Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [200,6,Mod(1,200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("200.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 200.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0767639626\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.1595208.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 20x^{2} + 33x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 40) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.0965878\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 200.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 24.1383 | 1.54847 | 0.774236 | − | 0.632897i | \(-0.218134\pi\) | ||||
0.774236 | + | 0.632897i | \(0.218134\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −179.876 | −1.38749 | −0.693743 | − | 0.720223i | \(-0.744040\pi\) | ||||
−0.693743 | + | 0.720223i | \(0.744040\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 339.657 | 1.39777 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −653.681 | −1.62886 | −0.814431 | − | 0.580260i | \(-0.802951\pi\) | ||||
−0.814431 | + | 0.580260i | \(0.802951\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 284.851 | 0.467477 | 0.233738 | − | 0.972300i | \(-0.424904\pi\) | ||||
0.233738 | + | 0.972300i | \(0.424904\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −383.672 | −0.321986 | −0.160993 | − | 0.986956i | \(-0.551470\pi\) | ||||
−0.160993 | + | 0.986956i | \(0.551470\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2563.29 | −1.62897 | −0.814485 | − | 0.580185i | \(-0.802980\pi\) | ||||
−0.814485 | + | 0.580185i | \(0.802980\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4341.90 | −2.14848 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −948.124 | −0.373719 | −0.186860 | − | 0.982387i | \(-0.559831\pi\) | ||||
−0.186860 | + | 0.982387i | \(0.559831\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2333.13 | 0.615929 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1524.26 | −0.336561 | −0.168281 | − | 0.985739i | \(-0.553822\pi\) | ||||
−0.168281 | + | 0.985739i | \(0.553822\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3103.88 | 0.580098 | 0.290049 | − | 0.957012i | \(-0.406328\pi\) | ||||
0.290049 | + | 0.957012i | \(0.406328\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −15778.7 | −2.52225 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9991.75 | −1.19988 | −0.599939 | − | 0.800046i | \(-0.704809\pi\) | ||||
−0.599939 | + | 0.800046i | \(0.704809\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6875.83 | 0.723875 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 15120.7 | 1.40479 | 0.702394 | − | 0.711788i | \(-0.252114\pi\) | ||||
0.702394 | + | 0.711788i | \(0.252114\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1754.92 | 0.144739 | 0.0723696 | − | 0.997378i | \(-0.476944\pi\) | ||||
0.0723696 | + | 0.997378i | \(0.476944\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 14760.7 | 0.974682 | 0.487341 | − | 0.873212i | \(-0.337967\pi\) | ||||
0.487341 | + | 0.873212i | \(0.337967\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15548.5 | 0.925118 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9261.18 | −0.498587 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8704.12 | −0.425633 | −0.212816 | − | 0.977092i | \(-0.568264\pi\) | ||||
−0.212816 | + | 0.977092i | \(0.568264\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −61873.3 | −2.52241 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12632.1 | −0.472438 | −0.236219 | − | 0.971700i | \(-0.575908\pi\) | ||||
−0.236219 | + | 0.971700i | \(0.575908\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 43098.3 | 1.48298 | 0.741490 | − | 0.670964i | \(-0.234119\pi\) | ||||
0.741490 | + | 0.670964i | \(0.234119\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −61096.2 | −1.93938 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −26125.5 | −0.711014 | −0.355507 | − | 0.934674i | \(-0.615692\pi\) | ||||
−0.355507 | + | 0.934674i | \(0.615692\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −22886.1 | −0.578694 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −46285.8 | −1.08969 | −0.544844 | − | 0.838538i | \(-0.683411\pi\) | ||||
−0.544844 | + | 0.838538i | \(0.683411\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −51303.2 | −1.12678 | −0.563388 | − | 0.826192i | \(-0.690502\pi\) | ||||
−0.563388 | + | 0.826192i | \(0.690502\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 117582. | 2.26002 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 39314.0 | 0.708729 | 0.354364 | − | 0.935107i | \(-0.384697\pi\) | ||||
0.354364 | + | 0.935107i | \(0.384697\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −26218.8 | −0.444017 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −69544.8 | −1.10808 | −0.554038 | − | 0.832492i | \(-0.686914\pi\) | ||||
−0.554038 | + | 0.832492i | \(0.686914\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −36793.1 | −0.521156 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13092.2 | −0.175201 | −0.0876007 | − | 0.996156i | \(-0.527920\pi\) | ||||
−0.0876007 | + | 0.996156i | \(0.527920\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −51238.0 | −0.648618 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 74922.5 | 0.898265 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −26258.1 | −0.283357 | −0.141678 | − | 0.989913i | \(-0.545250\pi\) | ||||
−0.141678 | + | 0.989913i | \(0.545250\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −222027. | −2.27677 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7382.54 | 0.0720116 | 0.0360058 | − | 0.999352i | \(-0.488537\pi\) | ||||
0.0360058 | + | 0.999352i | \(0.488537\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 44518.9 | 0.413477 | 0.206738 | − | 0.978396i | \(-0.433715\pi\) | ||||
