Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, 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("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.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: | \(32.1876970548\) |
Analytic rank: | \(1\) |
Dimension: | \(61\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.40 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.932122 | 0.659110 | 0.329555 | − | 0.944136i | \(-0.393101\pi\) | ||||
0.329555 | + | 0.944136i | \(0.393101\pi\) | |||||||
\(3\) | −1.74033 | −1.00478 | −0.502389 | − | 0.864641i | \(-0.667546\pi\) | ||||
−0.502389 | + | 0.864641i | \(0.667546\pi\) | |||||||
\(4\) | −1.13115 | −0.565574 | ||||||||
\(5\) | 4.00156 | 1.78955 | 0.894776 | − | 0.446516i | \(-0.147335\pi\) | ||||
0.894776 | + | 0.446516i | \(0.147335\pi\) | |||||||
\(6\) | −1.62220 | −0.662260 | ||||||||
\(7\) | −2.15132 | −0.813124 | −0.406562 | − | 0.913623i | \(-0.633273\pi\) | ||||
−0.406562 | + | 0.913623i | \(0.633273\pi\) | |||||||
\(8\) | −2.91861 | −1.03189 | ||||||||
\(9\) | 0.0287417 | 0.00958056 | ||||||||
\(10\) | 3.72994 | 1.17951 | ||||||||
\(11\) | −1.10471 | −0.333081 | −0.166541 | − | 0.986035i | \(-0.553260\pi\) | ||||
−0.166541 | + | 0.986035i | \(0.553260\pi\) | |||||||
\(12\) | 1.96857 | 0.568277 | ||||||||
\(13\) | −1.13002 | −0.313412 | −0.156706 | − | 0.987645i | \(-0.550088\pi\) | ||||
−0.156706 | + | 0.987645i | \(0.550088\pi\) | |||||||
\(14\) | −2.00530 | −0.535938 | ||||||||
\(15\) | −6.96403 | −1.79810 | ||||||||
\(16\) | −0.458207 | −0.114552 | ||||||||
\(17\) | 0.641226 | 0.155520 | 0.0777601 | − | 0.996972i | \(-0.475223\pi\) | ||||
0.0777601 | + | 0.996972i | \(0.475223\pi\) | |||||||
\(18\) | 0.0267907 | 0.00631464 | ||||||||
\(19\) | 5.81681 | 1.33447 | 0.667234 | − | 0.744849i | \(-0.267478\pi\) | ||||
0.667234 | + | 0.744849i | \(0.267478\pi\) | |||||||
\(20\) | −4.52636 | −1.01212 | ||||||||
\(21\) | 3.74401 | 0.817010 | ||||||||
\(22\) | −1.02972 | −0.219537 | ||||||||
\(23\) | −0.711332 | −0.148323 | −0.0741615 | − | 0.997246i | \(-0.523628\pi\) | ||||
−0.0741615 | + | 0.997246i | \(0.523628\pi\) | |||||||
\(24\) | 5.07934 | 1.03682 | ||||||||
\(25\) | 11.0125 | 2.20249 | ||||||||
\(26\) | −1.05332 | −0.206573 | ||||||||
\(27\) | 5.17096 | 0.995153 | ||||||||
\(28\) | 2.43347 | 0.459882 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −6.49132 | −1.18515 | ||||||||
\(31\) | 4.05496 | 0.728293 | 0.364146 | − | 0.931342i | \(-0.381361\pi\) | ||||
0.364146 | + | 0.931342i | \(0.381361\pi\) | |||||||
\(32\) | 5.41012 | 0.956383 | ||||||||
\(33\) | 1.92255 | 0.334673 | ||||||||
\(34\) | 0.597701 | 0.102505 | ||||||||
\(35\) | −8.60865 | −1.45513 | ||||||||
\(36\) | −0.0325111 | −0.00541852 | ||||||||
\(37\) | −5.22581 | −0.859118 | −0.429559 | − | 0.903039i | \(-0.641331\pi\) | ||||
−0.429559 | + | 0.903039i | \(0.641331\pi\) | |||||||
\(38\) | 5.42198 | 0.879560 | ||||||||
\(39\) | 1.96661 | 0.314910 | ||||||||
\(40\) | −11.6790 | −1.84661 | ||||||||
\(41\) | −5.27988 | −0.824579 | −0.412289 | − | 0.911053i | \(-0.635271\pi\) | ||||
−0.412289 | + | 0.911053i | \(0.635271\pi\) | |||||||
\(42\) | 3.48987 | 0.538499 | ||||||||
\(43\) | 1.20920 | 0.184402 | 0.0922008 | − | 0.995740i | \(-0.470610\pi\) | ||||
0.0922008 | + | 0.995740i | \(0.470610\pi\) | |||||||
\(44\) | 1.24959 | 0.188382 | ||||||||
\(45\) | 0.115011 | 0.0171449 | ||||||||
\(46\) | −0.663049 | −0.0977612 | ||||||||
\(47\) | −3.92896 | −0.573098 | −0.286549 | − | 0.958066i | \(-0.592508\pi\) | ||||
−0.286549 | + | 0.958066i | \(0.592508\pi\) | |||||||
\(48\) | 0.797430 | 0.115099 | ||||||||
\(49\) | −2.37180 | −0.338829 | ||||||||
\(50\) | 10.2650 | 1.45169 | ||||||||
\(51\) | −1.11594 | −0.156263 | ||||||||
\(52\) | 1.27823 | 0.177258 | ||||||||
\(53\) | −9.33718 | −1.28256 | −0.641280 | − | 0.767307i | \(-0.721596\pi\) | ||||
−0.641280 | + | 0.767307i | \(0.721596\pi\) | |||||||
\(54\) | 4.81997 | 0.655915 | ||||||||
\(55\) | −4.42054 | −0.596066 | ||||||||
\(56\) | 6.27888 | 0.839051 | ||||||||
\(57\) | −10.1232 | −1.34084 | ||||||||
\(58\) | −0.932122 | −0.122394 | ||||||||
\(59\) | 8.54483 | 1.11244 | 0.556221 | − | 0.831034i | \(-0.312251\pi\) | ||||
0.556221 | + | 0.831034i | \(0.312251\pi\) | |||||||
\(60\) | 7.87735 | 1.01696 | ||||||||
\(61\) | −12.3405 | −1.58004 | −0.790018 | − | 0.613084i | \(-0.789929\pi\) | ||||
−0.790018 | + | 0.613084i | \(0.789929\pi\) | |||||||
\(62\) | 3.77972 | 0.480025 | ||||||||
\(63\) | −0.0618327 | −0.00779018 | ||||||||
\(64\) | 5.95931 | 0.744913 | ||||||||
\(65\) | −4.52186 | −0.560868 | ||||||||
\(66\) | 1.79205 | 0.220586 | ||||||||
\(67\) | −10.2367 | −1.25062 | −0.625308 | − | 0.780378i | \(-0.715027\pi\) | ||||
−0.625308 | + | 0.780378i | \(0.715027\pi\) | |||||||
\(68\) | −0.725322 | −0.0879582 | ||||||||
\(69\) | 1.23795 | 0.149032 | ||||||||
\(70\) | −8.02431 | −0.959089 | ||||||||
\(71\) | −0.482849 | −0.0573036 | −0.0286518 | − | 0.999589i | \(-0.509121\pi\) | ||||
−0.0286518 | + | 0.999589i | \(0.509121\pi\) | |||||||
\(72\) | −0.0838858 | −0.00988604 | ||||||||
\(73\) | 2.63848 | 0.308811 | 0.154405 | − | 0.988008i | \(-0.450654\pi\) | ||||
0.154405 | + | 0.988008i | \(0.450654\pi\) | |||||||
\(74\) | −4.87109 | −0.566253 | ||||||||
\(75\) | −19.1653 | −2.21302 | ||||||||
\(76\) | −6.57967 | −0.754740 | ||||||||
\(77\) | 2.37658 | 0.270836 | ||||||||
\(78\) | 1.83312 | 0.207560 | ||||||||
\(79\) | −6.08175 | −0.684251 | −0.342125 | − | 0.939654i | \(-0.611147\pi\) | ||||
−0.342125 | + | 0.939654i | \(0.611147\pi\) | |||||||
\(80\) | −1.83354 | −0.204996 | ||||||||
\(81\) | −9.08540 | −1.00949 | ||||||||
\(82\) | −4.92149 | −0.543488 | ||||||||
\(83\) | 15.9310 | 1.74866 | 0.874330 | − | 0.485333i | \(-0.161301\pi\) | ||||
0.874330 | + | 0.485333i | \(0.161301\pi\) | |||||||
\(84\) | −4.23503 | −0.462080 | ||||||||
\(85\) | 2.56590 | 0.278311 | ||||||||
\(86\) | 1.12712 | 0.121541 | ||||||||
\(87\) | 1.74033 | 0.186583 | ||||||||
\(88\) | 3.22421 | 0.343702 | ||||||||
\(89\) | −9.49288 | −1.00624 | −0.503122 | − | 0.864216i | \(-0.667815\pi\) | ||||
−0.503122 | + | 0.864216i | \(0.667815\pi\) | |||||||
\(90\) | 0.107205 | 0.0113004 | ||||||||
\(91\) | 2.43105 | 0.254843 | ||||||||
\(92\) | 0.804622 | 0.0838877 | ||||||||
\(93\) | −7.05697 | −0.731773 | ||||||||
\(94\) | −3.66228 | −0.377735 | ||||||||
\(95\) | 23.2763 | 2.38810 | ||||||||
\(96\) | −9.41538 | −0.960954 | ||||||||
\(97\) | −12.9710 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(98\) | −2.21081 | −0.223326 | ||||||||
\(99\) | −0.0317511 | −0.00319110 | ||||||||
\(100\) | −12.4567 | −1.24567 | ||||||||
\(101\) | −7.82868 | −0.778983 | −0.389492 | − | 0.921030i | \(-0.627349\pi\) | ||||
−0.389492 | + | 0.921030i | \(0.627349\pi\) | |||||||
\(102\) | −1.04020 | −0.102995 | ||||||||
\(103\) | −6.75006 | −0.665103 | −0.332551 | − | 0.943085i | \(-0.607910\pi\) | ||||
−0.332551 | + | 0.943085i | \(0.607910\pi\) | |||||||
\(104\) | 3.29810 | 0.323406 | ||||||||
\(105\) | 14.9819 | 1.46208 | ||||||||
\(106\) | −8.70339 | −0.845348 | ||||||||
\(107\) | −0.698664 | −0.0675424 | −0.0337712 | − | 0.999430i | \(-0.510752\pi\) | ||||
−0.0337712 | + | 0.999430i | \(0.510752\pi\) | |||||||
