Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 26x^{8} - 3x^{7} + 220x^{6} + 42x^{5} - 675x^{4} - 67x^{3} + 628x^{2} - 48x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-2.53098\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.53098 | 0.684675 | 0.342338 | − | 0.939577i | \(-0.388781\pi\) | ||||
0.342338 | + | 0.939577i | \(0.388781\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.95354 | 0.738369 | 0.369185 | − | 0.929356i | \(-0.379637\pi\) | ||||
0.369185 | + | 0.929356i | \(0.379637\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.15240 | −0.648974 | −0.324487 | − | 0.945890i | \(-0.605192\pi\) | ||||
−0.324487 | + | 0.945890i | \(0.605192\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0320505 | −0.00888922 | −0.00444461 | − | 0.999990i | \(-0.501415\pi\) | ||||
−0.00444461 | + | 0.999990i | \(0.501415\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.53098 | −0.395297 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.27829 | −0.552567 | −0.276283 | − | 0.961076i | \(-0.589103\pi\) | ||||
−0.276283 | + | 0.961076i | \(0.589103\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.52833 | −1.26829 | −0.634143 | − | 0.773216i | \(-0.718647\pi\) | ||||
−0.634143 | + | 0.773216i | \(0.718647\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.95354 | −0.426298 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.90191 | 1.43915 | 0.719574 | − | 0.694416i | \(-0.244337\pi\) | ||||
0.719574 | + | 0.694416i | \(0.244337\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.65610 | −0.531220 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.80212 | −0.520341 | −0.260171 | − | 0.965563i | \(-0.583779\pi\) | ||||
−0.260171 | + | 0.965563i | \(0.583779\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.86516 | 0.334992 | 0.167496 | − | 0.985873i | \(-0.446432\pi\) | ||||
0.167496 | + | 0.985873i | \(0.446432\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.15240 | 0.374686 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.99083 | 0.505543 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.30674 | −1.20122 | −0.600611 | − | 0.799542i | \(-0.705076\pi\) | ||||
−0.600611 | + | 0.799542i | \(0.705076\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0320505 | 0.00513219 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.8322 | −1.84787 | −0.923936 | − | 0.382548i | \(-0.875047\pi\) | ||||
−0.923936 | + | 0.382548i | \(0.875047\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.12240 | 0.171165 | 0.0855825 | − | 0.996331i | \(-0.472725\pi\) | ||||
0.0855825 | + | 0.996331i | \(0.472725\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.53098 | 0.228225 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.929399 | −0.135567 | −0.0677834 | − | 0.997700i | \(-0.521593\pi\) | ||||
−0.0677834 | + | 0.997700i | \(0.521593\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.18367 | −0.454811 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.27829 | 0.319024 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.1295 | −1.52876 | −0.764379 | − | 0.644768i | \(-0.776954\pi\) | ||||
−0.764379 | + | 0.644768i | \(0.776954\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.29529 | −0.444337 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.52833 | 0.732245 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.11120 | 1.05599 | 0.527994 | − | 0.849248i | \(-0.322944\pi\) | ||||
0.527994 | + | 0.849248i | \(0.322944\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.44769 | −0.953580 | −0.476790 | − | 0.879017i | \(-0.658200\pi\) | ||||
−0.476790 | + | 0.879017i | \(0.658200\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.95354 | 0.246123 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0490687 | −0.00608623 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.5639 | 1.29058 | 0.645290 | − | 0.763938i | \(-0.276737\pi\) | ||||
0.645290 | + | 0.763938i | \(0.276737\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.90191 | −0.830892 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.98837 | −0.948045 | −0.474023 | − | 0.880513i | \(-0.657199\pi\) | ||||
−0.474023 | + | 0.880513i | \(0.657199\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.4948 | 1.22833 | 0.614164 | − | 0.789179i | \(-0.289493\pi\) | ||||
0.614164 | + | 0.789179i | \(0.289493\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.65610 | 0.306700 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.20481 | −0.479183 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.86119 | −0.659435 | −0.329717 | − | 0.944080i | \(-0.606953\pi\) | ||||
−0.329717 | + | 0.944080i | \(0.606953\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.0793 | −1.54541 | −0.772704 | − | 0.634767i | \(-0.781096\pi\) | ||||
−0.772704 | + | 0.634767i | \(0.781096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.48802 | −0.378329 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.80212 | 0.300419 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.24231 | 0.767684 | 0.383842 | − | 0.923399i | \(-0.374601\pi\) | ||||
0.383842 | + | 0.923399i | \(0.374601\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0626121 | −0.00656353 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.86516 | −0.193408 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.46376 | −0.868364 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.96086 | 0.300629 | 0.150315 | − | 0.988638i | \(-0.451971\pi\) | ||||
0.150315 | + | 0.988638i | \(0.451971\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.15240 | −0.216325 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.7676 | −1.07142 | −0.535709 | − | 0.844403i | \(-0.679955\pi\) | ||||
−0.535709 | + | 0.844403i | \(0.679955\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.59773 | −0.255962 | −0.127981 | − | 0.991777i | \(-0.540850\pi\) | ||||
−0.127981 | + | 0.991777i | \(0.540850\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.99083 | −0.291876 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.49290 | −0.240998 | −0.120499 | − | 0.992713i | \(-0.538449\pi\) | ||||
−0.120499 | + | 0.992713i | \(0.538449\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.57800 | 0.821624 | 0.410812 | − | 0.911720i | \(-0.365245\pi\) | ||||
