Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8024,2,Mod(1,8024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8024 = 2^{3} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8024.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: | \(64.0719625819\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8024.1 |
$q$-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 | ||||||||
\(3\) | −0.159636 | −0.0921659 | −0.0460829 | − | 0.998938i | \(-0.514674\pi\) | ||||
−0.0460829 | + | 0.998938i | \(0.514674\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.22368 | −0.547245 | −0.273623 | − | 0.961837i | \(-0.588222\pi\) | ||||
−0.273623 | + | 0.961837i | \(0.588222\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.18149 | 1.20249 | 0.601245 | − | 0.799065i | \(-0.294671\pi\) | ||||
0.601245 | + | 0.799065i | \(0.294671\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.97452 | −0.991505 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.68772 | −1.41340 | −0.706700 | − | 0.707514i | \(-0.749817\pi\) | ||||
−0.706700 | + | 0.707514i | \(0.749817\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.84748 | −1.34445 | −0.672225 | − | 0.740347i | \(-0.734661\pi\) | ||||
−0.672225 | + | 0.740347i | \(0.734661\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.195343 | 0.0504373 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.27761 | −1.21077 | −0.605383 | − | 0.795934i | \(-0.706980\pi\) | ||||
−0.605383 | + | 0.795934i | \(0.706980\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.507880 | −0.110829 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.783934 | −0.163462 | −0.0817308 | − | 0.996654i | \(-0.526045\pi\) | ||||
−0.0817308 | + | 0.996654i | \(0.526045\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.50261 | −0.700523 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.953748 | 0.183549 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.96119 | −0.735574 | −0.367787 | − | 0.929910i | \(-0.619884\pi\) | ||||
−0.367787 | + | 0.929910i | \(0.619884\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.08691 | 1.27285 | 0.636423 | − | 0.771340i | \(-0.280413\pi\) | ||||
0.636423 | + | 0.771340i | \(0.280413\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.748328 | 0.130267 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.89312 | −0.658057 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.25275 | −1.52114 | −0.760572 | − | 0.649254i | \(-0.775081\pi\) | ||||
−0.760572 | + | 0.649254i | \(0.775081\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.773833 | 0.123912 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.85024 | −0.445132 | −0.222566 | − | 0.974918i | \(-0.571443\pi\) | ||||
−0.222566 | + | 0.974918i | \(0.571443\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.32832 | −0.965060 | −0.482530 | − | 0.875880i | \(-0.660282\pi\) | ||||
−0.482530 | + | 0.875880i | \(0.660282\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.63985 | 0.542597 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.34943 | 0.342700 | 0.171350 | − | 0.985210i | \(-0.445187\pi\) | ||||
0.171350 | + | 0.985210i | \(0.445187\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.12188 | 0.445983 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.159636 | −0.0223535 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14.2699 | 1.96012 | 0.980060 | − | 0.198704i | \(-0.0636732\pi\) | ||||
0.980060 | + | 0.198704i | \(0.0636732\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.73625 | 0.773476 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.842496 | 0.111591 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.63395 | −0.209206 | −0.104603 | − | 0.994514i | \(-0.533357\pi\) | ||||
−0.104603 | + | 0.994514i | \(0.533357\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.46340 | −1.19228 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.93176 | 0.735744 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.5888 | 1.66013 | 0.830067 | − | 0.557663i | \(-0.188302\pi\) | ||||
0.830067 | + | 0.557663i | \(0.188302\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.125144 | 0.0150656 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.9418 | 1.41724 | 0.708618 | − | 0.705592i | \(-0.249319\pi\) | ||||
0.708618 | + | 0.705592i | \(0.249319\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.14024 | 0.601619 | 0.300810 | − | 0.953684i | \(-0.402743\pi\) | ||||
0.300810 | + | 0.953684i | \(0.402743\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.559143 | 0.0645643 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.9139 | −1.69960 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.220834 | 0.0248458 | 0.0124229 | − | 0.999923i | \(-0.496046\pi\) | ||||
0.0124229 | + | 0.999923i | \(0.496046\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.77130 | 0.974589 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.78113 | 0.854090 | 0.427045 | − | 0.904230i | \(-0.359555\pi\) | ||||
0.427045 | + | 0.904230i | \(0.359555\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.22368 | −0.132726 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.632348 | 0.0677948 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.9465 | −1.26632 | −0.633162 | − | 0.774019i | \(-0.718243\pi\) | ||||
−0.633162 | + | 0.774019i | \(0.718243\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.4222 | −1.61669 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.13132 | −0.117313 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.45809 | 0.662586 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.18393 | −0.120209 | −0.0601047 | − | 0.998192i | \(-0.519143\pi\) | ||||
−0.0601047 | + | 0.998192i | \(0.519143\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.9437 | 1.40139 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.42739 | −0.341038 | −0.170519 | − | 0.985354i | \(-0.554544\pi\) | ||||
−0.170519 | + | 0.985354i | \(0.554544\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.95890 | 0.587148 | 0.293574 | − | 0.955936i | \(-0.405155\pi\) | ||||
0.293574 | + | 0.955936i | \(0.405155\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.621482 | 0.0606504 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.0903576 | 0.00873520 | 0.00436760 | − | 0.999990i | \(-0.498610\pi\) | ||||
0.00436760 | + | 0.999990i | \(0.498610\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.7381 | 1.31588 | 0.657938 | − | 0.753072i | \(-0.271429\pi\) | ||||
