Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4027,2,Mod(1,4027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4027 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4027.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: | \(32.1557568940\) |
Analytic rank: | \(0\) |
Dimension: | \(174\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61961 | −1.85234 | −0.926170 | − | 0.377105i | \(-0.876920\pi\) | ||||
−0.926170 | + | 0.377105i | \(0.876920\pi\) | |||||||
\(3\) | 0.347361 | 0.200549 | 0.100274 | − | 0.994960i | \(-0.468028\pi\) | ||||
0.100274 | + | 0.994960i | \(0.468028\pi\) | |||||||
\(4\) | 4.86233 | 2.43117 | ||||||||
\(5\) | 3.06529 | 1.37084 | 0.685419 | − | 0.728149i | \(-0.259619\pi\) | ||||
0.685419 | + | 0.728149i | \(0.259619\pi\) | |||||||
\(6\) | −0.909948 | −0.371485 | ||||||||
\(7\) | −2.40365 | −0.908496 | −0.454248 | − | 0.890875i | \(-0.650092\pi\) | ||||
−0.454248 | + | 0.890875i | \(0.650092\pi\) | |||||||
\(8\) | −7.49819 | −2.65101 | ||||||||
\(9\) | −2.87934 | −0.959780 | ||||||||
\(10\) | −8.02984 | −2.53926 | ||||||||
\(11\) | −5.26667 | −1.58796 | −0.793981 | − | 0.607943i | \(-0.791995\pi\) | ||||
−0.793981 | + | 0.607943i | \(0.791995\pi\) | |||||||
\(12\) | 1.68898 | 0.487568 | ||||||||
\(13\) | −3.23857 | −0.898218 | −0.449109 | − | 0.893477i | \(-0.648259\pi\) | ||||
−0.449109 | + | 0.893477i | \(0.648259\pi\) | |||||||
\(14\) | 6.29663 | 1.68284 | ||||||||
\(15\) | 1.06476 | 0.274920 | ||||||||
\(16\) | 9.91762 | 2.47941 | ||||||||
\(17\) | −1.08454 | −0.263040 | −0.131520 | − | 0.991314i | \(-0.541986\pi\) | ||||
−0.131520 | + | 0.991314i | \(0.541986\pi\) | |||||||
\(18\) | 7.54274 | 1.77784 | ||||||||
\(19\) | 0.530031 | 0.121597 | 0.0607987 | − | 0.998150i | \(-0.480635\pi\) | ||||
0.0607987 | + | 0.998150i | \(0.480635\pi\) | |||||||
\(20\) | 14.9044 | 3.33274 | ||||||||
\(21\) | −0.834935 | −0.182198 | ||||||||
\(22\) | 13.7966 | 2.94145 | ||||||||
\(23\) | −6.75304 | −1.40811 | −0.704054 | − | 0.710147i | \(-0.748629\pi\) | ||||
−0.704054 | + | 0.710147i | \(0.748629\pi\) | |||||||
\(24\) | −2.60458 | −0.531657 | ||||||||
\(25\) | 4.39598 | 0.879196 | ||||||||
\(26\) | 8.48378 | 1.66381 | ||||||||
\(27\) | −2.04225 | −0.393032 | ||||||||
\(28\) | −11.6874 | −2.20871 | ||||||||
\(29\) | 8.35102 | 1.55075 | 0.775373 | − | 0.631504i | \(-0.217562\pi\) | ||||
0.775373 | + | 0.631504i | \(0.217562\pi\) | |||||||
\(30\) | −2.78925 | −0.509245 | ||||||||
\(31\) | −8.45447 | −1.51847 | −0.759233 | − | 0.650818i | \(-0.774426\pi\) | ||||
−0.759233 | + | 0.650818i | \(0.774426\pi\) | |||||||
\(32\) | −10.9839 | −1.94170 | ||||||||
\(33\) | −1.82944 | −0.318464 | ||||||||
\(34\) | 2.84107 | 0.487240 | ||||||||
\(35\) | −7.36789 | −1.24540 | ||||||||
\(36\) | −14.0003 | −2.33339 | ||||||||
\(37\) | 2.82376 | 0.464224 | 0.232112 | − | 0.972689i | \(-0.425436\pi\) | ||||
0.232112 | + | 0.972689i | \(0.425436\pi\) | |||||||
\(38\) | −1.38847 | −0.225240 | ||||||||
\(39\) | −1.12495 | −0.180137 | ||||||||
\(40\) | −22.9841 | −3.63410 | ||||||||
\(41\) | 3.29115 | 0.513991 | 0.256996 | − | 0.966413i | \(-0.417267\pi\) | ||||
0.256996 | + | 0.966413i | \(0.417267\pi\) | |||||||
\(42\) | 2.18720 | 0.337492 | ||||||||
\(43\) | 8.64744 | 1.31872 | 0.659361 | − | 0.751826i | \(-0.270827\pi\) | ||||
0.659361 | + | 0.751826i | \(0.270827\pi\) | |||||||
\(44\) | −25.6083 | −3.86060 | ||||||||
\(45\) | −8.82600 | −1.31570 | ||||||||
\(46\) | 17.6903 | 2.60829 | ||||||||
\(47\) | −8.21305 | −1.19800 | −0.598998 | − | 0.800750i | \(-0.704434\pi\) | ||||
−0.598998 | + | 0.800750i | \(0.704434\pi\) | |||||||
\(48\) | 3.44499 | 0.497242 | ||||||||
\(49\) | −1.22245 | −0.174635 | ||||||||
\(50\) | −11.5157 | −1.62857 | ||||||||
\(51\) | −0.376728 | −0.0527524 | ||||||||
\(52\) | −15.7470 | −2.18372 | ||||||||
\(53\) | 13.8081 | 1.89668 | 0.948341 | − | 0.317253i | \(-0.102760\pi\) | ||||
0.948341 | + | 0.317253i | \(0.102760\pi\) | |||||||
\(54\) | 5.34990 | 0.728029 | ||||||||
\(55\) | −16.1439 | −2.17684 | ||||||||
\(56\) | 18.0230 | 2.40843 | ||||||||
\(57\) | 0.184112 | 0.0243862 | ||||||||
\(58\) | −21.8764 | −2.87251 | ||||||||
\(59\) | −4.99471 | −0.650255 | −0.325128 | − | 0.945670i | \(-0.605407\pi\) | ||||
−0.325128 | + | 0.945670i | \(0.605407\pi\) | |||||||
\(60\) | 5.17722 | 0.668376 | ||||||||
\(61\) | −15.3035 | −1.95942 | −0.979708 | − | 0.200432i | \(-0.935765\pi\) | ||||
−0.979708 | + | 0.200432i | \(0.935765\pi\) | |||||||
\(62\) | 22.1474 | 2.81272 | ||||||||
\(63\) | 6.92094 | 0.871956 | ||||||||
\(64\) | 8.93821 | 1.11728 | ||||||||
\(65\) | −9.92715 | −1.23131 | ||||||||
\(66\) | 4.79240 | 0.589904 | ||||||||
\(67\) | 8.93521 | 1.09161 | 0.545805 | − | 0.837912i | \(-0.316224\pi\) | ||||
0.545805 | + | 0.837912i | \(0.316224\pi\) | |||||||
\(68\) | −5.27341 | −0.639495 | ||||||||
\(69\) | −2.34574 | −0.282394 | ||||||||
\(70\) | 19.3010 | 2.30691 | ||||||||
\(71\) | 1.95526 | 0.232047 | 0.116024 | − | 0.993246i | \(-0.462985\pi\) | ||||
0.116024 | + | 0.993246i | \(0.462985\pi\) | |||||||
\(72\) | 21.5898 | 2.54439 | ||||||||
\(73\) | −0.967541 | −0.113242 | −0.0566210 | − | 0.998396i | \(-0.518033\pi\) | ||||
−0.0566210 | + | 0.998396i | \(0.518033\pi\) | |||||||
\(74\) | −7.39715 | −0.859901 | ||||||||
\(75\) | 1.52699 | 0.176322 | ||||||||
\(76\) | 2.57719 | 0.295624 | ||||||||
\(77\) | 12.6593 | 1.44266 | ||||||||
\(78\) | 2.94693 | 0.333675 | ||||||||
\(79\) | −5.71184 | −0.642632 | −0.321316 | − | 0.946972i | \(-0.604125\pi\) | ||||
−0.321316 | + | 0.946972i | \(0.604125\pi\) | |||||||
\(80\) | 30.4004 | 3.39886 | ||||||||
\(81\) | 7.92862 | 0.880958 | ||||||||
\(82\) | −8.62151 | −0.952087 | ||||||||
\(83\) | 15.6220 | 1.71474 | 0.857369 | − | 0.514702i | \(-0.172097\pi\) | ||||
0.857369 | + | 0.514702i | \(0.172097\pi\) | |||||||
\(84\) | −4.05973 | −0.442953 | ||||||||
\(85\) | −3.32443 | −0.360586 | ||||||||
\(86\) | −22.6529 | −2.44272 | ||||||||
\(87\) | 2.90082 | 0.311000 | ||||||||
\(88\) | 39.4905 | 4.20970 | ||||||||
\(89\) | −3.10127 | −0.328734 | −0.164367 | − | 0.986399i | \(-0.552558\pi\) | ||||
−0.164367 | + | 0.986399i | \(0.552558\pi\) | |||||||
\(90\) | 23.1207 | 2.43713 | ||||||||
\(91\) | 7.78441 | 0.816028 | ||||||||
\(92\) | −32.8356 | −3.42334 | ||||||||
\(93\) | −2.93675 | −0.304527 | ||||||||
\(94\) | 21.5150 | 2.21910 | ||||||||
\(95\) | 1.62470 | 0.166690 | ||||||||
\(96\) | −3.81537 | −0.389405 | ||||||||
\(97\) | 9.74823 | 0.989783 | 0.494892 | − | 0.868955i | \(-0.335208\pi\) | ||||
0.494892 | + | 0.868955i | \(0.335208\pi\) | |||||||
\(98\) | 3.20232 | 0.323484 | ||||||||
\(99\) | 15.1645 | 1.52409 | ||||||||
\(100\) | 21.3747 | 2.13747 | ||||||||
\(101\) | 11.5866 | 1.15291 | 0.576454 | − | 0.817130i | \(-0.304436\pi\) | ||||
0.576454 | + | 0.817130i | \(0.304436\pi\) | |||||||
\(102\) | 0.986878 | 0.0977155 | ||||||||
\(103\) | 20.0076 | 1.97141 | 0.985706 | − | 0.168477i | \(-0.0538850\pi\) | ||||
0.985706 | + | 0.168477i | \(0.0538850\pi\) | |||||||
\(104\) | 24.2834 | 2.38119 | ||||||||
\(105\) | −2.55932 | −0.249764 | ||||||||
\(106\) | −36.1717 | −3.51330 | ||||||||
\(107\) | −1.14492 | −0.110684 | −0.0553419 | − | 0.998467i | \(-0.517625\pi\) | ||||
