Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0759064919\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34842 | 0.953477 | 0.476739 | − | 0.879045i | \(-0.341819\pi\) | ||||
0.476739 | + | 0.879045i | \(0.341819\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.181762 | −0.0908811 | ||||||||
\(5\) | −1.77320 | −0.793000 | −0.396500 | − | 0.918035i | \(-0.629775\pi\) | ||||
−0.396500 | + | 0.918035i | \(0.629775\pi\) | |||||||
\(6\) | −1.34842 | −0.550490 | ||||||||
\(7\) | 1.31404 | 0.496660 | 0.248330 | − | 0.968675i | \(-0.420118\pi\) | ||||
0.248330 | + | 0.968675i | \(0.420118\pi\) | |||||||
\(8\) | −2.94193 | −1.04013 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.39102 | −0.756107 | ||||||||
\(11\) | −1.43681 | −0.433215 | −0.216607 | − | 0.976259i | \(-0.569499\pi\) | ||||
−0.216607 | + | 0.976259i | \(0.569499\pi\) | |||||||
\(12\) | 0.181762 | 0.0524702 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 1.77188 | 0.473554 | ||||||||
\(15\) | 1.77320 | 0.457839 | ||||||||
\(16\) | −3.60344 | −0.900860 | ||||||||
\(17\) | −0.353504 | −0.0857373 | −0.0428687 | − | 0.999081i | \(-0.513650\pi\) | ||||
−0.0428687 | + | 0.999081i | \(0.513650\pi\) | |||||||
\(18\) | 1.34842 | 0.317826 | ||||||||
\(19\) | 6.34324 | 1.45524 | 0.727620 | − | 0.685980i | \(-0.240626\pi\) | ||||
0.727620 | + | 0.685980i | \(0.240626\pi\) | |||||||
\(20\) | 0.322301 | 0.0720687 | ||||||||
\(21\) | −1.31404 | −0.286747 | ||||||||
\(22\) | −1.93743 | −0.413061 | ||||||||
\(23\) | 3.44161 | 0.717624 | 0.358812 | − | 0.933410i | \(-0.383182\pi\) | ||||
0.358812 | + | 0.933410i | \(0.383182\pi\) | |||||||
\(24\) | 2.94193 | 0.600520 | ||||||||
\(25\) | −1.85576 | −0.371152 | ||||||||
\(26\) | 1.34842 | 0.264447 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.238843 | −0.0451370 | ||||||||
\(29\) | 8.26096 | 1.53402 | 0.767011 | − | 0.641634i | \(-0.221743\pi\) | ||||
0.767011 | + | 0.641634i | \(0.221743\pi\) | |||||||
\(30\) | 2.39102 | 0.436539 | ||||||||
\(31\) | 4.74752 | 0.852680 | 0.426340 | − | 0.904563i | \(-0.359803\pi\) | ||||
0.426340 | + | 0.904563i | \(0.359803\pi\) | |||||||
\(32\) | 1.02492 | 0.181181 | ||||||||
\(33\) | 1.43681 | 0.250117 | ||||||||
\(34\) | −0.476672 | −0.0817486 | ||||||||
\(35\) | −2.33006 | −0.393851 | ||||||||
\(36\) | −0.181762 | −0.0302937 | ||||||||
\(37\) | −11.3111 | −1.85954 | −0.929768 | − | 0.368147i | \(-0.879992\pi\) | ||||
−0.929768 | + | 0.368147i | \(0.879992\pi\) | |||||||
\(38\) | 8.55336 | 1.38754 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 5.21664 | 0.824823 | ||||||||
\(41\) | 0.305020 | 0.0476362 | 0.0238181 | − | 0.999716i | \(-0.492418\pi\) | ||||
0.0238181 | + | 0.999716i | \(0.492418\pi\) | |||||||
\(42\) | −1.77188 | −0.273407 | ||||||||
\(43\) | −6.02412 | −0.918669 | −0.459335 | − | 0.888263i | \(-0.651912\pi\) | ||||
−0.459335 | + | 0.888263i | \(0.651912\pi\) | |||||||
\(44\) | 0.261158 | 0.0393710 | ||||||||
\(45\) | −1.77320 | −0.264333 | ||||||||
\(46\) | 4.64073 | 0.684238 | ||||||||
\(47\) | −9.42424 | −1.37467 | −0.687333 | − | 0.726342i | \(-0.741219\pi\) | ||||
−0.687333 | + | 0.726342i | \(0.741219\pi\) | |||||||
\(48\) | 3.60344 | 0.520111 | ||||||||
\(49\) | −5.27330 | −0.753328 | ||||||||
\(50\) | −2.50234 | −0.353885 | ||||||||
\(51\) | 0.353504 | 0.0495005 | ||||||||
\(52\) | −0.181762 | −0.0252059 | ||||||||
\(53\) | 1.86199 | 0.255764 | 0.127882 | − | 0.991789i | \(-0.459182\pi\) | ||||
0.127882 | + | 0.991789i | \(0.459182\pi\) | |||||||
\(54\) | −1.34842 | −0.183497 | ||||||||
\(55\) | 2.54775 | 0.343539 | ||||||||
\(56\) | −3.86582 | −0.516592 | ||||||||
\(57\) | −6.34324 | −0.840183 | ||||||||
\(58\) | 11.1393 | 1.46266 | ||||||||
\(59\) | −8.84735 | −1.15183 | −0.575913 | − | 0.817511i | \(-0.695353\pi\) | ||||
−0.575913 | + | 0.817511i | \(0.695353\pi\) | |||||||
\(60\) | −0.322301 | −0.0416089 | ||||||||
\(61\) | 10.5977 | 1.35690 | 0.678449 | − | 0.734648i | \(-0.262653\pi\) | ||||
0.678449 | + | 0.734648i | \(0.262653\pi\) | |||||||
\(62\) | 6.40166 | 0.813011 | ||||||||
\(63\) | 1.31404 | 0.165553 | ||||||||
\(64\) | 8.58889 | 1.07361 | ||||||||
\(65\) | −1.77320 | −0.219939 | ||||||||
\(66\) | 1.93743 | 0.238481 | ||||||||
\(67\) | −10.5644 | −1.29065 | −0.645323 | − | 0.763910i | \(-0.723277\pi\) | ||||
−0.645323 | + | 0.763910i | \(0.723277\pi\) | |||||||
\(68\) | 0.0642537 | 0.00779190 | ||||||||
\(69\) | −3.44161 | −0.414321 | ||||||||
\(70\) | −3.14190 | −0.375528 | ||||||||
\(71\) | −6.44020 | −0.764311 | −0.382155 | − | 0.924098i | \(-0.624818\pi\) | ||||
−0.382155 | + | 0.924098i | \(0.624818\pi\) | |||||||
\(72\) | −2.94193 | −0.346710 | ||||||||
\(73\) | −9.96414 | −1.16621 | −0.583107 | − | 0.812395i | \(-0.698163\pi\) | ||||
−0.583107 | + | 0.812395i | \(0.698163\pi\) | |||||||
\(74\) | −15.2521 | −1.77302 | ||||||||
\(75\) | 1.85576 | 0.214285 | ||||||||
\(76\) | −1.15296 | −0.132254 | ||||||||
\(77\) | −1.88803 | −0.215161 | ||||||||
\(78\) | −1.34842 | −0.152679 | ||||||||
\(79\) | 16.5936 | 1.86692 | 0.933462 | − | 0.358676i | \(-0.116772\pi\) | ||||
0.933462 | + | 0.358676i | \(0.116772\pi\) | |||||||
\(80\) | 6.38962 | 0.714381 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.411296 | 0.0454200 | ||||||||
\(83\) | −9.14531 | −1.00383 | −0.501914 | − | 0.864917i | \(-0.667371\pi\) | ||||
−0.501914 | + | 0.864917i | \(0.667371\pi\) | |||||||
\(84\) | 0.238843 | 0.0260599 | ||||||||
\(85\) | 0.626834 | 0.0679896 | ||||||||
\(86\) | −8.12304 | −0.875930 | ||||||||
\(87\) | −8.26096 | −0.885668 | ||||||||
\(88\) | 4.22700 | 0.450600 | ||||||||
\(89\) | −9.98710 | −1.05863 | −0.529315 | − | 0.848425i | \(-0.677551\pi\) | ||||
−0.529315 | + | 0.848425i | \(0.677551\pi\) | |||||||
\(90\) | −2.39102 | −0.252036 | ||||||||
\(91\) | 1.31404 | 0.137749 | ||||||||
\(92\) | −0.625554 | −0.0652185 | ||||||||
\(93\) | −4.74752 | −0.492295 | ||||||||
\(94\) | −12.7078 | −1.31071 | ||||||||
\(95\) | −11.2478 | −1.15400 | ||||||||
\(96\) | −1.02492 | −0.104605 | ||||||||
\(97\) | −15.2494 | −1.54834 | −0.774169 | − | 0.632979i | \(-0.781832\pi\) | ||||
−0.774169 | + | 0.632979i | \(0.781832\pi\) | |||||||
\(98\) | −7.11062 | −0.718282 | ||||||||
\(99\) | −1.43681 | −0.144405 | ||||||||
\(100\) | 0.337307 | 0.0337307 | ||||||||
\(101\) | −9.89403 | −0.984493 | −0.492247 | − | 0.870456i | \(-0.663824\pi\) | ||||
−0.492247 | + | 0.870456i | \(0.663824\pi\) | |||||||
\(102\) | 0.476672 | 0.0471976 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −2.94193 | −0.288480 | ||||||||
\(105\) | 2.33006 | 0.227390 | ||||||||
\(106\) | 2.51075 | 0.243865 | ||||||||
\(107\) | 3.38176 | 0.326927 | 0.163463 | − | 0.986549i | \(-0.447733\pi\) | ||||
0.163463 | + | 0.986549i | \(0.447733\pi\) | |||||||
\(108\) | 0.181762 | 0.0174901 | ||||||||
\(109\) | 12.3011 | 1.17823 | 0.589114 | − | 0.808050i | \(-0.299477\pi\) | ||||
0.589114 | + | 0.808050i | \(0.299477\pi\) | |||||||
\(110\) | 3.43544 | 0.327557 | ||||||||
\(111\) | 11.3111 | 1.07360 | ||||||||
\(112\) | −4.73506 | −0.447421 | ||||||||
\(113\) | −6.68042 | −0.628441 | −0.314220 | − | 0.949350i | \(-0.601743\pi\) | ||||
−0.314220 | + | 0.949350i | \(0.601743\pi\) | |||||||
