Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + 6361 x^{6} - 14618 x^{5} - 7015 x^{4} + 15763 x^{3} + 1118 x^{2} + \cdots + 1552 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-1.34598\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.34598 | 0.601938 | 0.300969 | − | 0.953634i | \(-0.402690\pi\) | ||||
0.300969 | + | 0.953634i | \(0.402690\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −3.24510 | −1.22653 | −0.613266 | − | 0.789876i | \(-0.710145\pi\) | ||||
−0.613266 | + | 0.789876i | \(0.710145\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.34598 | −0.425635 | ||||||||
\(11\) | −3.77351 | −1.13776 | −0.568878 | − | 0.822422i | \(-0.692622\pi\) | ||||
−0.568878 | + | 0.822422i | \(0.692622\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 3.24510 | 0.867290 | ||||||||
\(15\) | −1.34598 | −0.347529 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.24113 | −1.75623 | −0.878116 | − | 0.478448i | \(-0.841199\pi\) | ||||
−0.878116 | + | 0.478448i | \(0.841199\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 0.661018 | 0.151648 | 0.0758240 | − | 0.997121i | \(-0.475841\pi\) | ||||
0.0758240 | + | 0.997121i | \(0.475841\pi\) | |||||||
\(20\) | 1.34598 | 0.300969 | ||||||||
\(21\) | 3.24510 | 0.708139 | ||||||||
\(22\) | 3.77351 | 0.804515 | ||||||||
\(23\) | −3.88709 | −0.810514 | −0.405257 | − | 0.914203i | \(-0.632818\pi\) | ||||
−0.405257 | + | 0.914203i | \(0.632818\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.18835 | −0.637670 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.24510 | −0.613266 | ||||||||
\(29\) | −2.76061 | −0.512632 | −0.256316 | − | 0.966593i | \(-0.582509\pi\) | ||||
−0.256316 | + | 0.966593i | \(0.582509\pi\) | |||||||
\(30\) | 1.34598 | 0.245740 | ||||||||
\(31\) | 7.79350 | 1.39975 | 0.699877 | − | 0.714263i | \(-0.253238\pi\) | ||||
0.699877 | + | 0.714263i | \(0.253238\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.77351 | 0.656883 | ||||||||
\(34\) | 7.24113 | 1.24184 | ||||||||
\(35\) | −4.36783 | −0.738297 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.09830 | −0.838156 | −0.419078 | − | 0.907950i | \(-0.637647\pi\) | ||||
−0.419078 | + | 0.907950i | \(0.637647\pi\) | |||||||
\(38\) | −0.661018 | −0.107231 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −1.34598 | −0.212817 | ||||||||
\(41\) | −11.1873 | −1.74716 | −0.873582 | − | 0.486677i | \(-0.838209\pi\) | ||||
−0.873582 | + | 0.486677i | \(0.838209\pi\) | |||||||
\(42\) | −3.24510 | −0.500730 | ||||||||
\(43\) | 0.261647 | 0.0399007 | 0.0199504 | − | 0.999801i | \(-0.493649\pi\) | ||||
0.0199504 | + | 0.999801i | \(0.493649\pi\) | |||||||
\(44\) | −3.77351 | −0.568878 | ||||||||
\(45\) | 1.34598 | 0.200646 | ||||||||
\(46\) | 3.88709 | 0.573120 | ||||||||
\(47\) | 0.430909 | 0.0628545 | 0.0314273 | − | 0.999506i | \(-0.489995\pi\) | ||||
0.0314273 | + | 0.999506i | \(0.489995\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 3.53068 | 0.504383 | ||||||||
\(50\) | 3.18835 | 0.450901 | ||||||||
\(51\) | 7.24113 | 1.01396 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −6.98136 | −0.958963 | −0.479481 | − | 0.877552i | \(-0.659175\pi\) | ||||
−0.479481 | + | 0.877552i | \(0.659175\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −5.07905 | −0.684859 | ||||||||
\(56\) | 3.24510 | 0.433645 | ||||||||
\(57\) | −0.661018 | −0.0875540 | ||||||||
\(58\) | 2.76061 | 0.362485 | ||||||||
\(59\) | 5.79920 | 0.754992 | 0.377496 | − | 0.926011i | \(-0.376785\pi\) | ||||
0.377496 | + | 0.926011i | \(0.376785\pi\) | |||||||
\(60\) | −1.34598 | −0.173765 | ||||||||
\(61\) | 12.2715 | 1.57120 | 0.785599 | − | 0.618736i | \(-0.212355\pi\) | ||||
0.785599 | + | 0.618736i | \(0.212355\pi\) | |||||||
\(62\) | −7.79350 | −0.989776 | ||||||||
\(63\) | −3.24510 | −0.408844 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.34598 | 0.166948 | ||||||||
\(66\) | −3.77351 | −0.464487 | ||||||||
\(67\) | −15.9624 | −1.95012 | −0.975061 | − | 0.221939i | \(-0.928762\pi\) | ||||
−0.975061 | + | 0.221939i | \(0.928762\pi\) | |||||||
\(68\) | −7.24113 | −0.878116 | ||||||||
\(69\) | 3.88709 | 0.467950 | ||||||||
\(70\) | 4.36783 | 0.522055 | ||||||||
\(71\) | 1.48957 | 0.176779 | 0.0883897 | − | 0.996086i | \(-0.471828\pi\) | ||||
0.0883897 | + | 0.996086i | \(0.471828\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −7.24146 | −0.847548 | −0.423774 | − | 0.905768i | \(-0.639295\pi\) | ||||
−0.423774 | + | 0.905768i | \(0.639295\pi\) | |||||||
\(74\) | 5.09830 | 0.592666 | ||||||||
\(75\) | 3.18835 | 0.368159 | ||||||||
\(76\) | 0.661018 | 0.0758240 | ||||||||
\(77\) | 12.2454 | 1.39549 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 9.27347 | 1.04335 | 0.521674 | − | 0.853145i | \(-0.325308\pi\) | ||||
0.521674 | + | 0.853145i | \(0.325308\pi\) | |||||||
\(80\) | 1.34598 | 0.150485 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.1873 | 1.23543 | ||||||||
\(83\) | 3.12239 | 0.342727 | 0.171363 | − | 0.985208i | \(-0.445183\pi\) | ||||
0.171363 | + | 0.985208i | \(0.445183\pi\) | |||||||
\(84\) | 3.24510 | 0.354070 | ||||||||
\(85\) | −9.74638 | −1.05714 | ||||||||
\(86\) | −0.261647 | −0.0282141 | ||||||||
\(87\) | 2.76061 | 0.295968 | ||||||||
\(88\) | 3.77351 | 0.402257 | ||||||||
\(89\) | 11.5122 | 1.22029 | 0.610144 | − | 0.792290i | \(-0.291112\pi\) | ||||
0.610144 | + | 0.792290i | \(0.291112\pi\) | |||||||
\(90\) | −1.34598 | −0.141878 | ||||||||
\(91\) | −3.24510 | −0.340179 | ||||||||
\(92\) | −3.88709 | −0.405257 | ||||||||
\(93\) | −7.79350 | −0.808149 | ||||||||
\(94\) | −0.430909 | −0.0444449 | ||||||||
\(95\) | 0.889714 | 0.0912828 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −4.13251 | −0.419593 | −0.209797 | − | 0.977745i | \(-0.567280\pi\) | ||||
−0.209797 | + | 0.977745i | \(0.567280\pi\) | |||||||
\(98\) | −3.53068 | −0.356653 | ||||||||
\(99\) | −3.77351 | −0.379252 | ||||||||
\(100\) | −3.18835 | −0.318835 | ||||||||
\(101\) | −10.6527 | −1.05999 | −0.529993 | − | 0.848002i | \(-0.677805\pi\) | ||||
−0.529993 | + | 0.848002i | \(0.677805\pi\) | |||||||
\(102\) | −7.24113 | −0.716979 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 4.36783 | 0.426256 | ||||||||
\(106\) | 6.98136 | 0.678089 | ||||||||
\(107\) | −13.5536 | −1.31027 | −0.655137 | − | 0.755510i | \(-0.727389\pi\) | ||||
−0.655137 | + | 0.755510i | \(0.727389\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −13.6544 | −1.30786 | −0.653928 | − | 0.756557i | \(-0.726880\pi\) | ||||
−0.653928 | + | 0.756557i | \(0.726880\pi\) | |||||||
\(110\) | 5.07905 | 0.484268 | ||||||||
\(111\) | 5.09830 | 0.483909 | ||||||||
\(112\) | −3.24510 | −0.306633 | ||||||||
\(113\) | −1.82889 | −0.172048 | −0.0860239 | − | 0.996293i | \(-0.527416\pi\) | ||||
−0.0860239 | + | 0.996293i | \(0.527416\pi\) | |||||||
\(114\) | 0.661018 | 0.0619100 | ||||||||
\(115\) | −5.23192 | −0.487879 | ||||||||
\(116\) | −2.76061 | −0.256316 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −5.79920 | −0.533860 | ||||||||
\(119\) | 23.4982 | 2.15408 | ||||||||
