Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(101,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.l (of order \(9\), degree \(6\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 301.1 | ||
Character | \(\chi\) | \(=\) | 950.301 |
Dual form | 950.2.l.j.101.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.766044 | − | 0.642788i | −0.541675 | − | 0.454519i | ||||
\(3\) | −2.56782 | + | 0.934611i | −1.48253 | + | 0.539598i | −0.951472 | − | 0.307735i | \(-0.900429\pi\) |
−0.531061 | + | 0.847333i | \(0.678207\pi\) | |||||||
\(4\) | 0.173648 | + | 0.984808i | 0.0868241 | + | 0.492404i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.56782 | + | 0.934611i | 1.04831 | + | 0.381553i | ||||
\(7\) | 1.06844 | + | 1.85059i | 0.403832 | + | 0.699457i | 0.994185 | − | 0.107688i | \(-0.0343448\pi\) |
−0.590353 | + | 0.807145i | \(0.701011\pi\) | |||||||
\(8\) | 0.500000 | − | 0.866025i | 0.176777 | − | 0.306186i | ||||
\(9\) | 3.42208 | − | 2.87147i | 1.14069 | − | 0.957157i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.926593 | − | 1.60491i | 0.279378 | − | 0.483898i | −0.691852 | − | 0.722039i | \(-0.743205\pi\) |
0.971230 | + | 0.238142i | \(0.0765383\pi\) | |||||||
\(12\) | −1.36631 | − | 2.36652i | −0.394420 | − | 0.683155i | ||||
\(13\) | −5.18051 | − | 1.88555i | −1.43681 | − | 0.522958i | −0.497938 | − | 0.867213i | \(-0.665909\pi\) |
−0.938876 | + | 0.344255i | \(0.888131\pi\) | |||||||
\(14\) | 0.371065 | − | 2.10441i | 0.0991712 | − | 0.562428i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.939693 | + | 0.342020i | −0.234923 | + | 0.0855050i | ||||
\(17\) | 2.82962 | + | 2.37433i | 0.686283 | + | 0.575860i | 0.917835 | − | 0.396963i | \(-0.129936\pi\) |
−0.231551 | + | 0.972823i | \(0.574380\pi\) | |||||||
\(18\) | −4.46721 | −1.05293 | ||||||||
\(19\) | 1.21370 | − | 4.18652i | 0.278443 | − | 0.960453i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.47314 | − | 3.75341i | −0.976120 | − | 0.819062i | ||||
\(22\) | −1.74143 | + | 0.633827i | −0.371273 | + | 0.135132i | ||||
\(23\) | −0.511133 | − | 2.89878i | −0.106579 | − | 0.604438i | −0.990578 | − | 0.136950i | \(-0.956270\pi\) |
0.883999 | − | 0.467488i | \(-0.154841\pi\) | |||||||
\(24\) | −0.474515 | + | 2.69111i | −0.0968599 | + | 0.549320i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.75649 | + | 4.77438i | 0.540592 | + | 0.936333i | ||||
\(27\) | −2.00467 | + | 3.47219i | −0.385799 | + | 0.668223i | ||||
\(28\) | −1.63694 | + | 1.37356i | −0.309353 | + | 0.259578i | ||||
\(29\) | −5.36998 | + | 4.50595i | −0.997181 | + | 0.836734i | −0.986591 | − | 0.163210i | \(-0.947815\pi\) |
−0.0105895 | + | 0.999944i | \(0.503371\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.12807 | + | 3.68592i | 0.382213 | + | 0.662012i | 0.991378 | − | 0.131031i | \(-0.0418289\pi\) |
−0.609166 | + | 0.793043i | \(0.708496\pi\) | |||||||
\(32\) | 0.939693 | + | 0.342020i | 0.166116 | + | 0.0604612i | ||||
\(33\) | −0.879364 | + | 4.98712i | −0.153078 | + | 0.868146i | ||||
\(34\) | −0.641422 | − | 3.63769i | −0.110003 | − | 0.623858i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.42208 | + | 2.87147i | 0.570347 | + | 0.478578i | ||||
\(37\) | −3.49650 | −0.574822 | −0.287411 | − | 0.957807i | \(-0.592795\pi\) | ||||
−0.287411 | + | 0.957807i | \(0.592795\pi\) | |||||||
\(38\) | −3.62079 | + | 2.42690i | −0.587370 | + | 0.393696i | ||||
\(39\) | 15.0649 | 2.41231 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.47464 | − | 0.536727i | 0.230301 | − | 0.0838227i | −0.224292 | − | 0.974522i | \(-0.572007\pi\) |
0.454593 | + | 0.890699i | \(0.349785\pi\) | |||||||
\(42\) | 1.01398 | + | 5.75056i | 0.156460 | + | 0.887331i | ||||
\(43\) | 0.404597 | − | 2.29458i | 0.0617005 | − | 0.349921i | −0.938291 | − | 0.345846i | \(-0.887592\pi\) |
0.999992 | − | 0.00407464i | \(-0.00129700\pi\) | |||||||
\(44\) | 1.74143 | + | 0.633827i | 0.262530 | + | 0.0955531i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.47175 | + | 2.54915i | −0.216998 | + | 0.375851i | ||||
\(47\) | 8.59234 | − | 7.20983i | 1.25332 | − | 1.05166i | 0.256961 | − | 0.966422i | \(-0.417279\pi\) |
0.996360 | − | 0.0852401i | \(-0.0271657\pi\) | |||||||
\(48\) | 2.09331 | − | 1.75649i | 0.302143 | − | 0.253528i | ||||
\(49\) | 1.21688 | − | 2.10770i | 0.173840 | − | 0.301099i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.48504 | − | 3.45227i | −1.32817 | − | 0.483415i | ||||
\(52\) | 0.957319 | − | 5.42923i | 0.132756 | − | 0.752898i | ||||
\(53\) | 1.11501 | + | 6.32356i | 0.153159 | + | 0.868607i | 0.960450 | + | 0.278453i | \(0.0898218\pi\) |
−0.807291 | + | 0.590154i | \(0.799067\pi\) | |||||||
\(54\) | 3.76755 | − | 1.37127i | 0.512698 | − | 0.186607i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.13688 | 0.285552 | ||||||||
\(57\) | 0.796188 | + | 11.8846i | 0.105458 | + | 1.57415i | ||||
\(58\) | 7.01002 | 0.920460 | ||||||||
\(59\) | 10.8207 | + | 9.07963i | 1.40873 | + | 1.18207i | 0.957062 | + | 0.289883i | \(0.0936165\pi\) |
0.451672 | + | 0.892184i | \(0.350828\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0461045 | − | 0.261472i | −0.00590308 | − | 0.0334780i | 0.981714 | − | 0.190362i | \(-0.0609662\pi\) |
−0.987617 | + | 0.156884i | \(0.949855\pi\) | |||||||
\(62\) | 0.739071 | − | 4.19148i | 0.0938621 | − | 0.532318i | ||||
\(63\) | 8.97020 | + | 3.26488i | 1.13014 | + | 0.411337i | ||||
\(64\) | −0.500000 | − | 0.866025i | −0.0625000 | − | 0.108253i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.87929 | − | 3.25511i | 0.477508 | − | 0.400677i | ||||
\(67\) | 11.3188 | − | 9.49761i | 1.38281 | − | 1.16032i | 0.414654 | − | 0.909979i | \(-0.363903\pi\) |
0.968158 | − | 0.250338i | \(-0.0805418\pi\) | |||||||
\(68\) | −1.84690 | + | 3.19893i | −0.223970 | + | 0.387927i | ||||
\(69\) | 4.02173 | + | 6.96585i | 0.484160 | + | 0.838589i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.722627 | − | 4.09822i | 0.0857601 | − | 0.486370i | −0.911430 | − | 0.411455i | \(-0.865021\pi\) |
0.997190 | − | 0.0749143i | \(-0.0238683\pi\) | |||||||
\(72\) | −0.775724 | − | 4.39935i | −0.0914199 | − | 0.518468i | ||||
\(73\) | 14.4815 | − | 5.27085i | 1.69494 | − | 0.616906i | 0.699703 | − | 0.714434i | \(-0.253316\pi\) |
0.995233 | + | 0.0975282i | \(0.0310936\pi\) | |||||||
\(74\) | 2.67848 | + | 2.24751i | 0.311367 | + | 0.261268i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.33367 | + | 0.468284i | 0.497106 | + | 0.0537159i | ||||
\(77\) | 3.96003 | 0.451288 | ||||||||
\(78\) | −11.5404 | − | 9.68352i | −1.30669 | − | 1.09644i | ||||
\(79\) | 2.70762 | − | 0.985493i | 0.304631 | − | 0.110877i | −0.185182 | − | 0.982704i | \(-0.559287\pi\) |
0.489813 | + | 0.871828i | \(0.337065\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.424681 | + | 2.40849i | −0.0471868 | + | 0.267610i | ||||
\(82\) | −1.47464 | − | 0.536727i | −0.162847 | − | 0.0592716i | ||||
\(83\) | 7.00947 | + | 12.1408i | 0.769389 | + | 1.33262i | 0.937894 | + | 0.346921i | \(0.112773\pi\) |
−0.168505 | + | 0.985701i | \(0.553894\pi\) | |||||||
\(84\) | 2.91964 | − | 5.05696i | 0.318558 | − | 0.551759i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.78487 | + | 1.49768i | −0.192467 | + | 0.161499i | ||||
\(87\) | 9.57786 | − | 16.5893i | 1.02685 | − | 1.77856i | ||||
\(88\) | −0.926593 | − | 1.60491i | −0.0987752 | − | 0.171084i | ||||
\(89\) | −1.86003 | − | 0.676995i | −0.197163 | − | 0.0717613i | 0.241552 | − | 0.970388i | \(-0.422344\pi\) |
−0.438714 | + | 0.898627i | \(0.644566\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.04567 | − | 11.6016i | −0.214445 | − | 1.21618i | ||||
\(92\) | 2.76599 | − | 1.00674i | 0.288374 | − | 0.104960i | ||||
\(93\) | −8.90941 | − | 7.47588i | −0.923863 | − | 0.775213i | ||||
\(94\) | −11.2165 | −1.15689 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.73262 | −0.278897 | ||||||||
\(97\) | 8.28096 | + | 6.94855i | 0.840805 | + | 0.705519i | 0.957745 | − | 0.287620i | \(-0.0928641\pi\) |
−0.116940 | + | 0.993139i | \(0.537309\pi\) | |||||||
\(98\) | −2.28698 | + | 0.832394i | −0.231020 | + | 0.0840845i | ||||
\(99\) | −1.43756 | − | 8.15281i | −0.144480 | − | 0.819388i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.37445 | − | 3.41202i | −0.932792 | − | 0.339509i | −0.169477 | − | 0.985534i | \(-0.554208\pi\) |
−0.763316 | + | 0.646026i | \(0.776430\pi\) | |||||||
\(102\) | 5.04688 | + | 8.74146i | 0.499716 | + | 0.865533i | ||||
\(103\) | −4.38758 | + | 7.59952i | −0.432322 | + | 0.748803i | −0.997073 | − | 0.0764583i | \(-0.975639\pi\) |
0.564751 | + | 0.825261i | \(0.308972\pi\) | |||||||
\(104\) | −4.22319 | + | 3.54368i | −0.414118 | + | 0.347486i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.21055 | − | 5.56084i | 0.311837 | − | 0.540117i | ||||
\(107\) | 2.85163 | + | 4.93917i | 0.275677 | + | 0.477487i | 0.970306 | − | 0.241882i | \(-0.0777645\pi\) |
−0.694628 | + | 0.719369i | \(0.744431\pi\) | |||||||
\(108\) | −3.76755 | − | 1.37127i | −0.362532 | − | 0.131951i | ||||
\(109\) | 0.137722 | − | 0.781060i | 0.0131914 | − | 0.0748119i | −0.977501 | − | 0.210929i | \(-0.932351\pi\) |
0.990693 | + | 0.136117i | \(0.0434623\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.97841 | − | 3.26787i | 0.852193 | − | 0.310173i | ||||
\(112\) | −1.63694 | − | 1.37356i | −0.154677 | − | 0.129789i | ||||
\(113\) | 4.98604 | 0.469047 | 0.234523 | − | 0.972110i | \(-0.424647\pi\) | ||||
0.234523 | + | 0.972110i | \(0.424647\pi\) | |||||||
