Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(8,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(36))
chi = DirichletCharacter(H, H._module([2, 27]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.r (of order \(36\), degree \(12\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{36})\) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{36}]$ |
Embedding invariants
Embedding label | 152.5 | ||
Character | \(\chi\) | \(=\) | 405.152 |
Dual form | 405.2.r.a.8.5 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{17}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.865920 | − | 0.606324i | −0.612298 | − | 0.428736i | 0.225863 | − | 0.974159i | \(-0.427480\pi\) |
−0.838161 | + | 0.545424i | \(0.816369\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.301851 | − | 0.829330i | −0.150926 | − | 0.414665i | ||||
\(5\) | −2.13636 | − | 0.660292i | −0.955407 | − | 0.295292i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.22161 | − | 2.61975i | −0.461725 | − | 0.990171i | −0.989996 | − | 0.141096i | \(-0.954937\pi\) |
0.528271 | − | 0.849076i | \(-0.322840\pi\) | |||||||
\(8\) | −0.788655 | + | 2.94330i | −0.278832 | + | 1.04061i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.44956 | + | 1.86708i | 0.458392 | + | 0.590424i | ||||
\(11\) | −1.51740 | − | 1.80836i | −0.457512 | − | 0.545242i | 0.487136 | − | 0.873326i | \(-0.338041\pi\) |
−0.944648 | + | 0.328084i | \(0.893597\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.11956 | + | 4.45519i | 0.865210 | + | 1.23565i | 0.970475 | + | 0.241203i | \(0.0775421\pi\) |
−0.105265 | + | 0.994444i | \(0.533569\pi\) | |||||||
\(14\) | −0.530600 | + | 3.00918i | −0.141809 | + | 0.804238i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.11535 | − | 0.935892i | 0.278838 | − | 0.233973i | ||||
\(17\) | 0.716894 | + | 2.67549i | 0.173872 | + | 0.648901i | 0.996741 | + | 0.0806688i | \(0.0257056\pi\) |
−0.822869 | + | 0.568232i | \(0.807628\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.35751 | + | 3.09316i | −1.22910 | + | 0.709619i | −0.966841 | − | 0.255379i | \(-0.917800\pi\) |
−0.262256 | + | 0.964998i | \(0.584466\pi\) | |||||||
\(20\) | 0.0972619 | + | 1.97105i | 0.0217484 | + | 0.440741i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.217491 | + | 2.48593i | 0.0463692 | + | 0.530002i | ||||
\(23\) | −0.646627 | − | 0.301527i | −0.134831 | − | 0.0628728i | 0.354032 | − | 0.935233i | \(-0.384810\pi\) |
−0.488863 | + | 0.872361i | \(0.662588\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.12803 | + | 2.82124i | 0.825606 | + | 0.564247i | ||||
\(26\) | − | 5.74930i | − | 1.12753i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.80389 | + | 1.80389i | −0.340903 | + | 0.340903i | ||||
\(29\) | −0.623300 | − | 3.53491i | −0.115744 | − | 0.656416i | −0.986379 | − | 0.164487i | \(-0.947403\pi\) |
0.870635 | − | 0.491929i | \(-0.163708\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.18043 | + | 1.88552i | −0.930432 | + | 0.338650i | −0.762381 | − | 0.647129i | \(-0.775970\pi\) |
−0.168051 | + | 0.985778i | \(0.553747\pi\) | |||||||
\(32\) | 4.53781 | − | 0.397007i | 0.802178 | − | 0.0701815i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.00144 | − | 2.75143i | 0.171745 | − | 0.471866i | ||||
\(35\) | 0.879991 | + | 6.40333i | 0.148746 | + | 1.08236i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.26173 | + | 1.14193i | −0.700624 | + | 0.187732i | −0.591510 | − | 0.806298i | \(-0.701468\pi\) |
−0.109114 | + | 0.994029i | \(0.534801\pi\) | |||||||
\(38\) | 6.51463 | + | 0.569956i | 1.05681 | + | 0.0924591i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.62828 | − | 5.76719i | 0.573682 | − | 0.911873i | ||||
\(41\) | −5.70140 | − | 1.00531i | −0.890409 | − | 0.157003i | −0.290314 | − | 0.956932i | \(-0.593760\pi\) |
−0.600095 | + | 0.799928i | \(0.704871\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.126221 | − | 1.44271i | 0.0192485 | − | 0.220012i | −0.980478 | − | 0.196629i | \(-0.937001\pi\) |
0.999727 | − | 0.0233831i | \(-0.00744375\pi\) | |||||||
\(44\) | −1.04170 | + | 1.80428i | −0.157042 | + | 0.272005i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.377104 | + | 0.653164i | 0.0556010 | + | 0.0963037i | ||||
\(47\) | −9.40770 | + | 4.38688i | −1.37225 | + | 0.639893i | −0.962244 | − | 0.272188i | \(-0.912253\pi\) |
−0.410010 | + | 0.912081i | \(0.634475\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.871236 | + | 1.03830i | −0.124462 | + | 0.148328i | ||||
\(50\) | −1.86396 | − | 4.94589i | −0.263604 | − | 0.699454i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.75318 | − | 3.93195i | 0.381797 | − | 0.545263i | ||||
\(53\) | 7.22940 | + | 7.22940i | 0.993035 | + | 0.993035i | 0.999976 | − | 0.00694140i | \(-0.00220953\pi\) |
−0.00694140 | + | 0.999976i | \(0.502210\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.04765 | + | 4.86523i | 0.276105 | + | 0.656027i | ||||
\(56\) | 8.67413 | − | 1.52948i | 1.15913 | − | 0.204386i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.60357 | + | 3.43887i | −0.210559 | + | 0.451546i | ||||
\(59\) | −6.27320 | − | 5.26384i | −0.816701 | − | 0.685293i | 0.135496 | − | 0.990778i | \(-0.456737\pi\) |
−0.952197 | + | 0.305484i | \(0.901182\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.64019 | + | 0.960952i | 0.338042 | + | 0.123037i | 0.505463 | − | 0.862848i | \(-0.331322\pi\) |
−0.167421 | + | 0.985885i | \(0.553544\pi\) | |||||||
\(62\) | 5.62907 | + | 1.50831i | 0.714893 | + | 0.191555i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.69194 | − | 3.86359i | −0.836493 | − | 0.482949i | ||||
\(65\) | −3.72276 | − | 11.5777i | −0.461751 | − | 1.43604i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.11610 | − | 4.28254i | 0.747201 | − | 0.523196i | −0.136847 | − | 0.990592i | \(-0.543697\pi\) |
0.884048 | + | 0.467396i | \(0.154808\pi\) | |||||||
\(68\) | 2.00246 | − | 1.40214i | 0.242834 | − | 0.170034i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.12049 | − | 6.07833i | 0.372970 | − | 0.726499i | ||||
\(71\) | 4.24004 | + | 2.44799i | 0.503200 | + | 0.290523i | 0.730034 | − | 0.683411i | \(-0.239504\pi\) |
−0.226834 | + | 0.973933i | \(0.572838\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.73088 | − | 1.80353i | −0.787790 | − | 0.211088i | −0.157574 | − | 0.987507i | \(-0.550367\pi\) |
−0.630216 | + | 0.776420i | \(0.717034\pi\) | |||||||
\(74\) | 4.38269 | + | 1.59517i | 0.509478 | + | 0.185435i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.18242 | + | 3.50947i | 0.479756 | + | 0.402563i | ||||
\(77\) | −2.88379 | + | 6.18430i | −0.328638 | + | 0.704767i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.8661 | + | 2.26863i | −1.44754 | + | 0.255241i | −0.841529 | − | 0.540212i | \(-0.818344\pi\) |
−0.606015 | + | 0.795453i | \(0.707233\pi\) | |||||||
\(80\) | −3.00075 | + | 1.26294i | −0.335494 | + | 0.141201i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.32741 | + | 4.32741i | 0.477883 | + | 0.477883i | ||||
\(83\) | 2.73492 | − | 3.90587i | 0.300196 | − | 0.428724i | −0.640509 | − | 0.767951i | \(-0.721276\pi\) |
0.940705 | + | 0.339227i | \(0.110165\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.235061 | − | 6.18915i | 0.0254960 | − | 0.671307i | ||||
\(86\) | −0.984048 | + | 1.17274i | −0.106113 | + | 0.126460i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.51925 | − | 3.03998i | 0.694955 | − | 0.324063i | ||||
\(89\) | −3.33276 | − | 5.77251i | −0.353272 | − | 0.611885i | 0.633549 | − | 0.773703i | \(-0.281598\pi\) |
−0.986821 | + | 0.161818i | \(0.948264\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.86060 | − | 13.6150i | 0.824014 | − | 1.42723i | ||||
\(92\) | −0.0548802 | + | 0.627283i | −0.00572165 | + | 0.0653988i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.8062 | + | 1.90542i | 1.11457 | + | 0.196529i | ||||
\(95\) | 13.4879 | − | 3.07057i | 1.38383 | − | 0.315033i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.2758 | − | 1.59893i | −1.85563 | − | 0.162346i | −0.896079 | − | 0.443894i | \(-0.853597\pi\) |
−0.959547 | + | 0.281548i | \(0.909152\pi\) | |||||||
\(98\) | 1.38397 | − | 0.370833i | 0.139802 | − | 0.0374597i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.09368 | − | 4.27509i | 0.109368 | − | 0.427509i | ||||
\(101\) | 1.15191 | − | 3.16484i | 0.114619 | − | 0.314913i | −0.869097 | − | 0.494641i | \(-0.835299\pi\) |
0.983716 | + | 0.179728i | \(0.0575217\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.61346 | + | 0.316137i | −0.356045 | + | 0.0311499i | −0.263775 | − | 0.964584i | \(-0.584968\pi\) |
−0.0922694 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(104\) | −15.5732 | + | 5.66819i | −1.52708 | + | 0.555812i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.87673 | − | 10.6434i | −0.182284 | − | 1.03378i | ||||
\(107\) | 4.03460 | − | 4.03460i | 0.390039 | − | 0.390039i | −0.484662 | − | 0.874701i | \(-0.661057\pi\) |
0.874701 | + | 0.484662i | \(0.161057\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 15.8226i | − | 1.51553i | −0.652527 | − | 0.757765i | \(-0.726291\pi\) | ||
0.652527 | − | 0.757765i | \(-0.273709\pi\) | |||||||
