Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2010,2,Mod(1,2010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2010, 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("2010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2010 = 2 \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2010.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: | \(16.0499308063\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.70292.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + 10x + 2 \) |
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 | 1.4 | ||
Root | \(-2.88727\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2010.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 4.33630 | 1.63897 | 0.819484 | − | 0.573101i | \(-0.194260\pi\) | ||||
0.819484 | + | 0.573101i | \(0.194260\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −4.74553 | −1.43083 | −0.715416 | − | 0.698699i | \(-0.753763\pi\) | ||||
−0.715416 | + | 0.698699i | \(0.753763\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0.409227 | 0.113499 | 0.0567495 | − | 0.998388i | \(-0.481926\pi\) | ||||
0.0567495 | + | 0.998388i | \(0.481926\pi\) | |||||||
\(14\) | −4.33630 | −1.15893 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.77453 | 1.40053 | 0.700265 | − | 0.713883i | \(-0.253065\pi\) | ||||
0.700265 | + | 0.713883i | \(0.253065\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −5.77453 | −1.32477 | −0.662384 | − | 0.749164i | \(-0.730455\pi\) | ||||
−0.662384 | + | 0.749164i | \(0.730455\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −4.33630 | −0.946259 | ||||||||
\(22\) | 4.74553 | 1.01175 | ||||||||
\(23\) | −9.36530 | −1.95280 | −0.976401 | − | 0.215968i | \(-0.930709\pi\) | ||||
−0.976401 | + | 0.215968i | \(0.930709\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.409227 | −0.0802560 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.33630 | 0.819484 | ||||||||
\(29\) | −1.30730 | −0.242760 | −0.121380 | − | 0.992606i | \(-0.538732\pi\) | ||||
−0.121380 | + | 0.992606i | \(0.538732\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 2.40923 | 0.432710 | 0.216355 | − | 0.976315i | \(-0.430583\pi\) | ||||
0.216355 | + | 0.976315i | \(0.430583\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.74553 | 0.826091 | ||||||||
\(34\) | −5.77453 | −0.990324 | ||||||||
\(35\) | −4.33630 | −0.732969 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.02900 | 0.497965 | 0.248982 | − | 0.968508i | \(-0.419904\pi\) | ||||
0.248982 | + | 0.968508i | \(0.419904\pi\) | |||||||
\(38\) | 5.77453 | 0.936753 | ||||||||
\(39\) | −0.409227 | −0.0655287 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 1.71653 | 0.268077 | 0.134038 | − | 0.990976i | \(-0.457205\pi\) | ||||
0.134038 | + | 0.990976i | \(0.457205\pi\) | |||||||
\(42\) | 4.33630 | 0.669106 | ||||||||
\(43\) | −9.49106 | −1.44737 | −0.723687 | − | 0.690129i | \(-0.757554\pi\) | ||||
−0.723687 | + | 0.690129i | \(0.757554\pi\) | |||||||
\(44\) | −4.74553 | −0.715416 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 9.36530 | 1.38084 | ||||||||
\(47\) | −1.51115 | −0.220424 | −0.110212 | − | 0.993908i | \(-0.535153\pi\) | ||||
−0.110212 | + | 0.993908i | \(0.535153\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 11.8035 | 1.68622 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −5.77453 | −0.808596 | ||||||||
\(52\) | 0.409227 | 0.0567495 | ||||||||
\(53\) | −10.6726 | −1.46600 | −0.732998 | − | 0.680231i | \(-0.761879\pi\) | ||||
−0.732998 | + | 0.680231i | \(0.761879\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 4.74553 | 0.639887 | ||||||||
\(56\) | −4.33630 | −0.579463 | ||||||||
\(57\) | 5.77453 | 0.764855 | ||||||||
\(58\) | 1.30730 | 0.171657 | ||||||||
\(59\) | 1.71653 | 0.223473 | 0.111737 | − | 0.993738i | \(-0.464359\pi\) | ||||
0.111737 | + | 0.993738i | \(0.464359\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 6.33630 | 0.811281 | 0.405640 | − | 0.914033i | \(-0.367049\pi\) | ||||
0.405640 | + | 0.914033i | \(0.367049\pi\) | |||||||
\(62\) | −2.40923 | −0.305972 | ||||||||
\(63\) | 4.33630 | 0.546323 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.409227 | −0.0507583 | ||||||||
\(66\) | −4.74553 | −0.584134 | ||||||||
\(67\) | −1.00000 | −0.122169 | ||||||||
\(68\) | 5.77453 | 0.700265 | ||||||||
\(69\) | 9.36530 | 1.12745 | ||||||||
\(70\) | 4.33630 | 0.518287 | ||||||||
\(71\) | 8.11084 | 0.962579 | 0.481290 | − | 0.876562i | \(-0.340169\pi\) | ||||
0.481290 | + | 0.876562i | \(0.340169\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −8.05800 | −0.943118 | −0.471559 | − | 0.881835i | \(-0.656309\pi\) | ||||
−0.471559 | + | 0.881835i | \(0.656309\pi\) | |||||||
\(74\) | −3.02900 | −0.352114 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −5.77453 | −0.662384 | ||||||||
\(77\) | −20.5781 | −2.34509 | ||||||||
\(78\) | 0.409227 | 0.0463358 | ||||||||
\(79\) | 7.64878 | 0.860554 | 0.430277 | − | 0.902697i | \(-0.358416\pi\) | ||||
0.430277 | + | 0.902697i | \(0.358416\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.71653 | −0.189559 | ||||||||
\(83\) | 8.57806 | 0.941565 | 0.470782 | − | 0.882249i | \(-0.343972\pi\) | ||||
0.470782 | + | 0.882249i | \(0.343972\pi\) | |||||||
\(84\) | −4.33630 | −0.473130 | ||||||||
\(85\) | −5.77453 | −0.626336 | ||||||||
\(86\) | 9.49106 | 1.02345 | ||||||||
\(87\) | 1.30730 | 0.140158 | ||||||||
\(88\) | 4.74553 | 0.505875 | ||||||||
\(89\) | −9.08700 | −0.963220 | −0.481610 | − | 0.876386i | \(-0.659948\pi\) | ||||
−0.481610 | + | 0.876386i | \(0.659948\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 1.77453 | 0.186021 | ||||||||
\(92\) | −9.36530 | −0.976401 | ||||||||
\(93\) | −2.40923 | −0.249825 | ||||||||
\(94\) | 1.51115 | 0.155863 | ||||||||
\(95\) | 5.77453 | 0.592454 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −4.74553 | −0.481836 | −0.240918 | − | 0.970546i | \(-0.577448\pi\) | ||||
−0.240918 | + | 0.970546i | \(0.577448\pi\) | |||||||
\(98\) | −11.8035 | −1.19234 | ||||||||
\(99\) | −4.74553 | −0.476944 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 8.52006 | 0.847778 | 0.423889 | − | 0.905714i | \(-0.360665\pi\) | ||||
0.423889 | + | 0.905714i | \(0.360665\pi\) | |||||||
\(102\) | 5.77453 | 0.571764 | ||||||||
\(103\) | −13.4911 | −1.32931 | −0.664657 | − | 0.747149i | \(-0.731422\pi\) | ||||
−0.664657 | + | 0.747149i | \(0.731422\pi\) | |||||||
\(104\) | −0.409227 | −0.0401280 | ||||||||
\(105\) | 4.33630 | 0.423180 | ||||||||
\(106\) | 10.6726 | 1.03662 | ||||||||
\(107\) | −8.81845 | −0.852512 | −0.426256 | − | 0.904603i | \(-0.640168\pi\) | ||||
−0.426256 | + | 0.904603i | \(0.640168\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −17.8854 | −1.71311 | −0.856554 | − | 0.516058i | \(-0.827399\pi\) | ||||
−0.856554 | + | 0.516058i | \(0.827399\pi\) | |||||||
\(110\) | −4.74553 | −0.452469 | ||||||||
\(111\) | −3.02900 | −0.287500 | ||||||||
\(112\) | 4.33630 | 0.409742 | ||||||||
\(113\) | −3.86908 | −0.363972 | −0.181986 | − | 0.983301i | \(-0.558253\pi\) | ||||
−0.181986 | + | 0.983301i | \(0.558253\pi\) | |||||||
