Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(151,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.f (of order \(2\), degree \(1\), 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: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{18} + x^{16} - 9x^{14} + 20x^{12} - 24x^{10} + 80x^{8} - 144x^{6} + 64x^{4} - 256x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.7 | ||
Root | \(0.611950 - 1.27496i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.151 |
Dual form | 380.2.f.a.151.8 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.611950 | − | 1.27496i | −0.432714 | − | 0.901531i | ||||
\(3\) | 3.21061 | 1.85365 | 0.926825 | − | 0.375495i | \(-0.122527\pi\) | ||||
0.926825 | + | 0.375495i | \(0.122527\pi\) | |||||||
\(4\) | −1.25103 | + | 1.56042i | −0.625517 | + | 0.780211i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.96474 | − | 4.09340i | −0.802100 | − | 1.67112i | ||||
\(7\) | − | 3.02772i | − | 1.14437i | −0.820125 | − | 0.572185i | \(-0.806096\pi\) | ||
0.820125 | − | 0.572185i | \(-0.193904\pi\) | |||||||
\(8\) | 2.75504 | + | 0.640115i | 0.974054 | + | 0.226315i | ||||
\(9\) | 7.30804 | 2.43601 | ||||||||
\(10\) | 0.611950 | + | 1.27496i | 0.193516 | + | 0.403177i | ||||
\(11\) | 0.488592i | 0.147316i | 0.997284 | + | 0.0736580i | \(0.0234673\pi\) | ||||
−0.997284 | + | 0.0736580i | \(0.976533\pi\) | |||||||
\(12\) | −4.01659 | + | 5.00991i | −1.15949 | + | 1.44624i | ||||
\(13\) | − | 0.943033i | − | 0.261550i | −0.991412 | − | 0.130775i | \(-0.958253\pi\) | ||
0.991412 | − | 0.130775i | \(-0.0417466\pi\) | |||||||
\(14\) | −3.86021 | + | 1.85281i | −1.03168 | + | 0.495185i | ||||
\(15\) | −3.21061 | −0.828977 | ||||||||
\(16\) | −0.869829 | − | 3.90428i | −0.217457 | − | 0.976070i | ||||
\(17\) | 3.16706 | 0.768126 | 0.384063 | − | 0.923307i | \(-0.374525\pi\) | ||||
0.384063 | + | 0.923307i | \(0.374525\pi\) | |||||||
\(18\) | −4.47216 | − | 9.31745i | −1.05410 | − | 2.19614i | ||||
\(19\) | −2.58768 | + | 3.50769i | −0.593655 | + | 0.804720i | ||||
\(20\) | 1.25103 | − | 1.56042i | 0.279740 | − | 0.348921i | ||||
\(21\) | − | 9.72083i | − | 2.12126i | ||||||
\(22\) | 0.622934 | − | 0.298994i | 0.132810 | − | 0.0637457i | ||||
\(23\) | − | 7.08696i | − | 1.47773i | −0.673852 | − | 0.738866i | \(-0.735361\pi\) | ||
0.673852 | − | 0.738866i | \(-0.264639\pi\) | |||||||
\(24\) | 8.84538 | + | 2.05516i | 1.80555 | + | 0.419508i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.20233 | + | 0.577089i | −0.235796 | + | 0.113177i | ||||
\(27\) | 13.8315 | 2.66187 | ||||||||
\(28\) | 4.72451 | + | 3.78777i | 0.892849 | + | 0.715822i | ||||
\(29\) | 8.80545i | 1.63513i | 0.575835 | + | 0.817566i | \(0.304677\pi\) | ||||
−0.575835 | + | 0.817566i | \(0.695323\pi\) | |||||||
\(30\) | 1.96474 | + | 4.09340i | 0.358710 | + | 0.747349i | ||||
\(31\) | −3.66325 | −0.657939 | −0.328969 | − | 0.944341i | \(-0.606701\pi\) | ||||
−0.328969 | + | 0.944341i | \(0.606701\pi\) | |||||||
\(32\) | −4.44550 | + | 3.49822i | −0.785861 | + | 0.618404i | ||||
\(33\) | 1.56868i | 0.273072i | ||||||||
\(34\) | −1.93809 | − | 4.03787i | −0.332379 | − | 0.692489i | ||||
\(35\) | 3.02772i | 0.511777i | ||||||||
\(36\) | −9.14261 | + | 11.4036i | −1.52377 | + | 1.90060i | ||||
\(37\) | 1.11751i | 0.183717i | 0.995772 | + | 0.0918584i | \(0.0292807\pi\) | ||||
−0.995772 | + | 0.0918584i | \(0.970719\pi\) | |||||||
\(38\) | 6.05569 | + | 1.15265i | 0.982363 | + | 0.186984i | ||||
\(39\) | − | 3.02772i | − | 0.484823i | ||||||
\(40\) | −2.75504 | − | 0.640115i | −0.435610 | − | 0.101211i | ||||
\(41\) | 1.56868i | 0.244987i | 0.992469 | + | 0.122493i | \(0.0390890\pi\) | ||||
−0.992469 | + | 0.122493i | \(0.960911\pi\) | |||||||
\(42\) | −12.3936 | + | 5.94866i | −1.91238 | + | 0.917899i | ||||
\(43\) | − | 3.58788i | − | 0.547147i | −0.961851 | − | 0.273573i | \(-0.911794\pi\) | ||
0.961851 | − | 0.273573i | \(-0.0882056\pi\) | |||||||
\(44\) | −0.762409 | − | 0.611245i | −0.114937 | − | 0.0921486i | ||||
\(45\) | −7.30804 | −1.08942 | ||||||||
\(46\) | −9.03557 | + | 4.33687i | −1.33222 | + | 0.639436i | ||||
\(47\) | − | 0.471362i | − | 0.0687552i | −0.999409 | − | 0.0343776i | \(-0.989055\pi\) | ||
0.999409 | − | 0.0343776i | \(-0.0109449\pi\) | |||||||
\(48\) | −2.79269 | − | 12.5351i | −0.403090 | − | 1.80929i | ||||
\(49\) | −2.16706 | −0.309581 | ||||||||
\(50\) | −0.611950 | − | 1.27496i | −0.0865428 | − | 0.180306i | ||||
\(51\) | 10.1682 | 1.42384 | ||||||||
\(52\) | 1.47153 | + | 1.17977i | 0.204064 | + | 0.163604i | ||||
\(53\) | 12.4070i | 1.70423i | 0.523351 | + | 0.852117i | \(0.324682\pi\) | ||||
−0.523351 | + | 0.852117i | \(0.675318\pi\) | |||||||
\(54\) | −8.46417 | − | 17.6345i | −1.15183 | − | 2.39976i | ||||
\(55\) | − | 0.488592i | − | 0.0658817i | ||||||
\(56\) | 1.93809 | − | 8.34148i | 0.258988 | − | 1.11468i | ||||
\(57\) | −8.30804 | + | 11.2618i | −1.10043 | + | 1.49167i | ||||
\(58\) | 11.2266 | − | 5.38850i | 1.47412 | − | 0.707545i | ||||
\(59\) | −8.65611 | −1.12693 | −0.563465 | − | 0.826140i | \(-0.690532\pi\) | ||||
−0.563465 | + | 0.826140i | \(0.690532\pi\) | |||||||
\(60\) | 4.01659 | − | 5.00991i | 0.518539 | − | 0.646777i | ||||
\(61\) | −8.62030 | −1.10372 | −0.551858 | − | 0.833938i | \(-0.686081\pi\) | ||||
−0.551858 | + | 0.833938i | \(0.686081\pi\) | |||||||
\(62\) | 2.24173 | + | 4.67049i | 0.284699 | + | 0.593152i | ||||
\(63\) | − | 22.1267i | − | 2.78770i | ||||||
\(64\) | 7.18051 | + | 3.52709i | 0.897563 | + | 0.440886i | ||||
\(65\) | 0.943033i | 0.116969i | ||||||||
\(66\) | 2.00000 | − | 0.959954i | 0.246183 | − | 0.118162i | ||||
\(67\) | −6.59410 | −0.805598 | −0.402799 | − | 0.915288i | \(-0.631963\pi\) | ||||
−0.402799 | + | 0.915288i | \(0.631963\pi\) | |||||||
\(68\) | −3.96210 | + | 4.94195i | −0.480476 | + | 0.599300i | ||||
\(69\) | − | 22.7535i | − | 2.73920i | ||||||
\(70\) | 3.86021 | − | 1.85281i | 0.461383 | − | 0.221453i | ||||
\(71\) | 13.9287 | 1.65304 | 0.826518 | − | 0.562911i | \(-0.190318\pi\) | ||||
0.826518 | + | 0.562911i | \(0.190318\pi\) | |||||||
\(72\) | 20.1340 | + | 4.67799i | 2.37281 | + | 0.551306i | ||||
\(73\) | −11.6960 | −1.36892 | −0.684458 | − | 0.729053i | \(-0.739961\pi\) | ||||
−0.684458 | + | 0.729053i | \(0.739961\pi\) | |||||||
\(74\) | 1.42477 | − | 0.683858i | 0.165626 | − | 0.0794969i | ||||
\(75\) | 3.21061 | 0.370730 | ||||||||
\(76\) | −2.23620 | − | 8.42611i | −0.256510 | − | 0.966542i | ||||
\(77\) | 1.47932 | 0.168584 | ||||||||
\(78\) | −3.86021 | + | 1.85281i | −0.437083 | + | 0.209790i | ||||
\(79\) | −10.5317 | −1.18491 | −0.592456 | − | 0.805603i | \(-0.701841\pi\) | ||||
−0.592456 | + | 0.805603i | \(0.701841\pi\) | |||||||
\(80\) | 0.869829 | + | 3.90428i | 0.0972499 | + | 0.436512i | ||||
\(81\) | 22.4834 | 2.49815 | ||||||||
\(82\) | 2.00000 | − | 0.959954i | 0.220863 | − | 0.106009i | ||||
\(83\) | 18.0674i | 1.98316i | 0.129499 | + | 0.991580i | \(0.458663\pi\) | ||||
−0.129499 | + | 0.991580i | \(0.541337\pi\) | |||||||
\(84\) | 15.1686 | + | 12.1611i | 1.65503 | + | 1.32688i | ||||
\(85\) | −3.16706 | −0.343516 | ||||||||
\(86\) | −4.57439 | + | 2.19560i | −0.493270 | + | 0.236758i | ||||
\(87\) | 28.2709i | 3.03096i | ||||||||
\(88\) | −0.312755 | + | 1.34609i | −0.0333398 | + | 0.143494i | ||||
\(89\) | 9.83998i | 1.04304i | 0.853240 | + | 0.521518i | \(0.174634\pi\) | ||||
−0.853240 | + | 0.521518i | \(0.825366\pi\) | |||||||
\(90\) | 4.47216 | + | 9.31745i | 0.471407 | + | 0.982145i | ||||
\(91\) | −2.85524 | −0.299310 | ||||||||
\(92\) | 11.0586 | + | 8.86602i | 1.15294 | + | 0.924347i | ||||
\(93\) | −11.7613 | −1.21959 | ||||||||
\(94\) | −0.600967 | + | 0.288450i | −0.0619850 | + | 0.0297514i | ||||
\(95\) | 2.58768 | − | 3.50769i | 0.265490 | − | 0.359882i | ||||
\(96\) | −14.2728 | + | 11.2314i | −1.45671 | + | 1.14630i | ||||
\(97\) | − | 1.71549i | − | 0.174182i | −0.996200 | − | 0.0870910i | \(-0.972243\pi\) | ||
0.996200 | − | 0.0870910i | \(-0.0277571\pi\) | |||||||
\(98\) | 1.32614 | + | 2.76291i | 0.133960 | + | 0.279096i | ||||
\(99\) | 3.57065i | 0.358864i | ||||||||
\(100\) | −1.25103 | + | 1.56042i | −0.125103 | + | 0.156042i | ||||
\(101\) | 9.47511 | 0.942808 | 0.471404 | − | 0.881917i | \(-0.343747\pi\) | ||||
0.471404 | + | 0.881917i | \(0.343747\pi\) | |||||||
\(102\) | −6.22244 | − | 12.9640i | −0.616114 | − | 1.28363i | ||||
\(103\) | 5.44549 | 0.536560 | 0.268280 | − | 0.963341i | \(-0.413545\pi\) | ||||
0.268280 | + | 0.963341i | \(0.413545\pi\) | |||||||
\(104\) | 0.603649 | − | 2.59810i | 0.0591927 | − | 0.254764i | ||||
\(105\) | 9.72083i | 0.948656i | ||||||||
\(106\) | 15.8184 | − | 7.59248i | 1.53642 | − | 0.737446i | ||||
\(107\) | 3.47686 | 0.336121 | 0.168060 | − | 0.985777i | \(-0.446250\pi\) | ||||
0.168060 | + | 0.985777i | \(0.446250\pi\) | |||||||
\(108\) | −17.3036 | + | 21.5829i | −1.66504 | + | 2.07682i | ||||
\(109\) | − | 12.5538i | − | 1.20244i | −0.799084 | − | 0.601219i | \(-0.794682\pi\) | ||
0.799084 | − | 0.601219i | \(-0.205318\pi\) | |||||||
\(110\) | −0.622934 | + | 0.298994i | −0.0593944 | + | 0.0285079i | ||||
\(111\) | 3.58788i | 0.340546i | ||||||||
