Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
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: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.56155 | 1.10418 | 0.552092 | − | 0.833783i | \(-0.313830\pi\) | ||||
0.552092 | + | 0.833783i | \(0.313830\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.438447 | 0.219224 | ||||||||
\(5\) | 0.561553 | 0.251134 | 0.125567 | − | 0.992085i | \(-0.459925\pi\) | ||||
0.125567 | + | 0.992085i | \(0.459925\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.43845 | −0.862121 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.876894 | 0.277298 | ||||||||
\(11\) | 5.12311 | 1.54467 | 0.772337 | − | 0.635213i | \(-0.219088\pi\) | ||||
0.772337 | + | 0.635213i | \(0.219088\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.561553 | 0.155747 | 0.0778734 | − | 0.996963i | \(-0.475187\pi\) | ||||
0.0778734 | + | 0.996963i | \(0.475187\pi\) | |||||||
\(14\) | −1.56155 | −0.417343 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.68466 | −1.17116 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 0.246211 | 0.0550545 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.00000 | 1.70561 | ||||||||
\(23\) | 4.56155 | 0.951150 | 0.475575 | − | 0.879675i | \(-0.342240\pi\) | ||||
0.475575 | + | 0.879675i | \(0.342240\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.68466 | −0.936932 | ||||||||
\(26\) | 0.876894 | 0.171973 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.438447 | −0.0828587 | ||||||||
\(29\) | −6.56155 | −1.21845 | −0.609225 | − | 0.792998i | \(-0.708519\pi\) | ||||
−0.609225 | + | 0.792998i | \(0.708519\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.56155 | 1.17849 | 0.589245 | − | 0.807955i | \(-0.299425\pi\) | ||||
0.589245 | + | 0.807955i | \(0.299425\pi\) | |||||||
\(32\) | −2.43845 | −0.431061 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.24621 | −1.07122 | ||||||||
\(35\) | −0.561553 | −0.0949197 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.56155 | −0.749915 | −0.374957 | − | 0.927042i | \(-0.622343\pi\) | ||||
−0.374957 | + | 0.927042i | \(0.622343\pi\) | |||||||
\(38\) | −6.24621 | −1.01327 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.36932 | −0.216508 | ||||||||
\(41\) | 1.12311 | 0.175400 | 0.0876998 | − | 0.996147i | \(-0.472048\pi\) | ||||
0.0876998 | + | 0.996147i | \(0.472048\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.12311 | −0.171272 | −0.0856360 | − | 0.996326i | \(-0.527292\pi\) | ||||
−0.0856360 | + | 0.996326i | \(0.527292\pi\) | |||||||
\(44\) | 2.24621 | 0.338629 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.12311 | 1.05024 | ||||||||
\(47\) | 10.0000 | 1.45865 | 0.729325 | − | 0.684167i | \(-0.239834\pi\) | ||||
0.729325 | + | 0.684167i | \(0.239834\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −7.31534 | −1.03455 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.246211 | 0.0341434 | ||||||||
\(53\) | −3.68466 | −0.506127 | −0.253063 | − | 0.967450i | \(-0.581438\pi\) | ||||
−0.253063 | + | 0.967450i | \(0.581438\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.87689 | 0.387920 | ||||||||
\(56\) | 2.43845 | 0.325851 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.2462 | −1.34539 | ||||||||
\(59\) | −3.68466 | −0.479702 | −0.239851 | − | 0.970810i | \(-0.577099\pi\) | ||||
−0.239851 | + | 0.970810i | \(0.577099\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.56155 | −1.09619 | −0.548097 | − | 0.836415i | \(-0.684648\pi\) | ||||
−0.548097 | + | 0.836415i | \(0.684648\pi\) | |||||||
\(62\) | 10.2462 | 1.30127 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.56155 | 0.695194 | ||||||||
\(65\) | 0.315342 | 0.0391133 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.12311 | −0.137209 | −0.0686046 | − | 0.997644i | \(-0.521855\pi\) | ||||
−0.0686046 | + | 0.997644i | \(0.521855\pi\) | |||||||
\(68\) | −1.75379 | −0.212678 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.876894 | −0.104809 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.56155 | −1.00205 | −0.501027 | − | 0.865432i | \(-0.667044\pi\) | ||||
−0.501027 | + | 0.865432i | \(0.667044\pi\) | |||||||
\(74\) | −7.12311 | −0.828044 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.75379 | −0.201173 | ||||||||
\(77\) | −5.12311 | −0.583832 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.2462 | −1.15279 | −0.576394 | − | 0.817172i | \(-0.695541\pi\) | ||||
−0.576394 | + | 0.817172i | \(0.695541\pi\) | |||||||
\(80\) | −2.63068 | −0.294119 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.75379 | 0.193674 | ||||||||
\(83\) | −7.68466 | −0.843501 | −0.421750 | − | 0.906712i | \(-0.638584\pi\) | ||||
−0.421750 | + | 0.906712i | \(0.638584\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.24621 | −0.243636 | ||||||||
\(86\) | −1.75379 | −0.189116 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −12.4924 | −1.33170 | ||||||||
\(89\) | −17.6847 | −1.87457 | −0.937285 | − | 0.348564i | \(-0.886669\pi\) | ||||
−0.937285 | + | 0.348564i | \(0.886669\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.561553 | −0.0588667 | ||||||||
\(92\) | 2.00000 | 0.208514 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 15.6155 | 1.61062 | ||||||||
\(95\) | −2.24621 | −0.230456 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.87689 | −0.901312 | −0.450656 | − | 0.892698i | \(-0.648810\pi\) | ||||
−0.450656 | + | 0.892698i | \(0.648810\pi\) | |||||||
\(98\) | 1.56155 | 0.157741 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.05398 | −0.205398 | ||||||||
\(101\) | −13.6847 | −1.36167 | −0.680837 | − | 0.732435i | \(-0.738384\pi\) | ||||
−0.680837 | + | 0.732435i | \(0.738384\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.24621 | −0.221326 | −0.110663 | − | 0.993858i | \(-0.535297\pi\) | ||||
−0.110663 | + | 0.993858i | \(0.535297\pi\) | |||||||
\(104\) | −1.36932 | −0.134273 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.75379 | −0.558857 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.24621 | −0.789844 | −0.394922 | − | 0.918715i | \(-0.629228\pi\) | ||||
−0.394922 | + | 0.918715i | \(0.629228\pi\) | |||||||
\(110\) | 4.49242 | 0.428336 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.68466 | 0.442659 | ||||||||
\(113\) | 5.36932 | 0.505103 | 0.252551 | − | 0.967583i | \(-0.418730\pi\) | ||||
0.252551 | + | 0.967583i | \(0.418730\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.56155 | 0.238866 | ||||||||
\(116\) | −2.87689 | −0.267113 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.75379 | −0.529679 | ||||||||
