Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1881,2,Mod(1,1881)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1881, 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("1881.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1881 = 3^{2} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1881.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: | \(15.0198606202\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.246832.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 209) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.71457\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1881.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.65432 | −1.87689 | −0.938443 | − | 0.345435i | \(-0.887732\pi\) | ||||
−0.938443 | + | 0.345435i | \(0.887732\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.04540 | 2.52270 | ||||||||
\(5\) | 1.06025 | 0.474159 | 0.237080 | − | 0.971490i | \(-0.423810\pi\) | ||||
0.237080 | + | 0.971490i | \(0.423810\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.36889 | −1.27332 | −0.636660 | − | 0.771145i | \(-0.719684\pi\) | ||||
−0.636660 | + | 0.771145i | \(0.719684\pi\) | |||||||
\(8\) | −8.08346 | −2.85793 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.81425 | −0.889943 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.15993 | −0.599056 | −0.299528 | − | 0.954087i | \(-0.596829\pi\) | ||||
−0.299528 | + | 0.954087i | \(0.596829\pi\) | |||||||
\(14\) | 8.94209 | 2.38987 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 11.3653 | 2.84131 | ||||||||
\(17\) | −3.67288 | −0.890805 | −0.445402 | − | 0.895330i | \(-0.646939\pi\) | ||||
−0.445402 | + | 0.895330i | \(0.646939\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 5.34940 | 1.19616 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.65432 | 0.565902 | ||||||||
\(23\) | −3.15468 | −0.657797 | −0.328898 | − | 0.944365i | \(-0.606677\pi\) | ||||
−0.328898 | + | 0.944365i | \(0.606677\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.87587 | −0.775173 | ||||||||
\(26\) | 5.73313 | 1.12436 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −16.9974 | −3.21220 | ||||||||
\(29\) | −7.17849 | −1.33301 | −0.666506 | − | 0.745499i | \(-0.732211\pi\) | ||||
−0.666506 | + | 0.745499i | \(0.732211\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.65295 | 0.835694 | 0.417847 | − | 0.908517i | \(-0.362785\pi\) | ||||
0.417847 | + | 0.908517i | \(0.362785\pi\) | |||||||
\(32\) | −14.0001 | −2.47489 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.74900 | 1.67194 | ||||||||
\(35\) | −3.57187 | −0.603756 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.27446 | 0.373918 | 0.186959 | − | 0.982368i | \(-0.440137\pi\) | ||||
0.186959 | + | 0.982368i | \(0.440137\pi\) | |||||||
\(38\) | 2.65432 | 0.430587 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.57050 | −1.35512 | ||||||||
\(41\) | 11.3852 | 1.77807 | 0.889034 | − | 0.457841i | \(-0.151377\pi\) | ||||
0.889034 | + | 0.457841i | \(0.151377\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.38838 | 1.43171 | 0.715857 | − | 0.698247i | \(-0.246036\pi\) | ||||
0.715857 | + | 0.698247i | \(0.246036\pi\) | |||||||
\(44\) | −5.04540 | −0.760623 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.37352 | 1.23461 | ||||||||
\(47\) | 5.77094 | 0.841778 | 0.420889 | − | 0.907112i | \(-0.361718\pi\) | ||||
0.420889 | + | 0.907112i | \(0.361718\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.34940 | 0.621342 | ||||||||
\(50\) | 10.2878 | 1.45491 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10.8977 | −1.51124 | ||||||||
\(53\) | 5.65820 | 0.777213 | 0.388607 | − | 0.921404i | \(-0.372957\pi\) | ||||
0.388607 | + | 0.921404i | \(0.372957\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.06025 | −0.142964 | ||||||||
\(56\) | 27.2322 | 3.63906 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 19.0540 | 2.50191 | ||||||||
\(59\) | 13.7944 | 1.79588 | 0.897939 | − | 0.440121i | \(-0.145064\pi\) | ||||
0.897939 | + | 0.440121i | \(0.145064\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.98152 | 0.893892 | 0.446946 | − | 0.894561i | \(-0.352512\pi\) | ||||
0.446946 | + | 0.894561i | \(0.352512\pi\) | |||||||
\(62\) | −12.3504 | −1.56850 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 14.4301 | 1.80377 | ||||||||
\(65\) | −2.29007 | −0.284048 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.81332 | −0.588041 | −0.294020 | − | 0.955799i | \(-0.594993\pi\) | ||||
−0.294020 | + | 0.955799i | \(0.594993\pi\) | |||||||
\(68\) | −18.5312 | −2.24723 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 9.48087 | 1.13318 | ||||||||
\(71\) | −15.2629 | −1.81137 | −0.905685 | − | 0.423951i | \(-0.860643\pi\) | ||||
−0.905685 | + | 0.423951i | \(0.860643\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.08806 | −0.946636 | −0.473318 | − | 0.880892i | \(-0.656944\pi\) | ||||
−0.473318 | + | 0.880892i | \(0.656944\pi\) | |||||||
\(74\) | −6.03713 | −0.701802 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.04540 | −0.578747 | ||||||||
\(77\) | 3.36889 | 0.383920 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.4291 | 1.51090 | 0.755448 | − | 0.655209i | \(-0.227419\pi\) | ||||
0.755448 | + | 0.655209i | \(0.227419\pi\) | |||||||
\(80\) | 12.0500 | 1.34724 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −30.2199 | −3.33723 | ||||||||
\(83\) | −9.96666 | −1.09398 | −0.546992 | − | 0.837138i | \(-0.684227\pi\) | ||||
−0.546992 | + | 0.837138i | \(0.684227\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.89418 | −0.422383 | ||||||||
\(86\) | −24.9197 | −2.68716 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.08346 | 0.861699 | ||||||||
\(89\) | 4.61626 | 0.489323 | 0.244661 | − | 0.969609i | \(-0.421323\pi\) | ||||
0.244661 | + | 0.969609i | \(0.421323\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.27655 | 0.762790 | ||||||||
\(92\) | −15.9166 | −1.65942 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −15.3179 | −1.57992 | ||||||||
\(95\) | −1.06025 | −0.108780 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.09907 | −0.416197 | −0.208099 | − | 0.978108i | \(-0.566727\pi\) | ||||
−0.208099 | + | 0.978108i | \(0.566727\pi\) | |||||||
\(98\) | −11.5447 | −1.16619 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −19.5553 | −1.95553 | ||||||||
\(101\) | 10.8730 | 1.08190 | 0.540950 | − | 0.841055i | \(-0.318065\pi\) | ||||
0.540950 | + | 0.841055i | \(0.318065\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.85864 | 0.872867 | 0.436434 | − | 0.899736i | \(-0.356241\pi\) | ||||
0.436434 | + | 0.899736i | \(0.356241\pi\) | |||||||
\(104\) | 17.4597 | 1.71206 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.0186 | −1.45874 | ||||||||
