Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1000,2,Mod(149,1000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1000, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1000.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1000 = 2^{3} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1000.o (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.98504020213\) |
Analytic rank: | \(0\) |
Dimension: | \(112\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 200) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 149.19 | ||
Character | \(\chi\) | \(=\) | 1000.149 |
Dual form | 1000.2.o.a.349.19 |
$q$-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 \(\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times\).
\(n\) | \(377\) | \(501\) | \(751\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.717591 | − | 1.21863i | 0.507414 | − | 0.861703i | ||||
\(3\) | 2.54275 | + | 1.84742i | 1.46806 | + | 1.06661i | 0.981170 | + | 0.193145i | \(0.0618687\pi\) |
0.486890 | + | 0.873463i | \(0.338131\pi\) | |||||||
\(4\) | −0.970125 | − | 1.74896i | −0.485063 | − | 0.874479i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.07598 | − | 1.77299i | 1.66401 | − | 0.723819i | ||||
\(7\) | 1.17589i | 0.444443i | 0.974996 | + | 0.222222i | \(0.0713308\pi\) | ||||
−0.974996 | + | 0.222222i | \(0.928669\pi\) | |||||||
\(8\) | −2.82749 | − | 0.0728129i | −0.999669 | − | 0.0257432i | ||||
\(9\) | 2.12559 | + | 6.54190i | 0.708531 | + | 2.18063i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.77756 | + | 1.22741i | 1.13898 | + | 0.370077i | 0.816981 | − | 0.576664i | \(-0.195646\pi\) |
0.321997 | + | 0.946741i | \(0.395646\pi\) | |||||||
\(12\) | 0.764270 | − | 6.23940i | 0.220626 | − | 1.80116i | ||||
\(13\) | 0.280944 | + | 0.864656i | 0.0779198 | + | 0.239812i | 0.982427 | − | 0.186645i | \(-0.0597614\pi\) |
−0.904508 | + | 0.426457i | \(0.859761\pi\) | |||||||
\(14\) | 1.43297 | + | 0.843806i | 0.382978 | + | 0.225517i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.11771 | + | 3.39342i | −0.529429 | + | 0.848355i | ||||
\(17\) | −3.27511 | − | 4.50780i | −0.794331 | − | 1.09330i | −0.993555 | − | 0.113348i | \(-0.963842\pi\) |
0.199225 | − | 0.979954i | \(-0.436158\pi\) | |||||||
\(18\) | 9.49747 | + | 2.10410i | 2.23858 | + | 0.495940i | ||||
\(19\) | 2.64864 | + | 3.64555i | 0.607641 | + | 0.836346i | 0.996381 | − | 0.0850017i | \(-0.0270896\pi\) |
−0.388740 | + | 0.921348i | \(0.627090\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.17235 | + | 2.98999i | −0.474047 | + | 0.652469i | ||||
\(22\) | 4.20650 | − | 3.72268i | 0.896829 | − | 0.793679i | ||||
\(23\) | 2.07468 | + | 0.674105i | 0.432601 | + | 0.140561i | 0.517220 | − | 0.855853i | \(-0.326967\pi\) |
−0.0846183 | + | 0.996413i | \(0.526967\pi\) | |||||||
\(24\) | −7.05510 | − | 5.40870i | −1.44012 | − | 1.10405i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.25530 | + | 0.278103i | 0.246184 | + | 0.0545404i | ||||
\(27\) | −3.76703 | + | 11.5937i | −0.724966 | + | 2.23122i | ||||
\(28\) | 2.05658 | − | 1.14076i | 0.388656 | − | 0.215583i | ||||
\(29\) | 3.65841 | − | 5.03536i | 0.679349 | − | 0.935044i | −0.320577 | − | 0.947223i | \(-0.603877\pi\) |
0.999926 | + | 0.0121788i | \(0.00387674\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.16778 | + | 0.848445i | −0.209740 | + | 0.152385i | −0.687696 | − | 0.725999i | \(-0.741378\pi\) |
0.477956 | + | 0.878384i | \(0.341378\pi\) | |||||||
\(32\) | 2.61567 | + | 5.01580i | 0.462390 | + | 0.886677i | ||||
\(33\) | 7.33789 | + | 10.0997i | 1.27736 | + | 1.75814i | ||||
\(34\) | −7.84354 | + | 0.756392i | −1.34516 | + | 0.129720i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9.37942 | − | 10.0640i | 1.56324 | − | 1.67734i | ||||
\(37\) | −2.16303 | − | 6.65712i | −0.355600 | − | 1.09442i | −0.955661 | − | 0.294470i | \(-0.904857\pi\) |
0.600061 | − | 0.799954i | \(-0.295143\pi\) | |||||||
\(38\) | 6.34322 | − | 0.611709i | 1.02901 | − | 0.0992323i | ||||
\(39\) | −0.883011 | + | 2.71763i | −0.141395 | + | 0.435169i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.97065 | + | 6.06503i | 0.307763 | + | 0.947198i | 0.978632 | + | 0.205622i | \(0.0659216\pi\) |
−0.670868 | + | 0.741577i | \(0.734078\pi\) | |||||||
\(42\) | 2.08483 | + | 4.79289i | 0.321697 | + | 0.739559i | ||||
\(43\) | −2.96089 | −0.451532 | −0.225766 | − | 0.974182i | \(-0.572488\pi\) | ||||
−0.225766 | + | 0.974182i | \(0.572488\pi\) | |||||||
\(44\) | −1.51803 | − | 7.79754i | −0.228852 | − | 1.17552i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.31026 | − | 2.04454i | 0.340629 | − | 0.301451i | ||||
\(47\) | 3.12538 | − | 4.30172i | 0.455884 | − | 0.627470i | −0.517765 | − | 0.855523i | \(-0.673236\pi\) |
0.973649 | + | 0.228053i | \(0.0732359\pi\) | |||||||
\(48\) | −11.6539 | + | 4.71632i | −1.68209 | + | 0.680743i | ||||
\(49\) | 5.61729 | 0.802470 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 17.5127i | − | 2.45227i | ||||||
\(52\) | 1.23970 | − | 1.33018i | 0.171915 | − | 0.184463i | ||||
\(53\) | −10.5708 | − | 7.68016i | −1.45202 | − | 1.05495i | −0.985355 | − | 0.170515i | \(-0.945457\pi\) |
−0.466661 | − | 0.884436i | \(-0.654543\pi\) | |||||||
\(54\) | 11.4253 | + | 12.9102i | 1.55479 | + | 1.75685i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.0856196 | − | 3.32481i | 0.0114414 | − | 0.444296i | ||||
\(57\) | 14.1629i | 1.87592i | ||||||||
\(58\) | −3.51101 | − | 8.07158i | −0.461019 | − | 1.05985i | ||||
\(59\) | −1.22277 | + | 0.397301i | −0.159191 | + | 0.0517242i | −0.387528 | − | 0.921858i | \(-0.626671\pi\) |
0.228338 | + | 0.973582i | \(0.426671\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.7321 | − | 4.78675i | −1.88625 | − | 0.612881i | −0.982948 | − | 0.183885i | \(-0.941133\pi\) |
−0.903306 | − | 0.428996i | \(-0.858867\pi\) | |||||||
\(62\) | 0.195950 | + | 2.03194i | 0.0248857 | + | 0.258056i | ||||
\(63\) | −7.69253 | + | 2.49945i | −0.969167 | + | 0.314902i | ||||
\(64\) | 7.98940 | + | 0.411755i | 0.998675 | + | 0.0514694i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 17.5735 | − | 1.69470i | 2.16314 | − | 0.208603i | ||||
\(67\) | 2.45652 | − | 1.78477i | 0.300112 | − | 0.218044i | −0.427530 | − | 0.904001i | \(-0.640616\pi\) |
0.727642 | + | 0.685957i | \(0.240616\pi\) | |||||||
\(68\) | −4.70669 | + | 10.1012i | −0.570770 | + | 1.22495i | ||||
\(69\) | 4.03005 | + | 5.54689i | 0.485161 | + | 0.667767i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.58201 | − | 1.14940i | −0.187750 | − | 0.136409i | 0.489940 | − | 0.871756i | \(-0.337019\pi\) |
−0.677690 | + | 0.735348i | \(0.737019\pi\) | |||||||
\(72\) | −5.53375 | − | 18.6519i | −0.652159 | − | 2.19815i | ||||
\(73\) | −4.01616 | − | 1.30493i | −0.470056 | − | 0.152731i | 0.0644044 | − | 0.997924i | \(-0.479485\pi\) |
−0.534461 | + | 0.845193i | \(0.679485\pi\) | |||||||
\(74\) | −9.66475 | − | 2.14116i | −1.12350 | − | 0.248905i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.80639 | − | 8.16901i | 0.436623 | − | 0.937049i | ||||
\(77\) | −1.44329 | + | 4.44199i | −0.164478 | + | 0.506211i | ||||
\(78\) | 2.67815 | + | 3.02621i | 0.303240 | + | 0.342651i | ||||
\(79\) | 2.23200 | + | 1.62164i | 0.251119 | + | 0.182449i | 0.706223 | − | 0.707990i | \(-0.250398\pi\) |
−0.455103 | + | 0.890439i | \(0.650398\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −14.3025 | + | 10.3914i | −1.58917 | + | 1.15460i | ||||
\(82\) | 8.80515 | + | 1.95072i | 0.972366 | + | 0.215421i | ||||
\(83\) | 7.65878 | − | 5.56443i | 0.840660 | − | 0.610775i | −0.0818950 | − | 0.996641i | \(-0.526097\pi\) |
0.922555 | + | 0.385866i | \(0.126097\pi\) | |||||||
\(84\) | 7.33683 | + | 0.898695i | 0.800513 | + | 0.0980557i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.12471 | + | 3.60824i | −0.229113 | + | 0.389086i | ||||
\(87\) | 18.6049 | − | 6.04509i | 1.99465 | − | 0.648101i | ||||
\(88\) | −10.5917 | − | 3.74553i | −1.12907 | − | 0.399275i | ||||
\(89\) | 0.806910 | − | 2.48341i | 0.0855323 | − | 0.263241i | −0.899139 | − | 0.437664i | \(-0.855806\pi\) |
0.984671 | + | 0.174423i | \(0.0558059\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.01674 | + | 0.330358i | −0.106583 | + | 0.0346309i | ||||
\(92\) | −0.833719 | − | 4.28250i | −0.0869213 | − | 0.446482i | ||||
\(93\) | −4.53682 | −0.470447 | ||||||||
\(94\) | −2.99946 | − | 6.89556i | −0.309371 | − | 0.711223i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.61528 | + | 17.5862i | −0.266920 | + | 1.79488i | ||||
\(97\) | 0.171369 | − | 0.235869i | 0.0173999 | − | 0.0239489i | −0.800228 | − | 0.599695i | \(-0.795288\pi\) |
0.817628 | + | 0.575746i | \(0.195288\pi\) | |||||||
\(98\) | 4.03092 | − | 6.84541i | 0.407184 | − | 0.691491i | ||||
\(99\) | 27.3214i | 2.74590i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.84171i | 0.780280i | 0.920756 | + | 0.390140i | \(0.127573\pi\) | ||||
−0.920756 | + | 0.390140i | \(0.872427\pi\) | |||||||
\(102\) | −21.3416 | − | 12.5670i | −2.11313 | − | 1.24432i | ||||
\(103\) | −7.73997 | + | 10.6532i | −0.762642 | + | 1.04969i | 0.234347 | + | 0.972153i | \(0.424705\pi\) |
−0.996990 | + | 0.0775342i | \(0.975295\pi\) | |||||||
\(104\) | −0.731407 | − | 2.46526i | −0.0717204 | − | 0.241739i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.9448 | + | 7.37074i | −1.64583 | + | 0.715909i | ||||
\(107\) | −7.00700 | −0.677392 | −0.338696 | − | 0.940896i | \(-0.609986\pi\) | ||||
−0.338696 | + | 0.940896i | \(0.609986\pi\) | |||||||
\(108\) | 23.9315 | − | 4.65899i | 2.30281 | − | 0.448312i | ||||
\(109\) | 2.56991 | − | 0.835013i | 0.246152 | − | 0.0799797i | −0.183342 | − | 0.983049i | \(-0.558692\pi\) |
