Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,26,Mod(1,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.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: | \(63.3594847924\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{106705}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 26676 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7}\cdot 3\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 2) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(163.829\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.75788e6 | −1.90974 | −0.954868 | − | 0.297031i | \(-0.904004\pi\) | ||||
−0.954868 | + | 0.297031i | \(0.904004\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.37041e8 | −0.251030 | −0.125515 | − | 0.992092i | \(-0.540058\pi\) | ||||
−0.125515 | + | 0.992092i | \(0.540058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.04153e10 | 0.830552 | 0.415276 | − | 0.909696i | \(-0.363685\pi\) | ||||
0.415276 | + | 0.909696i | \(0.363685\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.24285e12 | 2.64709 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.58704e12 | −0.248539 | −0.124270 | − | 0.992248i | \(-0.539659\pi\) | ||||
−0.124270 | + | 0.992248i | \(0.539659\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.57327e13 | −1.13964 | −0.569821 | − | 0.821769i | \(-0.692988\pi\) | ||||
−0.569821 | + | 0.821769i | \(0.692988\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.40901e14 | 0.479400 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.64685e15 | −0.685555 | −0.342777 | − | 0.939417i | \(-0.611368\pi\) | ||||
−0.342777 | + | 0.939417i | \(0.611368\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.95030e15 | −0.513111 | −0.256555 | − | 0.966530i | \(-0.582588\pi\) | ||||
−0.256555 | + | 0.966530i | \(0.582588\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.34664e16 | −1.58613 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.07650e16 | 0.102427 | 0.0512136 | − | 0.998688i | \(-0.483691\pi\) | ||||
0.0512136 | + | 0.998688i | \(0.483691\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.79243e17 | −0.936984 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.45323e18 | −3.14551 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.36741e18 | −0.717668 | −0.358834 | − | 0.933401i | \(-0.616826\pi\) | ||||
−0.358834 | + | 0.933401i | \(0.616826\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.42000e18 | 1.00786 | 0.503931 | − | 0.863744i | \(-0.331887\pi\) | ||||
0.503931 | + | 0.863744i | \(0.331887\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.54771e18 | 0.474645 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.16814e18 | −0.208493 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.01944e19 | 0.254590 | 0.127295 | − | 0.991865i | \(-0.459371\pi\) | ||||
0.127295 | + | 0.991865i | \(0.459371\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.68287e20 | 2.17642 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.58687e20 | 1.09835 | 0.549177 | − | 0.835706i | \(-0.314941\pi\) | ||||
0.549177 | + | 0.835706i | \(0.314941\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.83575e20 | −0.700582 | −0.350291 | − | 0.936641i | \(-0.613917\pi\) | ||||
−0.350291 | + | 0.936641i | \(0.613917\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.07362e20 | −0.664499 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.40203e21 | −1.76009 | −0.880045 | − | 0.474890i | \(-0.842488\pi\) | ||||
−0.880045 | + | 0.474890i | \(0.842488\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.15978e20 | −0.310184 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.89496e21 | 1.30923 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.99903e21 | −0.558946 | −0.279473 | − | 0.960154i | \(-0.590160\pi\) | ||||
−0.279473 | + | 0.960154i | \(0.590160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.54531e20 | 0.0623908 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.70202e21 | 0.979906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.16691e21 | 0.304905 | 0.152452 | − | 0.988311i | \(-0.451283\pi\) | ||||
0.152452 | + | 0.988311i | \(0.451283\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.42128e22 | 1.65031 | 0.825156 | − | 0.564904i | \(-0.191087\pi\) | ||||
0.825156 | + | 0.564904i | \(0.191087\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.82170e22 | 2.19855 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.31193e22 | 0.286084 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.67051e22 | −1.29452 | −0.647261 | − | 0.762268i | \(-0.724086\pi\) | ||||
−0.647261 | + | 0.762268i | \(0.724086\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.89236e22 | −0.195609 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.13159e22 | 0.371127 | 0.185564 | − | 0.982632i | \(-0.440589\pi\) | ||||
0.185564 | + | 0.982632i | \(0.440589\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.49147e22 | 0.178432 | 0.0892159 | − | 0.996012i | \(-0.471564\pi\) | ||||
0.0892159 | + | 0.996012i | \(0.471564\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.90875e23 | 1.78939 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.86857e22 | −0.206425 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.91588e23 | −0.555176 | −0.277588 | − | 0.960700i | \(-0.589535\pi\) | ||||
−0.277588 | + | 0.960700i | \(0.589535\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.41214e24 | 3.36000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.64916e24 | 1.69351 | 0.846753 | − | 0.531986i | \(-0.178554\pi\) | ||||
0.846753 | + | 0.531986i | \(0.178554\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.25686e23 | 0.172095 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.40374e24 | 1.37056 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.74435e23 | 0.375277 | 0.187639 | − | 0.982238i | \(-0.439917\pi\) | ||||
0.187639 | + | 0.982238i | \(0.439917\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.91174e24 | −0.946532 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.76982e24 | −1.92475 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.78393e23 | 0.128806 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.00608e25 | 1.47227 | 0.736134 | − | 0.676835i | \(-0.236649\pi\) | ||||
0.736134 | + | 0.676835i | \(0.236649\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.80235e24 | −0.657907 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.42151e25 | −1.25526 | −0.627628 | − | 0.778513i | \(-0.715974\pi\) | ||||
−0.627628 | + | 0.778513i | \(0.715974\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.03211e25 | −0.713283 | −0.356642 | − | 0.934241i | \(-0.616078\pi\) | ||||
