Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(0\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.80561 | −1.04247 | −0.521235 | − | 0.853413i | \(-0.674529\pi\) | ||||
−0.521235 | + | 0.853413i | \(0.674529\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.32735 | −0.593610 | −0.296805 | − | 0.954938i | \(-0.595921\pi\) | ||||
−0.296805 | + | 0.954938i | \(0.595921\pi\) | |||||||
\(6\) | 1.80561 | 0.737138 | ||||||||
\(7\) | −4.32567 | −1.63495 | −0.817474 | − | 0.575965i | \(-0.804626\pi\) | ||||
−0.817474 | + | 0.575965i | \(0.804626\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.260232 | 0.0867440 | ||||||||
\(10\) | 1.32735 | 0.419745 | ||||||||
\(11\) | 1.86526 | 0.562398 | 0.281199 | − | 0.959650i | \(-0.409268\pi\) | ||||
0.281199 | + | 0.959650i | \(0.409268\pi\) | |||||||
\(12\) | −1.80561 | −0.521235 | ||||||||
\(13\) | 3.09123 | 0.857353 | 0.428676 | − | 0.903458i | \(-0.358980\pi\) | ||||
0.428676 | + | 0.903458i | \(0.358980\pi\) | |||||||
\(14\) | 4.32567 | 1.15608 | ||||||||
\(15\) | 2.39668 | 0.618820 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.60385 | −1.11660 | −0.558299 | − | 0.829640i | \(-0.688546\pi\) | ||||
−0.558299 | + | 0.829640i | \(0.688546\pi\) | |||||||
\(18\) | −0.260232 | −0.0613372 | ||||||||
\(19\) | −5.39557 | −1.23783 | −0.618914 | − | 0.785458i | \(-0.712427\pi\) | ||||
−0.618914 | + | 0.785458i | \(0.712427\pi\) | |||||||
\(20\) | −1.32735 | −0.296805 | ||||||||
\(21\) | 7.81047 | 1.70439 | ||||||||
\(22\) | −1.86526 | −0.397675 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.80561 | 0.368569 | ||||||||
\(25\) | −3.23814 | −0.647627 | ||||||||
\(26\) | −3.09123 | −0.606240 | ||||||||
\(27\) | 4.94696 | 0.952042 | ||||||||
\(28\) | −4.32567 | −0.817474 | ||||||||
\(29\) | −1.23190 | −0.228758 | −0.114379 | − | 0.993437i | \(-0.536488\pi\) | ||||
−0.114379 | + | 0.993437i | \(0.536488\pi\) | |||||||
\(30\) | −2.39668 | −0.437572 | ||||||||
\(31\) | −2.10534 | −0.378130 | −0.189065 | − | 0.981965i | \(-0.560546\pi\) | ||||
−0.189065 | + | 0.981965i | \(0.560546\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.36794 | −0.586283 | ||||||||
\(34\) | 4.60385 | 0.789554 | ||||||||
\(35\) | 5.74168 | 0.970522 | ||||||||
\(36\) | 0.260232 | 0.0433720 | ||||||||
\(37\) | −5.10501 | −0.839259 | −0.419629 | − | 0.907696i | \(-0.637840\pi\) | ||||
−0.419629 | + | 0.907696i | \(0.637840\pi\) | |||||||
\(38\) | 5.39557 | 0.875277 | ||||||||
\(39\) | −5.58156 | −0.893765 | ||||||||
\(40\) | 1.32735 | 0.209873 | ||||||||
\(41\) | −7.15971 | −1.11816 | −0.559080 | − | 0.829114i | \(-0.688845\pi\) | ||||
−0.559080 | + | 0.829114i | \(0.688845\pi\) | |||||||
\(42\) | −7.81047 | −1.20518 | ||||||||
\(43\) | −12.5688 | −1.91672 | −0.958359 | − | 0.285567i | \(-0.907818\pi\) | ||||
−0.958359 | + | 0.285567i | \(0.907818\pi\) | |||||||
\(44\) | 1.86526 | 0.281199 | ||||||||
\(45\) | −0.345419 | −0.0514921 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 12.6346 | 1.84295 | 0.921474 | − | 0.388441i | \(-0.126986\pi\) | ||||
0.921474 | + | 0.388441i | \(0.126986\pi\) | |||||||
\(48\) | −1.80561 | −0.260618 | ||||||||
\(49\) | 11.7114 | 1.67306 | ||||||||
\(50\) | 3.23814 | 0.457942 | ||||||||
\(51\) | 8.31276 | 1.16402 | ||||||||
\(52\) | 3.09123 | 0.428676 | ||||||||
\(53\) | −7.01514 | −0.963603 | −0.481801 | − | 0.876280i | \(-0.660017\pi\) | ||||
−0.481801 | + | 0.876280i | \(0.660017\pi\) | |||||||
\(54\) | −4.94696 | −0.673195 | ||||||||
\(55\) | −2.47586 | −0.333845 | ||||||||
\(56\) | 4.32567 | 0.578042 | ||||||||
\(57\) | 9.74230 | 1.29040 | ||||||||
\(58\) | 1.23190 | 0.161756 | ||||||||
\(59\) | −4.28353 | −0.557668 | −0.278834 | − | 0.960339i | \(-0.589948\pi\) | ||||
−0.278834 | + | 0.960339i | \(0.589948\pi\) | |||||||
\(60\) | 2.39668 | 0.309410 | ||||||||
\(61\) | 5.88838 | 0.753929 | 0.376965 | − | 0.926228i | \(-0.376968\pi\) | ||||
0.376965 | + | 0.926228i | \(0.376968\pi\) | |||||||
\(62\) | 2.10534 | 0.267378 | ||||||||
\(63\) | −1.12568 | −0.141822 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.10315 | −0.508933 | ||||||||
\(66\) | 3.36794 | 0.414565 | ||||||||
\(67\) | −1.51476 | −0.185058 | −0.0925288 | − | 0.995710i | \(-0.529495\pi\) | ||||
−0.0925288 | + | 0.995710i | \(0.529495\pi\) | |||||||
\(68\) | −4.60385 | −0.558299 | ||||||||
\(69\) | −1.80561 | −0.217370 | ||||||||
\(70\) | −5.74168 | −0.686262 | ||||||||
\(71\) | −6.94658 | −0.824408 | −0.412204 | − | 0.911092i | \(-0.635241\pi\) | ||||
−0.412204 | + | 0.911092i | \(0.635241\pi\) | |||||||
\(72\) | −0.260232 | −0.0306686 | ||||||||
\(73\) | −6.83151 | −0.799568 | −0.399784 | − | 0.916609i | \(-0.630915\pi\) | ||||
−0.399784 | + | 0.916609i | \(0.630915\pi\) | |||||||
\(74\) | 5.10501 | 0.593445 | ||||||||
\(75\) | 5.84682 | 0.675132 | ||||||||
\(76\) | −5.39557 | −0.618914 | ||||||||
\(77\) | −8.06851 | −0.919491 | ||||||||
\(78\) | 5.58156 | 0.631987 | ||||||||
\(79\) | −1.92356 | −0.216418 | −0.108209 | − | 0.994128i | \(-0.534512\pi\) | ||||
−0.108209 | + | 0.994128i | \(0.534512\pi\) | |||||||
\(80\) | −1.32735 | −0.148402 | ||||||||
\(81\) | −9.71298 | −1.07922 | ||||||||
\(82\) | 7.15971 | 0.790658 | ||||||||
\(83\) | −8.12356 | −0.891677 | −0.445838 | − | 0.895113i | \(-0.647094\pi\) | ||||
−0.445838 | + | 0.895113i | \(0.647094\pi\) | |||||||
\(84\) | 7.81047 | 0.852193 | ||||||||
\(85\) | 6.11093 | 0.662823 | ||||||||
\(86\) | 12.5688 | 1.35532 | ||||||||
\(87\) | 2.22433 | 0.238473 | ||||||||
\(88\) | −1.86526 | −0.198838 | ||||||||
\(89\) | −15.2788 | −1.61955 | −0.809774 | − | 0.586742i | \(-0.800410\pi\) | ||||
−0.809774 | + | 0.586742i | \(0.800410\pi\) | |||||||
\(90\) | 0.345419 | 0.0364104 | ||||||||
\(91\) | −13.3716 | −1.40173 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 3.80142 | 0.394189 | ||||||||
\(94\) | −12.6346 | −1.30316 | ||||||||
\(95\) | 7.16182 | 0.734787 | ||||||||
\(96\) | 1.80561 | 0.184284 | ||||||||
\(97\) | −14.6172 | −1.48415 | −0.742074 | − | 0.670318i | \(-0.766158\pi\) | ||||
−0.742074 | + | 0.670318i | \(0.766158\pi\) | |||||||
\(98\) | −11.7114 | −1.18303 | ||||||||
\(99\) | 0.485401 | 0.0487846 | ||||||||
\(100\) | −3.23814 | −0.323814 | ||||||||
\(101\) | 0.695099 | 0.0691650 | 0.0345825 | − | 0.999402i | \(-0.488990\pi\) | ||||
0.0345825 | + | 0.999402i | \(0.488990\pi\) | |||||||
\(102\) | −8.31276 | −0.823086 | ||||||||
\(103\) | −8.30467 | −0.818284 | −0.409142 | − | 0.912471i | \(-0.634172\pi\) | ||||
−0.409142 | + | 0.912471i | \(0.634172\pi\) | |||||||
\(104\) | −3.09123 | −0.303120 | ||||||||
\(105\) | −10.3672 | −1.01174 | ||||||||
\(106\) | 7.01514 | 0.681370 | ||||||||
\(107\) | −19.5610 | −1.89103 | −0.945514 | − | 0.325580i | \(-0.894440\pi\) | ||||
−0.945514 | + | 0.325580i | \(0.894440\pi\) | |||||||
\(108\) | 4.94696 | 0.476021 | ||||||||
\(109\) | 1.42166 | 0.136170 | 0.0680850 | − | 0.997680i | \(-0.478311\pi\) | ||||
0.0680850 | + | 0.997680i | \(0.478311\pi\) | |||||||
\(110\) | 2.47586 | 0.236064 | ||||||||
\(111\) | 9.21766 | 0.874902 | ||||||||
\(112\) | −4.32567 | −0.408737 | ||||||||
\(113\) | −11.8348 | −1.11332 | −0.556662 | − | 0.830739i | \(-0.687918\pi\) | ||||
