Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(1,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, 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("1216.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.961.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 10x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 152) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.29707\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1 |
$q$-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 | ||||||||
\(3\) | 3.29707 | 1.90356 | 0.951782 | − | 0.306774i | \(-0.0992497\pi\) | ||||
0.951782 | + | 0.306774i | \(0.0992497\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.08387 | 1.37915 | 0.689575 | − | 0.724214i | \(-0.257797\pi\) | ||||
0.689575 | + | 0.724214i | \(0.257797\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.78680 | −0.675348 | −0.337674 | − | 0.941263i | \(-0.609640\pi\) | ||||
−0.337674 | + | 0.941263i | \(0.609640\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.87067 | 2.62356 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.08387 | −1.53285 | −0.766423 | − | 0.642337i | \(-0.777965\pi\) | ||||
−0.766423 | + | 0.642337i | \(0.777965\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.29707 | 0.359743 | 0.179871 | − | 0.983690i | \(-0.442432\pi\) | ||||
0.179871 | + | 0.983690i | \(0.442432\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.1677 | 2.62530 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.213198 | 0.0517082 | 0.0258541 | − | 0.999666i | \(-0.491769\pi\) | ||||
0.0258541 | + | 0.999666i | \(0.491769\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.89121 | −1.28557 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.72347 | 0.776397 | 0.388198 | − | 0.921576i | \(-0.373098\pi\) | ||||
0.388198 | + | 0.921576i | \(0.373098\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.51027 | 0.902054 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.0590 | 3.09055 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.870674 | −0.161680 | −0.0808401 | − | 0.996727i | \(-0.525760\pi\) | ||||
−0.0808401 | + | 0.996727i | \(0.525760\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −16.7619 | −2.91787 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.51027 | −0.931405 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.27653 | 0.684793 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.59414 | 1.34218 | 0.671090 | − | 0.741376i | \(-0.265827\pi\) | ||||
0.671090 | + | 0.741376i | \(0.265827\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.67801 | −0.560892 | −0.280446 | − | 0.959870i | \(-0.590482\pi\) | ||||
−0.280446 | + | 0.959870i | \(0.590482\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 24.2722 | 3.61828 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.65748 | 0.679363 | 0.339681 | − | 0.940541i | \(-0.389681\pi\) | ||||
0.339681 | + | 0.940541i | \(0.389681\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.80734 | −0.543906 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.702929 | 0.0984298 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.0384 | −1.51624 | −0.758122 | − | 0.652113i | \(-0.773883\pi\) | ||||
−0.758122 | + | 0.652113i | \(0.773883\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.6780 | −2.11402 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.29707 | −0.436708 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.70293 | −0.612269 | −0.306135 | − | 0.951988i | \(-0.599036\pi\) | ||||
−0.306135 | + | 0.951988i | \(0.599036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.51027 | −0.449444 | −0.224722 | − | 0.974423i | \(-0.572147\pi\) | ||||
−0.224722 | + | 0.974423i | \(0.572147\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −14.0633 | −1.77181 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.12933 | 0.137969 | 0.0689846 | − | 0.997618i | \(-0.478024\pi\) | ||||
0.0689846 | + | 0.997618i | \(0.478024\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.2765 | 1.47792 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.76189 | −1.03984 | −0.519922 | − | 0.854214i | \(-0.674039\pi\) | ||||
−0.519922 | + | 0.854214i | \(0.674039\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.80734 | 0.796739 | 0.398369 | − | 0.917225i | \(-0.369576\pi\) | ||||
0.398369 | + | 0.917225i | \(0.369576\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.8707 | 1.71712 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.08387 | 1.03520 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.5941 | −1.64197 | −0.820985 | − | 0.570950i | \(-0.806575\pi\) | ||||
−0.820985 | + | 0.570950i | \(0.806575\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.3355 | 3.25950 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.74135 | −1.06925 | −0.534626 | − | 0.845089i | \(-0.679547\pi\) | ||||
−0.534626 | + | 0.845089i | \(0.679547\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.657476 | 0.0713133 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.87067 | −0.307769 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.76189 | −0.716758 | −0.358379 | − | 0.933576i | \(-0.616671\pi\) | ||||
−0.358379 | + | 0.933576i | \(0.616671\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.31761 | −0.242951 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.08387 | −0.316399 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.16774 | 0.423170 | 0.211585 | − | 0.977360i | \(-0.432137\pi\) | ||||
0.211585 | + | 0.977360i | \(0.432137\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −40.0135 | −4.02151 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −19.1883 | −1.90931 | −0.954653 | − | 0.297722i | \(-0.903773\pi\) | ||||
−0.954653 | + | 0.297722i | \(0.903773\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.9091 | 1.56757 | 0.783785 | − | 0.621033i | \(-0.213287\pi\) | ||||
0.783785 | + | 0.621033i | \(0.213287\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −18.1677 | −1.77299 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.29707 | −0.318740 | −0.159370 | − | 0.987219i | \(-0.550946\pi\) | ||||
−0.159370 | + | 0.987219i | \(0.550946\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.44428 | −0.425685 | −0.212842 | − | 0.977087i | \(-0.568272\pi\) | ||||
