Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6038,2,Mod(1,6038)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6038, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6038.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6038 = 2 \cdot 3019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6038.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: | \(48.2136727404\) |
Analytic rank: | \(0\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6038.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.10090 | −1.21295 | −0.606476 | − | 0.795101i | \(-0.707418\pi\) | ||||
−0.606476 | + | 0.795101i | \(0.707418\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.50554 | −1.56773 | −0.783863 | − | 0.620934i | \(-0.786753\pi\) | ||||
−0.783863 | + | 0.620934i | \(0.786753\pi\) | |||||||
\(6\) | 2.10090 | 0.857687 | ||||||||
\(7\) | 3.00259 | 1.13487 | 0.567437 | − | 0.823417i | \(-0.307935\pi\) | ||||
0.567437 | + | 0.823417i | \(0.307935\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.41376 | 0.471255 | ||||||||
\(10\) | 3.50554 | 1.10855 | ||||||||
\(11\) | 1.00020 | 0.301571 | 0.150786 | − | 0.988566i | \(-0.451820\pi\) | ||||
0.150786 | + | 0.988566i | \(0.451820\pi\) | |||||||
\(12\) | −2.10090 | −0.606476 | ||||||||
\(13\) | 0.205336 | 0.0569501 | 0.0284750 | − | 0.999595i | \(-0.490935\pi\) | ||||
0.0284750 | + | 0.999595i | \(0.490935\pi\) | |||||||
\(14\) | −3.00259 | −0.802476 | ||||||||
\(15\) | 7.36478 | 1.90158 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.81052 | −1.65179 | −0.825897 | − | 0.563821i | \(-0.809331\pi\) | ||||
−0.825897 | + | 0.563821i | \(0.809331\pi\) | |||||||
\(18\) | −1.41376 | −0.333227 | ||||||||
\(19\) | −1.24499 | −0.285620 | −0.142810 | − | 0.989750i | \(-0.545614\pi\) | ||||
−0.142810 | + | 0.989750i | \(0.545614\pi\) | |||||||
\(20\) | −3.50554 | −0.783863 | ||||||||
\(21\) | −6.30813 | −1.37655 | ||||||||
\(22\) | −1.00020 | −0.213243 | ||||||||
\(23\) | −4.38251 | −0.913817 | −0.456909 | − | 0.889514i | \(-0.651043\pi\) | ||||
−0.456909 | + | 0.889514i | \(0.651043\pi\) | |||||||
\(24\) | 2.10090 | 0.428844 | ||||||||
\(25\) | 7.28882 | 1.45776 | ||||||||
\(26\) | −0.205336 | −0.0402698 | ||||||||
\(27\) | 3.33252 | 0.641343 | ||||||||
\(28\) | 3.00259 | 0.567437 | ||||||||
\(29\) | −5.03372 | −0.934739 | −0.467370 | − | 0.884062i | \(-0.654798\pi\) | ||||
−0.467370 | + | 0.884062i | \(0.654798\pi\) | |||||||
\(30\) | −7.36478 | −1.34462 | ||||||||
\(31\) | 5.72537 | 1.02831 | 0.514154 | − | 0.857698i | \(-0.328106\pi\) | ||||
0.514154 | + | 0.857698i | \(0.328106\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.10131 | −0.365792 | ||||||||
\(34\) | 6.81052 | 1.16799 | ||||||||
\(35\) | −10.5257 | −1.77917 | ||||||||
\(36\) | 1.41376 | 0.235627 | ||||||||
\(37\) | 7.15265 | 1.17589 | 0.587945 | − | 0.808901i | \(-0.299937\pi\) | ||||
0.587945 | + | 0.808901i | \(0.299937\pi\) | |||||||
\(38\) | 1.24499 | 0.201964 | ||||||||
\(39\) | −0.431391 | −0.0690778 | ||||||||
\(40\) | 3.50554 | 0.554275 | ||||||||
\(41\) | 1.01826 | 0.159026 | 0.0795129 | − | 0.996834i | \(-0.474664\pi\) | ||||
0.0795129 | + | 0.996834i | \(0.474664\pi\) | |||||||
\(42\) | 6.30813 | 0.973366 | ||||||||
\(43\) | −7.58576 | −1.15682 | −0.578409 | − | 0.815747i | \(-0.696326\pi\) | ||||
−0.578409 | + | 0.815747i | \(0.696326\pi\) | |||||||
\(44\) | 1.00020 | 0.150786 | ||||||||
\(45\) | −4.95601 | −0.738798 | ||||||||
\(46\) | 4.38251 | 0.646166 | ||||||||
\(47\) | 5.84435 | 0.852486 | 0.426243 | − | 0.904609i | \(-0.359837\pi\) | ||||
0.426243 | + | 0.904609i | \(0.359837\pi\) | |||||||
\(48\) | −2.10090 | −0.303238 | ||||||||
\(49\) | 2.01556 | 0.287937 | ||||||||
\(50\) | −7.28882 | −1.03079 | ||||||||
\(51\) | 14.3082 | 2.00355 | ||||||||
\(52\) | 0.205336 | 0.0284750 | ||||||||
\(53\) | −6.56170 | −0.901319 | −0.450660 | − | 0.892696i | \(-0.648811\pi\) | ||||
−0.450660 | + | 0.892696i | \(0.648811\pi\) | |||||||
\(54\) | −3.33252 | −0.453498 | ||||||||
\(55\) | −3.50624 | −0.472781 | ||||||||
\(56\) | −3.00259 | −0.401238 | ||||||||
\(57\) | 2.61559 | 0.346443 | ||||||||
\(58\) | 5.03372 | 0.660960 | ||||||||
\(59\) | 3.16104 | 0.411533 | 0.205766 | − | 0.978601i | \(-0.434031\pi\) | ||||
0.205766 | + | 0.978601i | \(0.434031\pi\) | |||||||
\(60\) | 7.36478 | 0.950789 | ||||||||
\(61\) | −4.70986 | −0.603036 | −0.301518 | − | 0.953461i | \(-0.597493\pi\) | ||||
−0.301518 | + | 0.953461i | \(0.597493\pi\) | |||||||
\(62\) | −5.72537 | −0.727123 | ||||||||
\(63\) | 4.24496 | 0.534814 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.719815 | −0.0892821 | ||||||||
\(66\) | 2.10131 | 0.258654 | ||||||||
\(67\) | 15.4818 | 1.89141 | 0.945703 | − | 0.325033i | \(-0.105376\pi\) | ||||
0.945703 | + | 0.325033i | \(0.105376\pi\) | |||||||
\(68\) | −6.81052 | −0.825897 | ||||||||
\(69\) | 9.20721 | 1.10842 | ||||||||
\(70\) | 10.5257 | 1.25806 | ||||||||
\(71\) | −12.0465 | −1.42965 | −0.714827 | − | 0.699302i | \(-0.753494\pi\) | ||||
−0.714827 | + | 0.699302i | \(0.753494\pi\) | |||||||
\(72\) | −1.41376 | −0.166614 | ||||||||
\(73\) | −7.76330 | −0.908626 | −0.454313 | − | 0.890842i | \(-0.650115\pi\) | ||||
−0.454313 | + | 0.890842i | \(0.650115\pi\) | |||||||
\(74\) | −7.15265 | −0.831479 | ||||||||
\(75\) | −15.3130 | −1.76820 | ||||||||
\(76\) | −1.24499 | −0.142810 | ||||||||
\(77\) | 3.00319 | 0.342245 | ||||||||
\(78\) | 0.431391 | 0.0488454 | ||||||||
\(79\) | 0.496972 | 0.0559137 | 0.0279569 | − | 0.999609i | \(-0.491100\pi\) | ||||
0.0279569 | + | 0.999609i | \(0.491100\pi\) | |||||||
\(80\) | −3.50554 | −0.391931 | ||||||||
\(81\) | −11.2426 | −1.24917 | ||||||||
\(82\) | −1.01826 | −0.112448 | ||||||||
\(83\) | 8.02145 | 0.880469 | 0.440234 | − | 0.897883i | \(-0.354895\pi\) | ||||
0.440234 | + | 0.897883i | \(0.354895\pi\) | |||||||
\(84\) | −6.30813 | −0.688274 | ||||||||
\(85\) | 23.8746 | 2.58956 | ||||||||
\(86\) | 7.58576 | 0.817993 | ||||||||
\(87\) | 10.5753 | 1.13379 | ||||||||
\(88\) | −1.00020 | −0.106622 | ||||||||
\(89\) | −8.27457 | −0.877103 | −0.438551 | − | 0.898706i | \(-0.644508\pi\) | ||||
−0.438551 | + | 0.898706i | \(0.644508\pi\) | |||||||
\(90\) | 4.95601 | 0.522409 | ||||||||
\(91\) | 0.616542 | 0.0646311 | ||||||||
\(92\) | −4.38251 | −0.456909 | ||||||||
\(93\) | −12.0284 | −1.24729 | ||||||||
\(94\) | −5.84435 | −0.602799 | ||||||||
\(95\) | 4.36436 | 0.447773 | ||||||||
\(96\) | 2.10090 | 0.214422 | ||||||||
\(97\) | −5.09387 | −0.517204 | −0.258602 | − | 0.965984i | \(-0.583262\pi\) | ||||
−0.258602 | + | 0.965984i | \(0.583262\pi\) | |||||||
\(98\) | −2.01556 | −0.203602 | ||||||||
\(99\) | 1.41405 | 0.142117 | ||||||||
\(100\) | 7.28882 | 0.728882 | ||||||||
\(101\) | 3.26281 | 0.324661 | 0.162331 | − | 0.986736i | \(-0.448099\pi\) | ||||
0.162331 | + | 0.986736i | \(0.448099\pi\) | |||||||
\(102\) | −14.3082 | −1.41672 | ||||||||
\(103\) | −16.2738 | −1.60350 | −0.801751 | − | 0.597658i | \(-0.796098\pi\) | ||||
−0.801751 | + | 0.597658i | \(0.796098\pi\) | |||||||
\(104\) | −0.205336 | −0.0201349 | ||||||||
\(105\) | 22.1134 | 2.15805 | ||||||||
\(106\) | 6.56170 | 0.637329 | ||||||||
\(107\) | 14.4097 | 1.39304 | 0.696521 | − | 0.717536i | \(-0.254730\pi\) | ||||
