Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(362,441)]
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([1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.362");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.s (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 | 374.4 | ||
Character | \(\chi\) | \(=\) | 441.374 |
Dual form | 441.2.s.d.362.4 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.80506 | − | 1.04215i | −1.27637 | − | 0.736913i | −0.300191 | − | 0.953879i | \(-0.597050\pi\) |
−0.976179 | + | 0.216966i | \(0.930384\pi\) | |||||||
\(3\) | 1.73189 | − | 0.0239080i | 0.999905 | − | 0.0138033i | ||||
\(4\) | 1.17216 | + | 2.03024i | 0.586081 | + | 1.01512i | ||||
\(5\) | −3.30465 | −1.47788 | −0.738942 | − | 0.673769i | \(-0.764674\pi\) | ||||
−0.738942 | + | 0.673769i | \(0.764674\pi\) | |||||||
\(6\) | −3.15107 | − | 1.76173i | −1.28642 | − | 0.719224i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 0.717672i | − | 0.253735i | ||||||
\(9\) | 2.99886 | − | 0.0828118i | 0.999619 | − | 0.0276039i | ||||
\(10\) | 5.96509 | + | 3.44395i | 1.88633 | + | 1.08907i | ||||
\(11\) | 2.66137i | 0.802434i | 0.915983 | + | 0.401217i | \(0.131413\pi\) | ||||
−0.915983 | + | 0.401217i | \(0.868587\pi\) | |||||||
\(12\) | 2.07859 | + | 3.48812i | 0.600037 | + | 1.00693i | ||||
\(13\) | 2.11249 | + | 1.21964i | 0.585899 | + | 0.338269i | 0.763474 | − | 0.645839i | \(-0.223492\pi\) |
−0.177576 | + | 0.984107i | \(0.556825\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.72328 | + | 0.0790075i | −1.47774 | + | 0.0203997i | ||||
\(16\) | 1.59640 | − | 2.76504i | 0.399100 | − | 0.691261i | ||||
\(17\) | 3.59017 | − | 6.21836i | 0.870744 | − | 1.50817i | 0.00951656 | − | 0.999955i | \(-0.496971\pi\) |
0.861228 | − | 0.508219i | \(-0.169696\pi\) | |||||||
\(18\) | −5.49942 | − | 2.97578i | −1.29623 | − | 0.701399i | ||||
\(19\) | 4.24746 | − | 2.45227i | 0.974433 | − | 0.562589i | 0.0738485 | − | 0.997269i | \(-0.476472\pi\) |
0.900585 | + | 0.434680i | \(0.143139\pi\) | |||||||
\(20\) | −3.87358 | − | 6.70924i | −0.866160 | − | 1.50023i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.77356 | − | 4.80394i | 0.591324 | − | 1.02420i | ||||
\(23\) | 4.99031i | 1.04055i | 0.853998 | + | 0.520276i | \(0.174171\pi\) | ||||
−0.853998 | + | 0.520276i | \(0.825829\pi\) | |||||||
\(24\) | −0.0171581 | − | 1.24293i | −0.00350238 | − | 0.253711i | ||||
\(25\) | 5.92072 | 1.18414 | ||||||||
\(26\) | −2.54211 | − | 4.40306i | −0.498549 | − | 0.863512i | ||||
\(27\) | 5.19170 | − | 0.215117i | 0.999143 | − | 0.0413993i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.50701 | − | 3.17947i | 1.02263 | − | 0.590413i | 0.107762 | − | 0.994177i | \(-0.465632\pi\) |
0.914863 | + | 0.403764i | \(0.132298\pi\) | |||||||
\(30\) | 10.4132 | + | 5.82191i | 1.90118 | + | 1.06293i | ||||
\(31\) | −2.30833 | + | 1.33271i | −0.414588 | + | 0.239362i | −0.692759 | − | 0.721169i | \(-0.743605\pi\) |
0.278171 | + | 0.960531i | \(0.410272\pi\) | |||||||
\(32\) | −7.00624 | + | 4.04505i | −1.23854 | + | 0.715071i | ||||
\(33\) | 0.0636281 | + | 4.60920i | 0.0110762 | + | 0.802358i | ||||
\(34\) | −12.9609 | + | 7.48301i | −2.22278 | + | 1.28333i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.68327 | + | 5.99134i | 0.613879 | + | 0.998556i | ||||
\(37\) | 0.844787 | + | 1.46321i | 0.138882 | + | 0.240551i | 0.927074 | − | 0.374879i | \(-0.122316\pi\) |
−0.788192 | + | 0.615430i | \(0.788982\pi\) | |||||||
\(38\) | −10.2226 | −1.65832 | ||||||||
\(39\) | 3.68775 | + | 2.06178i | 0.590512 | + | 0.330149i | ||||
\(40\) | 2.37166i | 0.374992i | ||||||||
\(41\) | 0.553137 | − | 0.958062i | 0.0863855 | − | 0.149624i | −0.819595 | − | 0.572943i | \(-0.805802\pi\) |
0.905981 | + | 0.423319i | \(0.139135\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.93481 | + | 5.08323i | 0.447554 | + | 0.775186i | 0.998226 | − | 0.0595356i | \(-0.0189620\pi\) |
−0.550672 | + | 0.834721i | \(0.685629\pi\) | |||||||
\(44\) | −5.40324 | + | 3.11956i | −0.814568 | + | 0.470291i | ||||
\(45\) | −9.91018 | + | 0.273664i | −1.47732 | + | 0.0407954i | ||||
\(46\) | 5.20066 | − | 9.00781i | 0.766796 | − | 1.32813i | ||||
\(47\) | 2.44098 | − | 4.22790i | 0.356053 | − | 0.616703i | −0.631244 | − | 0.775584i | \(-0.717455\pi\) |
0.987298 | + | 0.158881i | \(0.0507888\pi\) | |||||||
\(48\) | 2.69867 | − | 4.82691i | 0.389520 | − | 0.696704i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −10.6873 | − | 6.17029i | −1.51141 | − | 0.872610i | ||||
\(51\) | 6.06910 | − | 10.8553i | 0.849844 | − | 1.52005i | ||||
\(52\) | 5.71848i | 0.793011i | ||||||||
\(53\) | 8.94013 | + | 5.16159i | 1.22802 | + | 0.708999i | 0.966616 | − | 0.256230i | \(-0.0824806\pi\) |
0.261406 | + | 0.965229i | \(0.415814\pi\) | |||||||
\(54\) | −9.59551 | − | 5.02224i | −1.30578 | − | 0.683440i | ||||
\(55\) | − | 8.79491i | − | 1.18591i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.29748 | − | 4.34860i | 0.966575 | − | 0.575986i | ||||
\(58\) | −13.2540 | −1.74033 | ||||||||
\(59\) | −2.56820 | − | 4.44826i | −0.334351 | − | 0.579114i | 0.649009 | − | 0.760781i | \(-0.275184\pi\) |
−0.983360 | + | 0.181667i | \(0.941851\pi\) | |||||||
\(60\) | −6.86901 | − | 11.5270i | −0.886785 | − | 1.48813i | ||||
\(61\) | −4.44613 | − | 2.56698i | −0.569269 | − | 0.328668i | 0.187588 | − | 0.982248i | \(-0.439933\pi\) |
−0.756857 | + | 0.653580i | \(0.773266\pi\) | |||||||
\(62\) | 5.55556 | 0.705556 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 10.4766 | 1.30958 | ||||||||
\(65\) | −6.98103 | − | 4.03050i | −0.865891 | − | 0.499922i | ||||
\(66\) | 4.68863 | − | 8.38619i | 0.577130 | − | 1.03227i | ||||
\(67\) | −4.16544 | − | 7.21476i | −0.508890 | − | 0.881423i | −0.999947 | − | 0.0102956i | \(-0.996723\pi\) |
0.491057 | − | 0.871127i | \(-0.336611\pi\) | |||||||
\(68\) | 16.8330 | 2.04131 | ||||||||
\(69\) | 0.119308 | + | 8.64265i | 0.0143630 | + | 1.04045i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.07026i | 0.245695i | 0.992426 | + | 0.122848i | \(0.0392026\pi\) | ||||
−0.992426 | + | 0.122848i | \(0.960797\pi\) | |||||||
\(72\) | −0.0594317 | − | 2.15220i | −0.00700410 | − | 0.253639i | ||||
\(73\) | 6.94112 | + | 4.00746i | 0.812396 | + | 0.469037i | 0.847787 | − | 0.530336i | \(-0.177934\pi\) |
−0.0353910 | + | 0.999374i | \(0.511268\pi\) | |||||||
\(74\) | − | 3.52159i | − | 0.409376i | ||||||
\(75\) | 10.2540 | − | 0.141552i | 1.18403 | − | 0.0163451i | ||||
\(76\) | 9.95741 | + | 5.74891i | 1.14219 | + | 0.659445i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.50791 | − | 7.56483i | −0.510421 | − | 0.856548i | ||||
\(79\) | −2.50501 | + | 4.33881i | −0.281836 | + | 0.488155i | −0.971837 | − | 0.235654i | \(-0.924277\pi\) |
0.690001 | + | 0.723809i | \(0.257610\pi\) | |||||||
\(80\) | −5.27554 | + | 9.13750i | −0.589823 | + | 1.02160i | ||||
\(81\) | 8.98628 | − | 0.496681i | 0.998476 | − | 0.0551868i | ||||
\(82\) | −1.99689 | + | 1.15291i | −0.220520 | + | 0.127317i | ||||
\(83\) | 1.04482 | + | 1.80968i | 0.114684 | + | 0.198638i | 0.917653 | − | 0.397382i | \(-0.130081\pi\) |
−0.802970 | + | 0.596020i | \(0.796748\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.8643 | + | 20.5495i | −1.28686 | + | 2.22891i | ||||
\(86\) | − | 12.2341i | − | 1.31923i | ||||||
\(87\) | 9.46149 | − | 5.63814i | 1.01438 | − | 0.604472i | ||||
\(88\) | 1.90999 | 0.203606 | ||||||||
\(89\) | −0.541267 | − | 0.937501i | −0.0573741 | − | 0.0993749i | 0.835912 | − | 0.548864i | \(-0.184939\pi\) |
−0.893286 | + | 0.449489i | \(0.851606\pi\) | |||||||
\(90\) | 18.1737 | + | 9.83393i | 1.91567 | + | 1.03659i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −10.1315 | + | 5.84945i | −1.05629 | + | 0.609847i | ||||
\(93\) | −3.96589 | + | 2.36329i | −0.411244 | + | 0.245062i | ||||
\(94\) | −8.81223 | + | 5.08774i | −0.908912 | + | 0.524761i | ||||
\(95\) | −14.0364 | + | 8.10390i | −1.44010 | + | 0.831442i | ||||
\(96\) | −12.0373 | + | 7.17307i | −1.22855 | + | 0.732099i | ||||
\(97\) | −9.47203 | + | 5.46868i | −0.961739 | + | 0.555260i | −0.896708 | − | 0.442623i | \(-0.854048\pi\) |
−0.0650310 | + | 0.997883i | \(0.520715\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.220393 | + | 7.98108i | 0.0221503 | + | 0.802129i | ||||
\(100\) | 6.94004 | + | 12.0205i | 0.694004 | + | 1.20205i | ||||
\(101\) | 0.527915 | 0.0525295 | 0.0262647 | − | 0.999655i | \(-0.491639\pi\) | ||||
0.0262647 | + | 0.999655i | \(0.491639\pi\) | |||||||
\(102\) | −22.2680 | + | 13.2696i | −2.20486 | + | 1.31388i | ||||
\(103\) | − | 0.783733i | − | 0.0772235i | −0.999254 | − | 0.0386118i | \(-0.987706\pi\) | ||
0.999254 | − | 0.0386118i | \(-0.0122936\pi\) | |||||||
\(104\) | 0.875305 | − | 1.51607i | 0.0858308 | − | 0.148663i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.7583 | − | 18.6340i | −1.04494 | − | 1.80989i | ||||
\(107\) | 4.63398 | − | 2.67543i | 0.447984 | − | 0.258644i | −0.258994 | − | 0.965879i | \(-0.583391\pi\) |
0.706978 | + | 0.707235i | \(0.250058\pi\) | |||||||
\(108\) | 6.52225 | + | 10.2883i | 0.627603 | + | 0.989988i | ||||
\(109\) | −2.98261 | + | 5.16603i | −0.285682 | + | 0.494816i | −0.972774 | − | 0.231754i | \(-0.925553\pi\) |
0.687092 | + | 0.726570i | \(0.258887\pi\) | |||||||
\(110\) | −9.16563 | + | 15.8753i | −0.873909 | + | 1.51365i | ||||
\(111\) | 1.49806 | + | 2.51392i | 0.142189 | + | 0.238611i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0024 | + | 5.77487i | 0.940944 | + | 0.543254i | 0.890256 | − | 0.455461i | \(-0.150525\pi\) |
0.0506876 | + | 0.998715i | \(0.483859\pi\) | |||||||
