Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, 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("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(0\) |
Dimension: | \(179\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62553 | −1.85653 | −0.928265 | − | 0.371921i | \(-0.878699\pi\) | ||||
−0.928265 | + | 0.371921i | \(0.878699\pi\) | |||||||
\(3\) | −3.09813 | −1.78870 | −0.894352 | − | 0.447363i | \(-0.852363\pi\) | ||||
−0.894352 | + | 0.447363i | \(0.852363\pi\) | |||||||
\(4\) | 4.89340 | 2.44670 | ||||||||
\(5\) | −2.94807 | −1.31842 | −0.659208 | − | 0.751961i | \(-0.729108\pi\) | ||||
−0.659208 | + | 0.751961i | \(0.729108\pi\) | |||||||
\(6\) | 8.13422 | 3.32078 | ||||||||
\(7\) | 1.83284 | 0.692750 | 0.346375 | − | 0.938096i | \(-0.387413\pi\) | ||||
0.346375 | + | 0.938096i | \(0.387413\pi\) | |||||||
\(8\) | −7.59671 | −2.68584 | ||||||||
\(9\) | 6.59839 | 2.19946 | ||||||||
\(10\) | 7.74024 | 2.44768 | ||||||||
\(11\) | −3.15693 | −0.951849 | −0.475925 | − | 0.879486i | \(-0.657886\pi\) | ||||
−0.475925 | + | 0.879486i | \(0.657886\pi\) | |||||||
\(12\) | −15.1604 | −4.37642 | ||||||||
\(13\) | 4.64425 | 1.28808 | 0.644041 | − | 0.764991i | \(-0.277257\pi\) | ||||
0.644041 | + | 0.764991i | \(0.277257\pi\) | |||||||
\(14\) | −4.81218 | −1.28611 | ||||||||
\(15\) | 9.13349 | 2.35826 | ||||||||
\(16\) | 10.1586 | 2.53964 | ||||||||
\(17\) | 0.513047 | 0.124432 | 0.0622161 | − | 0.998063i | \(-0.480183\pi\) | ||||
0.0622161 | + | 0.998063i | \(0.480183\pi\) | |||||||
\(18\) | −17.3243 | −4.08337 | ||||||||
\(19\) | −2.75003 | −0.630899 | −0.315450 | − | 0.948942i | \(-0.602155\pi\) | ||||
−0.315450 | + | 0.948942i | \(0.602155\pi\) | |||||||
\(20\) | −14.4261 | −3.22577 | ||||||||
\(21\) | −5.67838 | −1.23912 | ||||||||
\(22\) | 8.28860 | 1.76714 | ||||||||
\(23\) | −4.64078 | −0.967670 | −0.483835 | − | 0.875159i | \(-0.660757\pi\) | ||||
−0.483835 | + | 0.875159i | \(0.660757\pi\) | |||||||
\(24\) | 23.5356 | 4.80418 | ||||||||
\(25\) | 3.69110 | 0.738221 | ||||||||
\(26\) | −12.1936 | −2.39136 | ||||||||
\(27\) | −11.1483 | −2.14549 | ||||||||
\(28\) | 8.96884 | 1.69495 | ||||||||
\(29\) | 0.719407 | 0.133590 | 0.0667952 | − | 0.997767i | \(-0.478723\pi\) | ||||
0.0667952 | + | 0.997767i | \(0.478723\pi\) | |||||||
\(30\) | −23.9802 | −4.37817 | ||||||||
\(31\) | −3.37968 | −0.607008 | −0.303504 | − | 0.952830i | \(-0.598157\pi\) | ||||
−0.303504 | + | 0.952830i | \(0.598157\pi\) | |||||||
\(32\) | −11.4782 | −2.02908 | ||||||||
\(33\) | 9.78056 | 1.70258 | ||||||||
\(34\) | −1.34702 | −0.231012 | ||||||||
\(35\) | −5.40335 | −0.913332 | ||||||||
\(36\) | 32.2886 | 5.38143 | ||||||||
\(37\) | −9.47375 | −1.55747 | −0.778737 | − | 0.627350i | \(-0.784140\pi\) | ||||
−0.778737 | + | 0.627350i | \(0.784140\pi\) | |||||||
\(38\) | 7.22027 | 1.17128 | ||||||||
\(39\) | −14.3885 | −2.30400 | ||||||||
\(40\) | 22.3956 | 3.54106 | ||||||||
\(41\) | −1.25001 | −0.195219 | −0.0976094 | − | 0.995225i | \(-0.531120\pi\) | ||||
−0.0976094 | + | 0.995225i | \(0.531120\pi\) | |||||||
\(42\) | 14.9088 | 2.30047 | ||||||||
\(43\) | 9.40106 | 1.43365 | 0.716824 | − | 0.697254i | \(-0.245595\pi\) | ||||
0.716824 | + | 0.697254i | \(0.245595\pi\) | |||||||
\(44\) | −15.4481 | −2.32889 | ||||||||
\(45\) | −19.4525 | −2.89981 | ||||||||
\(46\) | 12.1845 | 1.79651 | ||||||||
\(47\) | −4.35788 | −0.635662 | −0.317831 | − | 0.948147i | \(-0.602954\pi\) | ||||
−0.317831 | + | 0.948147i | \(0.602954\pi\) | |||||||
\(48\) | −31.4725 | −4.54267 | ||||||||
\(49\) | −3.64069 | −0.520098 | ||||||||
\(50\) | −9.69110 | −1.37053 | ||||||||
\(51\) | −1.58949 | −0.222572 | ||||||||
\(52\) | 22.7262 | 3.15155 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | 29.2701 | 3.98316 | ||||||||
\(55\) | 9.30683 | 1.25493 | ||||||||
\(56\) | −13.9236 | −1.86062 | ||||||||
\(57\) | 8.51993 | 1.12849 | ||||||||
\(58\) | −1.88882 | −0.248015 | ||||||||
\(59\) | 7.84428 | 1.02124 | 0.510619 | − | 0.859807i | \(-0.329416\pi\) | ||||
0.510619 | + | 0.859807i | \(0.329416\pi\) | |||||||
\(60\) | 44.6938 | 5.76995 | ||||||||
\(61\) | 0.0682438 | 0.00873772 | 0.00436886 | − | 0.999990i | \(-0.498609\pi\) | ||||
0.00436886 | + | 0.999990i | \(0.498609\pi\) | |||||||
\(62\) | 8.87345 | 1.12693 | ||||||||
\(63\) | 12.0938 | 1.52368 | ||||||||
\(64\) | 9.81921 | 1.22740 | ||||||||
\(65\) | −13.6916 | −1.69823 | ||||||||
\(66\) | −25.6791 | −3.16088 | ||||||||
\(67\) | 15.2544 | 1.86362 | 0.931811 | − | 0.362943i | \(-0.118228\pi\) | ||||
0.931811 | + | 0.362943i | \(0.118228\pi\) | |||||||
\(68\) | 2.51055 | 0.304448 | ||||||||
\(69\) | 14.3777 | 1.73088 | ||||||||
\(70\) | 14.1866 | 1.69563 | ||||||||
\(71\) | −3.31681 | −0.393632 | −0.196816 | − | 0.980440i | \(-0.563060\pi\) | ||||
−0.196816 | + | 0.980440i | \(0.563060\pi\) | |||||||
\(72\) | −50.1260 | −5.90741 | ||||||||
\(73\) | −3.94635 | −0.461885 | −0.230943 | − | 0.972967i | \(-0.574181\pi\) | ||||
−0.230943 | + | 0.972967i | \(0.574181\pi\) | |||||||
\(74\) | 24.8736 | 2.89150 | ||||||||
\(75\) | −11.4355 | −1.32046 | ||||||||
\(76\) | −13.4570 | −1.54362 | ||||||||
\(77\) | −5.78615 | −0.659393 | ||||||||
\(78\) | 37.7773 | 4.27744 | ||||||||
\(79\) | −9.41853 | −1.05967 | −0.529834 | − | 0.848101i | \(-0.677746\pi\) | ||||
−0.529834 | + | 0.848101i | \(0.677746\pi\) | |||||||
\(80\) | −29.9482 | −3.34831 | ||||||||
\(81\) | 14.7436 | 1.63818 | ||||||||
\(82\) | 3.28194 | 0.362429 | ||||||||
\(83\) | 6.55129 | 0.719097 | 0.359549 | − | 0.933126i | \(-0.382931\pi\) | ||||
0.359549 | + | 0.933126i | \(0.382931\pi\) | |||||||
\(84\) | −27.7866 | −3.03177 | ||||||||
\(85\) | −1.51250 | −0.164053 | ||||||||
\(86\) | −24.6827 | −2.66161 | ||||||||
\(87\) | −2.22881 | −0.238954 | ||||||||
\(88\) | 23.9822 | 2.55652 | ||||||||
\(89\) | −5.36837 | −0.569047 | −0.284523 | − | 0.958669i | \(-0.591835\pi\) | ||||
−0.284523 | + | 0.958669i | \(0.591835\pi\) | |||||||
\(90\) | 51.0731 | 5.38358 | ||||||||
\(91\) | 8.51218 | 0.892319 | ||||||||
\(92\) | −22.7092 | −2.36760 | ||||||||
\(93\) | 10.4707 | 1.08576 | ||||||||
\(94\) | 11.4417 | 1.18012 | ||||||||
\(95\) | 8.10727 | 0.831788 | ||||||||
\(96\) | 35.5609 | 3.62942 | ||||||||
\(97\) | 5.60546 | 0.569148 | 0.284574 | − | 0.958654i | \(-0.408148\pi\) | ||||
0.284574 | + | 0.958654i | \(0.408148\pi\) | |||||||
\(98\) | 9.55872 | 0.965577 | ||||||||
\(99\) | −20.8306 | −2.09356 | ||||||||
\(100\) | 18.0621 | 1.80621 | ||||||||
\(101\) | 3.52757 | 0.351007 | 0.175503 | − | 0.984479i | \(-0.443845\pi\) | ||||
0.175503 | + | 0.984479i | \(0.443845\pi\) | |||||||
\(102\) | 4.17324 | 0.413212 | ||||||||
\(103\) | 2.93263 | 0.288961 | 0.144481 | − | 0.989508i | \(-0.453849\pi\) | ||||
0.144481 | + | 0.989508i | \(0.453849\pi\) | |||||||
\(104\) | −35.2810 | −3.45958 | ||||||||
\(105\) | 16.7403 | 1.63368 | ||||||||
\(106\) | −2.62553 | −0.255014 | ||||||||
\(107\) | −4.68067 | −0.452498 | −0.226249 | − | 0.974070i | \(-0.572646\pi\) | ||||
−0.226249 | + | 0.974070i | \(0.572646\pi\) | |||||||
\(108\) | −54.5530 | −5.24936 | ||||||||
