Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(370,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 6, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.370");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.fm (of order \(12\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 622.3 | ||
Character | \(\chi\) | \(=\) | 819.622 |
Dual form | 819.2.fm.f.370.3 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0578232 | + | 0.215799i | −0.0408872 | + | 0.152593i | −0.983351 | − | 0.181714i | \(-0.941836\pi\) |
0.942464 | + | 0.334307i | \(0.108502\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.68883 | + | 0.975044i | 0.844413 | + | 0.487522i | ||||
\(5\) | 1.08760 | − | 1.08760i | 0.486390 | − | 0.486390i | −0.420775 | − | 0.907165i | \(-0.638242\pi\) |
0.907165 | + | 0.420775i | \(0.138242\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.643420 | − | 2.56632i | −0.243190 | − | 0.969979i | ||||
\(8\) | −0.624019 | + | 0.624019i | −0.220624 | + | 0.220624i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.171815 | + | 0.297592i | 0.0543326 | + | 0.0941068i | ||||
\(11\) | −4.17464 | − | 1.11859i | −1.25870 | − | 0.337268i | −0.433010 | − | 0.901389i | \(-0.642548\pi\) |
−0.825692 | + | 0.564121i | \(0.809215\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.01096 | − | 1.98346i | 0.835090 | − | 0.550113i | ||||
\(14\) | 0.591015 | + | 0.00954346i | 0.157955 | + | 0.00255060i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.85151 | + | 3.20690i | 0.462877 | + | 0.801726i | ||||
\(17\) | 3.78401 | − | 6.55410i | 0.917757 | − | 1.58960i | 0.114944 | − | 0.993372i | \(-0.463331\pi\) |
0.802813 | − | 0.596231i | \(-0.203336\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.31714 | − | 4.91565i | −0.302173 | − | 1.12773i | −0.935351 | − | 0.353720i | \(-0.884916\pi\) |
0.633178 | − | 0.774006i | \(-0.281750\pi\) | |||||||
\(20\) | 2.89722 | − | 0.776309i | 0.647839 | − | 0.173588i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.482783 | − | 0.836204i | 0.102930 | − | 0.178279i | ||||
\(23\) | 1.85976 | − | 1.07373i | 0.387787 | − | 0.223889i | −0.293414 | − | 0.955985i | \(-0.594791\pi\) |
0.681201 | + | 0.732097i | \(0.261458\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.63425i | 0.526850i | ||||||||
\(26\) | 0.253926 | + | 0.764453i | 0.0497989 | + | 0.149922i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.41565 | − | 4.96143i | 0.267533 | − | 0.937623i | ||||
\(29\) | 2.66646 | + | 4.61844i | 0.495148 | + | 0.857622i | 0.999984 | − | 0.00559304i | \(-0.00178033\pi\) |
−0.504836 | + | 0.863215i | \(0.668447\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.09410 | + | 1.09410i | −0.196507 | + | 0.196507i | −0.798501 | − | 0.601994i | \(-0.794373\pi\) |
0.601994 | + | 0.798501i | \(0.294373\pi\) | |||||||
\(32\) | −2.50396 | + | 0.670934i | −0.442642 | + | 0.118605i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.19557 | + | 1.19557i | 0.205038 | + | 0.205038i | ||||
\(35\) | −3.49092 | − | 2.09135i | −0.590073 | − | 0.353502i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.82556 | − | 0.757106i | −0.464519 | − | 0.124467i | 0.0189661 | − | 0.999820i | \(-0.493963\pi\) |
−0.483485 | + | 0.875353i | \(0.660629\pi\) | |||||||
\(38\) | 1.13695 | 0.184438 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.35737i | 0.214618i | ||||||||
\(41\) | 1.37894 | + | 0.369486i | 0.215354 | + | 0.0577039i | 0.364883 | − | 0.931053i | \(-0.381109\pi\) |
−0.149529 | + | 0.988757i | \(0.547776\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.58558 | − | 3.80219i | −1.00429 | − | 0.579828i | −0.0947764 | − | 0.995499i | \(-0.530214\pi\) |
−0.909515 | + | 0.415671i | \(0.863547\pi\) | |||||||
\(44\) | −5.95956 | − | 5.95956i | −0.898438 | − | 0.898438i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.124173 | + | 0.463422i | 0.0183084 | + | 0.0683278i | ||||
\(47\) | 5.26364 | + | 5.26364i | 0.767781 | + | 0.767781i | 0.977716 | − | 0.209934i | \(-0.0673250\pi\) |
−0.209934 | + | 0.977716i | \(0.567325\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.17202 | + | 3.30245i | −0.881717 | + | 0.471778i | ||||
\(50\) | −0.568470 | − | 0.152321i | −0.0803937 | − | 0.0215414i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.01895 | − | 0.413900i | 0.973353 | − | 0.0573976i | ||||
\(53\) | 13.1808 | 1.81053 | 0.905263 | − | 0.424851i | \(-0.139673\pi\) | ||||
0.905263 | + | 0.424851i | \(0.139673\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.75692 | + | 3.32376i | −0.776263 | + | 0.448176i | ||||
\(56\) | 2.00294 | + | 1.19993i | 0.267654 | + | 0.160347i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.15084 | + | 0.308366i | −0.151112 | + | 0.0404905i | ||||
\(59\) | −8.73809 | + | 2.34136i | −1.13760 | + | 0.304820i | −0.777987 | − | 0.628281i | \(-0.783759\pi\) |
−0.359616 | + | 0.933101i | \(0.617092\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.1891 | + | 5.88266i | 1.30458 | + | 0.753197i | 0.981185 | − | 0.193068i | \(-0.0618439\pi\) |
0.323391 | + | 0.946266i | \(0.395177\pi\) | |||||||
\(62\) | −0.172842 | − | 0.299371i | −0.0219510 | − | 0.0380202i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.82688i | 0.853360i | ||||||||
\(65\) | 1.11751 | − | 5.43193i | 0.138610 | − | 0.673748i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.28138 | + | 4.78216i | −0.156545 | + | 0.584234i | 0.842423 | + | 0.538817i | \(0.181128\pi\) |
−0.998968 | + | 0.0454175i | \(0.985538\pi\) | |||||||
\(68\) | 12.7811 | − | 7.37915i | 1.54993 | − | 0.894854i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.653167 | − | 0.632408i | 0.0780684 | − | 0.0755873i | ||||
\(71\) | 5.25942 | − | 1.40926i | 0.624179 | − | 0.167248i | 0.0671520 | − | 0.997743i | \(-0.478609\pi\) |
0.557027 | + | 0.830495i | \(0.311942\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.04396 | − | 8.04396i | −0.941474 | − | 0.941474i | 0.0569055 | − | 0.998380i | \(-0.481877\pi\) |
−0.998380 | + | 0.0569055i | \(0.981877\pi\) | |||||||
\(74\) | 0.326766 | − | 0.565975i | 0.0379857 | − | 0.0657932i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.56854 | − | 9.58594i | 0.294632 | − | 1.09958i | ||||
\(77\) | −0.184619 | + | 11.4332i | −0.0210392 | + | 1.30293i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.06635 | 1.02004 | 0.510022 | − | 0.860161i | \(-0.329637\pi\) | ||||
0.510022 | + | 0.860161i | \(0.329637\pi\) | |||||||
\(80\) | 5.50153 | + | 1.47413i | 0.615090 | + | 0.164813i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.159469 | + | 0.276209i | −0.0176104 | + | 0.0305022i | ||||
\(83\) | 1.13072 | − | 1.13072i | 0.124113 | − | 0.124113i | −0.642322 | − | 0.766435i | \(-0.722029\pi\) |
0.766435 | + | 0.642322i | \(0.222029\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.01275 | − | 11.2437i | −0.326778 | − | 1.21955i | ||||
\(86\) | 1.20131 | − | 1.20131i | 0.129540 | − | 0.129540i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.30308 | − | 1.90703i | 0.352109 | − | 0.203290i | ||||
\(89\) | −0.217351 | + | 0.811166i | −0.0230392 | + | 0.0859834i | −0.976488 | − | 0.215571i | \(-0.930839\pi\) |
0.953449 | + | 0.301554i | \(0.0975054\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.02751 | − | 6.45090i | −0.736683 | − | 0.676238i | ||||
\(92\) | 4.18775 | 0.436603 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.44025 | + | 0.831529i | −0.148551 | + | 0.0857657i | ||||
\(95\) | −6.77878 | − | 3.91373i | −0.695488 | − | 0.401540i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.35890 | + | 16.2676i | 0.442579 | + | 1.65173i | 0.722251 | + | 0.691631i | \(0.243108\pi\) |
−0.279672 | + | 0.960096i | \(0.590226\pi\) | |||||||
\(98\) | −0.355779 | − | 1.52288i | −0.0359391 | − | 0.153834i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.56851 | + | 4.44879i | −0.256851 | + | 0.444879i | ||||
\(101\) | −5.48585 | − | 9.50177i | −0.545863 | − | 0.945462i | −0.998552 | − | 0.0537934i | \(-0.982869\pi\) |
0.452690 | − | 0.891668i | \(-0.350465\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.70231 | 0.463332 | 0.231666 | − | 0.972795i | \(-0.425582\pi\) | ||||
0.231666 | + | 0.972795i | \(0.425582\pi\) | |||||||
\(104\) | −0.641180 | + | 3.11661i | −0.0628728 | + | 0.305609i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.762158 | + | 2.84441i | −0.0740274 | + | 0.276274i | ||||
\(107\) | −6.55307 | − | 11.3502i | −0.633509 | − | 1.09727i | −0.986829 | − | 0.161767i | \(-0.948281\pi\) |
0.353320 | − | 0.935503i | \(-0.385053\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.872057 | − | 0.872057i | −0.0835279 | − | 0.0835279i | 0.664108 | − | 0.747636i | \(-0.268811\pi\) |
−0.747636 | + | 0.664108i | \(0.768811\pi\) | |||||||
\(110\) | −0.384381 | − | 1.43453i | −0.0366493 | − | 0.136777i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.03865 | − | 6.81495i | 0.665090 | − | 0.643952i | ||||