\(114\) | −17.7043 | + | 0.244401i | −1.65816 | + | 0.0228902i | ||||
\(115\) | − | 16.4912i | − | 1.53782i | ||||||
\(116\) | 12.9102 | + | 7.45371i | 1.19868 | + | 0.692059i | ||||
\(117\) | 6.43605 | + | 3.48260i | 0.595013 | + | 0.321967i | ||||
\(118\) | 10.7058i | 0.985551i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.0567015 | + | 4.10744i | 0.00517612 | + | 0.374956i | ||||
\(121\) | 3.91709 | 0.356099 | ||||||||
\(122\) | 5.35036 | + | 9.26709i | 0.484399 | + | 0.839003i | ||||
\(123\) | 0.935065 | − | 1.67248i | 0.0843120 | − | 0.150802i | ||||
\(124\) | −5.41146 | − | 3.12431i | −0.485963 | − | 0.280571i | ||||
\(125\) | −3.04265 | −0.272143 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.0954 | −1.69444 | −0.847221 | − | 0.531241i | \(-0.821726\pi\) | ||||
−0.847221 | + | 0.531241i | \(0.821726\pi\) | |||||||
\(128\) | −4.89849 | − | 2.82815i | −0.432970 | − | 0.249975i | ||||
\(129\) | 5.20428 | + | 8.73341i | 0.458211 | + | 0.768934i | ||||
\(130\) | 8.40079 | + | 14.5506i | 0.736798 | + | 1.27617i | ||||
\(131\) | −4.15126 | −0.362697 | −0.181349 | − | 0.983419i | \(-0.558046\pi\) | ||||
−0.181349 | + | 0.983419i | \(0.558046\pi\) | |||||||
\(132\) | −9.28320 | + | 5.53190i | −0.807999 | + | 0.481490i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 17.3641i | 1.50003i | ||||||||
\(135\) | −17.1567 | + | 0.710887i | −1.47662 | + | 0.0611834i | ||||
\(136\) | −4.46274 | − | 2.57657i | −0.382677 | − | 0.220939i | ||||
\(137\) | − | 6.29419i | − | 0.537749i | −0.963175 | − | 0.268874i | \(-0.913348\pi\) | ||
0.963175 | − | 0.268874i | \(-0.0866516\pi\) | |||||||
\(138\) | 8.79160 | − | 15.7248i | 0.748390 | − | 1.33859i | ||||
\(139\) | 1.32575 | + | 0.765423i | 0.112449 | + | 0.0649223i | 0.555170 | − | 0.831737i | \(-0.312653\pi\) |
−0.442721 | + | 0.896660i | \(0.645987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.12642 | − | 7.38060i | 0.347507 | − | 0.621559i | ||||
\(142\) | 2.15753 | − | 3.73695i | 0.181056 | − | 0.313598i | ||||
\(143\) | −3.24593 | + | 5.62212i | −0.271438 | + | 0.470145i | ||||
\(144\) | 4.55839 | − | 8.42417i | 0.379866 | − | 0.702014i | ||||
\(145\) | −18.1987 | + | 10.5070i | −1.51132 | + | 0.872563i | ||||
\(146\) | −8.35276 | − | 14.4674i | −0.691279 | − | 1.19733i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.98045 | + | 3.43025i | −0.162792 | + | 0.281965i | ||||
\(149\) | 5.34815i | 0.438137i | 0.975709 | + | 0.219069i | \(0.0703019\pi\) | ||||
−0.975709 | + | 0.219069i | \(0.929698\pi\) | |||||||
\(150\) | −18.6566 | − | 10.4307i | −1.52331 | − | 0.851665i | ||||
\(151\) | 11.4877 | 0.934854 | 0.467427 | − | 0.884032i | \(-0.345181\pi\) | ||||
0.467427 | + | 0.884032i | \(0.345181\pi\) | |||||||
\(152\) | −1.75993 | − | 3.04828i | −0.142749 | − | 0.247248i | ||||
\(153\) | 10.2515 | − | 18.9453i | 0.828781 | − | 1.53163i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.62821 | − | 4.40415i | 0.612713 | − | 0.353750i | ||||
\(156\) | 0.136717 | + | 9.90376i | 0.0109461 | + | 0.792935i | ||||
\(157\) | −5.77243 | + | 3.33271i | −0.460690 | + | 0.265979i | −0.712334 | − | 0.701840i | \(-0.752362\pi\) |
0.251644 | + | 0.967820i | \(0.419029\pi\) | |||||||
\(158\) | 9.04340 | − | 5.22121i | 0.719454 | − | 0.415377i | ||||
\(159\) | 15.6067 | + | 8.72554i | 1.23769 | + | 0.691980i | ||||
\(160\) | 23.1532 | − | 13.3675i | 1.83042 | − | 1.05679i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −16.7384 | − | 8.46853i | −1.31509 | − | 0.665351i | ||||
\(163\) | 11.5460 | + | 19.9983i | 0.904356 | + | 1.56639i | 0.821779 | + | 0.569807i | \(0.192982\pi\) |
0.0825775 | + | 0.996585i | \(0.473685\pi\) | |||||||
\(164\) | 2.59346 | 0.202516 | ||||||||
\(165\) | −0.210269 | − | 15.2318i | −0.0163694 | − | 1.18579i | ||||
\(166\) | − | 4.35543i | − | 0.338047i | ||||||
\(167\) | −7.95418 | + | 13.7770i | −0.615513 | + | 1.06610i | 0.374782 | + | 0.927113i | \(0.377718\pi\) |
−0.990294 | + | 0.138986i | \(0.955616\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.52493 | − | 6.10536i | −0.271149 | − | 0.469643i | ||||
\(170\) | 42.8314 | − | 24.7287i | 3.28502 | − | 1.89661i | ||||
\(171\) | 12.5344 | − | 7.70575i | 0.958532 | − | 0.589273i | ||||
\(172\) | −6.88013 | + | 11.9167i | −0.524605 | + | 0.908643i | ||||
\(173\) | −9.33097 | + | 16.1617i | −0.709421 | + | 1.22875i | 0.255651 | + | 0.966769i | \(0.417710\pi\) |
−0.965072 | + | 0.261984i | \(0.915623\pi\) | |||||||
\(174\) | −22.9544 | + | 0.316876i | −1.74017 | + | 0.0240223i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.35882 | + | 4.24861i | 0.554692 | + | 0.320251i | ||||
\(177\) | −4.55418 | − | 7.64247i | −0.342313 | − | 0.574443i | ||||
\(178\) | 2.25633i | 0.169119i | ||||||||
\(179\) | −19.0792 | − | 11.0154i | −1.42604 | − | 0.823326i | −0.429237 | − | 0.903192i | \(-0.641218\pi\) |
−0.996806 | + | 0.0798653i | \(0.974551\pi\) | |||||||
\(180\) | −12.1719 | − | 19.7993i | −0.907242 | − | 1.47575i | ||||
\(181\) | − | 17.6986i | − | 1.31552i | −0.753226 | − | 0.657762i | \(-0.771503\pi\) | ||
0.753226 | − | 0.657762i | \(-0.228497\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.76157 | − | 4.33941i | −0.573751 | − | 0.320779i | ||||
\(184\) | 3.58141 | 0.264025 | ||||||||
\(185\) | −2.79173 | − | 4.83541i | −0.205252 | − | 0.355507i | ||||
\(186\) | 9.62159 | − | 0.132822i | 0.705489 | − | 0.00973899i | ||||
\(187\) | 16.5494 | + | 9.55479i | 1.21021 | + | 0.698715i | ||||
\(188\) | 11.4449 | 0.834704 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 33.7820 | 2.45080 | ||||||||
\(191\) | −13.2711 | − | 7.66209i | −0.960265 | − | 0.554409i | −0.0640104 | − | 0.997949i | \(-0.520389\pi\) |
−0.896255 | + | 0.443540i | \(0.853722\pi\) | |||||||
\(192\) | 18.1443 | − | 0.250475i | 1.30946 | − | 0.0180765i | ||||
\(193\) | −12.9333 | − | 22.4012i | −0.930962 | − | 1.61247i | −0.781681 | − | 0.623678i | \(-0.785638\pi\) |
−0.149280 | − | 0.988795i | \(-0.547696\pi\) | |||||||
\(194\) | 22.7968 | 1.63671 | ||||||||
\(195\) | −12.1867 | − | 6.81347i | −0.872709 | − | 0.487922i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.18301i | − | 0.298027i | −0.988835 | − | 0.149014i | \(-0.952390\pi\) | ||
0.988835 | − | 0.149014i | \(-0.0476098\pi\) | |||||||
\(198\) | 7.91967 | − | 14.6360i | 0.562827 | − | 1.04014i | ||||
\(199\) | −19.0592 | − | 11.0038i | −1.35107 | − | 0.780041i | −0.362671 | − | 0.931917i | \(-0.618135\pi\) |
−0.988399 | + | 0.151876i | \(0.951468\pi\) | |||||||
\(200\) | − | 4.24914i | − | 0.300459i | ||||||
\(201\) | −7.38656 | − | 12.3955i | −0.521008 | − | 0.874315i | ||||
\(202\) | −0.952918 | − | 0.550168i | −0.0670471 | − | 0.0387097i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 29.1529 | − | 0.402444i | 2.04111 | − | 0.0281767i | ||||
\(205\) | −1.82793 | + | 3.16606i | −0.127668 | + | 0.221127i | ||||
\(206\) | −0.816769 | + | 1.41469i | −0.0569070 | + | 0.0985658i | ||||
\(207\) | 0.413257 | + | 14.9652i | 0.0287233 | + | 1.04016i | ||||
\(208\) | 6.74474 | − | 3.89408i | 0.467664 | − | 0.270006i | ||||
\(209\) | 6.52641 | + | 11.3041i | 0.451441 | + | 0.781919i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.2926 | − | 21.2914i | 0.846257 | − | 1.46576i | −0.0382677 | − | 0.999268i | \(-0.512184\pi\) |
0.884525 | − | 0.466493i | \(-0.154483\pi\) | |||||||
\(212\) | 24.2009i | 1.66212i | ||||||||
\(213\) | 0.0494958 | + | 3.58546i | 0.00339140 | + | 0.245672i | ||||
\(214\) | −11.1528 | −0.762392 | ||||||||
\(215\) | −9.69851 | − | 16.7983i | −0.661433 | − | 1.14564i | ||||
\(216\) | −0.154384 | − | 3.72594i | −0.0105045 | − | 0.253518i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.7676 | − | 6.21666i | 0.729272 | − | 0.421045i | ||||
\(219\) | 12.1170 | + | 6.77451i | 0.818793 | + | 0.457779i | ||||
\(220\) | 17.8558 | − | 10.3091i | 1.20384 | − | 0.695036i | ||||
\(221\) | 15.1684 | − | 8.75747i | 1.02034 | − | 0.589091i | ||||
\(222\) | −0.0841940 | − | 6.09899i | −0.00565073 | − | 0.409337i | ||||
\(223\) | −7.31908 | + | 4.22567i | −0.490122 | + | 0.282972i | −0.724625 | − | 0.689143i | \(-0.757987\pi\) |
0.234503 | + | 0.972115i | \(0.424654\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 17.7554 | − | 0.490305i | 1.18369 | − | 0.0326870i | ||||
\(226\) | −12.0366 | − | 20.8480i | −0.800662 | − | 1.38679i | ||||
\(227\) | 5.82949 | 0.386917 | 0.193458 | − | 0.981108i | \(-0.438030\pi\) | ||||
0.193458 | + | 0.981108i | \(0.438030\pi\) | |||||||
\(228\) | 17.3825 | + | 9.71840i | 1.15119 | + | 0.643617i | ||||
\(229\) | − | 4.79826i | − | 0.317078i | −0.987353 | − | 0.158539i | \(-0.949322\pi\) | ||
0.987353 | − | 0.158539i | \(-0.0506783\pi\) | |||||||
\(230\) | −17.1864 | + | 29.7677i | −1.13324 | + | 1.96282i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.28182 | − | 3.95223i | −0.149809 | − | 0.259476i | ||||
\(233\) | −19.9587 | + | 11.5232i | −1.30754 | + | 0.754907i | −0.981685 | − | 0.190513i | \(-0.938985\pi\) |
−0.325853 | + | 0.945420i | \(0.605652\pi\) | |||||||
\(234\) | −7.98805 | − | 12.9936i | −0.522195 | − | 0.849421i | ||||
\(235\) | −8.06659 | + | 13.9717i | −0.526206 | + | 0.911416i | ||||
\(236\) | 6.02069 | − | 10.4281i | 0.391914 | − | 0.678815i | ||||
\(237\) | −4.23467 | + | 7.57422i | −0.275071 | + | 0.491998i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.91972 | + | 3.41775i | 0.382915 | + | 0.221076i | 0.679086 | − | 0.734059i | \(-0.262376\pi\) |
−0.296171 | + | 0.955135i | \(0.595710\pi\) | |||||||
\(240\) | −8.91818 | + | 15.9512i | −0.575666 | + | 1.02965i | ||||
\(241\) | − | 4.49308i | − | 0.289424i | −0.989474 | − | 0.144712i | \(-0.953774\pi\) | ||
