Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(43,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.dk (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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(168\) |
Relative dimension: | \(84\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 43.21 | ||
Character | \(\chi\) | \(=\) | 819.43 |
Dual form | 819.2.dk.a.400.21 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.46243 | + | 0.844334i | −1.03409 | + | 0.597035i | −0.918155 | − | 0.396222i | \(-0.870321\pi\) |
−0.115939 | + | 0.993256i | \(0.536988\pi\) | |||||||
\(3\) | −1.54593 | − | 0.781091i | −0.892543 | − | 0.450963i | ||||
\(4\) | 0.425801 | − | 0.737510i | 0.212901 | − | 0.368755i | ||||
\(5\) | −1.72850 | + | 0.997952i | −0.773010 | + | 0.446298i | −0.833947 | − | 0.551844i | \(-0.813924\pi\) |
0.0609373 | + | 0.998142i | \(0.480591\pi\) | |||||||
\(6\) | 2.92032 | − | 0.162991i | 1.19221 | − | 0.0665408i | ||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | − | 1.93926i | − | 0.685633i | ||||||
\(9\) | 1.77979 | + | 2.41502i | 0.593265 | + | 0.805007i | ||||
\(10\) | 1.68521 | − | 2.91887i | 0.532910 | − | 0.923028i | ||||
\(11\) | −2.41437 | + | 1.39394i | −0.727961 | + | 0.420288i | −0.817676 | − | 0.575679i | \(-0.804738\pi\) |
0.0897149 | + | 0.995967i | \(0.471404\pi\) | |||||||
\(12\) | −1.23432 | + | 0.807548i | −0.356318 | + | 0.233119i | ||||
\(13\) | 2.53374 | + | 2.56518i | 0.702733 | + | 0.711454i | ||||
\(14\) | −0.844334 | − | 1.46243i | −0.225658 | − | 0.390851i | ||||
\(15\) | 3.45163 | − | 0.192645i | 0.891208 | − | 0.0497408i | ||||
\(16\) | 2.48899 | + | 4.31106i | 0.622247 | + | 1.07776i | ||||
\(17\) | 1.71694 | + | 2.97383i | 0.416420 | + | 0.721261i | 0.995576 | − | 0.0939559i | \(-0.0299513\pi\) |
−0.579156 | + | 0.815216i | \(0.696618\pi\) | |||||||
\(18\) | −4.64191 | − | 2.02906i | −1.09411 | − | 0.478254i | ||||
\(19\) | 2.55074 | − | 1.47267i | 0.585179 | − | 0.337853i | −0.178010 | − | 0.984029i | \(-0.556966\pi\) |
0.763189 | + | 0.646175i | \(0.223633\pi\) | |||||||
\(20\) | 1.69972i | 0.380068i | ||||||||
\(21\) | 0.781091 | − | 1.54593i | 0.170448 | − | 0.337349i | ||||
\(22\) | 2.35390 | − | 4.07708i | 0.501853 | − | 0.869236i | ||||
\(23\) | −0.868177 | −0.181027 | −0.0905137 | − | 0.995895i | \(-0.528851\pi\) | ||||
−0.0905137 | + | 0.995895i | \(0.528851\pi\) | |||||||
\(24\) | −1.51474 | + | 2.99796i | −0.309195 | + | 0.611957i | ||||
\(25\) | −0.508185 | + | 0.880202i | −0.101637 | + | 0.176040i | ||||
\(26\) | −5.87129 | − | 1.61208i | −1.15145 | − | 0.316154i | ||||
\(27\) | −0.865086 | − | 5.12363i | −0.166486 | − | 0.986044i | ||||
\(28\) | 0.737510 | + | 0.425801i | 0.139376 | + | 0.0804689i | ||||
\(29\) | 1.23510 | + | 2.13925i | 0.229351 | + | 0.397248i | 0.957616 | − | 0.288048i | \(-0.0930062\pi\) |
−0.728265 | + | 0.685296i | \(0.759673\pi\) | |||||||
\(30\) | −4.88512 | + | 3.19606i | −0.891896 | + | 0.583519i | ||||
\(31\) | −5.38232 | + | 3.10748i | −0.966693 | + | 0.558121i | −0.898227 | − | 0.439533i | \(-0.855144\pi\) |
−0.0684669 | + | 0.997653i | \(0.521811\pi\) | |||||||
\(32\) | −3.92104 | − | 2.26382i | −0.693149 | − | 0.400190i | ||||
\(33\) | 4.82124 | − | 0.269087i | 0.839271 | − | 0.0468420i | ||||
\(34\) | −5.02182 | − | 2.89935i | −0.861235 | − | 0.497234i | ||||
\(35\) | −0.997952 | − | 1.72850i | −0.168685 | − | 0.292170i | ||||
\(36\) | 2.53894 | − | 0.284296i | 0.423157 | − | 0.0473827i | ||||
\(37\) | 5.93039 | + | 3.42391i | 0.974950 | + | 0.562888i | 0.900742 | − | 0.434355i | \(-0.143024\pi\) |
0.0742085 | + | 0.997243i | \(0.476357\pi\) | |||||||
\(38\) | −2.48685 | + | 4.30735i | −0.403420 | + | 0.698745i | ||||
\(39\) | −1.91334 | − | 5.94467i | −0.306380 | − | 0.951909i | ||||
\(40\) | 1.93529 | + | 3.35202i | 0.305996 | + | 0.530001i | ||||
\(41\) | − | 2.25951i | − | 0.352877i | −0.984312 | − | 0.176438i | \(-0.943542\pi\) | ||
0.984312 | − | 0.176438i | \(-0.0564576\pi\) | |||||||
\(42\) | 0.162991 | + | 2.92032i | 0.0251500 | + | 0.450614i | ||||
\(43\) | 2.62202 | 0.399855 | 0.199927 | − | 0.979811i | \(-0.435929\pi\) | ||||
0.199927 | + | 0.979811i | \(0.435929\pi\) | |||||||
\(44\) | 2.37416i | 0.357919i | ||||||||
\(45\) | −5.48646 | − | 2.39822i | −0.817873 | − | 0.357506i | ||||
\(46\) | 1.26965 | − | 0.733032i | 0.187199 | − | 0.108080i | ||||
\(47\) | −4.45571 | − | 2.57250i | −0.649932 | − | 0.375238i | 0.138498 | − | 0.990363i | \(-0.455772\pi\) |
−0.788430 | + | 0.615125i | \(0.789106\pi\) | |||||||
\(48\) | −0.480476 | − | 8.60871i | −0.0693508 | − | 1.24256i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | − | 1.71631i | − | 0.242723i | ||||||
\(51\) | −0.331440 | − | 5.93843i | −0.0464109 | − | 0.831546i | ||||
\(52\) | 2.97072 | − | 0.776399i | 0.411964 | − | 0.107667i | ||||
\(53\) | −5.32084 | −0.730874 | −0.365437 | − | 0.930836i | \(-0.619080\pi\) | ||||
−0.365437 | + | 0.930836i | \(0.619080\pi\) | |||||||
\(54\) | 5.59119 | + | 6.76253i | 0.760864 | + | 0.920264i | ||||
\(55\) | 2.78217 | − | 4.81885i | 0.375147 | − | 0.649774i | ||||
\(56\) | 1.93926 | 0.259145 | ||||||||
\(57\) | −5.09355 | + | 0.284285i | −0.674657 | + | 0.0376545i | ||||
\(58\) | −3.61248 | − | 2.08567i | −0.474342 | − | 0.273861i | ||||
\(59\) | −10.8539 | − | 6.26651i | −1.41306 | − | 0.815830i | −0.417384 | − | 0.908730i | \(-0.637053\pi\) |
−0.995675 | + | 0.0928996i | \(0.970386\pi\) | |||||||
\(60\) | 1.32763 | − | 2.62764i | 0.171397 | − | 0.339227i | ||||
\(61\) | −6.66360 | −0.853186 | −0.426593 | − | 0.904444i | \(-0.640286\pi\) | ||||
−0.426593 | + | 0.904444i | \(0.640286\pi\) | |||||||
\(62\) | 5.24751 | − | 9.08896i | 0.666435 | − | 1.15430i | ||||
\(63\) | −2.41502 | + | 1.77979i | −0.304264 | + | 0.224233i | ||||
\(64\) | −2.31029 | −0.288786 | ||||||||
\(65\) | −6.93951 | − | 1.90538i | −0.860740 | − | 0.236333i | ||||
\(66\) | −6.82353 | + | 4.46426i | −0.839919 | + | 0.549513i | ||||
\(67\) | − | 2.09482i | − | 0.255923i | −0.991779 | − | 0.127962i | \(-0.959157\pi\) | ||
0.991779 | − | 0.127962i | \(-0.0408434\pi\) | |||||||
\(68\) | 2.92431 | 0.354624 | ||||||||
\(69\) | 1.34214 | + | 0.678125i | 0.161575 | + | 0.0816367i | ||||
\(70\) | 2.91887 | + | 1.68521i | 0.348872 | + | 0.201421i | ||||
\(71\) | −8.10653 | + | 4.68031i | −0.962068 | + | 0.555450i | −0.896809 | − | 0.442418i | \(-0.854121\pi\) |
−0.0652591 | + | 0.997868i | \(0.520787\pi\) | |||||||
\(72\) | 4.68336 | − | 3.45149i | 0.551939 | − | 0.406762i | ||||
\(73\) | − | 11.1596i | − | 1.30614i | −0.757298 | − | 0.653069i | \(-0.773481\pi\) | ||
0.757298 | − | 0.653069i | \(-0.226519\pi\) | |||||||
\(74\) | −11.5637 | −1.34425 | ||||||||
\(75\) | 1.47314 | − | 0.963792i | 0.170103 | − | 0.111289i | ||||
\(76\) | − | 2.50826i | − | 0.287717i | ||||||
\(77\) | −1.39394 | − | 2.41437i | −0.158854 | − | 0.275143i | ||||
\(78\) | 7.81742 | + | 7.07817i | 0.885149 | + | 0.801445i | ||||
\(79\) | 1.52947 | − | 2.64913i | 0.172079 | − | 0.298050i | −0.767067 | − | 0.641567i | \(-0.778285\pi\) |
0.939147 | + | 0.343517i | \(0.111618\pi\) | |||||||
\(80\) | −8.60445 | − | 4.96778i | −0.962007 | − | 0.555415i | ||||
\(81\) | −2.66466 | + | 8.59649i | −0.296073 | + | 0.955165i | ||||
\(82\) | 1.90778 | + | 3.30438i | 0.210680 | + | 0.364908i | ||||
\(83\) | 10.1113 | + | 5.83777i | 1.10986 | + | 0.640779i | 0.938793 | − | 0.344481i | \(-0.111945\pi\) |
0.171068 | + | 0.985259i | \(0.445278\pi\) | |||||||
\(84\) | −0.807548 | − | 1.23432i | −0.0881107 | − | 0.134675i | ||||
\(85\) | −5.93548 | − | 3.42685i | −0.643794 | − | 0.371694i | ||||
\(86\) | −3.83453 | + | 2.21387i | −0.413488 | + | 0.238727i | ||||
\(87\) | −0.238424 | − | 4.27185i | −0.0255617 | − | 0.457990i | ||||
\(88\) | 2.70321 | + | 4.68210i | 0.288164 | + | 0.499114i | ||||
\(89\) | −15.1919 | − | 8.77105i | −1.61034 | − | 0.929729i | −0.989291 | − | 0.145956i | \(-0.953374\pi\) |
−0.621047 | − | 0.783773i | \(-0.713293\pi\) | |||||||
\(90\) | 10.0485 | − | 1.12517i | 1.05920 | − | 0.118603i | ||||
\(91\) | −2.56518 | + | 2.53374i | −0.268904 | + | 0.265608i | ||||
\(92\) | −0.369671 | + | 0.640289i | −0.0385409 | + | 0.0667547i | ||||
\(93\) | 10.7479 | − | 0.599871i | 1.11451 | − | 0.0622037i | ||||
\(94\) | 8.68821 | 0.896121 | ||||||||
\(95\) | −2.93931 | + | 5.09103i | −0.301566 | + | 0.522328i | ||||
\(96\) | 4.29341 | + | 6.56239i | 0.438195 | + | 0.669771i | ||||
\(97\) | − | 6.73005i | − | 0.683333i | −0.939821 | − | 0.341666i | \(-0.889009\pi\) | ||
0.939821 | − | 0.341666i | \(-0.110991\pi\) | |||||||
\(98\) | 1.46243 | − | 0.844334i | 0.147728 | − | 0.0852907i | ||||
\(99\) | −7.66348 | − | 3.34984i | −0.770209 | − | 0.336671i | ||||
\(100\) | 0.432772 | + | 0.749583i | 0.0432772 | + | 0.0749583i | ||||
\(101\) | 8.20621 | + | 14.2136i | 0.816549 | + | 1.41430i | 0.908211 | + | 0.418514i | \(0.137449\pi\) |
−0.0916619 | + | 0.995790i | \(0.529218\pi\) | |||||||
\(102\) | 5.49873 | + | 8.40469i | 0.544455 | + | 0.832188i | ||||
\(103\) | −7.50261 | − | 12.9949i | −0.739254 | − | 1.28043i | −0.952831 | − | 0.303500i | \(-0.901845\pi\) |
0.213577 | − | 0.976926i | \(-0.431489\pi\) | |||||||
\(104\) | 4.97456 | − | 4.91359i | 0.487796 | − | 0.481817i | ||||
\(105\) | 0.192645 | + | 3.45163i | 0.0188003 | + | 0.336845i | ||||
\(106\) | 7.78136 | − | 4.49257i | 0.755793 | − | 0.436357i | ||||
\(107\) | 0.0702618 | − | 0.121697i | 0.00679246 | − | 0.0117649i | −0.862609 | − | 0.505871i | \(-0.831171\pi\) |
0.869402 | + | 0.494106i | \(0.164505\pi\) | |||||||
\(108\) | −4.14708 | − | 1.54364i | −0.399053 | − | 0.148537i | ||||
\(109\) | − | 4.84617i | − | 0.464179i | −0.972694 | − | 0.232090i | \(-0.925444\pi\) | ||
0.972694 | − | 0.232090i | \(-0.0745563\pi\) | |||||||
\(110\) | 9.39632i | 0.895904i | ||||||||
\(111\) | −6.49358 | − | 9.92530i | −0.616343 | − | 0.942068i | ||||
\(112\) | −4.31106 | + | 2.48899i | −0.407356 | + | 0.235187i | ||||
\(113\) | 3.67709 | − | 6.36891i | 0.345912 | − | 0.599137i | −0.639607 | − | 0.768702i | \(-0.720903\pi\) |