\(112\) | −11.8210 | + | 2.63360i | −1.11698 | + | 0.248851i | ||||
\(113\) | 10.0974i | 0.949886i | 0.880016 | + | 0.474943i | \(0.157531\pi\) | ||||
−0.880016 | + | 0.474943i | \(0.842469\pi\) | |||||||
\(114\) | 19.4425 | + | 3.70071i | 1.82096 | + | 0.346603i | ||||
\(115\) | 7.08696i | 0.660862i | ||||||||
\(116\) | −13.7402 | − | 11.0159i | −1.27575 | − | 1.02280i | ||||
\(117\) | − | 6.89173i | − | 0.637141i | ||||||
\(118\) | 5.29711 | + | 11.0362i | 0.487638 | + | 1.01596i | ||||
\(119\) | − | 9.58897i | − | 0.879019i | ||||||
\(120\) | −8.84538 | − | 2.05516i | −0.807469 | − | 0.187610i | ||||
\(121\) | 10.7613 | 0.978298 | ||||||||
\(122\) | 5.27519 | + | 10.9905i | 0.477594 | + | 0.995034i | ||||
\(123\) | 5.03643i | 0.454119i | ||||||||
\(124\) | 4.58285 | − | 5.71621i | 0.411552 | − | 0.513331i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −28.2106 | + | 13.5404i | −2.51320 | + | 1.20628i | ||||
\(127\) | −4.63898 | −0.411643 | −0.205822 | − | 0.978590i | \(-0.565987\pi\) | ||||
−0.205822 | + | 0.978590i | \(0.565987\pi\) | |||||||
\(128\) | 0.102771 | − | 11.3132i | 0.00908376 | − | 0.999959i | ||||
\(129\) | − | 11.5193i | − | 1.01422i | ||||||
\(130\) | 1.20233 | − | 0.577089i | 0.105451 | − | 0.0506141i | ||||
\(131\) | − | 21.6381i | − | 1.89053i | −0.326306 | − | 0.945264i | \(-0.605804\pi\) | ||
0.326306 | − | 0.945264i | \(-0.394196\pi\) | |||||||
\(132\) | −2.44780 | − | 1.96247i | −0.213054 | − | 0.170811i | ||||
\(133\) | 10.6203 | + | 7.83476i | 0.920897 | + | 0.679360i | ||||
\(134\) | 4.03526 | + | 8.40720i | 0.348594 | + | 0.726272i | ||||
\(135\) | −13.8315 | −1.19042 | ||||||||
\(136\) | 8.72539 | + | 2.02728i | 0.748196 | + | 0.173838i | ||||
\(137\) | 12.5508 | 1.07229 | 0.536145 | − | 0.844126i | \(-0.319880\pi\) | ||||
0.536145 | + | 0.844126i | \(0.319880\pi\) | |||||||
\(138\) | −29.0097 | + | 13.9240i | −2.46947 | + | 1.18529i | ||||
\(139\) | − | 5.97381i | − | 0.506692i | −0.967376 | − | 0.253346i | \(-0.918469\pi\) | ||
0.967376 | − | 0.253346i | \(-0.0815310\pi\) | |||||||
\(140\) | −4.72451 | − | 3.78777i | −0.399294 | − | 0.320125i | ||||
\(141\) | − | 1.51336i | − | 0.127448i | ||||||
\(142\) | −8.52369 | − | 17.7585i | −0.715292 | − | 1.49026i | ||||
\(143\) | 0.460758 | 0.0385305 | ||||||||
\(144\) | −6.35675 | − | 28.5326i | −0.529729 | − | 2.37772i | ||||
\(145\) | − | 8.80545i | − | 0.731253i | ||||||
\(146\) | 7.15738 | + | 14.9119i | 0.592349 | + | 1.23412i | ||||
\(147\) | −6.95761 | −0.573854 | ||||||||
\(148\) | −1.74378 | − | 1.39804i | −0.143338 | − | 0.114918i | ||||
\(149\) | −20.3382 | −1.66617 | −0.833085 | − | 0.553146i | \(-0.813427\pi\) | ||||
−0.833085 | + | 0.553146i | \(0.813427\pi\) | |||||||
\(150\) | −1.96474 | − | 4.09340i | −0.160420 | − | 0.334224i | ||||
\(151\) | −1.35251 | −0.110066 | −0.0550330 | − | 0.998485i | \(-0.517526\pi\) | ||||
−0.0550330 | + | 0.998485i | \(0.517526\pi\) | |||||||
\(152\) | −9.37449 | + | 8.00743i | −0.760372 | + | 0.649488i | ||||
\(153\) | 23.1450 | 1.87117 | ||||||||
\(154\) | −0.905268 | − | 1.88607i | −0.0729486 | − | 0.151984i | ||||
\(155\) | 3.66325 | 0.294239 | ||||||||
\(156\) | 4.72451 | + | 3.78777i | 0.378264 | + | 0.303265i | ||||
\(157\) | 6.52895 | 0.521067 | 0.260534 | − | 0.965465i | \(-0.416102\pi\) | ||||
0.260534 | + | 0.965465i | \(0.416102\pi\) | |||||||
\(158\) | 6.44489 | + | 13.4275i | 0.512728 | + | 1.06823i | ||||
\(159\) | 39.8341i | 3.15905i | ||||||||
\(160\) | 4.44550 | − | 3.49822i | 0.351448 | − | 0.276559i | ||||
\(161\) | −21.4573 | −1.69107 | ||||||||
\(162\) | −13.7587 | − | 28.6654i | −1.08099 | − | 2.25216i | ||||
\(163\) | − | 9.64331i | − | 0.755322i | −0.925944 | − | 0.377661i | \(-0.876728\pi\) | ||
0.925944 | − | 0.377661i | \(-0.123272\pi\) | |||||||
\(164\) | −2.44780 | − | 1.96247i | −0.191141 | − | 0.153243i | ||||
\(165\) | − | 1.56868i | − | 0.122122i | ||||||
\(166\) | 23.0352 | − | 11.0564i | 1.78788 | − | 0.858141i | ||||
\(167\) | 0.429732 | 0.0332536 | 0.0166268 | − | 0.999862i | \(-0.494707\pi\) | ||||
0.0166268 | + | 0.999862i | \(0.494707\pi\) | |||||||
\(168\) | 6.22244 | − | 26.7813i | 0.480072 | − | 2.06622i | ||||
\(169\) | 12.1107 | 0.931591 | ||||||||
\(170\) | 1.93809 | + | 4.03787i | 0.148644 | + | 0.309691i | ||||
\(171\) | −18.9109 | + | 25.6344i | −1.44615 | + | 1.96031i | ||||
\(172\) | 5.59860 | + | 4.48856i | 0.426890 | + | 0.342249i | ||||
\(173\) | − | 17.1044i | − | 1.30042i | −0.759753 | − | 0.650212i | \(-0.774680\pi\) | ||
0.759753 | − | 0.650212i | \(-0.225320\pi\) | |||||||
\(174\) | 36.0442 | − | 17.3004i | 2.73251 | − | 1.31154i | ||||
\(175\) | − | 3.02772i | − | 0.228874i | ||||||
\(176\) | 1.90760 | − | 0.424991i | 0.143791 | − | 0.0320349i | ||||
\(177\) | −27.7914 | −2.08893 | ||||||||
\(178\) | 12.5456 | − | 6.02158i | 0.940330 | − | 0.451337i | ||||
\(179\) | 11.9559 | 0.893622 | 0.446811 | − | 0.894628i | \(-0.352560\pi\) | ||||
0.446811 | + | 0.894628i | \(0.352560\pi\) | |||||||
\(180\) | 9.14261 | − | 11.4036i | 0.681450 | − | 0.849976i | ||||
\(181\) | 17.8046i | 1.32341i | 0.749765 | + | 0.661704i | \(0.230166\pi\) | ||||
−0.749765 | + | 0.661704i | \(0.769834\pi\) | |||||||
\(182\) | 1.74726 | + | 3.64031i | 0.129516 | + | 0.269837i | ||||
\(183\) | −27.6765 | −2.04590 | ||||||||
\(184\) | 4.53647 | − | 19.5249i | 0.334433 | − | 1.43939i | ||||
\(185\) | − | 1.11751i | − | 0.0821606i | ||||||
\(186\) | 7.19732 | + | 14.9951i | 0.527733 | + | 1.09950i | ||||
\(187\) | 1.54740i | 0.113157i | ||||||||
\(188\) | 0.735524 | + | 0.589690i | 0.0536436 | + | 0.0430076i | ||||
\(189\) | − | 41.8778i | − | 3.04616i | ||||||
\(190\) | −6.05569 | − | 1.15265i | −0.439326 | − | 0.0836220i | ||||
\(191\) | 0.848579i | 0.0614010i | 0.999529 | + | 0.0307005i | \(0.00977381\pi\) | ||||
−0.999529 | + | 0.0307005i | \(0.990226\pi\) | |||||||
\(192\) | 23.0538 | + | 11.3241i | 1.66377 | + | 0.817247i | ||||
\(193\) | − | 23.0432i | − | 1.65869i | −0.558739 | − | 0.829343i | \(-0.688715\pi\) | ||
0.558739 | − | 0.829343i | \(-0.311285\pi\) | |||||||
\(194\) | −2.18718 | + | 1.04980i | −0.157030 | + | 0.0753710i | ||||
\(195\) | 3.02772i | 0.216819i | ||||||||
\(196\) | 2.71107 | − | 3.38153i | 0.193648 | − | 0.241538i | ||||
\(197\) | 1.14519 | 0.0815914 | 0.0407957 | − | 0.999168i | \(-0.487011\pi\) | ||||
0.0407957 | + | 0.999168i | \(0.487011\pi\) | |||||||
\(198\) | 4.55243 | − | 2.18506i | 0.323527 | − | 0.155285i | ||||
\(199\) | 1.56194i | 0.110723i | 0.998466 | + | 0.0553615i | \(0.0176311\pi\) | ||||
−0.998466 | + | 0.0553615i | \(0.982369\pi\) | |||||||
\(200\) | 2.75504 | + | 0.640115i | 0.194811 | + | 0.0452629i | ||||
\(201\) | −21.1711 | −1.49330 | ||||||||
\(202\) | −5.79829 | − | 12.0804i | −0.407967 | − | 0.849971i | ||||
\(203\) | 26.6604 | 1.87119 | ||||||||
\(204\) | −12.7208 | + | 15.8667i | −0.890633 | + | 1.11089i | ||||
\(205\) | − | 1.56868i | − | 0.109561i | ||||||
\(206\) | −3.33237 | − | 6.94277i | −0.232177 | − | 0.483726i | ||||
\(207\) | − | 51.7918i | − | 3.59978i | ||||||
\(208\) | −3.68187 | + | 0.820278i | −0.255291 | + | 0.0568760i | ||||
\(209\) | −1.71383 | − | 1.26432i | −0.118548 | − | 0.0874548i | ||||
\(210\) | 12.3936 | − | 5.94866i | 0.855243 | − | 0.410497i | ||||
\(211\) | −9.54786 | −0.657302 | −0.328651 | − | 0.944451i | \(-0.606594\pi\) | ||||
−0.328651 | + | 0.944451i | \(0.606594\pi\) | |||||||
\(212\) | −19.3602 | − | 15.5216i | −1.32966 | − | 1.06603i | ||||
\(213\) | 44.7198 | 3.06415 | ||||||||
\(214\) | −2.12767 | − | 4.43285i | −0.145444 | − | 0.303023i | ||||
\(215\) | 3.58788i | 0.244691i | ||||||||
\(216\) | 38.1063 | + | 8.85373i | 2.59280 | + | 0.602420i | ||||
\(217\) | 11.0913i | 0.752925i | ||||||||
\(218\) | −16.0056 | + | 7.68232i | −1.08404 | + | 0.520312i | ||||
\(219\) | −37.5514 | −2.53749 | ||||||||
\(220\) | 0.762409 | + | 0.611245i | 0.0514016 | + | 0.0412101i | ||||
\(221\) | − | 2.98665i | − | 0.200904i | ||||||
\(222\) | 4.57439 | − | 2.19560i | 0.307013 | − | 0.147359i | ||||
\(223\) | −8.65072 | −0.579295 | −0.289647 | − | 0.957133i | \(-0.593538\pi\) | ||||
−0.289647 | + | 0.957133i | \(0.593538\pi\) | |||||||
\(224\) | 10.5916 | + | 13.4597i | 0.707682 | + | 0.899314i | ||||
\(225\) | 7.30804 | 0.487203 | ||||||||
\(226\) | 12.8738 | − | 6.17913i | 0.856352 | − | 0.411029i | ||||
\(227\) | −2.31886 | −0.153908 | −0.0769541 | − | 0.997035i | \(-0.524519\pi\) | ||||
−0.0769541 | + | 0.997035i | \(0.524519\pi\) | |||||||
\(228\) | −7.17959 | − | 27.0530i | −0.475480 | − | 1.79163i | ||||
\(229\) | −16.7074 | −1.10406 | −0.552029 | − | 0.833825i | \(-0.686146\pi\) | ||||
−0.552029 | + | 0.833825i | \(0.686146\pi\) | |||||||
\(230\) | 9.03557 | − | 4.33687i | 0.595788 | − | 0.285964i | ||||
\(231\) | 4.74952 | 0.312495 | ||||||||
\(232\) | −5.63650 | + | 24.2594i | −0.370054 | + | 1.59271i | ||||
\(233\) | −20.0432 | −1.31308 | −0.656538 | − | 0.754293i | \(-0.727980\pi\) | ||||
−0.656538 | + | 0.754293i | \(0.727980\pi\) | |||||||
\(234\) | −8.78666 | + | 4.21740i | −0.574402 | + | 0.275700i | ||||
\(235\) | 0.471362i | 0.0307483i | ||||||||
