Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(99,950)]
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([9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.u (of order \(18\), degree \(6\), not 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: | \(48\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 149.8 | ||
Character | \(\chi\) | \(=\) | 950.149 |
Dual form | 950.2.u.h.899.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.642788 | − | 0.766044i | 0.454519 | − | 0.541675i | ||||
\(3\) | 0.934611 | + | 2.56782i | 0.539598 | + | 1.48253i | 0.847333 | + | 0.531061i | \(0.178207\pi\) |
−0.307735 | + | 0.951472i | \(0.599571\pi\) | |||||||
\(4\) | −0.173648 | − | 0.984808i | −0.0868241 | − | 0.492404i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.56782 | + | 0.934611i | 1.04831 | + | 0.381553i | ||||
\(7\) | −1.85059 | + | 1.06844i | −0.699457 | + | 0.403832i | −0.807145 | − | 0.590353i | \(-0.798989\pi\) |
0.107688 | + | 0.994185i | \(0.465655\pi\) | |||||||
\(8\) | −0.866025 | − | 0.500000i | −0.306186 | − | 0.176777i | ||||
\(9\) | −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 | \(0.0765383\pi\) | |||||||
\(12\) | 2.36652 | − | 1.36631i | 0.683155 | − | 0.394420i | ||||
\(13\) | −1.88555 | + | 5.18051i | −0.522958 | + | 1.43681i | 0.344255 | + | 0.938876i | \(0.388131\pi\) |
−0.867213 | + | 0.497938i | \(0.834091\pi\) | |||||||
\(14\) | −0.371065 | + | 2.10441i | −0.0991712 | + | 0.562428i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.939693 | + | 0.342020i | −0.234923 | + | 0.0855050i | ||||
\(17\) | −2.37433 | + | 2.82962i | −0.575860 | + | 0.686283i | −0.972823 | − | 0.231551i | \(-0.925620\pi\) |
0.396963 | + | 0.917835i | \(0.370064\pi\) | |||||||
\(18\) | 4.46721i | 1.05293i | ||||||||
\(19\) | −1.21370 | + | 4.18652i | −0.278443 | + | 0.960453i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.47314 | − | 3.75341i | −0.976120 | − | 0.819062i | ||||
\(22\) | −0.633827 | − | 1.74143i | −0.135132 | − | 0.371273i | ||||
\(23\) | −2.89878 | + | 0.511133i | −0.604438 | + | 0.106579i | −0.467488 | − | 0.883999i | \(-0.654841\pi\) |
−0.136950 | + | 0.990578i | \(0.543730\pi\) | |||||||
\(24\) | 0.474515 | − | 2.69111i | 0.0968599 | − | 0.549320i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.75649 | + | 4.77438i | 0.540592 | + | 0.936333i | ||||
\(27\) | −3.47219 | − | 2.00467i | −0.668223 | − | 0.385799i | ||||
\(28\) | 1.37356 | + | 1.63694i | 0.259578 | + | 0.309353i | ||||
\(29\) | 5.36998 | − | 4.50595i | 0.997181 | − | 0.836734i | 0.0105895 | − | 0.999944i | \(-0.496629\pi\) |
0.986591 | + | 0.163210i | \(0.0521848\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.12807 | + | 3.68592i | 0.382213 | + | 0.662012i | 0.991378 | − | 0.131031i | \(-0.0418289\pi\) |
−0.609166 | + | 0.793043i | \(0.708496\pi\) | |||||||
\(32\) | −0.342020 | + | 0.939693i | −0.0604612 | + | 0.166116i | ||||
\(33\) | 4.98712 | + | 0.879364i | 0.868146 | + | 0.153078i | ||||
\(34\) | 0.641422 | + | 3.63769i | 0.110003 | + | 0.623858i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.42208 | + | 2.87147i | 0.570347 | + | 0.478578i | ||||
\(37\) | − | 3.49650i | − | 0.574822i | −0.957807 | − | 0.287411i | \(-0.907205\pi\) | ||
0.957807 | − | 0.287411i | \(-0.0927945\pi\) | |||||||
\(38\) | 2.42690 | + | 3.62079i | 0.393696 | + | 0.587370i | ||||
\(39\) | −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 | \(0.349785\pi\) | |||||||
\(42\) | −5.75056 | + | 1.01398i | −0.887331 | + | 0.156460i | ||||
\(43\) | −2.29458 | − | 0.404597i | −0.349921 | − | 0.0617005i | −0.00407464 | − | 0.999992i | \(-0.501297\pi\) |
−0.345846 | + | 0.938291i | \(0.612408\pi\) | |||||||
\(44\) | −1.74143 | − | 0.633827i | −0.262530 | − | 0.0955531i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.47175 | + | 2.54915i | −0.216998 | + | 0.375851i | ||||
\(47\) | 7.20983 | + | 8.59234i | 1.05166 | + | 1.25332i | 0.966422 | + | 0.256961i | \(0.0827213\pi\) |
0.0852401 | + | 0.996360i | \(0.472834\pi\) | |||||||
\(48\) | −1.75649 | − | 2.09331i | −0.253528 | − | 0.302143i | ||||
\(49\) | −1.21688 | + | 2.10770i | −0.173840 | + | 0.301099i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.48504 | − | 3.45227i | −1.32817 | − | 0.483415i | ||||
\(52\) | 5.42923 | + | 0.957319i | 0.752898 | + | 0.132756i | ||||
\(53\) | 6.32356 | − | 1.11501i | 0.868607 | − | 0.153159i | 0.278453 | − | 0.960450i | \(-0.410178\pi\) |
0.590154 | + | 0.807291i | \(0.299067\pi\) | |||||||
\(54\) | −3.76755 | + | 1.37127i | −0.512698 | + | 0.186607i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.13688 | 0.285552 | ||||||||
\(57\) | −11.8846 | + | 0.796188i | −1.57415 | + | 0.105458i | ||||
\(58\) | − | 7.01002i | − | 0.920460i | ||||||
\(59\) | −10.8207 | − | 9.07963i | −1.40873 | − | 1.18207i | −0.957062 | − | 0.289883i | \(-0.906383\pi\) |
−0.451672 | − | 0.892184i | \(-0.649172\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0461045 | − | 0.261472i | −0.00590308 | − | 0.0334780i | 0.981714 | − | 0.190362i | \(-0.0609662\pi\) |
−0.987617 | + | 0.156884i | \(0.949855\pi\) | |||||||
\(62\) | 4.19148 | + | 0.739071i | 0.532318 | + | 0.0938621i | ||||
\(63\) | 3.26488 | − | 8.97020i | 0.411337 | − | 1.13014i | ||||
\(64\) | 0.500000 | + | 0.866025i | 0.0625000 | + | 0.108253i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.87929 | − | 3.25511i | 0.477508 | − | 0.400677i | ||||
\(67\) | 9.49761 | + | 11.3188i | 1.16032 | + | 1.38281i | 0.909979 | + | 0.414654i | \(0.136097\pi\) |
0.250338 | + | 0.968158i | \(0.419458\pi\) | |||||||
\(68\) | 3.19893 | + | 1.84690i | 0.387927 | + | 0.223970i | ||||
\(69\) | −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 | \(-0.0238683\pi\) | |||||||
\(72\) | 4.39935 | − | 0.775724i | 0.518468 | − | 0.0914199i | ||||
\(73\) | −5.27085 | − | 14.4815i | −0.616906 | − | 1.69494i | −0.714434 | − | 0.699703i | \(-0.753316\pi\) |
0.0975282 | − | 0.995233i | \(-0.468906\pi\) | |||||||
\(74\) | −2.67848 | − | 2.24751i | −0.311367 | − | 0.261268i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.33367 | + | 0.468284i | 0.497106 | + | 0.0537159i | ||||
\(77\) | 3.96003i | 0.451288i | ||||||||
\(78\) | −9.68352 | + | 11.5404i | −1.09644 | + | 1.30669i | ||||
\(79\) | −2.70762 | + | 0.985493i | −0.304631 | + | 0.110877i | −0.489813 | − | 0.871828i | \(-0.662935\pi\) |
0.185182 | + | 0.982704i | \(0.440713\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.424681 | + | 2.40849i | −0.0471868 | + | 0.267610i | ||||
\(82\) | 0.536727 | − | 1.47464i | 0.0592716 | − | 0.162847i | ||||
\(83\) | 12.1408 | − | 7.00947i | 1.33262 | − | 0.769389i | 0.346921 | − | 0.937894i | \(-0.387227\pi\) |
0.985701 | + | 0.168505i | \(0.0538940\pi\) | |||||||
\(84\) | −2.91964 | + | 5.05696i | −0.318558 | + | 0.551759i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.78487 | + | 1.49768i | −0.192467 | + | 0.161499i | ||||
\(87\) | 16.5893 | + | 9.57786i | 1.77856 | + | 1.02685i | ||||
\(88\) | −1.60491 | + | 0.926593i | −0.171084 | + | 0.0987752i | ||||
\(89\) | 1.86003 | + | 0.676995i | 0.197163 | + | 0.0717613i | 0.438714 | − | 0.898627i | \(-0.355434\pi\) |
−0.241552 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.04567 | − | 11.6016i | −0.214445 | − | 1.21618i | ||||
\(92\) | 1.00674 | + | 2.76599i | 0.104960 | + | 0.288374i | ||||
\(93\) | −7.47588 | + | 8.90941i | −0.775213 | + | 0.923863i | ||||
\(94\) | 11.2165 | 1.15689 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.73262 | −0.278897 | ||||||||
\(97\) | −6.94855 | + | 8.28096i | −0.705519 | + | 0.840805i | −0.993139 | − | 0.116940i | \(-0.962691\pi\) |
0.287620 | + | 0.957745i | \(0.407136\pi\) | |||||||
\(98\) | 0.832394 | + | 2.28698i | 0.0840845 | + | 0.231020i | ||||
\(99\) | 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 | \(0.776430\pi\) | |||||||
\(102\) | −8.74146 | + | 5.04688i | −0.865533 | + | 0.499716i | ||||
\(103\) | 7.59952 | + | 4.38758i | 0.748803 | + | 0.432322i | 0.825261 | − | 0.564751i | \(-0.191028\pi\) |
−0.0764583 | + | 0.997073i | \(0.524361\pi\) | |||||||
\(104\) | 4.22319 | − | 3.54368i | 0.414118 | − | 0.347486i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.21055 | − | 5.56084i | 0.311837 | − | 0.540117i | ||||
\(107\) | −4.93917 | + | 2.85163i | −0.477487 | + | 0.275677i | −0.719369 | − | 0.694628i | \(-0.755569\pi\) |
0.241882 | + | 0.970306i | \(0.422235\pi\) | |||||||
\(108\) | −1.37127 | + | 3.76755i | −0.131951 | + | 0.362532i | ||||
\(109\) | −0.137722 | + | 0.781060i | −0.0131914 | + | 0.0748119i | −0.990693 | − | 0.136117i | \(-0.956538\pi\) |
0.977501 | + | 0.210929i | \(0.0676488\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.97841 | − | 3.26787i | 0.852193 | − | 0.310173i | ||||
\(112\) | 1.37356 | − | 1.63694i | 0.129789 | − | 0.154677i | ||||
\(113\) | − | 4.98604i | − | 0.469047i | −0.972110 | − | 0.234523i | \(-0.924647\pi\) | ||
0.972110 | − | 0.234523i | \(-0.0753530\pi\) | |||||||