−0.356642 | + | 0.934241i | \(0.616078\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.32709e24 | 0.398167 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.74396e25 | 0.748582 | 0.374291 | − | 0.927311i | \(-0.377886\pi\) | ||||
0.374291 | + | 0.927311i | \(0.377886\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.65117e25 | −0.562292 | −0.281146 | − | 0.959665i | \(-0.590714\pi\) | ||||
−0.281146 | + | 0.959665i | \(0.590714\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.79205e25 | −0.486199 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.96039e25 | 1.51061 | 0.755306 | − | 0.655372i | \(-0.227488\pi\) | ||||
0.755306 | + | 0.655372i | \(0.227488\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.47524e24 | −0.0257123 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.14714e26 | −3.01674 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.00894e25 | −0.569389 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.01654e26 | −0.938228 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.78952e26 | −2.09757 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.91091e25 | 0.486241 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.18922e25 | 0.311953 | 0.155977 | − | 0.987761i | \(-0.450148\pi\) | ||||
0.155977 | + | 0.987761i | \(0.450148\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.22703e26 | 1.33793 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.39682e26 | 0.477805 | 0.238902 | − | 0.971044i | \(-0.423212\pi\) | ||||
0.238902 | + | 0.971044i | \(0.423212\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.50565e26 | −0.426165 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.36193e26 | 0.789616 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.92418e26 | −1.35320 | −0.676599 | − | 0.736352i | \(-0.736547\pi\) | ||||
−0.676599 | + | 0.736352i | \(0.736547\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.06682e26 | 1.31528 | 0.657639 | − | 0.753333i | \(-0.271555\pi\) | ||||
0.657639 | + | 0.753333i | \(0.271555\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.46460e27 | 3.36131 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.47665e26 | 0.283246 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.87391e26 | 0.180156 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.31239e26 | 0.592369 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.24039e26 | −0.290120 | −0.145060 | − | 0.989423i | \(-0.546337\pi\) | ||||
−0.145060 | + | 0.989423i | \(0.546337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.51382e27 | −1.45587 | −0.727934 | − | 0.685647i | \(-0.759519\pi\) | ||||
−0.727934 | + | 0.685647i | \(0.759519\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.69363e27 | −1.81473 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.05720e26 | −0.253003 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.75882e27 | 1.69338 | 0.846689 | − | 0.532088i | \(-0.178593\pi\) | ||||
0.846689 | + | 0.532088i | \(0.178593\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.51404e27 | 1.06744 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.27420e26 | 0.0850712 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.59899e26 | −0.169204 | −0.0846020 | − | 0.996415i | \(-0.526962\pi\) | ||||
−0.0846020 | + | 0.996415i | \(0.526962\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.23222e26 | −0.119150 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00207e28 | 1.64794 | 0.823970 | − | 0.566634i | \(-0.191755\pi\) | ||||
0.823970 | + | 0.566634i | \(0.191755\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.10835e27 | 0.298785 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.11028e28 | −1.35825 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.89989e27 | −0.835689 | −0.417845 | − | 0.908518i | \(-0.637214\pi\) | ||||
−0.417845 | + | 0.908518i | \(0.637214\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.49326e27 | −0.778214 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.32493e27 | −0.582288 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.08087e27 | 0.558207 | 0.279103 | − | 0.960261i | \(-0.409963\pi\) | ||||
0.279103 | + | 0.960261i | \(0.409963\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.80674e27 | 0.108621 | 0.0543104 | − | 0.998524i | \(-0.482704\pi\) | ||||
0.0543104 | + | 0.998524i | \(0.482704\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.01420e28 | −3.15166 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.39705e27 | −0.0639096 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.26047e27 | 0.170387 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.46157e28 | −2.61251 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.93091e28 | 1.51360 | 0.756798 | − | 0.653649i | \(-0.226763\pi\) | ||||
0.756798 | + | 0.653649i | \(0.226763\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.42443e28 | 0.383861 | 0.191931 | − | 0.981408i | \(-0.438525\pi\) | ||||
0.191931 | + | 0.981408i | \(0.438525\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.30621e28 | −0.546345 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.59073e28 | 0.748781 | 0.374390 | − | 0.927271i | \(-0.377852\pi\) | ||||
0.374390 | + | 0.927271i | \(0.377852\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.11996e28 | 1.49242 | 0.746209 | − | 0.665712i | \(-0.231872\pi\) | ||||
0.746209 | + | 0.665712i | \(0.231872\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.52417e29 | 2.47220 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.15902e28 | −0.596060 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.17466e28 | −0.275720 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.41443e28 | 0.271134 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.28066e28 | 0.127528 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.03285e29 | 0.913075 | 0.456537 | − | 0.889704i | \(-0.349089\pi\) | ||||
0.456537 | + | 0.889704i | \(0.349089\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.02072e28 | −0.708755 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.51573e28 | 0.175867 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.34436e29 | 0.837081 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.13758e28 | −0.340757 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.57657e29 | 0.781287 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.15542e29 | −0.511597 | −0.255799 | − | 0.966730i | \(-0.582338\pi\) | ||||
−0.255799 | + | 0.966730i | \(0.582338\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.26300e29 | −2.48028 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.01151e28 | 0.319502 | 0.159751 | − | 0.987157i | \(-0.448931\pi\) | ||||
0.159751 | + | 0.987157i | \(0.448931\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.69415e29 | 1.17374 | 0.586869 | − | 0.809682i | \(-0.300360\pi\) | ||||
