Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0080822603\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 33 x^{9} + 22 x^{8} + 417 x^{7} - 151 x^{6} - 2470 x^{5} + 272 x^{4} + 6584 x^{3} + \cdots + 242 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.54432\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.54432 | −1.13785 | −0.568927 | − | 0.822388i | \(-0.692641\pi\) | ||||
−0.568927 | + | 0.822388i | \(0.692641\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.525270 | −0.198533 | −0.0992667 | − | 0.995061i | \(-0.531650\pi\) | ||||
−0.0992667 | + | 0.995061i | \(0.531650\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.59056 | −1.68562 | −0.842809 | − | 0.538213i | \(-0.819100\pi\) | ||||
−0.842809 | + | 0.538213i | \(0.819100\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.57904 | 0.437947 | 0.218974 | − | 0.975731i | \(-0.429729\pi\) | ||||
0.218974 | + | 0.975731i | \(0.429729\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.54432 | −0.656940 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.20935 | 1.02092 | 0.510459 | − | 0.859902i | \(-0.329476\pi\) | ||||
0.510459 | + | 0.859902i | \(0.329476\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.78855 | −0.869153 | −0.434577 | − | 0.900635i | \(-0.643102\pi\) | ||||
−0.434577 | + | 0.900635i | \(0.643102\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.525270 | −0.114623 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.45151 | 0.511174 | 0.255587 | − | 0.966786i | \(-0.417731\pi\) | ||||
0.255587 | + | 0.966786i | \(0.417731\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.47356 | 0.294711 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.24006 | −0.787359 | −0.393679 | − | 0.919248i | \(-0.628798\pi\) | ||||
−0.393679 | + | 0.919248i | \(0.628798\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.76018 | 1.03456 | 0.517279 | − | 0.855817i | \(-0.326945\pi\) | ||||
0.517279 | + | 0.855817i | \(0.326945\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.59056 | −0.973192 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.33645 | 0.225902 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.67489 | −0.439749 | −0.219874 | − | 0.975528i | \(-0.570565\pi\) | ||||
−0.219874 | + | 0.975528i | \(0.570565\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.57904 | 0.252849 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.7672 | 1.68155 | 0.840774 | − | 0.541387i | \(-0.182101\pi\) | ||||
0.840774 | + | 0.541387i | \(0.182101\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.36680 | −1.27593 | −0.637963 | − | 0.770067i | \(-0.720223\pi\) | ||||
−0.637963 | + | 0.770067i | \(0.720223\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.54432 | −0.379285 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.77944 | −0.697153 | −0.348577 | − | 0.937280i | \(-0.613335\pi\) | ||||
−0.348577 | + | 0.937280i | \(0.613335\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.72409 | −0.960585 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.20935 | 0.589427 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.34459 | −0.322054 | −0.161027 | − | 0.986950i | \(-0.551481\pi\) | ||||
−0.161027 | + | 0.986950i | \(0.551481\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.2242 | 1.91799 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.78855 | −0.501806 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.25946 | 0.684723 | 0.342362 | − | 0.939568i | \(-0.388773\pi\) | ||||
0.342362 | + | 0.939568i | \(0.388773\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.02359 | −0.643205 | −0.321602 | − | 0.946875i | \(-0.604221\pi\) | ||||
−0.321602 | + | 0.946875i | \(0.604221\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.525270 | −0.0661778 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.01758 | −0.498320 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.91781 | −1.08948 | −0.544742 | − | 0.838604i | \(-0.683372\pi\) | ||||
−0.544742 | + | 0.838604i | \(0.683372\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.45151 | 0.295127 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.10616 | 0.605990 | 0.302995 | − | 0.952992i | \(-0.402013\pi\) | ||||
0.302995 | + | 0.952992i | \(0.402013\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.16373 | −0.253246 | −0.126623 | − | 0.991951i | \(-0.540414\pi\) | ||||
−0.126623 | + | 0.991951i | \(0.540414\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.47356 | 0.170151 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.93655 | 0.334651 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.52659 | 0.284263 | 0.142132 | − | 0.989848i | \(-0.454604\pi\) | ||||
0.142132 | + | 0.989848i | \(0.454604\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.01520 | 0.440726 | 0.220363 | − | 0.975418i | \(-0.429276\pi\) | ||||
0.220363 | + | 0.975418i | \(0.429276\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.7099 | −1.16165 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.24006 | −0.454582 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.2275 | 1.72011 | 0.860055 | − | 0.510201i | \(-0.170429\pi\) | ||||
0.860055 | + | 0.510201i | \(0.170429\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.829422 | −0.0869471 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.76018 | 0.597303 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.63928 | 0.988969 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.4673 | −1.67201 | −0.836003 | − | 0.548725i | \(-0.815113\pi\) | ||||
−0.836003 | + | 0.548725i | \(0.815113\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.59056 | −0.561873 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.51102 | −0.747374 | −0.373687 | − | 0.927555i | \(-0.621907\pi\) | ||||
−0.373687 | + | 0.927555i | \(0.621907\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.49723 | −0.147527 | −0.0737634 | − | 0.997276i | \(-0.523501\pi\) | ||||
−0.0737634 | + | 0.997276i | \(0.523501\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.33645 | 0.130425 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.29357 | 0.221728 | 0.110864 | − | 0.993836i | \(-0.464638\pi\) | ||||
0.110864 | + | 0.993836i | \(0.464638\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.3290 | 1.27669 | 0.638344 | − | 0.769751i | \(-0.279620\pi\) | ||||