\(114\) | −8.55336 | −0.801096 | ||||||||
\(115\) | −6.10266 | −0.569076 | ||||||||
\(116\) | −1.50153 | −0.139414 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −11.9299 | −1.09824 | ||||||||
\(119\) | −0.464518 | −0.0425823 | ||||||||
\(120\) | −5.21664 | −0.476212 | ||||||||
\(121\) | −8.93557 | −0.812325 | ||||||||
\(122\) | 14.2902 | 1.29377 | ||||||||
\(123\) | −0.305020 | −0.0275028 | ||||||||
\(124\) | −0.862920 | −0.0774925 | ||||||||
\(125\) | 12.1566 | 1.08732 | ||||||||
\(126\) | 1.77188 | 0.157851 | ||||||||
\(127\) | 9.99138 | 0.886591 | 0.443296 | − | 0.896375i | \(-0.353809\pi\) | ||||
0.443296 | + | 0.896375i | \(0.353809\pi\) | |||||||
\(128\) | 9.53161 | 0.842483 | ||||||||
\(129\) | 6.02412 | 0.530394 | ||||||||
\(130\) | −2.39102 | −0.209706 | ||||||||
\(131\) | −16.6646 | −1.45599 | −0.727997 | − | 0.685580i | \(-0.759549\pi\) | ||||
−0.727997 | + | 0.685580i | \(0.759549\pi\) | |||||||
\(132\) | −0.261158 | −0.0227309 | ||||||||
\(133\) | 8.33528 | 0.722760 | ||||||||
\(134\) | −14.2452 | −1.23060 | ||||||||
\(135\) | 1.77320 | 0.152613 | ||||||||
\(136\) | 1.03998 | 0.0891780 | ||||||||
\(137\) | −11.3796 | −0.972225 | −0.486113 | − | 0.873896i | \(-0.661586\pi\) | ||||
−0.486113 | + | 0.873896i | \(0.661586\pi\) | |||||||
\(138\) | −4.64073 | −0.395045 | ||||||||
\(139\) | 18.8994 | 1.60303 | 0.801514 | − | 0.597976i | \(-0.204028\pi\) | ||||
0.801514 | + | 0.597976i | \(0.204028\pi\) | |||||||
\(140\) | 0.423516 | 0.0357937 | ||||||||
\(141\) | 9.42424 | 0.793664 | ||||||||
\(142\) | −8.68409 | −0.728753 | ||||||||
\(143\) | −1.43681 | −0.120152 | ||||||||
\(144\) | −3.60344 | −0.300287 | ||||||||
\(145\) | −14.6483 | −1.21648 | ||||||||
\(146\) | −13.4358 | −1.11196 | ||||||||
\(147\) | 5.27330 | 0.434934 | ||||||||
\(148\) | 2.05593 | 0.168997 | ||||||||
\(149\) | 5.73376 | 0.469728 | 0.234864 | − | 0.972028i | \(-0.424535\pi\) | ||||
0.234864 | + | 0.972028i | \(0.424535\pi\) | |||||||
\(150\) | 2.50234 | 0.204315 | ||||||||
\(151\) | 13.5718 | 1.10446 | 0.552229 | − | 0.833692i | \(-0.313777\pi\) | ||||
0.552229 | + | 0.833692i | \(0.313777\pi\) | |||||||
\(152\) | −18.6614 | −1.51364 | ||||||||
\(153\) | −0.353504 | −0.0285791 | ||||||||
\(154\) | −2.54585 | −0.205151 | ||||||||
\(155\) | −8.41831 | −0.676175 | ||||||||
\(156\) | 0.181762 | 0.0145526 | ||||||||
\(157\) | −14.3910 | −1.14852 | −0.574262 | − | 0.818671i | \(-0.694711\pi\) | ||||
−0.574262 | + | 0.818671i | \(0.694711\pi\) | |||||||
\(158\) | 22.3751 | 1.78007 | ||||||||
\(159\) | −1.86199 | −0.147666 | ||||||||
\(160\) | −1.81738 | −0.143677 | ||||||||
\(161\) | 4.52241 | 0.356416 | ||||||||
\(162\) | 1.34842 | 0.105942 | ||||||||
\(163\) | −15.2265 | −1.19263 | −0.596317 | − | 0.802749i | \(-0.703370\pi\) | ||||
−0.596317 | + | 0.802749i | \(0.703370\pi\) | |||||||
\(164\) | −0.0554412 | −0.00432923 | ||||||||
\(165\) | −2.54775 | −0.198342 | ||||||||
\(166\) | −12.3317 | −0.957128 | ||||||||
\(167\) | 0.259202 | 0.0200576 | 0.0100288 | − | 0.999950i | \(-0.496808\pi\) | ||||
0.0100288 | + | 0.999950i | \(0.496808\pi\) | |||||||
\(168\) | 3.86582 | 0.298254 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.845235 | 0.0648266 | ||||||||
\(171\) | 6.34324 | 0.485080 | ||||||||
\(172\) | 1.09496 | 0.0834897 | ||||||||
\(173\) | 4.41019 | 0.335300 | 0.167650 | − | 0.985847i | \(-0.446382\pi\) | ||||
0.167650 | + | 0.985847i | \(0.446382\pi\) | |||||||
\(174\) | −11.1393 | −0.844464 | ||||||||
\(175\) | −2.43854 | −0.184336 | ||||||||
\(176\) | 5.17746 | 0.390266 | ||||||||
\(177\) | 8.84735 | 0.665008 | ||||||||
\(178\) | −13.4668 | −1.00938 | ||||||||
\(179\) | −7.72137 | −0.577122 | −0.288561 | − | 0.957462i | \(-0.593177\pi\) | ||||
−0.288561 | + | 0.957462i | \(0.593177\pi\) | |||||||
\(180\) | 0.322301 | 0.0240229 | ||||||||
\(181\) | 2.33128 | 0.173283 | 0.0866413 | − | 0.996240i | \(-0.472387\pi\) | ||||
0.0866413 | + | 0.996240i | \(0.472387\pi\) | |||||||
\(182\) | 1.77188 | 0.131340 | ||||||||
\(183\) | −10.5977 | −0.783405 | ||||||||
\(184\) | −10.1250 | −0.746423 | ||||||||
\(185\) | 20.0569 | 1.47461 | ||||||||
\(186\) | −6.40166 | −0.469392 | ||||||||
\(187\) | 0.507918 | 0.0371427 | ||||||||
\(188\) | 1.71297 | 0.124931 | ||||||||
\(189\) | −1.31404 | −0.0955823 | ||||||||
\(190\) | −15.1668 | −1.10032 | ||||||||
\(191\) | −1.18311 | −0.0856068 | −0.0428034 | − | 0.999084i | \(-0.513629\pi\) | ||||
−0.0428034 | + | 0.999084i | \(0.513629\pi\) | |||||||
\(192\) | −8.58889 | −0.619850 | ||||||||
\(193\) | −10.8098 | −0.778105 | −0.389052 | − | 0.921216i | \(-0.627197\pi\) | ||||
−0.389052 | + | 0.921216i | \(0.627197\pi\) | |||||||
\(194\) | −20.5625 | −1.47630 | ||||||||
\(195\) | 1.77320 | 0.126982 | ||||||||
\(196\) | 0.958486 | 0.0684633 | ||||||||
\(197\) | −16.6180 | −1.18398 | −0.591990 | − | 0.805945i | \(-0.701658\pi\) | ||||
−0.591990 | + | 0.805945i | \(0.701658\pi\) | |||||||
\(198\) | −1.93743 | −0.137687 | ||||||||
\(199\) | −6.93656 | −0.491719 | −0.245860 | − | 0.969305i | \(-0.579070\pi\) | ||||
−0.245860 | + | 0.969305i | \(0.579070\pi\) | |||||||
\(200\) | 5.45952 | 0.386046 | ||||||||
\(201\) | 10.5644 | 0.745154 | ||||||||
\(202\) | −13.3413 | −0.938692 | ||||||||
\(203\) | 10.8552 | 0.761888 | ||||||||
\(204\) | −0.0642537 | −0.00449866 | ||||||||
\(205\) | −0.540863 | −0.0377755 | ||||||||
\(206\) | 1.34842 | 0.0939489 | ||||||||
\(207\) | 3.44161 | 0.239208 | ||||||||
\(208\) | −3.60344 | −0.249853 | ||||||||
\(209\) | −9.11404 | −0.630432 | ||||||||
\(210\) | 3.14190 | 0.216811 | ||||||||
\(211\) | 5.71095 | 0.393158 | 0.196579 | − | 0.980488i | \(-0.437017\pi\) | ||||
0.196579 | + | 0.980488i | \(0.437017\pi\) | |||||||
\(212\) | −0.338440 | −0.0232441 | ||||||||
\(213\) | 6.44020 | 0.441275 | ||||||||
\(214\) | 4.56003 | 0.311717 | ||||||||
\(215\) | 10.6820 | 0.728504 | ||||||||
\(216\) | 2.94193 | 0.200173 | ||||||||
\(217\) | 6.23843 | 0.423493 | ||||||||
\(218\) | 16.5870 | 1.12341 | ||||||||
\(219\) | 9.96414 | 0.673314 | ||||||||
\(220\) | −0.463086 | −0.0312212 | ||||||||
\(221\) | −0.353504 | −0.0237792 | ||||||||
\(222\) | 15.2521 | 1.02366 | ||||||||
\(223\) | −7.00934 | −0.469380 | −0.234690 | − | 0.972070i | \(-0.575408\pi\) | ||||
−0.234690 | + | 0.972070i | \(0.575408\pi\) | |||||||
\(224\) | 1.34678 | 0.0899856 | ||||||||
\(225\) | −1.85576 | −0.123717 | ||||||||
\(226\) | −9.00801 | −0.599204 | ||||||||
\(227\) | −18.6169 | −1.23565 | −0.617823 | − | 0.786317i | \(-0.711985\pi\) | ||||
−0.617823 | + | 0.786317i | \(0.711985\pi\) | |||||||
\(228\) | 1.15296 | 0.0763568 | ||||||||
\(229\) | 5.28154 | 0.349014 | 0.174507 | − | 0.984656i | \(-0.444167\pi\) | ||||
0.174507 | + | 0.984656i | \(0.444167\pi\) | |||||||
\(230\) | −8.22895 | −0.542601 | ||||||||
\(231\) | 1.88803 | 0.124223 | ||||||||
\(232\) | −24.3032 | −1.59558 | ||||||||
\(233\) | −17.9516 | −1.17605 | −0.588023 | − | 0.808844i | \(-0.700094\pi\) | ||||
−0.588023 | + | 0.808844i | \(0.700094\pi\) | |||||||
\(234\) | 1.34842 | 0.0881490 | ||||||||
\(235\) | 16.7111 | 1.09011 | ||||||||
\(236\) | 1.60811 | 0.104679 | ||||||||
\(237\) | −16.5936 | −1.07787 | ||||||||