0.429495 | + | 0.903069i | \(0.358692\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.79844 | − | 20.9235i | 0.645280 | − | 1.98597i | ||||
\(112\) | −3.99027 | − | 2.49019i | −0.377045 | − | 0.235301i | ||||
\(113\) | −4.34695 | + | 1.41241i | −0.408926 | + | 0.132868i | −0.506255 | − | 0.862384i | \(-0.668970\pi\) |
0.0973282 | + | 0.995252i | \(0.468970\pi\) | |||||||
\(114\) | 17.2593 | + | 10.1632i | 1.61649 | + | 0.951868i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.3558 | − | 1.51347i | −1.14720 | − | 0.140522i | ||||
\(117\) | −5.05932 | + | 3.67581i | −0.467734 | + | 0.339829i | ||||
\(118\) | −0.393283 | + | 1.77520i | −0.0362047 | + | 0.163420i | ||||
\(119\) | 5.30066 | − | 3.85116i | 0.485911 | − | 0.353035i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.86428 | + | 2.80757i | 0.351299 | + | 0.255233i | ||||
\(122\) | −16.4049 | + | 14.5181i | −1.48523 | + | 1.31441i | ||||
\(123\) | −6.19378 | + | 19.0625i | −0.558474 | + | 1.71881i | ||||
\(124\) | 2.61679 | + | 1.21931i | 0.234995 | + | 0.109497i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.47418 | + | 11.1679i | −0.220417 | + | 0.994919i | ||||
\(127\) | 8.20787 | + | 2.66690i | 0.728330 | + | 0.236649i | 0.649631 | − | 0.760250i | \(-0.274923\pi\) |
0.0786992 | + | 0.996898i | \(0.474923\pi\) | |||||||
\(128\) | 6.23490 | − | 9.44066i | 0.551093 | − | 0.834444i | ||||
\(129\) | −7.52882 | − | 5.47001i | −0.662876 | − | 0.481607i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.11250 | − | 7.03676i | −0.446681 | − | 0.614804i | 0.524999 | − | 0.851103i | \(-0.324066\pi\) |
−0.971680 | + | 0.236299i | \(0.924066\pi\) | |||||||
\(132\) | 10.5454 | − | 22.6317i | 0.917855 | − | 1.96983i | ||||
\(133\) | −4.28675 | + | 3.11451i | −0.371708 | + | 0.270062i | ||||
\(134\) | −0.412194 | − | 4.27432i | −0.0356082 | − | 0.369245i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.93211 | + | 12.9842i | 0.765922 | + | 1.11339i | ||||
\(137\) | −3.46540 | + | 1.12598i | −0.296069 | + | 0.0961988i | −0.453285 | − | 0.891365i | \(-0.649748\pi\) |
0.157216 | + | 0.987564i | \(0.449748\pi\) | |||||||
\(138\) | 9.65155 | − | 0.930747i | 0.821594 | − | 0.0792305i | ||||
\(139\) | −13.2832 | − | 4.31597i | −1.12666 | − | 0.366075i | −0.314357 | − | 0.949305i | \(-0.601789\pi\) |
−0.812307 | + | 0.583230i | \(0.801789\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.8941 | − | 5.16432i | 1.33853 | − | 0.434914i | ||||
\(142\) | −2.53593 | + | 1.10309i | −0.212811 | + | 0.0925693i | ||||
\(143\) | 3.61112i | 0.301977i | ||||||||
\(144\) | −26.7008 | − | 6.64085i | −2.22507 | − | 0.553404i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.47219 | + | 3.95781i | −0.370121 | + | 0.327551i | ||||
\(147\) | 14.2834 | + | 10.3775i | 1.17807 | + | 0.855921i | ||||
\(148\) | −9.54463 | + | 10.2413i | −0.784563 | + | 0.841829i | ||||
\(149\) | 2.61363i | 0.214117i | 0.994253 | + | 0.107059i | \(0.0341433\pi\) | ||||
−0.994253 | + | 0.107059i | \(0.965857\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.6178 | 0.864067 | 0.432034 | − | 0.901857i | \(-0.357796\pi\) | ||||
0.432034 | + | 0.901857i | \(0.357796\pi\) | |||||||
\(152\) | −7.22357 | − | 10.5006i | −0.585909 | − | 0.851711i | ||||
\(153\) | 22.5280 | − | 31.0072i | 1.82128 | − | 2.50678i | ||||
\(154\) | 4.37745 | + | 4.94637i | 0.352745 | + | 0.398590i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.60965 | − | 1.09209i | 0.449132 | − | 0.0874372i | ||||
\(157\) | 3.90358 | 0.311539 | 0.155770 | − | 0.987793i | \(-0.450214\pi\) | ||||
0.155770 | + | 0.987793i | \(0.450214\pi\) | |||||||
\(158\) | 3.57784 | − | 1.55631i | 0.284638 | − | 0.123813i | ||||
\(159\) | −12.6906 | − | 39.0575i | −1.00643 | − | 3.09746i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.792671 | + | 2.43959i | −0.0624712 | + | 0.192267i | ||||
\(162\) | 2.39991 | + | 24.8863i | 0.188555 | + | 1.95525i | ||||
\(163\) | −6.06584 | − | 18.6687i | −0.475114 | − | 1.46225i | −0.845805 | − | 0.533493i | \(-0.820879\pi\) |
0.370691 | − | 0.928756i | \(-0.379121\pi\) | |||||||
\(164\) | 8.69571 | − | 9.33042i | 0.679021 | − | 0.728583i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.28511 | − | 13.3262i | −0.0997441 | − | 1.03431i | ||||
\(167\) | −9.89993 | − | 13.6261i | −0.766080 | − | 1.05442i | −0.996684 | − | 0.0813708i | \(-0.974070\pi\) |
0.230604 | − | 0.973048i | \(-0.425930\pi\) | |||||||
\(168\) | 6.36002 | − | 8.29599i | 0.490686 | − | 0.640050i | ||||
\(169\) | 9.84852 | − | 7.15537i | 0.757579 | − | 0.550413i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.2189 | + | 25.0761i | −1.39323 | + | 1.91762i | ||||
\(172\) | 2.87244 | + | 5.17848i | 0.219021 | + | 0.394855i | ||||
\(173\) | −3.14623 | + | 9.68309i | −0.239203 | + | 0.736192i | 0.757333 | + | 0.653029i | \(0.226502\pi\) |
−0.996536 | + | 0.0831625i | \(0.973498\pi\) | |||||||
\(174\) | 5.98396 | − | 27.0104i | 0.453643 | − | 2.04765i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.1649 | + | 10.2196i | −0.916964 | + | 0.770328i | ||||
\(177\) | −3.84317 | − | 1.24872i | −0.288871 | − | 0.0938598i | ||||
\(178\) | −2.44733 | − | 2.76540i | −0.183435 | − | 0.207276i | ||||
\(179\) | 8.87687 | − | 12.2180i | 0.663488 | − | 0.913214i | −0.336102 | − | 0.941826i | \(-0.609109\pi\) |
0.999591 | + | 0.0286120i | \(0.00910873\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.1217 | − | 15.3077i | −0.826668 | − | 1.13781i | −0.988534 | − | 0.150998i | \(-0.951751\pi\) |
0.161866 | − | 0.986813i | \(-0.448249\pi\) | |||||||
\(182\) | −0.327017 | + | 1.47609i | −0.0242401 | + | 0.109415i | ||||
\(183\) | −28.6170 | − | 39.3879i | −2.11543 | − | 2.91164i | ||||
\(184\) | −5.81706 | − | 2.05709i | −0.428839 | − | 0.151651i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.25559 | + | 5.52872i | −0.238711 | + | 0.405385i | ||||
\(187\) | −6.83904 | − | 21.0484i | −0.500120 | − | 1.53921i | ||||
\(188\) | −10.5555 | − | 1.29296i | −0.769841 | − | 0.0942986i | ||||
\(189\) | −13.6329 | − | 4.42960i | −0.991649 | − | 0.322206i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.692493 | − | 2.13127i | −0.0501070 | − | 0.154214i | 0.922872 | − | 0.385106i | \(-0.125835\pi\) |
−0.972979 | + | 0.230893i | \(0.925835\pi\) | |||||||
\(192\) | 19.5544 | + | 15.8068i | 1.41122 | + | 1.14075i | ||||
\(193\) | 22.6952i | 1.63363i | 0.576896 | + | 0.816817i | \(0.304264\pi\) | ||||
−0.576896 | + | 0.816817i | \(0.695736\pi\) | |||||||
\(194\) | −0.164465 | − | 0.378093i | −0.0118079 | − | 0.0271455i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.44948 | − | 9.82441i | −0.389248 | − | 0.701744i | ||||
\(197\) | 10.5031 | + | 7.63095i | 0.748315 | + | 0.543682i | 0.895304 | − | 0.445456i | \(-0.146958\pi\) |
−0.146989 | + | 0.989138i | \(0.546958\pi\) | |||||||
\(198\) | 33.2947 | + | 19.6056i | 2.36615 | + | 1.39331i | ||||
\(199\) | −18.2166 | −1.29134 | −0.645672 | − | 0.763615i | \(-0.723423\pi\) | ||||
−0.645672 | + | 0.763615i | \(0.723423\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.54353 | 0.673149 | ||||||||
\(202\) | 9.55616 | + | 5.62715i | 0.672369 | + | 0.395925i | ||||
\(203\) | 5.92102 | + | 4.30187i | 0.415574 | + | 0.301932i | ||||
\(204\) | −30.6290 | + | 16.9895i | −2.14446 | + | 1.18951i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.42814 | + | 17.0768i | 0.517543 | + | 1.18980i | ||||
\(207\) | 15.0052i | 1.04294i | ||||||||
\(208\) | −3.52910 | − | 0.877735i | −0.244699 | − | 0.0608599i | ||||
\(209\) | 5.53086 | + | 17.0222i | 0.382578 | + | 1.17745i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.67102 | − | 0.542946i | −0.115037 | − | 0.0373779i | 0.250933 | − | 0.968005i | \(-0.419263\pi\) |
−0.365970 | + | 0.930627i | \(0.619263\pi\) | |||||||
\(212\) | −3.17725 | + | 25.9387i | −0.218215 | + | 1.78148i | ||||
\(213\) | −1.89925 | − | 5.84528i | −0.130134 | − | 0.400512i | ||||
\(214\) | −5.02816 | + | 8.53895i | −0.343718 | + | 0.583711i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 11.4954 | − | 32.5069i | 0.782165 | − | 2.21181i | ||||
\(217\) | −0.997675 | − | 1.37318i | −0.0677266 | − | 0.0932177i | ||||
\(218\) | 0.826569 | − | 3.73097i | 0.0559823 | − | 0.252693i | ||||
\(219\) | −7.80136 | − | 10.7377i | −0.527167 | − | 0.725583i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.97757 | − | 4.09828i | 0.200293 | − | 0.275680i | ||||
\(222\) | −20.6195 | − | 23.2993i | −1.38389 | − | 1.56375i | ||||
\(223\) | 1.48230 | + | 0.481630i | 0.0992625 | + | 0.0322523i | 0.358227 | − | 0.933634i | \(-0.383381\pi\) |
−0.258965 | + | 0.965887i | \(0.583381\pi\) | |||||||
\(224\) | −5.89801 | + | 3.07573i | −0.394077 | + | 0.205506i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.39813 | + | 6.31086i | −0.0930020 | + | 0.419792i | ||||
\(227\) | 2.84981 | − | 8.77081i | 0.189148 | − | 0.582139i | −0.810847 | − | 0.585259i | \(-0.800993\pi\) |
0.999995 | + | 0.00311955i | \(0.000992986\pi\) | |||||||
\(228\) | 24.7703 | − | 13.7398i | 1.64045 | − | 0.909939i | ||||
\(229\) | 6.64077 | − | 9.14023i | 0.438834 | − | 0.604003i | −0.531118 | − | 0.847298i | \(-0.678228\pi\) |
0.969953 | + | 0.243294i | \(0.0782280\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.8761 | + | 8.62852i | −0.781393 | + | 0.567715i | ||||
\(232\) | −10.7107 | + | 13.9711i | −0.703195 | + | 0.917245i | ||||
\(233\) | 7.30682 | + | 10.0570i | 0.478685 | + | 0.658854i | 0.978252 | − | 0.207422i | \(-0.0665072\pi\) |
−0.499566 | + | 0.866276i | \(0.666507\pi\) | |||||||
\(234\) | 0.848934 | + | 8.80318i | 0.0554966 | + | 0.575482i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.88110 | + | 1.75314i | 0.122449 | + | 0.114119i | ||||
\(237\) | 2.67957 | + | 8.24687i | 0.174057 | + | 0.535692i | ||||
