Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.r (of order \(3\), degree \(2\), 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 673.2 | ||
Root | \(-0.173648 + 0.984808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.673 |
Dual form | 1008.2.r.h.337.2 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.592396 | + | 1.62760i | 0.342020 | + | 0.939693i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.673648 | − | 1.16679i | −0.301265 | − | 0.521806i | 0.675158 | − | 0.737673i | \(-0.264075\pi\) |
−0.976423 | + | 0.215867i | \(0.930742\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.29813 | + | 1.92836i | −0.766044 | + | 0.642788i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.826352 | − | 1.43128i | 0.249154 | − | 0.431548i | −0.714137 | − | 0.700006i | \(-0.753181\pi\) |
0.963291 | + | 0.268458i | \(0.0865140\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.68479 | + | 2.91815i | 0.467277 | + | 0.809348i | 0.999301 | − | 0.0373813i | \(-0.0119016\pi\) |
−0.532024 | + | 0.846729i | \(0.678568\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50000 | − | 1.78763i | 0.387298 | − | 0.461564i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.467911 | 0.113485 | 0.0567426 | − | 0.998389i | \(-0.481929\pi\) | ||||
0.0567426 | + | 0.998389i | \(0.481929\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.22668 | 0.740252 | 0.370126 | − | 0.928982i | \(-0.379315\pi\) | ||||
0.370126 | + | 0.928982i | \(0.379315\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.70574 | + | 0.300767i | 0.372222 | + | 0.0656328i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.47178 | + | 7.74535i | 0.932431 | + | 1.61502i | 0.779152 | + | 0.626835i | \(0.215650\pi\) |
0.153279 | + | 0.988183i | \(0.451017\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.59240 | − | 2.75811i | 0.318479 | − | 0.551622i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.50000 | − | 2.59808i | −0.866025 | − | 0.500000i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.13429 | + | 5.42874i | −0.582022 | + | 1.00809i | 0.413217 | + | 0.910632i | \(0.364405\pi\) |
−0.995239 | + | 0.0974595i | \(0.968928\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.61721 | + | 7.99724i | 0.829276 | + | 1.43635i | 0.898607 | + | 0.438754i | \(0.144580\pi\) |
−0.0693317 | + | 0.997594i | \(0.522087\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.81908 | + | 0.497079i | 0.490738 | + | 0.0865304i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.34730 | −0.227735 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.23442 | 1.51813 | 0.759065 | − | 0.651015i | \(-0.225657\pi\) | ||||
0.759065 | + | 0.651015i | \(0.225657\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.75150 | + | 4.47086i | −0.600720 | + | 0.715910i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.70574 | − | 2.95442i | −0.266391 | − | 0.461403i | 0.701536 | − | 0.712634i | \(-0.252498\pi\) |
−0.967927 | + | 0.251231i | \(0.919165\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.20574 | + | 3.82045i | −0.336372 | + | 0.582613i | −0.983747 | − | 0.179558i | \(-0.942533\pi\) |
0.647376 | + | 0.762171i | \(0.275867\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.79813 | + | 1.38241i | 0.566192 | + | 0.206077i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.67752 | − | 8.10170i | 0.682286 | − | 1.18175i | −0.291995 | − | 0.956420i | \(-0.594319\pi\) |
0.974281 | − | 0.225335i | \(-0.0723475\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.277189 | + | 0.761570i | 0.0388142 | + | 0.106641i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.573978 | −0.0788419 | −0.0394210 | − | 0.999223i | \(-0.512551\pi\) | ||||
−0.0394210 | + | 0.999223i | \(0.512551\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.22668 | −0.300246 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.91147 | + | 5.25173i | 0.253181 | + | 0.695609i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.19846 | − | 9.00400i | −0.676782 | − | 1.17222i | −0.975945 | − | 0.218019i | \(-0.930041\pi\) |
0.299162 | − | 0.954202i | \(-0.403293\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.81908 | + | 6.61484i | −0.488983 | + | 0.846943i | −0.999920 | − | 0.0126752i | \(-0.995965\pi\) |
0.510937 | + | 0.859618i | \(0.329299\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.520945 | + | 2.95442i | 0.0656328 | + | 0.372222i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.26991 | − | 3.93161i | 0.281548 | − | 0.487656i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.298133 | + | 0.516382i | 0.0364228 | + | 0.0630861i | 0.883662 | − | 0.468125i | \(-0.155070\pi\) |
−0.847239 | + | 0.531211i | \(0.821737\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.95723 | + | 11.8666i | −1.19871 | + | 1.42857i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.554378 | 0.0657925 | 0.0328963 | − | 0.999459i | \(-0.489527\pi\) | ||||
0.0328963 | + | 0.999459i | \(0.489527\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.04963 | 0.239891 | 0.119946 | − | 0.992780i | \(-0.461728\pi\) | ||||
0.119946 | + | 0.992780i | \(0.461728\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.43242 | + | 0.957882i | 0.627282 | + | 0.110607i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.826352 | − | 1.43128i | −0.0941715 | − | 0.163110i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.20187 | + | 2.08169i | −0.135221 | + | 0.234209i | −0.925682 | − | 0.378303i | \(-0.876508\pi\) |
0.790461 | + | 0.612512i | \(0.209841\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.56283 | − | 8.86327i | 0.173648 | − | 0.984808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.52481 | + | 13.0334i | −0.825956 | + | 1.43060i | 0.0752309 | + | 0.997166i | \(0.476031\pi\) |
−0.901187 | + | 0.433431i | \(0.857303\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.315207 | − | 0.545955i | −0.0341891 | − | 0.0592172i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.6925 | − | 1.88538i | −1.14636 | − | 0.202134i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.08647 | 0.963164 | 0.481582 | − | 0.876401i | \(-0.340062\pi\) | ||||
0.481582 | + | 0.876401i | \(0.340062\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.36959 | 0.353228 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.2811 | + | 12.2525i | −1.06610 | + | 1.27052i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.17365 | − | 3.76487i | −0.223012 | − | 0.386267i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.949493 | − | 1.64457i | 0.0964064 | − | 0.166981i | −0.813788 | − | 0.581161i | \(-0.802598\pi\) |
0.910195 | + | 0.414181i | \(0.135932\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.860967 | + | 4.88279i | 0.0865304 | + | 0.490738i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.854570 | − | 1.48016i | 0.0850329 | − | 0.147281i | −0.820372 | − | 0.571830i | \(-0.806234\pi\) |
0.905405 | + | 0.424548i | \(0.139567\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.81908 | − | 3.15074i | −0.179239 | − | 0.310451i | 0.762381 | − | 0.647128i | \(-0.224030\pi\) |
−0.941620 | + | 0.336677i | \(0.890697\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.798133 | − | 2.19285i | −0.0778898 | − | 0.214001i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.12836 | −0.689124 | −0.344562 | − | 0.938764i | \(-0.611973\pi\) | ||||
−0.344562 | + | 0.938764i | \(0.611973\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.403733 | 0.0386706 | 0.0193353 | − | 0.999813i | \(-0.493845\pi\) | ||||
0.0193353 | + | 0.999813i | \(0.493845\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.47044 | + | 15.0299i | 0.519231 | + | 1.42658i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.18479 | − | 12.4444i | −0.675888 | − | 1.17067i | −0.976208 | − | 0.216835i | \(-0.930427\pi\) |
