Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(53,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.53");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.bk (of order \(6\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 233.7 | ||
Character | \(\chi\) | \(=\) | 252.233 |
Dual form | 252.9.bk.a.53.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −349.907 | − | 202.019i | −0.559850 | − | 0.323230i | 0.193235 | − | 0.981152i | \(-0.438102\pi\) |
−0.753085 | + | 0.657923i | \(0.771435\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1821.32 | − | 1564.48i | −0.758568 | − | 0.651594i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10579.1 | − | 6107.83i | 0.722565 | − | 0.417173i | −0.0931312 | − | 0.995654i | \(-0.529688\pi\) |
0.815696 | + | 0.578481i | \(0.196354\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7958.67 | 0.278655 | 0.139327 | − | 0.990246i | \(-0.455506\pi\) | ||||
0.139327 | + | 0.990246i | \(0.455506\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −140355. | + | 81034.2i | −1.68048 | + | 0.970225i | −0.719138 | + | 0.694868i | \(0.755463\pi\) |
−0.961342 | + | 0.275358i | \(0.911204\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −35098.2 | + | 60791.9i | −0.269321 | + | 0.466478i | −0.968687 | − | 0.248286i | \(-0.920133\pi\) |
0.699365 | + | 0.714764i | \(0.253466\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −93110.9 | − | 53757.6i | −0.332728 | − | 0.192100i | 0.324324 | − | 0.945946i | \(-0.394863\pi\) |
−0.657051 | + | 0.753846i | \(0.728197\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −113689. | − | 196916.i | −0.291045 | − | 0.504105i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 813834.i | − | 1.15065i | −0.817924 | − | 0.575326i | \(-0.804875\pi\) | ||
0.817924 | − | 0.575326i | \(-0.195125\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −876420. | − | 1.51800e6i | −0.948999 | − | 1.64371i | −0.747539 | − | 0.664217i | \(-0.768765\pi\) |
−0.201459 | − | 0.979497i | \(-0.564568\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 321238. | + | 915362.i | 0.214070 | + | 0.609987i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.67953e6 | + | 2.90903e6i | −0.896149 | + | 1.55218i | −0.0637733 | + | 0.997964i | \(0.520313\pi\) |
−0.832376 | + | 0.554212i | \(0.813020\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.96551e6i | − | 0.695569i | −0.937575 | − | 0.347784i | \(-0.886934\pi\) | ||
0.937575 | − | 0.347784i | \(-0.113066\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.97887e6 | 1.16382 | 0.581910 | − | 0.813253i | \(-0.302305\pi\) | ||||
0.581910 | + | 0.813253i | \(0.302305\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.18444e6 | + | 1.83854e6i | 0.652592 | + | 0.376774i | 0.789448 | − | 0.613817i | \(-0.210367\pi\) |
−0.136857 | + | 0.990591i | \(0.543700\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 869617. | + | 5.69883e6i | 0.150850 | + | 0.988557i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.53376e6 | + | 2.61757e6i | −0.574586 | + | 0.331737i | −0.758979 | − | 0.651115i | \(-0.774301\pi\) |
0.184393 | + | 0.982853i | \(0.440968\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.93558e6 | −0.539371 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.47374e7 | − | 8.50867e6i | 1.21623 | − | 0.702188i | 0.252117 | − | 0.967697i | \(-0.418873\pi\) |
0.964108 | + | 0.265509i | \(0.0855399\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.69375e6 | − | 1.33260e7i | 0.555673 | − | 0.962453i | −0.442178 | − | 0.896927i | \(-0.645794\pi\) |
0.997851 | − | 0.0655259i | \(-0.0208725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.78479e6 | − | 1.60780e6i | −0.156005 | − | 0.0900696i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.19649e6 | − | 2.07238e6i | −0.0593759 | − | 0.102842i | 0.834810 | − | 0.550539i | \(-0.185578\pi\) |
−0.894185 | + | 0.447697i | \(0.852244\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.94900e7i | 1.94753i | 0.227554 | + | 0.973765i | \(0.426927\pi\) | ||||
−0.227554 | + | 0.973765i | \(0.573073\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 258100. | + | 447042.i | 0.00908859 | + | 0.0157419i | 0.870534 | − | 0.492108i | \(-0.163774\pi\) |
−0.861445 | + | 0.507850i | \(0.830440\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.88234e7 | − | 5.42641e6i | −0.819942 | − | 0.154365i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.00826e7 | + | 3.47840e7i | −0.515598 | + | 0.893042i | 0.484238 | + | 0.874936i | \(0.339097\pi\) |
−0.999836 | + | 0.0181054i | \(0.994237\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.77285e7i | − | 0.794981i | −0.917606 | − | 0.397490i | \(-0.869881\pi\) | ||
0.917606 | − | 0.397490i | \(-0.130119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.54817e7 | 1.25442 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.00892e7 | + | 4.62395e7i | 1.27648 | + | 0.736976i | 0.976199 | − | 0.216875i | \(-0.0695864\pi\) |
0.300280 | + | 0.953851i | \(0.402920\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.44953e7 | − | 1.24512e7i | −0.211379 | − | 0.181570i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.45622e7 | − | 1.41810e7i | 0.301559 | − | 0.174105i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.54164e8 | −1.74139 | −0.870697 | − | 0.491821i | \(-0.836332\pi\) | ||||
