Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3969,2,Mod(1,3969)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3969, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3969.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.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: | \(31.6926245622\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.14013.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + 6x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 567) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.53652\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3969.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.53652 | 1.08649 | 0.543243 | − | 0.839576i | \(-0.317196\pi\) | ||||
0.543243 | + | 0.839576i | \(0.317196\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.360904 | 0.180452 | ||||||||
\(5\) | 3.15761 | 1.41212 | 0.706062 | − | 0.708150i | \(-0.250470\pi\) | ||||
0.706062 | + | 0.708150i | \(0.250470\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.51851 | −0.890428 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.85173 | 1.53425 | ||||||||
\(11\) | −5.74916 | −1.73344 | −0.866719 | − | 0.498797i | \(-0.833775\pi\) | ||||
−0.866719 | + | 0.498797i | \(0.833775\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.360904 | −0.100097 | −0.0500484 | − | 0.998747i | \(-0.515938\pi\) | ||||
−0.0500484 | + | 0.998747i | \(0.515938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.59156 | −1.14789 | ||||||||
\(17\) | 2.77684 | 0.673483 | 0.336741 | − | 0.941597i | \(-0.390675\pi\) | ||||
0.336741 | + | 0.941597i | \(0.390675\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.23065 | −1.65883 | −0.829413 | − | 0.558636i | \(-0.811325\pi\) | ||||
−0.829413 | + | 0.558636i | \(0.811325\pi\) | |||||||
\(20\) | 1.13959 | 0.254820 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.83372 | −1.88336 | ||||||||
\(23\) | −0.824381 | −0.171895 | −0.0859476 | − | 0.996300i | \(-0.527392\pi\) | ||||
−0.0859476 | + | 0.996300i | \(0.527392\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.97047 | 0.994095 | ||||||||
\(26\) | −0.554537 | −0.108754 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.27819 | −0.794440 | −0.397220 | − | 0.917723i | \(-0.630025\pi\) | ||||
−0.397220 | + | 0.917723i | \(0.630025\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.98199 | −0.894791 | −0.447396 | − | 0.894336i | \(-0.647648\pi\) | ||||
−0.447396 | + | 0.894336i | \(0.647648\pi\) | |||||||
\(32\) | −2.01801 | −0.356738 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.26668 | 0.731730 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.49083 | 1.23149 | 0.615743 | − | 0.787947i | \(-0.288856\pi\) | ||||
0.615743 | + | 0.787947i | \(0.288856\pi\) | |||||||
\(38\) | −11.1101 | −1.80229 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.95246 | −1.25739 | ||||||||
\(41\) | −3.33138 | −0.520274 | −0.260137 | − | 0.965572i | \(-0.583768\pi\) | ||||
−0.260137 | + | 0.965572i | \(0.583768\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.86975 | −1.20013 | −0.600063 | − | 0.799953i | \(-0.704858\pi\) | ||||
−0.600063 | + | 0.799953i | \(0.704858\pi\) | |||||||
\(44\) | −2.07489 | −0.312802 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.26668 | −0.186762 | ||||||||
\(47\) | −3.48149 | −0.507828 | −0.253914 | − | 0.967227i | \(-0.581718\pi\) | ||||
−0.253914 | + | 0.967227i | \(0.581718\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.63725 | 1.08007 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.130252 | −0.0180626 | ||||||||
\(53\) | −2.91544 | −0.400467 | −0.200233 | − | 0.979748i | \(-0.564170\pi\) | ||||
−0.200233 | + | 0.979748i | \(0.564170\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.1536 | −2.44783 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.57354 | −0.863148 | ||||||||
\(59\) | 2.39878 | 0.312294 | 0.156147 | − | 0.987734i | \(-0.450093\pi\) | ||||
0.156147 | + | 0.987734i | \(0.450093\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.20113 | 0.409862 | 0.204931 | − | 0.978776i | \(-0.434303\pi\) | ||||
0.204931 | + | 0.978776i | \(0.434303\pi\) | |||||||
\(62\) | −7.65494 | −0.972178 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.08239 | 0.760298 | ||||||||
\(65\) | −1.13959 | −0.141349 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.89927 | 0.232033 | 0.116017 | − | 0.993247i | \(-0.462987\pi\) | ||||
0.116017 | + | 0.993247i | \(0.462987\pi\) | |||||||
\(68\) | 1.00217 | 0.121531 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.60957 | 0.191021 | 0.0955104 | − | 0.995428i | \(-0.469552\pi\) | ||||
0.0955104 | + | 0.995428i | \(0.469552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.4138 | −1.80404 | −0.902022 | − | 0.431689i | \(-0.857918\pi\) | ||||
−0.902022 | + | 0.431689i | \(0.857918\pi\) | |||||||
\(74\) | 11.5098 | 1.33799 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.60957 | −0.299338 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.47282 | 0.615740 | 0.307870 | − | 0.951428i | \(-0.400384\pi\) | ||||
0.307870 | + | 0.951428i | \(0.400384\pi\) | |||||||
\(80\) | −14.4983 | −1.62096 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.11874 | −0.565270 | ||||||||
\(83\) | −13.0348 | −1.43076 | −0.715380 | − | 0.698735i | \(-0.753746\pi\) | ||||
−0.715380 | + | 0.698735i | \(0.753746\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.76817 | 0.951041 | ||||||||
\(86\) | −12.0921 | −1.30392 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 14.4793 | 1.54350 | ||||||||
\(89\) | −14.2677 | −1.51237 | −0.756185 | − | 0.654358i | \(-0.772939\pi\) | ||||
−0.756185 | + | 0.654358i | \(0.772939\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.297522 | −0.0310188 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.34939 | −0.551748 | ||||||||
\(95\) | −22.8315 | −2.34247 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0053 | 1.62509 | 0.812547 | − | 0.582896i | \(-0.198080\pi\) | ||||
0.812547 | + | 0.582896i | \(0.198080\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.79386 | 0.179386 | ||||||||
\(101\) | 3.00749 | 0.299257 | 0.149628 | − | 0.988742i | \(-0.452192\pi\) | ||||
0.149628 | + | 0.988742i | \(0.452192\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.72063 | 0.957802 | 0.478901 | − | 0.877869i | \(-0.341035\pi\) | ||||
0.478901 | + | 0.877869i | \(0.341035\pi\) | |||||||