0.985519 | + | 0.169565i | \(0.0542363\pi\) | |||||||
\(114\) | 7.20893 | − | 4.71641i | 0.675178 | − | 0.441732i | ||||
\(115\) | 1.50065 | − | 0.866399i | 0.139936 | − | 0.0807921i | ||||
\(116\) | 2.10362 | 0.195316 | ||||||||
\(117\) | −1.68544 | + | 10.6845i | −0.155819 | + | 0.987786i | ||||
\(118\) | 21.1641 | 1.94832 | ||||||||
\(119\) | −2.97383 | + | 1.71694i | −0.272611 | + | 0.157392i | ||||
\(120\) | −0.373590 | − | 6.69363i | −0.0341039 | − | 0.611042i | ||||
\(121\) | −1.61387 | + | 2.79530i | −0.146715 | + | 0.254119i | ||||
\(122\) | 9.74505 | − | 5.62631i | 0.882275 | − | 0.509382i | ||||
\(123\) | −1.76488 | + | 3.49305i | −0.159134 | + | 0.314957i | ||||
\(124\) | 5.29269i | 0.475297i | ||||||||
\(125\) | − | 12.0081i | − | 1.07404i | ||||||
\(126\) | 2.02906 | − | 4.64191i | 0.180763 | − | 0.413534i | ||||
\(127\) | −9.45530 | + | 16.3771i | −0.839022 | + | 1.45323i | 0.0516908 | + | 0.998663i | \(0.483539\pi\) |
−0.890713 | + | 0.454566i | \(0.849794\pi\) | |||||||
\(128\) | 11.2207 | − | 6.47829i | 0.991781 | − | 0.572605i | ||||
\(129\) | −4.05346 | − | 2.04804i | −0.356888 | − | 0.180320i | ||||
\(130\) | 11.7573 | − | 3.07278i | 1.03118 | − | 0.269501i | ||||
\(131\) | 8.27462 | + | 14.3321i | 0.722957 | + | 1.25220i | 0.959809 | + | 0.280653i | \(0.0905510\pi\) |
−0.236852 | + | 0.971546i | \(0.576116\pi\) | |||||||
\(132\) | 1.85444 | − | 3.67029i | 0.161408 | − | 0.319458i | ||||
\(133\) | 1.47267 | + | 2.55074i | 0.127697 | + | 0.221177i | ||||
\(134\) | 1.76873 | + | 3.06353i | 0.152795 | + | 0.264649i | ||||
\(135\) | 6.60844 | + | 7.99290i | 0.568764 | + | 0.687919i | ||||
\(136\) | 5.76705 | − | 3.32960i | 0.494520 | − | 0.285511i | ||||
\(137\) | 13.6505i | 1.16624i | 0.812386 | + | 0.583119i | \(0.198168\pi\) | ||||
−0.812386 | + | 0.583119i | \(0.801832\pi\) | |||||||
\(138\) | −2.53535 | + | 0.141505i | −0.215823 | + | 0.0120457i | ||||
\(139\) | 3.26986 | − | 5.66357i | 0.277346 | − | 0.480378i | −0.693378 | − | 0.720574i | \(-0.743878\pi\) |
0.970724 | + | 0.240196i | \(0.0772118\pi\) | |||||||
\(140\) | −1.69972 | −0.143652 | ||||||||
\(141\) | 4.87885 | + | 7.45722i | 0.410873 | + | 0.628011i | ||||
\(142\) | 7.90349 | − | 13.6892i | 0.663246 | − | 1.14878i | ||||
\(143\) | −9.69310 | − | 2.66143i | −0.810578 | − | 0.222560i | ||||
\(144\) | −5.98140 | + | 13.6838i | −0.498450 | + | 1.14031i | ||||
\(145\) | −4.26973 | − | 2.46513i | −0.354582 | − | 0.204718i | ||||
\(146\) | 9.42247 | + | 16.3202i | 0.779810 | + | 1.35067i | ||||
\(147\) | 1.54593 | + | 0.781091i | 0.127506 | + | 0.0644233i | ||||
\(148\) | 5.05034 | − | 2.91581i | 0.415135 | − | 0.239678i | ||||
\(149\) | −11.5562 | − | 6.67200i | −0.946724 | − | 0.546591i | −0.0546620 | − | 0.998505i | \(-0.517408\pi\) |
−0.892062 | + | 0.451914i | \(0.850741\pi\) | |||||||
\(150\) | −1.34060 | + | 2.65330i | −0.109459 | + | 0.216641i | ||||
\(151\) | −8.62281 | − | 4.97838i | −0.701714 | − | 0.405135i | 0.106271 | − | 0.994337i | \(-0.466109\pi\) |
−0.807986 | + | 0.589202i | \(0.799442\pi\) | |||||||
\(152\) | −2.85589 | − | 4.94655i | −0.231643 | − | 0.401218i | ||||
\(153\) | −4.12607 | + | 9.43927i | −0.333573 | + | 0.763120i | ||||
\(154\) | 4.07708 | + | 2.35390i | 0.328540 | + | 0.189683i | ||||
\(155\) | 6.20224 | − | 10.7426i | 0.498176 | − | 0.862866i | ||||
\(156\) | −5.19896 | − | 1.12014i | −0.416250 | − | 0.0896831i | ||||
\(157\) | 4.45576 | + | 7.71761i | 0.355609 | + | 0.615932i | 0.987222 | − | 0.159351i | \(-0.0509403\pi\) |
−0.631613 | + | 0.775284i | \(0.717607\pi\) | |||||||
\(158\) | 5.16555i | 0.410949i | ||||||||
\(159\) | 8.22565 | + | 4.15606i | 0.652336 | + | 0.329597i | ||||
\(160\) | 9.03672 | 0.714415 | ||||||||
\(161\) | − | 0.868177i | − | 0.0684219i | ||||||
\(162\) | −3.36143 | − | 14.8216i | −0.264099 | − | 1.16450i | ||||
\(163\) | −3.27438 | + | 1.89046i | −0.256469 | + | 0.148072i | −0.622723 | − | 0.782443i | \(-0.713974\pi\) |
0.366254 | + | 0.930515i | \(0.380640\pi\) | |||||||
\(164\) | −1.66641 | − | 0.962104i | −0.130125 | − | 0.0751277i | ||||
\(165\) | −8.06500 | + | 5.27648i | −0.627859 | + | 0.410774i | ||||
\(166\) | −19.7161 | −1.53027 | ||||||||
\(167\) | − | 6.91053i | − | 0.534753i | −0.963592 | − | 0.267376i | \(-0.913843\pi\) | ||
0.963592 | − | 0.267376i | \(-0.0861567\pi\) | |||||||
\(168\) | −2.99796 | − | 1.51474i | −0.231298 | − | 0.116865i | ||||
\(169\) | −0.160326 | + | 12.9990i | −0.0123328 | + | 0.999924i | ||||
\(170\) | 11.5736 | 0.887658 | ||||||||
\(171\) | 8.09632 | + | 3.53904i | 0.619141 | + | 0.270637i | ||||
\(172\) | 1.11646 | − | 1.93377i | 0.0851294 | − | 0.147448i | ||||
\(173\) | 2.50499 | 0.190451 | 0.0952253 | − | 0.995456i | \(-0.469643\pi\) | ||||
0.0952253 | + | 0.995456i | \(0.469643\pi\) | |||||||
\(174\) | 3.95555 | + | 6.04597i | 0.299869 | + | 0.458344i | ||||
\(175\) | −0.880202 | − | 0.508185i | −0.0665370 | − | 0.0384152i | ||||
\(176\) | −12.0187 | − | 6.93900i | −0.905943 | − | 0.523047i | ||||
\(177\) | 11.8847 | + | 18.1655i | 0.893307 | + | 1.36540i | ||||
\(178\) | 29.6228 | 2.22032 | ||||||||
\(179\) | 3.24947 | − | 5.62826i | 0.242877 | − | 0.420676i | −0.718655 | − | 0.695366i | \(-0.755242\pi\) |
0.961533 | + | 0.274691i | \(0.0885755\pi\) | |||||||
\(180\) | −4.10485 | + | 3.02515i | −0.305958 | + | 0.225481i | ||||
\(181\) | 3.19266 | 0.237308 | 0.118654 | − | 0.992936i | \(-0.462142\pi\) | ||||
0.118654 | + | 0.992936i | \(0.462142\pi\) | |||||||
\(182\) | 1.61208 | − | 5.87129i | 0.119495 | − | 0.435209i | ||||
\(183\) | 10.3015 | + | 5.20487i | 0.761505 | + | 0.384755i | ||||
\(184\) | 1.68362i | 0.124118i | ||||||||
\(185\) | −13.6676 | −1.00486 | ||||||||
\(186\) | −15.2116 | + | 9.95211i | −1.11537 | + | 0.729724i | ||||
\(187\) | −8.29068 | − | 4.78663i | −0.606275 | − | 0.350033i | ||||
\(188\) | −3.79449 | + | 2.19075i | −0.276742 | + | 0.159777i | ||||
\(189\) | 5.12363 | − | 0.865086i | 0.372690 | − | 0.0629258i | ||||
\(190\) | − | 9.92703i | − | 0.720182i | ||||||
\(191\) | 1.41069 | 0.102074 | 0.0510368 | − | 0.998697i | \(-0.483747\pi\) | ||||
0.0510368 | + | 0.998697i | \(0.483747\pi\) | |||||||
\(192\) | 3.57154 | + | 1.80454i | 0.257754 | + | 0.130232i | ||||
\(193\) | 20.8476i | 1.50064i | 0.661074 | + | 0.750321i | \(0.270101\pi\) | ||||
−0.661074 | + | 0.750321i | \(0.729899\pi\) | |||||||
\(194\) | 5.68241 | + | 9.84223i | 0.407973 | + | 0.706631i | ||||
\(195\) | 9.23971 | + | 8.36596i | 0.661670 | + | 0.599099i | ||||
\(196\) | −0.425801 | + | 0.737510i | −0.0304144 | + | 0.0526793i | ||||
\(197\) | 24.1325 | + | 13.9329i | 1.71937 | + | 0.992678i | 0.920079 | + | 0.391733i | \(0.128124\pi\) |
0.799290 | + | 0.600946i | \(0.205209\pi\) | |||||||
\(198\) | 14.0357 | − | 1.57164i | 0.997473 | − | 0.111691i | ||||
\(199\) | −7.69090 | − | 13.3210i | −0.545194 | − | 0.944303i | −0.998595 | − | 0.0529966i | \(-0.983123\pi\) |
0.453401 | − | 0.891307i | \(-0.350211\pi\) | |||||||
\(200\) | 1.70694 | + | 0.985504i | 0.120699 | + | 0.0696857i | ||||
\(201\) | −1.63624 | + | 3.23844i | −0.115412 | + | 0.228422i | ||||
\(202\) | −24.0020 | − | 13.8576i | −1.68878 | − | 0.975016i | ||||
\(203\) | −2.13925 | + | 1.23510i | −0.150146 | + | 0.0866867i | ||||
\(204\) | −4.52077 | − | 2.28415i | −0.316517 | − | 0.159922i | ||||
\(205\) | 2.25488 | + | 3.90557i | 0.157488 | + | 0.272777i | ||||
\(206\) | 21.9441 | + | 12.6694i | 1.52892 | + | 0.882721i | ||||
\(207\) | −1.54518 | − | 2.09667i | −0.107397 | − | 0.145728i | ||||
\(208\) | −4.75220 | + | 17.3078i | −0.329505 | + | 1.20008i | ||||
\(209\) | −4.10562 | + | 7.11114i | −0.283992 | + | 0.491888i | ||||
\(210\) | −3.19606 | − | 4.88512i | −0.220549 | − | 0.337105i | ||||
\(211\) | −12.6991 | −0.874241 | −0.437121 | − | 0.899403i | \(-0.644002\pi\) | ||||
−0.437121 | + | 0.899403i | \(0.644002\pi\) | |||||||
\(212\) | −2.26562 | + | 3.92417i | −0.155604 | + | 0.269513i | ||||
\(213\) | 16.1879 | − | 0.903490i | 1.10917 | − | 0.0619061i | ||||
\(214\) | 0.237298i | 0.0162213i | ||||||||
\(215\) | −4.53218 | + | 2.61665i | −0.309092 | + | 0.178454i | ||||
\(216\) | −9.93607 | + | 1.67763i | −0.676064 | + | 0.114148i | ||||
\(217\) | −3.10748 | − | 5.38232i | −0.210950 | − | 0.365376i | ||||
\(218\) | 4.09179 | + | 7.08719i | 0.277131 | + | 0.480005i | ||||
\(219\) | −8.71670 | + | 17.2520i | −0.589020 | + | 1.16578i | ||||
\(220\) | −2.36930 | − | 4.10375i | −0.159738 | − | 0.276675i | ||||
\(221\) | −3.27814 | + | 11.9392i | −0.220511 | + | 0.803117i | ||||
\(222\) | 17.8767 | + | 9.03231i | 1.19980 | + | 0.606209i | ||||
\(223\) | 11.2449 | − | 6.49225i | 0.753014 | − | 0.434753i | −0.0737678 | − | 0.997275i | \(-0.523502\pi\) |
0.826782 | + | 0.562522i | \(0.190169\pi\) | |||||||
\(224\) | 2.26382 | − | 3.92104i | 0.151258 | − | 0.261986i | ||||
\(225\) | −3.03017 | + | 0.339302i | −0.202011 | + | 0.0226201i | ||||
\(226\) | 12.4188i | 0.826086i | ||||||||
\(227\) | − | 17.4205i | − | 1.15624i | −0.815951 | − | 0.578121i | \(-0.803786\pi\) | ||
0.815951 | − | 0.578121i | \(-0.196214\pi\) | |||||||
\(228\) | −1.95918 | + | 3.87759i | −0.129750 | + | 0.256800i | ||||
\(229\) | −17.6524 | + | 10.1916i | −1.16651 | + | 0.673482i | −0.952855 | − | 0.303428i | \(-0.901869\pi\) |
−0.213651 | + | 0.976910i | \(0.568536\pi\) | |||||||
\(230\) | −1.46306 | + | 2.53410i | −0.0964714 | + | 0.167093i | ||||
\(231\) | 0.269087 | + | 4.82124i | 0.0177046 | + | 0.317214i | ||||
\(232\) | 4.14856 | − | 2.39517i | 0.272367 | − | 0.157251i | ||||
\(233\) | 9.05169 | 0.592996 | 0.296498 | − | 0.955033i | \(-0.404181\pi\) | ||||
0.296498 | + | 0.955033i | \(0.404181\pi\) | |||||||
\(234\) | −6.55649 | − | 17.0485i | −0.428611 | − | 1.11449i | ||||
\(235\) | 10.2689 | 0.669871 | ||||||||
\(236\) | −9.24323 | + | 5.33658i | −0.601683 | + | 0.347382i | ||||
\(237\) | −4.43367 | + | 2.90070i | −0.287998 | + | 0.188421i | ||||
\(238\) | 2.89935 | − | 5.02182i | 0.187937 | − | 0.325516i | ||||
