Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,22,Mod(1,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.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: | \(178.865500344\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 4963x + 96223 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3\cdot 5\cdot 7 \) |
Twist minimal: | no (minimal twist has level 8) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(57.9766\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 64.1 |
$q$-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 | ||||||||
\(3\) | 7983.67 | 0.0780602 | 0.0390301 | − | 0.999238i | \(-0.487573\pi\) | ||||
0.0390301 | + | 0.999238i | \(0.487573\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.09730e7 | −1.41840 | −0.709199 | − | 0.705008i | \(-0.750943\pi\) | ||||
−0.709199 | + | 0.705008i | \(0.750943\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.17385e7 | 0.122750 | 0.0613751 | − | 0.998115i | \(-0.480451\pi\) | ||||
0.0613751 | + | 0.998115i | \(0.480451\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.03966e10 | −0.993907 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.72158e10 | −1.01385 | −0.506923 | − | 0.861991i | \(-0.669217\pi\) | ||||
−0.506923 | + | 0.861991i | \(0.669217\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.36850e11 | 0.476505 | 0.238253 | − | 0.971203i | \(-0.423425\pi\) | ||||
0.238253 | + | 0.971203i | \(0.423425\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.47278e11 | −0.110720 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.42283e12 | 0.893009 | 0.446505 | − | 0.894781i | \(-0.352669\pi\) | ||||
0.446505 | + | 0.894781i | \(0.352669\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.68680e9 | −0.000175373 0 | −8.76867e−5 | − | 1.00000i | \(-0.500028\pi\) | ||||
−8.76867e−5 | 1.00000i | \(0.500028\pi\) | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.32410e11 | 0.00958190 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.33703e14 | 1.67965 | 0.839823 | − | 0.542860i | \(-0.182659\pi\) | ||||
0.839823 | + | 0.542860i | \(0.182659\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.82489e14 | 1.01185 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.66515e14 | −0.155645 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.23982e15 | −1.43002 | −0.715010 | − | 0.699114i | \(-0.753578\pi\) | ||||
−0.715010 | + | 0.699114i | \(0.753578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.40473e15 | 1.40347 | 0.701735 | − | 0.712438i | \(-0.252409\pi\) | ||||
0.701735 | + | 0.712438i | \(0.252409\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.96303e14 | −0.0791410 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.84142e15 | −0.174109 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.61009e16 | 0.550467 | 0.275234 | − | 0.961377i | \(-0.411245\pi\) | ||||
0.275234 | + | 0.961377i | \(0.411245\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.89093e15 | 0.0371961 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.77168e16 | −0.671540 | −0.335770 | − | 0.941944i | \(-0.608997\pi\) | ||||
−0.335770 | + | 0.941944i | \(0.608997\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.01468e17 | 1.42163 | 0.710817 | − | 0.703377i | \(-0.248325\pi\) | ||||
0.710817 | + | 0.703377i | \(0.248325\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.22014e17 | 1.40976 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.62056e17 | 1.83598 | 0.917989 | − | 0.396607i | \(-0.129812\pi\) | ||||
0.917989 | + | 0.396607i | \(0.129812\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.50130e17 | −0.984932 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.92615e16 | 0.0697085 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.62651e17 | −0.363376 | −0.181688 | − | 0.983356i | \(-0.558156\pi\) | ||||
−0.181688 | + | 0.983356i | \(0.558156\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.70133e18 | 1.43804 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.74179e13 | −1.36897e−5 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.39502e18 | −1.88362 | −0.941809 | − | 0.336148i | \(-0.890876\pi\) | ||||
−0.941809 | + | 0.336148i | \(0.890876\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.50188e18 | 0.987524 | 0.493762 | − | 0.869597i | \(-0.335621\pi\) | ||||
0.493762 | + | 0.869597i | \(0.335621\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.53770e17 | −0.122002 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.33594e18 | −0.675874 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.03520e18 | −0.404489 | −0.202244 | − | 0.979335i | \(-0.564824\pi\) | ||||
−0.202244 | + | 0.979335i | \(0.564824\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.66418e18 | 0.131113 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.43147e19 | −1.61561 | −0.807803 | − | 0.589453i | \(-0.799343\pi\) | ||||
−0.807803 | + | 0.589453i | \(0.799343\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.48622e19 | −0.677095 | −0.338548 | − | 0.940949i | \(-0.609936\pi\) | ||||
−0.338548 | + | 0.940949i | \(0.609936\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.85204e18 | 0.0789855 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.00105e18 | −0.124450 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.70948e19 | 0.678441 | 0.339220 | − | 0.940707i | \(-0.389837\pi\) | ||||
0.339220 | + | 0.940707i | \(0.389837\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.07423e20 | 0.981757 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.31820e20 | 0.932528 | 0.466264 | − | 0.884646i | \(-0.345600\pi\) | ||||
0.466264 | + | 0.884646i | \(0.345600\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.29907e20 | −1.26664 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.58657e19 | −0.111628 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.97023e20 | 1.34965 | 0.674823 | − | 0.737979i | \(-0.264220\pi\) | ||||
0.674823 | + | 0.737979i | \(0.264220\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.17282e19 | 0.0584911 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.11333e19 | 0.109555 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.45164e17 | 0.000248749 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.80402e20 | −1.34990 | −0.674949 | − | 0.737864i | \(-0.735835\pi\) | ||||
−0.674949 | + | 0.737864i | \(0.735835\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.06749e20 | 1.00767 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.46191e19 | −0.0582085 | −0.0291042 | − | 0.999576i | \(-0.509265\pi\) | ||||
−0.0291042 | + | 0.999576i | \(0.509265\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.39481e19 | −0.0542171 | −0.0271085 | − | 0.999632i | \(-0.508630\pi\) | ||||
