Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(65,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("418.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.h (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.33774680449\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 41 x^{18} + 707 x^{16} + 6667 x^{14} + 37400 x^{12} + 126976 x^{10} + 253280 x^{8} + \cdots + 2304 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 373.8 | ||
Root | \(2.01980i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.373 |
Dual form | 418.2.h.b.65.8 |
$q$-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 \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(343\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 1.74919 | − | 1.00990i | 1.00990 | − | 0.583065i | 0.0987363 | − | 0.995114i | \(-0.468520\pi\) |
0.911162 | + | 0.412049i | \(0.135187\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.0648685 | + | 0.112356i | 0.0290101 | + | 0.0502469i | 0.880166 | − | 0.474666i | \(-0.157431\pi\) |
−0.851156 | + | 0.524913i | \(0.824098\pi\) | |||||||
\(6\) | 1.74919 | + | 1.00990i | 0.714106 | + | 0.412289i | ||||
\(7\) | 4.47991i | 1.69325i | 0.532191 | + | 0.846624i | \(0.321369\pi\) | ||||
−0.532191 | + | 0.846624i | \(0.678631\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.539789 | − | 0.934941i | 0.179930 | − | 0.311647i | ||||
\(10\) | −0.0648685 | + | 0.112356i | −0.0205132 | + | 0.0355300i | ||||
\(11\) | 0.0670646 | + | 3.31595i | 0.0202207 | + | 0.999796i | ||||
\(12\) | 2.01980i | 0.583065i | ||||||||
\(13\) | 1.96561 | − | 3.40453i | 0.545162 | − | 0.944248i | −0.453435 | − | 0.891289i | \(-0.649802\pi\) |
0.998597 | − | 0.0529585i | \(-0.0168651\pi\) | |||||||
\(14\) | −3.87972 | + | 2.23996i | −1.03690 | + | 0.598654i | ||||
\(15\) | 0.226935 | + | 0.131021i | 0.0585945 | + | 0.0338295i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.48638 | − | 1.43551i | 0.603035 | − | 0.348163i | −0.167199 | − | 0.985923i | \(-0.553472\pi\) |
0.770235 | + | 0.637761i | \(0.220139\pi\) | |||||||
\(18\) | 1.07958 | 0.254459 | ||||||||
\(19\) | −4.32001 | + | 0.580935i | −0.991079 | + | 0.133276i | ||||
\(20\) | −0.129737 | −0.0290101 | ||||||||
\(21\) | 4.52426 | + | 7.83624i | 0.987274 | + | 1.71001i | ||||
\(22\) | −2.83816 | + | 1.71605i | −0.605098 | + | 0.365864i | ||||
\(23\) | 2.80144 | − | 4.85224i | 0.584141 | − | 1.01176i | −0.410841 | − | 0.911707i | \(-0.634765\pi\) |
0.994982 | − | 0.100054i | \(-0.0319017\pi\) | |||||||
\(24\) | −1.74919 | + | 1.00990i | −0.357053 | + | 0.206145i | ||||
\(25\) | 2.49158 | − | 4.31555i | 0.498317 | − | 0.863110i | ||||
\(26\) | 3.93122 | 0.770975 | ||||||||
\(27\) | 3.87886i | 0.746487i | ||||||||
\(28\) | −3.87972 | − | 2.23996i | −0.733198 | − | 0.423312i | ||||
\(29\) | 1.99288 | − | 3.45178i | 0.370069 | − | 0.640979i | −0.619506 | − | 0.784992i | \(-0.712667\pi\) |
0.989576 | + | 0.144013i | \(0.0460006\pi\) | |||||||
\(30\) | 0.262042i | 0.0478422i | ||||||||
\(31\) | − | 6.05829i | − | 1.08810i | −0.839052 | − | 0.544051i | \(-0.816890\pi\) | ||
0.839052 | − | 0.544051i | \(-0.183110\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 3.46608 | + | 5.73251i | 0.603367 | + | 0.997902i | ||||
\(34\) | 2.48638 | + | 1.43551i | 0.426410 | + | 0.246188i | ||||
\(35\) | −0.503343 | + | 0.290605i | −0.0850806 | + | 0.0491213i | ||||
\(36\) | 0.539789 | + | 0.934941i | 0.0899648 | + | 0.155824i | ||||
\(37\) | 4.74193i | 0.779568i | 0.920906 | + | 0.389784i | \(0.127450\pi\) | ||||
−0.920906 | + | 0.389784i | \(0.872550\pi\) | |||||||
\(38\) | −2.66311 | − | 3.45077i | −0.432014 | − | 0.559789i | ||||
\(39\) | − | 7.94026i | − | 1.27146i | ||||||
\(40\) | −0.0648685 | − | 0.112356i | −0.0102566 | − | 0.0177650i | ||||
\(41\) | −2.41415 | − | 4.18143i | −0.377027 | − | 0.653030i | 0.613601 | − | 0.789616i | \(-0.289720\pi\) |
−0.990628 | + | 0.136586i | \(0.956387\pi\) | |||||||
\(42\) | −4.52426 | + | 7.83624i | −0.698108 | + | 1.20916i | ||||
\(43\) | −0.219263 | + | 0.126591i | −0.0334372 | + | 0.0193050i | −0.516625 | − | 0.856212i | \(-0.672812\pi\) |
0.483188 | + | 0.875517i | \(0.339479\pi\) | |||||||
\(44\) | −2.90523 | − | 1.59989i | −0.437979 | − | 0.241193i | ||||
\(45\) | 0.140061 | 0.0208791 | ||||||||
\(46\) | 5.60288 | 0.826100 | ||||||||
\(47\) | −1.82197 | + | 3.15574i | −0.265761 | + | 0.460312i | −0.967763 | − | 0.251864i | \(-0.918957\pi\) |
0.702002 | + | 0.712175i | \(0.252290\pi\) | |||||||
\(48\) | −1.74919 | − | 1.00990i | −0.252475 | − | 0.145766i | ||||
\(49\) | −13.0696 | −1.86709 | ||||||||
\(50\) | 4.98317 | 0.704726 | ||||||||
\(51\) | 2.89944 | − | 5.02198i | 0.406003 | − | 0.703217i | ||||
\(52\) | 1.96561 | + | 3.40453i | 0.272581 | + | 0.472124i | ||||
\(53\) | −0.112462 | − | 0.0649300i | −0.0154479 | − | 0.00891882i | 0.492256 | − | 0.870450i | \(-0.336172\pi\) |
−0.507704 | + | 0.861532i | \(0.669506\pi\) | |||||||
\(54\) | −3.35919 | + | 1.93943i | −0.457128 | + | 0.263923i | ||||
\(55\) | −0.368215 | + | 0.222636i | −0.0496501 | + | 0.0300202i | ||||
\(56\) | − | 4.47991i | − | 0.598654i | ||||||
\(57\) | −6.96986 | + | 5.37894i | −0.923181 | + | 0.712458i | ||||
\(58\) | 3.98577 | 0.523357 | ||||||||
\(59\) | 5.17436 | − | 2.98742i | 0.673645 | − | 0.388929i | −0.123812 | − | 0.992306i | \(-0.539512\pi\) |
0.797456 | + | 0.603377i | \(0.206178\pi\) | |||||||
\(60\) | −0.226935 | + | 0.131021i | −0.0292972 | + | 0.0169148i | ||||
\(61\) | −11.3345 | − | 6.54398i | −1.45123 | − | 0.837870i | −0.452682 | − | 0.891672i | \(-0.649533\pi\) |
−0.998552 | + | 0.0538016i | \(0.982866\pi\) | |||||||
\(62\) | 5.24664 | − | 3.02915i | 0.666324 | − | 0.384702i | ||||
\(63\) | 4.18846 | + | 2.41821i | 0.527696 | + | 0.304665i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.510025 | 0.0632608 | ||||||||
\(66\) | −3.23146 | + | 5.86797i | −0.397765 | + | 0.722297i | ||||
\(67\) | 3.51727 | + | 2.03070i | 0.429703 | + | 0.248089i | 0.699220 | − | 0.714906i | \(-0.253531\pi\) |
−0.269517 | + | 0.962996i | \(0.586864\pi\) | |||||||
\(68\) | 2.87102i | 0.348163i | ||||||||
\(69\) | − | 11.3167i | − | 1.36237i | ||||||
\(70\) | −0.503343 | − | 0.290605i | −0.0601610 | − | 0.0347340i | ||||
\(71\) | −12.5132 | + | 7.22450i | −1.48504 | + | 0.857390i | −0.999855 | − | 0.0170198i | \(-0.994582\pi\) |
−0.485188 | + | 0.874410i | \(0.661249\pi\) | |||||||
\(72\) | −0.539789 | + | 0.934941i | −0.0636147 | + | 0.110184i | ||||
\(73\) | −6.68675 | + | 3.86060i | −0.782625 | + | 0.451849i | −0.837360 | − | 0.546652i | \(-0.815902\pi\) |
0.0547346 | + | 0.998501i | \(0.482569\pi\) | |||||||
\(74\) | −4.10663 | + | 2.37096i | −0.477386 | + | 0.275619i | ||||
\(75\) | − | 10.0650i | − | 1.16220i | ||||||
\(76\) | 1.65690 | − | 4.03171i | 0.190060 | − | 0.462469i | ||||
\(77\) | −14.8552 | + | 0.300444i | −1.69290 | + | 0.0342387i | ||||
\(78\) | 6.87647 | − | 3.97013i | 0.778606 | − | 0.449529i | ||||
\(79\) | 2.26364 | + | 3.92074i | 0.254680 | + | 0.441118i | 0.964808 | − | 0.262954i | \(-0.0846966\pi\) |
−0.710129 | + | 0.704072i | \(0.751363\pi\) | |||||||
\(80\) | 0.0648685 | − | 0.112356i | 0.00725252 | − | 0.0125617i | ||||
\(81\) | 5.53662 | + | 9.58971i | 0.615180 | + | 1.06552i | ||||
\(82\) | 2.41415 | − | 4.18143i | 0.266598 | − | 0.461762i | ||||
\(83\) | − | 4.50822i | − | 0.494842i | −0.968908 | − | 0.247421i | \(-0.920417\pi\) | ||
0.968908 | − | 0.247421i | \(-0.0795830\pi\) | |||||||
\(84\) | −9.04852 | −0.987274 | ||||||||
\(85\) | 0.322575 | + | 0.186239i | 0.0349882 | + | 0.0202005i | ||||
\(86\) | −0.219263 | − | 0.126591i | −0.0236437 | − | 0.0136507i | ||||
\(87\) | − | 8.05044i | − | 0.863098i | ||||||
\(88\) | −0.0670646 | − | 3.31595i | −0.00714911 | − | 0.353481i | ||||
\(89\) | 14.4364 | + | 8.33488i | 1.53026 | + | 0.883496i | 0.999349 | + | 0.0360682i | \(0.0114834\pi\) |
0.530911 | + | 0.847428i | \(0.321850\pi\) | |||||||
\(90\) | 0.0700306 | + | 0.121297i | 0.00738187 | + | 0.0127858i | ||||
\(91\) | 15.2520 | + | 8.80576i | 1.59885 | + | 0.923094i | ||||
\(92\) | 2.80144 | + | 4.85224i | 0.292070 | + | 0.505881i | ||||
\(93\) | −6.11826 | − | 10.5971i | −0.634434 | − | 1.09887i | ||||
\(94\) | −3.64393 | −0.375843 | ||||||||
\(95\) | −0.345504 | − | 0.447693i | −0.0354480 | − | 0.0459324i | ||||
\(96\) | − | 2.01980i | − | 0.206145i | ||||||
\(97\) | 11.7545 | − | 6.78649i | 1.19349 | − | 0.689063i | 0.234396 | − | 0.972141i | \(-0.424689\pi\) |
0.959097 | + | 0.283078i | \(0.0913554\pi\) | |||||||
\(98\) | −6.53482 | − | 11.3186i | −0.660116 | − | 1.14335i | ||||
\(99\) | 3.13642 | + | 1.72721i | 0.315222 | + | 0.173591i | ||||
\(100\) | 2.49158 | + | 4.31555i | 0.249158 | + | 0.431555i | ||||
\(101\) | 0.321471 | + | 0.185601i | 0.0319876 | + | 0.0184680i | 0.515909 | − | 0.856644i | \(-0.327454\pi\) |
−0.483921 | + | 0.875112i | \(0.660788\pi\) | |||||||
\(102\) | 5.79888 | 0.574175 | ||||||||
\(103\) | − | 9.00448i | − | 0.887238i | −0.896215 | − | 0.443619i | \(-0.853694\pi\) | ||
0.896215 | − | 0.443619i | \(-0.146306\pi\) | |||||||
\(104\) | −1.96561 | + | 3.40453i | −0.192744 | + | 0.333842i | ||||
\(105\) | −0.586964 | + | 1.01665i | −0.0572818 | + | 0.0992150i | ||||
\(106\) | − | 0.129860i | − | 0.0126131i | ||||||
\(107\) | 10.5908 | 1.02385 | 0.511924 | − | 0.859031i | \(-0.328933\pi\) | ||||
0.511924 | + | 0.859031i | \(0.328933\pi\) | |||||||
\(108\) | −3.35919 | − | 1.93943i | −0.323239 | − | 0.186622i | ||||
\(109\) | −9.29222 | − | 16.0946i | −0.890033 | − | 1.54158i | −0.839834 | − | 0.542844i | \(-0.817348\pi\) |
−0.0501996 | − | 0.998739i | \(-0.515986\pi\) | |||||||
\(110\) | −0.376916 | − | 0.207566i | −0.0359375 | − | 0.0197906i | ||||
\(111\) | 4.78886 | + | 8.29456i | 0.454539 | + | 0.787284i | ||||