−0.870697 | + | 0.491821i | \(0.836332\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.65420e7 | − | 1.53240e7i | 0.255063 | − | 0.147261i | −0.367017 | − | 0.930214i | \(-0.619621\pi\) |
0.622080 | + | 0.782953i | \(0.286288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.10742e7 | + | 8.84631e7i | −0.453787 | + | 0.785983i | −0.998618 | − | 0.0525635i | \(-0.983261\pi\) |
0.544830 | + | 0.838546i | \(0.316594\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.11907e8 | + | 6.46093e7i | 0.853730 | + | 0.492901i | 0.861908 | − | 0.507066i | \(-0.169270\pi\) |
−0.00817787 | + | 0.999967i | \(0.502603\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.08266e8 | + | 1.87523e8i | 0.766987 | + | 1.32846i | 0.939190 | + | 0.343398i | \(0.111578\pi\) |
−0.172203 | + | 0.985061i | \(0.555089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.69205e8i | − | 1.03777i | −0.854845 | − | 0.518883i | \(-0.826348\pi\) | ||
0.854845 | − | 0.518883i | \(-0.173652\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.17201e7 | + | 3.76203e7i | 0.124185 | + | 0.215095i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.82408e8 | + | 7.19936e7i | 1.90695 | + | 0.359010i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.25683e7 | + | 5.64099e7i | −0.151933 | + | 0.263157i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.49697e8i | 1.02276i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.83510e8 | −1.47422 | −0.737109 | − | 0.675774i | \(-0.763809\pi\) | ||||
−0.737109 | + | 0.675774i | \(0.763809\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.17169e8 | + | 6.76477e7i | 0.397858 | + | 0.229704i | 0.685559 | − | 0.728017i | \(-0.259558\pi\) |
−0.287701 | + | 0.957720i | \(0.592891\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.59033e8 | − | 5.58111e7i | 0.508253 | − | 0.178367i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.07925e8 | + | 6.23103e7i | −0.306364 | + | 0.176880i | −0.645298 | − | 0.763931i | \(-0.723267\pi\) |
0.338934 | + | 0.940810i | \(0.389934\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.77388e6 | 0.0261823 | 0.0130912 | − | 0.999914i | \(-0.495833\pi\) | ||||
0.0130912 | + | 0.999914i | \(0.495833\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.41953e7 | − | 4.86102e7i | 0.201346 | − | 0.116247i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.64410e8 | + | 2.84766e8i | −0.371925 | + | 0.644193i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.34818e8 | + | 4.24247e8i | 1.49085 | + | 0.860744i | 0.999945 | − | 0.0104686i | \(-0.00333231\pi\) |
0.490907 | + | 0.871212i | \(0.336666\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.79475e8 | + | 3.10859e8i | 0.345220 | + | 0.597938i | 0.985394 | − | 0.170292i | \(-0.0544711\pi\) |
−0.640174 | + | 0.768230i | \(0.721138\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.08213e8i | 1.22698i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.59164e8 | + | 7.95296e8i | 0.755735 | + | 1.30897i | 0.945008 | + | 0.327047i | \(0.106054\pi\) |
−0.189273 | + | 0.981925i | \(0.560613\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.54822e7 | + | 2.43580e8i | 0.127225 | + | 0.362525i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.56877e7 | − | 1.65736e8i | 0.135552 | − | 0.234783i | −0.790256 | − | 0.612777i | \(-0.790053\pi\) |
0.925808 | + | 0.377994i | \(0.123386\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.09896e8i | − | 0.655565i | −0.944753 | − | 0.327782i | \(-0.893699\pi\) | ||
0.944753 | − | 0.327782i | \(-0.106301\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.52390e8 | −0.922351 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.29299e9 | + | 7.46508e8i | 1.44348 | + | 0.833393i | 0.998080 | − | 0.0619383i | \(-0.0197282\pi\) |
0.445400 | + | 0.895332i | \(0.353062\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.01006e8 | + | 5.36512e8i | −0.107695 | + | 0.572041i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.50876e9 | − | 8.71085e8i | 1.46963 | − | 0.848493i | 0.470213 | − | 0.882553i | \(-0.344177\pi\) |
0.999420 | + | 0.0340600i | \(0.0108437\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.60559e8 | −0.708628 | −0.354314 | − | 0.935126i | \(-0.615286\pi\) | ||||
−0.354314 | + | 0.935126i | \(0.615286\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.17536e9 | − | 6.78592e8i | 1.00342 | − | 0.579324i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.89886e8 | + | 1.71453e9i | −0.809503 | + | 1.40210i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.55485e9 | + | 8.97692e8i | 1.16830 | + | 0.674518i | 0.953279 | − | 0.302091i | \(-0.0976847\pi\) |
0.215021 | + | 0.976609i | \(0.431018\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.97709e8 | + | 6.88852e8i | 0.286640 | + | 0.496474i | 0.973005 | − | 0.230782i | \(-0.0741284\pi\) |
−0.686366 | + | 0.727256i | \(0.740795\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.47329e8i | − | 0.297004i | −0.988912 | − | 0.148502i | \(-0.952555\pi\) | ||
0.988912 | − | 0.148502i | \(-0.0474451\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.84277e8 | − | 1.35841e9i | −0.500100 | − | 0.866199i | −1.00000 | 0.000115831i | \(-0.999963\pi\) | |