−0.0271085 | + | 0.999632i | \(0.508630\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.26849e19 | −0.0135910 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.69439e20 | −0.378133 | −0.189066 | − | 0.981964i | \(-0.560546\pi\) | ||||
−0.189066 | + | 0.981964i | \(0.560546\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.27500e21 | 1.32505 | 0.662526 | − | 0.749039i | \(-0.269484\pi\) | ||||
0.662526 | + | 0.749039i | \(0.269484\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.28544e20 | 0.0429696 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.53293e20 | −0.0701938 | −0.0350969 | − | 0.999384i | \(-0.511174\pi\) | ||||
−0.0350969 | + | 0.999384i | \(0.511174\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.03358e22 | −2.38241 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.46243e21 | −0.473602 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.80959e20 | 0.109617 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.06345e20 | 0.0278836 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.60792e20 | −0.0524206 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.75063e20 | −0.0168128 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.02098e21 | −0.245589 | −0.122795 | − | 0.992432i | \(-0.539186\pi\) | ||||
−0.122795 | + | 0.992432i | \(0.539186\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.60846e21 | 0.110973 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.70668e22 | 1.00185 | 0.500925 | − | 0.865491i | \(-0.332993\pi\) | ||||
0.500925 | + | 0.865491i | \(0.332993\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.29960e17 | −2.15271e−5 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.15748e21 | 0.220766 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.34811e22 | −0.861296 | −0.430648 | − | 0.902520i | \(-0.641715\pi\) | ||||
−0.430648 | + | 0.902520i | \(0.641715\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.53132e22 | 1.42748 | 0.713738 | − | 0.700413i | \(-0.247001\pi\) | ||||
0.713738 | + | 0.700413i | \(0.247001\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.28564e21 | 0.143317 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.06570e22 | −0.483103 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00347e23 | 2.02834 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.39206e21 | −0.0768840 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.98352e22 | −1.06076 | −0.530381 | − | 0.847759i | \(-0.677951\pi\) | ||||
−0.530381 | + | 0.847759i | \(0.677951\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.73560e22 | −0.625341 | −0.312671 | − | 0.949862i | \(-0.601224\pi\) | ||||
−0.312671 | + | 0.949862i | \(0.601224\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.71723e22 | −0.887568 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.98374e23 | −1.99068 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.22945e21 | 0.0195547 | 0.00977733 | − | 0.999952i | \(-0.496888\pi\) | ||||
0.00977733 | + | 0.999952i | \(0.496888\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.69365e21 | −0.0283652 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.06134e22 | 0.206177 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.48202e23 | −0.876768 | −0.438384 | − | 0.898788i | \(-0.644449\pi\) | ||||
−0.438384 | + | 0.898788i | \(0.644449\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.15666e22 | 0.112253 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.25766e23 | −1.03547 | −0.517733 | − | 0.855542i | \(-0.673224\pi\) | ||||
−0.517733 | + | 0.855542i | \(0.673224\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.90967e23 | −0.772943 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.87269e19 | 0.000174305 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.37523e23 | 1.70182 | 0.850909 | − | 0.525313i | \(-0.176052\pi\) | ||||
0.850909 | + | 0.525313i | \(0.176052\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.42628e22 | 0.124205 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.90394e22 | −0.147036 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.13222e23 | −0.250597 | −0.125299 | − | 0.992119i | \(-0.539989\pi\) | ||||
−0.125299 | + | 0.992119i | \(0.539989\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.55968e23 | −0.504151 | −0.252075 | − | 0.967708i | \(-0.581113\pi\) | ||||
−0.252075 | + | 0.967708i | \(0.581113\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.39252e22 | 0.0770863 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.98692e23 | −0.780781 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.47388e23 | −0.905374 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.52759e22 | −0.0191054 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.48387e23 | −0.838062 | −0.419031 | − | 0.907972i | \(-0.637630\pi\) | ||||
−0.419031 | + | 0.907972i | \(0.637630\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.77062e24 | 1.77735 | 0.888674 | − | 0.458539i | \(-0.151627\pi\) | ||||
0.888674 | + | 0.458539i | \(0.151627\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.85678e22 | −0.0527589 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.04387e24 | −1.65409 | −0.827044 | − | 0.562137i | \(-0.809979\pi\) | ||||
−0.827044 | + | 0.562137i | \(0.809979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.13486e22 | −0.0592097 | −0.0296048 | − | 0.999562i | \(-0.509425\pi\) | ||||
−0.0296048 | + | 0.999562i | \(0.509425\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.81831e22 | −0.0315745 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.97216e23 | −0.175535 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.78766e24 | 0.952511 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.46938e24 | −1.66941 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.08763e20 | 0.000177802 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.52722e24 | −1.38825 | −0.694123 | − | 0.719856i | \(-0.744208\pi\) | ||||
−0.694123 | + | 0.719856i | \(0.744208\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.53794e23 | −0.126114 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.24008e24 | −2.01644 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.87560e23 | 0.172276 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.98492e23 | −0.0528542 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.75809e24 | 0.425523 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.37573e24 | −0.523114 | −0.261557 | − | 0.965188i | \(-0.584236\pi\) | ||||
−0.261557 | + | 0.965188i | \(0.584236\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.01625e24 | −1.00569 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.71337e24 | −1.22650 | −0.613252 | − | 0.789887i | \(-0.710139\pi\) | ||||
