Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(107,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.w (of order \(8\), degree \(4\), 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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 107.9 | ||
Character | \(\chi\) | \(=\) | 864.107 |
Dual form | 864.2.w.a.323.9 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.948429 | − | 1.04904i | −0.670641 | − | 0.741782i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.200965 | + | 1.98988i | −0.100482 | + | 0.994939i | ||||
\(5\) | 1.78263 | + | 0.738390i | 0.797217 | + | 0.330218i | 0.743841 | − | 0.668356i | \(-0.233002\pi\) |
0.0533761 | + | 0.998574i | \(0.483002\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.622002 | + | 0.622002i | −0.235095 | + | 0.235095i | −0.814815 | − | 0.579721i | \(-0.803162\pi\) |
0.579721 | + | 0.814815i | \(0.303162\pi\) | |||||||
\(8\) | 2.27806 | − | 1.67644i | 0.805416 | − | 0.592710i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.916100 | − | 2.57036i | −0.289696 | − | 0.812820i | ||||
\(11\) | 0.156498 | + | 0.0648236i | 0.0471859 | + | 0.0195450i | 0.406152 | − | 0.913806i | \(-0.366870\pi\) |
−0.358966 | + | 0.933351i | \(0.616870\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.19856 | + | 2.89359i | 0.332422 | + | 0.802538i | 0.998399 | + | 0.0565653i | \(0.0180149\pi\) |
−0.665977 | + | 0.745972i | \(0.731985\pi\) | |||||||
\(14\) | 1.24243 | + | 0.0625795i | 0.332053 | + | 0.0167251i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.91923 | − | 0.799791i | −0.979807 | − | 0.199948i | ||||
\(17\) | 4.81317 | 1.16736 | 0.583682 | − | 0.811982i | \(-0.301611\pi\) | ||||
0.583682 | + | 0.811982i | \(0.301611\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.67470 | + | 1.52211i | −0.843035 | + | 0.349196i | −0.762049 | − | 0.647519i | \(-0.775807\pi\) |
−0.0809854 | + | 0.996715i | \(0.525807\pi\) | |||||||
\(20\) | −1.82755 | + | 3.39883i | −0.408653 | + | 0.760001i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0804248 | − | 0.225653i | −0.0171466 | − | 0.0481094i | ||||
\(23\) | 1.56750 | − | 1.56750i | 0.326846 | − | 0.326846i | −0.524540 | − | 0.851386i | \(-0.675763\pi\) |
0.851386 | + | 0.524540i | \(0.175763\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.902976 | − | 0.902976i | −0.180595 | − | 0.180595i | ||||
\(26\) | 1.89874 | − | 4.00171i | 0.372373 | − | 0.784799i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.11271 | − | 1.36271i | −0.210282 | − | 0.257528i | ||||
\(29\) | 1.08392 | + | 2.61682i | 0.201279 | + | 0.485932i | 0.991999 | − | 0.126247i | \(-0.0402932\pi\) |
−0.790719 | + | 0.612179i | \(0.790293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.74627i | 0.493245i | 0.969112 | + | 0.246622i | \(0.0793207\pi\) | ||||
−0.969112 | + | 0.246622i | \(0.920679\pi\) | |||||||
\(32\) | 2.87810 | + | 4.86997i | 0.508780 | + | 0.860896i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.56495 | − | 5.04920i | −0.782882 | − | 0.865930i | ||||
\(35\) | −1.56808 | + | 0.649520i | −0.265054 | + | 0.109789i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.96490 | + | 4.74369i | −0.323028 | + | 0.779857i | 0.676048 | + | 0.736858i | \(0.263691\pi\) |
−0.999075 | + | 0.0429995i | \(0.986309\pi\) | |||||||
\(38\) | 5.08195 | + | 2.41129i | 0.824401 | + | 0.391163i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.29881 | − | 1.30637i | 0.837815 | − | 0.206556i | ||||
\(41\) | 3.95321 | + | 3.95321i | 0.617387 | + | 0.617387i | 0.944860 | − | 0.327473i | \(-0.106197\pi\) |
−0.327473 | + | 0.944860i | \(0.606197\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.627273 | + | 1.51437i | −0.0956582 | + | 0.230939i | −0.964464 | − | 0.264213i | \(-0.914888\pi\) |
0.868806 | + | 0.495152i | \(0.164888\pi\) | |||||||
\(44\) | −0.160442 | + | 0.298385i | −0.0241875 | + | 0.0449832i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.13103 | − | 0.157706i | −0.461645 | − | 0.0232525i | ||||
\(47\) | 9.33089i | 1.36105i | 0.732725 | + | 0.680525i | \(0.238248\pi\) | ||||
−0.732725 | + | 0.680525i | \(0.761752\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.22623i | 0.889461i | ||||||||
\(50\) | −0.0908483 | + | 1.80367i | −0.0128479 | + | 0.255077i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.99876 | + | 1.80349i | −0.831878 | + | 0.250099i | ||||
\(53\) | 0.182908 | − | 0.441579i | 0.0251243 | − | 0.0606555i | −0.910819 | − | 0.412805i | \(-0.864549\pi\) |
0.935944 | + | 0.352149i | \(0.114549\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.231113 | + | 0.231113i | 0.0311633 | + | 0.0311633i | ||||
\(56\) | −0.374210 | + | 2.45971i | −0.0500059 | + | 0.328692i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.71712 | − | 3.61895i | 0.225469 | − | 0.475191i | ||||
\(59\) | 3.02418 | − | 7.30102i | 0.393715 | − | 0.950512i | −0.595408 | − | 0.803423i | \(-0.703010\pi\) |
0.989123 | − | 0.147089i | \(-0.0469904\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.6637 | − | 4.83126i | 1.49338 | − | 0.618580i | 0.521334 | − | 0.853353i | \(-0.325435\pi\) |
0.972050 | + | 0.234773i | \(0.0754346\pi\) | |||||||
\(62\) | 2.88094 | − | 2.60464i | 0.365880 | − | 0.330790i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.37911 | − | 7.63805i | 0.297389 | − | 0.954756i | ||||
\(65\) | 6.04322i | 0.749569i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.45039 | + | 10.7442i | 0.543701 | + | 1.31261i | 0.922094 | + | 0.386966i | \(0.126477\pi\) |
−0.378393 | + | 0.925645i | \(0.623523\pi\) | |||||||
\(68\) | −0.967277 | + | 9.57761i | −0.117300 | + | 1.16146i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.16859 | + | 1.02895i | 0.259196 | + | 0.122984i | ||||
\(71\) | −6.22714 | − | 6.22714i | −0.739025 | − | 0.739025i | 0.233364 | − | 0.972389i | \(-0.425027\pi\) |
−0.972389 | + | 0.233364i | \(0.925027\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.573022 | + | 0.573022i | −0.0670672 | + | 0.0670672i | −0.739845 | − | 0.672778i | \(-0.765101\pi\) |
0.672778 | + | 0.739845i | \(0.265101\pi\) | |||||||
\(74\) | 6.83988 | − | 2.43779i | 0.795120 | − | 0.283388i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.29033 | − | 7.61810i | −0.262719 | − | 0.873856i | ||||
\(77\) | −0.137662 | + | 0.0570216i | −0.0156881 | + | 0.00649822i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.6432 | 1.42247 | 0.711233 | − | 0.702956i | \(-0.248137\pi\) | ||||
0.711233 | + | 0.702956i | \(0.248137\pi\) | |||||||
\(80\) | −6.39598 | − | 4.31965i | −0.715092 | − | 0.482952i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.397731 | − | 7.89640i | 0.0439221 | − | 0.872012i | ||||
\(83\) | −4.21199 | − | 10.1686i | −0.462326 | − | 1.11615i | −0.967440 | − | 0.253101i | \(-0.918550\pi\) |
0.505114 | − | 0.863053i | \(-0.331450\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.58010 | + | 3.55400i | 0.930643 | + | 0.385485i | ||||
\(86\) | 2.18356 | − | 0.778239i | 0.235459 | − | 0.0839197i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.465184 | − | 0.114687i | 0.0495888 | − | 0.0122257i | ||||
\(89\) | 6.68154 | − | 6.68154i | 0.708241 | − | 0.708241i | −0.257924 | − | 0.966165i | \(-0.583038\pi\) |
0.966165 | + | 0.257924i | \(0.0830384\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.54533 | − | 1.05431i | −0.266823 | − | 0.110522i | ||||
\(92\) | 2.80412 | + | 3.43415i | 0.292350 | + | 0.358034i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.78847 | − | 8.84969i | 1.00960 | − | 0.912776i | ||||
\(95\) | −7.67456 | −0.787393 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.92342 | −0.601432 | −0.300716 | − | 0.953714i | \(-0.597226\pi\) | ||||
−0.300716 | + | 0.953714i | \(0.597226\pi\) | |||||||
\(98\) | 6.53155 | − | 5.90513i | 0.659787 | − | 0.596509i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.97828 | − | 1.61535i | 0.197828 | − | 0.161535i | ||||
\(101\) | 4.59423 | + | 1.90299i | 0.457143 | + | 0.189355i | 0.599358 | − | 0.800481i | \(-0.295423\pi\) |
−0.142215 | + | 0.989836i | \(0.545423\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.254297 | − | 0.254297i | 0.0250566 | − | 0.0250566i | −0.694467 | − | 0.719524i | \(-0.744360\pi\) |
0.719524 | + | 0.694467i | \(0.244360\pi\) | |||||||
\(104\) | 7.58133 | + | 4.58245i | 0.743410 | + | 0.449347i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.636709 | + | 0.226929i | −0.0618426 | + | 0.0220413i | ||||
\(107\) | −4.13143 | − | 1.71129i | −0.399401 | − | 0.165437i | 0.173936 | − | 0.984757i | \(-0.444351\pi\) |
−0.573337 | + | 0.819320i | \(0.694351\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.89484 | + | 11.8172i | 0.468840 | + | 1.13188i | 0.964670 | + | 0.263461i | \(0.0848640\pi\) |
−0.495830 | + | 0.868420i | \(0.665136\pi\) | |||||||