\(107\) | 18.1669 | 1.75626 | 0.878131 | − | 0.478421i | \(-0.158791\pi\) | ||||
0.878131 | + | 0.478421i | \(0.158791\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.211303 | −0.0202392 | −0.0101196 | − | 0.999949i | \(-0.503221\pi\) | ||||
−0.0101196 | + | 0.999949i | \(0.503221\pi\) | |||||||
\(110\) | 2.81425 | 0.268328 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −38.2883 | −3.61790 | ||||||||
\(113\) | 0.198345 | 0.0186587 | 0.00932935 | − | 0.999956i | \(-0.497030\pi\) | ||||
0.00932935 | + | 0.999956i | \(0.497030\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.34476 | −0.311900 | ||||||||
\(116\) | −36.2184 | −3.36279 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −36.6147 | −3.37066 | ||||||||
\(119\) | 12.3735 | 1.13428 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −18.5312 | −1.67773 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 23.4760 | 2.10821 | ||||||||
\(125\) | −9.41066 | −0.841715 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.60331 | −0.319742 | −0.159871 | − | 0.987138i | \(-0.551108\pi\) | ||||
−0.159871 | + | 0.987138i | \(0.551108\pi\) | |||||||
\(128\) | −10.3020 | −0.910578 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.07857 | 0.533126 | ||||||||
\(131\) | −16.8741 | −1.47430 | −0.737150 | − | 0.675729i | \(-0.763829\pi\) | ||||
−0.737150 | + | 0.675729i | \(0.763829\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.36889 | 0.292119 | ||||||||
\(134\) | 12.7761 | 1.10369 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 29.6896 | 2.54586 | ||||||||
\(137\) | 6.10839 | 0.521875 | 0.260937 | − | 0.965356i | \(-0.415968\pi\) | ||||
0.260937 | + | 0.965356i | \(0.415968\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.3347 | 0.961398 | 0.480699 | − | 0.876886i | \(-0.340383\pi\) | ||||
0.480699 | + | 0.876886i | \(0.340383\pi\) | |||||||
\(140\) | −18.0215 | −1.52310 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 40.5125 | 3.39973 | ||||||||
\(143\) | 2.15993 | 0.180622 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.61101 | −0.632060 | ||||||||
\(146\) | 21.4683 | 1.77673 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.4755 | 0.943284 | ||||||||
\(149\) | −6.75698 | −0.553554 | −0.276777 | − | 0.960934i | \(-0.589266\pi\) | ||||
−0.276777 | + | 0.960934i | \(0.589266\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.46231 | 0.525895 | 0.262948 | − | 0.964810i | \(-0.415305\pi\) | ||||
0.262948 | + | 0.964810i | \(0.415305\pi\) | |||||||
\(152\) | 8.08346 | 0.655655 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.94209 | −0.720574 | ||||||||
\(155\) | 4.93330 | 0.396252 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.248382 | 0.0198230 | 0.00991152 | − | 0.999951i | \(-0.496845\pi\) | ||||
0.00991152 | + | 0.999951i | \(0.496845\pi\) | |||||||
\(158\) | −35.6452 | −2.83578 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −14.8436 | −1.17349 | ||||||||
\(161\) | 10.6278 | 0.837585 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.9710 | −1.32927 | −0.664637 | − | 0.747167i | \(-0.731414\pi\) | ||||
−0.664637 | + | 0.747167i | \(0.731414\pi\) | |||||||
\(164\) | 57.4428 | 4.48553 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 26.4547 | 2.05328 | ||||||||
\(167\) | 0.865538 | 0.0669773 | 0.0334887 | − | 0.999439i | \(-0.489338\pi\) | ||||
0.0334887 | + | 0.999439i | \(0.489338\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.33471 | −0.641132 | ||||||||
\(170\) | 10.3364 | 0.792765 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 47.3681 | 3.61178 | ||||||||
\(173\) | 4.14483 | 0.315125 | 0.157563 | − | 0.987509i | \(-0.449636\pi\) | ||||
0.157563 | + | 0.987509i | \(0.449636\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.0574 | 0.987043 | ||||||||
\(176\) | −11.3653 | −0.856688 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.2530 | −0.918403 | ||||||||
\(179\) | −2.04584 | −0.152913 | −0.0764567 | − | 0.997073i | \(-0.524361\pi\) | ||||
−0.0764567 | + | 0.997073i | \(0.524361\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.27519 | 0.392101 | 0.196051 | − | 0.980594i | \(-0.437188\pi\) | ||||
0.196051 | + | 0.980594i | \(0.437188\pi\) | |||||||
\(182\) | −19.3143 | −1.43167 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 25.5007 | 1.87994 | ||||||||
\(185\) | 2.41150 | 0.177297 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.67288 | 0.268588 | ||||||||
\(188\) | 29.1167 | 2.12355 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.81425 | 0.204167 | ||||||||
\(191\) | 16.1899 | 1.17146 | 0.585729 | − | 0.810507i | \(-0.300808\pi\) | ||||
0.585729 | + | 0.810507i | \(0.300808\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.0620 | −1.44409 | −0.722045 | − | 0.691846i | \(-0.756798\pi\) | ||||
−0.722045 | + | 0.691846i | \(0.756798\pi\) | |||||||
\(194\) | 10.8802 | 0.781155 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 21.9444 | 1.56746 | ||||||||
\(197\) | 23.8398 | 1.69851 | 0.849257 | − | 0.527979i | \(-0.177050\pi\) | ||||
0.849257 | + | 0.527979i | \(0.177050\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.90194 | −0.134825 | −0.0674125 | − | 0.997725i | \(-0.521474\pi\) | ||||
−0.0674125 | + | 0.997725i | \(0.521474\pi\) | |||||||
\(200\) | 31.3304 | 2.21539 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −28.8603 | −2.03060 | ||||||||
\(203\) | 24.1835 | 1.69735 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.0712 | 0.843087 | ||||||||
\(206\) | −23.5136 | −1.63827 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −24.5481 | −1.70211 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.3048 | 0.847100 | 0.423550 | − | 0.905873i | \(-0.360784\pi\) | ||||
0.423550 | + | 0.905873i | \(0.360784\pi\) | |||||||
\(212\) | 28.5479 | 1.96068 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −48.2207 | −3.29630 | ||||||||
\(215\) | 9.95405 | 0.678860 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.6753 | −1.06411 | ||||||||
\(218\) | 0.560865 | 0.0379866 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.34940 | −0.360656 | ||||||||
\(221\) | 7.93316 | 0.533642 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.8473 | 1.52997 | 0.764985 | − | 0.644048i | \(-0.222746\pi\) | ||||
0.764985 | + | 0.644048i | \(0.222746\pi\) | |||||||
\(224\) | 47.1647 | 3.15132 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.526470 | −0.0350202 | ||||||||
\(227\) | −4.00654 | −0.265923 | −0.132962 | − | 0.991121i | \(-0.542449\pi\) | ||||
−0.132962 | + | 0.991121i | \(0.542449\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.6024 | −1.62577 | −0.812887 | − | 0.582422i | \(-0.802105\pi\) | ||||
−0.812887 | + | 0.582422i | \(0.802105\pi\) | |||||||
\(230\) | 8.87805 | 0.585401 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 58.0270 | 3.80966 | ||||||||