\(112\) | 3.87972 | − | 2.23996i | 0.366599 | − | 0.211656i | ||||
\(113\) | 6.76377i | 0.636282i | 0.948043 | + | 0.318141i | \(0.103058\pi\) | ||||
−0.948043 | + | 0.318141i | \(0.896942\pi\) | |||||||
\(114\) | −8.14323 | − | 3.34661i | −0.762683 | − | 0.313438i | ||||
\(115\) | 0.726901 | 0.0677839 | ||||||||
\(116\) | 1.99288 | + | 3.45178i | 0.185035 | + | 0.320490i | ||||
\(117\) | −2.12203 | − | 3.67546i | −0.196181 | − | 0.339796i | ||||
\(118\) | 5.17436 | + | 2.98742i | 0.476339 | + | 0.275014i | ||||
\(119\) | 6.43097 | + | 11.1388i | 0.589526 | + | 1.02109i | ||||
\(120\) | −0.226935 | − | 0.131021i | −0.0207163 | − | 0.0119605i | ||||
\(121\) | −10.9910 | + | 0.444765i | −0.999182 | + | 0.0404332i | ||||
\(122\) | − | 13.0880i | − | 1.18493i | ||||||
\(123\) | −8.44564 | − | 4.87609i | −0.761518 | − | 0.439663i | ||||
\(124\) | 5.24664 | + | 3.02915i | 0.471162 | + | 0.272025i | ||||
\(125\) | 1.29519 | 0.115845 | ||||||||
\(126\) | 4.83641i | 0.430862i | ||||||||
\(127\) | −3.50584 | + | 6.07229i | −0.311093 | + | 0.538828i | −0.978599 | − | 0.205776i | \(-0.934028\pi\) |
0.667507 | + | 0.744604i | \(0.267362\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −0.255689 | + | 0.442866i | −0.0225121 | + | 0.0389922i | ||||
\(130\) | 0.255012 | + | 0.441694i | 0.0223661 | + | 0.0387392i | ||||
\(131\) | 6.86539 | − | 3.96374i | 0.599832 | − | 0.346313i | −0.169143 | − | 0.985591i | \(-0.554100\pi\) |
0.768976 | + | 0.639278i | \(0.220767\pi\) | |||||||
\(132\) | −6.69754 | + | 0.135457i | −0.582946 | + | 0.0117900i | ||||
\(133\) | −2.60254 | − | 19.3533i | −0.225669 | − | 1.67814i | ||||
\(134\) | 4.06140i | 0.350851i | ||||||||
\(135\) | −0.435812 | + | 0.251616i | −0.0375087 | + | 0.0216557i | ||||
\(136\) | −2.48638 | + | 1.43551i | −0.213205 | + | 0.123094i | ||||
\(137\) | −2.45790 | + | 4.25721i | −0.209992 | + | 0.363718i | −0.951712 | − | 0.306993i | \(-0.900677\pi\) |
0.741719 | + | 0.670710i | \(0.234011\pi\) | |||||||
\(138\) | 9.80053 | − | 5.65834i | 0.834277 | − | 0.481670i | ||||
\(139\) | −11.3003 | − | 6.52424i | −0.958481 | − | 0.553379i | −0.0627756 | − | 0.998028i | \(-0.519995\pi\) |
−0.895705 | + | 0.444649i | \(0.853329\pi\) | |||||||
\(140\) | − | 0.581211i | − | 0.0491213i | ||||||
\(141\) | 7.36000i | 0.619824i | ||||||||
\(142\) | −12.5132 | − | 7.22450i | −1.05008 | − | 0.606266i | ||||
\(143\) | 11.4211 | + | 6.28953i | 0.955078 | + | 0.525957i | ||||
\(144\) | −1.07958 | −0.0899648 | ||||||||
\(145\) | 0.517102 | 0.0429430 | ||||||||
\(146\) | −6.68675 | − | 3.86060i | −0.553400 | − | 0.319505i | ||||
\(147\) | −22.8613 | + | 13.1990i | −1.88557 | + | 1.08864i | ||||
\(148\) | −4.10663 | − | 2.37096i | −0.337563 | − | 0.194892i | ||||
\(149\) | 17.4584 | − | 10.0796i | 1.43025 | − | 0.825754i | 0.433109 | − | 0.901342i | \(-0.357417\pi\) |
0.997139 | + | 0.0755879i | \(0.0240834\pi\) | |||||||
\(150\) | 8.71653 | − | 5.03249i | 0.711702 | − | 0.410901i | ||||
\(151\) | −9.71609 | −0.790684 | −0.395342 | − | 0.918534i | \(-0.629374\pi\) | ||||
−0.395342 | + | 0.918534i | \(0.629374\pi\) | |||||||
\(152\) | 4.32001 | − | 0.580935i | 0.350399 | − | 0.0471200i | ||||
\(153\) | − | 3.09949i | − | 0.250579i | ||||||
\(154\) | −7.68777 | − | 12.7147i | −0.619498 | − | 1.02458i | ||||
\(155\) | 0.680683 | − | 0.392993i | 0.0546738 | − | 0.0315659i | ||||
\(156\) | 6.87647 | + | 3.97013i | 0.550558 | + | 0.317865i | ||||
\(157\) | −12.3175 | − | 21.3346i | −0.983046 | − | 1.70269i | −0.650315 | − | 0.759665i | \(-0.725363\pi\) |
−0.332731 | − | 0.943022i | \(-0.607970\pi\) | |||||||
\(158\) | −2.26364 | + | 3.92074i | −0.180086 | + | 0.311918i | ||||
\(159\) | −0.262291 | −0.0208010 | ||||||||
\(160\) | 0.129737 | 0.0102566 | ||||||||
\(161\) | 21.7376 | + | 12.5502i | 1.71316 | + | 0.989095i | ||||
\(162\) | −5.53662 | + | 9.58971i | −0.434998 | + | 0.753439i | ||||
\(163\) | 8.78657 | 0.688217 | 0.344109 | − | 0.938930i | \(-0.388181\pi\) | ||||
0.344109 | + | 0.938930i | \(0.388181\pi\) | |||||||
\(164\) | 4.82830 | 0.377027 | ||||||||
\(165\) | −0.419240 | + | 0.761293i | −0.0326378 | + | 0.0592666i | ||||
\(166\) | 3.90423 | − | 2.25411i | 0.303027 | − | 0.174953i | ||||
\(167\) | 1.15915 | − | 2.00771i | 0.0896979 | − | 0.155361i | −0.817686 | − | 0.575665i | \(-0.804743\pi\) |
0.907383 | + | 0.420304i | \(0.138077\pi\) | |||||||
\(168\) | −4.52426 | − | 7.83624i | −0.349054 | − | 0.604579i | ||||
\(169\) | −1.22724 | − | 2.12563i | −0.0944028 | − | 0.163510i | ||||
\(170\) | 0.372478i | 0.0285678i | ||||||||
\(171\) | −1.78875 | + | 4.35254i | −0.136789 | + | 0.332847i | ||||
\(172\) | − | 0.253183i | − | 0.0193050i | ||||||
\(173\) | 3.62502 | + | 6.27873i | 0.275605 | + | 0.477363i | 0.970288 | − | 0.241954i | \(-0.0777883\pi\) |
−0.694682 | + | 0.719317i | \(0.744455\pi\) | |||||||
\(174\) | 6.97189 | − | 4.02522i | 0.528537 | − | 0.305151i | ||||
\(175\) | 19.3333 | + | 11.1621i | 1.46146 | + | 0.843774i | ||||
\(176\) | 2.83816 | − | 1.71605i | 0.213934 | − | 0.129352i | ||||
\(177\) | 6.03398 | − | 10.4512i | 0.453542 | − | 0.785557i | ||||
\(178\) | 16.6698i | 1.24945i | ||||||||
\(179\) | 16.2846i | 1.21717i | 0.793489 | + | 0.608584i | \(0.208262\pi\) | ||||
−0.793489 | + | 0.608584i | \(0.791738\pi\) | |||||||
\(180\) | −0.0700306 | + | 0.121297i | −0.00521977 | + | 0.00904091i | ||||
\(181\) | 5.80563 | + | 3.35188i | 0.431529 | + | 0.249143i | 0.699998 | − | 0.714145i | \(-0.253184\pi\) |
−0.268469 | + | 0.963288i | \(0.586518\pi\) | |||||||
\(182\) | 17.6115i | 1.30545i | ||||||||
\(183\) | −26.4350 | −1.95413 | ||||||||
\(184\) | −2.80144 | + | 4.85224i | −0.206525 | + | 0.357712i | ||||
\(185\) | −0.532782 | + | 0.307602i | −0.0391709 | + | 0.0226153i | ||||
\(186\) | 6.11826 | − | 10.5971i | 0.448613 | − | 0.777020i | ||||
\(187\) | 4.92683 | + | 8.14842i | 0.360285 | + | 0.595872i | ||||
\(188\) | −1.82197 | − | 3.15574i | −0.132881 | − | 0.230156i | ||||
\(189\) | −17.3770 | −1.26399 | ||||||||
\(190\) | 0.214962 | − | 0.523062i | 0.0155950 | − | 0.0379469i | ||||
\(191\) | −14.4067 | −1.04243 | −0.521216 | − | 0.853425i | \(-0.674521\pi\) | ||||
−0.521216 | + | 0.853425i | \(0.674521\pi\) | |||||||
\(192\) | 1.74919 | − | 1.00990i | 0.126237 | − | 0.0728831i | ||||
\(193\) | −1.09475 | − | 1.89617i | −0.0788021 | − | 0.136489i | 0.823931 | − | 0.566690i | \(-0.191776\pi\) |
−0.902733 | + | 0.430201i | \(0.858443\pi\) | |||||||
\(194\) | 11.7545 | + | 6.78649i | 0.843927 | + | 0.487241i | ||||
\(195\) | 0.892132 | − | 0.515073i | 0.0638869 | − | 0.0368851i | ||||
\(196\) | 6.53482 | − | 11.3186i | 0.466773 | − | 0.808474i | ||||
\(197\) | 23.1367i | 1.64842i | 0.566284 | + | 0.824210i | \(0.308381\pi\) | ||||
−0.566284 | + | 0.824210i | \(0.691619\pi\) | |||||||
\(198\) | 0.0724014 | + | 3.57982i | 0.00514535 | + | 0.254407i | ||||
\(199\) | −0.412771 | + | 0.714940i | −0.0292606 | + | 0.0506808i | −0.880285 | − | 0.474446i | \(-0.842649\pi\) |
0.851024 | + | 0.525126i | \(0.175982\pi\) | |||||||
\(200\) | −2.49158 | + | 4.31555i | −0.176182 | + | 0.305155i | ||||
\(201\) | 8.20319 | 0.578609 | ||||||||
\(202\) | 0.371203i | 0.0261177i | ||||||||
\(203\) | 15.4637 | + | 8.92795i | 1.08534 | + | 0.626619i | ||||
\(204\) | 2.89944 | + | 5.02198i | 0.203001 | + | 0.351609i | ||||
\(205\) | 0.313205 | − | 0.542487i | 0.0218752 | − | 0.0378889i | ||||
\(206\) | 7.79811 | − | 4.50224i | 0.543320 | − | 0.313686i | ||||
\(207\) | −3.02437 | − | 5.23837i | −0.210208 | − | 0.364092i | ||||
\(208\) | −3.93122 | −0.272581 | ||||||||
\(209\) | −2.21607 | − | 14.2860i | −0.153289 | − | 0.988181i | ||||
\(210\) | −1.17393 | −0.0810087 | ||||||||
\(211\) | 10.8046 | + | 18.7142i | 0.743822 | + | 1.28834i | 0.950743 | + | 0.309981i | \(0.100323\pi\) |
−0.206920 | + | 0.978358i | \(0.566344\pi\) | |||||||
\(212\) | 0.112462 | − | 0.0649300i | 0.00772393 | − | 0.00445941i | ||||
\(213\) | −14.5920 | + | 25.2741i | −0.999828 | + | 1.73175i | ||||
\(214\) | 5.29538 | + | 9.17187i | 0.361985 | + | 0.626976i | ||||
\(215\) | −0.0284465 | − | 0.0164236i | −0.00194003 | − | 0.00112008i | ||||
\(216\) | − | 3.87886i | − | 0.263923i | ||||||
\(217\) | 27.1406 | 1.84243 | ||||||||
\(218\) | 9.29222 | − | 16.0946i | 0.629349 | − | 1.09006i | ||||
\(219\) | −7.79762 | + | 13.5059i | −0.526915 | + | 0.912643i | ||||
\(220\) | −0.00870076 | − | 0.430201i | −0.000586605 | − | 0.0290042i | ||||
\(221\) | − | 11.2866i | − | 0.759220i | ||||||
\(222\) | −4.78886 | + | 8.29456i | −0.321408 | + | 0.556694i | ||||
\(223\) | −21.3131 | + | 12.3051i | −1.42723 | + | 0.824011i | −0.996901 | − | 0.0786610i | \(-0.974936\pi\) |
−0.430328 | + | 0.902672i | \(0.641602\pi\) | |||||||
\(224\) | 3.87972 | + | 2.23996i | 0.259225 | + | 0.149663i | ||||
\(225\) | −2.68986 | − | 4.65897i | −0.179324 | − | 0.310598i | ||||
\(226\) | −5.85759 | + | 3.38188i | −0.389641 | + | 0.224959i | ||||
\(227\) | 9.38555 | 0.622941 | 0.311470 | − | 0.950256i | \(-0.399179\pi\) | ||||
0.311470 | + | 0.950256i | \(0.399179\pi\) | |||||||
\(228\) | −1.17337 | − | 8.72555i | −0.0777083 | − | 0.577863i | ||||
\(229\) | −24.5509 | −1.62237 | −0.811184 | − | 0.584791i | \(-0.801176\pi\) | ||||
−0.811184 | + | 0.584791i | \(0.801176\pi\) | |||||||
\(230\) | 0.363451 | + | 0.629515i | 0.0239652 | + | 0.0415090i | ||||
\(231\) | −25.6811 | + | 15.5277i | −1.68970 | + | 1.02165i | ||||
\(232\) | −1.99288 | + | 3.45178i | −0.130839 | + | 0.226620i | ||||
\(233\) | −23.7955 | + | 13.7383i | −1.55889 | + | 0.900027i | −0.561529 | + | 0.827457i | \(0.689787\pi\) |
−0.997363 | + | 0.0725695i | \(0.976880\pi\) | |||||||
\(234\) | 2.12203 | − | 3.67546i | 0.138721 | − | 0.240272i | ||||
\(235\) | −0.472753 | −0.0308390 | ||||||||
\(236\) | 5.97484i | 0.388929i | ||||||||
\(237\) | 7.91911 | + | 4.57210i | 0.514401 | + | 0.296990i | ||||