0.206738 | + | 0.978396i | \(0.433715\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −194929. | −1.64595 | −0.822974 | − | 0.568079i | \(-0.807687\pi\) | ||||
−0.822974 | + | 0.568079i | \(0.807687\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 213783. | 1.72348 | 0.861739 | − | 0.507351i | \(-0.169375\pi\) | ||||
0.861739 | + | 0.507351i | \(0.169375\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −241184. | −1.85798 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −148946. | −1.09732 | −0.548660 | − | 0.836046i | \(-0.684862\pi\) | ||||
−0.548660 | + | 0.836046i | \(0.684862\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 96751.8 | 0.653423 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 69013.4 | 0.446751 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 266248. | 1.65319 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 364987. | 2.17528 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 116757. | 0.642351 | 0.321175 | − | 0.947020i | \(-0.395922\pi\) | ||||
0.321175 | + | 0.947020i | \(0.395922\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 42360.8 | 0.224125 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 349111. | 1.77740 | 0.888700 | − | 0.458490i | \(-0.151610\pi\) | ||||
0.888700 | + | 0.458490i | \(0.151610\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 461074. | 2.26017 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 219776. | 1.00041 | 0.500205 | − | 0.865907i | \(-0.333258\pi\) | ||||
0.500205 | + | 0.865907i | \(0.333258\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 126594. | 0.555744 | 0.277872 | − | 0.960618i | \(-0.410371\pi\) | ||||
0.277872 | + | 0.960618i | \(0.410371\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 356299. | 1.50927 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −186202. | −0.761455 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 375313. | 1.43252 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −25809.9 | −0.0952403 | −0.0476202 | − | 0.998866i | \(-0.515164\pi\) | ||||
−0.0476202 | + | 0.998866i | \(0.515164\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −311270. | −1.11095 | −0.555475 | − | 0.831533i | \(-0.687464\pi\) | ||||
−0.555475 | + | 0.831533i | \(0.687464\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −130317. | −0.450061 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −429151. | −1.38951 | −0.694755 | − | 0.719247i | \(-0.744487\pi\) | ||||
−0.694755 | + | 0.719247i | \(0.744487\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −210102. | −0.659080 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 170545. | 0.518530 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −162467. | −0.478957 | −0.239479 | − | 0.970902i | \(-0.576977\pi\) | ||||
−0.239479 | + | 0.970902i | \(0.576977\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 280057. | 0.777060 | 0.388530 | − | 0.921436i | \(-0.372983\pi\) | ||||
0.388530 | + | 0.921436i | \(0.372983\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −290153. | −0.781465 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −870638. | −2.27692 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 742577. | 1.88637 | 0.943184 | − | 0.332271i | \(-0.107815\pi\) | ||||
0.943184 | + | 0.332271i | \(0.107815\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −304917. | −0.731557 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14556.0 | −0.0339554 | −0.0169777 | − | 0.999856i | \(-0.505404\pi\) | ||||
−0.0169777 | + | 0.999856i | \(0.505404\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −243243. | −0.551878 | −0.275939 | − | 0.961175i | \(-0.588989\pi\) | ||||
−0.275939 | + | 0.961175i | \(0.588989\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.04032e6 | 2.29635 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 250799. | 0.524471 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −419675. | −0.854592 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 75871.1 | 0.150485 | 0.0752425 | − | 0.997165i | \(-0.476027\pi\) | ||||
0.0752425 | + | 0.997165i | \(0.476027\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −370161. | −0.715314 | −0.357657 | − | 0.933853i | \(-0.616424\pi\) | ||||
−0.357657 | + | 0.933853i | \(0.616424\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 213848. | 0.392590 | 0.196295 | − | 0.980545i | \(-0.437109\pi\) | ||||
0.196295 | + | 0.980545i | \(0.437109\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 466075. | 0.834302 | 0.417151 | − | 0.908837i | \(-0.363029\pi\) | ||||
0.417151 | + | 0.908837i | \(0.363029\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −630626. | −1.10099 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 274178. | 0.466974 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −322037. | −0.522372 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.67557e6 | 2.65337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −228211. | −0.352883 | −0.176441 | − | 0.984311i | \(-0.556459\pi\) | ||||
−0.176441 | + | 0.984311i | \(0.556459\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.11726e6 | −1.68735 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −558315. | −0.804878 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.23837e6 | −1.74478 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −109289. | −0.150521 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −972750. | −1.30990 | −0.654951 | − | 0.755671i | \(-0.727311\pi\) | ||||
−0.654951 | + | 0.755671i | \(0.727311\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −357063. | −0.459917 | −0.229959 | − | 0.973200i | \(-0.573859\pi\) | ||||
−0.229959 | + | 0.973200i | \(0.573859\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −295196. | −0.371982 | −0.185991 | − | 0.982551i | \(-0.559549\pi\) | ||||
