Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [171,2,Mod(106,171)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(171, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("171.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 171 = 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 171.g (of order \(3\), 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: | \(1.36544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 106.5 | ||
Character | \(\chi\) | \(=\) | 171.106 |
Dual form | 171.2.g.c.121.5 |
$q$-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 \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(154\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.803309 | − | 1.39137i | −0.568025 | − | 0.983849i | −0.996761 | − | 0.0804188i | \(-0.974374\pi\) |
0.428736 | − | 0.903430i | \(-0.358959\pi\) | |||||||
\(3\) | −1.24014 | − | 1.20915i | −0.715996 | − | 0.698105i | ||||
\(4\) | −0.290611 | + | 0.503353i | −0.145306 | + | 0.251677i | ||||
\(5\) | 3.75880 | 1.68098 | 0.840492 | − | 0.541823i | \(-0.182266\pi\) | ||||
0.840492 | + | 0.541823i | \(0.182266\pi\) | |||||||
\(6\) | −0.686165 | + | 2.69682i | −0.280126 | + | 1.10097i | ||||
\(7\) | 2.27973 | − | 3.94861i | 0.861656 | − | 1.49243i | −0.00867312 | − | 0.999962i | \(-0.502761\pi\) |
0.870329 | − | 0.492470i | \(-0.163906\pi\) | |||||||
\(8\) | −2.27943 | −0.805902 | ||||||||
\(9\) | 0.0758986 | + | 2.99904i | 0.0252995 | + | 0.999680i | ||||
\(10\) | −3.01948 | − | 5.22989i | −0.954842 | − | 1.65383i | ||||
\(11\) | −1.29616 | + | 2.24501i | −0.390806 | + | 0.676896i | −0.992556 | − | 0.121789i | \(-0.961137\pi\) |
0.601750 | + | 0.798684i | \(0.294470\pi\) | |||||||
\(12\) | 0.969030 | − | 0.272836i | 0.279735 | − | 0.0787608i | ||||
\(13\) | 0.268857 | − | 0.465674i | 0.0745675 | − | 0.129155i | −0.826331 | − | 0.563185i | \(-0.809576\pi\) |
0.900898 | + | 0.434031i | \(0.142909\pi\) | |||||||
\(14\) | −7.32531 | −1.95777 | ||||||||
\(15\) | −4.66144 | − | 4.54496i | −1.20358 | − | 1.17350i | ||||
\(16\) | 2.41231 | + | 4.17825i | 0.603078 | + | 1.04456i | ||||
\(17\) | −1.73001 | + | 2.99646i | −0.419588 | + | 0.726748i | −0.995898 | − | 0.0904832i | \(-0.971159\pi\) |
0.576310 | + | 0.817231i | \(0.304492\pi\) | |||||||
\(18\) | 4.11181 | − | 2.51476i | 0.969163 | − | 0.592734i | ||||
\(19\) | −4.01417 | − | 1.69894i | −0.920915 | − | 0.389764i | ||||
\(20\) | −1.09235 | + | 1.89200i | −0.244256 | + | 0.423065i | ||||
\(21\) | −7.60165 | + | 2.14029i | −1.65882 | + | 0.467049i | ||||
\(22\) | 4.16486 | 0.887951 | ||||||||
\(23\) | 0.104462 | − | 0.180933i | 0.0217818 | − | 0.0377271i | −0.854929 | − | 0.518745i | \(-0.826399\pi\) |
0.876711 | + | 0.481018i | \(0.159733\pi\) | |||||||
\(24\) | 2.82682 | + | 2.75618i | 0.577022 | + | 0.562604i | ||||
\(25\) | 9.12855 | 1.82571 | ||||||||
\(26\) | −0.863901 | −0.169425 | ||||||||
\(27\) | 3.53217 | − | 3.81100i | 0.679767 | − | 0.733428i | ||||
\(28\) | 1.32503 | + | 2.29502i | 0.250407 | + | 0.433717i | ||||
\(29\) | −0.853801 | −0.158547 | −0.0792735 | − | 0.996853i | \(-0.525260\pi\) | ||||
−0.0792735 | + | 0.996853i | \(0.525260\pi\) | |||||||
\(30\) | −2.57916 | + | 10.1368i | −0.470887 | + | 1.85072i | ||||
\(31\) | 3.83524 | + | 6.64283i | 0.688829 | + | 1.19309i | 0.972217 | + | 0.234082i | \(0.0752084\pi\) |
−0.283388 | + | 0.959005i | \(0.591458\pi\) | |||||||
\(32\) | 1.59623 | − | 2.76475i | 0.282176 | − | 0.488744i | ||||
\(33\) | 4.32198 | − | 1.21688i | 0.752360 | − | 0.211831i | ||||
\(34\) | 5.55892 | 0.953347 | ||||||||
\(35\) | 8.56903 | − | 14.8420i | 1.44843 | − | 2.50876i | ||||
\(36\) | −1.53163 | − | 0.833350i | −0.255272 | − | 0.138892i | ||||
\(37\) | 4.41513 | 0.725843 | 0.362921 | − | 0.931820i | \(-0.381779\pi\) | ||||
0.362921 | + | 0.931820i | \(0.381779\pi\) | |||||||
\(38\) | 0.860764 | + | 6.94999i | 0.139634 | + | 1.12744i | ||||
\(39\) | −0.896491 | + | 0.252412i | −0.143554 | + | 0.0404183i | ||||
\(40\) | −8.56793 | −1.35471 | ||||||||
\(41\) | 0.939316 | 0.146697 | 0.0733483 | − | 0.997306i | \(-0.476632\pi\) | ||||
0.0733483 | + | 0.997306i | \(0.476632\pi\) | |||||||
\(42\) | 9.08441 | + | 8.85741i | 1.40176 | + | 1.36673i | ||||
\(43\) | −1.99417 | − | 3.45401i | −0.304108 | − | 0.526731i | 0.672954 | − | 0.739684i | \(-0.265025\pi\) |
−0.977062 | + | 0.212953i | \(0.931692\pi\) | |||||||
\(44\) | −0.753355 | − | 1.30485i | −0.113573 | − | 0.196713i | ||||
\(45\) | 0.285287 | + | 11.2728i | 0.0425281 | + | 1.68045i | ||||
\(46\) | −0.335660 | −0.0494904 | ||||||||
\(47\) | −3.14090 | −0.458147 | −0.229073 | − | 0.973409i | \(-0.573570\pi\) | ||||
−0.229073 | + | 0.973409i | \(0.573570\pi\) | |||||||
\(48\) | 2.06053 | − | 8.09847i | 0.297412 | − | 1.16891i | ||||
\(49\) | −6.89432 | − | 11.9413i | −0.984903 | − | 1.70590i | ||||
\(50\) | −7.33305 | − | 12.7012i | −1.03705 | − | 1.79622i | ||||
\(51\) | 5.76863 | − | 1.62419i | 0.807770 | − | 0.227432i | ||||
\(52\) | 0.156266 | + | 0.270660i | 0.0216701 | + | 0.0375338i | ||||
\(53\) | 5.68786 | + | 9.85167i | 0.781288 | + | 1.35323i | 0.931192 | + | 0.364530i | \(0.118770\pi\) |
−0.149903 | + | 0.988701i | \(0.547896\pi\) | |||||||
\(54\) | −8.13995 | − | 1.85315i | −1.10771 | − | 0.252182i | ||||
\(55\) | −4.87199 | + | 8.43853i | −0.656939 | + | 1.13785i | ||||
\(56\) | −5.19649 | + | 9.00059i | −0.694410 | + | 1.20275i | ||||
\(57\) | 2.92386 | + | 6.96068i | 0.387275 | + | 0.921964i | ||||
\(58\) | 0.685866 | + | 1.18796i | 0.0900587 | + | 0.155986i | ||||
\(59\) | 2.40432 | 0.313016 | 0.156508 | − | 0.987677i | \(-0.449976\pi\) | ||||
0.156508 | + | 0.987677i | \(0.449976\pi\) | |||||||
\(60\) | 3.64238 | − | 1.02553i | 0.470230 | − | 0.132396i | ||||
\(61\) | −7.18979 | −0.920558 | −0.460279 | − | 0.887774i | \(-0.652251\pi\) | ||||
−0.460279 | + | 0.887774i | \(0.652251\pi\) | |||||||
\(62\) | 6.16176 | − | 10.6725i | 0.782545 | − | 1.35541i | ||||
\(63\) | 12.0151 | + | 6.53730i | 1.51375 | + | 0.823623i | ||||
\(64\) | 4.52018 | 0.565023 | ||||||||
\(65\) | 1.01058 | − | 1.75037i | 0.125347 | − | 0.217107i | ||||
\(66\) | −5.16501 | − | 5.03595i | −0.635769 | − | 0.619883i | ||||
\(67\) | −0.140263 | + | 0.242942i | −0.0171358 | + | 0.0296801i | −0.874466 | − | 0.485087i | \(-0.838788\pi\) |
0.857330 | + | 0.514767i | \(0.172121\pi\) | |||||||
\(68\) | −1.00552 | − | 1.74161i | −0.121937 | − | 0.211201i | ||||
\(69\) | −0.348323 | + | 0.0980722i | −0.0419331 | + | 0.0118065i | ||||
\(70\) | −27.5343 | −3.29098 | ||||||||
\(71\) | 3.43003 | − | 5.94099i | 0.407070 | − | 0.705066i | −0.587490 | − | 0.809231i | \(-0.699884\pi\) |
0.994560 | + | 0.104165i | \(0.0332172\pi\) | |||||||
\(72\) | −0.173006 | − | 6.83611i | −0.0203889 | − | 0.805644i | ||||
\(73\) | −0.416690 | + | 0.721728i | −0.0487698 | + | 0.0844718i | −0.889380 | − | 0.457169i | \(-0.848863\pi\) |
0.840610 | + | 0.541641i | \(0.182197\pi\) | |||||||
\(74\) | −3.54671 | − | 6.14309i | −0.412297 | − | 0.714120i | ||||
\(75\) | −11.3207 | − | 11.0378i | −1.30720 | − | 1.27454i | ||||
\(76\) | 2.02173 | − | 1.52682i | 0.231908 | − | 0.175138i | ||||
\(77\) | 5.90977 | + | 10.2360i | 0.673481 | + | 1.16650i | ||||
\(78\) | 1.07136 | + | 1.04459i | 0.121307 | + | 0.118276i | ||||
\(79\) | 5.91744 | + | 10.2493i | 0.665764 | + | 1.15314i | 0.979077 | + | 0.203488i | \(0.0652278\pi\) |
−0.313313 | + | 0.949650i | \(0.601439\pi\) | |||||||
\(80\) | 9.06739 | + | 15.7052i | 1.01377 | + | 1.75589i | ||||
\(81\) | −8.98848 | + | 0.455246i | −0.998720 | + | 0.0505829i | ||||
\(82\) | −0.754561 | − | 1.30694i | −0.0833273 | − | 0.144327i | ||||
\(83\) | 3.63125 | − | 6.28951i | 0.398582 | − | 0.690364i | −0.594970 | − | 0.803748i | \(-0.702836\pi\) |
0.993551 | + | 0.113385i | \(0.0361692\pi\) | |||||||
\(84\) | 1.13180 | − | 4.44831i | 0.123490 | − | 0.485350i | ||||
\(85\) | −6.50274 | + | 11.2631i | −0.705322 | + | 1.22165i | ||||
\(86\) | −3.20387 | + | 5.54927i | −0.345483 | + | 0.598393i | ||||
\(87\) | 1.05883 | + | 1.03238i | 0.113519 | + | 0.110682i | ||||
\(88\) | 2.95450 | − | 5.11735i | 0.314951 | − | 0.545512i | ||||
\(89\) | −3.20392 | − | 5.54936i | −0.339615 | − | 0.588231i | 0.644745 | − | 0.764398i | \(-0.276963\pi\) |
−0.984360 | + | 0.176167i | \(0.943630\pi\) | |||||||
\(90\) | 15.4555 | − | 9.45247i | 1.62915 | − | 0.996378i | ||||
\(91\) | −1.22584 | − | 2.12322i | −0.128503 | − | 0.222574i | ||||
\(92\) | 0.0607154 | + | 0.105162i | 0.00633002 | + | 0.0109639i | ||||
\(93\) | 3.27596 | − | 12.8754i | 0.339701 | − | 1.33512i | ||||
\(94\) | 2.52311 | + | 4.37015i | 0.260239 | + | 0.450747i | ||||
\(95\) | −15.0885 | − | 6.38597i | −1.54804 | − | 0.655187i | ||||
\(96\) | −5.32256 | + | 1.49860i | −0.543232 | + | 0.152950i | ||||
\(97\) | 3.18119 | + | 5.50998i | 0.323001 | + | 0.559453i | 0.981106 | − | 0.193473i | \(-0.0619751\pi\) |
−0.658105 | + | 0.752926i | \(0.728642\pi\) | |||||||
\(98\) | −11.0765 | + | 19.1851i | −1.11890 | + | 1.93799i | ||||
\(99\) | −6.83125 | − | 3.71683i | −0.686566 | − | 0.373556i | ||||
\(100\) | −2.65286 | + | 4.59489i | −0.265286 | + | 0.459489i | ||||
\(101\) | −2.31014 | −0.229868 | −0.114934 | − | 0.993373i | \(-0.536666\pi\) | ||||
−0.114934 | + | 0.993373i | \(0.536666\pi\) | |||||||
\(102\) | −6.89384 | − | 6.72159i | −0.682592 | − | 0.665536i | ||||
\(103\) | −3.73572 | − | 6.47046i | −0.368092 | − | 0.637554i | 0.621175 | − | 0.783672i | \(-0.286655\pi\) |
−0.989267 | + | 0.146118i | \(0.953322\pi\) | |||||||
\(104\) | −0.612842 | + | 1.06147i | −0.0600941 | + | 0.104086i | ||||
\(105\) | −28.5731 | + | 8.04490i | −2.78845 | + | 0.785102i | ||||
\(106\) | 9.13823 | − | 15.8279i | 0.887583 | − | 1.53734i | ||||
\(107\) | −8.56202 | −0.827722 | −0.413861 | − | 0.910340i | \(-0.635820\pi\) | ||||
−0.413861 | + | 0.910340i | \(0.635820\pi\) | |||||||
\(108\) | 0.891793 | + | 2.88545i | 0.0858128 | + | 0.277653i | ||||
\(109\) | 5.16271 | − | 8.94207i | 0.494498 | − | 0.856495i | −0.505482 | − | 0.862837i | \(-0.668685\pi\) |
