Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,2,Mod(491,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.491");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.69520363885\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.312013725601644544.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{10} - 2x^{8} + 8x^{6} - 8x^{4} - 16x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 491.4 | ||
Root | \(-1.13556 + 0.842913i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.491 |
Dual form | 588.2.e.e.491.3 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.13556 | + | 0.842913i | −0.802962 | + | 0.596030i | ||||
\(3\) | 1.65140 | + | 0.522368i | 0.953438 | + | 0.301590i | ||||
\(4\) | 0.578995 | − | 1.91436i | 0.289497 | − | 0.957179i | ||||
\(5\) | − | 0.499464i | − | 0.223367i | −0.993744 | − | 0.111684i | \(-0.964376\pi\) | ||
0.993744 | − | 0.111684i | \(-0.0356243\pi\) | |||||||
\(6\) | −2.31558 | + | 0.798808i | −0.945331 | + | 0.326112i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.956154 | + | 2.66191i | 0.338051 | + | 0.941128i | ||||
\(9\) | 2.45426 | + | 1.72528i | 0.818087 | + | 0.575094i | ||||
\(10\) | 0.421005 | + | 0.567172i | 0.133134 | + | 0.179356i | ||||
\(11\) | −1.39050 | −0.419251 | −0.209626 | − | 0.977782i | \(-0.567224\pi\) | ||||
−0.209626 | + | 0.977782i | \(0.567224\pi\) | |||||||
\(12\) | 1.95615 | − | 2.85893i | 0.564693 | − | 0.825301i | ||||
\(13\) | 2.75054 | 0.762861 | 0.381431 | − | 0.924397i | \(-0.375432\pi\) | ||||
0.381431 | + | 0.924397i | \(0.375432\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.260904 | − | 0.824817i | 0.0673652 | − | 0.212967i | ||||
\(16\) | −3.32953 | − | 2.21681i | −0.832383 | − | 0.554202i | ||||
\(17\) | 5.82329i | 1.41235i | 0.708035 | + | 0.706177i | \(0.249582\pi\) | ||||
−0.708035 | + | 0.706177i | \(0.750418\pi\) | |||||||
\(18\) | −4.24123 | + | 0.109569i | −0.999666 | + | 0.0258256i | ||||
\(19\) | − | 2.48153i | − | 0.569302i | −0.958631 | − | 0.284651i | \(-0.908122\pi\) | ||
0.958631 | − | 0.284651i | \(-0.0918777\pi\) | |||||||
\(20\) | −0.956154 | − | 0.289187i | −0.213802 | − | 0.0646643i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.57899 | − | 1.17207i | 0.336643 | − | 0.249886i | ||||
\(23\) | 5.06405 | 1.05593 | 0.527964 | − | 0.849267i | \(-0.322956\pi\) | ||||
0.527964 | + | 0.849267i | \(0.322956\pi\) | |||||||
\(24\) | 0.188496 | + | 4.89535i | 0.0384767 | + | 0.999259i | ||||
\(25\) | 4.75054 | 0.950107 | ||||||||
\(26\) | −3.12340 | + | 2.31846i | −0.612549 | + | 0.454688i | ||||
\(27\) | 3.15174 | + | 4.13116i | 0.606553 | + | 0.795043i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.32275i | 1.17411i | 0.809549 | + | 0.587053i | \(0.199712\pi\) | ||||
−0.809549 | + | 0.587053i | \(0.800288\pi\) | |||||||
\(30\) | 0.398976 | + | 1.15655i | 0.0728428 | + | 0.211156i | ||||
\(31\) | − | 6.91514i | − | 1.24200i | −0.783812 | − | 0.620998i | \(-0.786727\pi\) | ||
0.783812 | − | 0.620998i | \(-0.213273\pi\) | |||||||
\(32\) | 5.64946 | − | 0.289187i | 0.998692 | − | 0.0511216i | ||||
\(33\) | −2.29627 | − | 0.726352i | −0.399730 | − | 0.126442i | ||||
\(34\) | −4.90852 | − | 6.61269i | −0.841805 | − | 1.13407i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.72381 | − | 3.69941i | 0.787302 | − | 0.616568i | ||||
\(37\) | 7.34308 | 1.20720 | 0.603598 | − | 0.797289i | \(-0.293733\pi\) | ||||
0.603598 | + | 0.797289i | \(0.293733\pi\) | |||||||
\(38\) | 2.09171 | + | 2.81793i | 0.339321 | + | 0.457128i | ||||
\(39\) | 4.54224 | + | 1.43679i | 0.727341 | + | 0.230071i | ||||
\(40\) | 1.32953 | − | 0.477565i | 0.210217 | − | 0.0755096i | ||||
\(41\) | − | 5.74438i | − | 0.897121i | −0.893753 | − | 0.448560i | \(-0.851937\pi\) | ||
0.893753 | − | 0.448560i | \(-0.148063\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.52627i | 0.537751i | 0.963175 | + | 0.268875i | \(0.0866520\pi\) | ||||
−0.963175 | + | 0.268875i | \(0.913348\pi\) | |||||||
\(44\) | −0.805091 | + | 2.66191i | −0.121372 | + | 0.401298i | ||||
\(45\) | 0.861717 | − | 1.22582i | 0.128457 | − | 0.182734i | ||||
\(46\) | −5.75054 | + | 4.26855i | −0.847870 | + | 0.629364i | ||||
\(47\) | −5.06405 | −0.738668 | −0.369334 | − | 0.929297i | \(-0.620414\pi\) | ||||
−0.369334 | + | 0.929297i | \(0.620414\pi\) | |||||||
\(48\) | −4.34041 | − | 5.40008i | −0.626484 | − | 0.779435i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.39452 | + | 4.00429i | −0.762900 | + | 0.566292i | ||||
\(51\) | −3.04190 | + | 9.61659i | −0.425951 | + | 1.34659i | ||||
\(52\) | 1.59255 | − | 5.26551i | 0.220846 | − | 0.730195i | ||||
\(53\) | − | 5.24491i | − | 0.720444i | −0.932867 | − | 0.360222i | \(-0.882701\pi\) | ||
0.932867 | − | 0.360222i | \(-0.117299\pi\) | |||||||
\(54\) | −7.06121 | − | 2.03454i | −0.960909 | − | 0.276866i | ||||
\(55\) | 0.694505i | 0.0936470i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.29627 | − | 4.09801i | 0.171696 | − | 0.542794i | ||||
\(58\) | −5.32953 | − | 7.17987i | −0.699802 | − | 0.942763i | ||||
\(59\) | −3.15174 | −0.410322 | −0.205161 | − | 0.978728i | \(-0.565772\pi\) | ||||
−0.205161 | + | 0.978728i | \(0.565772\pi\) | |||||||
\(60\) | −1.42793 | − | 0.977029i | −0.184345 | − | 0.126134i | ||||
\(61\) | −4.90852 | −0.628472 | −0.314236 | − | 0.949345i | \(-0.601748\pi\) | ||||
−0.314236 | + | 0.949345i | \(0.601748\pi\) | |||||||
\(62\) | 5.82886 | + | 7.85256i | 0.740267 | + | 0.997276i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.17154 | + | 5.09039i | −0.771443 | + | 0.636299i | ||||
\(65\) | − | 1.37379i | − | 0.170398i | ||||||
\(66\) | 3.21981 | − | 1.11074i | 0.396331 | − | 0.136723i | ||||
\(67\) | 10.7439i | 1.31257i | 0.754513 | + | 0.656286i | \(0.227873\pi\) | ||||
−0.754513 | + | 0.656286i | \(0.772127\pi\) | |||||||
\(68\) | 11.1479 | + | 3.37165i | 1.35188 | + | 0.408873i | ||||
\(69\) | 8.36279 | + | 2.64530i | 1.00676 | + | 0.318457i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.54224 | 0.539065 | 0.269532 | − | 0.962991i | \(-0.413131\pi\) | ||||
0.269532 | + | 0.962991i | \(0.413131\pi\) | |||||||
\(72\) | −2.24589 | + | 8.18266i | −0.264681 | + | 0.964336i | ||||
\(73\) | −9.97504 | −1.16749 | −0.583745 | − | 0.811937i | \(-0.698413\pi\) | ||||
−0.583745 | + | 0.811937i | \(0.698413\pi\) | |||||||
\(74\) | −8.33851 | + | 6.18958i | −0.969332 | + | 0.719524i | ||||
\(75\) | 7.84505 | + | 2.48153i | 0.905868 | + | 0.286542i | ||||
\(76\) | −4.75054 | − | 1.43679i | −0.544924 | − | 0.164811i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.36908 | + | 2.19715i | −0.721156 | + | 0.248778i | ||||
\(79\) | 2.13130i | 0.239790i | 0.992787 | + | 0.119895i | \(0.0382557\pi\) | ||||
−0.992787 | + | 0.119895i | \(0.961744\pi\) | |||||||
\(80\) | −1.10722 | + | 1.66298i | −0.123791 | + | 0.185927i | ||||
\(81\) | 3.04681 | + | 8.46859i | 0.338534 | + | 0.940954i | ||||
\(82\) | 4.84201 | + | 6.52309i | 0.534711 | + | 0.720354i | ||||
\(83\) | −12.0165 | −1.31899 | −0.659493 | − | 0.751710i | \(-0.729229\pi\) | ||||
−0.659493 | + | 0.751710i | \(0.729229\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.90852 | 0.315474 | ||||||||
\(86\) | −2.97234 | − | 4.00429i | −0.320515 | − | 0.431794i | ||||
\(87\) | −3.30281 | + | 10.4414i | −0.354098 | + | 1.11944i | ||||
\(88\) | −1.32953 | − | 3.70138i | −0.141728 | − | 0.394569i | ||||
\(89\) | 2.45163i | 0.259873i | 0.991522 | + | 0.129936i | \(0.0414773\pi\) | ||||
−0.991522 | + | 0.129936i | \(0.958523\pi\) | |||||||
\(90\) | 0.0547257 | + | 2.11834i | 0.00576860 | + | 0.223293i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.93206 | − | 9.69440i | 0.305688 | − | 1.01071i | ||||
\(93\) | 3.61225 | − | 11.4197i | 0.374573 | − | 1.18417i | ||||
\(94\) | 5.75054 | − | 4.26855i | 0.593122 | − | 0.440268i | ||||
\(95\) | −1.23944 | −0.127163 | ||||||||
\(96\) | 9.48059 | + | 2.47353i | 0.967609 | + | 0.252454i | ||||
\(97\) | 0.526031 | 0.0534104 | 0.0267052 | − | 0.999643i | \(-0.491498\pi\) | ||||
0.0267052 | + | 0.999643i | \(0.491498\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.41265 | − | 2.39900i | −0.342984 | − | 0.241109i | ||||
\(100\) | 2.75054 | − | 9.09422i | 0.275054 | − | 0.909422i | ||||
\(101\) | − | 16.0961i | − | 1.60162i | −0.598920 | − | 0.800809i | \(-0.704403\pi\) | ||
0.598920 | − | 0.800809i | \(-0.295597\pi\) | |||||||
\(102\) | −4.65169 | − | 13.4843i | −0.460586 | − | 1.33514i | ||||
\(103\) | 1.87663i | 0.184910i | 0.995717 | + | 0.0924550i | \(0.0294714\pi\) | ||||
−0.995717 | + | 0.0924550i | \(0.970529\pi\) | |||||||
\(104\) | 2.62993 | + | 7.32168i | 0.257886 | + | 0.717950i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.42101 | + | 5.95591i | 0.429406 | + | 0.578490i | ||||
\(107\) | −7.27848 | −0.703637 | −0.351819 | − | 0.936068i | \(-0.614437\pi\) | ||||
−0.351819 | + | 0.936068i | \(0.614437\pi\) | |||||||
\(108\) | 9.73337 | − | 3.64164i | 0.936594 | − | 0.350417i | ||||
\(109\) | −1.84201 | −0.176433 | −0.0882163 | − | 0.996101i | \(-0.528117\pi\) | ||||
−0.0882163 | + | 0.996101i | \(0.528117\pi\) | |||||||
\(110\) | −0.585407 | − | 0.788652i | −0.0558164 | − | 0.0751950i | ||||
\(111\) | 12.1264 | + | 3.83579i | 1.15099 | + | 0.364077i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.2728i | − | 0.966382i | −0.875515 | − | 0.483191i | \(-0.839478\pi\) | ||