−0.613252 | + | 0.789887i | \(0.710139\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.10829e24 | −0.517903 | −0.258952 | − | 0.965890i | \(-0.583377\pi\) | ||||
−0.258952 | + | 0.965890i | \(0.583377\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.38777e22 | −0.00971457 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.90742e24 | −0.542817 | −0.271408 | − | 0.962464i | \(-0.587489\pi\) | ||||
−0.271408 | + | 0.962464i | \(0.587489\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.05059e25 | −2.60415 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.55826e23 | 0.0529592 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.38784e23 | 0.0253997 | 0.0126998 | − | 0.999919i | \(-0.495957\pi\) | ||||
0.0126998 | + | 0.999919i | \(0.495957\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.14005e25 | 1.11107 | 0.555537 | − | 0.831492i | \(-0.312513\pi\) | ||||
0.555537 | + | 0.831492i | \(0.312513\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.59944e24 | 0.232281 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.70392e25 | 1.39703 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.11007e21 | −8.35663e−5 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.05241e24 | 0.0727934 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.80122e24 | 0.368931 | 0.184466 | − | 0.982839i | \(-0.440945\pi\) | ||||
0.184466 | + | 0.982839i | \(0.440945\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.91042e25 | −1.70290 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.83551e24 | −0.0988744 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.21415e25 | −1.09878 | −0.549388 | − | 0.835567i | \(-0.685139\pi\) | ||||
−0.549388 | + | 0.835567i | \(0.685139\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.47707e24 | 0.0675699 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.36832e25 | 1.42131 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.74763e25 | −1.45956 | −0.729779 | − | 0.683683i | \(-0.760377\pi\) | ||||
−0.729779 | + | 0.683683i | \(0.760377\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.43297e25 | 0.515412 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.16970e24 | 0.105354 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.64824e25 | −0.506549 | −0.253274 | − | 0.967394i | \(-0.581508\pi\) | ||||
−0.253274 | + | 0.967394i | \(0.581508\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.86168e25 | −0.813660 | −0.406830 | − | 0.913504i | \(-0.633366\pi\) | ||||
−0.406830 | + | 0.913504i | \(0.633366\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.73471e23 | 0.00456583 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.20807e25 | −1.02586 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.26085e25 | −1.18855 | −0.594277 | − | 0.804261i | \(-0.702562\pi\) | ||||
−0.594277 | + | 0.804261i | \(0.702562\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.65875e25 | −1.39492 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.45378e25 | 1.25429 | 0.627145 | − | 0.778903i | \(-0.284223\pi\) | ||||
0.627145 | + | 0.778903i | \(0.284223\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.56042e25 | −0.822711 | −0.411355 | − | 0.911475i | \(-0.634944\pi\) | ||||
−0.411355 | + | 0.911475i | \(0.634944\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.15894e21 | 1.94174e−5 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.29485e24 | −0.0824317 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.39935e25 | −0.202535 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.82721e24 | −0.105373 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.87863e25 | 0.736489 | 0.368244 | − | 0.929729i | \(-0.379959\pi\) | ||||
0.368244 | + | 0.929729i | \(0.379959\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.29046e26 | 2.67172 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.45228e25 | 0.157800 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.90374e25 | 0.800360 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.84824e25 | 0.174506 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.15898e23 | −0.00454377 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.70410e26 | −1.40070 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.65443e26 | 1.26969 | 0.634843 | − | 0.772641i | \(-0.281065\pi\) | ||||
0.634843 | + | 0.772641i | \(0.281065\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.90377e23 | −0.00423220 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.32700e24 | −0.0490842 | −0.0245421 | − | 0.999699i | \(-0.507813\pi\) | ||||
−0.0245421 | + | 0.999699i | \(0.507813\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.64901e25 | −0.479059 | −0.239530 | − | 0.970889i | \(-0.576993\pi\) | ||||
−0.239530 | + | 0.970889i | \(0.576993\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.95411e25 | 0.173048 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.82997e25 | 0.538803 | 0.269402 | − | 0.963028i | \(-0.413174\pi\) | ||||
0.269402 | + | 0.963028i | \(0.413174\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.82564e26 | 1.44982 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.14295e24 | −0.0295171 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.47893e22 | −0.000156610 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.14277e26 | 0.482153 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.61465e25 | 0.103434 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.07360e25 | 0.225367 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.46189e26 | 0.857187 | 0.428593 | − | 0.903498i | \(-0.359009\pi\) | ||||
0.428593 | + | 0.903498i | \(0.359009\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.67395e26 | −0.547113 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.86928e26 | 0.573726 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.89205e26 | 1.41051 | 0.705257 | − | 0.708952i | \(-0.250832\pi\) | ||||
0.705257 | + | 0.708952i | \(0.250832\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.02221e24 | −0.00547934 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.58594e26 | −1.42290 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.01708e26 | −0.243651 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.25175e25 | −0.185971 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.00972e26 | −0.214161 | −0.107080 | − | 0.994250i | \(-0.534150\pi\) | ||||
−0.107080 | + | 0.994250i | \(0.534150\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.95706e25 | 0.0989822 | 0.0494911 | − | 0.998775i | \(-0.484240\pi\) | ||||
0.0494911 | + | 0.998775i | \(0.484240\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.94391e25 | −0.0741655 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.88459e26 | 0.333873 | 0.166937 | − | 0.985968i | \(-0.446613\pi\) | ||||
