Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6030,2,Mod(1,6030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6030, 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("6030.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6030 = 2 \cdot 3^{2} \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6030.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1497924188\) |
Analytic rank: | \(0\) |
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: | no (minimal twist has level 2010) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.88727\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6030.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.33630 | 1.63897 | 0.819484 | − | 0.573101i | \(-0.194260\pi\) | ||||
0.819484 | + | 0.573101i | \(0.194260\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 4.74553 | 1.43083 | 0.715416 | − | 0.698699i | \(-0.246237\pi\) | ||||
0.715416 | + | 0.698699i | \(0.246237\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.409227 | 0.113499 | 0.0567495 | − | 0.998388i | \(-0.481926\pi\) | ||||
0.0567495 | + | 0.998388i | \(0.481926\pi\) | |||||||
\(14\) | 4.33630 | 1.15893 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.77453 | −1.40053 | −0.700265 | − | 0.713883i | \(-0.746935\pi\) | ||||
−0.700265 | + | 0.713883i | \(0.746935\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.77453 | −1.32477 | −0.662384 | − | 0.749164i | \(-0.730455\pi\) | ||||
−0.662384 | + | 0.749164i | \(0.730455\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.74553 | 1.01175 | ||||||||
\(23\) | 9.36530 | 1.95280 | 0.976401 | − | 0.215968i | \(-0.0692906\pi\) | ||||
0.976401 | + | 0.215968i | \(0.0692906\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.409227 | 0.0802560 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.33630 | 0.819484 | ||||||||
\(29\) | 1.30730 | 0.242760 | 0.121380 | − | 0.992606i | \(-0.461268\pi\) | ||||
0.121380 | + | 0.992606i | \(0.461268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.40923 | 0.432710 | 0.216355 | − | 0.976315i | \(-0.430583\pi\) | ||||
0.216355 | + | 0.976315i | \(0.430583\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.77453 | −0.990324 | ||||||||
\(35\) | 4.33630 | 0.732969 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 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 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −1.71653 | −0.268077 | −0.134038 | − | 0.990976i | \(-0.542795\pi\) | ||||
−0.134038 | + | 0.990976i | \(0.542795\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.49106 | −1.44737 | −0.723687 | − | 0.690129i | \(-0.757554\pi\) | ||||
−0.723687 | + | 0.690129i | \(0.757554\pi\) | |||||||
\(44\) | 4.74553 | 0.715416 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.36530 | 1.38084 | ||||||||
\(47\) | 1.51115 | 0.220424 | 0.110212 | − | 0.993908i | \(-0.464847\pi\) | ||||
0.110212 | + | 0.993908i | \(0.464847\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.8035 | 1.68622 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.409227 | 0.0567495 | ||||||||
\(53\) | 10.6726 | 1.46600 | 0.732998 | − | 0.680231i | \(-0.238121\pi\) | ||||
0.732998 | + | 0.680231i | \(0.238121\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.74553 | 0.639887 | ||||||||
\(56\) | 4.33630 | 0.579463 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.30730 | 0.171657 | ||||||||
\(59\) | −1.71653 | −0.223473 | −0.111737 | − | 0.993738i | \(-0.535641\pi\) | ||||
−0.111737 | + | 0.993738i | \(0.535641\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.33630 | 0.811281 | 0.405640 | − | 0.914033i | \(-0.367049\pi\) | ||||
0.405640 | + | 0.914033i | \(0.367049\pi\) | |||||||
\(62\) | 2.40923 | 0.305972 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.409227 | 0.0507583 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | −0.122169 | ||||||||
\(68\) | −5.77453 | −0.700265 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.33630 | 0.518287 | ||||||||
\(71\) | −8.11084 | −0.962579 | −0.481290 | − | 0.876562i | \(-0.659831\pi\) | ||||
−0.481290 | + | 0.876562i | \(0.659831\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.05800 | −0.943118 | −0.471559 | − | 0.881835i | \(-0.656309\pi\) | ||||
−0.471559 | + | 0.881835i | \(0.656309\pi\) | |||||||
\(74\) | 3.02900 | 0.352114 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.77453 | −0.662384 | ||||||||
\(77\) | 20.5781 | 2.34509 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.64878 | 0.860554 | 0.430277 | − | 0.902697i | \(-0.358416\pi\) | ||||
0.430277 | + | 0.902697i | \(0.358416\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.71653 | −0.189559 | ||||||||
\(83\) | −8.57806 | −0.941565 | −0.470782 | − | 0.882249i | \(-0.656028\pi\) | ||||
−0.470782 | + | 0.882249i | \(0.656028\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.77453 | −0.626336 | ||||||||
\(86\) | −9.49106 | −1.02345 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.74553 | 0.505875 | ||||||||
\(89\) | 9.08700 | 0.963220 | 0.481610 | − | 0.876386i | \(-0.340052\pi\) | ||||
0.481610 | + | 0.876386i | \(0.340052\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.77453 | 0.186021 | ||||||||
\(92\) | 9.36530 | 0.976401 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.51115 | 0.155863 | ||||||||
\(95\) | −5.77453 | −0.592454 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.74553 | −0.481836 | −0.240918 | − | 0.970546i | \(-0.577448\pi\) | ||||
−0.240918 | + | 0.970546i | \(0.577448\pi\) | |||||||
\(98\) | 11.8035 | 1.19234 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −8.52006 | −0.847778 | −0.423889 | − | 0.905714i | \(-0.639335\pi\) | ||||
−0.423889 | + | 0.905714i | \(0.639335\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.4911 | −1.32931 | −0.664657 | − | 0.747149i | \(-0.731422\pi\) | ||||
−0.664657 | + | 0.747149i | \(0.731422\pi\) | |||||||
\(104\) | 0.409227 | 0.0401280 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.6726 | 1.03662 | ||||||||
\(107\) | 8.81845 | 0.852512 | 0.426256 | − | 0.904603i | \(-0.359832\pi\) | ||||
0.426256 | + | 0.904603i | \(0.359832\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.8854 | −1.71311 | −0.856554 | − | 0.516058i | \(-0.827399\pi\) | ||||
−0.856554 | + | 0.516058i | \(0.827399\pi\) | |||||||
\(110\) | 4.74553 | 0.452469 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.33630 | 0.409742 | ||||||||
\(113\) | 3.86908 | 0.363972 | 0.181986 | − | 0.983301i | \(-0.441747\pi\) | ||||