\(114\) | −5.77453 | −0.540834 | ||||||||
\(115\) | 9.36530 | 0.873319 | ||||||||
\(116\) | −1.30730 | −0.121380 | ||||||||
\(117\) | 0.409227 | 0.0378330 | ||||||||
\(118\) | −1.71653 | −0.158019 | ||||||||
\(119\) | 25.0401 | 2.29542 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 11.5201 | 1.04728 | ||||||||
\(122\) | −6.33630 | −0.573662 | ||||||||
\(123\) | −1.71653 | −0.154774 | ||||||||
\(124\) | 2.40923 | 0.216355 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −4.33630 | −0.386309 | ||||||||
\(127\) | −9.23955 | −0.819877 | −0.409939 | − | 0.912113i | \(-0.634450\pi\) | ||||
−0.409939 | + | 0.912113i | \(0.634450\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 9.49106 | 0.835641 | ||||||||
\(130\) | 0.409227 | 0.0358916 | ||||||||
\(131\) | −18.9561 | −1.65620 | −0.828100 | − | 0.560580i | \(-0.810578\pi\) | ||||
−0.828100 | + | 0.560580i | \(0.810578\pi\) | |||||||
\(132\) | 4.74553 | 0.413045 | ||||||||
\(133\) | −25.0401 | −2.17125 | ||||||||
\(134\) | 1.00000 | 0.0863868 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −5.77453 | −0.495162 | ||||||||
\(137\) | −0.970999 | −0.0829581 | −0.0414790 | − | 0.999139i | \(-0.513207\pi\) | ||||
−0.0414790 | + | 0.999139i | \(0.513207\pi\) | |||||||
\(138\) | −9.36530 | −0.797228 | ||||||||
\(139\) | 9.41144 | 0.798268 | 0.399134 | − | 0.916893i | \(-0.369311\pi\) | ||||
0.399134 | + | 0.916893i | \(0.369311\pi\) | |||||||
\(140\) | −4.33630 | −0.366485 | ||||||||
\(141\) | 1.51115 | 0.127262 | ||||||||
\(142\) | −8.11084 | −0.680646 | ||||||||
\(143\) | −1.94200 | −0.162398 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 1.30730 | 0.108566 | ||||||||
\(146\) | 8.05800 | 0.666885 | ||||||||
\(147\) | −11.8035 | −0.973539 | ||||||||
\(148\) | 3.02900 | 0.248982 | ||||||||
\(149\) | −1.30730 | −0.107098 | −0.0535492 | − | 0.998565i | \(-0.517053\pi\) | ||||
−0.0535492 | + | 0.998565i | \(0.517053\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −15.3385 | −1.24823 | −0.624115 | − | 0.781332i | \(-0.714540\pi\) | ||||
−0.624115 | + | 0.781332i | \(0.714540\pi\) | |||||||
\(152\) | 5.77453 | 0.468376 | ||||||||
\(153\) | 5.77453 | 0.466843 | ||||||||
\(154\) | 20.5781 | 1.65823 | ||||||||
\(155\) | −2.40923 | −0.193514 | ||||||||
\(156\) | −0.409227 | −0.0327644 | ||||||||
\(157\) | −7.79615 | −0.622201 | −0.311100 | − | 0.950377i | \(-0.600698\pi\) | ||||
−0.311100 | + | 0.950377i | \(0.600698\pi\) | |||||||
\(158\) | −7.64878 | −0.608504 | ||||||||
\(159\) | 10.6726 | 0.846393 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −40.6108 | −3.20058 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −6.97100 | −0.546011 | −0.273005 | − | 0.962013i | \(-0.588018\pi\) | ||||
−0.273005 | + | 0.962013i | \(0.588018\pi\) | |||||||
\(164\) | 1.71653 | 0.134038 | ||||||||
\(165\) | −4.74553 | −0.369439 | ||||||||
\(166\) | −8.57806 | −0.665787 | ||||||||
\(167\) | 0.546851 | 0.0423166 | 0.0211583 | − | 0.999776i | \(-0.493265\pi\) | ||||
0.0211583 | + | 0.999776i | \(0.493265\pi\) | |||||||
\(168\) | 4.33630 | 0.334553 | ||||||||
\(169\) | −12.8325 | −0.987118 | ||||||||
\(170\) | 5.77453 | 0.442886 | ||||||||
\(171\) | −5.77453 | −0.441589 | ||||||||
\(172\) | −9.49106 | −0.723687 | ||||||||
\(173\) | −16.3147 | −1.24038 | −0.620191 | − | 0.784451i | \(-0.712945\pi\) | ||||
−0.620191 | + | 0.784451i | \(0.712945\pi\) | |||||||
\(174\) | −1.30730 | −0.0991064 | ||||||||
\(175\) | 4.33630 | 0.327794 | ||||||||
\(176\) | −4.74553 | −0.357708 | ||||||||
\(177\) | −1.71653 | −0.129022 | ||||||||
\(178\) | 9.08700 | 0.681100 | ||||||||
\(179\) | −1.92038 | −0.143536 | −0.0717679 | − | 0.997421i | \(-0.522864\pi\) | ||||
−0.0717679 | + | 0.997421i | \(0.522864\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 17.4032 | 1.29357 | 0.646785 | − | 0.762672i | \(-0.276113\pi\) | ||||
0.646785 | + | 0.762672i | \(0.276113\pi\) | |||||||
\(182\) | −1.77453 | −0.131537 | ||||||||
\(183\) | −6.33630 | −0.468393 | ||||||||
\(184\) | 9.36530 | 0.690419 | ||||||||
\(185\) | −3.02900 | −0.222697 | ||||||||
\(186\) | 2.40923 | 0.176653 | ||||||||
\(187\) | −27.4032 | −2.00392 | ||||||||
\(188\) | −1.51115 | −0.110212 | ||||||||
\(189\) | −4.33630 | −0.315420 | ||||||||
\(190\) | −5.77453 | −0.418929 | ||||||||
\(191\) | −2.50894 | −0.181540 | −0.0907702 | − | 0.995872i | \(-0.528933\pi\) | ||||
−0.0907702 | + | 0.995872i | \(0.528933\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 25.9382 | 1.86707 | 0.933536 | − | 0.358483i | \(-0.116706\pi\) | ||||
0.933536 | + | 0.358483i | \(0.116706\pi\) | |||||||
\(194\) | 4.74553 | 0.340709 | ||||||||
\(195\) | 0.409227 | 0.0293053 | ||||||||
\(196\) | 11.8035 | 0.843109 | ||||||||
\(197\) | −1.18155 | −0.0841817 | −0.0420909 | − | 0.999114i | \(-0.513402\pi\) | ||||
−0.0420909 | + | 0.999114i | \(0.513402\pi\) | |||||||
\(198\) | 4.74553 | 0.337250 | ||||||||
\(199\) | −16.5781 | −1.17519 | −0.587594 | − | 0.809156i | \(-0.699925\pi\) | ||||
−0.587594 | + | 0.809156i | \(0.699925\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 1.00000 | 0.0705346 | ||||||||
\(202\) | −8.52006 | −0.599470 | ||||||||
\(203\) | −5.66886 | −0.397876 | ||||||||
\(204\) | −5.77453 | −0.404298 | ||||||||
\(205\) | −1.71653 | −0.119888 | ||||||||
\(206\) | 13.4911 | 0.939967 | ||||||||
\(207\) | −9.36530 | −0.650934 | ||||||||
\(208\) | 0.409227 | 0.0283748 | ||||||||
\(209\) | 27.4032 | 1.89552 | ||||||||
\(210\) | −4.33630 | −0.299233 | ||||||||
\(211\) | −25.0617 | −1.72532 | −0.862661 | − | 0.505783i | \(-0.831204\pi\) | ||||
−0.862661 | + | 0.505783i | \(0.831204\pi\) | |||||||
\(212\) | −10.6726 | −0.732998 | ||||||||
\(213\) | −8.11084 | −0.555745 | ||||||||
\(214\) | 8.81845 | 0.602817 | ||||||||
\(215\) | 9.49106 | 0.647285 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 10.4471 | 0.709198 | ||||||||
\(218\) | 17.8854 | 1.21135 | ||||||||
\(219\) | 8.05800 | 0.544509 | ||||||||
\(220\) | 4.74553 | 0.319944 | ||||||||
\(221\) | 2.36309 | 0.158959 | ||||||||
\(222\) | 3.02900 | 0.203293 | ||||||||
\(223\) | −25.8586 | −1.73162 | −0.865809 | − | 0.500374i | \(-0.833196\pi\) | ||||
−0.865809 | + | 0.500374i | \(0.833196\pi\) | |||||||
\(224\) | −4.33630 | −0.289731 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 3.86908 | 0.257367 | ||||||||
\(227\) | 17.7127 | 1.17564 | 0.587818 | − | 0.808993i | \(-0.299987\pi\) | ||||
0.587818 | + | 0.808993i | \(0.299987\pi\) | |||||||
\(228\) | 5.77453 | 0.382428 | ||||||||
\(229\) | −15.8274 | −1.04590 | −0.522951 | − | 0.852363i | \(-0.675169\pi\) | ||||
−0.522951 | + | 0.852363i | \(0.675169\pi\) | |||||||
\(230\) | −9.36530 | −0.617530 | ||||||||
\(231\) | 20.5781 | 1.35394 | ||||||||
\(232\) | 1.30730 | 0.0858287 | ||||||||
\(233\) | −22.4322 | −1.46958 | −0.734792 | − | 0.678293i | \(-0.762720\pi\) | ||||
−0.734792 | + | 0.678293i | \(0.762720\pi\) | |||||||
\(234\) | −0.409227 | −0.0267520 | ||||||||
\(235\) | 1.51115 | 0.0985766 | ||||||||
\(236\) | 1.71653 | 0.111737 | ||||||||
\(237\) | −7.64878 | −0.496841 | ||||||||
\(238\) | −25.0401 | −1.62311 | ||||||||
