Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 373.8 | ||
Character | \(\chi\) | \(=\) | 784.373 |
Dual form | 784.2.x.n.557.8 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.13424 | − | 0.844695i | 0.802026 | − | 0.597290i | ||||
\(3\) | 1.26459 | + | 0.338847i | 0.730114 | + | 0.195633i | 0.604680 | − | 0.796469i | \(-0.293301\pi\) |
0.125434 | + | 0.992102i | \(0.459968\pi\) | |||||||
\(4\) | 0.572980 | − | 1.91617i | 0.286490 | − | 0.958083i | ||||
\(5\) | −3.57533 | + | 0.958008i | −1.59894 | + | 0.428434i | −0.944722 | − | 0.327874i | \(-0.893668\pi\) |
−0.654216 | + | 0.756308i | \(0.727001\pi\) | |||||||
\(6\) | 1.72057 | − | 0.683864i | 0.702420 | − | 0.279186i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.968683 | − | 2.65738i | −0.342481 | − | 0.939525i | ||||
\(9\) | −1.11370 | − | 0.642992i | −0.371232 | − | 0.214331i | ||||
\(10\) | −3.24604 | + | 4.10667i | −1.02649 | + | 1.29864i | ||||
\(11\) | 1.28693 | − | 4.80288i | 0.388023 | − | 1.44812i | −0.445322 | − | 0.895370i | \(-0.646911\pi\) |
0.833346 | − | 0.552752i | \(-0.186422\pi\) | |||||||
\(12\) | 1.37387 | − | 2.22902i | 0.396603 | − | 0.643463i | ||||
\(13\) | 3.14392 | − | 3.14392i | 0.871968 | − | 0.871968i | −0.120719 | − | 0.992687i | \(-0.538520\pi\) |
0.992687 | + | 0.120719i | \(0.0385201\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.84596 | −1.25122 | ||||||||
\(16\) | −3.34339 | − | 2.19585i | −0.835847 | − | 0.548962i | ||||
\(17\) | −3.33018 | − | 5.76804i | −0.807688 | − | 1.39896i | −0.914462 | − | 0.404673i | \(-0.867385\pi\) |
0.106774 | − | 0.994283i | \(-0.465948\pi\) | |||||||
\(18\) | −1.80633 | + | 0.211429i | −0.425755 | + | 0.0498342i | ||||
\(19\) | 1.26929 | + | 4.73707i | 0.291196 | + | 1.08676i | 0.944192 | + | 0.329396i | \(0.106845\pi\) |
−0.652996 | + | 0.757361i | \(0.726488\pi\) | |||||||
\(20\) | −0.212891 | + | 7.39985i | −0.0476039 | + | 1.65466i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.59729 | − | 6.53466i | −0.553744 | − | 1.39319i | ||||
\(23\) | 2.83059 | + | 1.63424i | 0.590219 | + | 0.340763i | 0.765184 | − | 0.643811i | \(-0.222648\pi\) |
−0.174965 | + | 0.984575i | \(0.555981\pi\) | |||||||
\(24\) | −0.324547 | − | 3.68874i | −0.0662478 | − | 0.752961i | ||||
\(25\) | 7.53510 | − | 4.35039i | 1.50702 | − | 0.870078i | ||||
\(26\) | 0.910292 | − | 6.22161i | 0.178523 | − | 1.22016i | ||||
\(27\) | −3.96774 | − | 3.96774i | −0.763592 | − | 0.763592i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0287696 | + | 0.0287696i | −0.00534239 | + | 0.00534239i | −0.709773 | − | 0.704431i | \(-0.751202\pi\) |
0.704431 | + | 0.709773i | \(0.251202\pi\) | |||||||
\(30\) | −5.49646 | + | 4.09336i | −1.00351 | + | 0.747342i | ||||
\(31\) | 2.29348 | + | 3.97242i | 0.411920 | + | 0.713467i | 0.995100 | − | 0.0988763i | \(-0.0315248\pi\) |
−0.583179 | + | 0.812343i | \(0.698191\pi\) | |||||||
\(32\) | −5.64701 | + | 0.333535i | −0.998260 | + | 0.0589612i | ||||
\(33\) | 3.25488 | − | 5.63762i | 0.566602 | − | 0.981384i | ||||
\(34\) | −8.64945 | − | 3.72933i | −1.48337 | − | 0.639575i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.87021 | + | 1.76560i | −0.311701 | + | 0.294267i | ||||
\(37\) | −1.28047 | + | 0.343100i | −0.210507 | + | 0.0564053i | −0.362532 | − | 0.931972i | \(-0.618087\pi\) |
0.152024 | + | 0.988377i | \(0.451421\pi\) | |||||||
\(38\) | 5.44105 | + | 4.30078i | 0.882656 | + | 0.697679i | ||||
\(39\) | 5.04110 | − | 2.91048i | 0.807221 | − | 0.466050i | ||||
\(40\) | 6.00915 | + | 8.57300i | 0.950130 | + | 1.35551i | ||||
\(41\) | − | 2.49919i | − | 0.390308i | −0.980773 | − | 0.195154i | \(-0.937479\pi\) | ||
0.980773 | − | 0.195154i | \(-0.0625207\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.947115 | − | 0.947115i | −0.144434 | − | 0.144434i | 0.631192 | − | 0.775626i | \(-0.282566\pi\) |
−0.775626 | + | 0.631192i | \(0.782566\pi\) | |||||||
\(44\) | −8.46573 | − | 5.21792i | −1.27626 | − | 0.786631i | ||||
\(45\) | 4.59782 | + | 1.23198i | 0.685403 | + | 0.183653i | ||||
\(46\) | 4.59099 | − | 0.537371i | 0.676905 | − | 0.0792311i | ||||
\(47\) | 0.399149 | − | 0.691346i | 0.0582218 | − | 0.100843i | −0.835445 | − | 0.549573i | \(-0.814790\pi\) |
0.893667 | + | 0.448730i | \(0.148124\pi\) | |||||||
\(48\) | −3.48397 | − | 3.90975i | −0.502868 | − | 0.564324i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.87182 | − | 11.2992i | 0.688979 | − | 1.59795i | ||||
\(51\) | −2.25684 | − | 8.42266i | −0.316021 | − | 1.17941i | ||||
\(52\) | −4.22288 | − | 7.82569i | −0.585608 | − | 1.08523i | ||||
\(53\) | −0.490386 | + | 1.83015i | −0.0673597 | + | 0.251390i | −0.991392 | − | 0.130923i | \(-0.958206\pi\) |
0.924033 | + | 0.382313i | \(0.124872\pi\) | |||||||
\(54\) | −7.85188 | − | 1.14882i | −1.06851 | − | 0.156334i | ||||
\(55\) | 18.4048i | 2.48170i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.42056i | 0.850424i | ||||||||
\(58\) | −0.00832996 | + | 0.0569331i | −0.00109378 | + | 0.00747569i | ||||
\(59\) | −1.40564 | + | 5.24593i | −0.182999 | + | 0.682962i | 0.812051 | + | 0.583587i | \(0.198351\pi\) |
−0.995050 | + | 0.0993754i | \(0.968316\pi\) | |||||||
\(60\) | −2.77664 | + | 9.28567i | −0.358462 | + | 1.19878i | ||||
\(61\) | 1.47985 | + | 5.52289i | 0.189476 | + | 0.707134i | 0.993628 | + | 0.112710i | \(0.0359531\pi\) |
−0.804152 | + | 0.594424i | \(0.797380\pi\) | |||||||
\(62\) | 5.95682 | + | 2.56837i | 0.756517 | + | 0.326183i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.12331 | + | 5.14831i | −0.765413 | + | 0.643539i | ||||
\(65\) | −8.22867 | + | 14.2525i | −1.02064 | + | 1.76780i | ||||
\(66\) | −1.07027 | − | 9.14377i | −0.131741 | − | 1.12552i | ||||
\(67\) | 10.5721 | + | 2.83278i | 1.29159 | + | 0.346079i | 0.838262 | − | 0.545267i | \(-0.183572\pi\) |
0.453323 | + | 0.891346i | \(0.350238\pi\) | |||||||
\(68\) | −12.9607 | + | 3.07621i | −1.57171 | + | 0.373045i | ||||
\(69\) | 3.02579 | + | 3.02579i | 0.364262 | + | 0.364262i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.16268i | 0.494019i | 0.969013 | + | 0.247010i | \(0.0794479\pi\) | ||||
−0.969013 | + | 0.247010i | \(0.920552\pi\) | |||||||
\(72\) | −0.629855 | + | 3.58236i | −0.0742291 | + | 0.422186i | ||||
\(73\) | 1.13427 | − | 0.654873i | 0.132757 | − | 0.0766471i | −0.432151 | − | 0.901801i | \(-0.642245\pi\) |
0.564907 | + | 0.825154i | \(0.308912\pi\) | |||||||
\(74\) | −1.16253 | + | 1.47076i | −0.135142 | + | 0.170972i | ||||
\(75\) | 11.0030 | − | 2.94823i | 1.27051 | − | 0.340433i | ||||
\(76\) | 9.80429 | + | 0.282066i | 1.12463 | + | 0.0323552i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.25932 | − | 7.55936i | 0.369046 | − | 0.855929i | ||||
\(79\) | −0.166127 | + | 0.287740i | −0.0186907 | + | 0.0323733i | −0.875219 | − | 0.483726i | \(-0.839283\pi\) |
0.856529 | + | 0.516099i | \(0.172616\pi\) | |||||||
\(80\) | 14.0574 | + | 4.64790i | 1.57166 | + | 0.519651i | ||||
\(81\) | −1.74414 | − | 3.02095i | −0.193794 | − | 0.335661i | ||||
\(82\) | −2.11106 | − | 2.83467i | −0.233127 | − | 0.313037i | ||||
\(83\) | 10.9693 | − | 10.9693i | 1.20403 | − | 1.20403i | 0.231104 | − | 0.972929i | \(-0.425766\pi\) |
0.972929 | − | 0.231104i | \(-0.0742339\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.4323 | + | 17.4323i | 1.89080 | + | 1.89080i | ||||
\(86\) | −1.87428 | − | 0.274228i | −0.202108 | − | 0.0295707i | ||||
\(87\) | −0.0461304 | + | 0.0266334i | −0.00494570 | + | 0.00285540i | ||||
\(88\) | −14.0097 | + | 1.23262i | −1.49344 | + | 0.131397i | ||||
\(89\) | −5.63762 | − | 3.25488i | −0.597587 | − | 0.345017i | 0.170505 | − | 0.985357i | \(-0.445460\pi\) |
−0.768092 | + | 0.640340i | \(0.778793\pi\) | |||||||
\(90\) | 6.25566 | − | 2.48640i | 0.659405 | − | 0.262090i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.75335 | − | 4.48750i | 0.495571 | − | 0.467854i | ||||
\(93\) | 1.55427 | + | 5.80063i | 0.161171 | + | 0.601498i | ||||
\(94\) | −0.131248 | − | 1.12131i | −0.0135372 | − | 0.115654i | ||||
\(95\) | −9.07629 | − | 15.7206i | −0.931208 | − | 1.61290i | ||||
\(96\) | −7.25420 | − | 1.49169i | −0.740378 | − | 0.152245i | ||||
\(97\) | −8.56512 | −0.869657 | −0.434828 | − | 0.900513i | \(-0.643191\pi\) | ||||
−0.434828 | + | 0.900513i | \(0.643191\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.52146 | + | 4.52146i | −0.454424 | + | 0.454424i | ||||
\(100\) | −4.01862 | − | 16.9312i | −0.401862 | − | 1.69312i | ||||
\(101\) | −2.23323 | + | 8.33453i | −0.222215 | + | 0.829317i | 0.761287 | + | 0.648416i | \(0.224568\pi\) |
−0.983501 | + | 0.180901i | \(0.942099\pi\) | |||||||
\(102\) | −9.67437 | − | 7.64693i | −0.957905 | − | 0.757159i | ||||
\(103\) | −2.51554 | − | 1.45235i | −0.247863 | − | 0.143104i | 0.370922 | − | 0.928664i | \(-0.379042\pi\) |
−0.618785 | + | 0.785560i | \(0.712375\pi\) | |||||||
\(104\) | −11.4001 | − | 5.30913i | −1.11787 | − | 0.520603i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.989703 | + | 2.49004i | 0.0961284 | + | 0.241854i | ||||
\(107\) | 16.0138 | − | 4.29089i | 1.54812 | − | 0.414816i | 0.619238 | − | 0.785203i | \(-0.287442\pi\) |
0.928877 | + | 0.370387i | \(0.120775\pi\) | |||||||
\(108\) | −9.87628 | + | 5.32941i | −0.950345 | + | 0.512823i | ||||
\(109\) | 17.5283 | + | 4.69669i | 1.67891 | + | 0.449861i | 0.967490 | − | 0.252910i | \(-0.0813877\pi\) |
0.711416 | + | 0.702772i | \(0.248054\pi\) | |||||||
\(110\) | 15.5464 | + | 20.8753i | 1.48229 | + | 1.99039i | ||||
\(111\) | −1.73553 | −0.164729 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.5180 | 1.08352 | 0.541760 | − | 0.840533i | \(-0.317758\pi\) | ||||
0.541760 | + | 0.840533i | \(0.317758\pi\) | |||||||
\(114\) | 5.42342 | + | 7.28243i | 0.507950 | + | 0.682062i | ||||
\(115\) | −11.6859 | − | 3.13123i | −1.08972 | − | 0.291989i | ||||