0.696521 | + | 0.717536i | \(0.254730\pi\) | |||||||
\(108\) | 3.33252 | 0.320671 | ||||||||
\(109\) | −17.3981 | −1.66643 | −0.833217 | − | 0.552946i | \(-0.813504\pi\) | ||||
−0.833217 | + | 0.552946i | \(0.813504\pi\) | |||||||
\(110\) | 3.50624 | 0.334307 | ||||||||
\(111\) | −15.0270 | −1.42630 | ||||||||
\(112\) | 3.00259 | 0.283718 | ||||||||
\(113\) | −17.8859 | −1.68257 | −0.841284 | − | 0.540593i | \(-0.818200\pi\) | ||||
−0.841284 | + | 0.540593i | \(0.818200\pi\) | |||||||
\(114\) | −2.61559 | −0.244972 | ||||||||
\(115\) | 15.3631 | 1.43261 | ||||||||
\(116\) | −5.03372 | −0.467370 | ||||||||
\(117\) | 0.290297 | 0.0268380 | ||||||||
\(118\) | −3.16104 | −0.290998 | ||||||||
\(119\) | −20.4492 | −1.87458 | ||||||||
\(120\) | −7.36478 | −0.672309 | ||||||||
\(121\) | −9.99960 | −0.909055 | ||||||||
\(122\) | 4.70986 | 0.426411 | ||||||||
\(123\) | −2.13926 | −0.192891 | ||||||||
\(124\) | 5.72537 | 0.514154 | ||||||||
\(125\) | −8.02354 | −0.717647 | ||||||||
\(126\) | −4.24496 | −0.378171 | ||||||||
\(127\) | 17.5216 | 1.55479 | 0.777395 | − | 0.629013i | \(-0.216541\pi\) | ||||
0.777395 | + | 0.629013i | \(0.216541\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 15.9369 | 1.40316 | ||||||||
\(130\) | 0.719815 | 0.0631320 | ||||||||
\(131\) | −7.20210 | −0.629250 | −0.314625 | − | 0.949216i | \(-0.601879\pi\) | ||||
−0.314625 | + | 0.949216i | \(0.601879\pi\) | |||||||
\(132\) | −2.10131 | −0.182896 | ||||||||
\(133\) | −3.73819 | −0.324142 | ||||||||
\(134\) | −15.4818 | −1.33743 | ||||||||
\(135\) | −11.6823 | −1.00545 | ||||||||
\(136\) | 6.81052 | 0.583997 | ||||||||
\(137\) | −12.4217 | −1.06126 | −0.530629 | − | 0.847604i | \(-0.678044\pi\) | ||||
−0.530629 | + | 0.847604i | \(0.678044\pi\) | |||||||
\(138\) | −9.20721 | −0.783769 | ||||||||
\(139\) | 5.91539 | 0.501737 | 0.250868 | − | 0.968021i | \(-0.419284\pi\) | ||||
0.250868 | + | 0.968021i | \(0.419284\pi\) | |||||||
\(140\) | −10.5257 | −0.889585 | ||||||||
\(141\) | −12.2784 | −1.03403 | ||||||||
\(142\) | 12.0465 | 1.01092 | ||||||||
\(143\) | 0.205377 | 0.0171745 | ||||||||
\(144\) | 1.41376 | 0.117814 | ||||||||
\(145\) | 17.6459 | 1.46541 | ||||||||
\(146\) | 7.76330 | 0.642495 | ||||||||
\(147\) | −4.23448 | −0.349254 | ||||||||
\(148\) | 7.15265 | 0.587945 | ||||||||
\(149\) | −2.03614 | −0.166807 | −0.0834036 | − | 0.996516i | \(-0.526579\pi\) | ||||
−0.0834036 | + | 0.996516i | \(0.526579\pi\) | |||||||
\(150\) | 15.3130 | 1.25031 | ||||||||
\(151\) | −19.3814 | −1.57724 | −0.788620 | − | 0.614881i | \(-0.789204\pi\) | ||||
−0.788620 | + | 0.614881i | \(0.789204\pi\) | |||||||
\(152\) | 1.24499 | 0.100982 | ||||||||
\(153\) | −9.62847 | −0.778416 | ||||||||
\(154\) | −3.00319 | −0.242004 | ||||||||
\(155\) | −20.0705 | −1.61210 | ||||||||
\(156\) | −0.431391 | −0.0345389 | ||||||||
\(157\) | −7.21945 | −0.576175 | −0.288088 | − | 0.957604i | \(-0.593019\pi\) | ||||
−0.288088 | + | 0.957604i | \(0.593019\pi\) | |||||||
\(158\) | −0.496972 | −0.0395370 | ||||||||
\(159\) | 13.7855 | 1.09326 | ||||||||
\(160\) | 3.50554 | 0.277137 | ||||||||
\(161\) | −13.1589 | −1.03707 | ||||||||
\(162\) | 11.2426 | 0.883299 | ||||||||
\(163\) | −1.52785 | −0.119670 | −0.0598352 | − | 0.998208i | \(-0.519058\pi\) | ||||
−0.0598352 | + | 0.998208i | \(0.519058\pi\) | |||||||
\(164\) | 1.01826 | 0.0795129 | ||||||||
\(165\) | 7.36624 | 0.573461 | ||||||||
\(166\) | −8.02145 | −0.622585 | ||||||||
\(167\) | 8.32014 | 0.643831 | 0.321916 | − | 0.946768i | \(-0.395673\pi\) | ||||
0.321916 | + | 0.946768i | \(0.395673\pi\) | |||||||
\(168\) | 6.30813 | 0.486683 | ||||||||
\(169\) | −12.9578 | −0.996757 | ||||||||
\(170\) | −23.8746 | −1.83109 | ||||||||
\(171\) | −1.76012 | −0.134600 | ||||||||
\(172\) | −7.58576 | −0.578409 | ||||||||
\(173\) | 3.17957 | 0.241738 | 0.120869 | − | 0.992668i | \(-0.461432\pi\) | ||||
0.120869 | + | 0.992668i | \(0.461432\pi\) | |||||||
\(174\) | −10.5753 | −0.801714 | ||||||||
\(175\) | 21.8853 | 1.65438 | ||||||||
\(176\) | 1.00020 | 0.0753928 | ||||||||
\(177\) | −6.64102 | −0.499170 | ||||||||
\(178\) | 8.27457 | 0.620205 | ||||||||
\(179\) | −12.5332 | −0.936777 | −0.468389 | − | 0.883522i | \(-0.655165\pi\) | ||||
−0.468389 | + | 0.883522i | \(0.655165\pi\) | |||||||
\(180\) | −4.95601 | −0.369399 | ||||||||
\(181\) | 14.3766 | 1.06861 | 0.534303 | − | 0.845293i | \(-0.320574\pi\) | ||||
0.534303 | + | 0.845293i | \(0.320574\pi\) | |||||||
\(182\) | −0.616542 | −0.0457011 | ||||||||
\(183\) | 9.89493 | 0.731454 | ||||||||
\(184\) | 4.38251 | 0.323083 | ||||||||
\(185\) | −25.0739 | −1.84347 | ||||||||
\(186\) | 12.0284 | 0.881966 | ||||||||
\(187\) | −6.81188 | −0.498134 | ||||||||
\(188\) | 5.84435 | 0.426243 | ||||||||
\(189\) | 10.0062 | 0.727843 | ||||||||
\(190\) | −4.36436 | −0.316624 | ||||||||
\(191\) | 21.3554 | 1.54522 | 0.772612 | − | 0.634879i | \(-0.218950\pi\) | ||||
0.772612 | + | 0.634879i | \(0.218950\pi\) | |||||||
\(192\) | −2.10090 | −0.151619 | ||||||||
\(193\) | −0.779713 | −0.0561250 | −0.0280625 | − | 0.999606i | \(-0.508934\pi\) | ||||
−0.0280625 | + | 0.999606i | \(0.508934\pi\) | |||||||
\(194\) | 5.09387 | 0.365718 | ||||||||
\(195\) | 1.51226 | 0.108295 | ||||||||
\(196\) | 2.01556 | 0.143968 | ||||||||
\(197\) | 2.04711 | 0.145850 | 0.0729252 | − | 0.997337i | \(-0.476767\pi\) | ||||
0.0729252 | + | 0.997337i | \(0.476767\pi\) | |||||||
\(198\) | −1.41405 | −0.100492 | ||||||||
\(199\) | −14.5252 | −1.02967 | −0.514833 | − | 0.857290i | \(-0.672146\pi\) | ||||
−0.514833 | + | 0.857290i | \(0.672146\pi\) | |||||||
\(200\) | −7.28882 | −0.515397 | ||||||||
\(201\) | −32.5257 | −2.29419 | ||||||||
\(202\) | −3.26281 | −0.229570 | ||||||||
\(203\) | −15.1142 | −1.06081 | ||||||||
\(204\) | 14.3082 | 1.00177 | ||||||||
\(205\) | −3.56956 | −0.249309 | ||||||||
\(206\) | 16.2738 | 1.13385 | ||||||||
\(207\) | −6.19584 | −0.430641 | ||||||||
\(208\) | 0.205336 | 0.0142375 | ||||||||
\(209\) | −1.24524 | −0.0861347 | ||||||||
\(210\) | −22.1134 | −1.52597 | ||||||||
\(211\) | 24.7555 | 1.70424 | 0.852121 | − | 0.523345i | \(-0.175316\pi\) | ||||
0.852121 | + | 0.523345i | \(0.175316\pi\) | |||||||
\(212\) | −6.56170 | −0.450660 | ||||||||
\(213\) | 25.3084 | 1.73410 | ||||||||
\(214\) | −14.4097 | −0.985029 | ||||||||
\(215\) | 26.5922 | 1.81357 | ||||||||
\(216\) | −3.33252 | −0.226749 | ||||||||
\(217\) | 17.1910 | 1.16700 | ||||||||
\(218\) | 17.3981 | 1.17835 | ||||||||
\(219\) | 16.3099 | 1.10212 | ||||||||
\(220\) | −3.50624 | −0.236391 | ||||||||
\(221\) | −1.39845 | −0.0940698 | ||||||||
\(222\) | 15.0270 | 1.00855 | ||||||||
\(223\) | 12.9017 | 0.863963 | 0.431982 | − | 0.901882i | \(-0.357815\pi\) | ||||
0.431982 | + | 0.901882i | \(0.357815\pi\) | |||||||
\(224\) | −3.00259 | −0.200619 | ||||||||
\(225\) | 10.3047 | 0.686978 | ||||||||
\(226\) | 17.8859 | 1.18976 | ||||||||
\(227\) | −12.4118 | −0.823798 | −0.411899 | − | 0.911230i | \(-0.635134\pi\) | ||||
−0.411899 | + | 0.911230i | \(0.635134\pi\) | |||||||
\(228\) | 2.61559 | 0.173222 | ||||||||
\(229\) | −21.0661 | −1.39209 | −0.696044 | − | 0.717999i | \(-0.745058\pi\) | ||||
−0.696044 | + | 0.717999i | \(0.745058\pi\) | |||||||