−0.185991 | + | 0.982551i | \(0.559549\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.83822e6 | 3.49958 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −492373. | −0.594162 | −0.297081 | − | 0.954852i | \(-0.596013\pi\) | ||||
−0.297081 | + | 0.954852i | \(0.596013\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 948974. | 1.09745 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −71796.0 | −0.0813028 | −0.0406514 | − | 0.999173i | \(-0.512943\pi\) | ||||
−0.0406514 | + | 0.999173i | \(0.512943\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 614304. | 0.681304 | 0.340652 | − | 0.940190i | \(-0.389352\pi\) | ||||
0.340652 | + | 0.940190i | \(0.389352\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.19983e6 | −1.30348 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −730156. | −0.761505 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.67869e6 | −1.71582 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −244276. | −0.244735 | −0.122368 | − | 0.992485i | \(-0.539049\pi\) | ||||
−0.122368 | + | 0.992485i | \(0.539049\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 619771. | 0.608737 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 951728. | 0.898835 | 0.449418 | − | 0.893322i | \(-0.351632\pi\) | ||||
0.449418 | + | 0.893322i | \(0.351632\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.79728e6 | 1.66481 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −517726. | −0.470434 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −258512. | −0.230458 | −0.115229 | − | 0.993339i | \(-0.536760\pi\) | ||||
−0.115229 | + | 0.993339i | \(0.536760\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −316023. | −0.271295 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 894716. | 0.753884 | 0.376942 | − | 0.926237i | \(-0.376976\pi\) | ||||
0.376942 | + | 0.926237i | \(0.376976\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 474149. | 0.392186 | 0.196093 | − | 0.980585i | \(-0.437175\pi\) | ||||
0.196093 | + | 0.980585i | \(0.437175\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.23680e6 | −1.00437 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 142752. | 0.111785 | 0.0558923 | − | 0.998437i | \(-0.482200\pi\) | ||||
0.0558923 | + | 0.998437i | \(0.482200\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.05426e6 | 0.810841 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −427838. | −0.323231 | −0.161616 | − | 0.986854i | \(-0.551670\pi\) | ||||
−0.161616 | + | 0.986854i | \(0.551670\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.30233e6 | −1.70884 | −0.854419 | − | 0.519585i | \(-0.826087\pi\) | ||||
−0.854419 | + | 0.519585i | \(0.826087\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.71985e6 | −1.94913 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.27265e6 | −0.896325 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −633825. | −0.438770 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.59390e6 | 1.08465 | 0.542326 | − | 0.840168i | \(-0.317544\pi\) | ||||
0.542326 | + | 0.840168i | \(0.317544\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.52513e6 | −1.00326 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −270074. | −0.174705 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −315668. | −0.200824 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 178202. | 0.111508 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −322680. | −0.195401 | −0.0977005 | − | 0.995216i | \(-0.531149\pi\) | ||||
−0.0977005 | + | 0.995216i | \(0.531149\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.07461e6 | 0.640257 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −660204. | −0.387059 | −0.193529 | − | 0.981094i | \(-0.561994\pi\) | ||||
−0.193529 | + | 0.981094i | \(0.561994\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.15378e6 | 0.665677 | 0.332838 | − | 0.942984i | \(-0.391994\pi\) | ||||
0.332838 | + | 0.942984i | \(0.391994\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.20296e6 | −0.672364 | −0.336182 | − | 0.941797i | \(-0.609136\pi\) | ||||
−0.336182 | + | 0.941797i | \(0.609136\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 996381. | 0.548212 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.70524e6 | −2.54870 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 983460. | 0.524506 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.16034e6 | 2.66876 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.65510e6 | −1.35236 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.82424e6 | 0.915193 | 0.457597 | − | 0.889160i | \(-0.348710\pi\) | ||||
0.457597 | + | 0.889160i | \(0.348710\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.39377e6 | −1.67715 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 485867. | 0.233047 | 0.116523 | − | 0.993188i | \(-0.462825\pi\) | ||||
0.116523 | + | 0.993188i | \(0.462825\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.59530e6 | −1.69917 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.02895e6 | −0.944899 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 226383. | 0.103898 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.35066e6 | 1.04801 | 0.524006 | − | 0.851715i | \(-0.324437\pi\) | ||||
0.524006 | + | 0.851715i | \(0.324437\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.62295e6 | −1.15273 | −0.576364 | − | 0.817193i | \(-0.695529\pi\) | ||||
−0.576364 | + | 0.817193i | \(0.695529\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 664597. | 0.287932 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 583638. | 0.249291 | 0.124646 | − | 0.992201i | \(-0.460221\pi\) | ||||
0.124646 | + | 0.992201i | \(0.460221\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.66587e6 | 0.691782 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.64503e6 | 0.673654 | 0.336827 | − | 0.941567i | \(-0.390646\pi\) | ||||