0.499900 | − | 0.866083i | \(-0.333370\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.27323e9 | + | 1.48225e9i | −0.749758 | + | 0.872847i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.97070e8 | + | 6.87745e8i | −0.224829 | + | 0.389415i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.57496e8i | 0.449414i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.18001e9 | 1.09984 | 0.549919 | − | 0.835218i | \(-0.314659\pi\) | ||||
0.549919 | + | 0.835218i | \(0.314659\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.39223e9 | − | 8.03806e8i | −0.651565 | − | 0.376181i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.78642e8 | + | 4.13591e9i | −0.351155 | + | 1.86523i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.11704e9 | + | 6.44924e8i | −0.468274 | + | 0.270358i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.17447e9 | −0.474921 | −0.237461 | − | 0.971397i | \(-0.576315\pi\) | ||||
−0.237461 | + | 0.971397i | \(0.576315\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.97460e9 | − | 1.14003e9i | 0.743661 | − | 0.429353i | −0.0797378 | − | 0.996816i | \(-0.525408\pi\) |
0.823399 | + | 0.567463i | \(0.192075\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.23665e9 | − | 2.14195e9i | 0.449682 | − | 0.778873i | −0.548683 | − | 0.836031i | \(-0.684870\pi\) |
0.998365 | + | 0.0571578i | \(0.0182038\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.39582e9 | + | 8.05875e8i | 0.473592 | + | 0.273429i | 0.717742 | − | 0.696309i | \(-0.245176\pi\) |
−0.244150 | + | 0.969737i | \(0.578509\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.42837e8 | − | 1.28663e9i | −0.243569 | − | 0.421874i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.26329e9i | 0.693662i | 0.937928 | + | 0.346831i | \(0.112742\pi\) | ||||
−0.937928 | + | 0.346831i | \(0.887258\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.25951e9 | − | 3.91359e9i | −0.669802 | − | 1.16013i | −0.977959 | − | 0.208796i | \(-0.933046\pi\) |
0.308157 | − | 0.951336i | \(-0.400288\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.46986e8 | − | 2.16974e9i | 0.235078 | − | 0.602203i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.79335e8 | + | 4.83822e8i | −0.0750477 | + | 0.129986i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.83085e8i | 0.172100i | 0.996291 | + | 0.0860499i | \(0.0274244\pi\) | ||||
−0.996291 | + | 0.0860499i | \(0.972576\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.31337e9 | −0.320556 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.48843e7 | − | 8.59346e6i | −0.00341190 | − | 0.00196986i | 0.498293 | − | 0.867009i | \(-0.333960\pi\) |
−0.501705 | + | 0.865039i | \(0.667294\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.61007e9 | − | 2.67069e9i | 1.69118 | − | 0.593505i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.49429e8 | + | 4.32683e8i | −0.156642 | + | 0.0904371i | −0.576272 | − | 0.817258i | \(-0.695493\pi\) |
0.419630 | + | 0.907695i | \(0.362160\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.11519e9 | 0.428909 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.41936e9 | + | 1.39682e9i | −0.462053 | + | 0.266766i | −0.712907 | − | 0.701258i | \(-0.752622\pi\) |
0.250854 | + | 0.968025i | \(0.419289\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.46401e9 | + | 5.99983e9i | −0.642246 | + | 1.11240i | 0.342684 | + | 0.939451i | \(0.388664\pi\) |
−0.984930 | + | 0.172952i | \(0.944669\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.40546e9 | − | 1.38879e9i | −0.420598 | − | 0.242832i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.02498e9 | + | 5.23942e9i | 0.513811 | + | 0.889947i | 0.999872 | + | 0.0160216i | \(0.00510006\pi\) |
−0.486061 | + | 0.873925i | \(0.661567\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4.17380e9i | − | 0.669432i | −0.942319 | − | 0.334716i | \(-0.891360\pi\) | ||
0.942319 | − | 0.334716i | \(-0.108640\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.92835e9 | + | 6.80410e9i | 0.612441 | + | 1.06078i | 0.990828 | + | 0.135131i | \(0.0431456\pi\) |
−0.378387 | + | 0.925648i | \(0.623521\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.07500e9 | + | 3.57983e9i | −0.453229 | + | 0.527636i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.64520e9 | − | 1.67060e10i | 1.38267 | − | 2.39486i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.07386e10i | − | 1.45706i | −0.685016 | − | 0.728528i | \(-0.740205\pi\) | ||
0.685016 | − | 0.728528i | \(-0.259795\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.87564e9 | −0.907872 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.41038e8 | − | 4.27839e8i | −0.0927162 | − | 0.0535297i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.24680e9 | − | 6.22486e9i | −0.882836 | − | 0.758339i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.38419e9 | + | 3.10856e9i | −0.622187 | + | 0.359220i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.62105e9 | −0.745372 | −0.372686 | − | 0.927957i | \(-0.621563\pi\) | ||||
−0.372686 | + | 0.927957i | \(0.621563\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.98990e9 | + | 5.19032e9i | −0.960977 | + | 0.554820i | −0.896474 | − | 0.443097i | \(-0.853880\pi\) |
