Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(68,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.68");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.i (of order \(6\), degree \(2\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 68.1 | ||
Character | \(\chi\) | \(=\) | 441.68 |
Dual form | 441.2.i.d.227.23 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.70883i | − | 1.91543i | −0.287716 | − | 0.957716i | \(-0.592896\pi\) | ||
0.287716 | − | 0.957716i | \(-0.407104\pi\) | |||||||
\(3\) | −0.572034 | − | 1.63486i | −0.330264 | − | 0.943889i | ||||
\(4\) | −5.33776 | −2.66888 | ||||||||
\(5\) | −0.601464 | − | 1.04177i | −0.268983 | − | 0.465892i | 0.699616 | − | 0.714519i | \(-0.253354\pi\) |
−0.968599 | + | 0.248626i | \(0.920021\pi\) | |||||||
\(6\) | −4.42857 | + | 1.54954i | −1.80795 | + | 0.632598i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 9.04141i | 3.19662i | ||||||||
\(9\) | −2.34556 | + | 1.87039i | −0.781852 | + | 0.623464i | ||||
\(10\) | −2.82197 | + | 1.62926i | −0.892385 | + | 0.515219i | ||||
\(11\) | 2.15351 | + | 1.24333i | 0.649309 | + | 0.374879i | 0.788191 | − | 0.615430i | \(-0.211018\pi\) |
−0.138882 | + | 0.990309i | \(0.544351\pi\) | |||||||
\(12\) | 3.05338 | + | 8.72650i | 0.881434 | + | 2.51912i | ||||
\(13\) | −1.63211 | − | 0.942300i | −0.452666 | − | 0.261347i | 0.256289 | − | 0.966600i | \(-0.417500\pi\) |
−0.708956 | + | 0.705253i | \(0.750833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.35909 | + | 1.57924i | −0.350915 | + | 0.407757i | ||||
\(16\) | 13.8161 | 3.45403 | ||||||||
\(17\) | −0.601863 | − | 1.04246i | −0.145973 | − | 0.252833i | 0.783762 | − | 0.621061i | \(-0.213298\pi\) |
−0.929736 | + | 0.368228i | \(0.879965\pi\) | |||||||
\(18\) | 5.06658 | + | 6.35371i | 1.19420 | + | 1.49758i | ||||
\(19\) | −6.46933 | − | 3.73507i | −1.48417 | − | 0.856883i | −0.484327 | − | 0.874887i | \(-0.660936\pi\) |
−0.999838 | + | 0.0180038i | \(0.994269\pi\) | |||||||
\(20\) | 3.21047 | + | 5.56070i | 0.717883 | + | 1.24341i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.36797 | − | 5.83350i | 0.718054 | − | 1.24371i | ||||
\(23\) | −2.63359 | + | 1.52050i | −0.549141 | + | 0.317047i | −0.748775 | − | 0.662824i | \(-0.769358\pi\) |
0.199634 | + | 0.979870i | \(0.436025\pi\) | |||||||
\(24\) | 14.7815 | − | 5.17199i | 3.01725 | − | 1.05573i | ||||
\(25\) | 1.77648 | − | 3.07696i | 0.355296 | − | 0.615391i | ||||
\(26\) | −2.55253 | + | 4.42111i | −0.500592 | + | 0.867052i | ||||
\(27\) | 4.39957 | + | 2.76473i | 0.846698 | + | 0.532073i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.173847 | + | 0.100371i | −0.0322826 | + | 0.0186384i | −0.516054 | − | 0.856556i | \(-0.672600\pi\) |
0.483772 | + | 0.875194i | \(0.339266\pi\) | |||||||
\(30\) | 4.27788 | + | 3.68154i | 0.781031 | + | 0.672154i | ||||
\(31\) | − | 3.50314i | − | 0.629183i | −0.949227 | − | 0.314592i | \(-0.898132\pi\) | ||
0.949227 | − | 0.314592i | \(-0.101868\pi\) | |||||||
\(32\) | − | 19.3427i | − | 3.41934i | ||||||
\(33\) | 0.800795 | − | 4.23193i | 0.139401 | − | 0.736684i | ||||
\(34\) | −2.82384 | + | 1.63034i | −0.484285 | + | 0.279602i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 12.5200 | − | 9.98370i | 2.08667 | − | 1.66395i | ||||
\(37\) | −0.865458 | + | 1.49902i | −0.142280 | + | 0.246437i | −0.928355 | − | 0.371695i | \(-0.878777\pi\) |
0.786075 | + | 0.618132i | \(0.212110\pi\) | |||||||
\(38\) | −10.1177 | + | 17.5243i | −1.64130 | + | 2.84282i | ||||
\(39\) | −0.606909 | + | 3.20731i | −0.0971832 | + | 0.513580i | ||||
\(40\) | 9.41904 | − | 5.43809i | 1.48928 | − | 0.859837i | ||||
\(41\) | −3.36029 | + | 5.82020i | −0.524790 | + | 0.908963i | 0.474793 | + | 0.880097i | \(0.342523\pi\) |
−0.999583 | + | 0.0288655i | \(0.990811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.00656005 | + | 0.0113623i | 0.00100040 | + | 0.00173274i | 0.866525 | − | 0.499133i | \(-0.166348\pi\) |
−0.865525 | + | 0.500866i | \(0.833015\pi\) | |||||||
\(44\) | −11.4949 | − | 6.63660i | −1.73293 | − | 1.00051i | ||||
\(45\) | 3.35928 | + | 1.31855i | 0.500772 | + | 0.196557i | ||||
\(46\) | 4.11878 | + | 7.13394i | 0.607281 | + | 1.05184i | ||||
\(47\) | −1.43481 | −0.209288 | −0.104644 | − | 0.994510i | \(-0.533370\pi\) | ||||
−0.104644 | + | 0.994510i | \(0.533370\pi\) | |||||||
\(48\) | −7.90329 | − | 22.5875i | −1.14074 | − | 3.26022i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8.33495 | − | 4.81219i | −1.17874 | − | 0.680546i | ||||
\(51\) | −1.35999 | + | 1.58028i | −0.190437 | + | 0.221284i | ||||
\(52\) | 8.71182 | + | 5.02977i | 1.20811 | + | 0.697504i | ||||
\(53\) | −8.58085 | + | 4.95416i | −1.17867 | + | 0.680506i | −0.955707 | − | 0.294321i | \(-0.904906\pi\) |
−0.222964 | + | 0.974827i | \(0.571573\pi\) | |||||||
\(54\) | 7.48919 | − | 11.9177i | 1.01915 | − | 1.62179i | ||||
\(55\) | − | 2.99128i | − | 0.403344i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.40565 | + | 12.7130i | −0.318636 | + | 1.68388i | ||||
\(58\) | 0.271887 | + | 0.470923i | 0.0357005 | + | 0.0618352i | ||||
\(59\) | 12.2191 | 1.59079 | 0.795394 | − | 0.606092i | \(-0.207264\pi\) | ||||
0.795394 | + | 0.606092i | \(0.207264\pi\) | |||||||
\(60\) | 7.25448 | − | 8.42958i | 0.936549 | − | 1.08825i | ||||
\(61\) | − | 11.2457i | − | 1.43986i | −0.694047 | − | 0.719930i | \(-0.744174\pi\) | ||
0.694047 | − | 0.719930i | \(-0.255826\pi\) | |||||||
\(62\) | −9.48942 | −1.20516 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −24.7638 | −3.09548 | ||||||||
\(65\) | 2.26704i | 0.281192i | ||||||||
\(66\) | −11.4636 | − | 2.16922i | −1.41107 | − | 0.267012i | ||||
\(67\) | −5.15865 | −0.630229 | −0.315115 | − | 0.949054i | \(-0.602043\pi\) | ||||
−0.315115 | + | 0.949054i | \(0.602043\pi\) | |||||||
\(68\) | 3.21260 | + | 5.56438i | 0.389585 | + | 0.674781i | ||||
\(69\) | 3.99231 | + | 3.43578i | 0.480618 | + | 0.413619i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.0452i | − | 1.42950i | −0.699379 | − | 0.714751i | \(-0.746540\pi\) | ||
0.699379 | − | 0.714751i | \(-0.253460\pi\) | |||||||
\(72\) | −16.9110 | − | 21.2071i | −1.99298 | − | 2.49928i | ||||
\(73\) | −7.51020 | + | 4.33602i | −0.879003 | + | 0.507493i | −0.870330 | − | 0.492470i | \(-0.836094\pi\) |
−0.00867336 | + | 0.999962i | \(0.502761\pi\) | |||||||
\(74\) | 4.06058 | + | 2.34438i | 0.472033 | + | 0.272528i | ||||
\(75\) | −6.04661 | − | 1.14418i | −0.698202 | − | 0.132119i | ||||
\(76\) | 34.5317 | + | 19.9369i | 3.96106 | + | 2.28692i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 8.68805 | + | 1.64401i | 0.983728 | + | 0.186148i | ||||
\(79\) | 5.49601 | 0.618350 | 0.309175 | − | 0.951005i | \(-0.399947\pi\) | ||||
0.309175 | + | 0.951005i | \(0.399947\pi\) | |||||||
\(80\) | −8.30991 | − | 14.3932i | −0.929076 | − | 1.60921i | ||||
\(81\) | 2.00326 | − | 8.77422i | 0.222584 | − | 0.974913i | ||||
\(82\) | 15.7659 | + | 9.10246i | 1.74106 | + | 1.00520i | ||||
\(83\) | −1.60854 | − | 2.78607i | −0.176560 | − | 0.305811i | 0.764140 | − | 0.645051i | \(-0.223164\pi\) |
−0.940700 | + | 0.339239i | \(0.889830\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.723998 | + | 1.25400i | −0.0785286 | + | 0.136016i | ||||
\(86\) | 0.0307786 | − | 0.0177700i | 0.00331894 | − | 0.00191619i | ||||
\(87\) | 0.263539 | + | 0.226801i | 0.0282543 | + | 0.0243156i | ||||
\(88\) | −11.2415 | + | 19.4708i | −1.19835 | + | 2.07559i | ||||
\(89\) | −3.98364 | + | 6.89986i | −0.422265 | + | 0.731384i | −0.996161 | − | 0.0875442i | \(-0.972098\pi\) |
0.573896 | + | 0.818928i | \(0.305431\pi\) | |||||||
\(90\) | 3.57172 | − | 9.09972i | 0.376492 | − | 0.959195i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 14.0574 | − | 8.11607i | 1.46559 | − | 0.846159i | ||||
\(93\) | −5.72716 | + | 2.00392i | −0.593879 | + | 0.207796i | ||||
\(94\) | 3.88665i | 0.400877i | ||||||||
\(95\) | 8.98604i | 0.921948i | ||||||||
\(96\) | −31.6227 | + | 11.0647i | −3.22748 | + | 1.12928i | ||||
\(97\) | −2.06260 | + | 1.19084i | −0.209425 | + | 0.120912i | −0.601044 | − | 0.799216i | \(-0.705249\pi\) |
0.391619 | + | 0.920128i | \(0.371915\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.37671 | + | 1.11162i | −0.741387 | + | 0.111722i | ||||
\(100\) | −9.48242 | + | 16.4240i | −0.948242 | + | 1.64240i | ||||
\(101\) | 4.73272 | − | 8.19730i | 0.470923 | − | 0.815662i | −0.528524 | − | 0.848918i | \(-0.677254\pi\) |
0.999447 | + | 0.0332561i | \(0.0105877\pi\) | |||||||
\(102\) | 4.28072 | + | 3.68398i | 0.423855 | + | 0.364768i | ||||
\(103\) | −14.9460 | + | 8.62908i | −1.47267 | + | 0.850249i | −0.999528 | − | 0.0307347i | \(-0.990215\pi\) |
−0.473147 | + | 0.880984i | \(0.656882\pi\) | |||||||
\(104\) | 8.51973 | − | 14.7566i | 0.835428 | − | 1.44700i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.4200 | + | 23.2441i | 1.30346 | + | 2.25766i | ||||
\(107\) | 8.55935 | + | 4.94175i | 0.827464 | + | 0.477737i | 0.852984 | − | 0.521938i | \(-0.174791\pi\) |
−0.0255196 | + | 0.999674i | \(0.508124\pi\) | |||||||
\(108\) | −23.4839 | − | 14.7575i | −2.25973 | − | 1.42004i | ||||
\(109\) | −5.20678 | − | 9.01841i | −0.498719 | − | 0.863807i | 0.501280 | − | 0.865285i | \(-0.332863\pi\) |
−0.999999 | + | 0.00147852i | \(0.999529\pi\) | |||||||
\(110\) | −8.10286 | −0.772578 | ||||||||
\(111\) | 2.94576 | + | 0.557417i | 0.279599 | + | 0.0529077i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.56137 | − | 5.52026i | −0.899458 | − | 0.519303i | −0.0224339 | − | 0.999748i | \(-0.507142\pi\) |
−0.877024 | + | 0.480446i | \(0.840475\pi\) | |||||||