\(113\) | −6.21370 | + | 10.7625i | −0.584536 | + | 1.01245i | 0.410397 | + | 0.911907i | \(0.365390\pi\) |
−0.994933 | + | 0.100539i | \(0.967943\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.854883 | − | 3.19047i | 0.0797183 | − | 0.297513i | ||||
\(116\) | 10.3996i | 0.965583i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 2.02106i | − | 0.186053i | ||||||
\(119\) | −19.2546 | − | 5.49395i | −1.76507 | − | 0.503630i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.65011 | + | 3.83944i | 0.604556 | + | 0.349040i | ||||
\(122\) | −1.85864 | + | 1.85864i | −0.168273 | + | 0.168273i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.91455 | + | 0.780950i | −0.261734 | + | 0.0701314i | ||||
\(125\) | 8.30301 | + | 8.30301i | 0.742644 | + | 0.742644i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.51334 | − | 3.18313i | 0.489230 | − | 0.282457i | −0.235025 | − | 0.971989i | \(-0.575517\pi\) |
0.724255 | + | 0.689532i | \(0.242184\pi\) | |||||||
\(128\) | −6.48115 | − | 1.73662i | −0.572858 | − | 0.153497i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.10759 | + | 0.555250i | 0.0971420 | + | 0.0486986i | ||||
\(131\) | 3.73498i | 0.326327i | 0.986599 | + | 0.163163i | \(0.0521698\pi\) | ||||
−0.986599 | + | 0.163163i | \(0.947830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.7677 | + | 6.54304i | −1.02039 | + | 0.567354i | ||||
\(134\) | −0.957894 | − | 0.553040i | −0.0827494 | − | 0.0477754i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.72859 | + | 6.45118i | 0.148225 | + | 0.553184i | ||||
\(137\) | −0.00793713 | − | 0.0296218i | −0.000678115 | − | 0.00253076i | 0.965586 | − | 0.260084i | \(-0.0837503\pi\) |
−0.966264 | + | 0.257553i | \(0.917084\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.85559 | − | 1.64867i | −0.242208 | − | 0.139839i | 0.373983 | − | 0.927435i | \(-0.377992\pi\) |
−0.616191 | + | 0.787597i | \(0.711325\pi\) | |||||||
\(140\) | −3.85639 | − | 6.93572i | −0.325924 | − | 0.586175i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.21647i | 0.102084i | ||||||||
\(143\) | −14.7884 | + | 4.91220i | −1.23667 | + | 0.410779i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.92305 | + | 2.12297i | 0.657974 | + | 0.176303i | ||||
\(146\) | 2.20101 | − | 1.27075i | 0.182157 | − | 0.105168i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.03366 | − | 4.03366i | −0.331565 | − | 0.331565i | ||||
\(149\) | −4.52646 | + | 1.21286i | −0.370822 | + | 0.0993615i | −0.439417 | − | 0.898283i | \(-0.644815\pi\) |
0.0685950 | + | 0.997645i | \(0.478148\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.74970 | + | 4.74970i | −0.386525 | + | 0.386525i | −0.873446 | − | 0.486921i | \(-0.838120\pi\) |
0.486921 | + | 0.873446i | \(0.338120\pi\) | |||||||
\(152\) | 3.88938 | + | 2.24553i | 0.315470 | + | 0.182137i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.45660 | − | 0.700945i | −0.197959 | − | 0.0564838i | ||||
\(155\) | 2.37989i | 0.191158i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.1115i | − | 1.36565i | −0.730584 | − | 0.682823i | \(-0.760752\pi\) | ||
0.730584 | − | 0.682823i | \(-0.239248\pi\) | |||||||
\(158\) | −0.524246 | + | 1.95651i | −0.0417068 | + | 0.155652i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.99360 | + | 3.45301i | −0.157608 | + | 0.272985i | ||||
\(161\) | −3.95215 | − | 4.08188i | −0.311473 | − | 0.321697i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.05271 | + | 18.8570i | 0.395759 | + | 1.47699i | 0.820484 | + | 0.571669i | \(0.193704\pi\) |
−0.424726 | + | 0.905322i | \(0.639630\pi\) | |||||||
\(164\) | 1.96852 | + | 1.96852i | 0.153716 | + | 0.153716i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.178627 | + | 0.309390i | 0.0138641 | + | 0.0240134i | ||||
\(167\) | −3.66374 | + | 13.6733i | −0.283508 | + | 1.05807i | 0.666414 | + | 0.745582i | \(0.267828\pi\) |
−0.949922 | + | 0.312486i | \(0.898838\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.13177 | − | 11.9442i | 0.394751 | − | 0.918788i | ||||
\(170\) | 2.60060 | 0.199457 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.41460 | − | 12.8425i | −0.565358 | − | 0.979228i | ||||
\(173\) | −9.66072 | + | 16.7329i | −0.734491 | + | 1.27218i | 0.220456 | + | 0.975397i | \(0.429246\pi\) |
−0.954946 | + | 0.296778i | \(0.904088\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.76034 | − | 1.69493i | 0.511034 | − | 0.128125i | ||||
\(176\) | −4.14216 | − | 15.4588i | −0.312227 | − | 1.16525i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.162481 | − | 0.0938085i | −0.0121785 | − | 0.00703124i | ||||
\(179\) | −3.56116 | + | 2.05604i | −0.266173 | + | 0.153675i | −0.627147 | − | 0.778901i | \(-0.715778\pi\) |
0.360974 | + | 0.932576i | \(0.382444\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.09652 | −0.155833 | −0.0779165 | − | 0.996960i | \(-0.524827\pi\) | ||||
−0.0779165 | + | 0.996960i | \(0.524827\pi\) | |||||||
\(182\) | 1.79845 | − | 1.14352i | 0.133310 | − | 0.0847633i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.490496 | + | 1.83056i | −0.0361598 | + | 0.134950i | ||||
\(185\) | −3.89650 | + | 2.24965i | −0.286477 | + | 0.165397i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.1283 | + | 23.1283i | −1.69131 | + | 1.69131i | ||||
\(188\) | 3.75709 | + | 14.0217i | 0.274014 | + | 1.02263i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.23655 | − | 1.23655i | 0.0897089 | − | 0.0897089i | ||||
\(191\) | −4.22074 | + | 7.31054i | −0.305402 | + | 0.528972i | −0.977351 | − | 0.211626i | \(-0.932124\pi\) |
0.671949 | + | 0.740598i | \(0.265458\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.96647 | + | 0.526915i | 0.141550 | + | 0.0379282i | 0.328898 | − | 0.944365i | \(-0.393323\pi\) |
−0.187348 | + | 0.982294i | \(0.559989\pi\) | |||||||
\(194\) | −3.76259 | −0.270138 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.6435 | − | 0.440734i | −0.974535 | − | 0.0314810i | ||||
\(197\) | −3.46988 | + | 12.9498i | −0.247219 | + | 0.922632i | 0.725037 | + | 0.688710i | \(0.241823\pi\) |
−0.972255 | + | 0.233922i | \(0.924844\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.76822 | + | 6.52675i | −0.267122 | + | 0.462669i | −0.968117 | − | 0.250497i | \(-0.919406\pi\) |
0.700995 | + | 0.713166i | \(0.252739\pi\) | |||||||
\(200\) | −1.64382 | − | 1.64382i | −0.116236 | − | 0.116236i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.36768 | − | 0.634419i | 0.166590 | − | 0.0446376i | ||||
\(203\) | 10.1367 | − | 9.81458i | 0.711460 | − | 0.688849i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.90159 | − | 1.09788i | 0.132813 | − | 0.0766794i | ||||
\(206\) | −0.271903 | + | 1.01475i | −0.0189444 | + | 0.0707013i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 11.9356 | + | 5.98347i | 0.827584 | + | 0.414879i | ||||
\(209\) | 21.9944i | 1.52139i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.48310 | + | 14.6932i | 0.584001 | + | 1.01152i | 0.994999 | + | 0.0998830i | \(0.0318469\pi\) |
−0.410998 | + | 0.911636i | \(0.634820\pi\) | |||||||
\(212\) | 22.2601 | + | 12.8519i | 1.52883 | + | 0.882671i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.82829 | − | 0.757839i | 0.193338 | − | 0.0518048i | ||||
\(215\) | −11.2977 | + | 3.02722i | −0.770499 | + | 0.206455i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.51179 | + | 2.10385i | 0.238396 | + | 0.142819i | ||||
\(218\) | 0.238614 | − | 0.137764i | 0.0161610 | − | 0.00933056i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.9632 | −0.873982 | ||||||||
\(221\) | −1.60629 | − | 27.2396i | −0.108051 | − | 1.83233i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.1895 | + | 3.26617i | 0.816269 | + | 0.218719i | 0.642715 | − | 0.766106i | \(-0.277808\pi\) |
0.173555 | + | 0.984824i | \(0.444475\pi\) | |||||||
\(224\) | 3.33293 | + | 5.99427i | 0.222691 | + | 0.400509i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.96323 | − | 1.96323i | −0.130592 | − | 0.130592i | ||||
\(227\) | −5.09212 | − | 19.0040i | −0.337976 | − | 1.26134i | −0.900607 | − | 0.434635i | \(-0.856878\pi\) |
0.562631 | − | 0.826708i | \(-0.309789\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.8246 | − | 19.8246i | −1.31004 | − | 1.31004i | −0.921379 | − | 0.388666i | \(-0.872936\pi\) |
−0.388666 | − | 0.921379i | \(-0.627064\pi\) | |||||||
\(230\) | 0.639068 | + | 0.368966i | 0.0421389 | + | 0.0243289i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.54591 | − | 1.21807i | −0.298454 | − | 0.0799704i | ||||
\(233\) | 10.8900i | 0.713427i | 0.934214 | + | 0.356714i | \(0.116103\pi\) | ||||
−0.934214 | + | 0.356714i | \(0.883897\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.4495 | 0.746882 | ||||||||
\(236\) | −17.0400 | − | 4.56586i | −1.10921 | − | 0.297212i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.29896 | − | 3.83746i | 0.149019 | − | 0.248745i | ||||
