Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, 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("6041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6041 = 7 \cdot 863 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2376278611\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.49223 | −1.76227 | −0.881136 | − | 0.472863i | \(-0.843221\pi\) | ||||
−0.881136 | + | 0.472863i | \(0.843221\pi\) | |||||||
\(3\) | 0.173328 | 0.100071 | 0.0500354 | − | 0.998747i | \(-0.484067\pi\) | ||||
0.0500354 | + | 0.998747i | \(0.484067\pi\) | |||||||
\(4\) | 4.21120 | 2.10560 | ||||||||
\(5\) | 2.29751 | 1.02748 | 0.513739 | − | 0.857947i | \(-0.328260\pi\) | ||||
0.513739 | + | 0.857947i | \(0.328260\pi\) | |||||||
\(6\) | −0.431973 | −0.176352 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −5.51083 | −1.94837 | ||||||||
\(9\) | −2.96996 | −0.989986 | ||||||||
\(10\) | −5.72592 | −1.81069 | ||||||||
\(11\) | 4.74692 | 1.43125 | 0.715625 | − | 0.698485i | \(-0.246142\pi\) | ||||
0.715625 | + | 0.698485i | \(0.246142\pi\) | |||||||
\(12\) | 0.729919 | 0.210709 | ||||||||
\(13\) | 4.44530 | 1.23290 | 0.616452 | − | 0.787392i | \(-0.288569\pi\) | ||||
0.616452 | + | 0.787392i | \(0.288569\pi\) | |||||||
\(14\) | −2.49223 | −0.666076 | ||||||||
\(15\) | 0.398222 | 0.102821 | ||||||||
\(16\) | 5.31183 | 1.32796 | ||||||||
\(17\) | 7.62429 | 1.84916 | 0.924581 | − | 0.380985i | \(-0.124415\pi\) | ||||
0.924581 | + | 0.380985i | \(0.124415\pi\) | |||||||
\(18\) | 7.40181 | 1.74462 | ||||||||
\(19\) | −5.56550 | −1.27681 | −0.638406 | − | 0.769700i | \(-0.720406\pi\) | ||||
−0.638406 | + | 0.769700i | \(0.720406\pi\) | |||||||
\(20\) | 9.67528 | 2.16346 | ||||||||
\(21\) | 0.173328 | 0.0378232 | ||||||||
\(22\) | −11.8304 | −2.52225 | ||||||||
\(23\) | 5.50036 | 1.14691 | 0.573453 | − | 0.819239i | \(-0.305604\pi\) | ||||
0.573453 | + | 0.819239i | \(0.305604\pi\) | |||||||
\(24\) | −0.955179 | −0.194975 | ||||||||
\(25\) | 0.278548 | 0.0557096 | ||||||||
\(26\) | −11.0787 | −2.17271 | ||||||||
\(27\) | −1.03476 | −0.199140 | ||||||||
\(28\) | 4.21120 | 0.795843 | ||||||||
\(29\) | −0.702971 | −0.130539 | −0.0652693 | − | 0.997868i | \(-0.520791\pi\) | ||||
−0.0652693 | + | 0.997868i | \(0.520791\pi\) | |||||||
\(30\) | −0.992461 | −0.181198 | ||||||||
\(31\) | 8.98471 | 1.61370 | 0.806851 | − | 0.590755i | \(-0.201170\pi\) | ||||
0.806851 | + | 0.590755i | \(0.201170\pi\) | |||||||
\(32\) | −2.21665 | −0.391852 | ||||||||
\(33\) | 0.822773 | 0.143226 | ||||||||
\(34\) | −19.0015 | −3.25873 | ||||||||
\(35\) | 2.29751 | 0.388350 | ||||||||
\(36\) | −12.5071 | −2.08452 | ||||||||
\(37\) | 9.07414 | 1.49178 | 0.745890 | − | 0.666070i | \(-0.232025\pi\) | ||||
0.745890 | + | 0.666070i | \(0.232025\pi\) | |||||||
\(38\) | 13.8705 | 2.25009 | ||||||||
\(39\) | 0.770494 | 0.123378 | ||||||||
\(40\) | −12.6612 | −2.00191 | ||||||||
\(41\) | −3.05811 | −0.477596 | −0.238798 | − | 0.971069i | \(-0.576753\pi\) | ||||
−0.238798 | + | 0.971069i | \(0.576753\pi\) | |||||||
\(42\) | −0.431973 | −0.0666548 | ||||||||
\(43\) | 4.67944 | 0.713608 | 0.356804 | − | 0.934179i | \(-0.383866\pi\) | ||||
0.356804 | + | 0.934179i | \(0.383866\pi\) | |||||||
\(44\) | 19.9902 | 3.01364 | ||||||||
\(45\) | −6.82350 | −1.01719 | ||||||||
\(46\) | −13.7082 | −2.02116 | ||||||||
\(47\) | 5.17442 | 0.754767 | 0.377383 | − | 0.926057i | \(-0.376824\pi\) | ||||
0.377383 | + | 0.926057i | \(0.376824\pi\) | |||||||
\(48\) | 0.920688 | 0.132890 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.694205 | −0.0981755 | ||||||||
\(51\) | 1.32150 | 0.185047 | ||||||||
\(52\) | 18.7201 | 2.59601 | ||||||||
\(53\) | 7.04975 | 0.968357 | 0.484179 | − | 0.874969i | \(-0.339119\pi\) | ||||
0.484179 | + | 0.874969i | \(0.339119\pi\) | |||||||
\(54\) | 2.57886 | 0.350938 | ||||||||
\(55\) | 10.9061 | 1.47058 | ||||||||
\(56\) | −5.51083 | −0.736415 | ||||||||
\(57\) | −0.964655 | −0.127772 | ||||||||
\(58\) | 1.75197 | 0.230044 | ||||||||
\(59\) | −11.8939 | −1.54845 | −0.774224 | − | 0.632912i | \(-0.781860\pi\) | ||||
−0.774224 | + | 0.632912i | \(0.781860\pi\) | |||||||
\(60\) | 1.67700 | 0.216499 | ||||||||
\(61\) | 1.14576 | 0.146699 | 0.0733495 | − | 0.997306i | \(-0.476631\pi\) | ||||
0.0733495 | + | 0.997306i | \(0.476631\pi\) | |||||||
\(62\) | −22.3920 | −2.84378 | ||||||||
\(63\) | −2.96996 | −0.374179 | ||||||||
\(64\) | −5.09927 | −0.637409 | ||||||||
\(65\) | 10.2131 | 1.26678 | ||||||||
\(66\) | −2.05054 | −0.252404 | ||||||||
\(67\) | −8.35343 | −1.02053 | −0.510267 | − | 0.860016i | \(-0.670453\pi\) | ||||
−0.510267 | + | 0.860016i | \(0.670453\pi\) | |||||||
\(68\) | 32.1074 | 3.89360 | ||||||||
\(69\) | 0.953366 | 0.114772 | ||||||||
\(70\) | −5.72592 | −0.684378 | ||||||||
\(71\) | −5.29454 | −0.628346 | −0.314173 | − | 0.949366i | \(-0.601727\pi\) | ||||
−0.314173 | + | 0.949366i | \(0.601727\pi\) | |||||||
\(72\) | 16.3669 | 1.92886 | ||||||||
\(73\) | −12.0571 | −1.41117 | −0.705586 | − | 0.708625i | \(-0.749316\pi\) | ||||
−0.705586 | + | 0.708625i | \(0.749316\pi\) | |||||||
\(74\) | −22.6148 | −2.62892 | ||||||||
\(75\) | 0.0482801 | 0.00557491 | ||||||||
\(76\) | −23.4374 | −2.68846 | ||||||||
\(77\) | 4.74692 | 0.540961 | ||||||||
\(78\) | −1.92025 | −0.217425 | ||||||||
\(79\) | 16.6769 | 1.87630 | 0.938149 | − | 0.346232i | \(-0.112539\pi\) | ||||
0.938149 | + | 0.346232i | \(0.112539\pi\) | |||||||
\(80\) | 12.2040 | 1.36445 | ||||||||
\(81\) | 8.73052 | 0.970058 | ||||||||
\(82\) | 7.62150 | 0.841654 | ||||||||
\(83\) | −5.73960 | −0.630003 | −0.315002 | − | 0.949091i | \(-0.602005\pi\) | ||||
−0.315002 | + | 0.949091i | \(0.602005\pi\) | |||||||
\(84\) | 0.729919 | 0.0796407 | ||||||||
\(85\) | 17.5169 | 1.89997 | ||||||||
\(86\) | −11.6622 | −1.25757 | ||||||||
\(87\) | −0.121844 | −0.0130631 | ||||||||
\(88\) | −26.1594 | −2.78861 | ||||||||
\(89\) | −4.50184 | −0.477194 | −0.238597 | − | 0.971119i | \(-0.576688\pi\) | ||||
−0.238597 | + | 0.971119i | \(0.576688\pi\) | |||||||
\(90\) | 17.0057 | 1.79256 | ||||||||
\(91\) | 4.44530 | 0.465994 | ||||||||
\(92\) | 23.1632 | 2.41493 | ||||||||
\(93\) | 1.55730 | 0.161485 | ||||||||
\(94\) | −12.8958 | −1.33010 | ||||||||
\(95\) | −12.7868 | −1.31190 | ||||||||
\(96\) | −0.384207 | −0.0392129 | ||||||||
\(97\) | −5.85081 | −0.594060 | −0.297030 | − | 0.954868i | \(-0.595996\pi\) | ||||
−0.297030 | + | 0.954868i | \(0.595996\pi\) | |||||||
\(98\) | −2.49223 | −0.251753 | ||||||||
\(99\) | −14.0981 | −1.41692 | ||||||||
\(100\) | 1.17302 | 0.117302 | ||||||||
\(101\) | 5.64318 | 0.561517 | 0.280759 | − | 0.959778i | \(-0.409414\pi\) | ||||
0.280759 | + | 0.959778i | \(0.409414\pi\) | |||||||
\(102\) | −3.29348 | −0.326104 | ||||||||
\(103\) | −4.24701 | −0.418470 | −0.209235 | − | 0.977865i | \(-0.567097\pi\) | ||||
−0.209235 | + | 0.977865i | \(0.567097\pi\) | |||||||
\(104\) | −24.4973 | −2.40216 | ||||||||
\(105\) | 0.398222 | 0.0388625 | ||||||||
\(106\) | −17.5696 | −1.70651 | ||||||||
\(107\) | −1.53811 | −0.148694 | −0.0743471 | − | 0.997232i | \(-0.523687\pi\) | ||||
−0.0743471 | + | 0.997232i | \(0.523687\pi\) | |||||||
\(108\) | −4.35758 | −0.419309 | ||||||||
