Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5225,2,Mod(1,5225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5225, 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("5225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5225 = 5^{2} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5225.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: | \(41.7218350561\) |
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: | \(\Z[a_1, a_2, a_3]\) |
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 | \(\chi\) | \(=\) | 5225.1 |
$q$-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 | \(0.887732\pi\) | |||||||
\(3\) | −0.121872 | −0.0703629 | −0.0351814 | − | 0.999381i | \(-0.511201\pi\) | ||||
−0.0351814 | + | 0.999381i | \(0.511201\pi\) | |||||||
\(4\) | 5.04540 | 2.52270 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.323487 | 0.132063 | ||||||||
\(7\) | 3.36889 | 1.27332 | 0.636660 | − | 0.771145i | \(-0.280316\pi\) | ||||
0.636660 | + | 0.771145i | \(0.280316\pi\) | |||||||
\(8\) | −8.08346 | −2.85793 | ||||||||
\(9\) | −2.98515 | −0.995049 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.614893 | −0.177504 | ||||||||
\(13\) | 2.15993 | 0.599056 | 0.299528 | − | 0.954087i | \(-0.403171\pi\) | ||||
0.299528 | + | 0.954087i | \(0.403171\pi\) | |||||||
\(14\) | −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 | \(0.646939\pi\) | |||||||
\(18\) | 7.92353 | 1.86759 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.410573 | −0.0895944 | ||||||||
\(22\) | −2.65432 | −0.565902 | ||||||||
\(23\) | −3.15468 | −0.657797 | −0.328898 | − | 0.944365i | \(-0.606677\pi\) | ||||
−0.328898 | + | 0.944365i | \(0.606677\pi\) | |||||||
\(24\) | 0.985147 | 0.201092 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.73313 | −1.12436 | ||||||||
\(27\) | 0.729422 | 0.140377 | ||||||||
\(28\) | 16.9974 | 3.21220 | ||||||||
\(29\) | 7.17849 | 1.33301 | 0.666506 | − | 0.745499i | \(-0.267789\pi\) | ||||
0.666506 | + | 0.745499i | \(0.267789\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | −0.121872 | −0.0212152 | ||||||||
\(34\) | 9.74900 | 1.67194 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −15.0613 | −2.51021 | ||||||||
\(37\) | −2.27446 | −0.373918 | −0.186959 | − | 0.982368i | \(-0.559863\pi\) | ||||
−0.186959 | + | 0.982368i | \(0.559863\pi\) | |||||||
\(38\) | 2.65432 | 0.430587 | ||||||||
\(39\) | −0.263235 | −0.0421513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.3852 | −1.77807 | −0.889034 | − | 0.457841i | \(-0.848623\pi\) | ||||
−0.889034 | + | 0.457841i | \(0.848623\pi\) | |||||||
\(42\) | 1.08979 | 0.168158 | ||||||||
\(43\) | −9.38838 | −1.43171 | −0.715857 | − | 0.698247i | \(-0.753964\pi\) | ||||
−0.715857 | + | 0.698247i | \(0.753964\pi\) | |||||||
\(44\) | 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 | \(0.361718\pi\) | |||||||
\(48\) | −1.38511 | −0.199923 | ||||||||
\(49\) | 4.34940 | 0.621342 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.447622 | 0.0626796 | ||||||||
\(52\) | 10.8977 | 1.51124 | ||||||||
\(53\) | 5.65820 | 0.777213 | 0.388607 | − | 0.921404i | \(-0.372957\pi\) | ||||
0.388607 | + | 0.921404i | \(0.372957\pi\) | |||||||
\(54\) | −1.93612 | −0.263472 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −27.2322 | −3.63906 | ||||||||
\(57\) | 0.121872 | 0.0161423 | ||||||||
\(58\) | −19.0540 | −2.50191 | ||||||||
\(59\) | −13.7944 | −1.79588 | −0.897939 | − | 0.440121i | \(-0.854936\pi\) | ||||
−0.897939 | + | 0.440121i | \(0.854936\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | −10.0566 | −1.26702 | ||||||||
\(64\) | 14.4301 | 1.80377 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.323487 | 0.0398185 | ||||||||
\(67\) | 4.81332 | 0.588041 | 0.294020 | − | 0.955799i | \(-0.405007\pi\) | ||||
0.294020 | + | 0.955799i | \(0.405007\pi\) | |||||||
\(68\) | −18.5312 | −2.24723 | ||||||||
\(69\) | 0.384467 | 0.0462844 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.2629 | 1.81137 | 0.905685 | − | 0.423951i | \(-0.139357\pi\) | ||||
0.905685 | + | 0.423951i | \(0.139357\pi\) | |||||||
\(72\) | 24.1303 | 2.84378 | ||||||||
\(73\) | 8.08806 | 0.946636 | 0.473318 | − | 0.880892i | \(-0.343056\pi\) | ||||
0.473318 | + | 0.880892i | \(0.343056\pi\) | |||||||
\(74\) | 6.03713 | 0.701802 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.04540 | −0.578747 | ||||||||
\(77\) | 3.36889 | 0.383920 | ||||||||
\(78\) | 0.698709 | 0.0791132 | ||||||||
\(79\) | 13.4291 | 1.51090 | 0.755448 | − | 0.655209i | \(-0.227419\pi\) | ||||
0.755448 | + | 0.655209i | \(0.227419\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.86655 | 0.985172 | ||||||||
\(82\) | 30.2199 | 3.33723 | ||||||||
\(83\) | −9.96666 | −1.09398 | −0.546992 | − | 0.837138i | \(-0.684227\pi\) | ||||
−0.546992 | + | 0.837138i | \(0.684227\pi\) | |||||||
\(84\) | −2.07150 | −0.226020 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 24.9197 | 2.68716 | ||||||||
\(87\) | −0.874858 | −0.0937946 | ||||||||
\(88\) | −8.08346 | −0.861699 | ||||||||
\(89\) | −4.61626 | −0.489323 | −0.244661 | − | 0.969609i | \(-0.578677\pi\) | ||||
−0.244661 | + | 0.969609i | \(0.578677\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.27655 | 0.762790 | ||||||||
\(92\) | −15.9166 | −1.65942 | ||||||||
\(93\) | −0.567064 | −0.0588018 | ||||||||
\(94\) | −15.3179 | −1.57992 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.70622 | 0.174140 | ||||||||
\(97\) | 4.09907 | 0.416197 | 0.208099 | − | 0.978108i | \(-0.433273\pi\) | ||||
0.208099 | + | 0.978108i | \(0.433273\pi\) | |||||||
\(98\) | −11.5447 | −1.16619 | ||||||||
\(99\) | −2.98515 | −0.300019 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.8730 | −1.08190 | −0.540950 | − | 0.841055i | \(-0.681935\pi\) | ||||
−0.540950 | + | 0.841055i | \(0.681935\pi\) | |||||||
\(102\) | −1.18813 | −0.117642 | ||||||||
\(103\) | −8.85864 | −0.872867 | −0.436434 | − | 0.899736i | \(-0.643759\pi\) | ||||
−0.436434 | + | 0.899736i | \(0.643759\pi\) | |||||||
\(104\) | −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 | \(0.158791\pi\) | |||||||