\(114\) | 34.4375 | + | 6.51650i | 3.22536 | + | 0.610326i | ||||
\(115\) | 3.16802 | + | 1.82906i | 0.295419 | + | 0.170560i | ||||
\(116\) | 0.927954 | − | 0.535755i | 0.0861584 | − | 0.0497436i | ||||
\(117\) | 5.59068 | − | 0.842474i | 0.516859 | − | 0.0778868i | ||||
\(118\) | − | 33.0994i | − | 3.04705i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −14.2785 | − | 12.2881i | −1.30345 | − | 1.12174i | ||||
\(121\) | −2.40825 | − | 4.17121i | −0.218932 | − | 0.379201i | ||||
\(122\) | −30.4626 | −2.75795 | ||||||||
\(123\) | 11.4374 | + | 2.16427i | 1.03128 | + | 0.195146i | ||||
\(124\) | 18.6989i | 1.67921i | ||||||||
\(125\) | −10.2886 | −0.920241 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.8634 | 1.23018 | 0.615090 | − | 0.788457i | \(-0.289119\pi\) | ||||
0.615090 | + | 0.788457i | \(0.289119\pi\) | |||||||
\(128\) | 28.3956i | 2.50984i | ||||||||
\(129\) | 0.0148233 | − | 0.0172244i | 0.00130512 | − | 0.00151653i | ||||
\(130\) | 6.14102 | 0.538603 | ||||||||
\(131\) | 6.17975 | + | 10.7036i | 0.539927 | + | 0.935181i | 0.998907 | + | 0.0467344i | \(0.0148814\pi\) |
−0.458981 | + | 0.888446i | \(0.651785\pi\) | |||||||
\(132\) | −4.27445 | + | 22.5890i | −0.372043 | + | 1.96612i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.9739i | 1.20716i | ||||||||
\(135\) | 0.234021 | − | 6.24622i | 0.0201413 | − | 0.537589i | ||||
\(136\) | 9.42529 | − | 5.44169i | 0.808212 | − | 0.466621i | ||||
\(137\) | −10.0991 | − | 5.83070i | −0.862822 | − | 0.498150i | 0.00213432 | − | 0.999998i | \(-0.499321\pi\) |
−0.864956 | + | 0.501847i | \(0.832654\pi\) | |||||||
\(138\) | 9.30693 | − | 10.8145i | 0.792259 | − | 0.920591i | ||||
\(139\) | −8.73893 | − | 5.04543i | −0.741227 | − | 0.427947i | 0.0812884 | − | 0.996691i | \(-0.474097\pi\) |
−0.822515 | + | 0.568743i | \(0.807430\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.820757 | + | 2.34571i | 0.0691202 | + | 0.197545i | ||||
\(142\) | −32.6284 | −2.73811 | ||||||||
\(143\) | −2.34318 | − | 4.05851i | −0.195947 | − | 0.339390i | ||||
\(144\) | −32.4065 | + | 25.8416i | −2.70054 | + | 2.15347i | ||||
\(145\) | 0.209126 | + | 0.120739i | 0.0173670 | + | 0.0100268i | ||||
\(146\) | 11.7455 | + | 20.3439i | 0.972067 | + | 1.68367i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.61960 | − | 8.00138i | 0.379729 | − | 0.657710i | ||||
\(149\) | −4.15010 | + | 2.39606i | −0.339990 | + | 0.196293i | −0.660267 | − | 0.751031i | \(-0.729557\pi\) |
0.320278 | + | 0.947324i | \(0.396224\pi\) | |||||||
\(150\) | −3.09939 | + | 16.3792i | −0.253064 | + | 1.33736i | ||||
\(151\) | 5.65924 | − | 9.80209i | 0.460542 | − | 0.797683i | −0.538446 | − | 0.842660i | \(-0.680988\pi\) |
0.998988 | + | 0.0449774i | \(0.0143216\pi\) | |||||||
\(152\) | 33.7703 | − | 58.4918i | 2.73913 | − | 4.74431i | ||||
\(153\) | 3.36151 | + | 1.31942i | 0.271762 | + | 0.106669i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.64946 | + | 2.10702i | −0.293132 | + | 0.169240i | ||||
\(156\) | 3.23953 | − | 17.1198i | 0.259370 | − | 1.37068i | ||||
\(157\) | − | 14.7316i | − | 1.17571i | −0.808966 | − | 0.587856i | \(-0.799972\pi\) | ||
0.808966 | − | 0.587856i | \(-0.200028\pi\) | |||||||
\(158\) | − | 14.8878i | − | 1.18441i | ||||||
\(159\) | 13.0079 | + | 11.1946i | 1.03159 | + | 0.887787i | ||||
\(160\) | −20.1506 | + | 11.6339i | −1.59304 | + | 0.919744i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −23.7679 | − | 5.42648i | −1.86738 | − | 0.426345i | ||||
\(163\) | 9.07900 | − | 15.7253i | 0.711122 | − | 1.23170i | −0.253314 | − | 0.967384i | \(-0.581521\pi\) |
0.964436 | − | 0.264316i | \(-0.0851460\pi\) | |||||||
\(164\) | 17.9364 | − | 31.0668i | 1.40060 | − | 2.42591i | ||||
\(165\) | −4.89033 | + | 1.71111i | −0.380712 | + | 0.133210i | ||||
\(166\) | −7.54700 | + | 4.35726i | −0.585761 | + | 0.338189i | ||||
\(167\) | −0.599436 | + | 1.03825i | −0.0463857 | + | 0.0803425i | −0.888286 | − | 0.459291i | \(-0.848104\pi\) |
0.841900 | + | 0.539633i | \(0.181437\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.72414 | − | 8.18245i | −0.363395 | − | 0.629419i | ||||
\(170\) | 3.39688 | + | 1.96119i | 0.260529 | + | 0.150416i | ||||
\(171\) | 22.1602 | − | 3.33938i | 1.69463 | − | 0.255369i | ||||
\(172\) | −0.0350159 | − | 0.0606494i | −0.00266994 | − | 0.00462447i | ||||
\(173\) | 18.0081 | 1.36913 | 0.684564 | − | 0.728953i | \(-0.259993\pi\) | ||||
0.684564 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(174\) | 0.614365 | − | 0.713882i | 0.0465749 | − | 0.0541193i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 29.7532 | + | 17.1780i | 2.24273 | + | 1.29484i | ||||
\(177\) | −6.98973 | − | 19.9765i | −0.525380 | − | 1.50153i | ||||
\(178\) | 18.6906 | + | 10.7910i | 1.40092 | + | 0.808819i | ||||
\(179\) | 13.1137 | − | 7.57118i | 0.980162 | − | 0.565897i | 0.0778428 | − | 0.996966i | \(-0.475197\pi\) |
0.902319 | + | 0.431069i | \(0.141863\pi\) | |||||||
\(180\) | −17.9310 | − | 7.03808i | −1.33650 | − | 0.524587i | ||||
\(181\) | − | 7.98716i | − | 0.593681i | −0.954927 | − | 0.296840i | \(-0.904067\pi\) | ||
0.954927 | − | 0.296840i | \(-0.0959329\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.3851 | + | 6.43290i | −1.35907 | + | 0.475534i | ||||
\(184\) | −13.7475 | − | 23.8114i | −1.01348 | − | 1.75540i | ||||
\(185\) | 2.08217 | 0.153084 | ||||||||
\(186\) | 5.42827 | + | 15.5139i | 0.398020 | + | 1.13753i | ||||
\(187\) | − | 2.99326i | − | 0.218889i | ||||||
\(188\) | 7.65865 | 0.558564 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 24.3416 | 1.76593 | ||||||||
\(191\) | 16.0170i | 1.15895i | 0.814991 | + | 0.579473i | \(0.196742\pi\) | ||||
−0.814991 | + | 0.579473i | \(0.803258\pi\) | |||||||
\(192\) | 14.1657 | + | 40.4855i | 1.02232 | + | 2.92179i | ||||
\(193\) | −13.7094 | −0.986821 | −0.493410 | − | 0.869797i | \(-0.664250\pi\) | ||||
−0.493410 | + | 0.869797i | \(0.664250\pi\) | |||||||
\(194\) | 3.22579 | + | 5.58724i | 0.231598 | + | 0.401140i | ||||
\(195\) | 3.70630 | − | 1.29682i | 0.265414 | − | 0.0928674i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.9248i | − | 1.34834i | −0.738577 | − | 0.674170i | \(-0.764502\pi\) | ||
0.738577 | − | 0.674170i | \(-0.235498\pi\) | |||||||
\(198\) | 3.01118 | + | 19.9822i | 0.213995 | + | 1.42008i | ||||
\(199\) | −21.5055 | + | 12.4162i | −1.52449 | + | 0.880163i | −0.524908 | + | 0.851159i | \(0.675900\pi\) |
−0.999579 | + | 0.0290036i | \(0.990767\pi\) | |||||||
\(200\) | 27.8200 | + | 16.0619i | 1.96717 | + | 1.13575i | ||||
\(201\) | 2.95092 | + | 8.43368i | 0.208142 | + | 0.594866i | ||||
\(202\) | −22.2051 | − | 12.8201i | −1.56235 | − | 0.902020i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.25929 | − | 8.43517i | 0.508252 | − | 0.590580i | ||||
\(205\) | 8.08439 | 0.564638 | ||||||||
\(206\) | 23.3747 | + | 40.4862i | 1.62859 | + | 2.82081i | ||||
\(207\) | 3.33329 | − | 8.49227i | 0.231679 | − | 0.590253i | ||||
\(208\) | −22.5495 | − | 13.0189i | −1.56352 | − | 0.902701i | ||||
\(209\) | −9.28786 | − | 16.0870i | −0.642454 | − | 1.11276i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.60761 | − | 6.24857i | 0.248358 | − | 0.430169i | −0.714712 | − | 0.699419i | \(-0.753442\pi\) |
0.963070 | + | 0.269250i | \(0.0867757\pi\) | |||||||
\(212\) | 45.8025 | − | 26.4441i | 3.14573 | − | 1.81619i | ||||
\(213\) | −19.6923 | + | 6.89026i | −1.34929 | + | 0.472113i | ||||
\(214\) | 13.3863 | − | 23.1858i | 0.915072 | − | 1.58495i | ||||
\(215\) | 0.00789127 | − | 0.0136681i | 0.000538180 | − | 0.000932155i | ||||
\(216\) | −24.9971 | + | 39.7784i | −1.70084 | + | 2.70657i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −24.4293 | + | 14.1043i | −1.65456 | + | 0.955262i | ||||
\(219\) | 11.3849 | + | 9.79781i | 0.769319 | + | 0.662074i | ||||
\(220\) | 15.9667i | 1.07648i | ||||||||
\(221\) | 2.26854i | 0.152599i | ||||||||
\(222\) | 1.50995 | − | 7.97956i | 0.101341 | − | 0.535553i | ||||
\(223\) | 21.0706 | − | 12.1651i | 1.41099 | − | 0.814635i | 0.415508 | − | 0.909590i | \(-0.363604\pi\) |
0.995482 | + | 0.0949545i | \(0.0302705\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.58828 | + | 10.5399i | 0.105886 | + | 0.702659i | ||||
\(226\) | −14.9534 | + | 25.9001i | −0.994688 | + | 1.72285i | ||||
\(227\) | 0.240288 | − | 0.416192i | 0.0159485 | − | 0.0276236i | −0.857941 | − | 0.513748i | \(-0.828257\pi\) |
0.873890 | + | 0.486125i | \(0.161590\pi\) | |||||||
\(228\) | 12.8408 | − | 67.8591i | 0.850401 | − | 4.49408i | ||||
\(229\) | 7.80442 | − | 4.50588i | 0.515730 | − | 0.297757i | −0.219456 | − | 0.975622i | \(-0.570428\pi\) |
0.735186 | + | 0.677865i | \(0.237095\pi\) | |||||||
\(230\) | 4.95460 | − | 8.58162i | 0.326697 | − | 0.565855i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.907493 | − | 1.57182i | −0.0595799 | − | 0.103195i | ||||
\(233\) | −9.62742 | − | 5.55840i | −0.630713 | − | 0.364143i | 0.150315 | − | 0.988638i | \(-0.451971\pi\) |
−0.781028 | + | 0.624496i | \(0.785305\pi\) | |||||||
\(234\) | −2.28212 | − | 15.1442i | −0.149187 | − | 0.990007i | ||||
\(235\) | 0.862985 | + | 1.49473i | 0.0562949 | + | 0.0975057i | ||||
\(236\) | −65.2225 | −4.24562 | ||||||||
\(237\) | −3.14390 | − | 8.98523i | −0.204219 | − | 0.583653i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0446 | + | 6.95395i | 0.779100 | + | 0.449813i | 0.836111 | − | 0.548560i | \(-0.184824\pi\) |
−0.0570114 | + | 0.998374i | \(0.518157\pi\) | |||||||
\(240\) | −18.7773 | + | 21.8189i | −1.21207 | + | 1.40841i | ||||
\(241\) | 10.7181 | + | 6.18807i | 0.690411 | + | 0.398609i | 0.803766 | − | 0.594946i | \(-0.202827\pi\) |