0.989474 | − | 0.144712i | \(-0.0462256\pi\) | |||||||
\(242\) | −7.07058 | − | 4.08220i | −0.454514 | − | 0.262414i | ||||
\(243\) | 15.5513 | − | 1.07504i | 0.997619 | − | 0.0689638i | ||||
\(244\) | − | 12.0356i | − | 0.770503i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.43083 | + | 2.04444i | −0.218741 | + | 0.130349i | ||||
\(247\) | 11.9636 | 0.761225 | ||||||||
\(248\) | 0.956451 | + | 1.65662i | 0.0607347 | + | 0.105196i | ||||
\(249\) | 1.85277 | + | 3.10917i | 0.117415 | + | 0.197036i | ||||
\(250\) | 5.49217 | + | 3.17091i | 0.347355 | + | 0.200546i | ||||
\(251\) | −0.467438 | −0.0295044 | −0.0147522 | − | 0.999891i | \(-0.504696\pi\) | ||||
−0.0147522 | + | 0.999891i | \(0.504696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.2811 | −0.834975 | ||||||||
\(254\) | 34.4683 | + | 19.9003i | 2.16273 | + | 1.24866i | ||||
\(255\) | −20.0563 | + | 35.8731i | −1.25597 | + | 2.24646i | ||||
\(256\) | −4.58192 | − | 7.93613i | −0.286370 | − | 0.496008i | ||||
\(257\) | 21.4865 | 1.34029 | 0.670146 | − | 0.742229i | \(-0.266231\pi\) | ||||
0.670146 | + | 0.742229i | \(0.266231\pi\) | |||||||
\(258\) | −0.292492 | − | 21.1880i | −0.0182097 | − | 1.31911i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 18.8976i | − | 1.17198i | ||||||
\(261\) | 16.2514 | − | 9.99083i | 1.00594 | − | 0.618417i | ||||
\(262\) | 7.49327 | + | 4.32624i | 0.462936 | + | 0.267276i | ||||
\(263\) | 11.0897i | 0.683819i | 0.939733 | + | 0.341909i | \(0.111074\pi\) | ||||
−0.939733 | + | 0.341909i | \(0.888926\pi\) | |||||||
\(264\) | 3.30789 | − | 0.0456641i | 0.203587 | − | 0.00281043i | ||||
\(265\) | −29.5440 | − | 17.0572i | −1.81487 | − | 1.04782i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.959826 | − | 1.61070i | −0.0587404 | − | 0.0985735i | ||||
\(268\) | 9.76514 | − | 16.9137i | 0.596501 | − | 1.03317i | ||||
\(269\) | 11.0288 | − | 19.1024i | 0.672435 | − | 1.16469i | −0.304776 | − | 0.952424i | \(-0.598582\pi\) |
0.977212 | − | 0.212268i | \(-0.0680850\pi\) | |||||||
\(270\) | 31.7098 | + | 16.5967i | 1.92980 | + | 1.01005i | ||||
\(271\) | 4.10874 | − | 2.37218i | 0.249588 | − | 0.144100i | −0.369988 | − | 0.929037i | \(-0.620638\pi\) |
0.619576 | + | 0.784937i | \(0.287305\pi\) | |||||||
\(272\) | −11.4627 | − | 19.8540i | −0.695028 | − | 1.20382i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.55950 | + | 11.3614i | −0.396274 | + | 0.686366i | ||||
\(275\) | 15.7572i | 0.950198i | ||||||||
\(276\) | −17.4068 | + | 10.3728i | −1.04777 | + | 0.624370i | ||||
\(277\) | −6.42658 | −0.386136 | −0.193068 | − | 0.981185i | \(-0.561844\pi\) | ||||
−0.193068 | + | 0.981185i | \(0.561844\pi\) | |||||||
\(278\) | −1.59537 | − | 2.76327i | −0.0956842 | − | 0.165730i | ||||
\(279\) | −6.81198 | + | 4.18777i | −0.407822 | + | 0.250715i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.0883 | + | 9.86595i | −1.01940 | + | 0.588553i | −0.913931 | − | 0.405869i | \(-0.866969\pi\) |
−0.105473 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(282\) | −15.1401 | + | 9.02207i | −0.901582 | + | 0.537257i | ||||
\(283\) | −4.85087 | + | 2.80065i | −0.288354 | + | 0.166481i | −0.637199 | − | 0.770699i | \(-0.719907\pi\) |
0.348845 | + | 0.937180i | \(0.386574\pi\) | |||||||
\(284\) | −4.20314 | + | 2.42668i | −0.249410 | + | 0.143997i | ||||
\(285\) | −24.1156 | + | 14.3706i | −1.42849 | + | 0.851241i | ||||
\(286\) | 11.7182 | − | 6.76551i | 0.692912 | − | 0.400053i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −20.6757 | + | 12.7107i | −1.21833 | + | 0.748987i | ||||
\(289\) | −17.2787 | − | 29.9275i | −1.01639 | − | 1.76044i | ||||
\(290\) | 43.7997 | 2.57201 | ||||||||
\(291\) | −16.2737 | + | 9.69758i | −0.953983 | + | 0.568482i | ||||
\(292\) | 18.7895i | 1.09957i | ||||||||
\(293\) | 15.0393 | − | 26.0488i | 0.878603 | − | 1.52178i | 0.0257278 | − | 0.999669i | \(-0.491810\pi\) |
0.852875 | − | 0.522115i | \(-0.174857\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.48701 | + | 14.6999i | 0.494133 | + | 0.855863i | ||||
\(296\) | 1.05011 | − | 0.606281i | 0.0610363 | − | 0.0352393i | ||||
\(297\) | 0.572507 | + | 13.8170i | 0.0332202 | + | 0.801747i | ||||
\(298\) | 5.57358 | − | 9.65373i | 0.322869 | − | 0.559225i | ||||
\(299\) | −6.08641 | + | 10.5420i | −0.351986 | + | 0.609658i | ||||
\(300\) | 12.3067 | + | 20.6522i | 0.710530 | + | 1.19236i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −20.7360 | − | 11.9719i | −1.19322 | − | 0.688906i | ||||
\(303\) | 0.914288 | − | 0.0126214i | 0.0525245 | − | 0.000725079i | ||||
\(304\) | − | 15.6592i | − | 0.898117i | ||||||
\(305\) | 14.6929 | + | 8.48296i | 0.841314 | + | 0.485733i | ||||
\(306\) | −38.2484 | + | 23.5138i | −2.18651 | + | 1.34419i | ||||
\(307\) | 23.4497i | 1.33835i | 0.743106 | + | 0.669173i | \(0.233352\pi\) | ||||
−0.743106 | + | 0.669173i | \(0.766648\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.0187375 | − | 1.35734i | −0.00106594 | − | 0.0772162i | ||||
\(310\) | −18.3592 | −1.04273 | ||||||||
\(311\) | 8.35507 | + | 14.4714i | 0.473773 | + | 0.820599i | 0.999549 | − | 0.0300243i | \(-0.00955846\pi\) |
−0.525776 | + | 0.850623i | \(0.676225\pi\) | |||||||
\(312\) | 1.47968 | − | 2.64659i | 0.0837705 | − | 0.149834i | ||||
\(313\) | −12.8757 | − | 7.43377i | −0.727776 | − | 0.420182i | 0.0898319 | − | 0.995957i | \(-0.471367\pi\) |
−0.817608 | + | 0.575775i | \(0.804700\pi\) | |||||||
\(314\) | 13.8928 | 0.784014 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.7451 | −0.660715 | ||||||||
\(317\) | −1.96761 | − | 1.13600i | −0.110512 | − | 0.0638040i | 0.443725 | − | 0.896163i | \(-0.353657\pi\) |
−0.554237 | + | 0.832359i | \(0.686990\pi\) | |||||||
\(318\) | −19.0777 | − | 32.0147i | −1.06982 | − | 1.79529i | ||||
\(319\) | 8.46176 | + | 14.6562i | 0.473768 | + | 0.820590i | ||||
\(320\) | −34.6216 | −1.93541 | ||||||||
\(321\) | 7.96157 | − | 4.74433i | 0.444371 | − | 0.264803i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 35.2163i | − | 1.95949i | ||||||
\(324\) | 11.5418 | + | 17.6621i | 0.641209 | + | 0.981230i | ||||
\(325\) | 12.5074 | + | 7.22117i | 0.693788 | + | 0.400559i | ||||
\(326\) | − | 48.1309i | − | 2.66573i | ||||||
\(327\) | −5.04203 | + | 9.01828i | −0.278825 | + | 0.498712i | ||||
\(328\) | −0.687575 | − | 0.396971i | −0.0379650 | − | 0.0219191i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −15.4943 | + | 27.7134i | −0.852932 | + | 1.52557i | ||||
\(331\) | 5.97440 | − | 10.3480i | 0.328383 | − | 0.568775i | −0.653808 | − | 0.756660i | \(-0.726830\pi\) |
0.982191 | + | 0.187885i | \(0.0601631\pi\) | |||||||
\(332\) | −2.44939 | + | 4.24247i | −0.134428 | + | 0.232836i | ||||
\(333\) | 2.65457 | + | 4.31801i | 0.145469 | + | 0.236626i | ||||
\(334\) | 28.7155 | − | 16.5789i | 1.57124 | − | 0.907158i | ||||
\(335\) | 13.7653 | + | 23.8423i | 0.752080 | + | 1.30264i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.34636 | − | 4.06402i | 0.127815 | − | 0.221381i | −0.795015 | − | 0.606590i | \(-0.792537\pi\) |
0.922830 | + | 0.385208i | \(0.125870\pi\) | |||||||
\(338\) | 14.6941i | 0.799251i | ||||||||
\(339\) | 17.4610 | + | 9.76228i | 0.948353 | + | 0.530214i | ||||
\(340\) | −55.6273 | −3.01681 | ||||||||
\(341\) | −3.54685 | − | 6.14332i | −0.192073 | − | 0.332679i | ||||
\(342\) | −30.6560 | + | 0.846548i | −1.65769 | + | 0.0457761i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.64810 | − | 2.10623i | 0.196692 | − | 0.113560i | ||||
\(345\) | −0.394272 | − | 28.5609i | −0.0212269 | − | 1.53767i | ||||
\(346\) | 33.6859 | − | 19.4486i | 1.81097 | − | 1.04556i | ||||
\(347\) | −6.40529 | + | 3.69809i | −0.343854 | + | 0.198524i | −0.661975 | − | 0.749526i | \(-0.730281\pi\) |
0.318121 | + | 0.948050i | \(0.396948\pi\) | |||||||
\(348\) | 22.5372 | + | 12.6003i | 1.20812 | + | 0.675448i | ||||
\(349\) | 18.0496 | − | 10.4209i | 0.966171 | − | 0.557819i | 0.0681042 | − | 0.997678i | \(-0.478305\pi\) |
0.898067 | + | 0.439859i | \(0.144972\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.2298 | + | 5.87760i | 0.599400 | + | 0.313723i | ||||
\(352\) | −10.7654 | − | 18.6462i | −0.573798 | − | 0.993847i | ||||
\(353\) | −7.09907 | −0.377845 | −0.188923 | − | 0.981992i | \(-0.560500\pi\) | ||||
−0.188923 | + | 0.981992i | \(0.560500\pi\) | |||||||
\(354\) | 0.255955 | + | 18.5413i | 0.0136038 | + | 0.985457i | ||||
\(355\) | − | 6.84150i | − | 0.363109i | ||||||
\(356\) | 1.26890 | − | 2.19780i | 0.0672517 | − | 0.116483i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.9593 | + | 39.7668i | 1.21344 | + | 2.10174i | ||||
\(359\) | −8.56701 | + | 4.94616i | −0.452149 | + | 0.261049i | −0.708737 | − | 0.705472i | \(-0.750735\pi\) |
0.256588 | + | 0.966521i | \(0.417402\pi\) | |||||||
\(360\) | 0.196401 | + | 7.11226i | 0.0103512 | + | 0.374849i | ||||
\(361\) | 2.52726 | − | 4.37734i | 0.133014 | − | 0.230386i | ||||
\(362\) | −18.4446 | + | 31.9470i | −0.969426 | + | 1.67910i | ||||
\(363\) | 6.78395 | − | 0.0936497i | 0.356065 | − | 0.00491533i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.9380 | − | 13.2432i | −1.20063 | − | 0.693183i | ||||
\(366\) | 9.48777 | + | 15.9216i | 0.495934 | + | 0.832237i | ||||
\(367\) | 31.2140i | 1.62936i | 0.579911 | + | 0.814680i | \(0.303087\pi\) | ||||
−0.579911 | + | 0.814680i | \(0.696913\pi\) | |||||||
\(368\) | 13.7984 | + | 7.96653i | 0.719293 | + | 0.415284i | ||||
\(369\) | 1.57944 | − | 2.91890i | 0.0822224 | − | 0.151952i | ||||
\(370\) | 11.6376i | 0.605011i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −9.44673 | − | 5.28157i | −0.489790 | − | 0.273837i | ||||