\(108\) | 3.68023 | 0.354130 | ||||||||
\(109\) | −0.211303 | −0.0202392 | −0.0101196 | − | 0.999949i | \(-0.503221\pi\) | ||||
−0.0101196 | + | 0.999949i | \(0.503221\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.277193 | 0.0263100 | ||||||||
\(112\) | 38.2883 | 3.61790 | ||||||||
\(113\) | 0.198345 | 0.0186587 | 0.00932935 | − | 0.999956i | \(-0.497030\pi\) | ||||
0.00932935 | + | 0.999956i | \(0.497030\pi\) | |||||||
\(114\) | −0.323487 | −0.0302973 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 36.2184 | 3.36279 | ||||||||
\(117\) | −6.44770 | −0.596090 | ||||||||
\(118\) | 36.6147 | 3.37066 | ||||||||
\(119\) | −12.3735 | −1.13428 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −18.5312 | −1.67773 | ||||||||
\(123\) | 1.38754 | 0.125110 | ||||||||
\(124\) | 23.4760 | 2.10821 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 26.6935 | 2.37804 | ||||||||
\(127\) | 3.60331 | 0.319742 | 0.159871 | − | 0.987138i | \(-0.448892\pi\) | ||||
0.159871 | + | 0.987138i | \(0.448892\pi\) | |||||||
\(128\) | −10.3020 | −0.910578 | ||||||||
\(129\) | 1.14418 | 0.100739 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.8741 | 1.47430 | 0.737150 | − | 0.675729i | \(-0.236171\pi\) | ||||
0.737150 | + | 0.675729i | \(0.236171\pi\) | |||||||
\(132\) | −0.614893 | −0.0535196 | ||||||||
\(133\) | −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 | \(0.415968\pi\) | |||||||
\(138\) | −1.02050 | −0.0868706 | ||||||||
\(139\) | 11.3347 | 0.961398 | 0.480699 | − | 0.876886i | \(-0.340383\pi\) | ||||
0.480699 | + | 0.876886i | \(0.340383\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.703316 | −0.0592299 | ||||||||
\(142\) | −40.5125 | −3.39973 | ||||||||
\(143\) | 2.15993 | 0.180622 | ||||||||
\(144\) | −33.9270 | −2.82725 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −21.4683 | −1.77673 | ||||||||
\(147\) | −0.530070 | −0.0437194 | ||||||||
\(148\) | −11.4755 | −0.943284 | ||||||||
\(149\) | 6.75698 | 0.553554 | 0.276777 | − | 0.960934i | \(-0.410734\pi\) | ||||
0.276777 | + | 0.960934i | \(0.410734\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 10.9641 | 0.886395 | ||||||||
\(154\) | −8.94209 | −0.720574 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.32813 | −0.106335 | ||||||||
\(157\) | −0.248382 | −0.0198230 | −0.00991152 | − | 0.999951i | \(-0.503155\pi\) | ||||
−0.00991152 | + | 0.999951i | \(0.503155\pi\) | |||||||
\(158\) | −35.6452 | −2.83578 | ||||||||
\(159\) | −0.689576 | −0.0546869 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.6278 | −0.837585 | ||||||||
\(162\) | −23.5346 | −1.84905 | ||||||||
\(163\) | 16.9710 | 1.32927 | 0.664637 | − | 0.747167i | \(-0.268586\pi\) | ||||
0.664637 | + | 0.747167i | \(0.268586\pi\) | |||||||
\(164\) | −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 | \(0.489338\pi\) | |||||||
\(168\) | 3.31885 | 0.256055 | ||||||||
\(169\) | −8.33471 | −0.641132 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.98515 | 0.228280 | ||||||||
\(172\) | −47.3681 | −3.61178 | ||||||||
\(173\) | 4.14483 | 0.315125 | 0.157563 | − | 0.987509i | \(-0.449636\pi\) | ||||
0.157563 | + | 0.987509i | \(0.449636\pi\) | |||||||
\(174\) | 2.32215 | 0.176042 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.3653 | 0.856688 | ||||||||
\(177\) | 1.68115 | 0.126363 | ||||||||
\(178\) | 12.2530 | 0.918403 | ||||||||
\(179\) | 2.04584 | 0.152913 | 0.0764567 | − | 0.997073i | \(-0.475639\pi\) | ||||
0.0764567 | + | 0.997073i | \(0.475639\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | −0.850852 | −0.0628968 | ||||||||
\(184\) | 25.5007 | 1.87994 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.50517 | 0.110364 | ||||||||
\(187\) | −3.67288 | −0.268588 | ||||||||
\(188\) | 29.1167 | 2.12355 | ||||||||
\(189\) | 2.45734 | 0.178745 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.1899 | −1.17146 | −0.585729 | − | 0.810507i | \(-0.699192\pi\) | ||||
−0.585729 | + | 0.810507i | \(0.699192\pi\) | |||||||
\(192\) | −1.75863 | −0.126918 | ||||||||
\(193\) | 20.0620 | 1.44409 | 0.722045 | − | 0.691846i | \(-0.243202\pi\) | ||||
0.722045 | + | 0.691846i | \(0.243202\pi\) | |||||||
\(194\) | −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 | \(0.177050\pi\) | |||||||
\(198\) | 7.92353 | 0.563101 | ||||||||
\(199\) | −1.90194 | −0.134825 | −0.0674125 | − | 0.997725i | \(-0.521474\pi\) | ||||
−0.0674125 | + | 0.997725i | \(0.521474\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.586609 | −0.0413762 | ||||||||
\(202\) | 28.8603 | 2.03060 | ||||||||
\(203\) | 24.1835 | 1.69735 | ||||||||
\(204\) | 2.25843 | 0.158122 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 23.5136 | 1.63827 | ||||||||
\(207\) | 9.41719 | 0.654540 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | −1.86012 | −0.127453 | ||||||||
\(214\) | −48.2207 | −3.29630 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.89625 | −0.401189 | ||||||||
\(217\) | 15.6753 | 1.06411 | ||||||||
\(218\) | 0.560865 | 0.0379866 | ||||||||
\(219\) | −0.985709 | −0.0666080 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.93316 | −0.533642 | ||||||||
\(222\) | −0.735757 | −0.0493808 | ||||||||
\(223\) | −22.8473 | −1.52997 | −0.764985 | − | 0.644048i | \(-0.777254\pi\) | ||||
−0.764985 | + | 0.644048i | \(0.777254\pi\) | |||||||
\(224\) | −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 | \(0.542449\pi\) | |||||||
\(228\) | 0.614893 | 0.0407223 | ||||||||
\(229\) | −24.6024 | −1.62577 | −0.812887 | − | 0.582422i | \(-0.802105\pi\) | ||||
−0.812887 | + | 0.582422i | \(0.802105\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.410573 | −0.0270137 | ||||||||
\(232\) | −58.0270 | −3.80966 | ||||||||
\(233\) | −16.2994 | −1.06781 | −0.533903 | − | 0.845545i | \(-0.679275\pi\) | ||||
−0.533903 | + | 0.845545i | \(0.679275\pi\) | |||||||
\(234\) | 17.1143 | 1.11879 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −69.5982 | −4.53046 | ||||||||
\(237\) | −1.63664 | −0.106311 | ||||||||
\(238\) | 32.8433 | 2.12891 | ||||||||