0.638344 | + | 0.769751i | \(0.279620\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.67489 | −0.253889 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.9368 | 1.78142 | 0.890711 | − | 0.454570i | \(-0.150207\pi\) | ||||
0.890711 | + | 0.454570i | \(0.150207\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.23741 | −0.581642 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.57904 | 0.145982 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.21104 | −0.202686 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.2544 | 1.84131 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.7672 | 0.970842 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.97240 | 0.802516 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.286281 | 0.0254034 | 0.0127017 | − | 0.999919i | \(-0.495957\pi\) | ||||
0.0127017 | + | 0.999919i | \(0.495957\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.36680 | −0.736656 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.5000 | −1.09213 | −0.546064 | − | 0.837744i | \(-0.683874\pi\) | ||||
−0.546064 | + | 0.837744i | \(0.683874\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.99001 | 0.172556 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.54432 | −0.218980 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.4508 | 1.06374 | 0.531872 | − | 0.846825i | \(-0.321489\pi\) | ||||
0.531872 | + | 0.846825i | \(0.321489\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.8333 | −1.17333 | −0.586663 | − | 0.809831i | \(-0.699559\pi\) | ||||
−0.586663 | + | 0.809831i | \(0.699559\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.77944 | −0.402502 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.82773 | −0.738212 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.7881 | 0.895899 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.72409 | −0.554594 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.9274 | 1.46867 | 0.734335 | − | 0.678787i | \(-0.237494\pi\) | ||||
0.734335 | + | 0.678787i | \(0.237494\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.27238 | 0.429061 | 0.214530 | − | 0.976717i | \(-0.431178\pi\) | ||||
0.214530 | + | 0.976717i | \(0.431178\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.20935 | 0.340306 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.6557 | −1.17718 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23.2595 | 1.85631 | 0.928155 | − | 0.372195i | \(-0.121395\pi\) | ||||
0.928155 | + | 0.372195i | \(0.121395\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.34459 | −0.185938 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.28770 | −0.101485 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.8496 | 1.71139 | 0.855696 | − | 0.517478i | \(-0.173129\pi\) | ||||
0.855696 | + | 0.517478i | \(0.173129\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 14.2242 | 1.10735 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5066 | −0.808202 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.78855 | −0.289718 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.0266 | 0.762310 | 0.381155 | − | 0.924511i | \(-0.375526\pi\) | ||||
0.381155 | + | 0.924511i | \(0.375526\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.774014 | −0.0585100 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.25946 | 0.395325 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.201597 | −0.0150681 | −0.00753404 | − | 0.999972i | \(-0.502398\pi\) | ||||
−0.00753404 | + | 0.999972i | \(0.502398\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.7308 | 0.871946 | 0.435973 | − | 0.899960i | \(-0.356404\pi\) | ||||
0.435973 | + | 0.899960i | \(0.356404\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.02359 | −0.371354 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.80576 | 0.500370 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.5326 | −1.72088 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.525270 | −0.0382078 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.0393 | 1.81178 | 0.905891 | − | 0.423511i | \(-0.139203\pi\) | ||||
0.905891 | + | 0.423511i | \(0.139203\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.7710 | −0.775315 | −0.387658 | − | 0.921803i | \(-0.626716\pi\) | ||||
−0.387658 | + | 0.921803i | \(0.626716\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.01758 | −0.287705 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.1738 | 0.796102 | 0.398051 | − | 0.917363i | \(-0.369687\pi\) | ||||
0.398051 | + | 0.917363i | \(0.369687\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.0987 | 1.63742 | 0.818710 | − | 0.574207i | \(-0.194690\pi\) | ||||
0.818710 | + | 0.574207i | \(0.194690\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.91781 | −0.629014 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.22717 | 0.156317 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −27.3951 | −1.91335 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.45151 | 0.170391 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.1801 | 1.46506 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.65386 | 0.595756 | 0.297878 | − | 0.954604i | \(-0.403721\pi\) | ||||
0.297878 | + | 0.954604i | \(0.403721\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.10616 | 0.349868 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 21.2878 | 1.45182 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.02565 | −0.205394 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.16373 | −0.146212 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.64673 | 0.447108 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.47630 | −0.232791 | −0.116395 | − | 0.993203i | \(-0.537134\pi\) | ||||
−0.116395 | + | 0.993203i | \(0.537134\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.47356 | 0.0982370 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.99391 | −0.331458 | −0.165729 | − | 0.986171i | \(-0.552998\pi\) | ||||
−0.165729 | + | 0.986171i | \(0.552998\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.724364 | −0.0478673 | −0.0239337 | − | 0.999714i | \(-0.507619\pi\) | ||||
−0.0239337 | + | 0.999714i | \(0.507619\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.93655 | 0.193211 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.07905 | 0.201716 | 0.100858 | − | 0.994901i | \(-0.467841\pi\) | ||||
