Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2008,2,Mod(1,2008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2008, 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("2008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2008 = 2^{3} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2008.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: | \(16.0339607259\) |
Analytic rank: | \(0\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 2008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.15136 | 1.81944 | 0.909720 | − | 0.415222i | \(-0.136296\pi\) | ||||
0.909720 | + | 0.415222i | \(0.136296\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.04418 | 1.80861 | 0.904306 | − | 0.426885i | \(-0.140389\pi\) | ||||
0.904306 | + | 0.426885i | \(0.140389\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.52087 | 1.33076 | 0.665381 | − | 0.746504i | \(-0.268269\pi\) | ||||
0.665381 | + | 0.746504i | \(0.268269\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.93109 | 2.31036 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.53748 | −1.66961 | −0.834806 | − | 0.550544i | \(-0.814420\pi\) | ||||
−0.834806 | + | 0.550544i | \(0.814420\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.479348 | 0.132947 | 0.0664735 | − | 0.997788i | \(-0.478825\pi\) | ||||
0.0664735 | + | 0.997788i | \(0.478825\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 12.7447 | 3.29066 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.91995 | −1.92087 | −0.960435 | − | 0.278503i | \(-0.910162\pi\) | ||||
−0.960435 | + | 0.278503i | \(0.910162\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.32818 | −1.22237 | −0.611184 | − | 0.791489i | \(-0.709306\pi\) | ||||
−0.611184 | + | 0.791489i | \(0.709306\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.0955 | 2.42124 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.98503 | −0.830936 | −0.415468 | − | 0.909608i | \(-0.636382\pi\) | ||||
−0.415468 | + | 0.909608i | \(0.636382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.3554 | 2.27108 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12.3883 | 2.38413 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.58479 | 0.851375 | 0.425687 | − | 0.904870i | \(-0.360032\pi\) | ||||
0.425687 | + | 0.904870i | \(0.360032\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0567383 | −0.0101905 | −0.00509525 | − | 0.999987i | \(-0.501622\pi\) | ||||
−0.00509525 | + | 0.999987i | \(0.501622\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −17.4506 | −3.03776 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14.2390 | 2.40683 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.74446 | −0.286787 | −0.143394 | − | 0.989666i | \(-0.545802\pi\) | ||||
−0.143394 | + | 0.989666i | \(0.545802\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.51060 | 0.241889 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.51530 | 0.705171 | 0.352586 | − | 0.935780i | \(-0.385303\pi\) | ||||
0.352586 | + | 0.935780i | \(0.385303\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.5560 | −1.76227 | −0.881135 | − | 0.472864i | \(-0.843220\pi\) | ||||
−0.881135 | + | 0.472864i | \(0.843220\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 28.0306 | 4.17855 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.2736 | 1.64442 | 0.822212 | − | 0.569181i | \(-0.192740\pi\) | ||||
0.822212 | + | 0.569181i | \(0.192740\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.39651 | 0.770929 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −24.9586 | −3.49491 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.14986 | 0.570027 | 0.285014 | − | 0.958523i | \(-0.408002\pi\) | ||||
0.285014 | + | 0.958523i | \(0.408002\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −22.3946 | −3.01968 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.7910 | −2.22403 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.02416 | −0.523901 | −0.261951 | − | 0.965081i | \(-0.584366\pi\) | ||||
−0.261951 | + | 0.965081i | \(0.584366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.3346 | −1.57929 | −0.789643 | − | 0.613566i | \(-0.789734\pi\) | ||||
−0.789643 | + | 0.613566i | \(0.789734\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 24.4034 | 3.07455 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.93857 | 0.240450 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.97615 | −0.730103 | −0.365051 | − | 0.930987i | \(-0.618949\pi\) | ||||
−0.365051 | + | 0.930987i | \(0.618949\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.5583 | −1.51184 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.10917 | 0.606347 | 0.303173 | − | 0.952935i | \(-0.401954\pi\) | ||||
0.303173 | + | 0.952935i | \(0.401954\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.78681 | 0.326171 | 0.163086 | − | 0.986612i | \(-0.447855\pi\) | ||||
0.163086 | + | 0.986612i | \(0.447855\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 35.7849 | 4.13209 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −19.4967 | −2.22186 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.61228 | −0.293904 | −0.146952 | − | 0.989144i | \(-0.546946\pi\) | ||||
−0.146952 | + | 0.989144i | \(0.546946\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 18.2467 | 2.02742 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.48896 | 0.163435 | 0.0817173 | − | 0.996656i | \(-0.473960\pi\) | ||||
0.0817173 | + | 0.996656i | \(0.473960\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −32.0297 | −3.47411 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.4483 | 1.54903 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.81110 | −0.721976 | −0.360988 | − | 0.932571i | \(-0.617560\pi\) | ||||
−0.360988 | + | 0.932571i | \(0.617560\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.68772 | 0.176921 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.178803 | −0.0185410 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −21.5481 | −2.21079 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.45770 | −0.554145 | −0.277072 | − | 0.960849i | \(-0.589364\pi\) | ||||
−0.277072 | + | 0.960849i | \(0.589364\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −38.3808 | −3.85741 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.79407 | 0.178517 | 0.0892585 | − | 0.996008i | \(-0.471550\pi\) | ||||
0.0892585 | + | 0.996008i | \(0.471550\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.62771 | 0.751581 | 0.375790 | − | 0.926705i | \(-0.377371\pi\) | ||||
