Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(91,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 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("552.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.n (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: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.14 | ||
Character | \(\chi\) | \(=\) | 552.91 |
Dual form | 552.2.n.a.91.16 |
$q$-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 \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0902148 | − | 1.41133i | 0.0637915 | − | 0.997963i | ||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.98372 | − | 0.254646i | −0.991861 | − | 0.127323i | ||||
\(5\) | 3.06098 | 1.36891 | 0.684457 | − | 0.729054i | \(-0.260040\pi\) | ||||
0.684457 | + | 0.729054i | \(0.260040\pi\) | |||||||
\(6\) | 0.0902148 | − | 1.41133i | 0.0368300 | − | 0.576174i | ||||
\(7\) | 0.892124 | 0.337191 | 0.168596 | − | 0.985685i | \(-0.446077\pi\) | ||||
0.168596 | + | 0.985685i | \(0.446077\pi\) | |||||||
\(8\) | −0.538352 | + | 2.77672i | −0.190336 | + | 0.981719i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.276146 | − | 4.32007i | 0.0873250 | − | 1.36612i | ||||
\(11\) | − | 3.95311i | − | 1.19191i | −0.803019 | − | 0.595953i | \(-0.796774\pi\) | ||
0.803019 | − | 0.595953i | \(-0.203226\pi\) | |||||||
\(12\) | −1.98372 | − | 0.254646i | −0.572651 | − | 0.0735100i | ||||
\(13\) | 4.14787i | 1.15041i | 0.818008 | + | 0.575207i | \(0.195078\pi\) | ||||
−0.818008 | + | 0.575207i | \(0.804922\pi\) | |||||||
\(14\) | 0.0804827 | − | 1.25908i | 0.0215099 | − | 0.336504i | ||||
\(15\) | 3.06098 | 0.790342 | ||||||||
\(16\) | 3.87031 | + | 1.01029i | 0.967578 | + | 0.252574i | ||||
\(17\) | − | 1.01396i | − | 0.245922i | −0.992411 | − | 0.122961i | \(-0.960761\pi\) | ||
0.992411 | − | 0.122961i | \(-0.0392391\pi\) | |||||||
\(18\) | 0.0902148 | − | 1.41133i | 0.0212638 | − | 0.332654i | ||||
\(19\) | 0.195663i | 0.0448882i | 0.999748 | + | 0.0224441i | \(0.00714478\pi\) | ||||
−0.999748 | + | 0.0224441i | \(0.992855\pi\) | |||||||
\(20\) | −6.07214 | − | 0.779468i | −1.35777 | − | 0.174294i | ||||
\(21\) | 0.892124 | 0.194677 | ||||||||
\(22\) | −5.57915 | − | 0.356629i | −1.18948 | − | 0.0760335i | ||||
\(23\) | 4.42425 | − | 1.85094i | 0.922521 | − | 0.385947i | ||||
\(24\) | −0.538352 | + | 2.77672i | −0.109891 | + | 0.566796i | ||||
\(25\) | 4.36961 | 0.873923 | ||||||||
\(26\) | 5.85403 | + | 0.374200i | 1.14807 | + | 0.0733866i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.76973 | − | 0.227176i | −0.334447 | − | 0.0429322i | ||||
\(29\) | 3.05624i | 0.567530i | 0.958894 | + | 0.283765i | \(0.0915835\pi\) | ||||
−0.958894 | + | 0.283765i | \(0.908416\pi\) | |||||||
\(30\) | 0.276146 | − | 4.32007i | 0.0504171 | − | 0.788733i | ||||
\(31\) | − | 2.58909i | − | 0.465015i | −0.972595 | − | 0.232507i | \(-0.925307\pi\) | ||
0.972595 | − | 0.232507i | \(-0.0746930\pi\) | |||||||
\(32\) | 1.77502 | − | 5.37115i | 0.313783 | − | 0.949495i | ||||
\(33\) | − | 3.95311i | − | 0.688147i | ||||||
\(34\) | −1.43104 | − | 0.0914745i | −0.245421 | − | 0.0156878i | ||||
\(35\) | 2.73077 | 0.461585 | ||||||||
\(36\) | −1.98372 | − | 0.254646i | −0.330620 | − | 0.0424410i | ||||
\(37\) | −6.01692 | −0.989176 | −0.494588 | − | 0.869128i | \(-0.664681\pi\) | ||||
−0.494588 | + | 0.869128i | \(0.664681\pi\) | |||||||
\(38\) | 0.276146 | + | 0.0176517i | 0.0447968 | + | 0.00286349i | ||||
\(39\) | 4.14787i | 0.664192i | ||||||||
\(40\) | −1.64789 | + | 8.49949i | −0.260554 | + | 1.34389i | ||||
\(41\) | −10.2344 | −1.59835 | −0.799174 | − | 0.601099i | \(-0.794730\pi\) | ||||
−0.799174 | + | 0.601099i | \(0.794730\pi\) | |||||||
\(42\) | 0.0804827 | − | 1.25908i | 0.0124188 | − | 0.194281i | ||||
\(43\) | − | 10.0034i | − | 1.52550i | −0.646691 | − | 0.762752i | \(-0.723847\pi\) | ||
0.646691 | − | 0.762752i | \(-0.276153\pi\) | |||||||
\(44\) | −1.00664 | + | 7.84187i | −0.151757 | + | 1.18221i | ||||
\(45\) | 3.06098 | 0.456304 | ||||||||
\(46\) | −2.21316 | − | 6.41108i | −0.326312 | − | 0.945262i | ||||
\(47\) | 7.33196i | 1.06948i | 0.845018 | + | 0.534738i | \(0.179590\pi\) | ||||
−0.845018 | + | 0.534738i | \(0.820410\pi\) | |||||||
\(48\) | 3.87031 | + | 1.01029i | 0.558631 | + | 0.145824i | ||||
\(49\) | −6.20412 | −0.886302 | ||||||||
\(50\) | 0.394204 | − | 6.16698i | 0.0557488 | − | 0.872143i | ||||
\(51\) | − | 1.01396i | − | 0.141983i | ||||||
\(52\) | 1.05624 | − | 8.22823i | 0.146474 | − | 1.14105i | ||||
\(53\) | 11.2321 | 1.54285 | 0.771425 | − | 0.636320i | \(-0.219544\pi\) | ||||
0.771425 | + | 0.636320i | \(0.219544\pi\) | |||||||
\(54\) | 0.0902148 | − | 1.41133i | 0.0122767 | − | 0.192058i | ||||
\(55\) | − | 12.1004i | − | 1.63162i | ||||||
\(56\) | −0.480276 | + | 2.47718i | −0.0641796 | + | 0.331027i | ||||
\(57\) | 0.195663i | 0.0259162i | ||||||||
\(58\) | 4.31337 | + | 0.275718i | 0.566374 | + | 0.0362036i | ||||
\(59\) | −4.35054 | −0.566393 | −0.283196 | − | 0.959062i | \(-0.591395\pi\) | ||||
−0.283196 | + | 0.959062i | \(0.591395\pi\) | |||||||
\(60\) | −6.07214 | − | 0.779468i | −0.783910 | − | 0.100629i | ||||
\(61\) | −7.63888 | −0.978059 | −0.489029 | − | 0.872267i | \(-0.662649\pi\) | ||||
−0.489029 | + | 0.872267i | \(0.662649\pi\) | |||||||
\(62\) | −3.65407 | − | 0.233574i | −0.464068 | − | 0.0296640i | ||||
\(63\) | 0.892124 | 0.112397 | ||||||||
\(64\) | −7.42035 | − | 2.98971i | −0.927544 | − | 0.373713i | ||||
\(65\) | 12.6966i | 1.57482i | ||||||||
\(66\) | −5.57915 | − | 0.356629i | −0.686746 | − | 0.0438980i | ||||
\(67\) | 3.60187i | 0.440039i | 0.975496 | + | 0.220019i | \(0.0706120\pi\) | ||||
−0.975496 | + | 0.220019i | \(0.929388\pi\) | |||||||
\(68\) | −0.258202 | + | 2.01142i | −0.0313116 | + | 0.243921i | ||||
\(69\) | 4.42425 | − | 1.85094i | 0.532618 | − | 0.222827i | ||||
\(70\) | 0.246356 | − | 3.85403i | 0.0294452 | − | 0.460645i | ||||
\(71\) | 10.5891i | 1.25669i | 0.777933 | + | 0.628347i | \(0.216268\pi\) | ||||
−0.777933 | + | 0.628347i | \(0.783732\pi\) | |||||||
\(72\) | −0.538352 | + | 2.77672i | −0.0634454 | + | 0.327240i | ||||
\(73\) | 3.24682 | 0.380011 | 0.190006 | − | 0.981783i | \(-0.439149\pi\) | ||||
0.190006 | + | 0.981783i | \(0.439149\pi\) | |||||||
\(74\) | −0.542815 | + | 8.49188i | −0.0631010 | + | 0.987161i | ||||
\(75\) | 4.36961 | 0.504560 | ||||||||
\(76\) | 0.0498249 | − | 0.388141i | 0.00571531 | − | 0.0445229i | ||||
\(77\) | − | 3.52666i | − | 0.401900i | ||||||
\(78\) | 5.85403 | + | 0.374200i | 0.662839 | + | 0.0423698i | ||||
\(79\) | −1.85136 | −0.208294 | −0.104147 | − | 0.994562i | \(-0.533211\pi\) | ||||
−0.104147 | + | 0.994562i | \(0.533211\pi\) | |||||||
\(80\) | 11.8470 | + | 3.09250i | 1.32453 | + | 0.345751i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.923296 | + | 14.4442i | −0.101961 | + | 1.59509i | ||||
\(83\) | 3.79082i | 0.416097i | 0.978119 | + | 0.208048i | \(0.0667111\pi\) | ||||
−0.978119 | + | 0.208048i | \(0.933289\pi\) | |||||||
\(84\) | −1.76973 | − | 0.227176i | −0.193093 | − | 0.0247869i | ||||
\(85\) | − | 3.10373i | − | 0.336646i | ||||||
\(86\) | −14.1181 | − | 0.902455i | −1.52240 | − | 0.0973142i | ||||
\(87\) | 3.05624i | 0.327663i | ||||||||
\(88\) | 10.9767 | + | 2.12816i | 1.17012 | + | 0.226863i | ||||
\(89\) | 10.7963i | 1.14440i | 0.820113 | + | 0.572202i | \(0.193911\pi\) | ||||
−0.820113 | + | 0.572202i | \(0.806089\pi\) | |||||||
\(90\) | 0.276146 | − | 4.32007i | 0.0291083 | − | 0.455375i | ||||
\(91\) | 3.70042i | 0.387909i | ||||||||
\(92\) | −9.24783 | + | 2.54513i | −0.964153 | + | 0.265348i | ||||
\(93\) | − | 2.58909i | − | 0.268476i | ||||||
\(94\) | 10.3478 | + | 0.661451i | 1.06730 | + | 0.0682235i | ||||
\(95\) | 0.598921i | 0.0614480i | ||||||||
\(96\) | 1.77502 | − | 5.37115i | 0.181162 | − | 0.548191i | ||||
\(97\) | 2.49750i | 0.253583i | 0.991929 | + | 0.126792i | \(0.0404679\pi\) | ||||
−0.991929 | + | 0.126792i | \(0.959532\pi\) | |||||||
\(98\) | −0.559703 | + | 8.75607i | −0.0565385 | + | 0.884497i | ||||
\(99\) | − | 3.95311i | − | 0.397302i | ||||||
\(100\) | −8.66810 | − | 1.11271i | −0.866810 | − | 0.111271i | ||||
\(101\) | − | 3.30462i | − | 0.328822i | −0.986392 | − | 0.164411i | \(-0.947428\pi\) | ||
0.986392 | − | 0.164411i | \(-0.0525723\pi\) | |||||||
\(102\) | −1.43104 | − | 0.0914745i | −0.141694 | − | 0.00905733i | ||||
\(103\) | −10.3779 | −1.02257 | −0.511284 | − | 0.859412i | \(-0.670830\pi\) | ||||
−0.511284 | + | 0.859412i | \(0.670830\pi\) | |||||||
\(104\) | −11.5175 | − | 2.23302i | −1.12938 | − | 0.218965i | ||||
\(105\) | 2.73077 | 0.266496 | ||||||||
\(106\) | 1.01330 | − | 15.8523i | 0.0984207 | − | 1.53971i | ||||
\(107\) | − | 18.3222i | − | 1.77127i | −0.464381 | − | 0.885635i | \(-0.653723\pi\) | ||
0.464381 | − | 0.885635i | \(-0.346277\pi\) | |||||||
\(108\) | −1.98372 | − | 0.254646i | −0.190884 | − | 0.0245033i | ||||
\(109\) | 12.4462 | 1.19213 | 0.596064 | − | 0.802937i | \(-0.296731\pi\) | ||||
0.596064 | + | 0.802937i | \(0.296731\pi\) | |||||||
\(110\) | −17.0777 | − | 1.09163i | −1.62829 | − | 0.104083i | ||||
\(111\) | −6.01692 | −0.571101 | ||||||||
\(112\) | 3.45280 | + | 0.901308i | 0.326259 | + | 0.0851656i | ||||