\(120\) | 1.34598 | 0.122870 | ||||||||
\(121\) | 3.23936 | 0.294487 | ||||||||
\(122\) | −12.2715 | −1.11101 | ||||||||
\(123\) | 11.1873 | 1.00873 | ||||||||
\(124\) | 7.79350 | 0.699877 | ||||||||
\(125\) | −11.0213 | −0.985777 | ||||||||
\(126\) | 3.24510 | 0.289097 | ||||||||
\(127\) | 5.03432 | 0.446724 | 0.223362 | − | 0.974736i | \(-0.428297\pi\) | ||||
0.223362 | + | 0.974736i | \(0.428297\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.261647 | −0.0230367 | ||||||||
\(130\) | −1.34598 | −0.118050 | ||||||||
\(131\) | 17.9193 | 1.56562 | 0.782809 | − | 0.622262i | \(-0.213786\pi\) | ||||
0.782809 | + | 0.622262i | \(0.213786\pi\) | |||||||
\(132\) | 3.77351 | 0.328442 | ||||||||
\(133\) | −2.14507 | −0.186001 | ||||||||
\(134\) | 15.9624 | 1.37894 | ||||||||
\(135\) | −1.34598 | −0.115843 | ||||||||
\(136\) | 7.24113 | 0.620922 | ||||||||
\(137\) | 3.26677 | 0.279099 | 0.139550 | − | 0.990215i | \(-0.455435\pi\) | ||||
0.139550 | + | 0.990215i | \(0.455435\pi\) | |||||||
\(138\) | −3.88709 | −0.330891 | ||||||||
\(139\) | 10.4650 | 0.887629 | 0.443814 | − | 0.896119i | \(-0.353625\pi\) | ||||
0.443814 | + | 0.896119i | \(0.353625\pi\) | |||||||
\(140\) | −4.36783 | −0.369149 | ||||||||
\(141\) | −0.430909 | −0.0362891 | ||||||||
\(142\) | −1.48957 | −0.125002 | ||||||||
\(143\) | −3.77351 | −0.315557 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −3.71571 | −0.308573 | ||||||||
\(146\) | 7.24146 | 0.599307 | ||||||||
\(147\) | −3.53068 | −0.291206 | ||||||||
\(148\) | −5.09830 | −0.419078 | ||||||||
\(149\) | 18.9960 | 1.55621 | 0.778104 | − | 0.628135i | \(-0.216181\pi\) | ||||
0.778104 | + | 0.628135i | \(0.216181\pi\) | |||||||
\(150\) | −3.18835 | −0.260328 | ||||||||
\(151\) | −2.86092 | −0.232818 | −0.116409 | − | 0.993201i | \(-0.537138\pi\) | ||||
−0.116409 | + | 0.993201i | \(0.537138\pi\) | |||||||
\(152\) | −0.661018 | −0.0536157 | ||||||||
\(153\) | −7.24113 | −0.585411 | ||||||||
\(154\) | −12.2454 | −0.986764 | ||||||||
\(155\) | 10.4899 | 0.842566 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −8.29324 | −0.661872 | −0.330936 | − | 0.943653i | \(-0.607364\pi\) | ||||
−0.330936 | + | 0.943653i | \(0.607364\pi\) | |||||||
\(158\) | −9.27347 | −0.737758 | ||||||||
\(159\) | 6.98136 | 0.553658 | ||||||||
\(160\) | −1.34598 | −0.106409 | ||||||||
\(161\) | 12.6140 | 0.994122 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 14.7826 | 1.15787 | 0.578933 | − | 0.815375i | \(-0.303469\pi\) | ||||
0.578933 | + | 0.815375i | \(0.303469\pi\) | |||||||
\(164\) | −11.1873 | −0.873582 | ||||||||
\(165\) | 5.07905 | 0.395403 | ||||||||
\(166\) | −3.12239 | −0.242344 | ||||||||
\(167\) | 1.14854 | 0.0888765 | 0.0444382 | − | 0.999012i | \(-0.485850\pi\) | ||||
0.0444382 | + | 0.999012i | \(0.485850\pi\) | |||||||
\(168\) | −3.24510 | −0.250365 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 9.74638 | 0.747513 | ||||||||
\(171\) | 0.661018 | 0.0505493 | ||||||||
\(172\) | 0.261647 | 0.0199504 | ||||||||
\(173\) | 17.4991 | 1.33044 | 0.665218 | − | 0.746650i | \(-0.268339\pi\) | ||||
0.665218 | + | 0.746650i | \(0.268339\pi\) | |||||||
\(174\) | −2.76061 | −0.209281 | ||||||||
\(175\) | 10.3465 | 0.782123 | ||||||||
\(176\) | −3.77351 | −0.284439 | ||||||||
\(177\) | −5.79920 | −0.435895 | ||||||||
\(178\) | −11.5122 | −0.862874 | ||||||||
\(179\) | −3.80501 | −0.284400 | −0.142200 | − | 0.989838i | \(-0.545418\pi\) | ||||
−0.142200 | + | 0.989838i | \(0.545418\pi\) | |||||||
\(180\) | 1.34598 | 0.100323 | ||||||||
\(181\) | 13.2055 | 0.981556 | 0.490778 | − | 0.871285i | \(-0.336713\pi\) | ||||
0.490778 | + | 0.871285i | \(0.336713\pi\) | |||||||
\(182\) | 3.24510 | 0.240543 | ||||||||
\(183\) | −12.2715 | −0.907132 | ||||||||
\(184\) | 3.88709 | 0.286560 | ||||||||
\(185\) | −6.86219 | −0.504518 | ||||||||
\(186\) | 7.79350 | 0.571447 | ||||||||
\(187\) | 27.3245 | 1.99816 | ||||||||
\(188\) | 0.430909 | 0.0314273 | ||||||||
\(189\) | 3.24510 | 0.236046 | ||||||||
\(190\) | −0.889714 | −0.0645467 | ||||||||
\(191\) | −14.5232 | −1.05086 | −0.525430 | − | 0.850837i | \(-0.676095\pi\) | ||||
−0.525430 | + | 0.850837i | \(0.676095\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 18.8956 | 1.36013 | 0.680066 | − | 0.733151i | \(-0.261951\pi\) | ||||
0.680066 | + | 0.733151i | \(0.261951\pi\) | |||||||
\(194\) | 4.13251 | 0.296697 | ||||||||
\(195\) | −1.34598 | −0.0963873 | ||||||||
\(196\) | 3.53068 | 0.252192 | ||||||||
\(197\) | −4.69606 | −0.334580 | −0.167290 | − | 0.985908i | \(-0.553502\pi\) | ||||
−0.167290 | + | 0.985908i | \(0.553502\pi\) | |||||||
\(198\) | 3.77351 | 0.268172 | ||||||||
\(199\) | −25.7438 | −1.82493 | −0.912465 | − | 0.409156i | \(-0.865823\pi\) | ||||
−0.912465 | + | 0.409156i | \(0.865823\pi\) | |||||||
\(200\) | 3.18835 | 0.225450 | ||||||||
\(201\) | 15.9624 | 1.12590 | ||||||||
\(202\) | 10.6527 | 0.749523 | ||||||||
\(203\) | 8.95845 | 0.628760 | ||||||||
\(204\) | 7.24113 | 0.506980 | ||||||||
\(205\) | −15.0578 | −1.05169 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | −3.88709 | −0.270171 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −2.49436 | −0.172538 | ||||||||
\(210\) | −4.36783 | −0.301409 | ||||||||
\(211\) | 16.6079 | 1.14334 | 0.571668 | − | 0.820485i | \(-0.306296\pi\) | ||||
0.571668 | + | 0.820485i | \(0.306296\pi\) | |||||||
\(212\) | −6.98136 | −0.479481 | ||||||||
\(213\) | −1.48957 | −0.102064 | ||||||||
\(214\) | 13.5536 | 0.926503 | ||||||||
\(215\) | 0.352170 | 0.0240178 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −25.2907 | −1.71684 | ||||||||
\(218\) | 13.6544 | 0.924794 | ||||||||
\(219\) | 7.24146 | 0.489332 | ||||||||
\(220\) | −5.07905 | −0.342429 | ||||||||
\(221\) | −7.24113 | −0.487091 | ||||||||
\(222\) | −5.09830 | −0.342176 | ||||||||
\(223\) | 4.74985 | 0.318074 | 0.159037 | − | 0.987273i | \(-0.449161\pi\) | ||||
0.159037 | + | 0.987273i | \(0.449161\pi\) | |||||||
\(224\) | 3.24510 | 0.216822 | ||||||||
\(225\) | −3.18835 | −0.212557 | ||||||||
\(226\) | 1.82889 | 0.121656 | ||||||||
\(227\) | 14.8843 | 0.987904 | 0.493952 | − | 0.869489i | \(-0.335552\pi\) | ||||
0.493952 | + | 0.869489i | \(0.335552\pi\) | |||||||
\(228\) | −0.661018 | −0.0437770 | ||||||||
\(229\) | −23.6580 | −1.56337 | −0.781683 | − | 0.623676i | \(-0.785639\pi\) | ||||
−0.781683 | + | 0.623676i | \(0.785639\pi\) | |||||||
\(230\) | 5.23192 | 0.344983 | ||||||||
\(231\) | −12.2454 | −0.805689 | ||||||||
\(232\) | 2.76061 | 0.181243 | ||||||||
\(233\) | −24.5541 | −1.60859 | −0.804297 | − | 0.594228i | \(-0.797458\pi\) | ||||
−0.804297 | + | 0.594228i | \(0.797458\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 0.579993 | 0.0378345 | ||||||||
\(236\) | 5.79920 | 0.377496 | ||||||||
\(237\) | −9.27347 | −0.602377 | ||||||||
\(238\) | −23.4982 | −1.52316 | ||||||||
\(239\) | −0.194543 | −0.0125839 | −0.00629195 | − | 0.999980i | \(-0.502003\pi\) | ||||
−0.00629195 | + | 0.999980i | \(0.502003\pi\) | |||||||
\(240\) | −1.34598 | −0.0868823 | ||||||||
\(241\) | 5.77889 | 0.372251 | 0.186126 | − | 0.982526i | \(-0.440407\pi\) | ||||