0.166937 | + | 0.985968i | \(0.446613\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.37256e27 | 2.29157 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.43656e24 | 0.00855673 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.21557e26 | 0.774123 | 0.387062 | − | 0.922054i | \(-0.373490\pi\) | ||||
0.387062 | + | 0.922054i | \(0.373490\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.14209e26 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.64740e24 | 0.00217660 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.70057e26 | 0.960390 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.38478e25 | −0.0516362 | −0.0258181 | − | 0.999667i | \(-0.508219\pi\) | ||||
−0.0258181 | + | 0.999667i | \(0.508219\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00060e26 | 0.667448 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.24429e25 | −0.0446045 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.92501e25 | −0.0191201 | −0.00956004 | − | 0.999954i | \(-0.503043\pi\) | ||||
−0.00956004 | + | 0.999954i | \(0.503043\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.39765e24 | −0.00131241 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.67351e26 | −0.681412 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.04774e27 | 1.72014 | 0.860070 | − | 0.510175i | \(-0.170419\pi\) | ||||
0.860070 | + | 0.510175i | \(0.170419\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.41186e25 | −0.0191707 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.75914e27 | 1.32347 | 0.661733 | − | 0.749740i | \(-0.269821\pi\) | ||||
0.661733 | + | 0.749740i | \(0.269821\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.47816e26 | 0.176519 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.09459e27 | −1.41297 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.73236e26 | 0.174609 | 0.0873046 | − | 0.996182i | \(-0.472175\pi\) | ||||
0.0873046 | + | 0.996182i | \(0.472175\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.47702e27 | 1.49994 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.36256e26 | 0.0782046 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.76840e27 | −0.962299 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.21691e27 | 0.627998 | 0.313999 | − | 0.949423i | \(-0.398331\pi\) | ||||
0.313999 | + | 0.949423i | \(0.398331\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.43266e21 | −1.68041e−6 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.15061e27 | −0.534455 | −0.267228 | − | 0.963633i | \(-0.586108\pi\) | ||||
−0.267228 | + | 0.963633i | \(0.586108\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.51696e27 | 0.668761 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.32721e27 | −1.39252 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.40425e27 | −0.558089 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.54628e26 | −0.0583705 | −0.0291852 | − | 0.999574i | \(-0.509291\pi\) | ||||
−0.0291852 | + | 0.999574i | \(0.509291\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.87465e26 | −0.0672330 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.78408e26 | −0.231215 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.08287e27 | −1.32270 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.61766e26 | 0.111429 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.10695e27 | −1.20302 | −0.601510 | − | 0.798866i | \(-0.705434\pi\) | ||||
−0.601510 | + | 0.798866i | \(0.705434\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.80891e27 | 1.33994 | 0.669969 | − | 0.742389i | \(-0.266307\pi\) | ||||
0.669969 | + | 0.742389i | \(0.266307\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.88314e27 | −1.82479 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.58144e27 | 0.903594 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.04734e26 | 0.121219 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.64919e26 | −0.0377111 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.51446e27 | −0.983092 | −0.491546 | − | 0.870852i | \(-0.663568\pi\) | ||||
−0.491546 | + | 0.870852i | \(0.663568\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.04253e27 | −0.838552 | −0.419276 | − | 0.907859i | \(-0.637716\pi\) | ||||
−0.419276 | + | 0.907859i | \(0.637716\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.01138e26 | 0.158332 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.56400e24 | −0.000294565 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.73290e26 | 0.0670145 | 0.0335072 | − | 0.999438i | \(-0.489332\pi\) | ||||
0.0335072 | + | 0.999438i | \(0.489332\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.71949e27 | 0.978931 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.67248e27 | −1.41548 | −0.707741 | − | 0.706472i | \(-0.750286\pi\) | ||||
−0.707741 | + | 0.706472i | \(0.750286\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.22970e28 | −1.91434 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.57541e26 | −0.0828034 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.22534e27 | −0.598790 | −0.299395 | − | 0.954129i | \(-0.596785\pi\) | ||||
−0.299395 | + | 0.954129i | \(0.596785\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.03382e27 | 0.680838 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.78075e26 | −0.0488143 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.72988e26 | −0.0829637 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.06069e27 | 0.948969 | 0.474484 | − | 0.880264i | \(-0.342635\pi\) | ||||
0.474484 | + | 0.880264i | \(0.342635\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.23601e27 | −0.138992 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.88705e27 | 1.06220 | 0.531101 | − | 0.847309i | \(-0.321779\pi\) | ||||
0.531101 | + | 0.847309i | \(0.321779\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.00097e28 | 1.02759 | 0.513794 | − | 0.857913i | \(-0.328239\pi\) | ||||
0.513794 | + | 0.857913i | \(0.328239\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.58375e27 | −0.155393 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.60212e28 | −1.50268 | −0.751342 | − | 0.659913i | \(-0.770593\pi\) | ||||
−0.751342 | + | 0.659913i | \(0.770593\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.53660e26 | −0.0496511 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.77992e25 | 0.00152644 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.75712e28 | −1.44132 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.26133e24 | −0.000177452 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.81000e27 | 0.361162 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.14679e27 | −0.657273 | −0.328636 | − | 0.944457i | \(-0.606589\pi\) | ||||
