Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(3649,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3800.3649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.d (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(30.3431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.59105344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 21x^{4} + 116x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3649.1 | ||
Root | \(3.08387i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.3649 |
Dual form | 3800.2.d.j.3649.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(951\) | \(1901\) | \(1977\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 3.29707i | − 1.90356i | −0.306774 | − | 0.951782i | \(-0.599250\pi\) | ||||
0.306774 | − | 0.951782i | \(-0.400750\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.78680i | 0.675348i | 0.941263 | + | 0.337674i | \(0.109640\pi\) | ||||
−0.941263 | + | 0.337674i | \(0.890360\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | 1.29707i | 0.359743i | 0.983690 | + | 0.179871i | \(0.0575681\pi\) | ||||
−0.983690 | + | 0.179871i | \(0.942432\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.213198i | 0.0517082i | 0.999666 | + | 0.0258541i | \(0.00823053\pi\) | ||||
−0.999666 | + | 0.0258541i | \(0.991769\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.89121 | 1.28557 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.72347i | 0.776397i | 0.921576 | + | 0.388198i | \(0.126902\pi\) | ||||
−0.921576 | + | 0.388198i | \(0.873098\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.0590i | 3.09055i | ||||||||
\(28\) | 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 | ||||||||
\(33\) | 16.7619i | 2.91787i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.00000i | − 0.328798i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) | ||||
0.986394 | − | 0.164399i | \(-0.0525685\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 3.67801i | 0.560892i | 0.959870 | + | 0.280446i | \(0.0904823\pi\) | ||||
−0.959870 | + | 0.280446i | \(0.909518\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 4.65748i | − 0.679363i | −0.940541 | − | 0.339681i | \(-0.889681\pi\) | ||||
0.940541 | − | 0.339681i | \(-0.110319\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.80734 | 0.543906 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.702929 | 0.0984298 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 11.0384i | − 1.51624i | −0.652113 | − | 0.758122i | \(-0.726117\pi\) | ||||
0.652113 | − | 0.758122i | \(-0.273883\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 3.29707i | − 0.436708i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.70293 | 0.612269 | 0.306135 | − | 0.951988i | \(-0.400964\pi\) | ||||
0.306135 | + | 0.951988i | \(0.400964\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.51027 | 0.449444 | 0.224722 | − | 0.974423i | \(-0.427853\pi\) | ||||
0.224722 | + | 0.974423i | \(0.427853\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 14.0633i | − 1.77181i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.12933i | 0.137969i | 0.997618 | + | 0.0689846i | \(0.0219759\pi\) | ||||
−0.997618 | + | 0.0689846i | \(0.978024\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.2765 | 1.47792 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.76189 | 1.03984 | 0.519922 | − | 0.854214i | \(-0.325961\pi\) | ||||
0.519922 | + | 0.854214i | \(0.325961\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 6.80734i | − 0.796739i | −0.917225 | − | 0.398369i | \(-0.869576\pi\) | ||||
0.917225 | − | 0.398369i | \(-0.130424\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 9.08387i | − 1.03520i | ||||||||
\(78\) | 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 | ||||||||
\(83\) | 9.74135i | 1.06925i | 0.845089 | + | 0.534626i | \(0.179547\pi\) | ||||
−0.845089 | + | 0.534626i | \(0.820453\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.87067i | 0.307769i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.76189 | 0.716758 | 0.358379 | − | 0.933576i | \(-0.383329\pi\) | ||||
0.358379 | + | 0.933576i | \(0.383329\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.31761 | −0.242951 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.16774i | 0.423170i | 0.977360 | + | 0.211585i | \(0.0678626\pi\) | ||||
−0.977360 | + | 0.211585i | \(0.932137\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 40.0135 | 4.02151 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.1883 | 1.90931 | 0.954653 | − | 0.297722i | \(-0.0962267\pi\) | ||||
0.954653 | + | 0.297722i | \(0.0962267\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.9091i | 1.56757i | 0.621033 | + | 0.783785i | \(0.286713\pi\) | ||||