\(239\) | 10.0403 | + | 10.0403i | 0.649451 | + | 0.649451i | 0.952860 | − | 0.303409i | \(-0.0981250\pi\) |
−0.303409 | + | 0.952860i | \(0.598125\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.1305 | + | 4.05421i | −0.974642 | + | 0.261155i | −0.710787 | − | 0.703408i | \(-0.751661\pi\) |
−0.263856 | + | 0.964562i | \(0.584994\pi\) | |||||||
\(242\) | −1.21308 | + | 1.21308i | −0.0779797 | + | 0.0779797i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.4717 | + | 19.8696i | 0.734400 | + | 1.27202i | ||||
\(245\) | −3.12095 | + | 10.3044i | −0.199390 | + | 0.658326i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.7159 | − | 12.1883i | −0.872719 | − | 0.775524i | ||||
\(248\) | − | 1.36548i | − | 0.0867082i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.27189 | + | 1.31168i | −0.143687 | + | 0.0829577i | ||||
\(251\) | 10.7847 | − | 18.6797i | 0.680727 | − | 1.17905i | −0.294033 | − | 0.955795i | \(-0.594997\pi\) |
0.974759 | − | 0.223258i | \(-0.0716692\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.96490 | + | 2.40214i | −0.563619 | + | 0.151021i | ||||
\(254\) | 0.368118 | + | 1.37383i | 0.0230977 | + | 0.0862020i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.07736 | + | 10.5263i | −0.379835 | + | 0.657893i | ||||
\(257\) | −1.05953 | − | 1.83517i | −0.0660920 | − | 0.114475i | 0.831086 | − | 0.556144i | \(-0.187720\pi\) |
−0.897178 | + | 0.441669i | \(0.854386\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.124957 | + | 7.73843i | −0.00776444 | + | 0.480843i | ||||
\(260\) | 7.18365 | − | 8.08396i | 0.445511 | − | 0.501346i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.806006 | − | 0.215969i | −0.0497952 | − | 0.0133426i | ||||
\(263\) | −5.53188 | − | 9.58150i | −0.341111 | − | 0.590821i | 0.643529 | − | 0.765422i | \(-0.277470\pi\) |
−0.984639 | + | 0.174601i | \(0.944136\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.3355 | − | 14.3355i | 0.880621 | − | 0.880621i | ||||
\(266\) | −0.731539 | − | 2.91779i | −0.0448536 | − | 0.178901i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.82684 | + | 6.82684i | −0.417016 | + | 0.417016i | ||||
\(269\) | −23.8459 | − | 13.7675i | −1.45391 | − | 0.839416i | −0.455211 | − | 0.890383i | \(-0.650436\pi\) |
−0.998700 | + | 0.0509670i | \(0.983770\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.80218 | − | 14.1899i | 0.230966 | − | 0.861978i | −0.748960 | − | 0.662616i | \(-0.769446\pi\) |
0.979926 | − | 0.199362i | \(-0.0638870\pi\) | |||||||
\(272\) | 28.0245 | 1.69923 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.00685131 | 0.000413903 | ||||||||
\(275\) | 2.94665 | − | 10.9971i | 0.177690 | − | 0.663148i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.50623 | + | 2.60167i | 0.270753 | + | 0.156319i | 0.629230 | − | 0.777219i | \(-0.283370\pi\) |
−0.358477 | + | 0.933539i | \(0.616704\pi\) | |||||||
\(278\) | 0.520902 | − | 0.520902i | 0.0312416 | − | 0.0312416i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.48344 | − | 0.873357i | 0.208175 | − | 0.0521931i | ||||
\(281\) | 10.7634 | − | 10.7634i | 0.642088 | − | 0.642088i | −0.308980 | − | 0.951068i | \(-0.599988\pi\) |
0.951068 | + | 0.308980i | \(0.0999877\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.03356 | − | 3.52223i | −0.120882 | − | 0.209375i | 0.799233 | − | 0.601021i | \(-0.205239\pi\) |
−0.920116 | + | 0.391646i | \(0.871906\pi\) | |||||||
\(284\) | 10.2563 | + | 2.74818i | 0.608601 | + | 0.163074i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.204938 | − | 3.47536i | −0.0121183 | − | 0.205502i | ||||
\(287\) | 0.0609819 | − | 3.77654i | 0.00359965 | − | 0.222922i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20.1375 | − | 34.8791i | −1.18456 | − | 2.05171i | ||||
\(290\) | −0.916273 | + | 1.58703i | −0.0538054 | + | 0.0931937i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.74163 | − | 21.4280i | −0.336003 | − | 1.25398i | ||||
\(293\) | 21.3183 | − | 5.71221i | 1.24543 | − | 0.333711i | 0.424858 | − | 0.905260i | \(-0.360324\pi\) |
0.820568 | + | 0.571549i | \(0.193657\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.95708 | + | 12.0500i | −0.405057 | + | 0.701579i | ||||
\(296\) | 2.23565 | − | 1.29075i | 0.129944 | − | 0.0750235i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 1.04694i | − | 0.0606475i | ||||||
\(299\) | 3.46996 | − | 6.92173i | 0.200673 | − | 0.400294i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.52034 | + | 19.3471i | −0.318187 | + | 1.11515i | ||||
\(302\) | −0.750339 | − | 1.29962i | −0.0431771 | − | 0.0747850i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 13.3253 | − | 13.3253i | 0.764259 | − | 0.764259i | ||||
\(305\) | 17.4796 | − | 4.68365i | 1.00088 | − | 0.268185i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.60326 | + | 9.60326i | 0.548087 | + | 0.548087i | 0.925887 | − | 0.377800i | \(-0.123319\pi\) |
−0.377800 | + | 0.925887i | \(0.623319\pi\) | |||||||
\(308\) | −11.4597 | + | 19.1287i | −0.652975 | + | 1.08996i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.513579 | − | 0.137613i | −0.0291693 | − | 0.00781590i | ||||
\(311\) | −16.2194 | −0.919715 | −0.459858 | − | 0.887993i | \(-0.652100\pi\) | ||||
−0.459858 | + | 0.887993i | \(0.652100\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.2234i | 1.36919i | 0.728926 | + | 0.684593i | \(0.240020\pi\) | ||||
−0.728926 | + | 0.684593i | \(0.759980\pi\) | |||||||
\(314\) | 3.69265 | + | 0.989442i | 0.208388 | + | 0.0558375i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.3115 | + | 8.84009i | 0.861338 | + | 0.497294i | ||||
\(317\) | 18.9182 | + | 18.9182i | 1.06255 | + | 1.06255i | 0.997909 | + | 0.0646418i | \(0.0205905\pi\) |
0.0646418 | + | 0.997909i | \(0.479410\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.96535 | − | 22.2630i | −0.333996 | − | 1.24649i | ||||
\(320\) | 7.42492 | + | 7.42492i | 0.415065 | + | 0.415065i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.10939 | − | 0.616844i | 0.0618241 | − | 0.0343754i | ||||
\(323\) | −37.2017 | − | 9.96817i | −2.06996 | − | 0.554644i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.22494 | + | 7.93163i | 0.289827 | + | 0.439968i | ||||
\(326\) | −4.36148 | −0.241560 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.09105 | + | 0.629918i | −0.0602432 | + | 0.0347814i | ||||
\(329\) | 10.1215 | − | 16.8949i | 0.558015 | − | 0.931448i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.9589 | − | 3.74029i | 0.767253 | − | 0.205585i | 0.146095 | − | 0.989271i | \(-0.453329\pi\) |
0.621157 | + | 0.783686i | \(0.286663\pi\) | |||||||
\(332\) | 3.01209 | − | 0.807087i | 0.165310 | − | 0.0442947i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.73883 | − | 1.58126i | −0.149862 | − | 0.0865229i | ||||
\(335\) | 3.80746 | + | 6.59471i | 0.208024 | + | 0.360307i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.15524i | 0.280824i | 0.990093 | + | 0.140412i | \(0.0448426\pi\) | ||||
−0.990093 | + | 0.140412i | \(0.955157\pi\) | |||||||
\(338\) | 2.28082 | + | 1.79809i | 0.124060 | + | 0.0978030i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.87512 | − | 21.9263i | 0.318623 | − | 1.18912i | ||||
\(341\) | 5.79134 | − | 3.34363i | 0.313619 | − | 0.181068i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.4463 | + | 13.7145i | 0.672040 | + | 0.740515i | ||||
\(344\) | 6.48216 | − | 1.73689i | 0.349495 | − | 0.0936469i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.05232 | − | 3.05232i | −0.164094 | − | 0.164094i | ||||
\(347\) | −11.9012 | + | 20.6134i | −0.638888 | + | 1.10659i | 0.346789 | + | 0.937943i | \(0.387272\pi\) |
−0.985677 | + | 0.168643i | \(0.946062\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.16538 | + | 11.8134i | −0.169439 | + | 0.632355i | 0.827993 | + | 0.560738i | \(0.189482\pi\) |
−0.997432 | + | 0.0716166i | \(0.977184\pi\) | |||||||
\(350\) | −0.0251399 | + | 1.55688i | −0.00134378 | + | 0.0832189i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.2036 | 0.597156 | ||||||||
\(353\) | 16.5186 | + | 4.42614i | 0.879196 | + | 0.235580i | 0.670060 | − | 0.742307i | \(-0.266268\pi\) |
0.209136 | + | 0.977887i | \(0.432935\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.18744 | − | 7.25286i | 0.222246 | − | 0.384942i | ||||
\(356\) | −1.15799 | + | 1.15799i | −0.0613734 | + | 0.0613734i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.237773 | − | 0.887382i | −0.0125667 | − | 0.0468996i | ||||
\(359\) | −14.6210 | + | 14.6210i | −0.771665 | + | 0.771665i | −0.978397 | − | 0.206733i | \(-0.933717\pi\) |
0.206733 | + | 0.978397i | \(0.433717\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.97423 | + | 3.44922i | −0.314433 | + | 0.181538i | ||||
\(362\) | 0.121228 | − | 0.452427i | 0.00637158 | − | 0.0237790i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.57833 | − | 17.7466i | −0.292384 | − | 0.930173i | ||||