0.657938 | + | 0.753072i | \(0.271429\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.47707 | 0.140197 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.40931 | 0.508865 | 0.254433 | − | 0.967091i | \(-0.418111\pi\) | ||||
0.254433 | + | 0.967091i | \(0.418111\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.959283 | 0.0894536 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.4189 | 1.33303 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.18149 | 0.291647 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9747 | 0.997698 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.455000 | 0.0410260 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.4045 | 0.930603 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.26004 | −0.200546 | −0.100273 | − | 0.994960i | \(-0.531972\pi\) | ||||
−0.100273 | + | 0.994960i | \(0.531972\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.01023 | 0.0889456 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.6204 | −1.45213 | −0.726065 | − | 0.687626i | \(-0.758653\pi\) | ||||
−0.726065 | + | 0.687626i | \(0.758653\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.7907 | −1.45593 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.16708 | −0.100446 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.42987 | −0.463905 | −0.231953 | − | 0.972727i | \(-0.574511\pi\) | ||||
−0.231953 | + | 0.972727i | \(0.574511\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.11995 | −0.603906 | −0.301953 | − | 0.953323i | \(-0.597639\pi\) | ||||
−0.301953 | + | 0.953323i | \(0.597639\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.375054 | −0.0315852 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.7236 | 1.90025 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.84722 | 0.402539 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.498365 | −0.0411044 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.3437 | −1.83047 | −0.915235 | − | 0.402921i | \(-0.867995\pi\) | ||||
−0.915235 | + | 0.402921i | \(0.867995\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.27022 | 0.754399 | 0.377200 | − | 0.926132i | \(-0.376887\pi\) | ||||
0.377200 | + | 0.926132i | \(0.376887\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.97452 | −0.240475 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.67208 | −0.696559 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.7248 | 1.49440 | 0.747200 | − | 0.664599i | \(-0.231398\pi\) | ||||
0.747200 | + | 0.664599i | \(0.231398\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.27799 | −0.180656 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.49408 | −0.196561 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.2420 | −1.27217 | −0.636085 | − | 0.771619i | \(-0.719447\pi\) | ||||
−0.636085 | + | 0.771619i | \(0.719447\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.915712 | −0.0712881 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.7205 | 0.829580 | 0.414790 | − | 0.909917i | \(-0.363855\pi\) | ||||
0.414790 | + | 0.909917i | \(0.363855\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4981 | 0.807546 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.6983 | 1.20048 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.79839 | 0.212757 | 0.106379 | − | 0.994326i | \(-0.466074\pi\) | ||||
0.106379 | + | 0.994326i | \(0.466074\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.1435 | −0.842372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.159636 | −0.0119990 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.84113 | −0.212356 | −0.106178 | − | 0.994347i | \(-0.533861\pi\) | ||||
−0.106178 | + | 0.994347i | \(0.533861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.93917 | 0.292796 | 0.146398 | − | 0.989226i | \(-0.453232\pi\) | ||||
0.146398 | + | 0.989226i | \(0.453232\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.260837 | 0.0192817 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.3224 | 0.832438 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.68772 | −0.342800 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.03434 | 0.220716 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.0138 | 1.59286 | 0.796430 | − | 0.604731i | \(-0.206719\pi\) | ||||
0.796430 | + | 0.604731i | \(0.206719\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.1683 | 0.731933 | 0.365966 | − | 0.930628i | \(-0.380738\pi\) | ||||
0.365966 | + | 0.930628i | \(0.380738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.946922 | −0.0678105 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.86530 | 0.631627 | 0.315813 | − | 0.948821i | \(-0.397723\pi\) | ||||
0.315813 | + | 0.948821i | \(0.397723\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.6876 | 1.60828 | 0.804141 | − | 0.594438i | \(-0.202626\pi\) | ||||
0.804141 | + | 0.594438i | \(0.202626\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.16926 | −0.153008 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.6025 | −0.884521 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.48777 | 0.243596 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.33183 | 0.162073 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.7399 | 1.71130 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.7486 | 0.946495 | 0.473248 | − | 0.880930i | \(-0.343082\pi\) | ||||
0.473248 | + | 0.880930i | \(0.343082\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.90635 | −0.130621 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.74382 | 0.528124 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.5469 | 1.53058 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.820567 | −0.0554488 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.84748 | −0.326077 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.793664 | 0.0531477 | 0.0265738 | − | 0.999647i | \(-0.491540\pi\) | ||||
0.0265738 | + | 0.999647i | \(0.491540\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.4186 | 0.694572 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.78020 | −0.582762 | −0.291381 | − | 0.956607i | \(-0.594115\pi\) | ||||
−0.291381 | + | 0.956607i | \(0.594115\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.98371 | 0.131087 | 0.0655436 | − | 0.997850i | \(-0.479122\pi\) | ||||
0.0655436 | + | 0.997850i | \(0.479122\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.38080 | 0.156645 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.1934 | −1.19189 | −0.595946 | − | 0.803025i | \(-0.703223\pi\) | ||||