0.300320 | − | 0.953839i | \(-0.402907\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.02481 | − | 10.4353i | 0.561817 | − | 0.973095i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.49912 | − | 3.45740i | −0.878194 | − | 0.319637i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.233956 | − | 0.405223i | 0.0214467 | − | 0.0371467i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.13429 | + | 7.16079i | 0.375844 | + | 0.650981i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.79813 | − | 4.52644i | 0.342466 | − | 0.408135i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0273 | −0.986315 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.7716 | 1.84318 | 0.921589 | − | 0.388167i | \(-0.126892\pi\) | ||||
0.921589 | + | 0.388167i | \(0.126892\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.52481 | − | 1.32683i | −0.662523 | − | 0.116821i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.58260 | − | 6.20524i | −0.313013 | − | 0.542154i | 0.666000 | − | 0.745952i | \(-0.268005\pi\) |
−0.979013 | + | 0.203797i | \(0.934672\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.61334 | − | 2.79439i | 0.139894 | − | 0.242304i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.00076i | 0.602529i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.28446 | + | 2.22475i | −0.109739 | + | 0.190074i | −0.915665 | − | 0.401943i | \(-0.868335\pi\) |
0.805925 | + | 0.592017i | \(0.201668\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.06670 | − | 5.31169i | −0.260114 | − | 0.450531i | 0.706158 | − | 0.708055i | \(-0.250427\pi\) |
−0.966272 | + | 0.257523i | \(0.917094\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.9572 | + | 2.81369i | 1.34384 | + | 0.236956i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.56893 | 0.465697 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.44562 | 0.701371 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.11334 | − | 1.32683i | 0.0918268 | − | 0.109435i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.215537 | − | 0.373321i | −0.0176575 | − | 0.0305837i | 0.857062 | − | 0.515214i | \(-0.172288\pi\) |
−0.874719 | + | 0.484630i | \(0.838954\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.23530 | + | 2.13960i | −0.100527 | + | 0.174118i | −0.911902 | − | 0.410408i | \(-0.865386\pi\) |
0.811375 | + | 0.584526i | \(0.198720\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.07532 | + | 0.902302i | −0.0869346 | + | 0.0729468i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.22075 | − | 10.7747i | 0.499663 | − | 0.865441i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.06670 | − | 8.77579i | −0.404367 | − | 0.700384i | 0.589881 | − | 0.807491i | \(-0.299175\pi\) |
−0.994248 | + | 0.107106i | \(0.965841\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.340022 | − | 0.934204i | −0.0269655 | − | 0.0740872i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.94356 | 0.704852 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.59627 | 0.203355 | 0.101678 | − | 0.994817i | \(-0.467579\pi\) | ||||
0.101678 | + | 0.994817i | \(0.467579\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.31908 | − | 3.62414i | −0.102690 | − | 0.282139i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.5915 | − | 20.0771i | −0.896979 | − | 1.55361i | −0.831337 | − | 0.555769i | \(-0.812424\pi\) |
−0.0656422 | − | 0.997843i | \(-0.520910\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.822948 | − | 1.42539i | 0.0633037 | − | 0.109645i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.41534 | + | 6.22221i | −0.567066 | + | 0.475825i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.37598 | − | 4.11532i | 0.180643 | − | 0.312882i | −0.761457 | − | 0.648215i | \(-0.775516\pi\) |
0.942100 | + | 0.335333i | \(0.108849\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.59240 | − | 2.75811i | −0.120374 | − | 0.208494i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.5753 | − | 13.7949i | 0.870054 | − | 1.03689i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.53209 | 0.637718 | 0.318859 | − | 0.947802i | \(-0.396700\pi\) | ||||
0.318859 | + | 0.947802i | \(0.396700\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.2344 | −1.28102 | −0.640512 | − | 0.767948i | \(-0.721278\pi\) | ||||
−0.640512 | + | 0.767948i | \(0.721278\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.0287 | − | 2.29731i | −0.963108 | − | 0.169822i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.22075 | − | 10.7747i | −0.457359 | − | 0.792169i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.386659 | − | 0.669713i | 0.0282753 | − | 0.0489743i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.50000 | + | 2.59808i | −0.327327 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.45471 | − | 11.1799i | 0.467046 | − | 0.808948i | −0.532245 | − | 0.846590i | \(-0.678651\pi\) |
0.999291 | + | 0.0376425i | \(0.0119848\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.319078 | + | 0.552659i | 0.0229677 | + | 0.0397813i | 0.877281 | − | 0.479977i | \(-0.159355\pi\) |
−0.854313 | + | 0.519759i | \(0.826022\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.74376 | + | 1.36543i | 0.554542 | + | 0.0977807i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.4456 | 0.815467 | 0.407733 | − | 0.913101i | \(-0.366319\pi\) | ||||
0.407733 | + | 0.913101i | \(0.366319\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.63816 | 0.257902 | 0.128951 | − | 0.991651i | \(-0.458839\pi\) | ||||
0.128951 | + | 0.991651i | \(0.458839\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.663848 | + | 0.791143i | −0.0468242 | + | 0.0558029i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.13429 | + | 5.42874i | 0.219984 | + | 0.381023i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.29813 | + | 3.98048i | −0.160509 | + | 0.278009i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −25.2126 | − | 9.17664i | −1.75240 | − | 0.637820i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.66637 | − | 4.61830i | 0.184437 | − | 0.319454i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.91147 | + | 5.04282i | 0.200434 | + | 0.347162i | 0.948668 | − | 0.316273i | \(-0.102431\pi\) |
−0.748234 | + | 0.663435i | \(0.769098\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.328411 | + | 0.902302i | 0.0225024 | + | 0.0618247i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.94356 | 0.405348 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.23442 | 0.626873 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.21419 | + | 3.33597i | 0.0820476 | + | 0.225424i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.788333 | + | 1.36543i | 0.0530290 | + | 0.0918490i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.54189 | − | 6.13473i | 0.237182 | − | 0.410812i | −0.722722 | − | 0.691139i | \(-0.757109\pi\) |
0.959905 | + | 0.280327i | \(0.0904428\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.65910 | + | 9.40923i | 0.110607 | + | 0.627282i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.97178 | + | 10.3434i | −0.396361 | + | 0.686517i | −0.993274 | − | 0.115789i | \(-0.963060\pi\) |
0.596913 | + | 0.802306i | \(0.296394\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.77631 | + | 15.2010i | 0.579955 | + | 1.00451i | 0.995484 | + | 0.0949315i | \(0.0302632\pi\) |
−0.415529 | + | 0.909580i | \(0.636403\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.84002 | − | 2.19285i | 0.121065 | − | 0.144279i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.2540 | 1.06484 | 0.532418 | − | 0.846481i | \(-0.321283\pi\) | ||||
0.532418 | + | 0.846481i | \(0.321283\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.6040 | −0.822195 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.10014 | − | 0.722965i | −0.266333 | − | 0.0469616i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.54963 | − | 13.0763i | −0.488345 | − | 0.845838i | 0.511565 | − | 0.859244i | \(-0.329066\pi\) |
