Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,8,Mod(1,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.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: | \(21.5545667584\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 757x^{6} - 1170x^{5} + 170343x^{4} + 424132x^{3} - 9973075x^{2} - 5161010x + 130545120 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-18.5379\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 21.5379 | 1.90370 | 0.951850 | − | 0.306564i | \(-0.0991795\pi\) | ||||
0.951850 | + | 0.306564i | \(0.0991795\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 335.881 | 2.62407 | ||||||||
\(5\) | 54.7305 | 0.195810 | 0.0979050 | − | 0.995196i | \(-0.468786\pi\) | ||||
0.0979050 | + | 0.995196i | \(0.468786\pi\) | |||||||
\(6\) | 581.523 | 1.09910 | ||||||||
\(7\) | −565.198 | −0.622812 | −0.311406 | − | 0.950277i | \(-0.600800\pi\) | ||||
−0.311406 | + | 0.950277i | \(0.600800\pi\) | |||||||
\(8\) | 4477.33 | 3.09175 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 1178.78 | 0.372763 | ||||||||
\(11\) | −890.150 | −0.201646 | −0.100823 | − | 0.994904i | \(-0.532148\pi\) | ||||
−0.100823 | + | 0.994904i | \(0.532148\pi\) | |||||||
\(12\) | 9068.80 | 1.51501 | ||||||||
\(13\) | 12435.5 | 1.56987 | 0.784934 | − | 0.619579i | \(-0.212697\pi\) | ||||
0.784934 | + | 0.619579i | \(0.212697\pi\) | |||||||
\(14\) | −12173.2 | −1.18565 | ||||||||
\(15\) | 1477.72 | 0.113051 | ||||||||
\(16\) | 53439.5 | 3.26169 | ||||||||
\(17\) | −2692.57 | −0.132922 | −0.0664608 | − | 0.997789i | \(-0.521171\pi\) | ||||
−0.0664608 | + | 0.997789i | \(0.521171\pi\) | |||||||
\(18\) | 15701.1 | 0.634567 | ||||||||
\(19\) | −56073.6 | −1.87551 | −0.937757 | − | 0.347291i | \(-0.887102\pi\) | ||||
−0.937757 | + | 0.347291i | \(0.887102\pi\) | |||||||
\(20\) | 18383.0 | 0.513819 | ||||||||
\(21\) | −15260.3 | −0.359581 | ||||||||
\(22\) | −19172.0 | −0.383873 | ||||||||
\(23\) | 12167.0 | 0.208514 | ||||||||
\(24\) | 120888. | 1.78502 | ||||||||
\(25\) | −75129.6 | −0.961658 | ||||||||
\(26\) | 267836. | 2.98856 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | −189839. | −1.63430 | ||||||||
\(29\) | −72626.2 | −0.552969 | −0.276484 | − | 0.961018i | \(-0.589169\pi\) | ||||
−0.276484 | + | 0.961018i | \(0.589169\pi\) | |||||||
\(30\) | 31827.1 | 0.215215 | ||||||||
\(31\) | 207276. | 1.24963 | 0.624817 | − | 0.780771i | \(-0.285173\pi\) | ||||
0.624817 | + | 0.780771i | \(0.285173\pi\) | |||||||
\(32\) | 577876. | 3.11752 | ||||||||
\(33\) | −24034.0 | −0.116420 | ||||||||
\(34\) | −57992.3 | −0.253043 | ||||||||
\(35\) | −30933.6 | −0.121953 | ||||||||
\(36\) | 244857. | 0.874691 | ||||||||
\(37\) | −160422. | −0.520664 | −0.260332 | − | 0.965519i | \(-0.583832\pi\) | ||||
−0.260332 | + | 0.965519i | \(0.583832\pi\) | |||||||
\(38\) | −1.20771e6 | −3.57042 | ||||||||
\(39\) | 335760. | 0.906364 | ||||||||
\(40\) | 245047. | 0.605395 | ||||||||
\(41\) | −562941. | −1.27561 | −0.637807 | − | 0.770196i | \(-0.720158\pi\) | ||||
−0.637807 | + | 0.770196i | \(0.720158\pi\) | |||||||
\(42\) | −328676. | −0.684534 | ||||||||
\(43\) | 7553.70 | 0.0144884 | 0.00724419 | − | 0.999974i | \(-0.497694\pi\) | ||||
0.00724419 | + | 0.999974i | \(0.497694\pi\) | |||||||
\(44\) | −298985. | −0.529133 | ||||||||
\(45\) | 39898.6 | 0.0652700 | ||||||||
\(46\) | 262052. | 0.396949 | ||||||||
\(47\) | 374615. | 0.526311 | 0.263156 | − | 0.964753i | \(-0.415237\pi\) | ||||
0.263156 | + | 0.964753i | \(0.415237\pi\) | |||||||
\(48\) | 1.44287e6 | 1.88314 | ||||||||
\(49\) | −504095. | −0.612105 | ||||||||
\(50\) | −1.61813e6 | −1.83071 | ||||||||
\(51\) | −72699.4 | −0.0767424 | ||||||||
\(52\) | 4.17687e6 | 4.11945 | ||||||||
\(53\) | 96348.3 | 0.0888952 | 0.0444476 | − | 0.999012i | \(-0.485847\pi\) | ||||
0.0444476 | + | 0.999012i | \(0.485847\pi\) | |||||||
\(54\) | 423931. | 0.366367 | ||||||||
\(55\) | −48718.4 | −0.0394842 | ||||||||
\(56\) | −2.53058e6 | −1.92558 | ||||||||
\(57\) | −1.51399e6 | −1.08283 | ||||||||
\(58\) | −1.56422e6 | −1.05269 | ||||||||
\(59\) | −1.29931e6 | −0.823625 | −0.411812 | − | 0.911269i | \(-0.635104\pi\) | ||||
−0.411812 | + | 0.911269i | \(0.635104\pi\) | |||||||
\(60\) | 496340. | 0.296654 | ||||||||
\(61\) | 1.20681e6 | 0.680747 | 0.340374 | − | 0.940290i | \(-0.389446\pi\) | ||||
0.340374 | + | 0.940290i | \(0.389446\pi\) | |||||||
\(62\) | 4.46429e6 | 2.37893 | ||||||||
\(63\) | −412029. | −0.207604 | ||||||||
\(64\) | 5.60599e6 | 2.67314 | ||||||||
\(65\) | 680604. | 0.307396 | ||||||||
\(66\) | −517643. | −0.221629 | ||||||||
\(67\) | 3.81931e6 | 1.55140 | 0.775699 | − | 0.631103i | \(-0.217398\pi\) | ||||
0.775699 | + | 0.631103i | \(0.217398\pi\) | |||||||
\(68\) | −904384. | −0.348796 | ||||||||
\(69\) | 328509. | 0.120386 | ||||||||
\(70\) | −666244. | −0.232162 | ||||||||
\(71\) | −649906. | −0.215499 | −0.107750 | − | 0.994178i | \(-0.534365\pi\) | ||||
−0.107750 | + | 0.994178i | \(0.534365\pi\) | |||||||
\(72\) | 3.26397e6 | 1.03058 | ||||||||
\(73\) | −2.81315e6 | −0.846374 | −0.423187 | − | 0.906042i | \(-0.639089\pi\) | ||||
−0.423187 | + | 0.906042i | \(0.639089\pi\) | |||||||
\(74\) | −3.45515e6 | −0.991187 | ||||||||
\(75\) | −2.02850e6 | −0.555214 | ||||||||
\(76\) | −1.88341e7 | −4.92149 | ||||||||
\(77\) | 503111. | 0.125587 | ||||||||
\(78\) | 7.23156e6 | 1.72544 | ||||||||
\(79\) | −807658. | −0.184303 | −0.0921516 | − | 0.995745i | \(-0.529374\pi\) | ||||
−0.0921516 | + | 0.995745i | \(0.529374\pi\) | |||||||
\(80\) | 2.92477e6 | 0.638670 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −1.21246e7 | −2.42839 | ||||||||
\(83\) | −4.40700e6 | −0.845999 | −0.422999 | − | 0.906130i | \(-0.639023\pi\) | ||||
−0.422999 | + | 0.906130i | \(0.639023\pi\) | |||||||
\(84\) | −5.12566e6 | −0.943566 | ||||||||
\(85\) | −147366. | −0.0260274 | ||||||||
\(86\) | 162691. | 0.0275815 | ||||||||
\(87\) | −1.96091e6 | −0.319257 | ||||||||
\(88\) | −3.98549e6 | −0.623437 | ||||||||
\(89\) | −1.28241e7 | −1.92824 | −0.964121 | − | 0.265464i | \(-0.914475\pi\) | ||||
−0.964121 | + | 0.265464i | \(0.914475\pi\) | |||||||
\(90\) | 859331. | 0.124254 | ||||||||
\(91\) | −7.02854e6 | −0.977733 | ||||||||
\(92\) | 4.08667e6 | 0.547157 | ||||||||
\(93\) | 5.59645e6 | 0.721477 | ||||||||
\(94\) | 8.06842e6 | 1.00194 | ||||||||
\(95\) | −3.06894e6 | −0.367244 | ||||||||
\(96\) | 1.56027e7 | 1.79990 | ||||||||
\(97\) | −2.57777e6 | −0.286776 | −0.143388 | − | 0.989667i | \(-0.545800\pi\) | ||||
−0.143388 | + | 0.989667i | \(0.545800\pi\) | |||||||
\(98\) | −1.08571e7 | −1.16526 | ||||||||
\(99\) | −648919. | −0.0672152 | ||||||||
\(100\) | −2.52346e7 | −2.52346 | ||||||||
\(101\) | 1.36859e7 | 1.32174 | 0.660872 | − | 0.750499i | \(-0.270187\pi\) | ||||
0.660872 | + | 0.750499i | \(0.270187\pi\) | |||||||
\(102\) | −1.56579e6 | −0.146094 | ||||||||
\(103\) | 1.78977e7 | 1.61386 | 0.806932 | − | 0.590645i | \(-0.201127\pi\) | ||||
0.806932 | + | 0.590645i | \(0.201127\pi\) | |||||||
\(104\) | 5.56780e7 | 4.85364 | ||||||||
\(105\) | −835206. | −0.0704095 | ||||||||
\(106\) | 2.07514e6 | 0.169230 | ||||||||
\(107\) | 2.05198e7 | 1.61931 | 0.809655 | − | 0.586907i | \(-0.199654\pi\) | ||||
0.809655 | + | 0.586907i | \(0.199654\pi\) | |||||||
\(108\) | 6.61115e6 | 0.505003 | ||||||||
\(109\) | −1.99672e7 | −1.47681 | −0.738405 | − | 0.674358i | \(-0.764421\pi\) | ||||
−0.738405 | + | 0.674358i | \(0.764421\pi\) | |||||||
\(110\) | −1.04929e6 | −0.0751661 | ||||||||