0.186126 | + | 0.982526i | \(0.440407\pi\) | |||||||
\(242\) | −3.23936 | −0.208234 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 12.2715 | 0.785599 | ||||||||
\(245\) | 4.75221 | 0.303608 | ||||||||
\(246\) | −11.1873 | −0.713277 | ||||||||
\(247\) | 0.661018 | 0.0420596 | ||||||||
\(248\) | −7.79350 | −0.494888 | ||||||||
\(249\) | −3.12239 | −0.197873 | ||||||||
\(250\) | 11.0213 | 0.697049 | ||||||||
\(251\) | −25.3501 | −1.60008 | −0.800042 | − | 0.599944i | \(-0.795190\pi\) | ||||
−0.800042 | + | 0.599944i | \(0.795190\pi\) | |||||||
\(252\) | −3.24510 | −0.204422 | ||||||||
\(253\) | 14.6680 | 0.922167 | ||||||||
\(254\) | −5.03432 | −0.315881 | ||||||||
\(255\) | 9.74638 | 0.610342 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.3251 | 1.33022 | 0.665111 | − | 0.746745i | \(-0.268384\pi\) | ||||
0.665111 | + | 0.746745i | \(0.268384\pi\) | |||||||
\(258\) | 0.261647 | 0.0162894 | ||||||||
\(259\) | 16.5445 | 1.02803 | ||||||||
\(260\) | 1.34598 | 0.0834738 | ||||||||
\(261\) | −2.76061 | −0.170877 | ||||||||
\(262\) | −17.9193 | −1.10706 | ||||||||
\(263\) | −24.8870 | −1.53460 | −0.767300 | − | 0.641288i | \(-0.778400\pi\) | ||||
−0.767300 | + | 0.641288i | \(0.778400\pi\) | |||||||
\(264\) | −3.77351 | −0.232243 | ||||||||
\(265\) | −9.39673 | −0.577237 | ||||||||
\(266\) | 2.14507 | 0.131523 | ||||||||
\(267\) | −11.5122 | −0.704534 | ||||||||
\(268\) | −15.9624 | −0.975061 | ||||||||
\(269\) | 27.1724 | 1.65673 | 0.828365 | − | 0.560189i | \(-0.189271\pi\) | ||||
0.828365 | + | 0.560189i | \(0.189271\pi\) | |||||||
\(270\) | 1.34598 | 0.0819134 | ||||||||
\(271\) | −9.83001 | −0.597130 | −0.298565 | − | 0.954389i | \(-0.596508\pi\) | ||||
−0.298565 | + | 0.954389i | \(0.596508\pi\) | |||||||
\(272\) | −7.24113 | −0.439058 | ||||||||
\(273\) | 3.24510 | 0.196402 | ||||||||
\(274\) | −3.26677 | −0.197353 | ||||||||
\(275\) | 12.0313 | 0.725513 | ||||||||
\(276\) | 3.88709 | 0.233975 | ||||||||
\(277\) | −1.13804 | −0.0683780 | −0.0341890 | − | 0.999415i | \(-0.510885\pi\) | ||||
−0.0341890 | + | 0.999415i | \(0.510885\pi\) | |||||||
\(278\) | −10.4650 | −0.627648 | ||||||||
\(279\) | 7.79350 | 0.466585 | ||||||||
\(280\) | 4.36783 | 0.261028 | ||||||||
\(281\) | −1.48374 | −0.0885125 | −0.0442562 | − | 0.999020i | \(-0.514092\pi\) | ||||
−0.0442562 | + | 0.999020i | \(0.514092\pi\) | |||||||
\(282\) | 0.430909 | 0.0256602 | ||||||||
\(283\) | 24.5874 | 1.46157 | 0.730784 | − | 0.682609i | \(-0.239155\pi\) | ||||
0.730784 | + | 0.682609i | \(0.239155\pi\) | |||||||
\(284\) | 1.48957 | 0.0883897 | ||||||||
\(285\) | −0.889714 | −0.0527021 | ||||||||
\(286\) | 3.77351 | 0.223132 | ||||||||
\(287\) | 36.3040 | 2.14295 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 35.4339 | 2.08435 | ||||||||
\(290\) | 3.71571 | 0.218194 | ||||||||
\(291\) | 4.13251 | 0.242252 | ||||||||
\(292\) | −7.24146 | −0.423774 | ||||||||
\(293\) | −23.1487 | −1.35236 | −0.676182 | − | 0.736735i | \(-0.736367\pi\) | ||||
−0.676182 | + | 0.736735i | \(0.736367\pi\) | |||||||
\(294\) | 3.53068 | 0.205914 | ||||||||
\(295\) | 7.80559 | 0.454459 | ||||||||
\(296\) | 5.09830 | 0.296333 | ||||||||
\(297\) | 3.77351 | 0.218961 | ||||||||
\(298\) | −18.9960 | −1.10041 | ||||||||
\(299\) | −3.88709 | −0.224796 | ||||||||
\(300\) | 3.18835 | 0.184080 | ||||||||
\(301\) | −0.849070 | −0.0489396 | ||||||||
\(302\) | 2.86092 | 0.164627 | ||||||||
\(303\) | 10.6527 | 0.611983 | ||||||||
\(304\) | 0.661018 | 0.0379120 | ||||||||
\(305\) | 16.5171 | 0.945765 | ||||||||
\(306\) | 7.24113 | 0.413948 | ||||||||
\(307\) | 19.4854 | 1.11209 | 0.556046 | − | 0.831152i | \(-0.312318\pi\) | ||||
0.556046 | + | 0.831152i | \(0.312318\pi\) | |||||||
\(308\) | 12.2454 | 0.697747 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −10.4899 | −0.595784 | ||||||||
\(311\) | −24.2475 | −1.37495 | −0.687474 | − | 0.726209i | \(-0.741280\pi\) | ||||
−0.687474 | + | 0.726209i | \(0.741280\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 17.0379 | 0.963042 | 0.481521 | − | 0.876435i | \(-0.340085\pi\) | ||||
0.481521 | + | 0.876435i | \(0.340085\pi\) | |||||||
\(314\) | 8.29324 | 0.468014 | ||||||||
\(315\) | −4.36783 | −0.246099 | ||||||||
\(316\) | 9.27347 | 0.521674 | ||||||||
\(317\) | −17.1424 | −0.962816 | −0.481408 | − | 0.876497i | \(-0.659874\pi\) | ||||
−0.481408 | + | 0.876497i | \(0.659874\pi\) | |||||||
\(318\) | −6.98136 | −0.391495 | ||||||||
\(319\) | 10.4172 | 0.583250 | ||||||||
\(320\) | 1.34598 | 0.0752423 | ||||||||
\(321\) | 13.5536 | 0.756487 | ||||||||
\(322\) | −12.6140 | −0.702950 | ||||||||
\(323\) | −4.78652 | −0.266329 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.18835 | −0.176858 | ||||||||
\(326\) | −14.7826 | −0.818735 | ||||||||
\(327\) | 13.6544 | 0.755091 | ||||||||
\(328\) | 11.1873 | 0.617716 | ||||||||
\(329\) | −1.39834 | −0.0770931 | ||||||||
\(330\) | −5.07905 | −0.279592 | ||||||||
\(331\) | −8.77403 | −0.482264 | −0.241132 | − | 0.970492i | \(-0.577519\pi\) | ||||
−0.241132 | + | 0.970492i | \(0.577519\pi\) | |||||||
\(332\) | 3.12239 | 0.171363 | ||||||||
\(333\) | −5.09830 | −0.279385 | ||||||||
\(334\) | −1.14854 | −0.0628452 | ||||||||
\(335\) | −21.4850 | −1.17385 | ||||||||
\(336\) | 3.24510 | 0.177035 | ||||||||
\(337\) | −4.00567 | −0.218203 | −0.109101 | − | 0.994031i | \(-0.534797\pi\) | ||||
−0.109101 | + | 0.994031i | \(0.534797\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 1.82889 | 0.0993319 | ||||||||
\(340\) | −9.74638 | −0.528572 | ||||||||
\(341\) | −29.4088 | −1.59258 | ||||||||
\(342\) | −0.661018 | −0.0357438 | ||||||||
\(343\) | 11.2583 | 0.607890 | ||||||||
\(344\) | −0.261647 | −0.0141070 | ||||||||
\(345\) | 5.23192 | 0.281677 | ||||||||
\(346\) | −17.4991 | −0.940760 | ||||||||
\(347\) | −15.7245 | −0.844137 | −0.422069 | − | 0.906564i | \(-0.638696\pi\) | ||||
−0.422069 | + | 0.906564i | \(0.638696\pi\) | |||||||
\(348\) | 2.76061 | 0.147984 | ||||||||
\(349\) | −9.84845 | −0.527175 | −0.263588 | − | 0.964635i | \(-0.584906\pi\) | ||||
−0.263588 | + | 0.964635i | \(0.584906\pi\) | |||||||
\(350\) | −10.3465 | −0.553045 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 3.77351 | 0.201129 | ||||||||
\(353\) | −3.60939 | −0.192108 | −0.0960541 | − | 0.995376i | \(-0.530622\pi\) | ||||
−0.0960541 | + | 0.995376i | \(0.530622\pi\) | |||||||
\(354\) | 5.79920 | 0.308224 | ||||||||
\(355\) | 2.00492 | 0.106410 | ||||||||
\(356\) | 11.5122 | 0.610144 | ||||||||
\(357\) | −23.4982 | −1.24366 | ||||||||
\(358\) | 3.80501 | 0.201101 | ||||||||
\(359\) | 6.53877 | 0.345103 | 0.172552 | − | 0.985000i | \(-0.444799\pi\) | ||||
0.172552 | + | 0.985000i | \(0.444799\pi\) | |||||||
\(360\) | −1.34598 | −0.0709391 | ||||||||
\(361\) | −18.5631 | −0.977003 | ||||||||
\(362\) | −13.2055 | −0.694065 | ||||||||
\(363\) | −3.23936 | −0.170022 | ||||||||
\(364\) | −3.24510 | −0.170090 | ||||||||
\(365\) | −9.74682 | −0.510172 | ||||||||
\(366\) | 12.2715 | 0.641439 | ||||||||
\(367\) | 30.8684 | 1.61132 | 0.805659 | − | 0.592379i | \(-0.201811\pi\) | ||||