0.100858 | + | 0.994901i | \(0.467841\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.1604 | 0.793258 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.52659 | 0.164120 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.7125 | −1.53383 | −0.766916 | − | 0.641748i | \(-0.778210\pi\) | ||||
−0.766916 | + | 0.641748i | \(0.778210\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.1304 | 0.910219 | 0.455109 | − | 0.890436i | \(-0.349600\pi\) | ||||
0.455109 | + | 0.890436i | \(0.349600\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.1082 | 1.09300 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.98227 | −0.380643 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.01520 | 0.254453 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.523099 | −0.0330177 | −0.0165089 | − | 0.999864i | \(-0.505255\pi\) | ||||
−0.0165089 | + | 0.999864i | \(0.505255\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.7053 | −0.861645 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.7099 | −0.670682 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.5504 | 1.21952 | 0.609761 | − | 0.792586i | \(-0.291266\pi\) | ||||
0.609761 | + | 0.792586i | \(0.291266\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.40504 | 0.0873048 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.24006 | −0.262453 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.94567 | 0.181638 | 0.0908189 | − | 0.995867i | \(-0.471052\pi\) | ||||
0.0908189 | + | 0.995867i | \(0.471052\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.96539 | 0.366451 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.2275 | 0.993106 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.57622 | 0.583872 | 0.291936 | − | 0.956438i | \(-0.405701\pi\) | ||||
0.291936 | + | 0.956438i | \(0.405701\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.1059 | −1.46433 | −0.732164 | − | 0.681128i | \(-0.761490\pi\) | ||||
−0.732164 | + | 0.681128i | \(0.761490\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.829422 | −0.0501989 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.23800 | −0.496770 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.19302 | −0.131766 | −0.0658828 | − | 0.997827i | \(-0.520986\pi\) | ||||
−0.0658828 | + | 0.997827i | \(0.520986\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.76018 | 0.344853 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.78076 | 0.404506 | 0.202253 | − | 0.979333i | \(-0.435174\pi\) | ||||
0.202253 | + | 0.979333i | \(0.435174\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.02725 | 0.239395 | 0.119697 | − | 0.992810i | \(-0.461808\pi\) | ||||
0.119697 | + | 0.992810i | \(0.461808\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.63928 | 0.570982 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.65566 | −0.333843 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.718627 | 0.0422722 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.4673 | −0.965333 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.8461 | 1.33468 | 0.667342 | − | 0.744751i | \(-0.267432\pi\) | ||||
0.667342 | + | 0.744751i | \(0.267432\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.3817 | −0.779115 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.59056 | −0.324397 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.87103 | 0.223867 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.39483 | 0.253314 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.51102 | −0.431497 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.7816 | 0.731873 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.74814 | −0.156845 | −0.0784223 | − | 0.996920i | \(-0.524988\pi\) | ||||
−0.0784223 | + | 0.996920i | \(0.524988\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.49723 | −0.0851746 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.22030 | 0.182606 | 0.0913032 | − | 0.995823i | \(-0.470897\pi\) | ||||
0.0913032 | + | 0.995823i | \(0.470897\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.2753 | −1.71126 | −0.855629 | − | 0.517589i | \(-0.826830\pi\) | ||||
−0.855629 | + | 0.517589i | \(0.826830\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.33645 | 0.0753006 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.1079 | 0.736214 | 0.368107 | − | 0.929783i | \(-0.380006\pi\) | ||||
0.368107 | + | 0.929783i | \(0.380006\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.7043 | 1.32719 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.29357 | 0.128015 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.9473 | −0.887333 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.32680 | 0.129068 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.3290 | 0.737096 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.51050 | 0.138408 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.4120 | 1.23188 | 0.615938 | − | 0.787795i | \(-0.288777\pi\) | ||||
0.615938 | + | 0.787795i | \(0.288777\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.67489 | −0.146583 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 22.6898 | 1.23967 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.50311 | 0.0818797 | 0.0409398 | − | 0.999162i | \(-0.486965\pi\) | ||||
0.0409398 | + | 0.999162i | \(0.486965\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.9368 | 1.02850 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −32.2026 | −1.74387 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.20885 | 0.389241 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.23741 | −0.335811 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.4505 | −1.58099 | −0.790493 | − | 0.612471i | \(-0.790175\pi\) | ||||
−0.790493 | + | 0.612471i | \(0.790175\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.58173 | 0.298783 | 0.149392 | − | 0.988778i | \(-0.452268\pi\) | ||||
0.149392 | + | 0.988778i | \(0.452268\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.57904 | 0.0842829 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.27363 | −0.493586 | −0.246793 | − | 0.969068i | \(-0.579377\pi\) | ||||
−0.246793 | + | 0.969068i | \(0.579377\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.9917 | −0.689528 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.21104 | −0.117021 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.7886 | 1.73052 | 0.865258 | − | 0.501326i | \(-0.167154\pi\) | ||||