\(238\) | −6.43097 | + | 11.1388i | −0.416858 | + | 0.722019i | ||||
\(239\) | 15.3803i | 0.994870i | 0.867501 | + | 0.497435i | \(0.165725\pi\) | ||||
−0.867501 | + | 0.497435i | \(0.834275\pi\) | |||||||
\(240\) | − | 0.262042i | − | 0.0169148i | ||||||
\(241\) | −5.04394 | + | 8.73636i | −0.324909 | + | 0.562758i | −0.981494 | − | 0.191493i | \(-0.938667\pi\) |
0.656585 | + | 0.754252i | \(0.272000\pi\) | |||||||
\(242\) | −5.88068 | − | 9.29611i | −0.378024 | − | 0.597576i | ||||
\(243\) | 9.29168 | + | 5.36456i | 0.596062 | + | 0.344136i | ||||
\(244\) | 11.3345 | − | 6.54398i | 0.725617 | − | 0.418935i | ||||
\(245\) | −0.847808 | − | 1.46845i | −0.0541645 | − | 0.0938156i | ||||
\(246\) | − | 9.75219i | − | 0.621777i | ||||||
\(247\) | −6.51364 | + | 15.8495i | −0.414453 | + | 1.00848i | ||||
\(248\) | 6.05829i | 0.384702i | ||||||||
\(249\) | −4.55284 | − | 7.88576i | −0.288525 | − | 0.499740i | ||||
\(250\) | 0.647593 | + | 1.12166i | 0.0409574 | + | 0.0709403i | ||||
\(251\) | −4.38439 | + | 7.59399i | −0.276740 | + | 0.479328i | −0.970573 | − | 0.240808i | \(-0.922588\pi\) |
0.693832 | + | 0.720137i | \(0.255921\pi\) | |||||||
\(252\) | −4.18846 | + | 2.41821i | −0.263848 | + | 0.152333i | ||||
\(253\) | 16.2776 | + | 8.96401i | 1.02337 | + | 0.563563i | ||||
\(254\) | −7.01167 | −0.439951 | ||||||||
\(255\) | 0.752330 | 0.0471127 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −27.4704 | − | 15.8601i | −1.71356 | − | 0.989324i | −0.929647 | − | 0.368452i | \(-0.879888\pi\) |
−0.783912 | − | 0.620872i | \(-0.786779\pi\) | |||||||
\(258\) | −0.511377 | −0.0318370 | ||||||||
\(259\) | −21.2434 | −1.32000 | ||||||||
\(260\) | −0.255012 | + | 0.441694i | −0.0158152 | + | 0.0273927i | ||||
\(261\) | −2.15147 | − | 3.72646i | −0.133173 | − | 0.230662i | ||||
\(262\) | 6.86539 | + | 3.96374i | 0.424145 | + | 0.244880i | ||||
\(263\) | 25.6515 | − | 14.8099i | 1.58174 | − | 0.913217i | 0.587133 | − | 0.809490i | \(-0.300256\pi\) |
0.994606 | − | 0.103727i | \(-0.0330769\pi\) | |||||||
\(264\) | −3.46608 | − | 5.73251i | −0.213322 | − | 0.352812i | ||||
\(265\) | − | 0.0168477i | − | 0.00103494i | ||||||
\(266\) | 15.4592 | − | 11.9305i | 0.947863 | − | 0.731506i | ||||
\(267\) | 33.6695 | 2.06054 | ||||||||
\(268\) | −3.51727 | + | 2.03070i | −0.214852 | + | 0.124045i | ||||
\(269\) | 12.2618 | − | 7.07936i | 0.747616 | − | 0.431636i | −0.0772161 | − | 0.997014i | \(-0.524603\pi\) |
0.824832 | + | 0.565378i | \(0.191270\pi\) | |||||||
\(270\) | −0.435812 | − | 0.251616i | −0.0265227 | − | 0.0153129i | ||||
\(271\) | 5.10308 | − | 2.94627i | 0.309990 | − | 0.178973i | −0.336932 | − | 0.941529i | \(-0.609389\pi\) |
0.646922 | + | 0.762556i | \(0.276056\pi\) | |||||||
\(272\) | −2.48638 | − | 1.43551i | −0.150759 | − | 0.0870406i | ||||
\(273\) | 35.5717 | 2.15290 | ||||||||
\(274\) | −4.91580 | −0.296974 | ||||||||
\(275\) | 14.4772 | + | 7.97254i | 0.873010 | + | 0.480762i | ||||
\(276\) | 9.80053 | + | 5.65834i | 0.589923 | + | 0.340592i | ||||
\(277\) | − | 19.5231i | − | 1.17303i | −0.809939 | − | 0.586514i | \(-0.800500\pi\) | ||
0.809939 | − | 0.586514i | \(-0.199500\pi\) | |||||||
\(278\) | − | 13.0485i | − | 0.782596i | ||||||
\(279\) | −5.66415 | − | 3.27020i | −0.339104 | − | 0.195782i | ||||
\(280\) | 0.503343 | − | 0.290605i | 0.0300805 | − | 0.0173670i | ||||
\(281\) | 5.67340 | − | 9.82662i | 0.338447 | − | 0.586207i | −0.645694 | − | 0.763596i | \(-0.723432\pi\) |
0.984141 | + | 0.177389i | \(0.0567651\pi\) | |||||||
\(282\) | −6.37395 | + | 3.68000i | −0.379563 | + | 0.219141i | ||||
\(283\) | 8.52486 | − | 4.92183i | 0.506750 | − | 0.292572i | −0.224747 | − | 0.974417i | \(-0.572155\pi\) |
0.731497 | + | 0.681845i | \(0.238822\pi\) | |||||||
\(284\) | − | 14.4490i | − | 0.857390i | ||||||
\(285\) | −1.05648 | − | 0.434179i | −0.0625804 | − | 0.0257185i | ||||
\(286\) | 0.263646 | + | 13.0357i | 0.0155897 | + | 0.770818i | ||||
\(287\) | 18.7325 | − | 10.8152i | 1.10574 | − | 0.638401i | ||||
\(288\) | −0.539789 | − | 0.934941i | −0.0318074 | − | 0.0550920i | ||||
\(289\) | −4.37862 | + | 7.58399i | −0.257566 | + | 0.446117i | ||||
\(290\) | 0.258551 | + | 0.447823i | 0.0151826 | + | 0.0262971i | ||||
\(291\) | 13.7073 | − | 23.7418i | 0.803538 | − | 1.39177i | ||||
\(292\) | − | 7.72120i | − | 0.451849i | ||||||
\(293\) | 2.93837 | 0.171661 | 0.0858307 | − | 0.996310i | \(-0.472646\pi\) | ||||
0.0858307 | + | 0.996310i | \(0.472646\pi\) | |||||||
\(294\) | −22.8613 | − | 13.1990i | −1.33330 | − | 0.769781i | ||||
\(295\) | 0.671307 | + | 0.387579i | 0.0390850 | + | 0.0225657i | ||||
\(296\) | − | 4.74193i | − | 0.275619i | ||||||
\(297\) | −12.8621 | + | 0.260134i | −0.746335 | + | 0.0150945i | ||||
\(298\) | 17.4584 | + | 10.0796i | 1.01134 | + | 0.583896i | ||||
\(299\) | −11.0131 | − | 19.0752i | −0.636902 | − | 1.10315i | ||||
\(300\) | 8.71653 | + | 5.03249i | 0.503249 | + | 0.290551i | ||||
\(301\) | −0.567118 | − | 0.982278i | −0.0326881 | − | 0.0566175i | ||||
\(302\) | −4.85804 | − | 8.41438i | −0.279549 | − | 0.484193i | ||||
\(303\) | 0.749754 | 0.0430723 | ||||||||
\(304\) | 2.66311 | + | 3.45077i | 0.152740 | + | 0.197915i | ||||
\(305\) | − | 1.69799i | − | 0.0972268i | ||||||
\(306\) | 2.68424 | − | 1.54975i | 0.153448 | − | 0.0885930i | ||||
\(307\) | 5.95515 | + | 10.3146i | 0.339879 | + | 0.588687i | 0.984410 | − | 0.175891i | \(-0.0562807\pi\) |
−0.644531 | + | 0.764578i | \(0.722947\pi\) | |||||||
\(308\) | 7.16739 | − | 13.0152i | 0.408400 | − | 0.741608i | ||||
\(309\) | −9.09361 | − | 15.7506i | −0.517317 | − | 0.896020i | ||||
\(310\) | 0.680683 | + | 0.392993i | 0.0386602 | + | 0.0223205i | ||||
\(311\) | −6.31922 | −0.358330 | −0.179165 | − | 0.983819i | \(-0.557340\pi\) | ||||
−0.179165 | + | 0.983819i | \(0.557340\pi\) | |||||||
\(312\) | 7.94026i | 0.449529i | ||||||||
\(313\) | −7.21873 | + | 12.5032i | −0.408027 | + | 0.706723i | −0.994669 | − | 0.103123i | \(-0.967116\pi\) |
0.586642 | + | 0.809847i | \(0.300450\pi\) | |||||||
\(314\) | 12.3175 | − | 21.3346i | 0.695119 | − | 1.20398i | ||||
\(315\) | 0.627462i | 0.0353535i | ||||||||
\(316\) | −4.52729 | −0.254680 | ||||||||
\(317\) | −3.32252 | − | 1.91826i | −0.186611 | − | 0.107740i | 0.403784 | − | 0.914854i | \(-0.367695\pi\) |
−0.590395 | + | 0.807114i | \(0.701028\pi\) | |||||||
\(318\) | −0.131145 | − | 0.227150i | −0.00735427 | − | 0.0127380i | ||||
\(319\) | 11.5796 | + | 6.37681i | 0.648331 | + | 0.357033i | ||||
\(320\) | 0.0648685 | + | 0.112356i | 0.00362626 | + | 0.00628087i | ||||
\(321\) | 18.5253 | − | 10.6956i | 1.03398 | − | 0.596970i | ||||
\(322\) | 25.1004i | 1.39879i | ||||||||
\(323\) | −9.90725 | + | 7.64585i | −0.551254 | + | 0.425426i | ||||
\(324\) | −11.0732 | −0.615180 | ||||||||
\(325\) | −9.79496 | − | 16.9654i | −0.543327 | − | 0.941069i | ||||
\(326\) | 4.39329 | + | 7.60939i | 0.243322 | + | 0.421445i | ||||
\(327\) | −32.5078 | − | 18.7684i | −1.79769 | − | 1.03789i | ||||
\(328\) | 2.41415 | + | 4.18143i | 0.133299 | + | 0.230881i | ||||
\(329\) | −14.1374 | − | 8.16225i | −0.779422 | − | 0.450000i | ||||
\(330\) | −0.868919 | + | 0.0175738i | −0.0478324 | + | 0.000967404i | ||||
\(331\) | − | 0.387307i | − | 0.0212883i | −0.999943 | − | 0.0106442i | \(-0.996612\pi\) | ||
0.999943 | − | 0.0106442i | \(-0.00338820\pi\) | |||||||
\(332\) | 3.90423 | + | 2.25411i | 0.214273 | + | 0.123710i | ||||
\(333\) | 4.43342 | + | 2.55964i | 0.242950 | + | 0.140267i | ||||
\(334\) | 2.31830 | 0.126852 | ||||||||
\(335\) | 0.526914i | 0.0287884i | ||||||||
\(336\) | 4.52426 | − | 7.83624i | 0.246818 | − | 0.427502i | ||||
\(337\) | −0.176938 | − | 0.306466i | −0.00963844 | − | 0.0166943i | 0.861166 | − | 0.508324i | \(-0.169735\pi\) |
−0.870804 | + | 0.491630i | \(0.836401\pi\) | |||||||
\(338\) | 1.22724 | − | 2.12563i | 0.0667528 | − | 0.115619i | ||||
\(339\) | 6.83071 | + | 11.8311i | 0.370993 | + | 0.642580i | ||||
\(340\) | −0.322575 | + | 0.186239i | −0.0174941 | + | 0.0101002i | ||||
\(341\) | 20.0890 | − | 0.406297i | 1.08788 | − | 0.0220022i | ||||
\(342\) | −4.66379 | + | 0.627164i | −0.252189 | + | 0.0339131i | ||||
\(343\) | − | 27.1914i | − | 1.46820i | ||||||
\(344\) | 0.219263 | − | 0.126591i | 0.0118218 | − | 0.00682535i | ||||
\(345\) | 1.27149 | − | 0.734096i | 0.0684548 | − | 0.0395224i | ||||
\(346\) | −3.62502 | + | 6.27873i | −0.194882 | + | 0.337546i | ||||
\(347\) | −16.9725 | + | 9.79909i | −0.911133 | + | 0.526043i | −0.880795 | − | 0.473497i | \(-0.842991\pi\) |
−0.0303372 | + | 0.999540i | \(0.509658\pi\) | |||||||
\(348\) | 6.97189 | + | 4.02522i | 0.373732 | + | 0.215775i | ||||
\(349\) | − | 2.72211i | − | 0.145711i | −0.997342 | − | 0.0728557i | \(-0.976789\pi\) | ||
0.997342 | − | 0.0728557i | \(-0.0232112\pi\) | |||||||
\(350\) | 22.3242i | 1.19328i | ||||||||
\(351\) | 13.2057 | + | 7.62433i | 0.704869 | + | 0.406956i | ||||
\(352\) | 2.90523 | + | 1.59989i | 0.154849 | + | 0.0852746i | ||||
\(353\) | 18.9919 | 1.01084 | 0.505418 | − | 0.862875i | \(-0.331338\pi\) | ||||
0.505418 | + | 0.862875i | \(0.331338\pi\) | |||||||
\(354\) | 12.0680 | 0.641405 | ||||||||
\(355\) | −1.62343 | − | 0.937285i | −0.0861625 | − | 0.0497459i | ||||
\(356\) | −14.4364 | + | 8.33488i | −0.765130 | + | 0.441748i | ||||
\(357\) | 22.4980 | + | 12.9892i | 1.19072 | + | 0.687464i | ||||
\(358\) | −14.1029 | + | 8.14230i | −0.745360 | + | 0.430334i | ||||
\(359\) | −22.2856 | + | 12.8666i | −1.17619 | + | 0.679072i | −0.955129 | − | 0.296189i | \(-0.904284\pi\) |
−0.221058 | + | 0.975261i | \(0.570951\pi\) | |||||||
\(360\) | −0.140061 | −0.00738187 | ||||||||
\(361\) | 18.3250 | − | 5.01929i | 0.964475 | − | 0.264173i | ||||
\(362\) | 6.70377i | 0.352342i | ||||||||
\(363\) | −18.7762 | + | 11.8778i | −0.985497 | + | 0.623422i | ||||
