Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [968,2,Mod(9,968)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(968, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("968.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 968 = 2^{3} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 968.i (of order \(5\), degree \(4\), 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: | \(7.72951891566\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 88) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 9.1 | ||
Root | \(-0.309017 - 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 968.9 |
Dual form | 968.2.i.j.753.1 |
$q$-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 \(\left(\mathbb{Z}/968\mathbb{Z}\right)^\times\).
\(n\) | \(485\) | \(727\) | \(849\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 | 0 | ||||||||
\(3\) | 2.42705 | − | 1.76336i | 1.40126 | − | 1.01807i | 0.406737 | − | 0.913545i | \(-0.366667\pi\) |
0.994522 | − | 0.104528i | \(-0.0333333\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.927051 | − | 2.85317i | −0.414590 | − | 1.27598i | −0.912617 | − | 0.408815i | \(-0.865942\pi\) |
0.498027 | − | 0.867161i | \(-0.334058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.61803 | + | 1.17557i | 0.611559 | + | 0.444324i | 0.849963 | − | 0.526842i | \(-0.176624\pi\) |
−0.238404 | + | 0.971166i | \(0.576624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.85410 | − | 5.70634i | 0.618034 | − | 1.90211i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.28115 | − | 5.29007i | −1.87999 | − | 1.36589i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.85410 | − | 5.70634i | −0.449686 | − | 1.38399i | −0.877262 | − | 0.480011i | \(-0.840633\pi\) |
0.427576 | − | 0.903979i | \(-0.359367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.23607 | + | 2.35114i | −0.742405 | + | 0.539389i | −0.893463 | − | 0.449136i | \(-0.851732\pi\) |
0.151058 | + | 0.988525i | \(0.451732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.00000 | 1.30931 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | 0.104257 | − | 0.994550i | \(-0.466753\pi\) | ||||
0.104257 | + | 0.994550i | \(0.466753\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.23607 | + | 2.35114i | −0.647214 | + | 0.470228i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.78115 | − | 8.55951i | −0.535233 | − | 1.64728i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.47214 | + | 4.70228i | 1.20185 | + | 0.873192i | 0.994465 | − | 0.105069i | \(-0.0335062\pi\) |
0.207380 | + | 0.978260i | \(0.433506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.16312 | + | 6.65740i | −0.388508 | + | 1.19570i | 0.545396 | + | 0.838179i | \(0.316379\pi\) |
−0.933904 | + | 0.357525i | \(0.883621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.85410 | − | 5.70634i | 0.313400 | − | 0.964547i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.809017 | + | 0.587785i | 0.133002 | + | 0.0966313i | 0.652297 | − | 0.757964i | \(-0.273806\pi\) |
−0.519295 | + | 0.854595i | \(0.673806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.23607 | + | 2.35114i | −0.505389 | + | 0.367187i | −0.811072 | − | 0.584947i | \(-0.801115\pi\) |
0.305683 | + | 0.952133i | \(0.401115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000 | 0.914991 | 0.457496 | − | 0.889212i | \(-0.348747\pi\) | ||||
0.457496 | + | 0.889212i | \(0.348747\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −18.0000 | −2.68328 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.47214 | − | 4.70228i | 0.944058 | − | 0.685898i | −0.00533600 | − | 0.999986i | \(-0.501699\pi\) |
0.949394 | + | 0.314087i | \(0.101699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.927051 | − | 2.85317i | −0.132436 | − | 0.407596i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −14.5623 | − | 10.5801i | −2.03913 | − | 1.48152i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.618034 | − | 1.90211i | 0.0848935 | − | 0.261275i | −0.899595 | − | 0.436726i | \(-0.856138\pi\) |
0.984488 | + | 0.175450i | \(0.0561381\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.70820 | + | 11.4127i | −0.491164 | + | 1.51165i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.809017 | + | 0.587785i | 0.105325 | + | 0.0765231i | 0.639201 | − | 0.769040i | \(-0.279265\pi\) |
−0.533876 | + | 0.845563i | \(0.679265\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.23607 | + | 3.80423i | 0.158262 | + | 0.487081i | 0.998477 | − | 0.0551729i | \(-0.0175710\pi\) |
−0.840215 | + | 0.542254i | \(0.817571\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.70820 | − | 7.05342i | 1.22312 | − | 0.888648i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | −0.610847 | −0.305424 | − | 0.952217i | \(-0.598798\pi\) | ||||
−0.305424 | + | 0.952217i | \(0.598798\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.42705 | − | 1.76336i | 0.292183 | − | 0.212283i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.927051 | + | 2.85317i | 0.110021 | + | 0.338609i | 0.990876 | − | 0.134777i | \(-0.0430317\pi\) |
−0.880855 | + | 0.473386i | \(0.843032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.9443 | − | 9.40456i | −1.51501 | − | 1.10072i | −0.963891 | − | 0.266296i | \(-0.914200\pi\) |
−0.551121 | − | 0.834425i | \(-0.685800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.70820 | + | 11.4127i | −0.428187 | + | 1.31782i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.618034 | − | 1.90211i | 0.0695343 | − | 0.214004i | −0.910251 | − | 0.414057i | \(-0.864111\pi\) |
0.979785 | + | 0.200053i | \(0.0641114\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.28115 | − | 5.29007i | −0.809017 | − | 0.587785i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.618034 | − | 1.90211i | −0.0678380 | − | 0.208784i | 0.911391 | − | 0.411542i | \(-0.135010\pi\) |
−0.979229 | + | 0.202758i | \(0.935010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.5623 | + | 10.5801i | −1.57950 | + | 1.14758i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 24.0000 | 2.57307 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.0000 | 1.59000 | 0.794998 | − | 0.606612i | \(-0.207472\pi\) | ||||
0.794998 | + | 0.606612i | \(0.207472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.48936 | + | 19.9722i | 0.672915 | + | 2.07102i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.70820 | + | 7.05342i | 0.996041 | + | 0.723666i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.16312 | + | 6.65740i | −0.219631 | + | 0.675956i | 0.779161 | + | 0.626824i | \(0.215646\pi\) |
−0.998792 | + | 0.0491321i | \(0.984354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.09017 | + | 9.51057i | −0.307483 | + | 0.946337i | 0.671255 | + | 0.741226i | \(0.265755\pi\) |