\(365\) | −17.4972 | −0.915846 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.401157 | − | 0.231608i | 0.0209402 | − | 0.0120898i | −0.489493 | − | 0.872007i | \(-0.662818\pi\) |
0.510434 | + | 0.859917i | \(0.329485\pi\) | |||||||
\(368\) | 6.88672 | + | 3.97605i | 0.358995 | + | 0.207266i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.260164 | − | 0.970945i | −0.0135253 | − | 0.0504770i | ||||
\(371\) | −8.48081 | − | 33.8263i | −0.440302 | − | 1.75617i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.348917 | + | 0.604342i | −0.0180662 | + | 0.0312916i | −0.874917 | − | 0.484273i | \(-0.839084\pi\) |
0.856851 | + | 0.515564i | \(0.172418\pi\) | |||||||
\(374\) | −3.65371 | − | 6.32841i | −0.188929 | − | 0.327234i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.56923 | −0.338782 | ||||||||
\(377\) | 17.1891 | + | 8.61712i | 0.885283 | + | 0.443804i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.85118 | − | 6.90871i | 0.0950889 | − | 0.354877i | −0.901944 | − | 0.431853i | \(-0.857860\pi\) |
0.997033 | + | 0.0769763i | \(0.0245266\pi\) | |||||||
\(380\) | −7.63212 | − | 13.2192i | −0.391519 | − | 0.678132i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.33355 | − | 1.33355i | −0.0682305 | − | 0.0682305i | ||||
\(383\) | −0.496583 | − | 1.85327i | −0.0253742 | − | 0.0946979i | 0.952078 | − | 0.305857i | \(-0.0989429\pi\) |
−0.977452 | + | 0.211159i | \(0.932276\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.2340 | + | 12.6355i | 0.623500 | + | 0.643967i | ||||
\(386\) | −0.227416 | + | 0.393895i | −0.0115751 | + | 0.0200487i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.50023 | + | 31.7233i | −0.431534 | + | 1.61051i | ||||
\(389\) | 6.17075i | 0.312870i | 0.987688 | + | 0.156435i | \(0.0500001\pi\) | ||||
−0.987688 | + | 0.156435i | \(0.950000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 16.2521i | − | 0.821903i | ||||||
\(392\) | 1.79067 | − | 5.91225i | 0.0904424 | − | 0.298614i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.59391 | − | 1.49759i | −0.130679 | − | 0.0754477i | ||||
\(395\) | 9.86057 | − | 9.86057i | 0.496139 | − | 0.496139i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.1243 | − | 8.07177i | 1.51189 | − | 0.405111i | 0.594830 | − | 0.803852i | \(-0.297220\pi\) |
0.917063 | + | 0.398741i | \(0.130553\pi\) | |||||||
\(398\) | −1.19058 | − | 1.19058i | −0.0596782 | − | 0.0596782i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.44780 | + | 4.87734i | −0.422390 | + | 0.243867i | ||||
\(401\) | −24.2526 | − | 6.49846i | −1.21112 | − | 0.324517i | −0.403916 | − | 0.914796i | \(-0.632351\pi\) |
−0.807199 | + | 0.590279i | \(0.799018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.12419 | + | 5.46441i | −0.0559999 | + | 0.272202i | ||||
\(404\) | − | 21.3958i | − | 1.06448i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.53184 | + | 2.75501i | 0.0760239 | + | 0.136729i | ||||
\(407\) | 10.9488 | + | 6.32129i | 0.542712 | + | 0.313335i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.92450 | − | 14.6464i | −0.194054 | − | 0.724219i | −0.992510 | − | 0.122165i | \(-0.961016\pi\) |
0.798456 | − | 0.602053i | \(-0.205651\pi\) | |||||||
\(410\) | 0.126966 | + | 0.473844i | 0.00627041 | + | 0.0234015i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.94138 | + | 4.58496i | 0.391244 | + | 0.225885i | ||||
\(413\) | 11.6310 | + | 20.9183i | 0.572322 | + | 1.02932i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.45954i | − | 0.120734i | ||||||
\(416\) | −6.20855 | + | 6.98666i | −0.304399 | + | 0.342549i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.74638 | − | 1.27179i | −0.232153 | − | 0.0622052i | ||||
\(419\) | 3.99149 | − | 2.30449i | 0.194997 | − | 0.112582i | −0.399323 | − | 0.916810i | \(-0.630755\pi\) |
0.594320 | + | 0.804229i | \(0.297421\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.6437 | + | 12.6437i | 0.616216 | + | 0.616216i | 0.944559 | − | 0.328342i | \(-0.106490\pi\) |
−0.328342 | + | 0.944559i | \(0.606490\pi\) | |||||||
\(422\) | −3.66129 | + | 0.981041i | −0.178229 | + | 0.0477563i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.22509 | + | 8.22509i | −0.399446 | + | 0.399446i | ||||
\(425\) | 17.2652 | + | 9.96804i | 0.837483 | + | 0.483521i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.54095 | − | 29.9334i | 0.413325 | − | 1.44858i | ||||
\(428\) | − | 25.5581i | − | 1.23540i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 2.61309i | − | 0.126014i | ||||||
\(431\) | −2.12448 | + | 7.92867i | −0.102333 | + | 0.381911i | −0.998029 | − | 0.0627557i | \(-0.980011\pi\) |
0.895696 | + | 0.444666i | \(0.146678\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.67779 | + | 15.0304i | −0.417028 | + | 0.722314i | −0.995639 | − | 0.0932901i | \(-0.970262\pi\) |
0.578611 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(434\) | −0.657073 | + | 0.636190i | −0.0315405 | + | 0.0305381i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.622458 | − | 2.32305i | −0.0298103 | − | 0.111254i | ||||
\(437\) | −7.72766 | − | 7.72766i | −0.369664 | − | 0.369664i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.78946 | + | 13.4917i | 0.371771 | + | 0.643926i | 0.989838 | − | 0.142199i | \(-0.0454174\pi\) |
−0.618067 | + | 0.786125i | \(0.712084\pi\) | |||||||
\(440\) | 1.51834 | − | 5.66652i | 0.0723840 | − | 0.270141i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.97116 | + | 1.22844i | 0.284019 | + | 0.0584311i | ||||
\(443\) | 30.0278 | 1.42667 | 0.713333 | − | 0.700825i | \(-0.247185\pi\) | ||||
0.713333 | + | 0.700825i | \(0.247185\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.645833 | + | 1.11862i | 0.0306154 | + | 0.0530274i | ||||
\(446\) | −1.40967 | + | 2.44162i | −0.0667499 | + | 0.115614i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 17.5200 | − | 4.39255i | 0.827741 | − | 0.207529i | ||||
\(449\) | −1.79908 | − | 6.71427i | −0.0849040 | − | 0.316866i | 0.910392 | − | 0.413747i | \(-0.135780\pi\) |
−0.995296 | + | 0.0968807i | \(0.969113\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.34327 | − | 3.08494i | −0.251605 | − | 0.145264i | ||||
\(452\) | −20.9877 | + | 12.1173i | −0.987179 | + | 0.569948i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.39550 | 0.206291 | ||||||||
\(455\) | −14.6591 | + | 0.627126i | −0.687230 | + | 0.0294001i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.76514 | − | 21.5158i | 0.269682 | − | 1.00647i | −0.689640 | − | 0.724152i | \(-0.742231\pi\) |
0.959322 | − | 0.282314i | \(-0.0911020\pi\) | |||||||
\(458\) | 5.42445 | − | 3.13181i | 0.253468 | − | 0.146340i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.55459 | − | 4.55459i | 0.212359 | − | 0.212359i | ||||
\(461\) | −3.01705 | − | 11.2598i | −0.140518 | − | 0.524420i | −0.999914 | − | 0.0131099i | \(-0.995827\pi\) |
0.859396 | − | 0.511311i | \(-0.170840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.6774 | − | 16.6774i | 0.775063 | − | 0.775063i | −0.203924 | − | 0.978987i | \(-0.565369\pi\) |
0.978987 | + | 0.203924i | \(0.0653694\pi\) | |||||||
\(464\) | −9.87392 | + | 17.1021i | −0.458385 | + | 0.793947i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.35005 | − | 0.629695i | −0.108864 | − | 0.0291700i | ||||
\(467\) | −17.0336 | −0.788223 | −0.394111 | − | 0.919063i | \(-0.628948\pi\) | ||||
−0.394111 | + | 0.919063i | \(0.628948\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.0970 | + | 0.211485i | 0.604765 | + | 0.00976549i | ||||
\(470\) | −0.662046 | + | 2.47079i | −0.0305379 | + | 0.113969i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.99168 | − | 6.91379i | 0.183732 | − | 0.318233i | ||||
\(473\) | 23.2393 | + | 23.2393i | 1.06855 | + | 1.06855i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.9491 | − | 3.46969i | 0.594143 | − | 0.159200i | ||||
\(476\) | −27.1609 | − | 28.0524i | −1.24492 | − | 1.28578i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.74724 | + | 1.58612i | −0.125656 | + | 0.0725475i | ||||
\(479\) | 8.69175 | − | 32.4380i | 0.397136 | − | 1.48213i | −0.420976 | − | 0.907072i | \(-0.638312\pi\) |
0.818111 | − | 0.575060i | \(-0.195021\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.0093 | + | 3.32477i | −0.456386 | + | 0.151596i | ||||
\(482\) | − | 3.49958i | − | 0.159402i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.48725 | + | 12.9683i | 0.340330 | + | 0.589468i | ||||
\(485\) | 22.4334 | + | 12.9519i | 1.01865 | + | 0.588117i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.78357 | + | 1.01381i | −0.171450 | + | 0.0459399i | −0.343523 | − | 0.939144i | \(-0.611620\pi\) |
0.172073 | + | 0.985084i | \(0.444954\pi\) | |||||||
\(488\) | −10.0291 | + | 2.68728i | −0.453994 | + | 0.121647i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.04323 | − | 1.26933i | −0.0923035 | − | 0.0573427i | ||||
\(491\) | 6.15458 | − | 3.55335i | 0.277752 | − | 0.160360i | −0.354653 | − | 0.934998i | \(-0.615401\pi\) |