\(104\) | 0.908940 | 0.0891289 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.47964 | −0.435101 | ||||||||
\(107\) | 10.4243 | 1.00775 | 0.503877 | − | 0.863775i | \(-0.331907\pi\) | ||||
0.503877 | + | 0.863775i | \(0.331907\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.67427 | −0.447714 | −0.223857 | − | 0.974622i | \(-0.571865\pi\) | ||||
−0.223857 | + | 0.974622i | \(0.571865\pi\) | |||||||
\(110\) | −27.8934 | −2.65953 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.68664 | 0.440882 | 0.220441 | − | 0.975400i | \(-0.429250\pi\) | ||||
0.220441 | + | 0.975400i | \(0.429250\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.60307 | −0.242737 | ||||||||
\(116\) | −1.54402 | −0.143358 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.68578 | 0.339304 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.0529 | 2.00481 | ||||||||
\(122\) | 4.91860 | 0.445310 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.79802 | −0.161467 | ||||||||
\(125\) | −0.0932326 | −0.00833898 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.15945 | −0.812770 | −0.406385 | − | 0.913702i | \(-0.633211\pi\) | ||||
−0.406385 | + | 0.913702i | \(0.633211\pi\) | |||||||
\(128\) | 13.3818 | 1.18279 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.75101 | −0.153574 | ||||||||
\(131\) | 9.21165 | 0.804825 | 0.402413 | − | 0.915458i | \(-0.368172\pi\) | ||||
0.402413 | + | 0.915458i | \(0.368172\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.91828 | 0.252101 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.99350 | −0.599688 | ||||||||
\(137\) | 6.82438 | 0.583046 | 0.291523 | − | 0.956564i | \(-0.405838\pi\) | ||||
0.291523 | + | 0.956564i | \(0.405838\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.68664 | −0.482334 | −0.241167 | − | 0.970484i | \(-0.577530\pi\) | ||||
−0.241167 | + | 0.970484i | \(0.577530\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.47314 | 0.207541 | ||||||||
\(143\) | 2.07489 | 0.173511 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.5088 | −1.12185 | ||||||||
\(146\) | −23.6836 | −1.96007 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.70347 | 0.222224 | ||||||||
\(149\) | 21.5885 | 1.76860 | 0.884301 | − | 0.466918i | \(-0.154636\pi\) | ||||
0.884301 | + | 0.466918i | \(0.154636\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.55553 | −0.452102 | −0.226051 | − | 0.974115i | \(-0.572582\pi\) | ||||
−0.226051 | + | 0.974115i | \(0.572582\pi\) | |||||||
\(152\) | 18.2105 | 1.47706 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.7311 | −1.26356 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.07120 | 0.484534 | 0.242267 | − | 0.970210i | \(-0.422109\pi\) | ||||
0.242267 | + | 0.970210i | \(0.422109\pi\) | |||||||
\(158\) | 8.40911 | 0.668993 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.37209 | −0.503758 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.85259 | −0.301758 | −0.150879 | − | 0.988552i | \(-0.548210\pi\) | ||||
−0.150879 | + | 0.988552i | \(0.548210\pi\) | |||||||
\(164\) | −1.20231 | −0.0938844 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −20.0283 | −1.55450 | ||||||||
\(167\) | −3.53837 | −0.273807 | −0.136904 | − | 0.990584i | \(-0.543715\pi\) | ||||
−0.136904 | + | 0.990584i | \(0.543715\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8697 | −0.989981 | ||||||||
\(170\) | 13.4725 | 1.03329 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.84022 | −0.216565 | ||||||||
\(173\) | −9.85358 | −0.749154 | −0.374577 | − | 0.927196i | \(-0.622212\pi\) | ||||
−0.374577 | + | 0.927196i | \(0.622212\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 26.3976 | 1.98979 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −21.9226 | −1.64317 | ||||||||
\(179\) | −19.8971 | −1.48718 | −0.743590 | − | 0.668636i | \(-0.766878\pi\) | ||||
−0.743590 | + | 0.668636i | \(0.766878\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0930 | 0.898869 | 0.449434 | − | 0.893313i | \(-0.351626\pi\) | ||||
0.449434 | + | 0.893313i | \(0.351626\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.07621 | 0.153060 | ||||||||
\(185\) | 23.6531 | 1.73901 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.9645 | −1.16744 | ||||||||
\(188\) | −1.25648 | −0.0916385 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −35.0812 | −2.54506 | ||||||||
\(191\) | 9.71964 | 0.703288 | 0.351644 | − | 0.936134i | \(-0.385623\pi\) | ||||
0.351644 | + | 0.936134i | \(0.385623\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.30185 | −0.165691 | −0.0828454 | − | 0.996562i | \(-0.526401\pi\) | ||||
−0.0828454 | + | 0.996562i | \(0.526401\pi\) | |||||||
\(194\) | 24.5925 | 1.76564 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.06470 | 0.360845 | 0.180422 | − | 0.983589i | \(-0.442254\pi\) | ||||
0.180422 | + | 0.983589i | \(0.442254\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.95332 | −0.705572 | −0.352786 | − | 0.935704i | \(-0.614766\pi\) | ||||
−0.352786 | + | 0.935704i | \(0.614766\pi\) | |||||||
\(200\) | −12.5182 | −0.885169 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.62108 | 0.325138 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.5192 | −0.734691 | ||||||||
\(206\) | 14.9360 | 1.04064 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.65711 | 0.114900 | ||||||||
\(209\) | 41.5702 | 2.87547 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.3007 | −1.60408 | −0.802042 | − | 0.597267i | \(-0.796253\pi\) | ||||
−0.802042 | + | 0.597267i | \(0.796253\pi\) | |||||||
\(212\) | −1.05219 | −0.0722650 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.0172 | 1.09491 | ||||||||
\(215\) | −24.8496 | −1.69473 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.18212 | −0.486435 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.55170 | −0.441715 | ||||||||
\(221\) | −1.00217 | −0.0674134 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.8754 | −0.795235 | −0.397618 | − | 0.917551i | \(-0.630163\pi\) | ||||
−0.397618 | + | 0.917551i | \(0.630163\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.20113 | 0.479012 | ||||||||
\(227\) | 5.96081 | 0.395633 | 0.197816 | − | 0.980239i | \(-0.436615\pi\) | ||||
0.197816 | + | 0.980239i | \(0.436615\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.7206 | −1.56750 | −0.783752 | − | 0.621074i | \(-0.786696\pi\) | ||||
−0.783752 | + | 0.621074i | \(0.786696\pi\) | |||||||