\(230\) | −15.3631 | −1.01301 | ||||||||
\(231\) | −6.30939 | −0.415127 | ||||||||
\(232\) | 5.03372 | 0.330480 | ||||||||
\(233\) | 13.5088 | 0.884989 | 0.442495 | − | 0.896771i | \(-0.354094\pi\) | ||||
0.442495 | + | 0.896771i | \(0.354094\pi\) | |||||||
\(234\) | −0.290297 | −0.0189773 | ||||||||
\(235\) | −20.4876 | −1.33646 | ||||||||
\(236\) | 3.16104 | 0.205766 | ||||||||
\(237\) | −1.04409 | −0.0678207 | ||||||||
\(238\) | 20.4492 | 1.32553 | ||||||||
\(239\) | −10.5268 | −0.680919 | −0.340460 | − | 0.940259i | \(-0.610583\pi\) | ||||
−0.340460 | + | 0.940259i | \(0.610583\pi\) | |||||||
\(240\) | 7.36478 | 0.475394 | ||||||||
\(241\) | −11.8794 | −0.765219 | −0.382609 | − | 0.923910i | \(-0.624974\pi\) | ||||
−0.382609 | + | 0.923910i | \(0.624974\pi\) | |||||||
\(242\) | 9.99960 | 0.642799 | ||||||||
\(243\) | 13.6219 | 0.873846 | ||||||||
\(244\) | −4.70986 | −0.301518 | ||||||||
\(245\) | −7.06562 | −0.451406 | ||||||||
\(246\) | 2.13926 | 0.136394 | ||||||||
\(247\) | −0.255641 | −0.0162661 | ||||||||
\(248\) | −5.72537 | −0.363561 | ||||||||
\(249\) | −16.8522 | −1.06797 | ||||||||
\(250\) | 8.02354 | 0.507453 | ||||||||
\(251\) | −5.87461 | −0.370802 | −0.185401 | − | 0.982663i | \(-0.559358\pi\) | ||||
−0.185401 | + | 0.982663i | \(0.559358\pi\) | |||||||
\(252\) | 4.24496 | 0.267407 | ||||||||
\(253\) | −4.38339 | −0.275581 | ||||||||
\(254\) | −17.5216 | −1.09940 | ||||||||
\(255\) | −50.1580 | −3.14101 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.2762 | 1.20242 | 0.601208 | − | 0.799092i | \(-0.294686\pi\) | ||||
0.601208 | + | 0.799092i | \(0.294686\pi\) | |||||||
\(258\) | −15.9369 | −0.992187 | ||||||||
\(259\) | 21.4765 | 1.33448 | ||||||||
\(260\) | −0.719815 | −0.0446411 | ||||||||
\(261\) | −7.11650 | −0.440500 | ||||||||
\(262\) | 7.20210 | 0.444947 | ||||||||
\(263\) | −17.1743 | −1.05901 | −0.529505 | − | 0.848307i | \(-0.677622\pi\) | ||||
−0.529505 | + | 0.848307i | \(0.677622\pi\) | |||||||
\(264\) | 2.10131 | 0.129327 | ||||||||
\(265\) | 23.0023 | 1.41302 | ||||||||
\(266\) | 3.73819 | 0.229203 | ||||||||
\(267\) | 17.3840 | 1.06388 | ||||||||
\(268\) | 15.4818 | 0.945703 | ||||||||
\(269\) | 25.2632 | 1.54033 | 0.770163 | − | 0.637848i | \(-0.220175\pi\) | ||||
0.770163 | + | 0.637848i | \(0.220175\pi\) | |||||||
\(270\) | 11.6823 | 0.710960 | ||||||||
\(271\) | 27.1284 | 1.64793 | 0.823967 | − | 0.566638i | \(-0.191756\pi\) | ||||
0.823967 | + | 0.566638i | \(0.191756\pi\) | |||||||
\(272\) | −6.81052 | −0.412948 | ||||||||
\(273\) | −1.29529 | −0.0783945 | ||||||||
\(274\) | 12.4217 | 0.750423 | ||||||||
\(275\) | 7.29027 | 0.439620 | ||||||||
\(276\) | 9.20721 | 0.554209 | ||||||||
\(277\) | −16.9599 | −1.01902 | −0.509510 | − | 0.860465i | \(-0.670173\pi\) | ||||
−0.509510 | + | 0.860465i | \(0.670173\pi\) | |||||||
\(278\) | −5.91539 | −0.354781 | ||||||||
\(279\) | 8.09433 | 0.484595 | ||||||||
\(280\) | 10.5257 | 0.629031 | ||||||||
\(281\) | 19.2714 | 1.14964 | 0.574819 | − | 0.818281i | \(-0.305073\pi\) | ||||
0.574819 | + | 0.818281i | \(0.305073\pi\) | |||||||
\(282\) | 12.2784 | 0.731167 | ||||||||
\(283\) | 19.8000 | 1.17699 | 0.588494 | − | 0.808501i | \(-0.299721\pi\) | ||||
0.588494 | + | 0.808501i | \(0.299721\pi\) | |||||||
\(284\) | −12.0465 | −0.714827 | ||||||||
\(285\) | −9.16906 | −0.543128 | ||||||||
\(286\) | −0.205377 | −0.0121442 | ||||||||
\(287\) | 3.05743 | 0.180474 | ||||||||
\(288\) | −1.41376 | −0.0833069 | ||||||||
\(289\) | 29.3832 | 1.72842 | ||||||||
\(290\) | −17.6459 | −1.03620 | ||||||||
\(291\) | 10.7017 | 0.627344 | ||||||||
\(292\) | −7.76330 | −0.454313 | ||||||||
\(293\) | 33.4163 | 1.95220 | 0.976101 | − | 0.217316i | \(-0.0697302\pi\) | ||||
0.976101 | + | 0.217316i | \(0.0697302\pi\) | |||||||
\(294\) | 4.23448 | 0.246960 | ||||||||
\(295\) | −11.0812 | −0.645170 | ||||||||
\(296\) | −7.15265 | −0.415740 | ||||||||
\(297\) | 3.33318 | 0.193411 | ||||||||
\(298\) | 2.03614 | 0.117950 | ||||||||
\(299\) | −0.899890 | −0.0520420 | ||||||||
\(300\) | −15.3130 | −0.884099 | ||||||||
\(301\) | −22.7769 | −1.31284 | ||||||||
\(302\) | 19.3814 | 1.11528 | ||||||||
\(303\) | −6.85482 | −0.393799 | ||||||||
\(304\) | −1.24499 | −0.0714049 | ||||||||
\(305\) | 16.5106 | 0.945394 | ||||||||
\(306\) | 9.62847 | 0.550423 | ||||||||
\(307\) | 23.9060 | 1.36438 | 0.682192 | − | 0.731173i | \(-0.261027\pi\) | ||||
0.682192 | + | 0.731173i | \(0.261027\pi\) | |||||||
\(308\) | 3.00319 | 0.171123 | ||||||||
\(309\) | 34.1895 | 1.94497 | ||||||||
\(310\) | 20.0705 | 1.13993 | ||||||||
\(311\) | 24.8251 | 1.40770 | 0.703852 | − | 0.710346i | \(-0.251462\pi\) | ||||
0.703852 | + | 0.710346i | \(0.251462\pi\) | |||||||
\(312\) | 0.431391 | 0.0244227 | ||||||||
\(313\) | −17.6837 | −0.999542 | −0.499771 | − | 0.866157i | \(-0.666583\pi\) | ||||
−0.499771 | + | 0.866157i | \(0.666583\pi\) | |||||||
\(314\) | 7.21945 | 0.407417 | ||||||||
\(315\) | −14.8809 | −0.838442 | ||||||||
\(316\) | 0.496972 | 0.0279569 | ||||||||
\(317\) | 8.17786 | 0.459314 | 0.229657 | − | 0.973272i | \(-0.426239\pi\) | ||||
0.229657 | + | 0.973272i | \(0.426239\pi\) | |||||||
\(318\) | −13.7855 | −0.773050 | ||||||||
\(319\) | −5.03473 | −0.281891 | ||||||||
\(320\) | −3.50554 | −0.195966 | ||||||||
\(321\) | −30.2734 | −1.68969 | ||||||||
\(322\) | 13.1589 | 0.733317 | ||||||||
\(323\) | 8.47901 | 0.471785 | ||||||||
\(324\) | −11.2426 | −0.624587 | ||||||||
\(325\) | 1.49666 | 0.0830198 | ||||||||
\(326\) | 1.52785 | 0.0846198 | ||||||||
\(327\) | 36.5516 | 2.02131 | ||||||||
\(328\) | −1.01826 | −0.0562241 | ||||||||
\(329\) | 17.5482 | 0.967464 | ||||||||
\(330\) | −7.36624 | −0.405498 | ||||||||
\(331\) | −4.88685 | −0.268606 | −0.134303 | − | 0.990940i | \(-0.542879\pi\) | ||||
−0.134303 | + | 0.990940i | \(0.542879\pi\) | |||||||
\(332\) | 8.02145 | 0.440234 | ||||||||
\(333\) | 10.1122 | 0.554143 | ||||||||
\(334\) | −8.32014 | −0.455258 | ||||||||
\(335\) | −54.2721 | −2.96520 | ||||||||
\(336\) | −6.30813 | −0.344137 | ||||||||
\(337\) | 16.9881 | 0.925400 | 0.462700 | − | 0.886515i | \(-0.346881\pi\) | ||||
0.462700 | + | 0.886515i | \(0.346881\pi\) | |||||||
\(338\) | 12.9578 | 0.704813 | ||||||||
\(339\) | 37.5765 | 2.04088 | ||||||||
\(340\) | 23.8746 | 1.29478 | ||||||||
\(341\) | 5.72651 | 0.310108 | ||||||||
\(342\) | 1.76012 | 0.0951764 | ||||||||
\(343\) | −14.9662 | −0.808101 | ||||||||
\(344\) | 7.58576 | 0.408997 | ||||||||
\(345\) | −32.2762 | −1.73769 | ||||||||
\(346\) | −3.17957 | −0.170935 | ||||||||
\(347\) | 24.4040 | 1.31008 | 0.655038 | − | 0.755596i | \(-0.272652\pi\) | ||||
0.655038 | + | 0.755596i | \(0.272652\pi\) | |||||||
\(348\) | 10.5753 | 0.566897 | ||||||||
\(349\) | −17.6222 | −0.943296 | −0.471648 | − | 0.881787i | \(-0.656341\pi\) | ||||
−0.471648 | + | 0.881787i | \(0.656341\pi\) | |||||||
\(350\) | −21.8853 | −1.16982 | ||||||||
\(351\) | 0.684287 | 0.0365245 | ||||||||
\(352\) | −1.00020 | −0.0533108 | ||||||||
\(353\) | −5.06883 | −0.269787 | −0.134893 | − | 0.990860i | \(-0.543069\pi\) | ||||
−0.134893 | + | 0.990860i | \(0.543069\pi\) | |||||||
\(354\) | 6.64102 | 0.352966 | ||||||||
\(355\) | 42.2294 | 2.24130 | ||||||||