\(373\) | 29.0463 | 1.50396 | 0.751981 | − | 0.659185i | \(-0.229099\pi\) | ||||
0.751981 | + | 0.659185i | \(0.229099\pi\) | |||||||
\(374\) | −19.9151 | − | 34.4939i | −1.02978 | − | 1.78364i | ||||
\(375\) | −5.26953 | + | 0.0727437i | −0.272117 | + | 0.00375647i | ||||
\(376\) | −3.03425 | − | 1.75182i | −0.156479 | − | 0.0903434i | ||||
\(377\) | 15.5113 | 0.798873 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.518354 | −0.0266261 | −0.0133130 | − | 0.999911i | \(-0.504238\pi\) | ||||
−0.0133130 | + | 0.999911i | \(0.504238\pi\) | |||||||
\(380\) | −32.9058 | − | 18.9981i | −1.68803 | − | 0.974584i | ||||
\(381\) | −33.0710 | + | 0.456532i | −1.69428 | + | 0.0233888i | ||||
\(382\) | 15.9701 | + | 27.6611i | 0.817102 | + | 1.41526i | ||||
\(383\) | −13.2102 | −0.675011 | −0.337505 | − | 0.941324i | \(-0.609583\pi\) | ||||
−0.337505 | + | 0.941324i | \(0.609583\pi\) | |||||||
\(384\) | −8.55125 | − | 4.78091i | −0.436379 | − | 0.243975i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 53.9140i | 2.74415i | ||||||||
\(387\) | 9.22201 | + | 15.0009i | 0.468781 | + | 0.762536i | ||||
\(388\) | −22.2055 | − | 12.8203i | −1.12731 | − | 0.650854i | ||||
\(389\) | − | 33.8236i | − | 1.71492i | −0.514549 | − | 0.857461i | \(-0.672040\pi\) | ||
0.514549 | − | 0.857461i | \(-0.327960\pi\) | |||||||
\(390\) | 14.8971 | + | 24.9991i | 0.754343 | + | 1.26588i | ||||
\(391\) | 31.0316 | + | 17.9161i | 1.56933 | + | 0.906055i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.18950 | + | 0.0992482i | −0.362662 | + | 0.00500641i | ||||
\(394\) | −4.35933 | + | 7.55059i | −0.219620 | + | 0.380393i | ||||
\(395\) | 8.27820 | − | 14.3383i | 0.416521 | − | 0.721436i | ||||
\(396\) | −15.9452 | + | 9.80256i | −0.801276 | + | 0.492597i | ||||
\(397\) | −7.42483 | + | 4.28673i | −0.372641 | + | 0.215145i | −0.674612 | − | 0.738173i | \(-0.735689\pi\) |
0.301970 | + | 0.953317i | \(0.402356\pi\) | |||||||
\(398\) | 22.9353 | + | 39.7251i | 1.14964 | + | 1.99124i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.45183 | − | 16.3710i | 0.472591 | − | 0.818552i | ||||
\(401\) | − | 16.1362i | − | 0.805801i | −0.915244 | − | 0.402900i | \(-0.868002\pi\) | ||
0.915244 | − | 0.402900i | \(-0.131998\pi\) | |||||||
\(402\) | 0.415140 | + | 30.0726i | 0.0207053 | + | 1.49989i | ||||
\(403\) | −6.50175 | −0.323875 | ||||||||
\(404\) | 0.618801 | + | 1.07180i | 0.0307865 | + | 0.0533238i | ||||
\(405\) | −29.6965 | + | 1.64136i | −1.47563 | + | 0.0815598i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.89416 | + | 2.24830i | −0.193026 | + | 0.111444i | ||||
\(408\) | −7.79056 | − | 4.35562i | −0.385690 | − | 0.215635i | ||||
\(409\) | −14.1364 | + | 8.16165i | −0.699000 | + | 0.403568i | −0.806975 | − | 0.590586i | \(-0.798897\pi\) |
0.107975 | + | 0.994154i | \(0.465563\pi\) | |||||||
\(410\) | 6.59903 | − | 3.80995i | 0.325903 | − | 0.188160i | ||||
\(411\) | −0.150481 | − | 10.9008i | −0.00742269 | − | 0.537697i | ||||
\(412\) | 1.59117 | − | 0.918662i | 0.0783913 | − | 0.0452592i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 14.8501 | − | 27.4438i | 0.729842 | − | 1.34879i | ||||
\(415\) | −3.45276 | − | 5.98035i | −0.169489 | − | 0.293564i | ||||
\(416\) | −19.7341 | −0.967544 | ||||||||
\(417\) | 2.31435 | + | 1.29393i | 0.113334 | + | 0.0633640i | ||||
\(418\) | − | 27.2060i | − | 1.33069i | ||||||
\(419\) | −0.589031 | + | 1.02023i | −0.0287760 | + | 0.0498415i | −0.880055 | − | 0.474872i | \(-0.842494\pi\) |
0.851279 | + | 0.524714i | \(0.175828\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.43544 | + | 5.95035i | 0.167433 | + | 0.290002i | 0.937517 | − | 0.347941i | \(-0.113119\pi\) |
−0.770084 | + | 0.637943i | \(0.779786\pi\) | |||||||
\(422\) | −44.3777 | + | 25.6215i | −2.16027 | + | 1.24724i | ||||
\(423\) | 6.97003 | − | 12.8810i | 0.338894 | − | 0.626296i | ||||
\(424\) | 3.70433 | − | 6.41609i | 0.179898 | − | 0.311593i | ||||
\(425\) | 21.2564 | − | 36.8172i | 1.03109 | − | 1.78589i | ||||
\(426\) | 3.64725 | − | 6.52355i | 0.176710 | − | 0.316067i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.8636 | + | 6.27208i | 0.525110 | + | 0.303172i | ||||
\(429\) | −5.48717 | + | 9.81447i | −0.264923 | + | 0.473847i | ||||
\(430\) | 40.4293i | 1.94967i | ||||||||
\(431\) | −0.702488 | − | 0.405582i | −0.0338377 | − | 0.0195362i | 0.482986 | − | 0.875628i | \(-0.339552\pi\) |
−0.516823 | + | 0.856092i | \(0.672886\pi\) | |||||||
\(432\) | 7.69321 | − | 14.6987i | 0.370140 | − | 0.707191i | ||||
\(433\) | 8.59662i | 0.413127i | 0.978433 | + | 0.206564i | \(0.0662280\pi\) | ||||
−0.978433 | + | 0.206564i | \(0.933772\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −31.2669 | + | 18.6321i | −1.49913 | + | 0.893341i | ||||
\(436\) | −13.9844 | −0.669731 | ||||||||
\(437\) | 12.2376 | + | 21.1961i | 0.585404 | + | 1.01395i | ||||
\(438\) | −14.8119 | − | 24.8562i | −0.707740 | − | 1.18767i | ||||
\(439\) | 23.8968 | + | 13.7968i | 1.14053 | + | 0.658486i | 0.946562 | − | 0.322522i | \(-0.104530\pi\) |
0.193969 | + | 0.981008i | \(0.437864\pi\) | |||||||
\(440\) | −6.31186 | −0.300906 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −36.5065 | −1.73643 | ||||||||
\(443\) | 10.6051 | + | 6.12286i | 0.503864 | + | 0.290906i | 0.730308 | − | 0.683118i | \(-0.239377\pi\) |
−0.226444 | + | 0.974024i | \(0.572710\pi\) | |||||||
\(444\) | −3.34791 | + | 5.98814i | −0.158885 | + | 0.284185i | ||||
\(445\) | 1.78870 | + | 3.09811i | 0.0847924 | + | 0.146865i | ||||
\(446\) | 17.6152 | 0.834103 | ||||||||
\(447\) | 0.127863 | + | 9.26238i | 0.00604773 | + | 0.438096i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.0163i | − | 1.03901i | −0.854466 | − | 0.519507i | \(-0.826116\pi\) | ||
0.854466 | − | 0.519507i | \(-0.173884\pi\) | |||||||
\(450\) | −32.5605 | − | 17.6188i | −1.53492 | − | 0.830557i | ||||
\(451\) | 2.54976 | + | 1.47211i | 0.120064 | + | 0.0693187i | ||||
\(452\) | 27.0763i | 1.27356i | ||||||||
\(453\) | 19.8954 | − | 0.274647i | 0.934765 | − | 0.0129041i | ||||
\(454\) | −10.5226 | − | 6.07522i | −0.493849 | − | 0.285124i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.12087 | − | 5.23720i | −0.146148 | − | 0.245254i | ||||
\(457\) | −12.0780 | + | 20.9196i | −0.564983 | + | 0.978579i | 0.432069 | + | 0.901841i | \(0.357784\pi\) |
−0.997051 | + | 0.0767380i | \(0.975550\pi\) | |||||||
\(458\) | −5.00051 | + | 8.66114i | −0.233659 | + | 0.404709i | ||||
\(459\) | 17.3014 | − | 33.0561i | 0.807561 | − | 1.54293i | ||||
\(460\) | 33.4812 | − | 19.3304i | 1.56107 | − | 0.901284i | ||||
\(461\) | −16.3899 | − | 28.3881i | −0.763352 | − | 1.32216i | −0.941114 | − | 0.338091i | \(-0.890219\pi\) |
0.177762 | − | 0.984074i | \(-0.443114\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.7659 | − | 27.3074i | 0.732704 | − | 1.26908i | −0.223020 | − | 0.974814i | \(-0.571591\pi\) |
0.955723 | − | 0.294266i | \(-0.0950753\pi\) | |||||||
\(464\) | − | 20.3028i | − | 0.942535i | ||||||
\(465\) | 13.1059 | − | 7.80986i | 0.607771 | − | 0.362174i | ||||
\(466\) | 48.0355 | 2.22520 | ||||||||
\(467\) | −16.5765 | − | 28.7114i | −0.767070 | − | 1.32860i | −0.939145 | − | 0.343521i | \(-0.888380\pi\) |
0.172075 | − | 0.985084i | \(-0.444953\pi\) | |||||||
\(468\) | 0.473558 | + | 17.1489i | 0.0218902 | + | 0.792709i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 29.1213 | − | 16.8132i | 1.34327 | − | 0.775536i | ||||
\(471\) | −9.91751 | + | 5.90988i | −0.456975 | + | 0.272313i | ||||
\(472\) | −3.19239 | + | 1.84313i | −0.146942 | + | 0.0848368i | ||||
\(473\) | −13.5284 | + | 7.81062i | −0.622036 | + | 0.359133i | ||||
\(474\) | 15.5373 | − | 9.25875i | 0.713652 | − | 0.425268i | ||||
\(475\) | 25.1480 | − | 14.5192i | 1.15387 | − | 0.666187i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 27.2376 | + | 14.7385i | 1.24712 | + | 0.674830i | ||||
\(478\) | −7.12364 | − | 12.3385i | −0.325828 | − | 0.564350i | ||||
\(479\) | −22.7945 | −1.04151 | −0.520754 | − | 0.853707i | \(-0.674349\pi\) | ||||
−0.520754 | + | 0.853707i | \(0.674349\pi\) | |||||||
\(480\) | 39.7790 | − | 23.7045i | 1.81566 | − | 1.08196i | ||||
\(481\) | 4.12136i | 0.187918i | ||||||||
\(482\) | −4.68247 | + | 8.11027i | −0.213281 | + | 0.369413i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.59146 | + | 7.95264i | 0.208703 | + | 0.361484i | ||||
\(485\) | 31.3017 | − | 18.0721i | 1.42134 | − | 0.820611i | ||||
\(486\) | −29.1915 | − | 14.2664i | −1.32415 | − | 0.647135i | ||||
\(487\) | 1.36560 | − | 2.36528i | 0.0618811 | − | 0.107181i | −0.833425 | − | 0.552632i | \(-0.813623\pi\) |
0.895306 | + | 0.445451i | \(0.146957\pi\) | |||||||
\(488\) | −1.84225 | + | 3.19087i | −0.0833946 | + | 0.144444i | ||||
\(489\) | 20.4746 | + | 34.3588i | 0.925892 | + | 1.55376i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.6775 | + | 12.5155i | 0.978291 | + | 0.564817i | 0.901754 | − | 0.432250i | \(-0.142280\pi\) |
0.0765375 | + | 0.997067i | \(0.475613\pi\) | |||||||
\(492\) | 4.49158 | − | 0.0620045i | 0.202496 | − | 0.00279538i | ||||
\(493\) | − | 45.6594i | − | 2.05640i | ||||||
\(494\) | −21.5950 | − | 12.4679i | −0.971605 | − | 0.560957i | ||||
\(495\) | −0.728322 | − | 26.3747i | −0.0327357 | − | 1.18545i | ||||
\(496\) | 8.51016i | 0.382118i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.104130 | − | 7.54311i | −0.00466616 | − | 0.338015i | ||||
\(499\) | 8.59962 | 0.384972 | 0.192486 | − | 0.981300i | \(-0.438345\pi\) | ||||
0.192486 | + | 0.981300i | \(0.438345\pi\) | |||||||
\(500\) | −3.56648 | − | 6.17732i | −0.159498 | − | 0.276258i | ||||
\(501\) | −13.4463 | + | 24.0504i | −0.600738 | + | 1.07449i | ||||
