Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.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: | \(32.1318017734\) |
Analytic rank: | \(1\) |
Dimension: | \(29\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-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 | ||||||||
\(3\) | −0.278789 | −0.160959 | −0.0804795 | − | 0.996756i | \(-0.525645\pi\) | ||||
−0.0804795 | + | 0.996756i | \(0.525645\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.533193 | −0.238451 | −0.119226 | − | 0.992867i | \(-0.538041\pi\) | ||||
−0.119226 | + | 0.992867i | \(0.538041\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.93823 | 0.732583 | 0.366292 | − | 0.930500i | \(-0.380627\pi\) | ||||
0.366292 | + | 0.930500i | \(0.380627\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.92228 | −0.974092 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.65384 | −1.10167 | −0.550837 | − | 0.834613i | \(-0.685691\pi\) | ||||
−0.550837 | + | 0.834613i | \(0.685691\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.69726 | 1.58013 | 0.790067 | − | 0.613020i | \(-0.210046\pi\) | ||||
0.790067 | + | 0.613020i | \(0.210046\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.148648 | 0.0383808 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.46842 | 1.56882 | 0.784411 | − | 0.620241i | \(-0.212965\pi\) | ||||
0.784411 | + | 0.620241i | \(0.212965\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.37548 | −1.00380 | −0.501902 | − | 0.864924i | \(-0.667366\pi\) | ||||
−0.501902 | + | 0.864924i | \(0.667366\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.540358 | −0.117916 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.89803 | −1.85537 | −0.927684 | − | 0.373366i | \(-0.878203\pi\) | ||||
−0.927684 | + | 0.373366i | \(0.878203\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.71571 | −0.943141 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.65107 | 0.317748 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.939891 | −0.174533 | −0.0872667 | − | 0.996185i | \(-0.527813\pi\) | ||||
−0.0872667 | + | 0.996185i | \(0.527813\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.67842 | 1.19948 | 0.599740 | − | 0.800195i | \(-0.295271\pi\) | ||||
0.599740 | + | 0.800195i | \(0.295271\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.01865 | 0.177324 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.03345 | −0.174685 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.254878 | 0.0419017 | 0.0209509 | − | 0.999781i | \(-0.493331\pi\) | ||||
0.0209509 | + | 0.999781i | \(0.493331\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.58833 | −0.254337 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.94692 | 0.304058 | 0.152029 | − | 0.988376i | \(-0.451419\pi\) | ||||
0.152029 | + | 0.988376i | \(0.451419\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.83373 | 0.279641 | 0.139821 | − | 0.990177i | \(-0.455347\pi\) | ||||
0.139821 | + | 0.990177i | \(0.455347\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.55814 | 0.232273 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.30907 | −0.774407 | −0.387203 | − | 0.921994i | \(-0.626559\pi\) | ||||
−0.387203 | + | 0.921994i | \(0.626559\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.24325 | −0.463322 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.80333 | −0.252516 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.23824 | 0.170085 | 0.0850424 | − | 0.996377i | \(-0.472897\pi\) | ||||
0.0850424 | + | 0.996377i | \(0.472897\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.94820 | 0.262695 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.21984 | 0.161571 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.09850 | −0.143012 | −0.0715062 | − | 0.997440i | \(-0.522781\pi\) | ||||
−0.0715062 | + | 0.997440i | \(0.522781\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.6922 | −1.62507 | −0.812536 | − | 0.582911i | \(-0.801914\pi\) | ||||
−0.812536 | + | 0.582911i | \(0.801914\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.66405 | −0.713604 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.03773 | −0.376785 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3763 | 1.38984 | 0.694920 | − | 0.719087i | \(-0.255440\pi\) | ||||
0.694920 | + | 0.719087i | \(0.255440\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.48068 | 0.298638 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.49053 | −1.12632 | −0.563159 | − | 0.826349i | \(-0.690414\pi\) | ||||
−0.563159 | + | 0.826349i | \(0.690414\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.549818 | −0.0643514 | −0.0321757 | − | 0.999482i | \(-0.510244\pi\) | ||||
−0.0321757 | + | 0.999482i | \(0.510244\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.31469 | 0.151807 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.08199 | −0.807067 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.46883 | −0.165256 | −0.0826282 | − | 0.996580i | \(-0.526331\pi\) | ||||
−0.0826282 | + | 0.996580i | \(0.526331\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.30653 | 0.922948 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.74985 | 0.301835 | 0.150917 | − | 0.988546i | \(-0.451777\pi\) | ||||
0.150917 | + | 0.988546i | \(0.451777\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.44891 | −0.374087 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.262032 | 0.0280927 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.78644 | 0.931360 | 0.465680 | − | 0.884953i | \(-0.345810\pi\) | ||||
0.465680 | + | 0.884953i | \(0.345810\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.0426 | 1.15758 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.86187 | −0.193067 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.33298 | 0.239358 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.40964 | −0.853870 | −0.426935 | − | 0.904282i | \(-0.640407\pi\) | ||||
−0.426935 | + | 0.904282i | \(0.640407\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.6775 | 1.07313 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.56448 | −0.752694 | −0.376347 | − | 0.926479i | \(-0.622820\pi\) | ||||
−0.376347 | + | 0.926479i | \(0.622820\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.15698 | −0.705198 | −0.352599 | − | 0.935775i | \(-0.614702\pi\) | ||||
−0.352599 | + | 0.935775i | \(0.614702\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.288115 | 0.0281172 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.6918 | −1.51698 | −0.758492 | − | 0.651682i | \(-0.774064\pi\) | ||||
