Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,3,Mod(263,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("294.263");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.h (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: | \(8.01091977219\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 263.2 | ||
Root | \(1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 294.263 |
Dual form | 294.3.h.b.275.2 |
$q$-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 \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(199\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | − | 0.707107i | 0.612372 | − | 0.353553i | ||||
\(3\) | −2.94949 | − | 0.548188i | −0.983163 | − | 0.182729i | ||||
\(4\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(5\) | 7.34847 | − | 4.24264i | 1.46969 | − | 0.848528i | 0.470272 | − | 0.882522i | \(-0.344156\pi\) |
0.999422 | + | 0.0339935i | \(0.0108226\pi\) | |||||||
\(6\) | −4.00000 | + | 1.41421i | −0.666667 | + | 0.235702i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | 8.39898 | + | 3.23375i | 0.933220 | + | 0.359306i | ||||
\(10\) | 6.00000 | − | 10.3923i | 0.600000 | − | 1.03923i | ||||
\(11\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | −3.89898 | + | 4.56048i | −0.324915 | + | 0.380040i | ||||
\(13\) | 1.00000 | 0.0769231 | 0.0384615 | − | 0.999260i | \(-0.487754\pi\) | ||||
0.0384615 | + | 0.999260i | \(0.487754\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −24.0000 | + | 8.48528i | −1.60000 | + | 0.565685i | ||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | 7.34847 | + | 4.24264i | 0.432263 | + | 0.249567i | 0.700310 | − | 0.713839i | \(-0.253045\pi\) |
−0.268047 | + | 0.963406i | \(0.586378\pi\) | |||||||
\(18\) | 12.5732 | − | 1.97846i | 0.698512 | − | 0.109914i | ||||
\(19\) | −15.5000 | − | 26.8468i | −0.815789 | − | 1.41299i | −0.908760 | − | 0.417320i | \(-0.862969\pi\) |
0.0929702 | − | 0.995669i | \(-0.470364\pi\) | |||||||
\(20\) | − | 16.9706i | − | 0.848528i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.34847 | − | 4.24264i | 0.319499 | − | 0.184463i | −0.331670 | − | 0.943395i | \(-0.607612\pi\) |
0.651169 | + | 0.758933i | \(0.274279\pi\) | |||||||
\(24\) | −1.55051 | + | 8.34242i | −0.0646046 | + | 0.347601i | ||||
\(25\) | 23.5000 | − | 40.7032i | 0.940000 | − | 1.62813i | ||||
\(26\) | 1.22474 | − | 0.707107i | 0.0471056 | − | 0.0271964i | ||||
\(27\) | −23.0000 | − | 14.1421i | −0.851852 | − | 0.523783i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 16.9706i | − | 0.585192i | −0.956236 | − | 0.292596i | \(-0.905481\pi\) | ||
0.956236 | − | 0.292596i | \(-0.0945191\pi\) | |||||||
\(30\) | −23.3939 | + | 27.3629i | −0.779796 | + | 0.912096i | ||||
\(31\) | −3.50000 | + | 6.06218i | −0.112903 | + | 0.195554i | −0.916940 | − | 0.399026i | \(-0.869348\pi\) |
0.804036 | + | 0.594580i | \(0.202682\pi\) | |||||||
\(32\) | −4.89898 | − | 2.82843i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.0000 | 0.352941 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 14.0000 | − | 11.3137i | 0.388889 | − | 0.314270i | ||||
\(37\) | 0.500000 | + | 0.866025i | 0.0135135 | + | 0.0234061i | 0.872703 | − | 0.488251i | \(-0.162365\pi\) |
−0.859190 | + | 0.511657i | \(0.829032\pi\) | |||||||
\(38\) | −37.9671 | − | 21.9203i | −0.999134 | − | 0.576850i | ||||
\(39\) | −2.94949 | − | 0.548188i | −0.0756279 | − | 0.0140561i | ||||
\(40\) | −12.0000 | − | 20.7846i | −0.300000 | − | 0.519615i | ||||
\(41\) | 33.9411i | 0.827832i | 0.910315 | + | 0.413916i | \(0.135839\pi\) | ||||
−0.910315 | + | 0.413916i | \(0.864161\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −31.0000 | −0.720930 | −0.360465 | − | 0.932773i | \(-0.617382\pi\) | ||||
−0.360465 | + | 0.932773i | \(0.617382\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 75.4393 | − | 11.8707i | 1.67643 | − | 0.263794i | ||||
\(46\) | 6.00000 | − | 10.3923i | 0.130435 | − | 0.225920i | ||||
\(47\) | 36.7423 | − | 21.2132i | 0.781752 | − | 0.451345i | −0.0552988 | − | 0.998470i | \(-0.517611\pi\) |
0.837051 | + | 0.547125i | \(0.184278\pi\) | |||||||
\(48\) | 4.00000 | + | 11.3137i | 0.0833333 | + | 0.235702i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 66.4680i | − | 1.32936i | ||||||
\(51\) | −19.3485 | − | 16.5420i | −0.379382 | − | 0.324352i | ||||
\(52\) | 1.00000 | − | 1.73205i | 0.0192308 | − | 0.0333087i | ||||
\(53\) | 22.0454 | + | 12.7279i | 0.415951 | + | 0.240149i | 0.693344 | − | 0.720607i | \(-0.256137\pi\) |
−0.277392 | + | 0.960757i | \(0.589470\pi\) | |||||||
\(54\) | −38.1691 | − | 1.05705i | −0.706836 | − | 0.0195750i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 31.0000 | + | 87.6812i | 0.543860 | + | 1.53827i | ||||
\(58\) | −12.0000 | − | 20.7846i | −0.206897 | − | 0.358355i | ||||
\(59\) | 7.34847 | + | 4.24264i | 0.124550 | + | 0.0719092i | 0.560981 | − | 0.827829i | \(-0.310424\pi\) |
−0.436430 | + | 0.899738i | \(0.643757\pi\) | |||||||
\(60\) | −9.30306 | + | 50.0545i | −0.155051 | + | 0.834242i | ||||
\(61\) | 25.0000 | + | 43.3013i | 0.409836 | + | 0.709857i | 0.994871 | − | 0.101151i | \(-0.0322526\pi\) |
−0.585035 | + | 0.811008i | \(0.698919\pi\) | |||||||
\(62\) | 9.89949i | 0.159669i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 7.34847 | − | 4.24264i | 0.113053 | − | 0.0652714i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −32.5000 | + | 56.2917i | −0.485075 | + | 0.840174i | −0.999853 | − | 0.0171494i | \(-0.994541\pi\) |
0.514778 | + | 0.857323i | \(0.327874\pi\) | |||||||
\(68\) | 14.6969 | − | 8.48528i | 0.216131 | − | 0.124784i | ||||
\(69\) | −24.0000 | + | 8.48528i | −0.347826 | + | 0.122975i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 59.3970i | 0.836577i | 0.908314 | + | 0.418289i | \(0.137370\pi\) | ||||
−0.908314 | + | 0.418289i | \(0.862630\pi\) | |||||||
\(72\) | 9.14643 | − | 23.7559i | 0.127034 | − | 0.329943i | ||||
\(73\) | −48.5000 | + | 84.0045i | −0.664384 | + | 1.15075i | 0.315068 | + | 0.949069i | \(0.397973\pi\) |
−0.979452 | + | 0.201677i | \(0.935361\pi\) | |||||||
\(74\) | 1.22474 | + | 0.707107i | 0.0165506 | + | 0.00955550i | ||||
\(75\) | −91.6260 | + | 107.171i | −1.22168 | + | 1.42895i | ||||
\(76\) | −62.0000 | −0.815789 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.00000 | + | 1.41421i | −0.0512821 | + | 0.0181309i | ||||
\(79\) | 51.5000 | + | 89.2006i | 0.651899 | + | 1.12912i | 0.982662 | + | 0.185408i | \(0.0593606\pi\) |
−0.330763 | + | 0.943714i | \(0.607306\pi\) | |||||||
\(80\) | −29.3939 | − | 16.9706i | −0.367423 | − | 0.212132i | ||||
\(81\) | 60.0857 | + | 54.3204i | 0.741799 | + | 0.670622i | ||||
\(82\) | 24.0000 | + | 41.5692i | 0.292683 | + | 0.506942i | ||||
\(83\) | 42.4264i | 0.511162i | 0.966788 | + | 0.255581i | \(0.0822667\pi\) | ||||
−0.966788 | + | 0.255581i | \(0.917733\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 72.0000 | 0.847059 | ||||||||
\(86\) | −37.9671 | + | 21.9203i | −0.441478 | + | 0.254887i | ||||
\(87\) | −9.30306 | + | 50.0545i | −0.106932 | + | 0.575339i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 102.879 | − | 59.3970i | 1.15594 | − | 0.667382i | 0.205612 | − | 0.978634i | \(-0.434082\pi\) |
0.950327 | + | 0.311252i | \(0.100748\pi\) | |||||||
\(90\) | 84.0000 | − | 67.8823i | 0.933333 | − | 0.754247i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 16.9706i | − | 0.184463i | ||||||
\(93\) | 13.6464 | − | 15.9617i | 0.146736 | − | 0.171631i | ||||
\(94\) | 30.0000 | − | 51.9615i | 0.319149 | − | 0.552782i | ||||
\(95\) | −227.803 | − | 131.522i | −2.39792 | − | 1.38444i | ||||
\(96\) | 12.8990 | + | 11.0280i | 0.134364 | + | 0.114875i | ||||
\(97\) | 166.000 | 1.71134 | 0.855670 | − | 0.517522i | \(-0.173145\pi\) | ||||
0.855670 | + | 0.517522i | \(0.173145\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −47.0000 | − | 81.4064i | −0.470000 | − | 0.814064i | ||||
\(101\) | −117.576 | − | 67.8823i | −1.16411 | − | 0.672101i | −0.211827 | − | 0.977307i | \(-0.567941\pi\) |
−0.952286 | + | 0.305206i | \(0.901275\pi\) | |||||||
\(102\) | −35.3939 | − | 6.57826i | −0.346999 | − | 0.0644927i | ||||
\(103\) | 32.5000 | + | 56.2917i | 0.315534 | + | 0.546521i | 0.979551 | − | 0.201197i | \(-0.0644830\pi\) |
−0.664017 | + | 0.747718i | \(0.731150\pi\) | |||||||
\(104\) | − | 2.82843i | − | 0.0271964i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 36.0000 | 0.339623 | ||||||||
\(107\) | 139.621 | − | 80.6102i | 1.30487 | − | 0.753366i | 0.323634 | − | 0.946183i | \(-0.395096\pi\) |
0.981235 | + | 0.192816i | \(0.0617622\pi\) | |||||||
\(108\) | −47.4949 | + | 25.6950i | −0.439768 | + | 0.237917i | ||||
\(109\) | −83.5000 | + | 144.626i | −0.766055 | + | 1.32685i | 0.173632 | + | 0.984811i | \(0.444450\pi\) |
−0.939687 | + | 0.342036i | \(0.888884\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.00000 | − | 2.82843i | −0.00900901 | − | 0.0254813i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 161.220i | − | 1.42673i | −0.700793 | − | 0.713364i | \(-0.747170\pi\) | ||
0.700793 | − | 0.713364i | \(-0.252830\pi\) | |||||||
\(114\) | 99.9671 | + | 85.4668i | 0.876904 | + | 0.749709i | ||||