−0.999910 | + | 0.0134062i | \(0.995733\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.81908 | − | 13.5430i | 0.503671 | − | 0.872384i | −0.496320 | − | 0.868140i | \(-0.665316\pi\) |
0.999991 | − | 0.00424420i | \(-0.00135097\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3516 | − | 2.70691i | 0.984808 | − | 0.173648i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.673648 | + | 1.16679i | −0.0430378 | + | 0.0745437i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.43629 | + | 9.41593i | 0.345903 | + | 0.599121i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −25.6707 | − | 4.52644i | −1.62682 | − | 0.286851i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.0651 | −1.20338 | −0.601690 | − | 0.798730i | \(-0.705506\pi\) | ||||
−0.601690 | + | 0.798730i | \(0.705506\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.7811 | 0.929277 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.701867 | − | 0.836452i | 0.0439526 | − | 0.0523807i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.2909 | − | 23.0204i | −0.829061 | − | 1.43598i | −0.898776 | − | 0.438409i | \(-0.855542\pi\) |
0.0697146 | − | 0.997567i | \(-0.477791\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.61721 | − | 7.99724i | 0.286900 | − | 0.496925i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.26558 | − | 18.5200i | −0.202134 | − | 1.14636i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.367059 | + | 0.635765i | −0.0226338 | + | 0.0392029i | −0.877120 | − | 0.480270i | \(-0.840539\pi\) |
0.854487 | + | 0.519473i | \(0.173872\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.386659 | + | 0.669713i | 0.0237523 | + | 0.0411402i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.38279 | + | 14.7891i | 0.329421 | + | 0.905078i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.8503 | −1.27126 | −0.635632 | − | 0.771992i | \(-0.719261\pi\) | ||||
−0.635632 | + | 0.771992i | \(0.719261\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.95811 | −0.422675 | −0.211338 | − | 0.977413i | \(-0.567782\pi\) | ||||
−0.211338 | + | 0.977413i | \(0.567782\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.99613 | + | 5.48432i | 0.120811 | + | 0.331926i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.63176 | − | 4.55834i | −0.158701 | − | 0.274878i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.93629 | + | 15.4781i | −0.536930 | + | 0.929989i | 0.462138 | + | 0.886808i | \(0.347083\pi\) |
−0.999067 | + | 0.0431811i | \(0.986251\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −26.0326 | − | 9.47508i | −1.55853 | − | 0.567258i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.1552 | + | 19.3214i | −0.665465 | + | 1.15262i | 0.313694 | + | 0.949524i | \(0.398433\pi\) |
−0.979159 | + | 0.203095i | \(0.934900\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.29726 | − | 16.1033i | −0.552665 | − | 0.957243i | −0.998081 | − | 0.0619196i | \(-0.980278\pi\) |
0.445417 | − | 0.895323i | \(-0.353056\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.84002 | − | 5.76811i | 0.286698 | − | 0.341674i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.41147 | −0.201373 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7811 | −0.987121 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.23917 | + | 0.571153i | 0.189884 | + | 0.0334816i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.54576 | − | 11.3376i | −0.382407 | − | 0.662349i | 0.608998 | − | 0.793171i | \(-0.291572\pi\) |
−0.991406 | + | 0.130822i | \(0.958238\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.00387 | + | 12.1311i | −0.407781 | + | 0.706298i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.43717 | + | 4.29385i | −0.431548 | + | 0.249154i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.0680 | + | 26.0986i | −0.871408 | + | 1.50932i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.20574 | + | 3.82045i | 0.127137 | + | 0.220207i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.91534 | + | 0.514054i | 0.167482 | + | 0.0295316i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.2909 | 0.589253 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.31046 | −0.360157 | −0.180078 | − | 0.983652i | \(-0.557635\pi\) | ||||
−0.180078 | + | 0.983652i | \(0.557635\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.05051 | − | 4.82721i | 0.230425 | − | 0.274610i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.76217 | − | 8.24833i | −0.270038 | − | 0.467720i | 0.698833 | − | 0.715285i | \(-0.253703\pi\) |
−0.968871 | + | 0.247565i | \(0.920370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.81433 | − | 15.2669i | 0.498215 | − | 0.862934i | −0.501782 | − | 0.864994i | \(-0.667322\pi\) |
0.999998 | + | 0.00205946i | \(0.000655547\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.09627 | − | 2.59808i | 0.174455 | − | 0.146385i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.03849 | + | 6.99486i | −0.226824 | + | 0.392871i | −0.956865 | − | 0.290533i | \(-0.906168\pi\) |
0.730041 | + | 0.683403i | \(0.239501\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.18004 | + | 8.97210i | 0.290027 | + | 0.502341i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.22281 | − | 11.6021i | −0.235694 | − | 0.647565i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.50980 | 0.0840075 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.7314 | 0.595273 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.239170 | + | 0.657115i | 0.0132261 | + | 0.0363385i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.67752 | − | 8.10170i | −0.257880 | − | 0.446661i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.5248 | − | 19.9616i | 0.633461 | − | 1.09719i | −0.353378 | − | 0.935481i | \(-0.614967\pi\) |
0.986839 | − | 0.161706i | \(-0.0516997\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.2219 | + | 17.8073i | −1.16295 | + | 0.975835i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.401674 | − | 0.695720i | 0.0219458 | − | 0.0380112i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.5116 | − | 25.1348i | −0.790498 | − | 1.36918i | −0.925659 | − | 0.378359i | \(-0.876489\pi\) |
0.135161 | − | 0.990824i | \(-0.456845\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.9982 | − | 19.0660i | 0.868905 | − | 1.03552i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.2618 | 0.826471 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 20.5535 | + | 3.62414i | 1.10656 | + | 0.195117i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.47313 | + | 11.2118i | 0.347496 | + | 0.601880i | 0.985804 | − | 0.167901i | \(-0.0536988\pi\) |
−0.638308 | + | 0.769781i | \(0.720365\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.731429 | + | 1.26687i | −0.0391525 | + | 0.0678141i | −0.884938 | − | 0.465710i | \(-0.845799\pi\) |
0.845785 | + | 0.533524i | \(0.179132\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 17.5089i | − | 0.934555i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.16637 | + | 12.4125i | −0.381428 | + | 0.660652i | −0.991267 | − | 0.131873i | \(-0.957901\pi\) |
0.609839 | + | 0.792525i | \(0.291234\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.373455 | − | 0.646844i | −0.0198210 | − | 0.0343309i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.798133 | + | 0.140732i | 0.0422417 | + | 0.00744835i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.9368 | 1.10500 | 0.552500 | − | 0.833513i | \(-0.313674\pi\) | ||||