\(119\) | 4.00000 | 0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.2462 | 1.38602 | ||||||||
\(122\) | −13.3693 | −1.21040 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.87689 | 0.258353 | ||||||||
\(125\) | −5.43845 | −0.486430 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 13.5616 | 1.19868 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.492423 | 0.0431883 | ||||||||
\(131\) | 18.0000 | 1.57267 | 0.786334 | − | 0.617802i | \(-0.211977\pi\) | ||||
0.786334 | + | 0.617802i | \(0.211977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | −1.75379 | −0.151504 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.75379 | 0.836380 | ||||||||
\(137\) | −10.5616 | −0.902334 | −0.451167 | − | 0.892439i | \(-0.648992\pi\) | ||||
−0.451167 | + | 0.892439i | \(0.648992\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.87689 | −0.583291 | −0.291645 | − | 0.956527i | \(-0.594203\pi\) | ||||
−0.291645 | + | 0.956527i | \(0.594203\pi\) | |||||||
\(140\) | −0.246211 | −0.0208086 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 18.7386 | 1.57251 | ||||||||
\(143\) | 2.87689 | 0.240578 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.68466 | −0.305994 | ||||||||
\(146\) | −13.3693 | −1.10645 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | −12.2462 | −1.00325 | −0.501624 | − | 0.865086i | \(-0.667264\pi\) | ||||
−0.501624 | + | 0.865086i | \(0.667264\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3693 | 0.925222 | 0.462611 | − | 0.886561i | \(-0.346913\pi\) | ||||
0.462611 | + | 0.886561i | \(0.346913\pi\) | |||||||
\(152\) | 9.75379 | 0.791137 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.00000 | −0.644658 | ||||||||
\(155\) | 3.68466 | 0.295959 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | −16.0000 | −1.27289 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.36932 | −0.108254 | ||||||||
\(161\) | −4.56155 | −0.359501 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.4384 | 1.05258 | 0.526290 | − | 0.850305i | \(-0.323583\pi\) | ||||
0.526290 | + | 0.850305i | \(0.323583\pi\) | |||||||
\(164\) | 0.492423 | 0.0384517 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0000 | −0.931381 | ||||||||
\(167\) | −20.4924 | −1.58575 | −0.792876 | − | 0.609383i | \(-0.791417\pi\) | ||||
−0.792876 | + | 0.609383i | \(0.791417\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6847 | −0.975743 | ||||||||
\(170\) | −3.50758 | −0.269019 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.492423 | −0.0375469 | ||||||||
\(173\) | −3.75379 | −0.285395 | −0.142698 | − | 0.989766i | \(-0.545578\pi\) | ||||
−0.142698 | + | 0.989766i | \(0.545578\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.68466 | 0.354127 | ||||||||
\(176\) | −24.0000 | −1.80907 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −27.6155 | −2.06987 | ||||||||
\(179\) | 1.75379 | 0.131084 | 0.0655422 | − | 0.997850i | \(-0.479122\pi\) | ||||
0.0655422 | + | 0.997850i | \(0.479122\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.87689 | 0.659814 | 0.329907 | − | 0.944013i | \(-0.392983\pi\) | ||||
0.329907 | + | 0.944013i | \(0.392983\pi\) | |||||||
\(182\) | −0.876894 | −0.0649997 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.1231 | −0.820006 | ||||||||
\(185\) | −2.56155 | −0.188329 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.4924 | −1.49855 | ||||||||
\(188\) | 4.38447 | 0.319770 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.50758 | −0.254466 | ||||||||
\(191\) | 1.75379 | 0.126900 | 0.0634499 | − | 0.997985i | \(-0.479790\pi\) | ||||
0.0634499 | + | 0.997985i | \(0.479790\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.2462 | 1.45735 | 0.728677 | − | 0.684857i | \(-0.240136\pi\) | ||||
0.728677 | + | 0.684857i | \(0.240136\pi\) | |||||||
\(194\) | −13.8617 | −0.995215 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.438447 | 0.0313177 | ||||||||
\(197\) | −0.876894 | −0.0624761 | −0.0312381 | − | 0.999512i | \(-0.509945\pi\) | ||||
−0.0312381 | + | 0.999512i | \(0.509945\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.56155 | 0.181584 | 0.0907918 | − | 0.995870i | \(-0.471060\pi\) | ||||
0.0907918 | + | 0.995870i | \(0.471060\pi\) | |||||||
\(200\) | 11.4233 | 0.807749 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −21.3693 | −1.50354 | ||||||||
\(203\) | 6.56155 | 0.460531 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.630683 | 0.0440488 | ||||||||
\(206\) | −3.50758 | −0.244385 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.63068 | −0.182405 | ||||||||
\(209\) | −20.4924 | −1.41749 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.68466 | 0.529034 | 0.264517 | − | 0.964381i | \(-0.414788\pi\) | ||||
0.264517 | + | 0.964381i | \(0.414788\pi\) | |||||||
\(212\) | −1.61553 | −0.110955 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.24621 | −0.426982 | ||||||||
\(215\) | −0.630683 | −0.0430122 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.56155 | −0.445427 | ||||||||
\(218\) | −12.8769 | −0.872133 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.26137 | 0.0850413 | ||||||||
\(221\) | −2.24621 | −0.151097 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.36932 | 0.493486 | 0.246743 | − | 0.969081i | \(-0.420640\pi\) | ||||
0.246743 | + | 0.969081i | \(0.420640\pi\) | |||||||
\(224\) | 2.43845 | 0.162926 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.38447 | 0.557727 | ||||||||
\(227\) | 0.246211 | 0.0163416 | 0.00817081 | − | 0.999967i | \(-0.497399\pi\) | ||||
0.00817081 | + | 0.999967i | \(0.497399\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.3693 | 1.14780 | 0.573898 | − | 0.818927i | \(-0.305430\pi\) | ||||
0.573898 | + | 0.818927i | \(0.305430\pi\) | |||||||
\(230\) | 4.00000 | 0.263752 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.0000 | 1.05045 | ||||||||
\(233\) | −13.9309 | −0.912642 | −0.456321 | − | 0.889815i | \(-0.650833\pi\) | ||||
−0.456321 | + | 0.889815i | \(0.650833\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.61553 | 0.366317 | ||||||||
\(236\) | −1.61553 | −0.105162 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.24621 | 0.404882 | ||||||||
\(239\) | −29.6847 | −1.92014 | −0.960070 | − | 0.279758i | \(-0.909746\pi\) | ||||
−0.960070 | + | 0.279758i | \(0.909746\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.8769 | −1.34480 | −0.672399 | − | 0.740188i | \(-0.734736\pi\) | ||||
−0.672399 | + | 0.740188i | \(0.734736\pi\) | |||||||