0.875515 | − | 0.483191i | \(-0.160522\pi\) | |||||||
\(114\) | 1.98227 | + | 5.74618i | 0.185656 | + | 0.538179i | ||||
\(115\) | − | 2.52931i | − | 0.235860i | ||||||
\(116\) | 12.1040 | + | 3.66084i | 1.12383 | + | 0.339900i | ||||
\(117\) | 6.75054 | + | 4.74545i | 0.624087 | + | 0.438717i | ||||
\(118\) | 3.57899 | − | 2.65665i | 0.329473 | − | 0.244564i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.44505 | − | 0.0941473i | 0.223202 | − | 0.00859443i | ||||
\(121\) | −9.06651 | −0.824229 | ||||||||
\(122\) | 5.57393 | − | 4.13746i | 0.504640 | − | 0.374588i | ||||
\(123\) | 3.00068 | − | 9.48628i | 0.270562 | − | 0.855349i | ||||
\(124\) | −13.2381 | − | 4.00383i | −1.18881 | − | 0.359555i | ||||
\(125\) | − | 4.87005i | − | 0.435590i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.51224i | 0.134190i | 0.997747 | + | 0.0670949i | \(0.0213730\pi\) | ||||
−0.997747 | + | 0.0670949i | \(0.978627\pi\) | |||||||
\(128\) | 2.71740 | − | 10.9825i | 0.240186 | − | 0.970727i | ||||
\(129\) | −1.84201 | + | 5.82329i | −0.162180 | + | 0.512712i | ||||
\(130\) | 1.15799 | + | 1.56003i | 0.101562 | + | 0.136823i | ||||
\(131\) | −6.65037 | −0.581045 | −0.290523 | − | 0.956868i | \(-0.593829\pi\) | ||||
−0.290523 | + | 0.956868i | \(0.593829\pi\) | |||||||
\(132\) | −2.72003 | + | 3.97533i | −0.236748 | + | 0.346008i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.05614 | − | 12.2003i | −0.782331 | − | 1.05395i | ||||
\(135\) | 2.06337 | − | 1.57418i | 0.177587 | − | 0.135484i | ||||
\(136\) | −15.5011 | + | 5.56796i | −1.32921 | + | 0.477448i | ||||
\(137\) | − | 12.1917i | − | 1.04161i | −0.853676 | − | 0.520805i | \(-0.825632\pi\) | ||
0.853676 | − | 0.520805i | \(-0.174368\pi\) | |||||||
\(138\) | −11.7262 | + | 4.04521i | −0.998201 | + | 0.344351i | ||||
\(139\) | 0.0477837i | 0.00405296i | 0.999998 | + | 0.00202648i | \(0.000645050\pi\) | ||||
−0.999998 | + | 0.00202648i | \(0.999355\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.36279 | − | 2.64530i | −0.704274 | − | 0.222774i | ||||
\(142\) | −5.15799 | + | 3.82872i | −0.432849 | + | 0.321299i | ||||
\(143\) | −3.82461 | −0.319830 | ||||||||
\(144\) | −4.34693 | − | 11.1850i | −0.362244 | − | 0.932083i | ||||
\(145\) | 3.15799 | 0.262257 | ||||||||
\(146\) | 11.3273 | − | 8.40809i | 0.937451 | − | 0.695859i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.25161 | − | 14.0573i | 0.349480 | − | 1.15550i | ||||
\(149\) | 2.29381i | 0.187917i | 0.995576 | + | 0.0939583i | \(0.0299520\pi\) | ||||
−0.995576 | + | 0.0939583i | \(0.970048\pi\) | |||||||
\(150\) | −11.0002 | + | 3.79477i | −0.898166 | + | 0.309841i | ||||
\(151\) | − | 13.1358i | − | 1.06897i | −0.845177 | − | 0.534487i | \(-0.820505\pi\) | ||
0.845177 | − | 0.534487i | \(-0.179495\pi\) | |||||||
\(152\) | 6.60561 | − | 2.37272i | 0.535786 | − | 0.192453i | ||||
\(153\) | −10.0468 | + | 14.2919i | −0.812236 | + | 1.15543i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.45387 | −0.277421 | ||||||||
\(156\) | 5.38047 | − | 7.86358i | 0.430782 | − | 0.629590i | ||||
\(157\) | 8.40960 | 0.671159 | 0.335579 | − | 0.942012i | \(-0.391068\pi\) | ||||
0.335579 | + | 0.942012i | \(0.391068\pi\) | |||||||
\(158\) | −1.79650 | − | 2.42022i | −0.142922 | − | 0.192542i | ||||
\(159\) | 2.73978 | − | 8.66146i | 0.217278 | − | 0.686899i | ||||
\(160\) | −0.144439 | − | 2.82170i | −0.0114189 | − | 0.223075i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −10.5981 | − | 7.04840i | −0.832667 | − | 0.553774i | ||||
\(163\) | − | 12.3599i | − | 0.968099i | −0.875041 | − | 0.484050i | \(-0.839165\pi\) | ||
0.875041 | − | 0.484050i | \(-0.160835\pi\) | |||||||
\(164\) | −10.9968 | − | 3.32596i | −0.858705 | − | 0.259714i | ||||
\(165\) | −0.362787 | + | 1.14691i | −0.0282429 | + | 0.0892866i | ||||
\(166\) | 13.6455 | − | 10.1289i | 1.05910 | − | 0.786155i | ||||
\(167\) | 2.36549 | 0.183047 | 0.0915237 | − | 0.995803i | \(-0.470826\pi\) | ||||
0.0915237 | + | 0.995803i | \(0.470826\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.43456 | −0.418043 | ||||||||
\(170\) | −3.30281 | + | 2.45163i | −0.253314 | + | 0.188032i | ||||
\(171\) | 4.28134 | − | 6.09033i | 0.327402 | − | 0.465739i | ||||
\(172\) | 6.75054 | + | 2.04169i | 0.514723 | + | 0.155677i | ||||
\(173\) | − | 9.56980i | − | 0.727579i | −0.931481 | − | 0.363789i | \(-0.881483\pi\) | ||
0.931481 | − | 0.363789i | \(-0.118517\pi\) | |||||||
\(174\) | −5.05067 | − | 14.6408i | −0.382890 | − | 1.10992i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.62971 | + | 3.08247i | 0.348977 | + | 0.232350i | ||||
\(177\) | −5.20480 | − | 1.64637i | −0.391217 | − | 0.123749i | ||||
\(178\) | −2.06651 | − | 2.78398i | −0.154892 | − | 0.208668i | ||||
\(179\) | −20.7541 | −1.55124 | −0.775619 | − | 0.631202i | \(-0.782562\pi\) | ||||
−0.775619 | + | 0.631202i | \(0.782562\pi\) | |||||||
\(180\) | −1.84772 | − | 2.35938i | −0.137721 | − | 0.175857i | ||||
\(181\) | −6.43456 | −0.478277 | −0.239138 | − | 0.970985i | \(-0.576865\pi\) | ||||
−0.239138 | + | 0.970985i | \(0.576865\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.10595 | − | 2.56406i | −0.599209 | − | 0.189541i | ||||
\(184\) | 4.84201 | + | 13.4801i | 0.356958 | + | 0.993763i | ||||
\(185\) | − | 3.66761i | − | 0.269648i | ||||||
\(186\) | 5.52387 | + | 16.0126i | 0.405030 | + | 1.17410i | ||||
\(187\) | − | 8.09727i | − | 0.592131i | ||||||
\(188\) | −2.93206 | + | 9.69440i | −0.213842 | + | 0.707037i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.40745 | − | 1.04474i | 0.102107 | − | 0.0757932i | ||||
\(191\) | 17.5338 | 1.26870 | 0.634350 | − | 0.773046i | \(-0.281268\pi\) | ||||
0.634350 | + | 0.773046i | \(0.281268\pi\) | |||||||
\(192\) | −12.8508 | + | 5.18247i | −0.927424 | + | 0.374013i | ||||
\(193\) | −2.18509 | −0.157286 | −0.0786432 | − | 0.996903i | \(-0.525059\pi\) | ||||
−0.0786432 | + | 0.996903i | \(0.525059\pi\) | |||||||
\(194\) | −0.597340 | + | 0.443399i | −0.0428865 | + | 0.0318342i | ||||
\(195\) | 0.717627 | − | 2.26869i | 0.0513903 | − | 0.162464i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 6.27706i | − | 0.447222i | −0.974678 | − | 0.223611i | \(-0.928215\pi\) | ||
0.974678 | − | 0.223611i | \(-0.0717845\pi\) | |||||||
\(198\) | 5.89742 | − | 0.152355i | 0.419111 | − | 0.0108274i | ||||
\(199\) | 0.865522i | 0.0613552i | 0.999529 | + | 0.0306776i | \(0.00976652\pi\) | ||||
−0.999529 | + | 0.0306776i | \(0.990233\pi\) | |||||||
\(200\) | 4.54224 | + | 12.6455i | 0.321185 | + | 0.894172i | ||||
\(201\) | −5.61225 | + | 17.7424i | −0.395858 | + | 1.25145i | ||||
\(202\) | 13.5676 | + | 18.2781i | 0.954612 | + | 1.28604i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 16.6484 | + | 11.3912i | 1.16562 | + | 0.797547i | ||||
\(205\) | −2.86911 | −0.200387 | ||||||||
\(206\) | −1.58184 | − | 2.13103i | −0.110212 | − | 0.148476i | ||||
\(207\) | 12.4285 | + | 8.73691i | 0.863841 | + | 0.607257i | ||||
\(208\) | −9.15799 | − | 6.09740i | −0.634992 | − | 0.422779i | ||||
\(209\) | 3.45056i | 0.238680i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.90417i | − | 0.268774i | −0.990929 | − | 0.134387i | \(-0.957094\pi\) | ||
0.990929 | − | 0.134387i | \(-0.0429065\pi\) | |||||||
\(212\) | −10.0406 | − | 3.03678i | −0.689594 | − | 0.208567i | ||||
\(213\) | 7.50107 | + | 2.37272i | 0.513965 | + | 0.162576i | ||||
\(214\) | 8.26516 | − | 6.13513i | 0.564994 | − | 0.419389i | ||||
\(215\) | 1.76124 | 0.120116 | ||||||||
\(216\) | −7.98324 | + | 12.3397i | −0.543191 | + | 0.839609i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.09171 | − | 1.55265i | 0.141669 | − | 0.105159i | ||||
\(219\) | −16.4728 | − | 5.21065i | −1.11313 | − | 0.352103i | ||||
\(220\) | 1.32953 | + | 0.402115i | 0.0896369 | + | 0.0271106i | ||||
\(221\) | 16.0172i | 1.07743i | ||||||||
\(222\) | −17.0035 | + | 5.86571i | −1.14120 | + | 0.393681i | ||||
\(223\) | − | 23.5017i | − | 1.57379i | −0.617085 | − | 0.786896i | \(-0.711687\pi\) | ||
0.617085 | − | 0.786896i | \(-0.288313\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.6591 | + | 8.19601i | 0.777271 | + | 0.546401i | ||||
\(226\) | 8.65906 | + | 11.6654i | 0.575992 | + | 0.775968i | ||||
\(227\) | 19.1678 | 1.27221 | 0.636107 | − | 0.771601i | \(-0.280544\pi\) | ||||
0.636107 | + | 0.771601i | \(0.280544\pi\) | |||||||
\(228\) | −7.09451 | − | 4.85425i | −0.469846 | − | 0.321481i | ||||
\(229\) | 11.4761 | 0.758363 | 0.379181 | − | 0.925322i | \(-0.376206\pi\) | ||||
0.379181 | + | 0.925322i | \(0.376206\pi\) | |||||||
\(230\) | 2.13199 | + | 2.87219i | 0.140579 | + | 0.189386i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.8306 | + | 6.04552i | −1.10498 | + | 0.396908i | ||||
\(233\) | 20.2174i | 1.32449i | 0.749288 | + | 0.662245i | \(0.230396\pi\) | ||||
−0.749288 | + | 0.662245i | \(0.769604\pi\) | |||||||
\(234\) | −11.6656 | + | 0.301373i | −0.762607 | + | 0.0197014i | ||||
\(235\) | 2.52931i | 0.164994i | ||||||||
\(236\) | −1.82484 | + | 6.03356i | −0.118787 | + | 0.392752i | ||||
\(237\) | −1.11332 | + | 3.51963i | −0.0723181 | + | 0.228625i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.90774 | 0.446824 | 0.223412 | − | 0.974724i | \(-0.428280\pi\) | ||||
0.223412 | + | 0.974724i | \(0.428280\pi\) | |||||||
\(240\) | −2.69715 | + | 2.16788i | −0.174100 | + | 0.139936i | ||||