\(110\) | 1.17680 | − | 5.45444i | 0.112204 | − | 0.520060i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.81433 | − | 1.77865i | −0.360420 | − | 0.168067i | ||||
\(113\) | 0.232615 | + | 2.65880i | 0.0218825 | + | 0.250119i | 0.999255 | + | 0.0385931i | \(0.0122876\pi\) |
−0.977372 | + | 0.211526i | \(0.932157\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.18233 | + | 1.07113i | 0.110253 | + | 0.0998836i | ||||
\(116\) | −2.74346 | + | 1.58394i | −0.254724 | + | 0.147065i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.24050 | + | 8.36165i | 0.206255 | + | 0.769753i | ||||
\(119\) | 6.13333 | − | 5.14648i | 0.562242 | − | 0.471777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.942447 | − | 5.34488i | 0.0856770 | − | 0.485898i | ||||
\(122\) | −1.70355 | − | 2.43292i | −0.154232 | − | 0.220266i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.12744 | + | 3.72713i | 0.280852 | + | 0.334707i | ||||
\(125\) | −6.95610 | − | 8.75287i | −0.622172 | − | 0.782880i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.846401 | + | 3.15881i | −0.0751059 | + | 0.280299i | −0.993257 | − | 0.115931i | \(-0.963015\pi\) |
0.918151 | + | 0.396230i | \(0.129682\pi\) | |||||||
\(128\) | −0.398073 | − | 0.853671i | −0.0351850 | − | 0.0754546i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.79622 | + | 12.2826i | −0.332950 | + | 1.07725i | ||||
\(131\) | −0.497235 | − | 1.36614i | −0.0434436 | − | 0.119360i | 0.916074 | − | 0.401010i | \(-0.131341\pi\) |
−0.959517 | + | 0.281649i | \(0.909118\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.6481 | + | 10.2567i | 1.27015 | + | 0.889368i | ||||
\(134\) | −7.89266 | −0.681822 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.44014 | −0.723736 | ||||||||
\(137\) | 13.0703 | + | 9.15193i | 1.11667 | + | 0.781902i | 0.978035 | − | 0.208442i | \(-0.0668391\pi\) |
0.138637 | + | 0.990343i | \(0.455728\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.12149 | − | 8.57623i | −0.264762 | − | 0.727426i | −0.998830 | − | 0.0483514i | \(-0.984603\pi\) |
0.734069 | − | 0.679075i | \(-0.237619\pi\) | |||||||
\(140\) | 5.04484 | − | 2.66266i | 0.426367 | − | 0.225035i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.18726 | − | 4.69060i | −0.183551 | − | 0.393626i | ||||
\(143\) | 3.32299 | − | 12.4016i | 0.277883 | − | 1.03707i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.00248 | + | 7.96338i | −0.0832517 | + | 0.661323i | ||||
\(146\) | 4.73488 | + | 5.64281i | 0.391861 | + | 0.467002i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.23344 | + | 3.18968i | 0.183588 | + | 0.262190i | ||||
\(149\) | −1.63395 | + | 9.26659i | −0.133858 | + | 0.759149i | 0.841789 | + | 0.539806i | \(0.181502\pi\) |
−0.975648 | + | 0.219343i | \(0.929609\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.808803 | + | 0.678666i | −0.0658194 | + | 0.0552291i | −0.675104 | − | 0.737723i | \(-0.735901\pi\) |
0.609284 | + | 0.792952i | \(0.291457\pi\) | |||||||
\(152\) | −4.87887 | − | 18.2082i | −0.395729 | − | 1.47688i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.24682 | − | 3.60660i | 0.503383 | − | 0.290628i | ||||
\(155\) | 12.3122 | − | 0.607549i | 0.988942 | − | 0.0487995i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.94520 | + | 22.2338i | 0.155244 | + | 1.77445i | 0.530652 | + | 0.847590i | \(0.321947\pi\) |
−0.375408 | + | 0.926860i | \(0.622497\pi\) | |||||||
\(158\) | 12.5165 | + | 5.83654i | 0.995759 | + | 0.464330i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.95651 | − | 2.14813i | −0.787131 | − | 0.169825i | ||||
\(161\) | 2.06235i | 0.162536i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.74889 | + | 1.74889i | −0.136983 | + | 0.136983i | −0.772274 | − | 0.635290i | \(-0.780881\pi\) |
0.635290 | + | 0.772274i | \(0.280881\pi\) | |||||||
\(164\) | 0.887241 | + | 5.03179i | 0.0692819 | + | 0.392917i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.73644 | + | 1.72392i | −0.367619 | + | 0.133802i | ||||
\(167\) | −7.25686 | + | 0.634893i | −0.561553 | + | 0.0491295i | −0.364399 | − | 0.931243i | \(-0.618725\pi\) |
−0.197154 | + | 0.980373i | \(0.563170\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.67082 | + | 15.5805i | −0.436217 | + | 1.19850i | ||||
\(170\) | −3.95617 | + | 5.21678i | −0.303424 | + | 0.400109i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.23458 | + | 0.330806i | −0.0941362 | + | 0.0252237i | ||||
\(173\) | −20.4232 | − | 1.78680i | −1.55275 | − | 0.135848i | −0.721760 | − | 0.692143i | \(-0.756667\pi\) |
−0.830985 | + | 0.556295i | \(0.812222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.34809 | − | 14.2608i | 0.177499 | − | 1.07802i | ||||
\(176\) | −3.38487 | − | 0.596843i | −0.255144 | − | 0.0449887i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.614106 | + | 7.01926i | −0.0460292 | + | 0.526116i | ||||
\(179\) | −7.17079 | + | 12.4202i | −0.535970 | + | 0.928327i | 0.463146 | + | 0.886282i | \(0.346721\pi\) |
−0.999116 | + | 0.0420450i | \(0.986613\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.03474 | + | 1.79221i | 0.0769112 | + | 0.133214i | 0.901916 | − | 0.431912i | \(-0.142161\pi\) |
−0.825005 | + | 0.565126i | \(0.808828\pi\) | |||||||
\(182\) | −15.0617 | + | 7.02339i | −1.11645 | + | 0.520609i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.39745 | − | 1.66542i | 0.103021 | − | 0.122776i | ||||
\(185\) | 9.85857 | + | 0.374424i | 0.724816 | + | 0.0275282i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.75043 | − | 5.35618i | 0.274259 | − | 0.391682i | ||||
\(188\) | 6.47790 | + | 6.47790i | 0.472449 | + | 0.472449i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13.5412 | − | 5.51919i | −0.982384 | − | 0.400404i | ||||
\(191\) | −22.9618 | + | 4.04878i | −1.66145 | + | 0.292959i | −0.923987 | − | 0.382424i | \(-0.875089\pi\) |
−0.737467 | + | 0.675383i | \(0.763978\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.131693 | + | 0.282417i | −0.00947948 | + | 0.0203288i | −0.910991 | − | 0.412427i | \(-0.864681\pi\) |
0.901511 | + | 0.432756i | \(0.142459\pi\) | |||||||
\(194\) | 14.8559 | + | 12.4656i | 1.06659 | + | 0.894977i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.12408 | + | 0.409130i | 0.0802911 | + | 0.0292236i | ||||
\(197\) | 3.13774 | + | 0.840756i | 0.223555 | + | 0.0599014i | 0.368858 | − | 0.929486i | \(-0.379749\pi\) |
−0.145303 | + | 0.989387i | \(0.546416\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.52277 | + | 3.18857i | 0.391499 | + | 0.226032i | 0.682809 | − | 0.730596i | \(-0.260758\pi\) |
−0.291310 | + | 0.956629i | \(0.594091\pi\) | |||||||
\(200\) | −11.5593 | + | 9.92504i | −0.817369 | + | 0.701807i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.91638 | + | 2.04207i | −0.205196 | + | 0.143679i | ||||
\(203\) | −8.49914 | + | 5.95116i | −0.596523 | + | 0.417690i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.5164 | + | 5.91229i | 0.804342 | + | 0.412932i | ||||
\(206\) | 3.32065 | + | 1.91718i | 0.231360 | + | 0.133576i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.64899 | + | 2.04954i | 0.530362 | + | 0.142110i | ||||
\(209\) | 13.7230 | + | 4.99477i | 0.949241 | + | 0.345495i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.91430 | + | 4.12359i | 0.338314 | + | 0.283879i | 0.796077 | − | 0.605195i | \(-0.206905\pi\) |
−0.457763 | + | 0.889074i | \(0.651349\pi\) | |||||||
\(212\) | 3.81335 | − | 8.17776i | 0.261902 | − | 0.561651i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.93991 | + | 1.04737i | −0.406044 | + | 0.0715965i | ||||
\(215\) | −1.22226 | + | 2.99880i | −0.0833578 | + | 0.204517i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.2680 | + | 11.2680i | 0.764925 | + | 0.764925i | ||||
\(218\) | −9.59362 | + | 13.7011i | −0.649762 | + | 0.927956i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.41679 | − | 3.16675i | 0.230360 | − | 0.213502i | ||||
\(221\) | −9.68341 | + | 11.5402i | −0.651376 | + | 0.776280i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.41489 | + | 4.39023i | −0.630467 | + | 0.293992i | −0.711464 | − | 0.702723i | \(-0.751968\pi\) |
0.0809965 | + | 0.996714i | \(0.474190\pi\) | |||||||
\(224\) | −6.58348 | − | 11.4029i | −0.439877 | − | 0.761889i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.41067 | − | 2.44335i | 0.0938361 | − | 0.162529i | ||||
\(227\) | −0.272304 | + | 3.11245i | −0.0180734 | + | 0.206580i | 0.981789 | + | 0.189976i | \(0.0608411\pi\) |
−0.999862 | + | 0.0166042i | \(0.994714\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.1368 | + | 4.07964i | 1.52892 | + | 0.269590i | 0.873933 | − | 0.486047i | \(-0.161562\pi\) |
0.654990 | + | 0.755638i | \(0.272673\pi\) | |||||||
\(230\) | −0.374350 | − | 1.64439i | −0.0246839 | − | 0.108428i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.8959 | + | 0.953265i | 0.715349 | + | 0.0625849i | ||||
\(233\) | 3.20411 | − | 0.858538i | 0.209908 | − | 0.0562447i | −0.152333 | − | 0.988329i | \(-0.548679\pi\) |
0.362241 | + | 0.932085i | \(0.382012\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.9948 | − | 3.16011i | 1.50002 | − | 0.206143i | ||||