−0.0645035 | + | 0.997917i | \(0.520546\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.95239e9 | − | 8.57780e9i | 0.515986 | − | 0.893714i | −0.483842 | − | 0.875155i | \(-0.660759\pi\) |
0.999828 | − | 0.0185583i | \(-0.00590761\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.20277e9 | − | 4.15852e9i | −0.713284 | − | 0.411814i | 0.0989920 | − | 0.995088i | \(-0.468438\pi\) |
−0.812276 | + | 0.583274i | \(0.801771\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.97076e9 | − | 8.60960e9i | −0.480021 | − | 0.831420i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.13766e10i | − | 1.04521i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.04816e8 | − | 1.56719e9i | −0.0811011 | − | 0.140471i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.92353e9 | − | 8.33055e9i | −0.249531 | − | 0.711034i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.72675e9 | + | 2.99081e9i | −0.143852 | + | 0.249159i | −0.928944 | − | 0.370220i | \(-0.879282\pi\) |
0.785092 | + | 0.619379i | \(0.212616\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.66854e8i | 0.0767682i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.00768e9 | 0.465787 | 0.232893 | − | 0.972502i | \(-0.425181\pi\) | ||||
0.232893 | + | 0.972502i | \(0.425181\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.85434e10 | − | 1.07061e10i | −1.37143 | − | 0.791793i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.33185e9 | − | 1.17399e10i | 0.529708 | − | 0.848180i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.66076e10 | + | 9.58841e9i | −1.14548 | + | 0.661346i | −0.947783 | − | 0.318917i | \(-0.896681\pi\) |
−0.197701 | + | 0.980262i | \(0.563348\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.40166e9 | 0.0944803 | 0.0472401 | − | 0.998884i | \(-0.484957\pi\) | ||||
0.0472401 | + | 0.998884i | \(0.484957\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.16222e10 | + | 6.71006e9i | −0.748493 | + | 0.432143i | −0.825149 | − | 0.564915i | \(-0.808909\pi\) |
0.0766559 | + | 0.997058i | \(0.475576\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.99791e9 | − | 1.73169e10i | 0.629500 | − | 1.09033i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.26658e9 | − | 7.31259e8i | −0.0762525 | − | 0.0440244i | 0.461389 | − | 0.887198i | \(-0.347351\pi\) |
−0.537641 | + | 0.843174i | \(0.680685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.02801e9 | + | 1.04408e10i | 0.354932 | + | 0.614760i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 2.08564e8i | − | 0.0117508i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.01014e10 | − | 1.74961e10i | −0.556823 | − | 0.964445i | −0.997759 | − | 0.0669071i | \(-0.978687\pi\) |
0.440936 | − | 0.897538i | \(-0.354646\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.23525e10 | + | 2.32554e9i | 0.652020 | + | 0.122752i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.22226e9 | + | 1.42414e10i | −0.424772 | + | 0.735727i | −0.996399 | − | 0.0847868i | \(-0.972979\pi\) |
0.571627 | + | 0.820514i | \(0.306312\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6.47703e9i | − | 0.320635i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.50115e10 | 0.727559 | 0.363780 | − | 0.931485i | \(-0.381486\pi\) | ||||
0.363780 | + | 0.931485i | \(0.381486\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.85696e9 | − | 5.69092e9i | −0.458087 | − | 0.264477i | 0.253153 | − | 0.967426i | \(-0.418533\pi\) |
−0.711240 | + | 0.702950i | \(0.751866\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.98928e9 | + | 7.72161e9i | 0.409149 | + | 0.351451i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.57517e10 | − | 9.09424e9i | 0.687905 | − | 0.397162i | −0.114922 | − | 0.993375i | \(-0.536662\pi\) |
0.802827 | + | 0.596212i | \(0.203328\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.74248e10 | 0.745523 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.40540e10 | − | 8.11411e9i | 0.577315 | − | 0.333313i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.04840e9 | − | 7.01203e9i | 0.162975 | − | 0.282281i | −0.772959 | − | 0.634456i | \(-0.781224\pi\) |
0.935934 | + | 0.352175i | \(0.114558\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.54624e9 | − | 3.77947e9i | −0.253171 | − | 0.146169i | 0.368044 | − | 0.929808i | \(-0.380028\pi\) |
−0.621215 | + | 0.783640i | \(0.713361\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.97514e9 | − | 1.20813e10i | −0.264443 | − | 0.458029i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.10331e10i | 1.49540i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.30352e9 | − | 3.98981e9i | −0.0823186 | − | 0.142580i | 0.821927 | − | 0.569593i | \(-0.192899\pi\) |
−0.904245 | + | 0.427013i | \(0.859566\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.01532e10 | − | 7.55940e9i | −1.38013 | − | 0.259829i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.62185e9 | + | 1.32014e10i | −0.256961 | + | 0.445070i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.03520e10i | − | 0.335868i | −0.985798 | − | 0.167934i | \(-0.946290\pi\) | ||
0.985798 | − | 0.167934i | \(-0.0537096\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.21723e10 | 1.02413 | 0.512063 | − | 0.858948i | \(-0.328882\pi\) | ||||
