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: | \(1\) |
Dimension: | \(101\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.14147 | −1.51425 | −0.757125 | − | 0.653270i | \(-0.773397\pi\) | ||||
−0.757125 | + | 0.653270i | \(0.773397\pi\) | |||||||
\(3\) | −2.96762 | −1.71335 | −0.856677 | − | 0.515853i | \(-0.827475\pi\) | ||||
−0.856677 | + | 0.515853i | \(0.827475\pi\) | |||||||
\(4\) | 2.58591 | 1.29295 | ||||||||
\(5\) | 4.08817 | 1.82828 | 0.914142 | − | 0.405395i | \(-0.132866\pi\) | ||||
0.914142 | + | 0.405395i | \(0.132866\pi\) | |||||||
\(6\) | 6.35507 | 2.59445 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.25470 | −0.443605 | ||||||||
\(9\) | 5.80675 | 1.93558 | ||||||||
\(10\) | −8.75470 | −2.76848 | ||||||||
\(11\) | −1.22122 | −0.368211 | −0.184105 | − | 0.982907i | \(-0.558939\pi\) | ||||
−0.184105 | + | 0.982907i | \(0.558939\pi\) | |||||||
\(12\) | −7.67398 | −2.21529 | ||||||||
\(13\) | −1.03810 | −0.287916 | −0.143958 | − | 0.989584i | \(-0.545983\pi\) | ||||
−0.143958 | + | 0.989584i | \(0.545983\pi\) | |||||||
\(14\) | 2.14147 | 0.572333 | ||||||||
\(15\) | −12.1321 | −3.13250 | ||||||||
\(16\) | −2.48490 | −0.621224 | ||||||||
\(17\) | 0.790038 | 0.191612 | 0.0958062 | − | 0.995400i | \(-0.469457\pi\) | ||||
0.0958062 | + | 0.995400i | \(0.469457\pi\) | |||||||
\(18\) | −12.4350 | −2.93096 | ||||||||
\(19\) | −6.74173 | −1.54666 | −0.773330 | − | 0.634004i | \(-0.781410\pi\) | ||||
−0.773330 | + | 0.634004i | \(0.781410\pi\) | |||||||
\(20\) | 10.5716 | 2.36389 | ||||||||
\(21\) | 2.96762 | 0.647587 | ||||||||
\(22\) | 2.61520 | 0.557563 | ||||||||
\(23\) | −1.01434 | −0.211504 | −0.105752 | − | 0.994393i | \(-0.533725\pi\) | ||||
−0.105752 | + | 0.994393i | \(0.533725\pi\) | |||||||
\(24\) | 3.72348 | 0.760053 | ||||||||
\(25\) | 11.7131 | 2.34262 | ||||||||
\(26\) | 2.22306 | 0.435977 | ||||||||
\(27\) | −8.32935 | −1.60298 | ||||||||
\(28\) | −2.58591 | −0.488691 | ||||||||
\(29\) | 0.298997 | 0.0555223 | 0.0277612 | − | 0.999615i | \(-0.491162\pi\) | ||||
0.0277612 | + | 0.999615i | \(0.491162\pi\) | |||||||
\(30\) | 25.9806 | 4.74338 | ||||||||
\(31\) | 4.85515 | 0.872012 | 0.436006 | − | 0.899944i | \(-0.356393\pi\) | ||||
0.436006 | + | 0.899944i | \(0.356393\pi\) | |||||||
\(32\) | 7.83075 | 1.38429 | ||||||||
\(33\) | 3.62410 | 0.630875 | ||||||||
\(34\) | −1.69185 | −0.290149 | ||||||||
\(35\) | −4.08817 | −0.691026 | ||||||||
\(36\) | 15.0157 | 2.50262 | ||||||||
\(37\) | 5.93905 | 0.976374 | 0.488187 | − | 0.872739i | \(-0.337658\pi\) | ||||
0.488187 | + | 0.872739i | \(0.337658\pi\) | |||||||
\(38\) | 14.4372 | 2.34203 | ||||||||
\(39\) | 3.08067 | 0.493303 | ||||||||
\(40\) | −5.12944 | −0.811036 | ||||||||
\(41\) | 3.01661 | 0.471115 | 0.235558 | − | 0.971860i | \(-0.424308\pi\) | ||||
0.235558 | + | 0.971860i | \(0.424308\pi\) | |||||||
\(42\) | −6.35507 | −0.980609 | ||||||||
\(43\) | −2.00668 | −0.306015 | −0.153008 | − | 0.988225i | \(-0.548896\pi\) | ||||
−0.153008 | + | 0.988225i | \(0.548896\pi\) | |||||||
\(44\) | −3.15795 | −0.476079 | ||||||||
\(45\) | 23.7389 | 3.53879 | ||||||||
\(46\) | 2.17218 | 0.320271 | ||||||||
\(47\) | −6.33631 | −0.924246 | −0.462123 | − | 0.886816i | \(-0.652912\pi\) | ||||
−0.462123 | + | 0.886816i | \(0.652912\pi\) | |||||||
\(48\) | 7.37422 | 1.06438 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −25.0833 | −3.54731 | ||||||||
\(51\) | −2.34453 | −0.328300 | ||||||||
\(52\) | −2.68442 | −0.372263 | ||||||||
\(53\) | 0.704090 | 0.0967141 | 0.0483571 | − | 0.998830i | \(-0.484601\pi\) | ||||
0.0483571 | + | 0.998830i | \(0.484601\pi\) | |||||||
\(54\) | 17.8371 | 2.42732 | ||||||||
\(55\) | −4.99253 | −0.673193 | ||||||||
\(56\) | 1.25470 | 0.167667 | ||||||||
\(57\) | 20.0069 | 2.64997 | ||||||||
\(58\) | −0.640294 | −0.0840747 | ||||||||
\(59\) | −13.3816 | −1.74214 | −0.871068 | − | 0.491162i | \(-0.836572\pi\) | ||||
−0.871068 | + | 0.491162i | \(0.836572\pi\) | |||||||
\(60\) | −31.3725 | −4.05017 | ||||||||
\(61\) | −5.54301 | −0.709710 | −0.354855 | − | 0.934921i | \(-0.615470\pi\) | ||||
−0.354855 | + | 0.934921i | \(0.615470\pi\) | |||||||
\(62\) | −10.3972 | −1.32044 | ||||||||
\(63\) | −5.80675 | −0.731581 | ||||||||
\(64\) | −11.7995 | −1.47494 | ||||||||
\(65\) | −4.24391 | −0.526393 | ||||||||
\(66\) | −7.76092 | −0.955303 | ||||||||
\(67\) | 8.30586 | 1.01472 | 0.507361 | − | 0.861733i | \(-0.330621\pi\) | ||||
0.507361 | + | 0.861733i | \(0.330621\pi\) | |||||||
\(68\) | 2.04297 | 0.247746 | ||||||||
\(69\) | 3.01017 | 0.362382 | ||||||||
\(70\) | 8.75470 | 1.04639 | ||||||||
\(71\) | −0.459341 | −0.0545138 | −0.0272569 | − | 0.999628i | \(-0.508677\pi\) | ||||
−0.0272569 | + | 0.999628i | \(0.508677\pi\) | |||||||
\(72\) | −7.28575 | −0.858634 | ||||||||
\(73\) | 2.60874 | 0.305329 | 0.152665 | − | 0.988278i | \(-0.451215\pi\) | ||||
0.152665 | + | 0.988278i | \(0.451215\pi\) | |||||||
\(74\) | −12.7183 | −1.47847 | ||||||||
\(75\) | −34.7600 | −4.01374 | ||||||||
\(76\) | −17.4335 | −1.99976 | ||||||||
\(77\) | 1.22122 | 0.139170 | ||||||||
\(78\) | −6.59718 | −0.746984 | ||||||||
\(79\) | 6.28955 | 0.707630 | 0.353815 | − | 0.935315i | \(-0.384884\pi\) | ||||
0.353815 | + | 0.935315i | \(0.384884\pi\) | |||||||
\(80\) | −10.1587 | −1.13577 | ||||||||
\(81\) | 7.29807 | 0.810897 | ||||||||
\(82\) | −6.45999 | −0.713386 | ||||||||
\(83\) | 7.99024 | 0.877043 | 0.438521 | − | 0.898721i | \(-0.355502\pi\) | ||||
0.438521 | + | 0.898721i | \(0.355502\pi\) | |||||||
\(84\) | 7.67398 | 0.837300 | ||||||||
\(85\) | 3.22981 | 0.350322 | ||||||||
\(86\) | 4.29724 | 0.463384 | ||||||||
\(87\) | −0.887308 | −0.0951294 | ||||||||
\(88\) | 1.53227 | 0.163340 | ||||||||
\(89\) | −13.3812 | −1.41841 | −0.709204 | − | 0.705003i | \(-0.750945\pi\) | ||||
−0.709204 | + | 0.705003i | \(0.750945\pi\) | |||||||
\(90\) | −50.8363 | −5.35862 | ||||||||
\(91\) | 1.03810 | 0.108822 | ||||||||
\(92\) | −2.62299 | −0.273465 | ||||||||
\(93\) | −14.4082 | −1.49406 | ||||||||
\(94\) | 13.5690 | 1.39954 | ||||||||
\(95\) | −27.5613 | −2.82773 | ||||||||
\(96\) | −23.2387 | −2.37179 | ||||||||
\(97\) | −2.42010 | −0.245724 | −0.122862 | − | 0.992424i | \(-0.539207\pi\) | ||||
−0.122862 | + | 0.992424i | \(0.539207\pi\) | |||||||
\(98\) | −2.14147 | −0.216321 | ||||||||
\(99\) | −7.09129 | −0.712702 | ||||||||
\(100\) | 30.2890 | 3.02890 | ||||||||
\(101\) | 0.782837 | 0.0778952 | 0.0389476 | − | 0.999241i | \(-0.487599\pi\) | ||||
0.0389476 | + | 0.999241i | \(0.487599\pi\) | |||||||
\(102\) | 5.02075 | 0.497128 | ||||||||
\(103\) | −7.37645 | −0.726823 | −0.363412 | − | 0.931629i | \(-0.618388\pi\) | ||||
−0.363412 | + | 0.931629i | \(0.618388\pi\) | |||||||
\(104\) | 1.30251 | 0.127721 | ||||||||
\(105\) | 12.1321 | 1.18397 | ||||||||
\(106\) | −1.50779 | −0.146449 | ||||||||
\(107\) | 5.21716 | 0.504362 | 0.252181 | − | 0.967680i | \(-0.418852\pi\) | ||||
0.252181 | + | 0.967680i | \(0.418852\pi\) | |||||||
\(108\) | −21.5389 | −2.07258 | ||||||||
\(109\) | −3.99109 | −0.382277 | −0.191138 | − | 0.981563i | \(-0.561218\pi\) | ||||
−0.191138 | + | 0.981563i | \(0.561218\pi\) | |||||||