\(233\) | −16.2994 | −1.06781 | −0.533903 | − | 0.845545i | \(-0.679275\pi\) | ||||
−0.533903 | + | 0.845545i | \(0.679275\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.11865 | 0.399137 | ||||||||
\(236\) | 69.5982 | 4.53046 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −32.8433 | −2.12891 | ||||||||
\(239\) | 15.4182 | 0.997324 | 0.498662 | − | 0.866797i | \(-0.333825\pi\) | ||||
0.498662 | + | 0.866797i | \(0.333825\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.1441 | 1.55526 | 0.777629 | − | 0.628723i | \(-0.216422\pi\) | ||||
0.777629 | + | 0.628723i | \(0.216422\pi\) | |||||||
\(242\) | −2.65432 | −0.170626 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 35.2245 | 2.25502 | ||||||||
\(245\) | 4.61146 | 0.294615 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.15993 | 0.137433 | ||||||||
\(248\) | −37.6119 | −2.38836 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 24.9789 | 1.57980 | ||||||||
\(251\) | 19.9099 | 1.25670 | 0.628350 | − | 0.777931i | \(-0.283731\pi\) | ||||
0.628350 | + | 0.777931i | \(0.283731\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.15468 | 0.198333 | ||||||||
\(254\) | 9.56433 | 0.600119 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.51547 | −0.0947166 | ||||||||
\(257\) | 22.3126 | 1.39182 | 0.695911 | − | 0.718128i | \(-0.255001\pi\) | ||||
0.695911 | + | 0.718128i | \(0.255001\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.66239 | −0.476118 | ||||||||
\(260\) | −11.5543 | −0.716568 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 44.7893 | 2.76709 | ||||||||
\(263\) | −13.7963 | −0.850716 | −0.425358 | − | 0.905025i | \(-0.639852\pi\) | ||||
−0.425358 | + | 0.905025i | \(0.639852\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.99912 | 0.368523 | ||||||||
\(266\) | −8.94209 | −0.548275 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −24.2851 | −1.48345 | ||||||||
\(269\) | 11.2028 | 0.683048 | 0.341524 | − | 0.939873i | \(-0.389057\pi\) | ||||
0.341524 | + | 0.939873i | \(0.389057\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.1234 | 1.04017 | 0.520085 | − | 0.854115i | \(-0.325900\pi\) | ||||
0.520085 | + | 0.854115i | \(0.325900\pi\) | |||||||
\(272\) | −41.7433 | −2.53106 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.2136 | −0.979499 | ||||||||
\(275\) | 3.87587 | 0.233723 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.7127 | −0.823919 | −0.411960 | − | 0.911202i | \(-0.635156\pi\) | ||||
−0.411960 | + | 0.911202i | \(0.635156\pi\) | |||||||
\(278\) | −30.0859 | −1.80443 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 28.8730 | 1.72549 | ||||||||
\(281\) | −25.8599 | −1.54267 | −0.771337 | − | 0.636427i | \(-0.780412\pi\) | ||||
−0.771337 | + | 0.636427i | \(0.780412\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.8711 | 1.71621 | 0.858103 | − | 0.513477i | \(-0.171643\pi\) | ||||
0.858103 | + | 0.513477i | \(0.171643\pi\) | |||||||
\(284\) | −77.0073 | −4.56954 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.73313 | −0.339007 | ||||||||
\(287\) | −38.3554 | −2.26405 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.50993 | −0.206467 | ||||||||
\(290\) | 20.2020 | 1.18630 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −40.8075 | −2.38808 | ||||||||
\(293\) | −6.37971 | −0.372707 | −0.186353 | − | 0.982483i | \(-0.559667\pi\) | ||||
−0.186353 | + | 0.982483i | \(0.559667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.6255 | 0.851532 | ||||||||
\(296\) | −18.3855 | −1.06863 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.9352 | 1.03896 | ||||||||
\(299\) | 6.81389 | 0.394057 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −31.6284 | −1.82303 | ||||||||
\(302\) | −17.1530 | −0.987045 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.3653 | −0.651842 | ||||||||
\(305\) | 7.40217 | 0.423847 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.4299 | 0.595264 | 0.297632 | − | 0.954681i | \(-0.403803\pi\) | ||||
0.297632 | + | 0.954681i | \(0.403803\pi\) | |||||||
\(308\) | 16.9974 | 0.968515 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −13.0945 | −0.743720 | ||||||||
\(311\) | 8.26224 | 0.468508 | 0.234254 | − | 0.972175i | \(-0.424735\pi\) | ||||
0.234254 | + | 0.972175i | \(0.424735\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.1167 | −1.36315 | −0.681577 | − | 0.731746i | \(-0.738706\pi\) | ||||
−0.681577 | + | 0.731746i | \(0.738706\pi\) | |||||||
\(314\) | −0.659285 | −0.0372056 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 67.7554 | 3.81154 | ||||||||
\(317\) | 11.7330 | 0.658989 | 0.329495 | − | 0.944157i | \(-0.393122\pi\) | ||||
0.329495 | + | 0.944157i | \(0.393122\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.17849 | 0.401918 | ||||||||
\(320\) | 15.2996 | 0.855273 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −28.2095 | −1.57205 | ||||||||
\(323\) | 3.67288 | 0.204365 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.37159 | 0.464372 | ||||||||
\(326\) | 45.0465 | 2.49489 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −92.0317 | −5.08160 | ||||||||
\(329\) | −19.4416 | −1.07185 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.95223 | −0.382129 | −0.191065 | − | 0.981577i | \(-0.561194\pi\) | ||||
−0.191065 | + | 0.981577i | \(0.561194\pi\) | |||||||
\(332\) | −50.2858 | −2.75979 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.29741 | −0.125709 | ||||||||
\(335\) | −5.10333 | −0.278825 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.4416 | 1.60379 | 0.801893 | − | 0.597468i | \(-0.203826\pi\) | ||||
0.801893 | + | 0.597468i | \(0.203826\pi\) | |||||||
\(338\) | 22.1230 | 1.20333 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −19.6477 | −1.06555 | ||||||||
\(341\) | −4.65295 | −0.251971 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.92959 | 0.482152 | ||||||||
\(344\) | −75.8905 | −4.09174 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.0017 | −0.591454 | ||||||||
\(347\) | 17.2180 | 0.924311 | 0.462155 | − | 0.886799i | \(-0.347076\pi\) | ||||
0.462155 | + | 0.886799i | \(0.347076\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.32405 | 0.231461 | 0.115731 | − | 0.993281i | \(-0.463079\pi\) | ||||
0.115731 | + | 0.993281i | \(0.463079\pi\) | |||||||
\(350\) | −34.6583 | −1.85257 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 14.0001 | 0.746207 | ||||||||
\(353\) | −23.4421 | −1.24770 | −0.623848 | − | 0.781545i | \(-0.714432\pi\) | ||||
−0.623848 | + | 0.781545i | \(0.714432\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.1825 | −0.858878 | ||||||||
\(356\) | 23.2909 | 1.23441 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.43031 | 0.287001 | ||||||||