0.805659 | + | 0.592379i | \(0.201811\pi\) | |||||||
\(368\) | −3.88709 | −0.202628 | ||||||||
\(369\) | −11.1873 | −0.582388 | ||||||||
\(370\) | 6.86219 | 0.356748 | ||||||||
\(371\) | 22.6552 | 1.17620 | ||||||||
\(372\) | −7.79350 | −0.404074 | ||||||||
\(373\) | 11.4169 | 0.591146 | 0.295573 | − | 0.955320i | \(-0.404489\pi\) | ||||
0.295573 | + | 0.955320i | \(0.404489\pi\) | |||||||
\(374\) | −27.3245 | −1.41291 | ||||||||
\(375\) | 11.0213 | 0.569138 | ||||||||
\(376\) | −0.430909 | −0.0222224 | ||||||||
\(377\) | −2.76061 | −0.142179 | ||||||||
\(378\) | −3.24510 | −0.166910 | ||||||||
\(379\) | −6.20355 | −0.318655 | −0.159327 | − | 0.987226i | \(-0.550933\pi\) | ||||
−0.159327 | + | 0.987226i | \(0.550933\pi\) | |||||||
\(380\) | 0.889714 | 0.0456414 | ||||||||
\(381\) | −5.03432 | −0.257916 | ||||||||
\(382\) | 14.5232 | 0.743070 | ||||||||
\(383\) | 2.81254 | 0.143714 | 0.0718570 | − | 0.997415i | \(-0.477107\pi\) | ||||
0.0718570 | + | 0.997415i | \(0.477107\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 16.4820 | 0.840002 | ||||||||
\(386\) | −18.8956 | −0.961759 | ||||||||
\(387\) | 0.261647 | 0.0133002 | ||||||||
\(388\) | −4.13251 | −0.209797 | ||||||||
\(389\) | −15.6657 | −0.794284 | −0.397142 | − | 0.917757i | \(-0.629998\pi\) | ||||
−0.397142 | + | 0.917757i | \(0.629998\pi\) | |||||||
\(390\) | 1.34598 | 0.0681561 | ||||||||
\(391\) | 28.1469 | 1.42345 | ||||||||
\(392\) | −3.53068 | −0.178326 | ||||||||
\(393\) | −17.9193 | −0.903910 | ||||||||
\(394\) | 4.69606 | 0.236584 | ||||||||
\(395\) | 12.4819 | 0.628031 | ||||||||
\(396\) | −3.77351 | −0.189626 | ||||||||
\(397\) | −3.89885 | −0.195678 | −0.0978388 | − | 0.995202i | \(-0.531193\pi\) | ||||
−0.0978388 | + | 0.995202i | \(0.531193\pi\) | |||||||
\(398\) | 25.7438 | 1.29042 | ||||||||
\(399\) | 2.14507 | 0.107388 | ||||||||
\(400\) | −3.18835 | −0.159418 | ||||||||
\(401\) | −28.2737 | −1.41192 | −0.705960 | − | 0.708251i | \(-0.749484\pi\) | ||||
−0.705960 | + | 0.708251i | \(0.749484\pi\) | |||||||
\(402\) | −15.9624 | −0.796134 | ||||||||
\(403\) | 7.79350 | 0.388222 | ||||||||
\(404\) | −10.6527 | −0.529993 | ||||||||
\(405\) | 1.34598 | 0.0668820 | ||||||||
\(406\) | −8.95845 | −0.444600 | ||||||||
\(407\) | 19.2385 | 0.953616 | ||||||||
\(408\) | −7.24113 | −0.358489 | ||||||||
\(409\) | −8.55426 | −0.422981 | −0.211491 | − | 0.977380i | \(-0.567832\pi\) | ||||
−0.211491 | + | 0.977380i | \(0.567832\pi\) | |||||||
\(410\) | 15.0578 | 0.743654 | ||||||||
\(411\) | −3.26677 | −0.161138 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | −18.8190 | −0.926023 | ||||||||
\(414\) | 3.88709 | 0.191040 | ||||||||
\(415\) | 4.20266 | 0.206300 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −10.4650 | −0.512473 | ||||||||
\(418\) | 2.49436 | 0.122003 | ||||||||
\(419\) | 7.01647 | 0.342777 | 0.171388 | − | 0.985204i | \(-0.445175\pi\) | ||||
0.171388 | + | 0.985204i | \(0.445175\pi\) | |||||||
\(420\) | 4.36783 | 0.213128 | ||||||||
\(421\) | −18.0352 | −0.878982 | −0.439491 | − | 0.898247i | \(-0.644841\pi\) | ||||
−0.439491 | + | 0.898247i | \(0.644841\pi\) | |||||||
\(422\) | −16.6079 | −0.808461 | ||||||||
\(423\) | 0.430909 | 0.0209515 | ||||||||
\(424\) | 6.98136 | 0.339045 | ||||||||
\(425\) | 23.0873 | 1.11990 | ||||||||
\(426\) | 1.48957 | 0.0721699 | ||||||||
\(427\) | −39.8221 | −1.92713 | ||||||||
\(428\) | −13.5536 | −0.655137 | ||||||||
\(429\) | 3.77351 | 0.182187 | ||||||||
\(430\) | −0.352170 | −0.0169831 | ||||||||
\(431\) | 28.1776 | 1.35727 | 0.678634 | − | 0.734477i | \(-0.262572\pi\) | ||||
0.678634 | + | 0.734477i | \(0.262572\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 18.6955 | 0.898451 | 0.449225 | − | 0.893418i | \(-0.351700\pi\) | ||||
0.449225 | + | 0.893418i | \(0.351700\pi\) | |||||||
\(434\) | 25.2907 | 1.21399 | ||||||||
\(435\) | 3.71571 | 0.178155 | ||||||||
\(436\) | −13.6544 | −0.653928 | ||||||||
\(437\) | −2.56944 | −0.122913 | ||||||||
\(438\) | −7.24146 | −0.346010 | ||||||||
\(439\) | −6.18598 | −0.295241 | −0.147620 | − | 0.989044i | \(-0.547161\pi\) | ||||
−0.147620 | + | 0.989044i | \(0.547161\pi\) | |||||||
\(440\) | 5.07905 | 0.242134 | ||||||||
\(441\) | 3.53068 | 0.168128 | ||||||||
\(442\) | 7.24113 | 0.344425 | ||||||||
\(443\) | 32.4240 | 1.54051 | 0.770255 | − | 0.637736i | \(-0.220129\pi\) | ||||
0.770255 | + | 0.637736i | \(0.220129\pi\) | |||||||
\(444\) | 5.09830 | 0.241955 | ||||||||
\(445\) | 15.4951 | 0.734538 | ||||||||
\(446\) | −4.74985 | −0.224912 | ||||||||
\(447\) | −18.9960 | −0.898478 | ||||||||
\(448\) | −3.24510 | −0.153317 | ||||||||
\(449\) | −25.2808 | −1.19308 | −0.596538 | − | 0.802585i | \(-0.703457\pi\) | ||||
−0.596538 | + | 0.802585i | \(0.703457\pi\) | |||||||
\(450\) | 3.18835 | 0.150300 | ||||||||
\(451\) | 42.2154 | 1.98785 | ||||||||
\(452\) | −1.82889 | −0.0860239 | ||||||||
\(453\) | 2.86092 | 0.134418 | ||||||||
\(454\) | −14.8843 | −0.698553 | ||||||||
\(455\) | −4.36783 | −0.204767 | ||||||||
\(456\) | 0.661018 | 0.0309550 | ||||||||
\(457\) | 16.3853 | 0.766470 | 0.383235 | − | 0.923651i | \(-0.374810\pi\) | ||||
0.383235 | + | 0.923651i | \(0.374810\pi\) | |||||||
\(458\) | 23.6580 | 1.10547 | ||||||||
\(459\) | 7.24113 | 0.337987 | ||||||||
\(460\) | −5.23192 | −0.243940 | ||||||||
\(461\) | 17.8016 | 0.829104 | 0.414552 | − | 0.910026i | \(-0.363938\pi\) | ||||
0.414552 | + | 0.910026i | \(0.363938\pi\) | |||||||
\(462\) | 12.2454 | 0.569708 | ||||||||
\(463\) | −13.5211 | −0.628378 | −0.314189 | − | 0.949360i | \(-0.601733\pi\) | ||||
−0.314189 | + | 0.949360i | \(0.601733\pi\) | |||||||
\(464\) | −2.76061 | −0.128158 | ||||||||
\(465\) | −10.4899 | −0.486456 | ||||||||
\(466\) | 24.5541 | 1.13745 | ||||||||
\(467\) | 30.5160 | 1.41211 | 0.706057 | − | 0.708155i | \(-0.250472\pi\) | ||||
0.706057 | + | 0.708155i | \(0.250472\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 51.7997 | 2.39189 | ||||||||
\(470\) | −0.579993 | −0.0267531 | ||||||||
\(471\) | 8.29324 | 0.382132 | ||||||||
\(472\) | −5.79920 | −0.266930 | ||||||||
\(473\) | −0.987326 | −0.0453973 | ||||||||
\(474\) | 9.27347 | 0.425945 | ||||||||
\(475\) | −2.10756 | −0.0967014 | ||||||||
\(476\) | 23.4982 | 1.07704 | ||||||||
\(477\) | −6.98136 | −0.319654 | ||||||||
\(478\) | 0.194543 | 0.00889817 | ||||||||
\(479\) | 8.25272 | 0.377076 | 0.188538 | − | 0.982066i | \(-0.439625\pi\) | ||||
0.188538 | + | 0.982066i | \(0.439625\pi\) | |||||||
\(480\) | 1.34598 | 0.0614351 | ||||||||
\(481\) | −5.09830 | −0.232463 | ||||||||
\(482\) | −5.77889 | −0.263221 | ||||||||
\(483\) | −12.6140 | −0.573957 | ||||||||
\(484\) | 3.23936 | 0.147244 | ||||||||
\(485\) | −5.56226 | −0.252569 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −3.27770 | −0.148527 | −0.0742634 | − | 0.997239i | \(-0.523661\pi\) | ||||
−0.0742634 | + | 0.997239i | \(0.523661\pi\) | |||||||
\(488\) | −12.2715 | −0.555503 | ||||||||
\(489\) | −14.7826 | −0.668494 | ||||||||
\(490\) | −4.75221 | −0.214683 | ||||||||