\(239\) | 9.23955 | 0.597657 | 0.298828 | − | 0.954307i | \(-0.403404\pi\) | ||||
0.298828 | + | 0.954307i | \(0.403404\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 6.17859 | 0.397998 | 0.198999 | − | 0.980000i | \(-0.436231\pi\) | ||||
0.198999 | + | 0.980000i | \(0.436231\pi\) | |||||||
\(242\) | −11.5201 | −0.740538 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.33630 | 0.405640 | ||||||||
\(245\) | −11.8035 | −0.754100 | ||||||||
\(246\) | 1.71653 | 0.109442 | ||||||||
\(247\) | −2.36309 | −0.150360 | ||||||||
\(248\) | −2.40923 | −0.152986 | ||||||||
\(249\) | −8.57806 | −0.543613 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −6.97100 | −0.440006 | −0.220003 | − | 0.975499i | \(-0.570607\pi\) | ||||
−0.220003 | + | 0.975499i | \(0.570607\pi\) | |||||||
\(252\) | 4.33630 | 0.273161 | ||||||||
\(253\) | 44.4433 | 2.79413 | ||||||||
\(254\) | 9.23955 | 0.579741 | ||||||||
\(255\) | 5.77453 | 0.361615 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.7090 | 0.917522 | 0.458761 | − | 0.888560i | \(-0.348293\pi\) | ||||
0.458761 | + | 0.888560i | \(0.348293\pi\) | |||||||
\(258\) | −9.49106 | −0.590888 | ||||||||
\(259\) | 13.1347 | 0.816149 | ||||||||
\(260\) | −0.409227 | −0.0253792 | ||||||||
\(261\) | −1.30730 | −0.0809200 | ||||||||
\(262\) | 18.9561 | 1.17111 | ||||||||
\(263\) | 8.79836 | 0.542530 | 0.271265 | − | 0.962505i | \(-0.412558\pi\) | ||||
0.271265 | + | 0.962505i | \(0.412558\pi\) | |||||||
\(264\) | −4.74553 | −0.292067 | ||||||||
\(265\) | 10.6726 | 0.655613 | ||||||||
\(266\) | 25.0401 | 1.53531 | ||||||||
\(267\) | 9.08700 | 0.556116 | ||||||||
\(268\) | −1.00000 | −0.0610847 | ||||||||
\(269\) | 28.8564 | 1.75940 | 0.879702 | − | 0.475526i | \(-0.157742\pi\) | ||||
0.879702 | + | 0.475526i | \(0.157742\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 13.8124 | 0.839046 | 0.419523 | − | 0.907745i | \(-0.362197\pi\) | ||||
0.419523 | + | 0.907745i | \(0.362197\pi\) | |||||||
\(272\) | 5.77453 | 0.350132 | ||||||||
\(273\) | −1.77453 | −0.107400 | ||||||||
\(274\) | 0.970999 | 0.0586602 | ||||||||
\(275\) | −4.74553 | −0.286166 | ||||||||
\(276\) | 9.36530 | 0.563725 | ||||||||
\(277\) | −3.28051 | −0.197107 | −0.0985535 | − | 0.995132i | \(-0.531422\pi\) | ||||
−0.0985535 | + | 0.995132i | \(0.531422\pi\) | |||||||
\(278\) | −9.41144 | −0.564461 | ||||||||
\(279\) | 2.40923 | 0.144237 | ||||||||
\(280\) | 4.33630 | 0.259144 | ||||||||
\(281\) | 0.363093 | 0.0216603 | 0.0108302 | − | 0.999941i | \(-0.496553\pi\) | ||||
0.0108302 | + | 0.999941i | \(0.496553\pi\) | |||||||
\(282\) | −1.51115 | −0.0899877 | ||||||||
\(283\) | 12.1570 | 0.722657 | 0.361328 | − | 0.932439i | \(-0.382323\pi\) | ||||
0.361328 | + | 0.932439i | \(0.382323\pi\) | |||||||
\(284\) | 8.11084 | 0.481290 | ||||||||
\(285\) | −5.77453 | −0.342054 | ||||||||
\(286\) | 1.94200 | 0.114833 | ||||||||
\(287\) | 7.44340 | 0.439370 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 16.3452 | 0.961483 | ||||||||
\(290\) | −1.30730 | −0.0767675 | ||||||||
\(291\) | 4.74553 | 0.278188 | ||||||||
\(292\) | −8.05800 | −0.471559 | ||||||||
\(293\) | −0.871287 | −0.0509012 | −0.0254506 | − | 0.999676i | \(-0.508102\pi\) | ||||
−0.0254506 | + | 0.999676i | \(0.508102\pi\) | |||||||
\(294\) | 11.8035 | 0.688396 | ||||||||
\(295\) | −1.71653 | −0.0999402 | ||||||||
\(296\) | −3.02900 | −0.176057 | ||||||||
\(297\) | 4.74553 | 0.275364 | ||||||||
\(298\) | 1.30730 | 0.0757300 | ||||||||
\(299\) | −3.83253 | −0.221641 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | −41.1561 | −2.37220 | ||||||||
\(302\) | 15.3385 | 0.882632 | ||||||||
\(303\) | −8.52006 | −0.489465 | ||||||||
\(304\) | −5.77453 | −0.331192 | ||||||||
\(305\) | −6.33630 | −0.362816 | ||||||||
\(306\) | −5.77453 | −0.330108 | ||||||||
\(307\) | 26.4583 | 1.51005 | 0.755026 | − | 0.655694i | \(-0.227624\pi\) | ||||
0.755026 | + | 0.655694i | \(0.227624\pi\) | |||||||
\(308\) | −20.5781 | −1.17254 | ||||||||
\(309\) | 13.4911 | 0.767480 | ||||||||
\(310\) | 2.40923 | 0.136835 | ||||||||
\(311\) | −26.1637 | −1.48361 | −0.741803 | − | 0.670618i | \(-0.766029\pi\) | ||||
−0.741803 | + | 0.670618i | \(0.766029\pi\) | |||||||
\(312\) | 0.409227 | 0.0231679 | ||||||||
\(313\) | 12.4404 | 0.703175 | 0.351588 | − | 0.936155i | \(-0.385642\pi\) | ||||
0.351588 | + | 0.936155i | \(0.385642\pi\) | |||||||
\(314\) | 7.79615 | 0.439962 | ||||||||
\(315\) | −4.33630 | −0.244323 | ||||||||
\(316\) | 7.64878 | 0.430277 | ||||||||
\(317\) | −31.2558 | −1.75550 | −0.877751 | − | 0.479116i | \(-0.840957\pi\) | ||||
−0.877751 | + | 0.479116i | \(0.840957\pi\) | |||||||
\(318\) | −10.6726 | −0.598490 | ||||||||
\(319\) | 6.20385 | 0.347349 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 8.81845 | 0.492198 | ||||||||
\(322\) | 40.6108 | 2.26315 | ||||||||
\(323\) | −33.3452 | −1.85538 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.409227 | 0.0226998 | ||||||||
\(326\) | 6.97100 | 0.386088 | ||||||||
\(327\) | 17.8854 | 0.989063 | ||||||||
\(328\) | −1.71653 | −0.0947795 | ||||||||
\(329\) | −6.55281 | −0.361268 | ||||||||
\(330\) | 4.74553 | 0.261233 | ||||||||
\(331\) | 28.6041 | 1.57222 | 0.786112 | − | 0.618084i | \(-0.212091\pi\) | ||||
0.786112 | + | 0.618084i | \(0.212091\pi\) | |||||||
\(332\) | 8.57806 | 0.470782 | ||||||||
\(333\) | 3.02900 | 0.165988 | ||||||||
\(334\) | −0.546851 | −0.0299224 | ||||||||
\(335\) | 1.00000 | 0.0546358 | ||||||||
\(336\) | −4.33630 | −0.236565 | ||||||||
\(337\) | −17.5751 | −0.957377 | −0.478689 | − | 0.877985i | \(-0.658888\pi\) | ||||
−0.478689 | + | 0.877985i | \(0.658888\pi\) | |||||||
\(338\) | 12.8325 | 0.697998 | ||||||||
\(339\) | 3.86908 | 0.210139 | ||||||||
\(340\) | −5.77453 | −0.313168 | ||||||||
\(341\) | −11.4331 | −0.619135 | ||||||||
\(342\) | 5.77453 | 0.312251 | ||||||||
\(343\) | 20.8296 | 1.12469 | ||||||||
\(344\) | 9.49106 | 0.511724 | ||||||||
\(345\) | −9.36530 | −0.504211 | ||||||||
\(346\) | 16.3147 | 0.877083 | ||||||||
\(347\) | −34.1122 | −1.83124 | −0.915620 | − | 0.402046i | \(-0.868299\pi\) | ||||
−0.915620 | + | 0.402046i | \(0.868299\pi\) | |||||||
\(348\) | 1.30730 | 0.0700788 | ||||||||
\(349\) | −12.9821 | −0.694917 | −0.347459 | − | 0.937695i | \(-0.612955\pi\) | ||||
−0.347459 | + | 0.937695i | \(0.612955\pi\) | |||||||
\(350\) | −4.33630 | −0.231785 | ||||||||
\(351\) | −0.409227 | −0.0218429 | ||||||||
\(352\) | 4.74553 | 0.252938 | ||||||||
\(353\) | 3.55286 | 0.189100 | 0.0945498 | − | 0.995520i | \(-0.469859\pi\) | ||||
0.0945498 | + | 0.995520i | \(0.469859\pi\) | |||||||
\(354\) | 1.71653 | 0.0912325 | ||||||||
\(355\) | −8.11084 | −0.430478 | ||||||||
\(356\) | −9.08700 | −0.481610 | ||||||||
\(357\) | −25.0401 | −1.32526 | ||||||||
\(358\) | 1.92038 | 0.101495 | ||||||||
\(359\) | −22.0230 | −1.16233 | −0.581165 | − | 0.813786i | \(-0.697403\pi\) | ||||
−0.581165 | + | 0.813786i | \(0.697403\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 14.3452 | 0.755011 | ||||||||
\(362\) | −17.4032 | −0.914693 | ||||||||
\(363\) | −11.5201 | −0.604646 | ||||||||
\(364\) | 1.77453 | 0.0930107 | ||||||||