\(239\) | −15.4182 | −0.997324 | −0.498662 | − | 0.866797i | \(-0.666175\pi\) | ||||
−0.498662 | + | 0.866797i | \(0.666175\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | −3.26885 | −0.209697 | ||||||||
\(244\) | 35.2245 | 2.25502 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.68296 | −0.234817 | ||||||||
\(247\) | −2.15993 | −0.137433 | ||||||||
\(248\) | −37.6119 | −2.38836 | ||||||||
\(249\) | 1.21466 | 0.0769758 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.9099 | −1.25670 | −0.628350 | − | 0.777931i | \(-0.716269\pi\) | ||||
−0.628350 | + | 0.777931i | \(0.716269\pi\) | |||||||
\(252\) | −50.7397 | −3.19630 | ||||||||
\(253\) | −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 | \(0.255001\pi\) | |||||||
\(258\) | −3.03702 | −0.189076 | ||||||||
\(259\) | −7.66239 | −0.476118 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.4289 | −1.32641 | ||||||||
\(262\) | −44.7893 | −2.76709 | ||||||||
\(263\) | −13.7963 | −0.850716 | −0.425358 | − | 0.905025i | \(-0.639852\pi\) | ||||
−0.425358 | + | 0.905025i | \(0.639852\pi\) | |||||||
\(264\) | 0.985147 | 0.0606316 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.94209 | 0.548275 | ||||||||
\(267\) | 0.562593 | 0.0344301 | ||||||||
\(268\) | 24.2851 | 1.48345 | ||||||||
\(269\) | −11.2028 | −0.683048 | −0.341524 | − | 0.939873i | \(-0.610943\pi\) | ||||
−0.341524 | + | 0.939873i | \(0.610943\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | −0.886808 | −0.0536721 | ||||||||
\(274\) | −16.2136 | −0.979499 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.93979 | 0.116762 | ||||||||
\(277\) | 13.7127 | 0.823919 | 0.411960 | − | 0.911202i | \(-0.364844\pi\) | ||||
0.411960 | + | 0.911202i | \(0.364844\pi\) | |||||||
\(278\) | −30.0859 | −1.80443 | ||||||||
\(279\) | −13.8897 | −0.831557 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.8599 | 1.54267 | 0.771337 | − | 0.636427i | \(-0.219588\pi\) | ||||
0.771337 | + | 0.636427i | \(0.219588\pi\) | |||||||
\(282\) | 1.86682 | 0.111168 | ||||||||
\(283\) | −28.8711 | −1.71621 | −0.858103 | − | 0.513477i | \(-0.828357\pi\) | ||||
−0.858103 | + | 0.513477i | \(0.828357\pi\) | |||||||
\(284\) | 77.0073 | 4.56954 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.73313 | −0.339007 | ||||||||
\(287\) | −38.3554 | −2.26405 | ||||||||
\(288\) | 41.7923 | 2.46264 | ||||||||
\(289\) | −3.50993 | −0.206467 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.499562 | −0.0292848 | ||||||||
\(292\) | 40.8075 | 2.38808 | ||||||||
\(293\) | −6.37971 | −0.372707 | −0.186353 | − | 0.982483i | \(-0.559667\pi\) | ||||
−0.186353 | + | 0.982483i | \(0.559667\pi\) | |||||||
\(294\) | 1.40697 | 0.0820563 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 18.3855 | 1.06863 | ||||||||
\(297\) | 0.729422 | 0.0423254 | ||||||||
\(298\) | −17.9352 | −1.03896 | ||||||||
\(299\) | −6.81389 | −0.394057 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −31.6284 | −1.82303 | ||||||||
\(302\) | −17.1530 | −0.987045 | ||||||||
\(303\) | 1.32511 | 0.0761256 | ||||||||
\(304\) | −11.3653 | −0.651842 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −29.1022 | −1.66366 | ||||||||
\(307\) | −10.4299 | −0.595264 | −0.297632 | − | 0.954681i | \(-0.596197\pi\) | ||||
−0.297632 | + | 0.954681i | \(0.596197\pi\) | |||||||
\(308\) | 16.9974 | 0.968515 | ||||||||
\(309\) | 1.07962 | 0.0614174 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.26224 | −0.468508 | −0.234254 | − | 0.972175i | \(-0.575265\pi\) | ||||
−0.234254 | + | 0.972175i | \(0.575265\pi\) | |||||||
\(312\) | 2.12785 | 0.120466 | ||||||||
\(313\) | 24.1167 | 1.36315 | 0.681577 | − | 0.731746i | \(-0.261294\pi\) | ||||
0.681577 | + | 0.731746i | \(0.261294\pi\) | |||||||
\(314\) | 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 | \(0.393122\pi\) | |||||||
\(318\) | 1.83035 | 0.102641 | ||||||||
\(319\) | 7.17849 | 0.401918 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.21404 | −0.123576 | ||||||||
\(322\) | 28.2095 | 1.57205 | ||||||||
\(323\) | 3.67288 | 0.204365 | ||||||||
\(324\) | 44.7353 | 2.48529 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −45.0465 | −2.49489 | ||||||||
\(327\) | 0.0257519 | 0.00142409 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 6.78959 | 0.372067 | ||||||||
\(334\) | −2.29741 | −0.125709 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.66627 | −0.254566 | ||||||||
\(337\) | −29.4416 | −1.60379 | −0.801893 | − | 0.597468i | \(-0.796174\pi\) | ||||
−0.801893 | + | 0.597468i | \(0.796174\pi\) | |||||||
\(338\) | 22.1230 | 1.20333 | ||||||||
\(339\) | −0.0241727 | −0.00131288 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.65295 | 0.251971 | ||||||||
\(342\) | −7.92353 | −0.428455 | ||||||||
\(343\) | −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 | \(0.347076\pi\) | |||||||
\(348\) | −4.41401 | −0.236616 | ||||||||
\(349\) | 4.32405 | 0.231461 | 0.115731 | − | 0.993281i | \(-0.463079\pi\) | ||||
0.115731 | + | 0.993281i | \(0.463079\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.57550 | 0.0840939 | ||||||||
\(352\) | −14.0001 | −0.746207 | ||||||||
\(353\) | −23.4421 | −1.24770 | −0.623848 | − | 0.781545i | \(-0.714432\pi\) | ||||
−0.623848 | + | 0.781545i | \(0.714432\pi\) | |||||||
\(354\) | −4.46231 | −0.237169 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −23.2909 | −1.23441 | ||||||||
\(357\) | 1.50799 | 0.0798111 | ||||||||
\(358\) | −5.43031 | −0.287001 | ||||||||
\(359\) | 8.20544 | 0.433066 | 0.216533 | − | 0.976275i | \(-0.430525\pi\) | ||||
0.216533 | + | 0.976275i | \(0.430525\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −14.0020 | −0.735930 | ||||||||
\(363\) | −0.121872 | −0.00639662 | ||||||||
\(364\) | 36.7131 | 1.92429 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.25843 | 0.118050 | ||||||||
\(367\) | −33.1494 | −1.73039 | −0.865193 | − | 0.501439i | \(-0.832804\pi\) | ||||
−0.865193 | + | 0.501439i | \(0.832804\pi\) | |||||||
\(368\) | −35.8538 | −1.86901 | ||||||||