\(241\) | 8.06651 | 0.519610 | 0.259805 | − | 0.965661i | \(-0.416342\pi\) | ||||
0.259805 | + | 0.965661i | \(0.416342\pi\) | |||||||
\(242\) | 10.2956 | − | 7.64228i | 0.661825 | − | 0.491265i | ||||
\(243\) | 0.607785 | + | 15.5766i | 0.0389894 | + | 0.999240i | ||||
\(244\) | −2.84201 | + | 9.39667i | −0.181941 | + | 0.601560i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.58866 | + | 13.3016i | 0.292562 | + | 0.848076i | ||||
\(247\) | − | 6.82553i | − | 0.434298i | ||||||
\(248\) | 18.4075 | − | 6.61194i | 1.16888 | − | 0.419859i | ||||
\(249\) | −19.8442 | − | 6.27706i | −1.25757 | − | 0.397793i | ||||
\(250\) | 4.10503 | + | 5.53023i | 0.259625 | + | 0.349763i | ||||
\(251\) | −20.4073 | −1.28810 | −0.644048 | − | 0.764985i | \(-0.722746\pi\) | ||||
−0.644048 | + | 0.764985i | \(0.722746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.04155 | −0.442699 | ||||||||
\(254\) | −1.27469 | − | 1.71724i | −0.0799811 | − | 0.107749i | ||||
\(255\) | 4.80315 | + | 1.51932i | 0.300785 | + | 0.0951436i | ||||
\(256\) | 6.17154 | + | 14.7618i | 0.385721 | + | 0.922615i | ||||
\(257\) | − | 27.2100i | − | 1.69731i | −0.528947 | − | 0.848655i | \(-0.677413\pi\) | ||
0.528947 | − | 0.848655i | \(-0.322587\pi\) | |||||||
\(258\) | −2.81681 | − | 8.16535i | −0.175367 | − | 0.508352i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.62993 | − | 0.795420i | −0.163102 | − | 0.0493299i | ||||
\(261\) | −10.9085 | + | 15.5177i | −0.675221 | + | 0.960521i | ||||
\(262\) | 7.55189 | − | 5.60568i | 0.466558 | − | 0.346320i | ||||
\(263\) | 3.60493 | 0.222290 | 0.111145 | − | 0.993804i | \(-0.464548\pi\) | ||||
0.111145 | + | 0.993804i | \(0.464548\pi\) | |||||||
\(264\) | −0.262104 | − | 6.80698i | −0.0161314 | − | 0.418941i | ||||
\(265\) | −2.61965 | −0.160924 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.28066 | + | 4.04864i | −0.0783749 | + | 0.247772i | ||||
\(268\) | 20.5676 | + | 6.22064i | 1.25637 | + | 0.379986i | ||||
\(269\) | 26.1653i | 1.59533i | 0.603102 | + | 0.797664i | \(0.293931\pi\) | ||||
−0.603102 | + | 0.797664i | \(0.706069\pi\) | |||||||
\(270\) | −1.01618 | + | 3.52682i | −0.0618428 | + | 0.214636i | ||||
\(271\) | 23.0619i | 1.40091i | 0.713696 | + | 0.700455i | \(0.247020\pi\) | ||||
−0.713696 | + | 0.700455i | \(0.752980\pi\) | |||||||
\(272\) | 12.9091 | − | 19.3888i | 0.782729 | − | 1.17562i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.2766 | + | 13.8444i | 0.620830 | + | 0.836373i | ||||
\(275\) | −6.60561 | −0.398333 | ||||||||
\(276\) | 9.90606 | − | 14.4778i | 0.596275 | − | 0.871458i | ||||
\(277\) | −20.2910 | −1.21917 | −0.609585 | − | 0.792721i | \(-0.708664\pi\) | ||||
−0.609585 | + | 0.792721i | \(0.708664\pi\) | |||||||
\(278\) | −0.0402775 | − | 0.0542613i | −0.00241569 | − | 0.00325438i | ||||
\(279\) | 11.9306 | − | 16.9716i | 0.714264 | − | 1.01606i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.6637i | 1.65028i | 0.564929 | + | 0.825140i | \(0.308904\pi\) | ||||
−0.564929 | + | 0.825140i | \(0.691096\pi\) | |||||||
\(282\) | 11.7262 | − | 4.04521i | 0.698286 | − | 0.240888i | ||||
\(283\) | 17.3707i | 1.03258i | 0.856413 | + | 0.516291i | \(0.172688\pi\) | ||||
−0.856413 | + | 0.516291i | \(0.827312\pi\) | |||||||
\(284\) | 2.62993 | − | 8.69547i | 0.156058 | − | 0.515981i | ||||
\(285\) | −2.04681 | − | 0.647442i | −0.121242 | − | 0.0383512i | ||||
\(286\) | 4.34308 | − | 3.22382i | 0.256812 | − | 0.190628i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 14.3642 | + | 9.03716i | 0.846417 | + | 0.532520i | ||||
\(289\) | −16.9107 | −0.994745 | ||||||||
\(290\) | −3.58609 | + | 2.66191i | −0.210582 | + | 0.156313i | ||||
\(291\) | 0.868689 | + | 0.274782i | 0.0509235 | + | 0.0161080i | ||||
\(292\) | −5.77550 | + | 19.0958i | −0.337985 | + | 1.11750i | ||||
\(293\) | − | 19.9672i | − | 1.16650i | −0.812294 | − | 0.583248i | \(-0.801782\pi\) | ||
0.812294 | − | 0.583248i | \(-0.198218\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.57418i | 0.0916525i | ||||||||
\(296\) | 7.02111 | + | 19.5466i | 0.408094 | + | 1.13612i | ||||
\(297\) | −4.38249 | − | 5.74438i | −0.254298 | − | 0.333323i | ||||
\(298\) | −1.93349 | − | 2.60476i | −0.112004 | − | 0.150890i | ||||
\(299\) | 13.9288 | 0.805526 | ||||||||
\(300\) | 9.29278 | − | 13.5814i | 0.536519 | − | 0.784124i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.0723 | + | 14.9165i | 0.637141 | + | 0.858346i | ||||
\(303\) | 8.40808 | − | 26.5811i | 0.483031 | − | 1.52704i | ||||
\(304\) | −5.50107 | + | 8.26233i | −0.315508 | + | 0.473877i | ||||
\(305\) | 2.45163i | 0.140380i | ||||||||
\(306\) | −0.638051 | − | 24.6979i | −0.0364749 | − | 1.41188i | ||||
\(307\) | 14.1529i | 0.807746i | 0.914815 | + | 0.403873i | \(0.132336\pi\) | ||||
−0.914815 | + | 0.403873i | \(0.867664\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.980294 | + | 3.09908i | −0.0557670 | + | 0.176300i | ||||
\(310\) | 3.92208 | − | 2.91131i | 0.222759 | − | 0.165351i | ||||
\(311\) | −24.5549 | −1.39238 | −0.696190 | − | 0.717857i | \(-0.745123\pi\) | ||||
−0.696190 | + | 0.717857i | \(0.745123\pi\) | |||||||
\(312\) | 0.518466 | + | 13.4648i | 0.0293524 | + | 0.762296i | ||||
\(313\) | 0.0520623 | 0.00294274 | 0.00147137 | − | 0.999999i | \(-0.499532\pi\) | ||||
0.00147137 | + | 0.999999i | \(0.499532\pi\) | |||||||
\(314\) | −9.54960 | + | 7.08856i | −0.538915 | + | 0.400031i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.08007 | + | 1.23401i | 0.229522 | + | 0.0694185i | ||||
\(317\) | − | 6.77653i | − | 0.380608i | −0.981725 | − | 0.190304i | \(-0.939053\pi\) | ||
0.981725 | − | 0.190304i | \(-0.0609473\pi\) | |||||||
\(318\) | 4.18968 | + | 12.1450i | 0.234946 | + | 0.681058i | ||||
\(319\) | − | 8.79177i | − | 0.492245i | ||||||
\(320\) | 2.54247 | + | 3.08247i | 0.142128 | + | 0.172315i | ||||
\(321\) | −12.0197 | − | 3.80205i | −0.670875 | − | 0.212210i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.4507 | 0.804056 | ||||||||
\(324\) | 17.9760 | − | 0.929412i | 0.998666 | − | 0.0516340i | ||||
\(325\) | 13.0665 | 0.724800 | ||||||||
\(326\) | 10.4183 | + | 14.0354i | 0.577016 | + | 0.777347i | ||||
\(327\) | −3.04190 | − | 0.962208i | −0.168218 | − | 0.0532102i | ||||
\(328\) | 15.2910 | − | 5.49251i | 0.844305 | − | 0.303273i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.554776 | − | 1.60818i | −0.0305394 | − | 0.0885274i | ||||
\(331\) | 17.8920i | 0.983431i | 0.870756 | + | 0.491715i | \(0.163630\pi\) | ||||
−0.870756 | + | 0.491715i | \(0.836370\pi\) | |||||||
\(332\) | −6.95752 | + | 23.0040i | −0.381843 | + | 1.26251i | ||||
\(333\) | 18.0218 | + | 12.6689i | 0.987591 | + | 0.694250i | ||||
\(334\) | −2.68616 | + | 1.99391i | −0.146980 | + | 0.109102i | ||||
\(335\) | 5.36618 | 0.293185 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.09362 | 0.386414 | 0.193207 | − | 0.981158i | \(-0.438111\pi\) | ||||
0.193207 | + | 0.981158i | \(0.438111\pi\) | |||||||
\(338\) | 6.17127 | − | 4.58086i | 0.335673 | − | 0.249166i | ||||
\(339\) | 5.36618 | − | 16.9645i | 0.291451 | − | 0.921385i | ||||
\(340\) | 1.68402 | − | 5.56796i | 0.0913288 | − | 0.301965i | ||||
\(341\) | 9.61549i | 0.520708i | ||||||||
\(342\) | 0.271898 | + | 10.5247i | 0.0147026 | + | 0.569112i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −9.38661 | + | 3.37165i | −0.506092 | + | 0.181787i | ||||
\(345\) | 1.32123 | − | 4.17692i | 0.0711328 | − | 0.224878i | ||||
\(346\) | 8.06651 | + | 10.8671i | 0.433659 | + | 0.584218i | ||||
\(347\) | −9.19079 | −0.493387 | −0.246694 | − | 0.969093i | \(-0.579344\pi\) | ||||
−0.246694 | + | 0.969093i | \(0.579344\pi\) | |||||||
\(348\) | 18.0763 | + | 12.3683i | 0.968990 | + | 0.663009i | ||||
\(349\) | −22.1330 | −1.18475 | −0.592377 | − | 0.805661i | \(-0.701810\pi\) | ||||
−0.592377 | + | 0.805661i | \(0.701810\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.66898 | + | 11.3629i | 0.462716 | + | 0.606507i | ||||
\(352\) | −7.85556 | + | 0.402115i | −0.418703 | + | 0.0214328i | ||||
\(353\) | − | 10.7266i | − | 0.570917i | −0.958391 | − | 0.285458i | \(-0.907854\pi\) | ||
0.958391 | − | 0.285458i | \(-0.0921459\pi\) | |||||||
\(354\) | 7.29811 | − | 2.51764i | 0.387890 | − | 0.133811i | ||||
\(355\) | − | 2.26869i | − | 0.120409i | ||||||
\(356\) | 4.69330 | + | 1.41948i | 0.248745 | + | 0.0752325i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 23.5676 | − | 17.4939i | 1.24559 | − | 0.924584i | ||||
\(359\) | 3.60493 | 0.190261 | 0.0951305 | − | 0.995465i | \(-0.469673\pi\) | ||||
0.0951305 | + | 0.995465i | \(0.469673\pi\) | |||||||
\(360\) | 4.08695 | + | 1.12174i | 0.215401 | + | 0.0591211i | ||||
\(361\) | 12.8420 | 0.675895 | ||||||||
\(362\) | 7.30683 | − | 5.42377i | 0.384038 | − | 0.285067i | ||||
\(363\) | −14.9725 | − | 4.73606i | −0.785851 | − | 0.248579i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.98218i | 0.260779i | ||||||||
\(366\) | 11.3661 | − | 3.92097i | 0.594114 | − | 0.204952i | ||||
\(367\) | 15.0266i | 0.784381i | 0.919884 | + | 0.392190i | \(0.128283\pi\) | ||||
−0.919884 | + | 0.392190i | \(0.871717\pi\) | |||||||
\(368\) | −16.8609 | − | 11.2260i | −0.878936 | − | 0.585197i | ||||
\(369\) | 9.91067 | − | 14.0982i | 0.515929 | − | 0.733923i | ||||
\(370\) | 3.09148 | + | 4.16479i | 0.160718 | + | 0.216517i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −19.7699 | − | 13.5271i | −1.02502 | − | 0.701346i | ||||