0.586869 | + | 0.809682i | \(0.300360\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.38320e29 | 0.394217 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.10753e28 | 0.105107 | 0.0525536 | − | 0.998618i | \(-0.483264\pi\) | ||||
0.0525536 | + | 0.998618i | \(0.483264\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.92136e29 | 0.441835 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.12576e29 | 1.06024 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.49097e29 | 1.20875 | 0.604374 | − | 0.796701i | \(-0.293423\pi\) | ||||
0.604374 | + | 0.796701i | \(0.293423\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.68781e29 | 0.283212 | 0.141606 | − | 0.989923i | \(-0.454773\pi\) | ||||
0.141606 | + | 0.989923i | \(0.454773\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.16165e30 | −3.27121 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.70060e28 | 0.0778653 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.73905e29 | 0.584763 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.89903e30 | −3.23415 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.65029e29 | −0.267530 | −0.133765 | − | 0.991013i | \(-0.542707\pi\) | ||||
−0.133765 | + | 0.991013i | \(0.542707\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.78495e28 | −0.0254572 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.96728e29 | −0.328655 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.11592e30 | 0.838433 | 0.419217 | − | 0.907886i | \(-0.362305\pi\) | ||||
0.419217 | + | 0.907886i | \(0.362305\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.10066e29 | 0.211450 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.06689e30 | −1.89973 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.53721e30 | −0.865541 | −0.432770 | − | 0.901504i | \(-0.642464\pi\) | ||||
−0.432770 | + | 0.901504i | \(0.642464\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.73948e29 | 0.140312 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.53715e30 | −0.716681 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.34612e30 | 0.996431 | 0.498216 | − | 0.867053i | \(-0.333989\pi\) | ||||
0.498216 | + | 0.867053i | \(0.333989\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.54578e30 | 0.598454 | 0.299227 | − | 0.954182i | \(-0.403271\pi\) | ||||
0.299227 | + | 0.954182i | \(0.403271\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.11849e30 | 1.80763 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.22414e29 | 0.232877 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.21614e30 | −0.358085 | −0.179042 | − | 0.983841i | \(-0.557300\pi\) | ||||
−0.179042 | + | 0.983841i | \(0.557300\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.91339e30 | 2.66790 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.09885e30 | 1.25500 | 0.627499 | − | 0.778617i | \(-0.284079\pi\) | ||||
0.627499 | + | 0.778617i | \(0.284079\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.56288e30 | 0.352042 | 0.176021 | − | 0.984386i | \(-0.443677\pi\) | ||||
0.176021 | + | 0.984386i | \(0.443677\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.19253e30 | −0.245986 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.82651e30 | 0.912240 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.05852e30 | −0.530015 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.76857e31 | −2.81164 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.17112e30 | −0.608706 | −0.304353 | − | 0.952559i | \(-0.598440\pi\) | ||||
−0.304353 | + | 0.952559i | \(0.598440\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.71038e29 | −0.0765402 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.34661e30 | 0.781783 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.03056e30 | −0.116730 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.58350e30 | −0.581870 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.49884e31 | 2.39721 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.68856e30 | −0.414278 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.69994e30 | −0.626986 | −0.313493 | − | 0.949591i | \(-0.601499\pi\) | ||||
−0.313493 | + | 0.949591i | \(0.601499\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.81433e31 | 1.36218 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.54260e31 | −1.06843 | −0.534217 | − | 0.845347i | \(-0.679394\pi\) | ||||
−0.534217 | + | 0.845347i | \(0.679394\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.62517e31 | 1.03895 | 0.519476 | − | 0.854485i | \(-0.326127\pi\) | ||||
0.519476 | + | 0.854485i | \(0.326127\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.34852e30 | −0.551900 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.29098e31 | −1.24963 | −0.624814 | − | 0.780773i | \(-0.714825\pi\) | ||||
−0.624814 | + | 0.780773i | \(0.714825\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.53755e30 | 0.178369 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.06567e31 | −1.42959 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.15239e30 | 0.351765 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.67327e31 | 1.06783 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.90256e31 | 1.07383 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.26433e31 | −1.46185 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.45199e31 | −1.09703 | −0.548517 | − | 0.836140i | \(-0.684807\pi\) | ||||
−0.548517 | + | 0.836140i | \(0.684807\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.28645e31 | 0.673922 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.18821e31 | 0.324964 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.27735e31 | −1.33981 | −0.669904 | − | 0.742448i | \(-0.733665\pi\) | ||||
−0.669904 | + | 0.742448i | \(0.733665\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.22355e32 | −2.88487 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.14347e31 | −0.250493 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.34411e31 | −1.08818 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.59330e30 | 0.0491037 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.40093e30 | −0.0775222 | −0.0387611 | − | 0.999249i | \(-0.512341\pi\) | ||||
−0.0387611 | + | 0.999249i | \(0.512341\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.98069e31 | 0.488651 | 0.244326 | − | 0.969693i | \(-0.421433\pi\) | ||||
0.244326 | + | 0.969693i | \(0.421433\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.34854e32 | 3.58476 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.46084e31 | 0.634209 | 0.317105 | − | 0.948391i | \(-0.397289\pi\) | ||||