−0.595946 | + | 0.803025i | \(0.703223\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.87495 | −0.187541 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.0352531 | −0.00228993 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.5927 | −1.59077 | −0.795384 | − | 0.606106i | \(-0.792731\pi\) | ||||
−0.795384 | + | 0.606106i | \(0.792731\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.4395 | −1.05896 | −0.529480 | − | 0.848323i | \(-0.677613\pi\) | ||||
−0.529480 | + | 0.848323i | \(0.677613\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.26146 | −0.273373 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.82018 | −0.244062 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 25.5831 | 1.62782 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.24215 | −0.0787179 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.30009 | 0.0820612 | 0.0410306 | − | 0.999158i | \(-0.486936\pi\) | ||||
0.0410306 | + | 0.999158i | \(0.486936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.67486 | 0.231037 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.195343 | 0.0122328 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.5662 | −0.846239 | −0.423119 | − | 0.906074i | \(-0.639065\pi\) | ||||
−0.423119 | + | 0.906074i | \(0.639065\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.4375 | −1.82916 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.7826 | 0.729326 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.0744 | 0.991189 | 0.495595 | − | 0.868554i | \(-0.334950\pi\) | ||||
0.495595 | + | 0.868554i | \(0.334950\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.4617 | −1.07267 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.90709 | 0.116712 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.6739 | −1.07760 | −0.538798 | − | 0.842435i | \(-0.681121\pi\) | ||||
−0.538798 | + | 0.842435i | \(0.681121\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.84698 | −0.172942 | −0.0864708 | − | 0.996254i | \(-0.527559\pi\) | ||||
−0.0864708 | + | 0.996254i | \(0.527559\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.46194 | 0.149003 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.4193 | 0.990119 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.46116 | 0.207961 | 0.103980 | − | 0.994579i | \(-0.466842\pi\) | ||||
0.103980 | + | 0.994579i | \(0.466842\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −21.0801 | −1.26203 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.4336 | −0.622415 | −0.311207 | − | 0.950342i | \(-0.600733\pi\) | ||||
−0.311207 | + | 0.950342i | \(0.600733\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.56408 | 0.330750 | 0.165375 | − | 0.986231i | \(-0.447117\pi\) | ||||
0.165375 | + | 0.986231i | \(0.447117\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.03094 | −0.0610678 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.06800 | −0.535267 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.188997 | 0.0110792 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.3845 | −0.606667 | −0.303333 | − | 0.952885i | \(-0.598100\pi\) | ||||
−0.303333 | + | 0.952885i | \(0.598100\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.22368 | −0.0712452 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.47090 | −0.259428 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.80011 | 0.219766 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.1335 | −1.16048 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.547135 | 0.0314321 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.99943 | 0.114487 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.67646 | 0.438119 | 0.219059 | − | 0.975712i | \(-0.429701\pi\) | ||||
0.219059 | + | 0.975712i | \(0.429701\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.951254 | −0.0541150 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.5562 | 0.882112 | 0.441056 | − | 0.897480i | \(-0.354604\pi\) | ||||
0.441056 | + | 0.897480i | \(0.354604\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.92757 | 0.561140 | 0.280570 | − | 0.959834i | \(-0.409477\pi\) | ||||
0.280570 | + | 0.959834i | \(0.409477\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.5801 | 0.652467 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.3994 | −1.65124 | −0.825619 | − | 0.564229i | \(-0.809174\pi\) | ||||
−0.825619 | + | 0.564229i | \(0.809174\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.5689 | 1.03966 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.0144243 | −0.000805087 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.27761 | −0.293654 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.9789 | 0.941818 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.19310 | −0.121279 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.47469 | 0.412093 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.0149 | −0.990189 | −0.495094 | − | 0.868839i | \(-0.664867\pi\) | ||||
−0.495094 | + | 0.868839i | \(0.664867\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 27.5225 | 1.50822 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.6283 | −0.908500 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.83733 | −0.426927 | −0.213463 | − | 0.976951i | \(-0.568474\pi\) | ||||
−0.213463 | + | 0.976951i | \(0.568474\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.863521 | −0.0469000 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −33.2214 | −1.79904 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.3382 | −0.666200 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.153136 | −0.00824456 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.37196 | −0.288382 | −0.144191 | − | 0.989550i | \(-0.546058\pi\) | ||||
−0.144191 | + | 0.989550i | \(0.546058\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.1222 | 1.66593 | 0.832966 | − | 0.553325i | \(-0.186641\pi\) | ||||
0.832966 | + | 0.553325i | \(0.186641\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.62328 | −0.246772 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.8396 | 1.64143 | 0.820713 | − | 0.571341i | \(-0.193577\pi\) | ||||
0.820713 | + | 0.571341i | \(0.193577\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.6130 | −0.775576 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.507880 | −0.0268799 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.3567 | −0.546603 | −0.273302 | − | 0.961928i | \(-0.588116\pi\) | ||||
