Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1911,2,Mod(1,1911)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1911, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1911.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1911 = 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1911.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: | \(15.2594118263\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 10x^{8} + 52x^{7} + 16x^{6} - 212x^{5} + 64x^{4} + 300x^{3} - 159x^{2} - 80x + 46 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.67947\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1911.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.67947 | 1.18756 | 0.593781 | − | 0.804626i | \(-0.297634\pi\) | ||||
0.593781 | + | 0.804626i | \(0.297634\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.820610 | 0.410305 | ||||||||
\(5\) | −1.01562 | −0.454201 | −0.227100 | − | 0.973871i | \(-0.572925\pi\) | ||||
−0.227100 | + | 0.973871i | \(0.572925\pi\) | |||||||
\(6\) | −1.67947 | −0.685640 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.98075 | −0.700300 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.70571 | −0.539392 | ||||||||
\(11\) | 4.05316 | 1.22207 | 0.611036 | − | 0.791603i | \(-0.290753\pi\) | ||||
0.611036 | + | 0.791603i | \(0.290753\pi\) | |||||||
\(12\) | −0.820610 | −0.236890 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.01562 | 0.262233 | ||||||||
\(16\) | −4.96782 | −1.24195 | ||||||||
\(17\) | −7.26007 | −1.76082 | −0.880412 | − | 0.474209i | \(-0.842734\pi\) | ||||
−0.880412 | + | 0.474209i | \(0.842734\pi\) | |||||||
\(18\) | 1.67947 | 0.395854 | ||||||||
\(19\) | 2.90686 | 0.666879 | 0.333440 | − | 0.942771i | \(-0.391791\pi\) | ||||
0.333440 | + | 0.942771i | \(0.391791\pi\) | |||||||
\(20\) | −0.833432 | −0.186361 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.80714 | 1.45129 | ||||||||
\(23\) | 9.53118 | 1.98739 | 0.993694 | − | 0.112127i | \(-0.0357664\pi\) | ||||
0.993694 | + | 0.112127i | \(0.0357664\pi\) | |||||||
\(24\) | 1.98075 | 0.404318 | ||||||||
\(25\) | −3.96851 | −0.793702 | ||||||||
\(26\) | 1.67947 | 0.329371 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.53200 | 1.21296 | 0.606481 | − | 0.795098i | \(-0.292581\pi\) | ||||
0.606481 | + | 0.795098i | \(0.292581\pi\) | |||||||
\(30\) | 1.70571 | 0.311418 | ||||||||
\(31\) | 9.86851 | 1.77244 | 0.886218 | − | 0.463268i | \(-0.153323\pi\) | ||||
0.886218 | + | 0.463268i | \(0.153323\pi\) | |||||||
\(32\) | −4.38180 | −0.774600 | ||||||||
\(33\) | −4.05316 | −0.705564 | ||||||||
\(34\) | −12.1930 | −2.09109 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.820610 | 0.136768 | ||||||||
\(37\) | 4.24217 | 0.697408 | 0.348704 | − | 0.937233i | \(-0.386622\pi\) | ||||
0.348704 | + | 0.937233i | \(0.386622\pi\) | |||||||
\(38\) | 4.88198 | 0.791961 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 2.01169 | 0.318077 | ||||||||
\(41\) | −8.83058 | −1.37911 | −0.689553 | − | 0.724236i | \(-0.742193\pi\) | ||||
−0.689553 | + | 0.724236i | \(0.742193\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.566950 | 0.0864590 | 0.0432295 | − | 0.999065i | \(-0.486235\pi\) | ||||
0.0432295 | + | 0.999065i | \(0.486235\pi\) | |||||||
\(44\) | 3.32606 | 0.501423 | ||||||||
\(45\) | −1.01562 | −0.151400 | ||||||||
\(46\) | 16.0073 | 2.36015 | ||||||||
\(47\) | 12.1032 | 1.76543 | 0.882717 | − | 0.469905i | \(-0.155712\pi\) | ||||
0.882717 | + | 0.469905i | \(0.155712\pi\) | |||||||
\(48\) | 4.96782 | 0.717043 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.66498 | −0.942570 | ||||||||
\(51\) | 7.26007 | 1.01661 | ||||||||
\(52\) | 0.820610 | 0.113798 | ||||||||
\(53\) | 8.89147 | 1.22134 | 0.610669 | − | 0.791886i | \(-0.290901\pi\) | ||||
0.610669 | + | 0.791886i | \(0.290901\pi\) | |||||||
\(54\) | −1.67947 | −0.228547 | ||||||||
\(55\) | −4.11648 | −0.555066 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.90686 | −0.385023 | ||||||||
\(58\) | 10.9703 | 1.44047 | ||||||||
\(59\) | 5.44378 | 0.708720 | 0.354360 | − | 0.935109i | \(-0.384699\pi\) | ||||
0.354360 | + | 0.935109i | \(0.384699\pi\) | |||||||
\(60\) | 0.833432 | 0.107596 | ||||||||
\(61\) | −5.51703 | −0.706384 | −0.353192 | − | 0.935551i | \(-0.614904\pi\) | ||||
−0.353192 | + | 0.935551i | \(0.614904\pi\) | |||||||
\(62\) | 16.5738 | 2.10488 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.57655 | 0.322069 | ||||||||
\(65\) | −1.01562 | −0.125973 | ||||||||
\(66\) | −6.80714 | −0.837901 | ||||||||
\(67\) | −3.03034 | −0.370214 | −0.185107 | − | 0.982718i | \(-0.559263\pi\) | ||||
−0.185107 | + | 0.982718i | \(0.559263\pi\) | |||||||
\(68\) | −5.95769 | −0.722476 | ||||||||
\(69\) | −9.53118 | −1.14742 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.18315 | −0.733805 | −0.366902 | − | 0.930259i | \(-0.619582\pi\) | ||||
−0.366902 | + | 0.930259i | \(0.619582\pi\) | |||||||
\(72\) | −1.98075 | −0.233433 | ||||||||
\(73\) | 3.99200 | 0.467229 | 0.233614 | − | 0.972329i | \(-0.424945\pi\) | ||||
0.233614 | + | 0.972329i | \(0.424945\pi\) | |||||||
\(74\) | 7.12458 | 0.828216 | ||||||||
\(75\) | 3.96851 | 0.458244 | ||||||||
\(76\) | 2.38540 | 0.273624 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.67947 | −0.190162 | ||||||||
\(79\) | 1.06343 | 0.119645 | 0.0598227 | − | 0.998209i | \(-0.480946\pi\) | ||||
0.0598227 | + | 0.998209i | \(0.480946\pi\) | |||||||
\(80\) | 5.04544 | 0.564097 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −14.8307 | −1.63777 | ||||||||
\(83\) | −8.02803 | −0.881191 | −0.440596 | − | 0.897706i | \(-0.645233\pi\) | ||||
−0.440596 | + | 0.897706i | \(0.645233\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.37350 | 0.799768 | ||||||||
\(86\) | 0.952174 | 0.102676 | ||||||||
\(87\) | −6.53200 | −0.700304 | ||||||||
\(88\) | −8.02827 | −0.855817 | ||||||||
\(89\) | 6.60402 | 0.700025 | 0.350013 | − | 0.936745i | \(-0.386177\pi\) | ||||
0.350013 | + | 0.936745i | \(0.386177\pi\) | |||||||
\(90\) | −1.70571 | −0.179797 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.82138 | 0.815436 | ||||||||
\(93\) | −9.86851 | −1.02332 | ||||||||
\(94\) | 20.3269 | 2.09656 | ||||||||
\(95\) | −2.95228 | −0.302897 | ||||||||
\(96\) | 4.38180 | 0.447215 | ||||||||
\(97\) | 1.63178 | 0.165682 | 0.0828410 | − | 0.996563i | \(-0.473601\pi\) | ||||
0.0828410 | + | 0.996563i | \(0.473601\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.05316 | 0.407357 | ||||||||
\(100\) | −3.25660 | −0.325660 | ||||||||
\(101\) | 15.5527 | 1.54755 | 0.773774 | − | 0.633461i | \(-0.218366\pi\) | ||||
0.773774 | + | 0.633461i | \(0.218366\pi\) | |||||||
\(102\) | 12.1930 | 1.20729 | ||||||||
\(103\) | 14.5504 | 1.43369 | 0.716847 | − | 0.697230i | \(-0.245584\pi\) | ||||
0.716847 | + | 0.697230i | \(0.245584\pi\) | |||||||
\(104\) | −1.98075 | −0.194228 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.9329 | 1.45041 | ||||||||
\(107\) | 18.7040 | 1.80818 | 0.904092 | − | 0.427338i | \(-0.140548\pi\) | ||||