−0.113355 | + | 0.993555i | \(0.536160\pi\) | |||||||
\(242\) | −11.2991 | + | 6.52354i | −0.726334 | + | 0.419349i | ||||
\(243\) | −15.4906 | + | 1.74410i | −0.993721 | + | 0.111884i | ||||
\(244\) | 60.0266i | 3.84281i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.86264 | − | 30.9821i | 0.373788 | − | 1.97534i | ||||
\(247\) | 7.03911 | + | 12.1921i | 0.447888 | + | 0.775764i | ||||
\(248\) | 31.6734 | 2.01126 | ||||||||
\(249\) | −3.63471 | + | 4.22347i | −0.230340 | + | 0.267652i | ||||
\(250\) | 27.8701i | 1.76266i | ||||||||
\(251\) | 19.7147 | 1.24438 | 0.622191 | − | 0.782866i | \(-0.286243\pi\) | ||||
0.622191 | + | 0.782866i | \(0.286243\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.56196 | −0.475416 | ||||||||
\(254\) | − | 37.5537i | − | 2.35633i | ||||||
\(255\) | 2.46427 | + | 0.466307i | 0.154319 | + | 0.0292013i | ||||
\(256\) | 27.3911 | 1.71195 | ||||||||
\(257\) | 5.62025 | + | 9.73456i | 0.350581 | + | 0.607225i | 0.986351 | − | 0.164654i | \(-0.0526506\pi\) |
−0.635770 | + | 0.771879i | \(0.719317\pi\) | |||||||
\(258\) | −0.0466580 | − | 0.0401538i | −0.00290480 | − | 0.00249987i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 12.1009i | − | 0.750466i | ||||||
\(261\) | 0.220036 | − | 0.560588i | 0.0136199 | − | 0.0346995i | ||||
\(262\) | 28.9943 | − | 16.7399i | 1.79127 | − | 1.03419i | ||||
\(263\) | 2.82146 | + | 1.62897i | 0.173979 | + | 0.100447i | 0.584461 | − | 0.811422i | \(-0.301306\pi\) |
−0.410482 | + | 0.911869i | \(0.634640\pi\) | |||||||
\(264\) | 38.2626 | + | 7.24032i | 2.35490 | + | 0.445611i | ||||
\(265\) | 10.3221 | + | 5.95949i | 0.634084 | + | 0.366089i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.5591 | + | 2.56575i | 0.829804 | + | 0.157021i | ||||
\(268\) | 27.5356 | 1.68200 | ||||||||
\(269\) | 0.121147 | + | 0.209832i | 0.00738644 | + | 0.0127937i | 0.869695 | − | 0.493590i | \(-0.164315\pi\) |
−0.862309 | + | 0.506383i | \(0.830982\pi\) | |||||||
\(270\) | −16.9199 | − | 0.633923i | −1.02971 | − | 0.0385793i | ||||
\(271\) | −0.929287 | − | 0.536524i | −0.0564502 | − | 0.0325915i | 0.471509 | − | 0.881861i | \(-0.343709\pi\) |
−0.527959 | + | 0.849270i | \(0.677043\pi\) | |||||||
\(272\) | −8.31542 | − | 14.4027i | −0.504196 | − | 0.873294i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.7944 | + | 27.3567i | −0.954173 | + | 1.65268i | ||||
\(275\) | 7.65136 | − | 4.41751i | 0.461394 | − | 0.266386i | ||||
\(276\) | −21.3100 | − | 18.3393i | −1.28271 | − | 1.10390i | ||||
\(277\) | 2.45076 | − | 4.24485i | 0.147252 | − | 0.255048i | −0.782959 | − | 0.622074i | \(-0.786290\pi\) |
0.930211 | + | 0.367025i | \(0.119624\pi\) | |||||||
\(278\) | −13.6672 | + | 23.6723i | −0.819704 | + | 1.41977i | ||||
\(279\) | 6.55226 | + | 8.21682i | 0.392273 | + | 0.491928i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.5613 | − | 6.67494i | 0.689691 | − | 0.398194i | −0.113805 | − | 0.993503i | \(-0.536304\pi\) |
0.803496 | + | 0.595310i | \(0.202971\pi\) | |||||||
\(282\) | 6.35413 | − | 2.22329i | 0.378383 | − | 0.132395i | ||||
\(283\) | − | 3.75657i | − | 0.223305i | −0.993747 | − | 0.111653i | \(-0.964386\pi\) | ||
0.993747 | − | 0.111653i | \(-0.0356144\pi\) | |||||||
\(284\) | 64.2943i | 3.81517i | ||||||||
\(285\) | 14.6909 | − | 5.14032i | 0.870216 | − | 0.304486i | ||||
\(286\) | −10.9938 | + | 6.34729i | −0.650078 | + | 0.375323i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 36.1785 | + | 45.3694i | 2.13184 | + | 2.67342i | ||||
\(289\) | 7.77552 | − | 13.4676i | 0.457384 | − | 0.792212i | ||||
\(290\) | 0.327061 | − | 0.566486i | 0.0192057 | − | 0.0332652i | ||||
\(291\) | 3.12674 | + | 2.69087i | 0.183293 | + | 0.157742i | ||||
\(292\) | 40.0876 | − | 23.1446i | 2.34595 | − | 1.35444i | ||||
\(293\) | −6.38430 | + | 11.0579i | −0.372975 | + | 0.646011i | −0.990022 | − | 0.140915i | \(-0.954995\pi\) |
0.617047 | + | 0.786926i | \(0.288329\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.34934 | − | 12.7294i | −0.427895 | − | 0.741136i | ||||
\(296\) | −13.5532 | − | 7.82496i | −0.787765 | − | 0.454816i | ||||
\(297\) | 6.03706 | + | 11.4240i | 0.350306 | + | 0.662889i | ||||
\(298\) | 6.49052 | + | 11.2419i | 0.375986 | + | 0.651227i | ||||
\(299\) | 5.73108 | 0.331437 | ||||||||
\(300\) | 32.2753 | + | 6.10736i | 1.86342 | + | 0.352609i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −26.5522 | − | 15.3299i | −1.52791 | − | 0.882137i | ||||
\(303\) | −16.1087 | − | 3.04821i | −0.925423 | − | 0.175115i | ||||
\(304\) | −89.3810 | − | 51.6042i | −5.12635 | − | 2.95970i | ||||
\(305\) | −11.7154 | + | 6.76387i | −0.670819 | + | 0.387298i | ||||
\(306\) | 3.57409 | − | 9.10575i | 0.204317 | − | 0.520541i | ||||
\(307\) | 10.7257i | 0.612148i | 0.952008 | + | 0.306074i | \(0.0990155\pi\) | ||||
−0.952008 | + | 0.306074i | \(0.900984\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.6570 | + | 19.4986i | 1.28891 | + | 1.10923i | ||||
\(310\) | 5.70755 | + | 9.88576i | 0.324167 | + | 0.561473i | ||||
\(311\) | −18.8349 | −1.06803 | −0.534013 | − | 0.845476i | \(-0.679317\pi\) | ||||
−0.534013 | + | 0.845476i | \(0.679317\pi\) | |||||||
\(312\) | −28.9986 | − | 5.48731i | −1.64172 | − | 0.310658i | ||||
\(313\) | − | 26.0702i | − | 1.47357i | −0.676125 | − | 0.736787i | \(-0.736342\pi\) | ||
0.676125 | − | 0.736787i | \(-0.263658\pi\) | |||||||
\(314\) | −39.9054 | −2.25199 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −29.3364 | −1.65030 | ||||||||
\(317\) | 13.8899i | 0.780134i | 0.920786 | + | 0.390067i | \(0.127548\pi\) | ||||
−0.920786 | + | 0.390067i | \(0.872452\pi\) | |||||||
\(318\) | 30.3242 | − | 35.2362i | 1.70050 | − | 1.97595i | ||||
\(319\) | −0.499177 | −0.0279485 | ||||||||
\(320\) | 14.8946 | + | 25.7981i | 0.832631 | + | 1.44216i | ||||
\(321\) | 3.18284 | − | 16.8202i | 0.177649 | − | 0.938813i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.99200i | 0.500328i | ||||||||
\(324\) | −10.6929 | + | 46.8347i | −0.594050 | + | 2.60193i | ||||
\(325\) | −5.79883 | + | 3.34796i | −0.321661 | + | 0.185711i | ||||
\(326\) | −42.5971 | − | 24.5935i | −2.35924 | − | 1.36211i | ||||
\(327\) | −11.7654 | + | 13.6712i | −0.650629 | + | 0.756019i | ||||
\(328\) | −52.6228 | − | 30.3818i | −2.90561 | − | 1.67755i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.63511 | + | 13.2471i | 0.255154 | + | 0.729227i | ||||
\(331\) | 4.48460 | 0.246496 | 0.123248 | − | 0.992376i | \(-0.460669\pi\) | ||||
0.123248 | + | 0.992376i | \(0.460669\pi\) | |||||||
\(332\) | 8.58600 | + | 14.8714i | 0.471218 | + | 0.816173i | ||||
\(333\) | −0.773772 | − | 5.13477i | −0.0424025 | − | 0.281384i | ||||
\(334\) | 2.81245 | + | 1.62377i | 0.153891 | + | 0.0888487i | ||||
\(335\) | 3.10274 | + | 5.37411i | 0.169521 | + | 0.293619i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.4010 | + | 28.4074i | −0.893420 | + | 1.54745i | −0.0576723 | + | 0.998336i | \(0.518368\pi\) |
−0.835748 | + | 0.549113i | \(0.814965\pi\) | |||||||
\(338\) | −22.1649 | + | 12.7969i | −1.20561 | + | 0.696059i | ||||
\(339\) | −3.55544 | + | 18.7893i | −0.193105 | + | 1.02050i | ||||
\(340\) | 3.86453 | − | 6.69356i | 0.209583 | − | 0.363009i | ||||
\(341\) | 4.35557 | − | 7.54407i | 0.235867 | − | 0.408534i | ||||
\(342\) | −9.04581 | − | 60.0282i | −0.489141 | − | 3.24595i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.102732 | + | 0.0593121i | −0.00553891 | + | 0.00319789i | ||||
\(345\) | 1.17804 | − | 6.22556i | 0.0634237 | − | 0.335173i | ||||
\(346\) | − | 48.7807i | − | 2.62247i | ||||||
\(347\) | − | 13.4075i | − | 0.719751i | −0.933000 | − | 0.359876i | \(-0.882819\pi\) | ||
0.933000 | − | 0.359876i | \(-0.117181\pi\) | |||||||
\(348\) | −1.40671 | − | 1.21061i | −0.0754074 | − | 0.0648954i | ||||
\(349\) | −19.3276 | + | 11.1588i | −1.03458 | + | 0.597316i | −0.918294 | − | 0.395899i | \(-0.870433\pi\) |
−0.116288 | + | 0.993215i | \(0.537100\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.57539 | − | 8.65807i | −0.244216 | − | 0.462134i | ||||
\(352\) | 24.0494 | − | 41.6548i | 1.28184 | − | 2.22021i | ||||
\(353\) | −8.60842 | + | 14.9102i | −0.458180 | + | 0.793591i | −0.998865 | − | 0.0476341i | \(-0.984832\pi\) |
0.540685 | + | 0.841225i | \(0.318165\pi\) | |||||||
\(354\) | −54.1130 | + | 18.9340i | −2.87607 | + | 1.00633i | ||||
\(355\) | −12.5483 | + | 7.24476i | −0.665994 | + | 0.384512i | ||||
\(356\) | 21.2637 | − | 36.8298i | 1.12697 | − | 1.95198i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.5090 | − | 35.5227i | −1.08394 | − | 1.87743i | ||||
\(359\) | −5.62867 | − | 3.24971i | −0.297070 | − | 0.171513i | 0.344056 | − | 0.938949i | \(-0.388199\pi\) |
−0.641126 | + | 0.767436i | \(0.721532\pi\) | |||||||
\(360\) | −11.9215 | + | 30.3726i | −0.628319 | + | 1.60078i | ||||
\(361\) | 18.4015 | + | 31.8722i | 0.968497 | + | 1.67749i | ||||
\(362\) | −21.6358 | −1.13715 | ||||||||
\(363\) | −5.44176 | + | 6.32324i | −0.285619 | + | 0.331884i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.03424 | + | 5.21592i | 0.472874 | + | 0.273014i | ||||
\(366\) | 17.4256 | + | 49.8022i | 0.910852 | + | 2.60320i | ||||
\(367\) | −7.79734 | − | 4.50180i | −0.407018 | − | 0.234992i | 0.282490 | − | 0.959270i | \(-0.408840\pi\) |
−0.689508 | + | 0.724278i | \(0.742173\pi\) | |||||||
\(368\) | −36.3860 | + | 21.0075i | −1.89675 | + | 1.09509i | ||||
\(369\) | −3.00431 | − | 19.9367i | −0.156398 | − | 1.03786i | ||||
\(370\) | − | 5.64024i | − | 0.293222i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 30.5702 | − | 10.6964i | 1.58499 | − | 0.554583i | ||||