\(110\) | 0.0232523 | − | 0.461641i | 0.00221702 | − | 0.0440158i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.93524 | − | 1.94029i | 0.277354 | − | 0.183341i | ||||
\(113\) | 12.6188 | 1.18708 | 0.593538 | − | 0.804806i | \(-0.297731\pi\) | ||||
0.593538 | + | 0.804806i | \(0.297731\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.95170 | − | 1.63685i | 0.368498 | − | 0.152637i | ||||
\(116\) | −5.42499 | + | 1.63099i | −0.503697 | + | 0.151433i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.5273 | + | 3.75202i | −0.969115 | + | 0.345401i | ||||
\(119\) | −2.99380 | + | 2.99380i | −0.274441 | + | 0.274441i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.75789 | − | 7.75789i | −0.705262 | − | 0.705262i | ||||
\(122\) | −16.1304 | − | 7.65357i | −1.46038 | − | 0.692921i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.46474 | − | 0.551904i | −0.490748 | − | 0.0495624i | ||||
\(125\) | −4.63488 | − | 11.1896i | −0.414556 | − | 1.00083i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 17.0615i | − | 1.51396i | −0.653438 | − | 0.756980i | \(-0.726674\pi\) | ||
0.653438 | − | 0.756980i | \(-0.273326\pi\) | |||||||
\(128\) | −10.2690 | + | 4.74837i | −0.907663 | + | 0.419700i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.33957 | − | 5.73156i | 0.556017 | − | 0.502691i | ||||
\(131\) | −11.9542 | + | 4.95158i | −1.04444 | + | 0.432621i | −0.837904 | − | 0.545818i | \(-0.816219\pi\) |
−0.206536 | + | 0.978439i | \(0.566219\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.33892 | − | 3.23243i | 0.116099 | − | 0.280287i | ||||
\(134\) | 7.05019 | − | 14.8587i | 0.609044 | − | 1.28360i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.9647 | − | 8.06897i | 0.940213 | − | 0.691909i | ||||
\(137\) | 0.560971 | + | 0.560971i | 0.0479270 | + | 0.0479270i | 0.730664 | − | 0.682737i | \(-0.239211\pi\) |
−0.682737 | + | 0.730664i | \(0.739211\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.35315 | + | 10.5094i | −0.369229 | + | 0.891398i | 0.624648 | + | 0.780907i | \(0.285243\pi\) |
−0.993877 | + | 0.110492i | \(0.964757\pi\) | |||||||
\(140\) | −0.977337 | − | 3.25082i | −0.0826001 | − | 0.274744i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.626511 | + | 12.4385i | −0.0525757 | + | 1.04382i | ||||
\(143\) | 0.530536i | 0.0443657i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.46519i | 0.453859i | ||||||||
\(146\) | 1.14459 | + | 0.0576517i | 0.0947272 | + | 0.00477128i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.04448 | − | 4.86322i | −0.743452 | − | 0.399755i | ||||
\(149\) | −7.37477 | + | 17.8043i | −0.604164 | + | 1.45858i | 0.265093 | + | 0.964223i | \(0.414597\pi\) |
−0.869258 | + | 0.494359i | \(0.835403\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.98204 | + | 2.98204i | 0.242675 | + | 0.242675i | 0.817956 | − | 0.575281i | \(-0.195107\pi\) |
−0.575281 | + | 0.817956i | \(0.695107\pi\) | |||||||
\(152\) | −5.81947 | + | 9.62787i | −0.472021 | + | 0.780924i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.190381 | + | 0.0903323i | 0.0153413 | + | 0.00727918i | ||||
\(155\) | −2.02782 | + | 4.89559i | −0.162878 | + | 0.393223i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.24732 | + | 1.34508i | −0.259164 | + | 0.107349i | −0.508483 | − | 0.861072i | \(-0.669793\pi\) |
0.249318 | + | 0.968422i | \(0.419793\pi\) | |||||||
\(158\) | −11.9911 | − | 13.2632i | −0.953964 | − | 1.05516i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.53465 | + | 10.8065i | 0.121325 | + | 0.854330i | ||||
\(161\) | 1.94998i | 0.153680i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.91012 | + | 16.6825i | 0.541242 | + | 1.30667i | 0.923847 | + | 0.382762i | \(0.125027\pi\) |
−0.382605 | + | 0.923912i | \(0.624973\pi\) | |||||||
\(164\) | −8.66085 | + | 7.07194i | −0.676299 | + | 0.552226i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.67253 | + | 14.0628i | −0.517889 | + | 1.09148i | ||||
\(167\) | −11.6859 | − | 11.6859i | −0.904286 | − | 0.904286i | 0.0915178 | − | 0.995803i | \(-0.470828\pi\) |
−0.995803 | + | 0.0915178i | \(0.970828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.25608 | − | 2.25608i | 0.173545 | − | 0.173545i | ||||
\(170\) | −4.40934 | − | 12.3716i | −0.338181 | − | 0.948856i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.88735 | − | 1.55253i | −0.220158 | − | 0.118379i | ||||
\(173\) | 20.9504 | − | 8.67794i | 1.59283 | − | 0.659772i | 0.602451 | − | 0.798156i | \(-0.294191\pi\) |
0.990379 | + | 0.138384i | \(0.0441908\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.12331 | 0.0849140 | ||||||||
\(176\) | −0.561506 | − | 0.379224i | −0.0423251 | − | 0.0285851i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.3462 | − | 0.672228i | −1.00034 | − | 0.0503856i | ||||
\(179\) | −0.893419 | − | 2.15690i | −0.0667773 | − | 0.161215i | 0.886968 | − | 0.461831i | \(-0.152807\pi\) |
−0.953745 | + | 0.300617i | \(0.902807\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.91096 | − | 3.69104i | −0.662347 | − | 0.274353i | 0.0260791 | − | 0.999660i | \(-0.491698\pi\) |
−0.688426 | + | 0.725307i | \(0.741698\pi\) | |||||||
\(182\) | 1.30805 | + | 3.67009i | 0.0969592 | + | 0.272045i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.943043 | − | 6.19868i | 0.0695220 | − | 0.456972i | ||||
\(185\) | −7.00539 | + | 7.00539i | −0.515046 | + | 0.515046i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.753251 | + | 0.312007i | 0.0550831 | + | 0.0228162i | ||||
\(188\) | −18.5673 | − | 1.87518i | −1.35416 | − | 0.136762i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.27877 | + | 8.05091i | 0.528058 | + | 0.584074i | ||||
\(191\) | 2.43569 | 0.176240 | 0.0881200 | − | 0.996110i | \(-0.471914\pi\) | ||||
0.0881200 | + | 0.996110i | \(0.471914\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.6589 | −1.70301 | −0.851504 | − | 0.524349i | \(-0.824309\pi\) | ||||
−0.851504 | + | 0.524349i | \(0.824309\pi\) | |||||||
\(194\) | 5.61795 | + | 6.21390i | 0.403345 | + | 0.446132i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12.3894 | − | 1.25125i | −0.884959 | − | 0.0893752i | ||||
\(197\) | 3.36182 | + | 1.39251i | 0.239520 | + | 0.0992122i | 0.499214 | − | 0.866478i | \(-0.333622\pi\) |
−0.259695 | + | 0.965691i | \(0.583622\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.56361 | − | 4.56361i | 0.323506 | − | 0.323506i | −0.526604 | − | 0.850110i | \(-0.676535\pi\) |
0.850110 | + | 0.526604i | \(0.176535\pi\) | |||||||
\(200\) | −3.57082 | − | 0.543250i | −0.252495 | − | 0.0384136i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.36099 | − | 6.62438i | −0.166119 | − | 0.466090i | ||||
\(203\) | −2.30187 | − | 0.953466i | −0.161560 | − | 0.0669202i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.12810 | + | 9.96612i | 0.288319 | + | 0.696064i | ||||
\(206\) | −0.507950 | − | 0.0255847i | −0.0353905 | − | 0.00178257i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.38318 | − | 12.2992i | −0.165244 | − | 0.852799i | ||||
\(209\) | −0.673752 | −0.0466044 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.67647 | + | 1.52284i | −0.253098 | + | 0.104837i | −0.505626 | − | 0.862753i | \(-0.668738\pi\) |
0.252527 | + | 0.967590i | \(0.418738\pi\) | |||||||
\(212\) | 0.841930 | + | 0.452706i | 0.0578240 | + | 0.0310920i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.12315 | + | 5.95707i | 0.145136 | + | 0.407217i | ||||
\(215\) | −2.23639 | + | 2.23639i | −0.152521 | + | 0.152521i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.70819 | − | 1.70819i | −0.115959 | − | 0.115959i | ||||
\(218\) | 7.75428 | − | 16.3426i | 0.525186 | − | 1.10686i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.506333 | + | 0.413441i | −0.0341369 | + | 0.0278742i | ||||
\(221\) | 5.76889 | + | 13.9273i | 0.388057 | + | 0.936854i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 15.1287i | − | 1.01309i | −0.862213 | − | 0.506545i | \(-0.830922\pi\) | ||
0.862213 | − | 0.506545i | \(-0.169078\pi\) | |||||||
\(224\) | −4.81931 | − | 1.23895i | −0.322004 | − | 0.0827806i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.9680 | − | 13.2376i | −0.796102 | − | 0.880552i | ||||
\(227\) | −14.4739 | + | 5.99529i | −0.960666 | + | 0.397921i | −0.807230 | − | 0.590237i | \(-0.799034\pi\) |
−0.153437 | + | 0.988158i | \(0.549034\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.24557 | + | 5.42129i | −0.148391 | + | 0.358249i | −0.980544 | − | 0.196298i | \(-0.937108\pi\) |
0.832153 | + | 0.554546i | \(0.187108\pi\) | |||||||
\(230\) | −5.46503 | − | 2.59306i | −0.360353 | − | 0.170981i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.85618 | + | 4.14415i | 0.450130 | + | 0.272077i | ||||
\(233\) | −21.4875 | − | 21.4875i | −1.40769 | − | 1.40769i | −0.771675 | − | 0.636017i | \(-0.780581\pi\) |
−0.636017 | − | 0.771675i | \(-0.719419\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.88984 | + | 16.6336i | −0.449444 | + | 1.08505i | ||||