0.865258 | + | 0.501326i | \(0.167154\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.64689 | −0.244573 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 20.2544 | 1.06308 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.50523 | 0.288157 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.93563 | −0.257638 | −0.128819 | − | 0.991668i | \(-0.541119\pi\) | ||||
−0.128819 | + | 0.991668i | \(0.541119\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.7672 | 0.560516 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.23154 | 0.0639385 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.9187 | 1.70446 | 0.852232 | − | 0.523165i | \(-0.175249\pi\) | ||||
0.852232 | + | 0.523165i | \(0.175249\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.97240 | 0.463333 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.69522 | −0.344821 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.820431 | 0.0421427 | 0.0210714 | − | 0.999778i | \(-0.493292\pi\) | ||||
0.0210714 | + | 0.999778i | \(0.493292\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.286281 | 0.0146666 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.99971 | 0.102180 | 0.0510901 | − | 0.998694i | \(-0.483730\pi\) | ||||
0.0510901 | + | 0.998694i | \(0.483730\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.47153 | −0.380784 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.36680 | −0.425309 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.8177 | −0.903395 | −0.451698 | − | 0.892171i | \(-0.649181\pi\) | ||||
−0.451698 | + | 0.892171i | \(0.649181\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.3192 | 0.521867 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.5000 | −0.630540 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.42845 | −0.323450 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.8025 | 1.64631 | 0.823156 | − | 0.567816i | \(-0.192211\pi\) | ||||
0.823156 | + | 0.567816i | \(0.192211\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.99001 | 0.0996252 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35.4145 | −1.76852 | −0.884258 | − | 0.466998i | \(-0.845336\pi\) | ||||
−0.884258 | + | 0.466998i | \(0.845336\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.09555 | 0.453082 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.54432 | −0.126428 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.9541 | 0.741248 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.5720 | −1.31390 | −0.656950 | − | 0.753934i | \(-0.728154\pi\) | ||||
−0.656950 | + | 0.753934i | \(0.728154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.4508 | 0.614153 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.76264 | −0.135940 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.2160 | −0.501482 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.8333 | −0.677420 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.4006 | −1.28975 | −0.644876 | − | 0.764287i | \(-0.723091\pi\) | ||||
−0.644876 | + | 0.764287i | \(0.723091\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.2066 | 1.47218 | 0.736090 | − | 0.676884i | \(-0.236670\pi\) | ||||
0.736090 | + | 0.676884i | \(0.236670\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.77944 | −0.232384 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.20271 | 0.300876 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.63874 | 0.127698 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.82773 | −0.426207 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.0759 | 1.25603 | 0.628015 | − | 0.778201i | \(-0.283868\pi\) | ||||
0.628015 | + | 0.778201i | \(0.283868\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.3412 | 1.07365 | 0.536825 | − | 0.843694i | \(-0.319624\pi\) | ||||
0.536825 | + | 0.843694i | \(0.319624\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.7881 | 0.517248 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.28766 | −0.444289 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.40123 | −0.114604 | −0.0573021 | − | 0.998357i | \(-0.518250\pi\) | ||||
−0.0573021 | + | 0.998357i | \(0.518250\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.72409 | −0.320195 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.06561 | 0.288186 | 0.144093 | − | 0.989564i | \(-0.453974\pi\) | ||||
0.144093 | + | 0.989564i | \(0.453974\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −41.2879 | −1.95723 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.9274 | 0.847937 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 40.4576 | 1.90931 | 0.954656 | − | 0.297713i | \(-0.0962237\pi\) | ||||
0.954656 | + | 0.297713i | \(0.0962237\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −60.1945 | −2.83445 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.27238 | 0.247718 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.11031 | 0.0989331 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.88373 | 0.228451 | 0.114226 | − | 0.993455i | \(-0.463561\pi\) | ||||
0.114226 | + | 0.993455i | \(0.463561\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.20935 | 0.196476 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.2825 | −0.572051 | −0.286026 | − | 0.958222i | \(-0.592334\pi\) | ||||
−0.286026 | + | 0.958222i | \(0.592334\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.0073 | −0.929818 | −0.464909 | − | 0.885359i | \(-0.653913\pi\) | ||||
−0.464909 | + | 0.885359i | \(0.653913\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.6557 | −0.679643 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.24777 | −0.335387 | −0.167693 | − | 0.985839i | \(-0.553632\pi\) | ||||
−0.167693 | + | 0.985839i | \(0.553632\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.68426 | 0.216299 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.2595 | 1.07174 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 46.7752 | 2.15072 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.58264 | −0.256149 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.34459 | −0.107351 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.0521512 | 0.00238285 | 0.00119143 | − | 0.999999i | \(-0.499621\pi\) | ||||
0.00119143 | + | 0.999999i | \(0.499621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.22375 | −0.192587 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.28770 | −0.0585925 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 41.8982 | 1.90250 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.29237 | −0.285135 | −0.142567 | − | 0.989785i | \(-0.545536\pi\) | ||||