\(113\) | 16.0203i | 1.50707i | 0.657410 | + | 0.753533i | \(0.271652\pi\) | ||||
−0.657410 | + | 0.753533i | \(0.728348\pi\) | |||||||
\(114\) | 0.276146 | + | 0.0176517i | 0.0258634 | + | 0.00165323i | ||||
\(115\) | 13.5426 | − | 5.66569i | 1.26285 | − | 0.528328i | ||||
\(116\) | 0.778260 | − | 6.06273i | 0.0722596 | − | 0.562911i | ||||
\(117\) | 4.14787i | 0.383471i | ||||||||
\(118\) | −0.392483 | + | 6.14007i | −0.0361310 | + | 0.565239i | ||||
\(119\) | − | 0.904581i | − | 0.0829228i | ||||||
\(120\) | −1.64789 | + | 8.49949i | −0.150431 | + | 0.775894i | ||||
\(121\) | −4.62705 | −0.420641 | ||||||||
\(122\) | −0.689140 | + | 10.7810i | −0.0623918 | + | 0.976067i | ||||
\(123\) | −10.2344 | −0.922807 | ||||||||
\(124\) | −0.659303 | + | 5.13604i | −0.0592071 | + | 0.461230i | ||||
\(125\) | −1.92960 | −0.172589 | ||||||||
\(126\) | 0.0804827 | − | 1.25908i | 0.00716997 | − | 0.112168i | ||||
\(127\) | 0.281251i | 0.0249569i | 0.999922 | + | 0.0124785i | \(0.00397212\pi\) | ||||
−0.999922 | + | 0.0124785i | \(0.996028\pi\) | |||||||
\(128\) | −4.88890 | + | 10.2029i | −0.432121 | + | 0.901815i | ||||
\(129\) | − | 10.0034i | − | 0.880751i | ||||||
\(130\) | 17.9191 | + | 1.14542i | 1.57161 | + | 0.100460i | ||||
\(131\) | 21.7964 | 1.90436 | 0.952179 | − | 0.305542i | \(-0.0988377\pi\) | ||||
0.952179 | + | 0.305542i | \(0.0988377\pi\) | |||||||
\(132\) | −1.00664 | + | 7.84187i | −0.0876171 | + | 0.682547i | ||||
\(133\) | 0.174556i | 0.0151359i | ||||||||
\(134\) | 5.08344 | + | 0.324942i | 0.439142 | + | 0.0280707i | ||||
\(135\) | 3.06098 | 0.263447 | ||||||||
\(136\) | 2.81549 | + | 0.545869i | 0.241427 | + | 0.0468079i | ||||
\(137\) | 19.1551i | 1.63653i | 0.574839 | + | 0.818267i | \(0.305065\pi\) | ||||
−0.574839 | + | 0.818267i | \(0.694935\pi\) | |||||||
\(138\) | −2.21316 | − | 6.41108i | −0.188396 | − | 0.545747i | ||||
\(139\) | −13.3472 | −1.13210 | −0.566048 | − | 0.824373i | \(-0.691528\pi\) | ||||
−0.566048 | + | 0.824373i | \(0.691528\pi\) | |||||||
\(140\) | −5.41710 | − | 0.695382i | −0.457828 | − | 0.0587705i | ||||
\(141\) | 7.33196i | 0.617462i | ||||||||
\(142\) | 14.9447 | + | 0.955293i | 1.25413 | + | 0.0801664i | ||||
\(143\) | 16.3970 | 1.37119 | ||||||||
\(144\) | 3.87031 | + | 1.01029i | 0.322526 | + | 0.0841912i | ||||
\(145\) | 9.35510i | 0.776899i | ||||||||
\(146\) | 0.292911 | − | 4.58234i | 0.0242415 | − | 0.379237i | ||||
\(147\) | −6.20412 | −0.511707 | ||||||||
\(148\) | 11.9359 | + | 1.53219i | 0.981125 | + | 0.125945i | ||||
\(149\) | 1.91404 | 0.156804 | 0.0784020 | − | 0.996922i | \(-0.475018\pi\) | ||||
0.0784020 | + | 0.996922i | \(0.475018\pi\) | |||||||
\(150\) | 0.394204 | − | 6.16698i | 0.0321866 | − | 0.503532i | ||||
\(151\) | 15.4992i | 1.26131i | 0.776064 | + | 0.630654i | \(0.217213\pi\) | ||||
−0.776064 | + | 0.630654i | \(0.782787\pi\) | |||||||
\(152\) | −0.543302 | − | 0.105336i | −0.0440676 | − | 0.00854385i | ||||
\(153\) | − | 1.01396i | − | 0.0819741i | ||||||
\(154\) | −4.97729 | − | 0.318157i | −0.401082 | − | 0.0256378i | ||||
\(155\) | − | 7.92517i | − | 0.636565i | ||||||
\(156\) | 1.05624 | − | 8.22823i | 0.0845669 | − | 0.658786i | ||||
\(157\) | −11.0597 | −0.882663 | −0.441331 | − | 0.897344i | \(-0.645494\pi\) | ||||
−0.441331 | + | 0.897344i | \(0.645494\pi\) | |||||||
\(158\) | −0.167020 | + | 2.61288i | −0.0132874 | + | 0.207870i | ||||
\(159\) | 11.2321 | 0.890765 | ||||||||
\(160\) | 5.43331 | − | 16.4410i | 0.429541 | − | 1.29978i | ||||
\(161\) | 3.94698 | − | 1.65126i | 0.311066 | − | 0.130138i | ||||
\(162\) | 0.0902148 | − | 1.41133i | 0.00708794 | − | 0.110885i | ||||
\(163\) | 10.0689 | 0.788659 | 0.394330 | − | 0.918969i | \(-0.370977\pi\) | ||||
0.394330 | + | 0.918969i | \(0.370977\pi\) | |||||||
\(164\) | 20.3023 | + | 2.60616i | 1.58534 | + | 0.203507i | ||||
\(165\) | − | 12.1004i | − | 0.942014i | ||||||
\(166\) | 5.35011 | + | 0.341988i | 0.415249 | + | 0.0265434i | ||||
\(167\) | − | 11.5383i | − | 0.892858i | −0.894819 | − | 0.446429i | \(-0.852696\pi\) | ||
0.894819 | − | 0.446429i | \(-0.147304\pi\) | |||||||
\(168\) | −0.480276 | + | 2.47718i | −0.0370541 | + | 0.191118i | ||||
\(169\) | −4.20486 | −0.323451 | ||||||||
\(170\) | −4.38039 | − | 0.280002i | −0.335961 | − | 0.0214752i | ||||
\(171\) | 0.195663i | 0.0149627i | ||||||||
\(172\) | −2.54733 | + | 19.8440i | −0.194232 | + | 1.51309i | ||||
\(173\) | − | 6.42949i | − | 0.488825i | −0.969671 | − | 0.244413i | \(-0.921405\pi\) | ||
0.969671 | − | 0.244413i | \(-0.0785951\pi\) | |||||||
\(174\) | 4.31337 | + | 0.275718i | 0.326996 | + | 0.0209021i | ||||
\(175\) | 3.89824 | 0.294679 | ||||||||
\(176\) | 3.99380 | − | 15.2997i | 0.301044 | − | 1.15326i | ||||
\(177\) | −4.35054 | −0.327007 | ||||||||
\(178\) | 15.2371 | + | 0.973984i | 1.14207 | + | 0.0730032i | ||||
\(179\) | −0.681542 | −0.0509408 | −0.0254704 | − | 0.999676i | \(-0.508108\pi\) | ||||
−0.0254704 | + | 0.999676i | \(0.508108\pi\) | |||||||
\(180\) | −6.07214 | − | 0.779468i | −0.452591 | − | 0.0580981i | ||||
\(181\) | 8.75811 | 0.650985 | 0.325492 | − | 0.945545i | \(-0.394470\pi\) | ||||
0.325492 | + | 0.945545i | \(0.394470\pi\) | |||||||
\(182\) | 5.22252 | + | 0.333832i | 0.387119 | + | 0.0247453i | ||||
\(183\) | −7.63888 | −0.564682 | ||||||||
\(184\) | 2.75773 | + | 13.2814i | 0.203303 | + | 0.979116i | ||||
\(185\) | −18.4177 | −1.35410 | ||||||||
\(186\) | −3.65407 | − | 0.233574i | −0.267930 | − | 0.0171265i | ||||
\(187\) | −4.00831 | −0.293116 | ||||||||
\(188\) | 1.86706 | − | 14.5446i | 0.136169 | − | 1.06077i | ||||
\(189\) | 0.892124 | 0.0648924 | ||||||||
\(190\) | 0.845278 | + | 0.0540316i | 0.0613229 | + | 0.00391986i | ||||
\(191\) | −7.03883 | −0.509312 | −0.254656 | − | 0.967032i | \(-0.581962\pi\) | ||||
−0.254656 | + | 0.967032i | \(0.581962\pi\) | |||||||
\(192\) | −7.42035 | − | 2.98971i | −0.535518 | − | 0.215763i | ||||
\(193\) | −21.4049 | −1.54076 | −0.770379 | − | 0.637586i | \(-0.779933\pi\) | ||||
−0.770379 | + | 0.637586i | \(0.779933\pi\) | |||||||
\(194\) | 3.52481 | + | 0.225312i | 0.253067 | + | 0.0161764i | ||||
\(195\) | 12.6966i | 0.909220i | ||||||||
\(196\) | 12.3072 | + | 1.57985i | 0.879089 | + | 0.112847i | ||||
\(197\) | 16.5652i | 1.18022i | 0.807323 | + | 0.590109i | \(0.200915\pi\) | ||||
−0.807323 | + | 0.590109i | \(0.799085\pi\) | |||||||
\(198\) | −5.57915 | − | 0.356629i | −0.396493 | − | 0.0253445i | ||||
\(199\) | −18.7514 | −1.32925 | −0.664627 | − | 0.747175i | \(-0.731409\pi\) | ||||
−0.664627 | + | 0.747175i | \(0.731409\pi\) | |||||||
\(200\) | −2.35239 | + | 12.1332i | −0.166339 | + | 0.857947i | ||||
\(201\) | 3.60187i | 0.254056i | ||||||||
\(202\) | −4.66392 | − | 0.298125i | −0.328152 | − | 0.0209760i | ||||
\(203\) | 2.72654i | 0.191366i | ||||||||
\(204\) | −0.258202 | + | 2.01142i | −0.0180778 | + | 0.140828i | ||||
\(205\) | −31.3274 | −2.18800 | ||||||||
\(206\) | −0.936243 | + | 14.6467i | −0.0652311 | + | 1.02049i | ||||
\(207\) | 4.42425 | − | 1.85094i | 0.307507 | − | 0.128649i | ||||
\(208\) | −4.19058 | + | 16.0536i | −0.290564 | + | 1.11311i | ||||
\(209\) | 0.773477 | 0.0535025 | ||||||||
\(210\) | 0.246356 | − | 3.85403i | 0.0170002 | − | 0.265954i | ||||
\(211\) | −4.73983 | −0.326303 | −0.163152 | − | 0.986601i | \(-0.552166\pi\) | ||||
−0.163152 | + | 0.986601i | \(0.552166\pi\) | |||||||
\(212\) | −22.2814 | − | 2.86022i | −1.53029 | − | 0.196441i | ||||
\(213\) | 10.5891i | 0.725553i | ||||||||
\(214\) | −25.8587 | − | 1.65293i | −1.76766 | − | 0.112992i | ||||
\(215\) | − | 30.6202i | − | 2.08828i | ||||||
\(216\) | −0.538352 | + | 2.77672i | −0.0366302 | + | 0.188932i | ||||
\(217\) | − | 2.30979i | − | 0.156799i | ||||||
\(218\) | 1.12283 | − | 17.5657i | 0.0760476 | − | 1.18970i | ||||
\(219\) | 3.24682 | 0.219400 | ||||||||
\(220\) | −3.08132 | + | 24.0038i | −0.207742 | + | 1.61834i | ||||
\(221\) | 4.20580 | 0.282912 | ||||||||
\(222\) | −0.542815 | + | 8.49188i | −0.0364314 | + | 0.569938i | ||||
\(223\) | − | 8.79654i | − | 0.589060i | −0.955642 | − | 0.294530i | \(-0.904837\pi\) | ||
0.955642 | − | 0.294530i | \(-0.0951631\pi\) | |||||||
\(224\) | 1.58354 | − | 4.79173i | 0.105805 | − | 0.320161i | ||||
\(225\) | 4.36961 | 0.291308 | ||||||||
\(226\) | 22.6100 | + | 1.44527i | 1.50400 | + | 0.0961380i | ||||
\(227\) | − | 23.9345i | − | 1.58859i | −0.607534 | − | 0.794294i | \(-0.707841\pi\) | ||
0.607534 | − | 0.794294i | \(-0.292159\pi\) | |||||||
\(228\) | 0.0498249 | − | 0.388141i | 0.00329973 | − | 0.0257053i | ||||
\(229\) | 8.58118 | 0.567060 | 0.283530 | − | 0.958963i | \(-0.408494\pi\) | ||||
0.283530 | + | 0.958963i | \(0.408494\pi\) | |||||||
\(230\) | −6.77443 | − | 19.6242i | −0.446693 | − | 1.29398i | ||||
\(231\) | − | 3.52666i | − | 0.232037i | ||||||
\(232\) | −8.48633 | − | 1.64533i | −0.557155 | − | 0.108021i | ||||
\(233\) | 6.59907 | 0.432319 | 0.216160 | − | 0.976358i | \(-0.430647\pi\) | ||||
0.216160 | + | 0.976358i | \(0.430647\pi\) | |||||||
\(234\) | 5.85403 | + | 0.374200i | 0.382690 | + | 0.0244622i | ||||
\(235\) | 22.4430i | 1.46402i | ||||||||
\(236\) | 8.63027 | + | 1.10785i | 0.561783 | + | 0.0721149i | ||||
\(237\) | −1.85136 | −0.120258 | ||||||||
\(238\) | −1.27667 | − | 0.0816066i | −0.0827539 | − | 0.00528977i | ||||
