Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [81,22,Mod(1,81)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(81, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("81.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.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: | \(226.376648873\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{19} - 30906825 x^{18} + 1599806295 x^{17} + 397632537600480 x^{16} + \cdots + 18\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | multiple of \( 2^{56}\cdot 3^{135}\cdot 5^{4}\cdot 7^{6} \) |
Twist minimal: | no (minimal twist has level 9) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Root | \(-1969.93\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 81.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1918.93 | 1.32509 | 0.662544 | − | 0.749023i | \(-0.269477\pi\) | ||||
0.662544 | + | 0.749023i | \(0.269477\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.58515e6 | 0.755857 | ||||||||
\(5\) | 1.00885e7 | 0.462001 | 0.231001 | − | 0.972954i | \(-0.425800\pi\) | ||||
0.231001 | + | 0.972954i | \(0.425800\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.43926e9 | 1.92579 | 0.962896 | − | 0.269873i | \(-0.0869816\pi\) | ||||
0.962896 | + | 0.269873i | \(0.0869816\pi\) | |||||||
\(8\) | −9.82502e8 | −0.323511 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.93592e10 | 0.612192 | ||||||||
\(11\) | −1.78976e10 | −0.208052 | −0.104026 | − | 0.994575i | \(-0.533173\pi\) | ||||
−0.104026 | + | 0.994575i | \(0.533173\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.16791e10 | −0.0234965 | −0.0117483 | − | 0.999931i | \(-0.503740\pi\) | ||||
−0.0117483 | + | 0.999931i | \(0.503740\pi\) | |||||||
\(14\) | 2.76184e12 | 2.55184 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.20965e12 | −1.18454 | ||||||||
\(17\) | −8.88490e11 | −0.106890 | −0.0534452 | − | 0.998571i | \(-0.517020\pi\) | ||||
−0.0534452 | + | 0.998571i | \(0.517020\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.75758e13 | −1.40603 | −0.703016 | − | 0.711174i | \(-0.748164\pi\) | ||||
−0.703016 | + | 0.711174i | \(0.748164\pi\) | |||||||
\(20\) | 1.59918e13 | 0.349207 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.43443e13 | −0.275687 | ||||||||
\(23\) | −2.58872e14 | −1.30299 | −0.651497 | − | 0.758651i | \(-0.725859\pi\) | ||||
−0.651497 | + | 0.758651i | \(0.725859\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.75059e14 | −0.786555 | ||||||||
\(26\) | −2.24114e13 | −0.0311350 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.28144e15 | 1.45562 | ||||||||
\(29\) | −2.84799e15 | −1.25707 | −0.628535 | − | 0.777781i | \(-0.716345\pi\) | ||||
−0.628535 | + | 0.777781i | \(0.716345\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.11887e15 | 0.902569 | 0.451284 | − | 0.892380i | \(-0.350966\pi\) | ||||
0.451284 | + | 0.892380i | \(0.350966\pi\) | |||||||
\(32\) | −7.93651e15 | −1.24610 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.70495e15 | −0.141639 | ||||||||
\(35\) | 1.45200e16 | 0.889718 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.25896e15 | 0.145608 | 0.0728040 | − | 0.997346i | \(-0.476805\pi\) | ||||
0.0728040 | + | 0.997346i | \(0.476805\pi\) | |||||||
\(38\) | −7.21054e16 | −1.86312 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.91201e15 | −0.149462 | ||||||||
\(41\) | −1.25337e17 | −1.45830 | −0.729150 | − | 0.684354i | \(-0.760084\pi\) | ||||
−0.729150 | + | 0.684354i | \(0.760084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.69863e17 | −1.19862 | −0.599309 | − | 0.800518i | \(-0.704558\pi\) | ||||
−0.599309 | + | 0.800518i | \(0.704558\pi\) | |||||||
\(44\) | −2.83704e16 | −0.157258 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.96757e17 | −1.72658 | ||||||||
\(47\) | −5.56420e16 | −0.154303 | −0.0771517 | − | 0.997019i | \(-0.524583\pi\) | ||||
−0.0771517 | + | 0.997019i | \(0.524583\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.51292e18 | 2.70868 | ||||||||
\(50\) | −7.19712e17 | −1.04225 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.85131e16 | −0.0177600 | ||||||||
\(53\) | 8.15800e17 | 0.640748 | 0.320374 | − | 0.947291i | \(-0.396191\pi\) | ||||
0.320374 | + | 0.947291i | \(0.396191\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.80561e17 | −0.0961203 | ||||||||
\(56\) | −1.41407e18 | −0.623014 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.46510e18 | −1.66573 | ||||||||
\(59\) | 4.14492e17 | 0.105577 | 0.0527886 | − | 0.998606i | \(-0.483189\pi\) | ||||
0.0527886 | + | 0.998606i | \(0.483189\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.64695e18 | −0.654586 | −0.327293 | − | 0.944923i | \(-0.606136\pi\) | ||||
−0.327293 | + | 0.944923i | \(0.606136\pi\) | |||||||
\(62\) | 7.90383e18 | 1.19598 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.30419e18 | −0.466661 | ||||||||
\(65\) | −1.17825e17 | −0.0108554 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.67422e18 | −0.246252 | −0.123126 | − | 0.992391i | \(-0.539292\pi\) | ||||
−0.123126 | + | 0.992391i | \(0.539292\pi\) | |||||||
\(68\) | −1.40839e18 | −0.0807939 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.78629e19 | 1.17895 | ||||||||
\(71\) | −3.18391e19 | −1.16077 | −0.580387 | − | 0.814340i | \(-0.697099\pi\) | ||||
−0.580387 | + | 0.814340i | \(0.697099\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.33473e19 | 0.908179 | 0.454089 | − | 0.890956i | \(-0.349965\pi\) | ||||
0.454089 | + | 0.890956i | \(0.349965\pi\) | |||||||
\(74\) | 8.17265e18 | 0.192943 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.95632e19 | −1.06276 | ||||||||
\(77\) | −2.57593e19 | −0.400665 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.42618e20 | 1.69468 | 0.847341 | − | 0.531049i | \(-0.178202\pi\) | ||||
0.847341 | + | 0.531049i | \(0.178202\pi\) | |||||||
\(80\) | −5.25577e19 | −0.547257 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.40512e20 | −1.93238 | ||||||||
\(83\) | −2.05840e20 | −1.45616 | −0.728082 | − | 0.685490i | \(-0.759588\pi\) | ||||
−0.728082 | + | 0.685490i | \(0.759588\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.96356e18 | −0.0493835 | ||||||||
\(86\) | −3.25956e20 | −1.58827 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.75844e19 | 0.0673071 | ||||||||
\(89\) | 3.19774e20 | 1.08705 | 0.543523 | − | 0.839395i | \(-0.317090\pi\) | ||||
0.543523 | + | 0.839395i | \(0.317090\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.68092e19 | −0.0452495 | ||||||||
\(92\) | −4.10350e20 | −0.984877 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.06773e20 | −0.204465 | ||||||||
\(95\) | −3.79085e20 | −0.649588 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.18447e20 | 0.163087 | 0.0815435 | − | 0.996670i | \(-0.474015\pi\) | ||||
0.0815435 | + | 0.996670i | \(0.474015\pi\) | |||||||
\(98\) | 2.90319e21 | 3.58923 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.94523e20 | −0.594523 | ||||||||
\(101\) | 1.12856e21 | 1.01660 | 0.508301 | − | 0.861180i | \(-0.330274\pi\) | ||||