\(238\) | −0.889430 | − | 9.22311i | −0.0576532 | − | 0.597845i | ||||
\(239\) | −8.53966 | + | 26.2824i | −0.552384 | + | 1.70006i | 0.150368 | + | 0.988630i | \(0.451954\pi\) |
−0.702752 | + | 0.711435i | \(0.748046\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.32369 | − | 4.07389i | −0.0852663 | − | 0.262423i | 0.899329 | − | 0.437273i | \(-0.144056\pi\) |
−0.984595 | + | 0.174851i | \(0.944056\pi\) | |||||||
\(242\) | 6.19437 | − | 2.69445i | 0.398189 | − | 0.173206i | ||||
\(243\) | −18.9940 | −1.21846 | ||||||||
\(244\) | 5.92016 | + | 30.4096i | 0.378999 | + | 1.94678i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 18.7855 | + | 21.2270i | 1.19772 | + | 1.35338i | ||||
\(247\) | −2.40802 | + | 3.31436i | −0.153219 | + | 0.210888i | ||||
\(248\) | 3.36368 | − | 2.31394i | 0.213594 | − | 0.146935i | ||||
\(249\) | 29.7542 | 1.88560 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.4000i | 0.845800i | 0.906176 | + | 0.422900i | \(0.138988\pi\) | ||||
−0.906176 | + | 0.422900i | \(0.861012\pi\) | |||||||
\(252\) | 11.8342 | + | 11.0291i | 0.745482 | + | 0.694770i | ||||
\(253\) | 7.00985 | + | 5.09295i | 0.440705 | + | 0.320191i | ||||
\(254\) | 9.13986 | − | 8.08862i | 0.573486 | − | 0.507525i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.03057 | − | 14.3726i | −0.439411 | − | 0.898286i | ||||
\(257\) | − | 7.81899i | − | 0.487735i | −0.969809 | − | 0.243868i | \(-0.921584\pi\) | ||
0.969809 | − | 0.243868i | \(-0.0784162\pi\) | |||||||
\(258\) | −12.0685 | + | 5.24963i | −0.751355 | + | 0.326827i | ||||
\(259\) | 7.82802 | − | 2.54348i | 0.486409 | − | 0.158044i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 40.7171 | + | 13.2298i | 2.52033 | + | 0.818904i | ||||
\(262\) | −12.2439 | + | 1.18074i | −0.756431 | + | 0.0729464i | ||||
\(263\) | 26.0980 | − | 8.47975i | 1.60927 | − | 0.522884i | 0.639894 | − | 0.768463i | \(-0.278978\pi\) |
0.969377 | + | 0.245579i | \(0.0789781\pi\) | |||||||
\(264\) | −20.0124 | − | 29.0912i | −1.23168 | − | 1.79044i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.719300 | + | 7.45891i | 0.0441031 | + | 0.457335i | ||||
\(267\) | 6.63968 | − | 4.82401i | 0.406342 | − | 0.295225i | ||||
\(268\) | −5.50461 | − | 2.56490i | −0.336248 | − | 0.156676i | ||||
\(269\) | 12.5408 | + | 17.2610i | 0.764629 | + | 1.05242i | 0.996815 | + | 0.0797498i | \(0.0254121\pi\) |
−0.232186 | + | 0.972671i | \(0.574588\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.864363 | + | 0.627996i | 0.0525063 | + | 0.0381481i | 0.613729 | − | 0.789517i | \(-0.289669\pi\) |
−0.561223 | + | 0.827665i | \(0.689669\pi\) | |||||||
\(272\) | 22.2326 | − | 1.56758i | 1.34805 | − | 0.0950485i | ||||
\(273\) | −3.19562 | − | 1.03832i | −0.193408 | − | 0.0628420i | ||||
\(274\) | −1.11459 | + | 5.03104i | −0.0673350 | + | 0.303936i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.79163 | − | 12.4296i | 0.348615 | − | 0.748173i | ||||
\(277\) | −5.48602 | + | 16.8842i | −0.329623 | + | 1.01448i | 0.639687 | + | 0.768635i | \(0.279064\pi\) |
−0.969310 | + | 0.245840i | \(0.920936\pi\) | |||||||
\(278\) | −14.7915 | + | 13.0902i | −0.887133 | + | 0.785098i | ||||
\(279\) | −8.03268 | − | 5.83608i | −0.480904 | − | 0.349397i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.77867 | + | 6.37807i | −0.523691 | + | 0.380484i | −0.817993 | − | 0.575229i | \(-0.804913\pi\) |
0.294301 | + | 0.955713i | \(0.404913\pi\) | |||||||
\(282\) | 5.11210 | − | 23.0750i | 0.304421 | − | 1.37410i | ||||
\(283\) | −18.7899 | + | 13.6517i | −1.11695 | + | 0.811509i | −0.983743 | − | 0.179580i | \(-0.942526\pi\) |
−0.133203 | + | 0.991089i | \(0.542526\pi\) | |||||||
\(284\) | −0.475502 | + | 3.88193i | −0.0282158 | + | 0.230350i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.40063 | + | 2.59131i | 0.260215 | + | 0.153228i | ||||
\(287\) | −7.13178 | + | 2.31726i | −0.420976 | + | 0.136783i | ||||
\(288\) | −27.2530 | + | 27.7730i | −1.60590 | + | 1.63654i | ||||
\(289\) | −4.34064 | + | 13.3591i | −0.255332 | + | 0.785830i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.871498 | − | 0.283167i | 0.0510881 | − | 0.0165995i | ||||
\(292\) | 1.61391 | + | 8.29005i | 0.0944470 | + | 0.485138i | ||||
\(293\) | 23.5633 | 1.37658 | 0.688291 | − | 0.725434i | \(-0.258361\pi\) | ||||
0.688291 | + | 0.725434i | \(0.258361\pi\) | |||||||
\(294\) | 22.8960 | − | 9.95939i | 1.33532 | − | 0.580844i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.63122 | + | 18.9804i | 0.327308 | + | 1.10322i | ||||
\(297\) | −28.4604 | + | 39.1724i | −1.65144 | + | 2.27301i | ||||
\(298\) | 3.18506 | + | 1.87552i | 0.184505 | + | 0.108646i | ||||
\(299\) | 1.98327i | 0.114696i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 3.48167i | − | 0.200680i | ||||||
\(302\) | 7.61927 | − | 12.9392i | 0.438440 | − | 0.744569i | ||||
\(303\) | −14.4869 | + | 19.9396i | −0.832252 | + | 1.14550i | ||||
\(304\) | −17.9799 | + | 1.26773i | −1.03122 | + | 0.0727094i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −21.6204 | − | 49.7038i | −1.23596 | − | 2.84138i | ||||
\(307\) | −29.1918 | −1.66607 | −0.833033 | − | 0.553223i | \(-0.813398\pi\) | ||||
−0.833033 | + | 0.553223i | \(0.813398\pi\) | |||||||
\(308\) | 9.16902 | − | 1.78503i | 0.522453 | − | 0.101712i | ||||
\(309\) | −39.3617 | + | 12.7894i | −2.23921 | + | 0.727563i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.303724 | − | 0.934766i | 0.0172226 | − | 0.0530057i | −0.942076 | − | 0.335400i | \(-0.891129\pi\) |
0.959298 | + | 0.282394i | \(0.0911286\pi\) | |||||||
\(312\) | 2.69458 | − | 7.61977i | 0.152551 | − | 0.431385i | ||||
\(313\) | 9.11237 | − | 2.96079i | 0.515062 | − | 0.167354i | −0.0399413 | − | 0.999202i | \(-0.512717\pi\) |
0.555003 | + | 0.831848i | \(0.312717\pi\) | |||||||
\(314\) | 2.80117 | − | 4.75702i | 0.158079 | − | 0.268454i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.670866 | − | 5.47686i | 0.0377392 | − | 0.308098i | ||||
\(317\) | −14.8949 | + | 10.8218i | −0.836580 | + | 0.607811i | −0.921413 | − | 0.388584i | \(-0.872964\pi\) |
0.0848334 | + | 0.996395i | \(0.472964\pi\) | |||||||
\(318\) | −56.7034 | − | 12.5622i | −3.17977 | − | 0.704455i | ||||
\(319\) | 20.0003 | − | 14.5311i | 1.11980 | − | 0.813584i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.8171 | − | 12.9449i | −0.994453 | − | 0.722512i | ||||
\(322\) | 2.40415 | + | 2.71660i | 0.133978 | + | 0.151390i | ||||
\(323\) | 7.75880 | − | 23.8791i | 0.431711 | − | 1.32867i | ||||
\(324\) | 32.0494 | + | 14.9336i | 1.78052 | + | 0.829643i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −27.1031 | − | 6.00450i | −1.50110 | − | 0.332559i | ||||
\(327\) | 8.07726 | + | 2.62446i | 0.446673 | + | 0.145133i | ||||
\(328\) | −5.13037 | − | 17.2923i | −0.283277 | − | 0.954807i | ||||
\(329\) | 5.05833 | + | 3.67509i | 0.278875 | + | 0.202614i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.25106 | + | 5.85108i | 0.233659 | + | 0.321604i | 0.909705 | − | 0.415255i | \(-0.136308\pi\) |
−0.676046 | + | 0.736860i | \(0.736308\pi\) | |||||||
\(332\) | −17.1619 | − | 7.99669i | −0.941883 | − | 0.438876i | ||||
\(333\) | 38.9525 | − | 28.3007i | 2.13458 | − | 1.55087i | ||||
\(334\) | −23.7093 | + | 2.28641i | −1.29731 | + | 0.125107i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.54586 | − | 13.7037i | −0.302551 | − | 0.747596i | ||||
\(337\) | 8.66935 | − | 2.81684i | 0.472250 | − | 0.153443i | −0.0632165 | − | 0.998000i | \(-0.520136\pi\) |
0.535466 | + | 0.844557i | \(0.320136\pi\) | |||||||
\(338\) | −1.65254 | − | 17.1363i | −0.0898865 | − | 0.932094i | ||||
\(339\) | −13.6625 | − | 4.43923i | −0.742047 | − | 0.241106i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.45277 | + | 1.77171i | −0.295284 | + | 0.0959436i | ||||
\(342\) | 17.4848 | + | 40.1965i | 0.945472 | + | 2.17358i | ||||
\(343\) | 14.8365i | 0.801096i | ||||||||
\(344\) | 8.37189 | + | 0.215591i | 0.451382 | + | 0.0116239i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.54241 | + | 10.7826i | 0.513003 | + | 0.579676i | ||||
\(347\) | 8.27687 | + | 6.01350i | 0.444326 | + | 0.322821i | 0.787351 | − | 0.616505i | \(-0.211452\pi\) |
−0.343026 | + | 0.939326i | \(0.611452\pi\) | |||||||
\(348\) | −28.6216 | − | 26.6746i | −1.53428 | − | 1.42991i | ||||
\(349\) | − | 4.76436i | − | 0.255030i | −0.991837 | − | 0.127515i | \(-0.959300\pi\) | ||
0.991837 | − | 0.127515i | \(-0.0407001\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.0829 | −0.591562 | ||||||||
\(352\) | 3.72445 | + | 22.1580i | 0.198514 | + | 1.18103i | ||||
\(353\) | 10.7305 | − | 14.7692i | 0.571126 | − | 0.786087i | −0.421562 | − | 0.906800i | \(-0.638518\pi\) |
0.992687 | + | 0.120713i | \(0.0385179\pi\) | |||||||
\(354\) | −4.27956 | + | 3.78734i | −0.227456 | + | 0.201295i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.12619 | + | 0.997969i | −0.271688 | + | 0.0528923i | ||||
\(357\) | 20.5930 | 1.08990 | ||||||||
\(358\) | −8.51923 | − | 19.5851i | −0.450255 | − | 1.03511i | ||||
\(359\) | 5.64467 | + | 17.3725i | 0.297914 | + | 0.916885i | 0.982227 | + | 0.187697i | \(0.0601022\pi\) |
−0.684313 | + | 0.729188i | \(0.739898\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.403370 | + | 1.24145i | −0.0212300 | + | 0.0653393i | ||||
\(362\) | −26.6353 | + | 2.56857i | −1.39992 | + | 0.135001i | ||||
\(363\) | 4.63917 | + | 14.2779i | 0.243493 | + | 0.749396i | ||||
\(364\) | 1.56414 | + | 1.45774i | 0.0819834 | + | 0.0764065i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −68.5347 | + | 6.60914i | −3.58237 | + | 0.345466i | ||||
\(367\) | −8.85005 | − | 12.1811i | −0.461969 | − | 0.635846i | 0.512947 | − | 0.858421i | \(-0.328554\pi\) |
−0.974916 | + | 0.222575i | \(0.928554\pi\) | |||||||