\(239\) | 14.2318i | 0.920576i | 0.887770 | + | 0.460288i | \(0.152254\pi\) | ||||
−0.887770 | + | 0.460288i | \(0.847746\pi\) | |||||||
\(240\) | 11.8470 | + | 3.09250i | 0.764718 | + | 0.199620i | ||||
\(241\) | − | 18.9358i | − | 1.21976i | −0.792492 | − | 0.609882i | \(-0.791217\pi\) | ||
0.792492 | − | 0.609882i | \(-0.208783\pi\) | |||||||
\(242\) | −0.417428 | + | 6.53031i | −0.0268333 | + | 0.419784i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 15.1534 | + | 1.94521i | 0.970099 | + | 0.124529i | ||||
\(245\) | −18.9907 | −1.21327 | ||||||||
\(246\) | −0.923296 | + | 14.4442i | −0.0588672 | + | 0.920927i | ||||
\(247\) | −0.811586 | −0.0516400 | ||||||||
\(248\) | 7.18918 | + | 1.39384i | 0.456514 | + | 0.0885091i | ||||
\(249\) | 3.79082i | 0.240233i | ||||||||
\(250\) | −0.174078 | + | 2.72331i | −0.0110097 | + | 0.172237i | ||||
\(251\) | − | 16.7334i | − | 1.05620i | −0.849182 | − | 0.528100i | \(-0.822904\pi\) | ||
0.849182 | − | 0.528100i | \(-0.177096\pi\) | |||||||
\(252\) | −1.76973 | − | 0.227176i | −0.111482 | − | 0.0143107i | ||||
\(253\) | −7.31695 | − | 17.4895i | −0.460013 | − | 1.09956i | ||||
\(254\) | 0.396938 | + | 0.0253730i | 0.0249061 | + | 0.00159204i | ||||
\(255\) | − | 3.10373i | − | 0.194363i | ||||||
\(256\) | 13.9586 | + | 7.82031i | 0.872413 | + | 0.488769i | ||||
\(257\) | 10.9984 | 0.686064 | 0.343032 | − | 0.939324i | \(-0.388546\pi\) | ||||
0.343032 | + | 0.939324i | \(0.388546\pi\) | |||||||
\(258\) | −14.1181 | − | 0.902455i | −0.878957 | − | 0.0561844i | ||||
\(259\) | −5.36784 | −0.333541 | ||||||||
\(260\) | 3.23313 | − | 25.1865i | 0.200510 | − | 1.56200i | ||||
\(261\) | 3.05624i | 0.189177i | ||||||||
\(262\) | 1.96635 | − | 30.7619i | 0.121482 | − | 1.90048i | ||||
\(263\) | −32.1667 | −1.98348 | −0.991742 | − | 0.128249i | \(-0.959064\pi\) | ||||
−0.991742 | + | 0.128249i | \(0.959064\pi\) | |||||||
\(264\) | 10.9767 | + | 2.12816i | 0.675567 | + | 0.130979i | ||||
\(265\) | 34.3813 | 2.11203 | ||||||||
\(266\) | 0.246356 | + | 0.0157475i | 0.0151051 | + | 0.000965542i | ||||
\(267\) | 10.7963i | 0.660721i | ||||||||
\(268\) | 0.917203 | − | 7.14511i | 0.0560271 | − | 0.436457i | ||||
\(269\) | 21.2979i | 1.29856i | 0.760550 | + | 0.649279i | \(0.224929\pi\) | ||||
−0.760550 | + | 0.649279i | \(0.775071\pi\) | |||||||
\(270\) | 0.276146 | − | 4.32007i | 0.0168057 | − | 0.262911i | ||||
\(271\) | − | 2.36324i | − | 0.143556i | −0.997421 | − | 0.0717782i | \(-0.977133\pi\) | ||
0.997421 | − | 0.0717782i | \(-0.0228674\pi\) | |||||||
\(272\) | 1.02440 | − | 3.92436i | 0.0621135 | − | 0.237949i | ||||
\(273\) | 3.70042i | 0.223959i | ||||||||
\(274\) | 27.0343 | + | 1.72808i | 1.63320 | + | 0.104397i | ||||
\(275\) | − | 17.2736i | − | 1.04163i | ||||||
\(276\) | −9.24783 | + | 2.54513i | −0.556654 | + | 0.153199i | ||||
\(277\) | − | 9.50918i | − | 0.571351i | −0.958326 | − | 0.285676i | \(-0.907782\pi\) | ||
0.958326 | − | 0.285676i | \(-0.0922180\pi\) | |||||||
\(278\) | −1.20412 | + | 18.8374i | −0.0722180 | + | 1.12979i | ||||
\(279\) | − | 2.58909i | − | 0.155005i | ||||||
\(280\) | −1.47012 | + | 7.58260i | −0.0878563 | + | 0.453147i | ||||
\(281\) | − | 22.7904i | − | 1.35956i | −0.733416 | − | 0.679780i | \(-0.762075\pi\) | ||
0.733416 | − | 0.679780i | \(-0.237925\pi\) | |||||||
\(282\) | 10.3478 | + | 0.661451i | 0.616205 | + | 0.0393888i | ||||
\(283\) | − | 17.0253i | − | 1.01205i | −0.862519 | − | 0.506025i | \(-0.831114\pi\) | ||
0.862519 | − | 0.506025i | \(-0.168886\pi\) | |||||||
\(284\) | 2.69647 | − | 21.0058i | 0.160006 | − | 1.24647i | ||||
\(285\) | 0.598921i | 0.0354770i | ||||||||
\(286\) | 1.47925 | − | 23.1416i | 0.0874699 | − | 1.36839i | ||||
\(287\) | −9.13037 | −0.538949 | ||||||||
\(288\) | 1.77502 | − | 5.37115i | 0.104594 | − | 0.316498i | ||||
\(289\) | 15.9719 | 0.939522 | ||||||||
\(290\) | 13.2032 | + | 0.843968i | 0.775316 | + | 0.0495595i | ||||
\(291\) | 2.49750i | 0.146406i | ||||||||
\(292\) | −6.44079 | − | 0.826790i | −0.376918 | − | 0.0483842i | ||||
\(293\) | −13.2959 | −0.776757 | −0.388378 | − | 0.921500i | \(-0.626965\pi\) | ||||
−0.388378 | + | 0.921500i | \(0.626965\pi\) | |||||||
\(294\) | −0.559703 | + | 8.75607i | −0.0326425 | + | 0.510665i | ||||
\(295\) | −13.3169 | −0.775342 | ||||||||
\(296\) | 3.23922 | − | 16.7073i | 0.188276 | − | 0.971093i | ||||
\(297\) | − | 3.95311i | − | 0.229382i | ||||||
\(298\) | 0.172674 | − | 2.70134i | 0.0100028 | − | 0.156485i | ||||
\(299\) | 7.67746 | + | 18.3513i | 0.443999 | + | 1.06128i | ||||
\(300\) | −8.66810 | − | 1.11271i | −0.500453 | − | 0.0642421i | ||||
\(301\) | − | 8.92427i | − | 0.514387i | ||||||
\(302\) | 21.8745 | + | 1.39826i | 1.25874 | + | 0.0804607i | ||||
\(303\) | − | 3.30462i | − | 0.189845i | ||||||
\(304\) | −0.197677 | + | 0.757277i | −0.0113376 | + | 0.0434328i | ||||
\(305\) | −23.3825 | −1.33888 | ||||||||
\(306\) | −1.43104 | − | 0.0914745i | −0.0818072 | − | 0.00522925i | ||||
\(307\) | −6.89668 | −0.393614 | −0.196807 | − | 0.980442i | \(-0.563057\pi\) | ||||
−0.196807 | + | 0.980442i | \(0.563057\pi\) | |||||||
\(308\) | −0.898051 | + | 6.99591i | −0.0511712 | + | 0.398629i | ||||
\(309\) | −10.3779 | −0.590380 | ||||||||
\(310\) | −11.1850 | − | 0.714967i | −0.635268 | − | 0.0406074i | ||||
\(311\) | − | 20.2868i | − | 1.15036i | −0.818026 | − | 0.575181i | \(-0.804932\pi\) | ||
0.818026 | − | 0.575181i | \(-0.195068\pi\) | |||||||
\(312\) | −11.5175 | − | 2.23302i | −0.652049 | − | 0.126420i | ||||
\(313\) | − | 28.1949i | − | 1.59367i | −0.604198 | − | 0.796835i | \(-0.706506\pi\) | ||
0.604198 | − | 0.796835i | \(-0.293494\pi\) | |||||||
\(314\) | −0.997751 | + | 15.6090i | −0.0563064 | + | 0.880865i | ||||
\(315\) | 2.73077 | 0.153862 | ||||||||
\(316\) | 3.67258 | + | 0.471441i | 0.206599 | + | 0.0265206i | ||||
\(317\) | − | 8.49011i | − | 0.476852i | −0.971161 | − | 0.238426i | \(-0.923369\pi\) | ||
0.971161 | − | 0.238426i | \(-0.0766315\pi\) | |||||||
\(318\) | 1.01330 | − | 15.8523i | 0.0568232 | − | 0.888951i | ||||
\(319\) | 12.0816 | 0.676442 | ||||||||
\(320\) | −22.7136 | − | 9.15144i | −1.26973 | − | 0.511581i | ||||
\(321\) | − | 18.3222i | − | 1.02264i | ||||||
\(322\) | −1.97441 | − | 5.71948i | −0.110029 | − | 0.318734i | ||||
\(323\) | 0.198395 | 0.0110390 | ||||||||
\(324\) | −1.98372 | − | 0.254646i | −0.110207 | − | 0.0141470i | ||||
\(325\) | 18.1246i | 1.00537i | ||||||||
\(326\) | 0.908366 | − | 14.2106i | 0.0503097 | − | 0.787053i | ||||
\(327\) | 12.4462 | 0.688275 | ||||||||
\(328\) | 5.50972 | − | 28.4181i | 0.304223 | − | 1.56913i | ||||
\(329\) | 6.54101i | 0.360618i | ||||||||
\(330\) | −17.0777 | − | 1.09163i | −0.940095 | − | 0.0600925i | ||||
\(331\) | −14.3840 | −0.790619 | −0.395309 | − | 0.918548i | \(-0.629363\pi\) | ||||
−0.395309 | + | 0.918548i | \(0.629363\pi\) | |||||||
\(332\) | 0.965318 | − | 7.51994i | 0.0529787 | − | 0.412710i | ||||
\(333\) | −6.01692 | −0.329725 | ||||||||
\(334\) | −16.2843 | − | 1.04092i | −0.891040 | − | 0.0569567i | ||||
\(335\) | 11.0253i | 0.602375i | ||||||||
\(336\) | 3.45280 | + | 0.901308i | 0.188365 | + | 0.0491704i | ||||
\(337\) | 29.2613i | 1.59396i | 0.604003 | + | 0.796982i | \(0.293571\pi\) | ||||
−0.604003 | + | 0.796982i | \(0.706429\pi\) | |||||||
\(338\) | −0.379341 | + | 5.93447i | −0.0206334 | + | 0.322792i | ||||
\(339\) | 16.0203i | 0.870105i | ||||||||
\(340\) | −0.790352 | + | 6.15693i | −0.0428629 | + | 0.333906i | ||||
\(341\) | −10.2350 | −0.554254 | ||||||||
\(342\) | 0.276146 | + | 0.0176517i | 0.0149323 | + | 0.000954495i | ||||
\(343\) | −11.7797 | −0.636044 | ||||||||
\(344\) | 27.7767 | + | 5.38535i | 1.49762 | + | 0.290359i | ||||
\(345\) | 13.5426 | − | 5.66569i | 0.729107 | − | 0.305030i | ||||
\(346\) | −9.07416 | − | 0.580035i | −0.487830 | − | 0.0311829i | ||||
\(347\) | 2.16372 | 0.116155 | 0.0580774 | − | 0.998312i | \(-0.481503\pi\) | ||||
0.0580774 | + | 0.998312i | \(0.481503\pi\) | |||||||
\(348\) | 0.778260 | − | 6.06273i | 0.0417191 | − | 0.324997i | ||||
\(349\) | − | 23.8000i | − | 1.27399i | −0.770869 | − | 0.636993i | \(-0.780178\pi\) | ||
0.770869 | − | 0.636993i | \(-0.219822\pi\) | |||||||
\(350\) | 0.351679 | − | 5.50171i | 0.0187980 | − | 0.294079i | ||||
\(351\) | 4.14787i | 0.221397i | ||||||||
\(352\) | −21.2327 | − | 7.01685i | −1.13171 | − | 0.373999i | ||||
\(353\) | 20.3453 | 1.08287 | 0.541436 | − | 0.840742i | \(-0.317881\pi\) | ||||
0.541436 | + | 0.840742i | \(0.317881\pi\) | |||||||
\(354\) | −0.392483 | + | 6.14007i | −0.0208603 | + | 0.326341i | ||||
\(355\) | 32.4130i | 1.72030i | ||||||||
\(356\) | 2.74923 | − | 21.4168i | 0.145709 | − | 1.13509i | ||||
\(357\) | − | 0.904581i | − | 0.0478755i | ||||||
\(358\) | −0.0614852 | + | 0.961883i | −0.00324959 | + | 0.0508371i | ||||
\(359\) | 11.3988 | 0.601608 | 0.300804 | − | 0.953686i | \(-0.402745\pi\) | ||||
0.300804 | + | 0.953686i | \(0.402745\pi\) | |||||||
\(360\) | −1.64789 | + | 8.49949i | −0.0868512 | + | 0.447963i | ||||
\(361\) | 18.9617 | 0.997985 | ||||||||
\(362\) | 0.790111 | − | 12.3606i | 0.0415273 | − | 0.649659i | ||||
\(363\) | −4.62705 | −0.242857 | ||||||||
\(364\) | 0.942297 | − | 7.34060i | 0.0493898 | − | 0.384752i | ||||