−0.758492 | + | 0.651682i | \(0.774064\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.48174 | 0.525055 | 0.262528 | − | 0.964924i | \(-0.415444\pi\) | ||||
0.262528 | + | 0.964924i | \(0.415444\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0710573 | −0.00674446 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.51716 | −0.424939 | −0.212469 | − | 0.977168i | \(-0.568151\pi\) | ||||
−0.212469 | + | 0.977168i | \(0.568151\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.74437 | 0.442414 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.6490 | −1.53920 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.5373 | 1.14929 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.35053 | 0.213684 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.542781 | −0.0489409 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.18034 | 0.463344 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.356947 | −0.0316739 | −0.0158370 | − | 0.999875i | \(-0.505041\pi\) | ||||
−0.0158370 | + | 0.999875i | \(0.505041\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.511224 | −0.0450108 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.5810 | −1.36132 | −0.680660 | − | 0.732600i | \(-0.738307\pi\) | ||||
−0.680660 | + | 0.732600i | \(0.738307\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.48070 | −0.735370 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.880337 | −0.0757673 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.3404 | −1.22518 | −0.612592 | − | 0.790399i | \(-0.709873\pi\) | ||||
−0.612592 | + | 0.790399i | \(0.709873\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.617329 | 0.0523612 | 0.0261806 | − | 0.999657i | \(-0.491666\pi\) | ||||
0.0261806 | + | 0.999657i | \(0.491666\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.48011 | 0.124648 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.8168 | −1.74079 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.501143 | 0.0416177 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.904184 | 0.0745758 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.7701 | 1.21001 | 0.605005 | − | 0.796222i | \(-0.293171\pi\) | ||||
0.605005 | + | 0.796222i | \(0.293171\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.9354 | −0.889909 | −0.444954 | − | 0.895553i | \(-0.646780\pi\) | ||||
−0.444954 | + | 0.895553i | \(0.646780\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.9025 | −1.52818 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.56089 | −0.286017 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.8967 | −0.869655 | −0.434827 | − | 0.900514i | \(-0.643191\pi\) | ||||
−0.434827 | + | 0.900514i | \(0.643191\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.345207 | −0.0273767 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.2465 | −1.35921 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.3000 | 0.885087 | 0.442544 | − | 0.896747i | \(-0.354076\pi\) | ||||
0.442544 | + | 0.896747i | \(0.354076\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.543137 | −0.0422832 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.2107 | −1.87348 | −0.936739 | − | 0.350028i | \(-0.886172\pi\) | ||||
−0.936739 | + | 0.350028i | \(0.886172\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.4587 | 1.49682 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.7864 | 0.977798 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.68096 | −0.279858 | −0.139929 | − | 0.990162i | \(-0.544687\pi\) | ||||
−0.139929 | + | 0.990162i | \(0.544687\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.14014 | −0.690929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.306250 | 0.0230191 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.3487 | 0.773496 | 0.386748 | − | 0.922185i | \(-0.373598\pi\) | ||||
0.386748 | + | 0.922185i | \(0.373598\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.27377 | 0.466325 | 0.233163 | − | 0.972438i | \(-0.425093\pi\) | ||||
0.233163 | + | 0.972438i | \(0.425093\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.53845 | 0.261570 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.135899 | −0.00999151 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.6346 | −1.72833 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.20015 | 0.232777 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.8440 | −0.929359 | −0.464680 | − | 0.885479i | \(-0.653830\pi\) | ||||
−0.464680 | + | 0.885479i | \(0.653830\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.6873 | 1.77703 | 0.888517 | − | 0.458844i | \(-0.151736\pi\) | ||||
0.888517 | + | 0.458844i | \(0.151736\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.846888 | 0.0606469 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.9025 | −1.41799 | −0.708996 | − | 0.705213i | \(-0.750851\pi\) | ||||
−0.708996 | + | 0.705213i | \(0.750851\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.4320 | −1.37750 | −0.688748 | − | 0.725001i | \(-0.741839\pi\) | ||||
−0.688748 | + | 0.725001i | \(0.741839\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.17160 | −0.223707 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.82173 | −0.127860 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.03808 | −0.0725029 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 26.0025 | 1.80730 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.9873 | 1.10586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.2368 | −1.80622 | −0.903109 | − | 0.429412i | \(-0.858721\pi\) | ||||
−0.903109 | + | 0.429412i | \(0.858721\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.64586 | 0.181291 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.977732 | −0.0666808 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.9443 | 0.878719 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.153283 | 0.0103579 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 36.8522 | 2.47895 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.20020 | 0.147336 | 0.0736681 | − | 0.997283i | \(-0.476529\pi\) | ||||
0.0736681 | + | 0.997283i | \(0.476529\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.7806 | 0.918706 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.32572 | −0.552598 | −0.276299 | − | 0.961072i | \(-0.589108\pi\) | ||||
−0.276299 | + | 0.961072i | \(0.589108\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.16853 | 0.605873 | 0.302937 | − | 0.953011i | \(-0.402033\pi\) | ||||