\(108\) | −5.84913 | −0.562833 | ||||||||
\(109\) | −12.5917 | −1.20607 | −0.603033 | − | 0.797716i | \(-0.706041\pi\) | ||||
−0.603033 | + | 0.797716i | \(0.706041\pi\) | |||||||
\(110\) | −4.12049 | −0.392873 | ||||||||
\(111\) | 9.09462 | 0.863223 | ||||||||
\(112\) | 0.985751 | 0.0931447 | ||||||||
\(113\) | 7.55301 | 0.710528 | 0.355264 | − | 0.934766i | \(-0.384391\pi\) | ||||
0.355264 | + | 0.934766i | \(0.384391\pi\) | |||||||
\(114\) | −9.43602 | −0.883764 | ||||||||
\(115\) | −2.84644 | −0.265432 | ||||||||
\(116\) | 1.13115 | 0.105024 | ||||||||
\(117\) | −0.0324788 | −0.00300267 | ||||||||
\(118\) | 7.96483 | 0.733222 | ||||||||
\(119\) | −1.37949 | −0.126457 | ||||||||
\(120\) | 20.3253 | 1.85544 | ||||||||
\(121\) | −9.77963 | −0.889057 | ||||||||
\(122\) | −11.5028 | −1.04142 | ||||||||
\(123\) | 9.18872 | 0.828519 | ||||||||
\(124\) | −4.58677 | −0.411904 | ||||||||
\(125\) | 24.0593 | 2.15193 | ||||||||
\(126\) | −0.0576356 | −0.00513459 | ||||||||
\(127\) | −5.78891 | −0.513683 | −0.256841 | − | 0.966454i | \(-0.582682\pi\) | ||||
−0.256841 | + | 0.966454i | \(0.582682\pi\) | |||||||
\(128\) | −5.26544 | −0.465404 | ||||||||
\(129\) | −2.10441 | −0.185283 | ||||||||
\(130\) | −4.21492 | −0.369673 | ||||||||
\(131\) | −9.86685 | −0.862071 | −0.431035 | − | 0.902335i | \(-0.641852\pi\) | ||||
−0.431035 | + | 0.902335i | \(0.641852\pi\) | |||||||
\(132\) | −2.17469 | −0.189282 | ||||||||
\(133\) | −12.5138 | −1.08509 | ||||||||
\(134\) | −9.54189 | −0.824294 | ||||||||
\(135\) | 20.6919 | 1.78088 | ||||||||
\(136\) | −1.87149 | −0.160479 | ||||||||
\(137\) | 0.368103 | 0.0314491 | 0.0157246 | − | 0.999876i | \(-0.494995\pi\) | ||||
0.0157246 | + | 0.999876i | \(0.494995\pi\) | |||||||
\(138\) | 1.15392 | 0.0982284 | ||||||||
\(139\) | −1.00000 | −0.0848189 | ||||||||
\(140\) | 9.73766 | 0.822983 | ||||||||
\(141\) | 6.83769 | 0.575837 | ||||||||
\(142\) | −0.450074 | −0.0377694 | ||||||||
\(143\) | 1.24834 | 0.104392 | ||||||||
\(144\) | −0.0131696 | −0.00109747 | ||||||||
\(145\) | −4.00156 | −0.332311 | ||||||||
\(146\) | 2.45939 | 0.203540 | ||||||||
\(147\) | 4.12772 | 0.340448 | ||||||||
\(148\) | 5.91117 | 0.485895 | ||||||||
\(149\) | −7.86801 | −0.644572 | −0.322286 | − | 0.946642i | \(-0.604451\pi\) | ||||
−0.322286 | + | 0.946642i | \(0.604451\pi\) | |||||||
\(150\) | −17.8644 | −1.45862 | ||||||||
\(151\) | 17.5929 | 1.43169 | 0.715845 | − | 0.698259i | \(-0.246042\pi\) | ||||
0.715845 | + | 0.698259i | \(0.246042\pi\) | |||||||
\(152\) | −16.9770 | −1.37702 | ||||||||
\(153\) | 0.0184299 | 0.00148997 | ||||||||
\(154\) | 2.21526 | 0.178511 | ||||||||
\(155\) | 16.2262 | 1.30332 | ||||||||
\(156\) | −2.22453 | −0.178105 | ||||||||
\(157\) | 17.3072 | 1.38127 | 0.690634 | − | 0.723204i | \(-0.257332\pi\) | ||||
0.690634 | + | 0.723204i | \(0.257332\pi\) | |||||||
\(158\) | −5.66894 | −0.450996 | ||||||||
\(159\) | 16.2497 | 1.28869 | ||||||||
\(160\) | 21.6489 | 1.71150 | ||||||||
\(161\) | 1.53031 | 0.120605 | ||||||||
\(162\) | −8.46870 | −0.665364 | ||||||||
\(163\) | 21.7632 | 1.70462 | 0.852312 | − | 0.523034i | \(-0.175200\pi\) | ||||
0.852312 | + | 0.523034i | \(0.175200\pi\) | |||||||
\(164\) | 5.97233 | 0.466360 | ||||||||
\(165\) | 7.69320 | 0.598914 | ||||||||
\(166\) | 14.8497 | 1.15256 | ||||||||
\(167\) | −6.84289 | −0.529519 | −0.264759 | − | 0.964315i | \(-0.585293\pi\) | ||||
−0.264759 | + | 0.964315i | \(0.585293\pi\) | |||||||
\(168\) | −10.9273 | −0.843061 | ||||||||
\(169\) | −11.7230 | −0.901773 | ||||||||
\(170\) | 2.39174 | 0.183438 | ||||||||
\(171\) | 0.167185 | 0.0127849 | ||||||||
\(172\) | −1.36779 | −0.104293 | ||||||||
\(173\) | −18.1776 | −1.38202 | −0.691008 | − | 0.722847i | \(-0.742833\pi\) | ||||
−0.691008 | + | 0.722847i | \(0.742833\pi\) | |||||||
\(174\) | 1.62220 | 0.122979 | ||||||||
\(175\) | −23.6914 | −1.79090 | ||||||||
\(176\) | 0.506183 | 0.0381550 | ||||||||
\(177\) | −14.8708 | −1.11776 | ||||||||
\(178\) | −8.84852 | −0.663225 | ||||||||
\(179\) | 10.3943 | 0.776904 | 0.388452 | − | 0.921469i | \(-0.373010\pi\) | ||||
0.388452 | + | 0.921469i | \(0.373010\pi\) | |||||||
\(180\) | −0.130095 | −0.00969671 | ||||||||
\(181\) | 4.53084 | 0.336775 | 0.168387 | − | 0.985721i | \(-0.446144\pi\) | ||||
0.168387 | + | 0.985721i | \(0.446144\pi\) | |||||||
\(182\) | 2.26603 | 0.167970 | ||||||||
\(183\) | 21.4765 | 1.58759 | ||||||||
\(184\) | 2.07610 | 0.153052 | ||||||||
\(185\) | −20.9114 | −1.53744 | ||||||||
\(186\) | −6.57795 | −0.482319 | ||||||||
\(187\) | −0.708366 | −0.0518009 | ||||||||
\(188\) | 4.44424 | 0.324130 | ||||||||
\(189\) | −11.1244 | −0.809183 | ||||||||
\(190\) | 21.6964 | 1.57402 | ||||||||
\(191\) | −9.57482 | −0.692810 | −0.346405 | − | 0.938085i | \(-0.612598\pi\) | ||||
−0.346405 | + | 0.938085i | \(0.612598\pi\) | |||||||
\(192\) | −10.3711 | −0.748473 | ||||||||
\(193\) | 9.45774 | 0.680783 | 0.340392 | − | 0.940284i | \(-0.389440\pi\) | ||||
0.340392 | + | 0.940284i | \(0.389440\pi\) | |||||||
\(194\) | −12.0906 | −0.868054 | ||||||||
\(195\) | 7.86952 | 0.563548 | ||||||||
\(196\) | 2.68286 | 0.191633 | ||||||||
\(197\) | 0.0556912 | 0.00396783 | 0.00198392 | − | 0.999998i | \(-0.499368\pi\) | ||||
0.00198392 | + | 0.999998i | \(0.499368\pi\) | |||||||
\(198\) | −0.0295959 | −0.00210329 | ||||||||
\(199\) | −8.82244 | −0.625407 | −0.312703 | − | 0.949851i | \(-0.601235\pi\) | ||||
−0.312703 | + | 0.949851i | \(0.601235\pi\) | |||||||
\(200\) | −32.1411 | −2.27272 | ||||||||
\(201\) | 17.8153 | 1.25659 | ||||||||
\(202\) | −7.29729 | −0.513435 | ||||||||
\(203\) | 2.15132 | 0.150993 | ||||||||
\(204\) | 1.26230 | 0.0883786 | ||||||||
\(205\) | −21.1277 | −1.47563 | ||||||||
\(206\) | −6.29188 | −0.438376 | ||||||||
\(207\) | −0.0204449 | −0.00142102 | ||||||||
\(208\) | 0.517785 | 0.0359019 | ||||||||
\(209\) | −6.42586 | −0.444486 | ||||||||
\(210\) | 13.9649 | 0.963672 | ||||||||
\(211\) | −11.0226 | −0.758825 | −0.379413 | − | 0.925228i | \(-0.623874\pi\) | ||||
−0.379413 | + | 0.925228i | \(0.623874\pi\) | |||||||
\(212\) | 10.5617 | 0.725383 | ||||||||
\(213\) | 0.840315 | 0.0575775 | ||||||||
\(214\) | −0.651240 | −0.0445179 | ||||||||
\(215\) | 4.83869 | 0.329996 | ||||||||
\(216\) | −15.0920 | −1.02688 | ||||||||
\(217\) | −8.72354 | −0.592193 | ||||||||
\(218\) | −11.7370 | −0.794930 | ||||||||
\(219\) | −4.59182 | −0.310287 | ||||||||
\(220\) | 5.00029 | 0.337120 | ||||||||
\(221\) | −0.724601 | −0.0487420 | ||||||||
\(222\) | 8.47730 | 0.568959 | ||||||||
\(223\) | −3.45379 | −0.231283 | −0.115642 | − | 0.993291i | \(-0.536892\pi\) | ||||
−0.115642 | + | 0.993291i | \(0.536892\pi\) | |||||||
\(224\) | −11.6389 | −0.777658 | ||||||||
\(225\) | 0.316517 | 0.0211011 | ||||||||
\(226\) | 7.04033 | 0.468316 | ||||||||
\(227\) | −14.8267 | −0.984081 | −0.492040 | − | 0.870572i | \(-0.663749\pi\) | ||||
−0.492040 | + | 0.870572i | \(0.663749\pi\) | |||||||
\(228\) | 11.4508 | 0.758347 | ||||||||
\(229\) | −25.5740 | −1.68998 | −0.844989 | − | 0.534783i | \(-0.820393\pi\) | ||||
−0.844989 | + | 0.534783i | \(0.820393\pi\) | |||||||
\(230\) | −2.65323 | −0.174949 | ||||||||
\(231\) | −4.13603 | −0.272131 | ||||||||
\(232\) | 2.91861 | 0.191616 | ||||||||