0.375790 | + | 0.926705i | \(0.377371\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 44.8723 | 4.37909 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.94989 | 0.671872 | 0.335936 | − | 0.941885i | \(-0.390947\pi\) | ||||
0.335936 | + | 0.941885i | \(0.390947\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.2310 | −1.26730 | −0.633650 | − | 0.773620i | \(-0.718444\pi\) | ||||
−0.633650 | + | 0.773620i | \(0.718444\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.49743 | −0.521793 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.5091 | 1.55304 | 0.776521 | − | 0.630092i | \(-0.216983\pi\) | ||||
0.776521 | + | 0.630092i | \(0.216983\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.1162 | −1.50284 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.32240 | 0.307156 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −27.8851 | −2.55622 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.6637 | 1.78761 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.2293 | 1.28302 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 25.7023 | 2.29888 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.48799 | 0.132037 | 0.0660187 | − | 0.997818i | \(-0.478970\pi\) | ||||
0.0660187 | + | 0.997818i | \(0.478970\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −36.4171 | −3.20635 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.69420 | 0.148023 | 0.0740116 | − | 0.997257i | \(-0.476420\pi\) | ||||
0.0740116 | + | 0.997257i | \(0.476420\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.7598 | −1.62668 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 50.1005 | 4.31196 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.76601 | 0.834367 | 0.417183 | − | 0.908822i | \(-0.363017\pi\) | ||||
0.417183 | + | 0.908822i | \(0.363017\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.40302 | 0.627916 | 0.313958 | − | 0.949437i | \(-0.398345\pi\) | ||||
0.313958 | + | 0.949437i | \(0.398345\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 35.5272 | 2.99193 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.65438 | −0.221970 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.5417 | 1.53981 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.0063 | 1.40266 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.2514 | 1.08560 | 0.542801 | − | 0.839862i | \(-0.317364\pi\) | ||||
0.542801 | + | 0.839862i | \(0.317364\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.04285 | −0.491760 | −0.245880 | − | 0.969300i | \(-0.579077\pi\) | ||||
−0.245880 | + | 0.969300i | \(0.579077\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −54.8939 | −4.43791 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.229460 | −0.0184307 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.09159 | 0.486162 | 0.243081 | − | 0.970006i | \(-0.421842\pi\) | ||||
0.243081 | + | 0.970006i | \(0.421842\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.0777 | 1.03713 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.0308 | −1.10578 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.28142 | −0.257021 | −0.128510 | − | 0.991708i | \(-0.541020\pi\) | ||||
−0.128510 | + | 0.991708i | \(0.541020\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −70.5734 | −5.49413 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.80322 | −0.603832 | −0.301916 | − | 0.953335i | \(-0.597626\pi\) | ||||
−0.301916 | + | 0.953335i | \(0.597626\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7702 | −0.982325 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −36.9301 | −2.82411 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.64285 | −0.657104 | −0.328552 | − | 0.944486i | \(-0.606561\pi\) | ||||
−0.328552 | + | 0.944486i | \(0.606561\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 39.9808 | 3.02226 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.6816 | −0.953207 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.5814 | −1.16461 | −0.582306 | − | 0.812970i | \(-0.697849\pi\) | ||||
−0.582306 | + | 0.812970i | \(0.697849\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.2473 | 0.836008 | 0.418004 | − | 0.908445i | \(-0.362730\pi\) | ||||
0.418004 | + | 0.908445i | \(0.362730\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −38.8709 | −2.87342 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.05491 | −0.518687 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 43.8566 | 3.20711 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 43.6175 | 3.17271 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.81146 | −0.131073 | −0.0655364 | − | 0.997850i | \(-0.520876\pi\) | ||||
−0.0655364 | + | 0.997850i | \(0.520876\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.19667 | 0.661991 | 0.330995 | − | 0.943632i | \(-0.392616\pi\) | ||||
0.330995 | + | 0.943632i | \(0.392616\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.10913 | 0.437484 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.9081 | 0.777169 | 0.388585 | − | 0.921413i | \(-0.372964\pi\) | ||||
0.388585 | + | 0.921413i | \(0.372964\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.1164 | 0.788023 | 0.394012 | − | 0.919105i | \(-0.371087\pi\) | ||||
0.394012 | + | 0.919105i | \(0.371087\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.8330 | −1.32838 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.1424 | 1.13298 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.2607 | 1.27538 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −27.6206 | −1.91976 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 29.5047 | 2.04088 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.5194 | 0.861868 | 0.430934 | − | 0.902383i | \(-0.358184\pi\) | ||||
0.430934 | + | 0.902383i | \(0.358184\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.1008 | 1.10321 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −46.7345 | −3.18726 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.199768 | −0.0135611 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.78225 | 0.593449 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.79641 | −0.255374 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.9011 | −0.863924 | −0.431962 | − | 0.901892i | \(-0.642179\pi\) | ||||
−0.431962 | + | 0.901892i | \(0.642179\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 78.7051 | 5.24701 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.4519 | −0.826463 | −0.413231 | − | 0.910626i | \(-0.635600\pi\) | ||||