\(356\) | −8.27457 | −0.438551 | ||||||||
\(357\) | 42.9617 | 2.27377 | ||||||||
\(358\) | 12.5332 | 0.662402 | ||||||||
\(359\) | −9.47904 | −0.500285 | −0.250142 | − | 0.968209i | \(-0.580477\pi\) | ||||
−0.250142 | + | 0.968209i | \(0.580477\pi\) | |||||||
\(360\) | 4.95601 | 0.261205 | ||||||||
\(361\) | −17.4500 | −0.918421 | ||||||||
\(362\) | −14.3766 | −0.755619 | ||||||||
\(363\) | 21.0081 | 1.10264 | ||||||||
\(364\) | 0.616542 | 0.0323156 | ||||||||
\(365\) | 27.2146 | 1.42448 | ||||||||
\(366\) | −9.89493 | −0.517216 | ||||||||
\(367\) | −4.88793 | −0.255148 | −0.127574 | − | 0.991829i | \(-0.540719\pi\) | ||||
−0.127574 | + | 0.991829i | \(0.540719\pi\) | |||||||
\(368\) | −4.38251 | −0.228454 | ||||||||
\(369\) | 1.43958 | 0.0749417 | ||||||||
\(370\) | 25.0739 | 1.30353 | ||||||||
\(371\) | −19.7021 | −1.02288 | ||||||||
\(372\) | −12.0284 | −0.623644 | ||||||||
\(373\) | −35.4079 | −1.83335 | −0.916676 | − | 0.399631i | \(-0.869138\pi\) | ||||
−0.916676 | + | 0.399631i | \(0.869138\pi\) | |||||||
\(374\) | 6.81188 | 0.352234 | ||||||||
\(375\) | 16.8566 | 0.870472 | ||||||||
\(376\) | −5.84435 | −0.301399 | ||||||||
\(377\) | −1.03361 | −0.0532335 | ||||||||
\(378\) | −10.0062 | −0.514663 | ||||||||
\(379\) | 8.19626 | 0.421014 | 0.210507 | − | 0.977592i | \(-0.432489\pi\) | ||||
0.210507 | + | 0.977592i | \(0.432489\pi\) | |||||||
\(380\) | 4.36436 | 0.223887 | ||||||||
\(381\) | −36.8110 | −1.88589 | ||||||||
\(382\) | −21.3554 | −1.09264 | ||||||||
\(383\) | 1.07701 | 0.0550327 | 0.0275163 | − | 0.999621i | \(-0.491240\pi\) | ||||
0.0275163 | + | 0.999621i | \(0.491240\pi\) | |||||||
\(384\) | 2.10090 | 0.107211 | ||||||||
\(385\) | −10.5278 | −0.536547 | ||||||||
\(386\) | 0.779713 | 0.0396864 | ||||||||
\(387\) | −10.7245 | −0.545156 | ||||||||
\(388\) | −5.09387 | −0.258602 | ||||||||
\(389\) | 37.1713 | 1.88466 | 0.942331 | − | 0.334683i | \(-0.108629\pi\) | ||||
0.942331 | + | 0.334683i | \(0.108629\pi\) | |||||||
\(390\) | −1.51226 | −0.0765761 | ||||||||
\(391\) | 29.8472 | 1.50944 | ||||||||
\(392\) | −2.01556 | −0.101801 | ||||||||
\(393\) | 15.1309 | 0.763251 | ||||||||
\(394\) | −2.04711 | −0.103132 | ||||||||
\(395\) | −1.74216 | −0.0876574 | ||||||||
\(396\) | 1.41405 | 0.0710585 | ||||||||
\(397\) | −6.57009 | −0.329743 | −0.164872 | − | 0.986315i | \(-0.552721\pi\) | ||||
−0.164872 | + | 0.986315i | \(0.552721\pi\) | |||||||
\(398\) | 14.5252 | 0.728084 | ||||||||
\(399\) | 7.85355 | 0.393169 | ||||||||
\(400\) | 7.28882 | 0.364441 | ||||||||
\(401\) | −15.0532 | −0.751722 | −0.375861 | − | 0.926676i | \(-0.622653\pi\) | ||||
−0.375861 | + | 0.926676i | \(0.622653\pi\) | |||||||
\(402\) | 32.5257 | 1.62223 | ||||||||
\(403\) | 1.17563 | 0.0585622 | ||||||||
\(404\) | 3.26281 | 0.162331 | ||||||||
\(405\) | 39.4113 | 1.95836 | ||||||||
\(406\) | 15.1142 | 0.750106 | ||||||||
\(407\) | 7.15408 | 0.354614 | ||||||||
\(408\) | −14.3082 | −0.708361 | ||||||||
\(409\) | 17.5973 | 0.870131 | 0.435066 | − | 0.900399i | \(-0.356725\pi\) | ||||
0.435066 | + | 0.900399i | \(0.356725\pi\) | |||||||
\(410\) | 3.56956 | 0.176288 | ||||||||
\(411\) | 26.0967 | 1.28726 | ||||||||
\(412\) | −16.2738 | −0.801751 | ||||||||
\(413\) | 9.49132 | 0.467037 | ||||||||
\(414\) | 6.19584 | 0.304509 | ||||||||
\(415\) | −28.1195 | −1.38033 | ||||||||
\(416\) | −0.205336 | −0.0100674 | ||||||||
\(417\) | −12.4276 | −0.608583 | ||||||||
\(418\) | 1.24524 | 0.0609065 | ||||||||
\(419\) | 2.96510 | 0.144855 | 0.0724273 | − | 0.997374i | \(-0.476925\pi\) | ||||
0.0724273 | + | 0.997374i | \(0.476925\pi\) | |||||||
\(420\) | 22.1134 | 1.07902 | ||||||||
\(421\) | 1.01231 | 0.0493369 | 0.0246685 | − | 0.999696i | \(-0.492147\pi\) | ||||
0.0246685 | + | 0.999696i | \(0.492147\pi\) | |||||||
\(422\) | −24.7555 | −1.20508 | ||||||||
\(423\) | 8.26254 | 0.401738 | ||||||||
\(424\) | 6.56170 | 0.318665 | ||||||||
\(425\) | −49.6406 | −2.40792 | ||||||||
\(426\) | −25.3084 | −1.22620 | ||||||||
\(427\) | −14.1418 | −0.684369 | ||||||||
\(428\) | 14.4097 | 0.696521 | ||||||||
\(429\) | −0.431476 | −0.0208319 | ||||||||
\(430\) | −26.5922 | −1.28239 | ||||||||
\(431\) | 2.33478 | 0.112462 | 0.0562311 | − | 0.998418i | \(-0.482092\pi\) | ||||
0.0562311 | + | 0.998418i | \(0.482092\pi\) | |||||||
\(432\) | 3.33252 | 0.160336 | ||||||||
\(433\) | 40.4137 | 1.94216 | 0.971079 | − | 0.238757i | \(-0.0767399\pi\) | ||||
0.971079 | + | 0.238757i | \(0.0767399\pi\) | |||||||
\(434\) | −17.1910 | −0.825192 | ||||||||
\(435\) | −37.0723 | −1.77748 | ||||||||
\(436\) | −17.3981 | −0.833217 | ||||||||
\(437\) | 5.45618 | 0.261004 | ||||||||
\(438\) | −16.3099 | −0.779317 | ||||||||
\(439\) | −16.8983 | −0.806512 | −0.403256 | − | 0.915087i | \(-0.632122\pi\) | ||||
−0.403256 | + | 0.915087i | \(0.632122\pi\) | |||||||
\(440\) | 3.50624 | 0.167153 | ||||||||
\(441\) | 2.84952 | 0.135692 | ||||||||
\(442\) | 1.39845 | 0.0665174 | ||||||||
\(443\) | 26.7150 | 1.26927 | 0.634635 | − | 0.772812i | \(-0.281150\pi\) | ||||
0.634635 | + | 0.772812i | \(0.281150\pi\) | |||||||
\(444\) | −15.0270 | −0.713149 | ||||||||
\(445\) | 29.0068 | 1.37506 | ||||||||
\(446\) | −12.9017 | −0.610914 | ||||||||
\(447\) | 4.27772 | 0.202329 | ||||||||
\(448\) | 3.00259 | 0.141859 | ||||||||
\(449\) | −36.9537 | −1.74395 | −0.871976 | − | 0.489548i | \(-0.837162\pi\) | ||||
−0.871976 | + | 0.489548i | \(0.837162\pi\) | |||||||
\(450\) | −10.3047 | −0.485767 | ||||||||
\(451\) | 1.01847 | 0.0479576 | ||||||||
\(452\) | −17.8859 | −0.841284 | ||||||||
\(453\) | 40.7184 | 1.91312 | ||||||||
\(454\) | 12.4118 | 0.582513 | ||||||||
\(455\) | −2.16131 | −0.101324 | ||||||||
\(456\) | −2.61559 | −0.122486 | ||||||||
\(457\) | −38.3405 | −1.79349 | −0.896747 | − | 0.442544i | \(-0.854076\pi\) | ||||
−0.896747 | + | 0.442544i | \(0.854076\pi\) | |||||||
\(458\) | 21.0661 | 0.984354 | ||||||||
\(459\) | −22.6962 | −1.05937 | ||||||||
\(460\) | 15.3631 | 0.716307 | ||||||||
\(461\) | 29.7056 | 1.38353 | 0.691764 | − | 0.722124i | \(-0.256834\pi\) | ||||
0.691764 | + | 0.722124i | \(0.256834\pi\) | |||||||
\(462\) | 6.30939 | 0.293539 | ||||||||
\(463\) | 28.9956 | 1.34754 | 0.673771 | − | 0.738940i | \(-0.264674\pi\) | ||||
0.673771 | + | 0.738940i | \(0.264674\pi\) | |||||||
\(464\) | −5.03372 | −0.233685 | ||||||||
\(465\) | 42.1661 | 1.95541 | ||||||||
\(466\) | −13.5088 | −0.625782 | ||||||||
\(467\) | 12.6310 | 0.584493 | 0.292247 | − | 0.956343i | \(-0.405597\pi\) | ||||
0.292247 | + | 0.956343i | \(0.405597\pi\) | |||||||
\(468\) | 0.290297 | 0.0134190 | ||||||||
\(469\) | 46.4856 | 2.14650 | ||||||||
\(470\) | 20.4876 | 0.945023 | ||||||||
\(471\) | 15.1673 | 0.698873 | ||||||||
\(472\) | −3.16104 | −0.145499 | ||||||||
\(473\) | −7.58727 | −0.348863 | ||||||||
\(474\) | 1.04409 | 0.0479565 | ||||||||
\(475\) | −9.07449 | −0.416366 | ||||||||
\(476\) | −20.4492 | −0.937288 | ||||||||
\(477\) | −9.27670 | −0.424751 | ||||||||
\(478\) | 10.5268 | 0.481483 | ||||||||
\(479\) | 30.4992 | 1.39355 | 0.696773 | − | 0.717292i | \(-0.254618\pi\) | ||||
0.696773 | + | 0.717292i | \(0.254618\pi\) | |||||||
\(480\) | −7.36478 | −0.336155 | ||||||||
\(481\) | 1.46870 | 0.0669670 | ||||||||