−0.556662 | + | 0.830739i | \(0.687918\pi\) | |||||||
\(114\) | −9.74230 | −0.912450 | ||||||||
\(115\) | −1.32735 | −0.123776 | ||||||||
\(116\) | −1.23190 | −0.114379 | ||||||||
\(117\) | 0.804436 | 0.0743702 | ||||||||
\(118\) | 4.28353 | 0.394331 | ||||||||
\(119\) | 19.9147 | 1.82558 | ||||||||
\(120\) | −2.39668 | −0.218786 | ||||||||
\(121\) | −7.52080 | −0.683709 | ||||||||
\(122\) | −5.88838 | −0.533108 | ||||||||
\(123\) | 12.9277 | 1.16565 | ||||||||
\(124\) | −2.10534 | −0.189065 | ||||||||
\(125\) | 10.9349 | 0.978048 | ||||||||
\(126\) | 1.12568 | 0.100283 | ||||||||
\(127\) | −5.38940 | −0.478232 | −0.239116 | − | 0.970991i | \(-0.576858\pi\) | ||||
−0.239116 | + | 0.970991i | \(0.576858\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 22.6943 | 1.99812 | ||||||||
\(130\) | 4.10315 | 0.359870 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | −3.36794 | −0.293141 | ||||||||
\(133\) | 23.3395 | 2.02379 | ||||||||
\(134\) | 1.51476 | 0.130856 | ||||||||
\(135\) | −6.56635 | −0.565141 | ||||||||
\(136\) | 4.60385 | 0.394777 | ||||||||
\(137\) | 10.1908 | 0.870660 | 0.435330 | − | 0.900271i | \(-0.356632\pi\) | ||||
0.435330 | + | 0.900271i | \(0.356632\pi\) | |||||||
\(138\) | 1.80561 | 0.153704 | ||||||||
\(139\) | 17.9403 | 1.52168 | 0.760838 | − | 0.648942i | \(-0.224788\pi\) | ||||
0.760838 | + | 0.648942i | \(0.224788\pi\) | |||||||
\(140\) | 5.74168 | 0.485261 | ||||||||
\(141\) | −22.8132 | −1.92122 | ||||||||
\(142\) | 6.94658 | 0.582944 | ||||||||
\(143\) | 5.76595 | 0.482173 | ||||||||
\(144\) | 0.260232 | 0.0216860 | ||||||||
\(145\) | 1.63516 | 0.135793 | ||||||||
\(146\) | 6.83151 | 0.565380 | ||||||||
\(147\) | −21.1462 | −1.74411 | ||||||||
\(148\) | −5.10501 | −0.419629 | ||||||||
\(149\) | 1.23929 | 0.101527 | 0.0507633 | − | 0.998711i | \(-0.483835\pi\) | ||||
0.0507633 | + | 0.998711i | \(0.483835\pi\) | |||||||
\(150\) | −5.84682 | −0.477391 | ||||||||
\(151\) | 11.4716 | 0.933547 | 0.466773 | − | 0.884377i | \(-0.345416\pi\) | ||||
0.466773 | + | 0.884377i | \(0.345416\pi\) | |||||||
\(152\) | 5.39557 | 0.437639 | ||||||||
\(153\) | −1.19807 | −0.0968581 | ||||||||
\(154\) | 8.06851 | 0.650179 | ||||||||
\(155\) | 2.79452 | 0.224461 | ||||||||
\(156\) | −5.58156 | −0.446882 | ||||||||
\(157\) | −3.98402 | −0.317960 | −0.158980 | − | 0.987282i | \(-0.550820\pi\) | ||||
−0.158980 | + | 0.987282i | \(0.550820\pi\) | |||||||
\(158\) | 1.92356 | 0.153031 | ||||||||
\(159\) | 12.6666 | 1.00453 | ||||||||
\(160\) | 1.32735 | 0.104936 | ||||||||
\(161\) | −4.32567 | −0.340910 | ||||||||
\(162\) | 9.71298 | 0.763123 | ||||||||
\(163\) | −10.5559 | −0.826803 | −0.413402 | − | 0.910549i | \(-0.635659\pi\) | ||||
−0.413402 | + | 0.910549i | \(0.635659\pi\) | |||||||
\(164\) | −7.15971 | −0.559080 | ||||||||
\(165\) | 4.47044 | 0.348023 | ||||||||
\(166\) | 8.12356 | 0.630511 | ||||||||
\(167\) | 8.81067 | 0.681790 | 0.340895 | − | 0.940101i | \(-0.389270\pi\) | ||||
0.340895 | + | 0.940101i | \(0.389270\pi\) | |||||||
\(168\) | −7.81047 | −0.602591 | ||||||||
\(169\) | −3.44430 | −0.264946 | ||||||||
\(170\) | −6.11093 | −0.468687 | ||||||||
\(171\) | −1.40410 | −0.107374 | ||||||||
\(172\) | −12.5688 | −0.958359 | ||||||||
\(173\) | 4.67939 | 0.355767 | 0.177884 | − | 0.984052i | \(-0.443075\pi\) | ||||
0.177884 | + | 0.984052i | \(0.443075\pi\) | |||||||
\(174\) | −2.22433 | −0.168626 | ||||||||
\(175\) | 14.0071 | 1.05884 | ||||||||
\(176\) | 1.86526 | 0.140599 | ||||||||
\(177\) | 7.73439 | 0.581352 | ||||||||
\(178\) | 15.2788 | 1.14519 | ||||||||
\(179\) | −9.43241 | −0.705011 | −0.352506 | − | 0.935810i | \(-0.614670\pi\) | ||||
−0.352506 | + | 0.935810i | \(0.614670\pi\) | |||||||
\(180\) | −0.345419 | −0.0257460 | ||||||||
\(181\) | −23.3758 | −1.73751 | −0.868753 | − | 0.495245i | \(-0.835078\pi\) | ||||
−0.868753 | + | 0.495245i | \(0.835078\pi\) | |||||||
\(182\) | 13.3716 | 0.991171 | ||||||||
\(183\) | −10.6321 | −0.785949 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 6.77614 | 0.498192 | ||||||||
\(186\) | −3.80142 | −0.278734 | ||||||||
\(187\) | −8.58738 | −0.627972 | ||||||||
\(188\) | 12.6346 | 0.921474 | ||||||||
\(189\) | −21.3989 | −1.55654 | ||||||||
\(190\) | −7.16182 | −0.519573 | ||||||||
\(191\) | 6.09532 | 0.441042 | 0.220521 | − | 0.975382i | \(-0.429224\pi\) | ||||
0.220521 | + | 0.975382i | \(0.429224\pi\) | |||||||
\(192\) | −1.80561 | −0.130309 | ||||||||
\(193\) | −7.79419 | −0.561038 | −0.280519 | − | 0.959848i | \(-0.590507\pi\) | ||||
−0.280519 | + | 0.959848i | \(0.590507\pi\) | |||||||
\(194\) | 14.6172 | 1.04945 | ||||||||
\(195\) | 7.40869 | 0.530547 | ||||||||
\(196\) | 11.7114 | 0.836529 | ||||||||
\(197\) | −13.9652 | −0.994982 | −0.497491 | − | 0.867469i | \(-0.665745\pi\) | ||||
−0.497491 | + | 0.867469i | \(0.665745\pi\) | |||||||
\(198\) | −0.485401 | −0.0344959 | ||||||||
\(199\) | 9.33175 | 0.661510 | 0.330755 | − | 0.943717i | \(-0.392697\pi\) | ||||
0.330755 | + | 0.943717i | \(0.392697\pi\) | |||||||
\(200\) | 3.23814 | 0.228971 | ||||||||
\(201\) | 2.73507 | 0.192917 | ||||||||
\(202\) | −0.695099 | −0.0489070 | ||||||||
\(203\) | 5.32878 | 0.374007 | ||||||||
\(204\) | 8.31276 | 0.582010 | ||||||||
\(205\) | 9.50346 | 0.663750 | ||||||||
\(206\) | 8.30467 | 0.578614 | ||||||||
\(207\) | 0.260232 | 0.0180874 | ||||||||
\(208\) | 3.09123 | 0.214338 | ||||||||
\(209\) | −10.0642 | −0.696152 | ||||||||
\(210\) | 10.3672 | 0.715408 | ||||||||
\(211\) | 8.01622 | 0.551859 | 0.275930 | − | 0.961178i | \(-0.411014\pi\) | ||||
0.275930 | + | 0.961178i | \(0.411014\pi\) | |||||||
\(212\) | −7.01514 | −0.481801 | ||||||||
\(213\) | 12.5428 | 0.859420 | ||||||||
\(214\) | 19.5610 | 1.33716 | ||||||||
\(215\) | 16.6832 | 1.13778 | ||||||||
\(216\) | −4.94696 | −0.336598 | ||||||||
\(217\) | 9.10699 | 0.618223 | ||||||||
\(218\) | −1.42166 | −0.0962867 | ||||||||
\(219\) | 12.3351 | 0.833526 | ||||||||
\(220\) | −2.47586 | −0.166922 | ||||||||
\(221\) | −14.2316 | −0.957318 | ||||||||
\(222\) | −9.21766 | −0.618649 | ||||||||
\(223\) | 4.89237 | 0.327617 | 0.163809 | − | 0.986492i | \(-0.447622\pi\) | ||||
0.163809 | + | 0.986492i | \(0.447622\pi\) | |||||||
\(224\) | 4.32567 | 0.289021 | ||||||||
\(225\) | −0.842667 | −0.0561778 | ||||||||
\(226\) | 11.8348 | 0.787239 | ||||||||
\(227\) | −26.2011 | −1.73903 | −0.869514 | − | 0.493908i | \(-0.835568\pi\) | ||||
−0.869514 | + | 0.493908i | \(0.835568\pi\) | |||||||
\(228\) | 9.74230 | 0.645200 | ||||||||
\(229\) | 18.3879 | 1.21511 | 0.607554 | − | 0.794279i | \(-0.292151\pi\) | ||||
0.607554 | + | 0.794279i | \(0.292151\pi\) | |||||||
\(230\) | 1.32735 | 0.0875230 | ||||||||
\(231\) | 14.5686 | 0.958542 | ||||||||
\(232\) | 1.23190 | 0.0808781 | ||||||||
\(233\) | 14.7959 | 0.969311 | 0.484655 | − | 0.874705i | \(-0.338945\pi\) | ||||
0.484655 | + | 0.874705i | \(0.338945\pi\) | |||||||
\(234\) | −0.804436 | −0.0525877 | ||||||||
\(235\) | −16.7706 | −1.09399 | ||||||||
\(236\) | −4.28353 | −0.278834 | ||||||||
\(237\) | 3.47321 | 0.225609 | ||||||||
\(238\) | −19.9147 | −1.29088 | ||||||||