\(114\) | 7.02934 | − | 9.61589i | 0.658358 | − | 0.900611i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.36998 | − | 4.50595i | −0.498590 | − | 0.418367i | ||||
\(117\) | −23.1424 | + | 8.42316i | −2.13952 | + | 0.778721i | ||||
\(118\) | −2.45285 | − | 13.9108i | −0.225803 | − | 1.28059i | ||||
\(119\) | −1.37064 | + | 7.77329i | −0.125646 | + | 0.712576i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.78285 | + | 6.55209i | 0.343895 | + | 0.595644i | ||||
\(122\) | −0.132753 | + | 0.229934i | −0.0120189 | + | 0.0208173i | ||||
\(123\) | −3.28500 | + | 2.75644i | −0.296198 | + | 0.248540i | ||||
\(124\) | −3.26039 | + | 2.73579i | −0.292792 | + | 0.245682i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.77294 | − | 8.26698i | −0.425208 | − | 0.736481i | ||||
\(127\) | −14.5787 | − | 5.30620i | −1.29365 | − | 0.470849i | −0.398725 | − | 0.917071i | \(-0.630547\pi\) |
−0.894923 | + | 0.446221i | \(0.852769\pi\) | |||||||
\(128\) | −0.173648 | + | 0.984808i | −0.0153485 | + | 0.0870455i | ||||
\(129\) | 1.10561 | + | 6.27023i | 0.0973436 | + | 0.552063i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.8928 | + | 14.1748i | 1.47593 | + | 1.23846i | 0.910399 | + | 0.413732i | \(0.135775\pi\) |
0.565535 | + | 0.824724i | \(0.308670\pi\) | |||||||
\(132\) | −5.06406 | −0.440770 | ||||||||
\(133\) | 9.04429 | − | 2.22697i | 0.784240 | − | 0.193103i | ||||
\(134\) | −14.7757 | −1.27642 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.47104 | − | 1.26336i | 0.297639 | − | 0.108332i | ||||
\(137\) | 2.42112 | + | 13.7309i | 0.206851 | + | 1.17311i | 0.894501 | + | 0.447066i | \(0.147531\pi\) |
−0.687650 | + | 0.726042i | \(0.741358\pi\) | |||||||
\(138\) | 1.39673 | − | 7.92127i | 0.118898 | − | 0.674303i | ||||
\(139\) | −11.5850 | − | 4.21658i | −0.982623 | − | 0.357646i | −0.199764 | − | 0.979844i | \(-0.564017\pi\) |
−0.782860 | + | 0.622198i | \(0.786240\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.3252 | + | 26.5441i | −1.29062 | + | 2.23541i | ||||
\(142\) | −3.18785 | + | 2.67493i | −0.267519 | + | 0.224475i | ||||
\(143\) | −7.82636 | + | 6.56709i | −0.654473 | + | 0.549168i | ||||
\(144\) | −2.23361 | + | 3.86872i | −0.186134 | + | 0.322393i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −14.4815 | − | 5.27085i | −1.19850 | − | 0.436218i | ||||
\(147\) | −1.15485 | + | 6.54950i | −0.0952507 | + | 0.540194i | ||||
\(148\) | −0.607162 | − | 3.44339i | −0.0499084 | − | 0.283045i | ||||
\(149\) | −21.1569 | + | 7.70049i | −1.73324 | + | 0.630849i | −0.998853 | − | 0.0478803i | \(-0.984753\pi\) |
−0.734389 | + | 0.678729i | \(0.762531\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.6452 | 1.84284 | 0.921420 | − | 0.388568i | \(-0.127030\pi\) | ||||
0.921420 | + | 0.388568i | \(0.127030\pi\) | |||||||
\(152\) | −3.01878 | − | 3.14436i | −0.244855 | − | 0.255041i | ||||
\(153\) | 16.5010 | 1.33403 | ||||||||
\(154\) | −3.03356 | − | 2.54546i | −0.244451 | − | 0.205119i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.61599 | + | 14.8360i | 0.209447 | + | 1.18783i | ||||
\(157\) | 2.58475 | − | 14.6588i | 0.206285 | − | 1.16990i | −0.689119 | − | 0.724648i | \(-0.742002\pi\) |
0.895405 | − | 0.445253i | \(-0.146886\pi\) | |||||||
\(158\) | −2.70762 | − | 0.985493i | −0.215407 | − | 0.0784016i | ||||
\(159\) | −8.77322 | − | 15.1957i | −0.695762 | − | 1.20510i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.81834 | − | 4.04307i | 0.379738 | − | 0.318638i | ||||
\(162\) | 1.87347 | − | 1.57203i | 0.147194 | − | 0.123510i | ||||
\(163\) | 5.53187 | − | 9.58148i | 0.433289 | − | 0.750479i | −0.563865 | − | 0.825867i | \(-0.690686\pi\) |
0.997154 | + | 0.0753878i | \(0.0240195\pi\) | |||||||
\(164\) | 0.784642 | + | 1.35904i | 0.0612703 | + | 0.106123i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.43436 | − | 13.8060i | 0.188943 | − | 1.07155i | ||||
\(167\) | −3.42470 | − | 19.4224i | −0.265011 | − | 1.50295i | −0.769003 | − | 0.639245i | \(-0.779247\pi\) |
0.503992 | − | 0.863708i | \(-0.331864\pi\) | |||||||
\(168\) | −5.48712 | + | 1.99715i | −0.423341 | + | 0.154083i | ||||
\(169\) | 13.3238 | + | 11.1800i | 1.02491 | + | 0.859998i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.86806 | − | 17.8117i | −0.601685 | − | 1.36210i | ||||
\(172\) | 2.32998 | 0.177659 | ||||||||
\(173\) | −4.64055 | − | 3.89388i | −0.352815 | − | 0.296047i | 0.449105 | − | 0.893479i | \(-0.351743\pi\) |
−0.801919 | + | 0.597433i | \(0.796188\pi\) | |||||||
\(174\) | −18.0005 | + | 6.55164i | −1.36461 | + | 0.496678i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.321803 | + | 1.82503i | −0.0242568 | + | 0.137567i | ||||
\(177\) | −36.2715 | − | 13.2018i | −2.72634 | − | 0.992305i | ||||
\(178\) | 0.989700 | + | 1.71421i | 0.0741812 | + | 0.128486i | ||||
\(179\) | 0.625049 | − | 1.08262i | 0.0467184 | − | 0.0809186i | −0.841721 | − | 0.539913i | \(-0.818457\pi\) |
0.888439 | + | 0.458995i | \(0.151790\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0955 | − | 10.1494i | 0.899054 | − | 0.754396i | −0.0709510 | − | 0.997480i | \(-0.522603\pi\) |
0.970005 | + | 0.243084i | \(0.0781590\pi\) | |||||||
\(182\) | −5.89028 | + | 10.2023i | −0.436617 | + | 0.756242i | ||||
\(183\) | 0.362763 | + | 0.628323i | 0.0268162 | + | 0.0464470i | ||||
\(184\) | −2.76599 | − | 1.00674i | −0.203911 | − | 0.0742176i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.01960 | + | 11.4537i | 0.148084 | + | 0.839827i | ||||
\(187\) | 6.43249 | − | 2.34123i | 0.470390 | − | 0.171208i | ||||
\(188\) | 8.59234 | + | 7.20983i | 0.626661 | + | 0.525831i | ||||
\(189\) | −8.56746 | −0.623191 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.05105 | −0.148409 | −0.0742045 | − | 0.997243i | \(-0.523642\pi\) | ||||
−0.0742045 | + | 0.997243i | \(0.523642\pi\) | |||||||
\(192\) | 2.09331 | + | 1.75649i | 0.151072 | + | 0.126764i | ||||
\(193\) | 0.773263 | − | 0.281445i | 0.0556607 | − | 0.0202588i | −0.314040 | − | 0.949410i | \(-0.601683\pi\) |
0.369700 | + | 0.929151i | \(0.379460\pi\) | |||||||
\(194\) | −1.87714 | − | 10.6458i | −0.134771 | − | 0.764324i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.28698 | + | 0.832394i | 0.163356 | + | 0.0594567i | ||||
\(197\) | 6.35099 | + | 11.0002i | 0.452489 | + | 0.783734i | 0.998540 | − | 0.0540180i | \(-0.0172028\pi\) |
−0.546051 | + | 0.837752i | \(0.683869\pi\) | |||||||
\(198\) | −4.13929 | + | 7.16946i | −0.294167 | + | 0.509511i | ||||
\(199\) | −3.91363 | + | 3.28392i | −0.277430 | + | 0.232791i | −0.770876 | − | 0.636985i | \(-0.780181\pi\) |
0.493446 | + | 0.869776i | \(0.335737\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20.1881 | + | 34.9669i | −1.42396 | + | 2.46637i | ||||
\(202\) | 4.98804 | + | 8.63954i | 0.350957 | + | 0.607876i | ||||
\(203\) | −14.0762 | − | 5.12330i | −0.987953 | − | 0.359585i | ||||
\(204\) | 1.75276 | − | 9.94042i | 0.122718 | − | 0.695969i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.24596 | − | 3.00128i | 0.574523 | − | 0.209109i | ||||
\(207\) | −10.0729 | − | 8.45217i | −0.700115 | − | 0.587466i | ||||
\(208\) | 5.51298 | 0.382256 | ||||||||
\(209\) | −5.59436 | − | 5.82708i | −0.386970 | − | 0.403068i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.9318 | − | 12.5293i | −1.02795 | − | 0.862551i | −0.0373426 | − | 0.999303i | \(-0.511889\pi\) |
−0.990605 | + | 0.136752i | \(0.956334\pi\) | |||||||
\(212\) | −6.03387 | + | 2.19615i | −0.414408 | + | 0.150832i | ||||
\(213\) | 1.97467 | + | 11.1989i | 0.135302 | + | 0.767335i | ||||
\(214\) | 0.990360 | − | 5.61661i | 0.0676996 | − | 0.383944i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.00467 | + | 3.47219i | 0.136400 | + | 0.236253i | ||||
\(217\) | −4.54742 | + | 7.87637i | −0.308699 | + | 0.534683i | ||||
\(218\) | −0.607556 | + | 0.509800i | −0.0411489 | + | 0.0345280i | ||||
\(219\) | −32.2598 | + | 27.0692i | −2.17992 | + | 1.82917i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.1819 | − | 17.6356i | −0.684911 | − | 1.18630i | ||||
\(222\) | −8.97841 | − | 3.26787i | −0.602591 | − | 0.219325i | ||||
\(223\) | −0.424827 | + | 2.40931i | −0.0284485 | + | 0.161340i | −0.995722 | − | 0.0923948i | \(-0.970548\pi\) |
0.967274 | + | 0.253734i | \(0.0816589\pi\) | |||||||
\(224\) | 0.371065 | + | 2.10441i | 0.0247928 | + | 0.140607i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.81953 | − | 3.20496i | −0.254071 | − | 0.213191i | ||||
\(227\) | 19.2300 | 1.27634 | 0.638169 | − | 0.769897i | \(-0.279692\pi\) | ||||
0.638169 | + | 0.769897i | \(0.279692\pi\) | |||||||
\(228\) | −11.5658 | + | 2.84783i | −0.765962 | + | 0.188602i | ||||
\(229\) | 20.3871 | 1.34722 | 0.673609 | − | 0.739088i | \(-0.264743\pi\) | ||||
0.673609 | + | 0.739088i | \(0.264743\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.1687 | + | 3.70109i | −0.669049 | + | 0.243514i | ||||
\(232\) | 1.21728 | + | 6.90352i | 0.0799181 | + | 0.453238i | ||||
\(233\) | −1.46196 | + | 8.29121i | −0.0957764 | + | 0.543175i | 0.898730 | + | 0.438502i | \(0.144491\pi\) |
−0.994507 | + | 0.104673i | \(0.966620\pi\) | |||||||
\(234\) | 23.1424 | + | 8.42316i | 1.51287 | + | 0.550639i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.06270 | + | 12.2330i | −0.459743 | + | 0.796298i | ||||
\(237\) | −6.03163 | + | 5.06114i | −0.391797 | + | 0.328756i | ||||
\(238\) | 6.04655 | − | 5.07365i | 0.391939 | − | 0.328876i | ||||
\(239\) | 6.60300 | − | 11.4367i | 0.427113 | − | 0.739781i | −0.569503 | − | 0.821990i | \(-0.692864\pi\) |