\(236\) | 13.9204 | + | 7.48500i | 0.906140 | + | 0.487232i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.98002 | + | 0.301205i | 0.387627 | + | 0.0195243i | ||||
\(239\) | − | 15.5320i | − | 1.00468i | −0.864671 | − | 0.502339i | \(-0.832473\pi\) | ||
0.864671 | − | 0.502339i | \(-0.167527\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 25.7287i | − | 1.65733i | −0.559743 | − | 0.828666i | \(-0.689100\pi\) | ||
0.559743 | − | 0.828666i | \(-0.310900\pi\) | |||||||
\(242\) | −0.780519 | + | 15.4961i | −0.0501737 | + | 0.996129i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.26963 | + | 24.1803i | 0.465390 | + | 1.54798i | ||||
\(245\) | −4.59739 | + | 11.0991i | −0.293716 | + | 0.709094i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.80874 | − | 8.80874i | −0.560487 | − | 0.560487i | ||||
\(248\) | 4.60395 | + | 6.25617i | 0.292351 | + | 0.397267i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.34246 | + | 15.4747i | −0.464378 | + | 0.978706i | ||||
\(251\) | 0.0305865 | − | 0.0738424i | 0.00193060 | − | 0.00466089i | −0.922911 | − | 0.385013i | \(-0.874197\pi\) |
0.924842 | + | 0.380352i | \(0.124197\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.346922 | − | 0.143700i | 0.0218108 | − | 0.00903432i | ||||
\(254\) | −17.8981 | + | 16.1816i | −1.12303 | + | 1.01532i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.7207 | + | 6.26912i | 0.920042 | + | 0.391820i | ||||
\(257\) | 27.2896i | 1.70228i | 0.524938 | + | 0.851141i | \(0.324089\pi\) | ||||
−0.524938 | + | 0.851141i | \(0.675911\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.72841 | − | 4.17275i | −0.107398 | − | 0.259282i | ||||
\(260\) | −12.0253 | − | 1.21447i | −0.745775 | − | 0.0753185i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.5321 | + | 7.84416i | 1.02136 | + | 0.484614i | ||||
\(263\) | −14.9965 | − | 14.9965i | −0.924725 | − | 0.924725i | 0.0726334 | − | 0.997359i | \(-0.476860\pi\) |
−0.997359 | + | 0.0726334i | \(0.976860\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.652115 | − | 0.652115i | 0.0400591 | − | 0.0400591i | ||||
\(266\) | −4.66081 | + | 1.66115i | −0.285773 | + | 0.101852i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −22.2740 | + | 6.69652i | −1.36060 | + | 0.409055i | ||||
\(269\) | 19.0608 | − | 7.89523i | 1.16216 | − | 0.481381i | 0.283564 | − | 0.958953i | \(-0.408483\pi\) |
0.878592 | + | 0.477573i | \(0.158483\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.04647 | 0.367297 | 0.183648 | − | 0.982992i | \(-0.441209\pi\) | ||||
0.183648 | + | 0.982992i | \(0.441209\pi\) | |||||||
\(272\) | −18.8639 | − | 3.84953i | −1.14379 | − | 0.233412i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.0564392 | − | 1.12052i | 0.00340962 | − | 0.0676932i | ||||
\(275\) | −0.0827798 | − | 0.199848i | −0.00499181 | − | 0.0120513i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.5872 | + | 7.28485i | 1.05671 | + | 0.437704i | 0.842283 | − | 0.539036i | \(-0.181211\pi\) |
0.214428 | + | 0.976740i | \(0.431211\pi\) | |||||||
\(278\) | 15.1535 | − | 5.40083i | 0.908844 | − | 0.323920i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.48330 | + | 4.10844i | −0.148406 | + | 0.245526i | ||||
\(281\) | −3.99083 | + | 3.99083i | −0.238073 | + | 0.238073i | −0.816052 | − | 0.577979i | \(-0.803842\pi\) |
0.577979 | + | 0.816052i | \(0.303842\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.8200 | − | 9.86659i | −1.41595 | − | 0.586508i | −0.462114 | − | 0.886821i | \(-0.652909\pi\) |
−0.953841 | + | 0.300313i | \(0.902909\pi\) | |||||||
\(284\) | 13.6427 | − | 11.1398i | 0.809544 | − | 0.661026i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.556553 | − | 0.503176i | 0.0329097 | − | 0.0297534i | ||||
\(287\) | −4.91780 | −0.290289 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.16656 | 0.362739 | ||||||||
\(290\) | 5.73320 | − | 5.18335i | 0.336665 | − | 0.304377i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.02509 | − | 1.25540i | −0.0599887 | − | 0.0734668i | ||||
\(293\) | 2.98858 | + | 1.23791i | 0.174595 | + | 0.0723195i | 0.468269 | − | 0.883586i | \(-0.344878\pi\) |
−0.293674 | + | 0.955906i | \(0.594878\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.7820 | − | 10.7820i | 0.627753 | − | 0.627753i | ||||
\(296\) | 3.47634 | + | 14.1004i | 0.202058 | + | 0.819571i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 25.6718 | − | 9.14966i | 1.48713 | − | 0.530026i | ||||
\(299\) | 6.41445 | + | 2.65695i | 0.370957 | + | 0.153656i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.551776 | − | 1.33211i | −0.0318039 | − | 0.0767813i | ||||
\(302\) | 0.300022 | − | 5.95652i | 0.0172643 | − | 0.342759i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 15.6194 | − | 3.02651i | 0.895832 | − | 0.173582i | ||||
\(305\) | 24.3595 | 1.39482 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.9645 | + | 11.5833i | −1.59602 | + | 0.661092i | −0.990845 | − | 0.135002i | \(-0.956896\pi\) |
−0.605173 | + | 0.796094i | \(0.706896\pi\) | |||||||
\(308\) | −0.0858008 | − | 0.285391i | −0.00488895 | − | 0.0162616i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.05891 | − | 2.51586i | 0.400919 | − | 0.142891i | ||||
\(311\) | 19.5213 | − | 19.5213i | 1.10695 | − | 1.10695i | 0.113401 | − | 0.993549i | \(-0.463826\pi\) |
0.993549 | − | 0.113401i | \(-0.0361745\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.3194 | − | 15.3194i | −0.865901 | − | 0.865901i | 0.126114 | − | 0.992016i | \(-0.459749\pi\) |
−0.992016 | + | 0.126114i | \(0.959749\pi\) | |||||||
\(314\) | 4.49090 | + | 2.13085i | 0.253436 | + | 0.120251i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.54083 | + | 25.1583i | −0.142933 | + | 1.41527i | ||||
\(317\) | −8.07700 | − | 19.4996i | −0.453649 | − | 1.09521i | −0.970924 | − | 0.239387i | \(-0.923053\pi\) |
0.517275 | − | 0.855819i | \(-0.326947\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.479791i | 0.0268631i | ||||||||
\(320\) | 9.88095 | − | 11.8591i | 0.552362 | − | 0.662945i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.04560 | − | 1.84941i | 0.113997 | − | 0.103064i | ||||
\(323\) | −17.6870 | + | 7.32618i | −0.984129 | + | 0.407639i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.53057 | − | 3.69512i | 0.0849007 | − | 0.204968i | ||||
\(326\) | 10.9468 | − | 23.0711i | 0.606289 | − | 1.27779i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.6329 | + | 2.37834i | 0.863185 | + | 0.131322i | ||||
\(329\) | −5.80383 | − | 5.80383i | −0.319976 | − | 0.319976i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.08547 | − | 19.5200i | 0.444417 | − | 1.07292i | −0.529965 | − | 0.848020i | \(-0.677795\pi\) |
0.974382 | − | 0.224899i | \(-0.0722052\pi\) | |||||||
\(332\) | 21.0808 | − | 6.33781i | 1.15696 | − | 0.347832i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.17572 | + | 23.3423i | −0.0643326 | + | 1.27723i | ||||
\(335\) | 22.4391i | 1.22598i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.13608i | 0.388727i | 0.980930 | + | 0.194364i | \(0.0622642\pi\) | ||||
−0.980930 | + | 0.194364i | \(0.937736\pi\) | |||||||
\(338\) | −4.50645 | − | 0.226984i | −0.245118 | − | 0.0123463i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.79632 | + | 16.3591i | −0.477047 | + | 0.887198i | ||||
\(341\) | −0.178023 | + | 0.429786i | −0.00964049 | + | 0.0232742i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.22674 | − | 8.22674i | −0.444202 | − | 0.444202i | ||||
\(344\) | 1.10978 | + | 4.50141i | 0.0598355 | + | 0.242700i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −28.9735 | − | 13.7474i | −1.55762 | − | 0.739064i | ||||
\(347\) | 10.8574 | − | 26.2122i | 0.582858 | − | 1.40714i | −0.307354 | − | 0.951595i | \(-0.599443\pi\) |
0.890211 | − | 0.455548i | \(-0.150557\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.7373 | − | 9.00387i | 1.16357 | − | 0.481966i | 0.284508 | − | 0.958674i | \(-0.408170\pi\) |
0.879062 | + | 0.476707i | \(0.158170\pi\) | |||||||
\(350\) | −1.06538 | − | 1.17839i | −0.0569467 | − | 0.0629877i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.134728 | + | 0.948708i | 0.00718100 | + | 0.0505663i | ||||
\(353\) | − | 20.0677i | − | 1.06810i | −0.845454 | − | 0.534048i | \(-0.820670\pi\) | ||
0.845454 | − | 0.534048i | \(-0.179330\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.50264 | − | 15.6988i | −0.345124 | − | 0.833204i | ||||
\(356\) | 11.9527 | + | 14.6382i | 0.633491 | + | 0.775823i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.41533 | + | 2.98290i | −0.0748026 | + | 0.157651i | ||||
\(359\) | 2.29736 | + | 2.29736i | 0.121250 | + | 0.121250i | 0.765128 | − | 0.643878i | \(-0.222676\pi\) |
−0.643878 | + | 0.765128i | \(0.722676\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.24841 | + | 2.24841i | −0.118337 | + | 0.118337i | ||||