0.999980 | + | 0.00634184i | \(0.00201868\pi\) | |||||||
\(110\) | 15.6549 | 1.49263 | ||||||||
\(111\) | −5.47538 | − | 5.33857i | −0.519700 | − | 0.506714i | ||||
\(112\) | 21.9977 | 2.07858 | ||||||||
\(113\) | −7.77287 | − | 13.4630i | −0.731210 | − | 1.26649i | −0.956366 | − | 0.292170i | \(-0.905623\pi\) |
0.225156 | − | 0.974323i | \(-0.427711\pi\) | |||||||
\(114\) | 7.33613 | − | 9.65976i | 0.687091 | − | 0.904719i | ||||
\(115\) | 0.392650 | − | 0.680090i | 0.0366148 | − | 0.0634187i | ||||
\(116\) | 0.248124 | − | 0.429764i | 0.0230377 | − | 0.0399026i | ||||
\(117\) | 1.41698 | + | 0.770969i | 0.131000 | + | 0.0712761i | ||||
\(118\) | −1.93141 | − | 3.34531i | −0.177801 | − | 0.307960i | ||||
\(119\) | 7.88789 | + | 13.6622i | 0.723082 | + | 1.25241i | ||||
\(120\) | 10.6254 | + | 10.3599i | 0.969966 | + | 0.945729i | ||||
\(121\) | 2.13996 | + | 3.70651i | 0.194541 | + | 0.336956i | ||||
\(122\) | 5.77562 | + | 10.0037i | 0.522900 | + | 0.905690i | ||||
\(123\) | −1.16488 | − | 1.13578i | −0.105034 | − | 0.102410i | ||||
\(124\) | −4.45825 | −0.400363 | ||||||||
\(125\) | 15.5184 | 1.38801 | ||||||||
\(126\) | −0.555980 | − | 21.9689i | −0.0495307 | − | 1.95714i | ||||
\(127\) | 6.30706 | + | 10.9241i | 0.559661 | + | 0.969361i | 0.997525 | + | 0.0703197i | \(0.0224020\pi\) |
−0.437864 | + | 0.899041i | \(0.644265\pi\) | |||||||
\(128\) | −6.82357 | − | 11.8188i | −0.603124 | − | 1.04464i | ||||
\(129\) | −1.70337 | + | 6.69472i | −0.149973 | + | 0.589437i | ||||
\(130\) | −3.24723 | −0.284801 | ||||||||
\(131\) | 19.7774 | 1.72796 | 0.863980 | − | 0.503526i | \(-0.167964\pi\) | ||||
0.863980 | + | 0.503526i | \(0.167964\pi\) | |||||||
\(132\) | −0.643496 | + | 2.52912i | −0.0560091 | + | 0.220131i | ||||
\(133\) | −15.8597 | + | 11.9773i | −1.37521 | + | 1.03856i | ||||
\(134\) | 0.450697 | 0.0389343 | ||||||||
\(135\) | 13.2767 | − | 14.3248i | 1.14268 | − | 1.23288i | ||||
\(136\) | 3.94344 | − | 6.83023i | 0.338147 | − | 0.585688i | ||||
\(137\) | 11.7148 | 1.00086 | 0.500430 | − | 0.865777i | \(-0.333175\pi\) | ||||
0.500430 | + | 0.865777i | \(0.333175\pi\) | |||||||
\(138\) | 0.416266 | + | 0.405864i | 0.0354349 | + | 0.0345495i | ||||
\(139\) | −8.92017 | + | 15.4502i | −0.756599 | + | 1.31047i | 0.187976 | + | 0.982174i | \(0.439807\pi\) |
−0.944575 | + | 0.328294i | \(0.893526\pi\) | |||||||
\(140\) | 4.98051 | + | 8.62650i | 0.420930 | + | 0.729072i | ||||
\(141\) | 3.89515 | + | 3.79782i | 0.328031 | + | 0.319834i | ||||
\(142\) | −11.0215 | −0.924904 | ||||||||
\(143\) | 0.696961 | + | 1.20717i | 0.0582828 | + | 0.100949i | ||||
\(144\) | −12.3476 | + | 7.55174i | −1.02897 | + | 0.629312i | ||||
\(145\) | −3.20927 | −0.266515 | ||||||||
\(146\) | 1.33892 | 0.110810 | ||||||||
\(147\) | −5.88895 | + | 23.1452i | −0.485712 | + | 1.90898i | ||||
\(148\) | −1.28309 | + | 2.22237i | −0.105469 | + | 0.182678i | ||||
\(149\) | −16.1092 | −1.31972 | −0.659859 | − | 0.751389i | \(-0.729384\pi\) | ||||
−0.659859 | + | 0.751389i | \(0.729384\pi\) | |||||||
\(150\) | −6.26370 | + | 24.6181i | −0.511429 | + | 2.01006i | ||||
\(151\) | −0.821225 | + | 1.42240i | −0.0668303 | + | 0.115754i | −0.897504 | − | 0.441005i | \(-0.854622\pi\) |
0.830674 | + | 0.556759i | \(0.187955\pi\) | |||||||
\(152\) | 9.15005 | + | 3.87262i | 0.742167 | + | 0.314111i | ||||
\(153\) | −9.11781 | − | 4.96093i | −0.737131 | − | 0.401068i | ||||
\(154\) | 9.49474 | − | 16.4454i | 0.765108 | − | 1.32521i | ||||
\(155\) | 14.4159 | + | 24.9690i | 1.15791 | + | 2.00556i | ||||
\(156\) | 0.133478 | − | 0.524605i | 0.0106868 | − | 0.0420021i | ||||
\(157\) | 10.6210 | 0.847648 | 0.423824 | − | 0.905745i | \(-0.360688\pi\) | ||||
0.423824 | + | 0.905745i | \(0.360688\pi\) | |||||||
\(158\) | 9.50707 | − | 16.4667i | 0.756342 | − | 1.31002i | ||||
\(159\) | 4.85842 | − | 19.0950i | 0.385298 | − | 1.51433i | ||||
\(160\) | 5.99991 | − | 10.3921i | 0.474334 | − | 0.821571i | ||||
\(161\) | −0.476288 | − | 0.824956i | −0.0375368 | − | 0.0650156i | ||||
\(162\) | 7.85394 | + | 12.1406i | 0.617064 | + | 0.953857i | ||||
\(163\) | −22.0892 | −1.73016 | −0.865080 | − | 0.501634i | \(-0.832732\pi\) | ||||
−0.865080 | + | 0.501634i | \(0.832732\pi\) | |||||||
\(164\) | −0.272976 | + | 0.472808i | −0.0213158 | + | 0.0369201i | ||||
\(165\) | 16.2454 | − | 4.57399i | 1.26471 | − | 0.356085i | ||||
\(166\) | −11.6681 | −0.905618 | ||||||||
\(167\) | −6.54741 | + | 11.3404i | −0.506654 | + | 0.877550i | 0.493316 | + | 0.869850i | \(0.335784\pi\) |
−0.999970 | + | 0.00770038i | \(0.997549\pi\) | |||||||
\(168\) | 17.3275 | − | 4.87864i | 1.33684 | − | 0.376395i | ||||
\(169\) | 6.35543 | + | 11.0079i | 0.488879 | + | 0.846764i | ||||
\(170\) | 20.8949 | 1.60256 | ||||||||
\(171\) | 4.79052 | − | 12.1676i | 0.366340 | − | 0.930481i | ||||
\(172\) | 2.31811 | 0.176755 | ||||||||
\(173\) | −6.28949 | − | 10.8937i | −0.478181 | − | 0.828234i | 0.521506 | − | 0.853248i | \(-0.325370\pi\) |
−0.999687 | + | 0.0250137i | \(0.992037\pi\) | |||||||
\(174\) | 0.585849 | − | 2.30255i | 0.0444131 | − | 0.174556i | ||||
\(175\) | 20.8106 | − | 36.0450i | 1.57313 | − | 2.72475i | ||||
\(176\) | −12.5069 | −0.942746 | ||||||||
\(177\) | −2.98170 | − | 2.90719i | −0.224118 | − | 0.218518i | ||||
\(178\) | −5.14748 | + | 8.91570i | −0.385820 | + | 0.668260i | ||||
\(179\) | −23.1728 | −1.73202 | −0.866008 | − | 0.500031i | \(-0.833322\pi\) | ||||
−0.866008 | + | 0.500031i | \(0.833322\pi\) | |||||||
\(180\) | −5.75710 | − | 3.13239i | −0.429109 | − | 0.233475i | ||||
\(181\) | 1.87031 | + | 3.23948i | 0.139019 | + | 0.240789i | 0.927126 | − | 0.374751i | \(-0.122272\pi\) |
−0.788106 | + | 0.615539i | \(0.788938\pi\) | |||||||
\(182\) | −1.96946 | + | 3.41120i | −0.145986 | + | 0.252855i | ||||
\(183\) | 8.91635 | + | 8.69355i | 0.659116 | + | 0.642646i | ||||
\(184\) | −0.238113 | + | 0.412425i | −0.0175540 | + | 0.0304044i | ||||
\(185\) | 16.5956 | 1.22013 | ||||||||
\(186\) | −20.5461 | + | 5.78487i | −1.50652 | + | 0.424168i | ||||
\(187\) | −4.48472 | − | 7.76776i | −0.327955 | − | 0.568035i | ||||
\(188\) | 0.912779 | − | 1.58098i | 0.0665712 | − | 0.115305i | ||||
\(189\) | −6.99576 | − | 22.6352i | −0.508867 | − | 1.64647i | ||||
\(190\) | 3.23544 | + | 26.1236i | 0.234723 | + | 1.89520i | ||||
\(191\) | −7.37837 | + | 12.7797i | −0.533880 | + | 0.924707i | 0.465337 | + | 0.885134i | \(0.345933\pi\) |
−0.999217 | + | 0.0395734i | \(0.987400\pi\) | |||||||
\(192\) | −5.60566 | − | 5.46559i | −0.404554 | − | 0.394445i | ||||
\(193\) | −5.67586 | −0.408558 | −0.204279 | − | 0.978913i | \(-0.565485\pi\) | ||||
−0.204279 | + | 0.978913i | \(0.565485\pi\) | |||||||
\(194\) | 5.11095 | − | 8.85243i | 0.366945 | − | 0.635568i | ||||
\(195\) | −3.36973 | + | 0.948766i | −0.241311 | + | 0.0679425i | ||||
\(196\) | 8.01426 | 0.572447 | ||||||||
\(197\) | −12.2959 | −0.876046 | −0.438023 | − | 0.898964i | \(-0.644321\pi\) | ||||
−0.438023 | + | 0.898964i | \(0.644321\pi\) | |||||||
\(198\) | 0.316107 | + | 12.4906i | 0.0224647 | + | 0.887667i | ||||
\(199\) | 0.0159042 | + | 0.0275469i | 0.00112742 | + | 0.00195275i | 0.866589 | − | 0.499023i | \(-0.166308\pi\) |
−0.865461 | + | 0.500976i | \(0.832974\pi\) | |||||||
\(200\) | −20.8079 | −1.47134 | ||||||||
\(201\) | 0.467699 | − | 0.131683i | 0.0329890 | − | 0.00928822i | ||||
\(202\) | 1.85576 | + | 3.21427i | 0.130571 | + | 0.226155i | ||||
\(203\) | −1.94644 | + | 3.37132i | −0.136613 | + | 0.236621i | ||||
\(204\) | −0.858887 | + | 3.37567i | −0.0601341 | + | 0.236344i | ||||
\(205\) | 3.53070 | 0.246595 | ||||||||
\(206\) | −6.00188 | + | 10.3956i | −0.418171 | + | 0.724293i | ||||
\(207\) | 0.550553 | + | 0.299552i | 0.0382661 | + | 0.0208203i | ||||
\(208\) | 2.59427 | 0.179880 | ||||||||
\(209\) | 9.01714 | − | 6.80977i | 0.623729 | − | 0.471041i | ||||
\(210\) | 34.1465 | + | 33.2932i | 2.35633 | + | 2.29745i | ||||
\(211\) | −22.3398 | −1.53794 | −0.768969 | − | 0.639286i | \(-0.779230\pi\) | ||||
−0.768969 | + | 0.639286i | \(0.779230\pi\) | |||||||
\(212\) | −6.61183 | −0.454102 | ||||||||
\(213\) | −11.4373 | + | 3.22023i | −0.783670 | + | 0.220647i | ||||
\(214\) | 6.87795 | + | 11.9130i | 0.470167 | + | 0.814353i | ||||
\(215\) | −7.49569 | − | 12.9829i | −0.511202 | − | 0.885427i | ||||
\(216\) | −8.05136 | + | 8.68694i | −0.547825 | + | 0.591071i | ||||
\(217\) | 34.9732 | 2.37414 | ||||||||
\(218\) | −16.5890 | −1.12355 | ||||||||
\(219\) | 1.38943 | − | 0.391202i | 0.0938892 | − | 0.0264350i | ||||
\(220\) | −2.83171 | − | 4.90466i | −0.190914 | − | 0.330672i | ||||
\(221\) | 0.930249 | + | 1.61124i | 0.0625753 | + | 0.108384i | ||||
\(222\) | −3.02951 | + | 11.9068i | −0.203327 | + | 0.799133i | ||||
\(223\) | 3.43392 | + | 5.94773i | 0.229952 | + | 0.398289i | 0.957794 | − | 0.287456i | \(-0.0928096\pi\) |
−0.727841 | + | 0.685746i | \(0.759476\pi\) | |||||||
\(224\) | −7.27795 | − | 12.6058i | −0.486278 | − | 0.842258i | ||||
\(225\) | 0.692844 | + | 27.3769i | 0.0461896 | + | 1.82513i | ||||
\(226\) | −12.4880 | + | 21.6299i | −0.830692 | + | 1.43880i | ||||
\(227\) | 4.44987 | − | 7.70739i | 0.295348 | − | 0.511558i | −0.679718 | − | 0.733474i | \(-0.737898\pi\) |
0.975066 | + | 0.221916i | \(0.0712311\pi\) | |||||||
\(228\) | −4.35339 | − | 0.551115i | −0.288310 | − | 0.0364985i | ||||
\(229\) | −4.13454 | − | 7.16123i | −0.273218 | − | 0.473228i | 0.696466 | − | 0.717590i | \(-0.254755\pi\) |
−0.969684 | + | 0.244362i | \(0.921421\pi\) | |||||||
\(230\) | −1.26168 | −0.0831926 | ||||||||
\(231\) | 5.04797 | − | 19.8399i | 0.332132 | − | 1.30537i | ||||
\(232\) | 1.94618 | 0.127773 | ||||||||
\(233\) | 0.668571 | − | 1.15800i | 0.0437995 | − | 0.0758630i | −0.843295 | − | 0.537452i | \(-0.819387\pi\) |
0.887094 | + | 0.461589i | \(0.152720\pi\) | |||||||
\(234\) | −0.0655689 | − | 2.59087i | −0.00428637 | − | 0.169371i | ||||
\(235\) | −11.8060 | −0.770138 | ||||||||
\(236\) | −0.698722 | + | 1.21022i | −0.0454829 | + | 0.0787788i | ||||