−0.328636 | + | 0.944457i | \(0.606589\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.81349e27 | 0.262300 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.44407e26 | 0.0160942 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.03660e28 | 1.91469 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.63338e28 | −0.986357 | −0.493179 | − | 0.869928i | \(-0.664165\pi\) | ||||
−0.493179 | + | 0.869928i | \(0.664165\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.18320e27 | −0.0684407 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.10020e28 | −0.609702 | −0.304851 | − | 0.952400i | \(-0.598607\pi\) | ||||
−0.304851 | + | 0.952400i | \(0.598607\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.40487e28 | −1.27702 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.80847e28 | −1.42927 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.06537e27 | −0.198316 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.04342e28 | −0.955657 | −0.477829 | − | 0.878453i | \(-0.658576\pi\) | ||||
−0.477829 | + | 0.878453i | \(0.658576\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.80244e27 | −0.0808288 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.67038e28 | 0.718375 | 0.359188 | − | 0.933265i | \(-0.383054\pi\) | ||||
0.359188 | + | 0.933265i | \(0.383054\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.00145e27 | 0.0825628 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.52462e27 | −0.0603361 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.42146e27 | 0.205864 | 0.102932 | − | 0.994688i | \(-0.467178\pi\) | ||||
0.102932 | + | 0.994688i | \(0.467178\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.28082e27 | −0.0831136 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.80424e23 | 2.72960e−5 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.29039e27 | 0.0769014 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.77418e28 | −1.86140 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.29141e27 | 0.132844 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.37414e28 | 0.408541 | 0.204271 | − | 0.978914i | \(-0.434518\pi\) | ||||
0.204271 | + | 0.978914i | \(0.434518\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.33678e28 | 0.952927 | 0.476463 | − | 0.879194i | \(-0.341919\pi\) | ||||
0.476463 | + | 0.879194i | \(0.341919\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.53380e26 | 0.00969548 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.75412e28 | 1.25331 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.18860e28 | 1.82121 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.68831e28 | 1.87214 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.36702e28 | −0.319992 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.38318e28 | 0.536343 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.03932e26 | −0.0195617 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.79800e28 | 0.998570 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.34113e28 | 1.86994 | 0.934971 | − | 0.354723i | \(-0.115425\pi\) | ||||
0.934971 | + | 0.354723i | \(0.115425\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.04356e27 | −0.0393541 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.01437e29 | −1.87945 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.90655e28 | −0.339923 | −0.169961 | − | 0.985451i | \(-0.554364\pi\) | ||||
−0.169961 | + | 0.985451i | \(0.554364\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.72009e28 | −0.981507 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.51844e25 | 0.000250788 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.23779e27 | 0.0832787 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.98140e27 | −0.0609480 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.85895e28 | 0.716247 | 0.358124 | − | 0.933674i | \(-0.383417\pi\) | ||||
0.358124 | + | 0.933674i | \(0.383417\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.77177e28 | 0.677416 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.16854e27 | −0.0706736 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.82251e28 | 0.635236 | 0.317618 | − | 0.948219i | \(-0.397117\pi\) | ||||
0.317618 | + | 0.948219i | \(0.397117\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.84523e27 | 0.0995628 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.85481e27 | 0.120511 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.25601e28 | −0.972952 | −0.486476 | − | 0.873694i | \(-0.661718\pi\) | ||||
−0.486476 | + | 0.873694i | \(0.661718\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.00348e28 | 0.341150 | 0.170575 | − | 0.985345i | \(-0.445437\pi\) | ||||
0.170575 | + | 0.985345i | \(0.445437\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.97488e27 | −0.0654193 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.61008e29 | 1.69956 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.52665e28 | 0.766047 | 0.383024 | − | 0.923739i | \(-0.374883\pi\) | ||||
0.383024 | + | 0.923739i | \(0.374883\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.41360e28 | 0.138740 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.20930e28 | 0.114468 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.03504e28 | 0.368408 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.62690e28 | 0.671756 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.52918e29 | −1.29945 | −0.649723 | − | 0.760171i | \(-0.725115\pi\) | ||||
−0.649723 | + | 0.760171i | \(0.725115\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.00177e25 | −0.000246131 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.63176e28 | −0.129118 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.89818e28 | 0.297706 | 0.148853 | − | 0.988859i | \(-0.452442\pi\) | ||||
0.148853 | + | 0.988859i | \(0.452442\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.10913e28 | −0.155481 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.49461e26 | −0.00462192 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.28684e29 | 0.884186 | 0.442093 | − | 0.896969i | \(-0.354236\pi\) | ||||
0.442093 | + | 0.896969i | \(0.354236\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.81454e29 | −1.20388 | −0.601942 | − | 0.798540i | \(-0.705606\pi\) | ||||
−0.601942 | + | 0.798540i | \(0.705606\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.27457e28 | 0.402024 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.39114e27 | −0.0395500 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.81972e29 | −1.68549 | −0.842743 | − | 0.538316i | \(-0.819061\pi\) | ||||
−0.842743 | + | 0.538316i | \(0.819061\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.37288e27 | −0.0137023 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.56808e29 | 0.874853 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.09843e28 | −0.436582 | −0.218291 | − | 0.975884i | \(-0.570048\pi\) | ||||