\(236\) | −2.47188 | + | 6.79145i | −0.160906 | + | 0.442085i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.43141 | + | 0.737653i | −0.546527 | + | 0.0478149i | ||||
\(239\) | 15.9837 | − | 5.81759i | 1.03390 | − | 0.376309i | 0.231335 | − | 0.972874i | \(-0.425691\pi\) |
0.802564 | + | 0.596566i | \(0.203468\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.22231 | + | 18.2746i | 0.207567 | + | 1.17717i | 0.893349 | + | 0.449364i | \(0.148349\pi\) |
−0.685782 | + | 0.727807i | \(0.740540\pi\) | |||||||
\(242\) | −4.05681 | + | 4.05681i | −0.260782 | + | 0.260782i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 2.47965i | − | 0.158744i | ||||||
\(245\) | 2.54685 | − | 1.64290i | 0.162712 | − | 0.104961i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.4937 | − | 14.2194i | −1.94027 | − | 0.904761i | ||||
\(248\) | −1.46409 | − | 16.7346i | −0.0929695 | − | 1.06265i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.716350 | + | 11.7969i | 0.0453060 | + | 0.746103i | ||||
\(251\) | 13.1493 | − | 7.59178i | 0.829979 | − | 0.479189i | −0.0238664 | − | 0.999715i | \(-0.507598\pi\) |
0.853846 | + | 0.520527i | \(0.174264\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.435919 | + | 1.62687i | 0.0274060 | + | 0.102281i | ||||
\(254\) | 2.64818 | − | 2.22208i | 0.166161 | − | 0.139426i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.85653 | + | 16.2002i | −0.178533 | + | 1.01251i | ||||
\(257\) | −4.98418 | − | 7.11815i | −0.310905 | − | 0.444018i | 0.633041 | − | 0.774118i | \(-0.281806\pi\) |
−0.943946 | + | 0.330100i | \(0.892917\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.19772 | + | 9.76966i | 0.509382 | + | 0.607057i | ||||
\(260\) | −8.47800 | + | 6.58213i | −0.525783 | + | 0.408207i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.397759 | + | 1.48446i | −0.0245736 | + | 0.0917099i | ||||
\(263\) | −9.97382 | − | 21.3889i | −0.615012 | − | 1.31890i | −0.929214 | − | 0.369541i | \(-0.879515\pi\) |
0.314203 | − | 0.949356i | \(-0.398263\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.6711 | − | 20.2181i | −0.655518 | − | 1.24199i | ||||
\(266\) | −6.46518 | − | 17.7629i | −0.396406 | − | 1.08912i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.39779 | − | 3.77957i | −0.329723 | − | 0.230874i | ||||
\(269\) | −10.2124 | −0.622659 | −0.311330 | − | 0.950302i | \(-0.600774\pi\) | ||||
−0.311330 | + | 0.950302i | \(0.600774\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.84409 | 0.294258 | 0.147129 | − | 0.989117i | \(-0.452997\pi\) | ||||
0.147129 | + | 0.989117i | \(0.452997\pi\) | |||||||
\(272\) | 3.30356 | + | 2.31318i | 0.200308 | + | 0.140257i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.76881 | − | 15.8497i | −0.348506 | − | 0.957514i | ||||
\(275\) | −1.16204 | − | 11.7459i | −0.0700734 | − | 0.708305i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.71185 | − | 12.2491i | −0.343192 | − | 0.735978i | 0.656642 | − | 0.754203i | \(-0.271976\pi\) |
−0.999834 | + | 0.0182248i | \(0.994199\pi\) | |||||||
\(278\) | −2.49701 | + | 9.31897i | −0.149761 | + | 0.558914i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −19.5409 | − | 2.45994i | −1.16779 | − | 0.147010i | ||||
\(281\) | 10.1156 | + | 12.0553i | 0.603445 | + | 0.719158i | 0.978130 | − | 0.207994i | \(-0.0666936\pi\) |
−0.374685 | + | 0.927152i | \(0.622249\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.2952 | − | 24.7001i | −1.02809 | − | 1.46827i | −0.877443 | − | 0.479680i | \(-0.840753\pi\) |
−0.150648 | − | 0.988587i | \(-0.548136\pi\) | |||||||
\(284\) | 0.750327 | − | 4.25532i | 0.0445237 | − | 0.252507i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.3968 | + | 8.72397i | −0.614777 | + | 0.515859i | ||||
\(287\) | 4.33122 | + | 16.1643i | 0.255664 | + | 0.954150i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.07815 | − | 4.66392i | 0.475185 | − | 0.274348i | ||||
\(290\) | 5.69646 | − | 6.28782i | 0.334508 | − | 0.369234i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.536001 | + | 6.12652i | 0.0313671 | + | 0.358527i | ||||
\(293\) | 6.65512 | + | 3.10333i | 0.388796 | + | 0.181299i | 0.607180 | − | 0.794564i | \(-0.292301\pi\) |
−0.218384 | + | 0.975863i | \(0.570078\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.92611 | + | 15.3876i | 0.577921 | + | 0.895899i | ||||
\(296\) | − | 13.4441i | − | 0.781424i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.03343 | − | 7.03343i | 0.407435 | − | 0.407435i | ||||
\(299\) | −0.673830 | − | 3.82148i | −0.0389686 | − | 0.221002i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.93374 | + | 1.43176i | −0.226737 | + | 0.0825254i | ||||
\(302\) | 1.11185 | − | 0.0972742i | 0.0639798 | − | 0.00559750i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.08065 | + | 8.46402i | −0.176687 | + | 0.485445i | ||||
\(305\) | −5.00588 | − | 3.79623i | −0.286636 | − | 0.217372i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.2129 | − | 3.54038i | 0.754099 | − | 0.202060i | 0.138764 | − | 0.990326i | \(-0.455687\pi\) |
0.615336 | + | 0.788265i | \(0.289020\pi\) | |||||||
\(308\) | 5.99930 | + | 0.524871i | 0.341842 | + | 0.0299073i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −11.0298 | − | 6.93911i | −0.626449 | − | 0.394115i | ||||
\(311\) | −3.80231 | − | 0.670449i | −0.215609 | − | 0.0380177i | 0.0648001 | − | 0.997898i | \(-0.479359\pi\) |
−0.280409 | + | 0.959881i | \(0.590470\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.14418 | − | 24.5081i | 0.121196 | − | 1.38528i | −0.655401 | − | 0.755281i | \(-0.727500\pi\) |
0.776597 | − | 0.629997i | \(-0.216944\pi\) | |||||||
\(314\) | 11.7965 | − | 20.4321i | 0.665714 | − | 1.15305i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.76508 | + | 9.98541i | 0.324311 | + | 0.561723i | ||||
\(317\) | −14.9555 | + | 6.97386i | −0.839984 | + | 0.391691i | −0.794493 | − | 0.607274i | \(-0.792263\pi\) |
−0.0454916 | + | 0.998965i | \(0.514485\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.44660 | + | 6.49101i | −0.304951 | + | 0.363427i | ||||
\(320\) | 11.7453 | + | 12.6726i | 0.656580 | + | 0.708422i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.25045 | − | 1.78583i | 0.0696849 | − | 0.0995203i | ||||
\(323\) | −12.1165 | − | 12.1165i | −0.674178 | − | 0.674178i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.308476 | + | 27.1922i | 0.0171112 | + | 1.50835i | ||||
\(326\) | 2.57479 | − | 0.454005i | 0.142604 | − | 0.0251450i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.45537 | − | 15.9881i | 0.411654 | − | 0.882794i | ||||
\(329\) | 22.9851 | + | 19.2867i | 1.26721 | + | 1.06331i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.3973 | − | 7.06005i | −1.06617 | − | 0.388056i | −0.251429 | − | 0.967876i | \(-0.580901\pi\) |
−0.814744 | + | 0.579820i | \(0.803123\pi\) | |||||||
\(332\) | −4.06479 | − | 1.08916i | −0.223084 | − | 0.0597752i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.66881 | + | 3.85024i | 0.364901 | + | 0.210676i | ||||
\(335\) | −15.8939 | + | 5.11062i | −0.868377 | + | 0.279223i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.57053 | + | 6.00115i | −0.466867 | + | 0.326904i | −0.783227 | − | 0.621735i | \(-0.786428\pi\) |
0.316361 | + | 0.948639i | \(0.397539\pi\) | |||||||
\(338\) | 14.3573 | − | 10.0531i | 0.780933 | − | 0.546815i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.20380 | + | 1.67326i | −0.282215 | + | 0.0907452i | ||||
\(341\) | 11.2705 | + | 6.50701i | 0.610330 | + | 0.352374i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.7602 | − | 4.22292i | −0.850968 | − | 0.228016i | ||||
\(344\) | 4.14679 | + | 1.50931i | 0.223580 | + | 0.0813765i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.6015 | + | 13.9303i | 0.892500 | + | 0.748896i | ||||
\(347\) | 4.85639 | − | 10.4146i | 0.260705 | − | 0.559083i | −0.731767 | − | 0.681554i | \(-0.761304\pi\) |
0.992472 | + | 0.122472i | \(0.0390821\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.6377 | − | 2.75735i | 0.837067 | − | 0.147597i | 0.261347 | − | 0.965245i | \(-0.415833\pi\) |
0.575719 | + | 0.817647i | \(0.304722\pi\) | |||||||
\(350\) | −10.6799 | + | 10.9250i | −0.570867 | + | 0.583968i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.60358 | − | 7.60358i | −0.405272 | − | 0.405272i | ||||
\(353\) | −4.97772 | + | 7.10893i | −0.264938 | + | 0.378370i | −0.929475 | − | 0.368885i | \(-0.879740\pi\) |
0.664538 | + | 0.747255i | \(0.268629\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.44184 | − | 8.02943i | −0.394972 | − | 0.426158i | ||||
\(356\) | −3.78131 | + | 4.50640i | −0.200409 | + | 0.238838i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.7400 | − | 6.40706i | 0.726180 | − | 0.338623i | ||||
\(359\) | −10.2032 | − | 17.6725i | −0.538505 | − | 0.932718i | −0.998985 | − | 0.0450476i | \(-0.985656\pi\) |
0.460480 | − | 0.887670i | \(-0.347677\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.63526 | − | 16.6888i | 0.507119 | − | 0.878356i | ||||
\(362\) | 0.190664 | − | 2.17930i | 0.0100211 | − | 0.114541i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.6640 | − | 2.40933i | −0.716189 | − | 0.126283i | ||||