\(116\) | 0.0386430 | + | 0.0716118i | 0.00358791 | + | 0.00664899i | ||||
\(117\) | −5.52289 | + | 1.47985i | −0.510592 | + | 0.136813i | ||||
\(118\) | 2.83688 | + | 7.13746i | 0.261156 | + | 0.657057i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.69420 | + | 12.8776i | 0.428520 | + | 1.17555i | ||||
\(121\) | −11.8852 | − | 6.86191i | −1.08047 | − | 0.623810i | ||||
\(122\) | 6.34366 | + | 5.01423i | 0.574328 | + | 0.453967i | ||||
\(123\) | 0.846844 | − | 3.16046i | 0.0763573 | − | 0.284969i | ||||
\(124\) | 8.92593 | − | 2.11857i | 0.801572 | − | 0.190253i | ||||
\(125\) | −9.68615 | + | 9.68615i | −0.866356 | + | 0.866356i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.0149 | −1.15489 | −0.577443 | − | 0.816431i | \(-0.695949\pi\) | ||||
−0.577443 | + | 0.816431i | \(0.695949\pi\) | |||||||
\(128\) | −2.59652 | + | 11.0117i | −0.229502 | + | 0.973308i | ||||
\(129\) | −0.876789 | − | 1.51864i | −0.0771970 | − | 0.133709i | ||||
\(130\) | 2.70575 | + | 23.1164i | 0.237310 | + | 2.02744i | ||||
\(131\) | −3.87868 | − | 14.4754i | −0.338882 | − | 1.26472i | −0.899599 | − | 0.436717i | \(-0.856141\pi\) |
0.560717 | − | 0.828007i | \(-0.310526\pi\) | |||||||
\(132\) | −8.93764 | − | 9.46714i | −0.777922 | − | 0.824009i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 14.3841 | − | 5.71715i | 1.24259 | − | 0.493886i | ||||
\(135\) | 17.9871 | + | 10.3849i | 1.54808 | + | 0.893786i | ||||
\(136\) | −12.1020 | + | 14.4370i | −1.03774 | + | 1.23796i | ||||
\(137\) | −5.15438 | + | 2.97588i | −0.440369 | + | 0.254247i | −0.703754 | − | 0.710444i | \(-0.748494\pi\) |
0.263385 | + | 0.964691i | \(0.415161\pi\) | |||||||
\(138\) | 5.98783 | + | 0.876088i | 0.509718 | + | 0.0745775i | ||||
\(139\) | −2.41458 | − | 2.41458i | −0.204802 | − | 0.204802i | 0.597252 | − | 0.802054i | \(-0.296259\pi\) |
−0.802054 | + | 0.597252i | \(0.796259\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.739022 | − | 0.739022i | 0.0622368 | − | 0.0622368i | ||||
\(142\) | 3.51619 | + | 4.72146i | 0.295073 | + | 0.396216i | ||||
\(143\) | −11.0539 | − | 19.1459i | −0.924372 | − | 1.60106i | ||||
\(144\) | 2.31160 | + | 4.59528i | 0.192634 | + | 0.382940i | ||||
\(145\) | 0.0752995 | − | 0.130423i | 0.00625328 | − | 0.0108310i | ||||
\(146\) | 0.733365 | − | 1.70090i | 0.0606937 | − | 0.140767i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.0762446 | + | 2.65018i | −0.00626727 | + | 0.217843i | ||||
\(149\) | 21.5493 | − | 5.77412i | 1.76539 | − | 0.473034i | 0.777590 | − | 0.628772i | \(-0.216442\pi\) |
0.987799 | + | 0.155737i | \(0.0497753\pi\) | |||||||
\(150\) | 9.98959 | − | 12.6381i | 0.815646 | − | 1.03190i | ||||
\(151\) | −13.5101 | + | 7.80005i | −1.09944 | + | 0.634759i | −0.936073 | − | 0.351807i | \(-0.885567\pi\) |
−0.163363 | + | 0.986566i | \(0.552234\pi\) | |||||||
\(152\) | 11.3586 | − | 7.96171i | 0.921306 | − | 0.645780i | ||||
\(153\) | 8.56512i | 0.692449i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0055 | − | 12.0055i | −0.964309 | − | 0.964309i | ||||
\(156\) | −2.68852 | − | 11.3272i | −0.215253 | − | 0.906904i | ||||
\(157\) | 9.86192 | + | 2.64249i | 0.787067 | + | 0.210894i | 0.629898 | − | 0.776678i | \(-0.283097\pi\) |
0.157169 | + | 0.987572i | \(0.449763\pi\) | |||||||
\(158\) | 0.0546257 | + | 0.466691i | 0.00434579 | + | 0.0371279i | ||||
\(159\) | −1.24028 | + | 2.14823i | −0.0983605 | + | 0.170365i | ||||
\(160\) | 19.8704 | − | 6.60238i | 1.57089 | − | 0.521964i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −4.53005 | − | 1.95319i | −0.355914 | − | 0.153457i | ||||
\(163\) | −3.05930 | − | 11.4174i | −0.239623 | − | 0.894283i | −0.976010 | − | 0.217724i | \(-0.930137\pi\) |
0.736388 | − | 0.676560i | \(-0.236530\pi\) | |||||||
\(164\) | −4.78887 | − | 1.43199i | −0.373948 | − | 0.111819i | ||||
\(165\) | −6.23640 | + | 23.2746i | −0.485503 | + | 1.81192i | ||||
\(166\) | 3.17604 | − | 21.7074i | 0.246509 | − | 1.68482i | ||||
\(167\) | − | 23.8433i | − | 1.84505i | −0.385938 | − | 0.922525i | \(-0.626122\pi\) | ||
0.385938 | − | 0.922525i | \(-0.373878\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 6.76851i | − | 0.520655i | ||||||
\(170\) | 34.4974 | + | 5.04736i | 2.64583 | + | 0.387115i | ||||
\(171\) | 1.63229 | − | 6.09179i | 0.124824 | − | 0.465851i | ||||
\(172\) | −2.35751 | + | 1.27215i | −0.179758 | + | 0.0970007i | ||||
\(173\) | 0.710136 | + | 2.65026i | 0.0539906 | + | 0.201496i | 0.987653 | − | 0.156659i | \(-0.0500725\pi\) |
−0.933662 | + | 0.358155i | \(0.883406\pi\) | |||||||
\(174\) | −0.0298256 | + | 0.0691747i | −0.00226108 | + | 0.00524412i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.8491 | + | 13.2320i | −1.11929 | + | 0.997399i | ||||
\(177\) | −3.55514 | + | 6.15768i | −0.267220 | + | 0.462839i | ||||
\(178\) | −9.14377 | + | 1.07027i | −0.685355 | + | 0.0802201i | ||||
\(179\) | 12.5494 | + | 3.36261i | 0.937990 | + | 0.251334i | 0.695258 | − | 0.718760i | \(-0.255290\pi\) |
0.242731 | + | 0.970094i | \(0.421957\pi\) | |||||||
\(180\) | 4.99514 | − | 8.10429i | 0.372316 | − | 0.604058i | ||||
\(181\) | −12.8301 | − | 12.8301i | −0.953652 | − | 0.953652i | 0.0453204 | − | 0.998973i | \(-0.485569\pi\) |
−0.998973 | + | 0.0453204i | \(0.985569\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.48566i | 0.553356i | ||||||||
\(184\) | 1.60085 | − | 9.10501i | 0.118016 | − | 0.671230i | ||||
\(185\) | 4.24940 | − | 2.45339i | 0.312422 | − | 0.180377i | ||||
\(186\) | 6.66268 | + | 5.26639i | 0.488531 | + | 0.386151i | ||||
\(187\) | −31.9889 | + | 8.57140i | −2.33926 | + | 0.626803i | ||||
\(188\) | −1.09603 | − | 1.16096i | −0.0799362 | − | 0.0846719i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −23.5738 | − | 10.1642i | −1.71022 | − | 0.737385i | ||||
\(191\) | 0.784437 | − | 1.35868i | 0.0567599 | − | 0.0983110i | −0.836249 | − | 0.548349i | \(-0.815256\pi\) |
0.893009 | + | 0.450038i | \(0.148590\pi\) | |||||||
\(192\) | −9.48799 | + | 4.43566i | −0.684736 | + | 0.320116i | ||||
\(193\) | 0.740598 | + | 1.28275i | 0.0533094 | + | 0.0923346i | 0.891449 | − | 0.453122i | \(-0.149690\pi\) |
−0.838139 | + | 0.545456i | \(0.816356\pi\) | |||||||
\(194\) | −9.71487 | + | 7.23492i | −0.697487 | + | 0.519437i | ||||
\(195\) | −15.2353 | + | 15.2353i | −1.09103 | + | 1.09103i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.91173 | + | 5.91173i | 0.421193 | + | 0.421193i | 0.885614 | − | 0.464421i | \(-0.153738\pi\) |
−0.464421 | + | 0.885614i | \(0.653738\pi\) | |||||||
\(198\) | −1.30914 | + | 8.94765i | −0.0930368 | + | 0.635882i | ||||
\(199\) | 12.7783 | − | 7.37753i | 0.905826 | − | 0.522979i | 0.0267404 | − | 0.999642i | \(-0.491487\pi\) |
0.879086 | + | 0.476663i | \(0.158154\pi\) | |||||||
\(200\) | −18.8598 | − | 15.8094i | −1.33359 | − | 1.11790i | ||||
\(201\) | 12.4095 | + | 7.16464i | 0.875300 | + | 0.505354i | ||||
\(202\) | 4.50713 | + | 11.3397i | 0.317120 | + | 0.797860i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −17.4323 | − | 0.501522i | −1.22051 | − | 0.0351136i | ||||
\(205\) | 2.39425 | + | 8.93545i | 0.167221 | + | 0.624079i | ||||
\(206\) | −4.08000 | + | 0.477560i | −0.284267 | + | 0.0332732i | ||||
\(207\) | −2.10161 | − | 3.64010i | −0.146072 | − | 0.253004i | ||||
\(208\) | −17.4149 | + | 3.60778i | −1.20751 | + | 0.250154i | ||||
\(209\) | 24.3850 | 1.68675 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.58986 | − | 5.58986i | 0.384822 | − | 0.384822i | −0.488014 | − | 0.872836i | \(-0.662279\pi\) |
0.872836 | + | 0.488014i | \(0.162279\pi\) | |||||||
\(212\) | 3.22588 | + | 1.98830i | 0.221555 | + | 0.136557i | ||||
\(213\) | −1.41051 | + | 5.26410i | −0.0966466 | + | 0.360690i | ||||
\(214\) | 14.5390 | − | 18.3937i | 0.993862 | − | 1.25737i | ||||
\(215\) | 4.29360 | + | 2.47891i | 0.292821 | + | 0.169060i | ||||
\(216\) | −6.70030 | + | 14.3873i | −0.455897 | + | 0.978929i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 23.8485 | − | 9.47891i | 1.61522 | − | 0.641993i | ||||
\(219\) | 1.65630 | − | 0.443803i | 0.111922 | − | 0.0299895i | ||||
\(220\) | 35.2666 | + | 10.5456i | 2.37767 | + | 0.710982i | ||||
\(221\) | −28.6041 | − | 7.66445i | −1.92412 | − | 0.515567i | ||||
\(222\) | −1.96850 | + | 1.46599i | −0.132117 | + | 0.0983910i | ||||
\(223\) | 16.4049 | 1.09855 | 0.549277 | − | 0.835640i | \(-0.314903\pi\) | ||||
0.549277 | + | 0.835640i | \(0.314903\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.1891 | −0.745938 | ||||||||
\(226\) | 13.0641 | − | 9.72918i | 0.869011 | − | 0.647175i | ||||
\(227\) | 5.59413 | + | 1.49894i | 0.371295 | + | 0.0994883i | 0.439641 | − | 0.898173i | \(-0.355106\pi\) |
−0.0683460 | + | 0.997662i | \(0.521772\pi\) | |||||||
\(228\) | 12.3029 | + | 3.67885i | 0.814777 | + | 0.243638i | ||||
\(229\) | 17.0126 | − | 4.55851i | 1.12422 | − | 0.301235i | 0.351632 | − | 0.936138i | \(-0.385627\pi\) |
0.772591 | + | 0.634904i | \(0.218960\pi\) | |||||||
\(230\) | −15.8995 | + | 6.31949i | −1.04838 | + | 0.416695i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.104320 | + | 0.0485831i | 0.00684897 | + | 0.00318964i | ||||
\(233\) | −9.30245 | − | 5.37077i | −0.609424 | − | 0.351851i | 0.163316 | − | 0.986574i | \(-0.447781\pi\) |
−0.772740 | + | 0.634723i | \(0.781114\pi\) | |||||||
\(234\) | −5.01423 | + | 6.34366i | −0.327791 | + | 0.414698i | ||||
\(235\) | −0.764775 | + | 2.85418i | −0.0498884 | + | 0.186186i | ||||
\(236\) | 9.24667 | + | 5.69926i | 0.601907 | + | 0.370990i | ||||
\(237\) | −0.307582 | + | 0.307582i | −0.0199796 | + | 0.0199796i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.00864 | −0.582721 | −0.291360 | − | 0.956613i | \(-0.594108\pi\) | ||||
−0.291360 | + | 0.956613i | \(0.594108\pi\) | |||||||
\(240\) | 16.2019 | + | 10.6410i | 1.04583 | + | 0.686874i | ||||
\(241\) | 4.86184 | + | 8.42096i | 0.313179 | + | 0.542442i | 0.979049 | − | 0.203626i | \(-0.0652727\pi\) |