\(239\) | 24.4982 | 1.58466 | 0.792328 | − | 0.610096i | \(-0.208869\pi\) | ||||
0.792328 | + | 0.610096i | \(0.208869\pi\) | |||||||
\(240\) | 2.39668 | 0.154705 | ||||||||
\(241\) | −11.3118 | −0.728657 | −0.364328 | − | 0.931271i | \(-0.618701\pi\) | ||||
−0.364328 | + | 0.931271i | \(0.618701\pi\) | |||||||
\(242\) | 7.52080 | 0.483455 | ||||||||
\(243\) | 2.69699 | 0.173012 | ||||||||
\(244\) | 5.88838 | 0.376965 | ||||||||
\(245\) | −15.5452 | −0.993143 | ||||||||
\(246\) | −12.9277 | −0.824237 | ||||||||
\(247\) | −16.6789 | −1.06126 | ||||||||
\(248\) | 2.10534 | 0.133689 | ||||||||
\(249\) | 14.6680 | 0.929546 | ||||||||
\(250\) | −10.9349 | −0.691584 | ||||||||
\(251\) | 3.76397 | 0.237580 | 0.118790 | − | 0.992919i | \(-0.462098\pi\) | ||||
0.118790 | + | 0.992919i | \(0.462098\pi\) | |||||||
\(252\) | −1.12568 | −0.0709110 | ||||||||
\(253\) | 1.86526 | 0.117268 | ||||||||
\(254\) | 5.38940 | 0.338161 | ||||||||
\(255\) | −11.0340 | −0.690973 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.54403 | 0.532962 | 0.266481 | − | 0.963840i | \(-0.414139\pi\) | ||||
0.266481 | + | 0.963840i | \(0.414139\pi\) | |||||||
\(258\) | −22.6943 | −1.41288 | ||||||||
\(259\) | 22.0826 | 1.37214 | ||||||||
\(260\) | −4.10315 | −0.254466 | ||||||||
\(261\) | −0.320579 | −0.0198434 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | −25.4440 | −1.56894 | −0.784472 | − | 0.620164i | \(-0.787066\pi\) | ||||
−0.784472 | + | 0.620164i | \(0.787066\pi\) | |||||||
\(264\) | 3.36794 | 0.207282 | ||||||||
\(265\) | 9.31155 | 0.572004 | ||||||||
\(266\) | −23.3395 | −1.43103 | ||||||||
\(267\) | 27.5876 | 1.68833 | ||||||||
\(268\) | −1.51476 | −0.0925288 | ||||||||
\(269\) | −22.4822 | −1.37077 | −0.685383 | − | 0.728182i | \(-0.740365\pi\) | ||||
−0.685383 | + | 0.728182i | \(0.740365\pi\) | |||||||
\(270\) | 6.56635 | 0.399615 | ||||||||
\(271\) | 9.69537 | 0.588952 | 0.294476 | − | 0.955659i | \(-0.404855\pi\) | ||||
0.294476 | + | 0.955659i | \(0.404855\pi\) | |||||||
\(272\) | −4.60385 | −0.279149 | ||||||||
\(273\) | 24.1440 | 1.46126 | ||||||||
\(274\) | −10.1908 | −0.615649 | ||||||||
\(275\) | −6.03998 | −0.364224 | ||||||||
\(276\) | −1.80561 | −0.108685 | ||||||||
\(277\) | −10.9550 | −0.658220 | −0.329110 | − | 0.944292i | \(-0.606749\pi\) | ||||
−0.329110 | + | 0.944292i | \(0.606749\pi\) | |||||||
\(278\) | −17.9403 | −1.07599 | ||||||||
\(279\) | −0.547876 | −0.0328005 | ||||||||
\(280\) | −5.74168 | −0.343131 | ||||||||
\(281\) | −4.00045 | −0.238647 | −0.119323 | − | 0.992855i | \(-0.538073\pi\) | ||||
−0.119323 | + | 0.992855i | \(0.538073\pi\) | |||||||
\(282\) | 22.8132 | 1.35851 | ||||||||
\(283\) | 20.2172 | 1.20179 | 0.600895 | − | 0.799328i | \(-0.294811\pi\) | ||||
0.600895 | + | 0.799328i | \(0.294811\pi\) | |||||||
\(284\) | −6.94658 | −0.412204 | ||||||||
\(285\) | −12.9315 | −0.765994 | ||||||||
\(286\) | −5.76595 | −0.340948 | ||||||||
\(287\) | 30.9705 | 1.82813 | ||||||||
\(288\) | −0.260232 | −0.0153343 | ||||||||
\(289\) | 4.19542 | 0.246790 | ||||||||
\(290\) | −1.63516 | −0.0960201 | ||||||||
\(291\) | 26.3929 | 1.54718 | ||||||||
\(292\) | −6.83151 | −0.399784 | ||||||||
\(293\) | −16.9710 | −0.991457 | −0.495729 | − | 0.868478i | \(-0.665099\pi\) | ||||
−0.495729 | + | 0.868478i | \(0.665099\pi\) | |||||||
\(294\) | 21.1462 | 1.23327 | ||||||||
\(295\) | 5.68575 | 0.331037 | ||||||||
\(296\) | 5.10501 | 0.296723 | ||||||||
\(297\) | 9.22737 | 0.535426 | ||||||||
\(298\) | −1.23929 | −0.0717901 | ||||||||
\(299\) | 3.09123 | 0.178770 | ||||||||
\(300\) | 5.84682 | 0.337566 | ||||||||
\(301\) | 54.3683 | 3.13373 | ||||||||
\(302\) | −11.4716 | −0.660117 | ||||||||
\(303\) | −1.25508 | −0.0721024 | ||||||||
\(304\) | −5.39557 | −0.309457 | ||||||||
\(305\) | −7.81595 | −0.447540 | ||||||||
\(306\) | 1.19807 | 0.0684890 | ||||||||
\(307\) | −34.3803 | −1.96219 | −0.981094 | − | 0.193533i | \(-0.938005\pi\) | ||||
−0.981094 | + | 0.193533i | \(0.938005\pi\) | |||||||
\(308\) | −8.06851 | −0.459746 | ||||||||
\(309\) | 14.9950 | 0.853036 | ||||||||
\(310\) | −2.79452 | −0.158718 | ||||||||
\(311\) | 13.1610 | 0.746290 | 0.373145 | − | 0.927773i | \(-0.378279\pi\) | ||||
0.373145 | + | 0.927773i | \(0.378279\pi\) | |||||||
\(312\) | 5.58156 | 0.315994 | ||||||||
\(313\) | 8.12702 | 0.459366 | 0.229683 | − | 0.973265i | \(-0.426231\pi\) | ||||
0.229683 | + | 0.973265i | \(0.426231\pi\) | |||||||
\(314\) | 3.98402 | 0.224831 | ||||||||
\(315\) | 1.49417 | 0.0841869 | ||||||||
\(316\) | −1.92356 | −0.108209 | ||||||||
\(317\) | −18.6763 | −1.04897 | −0.524484 | − | 0.851420i | \(-0.675742\pi\) | ||||
−0.524484 | + | 0.851420i | \(0.675742\pi\) | |||||||
\(318\) | −12.6666 | −0.710308 | ||||||||
\(319\) | −2.29781 | −0.128653 | ||||||||
\(320\) | −1.32735 | −0.0742012 | ||||||||
\(321\) | 35.3195 | 1.97134 | ||||||||
\(322\) | 4.32567 | 0.241060 | ||||||||
\(323\) | 24.8404 | 1.38216 | ||||||||
\(324\) | −9.71298 | −0.539610 | ||||||||
\(325\) | −10.0098 | −0.555245 | ||||||||
\(326\) | 10.5559 | 0.584638 | ||||||||
\(327\) | −2.56696 | −0.141953 | ||||||||
\(328\) | 7.15971 | 0.395329 | ||||||||
\(329\) | −54.6531 | −3.01312 | ||||||||
\(330\) | −4.47044 | −0.246090 | ||||||||
\(331\) | 25.5270 | 1.40309 | 0.701545 | − | 0.712625i | \(-0.252494\pi\) | ||||
0.701545 | + | 0.712625i | \(0.252494\pi\) | |||||||
\(332\) | −8.12356 | −0.445838 | ||||||||
\(333\) | −1.32849 | −0.0728006 | ||||||||
\(334\) | −8.81067 | −0.482098 | ||||||||
\(335\) | 2.01062 | 0.109852 | ||||||||
\(336\) | 7.81047 | 0.426096 | ||||||||
\(337\) | 33.7911 | 1.84072 | 0.920360 | − | 0.391072i | \(-0.127895\pi\) | ||||
0.920360 | + | 0.391072i | \(0.127895\pi\) | |||||||
\(338\) | 3.44430 | 0.187345 | ||||||||
\(339\) | 21.3690 | 1.16061 | ||||||||
\(340\) | 6.11093 | 0.331412 | ||||||||
\(341\) | −3.92700 | −0.212659 | ||||||||
\(342\) | 1.40410 | 0.0759250 | ||||||||
\(343\) | −20.3800 | −1.10041 | ||||||||
\(344\) | 12.5688 | 0.677662 | ||||||||
\(345\) | 2.39668 | 0.129033 | ||||||||
\(346\) | −4.67939 | −0.251566 | ||||||||
\(347\) | −1.10565 | −0.0593544 | −0.0296772 | − | 0.999560i | \(-0.509448\pi\) | ||||
−0.0296772 | + | 0.999560i | \(0.509448\pi\) | |||||||
\(348\) | 2.22433 | 0.119237 | ||||||||
\(349\) | 18.6252 | 0.996982 | 0.498491 | − | 0.866895i | \(-0.333888\pi\) | ||||
0.498491 | + | 0.866895i | \(0.333888\pi\) | |||||||
\(350\) | −14.0071 | −0.748711 | ||||||||
\(351\) | 15.2922 | 0.816236 | ||||||||
\(352\) | −1.86526 | −0.0994188 | ||||||||
\(353\) | 20.9570 | 1.11543 | 0.557714 | − | 0.830033i | \(-0.311678\pi\) | ||||
0.557714 | + | 0.830033i | \(0.311678\pi\) | |||||||
\(354\) | −7.73439 | −0.411078 | ||||||||
\(355\) | 9.22056 | 0.489376 | ||||||||
\(356\) | −15.2788 | −0.809774 | ||||||||
\(357\) | −35.9582 | −1.90311 | ||||||||
\(358\) | 9.43241 | 0.498518 | ||||||||
\(359\) | 8.79519 | 0.464193 | 0.232096 | − | 0.972693i | \(-0.425442\pi\) | ||||
0.232096 | + | 0.972693i | \(0.425442\pi\) | |||||||
\(360\) | 0.345419 | 0.0182052 | ||||||||
\(361\) | 10.1122 | 0.532221 | ||||||||
\(362\) | 23.3758 | 1.22860 | ||||||||
\(363\) | 13.5796 | 0.712746 | ||||||||