0.552500 | + | 0.833513i | \(0.313674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.58853 | −0.452028 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.20574 | + | 10.9710i | −0.483176 | + | 0.575827i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.38073 | − | 2.39149i | −0.0722707 | − | 0.125176i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.02869 | + | 10.4420i | −0.314695 | + | 0.545067i | −0.979373 | − | 0.202063i | \(-0.935236\pi\) |
0.664678 | + | 0.747130i | \(0.268569\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.61721 | + | 3.50038i | 0.500652 | + | 0.182222i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.286989 | + | 0.497079i | −0.0148997 | + | 0.0258071i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.390530 | + | 0.676417i | 0.0202209 | + | 0.0350235i | 0.875959 | − | 0.482386i | \(-0.160230\pi\) |
−0.855738 | + | 0.517410i | \(0.826896\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.53256 | − | 17.9480i | −0.337340 | − | 0.926833i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.1225 | −1.08786 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.92396 | 0.355660 | 0.177830 | − | 0.984061i | \(-0.443092\pi\) | ||||
0.177830 | + | 0.984061i | \(0.443092\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.3050 | + | 33.8077i | 0.630404 | + | 1.73202i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.86618 | + | 6.69642i | 0.197553 | + | 0.342171i | 0.947734 | − | 0.319061i | \(-0.103367\pi\) |
−0.750182 | + | 0.661232i | \(0.770034\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.11334 | + | 1.92836i | −0.0567411 | + | 0.0982785i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.29813 | − | 13.0334i | −0.116821 | − | 0.662523i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.69981 | + | 4.67620i | −0.136886 | + | 0.237093i | −0.926316 | − | 0.376747i | \(-0.877043\pi\) |
0.789431 | + | 0.613840i | \(0.210376\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.09240 | + | 3.62414i | 0.105817 | + | 0.183280i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.97730 | − | 9.50698i | 0.402402 | − | 0.479564i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.23854 | 0.162949 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.2344 | −1.46723 | −0.733617 | − | 0.679563i | \(-0.762169\pi\) | ||||
−0.733617 | + | 0.679563i | \(0.762169\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.50387 | + | 0.970481i | 0.275538 | + | 0.0485848i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.6989 | + | 23.7272i | 0.684092 | + | 1.18488i | 0.973721 | + | 0.227743i | \(0.0731346\pi\) |
−0.289629 | + | 0.957139i | \(0.593532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.5581 | + | 26.9474i | −0.775003 | + | 1.34235i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.3944 | + | 4.14722i | −0.566192 | + | 0.206077i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.63088 | − | 13.2171i | 0.378249 | − | 0.655146i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.51249 | + | 7.81586i | 0.223128 | + | 0.386469i | 0.955756 | − | 0.294160i | \(-0.0950398\pi\) |
−0.732628 | + | 0.680629i | \(0.761706\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.38191 | − | 0.772649i | −0.216144 | − | 0.0381120i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.3969 | −0.511599 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.2763 | 0.995325 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.82857 | − | 8.13798i | 0.334397 | − | 0.398518i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.0876485 | + | 0.151812i | 0.00428191 | + | 0.00741649i | 0.868158 | − | 0.496287i | \(-0.165304\pi\) |
−0.863877 | + | 0.503704i | \(0.831970\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.3525 | − | 21.3952i | 0.602025 | − | 1.04274i | −0.390490 | − | 0.920607i | \(-0.627694\pi\) |
0.992514 | − | 0.122130i | \(-0.0389724\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.87346 | + | 27.6387i | 0.236956 | + | 1.34384i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.745100 | − | 1.29055i | 0.0361427 | − | 0.0626009i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.81908 | + | 6.61484i | 0.184818 | + | 0.320114i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.29901 | + | 9.06396i | 0.159278 | + | 0.437612i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.3191 | 1.41225 | 0.706126 | − | 0.708086i | \(-0.250441\pi\) | ||||
0.706126 | + | 0.708086i | \(0.250441\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.6554 | 0.944578 | 0.472289 | − | 0.881444i | \(-0.343428\pi\) | ||||
0.472289 | + | 0.881444i | \(0.343428\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.00316 | + | 13.7461i | 0.239883 | + | 0.659073i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.4290 | + | 24.9918i | 0.690233 | + | 1.19552i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.9650 | + | 18.9919i | −0.523330 | + | 0.906434i | 0.476302 | + | 0.879282i | \(0.341977\pi\) |
−0.999631 | + | 0.0271516i | \(0.991356\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.81908 | + | 1.02606i | 0.134242 | + | 0.0488600i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.35504 | + | 16.2034i | −0.444471 | + | 0.769847i | −0.998015 | − | 0.0629732i | \(-0.979942\pi\) |
0.553544 | + | 0.832820i | \(0.313275\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.12108 | − | 10.6020i | −0.290167 | − | 0.502584i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.479933 | − | 0.571962i | 0.0227000 | − | 0.0270529i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.68004 | 0.315251 | 0.157625 | − | 0.987499i | \(-0.449616\pi\) | ||||
0.157625 | + | 0.987499i | \(0.449616\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.63816 | −0.265490 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.21419 | − | 0.743076i | −0.198000 | − | 0.0349128i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.26991 | − | 3.93161i | −0.106415 | − | 0.184317i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.71436 | − | 16.8258i | 0.454418 | − | 0.787076i | −0.544236 | − | 0.838932i | \(-0.683180\pi\) |
0.998655 | + | 0.0518563i | \(0.0165138\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.10560 | − | 1.21567i | −0.0982810 | − | 0.0567426i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.482926 | − | 0.836452i | 0.0224921 | − | 0.0389575i | −0.854560 | − | 0.519352i | \(-0.826173\pi\) |
0.877052 | + | 0.480395i | \(0.159507\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.222811 | − | 0.385920i | −0.0103549 | − | 0.0179352i | 0.860802 | − | 0.508941i | \(-0.169963\pi\) |
−0.871156 | + | 0.491006i | \(0.836629\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 21.2219 | + | 3.74200i | 0.984144 | + | 0.173531i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.2148 | 1.58327 | 0.791637 | − | 0.610992i | \(-0.209229\pi\) | ||||
0.791637 | + | 0.610992i | \(0.209229\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.596267 | 0.0275330 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.2819 | − | 13.4453i | 0.519844 | − | 0.619526i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.64543 | + | 6.31407i | 0.167617 | + | 0.290321i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.13816 | − | 8.89955i | 0.235755 | − | 0.408339i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.31908 | − | 1.10684i | 0.0603964 | − | 0.0506786i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.8965 | + | 18.8732i | −0.497872 | + | 0.862339i | −0.999997 | − | 0.00245553i | \(-0.999218\pi\) |
0.502125 | + | 0.864795i | \(0.332552\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.5581 | + | 26.9474i | 0.709388 | + | 1.22870i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.29813 | + | 14.5565i | 0.241073 | + | 0.662344i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.55850 | −0.116175 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.3928 | −0.878772 | −0.439386 | − | 0.898298i | \(-0.644804\pi\) | ||||