−0.273302 | + | 0.961928i | \(0.588116\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.85314 | 0.465955 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.75195 | −0.0919537 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.28999 | −0.329233 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.5607 | −1.12546 | −0.562730 | − | 0.826641i | \(-0.690249\pi\) | ||||
−0.562730 | + | 0.826641i | \(0.690249\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.47807 | 0.441351 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 45.3995 | 2.35702 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.3603 | 1.57200 | 0.785999 | − | 0.618228i | \(-0.212149\pi\) | ||||
0.785999 | + | 0.618228i | \(0.212149\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.66093 | −0.0857698 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.2018 | 0.988943 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.8141 | −0.555485 | −0.277743 | − | 0.960655i | \(-0.589586\pi\) | ||||
−0.277743 | + | 0.960655i | \(0.589586\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.360784 | 0.0184835 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.4602 | −0.841075 | −0.420537 | − | 0.907275i | \(-0.638158\pi\) | ||||
−0.420537 | + | 0.907275i | \(0.638158\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.2498 | 0.930097 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.8237 | 0.956862 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.4768 | −0.581894 | −0.290947 | − | 0.956739i | \(-0.593970\pi\) | ||||
−0.290947 | + | 0.956739i | \(0.593970\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.783934 | −0.0396453 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.65321 | 0.133837 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.270230 | −0.0135967 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.7362 | 1.49242 | 0.746208 | − | 0.665713i | \(-0.231872\pi\) | ||||
0.746208 | + | 0.665713i | \(0.231872\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.68039 | 0.134187 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.69858 | −0.384449 | −0.192224 | − | 0.981351i | \(-0.561570\pi\) | ||||
−0.192224 | + | 0.981351i | \(0.561570\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34.3537 | −1.71128 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.7332 | −0.533339 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 43.3743 | 2.14998 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.56107 | 0.274977 | 0.137489 | − | 0.990503i | \(-0.456097\pi\) | ||||
0.137489 | + | 0.990503i | \(0.456097\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.866803 | 0.0427562 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.18149 | 0.156551 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.52159 | −0.467396 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.13660 | 0.0556595 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.5828 | −1.49407 | −0.747034 | − | 0.664786i | \(-0.768523\pi\) | ||||
−0.747034 | + | 0.664786i | \(0.768523\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.9069 | 1.36010 | 0.680051 | − | 0.733165i | \(-0.261958\pi\) | ||||
0.680051 | + | 0.733165i | \(0.261958\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.98842 | −0.339789 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.50261 | −0.169902 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.19840 | −0.251568 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.62751 | −0.175138 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.0068 | −1.30087 | −0.650436 | − | 0.759561i | \(-0.725414\pi\) | ||||
−0.650436 | + | 0.759561i | \(0.725414\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.283178 | 0.0136087 | 0.00680433 | − | 0.999977i | \(-0.497834\pi\) | ||||
0.00680433 | + | 0.999977i | \(0.497834\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.773790 | −0.0371004 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.13730 | 0.197914 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.6030 | −1.31742 | −0.658709 | − | 0.752398i | \(-0.728897\pi\) | ||||
−0.658709 | + | 0.752398i | \(0.728897\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.28609 | −0.442195 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.0375 | −1.23708 | −0.618541 | − | 0.785753i | \(-0.712276\pi\) | ||||
−0.618541 | + | 0.785753i | \(0.712276\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.6186 | 0.692990 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.56686 | 0.168707 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.46706 | −0.210814 | −0.105407 | − | 0.994429i | \(-0.533614\pi\) | ||||
−0.105407 | + | 0.994429i | \(0.533614\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.3611 | 0.629149 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.47986 | −0.0695299 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 18.8718 | 0.884725 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.1249 | 1.31563 | 0.657813 | − | 0.753182i | \(-0.271482\pi\) | ||||
0.657813 | + | 0.753182i | \(0.271482\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.953748 | 0.0445171 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.0219 | 1.53798 | 0.768991 | − | 0.639260i | \(-0.220759\pi\) | ||||
0.768991 | + | 0.639260i | \(0.220759\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.77577 | 0.314897 | 0.157448 | − | 0.987527i | \(-0.449673\pi\) | ||||
0.157448 | + | 0.987527i | \(0.449673\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.38438 | 0.0641989 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.2140 | −1.35186 | −0.675932 | − | 0.736964i | \(-0.736259\pi\) | ||||
−0.675932 | + | 0.736964i | \(0.736259\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 43.2326 | 1.99630 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.98915 | −0.137733 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 29.6654 | 1.36401 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.4854 | 0.848169 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −42.4460 | −1.94347 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −42.9076 | −1.96050 | −0.980249 | − | 0.197769i | \(-0.936631\pi\) | ||||