−0.621033 | + | 0.783785i | \(0.713287\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 3.29707i | − 0.318740i | −0.987219 | − | 0.159370i | \(-0.949054\pi\) | ||||
0.987219 | − | 0.159370i | \(-0.0509463\pi\) | |||||||
\(108\) | 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 | ||||||||
\(113\) | 11.1883i | 1.05251i | 0.850328 | + | 0.526253i | \(0.176403\pi\) | ||||
−0.850328 | + | 0.526253i | \(0.823597\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 10.2088i | − 0.943806i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.380943 | −0.0349210 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.8458 | 1.34961 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 28.3355i | − 2.55493i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.7619i | 1.48738i | 0.668526 | + | 0.743688i | \(0.266925\pi\) | ||||
−0.668526 | + | 0.743688i | \(0.733075\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | 1.78680i | 0.154935i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.4015i | 1.82845i | 0.405205 | + | 0.914226i | \(0.367200\pi\) | ||||
−0.405205 | + | 0.914226i | \(0.632800\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8252 | 0.918183 | 0.459092 | − | 0.888389i | \(-0.348175\pi\) | ||||
0.459092 | + | 0.888389i | \(0.348175\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.3560 | −1.29321 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 6.59414i | − 0.551430i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 12.5531i | − 1.03536i | ||||||||
\(148\) | 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 | \(-0.724115\pi\) | ||||
−0.647332 | + | 0.762208i | \(0.724115\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 1.67801i | − 0.135659i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000i | 1.11732i | 0.829396 | + | 0.558661i | \(0.188685\pi\) | ||||
−0.829396 | + | 0.558661i | \(0.811315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −36.3944 | −2.88627 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.65310 | −0.524338 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 9.18828i | − 0.719682i | −0.933014 | − | 0.359841i | \(-0.882831\pi\) | ||||
0.933014 | − | 0.359841i | \(-0.117169\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 5.83226i | − 0.451313i | −0.974207 | − | 0.225657i | \(-0.927547\pi\) | ||||
0.974207 | − | 0.225657i | \(-0.0724528\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.3176 | 0.870585 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.87067 | −0.601885 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.18828i | 0.546515i | 0.961941 | + | 0.273257i | \(0.0881011\pi\) | ||||
−0.961941 | + | 0.273257i | \(0.911899\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 15.5059i | − 1.16549i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.87333 | 0.588480 | 0.294240 | − | 0.955732i | \(-0.404933\pi\) | ||||
0.294240 | + | 0.955732i | \(0.404933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.3355 | −1.66018 | −0.830092 | − | 0.557627i | \(-0.811712\pi\) | ||||
−0.830092 | + | 0.557627i | \(0.811712\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 11.5736i | − 0.855545i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.08387i | − 0.0792606i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −28.6942 | −2.08719 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.7370 | −1.71755 | −0.858773 | − | 0.512356i | \(-0.828773\pi\) | ||||
−0.858773 | + | 0.512356i | \(0.828773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.31495i | 0.526542i | 0.964722 | + | 0.263271i | \(0.0848013\pi\) | ||||
−0.964722 | + | 0.263271i | \(0.915199\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 8.59414i | − 0.612307i | −0.951982 | − | 0.306154i | \(-0.900958\pi\) | ||||
0.951982 | − | 0.306154i | \(-0.0990421\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | − 1.55572i | − 0.109190i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 29.3062i | − 2.03692i | ||||||||
\(208\) | 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 | ||||||||
\(213\) | − 28.8886i | − 1.97941i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −22.4443 | −1.51664 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.276533 | −0.0186016 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.7619i | 1.12246i | 0.827660 | + | 0.561229i | \(0.189671\pi\) | ||||
−0.827660 | + | 0.561229i | \(0.810329\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.27653i | 0.549333i | 0.961540 | + | 0.274666i | \(0.0885674\pi\) | ||||
−0.961540 | + | 0.274666i | \(0.911433\pi\) | |||||||
\(228\) | 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 | ||||||||
\(233\) | − 8.36306i | − 0.547882i | −0.961746 | − | 0.273941i | \(-0.911673\pi\) | ||||