\(115\) | 36.0000 | − | 62.3538i | 0.313043 | − | 0.542207i | ||||
\(116\) | −29.3939 | − | 16.9706i | −0.253395 | − | 0.146298i | ||||
\(117\) | 8.39898 | + | 3.23375i | 0.0717861 | + | 0.0276389i | ||||
\(118\) | 12.0000 | 0.101695 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 24.0000 | + | 67.8823i | 0.200000 | + | 0.565685i | ||||
\(121\) | −60.5000 | − | 104.789i | −0.500000 | − | 0.866025i | ||||
\(122\) | 61.2372 | + | 35.3553i | 0.501945 | + | 0.289798i | ||||
\(123\) | 18.6061 | − | 100.109i | 0.151269 | − | 0.813894i | ||||
\(124\) | 7.00000 | + | 12.1244i | 0.0564516 | + | 0.0977771i | ||||
\(125\) | − | 186.676i | − | 1.49341i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 113.000 | 0.889764 | 0.444882 | − | 0.895589i | \(-0.353246\pi\) | ||||
0.444882 | + | 0.895589i | \(0.353246\pi\) | |||||||
\(128\) | −9.79796 | + | 5.65685i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 91.4342 | + | 16.9938i | 0.708792 | + | 0.131735i | ||||
\(130\) | 6.00000 | − | 10.3923i | 0.0461538 | − | 0.0799408i | ||||
\(131\) | −73.4847 | + | 42.4264i | −0.560952 | + | 0.323866i | −0.753527 | − | 0.657416i | \(-0.771649\pi\) |
0.192576 | + | 0.981282i | \(0.438316\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 91.9239i | 0.685999i | ||||||||
\(135\) | −229.015 | − | 6.34231i | −1.69641 | − | 0.0469801i | ||||
\(136\) | 12.0000 | − | 20.7846i | 0.0882353 | − | 0.152828i | ||||
\(137\) | 161.666 | + | 93.3381i | 1.18005 | + | 0.681300i | 0.956025 | − | 0.293284i | \(-0.0947483\pi\) |
0.224021 | + | 0.974584i | \(0.428082\pi\) | |||||||
\(138\) | −23.3939 | + | 27.3629i | −0.169521 | + | 0.198282i | ||||
\(139\) | −113.000 | −0.812950 | −0.406475 | − | 0.913662i | \(-0.633242\pi\) | ||||
−0.406475 | + | 0.913662i | \(0.633242\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −120.000 | + | 42.4264i | −0.851064 | + | 0.300897i | ||||
\(142\) | 42.0000 | + | 72.7461i | 0.295775 | + | 0.512297i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.59592 | − | 35.5624i | −0.0388605 | − | 0.246961i | ||||
\(145\) | −72.0000 | − | 124.708i | −0.496552 | − | 0.860053i | ||||
\(146\) | 137.179i | 0.939580i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.00000 | 0.0135135 | ||||||||
\(149\) | −58.7878 | + | 33.9411i | −0.394549 | + | 0.227793i | −0.684129 | − | 0.729361i | \(-0.739818\pi\) |
0.289580 | + | 0.957154i | \(0.406484\pi\) | |||||||
\(150\) | −36.4370 | + | 196.047i | −0.242913 | + | 1.30698i | ||||
\(151\) | 29.0000 | − | 50.2295i | 0.192053 | − | 0.332646i | −0.753877 | − | 0.657015i | \(-0.771819\pi\) |
0.945930 | + | 0.324370i | \(0.105152\pi\) | |||||||
\(152\) | −75.9342 | + | 43.8406i | −0.499567 | + | 0.288425i | ||||
\(153\) | 48.0000 | + | 59.3970i | 0.313725 | + | 0.388215i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 59.3970i | 0.383206i | ||||||||
\(156\) | −3.89898 | + | 4.56048i | −0.0249935 | + | 0.0292338i | ||||
\(157\) | −59.0000 | + | 102.191i | −0.375796 | + | 0.650898i | −0.990446 | − | 0.137902i | \(-0.955964\pi\) |
0.614650 | + | 0.788800i | \(0.289297\pi\) | |||||||
\(158\) | 126.149 | + | 72.8320i | 0.798410 | + | 0.460962i | ||||
\(159\) | −58.0454 | − | 49.6259i | −0.365065 | − | 0.312113i | ||||
\(160\) | −48.0000 | −0.300000 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 112.000 | + | 24.0416i | 0.691358 | + | 0.148405i | ||||
\(163\) | 53.0000 | + | 91.7987i | 0.325153 | + | 0.563182i | 0.981543 | − | 0.191240i | \(-0.0612507\pi\) |
−0.656390 | + | 0.754422i | \(0.727917\pi\) | |||||||
\(164\) | 58.7878 | + | 33.9411i | 0.358462 | + | 0.206958i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 30.0000 | + | 51.9615i | 0.180723 | + | 0.313021i | ||||
\(167\) | 144.250i | 0.863771i | 0.901928 | + | 0.431886i | \(0.142152\pi\) | ||||
−0.901928 | + | 0.431886i | \(0.857848\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −168.000 | −0.994083 | ||||||||
\(170\) | 88.1816 | − | 50.9117i | 0.518715 | − | 0.299481i | ||||
\(171\) | −43.3684 | − | 275.609i | −0.253616 | − | 1.61175i | ||||
\(172\) | −31.0000 | + | 53.6936i | −0.180233 | + | 0.312172i | ||||
\(173\) | 66.1362 | − | 38.1838i | 0.382290 | − | 0.220715i | −0.296524 | − | 0.955025i | \(-0.595827\pi\) |
0.678814 | + | 0.734310i | \(0.262494\pi\) | |||||||
\(174\) | 24.0000 | + | 67.8823i | 0.137931 | + | 0.390128i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.3485 | − | 16.5420i | −0.109313 | − | 0.0934575i | ||||
\(178\) | 84.0000 | − | 145.492i | 0.471910 | − | 0.817372i | ||||
\(179\) | 139.621 | + | 80.6102i | 0.780005 | + | 0.450336i | 0.836432 | − | 0.548071i | \(-0.184637\pi\) |
−0.0564270 | + | 0.998407i | \(0.517971\pi\) | |||||||
\(180\) | 54.8786 | − | 142.535i | 0.304881 | − | 0.791863i | ||||
\(181\) | −215.000 | −1.18785 | −0.593923 | − | 0.804522i | \(-0.702421\pi\) | ||||
−0.593923 | + | 0.804522i | \(0.702421\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −50.0000 | − | 141.421i | −0.273224 | − | 0.772794i | ||||
\(184\) | −12.0000 | − | 20.7846i | −0.0652174 | − | 0.112960i | ||||
\(185\) | 7.34847 | + | 4.24264i | 0.0397215 | + | 0.0229332i | ||||
\(186\) | 5.42679 | − | 29.1985i | 0.0291763 | − | 0.156981i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 84.8528i | − | 0.451345i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −372.000 | −1.95789 | ||||||||
\(191\) | −154.318 | + | 89.0955i | −0.807947 | + | 0.466468i | −0.846242 | − | 0.532798i | \(-0.821141\pi\) |
0.0382955 | + | 0.999266i | \(0.487807\pi\) | |||||||
\(192\) | 23.5959 | + | 4.38551i | 0.122895 | + | 0.0228412i | ||||
\(193\) | 48.5000 | − | 84.0045i | 0.251295 | − | 0.435256i | −0.712587 | − | 0.701583i | \(-0.752477\pi\) |
0.963883 | + | 0.266327i | \(0.0858101\pi\) | |||||||
\(194\) | 203.308 | − | 117.380i | 1.04798 | − | 0.605050i | ||||
\(195\) | −24.0000 | + | 8.48528i | −0.123077 | + | 0.0435143i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 364.867i | − | 1.85212i | −0.377380 | − | 0.926059i | \(-0.623175\pi\) | ||
0.377380 | − | 0.926059i | \(-0.376825\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −53.0000 | + | 91.7987i | −0.266332 | + | 0.461300i | −0.967912 | − | 0.251291i | \(-0.919145\pi\) |
0.701580 | + | 0.712591i | \(0.252478\pi\) | |||||||
\(200\) | −115.126 | − | 66.4680i | −0.575630 | − | 0.332340i | ||||
\(201\) | 126.717 | − | 148.216i | 0.630432 | − | 0.737391i | ||||
\(202\) | −192.000 | −0.950495 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −48.0000 | + | 16.9706i | −0.235294 | + | 0.0831890i | ||||
\(205\) | 144.000 | + | 249.415i | 0.702439 | + | 1.21666i | ||||
\(206\) | 79.6084 | + | 45.9619i | 0.386449 | + | 0.223116i | ||||
\(207\) | 75.4393 | − | 11.8707i | 0.364441 | − | 0.0573465i | ||||
\(208\) | −2.00000 | − | 3.46410i | −0.00961538 | − | 0.0166543i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 62.0000 | 0.293839 | 0.146919 | − | 0.989148i | \(-0.453064\pi\) | ||||
0.146919 | + | 0.989148i | \(0.453064\pi\) | |||||||
\(212\) | 44.0908 | − | 25.4558i | 0.207976 | − | 0.120075i | ||||
\(213\) | 32.5607 | − | 175.191i | 0.152867 | − | 0.822492i | ||||
\(214\) | 114.000 | − | 197.454i | 0.532710 | − | 0.922681i | ||||
\(215\) | −227.803 | + | 131.522i | −1.05955 | + | 0.611730i | ||||
\(216\) | −40.0000 | + | 65.0538i | −0.185185 | + | 0.301175i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 236.174i | 1.08337i | ||||||||
\(219\) | 189.101 | − | 221.183i | 0.863473 | − | 1.00997i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.34847 | + | 4.24264i | 0.0332510 | + | 0.0191975i | ||||
\(222\) | −3.22474 | − | 2.75699i | −0.0145259 | − | 0.0124189i | ||||
\(223\) | 202.000 | 0.905830 | 0.452915 | − | 0.891554i | \(-0.350384\pi\) | ||||
0.452915 | + | 0.891554i | \(0.350384\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 329.000 | − | 265.872i | 1.46222 | − | 1.18165i | ||||
\(226\) | −114.000 | − | 197.454i | −0.504425 | − | 0.873689i | ||||
\(227\) | 14.6969 | + | 8.48528i | 0.0647442 | + | 0.0373801i | 0.532023 | − | 0.846730i | \(-0.321432\pi\) |
−0.467278 | + | 0.884110i | \(0.654765\pi\) | |||||||
\(228\) | 182.868 | + | 33.9877i | 0.802054 | + | 0.149069i | ||||
\(229\) | −0.500000 | − | 0.866025i | −0.00218341 | − | 0.00378177i | 0.864932 | − | 0.501890i | \(-0.167362\pi\) |
−0.867115 | + | 0.498108i | \(0.834028\pi\) | |||||||
\(230\) | − | 101.823i | − | 0.442710i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −48.0000 | −0.206897 | ||||||||
\(233\) | −286.590 | + | 165.463i | −1.23000 | + | 0.710142i | −0.967030 | − | 0.254662i | \(-0.918036\pi\) |
−0.262971 | + | 0.964804i | \(0.584702\pi\) | |||||||
\(234\) | 12.5732 | − | 1.97846i | 0.0537317 | − | 0.00845494i | ||||
\(235\) | 180.000 | − | 311.769i | 0.765957 | − | 1.32668i | ||||
\(236\) | 14.6969 | − | 8.48528i | 0.0622752 | − | 0.0359546i | ||||
\(237\) | −103.000 | − | 291.328i | −0.434599 | − | 1.22923i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 458.205i | 1.91718i | 0.284796 | + | 0.958588i | \(0.408074\pi\) | ||||
−0.284796 | + | 0.958588i | \(0.591926\pi\) | |||||||
\(240\) | 77.3939 | + | 66.1679i | 0.322474 | + | 0.275699i | ||||