\(110\) | 10.6914 | 1.01938 | ||||||||
\(111\) | −17.6248 | −1.67287 | ||||||||
\(112\) | 2.48490 | 0.234801 | ||||||||
\(113\) | 2.97109 | 0.279497 | 0.139748 | − | 0.990187i | \(-0.455371\pi\) | ||||
0.139748 | + | 0.990187i | \(0.455371\pi\) | |||||||
\(114\) | −42.8442 | −4.01272 | ||||||||
\(115\) | −4.14679 | −0.386690 | ||||||||
\(116\) | 0.773178 | 0.0717878 | ||||||||
\(117\) | −6.02797 | −0.557286 | ||||||||
\(118\) | 28.6563 | 2.63803 | ||||||||
\(119\) | −0.790038 | −0.0724227 | ||||||||
\(120\) | 15.2222 | 1.38959 | ||||||||
\(121\) | −9.50863 | −0.864421 | ||||||||
\(122\) | 11.8702 | 1.07468 | ||||||||
\(123\) | −8.95214 | −0.807187 | ||||||||
\(124\) | 12.5550 | 1.12747 | ||||||||
\(125\) | 27.4443 | 2.45469 | ||||||||
\(126\) | 12.4350 | 1.10780 | ||||||||
\(127\) | 11.0275 | 0.978529 | 0.489264 | − | 0.872135i | \(-0.337265\pi\) | ||||
0.489264 | + | 0.872135i | \(0.337265\pi\) | |||||||
\(128\) | 9.60691 | 0.849139 | ||||||||
\(129\) | 5.95505 | 0.524313 | ||||||||
\(130\) | 9.08823 | 0.797090 | ||||||||
\(131\) | −3.07149 | −0.268357 | −0.134179 | − | 0.990957i | \(-0.542840\pi\) | ||||
−0.134179 | + | 0.990957i | \(0.542840\pi\) | |||||||
\(132\) | 9.37159 | 0.815692 | ||||||||
\(133\) | 6.74173 | 0.584582 | ||||||||
\(134\) | −17.7868 | −1.53654 | ||||||||
\(135\) | −34.0518 | −2.93071 | ||||||||
\(136\) | −0.991265 | −0.0850003 | ||||||||
\(137\) | −15.4926 | −1.32363 | −0.661813 | − | 0.749669i | \(-0.730213\pi\) | ||||
−0.661813 | + | 0.749669i | \(0.730213\pi\) | |||||||
\(138\) | −6.44620 | −0.548737 | ||||||||
\(139\) | −0.313077 | −0.0265549 | −0.0132774 | − | 0.999912i | \(-0.504226\pi\) | ||||
−0.0132774 | + | 0.999912i | \(0.504226\pi\) | |||||||
\(140\) | −10.5716 | −0.893465 | ||||||||
\(141\) | 18.8037 | 1.58356 | ||||||||
\(142\) | 0.983667 | 0.0825475 | ||||||||
\(143\) | 1.26774 | 0.106014 | ||||||||
\(144\) | −14.4292 | −1.20243 | ||||||||
\(145\) | 1.22235 | 0.101511 | ||||||||
\(146\) | −5.58654 | −0.462345 | ||||||||
\(147\) | −2.96762 | −0.244765 | ||||||||
\(148\) | 15.3578 | 1.26241 | ||||||||
\(149\) | 0.793653 | 0.0650186 | 0.0325093 | − | 0.999471i | \(-0.489650\pi\) | ||||
0.0325093 | + | 0.999471i | \(0.489650\pi\) | |||||||
\(150\) | 74.4376 | 6.07780 | ||||||||
\(151\) | −12.0804 | −0.983093 | −0.491546 | − | 0.870851i | \(-0.663568\pi\) | ||||
−0.491546 | + | 0.870851i | \(0.663568\pi\) | |||||||
\(152\) | 8.45888 | 0.686106 | ||||||||
\(153\) | 4.58755 | 0.370882 | ||||||||
\(154\) | −2.61520 | −0.210739 | ||||||||
\(155\) | 19.8487 | 1.59428 | ||||||||
\(156\) | 7.96634 | 0.637818 | ||||||||
\(157\) | 18.7427 | 1.49583 | 0.747917 | − | 0.663792i | \(-0.231054\pi\) | ||||
0.747917 | + | 0.663792i | \(0.231054\pi\) | |||||||
\(158\) | −13.4689 | −1.07153 | ||||||||
\(159\) | −2.08947 | −0.165706 | ||||||||
\(160\) | 32.0134 | 2.53088 | ||||||||
\(161\) | 1.01434 | 0.0799412 | ||||||||
\(162\) | −15.6286 | −1.22790 | ||||||||
\(163\) | 0.965844 | 0.0756507 | 0.0378254 | − | 0.999284i | \(-0.487957\pi\) | ||||
0.0378254 | + | 0.999284i | \(0.487957\pi\) | |||||||
\(164\) | 7.80067 | 0.609130 | ||||||||
\(165\) | 14.8159 | 1.15342 | ||||||||
\(166\) | −17.1109 | −1.32806 | ||||||||
\(167\) | 24.9963 | 1.93427 | 0.967134 | − | 0.254266i | \(-0.0818340\pi\) | ||||
0.967134 | + | 0.254266i | \(0.0818340\pi\) | |||||||
\(168\) | −3.72348 | −0.287273 | ||||||||
\(169\) | −11.9224 | −0.917104 | ||||||||
\(170\) | −6.91655 | −0.530475 | ||||||||
\(171\) | −39.1475 | −2.99369 | ||||||||
\(172\) | −5.18908 | −0.395664 | ||||||||
\(173\) | −21.6920 | −1.64921 | −0.824606 | − | 0.565707i | \(-0.808603\pi\) | ||||
−0.824606 | + | 0.565707i | \(0.808603\pi\) | |||||||
\(174\) | 1.90015 | 0.144050 | ||||||||
\(175\) | −11.7131 | −0.885427 | ||||||||
\(176\) | 3.03460 | 0.228741 | ||||||||
\(177\) | 39.7115 | 2.98490 | ||||||||
\(178\) | 28.6556 | 2.14782 | ||||||||
\(179\) | −9.99625 | −0.747155 | −0.373577 | − | 0.927599i | \(-0.621869\pi\) | ||||
−0.373577 | + | 0.927599i | \(0.621869\pi\) | |||||||
\(180\) | 61.3867 | 4.57550 | ||||||||
\(181\) | −17.9866 | −1.33694 | −0.668468 | − | 0.743741i | \(-0.733050\pi\) | ||||
−0.668468 | + | 0.743741i | \(0.733050\pi\) | |||||||
\(182\) | −2.22306 | −0.164784 | ||||||||
\(183\) | 16.4495 | 1.21598 | ||||||||
\(184\) | 1.27270 | 0.0938244 | ||||||||
\(185\) | 24.2798 | 1.78509 | ||||||||
\(186\) | 30.8549 | 2.26239 | ||||||||
\(187\) | −0.964808 | −0.0705537 | ||||||||
\(188\) | −16.3851 | −1.19501 | ||||||||
\(189\) | 8.32935 | 0.605871 | ||||||||
\(190\) | 59.0218 | 4.28189 | ||||||||
\(191\) | −7.09796 | −0.513590 | −0.256795 | − | 0.966466i | \(-0.582667\pi\) | ||||
−0.256795 | + | 0.966466i | \(0.582667\pi\) | |||||||
\(192\) | 35.0165 | 2.52710 | ||||||||
\(193\) | 17.5611 | 1.26408 | 0.632039 | − | 0.774936i | \(-0.282218\pi\) | ||||
0.632039 | + | 0.774936i | \(0.282218\pi\) | |||||||
\(194\) | 5.18259 | 0.372088 | ||||||||
\(195\) | 12.5943 | 0.901897 | ||||||||
\(196\) | 2.58591 | 0.184708 | ||||||||
\(197\) | 9.60162 | 0.684087 | 0.342044 | − | 0.939684i | \(-0.388881\pi\) | ||||
0.342044 | + | 0.939684i | \(0.388881\pi\) | |||||||
\(198\) | 15.1858 | 1.07921 | ||||||||
\(199\) | −0.668850 | −0.0474135 | −0.0237067 | − | 0.999719i | \(-0.507547\pi\) | ||||
−0.0237067 | + | 0.999719i | \(0.507547\pi\) | |||||||
\(200\) | −14.6965 | −1.03920 | ||||||||
\(201\) | −24.6486 | −1.73858 | ||||||||
\(202\) | −1.67642 | −0.117953 | ||||||||
\(203\) | −0.298997 | −0.0209855 | ||||||||
\(204\) | −6.06274 | −0.424477 | ||||||||
\(205\) | 12.3324 | 0.861332 | ||||||||
\(206\) | 15.7965 | 1.10059 | ||||||||
\(207\) | −5.89001 | −0.409384 | ||||||||
\(208\) | 2.57957 | 0.178861 | ||||||||
\(209\) | 8.23311 | 0.569496 | ||||||||
\(210\) | −25.9806 | −1.79283 | ||||||||
\(211\) | 19.9415 | 1.37283 | 0.686415 | − | 0.727210i | \(-0.259184\pi\) | ||||
0.686415 | + | 0.727210i | \(0.259184\pi\) | |||||||
\(212\) | 1.82071 | 0.125047 | ||||||||
\(213\) | 1.36315 | 0.0934014 | ||||||||
\(214\) | −11.1724 | −0.763730 | ||||||||
\(215\) | −8.20363 | −0.559483 | ||||||||
\(216\) | 10.4509 | 0.711092 | ||||||||
\(217\) | −4.85515 | −0.329589 | ||||||||
\(218\) | 8.54681 | 0.578863 | ||||||||
\(219\) | −7.74173 | −0.523137 | ||||||||
\(220\) | −12.9102 | −0.870407 | ||||||||
\(221\) | −0.820137 | −0.0551684 | ||||||||
\(222\) | 37.7431 | 2.53315 | ||||||||
\(223\) | −14.9010 | −0.997845 | −0.498922 | − | 0.866647i | \(-0.666271\pi\) | ||||
−0.498922 | + | 0.866647i | \(0.666271\pi\) | |||||||
\(224\) | −7.83075 | −0.523214 | ||||||||
\(225\) | 68.0150 | 4.53433 | ||||||||
\(226\) | −6.36251 | −0.423228 | ||||||||
\(227\) | −25.3656 | −1.68358 | −0.841789 | − | 0.539807i | \(-0.818497\pi\) | ||||
−0.841789 | + | 0.539807i | \(0.818497\pi\) | |||||||
\(228\) | 51.7359 | 3.42629 | ||||||||
\(229\) | 7.44148 | 0.491747 | 0.245874 | − | 0.969302i | \(-0.420925\pi\) | ||||
0.245874 | + | 0.969302i | \(0.420925\pi\) | |||||||
\(230\) | 8.88023 | 0.585545 | ||||||||
\(231\) | −3.62410 | −0.238448 | ||||||||
\(232\) | −0.375153 | −0.0246300 | ||||||||
\(233\) | −14.6179 | −0.957648 | −0.478824 | − | 0.877911i | \(-0.658937\pi\) | ||||