\(109\) | −18.0590 | −1.72974 | −0.864870 | − | 0.501996i | \(-0.832599\pi\) | ||||
−0.864870 | + | 0.501996i | \(0.832599\pi\) | |||||||
\(110\) | −27.1805 | −2.59156 | ||||||||
\(111\) | 1.57280 | 0.149284 | ||||||||
\(112\) | 5.31183 | 0.501921 | ||||||||
\(113\) | 1.58533 | 0.149135 | 0.0745677 | − | 0.997216i | \(-0.476242\pi\) | ||||
0.0745677 | + | 0.997216i | \(0.476242\pi\) | |||||||
\(114\) | 2.40414 | 0.225168 | ||||||||
\(115\) | 12.6371 | 1.17842 | ||||||||
\(116\) | −2.96036 | −0.274862 | ||||||||
\(117\) | −13.2024 | −1.22056 | ||||||||
\(118\) | 29.6422 | 2.72879 | ||||||||
\(119\) | 7.62429 | 0.698918 | ||||||||
\(120\) | −2.19453 | −0.200333 | ||||||||
\(121\) | 11.5332 | 1.04847 | ||||||||
\(122\) | −2.85549 | −0.258524 | ||||||||
\(123\) | −0.530055 | −0.0477935 | ||||||||
\(124\) | 37.8365 | 3.39781 | ||||||||
\(125\) | −10.8476 | −0.970237 | ||||||||
\(126\) | 7.40181 | 0.659406 | ||||||||
\(127\) | 13.4958 | 1.19756 | 0.598780 | − | 0.800914i | \(-0.295652\pi\) | ||||
0.598780 | + | 0.800914i | \(0.295652\pi\) | |||||||
\(128\) | 17.1418 | 1.51514 | ||||||||
\(129\) | 0.811077 | 0.0714114 | ||||||||
\(130\) | −25.4534 | −2.23241 | ||||||||
\(131\) | 22.2050 | 1.94006 | 0.970031 | − | 0.242979i | \(-0.0781247\pi\) | ||||
0.970031 | + | 0.242979i | \(0.0781247\pi\) | |||||||
\(132\) | 3.46486 | 0.301578 | ||||||||
\(133\) | −5.56550 | −0.482590 | ||||||||
\(134\) | 20.8187 | 1.79846 | ||||||||
\(135\) | −2.37737 | −0.204611 | ||||||||
\(136\) | −42.0161 | −3.60285 | ||||||||
\(137\) | 15.8926 | 1.35779 | 0.678897 | − | 0.734233i | \(-0.262458\pi\) | ||||
0.678897 | + | 0.734233i | \(0.262458\pi\) | |||||||
\(138\) | −2.37601 | −0.202259 | ||||||||
\(139\) | 4.50633 | 0.382222 | 0.191111 | − | 0.981568i | \(-0.438791\pi\) | ||||
0.191111 | + | 0.981568i | \(0.438791\pi\) | |||||||
\(140\) | 9.67528 | 0.817710 | ||||||||
\(141\) | 0.896871 | 0.0755302 | ||||||||
\(142\) | 13.1952 | 1.10732 | ||||||||
\(143\) | 21.1015 | 1.76459 | ||||||||
\(144\) | −15.7759 | −1.31466 | ||||||||
\(145\) | −1.61508 | −0.134125 | ||||||||
\(146\) | 30.0489 | 2.48687 | ||||||||
\(147\) | 0.173328 | 0.0142958 | ||||||||
\(148\) | 38.2130 | 3.14109 | ||||||||
\(149\) | 0.463022 | 0.0379322 | 0.0189661 | − | 0.999820i | \(-0.493963\pi\) | ||||
0.0189661 | + | 0.999820i | \(0.493963\pi\) | |||||||
\(150\) | −0.120325 | −0.00982450 | ||||||||
\(151\) | −2.44742 | −0.199168 | −0.0995841 | − | 0.995029i | \(-0.531751\pi\) | ||||
−0.0995841 | + | 0.995029i | \(0.531751\pi\) | |||||||
\(152\) | 30.6705 | 2.48770 | ||||||||
\(153\) | −22.6438 | −1.83064 | ||||||||
\(154\) | −11.8304 | −0.953321 | ||||||||
\(155\) | 20.6425 | 1.65804 | ||||||||
\(156\) | 3.24471 | 0.259785 | ||||||||
\(157\) | 13.7617 | 1.09830 | 0.549151 | − | 0.835723i | \(-0.314951\pi\) | ||||
0.549151 | + | 0.835723i | \(0.314951\pi\) | |||||||
\(158\) | −41.5626 | −3.30655 | ||||||||
\(159\) | 1.22192 | 0.0969043 | ||||||||
\(160\) | −5.09277 | −0.402619 | ||||||||
\(161\) | 5.50036 | 0.433489 | ||||||||
\(162\) | −21.7585 | −1.70951 | ||||||||
\(163\) | −9.48515 | −0.742934 | −0.371467 | − | 0.928446i | \(-0.621145\pi\) | ||||
−0.371467 | + | 0.928446i | \(0.621145\pi\) | |||||||
\(164\) | −12.8783 | −1.00563 | ||||||||
\(165\) | 1.89033 | 0.147162 | ||||||||
\(166\) | 14.3044 | 1.11024 | ||||||||
\(167\) | −14.5005 | −1.12208 | −0.561041 | − | 0.827788i | \(-0.689599\pi\) | ||||
−0.561041 | + | 0.827788i | \(0.689599\pi\) | |||||||
\(168\) | −0.955179 | −0.0736937 | ||||||||
\(169\) | 6.76069 | 0.520053 | ||||||||
\(170\) | −43.6561 | −3.34827 | ||||||||
\(171\) | 16.5293 | 1.26403 | ||||||||
\(172\) | 19.7061 | 1.50257 | ||||||||
\(173\) | −18.9478 | −1.44057 | −0.720286 | − | 0.693678i | \(-0.755989\pi\) | ||||
−0.720286 | + | 0.693678i | \(0.755989\pi\) | |||||||
\(174\) | 0.303664 | 0.0230207 | ||||||||
\(175\) | 0.278548 | 0.0210563 | ||||||||
\(176\) | 25.2148 | 1.90064 | ||||||||
\(177\) | −2.06154 | −0.154955 | ||||||||
\(178\) | 11.2196 | 0.840946 | ||||||||
\(179\) | −8.94525 | −0.668600 | −0.334300 | − | 0.942467i | \(-0.608500\pi\) | ||||
−0.334300 | + | 0.942467i | \(0.608500\pi\) | |||||||
\(180\) | −28.7352 | −2.14179 | ||||||||
\(181\) | −11.0723 | −0.822994 | −0.411497 | − | 0.911411i | \(-0.634994\pi\) | ||||
−0.411497 | + | 0.911411i | \(0.634994\pi\) | |||||||
\(182\) | −11.0787 | −0.821208 | ||||||||
\(183\) | 0.198591 | 0.0146803 | ||||||||
\(184\) | −30.3116 | −2.23460 | ||||||||
\(185\) | 20.8479 | 1.53277 | ||||||||
\(186\) | −3.88115 | −0.284580 | ||||||||
\(187\) | 36.1919 | 2.64661 | ||||||||
\(188\) | 21.7905 | 1.58924 | ||||||||
\(189\) | −1.03476 | −0.0752677 | ||||||||
\(190\) | 31.8676 | 2.31192 | ||||||||
\(191\) | −9.74477 | −0.705107 | −0.352553 | − | 0.935792i | \(-0.614686\pi\) | ||||
−0.352553 | + | 0.935792i | \(0.614686\pi\) | |||||||
\(192\) | −0.883846 | −0.0637861 | ||||||||
\(193\) | 17.6514 | 1.27058 | 0.635288 | − | 0.772275i | \(-0.280881\pi\) | ||||
0.635288 | + | 0.772275i | \(0.280881\pi\) | |||||||
\(194\) | 14.5816 | 1.04690 | ||||||||
\(195\) | 1.77022 | 0.126768 | ||||||||
\(196\) | 4.21120 | 0.300800 | ||||||||
\(197\) | −18.0755 | −1.28782 | −0.643912 | − | 0.765099i | \(-0.722690\pi\) | ||||
−0.643912 | + | 0.765099i | \(0.722690\pi\) | |||||||
\(198\) | 35.1358 | 2.49699 | ||||||||
\(199\) | −3.02589 | −0.214500 | −0.107250 | − | 0.994232i | \(-0.534205\pi\) | ||||
−0.107250 | + | 0.994232i | \(0.534205\pi\) | |||||||
\(200\) | −1.53503 | −0.108543 | ||||||||
\(201\) | −1.44788 | −0.102126 | ||||||||
\(202\) | −14.0641 | −0.989546 | ||||||||
\(203\) | −0.702971 | −0.0493389 | ||||||||
\(204\) | 5.56511 | 0.389636 | ||||||||
\(205\) | −7.02603 | −0.490719 | ||||||||
\(206\) | 10.5845 | 0.737458 | ||||||||
\(207\) | −16.3358 | −1.13542 | ||||||||
\(208\) | 23.6127 | 1.63725 | ||||||||
\(209\) | −26.4189 | −1.82744 | ||||||||
\(210\) | −0.992461 | −0.0684863 | ||||||||
\(211\) | 4.69620 | 0.323300 | 0.161650 | − | 0.986848i | \(-0.448318\pi\) | ||||
0.161650 | + | 0.986848i | \(0.448318\pi\) | |||||||
\(212\) | 29.6879 | 2.03897 | ||||||||
\(213\) | −0.917691 | −0.0628791 | ||||||||
\(214\) | 3.83331 | 0.262040 | ||||||||
\(215\) | 10.7511 | 0.733216 | ||||||||
\(216\) | 5.70238 | 0.387998 | ||||||||
\(217\) | 8.98471 | 0.609922 | ||||||||
\(218\) | 45.0072 | 3.04827 | ||||||||
\(219\) | −2.08982 | −0.141217 | ||||||||
\(220\) | 45.9278 | 3.09645 | ||||||||
\(221\) | 33.8923 | 2.27984 | ||||||||
\(222\) | −3.91978 | −0.263078 | ||||||||
\(223\) | 22.1866 | 1.48572 | 0.742861 | − | 0.669445i | \(-0.233468\pi\) | ||||
0.742861 | + | 0.669445i | \(0.233468\pi\) | |||||||
\(224\) | −2.21665 | −0.148106 | ||||||||
\(225\) | −0.827276 | −0.0551517 | ||||||||
\(226\) | −3.95101 | −0.262817 | ||||||||
\(227\) | 5.94761 | 0.394756 | 0.197378 | − | 0.980327i | \(-0.436757\pi\) | ||||
0.197378 | + | 0.980327i | \(0.436757\pi\) | |||||||
\(228\) | −4.06236 | −0.269036 | ||||||||
\(229\) | −15.7376 | −1.03997 | −0.519986 | − | 0.854175i | \(-0.674063\pi\) | ||||
−0.519986 | + | 0.854175i | \(0.674063\pi\) | |||||||
\(230\) | −31.4946 | −2.07669 | ||||||||
\(231\) | 0.822773 | 0.0541345 | ||||||||