−0.142567 | + | 0.989785i | \(0.545536\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.8496 | 0.988073 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.3974 | −1.23643 | −0.618214 | − | 0.786010i | \(-0.712144\pi\) | ||||
−0.618214 | + | 0.786010i | \(0.712144\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.8479 | −0.803828 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.2242 | 0.639329 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.68211 | −0.120309 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.7237 | 1.46492 | 0.732458 | − | 0.680813i | \(-0.238373\pi\) | ||||
0.732458 | + | 0.680813i | \(0.238373\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.12421 | −0.0501261 | −0.0250630 | − | 0.999686i | \(-0.507979\pi\) | ||||
−0.0250630 | + | 0.999686i | \(0.507979\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.1104 | 0.850402 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.5066 | −0.466616 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.83949 | −0.214506 | −0.107253 | − | 0.994232i | \(-0.534206\pi\) | ||||
−0.107253 | + | 0.994232i | \(0.534206\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.13654 | 0.0502778 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.78855 | −0.167269 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.80944 | 0.167864 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.7198 | 1.17513 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.0266 | 0.440120 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.5789 | −1.60255 | −0.801275 | − | 0.598296i | \(-0.795844\pi\) | ||||
−0.801275 | + | 0.598296i | \(0.795844\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.8955 | 1.04488 | 0.522439 | − | 0.852677i | \(-0.325022\pi\) | ||||
0.522439 | + | 0.852677i | \(0.325022\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.774014 | −0.0337807 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.2466 | 1.05620 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.9901 | −0.738701 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.25946 | 0.228241 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.0018 | 0.736429 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.83558 | −0.252294 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.201597 | −0.00869956 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 37.5915 | 1.61918 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.0286 | −1.33402 | −0.667012 | − | 0.745047i | \(-0.732427\pi\) | ||||
−0.667012 | + | 0.745047i | \(0.732427\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.7308 | 0.503418 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −33.9132 | −1.45268 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.82578 | −0.163578 | −0.0817892 | − | 0.996650i | \(-0.526063\pi\) | ||||
−0.0817892 | + | 0.996650i | \(0.526063\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.02359 | −0.214402 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.0637 | 0.684335 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.32714 | −0.0564358 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.80576 | 0.288889 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.6847 | 1.04592 | 0.522962 | − | 0.852356i | \(-0.324827\pi\) | ||||
0.522962 | + | 0.852356i | \(0.324827\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.2115 | −0.558788 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23.5326 | −0.993549 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.9996 | −0.758592 | −0.379296 | − | 0.925275i | \(-0.623834\pi\) | ||||
−0.379296 | + | 0.925275i | \(0.623834\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −48.1812 | −2.02700 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.525270 | −0.0220593 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.9387 | −0.919718 | −0.459859 | − | 0.887992i | \(-0.652100\pi\) | ||||
−0.459859 | + | 0.887992i | \(0.652100\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.4601 | 0.814378 | 0.407189 | − | 0.913344i | \(-0.366509\pi\) | ||||
0.407189 | + | 0.913344i | \(0.366509\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.0393 | 1.04603 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.61243 | 0.150649 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.17908 | 0.340500 | 0.170250 | − | 0.985401i | \(-0.445543\pi\) | ||||
0.170250 | + | 0.985401i | \(0.445543\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.7710 | −0.447628 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.10907 | −0.0874988 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.1076 | 0.542861 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.01758 | −0.166107 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.61306 | −0.314225 | −0.157112 | − | 0.987581i | \(-0.550218\pi\) | ||||
−0.157112 | + | 0.987581i | \(0.550218\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.8227 | −0.899190 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.1738 | 0.459629 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.7438 | −0.892912 | −0.446456 | − | 0.894806i | \(-0.647314\pi\) | ||||
−0.446456 | + | 0.894806i | \(0.647314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.62560 | 0.230627 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.0987 | 0.945365 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.3506 | −1.60782 | −0.803911 | − | 0.594750i | \(-0.797251\pi\) | ||||
−0.803911 | + | 0.594750i | \(0.797251\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.4627 | 0.753109 | 0.376555 | − | 0.926394i | \(-0.377109\pi\) | ||||
0.376555 | + | 0.926394i | \(0.377109\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.91781 | −0.363161 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −51.5336 | −2.09514 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.84061 | 0.277652 | 0.138826 | − | 0.990317i | \(-0.455667\pi\) | ||||
0.138826 | + | 0.990317i | \(0.455667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.22717 | 0.0902496 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.54693 | −0.305316 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.6604 | 1.88460 | 0.942298 | − | 0.334776i | \(-0.108661\pi\) | ||||