\(373\) | 2.65692 | 0.137570 | 0.0687850 | − | 0.997632i | \(-0.478088\pi\) | ||||
0.0687850 | + | 0.997632i | \(0.478088\pi\) | |||||||
\(374\) | 6.82530 | + | 9.19494i | 0.352928 | + | 0.475459i | ||||
\(375\) | 2.54396 | − | 8.04241i | 0.131369 | − | 0.415308i | ||||
\(376\) | −4.84201 | − | 13.4801i | −0.249708 | − | 0.695181i | ||||
\(377\) | 17.3909i | 0.895679i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 17.7150i | − | 0.909957i | −0.890502 | − | 0.454979i | \(-0.849647\pi\) | ||
0.890502 | − | 0.454979i | \(-0.150353\pi\) | |||||||
\(380\) | −0.717627 | + | 2.37272i | −0.0368135 | + | 0.121718i | ||||
\(381\) | −0.789948 | + | 2.49732i | −0.0404703 | + | 0.127942i | ||||
\(382\) | −19.9107 | + | 14.7795i | −1.01872 | + | 0.756183i | ||||
\(383\) | −32.9217 | −1.68222 | −0.841111 | − | 0.540862i | \(-0.818098\pi\) | ||||
−0.841111 | + | 0.540862i | \(0.818098\pi\) | |||||||
\(384\) | 10.2244 | − | 16.7171i | 0.521764 | − | 0.853090i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.48130 | − | 1.84184i | 0.126295 | − | 0.0937473i | ||||
\(387\) | −6.08380 | + | 8.65438i | −0.309257 | + | 0.439927i | ||||
\(388\) | 0.304569 | − | 1.00701i | 0.0154622 | − | 0.0511233i | ||||
\(389\) | − | 6.82222i | − | 0.345900i | −0.984931 | − | 0.172950i | \(-0.944670\pi\) | ||
0.984931 | − | 0.172950i | \(-0.0553299\pi\) | |||||||
\(390\) | 1.09740 | + | 3.18113i | 0.0555689 | + | 0.161083i | ||||
\(391\) | 29.4894i | 1.49134i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.9824 | − | 3.47394i | −0.553991 | − | 0.175237i | ||||
\(394\) | 5.29102 | + | 7.12798i | 0.266558 | + | 0.359103i | ||||
\(395\) | 1.06451 | 0.0535612 | ||||||||
\(396\) | −6.56845 | + | 5.14402i | −0.330077 | + | 0.258497i | ||||
\(397\) | −20.8442 | −1.04614 | −0.523069 | − | 0.852290i | \(-0.675213\pi\) | ||||
−0.523069 | + | 0.852290i | \(0.675213\pi\) | |||||||
\(398\) | −0.729560 | − | 0.982853i | −0.0365695 | − | 0.0492660i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −15.8170 | − | 10.5310i | −0.790852 | − | 0.526551i | ||||
\(401\) | − | 3.82543i | − | 0.191033i | −0.995428 | − | 0.0955164i | \(-0.969550\pi\) | ||
0.995428 | − | 0.0955164i | \(-0.0304502\pi\) | |||||||
\(402\) | −8.58228 | − | 24.8782i | −0.428045 | − | 1.24081i | ||||
\(403\) | − | 19.0203i | − | 0.947471i | ||||||
\(404\) | −30.8136 | − | 9.31954i | −1.53304 | − | 0.463664i | ||||
\(405\) | 4.22976 | − | 1.52177i | 0.210178 | − | 0.0756175i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.2105 | −0.506118 | ||||||||
\(408\) | −28.5070 | + | 1.09767i | −1.41131 | + | 0.0543427i | ||||
\(409\) | −3.86911 | −0.191315 | −0.0956576 | − | 0.995414i | \(-0.530495\pi\) | ||||
−0.0956576 | + | 0.995414i | \(0.530495\pi\) | |||||||
\(410\) | 3.25805 | − | 2.41841i | 0.160904 | − | 0.119437i | ||||
\(411\) | 6.36857 | − | 20.1335i | 0.314139 | − | 0.993110i | ||||
\(412\) | 3.59255 | + | 1.08656i | 0.176992 | + | 0.0535310i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −21.4778 | + | 0.554862i | −1.05558 | + | 0.0272700i | ||||
\(415\) | 6.00184i | 0.294619i | ||||||||
\(416\) | 15.5390 | − | 0.795420i | 0.761864 | − | 0.0389987i | ||||
\(417\) | −0.0249607 | + | 0.0789102i | −0.00122233 | + | 0.00386425i | ||||
\(418\) | −2.90852 | − | 3.91832i | −0.142261 | − | 0.191651i | ||||
\(419\) | −13.5133 | −0.660170 | −0.330085 | − | 0.943951i | \(-0.607077\pi\) | ||||
−0.330085 | + | 0.943951i | \(0.607077\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.3825 | 0.554749 | 0.277374 | − | 0.960762i | \(-0.410536\pi\) | ||||
0.277374 | + | 0.960762i | \(0.410536\pi\) | |||||||
\(422\) | 3.29087 | + | 4.43342i | 0.160197 | + | 0.215815i | ||||
\(423\) | −12.4285 | − | 8.73691i | −0.604295 | − | 0.424803i | ||||
\(424\) | 13.9615 | − | 5.01494i | 0.678030 | − | 0.243547i | ||||
\(425\) | 27.6637i | 1.34189i | ||||||||
\(426\) | −10.5179 | + | 3.62838i | −0.509595 | + | 0.175796i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.21420 | + | 13.9336i | −0.203701 | + | 0.673507i | ||||
\(429\) | −6.31598 | − | 1.99786i | −0.304938 | − | 0.0964575i | ||||
\(430\) | −2.00000 | + | 1.48458i | −0.0964486 | + | 0.0715926i | ||||
\(431\) | 25.9245 | 1.24874 | 0.624370 | − | 0.781129i | \(-0.285356\pi\) | ||||
0.624370 | + | 0.781129i | \(0.285356\pi\) | |||||||
\(432\) | −1.33583 | − | 20.7416i | −0.0642704 | − | 0.997933i | ||||
\(433\) | 23.3825 | 1.12369 | 0.561845 | − | 0.827242i | \(-0.310092\pi\) | ||||
0.561845 | + | 0.827242i | \(0.310092\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.21511 | + | 1.64963i | 0.250046 | + | 0.0790939i | ||||
\(436\) | −1.06651 | + | 3.52627i | −0.0510768 | + | 0.168878i | ||||
\(437\) | − | 12.5666i | − | 0.601142i | ||||||
\(438\) | 23.0980 | − | 7.96814i | 1.10366 | − | 0.380733i | ||||
\(439\) | − | 17.6732i | − | 0.843494i | −0.906714 | − | 0.421747i | \(-0.861417\pi\) | ||
0.906714 | − | 0.421747i | \(-0.138583\pi\) | |||||||
\(440\) | −1.84871 | + | 0.664053i | −0.0881338 | + | 0.0316575i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.5011 | − | 18.1884i | −0.642180 | − | 0.865136i | ||||
\(443\) | −35.1362 | −1.66937 | −0.834685 | − | 0.550727i | \(-0.814350\pi\) | ||||
−0.834685 | + | 0.550727i | \(0.814350\pi\) | |||||||
\(444\) | 14.3642 | − | 20.9933i | 0.681694 | − | 0.996299i | ||||
\(445\) | 1.22450 | 0.0580471 | ||||||||
\(446\) | 19.8099 | + | 26.6876i | 0.938027 | + | 1.26370i | ||||
\(447\) | −1.19822 | + | 3.78801i | −0.0566737 | + | 0.179167i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.52733i | − | 0.260851i | −0.991458 | − | 0.130425i | \(-0.958366\pi\) | ||
0.991458 | − | 0.130425i | \(-0.0416343\pi\) | |||||||
\(450\) | −20.1481 | + | 0.520511i | −0.949790 | + | 0.0245371i | ||||
\(451\) | 7.98755i | 0.376119i | ||||||||
\(452\) | −19.6658 | − | 5.94789i | −0.925000 | − | 0.279765i | ||||
\(453\) | 6.86172 | − | 21.6925i | 0.322392 | − | 1.01920i | ||||
\(454\) | −21.7662 | + | 16.1568i | −1.02154 | + | 0.758277i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.1480 | − | 0.467760i | 0.568880 | − | 0.0219049i | ||||
\(457\) | 23.9522 | 1.12044 | 0.560219 | − | 0.828345i | \(-0.310717\pi\) | ||||
0.560219 | + | 0.828345i | \(0.310717\pi\) | |||||||
\(458\) | −13.0318 | + | 9.67336i | −0.608937 | + | 0.452007i | ||||
\(459\) | −24.0570 | + | 18.3535i | −1.12288 | + | 0.856668i | ||||
\(460\) | −4.84201 | − | 1.46446i | −0.225760 | − | 0.0682808i | ||||
\(461\) | 2.99679i | 0.139574i | 0.997562 | + | 0.0697871i | \(0.0222320\pi\) | ||||
−0.997562 | + | 0.0697871i | \(0.977768\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.4152i | − | 1.04172i | −0.853642 | − | 0.520861i | \(-0.825611\pi\) | ||
0.853642 | − | 0.520861i | \(-0.174389\pi\) | |||||||
\(464\) | 14.0163 | − | 21.0518i | 0.650691 | − | 0.977305i | ||||
\(465\) | −5.70373 | − | 1.80419i | −0.264504 | − | 0.0836674i | ||||
\(466\) | −17.0416 | − | 22.9581i | −0.789435 | − | 1.06352i | ||||
\(467\) | 12.0613 | 0.558130 | 0.279065 | − | 0.960272i | \(-0.409975\pi\) | ||||
0.279065 | + | 0.960272i | \(0.409975\pi\) | |||||||
\(468\) | 12.9930 | − | 10.1753i | 0.600602 | − | 0.470356i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.13199 | − | 2.87219i | −0.0983414 | − | 0.132484i | ||||
\(471\) | 13.8876 | + | 4.39291i | 0.639908 | + | 0.202414i | ||||
\(472\) | −3.01355 | − | 8.38966i | −0.138710 | − | 0.386165i | ||||
\(473\) | − | 4.90327i | − | 0.225452i | ||||||
\(474\) | −1.70250 | − | 4.93519i | −0.0781983 | − | 0.226681i | ||||
\(475\) | − | 11.7886i | − | 0.540898i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.04895 | − | 12.8724i | 0.414323 | − | 0.589386i | ||||
\(478\) | −7.84415 | + | 5.82262i | −0.358783 | + | 0.266321i | ||||
\(479\) | 13.4070 | 0.612583 | 0.306292 | − | 0.951938i | \(-0.400912\pi\) | ||||
0.306292 | + | 0.951938i | \(0.400912\pi\) | |||||||
\(480\) | 1.23544 | − | 4.73522i | 0.0563900 | − | 0.216132i | ||||
\(481\) | 20.1974 | 0.920922 | ||||||||
\(482\) | −9.16001 | + | 6.79937i | −0.417227 | + | 0.309703i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.24946 | + | 17.3566i | −0.238612 | + | 0.788934i | ||||
\(485\) | − | 0.262734i | − | 0.0119301i | ||||||
\(486\) | −13.8199 | − | 17.1759i | −0.626883 | − | 0.779113i | ||||
\(487\) | 12.2083i | 0.553212i | 0.960983 | + | 0.276606i | \(0.0892096\pi\) | ||||
−0.960983 | + | 0.276606i | \(0.910790\pi\) | |||||||
\(488\) | −4.69330 | − | 13.0661i | −0.212456 | − | 0.591473i | ||||
\(489\) | 6.45640 | − | 20.4111i | 0.291969 | − | 0.923023i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.8981 | −1.80058 | −0.900288 | − | 0.435294i | \(-0.856644\pi\) | ||||
−0.900288 | + | 0.435294i | \(0.856644\pi\) | |||||||
\(492\) | −16.4228 | − | 11.2369i | −0.740395 | − | 0.506598i | ||||
\(493\) | −36.8192 | −1.65825 | ||||||||
\(494\) | 5.75333 | + | 7.75081i | 0.258855 | + | 0.348725i | ||||
\(495\) | −1.19822 | + | 1.70450i | −0.0538558 | + | 0.0766114i | ||||
\(496\) | −15.3295 | + | 23.0242i | −0.688316 | + | 1.03382i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 27.8253 | − | 9.59891i | 1.24688 | − | 0.430138i | ||||
\(499\) | 8.47517i | 0.379401i | 0.981842 | + | 0.189700i | \(0.0607516\pi\) | ||||
−0.981842 | + | 0.189700i | \(0.939248\pi\) | |||||||