\(230\) | −3.99968 | −0.263731 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.7747 | 0.707392 | ||||||||
\(233\) | −13.8592 | −0.907948 | −0.453974 | − | 0.891015i | \(-0.649994\pi\) | ||||
−0.453974 | + | 0.891015i | \(0.649994\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.9932 | −0.717116 | ||||||||
\(236\) | 0.865728 | 0.0563541 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.3426 | 1.44522 | 0.722610 | − | 0.691256i | \(-0.242942\pi\) | ||||
0.722610 | + | 0.691256i | \(0.242942\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.72063 | 0.626161 | 0.313080 | − | 0.949727i | \(-0.398639\pi\) | ||||
0.313080 | + | 0.949727i | \(0.398639\pi\) | |||||||
\(242\) | 33.8847 | 2.17819 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.15530 | 0.0739604 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.60957 | 0.166043 | ||||||||
\(248\) | 12.5472 | 0.796747 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.143254 | −0.00906018 | ||||||||
\(251\) | −6.51950 | −0.411507 | −0.205754 | − | 0.978604i | \(-0.565965\pi\) | ||||
−0.205754 | + | 0.978604i | \(0.565965\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.73950 | 0.297970 | ||||||||
\(254\) | −14.0737 | −0.883063 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.39661 | 0.524788 | ||||||||
\(257\) | 5.53002 | 0.344953 | 0.172477 | − | 0.985014i | \(-0.444823\pi\) | ||||
0.172477 | + | 0.985014i | \(0.444823\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.411283 | −0.0255067 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.1539 | 0.874431 | ||||||||
\(263\) | 8.69499 | 0.536156 | 0.268078 | − | 0.963397i | \(-0.413612\pi\) | ||||
0.268078 | + | 0.963397i | \(0.413612\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.20581 | −0.565509 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.685455 | 0.0418709 | ||||||||
\(269\) | −3.77901 | −0.230410 | −0.115205 | − | 0.993342i | \(-0.536753\pi\) | ||||
−0.115205 | + | 0.993342i | \(0.536753\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.61990 | 0.402130 | 0.201065 | − | 0.979578i | \(-0.435560\pi\) | ||||
0.201065 | + | 0.979578i | \(0.435560\pi\) | |||||||
\(272\) | −12.7500 | −0.773083 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.4858 | 0.633472 | ||||||||
\(275\) | −28.5761 | −1.72320 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.2658 | −1.51808 | −0.759038 | − | 0.651046i | \(-0.774330\pi\) | ||||
−0.759038 | + | 0.651046i | \(0.774330\pi\) | |||||||
\(278\) | −8.73765 | −0.524049 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.42442 | 0.442904 | 0.221452 | − | 0.975171i | \(-0.428920\pi\) | ||||
0.221452 | + | 0.975171i | \(0.428920\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.4203 | 0.916640 | 0.458320 | − | 0.888787i | \(-0.348451\pi\) | ||||
0.458320 | + | 0.888787i | \(0.348451\pi\) | |||||||
\(284\) | 0.580900 | 0.0344701 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.18812 | 0.188518 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.28916 | −0.546421 | ||||||||
\(290\) | −20.7567 | −1.21887 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.56289 | −0.325543 | ||||||||
\(293\) | 30.5797 | 1.78649 | 0.893243 | − | 0.449574i | \(-0.148424\pi\) | ||||
0.893243 | + | 0.449574i | \(0.148424\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.57440 | 0.440999 | ||||||||
\(296\) | −18.8657 | −1.09655 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 33.1713 | 1.92156 | ||||||||
\(299\) | 0.297522 | 0.0172061 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −8.53620 | −0.491203 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 33.1999 | 1.90415 | ||||||||
\(305\) | 10.1079 | 0.578776 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.7794 | −1.64252 | −0.821262 | − | 0.570551i | \(-0.806730\pi\) | ||||
−0.821262 | + | 0.570551i | \(0.806730\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −24.1713 | −1.37284 | ||||||||
\(311\) | −2.57255 | −0.145876 | −0.0729380 | − | 0.997336i | \(-0.523238\pi\) | ||||
−0.0729380 | + | 0.997336i | \(0.523238\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.5145 | −1.04650 | −0.523250 | − | 0.852179i | \(-0.675281\pi\) | ||||
−0.523250 | + | 0.852179i | \(0.675281\pi\) | |||||||
\(314\) | 9.32854 | 0.526440 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.97516 | 0.111111 | ||||||||
\(317\) | 15.5182 | 0.871588 | 0.435794 | − | 0.900046i | \(-0.356468\pi\) | ||||
0.435794 | + | 0.900046i | \(0.356468\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.5960 | 1.37711 | ||||||||
\(320\) | 19.2058 | 1.07364 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.0784 | −1.11719 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.79386 | −0.0995056 | ||||||||
\(326\) | −5.91960 | −0.327856 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.39011 | 0.463266 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.5904 | 1.73636 | 0.868182 | − | 0.496246i | \(-0.165289\pi\) | ||||
0.868182 | + | 0.496246i | \(0.165289\pi\) | |||||||
\(332\) | −4.70433 | −0.258183 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.43679 | −0.297488 | ||||||||
\(335\) | 5.99716 | 0.327660 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4081 | −0.621440 | −0.310720 | − | 0.950502i | \(-0.600570\pi\) | ||||
−0.310720 | + | 0.950502i | \(0.600570\pi\) | |||||||
\(338\) | −19.7747 | −1.07560 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.16446 | 0.171617 | ||||||||
\(341\) | 28.6422 | 1.55106 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 19.8200 | 1.06862 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.1403 | −0.813945 | ||||||||
\(347\) | −4.08140 | −0.219101 | −0.109550 | − | 0.993981i | \(-0.534941\pi\) | ||||
−0.109550 | + | 0.993981i | \(0.534941\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.2779 | −1.29956 | −0.649782 | − | 0.760120i | \(-0.725140\pi\) | ||||
−0.649782 | + | 0.760120i | \(0.725140\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.6019 | 0.618383 | ||||||||
\(353\) | −34.0790 | −1.81384 | −0.906922 | − | 0.421299i | \(-0.861574\pi\) | ||||
−0.906922 | + | 0.421299i | \(0.861574\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.08239 | 0.269745 | ||||||||
\(356\) | −5.14926 | −0.272910 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −30.5724 | −1.61580 | ||||||||
\(359\) | 5.48931 | 0.289715 | 0.144857 | − | 0.989453i | \(-0.453728\pi\) | ||||