\(238\) | −0.626366 | −0.0406013 | ||||||||
\(239\) | 14.9158 | 0.964825 | 0.482412 | − | 0.875944i | \(-0.339761\pi\) | ||||
0.482412 | + | 0.875944i | \(0.339761\pi\) | |||||||
\(240\) | −6.38962 | −0.412448 | ||||||||
\(241\) | 23.7612 | 1.53060 | 0.765298 | − | 0.643676i | \(-0.222592\pi\) | ||||
0.765298 | + | 0.643676i | \(0.222592\pi\) | |||||||
\(242\) | −12.0489 | −0.774533 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.92626 | −0.123316 | ||||||||
\(245\) | 9.35062 | 0.597389 | ||||||||
\(246\) | −0.411296 | −0.0262233 | ||||||||
\(247\) | 6.34324 | 0.403611 | ||||||||
\(248\) | −13.9669 | −0.886899 | ||||||||
\(249\) | 9.14531 | 0.579561 | ||||||||
\(250\) | 16.3923 | 1.03674 | ||||||||
\(251\) | −31.5128 | −1.98907 | −0.994536 | − | 0.104394i | \(-0.966710\pi\) | ||||
−0.994536 | + | 0.104394i | \(0.966710\pi\) | |||||||
\(252\) | −0.238843 | −0.0150457 | ||||||||
\(253\) | −4.94494 | −0.310886 | ||||||||
\(254\) | 13.4726 | 0.845345 | ||||||||
\(255\) | −0.626834 | −0.0392538 | ||||||||
\(256\) | −4.32517 | −0.270323 | ||||||||
\(257\) | −2.46740 | −0.153912 | −0.0769562 | − | 0.997034i | \(-0.524520\pi\) | ||||
−0.0769562 | + | 0.997034i | \(0.524520\pi\) | |||||||
\(258\) | 8.12304 | 0.505719 | ||||||||
\(259\) | −14.8633 | −0.923557 | ||||||||
\(260\) | 0.322301 | 0.0199883 | ||||||||
\(261\) | 8.26096 | 0.511341 | ||||||||
\(262\) | −22.4709 | −1.38826 | ||||||||
\(263\) | −17.3388 | −1.06915 | −0.534577 | − | 0.845120i | \(-0.679529\pi\) | ||||
−0.534577 | + | 0.845120i | \(0.679529\pi\) | |||||||
\(264\) | −4.22700 | −0.260154 | ||||||||
\(265\) | −3.30169 | −0.202821 | ||||||||
\(266\) | 11.2395 | 0.689135 | ||||||||
\(267\) | 9.98710 | 0.611201 | ||||||||
\(268\) | 1.92021 | 0.117295 | ||||||||
\(269\) | −5.56357 | −0.339217 | −0.169608 | − | 0.985512i | \(-0.554250\pi\) | ||||
−0.169608 | + | 0.985512i | \(0.554250\pi\) | |||||||
\(270\) | 2.39102 | 0.145513 | ||||||||
\(271\) | 12.1362 | 0.737223 | 0.368611 | − | 0.929584i | \(-0.379833\pi\) | ||||
0.368611 | + | 0.929584i | \(0.379833\pi\) | |||||||
\(272\) | 1.27383 | 0.0772373 | ||||||||
\(273\) | −1.31404 | −0.0795293 | ||||||||
\(274\) | −15.3445 | −0.926995 | ||||||||
\(275\) | 2.66637 | 0.160788 | ||||||||
\(276\) | 0.625554 | 0.0376539 | ||||||||
\(277\) | 14.6007 | 0.877273 | 0.438636 | − | 0.898665i | \(-0.355462\pi\) | ||||
0.438636 | + | 0.898665i | \(0.355462\pi\) | |||||||
\(278\) | 25.4844 | 1.52845 | ||||||||
\(279\) | 4.74752 | 0.284227 | ||||||||
\(280\) | 6.85487 | 0.409657 | ||||||||
\(281\) | −12.5784 | −0.750362 | −0.375181 | − | 0.926952i | \(-0.622419\pi\) | ||||
−0.375181 | + | 0.926952i | \(0.622419\pi\) | |||||||
\(282\) | 12.7078 | 0.756741 | ||||||||
\(283\) | 25.5906 | 1.52120 | 0.760601 | − | 0.649219i | \(-0.224904\pi\) | ||||
0.760601 | + | 0.649219i | \(0.224904\pi\) | |||||||
\(284\) | 1.17058 | 0.0694614 | ||||||||
\(285\) | 11.2478 | 0.666265 | ||||||||
\(286\) | −1.93743 | −0.114562 | ||||||||
\(287\) | 0.400809 | 0.0236590 | ||||||||
\(288\) | 1.02492 | 0.0603937 | ||||||||
\(289\) | −16.8750 | −0.992649 | ||||||||
\(290\) | −19.7521 | −1.15989 | ||||||||
\(291\) | 15.2494 | 0.893933 | ||||||||
\(292\) | 1.81110 | 0.105987 | ||||||||
\(293\) | −2.42378 | −0.141599 | −0.0707994 | − | 0.997491i | \(-0.522555\pi\) | ||||
−0.0707994 | + | 0.997491i | \(0.522555\pi\) | |||||||
\(294\) | 7.11062 | 0.414700 | ||||||||
\(295\) | 15.6881 | 0.913398 | ||||||||
\(296\) | 33.2765 | 1.93416 | ||||||||
\(297\) | 1.43681 | 0.0833722 | ||||||||
\(298\) | 7.73152 | 0.447875 | ||||||||
\(299\) | 3.44161 | 0.199033 | ||||||||
\(300\) | −0.337307 | −0.0194744 | ||||||||
\(301\) | −7.91593 | −0.456267 | ||||||||
\(302\) | 18.3005 | 1.05308 | ||||||||
\(303\) | 9.89403 | 0.568397 | ||||||||
\(304\) | −22.8575 | −1.31097 | ||||||||
\(305\) | −18.7919 | −1.07602 | ||||||||
\(306\) | −0.476672 | −0.0272495 | ||||||||
\(307\) | −16.8670 | −0.962648 | −0.481324 | − | 0.876543i | \(-0.659844\pi\) | ||||
−0.481324 | + | 0.876543i | \(0.659844\pi\) | |||||||
\(308\) | 0.343172 | 0.0195540 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | −11.3514 | −0.644718 | ||||||||
\(311\) | 17.9486 | 1.01777 | 0.508887 | − | 0.860833i | \(-0.330057\pi\) | ||||
0.508887 | + | 0.860833i | \(0.330057\pi\) | |||||||
\(312\) | 2.94193 | 0.166554 | ||||||||
\(313\) | 5.70949 | 0.322720 | 0.161360 | − | 0.986896i | \(-0.448412\pi\) | ||||
0.161360 | + | 0.986896i | \(0.448412\pi\) | |||||||
\(314\) | −19.4051 | −1.09509 | ||||||||
\(315\) | −2.33006 | −0.131284 | ||||||||
\(316\) | −3.01609 | −0.169668 | ||||||||
\(317\) | 21.3040 | 1.19655 | 0.598275 | − | 0.801291i | \(-0.295853\pi\) | ||||
0.598275 | + | 0.801291i | \(0.295853\pi\) | |||||||
\(318\) | −2.51075 | −0.140796 | ||||||||
\(319\) | −11.8694 | −0.664561 | ||||||||
\(320\) | −15.2298 | −0.851374 | ||||||||
\(321\) | −3.38176 | −0.188751 | ||||||||
\(322\) | 6.09811 | 0.339834 | ||||||||
\(323\) | −2.24236 | −0.124768 | ||||||||
\(324\) | −0.181762 | −0.0100979 | ||||||||
\(325\) | −1.85576 | −0.102939 | ||||||||
\(326\) | −20.5318 | −1.13715 | ||||||||
\(327\) | −12.3011 | −0.680250 | ||||||||
\(328\) | −0.897350 | −0.0495479 | ||||||||
\(329\) | −12.3838 | −0.682742 | ||||||||
\(330\) | −3.43544 | −0.189115 | ||||||||
\(331\) | 12.7165 | 0.698962 | 0.349481 | − | 0.936943i | \(-0.386358\pi\) | ||||
0.349481 | + | 0.936943i | \(0.386358\pi\) | |||||||
\(332\) | 1.66227 | 0.0912290 | ||||||||
\(333\) | −11.3111 | −0.619845 | ||||||||
\(334\) | 0.349513 | 0.0191245 | ||||||||
\(335\) | 18.7328 | 1.02348 | ||||||||
\(336\) | 4.73506 | 0.258319 | ||||||||
\(337\) | −2.85191 | −0.155354 | −0.0776768 | − | 0.996979i | \(-0.524750\pi\) | ||||
−0.0776768 | + | 0.996979i | \(0.524750\pi\) | |||||||
\(338\) | 1.34842 | 0.0733444 | ||||||||
\(339\) | 6.68042 | 0.362830 | ||||||||
\(340\) | −0.113935 | −0.00617897 | ||||||||
\(341\) | −6.82129 | −0.369394 | ||||||||
\(342\) | 8.55336 | 0.462513 | ||||||||
\(343\) | −16.1276 | −0.870809 | ||||||||
\(344\) | 17.7225 | 0.955536 | ||||||||
\(345\) | 6.10266 | 0.328556 | ||||||||
\(346\) | 5.94678 | 0.319701 | ||||||||
\(347\) | −1.96473 | −0.105472 | −0.0527362 | − | 0.998608i | \(-0.516794\pi\) | ||||
−0.0527362 | + | 0.998608i | \(0.516794\pi\) | |||||||
\(348\) | 1.50153 | 0.0804905 | ||||||||
\(349\) | −21.7614 | −1.16486 | −0.582430 | − | 0.812881i | \(-0.697898\pi\) | ||||
−0.582430 | + | 0.812881i | \(0.697898\pi\) | |||||||
\(350\) | −3.28818 | −0.175761 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −1.47261 | −0.0784904 | ||||||||
\(353\) | −25.7299 | −1.36947 | −0.684733 | − | 0.728794i | \(-0.740081\pi\) | ||||
−0.684733 | + | 0.728794i | \(0.740081\pi\) | |||||||
\(354\) | 11.9299 | 0.634070 | ||||||||
\(355\) | 11.4198 | 0.606098 | ||||||||
\(356\) | 1.81528 | 0.0962095 | ||||||||
\(357\) | 0.464518 | 0.0245849 | ||||||||
\(358\) | −10.4116 | −0.550273 | ||||||||
\(359\) | −17.6557 | −0.931831 | −0.465916 | − | 0.884829i | \(-0.654275\pi\) | ||||
−0.465916 | + | 0.884829i | \(0.654275\pi\) | |||||||
\(360\) | 5.21664 | 0.274941 | ||||||||
\(361\) | 21.2367 | 1.11772 | ||||||||
\(362\) | 3.14354 | 0.165221 | ||||||||