−0.212842 | + | 0.977087i | \(0.568272\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.59414 | 0.625888 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.1883 | −1.05251 | −0.526253 | − | 0.850328i | \(-0.676403\pi\) | ||||
−0.526253 | + | 0.850328i | \(0.676403\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.4827 | 1.07077 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.2088 | 0.943806 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.380943 | −0.0349210 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.8458 | 1.34961 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 28.3355 | 2.55493 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.51027 | −0.135083 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.7619 | −1.48738 | −0.743688 | − | 0.668526i | \(-0.766925\pi\) | ||||
−0.743688 | + | 0.668526i | \(0.766925\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.1267 | −1.06769 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.67801 | 0.321350 | 0.160675 | − | 0.987007i | \(-0.448633\pi\) | ||||
0.160675 | + | 0.987007i | \(0.448633\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.78680 | 0.154935 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 49.5238 | 4.26233 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.4015 | 1.82845 | 0.914226 | − | 0.405205i | \(-0.132800\pi\) | ||||
0.914226 | + | 0.405205i | \(0.132800\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.8252 | −0.918183 | −0.459092 | − | 0.888389i | \(-0.651825\pi\) | ||||
−0.459092 | + | 0.888389i | \(0.651825\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.3560 | 1.29321 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.59414 | −0.551430 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.68505 | −0.222981 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.5531 | −1.03536 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.2516 | 1.74100 | 0.870500 | − | 0.492168i | \(-0.163795\pi\) | ||||
0.870500 | + | 0.492168i | \(0.163795\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.9091 | 1.29466 | 0.647332 | − | 0.762208i | \(-0.275885\pi\) | ||||
0.647332 | + | 0.762208i | \(0.275885\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.67801 | 0.135659 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0000 | −1.11732 | −0.558661 | − | 0.829396i | \(-0.688685\pi\) | ||||
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −36.3944 | −2.88627 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.65310 | −0.524338 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.18828 | 0.719682 | 0.359841 | − | 0.933014i | \(-0.382831\pi\) | ||||
0.359841 | + | 0.933014i | \(0.382831\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −51.6915 | −4.02418 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.83226 | 0.451313 | 0.225657 | − | 0.974207i | \(-0.427547\pi\) | ||||
0.225657 | + | 0.974207i | \(0.427547\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3176 | −0.870585 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.87067 | −0.601885 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.18828 | 0.546515 | 0.273257 | − | 0.961941i | \(-0.411899\pi\) | ||||
0.273257 | + | 0.961941i | \(0.411899\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.05896 | −0.609200 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.5059 | −1.16549 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.87333 | −0.588480 | −0.294240 | − | 0.955732i | \(-0.595067\pi\) | ||||
−0.294240 | + | 0.955732i | \(0.595067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.3355 | 1.66018 | 0.830092 | − | 0.557627i | \(-0.188288\pi\) | ||||
0.830092 | + | 0.557627i | \(0.188288\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.5736 | −0.855545 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.16774 | 0.453462 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.08387 | −0.0792606 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −28.6942 | −2.08719 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.7370 | 1.71755 | 0.858773 | − | 0.512356i | \(-0.171227\pi\) | ||||
0.858773 | + | 0.512356i | \(0.171227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.31495 | −0.526542 | −0.263271 | − | 0.964722i | \(-0.584801\pi\) | ||||
−0.263271 | + | 0.964722i | \(0.584801\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.1883 | 0.944433 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.59414 | 0.612307 | 0.306154 | − | 0.951982i | \(-0.400958\pi\) | ||||
0.306154 | + | 0.951982i | \(0.400958\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.06599 | 0.500895 | 0.250447 | − | 0.968130i | \(-0.419422\pi\) | ||||
0.250447 | + | 0.968130i | \(0.419422\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.72347 | 0.262633 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.55572 | 0.109190 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 26.5032 | 1.85107 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 29.3062 | 2.03692 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.08387 | 0.351659 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.55572 | −0.382472 | −0.191236 | − | 0.981544i | \(-0.561250\pi\) | ||||
−0.191236 | + | 0.981544i | \(0.561250\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −28.8886 | −1.97941 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.3425 | −0.773554 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.4443 | 1.51664 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.276533 | 0.0186016 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.7619 | 1.12246 | 0.561229 | − | 0.827660i | \(-0.310329\pi\) | ||||
0.561229 | + | 0.827660i | \(0.310329\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 35.4989 | 2.36659 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.27653 | 0.549333 | 0.274666 | − | 0.961540i | \(-0.411433\pi\) | ||||
0.274666 | + | 0.961540i | \(0.411433\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6986 | 0.839144 | 0.419572 | − | 0.907722i | \(-0.362180\pi\) | ||||
0.419572 | + | 0.907722i | \(0.362180\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 29.9502 | 1.97058 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.36306 | 0.547882 | 0.273941 | − | 0.961746i | \(-0.411673\pi\) | ||||
0.273941 | + | 0.961746i | \(0.411673\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.3631 | 0.936943 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −48.1179 | −3.12559 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.97508 | −0.451181 | −0.225590 | − | 0.974222i | \(-0.572431\pi\) | ||||