0.181986 | + | 0.983301i | \(0.441747\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.36530 | 0.873319 | ||||||||
\(116\) | 1.30730 | 0.121380 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.71653 | −0.158019 | ||||||||
\(119\) | −25.0401 | −2.29542 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.5201 | 1.04728 | ||||||||
\(122\) | 6.33630 | 0.573662 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.40923 | 0.216355 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.23955 | −0.819877 | −0.409939 | − | 0.912113i | \(-0.634450\pi\) | ||||
−0.409939 | + | 0.912113i | \(0.634450\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.409227 | 0.0358916 | ||||||||
\(131\) | 18.9561 | 1.65620 | 0.828100 | − | 0.560580i | \(-0.189422\pi\) | ||||
0.828100 | + | 0.560580i | \(0.189422\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −25.0401 | −2.17125 | ||||||||
\(134\) | −1.00000 | −0.0863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.77453 | −0.495162 | ||||||||
\(137\) | 0.970999 | 0.0829581 | 0.0414790 | − | 0.999139i | \(-0.486793\pi\) | ||||
0.0414790 | + | 0.999139i | \(0.486793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.41144 | 0.798268 | 0.399134 | − | 0.916893i | \(-0.369311\pi\) | ||||
0.399134 | + | 0.916893i | \(0.369311\pi\) | |||||||
\(140\) | 4.33630 | 0.366485 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.11084 | −0.680646 | ||||||||
\(143\) | 1.94200 | 0.162398 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.30730 | 0.108566 | ||||||||
\(146\) | −8.05800 | −0.666885 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.02900 | 0.248982 | ||||||||
\(149\) | 1.30730 | 0.107098 | 0.0535492 | − | 0.998565i | \(-0.482947\pi\) | ||||
0.0535492 | + | 0.998565i | \(0.482947\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.3385 | −1.24823 | −0.624115 | − | 0.781332i | \(-0.714540\pi\) | ||||
−0.624115 | + | 0.781332i | \(0.714540\pi\) | |||||||
\(152\) | −5.77453 | −0.468376 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 20.5781 | 1.65823 | ||||||||
\(155\) | 2.40923 | 0.193514 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.79615 | −0.622201 | −0.311100 | − | 0.950377i | \(-0.600698\pi\) | ||||
−0.311100 | + | 0.950377i | \(0.600698\pi\) | |||||||
\(158\) | 7.64878 | 0.608504 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 40.6108 | 3.20058 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.97100 | −0.546011 | −0.273005 | − | 0.962013i | \(-0.588018\pi\) | ||||
−0.273005 | + | 0.962013i | \(0.588018\pi\) | |||||||
\(164\) | −1.71653 | −0.134038 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.57806 | −0.665787 | ||||||||
\(167\) | −0.546851 | −0.0423166 | −0.0211583 | − | 0.999776i | \(-0.506735\pi\) | ||||
−0.0211583 | + | 0.999776i | \(0.506735\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8325 | −0.987118 | ||||||||
\(170\) | −5.77453 | −0.442886 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.49106 | −0.723687 | ||||||||
\(173\) | 16.3147 | 1.24038 | 0.620191 | − | 0.784451i | \(-0.287055\pi\) | ||||
0.620191 | + | 0.784451i | \(0.287055\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.33630 | 0.327794 | ||||||||
\(176\) | 4.74553 | 0.357708 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.08700 | 0.681100 | ||||||||
\(179\) | 1.92038 | 0.143536 | 0.0717679 | − | 0.997421i | \(-0.477136\pi\) | ||||
0.0717679 | + | 0.997421i | \(0.477136\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4032 | 1.29357 | 0.646785 | − | 0.762672i | \(-0.276113\pi\) | ||||
0.646785 | + | 0.762672i | \(0.276113\pi\) | |||||||
\(182\) | 1.77453 | 0.131537 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.36530 | 0.690419 | ||||||||
\(185\) | 3.02900 | 0.222697 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −27.4032 | −2.00392 | ||||||||
\(188\) | 1.51115 | 0.110212 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.77453 | −0.418929 | ||||||||
\(191\) | 2.50894 | 0.181540 | 0.0907702 | − | 0.995872i | \(-0.471067\pi\) | ||||
0.0907702 | + | 0.995872i | \(0.471067\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 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 | 0 | ||||||||
\(196\) | 11.8035 | 0.843109 | ||||||||
\(197\) | 1.18155 | 0.0841817 | 0.0420909 | − | 0.999114i | \(-0.486598\pi\) | ||||
0.0420909 | + | 0.999114i | \(0.486598\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.5781 | −1.17519 | −0.587594 | − | 0.809156i | \(-0.699925\pi\) | ||||
−0.587594 | + | 0.809156i | \(0.699925\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.52006 | −0.599470 | ||||||||
\(203\) | 5.66886 | 0.397876 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.71653 | −0.119888 | ||||||||
\(206\) | −13.4911 | −0.939967 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.409227 | 0.0283748 | ||||||||
\(209\) | −27.4032 | −1.89552 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.0617 | −1.72532 | −0.862661 | − | 0.505783i | \(-0.831204\pi\) | ||||
−0.862661 | + | 0.505783i | \(0.831204\pi\) | |||||||
\(212\) | 10.6726 | 0.732998 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.81845 | 0.602817 | ||||||||
\(215\) | −9.49106 | −0.647285 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.4471 | 0.709198 | ||||||||
\(218\) | −17.8854 | −1.21135 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.74553 | 0.319944 | ||||||||
\(221\) | −2.36309 | −0.158959 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.8586 | −1.73162 | −0.865809 | − | 0.500374i | \(-0.833196\pi\) | ||||
−0.865809 | + | 0.500374i | \(0.833196\pi\) | |||||||
\(224\) | 4.33630 | 0.289731 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.86908 | 0.257367 | ||||||||
\(227\) | −17.7127 | −1.17564 | −0.587818 | − | 0.808993i | \(-0.700013\pi\) | ||||
−0.587818 | + | 0.808993i | \(0.700013\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.8274 | −1.04590 | −0.522951 | − | 0.852363i | \(-0.675169\pi\) | ||||
−0.522951 | + | 0.852363i | \(0.675169\pi\) | |||||||
\(230\) | 9.36530 | 0.617530 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.30730 | 0.0858287 | ||||||||
\(233\) | 22.4322 | 1.46958 | 0.734792 | − | 0.678293i | \(-0.237280\pi\) | ||||
0.734792 | + | 0.678293i | \(0.237280\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.51115 | 0.0985766 | ||||||||
\(236\) | −1.71653 | −0.111737 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −25.0401 | −1.62311 | ||||||||
\(239\) | −9.23955 | −0.597657 | −0.298828 | − | 0.954307i | \(-0.596596\pi\) | ||||