−0.478824 | + | 0.877911i | \(0.658937\pi\) | |||||||
\(234\) | 12.9087 | 0.843870 | ||||||||
\(235\) | −25.9039 | −1.68978 | ||||||||
\(236\) | −34.6036 | −2.25250 | ||||||||
\(237\) | −18.6650 | −1.21242 | ||||||||
\(238\) | 1.69185 | 0.109666 | ||||||||
\(239\) | 9.59754 | 0.620813 | 0.310407 | − | 0.950604i | \(-0.399535\pi\) | ||||
0.310407 | + | 0.950604i | \(0.399535\pi\) | |||||||
\(240\) | 30.1470 | 1.94598 | ||||||||
\(241\) | 4.66658 | 0.300601 | 0.150301 | − | 0.988640i | \(-0.451976\pi\) | ||||
0.150301 | + | 0.988640i | \(0.451976\pi\) | |||||||
\(242\) | 20.3625 | 1.30895 | ||||||||
\(243\) | 3.33017 | 0.213630 | ||||||||
\(244\) | −14.3337 | −0.917622 | ||||||||
\(245\) | 4.08817 | 0.261183 | ||||||||
\(246\) | 19.1708 | 1.22228 | ||||||||
\(247\) | 6.99857 | 0.445308 | ||||||||
\(248\) | −6.09179 | −0.386829 | ||||||||
\(249\) | −23.7120 | −1.50269 | ||||||||
\(250\) | −58.7711 | −3.71701 | ||||||||
\(251\) | 4.16453 | 0.262863 | 0.131431 | − | 0.991325i | \(-0.458043\pi\) | ||||
0.131431 | + | 0.991325i | \(0.458043\pi\) | |||||||
\(252\) | −15.0157 | −0.945901 | ||||||||
\(253\) | 1.23873 | 0.0778781 | ||||||||
\(254\) | −23.6150 | −1.48174 | ||||||||
\(255\) | −9.58483 | −0.600225 | ||||||||
\(256\) | 3.02615 | 0.189134 | ||||||||
\(257\) | 22.9966 | 1.43449 | 0.717246 | − | 0.696820i | \(-0.245403\pi\) | ||||
0.717246 | + | 0.696820i | \(0.245403\pi\) | |||||||
\(258\) | −12.7526 | −0.793941 | ||||||||
\(259\) | −5.93905 | −0.369035 | ||||||||
\(260\) | −10.9744 | −0.680601 | ||||||||
\(261\) | 1.73620 | 0.107468 | ||||||||
\(262\) | 6.57751 | 0.406360 | ||||||||
\(263\) | −13.6389 | −0.841008 | −0.420504 | − | 0.907291i | \(-0.638147\pi\) | ||||
−0.420504 | + | 0.907291i | \(0.638147\pi\) | |||||||
\(264\) | −4.54718 | −0.279859 | ||||||||
\(265\) | 2.87843 | 0.176821 | ||||||||
\(266\) | −14.4372 | −0.885204 | ||||||||
\(267\) | 39.7104 | 2.43024 | ||||||||
\(268\) | 21.4782 | 1.31199 | ||||||||
\(269\) | 31.6968 | 1.93259 | 0.966294 | − | 0.257441i | \(-0.0828792\pi\) | ||||
0.966294 | + | 0.257441i | \(0.0828792\pi\) | |||||||
\(270\) | 72.9209 | 4.43783 | ||||||||
\(271\) | −9.47546 | −0.575593 | −0.287797 | − | 0.957692i | \(-0.592923\pi\) | ||||
−0.287797 | + | 0.957692i | \(0.592923\pi\) | |||||||
\(272\) | −1.96316 | −0.119034 | ||||||||
\(273\) | −3.08067 | −0.186451 | ||||||||
\(274\) | 33.1771 | 2.00430 | ||||||||
\(275\) | −14.3042 | −0.862577 | ||||||||
\(276\) | 7.78402 | 0.468543 | ||||||||
\(277\) | 0.716541 | 0.0430528 | 0.0215264 | − | 0.999768i | \(-0.493147\pi\) | ||||
0.0215264 | + | 0.999768i | \(0.493147\pi\) | |||||||
\(278\) | 0.670447 | 0.0402107 | ||||||||
\(279\) | 28.1927 | 1.68785 | ||||||||
\(280\) | 5.12944 | 0.306543 | ||||||||
\(281\) | −17.5181 | −1.04504 | −0.522522 | − | 0.852626i | \(-0.675009\pi\) | ||||
−0.522522 | + | 0.852626i | \(0.675009\pi\) | |||||||
\(282\) | −40.2677 | −2.39791 | ||||||||
\(283\) | 4.58582 | 0.272599 | 0.136299 | − | 0.990668i | \(-0.456479\pi\) | ||||
0.136299 | + | 0.990668i | \(0.456479\pi\) | |||||||
\(284\) | −1.18781 | −0.0704838 | ||||||||
\(285\) | 81.7914 | 4.84490 | ||||||||
\(286\) | −2.71483 | −0.160531 | ||||||||
\(287\) | −3.01661 | −0.178065 | ||||||||
\(288\) | 45.4712 | 2.67942 | ||||||||
\(289\) | −16.3758 | −0.963285 | ||||||||
\(290\) | −2.61763 | −0.153712 | ||||||||
\(291\) | 7.18194 | 0.421013 | ||||||||
\(292\) | 6.74595 | 0.394777 | ||||||||
\(293\) | 19.8669 | 1.16063 | 0.580317 | − | 0.814390i | \(-0.302929\pi\) | ||||
0.580317 | + | 0.814390i | \(0.302929\pi\) | |||||||
\(294\) | 6.35507 | 0.370635 | ||||||||
\(295\) | −54.7062 | −3.18512 | ||||||||
\(296\) | −7.45175 | −0.433124 | ||||||||
\(297\) | 10.1719 | 0.590236 | ||||||||
\(298\) | −1.69959 | −0.0984544 | ||||||||
\(299\) | 1.05298 | 0.0608956 | ||||||||
\(300\) | −89.8861 | −5.18958 | ||||||||
\(301\) | 2.00668 | 0.115663 | ||||||||
\(302\) | 25.8700 | 1.48865 | ||||||||
\(303\) | −2.32316 | −0.133462 | ||||||||
\(304\) | 16.7525 | 0.960823 | ||||||||
\(305\) | −22.6607 | −1.29755 | ||||||||
\(306\) | −9.82412 | −0.561608 | ||||||||
\(307\) | 8.65275 | 0.493839 | 0.246919 | − | 0.969036i | \(-0.420582\pi\) | ||||
0.246919 | + | 0.969036i | \(0.420582\pi\) | |||||||
\(308\) | 3.15795 | 0.179941 | ||||||||
\(309\) | 21.8905 | 1.24531 | ||||||||
\(310\) | −42.5054 | −2.41414 | ||||||||
\(311\) | −14.6622 | −0.831416 | −0.415708 | − | 0.909498i | \(-0.636466\pi\) | ||||
−0.415708 | + | 0.909498i | \(0.636466\pi\) | |||||||
\(312\) | −3.86534 | −0.218832 | ||||||||
\(313\) | −33.7333 | −1.90672 | −0.953360 | − | 0.301836i | \(-0.902400\pi\) | ||||
−0.953360 | + | 0.301836i | \(0.902400\pi\) | |||||||
\(314\) | −40.1371 | −2.26507 | ||||||||
\(315\) | −23.7389 | −1.33754 | ||||||||
\(316\) | 16.2642 | 0.914933 | ||||||||
\(317\) | −21.5073 | −1.20797 | −0.603986 | − | 0.796995i | \(-0.706422\pi\) | ||||
−0.603986 | + | 0.796995i | \(0.706422\pi\) | |||||||
\(318\) | 4.47454 | 0.250920 | ||||||||
\(319\) | −0.365140 | −0.0204439 | ||||||||
\(320\) | −48.2385 | −2.69661 | ||||||||
\(321\) | −15.4825 | −0.864151 | ||||||||
\(322\) | −2.17218 | −0.121051 | ||||||||
\(323\) | −5.32623 | −0.296359 | ||||||||
\(324\) | 18.8721 | 1.04845 | ||||||||
\(325\) | −12.1593 | −0.674478 | ||||||||
\(326\) | −2.06833 | −0.114554 | ||||||||
\(327\) | 11.8440 | 0.654976 | ||||||||
\(328\) | −3.78495 | −0.208989 | ||||||||
\(329\) | 6.33631 | 0.349332 | ||||||||
\(330\) | −31.7279 | −1.74656 | ||||||||
\(331\) | 9.33855 | 0.513293 | 0.256647 | − | 0.966505i | \(-0.417382\pi\) | ||||
0.256647 | + | 0.966505i | \(0.417382\pi\) | |||||||
\(332\) | 20.6620 | 1.13398 | ||||||||
\(333\) | 34.4866 | 1.88985 | ||||||||
\(334\) | −53.5288 | −2.92897 | ||||||||
\(335\) | 33.9557 | 1.85520 | ||||||||
\(336\) | −7.37422 | −0.402297 | ||||||||
\(337\) | 1.58249 | 0.0862039 | 0.0431019 | − | 0.999071i | \(-0.486276\pi\) | ||||
0.0431019 | + | 0.999071i | \(0.486276\pi\) | |||||||
\(338\) | 25.5314 | 1.38873 | ||||||||
\(339\) | −8.81706 | −0.478877 | ||||||||
\(340\) | 8.35198 | 0.452950 | ||||||||
\(341\) | −5.92919 | −0.321084 | ||||||||
\(342\) | 83.8334 | 4.53319 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 2.51779 | 0.135750 | ||||||||
\(345\) | 12.3061 | 0.662537 | ||||||||
\(346\) | 46.4528 | 2.49732 | ||||||||
\(347\) | 0.0859145 | 0.00461213 | 0.00230607 | − | 0.999997i | \(-0.499266\pi\) | ||||
0.00230607 | + | 0.999997i | \(0.499266\pi\) | |||||||
\(348\) | −2.29450 | −0.122998 | ||||||||
\(349\) | −22.4504 | −1.20174 | −0.600872 | − | 0.799345i | \(-0.705180\pi\) | ||||
−0.600872 | + | 0.799345i | \(0.705180\pi\) | |||||||
\(350\) | 25.0833 | 1.34076 | ||||||||
\(351\) | 8.64667 | 0.461525 | ||||||||
\(352\) | −9.56304 | −0.509712 | ||||||||
\(353\) | 17.5258 | 0.932805 | 0.466402 | − | 0.884573i | \(-0.345550\pi\) | ||||
0.466402 | + | 0.884573i | \(0.345550\pi\) | |||||||
\(354\) | −85.0410 | −4.51988 | ||||||||
\(355\) | −1.87786 | −0.0996667 | ||||||||
\(356\) | −34.6026 | −1.83394 | ||||||||
\(357\) | 2.34453 | 0.124086 | ||||||||
\(358\) | 21.4067 | 1.13138 | ||||||||
\(359\) | 24.2749 | 1.28118 | 0.640589 | − | 0.767884i | \(-0.278690\pi\) | ||||