\(111\) | −4.33139e6 | −0.300605 | ||||||||
\(112\) | −3.02039e7 | −2.03142 | ||||||||
\(113\) | 3.03308e7 | 1.97747 | 0.988734 | − | 0.149685i | \(-0.0478259\pi\) | ||||
0.988734 | + | 0.149685i | \(0.0478259\pi\) | |||||||
\(114\) | −3.26081e7 | −2.06138 | ||||||||
\(115\) | 665906. | 0.0408292 | ||||||||
\(116\) | −2.43938e7 | −1.45103 | ||||||||
\(117\) | 9.06551e6 | 0.523289 | ||||||||
\(118\) | −2.79843e7 | −1.56793 | ||||||||
\(119\) | 1.52183e6 | 0.0827853 | ||||||||
\(120\) | 6.61626e6 | 0.349525 | ||||||||
\(121\) | −1.86948e7 | −0.959339 | ||||||||
\(122\) | 2.59922e7 | 1.29594 | ||||||||
\(123\) | −1.51994e7 | −0.736476 | ||||||||
\(124\) | 6.96201e7 | 3.27913 | ||||||||
\(125\) | −8.38770e6 | −0.384112 | ||||||||
\(126\) | −8.87424e6 | −0.395216 | ||||||||
\(127\) | 1.95967e7 | 0.848926 | 0.424463 | − | 0.905445i | \(-0.360463\pi\) | ||||
0.424463 | + | 0.905445i | \(0.360463\pi\) | |||||||
\(128\) | 4.67731e7 | 1.97134 | ||||||||
\(129\) | 203950. | 0.00836487 | ||||||||
\(130\) | 1.46588e7 | 0.585189 | ||||||||
\(131\) | −1.49391e7 | −0.580597 | −0.290299 | − | 0.956936i | \(-0.593755\pi\) | ||||
−0.290299 | + | 0.956936i | \(0.593755\pi\) | |||||||
\(132\) | −8.07259e6 | −0.305495 | ||||||||
\(133\) | 3.16926e7 | 1.16809 | ||||||||
\(134\) | 8.22599e7 | 2.95339 | ||||||||
\(135\) | 1.07726e6 | 0.0376836 | ||||||||
\(136\) | −1.20555e7 | −0.410960 | ||||||||
\(137\) | 3.18774e7 | 1.05916 | 0.529578 | − | 0.848261i | \(-0.322350\pi\) | ||||
0.529578 | + | 0.848261i | \(0.322350\pi\) | |||||||
\(138\) | 7.07540e6 | 0.229179 | ||||||||
\(139\) | 4.39284e7 | 1.38737 | 0.693687 | − | 0.720277i | \(-0.255985\pi\) | ||||
0.693687 | + | 0.720277i | \(0.255985\pi\) | |||||||
\(140\) | −1.03900e7 | −0.320013 | ||||||||
\(141\) | 1.01146e7 | 0.303866 | ||||||||
\(142\) | −1.39976e7 | −0.410246 | ||||||||
\(143\) | −1.10695e7 | −0.316557 | ||||||||
\(144\) | 3.89574e7 | 1.08723 | ||||||||
\(145\) | −3.97487e6 | −0.108277 | ||||||||
\(146\) | −6.05893e7 | −1.61124 | ||||||||
\(147\) | −1.36106e7 | −0.353399 | ||||||||
\(148\) | −5.38827e7 | −1.36626 | ||||||||
\(149\) | 6.05704e7 | 1.50006 | 0.750030 | − | 0.661404i | \(-0.230039\pi\) | ||||
0.750030 | + | 0.661404i | \(0.230039\pi\) | |||||||
\(150\) | −4.36896e7 | −1.05696 | ||||||||
\(151\) | 1.59550e7 | 0.377117 | 0.188559 | − | 0.982062i | \(-0.439618\pi\) | ||||
0.188559 | + | 0.982062i | \(0.439618\pi\) | |||||||
\(152\) | −2.51060e8 | −5.79862 | ||||||||
\(153\) | −1.96288e6 | −0.0443072 | ||||||||
\(154\) | 1.08359e7 | 0.239081 | ||||||||
\(155\) | 1.13443e7 | 0.244691 | ||||||||
\(156\) | 1.12775e8 | 2.37836 | ||||||||
\(157\) | −3.40669e7 | −0.702562 | −0.351281 | − | 0.936270i | \(-0.614254\pi\) | ||||
−0.351281 | + | 0.936270i | \(0.614254\pi\) | |||||||
\(158\) | −1.73953e7 | −0.350858 | ||||||||
\(159\) | 2.60140e6 | 0.0513237 | ||||||||
\(160\) | 3.16275e7 | 0.610442 | ||||||||
\(161\) | −6.87676e6 | −0.129865 | ||||||||
\(162\) | 1.14461e7 | 0.211522 | ||||||||
\(163\) | −7.41885e7 | −1.34178 | −0.670888 | − | 0.741559i | \(-0.734087\pi\) | ||||
−0.670888 | + | 0.741559i | \(0.734087\pi\) | |||||||
\(164\) | −1.89081e8 | −3.34731 | ||||||||
\(165\) | −1.31540e6 | −0.0227962 | ||||||||
\(166\) | −9.49175e7 | −1.61053 | ||||||||
\(167\) | 1.05052e8 | 1.74540 | 0.872700 | − | 0.488258i | \(-0.162367\pi\) | ||||
0.872700 | + | 0.488258i | \(0.162367\pi\) | |||||||
\(168\) | −6.83255e7 | −1.11173 | ||||||||
\(169\) | 9.18943e7 | 1.46449 | ||||||||
\(170\) | −3.17395e6 | −0.0495483 | ||||||||
\(171\) | −4.08776e7 | −0.625172 | ||||||||
\(172\) | 2.53715e6 | 0.0380186 | ||||||||
\(173\) | 8.92240e7 | 1.31015 | 0.655074 | − | 0.755565i | \(-0.272638\pi\) | ||||
0.655074 | + | 0.755565i | \(0.272638\pi\) | |||||||
\(174\) | −4.22339e7 | −0.607769 | ||||||||
\(175\) | 4.24631e7 | 0.598933 | ||||||||
\(176\) | −4.75691e7 | −0.657705 | ||||||||
\(177\) | −3.50813e7 | −0.475520 | ||||||||
\(178\) | −2.76204e8 | −3.67079 | ||||||||
\(179\) | 4.09274e7 | 0.533369 | 0.266685 | − | 0.963784i | \(-0.414072\pi\) | ||||
0.266685 | + | 0.963784i | \(0.414072\pi\) | |||||||
\(180\) | 1.34012e7 | 0.171273 | ||||||||
\(181\) | 4.48333e7 | 0.561986 | 0.280993 | − | 0.959710i | \(-0.409336\pi\) | ||||
0.280993 | + | 0.959710i | \(0.409336\pi\) | |||||||
\(182\) | −1.51380e8 | −1.86131 | ||||||||
\(183\) | 3.25840e7 | 0.393029 | ||||||||
\(184\) | 5.44757e7 | 0.644674 | ||||||||
\(185\) | −8.77997e6 | −0.101951 | ||||||||
\(186\) | 1.20536e8 | 1.37348 | ||||||||
\(187\) | 2.39679e6 | 0.0268031 | ||||||||
\(188\) | 1.25826e8 | 1.38108 | ||||||||
\(189\) | −1.11248e7 | −0.119860 | ||||||||
\(190\) | −6.60984e7 | −0.699123 | ||||||||
\(191\) | 1.08477e8 | 1.12648 | 0.563239 | − | 0.826294i | \(-0.309555\pi\) | ||||
0.563239 | + | 0.826294i | \(0.309555\pi\) | |||||||
\(192\) | 1.51362e8 | 1.54334 | ||||||||
\(193\) | 8.81302e6 | 0.0882417 | 0.0441209 | − | 0.999026i | \(-0.485951\pi\) | ||||
0.0441209 | + | 0.999026i | \(0.485951\pi\) | |||||||
\(194\) | −5.55197e7 | −0.545935 | ||||||||
\(195\) | 1.83763e7 | 0.177475 | ||||||||
\(196\) | −1.69316e8 | −1.60621 | ||||||||
\(197\) | 1.04354e7 | 0.0972475 | 0.0486238 | − | 0.998817i | \(-0.484516\pi\) | ||||
0.0486238 | + | 0.998817i | \(0.484516\pi\) | |||||||
\(198\) | −1.39764e7 | −0.127958 | ||||||||
\(199\) | −1.41236e8 | −1.27046 | −0.635230 | − | 0.772323i | \(-0.719095\pi\) | ||||
−0.635230 | + | 0.772323i | \(0.719095\pi\) | |||||||
\(200\) | −3.36380e8 | −2.97320 | ||||||||
\(201\) | 1.03121e8 | 0.895700 | ||||||||
\(202\) | 2.94765e8 | 2.51620 | ||||||||
\(203\) | 4.10482e7 | 0.344396 | ||||||||
\(204\) | −2.44184e7 | −0.201378 | ||||||||
\(205\) | −3.08101e7 | −0.249778 | ||||||||
\(206\) | 3.85479e8 | 3.07231 | ||||||||
\(207\) | 8.86974e6 | 0.0695048 | ||||||||
\(208\) | 6.64549e8 | 5.12042 | ||||||||
\(209\) | 4.99139e7 | 0.378189 | ||||||||
\(210\) | −1.79886e7 | −0.134039 | ||||||||
\(211\) | 5.31949e7 | 0.389835 | 0.194918 | − | 0.980820i | \(-0.437556\pi\) | ||||
0.194918 | + | 0.980820i | \(0.437556\pi\) | |||||||
\(212\) | 3.23616e7 | 0.233267 | ||||||||
\(213\) | −1.75475e7 | −0.124419 | ||||||||
\(214\) | 4.41953e8 | 3.08268 | ||||||||
\(215\) | 413418. | 0.00283697 | ||||||||
\(216\) | 8.81273e7 | 0.595007 | ||||||||
\(217\) | −1.17152e8 | −0.778288 | ||||||||
\(218\) | −4.30052e8 | −2.81140 | ||||||||
\(219\) | −7.59550e7 | −0.488654 | ||||||||
\(220\) | −1.63636e7 | −0.103609 | ||||||||
\(221\) | −3.34836e7 | −0.208670 | ||||||||
\(222\) | −9.32890e7 | −0.572262 | ||||||||
\(223\) | −1.70709e8 | −1.03084 | −0.515419 | − | 0.856938i | \(-0.672364\pi\) | ||||
−0.515419 | + | 0.856938i | \(0.672364\pi\) | |||||||
\(224\) | −3.26614e8 | −1.94163 | ||||||||
\(225\) | −5.47695e7 | −0.320553 | ||||||||
\(226\) | 6.53262e8 | 3.76450 | ||||||||
\(227\) | −1.95923e8 | −1.11172 | −0.555860 | − | 0.831276i | \(-0.687611\pi\) | ||||
−0.555860 | + | 0.831276i | \(0.687611\pi\) | |||||||
\(228\) | −5.08520e8 | −2.84142 | ||||||||
\(229\) | −2.03625e8 | −1.12049 | −0.560244 | − | 0.828328i | \(-0.689293\pi\) | ||||
−0.560244 | + | 0.828328i | \(0.689293\pi\) | |||||||
\(230\) | 1.43422e7 | 0.0777265 | ||||||||
\(231\) | 1.35840e7 | 0.0725079 | ||||||||
\(232\) | −3.25172e8 | −1.70964 | ||||||||
\(233\) | 3.21437e7 | 0.166475 | 0.0832376 | − | 0.996530i | \(-0.473474\pi\) | ||||
0.0832376 | + | 0.996530i | \(0.473474\pi\) | |||||||
\(234\) | 1.95252e8 | 0.996186 | ||||||||