−0.978739 | + | 0.205110i | \(0.934245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.9443 | + | 9.40456i | 1.27544 | + | 0.926659i | 0.999405 | − | 0.0344892i | \(-0.0109804\pi\) |
0.276032 | + | 0.961148i | \(0.410980\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.56231 | − | 17.1190i | −0.542825 | − | 1.67065i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.61803 | + | 1.17557i | −0.156421 | + | 0.113647i | −0.663243 | − | 0.748404i | \(-0.730820\pi\) |
0.506822 | + | 0.862051i | \(0.330820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.00000 | 0.284747 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.66312 | − | 4.11450i | 0.532741 | − | 0.387059i | −0.288641 | − | 0.957437i | \(-0.593203\pi\) |
0.821382 | + | 0.570378i | \(0.193203\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.927051 | − | 2.85317i | −0.0864479 | − | 0.266059i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.70820 | − | 11.4127i | 0.339930 | − | 1.04620i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.70820 | + | 11.4127i | −0.334357 | + | 1.02905i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.42705 | − | 1.76336i | −0.217082 | − | 0.157719i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.23607 | + | 3.80423i | 0.109683 | + | 0.337570i | 0.990801 | − | 0.135326i | \(-0.0432083\pi\) |
−0.881118 | + | 0.472897i | \(0.843208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.5623 | − | 10.5801i | 1.28214 | − | 0.931529i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.00000 | −0.174741 | −0.0873704 | − | 0.996176i | \(-0.527846\pi\) | ||||
−0.0873704 | + | 0.996176i | \(0.527846\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −21.8435 | + | 15.8702i | −1.87999 | + | 1.36589i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.63525 | − | 14.2658i | −0.396017 | − | 1.21881i | −0.928167 | − | 0.372164i | \(-0.878616\pi\) |
0.532150 | − | 0.846650i | \(-0.321384\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.7984 | + | 12.9313i | 1.50964 | + | 1.09682i | 0.966337 | + | 0.257279i | \(0.0828258\pi\) |
0.543301 | + | 0.839538i | \(0.317174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.41641 | − | 22.8254i | 0.624574 | − | 1.92224i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.41641 | − | 22.8254i | 0.615899 | − | 1.89554i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.28115 | − | 5.29007i | −0.600539 | − | 0.436317i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.56231 | + | 17.1190i | 0.455682 | + | 1.40244i | 0.870333 | + | 0.492464i | \(0.163904\pi\) |
−0.414651 | + | 0.909981i | \(0.636096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.5623 | − | 10.5801i | 1.18506 | − | 0.860999i | 0.192330 | − | 0.981330i | \(-0.438396\pi\) |
0.992734 | + | 0.120331i | \(0.0383957\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −36.0000 | −2.91043 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.0000 | 1.68676 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.89919 | − | 6.46564i | 0.710232 | − | 0.516014i | −0.173016 | − | 0.984919i | \(-0.555351\pi\) |
0.883249 | + | 0.468905i | \(0.155351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.85410 | − | 5.70634i | −0.147040 | − | 0.452542i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.61803 | + | 1.17557i | 0.127519 | + | 0.0926479i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.23607 | + | 3.80423i | −0.0968163 | + | 0.297970i | −0.987723 | − | 0.156217i | \(-0.950070\pi\) |
0.890906 | + | 0.454187i | \(0.150070\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.94427 | − | 15.2169i | 0.382599 | − | 1.17752i | −0.555608 | − | 0.831445i | \(-0.687514\pi\) |
0.938207 | − | 0.346075i | \(-0.112486\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5172 | + | 7.64121i | 0.809017 | + | 0.587785i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.41641 | + | 22.8254i | 0.567147 | + | 1.74550i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.5623 | + | 10.5801i | −1.10715 | + | 0.804393i | −0.982213 | − | 0.187772i | \(-0.939873\pi\) |
−0.124939 | + | 0.992164i | \(0.539873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.00000 | −0.604743 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.00000 | 0.225494 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.04508 | − | 2.93893i | 0.302344 | − | 0.219666i | −0.426261 | − | 0.904600i | \(-0.640169\pi\) |
0.728604 | + | 0.684935i | \(0.240169\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.54508 | − | 4.75528i | −0.114845 | − | 0.353457i | 0.877069 | − | 0.480364i | \(-0.159495\pi\) |
−0.991915 | + | 0.126906i | \(0.959495\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.70820 | + | 7.05342i | 0.717651 | + | 0.521404i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.927051 | − | 2.85317i | 0.0681581 | − | 0.209769i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.56231 | − | 17.1190i | 0.404598 | − | 1.24523i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.28115 | + | 5.29007i | 0.526846 | + | 0.382776i | 0.819177 | − | 0.573541i | \(-0.194431\pi\) |
−0.292331 | + | 0.956317i | \(0.594431\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.23607 | + | 3.80423i | 0.0889741 | + | 0.273834i | 0.985636 | − | 0.168881i | \(-0.0540153\pi\) |
−0.896662 | + | 0.442715i | \(0.854015\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.1353 | + | 8.81678i | −0.855955 | + | 0.621888i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.94427 | + | 15.2169i | 0.347020 | + | 1.06802i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.70820 | + | 7.05342i | 0.678050 | + | 0.492632i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.85410 | − | 5.70634i | 0.128869 | − | 0.396618i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.18034 | − | 19.0211i | 0.425472 | − | 1.30947i | −0.477069 | − | 0.878866i | \(-0.658301\pi\) |
0.902541 | − | 0.430603i | \(-0.141699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.28115 | + | 5.29007i | 0.498896 | + | 0.362469i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.56231 | − | 17.1190i | −0.379346 | − | 1.16751i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.3262 | + | 8.22899i | −0.768875 | + | 0.558620i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −48.0000 | −3.24354 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.4615 | + | 17.0458i | −1.57110 | + | 1.14147i | −0.645002 | + | 0.764181i | \(0.723143\pi\) |
−0.926096 | + | 0.377288i | \(0.876857\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.41641 | + | 22.8254i | 0.494427 | + | 1.52169i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.5623 | − | 10.5801i | −0.966534 | − | 0.702228i | −0.0118751 | − | 0.999929i | \(-0.503780\pi\) |