\(239\) | −1.63695 | + | 0.945095i | −0.105886 | + | 0.0611331i | −0.552008 | − | 0.833839i | \(-0.686138\pi\) |
0.446122 | + | 0.894972i | \(0.352805\pi\) | |||||||
\(240\) | 9.42158 | + | 14.4007i | 0.608161 | + | 0.929561i | ||||
\(241\) | − | 7.29591i | − | 0.469971i | −0.971999 | − | 0.234985i | \(-0.924496\pi\) | ||
0.971999 | − | 0.234985i | \(-0.0755042\pi\) | |||||||
\(242\) | − | 5.45058i | − | 0.350377i | ||||||
\(243\) | 10.8340 | − | 11.2082i | 0.695002 | − | 0.719008i | ||||
\(244\) | −2.83737 | + | 4.91447i | −0.181644 | + | 0.314617i | ||||
\(245\) | 1.72850 | − | 0.997952i | 0.110430 | − | 0.0637568i | ||||
\(246\) | −0.368280 | − | 6.59849i | −0.0234807 | − | 0.420704i | ||||
\(247\) | 10.2406 | + | 2.81175i | 0.651592 | + | 0.178907i | ||||
\(248\) | 6.02623 | + | 10.4377i | 0.382666 | + | 0.662797i | ||||
\(249\) | −11.0716 | − | 16.9226i | −0.701631 | − | 1.07243i | ||||
\(250\) | 10.1388 | + | 17.5610i | 0.641237 | + | 1.11065i | ||||
\(251\) | 4.24362 | + | 7.35017i | 0.267855 | + | 0.463938i | 0.968308 | − | 0.249760i | \(-0.0803519\pi\) |
−0.700453 | + | 0.713699i | \(0.747019\pi\) | |||||||
\(252\) | 0.284296 | + | 2.53894i | 0.0179090 | + | 0.159938i | ||||
\(253\) | 2.09610 | − | 1.21019i | 0.131781 | − | 0.0760837i | ||||
\(254\) | − | 31.9337i | − | 2.00370i | ||||||
\(255\) | 6.49916 | + | 9.93383i | 0.406993 | + | 0.622080i | ||||
\(256\) | −8.62939 | + | 14.9465i | −0.539337 | + | 0.934159i | ||||
\(257\) | −14.8145 | −0.924106 | −0.462053 | − | 0.886852i | \(-0.652887\pi\) | ||||
−0.462053 | + | 0.886852i | \(0.652887\pi\) | |||||||
\(258\) | 7.65714 | − | 0.427366i | 0.476713 | − | 0.0266067i | ||||
\(259\) | −3.42391 | + | 5.93039i | −0.212752 | + | 0.368497i | ||||
\(260\) | −4.36008 | + | 4.30664i | −0.270401 | + | 0.267086i | ||||
\(261\) | −2.96811 | + | 6.79020i | −0.183722 | + | 0.420303i | ||||
\(262\) | −24.2021 | − | 13.9731i | −1.49521 | − | 0.863261i | ||||
\(263\) | 9.08834 | + | 15.7415i | 0.560411 | + | 0.970660i | 0.997460 | + | 0.0712226i | \(0.0226901\pi\) |
−0.437050 | + | 0.899437i | \(0.643977\pi\) | |||||||
\(264\) | −0.521830 | − | 9.34965i | −0.0321164 | − | 0.575431i | ||||
\(265\) | 9.19709 | − | 5.30994i | 0.564973 | − | 0.326187i | ||||
\(266\) | −4.30735 | − | 2.48685i | −0.264101 | − | 0.152479i | ||||
\(267\) | 16.6346 | + | 25.4257i | 1.01802 | + | 1.55603i | ||||
\(268\) | −1.54495 | − | 0.891978i | −0.0943729 | − | 0.0544862i | ||||
\(269\) | 1.10712 | + | 1.91759i | 0.0675022 | + | 0.116917i | 0.897801 | − | 0.440401i | \(-0.145164\pi\) |
−0.830299 | + | 0.557318i | \(0.811830\pi\) | |||||||
\(270\) | −16.4131 | − | 6.10932i | −0.998868 | − | 0.371802i | ||||
\(271\) | −27.8583 | − | 16.0840i | −1.69227 | − | 0.977032i | −0.952681 | − | 0.303971i | \(-0.901687\pi\) |
−0.739587 | − | 0.673061i | \(-0.764979\pi\) | |||||||
\(272\) | −8.54691 | + | 14.8037i | −0.518232 | + | 0.897605i | ||||
\(273\) | 5.94467 | − | 1.91334i | 0.359788 | − | 0.115801i | ||||
\(274\) | −11.5256 | − | 19.9629i | −0.696285 | − | 1.20600i | ||||
\(275\) | − | 2.83351i | − | 0.170867i | ||||||
\(276\) | 1.07161 | − | 0.701095i | 0.0645033 | − | 0.0422010i | ||||
\(277\) | −14.5777 | −0.875889 | −0.437945 | − | 0.899002i | \(-0.644293\pi\) | ||||
−0.437945 | + | 0.899002i | \(0.644293\pi\) | |||||||
\(278\) | 11.0434i | 0.662341i | ||||||||
\(279\) | −17.0841 | − | 7.46774i | −1.02280 | − | 0.447082i | ||||
\(280\) | −3.35202 | + | 1.93529i | −0.200322 | + | 0.115656i | ||||
\(281\) | −10.3688 | − | 5.98643i | −0.618551 | − | 0.357121i | 0.157754 | − | 0.987479i | \(-0.449575\pi\) |
−0.776305 | + | 0.630358i | \(0.782908\pi\) | |||||||
\(282\) | −13.4314 | − | 6.78628i | −0.799826 | − | 0.404117i | ||||
\(283\) | −0.829075 | −0.0492834 | −0.0246417 | − | 0.999696i | \(-0.507844\pi\) | ||||
−0.0246417 | + | 0.999696i | \(0.507844\pi\) | |||||||
\(284\) | 7.97152i | 0.473023i | ||||||||
\(285\) | 8.52051 | − | 5.57450i | 0.504711 | − | 0.330205i | ||||
\(286\) | 16.4226 | − | 4.29206i | 0.971090 | − | 0.253795i | ||||
\(287\) | 2.25951 | 0.133375 | ||||||||
\(288\) | −1.51149 | − | 13.4985i | −0.0890654 | − | 0.795409i | ||||
\(289\) | 2.60421 | − | 4.51062i | 0.153189 | − | 0.265331i | ||||
\(290\) | 8.32558 | 0.488895 | ||||||||
\(291\) | −5.25678 | + | 10.4042i | −0.308158 | + | 0.609904i | ||||
\(292\) | −8.23035 | − | 4.75179i | −0.481645 | − | 0.278078i | ||||
\(293\) | −8.27809 | − | 4.77936i | −0.483611 | − | 0.279213i | 0.238309 | − | 0.971189i | \(-0.423407\pi\) |
−0.721920 | + | 0.691976i | \(0.756740\pi\) | |||||||
\(294\) | −2.92032 | + | 0.162991i | −0.170316 | + | 0.00950582i | ||||
\(295\) | 25.0147 | 1.45641 | ||||||||
\(296\) | 6.63987 | − | 11.5006i | 0.385934 | − | 0.668458i | ||||
\(297\) | 9.23067 | + | 11.1645i | 0.535618 | + | 0.647829i | ||||
\(298\) | 22.5336 | 1.30534 | ||||||||
\(299\) | −2.19973 | − | 2.22703i | −0.127214 | − | 0.128793i | ||||
\(300\) | −0.0835426 | − | 1.49684i | −0.00482333 | − | 0.0864198i | ||||
\(301\) | 2.62202i | 0.151131i | ||||||||
\(302\) | 16.8137 | 0.967518 | ||||||||
\(303\) | −1.58413 | − | 28.3830i | −0.0910061 | − | 1.63056i | ||||
\(304\) | 12.6975 | + | 7.33091i | 0.728253 | + | 0.420457i | ||||
\(305\) | 11.5181 | − | 6.64995i | 0.659522 | − | 0.380775i | ||||
\(306\) | −1.93582 | − | 17.2881i | −0.110663 | − | 0.988292i | ||||
\(307\) | − | 20.1396i | − | 1.14943i | −0.818354 | − | 0.574714i | \(-0.805113\pi\) | ||
0.818354 | − | 0.574714i | \(-0.194887\pi\) | |||||||
\(308\) | −2.37416 | −0.135281 | ||||||||
\(309\) | 1.44831 | + | 25.9494i | 0.0823915 | + | 1.47621i | ||||
\(310\) | 20.9471i | 1.18971i | ||||||||
\(311\) | −9.02063 | − | 15.6242i | −0.511513 | − | 0.885966i | −0.999911 | − | 0.0133452i | \(-0.995752\pi\) |
0.488398 | − | 0.872621i | \(-0.337581\pi\) | |||||||
\(312\) | −11.5283 | + | 3.71047i | −0.652660 | + | 0.210064i | ||||
\(313\) | 7.49785 | − | 12.9867i | 0.423803 | − | 0.734049i | −0.572504 | − | 0.819902i | \(-0.694028\pi\) |
0.996308 | + | 0.0858526i | \(0.0273614\pi\) | |||||||
\(314\) | −13.0325 | − | 7.52431i | −0.735466 | − | 0.424621i | ||||
\(315\) | 2.39822 | − | 5.48646i | 0.135125 | − | 0.309127i | ||||
\(316\) | −1.30250 | − | 2.25600i | −0.0732716 | − | 0.126910i | ||||
\(317\) | −14.3390 | − | 8.27865i | −0.805361 | − | 0.464975i | 0.0399812 | − | 0.999200i | \(-0.487270\pi\) |
−0.845342 | + | 0.534225i | \(0.820604\pi\) | |||||||
\(318\) | −15.5385 | + | 0.867249i | −0.871358 | + | 0.0486329i | ||||
\(319\) | −5.96396 | − | 3.44329i | −0.333918 | − | 0.192787i | ||||
\(320\) | 3.99333 | − | 2.30555i | 0.223234 | − | 0.128884i | ||||
\(321\) | −0.203676 | + | 0.133254i | −0.0113681 | + | 0.00743752i | ||||
\(322\) | 0.733032 | + | 1.26965i | 0.0408503 | + | 0.0707547i | ||||
\(323\) | 8.75895 | + | 5.05698i | 0.487361 | + | 0.281378i | ||||
\(324\) | 5.20538 | + | 5.62561i | 0.289188 | + | 0.312534i | ||||
\(325\) | −3.54549 | + | 0.926616i | −0.196668 | + | 0.0513994i | ||||
\(326\) | 3.19236 | − | 5.52934i | 0.176809 | − | 0.306242i | ||||
\(327\) | −3.78530 | + | 7.49184i | −0.209328 | + | 0.414300i | ||||
\(328\) | −4.38179 | −0.241944 | ||||||||
\(329\) | 2.57250 | − | 4.45571i | 0.141827 | − | 0.245651i | ||||
\(330\) | 7.33938 | − | 14.5260i | 0.404019 | − | 0.799632i | ||||
\(331\) | 29.4568i | 1.61909i | 0.587055 | + | 0.809547i | \(0.300287\pi\) | ||||
−0.587055 | + | 0.809547i | \(0.699713\pi\) | |||||||
\(332\) | 8.61083 | − | 4.97146i | 0.472580 | − | 0.272844i | ||||
\(333\) | 2.28606 | + | 20.4159i | 0.125275 | + | 1.11878i | ||||
\(334\) | 5.83480 | + | 10.1062i | 0.319266 | + | 0.552985i | ||||
\(335\) | 2.09053 | + | 3.62090i | 0.114218 | + | 0.197831i | ||||
\(336\) | 8.60871 | − | 0.480476i | 0.469644 | − | 0.0262121i | ||||
\(337\) | 4.54514 | + | 7.87241i | 0.247590 | + | 0.428838i | 0.962857 | − | 0.270014i | \(-0.0870282\pi\) |
−0.715267 | + | 0.698851i | \(0.753695\pi\) | |||||||
\(338\) | −10.7410 | − | 19.1455i | −0.584236 | − | 1.04138i | ||||
\(339\) | −10.6592 | + | 6.97375i | −0.578930 | + | 0.378762i | ||||
\(340\) | −5.05468 | + | 2.91832i | −0.274128 | + | 0.158268i | ||||
\(341\) | 8.66329 | − | 15.0053i | 0.469143 | − | 0.812580i | ||||
\(342\) | −14.8284 | + | 1.66040i | −0.801830 | + | 0.0897844i | ||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | − | 5.08479i | − | 0.274154i | ||||||
\(345\) | −2.99663 | + | 0.167250i | −0.161333 | + | 0.00900445i | ||||
\(346\) | −3.66337 | + | 2.11505i | −0.196944 | + | 0.113706i | ||||
\(347\) | 9.90030 | − | 17.1478i | 0.531476 | − | 0.920543i | −0.467849 | − | 0.883808i | \(-0.654971\pi\) |
0.999325 | − | 0.0367349i | \(-0.0116957\pi\) | |||||||
\(348\) | −3.25205 | − | 1.64312i | −0.174328 | − | 0.0880804i | ||||
\(349\) | −4.28595 | + | 2.47449i | −0.229422 | + | 0.132457i | −0.610305 | − | 0.792166i | \(-0.708953\pi\) |
0.380884 | + | 0.924623i | \(0.375620\pi\) | |||||||
\(350\) | 1.71631 | 0.0917408 | ||||||||
\(351\) | 10.9512 | − | 15.2011i | 0.584529 | − | 0.811373i | ||||
\(352\) | 12.6225 | 0.672781 | ||||||||
\(353\) | −5.12091 | + | 2.95656i | −0.272559 | + | 0.157362i | −0.630050 | − | 0.776555i | \(-0.716966\pi\) |
0.357491 | + | 0.933917i | \(0.383632\pi\) | |||||||
\(354\) | −32.7183 | − | 16.5311i | −1.73896 | − | 0.878618i | ||||
\(355\) | 9.34144 | − | 16.1798i | 0.495792 | − | 0.858737i | ||||
\(356\) | −12.9375 | + | 7.46945i | −0.685684 | + | 0.395880i | ||||
\(357\) | 5.93843 | − | 0.331440i | 0.314295 | − | 0.0175417i | ||||
\(358\) | 10.9746i | 0.580024i | ||||||||
\(359\) | − | 12.9428i | − | 0.683097i | −0.939864 | − | 0.341549i | \(-0.889049\pi\) | ||
0.939864 | − | 0.341549i | \(-0.110951\pi\) | |||||||
\(360\) | −4.65078 | + | 10.6397i | −0.245118 | + | 0.560760i | ||||
\(361\) | −5.16249 | + | 8.94170i | −0.271710 | + | 0.470616i | ||||
\(362\) | −4.66904 | + | 2.69567i | −0.245399 | + | 0.141681i | ||||
\(363\) | 4.67831 | − | 3.06076i | 0.245548 | − | 0.160648i | ||||