\(114\) | −7.02934 | + | 9.61589i | −0.658358 | + | 0.900611i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.36998 | − | 4.50595i | −0.498590 | − | 0.418367i | ||||
\(117\) | −8.42316 | − | 23.1424i | −0.778721 | − | 2.13952i | ||||
\(118\) | −13.9108 | + | 2.45285i | −1.28059 | + | 0.225803i | ||||
\(119\) | 1.37064 | − | 7.77329i | 0.125646 | − | 0.712576i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.78285 | + | 6.55209i | 0.343895 | + | 0.595644i | ||||
\(122\) | −0.229934 | − | 0.132753i | −0.0208173 | − | 0.0120189i | ||||
\(123\) | 2.75644 | + | 3.28500i | 0.248540 | + | 0.296198i | ||||
\(124\) | 3.26039 | − | 2.73579i | 0.292792 | − | 0.245682i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.77294 | − | 8.26698i | −0.425208 | − | 0.736481i | ||||
\(127\) | 5.30620 | − | 14.5787i | 0.470849 | − | 1.29365i | −0.446221 | − | 0.894923i | \(-0.647231\pi\) |
0.917071 | − | 0.398725i | \(-0.130547\pi\) | |||||||
\(128\) | 0.984808 | + | 0.173648i | 0.0870455 | + | 0.0153485i | ||||
\(129\) | −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 | \(0.308670\pi\) | |||||||
\(132\) | − | 5.06406i | − | 0.440770i | ||||||
\(133\) | −2.22697 | − | 9.04429i | −0.193103 | − | 0.784240i | ||||
\(134\) | 14.7757 | 1.27642 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.47104 | − | 1.26336i | 0.297639 | − | 0.108332i | ||||
\(137\) | −13.7309 | + | 2.42112i | −1.17311 | + | 0.206851i | −0.726042 | − | 0.687650i | \(-0.758642\pi\) |
−0.447066 | + | 0.894501i | \(0.647531\pi\) | |||||||
\(138\) | −7.92127 | − | 1.39673i | −0.674303 | − | 0.118898i | ||||
\(139\) | 11.5850 | + | 4.21658i | 0.982623 | + | 0.357646i | 0.782860 | − | 0.622198i | \(-0.213760\pi\) |
0.199764 | + | 0.979844i | \(0.435983\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.3252 | + | 26.5441i | −1.29062 | + | 2.23541i | ||||
\(142\) | −2.67493 | − | 3.18785i | −0.224475 | − | 0.267519i | ||||
\(143\) | 6.56709 | + | 7.82636i | 0.549168 | + | 0.654473i | ||||
\(144\) | 2.23361 | − | 3.86872i | 0.186134 | − | 0.322393i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −14.4815 | − | 5.27085i | −1.19850 | − | 0.436218i | ||||
\(147\) | −6.54950 | − | 1.15485i | −0.540194 | − | 0.0952507i | ||||
\(148\) | −3.44339 | + | 0.607162i | −0.283045 | + | 0.0499084i | ||||
\(149\) | 21.1569 | − | 7.70049i | 1.73324 | − | 0.630849i | 0.734389 | − | 0.678729i | \(-0.237469\pi\) |
0.998853 | + | 0.0478803i | \(0.0152466\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.6452 | 1.84284 | 0.921420 | − | 0.388568i | \(-0.127030\pi\) | ||||
0.921420 | + | 0.388568i | \(0.127030\pi\) | |||||||
\(152\) | 3.14436 | − | 3.01878i | 0.255041 | − | 0.244855i | ||||
\(153\) | − | 16.5010i | − | 1.33403i | ||||||
\(154\) | 3.03356 | + | 2.54546i | 0.244451 | + | 0.205119i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.61599 | + | 14.8360i | 0.209447 | + | 1.18783i | ||||
\(157\) | 14.6588 | + | 2.58475i | 1.16990 | + | 0.206285i | 0.724648 | − | 0.689119i | \(-0.242002\pi\) |
0.445253 | + | 0.895405i | \(0.353114\pi\) | |||||||
\(158\) | −0.985493 | + | 2.70762i | −0.0784016 | + | 0.215407i | ||||
\(159\) | 8.77322 | + | 15.1957i | 0.695762 | + | 1.20510i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.81834 | − | 4.04307i | 0.379738 | − | 0.318638i | ||||
\(162\) | 1.57203 | + | 1.87347i | 0.123510 | + | 0.147194i | ||||
\(163\) | −9.58148 | − | 5.53187i | −0.750479 | − | 0.433289i | 0.0753878 | − | 0.997154i | \(-0.475981\pi\) |
−0.825867 | + | 0.563865i | \(0.809314\pi\) | |||||||
\(164\) | −0.784642 | − | 1.35904i | −0.0612703 | − | 0.106123i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.43436 | − | 13.8060i | 0.188943 | − | 1.07155i | ||||
\(167\) | 19.4224 | − | 3.42470i | 1.50295 | − | 0.265011i | 0.639245 | − | 0.769003i | \(-0.279247\pi\) |
0.863708 | + | 0.503992i | \(0.168136\pi\) | |||||||
\(168\) | 1.99715 | + | 5.48712i | 0.154083 | + | 0.423341i | ||||
\(169\) | −13.3238 | − | 11.1800i | −1.02491 | − | 0.859998i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.86806 | − | 17.8117i | −0.601685 | − | 1.36210i | ||||
\(172\) | 2.32998i | 0.177659i | ||||||||
\(173\) | −3.89388 | + | 4.64055i | −0.296047 | + | 0.352815i | −0.893479 | − | 0.449105i | \(-0.851743\pi\) |
0.597433 | + | 0.801919i | \(0.296188\pi\) | |||||||
\(174\) | 18.0005 | − | 6.55164i | 1.36461 | − | 0.496678i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.321803 | + | 1.82503i | −0.0242568 | + | 0.137567i | ||||
\(177\) | 13.2018 | − | 36.2715i | 0.992305 | − | 2.72634i | ||||
\(178\) | 1.71421 | − | 0.989700i | 0.128486 | − | 0.0741812i | ||||
\(179\) | −0.625049 | + | 1.08262i | −0.0467184 | + | 0.0809186i | −0.888439 | − | 0.458995i | \(-0.848210\pi\) |
0.841721 | + | 0.539913i | \(0.181543\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0955 | − | 10.1494i | 0.899054 | − | 0.754396i | −0.0709510 | − | 0.997480i | \(-0.522603\pi\) |
0.970005 | + | 0.243084i | \(0.0781590\pi\) | |||||||
\(182\) | −10.2023 | − | 5.89028i | −0.756242 | − | 0.436617i | ||||
\(183\) | 0.628323 | − | 0.362763i | 0.0464470 | − | 0.0268162i | ||||
\(184\) | 2.76599 | + | 1.00674i | 0.203911 | + | 0.0742176i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.01960 | + | 11.4537i | 0.148084 | + | 0.839827i | ||||
\(187\) | 2.34123 | + | 6.43249i | 0.171208 | + | 0.470390i | ||||
\(188\) | 7.20983 | − | 8.59234i | 0.525831 | − | 0.626661i | ||||
\(189\) | 8.56746 | 0.623191 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.05105 | −0.148409 | −0.0742045 | − | 0.997243i | \(-0.523642\pi\) | ||||
−0.0742045 | + | 0.997243i | \(0.523642\pi\) | |||||||
\(192\) | −1.75649 | + | 2.09331i | −0.126764 | + | 0.151072i | ||||
\(193\) | −0.281445 | − | 0.773263i | −0.0202588 | − | 0.0556607i | 0.929151 | − | 0.369700i | \(-0.120540\pi\) |
−0.949410 | + | 0.314040i | \(0.898317\pi\) | |||||||
\(194\) | 1.87714 | + | 10.6458i | 0.134771 | + | 0.764324i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.28698 | + | 0.832394i | 0.163356 | + | 0.0594567i | ||||
\(197\) | −11.0002 | + | 6.35099i | −0.783734 | + | 0.452489i | −0.837752 | − | 0.546051i | \(-0.816131\pi\) |
0.0540180 | + | 0.998540i | \(0.482797\pi\) | |||||||
\(198\) | 7.16946 | + | 4.13929i | 0.509511 | + | 0.294167i | ||||
\(199\) | 3.91363 | − | 3.28392i | 0.277430 | − | 0.232791i | −0.493446 | − | 0.869776i | \(-0.664263\pi\) |
0.770876 | + | 0.636985i | \(0.219819\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20.1881 | + | 34.9669i | −1.42396 | + | 2.46637i | ||||
\(202\) | −8.63954 | + | 4.98804i | −0.607876 | + | 0.350957i | ||||
\(203\) | −5.12330 | + | 14.0762i | −0.359585 | + | 0.987953i | ||||
\(204\) | −1.75276 | + | 9.94042i | −0.122718 | + | 0.695969i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.24596 | − | 3.00128i | 0.574523 | − | 0.209109i | ||||
\(207\) | 8.45217 | − | 10.0729i | 0.587466 | − | 0.700115i | ||||
\(208\) | − | 5.51298i | − | 0.382256i | ||||||
\(209\) | 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 | \(0.956334\pi\) | |||||||
\(212\) | −2.19615 | − | 6.03387i | −0.150832 | − | 0.414408i | ||||
\(213\) | 11.1989 | − | 1.97467i | 0.767335 | − | 0.135302i | ||||
\(214\) | −0.990360 | + | 5.61661i | −0.0676996 | + | 0.383944i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.00467 | + | 3.47219i | 0.136400 | + | 0.236253i | ||||
\(217\) | −7.87637 | − | 4.54742i | −0.534683 | − | 0.308699i | ||||
\(218\) | 0.509800 | + | 0.607556i | 0.0345280 | + | 0.0411489i | ||||
\(219\) | 32.2598 | − | 27.0692i | 2.17992 | − | 1.82917i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.1819 | − | 17.6356i | −0.684911 | − | 1.18630i | ||||
\(222\) | 3.26787 | − | 8.97841i | 0.219325 | − | 0.602591i | ||||
\(223\) | 2.40931 | + | 0.424827i | 0.161340 | + | 0.0284485i | 0.253734 | − | 0.967274i | \(-0.418341\pi\) |
−0.0923948 | + | 0.995722i | \(0.529452\pi\) | |||||||
\(224\) | −0.371065 | − | 2.10441i | −0.0247928 | − | 0.140607i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.81953 | − | 3.20496i | −0.254071 | − | 0.213191i | ||||
\(227\) | 19.2300i | 1.27634i | 0.769897 | + | 0.638169i | \(0.220308\pi\) | ||||
−0.769897 | + | 0.638169i | \(0.779692\pi\) | |||||||
\(228\) | 2.84783 | + | 11.5658i | 0.188602 | + | 0.765962i | ||||
\(229\) | −20.3871 | −1.34722 | −0.673609 | − | 0.739088i | \(-0.735257\pi\) | ||||
−0.673609 | + | 0.739088i | \(0.735257\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.1687 | + | 3.70109i | −0.669049 | + | 0.243514i | ||||
\(232\) | −6.90352 | + | 1.21728i | −0.453238 | + | 0.0799181i | ||||
\(233\) | 8.29121 | + | 1.46196i | 0.543175 | + | 0.0957764i | 0.438502 | − | 0.898730i | \(-0.355509\pi\) |
0.104673 | + | 0.994507i | \(0.466620\pi\) | |||||||
\(234\) | −23.1424 | − | 8.42316i | −1.51287 | − | 0.550639i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.06270 | + | 12.2330i | −0.459743 | + | 0.796298i | ||||