−0.0553419 | + | 0.998467i | \(0.517625\pi\) | |||||||
\(108\) | −9.93011 | −0.955526 | ||||||||
\(109\) | 20.4815 | 1.96177 | 0.980886 | − | 0.194585i | \(-0.0623359\pi\) | ||||
0.980886 | + | 0.194585i | \(0.0623359\pi\) | |||||||
\(110\) | 42.2906 | 4.03225 | ||||||||
\(111\) | 0.980865 | 0.0930996 | ||||||||
\(112\) | −23.8385 | −2.25253 | ||||||||
\(113\) | 12.0780 | 1.13620 | 0.568101 | − | 0.822959i | \(-0.307678\pi\) | ||||
0.568101 | + | 0.822959i | \(0.307678\pi\) | |||||||
\(114\) | −0.482301 | −0.0451716 | ||||||||
\(115\) | −20.7000 | −1.93029 | ||||||||
\(116\) | 40.6054 | 3.77012 | ||||||||
\(117\) | 9.32495 | 0.862092 | ||||||||
\(118\) | 13.0842 | 1.20449 | ||||||||
\(119\) | 2.60687 | 0.238971 | ||||||||
\(120\) | −7.98377 | −0.728815 | ||||||||
\(121\) | 16.7379 | 1.52162 | ||||||||
\(122\) | 40.0892 | 3.62950 | ||||||||
\(123\) | 1.14322 | 0.103080 | ||||||||
\(124\) | −41.1084 | −3.69165 | ||||||||
\(125\) | −1.85149 | −0.165602 | ||||||||
\(126\) | −18.1301 | −1.61516 | ||||||||
\(127\) | −1.66730 | −0.147949 | −0.0739745 | − | 0.997260i | \(-0.523568\pi\) | ||||
−0.0739745 | + | 0.997260i | \(0.523568\pi\) | |||||||
\(128\) | −1.44681 | −0.127881 | ||||||||
\(129\) | 3.00378 | 0.264468 | ||||||||
\(130\) | 26.0052 | 2.28081 | ||||||||
\(131\) | −5.87353 | −0.513173 | −0.256586 | − | 0.966521i | \(-0.582598\pi\) | ||||
−0.256586 | + | 0.966521i | \(0.582598\pi\) | |||||||
\(132\) | −8.89533 | −0.774239 | ||||||||
\(133\) | −1.27401 | −0.110471 | ||||||||
\(134\) | −23.4067 | −2.02203 | ||||||||
\(135\) | −6.26009 | −0.538783 | ||||||||
\(136\) | 8.13210 | 0.697322 | ||||||||
\(137\) | −11.2484 | −0.961013 | −0.480506 | − | 0.876991i | \(-0.659547\pi\) | ||||
−0.480506 | + | 0.876991i | \(0.659547\pi\) | |||||||
\(138\) | 6.14492 | 0.523090 | ||||||||
\(139\) | −10.8800 | −0.922833 | −0.461416 | − | 0.887184i | \(-0.652659\pi\) | ||||
−0.461416 | + | 0.887184i | \(0.652659\pi\) | |||||||
\(140\) | −35.8251 | −3.02778 | ||||||||
\(141\) | −2.85289 | −0.240257 | ||||||||
\(142\) | −5.12202 | −0.429831 | ||||||||
\(143\) | 17.0565 | 1.42634 | ||||||||
\(144\) | −28.5562 | −2.37968 | ||||||||
\(145\) | 25.5983 | 2.12582 | ||||||||
\(146\) | 2.53458 | 0.209763 | ||||||||
\(147\) | −0.424630 | −0.0350229 | ||||||||
\(148\) | 13.7301 | 1.12861 | ||||||||
\(149\) | 13.7210 | 1.12407 | 0.562036 | − | 0.827113i | \(-0.310018\pi\) | ||||
0.562036 | + | 0.827113i | \(0.310018\pi\) | |||||||
\(150\) | −4.00012 | −0.326608 | ||||||||
\(151\) | 7.63597 | 0.621406 | 0.310703 | − | 0.950507i | \(-0.399436\pi\) | ||||
0.310703 | + | 0.950507i | \(0.399436\pi\) | |||||||
\(152\) | −3.97427 | −0.322356 | ||||||||
\(153\) | 3.12277 | 0.252461 | ||||||||
\(154\) | −33.1623 | −2.67229 | ||||||||
\(155\) | −25.9154 | −2.08157 | ||||||||
\(156\) | −5.46990 | −0.437942 | ||||||||
\(157\) | −6.32759 | −0.504996 | −0.252498 | − | 0.967597i | \(-0.581252\pi\) | ||||
−0.252498 | + | 0.967597i | \(0.581252\pi\) | |||||||
\(158\) | 14.9628 | 1.19037 | ||||||||
\(159\) | 4.79638 | 0.380377 | ||||||||
\(160\) | −33.6688 | −2.66175 | ||||||||
\(161\) | 16.2320 | 1.27926 | ||||||||
\(162\) | −20.7699 | −1.63183 | ||||||||
\(163\) | −19.6986 | −1.54292 | −0.771458 | − | 0.636280i | \(-0.780472\pi\) | ||||
−0.771458 | + | 0.636280i | \(0.780472\pi\) | |||||||
\(164\) | 16.0027 | 1.24960 | ||||||||
\(165\) | −5.60775 | −0.436562 | ||||||||
\(166\) | −40.9235 | −3.17628 | ||||||||
\(167\) | 5.21277 | 0.403376 | 0.201688 | − | 0.979450i | \(-0.435357\pi\) | ||||
0.201688 | + | 0.979450i | \(0.435357\pi\) | |||||||
\(168\) | 6.26050 | 0.483008 | ||||||||
\(169\) | −2.51165 | −0.193204 | ||||||||
\(170\) | 8.70871 | 0.667927 | ||||||||
\(171\) | −1.52614 | −0.116707 | ||||||||
\(172\) | 42.0468 | 3.20604 | ||||||||
\(173\) | 21.1628 | 1.60898 | 0.804488 | − | 0.593969i | \(-0.202440\pi\) | ||||
0.804488 | + | 0.593969i | \(0.202440\pi\) | |||||||
\(174\) | −7.59899 | −0.576078 | ||||||||
\(175\) | −10.5664 | −0.798746 | ||||||||
\(176\) | −52.2329 | −3.93720 | ||||||||
\(177\) | −1.73497 | −0.130408 | ||||||||
\(178\) | 8.12411 | 0.608928 | ||||||||
\(179\) | −7.31645 | −0.546857 | −0.273429 | − | 0.961892i | \(-0.588158\pi\) | ||||
−0.273429 | + | 0.961892i | \(0.588158\pi\) | |||||||
\(180\) | −42.9150 | −3.19869 | ||||||||
\(181\) | −14.5776 | −1.08354 | −0.541771 | − | 0.840526i | \(-0.682246\pi\) | ||||
−0.541771 | + | 0.840526i | \(0.682246\pi\) | |||||||
\(182\) | −20.3921 | −1.51156 | ||||||||
\(183\) | −5.31584 | −0.392958 | ||||||||
\(184\) | 50.6356 | 3.73290 | ||||||||
\(185\) | 8.65565 | 0.636376 | ||||||||
\(186\) | 7.69313 | 0.564087 | ||||||||
\(187\) | 5.71193 | 0.417698 | ||||||||
\(188\) | −39.9346 | −2.91253 | ||||||||
\(189\) | 4.90887 | 0.357068 | ||||||||
\(190\) | −4.25606 | −0.308767 | ||||||||
\(191\) | −3.18751 | −0.230640 | −0.115320 | − | 0.993328i | \(-0.536789\pi\) | ||||
−0.115320 | + | 0.993328i | \(0.536789\pi\) | |||||||
\(192\) | 3.10478 | 0.224068 | ||||||||
\(193\) | 9.57637 | 0.689322 | 0.344661 | − | 0.938727i | \(-0.387994\pi\) | ||||
0.344661 | + | 0.938727i | \(0.387994\pi\) | |||||||
\(194\) | −25.5365 | −1.83342 | ||||||||
\(195\) | −3.44830 | −0.246938 | ||||||||
\(196\) | −5.94394 | −0.424567 | ||||||||
\(197\) | −20.1648 | −1.43668 | −0.718342 | − | 0.695690i | \(-0.755099\pi\) | ||||
−0.718342 | + | 0.695690i | \(0.755099\pi\) | |||||||
\(198\) | −39.7251 | −2.82314 | ||||||||
\(199\) | −3.45675 | −0.245043 | −0.122521 | − | 0.992466i | \(-0.539098\pi\) | ||||
−0.122521 | + | 0.992466i | \(0.539098\pi\) | |||||||
\(200\) | −32.9619 | −2.33076 | ||||||||
\(201\) | 3.10374 | 0.218921 | ||||||||
\(202\) | −30.3523 | −2.13558 | ||||||||
\(203\) | −20.0730 | −1.40885 | ||||||||
\(204\) | −1.83178 | −0.128250 | ||||||||
\(205\) | 10.0883 | 0.704599 | ||||||||
\(206\) | −52.4121 | −3.65173 | ||||||||
\(207\) | 19.4443 | 1.35147 | ||||||||
\(208\) | −32.1189 | −2.22705 | ||||||||
\(209\) | −2.79150 | −0.193092 | ||||||||
\(210\) | 6.70440 | 0.462647 | ||||||||
\(211\) | 8.35438 | 0.575139 | 0.287569 | − | 0.957760i | \(-0.407153\pi\) | ||||
0.287569 | + | 0.957760i | \(0.407153\pi\) | |||||||
\(212\) | 67.1394 | 4.61115 | ||||||||
\(213\) | 0.679182 | 0.0465368 | ||||||||
\(214\) | 2.99925 | 0.205024 | ||||||||
\(215\) | 26.5069 | 1.80776 | ||||||||
\(216\) | 15.3132 | 1.04193 | ||||||||
\(217\) | 20.3216 | 1.37952 | ||||||||
\(218\) | −53.6534 | −3.63387 | ||||||||
\(219\) | −0.336086 | −0.0227106 | ||||||||
\(220\) | −78.4969 | −5.29226 | ||||||||
\(221\) | 3.51237 | 0.236268 | ||||||||
\(222\) | −2.56948 | −0.172452 | ||||||||
\(223\) | −0.525797 | −0.0352100 | −0.0176050 | − | 0.999845i | \(-0.505604\pi\) | ||||
−0.0176050 | + | 0.999845i | \(0.505604\pi\) | |||||||
\(224\) | 26.4015 | 1.76402 | ||||||||
\(225\) | −12.6575 | −0.843835 | ||||||||
\(226\) | −31.6396 | −2.10463 | ||||||||
\(227\) | −6.09842 | −0.404767 | −0.202383 | − | 0.979306i | \(-0.564869\pi\) | ||||
−0.202383 | + | 0.979306i | \(0.564869\pi\) | |||||||
\(228\) | 0.895214 | 0.0592870 | ||||||||
\(229\) | −1.48962 | −0.0984369 | −0.0492185 | − | 0.998788i | \(-0.515673\pi\) | ||||