\(236\) | 10.8291 | − | 13.5072i | 0.704913 | − | 0.879242i | ||||
\(237\) | −33.8133 | −2.19641 | ||||||||
\(238\) | −12.2255 | + | 5.86797i | −0.792463 | + | 0.380364i | ||||
\(239\) | − | 19.1162i | − | 1.23652i | −0.785972 | − | 0.618262i | \(-0.787837\pi\) | ||
0.785972 | − | 0.618262i | \(-0.212163\pi\) | |||||||
\(240\) | 2.79269 | + | 12.5351i | 0.180267 | + | 0.809139i | ||||
\(241\) | − | 10.4803i | − | 0.675093i | −0.941309 | − | 0.337546i | \(-0.890403\pi\) | ||
0.941309 | − | 0.337546i | \(-0.109597\pi\) | |||||||
\(242\) | −6.58537 | − | 13.7202i | −0.423323 | − | 0.881966i | ||||
\(243\) | 30.6910 | 1.96883 | ||||||||
\(244\) | 10.7843 | − | 13.4513i | 0.690393 | − | 0.861131i | ||||
\(245\) | 2.16706 | 0.138449 | ||||||||
\(246\) | 6.42123 | − | 3.08204i | 0.409403 | − | 0.196504i | ||||
\(247\) | 3.30787 | + | 2.44027i | 0.210475 | + | 0.155271i | ||||
\(248\) | −10.0924 | − | 2.34490i | −0.640868 | − | 0.148901i | ||||
\(249\) | 58.0076i | 3.67608i | ||||||||
\(250\) | 0.611950 | + | 1.27496i | 0.0387031 | + | 0.0806354i | ||||
\(251\) | − | 25.7318i | − | 1.62418i | −0.583535 | − | 0.812088i | \(-0.698331\pi\) | ||
0.583535 | − | 0.812088i | \(-0.301669\pi\) | |||||||
\(252\) | 34.5269 | + | 27.6812i | 2.17499 | + | 1.74375i | ||||
\(253\) | 3.46263 | 0.217694 | ||||||||
\(254\) | 2.83883 | + | 5.91451i | 0.178124 | + | 0.371109i | ||||
\(255\) | −10.1682 | −0.636759 | ||||||||
\(256\) | −14.4868 | + | 6.79211i | −0.905425 | + | 0.424507i | ||||
\(257\) | − | 10.3042i | − | 0.642757i | −0.946951 | − | 0.321379i | \(-0.895854\pi\) | ||
0.946951 | − | 0.321379i | \(-0.104146\pi\) | |||||||
\(258\) | −14.6866 | + | 7.04924i | −0.914349 | + | 0.438866i | ||||
\(259\) | 3.38349 | 0.210240 | ||||||||
\(260\) | −1.47153 | − | 1.17977i | −0.0912604 | − | 0.0731660i | ||||
\(261\) | 64.3506i | 3.98320i | ||||||||
\(262\) | −27.5876 | + | 13.2414i | −1.70437 | + | 0.818059i | ||||
\(263\) | 3.62234i | 0.223363i | 0.993744 | + | 0.111681i | \(0.0356236\pi\) | ||||
−0.993744 | + | 0.111681i | \(0.964376\pi\) | |||||||
\(264\) | −1.00413 | + | 4.32178i | −0.0618002 | + | 0.265987i | ||||
\(265\) | − | 12.4070i | − | 0.762157i | ||||||
\(266\) | 3.48989 | − | 18.3349i | 0.213979 | − | 1.12419i | ||||
\(267\) | 31.5924i | 1.93342i | ||||||||
\(268\) | 8.24945 | − | 10.2896i | 0.503915 | − | 0.628536i | ||||
\(269\) | 14.9871i | 0.913778i | 0.889524 | + | 0.456889i | \(0.151036\pi\) | ||||
−0.889524 | + | 0.456889i | \(0.848964\pi\) | |||||||
\(270\) | 8.46417 | + | 17.6345i | 0.515113 | + | 1.07320i | ||||
\(271\) | 2.44027i | 0.148236i | 0.997249 | + | 0.0741179i | \(0.0236141\pi\) | ||||
−0.997249 | + | 0.0741179i | \(0.976386\pi\) | |||||||
\(272\) | −2.75480 | − | 12.3651i | −0.167035 | − | 0.749744i | ||||
\(273\) | −9.16706 | −0.554816 | ||||||||
\(274\) | −7.68048 | − | 16.0018i | −0.463995 | − | 0.966702i | ||||
\(275\) | 0.488592i | 0.0294632i | ||||||||
\(276\) | 35.5050 | + | 28.4654i | 2.13715 | + | 1.71341i | ||||
\(277\) | 22.7032 | 1.36410 | 0.682052 | − | 0.731303i | \(-0.261088\pi\) | ||||
0.682052 | + | 0.731303i | \(0.261088\pi\) | |||||||
\(278\) | −7.61635 | + | 3.65567i | −0.456798 | + | 0.219253i | ||||
\(279\) | −26.7712 | −1.60275 | ||||||||
\(280\) | −1.93809 | + | 8.34148i | −0.115823 | + | 0.498499i | ||||
\(281\) | − | 7.97768i | − | 0.475908i | −0.971276 | − | 0.237954i | \(-0.923523\pi\) | ||
0.971276 | − | 0.237954i | \(-0.0764768\pi\) | |||||||
\(282\) | −1.92947 | + | 0.926102i | −0.114898 | + | 0.0551486i | ||||
\(283\) | 6.56125i | 0.390026i | 0.980801 | + | 0.195013i | \(0.0624749\pi\) | ||||
−0.980801 | + | 0.195013i | \(0.937525\pi\) | |||||||
\(284\) | −17.4253 | + | 21.7347i | −1.03400 | + | 1.28972i | ||||
\(285\) | 8.30804 | − | 11.2618i | 0.492126 | − | 0.667094i | ||||
\(286\) | −0.281961 | − | 0.587447i | −0.0166727 | − | 0.0347365i | ||||
\(287\) | 4.74952 | 0.280355 | ||||||||
\(288\) | −32.4879 | + | 25.5651i | −1.91437 | + | 1.50644i | ||||
\(289\) | −6.96971 | −0.409983 | ||||||||
\(290\) | −11.2266 | + | 5.38850i | −0.659247 | + | 0.316424i | ||||
\(291\) | − | 5.50779i | − | 0.322872i | ||||||
\(292\) | 14.6321 | − | 18.2507i | 0.856280 | − | 1.06804i | ||||
\(293\) | 7.47982i | 0.436976i | 0.975840 | + | 0.218488i | \(0.0701124\pi\) | ||||
−0.975840 | + | 0.218488i | \(0.929888\pi\) | |||||||
\(294\) | 4.25771 | + | 8.87065i | 0.248315 | + | 0.517347i | ||||
\(295\) | 8.65611 | 0.503978 | ||||||||
\(296\) | −0.715332 | + | 3.07877i | −0.0415778 | + | 0.178950i | ||||
\(297\) | 6.75794i | 0.392136i | ||||||||
\(298\) | 12.4460 | + | 25.9303i | 0.720975 | + | 1.50210i | ||||
\(299\) | −6.68324 | −0.386502 | ||||||||
\(300\) | −4.01659 | + | 5.00991i | −0.231898 | + | 0.289247i | ||||
\(301\) | −10.8631 | −0.626138 | ||||||||
\(302\) | 0.827671 | + | 1.72440i | 0.0476271 | + | 0.0992279i | ||||
\(303\) | 30.4209 | 1.74764 | ||||||||
\(304\) | 15.9459 | + | 7.05193i | 0.914557 | + | 0.404456i | ||||
\(305\) | 8.62030 | 0.493597 | ||||||||
\(306\) | −14.1636 | − | 29.5089i | −0.809680 | − | 1.68691i | ||||
\(307\) | 12.2926 | 0.701574 | 0.350787 | − | 0.936455i | \(-0.385914\pi\) | ||||
0.350787 | + | 0.936455i | \(0.385914\pi\) | |||||||
\(308\) | −1.85068 | + | 2.30836i | −0.105452 | + | 0.131531i | ||||
\(309\) | 17.4834 | 0.994595 | ||||||||
\(310\) | −2.24173 | − | 4.67049i | −0.127321 | − | 0.265266i | ||||
\(311\) | − | 2.03330i | − | 0.115298i | −0.998337 | − | 0.0576490i | \(-0.981640\pi\) | ||
0.998337 | − | 0.0576490i | \(-0.0183604\pi\) | |||||||
\(312\) | 1.93809 | − | 8.34148i | 0.109722 | − | 0.472243i | ||||
\(313\) | 23.5095 | 1.32883 | 0.664417 | − | 0.747362i | \(-0.268680\pi\) | ||||
0.664417 | + | 0.747362i | \(0.268680\pi\) | |||||||
\(314\) | −3.99539 | − | 8.32414i | −0.225473 | − | 0.469758i | ||||
\(315\) | 22.1267i | 1.24670i | ||||||||
\(316\) | 13.1755 | − | 16.4339i | 0.741182 | − | 0.924480i | ||||
\(317\) | − | 10.5447i | − | 0.592250i | −0.955149 | − | 0.296125i | \(-0.904306\pi\) | ||
0.955149 | − | 0.296125i | \(-0.0956944\pi\) | |||||||
\(318\) | 50.7868 | − | 24.3765i | 2.84798 | − | 1.36697i | ||||
\(319\) | −4.30227 | −0.240881 | ||||||||
\(320\) | −7.18051 | − | 3.52709i | −0.401403 | − | 0.197170i | ||||
\(321\) | 11.1629 | 0.623050 | ||||||||
\(322\) | 13.1308 | + | 27.3571i | 0.731751 | + | 1.52455i | ||||
\(323\) | −8.19535 | + | 11.1091i | −0.456001 | + | 0.618126i | ||||
\(324\) | −28.1275 | + | 35.0835i | −1.56264 | + | 1.94909i | ||||
\(325\) | − | 0.943033i | − | 0.0523101i | ||||||
\(326\) | −12.2948 | + | 5.90123i | −0.680947 | + | 0.326839i | ||||
\(327\) | − | 40.3055i | − | 2.22890i | ||||||
\(328\) | −1.00413 | + | 4.32178i | −0.0554441 | + | 0.238630i | ||||
\(329\) | −1.42715 | −0.0786814 | ||||||||
\(330\) | −2.00000 | + | 0.959954i | −0.110096 | + | 0.0528437i | ||||
\(331\) | 1.08262 | 0.0595061 | 0.0297531 | − | 0.999557i | \(-0.490528\pi\) | ||||
0.0297531 | + | 0.999557i | \(0.490528\pi\) | |||||||
\(332\) | −28.1928 | − | 22.6030i | −1.54728 | − | 1.24050i | ||||
\(333\) | 8.16678i | 0.447537i | ||||||||
\(334\) | −0.262974 | − | 0.547890i | −0.0143893 | − | 0.0299792i | ||||
\(335\) | 6.59410 | 0.360274 | ||||||||
\(336\) | −37.9528 | + | 8.45546i | −2.07050 | + | 0.461283i | ||||
\(337\) | 0.257449i | 0.0140241i | 0.999975 | + | 0.00701206i | \(0.00223203\pi\) | ||||
−0.999975 | + | 0.00701206i | \(0.997768\pi\) | |||||||
\(338\) | −7.41114 | − | 15.4406i | −0.403113 | − | 0.839859i | ||||
\(339\) | 32.4190i | 1.76076i | ||||||||
\(340\) | 3.96210 | − | 4.94195i | 0.214875 | − | 0.268015i | ||||
\(341\) | − | 1.78983i | − | 0.0969249i | ||||||
\(342\) | 44.2553 | + | 8.42361i | 2.39305 | + | 0.455497i | ||||
\(343\) | − | 14.6328i | − | 0.790095i | ||||||
\(344\) | 2.29665 | − | 9.88476i | 0.123827 | − | 0.532950i | ||||
\(345\) | 22.7535i | 1.22501i | ||||||||
\(346\) | −21.8074 | + | 10.4671i | −1.17237 | + | 0.562712i | ||||
\(347\) | 16.9053i | 0.907523i | 0.891123 | + | 0.453762i | \(0.149918\pi\) | ||||
−0.891123 | + | 0.453762i | \(0.850082\pi\) | |||||||
\(348\) | −44.1145 | − | 35.3679i | −2.36479 | − | 1.89592i | ||||
\(349\) | −15.4709 | −0.828138 | −0.414069 | − | 0.910245i | \(-0.635893\pi\) | ||||
−0.414069 | + | 0.910245i | \(0.635893\pi\) | |||||||
\(350\) | −3.86021 | + | 1.85281i | −0.206337 | + | 0.0990369i | ||||
\(351\) | − | 13.0435i | − | 0.696212i | ||||||
\(352\) | −1.70920 | − | 2.17203i | −0.0911007 | − | 0.115770i | ||||
\(353\) | −16.0568 | −0.854620 | −0.427310 | − | 0.904105i | \(-0.640539\pi\) | ||||
−0.427310 | + | 0.904105i | \(0.640539\pi\) | |||||||
\(354\) | 17.0070 | + | 35.4329i | 0.903910 | + | 1.88324i | ||||
\(355\) | −13.9287 | −0.739260 | ||||||||
\(356\) | −15.3545 | − | 12.3102i | −0.813788 | − | 0.652437i | ||||
\(357\) | − | 30.7865i | − | 1.62939i | ||||||
\(358\) | −7.31639 | − | 15.2432i | −0.386683 | − | 0.805629i | ||||
\(359\) | 8.15765i | 0.430544i | 0.976554 | + | 0.215272i | \(0.0690639\pi\) | ||||
−0.976554 | + | 0.215272i | \(0.930936\pi\) | |||||||
\(360\) | −20.1340 | − | 4.67799i | −1.06115 | − | 0.246552i | ||||
\(361\) | −5.60782 | − | 18.1536i | −0.295148 | − | 0.955451i | ||||