0.640589 | + | 0.767884i | \(0.278690\pi\) | |||||||
\(360\) | −29.7854 | −1.56983 | ||||||||
\(361\) | 26.4509 | 1.39215 | ||||||||
\(362\) | 38.5179 | 2.02446 | ||||||||
\(363\) | 28.2180 | 1.48106 | ||||||||
\(364\) | 2.68442 | 0.140702 | ||||||||
\(365\) | 10.6649 | 0.558229 | ||||||||
\(366\) | −35.2262 | −1.84130 | ||||||||
\(367\) | −13.1637 | −0.687140 | −0.343570 | − | 0.939127i | \(-0.611636\pi\) | ||||
−0.343570 | + | 0.939127i | \(0.611636\pi\) | |||||||
\(368\) | 2.52053 | 0.131392 | ||||||||
\(369\) | 17.5167 | 0.911882 | ||||||||
\(370\) | −51.9946 | −2.70307 | ||||||||
\(371\) | −0.704090 | −0.0365545 | ||||||||
\(372\) | −37.2584 | −1.93176 | ||||||||
\(373\) | −5.30068 | −0.274459 | −0.137230 | − | 0.990539i | \(-0.543820\pi\) | ||||
−0.137230 | + | 0.990539i | \(0.543820\pi\) | |||||||
\(374\) | 2.06611 | 0.106836 | ||||||||
\(375\) | −81.4440 | −4.20575 | ||||||||
\(376\) | 7.95020 | 0.410000 | ||||||||
\(377\) | −0.310388 | −0.0159858 | ||||||||
\(378\) | −17.8371 | −0.917440 | ||||||||
\(379\) | −11.6288 | −0.597333 | −0.298666 | − | 0.954358i | \(-0.596542\pi\) | ||||
−0.298666 | + | 0.954358i | \(0.596542\pi\) | |||||||
\(380\) | −71.2710 | −3.65612 | ||||||||
\(381\) | −32.7253 | −1.67657 | ||||||||
\(382\) | 15.2001 | 0.777704 | ||||||||
\(383\) | −19.7281 | −1.00806 | −0.504029 | − | 0.863687i | \(-0.668150\pi\) | ||||
−0.504029 | + | 0.863687i | \(0.668150\pi\) | |||||||
\(384\) | −28.5096 | −1.45488 | ||||||||
\(385\) | 4.99253 | 0.254443 | ||||||||
\(386\) | −37.6067 | −1.91413 | ||||||||
\(387\) | −11.6523 | −0.592318 | ||||||||
\(388\) | −6.25817 | −0.317710 | ||||||||
\(389\) | −3.77387 | −0.191343 | −0.0956714 | − | 0.995413i | \(-0.530500\pi\) | ||||
−0.0956714 | + | 0.995413i | \(0.530500\pi\) | |||||||
\(390\) | −26.9704 | −1.36570 | ||||||||
\(391\) | −0.801367 | −0.0405269 | ||||||||
\(392\) | −1.25470 | −0.0633722 | ||||||||
\(393\) | 9.11500 | 0.459791 | ||||||||
\(394\) | −20.5616 | −1.03588 | ||||||||
\(395\) | 25.7127 | 1.29375 | ||||||||
\(396\) | −18.3374 | −0.921490 | ||||||||
\(397\) | 4.81283 | 0.241549 | 0.120774 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120774 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(398\) | 1.43232 | 0.0717959 | ||||||||
\(399\) | −20.0069 | −1.00160 | ||||||||
\(400\) | −29.1059 | −1.45529 | ||||||||
\(401\) | −25.8242 | −1.28960 | −0.644800 | − | 0.764351i | \(-0.723059\pi\) | ||||
−0.644800 | + | 0.764351i | \(0.723059\pi\) | |||||||
\(402\) | 52.7843 | 2.63264 | ||||||||
\(403\) | −5.04012 | −0.251066 | ||||||||
\(404\) | 2.02434 | 0.100715 | ||||||||
\(405\) | 29.8357 | 1.48255 | ||||||||
\(406\) | 0.640294 | 0.0317772 | ||||||||
\(407\) | −7.25286 | −0.359511 | ||||||||
\(408\) | 2.94169 | 0.145636 | ||||||||
\(409\) | −31.2218 | −1.54382 | −0.771909 | − | 0.635733i | \(-0.780698\pi\) | ||||
−0.771909 | + | 0.635733i | \(0.780698\pi\) | |||||||
\(410\) | −26.4095 | −1.30427 | ||||||||
\(411\) | 45.9762 | 2.26784 | ||||||||
\(412\) | −19.0748 | −0.939749 | ||||||||
\(413\) | 13.3816 | 0.658466 | ||||||||
\(414\) | 12.6133 | 0.619910 | ||||||||
\(415\) | 32.6654 | 1.60348 | ||||||||
\(416\) | −8.12908 | −0.398561 | ||||||||
\(417\) | 0.929094 | 0.0454979 | ||||||||
\(418\) | −17.6310 | −0.862360 | ||||||||
\(419\) | −18.6478 | −0.911003 | −0.455502 | − | 0.890235i | \(-0.650540\pi\) | ||||
−0.455502 | + | 0.890235i | \(0.650540\pi\) | |||||||
\(420\) | 31.3725 | 1.53082 | ||||||||
\(421\) | 16.7591 | 0.816786 | 0.408393 | − | 0.912806i | \(-0.366089\pi\) | ||||
0.408393 | + | 0.912806i | \(0.366089\pi\) | |||||||
\(422\) | −42.7042 | −2.07881 | ||||||||
\(423\) | −36.7933 | −1.78895 | ||||||||
\(424\) | −0.883425 | −0.0429029 | ||||||||
\(425\) | 9.25380 | 0.448875 | ||||||||
\(426\) | −2.91915 | −0.141433 | ||||||||
\(427\) | 5.54301 | 0.268245 | ||||||||
\(428\) | 13.4911 | 0.652117 | ||||||||
\(429\) | −3.76217 | −0.181639 | ||||||||
\(430\) | 17.5678 | 0.847197 | ||||||||
\(431\) | 15.6708 | 0.754838 | 0.377419 | − | 0.926043i | \(-0.376812\pi\) | ||||
0.377419 | + | 0.926043i | \(0.376812\pi\) | |||||||
\(432\) | 20.6976 | 0.995813 | ||||||||
\(433\) | 5.98440 | 0.287592 | 0.143796 | − | 0.989607i | \(-0.454069\pi\) | ||||
0.143796 | + | 0.989607i | \(0.454069\pi\) | |||||||
\(434\) | 10.3972 | 0.499081 | ||||||||
\(435\) | −3.62746 | −0.173923 | ||||||||
\(436\) | −10.3206 | −0.494266 | ||||||||
\(437\) | 6.83840 | 0.327125 | ||||||||
\(438\) | 16.5787 | 0.792161 | ||||||||
\(439\) | −0.831232 | −0.0396725 | −0.0198363 | − | 0.999803i | \(-0.506314\pi\) | ||||
−0.0198363 | + | 0.999803i | \(0.506314\pi\) | |||||||
\(440\) | 6.26416 | 0.298632 | ||||||||
\(441\) | 5.80675 | 0.276512 | ||||||||
\(442\) | 1.75630 | 0.0835387 | ||||||||
\(443\) | 41.1819 | 1.95661 | 0.978306 | − | 0.207167i | \(-0.0664244\pi\) | ||||
0.978306 | + | 0.207167i | \(0.0664244\pi\) | |||||||
\(444\) | −45.5762 | −2.16295 | ||||||||
\(445\) | −54.7047 | −2.59325 | ||||||||
\(446\) | 31.9101 | 1.51099 | ||||||||
\(447\) | −2.35526 | −0.111400 | ||||||||
\(448\) | 11.7995 | 0.557476 | ||||||||
\(449\) | 12.4920 | 0.589536 | 0.294768 | − | 0.955569i | \(-0.404758\pi\) | ||||
0.294768 | + | 0.955569i | \(0.404758\pi\) | |||||||
\(450\) | −145.652 | −6.86611 | ||||||||
\(451\) | −3.68393 | −0.173470 | ||||||||
\(452\) | 7.68297 | 0.361376 | ||||||||
\(453\) | 35.8501 | 1.68439 | ||||||||
\(454\) | 54.3199 | 2.54936 | ||||||||
\(455\) | 4.24391 | 0.198958 | ||||||||
\(456\) | −25.1027 | −1.17554 | ||||||||
\(457\) | −36.4861 | −1.70675 | −0.853373 | − | 0.521301i | \(-0.825447\pi\) | ||||
−0.853373 | + | 0.521301i | \(0.825447\pi\) | |||||||
\(458\) | −15.9357 | −0.744628 | ||||||||
\(459\) | −6.58051 | −0.307152 | ||||||||
\(460\) | −10.7232 | −0.499972 | ||||||||
\(461\) | 24.9288 | 1.16105 | 0.580526 | − | 0.814242i | \(-0.302847\pi\) | ||||
0.580526 | + | 0.814242i | \(0.302847\pi\) | |||||||
\(462\) | 7.76092 | 0.361070 | ||||||||
\(463\) | −20.1236 | −0.935224 | −0.467612 | − | 0.883934i | \(-0.654886\pi\) | ||||
−0.467612 | + | 0.883934i | \(0.654886\pi\) | |||||||
\(464\) | −0.742976 | −0.0344918 | ||||||||
\(465\) | −58.9033 | −2.73157 | ||||||||
\(466\) | 31.3038 | 1.45012 | ||||||||
\(467\) | −5.98664 | −0.277029 | −0.138514 | − | 0.990360i | \(-0.544233\pi\) | ||||
−0.138514 | + | 0.990360i | \(0.544233\pi\) | |||||||
\(468\) | −15.5878 | −0.720545 | ||||||||
\(469\) | −8.30586 | −0.383529 | ||||||||
\(470\) | 55.4725 | 2.55875 | ||||||||
\(471\) | −55.6213 | −2.56289 | ||||||||
\(472\) | 16.7900 | 0.772821 | ||||||||
\(473\) | 2.45059 | 0.112678 | ||||||||
\(474\) | 39.9705 | 1.83591 | ||||||||
\(475\) | −78.9665 | −3.62323 | ||||||||
\(476\) | −2.04297 | −0.0936392 | ||||||||
\(477\) | 4.08847 | 0.187198 | ||||||||
\(478\) | −20.5529 | −0.940066 | ||||||||
\(479\) | 3.18045 | 0.145319 | 0.0726593 | − | 0.997357i | \(-0.476851\pi\) | ||||
0.0726593 | + | 0.997357i | \(0.476851\pi\) | |||||||
\(480\) | −95.0035 | −4.33630 | ||||||||
\(481\) | −6.16531 | −0.281114 | ||||||||
\(482\) | −9.99336 | −0.455185 | ||||||||
\(483\) | −3.01017 | −0.136968 | ||||||||