−0.0492185 | + | 0.998788i | \(0.515673\pi\) | |||||||
\(230\) | 54.2259 | 3.57555 | ||||||||
\(231\) | 4.39733 | 0.289323 | ||||||||
\(232\) | −62.6175 | −4.11104 | ||||||||
\(233\) | −2.55413 | −0.167327 | −0.0836633 | − | 0.996494i | \(-0.526662\pi\) | ||||
−0.0836633 | + | 0.996494i | \(0.526662\pi\) | |||||||
\(234\) | −24.4277 | −1.59689 | ||||||||
\(235\) | −25.1754 | −1.64226 | ||||||||
\(236\) | −24.2859 | −1.58088 | ||||||||
\(237\) | −1.98407 | −0.128879 | ||||||||
\(238\) | −6.82896 | −0.442656 | ||||||||
\(239\) | 25.7873 | 1.66804 | 0.834020 | − | 0.551734i | \(-0.186034\pi\) | ||||
0.834020 | + | 0.551734i | \(0.186034\pi\) | |||||||
\(240\) | 10.5599 | 0.681638 | ||||||||
\(241\) | −1.15712 | −0.0745367 | −0.0372683 | − | 0.999305i | \(-0.511866\pi\) | ||||
−0.0372683 | + | 0.999305i | \(0.511866\pi\) | |||||||
\(242\) | −43.8466 | −2.81857 | ||||||||
\(243\) | 8.88085 | 0.569707 | ||||||||
\(244\) | −74.4108 | −4.76367 | ||||||||
\(245\) | −3.74714 | −0.239396 | ||||||||
\(246\) | −2.99478 | −0.190940 | ||||||||
\(247\) | −1.71654 | −0.109221 | ||||||||
\(248\) | 63.3932 | 4.02547 | ||||||||
\(249\) | 5.42647 | 0.343889 | ||||||||
\(250\) | 4.85017 | 0.306751 | ||||||||
\(251\) | 13.2403 | 0.835721 | 0.417861 | − | 0.908511i | \(-0.362780\pi\) | ||||
0.417861 | + | 0.908511i | \(0.362780\pi\) | |||||||
\(252\) | 33.6519 | 2.11987 | ||||||||
\(253\) | 35.5661 | 2.23602 | ||||||||
\(254\) | 4.36767 | 0.274052 | ||||||||
\(255\) | −1.15478 | −0.0723150 | ||||||||
\(256\) | −14.0863 | −0.880397 | ||||||||
\(257\) | −20.5888 | −1.28430 | −0.642148 | − | 0.766581i | \(-0.721956\pi\) | ||||
−0.642148 | + | 0.766581i | \(0.721956\pi\) | |||||||
\(258\) | −7.86873 | −0.489886 | ||||||||
\(259\) | −6.78736 | −0.421746 | ||||||||
\(260\) | −48.2691 | −2.99352 | ||||||||
\(261\) | −24.0454 | −1.48837 | ||||||||
\(262\) | 15.3863 | 0.950571 | ||||||||
\(263\) | 19.9625 | 1.23094 | 0.615470 | − | 0.788160i | \(-0.288966\pi\) | ||||
0.615470 | + | 0.788160i | \(0.288966\pi\) | |||||||
\(264\) | 13.7175 | 0.844251 | ||||||||
\(265\) | 42.3256 | 2.60004 | ||||||||
\(266\) | 3.33741 | 0.204630 | ||||||||
\(267\) | −1.07726 | −0.0659273 | ||||||||
\(268\) | 43.4460 | 2.65389 | ||||||||
\(269\) | 18.1424 | 1.10616 | 0.553081 | − | 0.833128i | \(-0.313452\pi\) | ||||
0.553081 | + | 0.833128i | \(0.313452\pi\) | |||||||
\(270\) | 16.3990 | 0.998009 | ||||||||
\(271\) | −19.2515 | −1.16945 | −0.584723 | − | 0.811233i | \(-0.698797\pi\) | ||||
−0.584723 | + | 0.811233i | \(0.698797\pi\) | |||||||
\(272\) | −10.7561 | −0.652183 | ||||||||
\(273\) | 2.70400 | 0.163653 | ||||||||
\(274\) | 29.4663 | 1.78012 | ||||||||
\(275\) | −23.1522 | −1.39613 | ||||||||
\(276\) | −11.4058 | −0.686548 | ||||||||
\(277\) | 12.1497 | 0.730002 | 0.365001 | − | 0.931007i | \(-0.381069\pi\) | ||||
0.365001 | + | 0.931007i | \(0.381069\pi\) | |||||||
\(278\) | 28.5014 | 1.70940 | ||||||||
\(279\) | 24.3433 | 1.45739 | ||||||||
\(280\) | 55.2458 | 3.30157 | ||||||||
\(281\) | 13.5051 | 0.805644 | 0.402822 | − | 0.915278i | \(-0.368029\pi\) | ||||
0.402822 | + | 0.915278i | \(0.368029\pi\) | |||||||
\(282\) | 7.47345 | 0.445038 | ||||||||
\(283\) | −1.74148 | −0.103520 | −0.0517601 | − | 0.998660i | \(-0.516483\pi\) | ||||
−0.0517601 | + | 0.998660i | \(0.516483\pi\) | |||||||
\(284\) | 9.50715 | 0.564146 | ||||||||
\(285\) | 0.564356 | 0.0334296 | ||||||||
\(286\) | −44.6813 | −2.64206 | ||||||||
\(287\) | −7.91079 | −0.466959 | ||||||||
\(288\) | 31.6264 | 1.86360 | ||||||||
\(289\) | −15.8238 | −0.930810 | ||||||||
\(290\) | −67.0574 | −3.93774 | ||||||||
\(291\) | 3.38615 | 0.198500 | ||||||||
\(292\) | −4.70451 | −0.275310 | ||||||||
\(293\) | 14.3713 | 0.839578 | 0.419789 | − | 0.907622i | \(-0.362104\pi\) | ||||
0.419789 | + | 0.907622i | \(0.362104\pi\) | |||||||
\(294\) | 1.11236 | 0.0648743 | ||||||||
\(295\) | −15.3102 | −0.891395 | ||||||||
\(296\) | −21.1731 | −1.23066 | ||||||||
\(297\) | 10.7559 | 0.624119 | ||||||||
\(298\) | −35.9437 | −2.08216 | ||||||||
\(299\) | 21.8702 | 1.26479 | ||||||||
\(300\) | 7.42474 | 0.428668 | ||||||||
\(301\) | −20.7855 | −1.19805 | ||||||||
\(302\) | −20.0032 | −1.15106 | ||||||||
\(303\) | 4.02472 | 0.231214 | ||||||||
\(304\) | 5.25665 | 0.301489 | ||||||||
\(305\) | −46.9097 | −2.68604 | ||||||||
\(306\) | −8.18042 | −0.467643 | ||||||||
\(307\) | −21.6167 | −1.23373 | −0.616865 | − | 0.787069i | \(-0.711598\pi\) | ||||
−0.616865 | + | 0.787069i | \(0.711598\pi\) | |||||||
\(308\) | 61.5536 | 3.50734 | ||||||||
\(309\) | 6.94987 | 0.395364 | ||||||||
\(310\) | 67.8880 | 3.85578 | ||||||||
\(311\) | 7.56380 | 0.428904 | 0.214452 | − | 0.976735i | \(-0.431204\pi\) | ||||
0.214452 | + | 0.976735i | \(0.431204\pi\) | |||||||
\(312\) | 8.43511 | 0.477544 | ||||||||
\(313\) | 32.4616 | 1.83484 | 0.917419 | − | 0.397922i | \(-0.130269\pi\) | ||||
0.917419 | + | 0.397922i | \(0.130269\pi\) | |||||||
\(314\) | 16.5758 | 0.935425 | ||||||||
\(315\) | 21.2147 | 1.19531 | ||||||||
\(316\) | −27.7729 | −1.56235 | ||||||||
\(317\) | 9.96783 | 0.559849 | 0.279925 | − | 0.960022i | \(-0.409691\pi\) | ||||
0.279925 | + | 0.960022i | \(0.409691\pi\) | |||||||
\(318\) | −12.5646 | −0.704589 | ||||||||
\(319\) | −43.9821 | −2.46252 | ||||||||
\(320\) | 27.3982 | 1.53160 | ||||||||
\(321\) | −0.397701 | −0.0221975 | ||||||||
\(322\) | −42.5214 | −2.36963 | ||||||||
\(323\) | −0.574841 | −0.0319850 | ||||||||
\(324\) | 38.5516 | 2.14176 | ||||||||
\(325\) | −14.2367 | −0.789710 | ||||||||
\(326\) | 51.6027 | 2.85801 | ||||||||
\(327\) | 7.11447 | 0.393431 | ||||||||
\(328\) | −24.6777 | −1.36260 | ||||||||
\(329\) | 19.7413 | 1.08838 | ||||||||
\(330\) | 14.6901 | 0.808663 | ||||||||
\(331\) | −16.5064 | −0.907274 | −0.453637 | − | 0.891187i | \(-0.649874\pi\) | ||||
−0.453637 | + | 0.891187i | \(0.649874\pi\) | |||||||
\(332\) | 75.9594 | 4.16881 | ||||||||
\(333\) | −8.13058 | −0.445553 | ||||||||
\(334\) | −13.6554 | −0.747190 | ||||||||
\(335\) | 27.3890 | 1.49642 | ||||||||
\(336\) | −8.28057 | −0.451742 | ||||||||
\(337\) | 34.1719 | 1.86146 | 0.930730 | − | 0.365707i | \(-0.119173\pi\) | ||||
0.930730 | + | 0.365707i | \(0.119173\pi\) | |||||||
\(338\) | 6.57953 | 0.357879 | ||||||||
\(339\) | 4.19542 | 0.227864 | ||||||||
\(340\) | −16.1645 | −0.876644 | ||||||||
\(341\) | 44.5269 | 2.41127 | ||||||||
\(342\) | 3.99788 | 0.216181 | ||||||||
\(343\) | 19.7639 | 1.06715 | ||||||||
\(344\) | −64.8401 | −3.49595 | ||||||||
\(345\) | −7.19037 | −0.387117 | ||||||||
\(346\) | −55.4381 | −2.98037 | ||||||||
\(347\) | 2.97617 | 0.159769 | 0.0798845 | − | 0.996804i | \(-0.474545\pi\) | ||||
0.0798845 | + | 0.996804i | \(0.474545\pi\) | |||||||
\(348\) | 14.1047 | 0.756093 | ||||||||
\(349\) | −36.5319 | −1.95551 | −0.977753 | − | 0.209757i | \(-0.932733\pi\) | ||||
−0.977753 | + | 0.209757i | \(0.932733\pi\) | |||||||
\(350\) | 27.6799 | 1.47955 | ||||||||
\(351\) | 6.61398 | 0.353028 | ||||||||
\(352\) | 57.8486 | 3.08334 | ||||||||
\(353\) | 3.93091 | 0.209221 | 0.104611 | − | 0.994513i | \(-0.466640\pi\) | ||||
0.104611 | + | 0.994513i | \(0.466640\pi\) | |||||||
\(354\) | 4.54492 | 0.241560 | ||||||||
\(355\) | 5.99345 | 0.318099 | ||||||||