\(237\) | 5.05452 | − | 19.8657i | 0.328327 | − | 1.29042i | ||||
\(238\) | 12.6728 | − | 21.9500i | 0.821457 | − | 1.42281i | ||||
\(239\) | 3.40198 | + | 5.89240i | 0.220056 | + | 0.381147i | 0.954825 | − | 0.297170i | \(-0.0960428\pi\) |
−0.734769 | + | 0.678317i | \(0.762709\pi\) | |||||||
\(240\) | 7.74513 | − | 30.4405i | 0.499946 | − | 1.96493i | ||||
\(241\) | 7.42157 | 0.478065 | 0.239033 | − | 0.971012i | \(-0.423170\pi\) | ||||
0.239033 | + | 0.971012i | \(0.423170\pi\) | |||||||
\(242\) | 3.43809 | − | 5.95495i | 0.221009 | − | 0.382799i | ||||
\(243\) | 11.6974 | + | 10.3039i | 0.750391 | + | 0.660994i | ||||
\(244\) | 2.08943 | − | 3.61900i | 0.133762 | − | 0.231683i | ||||
\(245\) | −25.9144 | − | 44.8850i | −1.65561 | − | 2.86760i | ||||
\(246\) | −0.644526 | + | 2.53317i | −0.0410935 | + | 0.161509i | ||||
\(247\) | −1.87039 | + | 1.41252i | −0.119010 | + | 0.0898768i | ||||
\(248\) | −8.74218 | − | 15.1419i | −0.555129 | − | 0.961511i | ||||
\(249\) | −12.1082 | + | 3.40914i | −0.767329 | + | 0.216046i | ||||
\(250\) | −12.4661 | − | 21.5919i | −0.788423 | − | 1.36559i | ||||
\(251\) | −7.83717 | − | 13.5744i | −0.494678 | − | 0.856807i | 0.505303 | − | 0.862942i | \(-0.331381\pi\) |
−0.999981 | + | 0.00613456i | \(0.998047\pi\) | |||||||
\(252\) | −6.78228 | + | 4.14800i | −0.427243 | + | 0.261300i | ||||
\(253\) | 0.270797 | + | 0.469035i | 0.0170249 | + | 0.0294880i | ||||
\(254\) | 10.1330 | − | 17.5509i | 0.635803 | − | 1.10124i | ||||
\(255\) | 21.6831 | − | 6.10500i | 1.35785 | − | 0.382310i | ||||
\(256\) | −6.44268 | + | 11.1591i | −0.402668 | + | 0.697441i | ||||
\(257\) | 3.69675 | − | 6.40296i | 0.230597 | − | 0.399406i | −0.727387 | − | 0.686228i | \(-0.759265\pi\) |
0.957984 | + | 0.286822i | \(0.0925987\pi\) | |||||||
\(258\) | 10.6832 | − | 3.00791i | 0.665105 | − | 0.187264i | ||||
\(259\) | 10.0653 | − | 17.4336i | 0.625427 | − | 1.08327i | ||||
\(260\) | 0.587371 | + | 1.01736i | 0.0364272 | + | 0.0630937i | ||||
\(261\) | −0.0648023 | − | 2.56058i | −0.00401116 | − | 0.158496i | ||||
\(262\) | −15.8874 | − | 27.5177i | −0.981525 | − | 1.70005i | ||||
\(263\) | −1.41631 | − | 2.45312i | −0.0873335 | − | 0.151266i | 0.819050 | − | 0.573723i | \(-0.194501\pi\) |
−0.906383 | + | 0.422457i | \(0.861168\pi\) | |||||||
\(264\) | −9.85166 | + | 2.77379i | −0.606328 | + | 0.170715i | ||||
\(265\) | 21.3795 | + | 37.0304i | 1.31333 | + | 2.27476i | ||||
\(266\) | 29.4051 | + | 12.4453i | 1.80294 | + | 0.763068i | ||||
\(267\) | −2.73671 | + | 10.7560i | −0.167484 | + | 0.658258i | ||||
\(268\) | −0.0815237 | − | 0.141203i | −0.00497985 | − | 0.00862536i | ||||
\(269\) | −5.71883 | + | 9.90530i | −0.348683 | + | 0.603937i | −0.986016 | − | 0.166652i | \(-0.946704\pi\) |
0.637333 | + | 0.770589i | \(0.280038\pi\) | |||||||
\(270\) | −30.5964 | − | 6.96562i | −1.86204 | − | 0.423914i | ||||
\(271\) | 13.8181 | − | 23.9337i | 0.839390 | − | 1.45387i | −0.0510155 | − | 0.998698i | \(-0.516246\pi\) |
0.890405 | − | 0.455168i | \(-0.150421\pi\) | |||||||
\(272\) | −16.6933 | −1.01218 | ||||||||
\(273\) | −1.04708 | + | 4.11532i | −0.0633722 | + | 0.249071i | ||||
\(274\) | −9.41058 | − | 16.2996i | −0.568514 | − | 0.984695i | ||||
\(275\) | −11.8320 | + | 20.4937i | −0.713499 | + | 1.23582i | ||||
\(276\) | 0.0518615 | − | 0.203830i | 0.00312170 | − | 0.0122691i | ||||
\(277\) | −5.19514 | + | 8.99825i | −0.312146 | + | 0.540653i | −0.978827 | − | 0.204691i | \(-0.934381\pi\) |
0.666681 | + | 0.745343i | \(0.267714\pi\) | |||||||
\(278\) | 28.6626 | 1.71907 | ||||||||
\(279\) | −19.6310 | + | 12.0062i | −1.17528 | + | 0.718793i | ||||
\(280\) | −19.5326 | + | 33.8314i | −1.16729 | + | 2.02181i | ||||
\(281\) | 8.50448 | 0.507335 | 0.253667 | − | 0.967292i | \(-0.418363\pi\) | ||||
0.253667 | + | 0.967292i | \(0.418363\pi\) | |||||||
\(282\) | 2.15517 | − | 8.47043i | 0.128339 | − | 0.504407i | ||||
\(283\) | −1.36691 | −0.0812541 | −0.0406270 | − | 0.999174i | \(-0.512936\pi\) | ||||
−0.0406270 | + | 0.999174i | \(0.512936\pi\) | |||||||
\(284\) | 1.99361 | + | 3.45304i | 0.118299 | + | 0.204900i | ||||
\(285\) | 10.9902 | + | 26.1638i | 0.651004 | + | 1.54981i | ||||
\(286\) | 1.11975 | − | 1.93947i | 0.0662123 | − | 0.114683i | ||||
\(287\) | 2.14139 | − | 3.70899i | 0.126402 | − | 0.218935i | ||||
\(288\) | 8.41276 | + | 4.57732i | 0.495726 | + | 0.269721i | ||||
\(289\) | 2.51415 | + | 4.35464i | 0.147891 | + | 0.256155i | ||||
\(290\) | 2.57803 | + | 4.46528i | 0.151387 | + | 0.262210i | ||||
\(291\) | 2.71729 | − | 10.6797i | 0.159290 | − | 0.626055i | ||||
\(292\) | −0.242189 | − | 0.419484i | −0.0141731 | − | 0.0245485i | ||||
\(293\) | −0.373905 | − | 0.647623i | −0.0218438 | − | 0.0378345i | 0.854897 | − | 0.518798i | \(-0.173620\pi\) |
−0.876741 | + | 0.480963i | \(0.840287\pi\) | |||||||
\(294\) | 36.9342 | − | 10.3990i | 2.15405 | − | 0.606484i | ||||
\(295\) | 9.03735 | 0.526175 | ||||||||
\(296\) | −10.0640 | −0.584958 | ||||||||
\(297\) | 3.97749 | + | 12.8694i | 0.230797 | + | 0.746759i | ||||
\(298\) | 12.9407 | + | 22.4139i | 0.749633 | + | 1.29840i | ||||
\(299\) | −0.0561705 | − | 0.0972901i | −0.00324842 | − | 0.00562643i | ||||
\(300\) | 8.84584 | − | 2.49059i | 0.510715 | − | 0.143794i | ||||
\(301\) | −18.1847 | −1.04815 | ||||||||
\(302\) | 2.63879 | 0.151845 | ||||||||
\(303\) | 2.86490 | + | 2.79332i | 0.164584 | + | 0.160472i | ||||
\(304\) | −2.58485 | − | 20.8706i | −0.148251 | − | 1.19701i | ||||
\(305\) | −27.0250 | −1.54744 | ||||||||
\(306\) | 0.421914 | + | 16.6714i | 0.0241192 | + | 0.953042i | ||||
\(307\) | 5.56496 | − | 9.63880i | 0.317609 | − | 0.550115i | −0.662379 | − | 0.749169i | \(-0.730453\pi\) |
0.979989 | + | 0.199053i | \(0.0637866\pi\) | |||||||
\(308\) | −6.86978 | −0.391442 | ||||||||
\(309\) | −3.19096 | + | 12.5413i | −0.181527 | + | 0.713452i | ||||
\(310\) | 23.1608 | − | 40.1157i | 1.31545 | − | 2.27842i | ||||
\(311\) | 6.07360 | + | 10.5198i | 0.344402 | + | 0.596522i | 0.985245 | − | 0.171150i | \(-0.0547483\pi\) |
−0.640843 | + | 0.767672i | \(0.721415\pi\) | |||||||
\(312\) | 2.04349 | − | 0.575357i | 0.115690 | − | 0.0325732i | ||||
\(313\) | −26.3132 | −1.48731 | −0.743656 | − | 0.668563i | \(-0.766910\pi\) | ||||
−0.743656 | + | 0.668563i | \(0.766910\pi\) | |||||||
\(314\) | −8.53194 | − | 14.7778i | −0.481485 | − | 0.833957i | ||||
\(315\) | 45.1621 | + | 24.5724i | 2.54460 | + | 1.38450i | ||||
\(316\) | −6.87870 | −0.386957 | ||||||||
\(317\) | −13.4516 | −0.755520 | −0.377760 | − | 0.925904i | \(-0.623306\pi\) | ||||
−0.377760 | + | 0.925904i | \(0.623306\pi\) | |||||||
\(318\) | −30.4710 | + | 8.57928i | −1.70873 | + | 0.481102i | ||||
\(319\) | 1.10666 | − | 1.91679i | 0.0619611 | − | 0.107320i | ||||
\(320\) | 16.9904 | 0.949795 | ||||||||
\(321\) | 10.6181 | + | 10.3528i | 0.592645 | + | 0.577836i | ||||
\(322\) | −0.765214 | + | 1.32539i | −0.0426437 | + | 0.0738610i | ||||
\(323\) | 12.0354 | − | 9.08913i | 0.669665 | − | 0.505733i | ||||
\(324\) | 2.38300 | − | 4.65668i | 0.132389 | − | 0.258704i | ||||
\(325\) | 2.45427 | − | 4.25093i | 0.136139 | − | 0.235799i | ||||
\(326\) | 17.7445 | + | 30.7343i | 0.982775 | + | 1.70222i | ||||
\(327\) | −17.2148 | + | 4.84693i | −0.951982 | + | 0.268036i | ||||
\(328\) | −2.14111 | −0.118223 | ||||||||
\(329\) | −7.16039 | + | 12.4022i | −0.394765 | + | 0.683753i | ||||
\(330\) | −19.4142 | − | 18.9291i | −1.06872 | − | 1.04201i | ||||
\(331\) | 2.15691 | − | 3.73589i | 0.118555 | − | 0.205343i | −0.800640 | − | 0.599145i | \(-0.795507\pi\) |
0.919195 | + | 0.393802i | \(0.128841\pi\) | |||||||
\(332\) | 2.11056 | + | 3.65560i | 0.115832 | + | 0.200627i | ||||
\(333\) | 0.335102 | + | 13.2412i | 0.0183635 | + | 0.725611i | ||||
\(334\) | 21.0384 | 1.15117 | ||||||||
\(335\) | −0.527219 | + | 0.913169i | −0.0288050 | + | 0.0498918i | ||||
\(336\) | −27.2802 | − | 26.5985i | −1.48826 | − | 1.45107i | ||||
\(337\) | −2.91534 | −0.158809 | −0.0794044 | − | 0.996842i | \(-0.525302\pi\) | ||||
−0.0794044 | + | 0.996842i | \(0.525302\pi\) | |||||||
\(338\) | 10.2108 | − | 17.6855i | 0.555392 | − | 0.961967i | ||||
\(339\) | −6.63938 | + | 26.0946i | −0.360602 | + | 1.41726i | ||||
\(340\) | −3.77954 | − | 6.54635i | −0.204974 | − | 0.355026i | ||||
\(341\) | −19.8843 | −1.07679 | ||||||||
\(342\) | −20.7780 | + | 3.10896i | −1.12354 | + | 0.168113i | ||||
\(343\) | −30.9525 | −1.67128 | ||||||||
\(344\) | 4.54558 | + | 7.87318i | 0.245082 | + | 0.424494i | ||||
\(345\) | −1.30927 | + | 0.368633i | −0.0704890 | + | 0.0198466i | ||||
\(346\) | −10.1048 | + | 17.5020i | −0.543238 | + | 0.940916i | ||||
\(347\) | −14.7943 | −0.794199 | −0.397099 | − | 0.917776i | \(-0.629983\pi\) | ||||
−0.397099 | + | 0.917776i | \(0.629983\pi\) | |||||||
\(348\) | −0.827359 | + | 0.232947i | −0.0443511 | + | 0.0124873i | ||||
\(349\) | 0.668641 | − | 1.15812i | 0.0357915 | − | 0.0619927i | −0.847575 | − | 0.530676i | \(-0.821938\pi\) |
0.883366 | + | 0.468683i | \(0.155271\pi\) | |||||||
\(350\) | −66.8694 | −3.57432 | ||||||||
\(351\) | −0.825036 | − | 2.66946i | −0.0440372 | − | 0.142485i | ||||
\(352\) | 4.13793 | + | 7.16711i | 0.220552 | + | 0.382008i | ||||
\(353\) | 10.3662 | − | 17.9549i | 0.551739 | − | 0.955641i | −0.446410 | − | 0.894829i | \(-0.647298\pi\) |
0.998149 | − | 0.0608121i | \(-0.0193691\pi\) | |||||||
\(354\) | −1.64976 | + | 6.48402i | −0.0876838 | + | 0.344622i | ||||
\(355\) | 12.8928 | − | 22.3310i | 0.684279 | − | 1.18521i | ||||
\(356\) | 3.72438 | 0.197392 | ||||||||
\(357\) | 6.73763 | − | 26.4808i | 0.356593 | − | 1.40151i | ||||
\(358\) | 18.6149 | + | 32.2420i | 0.983829 | + | 1.70404i | ||||
\(359\) | −2.38736 | + | 4.13504i | −0.126000 | + | 0.218239i | −0.922123 | − | 0.386896i | \(-0.873547\pi\) |
0.796123 | + | 0.605135i | \(0.206881\pi\) | |||||||
\(360\) | −0.650294 | − | 25.6956i | −0.0342735 | − | 1.35428i | ||||
\(361\) | 13.2272 | + | 13.6397i | 0.696168 | + | 0.717879i | ||||
\(362\) | 3.00488 | − | 5.20460i | 0.157933 | − | 0.273548i | ||||