0.961746 | − | 0.273941i | \(-0.0883274\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 48.1179i | 3.12559i | ||||||||
\(238\) | 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 | ||||||||
\(243\) | − 48.5443i | − 3.11412i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.29707i | 0.0825306i | ||||||||
\(248\) | 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 | ||||||||
\(253\) | − 18.9296i | − 1.19010i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.90909i | 0.618112i | 0.951044 | + | 0.309056i | \(0.100013\pi\) | ||||
−0.951044 | + | 0.309056i | \(0.899987\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.57360 | 0.222053 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.85279 | 0.424177 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 23.6780i | − 1.46005i | −0.683421 | − | 0.730024i | \(-0.739509\pi\) | ||||
0.683421 | − | 0.730024i | \(-0.260491\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 22.2944i | − 1.36440i | ||||||||
\(268\) | 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 | \(-0.458537\pi\) | ||||
0.129890 | + | 0.991528i | \(0.458537\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.64132i | 0.462474i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.93667i | 0.476868i | 0.971159 | + | 0.238434i | \(0.0766341\pi\) | ||||
−0.971159 | + | 0.238434i | \(0.923366\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 5.08387i | 0.302205i | 0.988518 | + | 0.151102i | \(0.0482823\pi\) | ||||
−0.988518 | + | 0.151102i | \(0.951718\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.3560i | 0.906438i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9545 | 0.997326 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.7413 | 0.805532 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.55572i | 0.207728i | 0.994592 | + | 0.103864i | \(0.0331206\pi\) | ||||
−0.994592 | + | 0.103864i | \(0.966879\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 81.6417i | − 4.73733i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.82960 | −0.279303 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.57188 | −0.378797 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 63.2651i | − 3.63449i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.3355i | 0.932316i | 0.884702 | + | 0.466158i | \(0.154362\pi\) | ||||
−0.884702 | + | 0.466158i | \(0.845638\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 52.4534 | 2.98397 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.3809 | −0.928878 | −0.464439 | − | 0.885605i | \(-0.653744\pi\) | ||||
−0.464439 | + | 0.885605i | \(0.653744\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.0590i | 1.69903i | 0.527562 | + | 0.849516i | \(0.323106\pi\) | ||||
−0.527562 | + | 0.849516i | \(0.676894\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 12.0179i | − 0.674991i | −0.941327 | − | 0.337496i | \(-0.890420\pi\) | ||||
0.941327 | − | 0.337496i | \(-0.109580\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.42640 | 0.247831 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.8707 | −0.606742 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.213198i | 0.0118627i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.6531i | 0.810318i | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 15.7413i | 0.862621i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.6147i | 0.632692i | 0.948644 | + | 0.316346i | \(0.102456\pi\) | ||||
−0.948644 | + | 0.316346i | \(0.897544\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 36.8886 | 2.00351 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.3106i | 1.04267i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2.91613i | − 0.156546i | −0.996932 | − | 0.0782730i | \(-0.975059\pi\) | ||||
0.996932 | − | 0.0782730i | \(-0.0249406\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | − 25.7592i | − 1.37103i | −0.728061 | − | 0.685513i | \(-0.759578\pi\) | ||||
0.728061 | − | 0.685513i | \(-0.240422\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.25600i | 0.0664743i | ||||||||
\(358\) | 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 | ||||||||
\(363\) | − 48.9475i | − 2.56908i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.18828i | 0.270826i | 0.990789 | + | 0.135413i | \(0.0432361\pi\) | ||||
−0.990789 | + | 0.135413i | \(0.956764\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −67.6417 | −3.52129 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.7235 | 1.02399 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 36.0091i | − 1.86448i | −0.361838 | − | 0.932241i | \(-0.617851\pi\) | ||||
0.361838 | − | 0.932241i | \(-0.382149\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 1.12933i | − 0.0581632i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.0384 | 1.28614 | 0.643069 | − | 0.765809i | \(-0.277661\pi\) | ||||