\(362\) | 22.7002 | − | 10.8955i | 1.19309 | − | 0.572657i | ||||
\(363\) | 34.5503 | 1.81342 | ||||||||
\(364\) | 3.57200 | − | 4.45537i | 0.187224 | − | 0.233525i | ||||
\(365\) | 11.6960 | 0.612197 | ||||||||
\(366\) | 16.9366 | + | 35.2863i | 0.885291 | + | 1.84444i | ||||
\(367\) | 3.05212i | 0.159319i | 0.996822 | + | 0.0796597i | \(0.0253834\pi\) | ||||
−0.996822 | + | 0.0796597i | \(0.974617\pi\) | |||||||
\(368\) | −27.6695 | + | 6.16444i | −1.44237 | + | 0.321344i | ||||
\(369\) | 11.4640i | 0.596791i | ||||||||
\(370\) | −1.42477 | + | 0.683858i | −0.0740704 | + | 0.0355521i | ||||
\(371\) | 37.5649 | 1.95027 | ||||||||
\(372\) | 14.7138 | − | 18.3525i | 0.762873 | − | 0.951535i | ||||
\(373\) | 22.1917i | 1.14904i | 0.818490 | + | 0.574521i | \(0.194812\pi\) | ||||
−0.818490 | + | 0.574521i | \(0.805188\pi\) | |||||||
\(374\) | 1.97287 | − | 0.946933i | 0.102015 | − | 0.0489647i | ||||
\(375\) | −3.21061 | −0.165795 | ||||||||
\(376\) | 0.301726 | − | 1.29862i | 0.0155603 | − | 0.0669713i | ||||
\(377\) | 8.30384 | 0.427669 | ||||||||
\(378\) | −53.3924 | + | 25.6271i | −2.74621 | + | 1.31812i | ||||
\(379\) | 23.4631 | 1.20522 | 0.602609 | − | 0.798037i | \(-0.294128\pi\) | ||||
0.602609 | + | 0.798037i | \(0.294128\pi\) | |||||||
\(380\) | 2.23620 | + | 8.42611i | 0.114715 | + | 0.432251i | ||||
\(381\) | −14.8940 | −0.763042 | ||||||||
\(382\) | 1.08190 | − | 0.519288i | 0.0553549 | − | 0.0265691i | ||||
\(383\) | 8.91696 | 0.455636 | 0.227818 | − | 0.973704i | \(-0.426841\pi\) | ||||
0.227818 | + | 0.973704i | \(0.426841\pi\) | |||||||
\(384\) | 0.329958 | − | 36.3225i | 0.0168381 | − | 1.85357i | ||||
\(385\) | −1.47932 | −0.0753930 | ||||||||
\(386\) | −29.3791 | + | 14.1013i | −1.49536 | + | 0.717737i | ||||
\(387\) | − | 26.2204i | − | 1.33286i | ||||||
\(388\) | 2.67689 | + | 2.14614i | 0.135899 | + | 0.108954i | ||||
\(389\) | 17.8050 | 0.902751 | 0.451375 | − | 0.892334i | \(-0.350934\pi\) | ||||
0.451375 | + | 0.892334i | \(0.350934\pi\) | |||||||
\(390\) | 3.86021 | − | 1.85281i | 0.195469 | − | 0.0938208i | ||||
\(391\) | − | 22.4448i | − | 1.13508i | ||||||
\(392\) | −5.97035 | − | 1.38717i | −0.301548 | − | 0.0700626i | ||||
\(393\) | − | 69.4716i | − | 3.50438i | ||||||
\(394\) | −0.700799 | − | 1.46007i | −0.0353058 | − | 0.0735572i | ||||
\(395\) | 10.5317 | 0.529908 | ||||||||
\(396\) | −5.57172 | − | 4.46700i | −0.279989 | − | 0.224475i | ||||
\(397\) | 14.6683 | 0.736179 | 0.368089 | − | 0.929790i | \(-0.380012\pi\) | ||||
0.368089 | + | 0.929790i | \(0.380012\pi\) | |||||||
\(398\) | 1.99141 | − | 0.955830i | 0.0998203 | − | 0.0479114i | ||||
\(399\) | 34.0977 | + | 25.1544i | 1.70702 | + | 1.25929i | ||||
\(400\) | −0.869829 | − | 3.90428i | −0.0434915 | − | 0.195214i | ||||
\(401\) | − | 18.1350i | − | 0.905621i | −0.891607 | − | 0.452810i | \(-0.850421\pi\) | ||
0.891607 | − | 0.452810i | \(-0.149579\pi\) | |||||||
\(402\) | 12.9557 | + | 26.9923i | 0.646170 | + | 1.34625i | ||||
\(403\) | 3.45457i | 0.172084i | ||||||||
\(404\) | −11.8537 | + | 14.7852i | −0.589743 | + | 0.735589i | ||||
\(405\) | −22.4834 | −1.11721 | ||||||||
\(406\) | −16.3148 | − | 33.9909i | −0.809692 | − | 1.68694i | ||||
\(407\) | −0.546004 | −0.0270644 | ||||||||
\(408\) | 28.0139 | + | 6.50883i | 1.38689 | + | 0.322235i | ||||
\(409\) | 6.24316i | 0.308704i | 0.988016 | + | 0.154352i | \(0.0493290\pi\) | ||||
−0.988016 | + | 0.154352i | \(0.950671\pi\) | |||||||
\(410\) | −2.00000 | + | 0.959954i | −0.0987730 | + | 0.0474087i | ||||
\(411\) | 40.2959 | 1.98765 | ||||||||
\(412\) | −6.81250 | + | 8.49726i | −0.335628 | + | 0.418630i | ||||
\(413\) | 26.2082i | 1.28962i | ||||||||
\(414\) | −66.0323 | + | 31.6940i | −3.24531 | + | 1.55768i | ||||
\(415\) | − | 18.0674i | − | 0.886896i | ||||||
\(416\) | 3.29894 | + | 4.19225i | 0.161744 | + | 0.205542i | ||||
\(417\) | − | 19.1796i | − | 0.939228i | ||||||
\(418\) | −0.563175 | + | 2.95876i | −0.0275458 | + | 0.144718i | ||||
\(419\) | − | 4.64669i | − | 0.227006i | −0.993538 | − | 0.113503i | \(-0.963793\pi\) | ||
0.993538 | − | 0.113503i | \(-0.0362071\pi\) | |||||||
\(420\) | −15.1686 | − | 12.1611i | −0.740151 | − | 0.593400i | ||||
\(421\) | 15.7441i | 0.767320i | 0.923474 | + | 0.383660i | \(0.125337\pi\) | ||||
−0.923474 | + | 0.383660i | \(0.874663\pi\) | |||||||
\(422\) | 5.84282 | + | 12.1731i | 0.284424 | + | 0.592578i | ||||
\(423\) | − | 3.44474i | − | 0.167489i | ||||||
\(424\) | −7.94191 | + | 34.1818i | −0.385693 | + | 1.66002i | ||||
\(425\) | 3.16706 | 0.153625 | ||||||||
\(426\) | −27.3663 | − | 57.0158i | −1.32590 | − | 2.76242i | ||||
\(427\) | 26.0998i | 1.26306i | ||||||||
\(428\) | −4.34967 | + | 5.42537i | −0.210249 | + | 0.262245i | ||||
\(429\) | 1.47932 | 0.0714221 | ||||||||
\(430\) | 4.57439 | − | 2.19560i | 0.220597 | − | 0.105881i | ||||
\(431\) | −14.2220 | −0.685050 | −0.342525 | − | 0.939509i | \(-0.611282\pi\) | ||||
−0.342525 | + | 0.939509i | \(0.611282\pi\) | |||||||
\(432\) | −12.0310 | − | 54.0019i | −0.578843 | − | 2.59817i | ||||
\(433\) | − | 30.9395i | − | 1.48686i | −0.668815 | − | 0.743429i | \(-0.733198\pi\) | ||
0.668815 | − | 0.743429i | \(-0.266802\pi\) | |||||||
\(434\) | 14.1409 | − | 6.78731i | 0.678785 | − | 0.325801i | ||||
\(435\) | − | 28.2709i | − | 1.35549i | ||||||
\(436\) | 19.5893 | + | 15.7053i | 0.938155 | + | 0.752146i | ||||
\(437\) | 24.8589 | + | 18.3388i | 1.18916 | + | 0.877263i | ||||
\(438\) | 22.9796 | + | 47.8764i | 1.09801 | + | 2.28762i | ||||
\(439\) | −24.9444 | −1.19053 | −0.595266 | − | 0.803529i | \(-0.702953\pi\) | ||||
−0.595266 | + | 0.803529i | \(0.702953\pi\) | |||||||
\(440\) | 0.312755 | − | 1.34609i | 0.0149100 | − | 0.0641723i | ||||
\(441\) | −15.8370 | −0.754143 | ||||||||
\(442\) | −3.80785 | + | 1.82768i | −0.181121 | + | 0.0869338i | ||||
\(443\) | − | 23.4764i | − | 1.11540i | −0.830044 | − | 0.557698i | \(-0.811685\pi\) | ||
0.830044 | − | 0.557698i | \(-0.188315\pi\) | |||||||
\(444\) | −5.59860 | − | 4.48856i | −0.265698 | − | 0.213018i | ||||
\(445\) | − | 9.83998i | − | 0.466460i | ||||||
\(446\) | 5.29381 | + | 11.0293i | 0.250669 | + | 0.522252i | ||||
\(447\) | −65.2981 | −3.08849 | ||||||||
\(448\) | 10.6790 | − | 21.7405i | 0.504536 | − | 1.02714i | ||||
\(449\) | − | 1.97053i | − | 0.0929951i | −0.998918 | − | 0.0464976i | \(-0.985194\pi\) | ||
0.998918 | − | 0.0464976i | \(-0.0148060\pi\) | |||||||
\(450\) | −4.47216 | − | 9.31745i | −0.210820 | − | 0.439229i | ||||
\(451\) | −0.766444 | −0.0360904 | ||||||||
\(452\) | −15.7562 | − | 12.6322i | −0.741112 | − | 0.594170i | ||||
\(453\) | −4.34240 | −0.204024 | ||||||||
\(454\) | 1.41903 | + | 2.95645i | 0.0665982 | + | 0.138753i | ||||
\(455\) | 2.85524 | 0.133856 | ||||||||
\(456\) | −30.0979 | + | 25.7088i | −1.40946 | + | 1.20392i | ||||
\(457\) | −9.40564 | −0.439977 | −0.219989 | − | 0.975502i | \(-0.570602\pi\) | ||||
−0.219989 | + | 0.975502i | \(0.570602\pi\) | |||||||
\(458\) | 10.2241 | + | 21.3013i | 0.477742 | + | 0.995343i | ||||
\(459\) | 43.8051 | 2.04465 | ||||||||
\(460\) | −11.0586 | − | 8.86602i | −0.515612 | − | 0.413380i | ||||
\(461\) | 18.2902 | 0.851861 | 0.425930 | − | 0.904756i | \(-0.359947\pi\) | ||||
0.425930 | + | 0.904756i | \(0.359947\pi\) | |||||||
\(462\) | −2.90647 | − | 6.05543i | −0.135221 | − | 0.281724i | ||||
\(463\) | 8.89549i | 0.413409i | 0.978403 | + | 0.206704i | \(0.0662738\pi\) | ||||
−0.978403 | + | 0.206704i | \(0.933726\pi\) | |||||||
\(464\) | 34.3790 | − | 7.65924i | 1.59600 | − | 0.355571i | ||||
\(465\) | 11.7613 | 0.545416 | ||||||||
\(466\) | 12.2655 | + | 25.5543i | 0.568187 | + | 1.18378i | ||||
\(467\) | − | 0.513185i | − | 0.0237474i | −0.999930 | − | 0.0118737i | \(-0.996220\pi\) | ||
0.999930 | − | 0.0118737i | \(-0.00377960\pi\) | |||||||
\(468\) | 10.7540 | + | 8.62178i | 0.497104 | + | 0.398542i | ||||
\(469\) | 19.9651i | 0.921901i | ||||||||
\(470\) | 0.600967 | − | 0.288450i | 0.0277205 | − | 0.0133052i | ||||
\(471\) | 20.9619 | 0.965876 | ||||||||
\(472\) | −23.8479 | − | 5.54090i | −1.09769 | − | 0.255041i | ||||
\(473\) | 1.75301 | 0.0806034 | ||||||||
\(474\) | 20.6921 | + | 43.1105i | 0.950418 | + | 1.98013i | ||||
\(475\) | −2.58768 | + | 3.50769i | −0.118731 | + | 0.160944i | ||||
\(476\) | 14.9628 | + | 11.9961i | 0.685820 | + | 0.549841i | ||||
\(477\) | 90.6710i | 4.15154i | ||||||||
\(478\) | −24.3723 | + | 11.6982i | −1.11476 | + | 0.535061i | ||||
\(479\) | 20.5748i | 0.940086i | 0.882643 | + | 0.470043i | \(0.155762\pi\) | ||||
−0.882643 | + | 0.470043i | \(0.844238\pi\) | |||||||
\(480\) | 14.2728 | − | 11.2314i | 0.651460 | − | 0.512643i | ||||
\(481\) | 1.05384 | 0.0480512 | ||||||||
\(482\) | −13.3619 | + | 6.41340i | −0.608617 | + | 0.292122i | ||||
\(483\) | −68.8911 | −3.13465 | ||||||||
\(484\) | −13.4627 | + | 16.7921i | −0.611942 | + | 0.763279i | ||||
\(485\) | 1.71549i | 0.0778965i | ||||||||
\(486\) | −18.7814 | − | 39.1298i | −0.851941 | − | 1.77496i | ||||
\(487\) | 1.51600 | 0.0686965 | 0.0343482 | − | 0.999410i | \(-0.489064\pi\) | ||||
0.0343482 | + | 0.999410i | \(0.489064\pi\) | |||||||