\(500\) | −9.32301 | − | 2.81973i | −0.416938 | − | 0.126102i | ||||
\(501\) | 3.90638 | + | 1.23566i | 0.174524 | + | 0.0552052i | ||||
\(502\) | 23.1737 | − | 17.2016i | 1.03429 | − | 0.767743i | ||||
\(503\) | 42.5519 | 1.89730 | 0.948648 | − | 0.316334i | \(-0.102452\pi\) | ||||
0.948648 | + | 0.316334i | \(0.102452\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.03941 | −0.357749 | ||||||||
\(506\) | 7.99611 | − | 5.93542i | 0.355470 | − | 0.263862i | ||||
\(507\) | −8.97464 | − | 2.83884i | −0.398578 | − | 0.126077i | ||||
\(508\) | 2.89497 | + | 0.875581i | 0.128444 | + | 0.0388476i | ||||
\(509\) | 17.2071i | 0.762692i | 0.924432 | + | 0.381346i | \(0.124539\pi\) | ||||
−0.924432 | + | 0.381346i | \(0.875461\pi\) | |||||||
\(510\) | −6.73492 | + | 2.32335i | −0.298227 | + | 0.102880i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −19.4511 | − | 11.5609i | −0.859626 | − | 0.510924i | ||||
\(513\) | 10.2516 | − | 7.82114i | 0.452619 | − | 0.345312i | ||||
\(514\) | 22.9356 | + | 30.8985i | 1.01165 | + | 1.36288i | ||||
\(515\) | 0.937311 | 0.0413029 | ||||||||
\(516\) | 10.0813 | + | 6.89792i | 0.443806 | + | 0.303664i | ||||
\(517\) | 7.04155 | 0.309687 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.99896 | − | 15.8036i | 0.219430 | − | 0.693701i | ||||
\(520\) | 3.65692 | − | 1.31356i | 0.160367 | − | 0.0576034i | ||||
\(521\) | 10.9436i | 0.479448i | 0.970841 | + | 0.239724i | \(0.0770569\pi\) | ||||
−0.970841 | + | 0.239724i | \(0.922943\pi\) | |||||||
\(522\) | −0.692777 | − | 26.8162i | −0.0303220 | − | 1.17371i | ||||
\(523\) | 5.53433i | 0.241999i | 0.992653 | + | 0.121000i | \(0.0386100\pi\) | ||||
−0.992653 | + | 0.121000i | \(0.961390\pi\) | |||||||
\(524\) | −3.85053 | + | 12.7312i | −0.168211 | + | 0.556164i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.09362 | + | 3.03864i | −0.178490 | + | 0.132491i | ||||
\(527\) | 40.2689 | 1.75414 | ||||||||
\(528\) | 6.03533 | + | 7.50880i | 0.262654 | + | 0.326779i | ||||
\(529\) | 2.64461 | 0.114983 | ||||||||
\(530\) | 2.97477 | − | 2.20814i | 0.129216 | − | 0.0959153i | ||||
\(531\) | −7.73521 | − | 5.43764i | −0.335679 | − | 0.235974i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 15.8001i | − | 0.684379i | ||||||
\(534\) | −1.95839 | − | 5.67695i | −0.0847476 | − | 0.245666i | ||||
\(535\) | 3.63534i | 0.157170i | ||||||||
\(536\) | −28.5992 | + | 10.2728i | −1.23530 | + | 0.443716i | ||||
\(537\) | −34.2735 | − | 10.8413i | −1.47901 | − | 0.467837i | ||||
\(538\) | −22.0551 | − | 29.7123i | −0.950863 | − | 1.28099i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.81887 | − | 4.86147i | −0.0782717 | − | 0.209204i | ||||
\(541\) | 12.5282 | 0.538628 | 0.269314 | − | 0.963052i | \(-0.413203\pi\) | ||||
0.269314 | + | 0.963052i | \(0.413203\pi\) | |||||||
\(542\) | −19.4392 | − | 26.1882i | −0.834984 | − | 1.12488i | ||||
\(543\) | −10.6260 | − | 3.36121i | −0.456007 | − | 0.144243i | ||||
\(544\) | 1.68402 | + | 32.8984i | 0.0722018 | + | 1.41051i | ||||
\(545\) | 0.920019i | 0.0394093i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.4911i | 1.60300i | 0.597992 | + | 0.801502i | \(0.295966\pi\) | ||||
−0.597992 | + | 0.801502i | \(0.704034\pi\) | |||||||
\(548\) | −23.3393 | − | 7.05895i | −0.997006 | − | 0.301543i | ||||
\(549\) | −12.0468 | − | 8.46859i | −0.514145 | − | 0.361430i | ||||
\(550\) | 7.50107 | − | 5.56796i | 0.319847 | − | 0.237418i | ||||
\(551\) | 15.6901 | 0.668420 | ||||||||
\(552\) | 0.954556 | + | 24.7903i | 0.0406286 | + | 1.05515i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 23.0417 | − | 17.1036i | 0.978947 | − | 0.726661i | ||||
\(555\) | 1.91584 | − | 6.05670i | 0.0813230 | − | 0.257093i | ||||
\(556\) | 0.0914752 | + | 0.0276665i | 0.00387941 | + | 0.00117332i | ||||
\(557\) | − | 30.0697i | − | 1.27409i | −0.770825 | − | 0.637046i | \(-0.780156\pi\) | ||
0.770825 | − | 0.637046i | \(-0.219844\pi\) | |||||||
\(558\) | 0.757684 | + | 29.3287i | 0.0320753 | + | 1.24158i | ||||
\(559\) | 9.69912i | 0.410229i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.22976 | − | 13.3719i | 0.178581 | − | 0.564560i | ||||
\(562\) | −23.3181 | − | 31.4138i | −0.983616 | − | 1.32511i | ||||
\(563\) | 6.83911 | 0.288234 | 0.144117 | − | 0.989561i | \(-0.453966\pi\) | ||||
0.144117 | + | 0.989561i | \(0.453966\pi\) | |||||||
\(564\) | −9.90606 | + | 14.4778i | −0.417120 | + | 0.609623i | ||||
\(565\) | −5.13089 | −0.215858 | ||||||||
\(566\) | −14.6420 | − | 19.7255i | −0.615449 | − | 0.829124i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.34308 | + | 12.0910i | 0.182232 | + | 0.507329i | ||||
\(569\) | − | 33.4870i | − | 1.40385i | −0.712252 | − | 0.701924i | \(-0.752324\pi\) | ||
0.712252 | − | 0.701924i | \(-0.247676\pi\) | |||||||
\(570\) | 2.87001 | − | 0.990072i | 0.120212 | − | 0.0414695i | ||||
\(571\) | 27.9973i | 1.17165i | 0.810438 | + | 0.585825i | \(0.199229\pi\) | ||||
−0.810438 | + | 0.585825i | \(0.800771\pi\) | |||||||
\(572\) | −2.21443 | + | 7.32168i | −0.0925901 | + | 0.306135i | ||||
\(573\) | 28.9553 | + | 9.15909i | 1.20963 | + | 0.382627i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.0570 | 1.00324 | ||||||||
\(576\) | −23.9289 | + | 1.84551i | −0.997039 | + | 0.0768964i | ||||
\(577\) | 37.6362 | 1.56682 | 0.783409 | − | 0.621507i | \(-0.213479\pi\) | ||||
0.783409 | + | 0.621507i | \(0.213479\pi\) | |||||||
\(578\) | 19.2031 | − | 14.2542i | 0.798743 | − | 0.592898i | ||||
\(579\) | −3.60847 | − | 1.14142i | −0.149963 | − | 0.0474359i | ||||
\(580\) | 1.82846 | − | 6.04552i | 0.0759227 | − | 0.251027i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.21807 | + | 0.420198i | −0.0504905 | + | 0.0174178i | ||||
\(583\) | 7.29304i | 0.302047i | ||||||||
\(584\) | −9.53767 | − | 26.5527i | −0.394672 | − | 1.09876i | ||||
\(585\) | 2.37018 | − | 3.37165i | 0.0979950 | − | 0.139401i | ||||
\(586\) | 16.8306 | + | 22.6739i | 0.695266 | + | 0.936652i | ||||
\(587\) | 19.7791 | 0.816373 | 0.408186 | − | 0.912899i | \(-0.366161\pi\) | ||||
0.408186 | + | 0.912899i | \(0.366161\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.1601 | −0.707071 | ||||||||
\(590\) | −1.32690 | − | 1.78758i | −0.0546276 | − | 0.0735935i | ||||
\(591\) | 3.27894 | − | 10.3660i | 0.134878 | − | 0.426399i | ||||
\(592\) | −24.4490 | − | 16.2782i | −1.00485 | − | 0.669029i | ||||
\(593\) | 22.5237i | 0.924939i | 0.886635 | + | 0.462469i | \(0.153036\pi\) | ||||
−0.886635 | + | 0.462469i | \(0.846964\pi\) | |||||||
\(594\) | 9.81860 | + | 2.82902i | 0.402862 | + | 0.116076i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.39118 | + | 1.32811i | 0.179870 | + | 0.0544013i | ||||
\(597\) | −0.452122 | + | 1.42933i | −0.0185041 | + | 0.0584984i | ||||
\(598\) | −15.8170 | + | 11.7408i | −0.646807 | + | 0.480117i | ||||
\(599\) | 26.7316 | 1.09223 | 0.546113 | − | 0.837712i | \(-0.316107\pi\) | ||||
0.546113 | + | 0.837712i | \(0.316107\pi\) | |||||||
\(600\) | 0.895459 | + | 23.2555i | 0.0365570 | + | 0.949403i | ||||
\(601\) | 31.1478 | 1.27055 | 0.635273 | − | 0.772288i | \(-0.280888\pi\) | ||||
0.635273 | + | 0.772288i | \(0.280888\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.5362 | + | 26.3682i | −0.754851 | + | 1.07380i | ||||
\(604\) | −25.1466 | − | 7.60555i | −1.02320 | − | 0.309465i | ||||
\(605\) | 4.52840i | 0.184106i | ||||||||
\(606\) | 12.8577 | + | 37.2717i | 0.522307 | + | 1.51406i | ||||
\(607\) | 12.5787i | 0.510552i | 0.966868 | + | 0.255276i | \(0.0821664\pi\) | ||||
−0.966868 | + | 0.255276i | \(0.917834\pi\) | |||||||
\(608\) | −0.717627 | − | 14.0193i | −0.0291036 | − | 0.568558i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.06651 | − | 2.78398i | −0.0836707 | − | 0.112720i | ||||
\(611\) | −13.9288 | −0.563501 | ||||||||
\(612\) | 21.5427 | + | 27.5081i | 0.870812 | + | 1.11195i | ||||
\(613\) | 4.54262 | 0.183475 | 0.0917374 | − | 0.995783i | \(-0.470758\pi\) | ||||
0.0917374 | + | 0.995783i | \(0.470758\pi\) | |||||||
\(614\) | −11.9296 | − | 16.0714i | −0.481440 | − | 0.648590i | ||||
\(615\) | −4.73806 | − | 1.49873i | −0.191057 | − | 0.0604348i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 35.4652i | − | 1.42777i | −0.700261 | − | 0.713887i | \(-0.746933\pi\) | ||
0.700261 | − | 0.713887i | \(-0.253067\pi\) | |||||||
\(618\) | −1.49907 | − | 4.34549i | −0.0603014 | − | 0.174801i | ||||
\(619\) | − | 41.4572i | − | 1.66631i | −0.553042 | − | 0.833153i | \(-0.686533\pi\) | ||
0.553042 | − | 0.833153i | \(-0.313467\pi\) | |||||||
\(620\) | −1.99977 | + | 6.61194i | −0.0803128 | + | 0.265542i | ||||
\(621\) | 15.9606 | + | 20.9204i | 0.640476 | + | 0.839508i | ||||
\(622\) | 27.8836 | − | 20.6976i | 1.11803 | − | 0.829900i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −11.9384 | − | 14.8531i | −0.477920 | − | 0.594600i | ||||
\(625\) | 21.3203 | 0.852810 | ||||||||
\(626\) | −0.0591199 | + | 0.0438840i | −0.00236291 | + | 0.00175396i | ||||
\(627\) | −1.80247 | + | 5.69827i | −0.0719835 | + | 0.227567i | ||||
\(628\) | 4.86911 | − | 16.0990i | 0.194299 | − | 0.642419i | ||||
\(629\) | 42.7609i | 1.70499i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.2919i | 0.887428i | 0.896168 | + | 0.443714i | \(0.146339\pi\) | ||||
−0.896168 | + | 0.443714i | \(0.853661\pi\) | |||||||
\(632\) | −5.67332 | + | 2.03785i | −0.225673 | + | 0.0810612i | ||||