\(368\) | −6.68111 | + | 5.61270i | −0.348277 | + | 0.292582i | ||||
\(369\) | −35.4880 | + | 25.7835i | −1.84743 | + | 1.34224i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.03100 | − | 12.4301i | 0.468866 | − | 0.645339i | ||||
\(372\) | 4.40129 | + | 7.93472i | 0.228196 | + | 0.411396i | ||||
\(373\) | 0.219092 | − | 0.674295i | 0.0113441 | − | 0.0349137i | −0.945224 | − | 0.326422i | \(-0.894157\pi\) |
0.956568 | + | 0.291508i | \(0.0941570\pi\) | |||||||
\(374\) | −30.5579 | − | 6.76988i | −1.58011 | − | 0.350062i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.15020 | + | 11.9355i | −0.471886 | + | 0.615526i | ||||
\(377\) | 5.38166 | + | 1.74861i | 0.277170 | + | 0.0900579i | ||||
\(378\) | −15.1809 | + | 13.4349i | −0.780822 | + | 0.691015i | ||||
\(379\) | 10.8210 | − | 14.8938i | 0.555838 | − | 0.765045i | −0.434952 | − | 0.900454i | \(-0.643235\pi\) |
0.990790 | + | 0.135408i | \(0.0432347\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.9437 | + | 21.9446i | 0.816821 | + | 1.12426i | ||||
\(382\) | −3.09416 | − | 0.685490i | −0.158311 | − | 0.0350727i | ||||
\(383\) | 10.5490 | + | 14.5194i | 0.539027 | + | 0.741907i | 0.988472 | − | 0.151401i | \(-0.0483783\pi\) |
−0.449445 | + | 0.893308i | \(0.648378\pi\) | |||||||
\(384\) | 33.2947 | − | 12.4868i | 1.69906 | − | 0.637214i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 27.6571 | + | 16.2859i | 1.40771 | + | 0.828929i | ||||
\(387\) | −6.29365 | − | 19.3699i | −0.319924 | − | 0.984625i | ||||
\(388\) | −0.578774 | − | 0.0708946i | −0.0293828 | − | 0.00359913i | ||||
\(389\) | 22.7077 | + | 7.37819i | 1.15133 | + | 0.374089i | 0.821643 | − | 0.570002i | \(-0.193058\pi\) |
0.329685 | + | 0.944091i | \(0.393058\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.75608 | − | 11.5600i | −0.189953 | − | 0.584616i | ||||
\(392\) | −15.8828 | − | 0.409011i | −0.802204 | − | 0.0206582i | ||||
\(393\) | − | 27.3377i | − | 1.37900i | ||||||
\(394\) | 16.8362 | − | 7.32350i | 0.848198 | − | 0.368953i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 47.7840 | − | 26.5052i | 2.40124 | − | 1.33194i | ||||
\(397\) | −1.16804 | − | 0.848630i | −0.0586222 | − | 0.0425915i | 0.558088 | − | 0.829782i | \(-0.311535\pi\) |
−0.616710 | + | 0.787190i | \(0.711535\pi\) | |||||||
\(398\) | −13.0721 | + | 22.1994i | −0.655246 | + | 1.11275i | ||||
\(399\) | −16.6539 | −0.833740 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.0682 | −1.30178 | −0.650891 | − | 0.759171i | \(-0.725605\pi\) | ||||
−0.650891 | + | 0.759171i | \(0.725605\pi\) | |||||||
\(402\) | 6.84836 | − | 11.6300i | 0.341565 | − | 0.580054i | ||||
\(403\) | −1.06170 | − | 0.771367i | −0.0528868 | − | 0.0384245i | ||||
\(404\) | 13.7148 | − | 7.60744i | 0.682338 | − | 0.378484i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.49126 | − | 4.12855i | 0.471043 | − | 0.204897i | ||||
\(407\) | − | 27.8026i | − | 1.37813i | ||||||
\(408\) | −1.27515 | + | 49.5171i | −0.0631294 | + | 2.45146i | ||||
\(409\) | 0.312601 | + | 0.962088i | 0.0154571 | + | 0.0475722i | 0.958488 | − | 0.285134i | \(-0.0920382\pi\) |
−0.943030 | + | 0.332706i | \(0.892038\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.8918 | − | 3.53897i | −0.537254 | − | 0.174564i | ||||
\(412\) | 26.1407 | + | 3.20200i | 1.28786 | + | 0.157751i | ||||
\(413\) | −0.467180 | − | 1.43783i | −0.0229884 | − | 0.0707512i | ||||
\(414\) | 18.2859 | + | 10.7676i | 0.898701 | + | 0.529200i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.60208 | + | 3.67081i | −0.176607 | + | 0.179976i | ||||
\(417\) | −25.8025 | − | 35.5140i | −1.26355 | − | 1.73913i | ||||
\(418\) | 24.7127 | + | 5.47494i | 1.20874 | + | 0.267788i | ||||
\(419\) | −19.6696 | − | 27.0728i | −0.960920 | − | 1.32259i | −0.946502 | − | 0.322697i | \(-0.895410\pi\) |
−0.0144183 | − | 0.999896i | \(-0.504590\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.1696 | + | 22.2556i | −0.788060 | + | 1.08467i | 0.206287 | + | 0.978492i | \(0.433862\pi\) |
−0.994347 | + | 0.106180i | \(0.966138\pi\) | |||||||
\(422\) | −1.86076 | + | 1.64674i | −0.0905803 | + | 0.0801620i | ||||
\(423\) | 34.7847 | + | 11.3022i | 1.69129 | + | 0.549533i | ||||
\(424\) | 29.3297 | + | 22.4853i | 1.42438 | + | 1.09198i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.48612 | − | 1.88004i | −0.411154 | − | 0.0910883i | ||||
\(427\) | 5.62868 | − | 17.3233i | 0.272391 | − | 0.838333i | ||||
\(428\) | 6.79767 | + | 12.2550i | 0.328578 | + | 0.592366i | ||||
\(429\) | −6.67126 | + | 9.18220i | −0.322092 | + | 0.443321i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.6348 | − | 15.7186i | 1.04211 | − | 0.757138i | 0.0714143 | − | 0.997447i | \(-0.477249\pi\) |
0.970696 | + | 0.240309i | \(0.0772488\pi\) | |||||||
\(432\) | −31.3649 | − | 37.3354i | −1.50904 | − | 1.79630i | ||||
\(433\) | 12.1996 | + | 16.7912i | 0.586273 | + | 0.806936i | 0.994366 | − | 0.106005i | \(-0.0338059\pi\) |
−0.408092 | + | 0.912941i | \(0.633806\pi\) | |||||||
\(434\) | −2.38933 | + | 0.230415i | −0.114691 | + | 0.0110603i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.95353 | − | 3.68459i | −0.189340 | − | 0.176460i | ||||
\(437\) | 3.03762 | + | 9.34882i | 0.145309 | + | 0.447215i | ||||
\(438\) | −18.6834 | + | 1.80174i | −0.892729 | + | 0.0860903i | ||||
\(439\) | 0.0935999 | − | 0.288071i | 0.00446728 | − | 0.0137489i | −0.948798 | − | 0.315883i | \(-0.897699\pi\) |
0.953265 | + | 0.302134i | \(0.0976992\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.9401 | + | 36.7478i | 0.568575 | + | 1.74989i | ||||
\(442\) | −2.85761 | − | 6.56946i | −0.135923 | − | 0.312477i | ||||
\(443\) | 33.9046 | 1.61086 | 0.805428 | − | 0.592693i | \(-0.201935\pi\) | ||||
0.805428 | + | 0.592693i | \(0.201935\pi\) | |||||||
\(444\) | −43.1896 | + | 8.40817i | −2.04969 | + | 0.399034i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.65062 | − | 1.46077i | 0.0781591 | − | 0.0691694i | ||||
\(447\) | −4.82848 | + | 6.64583i | −0.228379 | + | 0.314337i | ||||
\(448\) | −0.484177 | + | 9.39462i | −0.0228752 | + | 0.443854i | ||||
\(449\) | −12.6049 | −0.594860 | −0.297430 | − | 0.954744i | \(-0.596129\pi\) | ||||
−0.297430 | + | 0.954744i | \(0.596129\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.3298i | 1.19273i | ||||||||
\(452\) | 6.68733 | + | 6.23242i | 0.314545 | + | 0.293148i | ||||
\(453\) | 26.9986 | + | 19.6156i | 1.26850 | + | 0.921621i | ||||
\(454\) | −8.64339 | − | 9.76672i | −0.405654 | − | 0.458375i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.03124 | − | 40.0454i | 0.0482923 | − | 1.87530i | ||||
\(457\) | 2.58934i | 0.121124i | 0.998164 | + | 0.0605622i | \(0.0192893\pi\) | ||||
−0.998164 | + | 0.0605622i | \(0.980711\pi\) | |||||||
\(458\) | −6.37322 | − | 14.6516i | −0.297801 | − | 0.684624i | ||||
\(459\) | 64.5997 | − | 20.9897i | 3.01526 | − | 0.979716i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.49523 | + | 2.11043i | 0.302513 | + | 0.0982925i | 0.456340 | − | 0.889805i | \(-0.349160\pi\) |
−0.153827 | + | 0.988098i | \(0.549160\pi\) | |||||||
\(462\) | 1.99277 | + | 20.6644i | 0.0927121 | + | 0.961394i | ||||
\(463\) | −20.7530 | + | 6.74304i | −0.964472 | + | 0.313376i | −0.748582 | − | 0.663042i | \(-0.769265\pi\) |
−0.215889 | + | 0.976418i | \(0.569265\pi\) | |||||||
\(464\) | 9.33964 | + | 23.0780i | 0.433582 | + | 1.07137i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.4990 | − | 1.68752i | 0.810628 | − | 0.0781729i | ||||
\(467\) | −2.43118 | + | 1.76636i | −0.112502 | + | 0.0817373i | −0.642614 | − | 0.766190i | \(-0.722150\pi\) |
0.530112 | + | 0.847928i | \(0.322150\pi\) | |||||||
\(468\) | 11.3370 | + | 5.28254i | 0.524054 | + | 0.244186i | ||||
\(469\) | 2.09868 | + | 2.88859i | 0.0969081 | + | 0.133383i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.92583 | + | 7.21154i | 0.457358 | + | 0.332290i | ||||
\(472\) | 3.48629 | − | 1.03433i | 0.160469 | − | 0.0476089i | ||||
\(473\) | −11.1850 | − | 3.63421i | −0.514285 | − | 0.167101i | ||||
\(474\) | 11.9727 | + | 2.65247i | 0.549926 | + | 0.121832i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −11.8778 | − | 5.53453i | −0.544419 | − | 0.253675i | ||||
\(477\) | 27.7736 | − | 85.4782i | 1.27166 | − | 3.91378i | ||||
\(478\) | 25.9005 | + | 29.2667i | 1.18466 | + | 1.33863i | ||||
\(479\) | 15.3717 | + | 11.1682i | 0.702349 | + | 0.510287i | 0.880697 | − | 0.473681i | \(-0.157075\pi\) |
−0.178347 | + | 0.983968i | \(0.557075\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.14843 | − | 3.74055i | 0.234748 | − | 0.170555i | ||||
\(482\) | −5.91444 | − | 1.31030i | −0.269395 | − | 0.0596827i | ||||
\(483\) | −6.52251 | + | 4.73888i | −0.296785 | + | 0.215627i | ||||
\(484\) | 1.16148 | − | 9.48216i | 0.0527945 | − | 0.431007i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.6299 | + | 23.1466i | −0.618265 | + | 1.04995i | ||||
\(487\) | 1.80539 | − | 0.586607i | 0.0818101 | − | 0.0265817i | −0.267826 | − | 0.963467i | \(-0.586305\pi\) |
0.349636 | + | 0.936886i | \(0.386305\pi\) | |||||||
\(488\) | 41.3064 | + | 14.6072i | 1.86985 | + | 0.661236i | ||||
\(489\) | 19.0651 | − | 58.6762i | 0.862151 | − | 2.65343i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.3750 | − | 9.54451i | 1.32567 | − | 0.430738i | 0.441234 | − | 0.897392i | \(-0.354541\pi\) |
0.884440 | + | 0.466654i | \(0.154541\pi\) | |||||||
\(492\) | 39.3482 | − | 7.66034i | 1.77396 | − | 0.345355i | ||||
\(493\) | −34.6801 | −1.56191 | ||||||||
\(494\) | 2.31101 | + | 5.31285i | 0.103977 | + | 0.239036i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.406095 | − | 5.75955i | −0.0182342 | − | 0.258611i | ||||
\(497\) | 1.35156 | − | 1.86027i | 0.0606258 | − | 0.0834443i | ||||