\(362\) | 4.57937 | + | 12.8486i | 0.240686 | + | 0.675309i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.60947 | − | 4.85301i | 0.136773 | − | 0.254367i | ||||
\(365\) | −1.44460 | + | 0.598374i | −0.0756139 | + | 0.0313203i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.23365 | −0.377594 | −0.188797 | − | 0.982016i | \(-0.560459\pi\) | ||||
−0.188797 | + | 0.982016i | \(0.560459\pi\) | |||||||
\(368\) | −7.39706 | + | 4.88972i | −0.385598 | + | 0.254894i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 13.9930 | + | 0.704811i | 0.727463 | + | 0.0366414i | ||||
\(371\) | 0.160894 | + | 0.388432i | 0.00835319 | + | 0.0201664i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.5680 | + | 6.86267i | 0.857856 | + | 0.355336i | 0.767869 | − | 0.640607i | \(-0.221317\pi\) |
0.0899875 | + | 0.995943i | \(0.471317\pi\) | |||||||
\(374\) | −0.387098 | − | 1.08611i | −0.0200163 | − | 0.0561612i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.6427 | + | 21.2563i | 0.806709 | + | 1.09621i | ||||
\(377\) | −6.27286 | + | 6.27286i | −0.323069 | + | 0.323069i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.4951 | + | 8.48935i | 1.05276 | + | 0.436069i | 0.840877 | − | 0.541226i | \(-0.182040\pi\) |
0.211885 | + | 0.977295i | \(0.432040\pi\) | |||||||
\(380\) | 1.54232 | − | 15.2714i | 0.0791192 | − | 0.783408i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.31008 | − | 2.55513i | −0.118194 | − | 0.130732i | ||||
\(383\) | −2.58370 | −0.132021 | −0.0660103 | − | 0.997819i | \(-0.521027\pi\) | ||||
−0.0660103 | + | 0.997819i | \(0.521027\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.287506 | −0.0146526 | ||||||||
\(386\) | 22.4388 | + | 24.8191i | 1.14211 | + | 1.26326i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.19040 | − | 11.7869i | 0.0604334 | − | 0.598388i | ||||
\(389\) | −4.93427 | − | 2.04384i | −0.250177 | − | 0.103627i | 0.254071 | − | 0.967186i | \(-0.418230\pi\) |
−0.504248 | + | 0.863559i | \(0.668230\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.54464 | − | 7.54464i | 0.381549 | − | 0.381549i | ||||
\(392\) | 10.4379 | + | 14.1837i | 0.527193 | + | 0.716386i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.72765 | − | 4.84737i | −0.0870376 | − | 0.244207i | ||||
\(395\) | 22.5381 | + | 9.33559i | 1.13402 | + | 0.469725i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.50861 | − | 15.7132i | −0.326658 | − | 0.788622i | −0.998836 | − | 0.0482326i | \(-0.984641\pi\) |
0.672178 | − | 0.740389i | \(-0.265359\pi\) | |||||||
\(398\) | −9.11567 | − | 0.459144i | −0.456927 | − | 0.0230148i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.81678 | + | 4.26116i | 0.140839 | + | 0.213058i | ||||
\(401\) | 13.5140 | 0.674856 | 0.337428 | − | 0.941351i | \(-0.390443\pi\) | ||||
0.337428 | + | 0.941351i | \(0.390443\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.94658 | + | 3.29158i | −0.395847 | + | 0.163965i | ||||
\(404\) | −4.71000 | + | 8.75952i | −0.234331 | + | 0.435802i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.18294 | + | 3.31905i | 0.0587082 | + | 0.164722i | ||||
\(407\) | −0.615006 | + | 0.615006i | −0.0304847 | + | 0.0304847i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.3092 | − | 15.3092i | −0.756990 | − | 0.756990i | 0.218783 | − | 0.975773i | \(-0.429791\pi\) |
−0.975773 | + | 0.218783i | \(0.929791\pi\) | |||||||
\(410\) | 6.53964 | − | 13.7827i | 0.322970 | − | 0.680679i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.454915 | + | 0.557124i | 0.0224120 | + | 0.0274475i | ||||
\(413\) | 2.66020 | + | 6.42230i | 0.130900 | + | 0.316021i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 21.2370i | − | 1.04249i | ||||||
\(416\) | −10.6421 | + | 14.1650i | −0.521772 | + | 0.694496i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.639006 | + | 0.706792i | 0.0312548 | + | 0.0345703i | ||||
\(419\) | −7.00151 | + | 2.90012i | −0.342046 | + | 0.141680i | −0.547093 | − | 0.837072i | \(-0.684265\pi\) |
0.205046 | + | 0.978752i | \(0.434265\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.44827 | − | 10.7391i | 0.216796 | − | 0.523391i | −0.777643 | − | 0.628706i | \(-0.783585\pi\) |
0.994439 | + | 0.105315i | \(0.0335850\pi\) | |||||||
\(422\) | 5.08439 | + | 2.41245i | 0.247504 | + | 0.117436i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.323604 | − | 1.31258i | −0.0157156 | − | 0.0637444i | ||||
\(425\) | −4.34617 | − | 4.34617i | −0.210820 | − | 0.210820i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.24979 | + | 10.2599i | −0.205662 | + | 0.496511i | ||||
\(428\) | 4.23554 | − | 7.87713i | 0.204733 | − | 0.380756i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.46712 | + | 0.225003i | 0.215424 | + | 0.0108506i | ||||
\(431\) | 35.7388i | 1.72148i | 0.509046 | + | 0.860739i | \(0.329998\pi\) | ||||
−0.509046 | + | 0.860739i | \(0.670002\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 36.2711i | − | 1.74308i | −0.490326 | − | 0.871539i | \(-0.663122\pi\) | ||
0.490326 | − | 0.871539i | \(-0.336878\pi\) | |||||||
\(434\) | −0.171860 | + | 3.41205i | −0.00824955 | + | 0.163783i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −24.4984 | + | 7.36529i | −1.17326 | + | 0.352733i | ||||
\(437\) | −3.37419 | + | 8.14601i | −0.161409 | + | 0.389676i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.44721 | − | 4.44721i | −0.212254 | − | 0.212254i | 0.592970 | − | 0.805224i | \(-0.297955\pi\) |
−0.805224 | + | 0.592970i | \(0.797955\pi\) | |||||||
\(440\) | 0.913937 | + | 0.139043i | 0.0435702 | + | 0.00662861i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.13893 | − | 19.2609i | 0.434694 | − | 0.916146i | ||||
\(443\) | −0.302597 | + | 0.730534i | −0.0143768 | + | 0.0347087i | −0.930905 | − | 0.365262i | \(-0.880980\pi\) |
0.916528 | + | 0.399970i | \(0.130980\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.8443 | − | 6.97714i | 0.798497 | − | 0.330748i | ||||
\(446\) | −15.8706 | + | 14.3485i | −0.751493 | + | 0.679420i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.27107 | + | 6.23070i | 0.154544 | + | 0.294373i | ||||
\(449\) | 9.45413i | 0.446168i | 0.974799 | + | 0.223084i | \(0.0716124\pi\) | ||||
−0.974799 | + | 0.223084i | \(0.928388\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.362408 | + | 0.874930i | 0.0170651 | + | 0.0411988i | ||||
\(452\) | −2.53593 | + | 25.1099i | −0.119280 | + | 1.18107i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 20.0168 | + | 9.49758i | 0.939433 | + | 0.445744i | ||||
\(455\) | −3.75889 | − | 3.75889i | −0.176220 | − | 0.176220i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.41071 | + | 8.41071i | −0.393437 | + | 0.393437i | −0.875910 | − | 0.482474i | \(-0.839738\pi\) |
0.482474 | + | 0.875910i | \(0.339738\pi\) | |||||||
\(458\) | 7.81690 | − | 2.78601i | 0.365260 | − | 0.130182i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.46298 | + | 8.19236i | 0.114837 | + | 0.381971i | ||||
\(461\) | 22.6364 | − | 9.37632i | 1.05428 | − | 0.436699i | 0.212865 | − | 0.977082i | \(-0.431721\pi\) |
0.841419 | + | 0.540383i | \(0.181721\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.98464 | 0.138708 | 0.0693541 | − | 0.997592i | \(-0.477906\pi\) | ||||
0.0693541 | + | 0.997592i | \(0.477906\pi\) | |||||||
\(464\) | −2.15523 | − | 11.1228i | −0.100054 | − | 0.516364i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.16185 | + | 42.9206i | −0.100146 | + | 1.98826i | ||||
\(467\) | 14.7083 | + | 35.5089i | 0.680618 | + | 1.64316i | 0.762874 | + | 0.646547i | \(0.223788\pi\) |
−0.0822559 | + | 0.996611i | \(0.526212\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.45105 | − | 3.91475i | −0.436409 | − | 0.180767i | ||||
\(470\) | 23.9838 | − | 8.54803i | 1.10629 | − | 0.394291i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.35044 | − | 21.7020i | −0.246274 | − | 0.998917i | ||||
\(473\) | −0.196334 | + | 0.196334i | −0.00902744 | + | 0.00902744i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.69260 | + | 1.94374i | 0.215311 | + | 0.0891849i | ||||
\(476\) | −5.35564 | − | 6.55894i | −0.245476 | − | 0.300629i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16.2936 | + | 14.7310i | −0.745253 | + | 0.673778i | ||||
\(479\) | 39.8284 | 1.81980 | 0.909902 | − | 0.414823i | \(-0.136156\pi\) | ||||
0.909902 | + | 0.414823i | \(0.136156\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.0813 | −0.733246 | ||||||||
\(482\) | −26.9904 | + | 24.4019i | −1.22938 | + | 1.11147i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.9963 | − | 13.8782i | 0.772559 | − | 0.630826i | ||||
\(485\) | −10.5593 | − | 4.37380i | −0.479472 | − | 0.198604i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.5914 | − | 21.5914i | 0.978400 | − | 0.978400i | −0.0213713 | − | 0.999772i | \(-0.506803\pi\) |
0.999772 | + | 0.0213713i | \(0.00680320\pi\) | |||||||