\(356\) | −15.0794 | −0.799208 | ||||||||
\(357\) | 0.905523 | 0.0479254 | ||||||||
\(358\) | 19.1662 | 1.01297 | ||||||||
\(359\) | −13.4515 | −0.709943 | −0.354971 | − | 0.934877i | \(-0.615509\pi\) | ||||
−0.354971 | + | 0.934877i | \(0.615509\pi\) | |||||||
\(360\) | 66.1790 | 3.48794 | ||||||||
\(361\) | −18.7191 | −0.985214 | ||||||||
\(362\) | 38.1875 | 2.00709 | ||||||||
\(363\) | 5.81408 | 0.305160 | ||||||||
\(364\) | 37.8504 | 1.98390 | ||||||||
\(365\) | −2.96579 | −0.155237 | ||||||||
\(366\) | 13.9254 | 0.727893 | ||||||||
\(367\) | 32.0335 | 1.67214 | 0.836068 | − | 0.548625i | \(-0.184849\pi\) | ||||
0.836068 | + | 0.548625i | \(0.184849\pi\) | |||||||
\(368\) | −66.9741 | −3.49127 | ||||||||
\(369\) | −9.47634 | −0.493319 | ||||||||
\(370\) | −22.6744 | −1.17879 | ||||||||
\(371\) | −33.1898 | −1.72313 | ||||||||
\(372\) | −14.2795 | −0.740355 | ||||||||
\(373\) | −33.3827 | −1.72849 | −0.864246 | − | 0.503070i | \(-0.832204\pi\) | ||||
−0.864246 | + | 0.503070i | \(0.832204\pi\) | |||||||
\(374\) | −14.9630 | −0.773719 | ||||||||
\(375\) | −0.643134 | −0.0332113 | ||||||||
\(376\) | 61.5830 | 3.17590 | ||||||||
\(377\) | −27.0454 | −1.39291 | ||||||||
\(378\) | −12.8593 | −0.661411 | ||||||||
\(379\) | 0.880105 | 0.0452080 | 0.0226040 | − | 0.999744i | \(-0.492804\pi\) | ||||
0.0226040 | + | 0.999744i | \(0.492804\pi\) | |||||||
\(380\) | 7.89982 | 0.405252 | ||||||||
\(381\) | −0.579155 | −0.0296710 | ||||||||
\(382\) | 8.35001 | 0.427224 | ||||||||
\(383\) | 0.233986 | 0.0119561 | 0.00597806 | − | 0.999982i | \(-0.498097\pi\) | ||||
0.00597806 | + | 0.999982i | \(0.498097\pi\) | |||||||
\(384\) | −0.502566 | −0.0256464 | ||||||||
\(385\) | 38.8043 | 1.97765 | ||||||||
\(386\) | −25.0863 | −1.27686 | ||||||||
\(387\) | −24.8989 | −1.26568 | ||||||||
\(388\) | 47.3992 | 2.40633 | ||||||||
\(389\) | −8.86110 | −0.449276 | −0.224638 | − | 0.974442i | \(-0.572120\pi\) | ||||
−0.224638 | + | 0.974442i | \(0.572120\pi\) | |||||||
\(390\) | 9.03320 | 0.457414 | ||||||||
\(391\) | 7.32397 | 0.370389 | ||||||||
\(392\) | 9.16612 | 0.462959 | ||||||||
\(393\) | −2.04023 | −0.102916 | ||||||||
\(394\) | 52.8239 | 2.66123 | ||||||||
\(395\) | −17.5084 | −0.880944 | ||||||||
\(396\) | 73.7351 | 3.70533 | ||||||||
\(397\) | −27.1195 | −1.36109 | −0.680543 | − | 0.732708i | \(-0.738256\pi\) | ||||
−0.680543 | + | 0.732708i | \(0.738256\pi\) | |||||||
\(398\) | 9.05533 | 0.453903 | ||||||||
\(399\) | −0.442542 | −0.0221548 | ||||||||
\(400\) | 43.5977 | 2.17988 | ||||||||
\(401\) | 31.5321 | 1.57464 | 0.787320 | − | 0.616544i | \(-0.211468\pi\) | ||||
0.787320 | + | 0.616544i | \(0.211468\pi\) | |||||||
\(402\) | −8.13058 | −0.405516 | ||||||||
\(403\) | 27.3804 | 1.36391 | ||||||||
\(404\) | 56.3378 | 2.80291 | ||||||||
\(405\) | 24.3035 | 1.20765 | ||||||||
\(406\) | 52.5832 | 2.60966 | ||||||||
\(407\) | −14.8719 | −0.737170 | ||||||||
\(408\) | 2.82477 | 0.139847 | ||||||||
\(409\) | −17.4006 | −0.860403 | −0.430201 | − | 0.902733i | \(-0.641557\pi\) | ||||
−0.430201 | + | 0.902733i | \(0.641557\pi\) | |||||||
\(410\) | −26.4274 | −1.30516 | ||||||||
\(411\) | −3.90724 | −0.192730 | ||||||||
\(412\) | 97.2838 | 4.79283 | ||||||||
\(413\) | 12.0055 | 0.590754 | ||||||||
\(414\) | −50.9364 | −2.50339 | ||||||||
\(415\) | 47.8859 | 2.35063 | ||||||||
\(416\) | 35.5721 | 1.74407 | ||||||||
\(417\) | −3.77930 | −0.185073 | ||||||||
\(418\) | 7.31263 | 0.357672 | ||||||||
\(419\) | 30.6717 | 1.49841 | 0.749204 | − | 0.662339i | \(-0.230436\pi\) | ||||
0.749204 | + | 0.662339i | \(0.230436\pi\) | |||||||
\(420\) | −12.4442 | −0.607217 | ||||||||
\(421\) | −38.8655 | −1.89419 | −0.947095 | − | 0.320953i | \(-0.895997\pi\) | ||||
−0.947095 | + | 0.320953i | \(0.895997\pi\) | |||||||
\(422\) | −21.8852 | −1.06535 | ||||||||
\(423\) | 23.6482 | 1.14981 | ||||||||
\(424\) | −103.535 | −5.02812 | ||||||||
\(425\) | −4.76763 | −0.231264 | ||||||||
\(426\) | −1.77919 | −0.0862020 | ||||||||
\(427\) | 36.7844 | 1.78012 | ||||||||
\(428\) | −5.56700 | −0.269091 | ||||||||
\(429\) | 5.92476 | 0.286050 | ||||||||
\(430\) | −69.4376 | −3.34858 | ||||||||
\(431\) | −2.51248 | −0.121022 | −0.0605111 | − | 0.998168i | \(-0.519273\pi\) | ||||
−0.0605111 | + | 0.998168i | \(0.519273\pi\) | |||||||
\(432\) | −20.2543 | −0.974485 | ||||||||
\(433\) | −8.18697 | −0.393441 | −0.196720 | − | 0.980460i | \(-0.563029\pi\) | ||||
−0.196720 | + | 0.980460i | \(0.563029\pi\) | |||||||
\(434\) | −53.2346 | −2.55534 | ||||||||
\(435\) | 8.89183 | 0.426331 | ||||||||
\(436\) | 99.5879 | 4.76939 | ||||||||
\(437\) | −3.57932 | −0.171222 | ||||||||
\(438\) | 0.880412 | 0.0420677 | ||||||||
\(439\) | 22.0424 | 1.05203 | 0.526014 | − | 0.850476i | \(-0.323686\pi\) | ||||
0.526014 | + | 0.850476i | \(0.323686\pi\) | |||||||
\(440\) | 121.050 | 5.77082 | ||||||||
\(441\) | 3.51984 | 0.167611 | ||||||||
\(442\) | −9.20102 | −0.437648 | ||||||||
\(443\) | −10.0943 | −0.479595 | −0.239797 | − | 0.970823i | \(-0.577081\pi\) | ||||
−0.239797 | + | 0.970823i | \(0.577081\pi\) | |||||||
\(444\) | 4.76929 | 0.226341 | ||||||||
\(445\) | −9.50629 | −0.450641 | ||||||||
\(446\) | 1.37738 | 0.0652209 | ||||||||
\(447\) | 4.76615 | 0.225431 | ||||||||
\(448\) | −21.4844 | −1.01504 | ||||||||
\(449\) | −30.4818 | −1.43853 | −0.719263 | − | 0.694738i | \(-0.755520\pi\) | ||||
−0.719263 | + | 0.694738i | \(0.755520\pi\) | |||||||
\(450\) | 33.1577 | 1.56307 | ||||||||
\(451\) | −17.3334 | −0.816199 | ||||||||
\(452\) | 58.7272 | 2.76230 | ||||||||
\(453\) | 2.65244 | 0.124622 | ||||||||
\(454\) | 15.9755 | 0.749766 | ||||||||
\(455\) | 23.8614 | 1.11864 | ||||||||
\(456\) | −1.38051 | −0.0646481 | ||||||||
\(457\) | −13.5412 | −0.633430 | −0.316715 | − | 0.948521i | \(-0.602580\pi\) | ||||
−0.316715 | + | 0.948521i | \(0.602580\pi\) | |||||||
\(458\) | 3.90222 | 0.182339 | ||||||||
\(459\) | 2.21491 | 0.103383 | ||||||||
\(460\) | −100.650 | −4.69285 | ||||||||
\(461\) | 10.6284 | 0.495012 | 0.247506 | − | 0.968886i | \(-0.420389\pi\) | ||||
0.247506 | + | 0.968886i | \(0.420389\pi\) | |||||||
\(462\) | −11.5193 | −0.535925 | ||||||||
\(463\) | −14.1718 | −0.658622 | −0.329311 | − | 0.944222i | \(-0.606816\pi\) | ||||
−0.329311 | + | 0.944222i | \(0.606816\pi\) | |||||||
\(464\) | 82.8222 | 3.84493 | ||||||||
\(465\) | −9.00198 | −0.417457 | ||||||||
\(466\) | 6.69081 | 0.309946 | ||||||||
\(467\) | −23.1860 | −1.07292 | −0.536460 | − | 0.843926i | \(-0.680239\pi\) | ||||
−0.536460 | + | 0.843926i | \(0.680239\pi\) | |||||||
\(468\) | 45.3410 | 2.09589 | ||||||||
\(469\) | −21.4772 | −0.991723 | ||||||||
\(470\) | 65.9495 | 3.04202 | ||||||||
\(471\) | −2.19796 | −0.101276 | ||||||||
\(472\) | 37.4512 | 1.72383 | ||||||||
\(473\) | −45.5433 | −2.09408 | ||||||||
\(474\) | 5.19748 | 0.238728 | ||||||||
\(475\) | 2.33001 | 0.106908 | ||||||||
\(476\) | 12.6755 | 0.580978 | ||||||||
\(477\) | −39.7581 | −1.82040 | ||||||||
\(478\) | −67.5525 | −3.08978 | ||||||||
\(479\) | 17.4123 | 0.795590 | 0.397795 | − | 0.917474i | \(-0.369775\pi\) | ||||
0.397795 | + | 0.917474i | \(0.369775\pi\) | |||||||
\(480\) | −11.6952 | −0.533811 | ||||||||
\(481\) | −9.14497 | −0.416975 | ||||||||