\(488\) | −23.7493 | − | 5.51798i | −1.07508 | − | 0.249787i | ||||
\(489\) | − | 30.9610i | − | 1.40010i | ||||||
\(490\) | −1.32614 | − | 2.76291i | −0.0599087 | − | 0.124816i | ||||
\(491\) | 18.4129i | 0.830962i | 0.909602 | + | 0.415481i | \(0.136387\pi\) | ||||
−0.909602 | + | 0.415481i | \(0.863613\pi\) | |||||||
\(492\) | −7.85895 | − | 6.30074i | −0.354309 | − | 0.284059i | ||||
\(493\) | 27.8874i | 1.25599i | ||||||||
\(494\) | 1.08699 | − | 5.71072i | 0.0489058 | − | 0.256937i | ||||
\(495\) | − | 3.57065i | − | 0.160489i | ||||||
\(496\) | 3.18640 | + | 14.3023i | 0.143074 | + | 0.642194i | ||||
\(497\) | − | 42.1722i | − | 1.89168i | ||||||
\(498\) | 73.9572 | − | 35.4978i | 3.31410 | − | 1.59069i | ||||
\(499\) | 8.98900i | 0.402403i | 0.979550 | + | 0.201202i | \(0.0644846\pi\) | ||||
−0.979550 | + | 0.201202i | \(0.935515\pi\) | |||||||
\(500\) | 1.25103 | − | 1.56042i | 0.0559479 | − | 0.0697842i | ||||
\(501\) | 1.37970 | 0.0616406 | ||||||||
\(502\) | −32.8069 | + | 15.7466i | −1.46425 | + | 0.702804i | ||||
\(503\) | − | 10.0185i | − | 0.446703i | −0.974738 | − | 0.223352i | \(-0.928300\pi\) | ||
0.974738 | − | 0.223352i | \(-0.0716998\pi\) | |||||||
\(504\) | 14.1636 | − | 60.9599i | 0.630898 | − | 2.71537i | ||||
\(505\) | −9.47511 | −0.421637 | ||||||||
\(506\) | −2.11896 | − | 4.41471i | −0.0941991 | − | 0.196258i | ||||
\(507\) | 38.8827 | 1.72684 | ||||||||
\(508\) | 5.80353 | − | 7.23877i | 0.257490 | − | 0.321168i | ||||
\(509\) | − | 17.0538i | − | 0.755898i | −0.925826 | − | 0.377949i | \(-0.876629\pi\) | ||
0.925826 | − | 0.377949i | \(-0.123371\pi\) | |||||||
\(510\) | 6.22244 | + | 12.9640i | 0.275534 | + | 0.574058i | ||||
\(511\) | 35.4122i | 1.56654i | ||||||||
\(512\) | 17.5249 | + | 14.3136i | 0.774496 | + | 0.632578i | ||||
\(513\) | −35.7914 | + | 48.5165i | −1.58023 | + | 2.14206i | ||||
\(514\) | −13.1374 | + | 6.30565i | −0.579466 | + | 0.278130i | ||||
\(515\) | −5.44549 | −0.239957 | ||||||||
\(516\) | 17.9750 | + | 14.4110i | 0.791303 | + | 0.634410i | ||||
\(517\) | 0.230304 | 0.0101287 | ||||||||
\(518\) | −2.07053 | − | 4.31381i | −0.0909738 | − | 0.189538i | ||||
\(519\) | − | 54.9157i | − | 2.41053i | ||||||
\(520\) | −0.603649 | + | 2.59810i | −0.0264718 | + | 0.113934i | ||||
\(521\) | − | 15.1017i | − | 0.661618i | −0.943698 | − | 0.330809i | \(-0.892678\pi\) | ||
0.943698 | − | 0.330809i | \(-0.107322\pi\) | |||||||
\(522\) | 82.0443 | − | 39.3794i | 3.59098 | − | 1.72359i | ||||
\(523\) | 3.49037 | 0.152623 | 0.0763117 | − | 0.997084i | \(-0.475686\pi\) | ||||
0.0763117 | + | 0.997084i | \(0.475686\pi\) | |||||||
\(524\) | 33.7645 | + | 27.0700i | 1.47501 | + | 1.18256i | ||||
\(525\) | − | 9.72083i | − | 0.424252i | ||||||
\(526\) | 4.61833 | − | 2.21669i | 0.201369 | − | 0.0966523i | ||||
\(527\) | −11.6017 | −0.505380 | ||||||||
\(528\) | 6.12456 | − | 1.36448i | 0.266537 | − | 0.0593815i | ||||
\(529\) | −27.2250 | −1.18369 | ||||||||
\(530\) | −15.8184 | + | 7.59248i | −0.687108 | + | 0.329796i | ||||
\(531\) | −63.2592 | −2.74522 | ||||||||
\(532\) | −25.5119 | + | 6.77059i | −1.10608 | + | 0.293542i | ||||
\(533\) | 1.47932 | 0.0640763 | ||||||||
\(534\) | 40.2790 | − | 19.3330i | 1.74304 | − | 0.836620i | ||||
\(535\) | −3.47686 | −0.150318 | ||||||||
\(536\) | −18.1670 | − | 4.22098i | −0.784696 | − | 0.182319i | ||||
\(537\) | 38.3856 | 1.65646 | ||||||||
\(538\) | 19.1079 | − | 9.17134i | 0.823799 | − | 0.395405i | ||||
\(539\) | − | 1.05881i | − | 0.0456061i | ||||||
\(540\) | 17.3036 | − | 21.5829i | 0.744630 | − | 0.928781i | ||||
\(541\) | −0.859019 | −0.0369321 | −0.0184661 | − | 0.999829i | \(-0.505878\pi\) | ||||
−0.0184661 | + | 0.999829i | \(0.505878\pi\) | |||||||
\(542\) | 3.11124 | − | 1.49332i | 0.133639 | − | 0.0641437i | ||||
\(543\) | 57.1638i | 2.45313i | ||||||||
\(544\) | −14.0792 | + | 11.0791i | −0.603640 | + | 0.475012i | ||||
\(545\) | 12.5538i | 0.537747i | ||||||||
\(546\) | 5.60979 | + | 11.6876i | 0.240077 | + | 0.500184i | ||||
\(547\) | −16.9704 | −0.725600 | −0.362800 | − | 0.931867i | \(-0.618179\pi\) | ||||
−0.362800 | + | 0.931867i | \(0.618179\pi\) | |||||||
\(548\) | −15.7015 | + | 19.5846i | −0.670735 | + | 0.836612i | ||||
\(549\) | −62.9975 | −2.68867 | ||||||||
\(550\) | 0.622934 | − | 0.298994i | 0.0265620 | − | 0.0127491i | ||||
\(551\) | −30.8868 | − | 22.7857i | −1.31582 | − | 0.970703i | ||||
\(552\) | 14.5648 | − | 62.6868i | 0.619921 | − | 2.66813i | ||||
\(553\) | 31.8871i | 1.35598i | ||||||||
\(554\) | −13.8932 | − | 28.9456i | −0.590267 | − | 1.22978i | ||||
\(555\) | − | 3.58788i | − | 0.152297i | ||||||
\(556\) | 9.32165 | + | 7.47343i | 0.395326 | + | 0.316944i | ||||
\(557\) | 32.6593 | 1.38382 | 0.691910 | − | 0.721984i | \(-0.256769\pi\) | ||||
0.691910 | + | 0.721984i | \(0.256769\pi\) | |||||||
\(558\) | 16.3826 | + | 34.1321i | 0.693532 | + | 1.44493i | ||||
\(559\) | −3.38349 | −0.143106 | ||||||||
\(560\) | 11.8210 | − | 2.63360i | 0.499530 | − | 0.111290i | ||||
\(561\) | 4.96811i | 0.209754i | ||||||||
\(562\) | −10.1712 | + | 4.88194i | −0.429046 | + | 0.205932i | ||||
\(563\) | −9.10359 | −0.383671 | −0.191835 | − | 0.981427i | \(-0.561444\pi\) | ||||
−0.191835 | + | 0.981427i | \(0.561444\pi\) | |||||||
\(564\) | 2.36148 | + | 1.89327i | 0.0994364 | + | 0.0797209i | ||||
\(565\) | − | 10.0974i | − | 0.424802i | ||||||
\(566\) | 8.36532 | − | 4.01516i | 0.351621 | − | 0.168770i | ||||
\(567\) | − | 68.0733i | − | 2.85881i | ||||||
\(568\) | 38.3742 | + | 8.91598i | 1.61015 | + | 0.374106i | ||||
\(569\) | 29.8666i | 1.25207i | 0.779794 | + | 0.626037i | \(0.215324\pi\) | ||||
−0.779794 | + | 0.626037i | \(0.784676\pi\) | |||||||
\(570\) | −19.4425 | − | 3.70071i | −0.814356 | − | 0.155006i | ||||
\(571\) | 28.8364i | 1.20677i | 0.797451 | + | 0.603383i | \(0.206181\pi\) | ||||
−0.797451 | + | 0.603383i | \(0.793819\pi\) | |||||||
\(572\) | −0.576424 | + | 0.718977i | −0.0241015 | + | 0.0300619i | ||||
\(573\) | 2.72446i | 0.113816i | ||||||||
\(574\) | −2.90647 | − | 6.05543i | −0.121314 | − | 0.252749i | ||||
\(575\) | − | 7.08696i | − | 0.295547i | ||||||
\(576\) | 52.4755 | + | 25.7761i | 2.18648 | + | 1.07400i | ||||
\(577\) | 24.1255 | 1.00436 | 0.502180 | − | 0.864763i | \(-0.332532\pi\) | ||||
0.502180 | + | 0.864763i | \(0.332532\pi\) | |||||||
\(578\) | 4.26511 | + | 8.88608i | 0.177405 | + | 0.369612i | ||||
\(579\) | − | 73.9829i | − | 3.07462i | ||||||
\(580\) | 13.7402 | + | 11.0159i | 0.570531 | + | 0.457411i | ||||
\(581\) | 54.7031 | 2.26947 | ||||||||
\(582\) | −7.02220 | + | 3.37049i | −0.291079 | + | 0.139711i | ||||
\(583\) | −6.06196 | −0.251061 | ||||||||
\(584\) | −32.2230 | − | 7.48679i | −1.33340 | − | 0.309806i | ||||
\(585\) | 6.89173i | 0.284938i | ||||||||
\(586\) | 9.53645 | − | 4.57728i | 0.393947 | − | 0.189086i | ||||
\(587\) | 1.98430i | 0.0819010i | 0.999161 | + | 0.0409505i | \(0.0130386\pi\) | ||||
−0.999161 | + | 0.0409505i | \(0.986961\pi\) | |||||||
\(588\) | 8.70420 | − | 10.8568i | 0.358955 | − | 0.447727i | ||||
\(589\) | 9.47932 | − | 12.8496i | 0.390588 | − | 0.529457i | ||||
\(590\) | −5.29711 | − | 11.0362i | −0.218078 | − | 0.454352i | ||||
\(591\) | 3.67676 | 0.151242 | ||||||||
\(592\) | 4.36305 | − | 0.972039i | 0.179320 | − | 0.0399506i | ||||
\(593\) | −37.8922 | −1.55604 | −0.778022 | − | 0.628237i | \(-0.783777\pi\) | ||||
−0.778022 | + | 0.628237i | \(0.783777\pi\) | |||||||
\(594\) | 8.61609 | − | 4.13552i | 0.353522 | − | 0.169683i | ||||
\(595\) | 9.58897i | 0.393109i | ||||||||
\(596\) | 25.4438 | − | 31.7361i | 1.04222 | − | 1.29996i | ||||
\(597\) | 5.01479i | 0.205242i | ||||||||
\(598\) | 4.08981 | + | 8.52084i | 0.167245 | + | 0.348443i | ||||
\(599\) | 35.0029 | 1.43018 | 0.715091 | − | 0.699032i | \(-0.246385\pi\) | ||||
0.715091 | + | 0.699032i | \(0.246385\pi\) | |||||||
\(600\) | 8.84538 | + | 2.05516i | 0.361111 | + | 0.0839016i | ||||
\(601\) | − | 13.3793i | − | 0.545753i | −0.962049 | − | 0.272877i | \(-0.912025\pi\) | ||
0.962049 | − | 0.272877i | \(-0.0879751\pi\) | |||||||
\(602\) | 6.64766 | + | 13.8500i | 0.270939 | + | 0.564482i | ||||
\(603\) | −48.1900 | −1.96245 | ||||||||
\(604\) | 1.69204 | − | 2.11049i | 0.0688481 | − | 0.0858746i | ||||
\(605\) | −10.7613 | −0.437508 | ||||||||
\(606\) | −18.6161 | − | 38.7854i | −0.756227 | − | 1.57555i | ||||
\(607\) | 28.7047 | 1.16509 | 0.582543 | − | 0.812800i | \(-0.302058\pi\) | ||||
0.582543 | + | 0.812800i | \(0.302058\pi\) | |||||||
\(608\) | −0.767153 | − | 24.6457i | −0.0311121 | − | 0.999516i | ||||
\(609\) | 85.5963 | 3.46854 | ||||||||
\(610\) | −5.27519 | − | 10.9905i | −0.213586 | − | 0.444993i | ||||
\(611\) | −0.444510 | −0.0179830 | ||||||||
\(612\) | −28.9552 | + | 36.1160i | −1.17045 | + | 1.45990i | ||||
\(613\) | −9.72631 | −0.392842 | −0.196421 | − | 0.980520i | \(-0.562932\pi\) | ||||
−0.196421 | + | 0.980520i | \(0.562932\pi\) | |||||||
\(614\) | −7.52244 | − | 15.6725i | −0.303581 | − | 0.632491i | ||||
\(615\) | − | 5.03643i | − | 0.203088i | ||||||
\(616\) | 4.07558 | + | 0.946933i | 0.164210 | + | 0.0381530i | ||||
\(617\) | 9.50602 | 0.382698 | 0.191349 | − | 0.981522i | \(-0.438714\pi\) | ||||