0.508301 | + | 0.861180i | \(0.330274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.43842e20 | 0.618686 | 0.309343 | − | 0.950951i | \(-0.399891\pi\) | ||||
0.309343 | + | 0.950951i | \(0.399891\pi\) | |||||||
\(104\) | 1.14747e19 | 0.00760139 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.56546e21 | 0.849047 | ||||||||
\(107\) | 6.33311e20 | 0.311234 | 0.155617 | − | 0.987817i | \(-0.450263\pi\) | ||||
0.155617 | + | 0.987817i | \(0.450263\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.46747e21 | −1.80752 | −0.903760 | − | 0.428040i | \(-0.859204\pi\) | ||||
−0.903760 | + | 0.428040i | \(0.859204\pi\) | |||||||
\(110\) | −3.46484e20 | −0.127368 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.49803e21 | −2.28117 | ||||||||
\(113\) | 3.58005e21 | 0.992123 | 0.496061 | − | 0.868288i | \(-0.334779\pi\) | ||||
0.496061 | + | 0.868288i | \(0.334779\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.61163e21 | −0.601984 | ||||||||
\(116\) | −4.51448e21 | −0.950165 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.95382e20 | 0.139899 | ||||||||
\(119\) | −1.27877e21 | −0.205849 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.07993e21 | −0.956714 | ||||||||
\(122\) | −6.99825e21 | −0.867383 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.52902e21 | 0.682213 | ||||||||
\(125\) | −8.59438e21 | −0.825390 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.60955e21 | −0.456026 | −0.228013 | − | 0.973658i | \(-0.573223\pi\) | ||||
−0.228013 | + | 0.973658i | \(0.573223\pi\) | |||||||
\(128\) | 8.38462e21 | 0.627738 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.26098e20 | −0.0143844 | ||||||||
\(131\) | 3.13673e21 | 0.184131 | 0.0920657 | − | 0.995753i | \(-0.470653\pi\) | ||||
0.0920657 | + | 0.995753i | \(0.470653\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.40813e22 | −2.70773 | ||||||||
\(134\) | −7.05057e21 | −0.326305 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.72943e20 | 0.0345802 | ||||||||
\(137\) | −3.66042e22 | −1.34266 | −0.671328 | − | 0.741161i | \(-0.734276\pi\) | ||||
−0.671328 | + | 0.741161i | \(0.734276\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.78869e21 | −0.213861 | −0.106930 | − | 0.994267i | \(-0.534102\pi\) | ||||
−0.106930 | + | 0.994267i | \(0.534102\pi\) | |||||||
\(140\) | 2.30163e22 | 0.672500 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.10970e22 | −1.53813 | ||||||||
\(143\) | 2.09028e20 | 0.00488850 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.87320e22 | −0.580768 | ||||||||
\(146\) | 6.39913e22 | 1.20342 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.75108e21 | 0.110059 | ||||||||
\(149\) | −7.01638e22 | −1.06575 | −0.532877 | − | 0.846192i | \(-0.678889\pi\) | ||||
−0.532877 | + | 0.846192i | \(0.678889\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.43798e22 | −0.453988 | −0.226994 | − | 0.973896i | \(-0.572890\pi\) | ||||
−0.226994 | + | 0.973896i | \(0.572890\pi\) | |||||||
\(152\) | 3.69183e22 | 0.454867 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.94303e22 | −0.530916 | ||||||||
\(155\) | 4.15534e22 | 0.416988 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.01120e22 | 0.790381 | 0.395191 | − | 0.918599i | \(-0.370679\pi\) | ||||
0.395191 | + | 0.918599i | \(0.370679\pi\) | |||||||
\(158\) | 2.73673e23 | 2.24560 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.00677e22 | −0.575702 | ||||||||
\(161\) | −3.72583e23 | −2.50929 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.91470e22 | 0.172434 | 0.0862171 | − | 0.996276i | \(-0.472522\pi\) | ||||
0.0862171 | + | 0.996276i | \(0.472522\pi\) | |||||||
\(164\) | −1.98677e23 | −1.10227 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.94993e23 | −1.92954 | ||||||||
\(167\) | −3.95995e23 | −1.81622 | −0.908108 | − | 0.418737i | \(-0.862473\pi\) | ||||
−0.908108 | + | 0.418737i | \(0.862473\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.46928e23 | −0.999448 | ||||||||
\(170\) | −1.72005e22 | −0.0654374 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.69258e23 | −0.905983 | ||||||||
\(173\) | 1.74766e23 | 0.553316 | 0.276658 | − | 0.960968i | \(-0.410773\pi\) | ||||
0.276658 | + | 0.960968i | \(0.410773\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.39806e23 | −1.51474 | ||||||||
\(176\) | 9.32403e22 | 0.246445 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.13624e23 | 1.44043 | ||||||||
\(179\) | 8.15206e23 | 1.80431 | 0.902153 | − | 0.431416i | \(-0.141986\pi\) | ||||
0.902153 | + | 0.431416i | \(0.141986\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.90557e23 | 0.769236 | 0.384618 | − | 0.923076i | \(-0.374333\pi\) | ||||
0.384618 | + | 0.923076i | \(0.374333\pi\) | |||||||
\(182\) | −3.22558e22 | −0.0599595 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.54342e23 | 0.421532 | ||||||||
\(185\) | 4.29667e22 | 0.0672711 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.59018e22 | 0.0222388 | ||||||||
\(188\) | −8.82008e22 | −0.116631 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.27438e23 | −0.860762 | ||||||||
\(191\) | −8.48589e23 | −0.950270 | −0.475135 | − | 0.879913i | \(-0.657601\pi\) | ||||
−0.475135 | + | 0.879913i | \(0.657601\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.80489e23 | 0.984217 | 0.492109 | − | 0.870534i | \(-0.336226\pi\) | ||||
0.492109 | + | 0.870534i | \(0.336226\pi\) | |||||||
\(194\) | 2.27291e23 | 0.216104 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.39820e24 | 2.04737 | ||||||||
\(197\) | 9.48861e23 | 0.767905 | 0.383952 | − | 0.923353i | \(-0.374563\pi\) | ||||
0.383952 | + | 0.923353i | \(0.374563\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.82519e23 | −0.351202 | −0.175601 | − | 0.984461i | \(-0.556187\pi\) | ||||
−0.175601 | + | 0.984461i | \(0.556187\pi\) | |||||||
\(200\) | 3.68496e23 | 0.254459 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.16563e24 | 1.34709 | ||||||||
\(203\) | −4.09899e24 | −2.42086 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.26446e24 | −0.673736 | ||||||||
\(206\) | 1.61927e24 | 0.819813 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.08440e22 | 0.0278325 | ||||||||
\(209\) | 6.72517e23 | 0.292528 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.76646e23 | −0.305673 | −0.152837 | − | 0.988251i | \(-0.548841\pi\) | ||||
−0.152837 | + | 0.988251i | \(0.548841\pi\) | |||||||
\(212\) | 1.29316e24 | 0.484314 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.21528e24 | 0.412413 | ||||||||
\(215\) | −1.71367e24 | −0.553762 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.92812e24 | 1.73816 | ||||||||
\(218\) | −8.57276e24 | −2.39512 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.86215e23 | −0.0726532 | ||||||||
\(221\) | 1.03768e22 | 0.00251156 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.33639e24 | 0.734641 | 0.367321 | − | 0.930094i | \(-0.380275\pi\) | ||||
0.367321 | + | 0.930094i | \(0.380275\pi\) | |||||||
\(224\) | −1.14227e25 | −2.39974 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.86987e24 | 1.31465 | ||||||||
\(227\) | 1.29427e24 | 0.236458 | 0.118229 | − | 0.992986i | \(-0.462278\pi\) | ||||