\(365\) | 13.1887 | + | 8.29733i | 0.690328 | + | 0.434302i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.8506 | + | 2.26163i | 1.34939 | + | 0.118056i | 0.738818 | − | 0.673906i | \(-0.235385\pi\) |
0.610571 | + | 0.791962i | \(0.290940\pi\) | |||||||
\(368\) | −1.00341 | + | 0.268864i | −0.0523066 | + | 0.0140155i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.30971 | − | 6.30171i | −0.432001 | − | 0.327610i | ||||
\(371\) | 10.1077 | − | 27.7707i | 0.524766 | − | 1.44178i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.75950 | − | 0.416402i | 0.246438 | − | 0.0215605i | 0.0367323 | − | 0.999325i | \(-0.488305\pi\) |
0.209705 | + | 0.977765i | \(0.432750\pi\) | |||||||
\(374\) | −6.49515 | + | 2.36404i | −0.335856 | + | 0.122242i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.49248 | − | 31.1494i | −0.283253 | − | 1.60641i | ||||
\(377\) | 13.8043 | − | 13.8043i | 0.710956 | − | 0.710956i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 25.3002i | − | 1.29958i | −0.760112 | − | 0.649792i | \(-0.774856\pi\) | ||
0.760112 | − | 0.649792i | \(-0.225144\pi\) | |||||||
\(380\) | −6.61786 | − | 10.2591i | −0.339489 | − | 0.526280i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22.3379 | + | 10.4163i | 1.14291 | + | 0.532946i | ||||
\(383\) | 1.07406 | + | 12.2766i | 0.0548819 | + | 0.627303i | 0.972971 | + | 0.230929i | \(0.0741764\pi\) |
−0.918089 | + | 0.396375i | \(0.870268\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.2442 | − | 11.3077i | 0.522095 | − | 0.576295i | ||||
\(386\) | 0.285272 | − | 0.164702i | 0.0145200 | − | 0.00838310i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.19054 | + | 15.6393i | 0.212742 | + | 0.793965i | ||||
\(389\) | −6.83430 | + | 5.73466i | −0.346513 | + | 0.290759i | −0.799388 | − | 0.600815i | \(-0.794843\pi\) |
0.452875 | + | 0.891574i | \(0.350398\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.343168 | − | 1.94620i | 0.0173548 | − | 0.0984238i | ||||
\(392\) | −2.36892 | − | 3.38317i | −0.119649 | − | 0.170876i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.20727 | − | 2.63052i | −0.111200 | − | 0.132524i | ||||
\(395\) | 28.9844 | + | 3.64875i | 1.45836 | + | 0.183588i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.52782 | − | 13.1660i | 0.177056 | − | 0.660782i | −0.819136 | − | 0.573599i | \(-0.805547\pi\) |
0.996192 | − | 0.0871833i | \(-0.0277866\pi\) | |||||||
\(398\) | −2.84897 | − | 6.10964i | −0.142806 | − | 0.306249i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.24458 | − | 0.716715i | 0.362229 | − | 0.0358358i | ||||
\(401\) | 1.00354 | + | 2.75721i | 0.0501146 | + | 0.137689i | 0.962225 | − | 0.272257i | \(-0.0877700\pi\) |
−0.912110 | + | 0.409945i | \(0.865548\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.5610 | − | 17.1978i | −1.22347 | − | 0.856683i | ||||
\(404\) | −2.97240 | −0.147882 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.9679 | 0.544328 | ||||||||
\(407\) | 8.53175 | + | 5.97399i | 0.422903 | + | 0.296120i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.80467 | + | 26.9381i | 0.484810 | + | 1.33200i | 0.905325 | + | 0.424719i | \(0.139627\pi\) |
−0.420515 | + | 0.907285i | \(0.638151\pi\) | |||||||
\(410\) | −6.38754 | − | 12.1022i | −0.315458 | − | 0.597687i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.35291 | + | 2.90132i | 0.0666530 | + | 0.142938i | ||||
\(413\) | −6.12654 | + | 22.8645i | −0.301467 | + | 1.12509i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.42177 | + | 6.53847i | −0.413408 | + | 0.320961i | ||||
\(416\) | 15.9247 | + | 18.9783i | 0.780772 | + | 0.930488i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.85459 | − | 12.6457i | −0.433092 | − | 0.618519i | ||||
\(419\) | 2.30839 | − | 13.0915i | 0.112772 | − | 0.639563i | −0.875057 | − | 0.484020i | \(-0.839176\pi\) |
0.987829 | − | 0.155543i | \(-0.0497127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.93437 | − | 5.81863i | 0.337960 | − | 0.283582i | −0.457974 | − | 0.888966i | \(-0.651425\pi\) |
0.795934 | + | 0.605383i | \(0.206980\pi\) | |||||||
\(422\) | −1.75516 | − | 6.55035i | −0.0854399 | − | 0.318866i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −26.9798 | + | 15.5768i | −1.31025 | + | 0.756476i | ||||
\(425\) | −4.58882 | + | 13.0670i | −0.222590 | + | 0.633843i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.707831 | − | 8.09054i | −0.0342543 | − | 0.391529i | ||||
\(428\) | −4.56386 | − | 2.12816i | −0.220602 | − | 0.102869i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.87663 | − | 1.85564i | 0.138723 | − | 0.0894868i | ||||
\(431\) | − | 0.295969i | − | 0.0142563i | −0.999975 | − | 0.00712817i | \(-0.997731\pi\) | ||
0.999975 | − | 0.00712817i | \(-0.00226899\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.8171 | − | 12.8171i | 0.615949 | − | 0.615949i | −0.328541 | − | 0.944490i | \(-0.606557\pi\) |
0.944490 | + | 0.328541i | \(0.106557\pi\) | |||||||
\(434\) | −2.92514 | − | 16.5893i | −0.140411 | − | 0.796312i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.1221 | + | 4.77607i | −0.628437 | + | 0.228732i | ||||
\(437\) | 4.39698 | − | 0.384686i | 0.210336 | − | 0.0184020i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.75841 | + | 26.8110i | −0.465743 | + | 1.27962i | 0.455362 | + | 0.890306i | \(0.349510\pi\) |
−0.921105 | + | 0.389313i | \(0.872712\pi\) | |||||||
\(440\) | −15.9347 | + | 2.18986i | −0.759658 | + | 0.104398i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.3822 | − | 4.12164i | 0.731655 | − | 0.196046i | ||||
\(443\) | 40.1651 | + | 3.51399i | 1.90830 | + | 0.166955i | 0.979204 | − | 0.202878i | \(-0.0650296\pi\) |
0.929098 | + | 0.369833i | \(0.120585\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.30842 | + | 14.5327i | 0.156834 | + | 0.688917i | ||||
\(446\) | 10.8144 | + | 1.90688i | 0.512079 | + | 0.0902933i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.94671 | + | 22.2510i | −0.0919734 | + | 1.05126i | ||||
\(449\) | 3.91232 | − | 6.77634i | 0.184634 | − | 0.319795i | −0.758819 | − | 0.651301i | \(-0.774223\pi\) |
0.943453 | + | 0.331506i | \(0.107557\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.83332 | + | 11.8357i | 0.321768 | + | 0.557319i | ||||
\(452\) | 2.13480 | − | 0.995476i | 0.100413 | − | 0.0468232i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.12294 | − | 2.53003i | 0.0996347 | − | 0.118740i | ||||
\(455\) | −25.7829 | + | 23.8961i | −1.20872 | + | 1.12027i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.14363 | + | 4.48957i | −0.147053 | + | 0.210013i | −0.885920 | − | 0.463838i | \(-0.846472\pi\) |
0.738867 | + | 0.673851i | \(0.235361\pi\) | |||||||
\(458\) | −17.5610 | − | 17.5610i | −0.820573 | − | 0.820573i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.531434 | − | 1.30386i | 0.0247782 | − | 0.0607929i | ||||
\(461\) | −29.6880 | + | 5.23480i | −1.38271 | + | 0.243809i | −0.815019 | − | 0.579434i | \(-0.803274\pi\) |
−0.567689 | + | 0.823243i | \(0.692163\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.0761934 | − | 0.163397i | 0.00354101 | − | 0.00759371i | −0.904529 | − | 0.426411i | \(-0.859778\pi\) |
0.908070 | + | 0.418818i | \(0.137555\pi\) | |||||||
\(464\) | −4.00350 | − | 3.35933i | −0.185858 | − | 0.155953i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.29505 | − | 1.19930i | −0.152640 | − | 0.0555566i | ||||
\(467\) | 12.1916 | + | 3.26672i | 0.564158 | + | 0.151166i | 0.529616 | − | 0.848238i | \(-0.322336\pi\) |
0.0345422 | + | 0.999403i | \(0.489003\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.6907 | − | 10.7911i | −0.863055 | − | 0.498285i | ||||
\(470\) | −21.8277 | − | 11.2059i | −1.00684 | − | 0.516890i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 20.4404 | − | 14.3126i | 0.940848 | − | 0.658789i | ||||
\(473\) | −2.80048 | + | 1.96091i | −0.128766 | + | 0.0901629i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −30.8425 | − | 2.34615i | −1.41515 | − | 0.107649i | ||||
\(476\) | −6.11948 | − | 3.53308i | −0.280486 | − | 0.161939i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.3679 | − | 4.65373i | −0.794391 | − | 0.212857i | ||||
\(479\) | 33.4923 | + | 12.1902i | 1.53030 | + | 0.556985i | 0.963696 | − | 0.267003i | \(-0.0860335\pi\) |
0.566607 | + | 0.823988i | \(0.308256\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.3822 | − | 15.4245i | −0.838157 | − | 0.703297i | ||||
\(482\) | 8.29007 | − | 17.7781i | 0.377602 | − | 0.809771i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.71715 | + | 0.831760i | −0.214416 | + | 0.0378073i | ||||
\(485\) | 37.9878 | + | 15.4832i | 1.72494 | + | 0.703058i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.88907 | + | 4.88907i | 0.221545 | + | 0.221545i | 0.809149 | − | 0.587604i | \(-0.199929\pi\) |
−0.587604 | + | 0.809149i | \(0.699929\pi\) | |||||||
\(488\) | −4.91057 | + | 7.01302i | −0.222291 | + | 0.317464i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.20150 | − | 0.121592i | −0.144629 | − | 0.00549295i | ||||
\(491\) | 16.6934 | − | 19.8944i | 0.753361 | − | 0.897821i | −0.244048 | − | 0.969763i | \(-0.578475\pi\) |