\(232\) | 3.87395 | 0.254338 | ||||||||
\(233\) | −2.23207 | −0.146228 | −0.0731140 | − | 0.997324i | \(-0.523294\pi\) | ||||
−0.0731140 | + | 0.997324i | \(0.523294\pi\) | |||||||
\(234\) | 32.9033 | 2.15095 | ||||||||
\(235\) | 11.8883 | 0.775506 | ||||||||
\(236\) | −50.0874 | −3.26041 | ||||||||
\(237\) | 2.89057 | 0.187763 | ||||||||
\(238\) | −19.0015 | −1.23168 | ||||||||
\(239\) | −20.4047 | −1.31987 | −0.659936 | − | 0.751322i | \(-0.729416\pi\) | ||||
−0.659936 | + | 0.751322i | \(0.729416\pi\) | |||||||
\(240\) | 2.11529 | 0.136541 | ||||||||
\(241\) | −3.11638 | −0.200743 | −0.100372 | − | 0.994950i | \(-0.532003\pi\) | ||||
−0.100372 | + | 0.994950i | \(0.532003\pi\) | |||||||
\(242\) | −28.7434 | −1.84770 | ||||||||
\(243\) | 4.61752 | 0.296214 | ||||||||
\(244\) | 4.82501 | 0.308890 | ||||||||
\(245\) | 2.29751 | 0.146782 | ||||||||
\(246\) | 1.32102 | 0.0842251 | ||||||||
\(247\) | −24.7403 | −1.57419 | ||||||||
\(248\) | −49.5132 | −3.14409 | ||||||||
\(249\) | −0.994833 | −0.0630450 | ||||||||
\(250\) | 27.0346 | 1.70982 | ||||||||
\(251\) | −19.5061 | −1.23121 | −0.615606 | − | 0.788054i | \(-0.711089\pi\) | ||||
−0.615606 | + | 0.788054i | \(0.711089\pi\) | |||||||
\(252\) | −12.5071 | −0.787873 | ||||||||
\(253\) | 26.1098 | 1.64151 | ||||||||
\(254\) | −33.6347 | −2.11043 | ||||||||
\(255\) | 3.03616 | 0.190132 | ||||||||
\(256\) | −32.5229 | −2.03268 | ||||||||
\(257\) | 4.57248 | 0.285223 | 0.142612 | − | 0.989779i | \(-0.454450\pi\) | ||||
0.142612 | + | 0.989779i | \(0.454450\pi\) | |||||||
\(258\) | −2.02139 | −0.125846 | ||||||||
\(259\) | 9.07414 | 0.563839 | ||||||||
\(260\) | 43.0095 | 2.66734 | ||||||||
\(261\) | 2.08780 | 0.129231 | ||||||||
\(262\) | −55.3400 | −3.41892 | ||||||||
\(263\) | −13.0532 | −0.804896 | −0.402448 | − | 0.915443i | \(-0.631841\pi\) | ||||
−0.402448 | + | 0.915443i | \(0.631841\pi\) | |||||||
\(264\) | −4.53416 | −0.279058 | ||||||||
\(265\) | 16.1969 | 0.994965 | ||||||||
\(266\) | 13.8705 | 0.850454 | ||||||||
\(267\) | −0.780294 | −0.0477532 | ||||||||
\(268\) | −35.1780 | −2.14884 | ||||||||
\(269\) | −3.32800 | −0.202912 | −0.101456 | − | 0.994840i | \(-0.532350\pi\) | ||||
−0.101456 | + | 0.994840i | \(0.532350\pi\) | |||||||
\(270\) | 5.92495 | 0.360581 | ||||||||
\(271\) | 0.195976 | 0.0119047 | 0.00595233 | − | 0.999982i | \(-0.498105\pi\) | ||||
0.00595233 | + | 0.999982i | \(0.498105\pi\) | |||||||
\(272\) | 40.4990 | 2.45561 | ||||||||
\(273\) | 0.770494 | 0.0466324 | ||||||||
\(274\) | −39.6079 | −2.39280 | ||||||||
\(275\) | 1.32224 | 0.0797343 | ||||||||
\(276\) | 4.01482 | 0.241664 | ||||||||
\(277\) | −1.11536 | −0.0670153 | −0.0335076 | − | 0.999438i | \(-0.510668\pi\) | ||||
−0.0335076 | + | 0.999438i | \(0.510668\pi\) | |||||||
\(278\) | −11.2308 | −0.673580 | ||||||||
\(279\) | −26.6842 | −1.59754 | ||||||||
\(280\) | −12.6612 | −0.756650 | ||||||||
\(281\) | −10.2548 | −0.611751 | −0.305876 | − | 0.952071i | \(-0.598949\pi\) | ||||
−0.305876 | + | 0.952071i | \(0.598949\pi\) | |||||||
\(282\) | −2.23521 | −0.133105 | ||||||||
\(283\) | −14.3410 | −0.852485 | −0.426243 | − | 0.904609i | \(-0.640163\pi\) | ||||
−0.426243 | + | 0.904609i | \(0.640163\pi\) | |||||||
\(284\) | −22.2964 | −1.32305 | ||||||||
\(285\) | −2.21630 | −0.131283 | ||||||||
\(286\) | −52.5897 | −3.10969 | ||||||||
\(287\) | −3.05811 | −0.180514 | ||||||||
\(288\) | 6.58335 | 0.387928 | ||||||||
\(289\) | 41.1298 | 2.41940 | ||||||||
\(290\) | 4.02516 | 0.236365 | ||||||||
\(291\) | −1.01411 | −0.0594481 | ||||||||
\(292\) | −50.7747 | −2.97137 | ||||||||
\(293\) | −26.8965 | −1.57131 | −0.785655 | − | 0.618665i | \(-0.787674\pi\) | ||||
−0.785655 | + | 0.618665i | \(0.787674\pi\) | |||||||
\(294\) | −0.431973 | −0.0251932 | ||||||||
\(295\) | −27.3262 | −1.59099 | ||||||||
\(296\) | −50.0060 | −2.90654 | ||||||||
\(297\) | −4.91192 | −0.285018 | ||||||||
\(298\) | −1.15396 | −0.0668469 | ||||||||
\(299\) | 24.4508 | 1.41402 | ||||||||
\(300\) | 0.203317 | 0.0117385 | ||||||||
\(301\) | 4.67944 | 0.269719 | ||||||||
\(302\) | 6.09953 | 0.350988 | ||||||||
\(303\) | 0.978119 | 0.0561915 | ||||||||
\(304\) | −29.5630 | −1.69555 | ||||||||
\(305\) | 2.63238 | 0.150730 | ||||||||
\(306\) | 56.4336 | 3.22609 | ||||||||
\(307\) | −6.02151 | −0.343666 | −0.171833 | − | 0.985126i | \(-0.554969\pi\) | ||||
−0.171833 | + | 0.985126i | \(0.554969\pi\) | |||||||
\(308\) | 19.9902 | 1.13905 | ||||||||
\(309\) | −0.736124 | −0.0418766 | ||||||||
\(310\) | −51.4457 | −2.92192 | ||||||||
\(311\) | 29.9192 | 1.69656 | 0.848281 | − | 0.529546i | \(-0.177638\pi\) | ||||
0.848281 | + | 0.529546i | \(0.177638\pi\) | |||||||
\(312\) | −4.24606 | −0.240386 | ||||||||
\(313\) | 26.0398 | 1.47185 | 0.735927 | − | 0.677061i | \(-0.236747\pi\) | ||||
0.735927 | + | 0.677061i | \(0.236747\pi\) | |||||||
\(314\) | −34.2973 | −1.93551 | ||||||||
\(315\) | −6.82350 | −0.384461 | ||||||||
\(316\) | 70.2298 | 3.95074 | ||||||||
\(317\) | −32.8485 | −1.84495 | −0.922477 | − | 0.386052i | \(-0.873838\pi\) | ||||
−0.922477 | + | 0.386052i | \(0.873838\pi\) | |||||||
\(318\) | −3.04530 | −0.170772 | ||||||||
\(319\) | −3.33695 | −0.186833 | ||||||||
\(320\) | −11.7156 | −0.654923 | ||||||||
\(321\) | −0.266596 | −0.0148800 | ||||||||
\(322\) | −13.7082 | −0.763926 | ||||||||
\(323\) | −42.4330 | −2.36103 | ||||||||
\(324\) | 36.7660 | 2.04256 | ||||||||
\(325\) | 1.23823 | 0.0686846 | ||||||||
\(326\) | 23.6392 | 1.30925 | ||||||||
\(327\) | −3.13013 | −0.173097 | ||||||||
\(328\) | 16.8527 | 0.930535 | ||||||||
\(329\) | 5.17442 | 0.285275 | ||||||||
\(330\) | −4.71113 | −0.259339 | ||||||||
\(331\) | −17.0855 | −0.939106 | −0.469553 | − | 0.882904i | \(-0.655585\pi\) | ||||
−0.469553 | + | 0.882904i | \(0.655585\pi\) | |||||||
\(332\) | −24.1706 | −1.32654 | ||||||||
\(333\) | −26.9498 | −1.47684 | ||||||||
\(334\) | 36.1385 | 1.97741 | ||||||||
\(335\) | −19.1921 | −1.04858 | ||||||||
\(336\) | 0.920688 | 0.0502277 | ||||||||
\(337\) | 4.87510 | 0.265564 | 0.132782 | − | 0.991145i | \(-0.457609\pi\) | ||||
0.132782 | + | 0.991145i | \(0.457609\pi\) | |||||||
\(338\) | −16.8492 | −0.916474 | ||||||||
\(339\) | 0.274782 | 0.0149241 | ||||||||
\(340\) | 73.7672 | 4.00059 | ||||||||
\(341\) | 42.6497 | 2.30961 | ||||||||
\(342\) | −41.1948 | −2.22756 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −25.7876 | −1.39037 | ||||||||
\(345\) | 2.19037 | 0.117925 | ||||||||
\(346\) | 47.2221 | 2.53868 | ||||||||
\(347\) | −18.7327 | −1.00563 | −0.502813 | − | 0.864396i | \(-0.667701\pi\) | ||||
−0.502813 | + | 0.864396i | \(0.667701\pi\) | |||||||
\(348\) | −0.513112 | −0.0275057 | ||||||||
\(349\) | −12.6052 | −0.674743 | −0.337371 | − | 0.941372i | \(-0.609538\pi\) | ||||
−0.337371 | + | 0.941372i | \(0.609538\pi\) | |||||||
\(350\) | −0.694205 | −0.0371068 | ||||||||
\(351\) | −4.59982 | −0.245520 | ||||||||
\(352\) | −10.5222 | −0.560837 | ||||||||
\(353\) | 6.57308 | 0.349850 | 0.174925 | − | 0.984582i | \(-0.444032\pi\) | ||||
0.174925 | + | 0.984582i | \(0.444032\pi\) | |||||||
\(354\) | 5.13782 | 0.273072 | ||||||||
\(355\) | −12.1642 | −0.645611 | ||||||||