\(373\) | −5.75312 | − | 9.96470i | −0.297885 | − | 0.515953i | 0.677767 | − | 0.735277i | \(-0.262948\pi\) |
−0.975652 | + | 0.219324i | \(0.929615\pi\) | |||||||
\(374\) | −8.10824 | −0.419267 | ||||||||
\(375\) | 5.88543 | + | 16.8205i | 0.303922 | + | 0.868605i | ||||
\(376\) | − | 12.9727i | − | 0.669015i | ||||||
\(377\) | 0.378318 | 0.0194844 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.0982 | 0.878275 | 0.439138 | − | 0.898420i | \(-0.355284\pi\) | ||||
0.439138 | + | 0.898420i | \(0.355284\pi\) | |||||||
\(380\) | − | 47.9653i | − | 2.46057i | ||||||
\(381\) | −7.93035 | − | 22.6648i | −0.406284 | − | 1.16115i | ||||
\(382\) | 43.3872 | 2.21988 | ||||||||
\(383\) | −8.10778 | − | 14.0431i | −0.414288 | − | 0.717569i | 0.581065 | − | 0.813857i | \(-0.302636\pi\) |
−0.995353 | + | 0.0962885i | \(0.969303\pi\) | |||||||
\(384\) | 46.4229 | − | 16.2432i | 2.36901 | − | 0.828909i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 37.1363i | 1.89019i | ||||||||
\(387\) | −0.0366390 | − | 0.0143811i | −0.00186246 | − | 0.000731033i | ||||
\(388\) | 11.0097 | − | 6.35643i | 0.558931 | − | 0.322699i | ||||
\(389\) | 16.2358 | + | 9.37376i | 0.823189 | + | 0.475269i | 0.851515 | − | 0.524330i | \(-0.175684\pi\) |
−0.0283257 | + | 0.999599i | \(0.509018\pi\) | |||||||
\(390\) | −3.51287 | − | 10.0397i | −0.177881 | − | 0.508382i | ||||
\(391\) | 3.17012 | + | 1.83027i | 0.160320 | + | 0.0925607i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.9640 | − | 16.2259i | 0.704388 | − | 0.818487i | ||||
\(394\) | −51.2642 | −2.58265 | ||||||||
\(395\) | −3.30565 | − | 5.72556i | −0.166326 | − | 0.288084i | ||||
\(396\) | 39.3751 | − | 5.93353i | 1.97867 | − | 0.298171i | ||||
\(397\) | 26.8216 | + | 15.4854i | 1.34614 | + | 0.777192i | 0.987700 | − | 0.156362i | \(-0.0499767\pi\) |
0.358436 | + | 0.933554i | \(0.383310\pi\) | |||||||
\(398\) | 33.6334 | + | 58.2548i | 1.68589 | + | 2.92005i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 24.5441 | − | 42.5116i | 1.22720 | − | 2.12558i | ||||
\(401\) | 0.801065 | − | 0.462495i | 0.0400033 | − | 0.0230959i | −0.479865 | − | 0.877342i | \(-0.659314\pi\) |
0.519868 | + | 0.854246i | \(0.325981\pi\) | |||||||
\(402\) | 22.8454 | − | 7.99354i | 1.13943 | − | 0.398681i | ||||
\(403\) | −3.30101 | + | 5.71752i | −0.164435 | + | 0.284810i | ||||
\(404\) | −25.2621 | + | 43.7552i | −1.25684 | + | 2.17690i | ||||
\(405\) | −10.3456 | + | 3.19045i | −0.514076 | + | 0.158535i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.72755 | + | 2.15210i | −0.184768 | + | 0.106676i | ||||
\(408\) | −14.2880 | − | 12.2962i | −0.707362 | − | 0.608754i | ||||
\(409\) | 7.58159i | 0.374885i | 0.982276 | + | 0.187443i | \(0.0600199\pi\) | ||||
−0.982276 | + | 0.187443i | \(0.939980\pi\) | |||||||
\(410\) | − | 21.8992i | − | 1.08153i | ||||||
\(411\) | −3.75539 | + | 19.8460i | −0.185240 | + | 0.978929i | ||||
\(412\) | 79.7782 | − | 46.0599i | 3.93039 | − | 2.26921i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −23.0041 | − | 9.02931i | −1.13059 | − | 0.443766i | ||||
\(415\) | −1.93496 | + | 3.35145i | −0.0949834 | + | 0.164516i | ||||
\(416\) | −18.2266 | + | 31.5695i | −0.893635 | + | 1.54782i | ||||
\(417\) | −3.24962 | + | 17.1731i | −0.159134 | + | 0.840971i | ||||
\(418\) | −43.5770 | + | 25.1592i | −2.13142 | + | 1.23058i | ||||
\(419\) | −2.85061 | + | 4.93740i | −0.139262 | + | 0.241208i | −0.927217 | − | 0.374524i | \(-0.877806\pi\) |
0.787956 | + | 0.615732i | \(0.211140\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.86189 | − | 10.1531i | −0.285691 | − | 0.494832i | 0.687085 | − | 0.726577i | \(-0.258890\pi\) |
−0.972777 | + | 0.231745i | \(0.925557\pi\) | |||||||
\(422\) | −16.9263 | − | 9.77240i | −0.823959 | − | 0.475713i | ||||
\(423\) | 3.36542 | − | 2.68365i | 0.163632 | − | 0.130484i | ||||
\(424\) | −44.7926 | − | 77.5830i | −2.17532 | − | 3.76776i | ||||
\(425\) | −4.27680 | −0.207455 | ||||||||
\(426\) | 18.6645 | + | 53.3430i | 0.904300 | + | 2.58447i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −45.6877 | − | 26.3778i | −2.20840 | − | 1.27502i | ||||
\(429\) | −5.29473 | + | 6.15239i | −0.255632 | + | 0.297040i | ||||
\(430\) | −0.0370245 | − | 0.0213761i | −0.00178548 | − | 0.00103085i | ||||
\(431\) | 23.2973 | − | 13.4507i | 1.12219 | − | 0.647897i | 0.180231 | − | 0.983624i | \(-0.442315\pi\) |
0.941959 | + | 0.335728i | \(0.108982\pi\) | |||||||
\(432\) | 60.7851 | + | 38.1979i | 2.92452 | + | 1.83780i | ||||
\(433\) | 28.1028i | 1.35053i | 0.737574 | + | 0.675266i | \(0.235971\pi\) | ||||
−0.737574 | + | 0.675266i | \(0.764029\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.0777645 | − | 0.410959i | 0.00372852 | − | 0.0197040i | ||||
\(436\) | 27.7925 | + | 48.1381i | 1.33102 | + | 2.30539i | ||||
\(437\) | 22.7167 | 1.08669 | ||||||||
\(438\) | 26.5406 | − | 30.8397i | 1.26816 | − | 1.47358i | ||||
\(439\) | − | 9.32629i | − | 0.445120i | −0.974919 | − | 0.222560i | \(-0.928559\pi\) | ||
0.974919 | − | 0.222560i | \(-0.0714412\pi\) | |||||||
\(440\) | 27.0454 | 1.28934 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.14510 | 0.292292 | ||||||||
\(443\) | 11.3407i | 0.538812i | 0.963027 | + | 0.269406i | \(0.0868273\pi\) | ||||
−0.963027 | + | 0.269406i | \(0.913173\pi\) | |||||||
\(444\) | −15.7237 | − | 2.97536i | −0.746216 | − | 0.141204i | ||||
\(445\) | 9.58406 | 0.454328 | ||||||||
\(446\) | −32.9532 | − | 57.0766i | −1.56038 | − | 2.70265i | ||||
\(447\) | 6.29123 | + | 5.41422i | 0.297565 | + | 0.256084i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.3295i | 0.723444i | 0.932286 | + | 0.361722i | \(0.117811\pi\) | ||||
−0.932286 | + | 0.361722i | \(0.882189\pi\) | |||||||
\(450\) | 28.5508 | − | 4.30239i | 1.34590 | − | 0.202817i | ||||
\(451\) | −14.4729 | + | 8.35592i | −0.681501 | + | 0.393465i | ||||
\(452\) | 51.0363 | + | 29.4658i | 2.40054 | + | 1.38596i | ||||
\(453\) | −19.2624 | − | 3.64496i | −0.905024 | − | 0.171255i | ||||
\(454\) | −1.12739 | − | 0.650900i | −0.0529111 | − | 0.0305483i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −114.944 | − | 21.7505i | −5.38274 | − | 1.01856i | ||||
\(457\) | −9.17299 | −0.429094 | −0.214547 | − | 0.976714i | \(-0.568828\pi\) | ||||
−0.214547 | + | 0.976714i | \(0.568828\pi\) | |||||||
\(458\) | −12.2057 | − | 21.1408i | −0.570333 | − | 0.987846i | ||||
\(459\) | 0.234176 | − | 6.25036i | 0.0109304 | − | 0.291742i | ||||
\(460\) | −16.9101 | − | 9.76305i | −0.788438 | − | 0.455205i | ||||
\(461\) | −16.5365 | − | 28.6420i | −0.770181 | − | 1.33399i | −0.937464 | − | 0.348083i | \(-0.886833\pi\) |
0.167283 | − | 0.985909i | \(-0.446501\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.91594 | − | 6.78260i | 0.181989 | − | 0.315214i | −0.760569 | − | 0.649257i | \(-0.775080\pi\) |
0.942558 | + | 0.334043i | \(0.108413\pi\) | |||||||
\(464\) | −2.40190 | + | 1.38674i | −0.111505 | + | 0.0643776i | ||||
\(465\) | 5.53229 | + | 4.76108i | 0.256554 | + | 0.220790i | ||||
\(466\) | −15.0567 | + | 26.0790i | −0.697490 | + | 1.20809i | ||||
\(467\) | 10.3385 | − | 17.9068i | 0.478408 | − | 0.828627i | −0.521286 | − | 0.853382i | \(-0.674547\pi\) |
0.999694 | + | 0.0247555i | \(0.00788073\pi\) | |||||||
\(468\) | −29.8417 | + | 4.49692i | −1.37943 | + | 0.207870i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.04898 | − | 2.33768i | 0.186765 | − | 0.107829i | ||||
\(471\) | −24.0842 | + | 8.42698i | −1.10974 | + | 0.388295i | ||||
\(472\) | 110.478i | 5.08515i | ||||||||
\(473\) | 0.0326253i | 0.00150011i | ||||||||
\(474\) | −24.3394 | + | 8.51630i | −1.11795 | + | 0.391167i | ||||
\(475\) | −22.9853 | + | 13.2706i | −1.05464 | + | 0.608895i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.8606 | − | 27.6698i | 0.497274 | − | 1.26691i | ||||
\(478\) | 18.8371 | − | 32.6267i | 0.861587 | − | 1.49231i | ||||
\(479\) | 1.32999 | − | 2.30361i | 0.0607688 | − | 0.105255i | −0.834040 | − | 0.551703i | \(-0.813978\pi\) |
0.894809 | + | 0.446449i | \(0.147311\pi\) | |||||||
\(480\) | 30.5467 | + | 26.2884i | 1.39426 | + | 1.19990i | ||||
\(481\) | 2.82505 | − | 1.63104i | 0.128811 | − | 0.0743691i | ||||
\(482\) | 16.7624 | − | 29.0334i | 0.763508 | − | 1.32243i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.8547 | + | 22.2649i | 0.584303 | + | 1.01204i | ||||
\(485\) | 2.48116 | + | 1.43250i | 0.112664 | + | 0.0650465i | ||||
\(486\) | 4.72447 | + | 41.9613i | 0.214306 | + | 1.90341i | ||||
\(487\) | 0.521900 | + | 0.903957i | 0.0236495 | + | 0.0409622i | 0.877608 | − | 0.479379i | \(-0.159138\pi\) |
−0.853958 | + | 0.520341i | \(0.825805\pi\) | |||||||
\(488\) | 101.677 | 4.60269 | ||||||||
\(489\) | −30.9022 | − | 5.84753i | −1.39745 | − | 0.264434i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.0415 | + | 20.8085i | 1.62653 | + | 0.939076i | 0.985118 | + | 0.171878i | \(0.0549835\pi\) |
0.641410 | + | 0.767198i | \(0.278350\pi\) | |||||||
\(492\) | −61.0502 | − | 11.5524i | −2.75236 | − | 0.520820i | ||||
\(493\) | 0.209265 | + | 0.120819i | 0.00942480 | + | 0.00544141i | ||||
\(494\) | 33.0263 | − | 19.0677i | 1.48592 | − | 0.857898i | ||||
\(495\) | 5.59487 | + | 7.01621i | 0.251471 | + | 0.315355i | ||||
\(496\) | − | 48.3999i | − | 2.17322i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 11.4407 | + | 9.84581i | 0.512668 | + | 0.441201i | ||||
\(499\) | 16.1447 | + | 27.9635i | 0.722738 | + | 1.25182i | 0.959898 | + | 0.280348i | \(0.0904499\pi\) |
−0.237161 | + | 0.971470i | \(0.576217\pi\) | |||||||
\(500\) | 54.9181 | 2.45601 | ||||||||
\(501\) | 2.04030 | + | 0.386080i | 0.0911539 | + | 0.0172488i | ||||
\(502\) | − | 53.4038i | − | 2.38353i | ||||||