\(235\) | 2.05029e7 | 0.103057 | ||||||||
\(236\) | −4.36413e8 | −2.16125 | ||||||||
\(237\) | −2.18068e7 | −0.106407 | ||||||||
\(238\) | 3.27771e7 | 0.157598 | ||||||||
\(239\) | 4.43634e7 | 0.210200 | 0.105100 | − | 0.994462i | \(-0.466484\pi\) | ||||
0.105100 | + | 0.994462i | \(0.466484\pi\) | |||||||
\(240\) | 7.89688e7 | 0.368737 | ||||||||
\(241\) | 1.09153e8 | 0.502316 | 0.251158 | − | 0.967946i | \(-0.419189\pi\) | ||||
0.251158 | + | 0.967946i | \(0.419189\pi\) | |||||||
\(242\) | −4.02647e8 | −1.82629 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 4.05346e8 | 1.78633 | ||||||||
\(245\) | −2.75894e7 | −0.119856 | ||||||||
\(246\) | −3.27363e8 | −1.40203 | ||||||||
\(247\) | −6.97305e8 | −2.94431 | ||||||||
\(248\) | 9.28043e8 | 3.86356 | ||||||||
\(249\) | −1.18989e8 | −0.488438 | ||||||||
\(250\) | −1.80654e8 | −0.731234 | ||||||||
\(251\) | −1.36741e8 | −0.545810 | −0.272905 | − | 0.962041i | \(-0.587984\pi\) | ||||
−0.272905 | + | 0.962041i | \(0.587984\pi\) | |||||||
\(252\) | −1.38393e8 | −0.544768 | ||||||||
\(253\) | −1.08305e7 | −0.0420460 | ||||||||
\(254\) | 4.22072e8 | 1.61610 | ||||||||
\(255\) | −3.97888e6 | −0.0150269 | ||||||||
\(256\) | 2.89828e8 | 1.07969 | ||||||||
\(257\) | 4.31493e8 | 1.58565 | 0.792825 | − | 0.609449i | \(-0.208609\pi\) | ||||
0.792825 | + | 0.609449i | \(0.208609\pi\) | |||||||
\(258\) | 4.39265e6 | 0.0159242 | ||||||||
\(259\) | 9.06700e7 | 0.324276 | ||||||||
\(260\) | 2.28602e8 | 0.806629 | ||||||||
\(261\) | −5.29445e7 | −0.184323 | ||||||||
\(262\) | −3.21757e8 | −1.10528 | ||||||||
\(263\) | 2.44909e8 | 0.830157 | 0.415078 | − | 0.909786i | \(-0.363754\pi\) | ||||
0.415078 | + | 0.909786i | \(0.363754\pi\) | |||||||
\(264\) | −1.07608e8 | −0.359942 | ||||||||
\(265\) | 5.27319e6 | 0.0174066 | ||||||||
\(266\) | 6.82593e8 | 2.22370 | ||||||||
\(267\) | −3.46250e8 | −1.11327 | ||||||||
\(268\) | 1.28283e9 | 4.07098 | ||||||||
\(269\) | −6.20750e8 | −1.94439 | −0.972195 | − | 0.234171i | \(-0.924762\pi\) | ||||
−0.972195 | + | 0.234171i | \(0.924762\pi\) | |||||||
\(270\) | 2.32019e7 | 0.0717383 | ||||||||
\(271\) | 8.27788e7 | 0.252654 | 0.126327 | − | 0.991989i | \(-0.459681\pi\) | ||||
0.126327 | + | 0.991989i | \(0.459681\pi\) | |||||||
\(272\) | −1.43889e8 | −0.433549 | ||||||||
\(273\) | −1.89771e8 | −0.564495 | ||||||||
\(274\) | 6.86571e8 | 2.01632 | ||||||||
\(275\) | 6.68766e7 | 0.193914 | ||||||||
\(276\) | 1.10340e8 | 0.315901 | ||||||||
\(277\) | −5.28652e8 | −1.49448 | −0.747242 | − | 0.664552i | \(-0.768622\pi\) | ||||
−0.747242 | + | 0.664552i | \(0.768622\pi\) | |||||||
\(278\) | 9.46125e8 | 2.64114 | ||||||||
\(279\) | 1.51104e8 | 0.416545 | ||||||||
\(280\) | −1.38500e8 | −0.377047 | ||||||||
\(281\) | −9.61867e7 | −0.258608 | −0.129304 | − | 0.991605i | \(-0.541274\pi\) | ||||
−0.129304 | + | 0.991605i | \(0.541274\pi\) | |||||||
\(282\) | 2.17847e8 | 0.578469 | ||||||||
\(283\) | −3.04630e8 | −0.798950 | −0.399475 | − | 0.916744i | \(-0.630808\pi\) | ||||
−0.399475 | + | 0.916744i | \(0.630808\pi\) | |||||||
\(284\) | −2.18291e8 | −0.565486 | ||||||||
\(285\) | −8.28613e7 | −0.212029 | ||||||||
\(286\) | −2.38414e8 | −0.602630 | ||||||||
\(287\) | 3.18173e8 | 0.794468 | ||||||||
\(288\) | 4.21272e8 | 1.03917 | ||||||||
\(289\) | −4.03089e8 | −0.982332 | ||||||||
\(290\) | −8.56104e7 | −0.206126 | ||||||||
\(291\) | −6.95997e7 | −0.165570 | ||||||||
\(292\) | −9.44883e8 | −2.22095 | ||||||||
\(293\) | 5.54091e8 | 1.28690 | 0.643450 | − | 0.765488i | \(-0.277502\pi\) | ||||
0.643450 | + | 0.765488i | \(0.277502\pi\) | |||||||
\(294\) | −2.93143e8 | −0.672765 | ||||||||
\(295\) | −7.11117e7 | −0.161274 | ||||||||
\(296\) | −7.18261e8 | −1.60976 | ||||||||
\(297\) | −1.75208e7 | −0.0388067 | ||||||||
\(298\) | 1.30456e9 | 2.85566 | ||||||||
\(299\) | 1.51303e8 | 0.327340 | ||||||||
\(300\) | −6.81335e8 | −1.45692 | ||||||||
\(301\) | −4.26933e6 | −0.00902354 | ||||||||
\(302\) | 3.43636e8 | 0.717918 | ||||||||
\(303\) | 3.69518e8 | 0.763109 | ||||||||
\(304\) | −2.99654e9 | −6.11734 | ||||||||
\(305\) | 6.60495e7 | 0.133297 | ||||||||
\(306\) | −4.22764e7 | −0.0843477 | ||||||||
\(307\) | 6.73332e8 | 1.32814 | 0.664071 | − | 0.747669i | \(-0.268827\pi\) | ||||
0.664071 | + | 0.747669i | \(0.268827\pi\) | |||||||
\(308\) | 1.68985e8 | 0.329550 | ||||||||
\(309\) | 4.83238e8 | 0.931764 | ||||||||
\(310\) | 2.44333e8 | 0.465818 | ||||||||
\(311\) | −4.87910e8 | −0.919767 | −0.459884 | − | 0.887979i | \(-0.652109\pi\) | ||||
−0.459884 | + | 0.887979i | \(0.652109\pi\) | |||||||
\(312\) | 1.50331e9 | 2.80225 | ||||||||
\(313\) | −4.65266e8 | −0.857622 | −0.428811 | − | 0.903394i | \(-0.641067\pi\) | ||||
−0.428811 | + | 0.903394i | \(0.641067\pi\) | |||||||
\(314\) | −7.33731e8 | −1.33747 | ||||||||
\(315\) | −2.25506e7 | −0.0406509 | ||||||||
\(316\) | −2.71277e8 | −0.483625 | ||||||||
\(317\) | −4.54827e7 | −0.0801934 | −0.0400967 | − | 0.999196i | \(-0.512767\pi\) | ||||
−0.0400967 | + | 0.999196i | \(0.512767\pi\) | |||||||
\(318\) | 5.60288e7 | 0.0977049 | ||||||||
\(319\) | 6.46482e7 | 0.111504 | ||||||||
\(320\) | 3.06819e8 | 0.523428 | ||||||||
\(321\) | 5.54034e8 | 0.934909 | ||||||||
\(322\) | −1.48111e8 | −0.247225 | ||||||||
\(323\) | 1.50982e8 | 0.249297 | ||||||||
\(324\) | 1.78501e8 | 0.291564 | ||||||||
\(325\) | −9.34277e8 | −1.50968 | ||||||||
\(326\) | −1.59786e9 | −2.55434 | ||||||||
\(327\) | −5.39115e8 | −0.852636 | ||||||||
\(328\) | −2.52047e9 | −3.94388 | ||||||||
\(329\) | −2.11731e8 | −0.327793 | ||||||||
\(330\) | −2.83309e7 | −0.0433972 | ||||||||
\(331\) | 5.74770e8 | 0.871157 | 0.435578 | − | 0.900151i | \(-0.356544\pi\) | ||||
0.435578 | + | 0.900151i | \(0.356544\pi\) | |||||||
\(332\) | −1.48023e9 | −2.21996 | ||||||||
\(333\) | −1.16947e8 | −0.173555 | ||||||||
\(334\) | 2.26259e9 | 3.32272 | ||||||||
\(335\) | 2.09033e8 | 0.303779 | ||||||||
\(336\) | −8.15504e8 | −1.17284 | ||||||||
\(337\) | 6.94857e8 | 0.988987 | 0.494494 | − | 0.869181i | \(-0.335354\pi\) | ||||
0.494494 | + | 0.869181i | \(0.335354\pi\) | |||||||
\(338\) | 1.97921e9 | 2.78794 | ||||||||
\(339\) | 8.18932e8 | 1.14169 | ||||||||
\(340\) | −4.94974e7 | −0.0682977 | ||||||||
\(341\) | −1.84507e8 | −0.251983 | ||||||||
\(342\) | −8.80418e8 | −1.19014 | ||||||||
\(343\) | 7.50378e8 | 1.00404 | ||||||||
\(344\) | 3.38204e7 | 0.0447944 | ||||||||
\(345\) | 1.79795e7 | 0.0235727 | ||||||||
\(346\) | 1.92170e9 | 2.49413 | ||||||||
\(347\) | 1.21676e9 | 1.56334 | 0.781669 | − | 0.623694i | \(-0.214369\pi\) | ||||
0.781669 | + | 0.623694i | \(0.214369\pi\) | |||||||
\(348\) | −6.58633e8 | −0.837753 | ||||||||
\(349\) | −1.31017e9 | −1.64982 | −0.824912 | − | 0.565261i | \(-0.808775\pi\) | ||||
−0.824912 | + | 0.565261i | \(0.808775\pi\) | |||||||
\(350\) | 9.14565e8 | 1.14019 | ||||||||
\(351\) | 2.44769e8 | 0.302121 | ||||||||
\(352\) | −5.14396e8 | −0.628635 | ||||||||
\(353\) | −8.00528e8 | −0.968646 | −0.484323 | − | 0.874889i | \(-0.660934\pi\) | ||||
−0.484323 | + | 0.874889i | \(0.660934\pi\) | |||||||
\(354\) | −7.55577e8 | −0.905247 | ||||||||
\(355\) | −3.55697e7 | −0.0421969 | ||||||||
\(356\) | −4.30737e9 | −5.05985 | ||||||||
\(357\) | 4.10895e7 | 0.0477961 | ||||||||
\(358\) | 8.81490e8 | 1.01538 | ||||||||
\(359\) | 2.84701e7 | 0.0324757 | 0.0162378 | − | 0.999868i | \(-0.494831\pi\) | ||||
0.0162378 | + | 0.999868i | \(0.494831\pi\) | |||||||
\(360\) | 1.78639e8 | 0.201798 | ||||||||