0.317105 | + | 0.948391i | \(0.397289\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.03238e30 | −0.0931640 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.80511e31 | 1.08738 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.38054e31 | −0.504483 | −0.252242 | − | 0.967664i | \(-0.581168\pi\) | ||||
−0.252242 | + | 0.967664i | \(0.581168\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.85711e31 | −0.736717 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.78696e32 | 1.79177 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.78474e30 | −0.0447917 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.76735e31 | 0.679121 | 0.339560 | − | 0.940584i | \(-0.389722\pi\) | ||||
0.339560 | + | 0.940584i | \(0.389722\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.55911e32 | 2.90744 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.08010e31 | −0.464234 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.37205e32 | −1.69342 | −0.846708 | − | 0.532058i | \(-0.821419\pi\) | ||||
−0.846708 | + | 0.532058i | \(0.821419\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.39064e32 | −0.928591 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.30906e32 | 0.817884 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.38944e32 | 0.812551 | 0.406276 | − | 0.913751i | \(-0.366827\pi\) | ||||
0.406276 | + | 0.913751i | \(0.366827\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.08799e32 | −0.595748 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.79085e31 | 0.194425 | 0.0972125 | − | 0.995264i | \(-0.469007\pi\) | ||||
0.0972125 | + | 0.995264i | \(0.469007\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.07832e31 | 0.0518188 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.11732e32 | −1.85450 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.20209e32 | −0.929963 | −0.464982 | − | 0.885320i | \(-0.653939\pi\) | ||||
−0.464982 | + | 0.885320i | \(0.653939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.77283e31 | −0.0702195 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.45545e32 | −0.912481 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.99595e31 | 0.139366 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.18941e32 | 0.716877 | 0.358439 | − | 0.933553i | \(-0.383309\pi\) | ||||
0.358439 | + | 0.933553i | \(0.383309\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.64675e32 | 0.813863 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.99036e32 | 0.863810 | 0.431905 | − | 0.901919i | \(-0.357842\pi\) | ||||
0.431905 | + | 0.901919i | \(0.357842\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.23138e32 | −1.14860 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.30562e32 | −0.843460 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.63734e31 | −0.0632755 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.12330e31 | 0.160746 | 0.0803730 | − | 0.996765i | \(-0.474389\pi\) | ||||
0.0803730 | + | 0.996765i | \(0.474389\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.21719e33 | 2.58425 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.26738e32 | 0.253239 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.26003e32 | −0.425121 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.41805e33 | −2.51183 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.94461e32 | −0.491307 | −0.245654 | − | 0.969358i | \(-0.579003\pi\) | ||||
−0.245654 | + | 0.969358i | \(0.579003\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.01892e33 | 1.60182 | 0.800908 | − | 0.598787i | \(-0.204350\pi\) | ||||
0.800908 | + | 0.598787i | \(0.204350\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.14455e33 | −4.65912 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.59871e32 | 0.642354 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.04059e33 | 1.37067 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.35365e32 | −0.540925 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.79497e32 | 0.796565 | 0.398283 | − | 0.917263i | \(-0.369606\pi\) | ||||
0.398283 | + | 0.917263i | \(0.369606\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.24164e32 | −0.801195 | −0.400597 | − | 0.916254i | \(-0.631197\pi\) | ||||
−0.400597 | + | 0.916254i | \(0.631197\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.29411e32 | −0.344050 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.32899e31 | −0.0525566 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.13459e32 | 0.850908 | 0.425454 | − | 0.904980i | \(-0.360114\pi\) | ||||
0.425454 | + | 0.904980i | \(0.360114\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.32976e32 | −0.821085 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.52555e32 | 0.293211 | 0.146605 | − | 0.989195i | \(-0.453165\pi\) | ||||
0.146605 | + | 0.989195i | \(0.453165\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.19833e32 | −0.0942058 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.45409e32 | 0.554052 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.70918e32 | 0.260735 | 0.130367 | − | 0.991466i | \(-0.458384\pi\) | ||||
0.130367 | + | 0.991466i | \(0.458384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.10530e32 | −0.272984 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.41899e33 | 2.78032 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.99028e32 | 0.237608 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.76958e33 | 0.997512 | 0.498756 | − | 0.866742i | \(-0.333790\pi\) | ||||
0.498756 | + | 0.866742i | \(0.333790\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.04009e33 | 2.15642 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.01018e32 | 0.354379 | 0.177189 | − | 0.984177i | \(-0.443299\pi\) | ||||
0.177189 | + | 0.984177i | \(0.443299\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.20521e32 | 0.440830 | 0.220415 | − | 0.975406i | \(-0.429259\pi\) | ||||
0.220415 | + | 0.975406i | \(0.429259\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.06478e33 | 0.483169 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.84600e33 | 0.793908 | 0.396954 | − | 0.917838i | \(-0.370067\pi\) | ||||
0.396954 | + | 0.917838i | \(0.370067\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.63716e33 | −1.07517 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.36543e33 | −3.23390 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.74918e32 | 0.174122 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.38234e33 | 0.480777 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.48351e33 | −1.47958 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.88481e32 | 0.121668 | 0.0608339 | − | 0.998148i | \(-0.480624\pi\) | ||||
0.0608339 | + | 0.998148i | \(0.480624\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.75939e32 | −0.290141 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.75566e32 | −0.162463 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.37875e33 | −0.369583 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.26102e33 | −1.08493 | −0.542465 | − | 0.840078i | \(-0.682509\pi\) | ||||