0.632405 | + | 0.774638i | \(0.282068\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 40.3596 | 1.81770 | ||||||||
\(494\) | 3.42332 | − | 2.25510i | 0.154023 | − | 0.101462i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.53442 | − | 1.48294i | −0.248503 | − | 0.0665861i | ||||
\(497\) | −7.00063 | − | 12.5906i | −0.314021 | − | 0.564767i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.42530 | + | 5.42530i | 0.242870 | + | 0.242870i | 0.818036 | − | 0.575167i | \(-0.195063\pi\) |
−0.575167 | + | 0.818036i | \(0.695063\pi\) | |||||||
\(500\) | 5.92654 | + | 22.1181i | 0.265043 | + | 0.989153i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.40746 | + | 3.40746i | 0.152082 | + | 0.152082i | ||||
\(503\) | 11.4527 | + | 6.61222i | 0.510651 | + | 0.294824i | 0.733101 | − | 0.680120i | \(-0.238072\pi\) |
−0.222450 | + | 0.974944i | \(0.571406\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.3005 | − | 4.36772i | −0.725364 | − | 0.194361i | ||||
\(506\) | − | 2.07352i | − | 0.0921792i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.4148 | 0.550816 | ||||||||
\(509\) | 38.3913 | + | 10.2869i | 1.70167 | + | 0.455960i | 0.973358 | − | 0.229290i | \(-0.0736405\pi\) |
0.728308 | + | 0.685250i | \(0.240307\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.4677 | + | 25.8190i | −0.684253 | + | 1.14217i | ||||
\(512\) | −11.4092 | − | 11.4092i | −0.504221 | − | 0.504221i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.457294 | − | 0.122531i | 0.0201704 | − | 0.00540463i | ||||
\(515\) | 5.11423 | − | 5.11423i | 0.225360 | − | 0.225360i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.0860 | − | 27.8617i | −0.707460 | − | 1.22536i | ||||
\(518\) | −1.66272 | − | 0.474426i | −0.0730558 | − | 0.0208451i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.69228 | + | 4.08698i | 0.118064 | + | 0.179226i | ||||
\(521\) | 9.34550i | 0.409434i | 0.978821 | + | 0.204717i | \(0.0656274\pi\) | ||||
−0.978821 | + | 0.204717i | \(0.934373\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.9149 | − | 9.76580i | 0.739635 | − | 0.427028i | −0.0823016 | − | 0.996607i | \(-0.526227\pi\) |
0.821937 | + | 0.569579i | \(0.192894\pi\) | |||||||
\(524\) | −3.64177 | + | 6.30773i | −0.159091 | + | 0.275554i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.38755 | − | 0.639743i | 0.104102 | − | 0.0278941i | ||||
\(527\) | 3.03076 | + | 11.3110i | 0.132022 | + | 0.492713i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.19419 | + | 15.9248i | −0.399748 | + | 0.692383i | ||||
\(530\) | 2.26466 | + | 3.92251i | 0.0983706 | + | 0.170383i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −26.2533 | − | 0.423927i | −1.13822 | − | 0.0183796i | ||||
\(533\) | 4.88479 | − | 1.62256i | 0.211584 | − | 0.0702811i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.4716 | − | 5.21741i | −0.841833 | − | 0.225568i | ||||
\(536\) | −2.18456 | − | 3.78376i | −0.0943585 | − | 0.163434i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.34985 | − | 4.34985i | 0.187536 | − | 0.187536i | ||||
\(539\) | 29.4601 | − | 6.88256i | 1.26894 | − | 0.296453i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.184083 | + | 0.184083i | −0.00791436 | + | 0.00791436i | −0.711053 | − | 0.703139i | \(-0.751781\pi\) |
0.703139 | + | 0.711053i | \(0.251781\pi\) | |||||||
\(542\) | 2.84232 | + | 1.64102i | 0.122088 | + | 0.0704877i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.07764 | + | 18.9500i | −0.217702 | + | 0.812475i | ||||
\(545\) | −1.89690 | −0.0812542 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.9425 | −1.15198 | −0.575990 | − | 0.817457i | \(-0.695383\pi\) | ||||
−0.575990 | + | 0.817457i | \(0.695383\pi\) | |||||||
\(548\) | 0.0154781 | − | 0.0577651i | 0.000661192 | − | 0.00246760i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.20277 | + | 1.27177i | 0.0939265 | + | 0.0542285i | ||||
\(551\) | 19.1905 | − | 19.1905i | 0.817543 | − | 0.817543i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.83347 | − | 23.2672i | −0.248065 | − | 0.989421i | ||||
\(554\) | −0.822003 | + | 0.822003i | −0.0349236 | + | 0.0349236i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.21506 | − | 5.56864i | −0.136349 | − | 0.236163i | ||||
\(557\) | −29.5799 | − | 7.92591i | −1.25334 | − | 0.335832i | −0.429715 | − | 0.902965i | \(-0.641386\pi\) |
−0.823626 | + | 0.567133i | \(0.808052\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.3704 | + | 1.61400i | −1.15765 | + | 0.0682651i | ||||
\(560\) | 0.243299 | − | 15.0672i | 0.0102812 | − | 0.636705i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.70035 | + | 2.94510i | 0.0717250 | + | 0.124231i | ||||
\(563\) | −7.49329 | + | 12.9788i | −0.315804 | + | 0.546989i | −0.979608 | − | 0.200917i | \(-0.935608\pi\) |
0.663804 | + | 0.747907i | \(0.268941\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.94722 | + | 18.4633i | 0.208131 | + | 0.776756i | ||||
\(566\) | 0.877680 | − | 0.235174i | 0.0368917 | − | 0.00988509i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.40258 | + | 4.16138i | −0.100810 | + | 0.174608i | ||||
\(569\) | −6.07156 | + | 3.50542i | −0.254533 | + | 0.146955i | −0.621838 | − | 0.783146i | \(-0.713614\pi\) |
0.367305 | + | 0.930101i | \(0.380280\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.237494i | 0.00993882i | 0.999988 | + | 0.00496941i | \(0.00158182\pi\) | ||||
−0.999988 | + | 0.00496941i | \(0.998418\pi\) | |||||||
\(572\) | −29.7646 | − | 6.12345i | −1.24452 | − | 0.256034i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.811447 | + | 0.231531i | 0.0338692 | + | 0.00966393i | ||||
\(575\) | 2.82848 | + | 4.89908i | 0.117956 | + | 0.204306i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.41695 | − | 3.41695i | 0.142250 | − | 0.142250i | −0.632396 | − | 0.774645i | \(-0.717928\pi\) |
0.774645 | + | 0.632396i | \(0.217928\pi\) | |||||||
\(578\) | 8.69131 | − | 2.32883i | 0.361511 | − | 0.0968665i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 11.3107 | + | 11.3107i | 0.469649 | + | 0.469649i | ||||
\(581\) | −3.62932 | − | 2.17426i | −0.150570 | − | 0.0902037i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −55.0253 | − | 14.7440i | −2.27891 | − | 0.610633i | ||||
\(584\) | 10.0392 | 0.415424 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.93076i | 0.203688i | ||||||||
\(587\) | −7.16064 | − | 1.91869i | −0.295551 | − | 0.0791927i | 0.107997 | − | 0.994151i | \(-0.465556\pi\) |
−0.403548 | + | 0.914959i | \(0.632223\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.81931 | + | 3.93713i | 0.280985 | + | 0.162227i | ||||
\(590\) | −2.19810 | − | 2.19810i | −0.0904945 | − | 0.0904945i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.80357 | − | 10.4631i | −0.115226 | − | 0.430030i | ||||
\(593\) | 20.9219 | + | 20.9219i | 0.859161 | + | 0.859161i | 0.991239 | − | 0.132078i | \(-0.0421649\pi\) |
−0.132078 | + | 0.991239i | \(0.542165\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −26.9166 | + | 14.9661i | −1.10347 | + | 0.613551i | ||||
\(596\) | −8.82700 | − | 2.36519i | −0.361568 | − | 0.0968818i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.29306 | + | 1.14905i | 0.0528771 | + | 0.0469882i | ||||
\(599\) | 35.0083 | 1.43040 | 0.715199 | − | 0.698920i | \(-0.246336\pi\) | ||||
0.715199 | + | 0.698920i | \(0.246336\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.0031 | − | 14.4355i | 1.01990 | − | 0.588838i | 0.105823 | − | 0.994385i | \(-0.466252\pi\) |
0.914074 | + | 0.405547i | \(0.132919\pi\) | |||||||
\(602\) | −3.85589 | − | 2.31000i | −0.157154 | − | 0.0941485i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12.6526 | + | 3.39025i | −0.514826 | + | 0.137947i | ||||
\(605\) | 11.4084 | − | 3.05688i | 0.463819 | − | 0.124280i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.1458 | − | 12.7859i | −0.898871 | − | 0.518964i | −0.0220376 | − | 0.999757i | \(-0.507015\pi\) |
−0.876834 | + | 0.480793i | \(0.840349\pi\) | |||||||
\(608\) | 6.59615 | + | 11.4249i | 0.267509 | + | 0.463339i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.04291i | 0.163693i | ||||||||
\(611\) | 26.2889 | + | 5.40839i | 1.06353 | + | 0.218800i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.84627 | + | 25.5506i | −0.276518 | + | 1.03198i | 0.678299 | + | 0.734786i | \(0.262718\pi\) |
−0.954817 | + | 0.297194i | \(0.903949\pi\) | |||||||
\(614\) | −2.62767 | + | 1.51708i | −0.106044 | + | 0.0612245i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.01933 | − | 7.24974i | −0.282817 | − | 0.292100i | ||||
\(617\) | 41.2766 | − | 11.0600i | 1.66173 | − | 0.445260i | 0.698870 | − | 0.715249i | \(-0.253687\pi\) |
0.962864 | + | 0.269988i | \(0.0870199\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.36404 | − | 7.36404i | −0.295986 | − | 0.295986i | 0.543453 | − | 0.839439i | \(-0.317116\pi\) |