\(502\) | 0.843754 | + | 0.487141i | 0.0376586 | + | 0.0217422i | ||||
\(503\) | −39.0362 | −1.74054 | −0.870269 | − | 0.492577i | \(-0.836055\pi\) | ||||
−0.870269 | + | 0.492577i | \(0.836055\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.74457 | −0.0776325 | ||||||||
\(506\) | 23.9732 | + | 13.8409i | 1.06574 | + | 0.615304i | ||||
\(507\) | −6.25075 | − | 10.4895i | −0.277605 | − | 0.465856i | ||||
\(508\) | −22.3829 | − | 38.7683i | −0.993079 | − | 1.72006i | ||||
\(509\) | −32.5819 | −1.44417 | −0.722083 | − | 0.691806i | \(-0.756815\pi\) | ||||
−0.722083 | + | 0.691806i | \(0.756815\pi\) | |||||||
\(510\) | 73.5879 | − | 43.8513i | 3.25853 | − | 1.94177i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 30.4128i | 1.34407i | ||||||||
\(513\) | 21.5240 | − | 13.6451i | 0.950307 | − | 0.602448i | ||||
\(514\) | −38.7845 | − | 22.3922i | −1.71071 | − | 0.987679i | ||||
\(515\) | 2.58997i | 0.114128i | ||||||||
\(516\) | −11.6307 | + | 20.8029i | −0.512013 | + | 0.915797i | ||||
\(517\) | 11.2520 | + | 6.49636i | 0.494864 | + | 0.285710i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.7738 | + | 28.2133i | −0.692392 | + | 1.23843i | ||||
\(520\) | −2.89258 | + | 5.01009i | −0.126848 | + | 0.219707i | ||||
\(521\) | −3.68456 | + | 6.38185i | −0.161424 | + | 0.279594i | −0.935379 | − | 0.353646i | \(-0.884942\pi\) |
0.773956 | + | 0.633240i | \(0.218275\pi\) | |||||||
\(522\) | −39.7468 | + | 1.09758i | −1.73967 | + | 0.0480400i | ||||
\(523\) | −37.5991 | + | 21.7078i | −1.64409 | + | 0.949217i | −0.664735 | + | 0.747079i | \(0.731455\pi\) |
−0.979357 | + | 0.202138i | \(0.935211\pi\) | |||||||
\(524\) | −4.86594 | − | 8.42806i | −0.212570 | − | 0.368181i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.5571 | − | 20.0175i | 0.503915 | − | 0.872806i | ||||
\(527\) | 19.1387i | 0.833693i | ||||||||
\(528\) | 12.8462 | + | 7.18218i | 0.559059 | + | 0.312564i | ||||
\(529\) | −1.90322 | −0.0827487 | ||||||||
\(530\) | 35.5525 | + | 61.5787i | 1.54430 | + | 2.67481i | ||||
\(531\) | −8.07004 | − | 13.1270i | −0.350210 | − | 0.569664i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.33699 | − | 1.34926i | 0.101226 | − | 0.0584430i | ||||
\(534\) | 0.0539442 | + | 3.90770i | 0.00233440 | + | 0.169103i | ||||
\(535\) | −15.3137 | + | 8.84137i | −0.662069 | + | 0.382246i | ||||
\(536\) | −5.17783 | + | 2.98942i | −0.223648 | + | 0.129123i | ||||
\(537\) | −33.3063 | − | 18.6212i | −1.43727 | − | 0.803564i | ||||
\(538\) | −39.8151 | + | 22.9873i | −1.71655 | + | 0.991052i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −21.5537 | − | 33.9991i | −0.927526 | − | 1.46309i | ||||
\(541\) | 10.8221 | + | 18.7444i | 0.465278 | + | 0.805884i | 0.999214 | − | 0.0396402i | \(-0.0126212\pi\) |
−0.533936 | + | 0.845525i | \(0.679288\pi\) | |||||||
\(542\) | −9.88869 | −0.424755 | ||||||||
\(543\) | −0.423137 | − | 30.6519i | −0.0181585 | − | 1.31540i | ||||
\(544\) | 58.0897i | 2.49058i | ||||||||
\(545\) | 9.85648 | − | 17.0719i | 0.422205 | − | 0.731281i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.9092 | − | 20.6273i | −0.509200 | − | 0.881960i | −0.999943 | − | 0.0106561i | \(-0.996608\pi\) |
0.490743 | − | 0.871304i | \(-0.336725\pi\) | |||||||
\(548\) | 12.7787 | − | 7.37780i | 0.545880 | − | 0.315164i | ||||
\(549\) | −13.5459 | − | 7.32980i | −0.578125 | − | 0.312828i | ||||
\(550\) | 16.4214 | − | 28.4428i | 0.700213 | − | 1.21280i | ||||
\(551\) | 15.5938 | − | 27.0093i | 0.664320 | − | 1.15064i | ||||
\(552\) | 6.20259 | − | 0.0856243i | 0.264000 | − | 0.00364441i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 11.6004 | + | 6.69748i | 0.492852 | + | 0.284548i | ||||
\(555\) | −4.95056 | − | 8.30764i | −0.210140 | − | 0.352640i | ||||
\(556\) | 3.58880i | 0.152199i | ||||||||
\(557\) | −9.42040 | − | 5.43887i | −0.399155 | − | 0.230452i | 0.286964 | − | 0.957941i | \(-0.407354\pi\) |
−0.686119 | + | 0.727489i | \(0.740687\pi\) | |||||||
\(558\) | 16.6603 | − | 0.460066i | 0.705287 | − | 0.0194761i | ||||
\(559\) | 14.3177i | 0.605574i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 28.8901 | + | 16.1521i | 1.21974 | + | 0.681944i | ||||
\(562\) | 41.1273 | 1.73485 | ||||||||
\(563\) | 6.67759 | + | 11.5659i | 0.281427 | + | 0.487445i | 0.971736 | − | 0.236069i | \(-0.0758590\pi\) |
−0.690310 | + | 0.723514i | \(0.742526\pi\) | |||||||
\(564\) | 19.8212 | − | 0.273624i | 0.834625 | − | 0.0115217i | ||||
\(565\) | −33.0543 | − | 19.0839i | −1.39061 | − | 0.802867i | ||||
\(566\) | 11.6748 | 0.490729 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.48577 | 0.0623415 | ||||||||
\(569\) | −8.34729 | − | 4.81931i | −0.349937 | − | 0.202036i | 0.314721 | − | 0.949184i | \(-0.398089\pi\) |
−0.664657 | + | 0.747148i | \(0.731422\pi\) | |||||||
\(570\) | 58.5065 | − | 0.807659i | 2.45057 | − | 0.0338291i | ||||
\(571\) | 17.2031 | + | 29.7966i | 0.719926 | + | 1.24695i | 0.961028 | + | 0.276449i | \(0.0891578\pi\) |
−0.241102 | + | 0.970500i | \(0.577509\pi\) | |||||||
\(572\) | −15.2190 | −0.636339 | ||||||||
\(573\) | −23.1673 | − | 12.9526i | −0.967826 | − | 0.541102i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.5462i | 1.23216i | ||||||||
\(576\) | 31.4179 | − | 0.867589i | 1.30908 | − | 0.0361496i | ||||
\(577\) | 20.9017 | + | 12.0676i | 0.870149 | + | 0.502381i | 0.867398 | − | 0.497616i | \(-0.165791\pi\) |
0.00275107 | + | 0.999996i | \(0.499124\pi\) | |||||||
\(578\) | 72.0280i | 2.99597i | ||||||||
\(579\) | −22.9346 | − | 38.4871i | −0.953130 | − | 1.59947i | ||||
\(580\) | −42.6637 | − | 24.6319i | −1.77151 | − | 1.02278i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 39.4814 | − | 0.545025i | 1.63656 | − | 0.0225920i | ||||
\(583\) | −13.7369 | + | 23.7930i | −0.568925 | + | 0.985407i | ||||
\(584\) | 2.87604 | − | 4.98145i | 0.119011 | − | 0.206134i | ||||
\(585\) | −21.2689 | − | 11.5088i | −0.879360 | − | 0.475830i | ||||
\(586\) | −54.2935 | + | 31.3464i | −2.24284 | + | 1.29491i | ||||
\(587\) | −3.96848 | − | 6.87362i | −0.163797 | − | 0.283704i | 0.772431 | − | 0.635099i | \(-0.219041\pi\) |
−0.936227 | + | 0.351395i | \(0.885707\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.53634 | + | 11.3213i | −0.269325 | + | 0.466485i | ||||
\(590\) | − | 35.3790i | − | 1.45653i | ||||||
\(591\) | −0.100007 | − | 7.24450i | −0.00411375 | − | 0.297999i | ||||
\(592\) | 5.39447 | 0.221711 | ||||||||
\(593\) | 20.9147 | + | 36.2252i | 0.858862 | + | 1.48759i | 0.873015 | + | 0.487693i | \(0.162161\pi\) |
−0.0141532 | + | 0.999900i | \(0.504505\pi\) | |||||||
\(594\) | 13.3661 | − | 25.5372i | 0.548416 | − | 1.04781i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.8580 | + | 6.26889i | −0.444763 | + | 0.256784i | ||||
\(597\) | −33.2714 | − | 18.6017i | −1.36171 | − | 0.761317i | ||||
\(598\) | 21.9727 | − | 12.6859i | 0.898529 | − | 0.518766i | ||||
\(599\) | 7.57344 | − | 4.37253i | 0.309442 | − | 0.178657i | −0.337235 | − | 0.941421i | \(-0.609492\pi\) |
0.646677 | + | 0.762764i | \(0.276158\pi\) | |||||||
\(600\) | −0.101588 | − | 7.35902i | −0.00414732 | − | 0.300431i | ||||
\(601\) | 12.6427 | − | 7.29924i | 0.515705 | − | 0.297742i | −0.219471 | − | 0.975619i | \(-0.570433\pi\) |
0.735176 | + | 0.677877i | \(0.237100\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.0890 | − | 21.2911i | −0.533027 | − | 0.867040i | ||||
\(604\) | 13.4654 | + | 23.3228i | 0.547900 | + | 0.948990i | ||||
\(605\) | −12.9446 | −0.526273 | ||||||||
\(606\) | −1.66350 | − | 0.930045i | −0.0675750 | − | 0.0377805i | ||||
\(607\) | 10.9862i | 0.445918i | 0.974828 | + | 0.222959i | \(0.0715716\pi\) | ||||
−0.974828 | + | 0.222959i | \(0.928428\pi\) | |||||||
\(608\) | −19.8391 | + | 34.3624i | −0.804583 | + | 1.39358i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.6811 | − | 30.6245i | −0.715885 | − | 1.23995i | ||||
\(611\) | 10.3131 | − | 5.95426i | 0.417222 | − | 0.240883i | ||||
\(612\) | 50.4799 | − | 1.39397i | 2.04053 | − | 0.0563481i | ||||
\(613\) | −11.9068 | + | 20.6231i | −0.480909 | + | 0.832959i | −0.999760 | − | 0.0219056i | \(-0.993027\pi\) |
0.518851 | + | 0.854865i | \(0.326360\pi\) | |||||||
\(614\) | 24.4382 | − | 42.3282i | 0.986244 | − | 1.70823i | ||||
\(615\) | −3.09007 | + | 5.52696i | −0.124603 | + | 0.222868i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.5255 | − | 21.0880i | −1.47046 | − | 0.848971i | −0.471011 | − | 0.882127i | \(-0.656111\pi\) |
−0.999450 | + | 0.0331557i | \(0.989444\pi\) | |||||||
\(618\) | −1.38073 | + | 2.46960i | −0.0555411 | + | 0.0993419i | ||||
\(619\) | 26.1577i | 1.05137i | 0.850680 | + | 0.525683i | \(0.176190\pi\) | ||||
−0.850680 | + | 0.525683i | \(0.823810\pi\) | |||||||
\(620\) | 17.8830 | + | 10.3247i | 0.718198 | + | 0.414652i | ||||
\(621\) | 1.07350 | + | 25.9082i | 0.0430781 | + | 1.03966i | ||||
\(622\) | − | 34.8290i | − | 1.39652i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 11.5880 | − | 6.90535i | 0.463892 | − | 0.276435i | ||||
\(625\) | −19.5487 | −0.781947 | ||||||||
\(626\) | 15.4942 | + | 26.8368i | 0.619274 | + | 1.07261i | ||||
\(627\) | 11.5733 | + | 19.4213i | 0.462191 | + | 0.775613i | ||||
\(628\) | −13.5324 | − | 7.81295i | −0.540003 | − | 0.311771i | ||||
\(629\) | 12.1317 | 0.483724 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.2419 | −0.766009 | −0.383004 | − | 0.923746i | \(-0.625111\pi\) | ||||
−0.383004 | + | 0.923746i | \(0.625111\pi\) | |||||||
\(632\) | 3.11385 | + | 1.79778i | 0.123862 | + | 0.0715118i | ||||
\(633\) | 20.7803 | − | 37.1682i | 0.825944 | − | 1.47730i | ||||