0.118229 | + | 0.992986i | \(0.462278\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.68549e24 | 0.780698 | 0.390349 | − | 0.920667i | \(-0.372354\pi\) | ||||
0.390349 | + | 0.920667i | \(0.372354\pi\) | |||||||
\(230\) | −5.01155e24 | −0.797682 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.79816e24 | 0.406676 | ||||||||
\(233\) | −9.39232e24 | −1.30478 | −0.652388 | − | 0.757885i | \(-0.726233\pi\) | ||||
−0.652388 | + | 0.757885i | \(0.726233\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.61346e23 | −0.0712883 | ||||||||
\(236\) | 6.57031e23 | 0.0798013 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.45387e24 | −0.272768 | ||||||||
\(239\) | 5.80655e24 | 0.617647 | 0.308824 | − | 0.951119i | \(-0.400065\pi\) | ||||
0.308824 | + | 0.951119i | \(0.400065\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.05193e25 | −1.02520 | −0.512599 | − | 0.858628i | \(-0.671317\pi\) | ||||
−0.512599 | + | 0.858628i | \(0.671317\pi\) | |||||||
\(242\) | −1.35859e25 | −1.26773 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.78095e24 | −0.494773 | ||||||||
\(245\) | 1.52631e25 | 1.25141 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.38851e23 | 0.0330369 | ||||||||
\(248\) | −4.04680e24 | −0.291991 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.64920e25 | −1.09371 | ||||||||
\(251\) | 1.24868e25 | 0.794103 | 0.397052 | − | 0.917796i | \(-0.370033\pi\) | ||||
0.397052 | + | 0.917796i | \(0.370033\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.63318e24 | 0.271090 | ||||||||
\(254\) | −1.07644e25 | −0.604274 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.51160e25 | 1.29847 | ||||||||
\(257\) | 3.46865e25 | 1.72132 | 0.860662 | − | 0.509177i | \(-0.170050\pi\) | ||||
0.860662 | + | 0.509177i | \(0.170050\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.12975e24 | 0.280411 | ||||||||
\(260\) | −1.86770e23 | −0.00820515 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.01916e24 | 0.243990 | ||||||||
\(263\) | −4.29357e25 | −1.67218 | −0.836091 | − | 0.548591i | \(-0.815164\pi\) | ||||
−0.836091 | + | 0.548591i | \(0.815164\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.23022e24 | 0.296026 | ||||||||
\(266\) | −1.03778e26 | −3.58797 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.82417e24 | −0.186131 | ||||||||
\(269\) | 3.27085e25 | 1.00522 | 0.502610 | − | 0.864513i | \(-0.332373\pi\) | ||||
0.502610 | + | 0.864513i | \(0.332373\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.87108e25 | −0.816334 | −0.408167 | − | 0.912907i | \(-0.633832\pi\) | ||||
−0.408167 | + | 0.912907i | \(0.633832\pi\) | |||||||
\(272\) | 4.62872e24 | 0.126616 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.02409e25 | −1.77914 | ||||||||
\(275\) | 6.71266e24 | 0.163644 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.60016e23 | −0.00813362 | −0.00406681 | − | 0.999992i | \(-0.501295\pi\) | ||||
−0.00406681 | + | 0.999992i | \(0.501295\pi\) | |||||||
\(278\) | −1.30270e25 | −0.283384 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.42659e25 | −0.287833 | ||||||||
\(281\) | −7.31578e25 | −1.42182 | −0.710910 | − | 0.703283i | \(-0.751717\pi\) | ||||
−0.710910 | + | 0.703283i | \(0.751717\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.94047e25 | −1.07167 | −0.535837 | − | 0.844321i | \(-0.680004\pi\) | ||||
−0.535837 | + | 0.844321i | \(0.680004\pi\) | |||||||
\(284\) | −5.04696e25 | −0.877380 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.01110e23 | 0.00647770 | ||||||||
\(287\) | −1.80392e26 | −2.80838 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.83025e25 | −0.988574 | ||||||||
\(290\) | −5.51348e25 | −0.769568 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.28604e25 | 0.686453 | ||||||||
\(293\) | −6.94779e25 | −0.870436 | −0.435218 | − | 0.900325i | \(-0.643329\pi\) | ||||
−0.435218 | + | 0.900325i | \(0.643329\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.18162e24 | 0.0487768 | ||||||||
\(296\) | −4.18444e24 | −0.0471058 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.34640e26 | −1.41222 | ||||||||
\(299\) | 3.02339e24 | 0.0306158 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.44477e26 | −2.30829 | ||||||||
\(302\) | −6.59724e25 | −0.601574 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.95757e26 | 1.66550 | ||||||||
\(305\) | −3.67924e25 | −0.302419 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.34578e25 | 0.333514 | 0.166757 | − | 0.985998i | \(-0.446670\pi\) | ||||
0.166757 | + | 0.985998i | \(0.446670\pi\) | |||||||
\(308\) | −4.08323e25 | −0.302845 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.97381e25 | 0.552545 | ||||||||
\(311\) | 3.69095e25 | 0.247260 | 0.123630 | − | 0.992328i | \(-0.460546\pi\) | ||||
0.123630 | + | 0.992328i | \(0.460546\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.65069e25 | 0.103384 | 0.0516918 | − | 0.998663i | \(-0.483539\pi\) | ||||
0.0516918 | + | 0.998663i | \(0.483539\pi\) | |||||||
\(314\) | 1.72919e26 | 1.04732 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.26070e26 | 1.28094 | ||||||||
\(317\) | −1.87242e26 | −1.02632 | −0.513158 | − | 0.858294i | \(-0.671525\pi\) | ||||
−0.513158 | + | 0.858294i | \(0.671525\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.09722e25 | 0.261536 | ||||||||
\(320\) | −4.34229e25 | −0.215598 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.14962e26 | −3.32503 | ||||||||
\(323\) | 3.33857e25 | 0.150291 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.38035e24 | 0.0184813 | ||||||||
\(326\) | 5.59310e25 | 0.228490 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.23143e26 | 0.471776 | ||||||||
\(329\) | −8.00833e25 | −0.297156 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.10813e26 | 0.385831 | 0.192915 | − | 0.981215i | \(-0.438206\pi\) | ||||
0.192915 | + | 0.981215i | \(0.438206\pi\) | |||||||
\(332\) | −3.26287e26 | −1.10065 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.59888e26 | −2.40664 | ||||||||
\(335\) | −3.70674e25 | −0.113769 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.04643e26 | 1.45502 | 0.727512 | − | 0.686095i | \(-0.240677\pi\) | ||||
0.727512 | + | 0.686095i | \(0.240677\pi\) | |||||||
\(338\) | −4.73838e26 | −1.32436 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.42086e25 | −0.0373269 | ||||||||
\(341\) | −7.37180e25 | −0.187781 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.37359e27 | 3.29055 | ||||||||
\(344\) | 1.66891e26 | 0.387766 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.35364e26 | 0.733192 | ||||||||
\(347\) | 4.69718e26 | 0.996272 | 0.498136 | − | 0.867099i | \(-0.334018\pi\) | ||||
0.498136 | + | 0.867099i | \(0.334018\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.31480e26 | 0.262539 | 0.131269 | − | 0.991347i | \(-0.458095\pi\) | ||||
0.131269 | + | 0.991347i | \(0.458095\pi\) | |||||||
\(350\) | −1.03585e27 | −2.00717 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.42045e26 | 0.259255 | ||||||||
\(353\) | −6.81592e26 | −1.20751 | −0.603754 | − | 0.797171i | \(-0.706329\pi\) | ||||