0.144857 | + | 0.989453i | \(0.453728\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.2823 | 1.75170 | ||||||||
\(362\) | 18.5812 | 0.976608 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −48.6706 | −2.54754 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.6391 | −0.711955 | −0.355978 | − | 0.934495i | \(-0.615852\pi\) | ||||
−0.355978 | + | 0.934495i | \(0.615852\pi\) | |||||||
\(368\) | 3.78519 | 0.197317 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 36.3435 | 1.88941 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.92379 | 0.462056 | 0.231028 | − | 0.972947i | \(-0.425791\pi\) | ||||
0.231028 | + | 0.972947i | \(0.425791\pi\) | |||||||
\(374\) | −24.5298 | −1.26841 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.76817 | 0.452184 | ||||||||
\(377\) | 1.54402 | 0.0795209 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.7035 | 1.52576 | 0.762882 | − | 0.646537i | \(-0.223784\pi\) | ||||
0.762882 | + | 0.646537i | \(0.223784\pi\) | |||||||
\(380\) | −8.23999 | −0.422703 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.9344 | 0.764113 | ||||||||
\(383\) | −17.7101 | −0.904944 | −0.452472 | − | 0.891779i | \(-0.649458\pi\) | ||||
−0.452472 | + | 0.891779i | \(0.649458\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.53685 | −0.180021 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.77638 | 0.293251 | ||||||||
\(389\) | 21.3255 | 1.08125 | 0.540624 | − | 0.841264i | \(-0.318188\pi\) | ||||
0.540624 | + | 0.841264i | \(0.318188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.28917 | −0.115768 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.78203 | 0.392053 | ||||||||
\(395\) | 17.2810 | 0.869501 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.23566 | −0.112205 | −0.0561024 | − | 0.998425i | \(-0.517867\pi\) | ||||
−0.0561024 | + | 0.998425i | \(0.517867\pi\) | |||||||
\(398\) | −15.2935 | −0.766594 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −22.8222 | −1.14111 | ||||||||
\(401\) | 8.73702 | 0.436306 | 0.218153 | − | 0.975915i | \(-0.429997\pi\) | ||||
0.218153 | + | 0.975915i | \(0.429997\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.79802 | 0.0895656 | ||||||||
\(404\) | 1.08542 | 0.0540014 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −43.0660 | −2.13470 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.6920 | −1.41873 | −0.709363 | − | 0.704843i | \(-0.751017\pi\) | ||||
−0.709363 | + | 0.704843i | \(0.751017\pi\) | |||||||
\(410\) | −16.1630 | −0.798232 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.50821 | 0.172837 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −41.1589 | −2.02041 | ||||||||
\(416\) | 0.728309 | 0.0357083 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 63.8736 | 3.12416 | ||||||||
\(419\) | 8.64442 | 0.422307 | 0.211154 | − | 0.977453i | \(-0.432278\pi\) | ||||
0.211154 | + | 0.977453i | \(0.432278\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.4669 | 0.900024 | 0.450012 | − | 0.893022i | \(-0.351420\pi\) | ||||
0.450012 | + | 0.893022i | \(0.351420\pi\) | |||||||
\(422\) | −35.8020 | −1.74282 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.34257 | 0.356587 | ||||||||
\(425\) | 13.8022 | 0.669506 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.76216 | 0.181851 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −38.1819 | −1.84130 | ||||||||
\(431\) | −5.80736 | −0.279731 | −0.139865 | − | 0.990171i | \(-0.544667\pi\) | ||||
−0.139865 | + | 0.990171i | \(0.544667\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.63877 | 0.174868 | 0.0874341 | − | 0.996170i | \(-0.472133\pi\) | ||||
0.0874341 | + | 0.996170i | \(0.472133\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.68696 | −0.0807908 | ||||||||
\(437\) | 5.96081 | 0.285144 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.6619 | −0.890684 | −0.445342 | − | 0.895361i | \(-0.646918\pi\) | ||||
−0.445342 | + | 0.895361i | \(0.646918\pi\) | |||||||
\(440\) | 45.7200 | 2.17961 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.53986 | −0.0732437 | ||||||||
\(443\) | −26.0911 | −1.23962 | −0.619812 | − | 0.784750i | \(-0.712791\pi\) | ||||
−0.619812 | + | 0.784750i | \(0.712791\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −45.0517 | −2.13565 | ||||||||
\(446\) | −18.2468 | −0.864012 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.63824 | −0.266085 | −0.133042 | − | 0.991110i | \(-0.542475\pi\) | ||||
−0.133042 | + | 0.991110i | \(0.542475\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.1526 | 0.901862 | ||||||||
\(452\) | 1.69142 | 0.0795579 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.15892 | 0.429849 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.9923 | −0.935201 | −0.467601 | − | 0.883940i | \(-0.654881\pi\) | ||||
−0.467601 | + | 0.883940i | \(0.654881\pi\) | |||||||
\(458\) | −36.4473 | −1.70307 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.939457 | −0.0438024 | ||||||||
\(461\) | 37.4495 | 1.74420 | 0.872098 | − | 0.489332i | \(-0.162759\pi\) | ||||
0.872098 | + | 0.489332i | \(0.162759\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.45513 | 0.114099 | 0.0570497 | − | 0.998371i | \(-0.481831\pi\) | ||||
0.0570497 | + | 0.998371i | \(0.481831\pi\) | |||||||
\(464\) | 19.6436 | 0.911929 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.2950 | −0.986473 | ||||||||
\(467\) | 33.4107 | 1.54606 | 0.773032 | − | 0.634367i | \(-0.218739\pi\) | ||||
0.773032 | + | 0.634367i | \(0.218739\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −16.8913 | −0.779136 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.04135 | −0.278076 | ||||||||
\(473\) | 45.2445 | 2.08034 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35.9398 | −1.64903 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 34.3299 | 1.57021 | ||||||||
\(479\) | 34.6936 | 1.58519 | 0.792595 | − | 0.609748i | \(-0.208729\pi\) | ||||
0.792595 | + | 0.609748i | \(0.208729\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.70347 | −0.123268 | ||||||||
\(482\) | 14.9360 | 0.680315 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.95896 | 0.361771 | ||||||||
\(485\) | 50.5385 | 2.29483 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.959817 | 0.0434935 | 0.0217467 | − | 0.999764i | \(-0.493077\pi\) | ||||
0.0217467 | + | 0.999764i | \(0.493077\pi\) | |||||||
\(488\) | −8.06207 | −0.364953 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.7738 | 0.711862 | 0.355931 | − | 0.934512i | \(-0.384164\pi\) | ||||