\(359\) | −8.20544 | −0.433066 | −0.216533 | − | 0.976275i | \(-0.569475\pi\) | ||||
−0.216533 | + | 0.976275i | \(0.569475\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −14.0020 | −0.735930 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 36.7131 | 1.92429 | ||||||||
\(365\) | −8.57539 | −0.448856 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.1494 | 1.73039 | 0.865193 | − | 0.501439i | \(-0.167196\pi\) | ||||
0.865193 | + | 0.501439i | \(0.167196\pi\) | |||||||
\(368\) | −35.8538 | −1.86901 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.40088 | −0.332766 | ||||||||
\(371\) | −19.0618 | −0.989640 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.5840 | −0.858685 | −0.429343 | − | 0.903142i | \(-0.641255\pi\) | ||||
−0.429343 | + | 0.903142i | \(0.641255\pi\) | |||||||
\(374\) | −9.74900 | −0.504109 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −46.6492 | −2.40575 | ||||||||
\(377\) | 15.5050 | 0.798550 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.79467 | 0.297652 | 0.148826 | − | 0.988863i | \(-0.452451\pi\) | ||||
0.148826 | + | 0.988863i | \(0.452451\pi\) | |||||||
\(380\) | −5.34940 | −0.274418 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −42.9730 | −2.19869 | ||||||||
\(383\) | −5.89016 | −0.300973 | −0.150487 | − | 0.988612i | \(-0.548084\pi\) | ||||
−0.150487 | + | 0.988612i | \(0.548084\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.57187 | 0.182039 | ||||||||
\(386\) | 53.2508 | 2.71039 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −20.6814 | −1.04994 | ||||||||
\(389\) | −13.8055 | −0.699964 | −0.349982 | − | 0.936756i | \(-0.613812\pi\) | ||||
−0.349982 | + | 0.936756i | \(0.613812\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.5868 | 0.585968 | ||||||||
\(392\) | −35.1581 | −1.77575 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −63.2784 | −3.18792 | ||||||||
\(395\) | 14.2383 | 0.716405 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.48471 | 0.325458 | 0.162729 | − | 0.986671i | \(-0.447970\pi\) | ||||
0.162729 | + | 0.986671i | \(0.447970\pi\) | |||||||
\(398\) | 5.04835 | 0.253051 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −44.0502 | −2.20251 | ||||||||
\(401\) | −3.70806 | −0.185172 | −0.0925858 | − | 0.995705i | \(-0.529513\pi\) | ||||
−0.0925858 | + | 0.995705i | \(0.529513\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.0500 | −0.500628 | ||||||||
\(404\) | 54.8584 | 2.72931 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −64.1908 | −3.18573 | ||||||||
\(407\) | −2.27446 | −0.112741 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.0569 | 1.53567 | 0.767833 | − | 0.640650i | \(-0.221335\pi\) | ||||
0.767833 | + | 0.640650i | \(0.221335\pi\) | |||||||
\(410\) | −32.0407 | −1.58238 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 44.6954 | 2.20198 | ||||||||
\(413\) | −46.4717 | −2.28673 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.5672 | −0.518722 | ||||||||
\(416\) | 30.2392 | 1.48260 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.65432 | −0.129827 | ||||||||
\(419\) | 11.2871 | 0.551410 | 0.275705 | − | 0.961242i | \(-0.411089\pi\) | ||||
0.275705 | + | 0.961242i | \(0.411089\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.5194 | 1.68237 | 0.841186 | − | 0.540746i | \(-0.181858\pi\) | ||||
0.841186 | + | 0.540746i | \(0.181858\pi\) | |||||||
\(422\) | −32.6609 | −1.58991 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −45.7378 | −2.22122 | ||||||||
\(425\) | 14.2356 | 0.690528 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.5199 | −1.13821 | ||||||||
\(428\) | 91.6593 | 4.43052 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −26.4212 | −1.27414 | ||||||||
\(431\) | −18.1654 | −0.874996 | −0.437498 | − | 0.899219i | \(-0.644135\pi\) | ||||
−0.437498 | + | 0.899219i | \(0.644135\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.7804 | 0.518075 | 0.259037 | − | 0.965867i | \(-0.416595\pi\) | ||||
0.259037 | + | 0.965867i | \(0.416595\pi\) | |||||||
\(434\) | 41.6071 | 1.99720 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.06611 | −0.0510573 | ||||||||
\(437\) | 3.15468 | 0.150909 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.38742 | −0.0662180 | −0.0331090 | − | 0.999452i | \(-0.510541\pi\) | ||||
−0.0331090 | + | 0.999452i | \(0.510541\pi\) | |||||||
\(440\) | 8.57050 | 0.408583 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −21.0571 | −1.00159 | ||||||||
\(443\) | 7.26792 | 0.345310 | 0.172655 | − | 0.984982i | \(-0.444766\pi\) | ||||
0.172655 | + | 0.984982i | \(0.444766\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.89440 | 0.232017 | ||||||||
\(446\) | −60.6441 | −2.87158 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −48.6135 | −2.29677 | ||||||||
\(449\) | −21.4298 | −1.01134 | −0.505668 | − | 0.862728i | \(-0.668754\pi\) | ||||
−0.505668 | + | 0.862728i | \(0.668754\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.3852 | −0.536108 | ||||||||
\(452\) | 1.00073 | 0.0470703 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.6346 | 0.499108 | ||||||||
\(455\) | 7.71498 | 0.361684 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.6312 | −0.824754 | −0.412377 | − | 0.911013i | \(-0.635301\pi\) | ||||
−0.412377 | + | 0.911013i | \(0.635301\pi\) | |||||||
\(458\) | 65.3026 | 3.05139 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −16.8756 | −0.786831 | ||||||||
\(461\) | −34.2073 | −1.59320 | −0.796598 | − | 0.604510i | \(-0.793369\pi\) | ||||
−0.796598 | + | 0.604510i | \(0.793369\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.0009 | −0.511253 | −0.255626 | − | 0.966776i | \(-0.582282\pi\) | ||||
−0.255626 | + | 0.966776i | \(0.582282\pi\) | |||||||
\(464\) | −81.5854 | −3.78751 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 43.2637 | 2.00415 | ||||||||
\(467\) | −4.38453 | −0.202892 | −0.101446 | − | 0.994841i | \(-0.532347\pi\) | ||||
−0.101446 | + | 0.994841i | \(0.532347\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.2155 | 0.748764 | ||||||||
\(470\) | −16.2408 | −0.749134 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −111.506 | −5.13250 | ||||||||
\(473\) | −9.38838 | −0.431678 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.87587 | 0.177837 | ||||||||
\(476\) | 62.4294 | 2.86145 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −40.9249 | −1.87186 | ||||||||
\(479\) | 14.3683 | 0.656505 | 0.328253 | − | 0.944590i | \(-0.393540\pi\) | ||||
0.328253 | + | 0.944590i | \(0.393540\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.91266 | −0.223998 | ||||||||
\(482\) | −64.0861 | −2.91904 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.04540 | 0.229336 | ||||||||
\(485\) | −4.34604 | −0.197344 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.01712 | 0.0460899 | 0.0230449 | − | 0.999734i | \(-0.492664\pi\) | ||||