−0.603754 | + | 0.797171i | \(0.706329\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.21210e26 | −0.536279 | ||||||||
\(356\) | 5.06888e26 | 0.821651 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.56432e27 | 2.39086 | ||||||||
\(359\) | −7.00365e26 | −1.03952 | −0.519760 | − | 0.854313i | \(-0.673979\pi\) | ||||
−0.519760 | + | 0.854313i | \(0.673979\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.97731e26 | 0.976927 | ||||||||
\(362\) | 7.49452e26 | 1.01930 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.66451e25 | −0.0342021 | ||||||||
\(365\) | 3.36426e26 | 0.419579 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.83947e26 | −0.805432 | −0.402716 | − | 0.915325i | \(-0.631934\pi\) | ||||
−0.402716 | + | 0.915325i | \(0.631934\pi\) | |||||||
\(368\) | 1.34863e27 | 1.54344 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.24501e25 | 0.0891401 | ||||||||
\(371\) | 1.17415e27 | 1.23395 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.12611e26 | 0.807123 | 0.403562 | − | 0.914952i | \(-0.367772\pi\) | ||||
0.403562 | + | 0.914952i | \(0.367772\pi\) | |||||||
\(374\) | 3.05146e25 | 0.0294683 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.46684e25 | 0.0499188 | ||||||||
\(377\) | 3.32620e25 | 0.0295368 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.08255e27 | −0.909362 | −0.454681 | − | 0.890654i | \(-0.650247\pi\) | ||||
−0.454681 | + | 0.890654i | \(0.650247\pi\) | |||||||
\(380\) | −6.00905e26 | −0.490996 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.62838e27 | −1.25919 | ||||||||
\(383\) | −7.38183e25 | −0.0555363 | −0.0277681 | − | 0.999614i | \(-0.508840\pi\) | ||||
−0.0277681 | + | 0.999614i | \(0.508840\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.59873e26 | −0.185108 | ||||||||
\(386\) | 1.88149e27 | 1.30417 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.87755e26 | 0.123270 | ||||||||
\(389\) | −5.83122e26 | −0.372640 | −0.186320 | − | 0.982489i | \(-0.559656\pi\) | ||||
−0.186320 | + | 0.982489i | \(0.559656\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.30005e26 | 0.139278 | ||||||||
\(392\) | −1.48645e27 | −0.876286 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.82080e27 | 1.01754 | ||||||||
\(395\) | 1.43880e27 | 0.782945 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.64645e27 | 1.36572 | 0.682862 | − | 0.730547i | \(-0.260735\pi\) | ||||
0.682862 | + | 0.730547i | \(0.260735\pi\) | |||||||
\(398\) | −9.25922e26 | −0.465374 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.95392e27 | 0.931704 | ||||||||
\(401\) | 7.02503e25 | 0.0326311 | 0.0163156 | − | 0.999867i | \(-0.494806\pi\) | ||||
0.0163156 | + | 0.999867i | \(0.494806\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.81047e25 | −0.0212073 | ||||||||
\(404\) | 1.78894e27 | 0.768406 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.86569e27 | −3.20785 | ||||||||
\(407\) | −7.62252e25 | −0.0302941 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.55437e27 | −0.586760 | −0.293380 | − | 0.955996i | \(-0.594780\pi\) | ||||
−0.293380 | + | 0.955996i | \(0.594780\pi\) | |||||||
\(410\) | −2.42642e27 | −0.892760 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.33761e27 | 0.467638 | ||||||||
\(413\) | 5.96561e26 | 0.203320 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.07663e27 | −0.672749 | ||||||||
\(416\) | 9.26912e25 | 0.0292792 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.29051e27 | 0.387625 | ||||||||
\(419\) | 3.25686e27 | 0.954007 | 0.477003 | − | 0.878901i | \(-0.341723\pi\) | ||||
0.477003 | + | 0.878901i | \(0.341723\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.42448e27 | −1.23282 | −0.616411 | − | 0.787425i | \(-0.711414\pi\) | ||||
−0.616411 | + | 0.787425i | \(0.711414\pi\) | |||||||
\(422\) | −1.49033e27 | −0.405044 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.01525e26 | −0.207289 | ||||||||
\(425\) | 3.33236e26 | 0.0840752 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.24890e27 | −1.26060 | ||||||||
\(428\) | 1.00389e27 | 0.235249 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.28842e27 | −0.733784 | ||||||||
\(431\) | 5.08936e27 | 1.10829 | 0.554143 | − | 0.832421i | \(-0.313046\pi\) | ||||
0.554143 | + | 0.832421i | \(0.313046\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.54206e27 | 1.56447 | 0.782235 | − | 0.622983i | \(-0.214080\pi\) | ||||
0.782235 | + | 0.622983i | \(0.214080\pi\) | |||||||
\(434\) | 1.13757e28 | 2.30321 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.08159e27 | −1.36623 | ||||||||
\(437\) | 9.72731e27 | 1.83205 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.05560e27 | 0.907601 | 0.453800 | − | 0.891103i | \(-0.350068\pi\) | ||||
0.453800 | + | 0.891103i | \(0.350068\pi\) | |||||||
\(440\) | 1.77401e26 | 0.0310959 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.99123e25 | 0.00332803 | ||||||||
\(443\) | 2.30267e27 | 0.375832 | 0.187916 | − | 0.982185i | \(-0.439827\pi\) | ||||
0.187916 | + | 0.982185i | \(0.439827\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.22605e27 | 0.502216 | ||||||||
\(446\) | 6.40230e27 | 0.973464 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.19484e27 | −0.898691 | ||||||||
\(449\) | −6.87770e27 | −0.974668 | −0.487334 | − | 0.873216i | \(-0.662031\pi\) | ||||
−0.487334 | + | 0.873216i | \(0.662031\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.24322e27 | 0.303402 | ||||||||
\(452\) | 5.67490e27 | 0.749903 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.48362e27 | 0.313327 | ||||||||
\(455\) | −1.69581e26 | −0.0209053 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.63453e27 | −0.427886 | −0.213943 | − | 0.976846i | \(-0.568631\pi\) | ||||
−0.213943 | + | 0.976846i | \(0.568631\pi\) | |||||||
\(458\) | 8.99114e27 | 1.03449 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.13983e27 | −0.455014 | ||||||||
\(461\) | 2.08814e27 | 0.224336 | 0.112168 | − | 0.993689i | \(-0.464221\pi\) | ||||
0.112168 | + | 0.993689i | \(0.464221\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.23302e27 | −0.126581 | −0.0632906 | − | 0.997995i | \(-0.520159\pi\) | ||||
−0.0632906 | + | 0.997995i | \(0.520159\pi\) | |||||||
\(464\) | 1.48370e28 | 1.48905 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.80232e28 | −1.72894 | ||||||||
\(467\) | −3.72155e27 | −0.349057 | −0.174529 | − | 0.984652i | \(-0.555840\pi\) | ||||
−0.174529 | + | 0.984652i | \(0.555840\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.28815e27 | −0.474229 | ||||||||
\(470\) | −1.07719e27 | −0.0944633 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.07239e26 | −0.0341554 | ||||||||
\(473\) | 3.04015e27 | 0.249375 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.40931e28 | 1.10592 | ||||||||
\(476\) | −2.02703e27 | −0.155592 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.11424e28 | 0.818437 | ||||||||
\(479\) | 4.01585e27 | 0.288572 | 0.144286 | − | 0.989536i | \(-0.453911\pi\) | ||||
0.144286 | + | 0.989536i | \(0.453911\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.97408e25 | −0.00342129 | ||||||||