0.512063 | + | 0.858948i | \(0.328882\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.19138e10 | + | 1.84255e10i | 0.978190 | + | 0.564758i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.48610e10 | + | 1.22342e10i | −1.04864 | + | 0.368013i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.46168e10 | − | 8.43903e9i | 0.423588 | − | 0.244559i | −0.273023 | − | 0.962007i | \(-0.588024\pi\) |
0.696611 | + | 0.717449i | \(0.254690\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.06664e10 | 0.303435 | 0.151717 | − | 0.988424i | \(-0.451520\pi\) | ||||
0.151717 | + | 0.988424i | \(0.451520\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.53605e9 | − | 3.77359e9i | 0.179221 | − | 0.103473i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.32618e10 | + | 2.29702e10i | −0.357063 | + | 0.618452i | −0.987469 | − | 0.157814i | \(-0.949555\pi\) |
0.630405 | + | 0.776266i | \(0.282889\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.27728e10 | − | 2.46949e10i | −1.11059 | − | 0.641198i | −0.171606 | − | 0.985166i | \(-0.554895\pi\) |
−0.938981 | + | 0.343968i | \(0.888229\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.86825e10 | − | 3.23590e10i | −0.476425 | − | 0.825193i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.24668e8i | − | 0.00798829i | −0.999992 | − | 0.00399415i | \(-0.998729\pi\) | ||
0.999992 | − | 0.00399415i | \(-0.00127138\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.20050e10 | − | 2.07933e10i | −0.290173 | − | 0.502594i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.55663e9 | + | 7.28506e9i | 0.0596516 | + | 0.169976i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.80358e9 | − | 6.58799e9i | 0.0872022 | − | 0.151039i | −0.819125 | − | 0.573615i | \(-0.805541\pi\) |
0.906327 | + | 0.422576i | \(0.138874\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.90203e10i | 0.421127i | 0.977580 | + | 0.210563i | \(0.0675298\pi\) | ||||
−0.977580 | + | 0.210563i | \(0.932470\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.80548e10 | −1.69854 | −0.849270 | − | 0.527959i | \(-0.822957\pi\) | ||||
−0.849270 | + | 0.527959i | \(0.822957\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.41733e10 | + | 2.55034e10i | 0.928735 | + | 0.536206i | 0.886411 | − | 0.462898i | \(-0.153191\pi\) |
0.0423239 | + | 0.999104i | \(0.486524\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.06300e9 | + | 5.64636e9i | −0.0219707 | + | 0.116702i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.20928e10 | − | 2.43023e10i | 0.840936 | − | 0.485514i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.59612e10 | 0.313538 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.45961e10 | + | 2.57475e10i | −0.847139 | + | 0.489096i | −0.859684 | − | 0.510826i | \(-0.829340\pi\) |
0.0125458 | + | 0.999921i | \(0.496006\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.33668e10 | + | 2.31520e10i | −0.249716 | + | 0.432522i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.39431e10 | + | 3.11441e10i | 0.974920 | + | 0.562870i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.39213e10 | + | 4.14328e10i | 0.425273 | + | 0.736595i | 0.996446 | − | 0.0842348i | \(-0.0268446\pi\) |
−0.571172 | + | 0.820830i | \(0.693511\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 9.81309e9i | − | 0.168842i | −0.996430 | − | 0.0844209i | \(-0.973096\pi\) | ||
0.996430 | − | 0.0844209i | \(-0.0269040\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.59484e10 | + | 1.14226e11i | 1.11639 | + | 1.93365i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.74261e10 | − | 9.01372e10i | 1.26900 | − | 1.47733i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.88196e10 | + | 6.72376e10i | −0.626108 | + | 1.08445i | 0.362217 | + | 0.932094i | \(0.382020\pi\) |
−0.988325 | + | 0.152357i | \(0.951313\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.09735e11i | 1.71424i | 0.515114 | + | 0.857122i | \(0.327750\pi\) | ||||
−0.515114 | + | 0.857122i | \(0.672250\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.23829e10 | −0.190396 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.55015e10 | − | 1.47233e10i | −0.379922 | − | 0.219348i | 0.297862 | − | 0.954609i | \(-0.403726\pi\) |
−0.677784 | + | 0.735261i | \(0.737060\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.29305e8 | − | 1.21800e9i | 0.00336302 | − | 0.0178634i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.57424e10 | − | 2.06359e10i | 0.508106 | − | 0.293355i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.49179e10 | 0.628720 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.05467e9 | + | 4.07302e9i | −0.0957472 | + | 0.0552797i | −0.547109 | − | 0.837061i | \(-0.684272\pi\) |
0.451362 | + | 0.892341i | \(0.350938\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.87140e10 | + | 3.24137e10i | −0.250127 | + | 0.433233i | −0.963561 | − | 0.267490i | \(-0.913806\pi\) |
0.713434 | + | 0.700723i | \(0.247139\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.46021e11 | + | 1.42040e11i | 3.18955 | + | 1.84149i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.33757e10 | − | 5.78085e10i | −0.426195 | − | 0.738191i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1.56428e10i | − | 0.193824i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.61046e10 | − | 4.52144e10i | −0.318641 | − | 0.551902i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.40072e10 | + | 5.49769e10i | 0.521398 | + | 0.651366i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.06590e10 | + | 5.31030e10i | −0.357906 | + | 0.619912i | −0.987611 | − | 0.156923i | \(-0.949843\pi\) |