−0.839439 | + | 0.543453i | \(0.817116\pi\) | |||||||
\(620\) | −2.32050 | + | 4.01922i | −0.0931935 | + | 0.161416i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.937855 | − | 3.50012i | 0.0376046 | − | 0.140342i | ||||
\(623\) | 2.22156 | + | 0.0358728i | 0.0890050 | + | 0.00143722i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.88945 | 0.195578 | ||||||||
\(626\) | −5.22738 | − | 1.40067i | −0.208928 | − | 0.0559822i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.6845 | − | 28.8983i | 0.665782 | − | 1.15317i | ||||
\(629\) | −15.6541 | + | 15.6541i | −0.624169 | + | 0.624169i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.47681 | − | 12.9756i | −0.138410 | − | 0.516552i | −0.999961 | − | 0.00888079i | \(-0.997173\pi\) |
0.861551 | − | 0.507671i | \(-0.169494\pi\) | |||||||
\(632\) | −5.65758 | + | 5.65758i | −0.225046 | + | 0.225046i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.17644 | + | 2.98862i | −0.205583 | + | 0.118693i | ||||
\(635\) | 2.53434 | − | 9.45828i | 0.100572 | − | 0.375340i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.0334 | + | 22.1855i | −0.476782 | + | 0.879021i | ||||
\(638\) | 5.14927 | 0.203862 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.93765 | + | 5.16016i | −0.353292 | + | 0.203973i | ||||
\(641\) | 9.03607 | + | 5.21698i | 0.356903 | + | 0.206058i | 0.667722 | − | 0.744411i | \(-0.267270\pi\) |
−0.310818 | + | 0.950469i | \(0.600603\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.33827 | + | 8.72656i | 0.0922125 | + | 0.344142i | 0.996582 | − | 0.0826083i | \(-0.0263251\pi\) |
−0.904370 | + | 0.426750i | \(0.859658\pi\) | |||||||
\(644\) | −2.69448 | − | 10.7471i | −0.106177 | − | 0.423495i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.30225 | − | 7.45171i | 0.169270 | − | 0.293184i | ||||
\(647\) | −4.86550 | − | 8.42729i | −0.191283 | − | 0.331311i | 0.754393 | − | 0.656423i | \(-0.227931\pi\) |
−0.945676 | + | 0.325112i | \(0.894598\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 39.0974 | 1.53471 | ||||||||
\(650\) | −2.01376 | + | 0.668905i | −0.0789863 | + | 0.0262366i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.85322 | + | 36.7727i | −0.385882 | + | 1.44013i | ||||
\(653\) | −19.3917 | − | 33.5874i | −0.758855 | − | 1.31437i | −0.943435 | − | 0.331557i | \(-0.892426\pi\) |
0.184580 | − | 0.982817i | \(-0.440907\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.06217 | + | 4.06217i | 0.158722 | + | 0.158722i | ||||
\(656\) | 1.36821 | + | 5.10623i | 0.0534196 | + | 0.199365i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.06066 | + | 3.16113i | 0.119317 | + | 0.123233i | ||||
\(659\) | −16.5452 | + | 28.6571i | −0.644509 | + | 1.11632i | 0.339905 | + | 0.940460i | \(0.389605\pi\) |
−0.984415 | + | 0.175863i | \(0.943728\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.34087 | + | 12.4683i | −0.129945 | + | 0.484960i | −0.999968 | − | 0.00805129i | \(-0.997437\pi\) |
0.870023 | + | 0.493011i | \(0.164104\pi\) | |||||||
\(662\) | 3.22860i | 0.125483i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.41118i | 0.0547645i | ||||||||
\(665\) | −5.68229 | + | 19.9147i | −0.220350 | + | 0.772260i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.91794 | + | 5.72612i | 0.384024 | + | 0.221716i | ||||
\(668\) | −19.5194 | + | 19.5194i | −0.755229 | + | 0.755229i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.64329 | + | 0.440319i | −0.0634859 | + | 0.0170110i | ||||
\(671\) | −35.9554 | − | 35.9554i | −1.38804 | − | 1.38804i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.5255 | − | 13.0051i | 0.868295 | − | 0.501310i | 0.00151340 | − | 0.999999i | \(-0.499518\pi\) |
0.866781 | + | 0.498689i | \(0.166185\pi\) | |||||||
\(674\) | −1.11250 | − | 0.298092i | −0.0428517 | − | 0.0114821i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.3128 | − | 15.1680i | 0.781262 | − | 0.583386i | ||||
\(677\) | − | 41.0161i | − | 1.57638i | −0.615434 | − | 0.788188i | \(-0.711019\pi\) | ||
0.615434 | − | 0.788188i | \(-0.288981\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.9434 | − | 21.6533i | 1.49451 | − | 0.830976i | ||||
\(680\) | 8.89631 | + | 5.13629i | 0.341158 | + | 0.196968i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.386679 | + | 1.44311i | 0.0148067 | + | 0.0552594i | ||||
\(683\) | −8.69145 | − | 32.4369i | −0.332569 | − | 1.24116i | −0.906481 | − | 0.422247i | \(-0.861241\pi\) |
0.573912 | − | 0.818917i | \(-0.305425\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.0408491 | − | 0.0235842i | −0.00156076 | − | 0.000901107i | ||||
\(686\) | −3.67927 | + | 1.89289i | −0.140475 | + | 0.0722710i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 28.1591i | − | 1.07356i | ||||||
\(689\) | 39.6870 | − | 26.1437i | 1.51195 | − | 0.995994i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.3878 | − | 8.94624i | −1.27013 | − | 0.340331i | −0.440051 | − | 0.897973i | \(-0.645040\pi\) |
−0.830082 | + | 0.557642i | \(0.811706\pi\) | |||||||
\(692\) | −32.6305 | + | 18.8392i | −1.24043 | + | 0.716160i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.76020 | − | 3.76020i | −0.142735 | − | 0.142735i | ||||
\(695\) | −4.89884 | + | 1.31264i | −0.185823 | + | 0.0497912i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.63956 | − | 7.63956i | 0.289369 | − | 0.289369i | ||||
\(698\) | −2.36628 | − | 1.36617i | −0.0895651 | − | 0.0517104i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 13.0697 | + | 3.72918i | 0.493987 | + | 0.140950i | ||||
\(701\) | 4.79362i | 0.181053i | 0.995894 | + | 0.0905263i | \(0.0288549\pi\) | ||||
−0.995894 | + | 0.0905263i | \(0.971145\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.8867i | 0.561461i | ||||||||
\(704\) | 7.63649 | − | 28.4998i | 0.287811 | − | 1.07413i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.91032 | + | 3.30876i | −0.0718957 | + | 0.124527i | ||||
\(707\) | −20.8549 | + | 20.1921i | −0.784329 | + | 0.759402i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.76549 | + | 10.3209i | 0.103860 | + | 0.387611i | 0.998213 | − | 0.0597505i | \(-0.0190305\pi\) |
−0.894353 | + | 0.447361i | \(0.852364\pi\) | |||||||
\(710\) | 1.32303 | + | 1.32303i | 0.0496524 | + | 0.0496524i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.370552 | − | 0.641814i | −0.0138870 | − | 0.0240530i | ||||
\(713\) | −0.859994 | + | 3.20954i | −0.0322070 | + | 0.120198i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.7413 | + | 21.4263i | −0.401703 | + | 0.801300i | ||||
\(716\) | −8.01890 | −0.299680 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.30976 | − | 4.00062i | −0.0861995 | − | 0.149302i | ||||
\(719\) | −14.9272 | + | 25.8547i | −0.556690 | + | 0.964216i | 0.441080 | + | 0.897468i | \(0.354596\pi\) |
−0.997770 | + | 0.0667479i | \(0.978738\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.02556 | − | 12.0676i | −0.112678 | − | 0.449423i | ||||
\(722\) | −0.398890 | − | 1.48868i | −0.0148452 | − | 0.0554029i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.54065 | − | 2.04420i | −0.131587 | − | 0.0759720i | ||||
\(725\) | −12.1661 | + | 7.02412i | −0.451839 | + | 0.260869i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.2241 | −1.52892 | −0.764459 | − | 0.644672i | \(-0.776994\pi\) | ||||
−0.764459 | + | 0.644672i | \(0.776994\pi\) | |||||||
\(728\) | 8.41078 | − | 0.359819i | 0.311724 | − | 0.0133358i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.01175 | − | 3.77589i | 0.0374464 | − | 0.139752i | ||||
\(731\) | −49.8398 | + | 28.7750i | −1.84339 | + | 1.06428i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.3345 | + | 14.3345i | −0.529456 | + | 0.529456i | −0.920410 | − | 0.390954i | \(-0.872145\pi\) |
0.390954 | + | 0.920410i | \(0.372145\pi\) | |||||||
\(734\) | 0.0267847 | + | 0.0999617i | 0.000988640 | + | 0.00368965i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.93636 | + | 3.93636i | −0.145096 | + | 0.145096i | ||||
\(737\) | 10.6986 | − | 18.5305i | 0.394087 | − | 0.682579i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.4381 | + | 6.54818i | 0.898972 | + | 0.240879i | 0.678575 | − | 0.734532i | \(-0.262598\pi\) |
0.220397 | + | 0.975410i | \(0.429265\pi\) | |||||||
\(740\) | −8.77402 | −0.322539 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.79007 | + | 0.125791i | 0.285982 | + | 0.00461793i | ||||
\(743\) | −10.9162 | + | 40.7397i | −0.400476 | + | 1.49460i | 0.411774 | + | 0.911286i | \(0.364909\pi\) |
−0.812250 | + | 0.583310i | \(0.801757\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.60387 | + | 6.24209i | −0.132036 | + | 0.228693i | ||||
\(746\) | −0.110241 | − | 0.110241i | −0.00403621 | − | 0.00403621i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −61.6106 | + | 16.5085i | −2.25271 | + | 0.603611i | ||||
\(749\) | −24.9120 | + | 24.1203i | −0.910265 | + | 0.881335i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.23654 | + | 3.60067i | −0.227574 | + | 0.131390i | −0.609453 | − | 0.792823i | \(-0.708611\pi\) |