\(498\) | 21.3514 | − | 36.2594i | 0.956778 | − | 1.62482i | ||||
\(499\) | − | 10.5948i | − | 0.474289i | −0.971474 | − | 0.237145i | \(-0.923788\pi\) | ||
0.971474 | − | 0.237145i | \(-0.0762115\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 52.9371i | − | 2.36506i | ||||||
\(502\) | 16.3297 | + | 9.61572i | 0.728828 | + | 0.429171i | ||||
\(503\) | −15.5618 | + | 21.4189i | −0.693865 | + | 0.955024i | 0.306130 | + | 0.951990i | \(0.400966\pi\) |
−0.999995 | + | 0.00303389i | \(0.999034\pi\) | |||||||
\(504\) | 21.9325 | − | 6.50707i | 0.976953 | − | 0.289848i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 11.2366 | − | 4.88776i | 0.499529 | − | 0.217288i | ||||
\(507\) | 38.2613 | 1.69925 | ||||||||
\(508\) | −3.29836 | − | 16.9424i | −0.146341 | − | 0.751699i | ||||
\(509\) | 17.5095 | − | 5.68919i | 0.776096 | − | 0.252169i | 0.105923 | − | 0.994374i | \(-0.466220\pi\) |
0.670172 | + | 0.742205i | \(0.266220\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.53445 | − | 4.72255i | 0.0678800 | − | 0.208913i | ||||
\(512\) | −22.5600 | − | 1.74596i | −0.997019 | − | 0.0771615i | ||||
\(513\) | −52.2431 | + | 16.9748i | −2.30659 | + | 0.749456i | ||||
\(514\) | −9.52847 | − | 5.61084i | −0.420283 | − | 0.247484i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.26292 | + | 18.4742i | −0.0996196 | + | 0.813281i | ||||
\(517\) | 17.0863 | − | 12.4139i | 0.751453 | − | 0.545963i | ||||
\(518\) | 2.51776 | − | 11.3646i | 0.110624 | − | 0.499334i | ||||
\(519\) | −25.8888 | + | 18.8093i | −1.13639 | + | 0.825637i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.7039 | + | 23.7608i | 1.43278 | + | 1.04098i | 0.989490 | + | 0.144603i | \(0.0461906\pi\) |
0.443295 | + | 0.896376i | \(0.353809\pi\) | |||||||
\(522\) | 45.3405 | − | 40.1256i | 1.98450 | − | 1.75625i | ||||
\(523\) | 5.37852 | − | 16.5534i | 0.235186 | − | 0.723828i | −0.761911 | − | 0.647682i | \(-0.775738\pi\) |
0.997097 | − | 0.0761461i | \(-0.0242615\pi\) | |||||||
\(524\) | −7.34723 | + | 15.7681i | −0.320965 | + | 0.688832i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.39400 | − | 37.8888i | 0.365996 | − | 1.65203i | ||||
\(527\) | 7.64925 | + | 2.48539i | 0.333206 | + | 0.108265i | ||||
\(528\) | −49.8122 | + | 3.51216i | −2.16780 | + | 0.152847i | ||||
\(529\) | −14.7575 | − | 10.7220i | −0.641630 | − | 0.466172i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.19820 | − | 7.15471i | −0.225583 | − | 0.310488i | ||||
\(532\) | 9.60582 | + | 4.47589i | 0.416465 | + | 0.194054i | ||||
\(533\) | −4.69052 | + | 3.40786i | −0.203169 | + | 0.147611i | ||||
\(534\) | −1.11411 | − | 11.5530i | −0.0482124 | − | 0.499947i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.07573 | + | 4.86754i | −0.305625 | + | 0.210246i | ||||
\(537\) | 45.1434 | − | 14.6680i | 1.94808 | − | 0.632970i | ||||
\(538\) | 30.0340 | − | 2.89633i | 1.29486 | − | 0.124870i | ||||
\(539\) | 21.2197 | + | 6.89469i | 0.913996 | + | 0.296975i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.69917 | + | 2.50161i | −0.331013 | + | 0.107553i | −0.469808 | − | 0.882768i | \(-0.655677\pi\) |
0.138795 | + | 0.990321i | \(0.455677\pi\) | |||||||
\(542\) | 1.38556 | − | 0.602695i | 0.0595147 | − | 0.0258880i | ||||
\(543\) | − | 59.4701i | − | 2.55211i | ||||||
\(544\) | 14.0436 | − | 28.2182i | 0.602115 | − | 1.20985i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.55848 | + | 3.14920i | −0.152289 | + | 0.134773i | ||||
\(547\) | −20.7126 | − | 15.0486i | −0.885607 | − | 0.643431i | 0.0491221 | − | 0.998793i | \(-0.484358\pi\) |
−0.934729 | + | 0.355362i | \(0.884358\pi\) | |||||||
\(548\) | 5.33117 | + | 4.96851i | 0.227736 | + | 0.212244i | ||||
\(549\) | − | 106.551i | − | 4.54747i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.0465 | 1.19482 | ||||||||
\(552\) | −10.9911 | − | 15.9772i | −0.467810 | − | 0.680036i | ||||
\(553\) | −1.90686 | + | 2.62457i | −0.0810881 | + | 0.111608i | ||||
\(554\) | 16.6389 | + | 18.8014i | 0.706921 | + | 0.798796i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.33790 | + | 27.4188i | 0.226377 | + | 1.16281i | ||||
\(557\) | 1.74254 | 0.0738336 | 0.0369168 | − | 0.999318i | \(-0.488246\pi\) | ||||
0.0369168 | + | 0.999318i | \(0.488246\pi\) | |||||||
\(558\) | −12.8762 | + | 5.60095i | −0.545094 | + | 0.237107i | ||||
\(559\) | −0.831844 | − | 2.56015i | −0.0351832 | − | 0.108283i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.4952 | − | 66.1555i | 0.907529 | − | 2.79309i | ||||
\(562\) | 1.47303 | + | 15.2748i | 0.0621359 | + | 0.644329i | ||||
\(563\) | 7.94233 | + | 24.4440i | 0.334729 | + | 1.03019i | 0.966855 | + | 0.255325i | \(0.0821826\pi\) |
−0.632126 | + | 0.774866i | \(0.717817\pi\) | |||||||
\(564\) | −24.4515 | − | 22.7882i | −1.02959 | − | 0.959555i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.15288 | + | 32.6943i | 0.132525 | + | 1.37425i | ||||
\(567\) | −12.2191 | − | 16.8181i | −0.513154 | − | 0.706296i | ||||
\(568\) | 4.38943 | + | 3.36510i | 0.184176 | + | 0.141197i | ||||
\(569\) | −11.5604 | + | 8.39915i | −0.484639 | + | 0.352111i | −0.803119 | − | 0.595819i | \(-0.796828\pi\) |
0.318480 | + | 0.947930i | \(0.396828\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.7151 | − | 16.1245i | 0.490263 | − | 0.674789i | −0.490174 | − | 0.871625i | \(-0.663067\pi\) |
0.980436 | + | 0.196836i | \(0.0630666\pi\) | |||||||
\(572\) | 6.31571 | − | 3.50324i | 0.264073 | − | 0.146478i | ||||
\(573\) | 2.17652 | − | 6.69863i | 0.0909253 | − | 0.279839i | ||||
\(574\) | −2.29382 | + | 10.3539i | −0.0957424 | + | 0.432162i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 14.2885 | + | 53.1410i | 0.595356 | + | 2.21421i | ||||
\(577\) | −14.6528 | − | 4.76100i | −0.610006 | − | 0.198203i | −0.0123079 | − | 0.999924i | \(-0.503918\pi\) |
−0.597698 | + | 0.801721i | \(0.703918\pi\) | |||||||
\(578\) | 13.1650 | + | 14.8760i | 0.547593 | + | 0.618761i | ||||
\(579\) | −41.9275 | + | 57.7083i | −1.74245 | + | 2.39827i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.54313 | + | 9.00585i | 0.271455 | + | 0.373626i | ||||
\(582\) | 0.280303 | − | 1.26523i | 0.0116189 | − | 0.0524456i | ||||
\(583\) | −30.5054 | − | 41.9870i | −1.26340 | − | 1.73892i | ||||
\(584\) | 11.2606 | + | 3.98210i | 0.465969 | + | 0.164781i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.9088 | − | 28.7150i | 0.698497 | − | 1.18620i | ||||
\(587\) | 4.25364 | + | 13.0914i | 0.175567 | + | 0.540338i | 0.999659 | − | 0.0261173i | \(-0.00831433\pi\) |
−0.824092 | + | 0.566455i | \(0.808314\pi\) | |||||||
\(588\) | 4.29313 | − | 35.0485i | 0.177046 | − | 1.44538i | ||||
\(589\) | −6.18610 | − | 2.00998i | −0.254894 | − | 0.0828200i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.6092 | + | 38.8072i | 0.518675 | + | 1.59632i | ||||
\(592\) | 27.1711 | + | 6.75782i | 1.11672 | + | 0.277745i | ||||
\(593\) | 6.37493i | 0.261787i | 0.991396 | + | 0.130894i | \(0.0417846\pi\) | ||||
−0.991396 | + | 0.130894i | \(0.958215\pi\) | |||||||
\(594\) | 27.3138 | + | 62.7926i | 1.12070 | + | 2.57641i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.57114 | − | 2.53555i | 0.187241 | − | 0.103860i | ||||
\(597\) | −46.3205 | − | 33.6538i | −1.89577 | − | 1.37736i | ||||
\(598\) | 2.41688 | + | 1.42318i | 0.0988335 | + | 0.0581981i | ||||
\(599\) | 38.8351 | 1.58676 | 0.793380 | − | 0.608727i | \(-0.208319\pi\) | ||||
0.793380 | + | 0.608727i | \(0.208319\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.0478 | 1.67438 | 0.837188 | − | 0.546916i | \(-0.184198\pi\) | ||||
0.837188 | + | 0.546916i | \(0.184198\pi\) | |||||||
\(602\) | −4.24287 | − | 2.49842i | −0.172927 | − | 0.101828i | ||||
\(603\) | 16.8973 | + | 12.2766i | 0.688112 | + | 0.499942i | ||||
\(604\) | −10.3006 | − | 18.5702i | −0.419127 | − | 0.755609i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.9033 | + | 31.9627i | 0.564782 | + | 1.29840i | ||||
\(607\) | 28.6948i | 1.16469i | 0.812943 | + | 0.582343i | \(0.197864\pi\) | ||||
−0.812943 | + | 0.582343i | \(0.802136\pi\) | |||||||
\(608\) | −11.3574 | + | 22.8206i | −0.460601 | + | 0.925499i | ||||
\(609\) | 7.10833 | + | 21.8772i | 0.288044 | + | 0.886509i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.59756 | + | 1.49384i | 0.185997 | + | 0.0604342i | ||||
\(612\) | −76.0853 | − | 9.31976i | −3.07557 | − | 0.376729i | ||||
\(613\) | 2.30831 | + | 7.10423i | 0.0932316 | + | 0.286937i | 0.986789 | − | 0.162012i | \(-0.0517983\pi\) |
−0.893557 | + | 0.448949i | \(0.851798\pi\) | |||||||
\(614\) | −20.9478 | + | 35.5741i | −0.845385 | + | 1.43565i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.40432 | − | 12.4546i | 0.177455 | − | 0.501809i | ||||
\(617\) | 23.8187 | + | 32.7837i | 0.958906 | + | 1.31982i | 0.947456 | + | 0.319886i | \(0.103645\pi\) |
0.0114498 | + | 0.999934i | \(0.496355\pi\) | |||||||
\(618\) | −12.6601 | + | 57.1450i | −0.509263 | + | 2.29871i | ||||
\(619\) | −5.89273 | − | 8.11065i | −0.236849 | − | 0.325994i | 0.674003 | − | 0.738729i | \(-0.264574\pi\) |
−0.910851 | + | 0.412735i | \(0.864574\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.6308 | + | 21.5140i | −0.627242 | + | 0.863325i | ||||
\(622\) | −0.921185 | − | 1.04091i | −0.0369362 | − | 0.0417366i | ||||
\(623\) | 2.92021 | + | 0.948834i | 0.116996 | + | 0.0380142i | ||||
\(624\) | −7.35208 | − | 8.75159i | −0.294319 | − | 0.350344i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.93085 | − | 13.2293i | 0.117140 | − | 0.528748i | ||||
\(627\) | −17.3836 | + | 53.5012i | −0.694234 | + | 2.13663i | ||||
\(628\) | −3.78696 | − | 6.82719i | −0.151116 | − | 0.272435i | ||||
