Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,4,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(46.2574974445\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{65})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 35x^{2} + 36x + 194 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 7 \) |
Twist minimal: | no (minimal twist has level 49) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.11692\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-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 | ||||||||
\(3\) | −7.82220 | −1.50538 | −0.752691 | − | 0.658374i | \(-0.771245\pi\) | ||||
−0.752691 | + | 0.658374i | \(0.771245\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.07730 | 0.185799 | 0.0928996 | − | 0.995675i | \(-0.470386\pi\) | ||||
0.0928996 | + | 0.995675i | \(0.470386\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 34.1868 | 1.26618 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −49.1868 | −1.34822 | −0.674108 | − | 0.738633i | \(-0.735472\pi\) | ||||
−0.674108 | + | 0.738633i | \(0.735472\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 44.8559 | 0.956983 | 0.478492 | − | 0.878092i | \(-0.341184\pi\) | ||||
0.478492 | + | 0.878092i | \(0.341184\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −16.2490 | −0.279699 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −26.5179 | −0.378325 | −0.189163 | − | 0.981946i | \(-0.560577\pi\) | ||||
−0.189163 | + | 0.981946i | \(0.560577\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 77.7350 | 0.938612 | 0.469306 | − | 0.883036i | \(-0.344504\pi\) | ||||
0.469306 | + | 0.883036i | \(0.344504\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −55.7510 | −0.505430 | −0.252715 | − | 0.967541i | \(-0.581323\pi\) | ||||
−0.252715 | + | 0.967541i | \(0.581323\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −120.685 | −0.965479 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −56.2164 | −0.400698 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 121.436 | 0.777588 | 0.388794 | − | 0.921325i | \(-0.372892\pi\) | ||||
0.388794 | + | 0.921325i | \(0.372892\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 305.553 | 1.77029 | 0.885143 | − | 0.465319i | \(-0.154060\pi\) | ||||
0.885143 | + | 0.465319i | \(0.154060\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 384.749 | 2.02958 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 77.1868 | 0.342957 | 0.171479 | − | 0.985188i | \(-0.445146\pi\) | ||||
0.171479 | + | 0.985188i | \(0.445146\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −350.872 | −1.44063 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −248.720 | −0.947403 | −0.473702 | − | 0.880685i | \(-0.657083\pi\) | ||||
−0.473702 | + | 0.880685i | \(0.657083\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 147.179 | 0.521967 | 0.260984 | − | 0.965343i | \(-0.415953\pi\) | ||||
0.260984 | + | 0.965343i | \(0.415953\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 71.0161 | 0.235255 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 269.851 | 0.837484 | 0.418742 | − | 0.908105i | \(-0.362471\pi\) | ||||
0.418742 | + | 0.908105i | \(0.362471\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 207.428 | 0.569524 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −141.121 | −0.365744 | −0.182872 | − | 0.983137i | \(-0.558539\pi\) | ||||
−0.182872 | + | 0.983137i | \(0.558539\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −102.176 | −0.250497 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −608.058 | −1.41297 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −424.834 | −0.937434 | −0.468717 | − | 0.883348i | \(-0.655284\pi\) | ||||
−0.468717 | + | 0.883348i | \(0.655284\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 587.996 | 1.23418 | 0.617092 | − | 0.786891i | \(-0.288311\pi\) | ||||
0.617092 | + | 0.786891i | \(0.288311\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 93.1790 | 0.177807 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 179.634 | 0.327549 | 0.163775 | − | 0.986498i | \(-0.447633\pi\) | ||||
0.163775 | + | 0.986498i | \(0.447633\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 436.095 | 0.760865 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −674.872 | −1.12806 | −0.564032 | − | 0.825753i | \(-0.690750\pi\) | ||||
−0.564032 | + | 0.825753i | \(0.690750\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −237.489 | −0.380767 | −0.190383 | − | 0.981710i | \(-0.560973\pi\) | ||||
−0.190383 | + | 0.981710i | \(0.560973\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 944.021 | 1.45341 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −495.852 | −0.706174 | −0.353087 | − | 0.935591i | \(-0.614868\pi\) | ||||
−0.353087 | + | 0.935591i | \(0.614868\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −483.307 | −0.662973 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −24.4406 | −0.0323217 | −0.0161609 | − | 0.999869i | \(-0.505144\pi\) | ||||
−0.0161609 | + | 0.999869i | \(0.505144\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −55.0855 | −0.0702925 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −949.895 | −1.17057 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1072.29 | −1.27710 | −0.638552 | − | 0.769579i | \(-0.720466\pi\) | ||||
−0.638552 | + | 0.769579i | \(0.720466\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2390.09 | −2.66496 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 161.479 | 0.174393 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1667.43 | −1.74538 | −0.872690 | − | 0.488275i | \(-0.837626\pi\) | ||||
−0.872690 | + | 0.488275i | \(0.837626\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1681.54 | −1.70708 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 77.1187 | 0.0759762 | 0.0379881 | − | 0.999278i | \(-0.487905\pi\) | ||||
0.0379881 | + | 0.999278i | \(0.487905\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 164.693 | 0.157550 | 0.0787749 | − | 0.996892i | \(-0.474899\pi\) | ||||