\(365\) | 9.93845 | 0.520202 | ||||||||
\(366\) | −0.689140 | + | 10.7810i | −0.0360219 | + | 0.563532i | ||||
\(367\) | 1.55485 | 0.0811626 | 0.0405813 | − | 0.999176i | \(-0.487079\pi\) | ||||
0.0405813 | + | 0.999176i | \(0.487079\pi\) | |||||||
\(368\) | 18.9932 | − | 2.69390i | 0.990091 | − | 0.140429i | ||||
\(369\) | −10.2344 | −0.532783 | ||||||||
\(370\) | −1.66155 | + | 25.9935i | −0.0863798 | + | 1.35134i | ||||
\(371\) | 10.0204 | 0.520235 | ||||||||
\(372\) | −0.659303 | + | 5.13604i | −0.0341832 | + | 0.266291i | ||||
\(373\) | −9.25006 | −0.478950 | −0.239475 | − | 0.970903i | \(-0.576975\pi\) | ||||
−0.239475 | + | 0.970903i | \(0.576975\pi\) | |||||||
\(374\) | −0.361609 | + | 5.65706i | −0.0186983 | + | 0.292519i | ||||
\(375\) | −1.92960 | −0.0996441 | ||||||||
\(376\) | −20.3588 | − | 3.94717i | −1.04993 | − | 0.203560i | ||||
\(377\) | −12.6769 | −0.652894 | ||||||||
\(378\) | 0.0804827 | − | 1.25908i | 0.00413959 | − | 0.0647603i | ||||
\(379\) | 23.7934i | 1.22219i | 0.791559 | + | 0.611093i | \(0.209270\pi\) | ||||
−0.791559 | + | 0.611093i | \(0.790730\pi\) | |||||||
\(380\) | 0.152513 | − | 1.18809i | 0.00782376 | − | 0.0609479i | ||||
\(381\) | 0.281251i | 0.0144089i | ||||||||
\(382\) | −0.635007 | + | 9.93414i | −0.0324898 | + | 0.508275i | ||||
\(383\) | 13.8513 | 0.707766 | 0.353883 | − | 0.935290i | \(-0.384861\pi\) | ||||
0.353883 | + | 0.935290i | \(0.384861\pi\) | |||||||
\(384\) | −4.88890 | + | 10.2029i | −0.249485 | + | 0.520663i | ||||
\(385\) | − | 10.7950i | − | 0.550166i | ||||||
\(386\) | −1.93104 | + | 30.2094i | −0.0982872 | + | 1.53762i | ||||
\(387\) | − | 10.0034i | − | 0.508502i | ||||||
\(388\) | 0.635980 | − | 4.95436i | 0.0322870 | − | 0.251519i | ||||
\(389\) | 25.1821 | 1.27678 | 0.638392 | − | 0.769711i | \(-0.279600\pi\) | ||||
0.638392 | + | 0.769711i | \(0.279600\pi\) | |||||||
\(390\) | 17.9191 | + | 1.14542i | 0.907369 | + | 0.0580005i | ||||
\(391\) | −1.87678 | − | 4.48603i | −0.0949130 | − | 0.226869i | ||||
\(392\) | 3.34000 | − | 17.2271i | 0.168695 | − | 0.870100i | ||||
\(393\) | 21.7964 | 1.09948 | ||||||||
\(394\) | 23.3790 | + | 1.49442i | 1.17782 | + | 0.0752879i | ||||
\(395\) | −5.66697 | −0.285136 | ||||||||
\(396\) | −1.00664 | + | 7.84187i | −0.0505857 | + | 0.394069i | ||||
\(397\) | − | 34.8682i | − | 1.74998i | −0.484137 | − | 0.874992i | \(-0.660866\pi\) | ||
0.484137 | − | 0.874992i | \(-0.339134\pi\) | |||||||
\(398\) | −1.69166 | + | 26.4645i | −0.0847951 | + | 1.32655i | ||||
\(399\) | 0.174556i | 0.00873872i | ||||||||
\(400\) | 16.9118 | + | 4.41460i | 0.845588 | + | 0.220730i | ||||
\(401\) | − | 26.5370i | − | 1.32520i | −0.748976 | − | 0.662598i | \(-0.769454\pi\) | ||
0.748976 | − | 0.662598i | \(-0.230546\pi\) | |||||||
\(402\) | 5.08344 | + | 0.324942i | 0.253539 | + | 0.0162066i | ||||
\(403\) | 10.7392 | 0.534959 | ||||||||
\(404\) | −0.841509 | + | 6.55545i | −0.0418666 | + | 0.326146i | ||||
\(405\) | 3.06098 | 0.152101 | ||||||||
\(406\) | 3.84806 | + | 0.245975i | 0.190976 | + | 0.0122075i | ||||
\(407\) | 23.7855i | 1.17900i | ||||||||
\(408\) | 2.81549 | + | 0.545869i | 0.139388 | + | 0.0270246i | ||||
\(409\) | −24.6444 | −1.21859 | −0.609294 | − | 0.792944i | \(-0.708547\pi\) | ||||
−0.609294 | + | 0.792944i | \(0.708547\pi\) | |||||||
\(410\) | −2.82619 | + | 44.2134i | −0.139576 | + | 2.18354i | ||||
\(411\) | 19.1551i | 0.944853i | ||||||||
\(412\) | 20.5869 | + | 2.64270i | 1.01425 | + | 0.130197i | ||||
\(413\) | −3.88122 | −0.190982 | ||||||||
\(414\) | −2.21316 | − | 6.41108i | −0.108771 | − | 0.315087i | ||||
\(415\) | 11.6036i | 0.569600i | ||||||||
\(416\) | 22.2789 | + | 7.36257i | 1.09231 | + | 0.360980i | ||||
\(417\) | −13.3472 | −0.653616 | ||||||||
\(418\) | 0.0697791 | − | 1.09163i | 0.00341301 | − | 0.0533936i | ||||
\(419\) | − | 12.6674i | − | 0.618843i | −0.950925 | − | 0.309421i | \(-0.899865\pi\) | ||
0.950925 | − | 0.309421i | \(-0.100135\pi\) | |||||||
\(420\) | −5.41710 | − | 0.695382i | −0.264327 | − | 0.0339311i | ||||
\(421\) | 28.7090 | 1.39919 | 0.699594 | − | 0.714540i | \(-0.253364\pi\) | ||||
0.699594 | + | 0.714540i | \(0.253364\pi\) | |||||||
\(422\) | −0.427603 | + | 6.68948i | −0.0208154 | + | 0.325639i | ||||
\(423\) | 7.33196i | 0.356492i | ||||||||
\(424\) | −6.04683 | + | 31.1885i | −0.293660 | + | 1.51465i | ||||
\(425\) | − | 4.43063i | − | 0.214917i | ||||||
\(426\) | 14.9447 | + | 0.955293i | 0.724075 | + | 0.0462841i | ||||
\(427\) | −6.81483 | −0.329793 | ||||||||
\(428\) | −4.66567 | + | 36.3461i | −0.225524 | + | 1.75685i | ||||
\(429\) | 16.3970 | 0.791654 | ||||||||
\(430\) | −43.2154 | − | 2.76240i | −2.08403 | − | 0.133215i | ||||
\(431\) | 22.9516 | 1.10554 | 0.552770 | − | 0.833334i | \(-0.313571\pi\) | ||||
0.552770 | + | 0.833334i | \(0.313571\pi\) | |||||||
\(432\) | 3.87031 | + | 1.01029i | 0.186210 | + | 0.0486078i | ||||
\(433\) | − | 15.0677i | − | 0.724106i | −0.932157 | − | 0.362053i | \(-0.882076\pi\) | ||
0.932157 | − | 0.362053i | \(-0.117924\pi\) | |||||||
\(434\) | −3.25988 | − | 0.208377i | −0.156479 | − | 0.0100024i | ||||
\(435\) | 9.35510i | 0.448543i | ||||||||
\(436\) | −24.6898 | − | 3.16937i | −1.18243 | − | 0.151785i | ||||
\(437\) | 0.362160 | + | 0.865664i | 0.0173245 | + | 0.0414103i | ||||
\(438\) | 0.292911 | − | 4.58234i | 0.0139958 | − | 0.218953i | ||||
\(439\) | 22.4462i | 1.07130i | 0.844441 | + | 0.535649i | \(0.179933\pi\) | ||||
−0.844441 | + | 0.535649i | \(0.820067\pi\) | |||||||
\(440\) | 33.5994 | + | 6.51427i | 1.60179 | + | 0.310555i | ||||
\(441\) | −6.20412 | −0.295434 | ||||||||
\(442\) | 0.379425 | − | 5.93578i | 0.0180474 | − | 0.282336i | ||||
\(443\) | −28.7923 | −1.36796 | −0.683981 | − | 0.729500i | \(-0.739753\pi\) | ||||
−0.683981 | + | 0.729500i | \(0.739753\pi\) | |||||||
\(444\) | 11.9359 | + | 1.53219i | 0.566453 | + | 0.0727144i | ||||
\(445\) | 33.0472i | 1.56659i | ||||||||
\(446\) | −12.4149 | − | 0.793578i | −0.587860 | − | 0.0375770i | ||||
\(447\) | 1.91404 | 0.0905308 | ||||||||
\(448\) | −6.61987 | − | 2.66719i | −0.312760 | − | 0.126013i | ||||
\(449\) | 10.0261 | 0.473160 | 0.236580 | − | 0.971612i | \(-0.423973\pi\) | ||||
0.236580 | + | 0.971612i | \(0.423973\pi\) | |||||||
\(450\) | 0.394204 | − | 6.16698i | 0.0185829 | − | 0.290714i | ||||
\(451\) | 40.4578i | 1.90508i | ||||||||
\(452\) | 4.07952 | − | 31.7799i | 0.191884 | − | 1.49480i | ||||
\(453\) | 15.4992i | 0.728216i | ||||||||
\(454\) | −33.7795 | − | 2.15924i | −1.58535 | − | 0.101338i | ||||
\(455\) | 11.3269i | 0.531014i | ||||||||
\(456\) | −0.543302 | − | 0.105336i | −0.0254424 | − | 0.00493279i | ||||
\(457\) | 8.91212i | 0.416891i | 0.978034 | + | 0.208446i | \(0.0668404\pi\) | ||||
−0.978034 | + | 0.208446i | \(0.933160\pi\) | |||||||
\(458\) | 0.774149 | − | 12.1109i | 0.0361736 | − | 0.565905i | ||||
\(459\) | − | 1.01396i | − | 0.0473278i | ||||||
\(460\) | −28.3074 | + | 7.79059i | −1.31984 | + | 0.363238i | ||||
\(461\) | − | 36.2700i | − | 1.68926i | −0.535349 | − | 0.844631i | \(-0.679820\pi\) | ||
0.535349 | − | 0.844631i | \(-0.320180\pi\) | |||||||
\(462\) | −4.97729 | − | 0.318157i | −0.231565 | − | 0.0148020i | ||||
\(463\) | 29.5920i | 1.37525i | 0.726064 | + | 0.687627i | \(0.241348\pi\) | ||||
−0.726064 | + | 0.687627i | \(0.758652\pi\) | |||||||
\(464\) | −3.08770 | + | 11.8286i | −0.143343 | + | 0.549129i | ||||
\(465\) | − | 7.92517i | − | 0.367521i | ||||||
\(466\) | 0.595334 | − | 9.31348i | 0.0275783 | − | 0.431439i | ||||
\(467\) | 0.403565i | 0.0186747i | 0.999956 | + | 0.00933737i | \(0.00297222\pi\) | ||||
−0.999956 | + | 0.00933737i | \(0.997028\pi\) | |||||||
\(468\) | 1.05624 | − | 8.22823i | 0.0488247 | − | 0.380350i | ||||
\(469\) | 3.21331i | 0.148377i | ||||||||
\(470\) | 31.6745 | + | 2.02469i | 1.46104 | + | 0.0933920i | ||||
\(471\) | −11.0597 | −0.509606 | ||||||||
\(472\) | 2.34212 | − | 12.0802i | 0.107805 | − | 0.556038i | ||||
\(473\) | −39.5445 | −1.81826 | ||||||||
\(474\) | −0.167020 | + | 2.61288i | −0.00767147 | + | 0.120014i | ||||
\(475\) | 0.854973i | 0.0392288i | ||||||||
\(476\) | −0.230348 | + | 1.79444i | −0.0105580 | + | 0.0822479i | ||||
\(477\) | 11.2321 | 0.514284 | ||||||||
\(478\) | 20.0858 | + | 1.28391i | 0.918701 | + | 0.0587249i | ||||
\(479\) | 9.40765 | 0.429846 | 0.214923 | − | 0.976631i | \(-0.431050\pi\) | ||||
0.214923 | + | 0.976631i | \(0.431050\pi\) | |||||||
\(480\) | 5.43331 | − | 16.4410i | 0.247996 | − | 0.750426i | ||||
\(481\) | − | 24.9574i | − | 1.13796i | ||||||
\(482\) | −26.7248 | − | 1.70829i | −1.21728 | − | 0.0778105i | ||||
\(483\) | 3.94698 | − | 1.65126i | 0.179594 | − | 0.0751352i | ||||
\(484\) | 9.17878 | + | 1.17826i | 0.417217 | + | 0.0535573i | ||||
\(485\) | 7.64482i | 0.347133i | ||||||||
\(486\) | 0.0902148 | − | 1.41133i | 0.00409223 | − | 0.0640194i | ||||
\(487\) | 28.2242i | 1.27896i | 0.768808 | + | 0.639480i | \(0.220850\pi\) | ||||
−0.768808 | + | 0.639480i | \(0.779150\pi\) | |||||||
\(488\) | 4.11241 | − | 21.2110i | 0.186160 | − | 0.960179i | ||||
\(489\) | 10.0689 | 0.455333 | ||||||||
\(490\) | −1.71324 | + | 26.8022i | −0.0773963 | + | 1.21080i | ||||
\(491\) | 22.7769 | 1.02791 | 0.513953 | − | 0.857818i | \(-0.328180\pi\) | ||||