−0.413231 | + | 0.910626i | \(0.635600\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.6207 | −0.701834 | −0.350917 | − | 0.936407i | \(-0.614130\pi\) | ||||
−0.350917 | + | 0.936407i | \(0.614130\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −61.4413 | −4.04254 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.6738 | 1.28887 | 0.644436 | − | 0.764658i | \(-0.277092\pi\) | ||||
0.644436 | + | 0.764658i | \(0.277092\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 45.5925 | 2.97412 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.23223 | −0.534741 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.8440 | 1.67171 | 0.835855 | − | 0.548951i | \(-0.184972\pi\) | ||||
0.835855 | + | 0.548951i | \(0.184972\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3953 | 0.669618 | 0.334809 | − | 0.942286i | \(-0.391328\pi\) | ||||
0.334809 | + | 0.942286i | \(0.391328\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.3372 | 1.30463 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.8244 | 1.39431 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.55405 | −0.162510 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.69225 | 0.297359 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.0670 | 1.38734 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −100.937 | −6.32093 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.1531 | −1.31949 | −0.659746 | − | 0.751489i | \(-0.729336\pi\) | ||||
−0.659746 | + | 0.751489i | \(0.729336\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.14201 | −0.381646 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 31.7776 | 1.96699 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.8106 | −1.46822 | −0.734112 | − | 0.679028i | \(-0.762401\pi\) | ||||
−0.734112 | + | 0.679028i | \(0.762401\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.7828 | 1.03096 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.4643 | −1.31359 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.2857 | 1.05392 | 0.526962 | − | 0.849889i | \(-0.323331\pi\) | ||||
0.526962 | + | 0.849889i | \(0.323331\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.7163 | −1.74439 | −0.872194 | − | 0.489159i | \(-0.837304\pi\) | ||||
−0.872194 | + | 0.489159i | \(0.837304\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.31862 | 0.321897 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −62.8802 | −3.79182 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.14989 | −0.489679 | −0.244840 | − | 0.969564i | \(-0.578735\pi\) | ||||
−0.244840 | + | 0.969564i | \(0.578735\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.393259 | −0.0235438 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.1216 | 1.73725 | 0.868626 | − | 0.495469i | \(-0.165004\pi\) | ||||
0.868626 | + | 0.495469i | \(0.165004\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.474087 | −0.0281816 | −0.0140908 | − | 0.999901i | \(-0.504485\pi\) | ||||
−0.0140908 | + | 0.999901i | \(0.504485\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −67.9059 | −4.02240 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.8978 | 0.938416 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 45.7256 | 2.68974 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.1992 | −1.00823 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.8082 | 1.68299 | 0.841497 | − | 0.540261i | \(-0.181675\pi\) | ||||
0.841497 | + | 0.540261i | \(0.181675\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.2744 | −0.947533 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −68.5999 | −3.98057 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.91021 | −0.110470 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −40.6871 | −2.34516 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.65378 | 0.324801 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −49.8834 | −2.85632 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.9035 | −1.53546 | −0.767732 | − | 0.640771i | \(-0.778615\pi\) | ||||
−0.767732 | + | 0.640771i | \(0.778615\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.0377 | 1.36746 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.0223 | 0.908540 | 0.454270 | − | 0.890864i | \(-0.349900\pi\) | ||||
0.454270 | + | 0.890864i | \(0.349900\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.1881 | −0.915004 | −0.457502 | − | 0.889209i | \(-0.651256\pi\) | ||||
−0.457502 | + | 0.889209i | \(0.651256\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 98.6919 | 5.56066 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.76329 | 0.211367 | 0.105684 | − | 0.994400i | \(-0.466297\pi\) | ||||
0.105684 | + | 0.994400i | \(0.466297\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.3882 | −1.42147 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.9016 | 1.22243 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.1989 | 2.34801 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.44317 | 0.301933 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −41.6957 | −2.30578 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 39.6929 | 2.18834 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.1622 | 1.43800 | 0.719001 | − | 0.695009i | \(-0.244599\pi\) | ||||
0.719001 | + | 0.695009i | \(0.244599\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.0910 | −0.662583 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −24.1686 | −1.32047 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.6236 | 0.851070 | 0.425535 | − | 0.904942i | \(-0.360086\pi\) | ||||
0.425535 | + | 0.904942i | \(0.360086\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 52.0260 | 2.82567 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.314187 | 0.0170142 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.64569 | −0.304839 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −50.7879 | −2.73433 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.7409 | 1.48921 | 0.744604 | − | 0.667506i | \(-0.232638\pi\) | ||||
0.744604 | + | 0.667506i | \(0.232638\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.9806 | −1.23012 | −0.615062 | − | 0.788479i | \(-0.710869\pi\) | ||||
−0.615062 | + | 0.788479i | \(0.710869\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.93830 | 0.316963 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.88236 | −0.366311 | −0.183155 | − | 0.983084i | \(-0.558631\pi\) | ||||