0.336827 | + | 0.941567i | \(0.390646\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.09433e6 | 1.65354 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.42678e6 | 2.55992 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.62251e6 | −1.01637 | −0.508186 | − | 0.861247i | \(-0.669684\pi\) | ||||
−0.508186 | + | 0.861247i | \(0.669684\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.13584e6 | 1.96357 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.56566e6 | 0.590559 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.73068e6 | −1.38840 | −0.694202 | − | 0.719780i | \(-0.744243\pi\) | ||||
−0.694202 | + | 0.719780i | \(0.744243\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −434188. | −0.157335 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.00539e6 | −1.07474 | −0.537368 | − | 0.843348i | \(-0.680582\pi\) | ||||
−0.537368 | + | 0.843348i | \(0.680582\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.81831e6 | 0.994662 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −343090. | −0.119512 | −0.0597560 | − | 0.998213i | \(-0.519032\pi\) | ||||
−0.0597560 | + | 0.998213i | \(0.519032\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 596071. | 0.202311 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 190583. | 0.0638572 | 0.0319286 | − | 0.999490i | \(-0.489835\pi\) | ||||
0.0319286 | + | 0.999490i | \(0.489835\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 363768. | 0.120332 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.42694e6 | 2.75225 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.22551e6 | −1.66400 | −0.831999 | − | 0.554778i | \(-0.812803\pi\) | ||||
−0.831999 | + | 0.554778i | \(0.812803\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.11295e7 | 3.49981 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.60312e6 | −0.497859 | −0.248929 | − | 0.968522i | \(-0.580079\pi\) | ||||
−0.248929 | + | 0.968522i | \(0.580079\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 884146. | 0.271182 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.53142e6 | 1.95444 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.58732e6 | 1.35597 | 0.677986 | − | 0.735075i | \(-0.262853\pi\) | ||||
0.677986 | + | 0.735075i | \(0.262853\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.30501e6 | 1.54911 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.27221e6 | 0.655501 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.05575e6 | 0.860554 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.16854e6 | −1.71651 | −0.858256 | − | 0.513221i | \(-0.828452\pi\) | ||||
−0.858256 | + | 0.513221i | \(0.828452\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.15589e6 | −1.69272 | −0.846361 | − | 0.532610i | \(-0.821211\pi\) | ||||
−0.846361 | + | 0.532610i | \(0.821211\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.01358e6 | 1.36238 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.75236e6 | −2.05761 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.49460e6 | −1.17909 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.15900e6 | 0.300532 | 0.150266 | − | 0.988646i | \(-0.451987\pi\) | ||||
0.150266 | + | 0.988646i | \(0.451987\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.73906e6 | 1.72735 | 0.863673 | − | 0.504052i | \(-0.168158\pi\) | ||||
0.863673 | + | 0.504052i | \(0.168158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.43031e6 | 0.608777 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.69068e6 | −0.913998 | −0.456999 | − | 0.889467i | \(-0.651076\pi\) | ||||
−0.456999 | + | 0.889467i | \(0.651076\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.28114e6 | 1.29310 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.55124e6 | −1.10185 | −0.550923 | − | 0.834556i | \(-0.685724\pi\) | ||||
−0.550923 | + | 0.834556i | \(0.685724\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −623007. | −0.147477 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.31419e6 | −0.775822 | −0.387911 | − | 0.921697i | \(-0.626803\pi\) | ||||
−0.387911 | + | 0.921697i | \(0.626803\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.88409e6 | −2.28821 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.51352e6 | −1.72028 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.10489e6 | 0.919414 | 0.459707 | − | 0.888071i | \(-0.347954\pi\) | ||||
0.459707 | + | 0.888071i | \(0.347954\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −895158. | −0.198321 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.16525e6 | 1.78944 | 0.894720 | − | 0.446628i | \(-0.147375\pi\) | ||||
0.894720 | + | 0.446628i | \(0.147375\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.65614e6 | −1.22622 | −0.613109 | − | 0.789998i | \(-0.710081\pi\) | ||||
−0.613109 | + | 0.789998i | \(0.710081\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.77216e6 | 1.86129 | 0.930646 | − | 0.365921i | \(-0.119246\pi\) | ||||
0.930646 | + | 0.365921i | \(0.119246\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.69936e6 | 0.986522 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.03590e7 | −2.15162 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.14716e6 | −0.235760 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.95641e6 | −0.594935 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 417978. | 0.0832367 | 0.0416184 | − | 0.999134i | \(-0.486749\pi\) | ||||
0.0416184 | + | 0.999134i | \(0.486749\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.84616e6 | −0.560915 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.11666e6 | 0.802929 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.07076e6 | −1.35096 | −0.675482 | − | 0.737376i | \(-0.736064\pi\) | ||||
−0.675482 | + | 0.737376i | \(0.736064\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.92168e6 | −0.741652 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.00127e7 | −1.87433 | −0.937166 | − | 0.348883i | \(-0.886561\pi\) | ||||