\(109\) | 5.07450 | 0.486049 | 0.243025 | − | 0.970020i | \(-0.421860\pi\) | ||||
0.243025 | + | 0.970020i | \(0.421860\pi\) | |||||||
\(110\) | −24.4354 | −2.32982 | ||||||||
\(111\) | 29.3509 | 2.78586 | ||||||||
\(112\) | 18.6191 | 1.75934 | ||||||||
\(113\) | −7.44673 | −0.700529 | −0.350265 | − | 0.936651i | \(-0.613908\pi\) | ||||
−0.350265 | + | 0.936651i | \(0.613908\pi\) | |||||||
\(114\) | −22.3693 | −2.09508 | ||||||||
\(115\) | 13.6813 | 1.27579 | ||||||||
\(116\) | 3.52034 | 0.326856 | ||||||||
\(117\) | 30.6446 | 2.83309 | ||||||||
\(118\) | −20.5954 | −1.89596 | ||||||||
\(119\) | 0.940335 | 0.0862004 | ||||||||
\(120\) | −69.3844 | −6.33390 | ||||||||
\(121\) | −1.03382 | −0.0939834 | ||||||||
\(122\) | −0.179176 | −0.0162218 | ||||||||
\(123\) | 3.87269 | 0.349189 | ||||||||
\(124\) | −16.5381 | −1.48517 | ||||||||
\(125\) | 3.85871 | 0.345134 | ||||||||
\(126\) | −31.7527 | −2.82875 | ||||||||
\(127\) | −2.74007 | −0.243142 | −0.121571 | − | 0.992583i | \(-0.538793\pi\) | ||||
−0.121571 | + | 0.992583i | \(0.538793\pi\) | |||||||
\(128\) | −2.82421 | −0.249628 | ||||||||
\(129\) | −29.1257 | −2.56437 | ||||||||
\(130\) | 35.9476 | 3.15281 | ||||||||
\(131\) | −12.7274 | −1.11200 | −0.556000 | − | 0.831183i | \(-0.687664\pi\) | ||||
−0.556000 | + | 0.831183i | \(0.687664\pi\) | |||||||
\(132\) | 47.8602 | 4.16569 | ||||||||
\(133\) | −5.04037 | −0.437055 | ||||||||
\(134\) | −40.0509 | −3.45987 | ||||||||
\(135\) | 32.8659 | 2.82864 | ||||||||
\(136\) | −3.89747 | −0.334205 | ||||||||
\(137\) | 13.8335 | 1.18187 | 0.590937 | − | 0.806718i | \(-0.298758\pi\) | ||||
0.590937 | + | 0.806718i | \(0.298758\pi\) | |||||||
\(138\) | −37.7492 | −3.21342 | ||||||||
\(139\) | −20.7006 | −1.75580 | −0.877900 | − | 0.478844i | \(-0.841056\pi\) | ||||
−0.877900 | + | 0.478844i | \(0.841056\pi\) | |||||||
\(140\) | −26.4407 | −2.23465 | ||||||||
\(141\) | 13.5013 | 1.13701 | ||||||||
\(142\) | 8.70837 | 0.730790 | ||||||||
\(143\) | −14.6615 | −1.22606 | ||||||||
\(144\) | 67.0302 | 5.58585 | ||||||||
\(145\) | −2.12086 | −0.176128 | ||||||||
\(146\) | 10.3612 | 0.857503 | ||||||||
\(147\) | 11.2793 | 0.930302 | ||||||||
\(148\) | −46.3589 | −3.81067 | ||||||||
\(149\) | 22.1370 | 1.81354 | 0.906768 | − | 0.421631i | \(-0.138542\pi\) | ||||
0.906768 | + | 0.421631i | \(0.138542\pi\) | |||||||
\(150\) | 30.0243 | 2.45147 | ||||||||
\(151\) | −1.00000 | −0.0813788 | ||||||||
\(152\) | 20.8911 | 1.69450 | ||||||||
\(153\) | 3.38529 | 0.273684 | ||||||||
\(154\) | 15.1917 | 1.22418 | ||||||||
\(155\) | 9.96352 | 0.800290 | ||||||||
\(156\) | −70.4085 | −5.63719 | ||||||||
\(157\) | 9.03696 | 0.721228 | 0.360614 | − | 0.932715i | \(-0.382567\pi\) | ||||
0.360614 | + | 0.932715i | \(0.382567\pi\) | |||||||
\(158\) | 24.7286 | 1.96730 | ||||||||
\(159\) | −3.09813 | −0.245697 | ||||||||
\(160\) | 33.8385 | 2.67517 | ||||||||
\(161\) | −8.50583 | −0.670353 | ||||||||
\(162\) | −38.7097 | −3.04132 | ||||||||
\(163\) | 11.2227 | 0.879033 | 0.439517 | − | 0.898234i | \(-0.355150\pi\) | ||||
0.439517 | + | 0.898234i | \(0.355150\pi\) | |||||||
\(164\) | −6.11680 | −0.477642 | ||||||||
\(165\) | −28.8337 | −2.24470 | ||||||||
\(166\) | −17.2006 | −1.33503 | ||||||||
\(167\) | −15.1449 | −1.17195 | −0.585974 | − | 0.810330i | \(-0.699288\pi\) | ||||
−0.585974 | + | 0.810330i | \(0.699288\pi\) | |||||||
\(168\) | 43.1370 | 3.32809 | ||||||||
\(169\) | 8.56903 | 0.659156 | ||||||||
\(170\) | 3.97111 | 0.304570 | ||||||||
\(171\) | −18.1458 | −1.38764 | ||||||||
\(172\) | 46.0031 | 3.50771 | ||||||||
\(173\) | 22.1503 | 1.68405 | 0.842026 | − | 0.539437i | \(-0.181363\pi\) | ||||
0.842026 | + | 0.539437i | \(0.181363\pi\) | |||||||
\(174\) | 5.85181 | 0.443625 | ||||||||
\(175\) | 6.76521 | 0.511402 | ||||||||
\(176\) | −32.0699 | −2.41736 | ||||||||
\(177\) | −24.3026 | −1.82669 | ||||||||
\(178\) | 14.0948 | 1.05645 | ||||||||
\(179\) | −6.56444 | −0.490649 | −0.245325 | − | 0.969441i | \(-0.578895\pi\) | ||||
−0.245325 | + | 0.969441i | \(0.578895\pi\) | |||||||
\(180\) | −95.1889 | −7.09496 | ||||||||
\(181\) | 7.75561 | 0.576470 | 0.288235 | − | 0.957560i | \(-0.406932\pi\) | ||||
0.288235 | + | 0.957560i | \(0.406932\pi\) | |||||||
\(182\) | −22.3490 | −1.65662 | ||||||||
\(183\) | −0.211428 | −0.0156292 | ||||||||
\(184\) | 35.2547 | 2.59901 | ||||||||
\(185\) | 27.9293 | 2.05340 | ||||||||
\(186\) | −27.4911 | −2.01574 | ||||||||
\(187\) | −1.61965 | −0.118441 | ||||||||
\(188\) | −21.3248 | −1.55527 | ||||||||
\(189\) | −20.4330 | −1.48628 | ||||||||
\(190\) | −21.2859 | −1.54424 | ||||||||
\(191\) | −6.13645 | −0.444018 | −0.222009 | − | 0.975045i | \(-0.571261\pi\) | ||||
−0.222009 | + | 0.975045i | \(0.571261\pi\) | |||||||
\(192\) | −30.4212 | −2.19546 | ||||||||
\(193\) | 18.6602 | 1.34319 | 0.671595 | − | 0.740919i | \(-0.265610\pi\) | ||||
0.671595 | + | 0.740919i | \(0.265610\pi\) | |||||||
\(194\) | −14.7173 | −1.05664 | ||||||||
\(195\) | 42.4182 | 3.03763 | ||||||||
\(196\) | −17.8153 | −1.27252 | ||||||||
\(197\) | −18.2172 | −1.29792 | −0.648962 | − | 0.760821i | \(-0.724796\pi\) | ||||
−0.648962 | + | 0.760821i | \(0.724796\pi\) | |||||||
\(198\) | 54.6914 | 3.88675 | ||||||||
\(199\) | 3.98154 | 0.282244 | 0.141122 | − | 0.989992i | \(-0.454929\pi\) | ||||
0.141122 | + | 0.989992i | \(0.454929\pi\) | |||||||
\(200\) | −28.0402 | −1.98274 | ||||||||
\(201\) | −47.2601 | −3.33347 | ||||||||
\(202\) | −9.26174 | −0.651654 | ||||||||
\(203\) | 1.31856 | 0.0925447 | ||||||||
\(204\) | −7.77799 | −0.544568 | ||||||||
\(205\) | 3.68512 | 0.257380 | ||||||||
\(206\) | −7.69972 | −0.536465 | ||||||||
\(207\) | −30.6217 | −2.12836 | ||||||||
\(208\) | 47.1789 | 3.27127 | ||||||||
\(209\) | 8.68163 | 0.600521 | ||||||||
\(210\) | −43.9520 | −3.03298 | ||||||||
\(211\) | −20.7038 | −1.42531 | −0.712655 | − | 0.701514i | \(-0.752508\pi\) | ||||
−0.712655 | + | 0.701514i | \(0.752508\pi\) | |||||||
\(212\) | 4.89340 | 0.336080 | ||||||||
\(213\) | 10.2759 | 0.704092 | ||||||||
\(214\) | 12.2892 | 0.840075 | ||||||||
\(215\) | −27.7150 | −1.89014 | ||||||||
\(216\) | 84.6902 | 5.76244 | ||||||||
\(217\) | −6.19442 | −0.420505 | ||||||||
\(218\) | −13.3233 | −0.902365 | ||||||||
\(219\) | 12.2263 | 0.826176 | ||||||||
\(220\) | 45.5421 | 3.07045 | ||||||||
\(221\) | 2.38272 | 0.160279 | ||||||||
\(222\) | −77.0616 | −5.17203 | ||||||||
\(223\) | −23.1997 | −1.55357 | −0.776785 | − | 0.629766i | \(-0.783151\pi\) | ||||
−0.776785 | + | 0.629766i | \(0.783151\pi\) | |||||||
\(224\) | −21.0377 | −1.40564 | ||||||||
\(225\) | 24.3553 | 1.62369 | ||||||||
\(226\) | 19.5516 | 1.30055 | ||||||||
\(227\) | −8.38633 | −0.556620 | −0.278310 | − | 0.960491i | \(-0.589774\pi\) | ||||
−0.278310 | + | 0.960491i | \(0.589774\pi\) | |||||||
\(228\) | 41.6914 | 2.76108 | ||||||||
\(229\) | −12.3383 | −0.815336 | −0.407668 | − | 0.913130i | \(-0.633658\pi\) | ||||
−0.407668 | + | 0.913130i | \(0.633658\pi\) | |||||||
\(230\) | −35.9208 | −2.36854 | ||||||||
\(231\) | 17.9262 | 1.17946 | ||||||||
\(232\) | −5.46512 | −0.358803 | ||||||||
\(233\) | −10.7202 | −0.702306 | −0.351153 | − | 0.936318i | \(-0.614210\pi\) | ||||