\(369\) | 33.9865 | 1.76926 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.0618 | 0.989640 | ||||||||
\(372\) | −2.86107 | −0.148339 | ||||||||
\(373\) | 16.5840 | 0.858685 | 0.429343 | − | 0.903142i | \(-0.358745\pi\) | ||||
0.429343 | + | 0.903142i | \(0.358745\pi\) | |||||||
\(374\) | 9.74900 | 0.504109 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −46.6492 | −2.40575 | ||||||||
\(377\) | 15.5050 | 0.798550 | ||||||||
\(378\) | −6.52256 | −0.335484 | ||||||||
\(379\) | 5.79467 | 0.297652 | 0.148826 | − | 0.988863i | \(-0.452451\pi\) | ||||
0.148826 | + | 0.988863i | \(0.452451\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.439143 | −0.0224980 | ||||||||
\(382\) | 42.9730 | 2.19869 | ||||||||
\(383\) | −5.89016 | −0.300973 | −0.150487 | − | 0.988612i | \(-0.548084\pi\) | ||||
−0.150487 | + | 0.988612i | \(0.548084\pi\) | |||||||
\(384\) | 1.25553 | 0.0640709 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −53.2508 | −2.71039 | ||||||||
\(387\) | 28.0257 | 1.42463 | ||||||||
\(388\) | 20.6814 | 1.04994 | ||||||||
\(389\) | 13.8055 | 0.699964 | 0.349982 | − | 0.936756i | \(-0.386188\pi\) | ||||
0.349982 | + | 0.936756i | \(0.386188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.5868 | 0.585968 | ||||||||
\(392\) | −35.1581 | −1.77575 | ||||||||
\(393\) | −2.05649 | −0.103736 | ||||||||
\(394\) | −63.2784 | −3.18792 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −15.0613 | −0.756857 | ||||||||
\(397\) | −6.48471 | −0.325458 | −0.162729 | − | 0.986671i | \(-0.552030\pi\) | ||||
−0.162729 | + | 0.986671i | \(0.552030\pi\) | |||||||
\(398\) | 5.04835 | 0.253051 | ||||||||
\(399\) | 0.410573 | 0.0205544 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.70806 | 0.185172 | 0.0925858 | − | 0.995705i | \(-0.470487\pi\) | ||||
0.0925858 | + | 0.995705i | \(0.470487\pi\) | |||||||
\(402\) | 1.55705 | 0.0776584 | ||||||||
\(403\) | 10.0500 | 0.500628 | ||||||||
\(404\) | −54.8584 | −2.72931 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −64.1908 | −3.18573 | ||||||||
\(407\) | −2.27446 | −0.112741 | ||||||||
\(408\) | −3.61833 | −0.179134 | ||||||||
\(409\) | 31.0569 | 1.53567 | 0.767833 | − | 0.640650i | \(-0.221335\pi\) | ||||
0.767833 | + | 0.640650i | \(0.221335\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.744442 | −0.0367206 | ||||||||
\(412\) | −44.6954 | −2.20198 | ||||||||
\(413\) | −46.4717 | −2.28673 | ||||||||
\(414\) | −24.9962 | −1.22850 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −30.2392 | −1.48260 | ||||||||
\(417\) | −1.38138 | −0.0676467 | ||||||||
\(418\) | 2.65432 | 0.129827 | ||||||||
\(419\) | −11.2871 | −0.551410 | −0.275705 | − | 0.961242i | \(-0.588911\pi\) | ||||
−0.275705 | + | 0.961242i | \(0.588911\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | −17.2271 | −0.837611 | ||||||||
\(424\) | −45.7378 | −2.22122 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.93734 | 0.239215 | ||||||||
\(427\) | 23.5199 | 1.13821 | ||||||||
\(428\) | 91.6593 | 4.43052 | ||||||||
\(429\) | −0.263235 | −0.0127091 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.1654 | 0.874996 | 0.437498 | − | 0.899219i | \(-0.355865\pi\) | ||||
0.437498 | + | 0.899219i | \(0.355865\pi\) | |||||||
\(432\) | 8.29007 | 0.398856 | ||||||||
\(433\) | −10.7804 | −0.518075 | −0.259037 | − | 0.965867i | \(-0.583405\pi\) | ||||
−0.259037 | + | 0.965867i | \(0.583405\pi\) | |||||||
\(434\) | −41.6071 | −1.99720 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.06611 | −0.0510573 | ||||||||
\(437\) | 3.15468 | 0.150909 | ||||||||
\(438\) | 2.61638 | 0.125016 | ||||||||
\(439\) | −1.38742 | −0.0662180 | −0.0331090 | − | 0.999452i | \(-0.510541\pi\) | ||||
−0.0331090 | + | 0.999452i | \(0.510541\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.9836 | −0.618266 | ||||||||
\(442\) | 21.0571 | 1.00159 | ||||||||
\(443\) | 7.26792 | 0.345310 | 0.172655 | − | 0.984982i | \(-0.444766\pi\) | ||||
0.172655 | + | 0.984982i | \(0.444766\pi\) | |||||||
\(444\) | 1.39855 | 0.0663722 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 60.6441 | 2.87158 | ||||||||
\(447\) | −0.823487 | −0.0389496 | ||||||||
\(448\) | 48.6135 | 2.29677 | ||||||||
\(449\) | 21.4298 | 1.01134 | 0.505668 | − | 0.862728i | \(-0.331246\pi\) | ||||
0.505668 | + | 0.862728i | \(0.331246\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.3852 | −0.536108 | ||||||||
\(452\) | 1.00073 | 0.0470703 | ||||||||
\(453\) | −0.787575 | −0.0370035 | ||||||||
\(454\) | 10.6346 | 0.499108 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.985147 | −0.0461337 | ||||||||
\(457\) | 17.6312 | 0.824754 | 0.412377 | − | 0.911013i | \(-0.364699\pi\) | ||||
0.412377 | + | 0.911013i | \(0.364699\pi\) | |||||||
\(458\) | 65.3026 | 3.05139 | ||||||||
\(459\) | −2.67908 | −0.125049 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.2073 | 1.59320 | 0.796598 | − | 0.604510i | \(-0.206631\pi\) | ||||
0.796598 | + | 0.604510i | \(0.206631\pi\) | |||||||
\(462\) | 1.08979 | 0.0507017 | ||||||||
\(463\) | 11.0009 | 0.511253 | 0.255626 | − | 0.966776i | \(-0.417718\pi\) | ||||
0.255626 | + | 0.966776i | \(0.417718\pi\) | |||||||
\(464\) | 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 | \(0.532347\pi\) | |||||||
\(468\) | −32.5312 | −1.50376 | ||||||||
\(469\) | 16.2155 | 0.748764 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.0302708 | 0.00139481 | ||||||||
\(472\) | 111.506 | 5.13250 | ||||||||
\(473\) | −9.38838 | −0.431678 | ||||||||
\(474\) | 4.34415 | 0.199534 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −62.4294 | −2.86145 | ||||||||
\(477\) | −16.8905 | −0.773365 | ||||||||
\(478\) | 40.9249 | 1.87186 | ||||||||
\(479\) | −14.3683 | −0.656505 | −0.328253 | − | 0.944590i | \(-0.606460\pi\) | ||||
−0.328253 | + | 0.944590i | \(0.606460\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.91266 | −0.223998 | ||||||||
\(482\) | −64.0861 | −2.91904 | ||||||||
\(483\) | 1.29523 | 0.0589349 | ||||||||
\(484\) | 5.04540 | 0.229336 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.67657 | 0.393577 | ||||||||