\(241\) | −11.0000 | + | 19.0526i | −0.0456432 | + | 0.0790563i | −0.887944 | − | 0.459951i | \(-0.847867\pi\) |
0.842301 | + | 0.539007i | \(0.181200\pi\) | |||||||
\(242\) | −148.194 | − | 85.5599i | −0.612372 | − | 0.353553i | ||||
\(243\) | −147.444 | − | 193.156i | −0.606767 | − | 0.794880i | ||||
\(244\) | 100.000 | 0.409836 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −48.0000 | − | 135.765i | −0.195122 | − | 0.551888i | ||||
\(247\) | −15.5000 | − | 26.8468i | −0.0627530 | − | 0.108691i | ||||
\(248\) | 17.1464 | + | 9.89949i | 0.0691388 | + | 0.0399173i | ||||
\(249\) | 23.2577 | − | 125.136i | 0.0934042 | − | 0.502555i | ||||
\(250\) | −132.000 | − | 228.631i | −0.528000 | − | 0.914523i | ||||
\(251\) | − | 178.191i | − | 0.709924i | −0.934881 | − | 0.354962i | \(-0.884494\pi\) | ||
0.934881 | − | 0.354962i | \(-0.115506\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 138.396 | − | 79.9031i | 0.544867 | − | 0.314579i | ||||
\(255\) | −212.363 | − | 39.4695i | −0.832797 | − | 0.154783i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −242.499 | + | 140.007i | −0.943578 | + | 0.544775i | −0.891080 | − | 0.453846i | \(-0.850052\pi\) |
−0.0524977 | + | 0.998621i | \(0.516718\pi\) | |||||||
\(258\) | 124.000 | − | 43.8406i | 0.480620 | − | 0.169925i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 16.9706i | − | 0.0652714i | ||||||
\(261\) | 54.8786 | − | 142.535i | 0.210263 | − | 0.546113i | ||||
\(262\) | −60.0000 | + | 103.923i | −0.229008 | + | 0.396653i | ||||
\(263\) | −88.1816 | − | 50.9117i | −0.335291 | − | 0.193581i | 0.322897 | − | 0.946434i | \(-0.395343\pi\) |
−0.658188 | + | 0.752854i | \(0.728677\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 216.000 | 0.815094 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −336.000 | + | 118.794i | −1.25843 | + | 0.444921i | ||||
\(268\) | 65.0000 | + | 112.583i | 0.242537 | + | 0.420087i | ||||
\(269\) | 367.423 | + | 212.132i | 1.36589 | + | 0.788595i | 0.990400 | − | 0.138233i | \(-0.0441422\pi\) |
0.375487 | + | 0.926828i | \(0.377476\pi\) | |||||||
\(270\) | −284.969 | + | 154.170i | −1.05544 | + | 0.571001i | ||||
\(271\) | −125.000 | − | 216.506i | −0.461255 | − | 0.798916i | 0.537769 | − | 0.843092i | \(-0.319267\pi\) |
−0.999024 | + | 0.0441757i | \(0.985934\pi\) | |||||||
\(272\) | − | 33.9411i | − | 0.124784i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 264.000 | 0.963504 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.30306 | + | 50.0545i | −0.0337067 | + | 0.181357i | ||||
\(277\) | −191.500 | + | 331.688i | −0.691336 | + | 1.19743i | 0.280065 | + | 0.959981i | \(0.409644\pi\) |
−0.971400 | + | 0.237447i | \(0.923689\pi\) | |||||||
\(278\) | −138.396 | + | 79.9031i | −0.497828 | + | 0.287421i | ||||
\(279\) | −49.0000 | + | 39.5980i | −0.175627 | + | 0.141928i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 178.191i | 0.634131i | 0.948404 | + | 0.317066i | \(0.102698\pi\) | ||||
−0.948404 | + | 0.317066i | \(0.897302\pi\) | |||||||
\(282\) | −116.969 | + | 136.814i | −0.414785 | + | 0.485157i | ||||
\(283\) | 152.500 | − | 264.138i | 0.538869 | − | 0.933349i | −0.460096 | − | 0.887869i | \(-0.652185\pi\) |
0.998965 | − | 0.0454798i | \(-0.0144817\pi\) | |||||||
\(284\) | 102.879 | + | 59.3970i | 0.362248 | + | 0.209144i | ||||
\(285\) | 599.803 | + | 512.801i | 2.10457 | + | 1.79930i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −32.0000 | − | 39.5980i | −0.111111 | − | 0.137493i | ||||
\(289\) | −108.500 | − | 187.928i | −0.375433 | − | 0.650268i | ||||
\(290\) | −176.363 | − | 101.823i | −0.608149 | − | 0.351115i | ||||
\(291\) | −489.615 | − | 90.9992i | −1.68253 | − | 0.312712i | ||||
\(292\) | 97.0000 | + | 168.009i | 0.332192 | + | 0.575373i | ||||
\(293\) | − | 135.765i | − | 0.463360i | −0.972792 | − | 0.231680i | \(-0.925578\pi\) | ||
0.972792 | − | 0.231680i | \(-0.0744222\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 72.0000 | 0.244068 | ||||||||
\(296\) | 2.44949 | − | 1.41421i | 0.00827530 | − | 0.00477775i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −48.0000 | + | 83.1384i | −0.161074 | + | 0.278988i | ||||
\(299\) | 7.34847 | − | 4.24264i | 0.0245768 | − | 0.0141894i | ||||
\(300\) | 94.0000 | + | 265.872i | 0.313333 | + | 0.886240i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 82.0244i | − | 0.271604i | ||||||
\(303\) | 309.576 | + | 264.672i | 1.02170 | + | 0.873503i | ||||
\(304\) | −62.0000 | + | 107.387i | −0.203947 | + | 0.353247i | ||||
\(305\) | 367.423 | + | 212.132i | 1.20467 | + | 0.695515i | ||||
\(306\) | 100.788 | + | 38.8050i | 0.329372 | + | 0.126814i | ||||
\(307\) | 199.000 | 0.648208 | 0.324104 | − | 0.946021i | \(-0.394937\pi\) | ||||
0.324104 | + | 0.946021i | \(0.394937\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −65.0000 | − | 183.848i | −0.210356 | − | 0.594977i | ||||
\(310\) | 42.0000 | + | 72.7461i | 0.135484 | + | 0.234665i | ||||
\(311\) | −382.120 | − | 220.617i | −1.22868 | − | 0.709380i | −0.261929 | − | 0.965087i | \(-0.584358\pi\) |
−0.966754 | + | 0.255707i | \(0.917692\pi\) | |||||||
\(312\) | −1.55051 | + | 8.34242i | −0.00496958 | + | 0.0267385i | ||||
\(313\) | 59.5000 | + | 103.057i | 0.190096 | + | 0.329256i | 0.945282 | − | 0.326255i | \(-0.105787\pi\) |
−0.755186 | + | 0.655511i | \(0.772453\pi\) | |||||||
\(314\) | 166.877i | 0.531456i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 206.000 | 0.651899 | ||||||||
\(317\) | 176.363 | − | 101.823i | 0.556351 | − | 0.321209i | −0.195329 | − | 0.980738i | \(-0.562577\pi\) |
0.751680 | + | 0.659528i | \(0.229244\pi\) | |||||||
\(318\) | −106.182 | − | 19.7348i | −0.333904 | − | 0.0620590i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −58.7878 | + | 33.9411i | −0.183712 | + | 0.106066i | ||||
\(321\) | −456.000 | + | 161.220i | −1.42056 | + | 0.502244i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 263.044i | − | 0.814377i | ||||||
\(324\) | 154.171 | − | 49.7511i | 0.475838 | − | 0.153553i | ||||
\(325\) | 23.5000 | − | 40.7032i | 0.0723077 | − | 0.125241i | ||||
\(326\) | 129.823 | + | 74.9533i | 0.398230 | + | 0.229918i | ||||
\(327\) | 325.565 | − | 380.800i | 0.995611 | − | 1.16453i | ||||
\(328\) | 96.0000 | 0.292683 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −260.500 | − | 451.199i | −0.787009 | − | 1.36314i | −0.927791 | − | 0.373099i | \(-0.878295\pi\) |
0.140782 | − | 0.990041i | \(-0.455038\pi\) | |||||||
\(332\) | 73.4847 | + | 42.4264i | 0.221339 | + | 0.127790i | ||||
\(333\) | 1.39898 | + | 8.89060i | 0.00420114 | + | 0.0266985i | ||||
\(334\) | 102.000 | + | 176.669i | 0.305389 | + | 0.528950i | ||||
\(335\) | 551.543i | 1.64640i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 311.000 | 0.922849 | 0.461424 | − | 0.887180i | \(-0.347339\pi\) | ||||
0.461424 | + | 0.887180i | \(0.347339\pi\) | |||||||
\(338\) | −205.757 | + | 118.794i | −0.608749 | + | 0.351461i | ||||
\(339\) | −88.3791 | + | 475.518i | −0.260705 | + | 1.40271i | ||||
\(340\) | 72.0000 | − | 124.708i | 0.211765 | − | 0.366787i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −248.000 | − | 306.884i | −0.725146 | − | 0.897323i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 87.6812i | 0.254887i | ||||||||
\(345\) | −140.363 | + | 164.177i | −0.406850 | + | 0.475876i | ||||
\(346\) | 54.0000 | − | 93.5307i | 0.156069 | − | 0.270320i | ||||
\(347\) | −95.5301 | − | 55.1543i | −0.275303 | − | 0.158946i | 0.355992 | − | 0.934489i | \(-0.384143\pi\) |
−0.631295 | + | 0.775543i | \(0.717476\pi\) | |||||||
\(348\) | 77.3939 | + | 66.1679i | 0.222396 | + | 0.190138i | ||||
\(349\) | −50.0000 | −0.143266 | −0.0716332 | − | 0.997431i | \(-0.522821\pi\) | ||||
−0.0716332 | + | 0.997431i | \(0.522821\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23.0000 | − | 14.1421i | −0.0655271 | − | 0.0402910i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 139.621 | + | 80.6102i | 0.395527 | + | 0.228357i | 0.684552 | − | 0.728964i | \(-0.259998\pi\) |
−0.289025 | + | 0.957321i | \(0.593331\pi\) | |||||||
\(354\) | −35.3939 | − | 6.57826i | −0.0999827 | − | 0.0185826i | ||||
\(355\) | 252.000 | + | 436.477i | 0.709859 | + | 1.22951i | ||||
\(356\) | − | 237.588i | − | 0.667382i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 228.000 | 0.636872 | ||||||||
\(359\) | 352.727 | − | 203.647i | 0.982525 | − | 0.567261i | 0.0794936 | − | 0.996835i | \(-0.474670\pi\) |
0.903032 | + | 0.429574i | \(0.141336\pi\) | |||||||
\(360\) | −33.5755 | − | 213.375i | −0.0932653 | − | 0.592707i | ||||
\(361\) | −300.000 | + | 519.615i | −0.831025 | + | 1.43938i | ||||
\(362\) | −263.320 | + | 152.028i | −0.727404 | + | 0.419967i | ||||
\(363\) | 121.000 | + | 342.240i | 0.333333 | + | 0.942809i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 823.072i | 2.25499i | ||||||||
\(366\) | −161.237 | − | 137.850i | −0.440539 | − | 0.376639i | ||||
\(367\) | −267.500 | + | 463.324i | −0.728883 | + | 1.26246i | 0.228473 | + | 0.973550i | \(0.426627\pi\) |
−0.957356 | + | 0.288912i | \(0.906707\pi\) | |||||||
\(368\) | −29.3939 | − | 16.9706i | −0.0798747 | − | 0.0461157i | ||||
\(369\) | −109.757 | + | 285.071i | −0.297445 | + | 0.772550i | ||||