0.997409 | + | 0.0719426i | \(0.0229198\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.01076 | − | 4.20179i | 0.405824 | − | 0.189239i | ||||
\(494\) | 17.7835 | + | 30.8019i | 0.800117 | + | 1.38584i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.01336 | + | 6.95135i | −0.180205 | + | 0.312125i | ||||
\(497\) | 1.23344 | − | 14.0983i | 0.0553275 | − | 0.632396i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.0477 | + | 1.94801i | 0.494564 | + | 0.0872050i | 0.415367 | − | 0.909654i | \(-0.363653\pi\) |
0.0791972 | + | 0.996859i | \(0.474764\pi\) | |||||||
\(500\) | −5.15931 | + | 8.41096i | −0.230731 | + | 0.376150i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.9894 | − | 1.39889i | −0.713640 | − | 0.0624354i | ||||
\(503\) | −29.1890 | + | 7.82118i | −1.30147 | + | 0.348729i | −0.842008 | − | 0.539466i | \(-0.818626\pi\) |
−0.459467 | + | 0.888195i | \(0.651960\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.55060 | + | 6.00063i | −0.202499 | + | 0.267024i | ||||
\(506\) | 0.608940 | − | 1.67305i | 0.0270707 | − | 0.0743761i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.87518 | − | 0.251546i | 0.127566 | − | 0.0111605i | ||||
\(509\) | −22.0511 | + | 8.02596i | −0.977399 | + | 0.355744i | −0.780829 | − | 0.624745i | \(-0.785203\pi\) |
−0.196571 | + | 0.980490i | \(0.562981\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.49769 | + | 19.8364i | 0.154729 | + | 0.877511i | ||||
\(512\) | 10.9640 | − | 10.9640i | 0.484544 | − | 0.484544i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.18578i | 0.405167i | ||||||||
\(515\) | 7.92837 | + | 1.71056i | 0.349366 | + | 0.0753762i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.2083 | + | 10.3559i | 0.976719 | + | 0.455452i | ||||
\(518\) | −1.17499 | − | 13.4302i | −0.0516262 | − | 0.590090i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 37.0126 | − | 1.82639i | 1.62311 | − | 0.0800925i | ||||
\(521\) | 14.2319 | − | 8.21681i | 0.623512 | − | 0.359985i | −0.154723 | − | 0.987958i | \(-0.549449\pi\) |
0.778235 | + | 0.627973i | \(0.216115\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.78176 | + | 14.1137i | 0.165365 | + | 0.617150i | 0.997993 | + | 0.0633182i | \(0.0201683\pi\) |
−0.832629 | + | 0.553832i | \(0.813165\pi\) | |||||||
\(524\) | −0.982891 | + | 0.824743i | −0.0429378 | + | 0.0360291i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.33208 | + | 24.5685i | −0.188888 | + | 1.07124i | ||||
\(527\) | −8.75850 | − | 12.5084i | −0.381526 | − | 0.544876i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.4569 | − | 17.2291i | −0.628561 | − | 0.749090i | ||||
\(530\) | −3.01843 | + | 23.9774i | −0.131112 | + | 1.04151i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.08464 | − | 15.2441i | 0.177091 | − | 0.660914i | ||||
\(533\) | −13.3070 | − | 28.5370i | −0.576390 | − | 1.23607i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.2833 | + | 5.95532i | −0.487822 | + | 0.257471i | ||||
\(536\) | 7.78131 | + | 21.3790i | 0.336101 | + | 0.923431i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.84309 | + | 6.19200i | 0.381253 | + | 0.266956i | ||||
\(539\) | 3.19963 | 0.137818 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.4337 | −1.22246 | −0.611230 | − | 0.791453i | \(-0.709325\pi\) | ||||
−0.611230 | + | 0.791453i | \(0.709325\pi\) | |||||||
\(542\) | −4.19460 | − | 2.93709i | −0.180173 | − | 0.126159i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.31531 | + | 11.8562i | 0.185017 | + | 0.508331i | ||||
\(545\) | −10.4475 | + | 33.8027i | −0.447523 | + | 1.44795i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.44356 | + | 9.52924i | 0.189993 | + | 0.407441i | 0.978111 | − | 0.208083i | \(-0.0667224\pi\) |
−0.788118 | + | 0.615524i | \(0.788945\pi\) | |||||||
\(548\) | 3.64467 | − | 13.6021i | 0.155693 | − | 0.581053i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.11559 | + | 10.8756i | −0.260770 | + | 0.463737i | ||||
\(551\) | 14.2734 | + | 17.0103i | 0.608066 | + | 0.724665i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.6605 | + | 30.9344i | 0.921099 | + | 1.31547i | ||||
\(554\) | −2.48092 | + | 14.0700i | −0.105404 | + | 0.597776i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.17030 | + | 5.17749i | −0.261679 | + | 0.219575i | ||||
\(557\) | 4.48926 | + | 16.7541i | 0.190216 | + | 0.709896i | 0.993454 | + | 0.114237i | \(0.0364423\pi\) |
−0.803238 | + | 0.595659i | \(0.796891\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.82132 | − | 3.93829i | 0.288511 | − | 0.166572i | ||||
\(560\) | 6.97433 | + | 6.31840i | 0.294719 | + | 0.267001i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.44988 | − | 16.5722i | −0.0611596 | − | 0.699057i | ||||
\(563\) | −21.2542 | − | 9.91099i | −0.895758 | − | 0.417699i | −0.0804714 | − | 0.996757i | \(-0.525643\pi\) |
−0.815286 | + | 0.579058i | \(0.803420\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.25864 | − | 5.83373i | 0.0529512 | − | 0.245427i | ||||
\(566\) | 31.8748i | 1.33980i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.5491 | + | 10.5491i | −0.442630 | + | 0.442630i | ||||
\(569\) | −6.84027 | − | 38.7931i | −0.286759 | − | 1.62629i | −0.698934 | − | 0.715186i | \(-0.746342\pi\) |
0.412175 | − | 0.911105i | \(-0.364769\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.4980 | − | 11.4643i | 1.31815 | − | 0.479767i | 0.415285 | − | 0.909691i | \(-0.363682\pi\) |
0.902865 | + | 0.429924i | \(0.141460\pi\) | |||||||
\(572\) | −11.2880 | + | 0.987576i | −0.471977 | + | 0.0412926i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.05032 | − | 16.6231i | 0.252536 | − | 0.693836i | ||||
\(575\) | −1.81862 | − | 3.06900i | −0.0758415 | − | 0.127986i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.0819 | + | 5.64888i | −0.877651 | + | 0.235166i | −0.669393 | − | 0.742908i | \(-0.733446\pi\) |
−0.208257 | + | 0.978074i | \(0.566779\pi\) | |||||||
\(578\) | −9.82287 | − | 0.859390i | −0.408578 | − | 0.0357459i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.90687 | − | 1.57237i | 0.286792 | − | 0.0652891i | ||||
\(581\) | −13.5734 | − | 2.39335i | −0.563119 | − | 0.0992930i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.10351 | − | 24.0432i | 0.0871185 | − | 0.995769i | ||||
\(584\) | 10.6167 | − | 18.3886i | 0.439321 | − | 0.760927i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.88117 | − | 6.72239i | −0.160330 | − | 0.277699i | ||||
\(587\) | 22.1244 | − | 10.3168i | 0.913173 | − | 0.425819i | 0.0915170 | − | 0.995804i | \(-0.470828\pi\) |
0.821656 | + | 0.569984i | \(0.193051\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.9220 | − | 26.1256i | 0.903279 | − | 1.07649i | ||||
\(590\) | 0.734633 | − | 19.3428i | 0.0302444 | − | 0.796332i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.68461 | + | 5.26217i | −0.151437 | + | 0.216274i | ||||
\(593\) | 4.09490 | + | 4.09490i | 0.168157 | + | 0.168157i | 0.786169 | − | 0.618012i | \(-0.212062\pi\) |
−0.618012 | + | 0.786169i | \(0.712062\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.5012 | + | 6.94491i | −0.676481 | + | 0.284714i | ||||
\(596\) | 8.17827 | − | 1.44205i | 0.334995 | − | 0.0590687i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.73357 | + | 3.71765i | −0.0708910 | + | 0.152026i | ||||
\(599\) | −30.3866 | − | 25.4974i | −1.24156 | − | 1.04180i | −0.997400 | − | 0.0720615i | \(-0.977042\pi\) |
−0.244163 | − | 0.969734i | \(-0.578513\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.4811 | − | 8.18244i | −0.917022 | − | 0.333769i | −0.159969 | − | 0.987122i | \(-0.551139\pi\) |
−0.757053 | + | 0.653353i | \(0.773362\pi\) | |||||||
\(602\) | 4.27441 | + | 1.14533i | 0.174212 | + | 0.0466800i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.806976 | + | 0.465908i | 0.0328354 | + | 0.0189575i | ||||
\(605\) | −5.54258 | + | 10.7963i | −0.225338 | + | 0.438931i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.5308 | + | 18.5771i | −1.07685 | + | 0.754020i | −0.970691 | − | 0.240329i | \(-0.922745\pi\) |
−0.106160 | + | 0.994349i | \(0.533856\pi\) | |||||||
\(608\) | −23.0833 | + | 16.1631i | −0.936152 | + | 0.655501i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.03295 | + | 6.32242i | 0.0823116 | + | 0.255987i | ||||
\(611\) | −48.8923 | − | 28.2280i | −1.97797 | − | 1.14198i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.7737 | + | 3.95860i | 0.596704 | + | 0.159886i | 0.544515 | − | 0.838751i | \(-0.316714\pi\) |
0.0521885 | + | 0.998637i | \(0.483380\pi\) | |||||||
\(614\) | −13.5879 | − | 4.94560i | −0.548364 | − | 0.199588i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.9279 | − | 13.3651i | −0.641755 | − | 0.538497i | ||||
\(617\) | −11.3221 | + | 24.2804i | −0.455812 | + | 0.977492i | 0.535325 | + | 0.844646i | \(0.320189\pi\) |
−0.991137 | + | 0.132845i | \(0.957589\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.6300 | − | 3.28497i | 0.748802 | − | 0.132034i | 0.213792 | − | 0.976879i | \(-0.431419\pi\) |
0.535011 | + | 0.844845i | \(0.320308\pi\) | |||||||
\(620\) | −4.22032 | − | 10.0275i | −0.169492 | − | 0.402714i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.88598 | + | 2.88598i | 0.115717 | + | 0.115717i | ||||