\(363\) | 8.93557 | 0.468996 | ||||||||
\(364\) | −0.238843 | −0.0125188 | ||||||||
\(365\) | 17.6684 | 0.924807 | ||||||||
\(366\) | −14.2902 | −0.746959 | ||||||||
\(367\) | −6.64922 | −0.347087 | −0.173543 | − | 0.984826i | \(-0.555522\pi\) | ||||
−0.173543 | + | 0.984826i | \(0.555522\pi\) | |||||||
\(368\) | −12.4016 | −0.646479 | ||||||||
\(369\) | 0.305020 | 0.0158787 | ||||||||
\(370\) | 27.0451 | 1.40601 | ||||||||
\(371\) | 2.44673 | 0.127028 | ||||||||
\(372\) | 0.862920 | 0.0447403 | ||||||||
\(373\) | −29.8702 | −1.54662 | −0.773310 | − | 0.634028i | \(-0.781400\pi\) | ||||
−0.773310 | + | 0.634028i | \(0.781400\pi\) | |||||||
\(374\) | 0.684888 | 0.0354147 | ||||||||
\(375\) | −12.1566 | −0.627766 | ||||||||
\(376\) | 27.7255 | 1.42983 | ||||||||
\(377\) | 8.26096 | 0.425461 | ||||||||
\(378\) | −1.77188 | −0.0911356 | ||||||||
\(379\) | −11.5100 | −0.591228 | −0.295614 | − | 0.955307i | \(-0.595524\pi\) | ||||
−0.295614 | + | 0.955307i | \(0.595524\pi\) | |||||||
\(380\) | 2.04443 | 0.104877 | ||||||||
\(381\) | −9.99138 | −0.511874 | ||||||||
\(382\) | −1.59533 | −0.0816242 | ||||||||
\(383\) | 0.825078 | 0.0421595 | 0.0210798 | − | 0.999778i | \(-0.493290\pi\) | ||||
0.0210798 | + | 0.999778i | \(0.493290\pi\) | |||||||
\(384\) | −9.53161 | −0.486408 | ||||||||
\(385\) | 3.34785 | 0.170622 | ||||||||
\(386\) | −14.5761 | −0.741905 | ||||||||
\(387\) | −6.02412 | −0.306223 | ||||||||
\(388\) | 2.77176 | 0.140715 | ||||||||
\(389\) | −2.98428 | −0.151309 | −0.0756546 | − | 0.997134i | \(-0.524105\pi\) | ||||
−0.0756546 | + | 0.997134i | \(0.524105\pi\) | |||||||
\(390\) | 2.39102 | 0.121074 | ||||||||
\(391\) | −1.21662 | −0.0615272 | ||||||||
\(392\) | 15.5137 | 0.783560 | ||||||||
\(393\) | 16.6646 | 0.840619 | ||||||||
\(394\) | −22.4080 | −1.12890 | ||||||||
\(395\) | −29.4238 | −1.48047 | ||||||||
\(396\) | 0.261158 | 0.0131237 | ||||||||
\(397\) | 26.6402 | 1.33704 | 0.668518 | − | 0.743696i | \(-0.266929\pi\) | ||||
0.668518 | + | 0.743696i | \(0.266929\pi\) | |||||||
\(398\) | −9.35340 | −0.468843 | ||||||||
\(399\) | −8.33528 | −0.417286 | ||||||||
\(400\) | 6.68711 | 0.334356 | ||||||||
\(401\) | 31.7548 | 1.58576 | 0.792880 | − | 0.609377i | \(-0.208580\pi\) | ||||
0.792880 | + | 0.609377i | \(0.208580\pi\) | |||||||
\(402\) | 14.2452 | 0.710488 | ||||||||
\(403\) | 4.74752 | 0.236491 | ||||||||
\(404\) | 1.79836 | 0.0894718 | ||||||||
\(405\) | −1.77320 | −0.0881111 | ||||||||
\(406\) | 14.6374 | 0.726443 | ||||||||
\(407\) | 16.2519 | 0.805578 | ||||||||
\(408\) | −1.03998 | −0.0514869 | ||||||||
\(409\) | −5.03897 | −0.249161 | −0.124581 | − | 0.992209i | \(-0.539759\pi\) | ||||
−0.124581 | + | 0.992209i | \(0.539759\pi\) | |||||||
\(410\) | −0.729310 | −0.0360181 | ||||||||
\(411\) | 11.3796 | 0.561314 | ||||||||
\(412\) | −0.181762 | −0.00895478 | ||||||||
\(413\) | −11.6258 | −0.572067 | ||||||||
\(414\) | 4.64073 | 0.228079 | ||||||||
\(415\) | 16.2165 | 0.796035 | ||||||||
\(416\) | 1.02492 | 0.0502506 | ||||||||
\(417\) | −18.8994 | −0.925509 | ||||||||
\(418\) | −12.2896 | −0.601102 | ||||||||
\(419\) | 0.565038 | 0.0276039 | 0.0138020 | − | 0.999905i | \(-0.495607\pi\) | ||||
0.0138020 | + | 0.999905i | \(0.495607\pi\) | |||||||
\(420\) | −0.423516 | −0.0206655 | ||||||||
\(421\) | 9.09856 | 0.443437 | 0.221718 | − | 0.975111i | \(-0.428833\pi\) | ||||
0.221718 | + | 0.975111i | \(0.428833\pi\) | |||||||
\(422\) | 7.70076 | 0.374867 | ||||||||
\(423\) | −9.42424 | −0.458222 | ||||||||
\(424\) | −5.47786 | −0.266028 | ||||||||
\(425\) | 0.656018 | 0.0318215 | ||||||||
\(426\) | 8.68409 | 0.420746 | ||||||||
\(427\) | 13.9258 | 0.673917 | ||||||||
\(428\) | −0.614675 | −0.0297115 | ||||||||
\(429\) | 1.43681 | 0.0693699 | ||||||||
\(430\) | 14.4038 | 0.694612 | ||||||||
\(431\) | −25.2842 | −1.21790 | −0.608950 | − | 0.793209i | \(-0.708409\pi\) | ||||
−0.608950 | + | 0.793209i | \(0.708409\pi\) | |||||||
\(432\) | 3.60344 | 0.173370 | ||||||||
\(433\) | 4.45306 | 0.214000 | 0.107000 | − | 0.994259i | \(-0.465875\pi\) | ||||
0.107000 | + | 0.994259i | \(0.465875\pi\) | |||||||
\(434\) | 8.41203 | 0.403791 | ||||||||
\(435\) | 14.6483 | 0.702334 | ||||||||
\(436\) | −2.23587 | −0.107079 | ||||||||
\(437\) | 21.8309 | 1.04432 | ||||||||
\(438\) | 13.4358 | 0.641990 | ||||||||
\(439\) | −2.51681 | −0.120121 | −0.0600605 | − | 0.998195i | \(-0.519129\pi\) | ||||
−0.0600605 | + | 0.998195i | \(0.519129\pi\) | |||||||
\(440\) | −7.49532 | −0.357326 | ||||||||
\(441\) | −5.27330 | −0.251109 | ||||||||
\(442\) | −0.476672 | −0.0226730 | ||||||||
\(443\) | −5.58524 | −0.265363 | −0.132681 | − | 0.991159i | \(-0.542359\pi\) | ||||
−0.132681 | + | 0.991159i | \(0.542359\pi\) | |||||||
\(444\) | −2.05593 | −0.0975702 | ||||||||
\(445\) | 17.7091 | 0.839494 | ||||||||
\(446\) | −9.45154 | −0.447543 | ||||||||
\(447\) | −5.73376 | −0.271198 | ||||||||
\(448\) | 11.2861 | 0.533220 | ||||||||
\(449\) | 11.3162 | 0.534045 | 0.267023 | − | 0.963690i | \(-0.413960\pi\) | ||||
0.267023 | + | 0.963690i | \(0.413960\pi\) | |||||||
\(450\) | −2.50234 | −0.117962 | ||||||||
\(451\) | −0.438257 | −0.0206367 | ||||||||
\(452\) | 1.21425 | 0.0571134 | ||||||||
\(453\) | −13.5718 | −0.637659 | ||||||||
\(454\) | −25.1034 | −1.17816 | ||||||||
\(455\) | −2.33006 | −0.109235 | ||||||||
\(456\) | 18.6614 | 0.873900 | ||||||||
\(457\) | 14.1443 | 0.661641 | 0.330820 | − | 0.943694i | \(-0.392675\pi\) | ||||
0.330820 | + | 0.943694i | \(0.392675\pi\) | |||||||
\(458\) | 7.12174 | 0.332777 | ||||||||
\(459\) | 0.353504 | 0.0165002 | ||||||||
\(460\) | 1.10923 | 0.0517182 | ||||||||
\(461\) | 40.8724 | 1.90362 | 0.951809 | − | 0.306690i | \(-0.0992216\pi\) | ||||
0.951809 | + | 0.306690i | \(0.0992216\pi\) | |||||||
\(462\) | 2.54585 | 0.118444 | ||||||||
\(463\) | −14.3494 | −0.666875 | −0.333437 | − | 0.942772i | \(-0.608209\pi\) | ||||
−0.333437 | + | 0.942772i | \(0.608209\pi\) | |||||||
\(464\) | −29.7679 | −1.38194 | ||||||||
\(465\) | 8.41831 | 0.390390 | ||||||||
\(466\) | −24.2063 | −1.12133 | ||||||||
\(467\) | 31.3137 | 1.44902 | 0.724512 | − | 0.689262i | \(-0.242065\pi\) | ||||
0.724512 | + | 0.689262i | \(0.242065\pi\) | |||||||
\(468\) | −0.181762 | −0.00840196 | ||||||||
\(469\) | −13.8820 | −0.641012 | ||||||||
\(470\) | 22.5335 | 1.03940 | ||||||||
\(471\) | 14.3910 | 0.663101 | ||||||||
\(472\) | 26.0283 | 1.19805 | ||||||||
\(473\) | 8.65552 | 0.397981 | ||||||||
\(474\) | −22.3751 | −1.02772 | ||||||||
\(475\) | −11.7715 | −0.540115 | ||||||||
\(476\) | 0.0844319 | 0.00386993 | ||||||||
\(477\) | 1.86199 | 0.0852548 | ||||||||
\(478\) | 20.1128 | 0.919938 | ||||||||
\(479\) | −20.3107 | −0.928021 | −0.464010 | − | 0.885830i | \(-0.653590\pi\) | ||||
−0.464010 | + | 0.885830i | \(0.653590\pi\) | |||||||
\(480\) | 1.81738 | 0.0829518 | ||||||||
\(481\) | −11.3111 | −0.515742 | ||||||||
\(482\) | 32.0401 | 1.45939 | ||||||||
\(483\) | −4.52241 | −0.205777 | ||||||||
\(484\) | 1.62415 | 0.0738250 | ||||||||
\(485\) | 27.0402 | 1.22783 | ||||||||
\(486\) | −1.34842 | −0.0611656 | ||||||||
\(487\) | −35.9309 | −1.62819 | −0.814093 | − | 0.580734i | \(-0.802766\pi\) | ||||