\(629\) | −22.9248 | + | 31.5533i | −0.914073 | + | 1.25811i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.4964 | + | 17.7976i | −0.975184 | + | 0.708513i | −0.956627 | − | 0.291315i | \(-0.905907\pi\) |
−0.0185571 | + | 0.999828i | \(0.505907\pi\) | |||||||
\(632\) | −6.19287 | − | 4.74769i | −0.246339 | − | 0.188853i | ||||
\(633\) | −3.24593 | − | 4.46765i | −0.129014 | − | 0.177573i | ||||
\(634\) | 2.49930 | + | 25.9170i | 0.0992600 | + | 1.02929i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −55.9986 | + | 60.0860i | −2.22049 | + | 2.38256i | ||||
\(637\) | 1.57814 | + | 4.85702i | 0.0625283 | + | 0.192442i | ||||
\(638\) | −3.35597 | − | 34.8004i | −0.132864 | − | 1.37776i | ||||
\(639\) | 4.15654 | − | 12.7925i | 0.164430 | − | 0.506064i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.1688 | − | 37.4516i | −0.480637 | − | 1.47925i | −0.838201 | − | 0.545361i | \(-0.816393\pi\) |
0.357564 | − | 0.933889i | \(-0.383607\pi\) | |||||||
\(642\) | −28.5604 | + | 12.4233i | −1.12719 | + | 0.490310i | ||||
\(643\) | 15.6623 | 0.617660 | 0.308830 | − | 0.951117i | \(-0.400063\pi\) | ||||
0.308830 | + | 0.951117i | \(0.400063\pi\) | |||||||
\(644\) | 5.03573 | − | 0.980359i | 0.198436 | − | 0.0386316i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −23.5322 | − | 26.5906i | −0.925862 | − | 1.04619i | ||||
\(647\) | −19.5134 | + | 26.8579i | −0.767152 | + | 1.05589i | 0.229434 | + | 0.973324i | \(0.426313\pi\) |
−0.996585 | + | 0.0825693i | \(0.973687\pi\) | |||||||
\(648\) | 41.1969 | − | 28.3402i | 1.61837 | − | 1.11331i | ||||
\(649\) | −5.10673 | −0.200457 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 5.33479i | − | 0.209087i | ||||||
\(652\) | −26.7662 | + | 28.7199i | −1.04825 | + | 1.12476i | ||||
\(653\) | −3.13976 | − | 2.28117i | −0.122868 | − | 0.0892690i | 0.524654 | − | 0.851316i | \(-0.324195\pi\) |
−0.647522 | + | 0.762047i | \(0.724195\pi\) | |||||||
\(654\) | 8.99442 | − | 7.95991i | 0.351710 | − | 0.311257i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −24.7544 | − | 6.15677i | −0.966499 | − | 0.240381i | ||||
\(657\) | − | 29.0471i | − | 1.13323i | ||||||
\(658\) | 8.10839 | − | 3.52702i | 0.316098 | − | 0.137498i | ||||
\(659\) | −38.7539 | + | 12.5919i | −1.50964 | + | 0.490511i | −0.942811 | − | 0.333327i | \(-0.891829\pi\) |
−0.566826 | + | 0.823838i | \(0.691829\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.9253 | − | 11.6728i | −1.39733 | − | 0.454020i | −0.489004 | − | 0.872282i | \(-0.662640\pi\) |
−0.908327 | + | 0.418261i | \(0.862640\pi\) | |||||||
\(662\) | 10.1808 | − | 0.981789i | 0.395689 | − | 0.0381583i | ||||
\(663\) | 15.1425 | − | 4.92009i | 0.588085 | − | 0.191081i | ||||
\(664\) | −22.0603 | + | 15.1757i | −0.856105 | + | 0.588931i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.53608 | − | 67.7771i | −0.253268 | − | 2.62631i | ||||
\(667\) | 10.9844 | − | 7.98063i | 0.425318 | − | 0.309011i | ||||
\(668\) | −14.2273 | + | 30.5336i | −0.550471 | + | 1.18138i | ||||
\(669\) | 2.87936 | + | 3.96311i | 0.111323 | + | 0.153223i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −49.7762 | − | 36.1645i | −1.92159 | − | 1.39612i | ||||
\(672\) | −20.6794 | − | 3.07527i | −0.797724 | − | 0.118631i | ||||
\(673\) | −1.57662 | − | 0.512274i | −0.0607742 | − | 0.0197467i | 0.278472 | − | 0.960444i | \(-0.410172\pi\) |
−0.339246 | + | 0.940698i | \(0.610172\pi\) | |||||||
\(674\) | 2.78836 | − | 12.5861i | 0.107404 | − | 0.484798i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.0687 | − | 10.2831i | −0.848798 | − | 0.395502i | ||||
\(677\) | −0.0701106 | + | 0.215778i | −0.00269457 | + | 0.00829304i | −0.952395 | − | 0.304868i | \(-0.901388\pi\) |
0.949700 | + | 0.313161i | \(0.101388\pi\) | |||||||
\(678\) | −15.2139 | + | 13.4640i | −0.584286 | + | 0.517083i | ||||
\(679\) | 0.277355 | + | 0.201510i | 0.0106439 | + | 0.00773325i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.4497 | − | 17.0372i | 0.898596 | − | 0.652868i | ||||
\(682\) | −1.75380 | + | 7.91628i | −0.0671563 | + | 0.303130i | ||||
\(683\) | 24.0637 | − | 17.4833i | 0.920773 | − | 0.668981i | −0.0229435 | − | 0.999737i | \(-0.507304\pi\) |
0.943716 | + | 0.330756i | \(0.107304\pi\) | |||||||
\(684\) | 61.5317 | + | 7.53707i | 2.35272 | + | 0.288187i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.0802 | + | 10.6465i | 0.690306 | + | 0.406487i | ||||
\(687\) | 33.7717 | − | 10.9731i | 1.28847 | − | 0.418649i | ||||
\(688\) | 6.27032 | − | 10.0475i | 0.239054 | − | 0.383059i | ||||
\(689\) | 3.67089 | − | 11.2978i | 0.139850 | − | 0.430413i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.9436 | − | 9.72925i | 1.13911 | − | 0.370118i | 0.322077 | − | 0.946714i | \(-0.395619\pi\) |
0.817030 | + | 0.576595i | \(0.195619\pi\) | |||||||
\(692\) | 19.9876 | − | 3.89119i | 0.759813 | − | 0.147921i | ||||
\(693\) | −32.1269 | −1.22040 | ||||||||
\(694\) | 13.2676 | − | 5.77122i | 0.503633 | − | 0.219072i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −53.0452 | + | 15.7377i | −2.01067 | + | 0.596538i | ||||
\(697\) | 20.8859 | − | 28.7469i | 0.791108 | − | 1.08887i | ||||
\(698\) | −5.80600 | − | 3.41886i | −0.219760 | − | 0.129406i | ||||
\(699\) | 39.0712i | 1.47781i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.30506i | 0.0870611i | 0.999052 | + | 0.0435305i | \(0.0138606\pi\) | ||||
−0.999052 | + | 0.0435305i | \(0.986139\pi\) | |||||||
\(702\) | −7.95301 | + | 13.5060i | −0.300167 | + | 0.509751i | ||||
\(703\) | 18.5398 | − | 25.5178i | 0.699240 | − | 0.962422i | ||||
\(704\) | 29.6751 | + | 11.3617i | 1.11842 | + | 0.428209i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.2982 | − | 23.6748i | −0.387576 | − | 0.891012i | ||||
\(707\) | −9.22096 | −0.346790 | ||||||||
\(708\) | 1.54440 | + | 7.93297i | 0.0580419 | + | 0.298139i | ||||
\(709\) | −25.4956 | + | 8.28402i | −0.957508 | + | 0.311113i | −0.745763 | − | 0.666212i | \(-0.767915\pi\) |
−0.211745 | + | 0.977325i | \(0.567915\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.86429 | + | 18.0484i | −0.219928 | + | 0.676869i | ||||
\(712\) | −2.46235 | + | 6.96307i | −0.0922806 | + | 0.260952i | ||||
\(713\) | −2.99472 | + | 0.973045i | −0.112153 | + | 0.0364408i | ||||
\(714\) | 14.7773 | − | 25.0953i | 0.553028 | − | 0.939166i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −29.9804 | − | 3.67233i | −1.12042 | − | 0.137241i | ||||
\(717\) | −70.2688 | + | 51.0533i | −2.62424 | + | 1.90662i | ||||
\(718\) | 25.2212 | + | 5.58759i | 0.941248 | + | 0.208527i | ||||
\(719\) | 12.3313 | − | 8.95922i | 0.459880 | − | 0.334123i | −0.333604 | − | 0.942713i | \(-0.608265\pi\) |
0.793484 | + | 0.608591i | \(0.208265\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.5269 | − | 9.10133i | −0.466526 | − | 0.338951i | ||||
\(722\) | 1.22341 | + | 1.38241i | 0.0455306 | + | 0.0514480i | ||||
\(723\) | 4.16038 | − | 12.8043i | 0.154726 | − | 0.476198i | ||||
\(724\) | −15.9831 | + | 34.3017i | −0.594007 | + | 1.27481i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 20.7285 | + | 4.59226i | 0.769308 | + | 0.170435i | ||||
\(727\) | 2.11778 | + | 0.688107i | 0.0785440 | + | 0.0255205i | 0.348025 | − | 0.937485i | \(-0.386852\pi\) |
−0.269481 | + | 0.963006i | \(0.586852\pi\) | |||||||
\(728\) | 2.89887 | − | 0.860052i | 0.107439 | − | 0.0318756i | ||||
\(729\) | −5.38937 | − | 3.91560i | −0.199606 | − | 0.145022i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.69724 | + | 13.3471i | 0.358665 | + | 0.493661i | ||||
\(732\) | −41.1258 | + | 88.2612i | −1.52005 | + | 3.26223i | ||||
\(733\) | −40.0434 | + | 29.0933i | −1.47904 | + | 1.07458i | −0.501173 | + | 0.865347i | \(0.667098\pi\) |
−0.977865 | + | 0.209237i | \(0.932902\pi\) | |||||||
\(734\) | −21.1949 | + | 2.04393i | −0.782319 | + | 0.0754430i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.04551 | + | 12.1694i | 0.0753986 | + | 0.448571i | ||||
\(737\) | 11.4703 | − | 3.72692i | 0.422513 | − | 0.137283i | ||||
\(738\) | 5.95475 | + | 61.7488i | 0.219197 | + | 2.27301i | ||||
\(739\) | −17.2361 | − | 5.60033i | −0.634039 | − | 0.206012i | −0.0256753 | − | 0.999670i | \(-0.508174\pi\) |
−0.608363 | + | 0.793659i | \(0.708174\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.2460 | + | 3.97897i | −0.449869 | + | 0.146171i | ||||
\(742\) | −8.66715 | − | 19.9252i | −0.318181 | − | 0.731477i | ||||
\(743\) | 15.5632i | 0.570959i | 0.958385 | + | 0.285479i | \(0.0921528\pi\) | ||||
−0.958385 | + | 0.285479i | \(0.907847\pi\) | |||||||
\(744\) | 12.8278 | + | 0.330339i | 0.470291 | + | 0.0121108i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.664499 | − | 0.750860i | −0.0243290 | − | 0.0274910i | ||||
\(747\) | 52.6813 | + | 38.2752i | 1.92751 | + | 1.40042i | ||||
\(748\) | −30.1781 | + | 32.3808i | −1.10342 | + | 1.18396i | ||||
\(749\) | − | 8.23944i | − | 0.301062i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.5803 | 1.51729 | 0.758643 | − | 0.651507i | \(-0.225863\pi\) | ||||
0.758643 | + | 0.651507i | \(0.225863\pi\) | |||||||
\(752\) | 7.97886 | + | 19.7155i | 0.290959 | + | 0.718951i | ||||
\(753\) | −24.7554 | + | 34.0729i | −0.902137 | + | 1.24169i | ||||
\(754\) | 5.99274 | − | 5.30348i | 0.218243 | − | 0.193141i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.47844 | + | 28.1407i | 0.199249 | + | 1.02347i | ||||
\(757\) | 1.83755 | 0.0667870 | 0.0333935 | − | 0.999442i | \(-0.489369\pi\) | ||||
0.0333935 | + | 0.999442i | \(0.489369\pi\) | |||||||
\(758\) | −10.3850 | − | 23.8745i | −0.377202 | − | 0.867161i | ||||
\(759\) | 8.41550 | + | 25.9003i | 0.305463 | + | 0.940120i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.18935 | + | 28.2819i | −0.333114 | + | 1.02522i | 0.634530 | + | 0.772898i | \(0.281194\pi\) |