0.904092 | + | 0.427338i | \(0.140548\pi\) | |||||||
\(108\) | −0.820610 | −0.0789633 | ||||||||
\(109\) | −10.8252 | −1.03687 | −0.518433 | − | 0.855118i | \(-0.673484\pi\) | ||||
−0.518433 | + | 0.855118i | \(0.673484\pi\) | |||||||
\(110\) | −6.91350 | −0.659176 | ||||||||
\(111\) | −4.24217 | −0.402649 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.52791 | −0.896311 | −0.448155 | − | 0.893956i | \(-0.647919\pi\) | ||||
−0.448155 | + | 0.893956i | \(0.647919\pi\) | |||||||
\(114\) | −4.88198 | −0.457239 | ||||||||
\(115\) | −9.68009 | −0.902673 | ||||||||
\(116\) | 5.36023 | 0.497685 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 9.14265 | 0.841649 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.01169 | −0.183642 | ||||||||
\(121\) | 5.42807 | 0.493461 | ||||||||
\(122\) | −9.26568 | −0.838875 | ||||||||
\(123\) | 8.83058 | 0.796227 | ||||||||
\(124\) | 8.09820 | 0.727240 | ||||||||
\(125\) | 9.10863 | 0.814701 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.8621 | 0.963854 | 0.481927 | − | 0.876211i | \(-0.339937\pi\) | ||||
0.481927 | + | 0.876211i | \(0.339937\pi\) | |||||||
\(128\) | 13.0908 | 1.15708 | ||||||||
\(129\) | −0.566950 | −0.0499172 | ||||||||
\(130\) | −1.70571 | −0.149600 | ||||||||
\(131\) | 3.62137 | 0.316401 | 0.158200 | − | 0.987407i | \(-0.449431\pi\) | ||||
0.158200 | + | 0.987407i | \(0.449431\pi\) | |||||||
\(132\) | −3.32606 | −0.289497 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.08935 | −0.439653 | ||||||||
\(135\) | 1.01562 | 0.0874110 | ||||||||
\(136\) | 14.3804 | 1.23310 | ||||||||
\(137\) | −14.6162 | −1.24874 | −0.624372 | − | 0.781127i | \(-0.714645\pi\) | ||||
−0.624372 | + | 0.781127i | \(0.714645\pi\) | |||||||
\(138\) | −16.0073 | −1.36263 | ||||||||
\(139\) | −11.1222 | −0.943370 | −0.471685 | − | 0.881767i | \(-0.656354\pi\) | ||||
−0.471685 | + | 0.881767i | \(0.656354\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.1032 | −1.01927 | ||||||||
\(142\) | −10.3844 | −0.871439 | ||||||||
\(143\) | 4.05316 | 0.338942 | ||||||||
\(144\) | −4.96782 | −0.413985 | ||||||||
\(145\) | −6.63406 | −0.550928 | ||||||||
\(146\) | 6.70444 | 0.554863 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.48117 | 0.286150 | ||||||||
\(149\) | 5.23259 | 0.428671 | 0.214335 | − | 0.976760i | \(-0.431241\pi\) | ||||
0.214335 | + | 0.976760i | \(0.431241\pi\) | |||||||
\(150\) | 6.66498 | 0.544193 | ||||||||
\(151\) | −15.0293 | −1.22307 | −0.611535 | − | 0.791217i | \(-0.709448\pi\) | ||||
−0.611535 | + | 0.791217i | \(0.709448\pi\) | |||||||
\(152\) | −5.75775 | −0.467015 | ||||||||
\(153\) | −7.26007 | −0.586942 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.0227 | −0.805042 | ||||||||
\(156\) | −0.820610 | −0.0657014 | ||||||||
\(157\) | 1.33422 | 0.106482 | 0.0532410 | − | 0.998582i | \(-0.483045\pi\) | ||||
0.0532410 | + | 0.998582i | \(0.483045\pi\) | |||||||
\(158\) | 1.78600 | 0.142086 | ||||||||
\(159\) | −8.89147 | −0.705139 | ||||||||
\(160\) | 4.45026 | 0.351824 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.67947 | 0.131951 | ||||||||
\(163\) | −23.6878 | −1.85537 | −0.927686 | − | 0.373361i | \(-0.878205\pi\) | ||||
−0.927686 | + | 0.373361i | \(0.878205\pi\) | |||||||
\(164\) | −7.24647 | −0.565854 | ||||||||
\(165\) | 4.11648 | 0.320468 | ||||||||
\(166\) | −13.4828 | −1.04647 | ||||||||
\(167\) | −9.08825 | −0.703270 | −0.351635 | − | 0.936137i | \(-0.614374\pi\) | ||||
−0.351635 | + | 0.936137i | \(0.614374\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 12.3836 | 0.949775 | ||||||||
\(171\) | 2.90686 | 0.222293 | ||||||||
\(172\) | 0.465245 | 0.0354746 | ||||||||
\(173\) | −6.51688 | −0.495469 | −0.247735 | − | 0.968828i | \(-0.579686\pi\) | ||||
−0.247735 | + | 0.968828i | \(0.579686\pi\) | |||||||
\(174\) | −10.9703 | −0.831655 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −20.1353 | −1.51776 | ||||||||
\(177\) | −5.44378 | −0.409180 | ||||||||
\(178\) | 11.0912 | 0.831324 | ||||||||
\(179\) | −0.541948 | −0.0405071 | −0.0202536 | − | 0.999795i | \(-0.506447\pi\) | ||||
−0.0202536 | + | 0.999795i | \(0.506447\pi\) | |||||||
\(180\) | −0.833432 | −0.0621203 | ||||||||
\(181\) | 17.9887 | 1.33709 | 0.668543 | − | 0.743674i | \(-0.266918\pi\) | ||||
0.668543 | + | 0.743674i | \(0.266918\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.51703 | 0.407831 | ||||||||
\(184\) | −18.8788 | −1.39177 | ||||||||
\(185\) | −4.30845 | −0.316764 | ||||||||
\(186\) | −16.5738 | −1.21525 | ||||||||
\(187\) | −29.4262 | −2.15186 | ||||||||
\(188\) | 9.93202 | 0.724367 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.95825 | −0.359709 | ||||||||
\(191\) | −15.9819 | −1.15641 | −0.578204 | − | 0.815892i | \(-0.696246\pi\) | ||||
−0.578204 | + | 0.815892i | \(0.696246\pi\) | |||||||
\(192\) | −2.57655 | −0.185947 | ||||||||
\(193\) | −8.62801 | −0.621058 | −0.310529 | − | 0.950564i | \(-0.600506\pi\) | ||||
−0.310529 | + | 0.950564i | \(0.600506\pi\) | |||||||
\(194\) | 2.74052 | 0.196758 | ||||||||
\(195\) | 1.01562 | 0.0727304 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.179690 | −0.0128024 | −0.00640118 | − | 0.999980i | \(-0.502038\pi\) | ||||
−0.00640118 | + | 0.999980i | \(0.502038\pi\) | |||||||
\(198\) | 6.80714 | 0.483763 | ||||||||
\(199\) | 0.414150 | 0.0293583 | 0.0146791 | − | 0.999892i | \(-0.495327\pi\) | ||||
0.0146791 | + | 0.999892i | \(0.495327\pi\) | |||||||
\(200\) | 7.86061 | 0.555829 | ||||||||
\(201\) | 3.03034 | 0.213743 | ||||||||
\(202\) | 26.1202 | 1.83781 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.95769 | 0.417122 | ||||||||
\(205\) | 8.96855 | 0.626391 | ||||||||
\(206\) | 24.4369 | 1.70260 | ||||||||
\(207\) | 9.53118 | 0.662463 | ||||||||
\(208\) | −4.96782 | −0.344456 | ||||||||
\(209\) | 11.7820 | 0.814975 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.50902 | −0.585785 | −0.292893 | − | 0.956145i | \(-0.594618\pi\) | ||||
−0.292893 | + | 0.956145i | \(0.594618\pi\) | |||||||
\(212\) | 7.29643 | 0.501121 | ||||||||
\(213\) | 6.18315 | 0.423662 | ||||||||
\(214\) | 31.4128 | 2.14733 | ||||||||
\(215\) | −0.575808 | −0.0392698 | ||||||||
\(216\) | 1.98075 | 0.134773 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −18.1806 | −1.23134 | ||||||||
\(219\) | −3.99200 | −0.269755 | ||||||||
\(220\) | −3.37803 | −0.227747 | ||||||||
\(221\) | −7.26007 | −0.488365 | ||||||||
\(222\) | −7.12458 | −0.478171 | ||||||||
\(223\) | −22.6174 | −1.51457 | −0.757287 | − | 0.653083i | \(-0.773475\pi\) | ||||
−0.757287 | + | 0.653083i | \(0.773475\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.96851 | −0.264567 | ||||||||
\(226\) | −16.0018 | −1.06443 | ||||||||
\(227\) | −2.15420 | −0.142980 | −0.0714898 | − | 0.997441i | \(-0.522775\pi\) | ||||
−0.0714898 | + | 0.997441i | \(0.522775\pi\) | |||||||
\(228\) | −2.38540 | −0.157977 | ||||||||
\(229\) | 5.06718 | 0.334849 | 0.167424 | − | 0.985885i | \(-0.446455\pi\) | ||||
0.167424 | + | 0.985885i | \(0.446455\pi\) | |||||||