\(633\) | 2.03941 | − | 6.44735i | 0.0810594 | − | 0.256259i | ||||
\(634\) | 5.71202 | + | 7.69516i | 0.226853 | + | 0.305614i | ||||
\(635\) | 0.755312 | 0.0299736 | ||||||||
\(636\) | −14.9948 | − | 10.2599i | −0.594583 | − | 0.406830i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.41070 | + | 9.98359i | 0.293393 | + | 0.395254i | ||||
\(639\) | 11.1479 | + | 7.83664i | 0.441002 | + | 0.310013i | ||||
\(640\) | −5.48538 | − | 1.35724i | −0.216829 | − | 0.0536498i | ||||
\(641\) | 34.1111i | 1.34731i | 0.739048 | + | 0.673653i | \(0.235276\pi\) | ||||
−0.739048 | + | 0.673653i | \(0.764724\pi\) | |||||||
\(642\) | 16.8539 | − | 5.81411i | 0.665170 | − | 0.229465i | ||||
\(643\) | 24.2299i | 0.955533i | 0.878487 | + | 0.477766i | \(0.158553\pi\) | ||||
−0.878487 | + | 0.477766i | \(0.841447\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.90852 | + | 0.920019i | 0.114523 | + | 0.0362257i | ||||
\(646\) | −16.4096 | + | 12.1807i | −0.645627 | + | 0.479241i | ||||
\(647\) | −1.42818 | −0.0561477 | −0.0280738 | − | 0.999606i | \(-0.508937\pi\) | ||||
−0.0280738 | + | 0.999606i | \(0.508937\pi\) | |||||||
\(648\) | −19.6294 | + | 16.2076i | −0.771116 | + | 0.636695i | ||||
\(649\) | 4.38249 | 0.172028 | ||||||||
\(650\) | −14.8378 | + | 11.0139i | −0.581987 | + | 0.432002i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.6612 | − | 7.15630i | −0.926644 | − | 0.280262i | ||||
\(653\) | 5.02787i | 0.196756i | 0.995149 | + | 0.0983778i | \(0.0313654\pi\) | ||||
−0.995149 | + | 0.0983778i | \(0.968635\pi\) | |||||||
\(654\) | 4.26532 | − | 1.47141i | 0.166787 | − | 0.0575368i | ||||
\(655\) | 3.32162i | 0.129787i | ||||||||
\(656\) | −12.7342 | + | 19.1261i | −0.497186 | + | 0.746748i | ||||
\(657\) | −24.4814 | − | 17.2097i | −0.955109 | − | 0.671416i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.7930 | 0.771025 | 0.385512 | − | 0.922703i | \(-0.374025\pi\) | ||||
0.385512 | + | 0.922703i | \(0.374025\pi\) | |||||||
\(660\) | 1.98554 | + | 1.35856i | 0.0772869 | + | 0.0528818i | ||||
\(661\) | −22.6612 | −0.881419 | −0.440709 | − | 0.897650i | \(-0.645273\pi\) | ||||
−0.440709 | + | 0.897650i | \(0.645273\pi\) | |||||||
\(662\) | −15.0814 | − | 20.3174i | −0.586154 | − | 0.789658i | ||||
\(663\) | −8.36686 | + | 26.4508i | −0.324942 | + | 1.02726i | ||||
\(664\) | −11.4897 | − | 31.9870i | −0.445885 | − | 1.24134i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −31.1437 | + | 0.804573i | −1.20679 | + | 0.0311766i | ||||
\(667\) | 32.0187i | 1.23977i | ||||||||
\(668\) | 1.36961 | − | 4.52840i | 0.0529918 | − | 0.175209i | ||||
\(669\) | 12.2766 | − | 38.8108i | 0.474639 | − | 1.50051i | ||||
\(670\) | −6.09362 | + | 4.52322i | −0.235417 | + | 0.174747i | ||||
\(671\) | 6.82530 | 0.263488 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.2766 | −0.434680 | −0.217340 | − | 0.976096i | \(-0.569738\pi\) | ||||
−0.217340 | + | 0.976096i | \(0.569738\pi\) | |||||||
\(674\) | −8.05523 | + | 5.97930i | −0.310276 | + | 0.230314i | ||||
\(675\) | 14.9725 | + | 19.6252i | 0.576291 | + | 0.755376i | ||||
\(676\) | −3.14658 | + | 10.4037i | −0.121022 | + | 0.400142i | ||||
\(677\) | − | 10.0890i | − | 0.387750i | −0.981026 | − | 0.193875i | \(-0.937894\pi\) | ||
0.981026 | − | 0.193875i | \(-0.0621056\pi\) | |||||||
\(678\) | 8.20598 | + | 23.7874i | 0.315149 | + | 0.913551i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.78100 | + | 7.74223i | 0.106646 | + | 0.296901i | ||||
\(681\) | 31.6538 | + | 10.0127i | 1.21298 | + | 0.383686i | ||||
\(682\) | −8.10503 | − | 10.9190i | −0.310357 | − | 0.418109i | ||||
\(683\) | −6.23486 | −0.238570 | −0.119285 | − | 0.992860i | \(-0.538060\pi\) | ||||
−0.119285 | + | 0.992860i | \(0.538060\pi\) | |||||||
\(684\) | −9.18019 | − | 11.7223i | −0.351013 | − | 0.448212i | ||||
\(685\) | −6.08933 | −0.232662 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.9517 | + | 5.99476i | 0.723052 | + | 0.228714i | ||||
\(688\) | 7.81705 | − | 11.7408i | 0.298022 | − | 0.447614i | ||||
\(689\) | − | 14.4263i | − | 0.549599i | ||||||
\(690\) | 2.02044 | + | 5.85682i | 0.0769167 | + | 0.222966i | ||||
\(691\) | − | 17.0676i | − | 0.649283i | −0.945837 | − | 0.324641i | \(-0.894756\pi\) | ||
0.945837 | − | 0.324641i | \(-0.105244\pi\) | |||||||
\(692\) | −18.3200 | − | 5.54087i | −0.696423 | − | 0.210632i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.4367 | − | 7.74704i | 0.396172 | − | 0.294074i | ||||
\(695\) | 0.0238663 | 0.000905300 | ||||||||
\(696\) | −30.9521 | + | 1.19182i | −1.17324 | + | 0.0451757i | ||||
\(697\) | 33.4511 | 1.26705 | ||||||||
\(698\) | 25.1334 | − | 18.6562i | 0.951313 | − | 0.706148i | ||||
\(699\) | −10.5610 | + | 33.3872i | −0.399452 | + | 1.26282i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.4324i | 0.809489i | 0.914430 | + | 0.404744i | \(0.132640\pi\) | ||||
−0.914430 | + | 0.404744i | \(0.867360\pi\) | |||||||
\(702\) | −19.4221 | − | 5.59607i | −0.733040 | − | 0.211210i | ||||
\(703\) | − | 18.2221i | − | 0.687259i | ||||||
\(704\) | 8.58152 | − | 7.07818i | 0.323428 | − | 0.266769i | ||||
\(705\) | −1.32123 | + | 4.17692i | −0.0497605 | + | 0.157312i | ||||
\(706\) | 9.04155 | + | 12.1807i | 0.340283 | + | 0.458425i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.16529 | + | 9.01060i | −0.231706 | + | 0.338639i | ||||
\(709\) | −8.54262 | −0.320825 | −0.160412 | − | 0.987050i | \(-0.551282\pi\) | ||||
−0.160412 | + | 0.987050i | \(0.551282\pi\) | |||||||
\(710\) | 1.91231 | + | 2.57623i | 0.0717676 | + | 0.0966843i | ||||
\(711\) | −3.67709 | + | 5.23076i | −0.137902 | + | 0.196169i | ||||
\(712\) | −6.52603 | + | 2.34414i | −0.244573 | + | 0.0878503i | ||||
\(713\) | − | 35.0186i | − | 1.31146i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.91026i | 0.0714396i | ||||||||
\(716\) | −12.0165 | + | 39.7309i | −0.449079 | + | 1.48481i | ||||
\(717\) | 11.4075 | + | 3.60838i | 0.426019 | + | 0.134758i | ||||
\(718\) | −4.09362 | + | 3.03864i | −0.152772 | + | 0.113401i | ||||
\(719\) | 27.4731 | 1.02457 | 0.512287 | − | 0.858814i | \(-0.328798\pi\) | ||||
0.512287 | + | 0.858814i | \(0.328798\pi\) | |||||||
\(720\) | −5.58651 | + | 2.17114i | −0.208197 | + | 0.0809134i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −14.5829 | + | 10.8247i | −0.542719 | + | 0.402854i | ||||
\(723\) | 13.3211 | + | 4.21369i | 0.495416 | + | 0.156709i | ||||
\(724\) | −3.72557 | + | 12.3180i | −0.138460 | + | 0.457796i | ||||
\(725\) | 30.0365i | 1.11553i | ||||||||
\(726\) | 20.9942 | − | 7.24241i | 0.779169 | − | 0.268791i | ||||
\(727\) | − | 45.7930i | − | 1.69837i | −0.528096 | − | 0.849185i | \(-0.677094\pi\) | ||
0.528096 | − | 0.849185i | \(-0.322906\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.13303 | + | 26.0407i | −0.264186 | + | 0.964472i | ||||
\(730\) | −4.19954 | − | 5.65756i | −0.155432 | − | 0.209396i | ||||
\(731\) | −20.5345 | −0.759494 | ||||||||
\(732\) | −9.60183 | + | 14.0331i | −0.354894 | + | 0.518679i | ||||
\(733\) | −43.2932 | −1.59907 | −0.799535 | − | 0.600620i | \(-0.794920\pi\) | ||||
−0.799535 | + | 0.600620i | \(0.794920\pi\) | |||||||
\(734\) | −12.6661 | − | 17.0636i | −0.467514 | − | 0.629828i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 28.6091 | − | 1.46446i | 1.05455 | − | 0.0539807i | ||||
\(737\) | − | 14.9393i | − | 0.550297i | ||||||
\(738\) | 0.629405 | + | 24.3632i | 0.0231687 | + | 0.896822i | ||||
\(739\) | 5.17590i | 0.190399i | 0.995458 | + | 0.0951993i | \(0.0303488\pi\) | ||||
−0.995458 | + | 0.0951993i | \(0.969651\pi\) | |||||||
\(740\) | −7.02111 | − | 2.12353i | −0.258101 | − | 0.0780624i | ||||
\(741\) | 3.56544 | − | 11.2717i | 0.130980 | − | 0.414077i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −49.5492 | −1.81778 | −0.908891 | − | 0.417034i | \(-0.863070\pi\) | ||||
−0.908891 | + | 0.417034i | \(0.863070\pi\) | |||||||
\(744\) | 33.8521 | − | 1.30348i | 1.24108 | − | 0.0477879i | ||||
\(745\) | 1.14568 | 0.0419744 | ||||||||
\(746\) | −3.01709 | + | 2.23955i | −0.110464 | + | 0.0819958i | ||||
\(747\) | −29.4917 | − | 20.7319i | −1.07905 | − | 0.758541i | ||||
\(748\) | −15.5011 | − | 4.68828i | −0.566775 | − | 0.171420i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.89023 | + | 11.2770i | 0.142051 | + | 0.411777i | ||||
\(751\) | − | 30.5879i | − | 1.11617i | −0.829784 | − | 0.558084i | \(-0.811537\pi\) | ||
0.829784 | − | 0.558084i | \(-0.188463\pi\) | |||||||
\(752\) | 16.8609 | + | 11.2260i | 0.614854 | + | 0.409371i | ||||
\(753\) | −33.7006 | − | 10.6601i | −1.22812 | − | 0.388476i | ||||
\(754\) | −14.6591 | − | 19.7485i | −0.533851 | − | 0.719197i | ||||
\(755\) | −6.56086 | −0.238774 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.4533 | 1.68837 | 0.844187 | − | 0.536049i | \(-0.180084\pi\) | ||||
0.844187 | + | 0.536049i | \(0.180084\pi\) | |||||||
\(758\) | 14.9322 | + | 20.1164i | 0.542362 | + | 0.730662i | ||||
\(759\) | −11.6284 | − | 3.67829i | −0.422086 | − | 0.133513i | ||||
\(760\) | −1.18509 | − | 3.29927i | −0.0429878 | − | 0.119677i | ||||
\(761\) | − | 39.4484i | − | 1.43000i | −0.699122 | − | 0.715002i | \(-0.746426\pi\) | ||
0.699122 | − | 0.715002i | \(-0.253574\pi\) | |||||||
\(762\) | −1.20799 | − | 3.50172i | −0.0437609 | − | 0.126854i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.1520 | − | 33.5659i | 0.367285 | − | 1.21437i | ||||