−0.980249 | + | 0.197769i | \(0.936631\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 44.8526 | 2.04510 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.398145 | 0.0181162 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.44874 | 0.0657840 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.54390 | −0.0699608 | −0.0349804 | − | 0.999388i | \(-0.511137\pi\) | ||||
−0.0349804 | + | 0.999388i | \(0.511137\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.59280 | 0.117251 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.0195 | −0.632689 | −0.316345 | − | 0.948644i | \(-0.602456\pi\) | ||||
−0.316345 | + | 0.948644i | \(0.602456\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.96119 | −0.178403 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −17.0626 | −0.766906 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 37.9929 | 1.70421 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.41653 | 0.376776 | 0.188388 | − | 0.982095i | \(-0.439674\pi\) | ||||
0.188388 | + | 0.982095i | \(0.439674\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.71138 | −0.0764590 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.08466 | 0.315889 | 0.157945 | − | 0.987448i | \(-0.449513\pi\) | ||||
0.157945 | + | 0.987448i | \(0.449513\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.19402 | 0.186632 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.67587 | −0.0744282 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.3061 | −0.900050 | −0.450025 | − | 0.893016i | \(-0.648585\pi\) | ||||
−0.450025 | + | 0.893016i | \(0.648585\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.3536 | 0.723442 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.03351 | −0.222235 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.29177 | −0.321314 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.0135 | −0.484372 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.446723 | −0.0196090 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.9533 | 1.22465 | 0.612327 | − | 0.790604i | \(-0.290234\pi\) | ||||
0.612327 | + | 0.790604i | \(0.290234\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.6435 | 1.82094 | 0.910472 | − | 0.413570i | \(-0.135718\pi\) | ||||
0.910472 | + | 0.413570i | \(0.135718\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.77891 | 0.0776379 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.08691 | 0.308710 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3854 | −0.973280 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.97452 | −0.129083 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.8165 | 0.598458 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.110569 | −0.00478029 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.453547 | 0.0195720 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14.6345 | −0.630353 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.2704 | 1.08646 | 0.543229 | − | 0.839585i | \(-0.317202\pi\) | ||||
0.543229 | + | 0.839585i | \(0.317202\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.628833 | −0.0269858 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.8111 | −0.720107 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.7958 | 0.718137 | 0.359068 | − | 0.933311i | \(-0.383094\pi\) | ||||
0.359068 | + | 0.933311i | \(0.383094\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.86022 | 0.207429 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.9056 | 0.890608 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.702582 | 0.0298768 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.80746 | −0.0767224 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.1116 | 0.852157 | 0.426078 | − | 0.904686i | \(-0.359895\pi\) | ||||
0.426078 | + | 0.904686i | \(0.359895\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.6764 | 1.29747 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.748328 | 0.0315944 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.7409 | 0.831979 | 0.415990 | − | 0.909369i | \(-0.363435\pi\) | ||||
0.415990 | + | 0.909369i | \(0.363435\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.61925 | −0.278474 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 27.9058 | 1.17193 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.3605 | 1.10509 | 0.552546 | − | 0.833483i | \(-0.313656\pi\) | ||||
0.552546 | + | 0.833483i | \(0.313656\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.1151 | 1.76246 | 0.881230 | − | 0.472687i | \(-0.156716\pi\) | ||||
0.881230 | + | 0.472687i | \(0.156716\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.51419 | −0.146807 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.74582 | 0.114509 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.7502 | −0.530797 | −0.265398 | − | 0.964139i | \(-0.585503\pi\) | ||||
−0.265398 | + | 0.964139i | \(0.585503\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.62323 | −0.0674592 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.7556 | 1.02703 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −66.8932 | −2.77043 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.6441 | −0.729494 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.5005 | −1.01124 | −0.505621 | − | 0.862755i | \(-0.668737\pi\) | ||||
−0.505621 | + | 0.862755i | \(0.668737\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.4019 | −1.54112 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.41522 | −0.0582144 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.6831 | 1.75279 | 0.876393 | − | 0.481597i | \(-0.159943\pi\) | ||||
0.876393 | + | 0.481597i | \(0.159943\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.89312 | −0.159602 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.62176 | −0.148229 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.3736 | −1.48619 | −0.743093 | − | 0.669188i | \(-0.766642\pi\) | ||||
−0.743093 | + | 0.669188i | \(0.766642\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.42501 | 0.139709 | 0.0698545 | − | 0.997557i | \(-0.477746\pi\) | ||||
0.0698545 | + | 0.997557i | \(0.477746\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −40.4201 | −1.64603 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.4295 | −0.545985 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.78328 | 0.153559 | 0.0767793 | − | 0.997048i | \(-0.475536\pi\) | ||||
0.0767793 | + | 0.997048i | \(0.475536\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.01181 | 0.0815226 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.3888 | −0.460743 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.93993 | 0.280301 | 0.140151 | − | 0.990130i | \(-0.455241\pi\) | ||||