−0.351153 | + | 0.936318i | \(0.614210\pi\) | |||||||
\(234\) | −80.4582 | −5.25971 | ||||||||
\(235\) | 12.8473 | 0.838066 | ||||||||
\(236\) | 38.3852 | 2.49866 | ||||||||
\(237\) | 29.1798 | 1.89543 | ||||||||
\(238\) | −2.46888 | −0.160034 | ||||||||
\(239\) | −18.9842 | −1.22798 | −0.613992 | − | 0.789312i | \(-0.710437\pi\) | ||||
−0.613992 | + | 0.789312i | \(0.710437\pi\) | |||||||
\(240\) | 92.7832 | 5.98913 | ||||||||
\(241\) | 1.98619 | 0.127942 | 0.0639710 | − | 0.997952i | \(-0.479623\pi\) | ||||
0.0639710 | + | 0.997952i | \(0.479623\pi\) | |||||||
\(242\) | 2.71432 | 0.174483 | ||||||||
\(243\) | −12.2327 | −0.784728 | ||||||||
\(244\) | 0.333944 | 0.0213786 | ||||||||
\(245\) | 10.7330 | 0.685705 | ||||||||
\(246\) | −10.1679 | −0.648279 | ||||||||
\(247\) | −12.7718 | −0.812650 | ||||||||
\(248\) | 25.6744 | 1.63033 | ||||||||
\(249\) | −20.2967 | −1.28625 | ||||||||
\(250\) | −10.1312 | −0.640751 | ||||||||
\(251\) | −0.665703 | −0.0420188 | −0.0210094 | − | 0.999779i | \(-0.506688\pi\) | ||||
−0.0210094 | + | 0.999779i | \(0.506688\pi\) | |||||||
\(252\) | 59.1799 | 3.72798 | ||||||||
\(253\) | 14.6506 | 0.921076 | ||||||||
\(254\) | 7.19413 | 0.451400 | ||||||||
\(255\) | 4.68591 | 0.293443 | ||||||||
\(256\) | −12.2234 | −0.763960 | ||||||||
\(257\) | −16.0784 | −1.00294 | −0.501471 | − | 0.865174i | \(-0.667208\pi\) | ||||
−0.501471 | + | 0.865174i | \(0.667208\pi\) | |||||||
\(258\) | 76.4703 | 4.76083 | ||||||||
\(259\) | −17.3639 | −1.07894 | ||||||||
\(260\) | −66.9983 | −4.15506 | ||||||||
\(261\) | 4.74693 | 0.293827 | ||||||||
\(262\) | 33.4162 | 2.06446 | ||||||||
\(263\) | −10.1686 | −0.627021 | −0.313510 | − | 0.949585i | \(-0.601505\pi\) | ||||
−0.313510 | + | 0.949585i | \(0.601505\pi\) | |||||||
\(264\) | −74.3000 | −4.57285 | ||||||||
\(265\) | −2.94807 | −0.181098 | ||||||||
\(266\) | 13.2336 | 0.811406 | ||||||||
\(267\) | 16.6319 | 1.01786 | ||||||||
\(268\) | 74.6459 | 4.55973 | ||||||||
\(269\) | −18.5411 | −1.13047 | −0.565234 | − | 0.824931i | \(-0.691214\pi\) | ||||
−0.565234 | + | 0.824931i | \(0.691214\pi\) | |||||||
\(270\) | −86.2903 | −5.25146 | ||||||||
\(271\) | 10.6290 | 0.645664 | 0.322832 | − | 0.946456i | \(-0.395365\pi\) | ||||
0.322832 | + | 0.946456i | \(0.395365\pi\) | |||||||
\(272\) | 5.21183 | 0.316013 | ||||||||
\(273\) | −26.3718 | −1.59609 | ||||||||
\(274\) | −36.3202 | −2.19418 | ||||||||
\(275\) | −11.6525 | −0.702675 | ||||||||
\(276\) | 70.3560 | 4.23493 | ||||||||
\(277\) | −9.83047 | −0.590656 | −0.295328 | − | 0.955396i | \(-0.595429\pi\) | ||||
−0.295328 | + | 0.955396i | \(0.595429\pi\) | |||||||
\(278\) | 54.3500 | 3.25969 | ||||||||
\(279\) | −22.3004 | −1.33509 | ||||||||
\(280\) | 41.0476 | 2.45307 | ||||||||
\(281\) | 22.8333 | 1.36212 | 0.681062 | − | 0.732226i | \(-0.261519\pi\) | ||||
0.681062 | + | 0.732226i | \(0.261519\pi\) | |||||||
\(282\) | −35.4479 | −2.11089 | ||||||||
\(283\) | 31.8872 | 1.89549 | 0.947747 | − | 0.319022i | \(-0.103354\pi\) | ||||
0.947747 | + | 0.319022i | \(0.103354\pi\) | |||||||
\(284\) | −16.2305 | −0.963101 | ||||||||
\(285\) | −25.1173 | −1.48782 | ||||||||
\(286\) | 38.4943 | 2.27622 | ||||||||
\(287\) | −2.29107 | −0.135238 | ||||||||
\(288\) | −75.7377 | −4.46289 | ||||||||
\(289\) | −16.7368 | −0.984517 | ||||||||
\(290\) | 5.56838 | 0.326986 | ||||||||
\(291\) | −17.3664 | −1.01804 | ||||||||
\(292\) | −19.3111 | −1.13009 | ||||||||
\(293\) | −3.78095 | −0.220885 | −0.110443 | − | 0.993882i | \(-0.535227\pi\) | ||||
−0.110443 | + | 0.993882i | \(0.535227\pi\) | |||||||
\(294\) | −29.6141 | −1.72713 | ||||||||
\(295\) | −23.1255 | −1.34642 | ||||||||
\(296\) | 71.9693 | 4.18313 | ||||||||
\(297\) | 35.1943 | 2.04218 | ||||||||
\(298\) | −58.1214 | −3.36688 | ||||||||
\(299\) | −21.5529 | −1.24644 | ||||||||
\(300\) | −55.9585 | −3.23077 | ||||||||
\(301\) | 17.2307 | 0.993159 | ||||||||
\(302\) | 2.62553 | 0.151082 | ||||||||
\(303\) | −10.9289 | −0.627847 | ||||||||
\(304\) | −27.9363 | −1.60226 | ||||||||
\(305\) | −0.201187 | −0.0115200 | ||||||||
\(306\) | −8.88817 | −0.508103 | ||||||||
\(307\) | −33.5690 | −1.91588 | −0.957942 | − | 0.286961i | \(-0.907355\pi\) | ||||
−0.957942 | + | 0.286961i | \(0.907355\pi\) | |||||||
\(308\) | −28.3140 | −1.61334 | ||||||||
\(309\) | −9.08567 | −0.516866 | ||||||||
\(310\) | −26.1595 | −1.48576 | ||||||||
\(311\) | 0.989914 | 0.0561328 | 0.0280664 | − | 0.999606i | \(-0.491065\pi\) | ||||
0.0280664 | + | 0.999606i | \(0.491065\pi\) | |||||||
\(312\) | 109.305 | 6.18817 | ||||||||
\(313\) | −9.05645 | −0.511901 | −0.255950 | − | 0.966690i | \(-0.582388\pi\) | ||||
−0.255950 | + | 0.966690i | \(0.582388\pi\) | |||||||
\(314\) | −23.7268 | −1.33898 | ||||||||
\(315\) | −35.6534 | −2.00884 | ||||||||
\(316\) | −46.0887 | −2.59269 | ||||||||
\(317\) | −10.0173 | −0.562626 | −0.281313 | − | 0.959616i | \(-0.590770\pi\) | ||||
−0.281313 | + | 0.959616i | \(0.590770\pi\) | |||||||
\(318\) | 8.13422 | 0.456144 | ||||||||
\(319\) | −2.27111 | −0.127158 | ||||||||
\(320\) | −28.9477 | −1.61823 | ||||||||
\(321\) | 14.5013 | 0.809385 | ||||||||
\(322\) | 22.3323 | 1.24453 | ||||||||
\(323\) | −1.41089 | −0.0785042 | ||||||||
\(324\) | 72.1463 | 4.00813 | ||||||||
\(325\) | 17.1424 | 0.950889 | ||||||||
\(326\) | −29.4656 | −1.63195 | ||||||||
\(327\) | −15.7215 | −0.869398 | ||||||||
\(328\) | 9.49596 | 0.524327 | ||||||||
\(329\) | −7.98731 | −0.440354 | ||||||||
\(330\) | 75.7038 | 4.16736 | ||||||||
\(331\) | −18.0341 | −0.991243 | −0.495622 | − | 0.868539i | \(-0.665060\pi\) | ||||
−0.495622 | + | 0.868539i | \(0.665060\pi\) | |||||||
\(332\) | 32.0581 | 1.75942 | ||||||||
\(333\) | −62.5115 | −3.42561 | ||||||||
\(334\) | 39.7634 | 2.17576 | ||||||||
\(335\) | −44.9710 | −2.45703 | ||||||||
\(336\) | −57.6842 | −3.14693 | ||||||||
\(337\) | 20.7190 | 1.12864 | 0.564318 | − | 0.825558i | \(-0.309139\pi\) | ||||
0.564318 | + | 0.825558i | \(0.309139\pi\) | |||||||
\(338\) | −22.4982 | −1.22374 | ||||||||
\(339\) | 23.0709 | 1.25304 | ||||||||
\(340\) | −7.40126 | −0.401390 | ||||||||
\(341\) | 10.6694 | 0.577780 | ||||||||
\(342\) | 47.6422 | 2.57620 | ||||||||
\(343\) | −19.5027 | −1.05305 | ||||||||
\(344\) | −71.4171 | −3.85055 | ||||||||
\(345\) | −42.3865 | −2.28201 | ||||||||
\(346\) | −58.1561 | −3.12649 | ||||||||
\(347\) | 11.0897 | 0.595325 | 0.297662 | − | 0.954671i | \(-0.403793\pi\) | ||||
0.297662 | + | 0.954671i | \(0.403793\pi\) | |||||||
\(348\) | −10.9065 | −0.584648 | ||||||||
\(349\) | 7.67207 | 0.410676 | 0.205338 | − | 0.978691i | \(-0.434171\pi\) | ||||
0.205338 | + | 0.978691i | \(0.434171\pi\) | |||||||
\(350\) | −17.7623 | −0.949433 | ||||||||
\(351\) | −51.7753 | −2.76356 | ||||||||
\(352\) | 36.2358 | 1.93138 | ||||||||
\(353\) | 15.7014 | 0.835699 | 0.417850 | − | 0.908516i | \(-0.362784\pi\) | ||||
0.417850 | + | 0.908516i | \(0.362784\pi\) | |||||||
\(354\) | 63.8071 | 3.39131 | ||||||||
\(355\) | 9.77817 | 0.518971 | ||||||||
\(356\) | −26.2696 | −1.39229 | ||||||||
\(357\) | −2.91328 | −0.154187 | ||||||||
\(358\) | 17.2351 | 0.910904 | ||||||||
