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: | \(0\) |
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 | \(-0.512427\pi\) | ||||
−0.0390301 | + | 0.999238i | \(0.512427\pi\) | |||||||
\(4\) | 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 | \(-0.519549\pi\) | ||||
−0.0613751 | + | 0.998115i | \(0.519549\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.03966e10 | −0.993907 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.72158e10 | 1.01385 | 0.506923 | − | 0.861991i | \(-0.330783\pi\) | ||||
0.506923 | + | 0.861991i | \(0.330783\pi\) | |||||||
\(12\) | 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 | \(-0.499972\pi\) | ||||
8.76867e−5 | 1.00000i | \(0.499972\pi\) | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.32410e11 | 0.00958190 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.33703e14 | −1.67965 | −0.839823 | − | 0.542860i | \(-0.817341\pi\) | ||||
−0.839823 | + | 0.542860i | \(0.817341\pi\) | |||||||
\(24\) | 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 | \(-0.747591\pi\) | ||||
−0.701735 | + | 0.712438i | \(0.747591\pi\) | |||||||
\(32\) | 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 | \(-0.751675\pi\) | ||||
−0.710817 | + | 0.703377i | \(0.751675\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.22014e17 | 1.40976 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.62056e17 | −1.83598 | −0.917989 | − | 0.396607i | \(-0.870188\pi\) | ||||
−0.917989 | + | 0.396607i | \(0.870188\pi\) | |||||||
\(48\) | 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 | \(-0.109124\pi\) | ||||
0.941809 | + | 0.336148i | \(0.109124\pi\) | |||||||
\(60\) | 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 | \(-0.435176\pi\) | ||||
0.202244 | + | 0.979335i | \(0.435176\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.66418e18 | 0.131113 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.43147e19 | 1.61561 | 0.807803 | − | 0.589453i | \(-0.200657\pi\) | ||||
0.807803 | + | 0.589453i | \(0.200657\pi\) | |||||||
\(72\) | 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 | \(-0.610163\pi\) | ||||
−0.339220 | + | 0.940707i | \(0.610163\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.07423e20 | 0.981757 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.31820e20 | −0.932528 | −0.466264 | − | 0.884646i | \(-0.654400\pi\) | ||||
−0.466264 | + | 0.884646i | \(0.654400\pi\) | |||||||
\(84\) | 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 | \(-0.491370\pi\) | ||||
0.0271085 | + | 0.999632i | \(0.491370\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.26849e19 | −0.0135910 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.69439e20 | 0.378133 | 0.189066 | − | 0.981964i | \(-0.439454\pi\) | ||||
0.189066 | + | 0.981964i | \(0.439454\pi\) | |||||||
\(108\) | 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 | \(-0.460814\pi\) | ||||
0.122795 | + | 0.992432i | \(0.460814\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.60846e21 | 0.110973 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.70668e22 | −1.00185 | −0.500925 | − | 0.865491i | \(-0.667007\pi\) | ||||
−0.500925 | + | 0.865491i | \(0.667007\pi\) | |||||||
\(132\) | 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 | \(-0.752999\pi\) | ||||
−0.713738 | + | 0.700413i | \(0.752999\pi\) | |||||||
\(140\) | 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 | \(-0.398776\pi\) | ||||
0.312671 | + | 0.949862i | \(0.398776\pi\) | |||||||
\(152\) | 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 | \(-0.355551\pi\) | ||||
0.438384 | + | 0.898788i | \(0.355551\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.15666e22 | 0.112253 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.25766e23 | 1.03547 | 0.517733 | − | 0.855542i | \(-0.326776\pi\) | ||||
0.517733 | + | 0.855542i | \(0.326776\pi\) | |||||||
\(168\) | 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 | \(-0.460011\pi\) | ||||
0.125299 | + | 0.992119i | \(0.460011\pi\) | |||||||
\(180\) | 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 | \(-0.362370\pi\) | ||||
0.419031 | + | 0.907972i | \(0.362370\pi\) | |||||||
\(192\) | 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 | \(-0.490575\pi\) | ||||
0.0296048 | + | 0.999562i | \(0.490575\pi\) | |||||||
\(200\) | 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 | \(-0.255792\pi\) | ||||
0.694123 | + | 0.719856i | \(0.255792\pi\) | |||||||
\(212\) | 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 | \(-0.415764\pi\) | ||||
0.261557 | + | 0.965188i | \(0.415764\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.01625e24 | −1.00569 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.71337e24 | 1.22650 | 0.613252 | − | 0.789887i | \(-0.289861\pi\) | ||||
0.613252 | + | 0.789887i | \(0.289861\pi\) | |||||||
\(228\) | 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 | \(-0.504043\pi\) | ||||
−0.0126998 | + | 0.999919i | \(0.504043\pi\) | |||||||
\(240\) | 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 | \(-0.559055\pi\) | ||||