\(242\) | 23.8078 | 1.53042 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.75379 | −0.240312 | ||||||||
\(245\) | 0.561553 | 0.0358763 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.24621 | −0.142923 | ||||||||
\(248\) | −16.0000 | −1.01600 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.49242 | −0.537108 | ||||||||
\(251\) | −10.0000 | −0.631194 | −0.315597 | − | 0.948893i | \(-0.602205\pi\) | ||||
−0.315597 | + | 0.948893i | \(0.602205\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.3693 | 1.46922 | ||||||||
\(254\) | 1.56155 | 0.0979805 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.0540 | 0.628373 | ||||||||
\(257\) | −10.8078 | −0.674170 | −0.337085 | − | 0.941474i | \(-0.609441\pi\) | ||||
−0.337085 | + | 0.941474i | \(0.609441\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.56155 | 0.283441 | ||||||||
\(260\) | 0.138261 | 0.00857456 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 28.1080 | 1.73651 | ||||||||
\(263\) | −8.00000 | −0.493301 | −0.246651 | − | 0.969104i | \(-0.579330\pi\) | ||||
−0.246651 | + | 0.969104i | \(0.579330\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.06913 | −0.127106 | ||||||||
\(266\) | 6.24621 | 0.382980 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.492423 | −0.0300795 | ||||||||
\(269\) | −4.00000 | −0.243884 | −0.121942 | − | 0.992537i | \(-0.538912\pi\) | ||||
−0.121942 | + | 0.992537i | \(0.538912\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.31534 | −0.505121 | −0.252561 | − | 0.967581i | \(-0.581273\pi\) | ||||
−0.252561 | + | 0.967581i | \(0.581273\pi\) | |||||||
\(272\) | 18.7386 | 1.13620 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.4924 | −0.996344 | ||||||||
\(275\) | −24.0000 | −1.44725 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.3693 | −0.803284 | −0.401642 | − | 0.915797i | \(-0.631560\pi\) | ||||
−0.401642 | + | 0.915797i | \(0.631560\pi\) | |||||||
\(278\) | −10.7386 | −0.644060 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.36932 | 0.0818323 | ||||||||
\(281\) | −15.3693 | −0.916857 | −0.458428 | − | 0.888731i | \(-0.651587\pi\) | ||||
−0.458428 | + | 0.888731i | \(0.651587\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.0000 | −0.713326 | −0.356663 | − | 0.934233i | \(-0.616086\pi\) | ||||
−0.356663 | + | 0.934233i | \(0.616086\pi\) | |||||||
\(284\) | 5.26137 | 0.312205 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.49242 | 0.265643 | ||||||||
\(287\) | −1.12311 | −0.0662948 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −5.75379 | −0.337874 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.75379 | −0.219674 | ||||||||
\(293\) | −0.246211 | −0.0143838 | −0.00719191 | − | 0.999974i | \(-0.502289\pi\) | ||||
−0.00719191 | + | 0.999974i | \(0.502289\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.06913 | −0.120469 | ||||||||
\(296\) | 11.1231 | 0.646517 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.1231 | −1.10777 | ||||||||
\(299\) | 2.56155 | 0.148138 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.12311 | 0.0647347 | ||||||||
\(302\) | 17.7538 | 1.02162 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 18.7386 | 1.07473 | ||||||||
\(305\) | −4.80776 | −0.275292 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.12311 | 0.520683 | 0.260342 | − | 0.965517i | \(-0.416165\pi\) | ||||
0.260342 | + | 0.965517i | \(0.416165\pi\) | |||||||
\(308\) | −2.24621 | −0.127990 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.75379 | 0.326793 | ||||||||
\(311\) | 6.56155 | 0.372072 | 0.186036 | − | 0.982543i | \(-0.440436\pi\) | ||||
0.186036 | + | 0.982543i | \(0.440436\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.24621 | −0.240010 | −0.120005 | − | 0.992773i | \(-0.538291\pi\) | ||||
−0.120005 | + | 0.992773i | \(0.538291\pi\) | |||||||
\(314\) | 21.8617 | 1.23373 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.49242 | −0.252719 | ||||||||
\(317\) | −6.87689 | −0.386245 | −0.193122 | − | 0.981175i | \(-0.561861\pi\) | ||||
−0.193122 | + | 0.981175i | \(0.561861\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −33.6155 | −1.88211 | ||||||||
\(320\) | 3.12311 | 0.174587 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.12311 | −0.396955 | ||||||||
\(323\) | 16.0000 | 0.890264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.63068 | −0.145924 | ||||||||
\(326\) | 20.9848 | 1.16224 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.73863 | −0.151216 | ||||||||
\(329\) | −10.0000 | −0.551318 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.7386 | 1.68955 | 0.844774 | − | 0.535123i | \(-0.179735\pi\) | ||||
0.844774 | + | 0.535123i | \(0.179735\pi\) | |||||||
\(332\) | −3.36932 | −0.184915 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −32.0000 | −1.75096 | ||||||||
\(335\) | −0.630683 | −0.0344579 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.63068 | 0.361196 | 0.180598 | − | 0.983557i | \(-0.442197\pi\) | ||||
0.180598 | + | 0.983557i | \(0.442197\pi\) | |||||||
\(338\) | −19.8078 | −1.07740 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.984845 | −0.0534107 | ||||||||
\(341\) | 33.6155 | 1.82038 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 2.73863 | 0.147657 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.86174 | −0.315129 | ||||||||
\(347\) | −11.9309 | −0.640483 | −0.320241 | − | 0.947336i | \(-0.603764\pi\) | ||||
−0.320241 | + | 0.947336i | \(0.603764\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.7538 | −0.629166 | −0.314583 | − | 0.949230i | \(-0.601865\pi\) | ||||
−0.314583 | + | 0.949230i | \(0.601865\pi\) | |||||||
\(350\) | 7.31534 | 0.391021 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12.4924 | −0.665848 | ||||||||
\(353\) | −14.2462 | −0.758249 | −0.379125 | − | 0.925346i | \(-0.623775\pi\) | ||||
−0.379125 | + | 0.925346i | \(0.623775\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.73863 | 0.357650 | ||||||||
\(356\) | −7.75379 | −0.410950 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.73863 | 0.144741 | ||||||||
\(359\) | 11.1231 | 0.587055 | 0.293528 | − | 0.955951i | \(-0.405171\pi\) | ||||
0.293528 | + | 0.955951i | \(0.405171\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 13.8617 | 0.728557 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.246211 | −0.0129050 | ||||||||
\(365\) | −4.80776 | −0.251650 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.93087 | −0.309589 | −0.154794 | − | 0.987947i | \(-0.549472\pi\) | ||||
−0.154794 | + | 0.987947i | \(0.549472\pi\) | |||||||