0.302937 | + | 0.953011i | \(0.402033\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.97438 | 0.129905 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −27.9523 | −1.83121 | −0.915607 | − | 0.402074i | \(-0.868289\pi\) | ||||
−0.915607 | + | 0.402074i | \(0.868289\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.83076 | 0.184658 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.409494 | 0.0265995 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.06396 | 0.456930 | 0.228465 | − | 0.973552i | \(-0.426629\pi\) | ||||
0.228465 | + | 0.973552i | \(0.426629\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.7543 | −0.885995 | −0.442998 | − | 0.896523i | \(-0.646085\pi\) | ||||
−0.442998 | + | 0.896523i | \(0.646085\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.26897 | −0.466305 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.72928 | 0.110480 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.9282 | −1.58615 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.766627 | −0.0485830 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.33227 | −0.399690 | −0.199845 | − | 0.979828i | \(-0.564044\pi\) | ||||
−0.199845 | + | 0.979828i | \(0.564044\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.5120 | 2.04401 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.961520 | 0.0602127 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.48751 | −0.0927882 | −0.0463941 | − | 0.998923i | \(-0.514773\pi\) | ||||
−0.0463941 | + | 0.998923i | \(0.514773\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.494013 | 0.0306965 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.74662 | 0.170012 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.3815 | −1.01012 | −0.505062 | − | 0.863083i | \(-0.668531\pi\) | ||||
−0.505062 | + | 0.863083i | \(0.668531\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.660218 | −0.0405569 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.44956 | −0.149911 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.9069 | 1.82345 | 0.911726 | − | 0.410798i | \(-0.134750\pi\) | ||||
0.911726 | + | 0.410798i | \(0.134750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.5497 | 1.24830 | 0.624152 | − | 0.781303i | \(-0.285444\pi\) | ||||
0.624152 | + | 0.781303i | \(0.285444\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.07856 | −0.186323 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.2304 | 1.03903 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.7625 | 1.00716 | 0.503579 | − | 0.863949i | \(-0.332016\pi\) | ||||
0.503579 | + | 0.863949i | \(0.332016\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −19.5162 | −1.16840 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.6396 | 1.52953 | 0.764766 | − | 0.644308i | \(-0.222855\pi\) | ||||
0.764766 | + | 0.644308i | \(0.222855\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4338 | −0.739112 | −0.369556 | − | 0.929209i | \(-0.620490\pi\) | ||||
−0.369556 | + | 0.929209i | \(0.620490\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.650408 | −0.0385269 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.77359 | 0.222748 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.8405 | 1.46120 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.34452 | 0.137438 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.9618 | 0.757236 | 0.378618 | − | 0.925553i | \(-0.376399\pi\) | ||||
0.378618 | + | 0.925553i | \(0.376399\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.585711 | 0.0341014 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.03273 | −0.350054 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −50.6944 | −2.93173 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.55420 | 0.204861 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.10890 | 0.121153 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.76740 | 0.387500 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.0655 | 0.802759 | 0.401379 | − | 0.915912i | \(-0.368531\pi\) | ||||
0.401379 | + | 0.915912i | \(0.368531\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.99529 | 0.113508 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.2484 | −0.581133 | −0.290566 | − | 0.956855i | \(-0.593844\pi\) | ||||
−0.290566 | + | 0.956855i | \(0.593844\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.08174 | 0.400284 | 0.200142 | − | 0.979767i | \(-0.435860\pi\) | ||||
0.200142 | + | 0.979767i | \(0.435860\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.02003 | 0.170159 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.9770 | −1.29052 | −0.645260 | − | 0.763963i | \(-0.723251\pi\) | ||||
−0.645260 | + | 0.763963i | \(0.723251\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.43421 | 0.192279 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.37471 | 0.244172 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.3025 | −1.57479 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.8666 | −1.49029 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.52825 | −0.0845124 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.2902 | −0.567318 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.6362 | −1.24420 | −0.622098 | − | 0.782939i | \(-0.713720\pi\) | ||||
−0.622098 | + | 0.782939i | \(0.713720\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.744825 | −0.0408161 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.06577 | −0.331409 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.23572 | −0.339681 | −0.169841 | − | 0.985472i | \(-0.554325\pi\) | ||||
−0.169841 | + | 0.985472i | \(0.554325\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.25934 | 0.0683977 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.4019 | −1.32144 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.8538 | −1.07201 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.32268 | −0.0712106 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.9815 | 0.857932 | 0.428966 | − | 0.903321i | \(-0.358878\pi\) | ||||
0.428966 | + | 0.903321i | \(0.358878\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.07839 | −0.378897 | −0.189449 | − | 0.981891i | \(-0.560670\pi\) | ||||
−0.189449 | + | 0.981891i | \(0.560670\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.40655 | 0.502084 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.6725 | −0.727714 | −0.363857 | − | 0.931455i | \(-0.618540\pi\) | ||||