−0.542465 | + | 0.840078i | \(0.682509\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.33581e33 | 0.323135 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.52548e33 | 1.04027 | 0.520134 | − | 0.854084i | \(-0.325882\pi\) | ||||
0.520134 | + | 0.854084i | \(0.325882\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.25191e33 | 0.492000 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.95160e32 | 0.165154 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.56079e33 | 0.308241 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.45020e33 | −0.835840 | −0.417920 | − | 0.908484i | \(-0.637241\pi\) | ||||
−0.417920 | + | 0.908484i | \(0.637241\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.76151e34 | −3.14713 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.29032e33 | −0.389311 | −0.194656 | − | 0.980872i | \(-0.562359\pi\) | ||||
−0.194656 | + | 0.980872i | \(0.562359\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.94805e33 | 0.315107 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.70622e33 | −0.570600 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.35889e33 | 0.785421 | 0.392711 | − | 0.919662i | \(-0.371537\pi\) | ||||
0.392711 | + | 0.919662i | \(0.371537\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.06194e33 | 0.148197 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.21442e34 | 1.61400 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.41442e33 | 0.179055 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.62712e33 | 0.437452 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.38871e34 | 1.59595 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.14090e34 | −1.24961 | −0.624807 | − | 0.780779i | \(-0.714822\pi\) | ||||
−0.624807 | + | 0.780779i | \(0.714822\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.37717e34 | −1.43786 | −0.718928 | − | 0.695085i | \(-0.755367\pi\) | ||||
−0.718928 | + | 0.695085i | \(0.755367\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.49301e34 | 1.48618 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.27906e33 | −0.690944 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.09299e34 | −0.989509 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.34576e33 | 0.807111 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.51915e34 | −1.25173 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.38994e33 | −0.187916 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.42052e34 | −1.06603 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.07615e33 | 0.0770929 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.58682e34 | −1.08533 | −0.542667 | − | 0.839948i | \(-0.682585\pi\) | ||||
−0.542667 | + | 0.839948i | \(0.682585\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.17603e33 | −0.207437 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.26278e33 | 0.141152 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.29322e33 | 0.494176 | 0.247088 | − | 0.968993i | \(-0.420526\pi\) | ||||
0.247088 | + | 0.968993i | \(0.420526\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.67343e34 | 4.36853 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.76908e33 | 0.368243 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.86874e33 | −0.461103 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.45585e33 | 0.122050 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.56496e34 | 1.69381 | 0.846905 | − | 0.531744i | \(-0.178463\pi\) | ||||
0.846905 | + | 0.531744i | \(0.178463\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.75742e34 | 0.798413 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.48939e33 | −0.325395 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.62059e34 | −0.673471 | −0.336735 | − | 0.941599i | \(-0.609323\pi\) | ||||
−0.336735 | + | 0.941599i | \(0.609323\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.53858e33 | −0.379209 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.33659e34 | 2.79065 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.19926e34 | 1.52851 | 0.764257 | − | 0.644912i | \(-0.223106\pi\) | ||||
0.764257 | + | 0.644912i | \(0.223106\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.27922e34 | −0.794026 | −0.397013 | − | 0.917813i | \(-0.629953\pi\) | ||||
−0.397013 | + | 0.917813i | \(0.629953\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.66794e34 | −2.89057 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.00605e33 | −0.0959727 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.30064e34 | −0.397613 | −0.198807 | − | 0.980039i | \(-0.563707\pi\) | ||||
−0.198807 | + | 0.980039i | \(0.563707\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.50397e34 | −0.733074 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.01597e34 | 1.40655 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.17157e33 | 0.138920 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.94246e34 | 0.757291 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.13619e34 | −0.773440 | −0.386720 | − | 0.922197i | \(-0.626392\pi\) | ||||
−0.386720 | + | 0.922197i | \(0.626392\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.18803e34 | −0.517145 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.31206e34 | −1.42997 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.43753e34 | −1.39809 | −0.699046 | − | 0.715077i | \(-0.746392\pi\) | ||||
−0.699046 | + | 0.715077i | \(0.746392\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.86429e33 | 0.142933 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.42739e35 | −2.85012 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.82124e34 | 1.88075 | 0.940375 | − | 0.340140i | \(-0.110474\pi\) | ||||
0.940375 | + | 0.340140i | \(0.110474\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.10144e34 | 0.202316 | 0.101158 | − | 0.994870i | \(-0.467745\pi\) | ||||
0.101158 | + | 0.994870i | \(0.467745\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.94467e35 | −3.42672 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.39308e34 | 0.235523 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.06735e34 | −1.47103 | −0.735516 | − | 0.677508i | \(-0.763060\pi\) | ||||
−0.735516 | + | 0.677508i | \(0.763060\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.31105e34 | 1.13832 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.34220e35 | 2.00587 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.62922e34 | 0.377199 | 0.188599 | − | 0.982054i | \(-0.439605\pi\) | ||||
