||||||
\(884\) | −0.663360 | + | 1.14897i | −0.0223112 | + | 0.0386441i | ||||
\(885\) | 5.91823 | + | 9.11681i | 0.198939 | + | 0.306458i | ||||
\(886\) | 22.7142i | 0.763099i | ||||||||
\(887\) | −24.1827 | + | 41.8857i | −0.811976 | + | 1.40638i | 0.0995032 | + | 0.995037i | \(0.468275\pi\) |
−0.911479 | + | 0.411346i | \(0.865059\pi\) | |||||||
\(888\) | 4.46461 | − | 8.75845i | 0.149822 | − | 0.293914i | ||||
\(889\) | 22.4511 | + | 12.9622i | 0.752987 | + | 0.434737i | ||||
\(890\) | 8.61457 | − | 4.97362i | 0.288761 | − | 0.166716i | ||||
\(891\) | −20.5245 | − | 6.68491i | −0.687597 | − | 0.223953i | ||||
\(892\) | − | 15.2549i | − | 0.510773i | ||||||
\(893\) | 6.69694 | − | 7.13291i | 0.224105 | − | 0.238694i | ||||
\(894\) | 11.5383 | + | 17.7744i | 0.385900 | + | 0.594464i | ||||
\(895\) | 17.3871 | − | 10.0385i | 0.581187 | − | 0.335548i | ||||
\(896\) | 1.17084 | + | 2.02795i | 0.0391150 | + | 0.0677491i | ||||
\(897\) | −0.0899088 | − | 1.72140i | −0.00300197 | − | 0.0574759i | ||||
\(898\) | 12.2004 | + | 21.1316i | 0.407131 | + | 0.705172i | ||||
\(899\) | 1.11457 | + | 0.643496i | 0.0371729 | + | 0.0214618i | ||||
\(900\) | −1.22118 | + | 2.74020i | −0.0407060 | + | 0.0913401i | ||||
\(901\) | 36.8109i | 1.22635i | ||||||||
\(902\) | −4.34626 | − | 2.50931i | −0.144715 | − | 0.0835510i | ||||
\(903\) | −1.59625 | − | 30.5618i | −0.0531198 | − | 1.01703i | ||||
\(904\) | −9.99505 | −0.332430 | ||||||||
\(905\) | −11.7841 | −0.391718 | ||||||||
\(906\) | −27.7694 | + | 1.45040i | −0.922577 | + | 0.0481862i | ||||
\(907\) | −38.0067 | + | 21.9432i | −1.26199 | + | 0.728612i | −0.973460 | − | 0.228858i | \(-0.926501\pi\) |
−0.288533 | + | 0.957470i | \(0.593167\pi\) | |||||||
\(908\) | −0.870543 | + | 1.50782i | −0.0288900 | + | 0.0500389i | ||||
\(909\) | 1.42932 | + | 13.6456i | 0.0474075 | + | 0.452595i | ||||
\(910\) | 0.560495 | + | 0.970806i | 0.0185802 | + | 0.0321819i | ||||
\(911\) | 59.7244 | 1.97876 | 0.989378 | − | 0.145363i | \(-0.0464350\pi\) | ||||
0.989378 | + | 0.145363i | \(0.0464350\pi\) | |||||||
\(912\) | −7.43041 | − | 1.33756i | −0.246045 | − | 0.0442909i | ||||
\(913\) | 27.1216 | 0.897595 | ||||||||
\(914\) | 2.78960 | + | 4.83173i | 0.0922719 | + | 0.159820i | ||||
\(915\) | −1.96959 | + | 3.86385i | −0.0651128 | + | 0.127735i | ||||
\(916\) | 8.32269 | − | 14.4153i | 0.274989 | − | 0.476296i | ||||
\(917\) | −31.3357 | + | 18.0917i | −1.03480 | + | 0.597439i | ||||
\(918\) | 5.16793 | − | 13.4415i | 0.170567 | − | 0.443637i | ||||
\(919\) | 47.4923 | 1.56663 | 0.783313 | − | 0.621628i | \(-0.213528\pi\) | ||||
0.783313 | + | 0.621628i | \(0.213528\pi\) | |||||||
\(920\) | 2.07892 | 0.0685400 | ||||||||
\(921\) | −42.8441 | + | 2.23775i | −1.41176 | + | 0.0737363i | ||||
\(922\) | 13.2971 | + | 7.67711i | 0.437918 | + | 0.252832i | ||||
\(923\) | 2.56958i | 0.0845788i | ||||||||
\(924\) | −5.29666 | − | 8.15931i | −0.174247 | − | 0.268422i | ||||
\(925\) | 4.91536 | + | 2.83789i | 0.161616 | + | 0.0933091i | ||||
\(926\) | 14.5464 | + | 25.1950i | 0.478023 | + | 0.827960i | ||||