−0.439386 | + | 0.898298i | \(0.644804\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.53802 | + | 4.22567i | 0.0695516 | + | 0.191091i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.0783 | + | 22.6523i | 0.590216 | + | 1.02228i | 0.994203 | + | 0.107519i | \(0.0342908\pi\) |
−0.403987 | + | 0.914765i | \(0.632376\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.46657 | + | 2.54017i | −0.0660509 | + | 0.114403i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.11721 | − | 4.29385i | 0.230002 | − | 0.192994i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.277189 | − | 0.480105i | 0.0124336 | − | 0.0215357i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.15064 | − | 12.3853i | −0.320107 | − | 0.554441i | 0.660403 | − | 0.750911i | \(-0.270385\pi\) |
−0.980510 | + | 0.196470i | \(0.937052\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.8106 | − | 30.7599i | 1.15313 | − | 1.37425i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.7033 | −0.833937 | −0.416969 | − | 0.908921i | \(-0.636908\pi\) | ||||
−0.416969 | + | 0.908921i | \(0.636908\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.30272 | −0.102470 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.80747 | + | 0.495032i | 0.124684 | + | 0.0219851i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.8045 | + | 22.1781i | 0.567551 | + | 0.983027i | 0.996807 | + | 0.0798442i | \(0.0254423\pi\) |
−0.429257 | + | 0.903183i | \(0.641224\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.02481 | − | 1.77503i | 0.0453351 | − | 0.0785228i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.5201 | − | 8.38316i | −0.641077 | − | 0.370126i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.45084 | + | 4.24497i | −0.107997 | + | 0.187056i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.73055 | − | 13.3897i | −0.339989 | − | 0.588879i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.10560 | + | 1.42924i | 0.355796 | + | 0.0627365i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.2121 | −0.929320 | −0.464660 | − | 0.885489i | \(-0.653824\pi\) | ||||
−0.464660 | + | 0.885489i | \(0.653824\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.8057 | −0.909770 | −0.454885 | − | 0.890550i | \(-0.650320\pi\) | ||||
−0.454885 | + | 0.890550i | \(0.650320\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.54576 | − | 4.22567i | 0.154750 | − | 0.184423i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.16044 | + | 3.74200i | 0.0941104 | + | 0.163004i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −28.4937 | + | 49.3525i | −1.23885 | + | 2.14576i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.3097 | + | 10.6679i | 1.27193 | + | 0.462946i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.74763 | − | 9.95518i | 0.248957 | − | 0.431207i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.80200 | + | 8.31731i | 0.207609 | + | 0.359589i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.05438 | + | 13.8868i | 0.218112 | + | 0.599259i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.65270 | −0.0711870 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.7297 | 1.14920 | 0.574599 | − | 0.818435i | \(-0.305158\pi\) | ||||
0.574599 | + | 0.818435i | \(0.305158\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.2096 | − | 28.0507i | −0.438136 | − | 1.20377i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.271974 | − | 0.471073i | −0.0116501 | − | 0.0201786i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.3812 | − | 31.8372i | 0.785923 | − | 1.36126i | −0.142523 | − | 0.989792i | \(-0.545521\pi\) |
0.928446 | − | 0.371467i | \(-0.121145\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.97906 | − | 22.5663i | −0.169822 | − | 0.963108i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.1133 | + | 17.5168i | −0.430843 | + | 0.746242i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.20187 | + | 2.08169i | 0.0511086 | + | 0.0885226i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.8516 | − | 16.5077i | 0.587969 | − | 0.700714i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.3387 | 1.37024 | 0.685118 | − | 0.728432i | \(-0.259751\pi\) | ||||
0.685118 | + | 0.728432i | \(0.259751\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.8648 | −0.628716 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.31908 | + | 0.232589i | 0.0556915 | + | 0.00981992i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.87093 | − | 15.3649i | −0.373865 | − | 0.647553i | 0.616291 | − | 0.787518i | \(-0.288634\pi\) |
−0.990156 | + | 0.139965i | \(0.955301\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.68004 | + | 16.7663i | −0.407243 | + | 0.705365i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.89440 | − | 5.78509i | −0.289538 | − | 0.242951i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.3007 | − | 23.0374i | 0.557593 | − | 0.965779i | −0.440104 | − | 0.897947i | \(-0.645058\pi\) |
0.997697 | − | 0.0678320i | \(-0.0216082\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.00862 | − | 8.67518i | −0.209604 | − | 0.363045i | 0.741986 | − | 0.670416i | \(-0.233884\pi\) |
−0.951590 | + | 0.307371i | \(0.900551\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.0201 | + | 3.88273i | 0.919902 | + | 0.162203i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.4834 | 1.18784 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.9145 | −1.37025 | −0.685124 | − | 0.728427i | \(-0.740252\pi\) | ||||
−0.685124 | + | 0.728427i | \(0.740252\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.710485 | + | 0.846723i | −0.0295267 | + | 0.0351886i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.52481 | + | 13.0334i | 0.312182 | + | 0.540715i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.474308 | + | 0.821525i | −0.0196438 | + | 0.0340241i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.36500 | + | 13.4126i | 0.0977807 | + | 0.554542i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.53643 | + | 13.0535i | −0.311062 | + | 0.538774i | −0.978592 | − | 0.205808i | \(-0.934018\pi\) |
0.667531 | + | 0.744582i | \(0.267351\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.8983 | + | 25.8046i | 0.613873 | + | 1.06326i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.78034 | + | 18.6288i | 0.278906 | + | 0.766288i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.0009 | 1.68371 | 0.841853 | − | 0.539706i | \(-0.181465\pi\) | ||||
0.841853 | + | 0.539706i | \(0.181465\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.630415 | −0.0258445 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.15523 | + | 5.92145i | 0.0882077 | + | 0.242349i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.03684 | + | 5.25996i | 0.124082 | + | 0.214916i | 0.921374 | − | 0.388678i | \(-0.127068\pi\) |
−0.797292 | + | 0.603594i | \(0.793735\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.06758 | − | 12.2414i | 0.288293 | − | 0.499338i | −0.685110 | − | 0.728440i | \(-0.740246\pi\) |
0.973402 | + | 0.229102i | \(0.0735791\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.68092 | − | 0.611806i | −0.0684524 | − | 0.0249147i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.57011 | − | 9.64771i | 0.226457 | − | 0.392235i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.0449 | + | 39.9149i | 0.935363 | + | 1.62010i | 0.773986 | + | 0.633203i | \(0.218260\pi\) |
0.161377 | + | 0.986893i | \(0.448406\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.97906 | + | 8.31731i | −0.282806 | + | 0.337035i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.5226 | 1.27527 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.4938 | −1.07008 | −0.535038 | − | 0.844828i | \(-0.679703\pi\) | ||||