−0.184466 | + | 0.982839i | \(0.559055\pi\) | |||||||
\(252\) | 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 | \(-0.239623\pi\) | ||||
0.729779 | + | 0.683683i | \(0.239623\pi\) | |||||||
\(264\) | 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 | \(-0.366634\pi\) | ||||
0.406830 | + | 0.913504i | \(0.366634\pi\) | |||||||
\(272\) | 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 | \(-0.365056\pi\) | ||||
0.411355 | + | 0.911475i | \(0.365056\pi\) | |||||||
\(284\) | 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 | \(-0.718935\pi\) | ||||
−0.634843 | + | 0.772641i | \(0.718935\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.90377e23 | −0.00423220 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.32700e24 | 0.0490842 | 0.0245421 | − | 0.999699i | \(-0.492187\pi\) | ||||
0.0245421 | + | 0.999699i | \(0.492187\pi\) | |||||||
\(312\) | 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 | \(-0.640991\pi\) | ||||
−0.428593 | + | 0.903498i | \(0.640991\pi\) | |||||||
\(332\) | 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 | \(-0.465850\pi\) | ||||
0.107080 | + | 0.994250i | \(0.465850\pi\) | |||||||
\(348\) | 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 | \(-0.626510\pi\) | ||||
−0.387062 | + | 0.922054i | \(0.626510\pi\) | |||||||
\(360\) | 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 | \(-0.491781\pi\) | ||||
0.0258181 | + | 0.999667i | \(0.491781\pi\) | |||||||
\(368\) | 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 | \(-0.829581\pi\) | ||||
−0.860070 | + | 0.510175i | \(0.829581\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.41186e25 | −0.0191707 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.75914e27 | −1.32347 | −0.661733 | − | 0.749740i | \(-0.730179\pi\) | ||||
−0.661733 | + | 0.749740i | \(0.730179\pi\) | |||||||
\(384\) | 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 | \(-0.294566\pi\) | ||||
0.601510 | + | 0.798866i | \(0.294566\pi\) | |||||||
\(420\) | 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 | \(-0.336432\pi\) | ||||
0.491546 | + | 0.870852i | \(0.336432\pi\) | |||||||
\(432\) | 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 | \(-0.510668\pi\) | ||||
−0.0335072 | + | 0.999438i | \(0.510668\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.71949e27 | 0.978931 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.67248e27 | 1.41548 | 0.707741 | − | 0.706472i | \(-0.249714\pi\) | ||||
0.707741 | + | 0.706472i | \(0.249714\pi\) | |||||||
\(444\) | 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 | \(-0.671761\pi\) | ||||
−0.513794 | + | 0.857913i | \(0.671761\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.58375e27 | −0.155393 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.60212e28 | 1.50268 | 0.751342 | − | 0.659913i | \(-0.229407\pi\) | ||||
0.751342 | + | 0.659913i | \(0.229407\pi\) | |||||||
\(468\) | 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 | \(-0.393411\pi\) | ||||
0.328636 | + | 0.944457i | \(0.393411\pi\) | |||||||
\(480\) | 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 | \(-0.335835\pi\) | ||||
0.493179 | + | 0.869928i | \(0.335835\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.18320e27 | −0.0684407 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.10020e28 | 0.609702 | 0.304851 | − | 0.952400i | \(-0.401393\pi\) | ||||
0.304851 | + | 0.952400i | \(0.401393\pi\) | |||||||
\(492\) | 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 | \(-0.341424\pi\) | ||||
0.477829 | + | 0.878453i | \(0.341424\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.80244e27 | −0.0808288 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.67038e28 | −0.718375 | −0.359188 | − | 0.933265i | \(-0.616946\pi\) | ||||
−0.359188 | + | 0.933265i | \(0.616946\pi\) | |||||||
\(504\) | 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 | \(-0.658081\pi\) | ||||
−0.476463 | + | 0.879194i | \(0.658081\pi\) | |||||||
\(524\) | 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 | \(-0.445636\pi\) | ||||
0.169961 | + | 0.985451i | \(0.445636\pi\) | |||||||
\(548\) | 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 | \(-0.602883\pi\) | ||||
−0.317618 | + | 0.948219i | \(0.602883\pi\) | |||||||
\(564\) | 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 | \(-0.554563\pi\) | ||||
−0.170575 | + | 0.985345i | \(0.554563\pi\) | |||||||
\(572\) | 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 | \(-0.274885\pi\) | ||||
0.649723 | + | 0.760171i | \(0.274885\pi\) | |||||||
\(588\) | 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 | \(-0.645764\pi\) | ||||
−0.442093 | + | 0.896969i | \(0.645764\pi\) | |||||||
\(600\) | 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 | \(-0.180939\pi\) | ||||
0.842743 | + | 0.538316i | \(0.180939\pi\) | |||||||
\(608\) | 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 | \(-0.749447\pi\) | ||||
−0.705878 | + | 0.708333i | \(0.749447\pi\) | |||||||
\(620\) | 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 | \(-0.181035\pi\) | ||||
0.842581 | + | 0.538570i | \(0.181035\pi\) | |||||||