\(364\) | 0.776399 | + | 2.97072i | 0.0406944 | + | 0.155708i | ||||
\(365\) | 11.1368 | + | 19.2895i | 0.582926 | + | 1.00966i | ||||
\(366\) | −19.4598 | + | 1.08611i | −1.01718 | + | 0.0567717i | ||||
\(367\) | −6.03155 | − | 10.4470i | −0.314844 | − | 0.545327i | 0.664560 | − | 0.747235i | \(-0.268619\pi\) |
−0.979404 | + | 0.201908i | \(0.935286\pi\) | |||||||
\(368\) | −2.16088 | − | 3.74276i | −0.112644 | − | 0.195105i | ||||
\(369\) | 5.45677 | − | 4.02147i | 0.284068 | − | 0.209349i | ||||
\(370\) | 19.9879 | − | 11.5400i | 1.03912 | − | 0.599937i | ||||
\(371\) | − | 5.32084i | − | 0.276244i | ||||||
\(372\) | 4.13407 | − | 8.18212i | 0.214341 | − | 0.424223i | ||||
\(373\) | 8.63603 | − | 14.9580i | 0.447157 | − | 0.774498i | −0.551043 | − | 0.834477i | \(-0.685770\pi\) |
0.998200 | + | 0.0599786i | \(0.0191033\pi\) | |||||||
\(374\) | 16.1661 | 0.835927 | ||||||||
\(375\) | −9.37941 | + | 18.5637i | −0.484351 | + | 0.958623i | ||||
\(376\) | −4.98876 | + | 8.64078i | −0.257276 | + | 0.445614i | ||||
\(377\) | −2.35815 | + | 8.58854i | −0.121451 | + | 0.442332i | ||||
\(378\) | −6.76253 | + | 5.59119i | −0.347827 | + | 0.287580i | ||||
\(379\) | −2.37432 | − | 1.37082i | −0.121961 | − | 0.0704141i | 0.437778 | − | 0.899083i | \(-0.355765\pi\) |
−0.559739 | + | 0.828669i | \(0.689099\pi\) | |||||||
\(380\) | 2.50312 | + | 4.33553i | 0.128407 | + | 0.222408i | ||||
\(381\) | 27.4092 | − | 17.9323i | 1.40422 | − | 0.918701i | ||||
\(382\) | −2.06303 | + | 1.19109i | −0.105554 | + | 0.0609415i | ||||
\(383\) | −14.9816 | − | 8.64962i | −0.765523 | − | 0.441975i | 0.0657520 | − | 0.997836i | \(-0.479055\pi\) |
−0.831275 | + | 0.555861i | \(0.812389\pi\) | |||||||
\(384\) | −22.4066 | + | 1.25057i | −1.14343 | + | 0.0638180i | ||||
\(385\) | 4.81885 | + | 2.78217i | 0.245592 | + | 0.141792i | ||||
\(386\) | −17.6023 | − | 30.4881i | −0.895935 | − | 1.55180i | ||||
\(387\) | 4.66667 | + | 6.33225i | 0.237220 | + | 0.321886i | ||||
\(388\) | −4.96348 | − | 2.86566i | −0.251982 | − | 0.145482i | ||||
\(389\) | 15.1685 | − | 26.2725i | 0.769071 | − | 1.33207i | −0.168995 | − | 0.985617i | \(-0.554052\pi\) |
0.938067 | − | 0.346454i | \(-0.112614\pi\) | |||||||
\(390\) | −20.5761 | − | 4.43322i | −1.04191 | − | 0.224485i | ||||
\(391\) | −1.49061 | − | 2.58181i | −0.0753834 | − | 0.130568i | ||||
\(392\) | 1.93926i | 0.0979476i | ||||||||
\(393\) | −1.59734 | − | 28.6196i | −0.0805751 | − | 1.44367i | ||||
\(394\) | −47.0561 | −2.37065 | ||||||||
\(395\) | 6.10536i | 0.307194i | ||||||||
\(396\) | −5.73366 | + | 4.22553i | −0.288127 | + | 0.212341i | ||||
\(397\) | −22.6182 | + | 13.0586i | −1.13518 | + | 0.655394i | −0.945231 | − | 0.326401i | \(-0.894164\pi\) |
−0.189944 | + | 0.981795i | \(0.560831\pi\) | |||||||
\(398\) | 22.4948 | + | 12.9874i | 1.12756 | + | 0.650999i | ||||
\(399\) | −0.284285 | − | 5.09355i | −0.0142321 | − | 0.254996i | ||||
\(400\) | −5.05947 | −0.252973 | ||||||||
\(401\) | − | 26.8397i | − | 1.34031i | −0.742222 | − | 0.670154i | \(-0.766228\pi\) | ||
0.742222 | − | 0.670154i | \(-0.233772\pi\) | |||||||
\(402\) | −0.341437 | − | 6.11754i | −0.0170293 | − | 0.305115i | ||||
\(403\) | −21.6087 | − | 5.93308i | −1.07640 | − | 0.295548i | ||||
\(404\) | 13.9769 | 0.695375 | ||||||||
\(405\) | −3.97301 | − | 17.5183i | −0.197420 | − | 0.870489i | ||||
\(406\) | 2.08567 | − | 3.61248i | 0.103510 | − | 0.179284i | ||||
\(407\) | −19.0909 | −0.946301 | ||||||||
\(408\) | −11.5162 | + | 0.642749i | −0.570135 | + | 0.0318208i | ||||
\(409\) | 22.5686 | + | 13.0300i | 1.11595 | + | 0.644292i | 0.940363 | − | 0.340173i | \(-0.110486\pi\) |
0.175583 | + | 0.984465i | \(0.443819\pi\) | |||||||
\(410\) | −6.59522 | − | 3.80775i | −0.325715 | − | 0.188052i | ||||
\(411\) | 10.6623 | − | 21.1027i | 0.525930 | − | 1.04092i | ||||
\(412\) | −12.7785 | −0.629551 | ||||||||
\(413\) | 6.26651 | − | 10.8539i | 0.308355 | − | 0.534086i | ||||
\(414\) | 4.03000 | + | 1.76158i | 0.198064 | + | 0.0865770i | ||||
\(415\) | −23.3033 | −1.14391 | ||||||||
\(416\) | −4.12780 | − | 15.7941i | −0.202382 | − | 0.774370i | ||||
\(417\) | −9.47874 | + | 6.20142i | −0.464176 | + | 0.303685i | ||||
\(418\) | − | 13.8661i | − | 0.678212i | ||||||
\(419\) | 36.8955 | 1.80246 | 0.901232 | − | 0.433337i | \(-0.142664\pi\) | ||||
0.901232 | + | 0.433337i | \(0.142664\pi\) | |||||||
\(420\) | 2.62764 | + | 1.32763i | 0.128216 | + | 0.0647818i | ||||
\(421\) | −17.8529 | − | 10.3073i | −0.870095 | − | 0.502349i | −0.00271499 | − | 0.999996i | \(-0.500864\pi\) |
−0.867380 | + | 0.497647i | \(0.834198\pi\) | |||||||
\(422\) | 18.5715 | − | 10.7223i | 0.904048 | − | 0.521952i | ||||
\(423\) | −1.71759 | − | 15.3392i | −0.0835122 | − | 0.745815i | ||||
\(424\) | 10.3185i | 0.501111i | ||||||||
\(425\) | −3.49010 | −0.169295 | ||||||||
\(426\) | −22.9108 | + | 14.9893i | −1.11003 | + | 0.726232i | ||||
\(427\) | − | 6.66360i | − | 0.322474i | ||||||
\(428\) | −0.0598351 | − | 0.103637i | −0.00289224 | − | 0.00500951i | ||||
\(429\) | 12.9060 | + | 11.6856i | 0.623109 | + | 0.564185i | ||||
\(430\) | 4.41866 | − | 7.65335i | 0.213087 | − | 0.369077i | ||||
\(431\) | 20.8692 | + | 12.0488i | 1.00523 | + | 0.580372i | 0.909793 | − | 0.415063i | \(-0.136240\pi\) |
0.0954413 | + | 0.995435i | \(0.469574\pi\) | |||||||
\(432\) | 19.9351 | − | 16.4821i | 0.959127 | − | 0.792996i | ||||
\(433\) | −9.42304 | − | 16.3212i | −0.452842 | − | 0.784346i | 0.545719 | − | 0.837968i | \(-0.316257\pi\) |
−0.998561 | + | 0.0536222i | \(0.982923\pi\) | |||||||
\(434\) | 9.08896 | + | 5.24751i | 0.436284 | + | 0.251889i | ||||
\(435\) | 4.67521 | + | 7.14597i | 0.224159 | + | 0.342623i | ||||
\(436\) | −3.57410 | − | 2.06351i | −0.171168 | − | 0.0988241i | ||||
\(437\) | −2.21449 | + | 1.27854i | −0.105934 | + | 0.0611607i | ||||
\(438\) | −1.81892 | − | 32.5897i | −0.0869114 | − | 1.55720i | ||||
\(439\) | −16.4692 | − | 28.5254i | −0.786030 | − | 1.36144i | −0.928382 | − | 0.371628i | \(-0.878800\pi\) |
0.142351 | − | 0.989816i | \(-0.454534\pi\) | |||||||
\(440\) | −9.34503 | − | 5.39535i | −0.445507 | − | 0.257213i | ||||
\(441\) | −1.77979 | − | 2.41502i | −0.0847521 | − | 0.115001i | ||||
\(442\) | −5.28662 | − | 20.2281i | −0.251459 | − | 0.962152i | ||||
\(443\) | −10.9751 | + | 19.0093i | −0.521440 | + | 0.903161i | 0.478249 | + | 0.878225i | \(0.341272\pi\) |
−0.999689 | + | 0.0249368i | \(0.992062\pi\) | |||||||
\(444\) | −10.0850 | + | 0.562871i | −0.478612 | + | 0.0267127i | ||||
\(445\) | 35.0123 | 1.65974 | ||||||||
\(446\) | −10.9633 | + | 18.9889i | −0.519125 | + | 0.899151i | ||||
\(447\) | 12.6537 | + | 19.3409i | 0.598499 | + | 0.914793i | ||||
\(448\) | − | 2.31029i | − | 0.109151i | ||||||
\(449\) | −4.86626 | + | 2.80954i | −0.229653 | + | 0.132590i | −0.610412 | − | 0.792084i | \(-0.708996\pi\) |
0.380759 | + | 0.924674i | \(0.375663\pi\) | |||||||
\(450\) | 4.14493 | − | 3.05468i | 0.195394 | − | 0.143999i | ||||
\(451\) | 3.14962 | + | 5.45531i | 0.148310 | + | 0.256880i | ||||
\(452\) | −3.13142 | − | 5.42378i | −0.147290 | − | 0.255113i | ||||
\(453\) | 9.44169 | + | 14.4314i | 0.443609 | + | 0.678047i | ||||
\(454\) | 14.7088 | + | 25.4763i | 0.690316 | + | 1.19566i | ||||
\(455\) | 1.90538 | − | 6.93951i | 0.0893254 | − | 0.325329i | ||||
\(456\) | 0.551303 | + | 9.87773i | 0.0258172 | + | 0.462567i | ||||
\(457\) | −7.62429 | + | 4.40189i | −0.356649 | + | 0.205912i | −0.667610 | − | 0.744511i | \(-0.732683\pi\) |
0.310961 | + | 0.950423i | \(0.399349\pi\) | |||||||
\(458\) | 17.2103 | − | 29.8091i | 0.804185 | − | 1.39289i | ||||
\(459\) | 13.7515 | − | 11.3696i | 0.641867 | − | 0.530688i | ||||
\(460\) | − | 1.47566i | − | 0.0688028i | ||||||
\(461\) | 33.8740i | 1.57767i | 0.614605 | + | 0.788835i | \(0.289315\pi\) | ||||
−0.614605 | + | 0.788835i | \(0.710685\pi\) | |||||||
\(462\) | −4.46426 | − | 6.82353i | −0.207696 | − | 0.317459i | ||||
\(463\) | 7.57756 | − | 4.37491i | 0.352159 | − | 0.203319i | −0.313477 | − | 0.949596i | \(-0.601494\pi\) |
0.665636 | + | 0.746277i | \(0.268160\pi\) | |||||||
\(464\) | −6.14828 | + | 10.6491i | −0.285427 | + | 0.494373i | ||||
\(465\) | −17.9792 | + | 11.7628i | −0.833764 | + | 0.545486i | ||||
\(466\) | −13.2375 | + | 7.64266i | −0.613214 | + | 0.354039i | ||||
\(467\) | 14.8464 | 0.687008 | 0.343504 | − | 0.939151i | \(-0.388386\pi\) | ||||
0.343504 | + | 0.939151i | \(0.388386\pi\) | |||||||
\(468\) | 7.16229 | + | 5.79252i | 0.331077 | + | 0.267759i | ||||
\(469\) | 2.09482 | 0.0967298 | ||||||||
\(470\) | −15.0176 | + | 8.67042i | −0.692710 | + | 0.399936i | ||||
\(471\) | −0.860144 | − | 15.4112i | −0.0396333 | − | 0.710112i | ||||
\(472\) | −12.1524 | + | 21.0486i | −0.559360 | + | 0.968840i | ||||
\(473\) | −6.33054 | + | 3.65494i | −0.291079 | + | 0.168054i | ||||
\(474\) | 4.03476 | − | 7.98557i | 0.185323 | − | 0.366790i | ||||
\(475\) | 2.99355i | 0.137354i | ||||||||
\(476\) | 2.92431i | 0.134035i | ||||||||
\(477\) | −9.47001 | − | 12.8500i | −0.433602 | − | 0.588359i | ||||
\(478\) | 1.59595 | − | 2.76427i | 0.0729972 | − | 0.126435i | ||||
\(479\) | −16.3516 | + | 9.44061i | −0.747125 | + | 0.431353i | −0.824654 | − | 0.565637i | \(-0.808630\pi\) |
0.0775293 | + | 0.996990i | \(0.475297\pi\) | |||||||
\(480\) | −13.9701 | − | 7.05849i | −0.637646 | − | 0.322175i | ||||
\(481\) | 6.24310 | + | 23.8878i | 0.284661 | + | 1.08919i | ||||
\(482\) | 6.16019 | + | 10.6698i | 0.280589 | + | 0.485994i | ||||
\(483\) | −0.678125 | + | 1.34214i | −0.0308558 | + | 0.0610695i | ||||
\(484\) | 1.37438 | + | 2.38049i | 0.0624716 | + | 0.108204i | ||||
\(485\) | 6.71626 | + | 11.6329i | 0.304970 | + | 0.528223i | ||||
\(486\) | −6.38050 | + | 25.5388i | −0.289425 | + | 1.15846i | ||||
\(487\) | 19.0924 | − | 11.0230i | 0.865161 | − | 0.499501i | −0.000576209 | − | 1.00000i | \(-0.500183\pi\) |
0.865737 | + | 0.500499i | \(0.166850\pi\) | |||||||
\(488\) | 12.9225i | 0.584973i | ||||||||
\(489\) | 6.53858 | − | 0.364936i | 0.295685 | − | 0.0165030i | ||||