\(237\) | −5.06114 | − | 6.03163i | −0.328756 | − | 0.391797i | ||||
\(238\) | −5.07365 | − | 6.04655i | −0.328876 | − | 0.391939i | ||||
\(239\) | −6.60300 | + | 11.4367i | −0.427113 | + | 0.739781i | −0.996615 | − | 0.0822090i | \(-0.973803\pi\) |
0.569503 | + | 0.821990i | \(0.307136\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.63066 | + | 2.41336i | 0.427118 | + | 0.155458i | 0.546630 | − | 0.837375i | \(-0.315911\pi\) |
−0.119511 | + | 0.992833i | \(0.538133\pi\) | |||||||
\(242\) | 7.45076 | + | 1.31377i | 0.478953 | + | 0.0844523i | ||||
\(243\) | −18.4268 | + | 3.24914i | −1.18208 | + | 0.208432i | ||||
\(244\) | −0.249493 | + | 0.0908082i | −0.0159722 | + | 0.00581340i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.28826 | 0.273409 | ||||||||
\(247\) | −19.3998 | − | 14.1815i | −1.23438 | − | 0.902347i | ||||
\(248\) | − | 4.25614i | − | 0.270265i | ||||||
\(249\) | 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 | \(0.967908\pi\) | |||||||
\(252\) | −9.40086 | − | 1.65763i | −0.592199 | − | 0.104421i | ||||
\(253\) | −1.86567 | + | 5.12589i | −0.117294 | + | 0.322262i | ||||
\(254\) | −7.75715 | − | 13.4358i | −0.486727 | − | 0.843035i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.766044 | − | 0.642788i | 0.0478778 | − | 0.0401742i | ||||
\(257\) | 3.56140 | + | 4.24431i | 0.222154 | + | 0.264753i | 0.865597 | − | 0.500741i | \(-0.166939\pi\) |
−0.643443 | + | 0.765494i | \(0.722495\pi\) | |||||||
\(258\) | −5.51395 | − | 3.18348i | −0.343283 | − | 0.198195i | ||||
\(259\) | 3.73580 | + | 6.47060i | 0.232131 | + | 0.402063i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.43783 | + | 30.8395i | −0.336593 | + | 1.90892i | ||||
\(262\) | 21.7170 | − | 3.82930i | 1.34168 | − | 0.236575i | ||||
\(263\) | 0.606559 | + | 1.66651i | 0.0374020 | + | 0.102761i | 0.956988 | − | 0.290128i | \(-0.0936978\pi\) |
−0.919586 | + | 0.392889i | \(0.871476\pi\) | |||||||
\(264\) | −3.87929 | − | 3.25511i | −0.238754 | − | 0.200338i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.35980 | − | 4.10760i | −0.512572 | − | 0.251853i | ||||
\(267\) | 5.40895i | 0.331022i | ||||||||
\(268\) | 9.49761 | − | 11.3188i | 0.580159 | − | 0.691406i | ||||
\(269\) | −14.9736 | + | 5.44995i | −0.912957 | + | 0.332289i | −0.755433 | − | 0.655226i | \(-0.772573\pi\) |
−0.157524 | + | 0.987515i | \(0.550351\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.44844 | − | 13.8858i | 0.148732 | − | 0.843502i | −0.815562 | − | 0.578669i | \(-0.803572\pi\) |
0.964294 | − | 0.264832i | \(-0.0853166\pi\) | |||||||
\(272\) | 1.26336 | − | 3.47104i | 0.0766022 | − | 0.210463i | ||||
\(273\) | 27.8789 | − | 16.0959i | 1.68731 | − | 0.974168i | ||||
\(274\) | −6.97135 | + | 12.0747i | −0.421155 | + | 0.729461i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.16165 | + | 5.17024i | −0.370888 | + | 0.311212i | ||||
\(277\) | −19.2828 | − | 11.1329i | −1.15859 | − | 0.668912i | −0.207623 | − | 0.978209i | \(-0.566573\pi\) |
−0.950965 | + | 0.309297i | \(0.899906\pi\) | |||||||
\(278\) | 10.6768 | − | 6.16423i | 0.640349 | − | 0.369706i | ||||
\(279\) | −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 | \(-0.125500\pi\) | |||||||
\(282\) | 10.4831 | + | 28.8020i | 0.624258 | + | 1.71513i | ||||
\(283\) | −6.62536 | + | 7.89580i | −0.393837 | + | 0.469357i | −0.926131 | − | 0.377203i | \(-0.876886\pi\) |
0.532294 | + | 0.846560i | \(0.321330\pi\) | |||||||
\(284\) | −4.16145 | −0.246936 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.2166 | 0.604119 | ||||||||
\(287\) | −2.15550 | + | 2.56883i | −0.127235 | + | 0.151633i | ||||
\(288\) | −1.52788 | − | 4.19781i | −0.0900310 | − | 0.247358i | ||||
\(289\) | 0.582730 | + | 3.30482i | 0.0342782 | + | 0.194401i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −27.7582 | − | 10.1032i | −1.62722 | − | 0.592259i | ||||
\(292\) | −13.3463 | + | 7.70546i | −0.781030 | + | 0.450928i | ||||
\(293\) | −26.5315 | − | 15.3180i | −1.54999 | − | 0.894887i | −0.998141 | − | 0.0609422i | \(-0.980589\pi\) |
−0.551848 | − | 0.833945i | \(-0.686077\pi\) | |||||||
\(294\) | −5.09461 | + | 4.27488i | −0.297123 | + | 0.249316i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.74825 | + | 3.02806i | −0.101615 | + | 0.176003i | ||||
\(297\) | −6.43461 | + | 3.71503i | −0.373374 | + | 0.215568i | ||||
\(298\) | 7.70049 | − | 21.1569i | 0.446077 | − | 1.22559i | ||||
\(299\) | 2.81787 | − | 15.9809i | 0.162962 | − | 0.924201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.67862 | − | 1.70288i | 0.269671 | − | 0.0981523i | ||||
\(302\) | 14.5561 | − | 17.3472i | 0.837607 | − | 0.998221i | ||||
\(303\) | − | 27.2608i | − | 1.56609i | ||||||
\(304\) | −0.291364 | − | 4.34915i | −0.0167109 | − | 0.249441i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −12.6405 | − | 10.6066i | −0.722610 | − | 0.606342i | ||||
\(307\) | −2.73189 | − | 7.50580i | −0.155917 | − | 0.428379i | 0.836998 | − | 0.547206i | \(-0.184309\pi\) |
−0.992915 | + | 0.118828i | \(0.962086\pi\) | |||||||
\(308\) | 3.89987 | − | 0.687652i | 0.222216 | − | 0.0391826i | ||||
\(309\) | −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 | \(0.560945\pi\) | |||||||
\(312\) | 13.0466 | + | 7.53244i | 0.738617 | + | 0.426440i | ||||
\(313\) | −4.92589 | − | 5.87045i | −0.278428 | − | 0.331817i | 0.608649 | − | 0.793440i | \(-0.291712\pi\) |
−0.887076 | + | 0.461622i | \(0.847267\pi\) | |||||||
\(314\) | 11.4025 | − | 9.56787i | 0.643482 | − | 0.539946i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.44069 | + | 2.49535i | 0.0810454 | + | 0.140375i | ||||
\(317\) | 1.01446 | − | 2.78721i | 0.0569779 | − | 0.156545i | −0.907938 | − | 0.419104i | \(-0.862344\pi\) |
0.964916 | + | 0.262559i | \(0.0845664\pi\) | |||||||
\(318\) | 17.2799 | + | 3.04691i | 0.969008 | + | 0.170862i | ||||
\(319\) | −2.25584 | − | 12.7935i | −0.126303 | − | 0.716299i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.9387 | − | 10.0177i | −0.666352 | − | 0.559136i | ||||
\(322\) | − | 6.28990i | − | 0.350522i | ||||||
\(323\) | −8.96451 | − | 13.3745i | −0.498799 | − | 0.744177i | ||||
\(324\) | 2.44564 | 0.135869 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.3965 | + | 3.78402i | −0.575810 | + | 0.209578i | ||||
\(327\) | −2.13434 | + | 0.376342i | −0.118029 | + | 0.0208117i | ||||
\(328\) | −1.54544 | − | 0.272503i | −0.0853328 | − | 0.0150465i | ||||
\(329\) | −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 | \(0.189960\pi\) | |||||||
\(332\) | −9.01120 | − | 10.7391i | −0.494554 | − | 0.589386i | ||||
\(333\) | 10.0401 | + | 11.9653i | 0.550194 | + | 0.655696i | ||||
\(334\) | 9.86103 | − | 17.0798i | 0.539572 | − | 0.934565i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.48712 | + | 1.99715i | 0.299347 | + | 0.108953i | ||||
\(337\) | −30.8485 | − | 5.43943i | −1.68043 | − | 0.296304i | −0.749634 | − | 0.661853i | \(-0.769770\pi\) |
−0.930792 | + | 0.365549i | \(0.880881\pi\) | |||||||
\(338\) | −17.1287 | + | 3.02025i | −0.931679 | + | 0.164280i | ||||
\(339\) | 12.8033 | − | 4.66001i | 0.695378 | − | 0.253097i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.88742 | 0.427128 | ||||||||
\(342\) | −18.7021 | − | 5.42188i | −1.01129 | − | 0.293181i | ||||
\(343\) | − | 20.1588i | − | 1.08847i | ||||||
\(344\) | 1.78487 | + | 1.49768i | 0.0962337 | + | 0.0807497i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.05193 | + | 5.96578i | 0.0565520 | + | 0.320722i | ||||
\(347\) | 10.4564 | + | 1.84375i | 0.561330 | + | 0.0989776i | 0.447112 | − | 0.894478i | \(-0.352453\pi\) |
0.114218 | + | 0.993456i | \(0.463564\pi\) | |||||||
\(348\) | 6.55164 | − | 18.0005i | 0.351205 | − | 0.964927i | ||||
\(349\) | 18.4784 | + | 32.0056i | 0.989128 | + | 1.71322i | 0.621921 | + | 0.783080i | \(0.286352\pi\) |
0.367206 | + | 0.930139i | \(0.380314\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.9322 | − | 14.2078i | 0.903773 | − | 0.758356i | ||||
\(352\) | 1.19121 | + | 1.41962i | 0.0634915 | + | 0.0756662i | ||||
\(353\) | 26.7210 | + | 15.4274i | 1.42222 | + | 0.821117i | 0.996488 | − | 0.0837337i | \(-0.0266845\pi\) |
0.425729 | + | 0.904851i | \(0.360018\pi\) | |||||||
\(354\) | −19.2997 | − | 33.4280i | −1.02577 | − | 1.77668i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.343719 | − | 1.94933i | 0.0182171 | − | 0.103314i | ||||
\(357\) | 21.2414 | − | 3.74544i | 1.12422 | − | 0.198230i | ||||
\(358\) | 0.427559 | + | 1.17471i | 0.0225972 | + | 0.0620853i | ||||
\(359\) | 7.76753 | + | 6.51773i | 0.409954 | + | 0.343993i | 0.824326 | − | 0.566115i | \(-0.191554\pi\) |
−0.414372 | + | 0.910108i | \(0.635999\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.0538 | − | 10.1624i | −0.844939 | − | 0.534862i | ||||
\(362\) | − | 15.7896i | − | 0.829883i | ||||||
\(363\) | −13.2891 | + | 15.8373i | −0.697497 | + | 0.831245i | ||||