0.0787749 | + | 0.996892i | \(0.474899\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1022.62 | −0.923931 | −0.461966 | − | 0.886898i | \(-0.652856\pi\) | ||||
−0.461966 | + | 0.886898i | \(0.652856\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1362.52 | 1.19730 | 0.598649 | − | 0.801011i | \(-0.295704\pi\) | ||||
0.598649 | + | 0.801011i | \(0.295704\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −603.770 | −0.516282 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1538.41 | −1.28072 | −0.640360 | − | 0.768075i | \(-0.721215\pi\) | ||||
−0.640360 | + | 0.768075i | \(0.721215\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −115.811 | −0.0939084 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1533.48 | 1.21171 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1088.34 | 0.817685 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1945.54 | 1.42620 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −510.360 | −0.365184 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 170.358 | 0.119030 | 0.0595151 | − | 0.998227i | \(-0.481045\pi\) | ||||
0.0595151 | + | 0.998227i | \(0.481045\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1151.26 | −0.785760 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −751.935 | −0.501503 | −0.250751 | − | 0.968051i | \(-0.580678\pi\) | ||||
−0.250751 | + | 0.968051i | \(0.580678\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −116.778 | −0.0744493 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 518.623 | 0.323423 | 0.161711 | − | 0.986838i | \(-0.448299\pi\) | ||||
0.161711 | + | 0.986838i | \(0.448299\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2975.72 | −1.81581 | −0.907905 | − | 0.419177i | \(-0.862319\pi\) | ||||
−0.907905 | + | 0.419177i | \(0.862319\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2110.83 | −1.26073 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2206.32 | −1.29022 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 252.258 | 0.144475 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2717.94 | −1.49438 | −0.747188 | − | 0.664612i | \(-0.768597\pi\) | ||||
−0.747188 | + | 0.664612i | \(0.768597\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −707.650 | −0.381376 | −0.190688 | − | 0.981651i | \(-0.561072\pi\) | ||||
−0.190688 | + | 0.981651i | \(0.561072\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −906.561 | −0.479027 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 634.724 | 0.328918 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3117.91 | −1.58495 | −0.792473 | − | 0.609906i | \(-0.791207\pi\) | ||||
−0.792473 | + | 0.609906i | \(0.791207\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1103.87 | 0.550584 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1808.77 | −0.869167 | −0.434583 | − | 0.900632i | \(-0.643104\pi\) | ||||
−0.434583 | + | 0.900632i | \(0.643104\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 799.237 | 0.377094 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3147.38 | 1.45839 | 0.729197 | − | 0.684303i | \(-0.239894\pi\) | ||||
0.729197 | + | 0.684303i | \(0.239894\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −184.949 | −0.0841827 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2657.51 | 1.18845 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3284.36 | 1.44338 | 0.721691 | − | 0.692215i | \(-0.243365\pi\) | ||||
0.721691 | + | 0.692215i | \(0.243365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3323.13 | 1.41120 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2798.83 | −1.16868 | −0.584341 | − | 0.811508i | \(-0.698647\pi\) | ||||
−0.584341 | + | 0.811508i | \(0.698647\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3723.04 | 1.52890 | 0.764451 | − | 0.644682i | \(-0.223010\pi\) | ||||
0.764451 | + | 0.644682i | \(0.223010\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4599.42 | −1.85792 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 160.340 | 0.0637212 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1304.33 | 0.510064 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −959.650 | −0.363549 | −0.181774 | − | 0.983340i | \(-0.558184\pi\) | ||||
−0.181774 | + | 0.983340i | \(0.558184\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3790.25 | −1.41362 | −0.706808 | − | 0.707406i | \(-0.749865\pi\) | ||||
−0.706808 | + | 0.707406i | \(0.749865\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −728.865 | −0.267667 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5117.99 | 1.85097 | 0.925487 | − | 0.378779i | \(-0.123656\pi\) | ||||
0.925487 | + | 0.378779i | \(0.123656\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 864.855 | 0.308080 | 0.154040 | − | 0.988065i | \(-0.450772\pi\) | ||||
0.154040 | + | 0.988065i | \(0.450772\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1405.13 | −0.493087 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −516.665 | −0.176027 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1905.95 | −0.639963 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3823.53 | −1.26545 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1344.61 | 0.438707 | 0.219353 | − | 0.975645i | \(-0.429605\pi\) | ||||
0.219353 | + | 0.975645i | \(0.429605\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5278.98 | 1.69817 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 305.735 | 0.0969811 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1857.68 | 0.573200 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1189.48 | −0.362051 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −864.916 | −0.259727 | −0.129863 | − | 0.991532i | \(-0.541454\pi\) | ||||
−0.129863 | + | 0.991532i | \(0.541454\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4125.83 | −1.22247 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1715.34 | 0.501548 | 0.250774 | − | 0.968046i | \(-0.419315\pi\) | ||||
0.250774 | + | 0.968046i | \(0.419315\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1045.46 | −0.301685 | −0.150842 | − | 0.988558i | \(-0.548199\pi\) | ||||