0.0230449 | + | 0.999734i | \(0.492664\pi\) | |||||||
\(488\) | −56.4348 | −2.55468 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −12.2403 | −0.552959 | ||||||||
\(491\) | 2.41045 | 0.108782 | 0.0543910 | − | 0.998520i | \(-0.482678\pi\) | ||||
0.0543910 | + | 0.998520i | \(0.482678\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.3658 | 1.18745 | ||||||||
\(494\) | −5.73313 | −0.257946 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 52.8820 | 2.37447 | ||||||||
\(497\) | 51.4189 | 2.30645 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.07426 | 0.182389 | 0.0911945 | − | 0.995833i | \(-0.470931\pi\) | ||||
0.0911945 | + | 0.995833i | \(0.470931\pi\) | |||||||
\(500\) | −47.4805 | −2.12339 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −52.8471 | −2.35868 | ||||||||
\(503\) | 19.9553 | 0.889762 | 0.444881 | − | 0.895590i | \(-0.353246\pi\) | ||||
0.444881 | + | 0.895590i | \(0.353246\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.5281 | 0.512993 | ||||||||
\(506\) | −8.37352 | −0.372249 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.1801 | −0.806613 | ||||||||
\(509\) | 8.79239 | 0.389716 | 0.194858 | − | 0.980831i | \(-0.437575\pi\) | ||||
0.194858 | + | 0.980831i | \(0.437575\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.2478 | 1.20537 | ||||||||
\(512\) | 24.6266 | 1.08835 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −59.2247 | −2.61229 | ||||||||
\(515\) | 9.39239 | 0.413878 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.77094 | −0.253806 | ||||||||
\(518\) | 20.3384 | 0.893618 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 18.5117 | 0.811790 | ||||||||
\(521\) | −27.3483 | −1.19815 | −0.599075 | − | 0.800693i | \(-0.704465\pi\) | ||||
−0.599075 | + | 0.800693i | \(0.704465\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −41.7043 | −1.82360 | −0.911800 | − | 0.410634i | \(-0.865307\pi\) | ||||
−0.911800 | + | 0.410634i | \(0.865307\pi\) | |||||||
\(524\) | −85.1368 | −3.71922 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 36.6197 | 1.59670 | ||||||||
\(527\) | −17.0897 | −0.744441 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0480 | −0.567304 | ||||||||
\(530\) | −15.9236 | −0.691675 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16.9974 | 0.736930 | ||||||||
\(533\) | −24.5912 | −1.06516 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.2615 | 0.832748 | ||||||||
\(536\) | 38.9083 | 1.68058 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −29.7358 | −1.28200 | ||||||||
\(539\) | −4.34940 | −0.187342 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.7584 | −0.892472 | −0.446236 | − | 0.894915i | \(-0.647236\pi\) | ||||
−0.446236 | + | 0.894915i | \(0.647236\pi\) | |||||||
\(542\) | −45.4508 | −1.95228 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 51.4207 | 2.20464 | ||||||||
\(545\) | −0.224035 | −0.00959659 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.39396 | 0.230629 | 0.115315 | − | 0.993329i | \(-0.463212\pi\) | ||||
0.115315 | + | 0.993329i | \(0.463212\pi\) | |||||||
\(548\) | 30.8193 | 1.31653 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10.2878 | −0.438672 | ||||||||
\(551\) | 7.17849 | 0.305814 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −45.2412 | −1.92385 | ||||||||
\(554\) | 36.3980 | 1.54640 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 57.1881 | 2.42532 | ||||||||
\(557\) | 38.0076 | 1.61043 | 0.805217 | − | 0.592981i | \(-0.202049\pi\) | ||||
0.805217 | + | 0.592981i | \(0.202049\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.2782 | −0.857677 | ||||||||
\(560\) | −40.5952 | −1.71546 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 68.6404 | 2.89542 | ||||||||
\(563\) | 26.4313 | 1.11395 | 0.556973 | − | 0.830530i | \(-0.311963\pi\) | ||||
0.556973 | + | 0.830530i | \(0.311963\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.210295 | 0.00884719 | ||||||||
\(566\) | −76.6330 | −3.22112 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 123.377 | 5.17677 | ||||||||
\(569\) | −40.6105 | −1.70248 | −0.851239 | − | 0.524778i | \(-0.824148\pi\) | ||||
−0.851239 | + | 0.524778i | \(0.824148\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.44299 | 0.353328 | 0.176664 | − | 0.984271i | \(-0.443469\pi\) | ||||
0.176664 | + | 0.984271i | \(0.443469\pi\) | |||||||
\(572\) | 10.8977 | 0.455656 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 101.807 | 4.24936 | ||||||||
\(575\) | 12.2271 | 0.509906 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.9771 | 0.873288 | 0.436644 | − | 0.899634i | \(-0.356167\pi\) | ||||
0.436644 | + | 0.899634i | \(0.356167\pi\) | |||||||
\(578\) | 9.31648 | 0.387514 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −38.4006 | −1.59450 | ||||||||
\(581\) | 33.5766 | 1.39299 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.65820 | −0.234339 | ||||||||
\(584\) | 65.3795 | 2.70542 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.9338 | 0.699528 | ||||||||
\(587\) | 21.1452 | 0.872756 | 0.436378 | − | 0.899764i | \(-0.356261\pi\) | ||||
0.436378 | + | 0.899764i | \(0.356261\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.65295 | −0.191721 | ||||||||
\(590\) | −38.8208 | −1.59823 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 25.8498 | 1.06242 | ||||||||
\(593\) | −27.7731 | −1.14051 | −0.570253 | − | 0.821469i | \(-0.693155\pi\) | ||||
−0.570253 | + | 0.821469i | \(0.693155\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.1191 | 0.537829 | ||||||||
\(596\) | −34.0917 | −1.39645 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −18.0862 | −0.739600 | ||||||||
\(599\) | −23.0129 | −0.940281 | −0.470140 | − | 0.882592i | \(-0.655797\pi\) | ||||
−0.470140 | + | 0.882592i | \(0.655797\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.3322 | 0.951738 | 0.475869 | − | 0.879516i | \(-0.342134\pi\) | ||||
0.475869 | + | 0.879516i | \(0.342134\pi\) | |||||||
\(602\) | 83.9517 | 3.42162 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 32.6049 | 1.32668 | ||||||||
\(605\) | 1.06025 | 0.0431054 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.22857 | −0.131044 | −0.0655218 | − | 0.997851i | \(-0.520871\pi\) | ||||
−0.0655218 | + | 0.997851i | \(0.520871\pi\) | |||||||
\(608\) | 14.0001 | 0.567778 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.6477 | −0.795512 | ||||||||
\(611\) | −12.4648 | −0.504273 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.2202 | −0.695519 | −0.347759 | − | 0.937584i | \(-0.613057\pi\) | ||||
−0.347759 | + | 0.937584i | \(0.613057\pi\) | |||||||
\(614\) | −27.6842 | −1.11724 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −27.2322 | −1.09722 | ||||||||