\(490\) | −1.68521 | + | 2.91887i | −0.0761300 | + | 0.131861i | ||||
\(491\) | 7.33222 | 0.330898 | 0.165449 | − | 0.986218i | \(-0.447093\pi\) | ||||
0.165449 | + | 0.986218i | \(0.447093\pi\) | |||||||
\(492\) | 1.82467 | + | 2.78896i | 0.0822623 | + | 0.125736i | ||||
\(493\) | −4.24118 | + | 7.34594i | −0.191013 | + | 0.330844i | ||||
\(494\) | −17.3502 | + | 4.53448i | −0.780621 | + | 0.204016i | ||||
\(495\) | 16.5893 | − | 1.85758i | 0.745635 | − | 0.0834920i | ||||
\(496\) | −26.7931 | − | 15.4690i | −1.20304 | − | 0.694578i | ||||
\(497\) | −4.68031 | − | 8.10653i | −0.209940 | − | 0.363628i | ||||
\(498\) | 30.4797 | + | 15.4001i | 1.36583 | + | 0.690094i | ||||
\(499\) | −18.3962 | + | 10.6211i | −0.823527 | + | 0.475464i | −0.851631 | − | 0.524141i | \(-0.824386\pi\) |
0.0281039 | + | 0.999605i | \(0.491053\pi\) | |||||||
\(500\) | −8.85608 | − | 5.11306i | −0.396056 | − | 0.228663i | ||||
\(501\) | −5.39775 | + | 10.6832i | −0.241154 | + | 0.477290i | ||||
\(502\) | −12.4120 | − | 7.16607i | −0.553975 | − | 0.319837i | ||||
\(503\) | 18.2009 | + | 31.5248i | 0.811537 | + | 1.40562i | 0.911788 | + | 0.410661i | \(0.134702\pi\) |
−0.100251 | + | 0.994962i | \(0.531965\pi\) | |||||||
\(504\) | 3.45149 | + | 4.68336i | 0.153742 | + | 0.208614i | ||||
\(505\) | −28.3689 | − | 16.3788i | −1.26240 | − | 0.728847i | ||||
\(506\) | −2.04360 | + | 3.53962i | −0.0908492 | + | 0.157355i | ||||
\(507\) | 10.4013 | − | 19.9703i | 0.461936 | − | 0.886913i | ||||
\(508\) | 8.05216 | + | 13.9468i | 0.357257 | + | 0.618787i | ||||
\(509\) | 32.2063i | 1.42752i | 0.700392 | + | 0.713759i | \(0.253009\pi\) | ||||
−0.700392 | + | 0.713759i | \(0.746991\pi\) | |||||||
\(510\) | −17.8920 | − | 9.04006i | −0.792273 | − | 0.400301i | ||||
\(511\) | 11.1596 | 0.493674 | ||||||||
\(512\) | − | 3.23124i | − | 0.142802i | ||||||
\(513\) | −9.75203 | − | 11.7951i | −0.430562 | − | 0.520765i | ||||
\(514\) | 21.6652 | − | 12.5084i | 0.955613 | − | 0.551723i | ||||
\(515\) | 25.9366 | + | 14.9745i | 1.14290 | + | 0.659855i | ||||
\(516\) | −3.23642 | + | 2.11741i | −0.142475 | + | 0.0932138i | ||||
\(517\) | 14.3436 | 0.630833 | ||||||||
\(518\) | − | 11.5637i | − | 0.508080i | ||||||
\(519\) | −3.87253 | − | 1.95662i | −0.169985 | − | 0.0858862i | ||||
\(520\) | −3.69503 | + | 13.4575i | −0.162038 | + | 0.590151i | ||||
\(521\) | −1.22518 | −0.0536761 | −0.0268381 | − | 0.999640i | \(-0.508544\pi\) | ||||
−0.0268381 | + | 0.999640i | \(0.508544\pi\) | |||||||
\(522\) | −1.39254 | − | 12.4363i | −0.0609500 | − | 0.544321i | ||||
\(523\) | −8.12561 | + | 14.0740i | −0.355308 | + | 0.615412i | −0.987171 | − | 0.159669i | \(-0.948957\pi\) |
0.631863 | + | 0.775080i | \(0.282291\pi\) | |||||||
\(524\) | 14.0934 | 0.615672 | ||||||||
\(525\) | 0.963792 | + | 1.47314i | 0.0420633 | + | 0.0642929i | ||||
\(526\) | −26.5821 | − | 15.3472i | −1.15904 | − | 0.669169i | ||||
\(527\) | −18.4823 | − | 10.6708i | −0.805101 | − | 0.464825i | ||||
\(528\) | 13.1601 | + | 20.1149i | 0.572718 | + | 0.875388i | ||||
\(529\) | −22.2463 | −0.967229 | ||||||||
\(530\) | −8.96674 | + | 15.5308i | −0.389490 | + | 0.674617i | ||||
\(531\) | −4.18398 | − | 37.3656i | −0.181569 | − | 1.62153i | ||||
\(532\) | 2.50826 | 0.108747 | ||||||||
\(533\) | 5.79606 | − | 5.72502i | 0.251055 | − | 0.247978i | ||||
\(534\) | −45.7947 | − | 23.1381i | −1.98173 | − | 1.00128i | ||||
\(535\) | 0.280471i | 0.0121258i | ||||||||
\(536\) | −4.06241 | −0.175469 | ||||||||
\(537\) | −9.41964 | + | 6.16275i | −0.406487 | + | 0.265942i | ||||
\(538\) | −3.23817 | − | 1.86956i | −0.139607 | − | 0.0806024i | ||||
\(539\) | 2.41437 | − | 1.39394i | 0.103994 | − | 0.0600412i | ||||
\(540\) | 8.70873 | − | 1.47040i | 0.374764 | − | 0.0632760i | ||||
\(541\) | 27.6010i | 1.18666i | 0.804959 | + | 0.593331i | \(0.202187\pi\) | ||||
−0.804959 | + | 0.593331i | \(0.797813\pi\) | |||||||
\(542\) | 54.3210 | 2.33329 | ||||||||
\(543\) | −4.93562 | − | 2.49375i | −0.211808 | − | 0.107017i | ||||
\(544\) | − | 15.5474i | − | 0.666588i | ||||||
\(545\) | 4.83625 | + | 8.37663i | 0.207162 | + | 0.358815i | ||||
\(546\) | −7.07817 | + | 7.81742i | −0.302918 | + | 0.334555i | ||||
\(547\) | 5.42150 | − | 9.39032i | 0.231807 | − | 0.401501i | −0.726533 | − | 0.687131i | \(-0.758870\pi\) |
0.958340 | + | 0.285630i | \(0.0922030\pi\) | |||||||
\(548\) | 10.0674 | + | 5.81239i | 0.430056 | + | 0.248293i | ||||
\(549\) | −11.8598 | − | 16.0927i | −0.506166 | − | 0.686821i | ||||
\(550\) | 2.39243 | + | 4.14382i | 0.102014 | + | 0.176693i | ||||
\(551\) | 6.30081 | + | 3.63777i | 0.268423 | + | 0.154974i | ||||
\(552\) | 1.31506 | − | 2.60276i | 0.0559728 | − | 0.110781i | ||||
\(553\) | 2.64913 | + | 1.52947i | 0.112652 | + | 0.0650398i | ||||
\(554\) | 21.3189 | − | 12.3085i | 0.905752 | − | 0.522936i | ||||
\(555\) | 21.1291 | + | 10.6756i | 0.896882 | + | 0.453155i | ||||
\(556\) | −2.78462 | − | 4.82311i | −0.118094 | − | 0.204545i | ||||
\(557\) | 31.7563 | + | 18.3345i | 1.34556 | + | 0.776859i | 0.987617 | − | 0.156885i | \(-0.0501451\pi\) |
0.357942 | + | 0.933744i | \(0.383478\pi\) | |||||||
\(558\) | 31.2895 | − | 3.50363i | 1.32459 | − | 0.148320i | ||||
\(559\) | 6.64353 | + | 6.72597i | 0.280991 | + | 0.284478i | ||||
\(560\) | 4.96778 | − | 8.60445i | 0.209927 | − | 0.363604i | ||||
\(561\) | 9.07802 | + | 13.8756i | 0.383274 | + | 0.585827i | ||||
\(562\) | 20.2182 | 0.852854 | ||||||||
\(563\) | −3.59431 | + | 6.22552i | −0.151482 | + | 0.262374i | −0.931772 | − | 0.363043i | \(-0.881738\pi\) |
0.780291 | + | 0.625417i | \(0.215071\pi\) | |||||||
\(564\) | 7.57719 | − | 0.422904i | 0.319057 | − | 0.0178075i | ||||
\(565\) | 14.6782i | 0.617519i | ||||||||
\(566\) | 1.21246 | − | 0.700016i | 0.0509637 | − | 0.0294239i | ||||
\(567\) | −8.59649 | − | 2.66466i | −0.361019 | − | 0.111905i | ||||
\(568\) | 9.07634 | + | 15.7207i | 0.380835 | + | 0.659625i | ||||
\(569\) | −4.92801 | − | 8.53556i | −0.206593 | − | 0.357829i | 0.744046 | − | 0.668128i | \(-0.232904\pi\) |
−0.950639 | + | 0.310299i | \(0.899571\pi\) | |||||||
\(570\) | −7.75391 | + | 15.3465i | −0.324775 | + | 0.642793i | ||||
\(571\) | −1.02885 | − | 1.78201i | −0.0430558 | − | 0.0745749i | 0.843694 | − | 0.536824i | \(-0.180376\pi\) |
−0.886750 | + | 0.462249i | \(0.847043\pi\) | |||||||
\(572\) | −6.09017 | + | 6.01551i | −0.254643 | + | 0.251521i | ||||
\(573\) | −2.18082 | − | 1.10187i | −0.0911051 | − | 0.0460314i | ||||
\(574\) | −3.30438 | + | 1.90778i | −0.137922 | + | 0.0796294i | ||||
\(575\) | 0.441195 | − | 0.764171i | 0.0183991 | − | 0.0318681i | ||||
\(576\) | −4.11183 | − | 5.57939i | −0.171326 | − | 0.232475i | ||||
\(577\) | 23.3733i | 0.973045i | 0.873668 | + | 0.486523i | \(0.161735\pi\) | ||||
−0.873668 | + | 0.486523i | \(0.838265\pi\) | |||||||
\(578\) | 8.79529i | 0.365836i | ||||||||
\(579\) | 16.2838 | − | 32.2289i | 0.676733 | − | 1.33939i | ||||
\(580\) | −3.63612 | + | 2.09931i | −0.150981 | + | 0.0871692i | ||||
\(581\) | −5.83777 | + | 10.1113i | −0.242192 | + | 0.419488i | ||||
\(582\) | −1.09694 | − | 19.6539i | −0.0454695 | − | 0.814679i | ||||
\(583\) | 12.8465 | − | 7.41693i | 0.532048 | − | 0.307178i | ||||
\(584\) | −21.6415 | −0.895531 | ||||||||
\(585\) | −7.74937 | − | 20.1502i | −0.320397 | − | 0.833110i | ||||
\(586\) | 16.1415 | 0.666800 | ||||||||
\(587\) | −11.1307 | + | 6.42629i | −0.459411 | + | 0.265241i | −0.711797 | − | 0.702386i | \(-0.752118\pi\) |
0.252385 | + | 0.967627i | \(0.418785\pi\) | |||||||
\(588\) | 1.23432 | − | 0.807548i | 0.0509025 | − | 0.0333027i | ||||
\(589\) | −9.15259 | + | 15.8528i | −0.377126 | + | 0.653201i | ||||
\(590\) | −36.5823 | + | 21.1208i | −1.50607 | + | 0.869529i | ||||
\(591\) | −26.4243 | − | 40.3889i | −1.08695 | − | 1.66138i | ||||
\(592\) | 34.0883i | 1.40102i | ||||||||
\(593\) | − | 25.1789i | − | 1.03397i | −0.855993 | − | 0.516987i | \(-0.827054\pi\) | ||
0.855993 | − | 0.516987i | \(-0.172946\pi\) | |||||||
\(594\) | −22.9258 | − | 8.53350i | −0.940656 | − | 0.350134i | ||||
\(595\) | 3.42685 | − | 5.93548i | 0.140487 | − | 0.243331i | ||||
\(596\) | −9.84132 | + | 5.68189i | −0.403116 | + | 0.232739i | ||||
\(597\) | 1.48466 | + | 26.6007i | 0.0607630 | + | 1.08869i | ||||
\(598\) | 5.09732 | + | 1.39957i | 0.208445 | + | 0.0572326i | ||||
\(599\) | 8.91102 | + | 15.4343i | 0.364094 | + | 0.630630i | 0.988630 | − | 0.150366i | \(-0.0480453\pi\) |
−0.624536 | + | 0.780996i | \(0.714712\pi\) | |||||||
\(600\) | −1.86905 | − | 2.85680i | −0.0763035 | − | 0.116628i | ||||
\(601\) | 2.59386 | + | 4.49269i | 0.105806 | + | 0.183261i | 0.914067 | − | 0.405563i | \(-0.132925\pi\) |
−0.808261 | + | 0.588824i | \(0.799591\pi\) | |||||||
\(602\) | −2.21387 | − | 3.83453i | −0.0902304 | − | 0.156284i | ||||
\(603\) | 5.05904 | − | 3.72835i | 0.206020 | − | 0.151830i | ||||
\(604\) | −7.34321 | + | 4.23960i | −0.298791 | + | 0.172507i | ||||
\(605\) | − | 6.44225i | − | 0.261915i | ||||||
\(606\) | 26.2814 | + | 40.1706i | 1.06761 | + | 1.63182i | ||||
\(607\) | 12.5503 | − | 21.7377i | 0.509399 | − | 0.882305i | −0.490542 | − | 0.871418i | \(-0.663201\pi\) |
0.999941 | − | 0.0108872i | \(-0.00346558\pi\) | |||||||
\(608\) | −13.3354 | −0.540822 | ||||||||
\(609\) | 4.27185 | − | 0.238424i | 0.173104 | − | 0.00966142i | ||||
\(610\) | −11.2296 | + | 19.4502i | −0.454672 | + | 0.787515i | ||||
\(611\) | −4.69066 | − | 17.9478i | −0.189764 | − | 0.726088i | ||||
\(612\) | 5.20467 | + | 7.06227i | 0.210386 | + | 0.285475i | ||||
\(613\) | 20.1389 | + | 11.6272i | 0.813402 | + | 0.469618i | 0.848136 | − | 0.529779i | \(-0.177725\pi\) |
−0.0347336 | + | 0.999397i | \(0.511058\pi\) | |||||||
\(614\) | 17.0046 | + | 29.4528i | 0.686248 | + | 1.18862i | ||||
\(615\) | −0.435284 | − | 7.79901i | −0.0175524 | − | 0.314486i | ||||
\(616\) | −4.68210 | + | 2.70321i | −0.188647 | + | 0.108916i | ||||
\(617\) | −35.8852 | − | 20.7183i | −1.44468 | − | 0.834089i | −0.446527 | − | 0.894770i | \(-0.647339\pi\) |