−0.814093 | + | 0.580734i | \(0.802766\pi\) | |||||||
\(488\) | −31.1777 | −1.41135 | ||||||||
\(489\) | 15.2265 | 0.688567 | ||||||||
\(490\) | 12.6086 | 0.569597 | ||||||||
\(491\) | 29.6704 | 1.33901 | 0.669504 | − | 0.742809i | \(-0.266507\pi\) | ||||
0.669504 | + | 0.742809i | \(0.266507\pi\) | |||||||
\(492\) | 0.0554412 | 0.00249948 | ||||||||
\(493\) | −2.92028 | −0.131523 | ||||||||
\(494\) | 8.55336 | 0.384834 | ||||||||
\(495\) | 2.54775 | 0.114513 | ||||||||
\(496\) | −17.1074 | −0.768145 | ||||||||
\(497\) | −8.46267 | −0.379603 | ||||||||
\(498\) | 12.3317 | 0.552598 | ||||||||
\(499\) | 23.9104 | 1.07037 | 0.535187 | − | 0.844733i | \(-0.320241\pi\) | ||||
0.535187 | + | 0.844733i | \(0.320241\pi\) | |||||||
\(500\) | −2.20962 | −0.0988171 | ||||||||
\(501\) | −0.259202 | −0.0115803 | ||||||||
\(502\) | −42.4925 | −1.89653 | ||||||||
\(503\) | 0.217861 | 0.00971395 | 0.00485698 | − | 0.999988i | \(-0.498454\pi\) | ||||
0.00485698 | + | 0.999988i | \(0.498454\pi\) | |||||||
\(504\) | −3.86582 | −0.172197 | ||||||||
\(505\) | 17.5441 | 0.780703 | ||||||||
\(506\) | −6.66785 | −0.296422 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −1.81605 | −0.0805744 | ||||||||
\(509\) | −33.0449 | −1.46469 | −0.732344 | − | 0.680934i | \(-0.761574\pi\) | ||||
−0.732344 | + | 0.680934i | \(0.761574\pi\) | |||||||
\(510\) | −0.845235 | −0.0374276 | ||||||||
\(511\) | −13.0933 | −0.579212 | ||||||||
\(512\) | −24.8954 | −1.10023 | ||||||||
\(513\) | −6.34324 | −0.280061 | ||||||||
\(514\) | −3.32710 | −0.146752 | ||||||||
\(515\) | −1.77320 | −0.0781366 | ||||||||
\(516\) | −1.09496 | −0.0482028 | ||||||||
\(517\) | 13.5409 | 0.595526 | ||||||||
\(518\) | −20.0419 | −0.880591 | ||||||||
\(519\) | −4.41019 | −0.193586 | ||||||||
\(520\) | 5.21664 | 0.228765 | ||||||||
\(521\) | 4.74664 | 0.207954 | 0.103977 | − | 0.994580i | \(-0.466843\pi\) | ||||
0.103977 | + | 0.994580i | \(0.466843\pi\) | |||||||
\(522\) | 11.1393 | 0.487552 | ||||||||
\(523\) | 18.1701 | 0.794521 | 0.397261 | − | 0.917706i | \(-0.369961\pi\) | ||||
0.397261 | + | 0.917706i | \(0.369961\pi\) | |||||||
\(524\) | 3.02900 | 0.132322 | ||||||||
\(525\) | 2.43854 | 0.106427 | ||||||||
\(526\) | −23.3799 | −1.01941 | ||||||||
\(527\) | −1.67827 | −0.0731065 | ||||||||
\(528\) | −5.17746 | −0.225320 | ||||||||
\(529\) | −11.1554 | −0.485015 | ||||||||
\(530\) | −4.45206 | −0.193385 | ||||||||
\(531\) | −8.84735 | −0.383942 | ||||||||
\(532\) | −1.51504 | −0.0656852 | ||||||||
\(533\) | 0.305020 | 0.0132119 | ||||||||
\(534\) | 13.4668 | 0.582766 | ||||||||
\(535\) | −5.99653 | −0.259253 | ||||||||
\(536\) | 31.0797 | 1.34244 | ||||||||
\(537\) | 7.72137 | 0.333202 | ||||||||
\(538\) | −7.50203 | −0.323435 | ||||||||
\(539\) | 7.57674 | 0.326353 | ||||||||
\(540\) | −0.322301 | −0.0138696 | ||||||||
\(541\) | 3.29177 | 0.141524 | 0.0707622 | − | 0.997493i | \(-0.477457\pi\) | ||||
0.0707622 | + | 0.997493i | \(0.477457\pi\) | |||||||
\(542\) | 16.3647 | 0.702925 | ||||||||
\(543\) | −2.33128 | −0.100045 | ||||||||
\(544\) | −0.362312 | −0.0155340 | ||||||||
\(545\) | −21.8123 | −0.934334 | ||||||||
\(546\) | −1.77188 | −0.0758294 | ||||||||
\(547\) | −9.36019 | −0.400213 | −0.200106 | − | 0.979774i | \(-0.564129\pi\) | ||||
−0.200106 | + | 0.979774i | \(0.564129\pi\) | |||||||
\(548\) | 2.06838 | 0.0883569 | ||||||||
\(549\) | 10.5977 | 0.452299 | ||||||||
\(550\) | 3.59539 | 0.153308 | ||||||||
\(551\) | 52.4013 | 2.23237 | ||||||||
\(552\) | 10.1250 | 0.430947 | ||||||||
\(553\) | 21.8046 | 0.927227 | ||||||||
\(554\) | 19.6879 | 0.836460 | ||||||||
\(555\) | −20.0569 | −0.851367 | ||||||||
\(556\) | −3.43520 | −0.145685 | ||||||||
\(557\) | 41.6704 | 1.76563 | 0.882816 | − | 0.469720i | \(-0.155645\pi\) | ||||
0.882816 | + | 0.469720i | \(0.155645\pi\) | |||||||
\(558\) | 6.40166 | 0.271004 | ||||||||
\(559\) | −6.02412 | −0.254793 | ||||||||
\(560\) | 8.39622 | 0.354805 | ||||||||
\(561\) | −0.507918 | −0.0214443 | ||||||||
\(562\) | −16.9609 | −0.715453 | ||||||||
\(563\) | −14.4041 | −0.607059 | −0.303529 | − | 0.952822i | \(-0.598165\pi\) | ||||
−0.303529 | + | 0.952822i | \(0.598165\pi\) | |||||||
\(564\) | −1.71297 | −0.0721291 | ||||||||
\(565\) | 11.8457 | 0.498353 | ||||||||
\(566\) | 34.5069 | 1.45043 | ||||||||
\(567\) | 1.31404 | 0.0551845 | ||||||||
\(568\) | 18.9466 | 0.794983 | ||||||||
\(569\) | −37.5701 | −1.57502 | −0.787511 | − | 0.616301i | \(-0.788631\pi\) | ||||
−0.787511 | + | 0.616301i | \(0.788631\pi\) | |||||||
\(570\) | 15.1668 | 0.635268 | ||||||||
\(571\) | −1.75827 | −0.0735811 | −0.0367906 | − | 0.999323i | \(-0.511713\pi\) | ||||
−0.0367906 | + | 0.999323i | \(0.511713\pi\) | |||||||
\(572\) | 0.261158 | 0.0109196 | ||||||||
\(573\) | 1.18311 | 0.0494251 | ||||||||
\(574\) | 0.540459 | 0.0225583 | ||||||||
\(575\) | −6.38679 | −0.266347 | ||||||||
\(576\) | 8.58889 | 0.357871 | ||||||||
\(577\) | 37.1182 | 1.54525 | 0.772626 | − | 0.634861i | \(-0.218943\pi\) | ||||
0.772626 | + | 0.634861i | \(0.218943\pi\) | |||||||
\(578\) | −22.7546 | −0.946468 | ||||||||
\(579\) | 10.8098 | 0.449239 | ||||||||
\(580\) | 2.66252 | 0.110555 | ||||||||
\(581\) | −12.0173 | −0.498562 | ||||||||
\(582\) | 20.5625 | 0.852345 | ||||||||
\(583\) | −2.67533 | −0.110801 | ||||||||
\(584\) | 29.3138 | 1.21301 | ||||||||
\(585\) | −1.77320 | −0.0733128 | ||||||||
\(586\) | −3.26827 | −0.135011 | ||||||||
\(587\) | 18.6890 | 0.771378 | 0.385689 | − | 0.922629i | \(-0.373964\pi\) | ||||
0.385689 | + | 0.922629i | \(0.373964\pi\) | |||||||
\(588\) | −0.958486 | −0.0395273 | ||||||||
\(589\) | 30.1147 | 1.24085 | ||||||||
\(590\) | 21.1542 | 0.870904 | ||||||||
\(591\) | 16.6180 | 0.683572 | ||||||||
\(592\) | 40.7589 | 1.67518 | ||||||||
\(593\) | 18.5461 | 0.761597 | 0.380798 | − | 0.924658i | \(-0.375649\pi\) | ||||
0.380798 | + | 0.924658i | \(0.375649\pi\) | |||||||
\(594\) | 1.93743 | 0.0794935 | ||||||||
\(595\) | 0.823684 | 0.0337678 | ||||||||
\(596\) | −1.04218 | −0.0426894 | ||||||||
\(597\) | 6.93656 | 0.283894 | ||||||||
\(598\) | 4.64073 | 0.189774 | ||||||||
\(599\) | −19.3460 | −0.790457 | −0.395228 | − | 0.918583i | \(-0.629335\pi\) | ||||
−0.395228 | + | 0.918583i | \(0.629335\pi\) | |||||||
\(600\) | −5.45952 | −0.222884 | ||||||||
\(601\) | 33.1614 | 1.35268 | 0.676340 | − | 0.736590i | \(-0.263565\pi\) | ||||
0.676340 | + | 0.736590i | \(0.263565\pi\) | |||||||
\(602\) | −10.6740 | −0.435040 | ||||||||
\(603\) | −10.5644 | −0.430215 | ||||||||
\(604\) | −2.46684 | −0.100374 | ||||||||
\(605\) | 15.8446 | 0.644173 | ||||||||
\(606\) | 13.3413 | 0.541954 | ||||||||
\(607\) | −13.4535 | −0.546061 | −0.273030 | − | 0.962005i | \(-0.588026\pi\) | ||||
−0.273030 | + | 0.962005i | \(0.588026\pi\) | |||||||
\(608\) | 6.50129 | 0.263662 | ||||||||
\(609\) | −10.8552 | −0.439876 | ||||||||
\(610\) | −25.3393 | −1.02596 | ||||||||
\(611\) | −9.42424 | −0.381264 | ||||||||
\(612\) | 0.0642537 | 0.00259730 | ||||||||
\(613\) | 18.0184 | 0.727757 | 0.363878 | − | 0.931446i | \(-0.381452\pi\) | ||||
0.363878 | + | 0.931446i | \(0.381452\pi\) | |||||||
\(614\) | −22.7438 | −0.917863 | ||||||||
\(615\) | 0.540863 | 0.0218097 | ||||||||