0.996615 | + | 0.0822090i | \(0.0261975\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.63066 | + | 2.41336i | 0.427118 | + | 0.155458i | 0.546630 | − | 0.837375i | \(-0.315911\pi\) |
−0.119511 | + | 0.992833i | \(0.538133\pi\) | |||||||
\(242\) | 1.31377 | − | 7.45076i | 0.0844523 | − | 0.478953i | ||||
\(243\) | −3.24914 | − | 18.4268i | −0.208432 | − | 1.18208i | ||||
\(244\) | 0.249493 | − | 0.0908082i | 0.0159722 | − | 0.00581340i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.28826 | 0.273409 | ||||||||
\(247\) | −14.1815 | + | 19.3998i | −0.902347 | + | 1.23438i | ||||
\(248\) | 4.25614 | 0.270265 | ||||||||
\(249\) | −29.3460 | − | 24.6242i | −1.85973 | − | 1.56049i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.405222 | − | 2.29813i | −0.0255774 | − | 0.145057i | 0.969345 | − | 0.245705i | \(-0.0790194\pi\) |
−0.994922 | + | 0.100648i | \(0.967908\pi\) | |||||||
\(252\) | −1.65763 | + | 9.40086i | −0.104421 | + | 0.592199i | ||||
\(253\) | −5.12589 | − | 1.86567i | −0.322262 | − | 0.117294i | ||||
\(254\) | 7.75715 | + | 13.4358i | 0.486727 | + | 0.843035i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.766044 | − | 0.642788i | 0.0478778 | − | 0.0401742i | ||||
\(257\) | 4.24431 | − | 3.56140i | 0.264753 | − | 0.222154i | −0.500741 | − | 0.865597i | \(-0.666939\pi\) |
0.765494 | + | 0.643443i | \(0.222495\pi\) | |||||||
\(258\) | 3.18348 | − | 5.51395i | 0.198195 | − | 0.343283i | ||||
\(259\) | −3.73580 | − | 6.47060i | −0.232131 | − | 0.402063i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.43783 | + | 30.8395i | −0.336593 | + | 1.90892i | ||||
\(262\) | −3.82930 | − | 21.7170i | −0.236575 | − | 1.34168i | ||||
\(263\) | −1.66651 | + | 0.606559i | −0.102761 | + | 0.0374020i | −0.392889 | − | 0.919586i | \(-0.628524\pi\) |
0.290128 | + | 0.956988i | \(0.406302\pi\) | |||||||
\(264\) | 3.87929 | + | 3.25511i | 0.238754 | + | 0.200338i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.35980 | − | 4.10760i | −0.512572 | − | 0.251853i | ||||
\(267\) | 5.40895 | 0.331022 | ||||||||
\(268\) | 11.3188 | + | 9.49761i | 0.691406 | + | 0.580159i | ||||
\(269\) | 14.9736 | − | 5.44995i | 0.912957 | − | 0.332289i | 0.157524 | − | 0.987515i | \(-0.449649\pi\) |
0.755433 | + | 0.655226i | \(0.227427\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.44844 | − | 13.8858i | 0.148732 | − | 0.843502i | −0.815562 | − | 0.578669i | \(-0.803572\pi\) |
0.964294 | − | 0.264832i | \(-0.0853166\pi\) | |||||||
\(272\) | −3.47104 | − | 1.26336i | −0.210463 | − | 0.0766022i | ||||
\(273\) | 16.0959 | + | 27.8789i | 0.974168 | + | 1.68731i | ||||
\(274\) | 6.97135 | − | 12.0747i | 0.421155 | − | 0.729461i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.16165 | + | 5.17024i | −0.370888 | + | 0.311212i | ||||
\(277\) | −11.1329 | + | 19.2828i | −0.668912 | + | 1.15859i | 0.309297 | + | 0.950965i | \(0.399906\pi\) |
−0.978209 | + | 0.207623i | \(0.933427\pi\) | |||||||
\(278\) | 6.16423 | + | 10.6768i | 0.369706 | + | 0.640349i | ||||
\(279\) | 17.8665 | + | 6.50286i | 1.06964 | + | 0.389316i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.26898 | − | 7.19674i | −0.0757009 | − | 0.429321i | −0.998979 | − | 0.0451879i | \(-0.985611\pi\) |
0.923278 | − | 0.384133i | \(-0.125500\pi\) | |||||||
\(282\) | 28.8020 | − | 10.4831i | 1.71513 | − | 0.624258i | ||||
\(283\) | −7.89580 | − | 6.62536i | −0.469357 | − | 0.393837i | 0.377203 | − | 0.926131i | \(-0.376886\pi\) |
−0.846560 | + | 0.532294i | \(0.821330\pi\) | |||||||
\(284\) | 4.16145 | 0.246936 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.2166 | 0.604119 | ||||||||
\(287\) | 2.56883 | + | 2.15550i | 0.151633 | + | 0.127235i | ||||
\(288\) | 4.19781 | − | 1.52788i | 0.247358 | − | 0.0900310i | ||||
\(289\) | −0.582730 | − | 3.30482i | −0.0342782 | − | 0.194401i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −27.7582 | − | 10.1032i | −1.62722 | − | 0.592259i | ||||
\(292\) | 7.70546 | + | 13.3463i | 0.450928 | + | 0.781030i | ||||
\(293\) | 15.3180 | − | 26.5315i | 0.894887 | − | 1.54999i | 0.0609422 | − | 0.998141i | \(-0.480589\pi\) |
0.833945 | − | 0.551848i | \(-0.186077\pi\) | |||||||
\(294\) | 5.09461 | − | 4.27488i | 0.297123 | − | 0.249316i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.74825 | + | 3.02806i | −0.101615 | + | 0.176003i | ||||
\(297\) | 3.71503 | + | 6.43461i | 0.215568 | + | 0.373374i | ||||
\(298\) | 21.1569 | + | 7.70049i | 1.22559 | + | 0.446077i | ||||
\(299\) | −2.81787 | + | 15.9809i | −0.162962 | + | 0.924201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.67862 | − | 1.70288i | 0.269671 | − | 0.0981523i | ||||
\(302\) | −17.3472 | − | 14.5561i | −0.998221 | − | 0.837607i | ||||
\(303\) | 27.2608 | 1.56609 | ||||||||
\(304\) | 0.291364 | + | 4.34915i | 0.0167109 | + | 0.249441i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −12.6405 | − | 10.6066i | −0.722610 | − | 0.606342i | ||||
\(307\) | −7.50580 | + | 2.73189i | −0.428379 | + | 0.155917i | −0.547206 | − | 0.836998i | \(-0.684309\pi\) |
0.118828 | + | 0.992915i | \(0.462086\pi\) | |||||||
\(308\) | 0.687652 | + | 3.89987i | 0.0391826 | + | 0.222216i | ||||
\(309\) | 4.16395 | − | 23.6149i | 0.236879 | − | 1.34341i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.3155 | + | 23.0631i | 0.755052 | + | 1.30779i | 0.945348 | + | 0.326062i | \(0.105722\pi\) |
−0.190296 | + | 0.981727i | \(0.560945\pi\) | |||||||
\(312\) | 7.53244 | − | 13.0466i | 0.426440 | − | 0.738617i | ||||
\(313\) | 5.87045 | − | 4.92589i | 0.331817 | − | 0.278428i | −0.461622 | − | 0.887076i | \(-0.652733\pi\) |
0.793440 | + | 0.608649i | \(0.208288\pi\) | |||||||
\(314\) | −11.4025 | + | 9.56787i | −0.643482 | + | 0.539946i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.44069 | + | 2.49535i | 0.0810454 | + | 0.140375i | ||||
\(317\) | −2.78721 | − | 1.01446i | −0.156545 | − | 0.0569779i | 0.262559 | − | 0.964916i | \(-0.415434\pi\) |
−0.419104 | + | 0.907938i | \(0.637656\pi\) | |||||||
\(318\) | −3.04691 | + | 17.2799i | −0.170862 | + | 0.969008i | ||||
\(319\) | 2.25584 | + | 12.7935i | 0.126303 | + | 0.716299i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.9387 | − | 10.0177i | −0.666352 | − | 0.559136i | ||||
\(322\) | −6.28990 | −0.350522 | ||||||||
\(323\) | 13.3745 | − | 8.96451i | 0.744177 | − | 0.498799i | ||||
\(324\) | −2.44564 | −0.135869 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.3965 | + | 3.78402i | −0.575810 | + | 0.209578i | ||||
\(327\) | 0.376342 | + | 2.13434i | 0.0208117 | + | 0.118029i | ||||
\(328\) | 0.272503 | − | 1.54544i | 0.0150465 | − | 0.0853328i | ||||
\(329\) | 22.5228 | + | 8.19764i | 1.24172 | + | 0.451950i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.33020 | + | 2.30397i | −0.0731143 | + | 0.126638i | −0.900265 | − | 0.435343i | \(-0.856627\pi\) |
0.827150 | + | 0.561981i | \(0.189960\pi\) | |||||||
\(332\) | −10.7391 | + | 9.01120i | −0.589386 | + | 0.494554i | ||||
\(333\) | −11.9653 | + | 10.0401i | −0.655696 | + | 0.550194i | ||||
\(334\) | −9.86103 | + | 17.0798i | −0.539572 | + | 0.934565i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.48712 | + | 1.99715i | 0.299347 | + | 0.108953i | ||||
\(337\) | −5.43943 | + | 30.8485i | −0.296304 | + | 1.68043i | 0.365549 | + | 0.930792i | \(0.380881\pi\) |
−0.661853 | + | 0.749634i | \(0.730230\pi\) | |||||||
\(338\) | −3.02025 | − | 17.1287i | −0.164280 | − | 0.931679i | ||||
\(339\) | −12.8033 | + | 4.66001i | −0.695378 | + | 0.253097i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.88742 | 0.427128 | ||||||||
\(342\) | −5.42188 | + | 18.7021i | −0.293181 | + | 1.01129i | ||||
\(343\) | 20.1588 | 1.08847 | ||||||||
\(344\) | −1.78487 | − | 1.49768i | −0.0962337 | − | 0.0807497i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.05193 | + | 5.96578i | 0.0565520 | + | 0.320722i | ||||
\(347\) | 1.84375 | − | 10.4564i | 0.0989776 | − | 0.561330i | −0.894478 | − | 0.447112i | \(-0.852453\pi\) |
0.993456 | − | 0.114218i | \(-0.0364362\pi\) | |||||||
\(348\) | 18.0005 | + | 6.55164i | 0.964927 | + | 0.351205i | ||||
\(349\) | −18.4784 | − | 32.0056i | −0.989128 | − | 1.71322i | −0.621921 | − | 0.783080i | \(-0.713648\pi\) |
−0.367206 | − | 0.930139i | \(-0.619686\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.9322 | − | 14.2078i | 0.903773 | − | 0.758356i | ||||
\(352\) | 1.41962 | − | 1.19121i | 0.0756662 | − | 0.0634915i | ||||
\(353\) | −15.4274 | + | 26.7210i | −0.821117 | + | 1.42222i | 0.0837337 | + | 0.996488i | \(0.473315\pi\) |
−0.904851 | + | 0.425729i | \(0.860018\pi\) | |||||||
\(354\) | 19.2997 | + | 33.4280i | 1.02577 | + | 1.77668i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.343719 | − | 1.94933i | 0.0182171 | − | 0.103314i | ||||
\(357\) | −3.74544 | − | 21.2414i | −0.198230 | − | 1.12422i | ||||
\(358\) | −1.17471 | + | 0.427559i | −0.0620853 | + | 0.0225972i | ||||
\(359\) | −7.76753 | − | 6.51773i | −0.409954 | − | 0.343993i | 0.414372 | − | 0.910108i | \(-0.364001\pi\) |
−0.824326 | + | 0.566115i | \(0.808446\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.0538 | − | 10.1624i | −0.844939 | − | 0.534862i | ||||
\(362\) | −15.7896 | −0.829883 | ||||||||
\(363\) | −15.8373 | − | 13.2891i | −0.831245 | − | 0.697497i | ||||
\(364\) | 11.0701 | − | 4.02919i | 0.580231 | − | 0.211187i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.125986 | − | 0.714503i | 0.00658540 | − | 0.0373477i | ||||