\(482\) | −2.01858e28 | −1.35848 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.12227e28 | −0.723139 | ||||||||
\(485\) | 1.19495e27 | 0.0753463 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.76670e27 | −0.287848 | −0.143924 | − | 0.989589i | \(-0.545972\pi\) | ||||
−0.143924 | + | 0.989589i | \(0.545972\pi\) | |||||||
\(488\) | 3.58314e27 | 0.211766 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.92889e28 | 1.65823 | ||||||||
\(491\) | −1.70058e28 | −0.942413 | −0.471207 | − | 0.882023i | \(-0.656181\pi\) | ||||
−0.471207 | + | 0.882023i | \(0.656181\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.53041e27 | 0.134369 | ||||||||
\(494\) | 8.42126e26 | 0.0437768 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.14579e28 | −1.06913 | ||||||||
\(497\) | −4.58247e28 | −2.23541 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.63082e28 | 0.762693 | 0.381346 | − | 0.924432i | \(-0.375461\pi\) | ||||
0.381346 | + | 0.924432i | \(0.375461\pi\) | |||||||
\(500\) | −1.36234e28 | −0.623877 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.39613e28 | 1.05226 | ||||||||
\(503\) | −6.10168e27 | −0.262413 | −0.131207 | − | 0.991355i | \(-0.541885\pi\) | ||||
−0.131207 | + | 0.991355i | \(0.541885\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.13855e28 | 0.469671 | ||||||||
\(506\) | 8.89077e27 | 0.359219 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.89197e27 | −0.344690 | ||||||||
\(509\) | 1.08400e28 | 0.411615 | 0.205807 | − | 0.978592i | \(-0.434018\pi\) | ||||
0.205807 | + | 0.978592i | \(0.434018\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.79955e28 | 1.74896 | ||||||||
\(512\) | 3.06122e28 | 1.09285 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.65610e28 | 2.28091 | ||||||||
\(515\) | 8.51312e27 | 0.285833 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.95860e26 | 0.0321031 | ||||||||
\(518\) | 1.17626e28 | 0.371569 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.15763e26 | 0.00351185 | ||||||||
\(521\) | 6.28643e27 | 0.186899 | 0.0934497 | − | 0.995624i | \(-0.470211\pi\) | ||||
0.0934497 | + | 0.995624i | \(0.470211\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.14604e28 | 0.898454 | 0.449227 | − | 0.893418i | \(-0.351699\pi\) | ||||
0.449227 | + | 0.893418i | \(0.351699\pi\) | |||||||
\(524\) | 4.97217e27 | 0.139177 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.23907e28 | −2.21579 | ||||||||
\(527\) | −3.65957e27 | −0.0964760 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.75429e28 | 0.697792 | ||||||||
\(530\) | 1.57932e28 | 0.392260 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.57268e28 | −2.04665 | ||||||||
\(533\) | 1.46382e27 | 0.0342650 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.38918e27 | 0.143791 | ||||||||
\(536\) | 3.60993e27 | 0.0796651 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.27653e28 | 1.33201 | ||||||||
\(539\) | −2.70776e28 | −0.563545 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.83966e28 | −0.368270 | −0.184135 | − | 0.982901i | \(-0.558948\pi\) | ||||
−0.184135 | + | 0.982901i | \(0.558948\pi\) | |||||||
\(542\) | −5.50941e28 | −1.08171 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.05150e27 | 0.133197 | ||||||||
\(545\) | −4.50702e28 | −0.835076 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.24549e28 | −0.578646 | −0.289323 | − | 0.957231i | \(-0.593430\pi\) | ||||
−0.289323 | + | 0.957231i | \(0.593430\pi\) | |||||||
\(548\) | −5.80230e28 | −1.01486 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.28811e28 | 0.216843 | ||||||||
\(551\) | 1.07015e29 | 1.76748 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.05263e29 | 3.26361 | ||||||||
\(554\) | −6.90845e26 | −0.0107778 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.07611e28 | −0.161648 | ||||||||
\(557\) | 1.37986e28 | 0.203402 | 0.101701 | − | 0.994815i | \(-0.467571\pi\) | ||||
0.101701 | + | 0.994815i | \(0.467571\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.98385e27 | 0.0281634 | ||||||||
\(560\) | −7.56441e28 | −1.05390 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.40385e29 | −1.88404 | ||||||||
\(563\) | 1.51648e28 | 0.199756 | 0.0998778 | − | 0.995000i | \(-0.468155\pi\) | ||||
0.0998778 | + | 0.995000i | \(0.468155\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.61174e28 | 0.458362 | ||||||||
\(566\) | −1.13994e29 | −1.42006 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.12820e28 | 0.375523 | ||||||||
\(569\) | −9.58103e28 | −1.12910 | −0.564552 | − | 0.825398i | \(-0.690951\pi\) | ||||
−0.564552 | + | 0.825398i | \(0.690951\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.57951e28 | 0.860919 | 0.430459 | − | 0.902610i | \(-0.358352\pi\) | ||||
0.430459 | + | 0.902610i | \(0.358352\pi\) | |||||||
\(572\) | 3.31340e26 | 0.00369501 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.46159e29 | −3.72135 | ||||||||
\(575\) | 9.70921e28 | 1.02488 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.37885e28 | 0.445671 | 0.222835 | − | 0.974856i | \(-0.428469\pi\) | ||||
0.222835 | + | 0.974856i | \(0.428469\pi\) | |||||||
\(578\) | −1.31068e29 | −1.30995 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.55445e28 | −0.438977 | ||||||||
\(581\) | −2.96257e29 | −2.80427 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.46009e28 | −0.133309 | ||||||||
\(584\) | −3.27638e28 | −0.293806 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.33323e29 | −1.15340 | ||||||||
\(587\) | 1.06943e29 | 0.908766 | 0.454383 | − | 0.890806i | \(-0.349860\pi\) | ||||
0.454383 | + | 0.890806i | \(0.349860\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.54770e29 | −1.26904 | ||||||||
\(590\) | 8.02424e27 | 0.0646335 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.21877e28 | −0.172478 | ||||||||
\(593\) | −5.57095e28 | −0.425456 | −0.212728 | − | 0.977111i | \(-0.568235\pi\) | ||||
−0.212728 | + | 0.977111i | \(0.568235\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.29009e28 | −0.0951023 | ||||||||
\(596\) | −1.11220e29 | −0.805558 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.80167e27 | 0.0405687 | ||||||||
\(599\) | 6.50977e28 | 0.447285 | 0.223642 | − | 0.974671i | \(-0.428205\pi\) | ||||
0.223642 | + | 0.974671i | \(0.428205\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.78716e28 | −0.649344 | −0.324672 | − | 0.945827i | \(-0.605254\pi\) | ||||
−0.324672 | + | 0.945827i | \(0.605254\pi\) | |||||||
\(602\) | −4.69135e29 | −3.05868 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.44970e28 | −0.343150 | ||||||||
\(605\) | −7.14261e28 | −0.442003 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.65865e28 | −0.457795 | −0.228897 | − | 0.973451i | \(-0.573512\pi\) | ||||
−0.228897 | + | 0.973451i | \(0.573512\pi\) | |||||||
\(608\) | 2.98220e29 | 1.75206 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.06021e28 | −0.400732 | ||||||||
\(611\) | 6.49849e26 | 0.00362560 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.41320e29 | 0.761847 | 0.380923 | − | 0.924607i | \(-0.375606\pi\) | ||||