\(482\) | 3.03120 | 0.138067 | ||||||||
\(483\) | 5.63836 | 0.256554 | ||||||||
\(484\) | 81.3851 | 3.69932 | ||||||||
\(485\) | 29.8811 | 1.35683 | ||||||||
\(486\) | −23.2643 | −1.05529 | ||||||||
\(487\) | −32.5992 | −1.47721 | −0.738605 | − | 0.674138i | \(-0.764515\pi\) | ||||
−0.738605 | + | 0.674138i | \(0.764515\pi\) | |||||||
\(488\) | 114.749 | 5.19443 | ||||||||
\(489\) | −6.84253 | −0.309430 | ||||||||
\(490\) | 9.81604 | 0.443444 | ||||||||
\(491\) | 37.5041 | 1.69254 | 0.846269 | − | 0.532757i | \(-0.178844\pi\) | ||||
0.846269 | + | 0.532757i | \(0.178844\pi\) | |||||||
\(492\) | 5.55870 | 0.250606 | ||||||||
\(493\) | −9.05703 | −0.407908 | ||||||||
\(494\) | 4.49667 | 0.202315 | ||||||||
\(495\) | 46.4837 | 2.08929 | ||||||||
\(496\) | −83.8482 | −3.76490 | ||||||||
\(497\) | −4.69978 | −0.210814 | ||||||||
\(498\) | −14.2152 | −0.636999 | ||||||||
\(499\) | 12.0544 | 0.539627 | 0.269814 | − | 0.962913i | \(-0.413038\pi\) | ||||
0.269814 | + | 0.962913i | \(0.413038\pi\) | |||||||
\(500\) | −9.00255 | −0.402606 | ||||||||
\(501\) | 1.81071 | 0.0808966 | ||||||||
\(502\) | −34.6844 | −1.54804 | ||||||||
\(503\) | −5.70335 | −0.254300 | −0.127150 | − | 0.991884i | \(-0.540583\pi\) | ||||
−0.127150 | + | 0.991884i | \(0.540583\pi\) | |||||||
\(504\) | −51.8945 | −2.31156 | ||||||||
\(505\) | 35.5162 | 1.58045 | ||||||||
\(506\) | −93.1691 | −4.14187 | ||||||||
\(507\) | −0.872448 | −0.0387468 | ||||||||
\(508\) | −8.10698 | −0.359689 | ||||||||
\(509\) | 21.5555 | 0.955432 | 0.477716 | − | 0.878514i | \(-0.341465\pi\) | ||||
0.477716 | + | 0.878514i | \(0.341465\pi\) | |||||||
\(510\) | 3.02506 | 0.133952 | ||||||||
\(511\) | 2.32563 | 0.102880 | ||||||||
\(512\) | 39.7943 | 1.75868 | ||||||||
\(513\) | −1.08246 | −0.0477916 | ||||||||
\(514\) | 53.9346 | 2.37895 | ||||||||
\(515\) | 61.3291 | 2.70248 | ||||||||
\(516\) | 14.6054 | 0.642967 | ||||||||
\(517\) | 43.2555 | 1.90237 | ||||||||
\(518\) | 17.7802 | 0.781217 | ||||||||
\(519\) | 7.35112 | 0.322678 | ||||||||
\(520\) | 74.4356 | 3.26422 | ||||||||
\(521\) | 1.16743 | 0.0511460 | 0.0255730 | − | 0.999673i | \(-0.491859\pi\) | ||||
0.0255730 | + | 0.999673i | \(0.491859\pi\) | |||||||
\(522\) | 62.9895 | 2.75698 | ||||||||
\(523\) | −20.7155 | −0.905824 | −0.452912 | − | 0.891555i | \(-0.649615\pi\) | ||||
−0.452912 | + | 0.891555i | \(0.649615\pi\) | |||||||
\(524\) | −28.5591 | −1.24761 | ||||||||
\(525\) | −3.67036 | −0.160188 | ||||||||
\(526\) | −52.2939 | −2.28012 | ||||||||
\(527\) | 9.16923 | 0.399418 | ||||||||
\(528\) | −18.1437 | −0.789601 | ||||||||
\(529\) | 22.6036 | 0.982766 | ||||||||
\(530\) | −110.876 | −4.81617 | ||||||||
\(531\) | 14.3815 | 0.624102 | ||||||||
\(532\) | −6.19467 | −0.268573 | ||||||||
\(533\) | −10.6586 | −0.461676 | ||||||||
\(534\) | 2.82200 | 0.122120 | ||||||||
\(535\) | −3.50952 | −0.151730 | ||||||||
\(536\) | −66.9979 | −2.89387 | ||||||||
\(537\) | −2.54145 | −0.109672 | ||||||||
\(538\) | −47.5259 | −2.04899 | ||||||||
\(539\) | 6.43822 | 0.277314 | ||||||||
\(540\) | −30.4386 | −1.30987 | ||||||||
\(541\) | 0.555716 | 0.0238921 | 0.0119461 | − | 0.999929i | \(-0.496197\pi\) | ||||
0.0119461 | + | 0.999929i | \(0.496197\pi\) | |||||||
\(542\) | 50.4313 | 2.16621 | ||||||||
\(543\) | −5.06367 | −0.217303 | ||||||||
\(544\) | 11.9125 | 0.510744 | ||||||||
\(545\) | 62.7817 | 2.68927 | ||||||||
\(546\) | −7.08341 | −0.303142 | ||||||||
\(547\) | −21.6852 | −0.927190 | −0.463595 | − | 0.886047i | \(-0.653441\pi\) | ||||
−0.463595 | + | 0.886047i | \(0.653441\pi\) | |||||||
\(548\) | −54.6933 | −2.33638 | ||||||||
\(549\) | 44.0640 | 1.88061 | ||||||||
\(550\) | 60.6497 | 2.58611 | ||||||||
\(551\) | 4.42630 | 0.188567 | ||||||||
\(552\) | 17.5888 | 0.748630 | ||||||||
\(553\) | 13.7293 | 0.583829 | ||||||||
\(554\) | −31.8273 | −1.35221 | ||||||||
\(555\) | 3.00663 | 0.127624 | ||||||||
\(556\) | −52.9024 | −2.24356 | ||||||||
\(557\) | −21.6755 | −0.918420 | −0.459210 | − | 0.888328i | \(-0.651867\pi\) | ||||
−0.459210 | + | 0.888328i | \(0.651867\pi\) | |||||||
\(558\) | −63.7698 | −2.69959 | ||||||||
\(559\) | −28.0054 | −1.18450 | ||||||||
\(560\) | −73.0720 | −3.08785 | ||||||||
\(561\) | 1.98410 | 0.0837688 | ||||||||
\(562\) | −35.3779 | −1.49233 | ||||||||
\(563\) | −0.747473 | −0.0315022 | −0.0157511 | − | 0.999876i | \(-0.505014\pi\) | ||||
−0.0157511 | + | 0.999876i | \(0.505014\pi\) | |||||||
\(564\) | −13.8717 | −0.584105 | ||||||||
\(565\) | 37.0225 | 1.55755 | ||||||||
\(566\) | 4.56199 | 0.191755 | ||||||||
\(567\) | −19.0577 | −0.800347 | ||||||||
\(568\) | −14.6609 | −0.615159 | ||||||||
\(569\) | −14.7619 | −0.618850 | −0.309425 | − | 0.950924i | \(-0.600137\pi\) | ||||
−0.309425 | + | 0.950924i | \(0.600137\pi\) | |||||||
\(570\) | −1.47839 | −0.0619229 | ||||||||
\(571\) | −1.92429 | −0.0805289 | −0.0402644 | − | 0.999189i | \(-0.512820\pi\) | ||||
−0.0402644 | + | 0.999189i | \(0.512820\pi\) | |||||||
\(572\) | 82.9344 | 3.46766 | ||||||||
\(573\) | −1.10722 | −0.0462546 | ||||||||
\(574\) | 20.7231 | 0.864967 | ||||||||
\(575\) | −29.6863 | −1.23800 | ||||||||
\(576\) | −25.7362 | −1.07234 | ||||||||
\(577\) | 37.0975 | 1.54439 | 0.772194 | − | 0.635386i | \(-0.219159\pi\) | ||||
0.772194 | + | 0.635386i | \(0.219159\pi\) | |||||||
\(578\) | 41.4520 | 1.72418 | ||||||||
\(579\) | 3.32646 | 0.138243 | ||||||||
\(580\) | 124.467 | 5.16822 | ||||||||
\(581\) | −37.5499 | −1.55783 | ||||||||
\(582\) | −8.87039 | −0.367689 | ||||||||
\(583\) | −72.7225 | −3.01186 | ||||||||
\(584\) | 7.25480 | 0.300206 | ||||||||
\(585\) | 28.5837 | 1.18179 | ||||||||
\(586\) | −37.6470 | −1.55518 | ||||||||
\(587\) | 12.5276 | 0.517070 | 0.258535 | − | 0.966002i | \(-0.416760\pi\) | ||||
0.258535 | + | 0.966002i | \(0.416760\pi\) | |||||||
\(588\) | −2.06469 | −0.0851464 | ||||||||
\(589\) | −4.48113 | −0.184642 | ||||||||
\(590\) | 40.1067 | 1.65117 | ||||||||
\(591\) | −7.00447 | −0.288125 | ||||||||
\(592\) | 28.0050 | 1.15100 | ||||||||
\(593\) | 22.2827 | 0.915039 | 0.457520 | − | 0.889200i | \(-0.348738\pi\) | ||||
0.457520 | + | 0.889200i | \(0.348738\pi\) | |||||||
\(594\) | −28.1762 | −1.15608 | ||||||||
\(595\) | 7.99079 | 0.327590 | ||||||||
\(596\) | 66.7163 | 2.73281 | ||||||||
\(597\) | −1.20074 | −0.0491430 | ||||||||
\(598\) | −57.2914 | −2.34282 | ||||||||
\(599\) | 5.58545 | 0.228215 | 0.114108 | − | 0.993468i | \(-0.463599\pi\) | ||||
0.114108 | + | 0.993468i | \(0.463599\pi\) | |||||||
\(600\) | −11.4497 | −0.467431 | ||||||||
\(601\) | 10.0302 | 0.409142 | 0.204571 | − | 0.978852i | \(-0.434420\pi\) | ||||
0.204571 | + | 0.978852i | \(0.434420\pi\) | |||||||
\(602\) | 54.4497 | 2.21921 | ||||||||
\(603\) | −25.7275 | −1.04771 | ||||||||
\(604\) | 37.1286 | 1.51074 | ||||||||
\(605\) | 51.3063 | 2.08590 | ||||||||
\(606\) | −10.5432 | −0.428288 | ||||||||
\(607\) | −3.93795 | −0.159836 | −0.0799182 | − | 0.996801i | \(-0.525466\pi\) | ||||
−0.0799182 | + | 0.996801i | \(0.525466\pi\) | |||||||
\(608\) | −5.82180 | −0.236105 | ||||||||
\(609\) | −6.97256 | −0.282542 | ||||||||
\(610\) | 122.885 | 4.97546 | ||||||||
\(611\) | 26.5986 | 1.07606 | ||||||||