\(367\) | 11.0649 | + | 4.02729i | 0.577583 | + | 0.210223i | 0.614259 | − | 0.789104i | \(-0.289455\pi\) |
−0.0366766 | + | 0.999327i | \(0.511677\pi\) | |||||||
\(368\) | 1.47175 | + | 2.54915i | 0.0767203 | + | 0.132883i | ||||
\(369\) | 3.50516 | − | 6.07112i | 0.182472 | − | 0.316050i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.5110 | + | 8.81976i | −0.545703 | + | 0.457899i | ||||
\(372\) | 5.81521 | − | 10.0722i | 0.301504 | − | 0.522221i | ||||
\(373\) | −9.78613 | − | 16.9501i | −0.506706 | − | 0.877641i | −0.999970 | − | 0.00776129i | \(-0.997529\pi\) |
0.493263 | − | 0.869880i | \(-0.335804\pi\) | |||||||
\(374\) | −6.43249 | − | 2.34123i | −0.332616 | − | 0.121062i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.94773 | − | 11.0461i | −0.100446 | − | 0.569659i | ||||
\(377\) | 36.3154 | − | 13.2177i | 1.87034 | − | 0.680748i | ||||
\(378\) | 6.56306 | + | 5.50706i | 0.337567 | + | 0.283252i | ||||
\(379\) | 19.0901 | 0.980591 | 0.490296 | − | 0.871556i | \(-0.336889\pi\) | ||||
0.490296 | + | 0.871556i | \(0.336889\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 42.3947 | 2.17195 | ||||||||
\(382\) | 1.57120 | + | 1.31839i | 0.0803894 | + | 0.0674548i | ||||
\(383\) | −18.4874 | + | 6.72885i | −0.944660 | + | 0.343828i | −0.768004 | − | 0.640445i | \(-0.778750\pi\) |
−0.176655 | + | 0.984273i | \(0.556528\pi\) | |||||||
\(384\) | −0.474515 | − | 2.69111i | −0.0242150 | − | 0.137330i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.773263 | − | 0.281445i | −0.0393580 | − | 0.0143252i | ||||
\(387\) | −5.20426 | − | 9.01405i | −0.264548 | − | 0.458210i | ||||
\(388\) | −5.40502 | + | 9.36176i | −0.274398 | + | 0.475271i | ||||
\(389\) | −18.4221 | + | 15.4580i | −0.934038 | + | 0.783751i | −0.976538 | − | 0.215346i | \(-0.930912\pi\) |
0.0425001 | + | 0.999096i | \(0.486468\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.43636 | − | 9.41605i | 0.274928 | − | 0.476190i | ||||
\(392\) | −1.21688 | − | 2.10770i | −0.0614617 | − | 0.106455i | ||||
\(393\) | −56.6257 | − | 20.6101i | −2.85639 | − | 1.03964i | ||||
\(394\) | 2.20567 | − | 12.5090i | 0.111120 | − | 0.630194i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.77932 | − | 2.83144i | 0.390926 | − | 0.142285i | ||||
\(397\) | 1.94657 | + | 1.63337i | 0.0976956 | + | 0.0819763i | 0.690327 | − | 0.723497i | \(-0.257467\pi\) |
−0.592632 | + | 0.805474i | \(0.701911\pi\) | |||||||
\(398\) | 5.10888 | 0.256085 | ||||||||
\(399\) | −21.1428 | + | 14.1714i | −1.05846 | + | 0.709455i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.13717 | + | 0.954196i | 0.0567874 | + | 0.0476503i | 0.670740 | − | 0.741693i | \(-0.265977\pi\) |
−0.613952 | + | 0.789343i | \(0.710421\pi\) | |||||||
\(402\) | 37.9413 | − | 13.8095i | 1.89234 | − | 0.688755i | ||||
\(403\) | −4.07448 | − | 23.1075i | −0.202964 | − | 1.15107i | ||||
\(404\) | 1.73233 | − | 9.82452i | 0.0861865 | − | 0.488788i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.48977 | + | 12.9727i | 0.371711 | + | 0.643822i | ||||
\(407\) | −3.23984 | + | 5.61156i | −0.160593 | + | 0.278155i | ||||
\(408\) | −7.73227 | + | 6.48815i | −0.382805 | + | 0.321211i | ||||
\(409\) | 9.40691 | − | 7.89333i | 0.465142 | − | 0.390300i | −0.379877 | − | 0.925037i | \(-0.624034\pi\) |
0.845019 | + | 0.534737i | \(0.179589\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.0501 | − | 32.9957i | −0.939670 | − | 1.62756i | ||||
\(412\) | −8.24596 | − | 3.00128i | −0.406249 | − | 0.147863i | ||||
\(413\) | −5.24144 | + | 29.7257i | −0.257914 | + | 1.46271i | ||||
\(414\) | 2.28334 | + | 12.9495i | 0.112220 | + | 0.636432i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.22319 | − | 3.54368i | −0.207059 | − | 0.173743i | ||||
\(417\) | 33.6890 | 1.64976 | ||||||||
\(418\) | 0.539953 | + | 8.05979i | 0.0264099 | + | 0.394217i | ||||
\(419\) | −2.95132 | −0.144182 | −0.0720908 | − | 0.997398i | \(-0.522967\pi\) | ||||
−0.0720908 | + | 0.997398i | \(0.522967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.04747 | − | 2.56507i | 0.343472 | − | 0.125014i | −0.164524 | − | 0.986373i | \(-0.552609\pi\) |
0.507996 | + | 0.861359i | \(0.330386\pi\) | |||||||
\(422\) | 3.38477 | + | 19.1960i | 0.164768 | + | 0.934445i | ||||
\(423\) | 8.70091 | − | 49.3453i | 0.423053 | − | 2.39925i | ||||
\(424\) | 6.03387 | + | 2.19615i | 0.293031 | + | 0.106654i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.68583 | − | 9.84814i | 0.275479 | − | 0.477144i | ||||
\(427\) | 0.434617 | − | 0.364687i | 0.0210326 | − | 0.0176484i | ||||
\(428\) | −4.36895 | + | 3.66598i | −0.211181 | + | 0.177202i | ||||
\(429\) | 13.9590 | − | 24.1777i | 0.673948 | − | 1.16731i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.6407 | + | 8.24053i | 1.09056 | + | 0.396933i | 0.823829 | − | 0.566838i | \(-0.191833\pi\) |
0.266734 | + | 0.963770i | \(0.414056\pi\) | |||||||
\(432\) | 0.696214 | − | 3.94843i | 0.0334966 | − | 0.189969i | ||||
\(433\) | −6.14426 | − | 34.8458i | −0.295274 | − | 1.67458i | −0.666086 | − | 0.745875i | \(-0.732032\pi\) |
0.370812 | − | 0.928708i | \(-0.379080\pi\) | |||||||
\(434\) | 8.54636 | − | 3.11062i | 0.410238 | − | 0.149315i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.793109 | 0.0379830 | ||||||||
\(437\) | −12.7562 | − | 1.37839i | −0.610210 | − | 0.0659375i | ||||
\(438\) | 42.1122 | 2.01220 | ||||||||
\(439\) | 18.2221 | + | 15.2901i | 0.869692 | + | 0.729758i | 0.964033 | − | 0.265782i | \(-0.0856300\pi\) |
−0.0943411 | + | 0.995540i | \(0.530074\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.88792 | − | 10.7069i | −0.0899011 | − | 0.509855i | ||||
\(442\) | −3.53615 | + | 20.0545i | −0.168197 | + | 0.953895i | ||||
\(443\) | −12.8752 | − | 4.68618i | −0.611718 | − | 0.222647i | 0.0175367 | − | 0.999846i | \(-0.494418\pi\) |
−0.629255 | + | 0.777199i | \(0.716640\pi\) | |||||||
\(444\) | 4.77731 | + | 8.27454i | 0.226721 | + | 0.392692i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.87411 | − | 1.57257i | 0.0887418 | − | 0.0744632i | ||||
\(447\) | 47.1303 | − | 39.5470i | 2.22918 | − | 1.87051i | ||||
\(448\) | 1.06844 | − | 1.85059i | 0.0504790 | − | 0.0874321i | ||||
\(449\) | −7.58152 | − | 13.1316i | −0.357794 | − | 0.619717i | 0.629798 | − | 0.776759i | \(-0.283138\pi\) |
−0.987592 | + | 0.157042i | \(0.949804\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.505000 | − | 2.86400i | 0.0237795 | − | 0.134860i | ||||
\(452\) | 0.865816 | + | 4.91029i | 0.0407246 | + | 0.230961i | ||||
\(453\) | −58.1489 | + | 21.1645i | −2.73207 | + | 0.994393i | ||||
\(454\) | −14.7310 | − | 12.3608i | −0.691360 | − | 0.580120i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.6904 | + | 5.25277i | 0.500626 | + | 0.245983i | ||||
\(457\) | −33.5768 | −1.57066 | −0.785329 | − | 0.619079i | \(-0.787506\pi\) | ||||
−0.785329 | + | 0.619079i | \(0.787506\pi\) | |||||||
\(458\) | −15.6174 | − | 13.1046i | −0.729755 | − | 0.612337i | ||||
\(459\) | −13.9166 | + | 5.06522i | −0.649570 | + | 0.236424i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.57133 | − | 25.9253i | 0.212908 | − | 1.20746i | −0.671591 | − | 0.740922i | \(-0.734389\pi\) |
0.884500 | − | 0.466541i | \(-0.154500\pi\) | |||||||
\(462\) | 10.1687 | + | 3.70109i | 0.473089 | + | 0.172190i | ||||
\(463\) | 5.27461 | + | 9.13589i | 0.245132 | + | 0.424581i | 0.962169 | − | 0.272454i | \(-0.0878354\pi\) |
−0.717037 | + | 0.697035i | \(0.754502\pi\) | |||||||
\(464\) | 3.50501 | − | 6.07085i | 0.162716 | − | 0.281832i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.44942 | − | 5.41170i | 0.298763 | − | 0.250692i | ||||
\(467\) | 15.2584 | − | 26.4283i | 0.706074 | − | 1.22296i | −0.260229 | − | 0.965547i | \(-0.583798\pi\) |
0.966303 | − | 0.257408i | \(-0.0828686\pi\) | |||||||
\(468\) | −12.3138 | − | 21.3282i | −0.569207 | − | 0.985895i | ||||
\(469\) | 29.6696 | + | 10.7989i | 1.37002 | + | 0.498645i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.06313 | + | 40.0570i | 0.325452 | + | 1.84573i | ||||
\(472\) | 13.2735 | − | 4.83117i | 0.610964 | − | 0.222373i | ||||
\(473\) | −3.30770 | − | 2.77549i | −0.152088 | − | 0.127617i | ||||
\(474\) | 7.87374 | 0.361653 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.89321 | −0.361784 | ||||||||
\(477\) | 21.9736 | + | 18.4380i | 1.00610 | + | 0.844219i | ||||
\(478\) | −12.4096 | + | 4.51672i | −0.567601 | + | 0.206590i | ||||
\(479\) | 0.664874 | + | 3.77069i | 0.0303789 | + | 0.172287i | 0.996222 | − | 0.0868390i | \(-0.0276766\pi\) |
−0.965843 | + | 0.259126i | \(0.916565\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.1137 | + | 6.59284i | 0.825912 | + | 0.300607i | ||||
\(482\) | −3.52810 | − | 6.11085i | −0.160700 | − | 0.278341i | ||||
\(483\) | −8.59395 | + | 14.8852i | −0.391038 | + | 0.677298i | ||||
\(484\) | −5.79566 | + | 4.86314i | −0.263439 | + | 0.221052i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.35551 | + | 16.2042i | −0.424375 | + | 0.735039i | ||||
\(487\) | −17.7218 | − | 30.6951i | −0.803052 | − | 1.39093i | −0.917598 | − | 0.397509i | \(-0.869875\pi\) |
0.114546 | − | 0.993418i | \(-0.463459\pi\) | |||||||
\(488\) | −0.249493 | − | 0.0908082i | −0.0112940 | − | 0.00411069i | ||||
\(489\) | −5.24990 | + | 29.7737i | −0.237409 | + | 1.34641i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.02415 | + | 2.92055i | −0.362125 | + | 0.131803i | −0.516673 | − | 0.856183i | \(-0.672830\pi\) |
0.154549 | + | 0.987985i | \(0.450608\pi\) | |||||||