\(363\) | 1.82789 | − | 7.18413i | 0.0959395 | − | 0.377069i | ||||
\(364\) | 1.42497 | 0.0746888 | ||||||||
\(365\) | −1.56625 | + | 2.71283i | −0.0819814 | + | 0.141996i | ||||
\(366\) | 4.93338 | − | 19.3896i | 0.257872 | − | 1.01351i | ||||
\(367\) | 21.7614 | 1.13594 | 0.567969 | − | 0.823050i | \(-0.307729\pi\) | ||||
0.567969 | + | 0.823050i | \(0.307729\pi\) | |||||||
\(368\) | 1.00798 | 0.0525444 | ||||||||
\(369\) | 0.0712928 | + | 2.81705i | 0.00371135 | + | 0.146650i | ||||
\(370\) | −13.3314 | − | 23.0906i | −0.693065 | − | 1.20042i | ||||
\(371\) | 51.8671 | 2.69281 | ||||||||
\(372\) | 5.52886 | + | 5.39071i | 0.286658 | + | 0.279495i | ||||
\(373\) | 11.3702 | + | 19.6938i | 0.588727 | + | 1.01971i | 0.994399 | + | 0.105687i | \(0.0337041\pi\) |
−0.405672 | + | 0.914019i | \(0.632963\pi\) | |||||||
\(374\) | −7.20523 | + | 12.4798i | −0.372574 | + | 0.645317i | ||||
\(375\) | −19.2450 | − | 18.7641i | −0.993807 | − | 0.968974i | ||||
\(376\) | 7.15946 | 0.369221 | ||||||||
\(377\) | −0.229550 | + | 0.397593i | −0.0118224 | + | 0.0204771i | ||||
\(378\) | −25.8742 | + | 27.9168i | −1.33083 | + | 1.43588i | ||||
\(379\) | −21.1367 | −1.08572 | −0.542859 | − | 0.839824i | \(-0.682658\pi\) | ||||
−0.542859 | + | 0.839824i | \(0.682658\pi\) | |||||||
\(380\) | 7.59928 | − | 5.73899i | 0.389835 | − | 0.294404i | ||||
\(381\) | 5.38732 | − | 21.1737i | 0.276001 | − | 1.08476i | ||||
\(382\) | 23.7084 | 1.21303 | ||||||||
\(383\) | −9.57967 | −0.489498 | −0.244749 | − | 0.969586i | \(-0.578706\pi\) | ||||
−0.244749 | + | 0.969586i | \(0.578706\pi\) | |||||||
\(384\) | −5.82851 | + | 22.9077i | −0.297435 | + | 1.16900i | ||||
\(385\) | 22.2136 | + | 38.4751i | 1.13211 | + | 1.96087i | ||||
\(386\) | 4.55947 | + | 7.89724i | 0.232071 | + | 0.401959i | ||||
\(387\) | 10.2074 | − | 6.24276i | 0.518869 | − | 0.317337i | ||||
\(388\) | −3.69795 | −0.187735 | ||||||||
\(389\) | 34.4668 | 1.74754 | 0.873768 | − | 0.486343i | \(-0.161670\pi\) | ||||
0.873768 | + | 0.486343i | \(0.161670\pi\) | |||||||
\(390\) | 4.02702 | + | 3.92639i | 0.203916 | + | 0.198821i | ||||
\(391\) | 0.361439 | + | 0.626030i | 0.0182787 | + | 0.0316597i | ||||
\(392\) | 15.7152 | + | 27.2194i | 0.793735 | + | 1.37479i | ||||
\(393\) | −24.5268 | − | 23.9139i | −1.23721 | − | 1.20630i | ||||
\(394\) | 9.87741 | + | 17.1082i | 0.497617 | + | 0.861897i | ||||
\(395\) | 22.2425 | + | 38.5251i | 1.11914 | + | 1.93841i | ||||
\(396\) | 3.85612 | − | 2.35838i | 0.193777 | − | 0.118513i | ||||
\(397\) | 17.8313 | − | 30.8848i | 0.894928 | − | 1.55006i | 0.0610353 | − | 0.998136i | \(-0.480560\pi\) |
0.833893 | − | 0.551926i | \(-0.186107\pi\) | |||||||
\(398\) | 0.0255520 | − | 0.0442574i | 0.00128081 | − | 0.00221842i | ||||
\(399\) | 34.1506 | + | 4.32327i | 1.70967 | + | 0.216434i | ||||
\(400\) | 22.0209 | + | 38.1414i | 1.10105 | + | 1.90707i | ||||
\(401\) | 1.13355 | 0.0566066 | 0.0283033 | − | 0.999599i | \(-0.490990\pi\) | ||||
0.0283033 | + | 0.999599i | \(0.490990\pi\) | |||||||
\(402\) | −0.558928 | − | 0.544961i | −0.0278768 | − | 0.0271802i | ||||
\(403\) | 4.12452 | 0.205457 | ||||||||
\(404\) | 0.671354 | − | 1.16282i | 0.0334011 | − | 0.0578524i | ||||
\(405\) | −33.7859 | + | 1.71118i | −1.67883 | + | 0.0850290i | ||||
\(406\) | 6.25436 | 0.310399 | ||||||||
\(407\) | −5.72270 | + | 9.91201i | −0.283664 | + | 0.491320i | ||||
\(408\) | −13.1492 | + | 3.70223i | −0.650983 | + | 0.183288i | ||||
\(409\) | −6.71319 | + | 11.6276i | −0.331946 | + | 0.574947i | −0.982893 | − | 0.184176i | \(-0.941038\pi\) |
0.650947 | + | 0.759123i | \(0.274372\pi\) | |||||||
\(410\) | −2.83624 | − | 4.91251i | −0.140072 | − | 0.242612i | ||||
\(411\) | −14.5280 | − | 14.1649i | −0.716612 | − | 0.698705i | ||||
\(412\) | 4.34257 | 0.213943 | ||||||||
\(413\) | 5.48120 | − | 9.49371i | 0.269712 | − | 0.467155i | ||||
\(414\) | −0.0254761 | − | 1.00666i | −0.00125208 | − | 0.0494745i | ||||
\(415\) | 13.6491 | − | 23.6410i | 0.670010 | − | 1.16049i | ||||
\(416\) | −0.858315 | − | 1.48665i | −0.0420824 | − | 0.0728888i | ||||
\(417\) | 29.7439 | − | 8.37456i | 1.45657 | − | 0.410104i | ||||
\(418\) | −16.7185 | − | 7.07585i | −0.817727 | − | 0.346091i | ||||
\(419\) | 1.95049 | + | 3.37834i | 0.0952875 | + | 0.165043i | 0.909729 | − | 0.415203i | \(-0.136290\pi\) |
−0.814441 | + | 0.580246i | \(0.802956\pi\) | |||||||
\(420\) | 4.25422 | − | 16.7203i | 0.207585 | − | 0.815866i | ||||
\(421\) | −13.6227 | − | 23.5953i | −0.663932 | − | 1.14996i | −0.979574 | − | 0.201085i | \(-0.935553\pi\) |
0.315642 | − | 0.948878i | \(-0.397780\pi\) | |||||||
\(422\) | 17.9458 | + | 31.0830i | 0.873588 | + | 1.51310i | ||||
\(423\) | −0.238390 | − | 9.41967i | −0.0115909 | − | 0.458000i | ||||
\(424\) | −12.9651 | − | 22.4562i | −0.629642 | − | 1.09057i | ||||
\(425\) | −15.7925 | + | 27.3533i | −0.766047 | + | 1.32683i | ||||
\(426\) | 13.6682 | + | 13.3267i | 0.662228 | + | 0.645680i | ||||
\(427\) | −16.3908 | + | 28.3896i | −0.793205 | + | 1.37387i | ||||
\(428\) | 2.48822 | − | 4.30972i | 0.120273 | − | 0.208318i | ||||
\(429\) | 0.595326 | − | 2.33980i | 0.0287426 | − | 0.112966i | ||||
\(430\) | −12.0427 | + | 20.8586i | −0.580751 | + | 1.00589i | ||||
\(431\) | 20.2776 | + | 35.1217i | 0.976735 | + | 1.69176i | 0.674086 | + | 0.738653i | \(0.264538\pi\) |
0.302650 | + | 0.953102i | \(0.402129\pi\) | |||||||
\(432\) | 24.4440 | + | 5.56496i | 1.17606 | + | 0.267744i | ||||
\(433\) | −9.37164 | − | 16.2322i | −0.450372 | − | 0.780068i | 0.548037 | − | 0.836454i | \(-0.315375\pi\) |
−0.998409 | + | 0.0563866i | \(0.982042\pi\) | |||||||
\(434\) | −28.0943 | − | 48.6608i | −1.34857 | − | 2.33579i | ||||
\(435\) | 3.97994 | + | 3.88049i | 0.190824 | + | 0.186055i | ||||
\(436\) | 3.00068 | + | 5.19733i | 0.143707 | + | 0.248907i | ||||
\(437\) | −0.726722 | + | 0.548822i | −0.0347638 | + | 0.0262537i | ||||
\(438\) | −1.66045 | − | 1.61896i | −0.0793395 | − | 0.0773570i | ||||
\(439\) | −8.15172 | − | 14.1192i | −0.389060 | − | 0.673872i | 0.603263 | − | 0.797542i | \(-0.293867\pi\) |
−0.992323 | + | 0.123670i | \(0.960534\pi\) | |||||||
\(440\) | 11.1054 | − | 19.2351i | 0.529428 | − | 0.916997i | ||||
\(441\) | 35.2892 | − | 21.5827i | 1.68044 | − | 1.02775i | ||||
\(442\) | 1.49455 | − | 2.58864i | 0.0710887 | − | 0.123129i | ||||
\(443\) | −26.4906 | −1.25861 | −0.629303 | − | 0.777160i | \(-0.716659\pi\) | ||||
−0.629303 | + | 0.777160i | \(0.716659\pi\) | |||||||
\(444\) | 4.27839 | − | 1.20460i | 0.203043 | − | 0.0571680i | ||||
\(445\) | −12.0429 | − | 20.8589i | −0.570888 | − | 0.988807i | ||||
\(446\) | 5.51700 | − | 9.55573i | 0.261238 | − | 0.452477i | ||||
\(447\) | 19.9777 | + | 19.4785i | 0.944912 | + | 0.921301i | ||||
\(448\) | 10.3048 | − | 17.8484i | 0.486855 | − | 0.843258i | ||||
\(449\) | 19.2529 | 0.908602 | 0.454301 | − | 0.890848i | \(-0.349889\pi\) | ||||
0.454301 | + | 0.890848i | \(0.349889\pi\) | |||||||
\(450\) | 37.5349 | − | 22.9561i | 1.76941 | − | 1.08216i | ||||
\(451\) | −1.21750 | + | 2.10877i | −0.0573299 | + | 0.0992982i | ||||
\(452\) | 9.03553 | 0.424995 | ||||||||
\(453\) | 2.73834 | − | 0.770994i | 0.128658 | − | 0.0362244i | ||||
\(454\) | −14.2985 | −0.671061 | ||||||||
\(455\) | −4.60769 | − | 7.98075i | −0.216012 | − | 0.374143i | ||||
\(456\) | −6.66475 | − | 15.8664i | −0.312106 | − | 0.743013i | ||||
\(457\) | 18.2664 | − | 31.6384i | 0.854467 | − | 1.47998i | −0.0226720 | − | 0.999743i | \(-0.507217\pi\) |
0.877139 | − | 0.480237i | \(-0.159449\pi\) | |||||||
\(458\) | −6.64263 | + | 11.5054i | −0.310390 | + | 0.537610i | ||||
\(459\) | 5.30884 | + | 17.1771i | 0.247795 | + | 0.801757i | ||||
\(460\) | 0.228217 | + | 0.395283i | 0.0106407 | + | 0.0184302i | ||||
\(461\) | 2.91815 | + | 5.05439i | 0.135912 | + | 0.235406i | 0.925945 | − | 0.377657i | \(-0.123270\pi\) |
−0.790034 | + | 0.613064i | \(0.789937\pi\) | |||||||
\(462\) | −31.6598 | + | 8.91399i | −1.47295 | + | 0.414716i | ||||
\(463\) | 6.34039 | + | 10.9819i | 0.294663 | + | 0.510371i | 0.974906 | − | 0.222615i | \(-0.0714593\pi\) |
−0.680243 | + | 0.732986i | \(0.738126\pi\) | |||||||
\(464\) | −2.05964 | − | 3.56739i | −0.0956162 | − | 0.165612i | ||||
\(465\) | 12.3137 | − | 48.3961i | 0.571033 | − | 2.24432i | ||||
\(466\) | −2.14828 | −0.0995170 | ||||||||
\(467\) | −24.0640 | −1.11355 | −0.556774 | − | 0.830664i | \(-0.687961\pi\) | ||||
−0.556774 | + | 0.830664i | \(0.687961\pi\) | |||||||
\(468\) | −0.799860 | + | 0.489189i | −0.0369735 | + | 0.0226128i | ||||
\(469\) | 0.639521 | + | 1.10768i | 0.0295303 | + | 0.0511481i | ||||
\(470\) | 9.48386 | + | 16.4265i | 0.437458 | + | 0.757699i | ||||
\(471\) | −13.1715 | − | 12.8424i | −0.606912 | − | 0.591747i | ||||
\(472\) | −5.48049 | −0.252260 | ||||||||
\(473\) | 10.3390 | 0.475390 | ||||||||
\(474\) | −31.7009 | + | 8.92556i | −1.45607 | + | 0.409965i | ||||
\(475\) | −36.6436 | − | 15.5089i | −1.68132 | − | 0.711596i | ||||
\(476\) | −9.16923 | −0.420271 | ||||||||
\(477\) | −29.1138 | + | 17.8059i | −1.33303 | + | 0.815274i | ||||
\(478\) | 5.46568 | − | 9.46683i | 0.249994 | − | 0.433003i | ||||
\(479\) | 5.01131 | 0.228973 | 0.114486 | − | 0.993425i | \(-0.463478\pi\) | ||||
0.114486 | + | 0.993425i | \(0.463478\pi\) | |||||||
\(480\) | −20.0064 | + | 5.63292i | −0.913164 | + | 0.257106i | ||||
\(481\) | 1.18704 | − | 2.05601i | 0.0541243 | − | 0.0937460i | ||||
\(482\) | −5.96182 | − | 10.3262i | −0.271553 | − | 0.470344i | ||||
\(483\) | −0.406833 | + | 1.59897i | −0.0185115 | + | 0.0727555i | ||||
\(484\) | −2.48758 | −0.113072 | ||||||||
\(485\) | 11.9574 | + | 20.7109i | 0.542959 | + | 0.940433i | ||||
\(486\) | 4.93987 | − | 24.5527i | 0.224077 | − | 1.11373i | ||||
\(487\) | −31.5079 | −1.42776 | −0.713880 | − | 0.700268i | \(-0.753064\pi\) | ||||
−0.713880 | + | 0.700268i | \(0.753064\pi\) | |||||||
\(488\) | 16.3887 | 0.741879 | ||||||||
\(489\) | 27.3937 | + | 26.7092i | 1.23879 | + | 1.20783i | ||||
\(490\) | −41.6345 | + | 72.1130i | −1.88085 | + | 3.25773i | ||||