\(356\) | −18.9582 | −1.00478 | ||||||||
\(357\) | 1.32150 | 0.0699413 | ||||||||
\(358\) | 22.2936 | 1.17825 | ||||||||
\(359\) | −22.5557 | −1.19045 | −0.595223 | − | 0.803561i | \(-0.702936\pi\) | ||||
−0.595223 | + | 0.803561i | \(0.702936\pi\) | |||||||
\(360\) | 37.6031 | 1.98186 | ||||||||
\(361\) | 11.9747 | 0.630250 | ||||||||
\(362\) | 27.5946 | 1.45034 | ||||||||
\(363\) | 1.99903 | 0.104922 | ||||||||
\(364\) | 18.7201 | 0.981198 | ||||||||
\(365\) | −27.7012 | −1.44995 | ||||||||
\(366\) | −0.494935 | −0.0258707 | ||||||||
\(367\) | −31.6153 | −1.65031 | −0.825153 | − | 0.564909i | \(-0.808911\pi\) | ||||
−0.825153 | + | 0.564909i | \(0.808911\pi\) | |||||||
\(368\) | 29.2170 | 1.52304 | ||||||||
\(369\) | 9.08245 | 0.472813 | ||||||||
\(370\) | −51.9578 | −2.70116 | ||||||||
\(371\) | 7.04975 | 0.366005 | ||||||||
\(372\) | 6.55811 | 0.340022 | ||||||||
\(373\) | −19.9713 | −1.03408 | −0.517038 | − | 0.855963i | \(-0.672965\pi\) | ||||
−0.517038 | + | 0.855963i | \(0.672965\pi\) | |||||||
\(374\) | −90.1984 | −4.66405 | ||||||||
\(375\) | −1.88019 | −0.0970924 | ||||||||
\(376\) | −28.5153 | −1.47057 | ||||||||
\(377\) | −3.12492 | −0.160941 | ||||||||
\(378\) | 2.57886 | 0.132642 | ||||||||
\(379\) | 33.6280 | 1.72736 | 0.863678 | − | 0.504045i | \(-0.168155\pi\) | ||||
0.863678 | + | 0.504045i | \(0.168155\pi\) | |||||||
\(380\) | −53.8477 | −2.76233 | ||||||||
\(381\) | 2.33920 | 0.119841 | ||||||||
\(382\) | 24.2862 | 1.24259 | ||||||||
\(383\) | −1.36415 | −0.0697049 | −0.0348524 | − | 0.999392i | \(-0.511096\pi\) | ||||
−0.0348524 | + | 0.999392i | \(0.511096\pi\) | |||||||
\(384\) | 2.97116 | 0.151621 | ||||||||
\(385\) | 10.9061 | 0.555826 | ||||||||
\(386\) | −43.9913 | −2.23910 | ||||||||
\(387\) | −13.8977 | −0.706462 | ||||||||
\(388\) | −24.6390 | −1.25085 | ||||||||
\(389\) | −36.3694 | −1.84400 | −0.922000 | − | 0.387189i | \(-0.873446\pi\) | ||||
−0.922000 | + | 0.387189i | \(0.873446\pi\) | |||||||
\(390\) | −4.41179 | −0.223399 | ||||||||
\(391\) | 41.9364 | 2.12081 | ||||||||
\(392\) | −5.51083 | −0.278339 | ||||||||
\(393\) | 3.84875 | 0.194144 | ||||||||
\(394\) | 45.0482 | 2.26950 | ||||||||
\(395\) | 38.3153 | 1.92785 | ||||||||
\(396\) | −59.3702 | −2.98346 | ||||||||
\(397\) | 0.950346 | 0.0476965 | 0.0238483 | − | 0.999716i | \(-0.492408\pi\) | ||||
0.0238483 | + | 0.999716i | \(0.492408\pi\) | |||||||
\(398\) | 7.54122 | 0.378007 | ||||||||
\(399\) | −0.964655 | −0.0482932 | ||||||||
\(400\) | 1.47960 | 0.0739800 | ||||||||
\(401\) | −11.4641 | −0.572489 | −0.286244 | − | 0.958157i | \(-0.592407\pi\) | ||||
−0.286244 | + | 0.958157i | \(0.592407\pi\) | |||||||
\(402\) | 3.60845 | 0.179973 | ||||||||
\(403\) | 39.9397 | 1.98954 | ||||||||
\(404\) | 23.7646 | 1.18233 | ||||||||
\(405\) | 20.0584 | 0.996712 | ||||||||
\(406\) | 1.75197 | 0.0869486 | ||||||||
\(407\) | 43.0742 | 2.13511 | ||||||||
\(408\) | −7.28257 | −0.360541 | ||||||||
\(409\) | 27.2286 | 1.34637 | 0.673184 | − | 0.739475i | \(-0.264926\pi\) | ||||
0.673184 | + | 0.739475i | \(0.264926\pi\) | |||||||
\(410\) | 17.5105 | 0.864781 | ||||||||
\(411\) | 2.75463 | 0.135876 | ||||||||
\(412\) | −17.8850 | −0.881131 | ||||||||
\(413\) | −11.8939 | −0.585258 | ||||||||
\(414\) | 40.7127 | 2.00092 | ||||||||
\(415\) | −13.1868 | −0.647314 | ||||||||
\(416\) | −9.85366 | −0.483115 | ||||||||
\(417\) | 0.781073 | 0.0382493 | ||||||||
\(418\) | 65.8421 | 3.22044 | ||||||||
\(419\) | 21.5419 | 1.05239 | 0.526196 | − | 0.850363i | \(-0.323618\pi\) | ||||
0.526196 | + | 0.850363i | \(0.323618\pi\) | |||||||
\(420\) | 1.67700 | 0.0818290 | ||||||||
\(421\) | 39.6151 | 1.93072 | 0.965362 | − | 0.260916i | \(-0.0840245\pi\) | ||||
0.965362 | + | 0.260916i | \(0.0840245\pi\) | |||||||
\(422\) | −11.7040 | −0.569742 | ||||||||
\(423\) | −15.3678 | −0.747208 | ||||||||
\(424\) | −38.8499 | −1.88672 | ||||||||
\(425\) | 2.12373 | 0.103016 | ||||||||
\(426\) | 2.28710 | 0.110810 | ||||||||
\(427\) | 1.14576 | 0.0554470 | ||||||||
\(428\) | −6.47728 | −0.313091 | ||||||||
\(429\) | 3.65747 | 0.176584 | ||||||||
\(430\) | −26.7941 | −1.29213 | ||||||||
\(431\) | −11.3523 | −0.546820 | −0.273410 | − | 0.961898i | \(-0.588152\pi\) | ||||
−0.273410 | + | 0.961898i | \(0.588152\pi\) | |||||||
\(432\) | −5.49647 | −0.264449 | ||||||||
\(433\) | −13.8755 | −0.666812 | −0.333406 | − | 0.942783i | \(-0.608198\pi\) | ||||
−0.333406 | + | 0.942783i | \(0.608198\pi\) | |||||||
\(434\) | −22.3920 | −1.07485 | ||||||||
\(435\) | −0.279939 | −0.0134220 | ||||||||
\(436\) | −76.0502 | −3.64214 | ||||||||
\(437\) | −30.6123 | −1.46438 | ||||||||
\(438\) | 5.20832 | 0.248863 | ||||||||
\(439\) | −21.6239 | −1.03205 | −0.516027 | − | 0.856572i | \(-0.672590\pi\) | ||||
−0.516027 | + | 0.856572i | \(0.672590\pi\) | |||||||
\(440\) | −60.1015 | −2.86523 | ||||||||
\(441\) | −2.96996 | −0.141427 | ||||||||
\(442\) | −84.4673 | −4.01770 | ||||||||
\(443\) | 8.92232 | 0.423912 | 0.211956 | − | 0.977279i | \(-0.432017\pi\) | ||||
0.211956 | + | 0.977279i | \(0.432017\pi\) | |||||||
\(444\) | 6.62338 | 0.314332 | ||||||||
\(445\) | −10.3430 | −0.490306 | ||||||||
\(446\) | −55.2940 | −2.61825 | ||||||||
\(447\) | 0.0802545 | 0.00379591 | ||||||||
\(448\) | −5.09927 | −0.240918 | ||||||||
\(449\) | −13.4689 | −0.635639 | −0.317819 | − | 0.948151i | \(-0.602951\pi\) | ||||
−0.317819 | + | 0.948151i | \(0.602951\pi\) | |||||||
\(450\) | 2.06176 | 0.0971923 | ||||||||
\(451\) | −14.5166 | −0.683559 | ||||||||
\(452\) | 6.67615 | 0.314020 | ||||||||
\(453\) | −0.424206 | −0.0199309 | ||||||||
\(454\) | −14.8228 | −0.695668 | ||||||||
\(455\) | 10.2131 | 0.478798 | ||||||||
\(456\) | 5.31605 | 0.248947 | ||||||||
\(457\) | 31.7931 | 1.48722 | 0.743608 | − | 0.668615i | \(-0.233113\pi\) | ||||
0.743608 | + | 0.668615i | \(0.233113\pi\) | |||||||
\(458\) | 39.2217 | 1.83271 | ||||||||
\(459\) | −7.88931 | −0.368241 | ||||||||
\(460\) | 53.2176 | 2.48128 | ||||||||
\(461\) | 14.3153 | 0.666731 | 0.333366 | − | 0.942798i | \(-0.391816\pi\) | ||||
0.333366 | + | 0.942798i | \(0.391816\pi\) | |||||||
\(462\) | −2.05054 | −0.0953997 | ||||||||
\(463\) | 35.4821 | 1.64899 | 0.824496 | − | 0.565867i | \(-0.191459\pi\) | ||||
0.824496 | + | 0.565867i | \(0.191459\pi\) | |||||||
\(464\) | −3.73407 | −0.173350 | ||||||||
\(465\) | 3.57791 | 0.165922 | ||||||||
\(466\) | 5.56284 | 0.257693 | ||||||||
\(467\) | 3.44580 | 0.159452 | 0.0797262 | − | 0.996817i | \(-0.474595\pi\) | ||||
0.0797262 | + | 0.996817i | \(0.474595\pi\) | |||||||
\(468\) | −55.5978 | −2.57001 | ||||||||
\(469\) | −8.35343 | −0.385726 | ||||||||
\(470\) | −29.6283 | −1.36665 | ||||||||
\(471\) | 2.38528 | 0.109908 | ||||||||
\(472\) | 65.5450 | 3.01695 | ||||||||
\(473\) | 22.2129 | 1.02135 | ||||||||
\(474\) | −7.20396 | −0.330889 | ||||||||
\(475\) | −1.55026 | −0.0711307 | ||||||||
\(476\) | 32.1074 | 1.47164 | ||||||||
\(477\) | −20.9374 | −0.958660 | ||||||||
\(478\) | 50.8532 | 2.32597 | ||||||||
\(479\) | 27.2486 | 1.24502 | 0.622510 | − | 0.782612i | \(-0.286113\pi\) | ||||
0.622510 | + | 0.782612i | \(0.286113\pi\) | |||||||
\(480\) | −0.882718 | −0.0402904 | ||||||||