−0.998157 | + | 0.0606818i | \(0.980673\pi\) | |||||||
\(618\) | −24.0280 | − | 36.7264i | −0.966550 | − | 1.47735i | ||||
\(619\) | −38.8879 | − | 22.4519i | −1.56304 | − | 0.902419i | −0.996947 | − | 0.0780753i | \(-0.975123\pi\) |
−0.566089 | − | 0.824344i | \(-0.691544\pi\) | |||||||
\(620\) | −5.28184 | − | 9.14842i | −0.212124 | − | 0.367409i | ||||
\(621\) | 0.751048 | + | 4.44822i | 0.0301385 | + | 0.178501i | ||||
\(622\) | 26.3841 | + | 15.2328i | 1.05790 | + | 0.610782i | ||||
\(623\) | 8.77105 | − | 15.1919i | 0.351405 | − | 0.608651i | ||||
\(624\) | 20.8655 | − | 23.0447i | 0.835289 | − | 0.922528i | ||||
\(625\) | 9.44257 | + | 16.3550i | 0.377703 | + | 0.654201i | ||||
\(626\) | 25.3228i | 1.01210i | ||||||||
\(627\) | 11.9014 | − | 7.78646i | 0.475298 | − | 0.310961i | ||||
\(628\) | 7.58908 | 0.302837 | ||||||||
\(629\) | 23.5147i | 0.937591i | ||||||||
\(630\) | 1.12517 | + | 10.0485i | 0.0448279 | + | 0.400340i | ||||
\(631\) | −21.5239 | + | 12.4268i | −0.856852 | + | 0.494704i | −0.862957 | − | 0.505278i | \(-0.831390\pi\) |
0.00610493 | + | 0.999981i | \(0.498057\pi\) | |||||||
\(632\) | −5.13735 | − | 2.96605i | −0.204353 | − | 0.117983i | ||||
\(633\) | 19.6319 | + | 9.91914i | 0.780298 | + | 0.394250i | ||||
\(634\) | 27.9598 | 1.11043 | ||||||||
\(635\) | − | 37.7437i | − | 1.49781i | ||||||
\(636\) | 6.56763 | − | 4.29684i | 0.260423 | − | 0.170381i | ||||
\(637\) | −2.53374 | − | 2.56518i | −0.100390 | − | 0.101636i | ||||
\(638\) | 11.6292 | 0.460403 | ||||||||
\(639\) | −25.7310 | − | 11.2475i | −1.01790 | − | 0.444943i | ||||
\(640\) | −12.9300 | + | 22.3955i | −0.511104 | + | 0.885259i | ||||
\(641\) | −43.8503 | −1.73198 | −0.865991 | − | 0.500060i | \(-0.833311\pi\) | ||||
−0.865991 | + | 0.500060i | \(0.833311\pi\) | |||||||
\(642\) | 0.185351 | − | 0.366846i | 0.00731522 | − | 0.0144782i | ||||
\(643\) | −29.9017 | − | 17.2638i | −1.17921 | − | 0.680816i | −0.223377 | − | 0.974732i | \(-0.571708\pi\) |
−0.955831 | + | 0.293916i | \(0.905041\pi\) | |||||||
\(644\) | −0.640289 | − | 0.369671i | −0.0252309 | − | 0.0145671i | ||||
\(645\) | 9.05027 | − | 0.505121i | 0.356354 | − | 0.0198891i | ||||
\(646\) | −17.0791 | −0.671969 | ||||||||
\(647\) | −6.66984 | + | 11.5525i | −0.262218 | + | 0.454175i | −0.966831 | − | 0.255417i | \(-0.917787\pi\) |
0.704613 | + | 0.709592i | \(0.251121\pi\) | |||||||
\(648\) | 16.6708 | + | 5.16748i | 0.654893 | + | 0.202998i | ||||
\(649\) | 34.9405 | 1.37154 | ||||||||
\(650\) | 4.40265 | − | 4.34869i | 0.172686 | − | 0.170570i | ||||
\(651\) | 0.599871 | + | 10.7479i | 0.0235108 | + | 0.421244i | ||||
\(652\) | 3.21985i | 0.126099i | ||||||||
\(653\) | 11.4725 | 0.448953 | 0.224476 | − | 0.974480i | \(-0.427933\pi\) | ||||
0.224476 | + | 0.974480i | \(0.427933\pi\) | |||||||
\(654\) | −0.789882 | − | 14.1524i | −0.0308868 | − | 0.553401i | ||||
\(655\) | −28.6054 | − | 16.5154i | −1.11771 | − | 0.645308i | ||||
\(656\) | 9.74088 | − | 5.62390i | 0.380318 | − | 0.219576i | ||||
\(657\) | 26.9508 | − | 19.8619i | 1.05145 | − | 0.774886i | ||||
\(658\) | 8.68821i | 0.338702i | ||||||||
\(659\) | 9.77713 | 0.380863 | 0.190432 | − | 0.981700i | \(-0.439011\pi\) | ||||
0.190432 | + | 0.981700i | \(0.439011\pi\) | |||||||
\(660\) | 0.457372 | + | 8.19475i | 0.0178032 | + | 0.318980i | ||||
\(661\) | 39.3586i | 1.53087i | 0.643513 | + | 0.765435i | \(0.277476\pi\) | ||||
−0.643513 | + | 0.765435i | \(0.722524\pi\) | |||||||
\(662\) | −24.8714 | − | 43.0786i | −0.966655 | − | 1.67430i | ||||
\(663\) | 14.3934 | − | 15.8966i | 0.558992 | − | 0.617374i | ||||
\(664\) | 11.3210 | − | 19.6085i | 0.439339 | − | 0.760957i | ||||
\(665\) | −5.09103 | − | 2.93931i | −0.197422 | − | 0.113981i | ||||
\(666\) | −20.5810 | − | 27.9266i | −0.797499 | − | 1.08213i | ||||
\(667\) | −1.07228 | − | 1.85725i | −0.0415189 | − | 0.0719128i | ||||
\(668\) | −5.09658 | − | 2.94251i | −0.197193 | − | 0.113849i | ||||
\(669\) | −22.4549 | + | 1.25327i | −0.868155 | + | 0.0484541i | ||||
\(670\) | −6.11451 | − | 3.53021i | −0.236224 | − | 0.136384i | ||||
\(671\) | 16.0884 | − | 9.28865i | 0.621086 | − | 0.358584i | ||||
\(672\) | −6.56239 | + | 4.29341i | −0.253150 | + | 0.165622i | ||||
\(673\) | 8.30325 | + | 14.3817i | 0.320067 | + | 0.554372i | 0.980502 | − | 0.196511i | \(-0.0629613\pi\) |
−0.660435 | + | 0.750884i | \(0.729628\pi\) | |||||||
\(674\) | −13.2939 | − | 7.67524i | −0.512062 | − | 0.295639i | ||||
\(675\) | 4.94946 | + | 1.84230i | 0.190505 | + | 0.0709103i | ||||
\(676\) | 9.51863 | + | 5.65324i | 0.366101 | + | 0.217432i | ||||
\(677\) | −11.8222 | + | 20.4766i | −0.454364 | + | 0.786981i | −0.998651 | − | 0.0519177i | \(-0.983467\pi\) |
0.544288 | + | 0.838899i | \(0.316800\pi\) | |||||||
\(678\) | 9.70020 | − | 19.1986i | 0.372534 | − | 0.737317i | ||||
\(679\) | 6.73005 | 0.258276 | ||||||||
\(680\) | −6.64557 | + | 11.5105i | −0.254846 | + | 0.441406i | ||||
\(681\) | −13.6070 | + | 26.9309i | −0.521422 | + | 1.03199i | ||||
\(682\) | 29.2588i | 1.12038i | ||||||||
\(683\) | −21.0903 | + | 12.1765i | −0.806999 | + | 0.465921i | −0.845912 | − | 0.533322i | \(-0.820944\pi\) |
0.0389139 | + | 0.999243i | \(0.487610\pi\) | |||||||
\(684\) | 6.05750 | − | 4.46419i | 0.231614 | − | 0.170692i | ||||
\(685\) | −13.6225 | − | 23.5949i | −0.520490 | − | 0.901514i | ||||
\(686\) | 0.844334 | + | 1.46243i | 0.0322368 | + | 0.0558358i | ||||
\(687\) | 35.2500 | − | 1.96740i | 1.34487 | − | 0.0750610i | ||||
\(688\) | 6.52619 | + | 11.3037i | 0.248809 | + | 0.430949i | ||||
\(689\) | −13.4816 | − | 13.6489i | −0.513609 | − | 0.519983i | ||||
\(690\) | 4.24115 | − | 2.77475i | 0.161458 | − | 0.105633i | ||||
\(691\) | 30.3860 | − | 17.5434i | 1.15594 | − | 0.667381i | 0.205611 | − | 0.978634i | \(-0.434082\pi\) |
0.950327 | + | 0.311252i | \(0.100748\pi\) | |||||||
\(692\) | 1.06663 | − | 1.84745i | 0.0405471 | − | 0.0702296i | ||||
\(693\) | 3.34984 | − | 7.66348i | 0.127250 | − | 0.291112i | ||||
\(694\) | 33.4367i | 1.26924i | ||||||||
\(695\) | 13.0527i | 0.495116i | ||||||||
\(696\) | −8.28423 | + | 0.462366i | −0.314013 | + | 0.0175259i | ||||
\(697\) | 6.71941 | − | 3.87946i | 0.254516 | − | 0.146945i | ||||
\(698\) | 4.17860 | − | 7.23755i | 0.158162 | − | 0.273945i | ||||
\(699\) | −13.9933 | − | 7.07019i | −0.529274 | − | 0.267419i | ||||
\(700\) | −0.749583 | + | 0.432772i | −0.0283316 | + | 0.0163572i | ||||
\(701\) | −37.8901 | −1.43109 | −0.715544 | − | 0.698567i | \(-0.753821\pi\) | ||||
−0.715544 | + | 0.698567i | \(0.753821\pi\) | |||||||
\(702\) | −3.18052 | + | 31.4769i | −0.120041 | + | 1.18802i | ||||
\(703\) | 20.1692 | 0.760694 | ||||||||
\(704\) | 5.57789 | − | 3.22040i | 0.210225 | − | 0.121373i | ||||
\(705\) | −15.8750 | − | 8.02097i | −0.597889 | − | 0.302087i | ||||
\(706\) | 4.99265 | − | 8.64753i | 0.187901 | − | 0.325454i | ||||
\(707\) | −14.2136 | + | 8.20621i | −0.534557 | + | 0.308626i | ||||
\(708\) | 18.4577 | − | 1.03018i | 0.693684 | − | 0.0387164i | ||||
\(709\) | 20.8971i | 0.784808i | 0.919793 | + | 0.392404i | \(0.128356\pi\) | ||||
−0.919793 | + | 0.392404i | \(0.871644\pi\) | |||||||
\(710\) | 31.5492i | 1.18402i | ||||||||
\(711\) | 9.11985 | − | 1.02119i | 0.342021 | − | 0.0382976i | ||||
\(712\) | −17.0094 | + | 29.4611i | −0.637453 | + | 1.10410i | ||||
\(713\) | 4.67281 | − | 2.69785i | 0.174998 | − | 0.101035i | ||||
\(714\) | −8.40469 | + | 5.49873i | −0.314537 | + | 0.205785i | ||||
\(715\) | 19.4105 | − | 5.07296i | 0.725913 | − | 0.189718i | ||||
\(716\) | −2.76726 | − | 4.79304i | −0.103417 | − | 0.179124i | ||||
\(717\) | 3.26882 | − | 0.182442i | 0.122076 | − | 0.00681342i | ||||
\(718\) | 10.9281 | + | 18.9280i | 0.407833 | + | 0.706387i | ||||
\(719\) | 19.3354 | + | 33.4899i | 0.721089 | + | 1.24896i | 0.960564 | + | 0.278060i | \(0.0896915\pi\) |
−0.239475 | + | 0.970903i | \(0.576975\pi\) | |||||||
\(720\) | −3.31686 | − | 29.6216i | −0.123612 | − | 1.10393i | ||||
\(721\) | 12.9949 | − | 7.50261i | 0.483956 | − | 0.279412i | ||||
\(722\) | − | 17.4355i | − | 0.648881i | ||||||
\(723\) | −5.69877 | + | 11.2790i | −0.211939 | + | 0.419469i | ||||
\(724\) | 1.35944 | − | 2.35461i | 0.0505231 | − | 0.0875086i | ||||
\(725\) | −2.51063 | −0.0932424 | ||||||||
\(726\) | −4.25740 | + | 8.42622i | −0.158007 | + | 0.312726i | ||||
\(727\) | −25.6431 | + | 44.4151i | −0.951049 | + | 1.64726i | −0.207887 | + | 0.978153i | \(0.566659\pi\) |
−0.743162 | + | 0.669112i | \(0.766675\pi\) | |||||||
\(728\) | 4.91359 | + | 4.97456i | 0.182110 | + | 0.184370i | ||||
\(729\) | −25.5033 | + | 8.86477i | −0.944565 | + | 0.328325i | ||||
\(730\) | −32.5736 | − | 18.8063i | −1.20560 | − | 0.696054i | ||||
\(731\) | 4.50187 | + | 7.79746i | 0.166508 | + | 0.288400i | ||||
\(732\) | 8.22502 | − | 5.38118i | 0.304005 | − | 0.198894i | ||||
\(733\) | 41.6331 | − | 24.0369i | 1.53775 | − | 0.887822i | 0.538783 | − | 0.842444i | \(-0.318884\pi\) |
0.998970 | − | 0.0453780i | \(-0.0144492\pi\) | |||||||
\(734\) | 17.6414 | + | 10.1853i | 0.651158 | + | 0.375946i | ||||
\(735\) | −3.45163 | + | 0.192645i | −0.127315 | + | 0.00710583i | ||||
\(736\) | 3.40416 | + | 1.96539i | 0.125479 | + | 0.0724454i | ||||
\(737\) | 2.92005 | + | 5.05768i | 0.107561 | + | 0.186302i | ||||
\(738\) | −4.58468 | + | 10.4885i | −0.168765 | + | 0.386085i | ||||
\(739\) | 14.7473 | + | 8.51437i | 0.542489 | + | 0.313206i | 0.746087 | − | 0.665849i | \(-0.231930\pi\) |
−0.203598 | + | 0.979055i | \(0.565264\pi\) | |||||||
\(740\) | −5.81968 | + | 10.0800i | −0.213936 | + | 0.370548i | ||||
\(741\) | −13.6350 | − | 12.3456i | −0.500893 | − | 0.453526i | ||||
\(742\) | 4.49257 | + | 7.78136i | 0.164927 | + | 0.285663i | ||||
\(743\) | 33.9033i | 1.24379i | 0.783100 | + | 0.621896i | \(0.213637\pi\) | ||||
−0.783100 | + | 0.621896i | \(0.786363\pi\) | |||||||
\(744\) | −1.16331 | − | 20.8430i | −0.0426489 | − | 0.764143i | ||||
\(745\) | 26.6333 | 0.975769 | ||||||||