\(617\) | 27.4776 | 1.10621 | 0.553103 | − | 0.833113i | \(-0.313443\pi\) | ||||
0.553103 | + | 0.833113i | \(0.313443\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.53870 | −0.383393 | −0.191696 | − | 0.981454i | \(-0.561399\pi\) | ||||
−0.191696 | + | 0.981454i | \(0.561399\pi\) | |||||||
\(620\) | 24.8905 | 0.999625 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21.9306 | −0.879337 | ||||||||
\(623\) | −15.5517 | −0.623064 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.40166 | 0.376066 | ||||||||
\(626\) | 64.0133 | 2.55848 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.25319 | 0.0500076 | ||||||||
\(629\) | −8.35381 | −0.333088 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.16647 | 0.0464363 | 0.0232182 | − | 0.999730i | \(-0.492609\pi\) | ||||
0.0232182 | + | 0.999730i | \(0.492609\pi\) | |||||||
\(632\) | −108.554 | −4.31804 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −31.1430 | −1.23685 | ||||||||
\(635\) | −3.82042 | −0.151609 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.39438 | −0.372219 | ||||||||
\(638\) | −19.0540 | −0.754355 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.9227 | −0.431759 | ||||||||
\(641\) | −10.0249 | −0.395960 | −0.197980 | − | 0.980206i | \(-0.563438\pi\) | ||||
−0.197980 | + | 0.980206i | \(0.563438\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.7197 | −1.60583 | −0.802915 | − | 0.596094i | \(-0.796719\pi\) | ||||
−0.802915 | + | 0.596094i | \(0.796719\pi\) | |||||||
\(644\) | 53.6213 | 2.11298 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.74900 | −0.383569 | ||||||||
\(647\) | 16.6460 | 0.654423 | 0.327211 | − | 0.944951i | \(-0.393891\pi\) | ||||
0.327211 | + | 0.944951i | \(0.393891\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.7944 | −0.541477 | ||||||||
\(650\) | −22.2209 | −0.871574 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −85.6256 | −3.35336 | ||||||||
\(653\) | 34.7416 | 1.35954 | 0.679771 | − | 0.733424i | \(-0.262079\pi\) | ||||
0.679771 | + | 0.733424i | \(0.262079\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.8908 | −0.699053 | ||||||||
\(656\) | 129.396 | 5.05205 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 51.6043 | 2.01175 | ||||||||
\(659\) | 22.9537 | 0.894148 | 0.447074 | − | 0.894497i | \(-0.352466\pi\) | ||||
0.447074 | + | 0.894497i | \(0.352466\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.7141 | −0.883476 | −0.441738 | − | 0.897144i | \(-0.645638\pi\) | ||||
−0.441738 | + | 0.897144i | \(0.645638\pi\) | |||||||
\(662\) | 18.4534 | 0.717213 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 80.5651 | 3.12653 | ||||||||
\(665\) | 3.57187 | 0.138511 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.6459 | 0.876851 | ||||||||
\(668\) | 4.36698 | 0.168964 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.5459 | 0.523322 | ||||||||
\(671\) | −6.98152 | −0.269518 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.9448 | 0.807364 | 0.403682 | − | 0.914899i | \(-0.367730\pi\) | ||||
0.403682 | + | 0.914899i | \(0.367730\pi\) | |||||||
\(674\) | −78.1473 | −3.01012 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −42.0519 | −1.61738 | ||||||||
\(677\) | −11.4153 | −0.438726 | −0.219363 | − | 0.975643i | \(-0.570398\pi\) | ||||
−0.219363 | + | 0.975643i | \(0.570398\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.8093 | 0.529952 | ||||||||
\(680\) | 31.4784 | 1.20714 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.3504 | 0.472921 | ||||||||
\(683\) | 34.9550 | 1.33752 | 0.668759 | − | 0.743479i | \(-0.266826\pi\) | ||||
0.668759 | + | 0.743479i | \(0.266826\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.47643 | 0.247452 | ||||||||
\(686\) | −23.7020 | −0.904945 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 106.701 | 4.06795 | ||||||||
\(689\) | −12.2213 | −0.465594 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.8717 | −0.603789 | −0.301894 | − | 0.953341i | \(-0.597619\pi\) | ||||
−0.301894 | + | 0.953341i | \(0.597619\pi\) | |||||||
\(692\) | 20.9123 | 0.794967 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −45.7020 | −1.73483 | ||||||||
\(695\) | 12.0177 | 0.455855 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41.8165 | −1.58391 | ||||||||
\(698\) | −11.4774 | −0.434426 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 65.8795 | 2.49001 | ||||||||
\(701\) | 18.5830 | 0.701869 | 0.350935 | − | 0.936400i | \(-0.385864\pi\) | ||||
0.350935 | + | 0.936400i | \(0.385864\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.27446 | −0.0857828 | ||||||||
\(704\) | −14.4301 | −0.543857 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 62.2228 | 2.34178 | ||||||||
\(707\) | −36.6298 | −1.37760 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.8063 | 0.894064 | 0.447032 | − | 0.894518i | \(-0.352481\pi\) | ||||
0.447032 | + | 0.894518i | \(0.352481\pi\) | |||||||
\(710\) | 42.9535 | 1.61202 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −37.3153 | −1.39845 | ||||||||
\(713\) | −14.6786 | −0.549717 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.29007 | 0.0856437 | ||||||||
\(716\) | −10.3221 | −0.385755 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 21.7798 | 0.812816 | ||||||||
\(719\) | −37.0144 | −1.38040 | −0.690202 | − | 0.723616i | \(-0.742478\pi\) | ||||
−0.690202 | + | 0.723616i | \(0.742478\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.8437 | −1.11144 | ||||||||
\(722\) | −2.65432 | −0.0987835 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 26.6154 | 0.989154 | ||||||||
\(725\) | 27.8229 | 1.03332 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.0744 | −0.818694 | −0.409347 | − | 0.912379i | \(-0.634243\pi\) | ||||
−0.409347 | + | 0.912379i | \(0.634243\pi\) | |||||||
\(728\) | −58.8197 | −2.18000 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 22.7618 | 0.842452 | ||||||||
\(731\) | −34.4824 | −1.27538 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.7090 | −0.691031 | −0.345515 | − | 0.938413i | \(-0.612296\pi\) | ||||
−0.345515 | + | 0.938413i | \(0.612296\pi\) | |||||||
\(734\) | −87.9891 | −3.24774 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 44.1658 | 1.62797 | ||||||||
\(737\) | 4.81332 | 0.177301 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.91630 | −0.217635 | −0.108817 | − | 0.994062i | \(-0.534706\pi\) | ||||
−0.108817 | + | 0.994062i | \(0.534706\pi\) | |||||||
\(740\) | 12.1670 | 0.447267 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 50.5961 | 1.85744 | ||||||||
\(743\) | −14.0422 | −0.515159 | −0.257579 | − | 0.966257i | \(-0.582925\pi\) | ||||
−0.257579 | + | 0.966257i | \(0.582925\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.16411 | −0.262473 | ||||||||