\(484\) | −24.5884 | −1.11766 | ||||||||
\(485\) | −9.89379 | −0.449254 | ||||||||
\(486\) | −7.13146 | −0.323490 | ||||||||
\(487\) | −13.2634 | −0.601023 | −0.300511 | − | 0.953778i | \(-0.597157\pi\) | ||||
−0.300511 | + | 0.953778i | \(0.597157\pi\) | |||||||
\(488\) | 6.95484 | 0.314831 | ||||||||
\(489\) | −2.86625 | −0.129617 | ||||||||
\(490\) | −8.75470 | −0.395497 | ||||||||
\(491\) | 4.46870 | 0.201670 | 0.100835 | − | 0.994903i | \(-0.467849\pi\) | ||||
0.100835 | + | 0.994903i | \(0.467849\pi\) | |||||||
\(492\) | −23.1494 | −1.04366 | ||||||||
\(493\) | 0.236219 | 0.0106388 | ||||||||
\(494\) | −14.9873 | −0.674308 | ||||||||
\(495\) | −28.9904 | −1.30302 | ||||||||
\(496\) | −12.0646 | −0.541715 | ||||||||
\(497\) | 0.459341 | 0.0206043 | ||||||||
\(498\) | 50.7785 | 2.27544 | ||||||||
\(499\) | 10.8611 | 0.486209 | 0.243105 | − | 0.970000i | \(-0.421834\pi\) | ||||
0.243105 | + | 0.970000i | \(0.421834\pi\) | |||||||
\(500\) | 70.9683 | 3.17380 | ||||||||
\(501\) | −74.1793 | −3.31409 | ||||||||
\(502\) | −8.91822 | −0.398040 | ||||||||
\(503\) | 2.05559 | 0.0916540 | 0.0458270 | − | 0.998949i | \(-0.485408\pi\) | ||||
0.0458270 | + | 0.998949i | \(0.485408\pi\) | |||||||
\(504\) | 7.28575 | 0.324533 | ||||||||
\(505\) | 3.20037 | 0.142414 | ||||||||
\(506\) | −2.65270 | −0.117927 | ||||||||
\(507\) | 35.3810 | 1.57132 | ||||||||
\(508\) | 28.5160 | 1.26519 | ||||||||
\(509\) | 16.8368 | 0.746278 | 0.373139 | − | 0.927776i | \(-0.378282\pi\) | ||||
0.373139 | + | 0.927776i | \(0.378282\pi\) | |||||||
\(510\) | 20.5257 | 0.908891 | ||||||||
\(511\) | −2.60874 | −0.115404 | ||||||||
\(512\) | −25.6942 | −1.13554 | ||||||||
\(513\) | 56.1542 | 2.47927 | ||||||||
\(514\) | −49.2467 | −2.17218 | ||||||||
\(515\) | −30.1561 | −1.32884 | ||||||||
\(516\) | 15.3992 | 0.677912 | ||||||||
\(517\) | 7.73800 | 0.340317 | ||||||||
\(518\) | 12.7183 | 0.558811 | ||||||||
\(519\) | 64.3735 | 2.82568 | ||||||||
\(520\) | 5.32486 | 0.233510 | ||||||||
\(521\) | 21.0599 | 0.922653 | 0.461327 | − | 0.887230i | \(-0.347374\pi\) | ||||
0.461327 | + | 0.887230i | \(0.347374\pi\) | |||||||
\(522\) | −3.71802 | −0.162733 | ||||||||
\(523\) | −22.5602 | −0.986488 | −0.493244 | − | 0.869891i | \(-0.664189\pi\) | ||||
−0.493244 | + | 0.869891i | \(0.664189\pi\) | |||||||
\(524\) | −7.94259 | −0.346974 | ||||||||
\(525\) | 34.7600 | 1.51705 | ||||||||
\(526\) | 29.2072 | 1.27350 | ||||||||
\(527\) | 3.83576 | 0.167088 | ||||||||
\(528\) | −9.00552 | −0.391915 | ||||||||
\(529\) | −21.9711 | −0.955266 | ||||||||
\(530\) | −6.16409 | −0.267751 | ||||||||
\(531\) | −77.7036 | −3.37205 | ||||||||
\(532\) | 17.4335 | 0.755838 | ||||||||
\(533\) | −3.13153 | −0.135642 | ||||||||
\(534\) | −85.0387 | −3.67998 | ||||||||
\(535\) | 21.3286 | 0.922116 | ||||||||
\(536\) | −10.4214 | −0.450136 | ||||||||
\(537\) | 29.6650 | 1.28014 | ||||||||
\(538\) | −67.8779 | −2.92642 | ||||||||
\(539\) | −1.22122 | −0.0526015 | ||||||||
\(540\) | −88.0547 | −3.78927 | ||||||||
\(541\) | 38.5252 | 1.65633 | 0.828164 | − | 0.560486i | \(-0.189386\pi\) | ||||
0.828164 | + | 0.560486i | \(0.189386\pi\) | |||||||
\(542\) | 20.2914 | 0.871592 | ||||||||
\(543\) | 53.3775 | 2.29065 | ||||||||
\(544\) | 6.18659 | 0.265248 | ||||||||
\(545\) | −16.3162 | −0.698911 | ||||||||
\(546\) | 6.59718 | 0.282333 | ||||||||
\(547\) | 25.6941 | 1.09860 | 0.549301 | − | 0.835624i | \(-0.314894\pi\) | ||||
0.549301 | + | 0.835624i | \(0.314894\pi\) | |||||||
\(548\) | −40.0625 | −1.71139 | ||||||||
\(549\) | −32.1869 | −1.37370 | ||||||||
\(550\) | 30.6321 | 1.30616 | ||||||||
\(551\) | −2.01576 | −0.0858741 | ||||||||
\(552\) | −3.77688 | −0.160754 | ||||||||
\(553\) | −6.28955 | −0.267459 | ||||||||
\(554\) | −1.53445 | −0.0651927 | ||||||||
\(555\) | −72.0532 | −3.05849 | ||||||||
\(556\) | −0.809589 | −0.0343342 | ||||||||
\(557\) | −38.1445 | −1.61623 | −0.808117 | − | 0.589022i | \(-0.799513\pi\) | ||||
−0.808117 | + | 0.589022i | \(0.799513\pi\) | |||||||
\(558\) | −60.3738 | −2.55583 | ||||||||
\(559\) | 2.08313 | 0.0881068 | ||||||||
\(560\) | 10.1587 | 0.429282 | ||||||||
\(561\) | 2.86318 | 0.120884 | ||||||||
\(562\) | 37.5146 | 1.58246 | ||||||||
\(563\) | −2.27122 | −0.0957207 | −0.0478604 | − | 0.998854i | \(-0.515240\pi\) | ||||
−0.0478604 | + | 0.998854i | \(0.515240\pi\) | |||||||
\(564\) | 48.6247 | 2.04747 | ||||||||
\(565\) | 12.1463 | 0.510999 | ||||||||
\(566\) | −9.82042 | −0.412783 | ||||||||
\(567\) | −7.29807 | −0.306490 | ||||||||
\(568\) | 0.576338 | 0.0241826 | ||||||||
\(569\) | 6.49595 | 0.272324 | 0.136162 | − | 0.990687i | \(-0.456523\pi\) | ||||
0.136162 | + | 0.990687i | \(0.456523\pi\) | |||||||
\(570\) | −175.154 | −7.33640 | ||||||||
\(571\) | 45.6161 | 1.90898 | 0.954488 | − | 0.298249i | \(-0.0964027\pi\) | ||||
0.954488 | + | 0.298249i | \(0.0964027\pi\) | |||||||
\(572\) | 3.27826 | 0.137071 | ||||||||
\(573\) | 21.0640 | 0.879962 | ||||||||
\(574\) | 6.45999 | 0.269635 | ||||||||
\(575\) | −11.8811 | −0.495474 | ||||||||
\(576\) | −68.5170 | −2.85488 | ||||||||
\(577\) | −40.0053 | −1.66544 | −0.832721 | − | 0.553693i | \(-0.813218\pi\) | ||||
−0.832721 | + | 0.553693i | \(0.813218\pi\) | |||||||
\(578\) | 35.0684 | 1.45865 | ||||||||
\(579\) | −52.1147 | −2.16581 | ||||||||
\(580\) | 3.16088 | 0.131248 | ||||||||
\(581\) | −7.99024 | −0.331491 | ||||||||
\(582\) | −15.3799 | −0.637519 | ||||||||
\(583\) | −0.859846 | −0.0356112 | ||||||||
\(584\) | −3.27319 | −0.135446 | ||||||||
\(585\) | −24.6433 | −1.01888 | ||||||||
\(586\) | −42.5444 | −1.75749 | ||||||||
\(587\) | 12.0349 | 0.496734 | 0.248367 | − | 0.968666i | \(-0.420106\pi\) | ||||
0.248367 | + | 0.968666i | \(0.420106\pi\) | |||||||
\(588\) | −7.67398 | −0.316470 | ||||||||
\(589\) | −32.7321 | −1.34870 | ||||||||
\(590\) | 117.152 | 4.82307 | ||||||||
\(591\) | −28.4939 | −1.17208 | ||||||||
\(592\) | −14.7579 | −0.606547 | ||||||||
\(593\) | −22.4965 | −0.923821 | −0.461910 | − | 0.886927i | \(-0.652836\pi\) | ||||
−0.461910 | + | 0.886927i | \(0.652836\pi\) | |||||||
\(594\) | −21.7829 | −0.893764 | ||||||||
\(595\) | −3.22981 | −0.132409 | ||||||||
\(596\) | 2.05231 | 0.0840660 | ||||||||
\(597\) | 1.98489 | 0.0812361 | ||||||||
\(598\) | −2.25493 | −0.0922111 | ||||||||
\(599\) | −11.5702 | −0.472747 | −0.236373 | − | 0.971662i | \(-0.575959\pi\) | ||||
−0.236373 | + | 0.971662i | \(0.575959\pi\) | |||||||
\(600\) | 43.6135 | 1.78051 | ||||||||
\(601\) | −10.5903 | −0.431985 | −0.215993 | − | 0.976395i | \(-0.569299\pi\) | ||||
−0.215993 | + | 0.976395i | \(0.569299\pi\) | |||||||
\(602\) | −4.29724 | −0.175143 | ||||||||
\(603\) | 48.2300 | 1.96408 | ||||||||
\(604\) | −31.2389 | −1.27109 | ||||||||
\(605\) | −38.8729 | −1.58041 | ||||||||
\(606\) | 4.97498 | 0.202095 | ||||||||
\(607\) | 30.5891 | 1.24157 | 0.620787 | − | 0.783980i | \(-0.286813\pi\) | ||||
0.620787 | + | 0.783980i | \(0.286813\pi\) | |||||||
\(608\) | −52.7928 | −2.14103 | ||||||||
\(609\) | 0.887308 | 0.0359555 | ||||||||
\(610\) | 48.5274 | 1.96482 | ||||||||
\(611\) | 6.57770 | 0.266105 | ||||||||
\(612\) | 11.8630 | 0.479533 | ||||||||