\(365\) | 8.05800 | 0.421775 | ||||||||
\(366\) | 6.33630 | 0.331204 | ||||||||
\(367\) | −2.34300 | −0.122304 | −0.0611519 | − | 0.998128i | \(-0.519477\pi\) | ||||
−0.0611519 | + | 0.998128i | \(0.519477\pi\) | |||||||
\(368\) | −9.36530 | −0.488200 | ||||||||
\(369\) | 1.71653 | 0.0893590 | ||||||||
\(370\) | 3.02900 | 0.157470 | ||||||||
\(371\) | −46.2797 | −2.40272 | ||||||||
\(372\) | −2.40923 | −0.124913 | ||||||||
\(373\) | 16.9360 | 0.876912 | 0.438456 | − | 0.898753i | \(-0.355525\pi\) | ||||
0.438456 | + | 0.898753i | \(0.355525\pi\) | |||||||
\(374\) | 27.4032 | 1.41699 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 1.51115 | 0.0779316 | ||||||||
\(377\) | −0.534983 | −0.0275530 | ||||||||
\(378\) | 4.33630 | 0.223035 | ||||||||
\(379\) | 7.93378 | 0.407531 | 0.203765 | − | 0.979020i | \(-0.434682\pi\) | ||||
0.203765 | + | 0.979020i | \(0.434682\pi\) | |||||||
\(380\) | 5.77453 | 0.296227 | ||||||||
\(381\) | 9.23955 | 0.473356 | ||||||||
\(382\) | 2.50894 | 0.128368 | ||||||||
\(383\) | 26.3742 | 1.34766 | 0.673830 | − | 0.738887i | \(-0.264648\pi\) | ||||
0.673830 | + | 0.738887i | \(0.264648\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 20.5781 | 1.04876 | ||||||||
\(386\) | −25.9382 | −1.32022 | ||||||||
\(387\) | −9.49106 | −0.482458 | ||||||||
\(388\) | −4.74553 | −0.240918 | ||||||||
\(389\) | 39.4277 | 1.99907 | 0.999533 | − | 0.0305693i | \(-0.00973203\pi\) | ||||
0.999533 | + | 0.0305693i | \(0.00973203\pi\) | |||||||
\(390\) | −0.409227 | −0.0207220 | ||||||||
\(391\) | −54.0802 | −2.73496 | ||||||||
\(392\) | −11.8035 | −0.596168 | ||||||||
\(393\) | 18.9561 | 0.956208 | ||||||||
\(394\) | 1.18155 | 0.0595255 | ||||||||
\(395\) | −7.64878 | −0.384852 | ||||||||
\(396\) | −4.74553 | −0.238472 | ||||||||
\(397\) | −23.8073 | −1.19485 | −0.597426 | − | 0.801924i | \(-0.703810\pi\) | ||||
−0.597426 | + | 0.801924i | \(0.703810\pi\) | |||||||
\(398\) | 16.5781 | 0.830983 | ||||||||
\(399\) | 25.0401 | 1.25357 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −17.8109 | −0.889435 | −0.444717 | − | 0.895671i | \(-0.646696\pi\) | ||||
−0.444717 | + | 0.895671i | \(0.646696\pi\) | |||||||
\(402\) | −1.00000 | −0.0498755 | ||||||||
\(403\) | 0.985920 | 0.0491122 | ||||||||
\(404\) | 8.52006 | 0.423889 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 5.66886 | 0.281341 | ||||||||
\(407\) | −14.3742 | −0.712503 | ||||||||
\(408\) | 5.77453 | 0.285882 | ||||||||
\(409\) | 9.18155 | 0.453998 | 0.226999 | − | 0.973895i | \(-0.427109\pi\) | ||||
0.226999 | + | 0.973895i | \(0.427109\pi\) | |||||||
\(410\) | 1.71653 | 0.0847734 | ||||||||
\(411\) | 0.970999 | 0.0478959 | ||||||||
\(412\) | −13.4911 | −0.664657 | ||||||||
\(413\) | 7.44340 | 0.366266 | ||||||||
\(414\) | 9.36530 | 0.460280 | ||||||||
\(415\) | −8.57806 | −0.421081 | ||||||||
\(416\) | −0.409227 | −0.0200640 | ||||||||
\(417\) | −9.41144 | −0.460880 | ||||||||
\(418\) | −27.4032 | −1.34034 | ||||||||
\(419\) | −12.3013 | −0.600958 | −0.300479 | − | 0.953789i | \(-0.597146\pi\) | ||||
−0.300479 | + | 0.953789i | \(0.597146\pi\) | |||||||
\(420\) | 4.33630 | 0.211590 | ||||||||
\(421\) | 32.8363 | 1.60034 | 0.800171 | − | 0.599772i | \(-0.204742\pi\) | ||||
0.800171 | + | 0.599772i | \(0.204742\pi\) | |||||||
\(422\) | 25.0617 | 1.21999 | ||||||||
\(423\) | −1.51115 | −0.0734746 | ||||||||
\(424\) | 10.6726 | 0.518308 | ||||||||
\(425\) | 5.77453 | 0.280106 | ||||||||
\(426\) | 8.11084 | 0.392971 | ||||||||
\(427\) | 27.4761 | 1.32966 | ||||||||
\(428\) | −8.81845 | −0.426256 | ||||||||
\(429\) | 1.94200 | 0.0937606 | ||||||||
\(430\) | −9.49106 | −0.457700 | ||||||||
\(431\) | −41.0051 | −1.97515 | −0.987573 | − | 0.157158i | \(-0.949767\pi\) | ||||
−0.987573 | + | 0.157158i | \(0.949767\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 23.5274 | 1.13066 | 0.565328 | − | 0.824866i | \(-0.308749\pi\) | ||||
0.565328 | + | 0.824866i | \(0.308749\pi\) | |||||||
\(434\) | −10.4471 | −0.501479 | ||||||||
\(435\) | −1.30730 | −0.0626804 | ||||||||
\(436\) | −17.8854 | −0.856554 | ||||||||
\(437\) | 54.0802 | 2.58701 | ||||||||
\(438\) | −8.05800 | −0.385026 | ||||||||
\(439\) | −22.0691 | −1.05330 | −0.526651 | − | 0.850082i | \(-0.676553\pi\) | ||||
−0.526651 | + | 0.850082i | \(0.676553\pi\) | |||||||
\(440\) | −4.74553 | −0.226234 | ||||||||
\(441\) | 11.8035 | 0.562073 | ||||||||
\(442\) | −2.36309 | −0.112401 | ||||||||
\(443\) | 7.54906 | 0.358667 | 0.179333 | − | 0.983788i | \(-0.442606\pi\) | ||||
0.179333 | + | 0.983788i | \(0.442606\pi\) | |||||||
\(444\) | −3.02900 | −0.143750 | ||||||||
\(445\) | 9.08700 | 0.430765 | ||||||||
\(446\) | 25.8586 | 1.22444 | ||||||||
\(447\) | 1.30730 | 0.0618333 | ||||||||
\(448\) | 4.33630 | 0.204871 | ||||||||
\(449\) | 27.4398 | 1.29496 | 0.647481 | − | 0.762081i | \(-0.275822\pi\) | ||||
0.647481 | + | 0.762081i | \(0.275822\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −8.14585 | −0.383573 | ||||||||
\(452\) | −3.86908 | −0.181986 | ||||||||
\(453\) | 15.3385 | 0.720666 | ||||||||
\(454\) | −17.7127 | −0.831300 | ||||||||
\(455\) | −1.77453 | −0.0831913 | ||||||||
\(456\) | −5.77453 | −0.270417 | ||||||||
\(457\) | −14.3891 | −0.673095 | −0.336548 | − | 0.941666i | \(-0.609259\pi\) | ||||
−0.336548 | + | 0.941666i | \(0.609259\pi\) | |||||||
\(458\) | 15.8274 | 0.739564 | ||||||||
\(459\) | −5.77453 | −0.269532 | ||||||||
\(460\) | 9.36530 | 0.436660 | ||||||||
\(461\) | −14.5365 | −0.677033 | −0.338517 | − | 0.940960i | \(-0.609925\pi\) | ||||
−0.338517 | + | 0.940960i | \(0.609925\pi\) | |||||||
\(462\) | −20.5781 | −0.957378 | ||||||||
\(463\) | 11.6124 | 0.539674 | 0.269837 | − | 0.962906i | \(-0.413030\pi\) | ||||
0.269837 | + | 0.962906i | \(0.413030\pi\) | |||||||
\(464\) | −1.30730 | −0.0606900 | ||||||||
\(465\) | 2.40923 | 0.111725 | ||||||||
\(466\) | 22.4322 | 1.03915 | ||||||||
\(467\) | 8.88316 | 0.411063 | 0.205532 | − | 0.978650i | \(-0.434108\pi\) | ||||
0.205532 | + | 0.978650i | \(0.434108\pi\) | |||||||
\(468\) | 0.409227 | 0.0189165 | ||||||||
\(469\) | −4.33630 | −0.200232 | ||||||||
\(470\) | −1.51115 | −0.0697042 | ||||||||
\(471\) | 7.79615 | 0.359228 | ||||||||
\(472\) | −1.71653 | −0.0790097 | ||||||||
\(473\) | 45.0401 | 2.07095 | ||||||||
\(474\) | 7.64878 | 0.351320 | ||||||||
\(475\) | −5.77453 | −0.264954 | ||||||||
\(476\) | 25.0401 | 1.14771 | ||||||||
\(477\) | −10.6726 | −0.488665 | ||||||||
\(478\) | −9.23955 | −0.422607 | ||||||||
\(479\) | 24.5319 | 1.12089 | 0.560446 | − | 0.828191i | \(-0.310630\pi\) | ||||
0.560446 | + | 0.828191i | \(0.310630\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 1.23955 | 0.0565185 | ||||||||
\(482\) | −6.17859 | −0.281427 | ||||||||
\(483\) | 40.6108 | 1.84786 | ||||||||
\(484\) | 11.5201 | 0.523639 | ||||||||
\(485\) | 4.74553 | 0.215483 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −12.9553 | −0.587062 | −0.293531 | − | 0.955950i | \(-0.594830\pi\) | ||||
−0.293531 | + | 0.955950i | \(0.594830\pi\) | |||||||
\(488\) | −6.33630 | −0.286831 | ||||||||
\(489\) | 6.97100 | 0.315239 | ||||||||