\(364\) | −13.3716 | −0.700864 | ||||||||
\(365\) | 9.06782 | 0.474631 | ||||||||
\(366\) | 10.6321 | 0.555750 | ||||||||
\(367\) | 14.0713 | 0.734517 | 0.367259 | − | 0.930119i | \(-0.380296\pi\) | ||||
0.367259 | + | 0.930119i | \(0.380296\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −1.86319 | −0.0969935 | ||||||||
\(370\) | −6.77614 | −0.352275 | ||||||||
\(371\) | 30.3451 | 1.57544 | ||||||||
\(372\) | 3.80142 | 0.197094 | ||||||||
\(373\) | −10.6301 | −0.550407 | −0.275204 | − | 0.961386i | \(-0.588745\pi\) | ||||
−0.275204 | + | 0.961386i | \(0.588745\pi\) | |||||||
\(374\) | 8.58738 | 0.444043 | ||||||||
\(375\) | −19.7442 | −1.01959 | ||||||||
\(376\) | −12.6346 | −0.651580 | ||||||||
\(377\) | −3.80808 | −0.196126 | ||||||||
\(378\) | 21.3989 | 1.10064 | ||||||||
\(379\) | 33.8949 | 1.74106 | 0.870531 | − | 0.492113i | \(-0.163775\pi\) | ||||
0.870531 | + | 0.492113i | \(0.163775\pi\) | |||||||
\(380\) | 7.16182 | 0.367394 | ||||||||
\(381\) | 9.73116 | 0.498542 | ||||||||
\(382\) | −6.09532 | −0.311864 | ||||||||
\(383\) | 17.2663 | 0.882268 | 0.441134 | − | 0.897441i | \(-0.354576\pi\) | ||||
0.441134 | + | 0.897441i | \(0.354576\pi\) | |||||||
\(384\) | 1.80561 | 0.0921422 | ||||||||
\(385\) | 10.7097 | 0.545819 | ||||||||
\(386\) | 7.79419 | 0.396714 | ||||||||
\(387\) | −3.27079 | −0.166264 | ||||||||
\(388\) | −14.6172 | −0.742074 | ||||||||
\(389\) | −30.4112 | −1.54191 | −0.770955 | − | 0.636889i | \(-0.780221\pi\) | ||||
−0.770955 | + | 0.636889i | \(0.780221\pi\) | |||||||
\(390\) | −7.40869 | −0.375154 | ||||||||
\(391\) | −4.60385 | −0.232827 | ||||||||
\(392\) | −11.7114 | −0.591515 | ||||||||
\(393\) | 1.80561 | 0.0910810 | ||||||||
\(394\) | 13.9652 | 0.703559 | ||||||||
\(395\) | 2.55325 | 0.128468 | ||||||||
\(396\) | 0.485401 | 0.0243923 | ||||||||
\(397\) | −17.9691 | −0.901841 | −0.450920 | − | 0.892564i | \(-0.648904\pi\) | ||||
−0.450920 | + | 0.892564i | \(0.648904\pi\) | |||||||
\(398\) | −9.33175 | −0.467759 | ||||||||
\(399\) | −42.1420 | −2.10974 | ||||||||
\(400\) | −3.23814 | −0.161907 | ||||||||
\(401\) | −14.3336 | −0.715786 | −0.357893 | − | 0.933763i | \(-0.616505\pi\) | ||||
−0.357893 | + | 0.933763i | \(0.616505\pi\) | |||||||
\(402\) | −2.73507 | −0.136413 | ||||||||
\(403\) | −6.50808 | −0.324190 | ||||||||
\(404\) | 0.695099 | 0.0345825 | ||||||||
\(405\) | 12.8925 | 0.640635 | ||||||||
\(406\) | −5.32878 | −0.264463 | ||||||||
\(407\) | −9.52218 | −0.471997 | ||||||||
\(408\) | −8.31276 | −0.411543 | ||||||||
\(409\) | −18.9955 | −0.939265 | −0.469633 | − | 0.882862i | \(-0.655614\pi\) | ||||
−0.469633 | + | 0.882862i | \(0.655614\pi\) | |||||||
\(410\) | −9.50346 | −0.469342 | ||||||||
\(411\) | −18.4006 | −0.907637 | ||||||||
\(412\) | −8.30467 | −0.409142 | ||||||||
\(413\) | 18.5291 | 0.911759 | ||||||||
\(414\) | −0.260232 | −0.0127897 | ||||||||
\(415\) | 10.7828 | 0.529308 | ||||||||
\(416\) | −3.09123 | −0.151560 | ||||||||
\(417\) | −32.3932 | −1.58630 | ||||||||
\(418\) | 10.0642 | 0.492254 | ||||||||
\(419\) | −21.4193 | −1.04640 | −0.523200 | − | 0.852210i | \(-0.675262\pi\) | ||||
−0.523200 | + | 0.852210i | \(0.675262\pi\) | |||||||
\(420\) | −10.3672 | −0.505870 | ||||||||
\(421\) | 35.7201 | 1.74089 | 0.870446 | − | 0.492263i | \(-0.163830\pi\) | ||||
0.870446 | + | 0.492263i | \(0.163830\pi\) | |||||||
\(422\) | −8.01622 | −0.390223 | ||||||||
\(423\) | 3.28793 | 0.159865 | ||||||||
\(424\) | 7.01514 | 0.340685 | ||||||||
\(425\) | 14.9079 | 0.723139 | ||||||||
\(426\) | −12.5428 | −0.607702 | ||||||||
\(427\) | −25.4712 | −1.23264 | ||||||||
\(428\) | −19.5610 | −0.945514 | ||||||||
\(429\) | −10.4111 | −0.502651 | ||||||||
\(430\) | −16.6832 | −0.804533 | ||||||||
\(431\) | −5.92422 | −0.285360 | −0.142680 | − | 0.989769i | \(-0.545572\pi\) | ||||
−0.142680 | + | 0.989769i | \(0.545572\pi\) | |||||||
\(432\) | 4.94696 | 0.238011 | ||||||||
\(433\) | −27.6118 | −1.32694 | −0.663469 | − | 0.748204i | \(-0.730916\pi\) | ||||
−0.663469 | + | 0.748204i | \(0.730916\pi\) | |||||||
\(434\) | −9.10699 | −0.437149 | ||||||||
\(435\) | −2.95247 | −0.141560 | ||||||||
\(436\) | 1.42166 | 0.0680850 | ||||||||
\(437\) | −5.39557 | −0.258105 | ||||||||
\(438\) | −12.3351 | −0.589392 | ||||||||
\(439\) | 12.9467 | 0.617913 | 0.308956 | − | 0.951076i | \(-0.400020\pi\) | ||||
0.308956 | + | 0.951076i | \(0.400020\pi\) | |||||||
\(440\) | 2.47586 | 0.118032 | ||||||||
\(441\) | 3.04768 | 0.145128 | ||||||||
\(442\) | 14.2316 | 0.676926 | ||||||||
\(443\) | 32.0407 | 1.52230 | 0.761150 | − | 0.648576i | \(-0.224635\pi\) | ||||
0.761150 | + | 0.648576i | \(0.224635\pi\) | |||||||
\(444\) | 9.21766 | 0.437451 | ||||||||
\(445\) | 20.2803 | 0.961380 | ||||||||
\(446\) | −4.89237 | −0.231660 | ||||||||
\(447\) | −2.23768 | −0.105838 | ||||||||
\(448\) | −4.32567 | −0.204369 | ||||||||
\(449\) | 14.3905 | 0.679129 | 0.339565 | − | 0.940583i | \(-0.389720\pi\) | ||||
0.339565 | + | 0.940583i | \(0.389720\pi\) | |||||||
\(450\) | 0.842667 | 0.0397237 | ||||||||
\(451\) | −13.3547 | −0.628850 | ||||||||
\(452\) | −11.8348 | −0.556662 | ||||||||
\(453\) | −20.7133 | −0.973194 | ||||||||
\(454\) | 26.2011 | 1.22968 | ||||||||
\(455\) | 17.7489 | 0.832079 | ||||||||
\(456\) | −9.74230 | −0.456225 | ||||||||
\(457\) | 18.9587 | 0.886852 | 0.443426 | − | 0.896311i | \(-0.353763\pi\) | ||||
0.443426 | + | 0.896311i | \(0.353763\pi\) | |||||||
\(458\) | −18.3879 | −0.859211 | ||||||||
\(459\) | −22.7750 | −1.06305 | ||||||||
\(460\) | −1.32735 | −0.0618881 | ||||||||
\(461\) | −12.8900 | −0.600348 | −0.300174 | − | 0.953884i | \(-0.597045\pi\) | ||||
−0.300174 | + | 0.953884i | \(0.597045\pi\) | |||||||
\(462\) | −14.5686 | −0.677792 | ||||||||
\(463\) | 6.87915 | 0.319701 | 0.159851 | − | 0.987141i | \(-0.448899\pi\) | ||||
0.159851 | + | 0.987141i | \(0.448899\pi\) | |||||||
\(464\) | −1.23190 | −0.0571895 | ||||||||
\(465\) | −5.04582 | −0.233994 | ||||||||
\(466\) | −14.7959 | −0.685406 | ||||||||
\(467\) | −36.1072 | −1.67084 | −0.835421 | − | 0.549610i | \(-0.814776\pi\) | ||||
−0.835421 | + | 0.549610i | \(0.814776\pi\) | |||||||
\(468\) | 0.804436 | 0.0371851 | ||||||||
\(469\) | 6.55236 | 0.302560 | ||||||||
\(470\) | 16.7706 | 0.773569 | ||||||||
\(471\) | 7.19360 | 0.331463 | ||||||||
\(472\) | 4.28353 | 0.197165 | ||||||||
\(473\) | −23.4440 | −1.07796 | ||||||||
\(474\) | −3.47321 | −0.159530 | ||||||||
\(475\) | 17.4716 | 0.801652 | ||||||||
\(476\) | 19.9147 | 0.912790 | ||||||||
\(477\) | −1.82556 | −0.0835867 | ||||||||
\(478\) | −24.4982 | −1.12052 | ||||||||
\(479\) | −26.0091 | −1.18838 | −0.594192 | − | 0.804323i | \(-0.702528\pi\) | ||||
−0.594192 | + | 0.804323i | \(0.702528\pi\) | |||||||
\(480\) | −2.39668 | −0.109393 | ||||||||
\(481\) | −15.7808 | −0.719541 | ||||||||
\(482\) | 11.3118 | 0.515238 | ||||||||
\(483\) | 7.81047 | 0.355389 | ||||||||
\(484\) | −7.52080 | −0.341854 | ||||||||
\(485\) | 19.4021 | 0.881005 | ||||||||
\(486\) | −2.69699 | −0.122338 | ||||||||
\(487\) | −9.30524 | −0.421661 | −0.210830 | − | 0.977523i | \(-0.567617\pi\) | ||||