\(612\) | 15.1839 | 0.613774 | ||||||||
\(613\) | 5.60233 | 0.226276 | 0.113138 | − | 0.993579i | \(-0.463910\pi\) | ||||
0.113138 | + | 0.993579i | \(0.463910\pi\) | |||||||
\(614\) | 56.6272 | 2.28529 | ||||||||
\(615\) | 3.50429 | 0.141306 | ||||||||
\(616\) | −94.9215 | −3.82450 | ||||||||
\(617\) | −28.2994 | −1.13929 | −0.569645 | − | 0.821891i | \(-0.692919\pi\) | ||||
−0.569645 | + | 0.821891i | \(0.692919\pi\) | |||||||
\(618\) | −18.2059 | −0.732349 | ||||||||
\(619\) | −42.5156 | −1.70885 | −0.854424 | − | 0.519577i | \(-0.826090\pi\) | ||||
−0.854424 | + | 0.519577i | \(0.826090\pi\) | |||||||
\(620\) | −126.009 | −5.06065 | ||||||||
\(621\) | 13.7914 | 0.553431 | ||||||||
\(622\) | −19.8142 | −0.794476 | ||||||||
\(623\) | 7.45439 | 0.298654 | ||||||||
\(624\) | −11.1569 | −0.446632 | ||||||||
\(625\) | −27.6553 | −1.10621 | ||||||||
\(626\) | −85.0366 | −3.39875 | ||||||||
\(627\) | −0.969658 | −0.0387244 | ||||||||
\(628\) | −30.7668 | −1.22773 | ||||||||
\(629\) | −3.06249 | −0.122110 | ||||||||
\(630\) | −55.5741 | −2.21412 | ||||||||
\(631\) | −33.9475 | −1.35143 | −0.675714 | − | 0.737164i | \(-0.736165\pi\) | ||||
−0.675714 | + | 0.737164i | \(0.736165\pi\) | |||||||
\(632\) | 42.8284 | 1.70362 | ||||||||
\(633\) | 2.90198 | 0.115343 | ||||||||
\(634\) | −26.1118 | −1.03703 | ||||||||
\(635\) | −5.11076 | −0.202814 | ||||||||
\(636\) | 23.3216 | 0.924761 | ||||||||
\(637\) | 3.95898 | 0.156860 | ||||||||
\(638\) | 115.216 | 4.56143 | ||||||||
\(639\) | −5.62987 | −0.222714 | ||||||||
\(640\) | −4.43489 | −0.175304 | ||||||||
\(641\) | −22.5851 | −0.892059 | −0.446030 | − | 0.895018i | \(-0.647162\pi\) | ||||
−0.446030 | + | 0.895018i | \(0.647162\pi\) | |||||||
\(642\) | 1.04182 | 0.0411174 | ||||||||
\(643\) | −18.4075 | −0.725920 | −0.362960 | − | 0.931805i | \(-0.618234\pi\) | ||||
−0.362960 | + | 0.931805i | \(0.618234\pi\) | |||||||
\(644\) | 78.9253 | 3.11009 | ||||||||
\(645\) | 9.20746 | 0.362543 | ||||||||
\(646\) | 1.50586 | 0.0592472 | ||||||||
\(647\) | 40.3752 | 1.58731 | 0.793656 | − | 0.608367i | \(-0.208175\pi\) | ||||
0.793656 | + | 0.608367i | \(0.208175\pi\) | |||||||
\(648\) | −59.4503 | −2.33543 | ||||||||
\(649\) | 26.3055 | 1.03258 | ||||||||
\(650\) | 37.2946 | 1.46281 | ||||||||
\(651\) | 7.05893 | 0.276661 | ||||||||
\(652\) | −95.7813 | −3.75109 | ||||||||
\(653\) | 7.44790 | 0.291459 | 0.145729 | − | 0.989324i | \(-0.453447\pi\) | ||||
0.145729 | + | 0.989324i | \(0.453447\pi\) | |||||||
\(654\) | −18.6371 | −0.728768 | ||||||||
\(655\) | −18.0041 | −0.703477 | ||||||||
\(656\) | 32.6404 | 1.27439 | ||||||||
\(657\) | 2.78588 | 0.108687 | ||||||||
\(658\) | −51.7145 | −2.01604 | ||||||||
\(659\) | 38.7845 | 1.51083 | 0.755414 | − | 0.655247i | \(-0.227436\pi\) | ||||
0.755414 | + | 0.655247i | \(0.227436\pi\) | |||||||
\(660\) | −27.2667 | −1.06136 | ||||||||
\(661\) | −15.6365 | −0.608189 | −0.304094 | − | 0.952642i | \(-0.598354\pi\) | ||||
−0.304094 | + | 0.952642i | \(0.598354\pi\) | |||||||
\(662\) | 43.2403 | 1.68058 | ||||||||
\(663\) | 1.22006 | 0.0473832 | ||||||||
\(664\) | −117.137 | −4.54579 | ||||||||
\(665\) | −3.90521 | −0.151438 | ||||||||
\(666\) | 21.2989 | 0.825316 | ||||||||
\(667\) | −56.3948 | −2.18362 | ||||||||
\(668\) | 25.3462 | 0.980674 | ||||||||
\(669\) | −0.182641 | −0.00706132 | ||||||||
\(670\) | −71.7483 | −2.77188 | ||||||||
\(671\) | 80.5987 | 3.11148 | ||||||||
\(672\) | 9.17084 | 0.353773 | ||||||||
\(673\) | 49.2859 | 1.89983 | 0.949916 | − | 0.312505i | \(-0.101168\pi\) | ||||
0.949916 | + | 0.312505i | \(0.101168\pi\) | |||||||
\(674\) | −89.5168 | −3.44806 | ||||||||
\(675\) | −8.97771 | −0.345552 | ||||||||
\(676\) | −12.2125 | −0.469711 | ||||||||
\(677\) | 0.758392 | 0.0291474 | 0.0145737 | − | 0.999894i | \(-0.495361\pi\) | ||||
0.0145737 | + | 0.999894i | \(0.495361\pi\) | |||||||
\(678\) | −10.9903 | −0.422082 | ||||||||
\(679\) | −23.4314 | −0.899214 | ||||||||
\(680\) | 24.9272 | 0.955915 | ||||||||
\(681\) | −2.11835 | −0.0811755 | ||||||||
\(682\) | −116.643 | −4.46649 | ||||||||
\(683\) | 24.0650 | 0.920823 | 0.460411 | − | 0.887706i | \(-0.347702\pi\) | ||||
0.460411 | + | 0.887706i | \(0.347702\pi\) | |||||||
\(684\) | −7.42060 | −0.283734 | ||||||||
\(685\) | −34.4795 | −1.31739 | ||||||||
\(686\) | −51.7737 | −1.97673 | ||||||||
\(687\) | −0.517436 | −0.0197414 | ||||||||
\(688\) | 85.7621 | 3.26965 | ||||||||
\(689\) | −44.7184 | −1.70363 | ||||||||
\(690\) | 18.8359 | 0.717072 | ||||||||
\(691\) | 28.1699 | 1.07163 | 0.535817 | − | 0.844334i | \(-0.320004\pi\) | ||||
0.535817 | + | 0.844334i | \(0.320004\pi\) | |||||||
\(692\) | 102.901 | 3.91169 | ||||||||
\(693\) | −36.4503 | −1.38463 | ||||||||
\(694\) | −7.79638 | −0.295947 | ||||||||
\(695\) | −33.3504 | −1.26505 | ||||||||
\(696\) | −21.7509 | −0.824464 | ||||||||
\(697\) | −3.56939 | −0.135200 | ||||||||
\(698\) | 95.6991 | 3.62227 | ||||||||
\(699\) | −0.887204 | −0.0335572 | ||||||||
\(700\) | −51.3775 | −1.94189 | ||||||||
\(701\) | −8.73916 | −0.330074 | −0.165037 | − | 0.986287i | \(-0.552774\pi\) | ||||
−0.165037 | + | 0.986287i | \(0.552774\pi\) | |||||||
\(702\) | −17.3260 | −0.653929 | ||||||||
\(703\) | 1.49668 | 0.0564485 | ||||||||
\(704\) | −47.0746 | −1.77419 | ||||||||
\(705\) | −8.74493 | −0.329353 | ||||||||
\(706\) | −10.2974 | −0.387549 | ||||||||
\(707\) | −27.8501 | −1.04741 | ||||||||
\(708\) | −8.43598 | −0.317044 | ||||||||
\(709\) | 23.7809 | 0.893109 | 0.446554 | − | 0.894757i | \(-0.352651\pi\) | ||||
0.446554 | + | 0.894757i | \(0.352651\pi\) | |||||||
\(710\) | −15.7005 | −0.589228 | ||||||||
\(711\) | 16.4463 | 0.616785 | ||||||||
\(712\) | 23.2539 | 0.871478 | ||||||||
\(713\) | 57.0934 | 2.13816 | ||||||||
\(714\) | −2.37211 | −0.0887741 | ||||||||
\(715\) | 52.2831 | 1.95528 | ||||||||
\(716\) | −35.5750 | −1.32950 | ||||||||
\(717\) | 8.95749 | 0.334523 | ||||||||
\(718\) | 35.2376 | 1.31506 | ||||||||
\(719\) | −14.1369 | −0.527216 | −0.263608 | − | 0.964630i | \(-0.584912\pi\) | ||||
−0.263608 | + | 0.964630i | \(0.584912\pi\) | |||||||
\(720\) | −87.5330 | −3.26216 | ||||||||
\(721\) | −48.0914 | −1.79102 | ||||||||
\(722\) | 49.0366 | 1.82495 | ||||||||
\(723\) | −0.401938 | −0.0149482 | ||||||||
\(724\) | −70.8810 | −2.63427 | ||||||||
\(725\) | 36.7109 | 1.36341 | ||||||||
\(726\) | −15.2306 | −0.565260 | ||||||||
\(727\) | 8.26912 | 0.306685 | 0.153342 | − | 0.988173i | \(-0.450996\pi\) | ||||
0.153342 | + | 0.988173i | \(0.450996\pi\) | |||||||
\(728\) | −58.3689 | −2.16330 | ||||||||
\(729\) | −20.7010 | −0.766704 | ||||||||
\(730\) | 7.76920 | 0.287551 | ||||||||
\(731\) | −9.37852 | −0.346877 | ||||||||
\(732\) | −25.8474 | −0.955348 | ||||||||
\(733\) | 7.18909 | 0.265535 | 0.132767 | − | 0.991147i | \(-0.457614\pi\) | ||||
0.132767 | + | 0.991147i | \(0.457614\pi\) | |||||||
\(734\) | −83.9152 | −3.09737 | ||||||||
\(735\) | −1.30161 | −0.0480107 | ||||||||
\(736\) | 74.1747 | 2.73412 | ||||||||
\(737\) | −47.0588 | −1.73343 | ||||||||
\(738\) | 24.8243 | 0.913794 | ||||||||
\(739\) | −13.9348 | −0.512601 | −0.256300 | − | 0.966597i | \(-0.582504\pi\) | ||||
−0.256300 | + | 0.966597i | \(0.582504\pi\) | |||||||