−0.183155 | + | 0.983084i | \(0.558631\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.6624 | 1.09665 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −87.8761 | −4.65089 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.9320 | −0.788083 | −0.394041 | − | 0.919093i | \(-0.628923\pi\) | ||||
−0.394041 | + | 0.919093i | \(0.628923\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.38949 | 0.494184 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 61.9674 | 3.25244 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.2704 | 0.589917 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.32339 | −0.486677 | −0.243338 | − | 0.969941i | \(-0.578243\pi\) | ||||
−0.243338 | + | 0.969941i | \(0.578243\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 31.2959 | 1.62920 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.6111 | 0.758571 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.1887 | 1.04533 | 0.522665 | − | 0.852538i | \(-0.324938\pi\) | ||||
0.522665 | + | 0.852538i | \(0.324938\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 80.9972 | 4.18268 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.19771 | 0.113188 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.1073 | −0.981477 | −0.490739 | − | 0.871307i | \(-0.663273\pi\) | ||||
−0.490739 | + | 0.871307i | \(0.663273\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.68919 | 0.240234 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.05445 | −0.207173 | −0.103586 | − | 0.994620i | \(-0.533032\pi\) | ||||
−0.103586 | + | 0.994620i | \(0.533032\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −78.8482 | −4.01848 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −80.0956 | −4.07149 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.3037 | −0.522419 | −0.261209 | − | 0.965282i | \(-0.584121\pi\) | ||||
−0.261209 | + | 0.965282i | \(0.584121\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.5612 | 1.59612 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.33905 | 0.269319 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.5645 | −0.531558 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.7089 | 1.89256 | 0.946278 | − | 0.323353i | \(-0.104810\pi\) | ||||
0.946278 | + | 0.323353i | \(0.104810\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −59.1190 | −2.95965 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.4754 | 0.722867 | 0.361434 | − | 0.932398i | \(-0.382287\pi\) | ||||
0.361434 | + | 0.932398i | \(0.382287\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0271974 | −0.00135480 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 73.7931 | 3.66681 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.65991 | 0.478824 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.5803 | 0.622054 | 0.311027 | − | 0.950401i | \(-0.399327\pi\) | ||||
0.311027 | + | 0.950401i | \(0.399327\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 30.7763 | 1.51808 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.1685 | −0.697188 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.02162 | 0.295590 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 23.3296 | 1.14246 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.00486 | 0.195650 | 0.0978251 | − | 0.995204i | \(-0.468811\pi\) | ||||
0.0978251 | + | 0.995204i | \(0.468811\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.98847 | 0.340597 | 0.170299 | − | 0.985392i | \(-0.445527\pi\) | ||||
0.170299 | + | 0.985392i | \(0.445527\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 78.1384 | 3.79922 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −89.9340 | −4.36244 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −43.4286 | −2.10166 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.36491 | −0.403862 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.3992 | −0.597248 | −0.298624 | − | 0.954371i | \(-0.596528\pi\) | ||||
−0.298624 | + | 0.954371i | \(0.596528\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.9395 | 1.00629 | 0.503143 | − | 0.864203i | \(-0.332177\pi\) | ||||
0.503143 | + | 0.864203i | \(0.332177\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 58.4317 | 2.80159 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.2329 | 1.01571 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.17498 | 0.390170 | 0.195085 | − | 0.980786i | \(-0.437502\pi\) | ||||
0.195085 | + | 0.980786i | \(0.437502\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 37.4037 | 1.78113 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.88162 | −0.231933 | −0.115966 | − | 0.993253i | \(-0.536996\pi\) | ||||
−0.115966 | + | 0.993253i | \(0.536996\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.5453 | −1.30577 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 41.7601 | 1.97519 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.88168 | −0.183188 | −0.0915940 | − | 0.995796i | \(-0.529196\pi\) | ||||
−0.0915940 | + | 0.995796i | \(0.529196\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.0034 | −1.17736 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.0432 | −0.894728 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.82544 | 0.319981 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.5909 | −1.66487 | −0.832435 | − | 0.554123i | \(-0.813054\pi\) | ||||
−0.832435 | + | 0.554123i | \(0.813054\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −98.1147 | −4.57960 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.6008 | 0.959475 | 0.479738 | − | 0.877412i | \(-0.340732\pi\) | ||||
0.479738 | + | 0.877412i | \(0.340732\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.5277 | 0.768108 | 0.384054 | − | 0.923311i | \(-0.374528\pi\) | ||||
0.384054 | + | 0.923311i | \(0.374528\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.723112 | −0.0335335 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.4680 | −0.576950 | −0.288475 | − | 0.957487i | \(-0.593148\pi\) | ||||
−0.288475 | + | 0.957487i | \(0.593148\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.0412 | −0.971594 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.1968 | 0.884542 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 63.9910 | 2.94231 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −60.5035 | −2.77609 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.7631 | 1.31697 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.9698 | 0.775370 | 0.387685 | − | 0.921792i | \(-0.373275\pi\) | ||||