\(613\) | −8.50547 | −0.343533 | −0.171766 | − | 0.985138i | \(-0.554947\pi\) | ||||
−0.171766 | + | 0.985138i | \(0.554947\pi\) | |||||||
\(614\) | −18.5296 | −0.747795 | ||||||||
\(615\) | −36.5978 | −1.47577 | ||||||||
\(616\) | −1.53227 | −0.0617367 | ||||||||
\(617\) | 6.18369 | 0.248946 | 0.124473 | − | 0.992223i | \(-0.460276\pi\) | ||||
0.124473 | + | 0.992223i | \(0.460276\pi\) | |||||||
\(618\) | −46.8779 | −1.88570 | ||||||||
\(619\) | −24.6957 | −0.992605 | −0.496303 | − | 0.868150i | \(-0.665309\pi\) | ||||
−0.496303 | + | 0.868150i | \(0.665309\pi\) | |||||||
\(620\) | 51.3268 | 2.06134 | ||||||||
\(621\) | 8.44879 | 0.339038 | ||||||||
\(622\) | 31.3987 | 1.25897 | ||||||||
\(623\) | 13.3812 | 0.536108 | ||||||||
\(624\) | −7.65516 | −0.306452 | ||||||||
\(625\) | 53.6312 | 2.14525 | ||||||||
\(626\) | 72.2390 | 2.88725 | ||||||||
\(627\) | −24.4327 | −0.975749 | ||||||||
\(628\) | 48.4670 | 1.93404 | ||||||||
\(629\) | 4.69208 | 0.187085 | ||||||||
\(630\) | 50.8363 | 2.02537 | ||||||||
\(631\) | 7.87080 | 0.313331 | 0.156666 | − | 0.987652i | \(-0.449925\pi\) | ||||
0.156666 | + | 0.987652i | \(0.449925\pi\) | |||||||
\(632\) | −7.89153 | −0.313908 | ||||||||
\(633\) | −59.1787 | −2.35214 | ||||||||
\(634\) | 46.0573 | 1.82917 | ||||||||
\(635\) | 45.0821 | 1.78903 | ||||||||
\(636\) | −5.40317 | −0.214250 | ||||||||
\(637\) | −1.03810 | −0.0411309 | ||||||||
\(638\) | 0.781937 | 0.0309572 | ||||||||
\(639\) | −2.66728 | −0.105516 | ||||||||
\(640\) | 39.2747 | 1.55247 | ||||||||
\(641\) | −2.10803 | −0.0832620 | −0.0416310 | − | 0.999133i | \(-0.513255\pi\) | ||||
−0.0416310 | + | 0.999133i | \(0.513255\pi\) | |||||||
\(642\) | 33.1554 | 1.30854 | ||||||||
\(643\) | −31.3600 | −1.23672 | −0.618358 | − | 0.785896i | \(-0.712202\pi\) | ||||
−0.618358 | + | 0.785896i | \(0.712202\pi\) | |||||||
\(644\) | 2.62299 | 0.103360 | ||||||||
\(645\) | 24.3452 | 0.958592 | ||||||||
\(646\) | 11.4060 | 0.448762 | ||||||||
\(647\) | −43.6695 | −1.71682 | −0.858412 | − | 0.512961i | \(-0.828549\pi\) | ||||
−0.858412 | + | 0.512961i | \(0.828549\pi\) | |||||||
\(648\) | −9.15693 | −0.359718 | ||||||||
\(649\) | 16.3418 | 0.641473 | ||||||||
\(650\) | 26.0389 | 1.02133 | ||||||||
\(651\) | 14.4082 | 0.564703 | ||||||||
\(652\) | 2.49758 | 0.0978129 | ||||||||
\(653\) | 30.0767 | 1.17699 | 0.588496 | − | 0.808500i | \(-0.299720\pi\) | ||||
0.588496 | + | 0.808500i | \(0.299720\pi\) | |||||||
\(654\) | −25.3637 | −0.991797 | ||||||||
\(655\) | −12.5568 | −0.490633 | ||||||||
\(656\) | −7.49596 | −0.292668 | ||||||||
\(657\) | 15.1483 | 0.590990 | ||||||||
\(658\) | −13.5690 | −0.528976 | ||||||||
\(659\) | −36.8704 | −1.43627 | −0.718133 | − | 0.695906i | \(-0.755003\pi\) | ||||
−0.718133 | + | 0.695906i | \(0.755003\pi\) | |||||||
\(660\) | 38.3126 | 1.49132 | ||||||||
\(661\) | 20.1476 | 0.783651 | 0.391826 | − | 0.920039i | \(-0.371844\pi\) | ||||
0.391826 | + | 0.920039i | \(0.371844\pi\) | |||||||
\(662\) | −19.9983 | −0.777255 | ||||||||
\(663\) | 2.43385 | 0.0945229 | ||||||||
\(664\) | −10.0254 | −0.389061 | ||||||||
\(665\) | 27.5613 | 1.06878 | ||||||||
\(666\) | −73.8521 | −2.86171 | ||||||||
\(667\) | −0.303284 | −0.0117432 | ||||||||
\(668\) | 64.6380 | 2.50092 | ||||||||
\(669\) | 44.2204 | 1.70966 | ||||||||
\(670\) | −72.7153 | −2.80924 | ||||||||
\(671\) | 6.76922 | 0.261323 | ||||||||
\(672\) | 23.2387 | 0.896451 | ||||||||
\(673\) | −33.4916 | −1.29101 | −0.645504 | − | 0.763757i | \(-0.723352\pi\) | ||||
−0.645504 | + | 0.763757i | \(0.723352\pi\) | |||||||
\(674\) | −3.38887 | −0.130534 | ||||||||
\(675\) | −97.5625 | −3.75518 | ||||||||
\(676\) | −30.8301 | −1.18577 | ||||||||
\(677\) | −3.32961 | −0.127967 | −0.0639836 | − | 0.997951i | \(-0.520381\pi\) | ||||
−0.0639836 | + | 0.997951i | \(0.520381\pi\) | |||||||
\(678\) | 18.8815 | 0.725139 | ||||||||
\(679\) | 2.42010 | 0.0928751 | ||||||||
\(680\) | −4.05246 | −0.155405 | ||||||||
\(681\) | 75.2755 | 2.88456 | ||||||||
\(682\) | 12.6972 | 0.486201 | ||||||||
\(683\) | 42.7127 | 1.63436 | 0.817178 | − | 0.576385i | \(-0.195537\pi\) | ||||
0.817178 | + | 0.576385i | \(0.195537\pi\) | |||||||
\(684\) | −101.232 | −3.87070 | ||||||||
\(685\) | −63.3365 | −2.41996 | ||||||||
\(686\) | 2.14147 | 0.0817618 | ||||||||
\(687\) | −22.0835 | −0.842537 | ||||||||
\(688\) | 4.98639 | 0.190104 | ||||||||
\(689\) | −0.730913 | −0.0278456 | ||||||||
\(690\) | −26.3531 | −1.00325 | ||||||||
\(691\) | −39.4462 | −1.50060 | −0.750301 | − | 0.661096i | \(-0.770092\pi\) | ||||
−0.750301 | + | 0.661096i | \(0.770092\pi\) | |||||||
\(692\) | −56.0935 | −2.13236 | ||||||||
\(693\) | 7.09129 | 0.269376 | ||||||||
\(694\) | −0.183984 | −0.00698392 | ||||||||
\(695\) | −1.27991 | −0.0485499 | ||||||||
\(696\) | 1.11331 | 0.0421999 | ||||||||
\(697\) | 2.38324 | 0.0902715 | ||||||||
\(698\) | 48.0770 | 1.81974 | ||||||||
\(699\) | 43.3802 | 1.64079 | ||||||||
\(700\) | −30.2890 | −1.14482 | ||||||||
\(701\) | −17.6782 | −0.667697 | −0.333848 | − | 0.942627i | \(-0.608347\pi\) | ||||
−0.333848 | + | 0.942627i | \(0.608347\pi\) | |||||||
\(702\) | −18.5166 | −0.698865 | ||||||||
\(703\) | −40.0395 | −1.51012 | ||||||||
\(704\) | 14.4098 | 0.543090 | ||||||||
\(705\) | 76.8728 | 2.89520 | ||||||||
\(706\) | −37.5311 | −1.41250 | ||||||||
\(707\) | −0.782837 | −0.0294416 | ||||||||
\(708\) | 102.690 | 3.85933 | ||||||||
\(709\) | −48.6822 | −1.82830 | −0.914150 | − | 0.405376i | \(-0.867141\pi\) | ||||
−0.914150 | + | 0.405376i | \(0.867141\pi\) | |||||||
\(710\) | 4.02139 | 0.150920 | ||||||||
\(711\) | 36.5218 | 1.36968 | ||||||||
\(712\) | 16.7895 | 0.629213 | ||||||||
\(713\) | −4.92478 | −0.184434 | ||||||||
\(714\) | −5.02075 | −0.187897 | ||||||||
\(715\) | 5.18274 | 0.193823 | ||||||||
\(716\) | −25.8494 | −0.966036 | ||||||||
\(717\) | −28.4818 | −1.06367 | ||||||||
\(718\) | −51.9840 | −1.94002 | ||||||||
\(719\) | 22.8359 | 0.851635 | 0.425818 | − | 0.904809i | \(-0.359987\pi\) | ||||
0.425818 | + | 0.904809i | \(0.359987\pi\) | |||||||
\(720\) | −58.9889 | −2.19838 | ||||||||
\(721\) | 7.37645 | 0.274713 | ||||||||
\(722\) | −56.6440 | −2.10807 | ||||||||
\(723\) | −13.8486 | −0.515036 | ||||||||
\(724\) | −46.5118 | −1.72860 | ||||||||
\(725\) | 3.50218 | 0.130068 | ||||||||
\(726\) | −60.4280 | −2.24269 | ||||||||
\(727\) | −23.5966 | −0.875151 | −0.437575 | − | 0.899182i | \(-0.644163\pi\) | ||||
−0.437575 | + | 0.899182i | \(0.644163\pi\) | |||||||
\(728\) | −1.30251 | −0.0482741 | ||||||||
\(729\) | −31.7769 | −1.17692 | ||||||||
\(730\) | −22.8387 | −0.845298 | ||||||||
\(731\) | −1.58535 | −0.0586363 | ||||||||
\(732\) | 42.5370 | 1.57221 | ||||||||
\(733\) | 4.27307 | 0.157829 | 0.0789147 | − | 0.996881i | \(-0.474855\pi\) | ||||
0.0789147 | + | 0.996881i | \(0.474855\pi\) | |||||||
\(734\) | 28.1897 | 1.04050 | ||||||||
\(735\) | −12.1321 | −0.447500 | ||||||||
\(736\) | −7.94304 | −0.292784 | ||||||||
\(737\) | −10.1433 | −0.373632 | ||||||||
\(738\) | −37.5115 | −1.38082 | ||||||||
\(739\) | 7.51649 | 0.276499 | 0.138249 | − | 0.990397i | \(-0.455852\pi\) | ||||
0.138249 | + | 0.990397i | \(0.455852\pi\) | |||||||