\(364\) | −11.0701 | + | 4.02919i | −0.580231 | + | 0.211187i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.125986 | − | 0.714503i | 0.00658540 | − | 0.0373477i | ||||
\(367\) | −4.02729 | + | 11.0649i | −0.210223 | + | 0.577583i | −0.999327 | − | 0.0366766i | \(-0.988323\pi\) |
0.789104 | + | 0.614259i | \(0.210545\pi\) | |||||||
\(368\) | 2.54915 | − | 1.47175i | 0.132883 | − | 0.0767203i | ||||
\(369\) | −3.50516 | + | 6.07112i | −0.182472 | + | 0.316050i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.5110 | + | 8.81976i | −0.545703 | + | 0.457899i | ||||
\(372\) | 10.0722 | + | 5.81521i | 0.522221 | + | 0.301504i | ||||
\(373\) | −16.9501 | + | 9.78613i | −0.877641 | + | 0.506706i | −0.869880 | − | 0.493263i | \(-0.835804\pi\) |
−0.00776129 | + | 0.999970i | \(0.502471\pi\) | |||||||
\(374\) | 6.43249 | + | 2.34123i | 0.332616 | + | 0.121062i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.94773 | − | 11.0461i | −0.100446 | − | 0.569659i | ||||
\(377\) | 13.2177 | + | 36.3154i | 0.680748 | + | 1.87034i | ||||
\(378\) | 5.50706 | − | 6.56306i | 0.283252 | − | 0.337567i | ||||
\(379\) | −19.0901 | −0.980591 | −0.490296 | − | 0.871556i | \(-0.663111\pi\) | ||||
−0.490296 | + | 0.871556i | \(0.663111\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 42.3947 | 2.17195 | ||||||||
\(382\) | −1.31839 | + | 1.57120i | −0.0674548 | + | 0.0803894i | ||||
\(383\) | 6.72885 | + | 18.4874i | 0.343828 | + | 0.944660i | 0.984273 | + | 0.176655i | \(0.0565278\pi\) |
−0.640445 | + | 0.768004i | \(0.721250\pi\) | |||||||
\(384\) | 0.474515 | + | 2.69111i | 0.0242150 | + | 0.137330i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.773263 | − | 0.281445i | −0.0393580 | − | 0.0143252i | ||||
\(387\) | 9.01405 | − | 5.20426i | 0.458210 | − | 0.264548i | ||||
\(388\) | 9.36176 | + | 5.40502i | 0.475271 | + | 0.274398i | ||||
\(389\) | 18.4221 | − | 15.4580i | 0.934038 | − | 0.783751i | −0.0425001 | − | 0.999096i | \(-0.513532\pi\) |
0.976538 | + | 0.215346i | \(0.0690878\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.43636 | − | 9.41605i | 0.274928 | − | 0.476190i | ||||
\(392\) | 2.10770 | − | 1.21688i | 0.106455 | − | 0.0614617i | ||||
\(393\) | −20.6101 | + | 56.6257i | −1.03964 | + | 2.85639i | ||||
\(394\) | −2.20567 | + | 12.5090i | −0.111120 | + | 0.630194i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.77932 | − | 2.83144i | 0.390926 | − | 0.142285i | ||||
\(397\) | −1.63337 | + | 1.94657i | −0.0819763 | + | 0.0976956i | −0.805474 | − | 0.592632i | \(-0.798089\pi\) |
0.723497 | + | 0.690327i | \(0.242533\pi\) | |||||||
\(398\) | − | 5.10888i | − | 0.256085i | ||||||
\(399\) | 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 | \(0.710421\pi\) | |||||||
\(402\) | 13.8095 | + | 37.9413i | 0.688755 | + | 1.89234i | ||||
\(403\) | −23.1075 | + | 4.07448i | −1.15107 | + | 0.202964i | ||||
\(404\) | −1.73233 | + | 9.82452i | −0.0861865 | + | 0.488788i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.48977 | + | 12.9727i | 0.371711 | + | 0.643822i | ||||
\(407\) | −5.61156 | − | 3.23984i | −0.278155 | − | 0.160593i | ||||
\(408\) | 6.48815 | + | 7.73227i | 0.321211 | + | 0.382805i | ||||
\(409\) | −9.40691 | + | 7.89333i | −0.465142 | + | 0.390300i | −0.845019 | − | 0.534737i | \(-0.820411\pi\) |
0.379877 | + | 0.925037i | \(0.375966\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.0501 | − | 32.9957i | −0.939670 | − | 1.62756i | ||||
\(412\) | 3.00128 | − | 8.24596i | 0.147863 | − | 0.406249i | ||||
\(413\) | 29.7257 | + | 5.24144i | 1.46271 | + | 0.257914i | ||||
\(414\) | −2.28334 | − | 12.9495i | −0.112220 | − | 0.636432i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.22319 | − | 3.54368i | −0.207059 | − | 0.173743i | ||||
\(417\) | 33.6890i | 1.64976i | ||||||||
\(418\) | 8.05979 | − | 0.539953i | 0.394217 | − | 0.0264099i | ||||
\(419\) | 2.95132 | 0.144182 | 0.0720908 | − | 0.997398i | \(-0.477033\pi\) | ||||
0.0720908 | + | 0.997398i | \(0.477033\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.04747 | − | 2.56507i | 0.343472 | − | 0.125014i | −0.164524 | − | 0.986373i | \(-0.552609\pi\) |
0.507996 | + | 0.861359i | \(0.330386\pi\) | |||||||
\(422\) | −19.1960 | + | 3.38477i | −0.934445 | + | 0.164768i | ||||
\(423\) | −49.3453 | − | 8.70091i | −2.39925 | − | 0.423053i | ||||
\(424\) | −6.03387 | − | 2.19615i | −0.293031 | − | 0.106654i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.68583 | − | 9.84814i | 0.275479 | − | 0.477144i | ||||
\(427\) | 0.364687 | + | 0.434617i | 0.0176484 | + | 0.0210326i | ||||
\(428\) | 3.66598 | + | 4.36895i | 0.177202 | + | 0.211181i | ||||
\(429\) | −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 | \(0.414056\pi\) | |||||||
\(432\) | 3.94843 | + | 0.696214i | 0.189969 | + | 0.0334966i | ||||
\(433\) | −34.8458 | + | 6.14426i | −1.67458 | + | 0.295274i | −0.928708 | − | 0.370812i | \(-0.879080\pi\) |
−0.745875 | + | 0.666086i | \(0.767968\pi\) | |||||||
\(434\) | −8.54636 | + | 3.11062i | −0.410238 | + | 0.149315i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.793109 | 0.0379830 | ||||||||
\(437\) | 1.37839 | − | 12.7562i | 0.0659375 | − | 0.610210i | ||||
\(438\) | − | 42.1122i | − | 2.01220i | ||||||
\(439\) | −18.2221 | − | 15.2901i | −0.869692 | − | 0.729758i | 0.0943411 | − | 0.995540i | \(-0.469926\pi\) |
−0.964033 | + | 0.265782i | \(0.914370\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.88792 | − | 10.7069i | −0.0899011 | − | 0.509855i | ||||
\(442\) | −20.0545 | − | 3.53615i | −0.953895 | − | 0.168197i | ||||
\(443\) | −4.68618 | + | 12.8752i | −0.222647 | + | 0.611718i | −0.999846 | − | 0.0175367i | \(-0.994418\pi\) |
0.777199 | + | 0.629255i | \(0.216640\pi\) | |||||||
\(444\) | −4.77731 | − | 8.27454i | −0.226721 | − | 0.392692i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.87411 | − | 1.57257i | 0.0887418 | − | 0.0744632i | ||||
\(447\) | 39.5470 | + | 47.1303i | 1.87051 | + | 2.22918i | ||||
\(448\) | −1.85059 | − | 1.06844i | −0.0874321 | − | 0.0504790i | ||||
\(449\) | 7.58152 | + | 13.1316i | 0.357794 | + | 0.619717i | 0.987592 | − | 0.157042i | \(-0.0501957\pi\) |
−0.629798 | + | 0.776759i | \(0.716862\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.505000 | − | 2.86400i | 0.0237795 | − | 0.134860i | ||||
\(452\) | −4.91029 | + | 0.865816i | −0.230961 | + | 0.0407246i | ||||
\(453\) | 21.1645 | + | 58.1489i | 0.994393 | + | 2.73207i | ||||
\(454\) | 14.7310 | + | 12.3608i | 0.691360 | + | 0.580120i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.6904 | + | 5.25277i | 0.500626 | + | 0.245983i | ||||
\(457\) | − | 33.5768i | − | 1.57066i | −0.619079 | − | 0.785329i | \(-0.712494\pi\) | ||
0.619079 | − | 0.785329i | \(-0.287506\pi\) | |||||||
\(458\) | −13.1046 | + | 15.6174i | −0.612337 | + | 0.729755i | ||||
\(459\) | 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 | \(-0.154500\pi\) | |||||||
\(462\) | −3.70109 | + | 10.1687i | −0.172190 | + | 0.473089i | ||||
\(463\) | 9.13589 | − | 5.27461i | 0.424581 | − | 0.245132i | −0.272454 | − | 0.962169i | \(-0.587835\pi\) |
0.697035 | + | 0.717037i | \(0.254502\pi\) | |||||||
\(464\) | −3.50501 | + | 6.07085i | −0.162716 | + | 0.281832i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.44942 | − | 5.41170i | 0.298763 | − | 0.250692i | ||||
\(467\) | 26.4283 | + | 15.2584i | 1.22296 | + | 0.706074i | 0.965547 | − | 0.260229i | \(-0.0837981\pi\) |
0.257408 | + | 0.966303i | \(0.417131\pi\) | |||||||
\(468\) | −21.3282 | + | 12.3138i | −0.985895 | + | 0.569207i | ||||
\(469\) | −29.6696 | − | 10.7989i | −1.37002 | − | 0.498645i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.06313 | + | 40.0570i | 0.325452 | + | 1.84573i | ||||
\(472\) | 4.83117 | + | 13.2735i | 0.222373 | + | 0.610964i | ||||
\(473\) | −2.77549 | + | 3.30770i | −0.127617 | + | 0.152088i | ||||
\(474\) | −7.87374 | −0.361653 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.89321 | −0.361784 | ||||||||
\(477\) | −18.4380 | + | 21.9736i | −0.844219 | + | 1.00610i | ||||
\(478\) | 4.51672 | + | 12.4096i | 0.206590 | + | 0.567601i | ||||
\(479\) | −0.664874 | − | 3.77069i | −0.0303789 | − | 0.172287i | 0.965843 | − | 0.259126i | \(-0.0834345\pi\) |
−0.996222 | + | 0.0868390i | \(0.972323\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.1137 | + | 6.59284i | 0.825912 | + | 0.300607i | ||||
\(482\) | 6.11085 | − | 3.52810i | 0.278341 | − | 0.160700i | ||||
\(483\) | 14.8852 | + | 8.59395i | 0.677298 | + | 0.391038i | ||||
\(484\) | 5.79566 | − | 4.86314i | 0.263439 | − | 0.221052i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.35551 | + | 16.2042i | −0.424375 | + | 0.735039i | ||||
\(487\) | 30.6951 | − | 17.7218i | 1.39093 | − | 0.803052i | 0.397509 | − | 0.917598i | \(-0.369875\pi\) |
0.993418 | + | 0.114546i | \(0.0365414\pi\) | |||||||
\(488\) | −0.0908082 | + | 0.249493i | −0.00411069 | + | 0.0112940i | ||||
\(489\) | 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 | \(0.450608\pi\) | |||||||
\(492\) | 2.75644 | − | 3.28500i | 0.124270 | − | 0.148099i | ||||