\(927\) | −5.58154 | + | 4.05220i | −0.183322 | + | 0.133092i | ||||
\(928\) | 0.313727 | + | 0.543392i | 0.0102986 | + | 0.0178377i | ||||
\(929\) | 10.2174 | − | 5.89900i | 0.335221 | − | 0.193540i | −0.322936 | − | 0.946421i | \(-0.604670\pi\) |
0.658157 | + | 0.752881i | \(0.271336\pi\) | |||||||
\(930\) | −2.97985 | + | 1.93439i | −0.0977133 | + | 0.0634311i | ||||
\(931\) | −1.50888 | + | 6.43595i | −0.0494515 | + | 0.210930i | ||||
\(932\) | 8.67501i | 0.284160i | ||||||||
\(933\) | −8.85031 | + | 17.3621i | −0.289746 | + | 0.568410i | ||||
\(934\) | 26.5965 | − | 15.3555i | 0.870263 | − | 0.502446i | ||||
\(935\) | 5.75651 | + | 3.32352i | 0.188258 | + | 0.108691i | ||||
\(936\) | 0.149611 | + | 1.42832i | 0.00489019 | + | 0.0466862i | ||||
\(937\) | −24.8952 | + | 43.1198i | −0.813292 | + | 1.40866i | 0.0972554 | + | 0.995259i | \(0.468994\pi\) |
−0.910548 | + | 0.413404i | \(0.864340\pi\) | |||||||
\(938\) | 30.6242i | 0.999916i | ||||||||
\(939\) | 15.8832 | − | 10.3106i | 0.518327 | − | 0.336475i | ||||
\(940\) | 1.12231 | − | 1.94389i | 0.0366056 | − | 0.0634027i | ||||
\(941\) | 11.3241 | − | 19.6139i | 0.369155 | − | 0.639396i | −0.620278 | − | 0.784382i | \(-0.712980\pi\) |
0.989434 | + | 0.144986i | \(0.0463136\pi\) | |||||||
\(942\) | 2.42980 | − | 1.57732i | 0.0791671 | − | 0.0513918i | ||||
\(943\) | 4.35009i | 0.141659i | ||||||||
\(944\) | −3.13769 | + | 5.43465i | −0.102123 | + | 0.176883i | ||||
\(945\) | −7.65236 | − | 9.46016i | −0.248931 | − | 0.307739i | ||||
\(946\) | 15.6725 | + | 9.04852i | 0.509557 | + | 0.294193i | ||||
\(947\) | −16.7901 | + | 9.69377i | −0.545605 | + | 0.315005i | −0.747347 | − | 0.664433i | \(-0.768673\pi\) |
0.201742 | + | 0.979439i | \(0.435340\pi\) | |||||||
\(948\) | −9.22733 | + | 18.1017i | −0.299690 | + | 0.587917i | ||||
\(949\) | 5.56307i | 0.180585i | ||||||||
\(950\) | 0.994947 | − | 4.24383i | 0.0322803 | − | 0.137688i | ||||
\(951\) | 26.0057 | − | 16.8817i | 0.843291 | − | 0.547427i | ||||
\(952\) | 5.62033 | − | 3.24490i | 0.182156 | − | 0.105168i | ||||
\(953\) | 14.1707 | + | 24.5444i | 0.459034 | + | 0.795070i | 0.998910 | − | 0.0466745i | \(-0.0148623\pi\) |
−0.539876 | + | 0.841744i | \(0.681529\pi\) | |||||||
\(954\) | 23.4100 | + | 32.2451i | 0.757925 | + | 1.04397i | ||||
\(955\) | −3.68444 | − | 6.38163i | −0.119226 | − | 0.206505i | ||||
\(956\) | −16.5830 | − | 9.57417i | −0.536331 | − | 0.309651i | ||||
\(957\) | −1.41925 | − | 2.18630i | −0.0458777 | − | 0.0706729i | ||||
\(958\) | − | 25.7610i | − | 0.832299i | ||||||
\(959\) | −17.7470 | − | 10.2462i | −0.573080 | − | 0.330868i | ||||
\(960\) | −1.72969 | + | 0.0903420i | −0.0558256 | + | 0.00291577i | ||||
\(961\) | 26.7929 | 0.864286 | ||||||||
\(962\) | 2.71706 | 0.0876016 | ||||||||
\(963\) | −21.4744 | − | 29.5790i | −0.692002 | − | 0.953169i | ||||
\(964\) | 16.6382 | − | 9.60606i | 0.535880 | − | 0.309390i | ||||
\(965\) | 3.73601 | − | 6.47095i | 0.120266 | − | 0.208307i | ||||
\(966\) | −3.82934 | + | 7.51221i | −0.123207 | + | 0.241701i | ||||
\(967\) | −19.7510 | − | 34.2097i | −0.635150 | − | 1.10011i | −0.986483 | − | 0.163861i | \(-0.947605\pi\) |