\(740\) | 62.7854 | 2.30804 | ||||||||
\(741\) | −20.7691 | −0.762971 | ||||||||
\(742\) | 1.50779 | 0.0553527 | ||||||||
\(743\) | 11.1447 | 0.408859 | 0.204430 | − | 0.978881i | \(-0.434466\pi\) | ||||
0.204430 | + | 0.978881i | \(0.434466\pi\) | |||||||
\(744\) | 18.0781 | 0.662775 | ||||||||
\(745\) | 3.24458 | 0.118872 | ||||||||
\(746\) | 11.3513 | 0.415600 | ||||||||
\(747\) | 46.3973 | 1.69759 | ||||||||
\(748\) | −2.49490 | −0.0912227 | ||||||||
\(749\) | −5.21716 | −0.190631 | ||||||||
\(750\) | 174.410 | 6.36856 | ||||||||
\(751\) | 14.3356 | 0.523115 | 0.261557 | − | 0.965188i | \(-0.415764\pi\) | ||||
0.261557 | + | 0.965188i | \(0.415764\pi\) | |||||||
\(752\) | 15.7451 | 0.574164 | ||||||||
\(753\) | −12.3587 | −0.450377 | ||||||||
\(754\) | 0.664687 | 0.0242065 | ||||||||
\(755\) | −49.3869 | −1.79737 | ||||||||
\(756\) | 21.5389 | 0.783363 | ||||||||
\(757\) | −11.2079 | −0.407358 | −0.203679 | − | 0.979038i | \(-0.565290\pi\) | ||||
−0.203679 | + | 0.979038i | \(0.565290\pi\) | |||||||
\(758\) | 24.9028 | 0.904511 | ||||||||
\(759\) | −3.67607 | −0.133433 | ||||||||
\(760\) | 34.5813 | 1.25440 | ||||||||
\(761\) | −26.3959 | −0.956852 | −0.478426 | − | 0.878128i | \(-0.658792\pi\) | ||||
−0.478426 | + | 0.878128i | \(0.658792\pi\) | |||||||
\(762\) | 70.0803 | 2.53874 | ||||||||
\(763\) | 3.99109 | 0.144487 | ||||||||
\(764\) | −18.3547 | −0.664049 | ||||||||
\(765\) | 18.7547 | 0.678077 | ||||||||
\(766\) | 42.2472 | 1.52645 | ||||||||
\(767\) | 13.8914 | 0.501590 | ||||||||
\(768\) | −8.98045 | −0.324054 | ||||||||
\(769\) | −37.9918 | −1.37002 | −0.685009 | − | 0.728535i | \(-0.740202\pi\) | ||||
−0.685009 | + | 0.728535i | \(0.740202\pi\) | |||||||
\(770\) | −10.6914 | −0.385290 | ||||||||
\(771\) | −68.2452 | −2.45779 | ||||||||
\(772\) | 45.4115 | 1.63440 | ||||||||
\(773\) | −35.3793 | −1.27251 | −0.636253 | − | 0.771481i | \(-0.719517\pi\) | ||||
−0.636253 | + | 0.771481i | \(0.719517\pi\) | |||||||
\(774\) | 24.9530 | 0.896918 | ||||||||
\(775\) | 56.8689 | 2.04279 | ||||||||
\(776\) | 3.03652 | 0.109005 | ||||||||
\(777\) | 17.6248 | 0.632287 | ||||||||
\(778\) | 8.08164 | 0.289741 | ||||||||
\(779\) | −20.3372 | −0.728654 | ||||||||
\(780\) | 32.5677 | 1.16611 | ||||||||
\(781\) | 0.560955 | 0.0200726 | ||||||||
\(782\) | 1.71611 | 0.0613678 | ||||||||
\(783\) | −2.49045 | −0.0890014 | ||||||||
\(784\) | −2.48490 | −0.0887464 | ||||||||
\(785\) | 76.6234 | 2.73481 | ||||||||
\(786\) | −19.5195 | −0.696239 | ||||||||
\(787\) | −34.7939 | −1.24027 | −0.620134 | − | 0.784496i | \(-0.712922\pi\) | ||||
−0.620134 | + | 0.784496i | \(0.712922\pi\) | |||||||
\(788\) | 24.8289 | 0.884493 | ||||||||
\(789\) | 40.4749 | 1.44094 | ||||||||
\(790\) | −55.0631 | −1.95906 | ||||||||
\(791\) | −2.97109 | −0.105640 | ||||||||
\(792\) | 8.89748 | 0.316158 | ||||||||
\(793\) | 5.75418 | 0.204337 | ||||||||
\(794\) | −10.3065 | −0.365766 | ||||||||
\(795\) | −8.54209 | −0.302957 | ||||||||
\(796\) | −1.72958 | −0.0613035 | ||||||||
\(797\) | 19.6978 | 0.697731 | 0.348866 | − | 0.937173i | \(-0.386567\pi\) | ||||
0.348866 | + | 0.937173i | \(0.386567\pi\) | |||||||
\(798\) | 42.8442 | 1.51667 | ||||||||
\(799\) | −5.00593 | −0.177097 | ||||||||
\(800\) | 91.7224 | 3.24288 | ||||||||
\(801\) | −77.7014 | −2.74545 | ||||||||
\(802\) | 55.3019 | 1.95278 | ||||||||
\(803\) | −3.18583 | −0.112426 | ||||||||
\(804\) | −63.7390 | −2.24790 | ||||||||
\(805\) | 4.14679 | 0.146155 | ||||||||
\(806\) | 10.7933 | 0.380177 | ||||||||
\(807\) | −94.0640 | −3.31121 | ||||||||
\(808\) | −0.982229 | −0.0345547 | ||||||||
\(809\) | −52.0896 | −1.83137 | −0.915686 | − | 0.401893i | \(-0.868352\pi\) | ||||
−0.915686 | + | 0.401893i | \(0.868352\pi\) | |||||||
\(810\) | −63.8924 | −2.24495 | ||||||||
\(811\) | 11.5070 | 0.404067 | 0.202033 | − | 0.979379i | \(-0.435245\pi\) | ||||
0.202033 | + | 0.979379i | \(0.435245\pi\) | |||||||
\(812\) | −0.773178 | −0.0271332 | ||||||||
\(813\) | 28.1195 | 0.986195 | ||||||||
\(814\) | 15.5318 | 0.544390 | ||||||||
\(815\) | 3.94853 | 0.138311 | ||||||||
\(816\) | 5.82592 | 0.203948 | ||||||||
\(817\) | 13.5285 | 0.473301 | ||||||||
\(818\) | 66.8606 | 2.33773 | ||||||||
\(819\) | 6.02797 | 0.210634 | ||||||||
\(820\) | 31.8904 | 1.11366 | ||||||||
\(821\) | −7.50487 | −0.261922 | −0.130961 | − | 0.991388i | \(-0.541806\pi\) | ||||
−0.130961 | + | 0.991388i | \(0.541806\pi\) | |||||||
\(822\) | −98.4569 | −3.43408 | ||||||||
\(823\) | 6.46912 | 0.225499 | 0.112750 | − | 0.993623i | \(-0.464034\pi\) | ||||
0.112750 | + | 0.993623i | \(0.464034\pi\) | |||||||
\(824\) | 9.25527 | 0.322422 | ||||||||
\(825\) | 42.4494 | 1.47790 | ||||||||
\(826\) | −28.6563 | −0.997082 | ||||||||
\(827\) | −1.33834 | −0.0465387 | −0.0232694 | − | 0.999729i | \(-0.507408\pi\) | ||||
−0.0232694 | + | 0.999729i | \(0.507408\pi\) | |||||||
\(828\) | −15.2310 | −0.529315 | ||||||||
\(829\) | 0.343233 | 0.0119210 | 0.00596049 | − | 0.999982i | \(-0.498103\pi\) | ||||
0.00596049 | + | 0.999982i | \(0.498103\pi\) | |||||||
\(830\) | −69.9521 | −2.42807 | ||||||||
\(831\) | −2.12642 | −0.0737647 | ||||||||
\(832\) | 12.2491 | 0.424660 | ||||||||
\(833\) | 0.790038 | 0.0273732 | ||||||||
\(834\) | −1.98963 | −0.0688952 | ||||||||
\(835\) | 102.189 | 3.53639 | ||||||||
\(836\) | 21.2901 | 0.736332 | ||||||||
\(837\) | −40.4403 | −1.39782 | ||||||||
\(838\) | 39.9337 | 1.37949 | ||||||||
\(839\) | −19.0683 | −0.658309 | −0.329155 | − | 0.944276i | \(-0.606764\pi\) | ||||
−0.329155 | + | 0.944276i | \(0.606764\pi\) | |||||||
\(840\) | −15.2222 | −0.525216 | ||||||||
\(841\) | −28.9106 | −0.996917 | ||||||||
\(842\) | −35.8891 | −1.23682 | ||||||||
\(843\) | 51.9871 | 1.79053 | ||||||||
\(844\) | 51.5669 | 1.77500 | ||||||||
\(845\) | −48.7406 | −1.67673 | ||||||||
\(846\) | 78.7920 | 2.70892 | ||||||||
\(847\) | 9.50863 | 0.326720 | ||||||||
\(848\) | −1.74959 | −0.0600812 | ||||||||
\(849\) | −13.6090 | −0.467059 | ||||||||
\(850\) | −19.8168 | −0.679709 | ||||||||
\(851\) | −6.02421 | −0.206507 | ||||||||
\(852\) | 3.52498 | 0.120764 | ||||||||
\(853\) | −0.684623 | −0.0234410 | −0.0117205 | − | 0.999931i | \(-0.503731\pi\) | ||||
−0.0117205 | + | 0.999931i | \(0.503731\pi\) | |||||||
\(854\) | −11.8702 | −0.406190 | ||||||||
\(855\) | −160.042 | −5.47331 | ||||||||
\(856\) | −6.54600 | −0.223738 | ||||||||
\(857\) | 43.7317 | 1.49385 | 0.746923 | − | 0.664911i | \(-0.231531\pi\) | ||||
0.746923 | + | 0.664911i | \(0.231531\pi\) | |||||||
\(858\) | 8.05658 | 0.275047 | ||||||||
\(859\) | −24.3350 | −0.830300 | −0.415150 | − | 0.909753i | \(-0.636271\pi\) | ||||
−0.415150 | + | 0.909753i | \(0.636271\pi\) | |||||||
\(860\) | −21.2138 | −0.723385 | ||||||||
\(861\) | 8.95214 | 0.305088 | ||||||||
\(862\) | −33.5587 | −1.14301 | ||||||||
\(863\) | −1.00000 | −0.0340404 | ||||||||
\(864\) | −65.2251 | −2.21900 | ||||||||
\(865\) | −88.6805 | −3.01523 | ||||||||
\(866\) | −12.8154 | −0.435486 | ||||||||
\(867\) | 48.5972 | 1.65045 | ||||||||
\(868\) | −12.5550 | −0.426144 | ||||||||
\(869\) | −7.68090 | −0.260557 | ||||||||
\(870\) | 7.76811 | 0.263364 | ||||||||
\(871\) | −8.62229 | −0.292155 | ||||||||