0.629704 | + | 0.776835i | \(0.283176\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 8.74873e10i | − | 0.991652i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.06663e10 | −0.901038 | −0.450519 | − | 0.892767i | \(-0.648761\pi\) | ||||
−0.450519 | + | 0.892767i | \(0.648761\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.94745e10 | + | 2.85641e10i | 0.536754 | + | 0.309895i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.09957e10 | − | 3.19341e10i | 0.973017 | − | 0.341472i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.34971e10 | − | 2.51131e10i | 0.451897 | − | 0.260903i | −0.256734 | − | 0.966482i | \(-0.582646\pi\) |
0.708631 | + | 0.705579i | \(0.249313\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.16665e10 | 0.324304 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.37176e9 | − | 5.41079e9i | 0.0932798 | − | 0.0538551i | −0.452634 | − | 0.891696i | \(-0.649516\pi\) |
0.545914 | + | 0.837841i | \(0.316182\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.41826e10 | + | 5.92059e10i | −0.335437 | + | 0.580994i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.46519e11 | − | 8.45927e10i | −1.39780 | − | 0.807019i | −0.403636 | − | 0.914920i | \(-0.632254\pi\) |
−0.994162 | + | 0.107901i | \(0.965587\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.81136e10 | + | 1.52617e11i | 0.828893 | + | 1.43569i | 0.898907 | + | 0.438139i | \(0.144362\pi\) |
−0.0700140 | + | 0.997546i | \(0.522304\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.44467e10i | 0.223639i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.60526e10 | − | 2.78040e10i | −0.144825 | − | 0.250844i | 0.784483 | − | 0.620151i | \(-0.212929\pi\) |
−0.929308 | + | 0.369307i | \(0.879595\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.90253e10 | + | 6.87156e10i | −0.518005 | + | 0.603047i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.19753e10 | + | 5.53828e10i | −0.276784 | + | 0.479403i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.86668e11i | 1.57223i | 0.618079 | + | 0.786116i | \(0.287911\pi\) | ||||
−0.618079 | + | 0.786116i | \(0.712089\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.23043e11 | 1.02234 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.63636e10 | + | 5.56356e10i | 0.779282 | + | 0.449918i | 0.836176 | − | 0.548462i | \(-0.184786\pi\) |
−0.0568940 | + | 0.998380i | \(0.518120\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.19263e11 | − | 1.02445e11i | −0.951565 | − | 0.817375i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.32077e11 | + | 7.62549e10i | −1.02594 | + | 0.592326i | −0.915818 | − | 0.401593i | \(-0.868457\pi\) |
−0.110120 | + | 0.993918i | \(0.535123\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.43616e10 | −0.263375 | −0.131688 | − | 0.991291i | \(-0.542040\pi\) | ||||
−0.131688 | + | 0.991291i | \(0.542040\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.27917e10 | − | 1.31588e10i | 0.170120 | − | 0.0982189i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.62186e10 | + | 2.80914e10i | −0.119470 | + | 0.206927i | −0.919558 | − | 0.392955i | \(-0.871453\pi\) |
0.800088 | + | 0.599883i | \(0.204786\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.53439e10 | + | 1.46323e10i | 0.181848 | + | 0.104990i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.55918e9 | − | 1.48249e10i | −0.0606164 | − | 0.104991i | 0.834125 | − | 0.551576i | \(-0.185973\pi\) |
−0.894741 | + | 0.446585i | \(0.852640\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.04980e11i | 0.724376i | 0.932105 | + | 0.362188i | \(0.117970\pi\) | ||||
−0.932105 | + | 0.362188i | \(0.882030\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.24195e10 | + | 2.15112e10i | 0.0845945 | + | 0.146522i | 0.905218 | − | 0.424947i | \(-0.139707\pi\) |
−0.820624 | + | 0.571469i | \(0.806374\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.35274e10 | − | 2.09515e11i | −0.488087 | − | 1.39079i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.03342e9 | − | 1.04502e10i | 0.0395406 | − | 0.0684864i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 5.44397e11i | − | 3.47787i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.64527e11 | −1.03782 | −0.518908 | − | 0.854830i | \(-0.673661\pi\) | ||||
−0.518908 | + | 0.854830i | \(0.673661\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.34193e11 | + | 7.74761e10i | 0.825341 | + | 0.476511i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.92099e9 | + | 4.53551e10i | 0.0420350 | + | 0.275466i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.85646e11 | − | 1.07183e11i | 1.09965 | − | 0.634882i | 0.163519 | − | 0.986540i | \(-0.447716\pi\) |
0.936128 | + | 0.351659i | \(0.114382\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.59773e11 | −0.934672 | −0.467336 | − | 0.884080i | \(-0.654786\pi\) | ||||
−0.467336 | + | 0.884080i | \(0.654786\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.38290e11 | + | 7.98419e10i | −0.789177 | + | 0.455632i | −0.839673 | − | 0.543093i | \(-0.817253\pi\) |