\(503\) | 39.9702 | 1.78218 | 0.891091 | − | 0.453825i | \(-0.149941\pi\) | ||||
0.891091 | + | 0.453825i | \(0.149941\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.3862 | −0.506681 | ||||||||
\(506\) | 20.4841i | 0.910627i | ||||||||
\(507\) | −10.6748 | + | 12.4040i | −0.474085 | + | 0.550879i | ||||
\(508\) | −73.9996 | −3.28320 | ||||||||
\(509\) | −11.3631 | − | 19.6815i | −0.503661 | − | 0.872367i | −0.999991 | − | 0.00423260i | \(-0.998653\pi\) |
0.496330 | − | 0.868134i | \(-0.334681\pi\) | |||||||
\(510\) | 1.26315 | − | 6.67529i | 0.0559330 | − | 0.295587i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 17.4067i | − | 0.769277i | ||||||
\(513\) | −18.1358 | − | 34.3187i | −0.800716 | − | 1.51521i | ||||
\(514\) | 26.3692 | − | 15.2243i | 1.16310 | − | 0.671515i | ||||
\(515\) | 17.9790 | + | 10.3802i | 0.792249 | + | 0.457405i | ||||
\(516\) | −0.0791231 | + | 0.0919397i | −0.00348320 | + | 0.00404742i | ||||
\(517\) | −3.08988 | − | 1.78394i | −0.135893 | − | 0.0784576i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.3012 | − | 29.4407i | −0.452173 | − | 1.29230i | ||||
\(520\) | −20.4972 | −0.898863 | ||||||||
\(521\) | −15.0179 | − | 26.0118i | −0.657948 | − | 1.13960i | −0.981146 | − | 0.193268i | \(-0.938091\pi\) |
0.323198 | − | 0.946331i | \(-0.395242\pi\) | |||||||
\(522\) | −1.51854 | − | 0.596039i | −0.0664646 | − | 0.0260879i | ||||
\(523\) | −0.675300 | − | 0.389885i | −0.0295288 | − | 0.0170485i | 0.485163 | − | 0.874424i | \(-0.338760\pi\) |
−0.514692 | + | 0.857375i | \(0.672094\pi\) | |||||||
\(524\) | −32.9860 | − | 57.1334i | −1.44100 | − | 2.49588i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.41260 | − | 7.64285i | 0.192399 | − | 0.333244i | ||||
\(527\) | −3.65188 | + | 2.10841i | −0.159078 | + | 0.0918439i | ||||
\(528\) | 11.0639 | − | 58.4689i | 0.481494 | − | 2.54453i | ||||
\(529\) | −6.87614 | + | 11.9098i | −0.298963 | + | 0.517819i | ||||
\(530\) | 16.1433 | − | 27.9609i | 0.701218 | − | 1.21455i | ||||
\(531\) | −28.6605 | + | 22.8545i | −1.24376 | + | 0.991800i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.9688 | − | 6.33281i | 0.475110 | − | 0.274305i | ||||
\(534\) | 6.95018 | − | 36.7293i | 0.300764 | − | 1.58943i | ||||
\(535\) | − | 11.8891i | − | 0.514012i | ||||||
\(536\) | − | 46.6415i | − | 2.01460i | ||||||
\(537\) | −19.8793 | − | 17.1081i | −0.857855 | − | 0.738268i | ||||
\(538\) | 0.568399 | − | 0.328165i | 0.0245054 | − | 0.0141482i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.24915 | + | 33.3408i | −0.0537547 | + | 1.43476i | ||||
\(541\) | −1.02015 | + | 1.76696i | −0.0438598 | + | 0.0759674i | −0.887122 | − | 0.461535i | \(-0.847299\pi\) |
0.843262 | + | 0.537503i | \(0.180632\pi\) | |||||||
\(542\) | −1.45335 | + | 2.51728i | −0.0624268 | + | 0.108126i | ||||
\(543\) | −13.0579 | + | 4.56892i | −0.560368 | + | 0.196071i | ||||
\(544\) | −20.1640 | + | 11.6417i | −0.864522 | + | 0.499132i | ||||
\(545\) | −6.26338 | + | 10.8485i | −0.268294 | + | 0.464699i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.93590 | − | 15.4774i | −0.382071 | − | 0.661767i | 0.609287 | − | 0.792950i | \(-0.291456\pi\) |
−0.991358 | + | 0.131183i | \(0.958123\pi\) | |||||||
\(548\) | 53.9064 | + | 31.1229i | 2.30277 | + | 1.32950i | ||||
\(549\) | 21.0338 | + | 26.3773i | 0.897701 | + | 1.12576i | ||||
\(550\) | −11.9663 | − | 20.7262i | −0.510244 | − | 0.883769i | ||||
\(551\) | 1.49957 | 0.0638837 | ||||||||
\(552\) | −31.0643 | + | 36.0962i | −1.32218 | + | 1.53635i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −11.4986 | − | 6.63870i | −0.488527 | − | 0.282051i | ||||
\(555\) | −1.19107 | − | 3.40406i | −0.0505581 | − | 0.144494i | ||||
\(556\) | 46.6463 | + | 26.9313i | 1.97824 | + | 1.14214i | ||||
\(557\) | −37.2049 | + | 21.4802i | −1.57642 | + | 0.910147i | −0.581068 | + | 0.813855i | \(0.697365\pi\) |
−0.995353 | + | 0.0962924i | \(0.969302\pi\) | |||||||
\(558\) | 22.2580 | − | 17.7489i | 0.942254 | − | 0.751373i | ||||
\(559\) | − | 0.0247261i | − | 0.00104580i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.89357 | + | 1.71225i | −0.206607 | + | 0.0722911i | ||||
\(562\) | −18.0813 | − | 31.3177i | −0.762713 | − | 1.32106i | ||||
\(563\) | −1.54748 | −0.0652184 | −0.0326092 | − | 0.999468i | \(-0.510382\pi\) | ||||
−0.0326092 | + | 0.999468i | \(0.510382\pi\) | |||||||
\(564\) | −4.38100 | − | 12.5208i | −0.184474 | − | 0.527222i | ||||
\(565\) | 13.2810i | 0.558734i | ||||||||
\(566\) | −10.1759 | −0.427726 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 108.906 | 4.56958 | ||||||||
\(569\) | − | 9.99861i | − | 0.419164i | −0.977791 | − | 0.209582i | \(-0.932790\pi\) | ||
0.977791 | − | 0.209582i | \(-0.0672103\pi\) | |||||||
\(570\) | −13.9242 | − | 39.7952i | −0.583222 | − | 1.66684i | ||||
\(571\) | −2.79430 | −0.116938 | −0.0584689 | − | 0.998289i | \(-0.518622\pi\) | ||||
−0.0584689 | + | 0.998289i | \(0.518622\pi\) | |||||||
\(572\) | 12.5073 | + | 21.6634i | 0.522958 | + | 0.905790i | ||||
\(573\) | 26.1855 | − | 9.16224i | 1.09392 | − | 0.382758i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.8046i | 0.450582i | ||||||||
\(576\) | 58.0849 | − | 46.3181i | 2.42021 | − | 1.92992i | ||||
\(577\) | −3.23689 | + | 1.86882i | −0.134754 | + | 0.0778000i | −0.565861 | − | 0.824500i | \(-0.691456\pi\) |
0.431108 | + | 0.902300i | \(0.358123\pi\) | |||||||
\(578\) | −36.4814 | − | 21.0626i | −1.51743 | − | 0.876087i | ||||
\(579\) | 7.84221 | + | 22.4129i | 0.325911 | + | 0.931449i | ||||
\(580\) | −1.11626 | − | 0.644475i | −0.0463503 | − | 0.0267604i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.28910 | − | 8.46981i | 0.302143 | − | 0.351085i | ||||
\(583\) | −24.6386 | −1.02043 | ||||||||
\(584\) | −39.2037 | − | 67.9028i | −1.62226 | − | 2.80984i | ||||
\(585\) | −4.24026 | − | 5.31747i | −0.175313 | − | 0.219850i | ||||
\(586\) | 29.9540 | + | 17.2940i | 1.23739 | + | 0.714407i | ||||
\(587\) | 13.1249 | + | 22.7331i | 0.541725 | + | 0.938295i | 0.998805 | + | 0.0488692i | \(0.0155618\pi\) |
−0.457081 | + | 0.889425i | \(0.651105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.0845 | + | 22.6630i | −0.539136 | + | 0.933812i | ||||
\(590\) | −34.4819 | + | 19.9081i | −1.41960 | + | 0.819604i | ||||
\(591\) | −30.9395 | + | 10.8256i | −1.27268 | + | 0.445308i | ||||
\(592\) | −11.9573 | + | 20.7106i | −0.491441 | + | 0.851201i | ||||
\(593\) | −1.79833 | + | 3.11481i | −0.0738488 | + | 0.127910i | −0.900585 | − | 0.434680i | \(-0.856862\pi\) |
0.826736 | + | 0.562590i | \(0.190195\pi\) | |||||||
\(594\) | 30.9457 | − | 16.3534i | 1.26972 | − | 0.670987i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.1522 | − | 12.7896i | 0.907391 | − | 0.523882i | ||||
\(597\) | 32.6007 | + | 28.0561i | 1.33426 | + | 1.14826i | ||||
\(598\) | − | 15.5245i | − | 0.634845i | ||||||
\(599\) | − | 23.8330i | − | 0.973789i | −0.873461 | − | 0.486895i | \(-0.838130\pi\) | ||
0.873461 | − | 0.486895i | \(-0.161870\pi\) | |||||||
\(600\) | 10.3450 | − | 54.6699i | 0.422334 | − | 2.23189i | ||||
\(601\) | 14.6034 | − | 8.43126i | 0.595684 | − | 0.343918i | −0.171658 | − | 0.985157i | \(-0.554912\pi\) |
0.767342 | + | 0.641238i | \(0.221579\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.0999 | − | 9.64870i | 0.492746 | − | 0.392925i | ||||
\(604\) | −30.2076 | + | 52.3212i | −1.22913 | + | 2.12892i | ||||
\(605\) | −2.89695 | + | 5.01767i | −0.117778 | + | 0.203997i | ||||
\(606\) | −8.25708 | + | 43.6358i | −0.335421 | + | 1.77258i | ||||
\(607\) | −9.07737 | + | 5.24082i | −0.368439 | + | 0.212718i | −0.672776 | − | 0.739846i | \(-0.734898\pi\) |
0.304337 | + | 0.952564i | \(0.401565\pi\) | |||||||
\(608\) | −72.2463 | + | 125.134i | −2.92997 | + | 5.07487i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.3222 | + | 31.7349i | 0.741842 | + | 1.28491i | ||||
\(611\) | 2.34176 | + | 1.35202i | 0.0947377 | + | 0.0546968i | ||||
\(612\) | −17.9429 | − | 7.04275i | −0.725299 | − | 0.284686i | ||||
\(613\) | 23.9500 | + | 41.4827i | 0.967333 | + | 1.67547i | 0.703213 | + | 0.710979i | \(0.251748\pi\) |
0.264120 | + | 0.964490i | \(0.414919\pi\) | |||||||
\(614\) | 29.0541 | 1.17253 | ||||||||
\(615\) | −4.62454 | − | 13.2169i | −0.186480 | − | 0.532956i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.69477 | + | 2.71053i | 0.189004 | + | 0.109122i | 0.591516 | − | 0.806293i | \(-0.298530\pi\) |
−0.402512 | + | 0.915415i | \(0.631863\pi\) | |||||||
\(618\) | 52.8183 | − | 61.3739i | 2.12466 | − | 2.46882i | ||||
\(619\) | 27.9729 | + | 16.1501i | 1.12432 | + | 0.649129i | 0.942501 | − | 0.334202i | \(-0.108467\pi\) |
0.181823 | + | 0.983331i | \(0.441800\pi\) | |||||||
\(620\) | 19.4799 | − | 11.2467i | 0.782332 | − | 0.451680i | ||||
\(621\) | −15.7904 | − | 0.591605i | −0.633649 | − | 0.0237403i | ||||
\(622\) | 51.0204i | 2.04573i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −8.38513 | + | 44.3126i | −0.335674 | + | 1.77392i | ||||
\(625\) | −2.69418 | − | 4.66646i | −0.107767 | − | 0.186658i | ||||
\(626\) | −70.6196 | −2.82253 | ||||||||
\(627\) | −20.9871 | + | 24.3867i | −0.838146 | + | 0.973911i | ||||
\(628\) | 78.6338i | 3.13783i | ||||||||
\(629\) | 2.08355 | 0.0830765 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.3539 | −0.730656 | −0.365328 | − | 0.930879i | \(-0.619043\pi\) | ||||
−0.365328 | + | 0.930879i | \(0.619043\pi\) | |||||||
\(632\) | 49.6917i | 1.97663i | ||||||||
\(633\) | −12.2792 | − | 2.32356i | −0.488055 | − | 0.0923532i | ||||
\(634\) | 37.6253 | 1.49429 | ||||||||
\(635\) | −8.33836 | − | 14.4425i | −0.330898 | − | 0.573132i | ||||