−0.218291 | + | 0.975884i | \(0.570048\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.42721e28 | 0.0743532 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.47454e29 | 1.74946 | 0.874728 | − | 0.484614i | \(-0.161040\pi\) | ||||
0.874728 | + | 0.484614i | \(0.161040\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.90076e29 | 1.41176 | 0.705878 | − | 0.708333i | \(-0.250553\pi\) | ||||
0.705878 | + | 0.708333i | \(0.250553\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.55666e28 | −0.261428 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.64223e28 | 0.165669 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.24647e29 | −0.988006 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.26343e24 | 1.38792e−5 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.19514e29 | 0.491572 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.23594e29 | −1.68516 | −0.842581 | − | 0.538570i | \(-0.818965\pi\) | ||||
−0.842581 | + | 0.538570i | \(0.818965\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.81602e28 | −0.108367 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.35689e28 | 0.348343 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.30298e29 | −0.469325 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.60723e29 | 1.60576 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.43690e29 | −1.15920 | −0.579598 | − | 0.814902i | \(-0.696791\pi\) | ||||
−0.579598 | + | 0.814902i | \(0.696791\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.89646e29 | −0.619055 | −0.309527 | − | 0.950891i | \(-0.600171\pi\) | ||||
−0.309527 | + | 0.950891i | \(0.600171\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.98187e28 | −0.157404 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.06810e29 | 0.938370 | 0.469185 | − | 0.883100i | \(-0.344548\pi\) | ||||
0.469185 | + | 0.883100i | \(0.344548\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.44962e29 | 1.90970 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.69089e27 | 0.0134479 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.17693e29 | −0.326710 | −0.163355 | − | 0.986567i | \(-0.552232\pi\) | ||||
−0.163355 | + | 0.986567i | \(0.552232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.28609e29 | −1.42102 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.58483e29 | 0.672969 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.42901e29 | −0.864712 | −0.432356 | − | 0.901703i | \(-0.642318\pi\) | ||||
−0.432356 | + | 0.901703i | \(0.642318\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.95818e29 | 0.966897 | 0.483448 | − | 0.875373i | \(-0.339384\pi\) | ||||
0.483448 | + | 0.875373i | \(0.339384\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.40361e28 | 0.0332164 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.33172e25 | 3.05340e−5 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.08114e30 | −2.40193 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.89671e28 | −0.0408343 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.79851e29 | −1.00120 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.58339e29 | −1.93803 | −0.969017 | − | 0.246996i | \(-0.920557\pi\) | ||||
−0.969017 | + | 0.246996i | \(0.920557\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.03418e28 | −0.157490 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.12797e29 | −0.974461 | −0.487230 | − | 0.873273i | \(-0.661993\pi\) | ||||
−0.487230 | + | 0.873273i | \(0.661993\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.99406e28 | −0.165700 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.35973e28 | −0.0957411 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.75298e29 | −0.996495 | −0.498248 | − | 0.867035i | \(-0.666023\pi\) | ||||
−0.498248 | + | 0.867035i | \(0.666023\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.27280e29 | 1.22166 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.48156e28 | −0.0404276 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.09579e29 | −0.173151 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.46471e29 | −0.377787 | −0.188893 | − | 0.981998i | \(-0.560490\pi\) | ||||
−0.188893 | + | 0.981998i | \(0.560490\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.31838e28 | 0.123691 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.40348e30 | −2.02473 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.28422e29 | −0.599691 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.11956e28 | −0.0423724 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.94607e29 | 1.17922 | 0.589608 | − | 0.807690i | \(-0.299282\pi\) | ||||
0.589608 | + | 0.807690i | \(0.299282\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.54616e25 | −9.65373e−5 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.63712e29 | −0.203280 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.92806e27 | −0.00714510 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.52975e29 | −0.881039 | −0.440520 | − | 0.897743i | \(-0.645206\pi\) | ||||
−0.440520 | + | 0.897743i | \(0.645206\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.93592e29 | −0.674307 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.13728e30 | 2.35733 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.39810e29 | 0.685232 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.90638e27 | 0.00198270 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.85535e29 | 0.490419 | 0.245210 | − | 0.969470i | \(-0.421143\pi\) | ||||
0.245210 | + | 0.969470i | \(0.421143\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.78389e27 | −0.00665516 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.10175e28 | 0.0867307 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.56318e30 | −1.44697 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.86351e30 | 1.67579 | 0.837895 | − | 0.545831i | \(-0.183786\pi\) | ||||
0.837895 | + | 0.545831i | \(0.183786\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.10293e30 | −0.963625 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.49546e30 | 1.26953 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.73906e29 | 0.308440 | 0.154220 | − | 0.988037i | \(-0.450714\pi\) | ||||
0.154220 | + | 0.988037i | \(0.450714\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.36035e29 | 0.109052 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.26365e29 | 0.410089 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.38257e29 | −0.634762 | −0.317381 | − | 0.948298i | \(-0.602803\pi\) | ||||
−0.317381 | + | 0.948298i | \(0.602803\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.86242e24 | −6.52321e−6 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.60139e29 | −0.543889 | −0.271945 | − | 0.962313i | \(-0.587667\pi\) | ||||