\(361\) | 2.25037e9 | 2.51756 | ||||||||
\(362\) | 9.65615e8 | 1.06985 | ||||||||
\(363\) | −5.04760e8 | −0.553875 | ||||||||
\(364\) | −2.36076e9 | −2.56564 | ||||||||
\(365\) | −1.53965e8 | −0.165728 | ||||||||
\(366\) | 7.01790e8 | 0.748210 | ||||||||
\(367\) | −1.47636e8 | −0.155906 | −0.0779529 | − | 0.996957i | \(-0.524838\pi\) | ||||
−0.0779529 | + | 0.996957i | \(0.524838\pi\) | |||||||
\(368\) | 6.50198e8 | 0.680108 | ||||||||
\(369\) | −4.10384e8 | −0.425205 | ||||||||
\(370\) | −1.89102e8 | −0.194084 | ||||||||
\(371\) | −5.44558e7 | −0.0553650 | ||||||||
\(372\) | 1.87974e9 | 1.89321 | ||||||||
\(373\) | −1.17802e9 | −1.17537 | −0.587683 | − | 0.809091i | \(-0.699960\pi\) | ||||
−0.587683 | + | 0.809091i | \(0.699960\pi\) | |||||||
\(374\) | 5.16219e7 | 0.0510250 | ||||||||
\(375\) | −2.26468e8 | −0.221767 | ||||||||
\(376\) | 1.67727e9 | 1.62722 | ||||||||
\(377\) | −9.03147e8 | −0.868088 | ||||||||
\(378\) | −2.39605e8 | −0.228178 | ||||||||
\(379\) | −1.50793e9 | −1.42280 | −0.711399 | − | 0.702788i | \(-0.751938\pi\) | ||||
−0.711399 | + | 0.702788i | \(0.751938\pi\) | |||||||
\(380\) | −1.03080e9 | −0.963676 | ||||||||
\(381\) | 5.29111e8 | 0.490128 | ||||||||
\(382\) | 2.33638e9 | 2.14448 | ||||||||
\(383\) | −7.42514e7 | −0.0675319 | −0.0337659 | − | 0.999430i | \(-0.510750\pi\) | ||||
−0.0337659 | + | 0.999430i | \(0.510750\pi\) | |||||||
\(384\) | 1.26287e9 | 1.13815 | ||||||||
\(385\) | 2.75355e7 | 0.0245912 | ||||||||
\(386\) | 1.89814e8 | 0.167986 | ||||||||
\(387\) | 5.50665e6 | 0.00482946 | ||||||||
\(388\) | −8.65824e8 | −0.752521 | ||||||||
\(389\) | 1.56330e9 | 1.34654 | 0.673271 | − | 0.739396i | \(-0.264889\pi\) | ||||
0.673271 | + | 0.739396i | \(0.264889\pi\) | |||||||
\(390\) | 3.95787e8 | 0.337859 | ||||||||
\(391\) | −3.27605e7 | −0.0277161 | ||||||||
\(392\) | −2.25700e9 | −1.89247 | ||||||||
\(393\) | −4.03356e8 | −0.335208 | ||||||||
\(394\) | 2.24757e8 | 0.185130 | ||||||||
\(395\) | −4.42036e7 | −0.0360884 | ||||||||
\(396\) | −2.17960e8 | −0.176378 | ||||||||
\(397\) | −3.60628e8 | −0.289263 | −0.144631 | − | 0.989486i | \(-0.546200\pi\) | ||||
−0.144631 | + | 0.989486i | \(0.546200\pi\) | |||||||
\(398\) | −3.04194e9 | −2.41857 | ||||||||
\(399\) | 8.55701e8 | 0.674399 | ||||||||
\(400\) | −4.01488e9 | −3.13663 | ||||||||
\(401\) | −1.19634e9 | −0.926507 | −0.463253 | − | 0.886226i | \(-0.653318\pi\) | ||||
−0.463253 | + | 0.886226i | \(0.653318\pi\) | |||||||
\(402\) | 2.22102e9 | 1.70514 | ||||||||
\(403\) | 2.57759e9 | 1.96176 | ||||||||
\(404\) | 4.59682e9 | 3.46835 | ||||||||
\(405\) | 2.90860e7 | 0.0217567 | ||||||||
\(406\) | 8.84092e8 | 0.655626 | ||||||||
\(407\) | 1.42799e8 | 0.104990 | ||||||||
\(408\) | −3.25499e8 | −0.237268 | ||||||||
\(409\) | 6.44935e8 | 0.466106 | 0.233053 | − | 0.972464i | \(-0.425129\pi\) | ||||
0.233053 | + | 0.972464i | \(0.425129\pi\) | |||||||
\(410\) | −6.63584e8 | −0.475502 | ||||||||
\(411\) | 8.60688e8 | 0.611504 | ||||||||
\(412\) | 6.01150e9 | 4.23490 | ||||||||
\(413\) | 7.34365e8 | 0.512964 | ||||||||
\(414\) | 1.91036e8 | 0.132316 | ||||||||
\(415\) | −2.41197e8 | −0.165655 | ||||||||
\(416\) | 7.18620e9 | 4.89410 | ||||||||
\(417\) | 1.18607e9 | 0.801000 | ||||||||
\(418\) | 1.07504e9 | 0.719959 | ||||||||
\(419\) | −1.87982e9 | −1.24844 | −0.624218 | − | 0.781250i | \(-0.714582\pi\) | ||||
−0.624218 | + | 0.781250i | \(0.714582\pi\) | |||||||
\(420\) | −2.80530e8 | −0.184760 | ||||||||
\(421\) | 1.34590e9 | 0.879076 | 0.439538 | − | 0.898224i | \(-0.355142\pi\) | ||||
0.439538 | + | 0.898224i | \(0.355142\pi\) | |||||||
\(422\) | 1.14571e9 | 0.742130 | ||||||||
\(423\) | 2.73094e8 | 0.175437 | ||||||||
\(424\) | 4.31383e8 | 0.274841 | ||||||||
\(425\) | 2.02292e8 | 0.127825 | ||||||||
\(426\) | −3.77935e8 | −0.236856 | ||||||||
\(427\) | −6.82088e8 | −0.423978 | ||||||||
\(428\) | 6.89222e9 | 4.24919 | ||||||||
\(429\) | −2.98877e8 | −0.182764 | ||||||||
\(430\) | 8.90415e6 | 0.00540074 | ||||||||
\(431\) | −3.61149e8 | −0.217278 | −0.108639 | − | 0.994081i | \(-0.534649\pi\) | ||||
−0.108639 | + | 0.994081i | \(0.534649\pi\) | |||||||
\(432\) | 1.05185e9 | 0.627712 | ||||||||
\(433\) | −2.03487e9 | −1.20456 | −0.602281 | − | 0.798284i | \(-0.705741\pi\) | ||||
−0.602281 | + | 0.798284i | \(0.705741\pi\) | |||||||
\(434\) | −2.52321e9 | −1.48163 | ||||||||
\(435\) | −1.07322e8 | −0.0625136 | ||||||||
\(436\) | −6.70661e9 | −3.87526 | ||||||||
\(437\) | −6.82247e8 | −0.391072 | ||||||||
\(438\) | −1.63591e9 | −0.930251 | ||||||||
\(439\) | −2.51793e9 | −1.42043 | −0.710213 | − | 0.703987i | \(-0.751401\pi\) | ||||
−0.710213 | + | 0.703987i | \(0.751401\pi\) | |||||||
\(440\) | −2.18128e8 | −0.122075 | ||||||||
\(441\) | −3.67485e8 | −0.204035 | ||||||||
\(442\) | −7.21166e8 | −0.397244 | ||||||||
\(443\) | 8.85785e8 | 0.484078 | 0.242039 | − | 0.970267i | \(-0.422184\pi\) | ||||
0.242039 | + | 0.970267i | \(0.422184\pi\) | |||||||
\(444\) | −1.45483e9 | −0.788810 | ||||||||
\(445\) | −7.01869e8 | −0.377569 | ||||||||
\(446\) | −3.67672e9 | −1.96241 | ||||||||
\(447\) | 1.63540e9 | 0.866060 | ||||||||
\(448\) | −3.16849e9 | −1.66487 | ||||||||
\(449\) | −8.25873e8 | −0.430577 | −0.215289 | − | 0.976550i | \(-0.569069\pi\) | ||||
−0.215289 | + | 0.976550i | \(0.569069\pi\) | |||||||
\(450\) | −1.17962e9 | −0.610236 | ||||||||
\(451\) | 5.01102e8 | 0.257222 | ||||||||
\(452\) | 1.01876e10 | 5.18902 | ||||||||
\(453\) | 4.30784e8 | 0.217729 | ||||||||
\(454\) | −4.21978e9 | −2.11638 | ||||||||
\(455\) | −3.84676e8 | −0.191450 | ||||||||
\(456\) | −6.77861e9 | −3.34783 | ||||||||
\(457\) | −1.26103e9 | −0.618041 | −0.309021 | − | 0.951055i | \(-0.600001\pi\) | ||||
−0.309021 | + | 0.951055i | \(0.600001\pi\) | |||||||
\(458\) | −4.38566e9 | −2.13307 | ||||||||
\(459\) | −5.29979e7 | −0.0255808 | ||||||||
\(460\) | 2.23666e8 | 0.107139 | ||||||||
\(461\) | −2.91819e9 | −1.38727 | −0.693634 | − | 0.720328i | \(-0.743991\pi\) | ||||
−0.693634 | + | 0.720328i | \(0.743991\pi\) | |||||||
\(462\) | 2.92571e8 | 0.138033 | ||||||||
\(463\) | 8.59303e8 | 0.402358 | 0.201179 | − | 0.979554i | \(-0.435523\pi\) | ||||
0.201179 | + | 0.979554i | \(0.435523\pi\) | |||||||
\(464\) | −3.88111e9 | −1.80361 | ||||||||
\(465\) | 3.06297e8 | 0.141272 | ||||||||
\(466\) | 6.92307e8 | 0.316919 | ||||||||
\(467\) | 3.45880e9 | 1.57151 | 0.785754 | − | 0.618539i | \(-0.212275\pi\) | ||||
0.785754 | + | 0.618539i | \(0.212275\pi\) | |||||||
\(468\) | 3.04494e9 | 1.37315 | ||||||||
\(469\) | −2.15866e9 | −0.966229 | ||||||||
\(470\) | 4.41589e8 | 0.196189 | ||||||||
\(471\) | −9.19808e8 | −0.405624 | ||||||||
\(472\) | −5.81742e9 | −2.54644 | ||||||||
\(473\) | −6.72392e6 | −0.00292152 | ||||||||
\(474\) | −4.69672e8 | −0.202568 | ||||||||
\(475\) | 4.21278e9 | 1.80360 | ||||||||
\(476\) | 5.11156e8 | 0.217235 | ||||||||
\(477\) | 7.02379e7 | 0.0296317 | ||||||||
\(478\) | 9.55495e8 | 0.400157 | ||||||||
\(479\) | 2.91208e9 | 1.21068 | 0.605339 | − | 0.795968i | \(-0.293038\pi\) | ||||
0.605339 | + | 0.795968i | \(0.293038\pi\) | |||||||
\(480\) | 8.53941e8 | 0.352439 | ||||||||
\(481\) | −1.99493e9 | −0.817373 | ||||||||
\(482\) | 2.35093e9 | 0.956259 | ||||||||
\(483\) | −1.85673e8 | −0.0749778 | ||||||||
\(484\) | −6.27924e9 | −2.51738 | ||||||||
\(485\) | −1.41083e8 | −0.0561536 | ||||||||
\(486\) | 3.09045e8 | 0.122122 | ||||||||
\(487\) | 1.75754e9 | 0.689530 | 0.344765 | − | 0.938689i | \(-0.387959\pi\) | ||||