−0.954659 | + | 0.297701i | \(0.903780\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.48936 | + | 19.9722i | −0.428829 | + | 1.31980i | 0.470451 | + | 0.882426i | \(0.344091\pi\) |
−0.899280 | + | 0.437373i | \(0.855909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.94427 | + | 15.2169i | −0.323910 | + | 0.996893i | 0.648020 | + | 0.761623i | \(0.275597\pi\) |
−0.971930 | + | 0.235269i | \(0.924403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.4164 | − | 14.1068i | −1.26659 | − | 0.920229i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.85410 | − | 5.70634i | −0.120437 | − | 0.370667i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.61803 | − | 1.17557i | 0.104662 | − | 0.0760413i | −0.534223 | − | 0.845343i | \(-0.679396\pi\) |
0.638885 | + | 0.769302i | \(0.279396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.28115 | + | 5.29007i | −0.465176 | + | 0.337970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.85410 | − | 3.52671i | −0.307616 | − | 0.223496i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.01722 | + | 12.3637i | −0.253565 | + | 0.780392i | 0.740544 | + | 0.672008i | \(0.234568\pi\) |
−0.994109 | + | 0.108384i | \(0.965432\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.6869 | + | 51.3571i | −1.04498 | + | 3.21610i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.09017 | + | 5.87785i | 0.504651 | + | 0.366650i | 0.810791 | − | 0.585336i | \(-0.199037\pi\) |
−0.306140 | + | 0.951987i | \(0.599037\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.618034 | + | 1.90211i | 0.0384028 | + | 0.118192i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 38.8328 | − | 28.2137i | 2.40369 | − | 1.74638i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.0000 | 0.863277 | 0.431638 | − | 0.902047i | \(-0.357936\pi\) | ||||
0.431638 | + | 0.902047i | \(0.357936\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 36.4058 | − | 26.4503i | 2.22800 | − | 1.61873i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.03444 | + | 24.7275i | 0.489869 | + | 1.50766i | 0.824804 | + | 0.565419i | \(0.191286\pi\) |
−0.334935 | + | 0.942241i | \(0.608714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.618034 | + | 1.90211i | −0.0371341 | + | 0.114287i | −0.967905 | − | 0.251315i | \(-0.919137\pi\) |
0.930771 | + | 0.365602i | \(0.119137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 33.9787 | + | 24.6870i | 2.03425 | + | 1.47797i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.85410 | + | 5.70634i | 0.110606 | + | 0.340412i | 0.991005 | − | 0.133822i | \(-0.0427251\pi\) |
−0.880399 | + | 0.474234i | \(0.842725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.23607 | + | 2.35114i | −0.192364 | + | 0.139761i | −0.679799 | − | 0.733399i | \(-0.737933\pi\) |
0.487434 | + | 0.873160i | \(0.337933\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 36.0000 | 2.13246 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.00000 | −0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.3713 | + | 11.1679i | −0.904195 | + | 0.656936i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.48936 | + | 19.9722i | 0.380413 | + | 1.17079i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.70820 | − | 7.05342i | −0.567159 | − | 0.412065i | 0.266913 | − | 0.963721i | \(-0.413996\pi\) |
−0.834072 | + | 0.551655i | \(0.813996\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.927051 | − | 2.85317i | 0.0539750 | − | 0.166118i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.70820 | + | 7.05342i | 0.559572 | + | 0.406553i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.27051 | + | 28.5317i | 0.532577 | + | 1.63910i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.70820 | − | 7.05342i | 0.555890 | − | 0.403878i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.00000 | −0.228292 | −0.114146 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114146 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 48.0000 | 2.73062 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.70820 | − | 7.05342i | 0.550502 | − | 0.399963i | −0.277469 | − | 0.960735i | \(-0.589495\pi\) |
0.827970 | + | 0.560772i | \(0.189495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.78115 | − | 8.55951i | −0.157200 | − | 0.483812i | 0.841177 | − | 0.540760i | \(-0.181863\pi\) |
−0.998377 | + | 0.0569477i | \(0.981863\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −29.1246 | − | 21.1603i | −1.64099 | − | 1.19225i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.63525 | + | 14.2658i | −0.260342 | + | 0.801250i | 0.732388 | + | 0.680887i | \(0.238406\pi\) |
−0.992730 | + | 0.120362i | \(0.961594\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.85410 | + | 5.70634i | −0.103486 | + | 0.318497i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.4164 | + | 14.1068i | 1.08036 | + | 0.784926i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −33.9787 | + | 24.6870i | −1.87903 | + | 1.36519i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.0000 | 0.882109 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.0000 | −1.92377 | −0.961887 | − | 0.273447i | \(-0.911836\pi\) | ||||
−0.961887 | + | 0.273447i | \(0.911836\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.85410 | − | 3.52671i | 0.266003 | − | 0.193263i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.63525 | + | 14.2658i | 0.253251 | + | 0.779427i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.09017 | + | 5.87785i | 0.440700 | + | 0.320187i | 0.785913 | − | 0.618337i | \(-0.212193\pi\) |
−0.345213 | + | 0.938524i | \(0.612193\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.48936 | − | 19.9722i | 0.352453 | − | 1.08474i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.18034 | − | 19.0211i | 0.333707 | − | 1.02704i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.28115 | − | 5.29007i | −0.392004 | − | 0.284808i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.88854 | − | 30.4338i | −0.530845 | − | 1.63377i | −0.752460 | − | 0.658638i | \(-0.771133\pi\) |
0.221615 | − | 0.975134i | \(-0.428867\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.3262 | − | 8.22899i | 0.606280 | − | 0.440488i | −0.241823 | − | 0.970320i | \(-0.577745\pi\) |
0.848102 | + | 0.529833i | \(0.177745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.00000 | 0.159674 | 0.0798369 | − | 0.996808i | \(-0.474560\pi\) | ||||
0.0798369 | + | 0.996808i | \(0.474560\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.28115 | − | 5.29007i | 0.386443 | − | 0.280768i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.1246 | − | 34.2380i | −0.588777 | − | 1.81207i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.4164 | − | 14.1068i | −1.02476 | − | 0.744531i | −0.0575058 | − | 0.998345i | \(-0.518315\pi\) |