\(364\) | −15.2520 | + | 8.80576i | −0.799423 | + | 0.461547i | ||||
\(365\) | −0.867520 | − | 0.500863i | −0.0454081 | − | 0.0262164i | ||||
\(366\) | −13.2175 | − | 22.8934i | −0.690890 | − | 1.19666i | ||||
\(367\) | −1.47625 | + | 2.55694i | −0.0770596 | + | 0.133471i | −0.901980 | − | 0.431778i | \(-0.857887\pi\) |
0.824920 | + | 0.565249i | \(0.191220\pi\) | |||||||
\(368\) | −5.60288 | −0.292070 | ||||||||
\(369\) | −5.21253 | −0.271353 | ||||||||
\(370\) | −0.532782 | − | 0.307602i | −0.0276980 | − | 0.0159915i | ||||
\(371\) | 0.290881 | − | 0.503820i | 0.0151018 | − | 0.0261571i | ||||
\(372\) | 12.2365 | 0.634434 | ||||||||
\(373\) | −18.1589 | −0.940233 | −0.470117 | − | 0.882604i | \(-0.655788\pi\) | ||||
−0.470117 | + | 0.882604i | \(0.655788\pi\) | |||||||
\(374\) | −4.59333 | + | 8.34097i | −0.237515 | + | 0.431301i | ||||
\(375\) | 2.26553 | − | 1.30801i | 0.116992 | − | 0.0675452i | ||||
\(376\) | 1.82197 | − | 3.15574i | 0.0939608 | − | 0.162745i | ||||
\(377\) | −7.83446 | − | 13.5697i | −0.403495 | − | 0.698875i | ||||
\(378\) | −8.68849 | − | 15.0489i | −0.446888 | − | 0.774032i | ||||
\(379\) | − | 19.8897i | − | 1.02166i | −0.859681 | − | 0.510832i | \(-0.829338\pi\) | ||
0.859681 | − | 0.510832i | \(-0.170662\pi\) | |||||||
\(380\) | 0.560466 | − | 0.0753687i | 0.0287513 | − | 0.00386633i | ||||
\(381\) | 14.1621i | 0.725549i | ||||||||
\(382\) | −7.20335 | − | 12.4766i | −0.368555 | − | 0.638356i | ||||
\(383\) | 7.90191 | − | 4.56217i | 0.403769 | − | 0.233116i | −0.284340 | − | 0.958723i | \(-0.591774\pi\) |
0.688109 | + | 0.725607i | \(0.258441\pi\) | |||||||
\(384\) | 1.74919 | + | 1.00990i | 0.0892632 | + | 0.0515362i | ||||
\(385\) | −0.997389 | − | 1.64957i | −0.0508316 | − | 0.0840699i | ||||
\(386\) | 1.09475 | − | 1.89617i | 0.0557215 | − | 0.0965124i | ||||
\(387\) | 0.273330i | 0.0138942i | ||||||||
\(388\) | 13.5730i | 0.689063i | ||||||||
\(389\) | 9.99429 | − | 17.3106i | 0.506730 | − | 0.877683i | −0.493239 | − | 0.869894i | \(-0.664187\pi\) |
0.999970 | − | 0.00778918i | \(-0.00247940\pi\) | |||||||
\(390\) | 0.892132 | + | 0.515073i | 0.0451749 | + | 0.0260817i | ||||
\(391\) | − | 16.0860i | − | 0.813504i | ||||||
\(392\) | 13.0696 | 0.660116 | ||||||||
\(393\) | 8.00594 | − | 13.8667i | 0.403846 | − | 0.699482i | ||||
\(394\) | −20.0370 | + | 11.5683i | −1.00945 | + | 0.582805i | ||||
\(395\) | −0.293678 | + | 0.508666i | −0.0147766 | + | 0.0255938i | ||||
\(396\) | −3.06402 | + | 1.85261i | −0.153973 | + | 0.0930973i | ||||
\(397\) | −10.7075 | − | 18.5458i | −0.537392 | − | 0.930789i | −0.999043 | − | 0.0437283i | \(-0.986076\pi\) |
0.461652 | − | 0.887061i | \(-0.347257\pi\) | |||||||
\(398\) | −0.825542 | −0.0413807 | ||||||||
\(399\) | −24.0972 | − | 31.2244i | −1.20637 | − | 1.56317i | ||||
\(400\) | −4.98317 | −0.249158 | ||||||||
\(401\) | 0.706399 | − | 0.407840i | 0.0352759 | − | 0.0203665i | −0.482258 | − | 0.876029i | \(-0.660183\pi\) |
0.517534 | + | 0.855663i | \(0.326850\pi\) | |||||||
\(402\) | 4.10160 | + | 7.10417i | 0.204569 | + | 0.354324i | ||||
\(403\) | −20.6257 | − | 11.9082i | −1.02744 | − | 0.593192i | ||||
\(404\) | −0.321471 | + | 0.185601i | −0.0159938 | + | 0.00923402i | ||||
\(405\) | −0.718305 | + | 1.24414i | −0.0356929 | + | 0.0618219i | ||||
\(406\) | 17.8559i | 0.886174i | ||||||||
\(407\) | −15.7240 | + | 0.318015i | −0.779409 | + | 0.0157634i | ||||
\(408\) | −2.89944 | + | 5.02198i | −0.143544 | + | 0.248625i | ||||
\(409\) | 4.40138 | − | 7.62341i | 0.217634 | − | 0.376953i | −0.736450 | − | 0.676492i | \(-0.763499\pi\) |
0.954084 | + | 0.299539i | \(0.0968327\pi\) | |||||||
\(410\) | 0.626410 | 0.0309362 | ||||||||
\(411\) | 9.92891i | 0.489757i | ||||||||
\(412\) | 7.79811 | + | 4.50224i | 0.384185 | + | 0.221809i | ||||
\(413\) | 13.3834 | + | 23.1807i | 0.658553 | + | 1.14065i | ||||
\(414\) | 3.02437 | − | 5.23837i | 0.148640 | − | 0.257452i | ||||
\(415\) | 0.506524 | − | 0.292442i | 0.0248643 | − | 0.0143554i | ||||
\(416\) | −1.96561 | − | 3.40453i | −0.0963719 | − | 0.166921i | ||||
\(417\) | −26.3553 | −1.29062 | ||||||||
\(418\) | 11.2640 | − | 9.06216i | 0.550939 | − | 0.443245i | ||||
\(419\) | 12.3145 | 0.601601 | 0.300801 | − | 0.953687i | \(-0.402746\pi\) | ||||
0.300801 | + | 0.953687i | \(0.402746\pi\) | |||||||
\(420\) | −0.586964 | − | 1.01665i | −0.0286409 | − | 0.0496075i | ||||
\(421\) | −29.0645 | + | 16.7804i | −1.41652 | + | 0.817828i | −0.995991 | − | 0.0894517i | \(-0.971489\pi\) |
−0.420528 | + | 0.907279i | \(0.638155\pi\) | |||||||
\(422\) | −10.8046 | + | 18.7142i | −0.525962 | + | 0.910993i | ||||
\(423\) | 1.96695 | + | 3.40686i | 0.0956366 | + | 0.165647i | ||||
\(424\) | 0.112462 | + | 0.0649300i | 0.00546164 | + | 0.00315328i | ||||
\(425\) | − | 14.3068i | − | 0.693981i | ||||||
\(426\) | −29.1840 | −1.41397 | ||||||||
\(427\) | 29.3165 | − | 50.7776i | 1.41872 | − | 2.45730i | ||||
\(428\) | −5.29538 | + | 9.17187i | −0.255962 | + | 0.443339i | ||||
\(429\) | 26.3295 | − | 0.532510i | 1.27120 | − | 0.0257098i | ||||
\(430\) | − | 0.0328472i | − | 0.00158403i | ||||||
\(431\) | 9.43169 | − | 16.3362i | 0.454308 | − | 0.786885i | −0.544340 | − | 0.838865i | \(-0.683220\pi\) |
0.998648 | + | 0.0519795i | \(0.0165531\pi\) | |||||||
\(432\) | 3.35919 | − | 1.93943i | 0.161619 | − | 0.0933109i | ||||
\(433\) | −8.89336 | − | 5.13458i | −0.427387 | − | 0.246752i | 0.270846 | − | 0.962623i | \(-0.412697\pi\) |
−0.698233 | + | 0.715871i | \(0.746030\pi\) | |||||||
\(434\) | 13.5703 | + | 23.5045i | 0.651396 | + | 1.12825i | ||||
\(435\) | 0.904512 | − | 0.522220i | 0.0433680 | − | 0.0250386i | ||||
\(436\) | 18.5844 | 0.890033 | ||||||||
\(437\) | −9.28343 | + | 22.5892i | −0.444087 | + | 1.08059i | ||||
\(438\) | −15.5952 | −0.745170 | ||||||||
\(439\) | 15.8473 | + | 27.4484i | 0.756352 | + | 1.31004i | 0.944699 | + | 0.327938i | \(0.106354\pi\) |
−0.188347 | + | 0.982103i | \(0.560313\pi\) | |||||||
\(440\) | 0.368215 | − | 0.222636i | 0.0175540 | − | 0.0106137i | ||||
\(441\) | −7.05484 | + | 12.2193i | −0.335945 | + | 0.581873i | ||||
\(442\) | 9.77449 | − | 5.64331i | 0.464925 | − | 0.268425i | ||||
\(443\) | 5.62125 | − | 9.73630i | 0.267074 | − | 0.462585i | −0.701031 | − | 0.713131i | \(-0.747277\pi\) |
0.968105 | + | 0.250545i | \(0.0806099\pi\) | |||||||
\(444\) | −9.57773 | −0.454539 | ||||||||
\(445\) | 2.16269i | 0.102521i | ||||||||
\(446\) | −21.3131 | − | 12.3051i | −1.00920 | − | 0.582664i | ||||
\(447\) | 20.3588 | − | 35.2624i | 0.962936 | − | 1.66785i | ||||
\(448\) | 4.47991i | 0.211656i | ||||||||
\(449\) | 39.2910i | 1.85426i | 0.374743 | + | 0.927129i | \(0.377731\pi\) | ||||
−0.374743 | + | 0.927129i | \(0.622269\pi\) | |||||||
\(450\) | 2.68986 | − | 4.65897i | 0.126801 | − | 0.219626i | ||||
\(451\) | 13.7035 | − | 8.28562i | 0.645273 | − | 0.390155i | ||||
\(452\) | −5.85759 | − | 3.38188i | −0.275518 | − | 0.159070i | ||||
\(453\) | −16.9953 | + | 9.81226i | −0.798510 | + | 0.461020i | ||||
\(454\) | 4.69277 | + | 8.12812i | 0.220243 | + | 0.381472i | ||||
\(455\) | 2.28487i | 0.107116i | ||||||||
\(456\) | 6.96986 | − | 5.37894i | 0.326394 | − | 0.251892i | ||||
\(457\) | 17.9324i | 0.838842i | 0.907792 | + | 0.419421i | \(0.137767\pi\) | ||||
−0.907792 | + | 0.419421i | \(0.862233\pi\) | |||||||
\(458\) | −12.2754 | − | 21.2617i | −0.573594 | − | 0.993493i | ||||
\(459\) | 5.56815 | + | 9.64432i | 0.259899 | + | 0.450158i | ||||
\(460\) | −0.363451 | + | 0.629515i | −0.0169460 | + | 0.0293513i | ||||
\(461\) | −6.80571 | + | 3.92928i | −0.316973 | + | 0.183005i | −0.650043 | − | 0.759898i | \(-0.725249\pi\) |
0.333069 | + | 0.942902i | \(0.391916\pi\) | |||||||
\(462\) | −26.2880 | − | 14.4767i | −1.22303 | − | 0.673515i | ||||
\(463\) | 5.56513 | 0.258634 | 0.129317 | − | 0.991603i | \(-0.458722\pi\) | ||||
0.129317 | + | 0.991603i | \(0.458722\pi\) | |||||||
\(464\) | −3.98577 | −0.185035 | ||||||||
\(465\) | 0.793765 | − | 1.37484i | 0.0368100 | − | 0.0637568i | ||||
\(466\) | −23.7955 | − | 13.7383i | −1.10230 | − | 0.636415i | ||||
\(467\) | 11.6657 | 0.539826 | 0.269913 | − | 0.962885i | \(-0.413005\pi\) | ||||
0.269913 | + | 0.962885i | \(0.413005\pi\) | |||||||
\(468\) | 4.24405 | 0.196181 | ||||||||
\(469\) | −9.09735 | + | 15.7571i | −0.420077 | + | 0.727594i | ||||
\(470\) | −0.236377 | − | 0.409416i | −0.0109032 | − | 0.0188850i | ||||
\(471\) | −43.0915 | − | 24.8789i | −1.98555 | − | 1.14636i | ||||
\(472\) | −5.17436 | + | 2.98742i | −0.238169 | + | 0.137507i | ||||
\(473\) | −0.434475 | − | 0.718573i | −0.0199772 | − | 0.0330400i | ||||
\(474\) | 9.14420i | 0.420007i | ||||||||
\(475\) | −8.25662 | + | 20.0907i | −0.378840 | + | 0.921824i | ||||
\(476\) | −12.8619 | −0.589526 | ||||||||
\(477\) | −0.121411 | + | 0.0700970i | −0.00555905 | + | 0.00320952i | ||||
\(478\) | −13.3197 | + | 7.69016i | −0.609231 | + | 0.351740i | ||||
\(479\) | 27.3906 | + | 15.8140i | 1.25151 | + | 0.722560i | 0.971409 | − | 0.237411i | \(-0.0762989\pi\) |
0.280101 | + | 0.959971i | \(0.409632\pi\) | |||||||
\(480\) | 0.226935 | − | 0.131021i | 0.0103581 | − | 0.00598027i | ||||
\(481\) | 16.1441 | + | 9.32077i | 0.736106 | + | 0.424991i | ||||
\(482\) | −10.0879 | −0.459490 | ||||||||
\(483\) | 50.6978 | 2.30683 | ||||||||
\(484\) | 5.11032 | − | 9.74087i | 0.232287 | − | 0.442767i | ||||
\(485\) | 1.52500 | + | 0.880459i | 0.0692467 | + | 0.0399796i | ||||
\(486\) | 10.7291i | 0.486682i | ||||||||
\(487\) | 18.6345i | 0.844410i | 0.906500 | + | 0.422205i | \(0.138744\pi\) | ||||
−0.906500 | + | 0.422205i | \(0.861256\pi\) | |||||||
\(488\) | 11.3345 | + | 6.54398i | 0.513089 | + | 0.296232i | ||||
\(489\) | 15.3694 | − | 8.87354i | 0.695030 | − | 0.401275i | ||||
\(490\) | 0.847808 | − | 1.46845i | 0.0383001 | − | 0.0663376i | ||||