\(359\) | 11.6954 | 0.617262 | 0.308631 | − | 0.951182i | \(-0.400129\pi\) | ||||
0.308631 | + | 0.951182i | \(0.400129\pi\) | |||||||
\(360\) | 147.775 | 7.78843 | ||||||||
\(361\) | −11.4374 | −0.601966 | ||||||||
\(362\) | −20.3626 | −1.07023 | ||||||||
\(363\) | 3.20290 | 0.168109 | ||||||||
\(364\) | 41.6535 | 2.18324 | ||||||||
\(365\) | 11.6341 | 0.608957 | ||||||||
\(366\) | 0.555110 | 0.0290161 | ||||||||
\(367\) | 17.7022 | 0.924049 | 0.462024 | − | 0.886867i | \(-0.347123\pi\) | ||||
0.462024 | + | 0.886867i | \(0.347123\pi\) | |||||||
\(368\) | −47.1437 | −2.45754 | ||||||||
\(369\) | −8.24806 | −0.429377 | ||||||||
\(370\) | −73.3291 | −3.81220 | ||||||||
\(371\) | 1.83284 | 0.0951565 | ||||||||
\(372\) | 51.2372 | 2.65653 | ||||||||
\(373\) | −22.6795 | −1.17430 | −0.587149 | − | 0.809479i | \(-0.699750\pi\) | ||||
−0.587149 | + | 0.809479i | \(0.699750\pi\) | |||||||
\(374\) | 4.25244 | 0.219889 | ||||||||
\(375\) | −11.9548 | −0.617343 | ||||||||
\(376\) | 33.1055 | 1.70729 | ||||||||
\(377\) | 3.34110 | 0.172075 | ||||||||
\(378\) | 53.6475 | 2.75933 | ||||||||
\(379\) | −5.96614 | −0.306460 | −0.153230 | − | 0.988191i | \(-0.548968\pi\) | ||||
−0.153230 | + | 0.988191i | \(0.548968\pi\) | |||||||
\(380\) | 39.6721 | 2.03514 | ||||||||
\(381\) | 8.48908 | 0.434909 | ||||||||
\(382\) | 16.1114 | 0.824332 | ||||||||
\(383\) | 16.0768 | 0.821485 | 0.410742 | − | 0.911751i | \(-0.365270\pi\) | ||||
0.410742 | + | 0.911751i | \(0.365270\pi\) | |||||||
\(384\) | 8.74977 | 0.446510 | ||||||||
\(385\) | 17.0580 | 0.869354 | ||||||||
\(386\) | −48.9928 | −2.49367 | ||||||||
\(387\) | 62.0319 | 3.15326 | ||||||||
\(388\) | 27.4298 | 1.39254 | ||||||||
\(389\) | −10.0844 | −0.511299 | −0.255650 | − | 0.966769i | \(-0.582289\pi\) | ||||
−0.255650 | + | 0.966769i | \(0.582289\pi\) | |||||||
\(390\) | −111.370 | −5.63945 | ||||||||
\(391\) | −2.38094 | −0.120409 | ||||||||
\(392\) | 27.6572 | 1.39690 | ||||||||
\(393\) | 39.4311 | 1.98904 | ||||||||
\(394\) | 47.8298 | 2.40963 | ||||||||
\(395\) | 27.7665 | 1.39708 | ||||||||
\(396\) | −101.933 | −5.12231 | ||||||||
\(397\) | 3.38989 | 0.170134 | 0.0850669 | − | 0.996375i | \(-0.472890\pi\) | ||||
0.0850669 | + | 0.996375i | \(0.472890\pi\) | |||||||
\(398\) | −10.4536 | −0.523994 | ||||||||
\(399\) | 15.6157 | 0.781763 | ||||||||
\(400\) | 37.4963 | 1.87482 | ||||||||
\(401\) | 1.84242 | 0.0920059 | 0.0460029 | − | 0.998941i | \(-0.485352\pi\) | ||||
0.0460029 | + | 0.998941i | \(0.485352\pi\) | |||||||
\(402\) | 124.083 | 6.18869 | ||||||||
\(403\) | −15.6961 | −0.781877 | ||||||||
\(404\) | 17.2618 | 0.858808 | ||||||||
\(405\) | −43.4651 | −2.15980 | ||||||||
\(406\) | −3.46192 | −0.171812 | ||||||||
\(407\) | 29.9079 | 1.48248 | ||||||||
\(408\) | 12.0749 | 0.597794 | ||||||||
\(409\) | −14.1788 | −0.701098 | −0.350549 | − | 0.936544i | \(-0.614005\pi\) | ||||
−0.350549 | + | 0.936544i | \(0.614005\pi\) | |||||||
\(410\) | −9.67538 | −0.477833 | ||||||||
\(411\) | −42.8579 | −2.11402 | ||||||||
\(412\) | 14.3506 | 0.707001 | ||||||||
\(413\) | 14.3773 | 0.707462 | ||||||||
\(414\) | 80.3982 | 3.95135 | ||||||||
\(415\) | −19.3136 | −0.948070 | ||||||||
\(416\) | −53.3076 | −2.61362 | ||||||||
\(417\) | 64.1330 | 3.14061 | ||||||||
\(418\) | −22.7939 | −1.11488 | ||||||||
\(419\) | −1.73139 | −0.0845839 | −0.0422919 | − | 0.999105i | \(-0.513466\pi\) | ||||
−0.0422919 | + | 0.999105i | \(0.513466\pi\) | |||||||
\(420\) | 81.9168 | 3.99713 | ||||||||
\(421\) | −18.7536 | −0.913994 | −0.456997 | − | 0.889468i | \(-0.651075\pi\) | ||||
−0.456997 | + | 0.889468i | \(0.651075\pi\) | |||||||
\(422\) | 54.3585 | 2.64613 | ||||||||
\(423\) | −28.7550 | −1.39811 | ||||||||
\(424\) | −7.59671 | −0.368929 | ||||||||
\(425\) | 1.89371 | 0.0918584 | ||||||||
\(426\) | −26.9796 | −1.30717 | ||||||||
\(427\) | 0.125080 | 0.00605306 | ||||||||
\(428\) | −22.9044 | −1.10713 | ||||||||
\(429\) | 45.4233 | 2.19306 | ||||||||
\(430\) | 72.7664 | 3.50911 | ||||||||
\(431\) | 30.9135 | 1.48905 | 0.744526 | − | 0.667593i | \(-0.232676\pi\) | ||||
0.744526 | + | 0.667593i | \(0.232676\pi\) | |||||||
\(432\) | −113.251 | −5.44877 | ||||||||
\(433\) | 8.05092 | 0.386903 | 0.193451 | − | 0.981110i | \(-0.438032\pi\) | ||||
0.193451 | + | 0.981110i | \(0.438032\pi\) | |||||||
\(434\) | 16.2636 | 0.780679 | ||||||||
\(435\) | 6.57069 | 0.315041 | ||||||||
\(436\) | 24.8316 | 1.18922 | ||||||||
\(437\) | 12.7623 | 0.610503 | ||||||||
\(438\) | −32.1005 | −1.53382 | ||||||||
\(439\) | 5.99928 | 0.286330 | 0.143165 | − | 0.989699i | \(-0.454272\pi\) | ||||
0.143165 | + | 0.989699i | \(0.454272\pi\) | |||||||
\(440\) | −70.7013 | −3.37055 | ||||||||
\(441\) | −24.0227 | −1.14394 | ||||||||
\(442\) | −6.25589 | −0.297563 | ||||||||
\(443\) | −12.5365 | −0.595627 | −0.297814 | − | 0.954624i | \(-0.596257\pi\) | ||||
−0.297814 | + | 0.954624i | \(0.596257\pi\) | |||||||
\(444\) | 143.626 | 6.81617 | ||||||||
\(445\) | 15.8263 | 0.750240 | ||||||||
\(446\) | 60.9116 | 2.88425 | ||||||||
\(447\) | −68.5833 | −3.24388 | ||||||||
\(448\) | 17.9971 | 0.850282 | ||||||||
\(449\) | −13.3728 | −0.631103 | −0.315552 | − | 0.948908i | \(-0.602190\pi\) | ||||
−0.315552 | + | 0.948908i | \(0.602190\pi\) | |||||||
\(450\) | −63.9457 | −3.01443 | ||||||||
\(451\) | 3.94619 | 0.185819 | ||||||||
\(452\) | −36.4398 | −1.71399 | ||||||||
\(453\) | 3.09813 | 0.145563 | ||||||||
\(454\) | 22.0186 | 1.03338 | ||||||||
\(455\) | −25.0945 | −1.17645 | ||||||||
\(456\) | −64.7234 | −3.03095 | ||||||||
\(457\) | −23.3645 | −1.09294 | −0.546472 | − | 0.837477i | \(-0.684030\pi\) | ||||
−0.546472 | + | 0.837477i | \(0.684030\pi\) | |||||||
\(458\) | 32.3945 | 1.51370 | ||||||||
\(459\) | −5.71959 | −0.266968 | ||||||||
\(460\) | 66.9483 | 3.12148 | ||||||||
\(461\) | 13.7177 | 0.638896 | 0.319448 | − | 0.947604i | \(-0.396502\pi\) | ||||
0.319448 | + | 0.947604i | \(0.396502\pi\) | |||||||
\(462\) | −47.0658 | −2.18970 | ||||||||
\(463\) | 6.18162 | 0.287284 | 0.143642 | − | 0.989630i | \(-0.454119\pi\) | ||||
0.143642 | + | 0.989630i | \(0.454119\pi\) | |||||||
\(464\) | 7.30814 | 0.339272 | ||||||||
\(465\) | −30.8683 | −1.43148 | ||||||||
\(466\) | 28.1463 | 1.30385 | ||||||||
\(467\) | 0.687062 | 0.0317935 | 0.0158967 | − | 0.999874i | \(-0.494940\pi\) | ||||
0.0158967 | + | 0.999874i | \(0.494940\pi\) | |||||||
\(468\) | 149.956 | 6.93172 | ||||||||
\(469\) | 27.9589 | 1.29102 | ||||||||
\(470\) | −33.7310 | −1.55589 | ||||||||
\(471\) | −27.9977 | −1.29006 | ||||||||
\(472\) | −59.5907 | −2.74288 | ||||||||
\(473\) | −29.6784 | −1.36462 | ||||||||
\(474\) | −76.6124 | −3.51893 | ||||||||
\(475\) | −10.1506 | −0.465743 | ||||||||
\(476\) | 4.60144 | 0.210906 | ||||||||
\(477\) | 6.59839 | 0.302120 | ||||||||
\(478\) | 49.8435 | 2.27979 | ||||||||
\(479\) | −28.4118 | −1.29817 | −0.649085 | − | 0.760716i | \(-0.724848\pi\) | ||||
−0.649085 | + | 0.760716i | \(0.724848\pi\) | |||||||
\(480\) | −104.836 | −4.78509 | ||||||||
\(481\) | −43.9984 | −2.00616 | ||||||||
\(482\) | −5.21481 | −0.237528 | ||||||||
\(483\) | 26.3521 | 1.19906 | ||||||||