−0.535038 | + | 0.844828i | \(0.679703\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.84002 | − | 1.38241i | −0.316140 | − | 0.0557440i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.12495 | + | 1.94847i | 0.0452889 | + | 0.0784426i | 0.887781 | − | 0.460266i | \(-0.152246\pi\) |
−0.842492 | + | 0.538708i | \(0.818913\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.09539 | − | 5.36137i | 0.124414 | − | 0.215492i | −0.797090 | − | 0.603861i | \(-0.793628\pi\) |
0.921504 | + | 0.388369i | \(0.126962\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 46.4721i | − | 1.86486i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.54323 | − | 7.86911i | 0.182021 | − | 0.315269i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.533433 | − | 0.923933i | −0.0213373 | − | 0.0369573i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.09627 | + | 1.60392i | 0.363270 | + | 0.0640543i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.32089 | 0.172285 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.1661 | −1.04166 | −0.520829 | − | 0.853661i | \(-0.674377\pi\) | ||||
−0.520829 | + | 0.853661i | \(0.674377\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.48293 | + | 7.72605i | −0.257673 | + | 0.307083i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.9927 | − | 24.2361i | −0.555284 | − | 0.961781i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.68479 | − | 2.91815i | 0.0667539 | − | 0.115621i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.27403 | + | 1.06904i | −0.0504000 | + | 0.0422906i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.44444 | + | 4.23389i | −0.0965496 | + | 0.167229i | −0.910254 | − | 0.414050i | \(-0.864114\pi\) |
0.813705 | + | 0.581278i | \(0.197447\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.1839 | − | 34.9596i | −0.795976 | − | 1.37867i | −0.922218 | − | 0.386671i | \(-0.873625\pi\) |
0.126242 | − | 0.992000i | \(-0.459709\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.52094 | + | 9.67372i | 0.138637 | + | 0.380902i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.28075 | 0.0896657 | 0.0448329 | − | 0.998995i | \(-0.485724\pi\) | ||||
0.0448329 | + | 0.998995i | \(0.485724\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.1830 | −0.674493 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.47044 | + | 15.0299i | 0.214403 | + | 0.589068i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.7396 | − | 20.3336i | −0.459407 | − | 0.795717i | 0.539522 | − | 0.841971i | \(-0.318605\pi\) |
−0.998930 | + | 0.0462542i | \(0.985272\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.82682 | + | 8.36030i | −0.188599 | + | 0.326664i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.71032 | + | 3.95243i | −0.183767 | + | 0.154199i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.9812 | + | 41.5366i | −0.934174 | + | 1.61804i | −0.158073 | + | 0.987427i | \(0.550528\pi\) |
−0.776101 | + | 0.630609i | \(0.782805\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.6545 | − | 25.3824i | −0.569995 | − | 0.987260i | −0.996566 | − | 0.0828055i | \(-0.973612\pi\) |
0.426571 | − | 0.904454i | \(-0.359721\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.75537 | + | 2.09196i | −0.0681728 | + | 0.0812452i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.34730 | −0.168581 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −56.0634 | −2.17078 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.0831 | + | 2.13057i | 0.467158 | + | 0.0823726i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.31180 | + | 10.9324i | 0.243664 | + | 0.422039i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.1591 | + | 22.7922i | −0.507246 | + | 0.878576i | 0.492719 | + | 0.870189i | \(0.336003\pi\) |
−0.999965 | + | 0.00838731i | \(0.997330\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.3316 | + | 8.27433i | −0.551622 | + | 0.318479i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.9454 | + | 31.0823i | −0.689697 | + | 1.19459i | 0.282239 | + | 0.959344i | \(0.408923\pi\) |
−0.971936 | + | 0.235246i | \(0.924411\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.949493 | − | 1.64457i | −0.0364382 | − | 0.0631128i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.3726 | − | 3.59224i | −0.780679 | − | 0.137655i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −35.0642 | −1.34169 | −0.670847 | − | 0.741596i | \(-0.734069\pi\) | ||||
−0.670847 | + | 0.741596i | \(0.734069\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.46110 | 0.132242 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.5421 | + | 23.2893i | −0.745576 | + | 0.888543i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.967034 | − | 1.67495i | −0.0368411 | − | 0.0638106i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.03343 | − | 1.78996i | 0.0393136 | − | 0.0680932i | −0.845699 | − | 0.533660i | \(-0.820816\pi\) |
0.885013 | + | 0.465567i | \(0.154150\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.65910 | + | 1.69577i | 0.176985 | + | 0.0644171i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.13176 | + | 7.15642i | −0.156727 | + | 0.271458i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.798133 | − | 1.38241i | −0.0302315 | − | 0.0523624i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.62882 | + | 26.4550i | 0.364196 | + | 1.00062i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.36009 | −0.277987 | −0.138993 | − | 0.990293i | \(-0.544387\pi\) | ||||
−0.138993 | + | 0.990293i | \(0.544387\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29.7965 | 1.12380 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.46657 | − | 20.5142i | −0.281207 | − | 0.772610i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.854570 | − | 1.48016i | −0.0321394 | − | 0.0556671i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.55438 | + | 7.88841i | −0.171043 | + | 0.296256i | −0.938785 | − | 0.344504i | \(-0.888047\pi\) |
0.767742 | + | 0.640760i | \(0.221380\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.25221 | − | 7.10165i | −0.0469616 | − | 0.266333i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −41.2943 | + | 71.5239i | −1.54648 | + | 2.67859i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.75150 | − | 6.49778i | −0.140298 | − | 0.243003i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.8106 | − | 20.0341i | 0.627804 | − | 0.748188i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.9537 | 0.967908 | 0.483954 | − | 0.875093i | \(-0.339200\pi\) | ||||
0.483954 | + | 0.875093i | \(0.339200\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.63816 | −0.135492 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.6746 | + | 4.70345i | 0.992038 | + | 0.174923i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.98205 | + | 17.2894i | 0.370724 | + | 0.642113i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.08007 | + | 8.79894i | −0.188409 | + | 0.326335i | −0.944720 | − | 0.327878i | \(-0.893667\pi\) |
0.756311 | + | 0.654213i | \(0.227000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.5000 | + | 23.3827i | 0.500000 | + | 0.866025i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.03209 | + | 1.78763i | −0.0381732 | + | 0.0661179i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.3307 | − | 35.2138i | −0.750931 | − | 1.30065i | −0.947372 | − | 0.320135i | \(-0.896272\pi\) |
0.196441 | − | 0.980516i | \(-0.437062\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.29813 | − | 0.405223i | −0.0847679 | − | 0.0149469i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.985452 | 0.0362996 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.3618 | 0.932951 | 0.466475 | − | 0.884534i | \(-0.345524\pi\) | ||||
0.466475 | + | 0.884534i | \(0.345524\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.1049 | + | 14.4260i | −0.444684 | + | 0.529954i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.2221 | − | 19.4372i | −0.411699 | − | 0.713083i | 0.583377 | − | 0.812202i | \(-0.301731\pi\) |