0.410812 | + | 0.911720i | \(0.365245\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.30674 | 0.693525 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3592 | 1.63301 | 0.816507 | − | 0.577335i | \(-0.195907\pi\) | ||||
0.816507 | + | 0.577335i | \(0.195907\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.5667 | 0.985349 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.0320505 | −0.00296307 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.45074 | −0.407998 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.36715 | −0.578832 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.8322 | 1.06687 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.7213 | −1.04839 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.8473 | 1.76116 | 0.880580 | − | 0.473897i | \(-0.157153\pi\) | ||||
0.880580 | + | 0.473897i | \(0.157153\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.12240 | −0.0988221 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.00587 | 0.699476 | 0.349738 | − | 0.936847i | \(-0.386271\pi\) | ||||
0.349738 | + | 0.936847i | \(0.386271\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.7998 | −0.936463 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.53098 | −0.131766 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.5851 | 1.07522 | 0.537609 | − | 0.843194i | \(-0.319328\pi\) | ||||
0.537609 | + | 0.843194i | \(0.319328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.988330 | −0.0838291 | −0.0419145 | − | 0.999121i | \(-0.513346\pi\) | ||||
−0.0419145 | + | 0.999121i | \(0.513346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.929399 | 0.0782695 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.0689857 | 0.00576888 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.28999 | −0.356265 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.18367 | 0.262585 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.45810 | −0.692915 | −0.346457 | − | 0.938066i | \(-0.612615\pi\) | ||||
−0.346457 | + | 0.938066i | \(0.612615\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.136644 | −0.0111199 | −0.00555997 | − | 0.999985i | \(-0.501770\pi\) | ||||
−0.00555997 | + | 0.999985i | \(0.501770\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.27829 | −0.184189 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.85552 | 0.229361 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.3727 | 0.907639 | 0.453820 | − | 0.891094i | \(-0.350061\pi\) | ||||
0.453820 | + | 0.891094i | \(0.350061\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.1295 | 0.882629 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.4832 | 1.06262 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.0067 | −0.862114 | −0.431057 | − | 0.902325i | \(-0.641859\pi\) | ||||
−0.431057 | + | 0.902325i | \(0.641859\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.29529 | 0.256538 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9990 | −0.999921 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.52833 | −0.422762 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.6800 | −1.34418 | −0.672091 | − | 0.740468i | \(-0.734604\pi\) | ||||
−0.672091 | + | 0.740468i | \(0.734604\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.18880 | −0.392236 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.11120 | −0.609675 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.2929 | −1.74100 | −0.870498 | − | 0.492172i | \(-0.836203\pi\) | ||||
−0.870498 | + | 0.492172i | \(0.836203\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.4704 | 0.926918 | 0.463459 | − | 0.886118i | \(-0.346608\pi\) | ||||
0.463459 | + | 0.886118i | \(0.346608\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.44769 | 0.550549 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.1865 | −0.822446 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.90380 | 0.358602 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.95354 | −0.142099 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.6430 | −0.770103 | −0.385051 | − | 0.922895i | \(-0.625816\pi\) | ||||
−0.385051 | + | 0.922895i | \(0.625816\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.66898 | −0.264099 | −0.132050 | − | 0.991243i | \(-0.542156\pi\) | ||||
−0.132050 | + | 0.991243i | \(0.542156\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0490687 | 0.00351389 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.11526 | −0.364447 | −0.182223 | − | 0.983257i | \(-0.558329\pi\) | ||||
−0.182223 | + | 0.983257i | \(0.558329\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.690922 | −0.0489781 | −0.0244891 | − | 0.999700i | \(-0.507796\pi\) | ||||
−0.0244891 | + | 0.999700i | \(0.507796\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.5639 | −0.745117 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.47406 | −0.384204 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.1148 | −1.26519 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.90191 | 0.479716 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.8992 | 0.823085 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.3286 | 1.05526 | 0.527631 | − | 0.849474i | \(-0.323081\pi\) | ||||
0.527631 | + | 0.849474i | \(0.323081\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.98837 | 0.547354 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.71838 | 0.117192 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.64367 | 0.247348 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.4948 | −0.709175 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0730204 | 0.00491188 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.7330 | −1.58928 | −0.794641 | − | 0.607079i | \(-0.792341\pi\) | ||||
−0.794641 | + | 0.607079i | \(0.792341\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.65610 | −0.177073 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.9222 | −1.38866 | −0.694329 | − | 0.719658i | \(-0.744299\pi\) | ||||
−0.694329 | + | 0.719658i | \(0.744299\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.6369 | −0.768988 | −0.384494 | − | 0.923127i | \(-0.625624\pi\) | ||||
−0.384494 | + | 0.923127i | \(0.625624\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.20481 | 0.276656 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.90044 | −0.517575 | −0.258788 | − | 0.965934i | \(-0.583323\pi\) | ||||