\(616\) | 5.55445 | 0.223795 | ||||||||
\(617\) | −1.45961 | −0.0587618 | −0.0293809 | − | 0.999568i | \(-0.509354\pi\) | ||||
−0.0293809 | + | 0.999568i | \(0.509354\pi\) | |||||||
\(618\) | −1.34842 | −0.0542414 | ||||||||
\(619\) | 6.70749 | 0.269597 | 0.134798 | − | 0.990873i | \(-0.456961\pi\) | ||||
0.134798 | + | 0.990873i | \(0.456961\pi\) | |||||||
\(620\) | 1.53013 | 0.0614515 | ||||||||
\(621\) | −3.44161 | −0.138107 | ||||||||
\(622\) | 24.2023 | 0.970425 | ||||||||
\(623\) | −13.1234 | −0.525780 | ||||||||
\(624\) | 3.60344 | 0.144253 | ||||||||
\(625\) | −12.2774 | −0.491095 | ||||||||
\(626\) | 7.69880 | 0.307706 | ||||||||
\(627\) | 9.11404 | 0.363980 | ||||||||
\(628\) | 2.61573 | 0.104379 | ||||||||
\(629\) | 3.99852 | 0.159432 | ||||||||
\(630\) | −3.14190 | −0.125176 | ||||||||
\(631\) | −3.18769 | −0.126900 | −0.0634499 | − | 0.997985i | \(-0.520210\pi\) | ||||
−0.0634499 | + | 0.997985i | \(0.520210\pi\) | |||||||
\(632\) | −48.8172 | −1.94184 | ||||||||
\(633\) | −5.71095 | −0.226990 | ||||||||
\(634\) | 28.7267 | 1.14088 | ||||||||
\(635\) | −17.7167 | −0.703067 | ||||||||
\(636\) | 0.338440 | 0.0134200 | ||||||||
\(637\) | −5.27330 | −0.208936 | ||||||||
\(638\) | −16.0050 | −0.633644 | ||||||||
\(639\) | −6.44020 | −0.254770 | ||||||||
\(640\) | −16.9015 | −0.668089 | ||||||||
\(641\) | −6.11866 | −0.241672 | −0.120836 | − | 0.992672i | \(-0.538558\pi\) | ||||
−0.120836 | + | 0.992672i | \(0.538558\pi\) | |||||||
\(642\) | −4.56003 | −0.179970 | ||||||||
\(643\) | 24.8607 | 0.980409 | 0.490204 | − | 0.871608i | \(-0.336922\pi\) | ||||
0.490204 | + | 0.871608i | \(0.336922\pi\) | |||||||
\(644\) | −0.822003 | −0.0323914 | ||||||||
\(645\) | −10.6820 | −0.420602 | ||||||||
\(646\) | −3.02365 | −0.118964 | ||||||||
\(647\) | −16.4576 | −0.647015 | −0.323508 | − | 0.946226i | \(-0.604862\pi\) | ||||
−0.323508 | + | 0.946226i | \(0.604862\pi\) | |||||||
\(648\) | −2.94193 | −0.115570 | ||||||||
\(649\) | 12.7120 | 0.498989 | ||||||||
\(650\) | −2.50234 | −0.0981500 | ||||||||
\(651\) | −6.23843 | −0.244504 | ||||||||
\(652\) | 2.76761 | 0.108388 | ||||||||
\(653\) | −6.31354 | −0.247068 | −0.123534 | − | 0.992340i | \(-0.539423\pi\) | ||||
−0.123534 | + | 0.992340i | \(0.539423\pi\) | |||||||
\(654\) | −16.5870 | −0.648603 | ||||||||
\(655\) | 29.5497 | 1.15460 | ||||||||
\(656\) | −1.09912 | −0.0429135 | ||||||||
\(657\) | −9.96414 | −0.388738 | ||||||||
\(658\) | −16.6986 | −0.650979 | ||||||||
\(659\) | −6.57158 | −0.255993 | −0.127996 | − | 0.991775i | \(-0.540855\pi\) | ||||
−0.127996 | + | 0.991775i | \(0.540855\pi\) | |||||||
\(660\) | 0.463086 | 0.0180256 | ||||||||
\(661\) | −20.1062 | −0.782039 | −0.391020 | − | 0.920382i | \(-0.627878\pi\) | ||||
−0.391020 | + | 0.920382i | \(0.627878\pi\) | |||||||
\(662\) | 17.1472 | 0.666445 | ||||||||
\(663\) | 0.353504 | 0.0137290 | ||||||||
\(664\) | 26.9049 | 1.04411 | ||||||||
\(665\) | −14.7801 | −0.573148 | ||||||||
\(666\) | −15.2521 | −0.591008 | ||||||||
\(667\) | 28.4310 | 1.10085 | ||||||||
\(668\) | −0.0471131 | −0.00182286 | ||||||||
\(669\) | 7.00934 | 0.270997 | ||||||||
\(670\) | 25.2597 | 0.975866 | ||||||||
\(671\) | −15.2269 | −0.587828 | ||||||||
\(672\) | −1.34678 | −0.0519532 | ||||||||
\(673\) | −31.7768 | −1.22491 | −0.612453 | − | 0.790507i | \(-0.709817\pi\) | ||||
−0.612453 | + | 0.790507i | \(0.709817\pi\) | |||||||
\(674\) | −3.84558 | −0.148126 | ||||||||
\(675\) | 1.85576 | 0.0714282 | ||||||||
\(676\) | −0.181762 | −0.00699085 | ||||||||
\(677\) | −0.668684 | −0.0256996 | −0.0128498 | − | 0.999917i | \(-0.504090\pi\) | ||||
−0.0128498 | + | 0.999917i | \(0.504090\pi\) | |||||||
\(678\) | 9.00801 | 0.345950 | ||||||||
\(679\) | −20.0383 | −0.768998 | ||||||||
\(680\) | −1.84410 | −0.0707181 | ||||||||
\(681\) | 18.6169 | 0.713401 | ||||||||
\(682\) | −9.19797 | −0.352209 | ||||||||
\(683\) | −1.05659 | −0.0404294 | −0.0202147 | − | 0.999796i | \(-0.506435\pi\) | ||||
−0.0202147 | + | 0.999796i | \(0.506435\pi\) | |||||||
\(684\) | −1.15296 | −0.0440846 | ||||||||
\(685\) | 20.1783 | 0.770974 | ||||||||
\(686\) | −21.7468 | −0.830296 | ||||||||
\(687\) | −5.28154 | −0.201503 | ||||||||
\(688\) | 21.7075 | 0.827592 | ||||||||
\(689\) | 1.86199 | 0.0709363 | ||||||||
\(690\) | 8.22895 | 0.313271 | ||||||||
\(691\) | −13.3347 | −0.507274 | −0.253637 | − | 0.967299i | \(-0.581627\pi\) | ||||
−0.253637 | + | 0.967299i | \(0.581627\pi\) | |||||||
\(692\) | −0.801605 | −0.0304724 | ||||||||
\(693\) | −1.88803 | −0.0717202 | ||||||||
\(694\) | −2.64929 | −0.100566 | ||||||||
\(695\) | −33.5125 | −1.27120 | ||||||||
\(696\) | 24.3032 | 0.921210 | ||||||||
\(697\) | −0.107826 | −0.00408420 | ||||||||
\(698\) | −29.3435 | −1.11067 | ||||||||
\(699\) | 17.9516 | 0.678991 | ||||||||
\(700\) | 0.443235 | 0.0167527 | ||||||||
\(701\) | 1.20181 | 0.0453917 | 0.0226958 | − | 0.999742i | \(-0.492775\pi\) | ||||
0.0226958 | + | 0.999742i | \(0.492775\pi\) | |||||||
\(702\) | −1.34842 | −0.0508929 | ||||||||
\(703\) | −71.7491 | −2.70607 | ||||||||
\(704\) | −12.3406 | −0.465105 | ||||||||
\(705\) | −16.7111 | −0.629375 | ||||||||
\(706\) | −34.6948 | −1.30576 | ||||||||
\(707\) | −13.0012 | −0.488959 | ||||||||
\(708\) | −1.60811 | −0.0604366 | ||||||||
\(709\) | −47.2542 | −1.77467 | −0.887335 | − | 0.461125i | \(-0.847446\pi\) | ||||
−0.887335 | + | 0.461125i | \(0.847446\pi\) | |||||||
\(710\) | 15.3986 | 0.577901 | ||||||||
\(711\) | 16.5936 | 0.622308 | ||||||||
\(712\) | 29.3814 | 1.10111 | ||||||||
\(713\) | 16.3391 | 0.611904 | ||||||||
\(714\) | 0.626366 | 0.0234412 | ||||||||
\(715\) | 2.54775 | 0.0952806 | ||||||||
\(716\) | 1.40345 | 0.0524495 | ||||||||
\(717\) | −14.9158 | −0.557042 | ||||||||
\(718\) | −23.8073 | −0.888480 | ||||||||
\(719\) | 35.8071 | 1.33538 | 0.667690 | − | 0.744439i | \(-0.267283\pi\) | ||||
0.667690 | + | 0.744439i | \(0.267283\pi\) | |||||||
\(720\) | 6.38962 | 0.238127 | ||||||||
\(721\) | 1.31404 | 0.0489374 | ||||||||
\(722\) | 28.6361 | 1.06572 | ||||||||
\(723\) | −23.7612 | −0.883690 | ||||||||
\(724\) | −0.423738 | −0.0157481 | ||||||||
\(725\) | −15.3304 | −0.569355 | ||||||||
\(726\) | 12.0489 | 0.447177 | ||||||||
\(727\) | 49.9963 | 1.85426 | 0.927130 | − | 0.374741i | \(-0.122268\pi\) | ||||
0.927130 | + | 0.374741i | \(0.122268\pi\) | |||||||
\(728\) | −3.86582 | −0.143277 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 23.8245 | 0.881783 | ||||||||
\(731\) | 2.12955 | 0.0787642 | ||||||||
\(732\) | 1.92626 | 0.0711967 | ||||||||
\(733\) | 13.2200 | 0.488290 | 0.244145 | − | 0.969739i | \(-0.421493\pi\) | ||||
0.244145 | + | 0.969739i | \(0.421493\pi\) | |||||||
\(734\) | −8.96595 | −0.330939 | ||||||||
\(735\) | −9.35062 | −0.344903 | ||||||||
\(736\) | 3.52736 | 0.130020 | ||||||||
\(737\) | 15.1790 | 0.559127 | ||||||||
\(738\) | 0.411296 | 0.0151400 | ||||||||
\(739\) | −10.7562 | −0.395674 | −0.197837 | − | 0.980235i | \(-0.563392\pi\) | ||||
−0.197837 | + | 0.980235i | \(0.563392\pi\) | |||||||
\(740\) | −3.64558 | −0.134014 | ||||||||
\(741\) | −6.34324 | −0.233025 | ||||||||
\(742\) | 3.29922 | 0.121118 | ||||||||