\(481\) | 40.3373 | 1.83922 | ||||||||
\(482\) | 7.76672 | 0.353765 | ||||||||
\(483\) | 0.953366 | 0.0433797 | ||||||||
\(484\) | 48.5687 | 2.20767 | ||||||||
\(485\) | −13.4423 | −0.610383 | ||||||||
\(486\) | −11.5079 | −0.522010 | ||||||||
\(487\) | 23.9708 | 1.08622 | 0.543110 | − | 0.839662i | \(-0.317247\pi\) | ||||
0.543110 | + | 0.839662i | \(0.317247\pi\) | |||||||
\(488\) | −6.31406 | −0.285824 | ||||||||
\(489\) | −1.64404 | −0.0743461 | ||||||||
\(490\) | −5.72592 | −0.258671 | ||||||||
\(491\) | 29.4978 | 1.33122 | 0.665609 | − | 0.746300i | \(-0.268172\pi\) | ||||
0.665609 | + | 0.746300i | \(0.268172\pi\) | |||||||
\(492\) | −2.23217 | −0.100634 | ||||||||
\(493\) | −5.35966 | −0.241387 | ||||||||
\(494\) | 61.6585 | 2.77415 | ||||||||
\(495\) | −32.3906 | −1.45585 | ||||||||
\(496\) | 47.7253 | 2.14293 | ||||||||
\(497\) | −5.29454 | −0.237492 | ||||||||
\(498\) | 2.47935 | 0.111102 | ||||||||
\(499\) | 11.3620 | 0.508634 | 0.254317 | − | 0.967121i | \(-0.418149\pi\) | ||||
0.254317 | + | 0.967121i | \(0.418149\pi\) | |||||||
\(500\) | −45.6814 | −2.04293 | ||||||||
\(501\) | −2.51334 | −0.112288 | ||||||||
\(502\) | 48.6136 | 2.16973 | ||||||||
\(503\) | 38.8200 | 1.73090 | 0.865449 | − | 0.500997i | \(-0.167033\pi\) | ||||
0.865449 | + | 0.500997i | \(0.167033\pi\) | |||||||
\(504\) | 16.3669 | 0.729041 | ||||||||
\(505\) | 12.9652 | 0.576946 | ||||||||
\(506\) | −65.0715 | −2.89278 | ||||||||
\(507\) | 1.17182 | 0.0520421 | ||||||||
\(508\) | 56.8336 | 2.52158 | ||||||||
\(509\) | −40.3600 | −1.78893 | −0.894464 | − | 0.447141i | \(-0.852442\pi\) | ||||
−0.894464 | + | 0.447141i | \(0.852442\pi\) | |||||||
\(510\) | −7.56681 | −0.335064 | ||||||||
\(511\) | −12.0571 | −0.533373 | ||||||||
\(512\) | 46.7707 | 2.06699 | ||||||||
\(513\) | 5.75895 | 0.254264 | ||||||||
\(514\) | −11.3957 | −0.502641 | ||||||||
\(515\) | −9.75753 | −0.429968 | ||||||||
\(516\) | 3.41561 | 0.150364 | ||||||||
\(517\) | 24.5625 | 1.08026 | ||||||||
\(518\) | −22.6148 | −0.993638 | ||||||||
\(519\) | −3.28417 | −0.144159 | ||||||||
\(520\) | −56.2827 | −2.46816 | ||||||||
\(521\) | −18.6212 | −0.815811 | −0.407906 | − | 0.913024i | \(-0.633741\pi\) | ||||
−0.407906 | + | 0.913024i | \(0.633741\pi\) | |||||||
\(522\) | −5.20326 | −0.227741 | ||||||||
\(523\) | −14.9812 | −0.655081 | −0.327541 | − | 0.944837i | \(-0.606220\pi\) | ||||
−0.327541 | + | 0.944837i | \(0.606220\pi\) | |||||||
\(524\) | 93.5099 | 4.08500 | ||||||||
\(525\) | 0.0482801 | 0.00210712 | ||||||||
\(526\) | 32.5316 | 1.41845 | ||||||||
\(527\) | 68.5021 | 2.98400 | ||||||||
\(528\) | 4.37043 | 0.190199 | ||||||||
\(529\) | 7.25401 | 0.315392 | ||||||||
\(530\) | −40.3663 | −1.75340 | ||||||||
\(531\) | 35.3242 | 1.53294 | ||||||||
\(532\) | −23.4374 | −1.01614 | ||||||||
\(533\) | −13.5942 | −0.588830 | ||||||||
\(534\) | 1.94467 | 0.0841542 | ||||||||
\(535\) | −3.53381 | −0.152780 | ||||||||
\(536\) | 46.0343 | 1.98838 | ||||||||
\(537\) | −1.55046 | −0.0669073 | ||||||||
\(538\) | 8.29414 | 0.357586 | ||||||||
\(539\) | 4.74692 | 0.204464 | ||||||||
\(540\) | −10.0116 | −0.430830 | ||||||||
\(541\) | 26.6191 | 1.14444 | 0.572222 | − | 0.820099i | \(-0.306082\pi\) | ||||
0.572222 | + | 0.820099i | \(0.306082\pi\) | |||||||
\(542\) | −0.488416 | −0.0209793 | ||||||||
\(543\) | −1.91913 | −0.0823577 | ||||||||
\(544\) | −16.9004 | −0.724597 | ||||||||
\(545\) | −41.4908 | −1.77727 | ||||||||
\(546\) | −1.92025 | −0.0821790 | ||||||||
\(547\) | −33.7569 | −1.44334 | −0.721671 | − | 0.692236i | \(-0.756626\pi\) | ||||
−0.721671 | + | 0.692236i | \(0.756626\pi\) | |||||||
\(548\) | 66.9269 | 2.85897 | ||||||||
\(549\) | −3.40285 | −0.145230 | ||||||||
\(550\) | −3.29534 | −0.140514 | ||||||||
\(551\) | 3.91238 | 0.166673 | ||||||||
\(552\) | −5.25384 | −0.223618 | ||||||||
\(553\) | 16.6769 | 0.709174 | ||||||||
\(554\) | 2.77972 | 0.118099 | ||||||||
\(555\) | 3.61352 | 0.153386 | ||||||||
\(556\) | 18.9771 | 0.804808 | ||||||||
\(557\) | −42.8417 | −1.81526 | −0.907631 | − | 0.419769i | \(-0.862111\pi\) | ||||
−0.907631 | + | 0.419769i | \(0.862111\pi\) | |||||||
\(558\) | 66.5032 | 2.81530 | ||||||||
\(559\) | 20.8015 | 0.879811 | ||||||||
\(560\) | 12.2040 | 0.515712 | ||||||||
\(561\) | 6.27306 | 0.264849 | ||||||||
\(562\) | 25.5574 | 1.07807 | ||||||||
\(563\) | −28.9599 | −1.22051 | −0.610257 | − | 0.792204i | \(-0.708934\pi\) | ||||
−0.610257 | + | 0.792204i | \(0.708934\pi\) | |||||||
\(564\) | 3.77691 | 0.159036 | ||||||||
\(565\) | 3.64231 | 0.153233 | ||||||||
\(566\) | 35.7411 | 1.50231 | ||||||||
\(567\) | 8.73052 | 0.366647 | ||||||||
\(568\) | 29.1773 | 1.22425 | ||||||||
\(569\) | 29.9084 | 1.25382 | 0.626912 | − | 0.779090i | \(-0.284318\pi\) | ||||
0.626912 | + | 0.779090i | \(0.284318\pi\) | |||||||
\(570\) | 5.52354 | 0.231356 | ||||||||
\(571\) | −10.3344 | −0.432479 | −0.216240 | − | 0.976340i | \(-0.569379\pi\) | ||||
−0.216240 | + | 0.976340i | \(0.569379\pi\) | |||||||
\(572\) | 88.8626 | 3.71553 | ||||||||
\(573\) | −1.68904 | −0.0705606 | ||||||||
\(574\) | 7.62150 | 0.318115 | ||||||||
\(575\) | 1.53212 | 0.0638936 | ||||||||
\(576\) | 15.1446 | 0.631026 | ||||||||
\(577\) | 18.6240 | 0.775325 | 0.387663 | − | 0.921801i | \(-0.373283\pi\) | ||||
0.387663 | + | 0.921801i | \(0.373283\pi\) | |||||||
\(578\) | −102.505 | −4.26364 | ||||||||
\(579\) | 3.05948 | 0.127148 | ||||||||
\(580\) | −6.80144 | −0.282415 | ||||||||
\(581\) | −5.73960 | −0.238119 | ||||||||
\(582\) | 2.52739 | 0.104764 | ||||||||
\(583\) | 33.4646 | 1.38596 | ||||||||
\(584\) | 66.4443 | 2.74949 | ||||||||
\(585\) | −30.3325 | −1.25410 | ||||||||
\(586\) | 67.0322 | 2.76907 | ||||||||
\(587\) | −12.2949 | −0.507464 | −0.253732 | − | 0.967275i | \(-0.581658\pi\) | ||||
−0.253732 | + | 0.967275i | \(0.581658\pi\) | |||||||
\(588\) | 0.729919 | 0.0301013 | ||||||||
\(589\) | −50.0044 | −2.06039 | ||||||||
\(590\) | 68.1032 | 2.80377 | ||||||||
\(591\) | −3.13298 | −0.128874 | ||||||||
\(592\) | 48.2003 | 1.98102 | ||||||||
\(593\) | −15.9500 | −0.654990 | −0.327495 | − | 0.944853i | \(-0.606204\pi\) | ||||
−0.327495 | + | 0.944853i | \(0.606204\pi\) | |||||||
\(594\) | 12.2416 | 0.502280 | ||||||||
\(595\) | 17.5169 | 0.718122 | ||||||||
\(596\) | 1.94988 | 0.0798702 | ||||||||
\(597\) | −0.524472 | −0.0214652 | ||||||||
\(598\) | −60.9369 | −2.49190 | ||||||||
\(599\) | 12.3125 | 0.503075 | 0.251537 | − | 0.967848i | \(-0.419064\pi\) | ||||
0.251537 | + | 0.967848i | \(0.419064\pi\) | |||||||
\(600\) | −0.266063 | −0.0108620 | ||||||||
\(601\) | 8.93720 | 0.364556 | 0.182278 | − | 0.983247i | \(-0.441653\pi\) | ||||
0.182278 | + | 0.983247i | \(0.441653\pi\) | |||||||
\(602\) | −11.6622 | −0.475317 | ||||||||
\(603\) | 24.8093 | 1.01031 | ||||||||
\(604\) | −10.3066 | −0.419369 | ||||||||
\(605\) | 26.4977 | 1.07728 | ||||||||
\(606\) | −2.43770 | −0.0990247 | ||||||||
\(607\) | −2.79850 | −0.113587 | −0.0567937 | − | 0.998386i | \(-0.518088\pi\) | ||||
−0.0567937 | + | 0.998386i | \(0.518088\pi\) | |||||||
\(608\) | 12.3367 | 0.500321 | ||||||||
\(609\) | −0.121844 | −0.00493739 | ||||||||
\(610\) | −6.56051 | −0.265627 | ||||||||
\(611\) | 23.0018 | 0.930555 | ||||||||