−0.150842 | + | 0.988558i | \(0.548199\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1448.67 | 0.407320 | 0.203660 | − | 0.979042i | \(-0.434716\pi\) | ||||
0.203660 | + | 0.979042i | \(0.434716\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 560.560 | 0.155604 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3878.65 | 1.06306 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3153.12 | 0.853383 | 0.426691 | − | 0.904397i | \(-0.359679\pi\) | ||||
0.426691 | + | 0.904397i | \(0.359679\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −381.012 | −0.101839 | −0.0509194 | − | 0.998703i | \(-0.516215\pi\) | ||||
−0.0509194 | + | 0.998703i | \(0.516215\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5298.37 | 1.39873 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3486.87 | 0.898236 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 191.179 | 0.0486565 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3776.23 | −0.949617 | −0.474808 | − | 0.880089i | \(-0.657483\pi\) | ||||
−0.474808 | + | 0.880089i | \(0.657483\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2742.21 | 0.681428 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 430.890 | 0.105817 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4258.42 | 1.03359 | 0.516795 | − | 0.856109i | \(-0.327125\pi\) | ||||
0.516795 | + | 0.856109i | \(0.327125\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4151.50 | 0.984564 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4198.83 | −0.984451 | −0.492226 | − | 0.870468i | \(-0.663816\pi\) | ||||
−0.492226 | + | 0.870468i | \(0.663816\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −293.150 | −0.0679548 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8387.65 | 1.92253 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3740.59 | 0.847835 | 0.423917 | − | 0.905701i | \(-0.360655\pi\) | ||||
0.423917 | + | 0.905701i | \(0.360655\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4356.30 | −0.976480 | −0.488240 | − | 0.872709i | \(-0.662361\pi\) | ||||
−0.488240 | + | 0.872709i | \(0.662361\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5936.10 | 1.30167 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1344.30 | −0.291593 | −0.145797 | − | 0.989315i | \(-0.546575\pi\) | ||||
−0.145797 | + | 0.989315i | \(0.546575\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10445.9 | 2.24150 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4205.54 | 0.892817 | 0.446408 | − | 0.894829i | \(-0.352703\pi\) | ||||
0.446408 | + | 0.894829i | \(0.352703\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4752.03 | −0.998159 | −0.499079 | − | 0.866556i | \(-0.666328\pi\) | ||||
−0.499079 | + | 0.866556i | \(0.666328\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1263.12 | −0.262529 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4209.80 | −0.856870 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13043.0 | 2.62746 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4961.17 | −0.989196 | −0.494598 | − | 0.869122i | \(-0.664685\pi\) | ||||
−0.494598 | + | 0.869122i | \(0.664685\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −882.506 | −0.174174 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2765.10 | 0.540227 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2500.76 | −0.483688 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −603.237 | −0.114373 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1221.44 | 0.229310 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4234.00 | 0.787124 | 0.393562 | − | 0.919298i | \(-0.371243\pi\) | ||||
0.393562 | + | 0.919298i | \(0.371243\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1288.26 | −0.237173 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 684.700 | 0.124842 | 0.0624209 | − | 0.998050i | \(-0.480118\pi\) | ||||
0.0624209 | + | 0.998050i | \(0.480118\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5944.07 | −1.07341 | −0.536707 | − | 0.843768i | \(-0.680332\pi\) | ||||
−0.536707 | + | 0.843768i | \(0.680332\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2823.89 | −0.500333 | −0.250166 | − | 0.968203i | \(-0.580485\pi\) | ||||
−0.250166 | + | 0.968203i | \(0.580485\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5973.04 | −1.04836 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7999.16 | 1.39087 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2061.37 | −0.355101 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5413.43 | −0.923947 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10657.9 | −1.80239 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2812.97 | 0.467114 | 0.233557 | − | 0.972343i | \(-0.424963\pi\) | ||||
0.233557 | + | 0.972343i | \(0.424963\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2638.77 | 0.434245 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 373.154 | 0.0608584 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4260.10 | 0.688612 | 0.344306 | − | 0.938857i | \(-0.388114\pi\) | ||||
0.344306 | + | 0.938857i | \(0.388114\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12033.7 | 1.92797 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15029.2 | −2.38673 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 905.899 | 0.141368 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −36.0584 | −0.00557843 | −0.00278922 | − | 0.999996i | \(-0.500888\pi\) | ||||
−0.00278922 | + | 0.999996i | \(0.500888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −242.692 | −0.0372236 | −0.0186118 | − | 0.999827i | \(-0.505925\pi\) | ||||
−0.0186118 | + | 0.999827i | \(0.505925\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2521.63 | −0.383461 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −109.990 | −0.0165840 | −0.00829201 | − | 0.999966i | \(-0.502639\pi\) | ||||
−0.00829201 | + | 0.999966i | \(0.502639\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1401.91 | −0.209593 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12404.5 | −1.82363 | −0.911814 | − | 0.410604i | \(-0.865318\pi\) | ||||