0.355931 | + | 0.934512i | \(0.384164\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.8799 | −0.535042 | ||||||||
\(494\) | 4.00966 | 0.180403 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 22.8751 | 1.02712 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.1287 | −0.856320 | −0.428160 | − | 0.903703i | \(-0.640838\pi\) | ||||
−0.428160 | + | 0.903703i | \(0.640838\pi\) | |||||||
\(500\) | −0.0336480 | −0.00150478 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.0174 | −0.447097 | ||||||||
\(503\) | −33.3898 | −1.48878 | −0.744388 | − | 0.667747i | \(-0.767259\pi\) | ||||
−0.744388 | + | 0.667747i | \(0.767259\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.49648 | 0.422588 | ||||||||
\(506\) | 7.28235 | 0.323740 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.30568 | −0.146666 | ||||||||
\(509\) | 33.5176 | 1.48564 | 0.742822 | − | 0.669489i | \(-0.233487\pi\) | ||||
0.742822 | + | 0.669489i | \(0.233487\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −13.8619 | −0.612617 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.49701 | 0.374787 | ||||||||
\(515\) | 30.6939 | 1.35254 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.0157 | 0.880287 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.87007 | 0.125861 | ||||||||
\(521\) | −26.7243 | −1.17081 | −0.585407 | − | 0.810740i | \(-0.699065\pi\) | ||||
−0.585407 | + | 0.810740i | \(0.699065\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.0644 | 0.746173 | 0.373086 | − | 0.927797i | \(-0.378299\pi\) | ||||
0.373086 | + | 0.927797i | \(0.378299\pi\) | |||||||
\(524\) | 3.32452 | 0.145232 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.3600 | 0.582526 | ||||||||
\(527\) | −13.8342 | −0.602626 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3204 | −0.970452 | ||||||||
\(530\) | −14.1449 | −0.614417 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.20231 | 0.0520777 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.9158 | 1.42307 | ||||||||
\(536\) | −4.78334 | −0.206609 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.80654 | −0.250338 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.3426 | 0.530648 | 0.265324 | − | 0.964159i | \(-0.414521\pi\) | ||||
0.265324 | + | 0.964159i | \(0.414521\pi\) | |||||||
\(542\) | 10.1716 | 0.436909 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.60370 | −0.240257 | ||||||||
\(545\) | −14.7595 | −0.632227 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.4424 | 1.00233 | 0.501163 | − | 0.865353i | \(-0.332906\pi\) | ||||
0.501163 | + | 0.865353i | \(0.332906\pi\) | |||||||
\(548\) | 2.46294 | 0.105212 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −43.9078 | −1.87223 | ||||||||
\(551\) | 30.9341 | 1.31784 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −38.8215 | −1.64937 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.05233 | −0.0870381 | ||||||||
\(557\) | −24.5115 | −1.03858 | −0.519292 | − | 0.854597i | \(-0.673804\pi\) | ||||
−0.519292 | + | 0.854597i | \(0.673804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.84022 | 0.120129 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.4078 | 0.481209 | ||||||||
\(563\) | −13.3714 | −0.563538 | −0.281769 | − | 0.959482i | \(-0.590921\pi\) | ||||
−0.281769 | + | 0.959482i | \(0.590921\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.7985 | 0.622580 | ||||||||
\(566\) | 23.6936 | 0.995916 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.05372 | −0.170090 | ||||||||
\(569\) | −14.2488 | −0.597341 | −0.298670 | − | 0.954356i | \(-0.596543\pi\) | ||||
−0.298670 | + | 0.954356i | \(0.596543\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.3237 | −1.22716 | −0.613579 | − | 0.789633i | \(-0.710271\pi\) | ||||
−0.613579 | + | 0.789633i | \(0.710271\pi\) | |||||||
\(572\) | 0.748837 | 0.0313105 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.09756 | −0.170880 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.1001 | −0.753516 | −0.376758 | − | 0.926312i | \(-0.622961\pi\) | ||||
−0.376758 | + | 0.926312i | \(0.622961\pi\) | |||||||
\(578\) | −14.2730 | −0.593679 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.87539 | −0.202440 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.7613 | 0.694184 | ||||||||
\(584\) | 38.8197 | 1.60637 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 46.9865 | 1.94099 | ||||||||
\(587\) | 6.52804 | 0.269441 | 0.134721 | − | 0.990884i | \(-0.456986\pi\) | ||||
0.134721 | + | 0.990884i | \(0.456986\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.0230 | 1.48430 | ||||||||
\(590\) | 11.6382 | 0.479139 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −34.3946 | −1.41361 | ||||||||
\(593\) | −25.4405 | −1.04471 | −0.522357 | − | 0.852727i | \(-0.674947\pi\) | ||||
−0.522357 | + | 0.852727i | \(0.674947\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.79138 | 0.319147 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.457150 | 0.0186942 | ||||||||
\(599\) | 6.17931 | 0.252480 | 0.126240 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126240 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.9344 | −0.527607 | −0.263804 | − | 0.964576i | \(-0.584977\pi\) | ||||
−0.263804 | + | 0.964576i | \(0.584977\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.00501 | −0.0815828 | ||||||||
\(605\) | 69.6342 | 2.83103 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.0756 | −0.936608 | −0.468304 | − | 0.883567i | \(-0.655135\pi\) | ||||
−0.468304 | + | 0.883567i | \(0.655135\pi\) | |||||||
\(608\) | 14.5916 | 0.591766 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.5310 | 0.628832 | ||||||||
\(611\) | 1.25648 | 0.0508319 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.6273 | −0.711958 | −0.355979 | − | 0.934494i | \(-0.615853\pi\) | ||||
−0.355979 | + | 0.934494i | \(0.615853\pi\) | |||||||
\(614\) | −44.2201 | −1.78458 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.6441 | 0.871358 | 0.435679 | − | 0.900102i | \(-0.356508\pi\) | ||||
0.435679 | + | 0.900102i | \(0.356508\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.57941 | −0.385029 | −0.192514 | − | 0.981294i | \(-0.561664\pi\) | ||||
−0.192514 | + | 0.981294i | \(0.561664\pi\) | |||||||
\(620\) | −5.67743 | −0.228011 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.95278 | −0.158492 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.1468 | −1.00587 | ||||||||