\(488\) | 18.4713 | − | 30.5594i | 0.836156 | − | 1.38336i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 16.0037 | − | 5.70385i | 0.722971 | − | 0.257674i | ||||
\(491\) | 26.9379 | + | 11.1580i | 1.21569 | + | 0.503555i | 0.896037 | − | 0.443980i | \(-0.146434\pi\) |
0.319652 | + | 0.947535i | \(0.396434\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.21710 | + | 12.5952i | 0.234966 | + | 0.567259i | ||||
\(494\) | −0.886245 | + | 17.5952i | −0.0398741 | + | 0.791644i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.19644 | − | 10.7633i | 0.0986232 | − | 0.483284i | ||||
\(497\) | 7.74658 | 0.347482 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.3562 | − | 4.70388i | 0.508372 | − | 0.210575i | −0.113729 | − | 0.993512i | \(-0.536279\pi\) |
0.622101 | + | 0.782937i | \(0.286279\pi\) | |||||||
\(500\) | 23.1974 | − | 6.97413i | 1.03742 | − | 0.311892i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.106473 | + | 0.0379478i | −0.00475211 | + | 0.00169369i | ||||
\(503\) | 8.97393 | − | 8.97393i | 0.400128 | − | 0.400128i | −0.478150 | − | 0.878278i | \(-0.658693\pi\) |
0.878278 | + | 0.478150i | \(0.158693\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.78467 | + | 6.78467i | 0.301914 | + | 0.301914i | ||||
\(506\) | −0.479777 | − | 0.227645i | −0.0213287 | − | 0.0101201i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 33.9502 | + | 3.42876i | 1.50630 | + | 0.152126i | ||||
\(509\) | −2.41200 | − | 5.82308i | −0.106910 | − | 0.258104i | 0.861367 | − | 0.507983i | \(-0.169609\pi\) |
−0.968277 | + | 0.249880i | \(0.919609\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 0.712842i | − | 0.0315343i | ||||||
\(512\) | −7.38496 | − | 21.3884i | −0.326372 | − | 0.945241i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 28.6279 | − | 25.8823i | 1.26272 | − | 1.14162i | ||||
\(515\) | 0.641088 | − | 0.265547i | 0.0282497 | − | 0.0117014i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.604862 | + | 1.46027i | −0.0266018 | + | 0.0642224i | ||||
\(518\) | −2.73811 | + | 5.77073i | −0.120305 | + | 0.253551i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.1311 | + | 13.7668i | 0.444277 | + | 0.603714i | ||||
\(521\) | −0.969806 | − | 0.969806i | −0.0424880 | − | 0.0424880i | 0.685544 | − | 0.728032i | \(-0.259565\pi\) |
−0.728032 | + | 0.685544i | \(0.759565\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.6100 | + | 32.8575i | −0.595125 | + | 1.43676i | 0.283372 | + | 0.959010i | \(0.408547\pi\) |
−0.878497 | + | 0.477748i | \(0.841453\pi\) | |||||||
\(524\) | −7.45067 | − | 24.7824i | −0.325484 | − | 1.08263i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.50880 | + | 29.9551i | −0.0657867 | + | 1.30610i | ||||
\(527\) | 13.2183i | 0.575796i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.0859i | 0.786343i | ||||||||
\(530\) | −1.30258 | − | 0.0656092i | −0.0565804 | − | 0.00284988i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.16306 | + | 3.31388i | 0.267203 | + | 0.143675i | ||||
\(533\) | −6.70079 | + | 16.1771i | −0.290243 | + | 0.700709i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.10122 | − | 6.10122i | −0.263779 | − | 0.263779i | ||||
\(536\) | 28.1502 | + | 17.0151i | 1.21590 | + | 0.734940i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −26.3602 | − | 12.5074i | −1.13647 | − | 0.539233i | ||||
\(539\) | −0.403606 | + | 0.974392i | −0.0173846 | + | 0.0419700i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.0030 | + | 9.11394i | −0.945983 | + | 0.391839i | −0.801720 | − | 0.597700i | \(-0.796081\pi\) |
−0.144263 | + | 0.989539i | \(0.546081\pi\) | |||||||
\(542\) | −5.73464 | − | 6.34298i | −0.246324 | − | 0.272454i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.8528 | + | 23.4399i | 0.593932 | + | 1.00498i | ||||
\(545\) | 24.6800i | 1.05717i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.89886 | − | 6.99847i | −0.123946 | − | 0.299233i | 0.849711 | − | 0.527248i | \(-0.176776\pi\) |
−0.973657 | + | 0.228016i | \(0.926776\pi\) | |||||||
\(548\) | −1.22900 | + | 1.00353i | −0.0525003 | + | 0.0428686i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.131138 | + | 0.276381i | −0.00559173 | + | 0.0117849i | ||||
\(551\) | −7.96619 | − | 7.96619i | −0.339371 | − | 0.339371i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.86407 | + | 7.86407i | −0.334414 | + | 0.334414i | ||||
\(554\) | −9.03810 | − | 25.3588i | −0.383992 | − | 1.07739i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.0377 | − | 10.7743i | −0.849786 | − | 0.456930i | ||||
\(557\) | −5.71563 | + | 2.36749i | −0.242179 | + | 0.100314i | −0.500472 | − | 0.865753i | \(-0.666840\pi\) |
0.258293 | + | 0.966067i | \(0.416840\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.13379 | −0.217136 | ||||||||
\(560\) | 6.66515 | − | 1.29148i | 0.281654 | − | 0.0545750i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.97156 | + | 0.401517i | 0.336260 | + | 0.0169370i | ||||
\(563\) | −11.5978 | − | 27.9995i | −0.488787 | − | 1.18004i | −0.955331 | − | 0.295538i | \(-0.904501\pi\) |
0.466544 | − | 0.884498i | \(-0.345499\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.4947 | + | 9.31760i | 0.946358 | + | 0.391994i | ||||
\(566\) | 12.2412 | + | 34.3459i | 0.514536 | + | 1.44367i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.6252 | − | 3.74638i | −1.03325 | − | 0.157195i | ||||
\(569\) | −8.09693 | + | 8.09693i | −0.339441 | + | 0.339441i | −0.856157 | − | 0.516716i | \(-0.827154\pi\) |
0.516716 | + | 0.856157i | \(0.327154\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.74000 | + | 1.13495i | 0.114666 | + | 0.0474960i | 0.439279 | − | 0.898351i | \(-0.355234\pi\) |
−0.324613 | + | 0.945847i | \(0.605234\pi\) | |||||||
\(572\) | −1.05570 | − | 0.106619i | −0.0441411 | − | 0.00445797i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.66419 | + | 5.15897i | 0.194679 | + | 0.215331i | ||||
\(575\) | −2.83083 | −0.118054 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.87235 | 0.286100 | 0.143050 | − | 0.989715i | \(-0.454309\pi\) | ||||
0.143050 | + | 0.989715i | \(0.454309\pi\) | |||||||
\(578\) | −5.84855 | − | 6.46896i | −0.243267 | − | 0.269073i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10.8751 | − | 1.09831i | −0.451562 | − | 0.0456049i | ||||
\(581\) | 8.94478 | + | 3.70505i | 0.371092 | + | 0.153711i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.0572495 | − | 0.0572495i | 0.00237103 | − | 0.00237103i | ||||
\(584\) | −0.344743 | + | 2.26601i | −0.0142656 | + | 0.0937684i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.53584 | − | 4.30920i | −0.0634449 | − | 0.178012i | ||||
\(587\) | 38.8656 | + | 16.0987i | 1.60415 | + | 0.664463i | 0.991996 | − | 0.126272i | \(-0.0403012\pi\) |
0.612159 | + | 0.790735i | \(0.290301\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.18013 | − | 10.0917i | −0.172239 | − | 0.415822i | ||||
\(590\) | −21.5367 | − | 1.08478i | −0.886653 | − | 0.0446595i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.4948 | − | 17.0201i | 0.472435 | − | 0.699521i | ||||
\(593\) | −3.82382 | −0.157025 | −0.0785126 | − | 0.996913i | \(-0.525017\pi\) | ||||
−0.0785126 | + | 0.996913i | \(0.525017\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.54743 | + | 3.12625i | −0.309415 | + | 0.128164i | ||||
\(596\) | −33.9462 | − | 18.2529i | −1.39049 | − | 0.747668i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.29641 | − | 9.24894i | −0.134800 | − | 0.378217i | ||||
\(599\) | 24.3269 | − | 24.3269i | 0.993971 | − | 0.993971i | −0.00601064 | − | 0.999982i | \(-0.501913\pi\) |
0.999982 | + | 0.00601064i | \(0.00191326\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.3481 | − | 11.3481i | −0.462899 | − | 0.462899i | 0.436706 | − | 0.899604i | \(-0.356145\pi\) |
−0.899604 | + | 0.436706i | \(0.856145\pi\) | |||||||
\(602\) | −0.874110 | + | 1.84224i | −0.0356261 | + | 0.0750842i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.53317 | + | 5.33460i | −0.265831 | + | 0.217062i | ||||
\(605\) | −8.10111 | − | 19.5578i | −0.329357 | − | 0.795138i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.7633i | 1.37041i | 0.728349 | + | 0.685206i | \(0.240288\pi\) | ||||
−0.728349 | + | 0.685206i | \(0.759712\pi\) | |||||||
\(608\) | −17.9888 | − | 13.5149i | −0.729541 | − | 0.548101i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −23.1032 | − | 25.5540i | −0.935422 | − | 1.03465i | ||||
\(611\) | −26.9998 | + | 11.1837i | −1.09229 | + | 0.452443i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.90460 | + | 11.8407i | −0.198095 | + | 0.478243i | −0.991445 | − | 0.130522i | \(-0.958335\pi\) |
0.793351 | + | 0.608765i | \(0.208335\pi\) | |||||||
\(614\) | 38.6736 | + | 18.3499i | 1.56074 | + | 0.740543i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.218010 | + | 0.360681i | −0.00878387 | + | 0.0145323i | ||||