\(740\) | 42.0867 | 1.54714 | ||||||||
\(741\) | −0.596260 | −0.0219042 | ||||||||
\(742\) | 86.9442 | 3.19182 | ||||||||
\(743\) | −39.1786 | −1.43732 | −0.718661 | − | 0.695360i | \(-0.755245\pi\) | ||||
−0.718661 | + | 0.695360i | \(0.755245\pi\) | |||||||
\(744\) | 22.0203 | 0.807303 | ||||||||
\(745\) | 42.0589 | 1.54092 | ||||||||
\(746\) | 87.4496 | 3.20176 | ||||||||
\(747\) | −44.9811 | −1.64577 | ||||||||
\(748\) | 27.7733 | 1.01549 | ||||||||
\(749\) | 2.75200 | 0.100556 | ||||||||
\(750\) | 1.68476 | 0.0615186 | ||||||||
\(751\) | −19.2815 | −0.703593 | −0.351796 | − | 0.936077i | \(-0.614429\pi\) | ||||
−0.351796 | + | 0.936077i | \(0.614429\pi\) | |||||||
\(752\) | −81.4540 | −2.97032 | ||||||||
\(753\) | 4.59917 | 0.167603 | ||||||||
\(754\) | 70.8482 | 2.58014 | ||||||||
\(755\) | 23.4064 | 0.851847 | ||||||||
\(756\) | 23.8686 | 0.868091 | ||||||||
\(757\) | −22.0016 | −0.799661 | −0.399830 | − | 0.916589i | \(-0.630931\pi\) | ||||
−0.399830 | + | 0.916589i | \(0.630931\pi\) | |||||||
\(758\) | −2.30553 | −0.0837406 | ||||||||
\(759\) | 12.3543 | 0.448431 | ||||||||
\(760\) | −12.1823 | −0.441898 | ||||||||
\(761\) | 6.03626 | 0.218814 | 0.109407 | − | 0.993997i | \(-0.465105\pi\) | ||||
0.109407 | + | 0.993997i | \(0.465105\pi\) | |||||||
\(762\) | 1.51716 | 0.0549608 | ||||||||
\(763\) | −49.2304 | −1.78226 | ||||||||
\(764\) | −15.4987 | −0.560724 | ||||||||
\(765\) | 9.57218 | 0.346083 | ||||||||
\(766\) | −0.612951 | −0.0221468 | ||||||||
\(767\) | 16.1757 | 0.584071 | ||||||||
\(768\) | −4.89304 | −0.176563 | ||||||||
\(769\) | 52.9429 | 1.90917 | 0.954585 | − | 0.297940i | \(-0.0962996\pi\) | ||||
0.954585 | + | 0.297940i | \(0.0962996\pi\) | |||||||
\(770\) | −101.652 | −3.66328 | ||||||||
\(771\) | −7.15175 | −0.257564 | ||||||||
\(772\) | 46.5635 | 1.67586 | ||||||||
\(773\) | 9.25702 | 0.332952 | 0.166476 | − | 0.986046i | \(-0.446761\pi\) | ||||
0.166476 | + | 0.986046i | \(0.446761\pi\) | |||||||
\(774\) | 65.2254 | 2.34448 | ||||||||
\(775\) | −37.1657 | −1.33503 | ||||||||
\(776\) | −73.0941 | −2.62392 | ||||||||
\(777\) | −2.35766 | −0.0845806 | ||||||||
\(778\) | 23.2126 | 0.832212 | ||||||||
\(779\) | 1.74441 | 0.0625000 | ||||||||
\(780\) | −16.7668 | −0.600348 | ||||||||
\(781\) | −10.2977 | −0.368482 | ||||||||
\(782\) | −19.1859 | −0.686086 | ||||||||
\(783\) | −17.0549 | −0.609492 | ||||||||
\(784\) | −12.1237 | −0.432991 | ||||||||
\(785\) | −19.3959 | −0.692268 | ||||||||
\(786\) | 5.34461 | 0.190636 | ||||||||
\(787\) | 52.3457 | 1.86592 | 0.932961 | − | 0.359977i | \(-0.117216\pi\) | ||||
0.932961 | + | 0.359977i | \(0.117216\pi\) | |||||||
\(788\) | −98.0481 | −3.49282 | ||||||||
\(789\) | 6.93419 | 0.246864 | ||||||||
\(790\) | 45.8652 | 1.63181 | ||||||||
\(791\) | −29.0313 | −1.03223 | ||||||||
\(792\) | −113.707 | −4.04039 | ||||||||
\(793\) | 49.5616 | 1.75998 | ||||||||
\(794\) | 71.0423 | 2.52120 | ||||||||
\(795\) | 14.7023 | 0.521436 | ||||||||
\(796\) | −16.8079 | −0.595740 | ||||||||
\(797\) | −7.57678 | −0.268383 | −0.134192 | − | 0.990955i | \(-0.542844\pi\) | ||||
−0.134192 | + | 0.990955i | \(0.542844\pi\) | |||||||
\(798\) | 1.15928 | 0.0410382 | ||||||||
\(799\) | 8.90741 | 0.315121 | ||||||||
\(800\) | −48.2850 | −1.70713 | ||||||||
\(801\) | 8.92962 | 0.315513 | ||||||||
\(802\) | −82.6018 | −2.91677 | ||||||||
\(803\) | 5.09572 | 0.179824 | ||||||||
\(804\) | 15.0914 | 0.532234 | ||||||||
\(805\) | 49.7557 | 1.75366 | ||||||||
\(806\) | −71.7259 | −2.52644 | ||||||||
\(807\) | 6.30196 | 0.221839 | ||||||||
\(808\) | −86.8783 | −3.05637 | ||||||||
\(809\) | 5.66209 | 0.199069 | 0.0995343 | − | 0.995034i | \(-0.468265\pi\) | ||||
0.0995343 | + | 0.995034i | \(0.468265\pi\) | |||||||
\(810\) | −63.6656 | −2.23698 | ||||||||
\(811\) | 1.92817 | 0.0677072 | 0.0338536 | − | 0.999427i | \(-0.489222\pi\) | ||||
0.0338536 | + | 0.999427i | \(0.489222\pi\) | |||||||
\(812\) | −97.6014 | −3.42514 | ||||||||
\(813\) | −6.68722 | −0.234531 | ||||||||
\(814\) | 38.9584 | 1.36549 | ||||||||
\(815\) | −60.3820 | −2.11509 | ||||||||
\(816\) | −3.73624 | −0.130795 | ||||||||
\(817\) | 4.58341 | 0.160353 | ||||||||
\(818\) | 45.5826 | 1.59376 | ||||||||
\(819\) | −22.4140 | −0.783207 | ||||||||
\(820\) | 49.0528 | 1.71300 | ||||||||
\(821\) | −21.0029 | −0.733005 | −0.366503 | − | 0.930417i | \(-0.619445\pi\) | ||||
−0.366503 | + | 0.930417i | \(0.619445\pi\) | |||||||
\(822\) | 10.2354 | 0.357002 | ||||||||
\(823\) | −14.5339 | −0.506620 | −0.253310 | − | 0.967385i | \(-0.581519\pi\) | ||||
−0.253310 | + | 0.967385i | \(0.581519\pi\) | |||||||
\(824\) | −150.021 | −5.22623 | ||||||||
\(825\) | −8.04217 | −0.279992 | ||||||||
\(826\) | −31.4498 | −1.09428 | ||||||||
\(827\) | 42.2572 | 1.46943 | 0.734714 | − | 0.678377i | \(-0.237316\pi\) | ||||
0.734714 | + | 0.678377i | \(0.237316\pi\) | |||||||
\(828\) | 94.5448 | 3.28566 | ||||||||
\(829\) | 14.6924 | 0.510289 | 0.255145 | − | 0.966903i | \(-0.417877\pi\) | ||||
0.255145 | + | 0.966903i | \(0.417877\pi\) | |||||||
\(830\) | −125.442 | −4.35416 | ||||||||
\(831\) | 4.22032 | 0.146401 | ||||||||
\(832\) | −28.9470 | −1.00356 | ||||||||
\(833\) | 1.32579 | 0.0459360 | ||||||||
\(834\) | 9.90027 | 0.342818 | ||||||||
\(835\) | 15.9786 | 0.552963 | ||||||||
\(836\) | −13.5732 | −0.469439 | ||||||||
\(837\) | 17.2662 | 0.596806 | ||||||||
\(838\) | −80.3476 | −2.77556 | ||||||||
\(839\) | −17.4480 | −0.602371 | −0.301186 | − | 0.953566i | \(-0.597382\pi\) | ||||
−0.301186 | + | 0.953566i | \(0.597382\pi\) | |||||||
\(840\) | 19.1902 | 0.662126 | ||||||||
\(841\) | 40.7395 | 1.40481 | ||||||||
\(842\) | 101.812 | 3.50869 | ||||||||
\(843\) | 4.69113 | 0.161571 | ||||||||
\(844\) | 40.6218 | 1.39826 | ||||||||
\(845\) | −7.69892 | −0.264851 | ||||||||
\(846\) | −61.9489 | −2.12985 | ||||||||
\(847\) | −40.2320 | −1.38239 | ||||||||
\(848\) | 136.943 | 4.70264 | ||||||||
\(849\) | −0.604921 | −0.0207609 | ||||||||
\(850\) | 12.4893 | 0.428380 | ||||||||
\(851\) | −19.0690 | −0.653677 | ||||||||
\(852\) | 3.30241 | 0.113139 | ||||||||
\(853\) | 39.5495 | 1.35415 | 0.677074 | − | 0.735914i | \(-0.263247\pi\) | ||||
0.677074 | + | 0.735914i | \(0.263247\pi\) | |||||||
\(854\) | −96.3606 | −3.29739 | ||||||||
\(855\) | −4.67805 | −0.159986 | ||||||||
\(856\) | 8.58484 | 0.293424 | ||||||||
\(857\) | −7.14600 | −0.244103 | −0.122051 | − | 0.992524i | \(-0.538947\pi\) | ||||
−0.122051 | + | 0.992524i | \(0.538947\pi\) | |||||||
\(858\) | −15.5205 | −0.529862 | ||||||||
\(859\) | 29.8927 | 1.01992 | 0.509962 | − | 0.860197i | \(-0.329659\pi\) | ||||
0.509962 | + | 0.860197i | \(0.329659\pi\) | |||||||
\(860\) | 128.885 | 4.39496 | ||||||||
\(861\) | −2.74790 | −0.0936481 | ||||||||
\(862\) | 6.58172 | 0.224174 | ||||||||
\(863\) | 53.9154 | 1.83530 | 0.917650 | − | 0.397390i | \(-0.130084\pi\) | ||||
0.917650 | + | 0.397390i | \(0.130084\pi\) | |||||||
\(864\) | 22.4319 | 0.763148 | ||||||||
\(865\) | 64.8700 | 2.20565 | ||||||||
\(866\) | 21.4466 | 0.728787 | ||||||||
\(867\) | −5.49656 | −0.186673 | ||||||||
\(868\) | 98.8105 | 3.35385 | ||||||||
\(869\) | 30.0824 | 1.02048 | ||||||||
\(870\) | −23.2931 | −0.789710 | ||||||||