−0.665870 | + | 0.746068i | \(0.731939\pi\) | |||||||
\(242\) | −19.2768 | + | 2.25633i | −1.23916 | + | 0.145043i | ||||
\(243\) | 3.17488 | + | 11.8488i | 0.203669 | + | 0.760102i | ||||
\(244\) | 11.4307 | + | 0.328857i | 0.731776 | + | 0.0210529i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.70911 | − | 4.30004i | −0.108969 | − | 0.274160i | ||||
\(247\) | 18.8835 | + | 10.9024i | 1.20153 | + | 0.693704i | ||||
\(248\) | 8.33456 | − | 9.94264i | 0.529245 | − | 0.631359i | ||||
\(249\) | 17.5886 | − | 10.1548i | 1.11463 | − | 0.643532i | ||||
\(250\) | −2.80453 | + | 19.1682i | −0.177374 | + | 1.21231i | ||||
\(251\) | 16.0533 | + | 16.0533i | 1.01328 | + | 1.01328i | 0.999911 | + | 0.0133658i | \(0.00425458\pi\) |
0.0133658 | + | 0.999911i | \(0.495745\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.4918 | − | 11.4918i | 0.722486 | − | 0.722486i | ||||
\(254\) | −14.7620 | + | 10.9936i | −0.926248 | + | 0.689802i | ||||
\(255\) | 16.1379 | + | 27.9517i | 1.01060 | + | 1.75040i | ||||
\(256\) | 6.35649 | + | 14.6832i | 0.397281 | + | 0.917697i | ||||
\(257\) | −8.88786 | + | 15.3942i | −0.554409 | + | 0.960265i | 0.443540 | + | 0.896255i | \(0.353722\pi\) |
−0.997949 | + | 0.0640104i | \(0.979611\pi\) | |||||||
\(258\) | −2.27728 | − | 0.981879i | −0.141777 | − | 0.0611291i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 22.5953 | + | 23.9339i | 1.40130 | + | 1.48432i | ||||
\(261\) | 0.0505393 | − | 0.0135420i | 0.00312830 | − | 0.000838226i | ||||
\(262\) | −16.6267 | − | 13.1422i | −1.02720 | − | 0.811930i | ||||
\(263\) | −14.5176 | + | 8.38173i | −0.895192 | + | 0.516839i | −0.875637 | − | 0.482969i | \(-0.839558\pi\) |
−0.0195549 | + | 0.999809i | \(0.506225\pi\) | |||||||
\(264\) | −18.1342 | − | 3.18838i | −1.11608 | − | 0.196231i | ||||
\(265\) | − | 7.01318i | − | 0.430816i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.02639 | − | 6.02639i | −0.368809 | − | 0.368809i | ||||
\(268\) | 11.4857 | − | 18.6347i | 0.701599 | − | 1.13830i | ||||
\(269\) | −23.6071 | − | 6.32550i | −1.43935 | − | 0.385672i | −0.547043 | − | 0.837104i | \(-0.684247\pi\) |
−0.892306 | + | 0.451432i | \(0.850913\pi\) | |||||||
\(270\) | 29.1737 | − | 3.41475i | 1.77545 | − | 0.207815i | ||||
\(271\) | 5.49940 | − | 9.52524i | 0.334065 | − | 0.578617i | −0.649240 | − | 0.760584i | \(-0.724913\pi\) |
0.983305 | + | 0.181966i | \(0.0582462\pi\) | |||||||
\(272\) | −1.53166 | + | 26.5974i | −0.0928707 | + | 1.61270i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.33257 | + | 7.72924i | −0.201328 | + | 0.466940i | ||||
\(275\) | −11.1973 | − | 41.7888i | −0.675221 | − | 2.51996i | ||||
\(276\) | 7.53164 | − | 4.06420i | 0.453351 | − | 0.244636i | ||||
\(277\) | −7.25928 | + | 27.0920i | −0.436168 | + | 1.62780i | 0.302087 | + | 0.953280i | \(0.402317\pi\) |
−0.738256 | + | 0.674521i | \(0.764350\pi\) | |||||||
\(278\) | −4.77828 | − | 0.699117i | −0.286582 | − | 0.0419302i | ||||
\(279\) | − | 5.89875i | − | 0.353149i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3.39530i | − | 0.202547i | −0.994859 | − | 0.101273i | \(-0.967708\pi\) | ||
0.994859 | − | 0.101273i | \(-0.0322917\pi\) | |||||||
\(282\) | 0.213976 | − | 1.46247i | 0.0127421 | − | 0.0870890i | ||||
\(283\) | −1.34009 | + | 5.00130i | −0.0796603 | + | 0.297296i | −0.994250 | − | 0.107088i | \(-0.965847\pi\) |
0.914589 | + | 0.404384i | \(0.132514\pi\) | |||||||
\(284\) | 7.97639 | + | 2.38513i | 0.473311 | + | 0.141531i | ||||
\(285\) | −6.15095 | − | 22.9556i | −0.364351 | − | 1.35978i | ||||
\(286\) | −28.7101 | − | 12.3788i | −1.69767 | − | 0.731973i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.50351 | + | 3.25953i | 0.383223 | + | 0.192070i | ||||
\(289\) | −13.6802 | + | 23.6948i | −0.804719 | + | 1.39381i | ||||
\(290\) | −0.0247600 | − | 0.211535i | −0.00145396 | − | 0.0124218i | ||||
\(291\) | −10.8314 | − | 2.90227i | −0.634948 | − | 0.170134i | ||||
\(292\) | −0.604930 | − | 2.54869i | −0.0354009 | − | 0.149151i | ||||
\(293\) | 4.49832 | + | 4.49832i | 0.262795 | + | 0.262795i | 0.826188 | − | 0.563394i | \(-0.190505\pi\) |
−0.563394 | + | 0.826188i | \(0.690505\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 20.1026i | − | 1.17042i | ||||||
\(296\) | 2.15211 | + | 3.07033i | 0.125089 | + | 0.178459i | ||||
\(297\) | −24.1628 | + | 13.9504i | −1.40207 | + | 0.809483i | ||||
\(298\) | 19.5646 | − | 24.7518i | 1.13335 | − | 1.43383i | ||||
\(299\) | 14.0371 | − | 3.76123i | 0.811786 | − | 0.217517i | ||||
\(300\) | 0.655165 | − | 22.7728i | 0.0378260 | − | 1.31479i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −8.73495 | + | 20.2590i | −0.502640 | + | 1.16577i | ||||
\(303\) | −5.64826 | + | 9.78307i | −0.324484 | + | 0.562023i | ||||
\(304\) | 6.15814 | − | 18.6250i | 0.353194 | − | 1.06822i | ||||
\(305\) | −10.5819 | − | 18.3285i | −0.605920 | − | 1.04948i | ||||
\(306\) | 7.23492 | + | 9.71487i | 0.413593 | + | 0.555362i | ||||
\(307\) | −1.55316 | + | 1.55316i | −0.0886436 | + | 0.0886436i | −0.750038 | − | 0.661395i | \(-0.769965\pi\) |
0.661395 | + | 0.750038i | \(0.269965\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.68901 | − | 2.68901i | −0.152972 | − | 0.152972i | ||||
\(310\) | −23.7581 | − | 3.47609i | −1.34937 | − | 0.197428i | ||||
\(311\) | −0.719405 | + | 0.415348i | −0.0407937 | + | 0.0235522i | −0.520258 | − | 0.854009i | \(-0.674164\pi\) |
0.479464 | + | 0.877561i | \(0.340831\pi\) | |||||||
\(312\) | −12.6175 | − | 10.5768i | −0.714323 | − | 0.598791i | ||||
\(313\) | 15.5246 | + | 8.96316i | 0.877505 | + | 0.506628i | 0.869835 | − | 0.493343i | \(-0.164225\pi\) |
0.00766978 | + | 0.999971i | \(0.497559\pi\) | |||||||
\(314\) | 13.4178 | − | 5.33311i | 0.757213 | − | 0.300965i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.456170 | + | 0.483195i | 0.0256616 | + | 0.0271819i | ||||
\(317\) | −3.86320 | − | 14.4177i | −0.216979 | − | 0.809777i | −0.985460 | − | 0.169905i | \(-0.945654\pi\) |
0.768481 | − | 0.639872i | \(-0.221013\pi\) | |||||||
\(318\) | 0.407828 | + | 3.48425i | 0.0228699 | + | 0.195387i | ||||
\(319\) | 0.101153 | + | 0.175202i | 0.00566346 | + | 0.00980940i | ||||
\(320\) | 16.9607 | − | 24.2731i | 0.948134 | − | 1.35691i | ||||
\(321\) | 21.7049 | 1.21145 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.0966 | − | 23.0966i | 1.28513 | − | 1.28513i | ||||
\(324\) | −6.78800 | + | 1.61113i | −0.377111 | + | 0.0895073i | ||||
\(325\) | 10.0125 | − | 37.3671i | 0.555392 | − | 2.07275i | ||||
\(326\) | −13.1142 | − | 10.3659i | −0.726330 | − | 0.574114i | ||||
\(327\) | 20.5747 | + | 11.8788i | 1.13778 | + | 0.656900i | ||||
\(328\) | −6.64130 | + | 2.42093i | −0.366704 | + | 0.133673i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 12.5864 | + | 31.6667i | 0.692857 | + | 1.74319i | ||||
\(331\) | −5.36100 | + | 1.43647i | −0.294667 | + | 0.0789558i | −0.403124 | − | 0.915145i | \(-0.632076\pi\) |
0.108457 | + | 0.994101i | \(0.465409\pi\) | |||||||
\(332\) | −14.7338 | − | 27.3041i | −0.808621 | − | 1.49851i | ||||
\(333\) | 1.64666 | + | 0.441221i | 0.0902364 | + | 0.0241788i | ||||
\(334\) | −20.1403 | − | 27.0439i | −1.10203 | − | 1.47978i | ||||
\(335\) | −40.5125 | −2.21344 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.81586 | 0.534704 | 0.267352 | − | 0.963599i | \(-0.413851\pi\) | ||||
0.267352 | + | 0.963599i | \(0.413851\pi\) | |||||||
\(338\) | −5.71733 | − | 7.67709i | −0.310982 | − | 0.417578i | ||||
\(339\) | 14.5656 | + | 3.90283i | 0.791093 | + | 0.211973i | ||||
\(340\) | 43.3916 | − | 23.4149i | 2.35324 | − | 1.26985i | ||||
\(341\) | 22.0306 | − | 5.90307i | 1.19302 | − | 0.319669i | ||||
\(342\) | −3.29431 | − | 8.28832i | −0.178136 | − | 0.448181i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.59939 | + | 3.43430i | −0.0862332 | + | 0.185165i | ||||
\(345\) | −13.7169 | − | 7.91948i | −0.738495 | − | 0.426370i | ||||
\(346\) | 3.04413 | + | 2.40617i | 0.163653 | + | 0.129357i | ||||
\(347\) | 1.42570 | − | 5.32078i | 0.0765356 | − | 0.285635i | −0.917042 | − | 0.398792i | \(-0.869430\pi\) |
0.993577 | + | 0.113157i | \(0.0360963\pi\) | |||||||
\(348\) | 0.0246023 | + | 0.103654i | 0.00131882 | + | 0.00555644i | ||||
\(349\) | 5.79662 | − | 5.79662i | 0.310286 | − | 0.310286i | −0.534734 | − | 0.845020i | \(-0.679588\pi\) |
0.845020 | + | 0.534734i | \(0.179588\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −24.9485 | −1.33165 | ||||||||
\(352\) | −5.66537 | + | 27.5512i | −0.301965 | + | 1.46848i | ||||
\(353\) | 10.4845 | + | 18.1596i | 0.558031 | + | 0.966538i | 0.997661 | + | 0.0683590i | \(0.0217763\pi\) |
−0.439630 | + | 0.898179i | \(0.644890\pi\) | |||||||
\(354\) | 1.16900 | + | 9.98726i | 0.0621316 | + | 0.530817i | ||||
\(355\) | −3.98788 | − | 14.8830i | −0.211655 | − | 0.789906i | ||||
\(356\) | −9.46714 | + | 8.93764i | −0.501757 | + | 0.473694i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.0744 | − | 6.78646i | 0.902410 | − | 0.358676i | ||||
\(359\) | −27.4378 | − | 15.8412i | −1.44811 | − | 0.836068i | −0.449743 | − | 0.893158i | \(-0.648485\pi\) |
−0.998369 | + | 0.0570898i | \(0.981818\pi\) | |||||||
\(360\) | −1.17999 | − | 13.4116i | −0.0621909 | − | 0.706851i | ||||
\(361\) | −4.37421 | + | 2.52545i | −0.230221 | + | 0.132918i | ||||
\(362\) | −25.3898 | − | 3.71482i | −1.33446 | − | 0.195247i | ||||
\(363\) | −12.7048 | − | 12.7048i | −0.666829 | − | 0.666829i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.42803 | + | 3.42803i | −0.179431 | + | 0.179431i | ||||
\(366\) | 6.32310 | + | 8.49050i | 0.330514 | + | 0.443806i | ||||
\(367\) | 0.541748 | + | 0.938336i | 0.0282790 | + | 0.0489807i | 0.879819 | − | 0.475310i | \(-0.157664\pi\) |
−0.851540 | + | 0.524290i | \(0.824331\pi\) | |||||||
\(368\) | −5.87522 | − | 11.6795i | −0.306267 | − | 0.608834i | ||||