\(492\) | −3.28500 | − | 2.75644i | −0.148099 | − | 0.124270i | ||||
\(493\) | −25.8936 | −1.16619 | ||||||||
\(494\) | 23.3336 | − | 5.74541i | 1.04983 | − | 0.258498i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.26039 | − | 2.73579i | −0.146396 | − | 0.122841i | ||||
\(497\) | 8.35621 | − | 3.04141i | 0.374827 | − | 0.136426i | ||||
\(498\) | 6.65219 | + | 37.7265i | 0.298092 | + | 1.69056i | ||||
\(499\) | 6.45368 | − | 36.6007i | 0.288907 | − | 1.63847i | −0.402081 | − | 0.915604i | \(-0.631713\pi\) |
0.690988 | − | 0.722866i | \(-0.257176\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26.9465 | + | 46.6726i | 1.20388 | + | 2.08518i | ||||
\(502\) | −1.16679 | + | 2.02094i | −0.0520765 | + | 0.0901991i | ||||
\(503\) | 16.7933 | − | 14.0913i | 0.748778 | − | 0.628299i | −0.186402 | − | 0.982474i | \(-0.559683\pi\) |
0.935179 | + | 0.354175i | \(0.115238\pi\) | |||||||
\(504\) | 7.31257 | − | 6.13598i | 0.325728 | − | 0.273318i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.72743 | + | 4.72404i | 0.121249 | + | 0.210009i | ||||
\(507\) | −44.6620 | − | 16.2556i | −1.98351 | − | 0.721939i | ||||
\(508\) | 2.69403 | − | 15.2786i | 0.119528 | − | 0.677878i | ||||
\(509\) | −1.71368 | − | 9.71877i | −0.0759576 | − | 0.430777i | −0.998944 | − | 0.0459444i | \(-0.985370\pi\) |
0.922986 | − | 0.384833i | \(-0.125741\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.2268 | + | 21.1678i | 1.11597 | + | 0.936408i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 12.1033 | + | 12.6068i | 0.534374 | + | 0.556603i | ||||
\(514\) | −5.54056 | −0.244384 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.98298 | + | 2.17763i | −0.263386 | + | 0.0958647i | ||||
\(517\) | −3.60950 | − | 20.4705i | −0.158746 | − | 0.900291i | ||||
\(518\) | −1.29743 | + | 7.35809i | −0.0570058 | + | 0.323296i | ||||
\(519\) | 15.5554 | + | 5.66170i | 0.682805 | + | 0.248521i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.86829 | − | 4.96802i | 0.125662 | − | 0.217653i | −0.796330 | − | 0.604863i | \(-0.793228\pi\) |
0.921991 | + | 0.387210i | \(0.126561\pi\) | |||||||
\(522\) | 23.9889 | − | 20.1290i | 1.04996 | − | 0.881024i | ||||
\(523\) | −20.4665 | + | 17.1734i | −0.894937 | + | 0.750941i | −0.969194 | − | 0.246298i | \(-0.920786\pi\) |
0.0742573 | + | 0.997239i | \(0.476341\pi\) | |||||||
\(524\) | −11.0260 | + | 19.0976i | −0.481674 | + | 0.834283i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.66651 | + | 0.606559i | 0.0726632 | + | 0.0264472i | ||||
\(527\) | −2.72998 | + | 15.4825i | −0.118920 | + | 0.674428i | ||||
\(528\) | −0.879364 | − | 4.98712i | −0.0382694 | − | 0.217037i | ||||
\(529\) | 13.4713 | − | 4.90314i | 0.585707 | − | 0.213180i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 63.1012 | 2.73836 | ||||||||
\(532\) | 3.76366 | + | 8.52018i | 0.163175 | + | 0.369397i | ||||
\(533\) | −8.65143 | −0.374735 | ||||||||
\(534\) | −4.14350 | − | 3.47681i | −0.179307 | − | 0.150456i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.56577 | − | 14.5512i | −0.110824 | − | 0.628515i | ||||
\(537\) | −0.593190 | + | 3.36415i | −0.0255980 | + | 0.145174i | ||||
\(538\) | −14.9736 | − | 5.44995i | −0.645558 | − | 0.234964i | ||||
\(539\) | −2.25510 | − | 3.90595i | −0.0971342 | − | 0.168241i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.7434 | − | 19.9231i | 1.02081 | − | 0.856562i | 0.0310814 | − | 0.999517i | \(-0.490105\pi\) |
0.989729 | + | 0.142955i | \(0.0456604\pi\) | |||||||
\(542\) | −10.8012 | + | 9.06330i | −0.463952 | + | 0.389302i | ||||
\(543\) | −21.5735 | + | 37.3664i | −0.925807 | + | 1.60355i | ||||
\(544\) | 1.84690 | + | 3.19893i | 0.0791853 | + | 0.137153i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.59005 | − | 31.7027i | 0.239232 | − | 1.35675i | ||||
\(547\) | 3.02131 | + | 17.1347i | 0.129182 | + | 0.732627i | 0.978736 | + | 0.205125i | \(0.0657601\pi\) |
−0.849554 | + | 0.527502i | \(0.823129\pi\) | |||||||
\(548\) | −13.1019 | + | 4.76868i | −0.559683 | + | 0.203708i | ||||
\(549\) | −0.908582 | − | 0.762391i | −0.0387773 | − | 0.0325380i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.3467 | + | 27.9504i | 0.525986 | + | 1.19073i | ||||
\(552\) | 8.04347 | 0.342353 | ||||||||
\(553\) | 4.71667 | + | 3.95775i | 0.200573 | + | 0.168301i | ||||
\(554\) | 20.9230 | − | 7.61536i | 0.888934 | − | 0.323546i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.14081 | − | 12.1412i | 0.0907907 | − | 0.514900i | ||||
\(557\) | −11.1000 | − | 4.04009i | −0.470324 | − | 0.171184i | 0.0959752 | − | 0.995384i | \(-0.469403\pi\) |
−0.566299 | + | 0.824200i | \(0.691625\pi\) | |||||||
\(558\) | −9.50654 | − | 16.4658i | −0.402444 | − | 0.697053i | ||||
\(559\) | −6.42257 | + | 11.1242i | −0.271646 | + | 0.470504i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.3293 | + | 12.0238i | −0.604986 | + | 0.507643i | ||||
\(562\) | −3.65388 | + | 6.32870i | −0.154130 | + | 0.266960i | ||||
\(563\) | 15.6982 | + | 27.1901i | 0.661600 | + | 1.14592i | 0.980195 | + | 0.198034i | \(0.0634556\pi\) |
−0.318595 | + | 0.947891i | \(0.603211\pi\) | |||||||
\(564\) | −28.8020 | − | 10.4831i | −1.21278 | − | 0.441417i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.78983 | + | 10.1506i | 0.0752323 | + | 0.426663i | ||||
\(567\) | −4.91087 | + | 1.78741i | −0.206237 | + | 0.0750642i | ||||
\(568\) | −3.18785 | − | 2.67493i | −0.133759 | − | 0.112237i | ||||
\(569\) | 3.95114 | 0.165640 | 0.0828202 | − | 0.996565i | \(-0.473607\pi\) | ||||
0.0828202 | + | 0.996565i | \(0.473607\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.18380 | 0.0913891 | 0.0456946 | − | 0.998955i | \(-0.485450\pi\) | ||||
0.0456946 | + | 0.998955i | \(0.485450\pi\) | |||||||
\(572\) | −7.82636 | − | 6.56709i | −0.327236 | − | 0.274584i | ||||
\(573\) | 5.26674 | − | 1.91694i | 0.220021 | − | 0.0800812i | ||||
\(574\) | −0.582306 | − | 3.30242i | −0.0243050 | − | 0.137840i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.19781 | − | 1.52788i | −0.174909 | − | 0.0636615i | ||||
\(577\) | 6.51747 | + | 11.2886i | 0.271326 | + | 0.469950i | 0.969202 | − | 0.246269i | \(-0.0792046\pi\) |
−0.697876 | + | 0.716219i | \(0.745871\pi\) | |||||||
\(578\) | −1.67790 | + | 2.90621i | −0.0697916 | + | 0.120883i | ||||
\(579\) | −1.72256 | + | 1.44540i | −0.0715872 | + | 0.0600688i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.9784 | + | 25.9433i | −0.621408 | + | 1.07631i | ||||
\(582\) | 14.7699 | + | 25.5821i | 0.612230 | + | 1.06041i | ||||
\(583\) | 11.1819 | + | 4.06987i | 0.463106 | + | 0.168557i | ||||
\(584\) | 2.67608 | − | 15.1768i | 0.110737 | − | 0.628020i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.7884 | + | 10.4781i | −1.18924 | + | 0.432847i | ||||
\(587\) | 29.6918 | + | 24.9144i | 1.22551 | + | 1.02833i | 0.998517 | + | 0.0544318i | \(0.0173348\pi\) |
0.226996 | + | 0.973896i | \(0.427110\pi\) | |||||||
\(588\) | −6.65054 | −0.274263 | ||||||||
\(589\) | 18.0140 | − | 4.43558i | 0.742255 | − | 0.182765i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.5891 | − | 22.3109i | −1.09373 | − | 0.917750i | ||||
\(592\) | 3.28564 | − | 1.19588i | 0.135039 | − | 0.0491502i | ||||
\(593\) | 3.02318 | + | 17.1453i | 0.124147 | + | 0.704073i | 0.981811 | + | 0.189862i | \(0.0608040\pi\) |
−0.857664 | + | 0.514211i | \(0.828085\pi\) | |||||||
\(594\) | 1.29022 | − | 7.31717i | 0.0529382 | − | 0.300227i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.2574 | − | 19.4983i | −0.461119 | − | 0.798682i | ||||
\(597\) | 6.98031 | − | 12.0903i | 0.285685 | − | 0.494821i | ||||
\(598\) | 12.4310 | − | 10.4308i | 0.508339 | − | 0.426547i | ||||
\(599\) | −24.6574 | + | 20.6900i | −1.00747 | + | 0.845370i | −0.988002 | − | 0.154440i | \(-0.950643\pi\) |
−0.0194709 | + | 0.999810i | \(0.506198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.1105 | − | 31.3683i | −0.738742 | − | 1.27954i | −0.953062 | − | 0.302775i | \(-0.902087\pi\) |
0.214321 | − | 0.976763i | \(-0.431246\pi\) | |||||||
\(602\) | −4.67862 | − | 1.70288i | −0.190686 | − | 0.0694042i | ||||
\(603\) | 11.4618 | − | 65.0032i | 0.466761 | − | 2.64714i | ||||
\(604\) | 3.93230 | + | 22.3012i | 0.160003 | + | 0.907422i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −20.8830 | − | 17.5229i | −0.848314 | − | 0.711820i | ||||
\(607\) | −30.3654 | −1.23250 | −0.616248 | − | 0.787552i | \(-0.711348\pi\) | ||||
−0.616248 | + | 0.787552i | \(0.711348\pi\) | |||||||
\(608\) | 2.57238 | − | 3.51893i | 0.104324 | − | 0.142711i | ||||
\(609\) | 40.9334 | 1.65870 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −58.1072 | + | 21.1493i | −2.35076 | + | 0.855608i | ||||
\(612\) | 2.86537 | + | 16.2503i | 0.115826 | + | 0.656881i | ||||
\(613\) | 3.96373 | − | 22.4794i | 0.160094 | − | 0.907936i | −0.793886 | − | 0.608066i | \(-0.791946\pi\) |
0.953980 | − | 0.299870i | \(-0.0969434\pi\) | |||||||
\(614\) | 7.50580 | + | 2.73189i | 0.302910 | + | 0.110250i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.98002 | − | 3.42949i | 0.0797771 | − | 0.138178i | ||||
\(617\) | −30.4152 | + | 25.5214i | −1.22447 | + | 1.02745i | −0.225890 | + | 0.974153i | \(0.572529\pi\) |
−0.998579 | + | 0.0532981i | \(0.983027\pi\) | |||||||
\(618\) | −18.3691 | + | 15.4135i | −0.738915 | + | 0.620023i | ||||
\(619\) | −19.6707 | + | 34.0707i | −0.790633 | + | 1.36942i | 0.134943 | + | 0.990853i | \(0.456915\pi\) |
−0.925576 | + | 0.378562i | \(0.876419\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.0898 | + | 4.03635i | 0.445017 | + | 0.161973i | ||||