0.387685 | + | 0.921792i | \(0.373275\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.836203 | −0.0381276 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −44.2160 | −2.01190 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.0719 | −1.00223 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.2328 | 0.780893 | 0.390446 | − | 0.920626i | \(-0.372321\pi\) | ||||
0.390446 | + | 0.920626i | \(0.372321\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.3409 | −0.467634 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.7874 | −0.847865 | −0.423933 | − | 0.905694i | \(-0.639351\pi\) | ||||
−0.423933 | + | 0.905694i | \(0.639351\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −36.3113 | −1.63538 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −155.219 | −6.97656 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.9887 | 0.806904 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.7584 | 1.64553 | 0.822765 | − | 0.568381i | \(-0.192430\pi\) | ||||
0.822765 | + | 0.568381i | \(0.192430\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.5908 | −1.09864 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.0001 | −0.757996 | −0.378998 | − | 0.925397i | \(-0.623731\pi\) | ||||
−0.378998 | + | 0.925397i | \(0.623731\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.25555 | 0.322868 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −40.2436 | −1.78728 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.0726 | 0.490783 | 0.245391 | − | 0.969424i | \(-0.421084\pi\) | ||||
0.245391 | + | 0.969424i | \(0.421084\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.81198 | 0.434057 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −66.0070 | −2.91428 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 30.8478 | 1.35932 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −62.4273 | −2.74555 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −27.2368 | −1.19556 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.0217845 | −0.000954397 0 | −0.000477198 | − | 1.00000i | \(-0.500152\pi\) | ||||
−0.000477198 | 1.00000i | \(0.500152\pi\) | ||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.5812 | −1.46840 | −0.734201 | − | 0.678932i | \(-0.762443\pi\) | ||||
−0.734201 | + | 0.678932i | \(0.762443\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 125.994 | 5.49883 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.449365 | 0.0195746 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.11956 | −0.309546 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.8918 | −1.21040 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.16440 | 0.0937505 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.1066 | 1.21515 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −49.1028 | −2.11894 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −29.8830 | −1.28715 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.5095 | −0.580817 | −0.290409 | − | 0.956903i | \(-0.593791\pi\) | ||||
−0.290409 | + | 0.956903i | \(0.593791\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 35.4444 | 1.52107 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −53.5085 | −2.29205 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.1666 | 0.691233 | 0.345617 | − | 0.938376i | \(-0.387670\pi\) | ||||
0.345617 | + | 0.938376i | \(0.387670\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −85.4924 | −3.64873 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.4286 | −1.04069 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.19748 | −0.391117 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −22.2326 | −0.943720 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.9289 | −1.77659 | −0.888293 | − | 0.459278i | \(-0.848108\pi\) | ||||
−0.888293 | + | 0.459278i | \(0.848108\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.53933 | −0.234289 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 138.208 | 5.83515 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.70801 | 0.240564 | 0.120282 | − | 0.992740i | \(-0.461620\pi\) | ||||
0.120282 | + | 0.992740i | \(0.461620\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 66.7656 | 2.80885 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 64.2444 | 2.69801 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.7184 | 1.03625 | 0.518125 | − | 0.855305i | \(-0.326630\pi\) | ||||
0.518125 | + | 0.855305i | \(0.326630\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.8063 | −1.58214 | −0.791072 | − | 0.611723i | \(-0.790477\pi\) | ||||
−0.791072 | + | 0.611723i | \(0.790477\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.70858 | −0.238479 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −45.2515 | −1.88712 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.7099 | −1.56988 | −0.784942 | − | 0.619569i | \(-0.787307\pi\) | ||||
−0.784942 | + | 0.619569i | \(0.787307\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 28.9820 | 1.20445 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.24243 | 0.217493 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.9798 | −0.951725 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.4364 | 0.555526 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.98185 | 0.0817998 | 0.0408999 | − | 0.999163i | \(-0.486978\pi\) | ||||
0.0408999 | + | 0.999163i | \(0.486978\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.302312 | 0.0124566 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 34.3754 | 1.41401 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.4131 | −1.37211 | −0.686055 | − | 0.727550i | \(-0.740659\pi\) | ||||
−0.686055 | + | 0.727550i | \(0.740659\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −112.772 | −4.62321 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 35.0319 | 1.43376 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.4120 | 0.997447 | 0.498723 | − | 0.866761i | \(-0.333802\pi\) | ||||
0.498723 | + | 0.866761i | \(0.333802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.535645 | −0.0218494 | −0.0109247 | − | 0.999940i | \(-0.503478\pi\) | ||||
−0.0109247 | + | 0.999940i | \(0.503478\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −41.4212 | −1.68680 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 79.5234 | 3.23309 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.4095 | −1.55899 | −0.779497 | − | 0.626406i | \(-0.784525\pi\) | ||||
−0.779497 | + | 0.626406i | \(0.784525\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 50.8707 | 2.06139 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.40397 | 0.218621 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.0723 | −0.406815 | −0.203407 | − | 0.979094i | \(-0.565202\pi\) | ||||