\(487\) | −1.01712 | −0.0460899 | −0.0230449 | − | 0.999734i | \(-0.507336\pi\) | ||||
−0.0230449 | + | 0.999734i | \(0.507336\pi\) | |||||||
\(488\) | −56.4348 | −2.55468 | ||||||||
\(489\) | −2.06829 | −0.0935314 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.41045 | −0.108782 | −0.0543910 | − | 0.998520i | \(-0.517322\pi\) | ||||
−0.0543910 | + | 0.998520i | \(0.517322\pi\) | |||||||
\(492\) | 7.00067 | 0.315615 | ||||||||
\(493\) | −26.3658 | −1.18745 | ||||||||
\(494\) | 5.73313 | 0.257946 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 52.8820 | 2.37447 | ||||||||
\(497\) | 51.4189 | 2.30645 | ||||||||
\(498\) | −3.22409 | −0.144475 | ||||||||
\(499\) | 4.07426 | 0.182389 | 0.0911945 | − | 0.995833i | \(-0.470931\pi\) | ||||
0.0911945 | + | 0.995833i | \(0.470931\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.105485 | −0.00471272 | ||||||||
\(502\) | 52.8471 | 2.35868 | ||||||||
\(503\) | 19.9553 | 0.889762 | 0.444881 | − | 0.895590i | \(-0.353246\pi\) | ||||
0.444881 | + | 0.895590i | \(0.353246\pi\) | |||||||
\(504\) | 81.2923 | 3.62104 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.37352 | 0.372249 | ||||||||
\(507\) | 1.01577 | 0.0451118 | ||||||||
\(508\) | 18.1801 | 0.806613 | ||||||||
\(509\) | −8.79239 | −0.389716 | −0.194858 | − | 0.980831i | \(-0.562425\pi\) | ||||
−0.194858 | + | 0.980831i | \(0.562425\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.2478 | 1.20537 | ||||||||
\(512\) | 24.6266 | 1.08835 | ||||||||
\(513\) | −0.729422 | −0.0322048 | ||||||||
\(514\) | −59.2247 | −2.61229 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.77285 | 0.254135 | ||||||||
\(517\) | 5.77094 | 0.253806 | ||||||||
\(518\) | 20.3384 | 0.893618 | ||||||||
\(519\) | −0.505138 | −0.0221731 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.3483 | 1.19815 | 0.599075 | − | 0.800693i | \(-0.295535\pi\) | ||||
0.599075 | + | 0.800693i | \(0.295535\pi\) | |||||||
\(522\) | 56.8790 | 2.48953 | ||||||||
\(523\) | 41.7043 | 1.82360 | 0.911800 | − | 0.410634i | \(-0.134693\pi\) | ||||
0.911800 | + | 0.410634i | \(0.134693\pi\) | |||||||
\(524\) | 85.1368 | 3.71922 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 36.6197 | 1.59670 | ||||||||
\(527\) | −17.0897 | −0.744441 | ||||||||
\(528\) | −1.38511 | −0.0602790 | ||||||||
\(529\) | −13.0480 | −0.567304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 41.1783 | 1.78699 | ||||||||
\(532\) | −16.9974 | −0.736930 | ||||||||
\(533\) | −24.5912 | −1.06516 | ||||||||
\(534\) | −1.49330 | −0.0646214 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −38.9083 | −1.68058 | ||||||||
\(537\) | −0.249331 | −0.0107594 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | −0.642898 | −0.0275894 | ||||||||
\(544\) | 51.4207 | 2.20464 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.35387 | 0.100736 | ||||||||
\(547\) | −5.39396 | −0.230629 | −0.115315 | − | 0.993329i | \(-0.536788\pi\) | ||||
−0.115315 | + | 0.993329i | \(0.536788\pi\) | |||||||
\(548\) | 30.8193 | 1.31653 | ||||||||
\(549\) | −20.8409 | −0.889466 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.17849 | −0.305814 | ||||||||
\(552\) | −3.10783 | −0.132278 | ||||||||
\(553\) | 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 | \(0.202049\pi\) | |||||||
\(558\) | 36.8678 | 1.56074 | ||||||||
\(559\) | −20.2782 | −0.857677 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.447622 | 0.0188986 | ||||||||
\(562\) | −68.6404 | −2.89542 | ||||||||
\(563\) | 26.4313 | 1.11395 | 0.556973 | − | 0.830530i | \(-0.311963\pi\) | ||||
0.556973 | + | 0.830530i | \(0.311963\pi\) | |||||||
\(564\) | −3.54851 | −0.149419 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 76.6330 | 3.22112 | ||||||||
\(567\) | 29.8704 | 1.25444 | ||||||||
\(568\) | −123.377 | −5.17677 | ||||||||
\(569\) | 40.6105 | 1.70248 | 0.851239 | − | 0.524778i | \(-0.175852\pi\) | ||||
0.851239 | + | 0.524778i | \(0.175852\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 1.97309 | 0.0824271 | ||||||||
\(574\) | 101.807 | 4.24936 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −43.0761 | −1.79484 | ||||||||
\(577\) | −20.9771 | −0.873288 | −0.436644 | − | 0.899634i | \(-0.643833\pi\) | ||||
−0.436644 | + | 0.899634i | \(0.643833\pi\) | |||||||
\(578\) | 9.31648 | 0.387514 | ||||||||
\(579\) | −2.44499 | −0.101610 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.5766 | −1.39299 | ||||||||
\(582\) | 1.32600 | 0.0549643 | ||||||||
\(583\) | 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 | \(0.356261\pi\) | |||||||
\(588\) | −2.67441 | −0.110291 | ||||||||
\(589\) | −4.65295 | −0.191721 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.90540 | −0.119512 | ||||||||
\(592\) | −25.8498 | −1.06242 | ||||||||
\(593\) | −27.7731 | −1.14051 | −0.570253 | − | 0.821469i | \(-0.693155\pi\) | ||||
−0.570253 | + | 0.821469i | \(0.693155\pi\) | |||||||
\(594\) | −1.93612 | −0.0794399 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 34.0917 | 1.39645 | ||||||||
\(597\) | 0.231793 | 0.00948667 | ||||||||
\(598\) | 18.0862 | 0.739600 | ||||||||
\(599\) | 23.0129 | 0.940281 | 0.470140 | − | 0.882592i | \(-0.344203\pi\) | ||||
0.470140 | + | 0.882592i | \(0.344203\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | −14.3685 | −0.585129 | ||||||||
\(604\) | 32.6049 | 1.32668 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.51726 | −0.142879 | ||||||||
\(607\) | 3.22857 | 0.131044 | 0.0655218 | − | 0.997851i | \(-0.479129\pi\) | ||||
0.0655218 | + | 0.997851i | \(0.479129\pi\) | |||||||
\(608\) | 14.0001 | 0.567778 | ||||||||
\(609\) | −2.94730 | −0.119430 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.4648 | 0.504273 | ||||||||
\(612\) | 55.3182 | 2.23611 | ||||||||
\(613\) | 17.2202 | 0.695519 | 0.347759 | − | 0.937584i | \(-0.386943\pi\) | ||||
0.347759 | + | 0.937584i | \(0.386943\pi\) | |||||||
\(614\) | 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 | \(0.313443\pi\) | |||||||
\(618\) | −2.86565 | −0.115274 | ||||||||