\(368\) | −21.3693 | −1.11395 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.00000 | −0.207950 | ||||||||
\(371\) | 3.68466 | 0.191298 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.0000 | 0.724893 | 0.362446 | − | 0.932005i | \(-0.381942\pi\) | ||||
0.362446 | + | 0.932005i | \(0.381942\pi\) | |||||||
\(374\) | −32.0000 | −1.65468 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.3845 | −1.25753 | ||||||||
\(377\) | −3.68466 | −0.189770 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.1231 | 1.29049 | 0.645244 | − | 0.763977i | \(-0.276756\pi\) | ||||
0.645244 | + | 0.763977i | \(0.276756\pi\) | |||||||
\(380\) | −0.984845 | −0.0505215 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.73863 | 0.140121 | ||||||||
\(383\) | 2.63068 | 0.134422 | 0.0672108 | − | 0.997739i | \(-0.478590\pi\) | ||||
0.0672108 | + | 0.997739i | \(0.478590\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.87689 | −0.146620 | ||||||||
\(386\) | 31.6155 | 1.60919 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.89205 | −0.197589 | ||||||||
\(389\) | 0.876894 | 0.0444603 | 0.0222302 | − | 0.999753i | \(-0.492923\pi\) | ||||
0.0222302 | + | 0.999753i | \(0.492923\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.2462 | −0.922751 | ||||||||
\(392\) | −2.43845 | −0.123160 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.36932 | −0.0689852 | ||||||||
\(395\) | −5.75379 | −0.289505 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.8078 | 1.54620 | 0.773099 | − | 0.634286i | \(-0.218706\pi\) | ||||
0.773099 | + | 0.634286i | \(0.218706\pi\) | |||||||
\(398\) | 4.00000 | 0.200502 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 21.9460 | 1.09730 | ||||||||
\(401\) | −1.43845 | −0.0718326 | −0.0359163 | − | 0.999355i | \(-0.511435\pi\) | ||||
−0.0359163 | + | 0.999355i | \(0.511435\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.68466 | 0.183546 | ||||||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.2462 | 0.508511 | ||||||||
\(407\) | −23.3693 | −1.15837 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.24621 | −0.407749 | −0.203874 | − | 0.978997i | \(-0.565353\pi\) | ||||
−0.203874 | + | 0.978997i | \(0.565353\pi\) | |||||||
\(410\) | 0.984845 | 0.0486380 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.984845 | −0.0485198 | ||||||||
\(413\) | 3.68466 | 0.181310 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.31534 | −0.211832 | ||||||||
\(416\) | −1.36932 | −0.0671363 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −32.0000 | −1.56517 | ||||||||
\(419\) | −14.0000 | −0.683945 | −0.341972 | − | 0.939710i | \(-0.611095\pi\) | ||||
−0.341972 | + | 0.939710i | \(0.611095\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.12311 | −0.152211 | −0.0761054 | − | 0.997100i | \(-0.524249\pi\) | ||||
−0.0761054 | + | 0.997100i | \(0.524249\pi\) | |||||||
\(422\) | 12.0000 | 0.584151 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.98485 | 0.436343 | ||||||||
\(425\) | 18.7386 | 0.908957 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.56155 | 0.414323 | ||||||||
\(428\) | −1.75379 | −0.0847726 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.984845 | −0.0474934 | ||||||||
\(431\) | −0.630683 | −0.0303789 | −0.0151895 | − | 0.999885i | \(-0.504835\pi\) | ||||
−0.0151895 | + | 0.999885i | \(0.504835\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.2462 | −1.16520 | −0.582599 | − | 0.812760i | \(-0.697964\pi\) | ||||
−0.582599 | + | 0.812760i | \(0.697964\pi\) | |||||||
\(434\) | −10.2462 | −0.491834 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.61553 | −0.173152 | ||||||||
\(437\) | −18.2462 | −0.872835 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.1080 | −1.81879 | −0.909397 | − | 0.415930i | \(-0.863456\pi\) | ||||
−0.909397 | + | 0.415930i | \(0.863456\pi\) | |||||||
\(440\) | −7.01515 | −0.334434 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.50758 | −0.166838 | ||||||||
\(443\) | −26.7386 | −1.27039 | −0.635195 | − | 0.772351i | \(-0.719080\pi\) | ||||
−0.635195 | + | 0.772351i | \(0.719080\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.93087 | −0.470768 | ||||||||
\(446\) | 11.5076 | 0.544900 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.56155 | −0.262759 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.75379 | 0.270935 | ||||||||
\(452\) | 2.35416 | 0.110730 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.384472 | 0.0180442 | ||||||||
\(455\) | −0.315342 | −0.0147834 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.80776 | 0.318454 | 0.159227 | − | 0.987242i | \(-0.449100\pi\) | ||||
0.159227 | + | 0.987242i | \(0.449100\pi\) | |||||||
\(458\) | 27.1231 | 1.26738 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.12311 | 0.0523651 | ||||||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.8078 | 0.781123 | 0.390562 | − | 0.920577i | \(-0.372281\pi\) | ||||
0.390562 | + | 0.920577i | \(0.372281\pi\) | |||||||
\(464\) | 30.7386 | 1.42701 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.7538 | −1.00772 | ||||||||
\(467\) | −35.5464 | −1.64489 | −0.822446 | − | 0.568844i | \(-0.807391\pi\) | ||||
−0.822446 | + | 0.568844i | \(0.807391\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.12311 | 0.0518602 | ||||||||
\(470\) | 8.76894 | 0.404481 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.98485 | 0.413561 | ||||||||
\(473\) | −5.75379 | −0.264559 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.7386 | 0.859787 | ||||||||
\(476\) | 1.75379 | 0.0803848 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −46.3542 | −2.12019 | ||||||||
\(479\) | 22.4924 | 1.02771 | 0.513853 | − | 0.857879i | \(-0.328218\pi\) | ||||
0.513853 | + | 0.857879i | \(0.328218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.56155 | −0.116797 | ||||||||
\(482\) | −32.6004 | −1.48491 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.68466 | 0.303848 | ||||||||
\(485\) | −4.98485 | −0.226350 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.7386 | −1.03039 | −0.515193 | − | 0.857074i | \(-0.672280\pi\) | ||||
−0.515193 | + | 0.857074i | \(0.672280\pi\) | |||||||
\(488\) | 20.8769 | 0.945053 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.876894 | 0.0396140 | ||||||||
\(491\) | −17.8617 | −0.806089 | −0.403045 | − | 0.915180i | \(-0.632048\pi\) | ||||
−0.403045 | + | 0.915180i | \(0.632048\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.2462 | 1.18207 | ||||||||
\(494\) | −3.50758 | −0.157813 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −30.7386 | −1.38021 | ||||||||