\(623\) | −11.0512 | + | 15.7827i | −0.442757 | + | 0.632322i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.08124 | + | 23.2923i | 0.363250 | + | 0.931692i | ||||
\(626\) | −16.7165 | + | 19.9220i | −0.668126 | + | 0.796242i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.8520 | − | 8.32451i | 0.712371 | − | 0.332184i | ||||
\(629\) | −6.11042 | − | 10.5836i | −0.243638 | − | 0.421994i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.0126965 | − | 0.0219910i | 0.000505440 | − | 0.000875448i | −0.865773 | − | 0.500438i | \(-0.833172\pi\) |
0.866278 | + | 0.499562i | \(0.166506\pi\) | |||||||
\(632\) | 3.46961 | − | 39.6578i | 0.138014 | − | 1.57750i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17.1787 | + | 3.02907i | 0.682253 | + | 0.120300i | ||||
\(635\) | 3.89395 | − | 6.18947i | 0.154527 | − | 0.245622i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.34369 | − | 0.642490i | −0.290968 | − | 0.0254564i | ||||
\(638\) | 8.65198 | − | 2.31829i | 0.342535 | − | 0.0917820i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.286754 | + | 2.08659i | 0.0113349 | + | 0.0824797i | ||||
\(641\) | −9.97230 | + | 27.3987i | −0.393882 | + | 1.08218i | 0.571331 | + | 0.820720i | \(0.306427\pi\) |
−0.965214 | + | 0.261463i | \(0.915795\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.74781 | + | 0.152914i | −0.0689270 | + | 0.00603033i | −0.121567 | − | 0.992583i | \(-0.538792\pi\) |
0.0526401 | + | 0.998614i | \(0.483236\pi\) | |||||||
\(644\) | 1.71037 | − | 0.622522i | 0.0673979 | − | 0.0245308i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.14539 | + | 17.8384i | 0.123754 | + | 0.701842i | ||||
\(647\) | −14.7341 | + | 14.7341i | −0.579259 | + | 0.579259i | −0.934699 | − | 0.355440i | \(-0.884331\pi\) |
0.355440 | + | 0.934699i | \(0.384331\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.3315i | 0.758830i | ||||||||
\(650\) | 16.2201 | − | 23.7333i | 0.636206 | − | 0.930896i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.97831 | + | 0.922501i | 0.0774766 | + | 0.0361279i | ||||
\(653\) | −0.812604 | − | 9.28810i | −0.0317996 | − | 0.363471i | −0.995377 | − | 0.0960426i | \(-0.969382\pi\) |
0.963578 | − | 0.267429i | \(-0.0861741\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.160218 | + | 3.24688i | 0.00626023 | + | 0.126866i | ||||
\(656\) | −7.29994 | + | 4.21462i | −0.285015 | + | 0.164553i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.20920 | − | 30.6372i | −0.320028 | − | 1.19436i | ||||
\(659\) | 14.0775 | − | 11.8125i | 0.548383 | − | 0.460148i | −0.326010 | − | 0.945366i | \(-0.605704\pi\) |
0.874393 | + | 0.485218i | \(0.161260\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.43306 | − | 25.1412i | 0.172426 | − | 0.977878i | −0.768647 | − | 0.639674i | \(-0.779070\pi\) |
0.941073 | − | 0.338204i | \(-0.109819\pi\) | |||||||
\(662\) | 12.5159 | + | 17.8745i | 0.486443 | + | 0.694712i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.33923 | + | 11.1301i | 0.362432 | + | 0.431930i | ||||
\(665\) | −24.5211 | − | 31.5839i | −0.950886 | − | 1.22477i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.662829 | + | 2.47371i | −0.0256648 | + | 0.0957825i | ||||
\(668\) | 2.71703 | + | 5.82669i | 0.105125 | + | 0.225441i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16.8615 | + | 5.21146i | 0.651418 | + | 0.201336i | ||||
\(671\) | −2.26847 | − | 6.23257i | −0.0875733 | − | 0.240606i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.83098 | + | 2.68248i | 0.147673 | + | 0.103402i | 0.645078 | − | 0.764117i | \(-0.276825\pi\) |
−0.497405 | + | 0.867518i | \(0.665714\pi\) | |||||||
\(674\) | 11.0600 | 0.426017 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.6331 | 0.562810 | ||||||||
\(677\) | 32.1483 | + | 22.5105i | 1.23556 | + | 0.865147i | 0.994436 | − | 0.105347i | \(-0.0335953\pi\) |
0.241123 | + | 0.970495i | \(0.422484\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.1371 | + | 49.8312i | 0.696038 | + | 1.91235i | ||||
\(680\) | 18.0311 | + | 5.57296i | 0.691462 | + | 0.213713i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.81397 | − | 12.4681i | −0.222628 | − | 0.477428i | ||||
\(683\) | −9.77386 | + | 36.4765i | −0.373986 | + | 1.39574i | 0.480834 | + | 0.876812i | \(0.340334\pi\) |
−0.854820 | + | 0.518924i | \(0.826333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.8799 | − | 28.1820i | −0.835987 | − | 1.07678i | ||||
\(686\) | 11.0866 | + | 13.2125i | 0.423287 | + | 0.504454i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.20944 | − | 1.72726i | −0.0461096 | − | 0.0658513i | ||||
\(689\) | −9.65582 | + | 54.7609i | −0.367858 | + | 2.08622i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.1478 | − | 8.51501i | 0.386040 | − | 0.323926i | −0.429028 | − | 0.903291i | \(-0.641144\pi\) |
0.815068 | + | 0.579365i | \(0.196699\pi\) | |||||||
\(692\) | 4.68292 | + | 17.4769i | 0.178018 | + | 0.664372i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.5198 | + | 6.07363i | −0.399327 | + | 0.230552i | ||||
\(695\) | 1.00580 | + | 20.3830i | 0.0381522 | + | 0.773170i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.39761 | − | 15.9747i | −0.0529381 | − | 0.605086i | ||||
\(698\) | −15.2128 | − | 7.09386i | −0.575814 | − | 0.268507i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.5357 | + | 2.35731i | −0.473805 | + | 0.0890979i | ||||
\(701\) | − | 1.42181i | − | 0.0537011i | −0.999639 | − | 0.0268505i | \(-0.991452\pi\) | ||
0.999639 | − | 0.0268505i | \(-0.00854782\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.3001 | − | 19.3001i | 0.727916 | − | 0.727916i | ||||
\(704\) | 3.16755 | + | 17.9641i | 0.119381 | + | 0.677046i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.62062 | − | 3.13765i | 0.324441 | − | 0.118087i | ||||
\(707\) | −9.69826 | + | 0.848488i | −0.364741 | + | 0.0319107i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.4901 | − | 34.3163i | 0.469077 | − | 1.28878i | −0.449410 | − | 0.893325i | \(-0.648366\pi\) |
0.918487 | − | 0.395452i | \(-0.129412\pi\) | |||||||
\(710\) | 1.57560 | + | 11.4650i | 0.0591313 | + | 0.430274i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 19.6186 | − | 5.25679i | 0.735239 | − | 0.197007i | ||||
\(713\) | 3.91834 | + | 0.342810i | 0.146743 | + | 0.0128384i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.2878 | + | 24.3000i | −0.571730 | + | 0.908770i | ||||
\(716\) | 12.4649 | + | 2.19790i | 0.465836 | + | 0.0821395i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.88008 | + | 21.4894i | −0.0701639 | + | 0.801977i | ||||
\(719\) | −12.9014 | + | 22.3459i | −0.481142 | + | 0.833363i | −0.999766 | − | 0.0216398i | \(-0.993111\pi\) |
0.518624 | + | 0.855003i | \(0.326445\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.24243 | + | 9.08015i | 0.195238 | + | 0.338162i | ||||
\(722\) | −18.4622 | + | 8.60904i | −0.687090 | + | 0.320395i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.17400 | − | 1.39912i | 0.0436314 | − | 0.0519978i | ||||
\(725\) | 7.39982 | − | 16.3507i | 0.274822 | − | 0.607249i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.926059 | + | 1.32255i | −0.0343456 | + | 0.0490507i | −0.835958 | − | 0.548794i | \(-0.815087\pi\) |
0.801612 | + | 0.597845i | \(0.203976\pi\) | |||||||
\(728\) | 33.8736 | + | 33.8736i | 1.25544 | + | 1.25544i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.38948 | − | 15.1814i | −0.236485 | − | 0.561890i | ||||
\(731\) | 3.95045 | − | 0.696570i | 0.146112 | − | 0.0257636i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.62244 | + | 12.0574i | −0.207669 | + | 0.445349i | −0.982362 | − | 0.186990i | \(-0.940127\pi\) |
0.774692 | + | 0.632338i | \(0.217905\pi\) | |||||||
\(734\) | −21.0132 | − | 17.6322i | −0.775613 | − | 0.650816i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.05398 | − | 1.11156i | −0.112571 | − | 0.0409725i | ||||
\(737\) | −17.0249 | − | 4.56182i | −0.627122 | − | 0.168037i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.9063 | + | 17.8437i | 1.13691 | + | 0.656393i | 0.945663 | − | 0.325150i | \(-0.105415\pi\) |
0.191243 | + | 0.981543i | \(0.438748\pi\) | |||||||
\(740\) | −2.66530 | − | 8.28902i | −0.0979784 | − | 0.304711i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −25.5905 | + | 17.9187i | −0.939457 | + | 0.657815i | ||||
\(743\) | 28.8465 | − | 20.1985i | 1.05828 | − | 0.741012i | 0.0912848 | − | 0.995825i | \(-0.470903\pi\) |
0.966990 | + | 0.254813i | \(0.0820138\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.60936 | − | 18.7179i | 0.352060 | − | 0.685769i | ||||
\(746\) | −4.37382 | − | 2.52523i | −0.160137 | − | 0.0924551i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.57411 | − | 1.49358i | −0.203810 | − | 0.0546106i | ||||
\(749\) | −15.4983 | − | 5.64093i | −0.566296 | − | 0.206115i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.0262 | + | 15.9649i | 0.694275 | + | 0.582566i | 0.920138 | − | 0.391593i | \(-0.128076\pi\) |
−0.225864 | + | 0.974159i | \(0.572520\pi\) | |||||||
\(752\) | −6.38726 | + | 13.6975i | −0.232919 | + | 0.499497i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −20.3233 | + | 3.58354i | −0.740130 | + | 0.130505i | ||||