−0.258788 | + | 0.965934i | \(0.583323\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.42289 | −0.0928192 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.86119 | 0.380725 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.2822 | 1.37663 | 0.688316 | − | 0.725411i | \(-0.258350\pi\) | ||||
0.688316 | + | 0.725411i | \(0.258350\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.6365 | −1.13607 | −0.568033 | − | 0.823006i | \(-0.692295\pi\) | ||||
−0.568033 | + | 0.823006i | \(0.692295\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.87414 | −0.311398 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.177186 | 0.0112741 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.0793 | 0.892242 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.1497 | 1.83992 | 0.919958 | − | 0.392017i | \(-0.128223\pi\) | ||||
0.919958 | + | 0.392017i | \(0.128223\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.8557 | −0.933970 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.48802 | 0.218428 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.8771 | −1.80131 | −0.900653 | − | 0.434539i | \(-0.856911\pi\) | ||||
−0.900653 | + | 0.434539i | \(0.856911\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.2740 | −0.886945 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.80212 | −0.173447 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.69587 | 0.227897 | 0.113948 | − | 0.993487i | \(-0.463650\pi\) | ||||
0.113948 | + | 0.993487i | \(0.463650\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.0391 | −1.04670 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.24231 | −0.443222 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.9065 | −0.725952 | −0.362976 | − | 0.931799i | \(-0.618239\pi\) | ||||
−0.362976 | + | 0.931799i | \(0.618239\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.42035 | 0.572245 | 0.286123 | − | 0.958193i | \(-0.407634\pi\) | ||||
0.286123 | + | 0.958193i | \(0.407634\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0626121 | 0.00378945 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.71700 | 0.344748 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.72432 | −0.584278 | −0.292139 | − | 0.956376i | \(-0.594367\pi\) | ||||
−0.292139 | + | 0.956376i | \(0.594367\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.86516 | 0.111664 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.54649 | −0.569496 | −0.284748 | − | 0.958602i | \(-0.591910\pi\) | ||||
−0.284748 | + | 0.958602i | \(0.591910\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.881411 | 0.0523944 | 0.0261972 | − | 0.999657i | \(-0.491660\pi\) | ||||
0.0261972 | + | 0.999657i | \(0.491660\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.46376 | 0.501350 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −23.1146 | −1.36441 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.8094 | −0.694670 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.96086 | −0.173569 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.37269 | 0.430717 | 0.215358 | − | 0.976535i | \(-0.430908\pi\) | ||||
0.215358 | + | 0.976535i | \(0.430908\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.4181 | 0.723009 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.15240 | 0.124895 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.221210 | −0.0127929 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.19266 | 0.126383 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.7676 | 0.618583 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.4023 | −0.652892 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.3416 | −0.647299 | −0.323650 | − | 0.946177i | \(-0.604910\pi\) | ||||
−0.323650 | + | 0.946177i | \(0.604910\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.59773 | 0.147779 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.2572 | −1.31879 | −0.659397 | − | 0.751795i | \(-0.729188\pi\) | ||||
−0.659397 | + | 0.751795i | \(0.729188\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.6287 | 1.39210 | 0.696049 | − | 0.717994i | \(-0.254940\pi\) | ||||
0.696049 | + | 0.717994i | \(0.254940\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.99083 | 0.168514 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.6228 | 0.821299 | 0.410649 | − | 0.911793i | \(-0.365302\pi\) | ||||
0.410649 | + | 0.911793i | \(0.365302\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.03130 | 0.337688 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.49290 | 0.139140 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.5951 | 0.700812 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0851294 | 0.00472213 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.57800 | −0.474365 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.81562 | −0.100098 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.4030 | 0.791660 | 0.395830 | − | 0.918324i | \(-0.370457\pi\) | ||||
0.395830 | + | 0.918324i | \(0.370457\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.30674 | −0.400407 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.1731 | 0.883628 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.4014 | −1.00239 | −0.501193 | − | 0.865335i | \(-0.667105\pi\) | ||||
−0.501193 | + | 0.865335i | \(0.667105\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.3592 | −0.942821 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.01458 | −0.217402 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.8942 | −1.07419 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.5667 | −0.568891 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.12491 | 0.221437 | 0.110718 | − | 0.993852i | \(-0.464685\pi\) | ||||
0.110718 | + | 0.993852i | \(0.464685\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.8747 | −1.17093 | −0.585463 | − | 0.810699i | \(-0.699087\pi\) | ||||
−0.585463 | + | 0.810699i | \(0.699087\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.0320505 | 0.00171073 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.7177 | −1.10269 | −0.551347 | − | 0.834276i | \(-0.685886\pi\) | ||||
−0.551347 | + | 0.834276i | \(0.685886\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.2300 | −0.649103 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.45074 | 0.235558 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.2856 | −1.44008 | −0.720040 | − | 0.693933i | \(-0.755877\pi\) | ||||