0.344765 | + | 0.938689i | \(0.387959\pi\) | |||||||
\(488\) | 5.40330e9 | 2.10470 | ||||||||
\(489\) | −2.00309e9 | −0.774674 | ||||||||
\(490\) | −5.94217e8 | −0.228170 | ||||||||
\(491\) | −9.74766e8 | −0.371634 | −0.185817 | − | 0.982584i | \(-0.559493\pi\) | ||||
−0.185817 | + | 0.982584i | \(0.559493\pi\) | |||||||
\(492\) | −5.10520e9 | −1.93257 | ||||||||
\(493\) | 1.95551e8 | 0.0735015 | ||||||||
\(494\) | −1.50185e10 | −5.60508 | ||||||||
\(495\) | −3.55157e7 | −0.0131614 | ||||||||
\(496\) | 1.10767e10 | 4.07592 | ||||||||
\(497\) | 3.67325e8 | 0.134216 | ||||||||
\(498\) | −2.56277e9 | −0.929839 | ||||||||
\(499\) | −4.71158e7 | −0.0169752 | −0.00848760 | − | 0.999964i | \(-0.502702\pi\) | ||||
−0.00848760 | + | 0.999964i | \(0.502702\pi\) | |||||||
\(500\) | −2.81727e9 | −1.00794 | ||||||||
\(501\) | 2.83639e9 | 1.00771 | ||||||||
\(502\) | −2.94512e9 | −1.03906 | ||||||||
\(503\) | 5.67881e7 | 0.0198962 | 0.00994809 | − | 0.999951i | \(-0.496833\pi\) | ||||
0.00994809 | + | 0.999951i | \(0.496833\pi\) | |||||||
\(504\) | −1.84479e9 | −0.641859 | ||||||||
\(505\) | 7.49034e8 | 0.258810 | ||||||||
\(506\) | −2.33265e8 | −0.0800430 | ||||||||
\(507\) | 2.48115e9 | 0.845522 | ||||||||
\(508\) | 6.58217e9 | 2.22764 | ||||||||
\(509\) | −4.54481e9 | −1.52758 | −0.763789 | − | 0.645466i | \(-0.776663\pi\) | ||||
−0.763789 | + | 0.645466i | \(0.776663\pi\) | |||||||
\(510\) | −8.56967e7 | −0.0286067 | ||||||||
\(511\) | 1.58998e9 | 0.527132 | ||||||||
\(512\) | 2.55330e8 | 0.0840730 | ||||||||
\(513\) | −1.10370e9 | −0.360943 | ||||||||
\(514\) | 9.29345e9 | 3.01860 | ||||||||
\(515\) | 9.79550e8 | 0.316010 | ||||||||
\(516\) | 6.85029e7 | 0.0219500 | ||||||||
\(517\) | −3.33463e8 | −0.106128 | ||||||||
\(518\) | 1.95284e9 | 0.617324 | ||||||||
\(519\) | 2.40905e9 | 0.756414 | ||||||||
\(520\) | 3.04729e9 | 0.950390 | ||||||||
\(521\) | −1.70629e7 | −0.00528593 | −0.00264297 | − | 0.999997i | \(-0.500841\pi\) | ||||
−0.00264297 | + | 0.999997i | \(0.500841\pi\) | |||||||
\(522\) | −1.14031e9 | −0.350895 | ||||||||
\(523\) | −1.82834e8 | −0.0558856 | −0.0279428 | − | 0.999610i | \(-0.508896\pi\) | ||||
−0.0279428 | + | 0.999610i | \(0.508896\pi\) | |||||||
\(524\) | −5.01776e9 | −1.52353 | ||||||||
\(525\) | 1.14650e9 | 0.345794 | ||||||||
\(526\) | 5.27483e9 | 1.58037 | ||||||||
\(527\) | −5.58105e8 | −0.166104 | ||||||||
\(528\) | −1.28437e9 | −0.379726 | ||||||||
\(529\) | 1.48036e8 | 0.0434783 | ||||||||
\(530\) | 1.13573e8 | 0.0331369 | ||||||||
\(531\) | −9.47194e8 | −0.274542 | ||||||||
\(532\) | 1.06450e10 | 3.06516 | ||||||||
\(533\) | −7.00048e9 | −2.00255 | ||||||||
\(534\) | −7.45751e9 | −2.11933 | ||||||||
\(535\) | 1.12306e9 | 0.317077 | ||||||||
\(536\) | 1.71003e10 | 4.79653 | ||||||||
\(537\) | 1.10504e9 | 0.307941 | ||||||||
\(538\) | −1.33696e10 | −3.70154 | ||||||||
\(539\) | 4.48720e8 | 0.123428 | ||||||||
\(540\) | 3.61832e8 | 0.0988846 | ||||||||
\(541\) | −1.96073e9 | −0.532387 | −0.266194 | − | 0.963920i | \(-0.585766\pi\) | ||||
−0.266194 | + | 0.963920i | \(0.585766\pi\) | |||||||
\(542\) | 1.78288e9 | 0.480978 | ||||||||
\(543\) | 1.21050e9 | 0.324463 | ||||||||
\(544\) | −1.55597e9 | −0.414386 | ||||||||
\(545\) | −1.09282e9 | −0.289174 | ||||||||
\(546\) | −4.08726e9 | −1.07463 | ||||||||
\(547\) | −2.88969e9 | −0.754910 | −0.377455 | − | 0.926028i | \(-0.623201\pi\) | ||||
−0.377455 | + | 0.926028i | \(0.623201\pi\) | |||||||
\(548\) | 1.07070e10 | 2.77930 | ||||||||
\(549\) | 8.79767e8 | 0.226916 | ||||||||
\(550\) | 1.44038e9 | 0.369154 | ||||||||
\(551\) | 4.07241e9 | 1.03710 | ||||||||
\(552\) | 1.47084e9 | 0.372203 | ||||||||
\(553\) | 4.56486e8 | 0.114786 | ||||||||
\(554\) | −1.13861e10 | −2.84505 | ||||||||
\(555\) | −2.37059e8 | −0.0588615 | ||||||||
\(556\) | 1.47547e10 | 3.64057 | ||||||||
\(557\) | 4.50918e9 | 1.10562 | 0.552808 | − | 0.833309i | \(-0.313556\pi\) | ||||
0.552808 | + | 0.833309i | \(0.313556\pi\) | |||||||
\(558\) | 3.25447e9 | 0.792977 | ||||||||
\(559\) | 9.39344e7 | 0.0227449 | ||||||||
\(560\) | −1.65307e9 | −0.397772 | ||||||||
\(561\) | 6.47134e7 | 0.0154748 | ||||||||
\(562\) | −2.07166e9 | −0.492313 | ||||||||
\(563\) | −2.34598e9 | −0.554046 | −0.277023 | − | 0.960863i | \(-0.589348\pi\) | ||||
−0.277023 | + | 0.960863i | \(0.589348\pi\) | |||||||
\(564\) | 3.39731e9 | 0.797366 | ||||||||
\(565\) | 1.66002e9 | 0.387208 | ||||||||
\(566\) | −6.56108e9 | −1.52096 | ||||||||
\(567\) | −3.00369e8 | −0.0692014 | ||||||||
\(568\) | −2.90984e9 | −0.666270 | ||||||||
\(569\) | 5.31334e9 | 1.20913 | 0.604567 | − | 0.796554i | \(-0.293346\pi\) | ||||
0.604567 | + | 0.796554i | \(0.293346\pi\) | |||||||
\(570\) | −1.78466e9 | −0.403639 | ||||||||
\(571\) | −6.82398e9 | −1.53395 | −0.766975 | − | 0.641677i | \(-0.778239\pi\) | ||||
−0.766975 | + | 0.641677i | \(0.778239\pi\) | |||||||
\(572\) | −3.71804e9 | −0.830669 | ||||||||
\(573\) | 2.92889e9 | 0.650373 | ||||||||
\(574\) | 6.85278e9 | 1.51243 | ||||||||
\(575\) | −9.14101e8 | −0.200520 | ||||||||
\(576\) | 4.08676e9 | 0.891048 | ||||||||
\(577\) | 2.32589e9 | 0.504050 | 0.252025 | − | 0.967721i | \(-0.418903\pi\) | ||||
0.252025 | + | 0.967721i | \(0.418903\pi\) | |||||||
\(578\) | −8.68169e9 | −1.87006 | ||||||||
\(579\) | 2.37951e8 | 0.0509464 | ||||||||
\(580\) | −1.33509e9 | −0.284126 | ||||||||
\(581\) | 2.49083e9 | 0.526898 | ||||||||
\(582\) | −1.49903e9 | −0.315196 | ||||||||
\(583\) | −8.57644e7 | −0.0179253 | ||||||||
\(584\) | −1.25954e10 | −2.61677 | ||||||||
\(585\) | 4.96160e8 | 0.102465 | ||||||||
\(586\) | 1.19340e10 | 2.44987 | ||||||||
\(587\) | −2.10001e8 | −0.0428536 | −0.0214268 | − | 0.999770i | \(-0.506821\pi\) | ||||
−0.0214268 | + | 0.999770i | \(0.506821\pi\) | |||||||
\(588\) | −4.57153e9 | −0.927344 | ||||||||
\(589\) | −1.16227e10 | −2.34371 | ||||||||
\(590\) | −1.53160e9 | −0.307017 | ||||||||
\(591\) | 2.81757e8 | 0.0561459 | ||||||||
\(592\) | −8.57285e9 | −1.69824 | ||||||||
\(593\) | −6.51352e7 | −0.0128270 | −0.00641348 | − | 0.999979i | \(-0.502041\pi\) | ||||
−0.00641348 | + | 0.999979i | \(0.502041\pi\) | |||||||
\(594\) | −3.77362e8 | −0.0738763 | ||||||||
\(595\) | 8.32908e7 | 0.0162102 | ||||||||
\(596\) | 2.03445e10 | 3.93627 | ||||||||
\(597\) | −3.81338e9 | −0.733500 | ||||||||
\(598\) | 3.25876e9 | 0.623157 | ||||||||
\(599\) | −2.77059e7 | −0.00526718 | −0.00263359 | − | 0.999997i | \(-0.500838\pi\) | ||||
−0.00263359 | + | 0.999997i | \(0.500838\pi\) | |||||||
\(600\) | −9.08225e9 | −1.71658 | ||||||||
\(601\) | 6.25558e8 | 0.117546 | 0.0587729 | − | 0.998271i | \(-0.481281\pi\) | ||||
0.0587729 | + | 0.998271i | \(0.481281\pi\) | |||||||
\(602\) | −9.19525e7 | −0.0171781 | ||||||||
\(603\) | 2.78428e9 | 0.517132 | ||||||||
\(604\) | 5.35897e9 | 0.989583 | ||||||||
\(605\) | −1.02318e9 | −0.187848 | ||||||||
\(606\) | 7.95865e9 | 1.45273 | ||||||||
\(607\) | 5.77739e9 | 1.04851 | 0.524253 | − | 0.851562i | \(-0.324344\pi\) | ||||
0.524253 | + | 0.851562i | \(0.324344\pi\) | |||||||
\(608\) | −3.24036e10 | −5.84696 | ||||||||
\(609\) | 1.10830e9 | 0.198837 | ||||||||
\(610\) | 1.42257e9 | 0.253757 | ||||||||
\(611\) | 4.65854e9 | 0.826239 | ||||||||
\(612\) | −6.59296e8 | −0.116265 | ||||||||
\(613\) | −3.43198e8 | −0.0601774 | −0.0300887 | − | 0.999547i | \(-0.509579\pi\) | ||||
−0.0300887 | + | 0.999547i | \(0.509579\pi\) | |||||||
\(614\) | 1.45022e10 | 2.52838 | ||||||||
\(615\) | −8.31872e8 | −0.144209 | ||||||||