\(490\) | 11.8035 | 0.533229 | ||||||||
\(491\) | 27.6911 | 1.24968 | 0.624841 | − | 0.780752i | \(-0.285164\pi\) | ||||
0.624841 | + | 0.780752i | \(0.285164\pi\) | |||||||
\(492\) | −1.71653 | −0.0773871 | ||||||||
\(493\) | −7.54906 | −0.339993 | ||||||||
\(494\) | 2.36309 | 0.106321 | ||||||||
\(495\) | 4.74553 | 0.213296 | ||||||||
\(496\) | 2.40923 | 0.108177 | ||||||||
\(497\) | 35.1710 | 1.57764 | ||||||||
\(498\) | 8.57806 | 0.384392 | ||||||||
\(499\) | 32.7737 | 1.46715 | 0.733576 | − | 0.679607i | \(-0.237850\pi\) | ||||
0.733576 | + | 0.679607i | \(0.237850\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −0.546851 | −0.0244315 | ||||||||
\(502\) | 6.97100 | 0.311131 | ||||||||
\(503\) | 20.5677 | 0.917070 | 0.458535 | − | 0.888676i | \(-0.348374\pi\) | ||||
0.458535 | + | 0.888676i | \(0.348374\pi\) | |||||||
\(504\) | −4.33630 | −0.193154 | ||||||||
\(505\) | −8.52006 | −0.379138 | ||||||||
\(506\) | −44.4433 | −1.97575 | ||||||||
\(507\) | 12.8325 | 0.569913 | ||||||||
\(508\) | −9.23955 | −0.409939 | ||||||||
\(509\) | −1.97991 | −0.0877580 | −0.0438790 | − | 0.999037i | \(-0.513972\pi\) | ||||
−0.0438790 | + | 0.999037i | \(0.513972\pi\) | |||||||
\(510\) | −5.77453 | −0.255701 | ||||||||
\(511\) | −34.9419 | −1.54574 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.77453 | 0.254952 | ||||||||
\(514\) | −14.7090 | −0.648786 | ||||||||
\(515\) | 13.4911 | 0.594487 | ||||||||
\(516\) | 9.49106 | 0.417821 | ||||||||
\(517\) | 7.17121 | 0.315389 | ||||||||
\(518\) | −13.1347 | −0.577104 | ||||||||
\(519\) | 16.3147 | 0.716135 | ||||||||
\(520\) | 0.409227 | 0.0179458 | ||||||||
\(521\) | 22.6407 | 0.991905 | 0.495952 | − | 0.868350i | \(-0.334819\pi\) | ||||
0.495952 | + | 0.868350i | \(0.334819\pi\) | |||||||
\(522\) | 1.30730 | 0.0572191 | ||||||||
\(523\) | −23.8519 | −1.04297 | −0.521485 | − | 0.853261i | \(-0.674622\pi\) | ||||
−0.521485 | + | 0.853261i | \(0.674622\pi\) | |||||||
\(524\) | −18.9561 | −0.828100 | ||||||||
\(525\) | −4.33630 | −0.189252 | ||||||||
\(526\) | −8.79836 | −0.383627 | ||||||||
\(527\) | 13.9122 | 0.606023 | ||||||||
\(528\) | 4.74553 | 0.206523 | ||||||||
\(529\) | 64.7089 | 2.81343 | ||||||||
\(530\) | −10.6726 | −0.463588 | ||||||||
\(531\) | 1.71653 | 0.0744911 | ||||||||
\(532\) | −25.0401 | −1.08563 | ||||||||
\(533\) | 0.702450 | 0.0304265 | ||||||||
\(534\) | −9.08700 | −0.393233 | ||||||||
\(535\) | 8.81845 | 0.381255 | ||||||||
\(536\) | 1.00000 | 0.0431934 | ||||||||
\(537\) | 1.92038 | 0.0828704 | ||||||||
\(538\) | −28.8564 | −1.24409 | ||||||||
\(539\) | −56.0140 | −2.41269 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −4.49919 | −0.193435 | −0.0967175 | − | 0.995312i | \(-0.530834\pi\) | ||||
−0.0967175 | + | 0.995312i | \(0.530834\pi\) | |||||||
\(542\) | −13.8124 | −0.593295 | ||||||||
\(543\) | −17.4032 | −0.746844 | ||||||||
\(544\) | −5.77453 | −0.247581 | ||||||||
\(545\) | 17.8854 | 0.766125 | ||||||||
\(546\) | 1.77453 | 0.0759429 | ||||||||
\(547\) | 5.68015 | 0.242866 | 0.121433 | − | 0.992600i | \(-0.461251\pi\) | ||||
0.121433 | + | 0.992600i | \(0.461251\pi\) | |||||||
\(548\) | −0.970999 | −0.0414790 | ||||||||
\(549\) | 6.33630 | 0.270427 | ||||||||
\(550\) | 4.74553 | 0.202350 | ||||||||
\(551\) | 7.54906 | 0.321601 | ||||||||
\(552\) | −9.36530 | −0.398614 | ||||||||
\(553\) | 33.1674 | 1.41042 | ||||||||
\(554\) | 3.28051 | 0.139376 | ||||||||
\(555\) | 3.02900 | 0.128574 | ||||||||
\(556\) | 9.41144 | 0.399134 | ||||||||
\(557\) | −20.6412 | −0.874597 | −0.437299 | − | 0.899316i | \(-0.644065\pi\) | ||||
−0.437299 | + | 0.899316i | \(0.644065\pi\) | |||||||
\(558\) | −2.40923 | −0.101991 | ||||||||
\(559\) | −3.88400 | −0.164276 | ||||||||
\(560\) | −4.33630 | −0.183242 | ||||||||
\(561\) | 27.4032 | 1.15696 | ||||||||
\(562\) | −0.363093 | −0.0153162 | ||||||||
\(563\) | −2.50894 | −0.105739 | −0.0528696 | − | 0.998601i | \(-0.516837\pi\) | ||||
−0.0528696 | + | 0.998601i | \(0.516837\pi\) | |||||||
\(564\) | 1.51115 | 0.0636309 | ||||||||
\(565\) | 3.86908 | 0.162773 | ||||||||
\(566\) | −12.1570 | −0.510996 | ||||||||
\(567\) | 4.33630 | 0.182108 | ||||||||
\(568\) | −8.11084 | −0.340323 | ||||||||
\(569\) | 41.6138 | 1.74454 | 0.872270 | − | 0.489025i | \(-0.162647\pi\) | ||||
0.872270 | + | 0.489025i | \(0.162647\pi\) | |||||||
\(570\) | 5.77453 | 0.241869 | ||||||||
\(571\) | 11.5491 | 0.483313 | 0.241657 | − | 0.970362i | \(-0.422309\pi\) | ||||
0.241657 | + | 0.970362i | \(0.422309\pi\) | |||||||
\(572\) | −1.94200 | −0.0811990 | ||||||||
\(573\) | 2.50894 | 0.104812 | ||||||||
\(574\) | −7.44340 | −0.310681 | ||||||||
\(575\) | −9.36530 | −0.390560 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −40.6211 | −1.69108 | −0.845540 | − | 0.533912i | \(-0.820721\pi\) | ||||
−0.845540 | + | 0.533912i | \(0.820721\pi\) | |||||||
\(578\) | −16.3452 | −0.679871 | ||||||||
\(579\) | −25.9382 | −1.07795 | ||||||||
\(580\) | 1.30730 | 0.0542828 | ||||||||
\(581\) | 37.1971 | 1.54320 | ||||||||
\(582\) | −4.74553 | −0.196709 | ||||||||
\(583\) | 50.6472 | 2.09759 | ||||||||
\(584\) | 8.05800 | 0.333442 | ||||||||
\(585\) | −0.409227 | −0.0169194 | ||||||||
\(586\) | 0.871287 | 0.0359926 | ||||||||
\(587\) | 7.82220 | 0.322857 | 0.161428 | − | 0.986884i | \(-0.448390\pi\) | ||||
0.161428 | + | 0.986884i | \(0.448390\pi\) | |||||||
\(588\) | −11.8035 | −0.486769 | ||||||||
\(589\) | −13.9122 | −0.573240 | ||||||||
\(590\) | 1.71653 | 0.0706684 | ||||||||
\(591\) | 1.18155 | 0.0486023 | ||||||||
\(592\) | 3.02900 | 0.124491 | ||||||||
\(593\) | −12.4041 | −0.509374 | −0.254687 | − | 0.967024i | \(-0.581972\pi\) | ||||
−0.254687 | + | 0.967024i | \(0.581972\pi\) | |||||||
\(594\) | −4.74553 | −0.194711 | ||||||||
\(595\) | −25.0401 | −1.02655 | ||||||||
\(596\) | −1.30730 | −0.0535492 | ||||||||
\(597\) | 16.5781 | 0.678495 | ||||||||
\(598\) | 3.83253 | 0.156724 | ||||||||
\(599\) | 20.5134 | 0.838153 | 0.419077 | − | 0.907951i | \(-0.362354\pi\) | ||||
0.419077 | + | 0.907951i | \(0.362354\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 20.4984 | 0.836149 | 0.418074 | − | 0.908413i | \(-0.362705\pi\) | ||||
0.418074 | + | 0.908413i | \(0.362705\pi\) | |||||||
\(602\) | 41.1561 | 1.67740 | ||||||||
\(603\) | −1.00000 | −0.0407231 | ||||||||
\(604\) | −15.3385 | −0.624115 | ||||||||
\(605\) | −11.5201 | −0.468357 | ||||||||
\(606\) | 8.52006 | 0.346104 | ||||||||
\(607\) | 8.96430 | 0.363850 | 0.181925 | − | 0.983312i | \(-0.441767\pi\) | ||||
0.181925 | + | 0.983312i | \(0.441767\pi\) | |||||||
\(608\) | 5.77453 | 0.234188 | ||||||||
\(609\) | 5.66886 | 0.229714 | ||||||||
\(610\) | 6.33630 | 0.256549 | ||||||||
\(611\) | −0.618403 | −0.0250179 | ||||||||
\(612\) | 5.77453 | 0.233422 | ||||||||
\(613\) | −28.6904 | −1.15880 | −0.579398 | − | 0.815045i | \(-0.696712\pi\) | ||||
−0.579398 | + | 0.815045i | \(0.696712\pi\) | |||||||
\(614\) | −26.4583 | −1.06777 | ||||||||
\(615\) | 1.71653 | 0.0692172 | ||||||||
\(616\) | 20.5781 | 0.829114 | ||||||||
\(617\) | −2.85483 | −0.114931 | −0.0574656 | − | 0.998347i | \(-0.518302\pi\) | ||||