\(491\) | 13.4139 | − | 7.74450i | 0.605360 | − | 0.349504i | −0.165788 | − | 0.986161i | \(-0.553017\pi\) |
0.771147 | + | 0.636657i | \(0.219683\pi\) | |||||||
\(492\) | 8.44564 | − | 4.87609i | 0.380759 | − | 0.219831i | ||||
\(493\) | − | 11.4432i | − | 0.515377i | ||||||
\(494\) | −16.9829 | + | 2.28378i | −0.764097 | + | 0.102752i | ||||
\(495\) | 0.00939315 | + | 0.464435i | 0.000422191 | + | 0.0208748i | ||||
\(496\) | −5.24664 | + | 3.02915i | −0.235581 | + | 0.136013i | ||||
\(497\) | −32.3651 | − | 56.0580i | −1.45177 | − | 2.51455i | ||||
\(498\) | 4.55284 | − | 7.88576i | 0.204018 | − | 0.353369i | ||||
\(499\) | −7.05643 | − | 12.2221i | −0.315889 | − | 0.547136i | 0.663737 | − | 0.747966i | \(-0.268970\pi\) |
−0.979626 | + | 0.200830i | \(0.935636\pi\) | |||||||
\(500\) | −0.647593 | + | 1.12166i | −0.0289613 | + | 0.0501624i | ||||
\(501\) | − | 4.68250i | − | 0.209199i | ||||||
\(502\) | −8.76878 | −0.391370 | ||||||||
\(503\) | −3.02208 | − | 1.74480i | −0.134748 | − | 0.0777968i | 0.431111 | − | 0.902299i | \(-0.358122\pi\) |
−0.565859 | + | 0.824502i | \(0.691455\pi\) | |||||||
\(504\) | −4.18846 | − | 2.41821i | −0.186569 | − | 0.107716i | ||||
\(505\) | 0.0481588i | 0.00214304i | ||||||||
\(506\) | 0.375755 | + | 18.5789i | 0.0167043 | + | 0.825931i | ||||
\(507\) | −4.29335 | − | 2.47877i | −0.190674 | − | 0.110086i | ||||
\(508\) | −3.50584 | − | 6.07229i | −0.155546 | − | 0.269414i | ||||
\(509\) | 26.1640 | + | 15.1058i | 1.15970 | + | 0.669552i | 0.951232 | − | 0.308477i | \(-0.0998194\pi\) |
0.208467 | + | 0.978029i | \(0.433153\pi\) | |||||||
\(510\) | 0.376165 | + | 0.651537i | 0.0166569 | + | 0.0288505i | ||||
\(511\) | −17.2952 | − | 29.9561i | −0.765092 | − | 1.32518i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.25337 | − | 16.7567i | −0.0994885 | − | 0.739828i | ||||
\(514\) | − | 31.7201i | − | 1.39911i | ||||||
\(515\) | 1.01170 | − | 0.584107i | 0.0445810 | − | 0.0257389i | ||||
\(516\) | −0.255689 | − | 0.442866i | −0.0112561 | − | 0.0194961i | ||||
\(517\) | −10.5865 | − | 5.82991i | −0.465592 | − | 0.256399i | ||||
\(518\) | −10.6217 | − | 18.3974i | −0.466691 | − | 0.808333i | ||||
\(519\) | 12.6817 | + | 7.32181i | 0.556667 | + | 0.321392i | ||||
\(520\) | −0.510025 | −0.0223661 | ||||||||
\(521\) | 26.0601i | 1.14171i | 0.821050 | + | 0.570856i | \(0.193389\pi\) | ||||
−0.821050 | + | 0.570856i | \(0.806611\pi\) | |||||||
\(522\) | 2.15147 | − | 3.72646i | 0.0941674 | − | 0.163103i | ||||
\(523\) | −1.77172 | + | 3.06870i | −0.0774718 | + | 0.134185i | −0.902158 | − | 0.431405i | \(-0.858018\pi\) |
0.824687 | + | 0.565590i | \(0.191351\pi\) | |||||||
\(524\) | 7.92747i | 0.346313i | ||||||||
\(525\) | 45.0903 | 1.96790 | ||||||||
\(526\) | 25.6515 | + | 14.8099i | 1.11846 | + | 0.645742i | ||||
\(527\) | −8.69675 | − | 15.0632i | −0.378836 | − | 0.656164i | ||||
\(528\) | 3.23146 | − | 5.86797i | 0.140631 | − | 0.255370i | ||||
\(529\) | −4.19614 | − | 7.26792i | −0.182441 | − | 0.315997i | ||||
\(530\) | 0.0145905 | − | 0.00842383i | 0.000633771 | − | 0.000365908i | ||||
\(531\) | − | 6.45030i | − | 0.279919i | ||||||
\(532\) | 18.0617 | + | 7.42278i | 0.783074 | + | 0.321818i | ||||
\(533\) | −18.9811 | −0.822163 | ||||||||
\(534\) | 16.8348 | + | 29.1587i | 0.728512 | + | 1.26182i | ||||
\(535\) | 0.687007 | + | 1.18993i | 0.0297019 | + | 0.0514452i | ||||
\(536\) | −3.51727 | − | 2.03070i | −0.151923 | − | 0.0877128i | ||||
\(537\) | 16.4458 | + | 28.4849i | 0.709688 | + | 1.22922i | ||||
\(538\) | 12.2618 | + | 7.07936i | 0.528644 | + | 0.305213i | ||||
\(539\) | −0.876510 | − | 43.3382i | −0.0377539 | − | 1.86671i | ||||
\(540\) | − | 0.503232i | − | 0.0216557i | ||||||
\(541\) | 0.827614 | + | 0.477823i | 0.0355819 | + | 0.0205432i | 0.517685 | − | 0.855571i | \(-0.326794\pi\) |
−0.482104 | + | 0.876114i | \(0.660127\pi\) | |||||||
\(542\) | 5.10308 | + | 2.94627i | 0.219196 | + | 0.126553i | ||||
\(543\) | 13.5402 | 0.581067 | ||||||||
\(544\) | − | 2.87102i | − | 0.123094i | ||||||
\(545\) | 1.20555 | − | 2.08807i | 0.0516399 | − | 0.0894429i | ||||
\(546\) | 17.7858 | + | 30.8060i | 0.761164 | + | 1.31837i | ||||
\(547\) | −5.38930 | + | 9.33454i | −0.230430 | + | 0.399116i | −0.957935 | − | 0.286986i | \(-0.907347\pi\) |
0.727505 | + | 0.686102i | \(0.240680\pi\) | |||||||
\(548\) | −2.45790 | − | 4.25721i | −0.104996 | − | 0.181859i | ||||
\(549\) | −12.2365 | + | 7.06473i | −0.522240 | + | 0.301515i | ||||
\(550\) | 0.334194 | + | 16.5239i | 0.0142501 | + | 0.704582i | ||||
\(551\) | −6.60403 | + | 16.0695i | −0.281341 | + | 0.684582i | ||||
\(552\) | 11.3167i | 0.481670i | ||||||||
\(553\) | −17.5646 | + | 10.1409i | −0.746923 | + | 0.431236i | ||||
\(554\) | 16.9075 | − | 9.76153i | 0.718330 | − | 0.414728i | ||||
\(555\) | −0.621293 | + | 1.07611i | −0.0263724 | + | 0.0456784i | ||||
\(556\) | 11.3003 | − | 6.52424i | 0.479240 | − | 0.276690i | ||||
\(557\) | −11.4752 | − | 6.62520i | −0.486219 | − | 0.280719i | 0.236785 | − | 0.971562i | \(-0.423906\pi\) |
−0.723005 | + | 0.690843i | \(0.757240\pi\) | |||||||
\(558\) | − | 6.54040i | − | 0.276877i | ||||||
\(559\) | 0.995316i | 0.0420974i | ||||||||
\(560\) | 0.503343 | + | 0.290605i | 0.0212701 | + | 0.0122803i | ||||
\(561\) | 16.8471 | + | 9.27759i | 0.711283 | + | 0.391700i | ||||
\(562\) | 11.3468 | 0.478636 | ||||||||
\(563\) | −24.6625 | −1.03940 | −0.519701 | − | 0.854348i | \(-0.673957\pi\) | ||||
−0.519701 | + | 0.854348i | \(0.673957\pi\) | |||||||
\(564\) | −6.37395 | − | 3.68000i | −0.268392 | − | 0.154956i | ||||
\(565\) | −0.759947 | + | 0.438756i | −0.0319712 | + | 0.0184586i | ||||
\(566\) | 8.52486 | + | 4.92183i | 0.358326 | + | 0.206880i | ||||
\(567\) | −42.9611 | + | 24.8036i | −1.80420 | + | 1.04165i | ||||
\(568\) | 12.5132 | − | 7.22450i | 0.525042 | − | 0.303133i | ||||
\(569\) | 1.60056 | 0.0670990 | 0.0335495 | − | 0.999437i | \(-0.489319\pi\) | ||||
0.0335495 | + | 0.999437i | \(0.489319\pi\) | |||||||
\(570\) | −0.152230 | − | 1.13203i | −0.00637619 | − | 0.0474154i | ||||
\(571\) | − | 41.6813i | − | 1.74431i | −0.489231 | − | 0.872154i | \(-0.662723\pi\) | ||
0.489231 | − | 0.872154i | \(-0.337277\pi\) | |||||||
\(572\) | −11.1574 | + | 6.74618i | −0.466516 | + | 0.282072i | ||||
\(573\) | −25.2001 | + | 14.5493i | −1.05275 | + | 0.607805i | ||||
\(574\) | 18.7325 | + | 10.8152i | 0.781878 | + | 0.451417i | ||||
\(575\) | −13.9600 | − | 24.1795i | −0.582174 | − | 1.00836i | ||||
\(576\) | 0.539789 | − | 0.934941i | 0.0224912 | − | 0.0389559i | ||||
\(577\) | −25.1475 | −1.04690 | −0.523452 | − | 0.852055i | \(-0.675356\pi\) | ||||
−0.523452 | + | 0.852055i | \(0.675356\pi\) | |||||||
\(578\) | −8.75723 | −0.364253 | ||||||||
\(579\) | −3.82987 | − | 2.21118i | −0.159164 | − | 0.0918935i | ||||
\(580\) | −0.258551 | + | 0.447823i | −0.0107357 | + | 0.0185949i | ||||
\(581\) | 20.1964 | 0.837890 | ||||||||
\(582\) | 27.4146 | 1.13637 | ||||||||
\(583\) | 0.207762 | − | 0.377273i | 0.00860463 | − | 0.0156250i | ||||
\(584\) | 6.68675 | − | 3.86060i | 0.276700 | − | 0.159753i | ||||
\(585\) | 0.275306 | − | 0.476843i | 0.0113825 | − | 0.0197150i | ||||
\(586\) | 1.46919 | + | 2.54470i | 0.0606915 | + | 0.105121i | ||||
\(587\) | −6.80724 | − | 11.7905i | −0.280965 | − | 0.486645i | 0.690658 | − | 0.723182i | \(-0.257321\pi\) |
−0.971623 | + | 0.236536i | \(0.923988\pi\) | |||||||
\(588\) | − | 26.3980i | − | 1.08864i | ||||||
\(589\) | 3.51947 | + | 26.1719i | 0.145017 | + | 1.07839i | ||||
\(590\) | 0.775158i | 0.0319128i | ||||||||
\(591\) | 23.3657 | + | 40.4706i | 0.961136 | + | 1.66474i | ||||
\(592\) | 4.10663 | − | 2.37096i | 0.168781 | − | 0.0974460i | ||||
\(593\) | −6.91328 | − | 3.99138i | −0.283894 | − | 0.163906i | 0.351291 | − | 0.936266i | \(-0.385743\pi\) |
−0.635185 | + | 0.772360i | \(0.719076\pi\) | |||||||
\(594\) | −6.65633 | − | 11.0088i | −0.273113 | − | 0.451698i | ||||
\(595\) | −0.834335 | + | 1.44511i | −0.0342044 | + | 0.0592437i | ||||
\(596\) | 20.1592i | 0.825754i | ||||||||
\(597\) | 1.66743i | 0.0682432i | ||||||||
\(598\) | 11.0131 | − | 19.0752i | 0.450358 | − | 0.780043i | ||||
\(599\) | −27.4903 | − | 15.8715i | −1.12322 | − | 0.648493i | −0.181001 | − | 0.983483i | \(-0.557934\pi\) |
−0.942222 | + | 0.334990i | \(0.891267\pi\) | |||||||
\(600\) | 10.0650i | 0.410901i | ||||||||
\(601\) | 29.9977 | 1.22363 | 0.611815 | − | 0.791001i | \(-0.290440\pi\) | ||||
0.611815 | + | 0.791001i | \(0.290440\pi\) | |||||||
\(602\) | 0.567118 | − | 0.982278i | 0.0231140 | − | 0.0400346i | ||||
\(603\) | 3.79717 | − | 2.19230i | 0.154633 | − | 0.0892772i | ||||
\(604\) | 4.85804 | − | 8.41438i | 0.197671 | − | 0.342376i | ||||
\(605\) | −0.762942 | − | 1.20605i | −0.0310180 | − | 0.0490329i | ||||
\(606\) | 0.374877 | + | 0.649306i | 0.0152283 | + | 0.0263763i | ||||
\(607\) | −15.1457 | −0.614745 | −0.307373 | − | 0.951589i | \(-0.599450\pi\) | ||||
−0.307373 | + | 0.951589i | \(0.599450\pi\) | |||||||
\(608\) | −1.65690 | + | 4.03171i | −0.0671963 | + | 0.163507i | ||||
\(609\) | 36.0653 | 1.46144 | ||||||||
\(610\) | 1.47050 | − | 0.848996i | 0.0595390 | − | 0.0343749i | ||||
\(611\) | 7.16255 | + | 12.4059i | 0.289766 | + | 0.501889i | ||||
\(612\) | 2.68424 | + | 1.54975i | 0.108504 | + | 0.0626447i | ||||
\(613\) | 13.3958 | − | 7.73407i | 0.541051 | − | 0.312376i | −0.204454 | − | 0.978876i | \(-0.565542\pi\) |
0.745505 | + | 0.666500i | \(0.232208\pi\) | |||||||
\(614\) | −5.95515 | + | 10.3146i | −0.240330 | + | 0.416265i | ||||
\(615\) | − | 1.26522i | − | 0.0510186i | ||||||
\(616\) | 14.8552 | − | 0.300444i | 0.598531 | − | 0.0121052i | ||||
\(617\) | −11.6427 | + | 20.1657i | −0.468717 | + | 0.811842i | −0.999361 | − | 0.0357531i | \(-0.988617\pi\) |