\(616\) | 2.25259e9 | 0.388284 | ||||||||
\(617\) | 6.69767e9 | 1.14796 | 0.573978 | − | 0.818871i | \(-0.305399\pi\) | ||||
0.573978 | + | 0.818871i | \(0.305399\pi\) | |||||||
\(618\) | 1.04079e10 | 1.77380 | ||||||||
\(619\) | −9.34901e9 | −1.58434 | −0.792170 | − | 0.610301i | \(-0.791049\pi\) | ||||
−0.792170 | + | 0.610301i | \(0.791049\pi\) | |||||||
\(620\) | 3.81035e9 | 0.642087 | ||||||||
\(621\) | 2.39483e8 | 0.0401286 | ||||||||
\(622\) | −1.05085e10 | −1.75096 | ||||||||
\(623\) | 7.24814e9 | 1.20093 | ||||||||
\(624\) | 1.79428e10 | 2.95627 | ||||||||
\(625\) | 5.41043e9 | 0.886446 | ||||||||
\(626\) | −1.00209e10 | −1.63266 | ||||||||
\(627\) | 1.34767e9 | 0.218348 | ||||||||
\(628\) | −1.14425e10 | −1.84357 | ||||||||
\(629\) | 4.31947e8 | 0.0692075 | ||||||||
\(630\) | −4.85692e8 | −0.0773872 | ||||||||
\(631\) | 1.13983e10 | 1.80608 | 0.903038 | − | 0.429561i | \(-0.141332\pi\) | ||||
0.903038 | + | 0.429561i | \(0.141332\pi\) | |||||||
\(632\) | −3.61615e9 | −0.569819 | ||||||||
\(633\) | 1.43626e9 | 0.225072 | ||||||||
\(634\) | −9.79601e8 | −0.152664 | ||||||||
\(635\) | 1.07254e9 | 0.166228 | ||||||||
\(636\) | 8.73763e8 | 0.134677 | ||||||||
\(637\) | −6.26869e9 | −0.960924 | ||||||||
\(638\) | 1.39239e9 | 0.212270 | ||||||||
\(639\) | −4.73781e8 | −0.0718331 | ||||||||
\(640\) | 2.55992e9 | 0.386007 | ||||||||
\(641\) | −1.05373e10 | −1.58025 | −0.790124 | − | 0.612947i | \(-0.789984\pi\) | ||||
−0.790124 | + | 0.612947i | \(0.789984\pi\) | |||||||
\(642\) | 1.19327e10 | 1.77979 | ||||||||
\(643\) | 9.34452e9 | 1.38618 | 0.693089 | − | 0.720852i | \(-0.256249\pi\) | ||||
0.693089 | + | 0.720852i | \(0.256249\pi\) | |||||||
\(644\) | −2.30978e9 | −0.340776 | ||||||||
\(645\) | 1.11623e7 | 0.00163793 | ||||||||
\(646\) | 3.25184e9 | 0.474586 | ||||||||
\(647\) | −6.73299e9 | −0.977334 | −0.488667 | − | 0.872471i | \(-0.662517\pi\) | ||||
−0.488667 | + | 0.872471i | \(0.662517\pi\) | |||||||
\(648\) | 2.37944e9 | 0.343527 | ||||||||
\(649\) | 1.15658e9 | 0.166080 | ||||||||
\(650\) | −2.01224e10 | −2.87397 | ||||||||
\(651\) | −3.16310e9 | −0.449345 | ||||||||
\(652\) | −2.49185e10 | −3.52092 | ||||||||
\(653\) | 2.89741e9 | 0.407205 | 0.203603 | − | 0.979054i | \(-0.434735\pi\) | ||||
0.203603 | + | 0.979054i | \(0.434735\pi\) | |||||||
\(654\) | −1.16114e10 | −1.62316 | ||||||||
\(655\) | −8.17625e8 | −0.113687 | ||||||||
\(656\) | −3.00833e10 | −4.16065 | ||||||||
\(657\) | −2.05078e9 | −0.282125 | ||||||||
\(658\) | −4.56025e9 | −0.624020 | ||||||||
\(659\) | 4.09714e9 | 0.557675 | 0.278838 | − | 0.960338i | \(-0.410051\pi\) | ||||
0.278838 | + | 0.960338i | \(0.410051\pi\) | |||||||
\(660\) | −4.41817e8 | −0.0598189 | ||||||||
\(661\) | 1.19350e10 | 1.60738 | 0.803691 | − | 0.595047i | \(-0.202867\pi\) | ||||
0.803691 | + | 0.595047i | \(0.202867\pi\) | |||||||
\(662\) | 1.23793e10 | 1.65842 | ||||||||
\(663\) | −9.04057e8 | −0.120475 | ||||||||
\(664\) | −1.97316e10 | −2.61561 | ||||||||
\(665\) | 1.73456e9 | 0.228724 | ||||||||
\(666\) | −2.51880e9 | −0.330396 | ||||||||
\(667\) | −8.83643e8 | −0.115302 | ||||||||
\(668\) | 3.52849e10 | 4.58005 | ||||||||
\(669\) | −4.60915e9 | −0.595155 | ||||||||
\(670\) | 4.50213e9 | 0.578304 | ||||||||
\(671\) | −1.07424e9 | −0.137270 | ||||||||
\(672\) | −8.81858e9 | −1.12100 | ||||||||
\(673\) | −9.75181e9 | −1.23320 | −0.616599 | − | 0.787278i | \(-0.711490\pi\) | ||||
−0.616599 | + | 0.787278i | \(0.711490\pi\) | |||||||
\(674\) | 1.49658e10 | 1.88273 | ||||||||
\(675\) | −1.47878e9 | −0.185071 | ||||||||
\(676\) | 3.08656e10 | 3.84292 | ||||||||
\(677\) | −1.09587e10 | −1.35737 | −0.678684 | − | 0.734430i | \(-0.737449\pi\) | ||||
−0.678684 | + | 0.734430i | \(0.737449\pi\) | |||||||
\(678\) | 1.76381e10 | 2.17344 | ||||||||
\(679\) | 1.45695e9 | 0.178608 | ||||||||
\(680\) | −6.59805e8 | −0.0804701 | ||||||||
\(681\) | −5.28993e9 | −0.641852 | ||||||||
\(682\) | −3.97389e9 | −0.479701 | ||||||||
\(683\) | −5.39763e9 | −0.648233 | −0.324116 | − | 0.946017i | \(-0.605067\pi\) | ||||
−0.324116 | + | 0.946017i | \(0.605067\pi\) | |||||||
\(684\) | −1.37300e10 | −1.64050 | ||||||||
\(685\) | 1.74466e9 | 0.207393 | ||||||||
\(686\) | 1.61616e10 | 1.91139 | ||||||||
\(687\) | −5.49788e9 | −0.646914 | ||||||||
\(688\) | 4.03665e8 | 0.0472566 | ||||||||
\(689\) | 1.19814e9 | 0.139554 | ||||||||
\(690\) | 3.87240e8 | 0.0448754 | ||||||||
\(691\) | −1.91440e9 | −0.220729 | −0.110364 | − | 0.993891i | \(-0.535202\pi\) | ||||
−0.110364 | + | 0.993891i | \(0.535202\pi\) | |||||||
\(692\) | 2.99687e10 | 3.43792 | ||||||||
\(693\) | 3.66768e8 | 0.0418625 | ||||||||
\(694\) | 2.62065e10 | 2.97612 | ||||||||
\(695\) | 2.40422e9 | 0.271661 | ||||||||
\(696\) | −8.77963e9 | −0.987061 | ||||||||
\(697\) | 1.51576e9 | 0.169557 | ||||||||
\(698\) | −2.82183e10 | −3.14077 | ||||||||
\(699\) | 8.67879e8 | 0.0961145 | ||||||||
\(700\) | 1.42625e10 | 1.57164 | ||||||||
\(701\) | 1.00810e10 | 1.10532 | 0.552661 | − | 0.833406i | \(-0.313612\pi\) | ||||
0.552661 | + | 0.833406i | \(0.313612\pi\) | |||||||
\(702\) | 5.27181e9 | 0.575148 | ||||||||
\(703\) | 8.99542e9 | 0.976512 | ||||||||
\(704\) | −4.99017e9 | −0.539027 | ||||||||
\(705\) | 5.53578e8 | 0.0594999 | ||||||||
\(706\) | −1.72417e10 | −1.84401 | ||||||||
\(707\) | −7.73521e9 | −0.823198 | ||||||||
\(708\) | −1.17831e10 | −1.24780 | ||||||||
\(709\) | −1.08851e9 | −0.114702 | −0.0573509 | − | 0.998354i | \(-0.518265\pi\) | ||||
−0.0573509 | + | 0.998354i | \(0.518265\pi\) | |||||||
\(710\) | −7.66097e8 | −0.0803303 | ||||||||
\(711\) | −5.88783e8 | −0.0614344 | ||||||||
\(712\) | −5.74177e10 | −5.96164 | ||||||||
\(713\) | 2.52193e9 | 0.260567 | ||||||||
\(714\) | 8.84982e8 | 0.0909894 | ||||||||
\(715\) | −6.05840e8 | −0.0619850 | ||||||||
\(716\) | 1.37467e10 | 1.39960 | ||||||||
\(717\) | 1.19781e9 | 0.121359 | ||||||||
\(718\) | 6.13186e8 | 0.0618240 | ||||||||
\(719\) | 1.83367e10 | 1.83980 | 0.919899 | − | 0.392156i | \(-0.128271\pi\) | ||||
0.919899 | + | 0.392156i | \(0.128271\pi\) | |||||||
\(720\) | 2.13216e9 | 0.212890 | ||||||||
\(721\) | −1.01157e10 | −1.00513 | ||||||||
\(722\) | 4.84683e10 | 4.79267 | ||||||||
\(723\) | 2.94714e9 | 0.290012 | ||||||||
\(724\) | 1.50587e10 | 1.47469 | ||||||||
\(725\) | 5.45638e9 | 0.531767 | ||||||||
\(726\) | −1.08715e10 | −1.05441 | ||||||||
\(727\) | 1.27508e9 | 0.123074 | 0.0615369 | − | 0.998105i | \(-0.480400\pi\) | ||||
0.0615369 | + | 0.998105i | \(0.480400\pi\) | |||||||
\(728\) | −3.14691e10 | −3.02290 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −3.31608e9 | −0.315497 | ||||||||
\(731\) | −2.03389e7 | −0.00192582 | ||||||||
\(732\) | 1.09443e10 | 1.03134 | ||||||||
\(733\) | −1.44780e10 | −1.35782 | −0.678912 | − | 0.734220i | \(-0.737548\pi\) | ||||
−0.678912 | + | 0.734220i | \(0.737548\pi\) | |||||||
\(734\) | −3.17978e9 | −0.296798 | ||||||||
\(735\) | −7.44913e8 | −0.0691990 | ||||||||
\(736\) | 7.03102e9 | 0.650049 | ||||||||
\(737\) | −3.39976e9 | −0.312832 | ||||||||
\(738\) | −8.83881e9 | −0.809462 | ||||||||
\(739\) | −1.82585e9 | −0.166422 | −0.0832109 | − | 0.996532i | \(-0.526518\pi\) | ||||
−0.0832109 | + | 0.996532i | \(0.526518\pi\) | |||||||
\(740\) | −2.94903e9 | −0.267527 | ||||||||
\(741\) | −1.88272e10 | −1.69990 | ||||||||
\(742\) | −1.17286e9 | −0.105398 | ||||||||
\(743\) | −1.29792e9 | −0.116088 | −0.0580439 | − | 0.998314i | \(-0.518486\pi\) | ||||
−0.0580439 | + | 0.998314i | \(0.518486\pi\) | |||||||