\(746\) | 29.1668i | 1.06787i | ||||||||
\(747\) | 3.89773 | + | 34.8091i | 0.142610 | + | 1.27360i | ||||
\(748\) | −7.06037 | + | 4.07631i | −0.258153 | + | 0.149045i | ||||
\(749\) | 0.121697 | + | 0.0702618i | 0.00444671 | + | 0.00256731i | ||||
\(750\) | −1.95721 | − | 35.0674i | −0.0714672 | − | 1.28048i | ||||
\(751\) | 15.6334 | 0.570471 | 0.285235 | − | 0.958457i | \(-0.407928\pi\) | ||||
0.285235 | + | 0.958457i | \(0.407928\pi\) | |||||||
\(752\) | − | 25.6117i | − | 0.933964i | ||||||
\(753\) | −0.819192 | − | 14.6775i | −0.0298530 | − | 0.534877i | ||||
\(754\) | −3.80297 | − | 14.5512i | −0.138496 | − | 0.529924i | ||||
\(755\) | 19.8727 | 0.723243 | ||||||||
\(756\) | 1.54364 | − | 4.14708i | 0.0561417 | − | 0.150828i | ||||
\(757\) | −22.2713 | + | 38.5750i | −0.809465 | + | 1.40203i | 0.103771 | + | 0.994601i | \(0.466909\pi\) |
−0.913235 | + | 0.407433i | \(0.866424\pi\) | |||||||
\(758\) | 4.62971 | 0.168159 | ||||||||
\(759\) | −4.18569 | + | 0.233615i | −0.151931 | + | 0.00847969i | ||||
\(760\) | 9.87284 | + | 5.70008i | 0.358125 | + | 0.206764i | ||||
\(761\) | 45.8016 | + | 26.4436i | 1.66031 | + | 0.958578i | 0.972568 | + | 0.232619i | \(0.0747296\pi\) |
0.687738 | + | 0.725959i | \(0.258604\pi\) | |||||||
\(762\) | −24.9431 | + | 49.3673i | −0.903595 | + | 1.78839i | ||||
\(763\) | 4.84617 | 0.175443 | ||||||||
\(764\) | 0.600672 | − | 1.04039i | 0.0217315 | − | 0.0376401i | ||||
\(765\) | −2.28802 | − | 20.4334i | −0.0827235 | − | 0.738772i | ||||
\(766\) | 29.2127 | 1.05550 | ||||||||
\(767\) | −11.4263 | − | 43.7200i | −0.412578 | − | 1.57864i | ||||
\(768\) | 25.0150 | − | 16.3660i | 0.902653 | − | 0.590556i | ||||
\(769\) | 30.4285i | 1.09728i | 0.836059 | + | 0.548639i | \(0.184854\pi\) | ||||
−0.836059 | + | 0.548639i | \(0.815146\pi\) | |||||||
\(770\) | −9.39632 | −0.338620 | ||||||||
\(771\) | 22.9022 | + | 11.5715i | 0.824804 | + | 0.416737i | ||||
\(772\) | 15.3753 | + | 8.87693i | 0.553369 | + | 0.319488i | ||||
\(773\) | 16.8613 | − | 9.73487i | 0.606458 | − | 0.350139i | −0.165120 | − | 0.986274i | \(-0.552801\pi\) |
0.771578 | + | 0.636135i | \(0.219468\pi\) | |||||||
\(774\) | −12.1712 | − | 5.32024i | −0.437485 | − | 0.191232i | ||||
\(775\) | − | 6.31671i | − | 0.226903i | ||||||
\(776\) | −13.0513 | −0.468515 | ||||||||
\(777\) | 9.92530 | − | 6.49358i | 0.356068 | − | 0.232956i | ||||
\(778\) | 51.2290i | 1.83665i | ||||||||
\(779\) | −3.32751 | − | 5.76342i | −0.119221 | − | 0.206496i | ||||
\(780\) | 10.1043 | − | 3.25214i | 0.361790 | − | 0.116445i | ||||
\(781\) | 13.0481 | − | 22.6000i | 0.466898 | − | 0.808692i | ||||
\(782\) | 4.35983 | + | 2.51715i | 0.155907 | + | 0.0900131i | ||||
\(783\) | 9.89226 | − | 8.17881i | 0.353520 | − | 0.292287i | ||||
\(784\) | −2.48899 | − | 4.31106i | −0.0888925 | − | 0.153966i | ||||
\(785\) | −15.4036 | − | 8.89327i | −0.549778 | − | 0.317415i | ||||
\(786\) | 26.5005 | + | 40.5055i | 0.945242 | + | 1.44478i | ||||
\(787\) | 29.8286 | + | 17.2216i | 1.06328 | + | 0.613883i | 0.926337 | − | 0.376696i | \(-0.122940\pi\) |
0.136940 | + | 0.990579i | \(0.456273\pi\) | |||||||
\(788\) | 20.5513 | − | 11.8653i | 0.732110 | − | 0.422684i | ||||
\(789\) | −1.75442 | − | 31.4340i | −0.0624590 | − | 1.11908i | ||||
\(790\) | −5.15497 | − | 8.92867i | −0.183406 | − | 0.317668i | ||||
\(791\) | 6.36891 | + | 3.67709i | 0.226453 | + | 0.130742i | ||||
\(792\) | −6.49621 | + | 14.8615i | −0.230833 | + | 0.528080i | ||||
\(793\) | −16.8838 | − | 17.0934i | −0.599562 | − | 0.607003i | ||||
\(794\) | 22.0517 | − | 38.1947i | 0.782585 | − | 1.35548i | ||||
\(795\) | −18.3656 | + | 1.02504i | −0.651361 | + | 0.0363543i | ||||
\(796\) | −13.0992 | −0.464289 | ||||||||
\(797\) | −13.1008 | + | 22.6913i | −0.464056 | + | 0.803768i | −0.999158 | − | 0.0410189i | \(-0.986940\pi\) |
0.535103 | + | 0.844787i | \(0.320273\pi\) | |||||||
\(798\) | 4.71641 | + | 7.20893i | 0.166959 | + | 0.255193i | ||||
\(799\) | − | 17.6674i | − | 0.625027i | ||||||
\(800\) | 3.98523 | − | 2.30087i | 0.140899 | − | 0.0813482i | ||||
\(801\) | −5.85620 | − | 52.2994i | −0.206919 | − | 1.84791i | ||||
\(802\) | 22.6616 | + | 39.2511i | 0.800210 | + | 1.38601i | ||||
\(803\) | 15.5559 | + | 26.9435i | 0.548955 | + | 0.950817i | ||||
\(804\) | 1.69167 | + | 2.58568i | 0.0596606 | + | 0.0911899i | ||||
\(805\) | 0.866399 | + | 1.50065i | 0.0305365 | + | 0.0528908i | ||||
\(806\) | 36.6107 | − | 9.56823i | 1.28956 | − | 0.337026i | ||||
\(807\) | −0.213719 | − | 3.82921i | −0.00752327 | − | 0.134795i | ||||
\(808\) | 27.5639 | − | 15.9140i | 0.969693 | − | 0.559853i | ||||
\(809\) | 13.2872 | − | 23.0141i | 0.467154 | − | 0.809134i | −0.532142 | − | 0.846655i | \(-0.678613\pi\) |
0.999296 | + | 0.0375210i | \(0.0119461\pi\) | |||||||
\(810\) | 20.6015 | + | 22.2647i | 0.723863 | + | 0.782301i | ||||
\(811\) | − | 31.9095i | − | 1.12050i | −0.828325 | − | 0.560248i | \(-0.810706\pi\) | ||
0.828325 | − | 0.560248i | \(-0.189294\pi\) | |||||||
\(812\) | 2.10362i | 0.0738226i | ||||||||
\(813\) | 30.5039 | + | 46.6245i | 1.06982 | + | 1.63519i | ||||
\(814\) | 27.9191 | − | 16.1191i | 0.978564 | − | 0.564974i | ||||
\(815\) | 3.77318 | − | 6.53534i | 0.132169 | − | 0.228923i | ||||
\(816\) | 24.7759 | − | 16.2095i | 0.867331 | − | 0.567447i | ||||
\(817\) | 6.68810 | − | 3.86137i | 0.233987 | − | 0.135092i | ||||
\(818\) | −44.0067 | −1.53866 | ||||||||
\(819\) | −10.6845 | − | 1.68544i | −0.373348 | − | 0.0588939i | ||||
\(820\) | 3.84053 | 0.134117 | ||||||||
\(821\) | 20.3903 | − | 11.7723i | 0.711626 | − | 0.410858i | −0.100037 | − | 0.994984i | \(-0.531896\pi\) |
0.811663 | + | 0.584126i | \(0.198563\pi\) | |||||||
\(822\) | 2.22490 | + | 39.8637i | 0.0776024 | + | 1.39041i | ||||
\(823\) | 26.5995 | − | 46.0717i | 0.927202 | − | 1.60596i | 0.139220 | − | 0.990262i | \(-0.455541\pi\) |
0.787982 | − | 0.615699i | \(-0.211126\pi\) | |||||||
\(824\) | −25.2005 | + | 14.5495i | −0.877902 | + | 0.506857i | ||||
\(825\) | −2.21323 | + | 4.38041i | −0.0770548 | + | 0.152506i | ||||
\(826\) | 21.1641i | 0.736394i | ||||||||
\(827\) | − | 3.18210i | − | 0.110653i | −0.998468 | − | 0.0553263i | \(-0.982380\pi\) | ||
0.998468 | − | 0.0553263i | \(-0.0176199\pi\) | |||||||
\(828\) | −2.20425 | + | 0.246820i | −0.0766030 | + | 0.00857757i | ||||
\(829\) | 11.6734 | − | 20.2189i | 0.405433 | − | 0.702231i | −0.588938 | − | 0.808178i | \(-0.700454\pi\) |
0.994372 | + | 0.105947i | \(0.0337873\pi\) | |||||||
\(830\) | 34.0794 | − | 19.6757i | 1.18291 | − | 0.682955i | ||||
\(831\) | 22.5361 | + | 11.3865i | 0.781768 | + | 0.394993i | ||||
\(832\) | −5.85366 | − | 5.92630i | −0.202939 | − | 0.205458i | ||||
\(833\) | −1.71694 | − | 2.97383i | −0.0594886 | − | 0.103037i | ||||
\(834\) | 8.62592 | − | 17.0724i | 0.298691 | − | 0.591168i | ||||
\(835\) | 6.89637 | + | 11.9449i | 0.238659 | + | 0.413369i | ||||
\(836\) | 3.49636 | + | 6.05587i | 0.120924 | + | 0.209447i | ||||
\(837\) | 20.5778 | + | 24.8888i | 0.711272 | + | 0.860283i | ||||
\(838\) | −53.9571 | + | 31.1522i | −1.86392 | + | 1.07613i | ||||
\(839\) | 37.4890i | 1.29426i | 0.762378 | + | 0.647132i | \(0.224032\pi\) | ||||
−0.762378 | + | 0.647132i | \(0.775968\pi\) | |||||||
\(840\) | 6.69363 | − | 0.373590i | 0.230952 | − | 0.0128901i | ||||
\(841\) | 11.4491 | − | 19.8304i | 0.394796 | − | 0.683806i | ||||
\(842\) | 34.8114 | 1.19968 | ||||||||
\(843\) | 11.3535 | + | 17.3536i | 0.391035 | + | 0.597689i | ||||
\(844\) | −5.40729 | + | 9.36570i | −0.186127 | + | 0.322381i | ||||
\(845\) | −12.6953 | − | 22.6288i | −0.436730 | − | 0.778455i | ||||
\(846\) | 15.4632 | + | 20.9822i | 0.531637 | + | 0.721384i | ||||
\(847\) | −2.79530 | − | 1.61387i | −0.0960478 | − | 0.0554532i | ||||
\(848\) | −13.2435 | − | 22.9385i | −0.454784 | − | 0.787710i | ||||
\(849\) | 1.28169 | + | 0.647582i | 0.0439875 | + | 0.0222250i | ||||
\(850\) | 5.10403 | − | 2.94681i | 0.175067 | − | 0.101075i | ||||
\(851\) | −5.14863 | − | 2.97256i | −0.176493 | − | 0.101898i | ||||
\(852\) | 6.22648 | − | 12.3234i | 0.213316 | − | 0.422193i | ||||
\(853\) | −25.1870 | − | 14.5417i | −0.862385 | − | 0.497898i | 0.00242506 | − | 0.999997i | \(-0.499228\pi\) |
−0.864810 | + | 0.502099i | \(0.832561\pi\) | |||||||
\(854\) | 5.62631 | + | 9.74505i | 0.192528 | + | 0.333469i | ||||
\(855\) | −17.5263 | + | 1.96250i | −0.599387 | + | 0.0671160i | ||||
\(856\) | −0.236002 | − | 0.136256i | −0.00806640 | − | 0.00465714i | ||||
\(857\) | 0.703927 | − | 1.21924i | 0.0240457 | − | 0.0416484i | −0.853752 | − | 0.520680i | \(-0.825679\pi\) |
0.877798 | + | 0.479031i | \(0.159012\pi\) | |||||||
\(858\) | −28.7407 | − | 6.19233i | −0.981191 | − | 0.211403i | ||||
\(859\) | 2.51842 | + | 4.36204i | 0.0859275 | + | 0.148831i | 0.905786 | − | 0.423735i | \(-0.139281\pi\) |
−0.819859 | + | 0.572566i | \(0.805948\pi\) | |||||||
\(860\) | 4.45670i | 0.151972i | ||||||||
\(861\) | −3.49305 | − | 1.76488i | −0.119043 | − | 0.0601471i | ||||
\(862\) | −40.6930 | −1.38601 | ||||||||
\(863\) | 4.56933i | 0.155542i | 0.996971 | + | 0.0777708i | \(0.0247802\pi\) | ||||
−0.996971 | + | 0.0777708i | \(0.975220\pi\) | |||||||
\(864\) | −8.20692 | + | 22.0484i | −0.279205 | + | 0.750102i | ||||
\(865\) | −4.32988 | + | 2.49986i | −0.147220 | + | 0.0849976i | ||||
\(866\) | 27.5611 | + | 15.9124i | 0.936564 | + | 0.540725i | ||||
\(867\) | −7.54913 | + | 4.93898i | −0.256382 | + | 0.167737i | ||||
\(868\) | −5.29269 | −0.179645 | ||||||||
\(869\) | 8.52797i | 0.289292i | ||||||||
\(870\) | −12.8708 | − | 6.50303i | −0.436360 | − | 0.220473i | ||||
\(871\) | 5.37360 | − | 5.30773i | 0.182077 | − | 0.179846i | ||||
\(872\) | −9.39800 | −0.318257 | ||||||||
\(873\) | 16.2532 | − | 11.9781i | 0.550088 | − | 0.405397i | ||||
\(874\) | 2.15903 | − | 3.73954i | 0.0730302 | − | 0.126492i | ||||
\(875\) | 12.0081 | 0.405948 | ||||||||
\(876\) | 9.01195 | + | 13.7746i | 0.304486 | + | 0.465400i | ||||
\(877\) | 16.2684 | + | 9.39258i | 0.549346 | + | 0.317165i | 0.748858 | − | 0.662730i | \(-0.230602\pi\) |