−0.298828 | + | 0.954307i | \(0.596596\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.17859 | 0.397998 | 0.198999 | − | 0.980000i | \(-0.436231\pi\) | ||||
0.198999 | + | 0.980000i | \(0.436231\pi\) | |||||||
\(242\) | 11.5201 | 0.740538 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.33630 | 0.405640 | ||||||||
\(245\) | 11.8035 | 0.754100 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.36309 | −0.150360 | ||||||||
\(248\) | 2.40923 | 0.152986 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 6.97100 | 0.440006 | 0.220003 | − | 0.975499i | \(-0.429393\pi\) | ||||
0.220003 | + | 0.975499i | \(0.429393\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 44.4433 | 2.79413 | ||||||||
\(254\) | −9.23955 | −0.579741 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.7090 | −0.917522 | −0.458761 | − | 0.888560i | \(-0.651707\pi\) | ||||
−0.458761 | + | 0.888560i | \(0.651707\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.1347 | 0.816149 | ||||||||
\(260\) | 0.409227 | 0.0253792 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.9561 | 1.17111 | ||||||||
\(263\) | −8.79836 | −0.542530 | −0.271265 | − | 0.962505i | \(-0.587442\pi\) | ||||
−0.271265 | + | 0.962505i | \(0.587442\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.6726 | 0.655613 | ||||||||
\(266\) | −25.0401 | −1.53531 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.00000 | −0.0610847 | ||||||||
\(269\) | −28.8564 | −1.75940 | −0.879702 | − | 0.475526i | \(-0.842258\pi\) | ||||
−0.879702 | + | 0.475526i | \(0.842258\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.8124 | 0.839046 | 0.419523 | − | 0.907745i | \(-0.362197\pi\) | ||||
0.419523 | + | 0.907745i | \(0.362197\pi\) | |||||||
\(272\) | −5.77453 | −0.350132 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.970999 | 0.0586602 | ||||||||
\(275\) | 4.74553 | 0.286166 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.28051 | −0.197107 | −0.0985535 | − | 0.995132i | \(-0.531422\pi\) | ||||
−0.0985535 | + | 0.995132i | \(0.531422\pi\) | |||||||
\(278\) | 9.41144 | 0.564461 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.33630 | 0.259144 | ||||||||
\(281\) | −0.363093 | −0.0216603 | −0.0108302 | − | 0.999941i | \(-0.503447\pi\) | ||||
−0.0108302 | + | 0.999941i | \(0.503447\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1570 | 0.722657 | 0.361328 | − | 0.932439i | \(-0.382323\pi\) | ||||
0.361328 | + | 0.932439i | \(0.382323\pi\) | |||||||
\(284\) | −8.11084 | −0.481290 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.94200 | 0.114833 | ||||||||
\(287\) | −7.44340 | −0.439370 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.3452 | 0.961483 | ||||||||
\(290\) | 1.30730 | 0.0767675 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.05800 | −0.471559 | ||||||||
\(293\) | 0.871287 | 0.0509012 | 0.0254506 | − | 0.999676i | \(-0.491898\pi\) | ||||
0.0254506 | + | 0.999676i | \(0.491898\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.71653 | −0.0999402 | ||||||||
\(296\) | 3.02900 | 0.176057 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.30730 | 0.0757300 | ||||||||
\(299\) | 3.83253 | 0.221641 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −41.1561 | −2.37220 | ||||||||
\(302\) | −15.3385 | −0.882632 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.77453 | −0.331192 | ||||||||
\(305\) | 6.33630 | 0.362816 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.4583 | 1.51005 | 0.755026 | − | 0.655694i | \(-0.227624\pi\) | ||||
0.755026 | + | 0.655694i | \(0.227624\pi\) | |||||||
\(308\) | 20.5781 | 1.17254 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.40923 | 0.136835 | ||||||||
\(311\) | 26.1637 | 1.48361 | 0.741803 | − | 0.670618i | \(-0.233971\pi\) | ||||
0.741803 | + | 0.670618i | \(0.233971\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.4404 | 0.703175 | 0.351588 | − | 0.936155i | \(-0.385642\pi\) | ||||
0.351588 | + | 0.936155i | \(0.385642\pi\) | |||||||
\(314\) | −7.79615 | −0.439962 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.64878 | 0.430277 | ||||||||
\(317\) | 31.2558 | 1.75550 | 0.877751 | − | 0.479116i | \(-0.159043\pi\) | ||||
0.877751 | + | 0.479116i | \(0.159043\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.20385 | 0.347349 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 40.6108 | 2.26315 | ||||||||
\(323\) | 33.3452 | 1.85538 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.409227 | 0.0226998 | ||||||||
\(326\) | −6.97100 | −0.386088 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.71653 | −0.0947795 | ||||||||
\(329\) | 6.55281 | 0.361268 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.6041 | 1.57222 | 0.786112 | − | 0.618084i | \(-0.212091\pi\) | ||||
0.786112 | + | 0.618084i | \(0.212091\pi\) | |||||||
\(332\) | −8.57806 | −0.470782 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.546851 | −0.0299224 | ||||||||
\(335\) | −1.00000 | −0.0546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.5751 | −0.957377 | −0.478689 | − | 0.877985i | \(-0.658888\pi\) | ||||
−0.478689 | + | 0.877985i | \(0.658888\pi\) | |||||||
\(338\) | −12.8325 | −0.697998 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.77453 | −0.313168 | ||||||||
\(341\) | 11.4331 | 0.619135 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.8296 | 1.12469 | ||||||||
\(344\) | −9.49106 | −0.511724 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.3147 | 0.877083 | ||||||||
\(347\) | 34.1122 | 1.83124 | 0.915620 | − | 0.402046i | \(-0.131701\pi\) | ||||
0.915620 | + | 0.402046i | \(0.131701\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −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 | 0 | ||||||||
\(352\) | 4.74553 | 0.252938 | ||||||||
\(353\) | −3.55286 | −0.189100 | −0.0945498 | − | 0.995520i | \(-0.530141\pi\) | ||||
−0.0945498 | + | 0.995520i | \(0.530141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.11084 | −0.430478 | ||||||||
\(356\) | 9.08700 | 0.481610 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.92038 | 0.101495 | ||||||||
\(359\) | 22.0230 | 1.16233 | 0.581165 | − | 0.813786i | \(-0.302597\pi\) | ||||
0.581165 | + | 0.813786i | \(0.302597\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.3452 | 0.755011 | ||||||||
\(362\) | 17.4032 | 0.914693 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.77453 | 0.0930107 | ||||||||
\(365\) | −8.05800 | −0.421775 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.34300 | −0.122304 | −0.0611519 | − | 0.998128i | \(-0.519477\pi\) | ||||