−0.911814 | + | 0.410604i | \(0.865318\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −816.273 | −0.119008 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8513.20 | −1.23093 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −493.335 | −0.0707461 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13859.6 | −1.97130 | −0.985649 | − | 0.168807i | \(-0.946009\pi\) | ||||
−0.985649 | + | 0.168807i | \(0.946009\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8502.93 | −1.19958 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4898.06 | 0.679925 | 0.339963 | − | 0.940439i | \(-0.389586\pi\) | ||||
0.339963 | + | 0.940439i | \(0.389586\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3992.14 | 0.549742 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5447.11 | 0.744139 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9806.25 | 1.32906 | 0.664530 | − | 0.747262i | \(-0.268632\pi\) | ||||
0.664530 | + | 0.747262i | \(0.268632\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1332.57 | −0.179186 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10729.7 | −1.43149 | −0.715746 | − | 0.698361i | \(-0.753913\pi\) | ||||
−0.715746 | + | 0.698361i | \(0.753913\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5031.58 | 0.660903 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5264.05 | 0.686113 | 0.343057 | − | 0.939315i | \(-0.388538\pi\) | ||||
0.343057 | + | 0.939315i | \(0.388538\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1478.40 | 0.191217 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5881.79 | 0.754954 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1030.03 | −0.131206 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1214.90 | 0.153587 | 0.0767935 | − | 0.997047i | \(-0.475532\pi\) | ||||
0.0767935 | + | 0.997047i | \(0.475532\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2295.45 | 0.285859 | 0.142929 | − | 0.989733i | \(-0.454348\pi\) | ||||
0.142929 | + | 0.989733i | \(0.454348\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13705.8 | 1.69413 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1003.97 | −0.123180 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3796.57 | −0.462381 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4646.54 | 0.561753 | 0.280876 | − | 0.959744i | \(-0.409375\pi\) | ||||
0.280876 | + | 0.959744i | \(0.409375\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4056.77 | −0.486875 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −50.7703 | −0.00600535 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 23276.7 | 2.73349 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7541.24 | −0.879269 | −0.439634 | − | 0.898177i | \(-0.644892\pi\) | ||||
−0.439634 | + | 0.898177i | \(0.644892\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6243.63 | −0.722794 | −0.361397 | − | 0.932412i | \(-0.617700\pi\) | ||||
−0.361397 | + | 0.932412i | \(0.617700\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9225.32 | 1.06040 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3200.31 | 0.365265 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17258.2 | 1.94227 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11465.8 | −1.28141 | −0.640706 | − | 0.767786i | \(-0.721358\pi\) | ||||
−0.640706 | + | 0.767786i | \(0.721358\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5156.40 | 0.572289 | 0.286144 | − | 0.958187i | \(-0.407626\pi\) | ||||
0.286144 | + | 0.958187i | \(0.407626\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1973.21 | −0.217491 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4333.80 | −0.474402 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5064.25 | 0.550577 | 0.275289 | − | 0.961362i | \(-0.411227\pi\) | ||||
0.275289 | + | 0.961362i | \(0.411227\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12703.6 | −1.36246 | −0.681228 | − | 0.732071i | \(-0.738554\pi\) | ||||
−0.681228 | + | 0.732071i | \(0.738554\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2227.46 | −0.237285 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21260.2 | 2.24961 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13942.2 | 1.46542 | 0.732709 | − | 0.680542i | \(-0.238256\pi\) | ||||
0.732709 | + | 0.680542i | \(0.238256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12233.7 | 1.27730 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5535.38 | 0.574116 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15214.0 | −1.55729 | −0.778646 | − | 0.627464i | \(-0.784093\pi\) | ||||
−0.778646 | + | 0.627464i | \(0.784093\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1490.74 | 0.151594 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11430.2 | −1.15479 | −0.577394 | − | 0.816465i | \(-0.695930\pi\) | ||||
−0.577394 | + | 0.816465i | \(0.695930\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9347.88 | 0.938300 | 0.469150 | − | 0.883119i | \(-0.344560\pi\) | ||||
0.469150 | + | 0.883119i | \(0.344560\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4964.94 | −0.495147 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3630.84 | −0.359776 | −0.179888 | − | 0.983687i | \(-0.557573\pi\) | ||||
−0.179888 | + | 0.983687i | \(0.557573\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24388.9 | 2.38595 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7239.26 | −0.703724 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9381.43 | −0.906210 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4824.46 | −0.463096 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6521.25 | −0.622053 | −0.311027 | − | 0.950401i | \(-0.600673\pi\) | ||||
−0.311027 | + | 0.950401i | \(0.600673\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3462.28 | 0.328205 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3463.75 | −0.324290 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3666.29 | 0.341140 | 0.170570 | − | 0.985346i | \(-0.445439\pi\) | ||||
0.170570 | + | 0.985346i | \(0.445439\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14148.6 | 1.30843 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12470.7 | 1.14623 | 0.573113 | − | 0.819476i | \(-0.305736\pi\) | ||||