\(370\) | 12.0000 | 0.0324324 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −14.0000 | − | 39.5980i | −0.0376344 | − | 0.106446i | ||||
\(373\) | 192.500 | + | 333.420i | 0.516086 | + | 0.893887i | 0.999826 | + | 0.0186750i | \(0.00594477\pi\) |
−0.483740 | + | 0.875212i | \(0.660722\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −102.334 | + | 550.600i | −0.272890 | + | 1.46827i | ||||
\(376\) | −60.0000 | − | 103.923i | −0.159574 | − | 0.276391i | ||||
\(377\) | − | 16.9706i | − | 0.0450148i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −55.0000 | −0.145119 | −0.0725594 | − | 0.997364i | \(-0.523117\pi\) | ||||
−0.0725594 | + | 0.997364i | \(0.523117\pi\) | |||||||
\(380\) | −455.605 | + | 263.044i | −1.19896 | + | 0.692220i | ||||
\(381\) | −333.292 | − | 61.9453i | −0.874783 | − | 0.162586i | ||||
\(382\) | −126.000 | + | 218.238i | −0.329843 | + | 0.571305i | ||||
\(383\) | −360.075 | + | 207.889i | −0.940144 | + | 0.542792i | −0.890005 | − | 0.455950i | \(-0.849300\pi\) |
−0.0501383 | + | 0.998742i | \(0.515966\pi\) | |||||||
\(384\) | 32.0000 | − | 11.3137i | 0.0833333 | − | 0.0294628i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 137.179i | − | 0.355385i | ||||||
\(387\) | −260.368 | − | 100.246i | −0.672786 | − | 0.259034i | ||||
\(388\) | 166.000 | − | 287.520i | 0.427835 | − | 0.741032i | ||||
\(389\) | −330.681 | − | 190.919i | −0.850080 | − | 0.490794i | 0.0105979 | − | 0.999944i | \(-0.496627\pi\) |
−0.860678 | + | 0.509150i | \(0.829960\pi\) | |||||||
\(390\) | −23.3939 | + | 27.3629i | −0.0599843 | + | 0.0701612i | ||||
\(391\) | 72.0000 | 0.184143 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 240.000 | − | 84.8528i | 0.610687 | − | 0.215910i | ||||
\(394\) | −258.000 | − | 446.869i | −0.654822 | − | 1.13419i | ||||
\(395\) | 756.892 | + | 436.992i | 1.91618 | + | 1.10631i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −240.500 | − | 416.558i | −0.605793 | − | 1.04927i | −0.991926 | − | 0.126822i | \(-0.959522\pi\) |
0.386132 | − | 0.922443i | \(-0.373811\pi\) | |||||||
\(398\) | 149.907i | 0.376650i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −188.000 | −0.470000 | ||||||||
\(401\) | −66.1362 | + | 38.1838i | −0.164928 | + | 0.0952214i | −0.580192 | − | 0.814480i | \(-0.697023\pi\) |
0.415264 | + | 0.909701i | \(0.363689\pi\) | |||||||
\(402\) | 50.3916 | − | 271.129i | 0.125352 | − | 0.674449i | ||||
\(403\) | −3.50000 | + | 6.06218i | −0.00868486 | + | 0.0150426i | ||||
\(404\) | −235.151 | + | 135.765i | −0.582057 | + | 0.336051i | ||||
\(405\) | 672.000 | + | 144.250i | 1.65926 | + | 0.356172i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −46.7878 | + | 54.7257i | −0.114676 | + | 0.134132i | ||||
\(409\) | −24.5000 | + | 42.4352i | −0.0599022 | + | 0.103754i | −0.894421 | − | 0.447225i | \(-0.852412\pi\) |
0.834519 | + | 0.550979i | \(0.185746\pi\) | |||||||
\(410\) | 352.727 | + | 203.647i | 0.860309 | + | 0.496699i | ||||
\(411\) | −425.666 | − | 363.923i | −1.03568 | − | 0.885458i | ||||
\(412\) | 130.000 | 0.315534 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 84.0000 | − | 67.8823i | 0.202899 | − | 0.163967i | ||||
\(415\) | 180.000 | + | 311.769i | 0.433735 | + | 0.751251i | ||||
\(416\) | −4.89898 | − | 2.82843i | −0.0117764 | − | 0.00679910i | ||||
\(417\) | 333.292 | + | 61.9453i | 0.799262 | + | 0.148550i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 322.441i | − | 0.769548i | −0.923011 | − | 0.384774i | \(-0.874279\pi\) | ||
0.923011 | − | 0.384774i | \(-0.125721\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −313.000 | −0.743468 | −0.371734 | − | 0.928339i | \(-0.621237\pi\) | ||||
−0.371734 | + | 0.928339i | \(0.621237\pi\) | |||||||
\(422\) | 75.9342 | − | 43.8406i | 0.179939 | − | 0.103888i | ||||
\(423\) | 377.196 | − | 59.3537i | 0.891717 | − | 0.140316i | ||||
\(424\) | 36.0000 | − | 62.3538i | 0.0849057 | − | 0.147061i | ||||
\(425\) | 345.378 | − | 199.404i | 0.812654 | − | 0.469186i | ||||
\(426\) | −84.0000 | − | 237.588i | −0.197183 | − | 0.557718i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 322.441i | − | 0.753366i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −186.000 | + | 322.161i | −0.432558 | + | 0.749213i | ||||
\(431\) | −301.287 | − | 173.948i | −0.699042 | − | 0.403592i | 0.107948 | − | 0.994157i | \(-0.465572\pi\) |
−0.806991 | + | 0.590564i | \(0.798905\pi\) | |||||||
\(432\) | −2.98979 | + | 107.959i | −0.00692082 | + | 0.249904i | ||||
\(433\) | 97.0000 | 0.224018 | 0.112009 | − | 0.993707i | \(-0.464271\pi\) | ||||
0.112009 | + | 0.993707i | \(0.464271\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 144.000 | + | 407.294i | 0.331034 | + | 0.936307i | ||||
\(436\) | 167.000 | + | 289.252i | 0.383028 | + | 0.663423i | ||||
\(437\) | −227.803 | − | 131.522i | −0.521287 | − | 0.300965i | ||||
\(438\) | 75.1997 | − | 404.607i | 0.171689 | − | 0.923761i | ||||
\(439\) | 187.000 | + | 323.894i | 0.425968 | + | 0.737798i | 0.996510 | − | 0.0834699i | \(-0.0266002\pi\) |
−0.570542 | + | 0.821268i | \(0.693267\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.0000 | 0.0271493 | ||||||||
\(443\) | −521.741 | + | 301.227i | −1.17775 | + | 0.679972i | −0.955492 | − | 0.295017i | \(-0.904675\pi\) |
−0.222254 | + | 0.974989i | \(0.571341\pi\) | |||||||
\(444\) | −5.89898 | − | 1.09638i | −0.0132860 | − | 0.00246932i | ||||
\(445\) | 504.000 | − | 872.954i | 1.13258 | − | 1.96169i | ||||
\(446\) | 247.398 | − | 142.836i | 0.554705 | − | 0.320259i | ||||
\(447\) | 192.000 | − | 67.8823i | 0.429530 | − | 0.151862i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 42.4264i | − | 0.0944909i | −0.998883 | − | 0.0472454i | \(-0.984956\pi\) | ||
0.998883 | − | 0.0472454i | \(-0.0150443\pi\) | |||||||
\(450\) | 214.941 | − | 558.264i | 0.477647 | − | 1.24059i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −279.242 | − | 161.220i | −0.617792 | − | 0.356682i | ||||
\(453\) | −113.070 | + | 132.254i | −0.249604 | + | 0.291951i | ||||
\(454\) | 24.0000 | 0.0528634 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 248.000 | − | 87.6812i | 0.543860 | − | 0.192283i | ||||
\(457\) | −227.500 | − | 394.042i | −0.497812 | − | 0.862235i | 0.502185 | − | 0.864760i | \(-0.332530\pi\) |
−0.999997 | + | 0.00252486i | \(0.999196\pi\) | |||||||
\(458\) | −1.22474 | − | 0.707107i | −0.00267412 | − | 0.00154390i | ||||
\(459\) | −109.015 | − | 201.504i | −0.237505 | − | 0.439006i | ||||
\(460\) | −72.0000 | − | 124.708i | −0.156522 | − | 0.271104i | ||||
\(461\) | − | 220.617i | − | 0.478563i | −0.970950 | − | 0.239281i | \(-0.923088\pi\) | ||
0.970950 | − | 0.239281i | \(-0.0769118\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.00000 | −0.0151188 | −0.00755940 | − | 0.999971i | \(-0.502406\pi\) | ||||
−0.00755940 | + | 0.999971i | \(0.502406\pi\) | |||||||
\(464\) | −58.7878 | + | 33.9411i | −0.126698 | + | 0.0731490i | ||||
\(465\) | 32.5607 | − | 175.191i | 0.0700230 | − | 0.376754i | ||||
\(466\) | −234.000 | + | 405.300i | −0.502146 | + | 0.869742i | ||||
\(467\) | 536.438 | − | 309.713i | 1.14869 | − | 0.663197i | 0.200122 | − | 0.979771i | \(-0.435866\pi\) |
0.948568 | + | 0.316574i | \(0.102533\pi\) | |||||||
\(468\) | 14.0000 | − | 11.3137i | 0.0299145 | − | 0.0241746i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 509.117i | − | 1.08323i | ||||||
\(471\) | 230.040 | − | 269.068i | 0.488407 | − | 0.571270i | ||||
\(472\) | 12.0000 | − | 20.7846i | 0.0254237 | − | 0.0440352i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −332.149 | − | 283.970i | −0.700736 | − | 0.599094i | ||||
\(475\) | −1457.00 | −3.06737 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 144.000 | + | 178.191i | 0.301887 | + | 0.373566i | ||||
\(478\) | 324.000 | + | 561.184i | 0.677824 | + | 1.17403i | ||||
\(479\) | −580.529 | − | 335.169i | −1.21196 | − | 0.699726i | −0.248774 | − | 0.968561i | \(-0.580028\pi\) |
−0.963186 | + | 0.268836i | \(0.913361\pi\) | |||||||
\(480\) | 141.576 | + | 26.3130i | 0.294949 | + | 0.0548188i | ||||
\(481\) | 0.500000 | + | 0.866025i | 0.00103950 | + | 0.00180047i | ||||
\(482\) | 31.1127i | 0.0645492i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −242.000 | −0.500000 | ||||||||
\(485\) | 1219.85 | − | 704.278i | 2.51515 | − | 1.45212i | ||||
\(486\) | −317.164 | − | 132.308i | −0.652600 | − | 0.272238i | ||||
\(487\) | 231.500 | − | 400.970i | 0.475359 | − | 0.823347i | −0.524242 | − | 0.851569i | \(-0.675651\pi\) |
0.999602 | + | 0.0282226i | \(0.00898473\pi\) | |||||||
\(488\) | 122.474 | − | 70.7107i | 0.250972 | − | 0.144899i | ||||
\(489\) | −106.000 | − | 299.813i | −0.216769 | − | 0.613115i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 356.382i | − | 0.725829i | −0.931823 | − | 0.362914i | \(-0.881782\pi\) | ||
0.931823 | − | 0.362914i | \(-0.118218\pi\) | |||||||
\(492\) | −154.788 | − | 132.336i | −0.314609 | − | 0.268975i | ||||
\(493\) | 72.0000 | − | 124.708i | 0.146045 | − | 0.252957i | ||||
\(494\) | −37.9671 | − | 21.9203i | −0.0768565 | − | 0.0443731i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 28.0000 | 0.0564516 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −60.0000 | − | 169.706i | −0.120482 | − | 0.340774i | ||||