\(744\) | 2.50572e10 | 2.23062 | ||||||||
\(745\) | 3.31505e9 | 0.293727 | ||||||||
\(746\) | −2.53722e10 | −2.23754 | ||||||||
\(747\) | −3.21270e9 | −0.282000 | ||||||||
\(748\) | 8.05037e8 | 0.0703332 | ||||||||
\(749\) | −1.15977e10 | −1.00853 | ||||||||
\(750\) | −4.87765e9 | −0.422178 | ||||||||
\(751\) | −1.52504e10 | −1.31383 | −0.656917 | − | 0.753963i | \(-0.728140\pi\) | ||||
−0.656917 | + | 0.753963i | \(0.728140\pi\) | |||||||
\(752\) | 2.00192e10 | 1.71666 | ||||||||
\(753\) | −3.69201e9 | −0.315123 | ||||||||
\(754\) | −1.94519e10 | −1.65258 | ||||||||
\(755\) | 8.73224e8 | 0.0738433 | ||||||||
\(756\) | −3.73661e9 | −0.314522 | ||||||||
\(757\) | −1.60955e9 | −0.134856 | −0.0674280 | − | 0.997724i | \(-0.521479\pi\) | ||||
−0.0674280 | + | 0.997724i | \(0.521479\pi\) | |||||||
\(758\) | −3.24776e10 | −2.70858 | ||||||||
\(759\) | −2.92422e8 | −0.0242753 | ||||||||
\(760\) | −1.37406e10 | −1.13543 | ||||||||
\(761\) | −1.60947e9 | −0.132384 | −0.0661920 | − | 0.997807i | \(-0.521085\pi\) | ||||
−0.0661920 | + | 0.997807i | \(0.521085\pi\) | |||||||
\(762\) | 1.13959e10 | 0.933056 | ||||||||
\(763\) | 1.12854e10 | 0.919775 | ||||||||
\(764\) | 3.64356e10 | 2.95596 | ||||||||
\(765\) | −1.07430e8 | −0.00867579 | ||||||||
\(766\) | −1.59922e9 | −0.128560 | ||||||||
\(767\) | −1.61576e10 | −1.29298 | ||||||||
\(768\) | 7.82535e9 | 0.623361 | ||||||||
\(769\) | −1.07804e10 | −0.854855 | −0.427428 | − | 0.904050i | \(-0.640580\pi\) | ||||
−0.427428 | + | 0.904050i | \(0.640580\pi\) | |||||||
\(770\) | 5.93057e8 | 0.0468144 | ||||||||
\(771\) | 1.16503e10 | 0.915476 | ||||||||
\(772\) | 2.96013e9 | 0.231553 | ||||||||
\(773\) | −2.94937e9 | −0.229668 | −0.114834 | − | 0.993385i | \(-0.536634\pi\) | ||||
−0.114834 | + | 0.993385i | \(0.536634\pi\) | |||||||
\(774\) | 1.18602e8 | 0.00919385 | ||||||||
\(775\) | −1.55726e10 | −1.20172 | ||||||||
\(776\) | −1.15415e10 | −0.886638 | ||||||||
\(777\) | 2.44809e9 | 0.187221 | ||||||||
\(778\) | 3.36703e10 | 2.56341 | ||||||||
\(779\) | 3.15661e10 | 2.39243 | ||||||||
\(780\) | 6.17226e9 | 0.465707 | ||||||||
\(781\) | 5.78514e8 | 0.0434545 | ||||||||
\(782\) | −7.05593e8 | −0.0527631 | ||||||||
\(783\) | −1.42950e9 | −0.106419 | ||||||||
\(784\) | −2.69385e10 | −1.99649 | ||||||||
\(785\) | −1.86450e9 | −0.137569 | ||||||||
\(786\) | −8.68743e9 | −0.638135 | ||||||||
\(787\) | −1.46253e10 | −1.06953 | −0.534765 | − | 0.845001i | \(-0.679600\pi\) | ||||
−0.534765 | + | 0.845001i | \(0.679600\pi\) | |||||||
\(788\) | 3.50507e9 | 0.255185 | ||||||||
\(789\) | 6.61255e9 | 0.479291 | ||||||||
\(790\) | −9.52052e8 | −0.0687014 | ||||||||
\(791\) | −1.71429e10 | −1.23159 | ||||||||
\(792\) | −2.90542e9 | −0.207812 | ||||||||
\(793\) | 1.50074e10 | 1.06868 | ||||||||
\(794\) | −7.76717e9 | −0.550669 | ||||||||
\(795\) | 1.42376e8 | 0.0100497 | ||||||||
\(796\) | −4.74387e10 | −3.33378 | ||||||||
\(797\) | 4.11710e9 | 0.288063 | 0.144031 | − | 0.989573i | \(-0.453993\pi\) | ||||
0.144031 | + | 0.989573i | \(0.453993\pi\) | |||||||
\(798\) | 1.84300e10 | 1.28385 | ||||||||
\(799\) | −1.00868e9 | −0.0699582 | ||||||||
\(800\) | −4.34156e10 | −2.99799 | ||||||||
\(801\) | −9.34876e9 | −0.642747 | ||||||||
\(802\) | −2.57666e10 | −1.76379 | ||||||||
\(803\) | 2.50412e9 | 0.170668 | ||||||||
\(804\) | 3.46365e10 | 2.35038 | ||||||||
\(805\) | −3.76369e8 | −0.0254289 | ||||||||
\(806\) | 5.55159e10 | 3.73461 | ||||||||
\(807\) | −1.67602e10 | −1.12259 | ||||||||
\(808\) | 6.12761e10 | 4.08650 | ||||||||
\(809\) | −9.51685e9 | −0.631936 | −0.315968 | − | 0.948770i | \(-0.602329\pi\) | ||||
−0.315968 | + | 0.948770i | \(0.602329\pi\) | |||||||
\(810\) | 6.26453e8 | 0.0414181 | ||||||||
\(811\) | −1.01219e10 | −0.666327 | −0.333164 | − | 0.942869i | \(-0.608116\pi\) | ||||
−0.333164 | + | 0.942869i | \(0.608116\pi\) | |||||||
\(812\) | 1.37873e10 | 0.903719 | ||||||||
\(813\) | 2.23503e9 | 0.145870 | ||||||||
\(814\) | 3.07560e9 | 0.199869 | ||||||||
\(815\) | −4.06037e9 | −0.262733 | ||||||||
\(816\) | −3.88502e9 | −0.250309 | ||||||||
\(817\) | −4.23563e8 | −0.0271732 | ||||||||
\(818\) | 1.38905e10 | 0.887325 | ||||||||
\(819\) | −5.12381e9 | −0.325911 | ||||||||
\(820\) | −1.03485e10 | −0.655436 | ||||||||
\(821\) | 2.18569e10 | 1.37844 | 0.689218 | − | 0.724554i | \(-0.257954\pi\) | ||||
0.689218 | + | 0.724554i | \(0.257954\pi\) | |||||||
\(822\) | 1.85374e10 | 1.16412 | ||||||||
\(823\) | −3.86655e9 | −0.241782 | −0.120891 | − | 0.992666i | \(-0.538575\pi\) | ||||
−0.120891 | + | 0.992666i | \(0.538575\pi\) | |||||||
\(824\) | 8.01338e10 | 4.98966 | ||||||||
\(825\) | 1.80567e9 | 0.111956 | ||||||||
\(826\) | 1.58167e10 | 0.976529 | ||||||||
\(827\) | 1.12726e10 | 0.693035 | 0.346518 | − | 0.938044i | \(-0.387364\pi\) | ||||
0.346518 | + | 0.938044i | \(0.387364\pi\) | |||||||
\(828\) | 2.97918e9 | 0.182386 | ||||||||
\(829\) | −1.59797e10 | −0.974154 | −0.487077 | − | 0.873359i | \(-0.661937\pi\) | ||||
−0.487077 | + | 0.873359i | \(0.661937\pi\) | |||||||
\(830\) | −5.19489e9 | −0.315357 | ||||||||
\(831\) | −1.42736e10 | −0.862840 | ||||||||
\(832\) | 6.97135e10 | 4.19648 | ||||||||
\(833\) | 1.35731e9 | 0.0813620 | ||||||||
\(834\) | 2.55454e10 | 1.52486 | ||||||||
\(835\) | 5.74953e9 | 0.341766 | ||||||||
\(836\) | 1.67651e10 | 0.992396 | ||||||||
\(837\) | 4.07981e9 | 0.240492 | ||||||||
\(838\) | −4.04873e10 | −2.37665 | ||||||||
\(839\) | 2.40926e9 | 0.140837 | 0.0704186 | − | 0.997518i | \(-0.477567\pi\) | ||||
0.0704186 | + | 0.997518i | \(0.477567\pi\) | |||||||
\(840\) | −3.73949e9 | −0.217688 | ||||||||
\(841\) | −1.19753e10 | −0.694226 | ||||||||
\(842\) | 2.89879e10 | 1.67350 | ||||||||
\(843\) | −2.59704e9 | −0.149308 | ||||||||
\(844\) | 1.78672e10 | 1.02296 | ||||||||
\(845\) | 5.02943e9 | 0.286761 | ||||||||
\(846\) | 5.88188e9 | 0.333979 | ||||||||
\(847\) | 1.05663e10 | 0.597488 | ||||||||
\(848\) | 5.14880e9 | 0.289948 | ||||||||
\(849\) | −8.22500e9 | −0.461274 | ||||||||
\(850\) | 4.35694e9 | 0.243341 | ||||||||
\(851\) | −1.95185e9 | −0.108566 | ||||||||
\(852\) | −5.89386e9 | −0.326484 | ||||||||
\(853\) | 1.71764e10 | 0.947570 | 0.473785 | − | 0.880640i | \(-0.342887\pi\) | ||||
0.473785 | + | 0.880640i | \(0.342887\pi\) | |||||||
\(854\) | −1.46907e10 | −0.807126 | ||||||||
\(855\) | −2.23725e9 | −0.122415 | ||||||||
\(856\) | 9.18738e10 | 5.00649 | ||||||||
\(857\) | −4.41092e9 | −0.239385 | −0.119692 | − | 0.992811i | \(-0.538191\pi\) | ||||
−0.119692 | + | 0.992811i | \(0.538191\pi\) | |||||||
\(858\) | −6.43717e9 | −0.347928 | ||||||||
\(859\) | 2.39855e10 | 1.29114 | 0.645570 | − | 0.763701i | \(-0.276620\pi\) | ||||
0.645570 | + | 0.763701i | \(0.276620\pi\) | |||||||
\(860\) | 1.38859e8 | 0.00744441 | ||||||||
\(861\) | 8.59067e9 | 0.458687 | ||||||||
\(862\) | −7.77839e9 | −0.413632 | ||||||||
\(863\) | −1.76729e10 | −0.935985 | −0.467993 | − | 0.883732i | \(-0.655023\pi\) | ||||
−0.467993 | + | 0.883732i | \(0.655023\pi\) | |||||||
\(864\) | 1.13743e10 | 0.599968 | ||||||||
\(865\) | 4.88327e9 | 0.256540 | ||||||||
\(866\) | −4.38268e10 | −2.29312 | ||||||||
\(867\) | −1.08834e10 | −0.567150 | ||||||||
\(868\) | −3.93491e10 | −2.04228 | ||||||||
\(869\) | 7.18937e8 | 0.0371639 | ||||||||
\(870\) | −2.31148e9 | −0.119007 | ||||||||
\(871\) | 4.74952e10 | 2.43549 | ||||||||
\(872\) | −8.93997e10 | −4.56592 | ||||||||
\(873\) | −1.87919e9 | −0.0955920 | ||||||||
\(874\) | −1.46942e10 | −0.744483 | ||||||||