0.380923 | + | 0.924607i | \(0.375606\pi\) | |||||||
\(614\) | 8.33925e28 | 0.441935 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.53086e28 | 0.129619 | ||||||||
\(617\) | −1.53273e28 | −0.0771742 | −0.0385871 | − | 0.999255i | \(-0.512286\pi\) | ||||
−0.0385871 | + | 0.999255i | \(0.512286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.64333e29 | 1.28647 | 0.643234 | − | 0.765670i | \(-0.277592\pi\) | ||||
0.643234 | + | 0.765670i | \(0.277592\pi\) | |||||||
\(620\) | 6.58682e28 | 0.315183 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.08268e28 | 0.327641 | ||||||||
\(623\) | 4.60237e29 | 2.09342 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.21372e28 | 0.405224 | ||||||||
\(626\) | 3.16757e28 | 0.136992 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.42841e29 | 0.597415 | ||||||||
\(629\) | −3.78404e27 | −0.0155641 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.04710e29 | −1.61004 | −0.805019 | − | 0.593249i | \(-0.797845\pi\) | ||||
−0.805019 | + | 0.593249i | \(0.797845\pi\) | |||||||
\(632\) | −1.40122e29 | −0.548248 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.59305e29 | −1.35996 | ||||||||
\(635\) | −5.65922e28 | −0.210684 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.76695e28 | −0.0636445 | ||||||||
\(638\) | 9.78122e28 | 0.346558 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.45885e28 | 0.290016 | ||||||||
\(641\) | −2.25664e29 | −0.761118 | −0.380559 | − | 0.924757i | \(-0.624268\pi\) | ||||
−0.380559 | + | 0.924757i | \(0.624268\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.38638e28 | −0.0778978 | −0.0389489 | − | 0.999241i | \(-0.512401\pi\) | ||||
−0.0389489 | + | 0.999241i | \(0.512401\pi\) | |||||||
\(644\) | −5.90599e29 | −1.89667 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.40649e28 | 0.199149 | ||||||||
\(647\) | 3.52013e29 | 1.07662 | 0.538311 | − | 0.842746i | \(-0.319062\pi\) | ||||
0.538311 | + | 0.842746i | \(0.319062\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.41842e27 | −0.0219655 | ||||||||
\(650\) | 8.40559e27 | 0.0244894 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.62022e28 | 0.130336 | ||||||||
\(653\) | −7.92250e28 | −0.219925 | −0.109962 | − | 0.993936i | \(-0.535073\pi\) | ||||
−0.109962 | + | 0.993936i | \(0.535073\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.16450e28 | 0.0850689 | ||||||||
\(656\) | 6.52959e29 | 1.72741 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.53674e29 | −0.393758 | ||||||||
\(659\) | −6.58595e29 | −1.66082 | −0.830408 | − | 0.557156i | \(-0.811893\pi\) | ||||
−0.830408 | + | 0.557156i | \(0.811893\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.76931e29 | 1.40932 | 0.704658 | − | 0.709547i | \(-0.251101\pi\) | ||||
0.704658 | + | 0.709547i | \(0.251101\pi\) | |||||||
\(662\) | 2.12643e29 | 0.511259 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.02238e29 | 0.471085 | ||||||||
\(665\) | −5.45601e29 | −1.25097 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.37264e29 | 1.63795 | ||||||||
\(668\) | −6.27711e29 | −1.37280 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.11299e28 | −0.150753 | ||||||||
\(671\) | 6.52717e28 | 0.136188 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.30962e29 | 0.467071 | 0.233536 | − | 0.972348i | \(-0.424970\pi\) | ||||
0.233536 | + | 0.972348i | \(0.424970\pi\) | |||||||
\(674\) | 9.68375e29 | 1.92803 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.91417e29 | −0.755440 | ||||||||
\(677\) | 2.82785e29 | 0.537372 | 0.268686 | − | 0.963228i | \(-0.413411\pi\) | ||||
0.268686 | + | 0.963228i | \(0.413411\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.70475e29 | 0.314072 | ||||||||
\(680\) | 8.80672e27 | 0.0159761 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.41460e29 | −0.248827 | ||||||||
\(683\) | 6.52113e29 | 1.12955 | 0.564775 | − | 0.825245i | \(-0.308963\pi\) | ||||
0.564775 | + | 0.825245i | \(0.308963\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.69282e29 | −0.620308 | ||||||||
\(686\) | 2.63583e30 | 4.36027 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.84928e29 | 1.41981 | ||||||||
\(689\) | −9.52781e27 | −0.0150554 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.20725e30 | 1.85045 | 0.925223 | − | 0.379424i | \(-0.123878\pi\) | ||||
0.925223 | + | 0.379424i | \(0.123878\pi\) | |||||||
\(692\) | 2.77030e29 | 0.418228 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.01357e29 | 1.32015 | ||||||||
\(695\) | −6.84879e28 | −0.0988038 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.11360e29 | 0.155878 | ||||||||
\(698\) | 2.52302e29 | 0.347887 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.55673e29 | −1.14493 | ||||||||
\(701\) | −1.24828e30 | −1.64541 | −0.822705 | − | 0.568468i | \(-0.807536\pi\) | ||||
−0.822705 | + | 0.568468i | \(0.807536\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.60034e29 | −0.204730 | ||||||||
\(704\) | 7.70346e28 | 0.0970897 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.30793e30 | −1.60005 | ||||||||
\(707\) | 1.62429e30 | 1.95776 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.98119e29 | 0.816853 | 0.408427 | − | 0.912791i | \(-0.366078\pi\) | ||||
0.408427 | + | 0.912791i | \(0.366078\pi\) | |||||||
\(710\) | −6.16380e29 | −0.710617 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.14178e29 | −0.351671 | ||||||||
\(713\) | −1.06626e30 | −1.17604 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.10879e27 | 0.00225849 | ||||||||
\(716\) | 1.29222e30 | 1.36380 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.34395e30 | −1.37745 | ||||||||
\(719\) | −6.00175e29 | −0.606212 | −0.303106 | − | 0.952957i | \(-0.598024\pi\) | ||||
−0.303106 | + | 0.952957i | \(0.598024\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.21451e30 | 1.19146 | ||||||||
\(722\) | 1.33890e30 | 1.29451 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.19090e29 | 0.581432 | ||||||||
\(725\) | 1.06816e30 | 0.988755 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.90899e29 | −0.801157 | −0.400578 | − | 0.916263i | \(-0.631191\pi\) | ||||
−0.400578 | + | 0.916263i | \(0.631191\pi\) | |||||||
\(728\) | 1.65151e28 | 0.0146387 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.45578e29 | 0.555979 | ||||||||
\(731\) | 1.50922e29 | 0.128121 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.86535e30 | −1.53875 | −0.769375 | − | 0.638797i | \(-0.779432\pi\) | ||||
−0.769375 | + | 0.638797i | \(0.779432\pi\) | |||||||
\(734\) | −1.31245e30 | −1.06727 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.05454e30 | 1.62367 | ||||||||
\(737\) | 6.57597e28 | 0.0512332 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.76021e29 | 0.739082 | 0.369541 | − | 0.929214i | \(-0.379515\pi\) | ||||
0.369541 | + | 0.929214i | \(0.379515\pi\) | |||||||
\(740\) | 6.81085e28 | 0.0508473 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.25311e30 | 1.63509 | ||||||||
\(743\) | −1.30919e30 | −0.936742 | −0.468371 | − | 0.883532i | \(-0.655159\pi\) | ||||