\(622\) | 4.62442 | − | 26.2264i | 0.185422 | − | 1.05158i | ||||
\(623\) | −0.734486 | − | 4.16548i | −0.0294266 | − | 0.166886i | ||||
\(624\) | −14.1564 | + | 5.15249i | −0.566708 | + | 0.206265i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.66333 | −0.306288 | ||||||||
\(627\) | 19.8114 | + | 9.73436i | 0.791190 | + | 0.388753i | ||||
\(628\) | 14.8850 | 0.593974 | ||||||||
\(629\) | −9.89378 | − | 8.30186i | −0.394491 | − | 0.331017i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.418513 | + | 2.37351i | 0.0166607 | + | 0.0944878i | 0.992004 | − | 0.126204i | \(-0.0402795\pi\) |
−0.975344 | + | 0.220692i | \(0.929168\pi\) | |||||||
\(632\) | 0.500348 | − | 2.83761i | 0.0199028 | − | 0.112874i | ||||
\(633\) | 50.0522 | + | 18.2175i | 1.98940 | + | 0.724082i | ||||
\(634\) | 1.48304 | + | 2.56871i | 0.0588992 | + | 0.102016i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 13.4414 | − | 11.2786i | 0.532985 | − | 0.447227i | ||||
\(637\) | −10.2782 | + | 8.62445i | −0.407238 | + | 0.341713i | ||||
\(638\) | 6.49543 | − | 11.2504i | 0.257157 | − | 0.445408i | ||||
\(639\) | −9.29503 | − | 16.0995i | −0.367706 | − | 0.636885i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.88094 | + | 16.3386i | −0.113790 | + | 0.645337i | 0.873552 | + | 0.486731i | \(0.161811\pi\) |
−0.987342 | + | 0.158606i | \(0.949300\pi\) | |||||||
\(642\) | 2.70628 | + | 15.3481i | 0.106808 | + | 0.605740i | ||||
\(643\) | 32.3683 | − | 11.7811i | 1.27648 | − | 0.464601i | 0.387214 | − | 0.921990i | \(-0.373438\pi\) |
0.889267 | + | 0.457389i | \(0.151215\pi\) | |||||||
\(644\) | 4.81834 | + | 4.04307i | 0.189869 | + | 0.159319i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.0077 | − | 1.72975i | −0.629816 | − | 0.0680561i | ||||
\(647\) | 5.97186 | 0.234778 | 0.117389 | − | 0.993086i | \(-0.462548\pi\) | ||||
0.117389 | + | 0.993086i | \(0.462548\pi\) | |||||||
\(648\) | 1.87347 | + | 1.57203i | 0.0735969 | + | 0.0617551i | ||||
\(649\) | 24.5983 | − | 8.95307i | 0.965570 | − | 0.351439i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.31564 | − | 24.4752i | 0.169143 | − | 0.959258i | ||||
\(652\) | 10.3965 | + | 3.78402i | 0.407159 | + | 0.148194i | ||||
\(653\) | −4.22812 | − | 7.32332i | −0.165459 | − | 0.286584i | 0.771359 | − | 0.636400i | \(-0.219577\pi\) |
−0.936818 | + | 0.349816i | \(0.886244\pi\) | |||||||
\(654\) | 1.08363 | − | 1.87691i | 0.0423734 | − | 0.0733928i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.20214 | + | 1.00872i | −0.0469357 | + | 0.0393838i | ||||
\(657\) | 34.4220 | − | 59.6206i | 1.34293 | − | 2.32602i | ||||
\(658\) | −11.9841 | − | 20.7571i | −0.467191 | − | 0.809198i | ||||
\(659\) | 21.5906 | + | 7.85832i | 0.841049 | + | 0.306117i | 0.726385 | − | 0.687288i | \(-0.241199\pi\) |
0.114664 | + | 0.993404i | \(0.463421\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.06768 | + | 23.0690i | 0.158214 | + | 0.897278i | 0.955788 | + | 0.294057i | \(0.0950054\pi\) |
−0.797574 | + | 0.603222i | \(0.793883\pi\) | |||||||
\(662\) | 2.49995 | − | 0.909909i | 0.0971635 | − | 0.0353646i | ||||
\(663\) | 42.6279 | + | 35.7690i | 1.65553 | + | 1.38915i | ||||
\(664\) | 14.0189 | 0.544040 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.6196 | 0.605249 | ||||||||
\(667\) | 15.8065 | + | 13.2633i | 0.612032 | + | 0.513556i | ||||
\(668\) | 18.5327 | − | 6.74534i | 0.717051 | − | 0.260985i | ||||
\(669\) | −1.16089 | − | 6.58374i | −0.0448826 | − | 0.254542i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.462358 | − | 0.168285i | −0.0178491 | − | 0.00649655i | ||||
\(672\) | −2.91964 | − | 5.05696i | −0.112627 | − | 0.195076i | ||||
\(673\) | 0.0188863 | − | 0.0327120i | 0.000728012 | − | 0.00126095i | −0.865661 | − | 0.500630i | \(-0.833102\pi\) |
0.866389 | + | 0.499369i | \(0.166435\pi\) | |||||||
\(674\) | 23.9959 | − | 20.1349i | 0.924287 | − | 0.775569i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.69647 | + | 15.0627i | −0.334480 | + | 0.579336i | ||||
\(677\) | 15.5421 | + | 26.9197i | 0.597332 | + | 1.03461i | 0.993213 | + | 0.116307i | \(0.0371057\pi\) |
−0.395882 | + | 0.918302i | \(0.629561\pi\) | |||||||
\(678\) | 12.8033 | + | 4.66001i | 0.491706 | + | 0.178966i | ||||
\(679\) | −4.01122 | + | 22.7488i | −0.153937 | + | 0.873018i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −49.3791 | + | 17.9725i | −1.89221 | + | 0.688709i | ||||
\(682\) | −6.04212 | − | 5.06994i | −0.231365 | − | 0.194138i | ||||
\(683\) | −22.0437 | −0.843481 | −0.421740 | − | 0.906717i | \(-0.638581\pi\) | ||||
−0.421740 | + | 0.906717i | \(0.638581\pi\) | |||||||
\(684\) | 16.1749 | − | 10.8415i | 0.618461 | − | 0.414535i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.4425 | − | 12.9578i | −0.589598 | − | 0.494732i | ||||
\(687\) | −52.3505 | + | 19.0540i | −1.99730 | + | 0.726957i | ||||
\(688\) | 0.404597 | + | 2.29458i | 0.0154251 | + | 0.0874802i | ||||
\(689\) | 6.14705 | − | 34.8616i | 0.234184 | − | 1.32812i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.10144 | − | 7.10391i | −0.156026 | − | 0.270245i | 0.777406 | − | 0.628999i | \(-0.216535\pi\) |
−0.933432 | + | 0.358754i | \(0.883202\pi\) | |||||||
\(692\) | 3.02890 | − | 5.24622i | 0.115142 | − | 0.199431i | ||||
\(693\) | 13.5516 | − | 11.3711i | 0.514781 | − | 0.431953i | ||||
\(694\) | −8.13364 | + | 6.82494i | −0.308749 | + | 0.259071i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.57786 | − | 16.5893i | −0.363048 | − | 0.628817i | ||||
\(697\) | 5.44705 | + | 1.98256i | 0.206322 | + | 0.0750950i | ||||
\(698\) | −6.41749 | + | 36.3954i | −0.242906 | + | 1.37759i | ||||
\(699\) | −3.99499 | − | 22.6567i | −0.151104 | − | 0.856956i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.73064 | + | 2.29128i | 0.103135 | + | 0.0865405i | 0.692897 | − | 0.721037i | \(-0.256334\pi\) |
−0.589762 | + | 0.807577i | \(0.700778\pi\) | |||||||
\(702\) | −22.1034 | −0.834239 | ||||||||
\(703\) | −4.24372 | + | 14.6382i | −0.160055 | + | 0.552089i | ||||
\(704\) | −1.85319 | −0.0698446 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28.9940 | − | 10.5530i | 1.09120 | − | 0.397166i | ||||
\(707\) | −3.70177 | − | 20.9938i | −0.139219 | − | 0.789553i | ||||
\(708\) | 6.70271 | − | 38.0130i | 0.251903 | − | 1.42861i | ||||
\(709\) | −16.7368 | − | 6.09168i | −0.628562 | − | 0.228778i | 0.00804307 | − | 0.999968i | \(-0.497440\pi\) |
−0.636605 | + | 0.771190i | \(0.719662\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.43589 | − | 11.1473i | 0.241365 | − | 0.418056i | ||||
\(712\) | −1.51631 | + | 1.27233i | −0.0568261 | + | 0.0476827i | ||||
\(713\) | 9.59696 | − | 8.05281i | 0.359409 | − | 0.301580i | ||||
\(714\) | −10.7846 | + | 18.6794i | −0.403602 | + | 0.699060i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.17471 | + | 0.427559i | 0.0439009 | + | 0.0159786i | ||||
\(717\) | −6.26644 | + | 35.5387i | −0.234024 | + | 1.32722i | ||||
\(718\) | 1.76076 | + | 9.98574i | 0.0657108 | + | 0.372664i | ||||
\(719\) | −17.0854 | + | 6.21856i | −0.637176 | + | 0.231913i | −0.640352 | − | 0.768082i | \(-0.721211\pi\) |
0.00317562 | + | 0.999995i | \(0.498989\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.7515 | −0.698341 | ||||||||
\(722\) | 5.76570 | + | 18.1041i | 0.214577 | + | 0.673763i | ||||
\(723\) | −19.2819 | −0.717102 | ||||||||
\(724\) | 12.0955 | + | 10.1494i | 0.449527 | + | 0.377198i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.59003 | + | 20.3601i | 0.133239 | + | 0.755634i | ||||
\(727\) | 1.47717 | − | 8.37743i | 0.0547851 | − | 0.310702i | −0.945085 | − | 0.326825i | \(-0.894021\pi\) |
0.999870 | + | 0.0161233i | \(0.00513242\pi\) | |||||||
\(728\) | −11.0701 | − | 4.02919i | −0.410285 | − | 0.149332i | ||||
\(729\) | 21.8966 | + | 37.9260i | 0.810985 | + | 1.40467i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.59296 | − | 5.53215i | 0.243849 | − | 0.204614i | ||||
\(732\) | −0.555785 | + | 0.466359i | −0.0205424 | + | 0.0172371i | ||||
\(733\) | −25.4955 | + | 44.1595i | −0.941698 | + | 1.63107i | −0.179468 | + | 0.983764i | \(0.557438\pi\) |
−0.762230 | + | 0.647306i | \(0.775896\pi\) | |||||||
\(734\) | −5.88751 | − | 10.1975i | −0.217312 | − | 0.376395i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.511133 | − | 2.89878i | 0.0188406 | − | 0.106851i | ||||
\(737\) | −4.75484 | − | 26.9661i | −0.175147 | − | 0.993307i | ||||
\(738\) | −6.58755 | + | 2.39767i | −0.242491 | + | 0.0882596i | ||||
\(739\) | −1.19013 | − | 0.998640i | −0.0437798 | − | 0.0367356i | 0.620635 | − | 0.784099i | \(-0.286875\pi\) |
−0.664415 | + | 0.747364i | \(0.731319\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.2843 | − | 63.0694i | 0.671691 | − | 2.31691i | ||||
\(742\) | 13.7211 | 0.503718 | ||||||||
\(743\) | 7.59707 | + | 6.37470i | 0.278710 | + | 0.233865i | 0.771417 | − | 0.636330i | \(-0.219548\pi\) |
−0.492707 | + | 0.870195i | \(0.663993\pi\) | |||||||
\(744\) | −10.9290 | + | 3.97784i | −0.400677 | + | 0.145835i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.39869 | + | 19.2749i | −0.124435 | + | 0.705704i | ||||
\(747\) | 58.8488 | + | 21.4192i | 2.15317 | + | 0.783688i | ||||
\(748\) | 3.42266 | + | 5.92821i | 0.125145 | + | 0.216757i | ||||
\(749\) | −6.09358 | + | 10.5544i | −0.222655 | + | 0.385649i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.53634 | + | 2.96734i | −0.129043 | + | 0.108280i | −0.705025 | − | 0.709183i | \(-0.749064\pi\) |