\(755\) | 2.17601 | − | 0.915826i | 0.0791930 | − | 0.0333303i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.8009 | + | 17.8009i | 0.646986 | + | 0.646986i | 0.952263 | − | 0.305278i | \(-0.0987493\pi\) |
−0.305278 | + | 0.952263i | \(0.598749\pi\) | |||||||
\(758\) | −15.3401 | + | 21.9080i | −0.557178 | + | 0.795733i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.59972 | + | 42.1206i | −0.0580281 | + | 1.52788i | ||||
\(761\) | 31.3105 | − | 37.3144i | 1.13500 | − | 1.35265i | 0.207765 | − | 0.978179i | \(-0.433381\pi\) |
0.927240 | − | 0.374467i | \(-0.122174\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −41.4512 | + | 19.3290i | −1.50063 | + | 0.699757i | ||||
\(764\) | 10.2888 | + | 17.8207i | 0.372236 | + | 0.644731i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.51352 | − | 11.2818i | 0.235343 | − | 0.407626i | ||||
\(767\) | 3.88180 | − | 44.3691i | 0.140164 | − | 1.60208i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.1365 | − | 7.60612i | −1.55554 | − | 0.274284i | −0.671254 | − | 0.741227i | \(-0.734244\pi\) |
−0.884287 | + | 0.466944i | \(0.845355\pi\) | |||||||
\(770\) | −15.7268 | + | 3.58026i | −0.566756 | + | 0.129024i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.273968 | + | 0.0239691i | 0.00986034 | + | 0.000862668i | ||||
\(773\) | 22.0592 | − | 5.91076i | 0.793416 | − | 0.212595i | 0.160725 | − | 0.986999i | \(-0.448617\pi\) |
0.632691 | + | 0.774404i | \(0.281950\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.7045 | − | 6.83173i | −0.959252 | − | 0.245403i | ||||
\(776\) | 19.1194 | − | 52.5302i | 0.686347 | − | 1.88572i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.39502 | − | 0.821958i | 0.336828 | − | 0.0294686i | ||||
\(779\) | 33.6549 | − | 12.2494i | 1.20581 | − | 0.438879i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.00697 | − | 11.3821i | −0.0718150 | − | 0.407283i | ||||
\(782\) | −1.47719 | + | 1.47719i | −0.0528241 | + | 0.0528241i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.97345i | 0.0704805i | ||||||||
\(785\) | 10.5251 | − | 48.7837i | 0.375659 | − | 1.74116i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.6093 | − | 7.27876i | −0.556413 | − | 0.259460i | 0.124008 | − | 0.992281i | \(-0.460425\pi\) |
−0.680421 | + | 0.732822i | \(0.738203\pi\) | |||||||
\(788\) | −0.249868 | − | 2.85601i | −0.00890119 | − | 0.101741i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −22.8859 | − | 20.7335i | −0.814243 | − | 0.737664i | ||||
\(791\) | 6.68122 | − | 3.85740i | 0.237557 | − | 0.137153i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.95501 | + | 14.7603i | 0.140447 | + | 0.524154i | ||||
\(794\) | −11.0377 | + | 9.26170i | −0.391712 | + | 0.328685i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.977323 | − | 5.54267i | 0.0346403 | − | 0.196455i | ||||
\(797\) | −18.8617 | − | 26.9373i | −0.668115 | − | 0.954166i | −0.999941 | − | 0.0108262i | \(-0.996554\pi\) |
0.331827 | − | 0.943340i | \(-0.392335\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.4814 | − | 22.0252i | −0.653824 | − | 0.779197i | ||||
\(800\) | 19.8522 | + | 11.1634i | 0.701883 | + | 0.394685i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.802775 | − | 2.99600i | 0.0283470 | − | 0.105792i | ||||
\(803\) | 6.95197 | + | 14.9085i | 0.245330 | + | 0.526111i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.36175 | − | 4.40591i | 0.0479954 | − | 0.155288i | ||||
\(806\) | 10.8404 | + | 29.7838i | 0.381838 | + | 1.04909i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.40661 | + | 5.88637i | 0.295744 | + | 0.207082i | ||||
\(809\) | 0.589848 | 0.0207379 | 0.0103690 | − | 0.999946i | \(-0.496699\pi\) | ||||
0.0103690 | + | 0.999946i | \(0.496699\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.5224 | −1.70385 | −0.851925 | − | 0.523664i | \(-0.824565\pi\) | ||||
−0.851925 | + | 0.523664i | \(0.824565\pi\) | |||||||
\(812\) | 7.50095 | + | 5.25222i | 0.263232 | + | 0.184317i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.76564 | − | 10.3460i | −0.131985 | − | 0.362627i | ||||
\(815\) | 4.89102 | − | 2.58147i | 0.171325 | − | 0.0904249i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.78631 | + | 8.11977i | 0.132466 | + | 0.284075i | ||||
\(818\) | 7.84316 | − | 29.2711i | 0.274230 | − | 1.02344i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.42699 | − | 11.3355i | 0.0498327 | − | 0.395854i | ||||
\(821\) | −12.3182 | − | 14.6802i | −0.429907 | − | 0.512343i | 0.506989 | − | 0.861953i | \(-0.330759\pi\) |
−0.936895 | + | 0.349610i | \(0.886314\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.358433 | − | 0.511895i | −0.0124942 | − | 0.0178435i | 0.812856 | − | 0.582464i | \(-0.197911\pi\) |
−0.825351 | + | 0.564621i | \(0.809022\pi\) | |||||||
\(824\) | 1.91929 | − | 10.8848i | 0.0668615 | − | 0.379190i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.1684 | − | 16.0842i | 0.666954 | − | 0.559641i | ||||
\(827\) | −3.05127 | − | 11.3875i | −0.106103 | − | 0.395981i | 0.892365 | − | 0.451314i | \(-0.149045\pi\) |
−0.998468 | + | 0.0553328i | \(0.982378\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.0844 | + | 21.9880i | −1.32272 | + | 0.763675i | −0.984163 | − | 0.177269i | \(-0.943274\pi\) |
−0.338562 | + | 0.940944i | \(0.609941\pi\) | |||||||
\(830\) | 11.2570 | − | 0.555479i | 0.390736 | − | 0.0192809i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.66285 | − | 41.8666i | −0.126986 | − | 1.45146i | ||||
\(833\) | −3.40254 | − | 1.58663i | −0.117891 | − | 0.0549735i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.9225 | + | 3.43529i | 0.551019 | + | 0.118883i | ||||
\(836\) | − | 12.8886i | − | 0.445761i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.93659 | + | 9.93659i | −0.343254 | + | 0.343254i | ||||
\(839\) | −0.173429 | − | 0.983567i | −0.00598745 | − | 0.0339565i | 0.981668 | − | 0.190601i | \(-0.0610435\pi\) |
−0.987655 | + | 0.156644i | \(0.949932\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.1440 | − | 5.51197i | 0.522207 | − | 0.190068i | ||||
\(842\) | −9.53258 | + | 0.833993i | −0.328514 | + | 0.0287413i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.93642 | − | 5.32028i | 0.0666545 | − | 0.183132i | ||||
\(845\) | 22.4025 | − | 29.5410i | 0.770671 | − | 1.01624i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.1535 | + | 4.06038i | −0.520682 | + | 0.139516i | ||||
\(848\) | 14.8293 | + | 1.29739i | 0.509239 | + | 0.0445527i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 11.8964 | − | 8.53268i | 0.408043 | − | 0.292668i | ||||
\(851\) | 3.10007 | + | 0.546626i | 0.106269 | + | 0.0187381i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.394403 | − | 4.50805i | 0.0135041 | − | 0.154353i | −0.986449 | − | 0.164070i | \(-0.947538\pi\) |
0.999953 | + | 0.00971747i | \(0.00309322\pi\) | |||||||
\(854\) | −4.29256 | + | 7.43494i | −0.146889 | + | 0.254418i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.69313 | + | 15.0569i | 0.297125 | + | 0.514635i | ||||
\(857\) | −51.8892 | + | 24.1963i | −1.77250 | + | 0.826531i | −0.797831 | + | 0.602881i | \(0.794019\pi\) |
−0.974670 | + | 0.223650i | \(0.928203\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.9711 | − | 24.9924i | 0.715526 | − | 0.852730i | −0.278662 | − | 0.960389i | \(-0.589891\pi\) |
0.994188 | + | 0.107659i | \(0.0343354\pi\) | |||||||
\(860\) | 2.85594 | + | 0.108467i | 0.0973867 | + | 0.00369871i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.179453 | + | 0.256286i | −0.00611220 | + | 0.00872913i | ||||
\(863\) | −28.5706 | − | 28.5706i | −0.972554 | − | 0.972554i | 0.0270792 | − | 0.999633i | \(-0.491379\pi\) |
−0.999633 | + | 0.0270792i | \(0.991379\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 42.4513 | + | 17.3025i | 1.44339 | + | 0.588302i | ||||
\(866\) | −18.8698 | + | 3.32726i | −0.641223 | + | 0.113065i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.94365 | − | 12.7462i | 0.201741 | − | 0.432634i | ||||
\(869\) | 23.6254 | + | 19.8241i | 0.801437 | + | 0.672486i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.1591 | + | 13.8888i | 1.29297 | + | 0.470603i | ||||
\(872\) | 46.5707 | + | 12.4786i | 1.57708 | + | 0.422578i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.04068 | − | 2.33289i | −0.136678 | − | 0.0789111i | ||||
\(875\) | −14.4327 | + | 28.9158i | −0.487914 | + | 0.977532i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.1215 | + | 20.3911i | −0.983364 | + | 0.688559i | −0.950443 | − | 0.310899i | \(-0.899370\pi\) |
−0.0329214 | + | 0.999458i | \(0.510481\pi\) | |||||||
\(878\) | 24.7062 | − | 17.2994i | 0.833792 | − | 0.583828i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.83718 | + | 3.51007i | 0.230481 | + | 0.118324i | ||||
\(881\) | 30.9752 | + | 17.8836i | 1.04358 | + | 0.602512i | 0.920846 | − | 0.389927i | \(-0.127500\pi\) |
0.122736 | + | 0.992439i | \(0.460833\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.38029 | − | 0.905746i | −0.113756 | − | 0.0304808i | 0.201492 | − | 0.979490i | \(-0.435421\pi\) |
−0.315248 | + | 0.949009i | \(0.602088\pi\) | |||||||