\(871\) | −28.9373 | −0.980504 | ||||||||
\(872\) | −153.574 | −5.20067 | ||||||||
\(873\) | −28.0685 | −0.949974 | ||||||||
\(874\) | 9.37641 | 0.317162 | ||||||||
\(875\) | 4.45034 | 0.150449 | ||||||||
\(876\) | −1.63416 | −0.0552132 | ||||||||
\(877\) | 41.5953 | 1.40457 | 0.702287 | − | 0.711894i | \(-0.252162\pi\) | ||||
0.702287 | + | 0.711894i | \(0.252162\pi\) | |||||||
\(878\) | −57.7425 | −1.94871 | ||||||||
\(879\) | 4.99201 | 0.168376 | ||||||||
\(880\) | −160.109 | −5.39727 | ||||||||
\(881\) | 37.5685 | 1.26572 | 0.632858 | − | 0.774268i | \(-0.281882\pi\) | ||||
0.632858 | + | 0.774268i | \(0.281882\pi\) | |||||||
\(882\) | −9.22058 | −0.310473 | ||||||||
\(883\) | 35.4714 | 1.19371 | 0.596854 | − | 0.802350i | \(-0.296417\pi\) | ||||
0.596854 | + | 0.802350i | \(0.296417\pi\) | |||||||
\(884\) | 17.0783 | 0.574406 | ||||||||
\(885\) | −5.31817 | −0.178768 | ||||||||
\(886\) | 26.4431 | 0.888373 | ||||||||
\(887\) | −11.7456 | −0.394378 | −0.197189 | − | 0.980365i | \(-0.563181\pi\) | ||||
−0.197189 | + | 0.980365i | \(0.563181\pi\) | |||||||
\(888\) | −7.35471 | −0.246808 | ||||||||
\(889\) | 4.00762 | 0.134411 | ||||||||
\(890\) | 24.9027 | 0.834742 | ||||||||
\(891\) | −41.7575 | −1.39893 | ||||||||
\(892\) | −2.55660 | −0.0856014 | ||||||||
\(893\) | −4.35317 | −0.145673 | ||||||||
\(894\) | −12.4854 | −0.417576 | ||||||||
\(895\) | −22.4270 | −0.749652 | ||||||||
\(896\) | 3.47763 | 0.116180 | ||||||||
\(897\) | 7.59686 | 0.253652 | ||||||||
\(898\) | 79.8504 | 2.66464 | ||||||||
\(899\) | −70.6034 | −2.35476 | ||||||||
\(900\) | −61.5451 | −2.05150 | ||||||||
\(901\) | −14.9754 | −0.498904 | ||||||||
\(902\) | 45.4067 | 1.51188 | ||||||||
\(903\) | −7.22006 | −0.240268 | ||||||||
\(904\) | −90.5630 | −3.01208 | ||||||||
\(905\) | −44.6844 | −1.48536 | ||||||||
\(906\) | −6.94833 | −0.230843 | ||||||||
\(907\) | 21.0298 | 0.698284 | 0.349142 | − | 0.937070i | \(-0.386473\pi\) | ||||
0.349142 | + | 0.937070i | \(0.386473\pi\) | |||||||
\(908\) | −29.6526 | −0.984055 | ||||||||
\(909\) | −33.3617 | −1.10654 | ||||||||
\(910\) | −62.5076 | −2.07211 | ||||||||
\(911\) | 3.38392 | 0.112114 | 0.0560571 | − | 0.998428i | \(-0.482147\pi\) | ||||
0.0560571 | + | 0.998428i | \(0.482147\pi\) | |||||||
\(912\) | 1.82595 | 0.0604633 | ||||||||
\(913\) | −82.2760 | −2.72294 | ||||||||
\(914\) | 35.4726 | 1.17333 | ||||||||
\(915\) | −16.2946 | −0.538682 | ||||||||
\(916\) | −7.24303 | −0.239317 | ||||||||
\(917\) | 14.1179 | 0.466215 | ||||||||
\(918\) | −5.80219 | −0.191501 | ||||||||
\(919\) | −7.27860 | −0.240099 | −0.120049 | − | 0.992768i | \(-0.538305\pi\) | ||||
−0.120049 | + | 0.992768i | \(0.538305\pi\) | |||||||
\(920\) | 155.213 | 5.11721 | ||||||||
\(921\) | −7.50879 | −0.247423 | ||||||||
\(922\) | −27.8421 | −0.916931 | ||||||||
\(923\) | −6.33227 | −0.208429 | ||||||||
\(924\) | 21.3813 | 0.703393 | ||||||||
\(925\) | 12.4132 | 0.408144 | ||||||||
\(926\) | 37.1247 | 1.21999 | ||||||||
\(927\) | −57.6088 | −1.89212 | ||||||||
\(928\) | −91.7266 | −3.01107 | ||||||||
\(929\) | 16.6585 | 0.546546 | 0.273273 | − | 0.961936i | \(-0.411894\pi\) | ||||
0.273273 | + | 0.961936i | \(0.411894\pi\) | |||||||
\(930\) | 23.5816 | 0.773272 | ||||||||
\(931\) | −0.647934 | −0.0212352 | ||||||||
\(932\) | −12.4190 | −0.406799 | ||||||||
\(933\) | 2.62737 | 0.0860161 | ||||||||
\(934\) | 60.7381 | 1.98741 | ||||||||
\(935\) | 17.5087 | 0.572596 | ||||||||
\(936\) | −69.9202 | −2.28541 | ||||||||
\(937\) | 5.26000 | 0.171837 | 0.0859183 | − | 0.996302i | \(-0.472618\pi\) | ||||
0.0859183 | + | 0.996302i | \(0.472618\pi\) | |||||||
\(938\) | 56.2617 | 1.83701 | ||||||||
\(939\) | 11.2759 | 0.367975 | ||||||||
\(940\) | −122.411 | −3.99261 | ||||||||
\(941\) | −42.9123 | −1.39890 | −0.699451 | − | 0.714681i | \(-0.746572\pi\) | ||||
−0.699451 | + | 0.714681i | \(0.746572\pi\) | |||||||
\(942\) | 5.75778 | 0.187598 | ||||||||
\(943\) | −22.2253 | −0.723755 | ||||||||
\(944\) | −49.5356 | −1.61225 | ||||||||
\(945\) | 15.0471 | 0.489482 | ||||||||
\(946\) | 119.305 | 3.87895 | ||||||||
\(947\) | 57.0141 | 1.85271 | 0.926355 | − | 0.376651i | \(-0.122924\pi\) | ||||
0.926355 | + | 0.376651i | \(0.122924\pi\) | |||||||
\(948\) | −9.64720 | −0.313327 | ||||||||
\(949\) | 3.13345 | 0.101716 | ||||||||
\(950\) | −6.10370 | −0.198030 | ||||||||
\(951\) | 3.46243 | 0.112277 | ||||||||
\(952\) | −19.5468 | −0.633514 | ||||||||
\(953\) | −9.80633 | −0.317658 | −0.158829 | − | 0.987306i | \(-0.550772\pi\) | ||||
−0.158829 | + | 0.987306i | \(0.550772\pi\) | |||||||
\(954\) | 104.151 | 3.37200 | ||||||||
\(955\) | −9.77063 | −0.316170 | ||||||||
\(956\) | 125.386 | 4.05528 | ||||||||
\(957\) | −15.2777 | −0.493856 | ||||||||
\(958\) | −45.6135 | −1.47370 | ||||||||
\(959\) | 27.0372 | 0.873076 | ||||||||
\(960\) | 9.51705 | 0.307162 | ||||||||
\(961\) | 40.4780 | 1.30574 | ||||||||
\(962\) | 23.9562 | 0.772379 | ||||||||
\(963\) | 3.29662 | 0.106232 | ||||||||
\(964\) | −5.62631 | −0.181211 | ||||||||
\(965\) | 29.3543 | 0.944949 | ||||||||
\(966\) | −14.7703 | −0.475226 | ||||||||
\(967\) | −16.3832 | −0.526849 | −0.263424 | − | 0.964680i | \(-0.584852\pi\) | ||||
−0.263424 | + | 0.964680i | \(0.584852\pi\) | |||||||
\(968\) | −125.504 | −4.03384 | ||||||||
\(969\) | −0.199677 | −0.00641456 | ||||||||
\(970\) | −78.2768 | −2.51332 | ||||||||
\(971\) | 7.53526 | 0.241818 | 0.120909 | − | 0.992664i | \(-0.461419\pi\) | ||||
0.120909 | + | 0.992664i | \(0.461419\pi\) | |||||||
\(972\) | 43.1817 | 1.38505 | ||||||||
\(973\) | 26.1519 | 0.838390 | ||||||||
\(974\) | 85.3970 | 2.73630 | ||||||||
\(975\) | −4.94527 | −0.158376 | ||||||||
\(976\) | −151.775 | −4.85818 | ||||||||
\(977\) | 3.79906 | 0.121543 | 0.0607714 | − | 0.998152i | \(-0.480644\pi\) | ||||
0.0607714 | + | 0.998152i | \(0.480644\pi\) | |||||||
\(978\) | 17.9247 | 0.573170 | ||||||||
\(979\) | 16.3334 | 0.522018 | ||||||||
\(980\) | −18.2199 | −0.582012 | ||||||||
\(981\) | −58.9732 | −1.88287 | ||||||||
\(982\) | −98.2460 | −3.13516 | ||||||||
\(983\) | −45.2032 | −1.44176 | −0.720879 | − | 0.693061i | \(-0.756261\pi\) | ||||
−0.720879 | + | 0.693061i | \(0.756261\pi\) | |||||||
\(984\) | −8.57205 | −0.273267 | ||||||||
\(985\) | −61.8110 | −1.96946 | ||||||||
\(986\) | 23.7259 | 0.755585 | ||||||||
\(987\) | 6.85737 | 0.218272 | ||||||||
\(988\) | −8.34641 | −0.265535 | ||||||||
\(989\) | −58.3966 | −1.85690 | ||||||||
\(990\) | −121.769 | −3.87007 | ||||||||
\(991\) | 42.1534 | 1.33905 | 0.669524 | − | 0.742791i | \(-0.266498\pi\) | ||||
0.669524 | + | 0.742791i | \(0.266498\pi\) | |||||||
\(992\) | 92.8629 | 2.94840 | ||||||||
\(993\) | −5.73368 | −0.181953 | ||||||||
\(994\) | 12.3116 | 0.390499 | ||||||||
\(995\) | −10.5959 | −0.335914 | ||||||||
\(996\) | 26.3853 | 0.836051 | ||||||||
\(997\) | 57.6681 | 1.82637 | 0.913184 | − | 0.407547i | \(-0.133616\pi\) | ||||
0.913184 | + | 0.407547i | \(0.133616\pi\) | |||||||
\(998\) | −31.5777 | −0.999574 | ||||||||
\(999\) | −5.76684 | −0.182455 |
(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 | 4027.2.a.c.1.6 | ✓ | 174 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4027.2.a.c.1.6 | ✓ | 174 | 1.1 | even | 1 | trivial |