−0.995076 | + | 0.0991184i | \(0.968398\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.290393 | + | 0.502975i | −0.0106392 | + | 0.0184276i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.84002 | − | 44.4630i | −0.286851 | − | 1.62682i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.56418 | + | 6.17334i | −0.130232 | + | 0.225569i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.1086 | + | 20.9727i | 0.441849 | + | 0.765305i | 0.997827 | − | 0.0658924i | \(-0.0209894\pi\) |
−0.555978 | + | 0.831197i | \(0.687656\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.2941 | − | 31.0303i | −0.411580 | − | 1.13081i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.32863 | 0.121141 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.11793 | 0.331397 | 0.165698 | − | 0.986176i | \(-0.447012\pi\) | ||||
0.165698 | + | 0.986176i | \(0.447012\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.75624 | + | 24.0576i | 0.317832 | + | 0.873235i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.13610 | + | 15.8242i | 0.331183 | + | 0.573626i | 0.982744 | − | 0.184970i | \(-0.0592188\pi\) |
−0.651561 | + | 0.758596i | \(0.725886\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.201867 | − | 0.349643i | 0.00730806 | − | 0.0126579i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.77719 | + | 0.646844i | 0.0642544 | + | 0.0233867i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.5167 | − | 30.3398i | 0.632490 | − | 1.09550i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.26470 | − | 16.0469i | −0.334094 | − | 0.578667i | 0.649217 | − | 0.760604i | \(-0.275097\pi\) |
−0.983310 | + | 0.181936i | \(0.941764\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.5945 | − | 35.2694i | 1.06582 | − | 1.27020i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.96080 | −0.106493 | −0.0532463 | − | 0.998581i | \(-0.516957\pi\) | ||||
−0.0532463 | + | 0.998581i | \(0.516957\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.4097 | 1.05643 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.7515 | + | 2.77741i | 0.565082 | + | 0.0996392i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.50387 | − | 9.53298i | −0.197197 | − | 0.341555i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.458111 | − | 0.793471i | 0.0163925 | − | 0.0283926i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 28.2086 | − | 16.2862i | 1.00809 | − | 0.582022i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.82635 | + | 11.8236i | −0.243643 | + | 0.422002i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.7010 | − | 28.9270i | −0.595326 | − | 1.03113i | −0.993501 | − | 0.113825i | \(-0.963690\pi\) |
0.398175 | − | 0.917310i | \(-0.369644\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.25221 | − | 0.220799i | −0.0445799 | − | 0.00786064i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.3696 | −0.510924 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.7374 | −0.913962 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.860967 | + | 1.02606i | −0.0305354 | + | 0.0363906i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.6755 | − | 42.7391i | −0.874050 | − | 1.51390i | −0.857772 | − | 0.514031i | \(-0.828152\pi\) |
−0.0162779 | − | 0.999868i | \(-0.505182\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.18866 | − | 3.79088i | 0.0774293 | − | 0.134112i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.8819 | + | 17.5220i | −0.737826 | + | 0.619110i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.69372 | − | 2.93360i | 0.0597699 | − | 0.103525i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.02481 | − | 10.4353i | −0.212347 | − | 0.367795i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.3516 | − | 33.9358i | −0.434798 | − | 1.19460i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.8280 | 0.697115 | 0.348558 | − | 0.937287i | \(-0.386672\pi\) | ||||
0.348558 | + | 0.937287i | \(0.386672\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.8557 | 0.837686 | 0.418843 | − | 0.908059i | \(-0.362436\pi\) | ||||
0.418843 | + | 0.908059i | \(0.362436\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.12196 | − | 11.3250i | −0.144563 | − | 0.397185i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.74897 | − | 3.02931i | −0.0612638 | − | 0.106112i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.11721 | + | 12.3274i | −0.249000 | + | 0.431280i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.74376 | + | 6.49778i | −0.270589 | + | 0.227051i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.4714 | − | 44.1177i | 0.888957 | − | 1.53972i | 0.0478469 | − | 0.998855i | \(-0.484764\pi\) |
0.841110 | − | 0.540864i | \(-0.181903\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.80747 | + | 11.7909i | 0.237293 | + | 0.411004i | 0.959937 | − | 0.280217i | \(-0.0904064\pi\) |
−0.722643 | + | 0.691221i | \(0.757073\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.86009 | − | 6.98378i | 0.204022 | − | 0.243144i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.2158 | −1.25935 | −0.629673 | − | 0.776861i | \(-0.716811\pi\) | ||||
−0.629673 | + | 0.776861i | \(0.716811\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.3259 | 0.879606 | 0.439803 | − | 0.898094i | \(-0.355048\pi\) | ||||
0.439803 | + | 0.898094i | \(0.355048\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.4859 | − | 5.37549i | −1.05754 | − | 0.186474i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.233956 | − | 0.405223i | −0.00810608 | − | 0.0140401i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.6172 | + | 27.0498i | −0.540456 | + | 0.936097i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 47.9835i | − | 1.65855i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.35710 | − | 7.54671i | 0.150424 | − | 0.260541i | −0.780960 | − | 0.624582i | \(-0.785270\pi\) |
0.931383 | + | 0.364040i | \(0.118603\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.14749 | − | 8.91571i | −0.177500 | − | 0.307438i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −38.0558 | − | 6.71026i | −1.31071 | − | 0.231114i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.21751 | −0.0762847 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.26857 | 0.284111 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.7020 | − | 24.6717i | 0.710492 | − | 0.846731i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 41.2943 | + | 71.5239i | 1.41555 | + | 2.45181i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.99067 | − | 10.3761i | 0.205117 | − | 0.355272i | −0.745053 | − | 0.667005i | \(-0.767576\pi\) |
0.950170 | + | 0.311733i | \(0.100909\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.2554 | + | 4.46059i | 0.419125 | + | 0.152549i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.25015 | + | 5.62943i | −0.111023 | + | 0.192298i | −0.916183 | − | 0.400760i | \(-0.868746\pi\) |
0.805160 | + | 0.593058i | \(0.202079\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.7763 | − | 46.3779i | −0.913596 | − | 1.58239i | −0.808944 | − | 0.587886i | \(-0.799960\pi\) |
−0.104652 | − | 0.994509i | \(-0.533373\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.02094 | − | 5.55250i | −0.0688736 | − | 0.189229i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.69965 | −0.125937 | −0.0629687 | − | 0.998016i | \(-0.520057\pi\) | ||||
−0.0629687 | + | 0.998016i | \(0.520057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.40230 | −0.217685 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.94104 | − | 27.3128i | −0.337615 | − | 0.927590i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.98633 | + | 3.44042i | 0.0673816 | + | 0.116708i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.00459 | + | 1.73999i | −0.0340391 | + | 0.0589574i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.989266 | + | 5.61041i | 0.0334816 | + | 0.189884i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.51367 | + | 9.54996i | −0.186396 | + | 0.322847i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.89440 | + | 10.2094i | 0.199040 | + | 0.344747i | 0.948217 | − | 0.317622i | \(-0.102884\pi\) |