\(617\) | −34.8951 | − | 34.8951i | −1.40482 | − | 1.40482i | −0.783760 | − | 0.621064i | \(-0.786701\pi\) |
−0.621064 | − | 0.783760i | \(-0.713299\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.75222 | − | 11.4729i | 0.191008 | − | 0.461134i | −0.799142 | − | 0.601142i | \(-0.794713\pi\) |
0.990150 | + | 0.140008i | \(0.0447127\pi\) | |||||||
\(620\) | −9.33411 | − | 5.01896i | −0.374867 | − | 0.201566i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −38.9931 | − | 1.96403i | −1.56348 | − | 0.0787505i | ||||
\(623\) | 8.31186i | 0.333008i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 16.9843i | − | 0.679370i | ||||||
\(626\) | −1.54128 | + | 30.5999i | −0.0616018 | + | 1.22302i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.02396 | − | 6.73209i | −0.0807647 | − | 0.268640i | ||||
\(629\) | −9.45739 | + | 22.8322i | −0.377091 | + | 0.910378i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.46865 | − | 2.46865i | −0.0982753 | − | 0.0982753i | 0.656260 | − | 0.754535i | \(-0.272138\pi\) |
−0.754535 | + | 0.656260i | \(0.772138\pi\) | |||||||
\(632\) | 28.8019 | − | 21.1955i | 1.14568 | − | 0.843111i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.7954 | + | 26.9671i | −0.508169 | + | 1.07100i | ||||
\(635\) | 12.5980 | − | 30.4143i | 0.499937 | − | 1.20696i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.0162 | + | 7.46253i | −0.713826 | + | 0.295676i | ||||
\(638\) | 0.503320 | − | 0.455048i | 0.0199266 | − | 0.0180155i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21.8121 | + | 0.882038i | −0.862197 | + | 0.0348656i | ||||
\(641\) | − | 38.1577i | − | 1.50714i | −0.657368 | − | 0.753570i | \(-0.728330\pi\) | ||
0.657368 | − | 0.753570i | \(-0.271670\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.23595 | + | 2.98384i | 0.0487411 | + | 0.117671i | 0.946375 | − | 0.323071i | \(-0.104715\pi\) |
−0.897634 | + | 0.440742i | \(0.854715\pi\) | |||||||
\(644\) | −3.88021 | − | 0.391877i | −0.152902 | − | 0.0154421i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.4603 | + | 11.6059i | 0.962376 | + | 0.456630i | ||||
\(647\) | 21.3045 | + | 21.3045i | 0.837567 | + | 0.837567i | 0.988538 | − | 0.150971i | \(-0.0482401\pi\) |
−0.150971 | + | 0.988538i | \(0.548240\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.946557 | − | 0.946557i | 0.0371556 | − | 0.0371556i | ||||
\(650\) | −5.32796 | + | 1.89893i | −0.208980 | + | 0.0744823i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −34.5848 | + | 10.3977i | −1.35445 | + | 0.407205i | ||||
\(653\) | −13.2549 | + | 5.49034i | −0.518703 | + | 0.214854i | −0.626647 | − | 0.779303i | \(-0.715573\pi\) |
0.107944 | + | 0.994157i | \(0.465573\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.9661 | −0.975506 | ||||||||
\(656\) | −12.3318 | − | 18.6553i | −0.481475 | − | 0.728365i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.583923 | + | 11.5930i | −0.0227637 | + | 0.451941i | ||||
\(659\) | −11.5078 | − | 27.7824i | −0.448282 | − | 1.08225i | −0.972965 | − | 0.230951i | \(-0.925816\pi\) |
0.524683 | − | 0.851297i | \(-0.324184\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.8418 | + | 11.9467i | 1.12182 | + | 0.464671i | 0.864991 | − | 0.501787i | \(-0.167324\pi\) |
0.256824 | + | 0.966458i | \(0.417324\pi\) | |||||||
\(662\) | −28.1458 | + | 10.0314i | −1.09392 | + | 0.389882i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −26.6423 | − | 16.1036i | −1.03392 | − | 0.624942i | ||||
\(665\) | 4.77359 | − | 4.77359i | 0.185112 | − | 0.185112i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.80092 | + | 2.40282i | 0.224612 | + | 0.0930375i | ||||
\(668\) | 25.6021 | − | 20.9051i | 0.990574 | − | 0.808844i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 23.5394 | − | 21.2818i | 0.909408 | − | 0.822190i | ||||
\(671\) | 2.13853 | 0.0825569 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.9502 | −1.57851 | −0.789257 | − | 0.614063i | \(-0.789534\pi\) | ||||
−0.789257 | + | 0.614063i | \(0.789534\pi\) | |||||||
\(674\) | 7.48603 | − | 6.76807i | 0.288351 | − | 0.260696i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.03593 | + | 4.94272i | 0.155228 | + | 0.190104i | ||||
\(677\) | −38.6124 | − | 15.9938i | −1.48399 | − | 0.614690i | −0.513994 | − | 0.857794i | \(-0.671834\pi\) |
−0.970000 | + | 0.243104i | \(0.921834\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.68438 | − | 3.68438i | 0.141394 | − | 0.141394i | ||||
\(680\) | 25.5040 | − | 6.28780i | 0.978035 | − | 0.241126i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.619704 | − | 0.220868i | 0.0237297 | − | 0.00845748i | ||||
\(683\) | 19.6686 | + | 8.14698i | 0.752596 | + | 0.311736i | 0.725800 | − | 0.687905i | \(-0.241470\pi\) |
0.0267959 | + | 0.999641i | \(0.491470\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.585790 | + | 1.41422i | 0.0223819 | + | 0.0540346i | ||||
\(686\) | −0.827691 | + | 16.4326i | −0.0316014 | + | 0.627401i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.66960 | − | 5.43347i | 0.139902 | − | 0.207149i | ||||
\(689\) | 1.49698 | 0.0570302 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.338658 | + | 0.140277i | −0.0128832 | + | 0.00533638i | −0.389116 | − | 0.921189i | \(-0.627219\pi\) |
0.376233 | + | 0.926525i | \(0.377219\pi\) | |||||||
\(692\) | 13.0577 | + | 43.4327i | 0.496381 | + | 1.65106i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −37.7951 | + | 13.4705i | −1.43468 | + | 0.511334i | ||||
\(695\) | −15.5201 | + | 15.5201i | −0.588712 | + | 0.588712i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.0274 | + | 19.0274i | 0.720716 | + | 0.720716i | ||||
\(698\) | −30.0617 | − | 14.2637i | −1.13785 | − | 0.539889i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.225745 | + | 2.23524i | −0.00853236 | + | 0.0844842i | ||||
\(701\) | −17.6750 | − | 42.6712i | −0.667575 | − | 1.61167i | −0.785655 | − | 0.618665i | \(-0.787674\pi\) |
0.118080 | − | 0.993004i | \(-0.462326\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 20.4224i | − | 0.770247i | ||||||
\(704\) | 0.867452 | − | 1.04112i | 0.0326933 | − | 0.0392386i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.0518 | + | 19.0328i | −0.792295 | + | 0.716309i | ||||
\(707\) | −4.04128 | + | 1.67395i | −0.151988 | + | 0.0629555i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.95722 | − | 14.3820i | 0.223728 | − | 0.540127i | −0.771663 | − | 0.636032i | \(-0.780575\pi\) |
0.995390 | + | 0.0959051i | \(0.0305745\pi\) | |||||||
\(710\) | −10.3013 | + | 21.7107i | −0.386601 | + | 0.814787i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.01976 | − | 26.4221i | 0.150647 | − | 0.990211i | ||||
\(713\) | 4.30478 | + | 4.30478i | 0.161215 | + | 0.161215i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.391743 | + | 0.945751i | −0.0146504 | + | 0.0353691i | ||||
\(716\) | 4.47152 | − | 1.34433i | 0.167109 | − | 0.0502401i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.231137 | − | 4.58891i | 0.00862596 | − | 0.171256i | ||||
\(719\) | 26.6063i | 0.992249i | 0.868251 | + | 0.496124i | \(0.165244\pi\) | ||||
−0.868251 | + | 0.496124i | \(0.834756\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.316346i | 0.0117813i | ||||||||
\(722\) | 4.49112 | + | 0.226212i | 0.167142 | + | 0.00841873i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.13551 | − | 16.9900i | 0.339519 | − | 0.631427i | ||||
\(725\) | 1.38417 | − | 3.34169i | 0.0514068 | − | 0.124107i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.3093 | + | 32.3093i | 1.19828 | + | 1.19828i | 0.974680 | + | 0.223604i | \(0.0717823\pi\) |
0.223604 | + | 0.974680i | \(0.428218\pi\) | |||||||
\(728\) | −7.56589 | + | 1.86530i | −0.280411 | + | 0.0691328i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.99782 | + | 0.947929i | 0.0739426 | + | 0.0350844i | ||||
\(731\) | −3.01917 | + | 7.28891i | −0.111668 | + | 0.269590i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.7622 | + | 10.6711i | −0.951549 | + | 0.394145i | −0.803813 | − | 0.594882i | \(-0.797199\pi\) |
−0.147736 | + | 0.989027i | \(0.547199\pi\) | |||||||
\(734\) | 6.86060 | + | 7.58838i | 0.253230 | + | 0.280092i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.1451 | + | 3.12226i | 0.447674 | + | 0.115088i | ||||
\(737\) | 1.96993i | 0.0725634i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.64374 | + | 23.2821i | 0.354751 | + | 0.856444i | 0.996020 | + | 0.0891284i | \(0.0284081\pi\) |
−0.641269 | + | 0.767316i | \(0.721592\pi\) | |||||||
\(740\) | −12.5320 | − | 15.3477i | −0.460687 | − | 0.564193i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.254884 | − | 0.537184i | 0.00935708 | − | 0.0197207i | ||||
\(743\) | −12.1679 | − | 12.1679i | −0.446396 | − | 0.446396i | 0.447759 | − | 0.894154i | \(-0.352222\pi\) |
−0.894154 | + | 0.447759i | \(0.852222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.2930 | + | 26.2930i | −0.963301 | + | 0.963301i | ||||