\(491\) | 30.6070 | 1.38127 | 0.690636 | − | 0.723202i | \(-0.257331\pi\) | ||||
0.690636 | + | 0.723202i | \(0.257331\pi\) | |||||||
\(492\) | 0.910225 | − | 0.256279i | 0.0410361 | − | 0.0115539i | ||||
\(493\) | 1.47708 | − | 2.55838i | 0.0665244 | − | 0.115224i | ||||
\(494\) | 3.46785 | + | 1.46772i | 0.156026 | + | 0.0660357i | ||||
\(495\) | −25.6773 | − | 13.9708i | −1.15411 | − | 0.627942i | ||||
\(496\) | −18.5036 | + | 32.0492i | −0.830836 | + | 1.43905i | ||||
\(497\) | −15.6391 | − | 27.0877i | −0.701509 | − | 1.21505i | ||||
\(498\) | 14.4701 | + | 14.1085i | 0.648418 | + | 0.632216i | ||||
\(499\) | −10.9239 | −0.489021 | −0.244511 | − | 0.969647i | \(-0.578627\pi\) | ||||
−0.244511 | + | 0.969647i | \(0.578627\pi\) | |||||||
\(500\) | −4.50982 | + | 7.81123i | −0.201685 | + | 0.349329i | ||||
\(501\) | 21.8320 | − | 6.14693i | 0.975384 | − | 0.274625i | ||||
\(502\) | −12.5913 | + | 21.8088i | −0.561979 | + | 0.973376i | ||||
\(503\) | −15.0754 | − | 26.1113i | −0.672178 | − | 1.16425i | −0.977285 | − | 0.211928i | \(-0.932026\pi\) |
0.305108 | − | 0.952318i | \(-0.401307\pi\) | |||||||
\(504\) | −27.3875 | − | 14.9014i | −1.21994 | − | 0.663759i | ||||
\(505\) | −8.68336 | −0.386405 | ||||||||
\(506\) | 0.435068 | − | 0.753560i | 0.0193411 | − | 0.0334998i | ||||
\(507\) | 5.42864 | − | 21.3361i | 0.241094 | − | 0.947568i | ||||
\(508\) | −7.33160 | −0.325287 | ||||||||
\(509\) | −1.38957 | + | 2.40680i | −0.0615916 | + | 0.106680i | −0.895177 | − | 0.445711i | \(-0.852951\pi\) |
0.833585 | + | 0.552391i | \(0.186284\pi\) | |||||||
\(510\) | −25.9126 | − | 25.2651i | −1.14743 | − | 1.11876i | ||||
\(511\) | 1.89988 | + | 3.29069i | 0.0840457 | + | 0.145571i | ||||
\(512\) | −6.59240 | −0.291346 | ||||||||
\(513\) | −20.6534 | + | 9.29709i | −0.911871 | + | 0.410476i | ||||
\(514\) | −11.8785 | −0.523940 | ||||||||
\(515\) | −14.0418 | − | 24.3212i | −0.618757 | − | 1.07172i | ||||
\(516\) | −2.87479 | − | 2.80295i | −0.126555 | − | 0.123393i | ||||
\(517\) | 4.07109 | − | 7.05134i | 0.179046 | − | 0.310118i | ||||
\(518\) | −32.3422 | −1.42103 | ||||||||
\(519\) | −5.37231 | + | 21.1147i | −0.235818 | + | 0.926832i | ||||
\(520\) | −2.30355 | + | 3.98986i | −0.101017 | + | 0.174967i | ||||
\(521\) | 13.4298 | 0.588371 | 0.294186 | − | 0.955748i | \(-0.404952\pi\) | ||||
0.294186 | + | 0.955748i | \(0.404952\pi\) | |||||||
\(522\) | −3.51067 | + | 2.14711i | −0.153658 | + | 0.0939762i | ||||
\(523\) | 5.62130 | + | 9.73637i | 0.245802 | + | 0.425742i | 0.962357 | − | 0.271789i | \(-0.0876153\pi\) |
−0.716555 | + | 0.697531i | \(0.754282\pi\) | |||||||
\(524\) | −5.74753 | + | 9.95502i | −0.251082 | + | 0.434887i | ||||
\(525\) | −69.3921 | + | 19.5377i | −3.02852 | + | 0.852696i | ||||
\(526\) | −2.27547 | + | 3.94123i | −0.0992153 | + | 0.171846i | ||||
\(527\) | −26.5400 | −1.15610 | ||||||||
\(528\) | 15.5104 | + | 15.1228i | 0.675002 | + | 0.658136i | ||||
\(529\) | 11.4782 | + | 19.8808i | 0.499051 | + | 0.864382i | ||||
\(530\) | 34.3487 | − | 59.4938i | 1.49201 | − | 2.58424i | ||||
\(531\) | 0.182485 | + | 7.21065i | 0.00791916 | + | 0.312916i | ||||
\(532\) | −1.41980 | − | 11.4637i | −0.0615560 | − | 0.497016i | ||||
\(533\) | 0.252542 | − | 0.437415i | 0.0109388 | − | 0.0189465i | ||||
\(534\) | 17.1640 | − | 4.83263i | 0.742761 | − | 0.209128i | ||||
\(535\) | −32.1829 | −1.39139 | ||||||||
\(536\) | 0.319719 | − | 0.553770i | 0.0138098 | − | 0.0239192i | ||||
\(537\) | 28.7375 | + | 28.0194i | 1.24012 | + | 1.20913i | ||||
\(538\) | 18.3760 | 0.792244 | ||||||||
\(539\) | 35.7445 | 1.53962 | ||||||||
\(540\) | 3.35207 | + | 10.8458i | 0.144250 | + | 0.466730i | ||||
\(541\) | 9.55755 | + | 16.5542i | 0.410911 | + | 0.711719i | 0.994990 | − | 0.0999781i | \(-0.0318773\pi\) |
−0.584078 | + | 0.811697i | \(0.698544\pi\) | |||||||
\(542\) | −44.4008 | −1.90718 | ||||||||
\(543\) | 1.59757 | − | 6.27890i | 0.0685584 | − | 0.269454i | ||||
\(544\) | 5.52298 | + | 9.56608i | 0.236796 | + | 0.410142i | ||||
\(545\) | 19.4056 | − | 33.6114i | 0.831243 | − | 1.43976i | ||||
\(546\) | 6.56707 | − | 1.84900i | 0.281045 | − | 0.0791297i | ||||
\(547\) | −41.0410 | −1.75479 | −0.877393 | − | 0.479772i | \(-0.840719\pi\) | ||||
−0.877393 | + | 0.479772i | \(0.840719\pi\) | |||||||
\(548\) | −3.40444 | + | 5.89667i | −0.145431 | + | 0.251893i | ||||
\(549\) | −0.545695 | − | 21.5625i | −0.0232897 | − | 0.920263i | ||||
\(550\) | 38.0191 | 1.62114 | ||||||||
\(551\) | 3.42731 | + | 1.45056i | 0.146008 | + | 0.0617959i | ||||
\(552\) | 0.793979 | − | 0.223549i | 0.0337940 | − | 0.00951488i | ||||
\(553\) | 53.9607 | 2.29464 | ||||||||
\(554\) | 16.6932 | 0.709227 | ||||||||
\(555\) | −20.5809 | − | 20.0666i | −0.873608 | − | 0.851779i | ||||
\(556\) | −5.18460 | − | 8.97999i | −0.219876 | − | 0.380836i | ||||
\(557\) | −19.9467 | − | 34.5487i | −0.845169 | − | 1.46388i | −0.885475 | − | 0.464688i | \(-0.846167\pi\) |
0.0403059 | − | 0.999187i | \(-0.487167\pi\) | |||||||
\(558\) | 32.4749 | + | 17.6694i | 1.37477 | + | 0.748003i | ||||
\(559\) | −2.14459 | −0.0907064 | ||||||||
\(560\) | 82.6848 | 3.49407 | ||||||||
\(561\) | −3.83073 | + | 15.0558i | −0.161733 | + | 0.635658i | ||||
\(562\) | −6.83172 | − | 11.8329i | −0.288179 | − | 0.499140i | ||||
\(563\) | 4.46506 | + | 7.73371i | 0.188180 | + | 0.325937i | 0.944643 | − | 0.328099i | \(-0.106408\pi\) |
−0.756464 | + | 0.654036i | \(0.773075\pi\) | |||||||
\(564\) | −3.04362 | + | 0.856948i | −0.128160 | + | 0.0360840i | ||||
\(565\) | −29.2166 | − | 50.6047i | −1.22915 | − | 2.12896i | ||||
\(566\) | 1.09805 | + | 1.90187i | 0.0461544 | + | 0.0799417i | ||||
\(567\) | −18.6937 | + | 36.5298i | −0.785062 | + | 1.53411i | ||||
\(568\) | −7.81854 | + | 13.5421i | −0.328058 | + | 0.568214i | ||||
\(569\) | −2.87302 | + | 4.97622i | −0.120443 | + | 0.208614i | −0.919943 | − | 0.392053i | \(-0.871765\pi\) |
0.799499 | + | 0.600667i | \(0.205098\pi\) | |||||||
\(570\) | 27.5750 | − | 36.3091i | 1.15499 | − | 1.52082i | ||||
\(571\) | −6.75539 | − | 11.7007i | −0.282704 | − | 0.489658i | 0.689346 | − | 0.724433i | \(-0.257898\pi\) |
−0.972050 | + | 0.234774i | \(0.924565\pi\) | |||||||
\(572\) | −0.810179 | −0.0338753 | ||||||||
\(573\) | 24.6028 | − | 6.92706i | 1.02780 | − | 0.289382i | ||||
\(574\) | −6.88078 | −0.287198 | ||||||||
\(575\) | 0.953584 | − | 1.65166i | 0.0397672 | − | 0.0688788i | ||||
\(576\) | 0.343075 | + | 13.5562i | 0.0142948 | + | 0.564842i | ||||
\(577\) | −10.9961 | −0.457774 | −0.228887 | − | 0.973453i | \(-0.573509\pi\) | ||||
−0.228887 | + | 0.973453i | \(0.573509\pi\) | |||||||
\(578\) | 4.03928 | − | 6.99625i | 0.168012 | − | 0.291005i | ||||
\(579\) | 7.03887 | + | 6.86299i | 0.292525 | + | 0.285216i | ||||
\(580\) | 0.932648 | − | 1.61539i | 0.0387261 | − | 0.0670756i | ||||
\(581\) | −16.5565 | − | 28.6768i | −0.686881 | − | 1.18971i | ||||
\(582\) | −17.0422 | + | 4.79834i | −0.706424 | + | 0.198897i | ||||
\(583\) | −29.4895 | −1.22133 | ||||||||
\(584\) | 0.949817 | − | 1.64513i | 0.0393037 | − | 0.0680760i | ||||
\(585\) | 5.32614 | + | 2.89791i | 0.220209 | + | 0.119814i | ||||
\(586\) | −0.600723 | + | 1.04048i | −0.0248156 | + | 0.0429820i | ||||
\(587\) | 14.2331 | + | 24.6525i | 0.587464 | + | 1.01752i | 0.994563 | + | 0.104133i | \(0.0332068\pi\) |
−0.407100 | + | 0.913384i | \(0.633460\pi\) | |||||||
\(588\) | −9.93882 | − | 9.69047i | −0.409870 | − | 0.399628i | ||||
\(589\) | −4.10954 | − | 33.1813i | −0.169331 | − | 1.36721i | ||||
\(590\) | −7.25979 | − | 12.5743i | −0.298881 | − | 0.517677i | ||||
\(591\) | 15.2486 | + | 14.8676i | 0.627245 | + | 0.611572i | ||||
\(592\) | 10.6507 | + | 18.4475i | 0.437740 | + | 0.758188i | ||||
\(593\) | −2.56192 | − | 4.43738i | −0.105206 | − | 0.182222i | 0.808617 | − | 0.588336i | \(-0.200217\pi\) |
−0.913822 | + | 0.406114i | \(0.866883\pi\) | |||||||
\(594\) | 14.7110 | − | 15.8723i | 0.603600 | − | 0.651248i | ||||
\(595\) | 29.6490 | + | 51.3535i | 1.21549 | + | 2.10529i | ||||
\(596\) | 4.68152 | − | 8.10862i | 0.191762 | − | 0.332142i | ||||
\(597\) | 0.0135850 | − | 0.0533928i | 0.000555996 | − | 0.00218522i | ||||
\(598\) | −0.0902445 | + | 0.156308i | −0.00369037 | + | 0.00639191i | ||||
\(599\) | −13.5015 | + | 23.3853i | −0.551656 | + | 0.955497i | 0.446499 | + | 0.894784i | \(0.352671\pi\) |
−0.998155 | + | 0.0607125i | \(0.980663\pi\) | |||||||
\(600\) | 25.8048 | + | 25.1600i | 1.05348 | + | 1.02715i | ||||
\(601\) | 20.4168 | − | 35.3630i | 0.832819 | − | 1.44249i | −0.0629745 | − | 0.998015i | \(-0.520059\pi\) |
0.895794 | − | 0.444470i | \(-0.146608\pi\) | |||||||
\(602\) | 14.6079 | + | 25.3017i | 0.595374 | + | 1.03122i | ||||
\(603\) | −0.739238 | − | 0.402214i | −0.0301041 | − | 0.0163794i | ||||
\(604\) | −0.477314 | − | 0.826732i | −0.0194216 | − | 0.0336393i | ||||
\(605\) | 8.04366 | + | 13.9320i | 0.327021 | + | 0.566417i | ||||
\(606\) | 1.58514 | − | 6.23005i | 0.0643920 | − | 0.253078i | ||||
\(607\) | −0.992746 | − | 1.71949i | −0.0402943 | − | 0.0697918i | 0.845175 | − | 0.534490i | \(-0.179496\pi\) |
−0.885469 | + | 0.464698i | \(0.846163\pi\) | |||||||
\(608\) | −11.1047 | + | 8.38630i | −0.450355 | + | 0.340109i | ||||
\(609\) | 6.49030 | − | 1.82738i | 0.263000 | − | 0.0740492i | ||||
\(610\) | 21.7094 | + | 37.6018i | 0.878988 | + | 1.52245i | ||||
\(611\) | −0.844451 | + | 1.46263i | −0.0341628 | + | 0.0591718i | ||||
\(612\) | 5.14684 | − | 3.14777i | 0.208049 | − | 0.127241i | ||||
\(613\) | −14.2449 | + | 24.6729i | −0.575346 | + | 0.996528i | 0.420658 | + | 0.907219i | \(0.361799\pi\) |
−0.996004 | + | 0.0893089i | \(0.971534\pi\) | |||||||
\(614\) | −17.8815 | −0.721640 | ||||||||
\(615\) | −4.37856 | − | 4.26915i | −0.176561 | − | 0.172149i | ||||
\(616\) | −13.4709 | − | 23.3323i | −0.542759 | − | 0.940087i | ||||
\(617\) | −14.7097 | + | 25.4779i | −0.592189 | + | 1.02570i | 0.401748 | + | 0.915750i | \(0.368403\pi\) |
−0.993937 | + | 0.109951i | \(0.964931\pi\) | |||||||