0.573113 | + | 0.819476i | \(0.305736\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3220.22 | −0.294181 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3493.05 | −0.317174 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2303.93 | 0.206690 | 0.103345 | − | 0.994646i | \(-0.467045\pi\) | ||||
0.103345 | + | 0.994646i | \(0.467045\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24619.5 | −2.19544 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10520.4 | 0.932570 | 0.466285 | − | 0.884635i | \(-0.345592\pi\) | ||||
0.466285 | + | 0.884635i | \(0.345592\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 160.198 | 0.0141163 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1446.71 | 0.126727 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9662.22 | −0.841395 | −0.420698 | − | 0.907201i | \(-0.638215\pi\) | ||||
−0.420698 | + | 0.907201i | \(0.638215\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4369.98 | −0.376100 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 342.115 | 0.0292726 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13273.1 | −1.12911 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25690.9 | −2.17284 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8607.81 | 0.723829 | 0.361914 | − | 0.932211i | \(-0.382123\pi\) | ||||
0.361914 | + | 0.932211i | \(0.382123\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10482.7 | 0.876439 | 0.438219 | − | 0.898868i | \(-0.355609\pi\) | ||||
0.438219 | + | 0.898868i | \(0.355609\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8102.61 | −0.669744 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9058.83 | −0.744541 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14523.7 | −1.18696 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11156.6 | −0.906649 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2124.29 | −0.171666 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21893.0 | 1.75931 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20722.6 | 1.64683 | 0.823416 | − | 0.567438i | \(-0.192066\pi\) | ||||
0.823416 | + | 0.567438i | \(0.192066\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −29122.3 | −2.30158 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2830.35 | 0.222457 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4175.09 | 0.326351 | 0.163176 | − | 0.986597i | \(-0.447826\pi\) | ||||
0.163176 | + | 0.986597i | \(0.447826\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20101.7 | 1.56270 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9439.81 | 0.729854 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1254.21 | −0.0959248 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10161.7 | −0.773011 | −0.386505 | − | 0.922287i | \(-0.626318\pi\) | ||||
−0.386505 | + | 0.922287i | \(0.626318\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6601.85 | 0.499514 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10202.7 | −0.767841 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17104.4 | 1.28040 | 0.640201 | − | 0.768208i | \(-0.278851\pi\) | ||||
0.640201 | + | 0.768208i | \(0.278851\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3195.73 | −0.237957 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18257.6 | −1.34516 | −0.672581 | − | 0.740023i | \(-0.734815\pi\) | ||||
−0.672581 | + | 0.740023i | \(0.734815\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13630.5 | −0.998982 | −0.499491 | − | 0.866319i | \(-0.666480\pi\) | ||||
−0.499491 | + | 0.866319i | \(0.666480\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7506.57 | 0.547280 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6728.30 | 0.487981 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4442.08 | 0.320496 | 0.160248 | − | 0.987077i | \(-0.448771\pi\) | ||||
0.160248 | + | 0.987077i | \(0.448771\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29648.0 | 2.12803 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6941.27 | 0.493101 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3185.49 | 0.225135 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3103.38 | −0.218211 | −0.109106 | − | 0.994030i | \(-0.534799\pi\) | ||||
−0.109106 | + | 0.994030i | \(0.534799\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23752.1 | 1.66161 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −40033.9 | −2.78642 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5937.71 | 0.411185 | 0.205592 | − | 0.978638i | \(-0.434088\pi\) | ||||
0.205592 | + | 0.978638i | \(0.434088\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6765.07 | −0.463778 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2600.33 | 0.177373 | 0.0886866 | − | 0.996060i | \(-0.471733\pi\) | ||||
0.0886866 | + | 0.996060i | \(0.471733\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13881.4 | −0.942156 | −0.471078 | − | 0.882092i | \(-0.656135\pi\) | ||||
−0.471078 | + | 0.882092i | \(0.656135\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6141.11 | 0.414735 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2260.80 | 0.151925 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12284.6 | 0.821442 | 0.410721 | − | 0.911761i | \(-0.365277\pi\) | ||||
0.410721 | + | 0.911761i | \(0.365277\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12104.4 | 0.801459 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22062.0 | 1.45363 | 0.726815 | − | 0.686833i | \(-0.241000\pi\) | ||||
0.726815 | + | 0.686833i | \(0.241000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4041.46 | 0.264988 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12182.2 | −0.794871 | −0.397436 | − | 0.917630i | \(-0.630100\pi\) | ||||
−0.397436 | + | 0.917630i | \(0.630100\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23248.6 | −1.50960 | −0.754799 | − | 0.655956i | \(-0.772266\pi\) | ||||