0.530643 | + | 0.847595i | \(0.321950\pi\) | |||||||
\(618\) | 9.09361 | − | 15.7506i | 0.365799 | − | 0.633582i | ||||
\(619\) | 41.2500 | 1.65798 | 0.828990 | − | 0.559264i | \(-0.188916\pi\) | ||||
0.828990 | + | 0.559264i | \(0.188916\pi\) | |||||||
\(620\) | 0.785985i | 0.0315659i | ||||||||
\(621\) | 18.8212 | + | 10.8664i | 0.755267 | + | 0.436054i | ||||
\(622\) | −3.15961 | − | 5.47260i | −0.126689 | − | 0.219431i | ||||
\(623\) | −37.3396 | + | 64.6740i | −1.49598 | + | 2.59111i | ||||
\(624\) | −6.87647 | + | 3.97013i | −0.275279 | + | 0.158932i | ||||
\(625\) | −12.3739 | − | 21.4322i | −0.494956 | − | 0.857289i | ||||
\(626\) | −14.4375 | −0.577037 | ||||||||
\(627\) | −18.3037 | − | 22.7510i | −0.730980 | − | 0.908585i | ||||
\(628\) | 24.6351 | 0.983046 | ||||||||
\(629\) | 6.80709 | + | 11.7902i | 0.271416 | + | 0.470107i | ||||
\(630\) | −0.543398 | + | 0.313731i | −0.0216495 | + | 0.0124993i | ||||
\(631\) | 0.244717 | − | 0.423863i | 0.00974204 | − | 0.0168737i | −0.861113 | − | 0.508413i | \(-0.830232\pi\) |
0.870855 | + | 0.491539i | \(0.163566\pi\) | |||||||
\(632\) | −2.26364 | − | 3.92074i | −0.0900429 | − | 0.155959i | ||||
\(633\) | 37.7989 | + | 21.8232i | 1.50237 | + | 0.867394i | ||||
\(634\) | − | 3.83651i | − | 0.152367i | ||||||
\(635\) | −0.909674 | −0.0360993 | ||||||||
\(636\) | 0.131145 | − | 0.227150i | 0.00520025 | − | 0.00900710i | ||||
\(637\) | −25.6898 | + | 44.4960i | −1.01787 | + | 1.76300i | ||||
\(638\) | 0.267304 | + | 13.2166i | 0.0105827 | + | 0.523250i | ||||
\(639\) | 15.5988i | 0.617079i | ||||||||
\(640\) | −0.0648685 | + | 0.112356i | −0.00256415 | + | 0.00444124i | ||||
\(641\) | 22.5012 | − | 12.9911i | 0.888744 | − | 0.513116i | 0.0152123 | − | 0.999884i | \(-0.495158\pi\) |
0.873531 | + | 0.486768i | \(0.161824\pi\) | |||||||
\(642\) | 18.5253 | + | 10.6956i | 0.731135 | + | 0.422121i | ||||
\(643\) | 22.5233 | + | 39.0116i | 0.888234 | + | 1.53847i | 0.841962 | + | 0.539537i | \(0.181401\pi\) |
0.0462721 | + | 0.998929i | \(0.485266\pi\) | |||||||
\(644\) | −21.7376 | + | 12.5502i | −0.856582 | + | 0.494548i | ||||
\(645\) | −0.0663446 | −0.00261232 | ||||||||
\(646\) | −11.5751 | − | 4.75700i | −0.455417 | − | 0.187162i | ||||
\(647\) | −37.9571 | −1.49225 | −0.746125 | − | 0.665806i | \(-0.768088\pi\) | ||||
−0.746125 | + | 0.665806i | \(0.768088\pi\) | |||||||
\(648\) | −5.53662 | − | 9.58971i | −0.217499 | − | 0.376719i | ||||
\(649\) | 10.2531 | + | 16.9576i | 0.402471 | + | 0.665643i | ||||
\(650\) | 9.79496 | − | 16.9654i | 0.384190 | − | 0.665436i | ||||
\(651\) | 47.4743 | − | 27.4093i | 1.86066 | − | 1.07425i | ||||
\(652\) | −4.39329 | + | 7.60939i | −0.172054 | + | 0.298007i | ||||
\(653\) | 31.8364 | 1.24586 | 0.622928 | − | 0.782279i | \(-0.285943\pi\) | ||||
0.622928 | + | 0.782279i | \(0.285943\pi\) | |||||||
\(654\) | − | 37.5368i | − | 1.46780i | ||||||
\(655\) | 0.890696 | + | 0.514244i | 0.0348024 | + | 0.0200932i | ||||
\(656\) | −2.41415 | + | 4.18143i | −0.0942568 | + | 0.163258i | ||||
\(657\) | 8.33563i | 0.325204i | ||||||||
\(658\) | − | 16.3245i | − | 0.636396i | ||||||
\(659\) | 10.1845 | − | 17.6401i | 0.396732 | − | 0.687159i | −0.596589 | − | 0.802547i | \(-0.703478\pi\) |
0.993321 | + | 0.115388i | \(0.0368111\pi\) | |||||||
\(660\) | −0.449679 | − | 0.743719i | −0.0175037 | − | 0.0289492i | ||||
\(661\) | 43.3159 | + | 25.0084i | 1.68479 | + | 0.972715i | 0.958397 | + | 0.285439i | \(0.0921393\pi\) |
0.726396 | + | 0.687277i | \(0.241194\pi\) | |||||||
\(662\) | 0.335417 | − | 0.193653i | 0.0130364 | − | 0.00752655i | ||||
\(663\) | −11.3983 | − | 19.7425i | −0.442674 | − | 0.766735i | ||||
\(664\) | 4.50822i | 0.174953i | ||||||||
\(665\) | 2.00563 | − | 1.54783i | 0.0777749 | − | 0.0600222i | ||||
\(666\) | 5.11928i | 0.198368i | ||||||||
\(667\) | −11.1659 | − | 19.3399i | −0.432345 | − | 0.748844i | ||||
\(668\) | 1.15915 | + | 2.00771i | 0.0448489 | + | 0.0776806i | ||||
\(669\) | −24.8538 | + | 43.0481i | −0.960904 | + | 1.66434i | ||||
\(670\) | −0.456321 | + | 0.263457i | −0.0176292 | + | 0.0101782i | ||||
\(671\) | 20.9393 | − | 38.0235i | 0.808354 | − | 1.46788i | ||||
\(672\) | 9.04852 | 0.349054 | ||||||||
\(673\) | −31.7420 | −1.22356 | −0.611782 | − | 0.791026i | \(-0.709547\pi\) | ||||
−0.611782 | + | 0.791026i | \(0.709547\pi\) | |||||||
\(674\) | 0.176938 | − | 0.306466i | 0.00681541 | − | 0.0118046i | ||||
\(675\) | 16.7394 | + | 9.66451i | 0.644301 | + | 0.371987i | ||||
\(676\) | 2.45447 | 0.0944028 | ||||||||
\(677\) | 23.7389 | 0.912360 | 0.456180 | − | 0.889887i | \(-0.349217\pi\) | ||||
0.456180 | + | 0.889887i | \(0.349217\pi\) | |||||||
\(678\) | −6.83071 | + | 11.8311i | −0.262332 | + | 0.454372i | ||||
\(679\) | 30.4029 | + | 52.6593i | 1.16676 | + | 2.02088i | ||||
\(680\) | −0.322575 | − | 0.186239i | −0.0123702 | − | 0.00714194i | ||||
\(681\) | 16.4172 | − | 9.47845i | 0.629107 | − | 0.363215i | ||||
\(682\) | 10.3964 | + | 17.1944i | 0.398097 | + | 0.658408i | ||||
\(683\) | − | 14.0384i | − | 0.537166i | −0.963257 | − | 0.268583i | \(-0.913445\pi\) | ||
0.963257 | − | 0.268583i | \(-0.0865553\pi\) | |||||||
\(684\) | −2.87503 | − | 3.72538i | −0.109930 | − | 0.142443i | ||||
\(685\) | −0.637761 | −0.0243676 | ||||||||
\(686\) | 23.5485 | − | 13.5957i | 0.899085 | − | 0.519087i | ||||
\(687\) | −42.9443 | + | 24.7939i | −1.63843 | + | 0.945946i | ||||
\(688\) | 0.219263 | + | 0.126591i | 0.00835931 | + | 0.00482625i | ||||
\(689\) | −0.442113 | + | 0.255254i | −0.0168432 | + | 0.00972440i | ||||
\(690\) | 1.27149 | + | 0.734096i | 0.0484049 | + | 0.0279466i | ||||
\(691\) | −25.7327 | −0.978919 | −0.489460 | − | 0.872026i | \(-0.662806\pi\) | ||||
−0.489460 | + | 0.872026i | \(0.662806\pi\) | |||||||
\(692\) | −7.25005 | −0.275605 | ||||||||
\(693\) | −7.73775 | + | 14.0509i | −0.293933 | + | 0.533749i | ||||
\(694\) | −16.9725 | − | 9.79909i | −0.644268 | − | 0.371968i | ||||
\(695\) | − | 1.69287i | − | 0.0642143i | ||||||
\(696\) | 8.05044i | 0.305151i | ||||||||
\(697\) | −12.0050 | − | 6.93108i | −0.454721 | − | 0.262533i | ||||
\(698\) | 2.35742 | − | 1.36106i | 0.0892296 | − | 0.0515167i | ||||
\(699\) | −27.7486 | + | 48.0620i | −1.04955 | + | 1.81787i | ||||
\(700\) | −19.3333 | + | 11.1621i | −0.730730 | + | 0.421887i | ||||
\(701\) | −13.3777 | + | 7.72362i | −0.505269 | + | 0.291717i | −0.730887 | − | 0.682499i | \(-0.760893\pi\) |
0.225618 | + | 0.974216i | \(0.427560\pi\) | |||||||
\(702\) | 15.2487i | 0.575523i | ||||||||
\(703\) | −2.75475 | − | 20.4852i | −0.103897 | − | 0.772614i | ||||
\(704\) | 0.0670646 | + | 3.31595i | 0.00252759 | + | 0.124974i | ||||
\(705\) | −0.826937 | + | 0.477433i | −0.0311443 | + | 0.0179812i | ||||
\(706\) | 9.49593 | + | 16.4474i | 0.357384 | + | 0.619008i | ||||
\(707\) | −0.831479 | + | 1.44016i | −0.0312710 | + | 0.0541629i | ||||
\(708\) | 6.03398 | + | 10.4512i | 0.226771 | + | 0.392779i | ||||
\(709\) | −19.5140 | + | 33.7992i | −0.732863 | + | 1.26936i | 0.222791 | + | 0.974866i | \(0.428483\pi\) |
−0.955655 | + | 0.294490i | \(0.904850\pi\) | |||||||
\(710\) | − | 1.87457i | − | 0.0703514i | ||||||
\(711\) | 4.88756 | 0.183298 | ||||||||
\(712\) | −14.4364 | − | 8.33488i | −0.541029 | − | 0.312363i | ||||
\(713\) | −29.3963 | − | 16.9720i | −1.10090 | − | 0.635605i | ||||
\(714\) | 25.9785i | 0.972220i | ||||||||
\(715\) | 0.0342046 | + | 1.69121i | 0.00127918 | + | 0.0632478i | ||||
\(716\) | −14.1029 | − | 8.14230i | −0.527049 | − | 0.304292i | ||||
\(717\) | 15.5326 | + | 26.9032i | 0.580074 | + | 1.00472i | ||||
\(718\) | −22.2856 | − | 12.8666i | −0.831690 | − | 0.480176i | ||||
\(719\) | −3.76361 | − | 6.51877i | −0.140359 | − | 0.243109i | 0.787273 | − | 0.616605i | \(-0.211492\pi\) |
−0.927632 | + | 0.373496i | \(0.878159\pi\) | |||||||
\(720\) | −0.0700306 | − | 0.121297i | −0.00260989 | − | 0.00452046i | ||||
\(721\) | 40.3393 | 1.50231 | ||||||||
\(722\) | 13.5093 | + | 13.3603i | 0.502766 | + | 0.497219i | ||||
\(723\) | 20.3755i | 0.757772i | ||||||||
\(724\) | −5.80563 | + | 3.35188i | −0.215765 | + | 0.124572i | ||||
\(725\) | −9.93088 | − | 17.2008i | −0.368824 | − | 0.638821i | ||||
\(726\) | −19.6746 | − | 10.3218i | −0.730192 | − | 0.383078i | ||||
\(727\) | −11.1300 | − | 19.2777i | −0.412787 | − | 0.714969i | 0.582406 | − | 0.812898i | \(-0.302111\pi\) |
−0.995193 | + | 0.0979293i | \(0.968778\pi\) | |||||||
\(728\) | −15.2520 | − | 8.80576i | −0.565278 | − | 0.326363i | ||||
\(729\) | −11.5491 | −0.427745 | ||||||||
\(730\) | − | 1.00173i | − | 0.0370755i | ||||||
\(731\) | −0.363446 | + | 0.629508i | −0.0134425 | + | 0.0232832i | ||||
\(732\) | 13.2175 | − | 22.8934i | 0.488533 | − | 0.846164i | ||||
\(733\) | − | 43.1218i | − | 1.59274i | −0.604811 | − | 0.796369i | \(-0.706751\pi\) | ||
0.604811 | − | 0.796369i | \(-0.293249\pi\) | |||||||
\(734\) | −2.95250 | −0.108979 | ||||||||
\(735\) | −2.96596 | − | 1.71240i | −0.109401 | − | 0.0631628i | ||||
\(736\) | −2.80144 | − | 4.85224i | −0.103262 | − | 0.178856i | ||||
\(737\) | −6.49780 | + | 11.7993i | −0.239350 | + | 0.434632i | ||||
\(738\) | −2.60626 | − | 4.51418i | −0.0959379 | − | 0.166169i | ||||
\(739\) | −17.2620 | + | 9.96623i | −0.634993 | + | 0.366614i | −0.782683 | − | 0.622420i | \(-0.786150\pi\) |
0.147690 | + | 0.989034i | \(0.452816\pi\) | |||||||
\(740\) | − | 0.615204i | − | 0.0226153i | ||||||
\(741\) | 4.61277 | + | 34.3020i | 0.169454 | + | 1.26012i | ||||
\(742\) | 0.581762 | 0.0213571 | ||||||||
\(743\) | −8.67725 | − | 15.0294i | −0.318338 | − | 0.551377i | 0.661804 | − | 0.749677i | \(-0.269791\pi\) |
−0.980141 | + | 0.198300i | \(0.936458\pi\) | |||||||
\(744\) | 6.11826 | + | 10.5971i | 0.224306 | + | 0.388510i | ||||
\(745\) | 2.26500 | + | 1.30770i | 0.0829832 | + | 0.0479104i | ||||