\(618\) | 20.0130 | − | 5.63477i | 0.805041 | − | 0.226664i | ||||
\(619\) | −14.3363 | + | 24.8312i | −0.576224 | + | 0.998049i | 0.419684 | + | 0.907670i | \(0.362141\pi\) |
−0.995907 | + | 0.0903786i | \(0.971192\pi\) | |||||||
\(620\) | −16.7577 | −0.673004 | ||||||||
\(621\) | −0.320560 | − | 1.03719i | −0.0128636 | − | 0.0416210i | ||||
\(622\) | 9.75796 | − | 16.9013i | 0.391258 | − | 0.677679i | ||||
\(623\) | −29.2163 | −1.17053 | ||||||||
\(624\) | −3.21726 | − | 3.13687i | −0.128793 | − | 0.125575i | ||||
\(625\) | 12.6877 | 0.507508 | ||||||||
\(626\) | 21.1377 | + | 36.6115i | 0.844831 | + | 1.46329i | ||||
\(627\) | −19.4166 | − | 2.45803i | −0.775423 | − | 0.0981643i | ||||
\(628\) | −3.08658 | + | 5.34611i | −0.123168 | + | 0.213333i | ||||
\(629\) | −7.63820 | + | 13.2298i | −0.304555 | + | 0.527505i | ||||
\(630\) | −2.08982 | − | 82.5766i | −0.0832603 | − | 3.28993i | ||||
\(631\) | 9.49043 | + | 16.4379i | 0.377808 | + | 0.654383i | 0.990743 | − | 0.135750i | \(-0.0433446\pi\) |
−0.612935 | + | 0.790133i | \(0.710011\pi\) | |||||||
\(632\) | −13.4884 | − | 23.3626i | −0.536541 | − | 0.929316i | ||||
\(633\) | 27.7046 | + | 27.0123i | 1.10116 | + | 1.07364i | ||||
\(634\) | 10.8058 | + | 18.7162i | 0.429154 | + | 0.743317i | ||||
\(635\) | 23.7070 | + | 41.0616i | 0.940782 | + | 1.62948i | ||||
\(636\) | 8.19959 | + | 7.99471i | 0.325135 | + | 0.317011i | ||||
\(637\) | −7.41434 | −0.293767 | ||||||||
\(638\) | −3.55596 | −0.140782 | ||||||||
\(639\) | 18.0776 | + | 9.83589i | 0.715139 | + | 0.389102i | ||||
\(640\) | −25.6484 | − | 44.4243i | −1.01384 | − | 1.75603i | ||||
\(641\) | 2.73944 | + | 4.74484i | 0.108201 | + | 0.187410i | 0.915042 | − | 0.403359i | \(-0.132158\pi\) |
−0.806840 | + | 0.590770i | \(0.798824\pi\) | |||||||
\(642\) | 5.87496 | − | 23.0902i | 0.231866 | − | 0.911299i | ||||
\(643\) | 22.3400 | 0.881004 | 0.440502 | − | 0.897752i | \(-0.354801\pi\) | ||||
0.440502 | + | 0.897752i | \(0.354801\pi\) | |||||||
\(644\) | 0.553659 | 0.0218172 | ||||||||
\(645\) | −6.40262 | + | 25.1641i | −0.252103 | + | 0.990834i | ||||
\(646\) | −22.3145 | − | 9.44428i | −0.877951 | − | 0.371580i | ||||
\(647\) | 4.90902 | 0.192994 | 0.0964968 | − | 0.995333i | \(-0.469236\pi\) | ||||
0.0964968 | + | 0.995333i | \(0.469236\pi\) | |||||||
\(648\) | 20.4886 | − | 1.03770i | 0.804870 | − | 0.0407648i | ||||
\(649\) | −3.11638 | + | 5.39772i | −0.122328 | + | 0.211879i | ||||
\(650\) | −7.88616 | −0.309321 | ||||||||
\(651\) | −43.3717 | − | 42.2880i | −1.69987 | − | 1.65740i | ||||
\(652\) | 6.41937 | − | 11.1187i | 0.251402 | − | 0.435441i | ||||
\(653\) | −19.2926 | − | 33.4157i | −0.754977 | − | 1.30766i | −0.945386 | − | 0.325953i | \(-0.894315\pi\) |
0.190409 | − | 0.981705i | \(-0.439019\pi\) | |||||||
\(654\) | 20.5727 | + | 20.0586i | 0.804456 | + | 0.784355i | ||||
\(655\) | 74.3392 | 2.90467 | ||||||||
\(656\) | 2.26592 | + | 3.92470i | 0.0884695 | + | 0.153234i | ||||
\(657\) | −2.19612 | − | 1.19489i | −0.0856787 | − | 0.0466171i | ||||
\(658\) | 23.0080 | 0.896946 | ||||||||
\(659\) | −20.4933 | −0.798304 | −0.399152 | − | 0.916885i | \(-0.630696\pi\) | ||||
−0.399152 | + | 0.916885i | \(0.630696\pi\) | |||||||
\(660\) | −2.41877 | + | 9.50644i | −0.0941505 | + | 0.370038i | ||||
\(661\) | 23.2088 | − | 40.1988i | 0.902718 | − | 1.56355i | 0.0787667 | − | 0.996893i | \(-0.474902\pi\) |
0.823951 | − | 0.566660i | \(-0.191765\pi\) | |||||||
\(662\) | −6.93068 | −0.269368 | ||||||||
\(663\) | 0.794594 | − | 3.12297i | 0.0308595 | − | 0.121286i | ||||
\(664\) | −8.27720 | + | 14.3365i | −0.321218 | + | 0.556365i | ||||
\(665\) | −59.6133 | + | 45.0201i | −2.31170 | + | 1.74581i | ||||
\(666\) | 18.1542 | − | 11.1030i | 0.703460 | − | 0.430232i | ||||
\(667\) | −0.0891895 | + | 0.154481i | −0.00345343 | + | 0.00598152i | ||||
\(668\) | −3.80550 | − | 6.59132i | −0.147239 | − | 0.255026i | ||||
\(669\) | 2.93317 | − | 11.5282i | 0.113403 | − | 0.445704i | ||||
\(670\) | 1.69408 | 0.0654479 | ||||||||
\(671\) | 9.31909 | − | 16.1411i | 0.359760 | − | 0.623122i | ||||
\(672\) | −6.21663 | + | 24.4331i | −0.239812 | + | 0.942527i | ||||
\(673\) | 12.7950 | − | 22.1615i | 0.493209 | − | 0.854263i | −0.506760 | − | 0.862087i | \(-0.669157\pi\) |
0.999969 | + | 0.00782366i | \(0.00249037\pi\) | |||||||
\(674\) | 2.34192 | + | 4.05632i | 0.0902074 | + | 0.156244i | ||||
\(675\) | 32.2436 | − | 34.7890i | 1.24106 | − | 1.33903i | ||||
\(676\) | −7.38784 | −0.284148 | ||||||||
\(677\) | 15.8898 | − | 27.5220i | 0.610695 | − | 1.05775i | −0.380428 | − | 0.924810i | \(-0.624223\pi\) |
0.991123 | − | 0.132944i | \(-0.0424432\pi\) | |||||||
\(678\) | 41.6408 | − | 11.7242i | 1.59920 | − | 0.450265i | ||||
\(679\) | 29.0090 | 1.11326 | ||||||||
\(680\) | 14.8226 | − | 25.6735i | 0.568420 | − | 0.984532i | ||||
\(681\) | −14.8379 | + | 4.17769i | −0.568589 | + | 0.160089i | ||||
\(682\) | 15.9732 | + | 27.6664i | 0.611646 | + | 1.05940i | ||||
\(683\) | 46.5132 | 1.77978 | 0.889890 | − | 0.456176i | \(-0.150781\pi\) | ||||
0.889890 | + | 0.456176i | \(0.150781\pi\) | |||||||
\(684\) | 4.73243 | + | 5.94737i | 0.180949 | + | 0.227403i | ||||
\(685\) | 44.0334 | 1.68243 | ||||||||
\(686\) | 24.8644 | + | 43.0665i | 0.949329 | + | 1.64429i | ||||
\(687\) | −3.53161 | + | 13.8802i | −0.134739 | + | 0.529564i | ||||
\(688\) | 9.62113 | − | 16.6643i | 0.366802 | − | 0.635320i | ||||
\(689\) | 6.11689 | 0.233035 | ||||||||
\(690\) | 1.56466 | + | 1.52556i | 0.0595655 | + | 0.0580771i | ||||
\(691\) | −8.31573 | + | 14.4033i | −0.316345 | + | 0.547926i | −0.979723 | − | 0.200359i | \(-0.935789\pi\) |
0.663377 | + | 0.748285i | \(0.269122\pi\) | |||||||
\(692\) | 7.31118 | 0.277929 | ||||||||
\(693\) | −30.2497 | + | 18.5005i | −1.14909 | + | 0.702777i | ||||
\(694\) | 11.8844 | + | 20.5844i | 0.451125 | + | 0.781371i | ||||
\(695\) | −33.5291 | + | 58.0741i | −1.27183 | + | 2.20288i | ||||
\(696\) | −2.41354 | − | 2.35323i | −0.0914851 | − | 0.0891991i | ||||
\(697\) | −1.62502 | + | 2.81462i | −0.0615521 | + | 0.106611i | ||||
\(698\) | −2.14850 | −0.0813220 | ||||||||
\(699\) | −2.22932 | + | 0.627677i | −0.0843206 | + | 0.0237409i | ||||
\(700\) | 12.0956 | + | 20.9502i | 0.457170 | + | 0.791842i | ||||
\(701\) | 18.3672 | − | 31.8130i | 0.693721 | − | 1.20156i | −0.276889 | − | 0.960902i | \(-0.589303\pi\) |
0.970610 | − | 0.240658i | \(-0.0773632\pi\) | |||||||
\(702\) | −3.05145 | + | 3.29233i | −0.115169 | + | 0.124261i | ||||
\(703\) | −17.7231 | − | 7.50105i | −0.668439 | − | 0.282907i | ||||
\(704\) | −5.85887 | + | 10.1479i | −0.220814 | + | 0.382462i | ||||
\(705\) | 14.6411 | + | 14.2752i | 0.551415 | + | 0.537637i | ||||
\(706\) | −33.3092 | −1.25361 | ||||||||
\(707\) | −5.26650 | + | 9.12185i | −0.198067 | + | 0.343062i | ||||
\(708\) | 2.32986 | − | 0.655984i | 0.0875614 | − | 0.0246534i | ||||
\(709\) | −39.7998 | −1.49471 | −0.747356 | − | 0.664424i | \(-0.768677\pi\) | ||||
−0.747356 | + | 0.664424i | \(0.768677\pi\) | |||||||
\(710\) | −41.4276 | −1.55475 | ||||||||
\(711\) | −30.2890 | + | 18.5246i | −1.13593 | + | 0.694725i | ||||
\(712\) | 7.30313 | + | 12.6494i | 0.273696 | + | 0.474056i | ||||
\(713\) | 1.60254 | 0.0600157 | ||||||||
\(714\) | −42.2570 | + | 11.8977i | −1.58143 | + | 0.445260i | ||||
\(715\) | 2.61974 | + | 4.53752i | 0.0979726 | + | 0.169693i | ||||
\(716\) | 6.73427 | − | 11.6641i | 0.251671 | − | 0.435908i | ||||
\(717\) | 2.90588 | − | 11.4209i | 0.108522 | − | 0.426522i | ||||
\(718\) | 7.67116 | 0.286285 | ||||||||
\(719\) | 11.0069 | − | 19.0645i | 0.410487 | − | 0.710985i | −0.584456 | − | 0.811425i | \(-0.698692\pi\) |
0.994943 | + | 0.100441i | \(0.0320253\pi\) | |||||||
\(720\) | −46.4123 | + | 28.3855i | −1.72968 | + | 1.05786i | ||||
\(721\) | −34.0657 | −1.26867 | ||||||||
\(722\) | 8.35236 | − | 29.3608i | 0.310843 | − | 1.09270i | ||||
\(723\) | −9.20379 | − | 8.97381i | −0.342293 | − | 0.333740i | ||||
\(724\) | −2.17414 | −0.0808011 | ||||||||
\(725\) | −7.79397 | −0.289461 | ||||||||
\(726\) | −11.4642 | + | 3.22780i | −0.425475 | + | 0.119795i | ||||
\(727\) | 8.41740 | + | 14.5794i | 0.312184 | + | 0.540719i | 0.978835 | − | 0.204652i | \(-0.0656061\pi\) |
−0.666651 | + | 0.745370i | \(0.732273\pi\) | |||||||
\(728\) | 2.79423 | + | 4.83974i | 0.103561 | + | 0.179373i | ||||
\(729\) | −2.04751 | − | 26.9223i | −0.0758338 | − | 0.997120i | ||||
\(730\) | 5.03274 | 0.186270 | ||||||||
\(731\) | 13.7997 | 0.510401 | ||||||||
\(732\) | −6.96712 | + | 1.96163i | −0.257512 | + | 0.0725039i | ||||
\(733\) | 11.6819 | + | 20.2337i | 0.431481 | + | 0.747347i | 0.997001 | − | 0.0773873i | \(-0.0246578\pi\) |
−0.565520 | + | 0.824735i | \(0.691324\pi\) | |||||||
\(734\) | −17.4812 | − | 30.2783i | −0.645242 | − | 1.11759i | ||||
\(735\) | −22.1354 | + | 86.9981i | −0.816475 | + | 3.20897i | ||||
\(736\) | −0.333490 | − | 0.577621i | −0.0122926 | − | 0.0212914i | ||||
\(737\) | −0.363605 | − | 0.629782i | −0.0133935 | − | 0.0231983i | ||||
\(738\) | 3.86229 | − | 2.36215i | 0.142173 | − | 0.0869521i | ||||
\(739\) | 26.2097 | − | 45.3966i | 0.964141 | − | 1.66994i | 0.252235 | − | 0.967666i | \(-0.418834\pi\) |
0.711906 | − | 0.702275i | \(-0.247832\pi\) | |||||||
\(740\) | −4.82286 | + | 8.35343i | −0.177292 | + | 0.307078i | ||||
\(741\) | 4.02751 | + | 0.509860i | 0.147954 | + | 0.0187302i | ||||
\(742\) | −41.6653 | − | 72.1665i | −1.52958 | − | 2.64932i | ||||
\(743\) | 13.1393 | 0.482033 | 0.241016 | − | 0.970521i | \(-0.422519\pi\) | ||||
0.241016 | + | 0.970521i | \(0.422519\pi\) | |||||||
\(744\) | −7.46733 | + | 29.3487i | −0.273766 | + | 1.07598i | ||||
\(745\) | −60.5513 | −2.21843 | ||||||||
\(746\) | 18.2676 | − | 31.6404i | 0.668824 | − | 1.15844i | ||||
\(747\) | 19.1381 | + | 10.4129i | 0.700227 | + | 0.380988i | ||||
\(748\) | 5.21324 | 0.190615 | ||||||||
\(749\) | −19.5191 | + | 33.8080i | −0.713212 | + | 1.23532i | ||||
\(750\) | −10.6482 | + | 41.8503i | −0.388817 | + | 1.52816i | ||||