−0.0574656 | + | 0.998347i | \(0.518302\pi\) | |||||||
\(618\) | −13.4911 | −0.542690 | ||||||||
\(619\) | −25.7745 | −1.03597 | −0.517983 | − | 0.855391i | \(-0.673317\pi\) | ||||
−0.517983 | + | 0.855391i | \(0.673317\pi\) | |||||||
\(620\) | −2.40923 | −0.0967569 | ||||||||
\(621\) | 9.36530 | 0.375817 | ||||||||
\(622\) | 26.1637 | 1.04907 | ||||||||
\(623\) | −39.4040 | −1.57869 | ||||||||
\(624\) | −0.409227 | −0.0163822 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −12.4404 | −0.497220 | ||||||||
\(627\) | −27.4032 | −1.09438 | ||||||||
\(628\) | −7.79615 | −0.311100 | ||||||||
\(629\) | 17.4911 | 0.697414 | ||||||||
\(630\) | 4.33630 | 0.172762 | ||||||||
\(631\) | −29.1398 | −1.16004 | −0.580019 | − | 0.814603i | \(-0.696955\pi\) | ||||
−0.580019 | + | 0.814603i | \(0.696955\pi\) | |||||||
\(632\) | −7.64878 | −0.304252 | ||||||||
\(633\) | 25.0617 | 0.996115 | ||||||||
\(634\) | 31.2558 | 1.24133 | ||||||||
\(635\) | 9.23955 | 0.366660 | ||||||||
\(636\) | 10.6726 | 0.423196 | ||||||||
\(637\) | 4.83032 | 0.191384 | ||||||||
\(638\) | −6.20385 | −0.245613 | ||||||||
\(639\) | 8.11084 | 0.320860 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 31.0535 | 1.22654 | 0.613270 | − | 0.789873i | \(-0.289854\pi\) | ||||
0.613270 | + | 0.789873i | \(0.289854\pi\) | |||||||
\(642\) | −8.81845 | −0.348037 | ||||||||
\(643\) | −28.1273 | −1.10923 | −0.554616 | − | 0.832106i | \(-0.687135\pi\) | ||||
−0.554616 | + | 0.832106i | \(0.687135\pi\) | |||||||
\(644\) | −40.6108 | −1.60029 | ||||||||
\(645\) | −9.49106 | −0.373710 | ||||||||
\(646\) | 33.3452 | 1.31195 | ||||||||
\(647\) | 37.2641 | 1.46500 | 0.732501 | − | 0.680766i | \(-0.238353\pi\) | ||||
0.732501 | + | 0.680766i | \(0.238353\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −8.14585 | −0.319752 | ||||||||
\(650\) | −0.409227 | −0.0160512 | ||||||||
\(651\) | −10.4471 | −0.409456 | ||||||||
\(652\) | −6.97100 | −0.273005 | ||||||||
\(653\) | −11.1963 | −0.438145 | −0.219073 | − | 0.975709i | \(-0.570303\pi\) | ||||
−0.219073 | + | 0.975709i | \(0.570303\pi\) | |||||||
\(654\) | −17.8854 | −0.699373 | ||||||||
\(655\) | 18.9561 | 0.740675 | ||||||||
\(656\) | 1.71653 | 0.0670192 | ||||||||
\(657\) | −8.05800 | −0.314373 | ||||||||
\(658\) | 6.55281 | 0.255455 | ||||||||
\(659\) | −18.8727 | −0.735174 | −0.367587 | − | 0.929989i | \(-0.619816\pi\) | ||||
−0.367587 | + | 0.929989i | \(0.619816\pi\) | |||||||
\(660\) | −4.74553 | −0.184720 | ||||||||
\(661\) | 13.5290 | 0.526216 | 0.263108 | − | 0.964766i | \(-0.415252\pi\) | ||||
0.263108 | + | 0.964766i | \(0.415252\pi\) | |||||||
\(662\) | −28.6041 | −1.11173 | ||||||||
\(663\) | −2.36309 | −0.0917749 | ||||||||
\(664\) | −8.57806 | −0.332893 | ||||||||
\(665\) | 25.0401 | 0.971014 | ||||||||
\(666\) | −3.02900 | −0.117371 | ||||||||
\(667\) | 12.2433 | 0.474062 | ||||||||
\(668\) | 0.546851 | 0.0211583 | ||||||||
\(669\) | 25.8586 | 0.999750 | ||||||||
\(670\) | −1.00000 | −0.0386334 | ||||||||
\(671\) | −30.0691 | −1.16081 | ||||||||
\(672\) | 4.33630 | 0.167277 | ||||||||
\(673\) | −43.2358 | −1.66662 | −0.833308 | − | 0.552809i | \(-0.813556\pi\) | ||||
−0.833308 | + | 0.552809i | \(0.813556\pi\) | |||||||
\(674\) | 17.5751 | 0.676968 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −12.8325 | −0.493559 | ||||||||
\(677\) | 3.63691 | 0.139778 | 0.0698888 | − | 0.997555i | \(-0.477736\pi\) | ||||
0.0698888 | + | 0.997555i | \(0.477736\pi\) | |||||||
\(678\) | −3.86908 | −0.148591 | ||||||||
\(679\) | −20.5781 | −0.789714 | ||||||||
\(680\) | 5.77453 | 0.221443 | ||||||||
\(681\) | −17.7127 | −0.678753 | ||||||||
\(682\) | 11.4331 | 0.437794 | ||||||||
\(683\) | 42.9523 | 1.64352 | 0.821762 | − | 0.569831i | \(-0.192991\pi\) | ||||
0.821762 | + | 0.569831i | \(0.192991\pi\) | |||||||
\(684\) | −5.77453 | −0.220795 | ||||||||
\(685\) | 0.970999 | 0.0371000 | ||||||||
\(686\) | −20.8296 | −0.795277 | ||||||||
\(687\) | 15.8274 | 0.603852 | ||||||||
\(688\) | −9.49106 | −0.361843 | ||||||||
\(689\) | −4.36752 | −0.166389 | ||||||||
\(690\) | 9.36530 | 0.356531 | ||||||||
\(691\) | 43.0683 | 1.63839 | 0.819197 | − | 0.573512i | \(-0.194419\pi\) | ||||
0.819197 | + | 0.573512i | \(0.194419\pi\) | |||||||
\(692\) | −16.3147 | −0.620191 | ||||||||
\(693\) | −20.5781 | −0.781696 | ||||||||
\(694\) | 34.1122 | 1.29488 | ||||||||
\(695\) | −9.41144 | −0.356996 | ||||||||
\(696\) | −1.30730 | −0.0495532 | ||||||||
\(697\) | 9.91216 | 0.375450 | ||||||||
\(698\) | 12.9821 | 0.491381 | ||||||||
\(699\) | 22.4322 | 0.848464 | ||||||||
\(700\) | 4.33630 | 0.163897 | ||||||||
\(701\) | 42.5379 | 1.60663 | 0.803317 | − | 0.595552i | \(-0.203067\pi\) | ||||
0.803317 | + | 0.595552i | \(0.203067\pi\) | |||||||
\(702\) | 0.409227 | 0.0154453 | ||||||||
\(703\) | −17.4911 | −0.659688 | ||||||||
\(704\) | −4.74553 | −0.178854 | ||||||||
\(705\) | −1.51115 | −0.0569132 | ||||||||
\(706\) | −3.55286 | −0.133714 | ||||||||
\(707\) | 36.9456 | 1.38948 | ||||||||
\(708\) | −1.71653 | −0.0645111 | ||||||||
\(709\) | −22.8319 | −0.857468 | −0.428734 | − | 0.903431i | \(-0.641040\pi\) | ||||
−0.428734 | + | 0.903431i | \(0.641040\pi\) | |||||||
\(710\) | 8.11084 | 0.304394 | ||||||||
\(711\) | 7.64878 | 0.286851 | ||||||||
\(712\) | 9.08700 | 0.340550 | ||||||||
\(713\) | −22.5631 | −0.844996 | ||||||||
\(714\) | 25.0401 | 0.937103 | ||||||||
\(715\) | 1.94200 | 0.0726266 | ||||||||
\(716\) | −1.92038 | −0.0717679 | ||||||||
\(717\) | −9.23955 | −0.345057 | ||||||||
\(718\) | 22.0230 | 0.821891 | ||||||||
\(719\) | −11.3869 | −0.424661 | −0.212330 | − | 0.977198i | \(-0.568105\pi\) | ||||
−0.212330 | + | 0.977198i | \(0.568105\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | −58.5013 | −2.17870 | ||||||||
\(722\) | −14.3452 | −0.533874 | ||||||||
\(723\) | −6.17859 | −0.229784 | ||||||||
\(724\) | 17.4032 | 0.646785 | ||||||||
\(725\) | −1.30730 | −0.0485520 | ||||||||
\(726\) | 11.5201 | 0.427550 | ||||||||
\(727\) | 8.38761 | 0.311079 | 0.155540 | − | 0.987830i | \(-0.450288\pi\) | ||||
0.155540 | + | 0.987830i | \(0.450288\pi\) | |||||||
\(728\) | −1.77453 | −0.0657685 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.05800 | −0.298240 | ||||||||
\(731\) | −54.8064 | −2.02709 | ||||||||
\(732\) | −6.33630 | −0.234197 | ||||||||
\(733\) | −18.8244 | −0.695295 | −0.347648 | − | 0.937625i | \(-0.613019\pi\) | ||||
−0.347648 | + | 0.937625i | \(0.613019\pi\) | |||||||
\(734\) | 2.34300 | 0.0864819 | ||||||||
\(735\) | 11.8035 | 0.435380 | ||||||||
\(736\) | 9.36530 | 0.345210 | ||||||||
\(737\) | 4.74553 | 0.174804 | ||||||||
\(738\) | −1.71653 | −0.0631863 | ||||||||
\(739\) | −1.86238 | −0.0685086 | −0.0342543 | − | 0.999413i | \(-0.510906\pi\) | ||||
−0.0342543 | + | 0.999413i | \(0.510906\pi\) | |||||||
\(740\) | −3.02900 | −0.111348 | ||||||||
\(741\) | 2.36309 | 0.0868104 | ||||||||
\(742\) | 46.2797 | 1.69898 | ||||||||
\(743\) | 3.21504 | 0.117948 | 0.0589741 | − | 0.998260i | \(-0.481217\pi\) | ||||
0.0589741 | + | 0.998260i | \(0.481217\pi\) | |||||||
\(744\) | 2.40923 | 0.0883265 | ||||||||
\(745\) | 1.30730 | 0.0478959 | ||||||||