−0.967253 | + | 0.253814i | \(0.918315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.927051 | + | 2.85317i | −0.0487922 | + | 0.150167i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.8328 | + | 45.6507i | −0.776385 | + | 2.38947i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.6976 | − | 19.3969i | −1.39360 | − | 1.01251i | −0.995459 | − | 0.0951868i | \(-0.969655\pi\) |
−0.398142 | − | 0.917324i | \(-0.630345\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.41641 | + | 22.8254i | 0.386083 | + | 1.18824i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.23607 | − | 2.35114i | 0.168008 | − | 0.122065i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.0000 | −1.13912 | −0.569558 | − | 0.821951i | \(-0.692886\pi\) | ||||
−0.569558 | + | 0.821951i | \(0.692886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.00000 | −0.464758 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.72542 | + | 23.7764i | 0.396828 | + | 1.22131i | 0.927528 | + | 0.373753i | \(0.121929\pi\) |
−0.530700 | + | 0.847560i | \(0.678071\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.70820 | + | 7.05342i | 0.497366 | + | 0.361358i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.309017 | − | 0.951057i | 0.0157900 | − | 0.0485967i | −0.942851 | − | 0.333214i | \(-0.891867\pi\) |
0.958641 | + | 0.284618i | \(0.0918667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.1246 | − | 34.2380i | 0.565496 | − | 1.74042i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.5172 | − | 7.64121i | −0.533244 | − | 0.387425i | 0.288326 | − | 0.957532i | \(-0.406901\pi\) |
−0.821570 | + | 0.570108i | \(0.806901\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.85410 | − | 5.70634i | −0.0937660 | − | 0.288582i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.85410 | + | 3.52671i | −0.244857 | + | 0.177899i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.00000 | −0.301893 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.0000 | −1.30490 | −0.652451 | − | 0.757831i | \(-0.726259\pi\) | ||||
−0.652451 | + | 0.757831i | \(0.726259\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.4164 | + | 14.1068i | −0.972036 | + | 0.706226i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.85410 | − | 5.70634i | −0.0925894 | − | 0.284961i | 0.894029 | − | 0.448010i | \(-0.147867\pi\) |
−0.986618 | + | 0.163049i | \(0.947867\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.34346 | + | 25.6785i | −0.414590 | + | 1.27598i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.5066 | − | 32.3359i | 0.519517 | − | 1.59891i | −0.255393 | − | 0.966837i | \(-0.582205\pi\) |
0.774910 | − | 0.632071i | \(-0.217795\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −36.4058 | − | 26.4503i | −1.79576 | − | 1.30470i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.618034 | + | 1.90211i | 0.0304115 | + | 0.0935969i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.85410 | + | 3.52671i | −0.238278 | + | 0.173119i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 66.0000 | 3.23203 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0000 | −1.36789 | −0.683945 | − | 0.729534i | \(-0.739737\pi\) | ||||
−0.683945 | + | 0.729534i | \(0.739737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.2705 | + | 17.6336i | −1.18287 | + | 0.859407i | −0.992493 | − | 0.122304i | \(-0.960972\pi\) |
−0.190380 | + | 0.981711i | \(0.560972\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.8328 | − | 45.6507i | −0.721196 | − | 2.21961i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 19.4164 | + | 14.1068i | 0.941834 | + | 0.684283i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.47214 | + | 7.60845i | −0.119635 | + | 0.368199i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.03444 | + | 24.7275i | −0.387005 | + | 1.19108i | 0.548010 | + | 0.836472i | \(0.315386\pi\) |
−0.935015 | + | 0.354608i | \(0.884614\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.5172 | − | 7.64121i | −0.505425 | − | 0.367213i | 0.305660 | − | 0.952141i | \(-0.401123\pi\) |
−0.811085 | + | 0.584928i | \(0.801123\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.2492 | − | 68.4761i | −1.06677 | − | 3.28318i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.23607 | + | 2.35114i | −0.154802 | + | 0.112470i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.0000 | −1.52728 | −0.763638 | − | 0.645644i | \(-0.776589\pi\) | ||||
−0.763638 | + | 0.645644i | \(0.776589\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.0000 | −0.857143 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.28115 | − | 5.29007i | 0.345938 | − | 0.251339i | −0.401225 | − | 0.915980i | \(-0.631415\pi\) |
0.747163 | + | 0.664641i | \(0.231415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.9058 | − | 42.7975i | −0.659196 | − | 2.02880i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 43.6869 | + | 31.7404i | 2.06632 | + | 1.50127i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.48936 | + | 19.9722i | −0.306252 | + | 0.942546i | 0.672955 | + | 0.739683i | \(0.265025\pi\) |
−0.979207 | + | 0.202863i | \(0.934975\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.6869 | − | 51.3571i | 0.784020 | − | 2.41296i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.70820 | + | 11.4127i | 0.173462 | + | 0.533863i | 0.999560 | − | 0.0296647i | \(-0.00944396\pi\) |
−0.826097 | + | 0.563527i | \(0.809444\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −43.6869 | + | 31.7404i | −2.03913 | + | 1.48152i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.0000 | −1.30409 | −0.652045 | − | 0.758180i | \(-0.726089\pi\) | ||||
−0.652045 | + | 0.758180i | \(0.726089\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.0000 | 1.25480 | 0.627398 | − | 0.778699i | \(-0.284120\pi\) | ||||
0.627398 | + | 0.778699i | \(0.284120\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 50.9681 | − | 37.0305i | 2.36359 | − | 1.71725i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.1976 | − | 31.3849i | −0.471887 | − | 1.45232i | −0.850111 | − | 0.526604i | \(-0.823465\pi\) |
0.378224 | − | 0.925714i | \(-0.376535\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.09017 | − | 5.87785i | −0.373569 | − | 0.271414i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.1976 | − | 31.3849i | 0.469879 | − | 1.44614i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.94427 | − | 15.2169i | 0.226859 | − | 0.698199i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.70820 | − | 7.05342i | −0.444508 | − | 0.322954i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.47214 | + | 7.60845i | 0.112955 | + | 0.347639i | 0.991515 | − | 0.129993i | \(-0.0414954\pi\) |