0.942298 | + | 0.334776i | \(0.108661\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −27.3951 | −1.10468 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.4605 | 0.783452 | 0.391726 | − | 0.920082i | \(-0.371878\pi\) | ||||
0.391726 | + | 0.920082i | \(0.371878\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.6463 | −0.910232 | −0.455116 | − | 0.890432i | \(-0.650402\pi\) | ||||
−0.455116 | + | 0.890432i | \(0.650402\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.45151 | 0.0983756 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.52381 | −0.341499 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.1964 | −1.20786 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21.1801 | 0.845853 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.2595 | −0.448947 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.4338 | −1.64945 | −0.824727 | − | 0.565531i | \(-0.808671\pi\) | ||||
−0.824727 | + | 0.565531i | \(0.808671\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.65386 | 0.343960 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.728391 | −0.0289053 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.6176 | −0.420685 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.10616 | 0.201997 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.85111 | −0.231105 | −0.115552 | − | 0.993301i | \(-0.536864\pi\) | ||||
−0.115552 | + | 0.993301i | \(0.536864\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.42749 | −0.0562947 | −0.0281473 | − | 0.999604i | \(-0.508961\pi\) | ||||
−0.0281473 | + | 0.999604i | \(0.508961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.2878 | 0.838207 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.5140 | 0.413349 | 0.206675 | − | 0.978410i | \(-0.433736\pi\) | ||||
0.206675 | + | 0.978410i | \(0.433736\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29.4033 | −1.15418 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.02565 | −0.118584 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.1836 | 1.72904 | 0.864519 | − | 0.502601i | \(-0.167623\pi\) | ||||
0.864519 | + | 0.502601i | \(0.167623\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.8039 | 1.24268 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.16373 | −0.0844153 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.39910 | 0.366137 | 0.183069 | − | 0.983100i | \(-0.441397\pi\) | ||||
0.183069 | + | 0.983100i | \(0.441397\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.0872 | 1.83148 | 0.915739 | − | 0.401774i | \(-0.131606\pi\) | ||||
0.915739 | + | 0.401774i | \(0.131606\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.64673 | 0.258138 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.06322 | −0.196343 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.3945 | −0.402478 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.47630 | −0.134402 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.0847 | 1.08420 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.95242 | −0.345091 | −0.172545 | − | 0.985002i | \(-0.555199\pi\) | ||||
−0.172545 | + | 0.985002i | \(0.555199\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.47356 | 0.0567172 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.00580 | −0.307688 | −0.153844 | − | 0.988095i | \(-0.549165\pi\) | ||||
−0.153844 | + | 0.988095i | \(0.549165\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.64980 | 0.331949 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.99391 | −0.191367 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.64312 | −0.139400 | −0.0697001 | − | 0.997568i | \(-0.522204\pi\) | ||||
−0.0697001 | + | 0.997568i | \(0.522204\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.6788 | −1.21038 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.724364 | −0.0276362 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.70220 | −0.141043 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.2229 | −0.693230 | −0.346615 | − | 0.938008i | \(-0.612669\pi\) | ||||
−0.346615 | + | 0.938008i | \(0.612669\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.93655 | 0.111550 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35.1964 | 1.33507 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.3227 | 1.71672 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.07905 | 0.116461 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.3239 | −0.692085 | −0.346043 | − | 0.938219i | \(-0.612475\pi\) | ||||
−0.346043 | + | 0.938219i | \(0.612475\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.1339 | 0.382209 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.1604 | 0.457988 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.94531 | 0.148379 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.1399 | 1.24460 | 0.622298 | − | 0.782781i | \(-0.286199\pi\) | ||||
0.622298 | + | 0.782781i | \(0.286199\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.52659 | 0.0947545 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.1211 | 0.528840 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.4605 | 0.839977 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.7125 | −0.885558 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.6679 | −0.397847 | −0.198924 | − | 0.980015i | \(-0.563745\pi\) | ||||
−0.198924 | + | 0.980015i | \(0.563745\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.786451 | 0.0292890 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.1304 | 0.525515 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.24796 | −0.232043 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.3733 | 0.607254 | 0.303627 | − | 0.952791i | \(-0.401802\pi\) | ||||
0.303627 | + | 0.952791i | \(0.401802\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −35.2188 | −1.30261 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.1931 | 0.376492 | 0.188246 | − | 0.982122i | \(-0.439720\pi\) | ||||
0.188246 | + | 0.982122i | \(0.439720\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.1082 | 0.631047 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 49.8556 | 1.83645 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.0639 | −0.517349 | −0.258675 | − | 0.965964i | \(-0.583286\pi\) | ||||
−0.258675 | + | 0.965964i | \(0.583286\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.98227 | −0.219764 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.93010 | 0.327614 | 0.163807 | − | 0.986492i | \(-0.447623\pi\) | ||||