0.575982 | + | 0.817462i | \(0.304620\pi\) | |||||||
\(752\) | −5.60825 | + | 9.71378i | −0.204512 | + | 0.354225i | ||||
\(753\) | 3.18840 | + | 5.52247i | 0.116192 | + | 0.201250i | ||||
\(754\) | −36.3154 | − | 13.2177i | −1.32253 | − | 0.481362i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.48772 | − | 8.43730i | −0.0541080 | − | 0.306862i | ||||
\(757\) | −21.8372 | + | 7.94810i | −0.793688 | + | 0.288879i | −0.706868 | − | 0.707345i | \(-0.749893\pi\) |
−0.0868196 | + | 0.996224i | \(0.527670\pi\) | |||||||
\(758\) | −14.6238 | − | 12.2709i | −0.531162 | − | 0.445698i | ||||
\(759\) | 14.9060 | 0.541055 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.6042 | −0.928152 | −0.464076 | − | 0.885795i | \(-0.653614\pi\) | ||||
−0.464076 | + | 0.885795i | \(0.653614\pi\) | |||||||
\(762\) | −32.4762 | − | 27.2508i | −1.17649 | − | 0.987191i | ||||
\(763\) | 1.59257 | − | 0.579647i | 0.0576548 | − | 0.0209846i | ||||
\(764\) | −0.356162 | − | 2.01989i | −0.0128855 | − | 0.0730771i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.4874 | + | 6.72885i | 0.667975 | + | 0.243123i | ||||
\(767\) | −38.9365 | − | 67.4401i | −1.40592 | − | 2.43512i | ||||
\(768\) | −1.36631 | + | 2.36652i | −0.0493025 | + | 0.0853944i | ||||
\(769\) | 19.0328 | − | 15.9704i | 0.686339 | − | 0.575907i | −0.231512 | − | 0.972832i | \(-0.574367\pi\) |
0.917851 | + | 0.396925i | \(0.129923\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.57012 | + | 13.1118i | −0.272631 | + | 0.472211i | ||||
\(772\) | 0.411445 | + | 0.712643i | 0.0148082 | + | 0.0256486i | ||||
\(773\) | 34.6603 | + | 12.6153i | 1.24664 | + | 0.453741i | 0.879266 | − | 0.476330i | \(-0.158033\pi\) |
0.367378 | + | 0.930072i | \(0.380256\pi\) | |||||||
\(774\) | −1.80742 | + | 10.2504i | −0.0649664 | + | 0.368443i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.1581 | − | 3.69725i | 0.364655 | − | 0.132723i | ||||
\(777\) | 15.6404 | + | 13.1238i | 0.561095 | + | 0.470815i | ||||
\(778\) | 24.0483 | 0.862175 | ||||||||
\(779\) | −0.457233 | − | 6.82505i | −0.0163821 | − | 0.244533i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.90769 | − | 4.95714i | −0.211394 | − | 0.177380i | ||||
\(782\) | −10.2170 | + | 3.71869i | −0.365359 | + | 0.132980i | ||||
\(783\) | −4.88047 | − | 27.6785i | −0.174414 | − | 0.989150i | ||||
\(784\) | −0.422618 | + | 2.39678i | −0.0150935 | + | 0.0855994i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 30.1299 | + | 52.1865i | 1.07470 | + | 1.86143i | ||||
\(787\) | −25.0213 | + | 43.3382i | −0.891914 | + | 1.54484i | −0.0543351 | + | 0.998523i | \(0.517304\pi\) |
−0.837579 | + | 0.546317i | \(0.816029\pi\) | |||||||
\(788\) | −9.73028 | + | 8.16467i | −0.346627 | + | 0.290854i | ||||
\(789\) | 3.71240 | − | 3.11507i | 0.132165 | − | 0.110900i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.32727 | + | 9.22711i | 0.189416 | + | 0.328078i | ||||
\(792\) | −7.77932 | − | 2.83144i | −0.276426 | − | 0.100611i | ||||
\(793\) | −0.254173 | + | 1.44149i | −0.00902596 | + | 0.0511888i | ||||
\(794\) | −0.441252 | − | 2.50246i | −0.0156594 | − | 0.0888091i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.91363 | − | 3.28392i | −0.138715 | − | 0.116396i | ||||
\(797\) | −5.53339 | −0.196003 | −0.0980013 | − | 0.995186i | \(-0.531245\pi\) | ||||
−0.0980013 | + | 0.995186i | \(0.531245\pi\) | |||||||
\(798\) | 25.3055 | + | 2.73444i | 0.895805 | + | 0.0967981i | ||||
\(799\) | 41.4316 | 1.46574 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.30914 | + | 3.02428i | −0.293589 | + | 0.106858i | ||||
\(802\) | −0.257775 | − | 1.46191i | −0.00910234 | − | 0.0516219i | ||||
\(803\) | 4.95928 | − | 28.1254i | 0.175009 | − | 0.992525i | ||||
\(804\) | −37.9413 | − | 13.8095i | −1.33809 | − | 0.487023i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.7320 | + | 20.3204i | −0.413242 | + | 0.715757i | ||||
\(807\) | −33.3560 | + | 27.9890i | −1.17419 | + | 0.985260i | ||||
\(808\) | −7.64212 | + | 6.41250i | −0.268849 | + | 0.225591i | ||||
\(809\) | −6.93364 | + | 12.0094i | −0.243774 | + | 0.422229i | −0.961786 | − | 0.273802i | \(-0.911719\pi\) |
0.718012 | + | 0.696030i | \(0.245052\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.68087 | + | 2.79561i | 0.269712 | + | 0.0981670i | 0.473336 | − | 0.880882i | \(-0.343050\pi\) |
−0.203624 | + | 0.979049i | \(0.565272\pi\) | |||||||
\(812\) | 2.60117 | − | 14.7520i | 0.0912832 | − | 0.517693i | ||||
\(813\) | 6.69065 | + | 37.9446i | 0.234651 | + | 1.33077i | ||||
\(814\) | 6.08890 | − | 2.21618i | 0.213416 | − | 0.0776771i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 10.0938 | 0.353352 | ||||||||
\(817\) | −9.11526 | − | 4.47880i | −0.318902 | − | 0.156693i | ||||
\(818\) | −12.2798 | −0.429355 | ||||||||
\(819\) | −40.3141 | − | 33.8275i | −1.40869 | − | 1.18203i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.69213 | + | 43.6243i | 0.268457 | + | 1.52250i | 0.759006 | + | 0.651083i | \(0.225685\pi\) |
−0.490549 | + | 0.871414i | \(0.663204\pi\) | |||||||
\(822\) | −6.61601 | + | 37.5213i | −0.230760 | + | 1.30871i | ||||
\(823\) | 0.792059 | + | 0.288286i | 0.0276094 | + | 0.0100490i | 0.355788 | − | 0.934567i | \(-0.384213\pi\) |
−0.328179 | + | 0.944616i | \(0.606435\pi\) | |||||||
\(824\) | 4.38758 | + | 7.59952i | 0.152849 | + | 0.264742i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 23.1225 | − | 19.4021i | 0.804534 | − | 0.675084i | ||||
\(827\) | 10.8286 | − | 9.08627i | 0.376547 | − | 0.315961i | −0.434798 | − | 0.900528i | \(-0.643180\pi\) |
0.811345 | + | 0.584567i | \(0.198736\pi\) | |||||||
\(828\) | 6.57462 | − | 11.3876i | 0.228484 | − | 0.395746i | ||||
\(829\) | −23.8392 | − | 41.2907i | −0.827969 | − | 1.43408i | −0.899629 | − | 0.436655i | \(-0.856163\pi\) |
0.0716603 | − | 0.997429i | \(-0.477170\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.5655 | − | 59.9197i | 0.366511 | − | 2.07859i | ||||
\(832\) | 0.957319 | + | 5.42923i | 0.0331891 | + | 0.188225i | ||||
\(833\) | 8.44767 | − | 3.07470i | 0.292695 | − | 0.106532i | ||||
\(834\) | −25.8073 | − | 21.6549i | −0.893632 | − | 0.749847i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.76710 | − | 6.52123i | 0.164874 | − | 0.225541i | ||||
\(837\) | −17.0643 | −0.589828 | ||||||||
\(838\) | 2.26085 | + | 1.89707i | 0.0780996 | + | 0.0655333i | ||||
\(839\) | 0.221512 | − | 0.0806239i | 0.00764746 | − | 0.00278345i | −0.338194 | − | 0.941077i | \(-0.609816\pi\) |
0.345841 | + | 0.938293i | \(0.387594\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.49733 | − | 19.8343i | 0.120598 | − | 0.683943i | ||||
\(842\) | −7.04747 | − | 2.56507i | −0.242872 | − | 0.0883981i | ||||
\(843\) | 9.98466 | + | 17.2939i | 0.343890 | + | 0.595635i | ||||
\(844\) | 9.74604 | − | 16.8806i | 0.335473 | − | 0.581056i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −38.3838 | + | 32.2079i | −1.31966 | + | 1.10733i | ||||
\(847\) | −8.08348 | + | 14.0010i | −0.277752 | + | 0.481080i | ||||
\(848\) | −3.21055 | − | 5.56084i | −0.110251 | − | 0.190960i | ||||
\(849\) | 26.4672 | + | 9.63326i | 0.908350 | + | 0.330613i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.78718 | + | 10.1356i | 0.0612638 | + | 0.347444i | ||||
\(852\) | −10.6859 | + | 3.88933i | −0.366091 | + | 0.133246i | ||||
\(853\) | 2.93138 | + | 2.45972i | 0.100368 | + | 0.0842191i | 0.691591 | − | 0.722289i | \(-0.256910\pi\) |
−0.591223 | + | 0.806508i | \(0.701355\pi\) | |||||||
\(854\) | −0.567352 | −0.0194144 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.70326 | 0.194933 | ||||||||
\(857\) | 9.49966 | + | 7.97116i | 0.324502 | + | 0.272290i | 0.790455 | − | 0.612520i | \(-0.209844\pi\) |
−0.465953 | + | 0.884809i | \(0.654288\pi\) | |||||||
\(858\) | −26.2344 | + | 9.54853i | −0.895627 | + | 0.325982i | ||||
\(859\) | 6.20007 | + | 35.1623i | 0.211544 | + | 1.19972i | 0.886805 | + | 0.462145i | \(0.152920\pi\) |
−0.675261 | + | 0.737579i | \(0.735969\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.61085 | − | 3.13409i | −0.293457 | − | 0.106810i | ||||
\(862\) | −12.0469 | − | 20.8658i | −0.410317 | − | 0.710691i | ||||
\(863\) | 10.2181 | − | 17.6983i | 0.347830 | − | 0.602458i | −0.638034 | − | 0.770008i | \(-0.720252\pi\) |
0.985864 | + | 0.167550i | \(0.0535855\pi\) | |||||||
\(864\) | −3.07133 | + | 2.57715i | −0.104489 | + | 0.0876765i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.6917 | + | 30.6429i | −0.601188 | + | 1.04129i | ||||
\(867\) | 4.58507 | + | 7.94158i | 0.155717 | + | 0.269710i | ||||
\(868\) | −8.54636 | − | 3.11062i | −0.290082 | − | 0.105581i | ||||
\(869\) | 0.927238 | − | 5.25863i | 0.0314544 | − | 0.178387i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −76.5454 | + | 27.8602i | −2.59364 | + | 0.944008i | ||||
\(872\) | −0.607556 | − | 0.509800i | −0.0205745 | − | 0.0172640i | ||||
\(873\) | 48.2907 | 1.63439 | ||||||||
\(874\) | 8.88577 | + | 9.25541i | 0.300566 | + | 0.313069i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −32.2598 | − | 27.0692i | −1.08996 | − | 0.914584i | ||||
\(877\) | 49.5744 | − | 18.0436i | 1.67401 | − | 0.609289i | 0.681539 | − | 0.731782i | \(-0.261311\pi\) |
0.992469 | + | 0.122492i | \(0.0390886\pi\) | |||||||
\(878\) | −4.13061 | − | 23.4258i | −0.139401 | − | 0.790584i | ||||
\(879\) | −14.5372 | + | 82.4447i | −0.490328 | + | 2.78079i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.8483 | − | 27.4500i | −0.533941 | − | 0.924813i | −0.999214 | − | 0.0396459i | \(-0.987377\pi\) |