\(233\) | −12.2051 | −0.799582 | −0.399791 | − | 0.916606i | \(-0.630917\pi\) | ||||
−0.399791 | + | 0.916606i | \(0.630917\pi\) | |||||||
\(234\) | −0.0302742 | −0.00197909 | ||||||||
\(235\) | −15.7220 | −1.02559 | ||||||||
\(236\) | −9.66547 | −0.629169 | ||||||||
\(237\) | 10.5842 | 0.687521 | ||||||||
\(238\) | −1.28585 | −0.0833492 | ||||||||
\(239\) | −8.96006 | −0.579578 | −0.289789 | − | 0.957090i | \(-0.593585\pi\) | ||||
−0.289789 | + | 0.957090i | \(0.593585\pi\) | |||||||
\(240\) | 3.19096 | 0.205976 | ||||||||
\(241\) | 12.5515 | 0.808511 | 0.404255 | − | 0.914646i | \(-0.367531\pi\) | ||||
0.404255 | + | 0.914646i | \(0.367531\pi\) | |||||||
\(242\) | −9.11581 | −0.585986 | ||||||||
\(243\) | 0.298682 | 0.0191605 | ||||||||
\(244\) | 13.9589 | 0.893628 | ||||||||
\(245\) | −9.49091 | −0.606352 | ||||||||
\(246\) | 8.56501 | 0.546085 | ||||||||
\(247\) | −6.57313 | −0.418239 | ||||||||
\(248\) | −11.8349 | −0.751515 | ||||||||
\(249\) | −27.7252 | −1.75702 | ||||||||
\(250\) | 22.4262 | 1.41836 | ||||||||
\(251\) | −10.3939 | −0.656060 | −0.328030 | − | 0.944667i | \(-0.606385\pi\) | ||||
−0.328030 | + | 0.944667i | \(0.606385\pi\) | |||||||
\(252\) | 0.0699419 | 0.00440593 | ||||||||
\(253\) | 0.785813 | 0.0494036 | ||||||||
\(254\) | −5.39597 | −0.338573 | ||||||||
\(255\) | −4.46552 | −0.279641 | ||||||||
\(256\) | −16.8266 | −1.05167 | ||||||||
\(257\) | 10.8018 | 0.673800 | 0.336900 | − | 0.941540i | \(-0.390622\pi\) | ||||
0.336900 | + | 0.941540i | \(0.390622\pi\) | |||||||
\(258\) | −1.96156 | −0.122122 | ||||||||
\(259\) | 11.2424 | 0.698569 | ||||||||
\(260\) | 5.11489 | 0.317212 | ||||||||
\(261\) | −0.0287417 | −0.00177906 | ||||||||
\(262\) | −9.19711 | −0.568199 | ||||||||
\(263\) | 2.02945 | 0.125141 | 0.0625705 | − | 0.998041i | \(-0.480070\pi\) | ||||
0.0625705 | + | 0.998041i | \(0.480070\pi\) | |||||||
\(264\) | −5.61118 | −0.345344 | ||||||||
\(265\) | −37.3633 | −2.29521 | ||||||||
\(266\) | −11.6644 | −0.715192 | ||||||||
\(267\) | 16.5207 | 1.01105 | ||||||||
\(268\) | 11.5793 | 0.707317 | ||||||||
\(269\) | −0.426791 | −0.0260219 | −0.0130110 | − | 0.999915i | \(-0.504142\pi\) | ||||
−0.0130110 | + | 0.999915i | \(0.504142\pi\) | |||||||
\(270\) | 19.2874 | 1.17379 | ||||||||
\(271\) | 28.5499 | 1.73429 | 0.867143 | − | 0.498060i | \(-0.165954\pi\) | ||||
0.867143 | + | 0.498060i | \(0.165954\pi\) | |||||||
\(272\) | −0.293814 | −0.0178151 | ||||||||
\(273\) | −4.23082 | −0.256061 | ||||||||
\(274\) | 0.343117 | 0.0207284 | ||||||||
\(275\) | −12.1655 | −0.733610 | ||||||||
\(276\) | −1.40031 | −0.0842886 | ||||||||
\(277\) | 7.04733 | 0.423433 | 0.211716 | − | 0.977331i | \(-0.432095\pi\) | ||||
0.211716 | + | 0.977331i | \(0.432095\pi\) | |||||||
\(278\) | −0.932122 | −0.0559050 | ||||||||
\(279\) | 0.116546 | 0.00697745 | ||||||||
\(280\) | 25.1253 | 1.50152 | ||||||||
\(281\) | −10.1970 | −0.608300 | −0.304150 | − | 0.952624i | \(-0.598372\pi\) | ||||
−0.304150 | + | 0.952624i | \(0.598372\pi\) | |||||||
\(282\) | 6.37356 | 0.379540 | ||||||||
\(283\) | −17.1356 | −1.01861 | −0.509304 | − | 0.860587i | \(-0.670097\pi\) | ||||
−0.509304 | + | 0.860587i | \(0.670097\pi\) | |||||||
\(284\) | 0.546174 | 0.0324094 | ||||||||
\(285\) | −40.5084 | −2.39951 | ||||||||
\(286\) | 1.16361 | 0.0688056 | ||||||||
\(287\) | 11.3587 | 0.670485 | ||||||||
\(288\) | 0.155496 | 0.00916268 | ||||||||
\(289\) | −16.5888 | −0.975813 | ||||||||
\(290\) | −3.72994 | −0.219030 | ||||||||
\(291\) | 22.5739 | 1.32330 | ||||||||
\(292\) | −2.98451 | −0.174655 | ||||||||
\(293\) | −2.37102 | −0.138517 | −0.0692583 | − | 0.997599i | \(-0.522063\pi\) | ||||
−0.0692583 | + | 0.997599i | \(0.522063\pi\) | |||||||
\(294\) | 3.84753 | 0.224393 | ||||||||
\(295\) | 34.1926 | 1.99077 | ||||||||
\(296\) | 15.2521 | 0.886511 | ||||||||
\(297\) | −5.71239 | −0.331467 | ||||||||
\(298\) | −7.33394 | −0.424844 | ||||||||
\(299\) | 0.803823 | 0.0464863 | ||||||||
\(300\) | 21.6788 | 1.25163 | ||||||||
\(301\) | −2.60139 | −0.149941 | ||||||||
\(302\) | 16.3987 | 0.943641 | ||||||||
\(303\) | 13.6245 | 0.782706 | ||||||||
\(304\) | −2.66530 | −0.152865 | ||||||||
\(305\) | −49.3811 | −2.82756 | ||||||||
\(306\) | 0.0171789 | 0.000982054 0 | ||||||||
\(307\) | −2.97983 | −0.170068 | −0.0850341 | − | 0.996378i | \(-0.527100\pi\) | ||||
−0.0850341 | + | 0.996378i | \(0.527100\pi\) | |||||||
\(308\) | −2.68826 | −0.153178 | ||||||||
\(309\) | 11.7473 | 0.668281 | ||||||||
\(310\) | 15.1248 | 0.859030 | ||||||||
\(311\) | −25.2041 | −1.42919 | −0.714596 | − | 0.699538i | \(-0.753389\pi\) | ||||
−0.714596 | + | 0.699538i | \(0.753389\pi\) | |||||||
\(312\) | −5.73978 | −0.324951 | ||||||||
\(313\) | 11.6696 | 0.659605 | 0.329802 | − | 0.944050i | \(-0.393018\pi\) | ||||
0.329802 | + | 0.944050i | \(0.393018\pi\) | |||||||
\(314\) | 16.1325 | 0.910407 | ||||||||
\(315\) | −0.247427 | −0.0139409 | ||||||||
\(316\) | 6.87937 | 0.386995 | ||||||||
\(317\) | 13.5433 | 0.760667 | 0.380334 | − | 0.924849i | \(-0.375809\pi\) | ||||
0.380334 | + | 0.924849i | \(0.375809\pi\) | |||||||
\(318\) | 15.1467 | 0.849388 | ||||||||
\(319\) | 1.10471 | 0.0618516 | ||||||||
\(320\) | 23.8465 | 1.33306 | ||||||||
\(321\) | 1.21591 | 0.0678652 | ||||||||
\(322\) | 1.42643 | 0.0794920 | ||||||||
\(323\) | 3.72989 | 0.207537 | ||||||||
\(324\) | 10.2769 | 0.570941 | ||||||||
\(325\) | −12.4444 | −0.690289 | ||||||||
\(326\) | 20.2859 | 1.12353 | ||||||||
\(327\) | 21.9137 | 1.21183 | ||||||||
\(328\) | 15.4099 | 0.850871 | ||||||||
\(329\) | 8.45248 | 0.466000 | ||||||||
\(330\) | 7.17100 | 0.394750 | ||||||||
\(331\) | −14.1403 | −0.777219 | −0.388610 | − | 0.921402i | \(-0.627045\pi\) | ||||
−0.388610 | + | 0.921402i | \(0.627045\pi\) | |||||||
\(332\) | −18.0204 | −0.988997 | ||||||||
\(333\) | −0.150198 | −0.00823083 | ||||||||
\(334\) | −6.37841 | −0.349011 | ||||||||
\(335\) | −40.9629 | −2.23804 | ||||||||
\(336\) | −1.71553 | −0.0935899 | ||||||||
\(337\) | −0.644408 | −0.0351032 | −0.0175516 | − | 0.999846i | \(-0.505587\pi\) | ||||
−0.0175516 | + | 0.999846i | \(0.505587\pi\) | |||||||
\(338\) | −10.9273 | −0.594367 | ||||||||
\(339\) | −13.1447 | −0.713923 | ||||||||
\(340\) | −2.90242 | −0.157406 | ||||||||
\(341\) | −4.47954 | −0.242581 | ||||||||
\(342\) | 0.155837 | 0.00842668 | ||||||||
\(343\) | 20.1618 | 1.08863 | ||||||||
\(344\) | −3.52919 | −0.190281 | ||||||||
\(345\) | 4.95374 | 0.266700 | ||||||||
\(346\) | −16.9437 | −0.910900 | ||||||||
\(347\) | −5.27509 | −0.283182 | −0.141591 | − | 0.989925i | \(-0.545222\pi\) | ||||
−0.141591 | + | 0.989925i | \(0.545222\pi\) | |||||||
\(348\) | −1.96857 | −0.105526 | ||||||||
\(349\) | −30.0555 | −1.60883 | −0.804417 | − | 0.594065i | \(-0.797522\pi\) | ||||
−0.804417 | + | 0.594065i | \(0.797522\pi\) | |||||||
\(350\) | −22.0833 | −1.18040 | ||||||||
\(351\) | −5.84332 | −0.311893 | ||||||||
\(352\) | −5.97659 | −0.318553 | ||||||||
\(353\) | −5.09939 | −0.271413 | −0.135707 | − | 0.990749i | \(-0.543330\pi\) | ||||
−0.135707 | + | 0.990749i | \(0.543330\pi\) | |||||||
\(354\) | −13.8614 | −0.736726 | ||||||||
\(355\) | −1.93215 | −0.102548 | ||||||||
\(356\) | 10.7379 | 0.569105 | ||||||||
\(357\) | 2.40076 | 0.127062 | ||||||||