\(872\) | 5.00764 | 0.169580 | ||||||||
\(873\) | −14.0529 | −0.475620 | ||||||||
\(874\) | −14.6443 | −0.495349 | ||||||||
\(875\) | −27.4443 | −0.927785 | ||||||||
\(876\) | −20.0194 | −0.676392 | ||||||||
\(877\) | 13.7917 | 0.465713 | 0.232857 | − | 0.972511i | \(-0.425193\pi\) | ||||
0.232857 | + | 0.972511i | \(0.425193\pi\) | |||||||
\(878\) | 1.78006 | 0.0600741 | ||||||||
\(879\) | −58.9572 | −1.98858 | ||||||||
\(880\) | 12.4059 | 0.418204 | ||||||||
\(881\) | −53.9962 | −1.81918 | −0.909589 | − | 0.415509i | \(-0.863604\pi\) | ||||
−0.909589 | + | 0.415509i | \(0.863604\pi\) | |||||||
\(882\) | −12.4350 | −0.418708 | ||||||||
\(883\) | 17.8108 | 0.599383 | 0.299691 | − | 0.954036i | \(-0.403116\pi\) | ||||
0.299691 | + | 0.954036i | \(0.403116\pi\) | |||||||
\(884\) | −2.12080 | −0.0713301 | ||||||||
\(885\) | 162.347 | 5.45724 | ||||||||
\(886\) | −88.1899 | −2.96280 | ||||||||
\(887\) | 43.4881 | 1.46019 | 0.730094 | − | 0.683347i | \(-0.239476\pi\) | ||||
0.730094 | + | 0.683347i | \(0.239476\pi\) | |||||||
\(888\) | 22.1140 | 0.742096 | ||||||||
\(889\) | −11.0275 | −0.369849 | ||||||||
\(890\) | 117.149 | 3.92683 | ||||||||
\(891\) | −8.91252 | −0.298581 | ||||||||
\(892\) | −38.5326 | −1.29017 | ||||||||
\(893\) | 42.7177 | 1.42949 | ||||||||
\(894\) | 5.04372 | 0.168687 | ||||||||
\(895\) | −40.8663 | −1.36601 | ||||||||
\(896\) | −9.60691 | −0.320944 | ||||||||
\(897\) | −3.12485 | −0.104336 | ||||||||
\(898\) | −26.7514 | −0.892705 | ||||||||
\(899\) | 1.45168 | 0.0484161 | ||||||||
\(900\) | 175.880 | 5.86268 | ||||||||
\(901\) | 0.556258 | 0.0185316 | ||||||||
\(902\) | 7.88904 | 0.262676 | ||||||||
\(903\) | −5.95505 | −0.198172 | ||||||||
\(904\) | −3.72784 | −0.123986 | ||||||||
\(905\) | −73.5324 | −2.44430 | ||||||||
\(906\) | −76.7721 | −2.55058 | ||||||||
\(907\) | −34.3622 | −1.14098 | −0.570488 | − | 0.821306i | \(-0.693246\pi\) | ||||
−0.570488 | + | 0.821306i | \(0.693246\pi\) | |||||||
\(908\) | −65.5932 | −2.17679 | ||||||||
\(909\) | 4.54573 | 0.150773 | ||||||||
\(910\) | −9.08823 | −0.301272 | ||||||||
\(911\) | −39.4883 | −1.30831 | −0.654153 | − | 0.756362i | \(-0.726975\pi\) | ||||
−0.654153 | + | 0.756362i | \(0.726975\pi\) | |||||||
\(912\) | −49.7150 | −1.64623 | ||||||||
\(913\) | −9.75781 | −0.322936 | ||||||||
\(914\) | 78.1339 | 2.58444 | ||||||||
\(915\) | 67.2484 | 2.22316 | ||||||||
\(916\) | 19.2430 | 0.635806 | ||||||||
\(917\) | 3.07149 | 0.101430 | ||||||||
\(918\) | 14.0920 | 0.465105 | ||||||||
\(919\) | −49.0413 | −1.61772 | −0.808861 | − | 0.588000i | \(-0.799916\pi\) | ||||
−0.808861 | + | 0.588000i | \(0.799916\pi\) | |||||||
\(920\) | 5.20299 | 0.171538 | ||||||||
\(921\) | −25.6781 | −0.846121 | ||||||||
\(922\) | −53.3845 | −1.75812 | ||||||||
\(923\) | 0.476841 | 0.0156954 | ||||||||
\(924\) | −9.37159 | −0.308303 | ||||||||
\(925\) | 69.5647 | 2.28727 | ||||||||
\(926\) | 43.0942 | 1.41616 | ||||||||
\(927\) | −42.8332 | −1.40683 | ||||||||
\(928\) | 2.34137 | 0.0768592 | ||||||||
\(929\) | −16.7417 | −0.549278 | −0.274639 | − | 0.961547i | \(-0.588558\pi\) | ||||
−0.274639 | + | 0.961547i | \(0.588558\pi\) | |||||||
\(930\) | 126.140 | 4.13629 | ||||||||
\(931\) | −6.74173 | −0.220951 | ||||||||
\(932\) | −37.8004 | −1.23819 | ||||||||
\(933\) | 43.5117 | 1.42451 | ||||||||
\(934\) | 12.8202 | 0.419491 | ||||||||
\(935\) | −3.94429 | −0.128992 | ||||||||
\(936\) | 7.56332 | 0.247215 | ||||||||
\(937\) | 49.0794 | 1.60335 | 0.801677 | − | 0.597758i | \(-0.203942\pi\) | ||||
0.801677 | + | 0.597758i | \(0.203942\pi\) | |||||||
\(938\) | 17.7868 | 0.580759 | ||||||||
\(939\) | 100.108 | 3.26689 | ||||||||
\(940\) | −66.9850 | −2.18481 | ||||||||
\(941\) | 6.28288 | 0.204816 | 0.102408 | − | 0.994742i | \(-0.467345\pi\) | ||||
0.102408 | + | 0.994742i | \(0.467345\pi\) | |||||||
\(942\) | 119.111 | 3.88086 | ||||||||
\(943\) | −3.05987 | −0.0996429 | ||||||||
\(944\) | 33.2519 | 1.08226 | ||||||||
\(945\) | 34.0518 | 1.10770 | ||||||||
\(946\) | −5.24786 | −0.170623 | ||||||||
\(947\) | −5.61569 | −0.182485 | −0.0912427 | − | 0.995829i | \(-0.529084\pi\) | ||||
−0.0912427 | + | 0.995829i | \(0.529084\pi\) | |||||||
\(948\) | −48.2659 | −1.56760 | ||||||||
\(949\) | −2.70812 | −0.0879093 | ||||||||
\(950\) | 169.105 | 5.48648 | ||||||||
\(951\) | 63.8255 | 2.06968 | ||||||||
\(952\) | 0.991265 | 0.0321271 | ||||||||
\(953\) | 36.0636 | 1.16821 | 0.584107 | − | 0.811677i | \(-0.301445\pi\) | ||||
0.584107 | + | 0.811677i | \(0.301445\pi\) | |||||||
\(954\) | −8.75535 | −0.283465 | ||||||||
\(955\) | −29.0176 | −0.938989 | ||||||||
\(956\) | 24.8183 | 0.802683 | ||||||||
\(957\) | 1.08359 | 0.0350276 | ||||||||
\(958\) | −6.81085 | −0.220049 | ||||||||
\(959\) | 15.4926 | 0.500284 | ||||||||
\(960\) | 143.153 | 4.62026 | ||||||||
\(961\) | −7.42747 | −0.239596 | ||||||||
\(962\) | 13.2028 | 0.425677 | ||||||||
\(963\) | 30.2947 | 0.976234 | ||||||||
\(964\) | 12.0674 | 0.388663 | ||||||||
\(965\) | 71.7929 | 2.31109 | ||||||||
\(966\) | 6.44620 | 0.207403 | ||||||||
\(967\) | 27.0752 | 0.870679 | 0.435340 | − | 0.900266i | \(-0.356628\pi\) | ||||
0.435340 | + | 0.900266i | \(0.356628\pi\) | |||||||
\(968\) | 11.9305 | 0.383462 | ||||||||
\(969\) | 15.8062 | 0.507768 | ||||||||
\(970\) | 21.1873 | 0.680283 | ||||||||
\(971\) | −5.80383 | −0.186254 | −0.0931268 | − | 0.995654i | \(-0.529686\pi\) | ||||
−0.0931268 | + | 0.995654i | \(0.529686\pi\) | |||||||
\(972\) | 8.61150 | 0.276214 | ||||||||
\(973\) | 0.313077 | 0.0100368 | ||||||||
\(974\) | 28.4033 | 0.910099 | ||||||||
\(975\) | 36.0842 | 1.15562 | ||||||||
\(976\) | 13.7738 | 0.440889 | ||||||||
\(977\) | −41.1394 | −1.31616 | −0.658082 | − | 0.752946i | \(-0.728632\pi\) | ||||
−0.658082 | + | 0.752946i | \(0.728632\pi\) | |||||||
\(978\) | 6.13801 | 0.196272 | ||||||||
\(979\) | 16.3414 | 0.522273 | ||||||||
\(980\) | 10.5716 | 0.337698 | ||||||||
\(981\) | −23.1752 | −0.739929 | ||||||||
\(982\) | −9.56961 | −0.305379 | ||||||||
\(983\) | 59.5754 | 1.90016 | 0.950081 | − | 0.312005i | \(-0.101001\pi\) | ||||
0.950081 | + | 0.312005i | \(0.101001\pi\) | |||||||
\(984\) | 11.2323 | 0.358072 | ||||||||
\(985\) | 39.2530 | 1.25071 | ||||||||
\(986\) | −0.505856 | −0.0161098 | ||||||||
\(987\) | −18.8037 | −0.598529 | ||||||||
\(988\) | 18.0977 | 0.575763 | ||||||||
\(989\) | 2.03545 | 0.0647236 | ||||||||
\(990\) | 62.0821 | 1.97310 | ||||||||
\(991\) | −50.3745 | −1.60020 | −0.800100 | − | 0.599867i | \(-0.795220\pi\) | ||||
−0.800100 | + | 0.599867i | \(0.795220\pi\) | |||||||
\(992\) | 38.0195 | 1.20712 | ||||||||
\(993\) | −27.7132 | −0.879453 | ||||||||
\(994\) | −0.983667 | −0.0312000 | ||||||||
\(995\) | −2.73437 | −0.0866853 | ||||||||
\(996\) | −61.3170 | −1.94290 | ||||||||
\(997\) | −1.14652 | −0.0363108 | −0.0181554 | − | 0.999835i | \(-0.505779\pi\) | ||||
−0.0181554 | + | 0.999835i | \(0.505779\pi\) | |||||||
\(998\) | −23.2587 | −0.736242 | ||||||||
\(999\) | −49.4684 | −1.56511 |
(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.d.1.14 | ✓ | 101 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.d.1.14 | ✓ | 101 | 1.1 | even | 1 | trivial |