0.163807 | + | 0.986492i | \(0.447623\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −45.6130 | −1.67113 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.01520 | 0.146909 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.20475 | −0.0440204 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.7755 | 0.612146 | 0.306073 | − | 0.952008i | \(-0.400985\pi\) | ||||
0.306073 | + | 0.952008i | \(0.400985\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.523099 | −0.0190628 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.4146 | −0.488208 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.3838 | −1.03163 | −0.515814 | − | 0.856701i | \(-0.672510\pi\) | ||||
−0.515814 | + | 0.856701i | \(0.672510\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.7053 | −0.497471 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.5928 | 1.50774 | 0.753869 | − | 0.657025i | \(-0.228185\pi\) | ||||
0.753869 | + | 0.657025i | \(0.228185\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.00133 | −0.253465 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.7099 | −0.387218 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.30490 | 0.299873 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.5540 | −0.488770 | −0.244385 | − | 0.969678i | \(-0.578586\pi\) | ||||
−0.244385 | + | 0.969678i | \(0.578586\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.5504 | 0.704091 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.6981 | −1.31994 | −0.659970 | − | 0.751292i | \(-0.729431\pi\) | ||||
−0.659970 | + | 0.751292i | \(0.729431\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.48794 | 0.304896 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.40504 | 0.0504054 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −40.7919 | −1.46152 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.5463 | −1.02147 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.24006 | −0.151527 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −59.1795 | −2.11221 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.9838 | −0.747993 | −0.373996 | − | 0.927430i | \(-0.622013\pi\) | ||||
−0.373996 | + | 0.927430i | \(0.622013\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.94567 | 0.104869 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.94692 | −0.353672 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.93245 | −0.281690 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.96539 | 0.211570 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.30024 | 0.294010 | 0.147005 | − | 0.989136i | \(-0.453037\pi\) | ||||
0.147005 | + | 0.989136i | \(0.453037\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.1183 | −0.711736 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.2275 | 0.573370 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.0965 | 0.426876 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.27632 | 0.115475 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.57622 | 0.337099 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −40.2664 | −1.41569 | −0.707845 | − | 0.706368i | \(-0.750333\pi\) | ||||
−0.707845 | + | 0.706368i | \(0.750333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0881 | 0.389357 | 0.194679 | − | 0.980867i | \(-0.437634\pi\) | ||||
0.194679 | + | 0.980867i | \(0.437634\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.1059 | −0.845430 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −55.5923 | −1.94731 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.6981 | 1.10897 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.829422 | −0.0289824 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.0645 | 1.39826 | 0.699130 | − | 0.714995i | \(-0.253571\pi\) | ||||
0.699130 | + | 0.714995i | \(0.253571\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.7172 | 1.07073 | 0.535366 | − | 0.844620i | \(-0.320174\pi\) | ||||
0.535366 | + | 0.844620i | \(0.320174\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.23800 | −0.286810 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.1112 | 0.907977 | 0.453988 | − | 0.891008i | \(-0.350001\pi\) | ||||
0.453988 | + | 0.891008i | \(0.350001\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.46592 | −0.120376 | −0.0601882 | − | 0.998187i | \(-0.519170\pi\) | ||||
−0.0601882 | + | 0.998187i | \(0.519170\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.19302 | −0.0760749 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.3041 | −0.980677 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.54432 | 0.0880498 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.76018 | 0.199101 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.7905 | −0.855864 | −0.427932 | − | 0.903811i | \(-0.640758\pi\) | ||||
−0.427932 | + | 0.903811i | \(0.640758\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.0219 | −0.380066 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.78076 | 0.233542 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.7322 | 0.919616 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.6390 | −0.365561 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.02725 | 0.138215 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.55750 | −0.224788 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.4429 | −1.21354 | −0.606772 | − | 0.794876i | \(-0.707536\pi\) | ||||
−0.606772 | + | 0.794876i | \(0.707536\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.63928 | 0.329656 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.6459 | −0.671092 | −0.335546 | − | 0.942024i | \(-0.608921\pi\) | ||||
−0.335546 | + | 0.942024i | \(0.608921\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.37538 | −0.149286 | −0.0746430 | − | 0.997210i | \(-0.523782\pi\) | ||||
−0.0746430 | + | 0.997210i | \(0.523782\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.65566 | −0.192744 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.7669 | 0.366510 | 0.183255 | − | 0.983065i | \(-0.441337\pi\) | ||||
0.183255 | + | 0.983065i | \(0.441337\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.5109 | −0.867397 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.718627 | 0.0244059 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.1251 | −0.479160 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.0816 | −0.477136 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.4673 | −0.557335 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.71293 | −0.159326 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.0855 | −1.21852 | −0.609261 | − | 0.792970i | \(-0.708534\pi\) | ||||