0.513953 | + | 0.857818i | \(0.328180\pi\) | |||||||
\(492\) | 20.3023 | + | 2.60616i | 0.915297 | + | 0.117495i | ||||
\(493\) | 3.09892 | 0.139568 | ||||||||
\(494\) | −0.0732171 | + | 1.14542i | −0.00329419 | + | 0.0515348i | ||||
\(495\) | − | 12.1004i | − | 0.543872i | ||||||
\(496\) | 2.61575 | − | 10.0206i | 0.117450 | − | 0.449938i | ||||
\(497\) | 9.44678i | 0.423746i | ||||||||
\(498\) | 5.35011 | + | 0.341988i | 0.239744 | + | 0.0153248i | ||||
\(499\) | −17.9463 | −0.803386 | −0.401693 | − | 0.915774i | \(-0.631578\pi\) | ||||
−0.401693 | + | 0.915774i | \(0.631578\pi\) | |||||||
\(500\) | 3.82779 | + | 0.491365i | 0.171184 | + | 0.0219745i | ||||
\(501\) | − | 11.5383i | − | 0.515492i | ||||||
\(502\) | −23.6164 | − | 1.50960i | −1.05405 | − | 0.0673766i | ||||
\(503\) | −19.7331 | −0.879856 | −0.439928 | − | 0.898033i | \(-0.644996\pi\) | ||||
−0.439928 | + | 0.898033i | \(0.644996\pi\) | |||||||
\(504\) | −0.480276 | + | 2.47718i | −0.0213932 | + | 0.110342i | ||||
\(505\) | − | 10.1154i | − | 0.450128i | ||||||
\(506\) | −25.3437 | + | 8.74884i | −1.12666 | + | 0.388933i | ||||
\(507\) | −4.20486 | −0.186745 | ||||||||
\(508\) | 0.0716194 | − | 0.557923i | 0.00317760 | − | 0.0247538i | ||||
\(509\) | 18.5397i | 0.821756i | 0.911690 | + | 0.410878i | \(0.134778\pi\) | ||||
−0.911690 | + | 0.410878i | \(0.865222\pi\) | |||||||
\(510\) | −4.38039 | − | 0.280002i | −0.193967 | − | 0.0123987i | ||||
\(511\) | 2.89656 | 0.128136 | ||||||||
\(512\) | 12.2963 | − | 18.9947i | 0.543426 | − | 0.839457i | ||||
\(513\) | 0.195663i | 0.00863874i | ||||||||
\(514\) | 0.992222 | − | 15.5225i | 0.0437650 | − | 0.684666i | ||||
\(515\) | −31.7667 | −1.39981 | ||||||||
\(516\) | −2.54733 | + | 19.8440i | −0.112140 | + | 0.873583i | ||||
\(517\) | 28.9840 | 1.27472 | ||||||||
\(518\) | −0.484258 | + | 7.57581i | −0.0212771 | + | 0.332862i | ||||
\(519\) | − | 6.42949i | − | 0.282223i | ||||||
\(520\) | −35.2548 | − | 6.83522i | −1.54603 | − | 0.299744i | ||||
\(521\) | 17.7765i | 0.778803i | 0.921068 | + | 0.389401i | \(0.127318\pi\) | ||||
−0.921068 | + | 0.389401i | \(0.872682\pi\) | |||||||
\(522\) | 4.31337 | + | 0.275718i | 0.188791 | + | 0.0120679i | ||||
\(523\) | 23.3129i | 1.01940i | 0.860352 | + | 0.509701i | \(0.170244\pi\) | ||||
−0.860352 | + | 0.509701i | \(0.829756\pi\) | |||||||
\(524\) | −43.2379 | − | 5.55036i | −1.88886 | − | 0.242469i | ||||
\(525\) | 3.89824 | 0.170133 | ||||||||
\(526\) | −2.90191 | + | 45.3979i | −0.126529 | + | 1.97944i | ||||
\(527\) | −2.62525 | −0.114358 | ||||||||
\(528\) | 3.99380 | − | 15.2997i | 0.173808 | − | 0.665836i | ||||
\(529\) | 16.1481 | − | 16.3780i | 0.702090 | − | 0.712089i | ||||
\(530\) | 3.10170 | − | 48.5235i | 0.134729 | − | 2.10773i | ||||
\(531\) | −4.35054 | −0.188798 | ||||||||
\(532\) | 0.0444500 | − | 0.346270i | 0.00192715 | − | 0.0150127i | ||||
\(533\) | − | 42.4511i | − | 1.83876i | ||||||
\(534\) | 15.2371 | + | 0.973984i | 0.659376 | + | 0.0421484i | ||||
\(535\) | − | 56.0838i | − | 2.42472i | ||||||
\(536\) | −10.0014 | − | 1.93907i | −0.431994 | − | 0.0837552i | ||||
\(537\) | −0.681542 | −0.0294107 | ||||||||
\(538\) | 30.0585 | + | 1.92139i | 1.29591 | + | 0.0828370i | ||||
\(539\) | 24.5255i | 1.05639i | ||||||||
\(540\) | −6.07214 | − | 0.779468i | −0.261303 | − | 0.0335429i | ||||
\(541\) | 34.5138i | 1.48386i | 0.670475 | + | 0.741932i | \(0.266090\pi\) | ||||
−0.670475 | + | 0.741932i | \(0.733910\pi\) | |||||||
\(542\) | −3.33531 | − | 0.213199i | −0.143264 | − | 0.00915767i | ||||
\(543\) | 8.75811 | 0.375846 | ||||||||
\(544\) | −5.44616 | − | 1.79981i | −0.233502 | − | 0.0771661i | ||||
\(545\) | 38.0975 | 1.63192 | ||||||||
\(546\) | 5.22252 | + | 0.333832i | 0.223503 | + | 0.0142867i | ||||
\(547\) | 7.58510 | 0.324315 | 0.162158 | − | 0.986765i | \(-0.448155\pi\) | ||||
0.162158 | + | 0.986765i | \(0.448155\pi\) | |||||||
\(548\) | 4.87778 | − | 37.9985i | 0.208369 | − | 1.62321i | ||||
\(549\) | −7.63888 | −0.326020 | ||||||||
\(550\) | −24.3787 | − | 1.55833i | −1.03951 | − | 0.0664474i | ||||
\(551\) | −0.597994 | −0.0254754 | ||||||||
\(552\) | 2.75773 | + | 13.2814i | 0.117377 | + | 0.565293i | ||||
\(553\) | −1.65164 | −0.0702348 | ||||||||
\(554\) | −13.4206 | − | 0.857869i | −0.570188 | − | 0.0364474i | ||||
\(555\) | −18.4177 | −0.781788 | ||||||||
\(556\) | 26.4772 | + | 3.39882i | 1.12288 | + | 0.144142i | ||||
\(557\) | 23.6692 | 1.00290 | 0.501448 | − | 0.865188i | \(-0.332801\pi\) | ||||
0.501448 | + | 0.865188i | \(0.332801\pi\) | |||||||
\(558\) | −3.65407 | − | 0.233574i | −0.154689 | − | 0.00988799i | ||||
\(559\) | 41.4929 | 1.75496 | ||||||||
\(560\) | 10.5689 | + | 2.75889i | 0.446620 | + | 0.116584i | ||||
\(561\) | −4.00831 | −0.169231 | ||||||||
\(562\) | −32.1648 | − | 2.05603i | −1.35679 | − | 0.0867284i | ||||
\(563\) | 14.4822i | 0.610351i | 0.952296 | + | 0.305176i | \(0.0987152\pi\) | ||||
−0.952296 | + | 0.305176i | \(0.901285\pi\) | |||||||
\(564\) | 1.86706 | − | 14.5446i | 0.0786172 | − | 0.612437i | ||||
\(565\) | 49.0379i | 2.06304i | ||||||||
\(566\) | −24.0284 | − | 1.53593i | −1.00999 | − | 0.0645601i | ||||
\(567\) | 0.892124 | 0.0374657 | ||||||||
\(568\) | −29.4029 | − | 5.70066i | −1.23372 | − | 0.239194i | ||||
\(569\) | − | 11.4721i | − | 0.480935i | −0.970657 | − | 0.240467i | \(-0.922699\pi\) | ||
0.970657 | − | 0.240467i | \(-0.0773007\pi\) | |||||||
\(570\) | 0.845278 | + | 0.0540316i | 0.0354048 | + | 0.00226313i | ||||
\(571\) | − | 29.6426i | − | 1.24051i | −0.784402 | − | 0.620253i | \(-0.787030\pi\) | ||
0.784402 | − | 0.620253i | \(-0.212970\pi\) | |||||||
\(572\) | −32.5271 | − | 4.17543i | −1.36003 | − | 0.174584i | ||||
\(573\) | −7.03883 | −0.294052 | ||||||||
\(574\) | −0.823695 | + | 12.8860i | −0.0343803 | + | 0.537851i | ||||
\(575\) | 19.3323 | − | 8.08788i | 0.806212 | − | 0.337288i | ||||
\(576\) | −7.42035 | − | 2.98971i | −0.309181 | − | 0.124571i | ||||
\(577\) | −4.38359 | −0.182491 | −0.0912456 | − | 0.995828i | \(-0.529085\pi\) | ||||
−0.0912456 | + | 0.995828i | \(0.529085\pi\) | |||||||
\(578\) | 1.44090 | − | 22.5416i | 0.0599335 | − | 0.937609i | ||||
\(579\) | −21.4049 | −0.889557 | ||||||||
\(580\) | 2.38224 | − | 18.5579i | 0.0989172 | − | 0.770576i | ||||
\(581\) | 3.38188i | 0.140304i | ||||||||
\(582\) | 3.52481 | + | 0.225312i | 0.146108 | + | 0.00933948i | ||||
\(583\) | − | 44.4018i | − | 1.83893i | ||||||
\(584\) | −1.74793 | + | 9.01551i | −0.0723299 | + | 0.373064i | ||||
\(585\) | 12.6966i | 0.524939i | ||||||||
\(586\) | −1.19949 | + | 18.7650i | −0.0495505 | + | 0.775175i | ||||
\(587\) | 44.8384 | 1.85068 | 0.925339 | − | 0.379140i | \(-0.123780\pi\) | ||||
0.925339 | + | 0.379140i | \(0.123780\pi\) | |||||||
\(588\) | 12.3072 | + | 1.57985i | 0.507542 | + | 0.0651521i | ||||
\(589\) | 0.506590 | 0.0208737 | ||||||||
\(590\) | −1.20138 | + | 18.7946i | −0.0494602 | + | 0.773763i | ||||
\(591\) | 16.5652i | 0.681400i | ||||||||
\(592\) | −23.2874 | − | 6.07887i | −0.957104 | − | 0.249840i | ||||
\(593\) | 36.8434 | 1.51298 | 0.756489 | − | 0.654006i | \(-0.226913\pi\) | ||||
0.756489 | + | 0.654006i | \(0.226913\pi\) | |||||||
\(594\) | −5.57915 | − | 0.356629i | −0.228915 | − | 0.0146327i | ||||
\(595\) | − | 2.76891i | − | 0.113514i | ||||||
\(596\) | −3.79692 | − | 0.487402i | −0.155528 | − | 0.0199648i | ||||
\(597\) | −18.7514 | −0.767445 | ||||||||
\(598\) | 26.5924 | − | 9.17989i | 1.08744 | − | 0.375394i | ||||
\(599\) | − | 0.536356i | − | 0.0219149i | −0.999940 | − | 0.0109575i | \(-0.996512\pi\) | ||
0.999940 | − | 0.0109575i | \(-0.00348794\pi\) | |||||||
\(600\) | −2.35239 | + | 12.1332i | −0.0960359 | + | 0.495336i | ||||
\(601\) | 2.32091 | 0.0946721 | 0.0473360 | − | 0.998879i | \(-0.484927\pi\) | ||||
0.0473360 | + | 0.998879i | \(0.484927\pi\) | |||||||
\(602\) | −12.5951 | − | 0.805101i | −0.513339 | − | 0.0328135i | ||||
\(603\) | 3.60187i | 0.146680i | ||||||||
\(604\) | 3.94681 | − | 30.7461i | 0.160594 | − | 1.25104i | ||||
\(605\) | −14.1633 | −0.575821 | ||||||||
\(606\) | −4.66392 | − | 0.298125i | −0.189459 | − | 0.0121105i | ||||
\(607\) | 4.31945i | 0.175321i | 0.996150 | + | 0.0876605i | \(0.0279391\pi\) | ||||
−0.996150 | + | 0.0876605i | \(0.972061\pi\) | |||||||
\(608\) | 1.05094 | + | 0.347306i | 0.0426211 | + | 0.0140851i | ||||
\(609\) | 2.72654i | 0.110485i | ||||||||
\(610\) | −2.10945 | + | 33.0005i | −0.0854090 | + | 1.33615i | ||||
\(611\) | −30.4120 | −1.23034 | ||||||||
\(612\) | −0.258202 | + | 2.01142i | −0.0104372 | + | 0.0813070i | ||||
\(613\) | −4.29197 | −0.173351 | −0.0866756 | − | 0.996237i | \(-0.527624\pi\) | ||||
−0.0866756 | + | 0.996237i | \(0.527624\pi\) | |||||||
\(614\) | −0.622182 | + | 9.73351i | −0.0251092 | + | 0.392813i | ||||
\(615\) | −31.3274 | −1.26324 | ||||||||
\(616\) | 9.79255 | + | 1.89858i | 0.394553 | + | 0.0764961i | ||||
\(617\) | − | 36.9423i | − | 1.48724i | −0.668602 | − | 0.743621i | \(-0.733107\pi\) | ||
0.668602 | − | 0.743621i | \(-0.266893\pi\) | |||||||
\(618\) | −0.936243 | + | 14.6467i | −0.0376612 | + | 0.589178i | ||||
\(619\) | − | 2.34420i | − | 0.0942215i | −0.998890 | − | 0.0471108i | \(-0.984999\pi\) | ||
0.998890 | − | 0.0471108i | \(-0.0150014\pi\) | |||||||