−0.225590 | + | 0.974222i | \(0.572431\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.7413 | −1.27165 | −0.635826 | − | 0.771832i | \(-0.719340\pi\) | ||||
−0.635826 | + | 0.771832i | \(0.719340\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 48.5443 | 3.11412 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.7413 | −0.750127 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.29707 | −0.0825306 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −32.1179 | −2.03539 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.2722 | 0.648373 | 0.324186 | − | 0.945993i | \(-0.394910\pi\) | ||||
0.324186 | + | 0.945993i | \(0.394910\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.9296 | −1.19010 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.16774 | 0.135749 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.90909 | 0.618112 | 0.309056 | − | 0.951044i | \(-0.399987\pi\) | ||||
0.309056 | + | 0.951044i | \(0.399987\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.57360 | −0.222053 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.85279 | −0.424177 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.6780 | −1.46005 | −0.730024 | − | 0.683421i | \(-0.760491\pi\) | ||||
−0.730024 | + | 0.683421i | \(0.760491\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −34.0411 | −2.09113 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −22.2944 | −1.36440 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.02054 | 0.306108 | 0.153054 | − | 0.988218i | \(-0.451089\pi\) | ||||
0.153054 | + | 0.988218i | \(0.451089\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.27653 | −0.259781 | −0.129890 | − | 0.991528i | \(-0.541463\pi\) | ||||
−0.129890 | + | 0.991528i | \(0.541463\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.64132 | −0.462474 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −22.9296 | −1.38271 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.93667 | −0.476868 | −0.238434 | − | 0.971159i | \(-0.576634\pi\) | ||||
−0.238434 | + | 0.971159i | \(0.576634\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.8886 | 1.36542 | 0.682708 | − | 0.730691i | \(-0.260802\pi\) | ||||
0.682708 | + | 0.730691i | \(0.260802\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.08387 | −0.302205 | −0.151102 | − | 0.988518i | \(-0.548282\pi\) | ||||
−0.151102 | + | 0.988518i | \(0.548282\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.1677 | −0.602285 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.3560 | −0.906438 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9545 | −0.997326 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.7413 | 0.805532 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.55572 | 0.207728 | 0.103864 | − | 0.994592i | \(-0.466879\pi\) | ||||
0.103864 | + | 0.994592i | \(0.466879\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.5032 | −0.844411 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −81.6417 | −4.73733 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.82960 | 0.279303 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.57188 | 0.378797 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −63.2651 | −3.63449 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.8252 | −0.619850 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.3355 | 0.932316 | 0.466158 | − | 0.884702i | \(-0.345638\pi\) | ||||
0.466158 | + | 0.884702i | \(0.345638\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 52.4534 | 2.98397 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.3809 | 0.928878 | 0.464439 | − | 0.885605i | \(-0.346256\pi\) | ||||
0.464439 | + | 0.885605i | \(0.346256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.0590 | −1.69903 | −0.849516 | − | 0.527562i | \(-0.823106\pi\) | ||||
−0.849516 | + | 0.527562i | \(0.823106\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −43.3695 | −2.44360 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.0179 | 0.674991 | 0.337496 | − | 0.941327i | \(-0.390420\pi\) | ||||
0.337496 | + | 0.941327i | \(0.390420\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.42640 | 0.247831 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.8707 | −0.606742 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.213198 | −0.0118627 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.85014 | 0.324507 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.6531 | −0.810318 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.32199 | −0.458806 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.3176 | −0.786967 | −0.393483 | − | 0.919332i | \(-0.628730\pi\) | ||||
−0.393483 | + | 0.919332i | \(0.628730\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.7413 | 0.862621 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.48270 | 0.190280 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.6147 | 0.632692 | 0.316346 | − | 0.948644i | \(-0.397544\pi\) | ||||
0.316346 | + | 0.948644i | \(0.397544\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −36.8886 | −2.00351 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.3106 | 1.04267 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 37.8593 | 2.03827 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.91613 | −0.156546 | −0.0782730 | − | 0.996932i | \(-0.524941\pi\) | ||||
−0.0782730 | + | 0.996932i | \(0.524941\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.8252 | −0.686518 | −0.343259 | − | 0.939241i | \(-0.611531\pi\) | ||||
−0.343259 | + | 0.939241i | \(0.611531\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.8296 | 1.11180 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.7592 | 1.37103 | 0.685513 | − | 0.728061i | \(-0.259578\pi\) | ||||
0.685513 | + | 0.728061i | \(0.259578\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.0205 | −1.43410 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.25600 | −0.0664743 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.4220 | −1.18339 | −0.591694 | − | 0.806162i | \(-0.701541\pi\) | ||||
−0.591694 | + | 0.806162i | \(0.701541\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 48.9475 | 2.56908 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.9930 | 1.09882 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.18828 | −0.270826 | −0.135413 | − | 0.990789i | \(-0.543236\pi\) | ||||