0.643069 | + | 0.765809i | \(0.277661\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 55.2651 | 2.83132 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.7413i | 1.11093i | 0.831540 | + | 0.555466i | \(0.187460\pi\) | ||||
−0.831540 | + | 0.555466i | \(0.812540\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 28.9484i | − 1.47153i | ||||||||
\(388\) | 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 | ||||||||
\(393\) | − 12.1267i | − 0.611710i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 7.21054i | − 0.361887i | −0.983494 | − | 0.180943i | \(-0.942085\pi\) | ||||
0.983494 | − | 0.180943i | \(-0.0579151\pi\) | |||||||
\(398\) | 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 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.1677i | 0.503996i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.8030 | −1.62200 | −0.811001 | − | 0.585045i | \(-0.801077\pi\) | ||||
−0.811001 | + | 0.585045i | \(0.801077\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 70.5622 | 3.48058 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.40320i | 0.413495i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 35.6915i | − 1.74782i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.1883 | 0.839703 | 0.419851 | − | 0.907593i | \(-0.362082\pi\) | ||||
0.419851 | + | 0.907593i | \(0.362082\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.8912 | 0.969438 | 0.484719 | − | 0.874670i | \(-0.338922\pi\) | ||||
0.484719 | + | 0.874670i | \(0.338922\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 36.6575i | 1.78235i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.27215i | 0.303531i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21.7413 | −1.04968 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.55307 | 0.411987 | 0.205993 | − | 0.978553i | \(-0.433957\pi\) | ||||
0.205993 | + | 0.978553i | \(0.433957\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.5238i | 1.51494i | 0.652872 | + | 0.757468i | \(0.273564\pi\) | ||||
−0.652872 | + | 0.757468i | \(0.726436\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.72347i | 0.178118i | ||||||||
\(438\) | 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 | ||||||||
\(443\) | − 37.7549i | − 1.79379i | −0.442246 | − | 0.896894i | \(-0.645818\pi\) | ||||
0.442246 | − | 0.896894i | \(-0.354182\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 70.0681i | − 3.31411i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.3560 | −1.57417 | −0.787084 | − | 0.616846i | \(-0.788410\pi\) | ||||
−0.787084 | + | 0.616846i | \(0.788410\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −43.6915 | −2.05735 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 52.4534i | 2.46448i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.1223i | 1.50262i | 0.659951 | + | 0.751309i | \(0.270577\pi\) | ||||
−0.659951 | + | 0.751309i | \(0.729423\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.42374 | −0.159807 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.81000 | −0.363748 | −0.181874 | − | 0.983322i | \(-0.558216\pi\) | ||||
−0.181874 | + | 0.983322i | \(0.558216\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 18.4897i | − 0.859291i | −0.902998 | − | 0.429645i | \(-0.858639\pi\) | ||||
0.902998 | − | 0.429645i | \(-0.141361\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.0839i | 0.975645i | 0.872943 | + | 0.487823i | \(0.162209\pi\) | ||||
−0.872943 | + | 0.487823i | \(0.837791\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.01788 | −0.0931771 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 46.1590 | 2.12689 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 18.6986i | − 0.859760i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 86.8798i | 3.97795i | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 21.9357i | 0.998110i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 10.4675i | − 0.474326i | −0.971470 | − | 0.237163i | \(-0.923782\pi\) | ||||
0.971470 | − | 0.237163i | \(-0.0762176\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | − 0.185626i | − 0.00836018i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.6558i | 0.702257i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.8458 | 0.619821 | 0.309911 | − | 0.950766i | \(-0.399701\pi\) | ||||
0.309911 | + | 0.950766i | \(0.399701\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.2294 | −0.859104 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.76454i | 0.435379i | 0.976018 | + | 0.217690i | \(0.0698521\pi\) | ||||
−0.976018 | + | 0.217690i | \(0.930148\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 37.3150i | − 1.65722i | ||||||||