\(482\) | 11.8794 | 0.541091 | ||||||||
\(483\) | 27.6455 | 1.25791 | ||||||||
\(484\) | −9.99960 | −0.454527 | ||||||||
\(485\) | 17.8568 | 0.810834 | ||||||||
\(486\) | −13.6219 | −0.617902 | ||||||||
\(487\) | −17.6744 | −0.800902 | −0.400451 | − | 0.916318i | \(-0.631147\pi\) | ||||
−0.400451 | + | 0.916318i | \(0.631147\pi\) | |||||||
\(488\) | 4.70986 | 0.213205 | ||||||||
\(489\) | 3.20985 | 0.145155 | ||||||||
\(490\) | 7.06562 | 0.319192 | ||||||||
\(491\) | −42.6650 | −1.92544 | −0.962722 | − | 0.270493i | \(-0.912813\pi\) | ||||
−0.962722 | + | 0.270493i | \(0.912813\pi\) | |||||||
\(492\) | −2.13926 | −0.0964454 | ||||||||
\(493\) | 34.2823 | 1.54400 | ||||||||
\(494\) | 0.255641 | 0.0115018 | ||||||||
\(495\) | −4.95700 | −0.222800 | ||||||||
\(496\) | 5.72537 | 0.257077 | ||||||||
\(497\) | −36.1707 | −1.62248 | ||||||||
\(498\) | 16.8522 | 0.755167 | ||||||||
\(499\) | 4.97906 | 0.222894 | 0.111447 | − | 0.993770i | \(-0.464452\pi\) | ||||
0.111447 | + | 0.993770i | \(0.464452\pi\) | |||||||
\(500\) | −8.02354 | −0.358824 | ||||||||
\(501\) | −17.4797 | −0.780937 | ||||||||
\(502\) | 5.87461 | 0.262196 | ||||||||
\(503\) | −19.0518 | −0.849476 | −0.424738 | − | 0.905316i | \(-0.639634\pi\) | ||||
−0.424738 | + | 0.905316i | \(0.639634\pi\) | |||||||
\(504\) | −4.24496 | −0.189085 | ||||||||
\(505\) | −11.4379 | −0.508980 | ||||||||
\(506\) | 4.38339 | 0.194865 | ||||||||
\(507\) | 27.2231 | 1.20902 | ||||||||
\(508\) | 17.5216 | 0.777395 | ||||||||
\(509\) | −5.41836 | −0.240165 | −0.120082 | − | 0.992764i | \(-0.538316\pi\) | ||||
−0.120082 | + | 0.992764i | \(0.538316\pi\) | |||||||
\(510\) | 50.1580 | 2.22103 | ||||||||
\(511\) | −23.3100 | −1.03117 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.14894 | −0.183180 | ||||||||
\(514\) | −19.2762 | −0.850237 | ||||||||
\(515\) | 57.0483 | 2.51385 | ||||||||
\(516\) | 15.9369 | 0.701582 | ||||||||
\(517\) | 5.84552 | 0.257086 | ||||||||
\(518\) | −21.4765 | −0.943623 | ||||||||
\(519\) | −6.67995 | −0.293217 | ||||||||
\(520\) | 0.719815 | 0.0315660 | ||||||||
\(521\) | 15.0102 | 0.657608 | 0.328804 | − | 0.944398i | \(-0.393355\pi\) | ||||
0.328804 | + | 0.944398i | \(0.393355\pi\) | |||||||
\(522\) | 7.11650 | 0.311481 | ||||||||
\(523\) | 25.4656 | 1.11353 | 0.556766 | − | 0.830670i | \(-0.312042\pi\) | ||||
0.556766 | + | 0.830670i | \(0.312042\pi\) | |||||||
\(524\) | −7.20210 | −0.314625 | ||||||||
\(525\) | −45.9788 | −2.00668 | ||||||||
\(526\) | 17.1743 | 0.748833 | ||||||||
\(527\) | −38.9928 | −1.69855 | ||||||||
\(528\) | −2.10131 | −0.0914480 | ||||||||
\(529\) | −3.79357 | −0.164938 | ||||||||
\(530\) | −23.0023 | −0.999157 | ||||||||
\(531\) | 4.46897 | 0.193937 | ||||||||
\(532\) | −3.73819 | −0.162071 | ||||||||
\(533\) | 0.209086 | 0.00905654 | ||||||||
\(534\) | −17.3840 | −0.752280 | ||||||||
\(535\) | −50.5139 | −2.18391 | ||||||||
\(536\) | −15.4818 | −0.668713 | ||||||||
\(537\) | 26.3310 | 1.13627 | ||||||||
\(538\) | −25.2632 | −1.08917 | ||||||||
\(539\) | 2.01596 | 0.0868335 | ||||||||
\(540\) | −11.6823 | −0.502725 | ||||||||
\(541\) | −14.3607 | −0.617416 | −0.308708 | − | 0.951157i | \(-0.599897\pi\) | ||||
−0.308708 | + | 0.951157i | \(0.599897\pi\) | |||||||
\(542\) | −27.1284 | −1.16526 | ||||||||
\(543\) | −30.2038 | −1.29617 | ||||||||
\(544\) | 6.81052 | 0.291999 | ||||||||
\(545\) | 60.9897 | 2.61251 | ||||||||
\(546\) | 1.29529 | 0.0554333 | ||||||||
\(547\) | −5.74147 | −0.245488 | −0.122744 | − | 0.992438i | \(-0.539169\pi\) | ||||
−0.122744 | + | 0.992438i | \(0.539169\pi\) | |||||||
\(548\) | −12.4217 | −0.530629 | ||||||||
\(549\) | −6.65863 | −0.284183 | ||||||||
\(550\) | −7.29027 | −0.310858 | ||||||||
\(551\) | 6.26692 | 0.266980 | ||||||||
\(552\) | −9.20721 | −0.391885 | ||||||||
\(553\) | 1.49220 | 0.0634550 | ||||||||
\(554\) | 16.9599 | 0.720556 | ||||||||
\(555\) | 52.6777 | 2.23604 | ||||||||
\(556\) | 5.91539 | 0.250868 | ||||||||
\(557\) | 3.26352 | 0.138280 | 0.0691399 | − | 0.997607i | \(-0.477975\pi\) | ||||
0.0691399 | + | 0.997607i | \(0.477975\pi\) | |||||||
\(558\) | −8.09433 | −0.342660 | ||||||||
\(559\) | −1.55763 | −0.0658808 | ||||||||
\(560\) | −10.5257 | −0.444792 | ||||||||
\(561\) | 14.3110 | 0.604213 | ||||||||
\(562\) | −19.2714 | −0.812916 | ||||||||
\(563\) | −45.4495 | −1.91547 | −0.957735 | − | 0.287653i | \(-0.907125\pi\) | ||||
−0.957735 | + | 0.287653i | \(0.907125\pi\) | |||||||
\(564\) | −12.2784 | −0.517013 | ||||||||
\(565\) | 62.6999 | 2.63781 | ||||||||
\(566\) | −19.8000 | −0.832257 | ||||||||
\(567\) | −33.7568 | −1.41765 | ||||||||
\(568\) | 12.0465 | 0.505459 | ||||||||
\(569\) | 7.18806 | 0.301339 | 0.150670 | − | 0.988584i | \(-0.451857\pi\) | ||||
0.150670 | + | 0.988584i | \(0.451857\pi\) | |||||||
\(570\) | 9.16906 | 0.384050 | ||||||||
\(571\) | 19.5525 | 0.818249 | 0.409124 | − | 0.912479i | \(-0.365834\pi\) | ||||
0.409124 | + | 0.912479i | \(0.365834\pi\) | |||||||
\(572\) | 0.205377 | 0.00858726 | ||||||||
\(573\) | −44.8655 | −1.87428 | ||||||||
\(574\) | −3.05743 | −0.127615 | ||||||||
\(575\) | −31.9433 | −1.33213 | ||||||||
\(576\) | 1.41376 | 0.0589069 | ||||||||
\(577\) | 11.9721 | 0.498406 | 0.249203 | − | 0.968451i | \(-0.419831\pi\) | ||||
0.249203 | + | 0.968451i | \(0.419831\pi\) | |||||||
\(578\) | −29.3832 | −1.22218 | ||||||||
\(579\) | 1.63810 | 0.0680770 | ||||||||
\(580\) | 17.6459 | 0.732707 | ||||||||
\(581\) | 24.0851 | 0.999220 | ||||||||
\(582\) | −10.7017 | −0.443599 | ||||||||
\(583\) | −6.56301 | −0.271812 | ||||||||
\(584\) | 7.76330 | 0.321248 | ||||||||
\(585\) | −1.01765 | −0.0420746 | ||||||||
\(586\) | −33.4163 | −1.38042 | ||||||||
\(587\) | −15.7956 | −0.651955 | −0.325978 | − | 0.945377i | \(-0.605693\pi\) | ||||
−0.325978 | + | 0.945377i | \(0.605693\pi\) | |||||||
\(588\) | −4.23448 | −0.174627 | ||||||||
\(589\) | −7.12802 | −0.293705 | ||||||||
\(590\) | 11.0812 | 0.456204 | ||||||||
\(591\) | −4.30076 | −0.176910 | ||||||||
\(592\) | 7.15265 | 0.293972 | ||||||||
\(593\) | 20.1155 | 0.826044 | 0.413022 | − | 0.910721i | \(-0.364473\pi\) | ||||
0.413022 | + | 0.910721i | \(0.364473\pi\) | |||||||
\(594\) | −3.33318 | −0.136762 | ||||||||
\(595\) | 71.6855 | 2.93882 | ||||||||
\(596\) | −2.03614 | −0.0834036 | ||||||||
\(597\) | 30.5160 | 1.24894 | ||||||||
\(598\) | 0.899890 | 0.0367992 | ||||||||
\(599\) | 0.909511 | 0.0371616 | 0.0185808 | − | 0.999827i | \(-0.494085\pi\) | ||||
0.0185808 | + | 0.999827i | \(0.494085\pi\) | |||||||
\(600\) | 15.3130 | 0.625153 | ||||||||
\(601\) | 35.8855 | 1.46380 | 0.731899 | − | 0.681413i | \(-0.238634\pi\) | ||||
0.731899 | + | 0.681413i | \(0.238634\pi\) | |||||||
\(602\) | 22.7769 | 0.928318 | ||||||||
\(603\) | 21.8876 | 0.891334 | ||||||||
\(604\) | −19.3814 | −0.788620 | ||||||||
\(605\) | 35.0540 | 1.42515 | ||||||||
\(606\) | 6.85482 | 0.278458 | ||||||||
\(607\) | 32.2208 | 1.30780 | 0.653900 | − | 0.756581i | \(-0.273132\pi\) | ||||
0.653900 | + | 0.756581i | \(0.273132\pi\) | |||||||
\(608\) | 1.24499 | 0.0504909 | ||||||||
\(609\) | 31.7534 | 1.28671 | ||||||||
\(610\) | −16.5106 | −0.668495 | ||||||||
\(611\) | 1.20006 | 0.0485492 | ||||||||
\(612\) | −9.62847 | −0.389208 | ||||||||