−0.0611519 | + | 0.998128i | \(0.519477\pi\) | |||||||
\(368\) | 9.36530 | 0.488200 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.02900 | 0.157470 | ||||||||
\(371\) | 46.2797 | 2.40272 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.9360 | 0.876912 | 0.438456 | − | 0.898753i | \(-0.355525\pi\) | ||||
0.438456 | + | 0.898753i | \(0.355525\pi\) | |||||||
\(374\) | −27.4032 | −1.41699 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.51115 | 0.0779316 | ||||||||
\(377\) | 0.534983 | 0.0275530 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.93378 | 0.407531 | 0.203765 | − | 0.979020i | \(-0.434682\pi\) | ||||
0.203765 | + | 0.979020i | \(0.434682\pi\) | |||||||
\(380\) | −5.77453 | −0.296227 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.50894 | 0.128368 | ||||||||
\(383\) | −26.3742 | −1.34766 | −0.673830 | − | 0.738887i | \(-0.735352\pi\) | ||||
−0.673830 | + | 0.738887i | \(0.735352\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.5781 | 1.04876 | ||||||||
\(386\) | 25.9382 | 1.32022 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.74553 | −0.240918 | ||||||||
\(389\) | −39.4277 | −1.99907 | −0.999533 | − | 0.0305693i | \(-0.990268\pi\) | ||||
−0.999533 | + | 0.0305693i | \(0.990268\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −54.0802 | −2.73496 | ||||||||
\(392\) | 11.8035 | 0.596168 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.18155 | 0.0595255 | ||||||||
\(395\) | 7.64878 | 0.384852 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.8073 | −1.19485 | −0.597426 | − | 0.801924i | \(-0.703810\pi\) | ||||
−0.597426 | + | 0.801924i | \(0.703810\pi\) | |||||||
\(398\) | −16.5781 | −0.830983 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 17.8109 | 0.889435 | 0.444717 | − | 0.895671i | \(-0.353304\pi\) | ||||
0.444717 | + | 0.895671i | \(0.353304\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.985920 | 0.0491122 | ||||||||
\(404\) | −8.52006 | −0.423889 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.66886 | 0.281341 | ||||||||
\(407\) | 14.3742 | 0.712503 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 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 | 0 | ||||||||
\(412\) | −13.4911 | −0.664657 | ||||||||
\(413\) | −7.44340 | −0.366266 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.57806 | −0.421081 | ||||||||
\(416\) | 0.409227 | 0.0200640 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −27.4032 | −1.34034 | ||||||||
\(419\) | 12.3013 | 0.600958 | 0.300479 | − | 0.953789i | \(-0.402854\pi\) | ||||
0.300479 | + | 0.953789i | \(0.402854\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.8363 | 1.60034 | 0.800171 | − | 0.599772i | \(-0.204742\pi\) | ||||
0.800171 | + | 0.599772i | \(0.204742\pi\) | |||||||
\(422\) | −25.0617 | −1.21999 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.6726 | 0.518308 | ||||||||
\(425\) | −5.77453 | −0.280106 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.4761 | 1.32966 | ||||||||
\(428\) | 8.81845 | 0.426256 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.49106 | −0.457700 | ||||||||
\(431\) | 41.0051 | 1.97515 | 0.987573 | − | 0.157158i | \(-0.0502332\pi\) | ||||
0.987573 | + | 0.157158i | \(0.0502332\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.5274 | 1.13066 | 0.565328 | − | 0.824866i | \(-0.308749\pi\) | ||||
0.565328 | + | 0.824866i | \(0.308749\pi\) | |||||||
\(434\) | 10.4471 | 0.501479 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.8854 | −0.856554 | ||||||||
\(437\) | −54.0802 | −2.58701 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.0691 | −1.05330 | −0.526651 | − | 0.850082i | \(-0.676553\pi\) | ||||
−0.526651 | + | 0.850082i | \(0.676553\pi\) | |||||||
\(440\) | 4.74553 | 0.226234 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.36309 | −0.112401 | ||||||||
\(443\) | −7.54906 | −0.358667 | −0.179333 | − | 0.983788i | \(-0.557394\pi\) | ||||
−0.179333 | + | 0.983788i | \(0.557394\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.08700 | 0.430765 | ||||||||
\(446\) | −25.8586 | −1.22444 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.33630 | 0.204871 | ||||||||
\(449\) | −27.4398 | −1.29496 | −0.647481 | − | 0.762081i | \(-0.724178\pi\) | ||||
−0.647481 | + | 0.762081i | \(0.724178\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.14585 | −0.383573 | ||||||||
\(452\) | 3.86908 | 0.181986 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.7127 | −0.831300 | ||||||||
\(455\) | 1.77453 | 0.0831913 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.3891 | −0.673095 | −0.336548 | − | 0.941666i | \(-0.609259\pi\) | ||||
−0.336548 | + | 0.941666i | \(0.609259\pi\) | |||||||
\(458\) | −15.8274 | −0.739564 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.36530 | 0.436660 | ||||||||
\(461\) | 14.5365 | 0.677033 | 0.338517 | − | 0.940960i | \(-0.390075\pi\) | ||||
0.338517 | + | 0.940960i | \(0.390075\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.6124 | 0.539674 | 0.269837 | − | 0.962906i | \(-0.413030\pi\) | ||||
0.269837 | + | 0.962906i | \(0.413030\pi\) | |||||||
\(464\) | 1.30730 | 0.0606900 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.4322 | 1.03915 | ||||||||
\(467\) | −8.88316 | −0.411063 | −0.205532 | − | 0.978650i | \(-0.565892\pi\) | ||||
−0.205532 | + | 0.978650i | \(0.565892\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.33630 | −0.200232 | ||||||||
\(470\) | 1.51115 | 0.0697042 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.71653 | −0.0790097 | ||||||||
\(473\) | −45.0401 | −2.07095 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.77453 | −0.264954 | ||||||||
\(476\) | −25.0401 | −1.14771 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.23955 | −0.422607 | ||||||||
\(479\) | −24.5319 | −1.12089 | −0.560446 | − | 0.828191i | \(-0.689370\pi\) | ||||
−0.560446 | + | 0.828191i | \(0.689370\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.23955 | 0.0565185 | ||||||||
\(482\) | 6.17859 | 0.281427 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.5201 | 0.523639 | ||||||||
\(485\) | −4.74553 | −0.215483 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.9553 | −0.587062 | −0.293531 | − | 0.955950i | \(-0.594830\pi\) | ||||
−0.293531 | + | 0.955950i | \(0.594830\pi\) | |||||||
\(488\) | 6.33630 | 0.286831 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11.8035 | 0.533229 | ||||||||
\(491\) | −27.6911 | −1.24968 | −0.624841 | − | 0.780752i | \(-0.714836\pi\) | ||||