\(508\) | 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 | ||||||||
\(513\) | 16.0590i | 0.709020i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.6780i | 1.04136i | ||||||||
\(518\) | 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 | ||||||||
\(523\) | − 1.22023i | − 0.0533571i | −0.999644 | − | 0.0266785i | \(-0.991507\pi\) | ||||
0.999644 | − | 0.0266785i | \(-0.00849305\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.13579 | 0.397208 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −37.0152 | −1.60632 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.1472i | 0.482839i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 25.9589i | − 1.12021i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.3560 | −0.833723 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.1812 | 0.523713 | 0.261856 | − | 0.965107i | \(-0.415665\pi\) | ||||
0.261856 | + | 0.965107i | \(0.415665\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 73.6417i | 3.16027i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000i | 0.513083i | 0.966533 | + | 0.256541i | \(0.0825830\pi\) | ||||
−0.966533 | + | 0.256541i | \(0.917417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −27.6282 | −1.17914 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.870674 | −0.0370920 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 26.0768i | − 1.10890i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.60764i | 0.364718i | 0.983232 | + | 0.182359i | \(0.0583732\pi\) | ||||
−0.983232 | + | 0.182359i | \(0.941627\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.77064 | −0.201777 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.57360 | −0.150878 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.3560i | 0.815759i | 0.913036 | + | 0.407880i | \(0.133732\pi\) | ||||
−0.913036 | + | 0.407880i | \(0.866268\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 52.4167i | 2.20129i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.23811 | −0.387282 | −0.193641 | − | 0.981072i | \(-0.562030\pi\) | ||||
−0.193641 | + | 0.981072i | \(0.562030\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.3766 | 0.601640 | 0.300820 | − | 0.953681i | \(-0.402740\pi\) | ||||
0.300820 | + | 0.953681i | \(0.402740\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 78.2625i | 3.26946i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.19266i | 0.216173i | 0.994141 | + | 0.108087i | \(0.0344724\pi\) | ||||
−0.994141 | + | 0.108087i | \(0.965528\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.1179 | 1.00231 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.4059 | −0.722117 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 56.1179i | 2.32417i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.3079i | 1.25094i | 0.780248 | + | 0.625471i | \(0.215093\pi\) | ||||
−0.780248 | + | 0.625471i | \(0.784907\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.3355 | −1.16557 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.04107i | 0.165947i | 0.996552 | + | 0.0829735i | \(0.0264417\pi\) | ||||
−0.996552 | + | 0.0829735i | \(0.973558\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 23.2971i | − 0.953486i | ||||||||
\(598\) | 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 | ||||||||
\(603\) | − 8.88856i | − 0.361970i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 45.3062i | − 1.83892i | −0.393182 | − | 0.919461i | \(-0.628626\pi\) | ||||
0.393182 | − | 0.919461i | \(-0.371374\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.12933 | −0.207851 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.04107 | 0.244396 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 25.1607i | − 1.01623i | −0.861289 | − | 0.508116i | \(-0.830342\pi\) | ||||
0.861289 | − | 0.508116i | \(-0.169658\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.01350i | 0.242095i | 0.992647 | + | 0.121047i | \(0.0386253\pi\) | ||||
−0.992647 | + | 0.121047i | \(0.961375\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.2240 | −1.49616 | −0.748080 | − | 0.663608i | \(-0.769024\pi\) | ||||
−0.748080 | + | 0.663608i | \(0.769024\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −59.7950 | −2.39949 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0821i | 0.484061i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.7619i | 0.669405i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.426396 | 0.0170015 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.0135 | −0.478250 | −0.239125 | − | 0.970989i | \(-0.576861\pi\) | ||||
−0.239125 | + | 0.970989i | \(0.576861\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.3176i | 0.728060i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.93839i | 0.195666i | ||||||||