\(369\) | −1.60696 | + | 2.78334i | −0.0836551 | + | 0.144895i | ||||
\(370\) | 2.74745 | − | 6.37217i | 0.142833 | − | 0.331273i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 12.0055 | + | 0.345395i | 0.622459 | + | 0.0179079i | ||||
\(373\) | 2.04330 | − | 0.547500i | 0.105798 | − | 0.0283485i | −0.205532 | − | 0.978650i | \(-0.565892\pi\) |
0.311330 | + | 0.950302i | \(0.399226\pi\) | |||||||
\(374\) | −29.0427 | + | 36.7429i | −1.50176 | + | 1.89993i | ||||
\(375\) | −15.5312 | + | 8.96693i | −0.802026 | + | 0.463050i | ||||
\(376\) | −2.22382 | − | 0.390994i | −0.114685 | − | 0.0201640i | ||||
\(377\) | 0.180899i | 0.00931678i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.0857 | + | 19.0857i | 0.980369 | + | 0.980369i | 0.999811 | − | 0.0194423i | \(-0.00618906\pi\) |
−0.0194423 | + | 0.999811i | \(0.506189\pi\) | |||||||
\(380\) | −35.3238 | + | 8.38410i | −1.81207 | + | 0.430095i | ||||
\(381\) | −16.4586 | − | 4.41006i | −0.843198 | − | 0.225934i | ||||
\(382\) | −0.257938 | − | 2.20368i | −0.0131973 | − | 0.112750i | ||||
\(383\) | −16.5371 | + | 28.6431i | −0.845005 | + | 1.46359i | 0.0406110 | + | 0.999175i | \(0.487070\pi\) |
−0.885616 | + | 0.464417i | \(0.846264\pi\) | |||||||
\(384\) | −7.01483 | + | 13.0455i | −0.357974 | + | 0.665728i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.92355 | + | 0.829365i | 0.0979060 | + | 0.0422135i | ||||
\(387\) | 0.445810 | + | 1.66379i | 0.0226618 | + | 0.0845750i | ||||
\(388\) | −4.90764 | + | 16.4122i | −0.249148 | + | 0.833203i | ||||
\(389\) | −3.80114 | + | 14.1860i | −0.192725 | + | 0.719260i | 0.800119 | + | 0.599842i | \(0.204770\pi\) |
−0.992844 | + | 0.119419i | \(0.961897\pi\) | |||||||
\(390\) | −4.41124 | + | 30.1497i | −0.223372 | + | 1.52669i | ||||
\(391\) | − | 21.7693i | − | 1.10092i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 19.6198i | − | 0.989689i | ||||||
\(394\) | 11.6989 | + | 1.71168i | 0.589382 | + | 0.0862333i | ||||
\(395\) | 0.318301 | − | 1.18792i | 0.0160155 | − | 0.0597705i | ||||
\(396\) | 6.07316 | + | 11.2546i | 0.305188 | + | 0.565564i | ||||
\(397\) | −3.17304 | − | 11.8419i | −0.159250 | − | 0.594330i | −0.998704 | − | 0.0508988i | \(-0.983791\pi\) |
0.839453 | − | 0.543432i | \(-0.182875\pi\) | |||||||
\(398\) | 8.26178 | − | 19.1616i | 0.414126 | − | 0.960483i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −34.7456 | − | 2.00089i | −1.73728 | − | 0.100045i | ||||
\(401\) | −5.67996 | + | 9.83799i | −0.283644 | + | 0.491286i | −0.972279 | − | 0.233822i | \(-0.924877\pi\) |
0.688636 | + | 0.725108i | \(0.258210\pi\) | |||||||
\(402\) | 20.1272 | − | 2.35587i | 1.00386 | − | 0.117500i | ||||
\(403\) | 19.6995 | + | 5.27846i | 0.981301 | + | 0.262939i | ||||
\(404\) | 14.6907 | + | 9.05476i | 0.730892 | + | 0.450491i | ||||
\(405\) | 9.12999 | + | 9.12999i | 0.453673 | + | 0.453673i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.59147i | 0.326727i | ||||||||
\(408\) | −20.1960 | + | 14.1562i | −0.999851 | + | 0.700835i | ||||
\(409\) | 10.8729 | − | 6.27748i | 0.537631 | − | 0.310401i | −0.206487 | − | 0.978449i | \(-0.566203\pi\) |
0.744118 | + | 0.668048i | \(0.232870\pi\) | |||||||
\(410\) | 10.2634 | + | 8.11249i | 0.506872 | + | 0.400647i | ||||
\(411\) | −7.52657 | + | 2.01674i | −0.371258 | + | 0.0994784i | ||||
\(412\) | −4.22429 | + | 3.98802i | −0.208116 | + | 0.196476i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.45849 | − | 2.35351i | −0.268270 | − | 0.115669i | ||||
\(415\) | −28.7101 | + | 49.7274i | −1.40933 | + | 2.44102i | ||||
\(416\) | −16.7052 | + | 18.8024i | −0.819038 | + | 0.921863i | ||||
\(417\) | −2.23529 | − | 3.87163i | −0.109462 | − | 0.189595i | ||||
\(418\) | 27.6584 | − | 20.5979i | 1.35282 | − | 1.00748i | ||||
\(419\) | −12.7048 | + | 12.7048i | −0.620670 | + | 0.620670i | −0.945703 | − | 0.325033i | \(-0.894625\pi\) |
0.325033 | + | 0.945703i | \(0.394625\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.71277 | − | 8.71277i | −0.424635 | − | 0.424635i | 0.462161 | − | 0.886796i | \(-0.347074\pi\) |
−0.886796 | + | 0.462161i | \(0.847074\pi\) | |||||||
\(422\) | 1.61849 | − | 11.0619i | 0.0787867 | − | 0.538487i | ||||
\(423\) | −0.889060 | + | 0.513299i | −0.0432276 | + | 0.0249575i | ||||
\(424\) | 5.33842 | − | 0.469691i | 0.259257 | − | 0.0228102i | ||||
\(425\) | −50.1865 | − | 28.9752i | −2.43440 | − | 1.40550i | ||||
\(426\) | 2.84671 | + | 7.16218i | 0.137923 | + | 0.347009i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.953534 | − | 33.1438i | 0.0460908 | − | 1.60206i | ||||
\(429\) | −7.49115 | − | 27.9573i | −0.361676 | − | 1.34979i | ||||
\(430\) | 6.96387 | − | 0.815114i | 0.335828 | − | 0.0393083i | ||||
\(431\) | −8.49109 | − | 14.7070i | −0.409001 | − | 0.708411i | 0.585777 | − | 0.810472i | \(-0.300790\pi\) |
−0.994778 | + | 0.102061i | \(0.967456\pi\) | |||||||
\(432\) | 4.55314 | + | 21.9782i | 0.219063 | + | 1.05743i | ||||
\(433\) | −28.0125 | −1.34619 | −0.673097 | − | 0.739554i | \(-0.735037\pi\) | ||||
−0.673097 | + | 0.739554i | \(0.735037\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.139417 | − | 0.139417i | 0.00668451 | − | 0.00668451i | ||||
\(436\) | 19.0430 | − | 30.8960i | 0.911994 | − | 1.47965i | ||||
\(437\) | −4.14867 | + | 15.4830i | −0.198458 | + | 0.740654i | ||||
\(438\) | 1.50375 | − | 1.90244i | 0.0718520 | − | 0.0909023i | ||||
\(439\) | −26.2791 | − | 15.1722i | −1.25423 | − | 0.724131i | −0.282284 | − | 0.959331i | \(-0.591092\pi\) |
−0.971947 | + | 0.235200i | \(0.924425\pi\) | |||||||
\(440\) | 48.9084 | − | 17.8284i | 2.33162 | − | 0.849935i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −38.9179 | + | 15.4685i | −1.85114 | + | 0.735760i | ||||
\(443\) | −37.7206 | + | 10.1072i | −1.79216 | + | 0.480208i | −0.992710 | − | 0.120525i | \(-0.961542\pi\) |
−0.799450 | + | 0.600733i | \(0.794876\pi\) | |||||||
\(444\) | −0.994422 | + | 3.32556i | −0.0471932 | + | 0.157824i | ||||
\(445\) | 23.2746 | + | 6.23640i | 1.10332 | + | 0.295634i | ||||
\(446\) | 18.6070 | − | 13.8572i | 0.881069 | − | 0.656155i | ||||
\(447\) | 29.2077 | 1.38148 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.8779 | −1.17406 | −0.587030 | − | 0.809565i | \(-0.699703\pi\) | ||||
−0.587030 | + | 0.809565i | \(0.699703\pi\) | |||||||
\(450\) | −12.6910 | + | 9.45136i | −0.598261 | + | 0.445541i | ||||
\(451\) | −12.0033 | − | 3.21628i | −0.565214 | − | 0.151449i | ||||
\(452\) | 6.59957 | − | 22.0704i | 0.310417 | − | 1.03810i | ||||
\(453\) | −19.7278 | + | 5.28605i | −0.926893 | + | 0.248360i | ||||
\(454\) | 7.61121 | − | 3.02518i | 0.357212 | − | 0.141979i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 17.0619 | − | 6.21949i | 0.798994 | − | 0.291254i | ||||
\(457\) | −25.7420 | − | 14.8622i | −1.20416 | − | 0.695223i | −0.242683 | − | 0.970106i | \(-0.578028\pi\) |
−0.961478 | + | 0.274883i | \(0.911361\pi\) | |||||||
\(458\) | 15.4457 | − | 19.5409i | 0.721731 | − | 0.913085i | ||||
\(459\) | −9.67280 | + | 36.0994i | −0.451487 | + | 1.68497i | ||||
\(460\) | −12.6958 | + | 20.5980i | −0.591943 | + | 0.960389i | ||||
\(461\) | 2.73329 | − | 2.73329i | 0.127302 | − | 0.127302i | −0.640585 | − | 0.767887i | \(-0.721308\pi\) |
0.767887 | + | 0.640585i | \(0.221308\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.3082 | 1.59444 | 0.797219 | − | 0.603691i | \(-0.206304\pi\) | ||||
0.797219 | + | 0.603691i | \(0.206304\pi\) | |||||||
\(464\) | 0.159362 | − | 0.0330143i | 0.00739819 | − | 0.00153265i | ||||
\(465\) | −11.1141 | − | 19.2502i | −0.515404 | − | 0.892706i | ||||
\(466\) | −15.0878 | + | 1.76602i | −0.698930 | + | 0.0818091i | ||||
\(467\) | 2.88104 | + | 10.7522i | 0.133319 | + | 0.497552i | 0.999999 | − | 0.00131185i | \(-0.000417576\pi\) |
−0.866681 | + | 0.498863i | \(0.833751\pi\) | |||||||
\(468\) | −0.328857 | + | 11.4307i | −0.0152014 | + | 0.528385i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.54348 | + | 3.88331i | 0.0711953 | + | 0.179124i | ||||
\(471\) | 11.5759 | + | 6.68336i | 0.533391 | + | 0.307953i | ||||
\(472\) | 15.3020 | − | 1.34632i | 0.704333 | − | 0.0619695i | ||||
\(473\) | −5.76775 | + | 3.33001i | −0.265201 | + | 0.153114i | ||||
\(474\) | −0.0890574 | + | 0.608684i | −0.00409054 | + | 0.0279578i | ||||
\(475\) | 30.1723 | + | 30.1723i | 1.38440 | + | 1.38440i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.72291 | − | 1.72291i | 0.0788867 | − | 0.0788867i | ||||
\(478\) | −10.2179 | + | 7.60956i | −0.467357 | + | 0.348053i | ||||
\(479\) | −17.6331 | − | 30.5414i | −0.805677 | − | 1.39547i | −0.915833 | − | 0.401560i | \(-0.868468\pi\) |
0.110155 | − | 0.993914i | \(-0.464865\pi\) | |||||||
\(480\) | 27.3652 | − | 1.61630i | 1.24905 | − | 0.0737736i | ||||
\(481\) | −2.94701 | + | 5.10437i | −0.134372 | + | 0.232739i | ||||
\(482\) | 12.6276 | + | 5.44457i | 0.575172 | + | 0.247994i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −19.9585 | + | 18.8423i | −0.907206 | + | 0.856466i | ||||
\(485\) | 30.6232 | − | 8.20545i | 1.39053 | − | 0.372590i | ||||
\(486\) | 13.6097 | + | 10.7575i | 0.617349 | + | 0.487972i | ||||
\(487\) | 0.568713 | − | 0.328347i | 0.0257708 | − | 0.0148788i | −0.487059 | − | 0.873369i | \(-0.661930\pi\) |
0.512830 | + | 0.858490i | \(0.328597\pi\) | |||||||
\(488\) | 13.2429 | − | 9.28246i | 0.599478 | − | 0.420197i | ||||
\(489\) | − | 15.4751i | − | 0.699807i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.47946 | − | 9.47946i | −0.427802 | − | 0.427802i | 0.460077 | − | 0.887879i | \(-0.347822\pi\) |
−0.887879 | + | 0.460077i | \(0.847822\pi\) | |||||||
\(492\) | −5.57075 | − | 3.43358i | −0.251149 | − | 0.154798i | ||||
\(493\) | 0.261753 | + | 0.0701364i | 0.0117887 | + | 0.00315879i | ||||
\(494\) | 30.6276 | − | 3.58493i | 1.37800 | − | 0.161294i | ||||
\(495\) | 11.8341 | − | 20.4973i | 0.531905 | − | 0.921286i | ||||