−0.271945 | + | 0.962313i | \(0.587667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.16300e30 | 1.50458 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.37048e30 | −0.926846 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.05871e28 | −0.0464159 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.08974e30 | −0.696794 | −0.348397 | − | 0.937347i | \(-0.613274\pi\) | ||||
−0.348397 | + | 0.937347i | \(0.613274\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.63151e28 | 0.0287988 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.46676e30 | 0.886983 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.06224e30 | −1.80108 | −0.900540 | − | 0.434774i | \(-0.856828\pi\) | ||||
−0.900540 | + | 0.434774i | \(0.856828\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.32358e29 | −0.132929 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.46912e30 | −1.93055 | −0.965274 | − | 0.261241i | \(-0.915868\pi\) | ||||
−0.965274 | + | 0.261241i | \(0.915868\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.00444e29 | 0.162650 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.39026e30 | 1.25892 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.75151e30 | −0.897554 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.20768e29 | −0.359392 | −0.179696 | − | 0.983722i | \(-0.557511\pi\) | ||||
−0.179696 | + | 0.983722i | \(0.557511\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.76770e29 | −0.0857707 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.63916e30 | 0.773990 | 0.386995 | − | 0.922082i | \(-0.373513\pi\) | ||||
0.386995 | + | 0.922082i | \(0.373513\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.09021e30 | 1.42011 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.17924e28 | 0.00527452 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.70507e26 | 0.000117770 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.86494e30 | 1.63798 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.39480e29 | 0.222575 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.90526e28 | −0.0277363 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.22284e30 | −0.478227 | −0.239114 | − | 0.970992i | \(-0.576857\pi\) | ||||
−0.239114 | + | 0.970992i | \(0.576857\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.99199e29 | −0.113933 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.32367e28 | −0.00861630 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.30312e30 | 0.470560 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.14403e29 | 0.0402332 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.32063e30 | −0.452345 | −0.226173 | − | 0.974087i | \(-0.572621\pi\) | ||||
−0.226173 | + | 0.974087i | \(0.572621\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.91433e30 | 1.63954 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.12769e30 | −1.34142 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.16838e30 | 0.686470 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.48189e29 | −0.292441 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.31590e29 | −0.0395413 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.54086e30 | 1.62225 | 0.811124 | − | 0.584874i | \(-0.198856\pi\) | ||||
0.811124 | + | 0.584874i | \(0.198856\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.51703e30 | 1.28865 | 0.644323 | − | 0.764753i | \(-0.277139\pi\) | ||||
0.644323 | + | 0.764753i | \(0.277139\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.28467e29 | −0.0635145 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.59026e30 | 1.24361 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.44242e26 | −0.000249317 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.25900e29 | −0.0581347 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.49500e30 | −1.62921 | −0.814603 | − | 0.580019i | \(-0.803045\pi\) | ||||
−0.814603 | + | 0.580019i | \(0.803045\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.58977e30 | 1.61128 | 0.805642 | − | 0.592402i | \(-0.201820\pi\) | ||||
0.805642 | + | 0.592402i | \(0.201820\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.35959e29 | −0.0800791 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.99217e29 | 0.0695309 | 0.0347655 | − | 0.999395i | \(-0.488932\pi\) | ||||
0.0347655 | + | 0.999395i | \(0.488932\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.02375e30 | 0.685053 | 0.342526 | − | 0.939508i | \(-0.388717\pi\) | ||||
0.342526 | + | 0.939508i | \(0.388717\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.20009e29 | −0.0927787 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.08352e30 | −0.879554 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.99266e30 | 1.46870 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.06649e30 | −0.218443 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.48734e30 | −1.29588 | −0.647942 | − | 0.761690i | \(-0.724370\pi\) | ||||
−0.647942 | + | 0.761690i | \(0.724370\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.36360e30 | 1.04496 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.15249e29 | 0.0979101 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.91481e30 | 1.09634 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.89298e28 | 0.00342272 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.64089e29 | −0.0642210 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.37291e30 | 0.924590 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.83172e30 | −0.307535 | −0.153767 | − | 0.988107i | \(-0.549141\pi\) | ||||
−0.153767 | + | 0.988107i | \(0.549141\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.50922e27 | −0.000247234 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.04074e31 | 1.66358 | 0.831792 | − | 0.555088i | \(-0.187315\pi\) | ||||
0.831792 | + | 0.555088i | \(0.187315\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.40237e29 | 0.131061 | 0.0655306 | − | 0.997851i | \(-0.479126\pi\) | ||||
0.0655306 | + | 0.997851i | \(0.479126\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.22724e28 | −0.00643463 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.66021e30 | −0.989406 | −0.494703 | − | 0.869062i | \(-0.664723\pi\) | ||||
−0.494703 | + | 0.869062i | \(0.664723\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.66487e31 | −2.41386 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.11720e29 | −0.0158099 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.97957e30 | −0.687835 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.42944e30 | −0.192741 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.01929e31 | 1.34167 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.60600e28 | −0.00206377 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.99416e30 | 0.250187 | 0.125093 | − | 0.992145i | \(-0.460077\pi\) | ||||