\(499\) | 267.500 | + | 463.324i | 0.536072 | + | 0.928504i | 0.999111 | + | 0.0421660i | \(0.0134258\pi\) |
−0.463038 | + | 0.886338i | \(0.653241\pi\) | |||||||
\(500\) | −323.333 | − | 186.676i | −0.646665 | − | 0.373352i | ||||
\(501\) | 79.0760 | − | 425.463i | 0.157836 | − | 0.849228i | ||||
\(502\) | −126.000 | − | 218.238i | −0.250996 | − | 0.434738i | ||||
\(503\) | − | 627.911i | − | 1.24833i | −0.781292 | − | 0.624166i | \(-0.785439\pi\) | ||
0.781292 | − | 0.624166i | \(-0.214561\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1152.00 | −2.28119 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 495.514 | + | 92.0956i | 0.977346 | + | 0.181648i | ||||
\(508\) | 113.000 | − | 195.722i | 0.222441 | − | 0.385279i | ||||
\(509\) | 551.135 | − | 318.198i | 1.08278 | − | 0.625144i | 0.151135 | − | 0.988513i | \(-0.451707\pi\) |
0.931645 | + | 0.363370i | \(0.118374\pi\) | |||||||
\(510\) | −288.000 | + | 101.823i | −0.564706 | + | 0.199654i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | −23.1709 | + | 836.679i | −0.0451675 | + | 1.63095i | ||||
\(514\) | −198.000 | + | 342.946i | −0.385214 | + | 0.667210i | ||||
\(515\) | 477.650 | + | 275.772i | 0.927477 | + | 0.535479i | ||||
\(516\) | 120.868 | − | 141.375i | 0.234241 | − | 0.273982i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −216.000 | + | 76.3675i | −0.416185 | + | 0.147144i | ||||
\(520\) | −12.0000 | − | 20.7846i | −0.0230769 | − | 0.0399704i | ||||
\(521\) | 558.484 | + | 322.441i | 1.07195 | + | 0.618888i | 0.928712 | − | 0.370801i | \(-0.120917\pi\) |
0.143233 | + | 0.989689i | \(0.454250\pi\) | |||||||
\(522\) | −33.5755 | − | 213.375i | −0.0643209 | − | 0.408763i | ||||
\(523\) | 344.500 | + | 596.692i | 0.658700 | + | 1.14090i | 0.980952 | + | 0.194248i | \(0.0622266\pi\) |
−0.322253 | + | 0.946654i | \(0.604440\pi\) | |||||||
\(524\) | 169.706i | 0.323866i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −144.000 | −0.273764 | ||||||||
\(527\) | −51.4393 | + | 29.6985i | −0.0976078 | + | 0.0563539i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −228.500 | + | 395.774i | −0.431947 | + | 0.748154i | ||||
\(530\) | 264.545 | − | 152.735i | 0.499141 | − | 0.288179i | ||||
\(531\) | 48.0000 | + | 59.3970i | 0.0903955 | + | 0.111859i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 33.9411i | 0.0636794i | ||||||||
\(534\) | −327.514 | + | 383.080i | −0.613323 | + | 0.717379i | ||||
\(535\) | 684.000 | − | 1184.72i | 1.27850 | − | 2.21444i | ||||
\(536\) | 159.217 | + | 91.9239i | 0.297046 | + | 0.171500i | ||||
\(537\) | −367.621 | − | 314.297i | −0.684583 | − | 0.585284i | ||||
\(538\) | 600.000 | 1.11524 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −240.000 | + | 390.323i | −0.444444 | + | 0.722820i | ||||
\(541\) | −287.500 | − | 497.965i | −0.531423 | − | 0.920452i | −0.999327 | − | 0.0366729i | \(-0.988324\pi\) |
0.467904 | − | 0.883779i | \(-0.345009\pi\) | |||||||
\(542\) | −306.186 | − | 176.777i | −0.564919 | − | 0.326156i | ||||
\(543\) | 634.140 | + | 117.860i | 1.16785 | + | 0.217054i | ||||
\(544\) | −24.0000 | − | 41.5692i | −0.0441176 | − | 0.0764140i | ||||
\(545\) | 1417.04i | 2.60008i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 302.000 | 0.552102 | 0.276051 | − | 0.961143i | \(-0.410974\pi\) | ||||
0.276051 | + | 0.961143i | \(0.410974\pi\) | |||||||
\(548\) | 323.333 | − | 186.676i | 0.590023 | − | 0.340650i | ||||
\(549\) | 69.9490 | + | 444.530i | 0.127412 | + | 0.809709i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −455.605 | + | 263.044i | −0.826869 | + | 0.477393i | ||||
\(552\) | 24.0000 | + | 67.8823i | 0.0434783 | + | 0.122975i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 541.644i | 0.977696i | ||||||||
\(555\) | −19.3485 | − | 16.5420i | −0.0348621 | − | 0.0298053i | ||||
\(556\) | −113.000 | + | 195.722i | −0.203237 | + | 0.352018i | ||||
\(557\) | 117.576 | + | 67.8823i | 0.211087 | + | 0.121871i | 0.601817 | − | 0.798634i | \(-0.294444\pi\) |
−0.390729 | + | 0.920506i | \(0.627777\pi\) | |||||||
\(558\) | −32.0125 | + | 83.1457i | −0.0573701 | + | 0.149007i | ||||
\(559\) | −31.0000 | −0.0554562 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 126.000 | + | 218.238i | 0.224199 | + | 0.388325i | ||||
\(563\) | −521.741 | − | 301.227i | −0.926716 | − | 0.535040i | −0.0409448 | − | 0.999161i | \(-0.513037\pi\) |
−0.885772 | + | 0.464121i | \(0.846370\pi\) | |||||||
\(564\) | −46.5153 | + | 250.273i | −0.0824739 | + | 0.443746i | ||||
\(565\) | −684.000 | − | 1184.72i | −1.21062 | − | 2.09685i | ||||
\(566\) | − | 431.335i | − | 0.762076i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 168.000 | 0.295775 | ||||||||
\(569\) | −573.181 | + | 330.926i | −1.00735 | + | 0.581592i | −0.910414 | − | 0.413699i | \(-0.864237\pi\) |
−0.0969334 | + | 0.995291i | \(0.530903\pi\) | |||||||
\(570\) | 1097.21 | + | 203.926i | 1.92493 | + | 0.357765i | ||||
\(571\) | −56.5000 | + | 97.8609i | −0.0989492 | + | 0.171385i | −0.911250 | − | 0.411854i | \(-0.864881\pi\) |
0.812301 | + | 0.583239i | \(0.198215\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 504.000 | − | 178.191i | 0.879581 | − | 0.310979i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 398.808i | − | 0.693580i | ||||||
\(576\) | −67.1918 | − | 25.8700i | −0.116652 | − | 0.0449132i | ||||
\(577\) | −60.5000 | + | 104.789i | −0.104853 | + | 0.181610i | −0.913678 | − | 0.406439i | \(-0.866770\pi\) |
0.808825 | + | 0.588049i | \(0.200104\pi\) | |||||||
\(578\) | −265.770 | − | 153.442i | −0.459809 | − | 0.265471i | ||||
\(579\) | −189.101 | + | 221.183i | −0.326598 | + | 0.382009i | ||||
\(580\) | −288.000 | −0.496552 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −664.000 | + | 234.759i | −1.14089 | + | 0.403367i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 237.601 | + | 137.179i | 0.406850 | + | 0.234895i | ||||
\(585\) | 75.4393 | − | 11.8707i | 0.128956 | − | 0.0202919i | ||||
\(586\) | −96.0000 | − | 166.277i | −0.163823 | − | 0.283749i | ||||
\(587\) | − | 67.8823i | − | 0.115643i | −0.998327 | − | 0.0578213i | \(-0.981585\pi\) | ||
0.998327 | − | 0.0578213i | \(-0.0184154\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 217.000 | 0.368421 | ||||||||
\(590\) | 88.1816 | − | 50.9117i | 0.149460 | − | 0.0862910i | ||||
\(591\) | −200.016 | + | 1076.17i | −0.338436 | + | 1.82093i | ||||
\(592\) | 2.00000 | − | 3.46410i | 0.00337838 | − | 0.00585152i | ||||
\(593\) | −426.211 | + | 246.073i | −0.718737 | + | 0.414963i | −0.814288 | − | 0.580461i | \(-0.802872\pi\) |
0.0955505 | + | 0.995425i | \(0.469539\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 135.765i | 0.227793i | ||||||||
\(597\) | 206.646 | − | 241.705i | 0.346141 | − | 0.404867i | ||||
\(598\) | 6.00000 | − | 10.3923i | 0.0100334 | − | 0.0173784i | ||||
\(599\) | 88.1816 | + | 50.9117i | 0.147215 | + | 0.0849945i | 0.571798 | − | 0.820394i | \(-0.306246\pi\) |
−0.424583 | + | 0.905389i | \(0.639579\pi\) | |||||||
\(600\) | 303.126 | + | 259.158i | 0.505210 | + | 0.431929i | ||||
\(601\) | −791.000 | −1.31614 | −0.658070 | − | 0.752957i | \(-0.728627\pi\) | ||||
−0.658070 | + | 0.752957i | \(0.728627\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −455.000 | + | 367.696i | −0.754561 | + | 0.609777i | ||||
\(604\) | −58.0000 | − | 100.459i | −0.0960265 | − | 0.166323i | ||||
\(605\) | −889.165 | − | 513.360i | −1.46969 | − | 0.848528i | ||||
\(606\) | 566.302 | + | 105.252i | 0.934492 | + | 0.173683i | ||||
\(607\) | 56.5000 | + | 97.8609i | 0.0930807 | + | 0.161221i | 0.908806 | − | 0.417219i | \(-0.136995\pi\) |
−0.815725 | + | 0.578440i | \(0.803662\pi\) | |||||||
\(608\) | 175.362i | 0.288425i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 600.000 | 0.983607 | ||||||||
\(611\) | 36.7423 | − | 21.2132i | 0.0601348 | − | 0.0347188i | ||||
\(612\) | 150.879 | − | 23.7415i | 0.246534 | − | 0.0387933i | ||||
\(613\) | 287.000 | − | 497.099i | 0.468189 | − | 0.810928i | −0.531150 | − | 0.847278i | \(-0.678240\pi\) |
0.999339 | + | 0.0363503i | \(0.0115732\pi\) | |||||||
\(614\) | 243.724 | − | 140.714i | 0.396945 | − | 0.229176i | ||||
\(615\) | −288.000 | − | 814.587i | −0.468293 | − | 1.32453i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 661.852i | − | 1.07269i | −0.843998 | − | 0.536347i | \(-0.819804\pi\) | ||
0.843998 | − | 0.536347i | \(-0.180196\pi\) | |||||||
\(618\) | −209.608 | − | 179.205i | −0.339172 | − | 0.289975i | ||||
\(619\) | 476.500 | − | 825.322i | 0.769790 | − | 1.33332i | −0.167887 | − | 0.985806i | \(-0.553694\pi\) |
0.937677 | − | 0.347509i | \(-0.112972\pi\) | |||||||
\(620\) | 102.879 | + | 59.3970i | 0.165933 | + | 0.0958016i | ||||
\(621\) | −229.015 | − | 6.34231i | −0.368784 | − | 0.0102131i | ||||
\(622\) | −624.000 | −1.00322 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.00000 | + | 11.3137i | 0.00641026 | + | 0.0181309i | ||||
\(625\) | −204.500 | − | 354.204i | −0.327200 | − | 0.566727i | ||||
\(626\) | 145.745 | + | 84.1457i | 0.232819 | + | 0.134418i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 118.000 | + | 204.382i | 0.187898 | + | 0.325449i | ||||