\(638\) | 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 | ||||||||
\(643\) | − 40.7754i | − 1.60802i | −0.594613 | − | 0.804012i | \(-0.702695\pi\) | ||||
0.594613 | − | 0.804012i | \(-0.297305\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.9340i | 0.980257i | 0.871650 | + | 0.490129i | \(0.163050\pi\) | ||||
−0.871650 | + | 0.490129i | \(0.836950\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.9091 | −0.938514 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.3988i | 1.42440i | 0.701979 | + | 0.712198i | \(0.252300\pi\) | ||||
−0.701979 | + | 0.712198i | \(0.747700\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 53.5783i | 2.09029i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.8501 | −0.461616 | −0.230808 | − | 0.972999i | \(-0.574137\pi\) | ||||
−0.230808 | + | 0.972999i | \(0.574137\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.4854 | 1.34132 | 0.670662 | − | 0.741763i | \(-0.266010\pi\) | ||||
0.670662 | + | 0.741763i | \(0.266010\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.911749i | 0.0354094i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 3.24193i | − 0.125528i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 55.2651 | 2.13667 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.8458 | −0.688928 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 17.7003i | − 0.682295i | −0.940010 | − | 0.341148i | \(-0.889184\pi\) | ||||
0.940010 | − | 0.341148i | \(-0.110816\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 26.0590i | − 1.00153i | −0.865584 | − | 0.500764i | \(-0.833053\pi\) | ||||
0.865584 | − | 0.500764i | \(-0.166947\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.44693 | −0.285787 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.2883 | 1.04569 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0000i | 0.459167i | 0.973289 | + | 0.229584i | \(0.0737364\pi\) | ||||
−0.973289 | + | 0.229584i | \(0.926264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 41.8680i | − 1.59736i | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 71.4962i | 2.71592i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.83226i | 0.0694016i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27.5736 | −1.04293 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.55307 | 0.247506 | 0.123753 | − | 0.992313i | \(-0.460507\pi\) | ||||
0.123753 | + | 0.992313i | \(0.460507\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 2.00000i | − 0.0754314i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 34.2857i | 1.28944i | ||||||||
\(708\) | 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 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.9973i | 0.858852i | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 65.0886i | 2.42067i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.32464i | 0.0491283i | 0.999698 | + | 0.0245641i | \(0.00781979\pi\) | ||||
−0.999698 | + | 0.0245641i | \(0.992180\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −72.0475 | −2.66843 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.784146 | −0.0290027 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.7824i | 0.509065i | 0.967064 | + | 0.254533i | \(0.0819217\pi\) | ||||
−0.967064 | + | 0.254533i | \(0.918078\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 5.74135i | − 0.211485i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.5513 | −0.866350 | −0.433175 | − | 0.901310i | \(-0.642607\pi\) | ||||
−0.433175 | + | 0.901310i | \(0.642607\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.27653 | 0.157102 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.0411i | 0.515117i | 0.966263 | + | 0.257559i | \(0.0829180\pi\) | ||||
−0.966263 | + | 0.257559i | \(0.917082\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 76.6710i | − 2.80524i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.89121 | 0.215260 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.7056 | −0.646086 | −0.323043 | − | 0.946384i | \(-0.604706\pi\) | ||||
−0.323043 | + | 0.946384i | \(0.604706\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 33.8680i | − 1.23422i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.3220i | 1.10207i | 0.834482 | + | 0.551036i | \(0.185767\pi\) | ||||
−0.834482 | + | 0.551036i | \(0.814233\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | − 7.94104i | − 0.287485i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.10003i | 0.220259i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.0725 | 1.80566 | 0.902830 | − | 0.429999i | \(-0.141486\pi\) | ||||
0.902830 | + | 0.429999i | \(0.141486\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.6710 | 1.17662 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 11.8003i | − 0.424427i | −0.977223 | − | 0.212214i | \(-0.931933\pi\) | ||||