\(496\) | 1.05485 | − | 18.3175i | 0.0473640 | − | 0.822478i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 11.3719 | − | 26.3749i | 0.509587 | − | 1.18189i | ||||
\(499\) | 1.30062 | + | 4.85398i | 0.0582238 | + | 0.217294i | 0.988908 | − | 0.148530i | \(-0.0474540\pi\) |
−0.930684 | + | 0.365824i | \(0.880787\pi\) | |||||||
\(500\) | 13.0103 | + | 24.1103i | 0.581839 | + | 1.07824i | ||||
\(501\) | 8.07923 | − | 30.1521i | 0.360953 | − | 1.34710i | ||||
\(502\) | 31.7684 | + | 4.64808i | 1.41789 | + | 0.207454i | ||||
\(503\) | 24.0392i | 1.07185i | 0.844264 | + | 0.535927i | \(0.180038\pi\) | ||||
−0.844264 | + | 0.535927i | \(0.819962\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 31.9382i | − | 1.42123i | ||||||
\(506\) | 3.32735 | − | 22.7415i | 0.147919 | − | 1.01099i | ||||
\(507\) | 2.29349 | − | 8.55942i | 0.101857 | − | 0.380137i | ||||
\(508\) | −7.45728 | + | 24.9387i | −0.330863 | + | 1.10648i | ||||
\(509\) | 11.4618 | + | 42.7759i | 0.508034 | + | 1.89601i | 0.439221 | + | 0.898379i | \(0.355255\pi\) |
0.0688131 | + | 0.997630i | \(0.478079\pi\) | |||||||
\(510\) | 41.9149 | + | 18.0722i | 1.85602 | + | 0.800250i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 19.6126 | + | 11.2849i | 0.866760 | + | 0.498725i | ||||
\(513\) | 13.7592 | − | 23.8317i | 0.607484 | − | 1.05219i | ||||
\(514\) | 2.92250 | + | 24.9682i | 0.128906 | + | 1.10130i | ||||
\(515\) | 10.3852 | + | 2.78272i | 0.457628 | + | 0.122621i | ||||
\(516\) | −3.41236 | + | 0.809922i | −0.150221 | + | 0.0356548i | ||||
\(517\) | −2.80678 | − | 2.80678i | −0.123442 | − | 0.123442i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.59214i | 0.157677i | ||||||||
\(520\) | 45.8452 | + | 8.06055i | 2.01044 | + | 0.353478i | ||||
\(521\) | 34.2259 | − | 19.7603i | 1.49946 | − | 0.865715i | 0.499463 | − | 0.866335i | \(-0.333531\pi\) |
1.00000 | 0.000619517i | \(0.000197198\pi\) | ||||||||
\(522\) | 0.0458846 | − | 0.0580501i | 0.00200831 | − | 0.00254078i | ||||
\(523\) | 23.2840 | − | 6.23892i | 1.01814 | − | 0.272809i | 0.289111 | − | 0.957295i | \(-0.406640\pi\) |
0.729025 | + | 0.684487i | \(0.239974\pi\) | |||||||
\(524\) | −29.9597 | − | 0.861931i | −1.30880 | − | 0.0376536i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.38634 | + | 21.7698i | −0.409264 | + | 0.949208i | ||||
\(527\) | 15.2754 | − | 26.4577i | 0.665406 | − | 1.15252i | ||||
\(528\) | −23.2617 | + | 11.7015i | −1.01234 | + | 0.509244i | ||||
\(529\) | −6.15850 | − | 10.6668i | −0.267761 | − | 0.463776i | ||||
\(530\) | −5.92400 | − | 7.95459i | −0.257322 | − | 0.345525i | ||||
\(531\) | 4.93855 | − | 4.93855i | 0.214315 | − | 0.214315i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.85727 | − | 7.85727i | −0.340336 | − | 0.340336i | ||||
\(534\) | −11.9258 | − | 1.74488i | −0.516081 | − | 0.0755085i | ||||
\(535\) | −53.1441 | + | 30.6827i | −2.29762 | + | 1.32653i | ||||
\(536\) | −2.71323 | − | 30.8381i | −0.117194 | − | 1.33200i | ||||
\(537\) | 14.7305 | + | 8.50468i | 0.635670 | + | 0.367004i | ||||
\(538\) | −32.1191 | + | 12.7662i | −1.38475 | + | 0.550389i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 30.2054 | − | 28.5160i | 1.29983 | − | 1.22713i | ||||
\(541\) | 4.39167 | + | 16.3899i | 0.188812 | + | 0.704658i | 0.993782 | + | 0.111342i | \(0.0355148\pi\) |
−0.804970 | + | 0.593316i | \(0.797818\pi\) | |||||||
\(542\) | −1.80831 | − | 15.4492i | −0.0776736 | − | 0.663599i | ||||
\(543\) | −11.8774 | − | 20.5723i | −0.509708 | − | 0.882841i | ||||
\(544\) | 20.7294 | + | 31.4615i | 0.888767 | + | 1.34890i | ||||
\(545\) | −67.1689 | −2.87720 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.64831 | + | 5.64831i | −0.241504 | + | 0.241504i | −0.817472 | − | 0.575968i | \(-0.804625\pi\) |
0.575968 | + | 0.817472i | \(0.304625\pi\) | |||||||
\(548\) | 2.74893 | + | 11.5818i | 0.117429 | + | 0.494749i | ||||
\(549\) | 1.90307 | − | 7.10235i | 0.0812210 | − | 0.303121i | ||||
\(550\) | −47.9992 | − | 37.9401i | −2.04669 | − | 1.61777i | ||||
\(551\) | −0.172801 | − | 0.0997666i | −0.00736156 | − | 0.00425020i | ||||
\(552\) | 5.10964 | − | 10.9717i | 0.217481 | − | 0.466987i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14.6508 | + | 36.8606i | 0.622451 | + | 1.56606i | ||||
\(555\) | 6.20509 | − | 1.66265i | 0.263391 | − | 0.0705755i | ||||
\(556\) | −6.01023 | + | 3.24323i | −0.254891 | + | 0.137543i | ||||
\(557\) | −39.3752 | − | 10.5505i | −1.66838 | − | 0.447041i | −0.703707 | − | 0.710491i | \(-0.748473\pi\) |
−0.964673 | + | 0.263450i | \(0.915140\pi\) | |||||||
\(558\) | −4.98265 | − | 6.69057i | −0.210932 | − | 0.283234i | ||||
\(559\) | −5.95532 | −0.251883 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −43.3574 | −1.83055 | ||||||||
\(562\) | −2.86799 | − | 3.85107i | −0.120979 | − | 0.162448i | ||||
\(563\) | 36.0716 | + | 9.66535i | 1.52024 | + | 0.407346i | 0.919820 | − | 0.392341i | \(-0.128335\pi\) |
0.600417 | + | 0.799687i | \(0.295001\pi\) | |||||||
\(564\) | −0.992644 | − | 1.83953i | −0.0417979 | − | 0.0774583i | ||||
\(565\) | −41.1806 | + | 11.0343i | −1.73248 | + | 0.464217i | ||||
\(566\) | 2.70459 | + | 6.80462i | 0.113682 | + | 0.286020i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.0618 | − | 4.03232i | 0.464143 | − | 0.169192i | ||||
\(569\) | 27.4687 | + | 15.8591i | 1.15155 | + | 0.664847i | 0.949264 | − | 0.314480i | \(-0.101830\pi\) |
0.202284 | + | 0.979327i | \(0.435163\pi\) | |||||||
\(570\) | −26.3671 | − | 20.8414i | −1.10440 | − | 0.872951i | ||||
\(571\) | 5.22944 | − | 19.5165i | 0.218845 | − | 0.816741i | −0.765932 | − | 0.642921i | \(-0.777722\pi\) |
0.984777 | − | 0.173820i | \(-0.0556111\pi\) | |||||||
\(572\) | −43.0204 | + | 10.2109i | −1.79877 | + | 0.426938i | ||||
\(573\) | 1.45238 | − | 1.45238i | 0.0606741 | − | 0.0606741i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.4384 | 1.18596 | ||||||||
\(576\) | 10.1298 | − | 1.79641i | 0.422076 | − | 0.0748505i | ||||
\(577\) | 7.35619 | + | 12.7413i | 0.306242 | + | 0.530427i | 0.977537 | − | 0.210763i | \(-0.0675949\pi\) |
−0.671295 | + | 0.741190i | \(0.734262\pi\) | |||||||
\(578\) | 4.49833 | + | 38.4311i | 0.187106 | + | 1.59852i | ||||
\(579\) | 0.501899 | + | 1.87311i | 0.0208582 | + | 0.0778439i | ||||
\(580\) | −0.206766 | − | 0.219016i | −0.00858550 | − | 0.00909414i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −14.7369 | + | 5.85738i | −0.610864 | + | 0.242796i | ||||
\(583\) | 8.15888 | + | 4.71053i | 0.337906 | + | 0.195090i | ||||
\(584\) | −2.83900 | − | 2.37983i | −0.117478 | − | 0.0984780i | ||||
\(585\) | 18.3285 | − | 10.5819i | 0.757789 | − | 0.437510i | ||||
\(586\) | 8.90186 | + | 1.30244i | 0.367732 | + | 0.0538034i | ||||
\(587\) | −21.4287 | − | 21.4287i | −0.884458 | − | 0.884458i | 0.109526 | − | 0.993984i | \(-0.465067\pi\) |
−0.993984 | + | 0.109526i | \(0.965067\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.9065 | + | 15.9065i | −0.655416 | + | 0.655416i | ||||
\(590\) | −16.9805 | − | 22.8010i | −0.699078 | − | 0.938704i | ||||
\(591\) | 5.47277 | + | 9.47911i | 0.225120 | + | 0.389918i | ||||
\(592\) | 5.03449 | + | 1.66459i | 0.206916 | + | 0.0684144i | ||||
\(593\) | 15.1960 | − | 26.3202i | 0.624024 | − | 1.08084i | −0.364704 | − | 0.931123i | \(-0.618830\pi\) |
0.988729 | − | 0.149719i | \(-0.0478368\pi\) | |||||||
\(594\) | −15.6224 | + | 36.2332i | −0.640996 | + | 1.48667i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.28314 | − | 44.6005i | 0.0525595 | − | 1.82691i | ||||
\(597\) | 18.6592 | − | 4.99971i | 0.763668 | − | 0.204624i | ||||
\(598\) | 12.7443 | − | 16.1232i | 0.521152 | − | 0.659326i | ||||
\(599\) | 9.66590 | − | 5.58061i | 0.394938 | − | 0.228018i | −0.289360 | − | 0.957220i | \(-0.593442\pi\) |
0.684298 | + | 0.729203i | \(0.260109\pi\) | |||||||
\(600\) | −18.4929 | − | 26.3831i | −0.754971 | − | 1.07709i | ||||
\(601\) | 29.6441i | 1.20921i | 0.796527 | + | 0.604603i | \(0.206668\pi\) | ||||
−0.796527 | + | 0.604603i | \(0.793332\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.95262 | − | 9.95262i | −0.405302 | − | 0.405302i | ||||
\(604\) | 7.20520 | + | 30.3569i | 0.293175 | + | 1.23520i | ||||
\(605\) | 49.0673 | + | 13.1475i | 1.99487 | + | 0.534523i | ||||
\(606\) | 1.85726 | + | 15.8674i | 0.0754460 | + | 0.644568i | ||||
\(607\) | 11.4264 | − | 19.7911i | 0.463783 | − | 0.803296i | −0.535363 | − | 0.844622i | \(-0.679825\pi\) |
0.999146 | + | 0.0413263i | \(0.0131583\pi\) | |||||||
\(608\) | −8.74769 | − | 26.3269i | −0.354766 | − | 1.06770i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −27.4844 | − | 11.8503i | −1.11281 | − | 0.479804i | ||||
\(611\) | −0.918646 | − | 3.42843i | −0.0371644 | − | 0.138700i | ||||
\(612\) | 16.4122 | + | 4.90764i | 0.663424 | + | 0.198380i | ||||
\(613\) | 2.70264 | − | 10.0864i | 0.109159 | − | 0.407386i | −0.889625 | − | 0.456692i | \(-0.849034\pi\) |
0.998784 | + | 0.0493057i | \(0.0157009\pi\) | |||||||
\(614\) | −0.449703 | + | 3.07360i | −0.0181485 | + | 0.124040i | ||||
\(615\) | 12.1110i | 0.488362i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.6113i | 0.507713i | 0.967242 | + | 0.253857i | \(0.0816992\pi\) | ||||
−0.967242 | + | 0.253857i | \(0.918301\pi\) | |||||||
\(618\) | −5.32136 | − | 0.778576i | −0.214057 | − | 0.0313189i | ||||
\(619\) | 4.96797 | − | 18.5407i | 0.199680 | − | 0.745215i | −0.791326 | − | 0.611395i | \(-0.790609\pi\) |
0.991006 | − | 0.133820i | \(-0.0427245\pi\) | |||||||
\(620\) | −29.8836 | + | 16.1257i | −1.20015 | + | 0.647623i | ||||
\(621\) | −4.74680 | − | 17.7153i | −0.190482 | − | 0.710890i | ||||
\(622\) | −0.465131 | + | 1.07878i | −0.0186501 | + | 0.0432552i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −23.2453 | − | 1.33863i | −0.930557 | − | 0.0535880i | ||||