\(629\) | 8.48528i | 0.0134901i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 758.000 | 1.20127 | 0.600634 | − | 0.799524i | \(-0.294915\pi\) | ||||
0.600634 | + | 0.799524i | \(0.294915\pi\) | |||||||
\(632\) | 252.297 | − | 145.664i | 0.399205 | − | 0.230481i | ||||
\(633\) | −182.868 | − | 33.9877i | −0.288892 | − | 0.0536930i | ||||
\(634\) | 144.000 | − | 249.415i | 0.227129 | − | 0.393400i | ||||
\(635\) | 830.377 | − | 479.418i | 1.30768 | − | 0.754990i | ||||
\(636\) | −144.000 | + | 50.9117i | −0.226415 | + | 0.0800498i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −192.075 | + | 498.874i | −0.300587 | + | 0.780710i | ||||
\(640\) | −48.0000 | + | 83.1384i | −0.0750000 | + | 0.129904i | ||||
\(641\) | −933.256 | − | 538.815i | −1.45594 | − | 0.840586i | −0.457129 | − | 0.889400i | \(-0.651122\pi\) |
−0.998808 | + | 0.0488147i | \(0.984456\pi\) | |||||||
\(642\) | −444.484 | + | 519.894i | −0.692342 | + | 0.809804i | ||||
\(643\) | 1111.00 | 1.72784 | 0.863919 | − | 0.503631i | \(-0.168003\pi\) | ||||
0.863919 | + | 0.503631i | \(0.168003\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 744.000 | − | 263.044i | 1.15349 | − | 0.407820i | ||||
\(646\) | −186.000 | − | 322.161i | −0.287926 | − | 0.498702i | ||||
\(647\) | 293.939 | + | 169.706i | 0.454310 | + | 0.262296i | 0.709649 | − | 0.704556i | \(-0.248854\pi\) |
−0.255339 | + | 0.966852i | \(0.582187\pi\) | |||||||
\(648\) | 153.641 | − | 169.948i | 0.237101 | − | 0.262266i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 66.4680i | − | 0.102259i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 212.000 | 0.325153 | ||||||||
\(653\) | −558.484 | + | 322.441i | −0.855258 | + | 0.493784i | −0.862422 | − | 0.506191i | \(-0.831053\pi\) |
0.00716327 | + | 0.999974i | \(0.497720\pi\) | |||||||
\(654\) | 129.468 | − | 696.592i | 0.197963 | − | 1.06513i | ||||
\(655\) | −360.000 | + | 623.538i | −0.549618 | + | 0.951967i | ||||
\(656\) | 117.576 | − | 67.8823i | 0.179231 | − | 0.103479i | ||||
\(657\) | −679.000 | + | 548.715i | −1.03349 | + | 0.835182i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 873.984i | − | 1.32623i | −0.748519 | − | 0.663114i | \(-0.769235\pi\) | ||
0.748519 | − | 0.663114i | \(-0.230765\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −432.500 | + | 749.112i | −0.654312 | + | 1.13330i | 0.327754 | + | 0.944763i | \(0.393708\pi\) |
−0.982066 | + | 0.188538i | \(0.939625\pi\) | |||||||
\(662\) | −638.092 | − | 368.403i | −0.963885 | − | 0.556499i | ||||
\(663\) | −19.3485 | − | 16.5420i | −0.0291832 | − | 0.0249502i | ||||
\(664\) | 120.000 | 0.180723 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.00000 | + | 9.89949i | 0.0120120 | + | 0.0148641i | ||||
\(667\) | −72.0000 | − | 124.708i | −0.107946 | − | 0.186968i | ||||
\(668\) | 249.848 | + | 144.250i | 0.374024 | + | 0.215943i | ||||
\(669\) | −595.797 | − | 110.734i | −0.890578 | − | 0.165522i | ||||
\(670\) | 390.000 | + | 675.500i | 0.582090 | + | 1.00821i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −505.000 | −0.750371 | −0.375186 | − | 0.926950i | \(-0.622421\pi\) | ||||
−0.375186 | + | 0.926950i | \(0.622421\pi\) | |||||||
\(674\) | 380.896 | − | 219.910i | 0.565127 | − | 0.326276i | ||||
\(675\) | −1116.13 | + | 603.833i | −1.65353 | + | 0.894568i | ||||
\(676\) | −168.000 | + | 290.985i | −0.248521 | + | 0.430450i | ||||
\(677\) | 279.242 | − | 161.220i | 0.412469 | − | 0.238139i | −0.279381 | − | 0.960180i | \(-0.590129\pi\) |
0.691850 | + | 0.722041i | \(0.256796\pi\) | |||||||
\(678\) | 228.000 | + | 644.881i | 0.336283 | + | 0.951152i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 203.647i | − | 0.299481i | ||||||
\(681\) | −38.6969 | − | 33.0839i | −0.0568237 | − | 0.0485814i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 683.408 | + | 394.566i | 1.00060 | + | 0.577695i | 0.908425 | − | 0.418048i | \(-0.137286\pi\) |
0.0921720 | + | 0.995743i | \(0.470619\pi\) | |||||||
\(684\) | −520.737 | − | 200.493i | −0.761311 | − | 0.293118i | ||||
\(685\) | 1584.00 | 2.31241 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.00000 | + | 2.82843i | 0.00145560 | + | 0.00411707i | ||||
\(688\) | 62.0000 | + | 107.387i | 0.0901163 | + | 0.156086i | ||||
\(689\) | 22.0454 | + | 12.7279i | 0.0319962 | + | 0.0184730i | ||||
\(690\) | −55.8184 | + | 300.327i | −0.0808962 | + | 0.435257i | ||||
\(691\) | 92.5000 | + | 160.215i | 0.133864 | + | 0.231859i | 0.925163 | − | 0.379570i | \(-0.123928\pi\) |
−0.791299 | + | 0.611429i | \(0.790595\pi\) | |||||||
\(692\) | − | 152.735i | − | 0.220715i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −156.000 | −0.224784 | ||||||||
\(695\) | −830.377 | + | 479.418i | −1.19479 | + | 0.689811i | ||||
\(696\) | 141.576 | + | 26.3130i | 0.203413 | + | 0.0378061i | ||||
\(697\) | −144.000 | + | 249.415i | −0.206600 | + | 0.357841i | ||||
\(698\) | −61.2372 | + | 35.3553i | −0.0877324 | + | 0.0506523i | ||||
\(699\) | 936.000 | − | 330.926i | 1.33906 | − | 0.473428i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 93.3381i | − | 0.133150i | −0.997781 | − | 0.0665750i | \(-0.978793\pi\) | ||
0.997781 | − | 0.0665750i | \(-0.0212072\pi\) | |||||||
\(702\) | −38.1691 | − | 1.05705i | −0.0543720 | − | 0.00150577i | ||||
\(703\) | 15.5000 | − | 26.8468i | 0.0220484 | − | 0.0381889i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −701.816 | + | 820.886i | −0.995484 | + | 1.16438i | ||||
\(706\) | 228.000 | 0.322946 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −48.0000 | + | 16.9706i | −0.0677966 | + | 0.0239697i | ||||
\(709\) | −97.0000 | − | 168.009i | −0.136812 | − | 0.236966i | 0.789476 | − | 0.613782i | \(-0.210352\pi\) |
−0.926288 | + | 0.376815i | \(0.877019\pi\) | |||||||
\(710\) | 617.271 | + | 356.382i | 0.869396 | + | 0.501946i | ||||
\(711\) | 144.095 | + | 915.732i | 0.202665 | + | 1.28795i | ||||
\(712\) | −168.000 | − | 290.985i | −0.235955 | − | 0.408686i | ||||
\(713\) | 59.3970i | 0.0833057i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 279.242 | − | 161.220i | 0.390003 | − | 0.225168i | ||||
\(717\) | 251.183 | − | 1351.47i | 0.350324 | − | 1.88490i | ||||
\(718\) | 288.000 | − | 498.831i | 0.401114 | − | 0.694750i | ||||
\(719\) | 338.030 | − | 195.161i | 0.470139 | − | 0.271435i | −0.246159 | − | 0.969229i | \(-0.579169\pi\) |
0.716298 | + | 0.697795i | \(0.245835\pi\) | |||||||
\(720\) | −192.000 | − | 237.588i | −0.266667 | − | 0.329983i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 848.528i | 1.17525i | ||||||||
\(723\) | 42.8888 | − | 50.1653i | 0.0593206 | − | 0.0693849i | ||||
\(724\) | −215.000 | + | 372.391i | −0.296961 | + | 0.514352i | ||||
\(725\) | −690.756 | − | 398.808i | −0.952767 | − | 0.550080i | ||||
\(726\) | 390.194 | + | 333.596i | 0.537457 | + | 0.459499i | ||||
\(727\) | −425.000 | −0.584594 | −0.292297 | − | 0.956328i | \(-0.594420\pi\) | ||||
−0.292297 | + | 0.956328i | \(0.594420\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 329.000 | + | 650.538i | 0.451303 | + | 0.892371i | ||||
\(730\) | 582.000 | + | 1008.05i | 0.797260 | + | 1.38090i | ||||
\(731\) | −227.803 | − | 131.522i | −0.311631 | − | 0.179920i | ||||
\(732\) | −294.949 | − | 54.8188i | −0.402936 | − | 0.0748891i | ||||
\(733\) | 203.500 | + | 352.472i | 0.277626 | + | 0.480863i | 0.970794 | − | 0.239913i | \(-0.0771190\pi\) |
−0.693168 | + | 0.720776i | \(0.743786\pi\) | |||||||
\(734\) | 756.604i | 1.03080i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −48.0000 | −0.0652174 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 67.1510 | + | 426.749i | 0.0909905 | + | 0.578251i | ||||
\(739\) | −380.500 | + | 659.045i | −0.514885 | + | 0.891807i | 0.484966 | + | 0.874533i | \(0.338832\pi\) |
−0.999851 | + | 0.0172738i | \(0.994501\pi\) | |||||||
\(740\) | 14.6969 | − | 8.48528i | 0.0198607 | − | 0.0114666i | ||||
\(741\) | 31.0000 | + | 87.6812i | 0.0418354 | + | 0.118328i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 576.999i | − | 0.776580i | −0.921537 | − | 0.388290i | \(-0.873066\pi\) | ||
0.921537 | − | 0.388290i | \(-0.126934\pi\) | |||||||
\(744\) | −45.1464 | − | 38.5979i | −0.0606807 | − | 0.0518789i | ||||
\(745\) | −288.000 | + | 498.831i | −0.386577 | + | 0.669571i | ||||
\(746\) | 471.527 | + | 272.236i | 0.632073 | + | 0.364928i | ||||
\(747\) | −137.196 | + | 356.339i | −0.183663 | + | 0.477026i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 264.000 | + | 746.705i | 0.352000 | + | 0.995606i | ||||
\(751\) | −344.500 | − | 596.692i | −0.458722 | − | 0.794529i | 0.540172 | − | 0.841555i | \(-0.318359\pi\) |
−0.998894 | + | 0.0470253i | \(0.985026\pi\) | |||||||
\(752\) | −146.969 | − | 84.8528i | −0.195438 | − | 0.112836i | ||||
\(753\) | −97.6821 | + | 525.572i | −0.129724 | + | 0.697971i | ||||
\(754\) | −12.0000 | − | 20.7846i | −0.0159151 | − | 0.0275658i | ||||
\(755\) | − | 492.146i | − | 0.651849i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −142.000 | −0.187583 | −0.0937913 | − | 0.995592i | \(-0.529899\pi\) | ||||
−0.0937913 | + | 0.995592i | \(0.529899\pi\) | |||||||