\(613\) | 34.6671 | 1.40019 | 0.700096 | − | 0.714049i | \(-0.253140\pi\) | ||||
0.700096 | + | 0.714049i | \(0.253140\pi\) | |||||||
\(614\) | −23.9060 | −0.964766 | ||||||||
\(615\) | 7.49928 | 0.302400 | ||||||||
\(616\) | −3.00319 | −0.121002 | ||||||||
\(617\) | 10.4351 | 0.420103 | 0.210051 | − | 0.977690i | \(-0.432637\pi\) | ||||
0.210051 | + | 0.977690i | \(0.432637\pi\) | |||||||
\(618\) | −34.1895 | −1.37530 | ||||||||
\(619\) | 16.1814 | 0.650385 | 0.325192 | − | 0.945648i | \(-0.394571\pi\) | ||||
0.325192 | + | 0.945648i | \(0.394571\pi\) | |||||||
\(620\) | −20.0705 | −0.806052 | ||||||||
\(621\) | −14.6048 | −0.586070 | ||||||||
\(622\) | −24.8251 | −0.995397 | ||||||||
\(623\) | −24.8452 | −0.995400 | ||||||||
\(624\) | −0.431391 | −0.0172694 | ||||||||
\(625\) | −8.31723 | −0.332689 | ||||||||
\(626\) | 17.6837 | 0.706783 | ||||||||
\(627\) | 2.61611 | 0.104477 | ||||||||
\(628\) | −7.21945 | −0.288088 | ||||||||
\(629\) | −48.7133 | −1.94233 | ||||||||
\(630\) | 14.8809 | 0.592868 | ||||||||
\(631\) | −42.7927 | −1.70355 | −0.851776 | − | 0.523906i | \(-0.824474\pi\) | ||||
−0.851776 | + | 0.523906i | \(0.824474\pi\) | |||||||
\(632\) | −0.496972 | −0.0197685 | ||||||||
\(633\) | −52.0088 | −2.06717 | ||||||||
\(634\) | −8.17786 | −0.324784 | ||||||||
\(635\) | −61.4226 | −2.43748 | ||||||||
\(636\) | 13.7855 | 0.546629 | ||||||||
\(637\) | 0.413868 | 0.0163980 | ||||||||
\(638\) | 5.03473 | 0.199327 | ||||||||
\(639\) | −17.0309 | −0.673731 | ||||||||
\(640\) | 3.50554 | 0.138569 | ||||||||
\(641\) | 45.2345 | 1.78665 | 0.893327 | − | 0.449407i | \(-0.148365\pi\) | ||||
0.893327 | + | 0.449407i | \(0.148365\pi\) | |||||||
\(642\) | 30.2734 | 1.19479 | ||||||||
\(643\) | 20.5811 | 0.811639 | 0.405820 | − | 0.913953i | \(-0.366986\pi\) | ||||
0.405820 | + | 0.913953i | \(0.366986\pi\) | |||||||
\(644\) | −13.1589 | −0.518533 | ||||||||
\(645\) | −55.8674 | −2.19978 | ||||||||
\(646\) | −8.47901 | −0.333602 | ||||||||
\(647\) | 24.7330 | 0.972354 | 0.486177 | − | 0.873860i | \(-0.338391\pi\) | ||||
0.486177 | + | 0.873860i | \(0.338391\pi\) | |||||||
\(648\) | 11.2426 | 0.441650 | ||||||||
\(649\) | 3.16167 | 0.124107 | ||||||||
\(650\) | −1.49666 | −0.0587038 | ||||||||
\(651\) | −36.1164 | −1.41551 | ||||||||
\(652\) | −1.52785 | −0.0598352 | ||||||||
\(653\) | 6.66382 | 0.260775 | 0.130388 | − | 0.991463i | \(-0.458378\pi\) | ||||
0.130388 | + | 0.991463i | \(0.458378\pi\) | |||||||
\(654\) | −36.5516 | −1.42928 | ||||||||
\(655\) | 25.2473 | 0.986492 | ||||||||
\(656\) | 1.01826 | 0.0397565 | ||||||||
\(657\) | −10.9755 | −0.428194 | ||||||||
\(658\) | −17.5482 | −0.684100 | ||||||||
\(659\) | 33.5356 | 1.30636 | 0.653181 | − | 0.757202i | \(-0.273434\pi\) | ||||
0.653181 | + | 0.757202i | \(0.273434\pi\) | |||||||
\(660\) | 7.36624 | 0.286731 | ||||||||
\(661\) | 45.7292 | 1.77866 | 0.889329 | − | 0.457267i | \(-0.151172\pi\) | ||||
0.889329 | + | 0.457267i | \(0.151172\pi\) | |||||||
\(662\) | 4.88685 | 0.189933 | ||||||||
\(663\) | 2.93799 | 0.114102 | ||||||||
\(664\) | −8.02145 | −0.311293 | ||||||||
\(665\) | 13.1044 | 0.508166 | ||||||||
\(666\) | −10.1122 | −0.391839 | ||||||||
\(667\) | 22.0604 | 0.854181 | ||||||||
\(668\) | 8.32014 | 0.321916 | ||||||||
\(669\) | −27.1052 | −1.04795 | ||||||||
\(670\) | 54.2721 | 2.09672 | ||||||||
\(671\) | −4.71080 | −0.181858 | ||||||||
\(672\) | 6.30813 | 0.243342 | ||||||||
\(673\) | 36.7109 | 1.41510 | 0.707551 | − | 0.706663i | \(-0.249800\pi\) | ||||
0.707551 | + | 0.706663i | \(0.249800\pi\) | |||||||
\(674\) | −16.9881 | −0.654357 | ||||||||
\(675\) | 24.2901 | 0.934926 | ||||||||
\(676\) | −12.9578 | −0.498378 | ||||||||
\(677\) | −19.6727 | −0.756083 | −0.378042 | − | 0.925789i | \(-0.623402\pi\) | ||||
−0.378042 | + | 0.925789i | \(0.623402\pi\) | |||||||
\(678\) | −37.5765 | −1.44312 | ||||||||
\(679\) | −15.2948 | −0.586961 | ||||||||
\(680\) | −23.8746 | −0.915547 | ||||||||
\(681\) | 26.0758 | 0.999228 | ||||||||
\(682\) | −5.72651 | −0.219279 | ||||||||
\(683\) | 29.3426 | 1.12276 | 0.561382 | − | 0.827557i | \(-0.310270\pi\) | ||||
0.561382 | + | 0.827557i | \(0.310270\pi\) | |||||||
\(684\) | −1.76012 | −0.0672998 | ||||||||
\(685\) | 43.5448 | 1.66376 | ||||||||
\(686\) | 14.9662 | 0.571414 | ||||||||
\(687\) | 44.2577 | 1.68854 | ||||||||
\(688\) | −7.58576 | −0.289204 | ||||||||
\(689\) | −1.34736 | −0.0513302 | ||||||||
\(690\) | 32.2762 | 1.22874 | ||||||||
\(691\) | −5.83284 | −0.221892 | −0.110946 | − | 0.993826i | \(-0.535388\pi\) | ||||
−0.110946 | + | 0.993826i | \(0.535388\pi\) | |||||||
\(692\) | 3.17957 | 0.120869 | ||||||||
\(693\) | 4.24580 | 0.161285 | ||||||||
\(694\) | −24.4040 | −0.926364 | ||||||||
\(695\) | −20.7366 | −0.786586 | ||||||||
\(696\) | −10.5753 | −0.400857 | ||||||||
\(697\) | −6.93490 | −0.262678 | ||||||||
\(698\) | 17.6222 | 0.667011 | ||||||||
\(699\) | −28.3805 | −1.07345 | ||||||||
\(700\) | 21.8853 | 0.827188 | ||||||||
\(701\) | 44.7647 | 1.69074 | 0.845371 | − | 0.534180i | \(-0.179380\pi\) | ||||
0.845371 | + | 0.534180i | \(0.179380\pi\) | |||||||
\(702\) | −0.684287 | −0.0258268 | ||||||||
\(703\) | −8.90497 | −0.335857 | ||||||||
\(704\) | 1.00020 | 0.0376964 | ||||||||
\(705\) | 43.0424 | 1.62107 | ||||||||
\(706\) | 5.06883 | 0.190768 | ||||||||
\(707\) | 9.79688 | 0.368449 | ||||||||
\(708\) | −6.64102 | −0.249585 | ||||||||
\(709\) | 42.0611 | 1.57964 | 0.789819 | − | 0.613340i | \(-0.210175\pi\) | ||||
0.789819 | + | 0.613340i | \(0.210175\pi\) | |||||||
\(710\) | −42.2294 | −1.58484 | ||||||||
\(711\) | 0.702602 | 0.0263496 | ||||||||
\(712\) | 8.27457 | 0.310103 | ||||||||
\(713\) | −25.0915 | −0.939685 | ||||||||
\(714\) | −42.9617 | −1.60780 | ||||||||
\(715\) | −0.719959 | −0.0269249 | ||||||||
\(716\) | −12.5332 | −0.468389 | ||||||||
\(717\) | 22.1156 | 0.825923 | ||||||||
\(718\) | 9.47904 | 0.353755 | ||||||||
\(719\) | −49.3625 | −1.84091 | −0.920455 | − | 0.390848i | \(-0.872182\pi\) | ||||
−0.920455 | + | 0.390848i | \(0.872182\pi\) | |||||||
\(720\) | −4.95601 | −0.184700 | ||||||||
\(721\) | −48.8635 | −1.81977 | ||||||||
\(722\) | 17.4500 | 0.649422 | ||||||||
\(723\) | 24.9574 | 0.928174 | ||||||||
\(724\) | 14.3766 | 0.534303 | ||||||||
\(725\) | −36.6899 | −1.36263 | ||||||||
\(726\) | −21.0081 | −0.779685 | ||||||||
\(727\) | 19.5188 | 0.723911 | 0.361956 | − | 0.932195i | \(-0.382109\pi\) | ||||
0.361956 | + | 0.932195i | \(0.382109\pi\) | |||||||
\(728\) | −0.616542 | −0.0228506 | ||||||||
\(729\) | 5.10947 | 0.189240 | ||||||||
\(730\) | −27.2146 | −1.00726 | ||||||||
\(731\) | 51.6629 | 1.91082 | ||||||||
\(732\) | 9.89493 | 0.365727 | ||||||||
\(733\) | −45.2232 | −1.67036 | −0.835178 | − | 0.549979i | \(-0.814636\pi\) | ||||
−0.835178 | + | 0.549979i | \(0.814636\pi\) | |||||||
\(734\) | 4.88793 | 0.180417 | ||||||||
\(735\) | 14.8441 | 0.547534 | ||||||||
\(736\) | 4.38251 | 0.161542 | ||||||||
\(737\) | 15.4849 | 0.570394 | ||||||||
\(738\) | −1.43958 | −0.0529918 | ||||||||
\(739\) | −12.1355 | −0.446412 | −0.223206 | − | 0.974771i | \(-0.571652\pi\) | ||||
−0.223206 | + | 0.974771i | \(0.571652\pi\) | |||||||
\(740\) | −25.0739 | −0.921736 | ||||||||