0.140151 | + | 0.990130i | \(0.455241\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.556773 | −0.0224513 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.5832 | 1.43253 | 0.716263 | − | 0.697831i | \(-0.245851\pi\) | ||||
0.716263 | + | 0.697831i | \(0.245851\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.52750 | −0.262362 | −0.131181 | − | 0.991358i | \(-0.541877\pi\) | ||||
−0.131181 | + | 0.991358i | \(0.541877\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.747675 | −0.0300032 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −38.0076 | −1.52274 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.78137 | 0.191255 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.94938 | −0.157723 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.25275 | −0.368931 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.0434 | 1.39506 | 0.697528 | − | 0.716557i | \(-0.254283\pi\) | ||||
0.697528 | + | 0.716557i | \(0.254283\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.19478 | −0.0872345 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.76556 | 0.109748 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.1333 | −0.599602 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −35.5212 | −1.40520 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.8738 | −0.745469 | −0.372735 | − | 0.927938i | \(-0.621580\pi\) | ||||
−0.372735 | + | 0.927938i | \(0.621580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.6814 | −1.13108 | −0.565541 | − | 0.824720i | \(-0.691333\pi\) | ||||
−0.565541 | + | 0.824720i | \(0.691333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.23619 | −0.0486750 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.6276 | 1.16478 | 0.582390 | − | 0.812909i | \(-0.302118\pi\) | ||||
0.582390 | + | 0.812909i | \(0.302118\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.68772 | −0.184009 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.59930 | −0.141068 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.06063 | −0.158905 | −0.0794523 | − | 0.996839i | \(-0.525317\pi\) | ||||
−0.0794523 | + | 0.996839i | \(0.525317\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.3380 | 0.794671 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.2897 | −0.596509 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.5565 | 1.61881 | 0.809405 | − | 0.587250i | \(-0.199790\pi\) | ||||
0.809405 | + | 0.587250i | \(0.199790\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.98492 | −0.271682 | −0.135841 | − | 0.990731i | \(-0.543374\pi\) | ||||
−0.135841 | + | 0.990731i | \(0.543374\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.773833 | 0.0300532 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.5463 | 0.796753 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.10531 | 0.120238 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.126697 | −0.00489840 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.65950 | 0.295692 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.6607 | 1.76009 | 0.880046 | − | 0.474888i | \(-0.157511\pi\) | ||||
0.880046 | + | 0.474888i | \(0.157511\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.34061 | −0.128580 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.97767 | −0.114441 | −0.0572207 | − | 0.998362i | \(-0.518224\pi\) | ||||
−0.0572207 | + | 0.998362i | \(0.518224\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.76665 | −0.144551 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.40163 | 0.0537108 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.0810 | 0.959697 | 0.479849 | − | 0.877351i | \(-0.340692\pi\) | ||||
0.479849 | + | 0.877351i | \(0.340692\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.64441 | 0.253870 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.316671 | −0.0120818 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −69.1730 | −2.63528 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.91079 | −0.262899 | −0.131449 | − | 0.991323i | \(-0.541963\pi\) | ||||
−0.131449 | + | 0.991323i | \(0.541963\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 44.3617 | 1.68516 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.71252 | 0.330485 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.85024 | −0.107960 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.90433 | 0.109852 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.1939 | 1.78249 | 0.891244 | − | 0.453524i | \(-0.149833\pi\) | ||||
0.891244 | + | 0.453524i | \(0.149833\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48.8324 | 1.84175 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.458945 | 0.0172849 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.9042 | −0.410095 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.2058 | 1.84796 | 0.923982 | − | 0.382437i | \(-0.124915\pi\) | ||||
0.923982 | + | 0.382437i | \(0.124915\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.656875 | −0.0246347 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.55567 | −0.208061 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −27.8064 | −1.03990 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.92587 | 0.146614 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.1746 | −0.976147 | −0.488073 | − | 0.872803i | \(-0.662300\pi\) | ||||
−0.488073 | + | 0.872803i | \(0.662300\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.9582 | 0.706039 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.62433 | 0.0975999 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.8745 | 0.515286 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.0554 | 1.00343 | 0.501715 | − | 0.865033i | \(-0.332703\pi\) | ||||
0.501715 | + | 0.865033i | \(0.332703\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.6336 | −0.949393 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.32832 | −0.234061 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.9986 | 0.517050 | 0.258525 | − | 0.966005i | \(-0.416764\pi\) | ||||
0.258525 | + | 0.966005i | \(0.416764\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.609838 | 0.0224942 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −63.7004 | −2.34643 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.6598 | 0.907126 | 0.453563 | − | 0.891224i | \(-0.350153\pi\) | ||||