−0.135413 | + | 0.990789i | \(0.543236\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 67.6417 | 3.52129 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.7235 | 1.02399 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −36.0091 | −1.86448 | −0.932241 | − | 0.361838i | \(-0.882149\pi\) | ||||
−0.932241 | + | 0.361838i | \(0.882149\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.97946 | −0.257138 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.12933 | −0.0581632 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.0384 | −1.28614 | −0.643069 | − | 0.765809i | \(-0.722339\pi\) | ||||
−0.643069 | + | 0.765809i | \(0.722339\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −55.2651 | −2.83132 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.7413 | 1.11093 | 0.555466 | − | 0.831540i | \(-0.312540\pi\) | ||||
0.555466 | + | 0.831540i | \(0.312540\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 28.0135 | 1.42770 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −28.9484 | −1.47153 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.5103 | −0.583594 | −0.291797 | − | 0.956480i | \(-0.594253\pi\) | ||||
−0.291797 | + | 0.956480i | \(0.594253\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.793836 | 0.0401460 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.1267 | 0.611710 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −45.0065 | −2.26452 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.21054 | 0.361887 | 0.180943 | − | 0.983494i | \(-0.442085\pi\) | ||||
0.180943 | + | 0.983494i | \(0.442085\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.89121 | 0.294929 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.23811 | 0.0618285 | 0.0309142 | − | 0.999522i | \(-0.490158\pi\) | ||||
0.0309142 | + | 0.999522i | \(0.490158\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 90.4669 | 4.49534 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.1677 | −0.503996 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.8030 | 1.62200 | 0.811001 | − | 0.585045i | \(-0.198923\pi\) | ||||
0.811001 | + | 0.585045i | \(0.198923\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 70.5622 | 3.48058 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.40320 | 0.413495 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −30.0411 | −1.47466 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −35.6915 | −1.74782 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.1883 | −0.839703 | −0.419851 | − | 0.907593i | \(-0.637918\pi\) | ||||
−0.419851 | + | 0.907593i | \(0.637918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.8912 | −0.969438 | −0.484719 | − | 0.874670i | \(-0.661078\pi\) | ||||
−0.484719 | + | 0.874670i | \(0.661078\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 36.6575 | 1.78235 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.961581 | 0.0466435 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.27215 | 0.303531 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21.7413 | −1.04968 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.55307 | −0.411987 | −0.205993 | − | 0.978553i | \(-0.566043\pi\) | ||||
−0.205993 | + | 0.978553i | \(0.566043\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.5238 | −1.51494 | −0.757468 | − | 0.652872i | \(-0.773564\pi\) | ||||
−0.757468 | + | 0.652872i | \(0.773564\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.85279 | −0.424459 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.72347 | −0.178118 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.12667 | 0.196955 | 0.0984776 | − | 0.995139i | \(-0.468603\pi\) | ||||
0.0984776 | + | 0.995139i | \(0.468603\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −29.9663 | −1.42697 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 37.7549 | 1.79379 | 0.896894 | − | 0.442246i | \(-0.145818\pi\) | ||||
0.896894 | + | 0.442246i | \(0.145818\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.8528 | −0.988517 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 70.0681 | 3.31411 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.3560 | 1.57417 | 0.787084 | − | 0.616846i | \(-0.211590\pi\) | ||||
0.787084 | + | 0.616846i | \(0.211590\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −43.6915 | −2.05735 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 52.4534 | 2.46448 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.14721 | −0.335066 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.1223 | 1.50262 | 0.751309 | − | 0.659951i | \(-0.229423\pi\) | ||||
0.751309 | + | 0.659951i | \(0.229423\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.42374 | 0.159807 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.81000 | 0.363748 | 0.181874 | − | 0.983322i | \(-0.441784\pi\) | ||||
0.181874 | + | 0.983322i | \(0.441784\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.4897 | −0.859291 | −0.429645 | − | 0.902998i | \(-0.641361\pi\) | ||||
−0.429645 | + | 0.902998i | \(0.641361\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.0839 | 0.975645 | 0.487823 | − | 0.872943i | \(-0.337791\pi\) | ||||
0.487823 | + | 0.872943i | \(0.337791\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.01788 | −0.0931771 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −46.1590 | −2.12689 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.6986 | 0.859760 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.51027 | −0.206945 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −86.8798 | −3.97795 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.5238 | 1.16621 | 0.583105 | − | 0.812396i | \(-0.301837\pi\) | ||||
0.583105 | + | 0.812396i | \(0.301837\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.59414 | 0.118283 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −21.9357 | −0.998110 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.8528 | 0.583615 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.4675 | 0.474326 | 0.237163 | − | 0.971470i | \(-0.423782\pi\) | ||||
0.237163 | + | 0.971470i | \(0.423782\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 30.2944 | 1.36996 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.6710 | 0.571833 | 0.285917 | − | 0.958254i | \(-0.407702\pi\) | ||||