\(497\) | −12.0000 | −0.538274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.0000 | 1.07439 | 0.537194 | − | 0.843459i | \(-0.319484\pi\) | ||||
0.537194 | + | 0.843459i | \(0.319484\pi\) | |||||||
\(500\) | −2.38447 | −0.106637 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.6155 | −0.696955 | ||||||||
\(503\) | 19.1231 | 0.852657 | 0.426329 | − | 0.904568i | \(-0.359807\pi\) | ||||
0.426329 | + | 0.904568i | \(0.359807\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.68466 | −0.341963 | ||||||||
\(506\) | 36.4924 | 1.62229 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.438447 | 0.0194529 | ||||||||
\(509\) | 14.7386 | 0.653278 | 0.326639 | − | 0.945149i | \(-0.394084\pi\) | ||||
0.326639 | + | 0.945149i | \(0.394084\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.56155 | 0.378741 | ||||||||
\(512\) | −11.4233 | −0.504843 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −16.8769 | −0.744408 | ||||||||
\(515\) | −1.26137 | −0.0555824 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 51.2311 | 2.25314 | ||||||||
\(518\) | 7.12311 | 0.312971 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.768944 | −0.0337204 | ||||||||
\(521\) | −10.7386 | −0.470468 | −0.235234 | − | 0.971939i | \(-0.575586\pi\) | ||||
−0.235234 | + | 0.971939i | \(0.575586\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.4233 | −1.15541 | −0.577705 | − | 0.816246i | \(-0.696052\pi\) | ||||
−0.577705 | + | 0.816246i | \(0.696052\pi\) | |||||||
\(524\) | 7.89205 | 0.344766 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.4924 | −0.544696 | ||||||||
\(527\) | −26.2462 | −1.14330 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.19224 | −0.0953146 | ||||||||
\(530\) | −3.23106 | −0.140348 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.75379 | 0.0760364 | ||||||||
\(533\) | 0.630683 | 0.0273179 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.24621 | −0.0971122 | ||||||||
\(536\) | 2.73863 | 0.118291 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.24621 | −0.269293 | ||||||||
\(539\) | 5.12311 | 0.220668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.6155 | −1.70320 | −0.851602 | − | 0.524188i | \(-0.824369\pi\) | ||||
−0.851602 | + | 0.524188i | \(0.824369\pi\) | |||||||
\(542\) | −12.9848 | −0.557747 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.75379 | 0.418190 | ||||||||
\(545\) | −4.63068 | −0.198357 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.4924 | 1.04722 | 0.523610 | − | 0.851958i | \(-0.324585\pi\) | ||||
0.523610 | + | 0.851958i | \(0.324585\pi\) | |||||||
\(548\) | −4.63068 | −0.197813 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −37.4773 | −1.59804 | ||||||||
\(551\) | 26.2462 | 1.11813 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.2462 | 0.435713 | ||||||||
\(554\) | −20.8769 | −0.886974 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.01515 | −0.127871 | ||||||||
\(557\) | 10.4924 | 0.444578 | 0.222289 | − | 0.974981i | \(-0.428647\pi\) | ||||
0.222289 | + | 0.974981i | \(0.428647\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.630683 | −0.0266751 | ||||||||
\(560\) | 2.63068 | 0.111167 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −24.0000 | −1.01238 | ||||||||
\(563\) | 20.0000 | 0.842900 | 0.421450 | − | 0.906852i | \(-0.361521\pi\) | ||||
0.421450 | + | 0.906852i | \(0.361521\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.01515 | 0.126849 | ||||||||
\(566\) | −18.7386 | −0.787644 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −29.2614 | −1.22778 | ||||||||
\(569\) | 46.3542 | 1.94327 | 0.971634 | − | 0.236491i | \(-0.0759972\pi\) | ||||
0.971634 | + | 0.236491i | \(0.0759972\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.6155 | 0.737187 | 0.368593 | − | 0.929591i | \(-0.379839\pi\) | ||||
0.368593 | + | 0.929591i | \(0.379839\pi\) | |||||||
\(572\) | 1.26137 | 0.0527404 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.75379 | −0.0732017 | ||||||||
\(575\) | −21.3693 | −0.891162 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.3153 | 0.595955 | 0.297978 | − | 0.954573i | \(-0.403688\pi\) | ||||
0.297978 | + | 0.954573i | \(0.403688\pi\) | |||||||
\(578\) | −1.56155 | −0.0649520 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.61553 | −0.0670812 | ||||||||
\(581\) | 7.68466 | 0.318813 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.8769 | −0.781801 | ||||||||
\(584\) | 20.8769 | 0.863892 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.384472 | −0.0158824 | ||||||||
\(587\) | −8.24621 | −0.340358 | −0.170179 | − | 0.985413i | \(-0.554435\pi\) | ||||
−0.170179 | + | 0.985413i | \(0.554435\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.2462 | −1.08146 | ||||||||
\(590\) | −3.23106 | −0.133020 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 21.3693 | 0.878274 | ||||||||
\(593\) | −35.3002 | −1.44960 | −0.724802 | − | 0.688957i | \(-0.758069\pi\) | ||||
−0.724802 | + | 0.688957i | \(0.758069\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.24621 | 0.0920857 | ||||||||
\(596\) | −5.36932 | −0.219936 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.00000 | 0.163572 | ||||||||
\(599\) | 2.17708 | 0.0889531 | 0.0444766 | − | 0.999010i | \(-0.485838\pi\) | ||||
0.0444766 | + | 0.999010i | \(0.485838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.7538 | −0.479447 | −0.239724 | − | 0.970841i | \(-0.577057\pi\) | ||||
−0.239724 | + | 0.970841i | \(0.577057\pi\) | |||||||
\(602\) | 1.75379 | 0.0714791 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.98485 | 0.202830 | ||||||||
\(605\) | 8.56155 | 0.348077 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.5616 | 0.428680 | 0.214340 | − | 0.976759i | \(-0.431240\pi\) | ||||
0.214340 | + | 0.976759i | \(0.431240\pi\) | |||||||
\(608\) | 9.75379 | 0.395568 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.50758 | −0.303973 | ||||||||
\(611\) | 5.61553 | 0.227180 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.3693 | 0.863099 | 0.431549 | − | 0.902089i | \(-0.357967\pi\) | ||||
0.431549 | + | 0.902089i | \(0.357967\pi\) | |||||||
\(614\) | 14.2462 | 0.574930 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.4924 | 0.503334 | ||||||||
\(617\) | 25.9309 | 1.04394 | 0.521969 | − | 0.852965i | \(-0.325198\pi\) | ||||
0.521969 | + | 0.852965i | \(0.325198\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.1080 | 1.37091 | 0.685457 | − | 0.728113i | \(-0.259602\pi\) | ||||
0.685457 | + | 0.728113i | \(0.259602\pi\) | |||||||