0.453563 | + | 0.891224i | \(0.350153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.08399 | −0.150029 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.5789 | 1.26858 | 0.634288 | − | 0.773097i | \(-0.281293\pi\) | ||||
0.634288 | + | 0.773097i | \(0.281293\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.3415 | 1.00172 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −23.1451 | −0.846835 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.287472 | 0.0105040 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.8076 | 1.05120 | 0.525602 | − | 0.850731i | \(-0.323840\pi\) | ||||
0.525602 | + | 0.850731i | \(0.323840\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.207542 | −0.00756324 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.3438 | −0.412841 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.75998 | −0.173004 | −0.0865021 | − | 0.996252i | \(-0.527569\pi\) | ||||
−0.0865021 | + | 0.996252i | \(0.527569\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.586640 | −0.0212937 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.4235 | 0.704101 | 0.352050 | − | 0.935981i | \(-0.385485\pi\) | ||||
0.352050 | + | 0.935981i | \(0.385485\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.7078 | 1.58233 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.63985 | 0.131599 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.84748 | −0.175033 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.0219 | 1.01049 | 0.505247 | − | 0.862975i | \(-0.331401\pi\) | ||||
0.505247 | + | 0.862975i | \(0.331401\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.16566 | 0.0779943 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.6224 | 0.957541 | 0.478770 | − | 0.877940i | \(-0.341083\pi\) | ||||
0.478770 | + | 0.877940i | \(0.341083\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.8227 | −0.891657 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.69929 | 0.168586 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.0424 | 0.538951 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −55.9800 | −2.00312 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.77797 | −0.135014 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.9131 | −0.817803 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.3373 | 1.54481 | 0.772405 | − | 0.635131i | \(-0.219054\pi\) | ||||
0.772405 | + | 0.635131i | \(0.219054\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.56605 | −0.0913538 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.2097 | 0.611906 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.92055 | 0.281267 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.78752 | 0.0988631 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.1631 | 0.820479 | 0.410240 | − | 0.911978i | \(-0.365445\pi\) | ||||
0.410240 | + | 0.911978i | \(0.365445\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.34943 | 0.0831169 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 35.5350 | 1.25557 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.0960 | −0.850329 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.05195 | 0.107567 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.82139 | 0.0993176 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.8654 | −0.839064 | −0.419532 | − | 0.907741i | \(-0.637806\pi\) | ||||
−0.419532 | + | 0.907741i | \(0.637806\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.0771 | −1.37218 | −0.686092 | − | 0.727515i | \(-0.740675\pi\) | ||||
−0.686092 | + | 0.727515i | \(0.740675\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.454480 | 0.0159393 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.8749 | 0.696189 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.3984 | 1.16846 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 45.8737 | 1.60296 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.8685 | −0.763214 | −0.381607 | − | 0.924325i | \(-0.624629\pi\) | ||||
−0.381607 | + | 0.924325i | \(0.624629\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.21602 | 0.251535 | 0.125767 | − | 0.992060i | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.62110 | −0.0912551 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.47242 | −0.120748 | −0.0603739 | − | 0.998176i | \(-0.519229\pi\) | ||||
−0.0603739 | + | 0.998176i | \(0.519229\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.2692 | −0.877634 | −0.438817 | − | 0.898576i | \(-0.644602\pi\) | ||||
−0.438817 | + | 0.898576i | \(0.644602\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.552525 | −0.0191669 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.12188 | 0.108167 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.1185 | −0.453984 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.75912 | 0.233629 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.360262 | −0.0124376 | −0.00621882 | − | 0.999981i | \(-0.501980\pi\) | ||||
−0.00621882 | + | 0.999981i | \(0.501980\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.3090 | −0.458931 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.66557 | 0.0573654 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.8463 | −0.441926 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34.9158 | 1.19972 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.888227 | −0.0304839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.25355 | 0.248648 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.2029 | −0.725973 | −0.362987 | − | 0.931794i | \(-0.618243\pi\) | ||||
−0.362987 | + | 0.931794i | \(0.618243\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.2097 | −0.656958 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.7746 | 1.15372 | 0.576859 | − | 0.816844i | \(-0.304278\pi\) | ||||
0.576859 | + | 0.816844i | \(0.304278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.90816 | −0.235703 | −0.117852 | − | 0.993031i | \(-0.537601\pi\) | ||||
−0.117852 | + | 0.993031i | \(0.537601\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.44758 | 0.0493333 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.2974 | 1.09942 | 0.549708 | − | 0.835357i | \(-0.314739\pi\) | ||||
0.549708 | + | 0.835357i | \(0.314739\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.42432 | −0.116430 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.159636 | −0.00542152 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.03521 | −0.0351170 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −65.8714 | −2.23197 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.52161 | 0.119188 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33.1017 | 1.11904 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.8357 | 1.00748 | 0.503740 | − | 0.863856i | \(-0.331957\pi\) | ||||