\(612\) | −95.3578 | −3.85461 | ||||||||
\(613\) | −19.1133 | −0.771979 | −0.385990 | − | 0.922503i | \(-0.626140\pi\) | ||||
−0.385990 | + | 0.922503i | \(0.626140\pi\) | |||||||
\(614\) | 15.0070 | 0.605632 | ||||||||
\(615\) | −1.21781 | −0.0491067 | ||||||||
\(616\) | −26.1594 | −1.05399 | ||||||||
\(617\) | 10.8463 | 0.436654 | 0.218327 | − | 0.975876i | \(-0.429940\pi\) | ||||
0.218327 | + | 0.975876i | \(0.429940\pi\) | |||||||
\(618\) | 1.83459 | 0.0737980 | ||||||||
\(619\) | 37.8949 | 1.52312 | 0.761562 | − | 0.648092i | \(-0.224433\pi\) | ||||
0.761562 | + | 0.648092i | \(0.224433\pi\) | |||||||
\(620\) | 86.9296 | 3.49118 | ||||||||
\(621\) | −5.69156 | −0.228394 | ||||||||
\(622\) | −74.5655 | −2.98981 | ||||||||
\(623\) | −4.50184 | −0.180362 | ||||||||
\(624\) | 4.09273 | 0.163841 | ||||||||
\(625\) | −26.3152 | −1.05261 | ||||||||
\(626\) | −64.8970 | −2.59381 | ||||||||
\(627\) | −4.57914 | −0.182873 | ||||||||
\(628\) | 57.9533 | 2.31259 | ||||||||
\(629\) | 69.1839 | 2.75854 | ||||||||
\(630\) | 17.0057 | 0.677525 | ||||||||
\(631\) | −37.5224 | −1.49374 | −0.746871 | − | 0.664969i | \(-0.768445\pi\) | ||||
−0.746871 | + | 0.664969i | \(0.768445\pi\) | |||||||
\(632\) | −91.9035 | −3.65572 | ||||||||
\(633\) | 0.813982 | 0.0323529 | ||||||||
\(634\) | 81.8659 | 3.25131 | ||||||||
\(635\) | 31.0068 | 1.23047 | ||||||||
\(636\) | 5.14574 | 0.204042 | ||||||||
\(637\) | 4.44530 | 0.176129 | ||||||||
\(638\) | 8.31643 | 0.329251 | ||||||||
\(639\) | 15.7246 | 0.622054 | ||||||||
\(640\) | 39.3835 | 1.55677 | ||||||||
\(641\) | −45.0884 | −1.78089 | −0.890443 | − | 0.455096i | \(-0.849605\pi\) | ||||
−0.890443 | + | 0.455096i | \(0.849605\pi\) | |||||||
\(642\) | 0.664419 | 0.0262225 | ||||||||
\(643\) | −45.7955 | −1.80600 | −0.903000 | − | 0.429642i | \(-0.858640\pi\) | ||||
−0.903000 | + | 0.429642i | \(0.858640\pi\) | |||||||
\(644\) | 23.1632 | 0.912756 | ||||||||
\(645\) | 1.86346 | 0.0733736 | ||||||||
\(646\) | 105.753 | 4.16078 | ||||||||
\(647\) | −14.4987 | −0.570004 | −0.285002 | − | 0.958527i | \(-0.591994\pi\) | ||||
−0.285002 | + | 0.958527i | \(0.591994\pi\) | |||||||
\(648\) | −48.1124 | −1.89003 | ||||||||
\(649\) | −56.4591 | −2.21621 | ||||||||
\(650\) | −3.08595 | −0.121041 | ||||||||
\(651\) | 1.55730 | 0.0610354 | ||||||||
\(652\) | −39.9439 | −1.56432 | ||||||||
\(653\) | 31.3208 | 1.22568 | 0.612838 | − | 0.790209i | \(-0.290028\pi\) | ||||
0.612838 | + | 0.790209i | \(0.290028\pi\) | |||||||
\(654\) | 7.80100 | 0.305043 | ||||||||
\(655\) | 51.0163 | 1.99337 | ||||||||
\(656\) | −16.2442 | −0.634228 | ||||||||
\(657\) | 35.8089 | 1.39704 | ||||||||
\(658\) | −12.8958 | −0.502732 | ||||||||
\(659\) | 28.5345 | 1.11155 | 0.555774 | − | 0.831334i | \(-0.312422\pi\) | ||||
0.555774 | + | 0.831334i | \(0.312422\pi\) | |||||||
\(660\) | 7.96056 | 0.309864 | ||||||||
\(661\) | 26.4881 | 1.03027 | 0.515134 | − | 0.857109i | \(-0.327742\pi\) | ||||
0.515134 | + | 0.857109i | \(0.327742\pi\) | |||||||
\(662\) | 42.5811 | 1.65496 | ||||||||
\(663\) | 5.87447 | 0.228146 | ||||||||
\(664\) | 31.6300 | 1.22748 | ||||||||
\(665\) | −12.7868 | −0.495850 | ||||||||
\(666\) | 67.1651 | 2.60259 | ||||||||
\(667\) | −3.86660 | −0.149715 | ||||||||
\(668\) | −61.0645 | −2.36266 | ||||||||
\(669\) | 3.84555 | 0.148678 | ||||||||
\(670\) | 47.8311 | 1.84787 | ||||||||
\(671\) | 5.43881 | 0.209963 | ||||||||
\(672\) | −0.384207 | −0.0148211 | ||||||||
\(673\) | 19.5956 | 0.755354 | 0.377677 | − | 0.925938i | \(-0.376723\pi\) | ||||
0.377677 | + | 0.925938i | \(0.376723\pi\) | |||||||
\(674\) | −12.1499 | −0.467995 | ||||||||
\(675\) | −0.288230 | −0.0110940 | ||||||||
\(676\) | 28.4706 | 1.09502 | ||||||||
\(677\) | 13.2267 | 0.508343 | 0.254172 | − | 0.967159i | \(-0.418197\pi\) | ||||
0.254172 | + | 0.967159i | \(0.418197\pi\) | |||||||
\(678\) | −0.684819 | −0.0263003 | ||||||||
\(679\) | −5.85081 | −0.224534 | ||||||||
\(680\) | −96.5325 | −3.70185 | ||||||||
\(681\) | 1.03089 | 0.0395036 | ||||||||
\(682\) | −106.293 | −4.07016 | ||||||||
\(683\) | 16.4729 | 0.630317 | 0.315158 | − | 0.949039i | \(-0.397942\pi\) | ||||
0.315158 | + | 0.949039i | \(0.397942\pi\) | |||||||
\(684\) | 69.6082 | 2.66154 | ||||||||
\(685\) | 36.5133 | 1.39510 | ||||||||
\(686\) | −2.49223 | −0.0951537 | ||||||||
\(687\) | −2.72777 | −0.104071 | ||||||||
\(688\) | 24.8564 | 0.947642 | ||||||||
\(689\) | 31.3382 | 1.19389 | ||||||||
\(690\) | −5.45890 | −0.207817 | ||||||||
\(691\) | 35.4706 | 1.34937 | 0.674684 | − | 0.738107i | \(-0.264280\pi\) | ||||
0.674684 | + | 0.738107i | \(0.264280\pi\) | |||||||
\(692\) | −79.7929 | −3.03327 | ||||||||
\(693\) | −14.0981 | −0.535544 | ||||||||
\(694\) | 46.6862 | 1.77218 | ||||||||
\(695\) | 10.3533 | 0.392725 | ||||||||
\(696\) | 0.671464 | 0.0254518 | ||||||||
\(697\) | −23.3159 | −0.883153 | ||||||||
\(698\) | 31.4151 | 1.18908 | ||||||||
\(699\) | −0.386880 | −0.0146332 | ||||||||
\(700\) | 1.17302 | 0.0443361 | ||||||||
\(701\) | 8.17549 | 0.308784 | 0.154392 | − | 0.988010i | \(-0.450658\pi\) | ||||
0.154392 | + | 0.988010i | \(0.450658\pi\) | |||||||
\(702\) | 11.4638 | 0.432673 | ||||||||
\(703\) | −50.5021 | −1.90472 | ||||||||
\(704\) | −24.2058 | −0.912291 | ||||||||
\(705\) | 2.06057 | 0.0776055 | ||||||||
\(706\) | −16.3816 | −0.616530 | ||||||||
\(707\) | 5.64318 | 0.212233 | ||||||||
\(708\) | −8.68155 | −0.326273 | ||||||||
\(709\) | 5.62194 | 0.211136 | 0.105568 | − | 0.994412i | \(-0.466334\pi\) | ||||
0.105568 | + | 0.994412i | \(0.466334\pi\) | |||||||
\(710\) | 30.3161 | 1.13774 | ||||||||
\(711\) | −49.5297 | −1.85751 | ||||||||
\(712\) | 24.8089 | 0.929752 | ||||||||
\(713\) | 49.4192 | 1.85076 | ||||||||
\(714\) | −3.29348 | −0.123256 | ||||||||
\(715\) | 48.4808 | 1.81308 | ||||||||
\(716\) | −37.6703 | −1.40780 | ||||||||
\(717\) | −3.53670 | −0.132081 | ||||||||
\(718\) | 56.2140 | 2.09789 | ||||||||
\(719\) | 19.8931 | 0.741888 | 0.370944 | − | 0.928655i | \(-0.379034\pi\) | ||||
0.370944 | + | 0.928655i | \(0.379034\pi\) | |||||||
\(720\) | −36.2453 | −1.35078 | ||||||||
\(721\) | −4.24701 | −0.158167 | ||||||||
\(722\) | −29.8438 | −1.11067 | ||||||||
\(723\) | −0.540155 | −0.0200886 | ||||||||
\(724\) | −46.6275 | −1.73290 | ||||||||
\(725\) | −0.195811 | −0.00727225 | ||||||||
\(726\) | −4.98203 | −0.184901 | ||||||||
\(727\) | 28.2937 | 1.04936 | 0.524678 | − | 0.851301i | \(-0.324186\pi\) | ||||
0.524678 | + | 0.851301i | \(0.324186\pi\) | |||||||
\(728\) | −24.4973 | −0.907929 | ||||||||
\(729\) | −25.3912 | −0.940415 | ||||||||
\(730\) | 69.0377 | 2.55520 | ||||||||
\(731\) | 35.6774 | 1.31958 | ||||||||
\(732\) | 0.836309 | 0.0309109 | ||||||||
\(733\) | −50.8733 | −1.87905 | −0.939524 | − | 0.342483i | \(-0.888732\pi\) | ||||
−0.939524 | + | 0.342483i | \(0.888732\pi\) | |||||||
\(734\) | 78.7926 | 2.90829 | ||||||||
\(735\) | 0.398222 | 0.0146886 | ||||||||
\(736\) | −12.1924 | −0.449417 | ||||||||
\(737\) | −39.6530 | −1.46064 | ||||||||
\(738\) | −22.6355 | −0.833226 | ||||||||
\(739\) | 0.586872 | 0.0215884 | 0.0107942 | − | 0.999942i | \(-0.496564\pi\) | ||||
0.0107942 | + | 0.999942i | \(0.496564\pi\) | |||||||