\(620\) | 1.61553 | 0.0648812 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.2462 | 0.410836 | ||||||||
\(623\) | 17.6847 | 0.708521 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.3693 | 0.814773 | ||||||||
\(626\) | −6.63068 | −0.265015 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.13826 | 0.244943 | ||||||||
\(629\) | 18.2462 | 0.727524 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.8769 | 0.433002 | 0.216501 | − | 0.976282i | \(-0.430535\pi\) | ||||
0.216501 | + | 0.976282i | \(0.430535\pi\) | |||||||
\(632\) | 24.9848 | 0.993844 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.7386 | −0.426486 | ||||||||
\(635\) | 0.561553 | 0.0222845 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.561553 | 0.0222495 | ||||||||
\(638\) | −52.4924 | −2.07819 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.61553 | 0.301030 | ||||||||
\(641\) | 38.8769 | 1.53555 | 0.767773 | − | 0.640723i | \(-0.221365\pi\) | ||||
0.767773 | + | 0.640723i | \(0.221365\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.2462 | −0.877305 | −0.438652 | − | 0.898657i | \(-0.644544\pi\) | ||||
−0.438652 | + | 0.898657i | \(0.644544\pi\) | |||||||
\(644\) | −2.00000 | −0.0788110 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.9848 | 0.983016 | ||||||||
\(647\) | 35.5464 | 1.39747 | 0.698737 | − | 0.715379i | \(-0.253746\pi\) | ||||
0.698737 | + | 0.715379i | \(0.253746\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.8769 | −0.740983 | ||||||||
\(650\) | −4.10795 | −0.161127 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.89205 | 0.230750 | ||||||||
\(653\) | 4.24621 | 0.166167 | 0.0830835 | − | 0.996543i | \(-0.473523\pi\) | ||||
0.0830835 | + | 0.996543i | \(0.473523\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.1080 | 0.394950 | ||||||||
\(656\) | −5.26137 | −0.205422 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −15.6155 | −0.608757 | ||||||||
\(659\) | 50.1771 | 1.95462 | 0.977311 | − | 0.211810i | \(-0.0679359\pi\) | ||||
0.977311 | + | 0.211810i | \(0.0679359\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.5616 | −0.644170 | −0.322085 | − | 0.946711i | \(-0.604384\pi\) | ||||
−0.322085 | + | 0.946711i | \(0.604384\pi\) | |||||||
\(662\) | 48.0000 | 1.86557 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18.7386 | 0.727200 | ||||||||
\(665\) | 2.24621 | 0.0871043 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.9309 | −1.15893 | ||||||||
\(668\) | −8.98485 | −0.347634 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.984845 | −0.0380479 | ||||||||
\(671\) | −43.8617 | −1.69326 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.56155 | 0.330024 | 0.165012 | − | 0.986292i | \(-0.447234\pi\) | ||||
0.165012 | + | 0.986292i | \(0.447234\pi\) | |||||||
\(674\) | 10.3542 | 0.398827 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.56155 | −0.213906 | ||||||||
\(677\) | 20.9848 | 0.806513 | 0.403257 | − | 0.915087i | \(-0.367878\pi\) | ||||
0.403257 | + | 0.915087i | \(0.367878\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.87689 | 0.340664 | ||||||||
\(680\) | 5.47727 | 0.210044 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 52.4924 | 2.01004 | ||||||||
\(683\) | 8.38447 | 0.320823 | 0.160411 | − | 0.987050i | \(-0.448718\pi\) | ||||
0.160411 | + | 0.987050i | \(0.448718\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.93087 | −0.226607 | ||||||||
\(686\) | −1.56155 | −0.0596204 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.26137 | 0.200588 | ||||||||
\(689\) | −2.06913 | −0.0788276 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.7538 | 0.979720 | 0.489860 | − | 0.871801i | \(-0.337048\pi\) | ||||
0.489860 | + | 0.871801i | \(0.337048\pi\) | |||||||
\(692\) | −1.64584 | −0.0625654 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.6307 | −0.707211 | ||||||||
\(695\) | −3.86174 | −0.146484 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.49242 | −0.170163 | ||||||||
\(698\) | −18.3542 | −0.694715 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.05398 | 0.0776330 | ||||||||
\(701\) | −3.05398 | −0.115347 | −0.0576735 | − | 0.998335i | \(-0.518368\pi\) | ||||
−0.0576735 | + | 0.998335i | \(0.518368\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.2462 | 0.688169 | ||||||||
\(704\) | 28.4924 | 1.07385 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.2462 | −0.837247 | ||||||||
\(707\) | 13.6847 | 0.514665 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.2462 | 1.21103 | 0.605516 | − | 0.795833i | \(-0.292967\pi\) | ||||
0.605516 | + | 0.795833i | \(0.292967\pi\) | |||||||
\(710\) | 10.5227 | 0.394911 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 43.1231 | 1.61611 | ||||||||
\(713\) | 29.9309 | 1.12092 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.61553 | 0.0604173 | ||||||||
\(716\) | 0.768944 | 0.0287368 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.3693 | 0.648217 | ||||||||
\(719\) | 46.3542 | 1.72872 | 0.864359 | − | 0.502875i | \(-0.167724\pi\) | ||||
0.864359 | + | 0.502875i | \(0.167724\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.24621 | 0.0836533 | ||||||||
\(722\) | −4.68466 | −0.174345 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.89205 | 0.144647 | ||||||||
\(725\) | 30.7386 | 1.14160 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.36932 | 0.273313 | 0.136656 | − | 0.990619i | \(-0.456364\pi\) | ||||
0.136656 | + | 0.990619i | \(0.456364\pi\) | |||||||
\(728\) | 1.36932 | 0.0507503 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.50758 | −0.277868 | ||||||||
\(731\) | 4.49242 | 0.166158 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.4233 | −0.606608 | −0.303304 | − | 0.952894i | \(-0.598090\pi\) | ||||
−0.303304 | + | 0.952894i | \(0.598090\pi\) | |||||||
\(734\) | −9.26137 | −0.341843 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.1231 | −0.410003 | ||||||||
\(737\) | −5.75379 | −0.211944 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.1922 | −0.705998 | −0.352999 | − | 0.935624i | \(-0.614838\pi\) | ||||
−0.352999 | + | 0.935624i | \(0.614838\pi\) | |||||||
\(740\) | −1.12311 | −0.0412862 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.75379 | 0.211228 | ||||||||
\(743\) | 26.1771 | 0.960344 | 0.480172 | − | 0.877174i | \(-0.340574\pi\) | ||||
0.480172 | + | 0.877174i | \(0.340574\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.87689 | −0.251950 | ||||||||
\(746\) | 21.8617 | 0.800415 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.98485 | −0.328518 | ||||||||