\(626\) | −28.4479 | −1.13701 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.19112 | 0.0874352 | ||||||||
\(629\) | 20.8008 | 0.829384 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.1742 | −1.24103 | −0.620514 | − | 0.784196i | \(-0.713076\pi\) | ||||
−0.620514 | + | 0.784196i | \(0.713076\pi\) | |||||||
\(632\) | −13.7833 | −0.548272 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 23.8441 | 0.946968 | ||||||||
\(635\) | −28.9219 | −1.14773 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 37.7924 | 1.49621 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 42.2543 | 1.67025 | ||||||||
\(641\) | −8.25214 | −0.325940 | −0.162970 | − | 0.986631i | \(-0.552107\pi\) | ||||
−0.162970 | + | 0.986631i | \(0.552107\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.4318 | 0.963495 | 0.481748 | − | 0.876310i | \(-0.340002\pi\) | ||||
0.481748 | + | 0.876310i | \(0.340002\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −30.8509 | −1.21381 | ||||||||
\(647\) | 38.6864 | 1.52092 | 0.760461 | − | 0.649384i | \(-0.224973\pi\) | ||||
0.760461 | + | 0.649384i | \(0.224973\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.7910 | −0.541343 | ||||||||
\(650\) | −2.75631 | −0.108111 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.39041 | −0.0544528 | ||||||||
\(653\) | 7.65430 | 0.299536 | 0.149768 | − | 0.988721i | \(-0.452147\pi\) | ||||
0.149768 | + | 0.988721i | \(0.452147\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.0867 | 1.13651 | ||||||||
\(656\) | 15.2962 | 0.597217 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.5145 | 1.50031 | 0.750156 | − | 0.661261i | \(-0.229978\pi\) | ||||
0.750156 | + | 0.661261i | \(0.229978\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.2132 | 1.25295 | 0.626474 | − | 0.779443i | \(-0.284498\pi\) | ||||
0.626474 | + | 0.779443i | \(0.284498\pi\) | |||||||
\(662\) | 48.5393 | 1.88654 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 32.8284 | 1.27399 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.52686 | 0.136561 | ||||||||
\(668\) | −1.27701 | −0.0494091 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.21478 | 0.355998 | ||||||||
\(671\) | −18.4038 | −0.710470 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.26136 | 0.0486218 | 0.0243109 | − | 0.999704i | \(-0.492261\pi\) | ||||
0.0243109 | + | 0.999704i | \(0.492261\pi\) | |||||||
\(674\) | −17.5288 | −0.675186 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.64474 | −0.178644 | ||||||||
\(677\) | 14.8318 | 0.570031 | 0.285016 | − | 0.958523i | \(-0.408001\pi\) | ||||
0.285016 | + | 0.958523i | \(0.408001\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −22.0827 | −0.846833 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 44.0095 | 1.68521 | ||||||||
\(683\) | −5.53120 | −0.211646 | −0.105823 | − | 0.994385i | \(-0.533748\pi\) | ||||
−0.105823 | + | 0.994385i | \(0.533748\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.5487 | 0.823334 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 36.1344 | 1.37761 | ||||||||
\(689\) | 1.05219 | 0.0400854 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.63792 | 0.328602 | 0.164301 | − | 0.986410i | \(-0.447463\pi\) | ||||
0.164301 | + | 0.986410i | \(0.447463\pi\) | |||||||
\(692\) | −3.55620 | −0.135186 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.27116 | −0.238050 | ||||||||
\(695\) | −17.9562 | −0.681116 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.25070 | −0.350395 | ||||||||
\(698\) | −37.3035 | −1.41196 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.5897 | 1.00428 | 0.502140 | − | 0.864786i | \(-0.332546\pi\) | ||||
0.502140 | + | 0.864786i | \(0.332546\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −54.1636 | −2.04282 | ||||||||
\(704\) | −34.9686 | −1.31793 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −52.3632 | −1.97072 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.1261 | 0.380294 | 0.190147 | − | 0.981756i | \(-0.439104\pi\) | ||||
0.190147 | + | 0.981756i | \(0.439104\pi\) | |||||||
\(710\) | 7.80921 | 0.293074 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 35.9333 | 1.34666 | ||||||||
\(713\) | 4.10705 | 0.153810 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.55170 | 0.245020 | ||||||||
\(716\) | −7.18094 | −0.268364 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.43445 | 0.314771 | ||||||||
\(719\) | 32.3876 | 1.20785 | 0.603927 | − | 0.797040i | \(-0.293602\pi\) | ||||
0.603927 | + | 0.797040i | \(0.293602\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 51.1391 | 1.90320 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.36443 | 0.162203 | ||||||||
\(725\) | −21.2646 | −0.789749 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.2348 | 0.935907 | 0.467953 | − | 0.883753i | \(-0.344992\pi\) | ||||
0.467953 | + | 0.883753i | \(0.344992\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −74.7835 | −2.76786 | ||||||||
\(731\) | −21.8530 | −0.808264 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.84672 | 0.105146 | 0.0525731 | − | 0.998617i | \(-0.483258\pi\) | ||||
0.0525731 | + | 0.998617i | \(0.483258\pi\) | |||||||
\(734\) | −20.9568 | −0.773529 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.66361 | 0.0613215 | ||||||||
\(737\) | −10.9192 | −0.402215 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.5417 | 0.902779 | 0.451390 | − | 0.892327i | \(-0.350928\pi\) | ||||
0.451390 | + | 0.892327i | \(0.350928\pi\) | |||||||
\(740\) | 8.53649 | 0.313808 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.59070 | 0.168416 | 0.0842082 | − | 0.996448i | \(-0.473164\pi\) | ||||
0.0842082 | + | 0.996448i | \(0.473164\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 68.1681 | 2.49748 | ||||||||
\(746\) | 13.7116 | 0.502018 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.76165 | −0.210667 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.4356 | 1.14710 | 0.573551 | − | 0.819170i | \(-0.305566\pi\) | ||||
0.573551 | + | 0.819170i | \(0.305566\pi\) | |||||||
\(752\) | 15.9855 | 0.582930 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.37242 | 0.0863983 | ||||||||
\(755\) | −17.5422 | −0.638425 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.5432 | 1.07376 | 0.536882 | − | 0.843657i | \(-0.319602\pi\) | ||||
0.536882 | + | 0.843657i | \(0.319602\pi\) | |||||||