\(230\) | −16.2574 | −1.07198 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.9382 | −0.849437 | ||||||||
\(233\) | −8.97668 | −0.588082 | −0.294041 | − | 0.955793i | \(-0.595000\pi\) | ||||
−0.294041 | + | 0.955793i | \(0.595000\pi\) | |||||||
\(234\) | 1.67947 | 0.109790 | ||||||||
\(235\) | −12.2923 | −0.801862 | ||||||||
\(236\) | 4.46722 | 0.290791 | ||||||||
\(237\) | −1.06343 | −0.0690773 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.3970 | 1.77216 | 0.886081 | − | 0.463530i | \(-0.153417\pi\) | ||||
0.886081 | + | 0.463530i | \(0.153417\pi\) | |||||||
\(240\) | −5.04544 | −0.325682 | ||||||||
\(241\) | 1.42092 | 0.0915295 | 0.0457648 | − | 0.998952i | \(-0.485428\pi\) | ||||
0.0457648 | + | 0.998952i | \(0.485428\pi\) | |||||||
\(242\) | 9.11627 | 0.586016 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −4.52734 | −0.289833 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.8307 | 0.945569 | ||||||||
\(247\) | 2.90686 | 0.184959 | ||||||||
\(248\) | −19.5470 | −1.24124 | ||||||||
\(249\) | 8.02803 | 0.508756 | ||||||||
\(250\) | 15.2977 | 0.967508 | ||||||||
\(251\) | 12.7519 | 0.804895 | 0.402447 | − | 0.915443i | \(-0.368160\pi\) | ||||
0.402447 | + | 0.915443i | \(0.368160\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 38.6313 | 2.42873 | ||||||||
\(254\) | 18.2425 | 1.14464 | ||||||||
\(255\) | −7.37350 | −0.461746 | ||||||||
\(256\) | 16.8325 | 1.05203 | ||||||||
\(257\) | −12.7298 | −0.794064 | −0.397032 | − | 0.917805i | \(-0.629960\pi\) | ||||
−0.397032 | + | 0.917805i | \(0.629960\pi\) | |||||||
\(258\) | −0.952174 | −0.0592797 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.833432 | −0.0516872 | ||||||||
\(261\) | 6.53200 | 0.404321 | ||||||||
\(262\) | 6.08198 | 0.375746 | ||||||||
\(263\) | −28.9952 | −1.78792 | −0.893961 | − | 0.448144i | \(-0.852085\pi\) | ||||
−0.893961 | + | 0.448144i | \(0.852085\pi\) | |||||||
\(264\) | 8.02827 | 0.494106 | ||||||||
\(265\) | −9.03039 | −0.554733 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.60402 | −0.404160 | ||||||||
\(268\) | −2.48673 | −0.151901 | ||||||||
\(269\) | −1.34213 | −0.0818314 | −0.0409157 | − | 0.999163i | \(-0.513028\pi\) | ||||
−0.0409157 | + | 0.999163i | \(0.513028\pi\) | |||||||
\(270\) | 1.70571 | 0.103806 | ||||||||
\(271\) | 11.3410 | 0.688916 | 0.344458 | − | 0.938802i | \(-0.388063\pi\) | ||||
0.344458 | + | 0.938802i | \(0.388063\pi\) | |||||||
\(272\) | 36.0667 | 2.18687 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −24.5474 | −1.48296 | ||||||||
\(275\) | −16.0850 | −0.969961 | ||||||||
\(276\) | −7.82138 | −0.470792 | ||||||||
\(277\) | 13.0962 | 0.786875 | 0.393437 | − | 0.919351i | \(-0.371286\pi\) | ||||
0.393437 | + | 0.919351i | \(0.371286\pi\) | |||||||
\(278\) | −18.6793 | −1.12031 | ||||||||
\(279\) | 9.86851 | 0.590812 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.93491 | 0.175082 | 0.0875410 | − | 0.996161i | \(-0.472099\pi\) | ||||
0.0875410 | + | 0.996161i | \(0.472099\pi\) | |||||||
\(282\) | −20.3269 | −1.21045 | ||||||||
\(283\) | −21.2779 | −1.26484 | −0.632420 | − | 0.774626i | \(-0.717938\pi\) | ||||
−0.632420 | + | 0.774626i | \(0.717938\pi\) | |||||||
\(284\) | −5.07396 | −0.301084 | ||||||||
\(285\) | 2.95228 | 0.174878 | ||||||||
\(286\) | 6.80714 | 0.402515 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.38180 | −0.258200 | ||||||||
\(289\) | 35.7086 | 2.10050 | ||||||||
\(290\) | −11.1417 | −0.654262 | ||||||||
\(291\) | −1.63178 | −0.0956566 | ||||||||
\(292\) | 3.27588 | 0.191706 | ||||||||
\(293\) | −7.81571 | −0.456599 | −0.228299 | − | 0.973591i | \(-0.573317\pi\) | ||||
−0.228299 | + | 0.973591i | \(0.573317\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.52883 | −0.321901 | ||||||||
\(296\) | −8.40266 | −0.488395 | ||||||||
\(297\) | −4.05316 | −0.235188 | ||||||||
\(298\) | 8.78797 | 0.509073 | ||||||||
\(299\) | 9.53118 | 0.551202 | ||||||||
\(300\) | 3.25660 | 0.188020 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −25.2413 | −1.45247 | ||||||||
\(303\) | −15.5527 | −0.893478 | ||||||||
\(304\) | −14.4408 | −0.828234 | ||||||||
\(305\) | 5.60323 | 0.320840 | ||||||||
\(306\) | −12.1930 | −0.697030 | ||||||||
\(307\) | 1.63049 | 0.0930568 | 0.0465284 | − | 0.998917i | \(-0.485184\pi\) | ||||
0.0465284 | + | 0.998917i | \(0.485184\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.5504 | −0.827744 | ||||||||
\(310\) | −16.8328 | −0.956038 | ||||||||
\(311\) | 11.3479 | 0.643483 | 0.321741 | − | 0.946828i | \(-0.395732\pi\) | ||||
0.321741 | + | 0.946828i | \(0.395732\pi\) | |||||||
\(312\) | 1.98075 | 0.112138 | ||||||||
\(313\) | 5.83580 | 0.329859 | 0.164930 | − | 0.986305i | \(-0.447260\pi\) | ||||
0.164930 | + | 0.986305i | \(0.447260\pi\) | |||||||
\(314\) | 2.24077 | 0.126454 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.872664 | 0.0490912 | ||||||||
\(317\) | 23.6802 | 1.33001 | 0.665006 | − | 0.746838i | \(-0.268429\pi\) | ||||
0.665006 | + | 0.746838i | \(0.268429\pi\) | |||||||
\(318\) | −14.9329 | −0.837397 | ||||||||
\(319\) | 26.4752 | 1.48233 | ||||||||
\(320\) | −2.61681 | −0.146284 | ||||||||
\(321\) | −18.7040 | −1.04396 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.1040 | −1.17426 | ||||||||
\(324\) | 0.820610 | 0.0455895 | ||||||||
\(325\) | −3.96851 | −0.220133 | ||||||||
\(326\) | −39.7829 | −2.20337 | ||||||||
\(327\) | 10.8252 | 0.598634 | ||||||||
\(328\) | 17.4911 | 0.965787 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.91350 | 0.380576 | ||||||||
\(331\) | −19.2273 | −1.05683 | −0.528413 | − | 0.848987i | \(-0.677213\pi\) | ||||
−0.528413 | + | 0.848987i | \(0.677213\pi\) | |||||||
\(332\) | −6.58789 | −0.361557 | ||||||||
\(333\) | 4.24217 | 0.232469 | ||||||||
\(334\) | −15.2634 | −0.835177 | ||||||||
\(335\) | 3.07768 | 0.168152 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.8950 | −1.08375 | −0.541875 | − | 0.840459i | \(-0.682285\pi\) | ||||
−0.541875 | + | 0.840459i | \(0.682285\pi\) | |||||||
\(338\) | 1.67947 | 0.0913510 | ||||||||
\(339\) | 9.52791 | 0.517485 | ||||||||
\(340\) | 6.05077 | 0.328149 | ||||||||
\(341\) | 39.9986 | 2.16605 | ||||||||
\(342\) | 4.88198 | 0.263987 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.12298 | −0.0605472 | ||||||||
\(345\) | 9.68009 | 0.521159 | ||||||||
\(346\) | −10.9449 | −0.588401 | ||||||||
\(347\) | 16.6933 | 0.896145 | 0.448072 | − | 0.893997i | \(-0.352111\pi\) | ||||
0.448072 | + | 0.893997i | \(0.352111\pi\) | |||||||
\(348\) | −5.36023 | −0.287338 | ||||||||
\(349\) | 11.9128 | 0.637676 | 0.318838 | − | 0.947809i | \(-0.396707\pi\) | ||||
0.318838 | + | 0.947809i | \(0.396707\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −17.7601 | −0.946617 | ||||||||
\(353\) | −11.9997 | −0.638681 | −0.319340 | − | 0.947640i | \(-0.603461\pi\) | ||||
−0.319340 | + | 0.947640i | \(0.603461\pi\) | |||||||
\(354\) | −9.14265 | −0.485926 | ||||||||
\(355\) | 6.27976 | 0.333295 | ||||||||
\(356\) | 5.41933 | 0.287224 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.910184 | −0.0481047 | ||||||||