−0.609261 | + | 0.792970i | \(0.708534\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.8461 | 0.770580 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.9935 | −0.370379 | −0.185190 | − | 0.982703i | \(-0.559290\pi\) | ||||
−0.185190 | + | 0.982703i | \(0.559290\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.8415 | 1.81191 | 0.905956 | − | 0.423372i | \(-0.139154\pi\) | ||||
0.905956 | + | 0.423372i | \(0.139154\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.3817 | −0.449822 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −50.4057 | −1.69246 | −0.846229 | − | 0.532820i | \(-0.821132\pi\) | ||||
−0.846229 | + | 0.532820i | \(0.821132\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.150375 | −0.00504342 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.59056 | −0.187291 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.1072 | 0.605933 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.512927 | 0.0171453 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.87103 | 0.129250 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.4235 | −0.814569 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.86921 | −0.328791 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.39483 | 0.146251 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −29.8470 | −0.992147 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.2807 | 1.73595 | 0.867976 | − | 0.496607i | \(-0.165421\pi\) | ||||
0.867976 | + | 0.496607i | \(0.165421\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.51102 | −0.249125 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.9594 | −1.55584 | −0.777918 | − | 0.628366i | \(-0.783724\pi\) | ||||
−0.777918 | + | 0.628366i | \(0.783724\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.4473 | −0.742896 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.7816 | 0.422547 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.56586 | 0.216824 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.3643 | 1.33150 | 0.665748 | − | 0.746177i | \(-0.268113\pi\) | ||||
0.665748 | + | 0.746177i | \(0.268113\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.74814 | −0.0905543 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.06283 | 0.265391 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.94159 | −0.129599 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.49723 | −0.0491756 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.0090 | 0.787710 | 0.393855 | − | 0.919173i | \(-0.371141\pi\) | ||||
0.393855 | + | 0.919173i | \(0.371141\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.4746 | 0.834895 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.22030 | 0.105428 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 59.8745 | 1.95811 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.1221 | 0.657359 | 0.328680 | − | 0.944442i | \(-0.393396\pi\) | ||||
0.328680 | + | 0.944442i | \(0.393396\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.2753 | −0.987996 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.2819 | −0.856766 | −0.428383 | − | 0.903597i | \(-0.640917\pi\) | ||||
−0.428383 | + | 0.903597i | \(0.640917\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.3958 | 0.859564 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.33645 | 0.0434748 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.14635 | 0.199730 | 0.0998648 | − | 0.995001i | \(-0.468159\pi\) | ||||
0.0998648 | + | 0.995001i | \(0.468159\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.41662 | −0.110908 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.1079 | 0.425054 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.2709 | −1.01296 | −0.506481 | − | 0.862251i | \(-0.669054\pi\) | ||||
−0.506481 | + | 0.862251i | \(0.669054\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −63.7080 | −2.06154 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23.7043 | 0.766251 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.54003 | −0.211189 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.17965 | 0.0703114 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.29357 | 0.0739094 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.4049 | 0.882195 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.5240 | 0.370585 | 0.185293 | − | 0.982683i | \(-0.440677\pi\) | ||||
0.185293 | + | 0.982683i | \(0.440677\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.9473 | −0.512302 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.19367 | 0.166673 | 0.0833365 | − | 0.996521i | \(-0.473442\pi\) | ||||
0.0833365 | + | 0.996521i | \(0.473442\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.26622 | 0.232944 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.32680 | 0.0745173 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.7262 | 0.759067 | 0.379534 | − | 0.925178i | \(-0.376084\pi\) | ||||
0.379534 | + | 0.925178i | \(0.376084\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −90.7208 | −2.89945 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.3290 | 0.425562 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.9426 | 0.508490 | 0.254245 | − | 0.967140i | \(-0.418173\pi\) | ||||
0.254245 | + | 0.967140i | \(0.418173\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.4297 | −0.905847 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.51050 | 0.0799100 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.5113 | −0.652221 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.7291 | 1.29380 | 0.646902 | − | 0.762573i | \(-0.276064\pi\) | ||||
0.646902 | + | 0.762573i | \(0.276064\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.4120 | 0.711223 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −58.7703 | −1.86314 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.1173 | 1.42888 | 0.714440 | − | 0.699697i | \(-0.246681\pi\) | ||||
0.714440 | + | 0.699697i | \(0.246681\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.67489 | −0.0846297 |
(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 | 8016.2.a.be.1.1 | 11 | ||
4.3 | odd | 2 | 4008.2.a.k.1.1 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.k.1.1 | ✓ | 11 | 4.3 | odd | 2 | ||
8016.2.a.be.1.1 | 11 | 1.1 | even | 1 | trivial |