\(746\) | −16.9360 | −0.620071 | ||||||||
\(747\) | 8.57806 | 0.313855 | ||||||||
\(748\) | −27.4032 | −1.00196 | ||||||||
\(749\) | −38.2395 | −1.39724 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 14.9821 | 0.546705 | 0.273353 | − | 0.961914i | \(-0.411867\pi\) | ||||
0.273353 | + | 0.961914i | \(0.411867\pi\) | |||||||
\(752\) | −1.51115 | −0.0551060 | ||||||||
\(753\) | 6.97100 | 0.254037 | ||||||||
\(754\) | 0.534983 | 0.0194829 | ||||||||
\(755\) | 15.3385 | 0.558226 | ||||||||
\(756\) | −4.33630 | −0.157710 | ||||||||
\(757\) | 47.8749 | 1.74004 | 0.870021 | − | 0.493015i | \(-0.164105\pi\) | ||||
0.870021 | + | 0.493015i | \(0.164105\pi\) | |||||||
\(758\) | −7.93378 | −0.288168 | ||||||||
\(759\) | −44.4433 | −1.61319 | ||||||||
\(760\) | −5.77453 | −0.209464 | ||||||||
\(761\) | 10.3266 | 0.374337 | 0.187169 | − | 0.982328i | \(-0.440069\pi\) | ||||
0.187169 | + | 0.982328i | \(0.440069\pi\) | |||||||
\(762\) | −9.23955 | −0.334714 | ||||||||
\(763\) | −77.5564 | −2.80773 | ||||||||
\(764\) | −2.50894 | −0.0907702 | ||||||||
\(765\) | −5.77453 | −0.208779 | ||||||||
\(766\) | −26.3742 | −0.952939 | ||||||||
\(767\) | 0.702450 | 0.0253640 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −9.60264 | −0.346280 | −0.173140 | − | 0.984897i | \(-0.555391\pi\) | ||||
−0.173140 | + | 0.984897i | \(0.555391\pi\) | |||||||
\(770\) | −20.5781 | −0.741582 | ||||||||
\(771\) | −14.7090 | −0.529731 | ||||||||
\(772\) | 25.9382 | 0.933536 | ||||||||
\(773\) | −32.7151 | −1.17668 | −0.588340 | − | 0.808613i | \(-0.700218\pi\) | ||||
−0.588340 | + | 0.808613i | \(0.700218\pi\) | |||||||
\(774\) | 9.49106 | 0.341149 | ||||||||
\(775\) | 2.40923 | 0.0865420 | ||||||||
\(776\) | 4.74553 | 0.170355 | ||||||||
\(777\) | −13.1347 | −0.471204 | ||||||||
\(778\) | −39.4277 | −1.41355 | ||||||||
\(779\) | −9.91216 | −0.355140 | ||||||||
\(780\) | 0.409227 | 0.0146527 | ||||||||
\(781\) | −38.4902 | −1.37729 | ||||||||
\(782\) | 54.0802 | 1.93391 | ||||||||
\(783\) | 1.30730 | 0.0467192 | ||||||||
\(784\) | 11.8035 | 0.421555 | ||||||||
\(785\) | 7.79615 | 0.278257 | ||||||||
\(786\) | −18.9561 | −0.676141 | ||||||||
\(787\) | −15.3795 | −0.548219 | −0.274110 | − | 0.961698i | \(-0.588383\pi\) | ||||
−0.274110 | + | 0.961698i | \(0.588383\pi\) | |||||||
\(788\) | −1.18155 | −0.0420909 | ||||||||
\(789\) | −8.79836 | −0.313230 | ||||||||
\(790\) | 7.64878 | 0.272131 | ||||||||
\(791\) | −16.7775 | −0.596539 | ||||||||
\(792\) | 4.74553 | 0.168625 | ||||||||
\(793\) | 2.59299 | 0.0920796 | ||||||||
\(794\) | 23.8073 | 0.844889 | ||||||||
\(795\) | −10.6726 | −0.378518 | ||||||||
\(796\) | −16.5781 | −0.587594 | ||||||||
\(797\) | −24.5260 | −0.868756 | −0.434378 | − | 0.900731i | \(-0.643032\pi\) | ||||
−0.434378 | + | 0.900731i | \(0.643032\pi\) | |||||||
\(798\) | −25.0401 | −0.886411 | ||||||||
\(799\) | −8.72619 | −0.308710 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −9.08700 | −0.321073 | ||||||||
\(802\) | 17.8109 | 0.628925 | ||||||||
\(803\) | 38.2395 | 1.34944 | ||||||||
\(804\) | 1.00000 | 0.0352673 | ||||||||
\(805\) | 40.6108 | 1.43134 | ||||||||
\(806\) | −0.985920 | −0.0347276 | ||||||||
\(807\) | −28.8564 | −1.01579 | ||||||||
\(808\) | −8.52006 | −0.299735 | ||||||||
\(809\) | 26.0000 | 0.914111 | 0.457056 | − | 0.889438i | \(-0.348904\pi\) | ||||
0.457056 | + | 0.889438i | \(0.348904\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −36.9329 | −1.29689 | −0.648445 | − | 0.761261i | \(-0.724581\pi\) | ||||
−0.648445 | + | 0.761261i | \(0.724581\pi\) | |||||||
\(812\) | −5.66886 | −0.198938 | ||||||||
\(813\) | −13.8124 | −0.484424 | ||||||||
\(814\) | 14.3742 | 0.503816 | ||||||||
\(815\) | 6.97100 | 0.244183 | ||||||||
\(816\) | −5.77453 | −0.202149 | ||||||||
\(817\) | 54.8064 | 1.91743 | ||||||||
\(818\) | −9.18155 | −0.321025 | ||||||||
\(819\) | 1.77453 | 0.0620072 | ||||||||
\(820\) | −1.71653 | −0.0599438 | ||||||||
\(821\) | 45.4991 | 1.58793 | 0.793965 | − | 0.607963i | \(-0.208013\pi\) | ||||
0.793965 | + | 0.607963i | \(0.208013\pi\) | |||||||
\(822\) | −0.970999 | −0.0338675 | ||||||||
\(823\) | 28.9241 | 1.00823 | 0.504116 | − | 0.863636i | \(-0.331818\pi\) | ||||
0.504116 | + | 0.863636i | \(0.331818\pi\) | |||||||
\(824\) | 13.4911 | 0.469983 | ||||||||
\(825\) | 4.74553 | 0.165218 | ||||||||
\(826\) | −7.44340 | −0.258989 | ||||||||
\(827\) | −31.0767 | −1.08064 | −0.540321 | − | 0.841459i | \(-0.681697\pi\) | ||||
−0.540321 | + | 0.841459i | \(0.681697\pi\) | |||||||
\(828\) | −9.36530 | −0.325467 | ||||||||
\(829\) | 10.2217 | 0.355013 | 0.177507 | − | 0.984120i | \(-0.443197\pi\) | ||||
0.177507 | + | 0.984120i | \(0.443197\pi\) | |||||||
\(830\) | 8.57806 | 0.297749 | ||||||||
\(831\) | 3.28051 | 0.113800 | ||||||||
\(832\) | 0.409227 | 0.0141874 | ||||||||
\(833\) | 68.1599 | 2.36160 | ||||||||
\(834\) | 9.41144 | 0.325891 | ||||||||
\(835\) | −0.546851 | −0.0189246 | ||||||||
\(836\) | 27.4032 | 0.947760 | ||||||||
\(837\) | −2.40923 | −0.0832751 | ||||||||
\(838\) | 12.3013 | 0.424941 | ||||||||
\(839\) | −55.7870 | −1.92598 | −0.962991 | − | 0.269533i | \(-0.913131\pi\) | ||||
−0.962991 | + | 0.269533i | \(0.913131\pi\) | |||||||
\(840\) | −4.33630 | −0.149617 | ||||||||
\(841\) | −27.2910 | −0.941068 | ||||||||
\(842\) | −32.8363 | −1.13161 | ||||||||
\(843\) | −0.363093 | −0.0125056 | ||||||||
\(844\) | −25.0617 | −0.862661 | ||||||||
\(845\) | 12.8325 | 0.441453 | ||||||||
\(846\) | 1.51115 | 0.0519544 | ||||||||
\(847\) | 49.9545 | 1.71646 | ||||||||
\(848\) | −10.6726 | −0.366499 | ||||||||
\(849\) | −12.1570 | −0.417226 | ||||||||
\(850\) | −5.77453 | −0.198065 | ||||||||
\(851\) | −28.3675 | −0.972426 | ||||||||
\(852\) | −8.11084 | −0.277873 | ||||||||
\(853\) | 31.9880 | 1.09525 | 0.547624 | − | 0.836725i | \(-0.315533\pi\) | ||||
0.547624 | + | 0.836725i | \(0.315533\pi\) | |||||||
\(854\) | −27.4761 | −0.940214 | ||||||||
\(855\) | 5.77453 | 0.197485 | ||||||||
\(856\) | 8.81845 | 0.301409 | ||||||||
\(857\) | 29.4329 | 1.00541 | 0.502704 | − | 0.864458i | \(-0.332338\pi\) | ||||
0.502704 | + | 0.864458i | \(0.332338\pi\) | |||||||
\(858\) | −1.94200 | −0.0662987 | ||||||||
\(859\) | −14.5306 | −0.495776 | −0.247888 | − | 0.968789i | \(-0.579737\pi\) | ||||
−0.247888 | + | 0.968789i | \(0.579737\pi\) | |||||||
\(860\) | 9.49106 | 0.323643 | ||||||||
\(861\) | −7.44340 | −0.253670 | ||||||||
\(862\) | 41.0051 | 1.39664 | ||||||||
\(863\) | −20.9442 | −0.712949 | −0.356475 | − | 0.934305i | \(-0.616021\pi\) | ||||
−0.356475 | + | 0.934305i | \(0.616021\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 16.3147 | 0.554716 | ||||||||
\(866\) | −23.5274 | −0.799495 | ||||||||
\(867\) | −16.3452 | −0.555113 | ||||||||
\(868\) | 10.4471 | 0.354599 | ||||||||
\(869\) | −36.2975 | −1.23131 | ||||||||
\(870\) | 1.30730 | 0.0443217 | ||||||||
\(871\) | −0.409227 | −0.0138661 | ||||||||
\(872\) | 17.8854 | 0.605675 | ||||||||
\(873\) | −4.74553 | −0.160612 | ||||||||
\(874\) | −54.0802 | −1.82929 | ||||||||
\(875\) | −4.33630 | −0.146594 | ||||||||