0.188599 | + | 0.982054i | \(0.439605\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.82279e34 | 0.526552 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.11422e34 | 0.808679 | 0.404340 | − | 0.914609i | \(-0.367501\pi\) | ||||
0.404340 | + | 0.914609i | \(0.367501\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.66687e34 | 0.592779 | 0.296389 | − | 0.955067i | \(-0.404217\pi\) | ||||
0.296389 | + | 0.955067i | \(0.404217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.64090e34 | −0.322186 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.65962e34 | 0.311687 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.23797e34 | 0.814923 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.25125e34 | −0.243545 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.67886e34 | −0.174535 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.88083e33 | 0.0787417 | 0.0393709 | − | 0.999225i | \(-0.487465\pi\) | ||||
0.0393709 | + | 0.999225i | \(0.487465\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.81562e35 | −1.74373 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.48176e33 | −0.0783095 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.98227e34 | 0.353499 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.15094e35 | 0.982408 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.14908e34 | 0.258499 | 0.129250 | − | 0.991612i | \(-0.458743\pi\) | ||||
0.129250 | + | 0.991612i | \(0.458743\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.32480e34 | −0.657259 | −0.328630 | − | 0.944459i | \(-0.606587\pi\) | ||||
−0.328630 | + | 0.944459i | \(0.606587\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.42236e34 | −0.335859 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.33124e35 | 0.972641 | 0.486321 | − | 0.873780i | \(-0.338339\pi\) | ||||
0.486321 | + | 0.873780i | \(0.338339\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.07800e34 | −0.0757809 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.36321e35 | −1.59860 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.06756e35 | 1.34599 | 0.672997 | − | 0.739645i | \(-0.265007\pi\) | ||||
0.672997 | + | 0.739645i | \(0.265007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.91422e34 | −0.119943 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.83084e34 | 0.472325 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.57849e35 | 1.49726 | 0.748632 | − | 0.662986i | \(-0.230711\pi\) | ||||
0.748632 | + | 0.662986i | \(0.230711\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.31671e34 | −0.185434 | −0.0927170 | − | 0.995692i | \(-0.529555\pi\) | ||||
−0.0927170 | + | 0.995692i | \(0.529555\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.77142e35 | −1.49205 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.06335e34 | 0.106980 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.47201e34 | −0.0735087 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.03109e35 | 0.977016 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.85101e34 | −0.410168 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.87165e35 | −1.28216 | −0.641082 | − | 0.767472i | \(-0.721514\pi\) | ||||
−0.641082 | + | 0.767472i | \(0.721514\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.85047e35 | 2.94729 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.20244e35 | 1.32777 | 0.663885 | − | 0.747835i | \(-0.268907\pi\) | ||||
0.663885 | + | 0.747835i | \(0.268907\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.06003e35 | 1.22280 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.58411e35 | −0.610165 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.34050e35 | 1.61169 | 0.805843 | − | 0.592129i | \(-0.201712\pi\) | ||||
0.805843 | + | 0.592129i | \(0.201712\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.48896e34 | 0.339693 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.49388e35 | −2.24153 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.91372e35 | 0.636999 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.59659e35 | −1.15456 | −0.577279 | − | 0.816547i | \(-0.695886\pi\) | ||||
−0.577279 | + | 0.816547i | \(0.695886\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.76480e35 | −0.546425 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.10548e35 | −0.330174 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.61333e35 | −0.752982 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.22055e34 | −0.200727 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.01671e34 | −0.107745 | −0.0538723 | − | 0.998548i | \(-0.517156\pi\) | ||||
−0.0538723 | + | 0.998548i | \(0.517156\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.04654e34 | −0.130633 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.37752e35 | −0.843788 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.32357e35 | −1.04256 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.37128e34 | −0.0551957 | −0.0275979 | − | 0.999619i | \(-0.508786\pi\) | ||||
−0.0275979 | + | 0.999619i | \(0.508786\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.53988e35 | −1.46960 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.75812e34 | 0.103232 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.39402e34 | −0.0711032 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.14103e36 | −2.30839 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.41947e35 | 1.64503 | 0.822514 | − | 0.568744i | \(-0.192571\pi\) | ||||
0.822514 | + | 0.568744i | \(0.192571\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.13920e35 | −0.592419 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.96697e35 | −0.540859 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.81839e35 | 0.672443 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.07486e35 | −1.37390 | −0.686950 | − | 0.726705i | \(-0.741051\pi\) | ||||
−0.686950 | + | 0.726705i | \(0.741051\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.75615e36 | 2.88714 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.02321e35 | 0.480287 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.32041e35 | −1.43099 | −0.715493 | − | 0.698620i | \(-0.753798\pi\) | ||||
−0.715493 | + | 0.698620i | \(0.753798\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.00210e35 | −0.148702 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.24310e35 | 0.321740 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.24490e34 | 0.128188 | 0.0640939 | − | 0.997944i | \(-0.479584\pi\) | ||||
0.0640939 | + | 0.997944i | \(0.479584\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.33068e35 | −1.11674 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.86129e35 | −0.500463 | −0.250232 | − | 0.968186i | \(-0.580507\pi\) | ||||