−0.624841 | + | 0.780752i | \(0.714836\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.54906 | −0.339993 | ||||||||
\(494\) | −2.36309 | −0.106321 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.40923 | 0.108177 | ||||||||
\(497\) | −35.1710 | −1.57764 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 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 | 0 | ||||||||
\(502\) | 6.97100 | 0.311131 | ||||||||
\(503\) | −20.5677 | −0.917070 | −0.458535 | − | 0.888676i | \(-0.651626\pi\) | ||||
−0.458535 | + | 0.888676i | \(0.651626\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.52006 | −0.379138 | ||||||||
\(506\) | 44.4433 | 1.97575 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.23955 | −0.409939 | ||||||||
\(509\) | 1.97991 | 0.0877580 | 0.0438790 | − | 0.999037i | \(-0.486028\pi\) | ||||
0.0438790 | + | 0.999037i | \(0.486028\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.9419 | −1.54574 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.7090 | −0.648786 | ||||||||
\(515\) | −13.4911 | −0.594487 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.17121 | 0.315389 | ||||||||
\(518\) | 13.1347 | 0.577104 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.409227 | 0.0179458 | ||||||||
\(521\) | −22.6407 | −0.991905 | −0.495952 | − | 0.868350i | \(-0.665181\pi\) | ||||
−0.495952 | + | 0.868350i | \(0.665181\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.8519 | −1.04297 | −0.521485 | − | 0.853261i | \(-0.674622\pi\) | ||||
−0.521485 | + | 0.853261i | \(0.674622\pi\) | |||||||
\(524\) | 18.9561 | 0.828100 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.79836 | −0.383627 | ||||||||
\(527\) | −13.9122 | −0.606023 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 64.7089 | 2.81343 | ||||||||
\(530\) | 10.6726 | 0.463588 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −25.0401 | −1.08563 | ||||||||
\(533\) | −0.702450 | −0.0304265 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.81845 | 0.381255 | ||||||||
\(536\) | −1.00000 | −0.0431934 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −28.8564 | −1.24409 | ||||||||
\(539\) | 56.0140 | 2.41269 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.49919 | −0.193435 | −0.0967175 | − | 0.995312i | \(-0.530834\pi\) | ||||
−0.0967175 | + | 0.995312i | \(0.530834\pi\) | |||||||
\(542\) | 13.8124 | 0.593295 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.77453 | −0.247581 | ||||||||
\(545\) | −17.8854 | −0.766125 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.68015 | 0.242866 | 0.121433 | − | 0.992600i | \(-0.461251\pi\) | ||||
0.121433 | + | 0.992600i | \(0.461251\pi\) | |||||||
\(548\) | 0.970999 | 0.0414790 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.74553 | 0.202350 | ||||||||
\(551\) | −7.54906 | −0.321601 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33.1674 | 1.41042 | ||||||||
\(554\) | −3.28051 | −0.139376 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.41144 | 0.399134 | ||||||||
\(557\) | 20.6412 | 0.874597 | 0.437299 | − | 0.899316i | \(-0.355935\pi\) | ||||
0.437299 | + | 0.899316i | \(0.355935\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.88400 | −0.164276 | ||||||||
\(560\) | 4.33630 | 0.183242 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.363093 | −0.0153162 | ||||||||
\(563\) | 2.50894 | 0.105739 | 0.0528696 | − | 0.998601i | \(-0.483163\pi\) | ||||
0.0528696 | + | 0.998601i | \(0.483163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.86908 | 0.162773 | ||||||||
\(566\) | 12.1570 | 0.510996 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.11084 | −0.340323 | ||||||||
\(569\) | −41.6138 | −1.74454 | −0.872270 | − | 0.489025i | \(-0.837353\pi\) | ||||
−0.872270 | + | 0.489025i | \(0.837353\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.5491 | 0.483313 | 0.241657 | − | 0.970362i | \(-0.422309\pi\) | ||||
0.241657 | + | 0.970362i | \(0.422309\pi\) | |||||||
\(572\) | 1.94200 | 0.0811990 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.44340 | −0.310681 | ||||||||
\(575\) | 9.36530 | 0.390560 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.6211 | −1.69108 | −0.845540 | − | 0.533912i | \(-0.820721\pi\) | ||||
−0.845540 | + | 0.533912i | \(0.820721\pi\) | |||||||
\(578\) | 16.3452 | 0.679871 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.30730 | 0.0542828 | ||||||||
\(581\) | −37.1971 | −1.54320 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 50.6472 | 2.09759 | ||||||||
\(584\) | −8.05800 | −0.333442 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.871287 | 0.0359926 | ||||||||
\(587\) | −7.82220 | −0.322857 | −0.161428 | − | 0.986884i | \(-0.551610\pi\) | ||||
−0.161428 | + | 0.986884i | \(0.551610\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.9122 | −0.573240 | ||||||||
\(590\) | −1.71653 | −0.0706684 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.02900 | 0.124491 | ||||||||
\(593\) | 12.4041 | 0.509374 | 0.254687 | − | 0.967024i | \(-0.418028\pi\) | ||||
0.254687 | + | 0.967024i | \(0.418028\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.0401 | −1.02655 | ||||||||
\(596\) | 1.30730 | 0.0535492 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.83253 | 0.156724 | ||||||||
\(599\) | −20.5134 | −0.838153 | −0.419077 | − | 0.907951i | \(-0.637646\pi\) | ||||
−0.419077 | + | 0.907951i | \(0.637646\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.4984 | 0.836149 | 0.418074 | − | 0.908413i | \(-0.362705\pi\) | ||||
0.418074 | + | 0.908413i | \(0.362705\pi\) | |||||||
\(602\) | −41.1561 | −1.67740 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.3385 | −0.624115 | ||||||||
\(605\) | 11.5201 | 0.468357 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.96430 | 0.363850 | 0.181925 | − | 0.983312i | \(-0.441767\pi\) | ||||
0.181925 | + | 0.983312i | \(0.441767\pi\) | |||||||
\(608\) | −5.77453 | −0.234188 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.33630 | 0.256549 | ||||||||
\(611\) | 0.618403 | 0.0250179 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.6904 | −1.15880 | −0.579398 | − | 0.815045i | \(-0.696712\pi\) | ||||
−0.579398 | + | 0.815045i | \(0.696712\pi\) | |||||||
\(614\) | 26.4583 | 1.06777 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20.5781 | 0.829114 | ||||||||
\(617\) | 2.85483 | 0.114931 | 0.0574656 | − | 0.998347i | \(-0.481698\pi\) | ||||
0.0574656 | + | 0.998347i | \(0.481698\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.7745 | −1.03597 | −0.517983 | − | 0.855391i | \(-0.673317\pi\) | ||||