\(493\) | 25.8936i | 1.16619i | ||||||||
\(494\) | −23.3336 | + | 5.74541i | −1.04983 | + | 0.258498i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.26039 | − | 2.73579i | −0.146396 | − | 0.122841i | ||||
\(497\) | 3.04141 | + | 8.35621i | 0.136426 | + | 0.374827i | ||||
\(498\) | 37.7265 | − | 6.65219i | 1.69056 | − | 0.298092i | ||||
\(499\) | −6.45368 | + | 36.6007i | −0.288907 | + | 1.63847i | 0.402081 | + | 0.915604i | \(0.368287\pi\) |
−0.690988 | + | 0.722866i | \(0.742824\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26.9465 | + | 46.6726i | 1.20388 | + | 2.08518i | ||||
\(502\) | −2.02094 | − | 1.16679i | −0.0901991 | − | 0.0520765i | ||||
\(503\) | −14.0913 | − | 16.7933i | −0.628299 | − | 0.748778i | 0.354175 | − | 0.935179i | \(-0.384762\pi\) |
−0.982474 | + | 0.186402i | \(0.940317\pi\) | |||||||
\(504\) | −7.31257 | + | 6.13598i | −0.325728 | + | 0.273318i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.72743 | + | 4.72404i | 0.121249 | + | 0.210009i | ||||
\(507\) | 16.2556 | − | 44.6620i | 0.721939 | − | 1.98351i | ||||
\(508\) | −15.2786 | − | 2.69403i | −0.677878 | − | 0.119528i | ||||
\(509\) | 1.71368 | + | 9.71877i | 0.0759576 | + | 0.430777i | 0.998944 | + | 0.0459444i | \(0.0146297\pi\) |
−0.922986 | + | 0.384833i | \(0.874259\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.2268 | + | 21.1678i | 1.11597 | + | 0.936408i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 12.6068 | − | 12.1033i | 0.556603 | − | 0.534374i | ||||
\(514\) | 5.54056 | 0.244384 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.98298 | + | 2.17763i | −0.263386 | + | 0.0958647i | ||||
\(517\) | 20.4705 | − | 3.60950i | 0.900291 | − | 0.158746i | ||||
\(518\) | 7.35809 | + | 1.29743i | 0.323296 | + | 0.0570058i | ||||
\(519\) | −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 | \(0.126561\pi\) | |||||||
\(522\) | 20.1290 | + | 23.9889i | 0.881024 | + | 1.04996i | ||||
\(523\) | 17.1734 | + | 20.4665i | 0.750941 | + | 0.894937i | 0.997239 | − | 0.0742573i | \(-0.0236586\pi\) |
−0.246298 | + | 0.969194i | \(0.579214\pi\) | |||||||
\(524\) | 11.0260 | − | 19.0976i | 0.481674 | − | 0.834283i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.66651 | + | 0.606559i | 0.0726632 | + | 0.0264472i | ||||
\(527\) | −15.4825 | − | 2.72998i | −0.674428 | − | 0.118920i | ||||
\(528\) | −4.98712 | + | 0.879364i | −0.217037 | + | 0.0382694i | ||||
\(529\) | −13.4713 | + | 4.90314i | −0.585707 | + | 0.213180i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 63.1012 | 2.73836 | ||||||||
\(532\) | −8.52018 | + | 3.76366i | −0.369397 | + | 0.163175i | ||||
\(533\) | 8.65143i | 0.374735i | ||||||||
\(534\) | 4.14350 | + | 3.47681i | 0.179307 | + | 0.150456i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.56577 | − | 14.5512i | −0.110824 | − | 0.628515i | ||||
\(537\) | −3.36415 | − | 0.593190i | −0.145174 | − | 0.0255980i | ||||
\(538\) | −5.44995 | + | 14.9736i | −0.234964 | + | 0.645558i | ||||
\(539\) | 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 | \(0.0456604\pi\) | |||||||
\(542\) | −9.06330 | − | 10.8012i | −0.389302 | − | 0.463952i | ||||
\(543\) | 37.3664 | + | 21.5735i | 1.60355 | + | 0.925807i | ||||
\(544\) | −1.84690 | − | 3.19893i | −0.0791853 | − | 0.137153i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.59005 | − | 31.7027i | 0.239232 | − | 1.35675i | ||||
\(547\) | −17.1347 | + | 3.02131i | −0.732627 | + | 0.129182i | −0.527502 | − | 0.849554i | \(-0.676871\pi\) |
−0.205125 | + | 0.978736i | \(0.565760\pi\) | |||||||
\(548\) | 4.76868 | + | 13.1019i | 0.203708 | + | 0.559683i | ||||
\(549\) | 0.908582 | + | 0.762391i | 0.0387773 | + | 0.0325380i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.3467 | + | 27.9504i | 0.525986 | + | 1.19073i | ||||
\(552\) | 8.04347i | 0.342353i | ||||||||
\(553\) | 3.95775 | − | 4.71667i | 0.168301 | − | 0.200573i | ||||
\(554\) | −20.9230 | + | 7.61536i | −0.888934 | + | 0.323546i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.14081 | − | 12.1412i | 0.0907907 | − | 0.514900i | ||||
\(557\) | 4.04009 | − | 11.1000i | 0.171184 | − | 0.470324i | −0.824200 | − | 0.566299i | \(-0.808375\pi\) |
0.995384 | + | 0.0959752i | \(0.0305969\pi\) | |||||||
\(558\) | −16.4658 | + | 9.50654i | −0.697053 | + | 0.402444i | ||||
\(559\) | 6.42257 | − | 11.1242i | 0.271646 | − | 0.470504i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.3293 | + | 12.0238i | −0.604986 | + | 0.507643i | ||||
\(562\) | −6.32870 | − | 3.65388i | −0.266960 | − | 0.154130i | ||||
\(563\) | 27.1901 | − | 15.6982i | 1.14592 | − | 0.661600i | 0.198034 | − | 0.980195i | \(-0.436544\pi\) |
0.947891 | + | 0.318595i | \(0.103211\pi\) | |||||||
\(564\) | 28.8020 | + | 10.4831i | 1.21278 | + | 0.441417i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.78983 | + | 10.1506i | 0.0752323 | + | 0.426663i | ||||
\(567\) | −1.78741 | − | 4.91087i | −0.0750642 | − | 0.206237i | ||||
\(568\) | −2.67493 | + | 3.18785i | −0.112237 | + | 0.133759i | ||||
\(569\) | −3.95114 | −0.165640 | −0.0828202 | − | 0.996565i | \(-0.526393\pi\) | ||||
−0.0828202 | + | 0.996565i | \(0.526393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.18380 | 0.0913891 | 0.0456946 | − | 0.998955i | \(-0.485450\pi\) | ||||
0.0456946 | + | 0.998955i | \(0.485450\pi\) | |||||||
\(572\) | 6.56709 | − | 7.82636i | 0.274584 | − | 0.327236i | ||||
\(573\) | −1.91694 | − | 5.26674i | −0.0800812 | − | 0.220021i | ||||
\(574\) | 0.582306 | + | 3.30242i | 0.0243050 | + | 0.137840i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.19781 | − | 1.52788i | −0.174909 | − | 0.0636615i | ||||
\(577\) | −11.2886 | + | 6.51747i | −0.469950 | + | 0.271326i | −0.716219 | − | 0.697876i | \(-0.754129\pi\) |
0.246269 | + | 0.969202i | \(0.420795\pi\) | |||||||
\(578\) | 2.90621 | + | 1.67790i | 0.120883 | + | 0.0697916i | ||||
\(579\) | 1.72256 | − | 1.44540i | 0.0715872 | − | 0.0600688i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.9784 | + | 25.9433i | −0.621408 | + | 1.07631i | ||||
\(582\) | −25.5821 | + | 14.7699i | −1.06041 | + | 0.612230i | ||||
\(583\) | 4.06987 | − | 11.1819i | 0.168557 | − | 0.463106i | ||||
\(584\) | −2.67608 | + | 15.1768i | −0.110737 | + | 0.628020i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.7884 | + | 10.4781i | −1.18924 | + | 0.432847i | ||||
\(587\) | −24.9144 | + | 29.6918i | −1.02833 | + | 1.22551i | −0.0544318 | + | 0.998517i | \(0.517335\pi\) |
−0.973896 | + | 0.226996i | \(0.927110\pi\) | |||||||
\(588\) | 6.65054i | 0.274263i | ||||||||
\(589\) | −18.0140 | + | 4.43558i | −0.742255 | + | 0.182765i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.5891 | − | 22.3109i | −1.09373 | − | 0.917750i | ||||
\(592\) | 1.19588 | + | 3.28564i | 0.0491502 | + | 0.135039i | ||||
\(593\) | 17.1453 | − | 3.02318i | 0.704073 | − | 0.124147i | 0.189862 | − | 0.981811i | \(-0.439196\pi\) |
0.514211 | + | 0.857664i | \(0.328085\pi\) | |||||||
\(594\) | −1.29022 | + | 7.31717i | −0.0529382 | + | 0.300227i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.2574 | − | 19.4983i | −0.461119 | − | 0.798682i | ||||
\(597\) | 12.0903 | + | 6.98031i | 0.494821 | + | 0.285685i | ||||
\(598\) | −10.4308 | − | 12.4310i | −0.426547 | − | 0.508339i | ||||
\(599\) | 24.6574 | − | 20.6900i | 1.00747 | − | 0.845370i | 0.0194709 | − | 0.999810i | \(-0.493802\pi\) |
0.988002 | + | 0.154440i | \(0.0493574\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.1105 | − | 31.3683i | −0.738742 | − | 1.27954i | −0.953062 | − | 0.302775i | \(-0.902087\pi\) |
0.214321 | − | 0.976763i | \(-0.431246\pi\) | |||||||
\(602\) | 1.70288 | − | 4.67862i | 0.0694042 | − | 0.190686i | ||||
\(603\) | −65.0032 | − | 11.4618i | −2.64714 | − | 0.466761i | ||||
\(604\) | −3.93230 | − | 22.3012i | −0.160003 | − | 0.907422i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −20.8830 | − | 17.5229i | −0.848314 | − | 0.711820i | ||||
\(607\) | − | 30.3654i | − | 1.23250i | −0.787552 | − | 0.616248i | \(-0.788652\pi\) | ||
0.787552 | − | 0.616248i | \(-0.211348\pi\) | |||||||
\(608\) | −3.51893 | − | 2.57238i | −0.142711 | − | 0.104324i | ||||
\(609\) | −40.9334 | −1.65870 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −58.1072 | + | 21.1493i | −2.35076 | + | 0.855608i | ||||
\(612\) | −16.2503 | + | 2.86537i | −0.656881 | + | 0.115826i | ||||
\(613\) | −22.4794 | − | 3.96373i | −0.907936 | − | 0.160094i | −0.299870 | − | 0.953980i | \(-0.596943\pi\) |
−0.608066 | + | 0.793886i | \(0.708054\pi\) | |||||||
\(614\) | −7.50580 | − | 2.73189i | −0.302910 | − | 0.110250i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.98002 | − | 3.42949i | 0.0797771 | − | 0.138178i | ||||
\(617\) | −25.5214 | − | 30.4152i | −1.02745 | − | 1.22447i | −0.974153 | − | 0.225890i | \(-0.927471\pi\) |
−0.0532981 | − | 0.998579i | \(-0.516973\pi\) | |||||||
\(618\) | 15.4135 | + | 18.3691i | 0.620023 | + | 0.738915i | ||||