\(491\) | 7.49528 | 0.338257 | 0.169129 | − | 0.985594i | \(-0.445905\pi\) | ||||
0.169129 | + | 0.985594i | \(0.445905\pi\) | |||||||
\(492\) | 11.1873 | 0.504363 | ||||||||
\(493\) | 19.9899 | 0.900300 | ||||||||
\(494\) | −0.661018 | −0.0297406 | ||||||||
\(495\) | −5.07905 | −0.228286 | ||||||||
\(496\) | 7.79350 | 0.349939 | ||||||||
\(497\) | −4.83381 | −0.216826 | ||||||||
\(498\) | 3.12239 | 0.139918 | ||||||||
\(499\) | 14.3424 | 0.642054 | 0.321027 | − | 0.947070i | \(-0.395972\pi\) | ||||
0.321027 | + | 0.947070i | \(0.395972\pi\) | |||||||
\(500\) | −11.0213 | −0.492888 | ||||||||
\(501\) | −1.14854 | −0.0513129 | ||||||||
\(502\) | 25.3501 | 1.13143 | ||||||||
\(503\) | 36.3950 | 1.62277 | 0.811386 | − | 0.584511i | \(-0.198714\pi\) | ||||
0.811386 | + | 0.584511i | \(0.198714\pi\) | |||||||
\(504\) | 3.24510 | 0.144548 | ||||||||
\(505\) | −14.3383 | −0.638046 | ||||||||
\(506\) | −14.6680 | −0.652070 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 5.03432 | 0.223362 | ||||||||
\(509\) | −9.94797 | −0.440936 | −0.220468 | − | 0.975394i | \(-0.570758\pi\) | ||||
−0.220468 | + | 0.975394i | \(0.570758\pi\) | |||||||
\(510\) | −9.74638 | −0.431577 | ||||||||
\(511\) | 23.4993 | 1.03955 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.661018 | −0.0291847 | ||||||||
\(514\) | −21.3251 | −0.940609 | ||||||||
\(515\) | −1.34598 | −0.0593108 | ||||||||
\(516\) | −0.261647 | −0.0115184 | ||||||||
\(517\) | −1.62604 | −0.0715131 | ||||||||
\(518\) | −16.5445 | −0.726924 | ||||||||
\(519\) | −17.4991 | −0.768127 | ||||||||
\(520\) | −1.34598 | −0.0590249 | ||||||||
\(521\) | −8.19107 | −0.358857 | −0.179429 | − | 0.983771i | \(-0.557425\pi\) | ||||
−0.179429 | + | 0.983771i | \(0.557425\pi\) | |||||||
\(522\) | 2.76061 | 0.120828 | ||||||||
\(523\) | 22.4531 | 0.981805 | 0.490903 | − | 0.871214i | \(-0.336667\pi\) | ||||
0.490903 | + | 0.871214i | \(0.336667\pi\) | |||||||
\(524\) | 17.9193 | 0.782809 | ||||||||
\(525\) | −10.3465 | −0.451559 | ||||||||
\(526\) | 24.8870 | 1.08513 | ||||||||
\(527\) | −56.4338 | −2.45829 | ||||||||
\(528\) | 3.77351 | 0.164221 | ||||||||
\(529\) | −7.89055 | −0.343067 | ||||||||
\(530\) | 9.39673 | 0.408168 | ||||||||
\(531\) | 5.79920 | 0.251664 | ||||||||
\(532\) | −2.14507 | −0.0930006 | ||||||||
\(533\) | −11.1873 | −0.484576 | ||||||||
\(534\) | 11.5122 | 0.498181 | ||||||||
\(535\) | −18.2428 | −0.788704 | ||||||||
\(536\) | 15.9624 | 0.689472 | ||||||||
\(537\) | 3.80501 | 0.164198 | ||||||||
\(538\) | −27.1724 | −1.17149 | ||||||||
\(539\) | −13.3231 | −0.573865 | ||||||||
\(540\) | −1.34598 | −0.0579215 | ||||||||
\(541\) | −29.5197 | −1.26915 | −0.634576 | − | 0.772860i | \(-0.718825\pi\) | ||||
−0.634576 | + | 0.772860i | \(0.718825\pi\) | |||||||
\(542\) | 9.83001 | 0.422235 | ||||||||
\(543\) | −13.2055 | −0.566702 | ||||||||
\(544\) | 7.24113 | 0.310461 | ||||||||
\(545\) | −18.3785 | −0.787249 | ||||||||
\(546\) | −3.24510 | −0.138878 | ||||||||
\(547\) | 22.5800 | 0.965450 | 0.482725 | − | 0.875772i | \(-0.339647\pi\) | ||||
0.482725 | + | 0.875772i | \(0.339647\pi\) | |||||||
\(548\) | 3.26677 | 0.139550 | ||||||||
\(549\) | 12.2715 | 0.523733 | ||||||||
\(550\) | −12.0313 | −0.513015 | ||||||||
\(551\) | −1.82481 | −0.0777396 | ||||||||
\(552\) | −3.88709 | −0.165445 | ||||||||
\(553\) | −30.0934 | −1.27970 | ||||||||
\(554\) | 1.13804 | 0.0483505 | ||||||||
\(555\) | 6.86219 | 0.291284 | ||||||||
\(556\) | 10.4650 | 0.443814 | ||||||||
\(557\) | 22.8533 | 0.968327 | 0.484163 | − | 0.874978i | \(-0.339124\pi\) | ||||
0.484163 | + | 0.874978i | \(0.339124\pi\) | |||||||
\(558\) | −7.79350 | −0.329925 | ||||||||
\(559\) | 0.261647 | 0.0110665 | ||||||||
\(560\) | −4.36783 | −0.184574 | ||||||||
\(561\) | −27.3245 | −1.15364 | ||||||||
\(562\) | 1.48374 | 0.0625878 | ||||||||
\(563\) | 13.3416 | 0.562283 | 0.281142 | − | 0.959666i | \(-0.409287\pi\) | ||||
0.281142 | + | 0.959666i | \(0.409287\pi\) | |||||||
\(564\) | −0.430909 | −0.0181445 | ||||||||
\(565\) | −2.46165 | −0.103562 | ||||||||
\(566\) | −24.5874 | −1.03348 | ||||||||
\(567\) | −3.24510 | −0.136281 | ||||||||
\(568\) | −1.48957 | −0.0625010 | ||||||||
\(569\) | 19.8928 | 0.833950 | 0.416975 | − | 0.908918i | \(-0.363090\pi\) | ||||
0.416975 | + | 0.908918i | \(0.363090\pi\) | |||||||
\(570\) | 0.889714 | 0.0372660 | ||||||||
\(571\) | −31.0386 | −1.29893 | −0.649463 | − | 0.760393i | \(-0.725006\pi\) | ||||
−0.649463 | + | 0.760393i | \(0.725006\pi\) | |||||||
\(572\) | −3.77351 | −0.157778 | ||||||||
\(573\) | 14.5232 | 0.606714 | ||||||||
\(574\) | −36.3040 | −1.51530 | ||||||||
\(575\) | 12.3934 | 0.516841 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 6.32970 | 0.263509 | 0.131754 | − | 0.991282i | \(-0.457939\pi\) | ||||
0.131754 | + | 0.991282i | \(0.457939\pi\) | |||||||
\(578\) | −35.4339 | −1.47386 | ||||||||
\(579\) | −18.8956 | −0.785273 | ||||||||
\(580\) | −3.71571 | −0.154286 | ||||||||
\(581\) | −10.1325 | −0.420366 | ||||||||
\(582\) | −4.13251 | −0.171298 | ||||||||
\(583\) | 26.3442 | 1.09107 | ||||||||
\(584\) | 7.24146 | 0.299654 | ||||||||
\(585\) | 1.34598 | 0.0556492 | ||||||||
\(586\) | 23.1487 | 0.956266 | ||||||||
\(587\) | 6.56457 | 0.270949 | 0.135474 | − | 0.990781i | \(-0.456744\pi\) | ||||
0.135474 | + | 0.990781i | \(0.456744\pi\) | |||||||
\(588\) | −3.53068 | −0.145603 | ||||||||
\(589\) | 5.15165 | 0.212270 | ||||||||
\(590\) | −7.80559 | −0.321351 | ||||||||
\(591\) | 4.69606 | 0.193170 | ||||||||
\(592\) | −5.09830 | −0.209539 | ||||||||
\(593\) | −39.5198 | −1.62288 | −0.811442 | − | 0.584434i | \(-0.801317\pi\) | ||||
−0.811442 | + | 0.584434i | \(0.801317\pi\) | |||||||
\(594\) | −3.77351 | −0.154829 | ||||||||
\(595\) | 31.6280 | 1.29662 | ||||||||
\(596\) | 18.9960 | 0.778104 | ||||||||
\(597\) | 25.7438 | 1.05362 | ||||||||
\(598\) | 3.88709 | 0.158955 | ||||||||
\(599\) | 22.9693 | 0.938501 | 0.469250 | − | 0.883065i | \(-0.344524\pi\) | ||||
0.469250 | + | 0.883065i | \(0.344524\pi\) | |||||||
\(600\) | −3.18835 | −0.130164 | ||||||||
\(601\) | 10.4639 | 0.426833 | 0.213416 | − | 0.976961i | \(-0.431541\pi\) | ||||
0.213416 | + | 0.976961i | \(0.431541\pi\) | |||||||
\(602\) | 0.849070 | 0.0346055 | ||||||||
\(603\) | −15.9624 | −0.650040 | ||||||||
\(604\) | −2.86092 | −0.116409 | ||||||||
\(605\) | 4.36010 | 0.177263 | ||||||||
\(606\) | −10.6527 | −0.432737 | ||||||||
\(607\) | 3.58571 | 0.145539 | 0.0727697 | − | 0.997349i | \(-0.476816\pi\) | ||||
0.0727697 | + | 0.997349i | \(0.476816\pi\) | |||||||
\(608\) | −0.661018 | −0.0268078 | ||||||||
\(609\) | −8.95845 | −0.363015 | ||||||||
\(610\) | −16.5171 | −0.668757 | ||||||||
\(611\) | 0.430909 | 0.0174327 | ||||||||
\(612\) | −7.24113 | −0.292705 | ||||||||
\(613\) | −24.5872 | −0.993068 | −0.496534 | − | 0.868017i | \(-0.665394\pi\) | ||||
−0.496534 | + | 0.868017i | \(0.665394\pi\) | |||||||
\(614\) | −19.4854 | −0.786367 | ||||||||
\(615\) | 15.0578 | 0.607191 | ||||||||
\(616\) | −12.2454 | −0.493382 | ||||||||
\(617\) | −43.5235 | −1.75219 | −0.876094 | − | 0.482140i | \(-0.839860\pi\) | ||||