−0.517983 | + | 0.855391i | \(0.673317\pi\) | |||||||
\(620\) | 2.40923 | 0.0967569 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.1637 | 1.04907 | ||||||||
\(623\) | 39.4040 | 1.57869 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 12.4404 | 0.497220 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.79615 | −0.311100 | ||||||||
\(629\) | −17.4911 | −0.697414 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.1398 | −1.16004 | −0.580019 | − | 0.814603i | \(-0.696955\pi\) | ||||
−0.580019 | + | 0.814603i | \(0.696955\pi\) | |||||||
\(632\) | 7.64878 | 0.304252 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 31.2558 | 1.24133 | ||||||||
\(635\) | −9.23955 | −0.366660 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.83032 | 0.191384 | ||||||||
\(638\) | 6.20385 | 0.245613 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −31.0535 | −1.22654 | −0.613270 | − | 0.789873i | \(-0.710146\pi\) | ||||
−0.613270 | + | 0.789873i | \(0.710146\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.1273 | −1.10923 | −0.554616 | − | 0.832106i | \(-0.687135\pi\) | ||||
−0.554616 | + | 0.832106i | \(0.687135\pi\) | |||||||
\(644\) | 40.6108 | 1.60029 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 33.3452 | 1.31195 | ||||||||
\(647\) | −37.2641 | −1.46500 | −0.732501 | − | 0.680766i | \(-0.761647\pi\) | ||||
−0.732501 | + | 0.680766i | \(0.761647\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.14585 | −0.319752 | ||||||||
\(650\) | 0.409227 | 0.0160512 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.97100 | −0.273005 | ||||||||
\(653\) | 11.1963 | 0.438145 | 0.219073 | − | 0.975709i | \(-0.429697\pi\) | ||||
0.219073 | + | 0.975709i | \(0.429697\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.9561 | 0.740675 | ||||||||
\(656\) | −1.71653 | −0.0670192 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.55281 | 0.255455 | ||||||||
\(659\) | 18.8727 | 0.735174 | 0.367587 | − | 0.929989i | \(-0.380184\pi\) | ||||
0.367587 | + | 0.929989i | \(0.380184\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.5290 | 0.526216 | 0.263108 | − | 0.964766i | \(-0.415252\pi\) | ||||
0.263108 | + | 0.964766i | \(0.415252\pi\) | |||||||
\(662\) | 28.6041 | 1.11173 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.57806 | −0.332893 | ||||||||
\(665\) | −25.0401 | −0.971014 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.2433 | 0.474062 | ||||||||
\(668\) | −0.546851 | −0.0211583 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.00000 | −0.0386334 | ||||||||
\(671\) | 30.0691 | 1.16081 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.2358 | −1.66662 | −0.833308 | − | 0.552809i | \(-0.813556\pi\) | ||||
−0.833308 | + | 0.552809i | \(0.813556\pi\) | |||||||
\(674\) | −17.5751 | −0.676968 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.8325 | −0.493559 | ||||||||
\(677\) | −3.63691 | −0.139778 | −0.0698888 | − | 0.997555i | \(-0.522264\pi\) | ||||
−0.0698888 | + | 0.997555i | \(0.522264\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.5781 | −0.789714 | ||||||||
\(680\) | −5.77453 | −0.221443 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.4331 | 0.437794 | ||||||||
\(683\) | −42.9523 | −1.64352 | −0.821762 | − | 0.569831i | \(-0.807009\pi\) | ||||
−0.821762 | + | 0.569831i | \(0.807009\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.970999 | 0.0371000 | ||||||||
\(686\) | 20.8296 | 0.795277 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.49106 | −0.361843 | ||||||||
\(689\) | 4.36752 | 0.166389 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.0683 | 1.63839 | 0.819197 | − | 0.573512i | \(-0.194419\pi\) | ||||
0.819197 | + | 0.573512i | \(0.194419\pi\) | |||||||
\(692\) | 16.3147 | 0.620191 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 34.1122 | 1.29488 | ||||||||
\(695\) | 9.41144 | 0.356996 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.91216 | 0.375450 | ||||||||
\(698\) | −12.9821 | −0.491381 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.33630 | 0.163897 | ||||||||
\(701\) | −42.5379 | −1.60663 | −0.803317 | − | 0.595552i | \(-0.796933\pi\) | ||||
−0.803317 | + | 0.595552i | \(0.796933\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.4911 | −0.659688 | ||||||||
\(704\) | 4.74553 | 0.178854 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.55286 | −0.133714 | ||||||||
\(707\) | −36.9456 | −1.38948 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.8319 | −0.857468 | −0.428734 | − | 0.903431i | \(-0.641040\pi\) | ||||
−0.428734 | + | 0.903431i | \(0.641040\pi\) | |||||||
\(710\) | −8.11084 | −0.304394 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.08700 | 0.340550 | ||||||||
\(713\) | 22.5631 | 0.844996 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.94200 | 0.0726266 | ||||||||
\(716\) | 1.92038 | 0.0717679 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22.0230 | 0.821891 | ||||||||
\(719\) | 11.3869 | 0.424661 | 0.212330 | − | 0.977198i | \(-0.431895\pi\) | ||||
0.212330 | + | 0.977198i | \(0.431895\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −58.5013 | −2.17870 | ||||||||
\(722\) | 14.3452 | 0.533874 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17.4032 | 0.646785 | ||||||||
\(725\) | 1.30730 | 0.0485520 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.38761 | 0.311079 | 0.155540 | − | 0.987830i | \(-0.450288\pi\) | ||||
0.155540 | + | 0.987830i | \(0.450288\pi\) | |||||||
\(728\) | 1.77453 | 0.0657685 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.05800 | −0.298240 | ||||||||
\(731\) | 54.8064 | 2.02709 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.8244 | −0.695295 | −0.347648 | − | 0.937625i | \(-0.613019\pi\) | ||||
−0.347648 | + | 0.937625i | \(0.613019\pi\) | |||||||
\(734\) | −2.34300 | −0.0864819 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.36530 | 0.345210 | ||||||||
\(737\) | −4.74553 | −0.174804 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.86238 | −0.0685086 | −0.0342543 | − | 0.999413i | \(-0.510906\pi\) | ||||
−0.0342543 | + | 0.999413i | \(0.510906\pi\) | |||||||
\(740\) | 3.02900 | 0.111348 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 46.2797 | 1.69898 | ||||||||
\(743\) | −3.21504 | −0.117948 | −0.0589741 | − | 0.998260i | \(-0.518783\pi\) | ||||
−0.0589741 | + | 0.998260i | \(0.518783\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.30730 | 0.0478959 | ||||||||