\(619\) | 19.6707 | − | 34.0707i | 0.790633 | − | 1.36942i | −0.134943 | − | 0.990853i | \(-0.543085\pi\) |
0.925576 | − | 0.378562i | \(-0.123581\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.0898 | + | 4.03635i | 0.445017 | + | 0.161973i | ||||
\(622\) | 26.2264 | + | 4.62442i | 1.05158 | + | 0.185422i | ||||
\(623\) | −4.16548 | + | 0.734486i | −0.166886 | + | 0.0294266i | ||||
\(624\) | 14.1564 | − | 5.15249i | 0.566708 | − | 0.206265i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.66333 | −0.306288 | ||||||||
\(627\) | −9.73436 | + | 19.8114i | −0.388753 | + | 0.791190i | ||||
\(628\) | − | 14.8850i | − | 0.593974i | ||||||
\(629\) | 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 | \(0.929168\pi\) | |||||||
\(632\) | 2.83761 | + | 0.500348i | 0.112874 | + | 0.0199028i | ||||
\(633\) | 18.2175 | − | 50.0522i | 0.724082 | − | 1.98940i | ||||
\(634\) | −1.48304 | − | 2.56871i | −0.0588992 | − | 0.102016i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 13.4414 | − | 11.2786i | 0.532985 | − | 0.447227i | ||||
\(637\) | −8.62445 | − | 10.2782i | −0.341713 | − | 0.407238i | ||||
\(638\) | −11.2504 | − | 6.49543i | −0.445408 | − | 0.257157i | ||||
\(639\) | 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 | \(0.949300\pi\) | |||||||
\(642\) | −15.3481 | + | 2.70628i | −0.605740 | + | 0.106808i | ||||
\(643\) | −11.7811 | − | 32.3683i | −0.464601 | − | 1.27648i | −0.921990 | − | 0.387214i | \(-0.873438\pi\) |
0.457389 | − | 0.889267i | \(-0.348785\pi\) | |||||||
\(644\) | −4.81834 | − | 4.04307i | −0.189869 | − | 0.159319i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.0077 | − | 1.72975i | −0.629816 | − | 0.0680561i | ||||
\(647\) | 5.97186i | 0.234778i | 0.993086 | + | 0.117389i | \(0.0374525\pi\) | ||||
−0.993086 | + | 0.117389i | \(0.962548\pi\) | |||||||
\(648\) | 1.57203 | − | 1.87347i | 0.0617551 | − | 0.0735969i | ||||
\(649\) | −24.5983 | + | 8.95307i | −0.965570 | + | 0.351439i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.31564 | − | 24.4752i | 0.169143 | − | 0.959258i | ||||
\(652\) | −3.78402 | + | 10.3965i | −0.148194 | + | 0.407159i | ||||
\(653\) | −7.32332 | + | 4.22812i | −0.286584 | + | 0.165459i | −0.636400 | − | 0.771359i | \(-0.719577\pi\) |
0.349816 | + | 0.936818i | \(0.386244\pi\) | |||||||
\(654\) | −1.08363 | + | 1.87691i | −0.0423734 | + | 0.0733928i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.20214 | + | 1.00872i | −0.0469357 | + | 0.0393838i | ||||
\(657\) | 59.6206 | + | 34.4220i | 2.32602 | + | 1.34293i | ||||
\(658\) | −20.7571 | + | 11.9841i | −0.809198 | + | 0.467191i | ||||
\(659\) | −21.5906 | − | 7.85832i | −0.841049 | − | 0.306117i | −0.114664 | − | 0.993404i | \(-0.536579\pi\) |
−0.726385 | + | 0.687288i | \(0.758801\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.06768 | + | 23.0690i | 0.158214 | + | 0.897278i | 0.955788 | + | 0.294057i | \(0.0950054\pi\) |
−0.797574 | + | 0.603222i | \(0.793883\pi\) | |||||||
\(662\) | 0.909909 | + | 2.49995i | 0.0353646 | + | 0.0971635i | ||||
\(663\) | 35.7690 | − | 42.6279i | 1.38915 | − | 1.65553i | ||||
\(664\) | −14.0189 | −0.544040 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.6196 | 0.605249 | ||||||||
\(667\) | −13.2633 | + | 15.8065i | −0.513556 | + | 0.612032i | ||||
\(668\) | −6.74534 | − | 18.5327i | −0.260985 | − | 0.717051i | ||||
\(669\) | 1.16089 | + | 6.58374i | 0.0448826 | + | 0.254542i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.462358 | − | 0.168285i | −0.0178491 | − | 0.00649655i | ||||
\(672\) | 5.05696 | − | 2.91964i | 0.195076 | − | 0.112627i | ||||
\(673\) | −0.0327120 | − | 0.0188863i | −0.00126095 | − | 0.000728012i | 0.499369 | − | 0.866389i | \(-0.333565\pi\) |
−0.500630 | + | 0.865661i | \(0.666898\pi\) | |||||||
\(674\) | −23.9959 | + | 20.1349i | −0.924287 | + | 0.775569i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.69647 | + | 15.0627i | −0.334480 | + | 0.579336i | ||||
\(677\) | −26.9197 | + | 15.5421i | −1.03461 | + | 0.597332i | −0.918302 | − | 0.395882i | \(-0.870439\pi\) |
−0.116307 | + | 0.993213i | \(0.537106\pi\) | |||||||
\(678\) | 4.66001 | − | 12.8033i | 0.178966 | − | 0.491706i | ||||
\(679\) | 4.01122 | − | 22.7488i | 0.153937 | − | 0.873018i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −49.3791 | + | 17.9725i | −1.89221 | + | 0.688709i | ||||
\(682\) | 5.06994 | − | 6.04212i | 0.194138 | − | 0.231365i | ||||
\(683\) | 22.0437i | 0.843481i | 0.906717 | + | 0.421740i | \(0.138581\pi\) | ||||
−0.906717 | + | 0.421740i | \(0.861419\pi\) | |||||||
\(684\) | −16.1749 | + | 10.8415i | −0.618461 | + | 0.414535i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.4425 | − | 12.9578i | −0.589598 | − | 0.494732i | ||||
\(687\) | −19.0540 | − | 52.3505i | −0.726957 | − | 1.99730i | ||||
\(688\) | 2.29458 | − | 0.404597i | 0.0874802 | − | 0.0154251i | ||||
\(689\) | −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 | \(0.883202\pi\) | |||||||
\(692\) | 5.24622 | + | 3.02890i | 0.199431 | + | 0.115142i | ||||
\(693\) | −11.3711 | − | 13.5516i | −0.431953 | − | 0.514781i | ||||
\(694\) | 8.13364 | − | 6.82494i | 0.308749 | − | 0.259071i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.57786 | − | 16.5893i | −0.363048 | − | 0.628817i | ||||
\(697\) | −1.98256 | + | 5.44705i | −0.0750950 | + | 0.206322i | ||||
\(698\) | 36.3954 | + | 6.41749i | 1.37759 | + | 0.242906i | ||||
\(699\) | 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 | \(0.700778\pi\) | |||||||
\(702\) | − | 22.1034i | − | 0.834239i | ||||||
\(703\) | 14.6382 | + | 4.24372i | 0.552089 | + | 0.160055i | ||||
\(704\) | 1.85319 | 0.0698446 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28.9940 | − | 10.5530i | 1.09120 | − | 0.397166i | ||||
\(707\) | 20.9938 | − | 3.70177i | 0.789553 | − | 0.139219i | ||||
\(708\) | −38.0130 | − | 6.70271i | −1.42861 | − | 0.251903i | ||||
\(709\) | 16.7368 | + | 6.09168i | 0.628562 | + | 0.228778i | 0.636605 | − | 0.771190i | \(-0.280338\pi\) |
−0.00804307 | + | 0.999968i | \(0.502560\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.43589 | − | 11.1473i | 0.241365 | − | 0.418056i | ||||
\(712\) | −1.27233 | − | 1.51631i | −0.0476827 | − | 0.0568261i | ||||
\(713\) | −8.05281 | − | 9.59696i | −0.301580 | − | 0.359409i | ||||
\(714\) | 10.7846 | − | 18.6794i | 0.403602 | − | 0.699060i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.17471 | + | 0.427559i | 0.0439009 | + | 0.0159786i | ||||
\(717\) | −35.5387 | − | 6.26644i | −1.32722 | − | 0.234024i | ||||
\(718\) | 9.98574 | − | 1.76076i | 0.372664 | − | 0.0657108i | ||||
\(719\) | 17.0854 | − | 6.21856i | 0.637176 | − | 0.231913i | −0.00317562 | − | 0.999995i | \(-0.501011\pi\) |
0.640352 | + | 0.768082i | \(0.278789\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.7515 | −0.698341 | ||||||||
\(722\) | −18.1041 | + | 5.76570i | −0.673763 | + | 0.214577i | ||||
\(723\) | 19.2819i | 0.717102i | ||||||||
\(724\) | −12.0955 | − | 10.1494i | −0.449527 | − | 0.377198i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.59003 | + | 20.3601i | 0.133239 | + | 0.755634i | ||||
\(727\) | 8.37743 | + | 1.47717i | 0.310702 | + | 0.0547851i | 0.326825 | − | 0.945085i | \(-0.394021\pi\) |
−0.0161233 | + | 0.999870i | \(0.505132\pi\) | |||||||
\(728\) | −4.02919 | + | 11.0701i | −0.149332 | + | 0.410285i | ||||
\(729\) | −21.8966 | − | 37.9260i | −0.810985 | − | 1.40467i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.59296 | − | 5.53215i | 0.243849 | − | 0.204614i | ||||
\(732\) | −0.466359 | − | 0.555785i | −0.0172371 | − | 0.0205424i | ||||
\(733\) | 44.1595 | + | 25.4955i | 1.63107 | + | 0.941698i | 0.983764 | + | 0.179468i | \(0.0574377\pi\) |
0.647306 | + | 0.762230i | \(0.275896\pi\) | |||||||
\(734\) | 5.88751 | + | 10.1975i | 0.217312 | + | 0.376395i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.511133 | − | 2.89878i | 0.0188406 | − | 0.106851i | ||||
\(737\) | 26.9661 | − | 4.75484i | 0.993307 | − | 0.175147i | ||||
\(738\) | 2.39767 | + | 6.58755i | 0.0882596 | + | 0.242491i | ||||
\(739\) | 1.19013 | + | 0.998640i | 0.0437798 | + | 0.0367356i | 0.664415 | − | 0.747364i | \(-0.268681\pi\) |
−0.620635 | + | 0.784099i | \(0.713125\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.2843 | − | 63.0694i | 0.671691 | − | 2.31691i | ||||
\(742\) | 13.7211i | 0.503718i | ||||||||
\(743\) | 6.37470 | − | 7.59707i | 0.233865 | − | 0.278710i | −0.636330 | − | 0.771417i | \(-0.719548\pi\) |
0.870195 | + | 0.492707i | \(0.163993\pi\) | |||||||
\(744\) | 10.9290 | − | 3.97784i | 0.400677 | − | 0.145835i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.39869 | + | 19.2749i | −0.124435 | + | 0.705704i | ||||
\(747\) | −21.4192 | + | 58.8488i | −0.783688 | + | 2.15317i | ||||
\(748\) | 5.92821 | − | 3.42266i | 0.216757 | − | 0.125145i | ||||
\(749\) | 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 | \(0.304620\pi\) | |||||||