−0.199512 | + | 0.979895i | \(0.563936\pi\) | |||||||
\(878\) | 48.1700 | + | 27.8110i | 1.62566 | + | 0.938575i | ||||
\(879\) | 9.06423 | + | 13.8545i | 0.305729 | + | 0.467300i | ||||
\(880\) | 27.6991 | 0.933738 | ||||||||
\(881\) | −0.497153 | + | 0.861094i | −0.0167495 | + | 0.0290110i | −0.874279 | − | 0.485424i | \(-0.838665\pi\) |
0.857529 | + | 0.514435i | \(0.171998\pi\) | |||||||
\(882\) | 4.64191 | + | 2.02906i | 0.156301 | + | 0.0683220i | ||||
\(883\) | 15.3052 | 0.515061 | 0.257530 | − | 0.966270i | \(-0.417091\pi\) | ||||
0.257530 | + | 0.966270i | \(0.417091\pi\) | |||||||
\(884\) | 7.40944 | + | 7.50139i | 0.249206 | + | 0.252299i | ||||
\(885\) | −38.6710 | − | 19.5388i | −1.29991 | − | 0.656788i | ||||
\(886\) | − | 37.0665i | − | 1.24527i | ||||||
\(887\) | −26.5114 | −0.890166 | −0.445083 | − | 0.895489i | \(-0.646826\pi\) | ||||
−0.445083 | + | 0.895489i | \(0.646826\pi\) | |||||||
\(888\) | −19.2478 | + | 12.5928i | −0.645913 | + | 0.422585i | ||||
\(889\) | −16.3771 | − | 9.45530i | −0.549269 | − | 0.317121i | ||||
\(890\) | −51.2031 | + | 29.5621i | −1.71633 | + | 0.990924i | ||||
\(891\) | −5.54949 | − | 24.4695i | −0.185915 | − | 0.819759i | ||||
\(892\) | − | 11.0576i | − | 0.370237i | ||||||
\(893\) | −15.1538 | −0.507102 | ||||||||
\(894\) | −34.8353 | − | 17.6008i | −1.16507 | − | 0.588658i | ||||
\(895\) | 12.9713i | 0.433582i | ||||||||
\(896\) | 6.47829 | + | 11.2207i | 0.216424 | + | 0.374858i | ||||
\(897\) | 1.66112 | + | 5.16103i | 0.0554632 | + | 0.172322i | ||||
\(898\) | 4.74438 | − | 8.21751i | 0.158322 | − | 0.274222i | ||||
\(899\) | −13.2954 | − | 7.67608i | −0.443425 | − | 0.256012i | ||||
\(900\) | −1.04001 | + | 2.37926i | −0.0346671 | + | 0.0793086i | ||||
\(901\) | −9.13559 | − | 15.8233i | −0.304351 | − | 0.527151i | ||||
\(902\) | −9.21220 | − | 5.31867i | −0.306733 | − | 0.177092i | ||||
\(903\) | 2.04804 | − | 4.05346i | 0.0681545 | − | 0.134891i | ||||
\(904\) | −12.3510 | − | 7.13085i | −0.410788 | − | 0.237169i | ||||
\(905\) | −5.51851 | + | 3.18612i | −0.183442 | + | 0.105910i | ||||
\(906\) | −25.9928 | − | 13.1330i | −0.863551 | − | 0.436315i | ||||
\(907\) | −26.3334 | − | 45.6108i | −0.874386 | − | 1.51448i | −0.857415 | − | 0.514625i | \(-0.827931\pi\) |
−0.0169710 | − | 0.999856i | \(-0.505402\pi\) | |||||||
\(908\) | −12.8478 | − | 7.41769i | −0.426369 | − | 0.246165i | ||||
\(909\) | −19.7207 | + | 45.1154i | −0.654095 | + | 1.49638i | ||||
\(910\) | 3.07278 | + | 11.7573i | 0.101862 | + | 0.389751i | ||||
\(911\) | 5.84476 | − | 10.1234i | 0.193645 | − | 0.335404i | −0.752810 | − | 0.658238i | \(-0.771302\pi\) |
0.946456 | + | 0.322834i | \(0.104636\pi\) | |||||||
\(912\) | −13.9034 | − | 21.2510i | −0.460386 | − | 0.703690i | ||||
\(913\) | −32.5500 | −1.07725 | ||||||||
\(914\) | 7.43333 | − | 12.8749i | 0.245873 | − | 0.425864i | ||||
\(915\) | −23.0003 | + | 1.28371i | −0.760367 | + | 0.0424382i | ||||
\(916\) | 17.3585i | 0.573540i | ||||||||
\(917\) | −14.3321 | + | 8.27462i | −0.473287 | + | 0.273252i | ||||
\(918\) | −10.5109 | + | 28.2382i | −0.346911 | + | 0.931998i | ||||
\(919\) | 20.1980 | + | 34.9840i | 0.666272 | + | 1.15402i | 0.978939 | + | 0.204154i | \(0.0654442\pi\) |
−0.312667 | + | 0.949863i | \(0.601222\pi\) | |||||||
\(920\) | −1.68017 | − | 2.91015i | −0.0553937 | − | 0.0959447i | ||||
\(921\) | −15.7309 | + | 31.1344i | −0.518349 | + | 1.02591i | ||||
\(922\) | −28.6010 | − | 49.5384i | −0.941923 | − | 1.63146i | ||||
\(923\) | −32.5457 | − | 8.93605i | −1.07125 | − | 0.294134i | ||||
\(924\) | 3.67029 | + | 1.85444i | 0.120744 | + | 0.0610065i | ||||
\(925\) | −6.02747 | + | 3.47996i | −0.198182 | + | 0.114420i | ||||
\(926\) | −7.38777 | + | 12.7960i | −0.242777 | + | 0.420502i | ||||
\(927\) | 18.0299 | − | 41.2472i | 0.592179 | − | 1.35474i | ||||
\(928\) | − | 11.1841i | − | 0.367137i | ||||||
\(929\) | 31.2317i | 1.02468i | 0.858783 | + | 0.512340i | \(0.171221\pi\) | ||||
−0.858783 | + | 0.512340i | \(0.828779\pi\) | |||||||
\(930\) | 16.3615 | − | 32.3827i | 0.536516 | − | 1.06187i | ||||
\(931\) | −2.55074 | + | 1.47267i | −0.0835970 | + | 0.0482648i | ||||
\(932\) | 3.85422 | − | 6.67571i | 0.126249 | − | 0.218670i | ||||
\(933\) | 1.74135 | + | 31.1998i | 0.0570092 | + | 1.02144i | ||||
\(934\) | −21.7118 | + | 12.5353i | −0.710431 | + | 0.410168i | ||||
\(935\) | 19.1073 | 0.624875 | ||||||||
\(936\) | 20.7201 | + | 3.26850i | 0.677258 | + | 0.106834i | ||||
\(937\) | 18.3937 | 0.600895 | 0.300447 | − | 0.953798i | \(-0.402864\pi\) | ||||
0.300447 | + | 0.953798i | \(0.402864\pi\) | |||||||
\(938\) | −3.06353 | + | 1.76873i | −0.100028 | + | 0.0577511i | ||||
\(939\) | −21.7349 | + | 14.2200i | −0.709292 | + | 0.464051i | ||||
\(940\) | 4.37253 | − | 7.57344i | 0.142616 | − | 0.247018i | ||||
\(941\) | 23.8224 | − | 13.7539i | 0.776588 | − | 0.448363i | −0.0586318 | − | 0.998280i | \(-0.518674\pi\) |
0.835220 | + | 0.549916i | \(0.185340\pi\) | |||||||
\(942\) | 14.2701 | + | 21.8116i | 0.464946 | + | 0.710660i | ||||
\(943\) | 1.96166i | 0.0638803i | ||||||||
\(944\) | − | 62.3891i | − | 2.03059i | ||||||
\(945\) | −7.99290 | + | 6.60844i | −0.260009 | + | 0.214973i | ||||
\(946\) | 6.17199 | − | 10.6902i | 0.200669 | − | 0.347568i | ||||
\(947\) | 1.38427 | − | 0.799208i | 0.0449827 | − | 0.0259708i | −0.477340 | − | 0.878719i | \(-0.658399\pi\) |
0.522323 | + | 0.852748i | \(0.325066\pi\) | |||||||
\(948\) | 0.251436 | + | 4.50500i | 0.00816627 | + | 0.146315i | ||||
\(949\) | 28.6265 | − | 28.2756i | 0.929257 | − | 0.917866i | ||||
\(950\) | −2.52756 | − | 4.37786i | −0.0820049 | − | 0.142037i | ||||
\(951\) | 15.7008 | + | 23.9983i | 0.509133 | + | 0.778198i | ||||
\(952\) | 3.32960 | + | 5.76705i | 0.107913 | + | 0.186911i | ||||
\(953\) | 5.68885 | + | 9.85338i | 0.184280 | + | 0.319182i | 0.943334 | − | 0.331846i | \(-0.107671\pi\) |
−0.759054 | + | 0.651028i | \(0.774338\pi\) | |||||||
\(954\) | 24.6989 | + | 10.7963i | 0.799656 | + | 0.349543i | ||||
\(955\) | −2.43837 | + | 1.40780i | −0.0789039 | + | 0.0455552i | ||||
\(956\) | 1.60969i | 0.0520611i | ||||||||
\(957\) | 6.53034 | + | 9.98148i | 0.211096 | + | 0.322656i | ||||
\(958\) | 15.9421 | − | 27.6125i | 0.515065 | − | 0.892119i | ||||
\(959\) | −13.6505 | −0.440797 | ||||||||
\(960\) | −7.97426 | + | 0.445066i | −0.257368 | + | 0.0143644i | ||||
\(961\) | 3.81292 | − | 6.60418i | 0.122998 | − | 0.213038i | ||||
\(962\) | −29.2994 | − | 29.6630i | −0.944652 | − | 0.956375i | ||||
\(963\) | 0.418952 | − | 0.0469119i | 0.0135006 | − | 0.00151172i | ||||
\(964\) | −5.38080 | − | 3.10661i | −0.173304 | − | 0.100057i | ||||
\(965\) | −20.8049 | − | 36.0351i | −0.669732 | − | 1.16001i | ||||
\(966\) | −0.141505 | − | 2.53535i | −0.00455285 | − | 0.0815736i | ||||
\(967\) | −49.1602 | + | 28.3826i | −1.58088 | + | 0.912724i | −0.586153 | + | 0.810200i | \(0.699358\pi\) |
−0.994731 | + | 0.102524i | \(0.967308\pi\) | |||||||
\(968\) | 5.42083 | + | 3.12972i | 0.174232 | + | 0.100593i | ||||
\(969\) | −9.59075 | − | 14.6593i | −0.308099 | − | 0.470923i | ||||
\(970\) | −19.6441 | − | 11.3415i | −0.630735 | − | 0.364155i | ||||
\(971\) | −16.0791 | − | 27.8498i | −0.516002 | − | 0.893742i | −0.999827 | − | 0.0185771i | \(-0.994086\pi\) |
0.483825 | − | 0.875164i | \(-0.339247\pi\) | |||||||
\(972\) | −3.65303 | − | 12.7627i | −0.117171 | − | 0.409363i | ||||
\(973\) | 5.66357 | + | 3.26986i | 0.181566 | + | 0.104827i | ||||
\(974\) | −18.6142 | + | 32.2408i | −0.596439 | + | 1.03306i | ||||
\(975\) | 6.20484 | + | 1.33686i | 0.198714 | + | 0.0428139i | ||||
\(976\) | −16.5856 | − | 28.7271i | −0.530893 | − | 0.919534i | ||||
\(977\) | − | 7.35146i | − | 0.235194i | −0.993061 | − | 0.117597i | \(-0.962481\pi\) | ||
0.993061 | − | 0.117597i | \(-0.0375191\pi\) | |||||||
\(978\) | −9.25408 | + | 6.05444i | −0.295913 | + | 0.193600i | ||||
\(979\) | 48.9052 | 1.56302 | ||||||||
\(980\) | − | 1.69972i | − | 0.0542955i | ||||||
\(981\) | 11.7036 | − | 8.62520i | 0.373668 | − | 0.275381i | ||||
\(982\) | −10.7229 | + | 6.19084i | −0.342180 | + | 0.197558i | ||||
\(983\) | −17.6234 | − | 10.1749i | −0.562099 | − | 0.324528i | 0.191889 | − | 0.981417i | \(-0.438539\pi\) |
−0.753988 | + | 0.656889i | \(0.771872\pi\) | |||||||
\(984\) | 6.77393 | + | 3.42257i | 0.215945 | + | 0.109108i | ||||
\(985\) | −55.6175 | −1.77212 | ||||||||
\(986\) | − | 14.3239i | − | 0.456166i | ||||||
\(987\) | −7.45722 | + | 4.87885i | −0.237366 | + | 0.155295i | ||||
\(988\) | 6.43414 | − | 6.35527i | 0.204697 | − | 0.202188i | ||||
\(989\) | −2.27638 | −0.0723847 | ||||||||
\(990\) | −22.6923 | + | 16.7235i | −0.721209 | + | 0.531508i | ||||
\(991\) | −14.3598 | + | 24.8719i | −0.456154 | + | 0.790081i | −0.998754 | − | 0.0499099i | \(-0.984107\pi\) |
0.542600 | + | 0.839991i | \(0.317440\pi\) | |||||||
\(992\) | 28.1391 | 0.893417 | ||||||||
\(993\) | 23.0085 | − | 45.5382i | 0.730151 | − | 1.44511i | ||||
\(994\) | 13.6892 | + | 7.90349i | 0.434196 | + | 0.250683i | ||||
\(995\) | 26.5875 | + | 15.3503i | 0.842880 | + | 0.486637i | ||||
\(996\) | −17.1949 | + | 0.959695i | −0.544841 | + | 0.0304091i | ||||
\(997\) | 33.7710 | 1.06954 | 0.534768 | − | 0.844999i | \(-0.320399\pi\) | ||||
0.534768 | + | 0.844999i | \(0.320399\pi\) | |||||||
\(998\) | 17.9354 | − | 31.0651i | 0.567737 | − | 0.983349i | ||||
\(999\) | 12.4126 | − | 33.3471i | 0.392717 | − | 1.05506i |
(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 | 819.2.dk.a.43.21 | yes | 168 | |
9.4 | even | 3 | 819.2.bh.a.589.21 | ✓ | 168 | ||
13.10 | even | 6 | 819.2.bh.a.673.64 | yes | 168 | ||
117.49 | even | 6 | inner | 819.2.dk.a.400.21 | yes | 168 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
819.2.bh.a.589.21 | ✓ | 168 | 9.4 | even | 3 | ||
819.2.bh.a.673.64 | yes | 168 | 13.10 | even | 6 | ||
819.2.dk.a.43.21 | yes | 168 | 1.1 | even | 1 | trivial | |
819.2.dk.a.400.21 | yes | 168 | 117.49 | even | 6 | inner |