0.285917 | + | 0.958254i | \(0.407702\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.185626 | −0.00836018 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −123.397 | −5.54626 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.6558 | 0.702257 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.8458 | −0.619821 | −0.309911 | − | 0.950766i | \(-0.600299\pi\) | ||||
−0.309911 | + | 0.950766i | \(0.600299\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.2294 | 0.859104 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.76454 | 0.435379 | 0.217690 | − | 0.976018i | \(-0.430148\pi\) | ||||
0.217690 | + | 0.976018i | \(0.430148\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −59.1742 | −2.63322 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −37.3150 | −1.65722 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.1677 | 1.24851 | 0.624257 | − | 0.781219i | \(-0.285402\pi\) | ||||
0.624257 | + | 0.781219i | \(0.285402\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.1634 | −0.538076 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.0590 | −0.709020 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 49.0616 | 2.16191 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.6780 | −1.04136 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.7003 | 1.04033 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.2035 | −1.23562 | −0.617809 | − | 0.786328i | \(-0.711980\pi\) | ||||
−0.617809 | + | 0.786328i | \(0.711980\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.22023 | 0.0533571 | 0.0266785 | − | 0.999644i | \(-0.491507\pi\) | ||||
0.0266785 | + | 0.999644i | \(0.491507\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −26.5709 | −1.15965 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.13579 | −0.397208 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −37.0152 | −1.60632 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.1472 | 0.482839 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.1677 | −0.439590 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −25.9589 | −1.12021 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.3560 | 0.833723 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.1812 | −0.523713 | −0.261856 | − | 0.965107i | \(-0.584335\pi\) | ||||
−0.261856 | + | 0.965107i | \(0.584335\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 73.6417 | 3.16027 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.7056 | −0.587083 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000 | 0.513083 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −27.6282 | −1.17914 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.870674 | 0.0370920 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.0768 | 1.10890 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 20.3355 | 0.863193 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.60764 | −0.364718 | −0.182359 | − | 0.983232i | \(-0.558373\pi\) | ||||
−0.182359 | + | 0.983232i | \(0.558373\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.77064 | −0.201777 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.57360 | −0.150878 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.3560 | −0.815759 | −0.407880 | − | 0.913036i | \(-0.633732\pi\) | ||||
−0.407880 | + | 0.913036i | \(0.633732\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.5032 | −1.45156 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −52.4167 | −2.20129 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.23811 | 0.387282 | 0.193641 | − | 0.981072i | \(-0.437970\pi\) | ||||
0.193641 | + | 0.981072i | \(0.437970\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.3766 | 0.601640 | 0.300820 | − | 0.953681i | \(-0.402740\pi\) | ||||
0.300820 | + | 0.953681i | \(0.402740\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 78.2625 | 3.26946 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.7938 | 0.700351 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.19266 | 0.216173 | 0.108087 | − | 0.994141i | \(-0.465528\pi\) | ||||
0.108087 | + | 0.994141i | \(0.465528\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.1179 | −1.00231 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.4059 | 0.722117 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 56.1179 | 2.32417 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 31.4827 | 1.30165 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.3079 | 1.25094 | 0.625471 | − | 0.780248i | \(-0.284907\pi\) | ||||
0.625471 | + | 0.780248i | \(0.284907\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.3355 | 1.16557 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.04107 | −0.165947 | −0.0829735 | − | 0.996552i | \(-0.526442\pi\) | ||||
−0.0829735 | + | 0.996552i | \(0.526442\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.17478 | −0.0481613 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.2971 | 0.953486 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.29441 | 0.257183 | 0.128591 | − | 0.991698i | \(-0.458954\pi\) | ||||
0.128591 | + | 0.991698i | \(0.458954\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0358 | −0.409367 | −0.204684 | − | 0.978828i | \(-0.565617\pi\) | ||||
−0.204684 | + | 0.978828i | \(0.565617\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.88856 | 0.361970 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 45.7824 | 1.86132 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 45.3062 | 1.83892 | 0.919461 | − | 0.393182i | \(-0.128626\pi\) | ||||
0.919461 | + | 0.393182i | \(0.128626\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.12933 | 0.207851 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.04107 | 0.244396 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.1607 | −1.01623 | −0.508116 | − | 0.861289i | \(-0.669658\pi\) | ||||
−0.508116 | + | 0.861289i | \(0.669658\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 87.3830 | 3.52362 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.01350 | 0.242095 | 0.121047 | − | 0.992647i | \(-0.461375\pi\) | ||||
0.121047 | + | 0.992647i | \(0.461375\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.2240 | 1.49616 | 0.748080 | − | 0.663608i | \(-0.230976\pi\) | ||||