0.0504956 | + | 0.998724i | \(0.483920\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.03939e11 | − | 1.80028e11i | 0.585868 | − | 1.01475i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.93727e10 | + | 5.73729e10i | 0.546530 | + | 0.315540i | 0.747721 | − | 0.664013i | \(-0.231148\pi\) |
−0.201191 | + | 0.979552i | \(0.564481\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.73322e10 | − | 4.73407e10i | −0.148494 | − | 0.257199i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.04429e11i | 1.61415i | 0.590449 | + | 0.807075i | \(0.298951\pi\) | ||||
−0.590449 | + | 0.807075i | \(0.701049\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.54169e11 | − | 2.67028e11i | −0.807590 | − | 1.39879i | −0.914529 | − | 0.404521i | \(-0.867438\pi\) |
0.106939 | − | 0.994266i | \(-0.465895\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.69215e10 | − | 1.25989e10i | −0.342199 | − | 0.0644237i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.37497e10 | + | 7.57768e10i | −0.221041 | + | 0.382854i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.87969e11i | − | 0.927246i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.19224e11 | 1.55609 | 0.778047 | − | 0.628206i | \(-0.216211\pi\) | ||||
0.778047 | + | 0.628206i | \(0.216211\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.27203e11 | − | 1.88910e11i | −1.55762 | − | 0.899293i | −0.997484 | − | 0.0708939i | \(-0.977415\pi\) |
−0.560138 | − | 0.828399i | \(-0.689252\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.80783e11 | + | 2.41187e11i | 1.32096 | + | 1.13468i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.23257e11 | + | 7.11627e10i | −0.566410 | + | 0.327017i | −0.755714 | − | 0.654902i | \(-0.772710\pi\) |
0.189305 | + | 0.981918i | \(0.439377\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.03514e10 | 0.228691 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.60827e10 | + | 2.08323e10i | −0.160111 | + | 0.0924402i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.68290e10 | − | 8.11101e10i | 0.205401 | − | 0.355765i | −0.744860 | − | 0.667221i | \(-0.767484\pi\) |
0.950260 | + | 0.311457i | \(0.100817\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.41994e9 | − | 1.97451e9i | −0.0146582 | − | 0.00846290i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.59274e11 | + | 2.75870e11i | 0.674859 | + | 1.16889i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.68356e11i | − | 0.697199i | −0.937272 | − | 0.348599i | \(-0.886657\pi\) | ||
0.937272 | − | 0.348599i | \(-0.113343\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.17897e11 | − | 2.04203e11i | −0.482704 | − | 0.836068i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.23155e10 | − | 1.36144e10i | −0.289437 | − | 0.0544905i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.66170e9 | − | 4.61020e9i | 0.0105335 | − | 0.0182446i | −0.860711 | − | 0.509095i | \(-0.829980\pi\) |
0.871244 | + | 0.490850i | \(0.163314\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.88457e11i | 0.729212i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.92806e10 | −0.150298 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.42127e10 | − | 1.97527e10i | −0.128018 | − | 0.0739114i | 0.434623 | − | 0.900612i | \(-0.356882\pi\) |
−0.562642 | + | 0.826701i | \(0.690215\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.31421e11 | − | 8.12152e10i | 0.856370 | − | 0.300536i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.60257e11 | + | 9.25243e10i | −0.580049 | + | 0.334891i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.32747e9 | −0.0226513 | −0.0113256 | − | 0.999936i | \(-0.503605\pi\) | ||||
−0.0113256 | + | 0.999936i | \(0.503605\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.58456e11 | + | 3.22425e11i | −1.95578 | + | 1.12917i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.68943e10 | − | 1.67826e11i | 0.335647 | − | 0.581357i | −0.647962 | − | 0.761673i | \(-0.724378\pi\) |
0.983609 | + | 0.180315i | \(0.0577118\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.53155e10 | − | 1.46159e10i | −0.0858058 | − | 0.0495400i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.33208e11 | − | 4.03928e11i | −0.781927 | − | 1.35434i | −0.930818 | − | 0.365483i | \(-0.880904\pi\) |
0.148891 | − | 0.988854i | \(-0.452430\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.78453e11i | − | 0.585556i | −0.956181 | − | 0.292778i | \(-0.905420\pi\) | ||
0.956181 | − | 0.292778i | \(-0.0945796\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.71412e11 | − | 2.96894e11i | −0.556436 | − | 0.963775i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.02738e11 | − | 2.92750e11i | −0.326440 | − | 0.930184i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.81487e11 | − | 4.87549e11i | 0.884908 | − | 1.53271i | 0.0390887 | − | 0.999236i | \(-0.487555\pi\) |
0.845819 | − | 0.533470i | \(-0.179112\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.45029e11i | − | 0.446341i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.75340e11 | −0.838466 | −0.419233 | − | 0.907879i | \(-0.637701\pi\) | ||||
−0.419233 | + | 0.907879i | \(0.637701\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.54738e11 | − | 2.04808e11i | −1.05772 | − | 0.610673i | −0.132917 | − | 0.991127i | \(-0.542434\pi\) |