−0.250232 | + | 0.968186i | \(0.580507\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.81106e34 | 0.0728287 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.69882e36 | 4.48287 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.30431e35 | 0.621736 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.31819e35 | −0.602927 | −0.301463 | − | 0.953478i | \(-0.597475\pi\) | ||||
−0.301463 | + | 0.953478i | \(0.597475\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.65889e35 | 0.510911 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.44496e35 | 0.365466 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.46803e36 | 1.50674 | 0.753368 | − | 0.657599i | \(-0.228428\pi\) | ||||
0.753368 | + | 0.657599i | \(0.228428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.89561e34 | 0.0486166 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.26153e36 | 1.21225 | 0.606123 | − | 0.795371i | \(-0.292724\pi\) | ||||
0.606123 | + | 0.795371i | \(0.292724\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.02210e35 | −0.467012 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.06179e35 | 0.455550 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.98910e35 | −0.347482 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.78483e35 | −0.825039 | −0.412519 | − | 0.910949i | \(-0.635351\pi\) | ||||
−0.412519 | + | 0.910949i | \(0.635351\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.96165e36 | −1.60119 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.97217e36 | −1.55848 | −0.779238 | − | 0.626728i | \(-0.784394\pi\) | ||||
−0.779238 | + | 0.626728i | \(0.784394\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.23425e36 | −0.944350 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.45059e35 | −0.403813 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.85547e35 | −0.563578 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.32757e35 | −0.0922398 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.35457e36 | 2.25743 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.52153e35 | −0.425088 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.25189e35 | 0.142188 | 0.0710940 | − | 0.997470i | \(-0.477351\pi\) | ||||
0.0710940 | + | 0.997470i | \(0.477351\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.70224e36 | 1.65295 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.11702e36 | 1.25464 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.27529e36 | −1.88077 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.81568e35 | −0.267959 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.69113e36 | 1.99035 | 0.995177 | − | 0.0980978i | \(-0.0312758\pi\) | ||||
0.995177 | + | 0.0980978i | \(0.0312758\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.30893e36 | 1.20664 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.96123e36 | 0.993393 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.03258e34 | −0.0443473 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.48700e34 | −0.0213554 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.12420e36 | −1.90292 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.93815e36 | −1.31437 | −0.657185 | − | 0.753730i | \(-0.728253\pi\) | ||||
−0.657185 | + | 0.753730i | \(0.728253\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.44583e36 | 1.06088 | 0.530439 | − | 0.847723i | \(-0.322027\pi\) | ||||
0.530439 | + | 0.847723i | \(0.322027\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.71729e36 | −1.14289 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.04137e35 | 0.0424752 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.08753e35 | 0.359476 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.53060e36 | −2.50556 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.33815e36 | 1.24227 | 0.621136 | − | 0.783703i | \(-0.286672\pi\) | ||||
0.621136 | + | 0.783703i | \(0.286672\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.54036e36 | −0.917058 | −0.458529 | − | 0.888679i | \(-0.651623\pi\) | ||||
−0.458529 | + | 0.888679i | \(0.651623\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.26992e36 | −0.444734 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.63276e36 | 1.23429 | 0.617146 | − | 0.786849i | \(-0.288289\pi\) | ||||
0.617146 | + | 0.786849i | \(0.288289\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.07727e36 | 0.355135 | 0.177567 | − | 0.984109i | \(-0.443177\pi\) | ||||
0.177567 | + | 0.984109i | \(0.443177\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.13782e36 | 0.683847 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.85052e35 | 0.212648 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.37324e36 | −0.413682 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.08433e37 | −3.17024 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.96808e36 | 0.842269 | 0.421134 | − | 0.906998i | \(-0.361632\pi\) | ||||
0.421134 | + | 0.906998i | \(0.361632\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.76056e36 | −0.484953 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.96316e36 | −2.39671 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.88930e35 | −0.0750039 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.09185e36 | −0.779247 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.74735e36 | −0.672308 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.09743e35 | 0.0260769 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.13786e36 | 1.41630 | 0.708148 | − | 0.706064i | \(-0.249531\pi\) | ||||
0.708148 | + | 0.706064i | \(0.249531\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.52153e36 | 0.340961 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.16481e36 | 0.688791 | 0.344395 | − | 0.938825i | \(-0.388084\pi\) | ||||
0.344395 | + | 0.938825i | \(0.388084\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.65370e36 | −1.19514 | −0.597569 | − | 0.801818i | \(-0.703866\pi\) | ||||
−0.597569 | + | 0.801818i | \(0.703866\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.48442e36 | −1.74214 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.00828e36 | 1.59736 | 0.798682 | − | 0.601753i | \(-0.205531\pi\) | ||||
0.798682 | + | 0.601753i | \(0.205531\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.08261e36 | 0.209783 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.37651e36 | 1.01219 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.54351e35 | 0.137983 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.30052e36 | 1.47529 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.25649e37 | 3.89723 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.40613e36 | 0.403848 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.29560e36 | 0.537575 | 0.268788 | − | 0.963199i | \(-0.413377\pi\) | ||||