0.351334 | − | 0.936250i | \(-0.385728\pi\) | |||||||
\(968\) | −5.24761 | −0.168665 | ||||||||
\(969\) | −3.70695 | + | 20.5929i | −0.119084 | + | 0.661538i | ||||
\(970\) | −8.65112 | −0.277771 | ||||||||
\(971\) | −6.63173 | − | 11.4865i | −0.212822 | − | 0.368619i | 0.739774 | − | 0.672855i | \(-0.234932\pi\) |
−0.952597 | + | 0.304236i | \(0.901599\pi\) | |||||||
\(972\) | −4.02124 | − | 15.0609i | −0.128981 | − | 0.483077i | ||||
\(973\) | 8.77945 | − | 15.2065i | 0.281456 | − | 0.487496i | ||||
\(974\) | −16.6573 | + | 9.61708i | −0.533733 | + | 0.308151i | ||||
\(975\) | −0.828026 | + | 0.0432478i | −0.0265180 | + | 0.00138504i | ||||
\(976\) | −2.50391 | −0.0801481 | ||||||||
\(977\) | −44.3642 | −1.41934 | −0.709668 | − | 0.704537i | \(-0.751155\pi\) | ||||
−0.709668 | + | 0.704537i | \(0.751155\pi\) | |||||||
\(978\) | 1.12270 | + | 21.4952i | 0.0358998 | + | 0.687341i | ||||
\(979\) | −20.6613 | − | 11.9288i | −0.660338 | − | 0.381246i | ||||
\(980\) | 1.51654i | 0.0484442i | ||||||||
\(981\) | −1.97577 | − | 0.880507i | −0.0630813 | − | 0.0281124i | ||||
\(982\) | −18.7155 | − | 10.8054i | −0.597236 | − | 0.344814i | ||||
\(983\) | 0.420338 | + | 0.728047i | 0.0134067 | + | 0.0232211i | 0.872651 | − | 0.488345i | \(-0.162399\pi\) |
−0.859244 | + | 0.511566i | \(0.829066\pi\) | |||||||
\(984\) | −0.189038 | − | 3.61934i | −0.00602633 | − | 0.115380i | ||||
\(985\) | 10.1185 | + | 17.5258i | 0.322402 | + | 0.558417i | ||||
\(986\) | 1.50597 | − | 0.869474i | 0.0479600 | − | 0.0276897i | ||||
\(987\) | 4.95701 | + | 7.63608i | 0.157783 | + | 0.243059i | ||||
\(988\) | −0.603304 | − | 1.99754i | −0.0191937 | − | 0.0635502i | ||||
\(989\) | − | 15.6863i | − | 0.498796i | ||||||
\(990\) | 7.15609 | − | 0.749571i | 0.227436 | − | 0.0238229i | ||||
\(991\) | −3.01574 | + | 1.74114i | −0.0957982 | + | 0.0553091i | −0.547134 | − | 0.837045i | \(-0.684281\pi\) |
0.451336 | + | 0.892354i | \(0.350948\pi\) | |||||||
\(992\) | −1.77633 | − | 1.02556i | −0.0563985 | − | 0.0325617i | ||||
\(993\) | 8.15120 | − | 15.9906i | 0.258670 | − | 0.507447i | ||||
\(994\) | 6.28470 | − | 10.8854i | 0.199339 | − | 0.345265i | ||||
\(995\) | − | 11.2461i | − | 0.356526i | ||||||
\(996\) | 10.6645 | + | 16.4283i | 0.337919 | + | 0.520551i | ||||
\(997\) | 15.1353 | − | 26.2151i | 0.479339 | − | 0.830240i | −0.520380 | − | 0.853935i | \(-0.674210\pi\) |
0.999719 | + | 0.0236947i | \(0.00754296\pi\) | |||||||
\(998\) | 9.49912 | − | 16.4530i | 0.300689 | − | 0.520809i | ||||
\(999\) | −29.1315 | + | 4.59810i | −0.921681 | + | 0.145478i |
(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 | 570.2.s.b.221.11 | yes | 24 | |
3.2 | odd | 2 | 570.2.s.a.221.6 | ✓ | 24 | ||
19.8 | odd | 6 | 570.2.s.a.521.6 | yes | 24 | ||
57.8 | even | 6 | inner | 570.2.s.b.521.11 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.s.a.221.6 | ✓ | 24 | 3.2 | odd | 2 | ||
570.2.s.a.521.6 | yes | 24 | 19.8 | odd | 6 | ||
570.2.s.b.221.11 | yes | 24 | 1.1 | even | 1 | trivial | |
570.2.s.b.521.11 | yes | 24 | 57.8 | even | 6 | inner |