\(359\) | −6.50164 | −0.343143 | −0.171572 | − | 0.985172i | \(-0.554884\pi\) | ||||
−0.171572 | + | 0.985172i | \(0.554884\pi\) | |||||||
\(360\) | 2.01169 | 0.106026 | ||||||||
\(361\) | −10.5502 | −0.555272 | ||||||||
\(362\) | 30.2113 | 1.58787 | ||||||||
\(363\) | −5.42807 | −0.284900 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.05437 | −0.212216 | ||||||||
\(366\) | 9.26568 | 0.484325 | ||||||||
\(367\) | 11.2963 | 0.589660 | 0.294830 | − | 0.955550i | \(-0.404737\pi\) | ||||
0.294830 | + | 0.955550i | \(0.404737\pi\) | |||||||
\(368\) | −47.3492 | −2.46825 | ||||||||
\(369\) | −8.83058 | −0.459702 | ||||||||
\(370\) | −7.23590 | −0.376177 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.09820 | −0.419872 | ||||||||
\(373\) | −30.2400 | −1.56577 | −0.782884 | − | 0.622167i | \(-0.786252\pi\) | ||||
−0.782884 | + | 0.622167i | \(0.786252\pi\) | |||||||
\(374\) | −49.4203 | −2.55546 | ||||||||
\(375\) | −9.10863 | −0.470368 | ||||||||
\(376\) | −23.9734 | −1.23633 | ||||||||
\(377\) | 6.53200 | 0.336415 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.33348 | −0.119863 | −0.0599313 | − | 0.998203i | \(-0.519088\pi\) | ||||
−0.0599313 | + | 0.998203i | \(0.519088\pi\) | |||||||
\(380\) | −2.42267 | −0.124280 | ||||||||
\(381\) | −10.8621 | −0.556481 | ||||||||
\(382\) | −26.8411 | −1.37331 | ||||||||
\(383\) | 25.4474 | 1.30030 | 0.650151 | − | 0.759805i | \(-0.274705\pi\) | ||||
0.650151 | + | 0.759805i | \(0.274705\pi\) | |||||||
\(384\) | −13.0908 | −0.668039 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.4905 | −0.737545 | ||||||||
\(387\) | 0.566950 | 0.0288197 | ||||||||
\(388\) | 1.33905 | 0.0679802 | ||||||||
\(389\) | −7.31939 | −0.371108 | −0.185554 | − | 0.982634i | \(-0.559408\pi\) | ||||
−0.185554 | + | 0.982634i | \(0.559408\pi\) | |||||||
\(390\) | 1.70571 | 0.0863719 | ||||||||
\(391\) | −69.1970 | −3.49944 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.62137 | −0.182674 | ||||||||
\(394\) | −0.301783 | −0.0152036 | ||||||||
\(395\) | −1.08005 | −0.0543431 | ||||||||
\(396\) | 3.32606 | 0.167141 | ||||||||
\(397\) | 9.01082 | 0.452240 | 0.226120 | − | 0.974099i | \(-0.427396\pi\) | ||||
0.226120 | + | 0.974099i | \(0.427396\pi\) | |||||||
\(398\) | 0.695551 | 0.0348648 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.7148 | 0.985741 | ||||||||
\(401\) | 34.9597 | 1.74580 | 0.872902 | − | 0.487895i | \(-0.162235\pi\) | ||||
0.872902 | + | 0.487895i | \(0.162235\pi\) | |||||||
\(402\) | 5.08935 | 0.253834 | ||||||||
\(403\) | 9.86851 | 0.491585 | ||||||||
\(404\) | 12.7627 | 0.634967 | ||||||||
\(405\) | −1.01562 | −0.0504668 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.1942 | 0.852283 | ||||||||
\(408\) | −14.3804 | −0.711933 | ||||||||
\(409\) | −4.05390 | −0.200452 | −0.100226 | − | 0.994965i | \(-0.531957\pi\) | ||||
−0.100226 | + | 0.994965i | \(0.531957\pi\) | |||||||
\(410\) | 15.0624 | 0.743879 | ||||||||
\(411\) | 14.6162 | 0.720963 | ||||||||
\(412\) | 11.9402 | 0.588252 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 16.0073 | 0.786716 | ||||||||
\(415\) | 8.15346 | 0.400238 | ||||||||
\(416\) | −4.38180 | −0.214835 | ||||||||
\(417\) | 11.1222 | 0.544655 | ||||||||
\(418\) | 19.7874 | 0.967834 | ||||||||
\(419\) | 20.7873 | 1.01552 | 0.507762 | − | 0.861497i | \(-0.330473\pi\) | ||||
0.507762 | + | 0.861497i | \(0.330473\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.7027 | 0.960249 | 0.480125 | − | 0.877200i | \(-0.340591\pi\) | ||||
0.480125 | + | 0.877200i | \(0.340591\pi\) | |||||||
\(422\) | −14.2906 | −0.695657 | ||||||||
\(423\) | 12.1032 | 0.588478 | ||||||||
\(424\) | −17.6117 | −0.855302 | ||||||||
\(425\) | 28.8116 | 1.39757 | ||||||||
\(426\) | 10.3844 | 0.503126 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 15.3487 | 0.741907 | ||||||||
\(429\) | −4.05316 | −0.195688 | ||||||||
\(430\) | −0.967051 | −0.0466353 | ||||||||
\(431\) | 3.54528 | 0.170770 | 0.0853850 | − | 0.996348i | \(-0.472788\pi\) | ||||
0.0853850 | + | 0.996348i | \(0.472788\pi\) | |||||||
\(432\) | 4.96782 | 0.239014 | ||||||||
\(433\) | −10.2828 | −0.494159 | −0.247079 | − | 0.968995i | \(-0.579471\pi\) | ||||
−0.247079 | + | 0.968995i | \(0.579471\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.63406 | 0.318079 | ||||||||
\(436\) | −8.88327 | −0.425431 | ||||||||
\(437\) | 27.7058 | 1.32535 | ||||||||
\(438\) | −6.70444 | −0.320350 | ||||||||
\(439\) | 13.7824 | 0.657800 | 0.328900 | − | 0.944365i | \(-0.393322\pi\) | ||||
0.328900 | + | 0.944365i | \(0.393322\pi\) | |||||||
\(440\) | 8.15371 | 0.388713 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.1930 | −0.579964 | ||||||||
\(443\) | 16.2294 | 0.771082 | 0.385541 | − | 0.922691i | \(-0.374015\pi\) | ||||
0.385541 | + | 0.922691i | \(0.374015\pi\) | |||||||
\(444\) | −3.48117 | −0.165209 | ||||||||
\(445\) | −6.70721 | −0.317952 | ||||||||
\(446\) | −37.9852 | −1.79865 | ||||||||
\(447\) | −5.23259 | −0.247493 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.8213 | 1.87928 | 0.939642 | − | 0.342159i | \(-0.111158\pi\) | ||||
0.939642 | + | 0.342159i | \(0.111158\pi\) | |||||||
\(450\) | −6.66498 | −0.314190 | ||||||||
\(451\) | −35.7917 | −1.68537 | ||||||||
\(452\) | −7.81871 | −0.367761 | ||||||||
\(453\) | 15.0293 | 0.706140 | ||||||||
\(454\) | −3.61792 | −0.169797 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.75775 | 0.269631 | ||||||||
\(457\) | −3.04965 | −0.142656 | −0.0713282 | − | 0.997453i | \(-0.522724\pi\) | ||||
−0.0713282 | + | 0.997453i | \(0.522724\pi\) | |||||||
\(458\) | 8.51016 | 0.397654 | ||||||||
\(459\) | 7.26007 | 0.338871 | ||||||||
\(460\) | −7.94359 | −0.370372 | ||||||||
\(461\) | 14.0689 | 0.655252 | 0.327626 | − | 0.944808i | \(-0.393751\pi\) | ||||
0.327626 | + | 0.944808i | \(0.393751\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.2561 | 1.22022 | 0.610112 | − | 0.792315i | \(-0.291125\pi\) | ||||
0.610112 | + | 0.792315i | \(0.291125\pi\) | |||||||
\(464\) | −32.4498 | −1.50644 | ||||||||
\(465\) | 10.0227 | 0.464791 | ||||||||
\(466\) | −15.0760 | −0.698384 | ||||||||
\(467\) | 0.631924 | 0.0292419 | 0.0146210 | − | 0.999893i | \(-0.495346\pi\) | ||||
0.0146210 | + | 0.999893i | \(0.495346\pi\) | |||||||
\(468\) | 0.820610 | 0.0379327 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −20.6445 | −0.952261 | ||||||||
\(471\) | −1.33422 | −0.0614774 | ||||||||
\(472\) | −10.7827 | −0.496316 | ||||||||
\(473\) | 2.29794 | 0.105659 | ||||||||
\(474\) | −1.78600 | −0.0820337 | ||||||||
\(475\) | −11.5359 | −0.529303 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.89147 | 0.407112 | ||||||||
\(478\) | 46.0123 | 2.10455 | ||||||||
\(479\) | 17.2080 | 0.786253 | 0.393127 | − | 0.919484i | \(-0.371393\pi\) | ||||
0.393127 | + | 0.919484i | \(0.371393\pi\) | |||||||
\(480\) | −4.45026 | −0.203126 | ||||||||
\(481\) | 4.24217 | 0.193426 | ||||||||
\(482\) | 2.38639 | 0.108697 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.45433 | 0.202470 | ||||||||
\(485\) | −1.65727 | −0.0752529 | ||||||||