\(636\) | −69.4330 | − | 59.7539i | −2.75320 | − | 2.36940i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.35218i | 0.0535335i | ||||||||
\(639\) | 22.5293 | + | 28.2527i | 0.891244 | + | 1.11766i | ||||
\(640\) | 29.5816 | − | 17.0789i | 1.16931 | − | 0.675104i | ||||
\(641\) | −9.07003 | − | 5.23658i | −0.358245 | − | 0.206833i | 0.310066 | − | 0.950715i | \(-0.399649\pi\) |
−0.668310 | + | 0.743882i | \(0.732982\pi\) | |||||||
\(642\) | −45.5631 | − | 8.62177i | −1.79823 | − | 0.340274i | ||||
\(643\) | −3.37572 | − | 1.94897i | −0.133125 | − | 0.0768600i | 0.431958 | − | 0.901894i | \(-0.357823\pi\) |
−0.565084 | + | 0.825034i | \(0.691156\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.0268595 | − | 0.00508254i | −0.00105759 | − | 0.000200125i | ||||
\(646\) | 24.3578 | 0.958344 | ||||||||
\(647\) | 6.20269 | + | 10.7434i | 0.243853 | + | 0.422366i | 0.961809 | − | 0.273723i | \(-0.0882552\pi\) |
−0.717955 | + | 0.696089i | \(0.754922\pi\) | |||||||
\(648\) | 79.3313 | + | 18.1123i | 3.11643 | + | 0.711517i | ||||
\(649\) | 26.3140 | + | 15.1924i | 1.03291 | + | 0.596353i | ||||
\(650\) | 9.06905 | + | 15.7081i | 0.355717 | + | 0.616120i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −48.4615 | + | 83.9377i | −1.89790 | + | 3.28726i | ||||
\(653\) | 12.2749 | − | 7.08690i | 0.480353 | − | 0.277332i | −0.240211 | − | 0.970721i | \(-0.577216\pi\) |
0.720564 | + | 0.693389i | \(0.243883\pi\) | |||||||
\(654\) | 37.0330 | + | 31.8705i | 1.44810 | + | 1.24623i | ||||
\(655\) | 7.43379 | − | 12.8757i | 0.290462 | − | 0.503095i | ||||
\(656\) | −46.4263 | + | 80.4126i | −1.81264 | + | 3.13959i | ||||
\(657\) | 9.50554 | − | 24.2174i | 0.370846 | − | 0.944811i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.2962 | + | 9.98594i | −0.673763 | + | 0.388997i | −0.797501 | − | 0.603318i | \(-0.793845\pi\) |
0.123738 | + | 0.992315i | \(0.460512\pi\) | |||||||
\(660\) | 26.1034 | − | 9.13350i | 1.01607 | − | 0.355521i | ||||
\(661\) | − | 24.3056i | − | 0.945378i | −0.881229 | − | 0.472689i | \(-0.843283\pi\) | ||
0.881229 | − | 0.472689i | \(-0.156717\pi\) | |||||||
\(662\) | − | 12.1480i | − | 0.472146i | ||||||
\(663\) | 3.70876 | − | 1.29768i | 0.144036 | − | 0.0503978i | ||||
\(664\) | 25.1900 | − | 14.5435i | 0.977563 | − | 0.564396i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −13.9092 | + | 2.09602i | −0.538971 | + | 0.0812190i | ||||
\(667\) | 0.305228 | − | 0.528670i | 0.0118185 | − | 0.0204702i | ||||
\(668\) | 3.19964 | − | 5.54194i | 0.123798 | − | 0.214424i | ||||
\(669\) | −31.9413 | − | 27.4886i | −1.23492 | − | 1.06277i | ||||
\(670\) | 14.5575 | − | 8.40480i | 0.562407 | − | 0.324706i | ||||
\(671\) | 13.9821 | − | 24.2177i | 0.539773 | − | 0.934914i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.82521 | − | 3.16135i | −0.0703566 | − | 0.121861i | 0.828701 | − | 0.559692i | \(-0.189080\pi\) |
−0.899058 | + | 0.437830i | \(0.855747\pi\) | |||||||
\(674\) | 76.9508 | + | 44.4275i | 2.96403 | + | 1.71129i | ||||
\(675\) | 16.3227 | − | 8.62580i | 0.628262 | − | 0.332007i | ||||
\(676\) | 25.2163 | + | 43.6759i | 0.969858 | + | 1.67984i | ||||
\(677\) | −1.93735 | −0.0744585 | −0.0372292 | − | 0.999307i | \(-0.511853\pi\) | ||||
−0.0372292 | + | 0.999307i | \(0.511853\pi\) | |||||||
\(678\) | 50.8970 | + | 9.63109i | 1.95469 | + | 0.369880i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −11.3379 | − | 6.54597i | −0.434790 | − | 0.251026i | ||||
\(681\) | −0.817869 | − | 0.154763i | −0.0313408 | − | 0.00593053i | ||||
\(682\) | −20.4356 | − | 11.7985i | −0.782519 | − | 0.451788i | ||||
\(683\) | 16.8815 | − | 9.74656i | 0.645954 | − | 0.372942i | −0.140950 | − | 0.990017i | \(-0.545016\pi\) |
0.786905 | + | 0.617075i | \(0.211682\pi\) | |||||||
\(684\) | −118.286 | + | 17.8248i | −4.52277 | + | 0.681548i | ||||
\(685\) | 14.0278i | 0.535976i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.8309 | − | 10.1816i | −0.451377 | − | 0.388454i | ||||
\(688\) | 0.0906345 | + | 0.156983i | 0.00345541 | + | 0.00598494i | ||||
\(689\) | 18.6732 | 0.711393 | ||||||||
\(690\) | −16.8640 | − | 3.19112i | −0.642000 | − | 0.121484i | ||||
\(691\) | 41.3215i | 1.57194i | 0.618261 | + | 0.785972i | \(0.287837\pi\) | ||||
−0.618261 | + | 0.785972i | \(0.712163\pi\) | |||||||
\(692\) | −96.1226 | −3.65403 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −36.3186 | −1.37863 | ||||||||
\(695\) | 12.1386i | 0.460442i | ||||||||
\(696\) | −2.05060 | + | 2.38276i | −0.0777279 | + | 0.0903184i | ||||
\(697\) | 8.08975 | 0.306421 | ||||||||
\(698\) | 30.2273 | + | 52.3552i | 1.14412 | + | 1.98167i | ||||
\(699\) | −3.58001 | + | 18.9191i | −0.135408 | + | 0.715586i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27.3333i | − | 1.03236i | −0.856479 | − | 0.516182i | \(-0.827353\pi\) | ||
0.856479 | − | 0.516182i | \(-0.172647\pi\) | |||||||
\(702\) | −23.4532 | + | 12.3939i | −0.885186 | + | 0.467779i | ||||
\(703\) | 11.1979 | − | 6.46508i | 0.422335 | − | 0.243835i | ||||
\(704\) | −53.3293 | − | 30.7897i | −2.00992 | − | 1.16043i | ||||
\(705\) | 1.95003 | − | 2.26590i | 0.0734423 | − | 0.0853387i | ||||
\(706\) | 40.3893 | + | 23.3187i | 1.52007 | + | 0.877613i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 37.3094 | + | 106.630i | 1.40217 | + | 4.00739i | ||||
\(709\) | 2.71269 | 0.101877 | 0.0509387 | − | 0.998702i | \(-0.483779\pi\) | ||||
0.0509387 | + | 0.998702i | \(0.483779\pi\) | |||||||
\(710\) | 19.6248 | + | 33.9912i | 0.736506 | + | 1.27567i | ||||
\(711\) | −12.8912 | + | 10.2797i | −0.483458 | + | 0.385519i | ||||
\(712\) | −62.3845 | − | 36.0177i | −2.33796 | − | 1.34982i | ||||
\(713\) | 5.32654 | + | 9.22584i | 0.199480 | + | 0.345510i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.81868 | + | 4.88210i | −0.105413 | + | 0.182580i | ||||
\(716\) | −69.9976 | + | 40.4131i | −2.61593 | + | 1.51031i | ||||
\(717\) | 4.47884 | − | 23.6691i | 0.167265 | − | 0.883941i | ||||
\(718\) | −8.80292 | + | 15.2471i | −0.328522 | + | 0.569017i | ||||
\(719\) | 8.13931 | − | 14.0977i | 0.303545 | − | 0.525756i | −0.673391 | − | 0.739286i | \(-0.735163\pi\) |
0.976936 | + | 0.213531i | \(0.0684964\pi\) | |||||||
\(720\) | 46.4123 | + | 18.2172i | 1.72968 | + | 0.678915i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 86.3365 | − | 49.8464i | 3.21311 | − | 1.85509i | ||||
\(723\) | 3.98556 | − | 21.0623i | 0.148225 | − | 0.783317i | ||||
\(724\) | 42.6335i | 1.58446i | ||||||||
\(725\) | 0.713227i | 0.0264886i | ||||||||
\(726\) | 17.1286 | + | 14.7408i | 0.635701 | + | 0.547083i | ||||
\(727\) | 0.980123 | − | 0.565874i | 0.0363508 | − | 0.0209871i | −0.481714 | − | 0.876328i | \(-0.659986\pi\) |
0.518065 | + | 0.855341i | \(0.326652\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.7125 | + | 24.3273i | 0.433796 | + | 0.901011i | ||||
\(730\) | 14.1290 | − | 24.4722i | 0.522939 | − | 0.905757i | ||||
\(731\) | 0.00789650 | − | 0.0136771i | 0.000292063 | − | 0.000505867i | ||||
\(732\) | 98.1353 | − | 34.3372i | 3.62719 | − | 1.26914i | ||||
\(733\) | 33.2085 | − | 19.1729i | 1.22658 | − | 0.708169i | 0.260270 | − | 0.965536i | \(-0.416188\pi\) |
0.966314 | + | 0.257367i | \(0.0828549\pi\) | |||||||
\(734\) | −12.1946 | + | 21.1217i | −0.450111 | + | 0.779615i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 29.4106 | + | 50.9407i | 1.08409 | + | 1.87770i | ||||
\(737\) | −11.1092 | − | 6.41391i | −0.409213 | − | 0.236259i | ||||
\(738\) | −54.0051 | + | 8.13816i | −1.98795 | + | 0.299570i | ||||
\(739\) | −5.36489 | − | 9.29226i | −0.197351 | − | 0.341821i | 0.750318 | − | 0.661077i | \(-0.229900\pi\) |
−0.947669 | + | 0.319256i | \(0.896567\pi\) | |||||||
\(740\) | −11.1141 | −0.408562 | ||||||||
\(741\) | 15.9058 | − | 18.4823i | 0.584314 | − | 0.678963i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.3308 | − | 6.54185i | −0.415687 | − | 0.239997i | 0.277543 | − | 0.960713i | \(-0.410480\pi\) |
−0.693230 | + | 0.720716i | \(0.743813\pi\) | |||||||
\(744\) | −18.1182 | − | 51.7816i | −0.664246 | − | 1.89841i | ||||
\(745\) | 4.99228 | + | 2.88229i | 0.182903 | + | 0.105599i | ||||
\(746\) | −26.9927 | + | 15.5842i | −0.988272 | + | 0.570579i | ||||
\(747\) | 8.98397 | + | 3.52629i | 0.328706 | + | 0.129020i | ||||
\(748\) | 15.9773i | 0.584188i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 45.5637 | − | 15.9426i | 1.66375 | − | 0.582142i | ||||
\(751\) | −13.1677 | − | 22.8071i | −0.480495 | − | 0.832242i | 0.519254 | − | 0.854620i | \(-0.326210\pi\) |
−0.999750 | + | 0.0223774i | \(0.992876\pi\) | |||||||
\(752\) | −19.8235 | −0.722887 | ||||||||
\(753\) | −11.2775 | − | 32.2308i | −0.410974 | − | 1.17456i | ||||
\(754\) | − | 1.02480i | − | 0.0373209i | ||||||
\(755\) | −13.6153 | −0.495512 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.6280 | −1.18588 | −0.592942 | − | 0.805245i | \(-0.702034\pi\) | ||||
−0.592942 | + | 0.805245i | \(0.702034\pi\) | |||||||
\(758\) | − | 46.3161i | − | 1.68228i | ||||||
\(759\) | 4.32569 | + | 12.3628i | 0.157013 | + | 0.448740i | ||||
\(760\) | −81.2465 | −2.94712 | ||||||||
\(761\) | 12.6727 | + | 21.9498i | 0.459385 | + | 0.795679i | 0.998929 | − | 0.0462793i | \(-0.0147364\pi\) |
−0.539543 | + | 0.841958i | \(0.681403\pi\) | |||||||
\(762\) | −61.3951 | + | 21.4820i | −2.22411 | + | 0.778210i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 85.4946i | − | 3.09309i | ||||||
\(765\) | −0.647299 | − | 4.29549i | −0.0234031 | − | 0.155304i | ||||
\(766\) | −38.0403 | + | 21.9626i | −1.37445 | + | 0.793541i | ||||
\(767\) | −19.9429 | − | 11.5140i | −0.720097 | − | 0.415748i | ||||