0.381878 | + | 0.924213i | \(0.375277\pi\) | |||||||
\(752\) | −7.13433 | + | 26.6257i | −0.260162 | + | 0.970938i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.85350 | + | 3.21112i | −0.103918 | + | 0.116942i | ||||
\(755\) | 10.3315i | 0.376004i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.5449 | − | 19.9964i | −0.419607 | − | 0.726780i | 0.576293 | − | 0.817243i | \(-0.304499\pi\) |
−0.995900 | + | 0.0904628i | \(0.971165\pi\) | |||||||
\(758\) | 1.38385 | + | 0.798968i | 0.0502638 | + | 0.0290198i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.67233 | − | 1.78785i | 0.242031 | − | 0.0648520i | ||||
\(761\) | 5.76843 | − | 1.54565i | 0.209105 | − | 0.0560296i | −0.152746 | − | 0.988266i | \(-0.548812\pi\) |
0.361851 | + | 0.932236i | \(0.382145\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.67688 | + | 2.79908i | −0.0607071 | + | 0.101333i | ||||
\(764\) | −14.2562 | + | 8.23082i | −0.515771 | + | 0.297780i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.428649 | 0.0154877 | ||||||||
\(767\) | −21.6660 | + | 24.3814i | −0.782315 | + | 0.880362i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.9326 | + | 8.82426i | 1.18758 | + | 0.318211i | 0.797929 | − | 0.602752i | \(-0.205929\pi\) |
0.389650 | + | 0.920963i | \(0.372596\pi\) | |||||||
\(770\) | −3.43415 | + | 1.90945i | −0.123758 | + | 0.0688119i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.80726 | + | 2.80726i | 0.101036 | + | 0.101036i | ||||
\(773\) | −0.0200118 | − | 0.0746850i | −0.000719774 | − | 0.00268623i | 0.965565 | − | 0.260162i | \(-0.0837759\pi\) |
−0.966285 | + | 0.257476i | \(0.917109\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.88214 | − | 2.88214i | −0.103530 | − | 0.103530i | ||||
\(776\) | −12.8713 | − | 7.43127i | −0.462054 | − | 0.266767i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.33164 | − | 0.356813i | −0.0477417 | − | 0.0127924i | ||||
\(779\) | − | 7.26504i | − | 0.260297i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.5326 | −0.842063 | ||||||||
\(782\) | 3.50718 | + | 0.939747i | 0.125417 | + | 0.0336053i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −22.0182 | − | 13.6786i | −0.786363 | − | 0.488521i | ||||
\(785\) | −18.6105 | − | 18.6105i | −0.664236 | − | 0.664236i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.7109 | − | 3.67383i | 0.488742 | − | 0.130958i | −0.00602847 | − | 0.999982i | \(-0.501919\pi\) |
0.494770 | + | 0.869024i | \(0.335252\pi\) | |||||||
\(788\) | −18.4866 | + | 18.4866i | −0.658558 | + | 0.658558i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.55773 | + | 2.69807i | 0.0554216 | + | 0.0959931i | ||||
\(791\) | 31.6179 | + | 9.02159i | 1.12420 | + | 0.320771i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.3469 | − | 2.49715i | 1.50378 | − | 0.0886765i | ||||
\(794\) | 6.96753i | 0.247268i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.7277 | + | 7.34835i | −0.451122 | + | 0.260455i | ||||
\(797\) | −4.85453 | + | 8.40830i | −0.171956 | + | 0.297837i | −0.939104 | − | 0.343634i | \(-0.888342\pi\) |
0.767147 | + | 0.641471i | \(0.221676\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.4161 | − | 14.5808i | 1.92510 | − | 0.515830i | ||||
\(800\) | −1.76741 | − | 6.59606i | −0.0624873 | − | 0.233206i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.80472 | − | 4.85792i | 0.0990382 | − | 0.171539i | ||||
\(803\) | 24.5827 | + | 42.5786i | 0.867506 | + | 1.50256i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.73782 | − | 0.141095i | −0.307968 | − | 0.00497293i | ||||
\(806\) | −1.11421 | − | 0.558569i | −0.0392464 | − | 0.0196748i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.35256 | + | 2.50601i | 0.329022 | + | 0.0881612i | ||||
\(809\) | −22.8046 | − | 39.4988i | −0.801768 | − | 1.38870i | −0.918451 | − | 0.395534i | \(-0.870559\pi\) |
0.116683 | − | 0.993169i | \(-0.462774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.90491 | + | 6.90491i | −0.242464 | + | 0.242464i | −0.817869 | − | 0.575405i | \(-0.804845\pi\) |
0.575405 | + | 0.817869i | \(0.304845\pi\) | |||||||
\(812\) | 26.6888 | − | 6.69134i | 0.936595 | − | 0.234820i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.99722 | + | 1.99722i | −0.0700027 | + | 0.0700027i | ||||
\(815\) | 26.0042 | + | 15.0135i | 0.910886 | + | 0.525900i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.0161 | + | 37.3804i | −0.350417 | + | 1.30778i | ||||
\(818\) | 3.38761 | 0.118445 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.28193 | 0.149531 | ||||||||
\(821\) | −4.30181 | + | 16.0546i | −0.150134 | + | 0.560308i | 0.849339 | + | 0.527848i | \(0.177001\pi\) |
−0.999473 | + | 0.0324603i | \(0.989666\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.40900 | + | 4.85494i | 0.293119 | + | 0.169233i | 0.639348 | − | 0.768918i | \(-0.279204\pi\) |
−0.346228 | + | 0.938150i | \(0.612538\pi\) | |||||||
\(824\) | −2.93433 | + | 2.93433i | −0.102222 | + | 0.102222i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.18669 | + | 1.30039i | −0.180468 | + | 0.0452463i | ||||
\(827\) | 23.2961 | − | 23.2961i | 0.810086 | − | 0.810086i | −0.174560 | − | 0.984647i | \(-0.555850\pi\) |
0.984647 | + | 0.174560i | \(0.0558503\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.7204 | − | 25.4965i | −0.511261 | − | 0.885531i | −0.999915 | − | 0.0130527i | \(-0.995845\pi\) |
0.488653 | − | 0.872478i | \(-0.337488\pi\) | |||||||
\(830\) | 0.530767 | + | 0.142219i | 0.0184232 | + | 0.00493648i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.5408 | + | 20.5555i | 0.469444 | + | 0.712633i | ||||
\(833\) | −1.71043 | + | 52.9485i | −0.0592628 | + | 1.83456i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.8863 | + | 18.8557i | 0.376738 | + | 0.652529i | ||||
\(836\) | −21.4455 | + | 37.1447i | −0.741708 | + | 1.28468i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.266506 | + | 0.994613i | 0.00920629 | + | 0.0343583i | ||||
\(839\) | −18.5876 | + | 4.98054i | −0.641716 | + | 0.171947i | −0.564981 | − | 0.825104i | \(-0.691116\pi\) |
−0.0767354 | + | 0.997051i | \(0.524450\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.280024 | − | 0.485016i | 0.00965600 | − | 0.0167247i | ||||
\(842\) | −3.45960 | + | 1.99740i | −0.119226 | + | 0.0688350i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 33.0856i | 1.13885i | ||||||||
\(845\) | −7.40925 | − | 18.5719i | −0.254886 | − | 0.638892i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.57443 | − | 19.5367i | 0.191540 | − | 0.671289i | ||||
\(848\) | 24.4044 | + | 42.2697i | 0.838051 | + | 1.45155i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.14942 | + | 3.14942i | −0.108024 | + | 0.108024i | ||||
\(851\) | −6.06779 | + | 1.62586i | −0.208001 | + | 0.0557337i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.9327 | + | 14.9327i | 0.511287 | + | 0.511287i | 0.914921 | − | 0.403634i | \(-0.132253\pi\) |
−0.403634 | + | 0.914921i | \(0.632253\pi\) | |||||||
\(854\) | 5.96575 | + | 3.57398i | 0.204144 | + | 0.122299i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.1720 | + | 2.99353i | 0.381851 | + | 0.102317i | ||||
\(857\) | 5.36310 | 0.183200 | 0.0916001 | − | 0.995796i | \(-0.470802\pi\) | ||||
0.0916001 | + | 0.995796i | \(0.470802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.1000i | 0.719923i | 0.932967 | + | 0.359962i | \(0.117210\pi\) | ||||
−0.932967 | + | 0.359962i | \(0.882790\pi\) | |||||||
\(860\) | −22.0316 | − | 5.90334i | −0.751270 | − | 0.201302i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.58816 | − | 0.916923i | −0.0540929 | − | 0.0312305i | ||||
\(863\) | −0.437792 | − | 0.437792i | −0.0149026 | − | 0.0149026i | 0.699616 | − | 0.714519i | \(-0.253354\pi\) |
−0.714519 | + | 0.699616i | \(0.753354\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.69166 | + | 28.7056i | 0.261524 | + | 0.976021i | ||||
\(866\) | −2.74176 | − | 2.74176i | −0.0931690 | − | 0.0931690i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.87945 | + | 6.97718i | 0.131677 | + | 0.236821i | ||||
\(869\) | −37.8488 | − | 10.1416i | −1.28393 | − | 0.344029i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.62706 | + | 16.9405i | 0.190666 | + | 0.574006i | ||||
\(872\) | 1.08836 | 0.0368565 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.11446 | − | 1.22079i | 0.0715228 | − | 0.0412937i | ||||
\(875\) | 15.9659 | − | 26.6505i | 0.539745 | − | 0.900953i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.601435 | + | 0.161154i | −0.0203090 | + | 0.00544178i | −0.268959 | − | 0.963152i | \(-0.586680\pi\) |
0.248650 | + | 0.968593i | \(0.420013\pi\) | |||||||
\(878\) | −3.36192 | + | 0.900824i | −0.113459 | + | 0.0304013i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −21.3180 | − | 12.3079i | −0.718628 | − | 0.414900i | ||||