\(758\) | −67.3610 | + | 38.8909i | −0.0888667 | + | 0.0513072i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −372.000 | + | 644.323i | −0.489474 | + | 0.847793i | ||||
\(761\) | −962.649 | + | 555.786i | −1.26498 | + | 0.730336i | −0.974034 | − | 0.226403i | \(-0.927303\pi\) |
−0.290946 | + | 0.956740i | \(0.593970\pi\) | |||||||
\(762\) | −452.000 | + | 159.806i | −0.593176 | + | 0.209719i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 356.382i | 0.466468i | ||||||||
\(765\) | 604.727 | + | 232.830i | 0.790492 | + | 0.304353i | ||||
\(766\) | −294.000 | + | 509.223i | −0.383812 | + | 0.664782i | ||||
\(767\) | 7.34847 | + | 4.24264i | 0.00958079 | + | 0.00553147i | ||||
\(768\) | 31.1918 | − | 36.4838i | 0.0406144 | − | 0.0475050i | ||||
\(769\) | −1127.00 | −1.46554 | −0.732770 | − | 0.680477i | \(-0.761773\pi\) | ||||
−0.732770 | + | 0.680477i | \(0.761773\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 792.000 | − | 280.014i | 1.02724 | − | 0.363183i | ||||
\(772\) | −97.0000 | − | 168.009i | −0.125648 | − | 0.217628i | ||||
\(773\) | −396.817 | − | 229.103i | −0.513347 | − | 0.296381i | 0.220861 | − | 0.975305i | \(-0.429113\pi\) |
−0.734208 | + | 0.678924i | \(0.762447\pi\) | |||||||
\(774\) | −389.770 | + | 61.3321i | −0.503578 | + | 0.0792405i | ||||
\(775\) | 164.500 | + | 284.922i | 0.212258 | + | 0.367642i | ||||
\(776\) | − | 469.519i | − | 0.605050i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −540.000 | −0.694087 | ||||||||
\(779\) | 911.210 | − | 526.087i | 1.16972 | − | 0.675337i | ||||
\(780\) | −9.30306 | + | 50.0545i | −0.0119270 | + | 0.0641724i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 88.1816 | − | 50.9117i | 0.112764 | − | 0.0651045i | ||||
\(783\) | −240.000 | + | 390.323i | −0.306513 | + | 0.498497i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1001.26i | 1.27549i | ||||||||
\(786\) | 233.939 | − | 273.629i | 0.297632 | − | 0.348128i | ||||
\(787\) | −293.000 | + | 507.491i | −0.372300 | + | 0.644842i | −0.989919 | − | 0.141635i | \(-0.954764\pi\) |
0.617619 | + | 0.786477i | \(0.288097\pi\) | |||||||
\(788\) | −631.968 | − | 364.867i | −0.801990 | − | 0.463029i | ||||
\(789\) | 232.182 | + | 198.504i | 0.294273 | + | 0.251589i | ||||
\(790\) | 1236.00 | 1.56456 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.0000 | + | 43.3013i | 0.0315259 | + | 0.0546044i | ||||
\(794\) | −589.102 | − | 340.118i | −0.741942 | − | 0.428361i | ||||
\(795\) | −637.090 | − | 118.409i | −0.801371 | − | 0.148942i | ||||
\(796\) | 106.000 | + | 183.597i | 0.133166 | + | 0.230650i | ||||
\(797\) | − | 483.661i | − | 0.606852i | −0.952855 | − | 0.303426i | \(-0.901869\pi\) | ||
0.952855 | − | 0.303426i | \(-0.0981305\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 360.000 | 0.450563 | ||||||||
\(800\) | −230.252 | + | 132.936i | −0.287815 | + | 0.166170i | ||||
\(801\) | 1056.15 | − | 166.190i | 1.31854 | − | 0.207479i | ||||
\(802\) | −54.0000 | + | 93.5307i | −0.0673317 | + | 0.116622i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −130.000 | − | 367.696i | −0.161692 | − | 0.457333i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.89949i | 0.0122823i | ||||||||
\(807\) | −967.423 | − | 827.098i | −1.19879 | − | 1.02491i | ||||
\(808\) | −192.000 | + | 332.554i | −0.237624 | + | 0.411576i | ||||
\(809\) | 698.105 | + | 403.051i | 0.862923 | + | 0.498209i | 0.864990 | − | 0.501789i | \(-0.167325\pi\) |
−0.00206714 | + | 0.999998i | \(0.500658\pi\) | |||||||
\(810\) | 925.029 | − | 298.507i | 1.14201 | − | 0.368527i | ||||
\(811\) | −398.000 | −0.490752 | −0.245376 | − | 0.969428i | \(-0.578911\pi\) | ||||
−0.245376 | + | 0.969428i | \(0.578911\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 250.000 | + | 707.107i | 0.307503 | + | 0.869750i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 778.938 | + | 449.720i | 0.955752 | + | 0.551804i | ||||
\(816\) | −18.6061 | + | 100.109i | −0.0228016 | + | 0.122683i | ||||
\(817\) | 480.500 | + | 832.250i | 0.588127 | + | 1.01867i | ||||
\(818\) | 69.2965i | 0.0847145i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 576.000 | 0.702439 | ||||||||
\(821\) | 1403.56 | − | 810.344i | 1.70957 | − | 0.987021i | 0.774490 | − | 0.632586i | \(-0.218006\pi\) |
0.935081 | − | 0.354435i | \(-0.115327\pi\) | |||||||
\(822\) | −778.665 | − | 144.722i | −0.947281 | − | 0.176060i | ||||
\(823\) | 581.000 | − | 1006.32i | 0.705954 | − | 1.22275i | −0.260392 | − | 0.965503i | \(-0.583852\pi\) |
0.966346 | − | 0.257245i | \(-0.0828147\pi\) | |||||||
\(824\) | 159.217 | − | 91.9239i | 0.193224 | − | 0.111558i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 144.250i | 0.174425i | 0.996190 | + | 0.0872127i | \(0.0277960\pi\) | ||||
−0.996190 | + | 0.0872127i | \(0.972204\pi\) | |||||||
\(828\) | 54.8786 | − | 142.535i | 0.0662785 | − | 0.172144i | ||||
\(829\) | 623.500 | − | 1079.93i | 0.752111 | − | 1.30269i | −0.194687 | − | 0.980865i | \(-0.562369\pi\) |
0.946798 | − | 0.321829i | \(-0.104298\pi\) | |||||||
\(830\) | 440.908 | + | 254.558i | 0.531215 | + | 0.306697i | ||||
\(831\) | 746.655 | − | 873.332i | 0.898501 | − | 1.05094i | ||||
\(832\) | −8.00000 | −0.00961538 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 452.000 | − | 159.806i | 0.541966 | − | 0.191614i | ||||
\(835\) | 612.000 | + | 1060.02i | 0.732934 | + | 1.26948i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 166.232 | − | 89.9326i | 0.198605 | − | 0.107446i | ||||
\(838\) | −228.000 | − | 394.908i | −0.272076 | − | 0.471250i | ||||
\(839\) | 1001.26i | 1.19340i | 0.802464 | + | 0.596700i | \(0.203522\pi\) | ||||
−0.802464 | + | 0.596700i | \(0.796478\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 553.000 | 0.657551 | ||||||||
\(842\) | −383.345 | + | 221.324i | −0.455279 | + | 0.262856i | ||||
\(843\) | 97.6821 | − | 525.572i | 0.115874 | − | 0.623455i | ||||
\(844\) | 62.0000 | − | 107.387i | 0.0734597 | − | 0.127236i | ||||
\(845\) | −1234.54 | + | 712.764i | −1.46100 | + | 0.843507i | ||||
\(846\) | 420.000 | − | 339.411i | 0.496454 | − | 0.401195i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 101.823i | − | 0.120075i | ||||||
\(849\) | −594.594 | + | 695.473i | −0.700347 | + | 0.819167i | ||||
\(850\) | 282.000 | − | 488.438i | 0.331765 | − | 0.574633i | ||||
\(851\) | 7.34847 | + | 4.24264i | 0.00863510 | + | 0.00498548i | ||||
\(852\) | −270.879 | − | 231.588i | −0.317933 | − | 0.271816i | ||||
\(853\) | 337.000 | 0.395076 | 0.197538 | − | 0.980295i | \(-0.436705\pi\) | ||||
0.197538 | + | 0.980295i | \(0.436705\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1488.00 | − | 1841.31i | −1.74035 | − | 2.15357i | ||||
\(856\) | −228.000 | − | 394.908i | −0.266355 | − | 0.461341i | ||||
\(857\) | −969.998 | − | 560.029i | −1.13185 | − | 0.653476i | −0.187453 | − | 0.982274i | \(-0.560023\pi\) |
−0.944400 | + | 0.328798i | \(0.893356\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −545.000 | − | 943.968i | −0.634459 | − | 1.09891i | −0.986630 | − | 0.162979i | \(-0.947890\pi\) |
0.352171 | − | 0.935936i | \(-0.385444\pi\) | |||||||
\(860\) | 526.087i | 0.611730i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −492.000 | −0.570766 | ||||||||
\(863\) | 999.392 | − | 576.999i | 1.15804 | − | 0.668597i | 0.207209 | − | 0.978297i | \(-0.433562\pi\) |
0.950834 | + | 0.309700i | \(0.100229\pi\) | |||||||
\(864\) | 72.6765 | + | 134.336i | 0.0841164 | + | 0.155481i | ||||
\(865\) | 324.000 | − | 561.184i | 0.374566 | − | 0.648768i | ||||
\(866\) | 118.800 | − | 68.5894i | 0.137183 | − | 0.0792025i | ||||
\(867\) | 217.000 | + | 613.769i | 0.250288 | + | 0.707922i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 464.363 | + | 397.007i | 0.533751 | + | 0.456330i | ||||
\(871\) | −32.5000 | + | 56.2917i | −0.0373134 | + | 0.0646288i | ||||
\(872\) | 409.065 | + | 236.174i | 0.469111 | + | 0.270841i | ||||
\(873\) | 1394.23 | + | 536.803i | 1.59706 | + | 0.614894i | ||||
\(874\) | −372.000 | −0.425629 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −194.000 | − | 548.715i | −0.221461 | − | 0.626387i | ||||
\(877\) | 23.0000 | + | 39.8372i | 0.0262258 | + | 0.0454244i | 0.878840 | − | 0.477116i | \(-0.158318\pi\) |
−0.852615 | + | 0.522540i | \(0.824984\pi\) | |||||||
\(878\) | 458.055 | + | 264.458i | 0.521702 | + | 0.301205i | ||||
\(879\) | −74.4245 | + | 400.436i | −0.0846695 | + | 0.455559i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 924.896i | − | 1.04982i | −0.851156 | − | 0.524912i | \(-0.824098\pi\) | ||
0.851156 | − | 0.524912i | \(-0.175902\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 329.000 | 0.372593 | 0.186297 | − | 0.982494i | \(-0.440351\pi\) | ||||
0.186297 | + | 0.982494i | \(0.440351\pi\) | |||||||
\(884\) | 14.6969 | − | 8.48528i | 0.0166255 | − | 0.00959873i | ||||
\(885\) | −212.363 | − | 39.4695i | −0.239958 | − | 0.0445984i | ||||
\(886\) | −426.000 | + | 737.854i | −0.480813 | + | 0.832792i | ||||
\(887\) | 1219.85 | − | 704.278i | 1.37525 | − | 0.794000i | 0.383666 | − | 0.923472i | \(-0.374661\pi\) |
0.991583 | + | 0.129472i | \(0.0413281\pi\) | |||||||