\(768\) | −15.6687 | − | 44.7808i | −0.565394 | − | 1.61589i | ||||
\(769\) | 11.4964 | + | 6.63744i | 0.414570 | + | 0.239352i | 0.692752 | − | 0.721176i | \(-0.256398\pi\) |
−0.278181 | + | 0.960529i | \(0.589732\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.6997 | − | 14.7568i | 0.457368 | − | 0.531454i | ||||
\(772\) | 73.1772 | 2.63370 | ||||||||
\(773\) | −8.00680 | − | 13.8682i | −0.287985 | − | 0.498804i | 0.685344 | − | 0.728219i | \(-0.259652\pi\) |
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(774\) | −0.0389560 | + | 0.0992488i | −0.00140024 | + | 0.00356742i | ||||
\(775\) | −10.7790 | − | 6.22327i | −0.387194 | − | 0.223546i | ||||
\(776\) | −10.7669 | − | 18.6488i | −0.386509 | − | 0.669454i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25.3919 | − | 43.9801i | 0.910344 | − | 1.57676i | ||||
\(779\) | 43.4777 | − | 25.1019i | 1.55775 | − | 0.899367i | ||||
\(780\) | −19.7833 | + | 6.92213i | −0.708357 | + | 0.247852i | ||||
\(781\) | 14.9762 | − | 25.9395i | 0.535890 | − | 0.928189i | ||||
\(782\) | 4.95789 | − | 8.58731i | 0.177294 | − | 0.307082i | ||||
\(783\) | −1.04235 | − | 0.0390528i | −0.0372506 | − | 0.00139563i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.3469 | + | 8.86054i | −0.547755 | + | 0.316246i | ||||
\(786\) | −43.9531 | − | 37.8260i | −1.56776 | − | 1.34921i | ||||
\(787\) | 4.90354i | 0.174792i | 0.996174 | + | 0.0873961i | \(0.0278546\pi\) | ||||
−0.996174 | + | 0.0873961i | \(0.972145\pi\) | |||||||
\(788\) | 101.016i | 3.59855i | ||||||||
\(789\) | 1.04917 | − | 5.54453i | 0.0373516 | − | 0.197390i | ||||
\(790\) | −15.5096 | + | 8.95445i | −0.551806 | + | 0.318585i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −10.0506 | − | 66.6958i | −0.357131 | − | 2.36993i | ||||
\(793\) | −10.5968 | + | 18.3542i | −0.376303 | + | 0.651776i | ||||
\(794\) | 41.9474 | − | 72.6551i | 1.48866 | − | 2.57843i | ||||
\(795\) | 3.83834 | − | 20.2843i | 0.136132 | − | 0.719411i | ||||
\(796\) | 114.791 | − | 66.2748i | 4.06867 | − | 2.34905i | ||||
\(797\) | 21.3994 | − | 37.0649i | 0.758006 | − | 1.31290i | −0.185860 | − | 0.982576i | \(-0.559507\pi\) |
0.943866 | − | 0.330328i | \(-0.107159\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.863557 | + | 1.49572i | 0.0305505 | + | 0.0529149i | ||||
\(800\) | −59.5167 | − | 34.3620i | −2.10423 | − | 1.21488i | ||||
\(801\) | −3.56162 | − | 23.6350i | −0.125844 | − | 0.835101i | ||||
\(802\) | −1.25282 | − | 2.16995i | −0.0442386 | − | 0.0766235i | ||||
\(803\) | −21.5644 | −0.760993 | ||||||||
\(804\) | −15.7513 | − | 45.0169i | −0.555505 | − | 1.58763i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15.4878 | + | 8.94188i | 0.545534 | + | 0.314964i | ||||
\(807\) | 0.273747 | − | 0.318089i | 0.00963634 | − | 0.0111973i | ||||
\(808\) | 74.1152 | + | 42.7904i | 2.60736 | + | 1.50536i | ||||
\(809\) | 30.5649 | − | 17.6467i | 1.07461 | − | 0.620424i | 0.145169 | − | 0.989407i | \(-0.453627\pi\) |
0.929436 | + | 0.368983i | \(0.120294\pi\) | |||||||
\(810\) | 8.64240 | + | 28.0244i | 0.303663 | + | 0.984677i | ||||
\(811\) | − | 21.0223i | − | 0.738193i | −0.929391 | − | 0.369096i | \(-0.879667\pi\) | ||
0.929391 | − | 0.369096i | \(-0.120333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.345560 | + | 1.82617i | −0.0121193 | + | 0.0640465i | ||||
\(814\) | 5.82968 | + | 10.0973i | 0.204330 | + | 0.353910i | ||||
\(815\) | −21.8428 | −0.765119 | ||||||||
\(816\) | −18.7898 | + | 21.8334i | −0.657774 | + | 0.764322i | ||||
\(817\) | − | 0.0980089i | − | 0.00342890i | ||||||
\(818\) | 20.5372 | 0.718067 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −43.1525 | −1.50695 | ||||||||
\(821\) | − | 34.4820i | − | 1.20343i | −0.798710 | − | 0.601716i | \(-0.794484\pi\) | ||
0.798710 | − | 0.601716i | \(-0.205516\pi\) | |||||||
\(822\) | 53.7593 | + | 10.1727i | 1.87507 | + | 0.354814i | ||||
\(823\) | −38.9899 | −1.35910 | −0.679552 | − | 0.733628i | \(-0.737826\pi\) | ||||
−0.679552 | + | 0.733628i | \(0.737826\pi\) | |||||||
\(824\) | −78.0191 | − | 135.133i | −2.71792 | − | 4.70758i | ||||
\(825\) | −11.5989 | − | 9.98195i | −0.403820 | − | 0.347527i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.2537i | 1.64317i | 0.570086 | + | 0.821585i | \(0.306910\pi\) | ||||
−0.570086 | + | 0.821585i | \(0.693090\pi\) | |||||||
\(828\) | −17.7923 | + | 45.3297i | −0.618324 | + | 1.57531i | ||||
\(829\) | 42.5588 | − | 24.5713i | 1.47813 | − | 0.853397i | 0.478432 | − | 0.878124i | \(-0.341205\pi\) |
0.999694 | + | 0.0247275i | \(0.00787180\pi\) | |||||||
\(830\) | 9.07850 | + | 5.24147i | 0.315119 | + | 0.181934i | ||||
\(831\) | −8.34166 | − | 1.57847i | −0.289369 | − | 0.0547564i | ||||
\(832\) | 40.4174 | + | 23.3350i | 1.40122 | + | 0.808995i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 46.5190 | + | 8.80266i | 1.61082 | + | 0.304811i | ||||
\(835\) | 1.44216 | 0.0499079 | ||||||||
\(836\) | 49.5763 | + | 85.8687i | 1.71463 | + | 2.96983i | ||||
\(837\) | 9.68526 | − | 15.4123i | 0.334771 | − | 0.532728i | ||||
\(838\) | 13.3746 | + | 7.72182i | 0.462017 | + | 0.266746i | ||||
\(839\) | −26.0780 | − | 45.1684i | −0.900312 | − | 1.55939i | −0.827090 | − | 0.562070i | \(-0.810005\pi\) |
−0.0732219 | − | 0.997316i | \(-0.523328\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4799 | + | 25.0798i | −0.499305 | + | 0.864822i | ||||
\(842\) | −27.5030 | + | 15.8789i | −0.947816 | + | 0.547222i | ||||
\(843\) | −17.5261 | − | 15.0829i | −0.603631 | − | 0.519483i | ||||
\(844\) | −19.2565 | + | 33.3533i | −0.662838 | + | 1.14807i | ||||
\(845\) | −5.68280 | + | 9.84290i | −0.195494 | + | 0.338606i | ||||
\(846\) | −7.26956 | − | 9.11634i | −0.249932 | − | 0.313426i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −118.554 | + | 68.4472i | −4.07116 | + | 2.35049i | ||||
\(849\) | −6.14148 | + | 2.14889i | −0.210775 | + | 0.0737496i | ||||
\(850\) | 11.5851i | 0.397366i | ||||||||
\(851\) | − | 5.26372i | − | 0.180438i | ||||||
\(852\) | 105.112 | − | 36.7785i | 3.60109 | − | 1.26001i | ||||
\(853\) | 13.4028 | − | 7.73808i | 0.458902 | − | 0.264947i | −0.252681 | − | 0.967550i | \(-0.581312\pi\) |
0.711582 | + | 0.702603i | \(0.247979\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.8074 | − | 21.0772i | −0.574802 | − | 0.720827i | ||||
\(856\) | −44.6804 | + | 77.3886i | −1.52714 | + | 2.64509i | ||||
\(857\) | −24.4356 | + | 42.3238i | −0.834706 | + | 1.44575i | 0.0595642 | + | 0.998224i | \(0.481029\pi\) |
−0.894270 | + | 0.447528i | \(0.852304\pi\) | |||||||
\(858\) | 16.6658 | + | 14.3425i | 0.568960 | + | 0.489646i | ||||
\(859\) | −8.45000 | + | 4.87861i | −0.288310 | + | 0.166456i | −0.637180 | − | 0.770715i | \(-0.719899\pi\) |
0.348869 | + | 0.937171i | \(0.386566\pi\) | |||||||
\(860\) | −0.0421217 | + | 0.0729569i | −0.00143634 | + | 0.00248781i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −36.4356 | − | 63.1083i | −1.24100 | − | 2.14948i | ||||
\(863\) | −23.9462 | − | 13.8253i | −0.815138 | − | 0.470620i | 0.0335987 | − | 0.999435i | \(-0.489303\pi\) |
−0.848737 | + | 0.528815i | \(0.822637\pi\) | |||||||
\(864\) | 53.4774 | − | 85.0997i | 1.81934 | − | 2.89515i | ||||
\(865\) | −10.8312 | − | 18.7602i | −0.368272 | − | 0.637866i | ||||
\(866\) | 76.1256 | 2.58685 | ||||||||
\(867\) | −26.4655 | − | 5.00799i | −0.898817 | − | 0.170080i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.8357 | + | 6.83337i | 0.401500 | + | 0.231806i | ||||
\(870\) | −1.11322 | − | 0.210651i | −0.0377416 | − | 0.00714173i | ||||
\(871\) | 8.41949 | + | 4.86100i | 0.285284 | + | 0.164709i | ||||
\(872\) | 81.5391 | − | 47.0766i | 2.76126 | − | 1.59422i | ||||
\(873\) | 2.61060 | − | 6.65107i | 0.0883554 | − | 0.225104i | ||||
\(874\) | − | 61.5357i | − | 2.08148i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −60.7697 | − | 52.2983i | −2.05322 | − | 1.76700i | ||||
\(877\) | 0.932622 | + | 1.61535i | 0.0314924 | + | 0.0545465i | 0.881342 | − | 0.472479i | \(-0.156641\pi\) |
−0.849850 | + | 0.527025i | \(0.823307\pi\) | |||||||
\(878\) | −25.2633 | −0.852596 | ||||||||
\(879\) | 21.7302 | + | 4.11195i | 0.732942 | + | 0.138692i | ||||
\(880\) | − | 41.3279i | − | 1.39316i | ||||||
\(881\) | −0.0273875 | −0.000922707 | −0.000461353 | − | 1.00000i | \(-0.500147\pi\) | ||||
−0.000461353 | 1.00000i | \(0.500147\pi\) | ||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.2074 | 1.21848 | 0.609239 | − | 0.792987i | \(-0.291475\pi\) | ||||
0.609239 | + | 0.792987i | \(0.291475\pi\) | |||||||
\(884\) | − | 12.1089i | − | 0.407267i | ||||||
\(885\) | −16.6068 | + | 19.2968i | −0.558232 | + | 0.648656i | ||||
\(886\) | 30.7199 | 1.03206 | ||||||||
\(887\) | 12.6626 | + | 21.9323i | 0.425170 | + | 0.736415i | 0.996436 | − | 0.0843491i | \(-0.0268811\pi\) |
−0.571267 | + | 0.820765i | \(0.693548\pi\) | |||||||
\(888\) | −5.03984 | + | 26.6338i | −0.169126 | + | 0.893772i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 25.9616i | − | 0.870235i | ||||||
\(891\) | 15.2233 | − | 16.4047i | 0.510000 | − | 0.549578i | ||||
\(892\) | −112.470 | + | 64.9343i | −3.76576 | + | 2.17416i | ||||
\(893\) | 9.28223 | + | 5.35910i | 0.310618 | + | 0.179335i | ||||
\(894\) | 14.6662 | − | 17.0419i | 0.490511 | − | 0.569966i | ||||
\(895\) | −15.7748 | − | 9.10759i | −0.527294 | − | 0.304433i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.27837 | − | 9.36953i | −0.109462 | − | 0.312840i | ||||
\(898\) | 41.5250 | 1.38571 | ||||||||
\(899\) | 0.351613 | + | 0.609012i | 0.0117270 | + | 0.0203117i | ||||
\(900\) | −8.47787 | − | 56.2594i | −0.282596 | − | 1.87531i | ||||