\(484\) | −5.05888 | −0.229949 | ||||||||
\(485\) | −16.5253 | −0.750374 | ||||||||
\(486\) | 32.1173 | 1.45687 | ||||||||
\(487\) | 4.07601 | 0.184702 | 0.0923509 | − | 0.995727i | \(-0.470562\pi\) | ||||
0.0923509 | + | 0.995727i | \(0.470562\pi\) | |||||||
\(488\) | −0.518428 | −0.0234681 | ||||||||
\(489\) | −34.7695 | −1.57233 | ||||||||
\(490\) | −28.1798 | −1.27303 | ||||||||
\(491\) | −38.2986 | −1.72839 | −0.864196 | − | 0.503156i | \(-0.832172\pi\) | ||||
−0.864196 | + | 0.503156i | \(0.832172\pi\) | |||||||
\(492\) | 18.9506 | 0.854360 | ||||||||
\(493\) | 0.369089 | 0.0166230 | ||||||||
\(494\) | 33.5327 | 1.50871 | ||||||||
\(495\) | 61.4101 | 2.76018 | ||||||||
\(496\) | −34.3327 | −1.54158 | ||||||||
\(497\) | −6.07918 | −0.272689 | ||||||||
\(498\) | 53.2896 | 2.38797 | ||||||||
\(499\) | −31.0255 | −1.38889 | −0.694447 | − | 0.719544i | \(-0.744351\pi\) | ||||
−0.694447 | + | 0.719544i | \(0.744351\pi\) | |||||||
\(500\) | 18.8822 | 0.844439 | ||||||||
\(501\) | 46.9209 | 2.09627 | ||||||||
\(502\) | 1.74782 | 0.0780091 | ||||||||
\(503\) | −31.5136 | −1.40512 | −0.702561 | − | 0.711623i | \(-0.747960\pi\) | ||||
−0.702561 | + | 0.711623i | \(0.747960\pi\) | |||||||
\(504\) | −91.8732 | −4.09236 | ||||||||
\(505\) | −10.3995 | −0.462773 | ||||||||
\(506\) | −38.4656 | −1.71000 | ||||||||
\(507\) | −26.5479 | −1.17904 | ||||||||
\(508\) | −13.4083 | −0.594895 | ||||||||
\(509\) | −22.8584 | −1.01318 | −0.506590 | − | 0.862187i | \(-0.669094\pi\) | ||||
−0.506590 | + | 0.862187i | \(0.669094\pi\) | |||||||
\(510\) | −12.3030 | −0.544786 | ||||||||
\(511\) | −7.23304 | −0.319971 | ||||||||
\(512\) | 37.7412 | 1.66794 | ||||||||
\(513\) | 30.6581 | 1.35359 | ||||||||
\(514\) | 42.2143 | 1.86199 | ||||||||
\(515\) | −8.64561 | −0.380971 | ||||||||
\(516\) | −142.524 | −6.27425 | ||||||||
\(517\) | 13.7575 | 0.605054 | ||||||||
\(518\) | 45.5894 | 2.00308 | ||||||||
\(519\) | −68.6243 | −3.01227 | ||||||||
\(520\) | 104.011 | 4.56117 | ||||||||
\(521\) | −24.4911 | −1.07297 | −0.536486 | − | 0.843909i | \(-0.680249\pi\) | ||||
−0.536486 | + | 0.843909i | \(0.680249\pi\) | |||||||
\(522\) | −12.4632 | −0.545499 | ||||||||
\(523\) | 41.7013 | 1.82347 | 0.911735 | − | 0.410779i | \(-0.134743\pi\) | ||||
0.911735 | + | 0.410779i | \(0.134743\pi\) | |||||||
\(524\) | −62.2803 | −2.72073 | ||||||||
\(525\) | −20.9595 | −0.914747 | ||||||||
\(526\) | 26.6979 | 1.16408 | ||||||||
\(527\) | −1.73393 | −0.0755314 | ||||||||
\(528\) | 99.3565 | 4.32394 | ||||||||
\(529\) | −1.46314 | −0.0636146 | ||||||||
\(530\) | 7.74024 | 0.336214 | ||||||||
\(531\) | 51.7596 | 2.24618 | ||||||||
\(532\) | −24.6645 | −1.06934 | ||||||||
\(533\) | −5.80536 | −0.251458 | ||||||||
\(534\) | −43.6675 | −1.88968 | ||||||||
\(535\) | 13.7989 | 0.596580 | ||||||||
\(536\) | −115.883 | −5.00540 | ||||||||
\(537\) | 20.3375 | 0.877626 | ||||||||
\(538\) | 48.6801 | 2.09875 | ||||||||
\(539\) | 11.4934 | 0.495055 | ||||||||
\(540\) | 160.826 | 6.92084 | ||||||||
\(541\) | 0.825893 | 0.0355079 | 0.0177540 | − | 0.999842i | \(-0.494348\pi\) | ||||
0.0177540 | + | 0.999842i | \(0.494348\pi\) | |||||||
\(542\) | −27.9067 | −1.19869 | ||||||||
\(543\) | −24.0279 | −1.03113 | ||||||||
\(544\) | −5.88886 | −0.252483 | ||||||||
\(545\) | −14.9600 | −0.640815 | ||||||||
\(546\) | 69.2399 | 2.96320 | ||||||||
\(547\) | −20.8830 | −0.892891 | −0.446445 | − | 0.894811i | \(-0.647310\pi\) | ||||
−0.446445 | + | 0.894811i | \(0.647310\pi\) | |||||||
\(548\) | 67.6928 | 2.89169 | ||||||||
\(549\) | 0.450299 | 0.0192183 | ||||||||
\(550\) | 30.5941 | 1.30454 | ||||||||
\(551\) | −1.97839 | −0.0842821 | ||||||||
\(552\) | −109.223 | −4.64886 | ||||||||
\(553\) | −17.2627 | −0.734085 | ||||||||
\(554\) | 25.8102 | 1.09657 | ||||||||
\(555\) | −86.5284 | −3.67293 | ||||||||
\(556\) | −101.296 | −4.29592 | ||||||||
\(557\) | 27.2966 | 1.15659 | 0.578297 | − | 0.815826i | \(-0.303717\pi\) | ||||
0.578297 | + | 0.815826i | \(0.303717\pi\) | |||||||
\(558\) | 58.5505 | 2.47864 | ||||||||
\(559\) | 43.6608 | 1.84666 | ||||||||
\(560\) | −54.8903 | −2.31954 | ||||||||
\(561\) | 5.01789 | 0.211855 | ||||||||
\(562\) | −59.9496 | −2.52882 | ||||||||
\(563\) | −10.4374 | −0.439885 | −0.219942 | − | 0.975513i | \(-0.570587\pi\) | ||||
−0.219942 | + | 0.975513i | \(0.570587\pi\) | |||||||
\(564\) | 66.0671 | 2.78192 | ||||||||
\(565\) | 21.9535 | 0.923589 | ||||||||
\(566\) | −83.7207 | −3.51904 | ||||||||
\(567\) | 27.0227 | 1.13485 | ||||||||
\(568\) | 25.1968 | 1.05723 | ||||||||
\(569\) | 19.2063 | 0.805170 | 0.402585 | − | 0.915383i | \(-0.368112\pi\) | ||||
0.402585 | + | 0.915383i | \(0.368112\pi\) | |||||||
\(570\) | 65.9463 | 2.76219 | ||||||||
\(571\) | 23.6850 | 0.991185 | 0.495593 | − | 0.868555i | \(-0.334951\pi\) | ||||
0.495593 | + | 0.868555i | \(0.334951\pi\) | |||||||
\(572\) | −71.7448 | −2.99980 | ||||||||
\(573\) | 19.0115 | 0.794216 | ||||||||
\(574\) | 6.01528 | 0.251073 | ||||||||
\(575\) | −17.1296 | −0.714354 | ||||||||
\(576\) | 64.7910 | 2.69962 | ||||||||
\(577\) | 33.3582 | 1.38872 | 0.694360 | − | 0.719628i | \(-0.255688\pi\) | ||||
0.694360 | + | 0.719628i | \(0.255688\pi\) | |||||||
\(578\) | 43.9429 | 1.82778 | ||||||||
\(579\) | −57.8116 | −2.40257 | ||||||||
\(580\) | −10.3782 | −0.430932 | ||||||||
\(581\) | 12.0075 | 0.498154 | ||||||||
\(582\) | 45.5961 | 1.89002 | ||||||||
\(583\) | −3.15693 | −0.130747 | ||||||||
\(584\) | 29.9792 | 1.24055 | ||||||||
\(585\) | −90.3422 | −3.73519 | ||||||||
\(586\) | 9.92699 | 0.410080 | ||||||||
\(587\) | −3.41715 | −0.141041 | −0.0705204 | − | 0.997510i | \(-0.522466\pi\) | ||||
−0.0705204 | + | 0.997510i | \(0.522466\pi\) | |||||||
\(588\) | 55.1942 | 2.27617 | ||||||||
\(589\) | 9.29421 | 0.382961 | ||||||||
\(590\) | 60.7166 | 2.49966 | ||||||||
\(591\) | 56.4393 | 2.32160 | ||||||||
\(592\) | −96.2398 | −3.95543 | ||||||||
\(593\) | 35.2315 | 1.44679 | 0.723393 | − | 0.690437i | \(-0.242582\pi\) | ||||
0.723393 | + | 0.690437i | \(0.242582\pi\) | |||||||
\(594\) | −92.4036 | −3.79136 | ||||||||
\(595\) | −2.77217 | −0.113648 | ||||||||
\(596\) | 108.325 | 4.43718 | ||||||||
\(597\) | −12.3353 | −0.504851 | ||||||||
\(598\) | 56.5879 | 2.31405 | ||||||||
\(599\) | 6.46616 | 0.264200 | 0.132100 | − | 0.991236i | \(-0.457828\pi\) | ||||
0.132100 | + | 0.991236i | \(0.457828\pi\) | |||||||
\(600\) | 86.8722 | 3.54654 | ||||||||
\(601\) | 23.2793 | 0.949583 | 0.474791 | − | 0.880098i | \(-0.342524\pi\) | ||||
0.474791 | + | 0.880098i | \(0.342524\pi\) | |||||||
\(602\) | −45.2396 | −1.84383 | ||||||||
\(603\) | 100.655 | 4.09897 | ||||||||
\(604\) | −4.89340 | −0.199110 | ||||||||
\(605\) | 3.04776 | 0.123909 | ||||||||
\(606\) | 28.6941 | 1.16562 | ||||||||
\(607\) | −20.2975 | −0.823849 | −0.411925 | − | 0.911218i | \(-0.635143\pi\) | ||||
−0.411925 | + | 0.911218i | \(0.635143\pi\) | |||||||
\(608\) | 31.5654 | 1.28014 | ||||||||
\(609\) | −4.08506 | −0.165535 | ||||||||
\(610\) | 0.528223 | 0.0213871 | ||||||||
\(611\) | −20.2391 | −0.818785 | ||||||||
\(612\) | 16.5656 | 0.669623 | ||||||||
\(613\) | −26.6543 | −1.07656 | −0.538279 | − | 0.842767i | \(-0.680925\pi\) | ||||