\(876\) | 8.05800 | 0.272255 | ||||||||
\(877\) | −42.5789 | −1.43779 | −0.718893 | − | 0.695121i | \(-0.755351\pi\) | ||||
−0.718893 | + | 0.695121i | \(0.755351\pi\) | |||||||
\(878\) | 22.0691 | 0.744797 | ||||||||
\(879\) | 0.871287 | 0.0293878 | ||||||||
\(880\) | 4.74553 | 0.159972 | ||||||||
\(881\) | −40.1851 | −1.35387 | −0.676936 | − | 0.736042i | \(-0.736692\pi\) | ||||
−0.676936 | + | 0.736042i | \(0.736692\pi\) | |||||||
\(882\) | −11.8035 | −0.397446 | ||||||||
\(883\) | −38.1637 | −1.28431 | −0.642155 | − | 0.766575i | \(-0.721959\pi\) | ||||
−0.642155 | + | 0.766575i | \(0.721959\pi\) | |||||||
\(884\) | 2.36309 | 0.0794794 | ||||||||
\(885\) | 1.71653 | 0.0577005 | ||||||||
\(886\) | −7.54906 | −0.253616 | ||||||||
\(887\) | 22.4353 | 0.753303 | 0.376651 | − | 0.926355i | \(-0.377075\pi\) | ||||
0.376651 | + | 0.926355i | \(0.377075\pi\) | |||||||
\(888\) | 3.02900 | 0.101647 | ||||||||
\(889\) | −40.0655 | −1.34375 | ||||||||
\(890\) | −9.08700 | −0.304597 | ||||||||
\(891\) | −4.74553 | −0.158981 | ||||||||
\(892\) | −25.8586 | −0.865809 | ||||||||
\(893\) | 8.72619 | 0.292011 | ||||||||
\(894\) | −1.30730 | −0.0437228 | ||||||||
\(895\) | 1.92038 | 0.0641911 | ||||||||
\(896\) | −4.33630 | −0.144866 | ||||||||
\(897\) | 3.83253 | 0.127965 | ||||||||
\(898\) | −27.4398 | −0.915677 | ||||||||
\(899\) | −3.14959 | −0.105045 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −61.6293 | −2.05317 | ||||||||
\(902\) | 8.14585 | 0.271227 | ||||||||
\(903\) | 41.1561 | 1.36959 | ||||||||
\(904\) | 3.86908 | 0.128684 | ||||||||
\(905\) | −17.4032 | −0.578503 | ||||||||
\(906\) | −15.3385 | −0.509588 | ||||||||
\(907\) | 45.2945 | 1.50398 | 0.751990 | − | 0.659174i | \(-0.229094\pi\) | ||||
0.751990 | + | 0.659174i | \(0.229094\pi\) | |||||||
\(908\) | 17.7127 | 0.587818 | ||||||||
\(909\) | 8.52006 | 0.282593 | ||||||||
\(910\) | 1.77453 | 0.0588252 | ||||||||
\(911\) | −6.75528 | −0.223813 | −0.111906 | − | 0.993719i | \(-0.535696\pi\) | ||||
−0.111906 | + | 0.993719i | \(0.535696\pi\) | |||||||
\(912\) | 5.77453 | 0.191214 | ||||||||
\(913\) | −40.7075 | −1.34722 | ||||||||
\(914\) | 14.3891 | 0.475950 | ||||||||
\(915\) | 6.33630 | 0.209472 | ||||||||
\(916\) | −15.8274 | −0.522951 | ||||||||
\(917\) | −82.1993 | −2.71446 | ||||||||
\(918\) | 5.77453 | 0.190588 | ||||||||
\(919\) | −1.48511 | −0.0489891 | −0.0244946 | − | 0.999700i | \(-0.507798\pi\) | ||||
−0.0244946 | + | 0.999700i | \(0.507798\pi\) | |||||||
\(920\) | −9.36530 | −0.308765 | ||||||||
\(921\) | −26.4583 | −0.871829 | ||||||||
\(922\) | 14.5365 | 0.478735 | ||||||||
\(923\) | 3.31917 | 0.109252 | ||||||||
\(924\) | 20.5781 | 0.676969 | ||||||||
\(925\) | 3.02900 | 0.0995929 | ||||||||
\(926\) | −11.6124 | −0.381607 | ||||||||
\(927\) | −13.4911 | −0.443105 | ||||||||
\(928\) | 1.30730 | 0.0429143 | ||||||||
\(929\) | 30.3490 | 0.995717 | 0.497859 | − | 0.867258i | \(-0.334120\pi\) | ||||
0.497859 | + | 0.867258i | \(0.334120\pi\) | |||||||
\(930\) | −2.40923 | −0.0790017 | ||||||||
\(931\) | −68.1599 | −2.23385 | ||||||||
\(932\) | −22.4322 | −0.734792 | ||||||||
\(933\) | 26.1637 | 0.856560 | ||||||||
\(934\) | −8.88316 | −0.290666 | ||||||||
\(935\) | 27.4032 | 0.896181 | ||||||||
\(936\) | −0.409227 | −0.0133760 | ||||||||
\(937\) | −53.1992 | −1.73794 | −0.868971 | − | 0.494863i | \(-0.835218\pi\) | ||||
−0.868971 | + | 0.494863i | \(0.835218\pi\) | |||||||
\(938\) | 4.33630 | 0.141585 | ||||||||
\(939\) | −12.4404 | −0.405978 | ||||||||
\(940\) | 1.51115 | 0.0492883 | ||||||||
\(941\) | 32.2395 | 1.05098 | 0.525489 | − | 0.850801i | \(-0.323882\pi\) | ||||
0.525489 | + | 0.850801i | \(0.323882\pi\) | |||||||
\(942\) | −7.79615 | −0.254012 | ||||||||
\(943\) | −16.0758 | −0.523501 | ||||||||
\(944\) | 1.71653 | 0.0558683 | ||||||||
\(945\) | 4.33630 | 0.141060 | ||||||||
\(946\) | −45.0401 | −1.46438 | ||||||||
\(947\) | −27.7060 | −0.900325 | −0.450163 | − | 0.892947i | \(-0.648634\pi\) | ||||
−0.450163 | + | 0.892947i | \(0.648634\pi\) | |||||||
\(948\) | −7.64878 | −0.248421 | ||||||||
\(949\) | −3.29755 | −0.107043 | ||||||||
\(950\) | 5.77453 | 0.187351 | ||||||||
\(951\) | 31.2558 | 1.01354 | ||||||||
\(952\) | −25.0401 | −0.811555 | ||||||||
\(953\) | −50.3771 | −1.63187 | −0.815937 | − | 0.578140i | \(-0.803779\pi\) | ||||
−0.815937 | + | 0.578140i | \(0.803779\pi\) | |||||||
\(954\) | 10.6726 | 0.345538 | ||||||||
\(955\) | 2.50894 | 0.0811873 | ||||||||
\(956\) | 9.23955 | 0.298828 | ||||||||
\(957\) | −6.20385 | −0.200542 | ||||||||
\(958\) | −24.5319 | −0.792591 | ||||||||
\(959\) | −4.21055 | −0.135966 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −25.1956 | −0.812762 | ||||||||
\(962\) | −1.23955 | −0.0399646 | ||||||||
\(963\) | −8.81845 | −0.284171 | ||||||||
\(964\) | 6.17859 | 0.198999 | ||||||||
\(965\) | −25.9382 | −0.834980 | ||||||||
\(966\) | −40.6108 | −1.30663 | ||||||||
\(967\) | 2.23675 | 0.0719291 | 0.0359646 | − | 0.999353i | \(-0.488550\pi\) | ||||
0.0359646 | + | 0.999353i | \(0.488550\pi\) | |||||||
\(968\) | −11.5201 | −0.370269 | ||||||||
\(969\) | 33.3452 | 1.07120 | ||||||||
\(970\) | −4.74553 | −0.152370 | ||||||||
\(971\) | 37.2878 | 1.19662 | 0.598312 | − | 0.801263i | \(-0.295838\pi\) | ||||
0.598312 | + | 0.801263i | \(0.295838\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 40.8109 | 1.30834 | ||||||||
\(974\) | 12.9553 | 0.415116 | ||||||||
\(975\) | −0.409227 | −0.0131057 | ||||||||
\(976\) | 6.33630 | 0.202820 | ||||||||
\(977\) | 13.5261 | 0.432738 | 0.216369 | − | 0.976312i | \(-0.430579\pi\) | ||||
0.216369 | + | 0.976312i | \(0.430579\pi\) | |||||||
\(978\) | −6.97100 | −0.222908 | ||||||||
\(979\) | 43.1227 | 1.37821 | ||||||||
\(980\) | −11.8035 | −0.377050 | ||||||||
\(981\) | −17.8854 | −0.571036 | ||||||||
\(982\) | −27.6911 | −0.883659 | ||||||||
\(983\) | −59.9924 | −1.91346 | −0.956730 | − | 0.290976i | \(-0.906020\pi\) | ||||
−0.956730 | + | 0.290976i | \(0.906020\pi\) | |||||||
\(984\) | 1.71653 | 0.0547210 | ||||||||
\(985\) | 1.18155 | 0.0376472 | ||||||||
\(986\) | 7.54906 | 0.240411 | ||||||||
\(987\) | 6.55281 | 0.208578 | ||||||||
\(988\) | −2.36309 | −0.0751800 | ||||||||
\(989\) | 88.8867 | 2.82643 | ||||||||
\(990\) | −4.74553 | −0.150823 | ||||||||
\(991\) | 3.37353 | 0.107164 | 0.0535818 | − | 0.998563i | \(-0.482936\pi\) | ||||
0.0535818 | + | 0.998563i | \(0.482936\pi\) | |||||||
\(992\) | −2.40923 | −0.0764930 | ||||||||
\(993\) | −28.6041 | −0.907724 | ||||||||
\(994\) | −35.1710 | −1.11556 | ||||||||
\(995\) | 16.5781 | 0.525560 | ||||||||
\(996\) | −8.57806 | −0.271806 | ||||||||
\(997\) | −10.0647 | −0.318752 | −0.159376 | − | 0.987218i | \(-0.550948\pi\) | ||||
−0.159376 | + | 0.987218i | \(0.550948\pi\) | |||||||
\(998\) | −32.7737 | −1.03743 | ||||||||
\(999\) | −3.02900 | −0.0958333 |
(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 | 2010.2.a.r.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 6030.2.a.bu.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2010.2.a.r.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
6030.2.a.bu.1.4 | 4 | 3.2 | odd | 2 |