\(749\) | 4.00000 | 0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.00000 | −0.291924 | −0.145962 | − | 0.989290i | \(-0.546628\pi\) | ||||
−0.145962 | + | 0.989290i | \(0.546628\pi\) | |||||||
\(752\) | −46.8466 | −1.70832 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.75379 | −0.209541 | ||||||||
\(755\) | 6.38447 | 0.232355 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.4384 | 0.851885 | 0.425942 | − | 0.904750i | \(-0.359943\pi\) | ||||
0.425942 | + | 0.904750i | \(0.359943\pi\) | |||||||
\(758\) | 39.2311 | 1.42494 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.47727 | 0.198681 | ||||||||
\(761\) | 48.4233 | 1.75534 | 0.877671 | − | 0.479263i | \(-0.159096\pi\) | ||||
0.877671 | + | 0.479263i | \(0.159096\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.24621 | 0.298533 | ||||||||
\(764\) | 0.768944 | 0.0278194 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.10795 | 0.148426 | ||||||||
\(767\) | −2.06913 | −0.0747120 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.4924 | −0.811098 | −0.405549 | − | 0.914073i | \(-0.632920\pi\) | ||||
−0.405549 | + | 0.914073i | \(0.632920\pi\) | |||||||
\(770\) | −4.49242 | −0.161896 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.87689 | 0.319486 | ||||||||
\(773\) | 22.1080 | 0.795168 | 0.397584 | − | 0.917566i | \(-0.369849\pi\) | ||||
0.397584 | + | 0.917566i | \(0.369849\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −30.7386 | −1.10416 | ||||||||
\(776\) | 21.6458 | 0.777040 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.36932 | 0.0490924 | ||||||||
\(779\) | −4.49242 | −0.160958 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 61.4773 | 2.19983 | ||||||||
\(782\) | −28.4924 | −1.01889 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.68466 | −0.167309 | ||||||||
\(785\) | 7.86174 | 0.280598 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.94602 | 0.176307 | 0.0881534 | − | 0.996107i | \(-0.471903\pi\) | ||||
0.0881534 | + | 0.996107i | \(0.471903\pi\) | |||||||
\(788\) | −0.384472 | −0.0136962 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.98485 | −0.319666 | ||||||||
\(791\) | −5.36932 | −0.190911 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.80776 | −0.170729 | ||||||||
\(794\) | 48.1080 | 1.70729 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.12311 | 0.0398074 | ||||||||
\(797\) | 34.1080 | 1.20817 | 0.604083 | − | 0.796922i | \(-0.293540\pi\) | ||||
0.604083 | + | 0.796922i | \(0.293540\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.0000 | −1.41510 | ||||||||
\(800\) | 11.4233 | 0.403874 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.24621 | −0.0793165 | ||||||||
\(803\) | −43.8617 | −1.54785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.56155 | −0.0902829 | ||||||||
\(806\) | 5.75379 | 0.202669 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 33.3693 | 1.17393 | ||||||||
\(809\) | 56.1080 | 1.97265 | 0.986325 | − | 0.164811i | \(-0.0527013\pi\) | ||||
0.986325 | + | 0.164811i | \(0.0527013\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.0540 | −1.09045 | −0.545226 | − | 0.838289i | \(-0.683556\pi\) | ||||
−0.545226 | + | 0.838289i | \(0.683556\pi\) | |||||||
\(812\) | 2.87689 | 0.100959 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −36.4924 | −1.27906 | ||||||||
\(815\) | 7.54640 | 0.264339 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.49242 | 0.157170 | ||||||||
\(818\) | −12.8769 | −0.450230 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.276521 | 0.00965654 | ||||||||
\(821\) | −50.4233 | −1.75979 | −0.879893 | − | 0.475173i | \(-0.842386\pi\) | ||||
−0.879893 | + | 0.475173i | \(0.842386\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.9848 | 0.870917 | 0.435458 | − | 0.900209i | \(-0.356586\pi\) | ||||
0.435458 | + | 0.900209i | \(0.356586\pi\) | |||||||
\(824\) | 5.47727 | 0.190810 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.75379 | 0.200200 | ||||||||
\(827\) | −39.3002 | −1.36660 | −0.683301 | − | 0.730137i | \(-0.739456\pi\) | ||||
−0.683301 | + | 0.730137i | \(0.739456\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.4924 | −0.781194 | −0.390597 | − | 0.920562i | \(-0.627731\pi\) | ||||
−0.390597 | + | 0.920562i | \(0.627731\pi\) | |||||||
\(830\) | −6.73863 | −0.233901 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.12311 | 0.108274 | ||||||||
\(833\) | −4.00000 | −0.138592 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.5076 | −0.398236 | ||||||||
\(836\) | −8.98485 | −0.310747 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21.8617 | −0.755201 | ||||||||
\(839\) | 23.5464 | 0.812912 | 0.406456 | − | 0.913670i | \(-0.366764\pi\) | ||||
0.406456 | + | 0.913670i | \(0.366764\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0540 | 0.484620 | ||||||||
\(842\) | −4.87689 | −0.168069 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.36932 | 0.115977 | ||||||||
\(845\) | −7.12311 | −0.245042 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.2462 | −0.523866 | ||||||||
\(848\) | 17.2614 | 0.592758 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 29.2614 | 1.00366 | ||||||||
\(851\) | −20.8078 | −0.713281 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.2311 | 1.27477 | 0.637384 | − | 0.770547i | \(-0.280017\pi\) | ||||
0.637384 | + | 0.770547i | \(0.280017\pi\) | |||||||
\(854\) | 13.3693 | 0.457489 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.75379 | 0.333378 | ||||||||
\(857\) | −29.0540 | −0.992465 | −0.496232 | − | 0.868190i | \(-0.665284\pi\) | ||||
−0.496232 | + | 0.868190i | \(0.665284\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0000 | 1.50126 | 0.750630 | − | 0.660722i | \(-0.229750\pi\) | ||||
0.750630 | + | 0.660722i | \(0.229750\pi\) | |||||||
\(860\) | −0.276521 | −0.00942930 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.984845 | −0.0335440 | ||||||||
\(863\) | 9.68466 | 0.329670 | 0.164835 | − | 0.986321i | \(-0.447291\pi\) | ||||
0.164835 | + | 0.986321i | \(0.447291\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.10795 | −0.0716725 | ||||||||
\(866\) | −37.8617 | −1.28659 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.87689 | −0.0976482 | ||||||||
\(869\) | −52.4924 | −1.78068 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.630683 | −0.0213699 | ||||||||
\(872\) | 20.1080 | 0.680941 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −28.4924 | −0.963771 | ||||||||