\(634\) | 2.36776 | + | 4.10109i | 0.0940359 | + | 0.162875i | ||||
\(635\) | 63.1036 | 2.50419 | ||||||||
\(636\) | 0.578593 | + | 41.9131i | 0.0229427 | + | 1.66196i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 35.2738i | − | 1.39650i | ||||||
\(639\) | 0.171442 | + | 6.20842i | 0.00678215 | + | 0.245601i | ||||
\(640\) | 16.1878 | + | 9.34604i | 0.639879 | + | 0.369435i | ||||
\(641\) | 17.6072i | 0.695444i | 0.937598 | + | 0.347722i | \(0.113045\pi\) | ||||
−0.937598 | + | 0.347722i | \(0.886955\pi\) | |||||||
\(642\) | −19.3154 | + | 0.266642i | −0.762319 | + | 0.0105235i | ||||
\(643\) | −43.1158 | − | 24.8929i | −1.70032 | − | 0.981680i | −0.945428 | − | 0.325832i | \(-0.894355\pi\) |
−0.754893 | − | 0.655848i | \(-0.772311\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.1983 | − | 28.8609i | −0.677183 | − | 1.13640i | ||||
\(646\) | −36.7007 | + | 63.5675i | −1.44397 | + | 2.50103i | ||||
\(647\) | 5.77035 | − | 9.99454i | 0.226856 | − | 0.392926i | −0.730019 | − | 0.683427i | \(-0.760489\pi\) |
0.956875 | + | 0.290501i | \(0.0938221\pi\) | |||||||
\(648\) | −0.356454 | − | 6.44921i | −0.0140029 | − | 0.253349i | ||||
\(649\) | 11.8385 | − | 6.83495i | 0.464701 | − | 0.268295i | ||||
\(650\) | −15.0511 | − | 26.0693i | −0.590354 | − | 1.02252i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −27.0677 | + | 46.8826i | −1.06005 | + | 1.83606i | ||||
\(653\) | − | 21.0444i | − | 0.823529i | −0.911290 | − | 0.411765i | \(-0.864913\pi\) | ||
0.911290 | − | 0.411765i | \(-0.135087\pi\) | |||||||
\(654\) | 18.4996 | − | 11.0240i | 0.723391 | − | 0.431072i | ||||
\(655\) | 13.7185 | 0.536024 | ||||||||
\(656\) | −1.76606 | − | 3.05890i | −0.0689529 | − | 0.119430i | ||||
\(657\) | 21.1473 | + | 11.4430i | 0.825034 | + | 0.446433i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.8016 | + | 18.3607i | −1.23881 | + | 0.715230i | −0.968852 | − | 0.247641i | \(-0.920345\pi\) |
−0.269962 | + | 0.962871i | \(0.587011\pi\) | |||||||
\(660\) | 30.6777 | − | 18.2810i | 1.19413 | − | 0.711587i | ||||
\(661\) | −19.9819 | + | 11.5365i | −0.777205 | + | 0.448719i | −0.835439 | − | 0.549583i | \(-0.814786\pi\) |
0.0582339 | + | 0.998303i | \(0.481453\pi\) | |||||||
\(662\) | −21.5683 | + | 12.4525i | −0.838276 | + | 0.483979i | ||||
\(663\) | 26.0605 | − | 15.5296i | 1.01211 | − | 0.603119i | ||||
\(664\) | 1.29875 | − | 0.749836i | 0.0504015 | − | 0.0290993i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.291629 | − | 10.5607i | −0.0113004 | − | 0.409220i | ||||
\(667\) | 15.8666 | + | 27.4817i | 0.614356 | + | 1.06410i | ||||
\(668\) | −37.2943 | −1.44296 | ||||||||
\(669\) | −12.5748 | + | 7.49337i | −0.486169 | + | 0.289710i | ||||
\(670\) | − | 57.3823i | − | 2.21687i | ||||||
\(671\) | 6.83168 | − | 11.8328i | 0.263734 | − | 0.456801i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.7594 | + | 42.8846i | 0.954406 | + | 1.65308i | 0.735722 | + | 0.677284i | \(0.236843\pi\) |
0.218684 | + | 0.975796i | \(0.429824\pi\) | |||||||
\(674\) | −8.47065 | + | 4.89053i | −0.326277 | + | 0.188376i | ||||
\(675\) | 30.7386 | − | 1.27365i | 1.18313 | − | 0.0490227i | ||||
\(676\) | 8.26358 | − | 14.3129i | 0.317830 | − | 0.550498i | ||||
\(677\) | −14.9077 | + | 25.8208i | −0.572948 | + | 0.992374i | 0.423314 | + | 0.905983i | \(0.360867\pi\) |
−0.996261 | + | 0.0863911i | \(0.972467\pi\) | |||||||
\(678\) | −21.3444 | − | 35.8185i | −0.819727 | − | 1.37560i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 14.7478 | + | 8.51465i | 0.565553 | + | 0.326522i | ||||
\(681\) | 10.0960 | − | 0.139371i | 0.386880 | − | 0.00534072i | ||||
\(682\) | 14.7854i | 0.566163i | ||||||||
\(683\) | 26.1841 | + | 15.1174i | 1.00191 | + | 0.578451i | 0.908812 | − | 0.417207i | \(-0.136991\pi\) |
0.0930943 | + | 0.995657i | \(0.470324\pi\) | |||||||
\(684\) | 30.3369 | + | 16.4156i | 1.15996 | + | 0.627665i | ||||
\(685\) | 20.8001i | 0.794731i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.114717 | − | 8.31003i | −0.00437671 | − | 0.317048i | ||||
\(688\) | 18.7405 | 0.714474 | ||||||||
\(689\) | 12.5906 | + | 21.8076i | 0.479664 | + | 0.830802i | ||||
\(690\) | −29.0532 | + | 51.9651i | −1.10603 | + | 1.97828i | ||||
\(691\) | 26.7555 | + | 15.4473i | 1.01783 | + | 0.587642i | 0.913473 | − | 0.406899i | \(-0.133390\pi\) |
0.104352 | + | 0.994540i | \(0.466723\pi\) | |||||||
\(692\) | −43.7496 | −1.66311 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.4159 | 0.585180 | ||||||||
\(695\) | −4.38115 | − | 2.52946i | −0.166186 | − | 0.0959478i | ||||
\(696\) | −4.04634 | − | 6.79025i | −0.153376 | − | 0.257384i | ||||
\(697\) | −3.97172 | − | 6.87921i | −0.150439 | − | 0.260569i | ||||
\(698\) | −43.4407 | −1.64426 | ||||||||
\(699\) | −34.2907 | + | 20.4340i | −1.29699 | + | 0.772884i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.757329i | 0.0286039i | 0.999898 | + | 0.0143020i | \(0.00455261\pi\) | ||||
−0.999898 | + | 0.0143020i | \(0.995447\pi\) | |||||||
\(702\) | −14.1450 | − | 22.3125i | −0.533870 | − | 0.842132i | ||||
\(703\) | 7.17640 | + | 4.14329i | 0.270663 | + | 0.156267i | ||||
\(704\) | 27.8823i | 1.05085i | ||||||||
\(705\) | −13.6364 | + | 24.3903i | −0.513575 | + | 0.918592i | ||||
\(706\) | 12.8142 | + | 7.39831i | 0.482270 | + | 0.278439i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.1778 | − | 18.2043i | 0.382507 | − | 0.684160i | ||||
\(709\) | 10.7544 | − | 18.6271i | 0.403889 | − | 0.699556i | −0.590303 | − | 0.807182i | \(-0.700992\pi\) |
0.994191 | + | 0.107626i | \(0.0343249\pi\) | |||||||
\(710\) | −7.12988 | + | 12.3493i | −0.267580 | + | 0.463461i | ||||
\(711\) | −7.15287 | + | 13.2189i | −0.268254 | + | 0.495748i | ||||
\(712\) | −0.672819 | + | 0.388452i | −0.0252149 | + | 0.0145579i | ||||
\(713\) | −6.65065 | − | 11.5193i | −0.249069 | − | 0.431400i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.7267 | − | 18.5791i | 0.401155 | − | 0.694820i | ||||
\(716\) | − | 51.6471i | − | 1.93014i | ||||||
\(717\) | 10.3340 | + | 5.77763i | 0.385930 | + | 0.215770i | ||||
\(718\) | 20.6186 | 0.769480 | ||||||||
\(719\) | 22.1254 | + | 38.3224i | 0.825140 | + | 1.42918i | 0.901813 | + | 0.432127i | \(0.142237\pi\) |
−0.0766729 | + | 0.997056i | \(0.524430\pi\) | |||||||
\(720\) | −15.0639 | + | 27.8389i | −0.561398 | + | 1.03750i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −9.12371 | + | 5.26758i | −0.339549 | + | 0.196039i | ||||
\(723\) | −0.107420 | − | 7.78150i | −0.00399501 | − | 0.289397i | ||||
\(724\) | 35.9324 | − | 20.7456i | 1.33542 | − | 0.771003i | ||||
\(725\) | 32.6054 | − | 18.8248i | 1.21094 | − | 0.699134i | ||||
\(726\) | −12.3430 | − | 6.90086i | −0.458093 | − | 0.256115i | ||||
\(727\) | 2.95166 | − | 1.70414i | 0.109471 | − | 0.0632031i | −0.444265 | − | 0.895895i | \(-0.646535\pi\) |
0.553736 | + | 0.832692i | \(0.313202\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.9074 | − | 2.23365i | 0.996572 | − | 0.0827276i | ||||
\(730\) | 27.6029 | + | 47.8097i | 1.02163 | + | 1.76952i | ||||
\(731\) | 42.1458 | 1.55882 | ||||||||
\(732\) | −0.287748 | − | 20.8444i | −0.0106355 | − | 0.770429i | ||||
\(733\) | − | 6.30937i | − | 0.233042i | −0.993188 | − | 0.116521i | \(-0.962826\pi\) | ||
0.993188 | − | 0.116521i | \(-0.0371742\pi\) | |||||||
\(734\) | 32.5298 | − | 56.3432i | 1.20070 | − | 2.07967i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.1861 | − | 34.9633i | −0.744069 | − | 1.28876i | ||||
\(737\) | 19.2012 | − | 11.0858i | 0.707284 | − | 0.408351i | ||||
\(738\) | −5.89292 | + | 3.62277i | −0.216921 | + | 0.133356i | ||||
\(739\) | 2.45388 | − | 4.25024i | 0.0902674 | − | 0.156348i | −0.817356 | − | 0.576133i | \(-0.804561\pi\) |
0.907624 | + | 0.419785i | \(0.137895\pi\) | |||||||
\(740\) | 6.54471 | − | 11.3358i | 0.240588 | − | 0.416711i | ||||
\(741\) | 20.7196 | − | 0.286025i | 0.761153 | − | 0.0105074i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.1921 | + | 15.1220i | 0.960895 | + | 0.554773i | 0.896448 | − | 0.443148i | \(-0.146138\pi\) |
0.0644465 | + | 0.997921i | \(0.479472\pi\) | |||||||
\(744\) | 1.69607 | + | 2.84621i | 0.0621810 | + | 0.104347i | ||||
\(745\) | − | 17.6738i | − | 0.647516i | ||||||
\(746\) | −52.4304 | − | 30.2707i | −1.91961 | − | 1.10829i | ||||
\(747\) | 3.28312 | + | 5.34044i | 0.120123 | + | 0.195396i | ||||
\(748\) | 44.7990i | 1.63801i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 9.58762 | + | 5.36034i | 0.350091 | + | 0.195732i | ||||
\(751\) | −50.0642 | −1.82687 | −0.913435 | − | 0.406986i | \(-0.866580\pi\) | ||||
−0.913435 | + | 0.406986i | \(0.866580\pi\) | |||||||
\(752\) | −7.79355 | − | 13.4988i | −0.284202 | − | 0.492252i | ||||
\(753\) | −0.809549 | + | 0.0111755i | −0.0295016 | + | 0.000407258i | ||||
\(754\) | −27.9988 | − | 16.1651i | −1.01966 | − | 0.588700i | ||||
\(755\) | −37.9628 | −1.38161 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.2695 | 1.35458 | 0.677291 | − | 0.735716i | \(-0.263154\pi\) | ||||
0.677291 | + | 0.735716i | \(0.263154\pi\) | |||||||
\(758\) | 0.935660 | + | 0.540204i | 0.0339847 | + | 0.0196211i | ||||
\(759\) | −23.0013 | + | 0.317524i | −0.834895 | + | 0.0115254i | ||||
\(760\) | 5.81594 | + | 10.0735i | 0.210966 | + | 0.365405i | ||||
\(761\) | 10.5435 | 0.382201 | 0.191100 | − | 0.981570i | \(-0.438794\pi\) | ||||
0.191100 | + | 0.981570i | \(0.438794\pi\) | |||||||
\(762\) | 60.1710 | + | 33.6410i | 2.17976 | + | 1.21868i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 35.9248i | − | 1.29971i | ||||||
\(765\) | −33.8775 | + | 62.6075i | −1.22484 | + | 2.26358i | ||||
\(766\) | 23.8452 | + | 13.7671i | 0.861563 | + | 0.497424i | ||||