−0.878560 | + | 0.477632i | \(0.841495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.00000 | 0.273009 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.0000 | 0.953561 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.28115 | + | 5.29007i | −0.329941 | + | 0.239716i | −0.740405 | − | 0.672161i | \(-0.765366\pi\) |
0.410465 | + | 0.911876i | \(0.365366\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.70820 | + | 11.4127i | 0.167691 | + | 0.516099i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.47214 | − | 4.70228i | −0.292083 | − | 0.212211i | 0.432087 | − | 0.901832i | \(-0.357777\pi\) |
−0.724171 | + | 0.689621i | \(0.757777\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.8328 | − | 45.6507i | 0.668036 | − | 2.05600i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.85410 | + | 5.70634i | −0.0831678 | + | 0.255964i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.1803 | + | 11.7557i | 0.724331 | + | 0.526258i | 0.887765 | − | 0.460297i | \(-0.152257\pi\) |
−0.163434 | + | 0.986554i | \(0.552257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.8328 | − | 45.6507i | −0.662681 | − | 2.03952i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.2705 | − | 17.6336i | 1.08217 | − | 0.786241i | 0.104109 | − | 0.994566i | \(-0.466801\pi\) |
0.978060 | + | 0.208324i | \(0.0668010\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.0000 | 1.33498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 39.0000 | 1.73205 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.5172 | − | 7.64121i | 0.466168 | − | 0.338691i | −0.329778 | − | 0.944058i | \(-0.606974\pi\) |
0.795946 | + | 0.605368i | \(0.206974\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.88854 | − | 30.4338i | −0.437443 | − | 1.34631i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 29.1246 | + | 21.1603i | 1.28588 | + | 0.934249i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.8328 | − | 45.6507i | 0.653612 | − | 2.01161i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.6869 | + | 51.3571i | −0.732474 | + | 2.25432i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.9336 | − | 21.7481i | −1.31142 | − | 0.952800i | −0.999997 | − | 0.00252695i | \(-0.999196\pi\) |
−0.311419 | − | 0.950273i | \(-0.600804\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.5967 | + | 41.8465i | 0.594544 | + | 1.82982i | 0.556982 | + | 0.830525i | \(0.311959\pi\) |
0.0375627 | + | 0.999294i | \(0.488041\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −19.4164 | + | 14.1068i | −0.847402 | + | 0.615673i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 42.0000 | 1.82955 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.85410 | − | 3.52671i | 0.210650 | − | 0.153046i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.85410 | + | 3.52671i | 0.209861 | + | 0.152473i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.63525 | − | 14.2658i | 0.200026 | − | 0.615617i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.70820 | − | 11.4127i | 0.159428 | − | 0.490669i | −0.839154 | − | 0.543893i | \(-0.816950\pi\) |
0.998583 | + | 0.0532238i | \(0.0169497\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.1353 | − | 8.81678i | −0.520774 | − | 0.378364i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.9787 | + | 39.9444i | 0.555947 | + | 1.71103i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 24.0000 | 1.02430 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.0000 | −1.36325 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.23607 | − | 2.35114i | 0.137612 | − | 0.0999807i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.78115 | − | 8.55951i | −0.118053 | − | 0.363331i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.9787 | − | 24.6870i | −1.43972 | − | 1.04602i | −0.988100 | − | 0.153813i | \(-0.950845\pi\) |
−0.451624 | − | 0.892208i | \(-0.649155\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.70820 | + | 11.4127i | −0.156282 | + | 0.480987i | −0.998289 | − | 0.0584805i | \(-0.981374\pi\) |
0.842006 | + | 0.539468i | \(0.181374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.9894 | − | 12.3435i | −0.714748 | − | 0.519295i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.56231 | − | 17.1190i | −0.233595 | − | 0.718931i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.4164 | − | 14.1068i | 0.813978 | − | 0.591390i | −0.101003 | − | 0.994886i | \(-0.532205\pi\) |
0.914981 | + | 0.403496i | \(0.132205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.0000 | 1.12794 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.23607 | + | 2.35114i | −0.134953 | + | 0.0980494i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.10739 | − | 21.8743i | −0.295885 | − | 0.910639i | −0.982923 | − | 0.184018i | \(-0.941090\pi\) |
0.687038 | − | 0.726621i | \(-0.258910\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.70820 | + | 7.05342i | 0.403459 | + | 0.293130i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.23607 | − | 3.80423i | 0.0512807 | − | 0.157826i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.70820 | − | 7.05342i | −0.400700 | − | 0.291126i | 0.369126 | − | 0.929379i | \(-0.379657\pi\) |
−0.769826 | + | 0.638254i | \(0.779657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.65248 | − | 26.6296i | −0.356519 | − | 1.09725i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.5623 | − | 10.5801i | 0.599013 | − | 0.435209i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.00000 | −0.164260 | −0.0821302 | − | 0.996622i | \(-0.526172\pi\) | ||||
−0.0821302 | + | 0.996622i | \(0.526172\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.0000 | −1.47586 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.4164 | − | 14.1068i | 0.794661 | − | 0.577355i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.8328 | + | 45.6507i | 0.606052 | + | 1.86524i | 0.489388 | + | 0.872066i | \(0.337220\pi\) |
0.116664 | + | 0.993171i | \(0.462780\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.7426 | − | 22.3358i | −1.25402 | − | 0.911098i | −0.255571 | − | 0.966790i | \(-0.582263\pi\) |
−0.998448 | + | 0.0556925i | \(0.982263\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.27051 | + | 28.5317i | −0.377524 | + | 1.16190i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.56231 | + | 17.1190i | −0.225767 | + | 0.694839i | 0.772446 | + | 0.635081i | \(0.219033\pi\) |
−0.998213 | + | 0.0597588i | \(0.980967\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 38.8328 | + | 28.2137i | 1.57359 | + | 1.14328i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.9443 | − | 9.40456i | 0.522814 | − | 0.379847i | −0.294849 | − | 0.955544i | \(-0.595269\pi\) |