\(884\) | 12.4936 | + | 4.54730i | 0.420205 | + | 0.152942i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.6492 | − | 27.3959i | −1.09687 | − | 0.920383i | ||||
\(887\) | −12.0260 | + | 25.7899i | −0.403794 | + | 0.865939i | 0.594301 | + | 0.804243i | \(0.297429\pi\) |
−0.998095 | + | 0.0616962i | \(0.980349\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.30926 | − | 1.64147i | 0.312222 | − | 0.0550532i | ||||
\(890\) | 5.94671 | − | 14.5902i | 0.199334 | − | 0.489063i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.48285 | + | 6.48285i | 0.217062 | + | 0.217062i | ||||
\(893\) | 36.8325 | − | 52.6023i | 1.23255 | − | 1.76027i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.5203 | − | 21.7991i | 0.786197 | − | 0.728663i | ||||
\(896\) | −1.75011 | + | 2.08570i | −0.0584672 | + | 0.0696785i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.49641 | + | 3.49564i | −0.250159 | + | 0.116651i | ||||
\(899\) | 9.89411 | + | 17.1371i | 0.329987 | + | 0.571554i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.1594 | + | 24.5249i | −0.471719 | + | 0.817042i | ||||
\(902\) | 1.25913 | − | 14.3919i | 0.0419245 | − | 0.479199i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.00909 | − | 1.41222i | −0.266378 | − | 0.0469697i | ||||
\(905\) | −1.02718 | − | 4.51203i | −0.0341445 | − | 0.149985i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.6761 | + | 2.85879i | 1.08499 | + | 0.0949246i | 0.615596 | − | 0.788062i | \(-0.288915\pi\) |
0.469398 | + | 0.882987i | \(0.344471\pi\) | |||||||
\(908\) | 2.66344 | − | 0.713667i | 0.0883894 | − | 0.0236839i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 36.8147 | − | 5.05933i | 1.22039 | − | 0.167715i | ||||
\(911\) | −9.92857 | + | 27.2785i | −0.328948 | + | 0.903778i | 0.659430 | + | 0.751766i | \(0.270798\pi\) |
−0.988379 | + | 0.152012i | \(0.951425\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.2132 | + | 0.981025i | −0.371102 | + | 0.0324672i | ||||
\(914\) | 5.44427 | − | 1.98155i | 0.180080 | − | 0.0655439i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.60050 | − | 20.4195i | −0.118964 | − | 0.674678i | ||||
\(917\) | −2.97152 | + | 2.97152i | −0.0981282 | + | 0.0981282i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 28.2931i | − | 0.933302i | −0.884442 | − | 0.466651i | \(-0.845460\pi\) | ||
0.884442 | − | 0.466651i | \(-0.154540\pi\) | |||||||
\(920\) | −4.08511 | + | 2.63520i | −0.134682 | + | 0.0868798i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 28.8814 | + | 13.4676i | 0.951159 | + | 0.443533i | ||||
\(923\) | 2.32080 | + | 26.5268i | 0.0763899 | + | 0.873141i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.8142 | − | 7.30944i | −0.684366 | − | 0.240333i | ||||
\(926\) | −0.165049 | + | 0.0952911i | −0.00542385 | + | 0.00313146i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.23180 | − | 15.7933i | −0.138916 | − | 0.518440i | ||||
\(929\) | −25.1788 | + | 21.1275i | −0.826089 | + | 0.693171i | −0.954390 | − | 0.298564i | \(-0.903492\pi\) |
0.128300 | + | 0.991735i | \(0.459048\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.45603 | − | 8.25757i | 0.0477195 | − | 0.270631i | ||||
\(932\) | −1.67917 | − | 2.39811i | −0.0550032 | − | 0.0785527i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.57623 | − | 10.2208i | −0.280623 | − | 0.334433i | ||||
\(935\) | −11.5489 | + | 8.96631i | −0.377690 | + | 0.293230i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.30584 | + | 4.87347i | −0.0426600 | + | 0.159209i | −0.983970 | − | 0.178334i | \(-0.942929\pi\) |
0.941310 | + | 0.337543i | \(0.109596\pi\) | |||||||
\(938\) | 9.64174 | + | 20.6768i | 0.314814 | + | 0.675121i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.56179 | − | 18.1164i | −0.311871 | − | 0.590892i | ||||
\(941\) | −19.6715 | − | 54.0471i | −0.641274 | − | 1.76189i | −0.647687 | − | 0.761906i | \(-0.724264\pi\) |
0.00641343 | − | 0.999979i | \(-0.497959\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.38355 | + | 2.36919i | 0.110184 | + | 0.0771514i | ||||
\(944\) | −11.9232 | −0.388068 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.61394 | 0.117499 | ||||||||
\(947\) | 26.3740 | + | 18.4673i | 0.857041 | + | 0.600107i | 0.917354 | − | 0.398073i | \(-0.130321\pi\) |
−0.0603125 | + | 0.998180i | \(0.519210\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.9623 | − | 35.6136i | −0.420773 | − | 1.15607i | ||||
\(950\) | 25.2846 | + | 20.7321i | 0.820341 | + | 0.672638i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.3105 | + | 22.1110i | 0.334167 | + | 0.716623i | ||||
\(953\) | 5.59819 | − | 20.8927i | 0.181343 | − | 0.676782i | −0.814041 | − | 0.580808i | \(-0.802737\pi\) |
0.995384 | − | 0.0959743i | \(-0.0305967\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 51.7278 | + | 6.51184i | 1.67387 | + | 0.210718i | ||||
\(956\) | −9.64940 | − | 11.4997i | −0.312084 | − | 0.371927i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.6105 | − | 30.8629i | −0.698202 | − | 0.997136i | ||||
\(959\) | 8.00894 | − | 45.4210i | 0.258622 | − | 1.46672i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.465741 | + | 0.390803i | −0.0150239 | + | 0.0126065i | ||||
\(962\) | 6.56528 | + | 24.5020i | 0.211673 | + | 0.789975i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.1830 | − | 8.18857i | 0.456804 | − | 0.263736i | ||||
\(965\) | 0.467821 | − | 0.516387i | 0.0150597 | − | 0.0166231i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.961701 | + | 10.9923i | 0.0309262 | + | 0.353488i | 0.995854 | + | 0.0909711i | \(0.0289971\pi\) |
−0.964927 | + | 0.262517i | \(0.915447\pi\) | |||||||
\(968\) | 14.9883 | + | 6.98917i | 0.481743 | + | 0.224640i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23.5066 | − | 36.4402i | −0.754751 | − | 1.17002i | ||||
\(971\) | 21.9387i | 0.704047i | 0.935991 | + | 0.352023i | \(0.114506\pi\) | ||||
−0.935991 | + | 0.352023i | \(0.885494\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.6543 | + | 18.6543i | −0.598030 | + | 0.598030i | ||||
\(974\) | −1.26918 | − | 7.19790i | −0.0406673 | − | 0.230635i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.84410 | − | 1.39914i | 0.123046 | − | 0.0447853i | ||||
\(977\) | 5.48124 | − | 0.479546i | 0.175360 | − | 0.0153420i | 0.000862648 | − | 1.00000i | \(-0.499725\pi\) |
0.174498 | + | 0.984658i | \(0.444170\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.38167 | + | 14.7860i | −0.171999 | + | 0.472563i | ||||
\(980\) | −2.13128 | − | 1.61627i | −0.0680812 | − | 0.0516297i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −26.5176 | + | 7.10536i | −0.846209 | + | 0.226741i | ||||
\(983\) | 27.3904 | + | 2.39635i | 0.873618 | + | 0.0764316i | 0.515139 | − | 0.857106i | \(-0.327740\pi\) |
0.358478 | + | 0.933538i | \(0.383296\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.14819 | − | 3.86798i | −0.195898 | − | 0.123244i | ||||
\(986\) | −10.3502 | − | 1.82503i | −0.329619 | − | 0.0581207i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.58804 | + | 29.5815i | −0.0823366 | + | 0.941111i | ||||
\(989\) | −0.516635 | + | 0.894838i | −0.0164280 | + | 0.0284542i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.95205 | + | 13.7734i | 0.252605 | + | 0.437525i | 0.964242 | − | 0.265022i | \(-0.0853793\pi\) |
−0.711637 | + | 0.702547i | \(0.752046\pi\) | |||||||
\(992\) | −22.7592 | + | 10.6128i | −0.722606 | + | 0.336956i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.61620 | + | 11.4601i | −0.305007 | + | 0.363494i | ||||
\(995\) | −9.69322 | − | 10.4586i | −0.307296 | − | 0.331559i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.10376 | + | 3.00447i | −0.0666266 | + | 0.0951527i | −0.851083 | − | 0.525032i | \(-0.824053\pi\) |
0.784456 | + | 0.620185i | \(0.212942\pi\) | |||||||
\(998\) | −8.38532 | − | 8.38532i | −0.265433 | − | 0.265433i | ||||
\(999\) | 0 | 0 |
(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 | 405.2.r.a.152.5 | 192 | ||
3.2 | odd | 2 | 135.2.q.a.122.12 | yes | 192 | ||
5.3 | odd | 4 | inner | 405.2.r.a.233.5 | 192 | ||
15.2 | even | 4 | 675.2.ba.b.68.5 | 192 | |||
15.8 | even | 4 | 135.2.q.a.68.12 | yes | 192 | ||
15.14 | odd | 2 | 675.2.ba.b.257.5 | 192 | |||
27.2 | odd | 18 | inner | 405.2.r.a.332.5 | 192 | ||
27.25 | even | 9 | 135.2.q.a.2.12 | ✓ | 192 | ||
135.52 | odd | 36 | 675.2.ba.b.218.5 | 192 | |||
135.79 | even | 18 | 675.2.ba.b.407.5 | 192 | |||
135.83 | even | 36 | inner | 405.2.r.a.8.5 | 192 | ||
135.133 | odd | 36 | 135.2.q.a.83.12 | yes | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.q.a.2.12 | ✓ | 192 | 27.25 | even | 9 | ||
135.2.q.a.68.12 | yes | 192 | 15.8 | even | 4 | ||
135.2.q.a.83.12 | yes | 192 | 135.133 | odd | 36 | ||
135.2.q.a.122.12 | yes | 192 | 3.2 | odd | 2 | ||
405.2.r.a.8.5 | 192 | 135.83 | even | 36 | inner | ||
405.2.r.a.152.5 | 192 | 1.1 | even | 1 | trivial | ||
405.2.r.a.233.5 | 192 | 5.3 | odd | 4 | inner | ||
405.2.r.a.332.5 | 192 | 27.2 | odd | 18 | inner | ||
675.2.ba.b.68.5 | 192 | 15.2 | even | 4 | |||
675.2.ba.b.218.5 | 192 | 135.52 | odd | 36 | |||
675.2.ba.b.257.5 | 192 | 15.14 | odd | 2 | |||
675.2.ba.b.407.5 | 192 | 135.79 | even | 18 |