−0.720040 | + | 0.693933i | \(0.755877\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.5624 | 0.608548 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.36715 | 0.334189 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.0674 | 0.841006 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.1725 | 0.896398 | 0.448199 | − | 0.893934i | \(-0.352066\pi\) | ||||
0.448199 | + | 0.893934i | \(0.352066\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.8322 | −0.615957 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.7420 | −1.12879 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.5701 | 0.857967 | 0.428984 | − | 0.903312i | \(-0.358872\pi\) | ||||
0.428984 | + | 0.903312i | \(0.358872\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.7213 | 0.605287 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0898095 | 0.00462543 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.1485 | 1.65136 | 0.825680 | − | 0.564139i | \(-0.190792\pi\) | ||||
0.825680 | + | 0.564139i | \(0.190792\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.8473 | −1.01681 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 35.1609 | 1.79664 | 0.898319 | − | 0.439343i | \(-0.144789\pi\) | ||||
0.898319 | + | 0.439343i | \(0.144789\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.43749 | −0.328085 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.12240 | 0.0570550 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.1942 | −1.12529 | −0.562646 | − | 0.826698i | \(-0.690217\pi\) | ||||
−0.562646 | + | 0.826698i | \(0.690217\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.7246 | −0.795225 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.00587 | −0.403843 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.97336 | −0.451499 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.87019 | 0.495371 | 0.247685 | − | 0.968841i | \(-0.420330\pi\) | ||||
0.247685 | + | 0.968841i | \(0.420330\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.7998 | 0.540667 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.5475 | 0.976157 | 0.488079 | − | 0.872800i | \(-0.337698\pi\) | ||||
0.488079 | + | 0.872800i | \(0.337698\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0597793 | −0.00297782 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.53098 | 0.0760750 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.7271 | 0.779562 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.76824 | 0.334668 | 0.167334 | − | 0.985900i | \(-0.446484\pi\) | ||||
0.167334 | + | 0.985900i | \(0.446484\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.5851 | −0.620778 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.8456 | 0.779709 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.5552 | −1.05810 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.988330 | 0.0483987 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.13322 | 0.0553615 | 0.0276807 | − | 0.999617i | \(-0.491188\pi\) | ||||
0.0276807 | + | 0.999617i | \(0.491188\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.12164 | 0.200876 | 0.100438 | − | 0.994943i | \(-0.467976\pi\) | ||||
0.100438 | + | 0.994943i | \(0.467976\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.929399 | −0.0451889 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.05136 | 0.293534 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.5494 | −0.704094 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.0689857 | −0.00333066 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.83221 | −0.329096 | −0.164548 | − | 0.986369i | \(-0.552617\pi\) | ||||
−0.164548 | + | 0.986369i | \(0.552617\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.5894 | 1.51809 | 0.759046 | − | 0.651037i | \(-0.225666\pi\) | ||||
0.759046 | + | 0.651037i | \(0.225666\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.28999 | 0.205690 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −38.1560 | −1.82525 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.58677 | 0.218915 | 0.109457 | − | 0.993991i | \(-0.465089\pi\) | ||||
0.109457 | + | 0.993991i | \(0.465089\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.18367 | −0.151604 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.2286 | −1.43621 | −0.718103 | − | 0.695937i | \(-0.754989\pi\) | ||||
−0.718103 | + | 0.695937i | \(0.754989\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.0878 | 0.525614 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.45810 | 0.400054 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.1741 | −1.89593 | −0.947966 | − | 0.318370i | \(-0.896865\pi\) | ||||
−0.947966 | + | 0.318370i | \(0.896865\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.4676 | 1.19922 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.136644 | 0.00642010 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0958578 | −0.00449388 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.5905 | 1.38418 | 0.692092 | − | 0.721809i | \(-0.256689\pi\) | ||||
0.692092 | + | 0.721809i | \(0.256689\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.27829 | 0.106341 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.0716 | −0.608807 | −0.304404 | − | 0.952543i | \(-0.598457\pi\) | ||||
−0.304404 | + | 0.952543i | \(0.598457\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.0242 | −0.558810 | −0.279405 | − | 0.960173i | \(-0.590137\pi\) | ||||
−0.279405 | + | 0.960173i | \(0.590137\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.85552 | −0.132422 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.55381 | 0.349549 | 0.174774 | − | 0.984609i | \(-0.444080\pi\) | ||||
0.174774 | + | 0.984609i | \(0.444080\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.6369 | 0.952925 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.3727 | −0.524026 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.41587 | −0.111082 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.6838 | 0.673738 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.1295 | −0.509586 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.2810 | −1.20081 | −0.600405 | − | 0.799696i | \(-0.704994\pi\) | ||||
−0.600405 | + | 0.799696i | \(0.704994\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.234185 | 0.0106779 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.4832 | −0.613506 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.53301 | 0.205834 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.63742 | 0.300770 | 0.150385 | − | 0.988628i | \(-0.451949\pi\) | ||||