−0.203407 | + | 0.979094i | \(0.565202\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 57.5460 | 2.32048 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.1667 | −0.892396 | −0.446198 | − | 0.894934i | \(-0.647222\pi\) | ||||
−0.446198 | + | 0.894934i | \(0.647222\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.1859 | 1.25347 | 0.626734 | − | 0.779233i | \(-0.284391\pi\) | ||||
0.626734 | + | 0.779233i | \(0.284391\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −49.3677 | −1.98106 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −23.9810 | −0.960778 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 47.1677 | 1.88671 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 92.9800 | 3.71326 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.8160 | 0.550882 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.787730 | 0.0313590 | 0.0156795 | − | 0.999877i | \(-0.495009\pi\) | ||||
0.0156795 | + | 0.999877i | \(0.495009\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 39.4531 | 1.56812 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.01768 | 0.238804 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.58680 | 0.102493 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 35.4121 | 1.40088 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.1821 | −1.50810 | −0.754051 | − | 0.656816i | \(-0.771903\pi\) | ||||
−0.754051 | + | 0.656816i | \(0.771903\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.7804 | 0.977243 | 0.488622 | − | 0.872496i | \(-0.337500\pi\) | ||||
0.488622 | + | 0.872496i | \(0.337500\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −147.277 | −5.79904 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −44.2350 | −1.73906 | −0.869528 | − | 0.493883i | \(-0.835577\pi\) | ||||
−0.869528 | + | 0.493883i | \(0.835577\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.2837 | 0.874712 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.629542 | −0.0246737 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.69132 | −0.261852 | −0.130926 | − | 0.991392i | \(-0.541795\pi\) | ||||
−0.130926 | + | 0.991392i | \(0.541795\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.85166 | 0.267716 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19.3156 | 0.753574 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.5366 | −0.761040 | −0.380520 | − | 0.924773i | \(-0.624255\pi\) | ||||
−0.380520 | + | 0.924773i | \(0.624255\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −48.5989 | −1.89028 | −0.945139 | − | 0.326668i | \(-0.894074\pi\) | ||||
−0.945139 | + | 0.326668i | \(0.894074\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.9639 | −0.464638 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −75.8680 | −2.94204 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.2705 | −0.707438 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −40.6562 | −1.57186 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 68.3027 | 2.63680 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.2954 | 0.473954 | 0.236977 | − | 0.971515i | \(-0.423843\pi\) | ||||
0.236977 | + | 0.971515i | \(0.423843\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 140.674 | 5.41454 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.3173 | 0.703989 | 0.351995 | − | 0.936002i | \(-0.385504\pi\) | ||||
0.351995 | + | 0.936002i | \(0.385504\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.2158 | −0.737435 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −39.2405 | −1.50370 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.01922 | 0.115527 | 0.0577637 | − | 0.998330i | \(-0.481603\pi\) | ||||
0.0577637 | + | 0.998330i | \(0.481603\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.4955 | 1.50905 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.4696 | −1.27694 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.98923 | 0.0757834 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −42.6494 | −1.62246 | −0.811229 | − | 0.584728i | \(-0.801201\pi\) | ||||
−0.811229 | + | 0.584728i | \(0.801201\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −135.134 | −5.13330 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 29.9391 | 1.13566 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −35.7610 | −1.35454 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 61.9992 | 2.34503 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.4132 | −1.22423 | −0.612115 | − | 0.790769i | \(-0.709681\pi\) | ||||
−0.612115 | + | 0.790769i | \(0.709681\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.29480 | 0.350560 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 143.678 | 5.41124 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.31670 | 0.237564 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.2051 | −1.58505 | −0.792524 | − | 0.609841i | \(-0.791233\pi\) | ||||
−0.792524 | + | 0.609841i | \(0.791233\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.1059 | −0.679025 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.226104 | 0.00846766 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.7348 | −0.401458 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 81.4438 | 3.04158 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.1237 | 0.526725 | 0.263363 | − | 0.964697i | \(-0.415168\pi\) | ||||
0.263363 | + | 0.964697i | \(0.415168\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.8562 | 1.00018 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.7592 | 1.21833 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 52.0621 | 1.93354 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.03623 | 0.260959 | 0.130480 | − | 0.991451i | \(-0.458348\pi\) | ||||
0.130480 | + | 0.991451i | \(0.458348\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.34978 | 0.346288 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 91.5228 | 3.38509 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.5438 | −0.463315 | −0.231657 | − | 0.972797i | \(-0.574415\pi\) | ||||
−0.231657 | + | 0.972797i | \(0.574415\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 68.7767 | 2.53687 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.0928 | 1.21899 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.0521 | 0.553700 | 0.276850 | − | 0.960913i | \(-0.410709\pi\) | ||||