\(741\) | 0.537076 | 0.0197300 | ||||||||
\(742\) | 19.7021 | 0.723288 | ||||||||
\(743\) | 15.6314 | 0.573462 | 0.286731 | − | 0.958011i | \(-0.407431\pi\) | ||||
0.286731 | + | 0.958011i | \(0.407431\pi\) | |||||||
\(744\) | 12.0284 | 0.440983 | ||||||||
\(745\) | 7.13778 | 0.261508 | ||||||||
\(746\) | 35.4079 | 1.29638 | ||||||||
\(747\) | 11.3404 | 0.414925 | ||||||||
\(748\) | −6.81188 | −0.249067 | ||||||||
\(749\) | 43.2666 | 1.58093 | ||||||||
\(750\) | −16.8566 | −0.615517 | ||||||||
\(751\) | −21.4060 | −0.781116 | −0.390558 | − | 0.920578i | \(-0.627718\pi\) | ||||
−0.390558 | + | 0.920578i | \(0.627718\pi\) | |||||||
\(752\) | 5.84435 | 0.213122 | ||||||||
\(753\) | 12.3419 | 0.449765 | ||||||||
\(754\) | 1.03361 | 0.0376417 | ||||||||
\(755\) | 67.9424 | 2.47268 | ||||||||
\(756\) | 10.0062 | 0.363921 | ||||||||
\(757\) | −7.29388 | −0.265100 | −0.132550 | − | 0.991176i | \(-0.542317\pi\) | ||||
−0.132550 | + | 0.991176i | \(0.542317\pi\) | |||||||
\(758\) | −8.19626 | −0.297702 | ||||||||
\(759\) | 9.20904 | 0.334267 | ||||||||
\(760\) | −4.36436 | −0.158312 | ||||||||
\(761\) | 8.77669 | 0.318155 | 0.159077 | − | 0.987266i | \(-0.449148\pi\) | ||||
0.159077 | + | 0.987266i | \(0.449148\pi\) | |||||||
\(762\) | 36.8110 | 1.33352 | ||||||||
\(763\) | −52.2393 | −1.89119 | ||||||||
\(764\) | 21.3554 | 0.772612 | ||||||||
\(765\) | 33.7530 | 1.22034 | ||||||||
\(766\) | −1.07701 | −0.0389140 | ||||||||
\(767\) | 0.649077 | 0.0234368 | ||||||||
\(768\) | −2.10090 | −0.0758096 | ||||||||
\(769\) | 14.8253 | 0.534614 | 0.267307 | − | 0.963611i | \(-0.413866\pi\) | ||||
0.267307 | + | 0.963611i | \(0.413866\pi\) | |||||||
\(770\) | 10.5278 | 0.379396 | ||||||||
\(771\) | −40.4973 | −1.45847 | ||||||||
\(772\) | −0.779713 | −0.0280625 | ||||||||
\(773\) | 25.9202 | 0.932284 | 0.466142 | − | 0.884710i | \(-0.345644\pi\) | ||||
0.466142 | + | 0.884710i | \(0.345644\pi\) | |||||||
\(774\) | 10.7245 | 0.385483 | ||||||||
\(775\) | 41.7312 | 1.49903 | ||||||||
\(776\) | 5.09387 | 0.182859 | ||||||||
\(777\) | −45.1199 | −1.61867 | ||||||||
\(778\) | −37.1713 | −1.33266 | ||||||||
\(779\) | −1.26772 | −0.0454209 | ||||||||
\(780\) | 1.51226 | 0.0541475 | ||||||||
\(781\) | −12.0489 | −0.431143 | ||||||||
\(782\) | −29.8472 | −1.06733 | ||||||||
\(783\) | −16.7750 | −0.599488 | ||||||||
\(784\) | 2.01556 | 0.0719842 | ||||||||
\(785\) | 25.3081 | 0.903284 | ||||||||
\(786\) | −15.1309 | −0.539700 | ||||||||
\(787\) | 21.5205 | 0.767124 | 0.383562 | − | 0.923515i | \(-0.374697\pi\) | ||||
0.383562 | + | 0.923515i | \(0.374697\pi\) | |||||||
\(788\) | 2.04711 | 0.0729252 | ||||||||
\(789\) | 36.0813 | 1.28453 | ||||||||
\(790\) | 1.74216 | 0.0619831 | ||||||||
\(791\) | −53.7042 | −1.90950 | ||||||||
\(792\) | −1.41405 | −0.0502459 | ||||||||
\(793\) | −0.967106 | −0.0343429 | ||||||||
\(794\) | 6.57009 | 0.233164 | ||||||||
\(795\) | −48.3255 | −1.71393 | ||||||||
\(796\) | −14.5252 | −0.514833 | ||||||||
\(797\) | −3.15998 | −0.111932 | −0.0559662 | − | 0.998433i | \(-0.517824\pi\) | ||||
−0.0559662 | + | 0.998433i | \(0.517824\pi\) | |||||||
\(798\) | −7.85355 | −0.278013 | ||||||||
\(799\) | −39.8031 | −1.40813 | ||||||||
\(800\) | −7.28882 | −0.257699 | ||||||||
\(801\) | −11.6983 | −0.413339 | ||||||||
\(802\) | 15.0532 | 0.531547 | ||||||||
\(803\) | −7.76485 | −0.274016 | ||||||||
\(804\) | −32.5257 | −1.14709 | ||||||||
\(805\) | 46.1291 | 1.62584 | ||||||||
\(806\) | −1.17563 | −0.0414097 | ||||||||
\(807\) | −53.0754 | −1.86834 | ||||||||
\(808\) | −3.26281 | −0.114785 | ||||||||
\(809\) | −28.2805 | −0.994291 | −0.497145 | − | 0.867667i | \(-0.665618\pi\) | ||||
−0.497145 | + | 0.867667i | \(0.665618\pi\) | |||||||
\(810\) | −39.4113 | −1.38477 | ||||||||
\(811\) | −20.0316 | −0.703406 | −0.351703 | − | 0.936112i | \(-0.614397\pi\) | ||||
−0.351703 | + | 0.936112i | \(0.614397\pi\) | |||||||
\(812\) | −15.1142 | −0.530405 | ||||||||
\(813\) | −56.9940 | −1.99887 | ||||||||
\(814\) | −7.15408 | −0.250750 | ||||||||
\(815\) | 5.35594 | 0.187610 | ||||||||
\(816\) | 14.3082 | 0.500887 | ||||||||
\(817\) | 9.44417 | 0.330410 | ||||||||
\(818\) | −17.5973 | −0.615276 | ||||||||
\(819\) | 0.871645 | 0.0304577 | ||||||||
\(820\) | −3.56956 | −0.124654 | ||||||||
\(821\) | −36.6075 | −1.27761 | −0.638805 | − | 0.769369i | \(-0.720571\pi\) | ||||
−0.638805 | + | 0.769369i | \(0.720571\pi\) | |||||||
\(822\) | −26.0967 | −0.910228 | ||||||||
\(823\) | −2.39587 | −0.0835146 | −0.0417573 | − | 0.999128i | \(-0.513296\pi\) | ||||
−0.0417573 | + | 0.999128i | \(0.513296\pi\) | |||||||
\(824\) | 16.2738 | 0.566923 | ||||||||
\(825\) | −15.3161 | −0.533238 | ||||||||
\(826\) | −9.49132 | −0.330245 | ||||||||
\(827\) | −24.9206 | −0.866573 | −0.433287 | − | 0.901256i | \(-0.642646\pi\) | ||||
−0.433287 | + | 0.901256i | \(0.642646\pi\) | |||||||
\(828\) | −6.19584 | −0.215320 | ||||||||
\(829\) | −32.4953 | −1.12861 | −0.564305 | − | 0.825566i | \(-0.690856\pi\) | ||||
−0.564305 | + | 0.825566i | \(0.690856\pi\) | |||||||
\(830\) | 28.1195 | 0.976043 | ||||||||
\(831\) | 35.6309 | 1.23602 | ||||||||
\(832\) | 0.205336 | 0.00711876 | ||||||||
\(833\) | −13.7270 | −0.475612 | ||||||||
\(834\) | 12.4276 | 0.430333 | ||||||||
\(835\) | −29.1666 | −1.00935 | ||||||||
\(836\) | −1.24524 | −0.0430674 | ||||||||
\(837\) | 19.0799 | 0.659498 | ||||||||
\(838\) | −2.96510 | −0.102428 | ||||||||
\(839\) | −32.3198 | −1.11580 | −0.557902 | − | 0.829907i | \(-0.688394\pi\) | ||||
−0.557902 | + | 0.829907i | \(0.688394\pi\) | |||||||
\(840\) | −22.1134 | −0.762985 | ||||||||
\(841\) | −3.66162 | −0.126263 | ||||||||
\(842\) | −1.01231 | −0.0348865 | ||||||||
\(843\) | −40.4873 | −1.39446 | ||||||||
\(844\) | 24.7555 | 0.852121 | ||||||||
\(845\) | 45.4242 | 1.56264 | ||||||||
\(846\) | −8.26254 | −0.284072 | ||||||||
\(847\) | −30.0247 | −1.03166 | ||||||||
\(848\) | −6.56170 | −0.225330 | ||||||||
\(849\) | −41.5978 | −1.42763 | ||||||||
\(850\) | 49.6406 | 1.70266 | ||||||||
\(851\) | −31.3466 | −1.07455 | ||||||||
\(852\) | 25.3084 | 0.867051 | ||||||||
\(853\) | −9.31247 | −0.318853 | −0.159426 | − | 0.987210i | \(-0.550964\pi\) | ||||
−0.159426 | + | 0.987210i | \(0.550964\pi\) | |||||||
\(854\) | 14.1418 | 0.483922 | ||||||||
\(855\) | 6.17017 | 0.211015 | ||||||||
\(856\) | −14.4097 | −0.492515 | ||||||||
\(857\) | 36.2038 | 1.23670 | 0.618350 | − | 0.785903i | \(-0.287801\pi\) | ||||
0.618350 | + | 0.785903i | \(0.287801\pi\) | |||||||
\(858\) | 0.431476 | 0.0147304 | ||||||||
\(859\) | −31.8269 | −1.08592 | −0.542960 | − | 0.839759i | \(-0.682696\pi\) | ||||
−0.542960 | + | 0.839759i | \(0.682696\pi\) | |||||||
\(860\) | 26.5922 | 0.906786 | ||||||||
\(861\) | −6.42334 | −0.218907 | ||||||||
\(862\) | −2.33478 | −0.0795228 | ||||||||
\(863\) | 33.1246 | 1.12758 | 0.563788 | − | 0.825920i | \(-0.309344\pi\) | ||||
0.563788 | + | 0.825920i | \(0.309344\pi\) | |||||||
\(864\) | −3.33252 | −0.113374 | ||||||||
\(865\) | −11.1461 | −0.378979 | ||||||||
\(866\) | −40.4137 | −1.37331 | ||||||||
\(867\) | −61.7310 | −2.09649 | ||||||||
\(868\) | 17.1910 | 0.583499 | ||||||||
\(869\) | 0.497071 | 0.0168620 | ||||||||
\(870\) | 37.0723 | 1.25687 | ||||||||