−0.937166 | + | 0.348883i | \(0.886561\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 584816. | 0.108368 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.32571e6 | 1.51193 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.74452e6 | −1.39233 | −0.696166 | − | 0.717881i | \(-0.745112\pi\) | ||||
−0.696166 | + | 0.717881i | \(0.745112\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.76009e6 | 1.20326 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.20376e6 | −0.388370 | −0.194185 | − | 0.980965i | \(-0.562206\pi\) | ||||
−0.194185 | + | 0.980965i | \(0.562206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.00379e6 | −1.21008 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.40053e6 | 0.239607 | 0.119803 | − | 0.992798i | \(-0.461774\pi\) | ||||
0.119803 | + | 0.992798i | \(0.461774\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.22823e6 | 1.56339 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.98049e6 | −1.00333 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.64881e6 | −1.58762 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.79245e7 | 2.92099 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.60571e6 | 0.259162 | 0.129581 | − | 0.991569i | \(-0.458637\pi\) | ||||
0.129581 | + | 0.991569i | \(0.458637\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.80485e6 | −0.927977 | −0.463988 | − | 0.885841i | \(-0.653582\pi\) | ||||
−0.463988 | + | 0.885841i | \(0.653582\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.19087e6 | −0.186784 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.53740e6 | −0.860334 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.29057e6 | −0.660357 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.30714e6 | 0.656706 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −351356. | −0.0525790 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.01637e7 | −1.50689 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.37930e6 | −1.37777 | −0.688886 | − | 0.724870i | \(-0.741900\pi\) | ||||
−0.688886 | + | 0.724870i | \(0.741900\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.87146e6 | −0.854568 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.33685e6 | −0.333936 | −0.166968 | − | 0.985962i | \(-0.553398\pi\) | ||||
−0.166968 | + | 0.985962i | \(0.553398\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.46386e7 | 2.07286 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.90712e6 | 0.548248 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.07166e6 | −0.983351 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.02238e6 | 0.959061 | 0.479530 | − | 0.877525i | \(-0.340807\pi\) | ||||
0.479530 | + | 0.877525i | \(0.340807\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 499891. | 0.0676622 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.05386e6 | 0.812129 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.81010e6 | −0.240675 | −0.120338 | − | 0.992733i | \(-0.538398\pi\) | ||||
−0.120338 | + | 0.992733i | \(0.538398\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.71613e6 | 0.616068 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.62751e6 | 0.728678 | 0.364339 | − | 0.931266i | \(-0.381295\pi\) | ||||
0.364339 | + | 0.931266i | \(0.381295\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.16702e6 | −0.278145 | −0.139073 | − | 0.990282i | \(-0.544412\pi\) | ||||
−0.139073 | + | 0.990282i | \(0.544412\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.83140e6 | 0.233022 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.04992e7 | −1.31286 | −0.656430 | − | 0.754387i | \(-0.727934\pi\) | ||||
−0.656430 | + | 0.754387i | \(0.727934\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.93504e6 | −1.10764 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.25095e7 | 1.53744 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.68972e6 | 0.693297 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.47459e7 | −1.76634 | −0.883172 | − | 0.469050i | \(-0.844596\pi\) | ||||
−0.883172 | + | 0.469050i | \(0.844596\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.95614e6 | −0.944962 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.16192e6 | 0.607915 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.85519e6 | −0.566982 | −0.283491 | − | 0.958975i | \(-0.591493\pi\) | ||||
−0.283491 | + | 0.958975i | \(0.591493\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.12503e7 | 1.29189 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.48204e6 | −0.510398 | −0.255199 | − | 0.966889i | \(-0.582141\pi\) | ||||
−0.255199 | + | 0.966889i | \(0.582141\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.29562e6 | 0.485110 | 0.242555 | − | 0.970138i | \(-0.422015\pi\) | ||||
0.242555 | + | 0.970138i | \(0.422015\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.87372e6 | −0.993831 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.05706e7 | −1.16447 | −0.582235 | − | 0.813020i | \(-0.697822\pi\) | ||||
−0.582235 | + | 0.813020i | \(0.697822\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.61820e6 | 0.723097 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.20461e6 | 0.455641 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.30960e7 | −1.40763 | −0.703816 | − | 0.710383i | \(-0.748522\pi\) | ||||
−0.703816 | + | 0.710383i | \(0.748522\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.69519e7 | −1.79270 | −0.896348 | − | 0.443351i | \(-0.853789\pi\) | ||||
−0.896348 | + | 0.443351i | \(0.853789\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.27214e7 | 1.33447 | 0.667236 | − | 0.744846i | \(-0.267477\pi\) | ||||