\(358\) | 9.68873 | 0.512065 | ||||||||
\(359\) | −6.83839 | −0.360916 | −0.180458 | − | 0.983583i | \(-0.557758\pi\) | ||||
−0.180458 | + | 0.983583i | \(0.557758\pi\) | |||||||
\(360\) | −0.335674 | −0.0176916 | ||||||||
\(361\) | 14.8353 | 0.780803 | ||||||||
\(362\) | 4.22329 | 0.221971 | ||||||||
\(363\) | 17.0198 | 0.893306 | ||||||||
\(364\) | −2.74988 | −0.144133 | ||||||||
\(365\) | 10.5580 | 0.552633 | ||||||||
\(366\) | 20.0187 | 1.04639 | ||||||||
\(367\) | 14.6652 | 0.765519 | 0.382759 | − | 0.923848i | \(-0.374974\pi\) | ||||
0.382759 | + | 0.923848i | \(0.374974\pi\) | |||||||
\(368\) | 0.325937 | 0.0169907 | ||||||||
\(369\) | −0.151753 | −0.00789992 | ||||||||
\(370\) | −19.4920 | −1.01334 | ||||||||
\(371\) | 20.0873 | 1.04288 | ||||||||
\(372\) | 7.98248 | 0.413872 | ||||||||
\(373\) | 22.5622 | 1.16823 | 0.584114 | − | 0.811671i | \(-0.301442\pi\) | ||||
0.584114 | + | 0.811671i | \(0.301442\pi\) | |||||||
\(374\) | −0.660284 | −0.0341425 | ||||||||
\(375\) | −41.8710 | −2.16221 | ||||||||
\(376\) | 11.4671 | 0.591372 | ||||||||
\(377\) | 1.13002 | 0.0581992 | ||||||||
\(378\) | −10.3693 | −0.533340 | ||||||||
\(379\) | 0.139131 | 0.00714670 | 0.00357335 | − | 0.999994i | \(-0.498863\pi\) | ||||
0.00357335 | + | 0.999994i | \(0.498863\pi\) | |||||||
\(380\) | −26.3289 | −1.35065 | ||||||||
\(381\) | 10.0746 | 0.516138 | ||||||||
\(382\) | −8.92490 | −0.456638 | ||||||||
\(383\) | 22.1460 | 1.13161 | 0.565804 | − | 0.824540i | \(-0.308566\pi\) | ||||
0.565804 | + | 0.824540i | \(0.308566\pi\) | |||||||
\(384\) | 9.16359 | 0.467628 | ||||||||
\(385\) | 9.51002 | 0.484676 | ||||||||
\(386\) | 8.81577 | 0.448711 | ||||||||
\(387\) | 0.0347545 | 0.00176667 | ||||||||
\(388\) | 14.6722 | 0.744867 | ||||||||
\(389\) | 21.9416 | 1.11248 | 0.556241 | − | 0.831021i | \(-0.312243\pi\) | ||||
0.556241 | + | 0.831021i | \(0.312243\pi\) | |||||||
\(390\) | 7.33535 | 0.371440 | ||||||||
\(391\) | −0.456125 | −0.0230672 | ||||||||
\(392\) | 6.92237 | 0.349633 | ||||||||
\(393\) | 17.1716 | 0.866191 | ||||||||
\(394\) | 0.0519110 | 0.00261524 | ||||||||
\(395\) | −24.3365 | −1.22450 | ||||||||
\(396\) | 0.0359152 | 0.00180481 | ||||||||
\(397\) | 18.1890 | 0.912882 | 0.456441 | − | 0.889754i | \(-0.349124\pi\) | ||||
0.456441 | + | 0.889754i | \(0.349124\pi\) | |||||||
\(398\) | −8.22360 | −0.412212 | ||||||||
\(399\) | 21.7782 | 1.09027 | ||||||||
\(400\) | −5.04599 | −0.252299 | ||||||||
\(401\) | 8.95242 | 0.447062 | 0.223531 | − | 0.974697i | \(-0.428242\pi\) | ||||
0.223531 | + | 0.974697i | \(0.428242\pi\) | |||||||
\(402\) | 16.6060 | 0.828233 | ||||||||
\(403\) | −4.58221 | −0.228256 | ||||||||
\(404\) | 8.85540 | 0.440573 | ||||||||
\(405\) | −36.3558 | −1.80653 | ||||||||
\(406\) | 2.00530 | 0.0995212 | ||||||||
\(407\) | 5.77298 | 0.286156 | ||||||||
\(408\) | 3.25701 | 0.161246 | ||||||||
\(409\) | −22.9374 | −1.13418 | −0.567090 | − | 0.823656i | \(-0.691931\pi\) | ||||
−0.567090 | + | 0.823656i | \(0.691931\pi\) | |||||||
\(410\) | −19.6936 | −0.972600 | ||||||||
\(411\) | −0.640620 | −0.0315994 | ||||||||
\(412\) | 7.63532 | 0.376165 | ||||||||
\(413\) | −18.3827 | −0.904554 | ||||||||
\(414\) | −0.0190571 | −0.000936607 0 | ||||||||
\(415\) | 63.7490 | 3.12932 | ||||||||
\(416\) | −6.11357 | −0.299742 | ||||||||
\(417\) | 1.74033 | 0.0852242 | ||||||||
\(418\) | −5.98968 | −0.292965 | ||||||||
\(419\) | −22.2129 | −1.08517 | −0.542585 | − | 0.840001i | \(-0.682554\pi\) | ||||
−0.542585 | + | 0.840001i | \(0.682554\pi\) | |||||||
\(420\) | −16.9467 | −0.826916 | ||||||||
\(421\) | 15.1352 | 0.737643 | 0.368821 | − | 0.929500i | \(-0.379761\pi\) | ||||
0.368821 | + | 0.929500i | \(0.379761\pi\) | |||||||
\(422\) | −10.2744 | −0.500149 | ||||||||
\(423\) | −0.112925 | −0.00549060 | ||||||||
\(424\) | 27.2516 | 1.32345 | ||||||||
\(425\) | 7.06149 | 0.342532 | ||||||||
\(426\) | 0.783277 | 0.0379499 | ||||||||
\(427\) | 26.5484 | 1.28477 | ||||||||
\(428\) | 0.790293 | 0.0382003 | ||||||||
\(429\) | −2.17253 | −0.104891 | ||||||||
\(430\) | 4.51025 | 0.217504 | ||||||||
\(431\) | 2.95172 | 0.142179 | 0.0710897 | − | 0.997470i | \(-0.477352\pi\) | ||||
0.0710897 | + | 0.997470i | \(0.477352\pi\) | |||||||
\(432\) | −2.36937 | −0.113996 | ||||||||
\(433\) | −18.7423 | −0.900698 | −0.450349 | − | 0.892853i | \(-0.648700\pi\) | ||||
−0.450349 | + | 0.892853i | \(0.648700\pi\) | |||||||
\(434\) | −8.13141 | −0.390320 | ||||||||
\(435\) | 6.96403 | 0.333899 | ||||||||
\(436\) | 14.2431 | 0.682120 | ||||||||
\(437\) | −4.13768 | −0.197932 | ||||||||
\(438\) | −4.28014 | −0.204513 | ||||||||
\(439\) | −14.5131 | −0.692671 | −0.346335 | − | 0.938111i | \(-0.612574\pi\) | ||||
−0.346335 | + | 0.938111i | \(0.612574\pi\) | |||||||
\(440\) | 12.9019 | 0.615072 | ||||||||
\(441\) | −0.0681696 | −0.00324617 | ||||||||
\(442\) | −0.675417 | −0.0321263 | ||||||||
\(443\) | −8.46908 | −0.402378 | −0.201189 | − | 0.979552i | \(-0.564481\pi\) | ||||
−0.201189 | + | 0.979552i | \(0.564481\pi\) | |||||||
\(444\) | −10.2874 | −0.488217 | ||||||||
\(445\) | −37.9863 | −1.80072 | ||||||||
\(446\) | −3.21936 | −0.152441 | ||||||||
\(447\) | 13.6929 | 0.647652 | ||||||||
\(448\) | −12.8204 | −0.605707 | ||||||||
\(449\) | 11.3371 | 0.535031 | 0.267515 | − | 0.963554i | \(-0.413797\pi\) | ||||
0.267515 | + | 0.963554i | \(0.413797\pi\) | |||||||
\(450\) | 0.295032 | 0.0139080 | ||||||||
\(451\) | 5.83271 | 0.274652 | ||||||||
\(452\) | −8.54358 | −0.401856 | ||||||||
\(453\) | −30.6174 | −1.43853 | ||||||||
\(454\) | −13.8203 | −0.648617 | ||||||||
\(455\) | 9.72799 | 0.456055 | ||||||||
\(456\) | 29.5456 | 1.38360 | ||||||||
\(457\) | 9.56474 | 0.447420 | 0.223710 | − | 0.974656i | \(-0.428183\pi\) | ||||
0.223710 | + | 0.974656i | \(0.428183\pi\) | |||||||
\(458\) | −23.8381 | −1.11388 | ||||||||
\(459\) | 3.31576 | 0.154766 | ||||||||
\(460\) | 3.21974 | 0.150121 | ||||||||
\(461\) | 7.30349 | 0.340158 | 0.170079 | − | 0.985430i | \(-0.445598\pi\) | ||||
0.170079 | + | 0.985430i | \(0.445598\pi\) | |||||||
\(462\) | −3.85528 | −0.179364 | ||||||||
\(463\) | −7.18072 | −0.333716 | −0.166858 | − | 0.985981i | \(-0.553362\pi\) | ||||
−0.166858 | + | 0.985981i | \(0.553362\pi\) | |||||||
\(464\) | 0.458207 | 0.0212717 | ||||||||
\(465\) | −28.2389 | −1.30955 | ||||||||
\(466\) | −11.3766 | −0.527012 | ||||||||
\(467\) | −21.3523 | −0.988067 | −0.494033 | − | 0.869443i | \(-0.664478\pi\) | ||||
−0.494033 | + | 0.869443i | \(0.664478\pi\) | |||||||
\(468\) | 0.0367383 | 0.00169823 | ||||||||
\(469\) | 22.0225 | 1.01691 | ||||||||
\(470\) | −14.6548 | −0.675976 | ||||||||
\(471\) | −30.1203 | −1.38787 | ||||||||
\(472\) | −24.9391 | −1.14791 | ||||||||
\(473\) | −1.33581 | −0.0614207 | ||||||||
\(474\) | 9.86581 | 0.453152 | ||||||||
\(475\) | 64.0574 | 2.93916 | ||||||||
\(476\) | 1.56040 | 0.0715210 | ||||||||
\(477\) | −0.268366 | −0.0122876 | ||||||||
\(478\) | −8.35187 | −0.382006 | ||||||||
\(479\) | 6.88264 | 0.314476 | 0.157238 | − | 0.987561i | \(-0.449741\pi\) | ||||
0.157238 | + | 0.987561i | \(0.449741\pi\) | |||||||
\(480\) | −37.6762 | −1.71968 | ||||||||
\(481\) | 5.90529 | 0.269258 | ||||||||
\(482\) | 11.6995 | 0.532897 | ||||||||