\(875\) | 4.74071e9 | 0.239230 | ||||||||
\(876\) | −2.55119e10 | −1.28226 | ||||||||
\(877\) | −1.28667e10 | −0.644122 | −0.322061 | − | 0.946719i | \(-0.604376\pi\) | ||||
−0.322061 | + | 0.946719i | \(0.604376\pi\) | |||||||
\(878\) | −5.42310e10 | −2.70407 | ||||||||
\(879\) | 1.49605e10 | 0.742992 | ||||||||
\(880\) | −2.60348e9 | −0.128785 | ||||||||
\(881\) | −4.58163e8 | −0.0225738 | −0.0112869 | − | 0.999936i | \(-0.503593\pi\) | ||||
−0.0112869 | + | 0.999936i | \(0.503593\pi\) | |||||||
\(882\) | −7.91486e9 | −0.388421 | ||||||||
\(883\) | −3.51665e9 | −0.171897 | −0.0859483 | − | 0.996300i | \(-0.527392\pi\) | ||||
−0.0859483 | + | 0.996300i | \(0.527392\pi\) | |||||||
\(884\) | −1.12465e10 | −0.547564 | ||||||||
\(885\) | −1.92002e9 | −0.0931115 | ||||||||
\(886\) | 1.90780e10 | 0.921539 | ||||||||
\(887\) | −8.81338e9 | −0.424043 | −0.212021 | − | 0.977265i | \(-0.568005\pi\) | ||||
−0.212021 | + | 0.977265i | \(0.568005\pi\) | |||||||
\(888\) | −1.93930e10 | −0.929396 | ||||||||
\(889\) | −1.10760e10 | −0.528722 | ||||||||
\(890\) | −1.51168e10 | −0.718778 | ||||||||
\(891\) | −4.73062e8 | −0.0224051 | ||||||||
\(892\) | −5.73381e10 | −2.70499 | ||||||||
\(893\) | −2.10060e10 | −0.987104 | ||||||||
\(894\) | 3.52231e10 | 1.64872 | ||||||||
\(895\) | 2.23998e9 | 0.104439 | ||||||||
\(896\) | −2.64360e10 | −1.22777 | ||||||||
\(897\) | 4.08519e9 | 0.188990 | ||||||||
\(898\) | −1.77876e10 | −0.819690 | ||||||||
\(899\) | −1.50537e10 | −0.691009 | ||||||||
\(900\) | −1.83960e10 | −0.841154 | ||||||||
\(901\) | −2.59424e8 | −0.0118161 | ||||||||
\(902\) | 1.07927e10 | 0.489674 | ||||||||
\(903\) | −1.15272e8 | −0.00520975 | ||||||||
\(904\) | 1.35801e11 | 6.11383 | ||||||||
\(905\) | 2.45375e9 | 0.110042 | ||||||||
\(906\) | 9.27818e9 | 0.414490 | ||||||||
\(907\) | 2.98196e10 | 1.32701 | 0.663507 | − | 0.748170i | \(-0.269067\pi\) | ||||
0.663507 | + | 0.748170i | \(0.269067\pi\) | |||||||
\(908\) | −6.58070e10 | −2.91724 | ||||||||
\(909\) | 9.97699e9 | 0.440581 | ||||||||
\(910\) | −8.28511e9 | −0.364463 | ||||||||
\(911\) | −1.93274e10 | −0.846951 | −0.423475 | − | 0.905908i | \(-0.639190\pi\) | ||||
−0.423475 | + | 0.905908i | \(0.639190\pi\) | |||||||
\(912\) | −8.09066e10 | −3.53185 | ||||||||
\(913\) | 3.92289e9 | 0.170592 | ||||||||
\(914\) | −2.71599e10 | −1.17656 | ||||||||
\(915\) | 1.78334e9 | 0.0769591 | ||||||||
\(916\) | −6.83939e10 | −2.94024 | ||||||||
\(917\) | 8.44354e9 | 0.361603 | ||||||||
\(918\) | −1.14146e9 | −0.0486981 | ||||||||
\(919\) | 1.92553e9 | 0.0818361 | 0.0409180 | − | 0.999163i | \(-0.486972\pi\) | ||||
0.0409180 | + | 0.999163i | \(0.486972\pi\) | |||||||
\(920\) | 2.98148e9 | 0.126234 | ||||||||
\(921\) | 1.81800e10 | 0.766803 | ||||||||
\(922\) | −6.28517e10 | −2.64094 | ||||||||
\(923\) | −8.08193e9 | −0.338306 | ||||||||
\(924\) | 4.56261e9 | 0.190266 | ||||||||
\(925\) | 1.20524e10 | 0.500701 | ||||||||
\(926\) | 1.85076e10 | 0.765969 | ||||||||
\(927\) | 1.30474e10 | 0.537954 | ||||||||
\(928\) | −4.19690e10 | −1.72389 | ||||||||
\(929\) | −2.99271e10 | −1.22464 | −0.612321 | − | 0.790609i | \(-0.709764\pi\) | ||||
−0.612321 | + | 0.790609i | \(0.709764\pi\) | |||||||
\(930\) | 6.59699e9 | 0.268940 | ||||||||
\(931\) | 2.82664e10 | 1.14801 | ||||||||
\(932\) | 1.07965e10 | 0.436843 | ||||||||
\(933\) | −1.31736e10 | −0.531028 | ||||||||
\(934\) | 7.44954e10 | 2.99168 | ||||||||
\(935\) | 1.31178e8 | 0.00524831 | ||||||||
\(936\) | 4.05893e10 | 1.61788 | ||||||||
\(937\) | −6.02696e9 | −0.239337 | −0.119668 | − | 0.992814i | \(-0.538183\pi\) | ||||
−0.119668 | + | 0.992814i | \(0.538183\pi\) | |||||||
\(938\) | −4.64931e10 | −1.83941 | ||||||||
\(939\) | −1.25622e10 | −0.495149 | ||||||||
\(940\) | 6.88653e9 | 0.270429 | ||||||||
\(941\) | 1.83486e10 | 0.717860 | 0.358930 | − | 0.933364i | \(-0.383142\pi\) | ||||
0.358930 | + | 0.933364i | \(0.383142\pi\) | |||||||
\(942\) | −1.98107e10 | −0.772187 | ||||||||
\(943\) | −6.84930e9 | −0.265984 | ||||||||
\(944\) | −6.94342e10 | −2.68641 | ||||||||
\(945\) | −6.08865e8 | −0.0234698 | ||||||||
\(946\) | −1.44819e8 | −0.00556170 | ||||||||
\(947\) | 1.62700e10 | 0.622533 | 0.311267 | − | 0.950323i | \(-0.399247\pi\) | ||||
0.311267 | + | 0.950323i | \(0.399247\pi\) | |||||||
\(948\) | −7.32449e9 | −0.279221 | ||||||||
\(949\) | −3.49830e10 | −1.32870 | ||||||||
\(950\) | 9.07345e10 | 3.43352 | ||||||||
\(951\) | −1.22803e9 | −0.0462997 | ||||||||
\(952\) | 6.81375e9 | 0.255951 | ||||||||
\(953\) | 4.87166e10 | 1.82327 | 0.911636 | − | 0.410998i | \(-0.134820\pi\) | ||||
0.911636 | + | 0.410998i | \(0.134820\pi\) | |||||||
\(954\) | 1.51278e9 | 0.0564099 | ||||||||
\(955\) | 5.93703e9 | 0.220576 | ||||||||
\(956\) | 1.49008e10 | 0.551580 | ||||||||
\(957\) | 1.74550e9 | 0.0643767 | ||||||||
\(958\) | 6.27200e10 | 2.30477 | ||||||||
\(959\) | −1.80170e10 | −0.659656 | ||||||||
\(960\) | 8.28410e9 | 0.302201 | ||||||||
\(961\) | 1.54507e10 | 0.561587 | ||||||||
\(962\) | −4.29667e10 | −1.55603 | ||||||||
\(963\) | 1.49589e10 | 0.539770 | ||||||||
\(964\) | 3.66625e10 | 1.31811 | ||||||||
\(965\) | 4.82341e8 | 0.0172786 | ||||||||
\(966\) | −3.99900e9 | −0.142735 | ||||||||
\(967\) | 3.96535e10 | 1.41023 | 0.705113 | − | 0.709095i | \(-0.250896\pi\) | ||||
0.705113 | + | 0.709095i | \(0.250896\pi\) | |||||||
\(968\) | −8.37028e10 | −2.96603 | ||||||||
\(969\) | 4.07651e9 | 0.143931 | ||||||||
\(970\) | −3.03862e9 | −0.106900 | ||||||||
\(971\) | 4.46486e10 | 1.56509 | 0.782547 | − | 0.622591i | \(-0.213920\pi\) | ||||
0.782547 | + | 0.622591i | \(0.213920\pi\) | |||||||
\(972\) | 4.81953e9 | 0.168334 | ||||||||
\(973\) | −2.48282e10 | −0.864073 | ||||||||
\(974\) | 3.78536e10 | 1.31266 | ||||||||
\(975\) | −2.52255e10 | −0.871612 | ||||||||
\(976\) | 6.44915e10 | 2.22038 | ||||||||
\(977\) | 2.37557e10 | 0.814962 | 0.407481 | − | 0.913214i | \(-0.366407\pi\) | ||||
0.407481 | + | 0.913214i | \(0.366407\pi\) | |||||||
\(978\) | −4.31423e10 | −1.47475 | ||||||||
\(979\) | 1.14154e10 | 0.388821 | ||||||||
\(980\) | −9.26675e9 | −0.314511 | ||||||||
\(981\) | −1.45561e10 | −0.492270 | ||||||||
\(982\) | −2.09944e10 | −0.707479 | ||||||||
\(983\) | 2.14111e10 | 0.718955 | 0.359477 | − | 0.933154i | \(-0.382955\pi\) | ||||
0.359477 | + | 0.933154i | \(0.382955\pi\) | |||||||
\(984\) | −6.80527e10 | −2.27700 | ||||||||
\(985\) | 5.71137e8 | 0.0190420 | ||||||||
\(986\) | 4.21176e9 | 0.139925 | ||||||||
\(987\) | −5.71675e9 | −0.189251 | ||||||||
\(988\) | −2.34212e11 | −7.72609 | ||||||||
\(989\) | 9.19058e7 | 0.00302104 | ||||||||
\(990\) | −7.64934e8 | −0.0250554 | ||||||||
\(991\) | 1.26347e10 | 0.412387 | 0.206194 | − | 0.978511i | \(-0.433892\pi\) | ||||
0.206194 | + | 0.978511i | \(0.433892\pi\) | |||||||
\(992\) | 1.19780e11 | 3.89577 | ||||||||
\(993\) | 1.55188e10 | 0.502963 | ||||||||
\(994\) | 7.91141e9 | 0.255506 | ||||||||
\(995\) | −7.72994e9 | −0.248769 | ||||||||
\(996\) | −3.99662e10 | −1.28170 | ||||||||
\(997\) | −6.85313e9 | −0.219006 | −0.109503 | − | 0.993986i | \(-0.534926\pi\) | ||||
−0.109503 | + | 0.993986i | \(0.534926\pi\) | |||||||
\(998\) | −1.01478e9 | −0.0323157 | ||||||||
\(999\) | −3.15758e9 | −0.100202 |
(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 | 69.8.a.d.1.8 | ✓ | 8 | |
3.2 | odd | 2 | 207.8.a.e.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.8.a.d.1.8 | ✓ | 8 | 1.1 | even | 1 | trivial | |
207.8.a.e.1.1 | 8 | 3.2 | odd | 2 |