\(765\) | 7.13828 | + | 5.01802i | 0.258085 | + | 0.181427i | ||||
\(766\) | 37.3846 | − | 27.7502i | 1.35076 | − | 1.00265i | ||||
\(767\) | −8.66898 | −0.313019 | ||||||||
\(768\) | 2.48058 | + | 27.6016i | 0.0895101 | + | 0.995986i | ||||
\(769\) | 39.7256 | 1.43254 | 0.716270 | − | 0.697823i | \(-0.245848\pi\) | ||||
0.716270 | + | 0.697823i | \(0.245848\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.2136 | − | 44.9346i | 0.511891 | − | 1.61828i | ||||
\(772\) | −1.26516 | + | 4.18305i | −0.0455340 | + | 0.150551i | ||||
\(773\) | 21.9318i | 0.788833i | 0.918932 | + | 0.394416i | \(0.129053\pi\) | ||||
−0.918932 | + | 0.394416i | \(0.870947\pi\) | |||||||
\(774\) | −0.386369 | − | 14.9557i | −0.0138877 | − | 0.537571i | ||||
\(775\) | − | 32.8506i | − | 1.18003i | ||||||
\(776\) | 0.502967 | + | 1.40025i | 0.0180554 | + | 0.0502660i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.75054 | + | 7.74704i | 0.206167 | + | 0.277745i | ||||
\(779\) | −14.2548 | −0.510733 | ||||||||
\(780\) | −3.92758 | − | 2.68735i | −0.140630 | − | 0.0962227i | ||||
\(781\) | −6.31598 | −0.226004 | ||||||||
\(782\) | −24.8570 | − | 33.4870i | −0.888885 | − | 1.19749i | ||||
\(783\) | −26.1203 | + | 19.9277i | −0.933464 | + | 0.712157i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 4.20029i | − | 0.149915i | ||||||
\(786\) | 15.3994 | − | 5.31237i | 0.549280 | − | 0.189486i | ||||
\(787\) | − | 5.04447i | − | 0.179816i | −0.995950 | − | 0.0899080i | \(-0.971343\pi\) | ||
0.995950 | − | 0.0899080i | \(-0.0286573\pi\) | |||||||
\(788\) | −12.0165 | − | 3.63439i | −0.428072 | − | 0.129470i | ||||
\(789\) | 5.95319 | + | 1.88310i | 0.211939 | + | 0.0670402i | ||||
\(790\) | −1.20881 | + | 0.897287i | −0.0430076 | + | 0.0319240i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.12291 | − | 11.3780i | 0.110968 | − | 0.404299i | ||||
\(793\) | −13.5011 | −0.479437 | ||||||||
\(794\) | 23.6698 | − | 17.5698i | 0.840010 | − | 0.623529i | ||||
\(795\) | −4.32609 | − | 1.36842i | −0.153431 | − | 0.0485329i | ||||
\(796\) | 1.65692 | + | 0.501133i | 0.0587279 | + | 0.0177622i | ||||
\(797\) | 28.3335i | 1.00362i | 0.864977 | + | 0.501812i | \(0.167333\pi\) | ||||
−0.864977 | + | 0.501812i | \(0.832667\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 29.4894i | − | 1.04326i | ||||||
\(800\) | 26.8379 | − | 1.37379i | 0.948865 | − | 0.0485710i | ||||
\(801\) | −4.22976 | + | 6.01695i | −0.149451 | + | 0.212599i | ||||
\(802\) | 3.22450 | + | 4.34401i | 0.113861 | + | 0.153392i | ||||
\(803\) | 13.8703 | 0.489471 | ||||||||
\(804\) | 30.7159 | + | 21.0166i | 1.08327 | + | 0.741200i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16.0325 | + | 21.5987i | 0.564721 | + | 0.760783i | ||||
\(807\) | −13.6679 | + | 43.2095i | −0.481134 | + | 1.52105i | ||||
\(808\) | 42.8463 | − | 15.3903i | 1.50733 | − | 0.541429i | ||||
\(809\) | 20.2174i | 0.710808i | 0.934713 | + | 0.355404i | \(0.115657\pi\) | ||||
−0.934713 | + | 0.355404i | \(0.884343\pi\) | |||||||
\(810\) | −3.52042 | + | 5.29338i | −0.123695 | + | 0.185991i | ||||
\(811\) | − | 1.33368i | − | 0.0468317i | −0.999726 | − | 0.0234158i | \(-0.992546\pi\) | ||
0.999726 | − | 0.0234158i | \(-0.00745418\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0468 | + | 38.0845i | −0.422500 | + | 1.33568i | ||||
\(814\) | 11.5947 | − | 8.60660i | 0.406394 | − | 0.301661i | ||||
\(815\) | −6.17331 | −0.216242 | ||||||||
\(816\) | 31.4462 | − | 25.2754i | 1.10084 | − | 0.884817i | ||||
\(817\) | 8.75054 | 0.306142 | ||||||||
\(818\) | 4.39361 | − | 3.26133i | 0.153619 | − | 0.114030i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.66120 | + | 5.49251i | −0.0580117 | + | 0.191807i | ||||
\(821\) | 5.31136i | 0.185368i | 0.995696 | + | 0.0926838i | \(0.0295446\pi\) | ||||
−0.995696 | + | 0.0926838i | \(0.970455\pi\) | |||||||
\(822\) | 9.73885 | + | 28.2309i | 0.339681 | + | 0.984666i | ||||
\(823\) | 15.3007i | 0.533349i | 0.963787 | + | 0.266675i | \(0.0859249\pi\) | ||||
−0.963787 | + | 0.266675i | \(0.914075\pi\) | |||||||
\(824\) | −4.99543 | + | 1.79435i | −0.174024 | + | 0.0625091i | ||||
\(825\) | −10.9085 | − | 3.45056i | −0.379786 | − | 0.120133i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.288306 | 0.0100254 | 0.00501270 | − | 0.999987i | \(-0.498404\pi\) | ||||
0.00501270 | + | 0.999987i | \(0.498404\pi\) | |||||||
\(828\) | 23.9216 | − | 18.7340i | 0.831334 | − | 0.651051i | ||||
\(829\) | −41.1102 | −1.42782 | −0.713908 | − | 0.700239i | \(-0.753077\pi\) | ||||
−0.713908 | + | 0.700239i | \(0.753077\pi\) | |||||||
\(830\) | −5.05903 | − | 6.81545i | −0.175601 | − | 0.236568i | ||||
\(831\) | −33.5086 | − | 10.5994i | −1.16240 | − | 0.367689i | ||||
\(832\) | −16.9750 | + | 14.0013i | −0.588504 | + | 0.485408i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.0381700 | − | 0.110647i | −0.00132172 | − | 0.00383139i | ||||
\(835\) | − | 1.18148i | − | 0.0408868i | ||||||
\(836\) | 6.60561 | + | 1.99786i | 0.228460 | + | 0.0690974i | ||||
\(837\) | 28.5676 | − | 21.7948i | 0.987440 | − | 0.753337i | ||||
\(838\) | 15.3452 | − | 11.3906i | 0.530092 | − | 0.393481i | ||||
\(839\) | 25.7705 | 0.889695 | 0.444848 | − | 0.895606i | \(-0.353258\pi\) | ||||
0.444848 | + | 0.895606i | \(0.353258\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.9772 | −0.378523 | ||||||||
\(842\) | −12.9255 | + | 9.59445i | −0.445442 | + | 0.330647i | ||||
\(843\) | −14.4507 | + | 45.6840i | −0.497707 | + | 1.57344i | ||||
\(844\) | −7.47397 | − | 2.26049i | −0.257265 | − | 0.0778093i | ||||
\(845\) | 2.71437i | 0.0933771i | ||||||||
\(846\) | 21.4778 | − | 0.554862i | 0.738421 | − | 0.0190766i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.6270 | + | 17.4631i | −0.399271 | + | 0.599685i | ||||
\(849\) | −9.07391 | + | 28.6860i | −0.311416 | + | 0.984502i | ||||
\(850\) | −23.3181 | − | 31.4138i | −0.799805 | − | 1.07749i | ||||
\(851\) | 37.1857 | 1.27471 | ||||||||
\(852\) | 8.88532 | − | 12.9859i | 0.304406 | − | 0.444891i | ||||
\(853\) | −51.4656 | −1.76215 | −0.881074 | − | 0.472978i | \(-0.843179\pi\) | ||||
−0.881074 | + | 0.472978i | \(0.843179\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.04190 | − | 2.13838i | −0.104031 | − | 0.0731309i | ||||
\(856\) | −6.95935 | − | 19.3747i | −0.237866 | − | 0.662213i | ||||
\(857\) | 35.5762i | 1.21526i | 0.794220 | + | 0.607631i | \(0.207880\pi\) | ||||
−0.794220 | + | 0.607631i | \(0.792120\pi\) | |||||||
\(858\) | 8.85620 | − | 3.05513i | 0.302346 | − | 0.104301i | ||||
\(859\) | 51.3072i | 1.75058i | 0.483598 | + | 0.875290i | \(0.339330\pi\) | ||||
−0.483598 | + | 0.875290i | \(0.660670\pi\) | |||||||
\(860\) | 1.01975 | − | 3.37165i | 0.0347732 | − | 0.114972i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −29.4388 | + | 21.8521i | −1.00269 | + | 0.744286i | ||||
\(863\) | −11.7830 | −0.401099 | −0.200550 | − | 0.979684i | \(-0.564273\pi\) | ||||
−0.200550 | + | 0.979684i | \(0.564273\pi\) | |||||||
\(864\) | 19.0003 | + | 22.4274i | 0.646404 | + | 0.762995i | ||||
\(865\) | −4.77978 | −0.162517 | ||||||||
\(866\) | −26.5522 | + | 19.7094i | −0.902282 | + | 0.669753i | ||||
\(867\) | −27.9263 | − | 8.83360i | −0.948428 | − | 0.300005i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.96357i | − | 0.100532i | ||||||
\(870\) | −7.31257 | + | 2.52263i | −0.247919 | + | 0.0855251i | ||||
\(871\) | 29.5514i | 1.00131i | ||||||||
\(872\) | −1.76124 | − | 4.90327i | −0.0596433 | − | 0.166046i | ||||
\(873\) | 1.29102 | + | 0.907552i | 0.0436944 | + | 0.0307160i | ||||
\(874\) | 10.5925 | + | 14.2701i | 0.358298 | + | 0.482694i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −19.5127 | + | 28.5179i | −0.659273 | + | 0.963531i | ||||
\(877\) | 1.32863 | 0.0448646 | 0.0224323 | − | 0.999748i | \(-0.492859\pi\) | ||||
0.0224323 | + | 0.999748i | \(0.492859\pi\) | |||||||
\(878\) | 14.8969 | + | 20.0689i | 0.502747 | + | 0.677294i | ||||
\(879\) | 10.4302 | − | 32.9739i | 0.351803 | − | 1.11218i | ||||
\(880\) | 1.53958 | − | 2.31237i | 0.0518993 | − | 0.0779501i | ||||
\(881\) | − | 23.8258i | − | 0.802713i | −0.915922 | − | 0.401356i | \(-0.868539\pi\) | ||
0.915922 | − | 0.401356i | \(-0.131461\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 30.2235i | − | 1.01710i | −0.861032 | − | 0.508551i | \(-0.830181\pi\) | ||
0.861032 | − | 0.508551i | \(-0.169819\pi\) | |||||||
\(884\) | 30.6626 | + | 9.27385i | 1.03129 | + | 0.311913i | ||||
\(885\) | −0.822304 | + | 2.59961i | −0.0276414 | + | 0.0873850i | ||||
\(886\) | 39.8993 | − | 29.6167i | 1.34044 | − | 0.994994i | ||||
\(887\) | −21.9111 | −0.735704 | −0.367852 | − | 0.929884i | \(-0.619907\pi\) | ||||
−0.367852 | + | 0.929884i | \(0.619907\pi\) | |||||||
\(888\) | 1.38415 | + | 35.9470i | 0.0464489 | + | 1.20630i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.39050 | + | 1.03215i | −0.0466096 | + | 0.0345978i | ||||
\(891\) | −4.23658 | − | 11.7756i | −0.141931 | − | 0.394496i | ||||
\(892\) | −44.9907 | − | 13.6074i | −1.50640 | − | 0.455609i | ||||
\(893\) | 12.5666i | 0.420525i | ||||||||
\(894\) | −1.83232 | − | 5.31151i | −0.0612819 | − | 0.177643i | ||||
\(895\) | 10.3660i | 0.346496i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.0021 | + | 7.27599i | 0.768019 | + | 0.242938i | ||||
\(898\) | 4.65906 | + | 6.27662i | 0.155475 | + | 0.209453i | ||||