\(483\) | −2.66324 | −0.121181 | ||||||||
\(484\) | 11.0622 | 0.502828 | ||||||||
\(485\) | −51.9044 | −2.35686 | ||||||||
\(486\) | 0.278408 | 0.0126288 | ||||||||
\(487\) | 7.44550 | 0.337388 | 0.168694 | − | 0.985668i | \(-0.446045\pi\) | ||||
0.168694 | + | 0.985668i | \(0.446045\pi\) | |||||||
\(488\) | 36.0171 | 1.63042 | ||||||||
\(489\) | −37.8751 | −1.71277 | ||||||||
\(490\) | −8.84669 | −0.399653 | ||||||||
\(491\) | 9.05789 | 0.408777 | 0.204389 | − | 0.978890i | \(-0.434479\pi\) | ||||
0.204389 | + | 0.978890i | \(0.434479\pi\) | |||||||
\(492\) | −10.3938 | −0.468589 | ||||||||
\(493\) | −0.641226 | −0.0288794 | ||||||||
\(494\) | −6.12696 | −0.275665 | ||||||||
\(495\) | −0.127054 | −0.00571064 | ||||||||
\(496\) | −1.85801 | −0.0834272 | ||||||||
\(497\) | 1.03876 | 0.0465950 | ||||||||
\(498\) | −25.8433 | −1.15807 | ||||||||
\(499\) | 6.32078 | 0.282957 | 0.141478 | − | 0.989941i | \(-0.454814\pi\) | ||||
0.141478 | + | 0.989941i | \(0.454814\pi\) | |||||||
\(500\) | −27.2146 | −1.21707 | ||||||||
\(501\) | 11.9089 | 0.532049 | ||||||||
\(502\) | −9.68843 | −0.432416 | ||||||||
\(503\) | −4.52009 | −0.201541 | −0.100770 | − | 0.994910i | \(-0.532131\pi\) | ||||
−0.100770 | + | 0.994910i | \(0.532131\pi\) | |||||||
\(504\) | 0.180466 | 0.00803858 | ||||||||
\(505\) | −31.3269 | −1.39403 | ||||||||
\(506\) | 0.732473 | 0.0325624 | ||||||||
\(507\) | 20.4019 | 0.906082 | ||||||||
\(508\) | 6.54812 | 0.290526 | ||||||||
\(509\) | 20.5404 | 0.910436 | 0.455218 | − | 0.890380i | \(-0.349561\pi\) | ||||
0.455218 | + | 0.890380i | \(0.349561\pi\) | |||||||
\(510\) | −4.16241 | −0.184314 | ||||||||
\(511\) | −5.67623 | −0.251102 | ||||||||
\(512\) | −5.15361 | −0.227760 | ||||||||
\(513\) | 30.0785 | 1.32800 | ||||||||
\(514\) | 10.0686 | 0.444108 | ||||||||
\(515\) | −27.0108 | −1.19024 | ||||||||
\(516\) | 2.38040 | 0.104791 | ||||||||
\(517\) | 4.34035 | 0.190888 | ||||||||
\(518\) | 10.4793 | 0.460434 | ||||||||
\(519\) | 31.6349 | 1.38862 | ||||||||
\(520\) | 13.1976 | 0.578751 | ||||||||
\(521\) | 16.2114 | 0.710234 | 0.355117 | − | 0.934822i | \(-0.384441\pi\) | ||||
0.355117 | + | 0.934822i | \(0.384441\pi\) | |||||||
\(522\) | −0.0267907 | −0.00117260 | ||||||||
\(523\) | 7.64964 | 0.334495 | 0.167248 | − | 0.985915i | \(-0.446512\pi\) | ||||
0.167248 | + | 0.985915i | \(0.446512\pi\) | |||||||
\(524\) | 11.1609 | 0.487565 | ||||||||
\(525\) | 41.2308 | 1.79946 | ||||||||
\(526\) | 1.89169 | 0.0824817 | ||||||||
\(527\) | 2.60015 | 0.113264 | ||||||||
\(528\) | −0.880925 | −0.0383373 | ||||||||
\(529\) | −22.4940 | −0.978000 | ||||||||
\(530\) | −34.8271 | −1.51279 | ||||||||
\(531\) | 0.245593 | 0.0106578 | ||||||||
\(532\) | 14.1550 | 0.613698 | ||||||||
\(533\) | 5.96639 | 0.258433 | ||||||||
\(534\) | 15.3993 | 0.666394 | ||||||||
\(535\) | −2.79575 | −0.120871 | ||||||||
\(536\) | 29.8771 | 1.29049 | ||||||||
\(537\) | −18.0894 | −0.780617 | ||||||||
\(538\) | −0.397822 | −0.0171513 | ||||||||
\(539\) | 2.62014 | 0.112858 | ||||||||
\(540\) | −23.4056 | −1.00722 | ||||||||
\(541\) | 46.0016 | 1.97776 | 0.988882 | − | 0.148705i | \(-0.0475105\pi\) | ||||
0.988882 | + | 0.148705i | \(0.0475105\pi\) | |||||||
\(542\) | 26.6120 | 1.14308 | ||||||||
\(543\) | −7.88515 | −0.338384 | ||||||||
\(544\) | 3.46911 | 0.148737 | ||||||||
\(545\) | −50.3864 | −2.15832 | ||||||||
\(546\) | −3.94364 | −0.168772 | ||||||||
\(547\) | 16.3088 | 0.697312 | 0.348656 | − | 0.937251i | \(-0.386638\pi\) | ||||
0.348656 | + | 0.937251i | \(0.386638\pi\) | |||||||
\(548\) | −0.416379 | −0.0177868 | ||||||||
\(549\) | −0.354686 | −0.0151376 | ||||||||
\(550\) | −11.3398 | −0.483529 | ||||||||
\(551\) | −5.81681 | −0.247804 | ||||||||
\(552\) | −3.61310 | −0.153784 | ||||||||
\(553\) | 13.0838 | 0.556381 | ||||||||
\(554\) | 6.56897 | 0.279089 | ||||||||
\(555\) | 36.3927 | 1.54478 | ||||||||
\(556\) | 1.13115 | 0.0479714 | ||||||||
\(557\) | −44.2058 | −1.87306 | −0.936531 | − | 0.350585i | \(-0.885983\pi\) | ||||
−0.936531 | + | 0.350585i | \(0.885983\pi\) | |||||||
\(558\) | 0.108636 | 0.00459891 | ||||||||
\(559\) | −1.36643 | −0.0577937 | ||||||||
\(560\) | 3.94454 | 0.166687 | ||||||||
\(561\) | 1.23279 | 0.0520484 | ||||||||
\(562\) | −9.50482 | −0.400937 | ||||||||
\(563\) | 19.2680 | 0.812049 | 0.406025 | − | 0.913862i | \(-0.366915\pi\) | ||||
0.406025 | + | 0.913862i | \(0.366915\pi\) | |||||||
\(564\) | −7.73444 | −0.325679 | ||||||||
\(565\) | 30.2238 | 1.27153 | ||||||||
\(566\) | −15.9725 | −0.671375 | ||||||||
\(567\) | 19.5456 | 0.820840 | ||||||||
\(568\) | 1.40925 | 0.0591308 | ||||||||
\(569\) | 11.5693 | 0.485009 | 0.242504 | − | 0.970150i | \(-0.422031\pi\) | ||||
0.242504 | + | 0.970150i | \(0.422031\pi\) | |||||||
\(570\) | −37.7588 | −1.58154 | ||||||||
\(571\) | −15.4021 | −0.644557 | −0.322279 | − | 0.946645i | \(-0.604449\pi\) | ||||
−0.322279 | + | 0.946645i | \(0.604449\pi\) | |||||||
\(572\) | −1.41206 | −0.0590413 | ||||||||
\(573\) | 16.6633 | 0.696120 | ||||||||
\(574\) | 10.5877 | 0.441923 | ||||||||
\(575\) | −7.83353 | −0.326681 | ||||||||
\(576\) | 0.171280 | 0.00713669 | ||||||||
\(577\) | −45.3665 | −1.88863 | −0.944315 | − | 0.329042i | \(-0.893274\pi\) | ||||
−0.944315 | + | 0.329042i | \(0.893274\pi\) | |||||||
\(578\) | −15.4628 | −0.643168 | ||||||||
\(579\) | −16.4596 | −0.684037 | ||||||||
\(580\) | 4.52636 | 0.187947 | ||||||||
\(581\) | −34.2728 | −1.42188 | ||||||||
\(582\) | 21.0416 | 0.872202 | ||||||||
\(583\) | 10.3148 | 0.427197 | ||||||||
\(584\) | −7.70071 | −0.318657 | ||||||||
\(585\) | −0.129966 | −0.00537342 | ||||||||
\(586\) | −2.21008 | −0.0912977 | ||||||||
\(587\) | −43.3121 | −1.78768 | −0.893842 | − | 0.448383i | \(-0.852000\pi\) | ||||
−0.893842 | + | 0.448383i | \(0.852000\pi\) | |||||||
\(588\) | −4.66906 | −0.192549 | ||||||||
\(589\) | 23.5869 | 0.971883 | ||||||||
\(590\) | 31.8717 | 1.31214 | ||||||||
\(591\) | −0.0969209 | −0.00398679 | ||||||||
\(592\) | 2.39450 | 0.0984134 | ||||||||
\(593\) | 17.8552 | 0.733227 | 0.366614 | − | 0.930373i | \(-0.380517\pi\) | ||||
0.366614 | + | 0.930373i | \(0.380517\pi\) | |||||||
\(594\) | −5.32465 | −0.218473 | ||||||||
\(595\) | −5.52009 | −0.226302 | ||||||||
\(596\) | 8.89988 | 0.364553 | ||||||||
\(597\) | 15.3539 | 0.628395 | ||||||||
\(598\) | 0.749261 | 0.0306396 | ||||||||
\(599\) | 19.9486 | 0.815079 | 0.407540 | − | 0.913188i | \(-0.366387\pi\) | ||||
0.407540 | + | 0.913188i | \(0.366387\pi\) | |||||||
\(600\) | 55.9361 | 2.28358 | ||||||||
\(601\) | 17.9018 | 0.730230 | 0.365115 | − | 0.930962i | \(-0.381030\pi\) | ||||
0.365115 | + | 0.930962i | \(0.381030\pi\) | |||||||
\(602\) | −2.42481 | −0.0988278 | ||||||||
\(603\) | −0.294221 | −0.0119816 | ||||||||
\(604\) | −19.9002 | −0.809727 | ||||||||
\(605\) | −39.1337 | −1.59101 | ||||||||
\(606\) | 12.6997 | 0.515889 | ||||||||
\(607\) | 13.6079 | 0.552327 | 0.276164 | − | 0.961111i | \(-0.410937\pi\) | ||||
0.276164 | + | 0.961111i | \(0.410937\pi\) | |||||||
\(608\) | 31.4696 | 1.27626 | ||||||||
\(609\) | −3.74401 | −0.151715 | ||||||||
\(610\) | −46.0293 | −1.86367 | ||||||||
\(611\) | 4.43983 | 0.179616 | ||||||||
\(612\) | −0.0208470 | −0.000842689 0 | ||||||||