\(620\) | −2.01811 | + | 15.7213i | −0.0810494 | + | 0.631384i | ||||
\(621\) | 4.42425 | − | 1.85094i | 0.177539 | − | 0.0742756i | ||||
\(622\) | −28.6315 | − | 1.83017i | −1.14802 | − | 0.0733833i | ||||
\(623\) | 9.63161i | 0.385882i | ||||||||
\(624\) | −4.19058 | + | 16.0536i | −0.167757 | + | 0.642657i | ||||
\(625\) | −27.7545 | −1.11018 | ||||||||
\(626\) | −39.7924 | − | 2.54360i | −1.59042 | − | 0.101663i | ||||
\(627\) | 0.773477 | 0.0308897 | ||||||||
\(628\) | 21.9394 | + | 2.81632i | 0.875479 | + | 0.112383i | ||||
\(629\) | 6.10094i | 0.243260i | ||||||||
\(630\) | 0.246356 | − | 3.85403i | 0.00981507 | − | 0.153548i | ||||
\(631\) | 42.3515 | 1.68599 | 0.842993 | − | 0.537925i | \(-0.180791\pi\) | ||||
0.842993 | + | 0.537925i | \(0.180791\pi\) | |||||||
\(632\) | 0.996681 | − | 5.14070i | 0.0396458 | − | 0.204486i | ||||
\(633\) | −4.73983 | −0.188391 | ||||||||
\(634\) | −11.9824 | − | 0.765934i | −0.475881 | − | 0.0304191i | ||||
\(635\) | 0.860903i | 0.0341639i | ||||||||
\(636\) | −22.2814 | − | 2.86022i | −0.883516 | − | 0.113415i | ||||
\(637\) | − | 25.7339i | − | 1.01961i | ||||||
\(638\) | 1.08994 | − | 17.0512i | 0.0431513 | − | 0.675064i | ||||
\(639\) | 10.5891i | 0.418898i | ||||||||
\(640\) | −14.9648 | + | 31.2308i | −0.591537 | + | 1.23451i | ||||
\(641\) | 35.6357i | 1.40753i | 0.710435 | + | 0.703763i | \(0.248498\pi\) | ||||
−0.710435 | + | 0.703763i | \(0.751502\pi\) | |||||||
\(642\) | −25.8587 | − | 1.65293i | −1.02056 | − | 0.0652360i | ||||
\(643\) | − | 17.2554i | − | 0.680486i | −0.940338 | − | 0.340243i | \(-0.889491\pi\) | ||
0.940338 | − | 0.340243i | \(-0.110509\pi\) | |||||||
\(644\) | −8.25021 | + | 2.27057i | −0.325104 | + | 0.0894729i | ||||
\(645\) | − | 30.6202i | − | 1.20567i | ||||||
\(646\) | 0.0178982 | − | 0.280002i | 0.000704195 | − | 0.0110165i | ||||
\(647\) | − | 20.7332i | − | 0.815107i | −0.913181 | − | 0.407553i | \(-0.866382\pi\) | ||
0.913181 | − | 0.407553i | \(-0.133618\pi\) | |||||||
\(648\) | −0.538352 | + | 2.77672i | −0.0211485 | + | 0.109080i | ||||
\(649\) | 17.1982i | 0.675087i | ||||||||
\(650\) | 25.5799 | + | 1.63511i | 1.00332 | + | 0.0641342i | ||||
\(651\) | − | 2.30979i | − | 0.0905278i | ||||||
\(652\) | −19.9740 | − | 2.56401i | −0.782240 | − | 0.100415i | ||||
\(653\) | 41.9915i | 1.64325i | 0.570026 | + | 0.821626i | \(0.306933\pi\) | ||||
−0.570026 | + | 0.821626i | \(0.693067\pi\) | |||||||
\(654\) | 1.12283 | − | 17.5657i | 0.0439061 | − | 0.686873i | ||||
\(655\) | 66.7183 | 2.60690 | ||||||||
\(656\) | −39.6104 | − | 10.3398i | −1.54653 | − | 0.403701i | ||||
\(657\) | 3.24682 | 0.126670 | ||||||||
\(658\) | 9.23155 | + | 0.590096i | 0.359883 | + | 0.0230043i | ||||
\(659\) | − | 5.13261i | − | 0.199938i | −0.994991 | − | 0.0999690i | \(-0.968126\pi\) | ||
0.994991 | − | 0.0999690i | \(-0.0318744\pi\) | |||||||
\(660\) | −3.08132 | + | 24.0038i | −0.119940 | + | 0.934347i | ||||
\(661\) | 6.38665 | 0.248412 | 0.124206 | − | 0.992256i | \(-0.460362\pi\) | ||||
0.124206 | + | 0.992256i | \(0.460362\pi\) | |||||||
\(662\) | −1.29765 | + | 20.3007i | −0.0504347 | + | 0.789008i | ||||
\(663\) | 4.20580 | 0.163340 | ||||||||
\(664\) | −10.5260 | − | 2.04079i | −0.408490 | − | 0.0791982i | ||||
\(665\) | 0.534312i | 0.0207197i | ||||||||
\(666\) | −0.542815 | + | 8.49188i | −0.0210337 | + | 0.329054i | ||||
\(667\) | 5.65691 | + | 13.5216i | 0.219036 | + | 0.523558i | ||||
\(668\) | −2.93818 | + | 22.8887i | −0.113681 | + | 0.885591i | ||||
\(669\) | − | 8.79654i | − | 0.340094i | ||||||
\(670\) | 15.5603 | + | 0.994642i | 0.601148 | + | 0.0384264i | ||||
\(671\) | 30.1973i | 1.16575i | ||||||||
\(672\) | 1.58354 | − | 4.79173i | 0.0610863 | − | 0.184845i | ||||
\(673\) | 6.07738 | 0.234266 | 0.117133 | − | 0.993116i | \(-0.462630\pi\) | ||||
0.117133 | + | 0.993116i | \(0.462630\pi\) | |||||||
\(674\) | 41.2974 | + | 2.63980i | 1.59072 | + | 0.101681i | ||||
\(675\) | 4.36961 | 0.168187 | ||||||||
\(676\) | 8.34129 | + | 1.07075i | 0.320819 | + | 0.0411828i | ||||
\(677\) | 7.89600 | 0.303468 | 0.151734 | − | 0.988421i | \(-0.451514\pi\) | ||||
0.151734 | + | 0.988421i | \(0.451514\pi\) | |||||||
\(678\) | 22.6100 | + | 1.44527i | 0.868333 | + | 0.0555053i | ||||
\(679\) | 2.22808i | 0.0855060i | ||||||||
\(680\) | 8.61818 | + | 1.67090i | 0.330492 | + | 0.0640760i | ||||
\(681\) | − | 23.9345i | − | 0.917172i | ||||||
\(682\) | −0.923344 | + | 14.4449i | −0.0353567 | + | 0.553125i | ||||
\(683\) | 43.6655 | 1.67082 | 0.835408 | − | 0.549631i | \(-0.185232\pi\) | ||||
0.835408 | + | 0.549631i | \(0.185232\pi\) | |||||||
\(684\) | 0.0498249 | − | 0.388141i | 0.00190510 | − | 0.0148410i | ||||
\(685\) | 58.6335i | 2.24027i | ||||||||
\(686\) | −1.06270 | + | 16.6251i | −0.0405742 | + | 0.634749i | ||||
\(687\) | 8.58118 | 0.327392 | ||||||||
\(688\) | 10.1064 | − | 38.7163i | 0.385302 | − | 1.47604i | ||||
\(689\) | 46.5894i | 1.77492i | ||||||||
\(690\) | −6.77443 | − | 19.6242i | −0.257898 | − | 0.747081i | ||||
\(691\) | −15.7471 | −0.599049 | −0.299525 | − | 0.954089i | \(-0.596828\pi\) | ||||
−0.299525 | + | 0.954089i | \(0.596828\pi\) | |||||||
\(692\) | −1.63725 | + | 12.7543i | −0.0622388 | + | 0.484847i | ||||
\(693\) | − | 3.52666i | − | 0.133967i | ||||||
\(694\) | 0.195200 | − | 3.05373i | 0.00740968 | − | 0.115918i | ||||
\(695\) | −40.8556 | −1.54974 | ||||||||
\(696\) | −8.48633 | − | 1.64533i | −0.321673 | − | 0.0623662i | ||||
\(697\) | 10.3773i | 0.393070i | ||||||||
\(698\) | −33.5898 | − | 2.14712i | −1.27139 | − | 0.0812695i | ||||
\(699\) | 6.59907 | 0.249600 | ||||||||
\(700\) | −7.73302 | − | 0.992671i | −0.292281 | − | 0.0375194i | ||||
\(701\) | −35.7030 | −1.34849 | −0.674243 | − | 0.738510i | \(-0.735530\pi\) | ||||
−0.674243 | + | 0.738510i | \(0.735530\pi\) | |||||||
\(702\) | 5.85403 | + | 0.374200i | 0.220946 | + | 0.0141233i | ||||
\(703\) | − | 1.17729i | − | 0.0444023i | ||||||
\(704\) | −11.8186 | + | 29.3335i | −0.445431 | + | 1.10555i | ||||
\(705\) | 22.4430i | 0.845252i | ||||||||
\(706\) | 1.83545 | − | 28.7140i | 0.0690780 | − | 1.08067i | ||||
\(707\) | − | 2.94813i | − | 0.110876i | ||||||
\(708\) | 8.63027 | + | 1.10785i | 0.324345 | + | 0.0416355i | ||||
\(709\) | 25.5486 | 0.959499 | 0.479749 | − | 0.877406i | \(-0.340728\pi\) | ||||
0.479749 | + | 0.877406i | \(0.340728\pi\) | |||||||
\(710\) | 45.7456 | + | 2.92413i | 1.71680 | + | 0.109741i | ||||
\(711\) | −1.85136 | −0.0694313 | ||||||||
\(712\) | −29.9782 | − | 5.81220i | −1.12348 | − | 0.217821i | ||||
\(713\) | −4.79225 | − | 11.4548i | −0.179471 | − | 0.428986i | ||||
\(714\) | −1.27667 | − | 0.0816066i | −0.0477780 | − | 0.00305405i | ||||
\(715\) | 50.1909 | 1.87703 | ||||||||
\(716\) | 1.35199 | + | 0.173552i | 0.0505262 | + | 0.00648595i | ||||
\(717\) | 14.2318i | 0.531495i | ||||||||
\(718\) | 1.02834 | − | 16.0876i | 0.0383774 | − | 0.600382i | ||||
\(719\) | − | 12.9790i | − | 0.484036i | −0.970272 | − | 0.242018i | \(-0.922191\pi\) | ||
0.970272 | − | 0.242018i | \(-0.0778094\pi\) | |||||||
\(720\) | 11.8470 | + | 3.09250i | 0.441510 | + | 0.115250i | ||||
\(721\) | −9.25840 | −0.344801 | ||||||||
\(722\) | 1.71063 | − | 26.7613i | 0.0636630 | − | 0.995952i | ||||
\(723\) | − | 18.9358i | − | 0.704231i | ||||||
\(724\) | −17.3737 | − | 2.23022i | −0.645687 | − | 0.0828854i | ||||
\(725\) | 13.3546i | 0.495977i | ||||||||
\(726\) | −0.417428 | + | 6.53031i | −0.0154922 | + | 0.242362i | ||||
\(727\) | −25.5652 | −0.948160 | −0.474080 | − | 0.880482i | \(-0.657219\pi\) | ||||
−0.474080 | + | 0.880482i | \(0.657219\pi\) | |||||||
\(728\) | −10.2750 | − | 1.99213i | −0.380818 | − | 0.0738331i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.896595 | − | 14.0265i | 0.0331845 | − | 0.519143i | ||||
\(731\) | −10.1431 | −0.375156 | ||||||||
\(732\) | 15.1534 | + | 1.94521i | 0.560087 | + | 0.0718971i | ||||
\(733\) | −35.4883 | −1.31079 | −0.655395 | − | 0.755286i | \(-0.727498\pi\) | ||||
−0.655395 | + | 0.755286i | \(0.727498\pi\) | |||||||
\(734\) | 0.140271 | − | 2.19442i | 0.00517749 | − | 0.0809973i | ||||
\(735\) | −18.9907 | −0.700482 | ||||||||
\(736\) | −2.08852 | − | 27.0488i | −0.0769838 | − | 0.997032i | ||||
\(737\) | 14.2386 | 0.524485 | ||||||||
\(738\) | −0.923296 | + | 14.4442i | −0.0339870 | + | 0.531698i | ||||
\(739\) | −41.9864 | −1.54449 | −0.772247 | − | 0.635322i | \(-0.780867\pi\) | ||||
−0.772247 | + | 0.635322i | \(0.780867\pi\) | |||||||
\(740\) | 36.5356 | + | 4.69000i | 1.34308 | + | 0.172408i | ||||
\(741\) | −0.811586 | −0.0298144 | ||||||||
\(742\) | 0.903992 | − | 14.1422i | 0.0331866 | − | 0.519176i | ||||
\(743\) | −22.8728 | −0.839123 | −0.419561 | − | 0.907727i | \(-0.637816\pi\) | ||||
−0.419561 | + | 0.907727i | \(0.637816\pi\) | |||||||
\(744\) | 7.18918 | + | 1.39384i | 0.263568 | + | 0.0511007i | ||||
\(745\) | 5.85883 | 0.214651 | ||||||||
\(746\) | −0.834492 | + | 13.0549i | −0.0305529 | + | 0.477974i | ||||
\(747\) | 3.79082i | 0.138699i | ||||||||
\(748\) | 7.95137 | + | 1.02070i | 0.290731 | + | 0.0373205i | ||||
\(749\) | − | 16.3456i | − | 0.597257i | ||||||
\(750\) | −0.174078 | + | 2.72331i | −0.00635644 | + | 0.0994411i | ||||
\(751\) | 18.3558 | 0.669812 | 0.334906 | − | 0.942251i | \(-0.391295\pi\) | ||||