−0.754799 | + | 0.655956i | \(0.772266\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3134.12 | 0.202525 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14025.4 | 0.897628 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 29908.4 | 1.90499 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2046.83 | −0.129749 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19184.4 | −1.21033 | −0.605165 | − | 0.796100i | \(-0.706893\pi\) | ||||
−0.605165 | + | 0.796100i | \(0.706893\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10517.8 | −0.660421 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 353.884 | 0.0221157 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23071.7 | −1.42833 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19433.4 | −1.19746 | −0.598730 | − | 0.800951i | \(-0.704328\pi\) | ||||
−0.598730 | + | 0.800951i | \(0.704328\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5777.47 | −0.354341 | −0.177170 | − | 0.984180i | \(-0.556694\pi\) | ||||
−0.177170 | + | 0.984180i | \(0.556694\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2391.52 | −0.145994 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29231.5 | 1.77621 | 0.888106 | − | 0.459640i | \(-0.152021\pi\) | ||||
0.888106 | + | 0.459640i | \(0.152021\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20896.2 | 1.26386 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7093.27 | −0.425086 | −0.212543 | − | 0.977152i | \(-0.568174\pi\) | ||||
−0.212543 | + | 0.977152i | \(0.568174\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1561.99 | −0.0931788 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8118.98 | −0.482118 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19014.2 | −1.12396 | −0.561980 | − | 0.827151i | \(-0.689960\pi\) | ||||
−0.561980 | + | 0.827151i | \(0.689960\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21058.4 | −1.23915 | −0.619573 | − | 0.784939i | \(-0.712694\pi\) | ||||
−0.619573 | + | 0.784939i | \(0.712694\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9304.37 | 0.545025 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6770.16 | −0.393016 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6765.54 | 0.390988 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28921.6 | −1.66395 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9634.87 | 0.551853 | 0.275926 | − | 0.961179i | \(-0.411015\pi\) | ||||
0.275926 | + | 0.961179i | \(0.411015\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6784.46 | 0.386865 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8371.31 | 0.475237 | 0.237619 | − | 0.971359i | \(-0.423633\pi\) | ||||
0.237619 | + | 0.971359i | \(0.423633\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13417.8 | −0.755022 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12068.8 | 0.676137 | 0.338069 | − | 0.941121i | \(-0.390226\pi\) | ||||
0.338069 | + | 0.941121i | \(0.390226\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1077.33 | 0.0600917 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8177.78 | 0.454151 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6330.09 | −0.350011 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2981.29 | −0.164130 | −0.0820648 | − | 0.996627i | \(-0.526151\pi\) | ||||
−0.0820648 | + | 0.996627i | \(0.526151\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6181.46 | −0.337376 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6595.53 | 0.358427 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11331.8 | −0.613172 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28978.0 | −1.56132 | −0.780660 | − | 0.624956i | \(-0.785117\pi\) | ||||
−0.780660 | + | 0.624956i | \(0.785117\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6000.11 | 0.321904 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4384.81 | −0.234243 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16372.4 | −0.867249 | −0.433625 | − | 0.901094i | \(-0.642766\pi\) | ||||
−0.433625 | + | 0.901094i | \(0.642766\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16951.6 | −0.894141 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17034.9 | −0.894755 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4583.18 | −0.239722 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24664.3 | −1.28467 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23010.5 | −1.19353 | −0.596765 | − | 0.802416i | \(-0.703547\pi\) | ||||
−0.596765 | + | 0.802416i | \(0.703547\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2980.35 | 0.153306 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14655.5 | −0.750745 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24636.8 | 1.25685 | 0.628423 | − | 0.777872i | \(-0.283701\pi\) | ||||
0.628423 | + | 0.777872i | \(0.283701\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28395.6 | −1.44264 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3902.87 | −0.197473 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6904.76 | 0.347931 | 0.173965 | − | 0.984752i | \(-0.444342\pi\) | ||||
0.173965 | + | 0.984752i | \(0.444342\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8835.63 | −0.441607 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9234.89 | 0.459690 | 0.229845 | − | 0.973227i | \(-0.426178\pi\) | ||||
0.229845 | + | 0.973227i | \(0.426178\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27275.0 | −1.35219 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20216.9 | −0.998232 | −0.499116 | − | 0.866535i | \(-0.666342\pi\) | ||||
−0.499116 | + | 0.866535i | \(0.666342\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5645.97 | −0.277654 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −835.544 | −0.0409250 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24054.9 | −1.16881 | −0.584405 | − | 0.811462i | \(-0.698672\pi\) | ||||
−0.584405 | + | 0.811462i | \(0.698672\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29538.4 | 1.42954 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1470.00 | −0.0708593 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30328.2 | −1.45614 | −0.728069 | − | 0.685504i | \(-0.759582\pi\) | ||||