−0.468371 | + | 0.883532i | \(0.655159\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.07850e29 | −0.492380 | ||||||||
\(746\) | 1.55934e30 | 1.06951 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.52068e28 | 0.0168093 | ||||||||
\(749\) | 9.11499e29 | 0.599373 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.02067e30 | 0.652626 | 0.326313 | − | 0.945262i | \(-0.394194\pi\) | ||||
0.326313 | + | 0.945262i | \(0.394194\pi\) | |||||||
\(752\) | 2.89875e29 | 0.182778 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.38274e28 | 0.0391389 | ||||||||
\(755\) | −3.46841e29 | −0.209743 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.30425e30 | −0.767106 | −0.383553 | − | 0.923519i | \(-0.625300\pi\) | ||||
−0.383553 | + | 0.923519i | \(0.625300\pi\) | |||||||
\(758\) | −2.07734e30 | −1.20498 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.72452e29 | 0.210149 | ||||||||
\(761\) | −1.44355e30 | −0.803329 | −0.401664 | − | 0.915787i | \(-0.631568\pi\) | ||||
−0.401664 | + | 0.915787i | \(0.631568\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.42984e30 | −3.48091 | ||||||||
\(764\) | −1.34514e30 | −0.718268 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.41652e29 | −0.0735904 | ||||||||
\(767\) | −4.84089e27 | −0.00248070 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.69617e29 | −0.234163 | −0.117081 | − | 0.993122i | \(-0.537354\pi\) | ||||
−0.117081 | + | 0.993122i | \(0.537354\pi\) | |||||||
\(770\) | −4.98679e29 | −0.245284 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.55422e30 | 0.743927 | ||||||||
\(773\) | 1.85640e30 | 0.876572 | 0.438286 | − | 0.898835i | \(-0.355586\pi\) | ||||
0.438286 | + | 0.898835i | \(0.355586\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.54482e30 | −0.709920 | ||||||||
\(776\) | −1.16374e29 | −0.0527604 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.11897e30 | −0.493780 | ||||||||
\(779\) | 4.70962e30 | 2.05042 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.69844e29 | 0.241502 | ||||||||
\(782\) | 4.41364e29 | 0.184555 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.88178e30 | −3.20853 | ||||||||
\(785\) | 9.09098e29 | 0.365157 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.15728e30 | −1.23475 | −0.617374 | − | 0.786669i | \(-0.711804\pi\) | ||||
−0.617374 | + | 0.786669i | \(0.711804\pi\) | |||||||
\(788\) | 1.50408e30 | 0.580426 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.76096e30 | 1.03747 | ||||||||
\(791\) | 5.15262e30 | 1.91062 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.25931e28 | 0.0153805 | ||||||||
\(794\) | 5.07835e30 | 1.80970 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.64864e29 | −0.265459 | ||||||||
\(797\) | −4.17512e30 | −1.43007 | −0.715034 | − | 0.699090i | \(-0.753589\pi\) | ||||
−0.715034 | + | 0.699090i | \(0.753589\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.94374e28 | 0.0164936 | ||||||||
\(800\) | 2.97666e30 | 0.980130 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.34806e29 | 0.0432391 | ||||||||
\(803\) | −5.96838e29 | −0.188948 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.75882e30 | −1.15930 | ||||||||
\(806\) | −9.23096e28 | −0.0281015 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.10881e30 | −0.328882 | ||||||||
\(809\) | −1.58248e30 | −0.463318 | −0.231659 | − | 0.972797i | \(-0.574415\pi\) | ||||
−0.231659 | + | 0.972797i | \(0.574415\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.17280e30 | 1.76102 | 0.880508 | − | 0.474031i | \(-0.157202\pi\) | ||||
0.880508 | + | 0.474031i | \(0.157202\pi\) | |||||||
\(812\) | −6.49751e30 | −1.82982 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.46271e29 | −0.0401423 | ||||||||
\(815\) | 2.94050e29 | 0.0796648 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.38274e30 | 1.68529 | ||||||||
\(818\) | −2.98274e30 | −0.777509 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.00436e30 | −0.509248 | ||||||||
\(821\) | 1.86634e30 | 0.468154 | 0.234077 | − | 0.972218i | \(-0.424793\pi\) | ||||
0.234077 | + | 0.972218i | \(0.424793\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.55497e29 | −0.233631 | −0.116816 | − | 0.993154i | \(-0.537269\pi\) | ||||
−0.116816 | + | 0.993154i | \(0.537269\pi\) | |||||||
\(824\) | −8.29076e29 | −0.200151 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.14476e30 | 0.269416 | ||||||||
\(827\) | −6.36744e30 | −1.47964 | −0.739821 | − | 0.672803i | \(-0.765090\pi\) | ||||
−0.739821 | + | 0.672803i | \(0.765090\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.73773e30 | 0.393694 | 0.196847 | − | 0.980434i | \(-0.436930\pi\) | ||||
0.196847 | + | 0.980434i | \(0.436930\pi\) | |||||||
\(830\) | −3.98490e30 | −0.891451 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.02690e28 | 0.0109649 | ||||||||
\(833\) | −1.34421e30 | −0.289531 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.99501e30 | −0.839093 | ||||||||
\(836\) | 1.06604e30 | 0.221109 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.24969e30 | 1.26414 | ||||||||
\(839\) | −6.90704e29 | −0.137972 | −0.0689861 | − | 0.997618i | \(-0.521976\pi\) | ||||
−0.0689861 | + | 0.997618i | \(0.521976\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.97820e30 | 0.580225 | ||||||||
\(842\) | −8.49028e30 | −1.63360 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.23110e30 | −0.231045 | ||||||||
\(845\) | −2.49114e30 | −0.461746 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.01898e31 | −1.84243 | ||||||||
\(848\) | −4.25003e30 | −0.758989 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.39457e29 | 0.111407 | ||||||||
\(851\) | −1.10252e30 | −0.189726 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.91355e30 | −0.657061 | −0.328531 | − | 0.944493i | \(-0.606553\pi\) | ||||
−0.328531 | + | 0.944493i | \(0.606553\pi\) | |||||||
\(854\) | −1.00723e31 | −1.67040 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.22230e29 | −0.100688 | ||||||||
\(857\) | −9.77653e30 | −1.56274 | −0.781369 | − | 0.624069i | \(-0.785478\pi\) | ||||
−0.781369 | + | 0.624069i | \(0.785478\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.87242e30 | 0.448043 | 0.224022 | − | 0.974584i | \(-0.428081\pi\) | ||||
0.224022 | + | 0.974584i | \(0.428081\pi\) | |||||||
\(860\) | −2.71642e30 | −0.418565 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.76614e30 | 1.46858 | ||||||||
\(863\) | 1.04420e30 | 0.155122 | 0.0775608 | − | 0.996988i | \(-0.475287\pi\) | ||||
0.0775608 | + | 0.996988i | \(0.475287\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.76313e30 | 0.255633 | ||||||||
\(866\) | 1.44727e31 | 2.07306 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.39694e30 | 1.31380 | ||||||||
\(869\) | −2.55251e30 | −0.352582 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.29115e28 | 0.00578606 | ||||||||
\(872\) | 4.38930e30 | 0.584752 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.86660e31 | 2.42763 | ||||||||
\(875\) | −1.23695e31 | −1.58953 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.88930e30 | 0.738870 | 0.369435 | − | 0.929257i | \(-0.379551\pi\) | ||||