\(746\) | 16.9360 | 0.620071 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −27.4032 | −1.00196 | ||||||||
\(749\) | 38.2395 | 1.39724 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.9821 | 0.546705 | 0.273353 | − | 0.961914i | \(-0.411867\pi\) | ||||
0.273353 | + | 0.961914i | \(0.411867\pi\) | |||||||
\(752\) | 1.51115 | 0.0551060 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.534983 | 0.0194829 | ||||||||
\(755\) | −15.3385 | −0.558226 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.8749 | 1.74004 | 0.870021 | − | 0.493015i | \(-0.164105\pi\) | ||||
0.870021 | + | 0.493015i | \(0.164105\pi\) | |||||||
\(758\) | 7.93378 | 0.288168 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.77453 | −0.209464 | ||||||||
\(761\) | −10.3266 | −0.374337 | −0.187169 | − | 0.982328i | \(-0.559931\pi\) | ||||
−0.187169 | + | 0.982328i | \(0.559931\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −77.5564 | −2.80773 | ||||||||
\(764\) | 2.50894 | 0.0907702 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.3742 | −0.952939 | ||||||||
\(767\) | −0.702450 | −0.0253640 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.60264 | −0.346280 | −0.173140 | − | 0.984897i | \(-0.555391\pi\) | ||||
−0.173140 | + | 0.984897i | \(0.555391\pi\) | |||||||
\(770\) | 20.5781 | 0.741582 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 25.9382 | 0.933536 | ||||||||
\(773\) | 32.7151 | 1.17668 | 0.588340 | − | 0.808613i | \(-0.299782\pi\) | ||||
0.588340 | + | 0.808613i | \(0.299782\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.40923 | 0.0865420 | ||||||||
\(776\) | −4.74553 | −0.170355 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −39.4277 | −1.41355 | ||||||||
\(779\) | 9.91216 | 0.355140 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38.4902 | −1.37729 | ||||||||
\(782\) | −54.0802 | −1.93391 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11.8035 | 0.421555 | ||||||||
\(785\) | −7.79615 | −0.278257 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.3795 | −0.548219 | −0.274110 | − | 0.961698i | \(-0.588383\pi\) | ||||
−0.274110 | + | 0.961698i | \(0.588383\pi\) | |||||||
\(788\) | 1.18155 | 0.0420909 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.64878 | 0.272131 | ||||||||
\(791\) | 16.7775 | 0.596539 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.59299 | 0.0920796 | ||||||||
\(794\) | −23.8073 | −0.844889 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.5781 | −0.587594 | ||||||||
\(797\) | 24.5260 | 0.868756 | 0.434378 | − | 0.900731i | \(-0.356968\pi\) | ||||
0.434378 | + | 0.900731i | \(0.356968\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.72619 | −0.308710 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.8109 | 0.628925 | ||||||||
\(803\) | −38.2395 | −1.34944 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 40.6108 | 1.43134 | ||||||||
\(806\) | 0.985920 | 0.0347276 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.52006 | −0.299735 | ||||||||
\(809\) | −26.0000 | −0.914111 | −0.457056 | − | 0.889438i | \(-0.651096\pi\) | ||||
−0.457056 | + | 0.889438i | \(0.651096\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.9329 | −1.29689 | −0.648445 | − | 0.761261i | \(-0.724581\pi\) | ||||
−0.648445 | + | 0.761261i | \(0.724581\pi\) | |||||||
\(812\) | 5.66886 | 0.198938 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.3742 | 0.503816 | ||||||||
\(815\) | −6.97100 | −0.244183 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 54.8064 | 1.91743 | ||||||||
\(818\) | 9.18155 | 0.321025 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.71653 | −0.0599438 | ||||||||
\(821\) | −45.4991 | −1.58793 | −0.793965 | − | 0.607963i | \(-0.791987\pi\) | ||||
−0.793965 | + | 0.607963i | \(0.791987\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.9241 | 1.00823 | 0.504116 | − | 0.863636i | \(-0.331818\pi\) | ||||
0.504116 | + | 0.863636i | \(0.331818\pi\) | |||||||
\(824\) | −13.4911 | −0.469983 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.44340 | −0.258989 | ||||||||
\(827\) | 31.0767 | 1.08064 | 0.540321 | − | 0.841459i | \(-0.318303\pi\) | ||||
0.540321 | + | 0.841459i | \(0.318303\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.2217 | 0.355013 | 0.177507 | − | 0.984120i | \(-0.443197\pi\) | ||||
0.177507 | + | 0.984120i | \(0.443197\pi\) | |||||||
\(830\) | −8.57806 | −0.297749 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.409227 | 0.0141874 | ||||||||
\(833\) | −68.1599 | −2.36160 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.546851 | −0.0189246 | ||||||||
\(836\) | −27.4032 | −0.947760 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.3013 | 0.424941 | ||||||||
\(839\) | 55.7870 | 1.92598 | 0.962991 | − | 0.269533i | \(-0.0868695\pi\) | ||||
0.962991 | + | 0.269533i | \(0.0868695\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2910 | −0.941068 | ||||||||
\(842\) | 32.8363 | 1.13161 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −25.0617 | −0.862661 | ||||||||
\(845\) | −12.8325 | −0.441453 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 49.9545 | 1.71646 | ||||||||
\(848\) | 10.6726 | 0.366499 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.77453 | −0.198065 | ||||||||
\(851\) | 28.3675 | 0.972426 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.9880 | 1.09525 | 0.547624 | − | 0.836725i | \(-0.315533\pi\) | ||||
0.547624 | + | 0.836725i | \(0.315533\pi\) | |||||||
\(854\) | 27.4761 | 0.940214 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.81845 | 0.301409 | ||||||||
\(857\) | −29.4329 | −1.00541 | −0.502704 | − | 0.864458i | \(-0.667662\pi\) | ||||
−0.502704 | + | 0.864458i | \(0.667662\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.5306 | −0.495776 | −0.247888 | − | 0.968789i | \(-0.579737\pi\) | ||||
−0.247888 | + | 0.968789i | \(0.579737\pi\) | |||||||
\(860\) | −9.49106 | −0.323643 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 41.0051 | 1.39664 | ||||||||
\(863\) | 20.9442 | 0.712949 | 0.356475 | − | 0.934305i | \(-0.383979\pi\) | ||||
0.356475 | + | 0.934305i | \(0.383979\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.3147 | 0.554716 | ||||||||
\(866\) | 23.5274 | 0.799495 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.4471 | 0.354599 | ||||||||
\(869\) | 36.2975 | 1.23131 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.409227 | −0.0138661 | ||||||||
\(872\) | −17.8854 | −0.605675 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −54.0802 | −1.82929 | ||||||||