−0.538279 | + | 0.842767i | \(0.680925\pi\) | |||||||
\(614\) | 88.1364 | 3.55690 | ||||||||
\(615\) | −11.4170 | −0.460376 | ||||||||
\(616\) | 43.9557 | 1.77103 | ||||||||
\(617\) | −10.0512 | −0.404645 | −0.202322 | − | 0.979319i | \(-0.564849\pi\) | ||||
−0.202322 | + | 0.979319i | \(0.564849\pi\) | |||||||
\(618\) | 23.8547 | 0.959577 | ||||||||
\(619\) | 40.5056 | 1.62806 | 0.814030 | − | 0.580823i | \(-0.197269\pi\) | ||||
0.814030 | + | 0.580823i | \(0.197269\pi\) | |||||||
\(620\) | 48.7555 | 1.95807 | ||||||||
\(621\) | 51.7367 | 2.07612 | ||||||||
\(622\) | −2.59905 | −0.104212 | ||||||||
\(623\) | −9.83939 | −0.394207 | ||||||||
\(624\) | −146.166 | −5.85133 | ||||||||
\(625\) | −29.8313 | −1.19325 | ||||||||
\(626\) | 23.7780 | 0.950359 | ||||||||
\(627\) | −26.8968 | −1.07415 | ||||||||
\(628\) | 44.2215 | 1.76463 | ||||||||
\(629\) | −4.86048 | −0.193800 | ||||||||
\(630\) | 93.6090 | 3.72947 | ||||||||
\(631\) | −44.4387 | −1.76908 | −0.884539 | − | 0.466466i | \(-0.845527\pi\) | ||||
−0.884539 | + | 0.466466i | \(0.845527\pi\) | |||||||
\(632\) | 71.5498 | 2.84610 | ||||||||
\(633\) | 64.1431 | 2.54946 | ||||||||
\(634\) | 26.3006 | 1.04453 | ||||||||
\(635\) | 8.07791 | 0.320562 | ||||||||
\(636\) | −15.1604 | −0.601148 | ||||||||
\(637\) | −16.9082 | −0.669929 | ||||||||
\(638\) | 5.96287 | 0.236072 | ||||||||
\(639\) | −21.8856 | −0.865780 | ||||||||
\(640\) | 8.32598 | 0.329113 | ||||||||
\(641\) | −17.7327 | −0.700399 | −0.350199 | − | 0.936675i | \(-0.613886\pi\) | ||||
−0.350199 | + | 0.936675i | \(0.613886\pi\) | |||||||
\(642\) | −38.0736 | −1.50265 | ||||||||
\(643\) | −8.44158 | −0.332903 | −0.166452 | − | 0.986050i | \(-0.553231\pi\) | ||||
−0.166452 | + | 0.986050i | \(0.553231\pi\) | |||||||
\(644\) | −41.6224 | −1.64015 | ||||||||
\(645\) | 85.8645 | 3.38091 | ||||||||
\(646\) | 3.70434 | 0.145745 | ||||||||
\(647\) | 38.0905 | 1.49749 | 0.748745 | − | 0.662858i | \(-0.230657\pi\) | ||||
0.748745 | + | 0.662858i | \(0.230657\pi\) | |||||||
\(648\) | −112.003 | −4.39988 | ||||||||
\(649\) | −24.7638 | −0.972065 | ||||||||
\(650\) | −45.0079 | −1.76535 | ||||||||
\(651\) | 19.1911 | 0.752159 | ||||||||
\(652\) | 54.9174 | 2.15073 | ||||||||
\(653\) | 10.5246 | 0.411858 | 0.205929 | − | 0.978567i | \(-0.433978\pi\) | ||||
0.205929 | + | 0.978567i | \(0.433978\pi\) | |||||||
\(654\) | 41.2771 | 1.61406 | ||||||||
\(655\) | 37.5213 | 1.46608 | ||||||||
\(656\) | −12.6983 | −0.495786 | ||||||||
\(657\) | −26.0395 | −1.01590 | ||||||||
\(658\) | 20.9709 | 0.817531 | ||||||||
\(659\) | 45.7967 | 1.78399 | 0.891994 | − | 0.452048i | \(-0.149306\pi\) | ||||
0.891994 | + | 0.452048i | \(0.149306\pi\) | |||||||
\(660\) | −141.095 | −5.49212 | ||||||||
\(661\) | 19.0341 | 0.740342 | 0.370171 | − | 0.928964i | \(-0.379299\pi\) | ||||
0.370171 | + | 0.928964i | \(0.379299\pi\) | |||||||
\(662\) | 47.3490 | 1.84027 | ||||||||
\(663\) | −7.38196 | −0.286692 | ||||||||
\(664\) | −49.7682 | −1.93138 | ||||||||
\(665\) | 14.8593 | 0.576221 | ||||||||
\(666\) | 164.126 | 6.35974 | ||||||||
\(667\) | −3.33861 | −0.129271 | ||||||||
\(668\) | −74.1101 | −2.86741 | ||||||||
\(669\) | 71.8758 | 2.77888 | ||||||||
\(670\) | 118.073 | 4.56155 | ||||||||
\(671\) | −0.215441 | −0.00831699 | ||||||||
\(672\) | 65.1776 | 2.51428 | ||||||||
\(673\) | 25.3296 | 0.976385 | 0.488193 | − | 0.872736i | \(-0.337656\pi\) | ||||
0.488193 | + | 0.872736i | \(0.337656\pi\) | |||||||
\(674\) | −54.3983 | −2.09534 | ||||||||
\(675\) | −41.1494 | −1.58384 | ||||||||
\(676\) | 41.9317 | 1.61276 | ||||||||
\(677\) | 39.8768 | 1.53259 | 0.766295 | − | 0.642489i | \(-0.222098\pi\) | ||||
0.766295 | + | 0.642489i | \(0.222098\pi\) | |||||||
\(678\) | −60.5733 | −2.32631 | ||||||||
\(679\) | 10.2739 | 0.394277 | ||||||||
\(680\) | 11.4900 | 0.440622 | ||||||||
\(681\) | 25.9819 | 0.995629 | ||||||||
\(682\) | −28.0128 | −1.07267 | ||||||||
\(683\) | −48.3416 | −1.84974 | −0.924871 | − | 0.380282i | \(-0.875827\pi\) | ||||
−0.924871 | + | 0.380282i | \(0.875827\pi\) | |||||||
\(684\) | −88.7945 | −3.39514 | ||||||||
\(685\) | −40.7820 | −1.55820 | ||||||||
\(686\) | 51.2049 | 1.95501 | ||||||||
\(687\) | 38.2255 | 1.45840 | ||||||||
\(688\) | 95.5013 | 3.64095 | ||||||||
\(689\) | 4.64425 | 0.176932 | ||||||||
\(690\) | 111.287 | 4.23663 | ||||||||
\(691\) | −9.15136 | −0.348134 | −0.174067 | − | 0.984734i | \(-0.555691\pi\) | ||||
−0.174067 | + | 0.984734i | \(0.555691\pi\) | |||||||
\(692\) | 108.390 | 4.12037 | ||||||||
\(693\) | −38.1793 | −1.45031 | ||||||||
\(694\) | −29.1163 | −1.10524 | ||||||||
\(695\) | 61.0267 | 2.31488 | ||||||||
\(696\) | 16.9316 | 0.641792 | ||||||||
\(697\) | −0.641314 | −0.0242915 | ||||||||
\(698\) | −20.1432 | −0.762432 | ||||||||
\(699\) | 33.2127 | 1.25622 | ||||||||
\(700\) | 33.1049 | 1.25125 | ||||||||
\(701\) | 48.3637 | 1.82667 | 0.913335 | − | 0.407209i | \(-0.133498\pi\) | ||||
0.913335 | + | 0.407209i | \(0.133498\pi\) | |||||||
\(702\) | 135.938 | 5.13063 | ||||||||
\(703\) | 26.0531 | 0.982610 | ||||||||
\(704\) | −30.9985 | −1.16830 | ||||||||
\(705\) | −39.8026 | −1.49905 | ||||||||
\(706\) | −41.2244 | −1.55150 | ||||||||
\(707\) | 6.46549 | 0.243160 | ||||||||
\(708\) | −118.922 | −4.46937 | ||||||||
\(709\) | 30.8439 | 1.15837 | 0.579183 | − | 0.815198i | \(-0.303372\pi\) | ||||
0.579183 | + | 0.815198i | \(0.303372\pi\) | |||||||
\(710\) | −25.6729 | −0.963485 | ||||||||
\(711\) | −62.1472 | −2.33070 | ||||||||
\(712\) | 40.7820 | 1.52837 | ||||||||
\(713\) | 15.6844 | 0.587384 | ||||||||
\(714\) | 7.64889 | 0.286253 | ||||||||
\(715\) | 43.2232 | 1.61646 | ||||||||
\(716\) | −32.1224 | −1.20047 | ||||||||
\(717\) | 58.8153 | 2.19650 | ||||||||
\(718\) | −30.7067 | −1.14596 | ||||||||
\(719\) | −39.3826 | −1.46872 | −0.734362 | − | 0.678758i | \(-0.762518\pi\) | ||||
−0.734362 | + | 0.678758i | \(0.762518\pi\) | |||||||
\(720\) | −197.610 | −7.36448 | ||||||||
\(721\) | 5.37506 | 0.200178 | ||||||||
\(722\) | 30.0291 | 1.11757 | ||||||||
\(723\) | −6.15348 | −0.228851 | ||||||||
\(724\) | 37.9513 | 1.41045 | ||||||||
\(725\) | 2.65540 | 0.0986192 | ||||||||
\(726\) | −8.40930 | −0.312098 | ||||||||
\(727\) | −39.4690 | −1.46382 | −0.731912 | − | 0.681399i | \(-0.761372\pi\) | ||||
−0.731912 | + | 0.681399i | \(0.761372\pi\) | |||||||
\(728\) | −64.6645 | −2.39663 | ||||||||
\(729\) | −6.33230 | −0.234530 | ||||||||
\(730\) | −30.5457 | −1.13055 | ||||||||
\(731\) | 4.82319 | 0.178392 | ||||||||
\(732\) | −1.03460 | −0.0382400 | ||||||||
\(733\) | −16.4915 | −0.609128 | −0.304564 | − | 0.952492i | \(-0.598511\pi\) | ||||
−0.304564 | + | 0.952492i | \(0.598511\pi\) | |||||||
\(734\) | −46.4777 | −1.71552 | ||||||||
\(735\) | −33.2522 | −1.22652 | ||||||||
\(736\) | 53.2678 | 1.96348 | ||||||||
\(737\) | −48.1570 | −1.77389 | ||||||||
\(738\) | 21.6555 | 0.797150 | ||||||||
\(739\) | −37.9285 | −1.39522 | −0.697612 | − | 0.716476i | \(-0.745754\pi\) | ||||
−0.697612 | + | 0.716476i | \(0.745754\pi\) | |||||||
\(740\) | 136.669 | 5.02405 | ||||||||
\(741\) | 39.5687 | 1.45359 | ||||||||