−0.363857 | + | 0.931455i | \(0.618540\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.06028 | 0.268572 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.49527 | −0.184989 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.0638 | −0.795038 | −0.397519 | − | 0.917594i | \(-0.630129\pi\) | ||||
−0.397519 | + | 0.917594i | \(0.630129\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.144848 | 0.00762360 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.655301 | −0.0343944 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.293159 | 0.0153446 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.64083 | 0.190050 | 0.0950248 | − | 0.995475i | \(-0.469707\pi\) | ||||
0.0950248 | + | 0.995475i | \(0.469707\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.68944 | −0.296181 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.39999 | 0.124601 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.53608 | 0.441981 | 0.220991 | − | 0.975276i | \(-0.429071\pi\) | ||||
0.220991 | + | 0.975276i | \(0.429071\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.44422 | −0.0745794 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.35480 | −0.275786 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.9016 | 1.53594 | 0.767971 | − | 0.640485i | \(-0.221267\pi\) | ||||
0.767971 | + | 0.640485i | \(0.221267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.0995129 | 0.00509820 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.6657 | −1.20926 | −0.604629 | − | 0.796507i | \(-0.706679\pi\) | ||||
−0.604629 | + | 0.796507i | \(0.706679\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.77606 | 0.192446 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.35867 | −0.272396 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.0050 | −1.11570 | −0.557849 | − | 0.829942i | \(-0.688373\pi\) | ||||
−0.557849 | + | 0.829942i | \(0.688373\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −57.5562 | −2.91074 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.34382 | 0.219117 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.783170 | 0.0394056 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.9740 | −1.50435 | −0.752175 | − | 0.658963i | \(-0.770995\pi\) | ||||
−0.752175 | + | 0.658963i | \(0.770995\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.36433 | 0.118365 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.98771 | −0.448825 | −0.224412 | − | 0.974494i | \(-0.572046\pi\) | ||||
−0.224412 | + | 0.974494i | \(0.572046\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.0487 | 1.89534 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.42898 | −0.220078 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.931284 | −0.0461620 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.2282 | 0.950772 | 0.475386 | − | 0.879777i | \(-0.342308\pi\) | ||||
0.475386 | + | 0.879777i | \(0.342308\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.99795 | 0.197204 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.12915 | −0.104768 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.46620 | −0.0719728 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.172105 | −0.00842801 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.6843 | −0.961643 | −0.480822 | − | 0.876818i | \(-0.659662\pi\) | ||||
−0.480822 | + | 0.876818i | \(0.659662\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.3581 | −0.651033 | −0.325517 | − | 0.945536i | \(-0.605538\pi\) | ||||
−0.325517 | + | 0.945536i | \(0.605538\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.5146 | 0.754344 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −30.5032 | −1.47962 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.6005 | −1.19050 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.80351 | 0.280196 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 40.3852 | 1.94529 | 0.972644 | − | 0.232301i | \(-0.0746253\pi\) | ||||
0.972644 | + | 0.232301i | \(0.0746253\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.9912 | −1.39323 | −0.696614 | − | 0.717446i | \(-0.745311\pi\) | ||||
−0.696614 | + | 0.717446i | \(0.745311\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.139713 | −0.00669874 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 38.9332 | 1.86243 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.09475 | −0.0522497 | −0.0261248 | − | 0.999659i | \(-0.508317\pi\) | ||||
−0.0261248 | + | 0.999659i | \(0.508317\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.47768 | 0.451318 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.38223 | −0.255718 | −0.127859 | − | 0.991792i | \(-0.540810\pi\) | ||||
−0.127859 | + | 0.991792i | \(0.540810\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.68486 | −0.222084 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.11773 | −0.194762 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.5743 | −1.91482 | −0.957410 | − | 0.288733i | \(-0.906766\pi\) | ||||
−0.957410 | + | 0.288733i | \(0.906766\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.11373 | −0.334973 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.04867 | 0.143239 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.88784 | −0.276026 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.8573 | 0.601438 | 0.300719 | − | 0.953713i | \(-0.402773\pi\) | ||||
0.300719 | + | 0.953713i | \(0.402773\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.6798 | 0.498490 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.2492 | 1.31569 | 0.657847 | − | 0.753152i | \(-0.271467\pi\) | ||||
0.657847 | + | 0.753152i | \(0.271467\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.58957 | 0.259769 | 0.129885 | − | 0.991529i | \(-0.458539\pi\) | ||||
0.129885 | + | 0.991529i | \(0.458539\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.992737 | 0.0460371 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.4778 | 1.08642 | 0.543211 | − | 0.839596i | \(-0.317209\pi\) | ||||
0.543211 | + | 0.839596i | \(0.317209\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.0500 | 1.01817 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.03789 | 0.139979 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.70015 | −0.308073 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.6335 | 0.946729 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.61847 | −0.165678 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.58953 | 0.438157 | 0.219078 | − | 0.975707i | \(-0.429695\pi\) | ||||