0.817663 | + | 0.575697i | \(0.195269\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 36.0000 | 1.45166 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000 | 0.724653 | 0.362326 | − | 0.932051i | \(-0.381983\pi\) | ||||
0.362326 | + | 0.932051i | \(0.381983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.42705 | − | 1.76336i | 0.0975514 | − | 0.0708753i | −0.537940 | − | 0.842983i | \(-0.680797\pi\) |
0.635492 | + | 0.772108i | \(0.280797\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.78115 | − | 8.55951i | −0.111604 | − | 0.343481i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.2705 | + | 17.6336i | 0.972377 | + | 0.706474i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.96149 | + | 27.5806i | −0.358460 | + | 1.10323i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.85410 | − | 5.70634i | 0.0739279 | − | 0.227527i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.28115 | − | 5.29007i | −0.289858 | − | 0.210594i | 0.433348 | − | 0.901227i | \(-0.357332\pi\) |
−0.723206 | + | 0.690633i | \(0.757332\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.5410 | − | 57.0634i | −0.736939 | − | 2.26807i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.70820 | − | 7.05342i | 0.385258 | − | 0.279907i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.0000 | 0.712069 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.28115 | − | 5.29007i | 0.287588 | − | 0.208945i | −0.434632 | − | 0.900608i | \(-0.643122\pi\) |
0.722220 | + | 0.691663i | \(0.243122\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.16312 | + | 6.65740i | 0.0853051 | + | 0.262542i | 0.984606 | − | 0.174788i | \(-0.0559241\pi\) |
−0.899301 | + | 0.437330i | \(0.855924\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −43.6869 | − | 31.7404i | −1.72017 | − | 1.24978i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.63525 | − | 14.2658i | 0.182231 | − | 0.560848i | −0.817659 | − | 0.575703i | \(-0.804729\pi\) |
0.999890 | + | 0.0148545i | \(0.00472851\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.9787 | + | 39.9444i | −0.508676 | + | 1.56554i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.89919 | − | 6.46564i | −0.348252 | − | 0.253020i | 0.399883 | − | 0.916566i | \(-0.369051\pi\) |
−0.748135 | + | 0.663546i | \(0.769051\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.85410 | + | 5.70634i | 0.0724458 | + | 0.222965i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −77.6656 | + | 56.4274i | −3.03002 | + | 2.20144i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.0000 | 0.856998 | 0.428499 | − | 0.903542i | \(-0.359042\pi\) | ||||
0.428499 | + | 0.903542i | \(0.359042\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | −0.272268 | −0.136134 | − | 0.990690i | \(-0.543468\pi\) | ||||
−0.136134 | + | 0.990690i | \(0.543468\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.41641 | + | 22.8254i | 0.287596 | + | 0.885129i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.47214 | + | 4.70228i | 0.250602 | + | 0.182073i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −26.8845 | + | 82.7419i | −1.03941 | + | 3.19899i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.5066 | + | 32.3359i | −0.404999 | + | 1.24646i | 0.515897 | + | 0.856650i | \(0.327459\pi\) |
−0.920896 | + | 0.389808i | \(0.872541\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 29.1246 | + | 21.1603i | 1.12101 | + | 0.814459i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.27051 | − | 28.5317i | −0.356295 | − | 1.09656i | −0.955255 | − | 0.295783i | \(-0.904419\pi\) |
0.598960 | − | 0.800779i | \(-0.295581\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.3262 | + | 8.22899i | −0.434661 | + | 0.315800i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −54.0000 | −2.06928 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.00000 | 0.306111 | 0.153056 | − | 0.988218i | \(-0.451089\pi\) | ||||
0.153056 | + | 0.988218i | \(0.451089\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.4058 | + | 26.4503i | −1.39099 | + | 1.01062i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.4681 | + | 59.9166i | 0.742753 | + | 2.28596i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.96149 | + | 27.5806i | −0.340911 | + | 1.04922i | 0.622825 | + | 0.782361i | \(0.285985\pi\) |
−0.963736 | + | 0.266856i | \(0.914015\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.3951 | − | 62.7697i | 0.773631 | − | 2.38099i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.4164 | + | 14.1068i | 0.735449 | + | 0.534335i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.8328 | + | 45.6507i | 0.561029 | + | 1.72667i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.09017 | − | 5.87785i | 0.305562 | − | 0.222003i | −0.424428 | − | 0.905462i | \(-0.639525\pi\) |
0.729990 | + | 0.683458i | \(0.239525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.00000 | −0.150863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −72.0000 | −2.71168 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.1803 | + | 11.7557i | −0.608524 | + | 0.442119i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.87132 | + | 18.0701i | 0.220502 | + | 0.678636i | 0.998717 | + | 0.0506378i | \(0.0161254\pi\) |
−0.778215 | + | 0.627998i | \(0.783875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.70820 | − | 7.05342i | −0.364086 | − | 0.264524i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.16312 | + | 6.65740i | −0.0810094 | + | 0.249321i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.85410 | − | 5.70634i | 0.0692427 | − | 0.213107i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.6074 | + | 13.5191i | 0.693939 | + | 0.504176i | 0.877953 | − | 0.478748i | \(-0.158909\pi\) |
−0.184014 | + | 0.982924i | \(0.558909\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.88854 | + | 30.4338i | 0.368269 | + | 1.13341i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −32.0000 | −1.18845 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.0000 | −1.29808 | −0.649039 | − | 0.760755i | \(-0.724829\pi\) | ||||
−0.649039 | + | 0.760755i | \(0.724829\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.8435 | − | 15.8702i | 0.809017 | − | 0.587785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.1246 | − | 34.2380i | −0.411459 | − | 1.26634i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.23607 | − | 2.35114i | −0.119527 | − | 0.0868414i | 0.526416 | − | 0.850227i | \(-0.323536\pi\) |