0.334906 | + | 0.942251i | \(0.391295\pi\) | |||||||
\(752\) | −7.40744 | + | 28.3770i | −0.270122 | + | 1.03480i | ||||
\(753\) | − | 16.7334i | − | 0.609798i | ||||||
\(754\) | −1.14364 | + | 17.8913i | −0.0416491 | + | 0.651564i | ||||
\(755\) | 47.4428i | 1.72662i | ||||||||
\(756\) | −1.76973 | − | 0.227176i | −0.0643643 | − | 0.00826231i | ||||
\(757\) | 13.2658 | 0.482155 | 0.241078 | − | 0.970506i | \(-0.422499\pi\) | ||||
0.241078 | + | 0.970506i | \(0.422499\pi\) | |||||||
\(758\) | 33.5805 | + | 2.14652i | 1.21970 | + | 0.0779651i | ||||
\(759\) | −7.31695 | − | 17.4895i | −0.265589 | − | 0.634830i | ||||
\(760\) | −1.66304 | − | 0.322430i | −0.0603247 | − | 0.0116958i | ||||
\(761\) | 24.5251 | 0.889034 | 0.444517 | − | 0.895770i | \(-0.353375\pi\) | ||||
0.444517 | + | 0.895770i | \(0.353375\pi\) | |||||||
\(762\) | 0.396938 | + | 0.0253730i | 0.0143796 | + | 0.000919165i | ||||
\(763\) | 11.1035 | 0.401975 | ||||||||
\(764\) | 13.9631 | + | 1.79241i | 0.505167 | + | 0.0648472i | ||||
\(765\) | − | 3.10373i | − | 0.112215i | ||||||
\(766\) | 1.24959 | − | 19.5487i | 0.0451494 | − | 0.706324i | ||||
\(767\) | − | 18.0455i | − | 0.651586i | ||||||
\(768\) | 13.9586 | + | 7.82031i | 0.503688 | + | 0.282191i | ||||
\(769\) | − | 3.94832i | − | 0.142380i | −0.997463 | − | 0.0711901i | \(-0.977320\pi\) | ||
0.997463 | − | 0.0711901i | \(-0.0226797\pi\) | |||||||
\(770\) | −15.2354 | − | 0.973873i | −0.549046 | − | 0.0350959i | ||||
\(771\) | 10.9984 | 0.396099 | ||||||||
\(772\) | 42.4614 | + | 5.45068i | 1.52822 | + | 0.196174i | ||||
\(773\) | −16.8096 | −0.604599 | −0.302300 | − | 0.953213i | \(-0.597754\pi\) | ||||
−0.302300 | + | 0.953213i | \(0.597754\pi\) | |||||||
\(774\) | −14.1181 | − | 0.902455i | −0.507466 | − | 0.0324381i | ||||
\(775\) | − | 11.3133i | − | 0.406387i | ||||||
\(776\) | −6.93487 | − | 1.34454i | −0.248947 | − | 0.0482660i | ||||
\(777\) | −5.36784 | −0.192570 | ||||||||
\(778\) | 2.27180 | − | 35.5404i | 0.0814480 | − | 1.27418i | ||||
\(779\) | − | 2.00250i | − | 0.0717470i | ||||||
\(780\) | 3.23313 | − | 25.1865i | 0.115765 | − | 0.901821i | ||||
\(781\) | 41.8598 | 1.49786 | ||||||||
\(782\) | −6.50060 | + | 2.24406i | −0.232461 | + | 0.0802474i | ||||
\(783\) | 3.05624i | 0.109221i | ||||||||
\(784\) | −24.0119 | − | 6.26799i | −0.857566 | − | 0.223857i | ||||
\(785\) | −33.8536 | −1.20829 | ||||||||
\(786\) | 1.96635 | − | 30.7619i | 0.0701375 | − | 1.09724i | ||||
\(787\) | − | 41.0427i | − | 1.46302i | −0.681833 | − | 0.731508i | \(-0.738817\pi\) | ||
0.681833 | − | 0.731508i | \(-0.261183\pi\) | |||||||
\(788\) | 4.21826 | − | 32.8607i | 0.150269 | − | 1.17061i | ||||
\(789\) | −32.1667 | −1.14516 | ||||||||
\(790\) | −0.511244 | + | 7.99798i | −0.0181893 | + | 0.284555i | ||||
\(791\) | 14.2921i | 0.508169i | ||||||||
\(792\) | 10.9767 | + | 2.12816i | 0.390039 | + | 0.0756209i | ||||
\(793\) | − | 31.6851i | − | 1.12517i | ||||||
\(794\) | −49.2106 | − | 3.14563i | −1.74642 | − | 0.111634i | ||||
\(795\) | 34.3813 | 1.21938 | ||||||||
\(796\) | 37.1976 | + | 4.77498i | 1.31844 | + | 0.169245i | ||||
\(797\) | 34.5930 | 1.22535 | 0.612674 | − | 0.790336i | \(-0.290094\pi\) | ||||
0.612674 | + | 0.790336i | \(0.290094\pi\) | |||||||
\(798\) | 0.246356 | + | 0.0157475i | 0.00872092 | + | 0.000557456i | ||||
\(799\) | 7.43434 | 0.263008 | ||||||||
\(800\) | 7.75616 | − | 23.4699i | 0.274222 | − | 0.829785i | ||||
\(801\) | 10.7963i | 0.381468i | ||||||||
\(802\) | −37.4526 | − | 2.39403i | −1.32250 | − | 0.0845362i | ||||
\(803\) | − | 12.8350i | − | 0.452938i | ||||||
\(804\) | 0.917203 | − | 7.14511i | 0.0323473 | − | 0.251989i | ||||
\(805\) | 12.0816 | − | 5.05449i | 0.425822 | − | 0.178147i | ||||
\(806\) | 0.968837 | − | 15.1566i | 0.0341258 | − | 0.533870i | ||||
\(807\) | 21.2979i | 0.749723i | ||||||||
\(808\) | 9.17600 | + | 1.77905i | 0.322811 | + | 0.0625867i | ||||
\(809\) | −38.0524 | −1.33785 | −0.668926 | − | 0.743329i | \(-0.733246\pi\) | ||||
−0.668926 | + | 0.743329i | \(0.733246\pi\) | |||||||
\(810\) | 0.276146 | − | 4.32007i | 0.00970278 | − | 0.151792i | ||||
\(811\) | −28.4205 | −0.997978 | −0.498989 | − | 0.866608i | \(-0.666295\pi\) | ||||
−0.498989 | + | 0.866608i | \(0.666295\pi\) | |||||||
\(812\) | 0.694304 | − | 5.40871i | 0.0243653 | − | 0.189808i | ||||
\(813\) | − | 2.36324i | − | 0.0828823i | ||||||
\(814\) | 33.5693 | + | 2.14581i | 1.17660 | + | 0.0752105i | ||||
\(815\) | 30.8208 | 1.07961 | ||||||||
\(816\) | 1.02440 | − | 3.92436i | 0.0358613 | − | 0.137380i | ||||
\(817\) | 1.95730 | 0.0684772 | ||||||||
\(818\) | −2.22329 | + | 34.7815i | −0.0777356 | + | 1.21611i | ||||
\(819\) | 3.70042i | 0.129303i | ||||||||
\(820\) | 62.1449 | + | 7.97740i | 2.17019 | + | 0.278583i | ||||
\(821\) | − | 37.1955i | − | 1.29813i | −0.760733 | − | 0.649065i | \(-0.775160\pi\) | ||
0.760733 | − | 0.649065i | \(-0.224840\pi\) | |||||||
\(822\) | 27.0343 | + | 1.72808i | 0.942929 | + | 0.0602736i | ||||
\(823\) | 10.0207i | 0.349301i | 0.984630 | + | 0.174651i | \(0.0558796\pi\) | ||||
−0.984630 | + | 0.174651i | \(0.944120\pi\) | |||||||
\(824\) | 5.58698 | − | 28.8166i | 0.194632 | − | 1.00387i | ||||
\(825\) | − | 17.2736i | − | 0.601388i | ||||||
\(826\) | −0.350144 | + | 5.47770i | −0.0121831 | + | 0.190594i | ||||
\(827\) | − | 47.1667i | − | 1.64015i | −0.572258 | − | 0.820073i | \(-0.693933\pi\) | ||
0.572258 | − | 0.820073i | \(-0.306067\pi\) | |||||||
\(828\) | −9.24783 | + | 2.54513i | −0.321384 | + | 0.0884493i | ||||
\(829\) | − | 26.2155i | − | 0.910503i | −0.890363 | − | 0.455252i | \(-0.849549\pi\) | ||
0.890363 | − | 0.455252i | \(-0.150451\pi\) | |||||||
\(830\) | 16.3766 | + | 1.04682i | 0.568440 | + | 0.0363356i | ||||
\(831\) | − | 9.50918i | − | 0.329870i | ||||||
\(832\) | 12.4009 | − | 30.7787i | 0.429925 | − | 1.06706i | ||||
\(833\) | 6.29075i | 0.217962i | ||||||||
\(834\) | −1.20412 | + | 18.8374i | −0.0416951 | + | 0.652284i | ||||
\(835\) | − | 35.3184i | − | 1.22225i | ||||||
\(836\) | −1.53436 | − | 0.196963i | −0.0530671 | − | 0.00681211i | ||||
\(837\) | − | 2.58909i | − | 0.0894921i | ||||||
\(838\) | −17.8779 | − | 1.14279i | −0.617583 | − | 0.0394769i | ||||
\(839\) | −26.6221 | −0.919097 | −0.459549 | − | 0.888153i | \(-0.651989\pi\) | ||||
−0.459549 | + | 0.888153i | \(0.651989\pi\) | |||||||
\(840\) | −1.47012 | + | 7.58260i | −0.0507239 | + | 0.261625i | ||||
\(841\) | 19.6594 | 0.677910 | ||||||||
\(842\) | 2.58997 | − | 40.5179i | 0.0892563 | − | 1.39634i | ||||
\(843\) | − | 22.7904i | − | 0.784942i | ||||||
\(844\) | 9.40251 | + | 1.20698i | 0.323648 | + | 0.0415460i | ||||
\(845\) | −12.8710 | −0.442776 | ||||||||
\(846\) | 10.3478 | + | 0.661451i | 0.355766 | + | 0.0227412i | ||||
\(847\) | −4.12790 | −0.141836 | ||||||||
\(848\) | 43.4718 | + | 11.3478i | 1.49283 | + | 0.389684i | ||||
\(849\) | − | 17.0253i | − | 0.584307i | ||||||
\(850\) | −6.25310 | − | 0.399708i | −0.214479 | − | 0.0137099i | ||||
\(851\) | −26.6204 | + | 11.1369i | −0.912535 | + | 0.381770i | ||||
\(852\) | 2.69647 | − | 21.0058i | 0.0923796 | − | 0.719648i | ||||
\(853\) | − | 10.7592i | − | 0.368388i | −0.982890 | − | 0.184194i | \(-0.941032\pi\) | ||
0.982890 | − | 0.184194i | \(-0.0589675\pi\) | |||||||
\(854\) | −0.614798 | + | 9.61799i | −0.0210380 | + | 0.329121i | ||||
\(855\) | 0.598921i | 0.0204827i | ||||||||
\(856\) | 50.8755 | + | 9.86377i | 1.73889 | + | 0.337137i | ||||
\(857\) | −48.2719 | −1.64894 | −0.824469 | − | 0.565907i | \(-0.808526\pi\) | ||||
−0.824469 | + | 0.565907i | \(0.808526\pi\) | |||||||
\(858\) | 1.47925 | − | 23.1416i | 0.0505008 | − | 0.790042i | ||||
\(859\) | 41.1208 | 1.40302 | 0.701511 | − | 0.712659i | \(-0.252509\pi\) | ||||
0.701511 | + | 0.712659i | \(0.252509\pi\) | |||||||
\(860\) | −7.79733 | + | 60.7421i | −0.265887 | + | 2.07129i | ||||
\(861\) | −9.13037 | −0.311162 | ||||||||
\(862\) | 2.07057 | − | 32.3924i | 0.0705240 | − | 1.10329i | ||||
\(863\) | − | 26.4666i | − | 0.900934i | −0.892793 | − | 0.450467i | \(-0.851257\pi\) | ||
0.892793 | − | 0.450467i | \(-0.148743\pi\) | |||||||
\(864\) | 1.77502 | − | 5.37115i | 0.0603875 | − | 0.182730i | ||||
\(865\) | − | 19.6806i | − | 0.669159i | ||||||
\(866\) | −21.2655 | − | 1.35933i | −0.722632 | − | 0.0461918i | ||||
\(867\) | 15.9719 | 0.542433 | ||||||||
\(868\) | −0.588179 | + | 4.58198i | −0.0199641 | + | 0.155523i | ||||
\(869\) | 7.31861i | 0.248267i | ||||||||
\(870\) | 13.2032 | + | 0.843968i | 0.447629 | + | 0.0286132i | ||||
\(871\) | −14.9401 | −0.506226 | ||||||||
\(872\) | −6.70042 | + | 34.5596i | −0.226905 | + | 1.17033i | ||||
\(873\) | 2.49750i | 0.0845277i | ||||||||
\(874\) | 1.25441 | − | 0.433033i | 0.0424311 | − | 0.0146476i | ||||
\(875\) | −1.72144 | −0.0581953 | ||||||||
\(876\) | −6.44079 | − | 0.826790i | −0.217614 | − | 0.0279346i | ||||
\(877\) | 28.8502i | 0.974202i | 0.873346 | + | 0.487101i | \(0.161946\pi\) | ||||
−0.873346 | + | 0.487101i | \(0.838054\pi\) | |||||||
\(878\) | 31.6790 | + | 2.02498i | 1.06912 | + | 0.0683397i | ||||
\(879\) | −13.2959 | −0.448461 | ||||||||
\(880\) | 12.2250 | − | 46.8323i | 0.412103 | − | 1.57872i | ||||
\(881\) | − | 17.0655i | − | 0.574953i | −0.957788 | − | 0.287476i | \(-0.907184\pi\) | ||