\(613\) | −23.7023 | −0.957329 | −0.478664 | − | 0.877998i | \(-0.658879\pi\) | ||||
−0.478664 | + | 0.877998i | \(0.658879\pi\) | |||||||
\(614\) | −2.77757 | −0.112094 | ||||||||
\(615\) | 36.7692 | 1.48268 | ||||||||
\(616\) | −6.93632 | −0.279472 | ||||||||
\(617\) | 34.7167 | 1.39764 | 0.698822 | − | 0.715296i | \(-0.253708\pi\) | ||||
0.698822 | + | 0.715296i | \(0.253708\pi\) | |||||||
\(618\) | 10.9499 | 0.440471 | ||||||||
\(619\) | −38.4144 | −1.54400 | −0.772002 | − | 0.635620i | \(-0.780744\pi\) | ||||
−0.772002 | + | 0.635620i | \(0.780744\pi\) | |||||||
\(620\) | −18.3542 | −0.737123 | ||||||||
\(621\) | −3.67827 | −0.147604 | ||||||||
\(622\) | −23.4933 | −0.941994 | ||||||||
\(623\) | 20.4223 | 0.818201 | ||||||||
\(624\) | −0.901115 | −0.0360735 | ||||||||
\(625\) | 41.2122 | 1.64849 | ||||||||
\(626\) | 10.8775 | 0.434752 | ||||||||
\(627\) | 11.1831 | 0.446610 | ||||||||
\(628\) | −19.5771 | −0.781210 | ||||||||
\(629\) | −3.35093 | −0.133610 | ||||||||
\(630\) | −0.230632 | −0.00918861 | ||||||||
\(631\) | 6.36670 | 0.253454 | 0.126727 | − | 0.991938i | \(-0.459553\pi\) | ||||
0.126727 | + | 0.991938i | \(0.459553\pi\) | |||||||
\(632\) | 17.7503 | 0.706068 | ||||||||
\(633\) | 19.1829 | 0.762451 | ||||||||
\(634\) | 12.6240 | 0.501363 | ||||||||
\(635\) | −23.1647 | −0.919262 | ||||||||
\(636\) | −18.3809 | −0.728849 | ||||||||
\(637\) | 2.68020 | 0.106193 | ||||||||
\(638\) | 1.02972 | 0.0407670 | ||||||||
\(639\) | −0.0138779 | −0.000549001 0 | ||||||||
\(640\) | −21.0700 | −0.832864 | ||||||||
\(641\) | 30.7291 | 1.21373 | 0.606863 | − | 0.794806i | \(-0.292428\pi\) | ||||
0.606863 | + | 0.794806i | \(0.292428\pi\) | |||||||
\(642\) | 1.13337 | 0.0447306 | ||||||||
\(643\) | −40.0953 | −1.58120 | −0.790602 | − | 0.612330i | \(-0.790232\pi\) | ||||
−0.790602 | + | 0.612330i | \(0.790232\pi\) | |||||||
\(644\) | −1.73100 | −0.0682111 | ||||||||
\(645\) | −8.42091 | −0.331573 | ||||||||
\(646\) | 3.47671 | 0.136789 | ||||||||
\(647\) | 16.7772 | 0.659580 | 0.329790 | − | 0.944054i | \(-0.393022\pi\) | ||||
0.329790 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(648\) | 26.5168 | 1.04168 | ||||||||
\(649\) | −9.43952 | −0.370534 | ||||||||
\(650\) | −11.5997 | −0.454976 | ||||||||
\(651\) | 15.1818 | 0.595023 | ||||||||
\(652\) | −24.6174 | −0.964091 | ||||||||
\(653\) | 50.0384 | 1.95816 | 0.979078 | − | 0.203486i | \(-0.0652272\pi\) | ||||
0.979078 | + | 0.203486i | \(0.0652272\pi\) | |||||||
\(654\) | 20.4262 | 0.798729 | ||||||||
\(655\) | −39.4828 | −1.54272 | ||||||||
\(656\) | 2.41928 | 0.0944569 | ||||||||
\(657\) | 0.0758344 | 0.00295858 | ||||||||
\(658\) | 7.87874 | 0.307145 | ||||||||
\(659\) | −29.7121 | −1.15742 | −0.578709 | − | 0.815534i | \(-0.696443\pi\) | ||||
−0.578709 | + | 0.815534i | \(0.696443\pi\) | |||||||
\(660\) | −8.70215 | −0.338731 | ||||||||
\(661\) | 35.2423 | 1.37077 | 0.685384 | − | 0.728182i | \(-0.259635\pi\) | ||||
0.685384 | + | 0.728182i | \(0.259635\pi\) | |||||||
\(662\) | −13.1805 | −0.512273 | ||||||||
\(663\) | 1.26104 | 0.0489749 | ||||||||
\(664\) | −46.4965 | −1.80442 | ||||||||
\(665\) | −50.0749 | −1.94182 | ||||||||
\(666\) | −0.140003 | −0.00542502 | ||||||||
\(667\) | 0.711332 | 0.0275429 | ||||||||
\(668\) | 7.74032 | 0.299482 | ||||||||
\(669\) | 6.01073 | 0.232388 | ||||||||
\(670\) | −38.1824 | −1.47512 | ||||||||
\(671\) | 13.6326 | 0.526280 | ||||||||
\(672\) | 20.2555 | 0.781375 | ||||||||
\(673\) | 12.7537 | 0.491618 | 0.245809 | − | 0.969318i | \(-0.420946\pi\) | ||||
0.245809 | + | 0.969318i | \(0.420946\pi\) | |||||||
\(674\) | −0.600667 | −0.0231368 | ||||||||
\(675\) | 56.9451 | 2.19182 | ||||||||
\(676\) | 13.2605 | 0.510019 | ||||||||
\(677\) | −21.0530 | −0.809132 | −0.404566 | − | 0.914509i | \(-0.632577\pi\) | ||||
−0.404566 | + | 0.914509i | \(0.632577\pi\) | |||||||
\(678\) | −12.2525 | −0.470554 | ||||||||
\(679\) | 27.9049 | 1.07089 | ||||||||
\(680\) | −7.48888 | −0.287185 | ||||||||
\(681\) | 25.8033 | 0.988784 | ||||||||
\(682\) | −4.17548 | −0.159887 | ||||||||
\(683\) | 12.3201 | 0.471416 | 0.235708 | − | 0.971824i | \(-0.424259\pi\) | ||||
0.235708 | + | 0.971824i | \(0.424259\pi\) | |||||||
\(684\) | −0.189111 | −0.00723083 | ||||||||
\(685\) | 1.47298 | 0.0562799 | ||||||||
\(686\) | 18.7932 | 0.717530 | ||||||||
\(687\) | 44.5072 | 1.69805 | ||||||||
\(688\) | −0.554064 | −0.0211235 | ||||||||
\(689\) | 10.5512 | 0.401970 | ||||||||
\(690\) | 4.61749 | 0.175785 | ||||||||
\(691\) | −14.1582 | −0.538604 | −0.269302 | − | 0.963056i | \(-0.586793\pi\) | ||||
−0.269302 | + | 0.963056i | \(0.586793\pi\) | |||||||
\(692\) | 20.5615 | 0.781632 | ||||||||
\(693\) | 0.0683069 | 0.00259476 | ||||||||
\(694\) | −4.91703 | −0.186648 | ||||||||
\(695\) | −4.00156 | −0.151788 | ||||||||
\(696\) | −5.07934 | −0.192532 | ||||||||
\(697\) | −3.38560 | −0.128239 | ||||||||
\(698\) | −28.0154 | −1.06040 | ||||||||
\(699\) | 21.2409 | 0.803403 | ||||||||
\(700\) | 26.7985 | 1.01289 | ||||||||
\(701\) | 4.73015 | 0.178655 | 0.0893276 | − | 0.996002i | \(-0.471528\pi\) | ||||
0.0893276 | + | 0.996002i | \(0.471528\pi\) | |||||||
\(702\) | −5.44668 | −0.205572 | ||||||||
\(703\) | −30.3975 | −1.14646 | ||||||||
\(704\) | −6.58328 | −0.248117 | ||||||||
\(705\) | 27.3614 | 1.03049 | ||||||||
\(706\) | −4.75326 | −0.178891 | ||||||||
\(707\) | 16.8420 | 0.633410 | ||||||||
\(708\) | 16.8211 | 0.632175 | ||||||||
\(709\) | 3.71267 | 0.139432 | 0.0697161 | − | 0.997567i | \(-0.477791\pi\) | ||||
0.0697161 | + | 0.997567i | \(0.477791\pi\) | |||||||
\(710\) | −1.80100 | −0.0675903 | ||||||||
\(711\) | −0.174800 | −0.00655550 | ||||||||
\(712\) | 27.7060 | 1.03833 | ||||||||
\(713\) | −2.88443 | −0.108023 | ||||||||
\(714\) | 2.23780 | 0.0837475 | ||||||||
\(715\) | 4.99532 | 0.186814 | ||||||||
\(716\) | −11.7575 | −0.439397 | ||||||||
\(717\) | 15.5935 | 0.582348 | ||||||||
\(718\) | −6.37421 | −0.237884 | ||||||||
\(719\) | 29.5106 | 1.10056 | 0.550280 | − | 0.834980i | \(-0.314521\pi\) | ||||
0.550280 | + | 0.834980i | \(0.314521\pi\) | |||||||
\(720\) | −0.0526990 | −0.00196398 | ||||||||
\(721\) | 14.5216 | 0.540811 | ||||||||
\(722\) | 13.8283 | 0.514635 | ||||||||
\(723\) | −21.8437 | −0.812374 | ||||||||
\(724\) | −5.12505 | −0.190471 | ||||||||
\(725\) | −11.0125 | −0.408993 | ||||||||
\(726\) | 15.8645 | 0.588787 | ||||||||
\(727\) | −1.05323 | −0.0390623 | −0.0195311 | − | 0.999809i | \(-0.506217\pi\) | ||||
−0.0195311 | + | 0.999809i | \(0.506217\pi\) | |||||||
\(728\) | −7.09529 | −0.262969 | ||||||||
\(729\) | 26.7364 | 0.990237 | ||||||||
\(730\) | 9.84138 | 0.364246 | ||||||||
\(731\) | 0.775372 | 0.0286782 | ||||||||
\(732\) | −24.2931 | −0.897898 | ||||||||
\(733\) | 11.2175 | 0.414327 | 0.207163 | − | 0.978306i | \(-0.433577\pi\) | ||||
0.207163 | + | 0.978306i | \(0.433577\pi\) | |||||||
\(734\) | 13.6698 | 0.504561 | ||||||||
\(735\) | 16.5173 | 0.609250 | ||||||||
\(736\) | −3.84839 | −0.141854 | ||||||||
\(737\) | 11.3086 | 0.416557 | ||||||||
\(738\) | −0.141452 | −0.00520692 | ||||||||
\(739\) | −14.1682 | −0.521186 | −0.260593 | − | 0.965449i | \(-0.583918\pi\) | ||||
−0.260593 | + | 0.965449i | \(0.583918\pi\) | |||||||
\(740\) | 23.6539 | 0.869534 | ||||||||
\(741\) | 11.4394 | 0.420237 | ||||||||