0.219078 | + | 0.975707i | \(0.429695\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.45211 | 0.0662104 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.80813 | 0.218777 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.48396 | 0.203606 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.27219 | −0.420163 | −0.210081 | − | 0.977684i | \(-0.567373\pi\) | ||||
−0.210081 | + | 0.977684i | \(0.567373\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.15033 | −0.142463 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.1352 | 0.547655 | 0.273828 | − | 0.961779i | \(-0.411710\pi\) | ||||
0.273828 | + | 0.961779i | \(0.411710\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.07961 | −0.273812 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.69318 | −0.255889 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.3948 | −0.825122 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.6687 | −1.10432 | −0.552162 | − | 0.833737i | \(-0.686197\pi\) | ||||
−0.552162 | + | 0.833737i | \(0.686197\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.74968 | 0.301553 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.03332 | 0.179481 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.42488 | −0.240927 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.0468 | 1.33180 | 0.665902 | − | 0.746040i | \(-0.268047\pi\) | ||||
0.665902 | + | 0.746040i | \(0.268047\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.06568 | −0.0471427 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.22421 | −0.318957 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.81605 | 0.168155 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.3985 | 0.853143 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.02621 | 0.0450457 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.7233 | −1.12696 | −0.563479 | − | 0.826130i | \(-0.690537\pi\) | ||||
−0.563479 | + | 0.826130i | \(0.690537\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.5812 | 1.77449 | 0.887247 | − | 0.461296i | \(-0.152615\pi\) | ||||
0.887247 | + | 0.461296i | \(0.152615\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.54817 | 0.111211 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 43.1989 | 1.88177 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 56.1750 | 2.44239 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.21012 | 0.139307 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.0921 | 0.480453 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.36676 | 0.361726 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.88510 | −0.124501 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.8503 | 0.510429 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.0528 | 1.85098 | 0.925491 | − | 0.378768i | \(-0.123652\pi\) | ||||
0.925491 | + | 0.378768i | \(0.123652\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.74906 | −0.0750593 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.92282 | −0.125200 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.8613 | 0.635425 | 0.317713 | − | 0.948187i | \(-0.397085\pi\) | ||||
0.317713 | + | 0.948187i | \(0.397085\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 37.0902 | 1.58297 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.11248 | 0.175197 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.84694 | −0.121064 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.0378872 | 0.00160822 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.73500 | 0.327742 | 0.163871 | − | 0.986482i | \(-0.447602\pi\) | ||||
0.163871 | + | 0.986482i | \(0.447602\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.4472 | 0.441871 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.58906 | 0.278190 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.4246 | −0.607925 | −0.303963 | − | 0.952684i | \(-0.598310\pi\) | ||||
−0.303963 | + | 0.952684i | \(0.598310\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.40852 | 0.101327 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.1000 | 0.676136 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.0590 | −0.463618 | −0.231809 | − | 0.972761i | \(-0.574464\pi\) | ||||
−0.231809 | + | 0.972761i | \(0.574464\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.00340 | −0.376780 | −0.188390 | − | 0.982094i | \(-0.560327\pi\) | ||||
−0.188390 | + | 0.982094i | \(0.560327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.58077 | 0.149589 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 41.9605 | 1.74987 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.3685 | −0.473277 | −0.236638 | − | 0.971598i | \(-0.576046\pi\) | ||||
−0.236638 | + | 0.971598i | \(0.576046\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.88257 | −0.286030 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.32984 | 0.221119 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.52431 | −0.187378 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.87710 | 0.367023 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.8389 | −1.14904 | −0.574518 | − | 0.818492i | \(-0.694810\pi\) | ||||
−0.574518 | + | 0.818492i | \(0.694810\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.2213 | −1.20404 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.54859 | 0.228239 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.0177 | 0.863092 | 0.431546 | − | 0.902091i | \(-0.357968\pi\) | ||||
0.431546 | + | 0.902091i | \(0.357968\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.68480 | −0.274050 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.41742 | 0.221720 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.6730 | 1.33498 | 0.667491 | − | 0.744618i | \(-0.267368\pi\) | ||||
0.667491 | + | 0.744618i | \(0.267368\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.8085 | −0.848798 | −0.424399 | − | 0.905475i | \(-0.639515\pi\) | ||||
−0.424399 | + | 0.905475i | \(0.639515\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −33.2448 | −1.35383 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.25328 | −0.0509532 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.77008 | −0.355966 | −0.177983 | − | 0.984034i | \(-0.556957\pi\) | ||||
−0.177983 | + | 0.984034i | \(0.556957\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.507878 | 0.0205803 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.2471 | −1.22367 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.8737 | 1.40854 | 0.704268 | − | 0.709934i | \(-0.251275\pi\) | ||||