0.977223 | − | 0.212214i | \(-0.0680673\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 11.7824i | − 0.422692i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.59414 | 0.307917 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −44.5443 | −1.59392 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 13.9821i | − 0.499680i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.9475i | 1.17445i | 0.809423 | + | 0.587226i | \(0.199780\pi\) | ||||
−0.809423 | + | 0.587226i | \(0.800220\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −78.0681 | −2.77930 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.9912 | −0.710807 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.55307i | 0.161684i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 18.8208i | − 0.666668i | −0.942809 | − | 0.333334i | \(-0.891826\pi\) | ||||
0.942809 | − | 0.333334i | \(-0.108174\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.992965 | 0.0351286 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −53.2206 | −1.88046 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34.6076i | 1.22128i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 16.5531i | − 0.582696i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.2607 | 1.38033 | 0.690167 | − | 0.723650i | \(-0.257537\pi\) | ||||
0.690167 | + | 0.723650i | \(0.257537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.9182 | 1.19103 | 0.595515 | − | 0.803344i | \(-0.296948\pi\) | ||||
0.595515 | + | 0.803344i | \(0.296948\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 14.1000i | − 0.494510i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.67801i | 0.128677i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.2411 | 0.637397 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.6487 | 1.34885 | 0.674425 | − | 0.738344i | \(-0.264392\pi\) | ||||
0.674425 | + | 0.738344i | \(0.264392\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.47185i | 0.295310i | 0.989039 | + | 0.147655i | \(0.0471725\pi\) | ||||
−0.989039 | + | 0.147655i | \(0.952827\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 44.7299i | − 1.55541i | −0.628628 | − | 0.777706i | \(-0.716383\pi\) | ||||
0.628628 | − | 0.777706i | \(-0.283617\pi\) | |||||||
\(828\) | 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 | ||||||||
\(833\) | 0.811718i | 0.0281244i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 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 | ||||||||
\(843\) | − 75.4652i | − 2.59916i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.5264i | 0.911459i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.7619 | 0.575266 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.44693 | 0.255278 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.5238i | 1.49023i | 0.666938 | + | 0.745113i | \(0.267604\pi\) | ||||
−0.666938 | + | 0.745113i | \(0.732396\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 14.5531i | − 0.497123i | −0.968616 | − | 0.248562i | \(-0.920042\pi\) | ||||
0.968616 | − | 0.248562i | \(-0.0799579\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.3132 | 0.829557 | 0.414778 | − | 0.909922i | \(-0.363859\pi\) | ||||
0.414778 | + | 0.909922i | \(0.363859\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 50.6299 | 1.72546 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.4264i | 0.422999i | 0.977378 | + | 0.211500i | \(0.0678347\pi\) | ||||
−0.977378 | + | 0.211500i | \(0.932165\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 55.9003i | − 1.89847i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 74.1948 | 2.51688 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.46482 | −0.0496334 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 32.8030i | − 1.11021i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.6120i | 1.84412i | 0.387051 | + | 0.922058i | \(0.373494\pi\) | ||||
−0.387051 | + | 0.922058i | \(0.626506\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − 21.5460i | − 0.725082i | −0.931968 | − | 0.362541i | \(-0.881909\pi\) | ||||
0.931968 | − | 0.362541i | \(-0.118091\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 49.6147i | 1.66590i | 0.553350 | + | 0.832949i | \(0.313349\pi\) | ||||
−0.553350 | + | 0.832949i | \(0.686651\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.9502 | −1.00450 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −149.138 | −4.99631 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 4.65748i | − 0.155856i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.9235i | 0.531671i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.35337 | 0.0784022 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.6680i | 0.721064i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 11.0883i | − 0.368179i | −0.982909 | − | 0.184090i | \(-0.941066\pi\) | ||||