\(767\) | − | 12.5292i | − | 0.452403i | ||||||
\(768\) | −8.12511 | − | 13.6349i | −0.293190 | − | 0.492008i | ||||
\(769\) | −12.4720 | − | 7.20070i | −0.449751 | − | 0.259664i | 0.257974 | − | 0.966152i | \(-0.416945\pi\) |
−0.707725 | + | 0.706488i | \(0.750278\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.2122 | − | 0.513699i | 1.34016 | − | 0.0185004i | ||||
\(772\) | 30.3199 | − | 52.5156i | 1.09124 | − | 1.89008i | ||||
\(773\) | −10.9386 | + | 18.9462i | −0.393433 | + | 0.681446i | −0.992900 | − | 0.118954i | \(-0.962046\pi\) |
0.599467 | + | 0.800400i | \(0.295379\pi\) | |||||||
\(774\) | −1.01312 | − | 36.6882i | −0.0364160 | − | 1.31873i | ||||
\(775\) | −13.6669 | + | 7.89062i | −0.490931 | + | 0.283439i | ||||
\(776\) | 3.92472 | + | 6.79781i | 0.140889 | + | 0.244027i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.2493 | + | 61.0536i | −1.26375 | + | 2.18888i | ||||
\(779\) | − | 5.42577i | − | 0.194398i | ||||||
\(780\) | −0.451803 | − | 32.7285i | −0.0161771 | − | 1.17187i | ||||
\(781\) | −5.50974 | −0.197154 | ||||||||
\(782\) | −37.3425 | − | 64.6792i | −1.33537 | − | 2.31292i | ||||
\(783\) | 27.9068 | − | 17.6915i | 0.997306 | − | 0.632243i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.0759 | − | 11.0135i | 0.680847 | − | 0.393087i | ||||
\(786\) | 13.0809 | + | 7.31341i | 0.466581 | + | 0.260861i | ||||
\(787\) | 23.9804 | − | 13.8451i | 0.854807 | − | 0.493523i | −0.00746275 | − | 0.999972i | \(-0.502375\pi\) |
0.862270 | + | 0.506449i | \(0.169042\pi\) | |||||||
\(788\) | 8.49253 | − | 4.90316i | 0.302534 | − | 0.174668i | ||||
\(789\) | 0.265132 | + | 19.2061i | 0.00943894 | + | 0.683754i | ||||
\(790\) | −29.8853 | + | 17.2543i | −1.06327 | + | 0.613880i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.72780 | − | 0.158170i | 0.203528 | − | 0.00562033i | ||||
\(793\) | −6.26160 | − | 10.8454i | −0.222356 | − | 0.385132i | ||||
\(794\) | 17.8697 | 0.634171 | ||||||||
\(795\) | −51.5747 | − | 28.8349i | −1.82917 | − | 1.02267i | ||||
\(796\) | − | 51.5930i | − | 1.82867i | ||||||
\(797\) | 21.3285 | − | 36.9420i | 0.755493 | − | 1.30855i | −0.189636 | − | 0.981854i | \(-0.560731\pi\) |
0.945129 | − | 0.326697i | \(-0.105936\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.5271 | − | 30.3578i | −0.620063 | − | 1.07398i | ||||
\(800\) | −41.4820 | + | 23.9496i | −1.46661 | + | 0.846747i | ||||
\(801\) | −1.70082 | − | 2.76661i | −0.0600954 | − | 0.0977533i | ||||
\(802\) | −16.8163 | + | 29.1267i | −0.593805 | + | 1.02850i | ||||
\(803\) | −10.6653 | + | 18.4729i | −0.376372 | + | 0.651895i | ||||
\(804\) | 16.5077 | − | 29.5261i | 0.582183 | − | 1.04130i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.7360 | + | 6.77581i | 0.413384 | + | 0.238668i | ||||
\(807\) | 18.6438 | − | 33.3468i | 0.656295 | − | 1.17386i | ||||
\(808\) | − | 0.378870i | − | 0.0133286i | ||||||
\(809\) | 30.9391 | + | 17.8627i | 1.08776 | + | 0.628019i | 0.932979 | − | 0.359930i | \(-0.117199\pi\) |
0.154781 | + | 0.987949i | \(0.450533\pi\) | |||||||
\(810\) | 55.3146 | + | 27.9855i | 1.94356 | + | 0.983312i | ||||
\(811\) | 5.85377i | 0.205554i | 0.994704 | + | 0.102777i | \(0.0327728\pi\) | ||||
−0.994704 | + | 0.102777i | \(0.967227\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.05915 | − | 4.20658i | 0.247575 | − | 0.147531i | ||||
\(814\) | 9.37226 | 0.328498 | ||||||||
\(815\) | −38.1557 | − | 66.0875i | −1.33653 | − | 2.31495i | ||||
\(816\) | −20.3267 | − | 34.1107i | −0.711578 | − | 1.19411i | ||||
\(817\) | 24.9309 | + | 14.3939i | 0.872223 | + | 0.503578i | ||||
\(818\) | 34.0227 | 1.18958 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.57050 | −0.299295 | ||||||||
\(821\) | −15.2220 | − | 8.78841i | −0.531251 | − | 0.306718i | 0.210275 | − | 0.977642i | \(-0.432564\pi\) |
−0.741526 | + | 0.670925i | \(0.765897\pi\) | |||||||
\(822\) | −11.0887 | + | 19.8334i | −0.386762 | + | 0.691771i | ||||
\(823\) | −15.1893 | − | 26.3086i | −0.529465 | − | 0.917060i | −0.999409 | − | 0.0343640i | \(-0.989059\pi\) |
0.469945 | − | 0.882696i | \(-0.344274\pi\) | |||||||
\(824\) | −0.562464 | −0.0195943 | ||||||||
\(825\) | 0.376724 | + | 27.2898i | 0.0131158 | + | 0.950107i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.4454i | 0.537089i | 0.963267 | + | 0.268545i | \(0.0865426\pi\) | ||||
−0.963267 | + | 0.268545i | \(0.913457\pi\) | |||||||
\(828\) | −29.8987 | + | 18.3807i | −1.03905 | + | 0.638773i | ||||
\(829\) | −35.4158 | − | 20.4473i | −1.23004 | − | 0.710164i | −0.263002 | − | 0.964795i | \(-0.584713\pi\) |
−0.967038 | + | 0.254631i | \(0.918046\pi\) | |||||||
\(830\) | 14.3932i | 0.499595i | ||||||||
\(831\) | −11.1301 | + | 0.153647i | −0.386099 | + | 0.00532994i | ||||
\(832\) | 22.1318 | + | 12.7778i | 0.767281 | + | 0.442990i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.82907 | − | 4.74752i | −0.0979627 | − | 0.164393i | ||||
\(835\) | 26.2858 | − | 45.5283i | 0.909657 | − | 1.57557i | ||||
\(836\) | −15.3000 | + | 26.5004i | −0.529162 | + | 0.916535i | ||||
\(837\) | −11.6974 | + | 7.41560i | −0.404323 | + | 0.256321i | ||||
\(838\) | 2.12647 | − | 1.22772i | 0.0734577 | − | 0.0424108i | ||||
\(839\) | 16.8620 | + | 29.2058i | 0.582140 | + | 1.00830i | 0.995225 | + | 0.0976035i | \(0.0311177\pi\) |
−0.413086 | + | 0.910692i | \(0.635549\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.71808 | − | 9.90401i | 0.197175 | − | 0.341517i | ||||
\(842\) | − | 14.3210i | − | 0.493534i | ||||||
\(843\) | −29.3592 | + | 17.4953i | −1.01118 | + | 0.602568i | ||||
\(844\) | 57.6356 | 1.98390 | ||||||||
\(845\) | 11.6487 | + | 20.1761i | 0.400726 | + | 0.694079i | ||||
\(846\) | −26.0053 | + | 15.9872i | −0.894080 | + | 0.549650i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 28.5440 | − | 16.4799i | 0.980206 | − | 0.565922i | ||||
\(849\) | −8.33419 | + | 4.96638i | −0.286029 | + | 0.170446i | ||||
\(850\) | −76.7381 | + | 44.3048i | −2.63210 | + | 1.51964i | ||||
\(851\) | −7.30190 | + | 4.21575i | −0.250306 | + | 0.144514i | ||||
\(852\) | −7.22133 | + | 4.30322i | −0.247399 | + | 0.147426i | ||||
\(853\) | −37.6715 | + | 21.7497i | −1.28985 | + | 0.744694i | −0.978627 | − | 0.205643i | \(-0.934071\pi\) |
−0.311221 | + | 0.950337i | \(0.600738\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −41.4219 | + | 25.4648i | −1.41660 | + | 0.870878i | ||||
\(856\) | −1.92008 | − | 3.32568i | −0.0656271 | − | 0.113669i | ||||
\(857\) | −8.43068 | −0.287986 | −0.143993 | − | 0.989579i | \(-0.545994\pi\) | ||||
−0.143993 | + | 0.989579i | \(0.545994\pi\) | |||||||
\(858\) | 20.1328 | − | 11.9972i | 0.687324 | − | 0.409579i | ||||
\(859\) | 2.40096i | 0.0819197i | 0.999161 | + | 0.0409598i | \(0.0130416\pi\) | ||||
−0.999161 | + | 0.0409598i | \(0.986958\pi\) | |||||||
\(860\) | 22.7364 | − | 39.3807i | 0.775306 | − | 1.34287i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.845356 | + | 1.46420i | 0.0287929 | + | 0.0498708i | ||||
\(863\) | −8.12017 | + | 4.68818i | −0.276414 | + | 0.159588i | −0.631799 | − | 0.775132i | \(-0.717683\pi\) |
0.355385 | + | 0.934720i | \(0.384350\pi\) | |||||||
\(864\) | −35.5041 | + | 22.5079i | −1.20787 | + | 0.765733i | ||||
\(865\) | 30.8356 | − | 53.4089i | 1.04844 | − | 1.81596i | ||||
\(866\) | 8.95898 | − | 15.5174i | 0.304439 | − | 0.527303i | ||||
\(867\) | −30.6402 | − | 51.4179i | −1.04059 | − | 1.74625i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.5472 | − | 6.66678i | −0.391712 | − | 0.226155i | ||||
\(870\) | 75.8562 | − | 1.04716i | 2.57176 | − | 0.0355022i | ||||
\(871\) | − | 20.3214i | − | 0.688566i | ||||||
\(872\) | 3.70751 | + | 2.14053i | 0.125552 | + | 0.0724877i | ||||
\(873\) | −27.9524 | + | 17.1842i | −0.946045 | + | 0.581596i | ||||
\(874\) | − | 51.0137i | − | 1.72557i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.449220 | + | 32.5413i | 0.0151777 | + | 1.09947i | ||||
\(877\) | 3.43084 | 0.115851 | 0.0579256 | − | 0.998321i | \(-0.481551\pi\) | ||||
0.0579256 | + | 0.998321i | \(0.481551\pi\) | |||||||
\(878\) | −28.7568 | − | 49.8082i | −0.970493 | − | 1.68094i | ||||
\(879\) | 25.4235 | − | 45.4730i | 0.857513 | − | 1.53377i | ||||
\(880\) | −24.3183 | − | 14.0402i | −0.819770 | − | 0.473295i | ||||
\(881\) | −43.4962 | −1.46542 | −0.732712 | − | 0.680539i | \(-0.761746\pi\) | ||||
−0.732712 | + | 0.680539i | \(0.761746\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.6074 | 1.66942 | 0.834711 | − | 0.550688i | \(-0.185635\pi\) | ||||
0.834711 | + | 0.550688i | \(0.185635\pi\) | |||||||
\(884\) | 35.5596 | + | 20.5303i | 1.19600 | + | 0.690510i | ||||
\(885\) | 15.0500 | + | 25.2557i | 0.505900 | + | 0.848961i | ||||
\(886\) | −12.7619 | − | 22.1043i | −0.428745 | − | 0.742607i | ||||
\(887\) | −35.1532 | −1.18033 | −0.590164 | − | 0.807283i | \(-0.700937\pi\) | ||||
−0.590164 | + | 0.807283i | \(0.700937\pi\) | |||||||
\(888\) | 1.80417 | − | 1.07511i | 0.0605441 | − | 0.0360785i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 7.45638i | − | 0.249938i | ||||||
\(891\) | 1.32185 | + | 23.9159i | 0.0442838 | + | 0.801212i | ||||
\(892\) | −17.1583 | − | 9.90634i | −0.574502 | − | 0.331689i | ||||
\(893\) | − | 23.9438i | − | 0.801248i | ||||||
\(894\) | 9.42201 | − | 16.8524i | 0.315119 | − | 0.563629i | ||||
\(895\) | 63.0500 | + | 36.4019i | 2.10753 | + | 1.21678i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.2889 | + | 18.4030i | −0.343537 | + | 0.614458i | ||||
\(898\) | −22.9443 | + | 39.7407i | −0.765662 | + | 1.32617i | ||||
\(899\) | −8.47464 | + | 14.6785i | −0.282645 | + | 0.489556i | ||||