\(751\) | 24.1989 | − | 41.9138i | 0.883032 | − | 1.52946i | 0.0350783 | − | 0.999385i | \(-0.488832\pi\) |
0.847953 | − | 0.530071i | \(-0.177835\pi\) | |||||||
\(752\) | −7.57682 | − | 13.1234i | −0.276298 | − | 0.478563i | ||||
\(753\) | −6.69430 | + | 26.3105i | −0.243954 | + | 0.958807i | ||||
\(754\) | 0.737600 | 0.0268618 | ||||||||
\(755\) | −3.08682 | + | 5.34652i | −0.112341 | + | 0.194580i | ||||
\(756\) | 13.4265 | + | 3.05671i | 0.488319 | + | 0.111171i | ||||
\(757\) | −8.62645 | + | 14.9414i | −0.313533 | + | 0.543056i | −0.979125 | − | 0.203261i | \(-0.934846\pi\) |
0.665591 | + | 0.746317i | \(0.268179\pi\) | |||||||
\(758\) | 16.9793 | + | 29.4090i | 0.616715 | + | 1.06818i | ||||
\(759\) | 0.231308 | − | 0.909105i | 0.00839595 | − | 0.0329984i | ||||
\(760\) | 34.3932 | + | 14.5564i | 1.24757 | + | 0.528016i | ||||
\(761\) | 14.8377 | + | 25.6997i | 0.537867 | + | 0.931612i | 0.999019 | + | 0.0442911i | \(0.0141029\pi\) |
−0.461152 | + | 0.887321i | \(0.652564\pi\) | |||||||
\(762\) | −33.7882 | + | 9.51324i | −1.22402 | + | 0.344628i | ||||
\(763\) | −23.5391 | − | 40.7710i | −0.852174 | − | 1.47601i | ||||
\(764\) | −4.28847 | − | 7.42785i | −0.155151 | − | 0.268730i | ||||
\(765\) | −34.2720 | − | 18.6471i | −1.23911 | − | 0.674189i | ||||
\(766\) | 7.69544 | + | 13.3289i | 0.278048 | + | 0.481592i | ||||
\(767\) | 0.646418 | − | 1.11963i | 0.0233408 | − | 0.0404275i | ||||
\(768\) | 21.4828 | − | 6.04861i | 0.775195 | − | 0.218260i | ||||
\(769\) | 4.88919 | − | 8.46833i | 0.176309 | − | 0.305376i | −0.764305 | − | 0.644855i | \(-0.776918\pi\) |
0.940613 | + | 0.339479i | \(0.110251\pi\) | |||||||
\(770\) | 35.6888 | − | 61.8148i | 1.28614 | − | 2.22765i | ||||
\(771\) | −12.3267 | + | 3.47064i | −0.443934 | + | 0.124992i | ||||
\(772\) | 1.64947 | − | 2.85696i | 0.0593657 | − | 0.102824i | ||||
\(773\) | 10.7481 | + | 18.6163i | 0.386583 | + | 0.669581i | 0.991987 | − | 0.126337i | \(-0.0403220\pi\) |
−0.605405 | + | 0.795918i | \(0.706989\pi\) | |||||||
\(774\) | −16.8857 | − | 9.18736i | −0.606942 | − | 0.330233i | ||||
\(775\) | 35.0102 | + | 60.6394i | 1.25760 | + | 2.17823i | ||||
\(776\) | −7.25131 | − | 12.5596i | −0.260307 | − | 0.450865i | ||||
\(777\) | −33.5623 | + | 9.44964i | −1.20404 | + | 0.339004i | ||||
\(778\) | −27.6875 | − | 47.9561i | −0.992645 | − | 1.71931i | ||||
\(779\) | −3.77058 | − | 1.59584i | −0.135095 | − | 0.0571770i | ||||
\(780\) | 0.501716 | − | 1.97189i | 0.0179643 | − | 0.0706048i | ||||
\(781\) | 8.89172 | + | 15.4009i | 0.318171 | + | 0.551088i | ||||
\(782\) | 0.580694 | − | 1.00579i | 0.0207656 | − | 0.0359670i | ||||
\(783\) | −3.01577 | + | 3.25384i | −0.107775 | + | 0.116283i | ||||
\(784\) | 33.2625 | − | 57.6124i | 1.18795 | − | 2.05758i | ||||
\(785\) | 39.9222 | 1.42488 | ||||||||
\(786\) | −13.5706 | + | 53.3361i | −0.484046 | + | 1.90244i | ||||
\(787\) | 10.9841 | + | 19.0250i | 0.391541 | + | 0.678169i | 0.992653 | − | 0.120996i | \(-0.0386088\pi\) |
−0.601112 | + | 0.799165i | \(0.705275\pi\) | |||||||
\(788\) | 3.57332 | − | 6.18918i | 0.127294 | − | 0.220480i | ||||
\(789\) | −1.20978 | + | 4.75476i | −0.0430692 | + | 0.169274i | ||||
\(790\) | 35.7352 | − | 61.8951i | 1.27140 | − | 2.20213i | ||||
\(791\) | −70.8801 | −2.52021 | ||||||||
\(792\) | 15.5714 | + | 8.47228i | 0.553305 | + | 0.301049i | ||||
\(793\) | −1.93302 | + | 3.34810i | −0.0686437 | + | 0.118894i | ||||
\(794\) | −57.2963 | −2.03337 | ||||||||
\(795\) | 18.2618 | − | 71.7741i | 0.647680 | − | 2.54556i | ||||
\(796\) | −0.0184878 | −0.000655282 | ||||||||
\(797\) | −16.8742 | − | 29.2269i | −0.597713 | − | 1.03527i | −0.993158 | − | 0.116780i | \(-0.962743\pi\) |
0.395444 | − | 0.918490i | \(-0.370591\pi\) | |||||||
\(798\) | −21.4182 | − | 50.9891i | −0.758196 | − | 1.80499i | ||||
\(799\) | 5.43377 | − | 9.41157i | 0.192233 | − | 0.332957i | ||||
\(800\) | 14.5713 | − | 25.2382i | 0.515172 | − | 0.892305i | ||||
\(801\) | 16.3996 | − | 10.0299i | 0.579450 | − | 0.354388i | ||||
\(802\) | −0.910589 | − | 1.57719i | −0.0321540 | − | 0.0556924i | ||||
\(803\) | −1.08019 | − | 1.87094i | −0.0381191 | − | 0.0660242i | ||||
\(804\) | −0.0696354 | + | 0.273687i | −0.00245585 | + | 0.00965218i | ||||
\(805\) | −1.79027 | − | 3.10084i | −0.0630988 | − | 0.109290i | ||||
\(806\) | −3.31327 | − | 5.73875i | −0.116705 | − | 0.202139i | ||||
\(807\) | 19.0692 | − | 5.36903i | 0.671267 | − | 0.188999i | ||||
\(808\) | 5.26582 | 0.185251 | ||||||||
\(809\) | −11.4422 | −0.402288 | −0.201144 | − | 0.979562i | \(-0.564466\pi\) | ||||
−0.201144 | + | 0.979562i | \(0.564466\pi\) | |||||||
\(810\) | 29.5214 | + | 45.6341i | 1.03728 | + | 1.60342i | ||||
\(811\) | 18.0483 | + | 31.2606i | 0.633762 | + | 1.09771i | 0.986776 | + | 0.162090i | \(0.0518235\pi\) |
−0.353014 | + | 0.935618i | \(0.614843\pi\) | |||||||
\(812\) | −1.13131 | − | 1.95949i | −0.0397012 | − | 0.0687646i | ||||
\(813\) | −46.0758 | + | 12.9729i | −1.61595 | + | 0.454980i | ||||
\(814\) | 18.3884 | 0.644513 | ||||||||
\(815\) | −83.0288 | −2.90837 | ||||||||
\(816\) | 20.7020 | + | 20.1847i | 0.724715 | + | 0.706606i | ||||
\(817\) | 2.13680 | + | 17.2530i | 0.0747572 | + | 0.603605i | ||||
\(818\) | 21.5711 | 0.754215 | ||||||||
\(819\) | 6.27458 | − | 3.83750i | 0.219252 | − | 0.134093i | ||||
\(820\) | −1.02606 | + | 1.77719i | −0.0358316 | + | 0.0620621i | ||||
\(821\) | −29.8000 | −1.04003 | −0.520014 | − | 0.854158i | \(-0.674073\pi\) | ||||
−0.520014 | + | 0.854158i | \(0.674073\pi\) | |||||||
\(822\) | −8.03827 | + | 31.5926i | −0.280367 | + | 1.10192i | ||||
\(823\) | 1.97734 | − | 3.42485i | 0.0689256 | − | 0.119383i | −0.829503 | − | 0.558502i | \(-0.811376\pi\) |
0.898429 | + | 0.439120i | \(0.144710\pi\) | |||||||
\(824\) | 8.51534 | + | 14.7490i | 0.296646 | + | 0.513806i | ||||
\(825\) | 39.4534 | − | 11.1083i | 1.37359 | − | 0.386742i | ||||
\(826\) | −17.6124 | −0.612813 | ||||||||
\(827\) | −22.5669 | − | 39.0870i | −0.784728 | − | 1.35919i | −0.929161 | − | 0.369675i | \(-0.879469\pi\) |
0.144433 | − | 0.989515i | \(-0.453864\pi\) | |||||||
\(828\) | −0.310777 | + | 0.190070i | −0.0108003 | + | 0.00660538i | ||||
\(829\) | −37.7440 | −1.31090 | −0.655452 | − | 0.755237i | \(-0.727522\pi\) | ||||
−0.655452 | + | 0.755237i | \(0.727522\pi\) | |||||||
\(830\) | −43.8579 | −1.52233 | ||||||||
\(831\) | 17.3230 | − | 4.87738i | 0.600927 | − | 0.169194i | ||||
\(832\) | 1.21528 | − | 2.10493i | 0.0421323 | − | 0.0729754i | ||||
\(833\) | 47.7089 | 1.65302 | ||||||||
\(834\) | −35.5457 | − | 34.6575i | −1.23085 | − | 1.20009i | ||||
\(835\) | −24.6104 | + | 42.6264i | −0.851678 | + | 1.47515i | ||||
\(836\) | 0.807237 | + | 6.51780i | 0.0279189 | + | 0.225423i | ||||
\(837\) | 38.8626 | + | 8.84750i | 1.34329 | + | 0.305814i | ||||
\(838\) | 3.13369 | − | 5.42771i | 0.108251 | − | 0.187497i | ||||
\(839\) | 10.4100 | + | 18.0306i | 0.359392 | + | 0.622486i | 0.987859 | − | 0.155350i | \(-0.0496506\pi\) |
−0.628467 | + | 0.777836i | \(0.716317\pi\) | |||||||
\(840\) | 65.1304 | − | 18.3378i | 2.24721 | − | 0.632715i | ||||
\(841\) | −28.2710 | −0.974863 | ||||||||
\(842\) | −21.8865 | + | 37.9086i | −0.754260 | + | 1.30642i | ||||
\(843\) | −10.5467 | − | 10.2832i | −0.363249 | − | 0.354173i | ||||
\(844\) | 6.49221 | − | 11.2448i | 0.223471 | − | 0.387063i | ||||
\(845\) | 23.8888 | + | 41.3766i | 0.821799 | + | 1.42340i | ||||
\(846\) | −12.9148 | + | 7.89860i | −0.444019 | + | 0.271559i | ||||
\(847\) | 19.5141 | 0.670511 | ||||||||
\(848\) | −27.4418 | + | 47.5306i | −0.942356 | + | 1.63221i | ||||
\(849\) | 1.69516 | + | 1.65280i | 0.0581776 | + | 0.0567239i | ||||
\(850\) | 50.7449 | 1.74054 | ||||||||
\(851\) | 0.461212 | − | 0.798842i | 0.0158101 | − | 0.0273840i | ||||
\(852\) | 1.70289 | − | 6.69283i | 0.0583400 | − | 0.229293i | ||||
\(853\) | 14.2391 | + | 24.6629i | 0.487539 | + | 0.844442i | 0.999897 | − | 0.0143294i | \(-0.00456135\pi\) |
−0.512358 | + | 0.858772i | \(0.671228\pi\) | |||||||
\(854\) | 52.6674 | 1.80224 | ||||||||
\(855\) | 18.0066 | − | 45.7356i | 0.615813 | − | 1.56412i | ||||
\(856\) | 19.5166 | 0.667062 | ||||||||
\(857\) | −2.78592 | − | 4.82535i | −0.0951651 | − | 0.164831i | 0.814512 | − | 0.580146i | \(-0.197005\pi\) |
−0.909677 | + | 0.415315i | \(0.863671\pi\) | |||||||
\(858\) | −3.73376 | + | 1.05126i | −0.127468 | + | 0.0358894i | ||||
\(859\) | 3.07779 | − | 5.33088i | 0.105013 | − | 0.181887i | −0.808731 | − | 0.588179i | \(-0.799845\pi\) |
0.913743 | + | 0.406292i | \(0.133178\pi\) | |||||||
\(860\) | 8.71332 | 0.297122 | ||||||||
\(861\) | −7.14035 | + | 2.01041i | −0.243343 | + | 0.0685144i | ||||
\(862\) | 32.5783 | − | 56.4272i | 1.10962 | − | 1.92192i | ||||
\(863\) | 26.1393 | 0.889794 | 0.444897 | − | 0.895582i | \(-0.353240\pi\) | ||||
0.444897 | + | 0.895582i | \(0.353240\pi\) | |||||||
\(864\) | −4.89832 | − | 15.8488i | −0.166644 | − | 0.539188i | ||||
\(865\) | −23.6409 | − | 40.9473i | −0.803815 | − | 1.39225i | ||||
\(866\) | −15.0566 | + | 26.0789i | −0.511646 | + | 0.886196i | ||||
\(867\) | 2.14752 | − | 8.44036i | 0.0729337 | − | 0.286650i | ||||
\(868\) | −10.1636 | + | 17.6039i | −0.344975 | + | 0.597514i | ||||
\(869\) | −30.6797 | −1.04074 | ||||||||
\(870\) | 2.20209 | − | 8.65482i | 0.0746577 | − | 0.293426i | ||||
\(871\) | 0.0754211 | + | 0.130633i | 0.00255555 | + | 0.00442634i | ||||
\(872\) | −11.7681 | + | 20.3829i | −0.398517 | + | 0.690251i | ||||
\(873\) | −16.2832 | + | 9.95871i | −0.551103 | + | 0.337051i | ||||
\(874\) | 1.34740 | + | 0.570267i | 0.0455764 | + | 0.0192896i | ||||
\(875\) | 35.3777 | − | 61.2760i | 1.19598 | − | 2.07151i | ||||
\(876\) | −0.206872 | + | 0.813063i | −0.00698954 | + | 0.0274709i | ||||
\(877\) | 0.794874 | 0.0268410 | 0.0134205 | − | 0.999910i | \(-0.495728\pi\) | ||||
0.0134205 | + | 0.999910i | \(0.495728\pi\) | |||||||
\(878\) | −13.0967 | + | 22.6842i | −0.441992 | + | 0.765553i | ||||
\(879\) | −0.319380 | + | 1.25525i | −0.0107724 | + | 0.0423386i | ||||
\(880\) | −47.0110 | −1.58474 | ||||||||