0.748080 | + | 0.663608i | \(0.230976\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 59.7950 | 2.39949 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0821 | 0.484061 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.2088 | −1.08835 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.7619 | 0.669405 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.426396 | 0.0170015 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.0135 | 0.478250 | 0.239125 | − | 0.970989i | \(-0.423139\pi\) | ||||
0.239125 | + | 0.970989i | \(0.423139\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.3176 | −0.728060 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −51.6915 | −2.05132 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.93839 | −0.195666 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −68.9619 | −2.72809 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.97946 | 0.275672 | 0.137836 | − | 0.990455i | \(-0.455985\pi\) | ||||
0.137836 | + | 0.990455i | \(0.455985\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.7754 | 1.60802 | 0.804012 | − | 0.594613i | \(-0.202695\pi\) | ||||
0.804012 | + | 0.594613i | \(0.202695\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −37.3971 | −1.47251 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.9340 | −0.980257 | −0.490129 | − | 0.871650i | \(-0.663050\pi\) | ||||
−0.490129 | + | 0.871650i | \(0.663050\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.9091 | 0.938514 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.3988 | 1.42440 | 0.712198 | − | 0.701979i | \(-0.247700\pi\) | ||||
0.712198 | + | 0.701979i | \(0.247700\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.3425 | 0.443189 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 53.5783 | 2.09029 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.8501 | 0.461616 | 0.230808 | − | 0.972999i | \(-0.425863\pi\) | ||||
0.230808 | + | 0.972999i | \(0.425863\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.4854 | −1.34132 | −0.670662 | − | 0.741763i | \(-0.733990\pi\) | ||||
−0.670662 | + | 0.741763i | \(0.733990\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.911749 | 0.0354094 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.51027 | 0.213679 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.24193 | −0.125528 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 55.2651 | 2.13667 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.8458 | 0.688928 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.7003 | 0.682295 | 0.341148 | − | 0.940010i | \(-0.389184\pi\) | ||||
0.341148 | + | 0.940010i | \(0.389184\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 72.4302 | 2.78784 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.0590 | 1.00153 | 0.500764 | − | 0.865584i | \(-0.333053\pi\) | ||||
0.500764 | + | 0.865584i | \(0.333053\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.44693 | −0.285787 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.2883 | 1.04569 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 65.9994 | 2.52171 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.8680 | 1.59736 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.3176 | −0.545457 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.9367 | 0.530176 | 0.265088 | − | 0.964224i | \(-0.414599\pi\) | ||||
0.265088 | + | 0.964224i | \(0.414599\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 71.4962 | 2.71592 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −33.3836 | −1.26631 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.83226 | 0.0694016 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27.5736 | 1.04293 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.55307 | −0.247506 | −0.123753 | − | 0.992313i | \(-0.539493\pi\) | ||||
−0.123753 | + | 0.992313i | \(0.539493\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.00000 | −0.0754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 47.3560 | 1.78353 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 34.2857 | 1.28944 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.5238 | −0.883454 | −0.441727 | − | 0.897150i | \(-0.645634\pi\) | ||||
−0.441727 | + | 0.897150i | \(0.645634\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −114.866 | −4.30780 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.3355 | −0.760504 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.9973 | −0.858852 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.8842 | 0.555086 | 0.277543 | − | 0.960713i | \(-0.410480\pi\) | ||||
0.277543 | + | 0.960713i | \(0.410480\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.4264 | −1.05865 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −65.0886 | −2.42067 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.92697 | −0.145844 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.32464 | −0.0491283 | −0.0245641 | − | 0.999698i | \(-0.507820\pi\) | ||||
−0.0245641 | + | 0.999698i | \(0.507820\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 72.0475 | 2.66843 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.784146 | −0.0290027 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.7824 | 0.509065 | 0.254533 | − | 0.967064i | \(-0.418078\pi\) | ||||
0.254533 | + | 0.967064i | \(0.418078\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −38.7121 | −1.42792 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.74135 | −0.211485 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.5513 | 0.866350 | 0.433175 | − | 0.901310i | \(-0.357393\pi\) | ||||
0.433175 | + | 0.901310i | \(0.357393\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.27653 | −0.157102 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.0411 | 0.515117 | 0.257559 | − | 0.966263i | \(-0.417082\pi\) | ||||
0.257559 | + | 0.966263i | \(0.417082\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 65.5373 | 2.40110 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −76.6710 | −2.80524 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.89121 | 0.215260 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.7056 | 0.646086 | 0.323043 | − | 0.946384i | \(-0.395294\pi\) | ||||
0.323043 | + | 0.946384i | \(0.395294\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 33.8680 | 1.23422 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 49.0616 | 1.78553 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.3220 | −1.10207 | −0.551036 | − | 0.834482i | \(-0.685767\pi\) | ||||