0.667236 | + | 0.744846i | \(0.267477\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.21210e6 | −0.230184 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.35498e6 | 0.243090 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.04454e7 | 4.10866 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.83355e6 | 0.386344 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.32823e6 | 0.832682 | 0.416341 | − | 0.909209i | \(-0.363312\pi\) | ||||
0.416341 | + | 0.909209i | \(0.363312\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.50862e6 | −0.546429 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.42900e6 | 0.432471 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.57213e7 | −1.52313 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.18862e6 | −0.402648 | −0.201324 | − | 0.979525i | \(-0.564524\pi\) | ||||
−0.201324 | + | 0.979525i | \(0.564524\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −271198. | −0.0258677 | −0.0129339 | − | 0.999916i | \(-0.504117\pi\) | ||||
−0.0129339 | + | 0.999916i | \(0.504117\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.01692e7 | 0.955052 | 0.477526 | − | 0.878618i | \(-0.341534\pi\) | ||||
0.477526 | + | 0.878618i | \(0.341534\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.25735e6 | 0.769536 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.34768e7 | −1.24633 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.95062e6 | 0.821429 | 0.410714 | − | 0.911764i | \(-0.365279\pi\) | ||||
0.410714 | + | 0.911764i | \(0.365279\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.74255e7 | −1.57497 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.07182e7 | 0.961409 | 0.480705 | − | 0.876883i | \(-0.340381\pi\) | ||||
0.480705 | + | 0.876883i | \(0.340381\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.65131e6 | 0.414068 | 0.207034 | − | 0.978334i | \(-0.433619\pi\) | ||||
0.207034 | + | 0.978334i | \(0.433619\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.63806e6 | −0.233078 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.44519e6 | 0.125779 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.34805e7 | −2.02835 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.81725e7 | −2.41557 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.92139e6 | −0.844374 | −0.422187 | − | 0.906509i | \(-0.638737\pi\) | ||||
−0.422187 | + | 0.906509i | \(0.638737\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.45936e6 | 0.541649 | 0.270824 | − | 0.962629i | \(-0.412704\pi\) | ||||
0.270824 | + | 0.962629i | \(0.412704\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.72321e6 | 0.393154 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.61888e6 | −0.712169 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.26684e7 | 1.03913 | 0.519564 | − | 0.854432i | \(-0.326095\pi\) | ||||
0.519564 | + | 0.854432i | \(0.326095\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.12552e6 | −0.576003 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.47938e6 | −0.198973 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.07160e6 | 0.324392 | 0.162196 | − | 0.986759i | \(-0.448142\pi\) | ||||
0.162196 | + | 0.986759i | \(0.448142\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.99375e7 | 3.15898 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.80137e6 | −0.452323 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.18850e7 | −0.920043 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.11804e7 | −1.62795 | −0.813973 | − | 0.580903i | \(-0.802700\pi\) | ||||
−0.813973 | + | 0.580903i | \(0.802700\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.56117e7 | 1.95457 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.32794e6 | −0.0999150 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.87573e7 | −1.40138 | −0.700689 | − | 0.713467i | \(-0.747124\pi\) | ||||
−0.700689 | + | 0.713467i | \(0.747124\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.33533e7 | 0.990637 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.94287e6 | −0.216794 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.73303e6 | −0.125895 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.82800e7 | 1.31872 | 0.659362 | − | 0.751826i | \(-0.270826\pi\) | ||||
0.659362 | + | 0.751826i | \(0.270826\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00788e6 | −0.573693 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.48282e7 | 1.05498 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.45855e6 | 0.453210 | 0.226605 | − | 0.973987i | \(-0.427237\pi\) | ||||
0.226605 | + | 0.973987i | \(0.427237\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.25906e7 | −1.57438 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −673313. | −0.0466040 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.88365e6 | 0.129491 | 0.0647454 | − | 0.997902i | \(-0.479376\pi\) | ||||
0.0647454 | + | 0.997902i | \(0.479376\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.70778e7 | 1.15814 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.24002e7 | 1.50883 | 0.754417 | − | 0.656395i | \(-0.227920\pi\) | ||||
0.754417 | + | 0.656395i | \(0.227920\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.76247e7 | −1.17917 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.22827e6 | −0.148080 | −0.0740400 | − | 0.997255i | \(-0.523589\pi\) | ||||
−0.0740400 | + | 0.997255i | \(0.523589\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.36214e7 | −1.54883 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.50630e7 | 2.28373 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.92986e7 | 1.24861 | 0.624303 | − | 0.781183i | \(-0.285383\pi\) | ||||
0.624303 | + | 0.781183i | \(0.285383\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.89641e6 | −0.378966 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.22211e6 | −0.458062 | −0.229031 | − | 0.973419i | \(-0.573556\pi\) | ||||