−0.210830 | + | 0.977523i | \(0.567617\pi\) | |||||||
\(488\) | −5.88838 | −0.266554 | ||||||||
\(489\) | 19.0599 | 0.861918 | ||||||||
\(490\) | 15.5452 | 0.702258 | ||||||||
\(491\) | 38.4944 | 1.73723 | 0.868615 | − | 0.495488i | \(-0.165011\pi\) | ||||
0.868615 | + | 0.495488i | \(0.165011\pi\) | |||||||
\(492\) | 12.9277 | 0.582824 | ||||||||
\(493\) | 5.67147 | 0.255430 | ||||||||
\(494\) | 16.6789 | 0.750421 | ||||||||
\(495\) | −0.644297 | −0.0289590 | ||||||||
\(496\) | −2.10534 | −0.0945324 | ||||||||
\(497\) | 30.0486 | 1.34786 | ||||||||
\(498\) | −14.6680 | −0.657289 | ||||||||
\(499\) | 31.4539 | 1.40807 | 0.704036 | − | 0.710164i | \(-0.251379\pi\) | ||||
0.704036 | + | 0.710164i | \(0.251379\pi\) | |||||||
\(500\) | 10.9349 | 0.489024 | ||||||||
\(501\) | −15.9086 | −0.710745 | ||||||||
\(502\) | −3.76397 | −0.167994 | ||||||||
\(503\) | 34.8745 | 1.55498 | 0.777489 | − | 0.628896i | \(-0.216493\pi\) | ||||
0.777489 | + | 0.628896i | \(0.216493\pi\) | |||||||
\(504\) | 1.12568 | 0.0501416 | ||||||||
\(505\) | −0.922641 | −0.0410570 | ||||||||
\(506\) | −1.86526 | −0.0829210 | ||||||||
\(507\) | 6.21907 | 0.276199 | ||||||||
\(508\) | −5.38940 | −0.239116 | ||||||||
\(509\) | −43.6575 | −1.93508 | −0.967542 | − | 0.252709i | \(-0.918679\pi\) | ||||
−0.967542 | + | 0.252709i | \(0.918679\pi\) | |||||||
\(510\) | 11.0340 | 0.488592 | ||||||||
\(511\) | 29.5509 | 1.30725 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −26.6917 | −1.17847 | ||||||||
\(514\) | −8.54403 | −0.376861 | ||||||||
\(515\) | 11.0232 | 0.485741 | ||||||||
\(516\) | 22.6943 | 0.999060 | ||||||||
\(517\) | 23.5669 | 1.03647 | ||||||||
\(518\) | −22.0826 | −0.970253 | ||||||||
\(519\) | −8.44916 | −0.370877 | ||||||||
\(520\) | 4.10315 | 0.179935 | ||||||||
\(521\) | −24.3122 | −1.06514 | −0.532568 | − | 0.846387i | \(-0.678773\pi\) | ||||
−0.532568 | + | 0.846387i | \(0.678773\pi\) | |||||||
\(522\) | 0.320579 | 0.0140314 | ||||||||
\(523\) | 1.61571 | 0.0706502 | 0.0353251 | − | 0.999376i | \(-0.488753\pi\) | ||||
0.0353251 | + | 0.999376i | \(0.488753\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | −25.2914 | −1.10381 | ||||||||
\(526\) | 25.4440 | 1.10941 | ||||||||
\(527\) | 9.69265 | 0.422219 | ||||||||
\(528\) | −3.36794 | −0.146571 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −9.31155 | −0.404468 | ||||||||
\(531\) | −1.11471 | −0.0483743 | ||||||||
\(532\) | 23.3395 | 1.01189 | ||||||||
\(533\) | −22.1323 | −0.958657 | ||||||||
\(534\) | −27.5876 | −1.19383 | ||||||||
\(535\) | 25.9643 | 1.12253 | ||||||||
\(536\) | 1.51476 | 0.0654278 | ||||||||
\(537\) | 17.0313 | 0.734953 | ||||||||
\(538\) | 22.4822 | 0.969279 | ||||||||
\(539\) | 21.8448 | 0.940924 | ||||||||
\(540\) | −6.56635 | −0.282571 | ||||||||
\(541\) | 40.9612 | 1.76106 | 0.880529 | − | 0.473992i | \(-0.157188\pi\) | ||||
0.880529 | + | 0.473992i | \(0.157188\pi\) | |||||||
\(542\) | −9.69537 | −0.416452 | ||||||||
\(543\) | 42.2075 | 1.81130 | ||||||||
\(544\) | 4.60385 | 0.197388 | ||||||||
\(545\) | −1.88704 | −0.0808318 | ||||||||
\(546\) | −24.1440 | −1.03327 | ||||||||
\(547\) | −15.0983 | −0.645559 | −0.322779 | − | 0.946474i | \(-0.604617\pi\) | ||||
−0.322779 | + | 0.946474i | \(0.604617\pi\) | |||||||
\(548\) | 10.1908 | 0.435330 | ||||||||
\(549\) | 1.53234 | 0.0653988 | ||||||||
\(550\) | 6.03998 | 0.257545 | ||||||||
\(551\) | 6.64680 | 0.283163 | ||||||||
\(552\) | 1.80561 | 0.0768519 | ||||||||
\(553\) | 8.32070 | 0.353832 | ||||||||
\(554\) | 10.9550 | 0.465432 | ||||||||
\(555\) | −12.2351 | −0.519350 | ||||||||
\(556\) | 17.9403 | 0.760838 | ||||||||
\(557\) | 9.02869 | 0.382558 | 0.191279 | − | 0.981536i | \(-0.438737\pi\) | ||||
0.191279 | + | 0.981536i | \(0.438737\pi\) | |||||||
\(558\) | 0.547876 | 0.0231934 | ||||||||
\(559\) | −38.8529 | −1.64330 | ||||||||
\(560\) | 5.74168 | 0.242630 | ||||||||
\(561\) | 15.5055 | 0.654642 | ||||||||
\(562\) | 4.00045 | 0.168749 | ||||||||
\(563\) | 12.9216 | 0.544580 | 0.272290 | − | 0.962215i | \(-0.412219\pi\) | ||||
0.272290 | + | 0.962215i | \(0.412219\pi\) | |||||||
\(564\) | −22.8132 | −0.960609 | ||||||||
\(565\) | 15.7089 | 0.660880 | ||||||||
\(566\) | −20.2172 | −0.849793 | ||||||||
\(567\) | 42.0151 | 1.76447 | ||||||||
\(568\) | 6.94658 | 0.291472 | ||||||||
\(569\) | −29.4576 | −1.23493 | −0.617464 | − | 0.786599i | \(-0.711840\pi\) | ||||
−0.617464 | + | 0.786599i | \(0.711840\pi\) | |||||||
\(570\) | 12.9315 | 0.541639 | ||||||||
\(571\) | 30.0998 | 1.25964 | 0.629818 | − | 0.776743i | \(-0.283129\pi\) | ||||
0.629818 | + | 0.776743i | \(0.283129\pi\) | |||||||
\(572\) | 5.76595 | 0.241087 | ||||||||
\(573\) | −11.0058 | −0.459773 | ||||||||
\(574\) | −30.9705 | −1.29269 | ||||||||
\(575\) | −3.23814 | −0.135040 | ||||||||
\(576\) | 0.260232 | 0.0108430 | ||||||||
\(577\) | −26.2419 | −1.09246 | −0.546232 | − | 0.837634i | \(-0.683938\pi\) | ||||
−0.546232 | + | 0.837634i | \(0.683938\pi\) | |||||||
\(578\) | −4.19542 | −0.174507 | ||||||||
\(579\) | 14.0733 | 0.584866 | ||||||||
\(580\) | 1.63516 | 0.0678964 | ||||||||
\(581\) | 35.1398 | 1.45785 | ||||||||
\(582\) | −26.3929 | −1.09402 | ||||||||
\(583\) | −13.0851 | −0.541928 | ||||||||
\(584\) | 6.83151 | 0.282690 | ||||||||
\(585\) | −1.06777 | −0.0441469 | ||||||||
\(586\) | 16.9710 | 0.701066 | ||||||||
\(587\) | −23.9371 | −0.987992 | −0.493996 | − | 0.869464i | \(-0.664464\pi\) | ||||
−0.493996 | + | 0.869464i | \(0.664464\pi\) | |||||||
\(588\) | −21.1462 | −0.872056 | ||||||||
\(589\) | 11.3595 | 0.468060 | ||||||||
\(590\) | −5.68575 | −0.234079 | ||||||||
\(591\) | 25.2158 | 1.03724 | ||||||||
\(592\) | −5.10501 | −0.209815 | ||||||||
\(593\) | 13.8220 | 0.567600 | 0.283800 | − | 0.958884i | \(-0.408405\pi\) | ||||
0.283800 | + | 0.958884i | \(0.408405\pi\) | |||||||
\(594\) | −9.22737 | −0.378604 | ||||||||
\(595\) | −26.4338 | −1.08368 | ||||||||
\(596\) | 1.23929 | 0.0507633 | ||||||||
\(597\) | −16.8495 | −0.689605 | ||||||||
\(598\) | −3.09123 | −0.126410 | ||||||||
\(599\) | −8.67973 | −0.354644 | −0.177322 | − | 0.984153i | \(-0.556743\pi\) | ||||
−0.177322 | + | 0.984153i | \(0.556743\pi\) | |||||||
\(600\) | −5.84682 | −0.238695 | ||||||||
\(601\) | 18.9876 | 0.774521 | 0.387261 | − | 0.921970i | \(-0.373421\pi\) | ||||
0.387261 | + | 0.921970i | \(0.373421\pi\) | |||||||
\(602\) | −54.3683 | −2.21588 | ||||||||
\(603\) | −0.394189 | −0.0160526 | ||||||||
\(604\) | 11.4716 | 0.466773 | ||||||||
\(605\) | 9.98274 | 0.405856 | ||||||||
\(606\) | 1.25508 | 0.0509841 | ||||||||
\(607\) | −45.6586 | −1.85323 | −0.926613 | − | 0.376016i | \(-0.877294\pi\) | ||||
−0.926613 | + | 0.376016i | \(0.877294\pi\) | |||||||
\(608\) | 5.39557 | 0.218819 | ||||||||
\(609\) | −9.62171 | −0.389891 | ||||||||
\(610\) | 7.81595 | 0.316458 | ||||||||
\(611\) | 39.0565 | 1.58006 | ||||||||
\(612\) | −1.19807 | −0.0484290 | ||||||||
\(613\) | 40.7373 | 1.64536 | 0.822681 | − | 0.568503i | \(-0.192477\pi\) | ||||
0.822681 | + | 0.568503i | \(0.192477\pi\) | |||||||
\(614\) | 34.3803 | 1.38748 | ||||||||
\(615\) | −17.1595 | −0.691940 | ||||||||
\(616\) | 8.06851 | 0.325089 | ||||||||