\(899\) | 43.7227 | 1.45823 | ||||||||
\(900\) | 22.4406 | − | 17.5742i | 0.748021 | − | 0.585805i | ||||
\(901\) | 30.5426 | 1.01752 | ||||||||
\(902\) | −6.73281 | − | 9.07034i | −0.224178 | − | 0.302009i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27.3452 | − | 9.82235i | 0.909489 | − | 0.326687i | ||||
\(905\) | 3.21383i | 0.106831i | ||||||||
\(906\) | 10.4930 | + | 30.4169i | 0.348606 | + | 1.01053i | ||||
\(907\) | − | 48.9638i | − | 1.62581i | −0.582393 | − | 0.812907i | \(-0.697883\pi\) | ||
0.582393 | − | 0.812907i | \(-0.302117\pi\) | |||||||
\(908\) | 11.0981 | − | 36.6941i | 0.368302 | − | 1.21774i | ||||
\(909\) | 27.7702 | − | 39.5040i | 0.921081 | − | 1.31026i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.8251 | 1.71704 | 0.858522 | − | 0.512777i | \(-0.171383\pi\) | ||||
0.858522 | + | 0.512777i | \(0.171383\pi\) | |||||||
\(912\) | −13.4005 | + | 10.7708i | −0.443734 | + | 0.356658i | ||||
\(913\) | 16.7090 | 0.552987 | ||||||||
\(914\) | −27.1992 | + | 20.1896i | −0.899669 | + | 0.667814i | ||||
\(915\) | −1.28066 | + | 4.04864i | −0.0423372 | + | 0.133844i | ||||
\(916\) | 6.64461 | − | 21.9694i | 0.219544 | − | 0.725889i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 11.8477 | − | 41.1194i | 0.391033 | − | 1.35714i | ||||
\(919\) | − | 50.5037i | − | 1.66596i | −0.553301 | − | 0.832981i | \(-0.686632\pi\) | ||
0.553301 | − | 0.832981i | \(-0.313368\pi\) | |||||||
\(920\) | 6.73281 | − | 2.41841i | 0.221974 | − | 0.0797327i | ||||
\(921\) | −7.39300 | + | 23.3721i | −0.243608 | + | 0.770135i | ||||
\(922\) | −2.52603 | − | 3.40303i | −0.0831904 | − | 0.112073i | ||||
\(923\) | 12.4936 | 0.411232 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.8836 | 1.14696 | ||||||||
\(926\) | 18.8940 | + | 25.4538i | 0.620897 | + | 0.836463i | ||||
\(927\) | −3.23772 | + | 4.60575i | −0.106341 | + | 0.151273i | ||||
\(928\) | 1.82846 | + | 35.7201i | 0.0600221 | + | 1.17257i | ||||
\(929\) | − | 1.23566i | − | 0.0405407i | −0.999795 | − | 0.0202703i | \(-0.993547\pi\) | ||
0.999795 | − | 0.0202703i | \(-0.00645269\pi\) | |||||||
\(930\) | 7.99770 | − | 2.75898i | 0.262255 | − | 0.0904705i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 38.7034 | + | 11.7058i | 1.26777 | + | 0.383436i | ||||
\(933\) | −40.5500 | − | 12.8267i | −1.32755 | − | 0.419927i | ||||
\(934\) | −13.6963 | + | 10.1666i | −0.448158 | + | 0.332662i | ||||
\(935\) | −4.04430 | −0.132263 | ||||||||
\(936\) | −6.17741 | + | 22.5067i | −0.201915 | + | 0.735655i | ||||
\(937\) | −29.4139 | −0.960909 | −0.480455 | − | 0.877020i | \(-0.659528\pi\) | ||||
−0.480455 | + | 0.877020i | \(0.659528\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.0859759 | + | 0.0271957i | 0.00280572 | + | 0.000887499i | ||||
\(940\) | 4.84201 | + | 1.46446i | 0.157929 | + | 0.0477654i | ||||
\(941\) | − | 44.8636i | − | 1.46251i | −0.682103 | − | 0.731256i | \(-0.738934\pi\) | ||
0.682103 | − | 0.731256i | \(-0.261066\pi\) | |||||||
\(942\) | −19.4731 | + | 6.71765i | −0.634467 | + | 0.218873i | ||||
\(943\) | − | 29.0898i | − | 0.947295i | ||||||
\(944\) | 10.4938 | + | 6.98680i | 0.341545 | + | 0.227401i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.13303 | + | 5.56796i | 0.134376 | + | 0.181030i | ||||
\(947\) | 17.5576 | 0.570547 | 0.285273 | − | 0.958446i | \(-0.407916\pi\) | ||||
0.285273 | + | 0.958446i | \(0.407916\pi\) | |||||||
\(948\) | 6.09322 | + | 4.16915i | 0.197899 | + | 0.135408i | ||||
\(949\) | −27.4367 | −0.890633 | ||||||||
\(950\) | 9.93676 | + | 13.3867i | 0.322391 | + | 0.434321i | ||||
\(951\) | 3.53984 | − | 11.1908i | 0.114787 | − | 0.362886i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.1546i | 1.20356i | 0.798663 | + | 0.601778i | \(0.205541\pi\) | ||||
−0.798663 | + | 0.601778i | \(0.794459\pi\) | |||||||
\(954\) | 0.574679 | + | 22.2449i | 0.0186059 | + | 0.720204i | ||||
\(955\) | − | 8.75750i | − | 0.283386i | ||||||
\(956\) | 3.99954 | − | 13.2239i | 0.129354 | − | 0.427691i | ||||
\(957\) | 4.59255 | − | 14.5188i | 0.148456 | − | 0.469325i | ||||
\(958\) | −15.2245 | + | 11.3010i | −0.491881 | + | 0.365118i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.58846 | + | 6.41850i | 0.0835422 | + | 0.207156i | ||||
\(961\) | −16.8192 | −0.542555 | ||||||||
\(962\) | −22.9354 | + | 17.0247i | −0.739466 | + | 0.548897i | ||||
\(963\) | −17.8633 | − | 12.5574i | −0.575637 | − | 0.404658i | ||||
\(964\) | 4.67047 | − | 15.4422i | 0.150426 | − | 0.497360i | ||||
\(965\) | 1.09138i | 0.0351326i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53.9045i | 1.73345i | 0.498786 | + | 0.866725i | \(0.333779\pi\) | ||||
−0.498786 | + | 0.866725i | \(0.666221\pi\) | |||||||
\(968\) | −8.66898 | − | 24.1343i | −0.278632 | − | 0.775704i | ||||
\(969\) | 23.8639 | + | 7.54857i | 0.766618 | + | 0.242495i | ||||
\(970\) | 0.221462 | + | 0.298350i | 0.00711071 | + | 0.00957945i | ||||
\(971\) | 38.3565 | 1.23092 | 0.615460 | − | 0.788168i | \(-0.288970\pi\) | ||||
0.615460 | + | 0.788168i | \(0.288970\pi\) | |||||||
\(972\) | 30.1711 | + | 7.85526i | 0.967738 | + | 0.251957i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10.2906 | − | 13.8633i | −0.329731 | − | 0.444208i | ||||
\(975\) | 21.5781 | + | 6.82553i | 0.691052 | + | 0.218592i | ||||
\(976\) | 16.3431 | + | 10.8812i | 0.523129 | + | 0.348300i | ||||
\(977\) | − | 18.0025i | − | 0.575952i | −0.957638 | − | 0.287976i | \(-0.907018\pi\) | ||
0.957638 | − | 0.287976i | \(-0.0929824\pi\) | |||||||
\(978\) | 9.87316 | + | 28.6202i | 0.315709 | + | 0.915174i | ||||
\(979\) | − | 3.40899i | − | 0.108952i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.52078 | − | 3.17799i | −0.144337 | − | 0.101465i | ||||
\(982\) | 45.3067 | − | 33.6306i | 1.44580 | − | 1.07320i | ||||
\(983\) | −13.7569 | −0.438777 | −0.219388 | − | 0.975638i | \(-0.570406\pi\) | ||||
−0.219388 | + | 0.975638i | \(0.570406\pi\) | |||||||
\(984\) | 28.1207 | − | 1.08279i | 0.896457 | − | 0.0345182i | ||||
\(985\) | −3.13517 | −0.0998948 | ||||||||
\(986\) | 41.8104 | − | 31.0354i | 1.33151 | − | 0.988368i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.0665 | − | 3.95195i | −0.415701 | − | 0.125728i | ||||
\(989\) | 17.8572i | 0.567826i | ||||||||
\(990\) | −0.0760961 | − | 2.94555i | −0.00241849 | − | 0.0936157i | ||||
\(991\) | − | 1.85652i | − | 0.0589742i | −0.999565 | − | 0.0294871i | \(-0.990613\pi\) | ||
0.999565 | − | 0.0294871i | \(-0.00938739\pi\) | |||||||
\(992\) | −1.99977 | − | 39.0668i | −0.0634928 | − | 1.24037i | ||||
\(993\) | −9.34619 | + | 29.5468i | −0.296593 | + | 0.937640i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.432298 | 0.0137048 | ||||||||
\(996\) | −23.5062 | + | 34.3544i | −0.744823 | + | 1.08856i | ||||
\(997\) | 60.3495 | 1.91129 | 0.955644 | − | 0.294524i | \(-0.0951612\pi\) | ||||
0.955644 | + | 0.294524i | \(0.0951612\pi\) | |||||||
\(998\) | −7.14383 | − | 9.62407i | −0.226134 | − | 0.304644i | ||||
\(999\) | 23.1435 | + | 30.3355i | 0.732228 | + | 0.959772i |
(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 | 588.2.e.e.491.4 | 12 | ||
3.2 | odd | 2 | inner | 588.2.e.e.491.9 | 12 | ||
4.3 | odd | 2 | inner | 588.2.e.e.491.10 | 12 | ||
7.2 | even | 3 | 84.2.n.a.11.11 | yes | 24 | ||
7.3 | odd | 6 | 588.2.n.e.275.6 | 24 | |||
7.4 | even | 3 | 84.2.n.a.23.6 | yes | 24 | ||
7.5 | odd | 6 | 588.2.n.e.263.11 | 24 | |||
7.6 | odd | 2 | 588.2.e.d.491.4 | 12 | |||
12.11 | even | 2 | inner | 588.2.e.e.491.3 | 12 | ||
21.2 | odd | 6 | 84.2.n.a.11.2 | ✓ | 24 | ||
21.5 | even | 6 | 588.2.n.e.263.2 | 24 | |||
21.11 | odd | 6 | 84.2.n.a.23.7 | yes | 24 | ||
21.17 | even | 6 | 588.2.n.e.275.7 | 24 | |||
21.20 | even | 2 | 588.2.e.d.491.9 | 12 | |||
28.3 | even | 6 | 588.2.n.e.275.2 | 24 | |||
28.11 | odd | 6 | 84.2.n.a.23.2 | yes | 24 | ||
28.19 | even | 6 | 588.2.n.e.263.7 | 24 | |||
28.23 | odd | 6 | 84.2.n.a.11.7 | yes | 24 | ||
28.27 | even | 2 | 588.2.e.d.491.10 | 12 | |||
84.11 | even | 6 | 84.2.n.a.23.11 | yes | 24 | ||
84.23 | even | 6 | 84.2.n.a.11.6 | yes | 24 | ||
84.47 | odd | 6 | 588.2.n.e.263.6 | 24 | |||
84.59 | odd | 6 | 588.2.n.e.275.11 | 24 | |||
84.83 | odd | 2 | 588.2.e.d.491.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.2.n.a.11.2 | ✓ | 24 | 21.2 | odd | 6 | ||
84.2.n.a.11.6 | yes | 24 | 84.23 | even | 6 | ||
84.2.n.a.11.7 | yes | 24 | 28.23 | odd | 6 | ||
84.2.n.a.11.11 | yes | 24 | 7.2 | even | 3 | ||
84.2.n.a.23.2 | yes | 24 | 28.11 | odd | 6 | ||
84.2.n.a.23.6 | yes | 24 | 7.4 | even | 3 | ||
84.2.n.a.23.7 | yes | 24 | 21.11 | odd | 6 | ||
84.2.n.a.23.11 | yes | 24 | 84.11 | even | 6 | ||
588.2.e.d.491.3 | 12 | 84.83 | odd | 2 | |||
588.2.e.d.491.4 | 12 | 7.6 | odd | 2 | |||
588.2.e.d.491.9 | 12 | 21.20 | even | 2 | |||
588.2.e.d.491.10 | 12 | 28.27 | even | 2 | |||
588.2.e.e.491.3 | 12 | 12.11 | even | 2 | inner | ||
588.2.e.e.491.4 | 12 | 1.1 | even | 1 | trivial | ||
588.2.e.e.491.9 | 12 | 3.2 | odd | 2 | inner | ||
588.2.e.e.491.10 | 12 | 4.3 | odd | 2 | inner | ||
588.2.n.e.263.2 | 24 | 21.5 | even | 6 | |||
588.2.n.e.263.6 | 24 | 84.47 | odd | 6 | |||
588.2.n.e.263.7 | 24 | 28.19 | even | 6 | |||
588.2.n.e.263.11 | 24 | 7.5 | odd | 6 | |||
588.2.n.e.275.2 | 24 | 28.3 | even | 6 | |||
588.2.n.e.275.6 | 24 | 7.3 | odd | 6 | |||
588.2.n.e.275.7 | 24 | 21.17 | even | 6 | |||
588.2.n.e.275.11 | 24 | 84.59 | odd | 6 |