−0.551036 | + | 0.834482i | \(0.685767\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −62.4123 | −2.26542 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.5487 | 0.454890 | 0.227445 | − | 0.973791i | \(-0.426963\pi\) | ||||
0.227445 | + | 0.973791i | \(0.426963\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.94104 | 0.287485 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.17478 | 0.187095 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.10003 | −0.220259 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −50.0725 | −1.80566 | −0.902830 | − | 0.429999i | \(-0.858514\pi\) | ||||
−0.902830 | + | 0.429999i | \(0.858514\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.6710 | 1.17662 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.8003 | −0.424427 | −0.212214 | − | 0.977223i | \(-0.568067\pi\) | ||||
−0.212214 | + | 0.977223i | \(0.568067\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.7824 | −0.422692 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.59414 | −0.307917 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.5443 | 1.59392 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.9821 | −0.499680 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −43.1742 | −1.54095 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.9475 | 1.17445 | 0.587226 | − | 0.809423i | \(-0.300220\pi\) | ||||
0.587226 | + | 0.809423i | \(0.300220\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −78.0681 | −2.77930 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.9912 | 0.710807 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.55307 | −0.161684 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −112.236 | −3.98059 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.8208 | 0.666668 | 0.333334 | − | 0.942809i | \(-0.391826\pi\) | ||||
0.333334 | + | 0.942809i | \(0.391826\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.992965 | 0.0351286 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −53.2206 | −1.88046 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −34.6076 | −1.22128 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.5173 | −0.723140 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.5531 | 0.582696 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.2607 | −1.38033 | −0.690167 | − | 0.723650i | \(-0.742463\pi\) | ||||
−0.690167 | + | 0.723650i | \(0.742463\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.9182 | 1.19103 | 0.595515 | − | 0.803344i | \(-0.296948\pi\) | ||||
0.595515 | + | 0.803344i | \(0.296948\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.1000 | −0.494510 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.3355 | 0.992549 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.67801 | 0.128677 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.2411 | −0.637397 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.6487 | −1.34885 | −0.674425 | − | 0.738344i | \(-0.735608\pi\) | ||||
−0.674425 | + | 0.738344i | \(0.735608\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.47185 | 0.295310 | 0.147655 | − | 0.989039i | \(-0.452827\pi\) | ||||
0.147655 | + | 0.989039i | \(0.452827\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −75.6006 | −2.63208 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.7299 | −1.55541 | −0.777706 | − | 0.628628i | \(-0.783617\pi\) | ||||
−0.777706 | + | 0.628628i | \(0.783617\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.8566 | 1.34955 | 0.674773 | − | 0.738025i | \(-0.264242\pi\) | ||||
0.674773 | + | 0.738025i | \(0.264242\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.1677 | −0.907749 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.811718 | −0.0281244 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.9859 | 0.622429 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.53784 | 0.260235 | 0.130118 | − | 0.991499i | \(-0.458465\pi\) | ||||
0.130118 | + | 0.991499i | \(0.458465\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2419 | −0.973860 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 75.4652 | 2.59916 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34.9021 | −1.20067 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.5264 | −0.911459 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.7619 | −0.575266 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.44693 | 0.255278 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.5238 | 1.49023 | 0.745113 | − | 0.666938i | \(-0.232396\pi\) | ||||
0.745113 | + | 0.666938i | \(0.232396\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24.2722 | −0.830090 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.5531 | −0.497123 | −0.248562 | − | 0.968616i | \(-0.579958\pi\) | ||||
−0.248562 | + | 0.968616i | \(0.579958\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.3132 | −0.829557 | −0.414778 | − | 0.909922i | \(-0.636141\pi\) | ||||
−0.414778 | + | 0.909922i | \(0.636141\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −50.6299 | −1.72546 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.4264 | 0.422999 | 0.211500 | − | 0.977378i | \(-0.432165\pi\) | ||||
0.211500 | + | 0.977378i | \(0.432165\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.1677 | 0.753726 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −55.9003 | −1.89847 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 74.1948 | 2.51688 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.46482 | 0.0496334 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 32.8030 | 1.11021 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.69855 | 0.0912277 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −54.6120 | −1.84412 | −0.922058 | − | 0.387051i | \(-0.873494\pi\) | ||||
−0.922058 | + | 0.387051i | \(0.873494\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.7235 | 0.395423 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.4551 | 1.19451 | 0.597257 | − | 0.802050i | \(-0.296257\pi\) | ||||
0.597257 | + | 0.802050i | \(0.296257\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.5460 | 0.725082 | 0.362541 | − | 0.931968i | \(-0.381909\pi\) | ||||
0.362541 | + | 0.931968i | \(0.381909\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −47.8182 | −1.60739 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −49.6147 | −1.66590 | −0.832949 | − | 0.553350i | \(-0.813349\pi\) | ||||