\(875\) | 4.33630 | 0.146594 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −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 | 0 | ||||||||
\(880\) | 4.74553 | 0.159972 | ||||||||
\(881\) | 40.1851 | 1.35387 | 0.676936 | − | 0.736042i | \(-0.263308\pi\) | ||||
0.676936 | + | 0.736042i | \(0.263308\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.1637 | −1.28431 | −0.642155 | − | 0.766575i | \(-0.721959\pi\) | ||||
−0.642155 | + | 0.766575i | \(0.721959\pi\) | |||||||
\(884\) | −2.36309 | −0.0794794 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.54906 | −0.253616 | ||||||||
\(887\) | −22.4353 | −0.753303 | −0.376651 | − | 0.926355i | \(-0.622925\pi\) | ||||
−0.376651 | + | 0.926355i | \(0.622925\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.0655 | −1.34375 | ||||||||
\(890\) | 9.08700 | 0.304597 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −25.8586 | −0.865809 | ||||||||
\(893\) | −8.72619 | −0.292011 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.92038 | 0.0641911 | ||||||||
\(896\) | 4.33630 | 0.144866 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −27.4398 | −0.915677 | ||||||||
\(899\) | 3.14959 | 0.105045 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −61.6293 | −2.05317 | ||||||||
\(902\) | −8.14585 | −0.271227 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.86908 | 0.128684 | ||||||||
\(905\) | 17.4032 | 0.578503 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.2945 | 1.50398 | 0.751990 | − | 0.659174i | \(-0.229094\pi\) | ||||
0.751990 | + | 0.659174i | \(0.229094\pi\) | |||||||
\(908\) | −17.7127 | −0.587818 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.77453 | 0.0588252 | ||||||||
\(911\) | 6.75528 | 0.223813 | 0.111906 | − | 0.993719i | \(-0.464304\pi\) | ||||
0.111906 | + | 0.993719i | \(0.464304\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −40.7075 | −1.34722 | ||||||||
\(914\) | −14.3891 | −0.475950 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.8274 | −0.522951 | ||||||||
\(917\) | 82.1993 | 2.71446 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.48511 | −0.0489891 | −0.0244946 | − | 0.999700i | \(-0.507798\pi\) | ||||
−0.0244946 | + | 0.999700i | \(0.507798\pi\) | |||||||
\(920\) | 9.36530 | 0.308765 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.5365 | 0.478735 | ||||||||
\(923\) | −3.31917 | −0.109252 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.02900 | 0.0995929 | ||||||||
\(926\) | 11.6124 | 0.381607 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.30730 | 0.0429143 | ||||||||
\(929\) | −30.3490 | −0.995717 | −0.497859 | − | 0.867258i | \(-0.665880\pi\) | ||||
−0.497859 | + | 0.867258i | \(0.665880\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −68.1599 | −2.23385 | ||||||||
\(932\) | 22.4322 | 0.734792 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.88316 | −0.290666 | ||||||||
\(935\) | −27.4032 | −0.896181 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.1992 | −1.73794 | −0.868971 | − | 0.494863i | \(-0.835218\pi\) | ||||
−0.868971 | + | 0.494863i | \(0.835218\pi\) | |||||||
\(938\) | −4.33630 | −0.141585 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.51115 | 0.0492883 | ||||||||
\(941\) | −32.2395 | −1.05098 | −0.525489 | − | 0.850801i | \(-0.676118\pi\) | ||||
−0.525489 | + | 0.850801i | \(0.676118\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.0758 | −0.523501 | ||||||||
\(944\) | −1.71653 | −0.0558683 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −45.0401 | −1.46438 | ||||||||
\(947\) | 27.7060 | 0.900325 | 0.450163 | − | 0.892947i | \(-0.351366\pi\) | ||||
0.450163 | + | 0.892947i | \(0.351366\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.29755 | −0.107043 | ||||||||
\(950\) | −5.77453 | −0.187351 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −25.0401 | −0.811555 | ||||||||
\(953\) | 50.3771 | 1.63187 | 0.815937 | − | 0.578140i | \(-0.196221\pi\) | ||||
0.815937 | + | 0.578140i | \(0.196221\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.50894 | 0.0811873 | ||||||||
\(956\) | −9.23955 | −0.298828 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.5319 | −0.792591 | ||||||||
\(959\) | 4.21055 | 0.135966 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.1956 | −0.812762 | ||||||||
\(962\) | 1.23955 | 0.0399646 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.17859 | 0.198999 | ||||||||
\(965\) | 25.9382 | 0.834980 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.23675 | 0.0719291 | 0.0359646 | − | 0.999353i | \(-0.488550\pi\) | ||||
0.0359646 | + | 0.999353i | \(0.488550\pi\) | |||||||
\(968\) | 11.5201 | 0.370269 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.74553 | −0.152370 | ||||||||
\(971\) | −37.2878 | −1.19662 | −0.598312 | − | 0.801263i | \(-0.704162\pi\) | ||||
−0.598312 | + | 0.801263i | \(0.704162\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 40.8109 | 1.30834 | ||||||||
\(974\) | −12.9553 | −0.415116 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.33630 | 0.202820 | ||||||||
\(977\) | −13.5261 | −0.432738 | −0.216369 | − | 0.976312i | \(-0.569421\pi\) | ||||
−0.216369 | + | 0.976312i | \(0.569421\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43.1227 | 1.37821 | ||||||||
\(980\) | 11.8035 | 0.377050 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −27.6911 | −0.883659 | ||||||||
\(983\) | 59.9924 | 1.91346 | 0.956730 | − | 0.290976i | \(-0.0939800\pi\) | ||||
0.956730 | + | 0.290976i | \(0.0939800\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.18155 | 0.0376472 | ||||||||
\(986\) | −7.54906 | −0.240411 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.36309 | −0.0751800 | ||||||||
\(989\) | −88.8867 | −2.82643 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.37353 | 0.107164 | 0.0535818 | − | 0.998563i | \(-0.482936\pi\) | ||||
0.0535818 | + | 0.998563i | \(0.482936\pi\) | |||||||
\(992\) | 2.40923 | 0.0764930 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −35.1710 | −1.11556 | ||||||||
\(995\) | −16.5781 | −0.525560 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.0647 | −0.318752 | −0.159376 | − | 0.987218i | \(-0.550948\pi\) | ||||
−0.159376 | + | 0.987218i | \(0.550948\pi\) | |||||||
\(998\) | 32.7737 | 1.03743 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6030.2.a.bu.1.4 | 4 | ||
3.2 | odd | 2 | 2010.2.a.r.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2010.2.a.r.1.4 | ✓ | 4 | 3.2 | odd | 2 | ||
6030.2.a.bu.1.4 | 4 | 1.1 | even | 1 | trivial |