\(625\) | 3.59986 | − | 6.23513i | 0.143994 | − | 0.249405i | ||||
\(626\) | 25.1797 | − | 2.94726i | 1.00638 | − | 0.117796i | ||||
\(627\) | 30.8372 | + | 8.26280i | 1.23152 | + | 0.329984i | ||||
\(628\) | 10.7141 | − | 17.3830i | 0.427541 | − | 0.693657i | ||||
\(629\) | 6.24320 | + | 6.24320i | 0.248933 | + | 0.248933i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.4653i | 1.29242i | 0.763158 | + | 0.646212i | \(0.223648\pi\) | ||||
−0.763158 | + | 0.646212i | \(0.776352\pi\) | |||||||
\(632\) | 0.925557 | + | 0.162732i | 0.0368167 | + | 0.00647315i | ||||
\(633\) | 8.96300 | − | 5.17479i | 0.356247 | − | 0.205680i | ||||
\(634\) | −16.5603 | − | 13.0898i | −0.657695 | − | 0.519863i | ||||
\(635\) | 46.5326 | − | 12.4684i | 1.84659 | − | 0.494793i | ||||
\(636\) | 3.40571 | + | 3.60747i | 0.135045 | + | 0.143046i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.262723 | + | 0.113277i | 0.0104013 | + | 0.00448466i | ||||
\(639\) | 2.67657 | − | 4.63596i | 0.105883 | − | 0.183396i | ||||
\(640\) | −1.26591 | − | 41.8581i | −0.0500395 | − | 1.65459i | ||||
\(641\) | −8.48101 | − | 14.6895i | −0.334980 | − | 0.580202i | 0.648501 | − | 0.761214i | \(-0.275396\pi\) |
−0.983481 | + | 0.181012i | \(0.942063\pi\) | |||||||
\(642\) | 24.6185 | − | 18.3341i | 0.971616 | − | 0.723588i | ||||
\(643\) | 16.2770 | − | 16.2770i | 0.641904 | − | 0.641904i | −0.309119 | − | 0.951023i | \(-0.600034\pi\) |
0.951023 | + | 0.309119i | \(0.100034\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.58969 | + | 4.58969i | 0.180719 | + | 0.180719i | ||||
\(646\) | 6.68740 | − | 45.7066i | 0.263112 | − | 1.79830i | ||||
\(647\) | −12.2104 | + | 7.04966i | −0.480039 | + | 0.277151i | −0.720433 | − | 0.693525i | \(-0.756057\pi\) |
0.240394 | + | 0.970675i | \(0.422723\pi\) | |||||||
\(648\) | −6.33827 | + | 7.56119i | −0.248991 | + | 0.297032i | ||||
\(649\) | 23.3866 | + | 13.5023i | 0.918005 | + | 0.530010i | ||||
\(650\) | −20.2073 | − | 50.8406i | −0.792595 | − | 1.99413i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.6306 | − | 0.679845i | −0.925447 | − | 0.0266248i | ||||
\(653\) | 10.7159 | + | 39.9922i | 0.419345 | + | 1.56502i | 0.775971 | + | 0.630769i | \(0.217260\pi\) |
−0.356626 | + | 0.934247i | \(0.616073\pi\) | |||||||
\(654\) | 33.3705 | − | 3.90599i | 1.30489 | − | 0.152736i | ||||
\(655\) | 27.7351 | + | 48.0387i | 1.08370 | + | 1.87703i | ||||
\(656\) | −5.48785 | + | 8.35577i | −0.214265 | + | 0.326238i | ||||
\(657\) | −1.68431 | −0.0657113 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.32074 | − | 8.32074i | 0.324130 | − | 0.324130i | −0.526219 | − | 0.850349i | \(-0.676391\pi\) |
0.850349 | + | 0.526219i | \(0.176391\pi\) | |||||||
\(660\) | 41.0246 | + | 25.2858i | 1.59688 | + | 0.984250i | ||||
\(661\) | −5.29815 | + | 19.7730i | −0.206074 | + | 0.769079i | 0.783045 | + | 0.621964i | \(0.213665\pi\) |
−0.989120 | + | 0.147114i | \(0.953001\pi\) | |||||||
\(662\) | −4.86725 | + | 6.15771i | −0.189171 | + | 0.239326i | ||||
\(663\) | −33.5755 | − | 19.3848i | −1.30397 | − | 0.752845i | ||||
\(664\) | −39.7752 | − | 18.5237i | −1.54358 | − | 0.718860i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.24040 | − | 0.890477i | 0.0868136 | − | 0.0345053i | ||||
\(667\) | −0.128452 | + | 0.0344185i | −0.00497367 | + | 0.00133269i | ||||
\(668\) | −45.6877 | − | 13.6617i | −1.76771 | − | 0.528588i | ||||
\(669\) | 20.7456 | + | 5.55876i | 0.802070 | + | 0.214914i | ||||
\(670\) | −45.9508 | + | 34.2208i | −1.77523 | + | 1.32206i | ||||
\(671\) | 28.4302 | 1.09754 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.5406 | 0.984519 | 0.492259 | − | 0.870449i | \(-0.336171\pi\) | ||||
0.492259 | + | 0.870449i | \(0.336171\pi\) | |||||||
\(674\) | 11.1335 | − | 8.29141i | 0.428846 | − | 0.319373i | ||||
\(675\) | −47.1585 | − | 12.6361i | −1.81513 | − | 0.486363i | ||||
\(676\) | −12.9696 | − | 3.87822i | −0.498831 | − | 0.149162i | ||||
\(677\) | 23.3689 | − | 6.26167i | 0.898139 | − | 0.240656i | 0.219922 | − | 0.975517i | \(-0.429420\pi\) |
0.678217 | + | 0.734862i | \(0.262753\pi\) | |||||||
\(678\) | 19.8175 | − | 7.87673i | 0.761086 | − | 0.302504i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 29.4379 | − | 63.2107i | 1.12889 | − | 2.42402i | ||||
\(681\) | 6.56639 | + | 3.79111i | 0.251625 | + | 0.145276i | ||||
\(682\) | 20.0016 | − | 25.3046i | 0.765899 | − | 0.968963i | ||||
\(683\) | −1.96657 | + | 7.33934i | −0.0752487 | + | 0.280832i | −0.993290 | − | 0.115654i | \(-0.963104\pi\) |
0.918041 | + | 0.396486i | \(0.129770\pi\) | |||||||
\(684\) | −10.7376 | − | 6.61822i | −0.410563 | − | 0.253054i | ||||
\(685\) | 15.5777 | − | 15.5777i | 0.595194 | − | 0.595194i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.0587 | 0.879742 | ||||||||
\(688\) | 1.08685 | + | 5.24630i | 0.0414359 | + | 0.200013i | ||||
\(689\) | 4.21210 | + | 7.29558i | 0.160468 | + | 0.277939i | ||||
\(690\) | −22.2478 | + | 2.60408i | −0.846959 | + | 0.0991357i | ||||
\(691\) | 11.2258 | + | 41.8952i | 0.427049 | + | 1.59377i | 0.759407 | + | 0.650616i | \(0.225489\pi\) |
−0.332357 | + | 0.943154i | \(0.607844\pi\) | |||||||
\(692\) | 5.48524 | + | 0.157808i | 0.208518 | + | 0.00599898i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.87736 | − | 7.23930i | −0.109223 | − | 0.274800i | ||||
\(695\) | 10.9461 | + | 6.31973i | 0.415209 | + | 0.239721i | ||||
\(696\) | 0.115461 | + | 0.0967866i | 0.00437653 | + | 0.00366869i | ||||
\(697\) | −14.4155 | + | 8.32276i | −0.546024 | + | 0.315247i | ||||
\(698\) | 1.67835 | − | 11.4711i | 0.0635266 | − | 0.434188i | ||||
\(699\) | −9.94395 | − | 9.94395i | −0.376115 | − | 0.376115i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.2046 | + | 20.2046i | −0.763118 | + | 0.763118i | −0.976885 | − | 0.213767i | \(-0.931427\pi\) |
0.213767 | + | 0.976885i | \(0.431427\pi\) | |||||||
\(702\) | −28.2975 | + | 21.0739i | −1.06802 | + | 0.795383i | ||||
\(703\) | −3.25057 | − | 5.63016i | −0.122598 | − | 0.212345i | ||||
\(704\) | 16.8465 | + | 36.0350i | 0.634925 | + | 1.35812i | ||||
\(705\) | −1.93426 | + | 3.35024i | −0.0728484 | + | 0.126177i | ||||
\(706\) | 27.2312 | + | 11.7411i | 1.02486 | + | 0.441882i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9.76211 | + | 10.3405i | 0.366883 | + | 0.388618i | ||||
\(709\) | 21.1022 | − | 5.65431i | 0.792509 | − | 0.212352i | 0.160217 | − | 0.987082i | \(-0.448781\pi\) |
0.632293 | + | 0.774730i | \(0.282114\pi\) | |||||||
\(710\) | −17.0948 | − | 13.5122i | −0.641555 | − | 0.507105i | ||||
\(711\) | 0.370029 | − | 0.213636i | 0.0138772 | − | 0.00801199i | ||||
\(712\) | −3.18838 | + | 18.1342i | −0.119490 | + | 0.679609i | ||||
\(713\) | 14.9924i | 0.561469i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 57.8632 | + | 57.8632i | 2.16396 | + | 2.16396i | ||||
\(716\) | 13.6339 | − | 22.1201i | 0.509523 | − | 0.826668i | ||||
\(717\) | −11.3923 | − | 3.05255i | −0.425452 | − | 0.114000i | ||||
\(718\) | −44.5019 | + | 5.20891i | −1.66080 | + | 0.194395i | ||||
\(719\) | 0.769848 | − | 1.33342i | 0.0287105 | − | 0.0497280i | −0.851313 | − | 0.524658i | \(-0.824193\pi\) |
0.880024 | + | 0.474930i | \(0.157527\pi\) | |||||||
\(720\) | −12.6671 | − | 14.2151i | −0.472073 | − | 0.529766i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.82814 | + | 6.55932i | −0.105253 | + | 0.244113i | ||||
\(723\) | 3.29484 | + | 12.2965i | 0.122536 | + | 0.457312i | ||||
\(724\) | −31.9359 | + | 17.2332i | −1.18689 | + | 0.640467i | ||||
\(725\) | −0.0916229 | + | 0.341941i | −0.00340279 | + | 0.0126994i | ||||
\(726\) | −25.1419 | − | 3.67855i | −0.933104 | − | 0.136524i | ||||
\(727\) | 15.4144i | 0.571689i | 0.958276 | + | 0.285845i | \(0.0922741\pi\) | ||||
−0.958276 | + | 0.285845i | \(0.907726\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.5246i | 0.982393i | ||||||||
\(730\) | −0.992552 | + | 6.78384i | −0.0367360 | + | 0.251081i | ||||
\(731\) | −2.30894 | + | 8.61707i | −0.0853991 | + | 0.318714i | ||||
\(732\) | 14.3438 | + | 4.28913i | 0.530161 | + | 0.158531i | ||||
\(733\) | 0.205907 | + | 0.768456i | 0.00760535 | + | 0.0283836i | 0.969624 | − | 0.244599i | \(-0.0786564\pi\) |
−0.962019 | + | 0.272983i | \(0.911990\pi\) | |||||||
\(734\) | 1.40708 | + | 0.606681i | 0.0519362 | + | 0.0223930i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.5295 | − | 8.28449i | −0.609284 | − | 0.305370i | ||||
\(737\) | 27.2110 | − | 47.1309i | 1.00233 | − | 1.73609i | ||||
\(738\) | 0.528401 | + | 4.51435i | 0.0194507 | + | 0.166176i | ||||
\(739\) | −34.8153 | − | 9.32874i | −1.28070 | − | 0.343163i | −0.446581 | − | 0.894743i | \(-0.647358\pi\) |
−0.834122 | + | 0.551580i | \(0.814025\pi\) | |||||||
\(740\) | −2.26629 | − | 9.54830i | −0.0833104 | − | 0.351003i | ||||
\(741\) | 20.1858 | + | 20.1858i | 0.741542 | + | 0.741542i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.88298i | 0.215826i | 0.994160 | + | 0.107913i | \(0.0344167\pi\) | ||||
−0.994160 | + | 0.107913i | \(0.965583\pi\) | |||||||
\(744\) | 13.9089 | − | 9.74927i | 0.509924 | − | 0.357426i | ||||
\(745\) | −71.5143 | + | 41.2888i | −2.62008 | + | 1.51270i | ||||
\(746\) | 1.85511 | − | 2.34696i | 0.0679204 | − | 0.0859282i | ||||
\(747\) | −19.2696 | + | 5.16327i | −0.705037 | + | 0.188914i | ||||
\(748\) | −1.90476 | + | 66.2073i | −0.0696450 | + | 2.42078i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −10.0417 | + | 23.2897i | −0.366671 | + | 0.850420i | ||||
\(751\) | −15.7852 | + | 27.3409i | −0.576012 | + | 0.997682i | 0.419919 | + | 0.907562i | \(0.362058\pi\) |
−0.995931 | + | 0.0901203i | \(0.971275\pi\) | |||||||
\(752\) | −2.85260 | + | 1.43497i | −0.104024 | + | 0.0523279i | ||||
\(753\) | 14.8613 | + | 25.7405i | 0.541576 | + | 0.938038i | ||||
\(754\) | 0.152805 | + | 0.205182i | 0.00556482 | + | 0.00747229i | ||||