0.268788 | + | 0.963199i | \(0.413377\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.33233e36 | 1.16247 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.05386e36 | −1.24109 | −0.620547 | − | 0.784169i | \(-0.713090\pi\) | ||||
−0.620547 | + | 0.784169i | \(0.713090\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.91849e35 | 0.0736754 | 0.0368377 | − | 0.999321i | \(-0.488272\pi\) | ||||
0.0368377 | + | 0.999321i | \(0.488272\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.00381e36 | 0.146172 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.79484e36 | −1.10347 | −0.551737 | − | 0.834018i | \(-0.686035\pi\) | ||||
−0.551737 | + | 0.834018i | \(0.686035\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.88247e36 | 0.259093 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.24031e36 | −0.835093 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.94048e36 | 0.903121 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.10741e36 | −0.140127 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.81160e36 | 0.222924 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.04394e36 | −0.723309 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.29209e36 | 0.383188 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.81513e36 | 1.11122 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.47597e35 | −0.0272670 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.31417e37 | 1.40786 | 0.703932 | − | 0.710268i | \(-0.251426\pi\) | ||||
0.703932 | + | 0.710268i | \(0.251426\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.18823e37 | −3.32278 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.44767e37 | −1.46788 | −0.733940 | − | 0.679214i | \(-0.762321\pi\) | ||||
−0.733940 | + | 0.679214i | \(0.762321\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.26645e36 | −0.420903 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.24192e36 | 0.791161 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.24848e36 | 0.396842 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.03191e37 | 0.937990 | 0.468995 | − | 0.883201i | \(-0.344616\pi\) | ||||
0.468995 | + | 0.883201i | \(0.344616\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.35356e37 | 1.19738 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.91262e36 | −0.422953 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.84672e36 | −0.238546 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.31487e37 | −1.88813 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.17912e37 | −1.73015 | −0.865075 | − | 0.501642i | \(-0.832729\pi\) | ||||
−0.865075 | + | 0.501642i | \(0.832729\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.05921e36 | 0.159159 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.71170e37 | 2.04043 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.83858e35 | −0.0427723 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.08020e37 | −1.48375 | −0.741873 | − | 0.670540i | \(-0.766062\pi\) | ||||
−0.741873 | + | 0.670540i | \(0.766062\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.85686e37 | −1.98413 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.39454e37 | 1.61939 | 0.809695 | − | 0.586851i | \(-0.199632\pi\) | ||||
0.809695 | + | 0.586851i | \(0.199632\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.70826e36 | 0.112501 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.02254e37 | 0.655817 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.06134e36 | 0.503539 | 0.251769 | − | 0.967787i | \(-0.418988\pi\) | ||||
0.251769 | + | 0.967787i | \(0.418988\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.34248e36 | −0.203348 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.02727e37 | 2.38646 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.92589e37 | −1.11166 | −0.555829 | − | 0.831297i | \(-0.687599\pi\) | ||||
−0.555829 | + | 0.831297i | \(0.687599\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.75736e36 | −0.379957 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.21858e36 | −0.340637 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.10601e37 | −1.12390 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.03575e35 | 0.0157842 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.91144e37 | 1.98157 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.95205e36 | −0.0963606 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.29324e37 | −1.10311 | −0.551554 | − | 0.834139i | \(-0.685965\pi\) | ||||
−0.551554 | + | 0.834139i | \(0.685965\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.43309e37 | −0.671779 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.10199e37 | −0.960265 | −0.480132 | − | 0.877196i | \(-0.659411\pi\) | ||||
−0.480132 | + | 0.877196i | \(0.659411\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.45355e37 | 1.09241 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.69929e37 | −2.03927 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.52592e37 | −1.49139 | −0.745694 | − | 0.666289i | \(-0.767882\pi\) | ||||
−0.745694 | + | 0.666289i | \(0.767882\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.26220e36 | −0.0932712 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.70334e37 | −1.48844 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.31962e36 | −0.286794 | −0.143397 | − | 0.989665i | \(-0.545803\pi\) | ||||
−0.143397 | + | 0.989665i | \(0.545803\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.92076e36 | −0.187966 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.49617e37 | 2.79174 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.97619e36 | −0.0717587 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.16985e37 | −0.414200 | −0.207100 | − | 0.978320i | \(-0.566403\pi\) | ||||
−0.207100 | + | 0.978320i | \(0.566403\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.06819e37 | 2.09504 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.11277e37 | −0.374641 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.33411e37 | 0.766358 | 0.383179 | − | 0.923674i | \(-0.374829\pi\) | ||||
0.383179 | + | 0.923674i | \(0.374829\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.50092e37 | −0.800814 |
(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 | 16.26.a.c.1.1 | 2 | ||
4.3 | odd | 2 | 2.26.a.b.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 18.26.a.e.1.2 | 2 | |||
20.3 | even | 4 | 50.26.b.e.49.2 | 4 | |||
20.7 | even | 4 | 50.26.b.e.49.3 | 4 | |||
20.19 | odd | 2 | 50.26.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.26.a.b.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
16.26.a.c.1.1 | 2 | 1.1 | even | 1 | trivial | ||
18.26.a.e.1.2 | 2 | 12.11 | even | 2 | |||
50.26.a.c.1.1 | 2 | 20.19 | odd | 2 | |||
50.26.b.e.49.2 | 4 | 20.3 | even | 4 | |||
50.26.b.e.49.3 | 4 | 20.7 | even | 4 |