\(486\) | −1.67947 | −0.0761822 | ||||||||
\(487\) | −30.9293 | −1.40154 | −0.700770 | − | 0.713387i | \(-0.747160\pi\) | ||||
−0.700770 | + | 0.713387i | \(0.747160\pi\) | |||||||
\(488\) | 10.9278 | 0.494680 | ||||||||
\(489\) | 23.6878 | 1.07120 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.0434 | 1.03993 | 0.519966 | − | 0.854187i | \(-0.325944\pi\) | ||||
0.519966 | + | 0.854187i | \(0.325944\pi\) | |||||||
\(492\) | 7.24647 | 0.326696 | ||||||||
\(493\) | −47.4228 | −2.13581 | ||||||||
\(494\) | 4.88198 | 0.219650 | ||||||||
\(495\) | −4.11648 | −0.185022 | ||||||||
\(496\) | −49.0250 | −2.20129 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 13.4828 | 0.604180 | ||||||||
\(499\) | −12.7385 | −0.570252 | −0.285126 | − | 0.958490i | \(-0.592035\pi\) | ||||
−0.285126 | + | 0.958490i | \(0.592035\pi\) | |||||||
\(500\) | 7.47464 | 0.334276 | ||||||||
\(501\) | 9.08825 | 0.406033 | ||||||||
\(502\) | 21.4164 | 0.955863 | ||||||||
\(503\) | −12.7285 | −0.567536 | −0.283768 | − | 0.958893i | \(-0.591584\pi\) | ||||
−0.283768 | + | 0.958893i | \(0.591584\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.7957 | −0.702898 | ||||||||
\(506\) | 64.8801 | 2.88427 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 8.91354 | 0.395474 | ||||||||
\(509\) | −24.8747 | −1.10255 | −0.551276 | − | 0.834323i | \(-0.685859\pi\) | ||||
−0.551276 | + | 0.834323i | \(0.685859\pi\) | |||||||
\(510\) | −12.3836 | −0.548353 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 2.08800 | 0.0922776 | ||||||||
\(513\) | −2.90686 | −0.128341 | ||||||||
\(514\) | −21.3793 | −0.943001 | ||||||||
\(515\) | −14.7777 | −0.651185 | ||||||||
\(516\) | −0.465245 | −0.0204813 | ||||||||
\(517\) | 49.0562 | 2.15749 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.51688 | 0.286059 | ||||||||
\(520\) | 2.01169 | 0.0882186 | ||||||||
\(521\) | −36.7391 | −1.60957 | −0.804784 | − | 0.593568i | \(-0.797719\pi\) | ||||
−0.804784 | + | 0.593568i | \(0.797719\pi\) | |||||||
\(522\) | 10.9703 | 0.480156 | ||||||||
\(523\) | −19.5499 | −0.854858 | −0.427429 | − | 0.904049i | \(-0.640581\pi\) | ||||
−0.427429 | + | 0.904049i | \(0.640581\pi\) | |||||||
\(524\) | 2.97174 | 0.129821 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −48.6965 | −2.12327 | ||||||||
\(527\) | −71.6460 | −3.12095 | ||||||||
\(528\) | 20.1353 | 0.876278 | ||||||||
\(529\) | 67.8433 | 2.94971 | ||||||||
\(530\) | −15.1662 | −0.658780 | ||||||||
\(531\) | 5.44378 | 0.236240 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.83058 | −0.382495 | ||||||||
\(534\) | −11.0912 | −0.479965 | ||||||||
\(535\) | −18.9962 | −0.821279 | ||||||||
\(536\) | 6.00233 | 0.259261 | ||||||||
\(537\) | 0.541948 | 0.0233868 | ||||||||
\(538\) | −2.25407 | −0.0971799 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.833432 | 0.0358652 | ||||||||
\(541\) | −13.1112 | −0.563695 | −0.281847 | − | 0.959459i | \(-0.590947\pi\) | ||||
−0.281847 | + | 0.959459i | \(0.590947\pi\) | |||||||
\(542\) | 19.0468 | 0.818131 | ||||||||
\(543\) | −17.9887 | −0.771967 | ||||||||
\(544\) | 31.8121 | 1.36393 | ||||||||
\(545\) | 10.9943 | 0.470945 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.5723 | −1.22166 | −0.610831 | − | 0.791761i | \(-0.709165\pi\) | ||||
−0.610831 | + | 0.791761i | \(0.709165\pi\) | |||||||
\(548\) | −11.9942 | −0.512366 | ||||||||
\(549\) | −5.51703 | −0.235461 | ||||||||
\(550\) | −27.0142 | −1.15189 | ||||||||
\(551\) | 18.9876 | 0.808899 | ||||||||
\(552\) | 18.8788 | 0.803537 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 21.9946 | 0.934463 | ||||||||
\(555\) | 4.30845 | 0.182884 | ||||||||
\(556\) | −9.12696 | −0.387069 | ||||||||
\(557\) | 8.09164 | 0.342854 | 0.171427 | − | 0.985197i | \(-0.445162\pi\) | ||||
0.171427 | + | 0.985197i | \(0.445162\pi\) | |||||||
\(558\) | 16.5738 | 0.701626 | ||||||||
\(559\) | 0.566950 | 0.0239794 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 29.4262 | 1.24237 | ||||||||
\(562\) | 4.92909 | 0.207921 | ||||||||
\(563\) | 12.0169 | 0.506450 | 0.253225 | − | 0.967407i | \(-0.418509\pi\) | ||||
0.253225 | + | 0.967407i | \(0.418509\pi\) | |||||||
\(564\) | −9.93202 | −0.418213 | ||||||||
\(565\) | 9.67678 | 0.407105 | ||||||||
\(566\) | −35.7355 | −1.50208 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.2472 | 0.513883 | ||||||||
\(569\) | 33.6891 | 1.41232 | 0.706161 | − | 0.708051i | \(-0.250426\pi\) | ||||
0.706161 | + | 0.708051i | \(0.250426\pi\) | |||||||
\(570\) | 4.95825 | 0.207678 | ||||||||
\(571\) | −21.4169 | −0.896269 | −0.448135 | − | 0.893966i | \(-0.647912\pi\) | ||||
−0.448135 | + | 0.893966i | \(0.647912\pi\) | |||||||
\(572\) | 3.32606 | 0.139070 | ||||||||
\(573\) | 15.9819 | 0.667653 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −37.8245 | −1.57739 | ||||||||
\(576\) | 2.57655 | 0.107356 | ||||||||
\(577\) | −46.5340 | −1.93723 | −0.968617 | − | 0.248557i | \(-0.920044\pi\) | ||||
−0.968617 | + | 0.248557i | \(0.920044\pi\) | |||||||
\(578\) | 59.9714 | 2.49448 | ||||||||
\(579\) | 8.62801 | 0.358568 | ||||||||
\(580\) | −5.44398 | −0.226049 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.74052 | −0.113598 | ||||||||
\(583\) | 36.0385 | 1.49256 | ||||||||
\(584\) | −7.90714 | −0.327200 | ||||||||
\(585\) | −1.01562 | −0.0419909 | ||||||||
\(586\) | −13.1262 | −0.542240 | ||||||||
\(587\) | −1.76869 | −0.0730016 | −0.0365008 | − | 0.999334i | \(-0.511621\pi\) | ||||
−0.0365008 | + | 0.999334i | \(0.511621\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.6864 | 1.18200 | ||||||||
\(590\) | −9.28550 | −0.382278 | ||||||||
\(591\) | 0.179690 | 0.00739144 | ||||||||
\(592\) | −21.0743 | −0.866150 | ||||||||
\(593\) | 3.65783 | 0.150209 | 0.0751045 | − | 0.997176i | \(-0.476071\pi\) | ||||
0.0751045 | + | 0.997176i | \(0.476071\pi\) | |||||||
\(594\) | −6.80714 | −0.279300 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.29392 | 0.175886 | ||||||||
\(597\) | −0.414150 | −0.0169500 | ||||||||
\(598\) | 16.0073 | 0.654587 | ||||||||
\(599\) | 29.2941 | 1.19692 | 0.598461 | − | 0.801152i | \(-0.295779\pi\) | ||||
0.598461 | + | 0.801152i | \(0.295779\pi\) | |||||||
\(600\) | −7.86061 | −0.320908 | ||||||||
\(601\) | −17.0717 | −0.696368 | −0.348184 | − | 0.937426i | \(-0.613202\pi\) | ||||
−0.348184 | + | 0.937426i | \(0.613202\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.03034 | −0.123405 | ||||||||
\(604\) | −12.3332 | −0.501832 | ||||||||
\(605\) | −5.51288 | −0.224130 | ||||||||
\(606\) | −26.1202 | −1.06106 | ||||||||
\(607\) | −26.4068 | −1.07182 | −0.535909 | − | 0.844276i | \(-0.680031\pi\) | ||||
−0.535909 | + | 0.844276i | \(0.680031\pi\) | |||||||
\(608\) | −12.7373 | −0.516565 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.41045 | 0.381018 | ||||||||
\(611\) | 12.1032 | 0.489643 | ||||||||
\(612\) | −5.95769 | −0.240825 | ||||||||
\(613\) | −27.9308 | −1.12812 | −0.564058 | − | 0.825735i | \(-0.690760\pi\) | ||||
−0.564058 | + | 0.825735i | \(0.690760\pi\) | |||||||