\(619\) | −9.53870 | −0.383393 | −0.191696 | − | 0.981454i | \(-0.561399\pi\) | ||||
−0.191696 | + | 0.981454i | \(0.561399\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.30109 | −0.0923397 | ||||||||
\(622\) | 21.9306 | 0.879337 | ||||||||
\(623\) | −15.5517 | −0.623064 | ||||||||
\(624\) | −2.99173 | −0.119765 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −64.0133 | −2.55848 | ||||||||
\(627\) | 0.121872 | 0.00486710 | ||||||||
\(628\) | −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 | ||||||||
\(633\) | −1.49962 | −0.0596044 | ||||||||
\(634\) | −31.1430 | −1.23685 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.47919 | −0.137959 | ||||||||
\(637\) | 9.39438 | 0.372219 | ||||||||
\(638\) | −19.0540 | −0.754355 | ||||||||
\(639\) | −45.5619 | −1.80240 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.0249 | 0.395960 | 0.197980 | − | 0.980206i | \(-0.436562\pi\) | ||||
0.197980 | + | 0.980206i | \(0.436562\pi\) | |||||||
\(642\) | 5.87676 | 0.231937 | ||||||||
\(643\) | 40.7197 | 1.60583 | 0.802915 | − | 0.596094i | \(-0.203281\pi\) | ||||
0.802915 | + | 0.596094i | \(0.203281\pi\) | |||||||
\(644\) | −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 | \(0.393891\pi\) | |||||||
\(648\) | −71.6723 | −2.81555 | ||||||||
\(649\) | −13.7944 | −0.541477 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.91038 | −0.0748735 | ||||||||
\(652\) | 85.6256 | 3.35336 | ||||||||
\(653\) | 34.7416 | 1.35954 | 0.679771 | − | 0.733424i | \(-0.262079\pi\) | ||||
0.679771 | + | 0.733424i | \(0.262079\pi\) | |||||||
\(654\) | −0.0683538 | −0.00267285 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −129.396 | −5.05205 | ||||||||
\(657\) | −24.1441 | −0.941949 | ||||||||
\(658\) | −51.6043 | −2.01175 | ||||||||
\(659\) | −22.9537 | −0.894148 | −0.447074 | − | 0.894497i | \(-0.647534\pi\) | ||||
−0.447074 | + | 0.894497i | \(0.647534\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 0.966831 | 0.0375486 | ||||||||
\(664\) | 80.5651 | 3.12653 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −18.0217 | −0.698328 | ||||||||
\(667\) | −22.6459 | −0.876851 | ||||||||
\(668\) | 4.36698 | 0.168964 | ||||||||
\(669\) | 2.78445 | 0.107653 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.98152 | 0.269518 | ||||||||
\(672\) | 5.74806 | 0.221736 | ||||||||
\(673\) | −20.9448 | −0.807364 | −0.403682 | − | 0.914899i | \(-0.632270\pi\) | ||||
−0.403682 | + | 0.914899i | \(0.632270\pi\) | |||||||
\(674\) | 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 | \(0.570398\pi\) | |||||||
\(678\) | 0.0641619 | 0.00246412 | ||||||||
\(679\) | 13.8093 | 0.529952 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.488285 | 0.0187111 | ||||||||
\(682\) | −12.3504 | −0.472921 | ||||||||
\(683\) | 34.9550 | 1.33752 | 0.668759 | − | 0.743479i | \(-0.266826\pi\) | ||||
0.668759 | + | 0.743479i | \(0.266826\pi\) | |||||||
\(684\) | 15.0613 | 0.575882 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 23.7020 | 0.904945 | ||||||||
\(687\) | 2.99835 | 0.114394 | ||||||||
\(688\) | −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 | ||||||||
\(693\) | −10.0566 | −0.382019 | ||||||||
\(694\) | −45.7020 | −1.73483 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.07187 | 0.268059 | ||||||||
\(697\) | 41.8165 | 1.58391 | ||||||||
\(698\) | −11.4774 | −0.434426 | ||||||||
\(699\) | 1.98644 | 0.0751339 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.5830 | −0.701869 | −0.350935 | − | 0.936400i | \(-0.614136\pi\) | ||||
−0.350935 | + | 0.936400i | \(0.614136\pi\) | |||||||
\(702\) | −4.18188 | −0.157835 | ||||||||
\(703\) | 2.27446 | 0.0857828 | ||||||||
\(704\) | 14.4301 | 0.543857 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 62.2228 | 2.34178 | ||||||||
\(707\) | −36.6298 | −1.37760 | ||||||||
\(708\) | 8.48208 | 0.318776 | ||||||||
\(709\) | 23.8063 | 0.894064 | 0.447032 | − | 0.894518i | \(-0.352481\pi\) | ||||
0.447032 | + | 0.894518i | \(0.352481\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −40.0880 | −1.50342 | ||||||||
\(712\) | 37.3153 | 1.39845 | ||||||||
\(713\) | −14.6786 | −0.549717 | ||||||||
\(714\) | −4.00267 | −0.149796 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.3221 | 0.385755 | ||||||||
\(717\) | 1.87905 | 0.0701745 | ||||||||
\(718\) | −21.7798 | −0.812816 | ||||||||
\(719\) | 37.0144 | 1.38040 | 0.690202 | − | 0.723616i | \(-0.257522\pi\) | ||||
0.690202 | + | 0.723616i | \(0.257522\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.8437 | −1.11144 | ||||||||
\(722\) | −2.65432 | −0.0987835 | ||||||||
\(723\) | −2.94249 | −0.109432 | ||||||||
\(724\) | 26.6154 | 0.989154 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.323487 | 0.0120057 | ||||||||
\(727\) | 22.0744 | 0.818694 | 0.409347 | − | 0.912379i | \(-0.365757\pi\) | ||||
0.409347 | + | 0.912379i | \(0.365757\pi\) | |||||||
\(728\) | −58.8197 | −2.18000 | ||||||||
\(729\) | −26.2013 | −0.970417 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.4824 | 1.27538 | ||||||||
\(732\) | −4.29289 | −0.158670 | ||||||||
\(733\) | 18.7090 | 0.691031 | 0.345515 | − | 0.938413i | \(-0.387704\pi\) | ||||
0.345515 | + | 0.938413i | \(0.387704\pi\) | |||||||
\(734\) | 87.9891 | 3.24774 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 44.1658 | 1.62797 | ||||||||
\(737\) | 4.81332 | 0.177301 | ||||||||
\(738\) | −90.2109 | −3.32071 | ||||||||
\(739\) | −5.91630 | −0.217635 | −0.108817 | − | 0.994062i | \(-0.534706\pi\) | ||||
−0.108817 | + | 0.994062i | \(0.534706\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.263235 | 0.00967017 | ||||||||
\(742\) | −50.5961 | −1.85744 | ||||||||
\(743\) | −14.0422 | −0.515159 | −0.257579 | − | 0.966257i | \(-0.582925\pi\) | ||||
−0.257579 | + | 0.966257i | \(0.582925\pi\) | |||||||
\(744\) | 4.58384 | 0.168052 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −44.0191 | −1.61165 | ||||||||
\(747\) | 29.7520 | 1.08857 | ||||||||
\(748\) | −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 | ||||||||
\(753\) | 2.42646 | 0.0884250 | ||||||||