0.465273 | − | 0.885167i | \(-0.345956\pi\) | |||||||
\(882\) | −5.43606 | + | 9.41553i | −0.183042 | + | 0.317037i | ||||
\(883\) | −32.8546 | + | 27.5683i | −1.10564 | + | 0.927746i | −0.997792 | − | 0.0664209i | \(-0.978842\pi\) |
−0.107853 | + | 0.994167i | \(0.534398\pi\) | |||||||
\(884\) | 15.5996 | − | 13.0896i | 0.524672 | − | 0.440252i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.85074 | + | 11.8658i | 0.230155 | + | 0.398640i | ||||
\(887\) | 27.7243 | + | 10.0908i | 0.930889 | + | 0.338816i | 0.762562 | − | 0.646915i | \(-0.223941\pi\) |
0.168327 | + | 0.985731i | \(0.446163\pi\) | |||||||
\(888\) | 1.65914 | − | 9.40946i | 0.0556772 | − | 0.315761i | ||||
\(889\) | −5.75681 | − | 32.6485i | −0.193077 | − | 1.09499i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.47189 | + | 2.91326i | 0.116313 | + | 0.0975980i | ||||
\(892\) | −2.44648 | −0.0819142 | ||||||||
\(893\) | −19.7555 | − | 44.7226i | −0.661093 | − | 1.49658i | ||||
\(894\) | −61.5242 | −2.05768 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.00801 | + | 0.730855i | −0.0670828 | + | 0.0244161i | ||||
\(897\) | −7.70016 | − | 43.6698i | −0.257101 | − | 1.45809i | ||||
\(898\) | −2.63303 | + | 14.9327i | −0.0878655 | + | 0.498310i | ||||
\(899\) | −28.0363 | − | 10.2044i | −0.935063 | − | 0.340335i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.8592 | + | 20.5407i | −0.395086 | + | 0.684309i | ||||
\(902\) | −2.22779 | + | 1.86934i | −0.0741774 | + | 0.0622422i | ||||
\(903\) | −10.4223 | + | 8.74538i | −0.346834 | + | 0.291028i | ||||
\(904\) | 2.49302 | − | 4.31803i | 0.0829166 | − | 0.143616i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 58.1489 | + | 21.1645i | 1.93187 | + | 0.703142i | ||||
\(907\) | 4.82761 | − | 27.3787i | 0.160298 | − | 0.909095i | −0.793483 | − | 0.608593i | \(-0.791734\pi\) |
0.953781 | − | 0.300503i | \(-0.0971545\pi\) | |||||||
\(908\) | 3.33925 | + | 18.9378i | 0.110817 | + | 0.628473i | ||||
\(909\) | −41.8777 | + | 15.2422i | −1.38899 | + | 0.505553i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.5154 | 0.480915 | 0.240458 | − | 0.970660i | \(-0.422703\pi\) | ||||
0.240458 | + | 0.970660i | \(0.422703\pi\) | |||||||
\(912\) | −4.81294 | − | 10.8955i | −0.159372 | − | 0.360787i | ||||
\(913\) | 25.9797 | 0.859803 | ||||||||
\(914\) | 25.7213 | + | 21.5828i | 0.850786 | + | 0.713894i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.54019 | + | 20.0774i | 0.116971 | + | 0.663376i | ||||
\(917\) | −8.18273 | + | 46.4066i | −0.270218 | + | 1.53248i | ||||
\(918\) | 13.9166 | + | 5.06522i | 0.459315 | + | 0.167177i | ||||
\(919\) | −5.09200 | − | 8.81961i | −0.167970 | − | 0.290932i | 0.769736 | − | 0.638362i | \(-0.220388\pi\) |
−0.937706 | + | 0.347430i | \(0.887054\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.7203 | − | 14.0300i | 0.550953 | − | 0.462305i | ||||
\(922\) | −20.1663 | + | 16.9216i | −0.664142 | + | 0.557282i | ||||
\(923\) | −11.4710 | + | 19.8683i | −0.377572 | + | 0.653974i | ||||
\(924\) | −5.41063 | − | 9.37149i | −0.177997 | − | 0.308299i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.83185 | − | 10.3890i | 0.0601984 | − | 0.341402i | ||||
\(927\) | 6.80710 | + | 38.6050i | 0.223575 | + | 1.26795i | ||||
\(928\) | −6.58726 | + | 2.39757i | −0.216237 | + | 0.0787040i | ||||
\(929\) | −6.91896 | − | 5.80570i | −0.227004 | − | 0.190479i | 0.522191 | − | 0.852829i | \(-0.325115\pi\) |
−0.749195 | + | 0.662350i | \(0.769559\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.34697 | − | 7.65260i | −0.240787 | − | 0.250804i | ||||
\(932\) | −8.41911 | −0.275777 | ||||||||
\(933\) | −55.7469 | − | 46.7772i | −1.82507 | − | 1.53142i | ||||
\(934\) | −28.6764 | + | 10.4373i | −0.938320 | + | 0.341520i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.27655 | + | 24.2535i | −0.139783 | + | 0.792751i | ||||
\(937\) | −36.9882 | − | 13.4626i | −1.20835 | − | 0.439804i | −0.342219 | − | 0.939620i | \(-0.611179\pi\) |
−0.866131 | + | 0.499816i | \(0.833401\pi\) | |||||||
\(938\) | −15.7869 | − | 27.3437i | −0.515460 | − | 0.892802i | ||||
\(939\) | −10.4705 | + | 18.1354i | −0.341691 | + | 0.591827i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.3892 | − | 28.0169i | 1.08846 | − | 0.913324i | 0.0918617 | − | 0.995772i | \(-0.470718\pi\) |
0.996595 | + | 0.0824478i | \(0.0262738\pi\) | |||||||
\(942\) | 20.3375 | − | 35.2255i | 0.662630 | − | 1.14771i | ||||
\(943\) | −2.30959 | − | 4.00033i | −0.0752107 | − | 0.130269i | ||||
\(944\) | −13.2735 | − | 4.83117i | −0.432017 | − | 0.157241i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.749794 | + | 4.25229i | 0.0243779 | + | 0.138254i | ||||
\(947\) | −24.7470 | + | 9.00717i | −0.804170 | + | 0.292694i | −0.711213 | − | 0.702976i | \(-0.751854\pi\) |
−0.0929564 | + | 0.995670i | \(0.529632\pi\) | |||||||
\(948\) | −6.03163 | − | 5.06114i | −0.195898 | − | 0.164378i | ||||
\(949\) | −84.9601 | −2.75792 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.10520 | 0.262829 | ||||||||
\(952\) | 6.04655 | + | 5.07365i | 0.195970 | + | 0.164438i | ||||
\(953\) | −0.903804 | + | 0.328958i | −0.0292771 | + | 0.0106560i | −0.356617 | − | 0.934251i | \(-0.616070\pi\) |
0.327340 | + | 0.944907i | \(0.393848\pi\) | |||||||
\(954\) | −4.98100 | − | 28.2487i | −0.161266 | − | 0.914585i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.4096 | + | 4.51672i | 0.401354 | + | 0.146081i | ||||
\(957\) | −17.7496 | − | 30.7431i | −0.573762 | − | 0.993784i | ||||
\(958\) | 1.91443 | − | 3.31589i | 0.0618524 | − | 0.107131i | ||||
\(959\) | −22.8234 | + | 19.1511i | −0.737006 | + | 0.618422i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.44264 | − | 11.1590i | 0.207827 | − | 0.359967i | ||||
\(962\) | −9.63808 | − | 16.6936i | −0.310744 | − | 0.538225i | ||||
\(963\) | 23.9412 | + | 8.71388i | 0.771494 | + | 0.280801i | ||||
\(964\) | −1.22530 | + | 6.94900i | −0.0394641 | + | 0.223812i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16.1513 | − | 5.87861i | 0.519661 | − | 0.189141i | ||||
\(967\) | −13.8131 | − | 11.5906i | −0.444200 | − | 0.372728i | 0.393078 | − | 0.919505i | \(-0.371410\pi\) |
−0.837278 | + | 0.546777i | \(0.815855\pi\) | |||||||
\(968\) | 7.56570 | 0.243171 | ||||||||
\(969\) | −25.9650 | + | 35.5192i | −0.834117 | + | 1.14104i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.19208 | − | 6.87397i | −0.262896 | − | 0.220596i | 0.501806 | − | 0.864980i | \(-0.332669\pi\) |
−0.764702 | + | 0.644384i | \(0.777114\pi\) | |||||||
\(972\) | 17.5826 | − | 6.39955i | 0.563963 | − | 0.205266i | ||||
\(973\) | −4.57465 | − | 25.9442i | −0.146657 | − | 0.831731i | ||||
\(974\) | −6.15472 | + | 34.9052i | −0.197210 | + | 1.11843i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.132753 | + | 0.229934i | 0.00424931 | + | 0.00736002i | ||||
\(977\) | 25.2209 | − | 43.6839i | 0.806889 | − | 1.39757i | −0.108119 | − | 0.994138i | \(-0.534483\pi\) |
0.915008 | − | 0.403435i | \(-0.132184\pi\) | |||||||
\(978\) | 23.1598 | − | 19.4334i | 0.740569 | − | 0.621411i | ||||
\(979\) | −2.81000 | + | 2.35787i | −0.0898081 | + | 0.0753580i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.77149 | − | 3.06832i | −0.0565594 | − | 0.0979638i | ||||
\(982\) | 8.02415 | + | 2.92055i | 0.256061 | + | 0.0931985i | ||||
\(983\) | 8.69866 | − | 49.3325i | 0.277444 | − | 1.57346i | −0.453645 | − | 0.891182i | \(-0.649877\pi\) |
0.731090 | − | 0.682282i | \(-0.239012\pi\) | |||||||
\(984\) | 0.744648 | + | 4.22311i | 0.0237385 | + | 0.134628i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 19.8357 | + | 16.6441i | 0.631696 | + | 0.530056i | ||||
\(987\) | −65.4962 | −2.08477 | ||||||||
\(988\) | −21.5676 | − | 10.5973i | −0.686158 | − | 0.337145i | ||||
\(989\) | −6.85830 | −0.218081 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.6454 | + | 4.96651i | −0.433459 | + | 0.157766i | −0.549529 | − | 0.835475i | \(-0.685193\pi\) |
0.116069 | + | 0.993241i | \(0.462970\pi\) | |||||||
\(992\) | 0.739071 | + | 4.19148i | 0.0234655 | + | 0.133080i | ||||
\(993\) | 1.26240 | − | 7.15941i | 0.0400609 | − | 0.227197i | ||||
\(994\) | −8.35621 | − | 3.04141i | −0.265043 | − | 0.0964678i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 19.1542 | − | 33.1761i | 0.606925 | − | 1.05122i | ||||
\(997\) | −18.3966 | + | 15.4366i | −0.582627 | + | 0.488882i | −0.885809 | − | 0.464051i | \(-0.846395\pi\) |
0.303182 | + | 0.952933i | \(0.401951\pi\) | |||||||
\(998\) | −28.4703 | + | 23.8894i | −0.901210 | + | 0.756205i | ||||
\(999\) | 7.00933 | − | 12.1405i | 0.221766 | − | 0.384109i |
(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 | 950.2.l.j.301.1 | yes | 24 | |
5.2 | odd | 4 | 950.2.u.h.149.8 | 48 | |||
5.3 | odd | 4 | 950.2.u.h.149.1 | 48 | |||
5.4 | even | 2 | 950.2.l.k.301.4 | yes | 24 | ||
19.6 | even | 9 | inner | 950.2.l.j.101.1 | ✓ | 24 | |
95.44 | even | 18 | 950.2.l.k.101.4 | yes | 24 | ||
95.63 | odd | 36 | 950.2.u.h.899.8 | 48 | |||
95.82 | odd | 36 | 950.2.u.h.899.1 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.l.j.101.1 | ✓ | 24 | 19.6 | even | 9 | inner | |
950.2.l.j.301.1 | yes | 24 | 1.1 | even | 1 | trivial | |
950.2.l.k.101.4 | yes | 24 | 95.44 | even | 18 | ||
950.2.l.k.301.4 | yes | 24 | 5.4 | even | 2 | ||
950.2.u.h.149.1 | 48 | 5.3 | odd | 4 | |||
950.2.u.h.149.8 | 48 | 5.2 | odd | 4 | |||
950.2.u.h.899.1 | 48 | 95.82 | odd | 36 | |||
950.2.u.h.899.8 | 48 | 95.63 | odd | 36 |