\(614\) | 2.73835 | 0.110511 | ||||||||
\(615\) | −8.96855 | −0.361647 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.4751 | 1.30740 | 0.653699 | − | 0.756755i | \(-0.273216\pi\) | ||||
0.653699 | + | 0.756755i | \(0.273216\pi\) | |||||||
\(618\) | −24.4369 | −0.982998 | ||||||||
\(619\) | 7.57894 | 0.304624 | 0.152312 | − | 0.988332i | \(-0.451328\pi\) | ||||
0.152312 | + | 0.988332i | \(0.451328\pi\) | |||||||
\(620\) | −8.22473 | −0.330313 | ||||||||
\(621\) | −9.53118 | −0.382473 | ||||||||
\(622\) | 19.0585 | 0.764176 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.96782 | 0.198872 | ||||||||
\(625\) | 10.5916 | 0.423664 | ||||||||
\(626\) | 9.80104 | 0.391728 | ||||||||
\(627\) | −11.7820 | −0.470526 | ||||||||
\(628\) | 1.09487 | 0.0436901 | ||||||||
\(629\) | −30.7984 | −1.22801 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.5735 | −0.659780 | −0.329890 | − | 0.944019i | \(-0.607012\pi\) | ||||
−0.329890 | + | 0.944019i | \(0.607012\pi\) | |||||||
\(632\) | −2.10639 | −0.0837877 | ||||||||
\(633\) | 8.50902 | 0.338203 | ||||||||
\(634\) | 39.7701 | 1.57947 | ||||||||
\(635\) | −11.0318 | −0.437783 | ||||||||
\(636\) | −7.29643 | −0.289322 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 44.4642 | 1.76036 | ||||||||
\(639\) | −6.18315 | −0.244602 | ||||||||
\(640\) | −13.2954 | −0.525545 | ||||||||
\(641\) | −19.8649 | −0.784616 | −0.392308 | − | 0.919834i | \(-0.628323\pi\) | ||||
−0.392308 | + | 0.919834i | \(0.628323\pi\) | |||||||
\(642\) | −31.4128 | −1.23976 | ||||||||
\(643\) | −9.68565 | −0.381965 | −0.190982 | − | 0.981593i | \(-0.561167\pi\) | ||||
−0.190982 | + | 0.981593i | \(0.561167\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.575808 | 0.0226724 | ||||||||
\(646\) | −35.4435 | −1.39450 | ||||||||
\(647\) | 34.2542 | 1.34667 | 0.673337 | − | 0.739336i | \(-0.264860\pi\) | ||||
0.673337 | + | 0.739336i | \(0.264860\pi\) | |||||||
\(648\) | −1.98075 | −0.0778111 | ||||||||
\(649\) | 22.0645 | 0.866107 | ||||||||
\(650\) | −6.66498 | −0.261422 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.4385 | −0.761269 | ||||||||
\(653\) | −37.5001 | −1.46749 | −0.733746 | − | 0.679424i | \(-0.762230\pi\) | ||||
−0.733746 | + | 0.679424i | \(0.762230\pi\) | |||||||
\(654\) | 18.1806 | 0.710916 | ||||||||
\(655\) | −3.67795 | −0.143710 | ||||||||
\(656\) | 43.8687 | 1.71279 | ||||||||
\(657\) | 3.99200 | 0.155743 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.1575 | 1.56432 | 0.782158 | − | 0.623081i | \(-0.214119\pi\) | ||||
0.782158 | + | 0.623081i | \(0.214119\pi\) | |||||||
\(660\) | 3.37803 | 0.131490 | ||||||||
\(661\) | 30.8232 | 1.19888 | 0.599441 | − | 0.800419i | \(-0.295390\pi\) | ||||
0.599441 | + | 0.800419i | \(0.295390\pi\) | |||||||
\(662\) | −32.2916 | −1.25505 | ||||||||
\(663\) | 7.26007 | 0.281958 | ||||||||
\(664\) | 15.9015 | 0.617098 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.12458 | 0.276072 | ||||||||
\(667\) | 62.2576 | 2.41063 | ||||||||
\(668\) | −7.45792 | −0.288555 | ||||||||
\(669\) | 22.6174 | 0.874439 | ||||||||
\(670\) | 5.16887 | 0.199691 | ||||||||
\(671\) | −22.3614 | −0.863252 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.2528 | −1.05052 | −0.525260 | − | 0.850942i | \(-0.676032\pi\) | ||||
−0.525260 | + | 0.850942i | \(0.676032\pi\) | |||||||
\(674\) | −33.4130 | −1.28702 | ||||||||
\(675\) | 3.96851 | 0.152748 | ||||||||
\(676\) | 0.820610 | 0.0315619 | ||||||||
\(677\) | −0.689513 | −0.0265001 | −0.0132501 | − | 0.999912i | \(-0.504218\pi\) | ||||
−0.0132501 | + | 0.999912i | \(0.504218\pi\) | |||||||
\(678\) | 16.0018 | 0.614546 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −14.6050 | −0.560077 | ||||||||
\(681\) | 2.15420 | 0.0825493 | ||||||||
\(682\) | 67.1763 | 2.57231 | ||||||||
\(683\) | −0.746528 | −0.0285651 | −0.0142825 | − | 0.999898i | \(-0.504546\pi\) | ||||
−0.0142825 | + | 0.999898i | \(0.504546\pi\) | |||||||
\(684\) | 2.38540 | 0.0912080 | ||||||||
\(685\) | 14.8445 | 0.567181 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.06718 | −0.193325 | ||||||||
\(688\) | −2.81650 | −0.107378 | ||||||||
\(689\) | 8.89147 | 0.338738 | ||||||||
\(690\) | 16.2574 | 0.618909 | ||||||||
\(691\) | 36.8456 | 1.40167 | 0.700837 | − | 0.713321i | \(-0.252810\pi\) | ||||
0.700837 | + | 0.713321i | \(0.252810\pi\) | |||||||
\(692\) | −5.34782 | −0.203294 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.0359 | 1.06423 | ||||||||
\(695\) | 11.2959 | 0.428479 | ||||||||
\(696\) | 12.9382 | 0.490422 | ||||||||
\(697\) | 64.1106 | 2.42836 | ||||||||
\(698\) | 20.0071 | 0.757280 | ||||||||
\(699\) | 8.97668 | 0.339529 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.8455 | −0.749556 | −0.374778 | − | 0.927115i | \(-0.622281\pi\) | ||||
−0.374778 | + | 0.927115i | \(0.622281\pi\) | |||||||
\(702\) | −1.67947 | −0.0633874 | ||||||||
\(703\) | 12.3314 | 0.465087 | ||||||||
\(704\) | 10.4432 | 0.393592 | ||||||||
\(705\) | 12.2923 | 0.462955 | ||||||||
\(706\) | −20.1531 | −0.758473 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.46722 | −0.167889 | ||||||||
\(709\) | 6.77166 | 0.254315 | 0.127157 | − | 0.991883i | \(-0.459415\pi\) | ||||
0.127157 | + | 0.991883i | \(0.459415\pi\) | |||||||
\(710\) | 10.5466 | 0.395808 | ||||||||
\(711\) | 1.06343 | 0.0398818 | ||||||||
\(712\) | −13.0809 | −0.490227 | ||||||||
\(713\) | 94.0585 | 3.52252 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.11648 | −0.153948 | ||||||||
\(716\) | −0.444728 | −0.0166203 | ||||||||
\(717\) | −27.3970 | −1.02316 | ||||||||
\(718\) | −10.9193 | −0.407504 | ||||||||
\(719\) | 23.7828 | 0.886949 | 0.443475 | − | 0.896287i | \(-0.353746\pi\) | ||||
0.443475 | + | 0.896287i | \(0.353746\pi\) | |||||||
\(720\) | 5.04544 | 0.188032 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.7187 | −0.659420 | ||||||||
\(723\) | −1.42092 | −0.0528446 | ||||||||
\(724\) | 14.7617 | 0.548613 | ||||||||
\(725\) | −25.9223 | −0.962730 | ||||||||
\(726\) | −9.11627 | −0.338336 | ||||||||
\(727\) | 32.3712 | 1.20058 | 0.600290 | − | 0.799783i | \(-0.295052\pi\) | ||||
0.600290 | + | 0.799783i | \(0.295052\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.80919 | −0.252019 | ||||||||
\(731\) | −4.11609 | −0.152239 | ||||||||
\(732\) | 4.52734 | 0.167335 | ||||||||
\(733\) | −43.2848 | −1.59876 | −0.799379 | − | 0.600827i | \(-0.794838\pi\) | ||||
−0.799379 | + | 0.600827i | \(0.794838\pi\) | |||||||
\(734\) | 18.9717 | 0.700258 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −41.7637 | −1.53943 | ||||||||
\(737\) | −12.2824 | −0.452429 | ||||||||
\(738\) | −14.8307 | −0.545925 | ||||||||
\(739\) | 23.2717 | 0.856063 | 0.428032 | − | 0.903764i | \(-0.359207\pi\) | ||||
0.428032 | + | 0.903764i | \(0.359207\pi\) | |||||||
\(740\) | −3.53556 | −0.129970 | ||||||||
\(741\) | −2.90686 | −0.106786 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.9402 | 1.13509 | 0.567543 | − | 0.823344i | \(-0.307894\pi\) | ||||
0.567543 | + | 0.823344i | \(0.307894\pi\) | |||||||