\(752\) | −9.71378 | − | 5.60825i | −0.354225 | − | 0.204512i | ||||
\(753\) | 5.52247 | − | 3.18840i | 0.201250 | − | 0.116192i | ||||
\(754\) | 36.3154 | + | 13.2177i | 1.32253 | + | 0.481362i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.48772 | − | 8.43730i | −0.0541080 | − | 0.306862i | ||||
\(757\) | −7.94810 | − | 21.8372i | −0.288879 | − | 0.793688i | −0.996224 | − | 0.0868196i | \(-0.972330\pi\) |
0.707345 | − | 0.706868i | \(-0.249893\pi\) | |||||||
\(758\) | −12.2709 | + | 14.6238i | −0.445698 | + | 0.531162i | ||||
\(759\) | −14.9060 | −0.541055 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.6042 | −0.928152 | −0.464076 | − | 0.885795i | \(-0.653614\pi\) | ||||
−0.464076 | + | 0.885795i | \(0.653614\pi\) | |||||||
\(762\) | 27.2508 | − | 32.4762i | 0.987191 | − | 1.17649i | ||||
\(763\) | −0.579647 | − | 1.59257i | −0.0209846 | − | 0.0576548i | ||||
\(764\) | 0.356162 | + | 2.01989i | 0.0128855 | + | 0.0730771i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.4874 | + | 6.72885i | 0.667975 | + | 0.243123i | ||||
\(767\) | 67.4401 | − | 38.9365i | 2.43512 | − | 1.40592i | ||||
\(768\) | 2.36652 | + | 1.36631i | 0.0853944 | + | 0.0493025i | ||||
\(769\) | −19.0328 | + | 15.9704i | −0.686339 | + | 0.575907i | −0.917851 | − | 0.396925i | \(-0.870077\pi\) |
0.231512 | + | 0.972832i | \(0.425633\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.57012 | + | 13.1118i | −0.272631 | + | 0.472211i | ||||
\(772\) | −0.712643 | + | 0.411445i | −0.0256486 | + | 0.0148082i | ||||
\(773\) | 12.6153 | − | 34.6603i | 0.453741 | − | 1.24664i | −0.476330 | − | 0.879266i | \(-0.658033\pi\) |
0.930072 | − | 0.367378i | \(-0.119744\pi\) | |||||||
\(774\) | 1.80742 | − | 10.2504i | 0.0649664 | − | 0.368443i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.1581 | − | 3.69725i | 0.364655 | − | 0.132723i | ||||
\(777\) | −13.1238 | + | 15.6404i | −0.470815 | + | 0.561095i | ||||
\(778\) | − | 24.0483i | − | 0.862175i | ||||||
\(779\) | 0.457233 | + | 6.82505i | 0.0163821 | + | 0.244533i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.90769 | − | 4.95714i | −0.211394 | − | 0.177380i | ||||
\(782\) | −3.71869 | − | 10.2170i | −0.132980 | − | 0.365359i | ||||
\(783\) | −27.6785 | + | 4.88047i | −0.989150 | + | 0.174414i | ||||
\(784\) | 0.422618 | − | 2.39678i | 0.0150935 | − | 0.0855994i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 30.1299 | + | 52.1865i | 1.07470 | + | 1.86143i | ||||
\(787\) | −43.3382 | − | 25.0213i | −1.54484 | − | 0.891914i | −0.998523 | − | 0.0543351i | \(-0.982696\pi\) |
−0.546317 | − | 0.837579i | \(-0.683971\pi\) | |||||||
\(788\) | 8.16467 | + | 9.73028i | 0.290854 | + | 0.346627i | ||||
\(789\) | −3.71240 | + | 3.11507i | −0.132165 | + | 0.110900i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.32727 | + | 9.22711i | 0.189416 | + | 0.328078i | ||||
\(792\) | 2.83144 | − | 7.77932i | 0.100611 | − | 0.276426i | ||||
\(793\) | 1.44149 | + | 0.254173i | 0.0511888 | + | 0.00902596i | ||||
\(794\) | 0.441252 | + | 2.50246i | 0.0156594 | + | 0.0888091i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.91363 | − | 3.28392i | −0.138715 | − | 0.116396i | ||||
\(797\) | − | 5.53339i | − | 0.196003i | −0.995186 | − | 0.0980013i | \(-0.968755\pi\) | ||
0.995186 | − | 0.0980013i | \(-0.0312449\pi\) | |||||||
\(798\) | 2.73444 | − | 25.3055i | 0.0967981 | − | 0.895805i | ||||
\(799\) | −41.4316 | −1.46574 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.30914 | + | 3.02428i | −0.293589 | + | 0.106858i | ||||
\(802\) | 1.46191 | − | 0.257775i | 0.0516219 | − | 0.00910234i | ||||
\(803\) | −28.1254 | − | 4.95928i | −0.992525 | − | 0.175009i | ||||
\(804\) | 37.9413 | + | 13.8095i | 1.33809 | + | 0.487023i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.7320 | + | 20.3204i | −0.413242 | + | 0.715757i | ||||
\(807\) | −27.9890 | − | 33.3560i | −0.985260 | − | 1.17419i | ||||
\(808\) | 6.41250 | + | 7.64212i | 0.225591 | + | 0.268849i | ||||
\(809\) | 6.93364 | − | 12.0094i | 0.243774 | − | 0.422229i | −0.718012 | − | 0.696030i | \(-0.754948\pi\) |
0.961786 | + | 0.273802i | \(0.0882812\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.68087 | + | 2.79561i | 0.269712 | + | 0.0981670i | 0.473336 | − | 0.880882i | \(-0.343050\pi\) |
−0.203624 | + | 0.979049i | \(0.565272\pi\) | |||||||
\(812\) | 14.7520 | + | 2.60117i | 0.517693 | + | 0.0912832i | ||||
\(813\) | 37.9446 | − | 6.69065i | 1.33077 | − | 0.234651i | ||||
\(814\) | −6.08890 | + | 2.21618i | −0.213416 | + | 0.0776771i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 10.0938 | 0.353352 | ||||||||
\(817\) | 4.47880 | − | 9.11526i | 0.156693 | − | 0.318902i | ||||
\(818\) | 12.2798i | 0.429355i | ||||||||
\(819\) | 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 | \(0.663204\pi\) | |||||||
\(822\) | −37.5213 | − | 6.61601i | −1.30871 | − | 0.230760i | ||||
\(823\) | 0.288286 | − | 0.792059i | 0.0100490 | − | 0.0276094i | −0.934567 | − | 0.355788i | \(-0.884213\pi\) |
0.944616 | + | 0.328179i | \(0.106435\pi\) | |||||||
\(824\) | −4.38758 | − | 7.59952i | −0.152849 | − | 0.264742i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 23.1225 | − | 19.4021i | 0.804534 | − | 0.675084i | ||||
\(827\) | 9.08627 | + | 10.8286i | 0.315961 | + | 0.376547i | 0.900528 | − | 0.434798i | \(-0.143180\pi\) |
−0.584567 | + | 0.811345i | \(0.698736\pi\) | |||||||
\(828\) | −11.3876 | − | 6.57462i | −0.395746 | − | 0.228484i | ||||
\(829\) | 23.8392 | + | 41.2907i | 0.827969 | + | 1.43408i | 0.899629 | + | 0.436655i | \(0.143837\pi\) |
−0.0716603 | + | 0.997429i | \(0.522830\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.5655 | − | 59.9197i | 0.366511 | − | 2.07859i | ||||
\(832\) | −5.42923 | + | 0.957319i | −0.188225 | + | 0.0331891i | ||||
\(833\) | −3.07470 | − | 8.44767i | −0.106532 | − | 0.292695i | ||||
\(834\) | 25.8073 | + | 21.6549i | 0.893632 | + | 0.749847i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.76710 | − | 6.52123i | 0.164874 | − | 0.225541i | ||||
\(837\) | − | 17.0643i | − | 0.589828i | ||||||
\(838\) | 1.89707 | − | 2.26085i | 0.0655333 | − | 0.0780996i | ||||
\(839\) | −0.221512 | + | 0.0806239i | −0.00764746 | + | 0.00278345i | −0.345841 | − | 0.938293i | \(-0.612406\pi\) |
0.338194 | + | 0.941077i | \(0.390184\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.49733 | − | 19.8343i | 0.120598 | − | 0.683943i | ||||
\(842\) | 2.56507 | − | 7.04747i | 0.0883981 | − | 0.242872i | ||||
\(843\) | 17.2939 | − | 9.98466i | 0.595635 | − | 0.343890i | ||||
\(844\) | −9.74604 | + | 16.8806i | −0.335473 | + | 0.581056i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −38.3838 | + | 32.2079i | −1.31966 | + | 1.10733i | ||||
\(847\) | −14.0010 | − | 8.08348i | −0.481080 | − | 0.277752i | ||||
\(848\) | −5.56084 | + | 3.21055i | −0.190960 | + | 0.110251i | ||||
\(849\) | −26.4672 | − | 9.63326i | −0.908350 | − | 0.330613i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.78718 | + | 10.1356i | 0.0612638 | + | 0.347444i | ||||
\(852\) | −3.88933 | − | 10.6859i | −0.133246 | − | 0.366091i | ||||
\(853\) | 2.45972 | − | 2.93138i | 0.0842191 | − | 0.100368i | −0.722289 | − | 0.691591i | \(-0.756910\pi\) |
0.806508 | + | 0.591223i | \(0.201355\pi\) | |||||||
\(854\) | 0.567352 | 0.0194144 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.70326 | 0.194933 | ||||||||
\(857\) | −7.97116 | + | 9.49966i | −0.272290 | + | 0.324502i | −0.884809 | − | 0.465953i | \(-0.845712\pi\) |
0.612520 | + | 0.790455i | \(0.290156\pi\) | |||||||
\(858\) | 9.54853 | + | 26.2344i | 0.325982 | + | 0.895627i | ||||
\(859\) | −6.20007 | − | 35.1623i | −0.211544 | − | 1.19972i | −0.886805 | − | 0.462145i | \(-0.847080\pi\) |
0.675261 | − | 0.737579i | \(-0.264031\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.61085 | − | 3.13409i | −0.293457 | − | 0.106810i | ||||
\(862\) | 20.8658 | − | 12.0469i | 0.710691 | − | 0.410317i | ||||
\(863\) | −17.6983 | − | 10.2181i | −0.602458 | − | 0.347830i | 0.167550 | − | 0.985864i | \(-0.446415\pi\) |
−0.770008 | + | 0.638034i | \(0.779748\pi\) | |||||||
\(864\) | 3.07133 | − | 2.57715i | 0.104489 | − | 0.0876765i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.6917 | + | 30.6429i | −0.601188 | + | 1.04129i | ||||
\(867\) | −7.94158 | + | 4.58507i | −0.269710 | + | 0.155717i | ||||
\(868\) | −3.11062 | + | 8.54636i | −0.105581 | + | 0.290082i | ||||
\(869\) | −0.927238 | + | 5.25863i | −0.0314544 | + | 0.178387i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −76.5454 | + | 27.8602i | −2.59364 | + | 0.944008i | ||||
\(872\) | 0.509800 | − | 0.607556i | 0.0172640 | − | 0.0205745i | ||||
\(873\) | − | 48.2907i | − | 1.63439i | ||||||
\(874\) | −8.88577 | − | 9.25541i | −0.300566 | − | 0.313069i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −32.2598 | − | 27.0692i | −1.08996 | − | 0.914584i | ||||
\(877\) | 18.0436 | + | 49.5744i | 0.609289 | + | 1.67401i | 0.731782 | + | 0.681539i | \(0.238689\pi\) |