0.369435 | + | 0.929257i | \(0.379551\pi\) | |||||||
\(878\) | 9.70134e30 | 1.20265 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.40658e29 | 0.113858 | ||||||||
\(881\) | −1.18650e31 | −1.41913 | −0.709563 | − | 0.704642i | \(-0.751108\pi\) | ||||
−0.709563 | + | 0.704642i | \(0.751108\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.58382e30 | −0.418561 | −0.209280 | − | 0.977856i | \(-0.567112\pi\) | ||||
−0.209280 | + | 0.977856i | \(0.567112\pi\) | |||||||
\(884\) | 1.64487e28 | 0.00189838 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.41868e30 | 0.498010 | ||||||||
\(887\) | −1.13748e31 | −1.26691 | −0.633456 | − | 0.773779i | \(-0.718364\pi\) | ||||
−0.633456 | + | 0.773779i | \(0.718364\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.07360e30 | −0.878211 | ||||||||
\(890\) | 6.19056e30 | 0.665480 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.28866e30 | 0.555284 | ||||||||
\(893\) | 2.09079e30 | 0.216956 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.22423e30 | 0.833591 | ||||||||
\(896\) | 1.20676e31 | 1.20889 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.31978e31 | −1.29152 | ||||||||
\(899\) | −1.17305e31 | −1.13459 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.24830e29 | −0.0684898 | ||||||||
\(902\) | 4.30459e30 | 0.402035 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.51741e30 | −0.320962 | ||||||||
\(905\) | 3.94015e30 | 0.355388 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.42730e30 | 0.566438 | 0.283219 | − | 0.959055i | \(-0.408598\pi\) | ||||
0.283219 | + | 0.959055i | \(0.408598\pi\) | |||||||
\(908\) | 2.05161e30 | 0.178728 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.25414e29 | −0.0277014 | ||||||||
\(911\) | 2.02085e30 | 0.170056 | 0.0850278 | − | 0.996379i | \(-0.472902\pi\) | ||||
0.0850278 | + | 0.996379i | \(0.472902\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.68405e30 | 0.302958 | ||||||||
\(914\) | −6.97441e30 | −0.566986 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.42720e30 | 0.590096 | ||||||||
\(917\) | 4.51456e30 | 0.354599 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.04014e30 | −0.0798510 | −0.0399255 | − | 0.999203i | \(-0.512712\pi\) | ||||
−0.0399255 | + | 0.999203i | \(0.512712\pi\) | |||||||
\(920\) | 2.56594e30 | 0.194748 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.00699e30 | 0.297265 | ||||||||
\(923\) | 3.71852e29 | 0.0272742 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.59736e30 | −0.114529 | ||||||||
\(926\) | −2.36608e30 | −0.167731 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.26031e31 | 1.56644 | ||||||||
\(929\) | 1.20936e31 | 0.828684 | 0.414342 | − | 0.910121i | \(-0.364012\pi\) | ||||
0.414342 | + | 0.910121i | \(0.364012\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.68491e31 | −3.80849 | ||||||||
\(932\) | −1.48882e31 | −0.986224 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.14140e30 | −0.462531 | ||||||||
\(935\) | 1.60426e29 | 0.0102743 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.84764e31 | −1.78328 | −0.891638 | − | 0.452748i | \(-0.850444\pi\) | ||||
−0.891638 | + | 0.452748i | \(0.850444\pi\) | |||||||
\(938\) | −1.01476e31 | −0.628396 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.89817e29 | −0.0538838 | ||||||||
\(941\) | 2.38411e31 | 1.42770 | 0.713848 | − | 0.700301i | \(-0.246951\pi\) | ||||
0.713848 | + | 0.700301i | \(0.246951\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.24461e31 | 1.90016 | ||||||||
\(944\) | −2.15936e30 | −0.125060 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.83383e30 | 0.330443 | ||||||||
\(947\) | −3.03747e31 | −1.70152 | −0.850760 | − | 0.525555i | \(-0.823858\pi\) | ||||
−0.850760 | + | 0.525555i | \(0.823858\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.89467e29 | −0.0213391 | ||||||||
\(950\) | 2.70438e31 | 1.46544 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.25639e30 | 0.0665943 | ||||||||
\(953\) | −3.43245e30 | −0.179941 | −0.0899703 | − | 0.995944i | \(-0.528677\pi\) | ||||
−0.0899703 | + | 0.995944i | \(0.528677\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.56102e30 | −0.439026 | ||||||||
\(956\) | 9.20424e30 | 0.466853 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.70614e30 | 0.382384 | ||||||||
\(959\) | −5.26829e31 | −2.58568 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.86041e30 | −0.185370 | ||||||||
\(962\) | −9.54492e28 | −0.00453351 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.66746e31 | −0.774903 | ||||||||
\(965\) | 9.89169e30 | 0.454709 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.94184e31 | 0.873445 | 0.436722 | − | 0.899596i | \(-0.356139\pi\) | ||||
0.436722 | + | 0.899596i | \(0.356139\pi\) | |||||||
\(968\) | 6.95604e30 | 0.309507 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.29303e30 | 0.0998405 | ||||||||
\(971\) | 1.81095e31 | 0.780016 | 0.390008 | − | 0.920811i | \(-0.372472\pi\) | ||||
0.390008 | + | 0.920811i | \(0.372472\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.77068e30 | −0.411851 | ||||||||
\(974\) | −9.14697e30 | −0.381424 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.89993e31 | 0.775381 | ||||||||
\(977\) | −2.12590e31 | −0.858323 | −0.429161 | − | 0.903228i | \(-0.641191\pi\) | ||||
−0.429161 | + | 0.903228i | \(0.641191\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.72319e30 | −0.226162 | ||||||||
\(980\) | 2.41943e31 | 0.945888 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.26330e31 | −1.24878 | ||||||||
\(983\) | 3.74700e31 | 1.41864 | 0.709318 | − | 0.704888i | \(-0.249003\pi\) | ||||
0.709318 | + | 0.704888i | \(0.249003\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.57262e30 | 0.354773 | ||||||||
\(986\) | 4.85568e30 | 0.178050 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.95644e29 | 0.0249712 | ||||||||
\(989\) | 4.39728e31 | 1.56179 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.66143e31 | −1.27314 | −0.636572 | − | 0.771217i | \(-0.719648\pi\) | ||||
−0.636572 | + | 0.771217i | \(0.719648\pi\) | |||||||
\(992\) | −3.26894e31 | −1.12470 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.79344e31 | −2.96212 | ||||||||
\(995\) | −4.86791e30 | −0.162256 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.25970e31 | −1.39021 | −0.695105 | − | 0.718909i | \(-0.744642\pi\) | ||||
−0.695105 | + | 0.718909i | \(0.744642\pi\) | |||||||
\(998\) | 3.12943e31 | 1.01063 | ||||||||
\(999\) | 0 | 0 |
(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 | 81.22.a.c.1.17 | 20 | ||
3.2 | odd | 2 | 81.22.a.d.1.4 | 20 | |||
9.2 | odd | 6 | 27.22.c.a.10.17 | 40 | |||
9.4 | even | 3 | 9.22.c.a.7.4 | yes | 40 | ||
9.5 | odd | 6 | 27.22.c.a.19.17 | 40 | |||
9.7 | even | 3 | 9.22.c.a.4.4 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.22.c.a.4.4 | ✓ | 40 | 9.7 | even | 3 | ||
9.22.c.a.7.4 | yes | 40 | 9.4 | even | 3 | ||
27.22.c.a.10.17 | 40 | 9.2 | odd | 6 | |||
27.22.c.a.19.17 | 40 | 9.5 | odd | 6 | |||
81.22.a.c.1.17 | 20 | 1.1 | even | 1 | trivial | ||
81.22.a.d.1.4 | 20 | 3.2 | odd | 2 |