−0.229031 | + | 0.973419i | \(0.573556\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.49602e7 | 0.942612 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.08001e7 | 0.676028 | 0.338014 | − | 0.941141i | \(-0.390245\pi\) | ||||
0.338014 | + | 0.941141i | \(0.390245\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.84544e7 | −2.39130 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.59827e6 | −0.220854 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.50354e6 | 0.335603 | 0.167802 | − | 0.985821i | \(-0.446333\pi\) | ||||
0.167802 | + | 0.985821i | \(0.446333\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.29731e7 | 1.39182 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.91304e7 | 1.75347 | 0.876733 | − | 0.480977i | \(-0.159718\pi\) | ||||
0.876733 | + | 0.480977i | \(0.159718\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.33832e7 | 2.57792 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.87586e7 | −2.28836 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.02562e7 | 1.77495 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.55631e6 | −0.207298 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.40251e6 | 0.310927 | 0.155464 | − | 0.987842i | \(-0.450313\pi\) | ||||
0.155464 | + | 0.987842i | \(0.450313\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.24005e6 | −0.356858 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.67919e7 | 1.52251 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.22766e7 | 0.693259 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.19820e7 | 1.22580 | 0.612902 | − | 0.790159i | \(-0.290002\pi\) | ||||
0.612902 | + | 0.790159i | \(0.290002\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.66327e6 | −0.313834 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.44686e6 | −0.244891 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.35360e7 | 1.83536 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.15969e7 | 1.16737 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.37377e7 | 1.81236 | 0.906178 | − | 0.422896i | \(-0.138986\pi\) | ||||
0.906178 | + | 0.422896i | \(0.138986\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.30907e6 | 0.176666 | 0.0883331 | − | 0.996091i | \(-0.471846\pi\) | ||||
0.0883331 | + | 0.996091i | \(0.471846\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.14451e7 | 0.607289 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.49836e6 | −0.235776 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.74033e7 | −0.906615 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.00294e6 | 0.207263 | 0.103631 | − | 0.994616i | \(-0.466954\pi\) | ||||
0.103631 | + | 0.994616i | \(0.466954\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.17703e7 | −0.605740 | −0.302870 | − | 0.953032i | \(-0.597945\pi\) | ||||
−0.302870 | + | 0.953032i | \(0.597945\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.12347e7 | −0.571214 | −0.285607 | − | 0.958347i | \(-0.592195\pi\) | ||||
−0.285607 | + | 0.958347i | \(0.592195\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.44928e7 | 1.23781 | 0.618903 | − | 0.785468i | \(-0.287577\pi\) | ||||
0.618903 | + | 0.785468i | \(0.287577\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.44578e6 | 0.173095 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.96550e6 | −0.297875 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.24178e6 | 0.357299 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.20271e6 | −0.0589868 | −0.0294934 | − | 0.999565i | \(-0.509389\pi\) | ||||
−0.0294934 | + | 0.999565i | \(0.509389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.81878e7 | −0.886726 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.03273e7 | −0.500515 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.78917e7 | −2.29378 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.55742e7 | −2.64609 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.47341e6 | 0.448418 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.92510e7 | −1.84705 | −0.923523 | − | 0.383543i | \(-0.874704\pi\) | ||||
−0.923523 | + | 0.383543i | \(0.874704\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.29324e6 | 0.0601488 | 0.0300744 | − | 0.999548i | \(-0.490426\pi\) | ||||
0.0300744 | + | 0.999548i | \(0.490426\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.87256e7 | 1.32827 | 0.664134 | − | 0.747613i | \(-0.268800\pi\) | ||||
0.664134 | + | 0.747613i | \(0.268800\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.56525e7 | −3.01817 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.57964e6 | −0.392141 | −0.196070 | − | 0.980590i | \(-0.562818\pi\) | ||||
−0.196070 | + | 0.980590i | \(0.562818\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.07197e7 | −1.38793 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.56989e7 | −1.15442 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.44190e6 | −0.332383 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.91875e6 | −0.396067 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.79556e7 | −1.22735 | −0.613676 | − | 0.789558i | \(-0.710310\pi\) | ||||
−0.613676 | + | 0.789558i | \(0.710310\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.84739e7 | 1.67955 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.36409e6 | −0.232839 | −0.116420 | − | 0.993200i | \(-0.537142\pi\) | ||||
−0.116420 | + | 0.993200i | \(0.537142\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.40226e7 | 1.90009 | 0.950044 | − | 0.312117i | \(-0.101038\pi\) | ||||
0.950044 | + | 0.312117i | \(0.101038\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.88424e7 | 0.804133 | 0.402067 | − | 0.915610i | \(-0.368292\pi\) | ||||