\(755\) | 40.8306 | − | 40.8306i | 1.48598 | − | 1.48598i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.3777 | − | 20.3777i | −0.740639 | − | 0.740639i | 0.232062 | − | 0.972701i | \(-0.425453\pi\) |
−0.972701 | + | 0.232062i | \(0.925453\pi\) | |||||||
\(758\) | 37.7694 | + | 5.52609i | 1.37184 | + | 0.200717i | ||||
\(759\) | 18.4265 | − | 10.6385i | 0.668839 | − | 0.386154i | ||||
\(760\) | −32.9835 | + | 39.3474i | −1.19644 | + | 1.42728i | ||||
\(761\) | −8.10652 | − | 4.68030i | −0.293861 | − | 0.169661i | 0.345821 | − | 0.938301i | \(-0.387601\pi\) |
−0.639682 | + | 0.768640i | \(0.720934\pi\) | |||||||
\(762\) | −22.3931 | + | 8.90043i | −0.811215 | + | 0.322429i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.15400 | − | 2.28161i | −0.0779290 | − | 0.0825458i | ||||
\(765\) | −8.20545 | − | 30.6232i | −0.296669 | − | 1.10718i | ||||
\(766\) | 5.43772 | + | 46.4568i | 0.196473 | + | 1.67855i | ||||
\(767\) | 12.0736 | + | 20.9120i | 0.435951 | + | 0.755090i | ||||
\(768\) | 3.06304 | + | 20.7221i | 0.110528 | + | 0.747745i | ||||
\(769\) | 32.4675 | 1.17081 | 0.585404 | − | 0.810742i | \(-0.300936\pi\) | ||||
0.585404 | + | 0.810742i | \(0.300936\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.4558 | + | 16.4558i | −0.592642 | + | 0.592642i | ||||
\(772\) | 2.88232 | − | 0.684118i | 0.103737 | − | 0.0246219i | ||||
\(773\) | 1.80264 | − | 6.72754i | 0.0648364 | − | 0.241973i | −0.925901 | − | 0.377767i | \(-0.876692\pi\) |
0.990737 | + | 0.135794i | \(0.0433586\pi\) | |||||||
\(774\) | 1.91105 | + | 1.51055i | 0.0686911 | + | 0.0542956i | ||||
\(775\) | 34.5631 | + | 19.9550i | 1.24154 | + | 0.716806i | ||||
\(776\) | 8.29689 | + | 22.7608i | 0.297841 | + | 0.817064i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.67149 | + | 19.3011i | 0.275036 | + | 0.691978i | ||||
\(779\) | 11.8388 | − | 3.17221i | 0.424170 | − | 0.113656i | ||||
\(780\) | 20.4639 | + | 37.9230i | 0.732725 | + | 1.35786i | ||||
\(781\) | 19.9928 | + | 5.35707i | 0.715400 | + | 0.191691i | ||||
\(782\) | −18.3884 | − | 24.6915i | −0.657569 | − | 0.882967i | ||||
\(783\) | 0.228301 | 0.00815880 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −37.7912 | −1.34883 | ||||||||
\(786\) | −16.5728 | − | 22.2535i | −0.591131 | − | 0.793756i | ||||
\(787\) | 20.1266 | + | 5.39292i | 0.717437 | + | 0.192237i | 0.599028 | − | 0.800728i | \(-0.295554\pi\) |
0.118409 | + | 0.992965i | \(0.462221\pi\) | |||||||
\(788\) | 14.7152 | − | 7.94056i | 0.524206 | − | 0.282871i | ||||
\(789\) | −21.1990 | + | 5.68025i | −0.754703 | + | 0.202222i | ||||
\(790\) | −0.642399 | − | 1.61624i | −0.0228555 | − | 0.0575034i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 16.3951 | + | 7.63536i | 0.582574 | + | 0.271311i | ||||
\(793\) | 22.0161 | + | 12.7110i | 0.781815 | + | 0.451381i | ||||
\(794\) | −13.6018 | − | 10.7513i | −0.482710 | − | 0.381549i | ||||
\(795\) | 2.37639 | − | 8.86882i | 0.0842820 | − | 0.314545i | ||||
\(796\) | −6.81489 | − | 28.7124i | −0.241547 | − | 1.01769i | ||||
\(797\) | 8.46424 | − | 8.46424i | 0.299819 | − | 0.299819i | −0.541124 | − | 0.840943i | \(-0.682001\pi\) |
0.840943 | + | 0.541124i | \(0.182001\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.31695 | −0.188100 | ||||||||
\(800\) | −41.0998 | + | 27.0799i | −1.45310 | + | 0.957420i | ||||
\(801\) | 4.18573 | + | 7.24989i | 0.147895 | + | 0.256162i | ||||
\(802\) | 1.86768 | + | 15.9564i | 0.0659502 | + | 0.563441i | ||||
\(803\) | −1.68555 | − | 6.29055i | −0.0594817 | − | 0.221989i | ||||
\(804\) | 20.8390 | − | 19.6735i | 0.734936 | − | 0.693831i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26.8025 | − | 10.6530i | 0.944080 | − | 0.375238i | ||||
\(807\) | −27.7100 | − | 15.9984i | −0.975438 | − | 0.563169i | ||||
\(808\) | 24.3113 | − | 2.13898i | 0.855268 | − | 0.0752491i | ||||
\(809\) | 34.4318 | − | 19.8792i | 1.21056 | − | 0.698915i | 0.247676 | − | 0.968843i | \(-0.420333\pi\) |
0.962881 | + | 0.269927i | \(0.0869997\pi\) | |||||||
\(810\) | 18.0676 | + | 2.64350i | 0.634831 | + | 0.0928830i | ||||
\(811\) | −24.8317 | − | 24.8317i | −0.871960 | − | 0.871960i | 0.120726 | − | 0.992686i | \(-0.461478\pi\) |
−0.992686 | + | 0.120726i | \(0.961478\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.1821 | − | 10.1821i | 0.357102 | − | 0.357102i | ||||
\(814\) | 5.56778 | + | 7.47628i | 0.195151 | + | 0.262043i | ||||
\(815\) | 21.8760 | + | 37.8903i | 0.766283 | + | 1.32724i | ||||
\(816\) | −10.9494 | + | 33.1159i | −0.383305 | + | 1.15929i | ||||
\(817\) | 3.28438 | − | 5.68871i | 0.114906 | − | 0.199023i | ||||
\(818\) | 7.02989 | − | 16.3044i | 0.245794 | − | 0.570071i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18.4937 | + | 0.532056i | 0.645826 | + | 0.0185802i | ||||
\(821\) | −6.76852 | + | 1.81362i | −0.236223 | + | 0.0632958i | −0.374988 | − | 0.927030i | \(-0.622353\pi\) |
0.138765 | + | 0.990325i | \(0.455687\pi\) | |||||||
\(822\) | −6.83337 | + | 8.64512i | −0.238341 | + | 0.301533i | ||||
\(823\) | −33.7105 | + | 19.4628i | −1.17507 | + | 0.678430i | −0.954870 | − | 0.297024i | \(-0.904006\pi\) |
−0.220205 | + | 0.975454i | \(0.570673\pi\) | |||||||
\(824\) | −1.42267 | + | 8.09159i | −0.0495611 | + | 0.281884i | ||||
\(825\) | − | 56.6400i | − | 1.97195i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.4250 | + | 16.4250i | 0.571153 | + | 0.571153i | 0.932451 | − | 0.361297i | \(-0.117666\pi\) |
−0.361297 | + | 0.932451i | \(0.617666\pi\) | |||||||
\(828\) | −8.17921 | + | 1.94134i | −0.284247 | + | 0.0674661i | ||||
\(829\) | 12.2534 | + | 3.28329i | 0.425578 | + | 0.114033i | 0.465250 | − | 0.885180i | \(-0.345965\pi\) |
−0.0396717 | + | 0.999213i | \(0.512631\pi\) | |||||||
\(830\) | 9.44046 | + | 80.6539i | 0.327683 | + | 2.79954i | ||||
\(831\) | −18.3601 | + | 31.8006i | −0.636905 | + | 1.10315i | ||||
\(832\) | −3.06531 | + | 35.4371i | −0.106270 | + | 1.22856i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5.80569 | − | 2.50320i | −0.201035 | − | 0.0866789i | ||||
\(835\) | 22.8421 | + | 85.2477i | 0.790482 | + | 2.95012i | ||||
\(836\) | 13.9721 | − | 46.7258i | 0.483236 | − | 1.61605i | ||||
\(837\) | 6.66160 | − | 24.8614i | 0.230259 | − | 0.859336i | ||||
\(838\) | −3.67855 | + | 25.1419i | −0.127073 | + | 0.868513i | ||||
\(839\) | 29.4605i | 1.01709i | 0.861036 | + | 0.508544i | \(0.169816\pi\) | ||||
−0.861036 | + | 0.508544i | \(0.830184\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9983i | 0.999943i | ||||||||
\(842\) | −17.2420 | − | 2.52270i | −0.594198 | − | 0.0869379i | ||||
\(843\) | 1.15049 | − | 4.29368i | 0.0396249 | − | 0.147882i | ||||
\(844\) | −7.50822 | − | 13.9140i | −0.258444 | − | 0.478939i | ||||
\(845\) | 6.48429 | + | 24.1997i | 0.223066 | + | 0.832494i | ||||
\(846\) | −0.574822 | + | 1.33319i | −0.0197628 | + | 0.0458359i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.65828 | − | 5.04208i | 0.194306 | − | 0.173146i | ||||
\(849\) | −3.38935 | + | 5.87053i | −0.116322 | + | 0.201476i | ||||
\(850\) | −81.3985 | + | 9.52762i | −2.79195 | + | 0.326795i | ||||
\(851\) | −4.18518 | − | 1.12142i | −0.143466 | − | 0.0384417i | ||||
\(852\) | 9.27870 | + | 5.71900i | 0.317883 | + | 0.195930i | ||||
\(853\) | −8.56586 | − | 8.56586i | −0.293289 | − | 0.293289i | 0.545089 | − | 0.838378i | \(-0.316496\pi\) |
−0.838378 | + | 0.545089i | \(0.816496\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 23.3439i | 0.798346i | ||||||||
\(856\) | −26.9148 | − | 38.3983i | −0.919930 | − | 1.31243i | ||||
\(857\) | 15.7855 | − | 9.11375i | 0.539222 | − | 0.311320i | −0.205542 | − | 0.978648i | \(-0.565896\pi\) |
0.744764 | + | 0.667328i | \(0.232562\pi\) | |||||||
\(858\) | −32.1122 | − | 25.3825i | −1.09629 | − | 0.866543i | ||||
\(859\) | −21.4109 | + | 5.73702i | −0.730529 | + | 0.195745i | −0.604865 | − | 0.796328i | \(-0.706773\pi\) |
−0.125664 | + | 0.992073i | \(0.540106\pi\) | |||||||
\(860\) | 7.21015 | − | 6.80688i | 0.245864 | − | 0.232113i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.0538 | − | 9.50881i | −0.751156 | − | 0.323871i | ||||
\(863\) | −16.1931 | + | 28.0472i | −0.551218 | + | 0.954738i | 0.446969 | + | 0.894550i | \(0.352503\pi\) |
−0.998187 | + | 0.0601884i | \(0.980830\pi\) | |||||||
\(864\) | 23.7292 | + | 21.0825i | 0.807285 | + | 0.717241i | ||||
\(865\) | −5.07795 | − | 8.79526i | −0.172655 | − | 0.299048i | ||||
\(866\) | −31.7728 | + | 23.6620i | −1.07968 | + | 0.804068i | ||||
\(867\) | −25.3288 | + | 25.3288i | −0.860212 | + | 0.860212i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.16819 | + | 1.16819i | 0.0396280 | + | 0.0396280i | ||||
\(870\) | 0.0403667 | − | 0.275896i | 0.00136856 | − | 0.00935374i | ||||
\(871\) | 42.1439 | − | 24.3318i | 1.42799 | − | 0.824451i | ||||
\(872\) | −4.49848 | − | 51.1289i | −0.152338 | − | 1.73144i | ||||
\(873\) | 9.53894 | + | 5.50731i | 0.322844 | + | 0.186394i | ||||
\(874\) | 8.37288 | + | 21.0658i | 0.283217 | + | 0.712560i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.0986232 | − | 3.42803i | 0.00333217 | − | 0.115822i | ||||
\(877\) | −6.47093 | − | 24.1498i | −0.218508 | − | 0.815482i | −0.984902 | − | 0.173112i | \(-0.944618\pi\) |
0.766394 | − | 0.642370i | \(-0.222049\pi\) | |||||||
\(878\) | −42.6225 | + | 4.98893i | −1.43844 | + | 0.168368i | ||||
\(879\) | 4.16431 | + | 7.21279i | 0.140459 | + | 0.243281i | ||||
\(880\) | 40.4141 | − | 61.5343i | 1.36236 | − | 2.07432i | ||||
\(881\) | 5.28932 | 0.178202 | 0.0891008 | − | 0.996023i | \(-0.471601\pi\) | ||||
0.0891008 | + | 0.996023i | \(0.471601\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.0747 | − | 26.0747i | 0.877483 | − | 0.877483i | −0.115791 | − | 0.993274i | \(-0.536940\pi\) |
0.993274 | + | 0.115791i | \(0.0369401\pi\) | |||||||
\(884\) | −31.0759 | + | 50.4187i | −1.04520 | + | 1.69576i | ||||