−0.832949 | + | 0.553350i | \(0.813349\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.9502 | 1.00450 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −149.138 | −4.99631 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.65748 | −0.155856 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.2803 | −0.811602 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.9235 | 0.531671 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.35337 | −0.0784022 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.6680 | 0.721064 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 68.8798 | 2.28964 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.0883 | −0.368179 | −0.184090 | − | 0.982909i | \(-0.558934\pi\) | ||||
−0.184090 | + | 0.982909i | \(0.558934\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −151.025 | −5.00917 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.5443 | −0.415612 | −0.207806 | − | 0.978170i | \(-0.566632\pi\) | ||||
−0.207806 | + | 0.978170i | \(0.566632\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 49.5238 | 1.63900 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −35.6915 | −1.17993 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.57188 | −0.217023 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.8707 | −1.41417 | −0.707087 | − | 0.707127i | \(-0.749991\pi\) | ||||
−0.707087 | + | 0.707127i | \(0.749991\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 53.8593 | 1.77472 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.3648 | −0.374076 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.02054 | 0.296593 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 125.215 | 4.11261 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.9182 | −0.915967 | −0.457984 | − | 0.888961i | \(-0.651428\pi\) | ||||
−0.457984 | + | 0.888961i | \(0.651428\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.80734 | 0.124781 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 54.0091 | 1.76818 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.34252 | −0.109312 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.8982 | −0.356030 | −0.178015 | − | 0.984028i | \(-0.556968\pi\) | ||||
−0.178015 | + | 0.984028i | \(0.556968\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −99.1065 | −3.23422 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.9475 | 1.00886 | 0.504430 | − | 0.863453i | \(-0.331703\pi\) | ||||
0.504430 | + | 0.863453i | \(0.331703\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.0000 | 1.04206 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −88.4892 | −2.87855 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.2944 | −0.594489 | −0.297244 | − | 0.954801i | \(-0.596068\pi\) | ||||
−0.297244 | + | 0.954801i | \(0.596068\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.82960 | 0.286621 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 39.6238 | 1.28489 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.0616 | −0.747039 | −0.373519 | − | 0.927622i | \(-0.621849\pi\) | ||||
−0.373519 | + | 0.927622i | \(0.621849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 73.2018 | 2.36875 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.5941 | 0.471762 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −38.2402 | −1.23484 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.9502 | −0.836232 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.5584 | −0.726180 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.3766 | −0.848213 | −0.424107 | − | 0.905612i | \(-0.639412\pi\) | ||||
−0.424107 | + | 0.905612i | \(0.639412\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.702929 | −0.0225813 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.0000 | 0.641831 | 0.320915 | − | 0.947108i | \(-0.396010\pi\) | ||||
0.320915 | + | 0.947108i | \(0.396010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.3425 | 0.620093 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.2883 | 0.617720 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.4264 | −0.845455 | −0.422728 | − | 0.906257i | \(-0.638927\pi\) | ||||
−0.422728 | + | 0.906257i | \(0.638927\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.3766 | 1.09868 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34.9795 | −1.11681 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.4059 | −0.810321 | −0.405161 | − | 0.914246i | \(-0.632784\pi\) | ||||
−0.405161 | + | 0.914246i | \(0.632784\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.5032 | 0.844463 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.4382 | −0.873367 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.6950 | −0.435474 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.6504 | −0.941877 | −0.470939 | − | 0.882166i | \(-0.656085\pi\) | ||||
−0.470939 | + | 0.882166i | \(0.656085\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −47.2062 | −1.49804 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.7906 | 0.690809 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.7754 | 1.22803 | 0.614014 | − | 0.789295i | \(-0.289554\pi\) | ||||
0.614014 | + | 0.789295i | \(0.289554\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 32.1179 | 1.01617 |
(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 | 1216.2.a.v.1.3 | 3 | ||
4.3 | odd | 2 | 1216.2.a.u.1.1 | 3 | |||
8.3 | odd | 2 | 152.2.a.c.1.3 | ✓ | 3 | ||
8.5 | even | 2 | 304.2.a.g.1.1 | 3 | |||
24.5 | odd | 2 | 2736.2.a.bd.1.3 | 3 | |||
24.11 | even | 2 | 1368.2.a.n.1.3 | 3 | |||
40.3 | even | 4 | 3800.2.d.j.3649.6 | 6 | |||
40.19 | odd | 2 | 3800.2.a.r.1.1 | 3 | |||
40.27 | even | 4 | 3800.2.d.j.3649.1 | 6 | |||
40.29 | even | 2 | 7600.2.a.bv.1.3 | 3 | |||
56.27 | even | 2 | 7448.2.a.bf.1.1 | 3 | |||
152.37 | odd | 2 | 5776.2.a.bp.1.3 | 3 | |||
152.75 | even | 2 | 2888.2.a.o.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.a.c.1.3 | ✓ | 3 | 8.3 | odd | 2 | ||
304.2.a.g.1.1 | 3 | 8.5 | even | 2 | |||
1216.2.a.u.1.1 | 3 | 4.3 | odd | 2 | |||
1216.2.a.v.1.3 | 3 | 1.1 | even | 1 | trivial | ||
1368.2.a.n.1.3 | 3 | 24.11 | even | 2 | |||
2736.2.a.bd.1.3 | 3 | 24.5 | odd | 2 | |||
2888.2.a.o.1.1 | 3 | 152.75 | even | 2 | |||
3800.2.a.r.1.1 | 3 | 40.19 | odd | 2 | |||
3800.2.d.j.3649.1 | 6 | 40.27 | even | 4 | |||
3800.2.d.j.3649.6 | 6 | 40.3 | even | 4 | |||
5776.2.a.bp.1.3 | 3 | 152.37 | odd | 2 | |||
7448.2.a.bf.1.1 | 3 | 56.27 | even | 2 | |||
7600.2.a.bv.1.3 | 3 | 40.29 | even | 2 |