\(742\) | 18.7238 | 0.687373 | ||||||||
\(743\) | 25.8220 | 0.947318 | 0.473659 | − | 0.880708i | \(-0.342933\pi\) | ||||
0.473659 | + | 0.880708i | \(0.342933\pi\) | |||||||
\(744\) | 20.5966 | 0.755106 | ||||||||
\(745\) | −31.4843 | −1.15350 | ||||||||
\(746\) | 21.0308 | 0.769991 | ||||||||
\(747\) | 0.457885 | 0.0167531 | ||||||||
\(748\) | 0.801267 | 0.0292972 | ||||||||
\(749\) | 1.50305 | 0.0549204 | ||||||||
\(750\) | −39.0289 | −1.42513 | ||||||||
\(751\) | −0.579153 | −0.0211336 | −0.0105668 | − | 0.999944i | \(-0.503364\pi\) | ||||
−0.0105668 | + | 0.999944i | \(0.503364\pi\) | |||||||
\(752\) | 1.80028 | 0.0656494 | ||||||||
\(753\) | 18.0889 | 0.659195 | ||||||||
\(754\) | 1.05332 | 0.0383597 | ||||||||
\(755\) | 70.3990 | 2.56208 | ||||||||
\(756\) | 12.5834 | 0.457653 | ||||||||
\(757\) | 51.1370 | 1.85861 | 0.929303 | − | 0.369318i | \(-0.120409\pi\) | ||||
0.929303 | + | 0.369318i | \(0.120409\pi\) | |||||||
\(758\) | 0.129688 | 0.00471046 | ||||||||
\(759\) | −1.36757 | −0.0496397 | ||||||||
\(760\) | −67.9345 | −2.46424 | ||||||||
\(761\) | 0.854785 | 0.0309860 | 0.0154930 | − | 0.999880i | \(-0.495068\pi\) | ||||
0.0154930 | + | 0.999880i | \(0.495068\pi\) | |||||||
\(762\) | 9.39076 | 0.340191 | ||||||||
\(763\) | 27.0888 | 0.980682 | ||||||||
\(764\) | 10.8305 | 0.391835 | ||||||||
\(765\) | 0.0737484 | 0.00266638 | ||||||||
\(766\) | 20.6428 | 0.745854 | ||||||||
\(767\) | −9.65587 | −0.348653 | ||||||||
\(768\) | 29.2839 | 1.05669 | ||||||||
\(769\) | −15.6921 | −0.565872 | −0.282936 | − | 0.959139i | \(-0.591308\pi\) | ||||
−0.282936 | + | 0.959139i | \(0.591308\pi\) | |||||||
\(770\) | 8.86450 | 0.319455 | ||||||||
\(771\) | −18.7987 | −0.677020 | ||||||||
\(772\) | −10.6981 | −0.385033 | ||||||||
\(773\) | −27.8533 | −1.00182 | −0.500908 | − | 0.865501i | \(-0.667000\pi\) | ||||
−0.500908 | + | 0.865501i | \(0.667000\pi\) | |||||||
\(774\) | 0.0323954 | 0.00116443 | ||||||||
\(775\) | 44.6552 | 1.60406 | ||||||||
\(776\) | 37.8574 | 1.35900 | ||||||||
\(777\) | −19.5655 | −0.701908 | ||||||||
\(778\) | 20.4522 | 0.733248 | ||||||||
\(779\) | −30.7120 | −1.10037 | ||||||||
\(780\) | −8.90159 | −0.318728 | ||||||||
\(781\) | 0.533406 | 0.0190868 | ||||||||
\(782\) | −0.425164 | −0.0152038 | ||||||||
\(783\) | −5.17096 | −0.184795 | ||||||||
\(784\) | 1.08678 | 0.0388134 | ||||||||
\(785\) | 69.2559 | 2.47185 | ||||||||
\(786\) | 16.0060 | 0.570915 | ||||||||
\(787\) | 36.2276 | 1.29138 | 0.645688 | − | 0.763602i | \(-0.276571\pi\) | ||||
0.645688 | + | 0.763602i | \(0.276571\pi\) | |||||||
\(788\) | −0.0629950 | −0.00224410 | ||||||||
\(789\) | −3.53190 | −0.125739 | ||||||||
\(790\) | −22.6846 | −0.807081 | ||||||||
\(791\) | −16.2490 | −0.577747 | ||||||||
\(792\) | 0.0926691 | 0.00329285 | ||||||||
\(793\) | 13.9450 | 0.495203 | ||||||||
\(794\) | 16.9544 | 0.601689 | ||||||||
\(795\) | 65.0243 | 2.30618 | ||||||||
\(796\) | 9.97949 | 0.353714 | ||||||||
\(797\) | −50.1246 | −1.77550 | −0.887752 | − | 0.460323i | \(-0.847734\pi\) | ||||
−0.887752 | + | 0.460323i | \(0.847734\pi\) | |||||||
\(798\) | 20.2999 | 0.718610 | ||||||||
\(799\) | −2.51936 | −0.0891284 | ||||||||
\(800\) | 59.5788 | 2.10643 | ||||||||
\(801\) | −0.272841 | −0.00964037 | ||||||||
\(802\) | 8.34475 | 0.294663 | ||||||||
\(803\) | −2.91474 | −0.102859 | ||||||||
\(804\) | −20.1517 | −0.710697 | ||||||||
\(805\) | 6.12361 | 0.215829 | ||||||||
\(806\) | −4.27118 | −0.150446 | ||||||||
\(807\) | 0.742757 | 0.0261463 | ||||||||
\(808\) | 22.8489 | 0.803821 | ||||||||
\(809\) | −40.8190 | −1.43512 | −0.717560 | − | 0.696497i | \(-0.754741\pi\) | ||||
−0.717560 | + | 0.696497i | \(0.754741\pi\) | |||||||
\(810\) | −33.8880 | −1.19070 | ||||||||
\(811\) | −44.3385 | −1.55694 | −0.778468 | − | 0.627684i | \(-0.784003\pi\) | ||||
−0.778468 | + | 0.627684i | \(0.784003\pi\) | |||||||
\(812\) | −2.43347 | −0.0853980 | ||||||||
\(813\) | −49.6863 | −1.74257 | ||||||||
\(814\) | 5.38112 | 0.188608 | ||||||||
\(815\) | 87.0867 | 3.05051 | ||||||||
\(816\) | 0.511333 | 0.0179002 | ||||||||
\(817\) | 7.03369 | 0.246078 | ||||||||
\(818\) | −21.3804 | −0.747549 | ||||||||
\(819\) | 0.0698724 | 0.00244154 | ||||||||
\(820\) | 23.8986 | 0.834576 | ||||||||
\(821\) | −50.0851 | −1.74798 | −0.873992 | − | 0.485941i | \(-0.838477\pi\) | ||||
−0.873992 | + | 0.485941i | \(0.838477\pi\) | |||||||
\(822\) | −0.597136 | −0.0208275 | ||||||||
\(823\) | 7.71373 | 0.268884 | 0.134442 | − | 0.990921i | \(-0.457076\pi\) | ||||
0.134442 | + | 0.990921i | \(0.457076\pi\) | |||||||
\(824\) | 19.7008 | 0.686310 | ||||||||
\(825\) | 21.1720 | 0.737115 | ||||||||
\(826\) | −17.1349 | −0.596200 | ||||||||
\(827\) | −52.0043 | −1.80837 | −0.904183 | − | 0.427146i | \(-0.859519\pi\) | ||||
−0.904183 | + | 0.427146i | \(0.859519\pi\) | |||||||
\(828\) | 0.0231262 | 0.000803691 0 | ||||||||
\(829\) | 41.0699 | 1.42642 | 0.713209 | − | 0.700952i | \(-0.247241\pi\) | ||||
0.713209 | + | 0.700952i | \(0.247241\pi\) | |||||||
\(830\) | 59.4219 | 2.06256 | ||||||||
\(831\) | −12.2647 | −0.425456 | ||||||||
\(832\) | −6.73416 | −0.233465 | ||||||||
\(833\) | −1.52086 | −0.0526948 | ||||||||
\(834\) | 1.62220 | 0.0561721 | ||||||||
\(835\) | −27.3822 | −0.947601 | ||||||||
\(836\) | 7.26860 | 0.251390 | ||||||||
\(837\) | 20.9681 | 0.724763 | ||||||||
\(838\) | −20.7051 | −0.715247 | ||||||||
\(839\) | −5.53293 | −0.191018 | −0.0955090 | − | 0.995429i | \(-0.530448\pi\) | ||||
−0.0955090 | + | 0.995429i | \(0.530448\pi\) | |||||||
\(840\) | −43.7263 | −1.50870 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 14.1078 | 0.486188 | ||||||||
\(843\) | 17.7461 | 0.611207 | ||||||||
\(844\) | 12.4682 | 0.429172 | ||||||||
\(845\) | −46.9105 | −1.61377 | ||||||||
\(846\) | −0.105260 | −0.00361891 | ||||||||
\(847\) | 21.0391 | 0.722914 | ||||||||
\(848\) | 4.27836 | 0.146919 | ||||||||
\(849\) | 29.8216 | 1.02348 | ||||||||
\(850\) | 6.58217 | 0.225766 | ||||||||
\(851\) | 3.71729 | 0.127427 | ||||||||
\(852\) | −0.950521 | −0.0325643 | ||||||||
\(853\) | 35.3025 | 1.20873 | 0.604367 | − | 0.796706i | \(-0.293426\pi\) | ||||
0.604367 | + | 0.796706i | \(0.293426\pi\) | |||||||
\(854\) | 24.7463 | 0.846802 | ||||||||
\(855\) | 0.669000 | 0.0228793 | ||||||||
\(856\) | 2.03913 | 0.0696960 | ||||||||
\(857\) | −0.769176 | −0.0262745 | −0.0131373 | − | 0.999914i | \(-0.504182\pi\) | ||||
−0.0131373 | + | 0.999914i | \(0.504182\pi\) | |||||||
\(858\) | −2.02506 | −0.0691345 | ||||||||
\(859\) | −2.41712 | −0.0824710 | −0.0412355 | − | 0.999149i | \(-0.513129\pi\) | ||||
−0.0412355 | + | 0.999149i | \(0.513129\pi\) | |||||||
\(860\) | −5.47328 | −0.186637 | ||||||||
\(861\) | −19.7679 | −0.673689 | ||||||||
\(862\) | 2.75137 | 0.0937119 | ||||||||
\(863\) | 34.0792 | 1.16007 | 0.580035 | − | 0.814591i | \(-0.303039\pi\) | ||||
0.580035 | + | 0.814591i | \(0.303039\pi\) | |||||||
\(864\) | 27.9755 | 0.951747 | ||||||||
\(865\) | −72.7386 | −2.47319 | ||||||||
\(866\) | −17.4701 | −0.593659 | ||||||||
\(867\) | 28.8700 | 0.980477 | ||||||||
\(868\) | 9.86762 | 0.334929 | ||||||||
\(869\) | 6.71855 | 0.227911 | ||||||||
\(870\) | 6.49132 | 0.220076 | ||||||||
\(871\) | 11.5678 | 0.391959 | ||||||||