0.982909 | − | 0.184090i | \(-0.0589337\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −151.025 | −5.00917 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.5443 | 0.415612 | 0.207806 | − | 0.978170i | \(-0.433368\pi\) | ||||
0.207806 | + | 0.978170i | \(0.433368\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 49.5238i | − 1.63900i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.57188i | 0.217023i | ||||||||
\(918\) | 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 | ||||||||
\(923\) | 11.3648i | 0.374076i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 125.215i | − 4.11261i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.9182 | 0.915967 | 0.457984 | − | 0.888961i | \(-0.348572\pi\) | ||||
0.457984 | + | 0.888961i | \(0.348572\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.80734 | 0.124781 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 54.0091i | 1.76818i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 10.8982i | − 0.356030i | −0.984028 | − | 0.178015i | \(-0.943032\pi\) | ||||
0.984028 | − | 0.178015i | \(-0.0569676\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 99.1065 | 3.23422 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.9475 | −1.00886 | −0.504430 | − | 0.863453i | \(-0.668297\pi\) | ||||
−0.504430 | + | 0.863453i | \(0.668297\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.0000i | 1.04206i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 18.2944i | − 0.594489i | −0.954801 | − | 0.297244i | \(-0.903932\pi\) | ||||
0.954801 | − | 0.297244i | \(-0.0960676\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.82960 | 0.286621 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −39.6238 | −1.28489 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.0616i | 0.747039i | 0.927622 | + | 0.373519i | \(0.121849\pi\) | ||||
−0.927622 | + | 0.373519i | \(0.878151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 14.5941i | − 0.471762i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −38.2402 | −1.23484 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 25.9502i | 0.836232i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.3766i | 0.848213i | 0.905612 | + | 0.424107i | \(0.139412\pi\) | ||||
−0.905612 | + | 0.424107i | \(0.860588\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | 19.3425i | 0.620093i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 26.4264i | − 0.845455i | −0.906257 | − | 0.422728i | \(-0.861073\pi\) | ||||
0.906257 | − | 0.422728i | \(-0.138927\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.3766 | −1.09868 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 34.9795 | 1.11681 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 25.4059i | − 0.810321i | −0.914246 | − | 0.405161i | \(-0.867216\pi\) | ||||
0.914246 | − | 0.405161i | \(-0.132784\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 27.4382i | − 0.873367i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.6950 | −0.435474 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.6504 | 0.941877 | 0.470939 | − | 0.882166i | \(-0.343915\pi\) | ||||
0.470939 | + | 0.882166i | \(0.343915\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 47.2062i | 1.49804i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 38.7754i | − 1.22803i | −0.789295 | − | 0.614014i | \(-0.789554\pi\) | ||||
0.789295 | − | 0.614014i | \(-0.210446\pi\) | |||||||
\(998\) | 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 | 3800.2.d.j.3649.1 | 6 | ||
5.2 | odd | 4 | 3800.2.a.r.1.1 | 3 | |||
5.3 | odd | 4 | 152.2.a.c.1.3 | ✓ | 3 | ||
5.4 | even | 2 | inner | 3800.2.d.j.3649.6 | 6 | ||
15.8 | even | 4 | 1368.2.a.n.1.3 | 3 | |||
20.3 | even | 4 | 304.2.a.g.1.1 | 3 | |||
20.7 | even | 4 | 7600.2.a.bv.1.3 | 3 | |||
35.13 | even | 4 | 7448.2.a.bf.1.1 | 3 | |||
40.3 | even | 4 | 1216.2.a.v.1.3 | 3 | |||
40.13 | odd | 4 | 1216.2.a.u.1.1 | 3 | |||
60.23 | odd | 4 | 2736.2.a.bd.1.3 | 3 | |||
95.18 | even | 4 | 2888.2.a.o.1.1 | 3 | |||
380.303 | odd | 4 | 5776.2.a.bp.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.a.c.1.3 | ✓ | 3 | 5.3 | odd | 4 | ||
304.2.a.g.1.1 | 3 | 20.3 | even | 4 | |||
1216.2.a.u.1.1 | 3 | 40.13 | odd | 4 | |||
1216.2.a.v.1.3 | 3 | 40.3 | even | 4 | |||
1368.2.a.n.1.3 | 3 | 15.8 | even | 4 | |||
2736.2.a.bd.1.3 | 3 | 60.23 | odd | 4 | |||
2888.2.a.o.1.1 | 3 | 95.18 | even | 4 | |||
3800.2.a.r.1.1 | 3 | 5.2 | odd | 4 | |||
3800.2.d.j.3649.1 | 6 | 1.1 | even | 1 | trivial | ||
3800.2.d.j.3649.6 | 6 | 5.4 | even | 2 | inner | ||
5776.2.a.bp.1.3 | 3 | 380.303 | odd | 4 | |||
7448.2.a.bf.1.1 | 3 | 35.13 | even | 4 | |||
7600.2.a.bv.1.3 | 3 | 20.7 | even | 4 |