−0.876094 | + | 0.482140i | \(0.839860\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 18.6399 | 0.749202 | 0.374601 | − | 0.927186i | \(-0.377780\pi\) | ||||
0.374601 | + | 0.927186i | \(0.377780\pi\) | |||||||
\(620\) | 10.4899 | 0.421283 | ||||||||
\(621\) | 3.88709 | 0.155983 | ||||||||
\(622\) | 24.2475 | 0.972235 | ||||||||
\(623\) | −37.3582 | −1.49672 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 1.10733 | 0.0442934 | ||||||||
\(626\) | −17.0379 | −0.680973 | ||||||||
\(627\) | 2.49436 | 0.0996151 | ||||||||
\(628\) | −8.29324 | −0.330936 | ||||||||
\(629\) | 36.9175 | 1.47200 | ||||||||
\(630\) | 4.36783 | 0.174018 | ||||||||
\(631\) | 33.4063 | 1.32989 | 0.664943 | − | 0.746895i | \(-0.268456\pi\) | ||||
0.664943 | + | 0.746895i | \(0.268456\pi\) | |||||||
\(632\) | −9.27347 | −0.368879 | ||||||||
\(633\) | −16.6079 | −0.660106 | ||||||||
\(634\) | 17.1424 | 0.680813 | ||||||||
\(635\) | 6.77607 | 0.268900 | ||||||||
\(636\) | 6.98136 | 0.276829 | ||||||||
\(637\) | 3.53068 | 0.139891 | ||||||||
\(638\) | −10.4172 | −0.412420 | ||||||||
\(639\) | 1.48957 | 0.0589265 | ||||||||
\(640\) | −1.34598 | −0.0532043 | ||||||||
\(641\) | −35.5136 | −1.40270 | −0.701352 | − | 0.712815i | \(-0.747420\pi\) | ||||
−0.701352 | + | 0.712815i | \(0.747420\pi\) | |||||||
\(642\) | −13.5536 | −0.534917 | ||||||||
\(643\) | 37.5268 | 1.47991 | 0.739956 | − | 0.672655i | \(-0.234846\pi\) | ||||
0.739956 | + | 0.672655i | \(0.234846\pi\) | |||||||
\(644\) | 12.6140 | 0.497061 | ||||||||
\(645\) | −0.352170 | −0.0138667 | ||||||||
\(646\) | 4.78652 | 0.188323 | ||||||||
\(647\) | −1.85892 | −0.0730817 | −0.0365409 | − | 0.999332i | \(-0.511634\pi\) | ||||
−0.0365409 | + | 0.999332i | \(0.511634\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −21.8833 | −0.858996 | ||||||||
\(650\) | 3.18835 | 0.125057 | ||||||||
\(651\) | 25.2907 | 0.991221 | ||||||||
\(652\) | 14.7826 | 0.578933 | ||||||||
\(653\) | −17.1112 | −0.669612 | −0.334806 | − | 0.942287i | \(-0.608671\pi\) | ||||
−0.334806 | + | 0.942287i | \(0.608671\pi\) | |||||||
\(654\) | −13.6544 | −0.533930 | ||||||||
\(655\) | 24.1190 | 0.942406 | ||||||||
\(656\) | −11.1873 | −0.436791 | ||||||||
\(657\) | −7.24146 | −0.282516 | ||||||||
\(658\) | 1.39834 | 0.0545131 | ||||||||
\(659\) | 48.2990 | 1.88146 | 0.940731 | − | 0.339155i | \(-0.110141\pi\) | ||||
0.940731 | + | 0.339155i | \(0.110141\pi\) | |||||||
\(660\) | 5.07905 | 0.197702 | ||||||||
\(661\) | 12.4202 | 0.483091 | 0.241545 | − | 0.970389i | \(-0.422346\pi\) | ||||
0.241545 | + | 0.970389i | \(0.422346\pi\) | |||||||
\(662\) | 8.77403 | 0.341012 | ||||||||
\(663\) | 7.24113 | 0.281222 | ||||||||
\(664\) | −3.12239 | −0.121172 | ||||||||
\(665\) | −2.88721 | −0.111961 | ||||||||
\(666\) | 5.09830 | 0.197555 | ||||||||
\(667\) | 10.7307 | 0.415495 | ||||||||
\(668\) | 1.14854 | 0.0444382 | ||||||||
\(669\) | −4.74985 | −0.183640 | ||||||||
\(670\) | 21.4850 | 0.830039 | ||||||||
\(671\) | −46.3064 | −1.78764 | ||||||||
\(672\) | −3.24510 | −0.125182 | ||||||||
\(673\) | −11.3026 | −0.435682 | −0.217841 | − | 0.975984i | \(-0.569901\pi\) | ||||
−0.217841 | + | 0.975984i | \(0.569901\pi\) | |||||||
\(674\) | 4.00567 | 0.154293 | ||||||||
\(675\) | 3.18835 | 0.122720 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 8.16619 | 0.313852 | 0.156926 | − | 0.987610i | \(-0.449842\pi\) | ||||
0.156926 | + | 0.987610i | \(0.449842\pi\) | |||||||
\(678\) | −1.82889 | −0.0702382 | ||||||||
\(679\) | 13.4104 | 0.514645 | ||||||||
\(680\) | 9.74638 | 0.373757 | ||||||||
\(681\) | −14.8843 | −0.570366 | ||||||||
\(682\) | 29.4088 | 1.12612 | ||||||||
\(683\) | −34.0204 | −1.30176 | −0.650878 | − | 0.759183i | \(-0.725599\pi\) | ||||
−0.650878 | + | 0.759183i | \(0.725599\pi\) | |||||||
\(684\) | 0.661018 | 0.0252747 | ||||||||
\(685\) | 4.39700 | 0.168001 | ||||||||
\(686\) | −11.2583 | −0.429843 | ||||||||
\(687\) | 23.6580 | 0.902610 | ||||||||
\(688\) | 0.261647 | 0.00997519 | ||||||||
\(689\) | −6.98136 | −0.265968 | ||||||||
\(690\) | −5.23192 | −0.199176 | ||||||||
\(691\) | 19.5621 | 0.744177 | 0.372088 | − | 0.928197i | \(-0.378642\pi\) | ||||
0.372088 | + | 0.928197i | \(0.378642\pi\) | |||||||
\(692\) | 17.4991 | 0.665218 | ||||||||
\(693\) | 12.2454 | 0.465165 | ||||||||
\(694\) | 15.7245 | 0.596895 | ||||||||
\(695\) | 14.0856 | 0.534298 | ||||||||
\(696\) | −2.76061 | −0.104641 | ||||||||
\(697\) | 81.0088 | 3.06843 | ||||||||
\(698\) | 9.84845 | 0.372769 | ||||||||
\(699\) | 24.5541 | 0.928722 | ||||||||
\(700\) | 10.3465 | 0.391062 | ||||||||
\(701\) | 35.7782 | 1.35132 | 0.675661 | − | 0.737212i | \(-0.263858\pi\) | ||||
0.675661 | + | 0.737212i | \(0.263858\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −3.37007 | −0.127105 | ||||||||
\(704\) | −3.77351 | −0.142219 | ||||||||
\(705\) | −0.579993 | −0.0218438 | ||||||||
\(706\) | 3.60939 | 0.135841 | ||||||||
\(707\) | 34.5692 | 1.30011 | ||||||||
\(708\) | −5.79920 | −0.217947 | ||||||||
\(709\) | 7.42880 | 0.278994 | 0.139497 | − | 0.990222i | \(-0.455451\pi\) | ||||
0.139497 | + | 0.990222i | \(0.455451\pi\) | |||||||
\(710\) | −2.00492 | −0.0752435 | ||||||||
\(711\) | 9.27347 | 0.347782 | ||||||||
\(712\) | −11.5122 | −0.431437 | ||||||||
\(713\) | −30.2940 | −1.13452 | ||||||||
\(714\) | 23.4982 | 0.879398 | ||||||||
\(715\) | −5.07905 | −0.189946 | ||||||||
\(716\) | −3.80501 | −0.142200 | ||||||||
\(717\) | 0.194543 | 0.00726532 | ||||||||
\(718\) | −6.53877 | −0.244025 | ||||||||
\(719\) | 10.3305 | 0.385264 | 0.192632 | − | 0.981271i | \(-0.438298\pi\) | ||||
0.192632 | + | 0.981271i | \(0.438298\pi\) | |||||||
\(720\) | 1.34598 | 0.0501615 | ||||||||
\(721\) | 3.24510 | 0.120854 | ||||||||
\(722\) | 18.5631 | 0.690845 | ||||||||
\(723\) | −5.77889 | −0.214919 | ||||||||
\(724\) | 13.2055 | 0.490778 | ||||||||
\(725\) | 8.80178 | 0.326890 | ||||||||
\(726\) | 3.23936 | 0.120224 | ||||||||
\(727\) | −13.0139 | −0.482657 | −0.241328 | − | 0.970443i | \(-0.577583\pi\) | ||||
−0.241328 | + | 0.970443i | \(0.577583\pi\) | |||||||
\(728\) | 3.24510 | 0.120271 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 9.74682 | 0.360746 | ||||||||
\(731\) | −1.89462 | −0.0700750 | ||||||||
\(732\) | −12.2715 | −0.453566 | ||||||||
\(733\) | −3.85705 | −0.142463 | −0.0712317 | − | 0.997460i | \(-0.522693\pi\) | ||||
−0.0712317 | + | 0.997460i | \(0.522693\pi\) | |||||||
\(734\) | −30.8684 | −1.13937 | ||||||||
\(735\) | −4.75221 | −0.175288 | ||||||||
\(736\) | 3.88709 | 0.143280 | ||||||||
\(737\) | 60.2344 | 2.21876 | ||||||||
\(738\) | 11.1873 | 0.411811 | ||||||||
\(739\) | 19.4194 | 0.714356 | 0.357178 | − | 0.934036i | \(-0.383739\pi\) | ||||
0.357178 | + | 0.934036i | \(0.383739\pi\) | |||||||
\(740\) | −6.86219 | −0.252259 | ||||||||
\(741\) | −0.661018 | −0.0242831 | ||||||||
\(742\) | −22.6552 | −0.831699 | ||||||||
\(743\) | −44.8989 | −1.64718 | −0.823591 | − | 0.567184i | \(-0.808033\pi\) | ||||
−0.823591 | + | 0.567184i | \(0.808033\pi\) | |||||||
\(744\) | 7.79350 | 0.285724 | ||||||||