−0.122492 | + | 0.992469i | \(0.539089\pi\) | |||||||
\(878\) | −23.4258 | + | 4.13061i | −0.790584 | + | 0.139401i | ||||
\(879\) | 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 | \(-0.345956\pi\) | |||||||
\(882\) | −9.41553 | − | 5.43606i | −0.317037 | − | 0.183042i | ||||
\(883\) | 27.5683 | + | 32.8546i | 0.927746 | + | 1.10564i | 0.994167 | + | 0.107853i | \(0.0343976\pi\) |
−0.0664209 | + | 0.997792i | \(0.521158\pi\) | |||||||
\(884\) | −15.5996 | + | 13.0896i | −0.524672 | + | 0.440252i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.85074 | + | 11.8658i | 0.230155 | + | 0.398640i | ||||
\(887\) | −10.0908 | + | 27.7243i | −0.338816 | + | 0.930889i | 0.646915 | + | 0.762562i | \(0.276059\pi\) |
−0.985731 | + | 0.168327i | \(0.946163\pi\) | |||||||
\(888\) | −9.40946 | − | 1.65914i | −0.315761 | − | 0.0556772i | ||||
\(889\) | 5.75681 | + | 32.6485i | 0.193077 | + | 1.09499i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.47189 | + | 2.91326i | 0.116313 | + | 0.0975980i | ||||
\(892\) | − | 2.44648i | − | 0.0819142i | ||||||
\(893\) | −44.7226 | + | 19.7555i | −1.49658 | + | 0.661093i | ||||
\(894\) | 61.5242 | 2.05768 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.00801 | + | 0.730855i | −0.0670828 | + | 0.0244161i | ||||
\(897\) | 43.6698 | − | 7.70016i | 1.45809 | − | 0.257101i | ||||
\(898\) | 14.9327 | + | 2.63303i | 0.498310 | + | 0.0878655i | ||||
\(899\) | 28.0363 | + | 10.2044i | 0.935063 | + | 0.340335i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.8592 | + | 20.5407i | −0.395086 | + | 0.684309i | ||||
\(902\) | −1.86934 | − | 2.22779i | −0.0622422 | − | 0.0741774i | ||||
\(903\) | 8.74538 | + | 10.4223i | 0.291028 | + | 0.346834i | ||||
\(904\) | −2.49302 | + | 4.31803i | −0.0829166 | + | 0.143616i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 58.1489 | + | 21.1645i | 1.93187 | + | 0.703142i | ||||
\(907\) | 27.3787 | + | 4.82761i | 0.909095 | + | 0.160298i | 0.608593 | − | 0.793483i | \(-0.291734\pi\) |
0.300503 | + | 0.953781i | \(0.402846\pi\) | |||||||
\(908\) | 18.9378 | − | 3.33925i | 0.628473 | − | 0.110817i | ||||
\(909\) | 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 | \(0.422703\pi\) | |||||||
\(912\) | 10.8955 | − | 4.81294i | 0.360787 | − | 0.159372i | ||||
\(913\) | − | 25.9797i | − | 0.859803i | ||||||
\(914\) | −25.7213 | − | 21.5828i | −0.850786 | − | 0.713894i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.54019 | + | 20.0774i | 0.116971 | + | 0.663376i | ||||
\(917\) | −46.4066 | − | 8.18273i | −1.53248 | − | 0.270218i | ||||
\(918\) | 5.06522 | − | 13.9166i | 0.167177 | − | 0.459315i | ||||
\(919\) | 5.09200 | + | 8.81961i | 0.167970 | + | 0.290932i | 0.937706 | − | 0.347430i | \(-0.112946\pi\) |
−0.769736 | + | 0.638362i | \(0.779612\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.7203 | − | 14.0300i | 0.550953 | − | 0.462305i | ||||
\(922\) | −16.9216 | − | 20.1663i | −0.557282 | − | 0.664142i | ||||
\(923\) | 19.8683 | + | 11.4710i | 0.653974 | + | 0.377572i | ||||
\(924\) | 5.41063 | + | 9.37149i | 0.177997 | + | 0.308299i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.83185 | − | 10.3890i | 0.0601984 | − | 0.341402i | ||||
\(927\) | −38.6050 | + | 6.80710i | −1.26795 | + | 0.223575i | ||||
\(928\) | 2.39757 | + | 6.58726i | 0.0787040 | + | 0.216237i | ||||
\(929\) | 6.91896 | + | 5.80570i | 0.227004 | + | 0.190479i | 0.749195 | − | 0.662350i | \(-0.230441\pi\) |
−0.522191 | + | 0.852829i | \(0.674885\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.34697 | − | 7.65260i | −0.240787 | − | 0.250804i | ||||
\(932\) | − | 8.41911i | − | 0.275777i | ||||||
\(933\) | −46.7772 | + | 55.7469i | −1.53142 | + | 1.82507i | ||||
\(934\) | 28.6764 | − | 10.4373i | 0.938320 | − | 0.341520i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.27655 | + | 24.2535i | −0.139783 | + | 0.792751i | ||||
\(937\) | 13.4626 | − | 36.9882i | 0.439804 | − | 1.20835i | −0.499816 | − | 0.866131i | \(-0.666599\pi\) |
0.939620 | − | 0.342219i | \(-0.111179\pi\) | |||||||
\(938\) | −27.3437 | + | 15.7869i | −0.892802 | + | 0.515460i | ||||
\(939\) | 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 | \(0.0262738\pi\) | |||||||
\(942\) | 35.2255 | + | 20.3375i | 1.14771 | + | 0.662630i | ||||
\(943\) | −4.00033 | + | 2.30959i | −0.130269 | + | 0.0752107i | ||||
\(944\) | 13.2735 | + | 4.83117i | 0.432017 | + | 0.157241i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.749794 | + | 4.25229i | 0.0243779 | + | 0.138254i | ||||
\(947\) | −9.00717 | − | 24.7470i | −0.292694 | − | 0.804170i | −0.995670 | − | 0.0929564i | \(-0.970368\pi\) |
0.702976 | − | 0.711213i | \(-0.251854\pi\) | |||||||
\(948\) | −5.06114 | + | 6.03163i | −0.164378 | + | 0.195898i | ||||
\(949\) | 84.9601 | 2.75792 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.10520 | 0.262829 | ||||||||
\(952\) | −5.07365 | + | 6.04655i | −0.164438 | + | 0.195970i | ||||
\(953\) | 0.328958 | + | 0.903804i | 0.0106560 | + | 0.0292771i | 0.944907 | − | 0.327340i | \(-0.106152\pi\) |
−0.934251 | + | 0.356617i | \(0.883930\pi\) | |||||||
\(954\) | 4.98100 | + | 28.2487i | 0.161266 | + | 0.914585i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.4096 | + | 4.51672i | 0.401354 | + | 0.146081i | ||||
\(957\) | 30.7431 | − | 17.7496i | 0.993784 | − | 0.573762i | ||||
\(958\) | −3.31589 | − | 1.91443i | −0.107131 | − | 0.0618524i | ||||
\(959\) | 22.8234 | − | 19.1511i | 0.737006 | − | 0.618422i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.44264 | − | 11.1590i | 0.207827 | − | 0.359967i | ||||
\(962\) | 16.6936 | − | 9.63808i | 0.538225 | − | 0.310744i | ||||
\(963\) | 8.71388 | − | 23.9412i | 0.280801 | − | 0.771494i | ||||
\(964\) | 1.22530 | − | 6.94900i | 0.0394641 | − | 0.223812i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16.1513 | − | 5.87861i | 0.519661 | − | 0.189141i | ||||
\(967\) | 11.5906 | − | 13.8131i | 0.372728 | − | 0.444200i | −0.546777 | − | 0.837278i | \(-0.684145\pi\) |
0.919505 | + | 0.393078i | \(0.128590\pi\) | |||||||
\(968\) | − | 7.56570i | − | 0.243171i | ||||||
\(969\) | 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 | \(0.777114\pi\) | |||||||
\(972\) | 6.39955 | + | 17.5826i | 0.205266 | + | 0.563963i | ||||
\(973\) | −25.9442 | + | 4.57465i | −0.831731 | + | 0.146657i | ||||
\(974\) | 6.15472 | − | 34.9052i | 0.197210 | − | 1.11843i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.132753 | + | 0.229934i | 0.00424931 | + | 0.00736002i | ||||
\(977\) | 43.6839 | + | 25.2209i | 1.39757 | + | 0.806889i | 0.994138 | − | 0.108119i | \(-0.0344829\pi\) |
0.403435 | + | 0.915008i | \(0.367816\pi\) | |||||||
\(978\) | −19.4334 | − | 23.1598i | −0.621411 | − | 0.740569i | ||||
\(979\) | 2.81000 | − | 2.35787i | 0.0898081 | − | 0.0753580i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.77149 | − | 3.06832i | −0.0565594 | − | 0.0979638i | ||||
\(982\) | −2.92055 | + | 8.02415i | −0.0931985 | + | 0.256061i | ||||
\(983\) | −49.3325 | − | 8.69866i | −1.57346 | − | 0.277444i | −0.682282 | − | 0.731090i | \(-0.739012\pi\) |
−0.891182 | + | 0.453645i | \(0.850123\pi\) | |||||||
\(984\) | −0.744648 | − | 4.22311i | −0.0237385 | − | 0.134628i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 19.8357 | + | 16.6441i | 0.631696 | + | 0.530056i | ||||
\(987\) | − | 65.4962i | − | 2.08477i | ||||||
\(988\) | −10.5973 | + | 21.5676i | −0.337145 | + | 0.686158i | ||||
\(989\) | 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 | \(0.462970\pi\) | |||||||
\(992\) | −4.19148 | + | 0.739071i | −0.133080 | + | 0.0234655i | ||||
\(993\) | −7.15941 | − | 1.26240i | −0.227197 | − | 0.0400609i | ||||
\(994\) | 8.35621 | + | 3.04141i | 0.265043 | + | 0.0964678i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 19.1542 | − | 33.1761i | 0.606925 | − | 1.05122i | ||||
\(997\) | −15.4366 | − | 18.3966i | −0.488882 | − | 0.582627i | 0.464051 | − | 0.885809i | \(-0.346395\pi\) |
−0.952933 | + | 0.303182i | \(0.901951\pi\) | |||||||
\(998\) | 23.8894 | + | 28.4703i | 0.756205 | + | 0.901210i | ||||
\(999\) | −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.u.h.149.8 | 48 | ||
5.2 | odd | 4 | 950.2.l.k.301.4 | yes | 24 | ||
5.3 | odd | 4 | 950.2.l.j.301.1 | yes | 24 | ||
5.4 | even | 2 | inner | 950.2.u.h.149.1 | 48 | ||
19.6 | even | 9 | inner | 950.2.u.h.899.1 | 48 | ||
95.44 | even | 18 | inner | 950.2.u.h.899.8 | 48 | ||
95.63 | odd | 36 | 950.2.l.j.101.1 | ✓ | 24 | ||
95.82 | odd | 36 | 950.2.l.k.101.4 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.l.j.101.1 | ✓ | 24 | 95.63 | odd | 36 | ||
950.2.l.j.301.1 | yes | 24 | 5.3 | odd | 4 | ||
950.2.l.k.101.4 | yes | 24 | 95.82 | odd | 36 | ||
950.2.l.k.301.4 | yes | 24 | 5.2 | odd | 4 | ||
950.2.u.h.149.1 | 48 | 5.4 | even | 2 | inner | ||
950.2.u.h.149.8 | 48 | 1.1 | even | 1 | trivial | ||
950.2.u.h.899.1 | 48 | 19.6 | even | 9 | inner | ||
950.2.u.h.899.8 | 48 | 95.44 | even | 18 | inner |