0.704268 | + | 0.709934i | \(0.251275\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.289407 | 0.0116700 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.6845 | 0.792466 | 0.396233 | − | 0.918150i | \(-0.370317\pi\) | ||||
0.396233 | + | 0.918150i | \(0.370317\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.3438 | −0.857879 | −0.428939 | − | 0.903333i | \(-0.641113\pi\) | ||||
−0.428939 | + | 0.903333i | \(0.641113\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.6912 | −0.589539 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.0302 | 0.682299 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.8164 | 0.832656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.45709 | −0.177999 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.64866 | 0.0657364 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 49.9643 | 1.98905 | 0.994524 | − | 0.104512i | \(-0.0333281\pi\) | ||||
0.994524 | + | 0.104512i | \(0.0333281\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.31455 | 0.290727 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.190321 | 0.00755268 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.4776 | −0.732111 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 27.7339 | 1.09714 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.3561 | −1.19899 | −0.599497 | − | 0.800377i | \(-0.704633\pi\) | ||||
−0.599497 | + | 0.800377i | \(0.704633\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.9321 | 1.53533 | 0.767665 | − | 0.640851i | \(-0.221418\pi\) | ||||
0.767665 | + | 0.640851i | \(0.221418\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.272581 | 0.0107329 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.0572 | −0.749215 | −0.374608 | − | 0.927183i | \(-0.622223\pi\) | ||||
−0.374608 | + | 0.927183i | \(0.622223\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.01373 | 0.157553 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.60874 | −0.141438 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.4775 | −1.27094 | −0.635472 | − | 0.772124i | \(-0.719194\pi\) | ||||
−0.635472 | + | 0.772124i | \(0.719194\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.30768 | 0.324608 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.60672 | 0.0626842 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.3863 | −0.521454 | −0.260727 | − | 0.965413i | \(-0.583962\pi\) | ||||
−0.260727 | + | 0.965413i | \(0.583962\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.9688 | −0.582220 | −0.291110 | − | 0.956690i | \(-0.594025\pi\) | ||||
−0.291110 | + | 0.956690i | \(0.594025\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.2740 | −0.399009 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.52185 | 0.175350 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.36318 | 0.323824 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.613392 | −0.0237151 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 46.3753 | 1.79030 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.08519 | 0.234567 | 0.117283 | − | 0.993098i | \(-0.462581\pi\) | ||||
0.117283 | + | 0.993098i | \(0.462581\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.78595 | −0.299681 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.3791 | 1.01383 | 0.506916 | − | 0.861995i | \(-0.330785\pi\) | ||||
0.506916 | + | 0.861995i | \(0.330785\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.2998 | −0.625531 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.32112 | 0.0889456 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.12382 | 0.310850 | 0.155425 | − | 0.987848i | \(-0.450325\pi\) | ||||
0.155425 | + | 0.987848i | \(0.450325\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.64620 | 0.292146 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.55609 | −0.0975208 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.05455 | 0.268757 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.85362 | 0.222682 | 0.111341 | − | 0.993782i | \(-0.464485\pi\) | ||||
0.111341 | + | 0.993782i | \(0.464485\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 20.6955 | 0.786158 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.329155 | −0.0124856 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.5935 | 0.477013 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.79279 | 0.294751 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.6736 | 1.27184 | 0.635918 | − | 0.771757i | \(-0.280622\pi\) | ||||
0.635918 | + | 0.771757i | \(0.280622\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.11522 | −0.0420611 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.789184 | −0.0297224 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.6617 | −0.551411 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.1190 | 0.417581 | 0.208791 | − | 0.977960i | \(-0.433047\pi\) | ||||
0.208791 | + | 0.977960i | \(0.433047\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.29233 | 0.160975 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −59.4248 | −2.22548 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.0994 | 0.415094 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.96936 | −0.0735470 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.7212 | 0.474422 | 0.237211 | − | 0.971458i | \(-0.423767\pi\) | ||||
0.237211 | + | 0.971458i | \(0.423767\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.8719 | −0.516616 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.83456 | 0.142609 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.43225 | 0.164610 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.8102 | −1.36521 | −0.682607 | − | 0.730785i | \(-0.739154\pi\) | ||||
−0.682607 | + | 0.730785i | \(0.739154\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.8931 | −0.847892 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.8613 | 0.438708 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.36736 | 0.0874403 | 0.0437202 | − | 0.999044i | \(-0.486079\pi\) | ||||
0.0437202 | + | 0.999044i | \(0.486079\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.482104 | −0.0177827 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −41.5672 | −1.53115 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.2838 | 0.930079 | 0.465039 | − | 0.885290i | \(-0.346040\pi\) | ||||
0.465039 | + | 0.885290i | \(0.346040\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.94973 | 0.255305 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.3022 | −1.40517 | −0.702586 | − | 0.711599i | \(-0.747971\pi\) | ||||