\(758\) | 45.6401 | 1.65772 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 57.5015 | 2.08580 | ||||||||
\(761\) | −46.4873 | −1.68516 | −0.842582 | − | 0.538567i | \(-0.818966\pi\) | ||||
−0.842582 | + | 0.538567i | \(0.818966\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.50785 | 0.126910 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.2120 | −0.983209 | ||||||||
\(767\) | −0.865728 | −0.0312596 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.1706 | 0.511006 | 0.255503 | − | 0.966808i | \(-0.417759\pi\) | ||||
0.255503 | + | 0.966808i | \(0.417759\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.830747 | −0.0298992 | ||||||||
\(773\) | −34.0085 | −1.22320 | −0.611600 | − | 0.791167i | \(-0.709474\pi\) | ||||
−0.611600 | + | 0.791167i | \(0.709474\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.7628 | −0.889507 | ||||||||
\(776\) | −40.3096 | −1.44703 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32.7672 | 1.17476 | ||||||||
\(779\) | 24.0880 | 0.863043 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.25368 | −0.331123 | ||||||||
\(782\) | −3.51737 | −0.125781 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.1705 | 0.684223 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.1059 | −1.03751 | −0.518757 | − | 0.854921i | \(-0.673605\pi\) | ||||
−0.518757 | + | 0.854921i | \(0.673605\pi\) | |||||||
\(788\) | 1.82787 | 0.0651151 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 26.5527 | 0.944701 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.15530 | −0.0410259 | ||||||||
\(794\) | −3.43515 | −0.121909 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.59219 | −0.127322 | ||||||||
\(797\) | −18.5038 | −0.655439 | −0.327720 | − | 0.944775i | \(-0.606280\pi\) | ||||
−0.327720 | + | 0.944775i | \(0.606280\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.66754 | −0.342013 | ||||||||
\(800\) | −10.0305 | −0.354631 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13.4246 | 0.474040 | ||||||||
\(803\) | 88.6162 | 3.12720 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.76270 | 0.0973118 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.57440 | −0.266466 | ||||||||
\(809\) | 41.0813 | 1.44434 | 0.722172 | − | 0.691714i | \(-0.243144\pi\) | ||||
0.722172 | + | 0.691714i | \(0.243144\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.1361 | −1.51471 | −0.757357 | − | 0.653001i | \(-0.773510\pi\) | ||||
−0.757357 | + | 0.653001i | \(0.773510\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −66.1719 | −2.31932 | ||||||||
\(815\) | −12.1650 | −0.426120 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56.9034 | 1.99080 | ||||||||
\(818\) | −44.0859 | −1.54143 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.79641 | −0.132576 | ||||||||
\(821\) | 13.1748 | 0.459802 | 0.229901 | − | 0.973214i | \(-0.426160\pi\) | ||||
0.229901 | + | 0.973214i | \(0.426160\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.9817 | −0.417654 | −0.208827 | − | 0.977953i | \(-0.566965\pi\) | ||||
−0.208827 | + | 0.977953i | \(0.566965\pi\) | |||||||
\(824\) | −24.4815 | −0.852853 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.9879 | 1.04278 | 0.521391 | − | 0.853318i | \(-0.325413\pi\) | ||||
0.521391 | + | 0.853318i | \(0.325413\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.9238 | 0.935102 | 0.467551 | − | 0.883966i | \(-0.345136\pi\) | ||||
0.467551 | + | 0.883966i | \(0.345136\pi\) | |||||||
\(830\) | −63.2416 | −2.19515 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.19516 | −0.0761034 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.1728 | −0.386650 | ||||||||
\(836\) | 15.0028 | 0.518884 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.2823 | 0.458831 | ||||||||
\(839\) | −11.2238 | −0.387490 | −0.193745 | − | 0.981052i | \(-0.562063\pi\) | ||||
−0.193745 | + | 0.981052i | \(0.562063\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.6971 | −0.368864 | ||||||||
\(842\) | 28.3749 | 0.977864 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.40930 | −0.289460 | ||||||||
\(845\) | −40.6376 | −1.39798 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 13.3864 | 0.459691 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 21.2074 | 0.727408 | ||||||||
\(851\) | −6.17529 | −0.211686 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.1934 | −0.417496 | −0.208748 | − | 0.977970i | \(-0.566939\pi\) | ||||
−0.208748 | + | 0.977970i | \(0.566939\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −26.2537 | −0.897332 | ||||||||
\(857\) | −37.4382 | −1.27887 | −0.639433 | − | 0.768847i | \(-0.720831\pi\) | ||||
−0.639433 | + | 0.768847i | \(0.720831\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.757734 | 0.0258535 | 0.0129268 | − | 0.999916i | \(-0.495885\pi\) | ||||
0.0129268 | + | 0.999916i | \(0.495885\pi\) | |||||||
\(860\) | −8.96830 | −0.305817 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.92314 | −0.303923 | ||||||||
\(863\) | 23.5592 | 0.801965 | 0.400983 | − | 0.916086i | \(-0.368669\pi\) | ||||
0.400983 | + | 0.916086i | \(0.368669\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.1137 | −1.05790 | ||||||||
\(866\) | 5.59106 | 0.189992 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.4641 | −1.06735 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.685455 | −0.0232258 | ||||||||
\(872\) | 11.7722 | 0.398657 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.15892 | 0.309805 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.6739 | 1.23839 | 0.619196 | − | 0.785237i | \(-0.287459\pi\) | ||||
0.619196 | + | 0.785237i | \(0.287459\pi\) | |||||||
\(878\) | −28.6744 | −0.967716 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 83.3532 | 2.80984 | ||||||||
\(881\) | −39.4357 | −1.32862 | −0.664311 | − | 0.747456i | \(-0.731275\pi\) | ||||
−0.664311 | + | 0.747456i | \(0.731275\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.76912 | −0.295105 | −0.147552 | − | 0.989054i | \(-0.547139\pi\) | ||||
−0.147552 | + | 0.989054i | \(0.547139\pi\) | |||||||
\(884\) | −0.361688 | −0.0121649 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −40.0895 | −1.34683 | ||||||||
\(887\) | 7.82601 | 0.262772 | 0.131386 | − | 0.991331i | \(-0.458057\pi\) | ||||
0.131386 | + | 0.991331i | \(0.458057\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −69.2230 | −2.32036 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.28587 | −0.143502 | ||||||||