\(871\) | 3.17898 | 0.107716 | ||||||||
\(872\) | 17.3981 | 0.589173 | ||||||||
\(873\) | −7.20153 | −0.243735 | ||||||||
\(874\) | −5.45618 | −0.184558 | ||||||||
\(875\) | −24.0914 | −0.814439 | ||||||||
\(876\) | 16.3099 | 0.551060 | ||||||||
\(877\) | −33.0020 | −1.11440 | −0.557199 | − | 0.830379i | \(-0.688124\pi\) | ||||
−0.557199 | + | 0.830379i | \(0.688124\pi\) | |||||||
\(878\) | 16.8983 | 0.570290 | ||||||||
\(879\) | −70.2042 | −2.36793 | ||||||||
\(880\) | −3.50624 | −0.118195 | ||||||||
\(881\) | 18.0075 | 0.606688 | 0.303344 | − | 0.952881i | \(-0.401897\pi\) | ||||
0.303344 | + | 0.952881i | \(0.401897\pi\) | |||||||
\(882\) | −2.84952 | −0.0959485 | ||||||||
\(883\) | 30.0777 | 1.01220 | 0.506098 | − | 0.862476i | \(-0.331087\pi\) | ||||
0.506098 | + | 0.862476i | \(0.331087\pi\) | |||||||
\(884\) | −1.39845 | −0.0470349 | ||||||||
\(885\) | 23.2804 | 0.782561 | ||||||||
\(886\) | −26.7150 | −0.897509 | ||||||||
\(887\) | −38.6262 | −1.29694 | −0.648470 | − | 0.761240i | \(-0.724591\pi\) | ||||
−0.648470 | + | 0.761240i | \(0.724591\pi\) | |||||||
\(888\) | 15.0270 | 0.504273 | ||||||||
\(889\) | 52.6102 | 1.76449 | ||||||||
\(890\) | −29.0068 | −0.972311 | ||||||||
\(891\) | −11.2448 | −0.376715 | ||||||||
\(892\) | 12.9017 | 0.431982 | ||||||||
\(893\) | −7.27615 | −0.243487 | ||||||||
\(894\) | −4.27772 | −0.143068 | ||||||||
\(895\) | 43.9357 | 1.46861 | ||||||||
\(896\) | −3.00259 | −0.100310 | ||||||||
\(897\) | 1.89058 | 0.0631245 | ||||||||
\(898\) | 36.9537 | 1.23316 | ||||||||
\(899\) | −28.8199 | −0.961199 | ||||||||
\(900\) | 10.3047 | 0.343489 | ||||||||
\(901\) | 44.6886 | 1.48879 | ||||||||
\(902\) | −1.01847 | −0.0339112 | ||||||||
\(903\) | 47.8520 | 1.59241 | ||||||||
\(904\) | 17.8859 | 0.594878 | ||||||||
\(905\) | −50.3979 | −1.67528 | ||||||||
\(906\) | −40.7184 | −1.35278 | ||||||||
\(907\) | −10.1871 | −0.338259 | −0.169129 | − | 0.985594i | \(-0.554096\pi\) | ||||
−0.169129 | + | 0.985594i | \(0.554096\pi\) | |||||||
\(908\) | −12.4118 | −0.411899 | ||||||||
\(909\) | 4.61284 | 0.152998 | ||||||||
\(910\) | 2.16131 | 0.0716468 | ||||||||
\(911\) | 32.2951 | 1.06998 | 0.534992 | − | 0.844857i | \(-0.320315\pi\) | ||||
0.534992 | + | 0.844857i | \(0.320315\pi\) | |||||||
\(912\) | 2.61559 | 0.0866108 | ||||||||
\(913\) | 8.02305 | 0.265524 | ||||||||
\(914\) | 38.3405 | 1.26819 | ||||||||
\(915\) | −34.6871 | −1.14672 | ||||||||
\(916\) | −21.0661 | −0.696044 | ||||||||
\(917\) | −21.6250 | −0.714119 | ||||||||
\(918\) | 22.6962 | 0.749085 | ||||||||
\(919\) | 10.5091 | 0.346663 | 0.173332 | − | 0.984864i | \(-0.444547\pi\) | ||||
0.173332 | + | 0.984864i | \(0.444547\pi\) | |||||||
\(920\) | −15.3631 | −0.506506 | ||||||||
\(921\) | −50.2239 | −1.65493 | ||||||||
\(922\) | −29.7056 | −0.978302 | ||||||||
\(923\) | −2.47358 | −0.0814189 | ||||||||
\(924\) | −6.30939 | −0.207564 | ||||||||
\(925\) | 52.1344 | 1.71417 | ||||||||
\(926\) | −28.9956 | −0.952856 | ||||||||
\(927\) | −23.0073 | −0.755658 | ||||||||
\(928\) | 5.03372 | 0.165240 | ||||||||
\(929\) | −25.1154 | −0.824009 | −0.412004 | − | 0.911182i | \(-0.635171\pi\) | ||||
−0.412004 | + | 0.911182i | \(0.635171\pi\) | |||||||
\(930\) | −42.1661 | −1.38268 | ||||||||
\(931\) | −2.50934 | −0.0822405 | ||||||||
\(932\) | 13.5088 | 0.442495 | ||||||||
\(933\) | −52.1550 | −1.70748 | ||||||||
\(934\) | −12.6310 | −0.413299 | ||||||||
\(935\) | 23.8793 | 0.780937 | ||||||||
\(936\) | −0.290297 | −0.00948867 | ||||||||
\(937\) | 18.2646 | 0.596679 | 0.298340 | − | 0.954460i | \(-0.403567\pi\) | ||||
0.298340 | + | 0.954460i | \(0.403567\pi\) | |||||||
\(938\) | −46.4856 | −1.51781 | ||||||||
\(939\) | 37.1516 | 1.21240 | ||||||||
\(940\) | −20.4876 | −0.668232 | ||||||||
\(941\) | 25.9106 | 0.844660 | 0.422330 | − | 0.906442i | \(-0.361212\pi\) | ||||
0.422330 | + | 0.906442i | \(0.361212\pi\) | |||||||
\(942\) | −15.1673 | −0.494178 | ||||||||
\(943\) | −4.46255 | −0.145321 | ||||||||
\(944\) | 3.16104 | 0.102883 | ||||||||
\(945\) | −35.0771 | −1.14106 | ||||||||
\(946\) | 7.58727 | 0.246683 | ||||||||
\(947\) | 31.0640 | 1.00944 | 0.504721 | − | 0.863282i | \(-0.331595\pi\) | ||||
0.504721 | + | 0.863282i | \(0.331595\pi\) | |||||||
\(948\) | −1.04409 | −0.0339104 | ||||||||
\(949\) | −1.59409 | −0.0517463 | ||||||||
\(950\) | 9.07449 | 0.294415 | ||||||||
\(951\) | −17.1808 | −0.557127 | ||||||||
\(952\) | 20.4492 | 0.662763 | ||||||||
\(953\) | 30.4592 | 0.986670 | 0.493335 | − | 0.869839i | \(-0.335778\pi\) | ||||
0.493335 | + | 0.869839i | \(0.335778\pi\) | |||||||
\(954\) | 9.27670 | 0.300344 | ||||||||
\(955\) | −74.8623 | −2.42249 | ||||||||
\(956\) | −10.5268 | −0.340460 | ||||||||
\(957\) | 10.5774 | 0.341920 | ||||||||
\(958\) | −30.4992 | −0.985386 | ||||||||
\(959\) | −37.2973 | −1.20439 | ||||||||
\(960\) | 7.36478 | 0.237697 | ||||||||
\(961\) | 1.77988 | 0.0574153 | ||||||||
\(962\) | −1.46870 | −0.0473528 | ||||||||
\(963\) | 20.3720 | 0.656478 | ||||||||
\(964\) | −11.8794 | −0.382609 | ||||||||
\(965\) | 2.73332 | 0.0879886 | ||||||||
\(966\) | −27.6455 | −0.889479 | ||||||||
\(967\) | −31.7794 | −1.02196 | −0.510978 | − | 0.859594i | \(-0.670717\pi\) | ||||
−0.510978 | + | 0.859594i | \(0.670717\pi\) | |||||||
\(968\) | 9.99960 | 0.321399 | ||||||||
\(969\) | −17.8135 | −0.572253 | ||||||||
\(970\) | −17.8568 | −0.573346 | ||||||||
\(971\) | −28.9408 | −0.928754 | −0.464377 | − | 0.885638i | \(-0.653722\pi\) | ||||
−0.464377 | + | 0.885638i | \(0.653722\pi\) | |||||||
\(972\) | 13.6219 | 0.436923 | ||||||||
\(973\) | 17.7615 | 0.569408 | ||||||||
\(974\) | 17.6744 | 0.566323 | ||||||||
\(975\) | −3.14433 | −0.100699 | ||||||||
\(976\) | −4.70986 | −0.150759 | ||||||||
\(977\) | 3.49262 | 0.111739 | 0.0558694 | − | 0.998438i | \(-0.482207\pi\) | ||||
0.0558694 | + | 0.998438i | \(0.482207\pi\) | |||||||
\(978\) | −3.20985 | −0.102640 | ||||||||
\(979\) | −8.27622 | −0.264509 | ||||||||
\(980\) | −7.06562 | −0.225703 | ||||||||
\(981\) | −24.5968 | −0.785315 | ||||||||
\(982\) | 42.6650 | 1.36149 | ||||||||
\(983\) | 15.0208 | 0.479090 | 0.239545 | − | 0.970885i | \(-0.423002\pi\) | ||||
0.239545 | + | 0.970885i | \(0.423002\pi\) | |||||||
\(984\) | 2.13926 | 0.0681972 | ||||||||
\(985\) | −7.17622 | −0.228653 | ||||||||
\(986\) | −34.2823 | −1.09177 | ||||||||
\(987\) | −36.8670 | −1.17349 | ||||||||
\(988\) | −0.255641 | −0.00813304 | ||||||||
\(989\) | 33.2447 | 1.05712 | ||||||||
\(990\) | 4.95700 | 0.157544 | ||||||||
\(991\) | 26.3069 | 0.835667 | 0.417833 | − | 0.908524i | \(-0.362790\pi\) | ||||
0.417833 | + | 0.908524i | \(0.362790\pi\) | |||||||
\(992\) | −5.72537 | −0.181781 | ||||||||
\(993\) | 10.2668 | 0.325806 | ||||||||
\(994\) | 36.1707 | 1.14726 | ||||||||
\(995\) | 50.9188 | 1.61423 | ||||||||
\(996\) | −16.8522 | −0.533984 | ||||||||
\(997\) | −35.8211 | −1.13447 | −0.567233 | − | 0.823558i | \(-0.691986\pi\) | ||||
−0.567233 | + | 0.823558i | \(0.691986\pi\) | |||||||
\(998\) | −4.97906 | −0.157610 | ||||||||
\(999\) | 23.8363 | 0.754148 |
(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 | 6038.2.a.d.1.16 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6038.2.a.d.1.16 | ✓ | 69 | 1.1 | even | 1 | trivial |