0.191349 | + | 0.981522i | \(0.438714\pi\) | |||||||
\(618\) | −10.6990 | − | 22.2906i | −0.430375 | − | 0.896658i | ||||
\(619\) | − | 37.7438i | − | 1.51705i | −0.651643 | − | 0.758526i | \(-0.725920\pi\) | ||
0.651643 | − | 0.758526i | \(-0.274080\pi\) | |||||||
\(620\) | −4.58285 | + | 5.71621i | −0.184052 | + | 0.229569i | ||||
\(621\) | − | 98.0230i | − | 3.93353i | ||||||
\(622\) | −2.59237 | + | 1.24428i | −0.103945 | + | 0.0498911i | ||||
\(623\) | 29.7927 | 1.19362 | ||||||||
\(624\) | −11.8210 | + | 2.63360i | −0.473221 | + | 0.105428i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −14.3866 | − | 29.9736i | −0.575005 | − | 1.19798i | ||||
\(627\) | −5.50245 | − | 4.05924i | −0.219747 | − | 0.162111i | ||||
\(628\) | −8.16794 | + | 10.1879i | −0.325936 | + | 0.406542i | ||||
\(629\) | 3.53921i | 0.141118i | ||||||||
\(630\) | 28.2106 | − | 13.5404i | 1.12394 | − | 0.539464i | ||||
\(631\) | 24.8879i | 0.990773i | 0.868673 | + | 0.495386i | \(0.164973\pi\) | ||||
−0.868673 | + | 0.495386i | \(0.835027\pi\) | |||||||
\(632\) | −29.0153 | − | 6.74151i | −1.15417 | − | 0.268163i | ||||
\(633\) | −30.6545 | −1.21841 | ||||||||
\(634\) | −13.4441 | + | 6.45284i | −0.533932 | + | 0.256275i | ||||
\(635\) | 4.63898 | 0.184092 | ||||||||
\(636\) | −62.1580 | − | 49.8338i | −2.46473 | − | 1.97604i | ||||
\(637\) | 2.04361i | 0.0809709i | ||||||||
\(638\) | 2.63278 | + | 5.48521i | 0.104233 | + | 0.217162i | ||||
\(639\) | 101.792 | 4.02682 | ||||||||
\(640\) | −0.102771 | + | 11.3132i | −0.00406238 | + | 0.447195i | ||||
\(641\) | 17.6954i | 0.698925i | 0.936950 | + | 0.349463i | \(0.113636\pi\) | ||||
−0.936950 | + | 0.349463i | \(0.886364\pi\) | |||||||
\(642\) | −6.83111 | − | 14.2322i | −0.269602 | − | 0.561699i | ||||
\(643\) | − | 10.2796i | − | 0.405389i | −0.979242 | − | 0.202695i | \(-0.935030\pi\) | ||
0.979242 | − | 0.202695i | \(-0.0649699\pi\) | |||||||
\(644\) | 26.8438 | − | 33.4824i | 1.05779 | − | 1.31939i | ||||
\(645\) | 11.5193i | 0.453572i | ||||||||
\(646\) | 19.1788 | + | 3.65051i | 0.754578 | + | 0.143628i | ||||
\(647\) | 31.9257i | 1.25513i | 0.778565 | + | 0.627564i | \(0.215948\pi\) | ||||
−0.778565 | + | 0.627564i | \(0.784052\pi\) | |||||||
\(648\) | 61.9426 | + | 14.3919i | 2.43334 | + | 0.565369i | ||||
\(649\) | − | 4.22930i | − | 0.166015i | ||||||
\(650\) | −1.20233 | + | 0.577089i | −0.0471592 | + | 0.0226353i | ||||
\(651\) | 35.6098i | 1.39566i | ||||||||
\(652\) | 15.0476 | + | 12.0641i | 0.589311 | + | 0.472467i | ||||
\(653\) | 5.72631 | 0.224088 | 0.112044 | − | 0.993703i | \(-0.464260\pi\) | ||||
0.112044 | + | 0.993703i | \(0.464260\pi\) | |||||||
\(654\) | −51.3878 | + | 24.6650i | −2.00942 | + | 0.964476i | ||||
\(655\) | 21.6381i | 0.845470i | ||||||||
\(656\) | 6.12456 | − | 1.36448i | 0.239124 | − | 0.0532741i | ||||
\(657\) | −85.4750 | −3.33470 | ||||||||
\(658\) | 0.873345 | + | 1.81956i | 0.0340465 | + | 0.0709337i | ||||
\(659\) | −0.928171 | −0.0361564 | −0.0180782 | − | 0.999837i | \(-0.505755\pi\) | ||||
−0.0180782 | + | 0.999837i | \(0.505755\pi\) | |||||||
\(660\) | 2.44780 | + | 1.96247i | 0.0952805 | + | 0.0763891i | ||||
\(661\) | − | 15.5689i | − | 0.605560i | −0.953060 | − | 0.302780i | \(-0.902085\pi\) | ||
0.953060 | − | 0.302780i | \(-0.0979147\pi\) | |||||||
\(662\) | −0.662509 | − | 1.38029i | −0.0257491 | − | 0.0536466i | ||||
\(663\) | − | 9.58897i | − | 0.372405i | ||||||
\(664\) | −11.5652 | + | 49.7765i | −0.448818 | + | 1.93170i | ||||
\(665\) | −10.6203 | − | 7.83476i | −0.411837 | − | 0.303819i | ||||
\(666\) | 10.4123 | − | 4.99766i | 0.403468 | − | 0.193656i | ||||
\(667\) | 62.4039 | 2.41629 | ||||||||
\(668\) | −0.537609 | + | 0.670562i | −0.0208007 | + | 0.0259448i | ||||
\(669\) | −27.7741 | −1.07381 | ||||||||
\(670\) | −4.03526 | − | 8.40720i | −0.155896 | − | 0.324799i | ||||
\(671\) | − | 4.21181i | − | 0.162595i | ||||||
\(672\) | 34.0056 | + | 43.2139i | 1.31179 | + | 1.66701i | ||||
\(673\) | − | 14.6637i | − | 0.565244i | −0.959231 | − | 0.282622i | \(-0.908796\pi\) | ||
0.959231 | − | 0.282622i | \(-0.0912041\pi\) | |||||||
\(674\) | 0.328236 | − | 0.157546i | 0.0126432 | − | 0.00606843i | ||||
\(675\) | 13.8315 | 0.532373 | ||||||||
\(676\) | −15.1509 | + | 18.8978i | −0.582726 | + | 0.726838i | ||||
\(677\) | − | 20.0120i | − | 0.769123i | −0.923099 | − | 0.384562i | \(-0.874353\pi\) | ||
0.923099 | − | 0.384562i | \(-0.125647\pi\) | |||||||
\(678\) | 41.3328 | − | 19.8388i | 1.58738 | − | 0.761904i | ||||
\(679\) | −5.19403 | −0.199328 | ||||||||
\(680\) | −8.72539 | − | 2.02728i | −0.334603 | − | 0.0777428i | ||||
\(681\) | −7.44496 | −0.285292 | ||||||||
\(682\) | −2.28196 | + | 1.09529i | −0.0873808 | + | 0.0419408i | ||||
\(683\) | −39.0637 | −1.49473 | −0.747366 | − | 0.664412i | \(-0.768682\pi\) | ||||
−0.747366 | + | 0.664412i | \(0.768682\pi\) | |||||||
\(684\) | −16.3423 | − | 61.5784i | −0.624862 | − | 2.35451i | ||||
\(685\) | −12.5508 | −0.479542 | ||||||||
\(686\) | −18.6561 | + | 8.95452i | −0.712295 | + | 0.341885i | ||||
\(687\) | −53.6411 | −2.04654 | ||||||||
\(688\) | −14.0081 | + | 3.12084i | −0.534053 | + | 0.118981i | ||||
\(689\) | 11.7002 | 0.445743 | ||||||||
\(690\) | 29.0097 | − | 13.9240i | 1.10438 | − | 0.530078i | ||||
\(691\) | 36.4683i | 1.38732i | 0.720302 | + | 0.693660i | \(0.244003\pi\) | ||||
−0.720302 | + | 0.693660i | \(0.755997\pi\) | |||||||
\(692\) | 26.6901 | + | 21.3982i | 1.01461 | + | 0.813438i | ||||
\(693\) | 10.8109 | 0.410673 | ||||||||
\(694\) | 21.5535 | − | 10.3452i | 0.818161 | − | 0.392698i | ||||
\(695\) | 5.97381i | 0.226599i | ||||||||
\(696\) | −18.0966 | + | 77.8875i | −0.685951 | + | 2.95232i | ||||
\(697\) | 4.96811i | 0.188181i | ||||||||
\(698\) | 9.46742 | + | 19.7247i | 0.358347 | + | 0.746592i | ||||
\(699\) | −64.3511 | −2.43398 | ||||||||
\(700\) | 4.72451 | + | 3.78777i | 0.178570 | + | 0.143164i | ||||
\(701\) | −32.9543 | −1.24467 | −0.622333 | − | 0.782753i | \(-0.713815\pi\) | ||||
−0.622333 | + | 0.782753i | \(0.713815\pi\) | |||||||
\(702\) | −16.6300 | + | 7.98199i | −0.627657 | + | 0.301261i | ||||
\(703\) | −3.91987 | − | 2.89175i | −0.147841 | − | 0.109064i | ||||
\(704\) | −1.72330 | + | 3.50834i | −0.0649495 | + | 0.132225i | ||||
\(705\) | 1.51336i | 0.0569965i | ||||||||
\(706\) | 9.82599 | + | 20.4718i | 0.369806 | + | 0.770466i | ||||
\(707\) | − | 28.6879i | − | 1.07892i | ||||||
\(708\) | 34.7680 | − | 43.3663i | 1.30666 | − | 1.62981i | ||||
\(709\) | 0.863080 | 0.0324137 | 0.0162068 | − | 0.999869i | \(-0.494841\pi\) | ||||
0.0162068 | + | 0.999869i | \(0.494841\pi\) | |||||||
\(710\) | 8.52369 | + | 17.7585i | 0.319888 | + | 0.666466i | ||||
\(711\) | −76.9663 | −2.88646 | ||||||||
\(712\) | −6.29872 | + | 27.1096i | −0.236054 | + | 1.01597i | ||||
\(713\) | 25.9613i | 0.972258i | ||||||||
\(714\) | −39.2515 | + | 18.8398i | −1.46895 | + | 0.705062i | ||||
\(715\) | −0.460758 | −0.0172314 | ||||||||
\(716\) | −14.9572 | + | 18.6562i | −0.558976 | + | 0.697214i | ||||
\(717\) | − | 61.3747i | − | 2.29208i | ||||||
\(718\) | 10.4007 | − | 4.99208i | 0.388149 | − | 0.186303i | ||||
\(719\) | 30.5363i | 1.13881i | 0.822057 | + | 0.569405i | \(0.192827\pi\) | ||||
−0.822057 | + | 0.569405i | \(0.807173\pi\) | |||||||
\(720\) | 6.35675 | + | 28.5326i | 0.236902 | + | 1.06335i | ||||
\(721\) | − | 16.4874i | − | 0.614023i | ||||||
\(722\) | −19.7133 | + | 18.2588i | −0.733654 | + | 0.679523i | ||||
\(723\) | − | 33.6481i | − | 1.25139i | ||||||
\(724\) | −27.7827 | − | 22.2742i | −1.03254 | − | 0.827814i | ||||
\(725\) | 8.80545i | 0.327026i | ||||||||
\(726\) | −21.1431 | − | 44.0502i | −0.784693 | − | 1.63486i | ||||
\(727\) | 5.68270i | 0.210760i | 0.994432 | + | 0.105380i | \(0.0336058\pi\) | ||||
−0.994432 | + | 0.105380i | \(0.966394\pi\) | |||||||
\(728\) | −7.86630 | − | 1.82768i | −0.291544 | − | 0.0677383i | ||||
\(729\) | 31.0870 | 1.15137 | ||||||||
\(730\) | −7.15738 | − | 14.9119i | −0.264907 | − | 0.551915i | ||||
\(731\) | − | 11.3630i | − | 0.420277i | ||||||
\(732\) | 34.6242 | − | 43.1869i | 1.27975 | − | 1.59623i | ||||
\(733\) | 25.1533 | 0.929059 | 0.464529 | − | 0.885558i | \(-0.346224\pi\) | ||||
0.464529 | + | 0.885558i | \(0.346224\pi\) | |||||||
\(734\) | 3.89132 | − | 1.86775i | 0.143631 | − | 0.0689398i | ||||
\(735\) | 6.95761 | 0.256635 | ||||||||
\(736\) | 24.7917 | + | 31.5051i | 0.913836 | + | 1.16129i | ||||
\(737\) | − | 3.22182i | − | 0.118677i | ||||||
\(738\) | 14.6161 | − | 7.01539i | 0.538026 | − | 0.258240i | ||||
\(739\) | 29.1790i | 1.07337i | 0.843784 | + | 0.536683i | \(0.180323\pi\) | ||||
−0.843784 | + | 0.536683i | \(0.819677\pi\) | |||||||
\(740\) | 1.74378 | + | 1.39804i | 0.0641026 | + | 0.0513929i | ||||
\(741\) | 10.6203 | + | 7.83476i | 0.390146 | + | 0.287817i | ||||
\(742\) | −22.9879 | − | 47.8937i | −0.843911 | − | 1.75823i | ||||
\(743\) | −42.1946 | −1.54797 | −0.773985 | − | 0.633204i | \(-0.781740\pi\) | ||||
−0.773985 | + | 0.633204i | \(0.781740\pi\) | |||||||
\(744\) | −32.4028 | − | 7.52857i | −1.18794 | − | 0.276011i | ||||
\(745\) | 20.3382 | 0.745134 | ||||||||