−0.702586 | + | 0.711599i | \(0.747971\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.87529 | −0.288528 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.03581 | −0.294015 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30.4144 | −1.11132 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.1161 | 0.442121 | 0.221061 | − | 0.975260i | \(-0.429048\pi\) | ||||
0.221061 | + | 0.975260i | \(0.429048\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.76537 | 0.0643336 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.83066 | 0.212200 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.5424 | −0.383171 | −0.191586 | − | 0.981476i | \(-0.561363\pi\) | ||||
−0.191586 | + | 0.981476i | \(0.561363\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.06398 | −0.329002 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 52.0276 | 1.88600 | 0.942999 | − | 0.332796i | \(-0.107992\pi\) | ||||
0.942999 | + | 0.332796i | \(0.107992\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.6249 | 0.384647 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.0787 | 0.364396 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.25843 | −0.225979 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.4385 | 0.628848 | 0.314424 | − | 0.949283i | \(-0.398189\pi\) | ||||
0.314424 | + | 0.949283i | \(0.398189\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.414701 | 0.0149351 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.9057 | 0.715960 | 0.357980 | − | 0.933729i | \(-0.383466\pi\) | ||||
0.357980 | + | 0.933729i | \(0.383466\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31.4935 | −1.13128 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.137726 | −0.00494088 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.51872 | −0.305215 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.6768 | 1.24083 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.55182 | −0.0554576 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.81006 | 0.207370 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.53287 | −0.0902869 | −0.0451435 | − | 0.998981i | \(-0.514374\pi\) | ||||
−0.0451435 | + | 0.998981i | \(0.514374\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.56698 | 0.162589 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.75531 | −0.311303 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −72.3108 | −2.56783 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.184062 | 0.00652800 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.3327 | 0.755643 | 0.377821 | − | 0.925879i | \(-0.376673\pi\) | ||||
0.377821 | + | 0.925879i | \(0.376673\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.3413 | −1.21491 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25.6764 | −0.907231 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.00895 | 0.0708942 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.19568 | 0.324105 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.33771 | −0.293501 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.4011 | 1.35011 | 0.675055 | − | 0.737767i | \(-0.264120\pi\) | ||||
0.675055 | + | 0.737767i | \(0.264120\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.1146 | 1.12770 | 0.563848 | − | 0.825879i | \(-0.309320\pi\) | ||||
0.563848 | + | 0.825879i | \(0.309320\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.72903 | −0.200926 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.02510 | −0.211050 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.02346 | −0.280705 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −32.2696 | −1.12759 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.2674 | 1.37044 | 0.685221 | − | 0.728335i | \(-0.259706\pi\) | ||||
0.685221 | + | 0.728335i | \(0.259706\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.6875 | 0.721121 | 0.360560 | − | 0.932736i | \(-0.382585\pi\) | ||||
0.360560 | + | 0.932736i | \(0.382585\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.80366 | −0.167242 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.8318 | 1.28077 | 0.640384 | − | 0.768055i | \(-0.278775\pi\) | ||||
0.640384 | + | 0.768055i | \(0.278775\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.0684 | 1.53056 | 0.765280 | − | 0.643698i | \(-0.222601\pi\) | ||||
0.765280 | + | 0.643698i | \(0.222601\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.67319 | −0.162111 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.9787 | −0.726870 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.9090 | 0.446733 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.0265 | 0.381132 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.5740 | 0.606722 | 0.303361 | − | 0.952876i | \(-0.401891\pi\) | ||||
0.303361 | + | 0.952876i | \(0.401891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1166 | −0.969538 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.14805 | −0.246192 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.3752 | −0.356919 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.55587 | 0.156541 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.46640 | 0.118967 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.26791 | −0.0777431 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.84226 | −0.165796 | −0.0828978 | − | 0.996558i | \(-0.526418\pi\) | ||||
−0.0828978 | + | 0.996558i | \(0.526418\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.81760 | −0.233157 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.42035 | −0.150996 | −0.0754981 | − | 0.997146i | \(-0.524055\pi\) | ||||
−0.0754981 | + | 0.997146i | \(0.524055\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.9824 | −0.750030 | −0.375015 | − | 0.927019i | \(-0.622362\pi\) | ||||
−0.375015 | + | 0.927019i | \(0.622362\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.05204 | −0.0358533 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.8318 | 0.709124 | 0.354562 | − | 0.935033i | \(-0.384630\pi\) | ||||
0.354562 | + | 0.935033i | \(0.384630\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.96266 | 0.0667324 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.92526 | −0.235194 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.36687 | 0.182059 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 64.8138 | 2.19613 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.5753 | 0.831748 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.0407 | 0.339438 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.7896 | −0.735784 | −0.367892 | − | 0.929869i | \(-0.619920\pi\) | ||||