\(893\) | 25.1734 | 0.842397 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −62.8272 | −2.10008 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.66329 | −0.289098 | ||||||||
\(899\) | 21.3139 | 0.710858 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.09571 | −0.269707 | ||||||||
\(902\) | 29.4285 | 0.979860 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.8033 | −0.392573 | ||||||||
\(905\) | 38.1851 | 1.26931 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.9332 | 1.72442 | 0.862208 | − | 0.506555i | \(-0.169081\pi\) | ||||
0.862208 | + | 0.506555i | \(0.169081\pi\) | |||||||
\(908\) | 2.15128 | 0.0713927 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.1524 | 1.19778 | 0.598891 | − | 0.800830i | \(-0.295608\pi\) | ||||
0.598891 | + | 0.800830i | \(0.295608\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 74.9394 | 2.48013 | ||||||||
\(914\) | −30.7187 | −1.01608 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.56086 | −0.282859 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.1768 | −0.368690 | −0.184345 | − | 0.982862i | \(-0.559016\pi\) | ||||
−0.184345 | + | 0.982862i | \(0.559016\pi\) | |||||||
\(920\) | 6.55585 | 0.216140 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 57.5420 | 1.89504 | ||||||||
\(923\) | −0.580900 | −0.0191206 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37.2330 | 1.22421 | ||||||||
\(926\) | 3.77236 | 0.123967 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.63345 | 0.283407 | ||||||||
\(929\) | 32.8384 | 1.07739 | 0.538696 | − | 0.842500i | \(-0.318917\pi\) | ||||
0.538696 | + | 0.842500i | \(0.318917\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5.00185 | −0.163841 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 51.3364 | 1.67978 | ||||||||
\(935\) | −50.4096 | −1.64857 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.9566 | −0.847965 | −0.423983 | − | 0.905670i | \(-0.639368\pi\) | ||||
−0.423983 | + | 0.905670i | \(0.639368\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.96748 | −0.129405 | ||||||||
\(941\) | 29.4679 | 0.960627 | 0.480314 | − | 0.877097i | \(-0.340523\pi\) | ||||
0.480314 | + | 0.877097i | \(0.340523\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.74632 | 0.0894326 | ||||||||
\(944\) | −11.0141 | −0.358479 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 69.5192 | 2.26026 | ||||||||
\(947\) | −11.5227 | −0.374439 | −0.187219 | − | 0.982318i | \(-0.559948\pi\) | ||||
−0.187219 | + | 0.982318i | \(0.559948\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.56289 | 0.180579 | ||||||||
\(950\) | −55.2223 | −1.79165 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.2912 | 0.948835 | 0.474417 | − | 0.880300i | \(-0.342659\pi\) | ||||
0.474417 | + | 0.880300i | \(0.342659\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.6908 | 0.993130 | ||||||||
\(956\) | 8.06352 | 0.260793 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 53.3075 | 1.72229 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.17981 | −0.199349 | ||||||||
\(962\) | −4.15394 | −0.133929 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.50821 | 0.112992 | ||||||||
\(965\) | −7.26834 | −0.233976 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.0803 | 1.35321 | 0.676606 | − | 0.736345i | \(-0.263450\pi\) | ||||
0.676606 | + | 0.736345i | \(0.263450\pi\) | |||||||
\(968\) | −55.5403 | −1.78513 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 77.6536 | 2.49331 | ||||||||
\(971\) | −35.1549 | −1.12817 | −0.564087 | − | 0.825715i | \(-0.690772\pi\) | ||||
−0.564087 | + | 0.825715i | \(0.690772\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.47478 | 0.0472551 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.6981 | −0.470476 | ||||||||
\(977\) | −4.43025 | −0.141736 | −0.0708682 | − | 0.997486i | \(-0.522577\pi\) | ||||
−0.0708682 | + | 0.997486i | \(0.522577\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 82.0271 | 2.62160 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 24.2368 | 0.773428 | ||||||||
\(983\) | 22.1601 | 0.706798 | 0.353399 | − | 0.935473i | \(-0.385026\pi\) | ||||
0.353399 | + | 0.935473i | \(0.385026\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.9923 | 0.509558 | ||||||||
\(986\) | −18.2537 | −0.581316 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.941804 | 0.0299628 | ||||||||
\(989\) | 6.48767 | 0.206296 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.7203 | −1.16646 | −0.583229 | − | 0.812307i | \(-0.698211\pi\) | ||||
−0.583229 | + | 0.812307i | \(0.698211\pi\) | |||||||
\(992\) | 10.0537 | 0.319206 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −31.4286 | −0.996355 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.9031 | −1.26374 | −0.631872 | − | 0.775073i | \(-0.717713\pi\) | ||||
−0.631872 | + | 0.775073i | \(0.717713\pi\) | |||||||
\(998\) | −29.3918 | −0.930380 | ||||||||
\(999\) | 0 | 0 |
(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 | 3969.2.a.x.1.3 | 4 | ||
3.2 | odd | 2 | 3969.2.a.s.1.2 | 4 | |||
7.2 | even | 3 | 567.2.e.c.487.2 | yes | 8 | ||
7.4 | even | 3 | 567.2.e.c.163.2 | ✓ | 8 | ||
7.6 | odd | 2 | 3969.2.a.w.1.3 | 4 | |||
21.2 | odd | 6 | 567.2.e.d.487.3 | yes | 8 | ||
21.11 | odd | 6 | 567.2.e.d.163.3 | yes | 8 | ||
21.20 | even | 2 | 3969.2.a.t.1.2 | 4 | |||
63.2 | odd | 6 | 567.2.g.k.109.3 | 8 | |||
63.4 | even | 3 | 567.2.g.j.541.2 | 8 | |||
63.11 | odd | 6 | 567.2.h.j.352.2 | 8 | |||
63.16 | even | 3 | 567.2.g.j.109.2 | 8 | |||
63.23 | odd | 6 | 567.2.h.j.298.2 | 8 | |||
63.25 | even | 3 | 567.2.h.k.352.3 | 8 | |||
63.32 | odd | 6 | 567.2.g.k.541.3 | 8 | |||
63.58 | even | 3 | 567.2.h.k.298.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
567.2.e.c.163.2 | ✓ | 8 | 7.4 | even | 3 | ||
567.2.e.c.487.2 | yes | 8 | 7.2 | even | 3 | ||
567.2.e.d.163.3 | yes | 8 | 21.11 | odd | 6 | ||
567.2.e.d.487.3 | yes | 8 | 21.2 | odd | 6 | ||
567.2.g.j.109.2 | 8 | 63.16 | even | 3 | |||
567.2.g.j.541.2 | 8 | 63.4 | even | 3 | |||
567.2.g.k.109.3 | 8 | 63.2 | odd | 6 | |||
567.2.g.k.541.3 | 8 | 63.32 | odd | 6 | |||
567.2.h.j.298.2 | 8 | 63.23 | odd | 6 | |||
567.2.h.j.352.2 | 8 | 63.11 | odd | 6 | |||
567.2.h.k.298.3 | 8 | 63.58 | even | 3 | |||
567.2.h.k.352.3 | 8 | 63.25 | even | 3 | |||
3969.2.a.s.1.2 | 4 | 3.2 | odd | 2 | |||
3969.2.a.t.1.2 | 4 | 21.20 | even | 2 | |||
3969.2.a.w.1.3 | 4 | 7.6 | odd | 2 | |||
3969.2.a.x.1.3 | 4 | 1.1 | even | 1 | trivial |