0.276850 | + | 0.960913i | \(0.410709\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.04874 | −0.295678 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.8186 | 1.60755 | 0.803774 | − | 0.594935i | \(-0.202822\pi\) | ||||
0.803774 | + | 0.594935i | \(0.202822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 53.5912 | 1.96343 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.3201 | 0.377593 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.4697 | 0.894102 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.5683 | 1.69930 | 0.849650 | − | 0.527346i | \(-0.176813\pi\) | ||||
0.849650 | + | 0.527346i | \(0.176813\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.15136 | −0.114842 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.4384 | −0.889403 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.6548 | 1.11417 | 0.557083 | − | 0.830457i | \(-0.311920\pi\) | ||||
0.557083 | + | 0.830457i | \(0.311920\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 69.5412 | 2.52418 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.2379 | 0.914873 | 0.457437 | − | 0.889242i | \(-0.348768\pi\) | ||||
0.457437 | + | 0.889242i | \(0.348768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46.5846 | −1.68648 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −222.001 | −8.02645 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.92897 | −0.0696511 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.00969 | 0.252776 | 0.126388 | − | 0.991981i | \(-0.459662\pi\) | ||||
0.126388 | + | 0.991981i | \(0.459662\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −66.6610 | −2.40074 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.9877 | 0.754873 | 0.377437 | − | 0.926035i | \(-0.376806\pi\) | ||||
0.377437 | + | 0.926035i | \(0.376806\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.644285 | −0.0231434 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −19.3557 | −0.694382 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.0583 | −0.861979 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.2919 | −1.01236 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 56.7978 | 2.02979 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.6355 | 0.879278 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.8551 | 1.24245 | 0.621225 | − | 0.783632i | \(-0.286635\pi\) | ||||
0.621225 | + | 0.783632i | \(0.286635\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −75.0359 | −2.67135 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 58.1262 | 2.06673 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.91257 | −0.209962 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 52.8886 | 1.87577 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.7830 | −1.33834 | −0.669171 | − | 0.743109i | \(-0.733351\pi\) | ||||
−0.669171 | + | 0.743109i | \(0.733351\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −89.2864 | −3.15873 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −47.2084 | −1.66803 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.4319 | −0.544580 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −56.7429 | −1.99992 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 54.4734 | 1.91755 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.97233 | 0.209976 | 0.104988 | − | 0.994473i | \(-0.466520\pi\) | ||||
0.104988 | + | 0.994473i | \(0.466520\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.0374 | 0.528035 | 0.264017 | − | 0.964518i | \(-0.414952\pi\) | ||||
0.264017 | + | 0.964518i | \(0.414952\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −90.4954 | −3.17381 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.2706 | −0.464850 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 61.5723 | 2.15414 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.6977 | 0.408752 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.73076 | 0.269805 | 0.134903 | − | 0.990859i | \(-0.456928\pi\) | ||||
0.134903 | + | 0.990859i | \(0.456928\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.1506 | −1.39956 | −0.699782 | − | 0.714357i | \(-0.746719\pi\) | ||||
−0.699782 | + | 0.714357i | \(0.746719\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −198.158 | −6.89898 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −51.3430 | −1.78537 | −0.892686 | − | 0.450680i | \(-0.851182\pi\) | ||||
−0.892686 | + | 0.450680i | \(0.851182\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.3083 | 0.566411 | 0.283205 | − | 0.959059i | \(-0.408602\pi\) | ||||
0.283205 | + | 0.959059i | \(0.408602\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.6833 | −0.890942 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −42.7401 | −1.48086 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.5576 | −1.09210 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.702891 | −0.0242955 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.5986 | 0.780191 | 0.390096 | − | 0.920774i | \(-0.372442\pi\) | ||||
0.390096 | + | 0.920774i | \(0.372442\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.97967 | −0.275161 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 91.7729 | 3.16083 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −51.6451 | −1.77664 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 69.2332 | 2.37888 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.49402 | −0.0512747 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.95172 | 0.238302 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.4187 | 1.52087 | 0.760434 | − | 0.649416i | \(-0.224986\pi\) | ||||
0.760434 | + | 0.649416i | \(0.224986\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −149.352 | −5.10773 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.4871 | −1.17806 | −0.589028 | − | 0.808113i | \(-0.700489\pi\) | ||||
−0.589028 | + | 0.808113i | \(0.700489\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.7049 | −0.365247 | −0.182624 | − | 0.983183i | \(-0.558459\pi\) | ||||
−0.182624 | + | 0.983183i | \(0.558459\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 50.0996 | 1.70739 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.1619 | 0.788439 | 0.394220 | − | 0.919016i | \(-0.371015\pi\) | ||||
0.394220 | + | 0.919016i | \(0.371015\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.9532 | −1.18844 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 144.098 | 4.89383 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.4654 | 0.490706 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.86465 | −0.0970650 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −37.8278 | −1.28028 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 90.4943 | 3.05927 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.4215 | 1.46624 | 0.733119 | − | 0.680100i | \(-0.238064\pi\) | ||||