\(746\) | 28.2934 | − | 13.5802i | 1.03590 | − | 0.497207i | ||||
\(747\) | 132.038i | 4.83101i | ||||||||
\(748\) | −2.41460 | − | 1.93585i | −0.0882864 | − | 0.0707817i | ||||
\(749\) | − | 10.5269i | − | 0.384646i | ||||||
\(750\) | 1.96474 | + | 4.09340i | 0.0717420 | + | 0.149470i | ||||
\(751\) | −37.9019 | −1.38306 | −0.691529 | − | 0.722348i | \(-0.743063\pi\) | ||||
−0.691529 | + | 0.722348i | \(0.743063\pi\) | |||||||
\(752\) | −1.84033 | + | 0.410005i | −0.0671099 | + | 0.0149513i | ||||
\(753\) | − | 82.6149i | − | 3.01065i | ||||||
\(754\) | −5.08153 | − | 10.5870i | −0.185059 | − | 0.385557i | ||||
\(755\) | 1.35251 | 0.0492230 | ||||||||
\(756\) | 65.3469 | + | 52.3905i | 2.37665 | + | 1.90542i | ||||
\(757\) | 9.06683 | 0.329540 | 0.164770 | − | 0.986332i | \(-0.447312\pi\) | ||||
0.164770 | + | 0.986332i | \(0.447312\pi\) | |||||||
\(758\) | −14.3582 | − | 29.9144i | −0.521515 | − | 1.08654i | ||||
\(759\) | 11.1172 | 0.403528 | ||||||||
\(760\) | 9.37449 | − | 8.00743i | 0.340049 | − | 0.290460i | ||||
\(761\) | 35.1190 | 1.27306 | 0.636531 | − | 0.771251i | \(-0.280369\pi\) | ||||
0.636531 | + | 0.771251i | \(0.280369\pi\) | |||||||
\(762\) | 9.11438 | + | 18.9892i | 0.330179 | + | 0.687906i | ||||
\(763\) | −38.0094 | −1.37603 | ||||||||
\(764\) | −1.32414 | − | 1.06160i | −0.0479057 | − | 0.0384074i | ||||
\(765\) | −23.1450 | −0.836811 | ||||||||
\(766\) | −5.45674 | − | 11.3687i | −0.197160 | − | 0.410770i | ||||
\(767\) | 8.16300i | 0.294749i | ||||||||
\(768\) | −46.5115 | + | 21.8069i | −1.67834 | + | 0.786887i | ||||
\(769\) | −34.2519 | −1.23515 | −0.617577 | − | 0.786511i | \(-0.711886\pi\) | ||||
−0.617577 | + | 0.786511i | \(0.711886\pi\) | |||||||
\(770\) | 0.905268 | + | 1.88607i | 0.0326236 | + | 0.0679691i | ||||
\(771\) | − | 33.0828i | − | 1.19145i | ||||||
\(772\) | 35.9571 | + | 28.8278i | 1.29413 | + | 1.03754i | ||||
\(773\) | − | 9.33048i | − | 0.335594i | −0.985822 | − | 0.167797i | \(-0.946335\pi\) | ||
0.985822 | − | 0.167797i | \(-0.0536653\pi\) | |||||||
\(774\) | −33.4299 | + | 16.0456i | −1.20161 | + | 0.576746i | ||||
\(775\) | −3.66325 | −0.131588 | ||||||||
\(776\) | 1.09811 | − | 4.72626i | 0.0394199 | − | 0.169663i | ||||
\(777\) | 10.8631 | 0.389711 | ||||||||
\(778\) | −10.8958 | − | 22.7007i | −0.390633 | − | 0.813858i | ||||
\(779\) | −5.50245 | − | 4.05924i | −0.197146 | − | 0.145437i | ||||
\(780\) | −4.72451 | − | 3.78777i | −0.169165 | − | 0.135624i | ||||
\(781\) | 6.80546i | 0.243519i | ||||||||
\(782\) | −28.6162 | + | 13.7351i | −1.02331 | + | 0.491167i | ||||
\(783\) | 121.792i | 4.35250i | ||||||||
\(784\) | 1.88498 | + | 8.46082i | 0.0673205 | + | 0.302172i | ||||
\(785\) | −6.52895 | −0.233028 | ||||||||
\(786\) | −88.5733 | + | 42.5131i | −3.15930 | + | 1.51639i | ||||
\(787\) | 4.73061 | 0.168628 | 0.0843141 | − | 0.996439i | \(-0.473130\pi\) | ||||
0.0843141 | + | 0.996439i | \(0.473130\pi\) | |||||||
\(788\) | −1.43267 | + | 1.78698i | −0.0510368 | + | 0.0636585i | ||||
\(789\) | 11.6299i | 0.414037i | ||||||||
\(790\) | −6.44489 | − | 13.4275i | −0.229299 | − | 0.477729i | ||||
\(791\) | 30.5722 | 1.08702 | ||||||||
\(792\) | −2.28563 | + | 9.83729i | −0.0812162 | + | 0.349553i | ||||
\(793\) | 8.12923i | 0.288677i | ||||||||
\(794\) | −8.97624 | − | 18.7014i | −0.318555 | − | 0.663688i | ||||
\(795\) | − | 39.8341i | − | 1.41277i | ||||||
\(796\) | −2.43729 | − | 1.95404i | −0.0863873 | − | 0.0692591i | ||||
\(797\) | 21.3976i | 0.757940i | 0.925409 | + | 0.378970i | \(0.123722\pi\) | ||||
−0.925409 | + | 0.378970i | \(0.876278\pi\) | |||||||
\(798\) | 11.2047 | − | 58.8663i | 0.396642 | − | 2.08385i | ||||
\(799\) | − | 1.49283i | − | 0.0528127i | ||||||
\(800\) | −4.44550 | + | 3.49822i | −0.157172 | + | 0.123681i | ||||
\(801\) | 71.9110i | 2.54085i | ||||||||
\(802\) | −23.1214 | + | 11.0977i | −0.816446 | + | 0.391875i | ||||
\(803\) | − | 5.71458i | − | 0.201663i | ||||||
\(804\) | 26.4858 | − | 33.0359i | 0.934082 | − | 1.16509i | ||||
\(805\) | 21.4573 | 0.756270 | ||||||||
\(806\) | 4.40442 | − | 2.11402i | 0.155139 | − | 0.0744632i | ||||
\(807\) | 48.1177i | 1.69382i | ||||||||
\(808\) | 26.1043 | + | 6.06516i | 0.918347 | + | 0.213371i | ||||
\(809\) | 37.8352 | 1.33021 | 0.665107 | − | 0.746748i | \(-0.268386\pi\) | ||||
0.665107 | + | 0.746748i | \(0.268386\pi\) | |||||||
\(810\) | 13.7587 | + | 28.6654i | 0.483432 | + | 1.00720i | ||||
\(811\) | 42.0985 | 1.47828 | 0.739139 | − | 0.673552i | \(-0.235232\pi\) | ||||
0.739139 | + | 0.673552i | \(0.235232\pi\) | |||||||
\(812\) | −33.3531 | + | 41.6015i | −1.17046 | + | 1.45993i | ||||
\(813\) | 7.83476i | 0.274777i | ||||||||
\(814\) | 0.334127 | + | 0.696132i | 0.0117112 | + | 0.0243994i | ||||
\(815\) | 9.64331i | 0.337790i | ||||||||
\(816\) | −8.84462 | − | 39.6996i | −0.309623 | − | 1.38976i | ||||
\(817\) | 12.5852 | + | 9.28429i | 0.440300 | + | 0.324816i | ||||
\(818\) | 7.95976 | − | 3.82050i | 0.278307 | − | 0.133581i | ||||
\(819\) | −20.8662 | −0.729124 | ||||||||
\(820\) | 2.44780 | + | 1.96247i | 0.0854809 | + | 0.0685325i | ||||
\(821\) | 29.9355 | 1.04476 | 0.522379 | − | 0.852713i | \(-0.325045\pi\) | ||||
0.522379 | + | 0.852713i | \(0.325045\pi\) | |||||||
\(822\) | −24.6591 | − | 51.3755i | −0.860084 | − | 1.79193i | ||||
\(823\) | − | 0.318164i | − | 0.0110905i | −0.999985 | − | 0.00554526i | \(-0.998235\pi\) | ||
0.999985 | − | 0.00554526i | \(-0.00176512\pi\) | |||||||
\(824\) | 15.0026 | + | 3.48574i | 0.522639 | + | 0.121432i | ||||
\(825\) | 1.56868i | 0.0546144i | ||||||||
\(826\) | 33.4144 | − | 16.0381i | 1.16264 | − | 0.558038i | ||||
\(827\) | 20.0096 | 0.695802 | 0.347901 | − | 0.937531i | \(-0.386895\pi\) | ||||
0.347901 | + | 0.937531i | \(0.386895\pi\) | |||||||
\(828\) | 80.8170 | + | 64.7933i | 2.80859 | + | 2.25172i | ||||
\(829\) | − | 3.63983i | − | 0.126417i | −0.998000 | − | 0.0632083i | \(-0.979867\pi\) | ||
0.998000 | − | 0.0632083i | \(-0.0201333\pi\) | |||||||
\(830\) | −23.0352 | + | 11.0564i | −0.799564 | + | 0.383772i | ||||
\(831\) | 72.8913 | 2.52857 | ||||||||
\(832\) | 3.32616 | − | 6.77146i | 0.115314 | − | 0.234758i | ||||
\(833\) | −6.86323 | −0.237797 | ||||||||
\(834\) | −24.4532 | + | 11.7370i | −0.846744 | + | 0.406417i | ||||
\(835\) | −0.429732 | −0.0148715 | ||||||||
\(836\) | 4.11693 | − | 1.09259i | 0.142387 | − | 0.0377880i | ||||
\(837\) | −50.6681 | −1.75135 | ||||||||
\(838\) | −5.92433 | + | 2.84354i | −0.204653 | + | 0.0982285i | ||||
\(839\) | −35.9639 | −1.24161 | −0.620806 | − | 0.783964i | \(-0.713195\pi\) | ||||
−0.620806 | + | 0.783964i | \(0.713195\pi\) | |||||||
\(840\) | −6.22244 | + | 26.7813i | −0.214695 | + | 0.924042i | ||||
\(841\) | −48.5360 | −1.67366 | ||||||||
\(842\) | 20.0731 | − | 9.63460i | 0.691763 | − | 0.332030i | ||||
\(843\) | − | 25.6132i | − | 0.882167i | ||||||
\(844\) | 11.9447 | − | 14.8987i | 0.411153 | − | 0.512834i | ||||
\(845\) | −12.1107 | −0.416620 | ||||||||
\(846\) | −4.39189 | + | 2.10801i | −0.150996 | + | 0.0724748i | ||||
\(847\) | − | 32.5821i | − | 1.11953i | ||||||
\(848\) | 48.4404 | − | 10.7920i | 1.66345 | − | 0.370598i | ||||
\(849\) | 21.0657i | 0.722971i | ||||||||
\(850\) | −1.93809 | − | 4.03787i | −0.0664758 | − | 0.138498i | ||||
\(851\) | 7.91972 | 0.271484 | ||||||||
\(852\) | −55.9459 | + | 69.7817i | −1.91668 | + | 2.39068i | ||||
\(853\) | −26.7120 | −0.914602 | −0.457301 | − | 0.889312i | \(-0.651184\pi\) | ||||
−0.457301 | + | 0.889312i | \(0.651184\pi\) | |||||||
\(854\) | 33.2762 | − | 15.9718i | 1.13869 | − | 0.546543i | ||||
\(855\) | 18.9109 | − | 25.6344i | 0.646739 | − | 0.876677i | ||||
\(856\) | 9.57889 | + | 2.22559i | 0.327400 | + | 0.0760691i | ||||
\(857\) | − | 19.2855i | − | 0.658780i | −0.944194 | − | 0.329390i | \(-0.893157\pi\) | ||
0.944194 | − | 0.329390i | \(-0.106843\pi\) | |||||||
\(858\) | −0.905268 | − | 1.88607i | −0.0309054 | − | 0.0643892i | ||||
\(859\) | 27.1922i | 0.927787i | 0.885891 | + | 0.463893i | \(0.153548\pi\) | ||||
−0.885891 | + | 0.463893i | \(0.846452\pi\) | |||||||
\(860\) | −5.59860 | − | 4.48856i | −0.190911 | − | 0.153059i | ||||
\(861\) | 15.2489 | 0.519680 | ||||||||
\(862\) | 8.70316 | + | 18.1324i | 0.296431 | + | 0.617593i | ||||
\(863\) | 40.1609 | 1.36709 | 0.683547 | − | 0.729907i | \(-0.260437\pi\) | ||||
0.683547 | + | 0.729907i | \(0.260437\pi\) | |||||||
\(864\) | −61.4878 | + | 48.3855i | −2.09186 | + | 1.64611i | ||||
\(865\) | 17.1044i | 0.581568i | ||||||||
\(866\) | −39.4466 | + | 18.9334i | −1.34045 | + | 0.643385i | ||||
\(867\) | −22.3770 | −0.759964 | ||||||||
\(868\) | −17.3071 | − | 13.8756i | −0.587440 | − | 0.470967i | ||||
\(869\) | − | 5.14571i | − | 0.174556i | ||||||
\(870\) | −36.0442 | + | 17.3004i | −1.22201 | + | 0.586538i | ||||
\(871\) | 6.21846i | 0.210704i | ||||||||
\(872\) | 8.03589 | − | 34.5863i | 0.272130 | − | 1.17124i | ||||
\(873\) | − | 12.5369i | − | 0.424310i | ||||||
\(874\) | 8.16878 | − | 42.9164i | 0.276313 | − | 1.45167i | ||||
\(875\) | 3.02772i | 0.102355i | ||||||||
\(876\) | 46.9781 | − | 58.5960i | 1.58724 | − | 1.97978i | ||||
\(877\) | − | 30.1261i | − | 1.01729i | −0.860977 | − | 0.508644i | \(-0.830147\pi\) | ||