−0.749178 | + | 0.662369i | \(0.769551\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.5753 | − | 17.3702i | 0.491613 | − | 0.585882i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.4858 | 1.66722 | 0.833609 | − | 0.552355i | \(-0.186271\pi\) | ||||
0.833609 | + | 0.552355i | \(0.186271\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.5357 | 0.724734 | 0.362367 | − | 0.932035i | \(-0.381969\pi\) | ||||
0.362367 | + | 0.932035i | \(0.381969\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23.8935 | − | 4.21307i | −0.803172 | − | 0.141621i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.94238 | + | 10.2925i | 0.199526 | + | 0.345589i | 0.948375 | − | 0.317152i | \(-0.102727\pi\) |
−0.748849 | + | 0.662741i | \(0.769393\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.3858 | − | 17.9887i | 0.348328 | − | 0.603322i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.3944 | − | 9.56104i | −0.381727 | − | 0.320307i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.0929 | − | 26.1416i | 0.505063 | − | 0.874795i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.74763 | − | 9.95518i | −0.192122 | − | 0.332765i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −51.4043 | − | 9.06396i | −1.71634 | − | 0.302637i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −57.8866 | −1.93063 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.268571 | −0.00894739 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.91147 | + | 5.85327i | −0.163444 | + | 0.194785i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.6099 | + | 20.1090i | 0.385927 | + | 0.668446i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.0107 | + | 22.5353i | −0.432014 | + | 0.748271i | −0.997047 | − | 0.0767980i | \(-0.975530\pi\) |
0.565032 | + | 0.825069i | \(0.308864\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.890367 | + | 5.04952i | 0.0295316 | + | 0.167482i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.01636 | + | 3.49244i | −0.0668050 | + | 0.115710i | −0.897493 | − | 0.441028i | \(-0.854614\pi\) |
0.830688 | + | 0.556738i | \(0.187947\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.4363 | + | 21.5403i | 0.411581 | + | 0.712879i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.09627 | + | 16.7494i | 0.201536 | + | 0.553717i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.16519 | −0.236615 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.4270 | −0.904732 | −0.452366 | − | 0.891832i | \(-0.649420\pi\) | ||||
−0.452366 | + | 0.891832i | \(0.649420\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.73829 | − | 10.2709i | −0.123181 | − | 0.338437i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.934011 | + | 1.61775i | 0.0307434 | + | 0.0532491i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.7049 | − | 25.4696i | 0.483493 | − | 0.837434i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.2562 | + | 3.73297i | 0.336859 | + | 0.122607i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.83837 | + | 6.64826i | −0.125933 | + | 0.218122i | −0.922097 | − | 0.386958i | \(-0.873526\pi\) |
0.796164 | + | 0.605081i | \(0.206859\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.61334 | − | 2.79439i | −0.0528751 | − | 0.0915824i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.6038 | − | 12.6372i | 0.347154 | − | 0.413722i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.04189 | −0.0340734 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.02465 | −0.0661425 | −0.0330713 | − | 0.999453i | \(-0.510529\pi\) | ||||
−0.0330713 | + | 0.999453i | \(0.510529\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.0699 | + | 5.30213i | 0.981293 | + | 0.173028i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.06964 | + | 5.31677i | 0.100067 | + | 0.173322i | 0.911712 | − | 0.410829i | \(-0.134761\pi\) |
−0.811645 | + | 0.584151i | \(0.801427\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.2554 | − | 26.4231i | 0.496783 | − | 0.860454i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.06283 | + | 3.50038i | 0.197224 | + | 0.113867i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.78224 | − | 4.81898i | 0.0904107 | − | 0.156596i | −0.817273 | − | 0.576250i | \(-0.804515\pi\) |
0.907684 | + | 0.419654i | \(0.137849\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.45320 | + | 5.98112i | 0.112096 | + | 0.194155i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.7772 | − | 2.42929i | −0.446756 | − | 0.0787751i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.72018 | −0.282474 | −0.141237 | − | 0.989976i | \(-0.545108\pi\) | ||||
−0.141237 | + | 0.989976i | \(0.545108\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.3928 | −0.562818 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.5343 | + | 13.7461i | −0.372851 | + | 0.444347i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.28446 | + | 2.22475i | 0.0414775 | + | 0.0718411i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.1373 | + | 47.0031i | −0.875396 | + | 1.51623i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.3819 | − | 13.7461i | 0.527900 | − | 0.442960i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.429892 | − | 0.744596i | 0.0138387 | − | 0.0239694i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.8849 | − | 50.0301i | −0.928876 | − | 1.60886i | −0.785206 | − | 0.619235i | \(-0.787443\pi\) |
−0.143670 | − | 0.989626i | \(-0.545890\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.894400 | + | 2.45734i | 0.0287323 | + | 0.0789413i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.7192 | 0.985828 | 0.492914 | − | 0.870078i | \(-0.335932\pi\) | ||||
0.492914 | + | 0.870078i | \(0.335932\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.13341 | −0.196628 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.35726 | + | 17.4664i | 0.203595 | + | 0.559373i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.15002 | − | 8.92009i | −0.164764 | − | 0.285379i | 0.771808 | − | 0.635856i | \(-0.219353\pi\) |
−0.936571 | + | 0.350477i | \(0.886019\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.50862 | − | 13.0053i | 0.239976 | − | 0.415651i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.927833 | + | 0.778544i | −0.0296234 | + | 0.0248570i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.84817 | − | 11.8614i | 0.218423 | − | 0.378319i | −0.735903 | − | 0.677087i | \(-0.763242\pi\) |
0.954326 | + | 0.298767i | \(0.0965755\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.71032 | − | 13.3547i | −0.245671 | − | 0.425515i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.4153 | − | 12.4125i | 0.331524 | − | 0.395095i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −39.4543 | −1.25457 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.9813 | −1.84184 | −0.920919 | − | 0.389754i | \(-0.872560\pi\) | ||||
−0.920919 | + | 0.389754i | \(0.872560\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 39.3166 | + | 6.93258i | 1.24767 | + | 0.219999i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.45084 | − | 4.24497i | −0.0776968 | − | 0.134575i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.10876 | + | 14.0448i | −0.256807 | + | 0.444803i | −0.965385 | − | 0.260830i | \(-0.916004\pi\) |
0.708578 | + | 0.705633i | \(0.249337\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −41.5549 | − | 23.9917i | −1.31474 | − | 0.759065i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))