\(743\) | −10.3190 | −0.378569 | −0.189284 | − | 0.981922i | \(-0.560617\pi\) | ||||
−0.189284 | + | 0.981922i | \(0.560617\pi\) | |||||||
\(744\) | 13.9669 | 0.512051 | ||||||||
\(745\) | −10.1671 | −0.372494 | ||||||||
\(746\) | −40.2776 | −1.47467 | ||||||||
\(747\) | −9.14531 | −0.334609 | ||||||||
\(748\) | −0.0923204 | −0.00337557 | ||||||||
\(749\) | 4.44376 | 0.162372 | ||||||||
\(750\) | −16.3923 | −0.598561 | ||||||||
\(751\) | 1.24818 | 0.0455469 | 0.0227734 | − | 0.999741i | \(-0.492750\pi\) | ||||
0.0227734 | + | 0.999741i | \(0.492750\pi\) | |||||||
\(752\) | 33.9597 | 1.23838 | ||||||||
\(753\) | 31.5128 | 1.14839 | ||||||||
\(754\) | 11.1393 | 0.405668 | ||||||||
\(755\) | −24.0655 | −0.875835 | ||||||||
\(756\) | 0.238843 | 0.00868663 | ||||||||
\(757\) | 48.6549 | 1.76839 | 0.884196 | − | 0.467116i | \(-0.154707\pi\) | ||||
0.884196 | + | 0.467116i | \(0.154707\pi\) | |||||||
\(758\) | −15.5203 | −0.563723 | ||||||||
\(759\) | 4.94494 | 0.179490 | ||||||||
\(760\) | 33.0904 | 1.20032 | ||||||||
\(761\) | 26.1629 | 0.948405 | 0.474203 | − | 0.880416i | \(-0.342736\pi\) | ||||
0.474203 | + | 0.880416i | \(0.342736\pi\) | |||||||
\(762\) | −13.4726 | −0.488060 | ||||||||
\(763\) | 16.1641 | 0.585179 | ||||||||
\(764\) | 0.215045 | 0.00778004 | ||||||||
\(765\) | 0.626834 | 0.0226632 | ||||||||
\(766\) | 1.11255 | 0.0401982 | ||||||||
\(767\) | −8.84735 | −0.319459 | ||||||||
\(768\) | 4.32517 | 0.156071 | ||||||||
\(769\) | −11.1726 | −0.402893 | −0.201446 | − | 0.979500i | \(-0.564564\pi\) | ||||
−0.201446 | + | 0.979500i | \(0.564564\pi\) | |||||||
\(770\) | 4.51431 | 0.162684 | ||||||||
\(771\) | 2.46740 | 0.0888614 | ||||||||
\(772\) | 1.96481 | 0.0707150 | ||||||||
\(773\) | 31.2693 | 1.12468 | 0.562339 | − | 0.826907i | \(-0.309902\pi\) | ||||
0.562339 | + | 0.826907i | \(0.309902\pi\) | |||||||
\(774\) | −8.12304 | −0.291977 | ||||||||
\(775\) | −8.81026 | −0.316474 | ||||||||
\(776\) | 44.8626 | 1.61047 | ||||||||
\(777\) | 14.8633 | 0.533216 | ||||||||
\(778\) | −4.02407 | −0.144270 | ||||||||
\(779\) | 1.93482 | 0.0693221 | ||||||||
\(780\) | −0.322301 | −0.0115402 | ||||||||
\(781\) | 9.25334 | 0.331111 | ||||||||
\(782\) | −1.64052 | −0.0586648 | ||||||||
\(783\) | −8.26096 | −0.295223 | ||||||||
\(784\) | 19.0020 | 0.678643 | ||||||||
\(785\) | 25.5181 | 0.910779 | ||||||||
\(786\) | 22.4709 | 0.801511 | ||||||||
\(787\) | 32.6223 | 1.16286 | 0.581430 | − | 0.813597i | \(-0.302493\pi\) | ||||
0.581430 | + | 0.813597i | \(0.302493\pi\) | |||||||
\(788\) | 3.02052 | 0.107601 | ||||||||
\(789\) | 17.3388 | 0.617276 | ||||||||
\(790\) | −39.6756 | −1.41159 | ||||||||
\(791\) | −8.77833 | −0.312122 | ||||||||
\(792\) | 4.22700 | 0.150200 | ||||||||
\(793\) | 10.5977 | 0.376336 | ||||||||
\(794\) | 35.9223 | 1.27483 | ||||||||
\(795\) | 3.30169 | 0.117099 | ||||||||
\(796\) | 1.26080 | 0.0446880 | ||||||||
\(797\) | 20.3390 | 0.720443 | 0.360221 | − | 0.932867i | \(-0.382701\pi\) | ||||
0.360221 | + | 0.932867i | \(0.382701\pi\) | |||||||
\(798\) | −11.2395 | −0.397872 | ||||||||
\(799\) | 3.33151 | 0.117860 | ||||||||
\(800\) | −1.90200 | −0.0672457 | ||||||||
\(801\) | −9.98710 | −0.352877 | ||||||||
\(802\) | 42.8189 | 1.51199 | ||||||||
\(803\) | 14.3166 | 0.505221 | ||||||||
\(804\) | −1.92021 | −0.0677205 | ||||||||
\(805\) | −8.01914 | −0.282637 | ||||||||
\(806\) | 6.40166 | 0.225489 | ||||||||
\(807\) | 5.56357 | 0.195847 | ||||||||
\(808\) | 29.1076 | 1.02400 | ||||||||
\(809\) | 30.2112 | 1.06217 | 0.531084 | − | 0.847319i | \(-0.321785\pi\) | ||||
0.531084 | + | 0.847319i | \(0.321785\pi\) | |||||||
\(810\) | −2.39102 | −0.0840119 | ||||||||
\(811\) | 0.407187 | 0.0142983 | 0.00714913 | − | 0.999974i | \(-0.497724\pi\) | ||||
0.00714913 | + | 0.999974i | \(0.497724\pi\) | |||||||
\(812\) | −1.97307 | −0.0692412 | ||||||||
\(813\) | −12.1362 | −0.425636 | ||||||||
\(814\) | 21.9144 | 0.768101 | ||||||||
\(815\) | 26.9997 | 0.945758 | ||||||||
\(816\) | −1.27383 | −0.0445930 | ||||||||
\(817\) | −38.2124 | −1.33688 | ||||||||
\(818\) | −6.79465 | −0.237569 | ||||||||
\(819\) | 1.31404 | 0.0459163 | ||||||||
\(820\) | 0.0983084 | 0.00343308 | ||||||||
\(821\) | −48.9320 | −1.70774 | −0.853869 | − | 0.520489i | \(-0.825750\pi\) | ||||
−0.853869 | + | 0.520489i | \(0.825750\pi\) | |||||||
\(822\) | 15.3445 | 0.535201 | ||||||||
\(823\) | −16.8822 | −0.588477 | −0.294239 | − | 0.955732i | \(-0.595066\pi\) | ||||
−0.294239 | + | 0.955732i | \(0.595066\pi\) | |||||||
\(824\) | −2.94193 | −0.102487 | ||||||||
\(825\) | −2.66637 | −0.0928313 | ||||||||
\(826\) | −15.6764 | −0.545453 | ||||||||
\(827\) | −51.6212 | −1.79504 | −0.897522 | − | 0.440970i | \(-0.854635\pi\) | ||||
−0.897522 | + | 0.440970i | \(0.854635\pi\) | |||||||
\(828\) | −0.625554 | −0.0217395 | ||||||||
\(829\) | 15.6165 | 0.542384 | 0.271192 | − | 0.962525i | \(-0.412582\pi\) | ||||
0.271192 | + | 0.962525i | \(0.412582\pi\) | |||||||
\(830\) | 21.8666 | 0.759002 | ||||||||
\(831\) | −14.6007 | −0.506494 | ||||||||
\(832\) | 8.58889 | 0.297766 | ||||||||
\(833\) | 1.86413 | 0.0645883 | ||||||||
\(834\) | −25.4844 | −0.882452 | ||||||||
\(835\) | −0.459617 | −0.0159057 | ||||||||
\(836\) | 1.65659 | 0.0572943 | ||||||||
\(837\) | −4.74752 | −0.164098 | ||||||||
\(838\) | 0.761909 | 0.0263197 | ||||||||
\(839\) | −46.8734 | −1.61825 | −0.809124 | − | 0.587638i | \(-0.800058\pi\) | ||||
−0.809124 | + | 0.587638i | \(0.800058\pi\) | |||||||
\(840\) | −6.85487 | −0.236515 | ||||||||
\(841\) | 39.2435 | 1.35322 | ||||||||
\(842\) | 12.2687 | 0.422807 | ||||||||
\(843\) | 12.5784 | 0.433222 | ||||||||
\(844\) | −1.03803 | −0.0357306 | ||||||||
\(845\) | −1.77320 | −0.0610000 | ||||||||
\(846\) | −12.7078 | −0.436904 | ||||||||
\(847\) | −11.7417 | −0.403450 | ||||||||
\(848\) | −6.70957 | −0.230408 | ||||||||
\(849\) | −25.5906 | −0.878267 | ||||||||
\(850\) | 0.884588 | 0.0303411 | ||||||||
\(851\) | −38.9284 | −1.33445 | ||||||||
\(852\) | −1.17058 | −0.0401035 | ||||||||
\(853\) | −35.8127 | −1.22620 | −0.613102 | − | 0.790004i | \(-0.710078\pi\) | ||||
−0.613102 | + | 0.790004i | \(0.710078\pi\) | |||||||
\(854\) | 18.7778 | 0.642565 | ||||||||
\(855\) | −11.2478 | −0.384668 | ||||||||
\(856\) | −9.94890 | −0.340046 | ||||||||
\(857\) | −13.4408 | −0.459128 | −0.229564 | − | 0.973294i | \(-0.573730\pi\) | ||||
−0.229564 | + | 0.973294i | \(0.573730\pi\) | |||||||
\(858\) | 1.93743 | 0.0661426 | ||||||||
\(859\) | −3.72029 | −0.126935 | −0.0634674 | − | 0.997984i | \(-0.520216\pi\) | ||||
−0.0634674 | + | 0.997984i | \(0.520216\pi\) | |||||||
\(860\) | −1.94158 | −0.0662073 | ||||||||
\(861\) | −0.400809 | −0.0136595 | ||||||||
\(862\) | −34.0938 | −1.16124 | ||||||||
\(863\) | −13.8630 | −0.471901 | −0.235950 | − | 0.971765i | \(-0.575820\pi\) | ||||
−0.235950 | + | 0.971765i | \(0.575820\pi\) | |||||||
\(864\) | −1.02492 | −0.0348683 | ||||||||
\(865\) | −7.82014 | −0.265893 | ||||||||
\(866\) | 6.00459 | 0.204044 | ||||||||
\(867\) | 16.8750 | 0.573106 | ||||||||
\(868\) | −1.13391 | −0.0384875 | ||||||||
\(869\) | −23.8419 | −0.808779 | ||||||||
\(870\) | 19.7521 | 0.669660 | ||||||||
\(871\) | −10.5644 | −0.357961 | ||||||||