\(901\) | 10.3290 | + | 5.96345i | 0.344109 | + | 0.198671i | ||||
\(902\) | 22.6348 | + | 39.2046i | 0.753655 | + | 1.30537i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 49.9110 | − | 86.4483i | 1.66001 | − | 2.87523i | ||||
\(905\) | −8.32075 | + | 4.80399i | −0.276591 | + | 0.159690i | ||||
\(906\) | −9.87357 | + | 52.1784i | −0.328027 | + | 1.73351i | ||||
\(907\) | 19.4060 | − | 33.6122i | 0.644366 | − | 1.11608i | −0.340081 | − | 0.940396i | \(-0.610455\pi\) |
0.984447 | − | 0.175679i | \(-0.0562121\pi\) | |||||||
\(908\) | −1.28260 | + | 2.22153i | −0.0425646 | + | 0.0737240i | ||||
\(909\) | 4.23134 | + | 28.0793i | 0.140345 | + | 0.931331i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.6110 | + | 25.1788i | −1.44490 | + | 0.834211i | −0.998171 | − | 0.0604602i | \(-0.980743\pi\) |
−0.446725 | + | 0.894671i | \(0.647410\pi\) | |||||||
\(912\) | −33.2368 | + | 175.645i | −1.10058 | + | 5.81619i | ||||
\(913\) | − | 7.99980i | − | 0.264755i | ||||||
\(914\) | 24.8481i | 0.821901i | ||||||||
\(915\) | 17.7596 | + | 15.2838i | 0.587113 | + | 0.505268i | ||||
\(916\) | −41.6581 | + | 24.0513i | −1.37642 | + | 0.794677i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −16.9312 | − | 0.634343i | −0.558812 | − | 0.0209364i | ||||
\(919\) | 1.49845 | − | 2.59539i | 0.0494293 | − | 0.0856140i | −0.840252 | − | 0.542196i | \(-0.817593\pi\) |
0.889681 | + | 0.456582i | \(0.150926\pi\) | |||||||
\(920\) | −16.5372 | + | 28.6434i | −0.545217 | + | 0.944343i | ||||
\(921\) | 17.5351 | − | 6.13546i | 0.577800 | − | 0.202170i | ||||
\(922\) | −77.5863 | + | 44.7945i | −2.55517 | + | 1.47523i | ||||
\(923\) | −11.3502 | + | 19.6591i | −0.373596 | + | 0.647088i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.07494 | + | 5.32595i | 0.101103 | + | 0.175116i | ||||
\(926\) | −18.3729 | − | 10.6076i | −0.603771 | − | 0.348588i | ||||
\(927\) | 18.9169 | − | 48.1949i | 0.621313 | − | 1.58293i | ||||
\(928\) | 1.94144 | + | 3.36268i | 0.0637310 | + | 0.110385i | ||||
\(929\) | −32.2215 | −1.05715 | −0.528577 | − | 0.848885i | \(-0.677274\pi\) | ||||
−0.528577 | + | 0.848885i | \(0.677274\pi\) | |||||||
\(930\) | 12.8970 | − | 14.9860i | 0.422908 | − | 0.491412i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 51.3888 | + | 29.6694i | 1.68330 | + | 0.971852i | ||||
\(933\) | 10.7742 | + | 30.7924i | 0.352730 | + | 1.00810i | ||||
\(934\) | −48.5064 | − | 28.0052i | −1.58718 | − | 0.916358i | ||||
\(935\) | −3.11828 | + | 1.80034i | −0.101979 | + | 0.0588774i | ||||
\(936\) | 7.61716 | + | 50.5476i | 0.248975 | + | 1.65220i | ||||
\(937\) | − | 3.07038i | − | 0.100305i | −0.998742 | − | 0.0501525i | \(-0.984029\pi\) | ||
0.998742 | − | 0.0501525i | \(-0.0159708\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −42.6212 | + | 14.9130i | −1.39089 | + | 0.486668i | ||||
\(940\) | −4.60640 | − | 7.97852i | −0.150244 | − | 0.260231i | ||||
\(941\) | 38.8272 | 1.26573 | 0.632865 | − | 0.774263i | \(-0.281879\pi\) | ||||
0.632865 | + | 0.774263i | \(0.281879\pi\) | |||||||
\(942\) | 22.8273 | + | 65.2399i | 0.743752 | + | 2.12563i | ||||
\(943\) | − | 20.4373i | − | 0.665532i | ||||||
\(944\) | 168.820 | 5.49464 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.0883763 | 0.00287336 | ||||||||
\(947\) | 18.7513i | 0.609337i | 0.952459 | + | 0.304668i | \(0.0985456\pi\) | ||||
−0.952459 | + | 0.304668i | \(0.901454\pi\) | |||||||
\(948\) | 16.7814 | + | 47.9610i | 0.545034 | + | 1.55770i | ||||
\(949\) | 16.3433 | 0.530527 | ||||||||
\(950\) | 35.9477 | + | 62.2632i | 1.16630 | + | 2.02008i | ||||
\(951\) | 22.7081 | − | 7.94549i | 0.736360 | − | 0.257650i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 47.6453i | − | 1.54338i | −0.635997 | − | 0.771692i | \(-0.719411\pi\) | ||
0.635997 | − | 0.771692i | \(-0.280589\pi\) | |||||||
\(954\) | −74.9528 | − | 29.4196i | −2.42669 | − | 0.952495i | ||||
\(955\) | 16.6859 | − | 9.63362i | 0.539944 | − | 0.311737i | ||||
\(956\) | −64.2911 | − | 37.1185i | −2.07932 | − | 1.20050i | ||||
\(957\) | 0.285546 | + | 0.816086i | 0.00923039 | + | 0.0263803i | ||||
\(958\) | −6.24009 | − | 3.60272i | −0.201608 | − | 0.116398i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 33.6562 | − | 39.1080i | 1.08625 | − | 1.26220i | ||||
\(961\) | 18.7280 | 0.604129 | ||||||||
\(962\) | −4.41821 | − | 7.65257i | −0.142449 | − | 0.246729i | ||||
\(963\) | −29.3194 | + | 4.41822i | −0.944806 | + | 0.142375i | ||||
\(964\) | −57.2104 | − | 33.0304i | −1.84262 | − | 1.06384i | ||||
\(965\) | 8.24569 | + | 14.2819i | 0.265438 | + | 0.459752i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.8005 | − | 44.6878i | 0.829689 | − | 1.43706i | −0.0685936 | − | 0.997645i | \(-0.521851\pi\) |
0.898282 | − | 0.439419i | \(-0.144815\pi\) | |||||||
\(968\) | 37.7137 | − | 21.7740i | 1.21216 | − | 0.699843i | ||||
\(969\) | 14.7007 | − | 5.14372i | 0.472254 | − | 0.165240i | ||||
\(970\) | 3.88040 | − | 6.72104i | 0.124592 | − | 0.215800i | ||||
\(971\) | 14.1933 | − | 24.5836i | 0.455485 | − | 0.788924i | −0.543231 | − | 0.839584i | \(-0.682799\pi\) |
0.998716 | + | 0.0506597i | \(0.0161324\pi\) | |||||||
\(972\) | 82.6849 | − | 9.30958i | 2.65212 | − | 0.298605i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.44867 | − | 1.41374i | 0.0784603 | − | 0.0452991i | ||||
\(975\) | 8.79058 | + | 7.56516i | 0.281524 | + | 0.242279i | ||||
\(976\) | − | 155.372i | − | 4.97332i | ||||||
\(977\) | − | 41.1908i | − | 1.31781i | −0.752227 | − | 0.658904i | \(-0.771020\pi\) | ||
0.752227 | − | 0.658904i | \(-0.228980\pi\) | |||||||
\(978\) | −15.8400 | + | 83.7087i | −0.506506 | + | 2.67671i | ||||
\(979\) | −17.1576 | + | 9.90597i | −0.548361 | + | 0.316596i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.0808 | + | 11.4144i | 0.928477 | + | 0.364435i | ||||
\(982\) | 56.3668 | − | 97.6302i | 1.79874 | − | 3.11550i | ||||
\(983\) | 26.4017 | − | 45.7291i | 0.842085 | − | 1.45853i | −0.0460447 | − | 0.998939i | \(-0.514662\pi\) |
0.888129 | − | 0.459594i | \(-0.152005\pi\) | |||||||
\(984\) | −19.5681 | + | 103.411i | −0.623807 | + | 3.29661i | ||||
\(985\) | −19.7153 | + | 11.3826i | −0.628181 | + | 0.362680i | ||||
\(986\) | 0.327278 | − | 0.566862i | 0.0104227 | − | 0.0180526i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −37.5731 | − | 65.0784i | −1.19536 | − | 2.07042i | ||||
\(989\) | −0.0345529 | − | 0.0199491i | −0.00109872 | − | 0.000634346i | ||||
\(990\) | 19.0057 | − | 15.1555i | 0.604041 | − | 0.481675i | ||||
\(991\) | −8.24486 | − | 14.2805i | −0.261907 | − | 0.453636i | 0.704842 | − | 0.709364i | \(-0.251018\pi\) |
−0.966749 | + | 0.255729i | \(0.917685\pi\) | |||||||
\(992\) | −67.7603 | −2.15139 | ||||||||
\(993\) | −2.56534 | − | 7.33171i | −0.0814087 | − | 0.232665i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.8696 | + | 14.9358i | 0.820122 | + | 0.473498i | ||||
\(996\) | 19.4012 | − | 22.5439i | 0.614750 | − | 0.714329i | ||||
\(997\) | −42.4857 | − | 24.5291i | −1.34553 | − | 0.776845i | −0.357921 | − | 0.933752i | \(-0.616514\pi\) |
−0.987613 | + | 0.156907i | \(0.949848\pi\) | |||||||
\(998\) | 75.7484 | − | 43.7333i | 2.39777 | − | 1.38435i | ||||
\(999\) | −7.95203 | + | 4.20227i | −0.251591 | + | 0.132954i |
(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 | 441.2.i.d.68.1 | 48 | ||
3.2 | odd | 2 | 1323.2.i.d.1097.21 | 48 | |||
7.2 | even | 3 | 441.2.o.e.293.2 | yes | 48 | ||
7.3 | odd | 6 | 441.2.s.d.374.24 | 48 | |||
7.4 | even | 3 | 441.2.s.d.374.23 | 48 | |||
7.5 | odd | 6 | 441.2.o.e.293.1 | yes | 48 | ||
7.6 | odd | 2 | inner | 441.2.i.d.68.2 | 48 | ||
9.2 | odd | 6 | 441.2.s.d.362.24 | 48 | |||
9.7 | even | 3 | 1323.2.s.d.656.1 | 48 | |||
21.2 | odd | 6 | 1323.2.o.e.881.24 | 48 | |||
21.5 | even | 6 | 1323.2.o.e.881.23 | 48 | |||
21.11 | odd | 6 | 1323.2.s.d.962.2 | 48 | |||
21.17 | even | 6 | 1323.2.s.d.962.1 | 48 | |||
21.20 | even | 2 | 1323.2.i.d.1097.6 | 48 | |||
63.2 | odd | 6 | 441.2.o.e.146.1 | ✓ | 48 | ||
63.11 | odd | 6 | inner | 441.2.i.d.227.24 | 48 | ||
63.16 | even | 3 | 1323.2.o.e.440.23 | 48 | |||
63.20 | even | 6 | 441.2.s.d.362.23 | 48 | |||
63.25 | even | 3 | 1323.2.i.d.521.6 | 48 | |||
63.34 | odd | 6 | 1323.2.s.d.656.2 | 48 | |||
63.38 | even | 6 | inner | 441.2.i.d.227.23 | 48 | ||
63.47 | even | 6 | 441.2.o.e.146.2 | yes | 48 | ||
63.52 | odd | 6 | 1323.2.i.d.521.21 | 48 | |||
63.61 | odd | 6 | 1323.2.o.e.440.24 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.1 | 48 | 1.1 | even | 1 | trivial | ||
441.2.i.d.68.2 | 48 | 7.6 | odd | 2 | inner | ||
441.2.i.d.227.23 | 48 | 63.38 | even | 6 | inner | ||
441.2.i.d.227.24 | 48 | 63.11 | odd | 6 | inner | ||
441.2.o.e.146.1 | ✓ | 48 | 63.2 | odd | 6 | ||
441.2.o.e.146.2 | yes | 48 | 63.47 | even | 6 | ||
441.2.o.e.293.1 | yes | 48 | 7.5 | odd | 6 | ||
441.2.o.e.293.2 | yes | 48 | 7.2 | even | 3 | ||
441.2.s.d.362.23 | 48 | 63.20 | even | 6 | |||
441.2.s.d.362.24 | 48 | 9.2 | odd | 6 | |||
441.2.s.d.374.23 | 48 | 7.4 | even | 3 | |||
441.2.s.d.374.24 | 48 | 7.3 | odd | 6 | |||
1323.2.i.d.521.6 | 48 | 63.25 | even | 3 | |||
1323.2.i.d.521.21 | 48 | 63.52 | odd | 6 | |||
1323.2.i.d.1097.6 | 48 | 21.20 | even | 2 | |||
1323.2.i.d.1097.21 | 48 | 3.2 | odd | 2 | |||
1323.2.o.e.440.23 | 48 | 63.16 | even | 3 | |||
1323.2.o.e.440.24 | 48 | 63.61 | odd | 6 | |||
1323.2.o.e.881.23 | 48 | 21.5 | even | 6 | |||
1323.2.o.e.881.24 | 48 | 21.2 | odd | 6 | |||
1323.2.s.d.656.1 | 48 | 9.7 | even | 3 | |||
1323.2.s.d.656.2 | 48 | 63.34 | odd | 6 | |||
1323.2.s.d.962.1 | 48 | 21.17 | even | 6 | |||
1323.2.s.d.962.2 | 48 | 21.11 | odd | 6 |