\(745\) | 25.5681 | 0.936742 | ||||||||
\(746\) | −11.4169 | −0.418003 | ||||||||
\(747\) | 3.12239 | 0.114242 | ||||||||
\(748\) | 27.3245 | 0.999081 | ||||||||
\(749\) | 43.9827 | 1.60709 | ||||||||
\(750\) | −11.0213 | −0.402442 | ||||||||
\(751\) | −24.8939 | −0.908390 | −0.454195 | − | 0.890902i | \(-0.650073\pi\) | ||||
−0.454195 | + | 0.890902i | \(0.650073\pi\) | |||||||
\(752\) | 0.430909 | 0.0157136 | ||||||||
\(753\) | 25.3501 | 0.923809 | ||||||||
\(754\) | 2.76061 | 0.100535 | ||||||||
\(755\) | −3.85072 | −0.140142 | ||||||||
\(756\) | 3.24510 | 0.118023 | ||||||||
\(757\) | −31.0682 | −1.12919 | −0.564596 | − | 0.825367i | \(-0.690968\pi\) | ||||
−0.564596 | + | 0.825367i | \(0.690968\pi\) | |||||||
\(758\) | 6.20355 | 0.225323 | ||||||||
\(759\) | −14.6680 | −0.532413 | ||||||||
\(760\) | −0.889714 | −0.0322733 | ||||||||
\(761\) | 52.5673 | 1.90556 | 0.952781 | − | 0.303659i | \(-0.0982084\pi\) | ||||
0.952781 | + | 0.303659i | \(0.0982084\pi\) | |||||||
\(762\) | 5.03432 | 0.182374 | ||||||||
\(763\) | 44.3100 | 1.60413 | ||||||||
\(764\) | −14.5232 | −0.525430 | ||||||||
\(765\) | −9.74638 | −0.352381 | ||||||||
\(766\) | −2.81254 | −0.101621 | ||||||||
\(767\) | 5.79920 | 0.209397 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 47.6484 | 1.71824 | 0.859122 | − | 0.511771i | \(-0.171010\pi\) | ||||
0.859122 | + | 0.511771i | \(0.171010\pi\) | |||||||
\(770\) | −16.4820 | −0.593971 | ||||||||
\(771\) | −21.3251 | −0.768004 | ||||||||
\(772\) | 18.8956 | 0.680066 | ||||||||
\(773\) | 52.2759 | 1.88023 | 0.940117 | − | 0.340853i | \(-0.110716\pi\) | ||||
0.940117 | + | 0.340853i | \(0.110716\pi\) | |||||||
\(774\) | −0.261647 | −0.00940470 | ||||||||
\(775\) | −24.8484 | −0.892582 | ||||||||
\(776\) | 4.13251 | 0.148349 | ||||||||
\(777\) | −16.5445 | −0.593531 | ||||||||
\(778\) | 15.6657 | 0.561644 | ||||||||
\(779\) | −7.39502 | −0.264954 | ||||||||
\(780\) | −1.34598 | −0.0481936 | ||||||||
\(781\) | −5.62091 | −0.201132 | ||||||||
\(782\) | −28.1469 | −1.00653 | ||||||||
\(783\) | 2.76061 | 0.0986561 | ||||||||
\(784\) | 3.53068 | 0.126096 | ||||||||
\(785\) | −11.1625 | −0.398406 | ||||||||
\(786\) | 17.9193 | 0.639161 | ||||||||
\(787\) | −25.6614 | −0.914730 | −0.457365 | − | 0.889279i | \(-0.651207\pi\) | ||||
−0.457365 | + | 0.889279i | \(0.651207\pi\) | |||||||
\(788\) | −4.69606 | −0.167290 | ||||||||
\(789\) | 24.8870 | 0.886002 | ||||||||
\(790\) | −12.4819 | −0.444085 | ||||||||
\(791\) | 5.93494 | 0.211022 | ||||||||
\(792\) | 3.77351 | 0.134086 | ||||||||
\(793\) | 12.2715 | 0.435772 | ||||||||
\(794\) | 3.89885 | 0.138365 | ||||||||
\(795\) | 9.39673 | 0.333268 | ||||||||
\(796\) | −25.7438 | −0.912465 | ||||||||
\(797\) | −34.2164 | −1.21201 | −0.606003 | − | 0.795462i | \(-0.707228\pi\) | ||||
−0.606003 | + | 0.795462i | \(0.707228\pi\) | |||||||
\(798\) | −2.14507 | −0.0759347 | ||||||||
\(799\) | −3.12027 | −0.110387 | ||||||||
\(800\) | 3.18835 | 0.112725 | ||||||||
\(801\) | 11.5122 | 0.406763 | ||||||||
\(802\) | 28.2737 | 0.998379 | ||||||||
\(803\) | 27.3257 | 0.964303 | ||||||||
\(804\) | 15.9624 | 0.562952 | ||||||||
\(805\) | 16.9781 | 0.598400 | ||||||||
\(806\) | −7.79350 | −0.274514 | ||||||||
\(807\) | −27.1724 | −0.956514 | ||||||||
\(808\) | 10.6527 | 0.374761 | ||||||||
\(809\) | 14.0727 | 0.494772 | 0.247386 | − | 0.968917i | \(-0.420429\pi\) | ||||
0.247386 | + | 0.968917i | \(0.420429\pi\) | |||||||
\(810\) | −1.34598 | −0.0472927 | ||||||||
\(811\) | −28.9741 | −1.01742 | −0.508709 | − | 0.860938i | \(-0.669877\pi\) | ||||
−0.508709 | + | 0.860938i | \(0.669877\pi\) | |||||||
\(812\) | 8.95845 | 0.314380 | ||||||||
\(813\) | 9.83001 | 0.344753 | ||||||||
\(814\) | −19.2385 | −0.674309 | ||||||||
\(815\) | 19.8971 | 0.696964 | ||||||||
\(816\) | 7.24113 | 0.253490 | ||||||||
\(817\) | 0.172953 | 0.00605087 | ||||||||
\(818\) | 8.55426 | 0.299093 | ||||||||
\(819\) | −3.24510 | −0.113393 | ||||||||
\(820\) | −15.0578 | −0.525843 | ||||||||
\(821\) | −0.124312 | −0.00433852 | −0.00216926 | − | 0.999998i | \(-0.500690\pi\) | ||||
−0.00216926 | + | 0.999998i | \(0.500690\pi\) | |||||||
\(822\) | 3.26677 | 0.113942 | ||||||||
\(823\) | 17.7601 | 0.619079 | 0.309540 | − | 0.950887i | \(-0.399825\pi\) | ||||
0.309540 | + | 0.950887i | \(0.399825\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | −12.0313 | −0.418875 | ||||||||
\(826\) | 18.8190 | 0.654797 | ||||||||
\(827\) | 12.4195 | 0.431869 | 0.215935 | − | 0.976408i | \(-0.430720\pi\) | ||||
0.215935 | + | 0.976408i | \(0.430720\pi\) | |||||||
\(828\) | −3.88709 | −0.135086 | ||||||||
\(829\) | 39.5635 | 1.37410 | 0.687049 | − | 0.726611i | \(-0.258906\pi\) | ||||
0.687049 | + | 0.726611i | \(0.258906\pi\) | |||||||
\(830\) | −4.20266 | −0.145876 | ||||||||
\(831\) | 1.13804 | 0.0394780 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −25.5661 | −0.885814 | ||||||||
\(834\) | 10.4650 | 0.362373 | ||||||||
\(835\) | 1.54590 | 0.0534982 | ||||||||
\(836\) | −2.49436 | −0.0862692 | ||||||||
\(837\) | −7.79350 | −0.269383 | ||||||||
\(838\) | −7.01647 | −0.242380 | ||||||||
\(839\) | −17.5349 | −0.605371 | −0.302685 | − | 0.953091i | \(-0.597883\pi\) | ||||
−0.302685 | + | 0.953091i | \(0.597883\pi\) | |||||||
\(840\) | −4.36783 | −0.150704 | ||||||||
\(841\) | −21.3790 | −0.737209 | ||||||||
\(842\) | 18.0352 | 0.621534 | ||||||||
\(843\) | 1.48374 | 0.0511027 | ||||||||
\(844\) | 16.6079 | 0.571668 | ||||||||
\(845\) | 1.34598 | 0.0463030 | ||||||||
\(846\) | −0.430909 | −0.0148150 | ||||||||
\(847\) | −10.5121 | −0.361199 | ||||||||
\(848\) | −6.98136 | −0.239741 | ||||||||
\(849\) | −24.5874 | −0.843837 | ||||||||
\(850\) | −23.0873 | −0.791886 | ||||||||
\(851\) | 19.8175 | 0.679337 | ||||||||
\(852\) | −1.48957 | −0.0510318 | ||||||||
\(853\) | 44.9350 | 1.53854 | 0.769272 | − | 0.638922i | \(-0.220619\pi\) | ||||
0.769272 | + | 0.638922i | \(0.220619\pi\) | |||||||
\(854\) | 39.8221 | 1.36268 | ||||||||
\(855\) | 0.889714 | 0.0304276 | ||||||||
\(856\) | 13.5536 | 0.463252 | ||||||||
\(857\) | −18.4177 | −0.629138 | −0.314569 | − | 0.949235i | \(-0.601860\pi\) | ||||
−0.314569 | + | 0.949235i | \(0.601860\pi\) | |||||||
\(858\) | −3.77351 | −0.128825 | ||||||||
\(859\) | 33.2889 | 1.13580 | 0.567902 | − | 0.823096i | \(-0.307755\pi\) | ||||
0.567902 | + | 0.823096i | \(0.307755\pi\) | |||||||
\(860\) | 0.352170 | 0.0120089 | ||||||||
\(861\) | −36.3040 | −1.23724 | ||||||||
\(862\) | −28.1776 | −0.959733 | ||||||||
\(863\) | −39.3854 | −1.34070 | −0.670348 | − | 0.742047i | \(-0.733855\pi\) | ||||
−0.670348 | + | 0.742047i | \(0.733855\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 23.5534 | 0.800840 | ||||||||
\(866\) | −18.6955 | −0.635301 | ||||||||
\(867\) | −35.4339 | −1.20340 | ||||||||
\(868\) | −25.2907 | −0.858422 | ||||||||
\(869\) | −34.9935 | −1.18707 | ||||||||
\(870\) | −3.71571 | −0.125974 | ||||||||
\(871\) | −15.9624 | −0.540866 | ||||||||
\(872\) | 13.6544 | 0.462397 | ||||||||
\(873\) | −4.13251 | −0.139864 | ||||||||