\(875\) | 5.43845 | 0.183853 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.2311 | 1.66241 | 0.831207 | − | 0.555963i | \(-0.187650\pi\) | ||||
0.831207 | + | 0.555963i | \(0.187650\pi\) | |||||||
\(878\) | −59.5076 | −2.00828 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13.4773 | −0.454319 | ||||||||
\(881\) | 20.4233 | 0.688078 | 0.344039 | − | 0.938955i | \(-0.388205\pi\) | ||||
0.344039 | + | 0.938955i | \(0.388205\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.6695 | −1.09942 | −0.549708 | − | 0.835357i | \(-0.685261\pi\) | ||||
−0.549708 | + | 0.835357i | \(0.685261\pi\) | |||||||
\(884\) | −0.984845 | −0.0331239 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −41.7538 | −1.40275 | ||||||||
\(887\) | −45.9309 | −1.54221 | −0.771104 | − | 0.636709i | \(-0.780295\pi\) | ||||
−0.771104 | + | 0.636709i | \(0.780295\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −15.5076 | −0.519815 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.23106 | 0.108184 | ||||||||
\(893\) | −40.0000 | −1.33855 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.984845 | 0.0329197 | ||||||||
\(896\) | −13.5616 | −0.453060 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.36932 | −0.312658 | ||||||||
\(899\) | −43.0540 | −1.43593 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.7386 | 0.491015 | ||||||||
\(902\) | 8.98485 | 0.299163 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.0928 | −0.435460 | ||||||||
\(905\) | 4.98485 | 0.165702 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.6847 | 1.05207 | 0.526036 | − | 0.850462i | \(-0.323678\pi\) | ||||
0.526036 | + | 0.850462i | \(0.323678\pi\) | |||||||
\(908\) | 0.107951 | 0.00358247 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.492423 | −0.0163236 | ||||||||
\(911\) | −38.2462 | −1.26715 | −0.633577 | − | 0.773680i | \(-0.718414\pi\) | ||||
−0.633577 | + | 0.773680i | \(0.718414\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.3693 | −1.30293 | ||||||||
\(914\) | 10.6307 | 0.351632 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.61553 | 0.251624 | ||||||||
\(917\) | −18.0000 | −0.594412 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.0540 | 1.42022 | 0.710110 | − | 0.704091i | \(-0.248645\pi\) | ||||
0.710110 | + | 0.704091i | \(0.248645\pi\) | |||||||
\(920\) | −6.24621 | −0.205931 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −21.8617 | −0.719978 | ||||||||
\(923\) | 6.73863 | 0.221805 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.3693 | 0.702619 | ||||||||
\(926\) | 26.2462 | 0.862504 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16.0000 | 0.525226 | ||||||||
\(929\) | −30.4924 | −1.00042 | −0.500212 | − | 0.865903i | \(-0.666745\pi\) | ||||
−0.500212 | + | 0.865903i | \(0.666745\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.00000 | −0.131095 | ||||||||
\(932\) | −6.10795 | −0.200073 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −55.5076 | −1.81626 | ||||||||
\(935\) | −11.5076 | −0.376338 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.8617 | 1.62891 | 0.814456 | − | 0.580225i | \(-0.197036\pi\) | ||||
0.814456 | + | 0.580225i | \(0.197036\pi\) | |||||||
\(938\) | 1.75379 | 0.0572632 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.46211 | 0.0803053 | ||||||||
\(941\) | 15.3693 | 0.501025 | 0.250513 | − | 0.968113i | \(-0.419401\pi\) | ||||
0.250513 | + | 0.968113i | \(0.419401\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.12311 | 0.166831 | ||||||||
\(944\) | 17.2614 | 0.561810 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.98485 | −0.292123 | ||||||||
\(947\) | 35.6155 | 1.15735 | 0.578675 | − | 0.815559i | \(-0.303570\pi\) | ||||
0.578675 | + | 0.815559i | \(0.303570\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.80776 | −0.156067 | ||||||||
\(950\) | 29.2614 | 0.949364 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.75379 | −0.316122 | ||||||||
\(953\) | −42.9848 | −1.39242 | −0.696208 | − | 0.717840i | \(-0.745131\pi\) | ||||
−0.696208 | + | 0.717840i | \(0.745131\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.984845 | 0.0318688 | ||||||||
\(956\) | −13.0152 | −0.420940 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 35.1231 | 1.13478 | ||||||||
\(959\) | 10.5616 | 0.341050 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0540 | 0.388838 | ||||||||
\(962\) | −4.00000 | −0.128965 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.15342 | −0.294812 | ||||||||
\(965\) | 11.3693 | 0.365991 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.6155 | 1.20963 | 0.604817 | − | 0.796365i | \(-0.293246\pi\) | ||||
0.604817 | + | 0.796365i | \(0.293246\pi\) | |||||||
\(968\) | −37.1771 | −1.19492 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.78410 | −0.249932 | ||||||||
\(971\) | −61.2311 | −1.96500 | −0.982499 | − | 0.186268i | \(-0.940361\pi\) | ||||
−0.982499 | + | 0.186268i | \(0.940361\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.87689 | 0.220463 | ||||||||
\(974\) | −35.5076 | −1.13774 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 40.1080 | 1.28382 | ||||||||
\(977\) | −59.6155 | −1.90727 | −0.953635 | − | 0.300966i | \(-0.902691\pi\) | ||||
−0.953635 | + | 0.300966i | \(0.902691\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −90.6004 | −2.89560 | ||||||||
\(980\) | 0.246211 | 0.00786493 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −27.8920 | −0.890071 | ||||||||
\(983\) | −30.4924 | −0.972557 | −0.486279 | − | 0.873804i | \(-0.661646\pi\) | ||||
−0.486279 | + | 0.873804i | \(0.661646\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.492423 | −0.0156899 | ||||||||
\(986\) | 40.9848 | 1.30522 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.984845 | −0.0313321 | ||||||||
\(989\) | −5.12311 | −0.162905 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.9848 | 1.04780 | 0.523899 | − | 0.851780i | \(-0.324477\pi\) | ||||
0.523899 | + | 0.851780i | \(0.324477\pi\) | |||||||
\(992\) | −16.0000 | −0.508001 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −18.7386 | −0.594353 | ||||||||
\(995\) | 1.43845 | 0.0456018 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.0000 | −0.443384 | −0.221692 | − | 0.975117i | \(-0.571158\pi\) | ||||
−0.221692 | + | 0.975117i | \(0.571158\pi\) | |||||||
\(998\) | 37.4773 | 1.18632 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.h.1.2 | 2 | ||
3.2 | odd | 2 | 2667.2.a.i.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.i.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
8001.2.a.h.1.2 | 2 | 1.1 | even | 1 | trivial |