−0.967644 | + | 0.252320i | \(0.918806\pi\) | |||||||
\(762\) | 38.1835 | − | 3.68223i | 1.38324 | − | 0.133393i | ||||
\(763\) | 0.981880 | + | 3.02192i | 0.0355464 | + | 0.109401i | ||||
\(764\) | −3.05570 | + | 3.27874i | −0.110552 | + | 0.118621i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25.2637 | − | 2.43630i | 0.912813 | − | 0.0880272i | ||||
\(767\) | −0.687057 | − | 0.945653i | −0.0248082 | − | 0.0341455i | ||||
\(768\) | 8.67516 | − | 49.5344i | 0.313038 | − | 1.78742i | ||||
\(769\) | 7.63237 | − | 5.54524i | 0.275230 | − | 0.199966i | −0.441604 | − | 0.897210i | \(-0.645590\pi\) |
0.716834 | + | 0.697244i | \(0.245590\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.4450 | − | 19.8818i | 0.520222 | − | 0.716025i | ||||
\(772\) | 39.6929 | − | 22.0172i | 1.42858 | − | 0.792415i | ||||
\(773\) | −7.49873 | + | 23.0787i | −0.269711 | + | 0.830084i | 0.720860 | + | 0.693081i | \(0.243747\pi\) |
−0.990571 | + | 0.137003i | \(0.956253\pi\) | |||||||
\(774\) | −28.1210 | − | 6.23000i | −1.01079 | − | 0.223933i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.501718 | + | 0.654439i | −0.0180106 | + | 0.0234930i | ||||
\(777\) | 24.6036 | + | 7.99420i | 0.882649 | + | 0.286790i | ||||
\(778\) | 25.2862 | − | 22.3778i | 0.906553 | − | 0.802284i | ||||
\(779\) | −16.8908 | + | 23.2482i | −0.605176 | + | 0.832953i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.56537 | − | 6.28370i | −0.163362 | − | 0.224848i | ||||
\(782\) | −16.7827 | − | 3.71810i | −0.600150 | − | 0.132959i | ||||
\(783\) | 44.5974 | + | 61.3830i | 1.59378 | + | 2.19365i | ||||
\(784\) | −11.8958 | + | 19.0618i | −0.424851 | + | 0.680779i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −33.3146 | − | 19.6173i | −1.18829 | − | 0.699725i | ||||
\(787\) | −11.5135 | − | 35.4350i | −0.410413 | − | 1.26312i | −0.916290 | − | 0.400515i | \(-0.868831\pi\) |
0.505877 | − | 0.862606i | \(-0.331169\pi\) | |||||||
\(788\) | 3.15689 | − | 25.7725i | 0.112460 | − | 0.918106i | ||||
\(789\) | 82.0264 | + | 26.6520i | 2.92022 | + | 0.948837i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.66083 | − | 5.11151i | −0.0590524 | − | 0.181745i | ||||
\(792\) | 1.98935 | − | 77.2510i | 0.0706885 | − | 2.74499i | ||||
\(793\) | − | 14.0830i | − | 0.500103i | ||||||
\(794\) | −1.87234 | + | 0.814440i | −0.0664469 | + | 0.0289034i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.6724 | + | 31.8602i | 0.626383 | + | 1.12925i | ||||
\(797\) | −4.03520 | − | 2.93174i | −0.142934 | − | 0.103848i | 0.514020 | − | 0.857778i | \(-0.328156\pi\) |
−0.656954 | + | 0.753930i | \(0.728156\pi\) | |||||||
\(798\) | −11.9507 | + | 20.2950i | −0.423051 | + | 0.718436i | ||||
\(799\) | −29.6272 | −1.04814 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.9614 | 0.634635 | ||||||||
\(802\) | −18.7063 | + | 31.7675i | −0.660542 | + | 1.12175i | ||||
\(803\) | −13.5696 | − | 9.85892i | −0.478862 | − | 0.347914i | ||||
\(804\) | −9.25842 | − | 16.6912i | −0.326519 | − | 0.588655i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.70187 | + | 0.740289i | −0.0599460 | + | 0.0260756i | ||||
\(807\) | 67.0587i | 2.36058i | ||||||||
\(808\) | 0.570978 | − | 22.1724i | 0.0200869 | − | 0.780021i | ||||
\(809\) | −2.74204 | − | 8.43914i | −0.0964051 | − | 0.296704i | 0.891212 | − | 0.453587i | \(-0.149856\pi\) |
−0.987617 | + | 0.156882i | \(0.949856\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.7338 | − | 6.73681i | −0.728062 | − | 0.236562i | −0.0785467 | − | 0.996910i | \(-0.525028\pi\) |
−0.649515 | + | 0.760349i | \(0.725028\pi\) | |||||||
\(812\) | 1.77967 | − | 14.5290i | 0.0624541 | − | 0.509867i | ||||
\(813\) | 1.03769 | + | 3.19368i | 0.0363934 | + | 0.112007i | ||||
\(814\) | −33.8812 | − | 19.9509i | −1.18753 | − | 0.699280i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 59.4280 | + | 37.0870i | 2.08040 | + | 1.29830i | ||||
\(817\) | −7.84235 | − | 10.7941i | −0.274369 | − | 0.377637i | ||||
\(818\) | 1.39675 | + | 0.309440i | 0.0488362 | + | 0.0108193i | ||||
\(819\) | −4.32233 | − | 5.94918i | −0.151035 | − | 0.207881i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.5298 | − | 29.6332i | 0.751394 | − | 1.03420i | −0.246488 | − | 0.969146i | \(-0.579276\pi\) |
0.997881 | − | 0.0650589i | \(-0.0207235\pi\) | |||||||
\(822\) | −12.1286 | + | 10.7336i | −0.423033 | + | 0.374377i | ||||
\(823\) | 5.63427 | + | 1.83068i | 0.196398 | + | 0.0638136i | 0.405564 | − | 0.914066i | \(-0.367075\pi\) |
−0.209166 | + | 0.977880i | \(0.567075\pi\) | |||||||
\(824\) | 22.6604 | − | 29.5581i | 0.789412 | − | 1.02971i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.08743 | − | 0.462456i | −0.0726311 | − | 0.0160909i | ||||
\(827\) | −4.70692 | + | 14.4864i | −0.163676 | + | 0.503742i | −0.998936 | − | 0.0461123i | \(-0.985317\pi\) |
0.835261 | + | 0.549854i | \(0.185317\pi\) | |||||||
\(828\) | 26.2435 | − | 14.5570i | 0.912026 | − | 0.505889i | ||||
\(829\) | 25.2244 | − | 34.7183i | 0.876078 | − | 1.20582i | −0.101414 | − | 0.994844i | \(-0.532337\pi\) |
0.977492 | − | 0.210974i | \(-0.0676634\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −45.1419 | + | 32.7975i | −1.56595 | + | 1.13773i | ||||
\(832\) | 1.88854 | + | 7.02376i | 0.0654735 | + | 0.243505i | ||||
\(833\) | −18.3972 | − | 25.3216i | −0.637427 | − | 0.877343i | ||||
\(834\) | −61.7941 | + | 5.95912i | −2.13976 | + | 0.206347i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 24.4056 | − | 26.1870i | 0.844085 | − | 0.905695i | ||||
\(837\) | −5.43757 | − | 16.7351i | −0.187950 | − | 0.578450i | ||||
\(838\) | −47.1065 | + | 4.54271i | −1.62727 | + | 0.156925i | ||||
\(839\) | 14.0891 | − | 43.3617i | 0.486409 | − | 1.49701i | −0.343521 | − | 0.939145i | \(-0.611620\pi\) |
0.829930 | − | 0.557868i | \(-0.188380\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.00946 | − | 9.26218i | −0.103775 | − | 0.319385i | ||||
\(842\) | 15.5182 | + | 35.6753i | 0.534792 | + | 1.22945i | ||||
\(843\) | −34.1050 | −1.17464 | ||||||||
\(844\) | 0.671504 | + | 3.44926i | 0.0231141 | + | 0.118729i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 38.7344 | − | 34.2793i | 1.33172 | − | 1.17855i | ||||
\(847\) | −3.30138 | + | 4.54396i | −0.113437 | + | 0.156132i | ||||
\(848\) | 48.4480 | − | 19.6069i | 1.66371 | − | 0.673303i | ||||
\(849\) | −72.9986 | −2.50531 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 15.2695i | − | 0.523433i | ||||||
\(852\) | −8.38064 | + | 8.99235i | −0.287116 | + | 0.308073i | ||||
\(853\) | −39.8951 | − | 28.9855i | −1.36598 | − | 0.992445i | −0.998039 | − | 0.0625971i | \(-0.980062\pi\) |
−0.367944 | − | 0.929848i | \(-0.619938\pi\) | |||||||
\(854\) | −17.0716 | − | 19.2903i | −0.584179 | − | 0.660101i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.8122 | + | 0.510200i | 0.677168 | + | 0.0174383i | ||||
\(857\) | 57.0345i | 1.94826i | 0.225989 | + | 0.974130i | \(0.427439\pi\) | ||||
−0.225989 | + | 0.974130i | \(0.572561\pi\) | |||||||
\(858\) | 6.40248 | + | 14.7189i | 0.218577 | + | 0.502494i | ||||
\(859\) | 20.6564 | − | 6.71166i | 0.704786 | − | 0.228999i | 0.0653714 | − | 0.997861i | \(-0.479177\pi\) |
0.639415 | + | 0.768862i | \(0.279177\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.4153 | − | 7.28318i | −0.763912 | − | 0.248210i | ||||
\(862\) | −3.63023 | − | 37.6443i | −0.123646 | − | 1.28217i | ||||
\(863\) | 17.9981 | − | 5.84794i | 0.612663 | − | 0.199066i | 0.0137830 | − | 0.999905i | \(-0.495613\pi\) |
0.598880 | + | 0.800839i | \(0.295613\pi\) | |||||||
\(864\) | −68.0052 | + | 11.4307i | −2.31358 | + | 0.388881i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 29.2166 | − | 2.81751i | 0.992822 | − | 0.0957428i | ||||
\(867\) | −35.7171 | + | 25.9500i | −1.21302 | + | 0.881307i | ||||
\(868\) | −1.43377 | + | 3.07705i | −0.0486653 | + | 0.104442i | ||||
\(869\) | 6.44110 | + | 8.86542i | 0.218499 | + | 0.300739i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.23335 | + | 1.62262i | 0.0756742 | + | 0.0549805i | ||||
\(872\) | −7.32718 | + | 2.17387i | −0.248130 | + | 0.0736165i | ||||
\(873\) | 1.90729 | + | 0.619716i | 0.0645520 | + | 0.0209742i | ||||
\(874\) | 13.5725 | + | 3.00690i | 0.459098 | + | 0.101710i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.2114 | + | 24.0611i | −0.378799 | + | 0.812950i | ||||
\(877\) | 4.30447 | − | 13.2478i | 0.145352 | − | 0.447347i | −0.851704 | − | 0.524023i | \(-0.824431\pi\) |
0.997056 | + | 0.0766761i | \(0.0244307\pi\) | |||||||
\(878\) | −0.283886 | − | 0.320781i | −0.00958068 | − | 0.0108258i | ||||
\(879\) | 59.9157 | + | 43.5313i | 2.02091 | + | 1.46827i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.7294 | + | 23.7793i | −1.10268 | + | 0.801145i | −0.981496 | − | 0.191485i | \(-0.938670\pi\) |
−0.121186 | + | 0.992630i | \(0.538670\pi\) | |||||||
\(882\) | 53.3501 | + | 11.8193i | 1.79639 | + | 0.397977i | ||||
\(883\) | −3.31224 | + | 2.40648i | −0.111466 | + | 0.0809845i | −0.642122 | − | 0.766603i | \(-0.721946\pi\) |
0.530656 | + | 0.847587i | \(0.321946\pi\) | |||||||
\(884\) | −10.0563 | − | 1.23181i | −0.338231 | − | 0.0414303i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.3297 | − | 41.3172i | 0.817371 | − | 1.38808i | ||||
\(887\) | −5.39637 | + | 1.75339i | −0.181192 | + | 0.0588730i | −0.398208 | − | 0.917295i | \(-0.630368\pi\) |
0.217016 | + | 0.976168i | \(0.430368\pi\) | |||||||
\(888\) | −20.7460 | + | 58.6658i | −0.696191 | + | 1.96870i | ||||
\(889\) | −3.13597 | + | 9.65152i | −0.105177 | + | 0.323701i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −66.7832 | + | 21.6992i | −2.23732 | + | 0.726950i | ||||
\(892\) | −0.595670 | − | 3.05973i | −0.0199445 | − | 0.102447i | ||||