\(874\) | 2.56944 | 0.0869125 | ||||||||
\(875\) | 35.7653 | 1.20909 | ||||||||
\(876\) | 7.24146 | 0.244666 | ||||||||
\(877\) | 53.7415 | 1.81472 | 0.907361 | − | 0.420352i | \(-0.138094\pi\) | ||||
0.907361 | + | 0.420352i | \(0.138094\pi\) | |||||||
\(878\) | 6.18598 | 0.208767 | ||||||||
\(879\) | 23.1487 | 0.780788 | ||||||||
\(880\) | −5.07905 | −0.171215 | ||||||||
\(881\) | 22.6595 | 0.763418 | 0.381709 | − | 0.924282i | \(-0.375336\pi\) | ||||
0.381709 | + | 0.924282i | \(0.375336\pi\) | |||||||
\(882\) | −3.53068 | −0.118884 | ||||||||
\(883\) | 31.9862 | 1.07642 | 0.538210 | − | 0.842811i | \(-0.319101\pi\) | ||||
0.538210 | + | 0.842811i | \(0.319101\pi\) | |||||||
\(884\) | −7.24113 | −0.243546 | ||||||||
\(885\) | −7.80559 | −0.262382 | ||||||||
\(886\) | −32.4240 | −1.08930 | ||||||||
\(887\) | −51.3286 | −1.72345 | −0.861723 | − | 0.507378i | \(-0.830615\pi\) | ||||
−0.861723 | + | 0.507378i | \(0.830615\pi\) | |||||||
\(888\) | −5.09830 | −0.171088 | ||||||||
\(889\) | −16.3369 | −0.547921 | ||||||||
\(890\) | −15.4951 | −0.519397 | ||||||||
\(891\) | −3.77351 | −0.126417 | ||||||||
\(892\) | 4.74985 | 0.159037 | ||||||||
\(893\) | 0.284839 | 0.00953176 | ||||||||
\(894\) | 18.9960 | 0.635320 | ||||||||
\(895\) | −5.12145 | −0.171191 | ||||||||
\(896\) | 3.24510 | 0.108411 | ||||||||
\(897\) | 3.88709 | 0.129786 | ||||||||
\(898\) | 25.2808 | 0.843632 | ||||||||
\(899\) | −21.5148 | −0.717559 | ||||||||
\(900\) | −3.18835 | −0.106278 | ||||||||
\(901\) | 50.5529 | 1.68416 | ||||||||
\(902\) | −42.2154 | −1.40562 | ||||||||
\(903\) | 0.849070 | 0.0282553 | ||||||||
\(904\) | 1.82889 | 0.0608281 | ||||||||
\(905\) | 17.7743 | 0.590836 | ||||||||
\(906\) | −2.86092 | −0.0950476 | ||||||||
\(907\) | 21.3592 | 0.709220 | 0.354610 | − | 0.935014i | \(-0.384614\pi\) | ||||
0.354610 | + | 0.935014i | \(0.384614\pi\) | |||||||
\(908\) | 14.8843 | 0.493952 | ||||||||
\(909\) | −10.6527 | −0.353328 | ||||||||
\(910\) | 4.36783 | 0.144792 | ||||||||
\(911\) | 24.3445 | 0.806570 | 0.403285 | − | 0.915074i | \(-0.367868\pi\) | ||||
0.403285 | + | 0.915074i | \(0.367868\pi\) | |||||||
\(912\) | −0.661018 | −0.0218885 | ||||||||
\(913\) | −11.7824 | −0.389939 | ||||||||
\(914\) | −16.3853 | −0.541976 | ||||||||
\(915\) | −16.5171 | −0.546038 | ||||||||
\(916\) | −23.6580 | −0.781683 | ||||||||
\(917\) | −58.1500 | −1.92028 | ||||||||
\(918\) | −7.24113 | −0.238993 | ||||||||
\(919\) | 18.3753 | 0.606146 | 0.303073 | − | 0.952967i | \(-0.401987\pi\) | ||||
0.303073 | + | 0.952967i | \(0.401987\pi\) | |||||||
\(920\) | 5.23192 | 0.172491 | ||||||||
\(921\) | −19.4854 | −0.642066 | ||||||||
\(922\) | −17.8016 | −0.586265 | ||||||||
\(923\) | 1.48957 | 0.0490298 | ||||||||
\(924\) | −12.2454 | −0.402845 | ||||||||
\(925\) | 16.2552 | 0.534467 | ||||||||
\(926\) | 13.5211 | 0.444330 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 2.76061 | 0.0906214 | ||||||||
\(929\) | −27.2635 | −0.894487 | −0.447243 | − | 0.894412i | \(-0.647594\pi\) | ||||
−0.447243 | + | 0.894412i | \(0.647594\pi\) | |||||||
\(930\) | 10.4899 | 0.343976 | ||||||||
\(931\) | 2.33385 | 0.0764887 | ||||||||
\(932\) | −24.5541 | −0.804297 | ||||||||
\(933\) | 24.2475 | 0.793826 | ||||||||
\(934\) | −30.5160 | −0.998515 | ||||||||
\(935\) | 36.7780 | 1.20277 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −18.9150 | −0.617925 | −0.308962 | − | 0.951074i | \(-0.599982\pi\) | ||||
−0.308962 | + | 0.951074i | \(0.599982\pi\) | |||||||
\(938\) | −51.7997 | −1.69132 | ||||||||
\(939\) | −17.0379 | −0.556012 | ||||||||
\(940\) | 0.579993 | 0.0189173 | ||||||||
\(941\) | 12.5725 | 0.409853 | 0.204927 | − | 0.978777i | \(-0.434304\pi\) | ||||
0.204927 | + | 0.978777i | \(0.434304\pi\) | |||||||
\(942\) | −8.29324 | −0.270208 | ||||||||
\(943\) | 43.4861 | 1.41610 | ||||||||
\(944\) | 5.79920 | 0.188748 | ||||||||
\(945\) | 4.36783 | 0.142085 | ||||||||
\(946\) | 0.987326 | 0.0321007 | ||||||||
\(947\) | −18.5027 | −0.601258 | −0.300629 | − | 0.953741i | \(-0.597197\pi\) | ||||
−0.300629 | + | 0.953741i | \(0.597197\pi\) | |||||||
\(948\) | −9.27347 | −0.301188 | ||||||||
\(949\) | −7.24146 | −0.235068 | ||||||||
\(950\) | 2.10756 | 0.0683782 | ||||||||
\(951\) | 17.1424 | 0.555882 | ||||||||
\(952\) | −23.4982 | −0.761581 | ||||||||
\(953\) | 41.8571 | 1.35589 | 0.677943 | − | 0.735115i | \(-0.262872\pi\) | ||||
0.677943 | + | 0.735115i | \(0.262872\pi\) | |||||||
\(954\) | 6.98136 | 0.226030 | ||||||||
\(955\) | −19.5478 | −0.632553 | ||||||||
\(956\) | −0.194543 | −0.00629195 | ||||||||
\(957\) | −10.4172 | −0.336739 | ||||||||
\(958\) | −8.25272 | −0.266633 | ||||||||
\(959\) | −10.6010 | −0.342325 | ||||||||
\(960\) | −1.34598 | −0.0434412 | ||||||||
\(961\) | 29.7387 | 0.959313 | ||||||||
\(962\) | 5.09830 | 0.164376 | ||||||||
\(963\) | −13.5536 | −0.436758 | ||||||||
\(964\) | 5.77889 | 0.186126 | ||||||||
\(965\) | 25.4330 | 0.818716 | ||||||||
\(966\) | 12.6140 | 0.405849 | ||||||||
\(967\) | 12.5222 | 0.402687 | 0.201343 | − | 0.979521i | \(-0.435469\pi\) | ||||
0.201343 | + | 0.979521i | \(0.435469\pi\) | |||||||
\(968\) | −3.23936 | −0.104117 | ||||||||
\(969\) | 4.78652 | 0.153765 | ||||||||
\(970\) | 5.56226 | 0.178593 | ||||||||
\(971\) | 36.4400 | 1.16942 | 0.584708 | − | 0.811244i | \(-0.301209\pi\) | ||||
0.584708 | + | 0.811244i | \(0.301209\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −33.9600 | −1.08871 | ||||||||
\(974\) | 3.27770 | 0.105024 | ||||||||
\(975\) | 3.18835 | 0.102109 | ||||||||
\(976\) | 12.2715 | 0.392800 | ||||||||
\(977\) | −53.3142 | −1.70567 | −0.852836 | − | 0.522179i | \(-0.825119\pi\) | ||||
−0.852836 | + | 0.522179i | \(0.825119\pi\) | |||||||
\(978\) | 14.7826 | 0.472697 | ||||||||
\(979\) | −43.4413 | −1.38839 | ||||||||
\(980\) | 4.75221 | 0.151804 | ||||||||
\(981\) | −13.6544 | −0.435952 | ||||||||
\(982\) | −7.49528 | −0.239184 | ||||||||
\(983\) | −0.0934276 | −0.00297988 | −0.00148994 | − | 0.999999i | \(-0.500474\pi\) | ||||
−0.00148994 | + | 0.999999i | \(0.500474\pi\) | |||||||
\(984\) | −11.1873 | −0.356638 | ||||||||
\(985\) | −6.32078 | −0.201397 | ||||||||
\(986\) | −19.9899 | −0.636609 | ||||||||
\(987\) | 1.39834 | 0.0445097 | ||||||||
\(988\) | 0.661018 | 0.0210298 | ||||||||
\(989\) | −1.01704 | −0.0323401 | ||||||||
\(990\) | 5.07905 | 0.161423 | ||||||||
\(991\) | 13.1691 | 0.418331 | 0.209165 | − | 0.977880i | \(-0.432925\pi\) | ||||
0.209165 | + | 0.977880i | \(0.432925\pi\) | |||||||
\(992\) | −7.79350 | −0.247444 | ||||||||
\(993\) | 8.77403 | 0.278435 | ||||||||
\(994\) | 4.83381 | 0.153319 | ||||||||
\(995\) | −34.6505 | −1.09850 | ||||||||
\(996\) | −3.12239 | −0.0989367 | ||||||||
\(997\) | 45.6533 | 1.44586 | 0.722928 | − | 0.690924i | \(-0.242796\pi\) | ||||
0.722928 | + | 0.690924i | \(0.242796\pi\) | |||||||
\(998\) | −14.3424 | −0.454000 | ||||||||
\(999\) | 5.09830 | 0.161303 |
(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 | 8034.2.a.z.1.10 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.z.1.10 | ✓ | 14 | 1.1 | even | 1 | trivial |