0.150385 | + | 0.988628i | \(0.451949\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.0067 | 0.497742 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.0991 | 0.591156 | 0.295578 | − | 0.955319i | \(-0.404488\pi\) | ||||
0.295578 | + | 0.955319i | \(0.404488\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.38405 | 0.287523 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.29529 | −0.148112 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.6056 | −0.700008 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.1353 | 0.990912 | 0.495456 | − | 0.868633i | \(-0.335001\pi\) | ||||
0.495456 | + | 0.868633i | \(0.335001\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.7703 | 1.01528 | 0.507639 | − | 0.861570i | \(-0.330518\pi\) | ||||
0.507639 | + | 0.861570i | \(0.330518\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.4850 | −0.733573 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9990 | 0.577305 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.95493 | 0.0866506 | 0.0433253 | − | 0.999061i | \(-0.486205\pi\) | ||||
0.0433253 | + | 0.999061i | \(0.486205\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.5021 | 0.906960 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.52833 | 0.244082 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.97707 | −0.175251 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.00044 | 0.0879794 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.6800 | 0.776064 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.26095 | −0.318108 | −0.159054 | − | 0.987270i | \(-0.550844\pi\) | ||||
−0.159054 | + | 0.987270i | \(0.550844\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.6991 | −1.12374 | −0.561871 | − | 0.827225i | \(-0.689918\pi\) | ||||
−0.561871 | + | 0.827225i | \(0.689918\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.18880 | 0.226458 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.24937 | −0.185106 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.6364 | 1.07115 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.11120 | 0.351996 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.379227 | 0.0164261 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.81659 | −0.165006 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.2929 | 1.00516 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.85256 | 0.295160 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.5546 | 0.926703 | 0.463352 | − | 0.886174i | \(-0.346647\pi\) | ||||
0.463352 | + | 0.886174i | \(0.346647\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.4704 | −0.535156 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.1328 | 0.562545 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.8562 | −0.506936 | −0.253468 | − | 0.967344i | \(-0.581571\pi\) | ||||
−0.253468 | + | 0.967344i | \(0.581571\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.44769 | −0.317860 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.4911 | 0.659941 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.4501 | −0.486907 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.1865 | 0.474840 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −44.9125 | −1.90300 | −0.951502 | − | 0.307642i | \(-0.900460\pi\) | ||||
−0.951502 | + | 0.307642i | \(0.900460\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.0359736 | −0.00152152 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.90380 | −0.207039 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.14999 | −0.343481 | −0.171741 | − | 0.985142i | \(-0.554939\pi\) | ||||
−0.171741 | + | 0.985142i | \(0.554939\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.5766 | 1.11808 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.95354 | 0.0820410 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.1874 | 1.64282 | 0.821410 | − | 0.570338i | \(-0.193188\pi\) | ||||
0.821410 | + | 0.570338i | \(0.193188\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.40716 | 0.268131 | 0.134066 | − | 0.990972i | \(-0.457197\pi\) | ||||
0.134066 | + | 0.990972i | \(0.457197\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.6430 | 0.444619 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.3322 | −0.764504 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 45.5385 | 1.89579 | 0.947895 | − | 0.318582i | \(-0.103207\pi\) | ||||
0.947895 | + | 0.318582i | \(0.103207\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.66898 | 0.152478 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.5046 | −1.14108 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.9552 | 0.992125 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0490687 | −0.00202874 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.1537 | −1.49222 | −0.746111 | − | 0.665821i | \(-0.768081\pi\) | ||||
−0.746111 | + | 0.665821i | \(0.768081\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.3112 | −0.424866 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.11526 | 0.210414 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.9600 | 0.860724 | 0.430362 | − | 0.902656i | \(-0.358386\pi\) | ||||
0.430362 | + | 0.902656i | \(0.358386\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.81399 | −0.279346 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.690922 | 0.0282775 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.3654 | 0.913826 | 0.456913 | − | 0.889512i | \(-0.348955\pi\) | ||||
0.456913 | + | 0.889512i | \(0.348955\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.29446 | 0.338338 | 0.169169 | − | 0.985587i | \(-0.445892\pi\) | ||||
0.169169 | + | 0.985587i | \(0.445892\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.5639 | 0.430193 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.74799 | −0.396312 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.58092 | −0.185934 | −0.0929670 | − | 0.995669i | \(-0.529635\pi\) | ||||
−0.0929670 | + | 0.995669i | \(0.529635\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.47406 | 0.221820 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.0297877 | 0.00120508 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.46801 | 0.342020 | 0.171010 | − | 0.985269i | \(-0.445297\pi\) | ||||
0.171010 | + | 0.985269i | \(0.445297\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18.1148 | 0.730459 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.3651 | 0.940642 | 0.470321 | − | 0.882495i | \(-0.344138\pi\) | ||||