0.957788 | − | 0.287476i | \(-0.0928163\pi\) | |||||||
\(882\) | −0.559703 | + | 8.75607i | −0.0188462 | + | 0.294832i | ||||
\(883\) | 2.35287 | 0.0791805 | 0.0395902 | − | 0.999216i | \(-0.487395\pi\) | ||||
0.0395902 | + | 0.999216i | \(0.487395\pi\) | |||||||
\(884\) | −8.34313 | − | 1.07099i | −0.280610 | − | 0.0360213i | ||||
\(885\) | −13.3169 | −0.447644 | ||||||||
\(886\) | −2.59749 | + | 40.6355i | −0.0872644 | + | 1.36518i | ||||
\(887\) | − | 5.60160i | − | 0.188083i | −0.995568 | − | 0.0940417i | \(-0.970021\pi\) | ||
0.995568 | − | 0.0940417i | \(-0.0299787\pi\) | |||||||
\(888\) | 3.23922 | − | 16.7073i | 0.108701 | − | 0.560661i | ||||
\(889\) | 0.250910i | 0.00841526i | ||||||||
\(890\) | 46.6406 | + | 2.98135i | 1.56340 | + | 0.0999350i | ||||
\(891\) | − | 3.95311i | − | 0.132434i | ||||||
\(892\) | −2.24001 | + | 17.4499i | −0.0750010 | + | 0.584266i | ||||
\(893\) | −1.43459 | −0.0480069 | ||||||||
\(894\) | 0.172674 | − | 2.70134i | 0.00577509 | − | 0.0903464i | ||||
\(895\) | −2.08619 | −0.0697336 | ||||||||
\(896\) | −4.36150 | + | 9.10223i | −0.145707 | + | 0.304084i | ||||
\(897\) | 7.67746 | + | 18.3513i | 0.256343 | + | 0.612731i | ||||
\(898\) | 0.904500 | − | 14.1501i | 0.0301836 | − | 0.472196i | ||||
\(899\) | 7.91289 | 0.263910 | ||||||||
\(900\) | −8.66810 | − | 1.11271i | −0.288937 | − | 0.0370902i | ||||
\(901\) | − | 11.3890i | − | 0.379422i | ||||||
\(902\) | 57.0994 | + | 3.64989i | 1.90120 | + | 0.121528i | ||||
\(903\) | − | 8.92427i | − | 0.296981i | ||||||
\(904\) | −44.4840 | − | 8.62457i | −1.47951 | − | 0.286849i | ||||
\(905\) | 26.8084 | 0.891142 | ||||||||
\(906\) | 21.8745 | + | 1.39826i | 0.726733 | + | 0.0464540i | ||||
\(907\) | − | 53.9169i | − | 1.79028i | −0.445783 | − | 0.895141i | \(-0.647075\pi\) | ||
0.445783 | − | 0.895141i | \(-0.352925\pi\) | |||||||
\(908\) | −6.09483 | + | 47.4794i | −0.202264 | + | 1.57566i | ||||
\(909\) | − | 3.30462i | − | 0.109607i | ||||||
\(910\) | 15.9860 | + | 1.02185i | 0.529932 | + | 0.0338742i | ||||
\(911\) | −27.6108 | −0.914785 | −0.457393 | − | 0.889265i | \(-0.651217\pi\) | ||||
−0.457393 | + | 0.889265i | \(0.651217\pi\) | |||||||
\(912\) | −0.197677 | + | 0.757277i | −0.00654576 | + | 0.0250760i | ||||
\(913\) | 14.9855 | 0.495948 | ||||||||
\(914\) | 12.5780 | + | 0.804005i | 0.416042 | + | 0.0265941i | ||||
\(915\) | −23.3825 | −0.773001 | ||||||||
\(916\) | −17.0227 | − | 2.18517i | −0.562445 | − | 0.0721999i | ||||
\(917\) | 19.4451 | 0.642132 | ||||||||
\(918\) | −1.43104 | − | 0.0914745i | −0.0472314 | − | 0.00301911i | ||||
\(919\) | 19.0333 | 0.627850 | 0.313925 | − | 0.949448i | \(-0.398356\pi\) | ||||
0.313925 | + | 0.949448i | \(0.398356\pi\) | |||||||
\(920\) | 8.44136 | + | 40.6541i | 0.278304 | + | 1.34032i | ||||
\(921\) | −6.89668 | −0.227253 | ||||||||
\(922\) | −51.1890 | − | 3.27209i | −1.68582 | − | 0.107761i | ||||
\(923\) | −43.9222 | −1.44572 | ||||||||
\(924\) | −0.898051 | + | 6.99591i | −0.0295437 | + | 0.230149i | ||||
\(925\) | −26.2916 | −0.864463 | ||||||||
\(926\) | 41.7641 | + | 2.66963i | 1.37245 | + | 0.0877295i | ||||
\(927\) | −10.3779 | −0.340856 | ||||||||
\(928\) | 16.4155 | + | 5.42489i | 0.538866 | + | 0.178081i | ||||
\(929\) | −21.7196 | −0.712596 | −0.356298 | − | 0.934372i | \(-0.615961\pi\) | ||||
−0.356298 | + | 0.934372i | \(0.615961\pi\) | |||||||
\(930\) | −11.1850 | − | 0.714967i | −0.366772 | − | 0.0234447i | ||||
\(931\) | − | 1.21392i | − | 0.0397845i | ||||||
\(932\) | −13.0907 | − | 1.68043i | −0.428801 | − | 0.0550442i | ||||
\(933\) | − | 20.2868i | − | 0.664161i | ||||||
\(934\) | 0.569564 | + | 0.0364075i | 0.0186367 | + | 0.00119129i | ||||
\(935\) | −12.2694 | −0.401251 | ||||||||
\(936\) | −11.5175 | − | 2.23302i | −0.376461 | − | 0.0729884i | ||||
\(937\) | 16.7401i | 0.546875i | 0.961890 | + | 0.273437i | \(0.0881606\pi\) | ||||
−0.961890 | + | 0.273437i | \(0.911839\pi\) | |||||||
\(938\) | 4.53506 | + | 0.289888i | 0.148075 | + | 0.00946519i | ||||
\(939\) | − | 28.1949i | − | 0.920105i | ||||||
\(940\) | 5.71503 | − | 44.5207i | 0.186404 | − | 1.45210i | ||||
\(941\) | 38.9995 | 1.27135 | 0.635674 | − | 0.771958i | \(-0.280722\pi\) | ||||
0.635674 | + | 0.771958i | \(0.280722\pi\) | |||||||
\(942\) | −0.997751 | + | 15.6090i | −0.0325085 | + | 0.508568i | ||||
\(943\) | −45.2797 | + | 18.9433i | −1.47451 | + | 0.616878i | ||||
\(944\) | −16.8380 | − | 4.39533i | −0.548029 | − | 0.143056i | ||||
\(945\) | 2.73077 | 0.0888321 | ||||||||
\(946\) | −3.56750 | + | 55.8105i | −0.115989 | + | 1.81456i | ||||
\(947\) | 35.7861 | 1.16289 | 0.581446 | − | 0.813585i | \(-0.302487\pi\) | ||||
0.581446 | + | 0.813585i | \(0.302487\pi\) | |||||||
\(948\) | 3.67258 | + | 0.471441i | 0.119280 | + | 0.0153117i | ||||
\(949\) | 13.4674i | 0.437170i | ||||||||
\(950\) | 1.20665 | + | 0.0771312i | 0.0391489 | + | 0.00250247i | ||||
\(951\) | − | 8.49011i | − | 0.275311i | ||||||
\(952\) | 2.51177 | + | 0.486983i | 0.0814069 | + | 0.0157832i | ||||
\(953\) | − | 4.44958i | − | 0.144136i | −0.997400 | − | 0.0720681i | \(-0.977040\pi\) | ||
0.997400 | − | 0.0720681i | \(-0.0229599\pi\) | |||||||
\(954\) | 1.01330 | − | 15.8523i | 0.0328069 | − | 0.513236i | ||||
\(955\) | −21.5457 | −0.697204 | ||||||||
\(956\) | 3.62406 | − | 28.2319i | 0.117211 | − | 0.913084i | ||||
\(957\) | 12.0816 | 0.390544 | ||||||||
\(958\) | 0.848709 | − | 13.2773i | 0.0274205 | − | 0.428971i | ||||
\(959\) | 17.0887i | 0.551824i | ||||||||
\(960\) | −22.7136 | − | 9.15144i | −0.733078 | − | 0.295361i | ||||
\(961\) | 24.2966 | 0.783761 | ||||||||
\(962\) | −35.2233 | − | 2.25153i | −1.13564 | − | 0.0725922i | ||||
\(963\) | − | 18.3222i | − | 0.590424i | ||||||
\(964\) | −4.82194 | + | 37.5634i | −0.155304 | + | 1.20984i | ||||
\(965\) | −65.5200 | −2.10916 | ||||||||
\(966\) | −1.97441 | − | 5.71948i | −0.0635256 | − | 0.184021i | ||||
\(967\) | 19.1093i | 0.614514i | 0.951627 | + | 0.307257i | \(0.0994110\pi\) | ||||
−0.951627 | + | 0.307257i | \(0.900589\pi\) | |||||||
\(968\) | 2.49098 | − | 12.8480i | 0.0800631 | − | 0.412951i | ||||
\(969\) | 0.198395 | 0.00637338 | ||||||||
\(970\) | 10.7894 | + | 0.689676i | 0.346426 | + | 0.0221441i | ||||
\(971\) | 52.6143i | 1.68847i | 0.535972 | + | 0.844236i | \(0.319945\pi\) | ||||
−0.535972 | + | 0.844236i | \(0.680055\pi\) | |||||||
\(972\) | −1.98372 | − | 0.254646i | −0.0636279 | − | 0.00816778i | ||||
\(973\) | −11.9074 | −0.381732 | ||||||||
\(974\) | 39.8337 | + | 2.54624i | 1.27635 | + | 0.0815867i | ||||
\(975\) | 18.1246i | 0.580452i | ||||||||
\(976\) | −29.5648 | − | 7.71752i | −0.946348 | − | 0.247032i | ||||
\(977\) | − | 4.07699i | − | 0.130435i | −0.997871 | − | 0.0652173i | \(-0.979226\pi\) | ||
0.997871 | − | 0.0652173i | \(-0.0207741\pi\) | |||||||
\(978\) | 0.908366 | − | 14.2106i | 0.0290463 | − | 0.454405i | ||||
\(979\) | 42.6788 | 1.36402 | ||||||||
\(980\) | 37.6723 | + | 4.83591i | 1.20340 | + | 0.154477i | ||||
\(981\) | 12.4462 | 0.397376 | ||||||||
\(982\) | 2.05481 | − | 32.1458i | 0.0655717 | − | 1.02581i | ||||
\(983\) | −3.92937 | −0.125327 | −0.0626637 | − | 0.998035i | \(-0.519960\pi\) | ||||
−0.0626637 | + | 0.998035i | \(0.519960\pi\) | |||||||
\(984\) | 5.50972 | − | 28.4181i | 0.175643 | − | 0.905937i | ||||
\(985\) | 50.7057i | 1.61562i | ||||||||
\(986\) | 0.279568 | − | 4.37361i | 0.00890327 | − | 0.139284i | ||||
\(987\) | 6.54101i | 0.208203i | ||||||||
\(988\) | 1.60996 | + | 0.206667i | 0.0512197 | + | 0.00657497i | ||||
\(989\) | −18.5157 | − | 44.2576i | −0.588764 | − | 1.40731i | ||||
\(990\) | −17.0777 | − | 1.09163i | −0.542764 | − | 0.0346944i | ||||
\(991\) | 40.8198i | 1.29668i | 0.761350 | + | 0.648341i | \(0.224537\pi\) | ||||
−0.761350 | + | 0.648341i | \(0.775463\pi\) | |||||||
\(992\) | −13.9064 | − | 4.59570i | −0.441529 | − | 0.145913i | ||||
\(993\) | −14.3840 | −0.456464 | ||||||||
\(994\) | 13.3326 | + | 0.852239i | 0.422883 | + | 0.0270314i | ||||
\(995\) | −57.3978 | −1.81963 | ||||||||
\(996\) | 0.965318 | − | 7.51994i | 0.0305873 | − | 0.238278i | ||||
\(997\) | 16.7467i | 0.530374i | 0.964197 | + | 0.265187i | \(0.0854337\pi\) | ||||
−0.964197 | + | 0.265187i | \(0.914566\pi\) | |||||||
\(998\) | −1.61902 | + | 25.3282i | −0.0512492 | + | 0.801749i | ||||
\(999\) | −6.01692 | −0.190367 |
(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 | 552.2.n.a.91.14 | yes | 24 | |
4.3 | odd | 2 | 2208.2.n.a.367.22 | 24 | |||
8.3 | odd | 2 | inner | 552.2.n.a.91.15 | yes | 24 | |
8.5 | even | 2 | 2208.2.n.a.367.4 | 24 | |||
23.22 | odd | 2 | inner | 552.2.n.a.91.13 | ✓ | 24 | |
92.91 | even | 2 | 2208.2.n.a.367.3 | 24 | |||
184.45 | odd | 2 | 2208.2.n.a.367.21 | 24 | |||
184.91 | even | 2 | inner | 552.2.n.a.91.16 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.n.a.91.13 | ✓ | 24 | 23.22 | odd | 2 | inner | |
552.2.n.a.91.14 | yes | 24 | 1.1 | even | 1 | trivial | |
552.2.n.a.91.15 | yes | 24 | 8.3 | odd | 2 | inner | |
552.2.n.a.91.16 | yes | 24 | 184.91 | even | 2 | inner | |
2208.2.n.a.367.3 | 24 | 92.91 | even | 2 | |||
2208.2.n.a.367.4 | 24 | 8.5 | even | 2 | |||
2208.2.n.a.367.21 | 24 | 184.45 | odd | 2 | |||
2208.2.n.a.367.22 | 24 | 4.3 | odd | 2 |