\(754\) | −41.1553 | −1.49879 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 12.3983 | 0.450920 | ||||||||
\(757\) | −49.2829 | −1.79122 | −0.895609 | − | 0.444843i | \(-0.853259\pi\) | ||||
−0.895609 | + | 0.444843i | \(0.853259\pi\) | |||||||
\(758\) | −15.3809 | −0.558659 | ||||||||
\(759\) | 0.384467 | 0.0139553 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.25922 | −0.263146 | −0.131573 | − | 0.991306i | \(-0.542003\pi\) | ||||
−0.131573 | + | 0.991306i | \(0.542003\pi\) | |||||||
\(762\) | 1.16562 | 0.0422261 | ||||||||
\(763\) | −0.711856 | −0.0257709 | ||||||||
\(764\) | −81.6843 | −2.95524 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.6344 | 0.564892 | ||||||||
\(767\) | −29.7949 | −1.07583 | ||||||||
\(768\) | 0.184693 | 0.00666453 | ||||||||
\(769\) | −21.5123 | −0.775755 | −0.387877 | − | 0.921711i | \(-0.626792\pi\) | ||||
−0.387877 | + | 0.921711i | \(0.626792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.71928 | −0.0979325 | ||||||||
\(772\) | 101.221 | 3.64301 | ||||||||
\(773\) | −4.54038 | −0.163306 | −0.0816530 | − | 0.996661i | \(-0.526020\pi\) | ||||
−0.0816530 | + | 0.996661i | \(0.526020\pi\) | |||||||
\(774\) | −74.3891 | −2.67386 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −33.1346 | −1.18946 | ||||||||
\(777\) | 0.933831 | 0.0335010 | ||||||||
\(778\) | −36.6440 | −1.31375 | ||||||||
\(779\) | 11.3852 | 0.407917 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.2629 | 0.546149 | ||||||||
\(782\) | −30.7550 | −1.09980 | ||||||||
\(783\) | 5.23615 | 0.187125 | ||||||||
\(784\) | 49.4320 | 1.76543 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.45856 | 0.194701 | ||||||||
\(787\) | 7.25028 | 0.258444 | 0.129222 | − | 0.991616i | \(-0.458752\pi\) | ||||
0.129222 | + | 0.991616i | \(0.458752\pi\) | |||||||
\(788\) | 120.281 | 4.28484 | ||||||||
\(789\) | 1.68138 | 0.0598588 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.668201 | 0.0237585 | ||||||||
\(792\) | 24.1303 | 0.857433 | ||||||||
\(793\) | 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 | \(0.608452\pi\) | |||||||
\(798\) | −1.08979 | −0.0385782 | ||||||||
\(799\) | −21.1960 | −0.749860 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.7802 | 0.486900 | ||||||||
\(802\) | −9.84236 | −0.347546 | ||||||||
\(803\) | 8.08806 | 0.285422 | ||||||||
\(804\) | −2.95968 | −0.104380 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −26.6760 | −0.939622 | ||||||||
\(807\) | 1.36531 | 0.0480612 | ||||||||
\(808\) | 87.8911 | 3.09200 | ||||||||
\(809\) | −19.4948 | −0.685399 | −0.342700 | − | 0.939445i | \(-0.611341\pi\) | ||||
−0.342700 | + | 0.939445i | \(0.611341\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | −2.08686 | −0.0731893 | ||||||||
\(814\) | 6.03713 | 0.211601 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.08734 | 0.178092 | ||||||||
\(817\) | 9.38838 | 0.328458 | ||||||||
\(818\) | −82.4350 | −2.88227 | ||||||||
\(819\) | −21.7216 | −0.759014 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.37419 | 0.187561 | 0.0937803 | − | 0.995593i | \(-0.470105\pi\) | ||||
0.0937803 | + | 0.995593i | \(0.470105\pi\) | |||||||
\(822\) | 1.97598 | 0.0689204 | ||||||||
\(823\) | −26.3196 | −0.917445 | −0.458723 | − | 0.888580i | \(-0.651693\pi\) | ||||
−0.458723 | + | 0.888580i | \(0.651693\pi\) | |||||||
\(824\) | 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 | \(0.454956\pi\) | |||||||
\(828\) | 47.5135 | 1.65121 | ||||||||
\(829\) | −21.5948 | −0.750017 | −0.375009 | − | 0.927021i | \(-0.622360\pi\) | ||||
−0.375009 | + | 0.927021i | \(0.622360\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.67120 | −0.0579733 | ||||||||
\(832\) | 31.1681 | 1.08056 | ||||||||
\(833\) | −15.9748 | −0.553495 | ||||||||
\(834\) | 3.66663 | 0.126965 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.04540 | −0.174499 | ||||||||
\(837\) | 3.39396 | 0.117313 | ||||||||
\(838\) | 29.9595 | 1.03493 | ||||||||
\(839\) | −4.35109 | −0.150216 | −0.0751082 | − | 0.997175i | \(-0.523930\pi\) | ||||
−0.0751082 | + | 0.997175i | \(0.523930\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.5308 | 0.776923 | ||||||||
\(842\) | −91.6254 | −3.15762 | ||||||||
\(843\) | −3.15160 | −0.108547 | ||||||||
\(844\) | 62.0828 | 2.13698 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 45.7262 | 1.57210 | ||||||||
\(847\) | 3.36889 | 0.115756 | ||||||||
\(848\) | 64.3069 | 2.20831 | ||||||||
\(849\) | 3.51858 | 0.120757 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.17519 | 0.245962 | ||||||||
\(852\) | −9.38504 | −0.321526 | ||||||||
\(853\) | −19.5022 | −0.667744 | −0.333872 | − | 0.942618i | \(-0.608355\pi\) | ||||
−0.333872 | + | 0.942618i | \(0.608355\pi\) | |||||||
\(854\) | −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 | \(0.573202\pi\) | |||||||
\(858\) | 0.698709 | 0.0238535 | ||||||||
\(859\) | 21.6016 | 0.737036 | 0.368518 | − | 0.929621i | \(-0.379865\pi\) | ||||
0.368518 | + | 0.929621i | \(0.379865\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.67445 | 0.159305 | ||||||||
\(862\) | −48.2167 | −1.64227 | ||||||||
\(863\) | 2.72425 | 0.0927345 | 0.0463673 | − | 0.998924i | \(-0.485236\pi\) | ||||
0.0463673 | + | 0.998924i | \(0.485236\pi\) | |||||||
\(864\) | −10.2120 | −0.347418 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 28.6147 | 0.972367 | ||||||||
\(867\) | 0.427763 | 0.0145276 | ||||||||
\(868\) | 79.0879 | 2.68442 | ||||||||
\(869\) | 13.4291 | 0.455552 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.3964 | 0.352269 | ||||||||
\(872\) | 1.70806 | 0.0578422 | ||||||||
\(873\) | −12.2363 | −0.414137 | ||||||||
\(874\) | −8.37352 | −0.283239 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.97329 | −0.168032 | ||||||||
\(877\) | −1.29130 | −0.0436041 | −0.0218021 | − | 0.999762i | \(-0.506940\pi\) | ||||
−0.0218021 | + | 0.999762i | \(0.506940\pi\) | |||||||
\(878\) | 3.68266 | 0.124284 | ||||||||
\(879\) | 0.777508 | 0.0262247 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.9873 | 0.841844 | 0.420922 | − | 0.907097i | \(-0.361707\pi\) | ||||