\(742\) | −4.81218 | −0.176661 | ||||||||
\(743\) | 7.36474 | 0.270186 | 0.135093 | − | 0.990833i | \(-0.456867\pi\) | ||||
0.135093 | + | 0.990833i | \(0.456867\pi\) | |||||||
\(744\) | −79.5427 | −2.91618 | ||||||||
\(745\) | −65.2614 | −2.39099 | ||||||||
\(746\) | 59.5456 | 2.18012 | ||||||||
\(747\) | 43.2280 | 1.58163 | ||||||||
\(748\) | −7.92561 | −0.289789 | ||||||||
\(749\) | −8.57894 | −0.313468 | ||||||||
\(750\) | 31.3876 | 1.14611 | ||||||||
\(751\) | 26.8126 | 0.978405 | 0.489202 | − | 0.872170i | \(-0.337288\pi\) | ||||
0.489202 | + | 0.872170i | \(0.337288\pi\) | |||||||
\(752\) | −44.2698 | −1.61435 | ||||||||
\(753\) | 2.06243 | 0.0751592 | ||||||||
\(754\) | −8.77216 | −0.319463 | ||||||||
\(755\) | 2.94807 | 0.107291 | ||||||||
\(756\) | −99.9870 | −3.63649 | ||||||||
\(757\) | 12.9176 | 0.469499 | 0.234750 | − | 0.972056i | \(-0.424573\pi\) | ||||
0.234750 | + | 0.972056i | \(0.424573\pi\) | |||||||
\(758\) | 15.6643 | 0.568952 | ||||||||
\(759\) | −45.3894 | −1.64753 | ||||||||
\(760\) | −61.5885 | −2.23405 | ||||||||
\(761\) | 15.2719 | 0.553605 | 0.276802 | − | 0.960927i | \(-0.410725\pi\) | ||||
0.276802 | + | 0.960927i | \(0.410725\pi\) | |||||||
\(762\) | −22.2883 | −0.807421 | ||||||||
\(763\) | 9.30077 | 0.336710 | ||||||||
\(764\) | −30.0281 | −1.08638 | ||||||||
\(765\) | −9.98005 | −0.360830 | ||||||||
\(766\) | −42.2100 | −1.52511 | ||||||||
\(767\) | 36.4308 | 1.31544 | ||||||||
\(768\) | 37.8695 | 1.36650 | ||||||||
\(769\) | 18.3002 | 0.659921 | 0.329960 | − | 0.943995i | \(-0.392965\pi\) | ||||
0.329960 | + | 0.943995i | \(0.392965\pi\) | |||||||
\(770\) | −44.7862 | −1.61398 | ||||||||
\(771\) | 49.8129 | 1.79397 | ||||||||
\(772\) | 91.3117 | 3.28638 | ||||||||
\(773\) | −8.64714 | −0.311016 | −0.155508 | − | 0.987835i | \(-0.549701\pi\) | ||||
−0.155508 | + | 0.987835i | \(0.549701\pi\) | |||||||
\(774\) | −162.866 | −5.85411 | ||||||||
\(775\) | −12.4747 | −0.448106 | ||||||||
\(776\) | −42.5831 | −1.52864 | ||||||||
\(777\) | 53.7956 | 1.92991 | ||||||||
\(778\) | 26.4769 | 0.949242 | ||||||||
\(779\) | 3.43756 | 0.123163 | ||||||||
\(780\) | 207.569 | 7.43217 | ||||||||
\(781\) | 10.4709 | 0.374679 | ||||||||
\(782\) | 6.25123 | 0.223543 | ||||||||
\(783\) | −8.02014 | −0.286616 | ||||||||
\(784\) | −36.9842 | −1.32086 | ||||||||
\(785\) | −26.6416 | −0.950879 | ||||||||
\(786\) | −103.528 | −3.69271 | ||||||||
\(787\) | −7.44912 | −0.265533 | −0.132766 | − | 0.991147i | \(-0.542386\pi\) | ||||
−0.132766 | + | 0.991147i | \(0.542386\pi\) | |||||||
\(788\) | −89.1442 | −3.17563 | ||||||||
\(789\) | 31.5035 | 1.12155 | ||||||||
\(790\) | −72.9017 | −2.59373 | ||||||||
\(791\) | −13.6487 | −0.485291 | ||||||||
\(792\) | 158.244 | 5.62296 | ||||||||
\(793\) | 0.316941 | 0.0112549 | ||||||||
\(794\) | −8.90026 | −0.315858 | ||||||||
\(795\) | 9.13349 | 0.323931 | ||||||||
\(796\) | 19.4833 | 0.690566 | ||||||||
\(797\) | 48.1292 | 1.70482 | 0.852412 | − | 0.522870i | \(-0.175139\pi\) | ||||
0.852412 | + | 0.522870i | \(0.175139\pi\) | |||||||
\(798\) | −40.9995 | −1.45137 | ||||||||
\(799\) | −2.23580 | −0.0790968 | ||||||||
\(800\) | −42.3672 | −1.49791 | ||||||||
\(801\) | −35.4226 | −1.25160 | ||||||||
\(802\) | −4.83732 | −0.170812 | ||||||||
\(803\) | 12.4583 | 0.439645 | ||||||||
\(804\) | −231.263 | −8.15600 | ||||||||
\(805\) | 25.0758 | 0.883804 | ||||||||
\(806\) | 41.2105 | 1.45158 | ||||||||
\(807\) | 57.4425 | 2.02207 | ||||||||
\(808\) | −26.7979 | −0.942748 | ||||||||
\(809\) | 6.18950 | 0.217611 | 0.108806 | − | 0.994063i | \(-0.465297\pi\) | ||||
0.108806 | + | 0.994063i | \(0.465297\pi\) | |||||||
\(810\) | 114.119 | 4.00973 | ||||||||
\(811\) | 28.2244 | 0.991094 | 0.495547 | − | 0.868581i | \(-0.334968\pi\) | ||||
0.495547 | + | 0.868581i | \(0.334968\pi\) | |||||||
\(812\) | 6.45224 | 0.226429 | ||||||||
\(813\) | −32.9299 | −1.15490 | ||||||||
\(814\) | −78.5241 | −2.75227 | ||||||||
\(815\) | −33.0854 | −1.15893 | ||||||||
\(816\) | −16.1469 | −0.565254 | ||||||||
\(817\) | −25.8532 | −0.904488 | ||||||||
\(818\) | 37.2269 | 1.30161 | ||||||||
\(819\) | 56.1667 | 1.96262 | ||||||||
\(820\) | 18.0327 | 0.629731 | ||||||||
\(821\) | 49.0116 | 1.71052 | 0.855258 | − | 0.518203i | \(-0.173399\pi\) | ||||
0.855258 | + | 0.518203i | \(0.173399\pi\) | |||||||
\(822\) | 112.525 | 3.92475 | ||||||||
\(823\) | −30.8178 | −1.07424 | −0.537121 | − | 0.843505i | \(-0.680488\pi\) | ||||
−0.537121 | + | 0.843505i | \(0.680488\pi\) | |||||||
\(824\) | −22.2784 | −0.776104 | ||||||||
\(825\) | 36.1011 | 1.25688 | ||||||||
\(826\) | −37.7481 | −1.31342 | ||||||||
\(827\) | 31.6319 | 1.09995 | 0.549974 | − | 0.835182i | \(-0.314638\pi\) | ||||
0.549974 | + | 0.835182i | \(0.314638\pi\) | |||||||
\(828\) | −149.844 | −5.20745 | ||||||||
\(829\) | 1.49897 | 0.0520612 | 0.0260306 | − | 0.999661i | \(-0.491713\pi\) | ||||
0.0260306 | + | 0.999661i | \(0.491713\pi\) | |||||||
\(830\) | 50.7085 | 1.76012 | ||||||||
\(831\) | 30.4561 | 1.05651 | ||||||||
\(832\) | 45.6028 | 1.58099 | ||||||||
\(833\) | −1.86784 | −0.0647169 | ||||||||
\(834\) | −168.383 | −5.83063 | ||||||||
\(835\) | 44.6482 | 1.54512 | ||||||||
\(836\) | 42.4827 | 1.46930 | ||||||||
\(837\) | 37.6776 | 1.30233 | ||||||||
\(838\) | 4.54581 | 0.157032 | ||||||||
\(839\) | 9.02087 | 0.311435 | 0.155718 | − | 0.987802i | \(-0.450231\pi\) | ||||
0.155718 | + | 0.987802i | \(0.450231\pi\) | |||||||
\(840\) | −127.171 | −4.38781 | ||||||||
\(841\) | −28.4825 | −0.982154 | ||||||||
\(842\) | 49.2381 | 1.69686 | ||||||||
\(843\) | −70.7406 | −2.43644 | ||||||||
\(844\) | −101.312 | −3.48731 | ||||||||
\(845\) | −25.2621 | −0.869042 | ||||||||
\(846\) | 75.4970 | 2.59564 | ||||||||
\(847\) | −1.89483 | −0.0651070 | ||||||||
\(848\) | 10.1586 | 0.348847 | ||||||||
\(849\) | −98.7905 | −3.39048 | ||||||||
\(850\) | −4.97199 | −0.170538 | ||||||||
\(851\) | 43.9656 | 1.50712 | ||||||||
\(852\) | 50.2840 | 1.72270 | ||||||||
\(853\) | 51.1432 | 1.75111 | 0.875556 | − | 0.483117i | \(-0.160495\pi\) | ||||
0.875556 | + | 0.483117i | \(0.160495\pi\) | |||||||
\(854\) | −0.328402 | −0.0112377 | ||||||||
\(855\) | 53.4949 | 1.82949 | ||||||||
\(856\) | 35.5577 | 1.21534 | ||||||||
\(857\) | 9.49639 | 0.324390 | 0.162195 | − | 0.986759i | \(-0.448143\pi\) | ||||
0.162195 | + | 0.986759i | \(0.448143\pi\) | |||||||
\(858\) | −119.260 | −4.07148 | ||||||||
\(859\) | 5.28903 | 0.180460 | 0.0902298 | − | 0.995921i | \(-0.471240\pi\) | ||||
0.0902298 | + | 0.995921i | \(0.471240\pi\) | |||||||
\(860\) | −135.620 | −4.62462 | ||||||||
\(861\) | 7.09803 | 0.241900 | ||||||||
\(862\) | −81.1644 | −2.76447 | ||||||||
\(863\) | 20.2943 | 0.690826 | 0.345413 | − | 0.938451i | \(-0.387739\pi\) | ||||
0.345413 | + | 0.938451i | \(0.387739\pi\) | |||||||
\(864\) | 127.962 | 4.35336 | ||||||||
\(865\) | −65.3004 | −2.22028 | ||||||||
\(866\) | −21.1379 | −0.718296 | ||||||||
\(867\) | 51.8527 | 1.76101 | ||||||||
\(868\) | −30.3118 | −1.02885 | ||||||||
\(869\) | 29.7336 | 1.00864 | ||||||||
\(870\) | −17.2515 | −0.584882 | ||||||||
\(871\) | 70.8452 | 2.40050 | ||||||||