\(900\) | 21.8076 | + | 35.4730i | 0.726920 | + | 1.18243i | ||||
\(901\) | 64.1932 | − | 37.0620i | 2.13859 | − | 1.23471i | ||||
\(902\) | −3.06832 | − | 5.31448i | −0.102164 | − | 0.176953i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.14446 | − | 7.17842i | 0.137843 | − | 0.238751i | ||||
\(905\) | 58.4876i | 1.94419i | ||||||||
\(906\) | −36.1985 | − | 20.2382i | −1.20262 | − | 0.672370i | ||||
\(907\) | 38.1633 | 1.26719 | 0.633596 | − | 0.773664i | \(-0.281578\pi\) | ||||
0.633596 | + | 0.773664i | \(0.281578\pi\) | |||||||
\(908\) | 6.83310 | + | 11.8353i | 0.226765 | + | 0.392768i | ||||
\(909\) | 1.58314 | − | 0.0437176i | 0.0525095 | − | 0.00145002i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.9027 | + | 23.0378i | −1.32203 | + | 0.763277i | −0.984053 | − | 0.177876i | \(-0.943077\pi\) |
−0.337981 | + | 0.941153i | \(0.609744\pi\) | |||||||
\(912\) | −0.374380 | − | 27.1200i | −0.0123970 | − | 0.898031i | ||||
\(913\) | −4.81623 | + | 2.78065i | −0.159394 | + | 0.0920261i | ||||
\(914\) | 43.6028 | − | 25.1741i | 1.44225 | − | 0.832686i | ||||
\(915\) | 25.6493 | + | 14.3402i | 0.847939 | + | 0.474074i | ||||
\(916\) | 9.74163 | − | 5.62433i | 0.321872 | − | 0.185833i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −65.6796 | + | 41.6376i | −2.16775 | + | 1.37425i | ||||
\(919\) | −5.27574 | − | 9.13785i | −0.174031 | − | 0.301430i | 0.765795 | − | 0.643085i | \(-0.222346\pi\) |
−0.939825 | + | 0.341655i | \(0.889013\pi\) | |||||||
\(920\) | −11.8353 | −0.390198 | ||||||||
\(921\) | 0.560636 | + | 40.6122i | 0.0184736 | + | 1.33822i | ||||
\(922\) | 68.3229i | 2.25009i | ||||||||
\(923\) | −2.52499 | + | 4.37340i | −0.0831109 | + | 0.143952i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.00175 | + | 8.66328i | 0.164456 | + | 0.284847i | ||||
\(926\) | −56.9168 | + | 32.8609i | −1.87040 | + | 1.07988i | ||||
\(927\) | −0.0649024 | − | 2.35030i | −0.00213167 | − | 0.0771941i | ||||
\(928\) | −25.7223 | + | 44.5523i | −0.844375 | + | 1.46250i | ||||
\(929\) | 26.4514 | − | 45.8152i | 0.867843 | − | 1.50315i | 0.00364718 | − | 0.999993i | \(-0.498839\pi\) |
0.864196 | − | 0.503155i | \(-0.167828\pi\) | |||||||
\(930\) | −31.7960 | + | 0.438931i | −1.04263 | + | 0.0143931i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −46.7896 | − | 27.0140i | −1.53265 | − | 0.884873i | ||||
\(933\) | 14.8160 | + | 24.8631i | 0.485055 | + | 0.813981i | ||||
\(934\) | 69.1010i | 2.26106i | ||||||||
\(935\) | −54.6899 | − | 31.5752i | −1.78855 | − | 1.03262i | ||||
\(936\) | 2.49937 | − | 4.61897i | 0.0816944 | − | 0.150976i | ||||
\(937\) | − | 10.3265i | − | 0.337353i | −0.985671 | − | 0.168676i | \(-0.946051\pi\) | ||
0.985671 | − | 0.168676i | \(-0.0539493\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.4769 | − | 12.5666i | −0.733507 | − | 0.410096i | ||||
\(940\) | −37.8214 | −1.23360 | ||||||||
\(941\) | −0.505336 | − | 0.875268i | −0.0164735 | − | 0.0285329i | 0.857671 | − | 0.514199i | \(-0.171911\pi\) |
−0.874145 | + | 0.485666i | \(0.838577\pi\) | |||||||
\(942\) | 24.0607 | − | 0.332148i | 0.783940 | − | 0.0108220i | ||||
\(943\) | 4.78103 | + | 2.76033i | 0.155692 | + | 0.0898887i | ||||
\(944\) | −16.3995 | −0.533758 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.5594 | 1.05860 | ||||||||
\(947\) | −9.36454 | − | 5.40662i | −0.304307 | − | 0.175692i | 0.340069 | − | 0.940400i | \(-0.389549\pi\) |
−0.644376 | + | 0.764709i | \(0.722883\pi\) | |||||||
\(948\) | −20.3412 | + | 0.280802i | −0.660652 | + | 0.00912003i | ||||
\(949\) | 9.77535 | + | 16.9314i | 0.317321 | + | 0.549616i | ||||
\(950\) | −60.5249 | −1.96369 | ||||||||
\(951\) | −3.43483 | − | 1.92038i | −0.111382 | − | 0.0622725i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 26.7466i | − | 0.866408i | −0.901296 | − | 0.433204i | \(-0.857383\pi\) | ||
0.901296 | − | 0.433204i | \(-0.142617\pi\) | |||||||
\(954\) | −33.8058 | − | 54.9896i | −1.09450 | − | 1.78036i | ||||
\(955\) | 43.8564 | + | 25.3205i | 1.41916 | + | 0.819353i | ||||
\(956\) | 16.0246i | 0.518274i | ||||||||
\(957\) | 15.0052 | + | 25.1806i | 0.485049 | + | 0.813972i | ||||
\(958\) | 41.1454 | + | 23.7553i | 1.32935 | + | 0.767500i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −59.9607 | + | 0.827734i | −1.93522 | + | 0.0267150i | ||||
\(961\) | −11.9478 | + | 20.6941i | −0.385411 | + | 0.667552i | ||||
\(962\) | 4.29509 | − | 7.43931i | 0.138479 | − | 0.239853i | ||||
\(963\) | 13.6751 | − | 8.40699i | 0.440674 | − | 0.270911i | ||||
\(964\) | 9.12204 | − | 5.26661i | 0.293801 | − | 0.169626i | ||||
\(965\) | 42.7402 | + | 74.0281i | 1.37585 | + | 2.38305i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.62313 | − | 2.81134i | 0.0521962 | − | 0.0904065i | −0.838747 | − | 0.544522i | \(-0.816711\pi\) |
0.890943 | + | 0.454115i | \(0.150045\pi\) | |||||||
\(968\) | − | 2.81119i | − | 0.0903549i | ||||||
\(969\) | −0.841950 | − | 60.9906i | −0.0270473 | − | 1.95930i | ||||
\(970\) | −75.3354 | −2.41887 | ||||||||
\(971\) | −4.41423 | − | 7.64567i | −0.141659 | − | 0.245361i | 0.786462 | − | 0.617638i | \(-0.211910\pi\) |
−0.928122 | + | 0.372277i | \(0.878577\pi\) | |||||||
\(972\) | 20.4113 | + | 30.3129i | 0.654692 | + | 0.972286i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.92997 | + | 2.84632i | −0.157966 | + | 0.0912019i | ||||
\(975\) | 21.8341 | + | 12.2072i | 0.699251 | + | 0.390944i | ||||
\(976\) | −14.1956 | + | 8.19584i | −0.454390 | + | 0.262342i | ||||
\(977\) | −36.2748 | + | 20.9433i | −1.16053 | + | 0.670035i | −0.951432 | − | 0.307859i | \(-0.900388\pi\) |
−0.209102 | + | 0.977894i | \(0.567054\pi\) | |||||||
\(978\) | −1.15071 | − | 83.3573i | −0.0367958 | − | 2.66547i | ||||
\(979\) | 2.49504 | − | 1.44051i | 0.0797419 | − | 0.0460390i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.51661 | + | 15.7392i | −0.271914 | + | 0.502513i | ||||
\(982\) | −26.0861 | − | 45.1825i | −0.832441 | − | 1.44183i | ||||
\(983\) | −4.70388 | −0.150031 | −0.0750153 | − | 0.997182i | \(-0.523901\pi\) | ||||
−0.0750153 | + | 0.997182i | \(0.523901\pi\) | |||||||
\(984\) | −1.20029 | − | 0.671071i | −0.0382639 | − | 0.0213929i | ||||
\(985\) | 13.8234i | 0.440450i | ||||||||
\(986\) | −47.5840 | + | 82.4179i | −1.51538 | + | 2.62472i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.0233 | + | 24.2890i | 0.446139 | + | 0.772736i | ||||
\(989\) | −25.3669 | + | 14.6456i | −0.806621 | + | 0.465703i | ||||
\(990\) | −26.1718 | + | 48.3669i | −0.831793 | + | 1.53720i | ||||
\(991\) | −18.9327 | + | 32.7924i | −0.601418 | + | 1.04169i | 0.391189 | + | 0.920310i | \(0.372064\pi\) |
−0.992607 | + | 0.121375i | \(0.961269\pi\) | |||||||
\(992\) | 10.7818 | − | 18.6746i | 0.342322 | − | 0.592919i | ||||
\(993\) | 10.0996 | − | 18.0643i | 0.320500 | − | 0.573254i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 62.9840 | + | 36.3638i | 1.99673 | + | 1.15281i | ||||
\(996\) | −4.14063 | + | 7.40603i | −0.131201 | + | 0.234669i | ||||
\(997\) | − | 3.67583i | − | 0.116415i | −0.998305 | − | 0.0582073i | \(-0.981462\pi\) | ||
0.998305 | − | 0.0582073i | \(-0.0185384\pi\) | |||||||
\(998\) | −15.5228 | − | 8.96211i | −0.491367 | − | 0.283691i | ||||
\(999\) | 4.70064 | + | 7.41484i | 0.148722 | + | 0.234595i |
(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.s.d.374.4 | 48 | ||
3.2 | odd | 2 | 1323.2.s.d.962.22 | 48 | |||
7.2 | even | 3 | 441.2.i.d.68.21 | 48 | |||
7.3 | odd | 6 | 441.2.o.e.293.22 | yes | 48 | ||
7.4 | even | 3 | 441.2.o.e.293.21 | yes | 48 | ||
7.5 | odd | 6 | 441.2.i.d.68.22 | 48 | |||
7.6 | odd | 2 | inner | 441.2.s.d.374.3 | 48 | ||
9.2 | odd | 6 | 441.2.i.d.227.4 | 48 | |||
9.7 | even | 3 | 1323.2.i.d.521.16 | 48 | |||
21.2 | odd | 6 | 1323.2.i.d.1097.23 | 48 | |||
21.5 | even | 6 | 1323.2.i.d.1097.16 | 48 | |||
21.11 | odd | 6 | 1323.2.o.e.881.3 | 48 | |||
21.17 | even | 6 | 1323.2.o.e.881.4 | 48 | |||
21.20 | even | 2 | 1323.2.s.d.962.21 | 48 | |||
63.2 | odd | 6 | inner | 441.2.s.d.362.3 | 48 | ||
63.11 | odd | 6 | 441.2.o.e.146.22 | yes | 48 | ||
63.16 | even | 3 | 1323.2.s.d.656.21 | 48 | |||
63.20 | even | 6 | 441.2.i.d.227.3 | 48 | |||
63.25 | even | 3 | 1323.2.o.e.440.4 | 48 | |||
63.34 | odd | 6 | 1323.2.i.d.521.23 | 48 | |||
63.38 | even | 6 | 441.2.o.e.146.21 | ✓ | 48 | ||
63.47 | even | 6 | inner | 441.2.s.d.362.4 | 48 | ||
63.52 | odd | 6 | 1323.2.o.e.440.3 | 48 | |||
63.61 | odd | 6 | 1323.2.s.d.656.22 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.21 | 48 | 7.2 | even | 3 | |||
441.2.i.d.68.22 | 48 | 7.5 | odd | 6 | |||
441.2.i.d.227.3 | 48 | 63.20 | even | 6 | |||
441.2.i.d.227.4 | 48 | 9.2 | odd | 6 | |||
441.2.o.e.146.21 | ✓ | 48 | 63.38 | even | 6 | ||
441.2.o.e.146.22 | yes | 48 | 63.11 | odd | 6 | ||
441.2.o.e.293.21 | yes | 48 | 7.4 | even | 3 | ||
441.2.o.e.293.22 | yes | 48 | 7.3 | odd | 6 | ||
441.2.s.d.362.3 | 48 | 63.2 | odd | 6 | inner | ||
441.2.s.d.362.4 | 48 | 63.47 | even | 6 | inner | ||
441.2.s.d.374.3 | 48 | 7.6 | odd | 2 | inner | ||
441.2.s.d.374.4 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.i.d.521.16 | 48 | 9.7 | even | 3 | |||
1323.2.i.d.521.23 | 48 | 63.34 | odd | 6 | |||
1323.2.i.d.1097.16 | 48 | 21.5 | even | 6 | |||
1323.2.i.d.1097.23 | 48 | 21.2 | odd | 6 | |||
1323.2.o.e.440.3 | 48 | 63.52 | odd | 6 | |||
1323.2.o.e.440.4 | 48 | 63.25 | even | 3 | |||
1323.2.o.e.881.3 | 48 | 21.11 | odd | 6 | |||
1323.2.o.e.881.4 | 48 | 21.17 | even | 6 | |||
1323.2.s.d.656.21 | 48 | 63.16 | even | 3 | |||
1323.2.s.d.656.22 | 48 | 63.61 | odd | 6 | |||
1323.2.s.d.962.21 | 48 | 21.20 | even | 2 | |||
1323.2.s.d.962.22 | 48 | 3.2 | odd | 2 |