0.125093 | + | 0.992145i | \(0.460077\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.69331e29 | 0.0574905 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.25457e30 | −0.867690 | −0.433845 | − | 0.900987i | \(-0.642843\pi\) | ||||
−0.433845 | + | 0.900987i | \(0.642843\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.43622e30 | −0.868491 | −0.434245 | − | 0.900795i | \(-0.642985\pi\) | ||||
−0.434245 | + | 0.900795i | \(0.642985\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.82863e30 | 0.208555 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.32005e30 | 0.592540 | 0.296270 | − | 0.955104i | \(-0.404257\pi\) | ||||
0.296270 | + | 0.955104i | \(0.404257\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.77140e29 | −0.0301461 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.36897e30 | −0.995350 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.10293e27 | −0.000321982 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.50684e30 | 0.355446 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.31009e29 | 0.0624762 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.07502e31 | −2.00699 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.43418e30 | −0.324498 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.47557e29 | 0.0136220 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.92809e30 | 0.715086 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.82478e30 | 0.337077 | 0.168539 | − | 0.985695i | \(-0.446095\pi\) | ||||
0.168539 | + | 0.985695i | \(0.446095\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.71820e29 | 0.0578538 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.98935e30 | −0.335706 | −0.167853 | − | 0.985812i | \(-0.553683\pi\) | ||||
−0.167853 | + | 0.985812i | \(0.553683\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.14968e31 | −0.945440 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.36050e30 | −0.109339 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.56568e30 | 0.122977 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.24335e31 | −1.72220 | −0.861102 | − | 0.508432i | \(-0.830225\pi\) | ||||
−0.861102 | + | 0.508432i | \(0.830225\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.32085e30 | 0.0991119 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.04959e31 | −0.769844 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.76850e30 | 0.556992 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.68810e29 | 0.0538867 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.26649e30 | −0.360875 | −0.180437 | − | 0.983586i | \(-0.557751\pi\) | ||||
−0.180437 | + | 0.983586i | \(0.557751\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.57835e27 | 0.000172731 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.84963e28 | −0.00383152 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.00515e31 | 1.28418 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.29722e30 | −0.206482 | −0.103241 | − | 0.994656i | \(-0.532921\pi\) | ||||
−0.103241 | + | 0.994656i | \(0.532921\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.10672e29 | −0.0373955 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.14709e31 | 1.28576 | 0.642879 | − | 0.765968i | \(-0.277740\pi\) | ||||
0.642879 | + | 0.765968i | \(0.277740\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.92603e31 | −1.12795 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.73139e29 | 0.0270991 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.56465e31 | 0.876483 | 0.438242 | − | 0.898857i | \(-0.355601\pi\) | ||||
0.438242 | + | 0.898857i | \(0.355601\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.88861e30 | −0.322639 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.84793e29 | 0.0420591 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.71750e30 | −0.247307 | −0.123654 | − | 0.992325i | \(-0.539461\pi\) | ||||
−0.123654 | + | 0.992325i | \(0.539461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.31798e31 | 1.18871 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.25590e30 | 0.113173 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.15412e30 | −0.105724 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.01951e31 | 0.969728 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.99956e30 | 0.375829 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.48413e31 | −2.52099 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.43670e31 | −1.54584 | −0.772919 | − | 0.634505i | \(-0.781204\pi\) | ||||
−0.772919 | + | 0.634505i | \(0.781204\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.77747e26 | −1.22250e−5 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.39842e31 | −1.89450 | −0.947249 | − | 0.320497i | \(-0.896150\pi\) | ||||
−0.947249 | + | 0.320497i | \(0.896150\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.15696e30 | 0.175223 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.12354e29 | 0.0376370 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.85934e31 | −0.750700 | −0.375350 | − | 0.926883i | \(-0.622477\pi\) | ||||
−0.375350 | + | 0.926883i | \(0.622477\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.46266e31 | −1.36833 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.40489e31 | −1.31698 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.18619e31 | −0.827704 | −0.413852 | − | 0.910344i | \(-0.635817\pi\) | ||||
−0.413852 | + | 0.910344i | \(0.635817\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.33049e31 | 2.34616 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.84897e29 | 0.0175922 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.72306e31 | 2.38784 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.68993e30 | −0.302164 | −0.151082 | − | 0.988521i | \(-0.548276\pi\) | ||||
−0.151082 | + | 0.988521i | \(0.548276\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.96550e30 | 0.0669122 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.51961e30 | 0.0839829 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.31572e31 | −0.429403 | −0.214701 | − | 0.976680i | \(-0.568878\pi\) | ||||
−0.214701 | + | 0.976680i | \(0.568878\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.68104e30 | −0.0856773 |
(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 | 64.22.a.l.1.2 | 3 | ||
4.3 | odd | 2 | 64.22.a.m.1.2 | 3 | |||
8.3 | odd | 2 | 16.22.a.f.1.2 | 3 | |||
8.5 | even | 2 | 8.22.a.b.1.2 | ✓ | 3 | ||
24.5 | odd | 2 | 72.22.a.f.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.22.a.b.1.2 | ✓ | 3 | 8.5 | even | 2 | ||
16.22.a.f.1.2 | 3 | 8.3 | odd | 2 | |||
64.22.a.l.1.2 | 3 | 1.1 | even | 1 | trivial | ||
64.22.a.m.1.2 | 3 | 4.3 | odd | 2 | |||
72.22.a.f.1.1 | 3 | 24.5 | odd | 2 |