0.420922 | + | 0.907097i | \(0.361707\pi\) | |||||||
\(882\) | 34.4626 | 1.16041 | ||||||||
\(883\) | −15.5046 | −0.521772 | −0.260886 | − | 0.965370i | \(-0.584015\pi\) | ||||
−0.260886 | + | 0.965370i | \(0.584015\pi\) | |||||||
\(884\) | −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 | \(0.446414\pi\) | |||||||
\(888\) | −2.24068 | −0.0751921 | ||||||||
\(889\) | 12.1391 | 0.407134 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.86655 | 0.297040 | ||||||||
\(892\) | −115.274 | −3.85966 | ||||||||
\(893\) | −5.77094 | −0.193117 | ||||||||
\(894\) | 2.18580 | 0.0731040 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −34.7063 | −1.15946 | ||||||||
\(897\) | 0.830422 | 0.0277270 | ||||||||
\(898\) | −56.8815 | −1.89816 | ||||||||
\(899\) | 33.4012 | 1.11399 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.7819 | −0.692345 | ||||||||
\(902\) | 30.2199 | 1.00621 | ||||||||
\(903\) | 3.85461 | 0.128274 | ||||||||
\(904\) | −1.60331 | −0.0533253 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.09047 | 0.0694513 | ||||||||
\(907\) | −11.8887 | −0.394758 | −0.197379 | − | 0.980327i | \(-0.563243\pi\) | ||||
−0.197379 | + | 0.980327i | \(0.563243\pi\) | |||||||
\(908\) | −20.2146 | −0.670845 | ||||||||
\(909\) | 32.4574 | 1.07654 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.7166 | −0.785767 | −0.392883 | − | 0.919588i | \(-0.628522\pi\) | ||||
−0.392883 | + | 0.919588i | \(0.628522\pi\) | |||||||
\(912\) | 1.38511 | 0.0458655 | ||||||||
\(913\) | −9.96666 | −0.329848 | ||||||||
\(914\) | −46.7989 | −1.54797 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −124.129 | −4.10134 | ||||||||
\(917\) | 56.8471 | 1.87726 | ||||||||
\(918\) | 7.11113 | 0.234702 | ||||||||
\(919\) | 18.1426 | 0.598470 | 0.299235 | − | 0.954179i | \(-0.403269\pi\) | ||||
0.299235 | + | 0.954179i | \(0.403269\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.27111 | 0.0418845 | ||||||||
\(922\) | −90.7972 | −2.99024 | ||||||||
\(923\) | 32.9667 | 1.08511 | ||||||||
\(924\) | −2.07150 | −0.0681475 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −29.1997 | −0.959563 | ||||||||
\(927\) | 26.4443 | 0.868546 | ||||||||
\(928\) | −100.500 | −3.29906 | ||||||||
\(929\) | −50.5019 | −1.65691 | −0.828457 | − | 0.560053i | \(-0.810781\pi\) | ||||
−0.828457 | + | 0.560053i | \(0.810781\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.34940 | −0.142546 | ||||||||
\(932\) | −82.2368 | −2.69376 | ||||||||
\(933\) | 1.00694 | 0.0329656 | ||||||||
\(934\) | 11.6379 | 0.380805 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 52.1197 | 1.70359 | ||||||||
\(937\) | 39.6587 | 1.29559 | 0.647797 | − | 0.761813i | \(-0.275691\pi\) | ||||
0.647797 | + | 0.761813i | \(0.275691\pi\) | |||||||
\(938\) | −43.0412 | −1.40534 | ||||||||
\(939\) | −2.93915 | −0.0959154 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.8809 | −1.13709 | −0.568543 | − | 0.822653i | \(-0.692493\pi\) | ||||
−0.568543 | + | 0.822653i | \(0.692493\pi\) | |||||||
\(942\) | −0.0803484 | −0.00261789 | ||||||||
\(943\) | 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 | \(0.336113\pi\) | |||||||
\(948\) | −8.25748 | −0.268191 | ||||||||
\(949\) | 17.4696 | 0.567088 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.42992 | −0.0463684 | ||||||||
\(952\) | 100.021 | 3.24169 | ||||||||
\(953\) | 6.65804 | 0.215675 | 0.107838 | − | 0.994169i | \(-0.465607\pi\) | ||||
0.107838 | + | 0.994169i | \(0.465607\pi\) | |||||||
\(954\) | 44.8329 | 1.45152 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −77.7912 | −2.51595 | ||||||||
\(957\) | −0.874858 | −0.0282801 | ||||||||
\(958\) | 38.1381 | 1.23219 | ||||||||
\(959\) | 20.5785 | 0.664513 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.35006 | −0.301615 | ||||||||
\(962\) | 13.0398 | 0.420419 | ||||||||
\(963\) | −54.2309 | −1.74757 | ||||||||
\(964\) | 121.817 | 3.92345 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.43794 | −0.110614 | ||||||||
\(967\) | 20.0020 | 0.643221 | 0.321611 | − | 0.946872i | \(-0.395776\pi\) | ||||
0.321611 | + | 0.946872i | \(0.395776\pi\) | |||||||
\(968\) | −8.08346 | −0.259812 | ||||||||
\(969\) | −0.447622 | −0.0143797 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.491941 | −0.0157871 | −0.00789357 | − | 0.999969i | \(-0.502513\pi\) | ||||
−0.00789357 | + | 0.999969i | \(0.502513\pi\) | |||||||
\(972\) | −16.4927 | −0.529002 | ||||||||
\(973\) | 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 | \(0.623505\pi\) | |||||||
\(978\) | 5.48991 | 0.175548 | ||||||||
\(979\) | −4.61626 | −0.147536 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.630771 | 0.0201390 | ||||||||
\(982\) | 6.39809 | 0.204171 | ||||||||
\(983\) | −39.5609 | −1.26180 | −0.630899 | − | 0.775865i | \(-0.717314\pi\) | ||||
−0.630899 | + | 0.775865i | \(0.717314\pi\) | |||||||
\(984\) | −11.2161 | −0.357556 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 69.9831 | 2.22872 | ||||||||
\(987\) | −2.36939 | −0.0754186 | ||||||||
\(988\) | −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 | ||||||||
\(993\) | 0.847283 | 0.0268877 | ||||||||
\(994\) | −136.482 | −4.32895 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.12843 | 0.194187 | ||||||||
\(997\) | −41.1821 | −1.30425 | −0.652125 | − | 0.758111i | \(-0.726122\pi\) | ||||
−0.652125 | + | 0.758111i | \(0.726122\pi\) | |||||||
\(998\) | −10.8144 | −0.342323 | ||||||||
\(999\) | −1.65904 | −0.0524897 |
(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 | 5225.2.a.h.1.1 | 5 | ||
5.4 | even | 2 | 209.2.a.c.1.5 | ✓ | 5 | ||
15.14 | odd | 2 | 1881.2.a.k.1.1 | 5 | |||
20.19 | odd | 2 | 3344.2.a.t.1.3 | 5 | |||
55.54 | odd | 2 | 2299.2.a.n.1.1 | 5 | |||
95.94 | odd | 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 | 5.4 | even | 2 | ||
1881.2.a.k.1.1 | 5 | 15.14 | odd | 2 | |||
2299.2.a.n.1.1 | 5 | 55.54 | odd | 2 | |||
3344.2.a.t.1.3 | 5 | 20.19 | odd | 2 | |||
3971.2.a.h.1.1 | 5 | 95.94 | odd | 2 | |||
5225.2.a.h.1.1 | 5 | 1.1 | even | 1 | trivial |