\(885\) | 6.81169 | − | 25.4216i | 0.228973 | − | 0.854537i | ||||
\(886\) | −34.2465 | + | 43.3264i | −1.15054 | + | 1.45558i | ||||
\(887\) | −22.3247 | − | 12.8892i | −0.749590 | − | 0.432776i | 0.0759555 | − | 0.997111i | \(-0.475799\pi\) |
−0.825546 | + | 0.564335i | \(0.809133\pi\) | |||||||
\(888\) | 1.68118 | + | 4.61195i | 0.0564166 | + | 0.154767i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 31.6667 | − | 12.5864i | 1.06147 | − | 0.421896i | ||||
\(891\) | −16.7538 | + | 4.48918i | −0.561275 | + | 0.150393i | ||||
\(892\) | 9.39968 | − | 31.4346i | 0.314725 | − | 1.05251i | ||||
\(893\) | 3.78159 | + | 1.01327i | 0.126546 | + | 0.0339079i | ||||
\(894\) | 33.1284 | − | 24.6716i | 1.10798 | − | 0.825141i | ||||
\(895\) | −48.0899 | −1.60747 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.0257 | 0.635250 | ||||||||
\(898\) | −28.2174 | + | 21.0142i | −0.941627 | + | 0.701255i | ||||
\(899\) | −0.180267 | − | 0.0483025i | −0.00601226 | − | 0.00161098i | ||||
\(900\) | −6.41111 | + | 21.4401i | −0.213704 | + | 0.714671i | ||||
\(901\) | 12.1894 | − | 3.26615i | 0.406089 | − | 0.108811i | ||||
\(902\) | −16.3314 | + | 6.49113i | −0.543775 | + | 0.216131i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.1573 | − | 30.6076i | −0.371085 | − | 1.01799i | ||||
\(905\) | 58.1631 | + | 33.5805i | 1.93341 | + | 1.11625i | ||||
\(906\) | −17.9109 | + | 22.6596i | −0.595049 | + | 0.752815i | ||||
\(907\) | 1.50772 | − | 5.62687i | 0.0500629 | − | 0.186837i | −0.936366 | − | 0.351024i | \(-0.885833\pi\) |
0.986429 | + | 0.164187i | \(0.0525001\pi\) | |||||||
\(908\) | 6.07755 | − | 9.86042i | 0.201690 | − | 0.327230i | ||||
\(909\) | 7.84617 | − | 7.84617i | 0.260241 | − | 0.260241i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.69169 | −0.122311 | −0.0611556 | − | 0.998128i | \(-0.519479\pi\) | ||||
−0.0611556 | + | 0.998128i | \(0.519479\pi\) | |||||||
\(912\) | 14.0986 | − | 21.4664i | 0.466851 | − | 0.710825i | ||||
\(913\) | −38.5674 | − | 66.8007i | −1.27639 | − | 2.21078i | ||||
\(914\) | −41.7515 | + | 4.88697i | −1.38102 | + | 0.161647i | ||||
\(915\) | −7.17132 | − | 26.7637i | −0.237076 | − | 0.884782i | ||||
\(916\) | 1.01300 | − | 35.2109i | 0.0334706 | − | 1.16340i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 19.5217 | + | 49.1157i | 0.644313 | + | 1.62106i | ||||
\(919\) | 1.02757 | + | 0.593266i | 0.0338963 | + | 0.0195701i | 0.516852 | − | 0.856075i | \(-0.327104\pi\) |
−0.482956 | + | 0.875645i | \(0.660437\pi\) | |||||||
\(920\) | 2.99909 | + | 34.0871i | 0.0988770 | + | 1.12382i | ||||
\(921\) | −2.49040 | + | 1.43783i | −0.0820616 | + | 0.0473783i | ||||
\(922\) | 0.791397 | − | 5.40899i | 0.0260633 | − | 0.178136i | ||||
\(923\) | 13.0871 | + | 13.0871i | 0.430769 | + | 0.430769i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.15582 | + | 8.15582i | −0.268162 | + | 0.268162i | ||||
\(926\) | 38.9136 | − | 28.9800i | 1.27878 | − | 0.952341i | ||||
\(927\) | 1.86769 | + | 3.23494i | 0.0613431 | + | 0.106249i | ||||
\(928\) | 0.152867 | − | 0.172058i | 0.00501810 | − | 0.00564809i | ||||
\(929\) | 3.35968 | − | 5.81914i | 0.110228 | − | 0.190920i | −0.805634 | − | 0.592413i | \(-0.798175\pi\) |
0.915862 | + | 0.401493i | \(0.131509\pi\) | |||||||
\(930\) | −28.8665 | − | 12.4462i | −0.946571 | − | 0.408127i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −15.6214 | + | 14.7477i | −0.511696 | + | 0.483077i | ||||
\(933\) | −1.05049 | + | 0.281479i | −0.0343916 | + | 0.00921521i | ||||
\(934\) | 12.3501 | + | 9.76190i | 0.404107 | + | 0.319419i | ||||
\(935\) | 106.160 | − | 61.2912i | 3.47179 | − | 2.00444i | ||||
\(936\) | 9.28246 | + | 13.2429i | 0.303407 | + | 0.432858i | ||||
\(937\) | − | 0.936781i | − | 0.0306033i | −0.999883 | − | 0.0153017i | \(-0.995129\pi\) | ||
0.999883 | − | 0.0153017i | \(-0.00487086\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.5952 | + | 16.5952i | 0.541565 | + | 0.541565i | ||||
\(940\) | 5.03088 | + | 3.10082i | 0.164089 | + | 0.101138i | ||||
\(941\) | −43.4351 | − | 11.6384i | −1.41594 | − | 0.379401i | −0.531900 | − | 0.846807i | \(-0.678522\pi\) |
−0.884042 | + | 0.467407i | \(0.845188\pi\) | |||||||
\(942\) | 18.7752 | − | 2.19762i | 0.611730 | − | 0.0716024i | ||||
\(943\) | 4.08429 | − | 7.07419i | 0.133003 | − | 0.230367i | ||||
\(944\) | 16.2189 | − | 14.4526i | 0.527880 | − | 0.470392i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.72914 | + | 8.64901i | −0.121245 | + | 0.281203i | ||||
\(947\) | −10.8867 | − | 40.6298i | −0.353771 | − | 1.32029i | −0.882024 | − | 0.471204i | \(-0.843820\pi\) |
0.528254 | − | 0.849087i | \(-0.322847\pi\) | |||||||
\(948\) | 0.413141 | + | 0.765618i | 0.0134182 | + | 0.0248661i | ||||
\(949\) | 1.50720 | − | 5.62494i | 0.0489257 | − | 0.182593i | ||||
\(950\) | 59.7090 | + | 8.73610i | 1.93721 | + | 0.283437i | ||||
\(951\) | − | 19.5415i | − | 0.633678i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.7372i | 1.22243i | 0.791466 | + | 0.611214i | \(0.209318\pi\) | ||||
−0.791466 | + | 0.611214i | \(0.790682\pi\) | |||||||
\(954\) | 0.498852 | − | 3.40952i | 0.0161509 | − | 0.110387i | ||||
\(955\) | −1.50299 | + | 5.60925i | −0.0486357 | + | 0.181511i | ||||
\(956\) | −5.16177 | + | 17.2621i | −0.166944 | + | 0.558295i | ||||
\(957\) | 0.0685505 | + | 0.255834i | 0.00221592 | + | 0.00826994i | ||||
\(958\) | −45.7983 | − | 19.7466i | −1.47968 | − | 0.637983i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 29.6733 | − | 24.9485i | 0.957702 | − | 0.805210i | ||||
\(961\) | 4.97994 | − | 8.62550i | 0.160643 | − | 0.278242i | ||||
\(962\) | 0.969035 | + | 8.27888i | 0.0312429 | + | 0.266922i | ||||
\(963\) | −20.5935 | − | 5.51802i | −0.663617 | − | 0.177816i | ||||
\(964\) | 18.9217 | − | 4.49106i | 0.609427 | − | 0.144647i | ||||
\(965\) | −3.87677 | − | 3.87677i | −0.124798 | − | 0.124798i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.4709i | 0.368880i | 0.982844 | + | 0.184440i | \(0.0590471\pi\) | ||||
−0.982844 | + | 0.184440i | \(0.940953\pi\) | |||||||
\(968\) | −6.72172 | + | 38.2304i | −0.216044 | + | 1.22877i | ||||
\(969\) | 37.0341 | − | 21.3816i | 1.18971 | − | 0.686877i | ||||
\(970\) | 27.8028 | − | 35.1742i | 0.892693 | − | 1.12937i | ||||
\(971\) | −54.4578 | + | 14.5919i | −1.74763 | + | 0.468277i | −0.984119 | − | 0.177512i | \(-0.943195\pi\) |
−0.763516 | + | 0.645789i | \(0.776529\pi\) | |||||||
\(972\) | 24.5235 | + | 0.705531i | 0.786590 | + | 0.0226299i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.367702 | − | 0.852812i | 0.0117819 | − | 0.0273258i | ||||
\(975\) | 25.3234 | − | 43.8615i | 0.810999 | − | 1.40469i | ||||
\(976\) | 7.17971 | − | 21.7147i | 0.229817 | − | 0.695071i | ||||
\(977\) | 7.50978 | + | 13.0073i | 0.240259 | + | 0.416141i | 0.960788 | − | 0.277284i | \(-0.0894343\pi\) |
−0.720529 | + | 0.693425i | \(0.756101\pi\) | |||||||
\(978\) | −13.0717 | − | 17.5524i | −0.417987 | − | 0.561263i | ||||
\(979\) | −22.8880 | + | 22.8880i | −0.731504 | + | 0.731504i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.5012 | − | 16.5012i | −0.526844 | − | 0.526844i | ||||
\(982\) | −18.7592 | − | 2.74468i | −0.598630 | − | 0.0875863i | ||||
\(983\) | 34.9121 | − | 20.1565i | 1.11352 | − | 0.642893i | 0.173783 | − | 0.984784i | \(-0.444401\pi\) |
0.939740 | + | 0.341891i | \(0.111067\pi\) | |||||||
\(984\) | −9.21887 | + | 0.811105i | −0.293887 | + | 0.0258571i | ||||
\(985\) | −26.7999 | − | 15.4729i | −0.853915 | − | 0.493008i | ||||
\(986\) | 0.356133 | − | 0.141550i | 0.0113416 | − | 0.00450787i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 31.7107 | − | 29.9371i | 1.00885 | − | 0.952427i | ||||
\(989\) | −1.13308 | − | 4.22871i | −0.0360299 | − | 0.134465i | ||||
\(990\) | −3.89130 | − | 33.2450i | −0.123674 | − | 1.05660i | ||||
\(991\) | −8.85004 | − | 15.3287i | −0.281131 | − | 0.486933i | 0.690533 | − | 0.723301i | \(-0.257376\pi\) |
−0.971664 | + | 0.236368i | \(0.924043\pi\) | |||||||
\(992\) | −14.2762 | − | 21.6673i | −0.453271 | − | 0.687939i | ||||
\(993\) | −7.26623 | −0.230587 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −38.6188 | + | 38.6188i | −1.22430 | + | 1.22430i | ||||
\(996\) | −9.38033 | − | 39.5211i | −0.297227 | − | 1.25227i | ||||
\(997\) | −10.2577 | + | 38.2824i | −0.324866 | + | 1.21242i | 0.589580 | + | 0.807710i | \(0.299293\pi\) |
−0.914446 | + | 0.404707i | \(0.867374\pi\) | |||||||
\(998\) | 5.57535 | + | 4.40693i | 0.176485 | + | 0.139499i | ||||
\(999\) | 6.44188 | + | 3.71922i | 0.203812 | + | 0.117671i |
(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 | 784.2.x.n.373.8 | 40 | ||
7.2 | even | 3 | 784.2.m.i.197.1 | ✓ | 20 | ||
7.3 | odd | 6 | inner | 784.2.x.n.165.6 | 40 | ||
7.4 | even | 3 | inner | 784.2.x.n.165.5 | 40 | ||
7.5 | odd | 6 | 784.2.m.i.197.2 | yes | 20 | ||
7.6 | odd | 2 | inner | 784.2.x.n.373.7 | 40 | ||
16.13 | even | 4 | inner | 784.2.x.n.765.5 | 40 | ||
112.13 | odd | 4 | inner | 784.2.x.n.765.6 | 40 | ||
112.45 | odd | 12 | inner | 784.2.x.n.557.7 | 40 | ||
112.61 | odd | 12 | 784.2.m.i.589.2 | yes | 20 | ||
112.93 | even | 12 | 784.2.m.i.589.1 | yes | 20 | ||
112.109 | even | 12 | inner | 784.2.x.n.557.8 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
784.2.m.i.197.1 | ✓ | 20 | 7.2 | even | 3 | ||
784.2.m.i.197.2 | yes | 20 | 7.5 | odd | 6 | ||
784.2.m.i.589.1 | yes | 20 | 112.93 | even | 12 | ||
784.2.m.i.589.2 | yes | 20 | 112.61 | odd | 12 | ||
784.2.x.n.165.5 | 40 | 7.4 | even | 3 | inner | ||
784.2.x.n.165.6 | 40 | 7.3 | odd | 6 | inner | ||
784.2.x.n.373.7 | 40 | 7.6 | odd | 2 | inner | ||
784.2.x.n.373.8 | 40 | 1.1 | even | 1 | trivial | ||
784.2.x.n.557.7 | 40 | 112.45 | odd | 12 | inner | ||
784.2.x.n.557.8 | 40 | 112.109 | even | 12 | inner | ||
784.2.x.n.765.5 | 40 | 16.13 | even | 4 | inner | ||
784.2.x.n.765.6 | 40 | 112.13 | odd | 4 | inner |