−0.645943 | + | 0.763386i | \(0.723536\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.34346 | + | 25.6785i | −0.307753 | + | 0.947167i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.03444 | + | 24.7275i | −0.295552 | + | 0.909615i | 0.687484 | + | 0.726200i | \(0.258715\pi\) |
−0.983036 | + | 0.183415i | \(0.941285\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.1246 | − | 34.2380i | −0.408122 | − | 1.25607i | −0.918260 | − | 0.395979i | \(-0.870405\pi\) |
0.510137 | − | 0.860093i | \(-0.329595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 43.6869 | − | 31.7404i | 1.60056 | − | 1.16288i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.0000 | −0.439057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.00000 | −0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.6074 | + | 13.5191i | −0.678993 | + | 0.493318i | −0.873024 | − | 0.487678i | \(-0.837844\pi\) |
0.194030 | + | 0.980996i | \(0.437844\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.0517 | + | 37.0912i | 0.439187 | + | 1.35168i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −43.6869 | − | 31.7404i | −1.58993 | − | 1.15515i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.09017 | − | 9.51057i | 0.112314 | − | 0.345667i | −0.879063 | − | 0.476705i | \(-0.841831\pi\) |
0.991377 | + | 0.131038i | \(0.0418309\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.6525 | − | 16.4580i | −0.820075 | − | 0.595819i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 33.3738 | + | 102.714i | 1.20663 | + | 3.71364i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.0000 | 0.576975 | 0.288487 | − | 0.957484i | \(-0.406848\pi\) | ||||
0.288487 | + | 0.957484i | \(0.406848\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.0000 | 1.08042 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.85410 | − | 3.52671i | 0.174590 | − | 0.126847i | −0.497059 | − | 0.867717i | \(-0.665587\pi\) |
0.671648 | + | 0.740870i | \(0.265587\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.65248 | − | 26.6296i | −0.310806 | − | 0.956563i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.85410 | + | 3.52671i | 0.174140 | + | 0.126520i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.94427 | − | 15.2169i | 0.177147 | − | 0.545202i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.2492 | − | 68.4761i | 0.795122 | − | 2.44714i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.6976 | − | 19.3969i | −0.952877 | − | 0.692306i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.41641 | + | 22.8254i | 0.264366 | + | 0.813636i | 0.991839 | + | 0.127499i | \(0.0406950\pi\) |
−0.727472 | + | 0.686137i | \(0.759305\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 33.9787 | − | 24.6870i | 1.20967 | − | 0.878880i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.0000 | 0.497783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.5623 | + | 10.5801i | −0.516472 | + | 0.375239i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.309017 | + | 0.951057i | 0.0109459 | + | 0.0336882i | 0.956380 | − | 0.292124i | \(-0.0943621\pi\) |
−0.945434 | + | 0.325813i | \(0.894362\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.8328 | − | 28.2137i | −1.37381 | − | 0.998129i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 27.8115 | − | 85.5951i | 0.982672 | − | 3.02435i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.85410 | − | 5.70634i | 0.0653485 | − | 0.201122i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 63.1033 | + | 45.8472i | 2.22134 | + | 1.61390i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.70820 | + | 11.4127i | 0.130374 | + | 0.401248i | 0.994842 | − | 0.101439i | \(-0.0323447\pi\) |
−0.864468 | + | 0.502687i | \(0.832345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.0344 | − | 15.2824i | 0.738619 | − | 0.536638i | −0.153659 | − | 0.988124i | \(-0.549106\pi\) |
0.892278 | + | 0.451486i | \(0.149106\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.0000 | 0.420342 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.4164 | + | 14.1068i | −0.679294 | + | 0.493536i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.5066 | + | 19.9847i | 0.959986 | + | 0.697471i | 0.953148 | − | 0.302506i | \(-0.0978232\pi\) |
0.00683865 | + | 0.999977i | \(0.497823\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.57953 | + | 29.4828i | −0.333921 | + | 1.02770i | 0.633330 | + | 0.773882i | \(0.281688\pi\) |
−0.967251 | + | 0.253822i | \(0.918312\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.94427 | + | 15.2169i | −0.171929 | + | 0.529144i | −0.999480 | − | 0.0322473i | \(-0.989734\pi\) |
0.827551 | + | 0.561391i | \(0.189734\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.3156 | + | 20.5725i | 0.983441 | + | 0.714512i | 0.958475 | − | 0.285176i | \(-0.0920522\pi\) |
0.0249662 | + | 0.999688i | \(0.492052\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.85410 | + | 5.70634i | 0.0643181 | + | 0.197951i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.5623 | + | 10.5801i | −0.504554 | + | 0.366580i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −48.0000 | −1.66111 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 63.0000 | 2.17760 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.9894 | + | 12.3435i | −0.586538 | + | 0.426145i | −0.841075 | − | 0.540918i | \(-0.818077\pi\) |
0.254537 | + | 0.967063i | \(0.418077\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.8156 | + | 33.2870i | 0.372952 | + | 1.14783i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.5623 | + | 10.5801i | 0.501552 | + | 0.364399i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.0517 | − | 37.0912i | 0.414590 | − | 1.27598i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.70820 | + | 11.4127i | −0.127265 | + | 0.391682i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.809017 | + | 0.587785i | 0.0277327 | + | 0.0201490i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.03444 | − | 24.7275i | −0.275094 | − | 0.846652i | −0.989194 | − | 0.146609i | \(-0.953164\pi\) |
0.714100 | − | 0.700043i | \(-0.246836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 58.2492 | − | 42.3205i | 1.99208 | − | 1.44733i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.0000 | −0.819824 | −0.409912 | − | 0.912125i | \(-0.634441\pi\) | ||||
−0.409912 | + | 0.912125i | \(0.634441\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0000 | 0.375315 | 0.187658 | − | 0.982235i | \(-0.439910\pi\) | ||||
0.187658 | + | 0.982235i | \(0.439910\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.4164 | + | 14.1068i | −0.661709 | + | 0.480760i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.94427 | − | 15.2169i | −0.168305 | − | 0.517989i | 0.830960 | − | 0.556333i | \(-0.187792\pi\) |