\(746\) | 44.0191 | 1.61165 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18.5312 | 0.677566 | ||||||||
\(749\) | −61.2023 | −2.23628 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.91166 | 0.179229 | 0.0896145 | − | 0.995977i | \(-0.471437\pi\) | ||||
0.0896145 | + | 0.995977i | \(0.471437\pi\) | |||||||
\(752\) | 65.5882 | 2.39176 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −41.1553 | −1.49879 | ||||||||
\(755\) | 6.85168 | 0.249358 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.2829 | 1.79122 | 0.895609 | − | 0.444843i | \(-0.146741\pi\) | ||||
0.895609 | + | 0.444843i | \(0.146741\pi\) | |||||||
\(758\) | −15.3809 | −0.558659 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.57050 | 0.310885 | ||||||||
\(761\) | 7.25922 | 0.263146 | 0.131573 | − | 0.991306i | \(-0.457997\pi\) | ||||
0.131573 | + | 0.991306i | \(0.457997\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.711856 | 0.0257709 | ||||||||
\(764\) | 81.6843 | 2.95524 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.6344 | 0.564892 | ||||||||
\(767\) | −29.7949 | −1.07583 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.5123 | −0.775755 | −0.387877 | − | 0.921711i | \(-0.626792\pi\) | ||||
−0.387877 | + | 0.921711i | \(0.626792\pi\) | |||||||
\(770\) | −9.48087 | −0.341667 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −101.221 | −3.64301 | ||||||||
\(773\) | −4.54038 | −0.163306 | −0.0816530 | − | 0.996661i | \(-0.526020\pi\) | ||||
−0.0816530 | + | 0.996661i | \(0.526020\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.0342 | −0.647808 | ||||||||
\(776\) | 33.1346 | 1.18946 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 36.6440 | 1.31375 | ||||||||
\(779\) | −11.3852 | −0.407917 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.2629 | 0.546149 | ||||||||
\(782\) | −30.7550 | −1.09980 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 49.4320 | 1.76543 | ||||||||
\(785\) | 0.263348 | 0.00939928 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.25028 | −0.258444 | −0.129222 | − | 0.991616i | \(-0.541248\pi\) | ||||
−0.129222 | + | 0.991616i | \(0.541248\pi\) | |||||||
\(788\) | 120.281 | 4.28484 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −37.7929 | −1.34461 | ||||||||
\(791\) | −0.668201 | −0.0237585 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.0796 | −0.535491 | ||||||||
\(794\) | −17.2125 | −0.610848 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.59605 | −0.340123 | ||||||||
\(797\) | −18.8674 | −0.668319 | −0.334159 | − | 0.942517i | \(-0.608452\pi\) | ||||
−0.334159 | + | 0.942517i | \(0.608452\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.1960 | −0.749860 | ||||||||
\(800\) | 54.2624 | 1.91847 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.84236 | 0.347546 | ||||||||
\(803\) | 8.08806 | 0.285422 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.2681 | 0.397149 | ||||||||
\(806\) | 26.6760 | 0.939622 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −87.8911 | −3.09200 | ||||||||
\(809\) | 19.4948 | 0.685399 | 0.342700 | − | 0.939445i | \(-0.388659\pi\) | ||||
0.342700 | + | 0.939445i | \(0.388659\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.28635 | 0.150514 | 0.0752570 | − | 0.997164i | \(-0.476022\pi\) | ||||
0.0752570 | + | 0.997164i | \(0.476022\pi\) | |||||||
\(812\) | 122.016 | 4.28191 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.03713 | 0.211601 | ||||||||
\(815\) | −17.9936 | −0.630287 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.38838 | −0.328458 | ||||||||
\(818\) | −82.4350 | −2.88227 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 60.9039 | 2.12686 | ||||||||
\(821\) | −5.37419 | −0.187561 | −0.0937803 | − | 0.995593i | \(-0.529895\pi\) | ||||
−0.0937803 | + | 0.995593i | \(0.529895\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.3196 | 0.917445 | 0.458723 | − | 0.888580i | \(-0.348307\pi\) | ||||
0.458723 | + | 0.888580i | \(0.348307\pi\) | |||||||
\(824\) | −71.6084 | −2.49460 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 123.351 | 4.29192 | ||||||||
\(827\) | 8.11186 | 0.282077 | 0.141039 | − | 0.990004i | \(-0.454956\pi\) | ||||
0.141039 | + | 0.990004i | \(0.454956\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.5948 | −0.750017 | −0.375009 | − | 0.927021i | \(-0.622360\pi\) | ||||
−0.375009 | + | 0.927021i | \(0.622360\pi\) | |||||||
\(830\) | 28.0486 | 0.973582 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −31.1681 | −1.08056 | ||||||||
\(833\) | −15.9748 | −0.553495 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.917688 | 0.0317579 | ||||||||
\(836\) | 5.04540 | 0.174499 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −29.9595 | −1.03493 | ||||||||
\(839\) | 4.35109 | 0.150216 | 0.0751082 | − | 0.997175i | \(-0.476070\pi\) | ||||
0.0751082 | + | 0.997175i | \(0.476070\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.5308 | 0.776923 | ||||||||
\(842\) | −91.6254 | −3.15762 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 62.0828 | 2.13698 | ||||||||
\(845\) | −8.83689 | −0.303998 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.36889 | −0.115756 | ||||||||
\(848\) | 64.3069 | 2.20831 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −37.7858 | −1.29604 | ||||||||
\(851\) | −7.17519 | −0.245962 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.5022 | 0.667744 | 0.333872 | − | 0.942618i | \(-0.391645\pi\) | ||||
0.333872 | + | 0.942618i | \(0.391645\pi\) | |||||||
\(854\) | 62.4294 | 2.13629 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −146.851 | −5.01928 | ||||||||
\(857\) | −13.3462 | −0.455898 | −0.227949 | − | 0.973673i | \(-0.573202\pi\) | ||||
−0.227949 | + | 0.973673i | \(0.573202\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.6016 | 0.737036 | 0.368518 | − | 0.929621i | \(-0.379865\pi\) | ||||
0.368518 | + | 0.929621i | \(0.379865\pi\) | |||||||
\(860\) | 50.2221 | 1.71256 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 48.2167 | 1.64227 | ||||||||
\(863\) | 2.72425 | 0.0927345 | 0.0463673 | − | 0.998924i | \(-0.485236\pi\) | ||||
0.0463673 | + | 0.998924i | \(0.485236\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.39456 | 0.149420 | ||||||||
\(866\) | −28.6147 | −0.972367 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −79.0879 | −2.68442 | ||||||||
\(869\) | −13.4291 | −0.455552 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.3964 | 0.352269 | ||||||||
\(872\) | 1.70806 | 0.0578422 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.37352 | −0.283239 | ||||||||
\(875\) | 31.7034 | 1.07177 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.29130 | 0.0436041 | 0.0218021 | − | 0.999762i | \(-0.493060\pi\) | ||||
0.0218021 | + | 0.999762i | \(0.493060\pi\) | |||||||