\(746\) | −9.07946 | − | 15.7261i | −0.332423 | − | 0.575773i | ||||
\(747\) | −4.21492 | − | 2.43349i | −0.154216 | − | 0.0890366i | ||||
\(748\) | −9.52016 | + | 0.192544i | −0.348091 | + | 0.00704010i | ||||
\(749\) | 47.4457i | 1.73363i | ||||||||
\(750\) | 2.26553 | + | 1.30801i | 0.0827256 | + | 0.0477617i | ||||
\(751\) | 30.4579 | + | 17.5849i | 1.11142 | + | 0.641680i | 0.939198 | − | 0.343377i | \(-0.111571\pi\) |
0.172225 | + | 0.985058i | \(0.444904\pi\) | |||||||
\(752\) | 3.64393 | 0.132881 | ||||||||
\(753\) | 17.7112i | 0.645431i | ||||||||
\(754\) | 7.83446 | − | 13.5697i | 0.285314 | − | 0.494179i | ||||
\(755\) | −0.630268 | − | 1.09166i | −0.0229378 | − | 0.0397295i | ||||
\(756\) | 8.68849 | − | 15.0489i | 0.315997 | − | 0.547323i | ||||
\(757\) | −5.34556 | − | 9.25878i | −0.194288 | − | 0.336516i | 0.752379 | − | 0.658730i | \(-0.228906\pi\) |
−0.946667 | + | 0.322214i | \(0.895573\pi\) | |||||||
\(758\) | 17.2250 | − | 9.94483i | 0.625638 | − | 0.361213i | ||||
\(759\) | 37.5255 | − | 0.758948i | 1.36209 | − | 0.0275481i | ||||
\(760\) | 0.345504 | + | 0.447693i | 0.0125328 | + | 0.0162395i | ||||
\(761\) | 23.8022i | 0.862828i | 0.902154 | + | 0.431414i | \(0.141985\pi\) | ||||
−0.902154 | + | 0.431414i | \(0.858015\pi\) | |||||||
\(762\) | −12.2648 | + | 7.08107i | −0.444306 | + | 0.256520i | ||||
\(763\) | 72.1024 | − | 41.6284i | 2.61028 | − | 1.50705i | ||||
\(764\) | 7.20335 | − | 12.4766i | 0.260608 | − | 0.451386i | ||||
\(765\) | 0.348245 | − | 0.201059i | 0.0125908 | − | 0.00726932i | ||||
\(766\) | 7.90191 | + | 4.56217i | 0.285508 | + | 0.164838i | ||||
\(767\) | − | 23.4884i | − | 0.848117i | ||||||
\(768\) | 2.01980i | 0.0728831i | ||||||||
\(769\) | 12.9558 | + | 7.48002i | 0.467197 | + | 0.269736i | 0.715066 | − | 0.699057i | \(-0.246397\pi\) |
−0.247868 | + | 0.968794i | \(0.579730\pi\) | |||||||
\(770\) | 0.929876 | − | 1.68855i | 0.0335104 | − | 0.0608511i | ||||
\(771\) | −64.0682 | −2.30736 | ||||||||
\(772\) | 2.18951 | 0.0788021 | ||||||||
\(773\) | 24.5501 | + | 14.1740i | 0.883004 | + | 0.509803i | 0.871648 | − | 0.490133i | \(-0.163052\pi\) |
0.0113563 | + | 0.999936i | \(0.496385\pi\) | |||||||
\(774\) | −0.236711 | + | 0.136665i | −0.00850840 | + | 0.00491233i | ||||
\(775\) | −26.1449 | − | 15.0948i | −0.939152 | − | 0.542219i | ||||
\(776\) | −11.7545 | + | 6.78649i | −0.421963 | + | 0.243621i | ||||
\(777\) | −37.1589 | + | 21.4537i | −1.33307 | + | 0.769647i | ||||
\(778\) | 19.9886 | 0.716625 | ||||||||
\(779\) | 12.8583 | + | 16.6614i | 0.460697 | + | 0.596956i | ||||
\(780\) | 1.03015i | 0.0368851i | ||||||||
\(781\) | −24.7952 | − | 41.0086i | −0.887243 | − | 1.46740i | ||||
\(782\) | 13.9309 | − | 8.04300i | 0.498167 | − | 0.287617i | ||||
\(783\) | 13.3890 | + | 7.73013i | 0.478483 | + | 0.276252i | ||||
\(784\) | 6.53482 | + | 11.3186i | 0.233386 | + | 0.404237i | ||||
\(785\) | 1.59804 | − | 2.76789i | 0.0570365 | − | 0.0987902i | ||||
\(786\) | 16.0119 | 0.571125 | ||||||||
\(787\) | −17.8108 | −0.634887 | −0.317444 | − | 0.948277i | \(-0.602824\pi\) | ||||
−0.317444 | + | 0.948277i | \(0.602824\pi\) | |||||||
\(788\) | −20.0370 | − | 11.5683i | −0.713787 | − | 0.412105i | ||||
\(789\) | 29.9130 | − | 51.8108i | 1.06493 | − | 1.84451i | ||||
\(790\) | −0.587357 | −0.0208972 | ||||||||
\(791\) | −30.3011 | −1.07738 | ||||||||
\(792\) | −3.13642 | − | 1.72721i | −0.111448 | − | 0.0613737i | ||||
\(793\) | −44.5584 | + | 25.7258i | −1.58231 | + | 0.913550i | ||||
\(794\) | 10.7075 | − | 18.5458i | 0.379993 | − | 0.658168i | ||||
\(795\) | −0.0170144 | − | 0.0294698i | −0.000603439 | − | 0.00104519i | ||||
\(796\) | −0.412771 | − | 0.714940i | −0.0146303 | − | 0.0253404i | ||||
\(797\) | − | 21.4014i | − | 0.758075i | −0.925381 | − | 0.379038i | \(-0.876255\pi\) | ||
0.925381 | − | 0.379038i | \(-0.123745\pi\) | |||||||
\(798\) | 14.9925 | − | 36.4810i | 0.530729 | − | 1.29141i | ||||
\(799\) | 10.4618i | 0.370112i | ||||||||
\(800\) | −2.49158 | − | 4.31555i | −0.0880908 | − | 0.152578i | ||||
\(801\) | 15.5853 | − | 8.99815i | 0.550678 | − | 0.317934i | ||||
\(802\) | 0.706399 | + | 0.407840i | 0.0249438 | + | 0.0144013i | ||||
\(803\) | −13.2500 | − | 21.9140i | −0.467582 | − | 0.773329i | ||||
\(804\) | −4.10160 | + | 7.10417i | −0.144652 | + | 0.250545i | ||||
\(805\) | 3.25646i | 0.114775i | ||||||||
\(806\) | − | 23.8165i | − | 0.838900i | ||||||
\(807\) | 14.2989 | − | 24.7664i | 0.503344 | − | 0.871817i | ||||
\(808\) | −0.321471 | − | 0.185601i | −0.0113093 | − | 0.00652944i | ||||
\(809\) | − | 32.9671i | − | 1.15906i | −0.814950 | − | 0.579531i | \(-0.803236\pi\) | ||
0.814950 | − | 0.579531i | \(-0.196764\pi\) | |||||||
\(810\) | −1.43661 | −0.0504773 | ||||||||
\(811\) | 9.10086 | − | 15.7632i | 0.319574 | − | 0.553519i | −0.660825 | − | 0.750540i | \(-0.729793\pi\) |
0.980399 | + | 0.197021i | \(0.0631267\pi\) | |||||||
\(812\) | −15.4637 | + | 8.92795i | −0.542668 | + | 0.313310i | ||||
\(813\) | 5.95086 | − | 10.3072i | 0.208706 | − | 0.361489i | ||||
\(814\) | −8.13740 | − | 13.4584i | −0.285216 | − | 0.471715i | ||||
\(815\) | 0.569972 | + | 0.987220i | 0.0199652 | + | 0.0345808i | ||||
\(816\) | −5.79888 | −0.203001 | ||||||||
\(817\) | 0.873676 | − | 0.674253i | 0.0305661 | − | 0.0235891i | ||||
\(818\) | 8.80275 | 0.307781 | ||||||||
\(819\) | 16.4657 | − | 9.50650i | 0.575359 | − | 0.332184i | ||||
\(820\) | 0.313205 | + | 0.542487i | 0.0109376 | + | 0.0189445i | ||||
\(821\) | −19.4920 | − | 11.2537i | −0.680276 | − | 0.392758i | 0.119683 | − | 0.992812i | \(-0.461812\pi\) |
−0.799959 | + | 0.600055i | \(0.795146\pi\) | |||||||
\(822\) | −8.59869 | + | 4.96445i | −0.299914 | + | 0.173155i | ||||
\(823\) | −12.4961 | + | 21.6439i | −0.435587 | + | 0.754459i | −0.997343 | − | 0.0728437i | \(-0.976793\pi\) |
0.561756 | + | 0.827303i | \(0.310126\pi\) | |||||||
\(824\) | 9.00448i | 0.313686i | ||||||||
\(825\) | 33.3750 | − | 0.675004i | 1.16197 | − | 0.0235006i | ||||
\(826\) | −13.3834 | + | 23.1807i | −0.465668 | + | 0.806560i | ||||
\(827\) | −19.1720 | + | 33.2068i | −0.666674 | + | 1.15471i | 0.312154 | + | 0.950032i | \(0.398950\pi\) |
−0.978828 | + | 0.204683i | \(0.934384\pi\) | |||||||
\(828\) | 6.04874 | 0.210208 | ||||||||
\(829\) | − | 38.5814i | − | 1.33999i | −0.742366 | − | 0.669994i | \(-0.766297\pi\) | ||
0.742366 | − | 0.669994i | \(-0.233703\pi\) | |||||||
\(830\) | 0.506524 | + | 0.292442i | 0.0175817 | + | 0.0101508i | ||||
\(831\) | −19.7163 | − | 34.1496i | −0.683951 | − | 1.18464i | ||||
\(832\) | 1.96561 | − | 3.40453i | 0.0681452 | − | 0.118031i | ||||
\(833\) | −32.4960 | + | 18.7616i | −1.12592 | + | 0.650051i | ||||
\(834\) | −13.1776 | − | 22.8243i | −0.456304 | − | 0.790343i | ||||
\(835\) | 0.300770 | 0.0104086 | ||||||||
\(836\) | 13.4801 | + | 5.22382i | 0.466217 | + | 0.180669i | ||||
\(837\) | 23.4993 | 0.812254 | ||||||||
\(838\) | 6.15724 | + | 10.6646i | 0.212698 | + | 0.368404i | ||||
\(839\) | −29.1071 | + | 16.8050i | −1.00489 | + | 0.580173i | −0.909691 | − | 0.415286i | \(-0.863682\pi\) |
−0.0951975 | + | 0.995458i | \(0.530348\pi\) | |||||||
\(840\) | 0.586964 | − | 1.01665i | 0.0202522 | − | 0.0350778i | ||||
\(841\) | 6.55682 | + | 11.3567i | 0.226097 | + | 0.391612i | ||||
\(842\) | −29.0645 | − | 16.7804i | −1.00163 | − | 0.578292i | ||||
\(843\) | − | 22.9182i | − | 0.789346i | ||||||
\(844\) | −21.6093 | −0.743822 | ||||||||
\(845\) | 0.159218 | − | 0.275774i | 0.00547726 | − | 0.00948690i | ||||
\(846\) | −1.96695 | + | 3.40686i | −0.0676253 | + | 0.117130i | ||||
\(847\) | −1.99251 | − | 49.2388i | −0.0684635 | − | 1.69186i | ||||
\(848\) | 0.129860i | 0.00445941i | ||||||||
\(849\) | 9.94109 | − | 17.2185i | 0.341177 | − | 0.590936i | ||||
\(850\) | 12.3900 | − | 7.15339i | 0.424975 | − | 0.245359i | ||||
\(851\) | 23.0090 | + | 13.2842i | 0.788737 | + | 0.455377i | ||||
\(852\) | −14.5920 | − | 25.2741i | −0.499914 | − | 0.865877i | ||||
\(853\) | 4.36144 | − | 2.51808i | 0.149333 | − | 0.0862173i | −0.423472 | − | 0.905909i | \(-0.639189\pi\) |
0.572805 | + | 0.819692i | \(0.305855\pi\) | |||||||
\(854\) | 58.6329 | 2.00638 | ||||||||
\(855\) | −0.605066 | + | 0.0813664i | −0.0206928 | + | 0.00278267i | ||||
\(856\) | −10.5908 | −0.361985 | ||||||||
\(857\) | −18.6540 | − | 32.3096i | −0.637207 | − | 1.10367i | −0.986043 | − | 0.166491i | \(-0.946756\pi\) |
0.348836 | − | 0.937184i | \(-0.386577\pi\) | |||||||
\(858\) | 13.6259 | + | 22.5357i | 0.465181 | + | 0.769357i | ||||
\(859\) | −8.20513 | + | 14.2117i | −0.279955 | + | 0.484897i | −0.971373 | − | 0.237558i | \(-0.923653\pi\) |
0.691418 | + | 0.722455i | \(0.256986\pi\) | |||||||
\(860\) | 0.0284465 | − | 0.0164236i | 0.000970017 | − | 0.000560040i | ||||
\(861\) | 21.8445 | − | 37.8358i | 0.744458 | − | 1.28944i | ||||
\(862\) | 18.8634 | 0.642489 | ||||||||
\(863\) | − | 33.2130i | − | 1.13058i | −0.824891 | − | 0.565292i | \(-0.808763\pi\) | ||
0.824891 | − | 0.565292i | \(-0.191237\pi\) | |||||||
\(864\) | 3.35919 | + | 1.93943i | 0.114282 | + | 0.0659808i | ||||
\(865\) | −0.470300 | + | 0.814583i | −0.0159907 | + | 0.0276967i | ||||
\(866\) | − | 10.2692i | − | 0.348960i | ||||||
\(867\) | 17.6878i | 0.600710i | ||||||||
\(868\) | −13.5703 | + | 23.5045i | −0.460607 | + | 0.797794i | ||||
\(869\) | −12.8492 | + | 7.76906i | −0.435878 | + | 0.263547i | ||||
\(870\) | 0.904512 | + | 0.522220i | 0.0306658 | + | 0.0177049i | ||||
\(871\) | 13.8272 | − | 7.98312i | 0.468516 | − | 0.270498i | ||||
\(872\) | 9.29222 | + | 16.0946i | 0.314674 | + | 0.545032i | ||||
\(873\) | − | 14.6531i | − | 0.495932i | ||||||
\(874\) | −24.2045 | + | 3.25491i | −0.818730 | + | 0.110099i | ||||
\(875\) | 5.80233i | 0.196154i | ||||||||
\(876\) | −7.79762 | − | 13.5059i | −0.263457 | − | 0.456321i | ||||