−0.999265 | + | 0.0383432i | \(0.987792\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 43.6869 | + | 31.7404i | 1.48540 | + | 1.07921i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.6140 | + | 54.2102i | −0.598202 | + | 1.84108i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 33.9787 | + | 24.6870i | 1.15001 | + | 0.835528i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.85410 | − | 5.70634i | −0.0626801 | − | 0.192909i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.3050 | + | 32.9160i | −1.52984 | + | 1.11149i | −0.573512 | + | 0.819197i | \(0.694419\pi\) |
−0.956328 | + | 0.292296i | \(0.905581\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −36.0000 | −1.21425 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.0000 | −0.640126 | −0.320063 | − | 0.947396i | \(-0.603704\pi\) | ||||
−0.320063 | + | 0.947396i | \(0.603704\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.6525 | − | 16.4580i | 0.762317 | − | 0.553855i | −0.137303 | − | 0.990529i | \(-0.543844\pi\) |
0.899620 | + | 0.436674i | \(0.143844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.78115 | − | 8.55951i | −0.0934874 | − | 0.287725i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.5066 | + | 19.9847i | 0.923580 | + | 0.671021i | 0.944413 | − | 0.328762i | \(-0.106632\pi\) |
−0.0208321 | + | 0.999783i | \(0.506632\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.47214 | + | 7.60845i | −0.0829128 | + | 0.255179i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.88854 | + | 30.4338i | −0.330908 | + | 1.01843i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.1353 | − | 8.81678i | −0.405637 | − | 0.294712i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −45.3050 | + | 32.9160i | −1.51100 | + | 1.09781i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 36.0000 | 1.19800 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.1353 | + | 8.81678i | −0.403390 | + | 0.293080i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.65248 | + | 26.6296i | 0.287301 | + | 0.884221i | 0.985700 | + | 0.168512i | \(0.0538962\pi\) |
−0.698399 | + | 0.715709i | \(0.746104\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 48.5410 | + | 35.2671i | 1.61000 | + | 1.16974i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.1246 | − | 34.2380i | 0.368575 | − | 1.13436i | −0.579137 | − | 0.815230i | \(-0.696610\pi\) |
0.947712 | − | 0.319127i | \(-0.103390\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.1246 | − | 34.2380i | 0.367768 | − | 1.13187i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.23607 | − | 2.35114i | −0.106864 | − | 0.0776415i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.4508 | − | 47.5528i | −0.509677 | − | 1.56862i | −0.792764 | − | 0.609529i | \(-0.791359\pi\) |
0.283087 | − | 0.959094i | \(-0.408641\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.70820 | + | 7.05342i | −0.319896 | + | 0.232418i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 77.6656 | − | 56.4274i | 2.55087 | − | 1.85332i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.79837 | − | 20.9232i | −0.223047 | − | 0.686469i | −0.998484 | − | 0.0550438i | \(-0.982470\pi\) |
0.775437 | − | 0.631426i | \(-0.217530\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.70820 | + | 7.05342i | 0.318174 | + | 0.231167i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.1246 | − | 34.2380i | 0.364203 | − | 1.12090i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.23607 | − | 3.80423i | 0.0403806 | − | 0.124279i | −0.928834 | − | 0.370496i | \(-0.879188\pi\) |
0.969215 | + | 0.246217i | \(0.0791877\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.8435 | − | 15.8702i | −0.712834 | − | 0.517904i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.09017 | + | 9.51057i | 0.100737 | + | 0.310036i | 0.988706 | − | 0.149867i | \(-0.0478844\pi\) |
−0.887970 | + | 0.459902i | \(0.847884\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.23607 | + | 2.35114i | −0.105381 | + | 0.0765637i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −54.0000 | −1.75662 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.0000 | 1.52729 | 0.763647 | − | 0.645634i | \(-0.223407\pi\) | ||||
0.763647 | + | 0.645634i | \(0.223407\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.9058 | + | 42.7975i | 0.450925 | + | 1.38781i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.5066 | + | 19.9847i | 0.891025 | + | 0.647368i | 0.936145 | − | 0.351614i | \(-0.114367\pi\) |
−0.0451197 | + | 0.998982i | \(0.514367\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.34346 | − | 25.6785i | 0.269988 | − | 0.830938i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.27051 | − | 28.5317i | 0.299360 | − | 0.921337i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.5623 | − | 10.5801i | −0.469752 | − | 0.341295i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.70820 | + | 11.4127i | 0.119495 | + | 0.367768i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.70820 | − | 7.05342i | 0.312518 | − | 0.227058i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.00000 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 72.0000 | 2.31297 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.8779 | + | 31.1526i | −1.37602 | + | 0.999735i | −0.378777 | + | 0.925488i | \(0.623655\pi\) |
−0.997240 | + | 0.0742473i | \(0.976345\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.5967 | + | 41.8465i | 0.435892 | + | 1.34154i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.39919 | + | 10.4616i | −0.108750 | + | 0.334697i | −0.990592 | − | 0.136847i | \(-0.956303\pi\) |
0.881843 | + | 0.471544i | \(0.156303\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.9574 | + | 79.8887i | −0.828757 | + | 2.55065i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.2254 | − | 14.6946i | −0.645091 | − | 0.468686i | 0.216505 | − | 0.976282i | \(-0.430534\pi\) |
−0.861595 | + | 0.507596i | \(0.830534\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.56231 | − | 17.1190i | −0.177230 | − | 0.545457i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 38.8328 | − | 28.2137i | 1.23606 | − | 0.898052i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.00000 | 0.190789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −84.9468 | + | 61.7175i | −2.69570 | + | 1.95854i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.41641 | − | 22.8254i | −0.235116 | − | 0.723612i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.61803 | − | 1.17557i | −0.0512437 | − | 0.0372307i | 0.561869 | − | 0.827227i | \(-0.310083\pi\) |
−0.613112 | + | 0.789996i | \(0.710083\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.78115 | − | 8.55951i | 0.0879918 | − | 0.270811i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))