0.733119 | + | 0.680100i | \(0.238064\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 90.7852 | 3.06211 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.13169 | 0.172891 | 0.0864454 | − | 0.996257i | \(-0.472449\pi\) | ||||
0.0864454 | + | 0.996257i | \(0.472449\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.4895 | 0.790486 | 0.395243 | − | 0.918577i | \(-0.370660\pi\) | ||||
0.395243 | + | 0.918577i | \(0.370660\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −51.2866 | −1.72398 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.5715 | −0.489263 | −0.244632 | − | 0.969616i | \(-0.578667\pi\) | ||||
−0.244632 | + | 0.969616i | \(0.578667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.23900 | 0.175711 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −101.041 | −3.38500 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −60.0678 | −2.01009 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −63.0141 | −2.10633 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.01978 | −0.200994 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.260134 | −0.00867594 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.8667 | −1.09495 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −128.220 | −4.26689 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 45.4862 | 1.51201 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.5526 | −0.450006 | −0.225003 | − | 0.974358i | \(-0.572239\pi\) | ||||
−0.225003 | + | 0.974358i | \(0.572239\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.4349 | 0.412439 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.1056 | −0.765522 | −0.382761 | − | 0.923847i | \(-0.625027\pi\) | ||||
−0.382761 | + | 0.923847i | \(0.625027\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.24508 | −0.272872 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −157.201 | −5.19690 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.96506 | 0.196984 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.0667 | −0.925834 | −0.462917 | − | 0.886402i | \(-0.653197\pi\) | ||||
−0.462917 | + | 0.886402i | \(0.653197\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −84.7827 | −2.79369 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.44907 | 0.0806121 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.8090 | −0.651316 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 52.8684 | 1.73642 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.0125 | 0.361309 | 0.180654 | − | 0.983547i | \(-0.442178\pi\) | ||||
0.180654 | + | 0.983547i | \(0.442178\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.7535 | −0.942359 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 50.4920 | 1.65303 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 177.364 | 5.80042 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.1633 | 1.21407 | 0.607037 | − | 0.794674i | \(-0.292358\pi\) | ||||
0.607037 | + | 0.794674i | \(0.292358\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −51.0145 | −1.66480 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.3274 | 0.499660 | 0.249830 | − | 0.968290i | \(-0.419625\pi\) | ||||
0.249830 | + | 0.968290i | \(0.419625\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.9936 | −0.585952 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 176.397 | 5.73820 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.476399 | 0.0154809 | 0.00774045 | − | 0.999970i | \(-0.497536\pi\) | ||||
0.00774045 | + | 0.999970i | \(0.497536\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.33585 | 0.0433635 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.8595 | 0.384570 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.8116 | 1.58116 | 0.790581 | − | 0.612357i | \(-0.209778\pi\) | ||||
0.790581 | + | 0.612357i | \(0.209778\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.32588 | −0.237060 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −80.0074 | −2.58627 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 34.3848 | 1.11034 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9968 | −0.999896 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 48.1703 | 1.55227 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 37.1930 | 1.19728 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.1506 | 0.326421 | 0.163211 | − | 0.986591i | \(-0.447815\pi\) | ||||
0.163211 | + | 0.986591i | \(0.447815\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 132.984 | 4.27207 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.7954 | −0.763631 | −0.381815 | − | 0.924239i | \(-0.624701\pi\) | ||||
−0.381815 | + | 0.924239i | \(0.624701\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.0651 | 0.835607 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.1534 | 0.549349 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.16766 | −0.101342 | −0.0506712 | − | 0.998715i | \(-0.516136\pi\) | ||||
−0.0506712 | + | 0.998715i | \(0.516136\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37.7163 | 1.20542 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −91.7053 | −2.92792 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 55.7595 | 1.77845 | 0.889227 | − | 0.457467i | \(-0.151243\pi\) | ||||
0.889227 | + | 0.457467i | \(0.151243\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 44.1143 | 1.40560 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 125.087 | 3.98155 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 46.0509 | 1.46433 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.3174 | 1.43956 | 0.719778 | − | 0.694204i | \(-0.244244\pi\) | ||||
0.719778 | + | 0.694204i | \(0.244244\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 82.4465 | 2.61636 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 44.9569 | 1.42523 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.1146 | 1.14376 | 0.571880 | − | 0.820337i | \(-0.306214\pi\) | ||||
0.571880 | + | 0.820337i | \(0.306214\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.6109 | −0.683738 |
(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 | 2008.2.a.d.1.21 | ✓ | 23 | |
4.3 | odd | 2 | 4016.2.a.m.1.3 | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.d.1.21 | ✓ | 23 | 1.1 | even | 1 | trivial | |
4016.2.a.m.1.3 | 23 | 4.3 | odd | 2 |