\(877\) | −18.7099 | − | 32.4064i | −0.631787 | − | 1.09429i | −0.987186 | − | 0.159573i | \(-0.948988\pi\) |
0.355399 | − | 0.934715i | \(-0.384345\pi\) | |||||||
\(878\) | −15.8473 | + | 27.4484i | −0.534822 | + | 0.926339i | ||||
\(879\) | 5.13978 | − | 2.96745i | 0.173361 | − | 0.100090i | ||||
\(880\) | 0.376916 | + | 0.207566i | 0.0127058 | + | 0.00699703i | ||||
\(881\) | −28.4239 | −0.957627 | −0.478813 | − | 0.877917i | \(-0.658933\pi\) | ||||
−0.478813 | + | 0.877917i | \(0.658933\pi\) | |||||||
\(882\) | −14.1097 | −0.475098 | ||||||||
\(883\) | −13.6042 | + | 23.5631i | −0.457817 | + | 0.792963i | −0.998845 | − | 0.0480416i | \(-0.984702\pi\) |
0.541028 | + | 0.841005i | \(0.318035\pi\) | |||||||
\(884\) | 9.77449 | + | 5.64331i | 0.328752 | + | 0.189805i | ||||
\(885\) | 1.56566 | 0.0526291 | ||||||||
\(886\) | 11.2425 | 0.377699 | ||||||||
\(887\) | 4.78008 | − | 8.27934i | 0.160499 | − | 0.277993i | −0.774548 | − | 0.632515i | \(-0.782023\pi\) |
0.935048 | + | 0.354521i | \(0.115356\pi\) | |||||||
\(888\) | −4.78886 | − | 8.29456i | −0.160704 | − | 0.278347i | ||||
\(889\) | −27.2033 | − | 15.7058i | −0.912370 | − | 0.526757i | ||||
\(890\) | −1.87294 | + | 1.08134i | −0.0627812 | + | 0.0362467i | ||||
\(891\) | −31.4277 | + | 19.0023i | −1.05287 | + | 0.636600i | ||||
\(892\) | − | 24.6102i | − | 0.824011i | ||||||
\(893\) | 6.03764 | − | 14.6913i | 0.202042 | − | 0.491625i | ||||
\(894\) | 40.7175 | 1.36180 | ||||||||
\(895\) | −1.82967 | + | 1.05636i | −0.0611590 | + | 0.0353102i | ||||
\(896\) | −3.87972 | + | 2.23996i | −0.129612 | + | 0.0748317i | ||||
\(897\) | −38.5280 | − | 22.2442i | −1.28641 | − | 0.742711i | ||||
\(898\) | −34.0270 | + | 19.6455i | −1.13550 | + | 0.655579i | ||||
\(899\) | −20.9119 | − | 12.0735i | −0.697450 | − | 0.402673i | ||||
\(900\) | 5.37972 | 0.179324 | ||||||||
\(901\) | −0.372831 | −0.0124208 | ||||||||
\(902\) | 14.0273 | + | 7.72477i | 0.467058 | + | 0.257207i | ||||
\(903\) | −1.98400 | − | 1.14546i | −0.0660234 | − | 0.0381186i | ||||
\(904\) | − | 6.76377i | − | 0.224959i | ||||||
\(905\) | 0.869727i | 0.0289107i | ||||||||
\(906\) | −16.9953 | − | 9.81226i | −0.564632 | − | 0.325990i | ||||
\(907\) | 0.627538 | − | 0.362309i | 0.0208371 | − | 0.0120303i | −0.489545 | − | 0.871978i | \(-0.662837\pi\) |
0.510382 | + | 0.859948i | \(0.329504\pi\) | |||||||
\(908\) | −4.69277 | + | 8.12812i | −0.155735 | + | 0.269741i | ||||
\(909\) | 0.347053 | − | 0.200371i | 0.0115110 | − | 0.00664589i | ||||
\(910\) | −1.97875 | + | 1.14243i | −0.0655950 | + | 0.0378713i | ||||
\(911\) | 33.6066i | 1.11344i | 0.830702 | + | 0.556718i | \(0.187940\pi\) | ||||
−0.830702 | + | 0.556718i | \(0.812060\pi\) | |||||||
\(912\) | 8.14323 | + | 3.34661i | 0.269649 | + | 0.110817i | ||||
\(913\) | 14.9490 | − | 0.302342i | 0.494740 | − | 0.0100061i | ||||
\(914\) | −15.5299 | + | 8.96620i | −0.513684 | + | 0.296576i | ||||
\(915\) | −1.71480 | − | 2.97012i | −0.0566895 | − | 0.0981891i | ||||
\(916\) | 12.2754 | − | 21.2617i | 0.405592 | − | 0.702506i | ||||
\(917\) | 17.7572 | + | 30.7564i | 0.586394 | + | 1.01566i | ||||
\(918\) | −5.56815 | + | 9.64432i | −0.183776 | + | 0.318310i | ||||
\(919\) | − | 35.4628i | − | 1.16981i | −0.811102 | − | 0.584904i | \(-0.801132\pi\) | ||
0.811102 | − | 0.584904i | \(-0.198868\pi\) | |||||||
\(920\) | −0.726901 | −0.0239652 | ||||||||
\(921\) | 20.8335 | + | 12.0282i | 0.686486 | + | 0.396343i | ||||
\(922\) | −6.80571 | − | 3.92928i | −0.224134 | − | 0.129404i | ||||
\(923\) | 56.8021i | 1.86967i | ||||||||
\(924\) | −0.606835 | − | 30.0044i | −0.0199634 | − | 0.987072i | ||||
\(925\) | 20.4640 | + | 11.8149i | 0.672853 | + | 0.388472i | ||||
\(926\) | 2.78257 | + | 4.81955i | 0.0914408 | + | 0.158380i | ||||
\(927\) | −8.41866 | − | 4.86052i | −0.276505 | − | 0.159640i | ||||
\(928\) | −1.99288 | − | 3.45178i | −0.0654196 | − | 0.113310i | ||||
\(929\) | 6.04455 | + | 10.4695i | 0.198315 | + | 0.343492i | 0.947982 | − | 0.318323i | \(-0.103120\pi\) |
−0.749667 | + | 0.661815i | \(0.769786\pi\) | |||||||
\(930\) | 1.58753 | 0.0520572 | ||||||||
\(931\) | 56.4610 | − | 7.59260i | 1.85043 | − | 0.248837i | ||||
\(932\) | − | 27.4766i | − | 0.900027i | ||||||
\(933\) | −11.0535 | + | 6.38177i | −0.361877 | + | 0.208930i | ||||
\(934\) | 5.83287 | + | 10.1028i | 0.190857 | + | 0.330575i | ||||
\(935\) | −0.595925 | + | 1.08213i | −0.0194888 | + | 0.0353895i | ||||
\(936\) | 2.12203 | + | 3.67546i | 0.0693606 | + | 0.120136i | ||||
\(937\) | 6.31515 | + | 3.64605i | 0.206307 | + | 0.119111i | 0.599594 | − | 0.800304i | \(-0.295329\pi\) |
−0.393287 | + | 0.919416i | \(0.628662\pi\) | |||||||
\(938\) | −18.1947 | −0.594078 | ||||||||
\(939\) | 29.1607i | 0.951625i | ||||||||
\(940\) | 0.236377 | − | 0.409416i | 0.00770975 | − | 0.0133537i | ||||
\(941\) | 0.960244 | − | 1.66319i | 0.0313031 | − | 0.0542185i | −0.849949 | − | 0.526864i | \(-0.823368\pi\) |
0.881253 | + | 0.472646i | \(0.156701\pi\) | |||||||
\(942\) | − | 49.7578i | − | 1.62120i | ||||||
\(943\) | −27.0524 | −0.880947 | ||||||||
\(944\) | −5.17436 | − | 2.98742i | −0.168411 | − | 0.0972322i | ||||
\(945\) | −1.12722 | − | 1.95240i | −0.0366684 | − | 0.0635116i | ||||
\(946\) | 0.405065 | − | 0.735553i | 0.0131698 | − | 0.0239149i | ||||
\(947\) | −21.1607 | − | 36.6513i | −0.687629 | − | 1.19101i | −0.972603 | − | 0.232473i | \(-0.925318\pi\) |
0.284974 | − | 0.958535i | \(-0.408015\pi\) | |||||||
\(948\) | −7.91911 | + | 4.57210i | −0.257201 | + | 0.148495i | ||||
\(949\) | 30.3537i | 0.985323i | ||||||||
\(950\) | −21.5274 | + | 2.89489i | −0.698440 | + | 0.0939228i | ||||
\(951\) | −7.74897 | −0.251278 | ||||||||
\(952\) | −6.43097 | − | 11.1388i | −0.208429 | − | 0.361009i | ||||
\(953\) | 14.4815 | + | 25.0828i | 0.469103 | + | 0.812511i | 0.999376 | − | 0.0353162i | \(-0.0112438\pi\) |
−0.530273 | + | 0.847827i | \(0.677911\pi\) | |||||||
\(954\) | −0.121411 | − | 0.0700970i | −0.00393084 | − | 0.00226947i | ||||
\(955\) | −0.934541 | − | 1.61867i | −0.0302410 | − | 0.0523790i | ||||
\(956\) | −13.3197 | − | 7.69016i | −0.430791 | − | 0.248717i | ||||
\(957\) | 26.6948 | − | 0.539900i | 0.862922 | − | 0.0174525i | ||||
\(958\) | 31.6280i | 1.02185i | ||||||||
\(959\) | −19.0719 | − | 11.0112i | −0.615864 | − | 0.355569i | ||||
\(960\) | 0.226935 | + | 0.131021i | 0.00732431 | + | 0.00422869i | ||||
\(961\) | −5.70293 | −0.183966 | ||||||||
\(962\) | 18.6415i | 0.601028i | ||||||||
\(963\) | 5.71677 | − | 9.90174i | 0.184220 | − | 0.319079i | ||||
\(964\) | −5.04394 | − | 8.73636i | −0.162454 | − | 0.281379i | ||||
\(965\) | 0.142030 | − | 0.246003i | 0.00457211 | − | 0.00791913i | ||||
\(966\) | 25.3489 | + | 43.9055i | 0.815587 | + | 1.41264i | ||||
\(967\) | 50.6423 | − | 29.2384i | 1.62855 | − | 0.940242i | 0.644021 | − | 0.765008i | \(-0.277265\pi\) |
0.984527 | − | 0.175234i | \(-0.0560682\pi\) | |||||||
\(968\) | 10.9910 | − | 0.444765i | 0.353264 | − | 0.0142953i | ||||
\(969\) | −9.60818 | + | 23.3794i | −0.308659 | + | 0.751054i | ||||
\(970\) | 1.76092i | 0.0565397i | ||||||||
\(971\) | −2.18314 | + | 1.26044i | −0.0700603 | + | 0.0404493i | −0.534621 | − | 0.845092i | \(-0.679546\pi\) |
0.464561 | + | 0.885541i | \(0.346212\pi\) | |||||||
\(972\) | −9.29168 | + | 5.36456i | −0.298031 | + | 0.172068i | ||||
\(973\) | 29.2281 | − | 50.6245i | 0.937008 | − | 1.62295i | ||||
\(974\) | −16.1380 | + | 9.31725i | −0.517094 | + | 0.298544i | ||||
\(975\) | −34.2666 | − | 19.7838i | −1.09741 | − | 0.633589i | ||||
\(976\) | 13.0880i | 0.418935i | ||||||||
\(977\) | − | 36.1199i | − | 1.15558i | −0.816186 | − | 0.577789i | \(-0.803916\pi\) | ||
0.816186 | − | 0.577789i | \(-0.196084\pi\) | |||||||
\(978\) | 15.3694 | + | 8.87354i | 0.491460 | + | 0.283745i | ||||
\(979\) | −26.6699 | + | 48.4295i | −0.852372 | + | 1.54781i | ||||
\(980\) | 1.69562 | 0.0541645 | ||||||||
\(981\) | −20.0633 | −0.640573 | ||||||||
\(982\) | 13.4139 | + | 7.74450i | 0.428054 | + | 0.247137i | ||||
\(983\) | −12.7193 | + | 7.34349i | −0.405682 | + | 0.234221i | −0.688933 | − | 0.724825i | \(-0.741921\pi\) |
0.283250 | + | 0.959046i | \(0.408587\pi\) | |||||||
\(984\) | 8.44564 | + | 4.87609i | 0.269237 | + | 0.155444i | ||||
\(985\) | −2.59954 | + | 1.50084i | −0.0828281 | + | 0.0478208i | ||||
\(986\) | 9.91013 | − | 5.72162i | 0.315603 | − | 0.182213i | ||||
\(987\) | −32.9722 | −1.04952 | ||||||||
\(988\) | −10.4693 | − | 13.5657i | −0.333072 | − | 0.431584i | ||||
\(989\) | 1.41855i | 0.0451073i | ||||||||
\(990\) | −0.397516 | + | 0.240352i | −0.0126339 | + | 0.00763890i | ||||
\(991\) | 0.982105 | − | 0.567019i | 0.0311976 | − | 0.0180119i | −0.484320 | − | 0.874891i | \(-0.660933\pi\) |
0.515518 | + | 0.856879i | \(0.327600\pi\) | |||||||
\(992\) | −5.24664 | − | 3.02915i | −0.166581 | − | 0.0961755i | ||||
\(993\) | −0.391140 | − | 0.677475i | −0.0124125 | − | 0.0214990i | ||||
\(994\) | 32.3651 | − | 56.0580i | 1.02656 | − | 1.77805i | ||||
\(995\) | −0.107103 | −0.00339540 | ||||||||
\(996\) | 9.10569 | 0.288525 | ||||||||
\(997\) | 43.6376 | + | 25.1942i | 1.38202 | + | 0.797907i | 0.992398 | − | 0.123069i | \(-0.0392738\pi\) |
0.389618 | + | 0.920977i | \(0.372607\pi\) | |||||||
\(998\) | 7.05643 | − | 12.2221i | 0.223368 | − | 0.386884i | ||||
\(999\) | −18.3933 | −0.581938 |
(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 | 418.2.h.b.373.8 | yes | 20 | |
11.10 | odd | 2 | 418.2.h.a.373.8 | yes | 20 | ||
19.8 | odd | 6 | 418.2.h.a.65.8 | ✓ | 20 | ||
209.65 | even | 6 | inner | 418.2.h.b.65.8 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.h.a.65.8 | ✓ | 20 | 19.8 | odd | 6 | ||
418.2.h.a.373.8 | yes | 20 | 11.10 | odd | 2 | ||
418.2.h.b.65.8 | yes | 20 | 209.65 | even | 6 | inner | |
418.2.h.b.373.8 | yes | 20 | 1.1 | even | 1 | trivial |