0.470321 | + | 0.882495i | \(0.344138\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.4277 | −0.459318 | −0.229659 | − | 0.973271i | \(-0.573761\pi\) | ||||
−0.229659 | + | 0.973271i | \(0.573761\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.90191 | −0.276964 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.1482 | 0.566834 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.66464 | −0.186586 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.8992 | −0.475208 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.6469 | 0.663755 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.40993 | −0.135747 | −0.0678736 | − | 0.997694i | \(-0.521621\pi\) | ||||
−0.0678736 | + | 0.997694i | \(0.521621\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.3286 | −0.609255 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 30.3858 | 1.20582 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.102038 | 0.00404291 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.98837 | −0.316015 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.8009 | −0.782088 | −0.391044 | − | 0.920372i | \(-0.627886\pi\) | ||||
−0.391044 | + | 0.920372i | \(0.627886\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.9862 | −1.57690 | −0.788451 | − | 0.615097i | \(-0.789117\pi\) | ||||
−0.788451 | + | 0.615097i | \(0.789117\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.71838 | −0.0676611 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.7997 | −0.935664 | −0.467832 | − | 0.883817i | \(-0.654965\pi\) | ||||
−0.467832 | + | 0.883817i | \(0.654965\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.4586 | −0.685309 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.64367 | −0.142807 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.24958 | −0.127166 | −0.0635829 | − | 0.997977i | \(-0.520253\pi\) | ||||
−0.0635829 | + | 0.997977i | \(0.520253\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.2568 | 0.478914 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.4948 | 0.409443 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 47.1312 | 1.83597 | 0.917985 | − | 0.396616i | \(-0.129816\pi\) | ||||
0.917985 | + | 0.396616i | \(0.129816\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 49.8545 | 1.93912 | 0.969558 | − | 0.244861i | \(-0.0787424\pi\) | ||||
0.969558 | + | 0.244861i | \(0.0787424\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.0730204 | −0.00283588 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.5343 | −0.641173 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.3400 | −0.748848 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.7330 | 0.917573 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.0305 | 0.618849 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.5519 | 1.13914 | 0.569571 | − | 0.821942i | \(-0.307109\pi\) | ||||
0.569571 | + | 0.821942i | \(0.307109\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.65610 | 0.102233 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.97155 | −0.0757729 | −0.0378864 | − | 0.999282i | \(-0.512063\pi\) | ||||
−0.0378864 | + | 0.999282i | \(0.512063\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.78416 | 0.221976 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.9222 | 0.801742 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.7594 | 0.564751 | 0.282375 | − | 0.959304i | \(-0.408878\pi\) | ||||
0.282375 | + | 0.959304i | \(0.408878\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.2676 | 0.736175 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.6369 | 0.443976 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.356707 | 0.0135895 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.62826 | −0.328234 | −0.164117 | − | 0.986441i | \(-0.552478\pi\) | ||||
−0.164117 | + | 0.986441i | \(0.552478\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.20481 | −0.159728 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.51311 | −0.0573957 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.9571 | 1.02107 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.90044 | 0.298822 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.1406 | −1.25170 | −0.625851 | − | 0.779943i | \(-0.715248\pi\) | ||||
−0.625851 | + | 0.779943i | \(0.715248\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.3941 | 1.52349 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.42289 | 0.0535892 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.0350 | −0.791102 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.0277 | 1.31549 | 0.657746 | − | 0.753240i | \(-0.271510\pi\) | ||||
0.657746 | + | 0.753240i | \(0.271510\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.86119 | −0.219812 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.8732 | 0.482104 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.105616 | 0.00394981 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.2822 | −0.794798 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.7903 | 1.70769 | 0.853846 | − | 0.520526i | \(-0.174264\pi\) | ||||
0.853846 | + | 0.520526i | \(0.174264\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.07477 | −0.188994 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.6365 | 0.655908 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.44271 | 0.276415 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.5668 | 0.466076 | 0.233038 | − | 0.972468i | \(-0.425133\pi\) | ||||
0.233038 | + | 0.972468i | \(0.425133\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.55716 | −0.0945800 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.3051 | 1.30402 | 0.652012 | − | 0.758209i | \(-0.273925\pi\) | ||||
0.652012 | + | 0.758209i | \(0.273925\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.87414 | 0.179785 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.7377 | −0.837553 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.2423 | −1.11248 | −0.556241 | − | 0.831021i | \(-0.687757\pi\) | ||||
−0.556241 | + | 0.831021i | \(0.687757\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.177186 | −0.00650908 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.5002 | 0.605332 | 0.302666 | − | 0.953097i | \(-0.402123\pi\) | ||||