\(872\) | −38.5495 | −1.30545 | ||||||||
\(873\) | 36.9870 | 1.25182 | ||||||||
\(874\) | −33.5077 | −1.13342 | ||||||||
\(875\) | 7.07242 | 0.239091 | ||||||||
\(876\) | 59.8281 | 2.02140 | ||||||||
\(877\) | 52.5660 | 1.77503 | 0.887513 | − | 0.460782i | \(-0.152431\pi\) | ||||
0.887513 | + | 0.460782i | \(0.152431\pi\) | |||||||
\(878\) | −15.7513 | −0.531580 | ||||||||
\(879\) | 11.7139 | 0.395099 | ||||||||
\(880\) | 94.5441 | 3.18708 | ||||||||
\(881\) | −9.22078 | −0.310656 | −0.155328 | − | 0.987863i | \(-0.549643\pi\) | ||||
−0.155328 | + | 0.987863i | \(0.549643\pi\) | |||||||
\(882\) | 63.0722 | 2.12375 | ||||||||
\(883\) | 27.5680 | 0.927738 | 0.463869 | − | 0.885904i | \(-0.346461\pi\) | ||||
0.463869 | + | 0.885904i | \(0.346461\pi\) | |||||||
\(884\) | 11.6596 | 0.392155 | ||||||||
\(885\) | 71.6456 | 2.40834 | ||||||||
\(886\) | 32.9149 | 1.10580 | ||||||||
\(887\) | 53.3759 | 1.79219 | 0.896093 | − | 0.443866i | \(-0.146393\pi\) | ||||
0.896093 | + | 0.443866i | \(0.146393\pi\) | |||||||
\(888\) | −222.970 | −7.48238 | ||||||||
\(889\) | −5.02212 | −0.168436 | ||||||||
\(890\) | −41.5525 | −1.39284 | ||||||||
\(891\) | −46.5444 | −1.55930 | ||||||||
\(892\) | −113.526 | −3.80112 | ||||||||
\(893\) | 11.9843 | 0.401039 | ||||||||
\(894\) | 180.067 | 6.02235 | ||||||||
\(895\) | 19.3524 | 0.646880 | ||||||||
\(896\) | −5.17634 | −0.172929 | ||||||||
\(897\) | 66.7737 | 2.22951 | ||||||||
\(898\) | 35.1108 | 1.17166 | ||||||||
\(899\) | −2.43136 | −0.0810905 | ||||||||
\(900\) | 119.180 | 3.97268 | ||||||||
\(901\) | 0.513047 | 0.0170921 | ||||||||
\(902\) | −10.3608 | −0.344978 | ||||||||
\(903\) | −53.3828 | −1.77647 | ||||||||
\(904\) | 56.5706 | 1.88151 | ||||||||
\(905\) | −22.8641 | −0.760027 | ||||||||
\(906\) | −8.13422 | −0.270241 | ||||||||
\(907\) | −50.0678 | −1.66247 | −0.831237 | − | 0.555918i | \(-0.812367\pi\) | ||||
−0.831237 | + | 0.555918i | \(0.812367\pi\) | |||||||
\(908\) | −41.0377 | −1.36188 | ||||||||
\(909\) | 23.2763 | 0.772026 | ||||||||
\(910\) | 65.8863 | 2.18411 | ||||||||
\(911\) | −24.3099 | −0.805424 | −0.402712 | − | 0.915327i | \(-0.631932\pi\) | ||||
−0.402712 | + | 0.915327i | \(0.631932\pi\) | |||||||
\(912\) | 86.5503 | 2.86597 | ||||||||
\(913\) | −20.6819 | −0.684472 | ||||||||
\(914\) | 61.3441 | 2.02908 | ||||||||
\(915\) | 0.623304 | 0.0206058 | ||||||||
\(916\) | −60.3761 | −1.99488 | ||||||||
\(917\) | −23.3274 | −0.770337 | ||||||||
\(918\) | 15.0169 | 0.495633 | ||||||||
\(919\) | −11.5013 | −0.379394 | −0.189697 | − | 0.981843i | \(-0.560751\pi\) | ||||
−0.189697 | + | 0.981843i | \(0.560751\pi\) | |||||||
\(920\) | −103.933 | −3.42657 | ||||||||
\(921\) | 104.001 | 3.42695 | ||||||||
\(922\) | −36.0162 | −1.18613 | ||||||||
\(923\) | −15.4041 | −0.507031 | ||||||||
\(924\) | 87.7202 | 2.88578 | ||||||||
\(925\) | −34.9686 | −1.14976 | ||||||||
\(926\) | −16.2300 | −0.533351 | ||||||||
\(927\) | 19.3507 | 0.635559 | ||||||||
\(928\) | −8.25749 | −0.271066 | ||||||||
\(929\) | −29.0660 | −0.953626 | −0.476813 | − | 0.879005i | \(-0.658208\pi\) | ||||
−0.476813 | + | 0.879005i | \(0.658208\pi\) | |||||||
\(930\) | 81.0455 | 2.65759 | ||||||||
\(931\) | 10.0120 | 0.328130 | ||||||||
\(932\) | −52.4584 | −1.71833 | ||||||||
\(933\) | −3.06688 | −0.100405 | ||||||||
\(934\) | −1.80390 | −0.0590255 | ||||||||
\(935\) | 4.77484 | 0.156154 | ||||||||
\(936\) | −232.798 | −7.60923 | ||||||||
\(937\) | −47.8839 | −1.56430 | −0.782150 | − | 0.623090i | \(-0.785877\pi\) | ||||
−0.782150 | + | 0.623090i | \(0.785877\pi\) | |||||||
\(938\) | −73.4070 | −2.39682 | ||||||||
\(939\) | 28.0580 | 0.915639 | ||||||||
\(940\) | 62.8671 | 2.05050 | ||||||||
\(941\) | 31.6061 | 1.03033 | 0.515165 | − | 0.857091i | \(-0.327731\pi\) | ||||
0.515165 | + | 0.857091i | \(0.327731\pi\) | |||||||
\(942\) | 73.5086 | 2.39504 | ||||||||
\(943\) | 5.80103 | 0.188907 | ||||||||
\(944\) | 79.6867 | 2.59358 | ||||||||
\(945\) | 60.2380 | 1.95954 | ||||||||
\(946\) | 77.9216 | 2.53345 | ||||||||
\(947\) | −39.1461 | −1.27208 | −0.636039 | − | 0.771657i | \(-0.719428\pi\) | ||||
−0.636039 | + | 0.771657i | \(0.719428\pi\) | |||||||
\(948\) | 142.789 | 4.63756 | ||||||||
\(949\) | −18.3278 | −0.594946 | ||||||||
\(950\) | 26.6508 | 0.864666 | ||||||||
\(951\) | 31.0348 | 1.00637 | ||||||||
\(952\) | −7.14345 | −0.231521 | ||||||||
\(953\) | −17.0366 | −0.551870 | −0.275935 | − | 0.961176i | \(-0.588987\pi\) | ||||
−0.275935 | + | 0.961176i | \(0.588987\pi\) | |||||||
\(954\) | −17.3243 | −0.560894 | ||||||||
\(955\) | 18.0907 | 0.585400 | ||||||||
\(956\) | −92.8971 | −3.00451 | ||||||||
\(957\) | 7.03620 | 0.227448 | ||||||||
\(958\) | 74.5961 | 2.41009 | ||||||||
\(959\) | 25.3546 | 0.818743 | ||||||||
\(960\) | 89.6837 | 2.89453 | ||||||||
\(961\) | −19.5778 | −0.631541 | ||||||||
\(962\) | 115.519 | 3.72449 | ||||||||
\(963\) | −30.8849 | −0.995252 | ||||||||
\(964\) | 9.71925 | 0.313036 | ||||||||
\(965\) | −55.0115 | −1.77088 | ||||||||
\(966\) | −69.1883 | −2.22610 | ||||||||
\(967\) | −4.90118 | −0.157611 | −0.0788057 | − | 0.996890i | \(-0.525111\pi\) | ||||
−0.0788057 | + | 0.996890i | \(0.525111\pi\) | |||||||
\(968\) | 7.85361 | 0.252425 | ||||||||
\(969\) | 4.37113 | 0.140421 | ||||||||
\(970\) | 43.3876 | 1.39309 | ||||||||
\(971\) | 18.3675 | 0.589441 | 0.294721 | − | 0.955583i | \(-0.404773\pi\) | ||||
0.294721 | + | 0.955583i | \(0.404773\pi\) | |||||||
\(972\) | −59.8595 | −1.92000 | ||||||||
\(973\) | −37.9409 | −1.21633 | ||||||||
\(974\) | −10.7017 | −0.342904 | ||||||||
\(975\) | −53.1093 | −1.70086 | ||||||||
\(976\) | 0.693260 | 0.0221907 | ||||||||
\(977\) | 14.6595 | 0.469001 | 0.234500 | − | 0.972116i | \(-0.424655\pi\) | ||||
0.234500 | + | 0.972116i | \(0.424655\pi\) | |||||||
\(978\) | 91.2883 | 2.91908 | ||||||||
\(979\) | 16.9476 | 0.541646 | ||||||||
\(980\) | 52.5208 | 1.67772 | ||||||||
\(981\) | 33.4836 | 1.06905 | ||||||||
\(982\) | 100.554 | 3.20881 | ||||||||
\(983\) | 50.6466 | 1.61537 | 0.807687 | − | 0.589611i | \(-0.200719\pi\) | ||||
0.807687 | + | 0.589611i | \(0.200719\pi\) | |||||||
\(984\) | −29.4197 | −0.937866 | ||||||||
\(985\) | 53.7056 | 1.71120 | ||||||||
\(986\) | −0.969055 | −0.0308610 | ||||||||
\(987\) | 24.7457 | 0.787664 | ||||||||
\(988\) | −62.4976 | −1.98831 | ||||||||
\(989\) | −43.6283 | −1.38730 | ||||||||
\(990\) | −161.234 | −5.12435 | ||||||||
\(991\) | 5.89768 | 0.187346 | 0.0936730 | − | 0.995603i | \(-0.470139\pi\) | ||||
0.0936730 | + | 0.995603i | \(0.470139\pi\) | |||||||
\(992\) | 38.7926 | 1.23167 | ||||||||
\(993\) | 55.8719 | 1.77304 | ||||||||
\(994\) | 15.9611 | 0.506255 | ||||||||
\(995\) | −11.7378 | −0.372115 | ||||||||
\(996\) | −99.3200 | −3.14708 | ||||||||
\(997\) | −13.2462 | −0.419510 | −0.209755 | − | 0.977754i | \(-0.567267\pi\) | ||||
−0.209755 | + | 0.977754i | \(0.567267\pi\) | |||||||
\(998\) | 81.4584 | 2.57852 | ||||||||
\(999\) | 105.616 | 3.34154 |
(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 | 8003.2.a.d.1.9 | ✓ | 179 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.d.1.9 | ✓ | 179 | 1.1 | even | 1 | trivial |