\(878\) | 3.68266 | 0.124284 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −12.0500 | −0.406207 | ||||||||
\(881\) | −24.9873 | −0.841844 | −0.420922 | − | 0.907097i | \(-0.638293\pi\) | ||||
−0.420922 | + | 0.907097i | \(0.638293\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.5046 | 0.521772 | 0.260886 | − | 0.965370i | \(-0.415985\pi\) | ||||
0.260886 | + | 0.965370i | \(0.415985\pi\) | |||||||
\(884\) | 40.0260 | 1.34622 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.2914 | −0.648107 | ||||||||
\(887\) | 9.98029 | 0.335105 | 0.167553 | − | 0.985863i | \(-0.446414\pi\) | ||||
0.167553 | + | 0.985863i | \(0.446414\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.1391 | 0.407134 | ||||||||
\(890\) | −12.9913 | −0.435469 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 115.274 | 3.85966 | ||||||||
\(893\) | −5.77094 | −0.193117 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.16911 | −0.0725053 | ||||||||
\(896\) | 34.7063 | 1.15946 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 56.8815 | 1.89816 | ||||||||
\(899\) | −33.4012 | −1.11399 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.7819 | −0.692345 | ||||||||
\(902\) | 30.2199 | 1.00621 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.60331 | −0.0533253 | ||||||||
\(905\) | 5.59303 | 0.185919 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.8887 | 0.394758 | 0.197379 | − | 0.980327i | \(-0.436757\pi\) | ||||
0.197379 | + | 0.980327i | \(0.436757\pi\) | |||||||
\(908\) | −20.2146 | −0.670845 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −20.4780 | −0.678839 | ||||||||
\(911\) | 23.7166 | 0.785767 | 0.392883 | − | 0.919588i | \(-0.371478\pi\) | ||||
0.392883 | + | 0.919588i | \(0.371478\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.96666 | 0.329848 | ||||||||
\(914\) | 46.7989 | 1.54797 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −124.129 | −4.10134 | ||||||||
\(917\) | 56.8471 | 1.87726 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.1426 | 0.598470 | 0.299235 | − | 0.954179i | \(-0.403269\pi\) | ||||
0.299235 | + | 0.954179i | \(0.403269\pi\) | |||||||
\(920\) | 27.0372 | 0.891390 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 90.7972 | 2.99024 | ||||||||
\(923\) | 32.9667 | 1.08511 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.81549 | −0.289852 | ||||||||
\(926\) | 29.1997 | 0.959563 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 100.500 | 3.29906 | ||||||||
\(929\) | 50.5019 | 1.65691 | 0.828457 | − | 0.560053i | \(-0.189219\pi\) | ||||
0.828457 | + | 0.560053i | \(0.189219\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.34940 | −0.142546 | ||||||||
\(932\) | −82.2368 | −2.69376 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.6379 | 0.380805 | ||||||||
\(935\) | 3.89418 | 0.127353 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.6587 | −1.29559 | −0.647797 | − | 0.761813i | \(-0.724309\pi\) | ||||
−0.647797 | + | 0.761813i | \(0.724309\pi\) | |||||||
\(938\) | −43.0412 | −1.40534 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 30.8711 | 1.00690 | ||||||||
\(941\) | 34.8809 | 1.13709 | 0.568543 | − | 0.822653i | \(-0.307507\pi\) | ||||
0.568543 | + | 0.822653i | \(0.307507\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.9166 | −1.16961 | ||||||||
\(944\) | 156.777 | 5.10265 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.9197 | 0.810210 | ||||||||
\(947\) | 30.3067 | 0.984835 | 0.492417 | − | 0.870359i | \(-0.336113\pi\) | ||||
0.492417 | + | 0.870359i | \(0.336113\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.4696 | 0.567088 | ||||||||
\(950\) | −10.2878 | −0.333780 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −100.021 | −3.24169 | ||||||||
\(953\) | 6.65804 | 0.215675 | 0.107838 | − | 0.994169i | \(-0.465607\pi\) | ||||
0.107838 | + | 0.994169i | \(0.465607\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.1653 | 0.555457 | ||||||||
\(956\) | 77.7912 | 2.51595 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −38.1381 | −1.23219 | ||||||||
\(959\) | −20.5785 | −0.664513 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.35006 | −0.301615 | ||||||||
\(962\) | 13.0398 | 0.420419 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 121.817 | 3.92345 | ||||||||
\(965\) | −21.2707 | −0.684729 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.0020 | −0.643221 | −0.321611 | − | 0.946872i | \(-0.604224\pi\) | ||||
−0.321611 | + | 0.946872i | \(0.604224\pi\) | |||||||
\(968\) | −8.08346 | −0.259812 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.5358 | 0.370392 | ||||||||
\(971\) | 0.491941 | 0.0157871 | 0.00789357 | − | 0.999969i | \(-0.497487\pi\) | ||||
0.00789357 | + | 0.999969i | \(0.497487\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −38.1853 | −1.22417 | ||||||||
\(974\) | −2.69975 | −0.0865055 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 79.3467 | 2.53983 | ||||||||
\(977\) | −23.6515 | −0.756679 | −0.378339 | − | 0.925667i | \(-0.623505\pi\) | ||||
−0.378339 | + | 0.925667i | \(0.623505\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.61626 | −0.147536 | ||||||||
\(980\) | 23.2666 | 0.743225 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.39809 | −0.204171 | ||||||||
\(983\) | −39.5609 | −1.26180 | −0.630899 | − | 0.775865i | \(-0.717314\pi\) | ||||
−0.630899 | + | 0.775865i | \(0.717314\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.2762 | 0.805366 | ||||||||
\(986\) | −69.9831 | −2.22872 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.8977 | 0.346702 | ||||||||
\(989\) | −29.6173 | −0.941777 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.6096 | −0.432322 | −0.216161 | − | 0.976358i | \(-0.569354\pi\) | ||||
−0.216161 | + | 0.976358i | \(0.569354\pi\) | |||||||
\(992\) | −65.1417 | −2.06825 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −136.482 | −4.32895 | ||||||||
\(995\) | −2.01654 | −0.0639285 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.1821 | 1.30425 | 0.652125 | − | 0.758111i | \(-0.273878\pi\) | ||||
0.652125 | + | 0.758111i | \(0.273878\pi\) | |||||||
\(998\) | −10.8144 | −0.342323 | ||||||||
\(999\) | 0 | 0 |
(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 | 1881.2.a.k.1.1 | 5 | ||
3.2 | odd | 2 | 209.2.a.c.1.5 | ✓ | 5 | ||
12.11 | even | 2 | 3344.2.a.t.1.3 | 5 | |||
15.14 | odd | 2 | 5225.2.a.h.1.1 | 5 | |||
33.32 | even | 2 | 2299.2.a.n.1.1 | 5 | |||
57.56 | even | 2 | 3971.2.a.h.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
209.2.a.c.1.5 | ✓ | 5 | 3.2 | odd | 2 | ||
1881.2.a.k.1.1 | 5 | 1.1 | even | 1 | trivial | ||
2299.2.a.n.1.1 | 5 | 33.32 | even | 2 | |||
3344.2.a.t.1.3 | 5 | 12.11 | even | 2 | |||
3971.2.a.h.1.1 | 5 | 57.56 | even | 2 | |||
5225.2.a.h.1.1 | 5 | 15.14 | odd | 2 |