\(740\) | 87.7948 | 3.22740 | ||||||||
\(741\) | −4.28818 | −0.157530 | ||||||||
\(742\) | −17.5696 | −0.645000 | ||||||||
\(743\) | −46.8964 | −1.72046 | −0.860230 | − | 0.509906i | \(-0.829680\pi\) | ||||
−0.860230 | + | 0.509906i | \(0.829680\pi\) | |||||||
\(744\) | −8.58201 | −0.314632 | ||||||||
\(745\) | 1.06380 | 0.0389745 | ||||||||
\(746\) | 49.7731 | 1.82232 | ||||||||
\(747\) | 17.0464 | 0.623694 | ||||||||
\(748\) | 152.411 | 5.57271 | ||||||||
\(749\) | −1.53811 | −0.0562011 | ||||||||
\(750\) | 4.68586 | 0.171103 | ||||||||
\(751\) | −3.87881 | −0.141540 | −0.0707700 | − | 0.997493i | \(-0.522546\pi\) | ||||
−0.0707700 | + | 0.997493i | \(0.522546\pi\) | |||||||
\(752\) | 27.4857 | 1.00230 | ||||||||
\(753\) | −3.38094 | −0.123208 | ||||||||
\(754\) | 7.78801 | 0.283623 | ||||||||
\(755\) | −5.62297 | −0.204641 | ||||||||
\(756\) | −4.35758 | −0.158484 | ||||||||
\(757\) | 7.16382 | 0.260373 | 0.130187 | − | 0.991489i | \(-0.458442\pi\) | ||||
0.130187 | + | 0.991489i | \(0.458442\pi\) | |||||||
\(758\) | −83.8087 | −3.04407 | ||||||||
\(759\) | 4.52555 | 0.164267 | ||||||||
\(760\) | 70.4657 | 2.55606 | ||||||||
\(761\) | 51.2063 | 1.85623 | 0.928114 | − | 0.372296i | \(-0.121430\pi\) | ||||
0.928114 | + | 0.372296i | \(0.121430\pi\) | |||||||
\(762\) | −5.82982 | −0.211192 | ||||||||
\(763\) | −18.0590 | −0.653780 | ||||||||
\(764\) | −41.0372 | −1.48467 | ||||||||
\(765\) | −52.0244 | −1.88095 | ||||||||
\(766\) | 3.39978 | 0.122839 | ||||||||
\(767\) | −52.8717 | −1.90909 | ||||||||
\(768\) | −5.63712 | −0.203412 | ||||||||
\(769\) | 10.7227 | 0.386672 | 0.193336 | − | 0.981133i | \(-0.438069\pi\) | ||||
0.193336 | + | 0.981133i | \(0.438069\pi\) | |||||||
\(770\) | −27.1805 | −0.979516 | ||||||||
\(771\) | 0.792538 | 0.0285425 | ||||||||
\(772\) | 74.3337 | 2.67533 | ||||||||
\(773\) | −38.1132 | −1.37084 | −0.685419 | − | 0.728149i | \(-0.740381\pi\) | ||||
−0.685419 | + | 0.728149i | \(0.740381\pi\) | |||||||
\(774\) | 34.6364 | 1.24498 | ||||||||
\(775\) | 2.50267 | 0.0898987 | ||||||||
\(776\) | 32.2428 | 1.15745 | ||||||||
\(777\) | 1.57280 | 0.0564239 | ||||||||
\(778\) | 90.6408 | 3.24963 | ||||||||
\(779\) | 17.0199 | 0.609801 | ||||||||
\(780\) | 7.45475 | 0.266923 | ||||||||
\(781\) | −25.1327 | −0.899320 | ||||||||
\(782\) | −104.515 | −3.73745 | ||||||||
\(783\) | 0.727406 | 0.0259954 | ||||||||
\(784\) | 5.31183 | 0.189708 | ||||||||
\(785\) | 31.6176 | 1.12848 | ||||||||
\(786\) | −9.59197 | −0.342134 | ||||||||
\(787\) | 18.9969 | 0.677167 | 0.338583 | − | 0.940936i | \(-0.390052\pi\) | ||||
0.338583 | + | 0.940936i | \(0.390052\pi\) | |||||||
\(788\) | −76.1195 | −2.71165 | ||||||||
\(789\) | −2.26249 | −0.0805466 | ||||||||
\(790\) | −95.4906 | −3.39740 | ||||||||
\(791\) | 1.58533 | 0.0563679 | ||||||||
\(792\) | 77.6924 | 2.76068 | ||||||||
\(793\) | 5.09323 | 0.180866 | ||||||||
\(794\) | −2.36848 | −0.0840542 | ||||||||
\(795\) | 2.80737 | 0.0995670 | ||||||||
\(796\) | −12.7427 | −0.451652 | ||||||||
\(797\) | −3.70336 | −0.131180 | −0.0655899 | − | 0.997847i | \(-0.520893\pi\) | ||||
−0.0655899 | + | 0.997847i | \(0.520893\pi\) | |||||||
\(798\) | 2.40414 | 0.0851057 | ||||||||
\(799\) | 39.4513 | 1.39569 | ||||||||
\(800\) | −0.617443 | −0.0218299 | ||||||||
\(801\) | 13.3703 | 0.472416 | ||||||||
\(802\) | 28.5711 | 1.00888 | ||||||||
\(803\) | −57.2338 | −2.01974 | ||||||||
\(804\) | −6.09732 | −0.215036 | ||||||||
\(805\) | 12.6371 | 0.445401 | ||||||||
\(806\) | −99.5390 | −3.50611 | ||||||||
\(807\) | −0.576835 | −0.0203055 | ||||||||
\(808\) | −31.0986 | −1.09404 | ||||||||
\(809\) | −28.9623 | −1.01826 | −0.509130 | − | 0.860690i | \(-0.670033\pi\) | ||||
−0.509130 | + | 0.860690i | \(0.670033\pi\) | |||||||
\(810\) | −49.9902 | −1.75648 | ||||||||
\(811\) | 22.9619 | 0.806303 | 0.403151 | − | 0.915133i | \(-0.367915\pi\) | ||||
0.403151 | + | 0.915133i | \(0.367915\pi\) | |||||||
\(812\) | −2.96036 | −0.103888 | ||||||||
\(813\) | 0.0339680 | 0.00119131 | ||||||||
\(814\) | −107.351 | −3.76264 | ||||||||
\(815\) | −21.7922 | −0.763348 | ||||||||
\(816\) | 7.01960 | 0.245735 | ||||||||
\(817\) | −26.0434 | −0.911144 | ||||||||
\(818\) | −67.8599 | −2.37267 | ||||||||
\(819\) | −13.2024 | −0.461327 | ||||||||
\(820\) | −29.5880 | −1.03326 | ||||||||
\(821\) | 17.4961 | 0.610616 | 0.305308 | − | 0.952254i | \(-0.401241\pi\) | ||||
0.305308 | + | 0.952254i | \(0.401241\pi\) | |||||||
\(822\) | −6.86516 | −0.239450 | ||||||||
\(823\) | 1.39813 | 0.0487357 | 0.0243678 | − | 0.999703i | \(-0.492243\pi\) | ||||
0.0243678 | + | 0.999703i | \(0.492243\pi\) | |||||||
\(824\) | 23.4045 | 0.815335 | ||||||||
\(825\) | 0.229182 | 0.00797908 | ||||||||
\(826\) | 29.6422 | 1.03138 | ||||||||
\(827\) | −14.2691 | −0.496186 | −0.248093 | − | 0.968736i | \(-0.579804\pi\) | ||||
−0.248093 | + | 0.968736i | \(0.579804\pi\) | |||||||
\(828\) | −68.7936 | −2.39074 | ||||||||
\(829\) | 44.3472 | 1.54024 | 0.770121 | − | 0.637898i | \(-0.220196\pi\) | ||||
0.770121 | + | 0.637898i | \(0.220196\pi\) | |||||||
\(830\) | 32.8645 | 1.14074 | ||||||||
\(831\) | −0.193322 | −0.00670628 | ||||||||
\(832\) | −22.6678 | −0.785864 | ||||||||
\(833\) | 7.62429 | 0.264166 | ||||||||
\(834\) | −1.94661 | −0.0674057 | ||||||||
\(835\) | −33.3150 | −1.15291 | ||||||||
\(836\) | −111.256 | −3.84785 | ||||||||
\(837\) | −9.29702 | −0.321352 | ||||||||
\(838\) | −53.6874 | −1.85460 | ||||||||
\(839\) | −10.3940 | −0.358839 | −0.179420 | − | 0.983773i | \(-0.557422\pi\) | ||||
−0.179420 | + | 0.983773i | \(0.557422\pi\) | |||||||
\(840\) | −2.19453 | −0.0757186 | ||||||||
\(841\) | −28.5058 | −0.982960 | ||||||||
\(842\) | −98.7300 | −3.40246 | ||||||||
\(843\) | −1.77745 | −0.0612185 | ||||||||
\(844\) | 19.7767 | 0.680740 | ||||||||
\(845\) | 15.5327 | 0.534342 | ||||||||
\(846\) | 38.3001 | 1.31678 | ||||||||
\(847\) | 11.5332 | 0.396286 | ||||||||
\(848\) | 37.4471 | 1.28594 | ||||||||
\(849\) | −2.48570 | −0.0853089 | ||||||||
\(850\) | −5.29282 | −0.181542 | ||||||||
\(851\) | 49.9111 | 1.71093 | ||||||||
\(852\) | −3.86458 | −0.132398 | ||||||||
\(853\) | 40.3933 | 1.38304 | 0.691520 | − | 0.722357i | \(-0.256941\pi\) | ||||
0.691520 | + | 0.722357i | \(0.256941\pi\) | |||||||
\(854\) | −2.85549 | −0.0977127 | ||||||||
\(855\) | 37.9762 | 1.29876 | ||||||||
\(856\) | 8.47623 | 0.289712 | ||||||||
\(857\) | 33.6418 | 1.14918 | 0.574591 | − | 0.818441i | \(-0.305161\pi\) | ||||
0.574591 | + | 0.818441i | \(0.305161\pi\) | |||||||
\(858\) | −9.11525 | −0.311190 | ||||||||
\(859\) | −29.5627 | −1.00867 | −0.504333 | − | 0.863509i | \(-0.668262\pi\) | ||||
−0.504333 | + | 0.863509i | \(0.668262\pi\) | |||||||
\(860\) | 45.2749 | 1.54386 | ||||||||
\(861\) | −0.530055 | −0.0180642 | ||||||||
\(862\) | 28.2925 | 0.963646 | ||||||||
\(863\) | −1.00000 | −0.0340404 | ||||||||
\(864\) | 2.29370 | 0.0780332 | ||||||||
\(865\) | −43.5326 | −1.48015 | ||||||||
\(866\) | 34.5808 | 1.17510 | ||||||||
\(867\) | 7.12894 | 0.242112 | ||||||||
\(868\) | 37.8365 | 1.28425 | ||||||||
\(869\) | 79.1639 | 2.68545 | ||||||||
\(870\) | 0.697672 | 0.0236533 | ||||||||
\(871\) | −37.1335 | −1.25822 | ||||||||