0.503740 | + | 0.863856i | \(0.331957\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.65773 | 0.0559139 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.8307 | −1.67884 | −0.839419 | − | 0.543485i | \(-0.817105\pi\) | ||||
−0.839419 | + | 0.543485i | \(0.817105\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.5600 | 0.994773 | 0.497387 | − | 0.867529i | \(-0.334293\pi\) | ||||
0.497387 | + | 0.867529i | \(0.334293\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.195343 | 0.00656638 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45.2555 | −1.51953 | −0.759766 | − | 0.650197i | \(-0.774686\pi\) | ||||
−0.759766 | + | 0.650197i | \(0.774686\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.19030 | −0.241155 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −41.1173 | −1.37748 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.3994 | −0.414929 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.47663 | 0.116211 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.606634 | −0.0202549 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.0726 | −0.936272 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.2699 | 0.475399 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.21403 | 0.106956 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.82027 | −0.160231 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.155456 | −0.00516185 | −0.00258092 | − | 0.999997i | \(-0.500822\pi\) | ||||
−0.00258092 | + | 0.999997i | \(0.500822\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.1948 | 0.338141 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.8398 | 1.28682 | 0.643410 | − | 0.765522i | \(-0.277519\pi\) | ||||
0.643410 | + | 0.765522i | \(0.277519\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.4757 | −1.20717 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.319181 | −0.0105518 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −52.8776 | −1.74617 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.5612 | −1.37098 | −0.685489 | − | 0.728083i | \(-0.740411\pi\) | ||||
−0.685489 | + | 0.728083i | \(0.740411\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.22544 | −0.0403796 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −57.8879 | −1.90540 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.4088 | 1.06560 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.7248 | −0.582160 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.44937 | 0.277215 | 0.138607 | − | 0.990347i | \(-0.455737\pi\) | ||||
0.138607 | + | 0.990347i | \(0.455737\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.4761 | −0.539982 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.48333 | −0.0813006 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.73625 | 0.187595 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.2953 | −0.499676 | −0.249838 | − | 0.968288i | \(-0.580377\pi\) | ||||
−0.249838 | + | 0.968288i | \(0.580377\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.58480 | −0.0517179 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.8519 | −0.484160 | −0.242080 | − | 0.970256i | \(-0.577830\pi\) | ||||
−0.242080 | + | 0.970256i | \(0.577830\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.23440 | 0.0727620 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.71305 | −0.120786 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.0834 | 0.685118 | 0.342559 | − | 0.939496i | \(-0.388706\pi\) | ||||
0.342559 | + | 0.939496i | \(0.388706\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.9172 | −0.808847 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.69321 | 0.152188 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.6820 | 0.443202 | 0.221601 | − | 0.975137i | \(-0.428872\pi\) | ||||
0.221601 | + | 0.975137i | \(0.428872\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26.9377 | −0.871685 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.96427 | −0.0958212 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.2751 | −0.557842 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.2242 | 0.620136 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.268770 | −0.00866099 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.4428 | −0.400547 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.3058 | −0.878096 | −0.439048 | − | 0.898464i | \(-0.644684\pi\) | ||||
−0.439048 | + | 0.898464i | \(0.644684\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.842496 | 0.0270649 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.4805 | −1.29908 | −0.649541 | − | 0.760327i | \(-0.725039\pi\) | ||||
−0.649541 | + | 0.760327i | \(0.725039\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.6521 | −0.726192 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.71044 | −0.0868035 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.6264 | −0.883847 | −0.441923 | − | 0.897053i | \(-0.645704\pi\) | ||||
−0.441923 | + | 0.897053i | \(0.645704\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 56.0017 | 1.78982 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −40.8644 | −1.30470 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.1145 | 0.737237 | 0.368619 | − | 0.929581i | \(-0.379831\pi\) | ||||
0.368619 | + | 0.929581i | \(0.379831\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.8483 | −0.345655 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.19323 | −0.0379809 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.96099 | 0.157750 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.2053 | −1.78542 | −0.892710 | − | 0.450633i | \(-0.851198\pi\) | ||||
−0.892710 | + | 0.450633i | \(0.851198\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.87583 | 0.0912616 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.7623 | −0.880125 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.8504 | 0.850360 | 0.425180 | − | 0.905109i | \(-0.360211\pi\) | ||||
0.425180 | + | 0.905109i | \(0.360211\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.82479 | −0.279204 |
(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 | 8024.2.a.bb.1.16 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8024.2.a.bb.1.16 | ✓ | 32 | 1.1 | even | 1 | trivial |