\(746\) | −8.51432 | − | 23.8892i | −0.311731 | − | 0.874645i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.772232 | + | 1.43617i | −0.0282356 | + | 0.0525117i | ||||
\(749\) | 3.63419 | − | 1.50533i | 0.132790 | − | 0.0550035i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.0598 | 0.768485 | 0.384242 | − | 0.923232i | \(-0.374463\pi\) | ||||
0.384242 | + | 0.923232i | \(0.374463\pi\) | |||||||
\(752\) | 7.46276 | − | 36.5699i | 0.272139 | − | 1.33357i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.5298 | + | 0.631111i | 0.456310 | + | 0.0229837i | ||||
\(755\) | 3.11397 | + | 7.51778i | 0.113329 | + | 0.273600i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.7664 | − | 13.1581i | −1.15457 | − | 0.478238i | −0.278505 | − | 0.960435i | \(-0.589839\pi\) |
−0.876063 | + | 0.482197i | \(0.839839\pi\) | |||||||
\(758\) | −10.5325 | − | 29.5517i | −0.382557 | − | 1.07337i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17.4831 | + | 12.8659i | −0.634179 | + | 0.466696i | ||||
\(761\) | −15.4825 | + | 15.4825i | −0.561240 | + | 0.561240i | −0.929660 | − | 0.368419i | \(-0.879899\pi\) |
0.368419 | + | 0.929660i | \(0.379899\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.3949 | − | 4.30571i | −0.376321 | − | 0.155877i | ||||
\(764\) | −0.489487 | + | 4.84672i | −0.0177090 | + | 0.175348i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.45045 | + | 2.71040i | 0.0885384 | + | 0.0979306i | ||||
\(767\) | 24.7509 | 0.893701 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.8973 | 0.609333 | 0.304666 | − | 0.952459i | \(-0.401455\pi\) | ||||
0.304666 | + | 0.952459i | \(0.401455\pi\) | |||||||
\(770\) | 0.272679 | + | 0.301605i | 0.00982666 | + | 0.0108691i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.75461 | − | 47.0784i | 0.171122 | − | 1.69439i | ||||
\(773\) | −28.9525 | − | 11.9925i | −1.04135 | − | 0.431341i | −0.204553 | − | 0.978856i | \(-0.565574\pi\) |
−0.836796 | + | 0.547515i | \(0.815574\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.47982 | − | 2.47982i | 0.0890777 | − | 0.0890777i | ||||
\(776\) | −13.4939 | + | 9.93025i | −0.484403 | + | 0.356475i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.53574 | + | 7.11468i | 0.0909105 | + | 0.255074i | ||||
\(779\) | −20.5441 | − | 8.50964i | −0.736068 | − | 0.304889i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.570869 | − | 1.37820i | −0.0204273 | − | 0.0493159i | ||||
\(782\) | −15.0702 | − | 0.759065i | −0.538908 | − | 0.0271441i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.97968 | − | 24.4020i | 0.177846 | − | 0.871500i | ||||
\(785\) | −6.78198 | −0.242059 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.7032 | − | 7.33292i | 0.631052 | − | 0.261390i | −0.0441479 | − | 0.999025i | \(-0.514057\pi\) |
0.675200 | + | 0.737635i | \(0.264057\pi\) | |||||||
\(788\) | −3.44653 | + | 6.40976i | −0.122778 | + | 0.228338i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −11.5824 | − | 32.4975i | −0.412083 | − | 1.15621i | ||||
\(791\) | −7.84892 | + | 7.84892i | −0.279075 | + | 0.279075i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.9594 | + | 27.9594i | 0.992867 | + | 0.992867i | ||||
\(794\) | −10.3108 | + | 21.7306i | −0.365916 | + | 0.771191i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.16391 | + | 9.99816i | 0.289362 | + | 0.354375i | ||||
\(797\) | −2.51784 | − | 6.07859i | −0.0891863 | − | 0.215315i | 0.872992 | − | 0.487734i | \(-0.162176\pi\) |
−0.962179 | + | 0.272419i | \(0.912176\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.9111i | 1.58884i | ||||||||
\(800\) | 1.79861 | − | 6.99632i | 0.0635905 | − | 0.247357i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.8171 | − | 14.1767i | −0.452586 | − | 0.500596i | ||||
\(803\) | −0.126822 | + | 0.0525315i | −0.00447546 | + | 0.00185379i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.43984 | + | 3.47609i | −0.0507478 | + | 0.122516i | ||||
\(806\) | 10.9898 | + | 5.21444i | 0.387098 | + | 0.183671i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13.6562 | − | 3.36681i | 0.480423 | − | 0.118444i | ||||
\(809\) | −26.1388 | − | 26.1388i | −0.918990 | − | 0.918990i | 0.0779658 | − | 0.996956i | \(-0.475158\pi\) |
−0.996956 | + | 0.0779658i | \(0.975158\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.0990278 | − | 0.239074i | 0.00347734 | − | 0.00839503i | −0.922131 | − | 0.386877i | \(-0.873554\pi\) |
0.925609 | + | 0.378482i | \(0.123554\pi\) | |||||||
\(812\) | 2.35988 | − | 4.38883i | 0.0828154 | − | 0.154018i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.22845 | + | 0.0618756i | 0.0430573 | + | 0.00216874i | ||||
\(815\) | 34.8411i | 1.22043i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.51964i | − | 0.228093i | ||||||
\(818\) | −1.54025 | + | 30.5796i | −0.0538537 | + | 1.06919i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.6610 | + | 6.21158i | −0.721512 | + | 0.216918i | ||||
\(821\) | −18.4263 | + | 44.4851i | −0.643083 | + | 1.55254i | 0.179416 | + | 0.983773i | \(0.442579\pi\) |
−0.822499 | + | 0.568767i | \(0.807421\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.9395 | + | 19.9395i | 0.695048 | + | 0.695048i | 0.963338 | − | 0.268290i | \(-0.0864585\pi\) |
−0.268290 | + | 0.963338i | \(0.586459\pi\) | |||||||
\(824\) | 0.152991 | − | 1.00562i | 0.00532968 | − | 0.0350323i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.21423 | − | 8.88175i | 0.146632 | − | 0.309036i | ||||
\(827\) | 9.96943 | − | 24.0683i | 0.346671 | − | 0.836938i | −0.650337 | − | 0.759645i | \(-0.725372\pi\) |
0.997008 | − | 0.0772925i | \(-0.0246275\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.308480 | + | 0.127777i | −0.0107140 | + | 0.00443787i | −0.388034 | − | 0.921645i | \(-0.626846\pi\) |
0.377320 | + | 0.926083i | \(0.376846\pi\) | |||||||
\(830\) | −22.2785 | + | 20.1418i | −0.773298 | + | 0.699133i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24.9529 | − | 2.27052i | 0.865087 | − | 0.0787160i | ||||
\(833\) | 29.9679i | 1.03832i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.2030 | − | 29.4605i | −0.422301 | − | 1.01952i | ||||
\(836\) | 0.135401 | − | 1.34068i | 0.00468293 | − | 0.0463686i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.68278 | + | 4.59430i | 0.334486 | + | 0.158707i | ||||
\(839\) | −38.2282 | − | 38.2282i | −1.31978 | − | 1.31978i | −0.913944 | − | 0.405841i | \(-0.866979\pi\) |
−0.405841 | − | 0.913944i | \(-0.633021\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.8332 | − | 14.8332i | 0.511491 | − | 0.511491i | ||||
\(842\) | −15.4846 | + | 5.51885i | −0.533634 | + | 0.190192i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.29143 | − | 7.62175i | −0.0788742 | − | 0.262352i | ||||
\(845\) | 5.68763 | − | 2.35589i | 0.195660 | − | 0.0810452i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.65084 | 0.331607 | ||||||||
\(848\) | −1.07003 | + | 1.58436i | −0.0367449 | + | 0.0544071i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.437268 | + | 8.68134i | −0.0149982 | + | 0.297768i | ||||
\(851\) | 4.35575 | + | 10.5157i | 0.149313 | + | 0.360474i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.42158 | + | 2.24569i | 0.185631 | + | 0.0768911i | 0.473563 | − | 0.880760i | \(-0.342968\pi\) |
−0.287932 | + | 0.957651i | \(0.592968\pi\) | |||||||
\(854\) | 14.7937 | − | 5.27259i | 0.506229 | − | 0.180424i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.2805 | + | 3.02766i | −0.419740 | + | 0.103483i | ||||
\(857\) | 16.3557 | − | 16.3557i | 0.558701 | − | 0.558701i | −0.370236 | − | 0.928938i | \(-0.620723\pi\) |
0.928938 | + | 0.370236i | \(0.120723\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.2965 | + | 12.5492i | 1.03370 | + | 0.428175i | 0.834048 | − | 0.551691i | \(-0.186017\pi\) |
0.199657 | + | 0.979866i | \(0.436017\pi\) | |||||||
\(860\) | −4.00071 | − | 4.89958i | −0.136423 | − | 0.167074i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 37.4914 | − | 33.8957i | 1.27696 | − | 1.15449i | ||||
\(863\) | 8.63755 | 0.294026 | 0.147013 | − | 0.989135i | \(-0.453034\pi\) | ||||
0.147013 | + | 0.989135i | \(0.453034\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 43.7546 | 1.48770 | ||||||||
\(866\) | −38.0498 | + | 34.4006i | −1.29298 | + | 1.16898i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.74237 | − | 3.05580i | 0.127024 | − | 0.103720i | ||||
\(869\) | 1.97863 | + | 0.819575i | 0.0671204 | + | 0.0278022i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.7552 | + | 25.7552i | −0.872681 | + | 0.872681i | ||||
\(872\) | 30.9615 | + | 18.7144i | 1.04849 | + | 0.633748i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11.7457 | − | 4.18626i | 0.397303 | − | 0.141602i | ||||
\(875\) | 9.84285 | + | 4.07704i | 0.332749 | + | 0.137829i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.3895 | + | 37.1535i | 0.519666 | + | 1.25458i | 0.938109 | + | 0.346341i | \(0.112576\pi\) |