\(881\) | 36.2565 | 1.22151 | 0.610756 | − | 0.791819i | \(-0.290866\pi\) | ||||
0.610756 | + | 0.791819i | \(0.290866\pi\) | |||||||
\(882\) | −58.3777 | − | 31.7629i | −1.96568 | − | 1.06951i | ||||
\(883\) | −27.3417 | − | 47.3571i | −0.920120 | − | 1.59369i | −0.799227 | − | 0.601029i | \(-0.794758\pi\) |
−0.120893 | − | 0.992666i | \(-0.538576\pi\) | |||||||
\(884\) | −1.08136 | −0.0363701 | ||||||||
\(885\) | −11.2076 | − | 10.9275i | −0.376739 | − | 0.367325i | ||||
\(886\) | 21.2801 | + | 36.8583i | 0.714920 | + | 1.23828i | ||||
\(887\) | 25.1527 | − | 43.5658i | 0.844545 | − | 1.46280i | −0.0414702 | − | 0.999140i | \(-0.513204\pi\) |
0.886015 | − | 0.463656i | \(-0.153463\pi\) | |||||||
\(888\) | 12.4808 | + | 12.1689i | 0.418827 | + | 0.408362i | ||||
\(889\) | 57.5135 | 1.92894 | ||||||||
\(890\) | −19.3483 | + | 33.5123i | −0.648558 | + | 1.12333i | ||||
\(891\) | 10.6284 | − | 20.7693i | 0.356066 | − | 0.695797i | ||||
\(892\) | −3.99174 | −0.133653 | ||||||||
\(893\) | 12.6081 | + | 5.33620i | 0.421914 | + | 0.178569i | ||||
\(894\) | 11.0536 | − | 43.4437i | 0.369687 | − | 1.45297i | ||||
\(895\) | −87.1018 | −2.91149 | ||||||||
\(896\) | −62.2235 | −2.07874 | ||||||||
\(897\) | −0.0479793 | + | 0.188572i | −0.00160198 | + | 0.00629624i | ||||
\(898\) | −15.4661 | − | 26.7880i | −0.516109 | − | 0.893927i | ||||
\(899\) | −3.27453 | − | 5.67166i | −0.109212 | − | 0.189160i | ||||
\(900\) | −13.9816 | − | 7.60728i | −0.466053 | − | 0.253576i | ||||
\(901\) | −39.3602 | −1.31128 | ||||||||
\(902\) | 3.91212 | 0.130259 | ||||||||
\(903\) | 22.5516 | + | 21.9881i | 0.750469 | + | 0.731717i | ||||
\(904\) | 17.7177 | + | 30.6880i | 0.589284 | + | 1.02067i | ||||
\(905\) | 7.03013 | + | 12.1765i | 0.233689 | + | 0.404762i | ||||
\(906\) | −3.27247 | − | 3.19070i | −0.108721 | − | 0.106004i | ||||
\(907\) | 6.06193 | + | 10.4996i | 0.201283 | + | 0.348633i | 0.948942 | − | 0.315450i | \(-0.102156\pi\) |
−0.747659 | + | 0.664083i | \(0.768822\pi\) | |||||||
\(908\) | 2.58636 | + | 4.47971i | 0.0858314 | + | 0.148664i | ||||
\(909\) | −0.175337 | − | 6.92822i | −0.00581555 | − | 0.229794i | ||||
\(910\) | −7.40280 | + | 12.8220i | −0.245400 | + | 0.425046i | ||||
\(911\) | 10.4969 | − | 18.1811i | 0.347777 | − | 0.602367i | −0.638077 | − | 0.769972i | \(-0.720270\pi\) |
0.985854 | + | 0.167605i | \(0.0536034\pi\) | |||||||
\(912\) | −22.0302 | + | 29.0080i | −0.729492 | + | 0.960549i | ||||
\(913\) | 9.41334 | + | 16.3044i | 0.311536 | + | 0.539596i | ||||
\(914\) | −58.6943 | −1.94144 | ||||||||
\(915\) | 33.5147 | + | 32.6773i | 1.10796 | + | 1.08028i | ||||
\(916\) | 4.80617 | 0.158800 | ||||||||
\(917\) | 45.0871 | − | 78.0932i | 1.48891 | − | 2.57886i | ||||
\(918\) | 19.6351 | − | 21.1851i | 0.648054 | − | 0.699212i | ||||
\(919\) | −5.58553 | −0.184250 | −0.0921248 | − | 0.995747i | \(-0.529366\pi\) | ||||
−0.0921248 | + | 0.995747i | \(0.529366\pi\) | |||||||
\(920\) | −0.895020 | + | 1.55022i | −0.0295079 | + | 0.0511093i | ||||
\(921\) | −18.5561 | + | 5.22458i | −0.611445 | + | 0.172156i | ||||
\(922\) | 4.68836 | − | 8.12048i | 0.154403 | − | 0.267434i | ||||
\(923\) | −1.84438 | − | 3.19455i | −0.0607084 | − | 0.105150i | ||||
\(924\) | 8.51949 | + | 8.30661i | 0.280271 | + | 0.273267i | ||||
\(925\) | 40.3037 | 1.32518 | ||||||||
\(926\) | 10.1866 | − | 17.6437i | 0.334752 | − | 0.579808i | ||||
\(927\) | 19.1216 | − | 11.6947i | 0.628037 | − | 0.384104i | ||||
\(928\) | −1.36286 | + | 2.36055i | −0.0447382 | + | 0.0774889i | ||||
\(929\) | −10.8938 | − | 18.8685i | −0.357413 | − | 0.619057i | 0.630115 | − | 0.776502i | \(-0.283008\pi\) |
−0.987528 | + | 0.157445i | \(0.949674\pi\) | |||||||
\(930\) | −77.2287 | + | 21.7442i | −2.53243 | + | 0.713019i | ||||
\(931\) | 7.38742 | + | 59.6476i | 0.242113 | + | 1.95487i | ||||
\(932\) | 0.388588 | + | 0.673054i | 0.0127286 | + | 0.0220466i | ||||
\(933\) | 5.18791 | − | 20.3899i | 0.169844 | − | 0.667536i | ||||
\(934\) | 19.3308 | + | 33.4819i | 0.632523 | + | 1.09556i | ||||
\(935\) | −16.8571 | − | 29.1974i | −0.551288 | − | 0.954858i | ||||
\(936\) | −3.22991 | − | 1.75737i | −0.105573 | − | 0.0574415i | ||||
\(937\) | −23.1526 | − | 40.1014i | −0.756362 | − | 1.31006i | −0.944694 | − | 0.327952i | \(-0.893642\pi\) |
0.188333 | − | 0.982105i | \(-0.439692\pi\) | |||||||
\(938\) | 1.02747 | − | 1.77962i | 0.0335480 | − | 0.0581068i | ||||
\(939\) | 32.6321 | + | 31.8167i | 1.06491 | + | 1.03830i | ||||
\(940\) | 3.43095 | − | 5.94258i | 0.111905 | − | 0.193826i | ||||
\(941\) | −13.1076 | + | 22.7030i | −0.427295 | + | 0.740097i | −0.996632 | − | 0.0820075i | \(-0.973867\pi\) |
0.569336 | + | 0.822105i | \(0.307200\pi\) | |||||||
\(942\) | −7.28776 | + | 28.6429i | −0.237448 | + | 0.933237i | ||||
\(943\) | 0.0981225 | − | 0.169953i | 0.00319531 | − | 0.00553444i | ||||
\(944\) | 5.79997 | + | 10.0458i | 0.188773 | + | 0.326965i | ||||
\(945\) | −26.2956 | − | 85.0812i | −0.855397 | − | 2.76769i | ||||
\(946\) | −8.30544 | − | 14.3855i | −0.270033 | − | 0.467711i | ||||
\(947\) | 17.9942 | + | 31.1669i | 0.584733 | + | 1.01279i | 0.994909 | + | 0.100781i | \(0.0321342\pi\) |
−0.410175 | + | 0.912007i | \(0.634532\pi\) | |||||||
\(948\) | 8.53056 | + | 8.31740i | 0.277060 | + | 0.270137i | ||||
\(949\) | 0.224060 | + | 0.388083i | 0.00727329 | + | 0.0125977i | ||||
\(950\) | 7.85753 | + | 63.4433i | 0.254932 | + | 2.05837i | ||||
\(951\) | 16.6819 | + | 16.2651i | 0.540949 | + | 0.527432i | ||||
\(952\) | −17.9799 | − | 31.1421i | −0.582733 | − | 1.00932i | ||||
\(953\) | −6.73210 | + | 11.6603i | −0.218074 | + | 0.377716i | −0.954219 | − | 0.299108i | \(-0.903311\pi\) |
0.736145 | + | 0.676824i | \(0.236644\pi\) | |||||||
\(954\) | 48.1620 | + | 26.2046i | 1.55930 | + | 0.848405i | ||||
\(955\) | −27.7338 | + | 48.0363i | −0.897444 | + | 1.55442i | ||||
\(956\) | −3.95461 | −0.127901 | ||||||||
\(957\) | −3.69011 | + | 1.03897i | −0.119284 | + | 0.0335851i | ||||
\(958\) | −4.02563 | − | 6.97260i | −0.130062 | − | 0.225274i | ||||
\(959\) | 26.7065 | − | 46.2570i | 0.862397 | − | 1.49372i | ||||
\(960\) | −21.0705 | − | 20.5440i | −0.680049 | − | 0.663056i | ||||
\(961\) | −13.9181 | + | 24.1069i | −0.448971 | + | 0.777641i | ||||
\(962\) | −3.81423 | −0.122976 | ||||||||
\(963\) | −0.649845 | − | 25.6778i | −0.0209410 | − | 0.827457i | ||||
\(964\) | −2.15679 | + | 3.73567i | −0.0694655 | + | 0.120318i | ||||
\(965\) | −21.3344 | −0.686779 | ||||||||
\(966\) | 2.55157 | − | 0.718409i | 0.0820954 | − | 0.0231144i | ||||
\(967\) | 12.6766 | 0.407653 | 0.203826 | − | 0.979007i | \(-0.434662\pi\) | ||||
0.203826 | + | 0.979007i | \(0.434662\pi\) | |||||||
\(968\) | −4.87789 | − | 8.44875i | −0.156781 | − | 0.271553i | ||||
\(969\) | −25.9157 | − | 3.28078i | −0.832532 | − | 0.105394i | ||||
\(970\) | 19.2110 | − | 33.2745i | 0.616829 | − | 1.06838i | ||||
\(971\) | 5.76415 | − | 9.98379i | 0.184980 | − | 0.320395i | −0.758590 | − | 0.651569i | \(-0.774111\pi\) |
0.943570 | + | 0.331174i | \(0.107445\pi\) | |||||||
\(972\) | −8.58589 | + | 2.89352i | −0.275393 | + | 0.0928098i | ||||
\(973\) | 40.6711 | + | 70.4445i | 1.30386 | + | 2.25835i | ||||
\(974\) | 25.3106 | + | 43.8392i | 0.811004 | + | 1.40470i | ||||
\(975\) | −8.18367 | + | 2.30416i | −0.262087 | + | 0.0737921i | ||||
\(976\) | −17.3440 | − | 30.0407i | −0.555168 | − | 0.961580i | ||||
\(977\) | −19.0964 | − | 33.0759i | −0.610947 | − | 1.05819i | −0.991081 | − | 0.133260i | \(-0.957455\pi\) |
0.380134 | − | 0.924932i | \(-0.375878\pi\) | |||||||
\(978\) | 15.1568 | − | 59.5706i | 0.484662 | − | 1.90486i | ||||
\(979\) | 16.6111 | 0.530895 | ||||||||
\(980\) | 30.1240 | 0.962276 | ||||||||
\(981\) | 27.2095 | + | 14.8045i | 0.868732 | + | 0.472671i | ||||
\(982\) | −24.5868 | − | 42.5857i | −0.784598 | − | 1.35896i | ||||
\(983\) | 7.91585 | + | 13.7107i | 0.252476 | + | 0.437302i | 0.964207 | − | 0.265150i | \(-0.0854216\pi\) |
−0.711731 | + | 0.702453i | \(0.752088\pi\) | |||||||
\(984\) | 2.65528 | + | 2.58893i | 0.0846471 | + | 0.0825320i | ||||
\(985\) | −46.2178 | −1.47262 | ||||||||
\(986\) | −4.74621 | −0.151150 | ||||||||
\(987\) | 23.8760 | − | 6.72242i | 0.759981 | − | 0.213977i | ||||
\(988\) | −0.167442 | − | 1.35196i | −0.00532704 | − | 0.0430117i | ||||
\(989\) | −0.833258 | −0.0264961 | ||||||||
\(990\) | 1.18818 | + | 46.9495i | 0.0377629 | + | 1.49215i | ||||
\(991\) | −10.1647 | + | 17.6058i | −0.322893 | + | 0.559267i | −0.981084 | − | 0.193584i | \(-0.937989\pi\) |
0.658191 | + | 0.752851i | \(0.271322\pi\) | |||||||
\(992\) | 24.4877 | 0.777485 | ||||||||
\(993\) | −7.19213 | + | 2.02498i | −0.228235 | + | 0.0642610i | ||||
\(994\) | −25.1260 | + | 43.5196i | −0.796950 | + | 1.38036i | ||||
\(995\) | 0.0597808 | + | 0.103543i | 0.00189518 | + | 0.00328255i | ||||
\(996\) | 1.80279 | − | 7.08546i | 0.0571235 | − | 0.224511i | ||||
\(997\) | 36.2674 | 1.14860 | 0.574300 | − | 0.818645i | \(-0.305274\pi\) | ||||
0.574300 | + | 0.818645i | \(0.305274\pi\) | |||||||
\(998\) | 8.77527 | + | 15.1992i | 0.277776 | + | 0.481123i | ||||
\(999\) | 15.5950 | − | 16.8261i | 0.493404 | − | 0.532354i |
(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 | 171.2.g.c.106.5 | ✓ | 32 | |
3.2 | odd | 2 | 513.2.g.c.505.12 | 32 | |||
9.4 | even | 3 | 171.2.h.c.49.12 | yes | 32 | ||
9.5 | odd | 6 | 513.2.h.c.334.5 | 32 | |||
19.7 | even | 3 | 171.2.h.c.7.12 | yes | 32 | ||
57.26 | odd | 6 | 513.2.h.c.235.5 | 32 | |||
171.121 | even | 3 | inner | 171.2.g.c.121.5 | yes | 32 | |
171.140 | odd | 6 | 513.2.g.c.64.12 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.2.g.c.106.5 | ✓ | 32 | 1.1 | even | 1 | trivial | |
171.2.g.c.121.5 | yes | 32 | 171.121 | even | 3 | inner | |
171.2.h.c.7.12 | yes | 32 | 19.7 | even | 3 | ||
171.2.h.c.49.12 | yes | 32 | 9.4 | even | 3 | ||
513.2.g.c.64.12 | 32 | 171.140 | odd | 6 | |||
513.2.g.c.505.12 | 32 | 3.2 | odd | 2 | |||
513.2.h.c.235.5 | 32 | 57.26 | odd | 6 | |||
513.2.h.c.334.5 | 32 | 9.5 | odd | 6 |