\(617\) | −26.6199 | −1.07168 | −0.535839 | − | 0.844320i | \(-0.680005\pi\) | ||||
−0.535839 | + | 0.844320i | \(0.680005\pi\) | |||||||
\(618\) | −14.9950 | −0.603188 | ||||||||
\(619\) | 0.230345 | 0.00925836 | 0.00462918 | − | 0.999989i | \(-0.498526\pi\) | ||||
0.00462918 | + | 0.999989i | \(0.498526\pi\) | |||||||
\(620\) | 2.79452 | 0.112231 | ||||||||
\(621\) | 4.94696 | 0.198515 | ||||||||
\(622\) | −13.1610 | −0.527706 | ||||||||
\(623\) | 66.0910 | 2.64788 | ||||||||
\(624\) | −5.58156 | −0.223441 | ||||||||
\(625\) | 1.67622 | 0.0670488 | ||||||||
\(626\) | −8.12702 | −0.324821 | ||||||||
\(627\) | 18.1720 | 0.725718 | ||||||||
\(628\) | −3.98402 | −0.158980 | ||||||||
\(629\) | 23.5027 | 0.937114 | ||||||||
\(630\) | −1.49417 | −0.0595291 | ||||||||
\(631\) | 18.7253 | 0.745444 | 0.372722 | − | 0.927943i | \(-0.378424\pi\) | ||||
0.372722 | + | 0.927943i | \(0.378424\pi\) | |||||||
\(632\) | 1.92356 | 0.0765153 | ||||||||
\(633\) | −14.4742 | −0.575297 | ||||||||
\(634\) | 18.6763 | 0.741732 | ||||||||
\(635\) | 7.15363 | 0.283883 | ||||||||
\(636\) | 12.6666 | 0.502264 | ||||||||
\(637\) | 36.2026 | 1.43440 | ||||||||
\(638\) | 2.29781 | 0.0909713 | ||||||||
\(639\) | −1.80772 | −0.0715124 | ||||||||
\(640\) | 1.32735 | 0.0524682 | ||||||||
\(641\) | 44.5802 | 1.76081 | 0.880406 | − | 0.474220i | \(-0.157270\pi\) | ||||
0.880406 | + | 0.474220i | \(0.157270\pi\) | |||||||
\(642\) | −35.3195 | −1.39395 | ||||||||
\(643\) | −3.84811 | −0.151755 | −0.0758773 | − | 0.997117i | \(-0.524176\pi\) | ||||
−0.0758773 | + | 0.997117i | \(0.524176\pi\) | |||||||
\(644\) | −4.32567 | −0.170455 | ||||||||
\(645\) | −30.1233 | −1.18610 | ||||||||
\(646\) | −24.8404 | −0.977332 | ||||||||
\(647\) | −20.6529 | −0.811951 | −0.405976 | − | 0.913884i | \(-0.633068\pi\) | ||||
−0.405976 | + | 0.913884i | \(0.633068\pi\) | |||||||
\(648\) | 9.71298 | 0.381562 | ||||||||
\(649\) | −7.98991 | −0.313631 | ||||||||
\(650\) | 10.0098 | 0.392618 | ||||||||
\(651\) | −16.4437 | −0.644479 | ||||||||
\(652\) | −10.5559 | −0.413402 | ||||||||
\(653\) | −5.73340 | −0.224365 | −0.112183 | − | 0.993688i | \(-0.535784\pi\) | ||||
−0.112183 | + | 0.993688i | \(0.535784\pi\) | |||||||
\(654\) | 2.56696 | 0.100376 | ||||||||
\(655\) | 1.32735 | 0.0518639 | ||||||||
\(656\) | −7.15971 | −0.279540 | ||||||||
\(657\) | −1.77778 | −0.0693577 | ||||||||
\(658\) | 54.6531 | 2.13060 | ||||||||
\(659\) | 14.8658 | 0.579091 | 0.289545 | − | 0.957164i | \(-0.406496\pi\) | ||||
0.289545 | + | 0.957164i | \(0.406496\pi\) | |||||||
\(660\) | 4.47044 | 0.174012 | ||||||||
\(661\) | 7.57387 | 0.294590 | 0.147295 | − | 0.989093i | \(-0.452943\pi\) | ||||
0.147295 | + | 0.989093i | \(0.452943\pi\) | |||||||
\(662\) | −25.5270 | −0.992134 | ||||||||
\(663\) | 25.6967 | 0.997975 | ||||||||
\(664\) | 8.12356 | 0.315255 | ||||||||
\(665\) | −30.9797 | −1.20134 | ||||||||
\(666\) | 1.32849 | 0.0514778 | ||||||||
\(667\) | −1.23190 | −0.0476993 | ||||||||
\(668\) | 8.81067 | 0.340895 | ||||||||
\(669\) | −8.83371 | −0.341531 | ||||||||
\(670\) | −2.01062 | −0.0776771 | ||||||||
\(671\) | 10.9834 | 0.424008 | ||||||||
\(672\) | −7.81047 | −0.301296 | ||||||||
\(673\) | −1.14253 | −0.0440412 | −0.0220206 | − | 0.999758i | \(-0.507010\pi\) | ||||
−0.0220206 | + | 0.999758i | \(0.507010\pi\) | |||||||
\(674\) | −33.7911 | −1.30159 | ||||||||
\(675\) | −16.0189 | −0.616569 | ||||||||
\(676\) | −3.44430 | −0.132473 | ||||||||
\(677\) | 19.7553 | 0.759258 | 0.379629 | − | 0.925139i | \(-0.376052\pi\) | ||||
0.379629 | + | 0.925139i | \(0.376052\pi\) | |||||||
\(678\) | −21.3690 | −0.820673 | ||||||||
\(679\) | 63.2290 | 2.42651 | ||||||||
\(680\) | −6.11093 | −0.234343 | ||||||||
\(681\) | 47.3090 | 1.81289 | ||||||||
\(682\) | 3.92700 | 0.150373 | ||||||||
\(683\) | −11.2425 | −0.430181 | −0.215090 | − | 0.976594i | \(-0.569005\pi\) | ||||
−0.215090 | + | 0.976594i | \(0.569005\pi\) | |||||||
\(684\) | −1.40410 | −0.0536871 | ||||||||
\(685\) | −13.5268 | −0.516832 | ||||||||
\(686\) | 20.3800 | 0.778111 | ||||||||
\(687\) | −33.2014 | −1.26671 | ||||||||
\(688\) | −12.5688 | −0.479179 | ||||||||
\(689\) | −21.6854 | −0.826148 | ||||||||
\(690\) | −2.39668 | −0.0912401 | ||||||||
\(691\) | 15.5094 | 0.590005 | 0.295003 | − | 0.955496i | \(-0.404679\pi\) | ||||
0.295003 | + | 0.955496i | \(0.404679\pi\) | |||||||
\(692\) | 4.67939 | 0.177884 | ||||||||
\(693\) | −2.09968 | −0.0797603 | ||||||||
\(694\) | 1.10565 | 0.0419699 | ||||||||
\(695\) | −23.8131 | −0.903282 | ||||||||
\(696\) | −2.22433 | −0.0843130 | ||||||||
\(697\) | 32.9622 | 1.24853 | ||||||||
\(698\) | −18.6252 | −0.704973 | ||||||||
\(699\) | −26.7156 | −1.01048 | ||||||||
\(700\) | 14.0071 | 0.529419 | ||||||||
\(701\) | 8.20626 | 0.309946 | 0.154973 | − | 0.987919i | \(-0.450471\pi\) | ||||
0.154973 | + | 0.987919i | \(0.450471\pi\) | |||||||
\(702\) | −15.2922 | −0.577166 | ||||||||
\(703\) | 27.5444 | 1.03886 | ||||||||
\(704\) | 1.86526 | 0.0702997 | ||||||||
\(705\) | 30.2811 | 1.14045 | ||||||||
\(706\) | −20.9570 | −0.788727 | ||||||||
\(707\) | −3.00677 | −0.113081 | ||||||||
\(708\) | 7.73439 | 0.290676 | ||||||||
\(709\) | −23.7026 | −0.890169 | −0.445085 | − | 0.895489i | \(-0.646826\pi\) | ||||
−0.445085 | + | 0.895489i | \(0.646826\pi\) | |||||||
\(710\) | −9.22056 | −0.346041 | ||||||||
\(711\) | −0.500573 | −0.0187729 | ||||||||
\(712\) | 15.2788 | 0.572597 | ||||||||
\(713\) | −2.10534 | −0.0788455 | ||||||||
\(714\) | 35.9582 | 1.34570 | ||||||||
\(715\) | −7.65345 | −0.286223 | ||||||||
\(716\) | −9.43241 | −0.352506 | ||||||||
\(717\) | −44.2342 | −1.65196 | ||||||||
\(718\) | −8.79519 | −0.328234 | ||||||||
\(719\) | −2.73616 | −0.102041 | −0.0510207 | − | 0.998698i | \(-0.516247\pi\) | ||||
−0.0510207 | + | 0.998698i | \(0.516247\pi\) | |||||||
\(720\) | −0.345419 | −0.0128730 | ||||||||
\(721\) | 35.9232 | 1.33785 | ||||||||
\(722\) | −10.1122 | −0.376337 | ||||||||
\(723\) | 20.4247 | 0.759603 | ||||||||
\(724\) | −23.3758 | −0.868753 | ||||||||
\(725\) | 3.98906 | 0.148150 | ||||||||
\(726\) | −13.5796 | −0.503988 | ||||||||
\(727\) | −33.0449 | −1.22557 | −0.612783 | − | 0.790251i | \(-0.709950\pi\) | ||||
−0.612783 | + | 0.790251i | \(0.709950\pi\) | |||||||
\(728\) | 13.3716 | 0.495586 | ||||||||
\(729\) | 24.2692 | 0.898860 | ||||||||
\(730\) | −9.06782 | −0.335615 | ||||||||
\(731\) | 57.8646 | 2.14020 | ||||||||
\(732\) | −10.6321 | −0.392974 | ||||||||
\(733\) | 50.8481 | 1.87812 | 0.939059 | − | 0.343757i | \(-0.111700\pi\) | ||||
0.939059 | + | 0.343757i | \(0.111700\pi\) | |||||||
\(734\) | −14.0713 | −0.519382 | ||||||||
\(735\) | 28.0685 | 1.03532 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −2.82543 | −0.104076 | ||||||||
\(738\) | 1.86319 | 0.0685848 | ||||||||
\(739\) | −35.3951 | −1.30203 | −0.651015 | − | 0.759065i | \(-0.725657\pi\) | ||||
−0.651015 | + | 0.759065i | \(0.725657\pi\) | |||||||
\(740\) | 6.77614 | 0.249096 | ||||||||
\(741\) | 30.1157 | 1.10633 | ||||||||
\(742\) | −30.3451 | −1.11401 | ||||||||
\(743\) | 42.6682 | 1.56534 | 0.782672 | − | 0.622434i | \(-0.213856\pi\) | ||||