\(872\) | 36.7503 | 1.24452 | ||||||||
\(873\) | −0.372809 | −0.0126177 | ||||||||
\(874\) | −3.85683 | −0.130459 | ||||||||
\(875\) | −51.7593 | −1.74978 | ||||||||
\(876\) | 5.19403 | 0.175490 | ||||||||
\(877\) | 34.8514 | 1.17685 | 0.588424 | − | 0.808553i | \(-0.299749\pi\) | ||||
0.588424 | + | 0.808553i | \(0.299749\pi\) | |||||||
\(878\) | −13.5279 | −0.456546 | ||||||||
\(879\) | 4.12636 | 0.139179 | ||||||||
\(880\) | 2.02552 | 0.0682804 | ||||||||
\(881\) | 17.1367 | 0.577351 | 0.288675 | − | 0.957427i | \(-0.406785\pi\) | ||||
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(882\) | −0.0635424 | −0.00213958 | ||||||||
\(883\) | 55.6457 | 1.87263 | 0.936314 | − | 0.351163i | \(-0.114214\pi\) | ||||
0.936314 | + | 0.351163i | \(0.114214\pi\) | |||||||
\(884\) | 0.819632 | 0.0275672 | ||||||||
\(885\) | −59.5064 | −2.00029 | ||||||||
\(886\) | −7.89422 | −0.265211 | ||||||||
\(887\) | 37.1510 | 1.24741 | 0.623704 | − | 0.781661i | \(-0.285627\pi\) | ||||
0.623704 | + | 0.781661i | \(0.285627\pi\) | |||||||
\(888\) | −26.5437 | −0.890748 | ||||||||
\(889\) | 12.4538 | 0.417688 | ||||||||
\(890\) | −35.4079 | −1.18688 | ||||||||
\(891\) | 10.0367 | 0.336242 | ||||||||
\(892\) | 3.90675 | 0.130808 | ||||||||
\(893\) | −22.8540 | −0.764781 | ||||||||
\(894\) | 12.7635 | 0.426874 | ||||||||
\(895\) | 41.5933 | 1.39031 | ||||||||
\(896\) | 11.3277 | 0.378431 | ||||||||
\(897\) | −1.39892 | −0.0467084 | ||||||||
\(898\) | 10.5676 | 0.352644 | ||||||||
\(899\) | −4.05496 | −0.135241 | ||||||||
\(900\) | −0.358028 | −0.0119343 | ||||||||
\(901\) | −5.98724 | −0.199464 | ||||||||
\(902\) | 5.43680 | 0.181026 | ||||||||
\(903\) | 4.52726 | 0.150658 | ||||||||
\(904\) | −22.0443 | −0.733183 | ||||||||
\(905\) | 18.1304 | 0.602675 | ||||||||
\(906\) | −28.5392 | −0.948151 | ||||||||
\(907\) | −11.0585 | −0.367192 | −0.183596 | − | 0.983002i | \(-0.558774\pi\) | ||||
−0.183596 | + | 0.983002i | \(0.558774\pi\) | |||||||
\(908\) | 16.7712 | 0.556571 | ||||||||
\(909\) | −0.225009 | −0.00746309 | ||||||||
\(910\) | 9.06767 | 0.300590 | ||||||||
\(911\) | 34.6013 | 1.14639 | 0.573196 | − | 0.819418i | \(-0.305703\pi\) | ||||
0.573196 | + | 0.819418i | \(0.305703\pi\) | |||||||
\(912\) | 4.63850 | 0.153596 | ||||||||
\(913\) | −17.5991 | −0.582446 | ||||||||
\(914\) | 8.91551 | 0.294899 | ||||||||
\(915\) | 85.9394 | 2.84107 | ||||||||
\(916\) | 28.9280 | 0.955808 | ||||||||
\(917\) | 21.2268 | 0.700971 | ||||||||
\(918\) | 3.09069 | 0.102008 | ||||||||
\(919\) | 12.2658 | 0.404612 | 0.202306 | − | 0.979322i | \(-0.435156\pi\) | ||||
0.202306 | + | 0.979322i | \(0.435156\pi\) | |||||||
\(920\) | 8.30765 | 0.273895 | ||||||||
\(921\) | 5.18589 | 0.170881 | ||||||||
\(922\) | 6.80775 | 0.224201 | ||||||||
\(923\) | 0.545631 | 0.0179597 | ||||||||
\(924\) | 4.67846 | 0.153910 | ||||||||
\(925\) | −57.5491 | −1.89220 | ||||||||
\(926\) | −6.69331 | −0.219956 | ||||||||
\(927\) | −0.194008 | −0.00637206 | ||||||||
\(928\) | −5.41012 | −0.177596 | ||||||||
\(929\) | −3.00251 | −0.0985091 | −0.0492546 | − | 0.998786i | \(-0.515685\pi\) | ||||
−0.0492546 | + | 0.998786i | \(0.515685\pi\) | |||||||
\(930\) | −26.3221 | −0.863135 | ||||||||
\(931\) | −13.7963 | −0.452156 | ||||||||
\(932\) | 13.8058 | 0.452223 | ||||||||
\(933\) | 43.8633 | 1.43602 | ||||||||
\(934\) | −19.9030 | −0.651245 | ||||||||
\(935\) | −2.83457 | −0.0927003 | ||||||||
\(936\) | 0.0947930 | 0.00309841 | ||||||||
\(937\) | −9.65067 | −0.315274 | −0.157637 | − | 0.987497i | \(-0.550388\pi\) | ||||
−0.157637 | + | 0.987497i | \(0.550388\pi\) | |||||||
\(938\) | 20.5277 | 0.670253 | ||||||||
\(939\) | −20.3089 | −0.662757 | ||||||||
\(940\) | 17.7839 | 0.580047 | ||||||||
\(941\) | −18.8891 | −0.615766 | −0.307883 | − | 0.951424i | \(-0.599620\pi\) | ||||
−0.307883 | + | 0.951424i | \(0.599620\pi\) | |||||||
\(942\) | −28.0758 | −0.914758 | ||||||||
\(943\) | 3.75575 | 0.122304 | ||||||||
\(944\) | −3.91530 | −0.127432 | ||||||||
\(945\) | −44.5150 | −1.44807 | ||||||||
\(946\) | −1.24514 | −0.0404830 | ||||||||
\(947\) | −20.4373 | −0.664121 | −0.332061 | − | 0.943258i | \(-0.607744\pi\) | ||||
−0.332061 | + | 0.943258i | \(0.607744\pi\) | |||||||
\(948\) | −11.9724 | −0.388844 | ||||||||
\(949\) | −2.98155 | −0.0967852 | ||||||||
\(950\) | 59.7094 | 1.93723 | ||||||||
\(951\) | −23.5698 | −0.764302 | ||||||||
\(952\) | 4.02618 | 0.130489 | ||||||||
\(953\) | −24.8443 | −0.804786 | −0.402393 | − | 0.915467i | \(-0.631821\pi\) | ||||
−0.402393 | + | 0.915467i | \(0.631821\pi\) | |||||||
\(954\) | −0.250150 | −0.00809890 | ||||||||
\(955\) | −38.3142 | −1.23982 | ||||||||
\(956\) | 10.1352 | 0.327795 | ||||||||
\(957\) | −1.92255 | −0.0621472 | ||||||||
\(958\) | 6.41546 | 0.207274 | ||||||||
\(959\) | −0.791908 | −0.0255721 | ||||||||
\(960\) | −41.5008 | −1.33943 | ||||||||
\(961\) | −14.5573 | −0.469589 | ||||||||
\(962\) | 5.50445 | 0.177471 | ||||||||
\(963\) | −0.0200808 | −0.000647094 0 | ||||||||
\(964\) | −14.1976 | −0.457273 | ||||||||
\(965\) | 37.8457 | 1.21830 | ||||||||
\(966\) | −2.48246 | −0.0798719 | ||||||||
\(967\) | −0.618562 | −0.0198916 | −0.00994581 | − | 0.999951i | \(-0.503166\pi\) | ||||
−0.00994581 | + | 0.999951i | \(0.503166\pi\) | |||||||
\(968\) | 28.5429 | 0.917405 | ||||||||
\(969\) | −6.49123 | −0.208528 | ||||||||
\(970\) | −48.3812 | −1.55343 | ||||||||
\(971\) | 33.9845 | 1.09062 | 0.545308 | − | 0.838236i | \(-0.316413\pi\) | ||||
0.545308 | + | 0.838236i | \(0.316413\pi\) | |||||||
\(972\) | −0.337854 | −0.0108367 | ||||||||
\(973\) | 2.15132 | 0.0689683 | ||||||||
\(974\) | 6.94011 | 0.222376 | ||||||||
\(975\) | 21.6573 | 0.693588 | ||||||||
\(976\) | 5.65449 | 0.180996 | ||||||||
\(977\) | −59.5556 | −1.90535 | −0.952676 | − | 0.303987i | \(-0.901682\pi\) | ||||
−0.952676 | + | 0.303987i | \(0.901682\pi\) | |||||||
\(978\) | −35.3042 | −1.12890 | ||||||||
\(979\) | 10.4868 | 0.335161 | ||||||||
\(980\) | 10.7356 | 0.342937 | ||||||||
\(981\) | −0.361907 | −0.0115548 | ||||||||
\(982\) | 8.44306 | 0.269429 | ||||||||
\(983\) | −33.8426 | −1.07941 | −0.539706 | − | 0.841853i | \(-0.681465\pi\) | ||||
−0.539706 | + | 0.841853i | \(0.681465\pi\) | |||||||
\(984\) | −26.8183 | −0.854937 | ||||||||
\(985\) | 0.222852 | 0.00710064 | ||||||||
\(986\) | −0.597701 | −0.0190347 | ||||||||
\(987\) | −14.7101 | −0.468227 | ||||||||
\(988\) | 7.43519 | 0.236545 | ||||||||
\(989\) | −0.860144 | −0.0273510 | ||||||||
\(990\) | −0.118430 | −0.00376394 | ||||||||
\(991\) | −34.8968 | −1.10853 | −0.554267 | − | 0.832339i | \(-0.687001\pi\) | ||||
−0.554267 | + | 0.832339i | \(0.687001\pi\) | |||||||
\(992\) | 21.9378 | 0.696527 | ||||||||
\(993\) | 24.6087 | 0.780934 | ||||||||
\(994\) | 0.968255 | 0.0307112 | ||||||||
\(995\) | −35.3035 | −1.11920 | ||||||||
\(996\) | 31.3614 | 0.993723 | ||||||||
\(997\) | 52.6927 | 1.66879 | 0.834397 | − | 0.551164i | \(-0.185816\pi\) | ||||
0.834397 | + | 0.551164i | \(0.185816\pi\) | |||||||
\(998\) | 5.89174 | 0.186500 | ||||||||
\(999\) | −27.0225 | −0.854953 |
(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 | 4031.2.a.c.1.40 | ✓ | 61 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.c.1.40 | ✓ | 61 | 1.1 | even | 1 | trivial |