\(744\) | 19.5470 | 0.716628 | ||||||||
\(745\) | −5.31435 | −0.194703 | ||||||||
\(746\) | −50.7871 | −1.85945 | ||||||||
\(747\) | −8.02803 | −0.293730 | ||||||||
\(748\) | −24.1474 | −0.882918 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −15.2977 | −0.558591 | ||||||||
\(751\) | 13.4036 | 0.489106 | 0.244553 | − | 0.969636i | \(-0.421359\pi\) | ||||
0.244553 | + | 0.969636i | \(0.421359\pi\) | |||||||
\(752\) | −60.1265 | −2.19259 | ||||||||
\(753\) | −12.7519 | −0.464706 | ||||||||
\(754\) | 10.9703 | 0.399514 | ||||||||
\(755\) | 15.2642 | 0.555520 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.8271 | 1.15677 | 0.578387 | − | 0.815762i | \(-0.303682\pi\) | ||||
0.578387 | + | 0.815762i | \(0.303682\pi\) | |||||||
\(758\) | −3.91900 | −0.142344 | ||||||||
\(759\) | −38.6313 | −1.40223 | ||||||||
\(760\) | 5.84771 | 0.212119 | ||||||||
\(761\) | 3.91844 | 0.142043 | 0.0710216 | − | 0.997475i | \(-0.477374\pi\) | ||||
0.0710216 | + | 0.997475i | \(0.477374\pi\) | |||||||
\(762\) | −18.2425 | −0.660857 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −13.1149 | −0.474481 | ||||||||
\(765\) | 7.37350 | 0.266589 | ||||||||
\(766\) | 42.7381 | 1.54419 | ||||||||
\(767\) | 5.44378 | 0.196564 | ||||||||
\(768\) | −16.8325 | −0.607391 | ||||||||
\(769\) | −10.6889 | −0.385453 | −0.192727 | − | 0.981252i | \(-0.561733\pi\) | ||||
−0.192727 | + | 0.981252i | \(0.561733\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.7298 | 0.458453 | ||||||||
\(772\) | −7.08023 | −0.254823 | ||||||||
\(773\) | −11.7012 | −0.420862 | −0.210431 | − | 0.977609i | \(-0.567487\pi\) | ||||
−0.210431 | + | 0.977609i | \(0.567487\pi\) | |||||||
\(774\) | 0.952174 | 0.0342252 | ||||||||
\(775\) | −39.1632 | −1.40679 | ||||||||
\(776\) | −3.23214 | −0.116027 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.2927 | −0.440714 | ||||||||
\(779\) | −25.6693 | −0.919697 | ||||||||
\(780\) | 0.833432 | 0.0298416 | ||||||||
\(781\) | −25.0613 | −0.896763 | ||||||||
\(782\) | −116.214 | −4.15581 | ||||||||
\(783\) | −6.53200 | −0.233435 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.35506 | −0.0483642 | ||||||||
\(786\) | −6.08198 | −0.216937 | ||||||||
\(787\) | 12.8318 | 0.457403 | 0.228702 | − | 0.973497i | \(-0.426552\pi\) | ||||
0.228702 | + | 0.973497i | \(0.426552\pi\) | |||||||
\(788\) | −0.147455 | −0.00525287 | ||||||||
\(789\) | 28.9952 | 1.03226 | ||||||||
\(790\) | −1.81390 | −0.0645358 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −8.02827 | −0.285272 | ||||||||
\(793\) | −5.51703 | −0.195916 | ||||||||
\(794\) | 15.1334 | 0.537063 | ||||||||
\(795\) | 9.03039 | 0.320275 | ||||||||
\(796\) | 0.339856 | 0.0120459 | ||||||||
\(797\) | −1.12352 | −0.0397970 | −0.0198985 | − | 0.999802i | \(-0.506334\pi\) | ||||
−0.0198985 | + | 0.999802i | \(0.506334\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −87.8701 | −3.10862 | ||||||||
\(800\) | 17.3892 | 0.614801 | ||||||||
\(801\) | 6.60402 | 0.233342 | ||||||||
\(802\) | 58.7137 | 2.07325 | ||||||||
\(803\) | 16.1802 | 0.570987 | ||||||||
\(804\) | 2.48673 | 0.0877000 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16.5738 | 0.583788 | ||||||||
\(807\) | 1.34213 | 0.0472454 | ||||||||
\(808\) | −30.8059 | −1.08375 | ||||||||
\(809\) | 7.84953 | 0.275975 | 0.137987 | − | 0.990434i | \(-0.455937\pi\) | ||||
0.137987 | + | 0.990434i | \(0.455937\pi\) | |||||||
\(810\) | −1.70571 | −0.0599325 | ||||||||
\(811\) | −7.38224 | −0.259225 | −0.129613 | − | 0.991565i | \(-0.541373\pi\) | ||||
−0.129613 | + | 0.991565i | \(0.541373\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.3410 | −0.397746 | ||||||||
\(814\) | 28.8771 | 1.01214 | ||||||||
\(815\) | 24.0579 | 0.842712 | ||||||||
\(816\) | −36.0667 | −1.26259 | ||||||||
\(817\) | 1.64804 | 0.0576577 | ||||||||
\(818\) | −6.80839 | −0.238050 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.35969 | 0.257011 | ||||||||
\(821\) | −27.7269 | −0.967674 | −0.483837 | − | 0.875158i | \(-0.660757\pi\) | ||||
−0.483837 | + | 0.875158i | \(0.660757\pi\) | |||||||
\(822\) | 24.5474 | 0.856188 | ||||||||
\(823\) | −8.41214 | −0.293229 | −0.146614 | − | 0.989194i | \(-0.546838\pi\) | ||||
−0.146614 | + | 0.989194i | \(0.546838\pi\) | |||||||
\(824\) | −28.8207 | −1.00402 | ||||||||
\(825\) | 16.0850 | 0.560007 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.80644 | −0.236683 | −0.118342 | − | 0.992973i | \(-0.537758\pi\) | ||||
−0.118342 | + | 0.992973i | \(0.537758\pi\) | |||||||
\(828\) | 7.82138 | 0.271812 | ||||||||
\(829\) | −50.0143 | −1.73707 | −0.868534 | − | 0.495629i | \(-0.834938\pi\) | ||||
−0.868534 | + | 0.495629i | \(0.834938\pi\) | |||||||
\(830\) | 13.6935 | 0.475308 | ||||||||
\(831\) | −13.0962 | −0.454302 | ||||||||
\(832\) | 2.57655 | 0.0893259 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 18.6793 | 0.646812 | ||||||||
\(835\) | 9.23025 | 0.319426 | ||||||||
\(836\) | 9.66840 | 0.334388 | ||||||||
\(837\) | −9.86851 | −0.341106 | ||||||||
\(838\) | 34.9115 | 1.20600 | ||||||||
\(839\) | 18.8435 | 0.650552 | 0.325276 | − | 0.945619i | \(-0.394543\pi\) | ||||
0.325276 | + | 0.945619i | \(0.394543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.6670 | 0.471276 | ||||||||
\(842\) | 33.0900 | 1.14036 | ||||||||
\(843\) | −2.93491 | −0.101084 | ||||||||
\(844\) | −6.98259 | −0.240351 | ||||||||
\(845\) | −1.01562 | −0.0349385 | ||||||||
\(846\) | 20.3269 | 0.698855 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −44.1712 | −1.51685 | ||||||||
\(849\) | 21.2779 | 0.730256 | ||||||||
\(850\) | 48.3882 | 1.65970 | ||||||||
\(851\) | 40.4329 | 1.38602 | ||||||||
\(852\) | 5.07396 | 0.173831 | ||||||||
\(853\) | −41.3669 | −1.41638 | −0.708189 | − | 0.706023i | \(-0.750487\pi\) | ||||
−0.708189 | + | 0.706023i | \(0.750487\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.95228 | −0.100966 | ||||||||
\(856\) | −37.0479 | −1.26627 | ||||||||
\(857\) | 29.5295 | 1.00871 | 0.504355 | − | 0.863497i | \(-0.331730\pi\) | ||||
0.504355 | + | 0.863497i | \(0.331730\pi\) | |||||||
\(858\) | −6.80714 | −0.232392 | ||||||||
\(859\) | −36.0619 | −1.23041 | −0.615207 | − | 0.788365i | \(-0.710928\pi\) | ||||
−0.615207 | + | 0.788365i | \(0.710928\pi\) | |||||||
\(860\) | −0.472514 | −0.0161126 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.95418 | 0.202800 | ||||||||
\(863\) | −2.68662 | −0.0914537 | −0.0457269 | − | 0.998954i | \(-0.514560\pi\) | ||||
−0.0457269 | + | 0.998954i | \(0.514560\pi\) | |||||||
\(864\) | 4.38180 | 0.149072 | ||||||||
\(865\) | 6.61870 | 0.225043 | ||||||||
\(866\) | −17.2696 | −0.586844 | ||||||||
\(867\) | −35.7086 | −1.21273 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.31026 | 0.146215 | ||||||||
\(870\) | 11.1417 | 0.377738 | ||||||||
\(871\) | −3.03034 | −0.102679 | ||||||||
\(872\) | 21.4420 | 0.726116 | ||||||||
\(873\) | 1.63178 | 0.0552273 | ||||||||
\(874\) | 46.5310 | 1.57393 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.27588 | −0.110682 | ||||||||