0.782672 | + | 0.622434i | \(0.213856\pi\) | |||||||
\(744\) | −3.80142 | −0.139367 | ||||||||
\(745\) | −1.64497 | −0.0602672 | ||||||||
\(746\) | 10.6301 | 0.389197 | ||||||||
\(747\) | −2.11401 | −0.0773476 | ||||||||
\(748\) | −8.58738 | −0.313986 | ||||||||
\(749\) | 84.6142 | 3.09174 | ||||||||
\(750\) | 19.7442 | 0.720956 | ||||||||
\(751\) | −39.3070 | −1.43433 | −0.717166 | − | 0.696902i | \(-0.754561\pi\) | ||||
−0.717166 | + | 0.696902i | \(0.754561\pi\) | |||||||
\(752\) | 12.6346 | 0.460737 | ||||||||
\(753\) | −6.79627 | −0.247670 | ||||||||
\(754\) | 3.80808 | 0.138682 | ||||||||
\(755\) | −15.2269 | −0.554162 | ||||||||
\(756\) | −21.3989 | −0.778270 | ||||||||
\(757\) | 4.41370 | 0.160419 | 0.0802094 | − | 0.996778i | \(-0.474441\pi\) | ||||
0.0802094 | + | 0.996778i | \(0.474441\pi\) | |||||||
\(758\) | −33.8949 | −1.23112 | ||||||||
\(759\) | −3.36794 | −0.122248 | ||||||||
\(760\) | −7.16182 | −0.259787 | ||||||||
\(761\) | −1.03158 | −0.0373948 | −0.0186974 | − | 0.999825i | \(-0.505952\pi\) | ||||
−0.0186974 | + | 0.999825i | \(0.505952\pi\) | |||||||
\(762\) | −9.73116 | −0.352523 | ||||||||
\(763\) | −6.14961 | −0.222631 | ||||||||
\(764\) | 6.09532 | 0.220521 | ||||||||
\(765\) | 1.59026 | 0.0574959 | ||||||||
\(766\) | −17.2663 | −0.623857 | ||||||||
\(767\) | −13.2414 | −0.478118 | ||||||||
\(768\) | −1.80561 | −0.0651544 | ||||||||
\(769\) | −1.97869 | −0.0713535 | −0.0356767 | − | 0.999363i | \(-0.511359\pi\) | ||||
−0.0356767 | + | 0.999363i | \(0.511359\pi\) | |||||||
\(770\) | −10.7097 | −0.385952 | ||||||||
\(771\) | −15.4272 | −0.555597 | ||||||||
\(772\) | −7.79419 | −0.280519 | ||||||||
\(773\) | −15.0376 | −0.540864 | −0.270432 | − | 0.962739i | \(-0.587167\pi\) | ||||
−0.270432 | + | 0.962739i | \(0.587167\pi\) | |||||||
\(774\) | 3.27079 | 0.117566 | ||||||||
\(775\) | 6.81737 | 0.244887 | ||||||||
\(776\) | 14.6172 | 0.524726 | ||||||||
\(777\) | −39.8726 | −1.43042 | ||||||||
\(778\) | 30.4112 | 1.09030 | ||||||||
\(779\) | 38.6307 | 1.38409 | ||||||||
\(780\) | 7.40869 | 0.265274 | ||||||||
\(781\) | −12.9572 | −0.463645 | ||||||||
\(782\) | 4.60385 | 0.164633 | ||||||||
\(783\) | −6.09415 | −0.217787 | ||||||||
\(784\) | 11.7114 | 0.418264 | ||||||||
\(785\) | 5.28820 | 0.188744 | ||||||||
\(786\) | −1.80561 | −0.0644040 | ||||||||
\(787\) | −19.6755 | −0.701355 | −0.350677 | − | 0.936496i | \(-0.614049\pi\) | ||||
−0.350677 | + | 0.936496i | \(0.614049\pi\) | |||||||
\(788\) | −13.9652 | −0.497491 | ||||||||
\(789\) | 45.9420 | 1.63558 | ||||||||
\(790\) | −2.55325 | −0.0908404 | ||||||||
\(791\) | 51.1934 | 1.82023 | ||||||||
\(792\) | −0.485401 | −0.0172480 | ||||||||
\(793\) | 18.2023 | 0.646383 | ||||||||
\(794\) | 17.9691 | 0.637698 | ||||||||
\(795\) | −16.8130 | −0.596297 | ||||||||
\(796\) | 9.33175 | 0.330755 | ||||||||
\(797\) | −45.3541 | −1.60652 | −0.803262 | − | 0.595626i | \(-0.796904\pi\) | ||||
−0.803262 | + | 0.595626i | \(0.796904\pi\) | |||||||
\(798\) | 42.1420 | 1.49181 | ||||||||
\(799\) | −58.1678 | −2.05783 | ||||||||
\(800\) | 3.23814 | 0.114485 | ||||||||
\(801\) | −3.97603 | −0.140486 | ||||||||
\(802\) | 14.3336 | 0.506137 | ||||||||
\(803\) | −12.7426 | −0.449675 | ||||||||
\(804\) | 2.73507 | 0.0964585 | ||||||||
\(805\) | 5.74168 | 0.202368 | ||||||||
\(806\) | 6.50808 | 0.229237 | ||||||||
\(807\) | 40.5942 | 1.42898 | ||||||||
\(808\) | −0.695099 | −0.0244535 | ||||||||
\(809\) | 42.9213 | 1.50903 | 0.754517 | − | 0.656281i | \(-0.227871\pi\) | ||||
0.754517 | + | 0.656281i | \(0.227871\pi\) | |||||||
\(810\) | −12.8925 | −0.452997 | ||||||||
\(811\) | −16.2139 | −0.569347 | −0.284674 | − | 0.958625i | \(-0.591885\pi\) | ||||
−0.284674 | + | 0.958625i | \(0.591885\pi\) | |||||||
\(812\) | 5.32878 | 0.187004 | ||||||||
\(813\) | −17.5061 | −0.613965 | ||||||||
\(814\) | 9.52218 | 0.333752 | ||||||||
\(815\) | 14.0114 | 0.490799 | ||||||||
\(816\) | 8.31276 | 0.291005 | ||||||||
\(817\) | 67.8156 | 2.37257 | ||||||||
\(818\) | 18.9955 | 0.664161 | ||||||||
\(819\) | −3.47973 | −0.121591 | ||||||||
\(820\) | 9.50346 | 0.331875 | ||||||||
\(821\) | −33.4633 | −1.16788 | −0.583939 | − | 0.811797i | \(-0.698489\pi\) | ||||
−0.583939 | + | 0.811797i | \(0.698489\pi\) | |||||||
\(822\) | 18.4006 | 0.641796 | ||||||||
\(823\) | 6.83737 | 0.238336 | 0.119168 | − | 0.992874i | \(-0.461977\pi\) | ||||
0.119168 | + | 0.992874i | \(0.461977\pi\) | |||||||
\(824\) | 8.30467 | 0.289307 | ||||||||
\(825\) | 10.9058 | 0.379693 | ||||||||
\(826\) | −18.5291 | −0.644711 | ||||||||
\(827\) | 17.7194 | 0.616163 | 0.308081 | − | 0.951360i | \(-0.400313\pi\) | ||||
0.308081 | + | 0.951360i | \(0.400313\pi\) | |||||||
\(828\) | 0.260232 | 0.00904368 | ||||||||
\(829\) | 23.4735 | 0.815268 | 0.407634 | − | 0.913145i | \(-0.366354\pi\) | ||||
0.407634 | + | 0.913145i | \(0.366354\pi\) | |||||||
\(830\) | −10.7828 | −0.374277 | ||||||||
\(831\) | 19.7804 | 0.686175 | ||||||||
\(832\) | 3.09123 | 0.107169 | ||||||||
\(833\) | −53.9175 | −1.86813 | ||||||||
\(834\) | 32.3932 | 1.12168 | ||||||||
\(835\) | −11.6949 | −0.404717 | ||||||||
\(836\) | −10.0642 | −0.348076 | ||||||||
\(837\) | −10.4150 | −0.359995 | ||||||||
\(838\) | 21.4193 | 0.739916 | ||||||||
\(839\) | −29.4810 | −1.01780 | −0.508899 | − | 0.860826i | \(-0.669947\pi\) | ||||
−0.508899 | + | 0.860826i | \(0.669947\pi\) | |||||||
\(840\) | 10.3672 | 0.357704 | ||||||||
\(841\) | −27.4824 | −0.947670 | ||||||||
\(842\) | −35.7201 | −1.23100 | ||||||||
\(843\) | 7.22326 | 0.248782 | ||||||||
\(844\) | 8.01622 | 0.275930 | ||||||||
\(845\) | 4.57180 | 0.157275 | ||||||||
\(846\) | −3.28793 | −0.113041 | ||||||||
\(847\) | 32.5325 | 1.11783 | ||||||||
\(848\) | −7.01514 | −0.240901 | ||||||||
\(849\) | −36.5044 | −1.25283 | ||||||||
\(850\) | −14.9079 | −0.511337 | ||||||||
\(851\) | −5.10501 | −0.174998 | ||||||||
\(852\) | 12.5428 | 0.429710 | ||||||||
\(853\) | 1.41702 | 0.0485178 | 0.0242589 | − | 0.999706i | \(-0.492277\pi\) | ||||
0.0242589 | + | 0.999706i | \(0.492277\pi\) | |||||||
\(854\) | 25.4712 | 0.871605 | ||||||||
\(855\) | 1.86373 | 0.0637384 | ||||||||
\(856\) | 19.5610 | 0.668580 | ||||||||
\(857\) | −56.0332 | −1.91406 | −0.957029 | − | 0.289993i | \(-0.906347\pi\) | ||||
−0.957029 | + | 0.289993i | \(0.906347\pi\) | |||||||
\(858\) | 10.4111 | 0.355428 | ||||||||
\(859\) | 7.04163 | 0.240257 | 0.120129 | − | 0.992758i | \(-0.461669\pi\) | ||||
0.120129 | + | 0.992758i | \(0.461669\pi\) | |||||||
\(860\) | 16.6832 | 0.568891 | ||||||||
\(861\) | −55.9207 | −1.90577 | ||||||||
\(862\) | 5.92422 | 0.201780 | ||||||||
\(863\) | 23.1308 | 0.787382 | 0.393691 | − | 0.919243i | \(-0.371198\pi\) | ||||
0.393691 | + | 0.919243i | \(0.371198\pi\) | |||||||
\(864\) | −4.94696 | −0.168299 | ||||||||
\(865\) | −6.21120 | −0.211187 | ||||||||
\(866\) | 27.6118 | 0.938286 | ||||||||
\(867\) | −7.57530 | −0.257271 | ||||||||
\(868\) | 9.10699 | 0.309111 | ||||||||
\(869\) | −3.58795 | −0.121713 | ||||||||
\(870\) | 2.95247 | 0.100098 | ||||||||
\(871\) | −4.68248 | −0.158660 | ||||||||
\(872\) | −1.42166 | −0.0481434 | ||||||||
\(873\) | −3.80385 | −0.128741 | ||||||||