0.402067 | + | 0.915610i | \(0.368292\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.10017e7 | −0.891253 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.71387e7 | 0.723243 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.78359e7 | −1.58773 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.51913e6 | −0.270526 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.73113e6 | −0.195239 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.33952e6 | 0.137048 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.61969e6 | −0.310970 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.40217e7 | 1.77684 | 0.888421 | − | 0.459029i | \(-0.151803\pi\) | ||||
0.888421 | + | 0.459029i | \(0.151803\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.50753e6 | 0.100655 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.02447e7 | −1.20741 | −0.603703 | − | 0.797209i | \(-0.706309\pi\) | ||||
−0.603703 | + | 0.797209i | \(0.706309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.54601e7 | 1.80490 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.27967e7 | −2.46612 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.35173e7 | −0.918543 | −0.459272 | − | 0.888296i | \(-0.651890\pi\) | ||||
−0.459272 | + | 0.888296i | \(0.651890\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.78895e6 | −0.302573 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.31846e7 | −0.509404 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.51211e7 | 0.577943 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.07876e7 | 1.55056 | 0.775281 | − | 0.631616i | \(-0.217608\pi\) | ||||
0.775281 | + | 0.631616i | \(0.217608\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.98551e7 | −1.50699 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.59362e7 | −0.599350 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.42613e7 | −0.530654 | −0.265327 | − | 0.964159i | \(-0.585480\pi\) | ||||
−0.265327 | + | 0.964159i | \(0.585480\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.78504e7 | 1.03078 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.24934e7 | 0.828095 | 0.414048 | − | 0.910255i | \(-0.364115\pi\) | ||||
0.414048 | + | 0.910255i | \(0.364115\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.43363e7 | −0.524997 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.45401e7 | 0.889205 | 0.444603 | − | 0.895728i | \(-0.353345\pi\) | ||||
0.444603 | + | 0.895728i | \(0.353345\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.46138e7 | −0.526742 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.90375e7 | −1.04114 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.06466e7 | −1.44975 | −0.724873 | − | 0.688882i | \(-0.758102\pi\) | ||||
−0.724873 | + | 0.688882i | \(0.758102\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.40509e7 | 0.848891 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.95324e7 | −1.38806 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.89951e7 | −0.663486 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.62089e7 | −2.30065 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.22263e7 | 1.45217 | 0.726084 | − | 0.687606i | \(-0.241338\pi\) | ||||
0.726084 | + | 0.687606i | \(0.241338\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.37390e7 | 0.812183 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.00999e7 | 1.36488 | 0.682442 | − | 0.730940i | \(-0.260918\pi\) | ||||
0.682442 | + | 0.730940i | \(0.260918\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.27712e7 | −0.771087 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.75634e7 | −0.588671 | −0.294336 | − | 0.955702i | \(-0.595098\pi\) | ||||
−0.294336 | + | 0.955702i | \(0.595098\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.55813e6 | 0.285379 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.26127e7 | 2.40902 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.46862e6 | −0.114491 | −0.0572456 | − | 0.998360i | \(-0.518232\pi\) | ||||
−0.0572456 | + | 0.998360i | \(0.518232\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.40896e7 | −2.09409 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.66388e6 | −0.0540918 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.88098e7 | −0.608414 | −0.304207 | − | 0.952606i | \(-0.598391\pi\) | ||||
−0.304207 | + | 0.952606i | \(0.598391\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.40341e7 | 1.41715 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.29454e7 | 0.412455 | 0.206227 | − | 0.978504i | \(-0.433881\pi\) | ||||
0.206227 | + | 0.978504i | \(0.433881\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.33121e7 | −0.739039 |
(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 | 200.6.a.j.1.4 | 4 | ||
4.3 | odd | 2 | 400.6.a.ba.1.1 | 4 | |||
5.2 | odd | 4 | 40.6.c.a.9.2 | ✓ | 8 | ||
5.3 | odd | 4 | 40.6.c.a.9.7 | yes | 8 | ||
5.4 | even | 2 | 200.6.a.k.1.1 | 4 | |||
15.2 | even | 4 | 360.6.f.b.289.1 | 8 | |||
15.8 | even | 4 | 360.6.f.b.289.2 | 8 | |||
20.3 | even | 4 | 80.6.c.d.49.2 | 8 | |||
20.7 | even | 4 | 80.6.c.d.49.7 | 8 | |||
20.19 | odd | 2 | 400.6.a.z.1.4 | 4 | |||
40.3 | even | 4 | 320.6.c.i.129.7 | 8 | |||
40.13 | odd | 4 | 320.6.c.j.129.2 | 8 | |||
40.27 | even | 4 | 320.6.c.i.129.2 | 8 | |||
40.37 | odd | 4 | 320.6.c.j.129.7 | 8 | |||
60.23 | odd | 4 | 720.6.f.n.289.2 | 8 | |||
60.47 | odd | 4 | 720.6.f.n.289.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.c.a.9.2 | ✓ | 8 | 5.2 | odd | 4 | ||
40.6.c.a.9.7 | yes | 8 | 5.3 | odd | 4 | ||
80.6.c.d.49.2 | 8 | 20.3 | even | 4 | |||
80.6.c.d.49.7 | 8 | 20.7 | even | 4 | |||
200.6.a.j.1.4 | 4 | 1.1 | even | 1 | trivial | ||
200.6.a.k.1.1 | 4 | 5.4 | even | 2 | |||
320.6.c.i.129.2 | 8 | 40.27 | even | 4 | |||
320.6.c.i.129.7 | 8 | 40.3 | even | 4 | |||
320.6.c.j.129.2 | 8 | 40.13 | odd | 4 | |||
320.6.c.j.129.7 | 8 | 40.37 | odd | 4 | |||
360.6.f.b.289.1 | 8 | 15.2 | even | 4 | |||
360.6.f.b.289.2 | 8 | 15.8 | even | 4 | |||
400.6.a.z.1.4 | 4 | 20.19 | odd | 2 | |||
400.6.a.ba.1.1 | 4 | 4.3 | odd | 2 | |||
720.6.f.n.289.1 | 8 | 60.47 | odd | 4 | |||
720.6.f.n.289.2 | 8 | 60.23 | odd | 4 |