\(888\) | −8.00000 | + | 2.82843i | −0.00900901 | + | 0.00318517i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 1425.53i | − | 1.60172i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 202.000 | − | 349.874i | 0.226457 | − | 0.392236i | ||||
\(893\) | −1139.01 | − | 657.609i | −1.27549 | − | 0.736405i | ||||
\(894\) | 187.151 | − | 218.903i | 0.209341 | − | 0.244858i | ||||
\(895\) | 1368.00 | 1.52849 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.0000 | + | 8.48528i | −0.0267559 | + | 0.00945962i | ||||
\(898\) | −30.0000 | − | 51.9615i | −0.0334076 | − | 0.0578636i | ||||
\(899\) | 102.879 | + | 59.3970i | 0.114437 | + | 0.0660700i | ||||
\(900\) | −131.504 | − | 835.717i | −0.146116 | − | 0.928574i | ||||
\(901\) | 108.000 | + | 187.061i | 0.119867 | + | 0.207615i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −456.000 | −0.504425 | ||||||||
\(905\) | −1579.92 | + | 912.168i | −1.74577 | + | 1.00792i | ||||
\(906\) | −44.9648 | + | 241.930i | −0.0496300 | + | 0.267031i | ||||
\(907\) | 87.5000 | − | 151.554i | 0.0964719 | − | 0.167094i | −0.813750 | − | 0.581215i | \(-0.802578\pi\) |
0.910222 | + | 0.414121i | \(0.135911\pi\) | |||||||
\(908\) | 29.3939 | − | 16.9706i | 0.0323721 | − | 0.0186900i | ||||
\(909\) | −768.000 | − | 950.352i | −0.844884 | − | 1.04549i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1450.98i | 1.59274i | 0.604812 | + | 0.796368i | \(0.293248\pi\) | ||||
−0.604812 | + | 0.796368i | \(0.706752\pi\) | |||||||
\(912\) | 241.737 | − | 282.750i | 0.265062 | − | 0.310032i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −557.259 | − | 321.734i | −0.609692 | − | 0.352006i | ||||
\(915\) | −967.423 | − | 827.098i | −1.05729 | − | 0.903933i | ||||
\(916\) | −2.00000 | −0.00218341 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −276.000 | − | 169.706i | −0.300654 | − | 0.184865i | ||||
\(919\) | −548.500 | − | 950.030i | −0.596844 | − | 1.03376i | −0.993284 | − | 0.115704i | \(-0.963088\pi\) |
0.396439 | − | 0.918061i | \(-0.370246\pi\) | |||||||
\(920\) | −176.363 | − | 101.823i | −0.191699 | − | 0.110678i | ||||
\(921\) | −586.948 | − | 109.089i | −0.637295 | − | 0.118447i | ||||
\(922\) | −156.000 | − | 270.200i | −0.169197 | − | 0.293058i | ||||
\(923\) | 59.3970i | 0.0643521i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 47.0000 | 0.0508108 | ||||||||
\(926\) | −8.57321 | + | 4.94975i | −0.00925833 | + | 0.00534530i | ||||
\(927\) | 90.9337 | + | 577.889i | 0.0980946 | + | 0.623397i | ||||
\(928\) | −48.0000 | + | 83.1384i | −0.0517241 | + | 0.0895888i | ||||
\(929\) | −492.347 | + | 284.257i | −0.529976 | + | 0.305982i | −0.741007 | − | 0.671498i | \(-0.765651\pi\) |
0.211031 | + | 0.977479i | \(0.432318\pi\) | |||||||
\(930\) | −84.0000 | − | 237.588i | −0.0903226 | − | 0.255471i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 661.852i | 0.710142i | ||||||||
\(933\) | 1006.12 | + | 860.182i | 1.07837 | + | 0.921953i | ||||
\(934\) | 438.000 | − | 758.638i | 0.468951 | − | 0.812247i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.14643 | − | 23.7559i | 0.00977182 | − | 0.0253802i | ||||
\(937\) | 1.00000 | 0.00106724 | 0.000533618 | − | 1.00000i | \(-0.499830\pi\) | ||||
0.000533618 | 1.00000i | \(0.499830\pi\) | ||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −119.000 | − | 336.583i | −0.126731 | − | 0.358448i | ||||
\(940\) | −360.000 | − | 623.538i | −0.382979 | − | 0.663339i | ||||
\(941\) | 330.681 | + | 190.919i | 0.351415 | + | 0.202889i | 0.665308 | − | 0.746569i | \(-0.268300\pi\) |
−0.313894 | + | 0.949458i | \(0.601634\pi\) | |||||||
\(942\) | 91.4801 | − | 492.203i | 0.0971126 | − | 0.522508i | ||||
\(943\) | 144.000 | + | 249.415i | 0.152704 | + | 0.264491i | ||||
\(944\) | − | 33.9411i | − | 0.0359546i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1455.00 | + | 840.043i | −1.53643 | + | 0.887057i | −0.537384 | + | 0.843338i | \(0.680587\pi\) |
−0.999044 | + | 0.0437190i | \(0.986079\pi\) | |||||||
\(948\) | −607.595 | − | 112.927i | −0.640923 | − | 0.119121i | ||||
\(949\) | −48.5000 | + | 84.0045i | −0.0511064 | + | 0.0885189i | ||||
\(950\) | −1784.45 | + | 1030.25i | −1.87837 | + | 1.08448i | ||||
\(951\) | −576.000 | + | 203.647i | −0.605678 | + | 0.214140i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 195.161i | − | 0.204786i | −0.994744 | − | 0.102393i | \(-0.967350\pi\) | ||
0.994744 | − | 0.102393i | \(-0.0326500\pi\) | |||||||
\(954\) | 302.363 | + | 116.415i | 0.316943 | + | 0.122028i | ||||
\(955\) | −756.000 | + | 1309.43i | −0.791623 | + | 1.37113i | ||||
\(956\) | 793.635 | + | 458.205i | 0.830162 | + | 0.479294i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −948.000 | −0.989562 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 192.000 | − | 67.8823i | 0.200000 | − | 0.0707107i | ||||
\(961\) | 456.000 | + | 789.815i | 0.474506 | + | 0.821868i | ||||
\(962\) | 1.22474 | + | 0.707107i | 0.00127312 | + | 0.000735038i | ||||
\(963\) | 1433.35 | − | 225.544i | 1.48842 | − | 0.234210i | ||||
\(964\) | 22.0000 | + | 38.1051i | 0.0228216 | + | 0.0395281i | ||||
\(965\) | − | 823.072i | − | 0.852925i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −223.000 | −0.230610 | −0.115305 | − | 0.993330i | \(-0.536785\pi\) | ||||
−0.115305 | + | 0.993330i | \(0.536785\pi\) | |||||||
\(968\) | −296.388 | + | 171.120i | −0.306186 | + | 0.176777i | ||||
\(969\) | −144.197 | + | 775.845i | −0.148811 | + | 0.800665i | ||||
\(970\) | 996.000 | − | 1725.12i | 1.02680 | − | 1.77848i | ||||
\(971\) | −492.347 | + | 284.257i | −0.507052 | + | 0.292747i | −0.731621 | − | 0.681712i | \(-0.761236\pi\) |
0.224569 | + | 0.974458i | \(0.427903\pi\) | |||||||
\(972\) | −482.000 | + | 62.2254i | −0.495885 | + | 0.0640179i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 654.781i | − | 0.672260i | ||||||
\(975\) | −91.6260 | + | 107.171i | −0.0939754 | + | 0.109919i | ||||
\(976\) | 100.000 | − | 173.205i | 0.102459 | − | 0.177464i | ||||
\(977\) | 1396.21 | + | 806.102i | 1.42908 | + | 0.825079i | 0.997048 | − | 0.0767807i | \(-0.0244641\pi\) |
0.432030 | + | 0.901859i | \(0.357797\pi\) | |||||||
\(978\) | −341.823 | − | 292.241i | −0.349512 | − | 0.298815i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1169.00 | + | 944.695i | −1.19164 | + | 0.962991i | ||||
\(982\) | −252.000 | − | 436.477i | −0.256619 | − | 0.444477i | ||||
\(983\) | 1491.74 | + | 861.256i | 1.51754 | + | 0.876151i | 0.999787 | + | 0.0206186i | \(0.00656358\pi\) |
0.517750 | + | 0.855532i | \(0.326770\pi\) | |||||||
\(984\) | −283.151 | − | 52.6261i | −0.287755 | − | 0.0534818i | ||||
\(985\) | −1548.00 | − | 2681.21i | −1.57157 | − | 2.72205i | ||||
\(986\) | − | 203.647i | − | 0.206538i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −62.0000 | −0.0627530 | ||||||||
\(989\) | −227.803 | + | 131.522i | −0.230336 | + | 0.132985i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 447.500 | − | 775.093i | 0.451564 | − | 0.782132i | −0.546919 | − | 0.837185i | \(-0.684200\pi\) |
0.998483 | + | 0.0550534i | \(0.0175329\pi\) | |||||||
\(992\) | 34.2929 | − | 19.7990i | 0.0345694 | − | 0.0199587i | ||||
\(993\) | 521.000 | + | 1473.61i | 0.524673 | + | 1.48400i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 899.440i | 0.903960i | ||||||||
\(996\) | −193.485 | − | 165.420i | −0.194262 | − | 0.166084i | ||||
\(997\) | 203.500 | − | 352.472i | 0.204112 | − | 0.353533i | −0.745737 | − | 0.666240i | \(-0.767903\pi\) |
0.949850 | + | 0.312707i | \(0.101236\pi\) | |||||||
\(998\) | 655.239 | + | 378.302i | 0.656552 | + | 0.379060i | ||||
\(999\) | 0.747449 | − | 26.9897i | 0.000748197 | − | 0.0270167i |
(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 | 294.3.h.b.263.2 | 4 | ||
3.2 | odd | 2 | inner | 294.3.h.b.263.1 | 4 | ||
7.2 | even | 3 | inner | 294.3.h.b.275.1 | 4 | ||
7.3 | odd | 6 | 294.3.b.b.197.2 | 2 | |||
7.4 | even | 3 | 294.3.b.c.197.2 | 2 | |||
7.5 | odd | 6 | 42.3.h.a.23.1 | yes | 4 | ||
7.6 | odd | 2 | 42.3.h.a.11.2 | yes | 4 | ||
21.2 | odd | 6 | inner | 294.3.h.b.275.2 | 4 | ||
21.5 | even | 6 | 42.3.h.a.23.2 | yes | 4 | ||
21.11 | odd | 6 | 294.3.b.c.197.1 | 2 | |||
21.17 | even | 6 | 294.3.b.b.197.1 | 2 | |||
21.20 | even | 2 | 42.3.h.a.11.1 | ✓ | 4 | ||
28.19 | even | 6 | 336.3.bn.c.65.2 | 4 | |||
28.27 | even | 2 | 336.3.bn.c.305.1 | 4 | |||
84.47 | odd | 6 | 336.3.bn.c.65.1 | 4 | |||
84.83 | odd | 2 | 336.3.bn.c.305.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.h.a.11.1 | ✓ | 4 | 21.20 | even | 2 | ||
42.3.h.a.11.2 | yes | 4 | 7.6 | odd | 2 | ||
42.3.h.a.23.1 | yes | 4 | 7.5 | odd | 6 | ||
42.3.h.a.23.2 | yes | 4 | 21.5 | even | 6 | ||
294.3.b.b.197.1 | 2 | 21.17 | even | 6 | |||
294.3.b.b.197.2 | 2 | 7.3 | odd | 6 | |||
294.3.b.c.197.1 | 2 | 21.11 | odd | 6 | |||
294.3.b.c.197.2 | 2 | 7.4 | even | 3 | |||
294.3.h.b.263.1 | 4 | 3.2 | odd | 2 | inner | ||
294.3.h.b.263.2 | 4 | 1.1 | even | 1 | trivial | ||
294.3.h.b.275.1 | 4 | 7.2 | even | 3 | inner | ||
294.3.h.b.275.2 | 4 | 21.2 | odd | 6 | inner | ||
336.3.bn.c.65.1 | 4 | 84.47 | odd | 6 | |||
336.3.bn.c.65.2 | 4 | 28.19 | even | 6 | |||
336.3.bn.c.305.1 | 4 | 28.27 | even | 2 | |||
336.3.bn.c.305.2 | 4 | 84.83 | odd | 2 |