\(632\) | 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 | \(-0.399829\pi\) | ||||
0.309527 | + | 0.950891i | \(0.399829\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.98187e28 | −0.157404 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.06810e29 | −0.938370 | −0.469185 | − | 0.883100i | \(-0.655452\pi\) | ||||
−0.469185 | + | 0.883100i | \(0.655452\pi\) | |||||||
\(648\) | 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 | \(-0.357682\pi\) | ||||
0.432356 | + | 0.901703i | \(0.357682\pi\) | |||||||
\(660\) | 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 | \(-0.333977\pi\) | ||||
0.498248 | + | 0.867035i | \(0.333977\pi\) | |||||||
\(684\) | 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 | \(-0.439510\pi\) | ||||
0.188893 | + | 0.981998i | \(0.439510\pi\) | |||||||
\(692\) | 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 | \(-0.578857\pi\) | ||||
−0.245210 | + | 0.969470i | \(0.578857\pi\) | |||||||
\(720\) | 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 | \(-0.816214\pi\) | ||||
−0.837895 | + | 0.545831i | \(0.816214\pi\) | |||||||
\(728\) | 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 | \(-0.397197\pi\) | ||||
0.317381 | + | 0.948298i | \(0.397197\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.86242e24 | −6.52321e−6 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.60139e29 | 0.543889 | 0.271945 | − | 0.962313i | \(-0.412333\pi\) | ||||
0.271945 | + | 0.962313i | \(0.412333\pi\) | |||||||
\(744\) | 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 | \(-0.386726\pi\) | ||||
0.348397 | + | 0.937347i | \(0.386726\pi\) | |||||||
\(752\) | 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 | \(-0.423143\pi\) | ||||
0.239114 | + | 0.970992i | \(0.423143\pi\) | |||||||
\(788\) | 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 | \(-0.722861\pi\) | ||||
−0.644323 | + | 0.764753i | \(0.722861\pi\) | |||||||
\(812\) | 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 | \(-0.798180\pi\) | ||||
−0.805642 | + | 0.592402i | \(0.798180\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.35959e29 | −0.0800791 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.99217e29 | −0.0695309 | −0.0347655 | − | 0.999395i | \(-0.511068\pi\) | ||||
−0.0347655 | + | 0.999395i | \(0.511068\pi\) | |||||||
\(828\) | 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 | \(-0.275630\pi\) | ||||
0.647942 | + | 0.761690i | \(0.275630\pi\) | |||||||
\(840\) | 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 | \(-0.520874\pi\) | ||||
−0.0655306 | + | 0.997851i | \(0.520874\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.22724e28 | −0.00643463 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.66021e30 | 0.989406 | 0.494703 | − | 0.869062i | \(-0.335277\pi\) | ||||
0.494703 | + | 0.869062i | \(0.335277\pi\) | |||||||
\(864\) | 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 | \(-0.357015\pi\) | ||||
0.434245 | + | 0.900795i | \(0.357015\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.82863e30 | 0.208555 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.32005e30 | −0.592540 | −0.296270 | − | 0.955104i | \(-0.595743\pi\) | ||||
−0.296270 | + | 0.955104i | \(0.595743\pi\) | |||||||
\(888\) | 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 | \(-0.553905\pi\) | ||||
−0.168539 | + | 0.985695i | \(0.553905\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.71820e29 | 0.0578538 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.98935e30 | 0.335706 | 0.167853 | − | 0.985812i | \(-0.446317\pi\) | ||||
0.167853 | + | 0.985812i | \(0.446317\pi\) | |||||||
\(912\) | 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 | \(-0.169775\pi\) | ||||
0.861102 | + | 0.508432i | \(0.169775\pi\) | |||||||
\(920\) | 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 | \(-0.644399\pi\) | ||||
−0.438242 | + | 0.898857i | \(0.644399\pi\) | |||||||
\(948\) | 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 | \(-0.218796\pi\) | ||||
0.772919 | + | 0.634505i | \(0.218796\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.77747e26 | −1.22250e−5 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.39842e31 | 1.89450 | 0.947249 | − | 0.320497i | \(-0.103850\pi\) | ||||
0.947249 | + | 0.320497i | \(0.103850\pi\) | |||||||
\(972\) | 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 | \(-0.364183\pi\) | ||||
0.413852 | + | 0.910344i | \(0.364183\pi\) | |||||||
\(984\) | 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 | \(-0.451724\pi\) | ||||
0.151082 | + | 0.988521i | \(0.451724\pi\) | |||||||
\(992\) | 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.m.1.2 | 3 | ||
4.3 | odd | 2 | 64.22.a.l.1.2 | 3 | |||
8.3 | odd | 2 | 8.22.a.b.1.2 | ✓ | 3 | ||
8.5 | even | 2 | 16.22.a.f.1.2 | 3 | |||
24.11 | even | 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 | 8.3 | odd | 2 | ||
16.22.a.f.1.2 | 3 | 8.5 | even | 2 | |||
64.22.a.l.1.2 | 3 | 4.3 | odd | 2 | |||
64.22.a.m.1.2 | 3 | 1.1 | even | 1 | trivial | ||
72.22.a.f.1.1 | 3 | 24.11 | even | 2 |