\(872\) | −36.1889 | −1.22551 | ||||||||
\(873\) | −15.2494 | −0.516112 | ||||||||
\(874\) | 29.4373 | 0.995731 | ||||||||
\(875\) | 15.9743 | 0.540030 | ||||||||
\(876\) | −1.81110 | −0.0611915 | ||||||||
\(877\) | 49.0616 | 1.65669 | 0.828347 | − | 0.560216i | \(-0.189282\pi\) | ||||
0.828347 | + | 0.560216i | \(0.189282\pi\) | |||||||
\(878\) | −3.39372 | −0.114533 | ||||||||
\(879\) | 2.42378 | 0.0817521 | ||||||||
\(880\) | −9.18068 | −0.309481 | ||||||||
\(881\) | 8.49791 | 0.286302 | 0.143151 | − | 0.989701i | \(-0.454277\pi\) | ||||
0.143151 | + | 0.989701i | \(0.454277\pi\) | |||||||
\(882\) | −7.11062 | −0.239427 | ||||||||
\(883\) | −17.6196 | −0.592946 | −0.296473 | − | 0.955041i | \(-0.595810\pi\) | ||||
−0.296473 | + | 0.955041i | \(0.595810\pi\) | |||||||
\(884\) | 0.0642537 | 0.00216108 | ||||||||
\(885\) | −15.6881 | −0.527351 | ||||||||
\(886\) | −7.53125 | −0.253017 | ||||||||
\(887\) | −38.3575 | −1.28792 | −0.643960 | − | 0.765059i | \(-0.722710\pi\) | ||||
−0.643960 | + | 0.765059i | \(0.722710\pi\) | |||||||
\(888\) | −33.2765 | −1.11669 | ||||||||
\(889\) | 13.1291 | 0.440335 | ||||||||
\(890\) | 23.8794 | 0.800438 | ||||||||
\(891\) | −1.43681 | −0.0481350 | ||||||||
\(892\) | 1.27403 | 0.0426578 | ||||||||
\(893\) | −59.7802 | −2.00047 | ||||||||
\(894\) | −7.73152 | −0.258581 | ||||||||
\(895\) | 13.6915 | 0.457657 | ||||||||
\(896\) | 12.5249 | 0.418428 | ||||||||
\(897\) | −3.44161 | −0.114912 | ||||||||
\(898\) | 15.2590 | 0.509200 | ||||||||
\(899\) | 39.2191 | 1.30803 | ||||||||
\(900\) | 0.337307 | 0.0112436 | ||||||||
\(901\) | −0.658222 | −0.0219285 | ||||||||
\(902\) | −0.590954 | −0.0196766 | ||||||||
\(903\) | 7.91593 | 0.263426 | ||||||||
\(904\) | 19.6533 | 0.653660 | ||||||||
\(905\) | −4.13383 | −0.137413 | ||||||||
\(906\) | −18.3005 | −0.607994 | ||||||||
\(907\) | −18.2145 | −0.604803 | −0.302401 | − | 0.953181i | \(-0.597788\pi\) | ||||
−0.302401 | + | 0.953181i | \(0.597788\pi\) | |||||||
\(908\) | 3.38385 | 0.112297 | ||||||||
\(909\) | −9.89403 | −0.328164 | ||||||||
\(910\) | −3.14190 | −0.104153 | ||||||||
\(911\) | −24.0806 | −0.797825 | −0.398913 | − | 0.916989i | \(-0.630612\pi\) | ||||
−0.398913 | + | 0.916989i | \(0.630612\pi\) | |||||||
\(912\) | 22.8575 | 0.756887 | ||||||||
\(913\) | 13.1401 | 0.434873 | ||||||||
\(914\) | 19.0724 | 0.630860 | ||||||||
\(915\) | 18.7919 | 0.621240 | ||||||||
\(916\) | −0.959984 | −0.0317188 | ||||||||
\(917\) | −21.8980 | −0.723135 | ||||||||
\(918\) | 0.476672 | 0.0157325 | ||||||||
\(919\) | 23.7210 | 0.782482 | 0.391241 | − | 0.920288i | \(-0.372046\pi\) | ||||
0.391241 | + | 0.920288i | \(0.372046\pi\) | |||||||
\(920\) | 17.9536 | 0.591913 | ||||||||
\(921\) | 16.8670 | 0.555785 | ||||||||
\(922\) | 55.1132 | 1.81506 | ||||||||
\(923\) | −6.44020 | −0.211982 | ||||||||
\(924\) | −0.343172 | −0.0112895 | ||||||||
\(925\) | 20.9907 | 0.690170 | ||||||||
\(926\) | −19.3491 | −0.635850 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 8.46679 | 0.277936 | ||||||||
\(929\) | −10.8802 | −0.356966 | −0.178483 | − | 0.983943i | \(-0.557119\pi\) | ||||
−0.178483 | + | 0.983943i | \(0.557119\pi\) | |||||||
\(930\) | 11.3514 | 0.372228 | ||||||||
\(931\) | −33.4498 | −1.09627 | ||||||||
\(932\) | 3.26292 | 0.106880 | ||||||||
\(933\) | −17.9486 | −0.587612 | ||||||||
\(934\) | 42.2240 | 1.38161 | ||||||||
\(935\) | −0.900641 | −0.0294541 | ||||||||
\(936\) | −2.94193 | −0.0961601 | ||||||||
\(937\) | −7.41462 | −0.242225 | −0.121113 | − | 0.992639i | \(-0.538646\pi\) | ||||
−0.121113 | + | 0.992639i | \(0.538646\pi\) | |||||||
\(938\) | −18.7188 | −0.611191 | ||||||||
\(939\) | −5.70949 | −0.186322 | ||||||||
\(940\) | −3.03744 | −0.0990704 | ||||||||
\(941\) | −55.1308 | −1.79721 | −0.898607 | − | 0.438755i | \(-0.855420\pi\) | ||||
−0.898607 | + | 0.438755i | \(0.855420\pi\) | |||||||
\(942\) | 19.4051 | 0.632252 | ||||||||
\(943\) | 1.04976 | 0.0341849 | ||||||||
\(944\) | 31.8809 | 1.03763 | ||||||||
\(945\) | 2.33006 | 0.0757968 | ||||||||
\(946\) | 11.6713 | 0.379466 | ||||||||
\(947\) | 42.1126 | 1.36848 | 0.684238 | − | 0.729259i | \(-0.260135\pi\) | ||||
0.684238 | + | 0.729259i | \(0.260135\pi\) | |||||||
\(948\) | 3.01609 | 0.0979579 | ||||||||
\(949\) | −9.96414 | −0.323450 | ||||||||
\(950\) | −15.8730 | −0.514987 | ||||||||
\(951\) | −21.3040 | −0.690828 | ||||||||
\(952\) | 1.36658 | 0.0442912 | ||||||||
\(953\) | −32.6027 | −1.05611 | −0.528053 | − | 0.849211i | \(-0.677078\pi\) | ||||
−0.528053 | + | 0.849211i | \(0.677078\pi\) | |||||||
\(954\) | 2.51075 | 0.0812885 | ||||||||
\(955\) | 2.09789 | 0.0678862 | ||||||||
\(956\) | −2.71113 | −0.0876843 | ||||||||
\(957\) | 11.8694 | 0.383685 | ||||||||
\(958\) | −27.3874 | −0.884847 | ||||||||
\(959\) | −14.9533 | −0.482866 | ||||||||
\(960\) | 15.2298 | 0.491541 | ||||||||
\(961\) | −8.46102 | −0.272936 | ||||||||
\(962\) | −15.2521 | −0.491749 | ||||||||
\(963\) | 3.38176 | 0.108976 | ||||||||
\(964\) | −4.31889 | −0.139102 | ||||||||
\(965\) | 19.1679 | 0.617037 | ||||||||
\(966\) | −6.09811 | −0.196203 | ||||||||
\(967\) | −44.1023 | −1.41824 | −0.709118 | − | 0.705090i | \(-0.750907\pi\) | ||||
−0.709118 | + | 0.705090i | \(0.750907\pi\) | |||||||
\(968\) | 26.2879 | 0.844924 | ||||||||
\(969\) | 2.24236 | 0.0720350 | ||||||||
\(970\) | 36.4615 | 1.17071 | ||||||||
\(971\) | −16.5951 | −0.532562 | −0.266281 | − | 0.963895i | \(-0.585795\pi\) | ||||
−0.266281 | + | 0.963895i | \(0.585795\pi\) | |||||||
\(972\) | 0.181762 | 0.00583003 | ||||||||
\(973\) | 24.8346 | 0.796161 | ||||||||
\(974\) | −48.4500 | −1.55244 | ||||||||
\(975\) | 1.85576 | 0.0594318 | ||||||||
\(976\) | −38.1882 | −1.22237 | ||||||||
\(977\) | −32.9020 | −1.05263 | −0.526313 | − | 0.850291i | \(-0.676426\pi\) | ||||
−0.526313 | + | 0.850291i | \(0.676426\pi\) | |||||||
\(978\) | 20.5318 | 0.656533 | ||||||||
\(979\) | 14.3496 | 0.458615 | ||||||||
\(980\) | −1.69959 | −0.0542914 | ||||||||
\(981\) | 12.3011 | 0.392743 | ||||||||
\(982\) | 40.0082 | 1.27671 | ||||||||
\(983\) | 53.4386 | 1.70443 | 0.852214 | − | 0.523194i | \(-0.175260\pi\) | ||||
0.852214 | + | 0.523194i | \(0.175260\pi\) | |||||||
\(984\) | 0.897350 | 0.0286065 | ||||||||
\(985\) | 29.4670 | 0.938896 | ||||||||
\(986\) | −3.93777 | −0.125404 | ||||||||
\(987\) | 12.3838 | 0.394182 | ||||||||
\(988\) | −1.15296 | −0.0366806 | ||||||||
\(989\) | −20.7326 | −0.659259 | ||||||||
\(990\) | 3.43544 | 0.109186 | ||||||||
\(991\) | −42.9357 | −1.36390 | −0.681948 | − | 0.731401i | \(-0.738867\pi\) | ||||
−0.681948 | + | 0.731401i | \(0.738867\pi\) | |||||||
\(992\) | 4.86581 | 0.154490 | ||||||||
\(993\) | −12.7165 | −0.403546 | ||||||||
\(994\) | −11.4112 | −0.361943 | ||||||||
\(995\) | 12.2999 | 0.389933 | ||||||||
\(996\) | −1.66227 | −0.0526711 | ||||||||
\(997\) | 13.8936 | 0.440016 | 0.220008 | − | 0.975498i | \(-0.429392\pi\) | ||||
0.220008 | + | 0.975498i | \(0.429392\pi\) | |||||||
\(998\) | 32.2412 | 1.02058 | ||||||||
\(999\) | 11.3111 | 0.357868 |
(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 | 4017.2.a.h.1.18 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.h.1.18 | ✓ | 25 | 1.1 | even | 1 | trivial |