0.860977 | − | 0.508644i | \(-0.169853\pi\) | |||||||
\(878\) | 15.2647 | + | 31.8030i | 0.515160 | + | 1.07330i | ||||
\(879\) | 24.0148i | 0.810000i | ||||||||
\(880\) | −1.90760 | + | 0.424991i | −0.0643051 | + | 0.0143265i | ||||
\(881\) | −34.6286 | −1.16667 | −0.583333 | − | 0.812233i | \(-0.698252\pi\) | ||||
−0.583333 | + | 0.812233i | \(0.698252\pi\) | |||||||
\(882\) | 9.69145 | + | 20.1915i | 0.326328 | + | 0.679883i | ||||
\(883\) | − | 21.0760i | − | 0.709265i | −0.935006 | − | 0.354632i | \(-0.884606\pi\) | ||
0.935006 | − | 0.354632i | \(-0.115394\pi\) | |||||||
\(884\) | 4.66043 | + | 3.73640i | 0.156747 | + | 0.125669i | ||||
\(885\) | 27.7914 | 0.934198 | ||||||||
\(886\) | −29.9314 | + | 14.3664i | −1.00556 | + | 0.482648i | ||||
\(887\) | −26.9404 | −0.904570 | −0.452285 | − | 0.891873i | \(-0.649391\pi\) | ||||
−0.452285 | + | 0.891873i | \(0.649391\pi\) | |||||||
\(888\) | −2.29665 | + | 9.88476i | −0.0770707 | + | 0.331711i | ||||
\(889\) | 14.0455i | 0.471072i | ||||||||
\(890\) | −12.5456 | + | 6.02158i | −0.420528 | + | 0.201844i | ||||
\(891\) | 10.9852i | 0.368018i | ||||||||
\(892\) | 10.8223 | − | 13.4988i | 0.362359 | − | 0.451972i | ||||
\(893\) | 1.65339 | + | 1.21973i | 0.0553287 | + | 0.0408169i | ||||
\(894\) | 39.9592 | + | 83.2523i | 1.33643 | + | 2.78437i | ||||
\(895\) | −11.9559 | −0.399640 | ||||||||
\(896\) | −34.2533 | − | 0.311161i | −1.14432 | − | 0.0103952i | ||||
\(897\) | −21.4573 | −0.716438 | ||||||||
\(898\) | −2.51234 | + | 1.20587i | −0.0838380 | + | 0.0402403i | ||||
\(899\) | − | 32.2566i | − | 1.07582i | ||||||
\(900\) | −9.14261 | + | 11.4036i | −0.304754 | + | 0.380121i | ||||
\(901\) | 39.2938i | 1.30907i | ||||||||
\(902\) | 0.469026 | + | 0.977183i | 0.0156168 | + | 0.0325367i | ||||
\(903\) | −34.8772 | −1.16064 | ||||||||
\(904\) | −6.46351 | + | 27.8188i | −0.214973 | + | 0.925241i | ||||
\(905\) | − | 17.8046i | − | 0.591846i | ||||||
\(906\) | 2.65733 | + | 5.53637i | 0.0882839 | + | 0.183934i | ||||
\(907\) | 13.8276 | 0.459137 | 0.229569 | − | 0.973292i | \(-0.426268\pi\) | ||||
0.229569 | + | 0.973292i | \(0.426268\pi\) | |||||||
\(908\) | 2.90097 | − | 3.61840i | 0.0962721 | − | 0.120081i | ||||
\(909\) | 69.2445 | 2.29670 | ||||||||
\(910\) | −1.74726 | − | 3.64031i | −0.0579212 | − | 0.120675i | ||||
\(911\) | 4.76877 | 0.157996 | 0.0789982 | − | 0.996875i | \(-0.474828\pi\) | ||||
0.0789982 | + | 0.996875i | \(0.474828\pi\) | |||||||
\(912\) | 51.1960 | + | 22.6410i | 1.69527 | + | 0.749720i | ||||
\(913\) | −8.82760 | −0.292151 | ||||||||
\(914\) | 5.75578 | + | 11.9918i | 0.190384 | + | 0.396653i | ||||
\(915\) | 27.6765 | 0.914955 | ||||||||
\(916\) | 20.9016 | − | 26.0706i | 0.690607 | − | 0.861398i | ||||
\(917\) | −65.5140 | −2.16346 | ||||||||
\(918\) | −26.8066 | − | 55.8497i | −0.884749 | − | 1.84331i | ||||
\(919\) | − | 46.6300i | − | 1.53818i | −0.639140 | − | 0.769091i | \(-0.720709\pi\) | ||
0.639140 | − | 0.769091i | \(-0.279291\pi\) | |||||||
\(920\) | −4.53647 | + | 19.5249i | −0.149563 | + | 0.643716i | ||||
\(921\) | 39.4667 | 1.30047 | ||||||||
\(922\) | −11.1927 | − | 23.3193i | −0.368612 | − | 0.767979i | ||||
\(923\) | − | 13.1353i | − | 0.432352i | ||||||
\(924\) | −5.94181 | + | 7.41125i | −0.195471 | + | 0.243812i | ||||
\(925\) | 1.11751i | 0.0367434i | ||||||||
\(926\) | 11.3414 | − | 5.44360i | 0.372701 | − | 0.178888i | ||||
\(927\) | 39.7959 | 1.30707 | ||||||||
\(928\) | −30.8034 | − | 39.1446i | −1.01117 | − | 1.28499i | ||||
\(929\) | 23.0589 | 0.756537 | 0.378268 | − | 0.925696i | \(-0.376520\pi\) | ||||
0.378268 | + | 0.925696i | \(0.376520\pi\) | |||||||
\(930\) | −7.19732 | − | 14.9951i | −0.236009 | − | 0.491710i | ||||
\(931\) | 5.60767 | − | 7.60139i | 0.183784 | − | 0.249126i | ||||
\(932\) | 25.0748 | − | 31.2759i | 0.821351 | − | 1.02448i | ||||
\(933\) | − | 6.52815i | − | 0.213722i | ||||||
\(934\) | −0.654289 | + | 0.314044i | −0.0214090 | + | 0.0102758i | ||||
\(935\) | − | 1.54740i | − | 0.0506054i | ||||||
\(936\) | 4.41150 | − | 18.9870i | 0.144194 | − | 0.620609i | ||||
\(937\) | 8.32894 | 0.272095 | 0.136047 | − | 0.990702i | \(-0.456560\pi\) | ||||
0.136047 | + | 0.990702i | \(0.456560\pi\) | |||||||
\(938\) | 25.4546 | − | 12.2176i | 0.831123 | − | 0.398920i | ||||
\(939\) | 75.4798 | 2.46319 | ||||||||
\(940\) | −0.735524 | − | 0.589690i | −0.0239901 | − | 0.0192336i | ||||
\(941\) | 45.6945i | 1.48960i | 0.667289 | + | 0.744799i | \(0.267454\pi\) | ||||
−0.667289 | + | 0.744799i | \(0.732546\pi\) | |||||||
\(942\) | −12.8277 | − | 26.7256i | −0.417948 | − | 0.870767i | ||||
\(943\) | 11.1172 | 0.362025 | ||||||||
\(944\) | 7.52934 | + | 33.7959i | 0.245059 | + | 1.09996i | ||||
\(945\) | 41.8778i | 1.36228i | ||||||||
\(946\) | −1.07275 | − | 2.23501i | −0.0348782 | − | 0.0726665i | ||||
\(947\) | − | 48.3372i | − | 1.57075i | −0.619021 | − | 0.785375i | \(-0.712470\pi\) | ||
0.619021 | − | 0.785375i | \(-0.287530\pi\) | |||||||
\(948\) | 42.3016 | − | 52.7630i | 1.37389 | − | 1.71366i | ||||
\(949\) | 11.0297i | 0.358040i | ||||||||
\(950\) | 6.05569 | + | 1.15265i | 0.196473 | + | 0.0373969i | ||||
\(951\) | − | 33.8550i | − | 1.09782i | ||||||
\(952\) | 6.13804 | − | 26.4180i | 0.198935 | − | 0.856213i | ||||
\(953\) | − | 4.66986i | − | 0.151272i | −0.997136 | − | 0.0756358i | \(-0.975901\pi\) | ||
0.997136 | − | 0.0756358i | \(-0.0240986\pi\) | |||||||
\(954\) | 115.602 | − | 55.4861i | 3.74274 | − | 1.79643i | ||||
\(955\) | − | 0.848579i | − | 0.0274594i | ||||||
\(956\) | 29.8293 | + | 23.9150i | 0.964749 | + | 0.773467i | ||||
\(957\) | −13.8129 | −0.446509 | ||||||||
\(958\) | 26.2320 | − | 12.5908i | 0.847517 | − | 0.406789i | ||||
\(959\) | − | 38.0003i | − | 1.22709i | ||||||
\(960\) | −23.0538 | − | 11.3241i | −0.744059 | − | 0.365484i | ||||
\(961\) | −17.5806 | −0.567116 | ||||||||
\(962\) | −0.644901 | − | 1.34361i | −0.0207924 | − | 0.0433196i | ||||
\(963\) | 25.4090 | 0.818795 | ||||||||
\(964\) | 16.3536 | + | 13.1112i | 0.526715 | + | 0.422282i | ||||
\(965\) | 23.0432i | 0.741787i | ||||||||
\(966\) | 42.1579 | + | 87.8332i | 1.35641 | + | 2.82599i | ||||
\(967\) | − | 4.19050i | − | 0.134757i | −0.997727 | − | 0.0673787i | \(-0.978536\pi\) | ||
0.997727 | − | 0.0673787i | \(-0.0214636\pi\) | |||||||
\(968\) | 29.6478 | + | 6.88845i | 0.952915 | + | 0.221403i | ||||
\(969\) | −26.3121 | + | 35.6670i | −0.845267 | + | 1.14579i | ||||
\(970\) | 2.18718 | − | 1.04980i | 0.0702262 | − | 0.0337069i | ||||
\(971\) | 9.15781 | 0.293888 | 0.146944 | − | 0.989145i | \(-0.453056\pi\) | ||||
0.146944 | + | 0.989145i | \(0.453056\pi\) | |||||||
\(972\) | −38.3955 | + | 47.8910i | −1.23154 | + | 1.53610i | ||||
\(973\) | −18.0870 | −0.579842 | ||||||||
\(974\) | −0.927716 | − | 1.93283i | −0.0297259 | − | 0.0619320i | ||||
\(975\) | − | 3.02772i | − | 0.0969645i | ||||||
\(976\) | 7.49819 | + | 33.6560i | 0.240011 | + | 1.07730i | ||||
\(977\) | − | 20.6015i | − | 0.659099i | −0.944138 | − | 0.329549i | \(-0.893103\pi\) | ||
0.944138 | − | 0.329549i | \(-0.106897\pi\) | |||||||
\(978\) | −39.4739 | + | 18.9466i | −1.26224 | + | 0.605844i | ||||
\(979\) | −4.80773 | −0.153656 | ||||||||
\(980\) | −2.71107 | + | 3.38153i | −0.0866019 | + | 0.108019i | ||||
\(981\) | − | 91.7439i | − | 2.92916i | ||||||
\(982\) | 23.4757 | − | 11.2678i | 0.749138 | − | 0.359569i | ||||
\(983\) | 28.8332 | 0.919636 | 0.459818 | − | 0.888013i | \(-0.347915\pi\) | ||||
0.459818 | + | 0.888013i | \(0.347915\pi\) | |||||||
\(984\) | −3.22389 | + | 13.8756i | −0.102774 | + | 0.442337i | ||||
\(985\) | −1.14519 | −0.0364888 | ||||||||
\(986\) | 35.5553 | − | 17.0657i | 1.13231 | − | 0.543483i | ||||
\(987\) | −4.58203 | −0.145848 | ||||||||
\(988\) | −7.94611 | + | 2.10881i | −0.252799 | + | 0.0670903i | ||||
\(989\) | −25.4272 | −0.808536 | ||||||||
\(990\) | −4.55243 | + | 2.18506i | −0.144686 | + | 0.0694458i | ||||
\(991\) | −33.2449 | −1.05606 | −0.528029 | − | 0.849226i | \(-0.677069\pi\) | ||||
−0.528029 | + | 0.849226i | \(0.677069\pi\) | |||||||
\(992\) | 16.2850 | − | 12.8149i | 0.517048 | − | 0.406872i | ||||
\(993\) | 3.47587 | 0.110303 | ||||||||
\(994\) | −53.7678 | + | 25.8073i | −1.70541 | + | 0.818558i | ||||
\(995\) | − | 1.56194i | − | 0.0495168i | ||||||
\(996\) | −90.5163 | − | 72.5694i | −2.86812 | − | 2.29945i | ||||
\(997\) | −55.1366 | −1.74619 | −0.873097 | − | 0.487546i | \(-0.837892\pi\) | ||||
−0.873097 | + | 0.487546i | \(0.837892\pi\) | |||||||
\(998\) | 11.4606 | − | 5.50082i | 0.362779 | − | 0.174125i | ||||
\(999\) | 15.4567i | 0.489030i |
(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 | 380.2.f.a.151.7 | ✓ | 20 | |
4.3 | odd | 2 | inner | 380.2.f.a.151.13 | yes | 20 | |
19.18 | odd | 2 | inner | 380.2.f.a.151.14 | yes | 20 | |
76.75 | even | 2 | inner | 380.2.f.a.151.8 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.f.a.151.7 | ✓ | 20 | 1.1 | even | 1 | trivial | |
380.2.f.a.151.8 | yes | 20 | 76.75 | even | 2 | inner | |
380.2.f.a.151.13 | yes | 20 | 4.3 | odd | 2 | inner | |
380.2.f.a.151.14 | yes | 20 | 19.18 | odd | 2 | inner |