\(874\) | 5.39557 | 0.182508 | ||||||||
\(875\) | −47.3008 | −1.59906 | ||||||||
\(876\) | 12.3351 | 0.416763 | ||||||||
\(877\) | −16.8562 | −0.569193 | −0.284597 | − | 0.958647i | \(-0.591860\pi\) | ||||
−0.284597 | + | 0.958647i | \(0.591860\pi\) | |||||||
\(878\) | −12.9467 | −0.436930 | ||||||||
\(879\) | 30.6431 | 1.03356 | ||||||||
\(880\) | −2.47586 | −0.0834612 | ||||||||
\(881\) | −21.9186 | −0.738455 | −0.369228 | − | 0.929339i | \(-0.620378\pi\) | ||||
−0.369228 | + | 0.929339i | \(0.620378\pi\) | |||||||
\(882\) | −3.04768 | −0.102621 | ||||||||
\(883\) | 4.35752 | 0.146642 | 0.0733212 | − | 0.997308i | \(-0.476640\pi\) | ||||
0.0733212 | + | 0.997308i | \(0.476640\pi\) | |||||||
\(884\) | −14.2316 | −0.478659 | ||||||||
\(885\) | −10.2663 | −0.345096 | ||||||||
\(886\) | −32.0407 | −1.07643 | ||||||||
\(887\) | 27.2783 | 0.915915 | 0.457957 | − | 0.888974i | \(-0.348581\pi\) | ||||
0.457957 | + | 0.888974i | \(0.348581\pi\) | |||||||
\(888\) | −9.21766 | −0.309325 | ||||||||
\(889\) | 23.3127 | 0.781884 | ||||||||
\(890\) | −20.2803 | −0.679798 | ||||||||
\(891\) | −18.1172 | −0.606951 | ||||||||
\(892\) | 4.89237 | 0.163809 | ||||||||
\(893\) | −68.1709 | −2.28125 | ||||||||
\(894\) | 2.23768 | 0.0748391 | ||||||||
\(895\) | 12.5201 | 0.418502 | ||||||||
\(896\) | 4.32567 | 0.144510 | ||||||||
\(897\) | −5.58156 | −0.186363 | ||||||||
\(898\) | −14.3905 | −0.480217 | ||||||||
\(899\) | 2.59356 | 0.0865001 | ||||||||
\(900\) | −0.842667 | −0.0280889 | ||||||||
\(901\) | 32.2966 | 1.07596 | ||||||||
\(902\) | 13.3547 | 0.444664 | ||||||||
\(903\) | −98.1679 | −3.26682 | ||||||||
\(904\) | 11.8348 | 0.393619 | ||||||||
\(905\) | 31.0278 | 1.03140 | ||||||||
\(906\) | 20.7133 | 0.688152 | ||||||||
\(907\) | −21.6796 | −0.719860 | −0.359930 | − | 0.932979i | \(-0.617199\pi\) | ||||
−0.359930 | + | 0.932979i | \(0.617199\pi\) | |||||||
\(908\) | −26.2011 | −0.869514 | ||||||||
\(909\) | 0.180887 | 0.00599964 | ||||||||
\(910\) | −17.7489 | −0.588369 | ||||||||
\(911\) | 5.85292 | 0.193916 | 0.0969580 | − | 0.995288i | \(-0.469089\pi\) | ||||
0.0969580 | + | 0.995288i | \(0.469089\pi\) | |||||||
\(912\) | 9.74230 | 0.322600 | ||||||||
\(913\) | −15.1526 | −0.501477 | ||||||||
\(914\) | −18.9587 | −0.627099 | ||||||||
\(915\) | 14.1126 | 0.466547 | ||||||||
\(916\) | 18.3879 | 0.607554 | ||||||||
\(917\) | 4.32567 | 0.142846 | ||||||||
\(918\) | 22.7750 | 0.751688 | ||||||||
\(919\) | 33.3285 | 1.09941 | 0.549703 | − | 0.835360i | \(-0.314741\pi\) | ||||
0.549703 | + | 0.835360i | \(0.314741\pi\) | |||||||
\(920\) | 1.32735 | 0.0437615 | ||||||||
\(921\) | 62.0775 | 2.04552 | ||||||||
\(922\) | 12.8900 | 0.424510 | ||||||||
\(923\) | −21.4735 | −0.706808 | ||||||||
\(924\) | 14.5686 | 0.479271 | ||||||||
\(925\) | 16.5307 | 0.543527 | ||||||||
\(926\) | −6.87915 | −0.226063 | ||||||||
\(927\) | −2.16114 | −0.0709812 | ||||||||
\(928\) | 1.23190 | 0.0404391 | ||||||||
\(929\) | 3.80199 | 0.124739 | 0.0623697 | − | 0.998053i | \(-0.480134\pi\) | ||||
0.0623697 | + | 0.998053i | \(0.480134\pi\) | |||||||
\(930\) | 5.04582 | 0.165459 | ||||||||
\(931\) | −63.1897 | −2.07096 | ||||||||
\(932\) | 14.7959 | 0.484655 | ||||||||
\(933\) | −23.7636 | −0.777985 | ||||||||
\(934\) | 36.1072 | 1.18146 | ||||||||
\(935\) | 11.3985 | 0.372770 | ||||||||
\(936\) | −0.804436 | −0.0262938 | ||||||||
\(937\) | 5.73284 | 0.187284 | 0.0936418 | − | 0.995606i | \(-0.470149\pi\) | ||||
0.0936418 | + | 0.995606i | \(0.470149\pi\) | |||||||
\(938\) | −6.55236 | −0.213942 | ||||||||
\(939\) | −14.6742 | −0.478876 | ||||||||
\(940\) | −16.7706 | −0.546996 | ||||||||
\(941\) | 3.58081 | 0.116731 | 0.0583656 | − | 0.998295i | \(-0.481411\pi\) | ||||
0.0583656 | + | 0.998295i | \(0.481411\pi\) | |||||||
\(942\) | −7.19360 | −0.234380 | ||||||||
\(943\) | −7.15971 | −0.233152 | ||||||||
\(944\) | −4.28353 | −0.139417 | ||||||||
\(945\) | 28.4039 | 0.923977 | ||||||||
\(946\) | 23.4440 | 0.762231 | ||||||||
\(947\) | −2.86742 | −0.0931786 | −0.0465893 | − | 0.998914i | \(-0.514835\pi\) | ||||
−0.0465893 | + | 0.998914i | \(0.514835\pi\) | |||||||
\(948\) | 3.47321 | 0.112805 | ||||||||
\(949\) | −21.1178 | −0.685512 | ||||||||
\(950\) | −17.4716 | −0.566854 | ||||||||
\(951\) | 33.7222 | 1.09352 | ||||||||
\(952\) | −19.9147 | −0.645440 | ||||||||
\(953\) | 48.6769 | 1.57680 | 0.788400 | − | 0.615163i | \(-0.210910\pi\) | ||||
0.788400 | + | 0.615163i | \(0.210910\pi\) | |||||||
\(954\) | 1.82556 | 0.0591047 | ||||||||
\(955\) | −8.09064 | −0.261807 | ||||||||
\(956\) | 24.4982 | 0.792328 | ||||||||
\(957\) | 4.14896 | 0.134117 | ||||||||
\(958\) | 26.0091 | 0.840314 | ||||||||
\(959\) | −44.0821 | −1.42348 | ||||||||
\(960\) | 2.39668 | 0.0773526 | ||||||||
\(961\) | −26.5676 | −0.857018 | ||||||||
\(962\) | 15.7808 | 0.508792 | ||||||||
\(963\) | −5.09038 | −0.164035 | ||||||||
\(964\) | −11.3118 | −0.364328 | ||||||||
\(965\) | 10.3456 | 0.333038 | ||||||||
\(966\) | −7.81047 | −0.251298 | ||||||||
\(967\) | −30.6244 | −0.984815 | −0.492408 | − | 0.870365i | \(-0.663883\pi\) | ||||
−0.492408 | + | 0.870365i | \(0.663883\pi\) | |||||||
\(968\) | 7.52080 | 0.241728 | ||||||||
\(969\) | −44.8521 | −1.44086 | ||||||||
\(970\) | −19.4021 | −0.622965 | ||||||||
\(971\) | 33.7515 | 1.08314 | 0.541568 | − | 0.840657i | \(-0.317831\pi\) | ||||
0.541568 | + | 0.840657i | \(0.317831\pi\) | |||||||
\(972\) | 2.69699 | 0.0865059 | ||||||||
\(973\) | −77.6038 | −2.48786 | ||||||||
\(974\) | 9.30524 | 0.298159 | ||||||||
\(975\) | 18.0739 | 0.578827 | ||||||||
\(976\) | 5.88838 | 0.188482 | ||||||||
\(977\) | −13.2095 | −0.422609 | −0.211304 | − | 0.977420i | \(-0.567771\pi\) | ||||
−0.211304 | + | 0.977420i | \(0.567771\pi\) | |||||||
\(978\) | −19.0599 | −0.609468 | ||||||||
\(979\) | −28.4990 | −0.910830 | ||||||||
\(980\) | −15.5452 | −0.496572 | ||||||||
\(981\) | 0.369960 | 0.0118119 | ||||||||
\(982\) | −38.4944 | −1.22841 | ||||||||
\(983\) | −24.8987 | −0.794144 | −0.397072 | − | 0.917788i | \(-0.629974\pi\) | ||||
−0.397072 | + | 0.917788i | \(0.629974\pi\) | |||||||
\(984\) | −12.9277 | −0.412119 | ||||||||
\(985\) | 18.5368 | 0.590631 | ||||||||
\(986\) | −5.67147 | −0.180617 | ||||||||
\(987\) | 98.6823 | 3.14109 | ||||||||
\(988\) | −16.6789 | −0.530628 | ||||||||
\(989\) | −12.5688 | −0.399663 | ||||||||
\(990\) | 0.644297 | 0.0204771 | ||||||||
\(991\) | −11.4892 | −0.364965 | −0.182483 | − | 0.983209i | \(-0.558413\pi\) | ||||
−0.182483 | + | 0.983209i | \(0.558413\pi\) | |||||||
\(992\) | 2.10534 | 0.0668445 | ||||||||
\(993\) | −46.0918 | −1.46268 | ||||||||
\(994\) | −30.0486 | −0.953084 | ||||||||
\(995\) | −12.3865 | −0.392679 | ||||||||
\(996\) | 14.6680 | 0.464773 | ||||||||
\(997\) | −44.7377 | −1.41686 | −0.708428 | − | 0.705783i | \(-0.750595\pi\) | ||||
−0.708428 | + | 0.705783i | \(0.750595\pi\) | |||||||
\(998\) | −31.4539 | −0.995657 | ||||||||
\(999\) | −25.2543 | −0.799010 |
(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 | 6026.2.a.j.1.9 | ✓ | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.j.1.9 | ✓ | 33 | 1.1 | even | 1 | trivial |