0.302666 | + | 0.953097i | \(0.402123\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.9492 | −0.474422 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.0793 | −0.515136 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.86999 | −0.177946 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.4211 | 1.58446 | 0.792229 | − | 0.610224i | \(-0.208920\pi\) | ||||
0.792229 | + | 0.610224i | \(0.208920\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −29.1497 | −1.06228 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.209199 | −0.00761354 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.8584 | −0.394655 | −0.197327 | − | 0.980338i | \(-0.563226\pi\) | ||||
−0.197327 | + | 0.980338i | \(0.563226\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.8557 | 0.539228 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.4505 | −1.53883 | −0.769415 | − | 0.638750i | \(-0.779452\pi\) | ||||
−0.769415 | + | 0.638750i | \(0.779452\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.7575 | 0.606662 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.48802 | −0.126110 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.259968 | −0.00938691 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.3994 | 0.879865 | 0.439933 | − | 0.898031i | \(-0.355002\pi\) | ||||
0.439933 | + | 0.898031i | \(0.355002\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.8771 | 1.03998 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.70612 | −0.241203 | −0.120601 | − | 0.992701i | \(-0.538482\pi\) | ||||
−0.120601 | + | 0.992701i | \(0.538482\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.95405 | −0.177955 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.2740 | 0.512078 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 65.4120 | 2.34363 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.1942 | 0.615257 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.80212 | 0.100140 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.4114 | 0.621438 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.6064 | −1.59005 | −0.795023 | − | 0.606579i | \(-0.792541\pi\) | ||||
−0.795023 | + | 0.606579i | \(0.792541\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.69587 | −0.131576 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33.9119 | 1.20577 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.238703 | 0.00847658 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17.0391 | 0.604314 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.7264 | 0.840433 | 0.420217 | − | 0.907424i | \(-0.361954\pi\) | ||||
0.420217 | + | 0.907424i | \(0.361954\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.11744 | 0.0749097 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.24231 | 0.255895 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.5891 | −0.797153 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.6425 | 0.727552 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.9065 | 0.419128 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.3941 | −1.38502 | −0.692512 | − | 0.721407i | \(-0.743496\pi\) | ||||
−0.692512 | + | 0.721407i | \(0.743496\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.3386 | −1.41648 | −0.708240 | − | 0.705971i | \(-0.750511\pi\) | ||||
−0.708240 | + | 0.705971i | \(0.750511\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.42035 | −0.330386 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.8511 | −0.590268 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.20502 | −0.217086 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.0626121 | −0.00218784 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.3862 | −1.47929 | −0.739645 | − | 0.672997i | \(-0.765007\pi\) | ||||
−0.739645 | + | 0.672997i | \(0.765007\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.66255 | −0.232242 | −0.116121 | − | 0.993235i | \(-0.537046\pi\) | ||||
−0.116121 | + | 0.993235i | \(0.537046\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.71700 | −0.199040 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.1082 | −0.664456 | −0.332228 | − | 0.943199i | \(-0.607800\pi\) | ||||
−0.332228 | + | 0.943199i | \(0.607800\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.4467 | −1.75209 | −0.876044 | − | 0.482231i | \(-0.839827\pi\) | ||||
−0.876044 | + | 0.482231i | \(0.839827\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.72432 | 0.337333 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.25333 | 0.251313 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.53098 | −0.0529818 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.86516 | −0.0644693 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.7449 | −0.957862 | −0.478931 | − | 0.877853i | \(-0.658976\pi\) | ||||
−0.478931 | + | 0.877853i | \(0.658976\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.1481 | −0.729245 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.54649 | 0.328799 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.9012 | −0.684621 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.4385 | −0.427392 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.881411 | −0.0302499 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −50.4305 | −1.72873 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.0988 | 1.68111 | 0.840556 | − | 0.541725i | \(-0.182229\pi\) | ||||
0.840556 | + | 0.541725i | \(0.182229\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.46376 | −0.289455 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.7973 | 1.63272 | 0.816362 | − | 0.577541i | \(-0.195988\pi\) | ||||
0.816362 | + | 0.577541i | \(0.195988\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.6308 | 1.18159 | 0.590794 | − | 0.806822i | \(-0.298814\pi\) | ||||
0.590794 | + | 0.806822i | \(0.298814\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.1146 | 0.787743 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 53.2646 | 1.81315 | 0.906574 | − | 0.422047i | \(-0.138688\pi\) | ||||
0.906574 | + | 0.422047i | \(0.138688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27.0677 | −0.920329 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.8094 | 0.401068 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.6156 | 0.427956 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.338577 | −0.0114722 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.96086 | 0.100210 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −22.8981 | −0.774098 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.6892 | −1.67789 | −0.838943 | − | 0.544219i | \(-0.816826\pi\) | ||||