−0.728069 | + | 0.685504i | \(0.759582\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −21450.1 | −1.02581 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33834.1 | −1.61168 | −0.805839 | − | 0.592135i | \(-0.798285\pi\) | ||||
−0.805839 | + | 0.592135i | \(0.798285\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1883.20 | −0.0890027 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19056.3 | −0.897109 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31738.1 | 1.48830 | 0.744151 | − | 0.668011i | \(-0.232854\pi\) | ||||
0.744151 | + | 0.668011i | \(0.232854\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33310.2 | −1.55595 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27494.2 | 1.27930 | 0.639650 | − | 0.768667i | \(-0.279080\pi\) | ||||
0.639650 | + | 0.768667i | \(0.279080\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −36875.6 | −1.70917 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19334.2 | −0.889244 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33194.8 | 1.52087 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6826.68 | −0.311578 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6476.84 | −0.294482 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 468.356 | 0.0212136 | 0.0106068 | − | 0.999944i | \(-0.496624\pi\) | ||||
0.0106068 | + | 0.999944i | \(0.496624\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 32844.0 | 1.48198 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26375.1 | 1.18109 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2293.07 | 0.102298 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37723.8 | 1.67659 | 0.838297 | − | 0.545214i | \(-0.183551\pi\) | ||||
0.838297 | + | 0.545214i | \(0.183551\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7155.87 | −0.316841 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −36658.1 | −1.61704 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11681.3 | 0.513356 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29259.6 | −1.27632 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7797.13 | −0.338854 | −0.169427 | − | 0.985543i | \(-0.554192\pi\) | ||||
−0.169427 | + | 0.985543i | \(0.554192\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16925.9 | −0.732860 | −0.366430 | − | 0.930446i | \(-0.619420\pi\) | ||||
−0.366430 | + | 0.930446i | \(0.619420\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34075.8 | 1.46998 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3757.36 | −0.161490 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11441.0 | 0.489925 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30009.3 | −1.27568 | −0.637840 | − | 0.770169i | \(-0.720172\pi\) | ||||
−0.637840 | + | 0.770169i | \(0.720172\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23385.6 | 0.990486 | 0.495243 | − | 0.868754i | \(-0.335079\pi\) | ||||
0.495243 | + | 0.868754i | \(0.335079\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −46433.3 | −1.95952 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37325.9 | 1.56947 | 0.784734 | − | 0.619833i | \(-0.212800\pi\) | ||||
0.784734 | + | 0.619833i | \(0.212800\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24671.3 | −1.03362 | −0.516809 | − | 0.856100i | \(-0.672880\pi\) | ||||
−0.516809 | + | 0.856100i | \(0.672880\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10515.4 | 0.438960 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6538.05 | 0.270969 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17177.1 | −0.709350 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14147.4 | −0.582147 | −0.291074 | − | 0.956701i | \(-0.594013\pi\) | ||||
−0.291074 | + | 0.956701i | \(0.594013\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9642.35 | −0.395356 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32896.6 | −1.34403 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −384.195 | −0.0156411 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 37171.3 | 1.50261 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4303.24 | −0.173341 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27963.6 | 1.12246 | 0.561229 | − | 0.827661i | \(-0.310329\pi\) | ||||
0.561229 | + | 0.827661i | \(0.310329\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5520.44 | 0.220813 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33855.8 | 1.34947 | 0.674734 | − | 0.738061i | \(-0.264259\pi\) | ||||
0.674734 | + | 0.738061i | \(0.264259\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24282.7 | 0.964511 | 0.482255 | − | 0.876031i | \(-0.339818\pi\) | ||||
0.482255 | + | 0.876031i | \(0.339818\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19667.0 | 0.775750 | 0.387875 | − | 0.921712i | \(-0.373209\pi\) | ||||
0.387875 | + | 0.921712i | \(0.373209\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6822.59 | 0.268179 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 32929.9 | 1.28992 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24389.4 | 0.952075 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8057.65 | 0.313459 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −57004.0 | −2.20996 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36061.0 | −1.38848 | −0.694238 | − | 0.719745i | \(-0.744259\pi\) | ||||
−0.694238 | + | 0.719745i | \(0.744259\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 38807.2 | 1.48912 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15889.7 | −0.607646 | −0.303823 | − | 0.952728i | \(-0.598263\pi\) | ||||
−0.303823 | + | 0.952728i | \(0.598263\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14861.3 | −0.566390 | −0.283195 | − | 0.959062i | \(-0.591394\pi\) | ||||
−0.283195 | + | 0.959062i | \(0.591394\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6903.13 | 0.262199 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38189.9 | 1.44565 | 0.722824 | − | 0.691032i | \(-0.242844\pi\) | ||||