−0.418443 | + | 0.908243i | \(0.637424\pi\) | |||||||
\(878\) | −0.447433 | + | 8.88317i | −0.0151001 | + | 0.299792i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.720943 | − | 1.09063i | −0.0243030 | − | 0.0367650i | ||||
\(881\) | 6.48388 | 0.218447 | 0.109224 | − | 0.994017i | \(-0.465164\pi\) | ||||
0.109224 | + | 0.994017i | \(0.465164\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.658325 | − | 0.272687i | 0.0221544 | − | 0.00917665i | −0.371579 | − | 0.928401i | \(-0.621183\pi\) |
0.393733 | + | 0.919225i | \(0.371183\pi\) | |||||||
\(884\) | −28.8730 | + | 8.68048i | −0.971105 | + | 0.291956i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.05335 | − | 0.375424i | 0.0353880 | − | 0.0126126i | ||||
\(887\) | −8.84672 | + | 8.84672i | −0.297044 | + | 0.297044i | −0.839855 | − | 0.542811i | \(-0.817360\pi\) |
0.542811 | + | 0.839855i | \(0.317360\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.6123 | + | 10.6123i | 0.355924 | + | 0.355924i | ||||
\(890\) | −23.2949 | − | 11.0530i | −0.780847 | − | 0.370498i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 30.1042 | + | 3.04033i | 1.00796 | + | 0.101798i | ||||
\(893\) | −14.2027 | − | 34.2883i | −0.475274 | − | 1.14741i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 4.50466i | − | 0.150574i | ||||||
\(896\) | 3.43386 | − | 9.34085i | 0.114717 | − | 0.312056i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.91775 | − | 8.96657i | 0.330960 | − | 0.299218i | ||||
\(899\) | −7.18650 | + | 2.97675i | −0.239683 | + | 0.0992801i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.880366 | − | 2.12539i | 0.0293293 | − | 0.0708071i | ||||
\(902\) | 0.574117 | − | 1.20999i | 0.0191160 | − | 0.0402882i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 28.7464 | − | 21.1546i | 0.956090 | − | 0.703592i | ||||
\(905\) | −13.1595 | − | 13.1595i | −0.437438 | − | 0.437438i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.3164 | + | 29.7344i | −0.408958 | + | 0.987313i | 0.576454 | + | 0.817130i | \(0.304436\pi\) |
−0.985412 | + | 0.170183i | \(0.945564\pi\) | |||||||
\(908\) | −9.02114 | − | 30.0061i | −0.299377 | − | 0.995788i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.378181 | + | 7.50827i | −0.0125366 | + | 0.248897i | ||||
\(911\) | 8.91656i | 0.295419i | 0.989031 | + | 0.147709i | \(0.0471901\pi\) | ||||
−0.989031 | + | 0.147709i | \(0.952810\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.86441i | − | 0.0617029i | ||||||
\(914\) | 16.8001 | + | 0.846200i | 0.555699 | + | 0.0279898i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.3364 | − | 5.55790i | −0.341525 | − | 0.183638i | ||||
\(917\) | 4.35562 | − | 10.5154i | 0.143835 | − | 0.347249i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.38230 | − | 6.38230i | −0.210533 | − | 0.210533i | 0.593961 | − | 0.804494i | \(-0.297563\pi\) |
−0.804494 | + | 0.593961i | \(0.797563\pi\) | |||||||
\(920\) | 6.25814 | − | 10.3536i | 0.206325 | − | 0.341349i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −31.3052 | − | 14.8537i | −1.03098 | − | 0.489181i | ||||
\(923\) | 10.5552 | − | 25.4824i | 0.347427 | − | 0.838764i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.05770 | − | 2.50918i | 0.199176 | − | 0.0825013i | ||||
\(926\) | −2.83072 | − | 3.13101i | −0.0930233 | − | 0.102891i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.62420 | + | 12.8101i | −0.315930 | + | 0.420513i | ||||
\(929\) | 16.9849i | 0.557256i | 0.960399 | + | 0.278628i | \(0.0898797\pi\) | ||||
−0.960399 | + | 0.278628i | \(0.910120\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.47702 | − | 22.8795i | −0.310597 | − | 0.749847i | ||||
\(932\) | 47.0757 | − | 38.4392i | 1.54202 | − | 1.25912i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23.3005 | − | 49.1073i | 0.762416 | − | 1.60684i | ||||
\(935\) | 1.11239 | + | 1.11239i | 0.0363789 | + | 0.0363789i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.3804 | − | 25.3804i | 0.829140 | − | 0.829140i | −0.158258 | − | 0.987398i | \(-0.550588\pi\) |
0.987398 | + | 0.158258i | \(0.0505877\pi\) | |||||||
\(938\) | 4.85692 | + | 13.6274i | 0.158584 | + | 0.444950i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −31.7141 | − | 17.0527i | −1.03440 | − | 0.556198i | ||||
\(941\) | −38.0076 | + | 15.7433i | −1.23901 | + | 0.513216i | −0.903406 | − | 0.428786i | \(-0.858942\pi\) |
−0.335607 | + | 0.942002i | \(0.608942\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.3933 | 0.403582 | ||||||||
\(944\) | −17.6918 | + | 26.1957i | −0.575817 | + | 0.852596i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.392170 | + | 0.0197531i | 0.0127506 | + | 0.000642229i | ||||
\(947\) | 10.0319 | + | 24.2192i | 0.325993 | + | 0.787017i | 0.998882 | + | 0.0472735i | \(0.0150532\pi\) |
−0.672889 | + | 0.739744i | \(0.734947\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.34490 | − | 0.971288i | −0.0761185 | − | 0.0315293i | ||||
\(950\) | −2.41154 | − | 6.76622i | −0.0782407 | − | 0.219525i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.80114 | + | 11.8390i | −0.0583751 | + | 0.383703i | ||||
\(953\) | −7.72678 | + | 7.72678i | −0.250295 | + | 0.250295i | −0.821092 | − | 0.570797i | \(-0.806634\pi\) |
0.570797 | + | 0.821092i | \(0.306634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.34193 | + | 1.79849i | 0.140502 | + | 0.0581977i | ||||
\(956\) | 30.9067 | + | 3.12138i | 0.999594 | + | 0.100953i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −37.7744 | − | 41.7815i | −1.22043 | − | 1.34990i | ||||
\(959\) | −0.697850 | −0.0225348 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.4580 | 0.756710 | ||||||||
\(962\) | 15.2520 | + | 16.8700i | 0.491745 | + | 0.543909i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 51.1970 | + | 5.17057i | 1.64894 | + | 0.166533i | ||||
\(965\) | −42.1752 | − | 17.4695i | −1.35767 | − | 0.562364i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.9131 | + | 14.9131i | −0.479574 | + | 0.479574i | −0.904995 | − | 0.425421i | \(-0.860126\pi\) |
0.425421 | + | 0.904995i | \(0.360126\pi\) | |||||||
\(968\) | −30.6785 | − | 4.66731i | −0.986046 | − | 0.150013i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.42645 | + | 15.2253i | 0.174233 | + | 0.488856i | ||||
\(971\) | 8.02125 | + | 3.32251i | 0.257414 | + | 0.106624i | 0.507659 | − | 0.861558i | \(-0.330511\pi\) |
−0.250245 | + | 0.968183i | \(0.580511\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.82922 | − | 9.24455i | −0.122759 | − | 0.296367i | ||||
\(974\) | −43.1282 | − | 2.17231i | −1.38192 | − | 0.0696052i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −49.5767 | + | 9.60629i | −1.58691 | + | 0.307490i | ||||
\(977\) | 29.7718 | 0.952484 | 0.476242 | − | 0.879314i | \(-0.341999\pi\) | ||||
0.476242 | + | 0.879314i | \(0.341999\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.47877 | − | 0.612526i | 0.0472616 | − | 0.0195764i | ||||
\(980\) | −21.1619 | − | 11.3788i | −0.675992 | − | 0.363481i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.8434 | − | 38.8415i | −0.441762 | − | 1.23948i | ||||
\(983\) | 23.9283 | − | 23.9283i | 0.763194 | − | 0.763194i | −0.213704 | − | 0.976898i | \(-0.568553\pi\) |
0.976898 | + | 0.213704i | \(0.0685528\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.96467 | + | 4.96467i | 0.158187 | + | 0.158187i | ||||
\(986\) | 8.26480 | − | 17.4186i | 0.263205 | − | 0.554721i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 19.2986 | − | 15.7581i | 0.613969 | − | 0.501331i | ||||
\(989\) | 1.39053 | + | 3.35703i | 0.0442161 | + | 0.106747i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 44.7052i | − | 1.42011i | −0.704148 | − | 0.710054i | \(-0.748671\pi\) | ||
0.704148 | − | 0.710054i | \(-0.251329\pi\) | |||||||
\(992\) | −13.3742 | + | 7.90403i | −0.424633 | + | 0.250953i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.34709 | − | 8.12647i | −0.233035 | − | 0.257756i | ||||
\(995\) | 11.5050 | − | 4.76552i | 0.364732 | − | 0.151077i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.1630 | + | 24.5356i | −0.321864 | + | 0.777049i | 0.677281 | + | 0.735724i | \(0.263158\pi\) |
−0.999146 | + | 0.0413253i | \(0.986842\pi\) | |||||||
\(998\) | −15.7051 | − | 7.45176i | −0.497135 | − | 0.235881i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 864.2.w.a.107.9 | ✓ | 128 | |
3.2 | odd | 2 | inner | 864.2.w.a.107.24 | yes | 128 | |
32.3 | odd | 8 | inner | 864.2.w.a.323.24 | yes | 128 | |
96.35 | even | 8 | inner | 864.2.w.a.323.9 | yes | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.w.a.107.9 | ✓ | 128 | 1.1 | even | 1 | trivial | |
864.2.w.a.107.24 | yes | 128 | 3.2 | odd | 2 | inner | |
864.2.w.a.323.9 | yes | 128 | 96.35 | even | 8 | inner | |
864.2.w.a.323.24 | yes | 128 | 32.3 | odd | 8 | inner |