−0.838943 | + | 0.544219i | \(0.816826\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.37269 | −0.248675 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.172379 | 0.00580759 | 0.00290379 | − | 0.999996i | \(-0.499076\pi\) | ||||
0.00290379 | + | 0.999996i | \(0.499076\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.2229 | 1.85840 | 0.929200 | − | 0.369578i | \(-0.120498\pi\) | ||||
0.929200 | + | 0.369578i | \(0.120498\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.4181 | −0.417429 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.2457 | −1.31774 | −0.658871 | − | 0.752256i | \(-0.728966\pi\) | ||||
−0.658871 | + | 0.752256i | \(0.728966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.7725 | 1.30039 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.15240 | −0.0721083 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.13802 | 0.171937 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −35.6610 | −1.19202 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.221210 | 0.00738598 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.22640 | −0.174310 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.3563 | 0.844740 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.19266 | −0.0729673 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.0919 | 0.634638 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.0928 | 0.567559 | 0.283779 | − | 0.958890i | \(-0.408412\pi\) | ||||
0.283779 | + | 0.958890i | \(0.408412\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.7676 | −0.357139 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.5880 | −0.615850 | −0.307925 | − | 0.951411i | \(-0.599635\pi\) | ||||
−0.307925 | + | 0.951411i | \(0.599635\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.3044 | 1.00293 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.4023 | 0.376948 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.6398 | 0.516472 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.4303 | 0.838868 | 0.419434 | − | 0.907786i | \(-0.362229\pi\) | ||||
0.419434 | + | 0.907786i | \(0.362229\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.3416 | 0.373718 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.256032 | 0.00842738 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.4074 | 0.638112 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.59773 | −0.0853205 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.00391 | 0.196982 | 0.0984909 | − | 0.995138i | \(-0.468598\pi\) | ||||
0.0984909 | + | 0.995138i | \(0.468598\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.6004 | 0.576830 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.2572 | 0.761406 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.50763 | 0.245526 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.8575 | −1.56344 | −0.781719 | − | 0.623631i | \(-0.785657\pi\) | ||||
−0.781719 | + | 0.623631i | \(0.785657\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.6287 | −0.803728 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.11153 | −0.0362348 | −0.0181174 | − | 0.999836i | \(-0.505767\pi\) | ||||
−0.0181174 | + | 0.999836i | \(0.505767\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −81.6644 | −2.65936 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.99083 | −0.0972919 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.8001 | −0.513434 | −0.256717 | − | 0.966487i | \(-0.582641\pi\) | ||||
−0.256717 | + | 0.966487i | \(0.582641\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.336365 | −0.0109189 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.6228 | −0.474177 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.6651 | 0.410263 | 0.205131 | − | 0.978734i | \(-0.434238\pi\) | ||||
0.205131 | + | 0.978734i | \(0.434238\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.2943 | −0.527270 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.03130 | −0.194964 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.5855 | 0.793908 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.5212 | −0.887780 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.49290 | −0.0803327 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.61714 | −0.180822 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.0282 | −0.997801 | −0.498901 | − | 0.866659i | \(-0.666263\pi\) | ||||
−0.498901 | + | 0.866659i | \(0.666263\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.5951 | −0.404614 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.5965 | 0.404242 | 0.202121 | − | 0.979361i | \(-0.435217\pi\) | ||||
0.202121 | + | 0.979361i | \(0.435217\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.93074 | −0.0618968 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.0851294 | −0.00272632 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.7953 | −0.697295 | −0.348647 | − | 0.937254i | \(-0.613359\pi\) | ||||
−0.348647 | + | 0.937254i | \(0.613359\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.5884 | −0.498207 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.57800 | 0.273875 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.0842 | 1.02333 | 0.511664 | − | 0.859186i | \(-0.329029\pi\) | ||||
0.511664 | + | 0.859186i | \(0.329029\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.83136 | −0.249528 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.81562 | 0.0577918 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.74673 | 0.246332 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.9196 | 1.07749 | 0.538745 | − | 0.842469i | \(-0.318899\pi\) | ||||
0.538745 | + | 0.842469i | \(0.318899\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.4030 | −0.457065 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.05779 | −0.0335341 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55.7384 | −1.76525 | −0.882626 | − | 0.470076i | \(-0.844226\pi\) | ||||
−0.882626 | + | 0.470076i | \(0.844226\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.30674 | 0.231175 |
(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 | 4008.2.a.j.1.9 | ✓ | 10 | |
4.3 | odd | 2 | 8016.2.a.bd.1.9 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.j.1.9 | ✓ | 10 | 1.1 | even | 1 | trivial | |
8016.2.a.bd.1.9 | 10 | 4.3 | odd | 2 |