0.722824 | + | 0.691032i | \(0.242844\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23772.3 | 0.893831 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20976.8 | 0.786073 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5813.99 | −0.217140 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19561.4 | 0.728135 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37105.0 | 1.37655 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3742.22 | 0.138370 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7733.86 | 0.284069 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16865.5 | −0.617431 | −0.308715 | − | 0.951154i | \(-0.599899\pi\) | ||||
−0.308715 | + | 0.951154i | \(0.599899\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2636.44 | 0.0961993 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26754.1 | −0.973000 | −0.486500 | − | 0.873681i | \(-0.661727\pi\) | ||||
−0.486500 | + | 0.873681i | \(0.661727\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1202.15 | 0.0435766 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9554.37 | −0.345200 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41527.5 | 1.49061 | 0.745303 | − | 0.666726i | \(-0.232305\pi\) | ||||
0.745303 | + | 0.666726i | \(0.232305\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33119.2 | −1.18492 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30272.0 | −1.07954 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9315.27 | −0.331118 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5630.31 | 0.199486 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4584.68 | 0.161914 | 0.0809572 | − | 0.996718i | \(-0.474202\pi\) | ||||
0.0809572 | + | 0.996718i | \(0.474202\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5355.86 | −0.187935 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2709.48 | 0.0947694 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6928.18 | −0.241552 | −0.120776 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120776 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 46495.7 | 1.61590 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20944.9 | 0.725596 | 0.362798 | − | 0.931868i | \(-0.381822\pi\) | ||||
0.362798 | + | 0.931868i | \(0.381822\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13866.4 | 0.478846 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29278.9 | −1.00468 | −0.502342 | − | 0.864669i | \(-0.667528\pi\) | ||||
−0.502342 | + | 0.864669i | \(0.667528\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10652.8 | −0.364387 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22089.0 | 0.753192 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2136.81 | 0.0726316 | 0.0363158 | − | 0.999340i | \(-0.488438\pi\) | ||||
0.0363158 | + | 0.999340i | \(0.488438\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1993.48 | −0.0675470 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 46722.3 | 1.57818 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63571.4 | 2.13391 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34960.2 | −1.16986 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7873.47 | −0.262649 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3921.32 | 0.130405 | 0.0652023 | − | 0.997872i | \(-0.479231\pi\) | ||||
0.0652023 | + | 0.997872i | \(0.479231\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16124.4 | 0.534562 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47809.1 | −1.58009 | −0.790045 | − | 0.613049i | \(-0.789943\pi\) | ||||
−0.790045 | + | 0.613049i | \(0.789943\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 42344.9 | 1.39089 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51329.1 | −1.68082 | −0.840411 | − | 0.541949i | \(-0.817686\pi\) | ||||
−0.840411 | + | 0.541949i | \(0.817686\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 52742.4 | 1.72181 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46580.1 | 1.51599 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16326.3 | 0.529734 | 0.264867 | − | 0.964285i | \(-0.414672\pi\) | ||||
0.264867 | + | 0.964285i | \(0.414672\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10631.6 | 0.343909 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8205.37 | −0.263818 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33770.0 | −1.08248 | −0.541242 | − | 0.840867i | \(-0.682046\pi\) | ||||
−0.541242 | + | 0.840867i | \(0.682046\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22003.6 | −0.703185 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1796.56 | 0.0572410 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50695.4 | 1.61037 | 0.805185 | − | 0.593023i | \(-0.202066\pi\) | ||||
0.805185 | + | 0.593023i | \(0.202066\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4339.16 | −0.137422 |
(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 | 784.4.a.bf.1.1 | 4 | ||
4.3 | odd | 2 | 49.4.a.e.1.2 | yes | 4 | ||
7.6 | odd | 2 | inner | 784.4.a.bf.1.4 | 4 | ||
12.11 | even | 2 | 441.4.a.u.1.3 | 4 | |||
20.19 | odd | 2 | 1225.4.a.bb.1.3 | 4 | |||
28.3 | even | 6 | 49.4.c.e.30.4 | 8 | |||
28.11 | odd | 6 | 49.4.c.e.30.3 | 8 | |||
28.19 | even | 6 | 49.4.c.e.18.4 | 8 | |||
28.23 | odd | 6 | 49.4.c.e.18.3 | 8 | |||
28.27 | even | 2 | 49.4.a.e.1.1 | ✓ | 4 | ||
84.11 | even | 6 | 441.4.e.y.226.2 | 8 | |||
84.23 | even | 6 | 441.4.e.y.361.2 | 8 | |||
84.47 | odd | 6 | 441.4.e.y.361.1 | 8 | |||
84.59 | odd | 6 | 441.4.e.y.226.1 | 8 | |||
84.83 | odd | 2 | 441.4.a.u.1.4 | 4 | |||
140.139 | even | 2 | 1225.4.a.bb.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.4.a.e.1.1 | ✓ | 4 | 28.27 | even | 2 | ||
49.4.a.e.1.2 | yes | 4 | 4.3 | odd | 2 | ||
49.4.c.e.18.3 | 8 | 28.23 | odd | 6 | |||
49.4.c.e.18.4 | 8 | 28.19 | even | 6 | |||
49.4.c.e.30.3 | 8 | 28.11 | odd | 6 | |||
49.4.c.e.30.4 | 8 | 28.3 | even | 6 | |||
441.4.a.u.1.3 | 4 | 12.11 | even | 2 | |||
441.4.a.u.1.4 | 4 | 84.83 | odd | 2 | |||
441.4.e.y.226.1 | 8 | 84.59 | odd | 6 | |||
441.4.e.y.226.2 | 8 | 84.11 | even | 6 | |||
441.4.e.y.361.1 | 8 | 84.47 | odd | 6 | |||
441.4.e.y.361.2 | 8 | 84.23 | even | 6 | |||
784.4.a.bf.1.1 | 4 | 1.1 | even | 1 | trivial | ||
784.4.a.bf.1.4 | 4 | 7.6 | odd | 2 | inner | ||
1225.4.a.bb.1.3 | 4 | 20.19 | odd | 2 | |||
1225.4.a.bb.1.4 | 4 | 140.139 | even | 2 |