\(877\) | −6.40742 | −0.216363 | −0.108182 | − | 0.994131i | \(-0.534503\pi\) | ||||
−0.108182 | + | 0.994131i | \(0.534503\pi\) | |||||||
\(878\) | 23.1472 | 0.781179 | ||||||||
\(879\) | 7.81571 | 0.263618 | ||||||||
\(880\) | 20.4499 | 0.689367 | ||||||||
\(881\) | 13.3454 | 0.449617 | 0.224808 | − | 0.974403i | \(-0.427824\pi\) | ||||
0.224808 | + | 0.974403i | \(0.427824\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.8329 | −0.499167 | −0.249584 | − | 0.968353i | \(-0.580294\pi\) | ||||
−0.249584 | + | 0.968353i | \(0.580294\pi\) | |||||||
\(884\) | −5.95769 | −0.200379 | ||||||||
\(885\) | 5.52883 | 0.185850 | ||||||||
\(886\) | 27.2568 | 0.915709 | ||||||||
\(887\) | −32.8467 | −1.10288 | −0.551442 | − | 0.834213i | \(-0.685922\pi\) | ||||
−0.551442 | + | 0.834213i | \(0.685922\pi\) | |||||||
\(888\) | 8.40266 | 0.281975 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −11.2645 | −0.377588 | ||||||||
\(891\) | 4.05316 | 0.135786 | ||||||||
\(892\) | −18.5601 | −0.621437 | ||||||||
\(893\) | 35.1823 | 1.17733 | ||||||||
\(894\) | −8.78797 | −0.293914 | ||||||||
\(895\) | 0.550416 | 0.0183984 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.53118 | −0.318237 | ||||||||
\(898\) | 66.8786 | 2.23177 | ||||||||
\(899\) | 64.4611 | 2.14990 | ||||||||
\(900\) | −3.25660 | −0.108553 | ||||||||
\(901\) | −64.5527 | −2.15056 | ||||||||
\(902\) | −60.1110 | −2.00148 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.8724 | 0.627686 | ||||||||
\(905\) | −18.2697 | −0.607306 | ||||||||
\(906\) | 25.2413 | 0.838586 | ||||||||
\(907\) | −6.78020 | −0.225133 | −0.112566 | − | 0.993644i | \(-0.535907\pi\) | ||||
−0.112566 | + | 0.993644i | \(0.535907\pi\) | |||||||
\(908\) | −1.76776 | −0.0586653 | ||||||||
\(909\) | 15.5527 | 0.515850 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.2486 | 0.637736 | 0.318868 | − | 0.947799i | \(-0.396697\pi\) | ||||
0.318868 | + | 0.947799i | \(0.396697\pi\) | |||||||
\(912\) | 14.4408 | 0.478181 | ||||||||
\(913\) | −32.5389 | −1.07688 | ||||||||
\(914\) | −5.12178 | −0.169413 | ||||||||
\(915\) | −5.60323 | −0.185237 | ||||||||
\(916\) | 4.15818 | 0.137390 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 12.1930 | 0.402430 | ||||||||
\(919\) | 23.6687 | 0.780757 | 0.390379 | − | 0.920654i | \(-0.372344\pi\) | ||||
0.390379 | + | 0.920654i | \(0.372344\pi\) | |||||||
\(920\) | 19.1738 | 0.632142 | ||||||||
\(921\) | −1.63049 | −0.0537264 | ||||||||
\(922\) | 23.6282 | 0.778152 | ||||||||
\(923\) | −6.18315 | −0.203521 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.8351 | −0.553534 | ||||||||
\(926\) | 44.0962 | 1.44909 | ||||||||
\(927\) | 14.5504 | 0.477898 | ||||||||
\(928\) | −28.6219 | −0.939560 | ||||||||
\(929\) | −18.2611 | −0.599126 | −0.299563 | − | 0.954076i | \(-0.596841\pi\) | ||||
−0.299563 | + | 0.954076i | \(0.596841\pi\) | |||||||
\(930\) | 16.8328 | 0.551969 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.36635 | −0.241293 | ||||||||
\(933\) | −11.3479 | −0.371515 | ||||||||
\(934\) | 1.06129 | 0.0347266 | ||||||||
\(935\) | 29.8859 | 0.977375 | ||||||||
\(936\) | −1.98075 | −0.0647427 | ||||||||
\(937\) | 2.02078 | 0.0660159 | 0.0330079 | − | 0.999455i | \(-0.489491\pi\) | ||||
0.0330079 | + | 0.999455i | \(0.489491\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.83580 | −0.190444 | ||||||||
\(940\) | −10.0872 | −0.329008 | ||||||||
\(941\) | −26.6332 | −0.868217 | −0.434108 | − | 0.900861i | \(-0.642937\pi\) | ||||
−0.434108 | + | 0.900861i | \(0.642937\pi\) | |||||||
\(942\) | −2.24077 | −0.0730083 | ||||||||
\(943\) | −84.1658 | −2.74082 | ||||||||
\(944\) | −27.0437 | −0.880198 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.85931 | 0.125477 | ||||||||
\(947\) | 3.57351 | 0.116124 | 0.0580618 | − | 0.998313i | \(-0.481508\pi\) | ||||
0.0580618 | + | 0.998313i | \(0.481508\pi\) | |||||||
\(948\) | −0.872664 | −0.0283428 | ||||||||
\(949\) | 3.99200 | 0.129586 | ||||||||
\(950\) | −19.3742 | −0.628581 | ||||||||
\(951\) | −23.6802 | −0.767883 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.18119 | −0.167835 | −0.0839176 | − | 0.996473i | \(-0.526743\pi\) | ||||
−0.0839176 | + | 0.996473i | \(0.526743\pi\) | |||||||
\(954\) | 14.9329 | 0.483472 | ||||||||
\(955\) | 16.2316 | 0.525242 | ||||||||
\(956\) | 22.4822 | 0.727128 | ||||||||
\(957\) | −26.4752 | −0.855822 | ||||||||
\(958\) | 28.9003 | 0.933725 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.61681 | 0.0844571 | ||||||||
\(961\) | 66.3874 | 2.14153 | ||||||||
\(962\) | 7.12458 | 0.229706 | ||||||||
\(963\) | 18.7040 | 0.602728 | ||||||||
\(964\) | 1.16602 | 0.0375551 | ||||||||
\(965\) | 8.76281 | 0.282085 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.3558 | −1.07265 | −0.536325 | − | 0.844012i | \(-0.680188\pi\) | ||||
−0.536325 | + | 0.844012i | \(0.680188\pi\) | |||||||
\(968\) | −10.7516 | −0.345570 | ||||||||
\(969\) | 21.1040 | 0.677958 | ||||||||
\(970\) | −2.78334 | −0.0893676 | ||||||||
\(971\) | −11.0917 | −0.355949 | −0.177975 | − | 0.984035i | \(-0.556954\pi\) | ||||
−0.177975 | + | 0.984035i | \(0.556954\pi\) | |||||||
\(972\) | −0.820610 | −0.0263211 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −51.9447 | −1.66442 | ||||||||
\(975\) | 3.96851 | 0.127094 | ||||||||
\(976\) | 27.4076 | 0.877297 | ||||||||
\(977\) | 31.3247 | 1.00217 | 0.501083 | − | 0.865399i | \(-0.332935\pi\) | ||||
0.501083 | + | 0.865399i | \(0.332935\pi\) | |||||||
\(978\) | 39.7829 | 1.27212 | ||||||||
\(979\) | 26.7671 | 0.855481 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.8252 | −0.345622 | ||||||||
\(982\) | 38.7006 | 1.23499 | ||||||||
\(983\) | −19.7083 | −0.628596 | −0.314298 | − | 0.949324i | \(-0.601769\pi\) | ||||
−0.314298 | + | 0.949324i | \(0.601769\pi\) | |||||||
\(984\) | −17.4911 | −0.557597 | ||||||||
\(985\) | 0.182497 | 0.00581484 | ||||||||
\(986\) | −79.6450 | −2.53641 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.38540 | 0.0758897 | ||||||||
\(989\) | 5.40370 | 0.171828 | ||||||||
\(990\) | −6.91350 | −0.219725 | ||||||||
\(991\) | −36.9147 | −1.17263 | −0.586316 | − | 0.810082i | \(-0.699422\pi\) | ||||
−0.586316 | + | 0.810082i | \(0.699422\pi\) | |||||||
\(992\) | −43.2418 | −1.37293 | ||||||||
\(993\) | 19.2273 | 0.610159 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.420620 | −0.0133346 | ||||||||
\(996\) | 6.58789 | 0.208745 | ||||||||
\(997\) | 1.04532 | 0.0331057 | 0.0165528 | − | 0.999863i | \(-0.494731\pi\) | ||||
0.0165528 | + | 0.999863i | \(0.494731\pi\) | |||||||
\(998\) | −21.3938 | −0.677210 | ||||||||
\(999\) | −4.24217 | −0.134216 |
(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 | 1911.2.a.x.1.7 | ✓ | 10 | |
3.2 | odd | 2 | 5733.2.a.bw.1.4 | 10 | |||
7.6 | odd | 2 | 1911.2.a.y.1.7 | yes | 10 | ||
21.20 | even | 2 | 5733.2.a.bx.1.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1911.2.a.x.1.7 | ✓ | 10 | 1.1 | even | 1 | trivial | |
1911.2.a.y.1.7 | yes | 10 | 7.6 | odd | 2 | ||
5733.2.a.bw.1.4 | 10 | 3.2 | odd | 2 | |||
5733.2.a.bx.1.4 | 10 | 21.20 | even | 2 |