\(881\) | −9.21121 | − | 15.9543i | −0.310333 | − | 0.537513i | 0.668101 | − | 0.744070i | \(-0.267107\pi\) |
−0.978435 | + | 0.206557i | \(0.933774\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 15.8935i | − | 0.534859i | −0.963577 | − | 0.267429i | \(-0.913826\pi\) | ||
0.963577 | − | 0.267429i | \(-0.0861742\pi\) | |||||||
\(884\) | 23.8470 | − | 47.5691i | 0.802062 | − | 1.59992i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.73631 | + | 6.47998i | −0.0583324 | + | 0.217699i | ||||
\(887\) | −29.3404 | + | 16.9397i | −0.985154 | + | 0.568779i | −0.903822 | − | 0.427908i | \(-0.859251\pi\) |
−0.0813318 | + | 0.996687i | \(0.525917\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.7163 | − | 12.1009i | −0.392953 | − | 0.405852i | ||||
\(890\) | −0.278740 | + | 0.0746883i | −0.00934340 | + | 0.00250356i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17.4013 | + | 17.4013i | 0.582638 | + | 0.582638i | ||||
\(893\) | 18.9412 | − | 32.8072i | 0.633844 | − | 1.09785i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.63697 | + | 6.10926i | −0.0547179 | + | 0.204210i | ||||
\(896\) | −0.286621 | + | 17.7501i | −0.00957535 | + | 0.592989i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.55296 | 0.0518231 | ||||||||
\(899\) | −7.97042 | − | 2.13567i | −0.265828 | − | 0.0712285i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 49.8764 | − | 86.3885i | 1.66162 | − | 2.87802i | ||||
\(902\) | 0.974693 | − | 0.974693i | 0.0324537 | − | 0.0324537i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.83850 | − | 10.5934i | −0.0944073 | − | 0.352333i | ||||
\(905\) | −2.28017 | + | 2.28017i | −0.0757956 | + | 0.0757956i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.0978 | − | 21.4184i | 1.23181 | − | 0.711187i | 0.264404 | − | 0.964412i | \(-0.414825\pi\) |
0.967407 | + | 0.253225i | \(0.0814914\pi\) | |||||||
\(908\) | 9.93007 | − | 37.0595i | 0.329541 | − | 1.22986i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.712304 | − | 3.19969i | 0.0236127 | − | 0.106069i | ||||
\(911\) | 9.59124 | 0.317772 | 0.158886 | − | 0.987297i | \(-0.449210\pi\) | ||||
0.158886 | + | 0.987297i | \(0.449210\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.98517 | + | 3.45554i | −0.198080 | + | 0.114362i | ||||
\(914\) | 4.30973 | + | 2.48822i | 0.142553 | + | 0.0823032i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.1504 | − | 52.8101i | −0.467543 | − | 1.74489i | ||||
\(917\) | 9.58517 | − | 2.40316i | 0.316530 | − | 0.0793594i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.74479 | + | 6.48617i | −0.123529 | + | 0.213959i | −0.921157 | − | 0.389191i | \(-0.872755\pi\) |
0.797628 | + | 0.603150i | \(0.206088\pi\) | |||||||
\(920\) | 1.45745 | + | 2.52438i | 0.0480507 | + | 0.0832262i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.60431 | 0.0857683 | ||||||||
\(923\) | 13.0407 | − | 14.6751i | 0.429240 | − | 0.483036i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.99441 | − | 7.44323i | 0.0655757 | − | 0.244732i | ||||
\(926\) | 2.63462 | + | 4.56330i | 0.0865791 | + | 0.149959i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.77536 | − | 9.77536i | −0.320892 | − | 0.320892i | ||||
\(929\) | 9.80192 | + | 36.5812i | 0.321590 | + | 1.20019i | 0.917695 | + | 0.397285i | \(0.130048\pi\) |
−0.596105 | + | 0.802907i | \(0.703286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.3631 | + | 25.9897i | 0.798468 | + | 0.851777i | ||||
\(932\) | −10.6182 | + | 18.3913i | −0.347811 | + | 0.602427i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.984940 | − | 3.67585i | 0.0322282 | − | 0.120277i | ||||
\(935\) | 50.3086i | 1.64527i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 9.27559i | − | 0.303020i | −0.988456 | − | 0.151510i | \(-0.951586\pi\) | ||
0.988456 | − | 0.151510i | \(-0.0484136\pi\) | |||||||
\(938\) | −0.802951 | + | 2.81410i | −0.0262173 | + | 0.0918837i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 19.3362 | + | 11.1637i | 0.630676 | + | 0.364121i | ||||
\(941\) | 38.7691 | − | 38.7691i | 1.26384 | − | 1.26384i | 0.314617 | − | 0.949219i | \(-0.398124\pi\) |
0.949219 | − | 0.314617i | \(-0.101876\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.96122 | − | 0.793458i | 0.0964307 | − | 0.0258385i | ||||
\(944\) | −23.6872 | − | 23.6872i | −0.770951 | − | 0.770951i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.35881 | + | 3.67126i | −0.206743 | + | 0.119363i | ||||
\(947\) | −50.1290 | − | 13.4320i | −1.62898 | − | 0.436483i | −0.675354 | − | 0.737493i | \(-0.736009\pi\) |
−0.953621 | + | 0.301011i | \(0.902676\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40.1749 | − | 8.26517i | −1.30413 | − | 0.268299i | ||||
\(950\) | 2.99502i | 0.0971714i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 15.4436 | − | 8.58693i | 0.500530 | − | 0.278304i | ||||
\(953\) | −12.2620 | − | 7.07949i | −0.397206 | − | 0.229327i | 0.288072 | − | 0.957609i | \(-0.406986\pi\) |
−0.685278 | + | 0.728282i | \(0.740319\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.36046 | + | 12.5414i | 0.108742 | + | 0.405831i | ||||
\(956\) | 7.16655 | + | 26.7459i | 0.231783 | + | 0.865026i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.49752 | + | 3.75134i | 0.209925 | + | 0.121200i | ||||
\(959\) | −0.0709121 | + | 0.0394285i | −0.00228987 | + | 0.00127321i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.6059i | 0.922770i | ||||||||
\(962\) | −0.138710 | − | 2.35225i | −0.00447219 | − | 0.0758397i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −29.5058 | − | 7.90606i | −0.950319 | − | 0.254637i | ||||
\(965\) | 2.71181 | − | 1.56566i | 0.0872962 | − | 0.0504005i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.4554 | − | 24.4554i | −0.786433 | − | 0.786433i | 0.194474 | − | 0.980908i | \(-0.437700\pi\) |
−0.980908 | + | 0.194474i | \(0.937700\pi\) | |||||||
\(968\) | −6.54568 | + | 1.75391i | −0.210386 | + | 0.0563728i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.09219 | + | 4.09219i | −0.131392 | + | 0.131392i | ||||
\(971\) | 4.45063 | + | 2.56957i | 0.142828 | + | 0.0824615i | 0.569711 | − | 0.821845i | \(-0.307055\pi\) |
−0.426883 | + | 0.904307i | \(0.640389\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.39369 | + | 8.38915i | −0.0767381 | + | 0.268944i | ||||
\(974\) | − | 0.875113i | − | 0.0280404i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 43.5671i | 1.39455i | ||||||||
\(977\) | 4.45430 | − | 16.6237i | 0.142506 | − | 0.531839i | −0.857348 | − | 0.514737i | \(-0.827889\pi\) |
0.999854 | − | 0.0171015i | \(-0.00544385\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.81473 | − | 3.14320i | 0.0579989 | − | 0.100457i | ||||
\(980\) | −15.3180 | + | 14.3593i | −0.489316 | + | 0.458692i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.410932 | + | 1.53362i | 0.0131134 | + | 0.0489398i | ||||
\(983\) | 13.7631 | + | 13.7631i | 0.438975 | + | 0.438975i | 0.891667 | − | 0.452692i | \(-0.149536\pi\) |
−0.452692 | + | 0.891667i | \(0.649536\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.3103 | + | 17.8580i | 0.328514 | + | 0.569003i | ||||
\(986\) | −2.33372 | + | 8.70957i | −0.0743209 | + | 0.277369i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.2795 | − | 33.9575i | −0.358850 | − | 1.08033i | ||||
\(989\) | −16.3301 | −0.519268 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.9230 | − | 39.7039i | −0.728174 | − | 1.26124i | −0.957654 | − | 0.287922i | \(-0.907036\pi\) |
0.229480 | − | 0.973313i | \(-0.426298\pi\) | |||||||
\(992\) | 2.00552 | − | 3.47366i | 0.0636753 | − | 0.110289i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.12185 | − | 0.782700i | 0.0990190 | − | 0.0248257i | ||||
\(995\) | 3.00017 | + | 11.1968i | 0.0951119 | + | 0.354963i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.8851 | − | 15.5221i | −0.851461 | − | 0.491591i | 0.00968271 | − | 0.999953i | \(-0.496918\pi\) |
−0.861143 | + | 0.508362i | \(0.830251\pi\) | |||||||
\(998\) | −1.48448 | + | 0.857066i | −0.0469905 | + | 0.0271300i | ||||
\(999\) | 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 | 819.2.fm.f.622.3 | 32 | ||
3.2 | odd | 2 | 273.2.by.c.76.6 | ✓ | 32 | ||
7.6 | odd | 2 | 819.2.fm.e.622.3 | 32 | |||
13.6 | odd | 12 | 819.2.fm.e.370.3 | 32 | |||
21.20 | even | 2 | 273.2.by.d.76.6 | yes | 32 | ||
39.32 | even | 12 | 273.2.by.d.97.6 | yes | 32 | ||
91.6 | even | 12 | inner | 819.2.fm.f.370.3 | 32 | ||
273.188 | odd | 12 | 273.2.by.c.97.6 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.by.c.76.6 | ✓ | 32 | 3.2 | odd | 2 | ||
273.2.by.c.97.6 | yes | 32 | 273.188 | odd | 12 | ||
273.2.by.d.76.6 | yes | 32 | 21.20 | even | 2 | ||
273.2.by.d.97.6 | yes | 32 | 39.32 | even | 12 | ||
819.2.fm.e.370.3 | 32 | 13.6 | odd | 12 | |||
819.2.fm.e.622.3 | 32 | 7.6 | odd | 2 | |||
819.2.fm.f.370.3 | 32 | 91.6 | even | 12 | inner | ||
819.2.fm.f.622.3 | 32 | 1.1 | even | 1 | trivial |