\(893\) | 23.9601 | 0.801795 | ||||||||
\(894\) | 4.63394 | + | 10.6531i | 0.154982 | + | 0.356294i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11.1011 | + | 7.33153i | 0.370863 | + | 0.244929i | ||||
\(897\) | −3.66394 | + | 5.04297i | −0.122335 | + | 0.168380i | ||||
\(898\) | −9.04513 | + | 15.3607i | −0.301840 | + | 0.512592i | ||||
\(899\) | 8.98418i | 0.299639i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 72.8046i | 2.42547i | ||||||||
\(902\) | 30.8677 | + | 18.1765i | 1.02778 | + | 0.605210i | ||||
\(903\) | 6.43211 | − | 8.85304i | 0.214047 | − | 0.294611i | ||||
\(904\) | 12.3938 | − | 3.67706i | 0.412211 | − | 0.122297i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 43.2781 | − | 18.8253i | 1.43782 | − | 0.625429i | ||||
\(907\) | 49.8362 | 1.65478 | 0.827392 | − | 0.561625i | \(-0.189824\pi\) | ||||
0.827392 | + | 0.561625i | \(0.189824\pi\) | |||||||
\(908\) | −18.1045 | + | 3.52458i | −0.600817 | + | 0.116967i | ||||
\(909\) | −51.2997 | + | 16.6683i | −1.70150 | + | 0.552852i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.08071 | − | 3.32610i | 0.0358057 | − | 0.110199i | −0.931556 | − | 0.363597i | \(-0.881548\pi\) |
0.967362 | + | 0.253399i | \(0.0815485\pi\) | |||||||
\(912\) | −48.0606 | − | 29.9930i | −1.59145 | − | 0.993166i | ||||
\(913\) | 35.7613 | − | 11.6196i | 1.18353 | − | 0.384551i | ||||
\(914\) | 3.15545 | + | 1.85809i | 0.104373 | + | 0.0614602i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.4283 | − | 2.74726i | −0.741051 | − | 0.0907720i | ||||
\(917\) | 8.27442 | − | 6.01172i | 0.273246 | − | 0.198525i | ||||
\(918\) | 20.7775 | − | 93.7853i | 0.685759 | − | 3.09538i | ||||
\(919\) | −35.2395 | + | 25.6030i | −1.16244 | + | 0.844564i | −0.990085 | − | 0.140471i | \(-0.955138\pi\) |
−0.172357 | + | 0.985034i | \(0.555138\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −74.2277 | − | 53.9296i | −2.44589 | − | 1.77704i | ||||
\(922\) | 7.23276 | − | 6.40087i | 0.238198 | − | 0.210801i | ||||
\(923\) | 0.549378 | − | 1.69081i | 0.0180830 | − | 0.0556538i | ||||
\(924\) | 26.6123 | + | 12.4001i | 0.875479 | + | 0.407935i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.67486 | + | 30.1290i | −0.219349 | + | 0.990099i | ||||
\(927\) | −86.1439 | − | 27.9899i | −2.82934 | − | 0.919307i | ||||
\(928\) | 34.8256 | + | 5.17898i | 1.14321 | + | 0.170008i | ||||
\(929\) | −20.6493 | − | 15.0026i | −0.677483 | − | 0.492220i | 0.195039 | − | 0.980795i | \(-0.437517\pi\) |
−0.872522 | + | 0.488576i | \(0.837517\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.8782 | + | 20.4781i | 0.487614 | + | 0.671143i | ||||
\(932\) | 10.5007 | − | 22.5358i | 0.343962 | − | 0.738186i | ||||
\(933\) | 2.49920 | − | 1.81577i | 0.0818201 | − | 0.0594458i | ||||
\(934\) | 0.407943 | + | 4.23024i | 0.0133483 | + | 0.138418i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 14.5728 | − | 10.0249i | 0.476327 | − | 0.327675i | ||||
\(937\) | −3.76427 | + | 1.22309i | −0.122973 | + | 0.0399565i | −0.369857 | − | 0.929089i | \(-0.620593\pi\) |
0.246884 | + | 0.969045i | \(0.420593\pi\) | |||||||
\(938\) | 5.02612 | − | 0.484694i | 0.164109 | − | 0.0158258i | ||||
\(939\) | 28.6403 | + | 9.30581i | 0.934642 | + | 0.303684i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.54079 | − | 2.45015i | 0.245823 | − | 0.0798727i | −0.183514 | − | 0.983017i | \(-0.558747\pi\) |
0.429337 | + | 0.903144i | \(0.358747\pi\) | |||||||
\(942\) | 15.9109 | − | 6.92099i | 0.518405 | − | 0.225498i | ||||
\(943\) | 13.9114i | 0.453018i | ||||||||
\(944\) | 1.24126 | − | 4.99073i | 0.0403996 | − | 0.162434i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.4550 | + | 11.0225i | −0.404947 | + | 0.358371i | ||||
\(947\) | −0.630350 | − | 0.457976i | −0.0204836 | − | 0.0148822i | 0.577496 | − | 0.816393i | \(-0.304030\pi\) |
−0.597980 | + | 0.801511i | \(0.704030\pi\) | |||||||
\(948\) | 11.8239 | − | 12.6870i | 0.384023 | − | 0.412053i | ||||
\(949\) | − | 3.83921i | − | 0.124626i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −57.8664 | −1.87645 | ||||||||
\(952\) | −15.2680 | + | 10.5031i | −0.494838 | + | 0.340409i | ||||
\(953\) | −6.29429 | + | 8.66334i | −0.203892 | + | 0.280633i | −0.898702 | − | 0.438560i | \(-0.855489\pi\) |
0.694810 | + | 0.719194i | \(0.255489\pi\) | |||||||
\(954\) | −84.2364 | − | 95.1842i | −2.72725 | − | 3.08170i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 54.2513 | − | 10.5617i | 1.75461 | − | 0.341589i | ||||
\(957\) | 77.7008 | 2.51171 | ||||||||
\(958\) | 24.6405 | − | 10.7182i | 0.796097 | − | 0.346290i | ||||
\(959\) | −1.32402 | − | 4.07492i | −0.0427549 | − | 0.131586i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.93566 | + | 27.5011i | −0.288247 | + | 0.887134i | ||||
\(962\) | −0.863887 | − | 8.95823i | −0.0278528 | − | 0.288825i | ||||
\(963\) | −14.8940 | − | 45.8391i | −0.479953 | − | 1.47714i | ||||
\(964\) | −5.84093 | + | 6.26726i | −0.188124 | + | 0.201855i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.09445 | + | 11.3491i | 0.0352134 | + | 0.365152i | ||||
\(967\) | −5.37219 | − | 7.39419i | −0.172758 | − | 0.237781i | 0.713854 | − | 0.700294i | \(-0.246948\pi\) |
−0.886612 | + | 0.462513i | \(0.846948\pi\) | |||||||
\(968\) | −10.7218 | − | 8.21973i | −0.344612 | − | 0.264192i | ||||
\(969\) | 63.8435 | − | 46.3850i | 2.05095 | − | 1.49010i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.2665 | + | 21.0125i | −0.489924 | + | 0.674323i | −0.980374 | − | 0.197147i | \(-0.936833\pi\) |
0.490450 | + | 0.871469i | \(0.336833\pi\) | |||||||
\(972\) | 18.4265 | + | 33.2196i | 0.591031 | + | 1.06552i | ||||
\(973\) | 5.07508 | − | 15.6195i | 0.162700 | − | 0.500738i | ||||
\(974\) | 0.580675 | − | 2.62105i | 0.0186060 | − | 0.0839839i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 47.4419 | − | 39.8552i | 1.51858 | − | 1.27574i | ||||
\(977\) | −29.0332 | − | 9.43346i | −0.928855 | − | 0.301803i | −0.194760 | − | 0.980851i | \(-0.562393\pi\) |
−0.734094 | + | 0.679048i | \(0.762393\pi\) | |||||||
\(978\) | −57.8237 | − | 65.3388i | −1.84900 | − | 2.08930i | ||||
\(979\) | 6.09631 | − | 8.39085i | 0.194839 | − | 0.268173i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.9251 | + | 15.0372i | 0.348813 | + | 0.480100i | ||||
\(982\) | 9.44799 | − | 42.6463i | 0.301498 | − | 1.36090i | ||||
\(983\) | 23.5163 | + | 32.3674i | 0.750052 | + | 1.03236i | 0.997977 | + | 0.0635791i | \(0.0202515\pi\) |
−0.247924 | + | 0.968779i | \(0.579748\pi\) | |||||||
\(984\) | 18.9008 | − | 53.4480i | 0.602537 | − | 1.70386i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −24.8861 | + | 42.2623i | −0.792536 | + | 1.34590i | ||||
\(987\) | 6.07265 | + | 18.6897i | 0.193295 | + | 0.594900i | ||||
\(988\) | 8.13276 | + | 0.996190i | 0.258738 | + | 0.0316930i | ||||
\(989\) | −6.14291 | − | 1.99595i | −0.195333 | − | 0.0634676i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.8786 | + | 45.7916i | 0.472634 | + | 1.45462i | 0.849122 | + | 0.528197i | \(0.177132\pi\) |
−0.376488 | + | 0.926422i | \(0.622868\pi\) | |||||||
\(992\) | −7.31018 | − | 3.63812i | −0.232098 | − | 0.115510i | ||||
\(993\) | 22.7314i | 0.721358i | ||||||||
\(994\) | −1.29711 | − | 2.98197i | −0.0411418 | − | 0.0945822i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −28.8653 | − | 52.0389i | −0.914633 | − | 1.64892i | ||||
\(997\) | −0.969621 | − | 0.704471i | −0.0307082 | − | 0.0223108i | 0.572325 | − | 0.820027i | \(-0.306041\pi\) |
−0.603033 | + | 0.797716i | \(0.706041\pi\) | |||||||
\(998\) | −12.9112 | − | 7.60275i | −0.408696 | − | 0.240661i | ||||
\(999\) | 85.3292 | 2.69970 |
(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 | 1000.2.o.a.149.19 | 112 | ||
5.2 | odd | 4 | 1000.2.t.b.101.47 | 224 | |||
5.3 | odd | 4 | 1000.2.t.b.101.10 | 224 | |||
5.4 | even | 2 | 200.2.o.a.29.10 | ✓ | 112 | ||
8.5 | even | 2 | inner | 1000.2.o.a.149.13 | 112 | ||
20.19 | odd | 2 | 800.2.be.a.529.27 | 112 | |||
25.6 | even | 5 | 200.2.o.a.69.16 | yes | 112 | ||
25.8 | odd | 20 | 1000.2.t.b.901.55 | 224 | |||
25.17 | odd | 20 | 1000.2.t.b.901.2 | 224 | |||
25.19 | even | 10 | inner | 1000.2.o.a.349.13 | 112 | ||
40.13 | odd | 4 | 1000.2.t.b.101.55 | 224 | |||
40.19 | odd | 2 | 800.2.be.a.529.2 | 112 | |||
40.29 | even | 2 | 200.2.o.a.29.16 | yes | 112 | ||
40.37 | odd | 4 | 1000.2.t.b.101.2 | 224 | |||
100.31 | odd | 10 | 800.2.be.a.369.2 | 112 | |||
200.69 | even | 10 | inner | 1000.2.o.a.349.19 | 112 | ||
200.117 | odd | 20 | 1000.2.t.b.901.47 | 224 | |||
200.131 | odd | 10 | 800.2.be.a.369.27 | 112 | |||
200.133 | odd | 20 | 1000.2.t.b.901.10 | 224 | |||
200.181 | even | 10 | 200.2.o.a.69.10 | yes | 112 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.2.o.a.29.10 | ✓ | 112 | 5.4 | even | 2 | ||
200.2.o.a.29.16 | yes | 112 | 40.29 | even | 2 | ||
200.2.o.a.69.10 | yes | 112 | 200.181 | even | 10 | ||
200.2.o.a.69.16 | yes | 112 | 25.6 | even | 5 | ||
800.2.be.a.369.2 | 112 | 100.31 | odd | 10 | |||
800.2.be.a.369.27 | 112 | 200.131 | odd | 10 | |||
800.2.be.a.529.2 | 112 | 40.19 | odd | 2 | |||
800.2.be.a.529.27 | 112 | 20.19 | odd | 2 | |||
1000.2.o.a.149.13 | 112 | 8.5 | even | 2 | inner | ||
1000.2.o.a.149.19 | 112 | 1.1 | even | 1 | trivial | ||
1000.2.o.a.349.13 | 112 | 25.19 | even | 10 | inner | ||
1000.2.o.a.349.19 | 112 | 200.69 | even | 10 | inner | ||
1000.2.t.b.101.2 | 224 | 40.37 | odd | 4 | |||
1000.2.t.b.101.10 | 224 | 5.3 | odd | 4 | |||
1000.2.t.b.101.47 | 224 | 5.2 | odd | 4 | |||
1000.2.t.b.101.55 | 224 | 40.13 | odd | 4 | |||
1000.2.t.b.901.2 | 224 | 25.17 | odd | 20 | |||
1000.2.t.b.901.10 | 224 | 200.133 | odd | 20 | |||
1000.2.t.b.901.47 | 224 | 200.117 | odd | 20 | |||
1000.2.t.b.901.55 | 224 | 25.8 | odd | 20 |