\(872\) | 99.5201 | 3.37018 | ||||||||
\(873\) | 17.3767 | 0.588111 | ||||||||
\(874\) | 76.2927 | 2.58064 | ||||||||
\(875\) | −10.8476 | −0.366715 | ||||||||
\(876\) | −8.80067 | −0.297347 | ||||||||
\(877\) | 6.11912 | 0.206628 | 0.103314 | − | 0.994649i | \(-0.467055\pi\) | ||||
0.103314 | + | 0.994649i | \(0.467055\pi\) | |||||||
\(878\) | 53.8918 | 1.81876 | ||||||||
\(879\) | −4.66191 | −0.157242 | ||||||||
\(880\) | 57.9313 | 1.95286 | ||||||||
\(881\) | −42.3782 | −1.42776 | −0.713878 | − | 0.700270i | \(-0.753063\pi\) | ||||
−0.713878 | + | 0.700270i | \(0.753063\pi\) | |||||||
\(882\) | 7.40181 | 0.249232 | ||||||||
\(883\) | 14.4968 | 0.487855 | 0.243928 | − | 0.969793i | \(-0.421564\pi\) | ||||
0.243928 | + | 0.969793i | \(0.421564\pi\) | |||||||
\(884\) | 142.727 | 4.80044 | ||||||||
\(885\) | −4.73640 | −0.159212 | ||||||||
\(886\) | −22.2365 | −0.747048 | ||||||||
\(887\) | 20.6720 | 0.694097 | 0.347048 | − | 0.937847i | \(-0.387184\pi\) | ||||
0.347048 | + | 0.937847i | \(0.387184\pi\) | |||||||
\(888\) | −8.66743 | −0.290860 | ||||||||
\(889\) | 13.4958 | 0.452635 | ||||||||
\(890\) | 25.7772 | 0.864053 | ||||||||
\(891\) | 41.4431 | 1.38839 | ||||||||
\(892\) | 93.4322 | 3.12834 | ||||||||
\(893\) | −28.7982 | −0.963696 | ||||||||
\(894\) | −0.200013 | −0.00668942 | ||||||||
\(895\) | −20.5518 | −0.686971 | ||||||||
\(896\) | 17.1418 | 0.572669 | ||||||||
\(897\) | 4.23800 | 0.141503 | ||||||||
\(898\) | 33.5677 | 1.12017 | ||||||||
\(899\) | −6.31600 | −0.210650 | ||||||||
\(900\) | −3.48383 | −0.116128 | ||||||||
\(901\) | 53.7493 | 1.79065 | ||||||||
\(902\) | 36.1786 | 1.20462 | ||||||||
\(903\) | 0.811077 | 0.0269910 | ||||||||
\(904\) | −8.73648 | −0.290571 | ||||||||
\(905\) | −25.4386 | −0.845608 | ||||||||
\(906\) | 1.05722 | 0.0351237 | ||||||||
\(907\) | 12.8102 | 0.425356 | 0.212678 | − | 0.977122i | \(-0.431781\pi\) | ||||
0.212678 | + | 0.977122i | \(0.431781\pi\) | |||||||
\(908\) | 25.0466 | 0.831200 | ||||||||
\(909\) | −16.7600 | −0.555894 | ||||||||
\(910\) | −25.4534 | −0.843773 | ||||||||
\(911\) | −37.6111 | −1.24611 | −0.623055 | − | 0.782178i | \(-0.714109\pi\) | ||||
−0.623055 | + | 0.782178i | \(0.714109\pi\) | |||||||
\(912\) | −5.12409 | −0.169675 | ||||||||
\(913\) | −27.2454 | −0.901692 | ||||||||
\(914\) | −79.2356 | −2.62088 | ||||||||
\(915\) | 0.456266 | 0.0150837 | ||||||||
\(916\) | −66.2743 | −2.18977 | ||||||||
\(917\) | 22.2050 | 0.733275 | ||||||||
\(918\) | 19.6620 | 0.648941 | ||||||||
\(919\) | 51.8458 | 1.71024 | 0.855118 | − | 0.518433i | \(-0.173484\pi\) | ||||
0.855118 | + | 0.518433i | \(0.173484\pi\) | |||||||
\(920\) | −69.6411 | −2.29600 | ||||||||
\(921\) | −1.04370 | −0.0343909 | ||||||||
\(922\) | −35.6771 | −1.17496 | ||||||||
\(923\) | −23.5358 | −0.774690 | ||||||||
\(924\) | 3.46486 | 0.113986 | ||||||||
\(925\) | 2.52758 | 0.0831064 | ||||||||
\(926\) | −88.4295 | −2.90597 | ||||||||
\(927\) | 12.6134 | 0.414279 | ||||||||
\(928\) | 1.55824 | 0.0511517 | ||||||||
\(929\) | 15.5155 | 0.509048 | 0.254524 | − | 0.967066i | \(-0.418081\pi\) | ||||
0.254524 | + | 0.967066i | \(0.418081\pi\) | |||||||
\(930\) | −8.91697 | −0.292399 | ||||||||
\(931\) | −5.56550 | −0.182402 | ||||||||
\(932\) | −9.39972 | −0.307898 | ||||||||
\(933\) | 5.18583 | 0.169777 | ||||||||
\(934\) | −8.58771 | −0.280998 | ||||||||
\(935\) | 83.1512 | 2.71933 | ||||||||
\(936\) | 72.7559 | 2.37810 | ||||||||
\(937\) | −45.3080 | −1.48015 | −0.740073 | − | 0.672526i | \(-0.765209\pi\) | ||||
−0.740073 | + | 0.672526i | \(0.765209\pi\) | |||||||
\(938\) | 20.8187 | 0.679753 | ||||||||
\(939\) | 4.51341 | 0.147290 | ||||||||
\(940\) | 50.0640 | 1.63291 | ||||||||
\(941\) | −20.3497 | −0.663380 | −0.331690 | − | 0.943388i | \(-0.607619\pi\) | ||||
−0.331690 | + | 0.943388i | \(0.607619\pi\) | |||||||
\(942\) | −5.94467 | −0.193688 | ||||||||
\(943\) | −16.8207 | −0.547758 | ||||||||
\(944\) | −63.1782 | −2.05627 | ||||||||
\(945\) | −2.37737 | −0.0773358 | ||||||||
\(946\) | −55.3597 | −1.79990 | ||||||||
\(947\) | 33.8198 | 1.09900 | 0.549498 | − | 0.835495i | \(-0.314819\pi\) | ||||
0.549498 | + | 0.835495i | \(0.314819\pi\) | |||||||
\(948\) | 12.1728 | 0.395354 | ||||||||
\(949\) | −53.5972 | −1.73984 | ||||||||
\(950\) | 3.86360 | 0.125352 | ||||||||
\(951\) | −5.69355 | −0.184626 | ||||||||
\(952\) | −42.0161 | −1.36175 | ||||||||
\(953\) | 54.0496 | 1.75084 | 0.875419 | − | 0.483365i | \(-0.160586\pi\) | ||||
0.875419 | + | 0.483365i | \(0.160586\pi\) | |||||||
\(954\) | 52.1809 | 1.68942 | ||||||||
\(955\) | −22.3887 | −0.724481 | ||||||||
\(956\) | −85.9284 | −2.77912 | ||||||||
\(957\) | −0.578386 | −0.0186966 | ||||||||
\(958\) | −67.9097 | −2.19406 | ||||||||
\(959\) | 15.8926 | 0.513198 | ||||||||
\(960\) | −2.03064 | −0.0655387 | ||||||||
\(961\) | 49.7250 | 1.60403 | ||||||||
\(962\) | −100.530 | −3.24121 | ||||||||
\(963\) | 4.56811 | 0.147205 | ||||||||
\(964\) | −13.1237 | −0.422686 | ||||||||
\(965\) | 40.5543 | 1.30549 | ||||||||
\(966\) | −2.37601 | −0.0764468 | ||||||||
\(967\) | −24.7111 | −0.794655 | −0.397327 | − | 0.917677i | \(-0.630062\pi\) | ||||
−0.397327 | + | 0.917677i | \(0.630062\pi\) | |||||||
\(968\) | −63.5576 | −2.04282 | ||||||||
\(969\) | −7.35481 | −0.236271 | ||||||||
\(970\) | 33.5013 | 1.07566 | ||||||||
\(971\) | 3.66325 | 0.117559 | 0.0587796 | − | 0.998271i | \(-0.481279\pi\) | ||||
0.0587796 | + | 0.998271i | \(0.481279\pi\) | |||||||
\(972\) | 19.4453 | 0.623709 | ||||||||
\(973\) | 4.50633 | 0.144466 | ||||||||
\(974\) | −59.7406 | −1.91421 | ||||||||
\(975\) | 0.214620 | 0.00687333 | ||||||||
\(976\) | 6.08606 | 0.194810 | ||||||||
\(977\) | −8.76216 | −0.280326 | −0.140163 | − | 0.990128i | \(-0.544763\pi\) | ||||
−0.140163 | + | 0.990128i | \(0.544763\pi\) | |||||||
\(978\) | 4.09732 | 0.131018 | ||||||||
\(979\) | −21.3699 | −0.682984 | ||||||||
\(980\) | 9.67528 | 0.309065 | ||||||||
\(981\) | 53.6345 | 1.71242 | ||||||||
\(982\) | −73.5153 | −2.34597 | ||||||||
\(983\) | 55.7992 | 1.77972 | 0.889860 | − | 0.456234i | \(-0.150802\pi\) | ||||
0.889860 | + | 0.456234i | \(0.150802\pi\) | |||||||
\(984\) | 2.92104 | 0.0931194 | ||||||||
\(985\) | −41.5286 | −1.32321 | ||||||||
\(986\) | 13.3575 | 0.425389 | ||||||||
\(987\) | 0.896871 | 0.0285477 | ||||||||
\(988\) | −104.186 | −3.31461 | ||||||||
\(989\) | 25.7386 | 0.818441 | ||||||||
\(990\) | 80.7248 | 2.56560 | ||||||||
\(991\) | 24.6850 | 0.784146 | 0.392073 | − | 0.919934i | \(-0.371758\pi\) | ||||
0.392073 | + | 0.919934i | \(0.371758\pi\) | |||||||
\(992\) | −19.9159 | −0.632332 | ||||||||
\(993\) | −2.96140 | −0.0939771 | ||||||||
\(994\) | 13.1952 | 0.418526 | ||||||||
\(995\) | −6.95202 | −0.220394 | ||||||||
\(996\) | −4.18945 | −0.132748 | ||||||||
\(997\) | −27.8325 | −0.881463 | −0.440731 | − | 0.897639i | \(-0.645281\pi\) | ||||
−0.440731 | + | 0.897639i | \(0.645281\pi\) | |||||||
\(998\) | −28.3168 | −0.896352 | ||||||||
\(999\) | −9.38955 | −0.297072 |
(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 | 6041.2.a.f.1.13 | ✓ | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.f.1.13 | ✓ | 132 | 1.1 | even | 1 | trivial |