−0.367892 | + | 0.929869i | \(0.619920\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.61361 | −0.121884 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.1565 | −1.52136 | −0.760680 | − | 0.649127i | \(-0.775134\pi\) | ||||
−0.760680 | + | 0.649127i | \(0.775134\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.9428 | −1.27688 | −0.638438 | − | 0.769673i | \(-0.720419\pi\) | ||||
−0.638438 | + | 0.769673i | \(0.720419\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.163290 | −0.00548893 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.2579 | 1.48603 | 0.743017 | − | 0.669272i | \(-0.233394\pi\) | ||||
0.743017 | + | 0.669272i | \(0.233394\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.691846 | −0.0232038 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −30.3507 | −1.01679 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.2297 | 0.777353 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.51783 | −0.184441 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.1330 | 0.471889 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.27699 | −0.209349 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.00943 | 0.266833 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.990872 | −0.0329742 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.34513 | −0.111196 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.79259 | −0.0927266 | −0.0463633 | − | 0.998925i | \(-0.514763\pi\) | ||||
−0.0463633 | + | 0.998925i | \(0.514763\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.1055 | 0.733193 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.6731 | 1.57948 | 0.789740 | − | 0.613442i | \(-0.210215\pi\) | ||||
0.789740 | + | 0.613442i | \(0.210215\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.0475 | −0.332523 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.88668 | −0.0623716 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.1996 | −0.997280 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.7545 | 0.915537 | 0.457769 | − | 0.889071i | \(-0.348649\pi\) | ||||
0.457769 | + | 0.889071i | \(0.348649\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.92130 | −0.129211 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −54.0699 | −1.77973 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.20193 | −0.0395192 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.9147 | 0.686928 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.05342 | 0.231415 | 0.115708 | − | 0.993283i | \(-0.463086\pi\) | ||||
0.115708 | + | 0.993283i | \(0.463086\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.1908 | 0.465085 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.85714 | 0.0935385 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.6018 | 0.412122 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.1812 | −0.724627 | −0.362314 | − | 0.932056i | \(-0.618013\pi\) | ||||
−0.362314 | + | 0.932056i | \(0.618013\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.97431 | −0.0644293 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.2794 | −0.791487 | −0.395744 | − | 0.918361i | \(-0.629513\pi\) | ||||
−0.395744 | + | 0.918361i | \(0.629513\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.3238 | −0.564140 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.70630 | −0.0555059 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.0102 | 0.585254 | 0.292627 | − | 0.956227i | \(-0.405471\pi\) | ||||
0.292627 | + | 0.956227i | \(0.405471\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.13246 | −0.101684 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.40575 | 0.207721 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.0273 | 0.713535 | 0.356767 | − | 0.934193i | \(-0.383879\pi\) | ||||
0.356767 | + | 0.934193i | \(0.383879\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.84833 | 0.221607 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.957421 | −0.0309490 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27.7951 | −0.897549 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.6013 | 0.438753 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 45.8558 | 1.47768 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.1631 | −0.423735 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.6765 | −1.21160 | −0.605798 | − | 0.795618i | \(-0.707146\pi\) | ||||
−0.605798 | + | 0.795618i | \(0.707146\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.89042 | 0.253477 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.57685 | −0.243153 | −0.121576 | − | 0.992582i | \(-0.538795\pi\) | ||||
−0.121576 | + | 0.992582i | \(0.538795\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.19653 | 0.0383589 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.49011 | 0.239876 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.1260 | 0.675881 | 0.337940 | − | 0.941168i | \(-0.390270\pi\) | ||||
0.337940 | + | 0.941168i | \(0.390270\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.1042 | −1.02605 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.0192 | −0.511452 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.5187 | −0.750130 | −0.375065 | − | 0.926999i | \(-0.622380\pi\) | ||||
−0.375065 | + | 0.926999i | \(0.622380\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.6118 | 0.338121 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.86880 | 0.0913149 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.3166 | −0.518838 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.5701 | −1.22522 | −0.612610 | − | 0.790385i | \(-0.709880\pi\) | ||||
−0.612610 | + | 0.790385i | \(0.709880\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.31072 | 0.200265 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.3610 | 0.328465 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57.5477 | 1.82255 | 0.911277 | − | 0.411795i | \(-0.135098\pi\) | ||||
0.911277 | + | 0.411795i | \(0.135098\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.420821 | 0.0133142 |
(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 | 4024.2.a.e.1.16 | ✓ | 29 | |
4.3 | odd | 2 | 8048.2.a.w.1.14 | 29 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.e.1.16 | ✓ | 29 | 1.1 | even | 1 | trivial | |
8048.2.a.w.1.14 | 29 | 4.3 | odd | 2 |