−0.924800 | + | 0.380454i | \(0.875768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.61877e10 | − | 5.10920e11i | 0.283806 | − | 1.50749i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.17290e11 | − | 6.77176e10i | 0.338907 | − | 0.195668i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.47102e11 | 1.27850 | 0.639250 | − | 0.768999i | \(-0.279245\pi\) | ||||
0.639250 | + | 0.768999i | \(0.279245\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.97227e11 | + | 1.71604e11i | −0.832472 | + | 0.480628i | −0.854698 | − | 0.519125i | \(-0.826258\pi\) |
0.0222260 | + | 0.999753i | \(0.492925\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.99280e11 | + | 3.45162e11i | −0.552403 | + | 0.956790i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.19487e11 | + | 6.89859e10i | 0.324468 | + | 0.187331i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.02277e11 | + | 5.23559e11i | 0.812457 | + | 1.40722i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 3.71039e11i | − | 0.977105i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.26115e10 | + | 9.11257e10i | 0.137145 | + | 0.237543i | 0.926415 | − | 0.376504i | \(-0.122874\pi\) |
−0.789270 | + | 0.614047i | \(0.789541\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.64717e11 | + | 3.08177e11i | −0.676202 | + | 0.787215i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.12320e10 | − | 1.06057e11i | 0.154841 | − | 0.268192i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 3.01194e11i | − | 0.746471i | −0.927737 | − | 0.373236i | \(-0.878248\pi\) | ||
0.927737 | − | 0.373236i | \(-0.121752\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.95937e11 | −1.46222 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.46091e9 | + | 3.15286e9i | 0.0131342 | + | 0.00758302i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.92969e10 | − | 1.02499e11i | 0.0459519 | − | 0.244082i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.30511e10 | + | 1.33086e10i | −0.0538143 | + | 0.0310697i | −0.526666 | − | 0.850072i | \(-0.676558\pi\) |
0.472851 | + | 0.881142i | \(0.343225\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.25219e11 | 0.520622 | 0.260311 | − | 0.965525i | \(-0.416175\pi\) | ||||
0.260311 | + | 0.965525i | \(0.416175\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.69635e10 | + | 3.86614e10i | −0.151778 | + | 0.0876289i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.39651e11 | + | 2.41883e11i | −0.313442 | + | 0.542897i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.98848e11 | + | 1.72540e11i | 0.657776 | + | 0.379767i | 0.791429 | − | 0.611261i | \(-0.209337\pi\) |
−0.133653 | + | 0.991028i | \(0.542671\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.74635e10 | − | 4.75681e10i | −0.0598626 | − | 0.103685i | 0.834541 | − | 0.550946i | \(-0.185733\pi\) |
−0.894404 | + | 0.447261i | \(0.852400\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.15387e11i | 0.674251i | 0.941460 | + | 0.337126i | \(0.109455\pi\) | ||||
−0.941460 | + | 0.337126i | \(0.890545\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.83826e11 | − | 3.18396e11i | −0.389214 | − | 0.674139i | 0.603130 | − | 0.797643i | \(-0.293920\pi\) |
−0.992344 | + | 0.123504i | \(0.960587\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.83856e11 | − | 7.29393e11i | −1.21262 | − | 1.51489i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.03008e11 | + | 1.78416e11i | −0.211898 | + | 0.367018i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 4.42480e11i | − | 0.892988i | −0.894787 | − | 0.446494i | \(-0.852672\pi\) | ||
0.894787 | − | 0.446494i | \(-0.147328\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.62079e11 | −0.323998 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.63266e11 | + | 1.51997e11i | 0.516379 | + | 0.298131i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.47569e11 | − | 5.17882e10i | 0.286723 | − | 0.100623i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.12765e11 | − | 1.80575e11i | 0.596347 | − | 0.344301i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.10112e11 | 1.53020 | 0.765102 | − | 0.643910i | \(-0.222689\pi\) | ||||
0.765102 | + | 0.643910i | \(0.222689\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.23929e10 | − | 1.87020e10i | 0.0600518 | − | 0.0346709i | −0.469673 | − | 0.882840i | \(-0.655628\pi\) |
0.529725 | + | 0.848169i | \(0.322295\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.53311e11 | + | 4.38747e11i | −0.465244 | + | 0.805827i | −0.999213 | − | 0.0396779i | \(-0.987367\pi\) |
0.533968 | + | 0.845504i | \(0.320700\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.18246e11 | + | 5.30150e11i | 1.65545 | + | 0.955774i | 0.974775 | + | 0.223189i | \(0.0716466\pi\) |
0.680675 | + | 0.732586i | \(0.261687\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.01617e11 | − | 5.22416e11i | −0.538755 | − | 0.933151i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.90644e11i | 0.860374i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.52247e9 | − | 1.64934e10i | −0.0165454 | − | 0.0286574i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.90645e11 | − | 4.54778e11i | 0.666423 | − | 0.775830i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.16539e11 | + | 5.48262e11i | −0.535093 | + | 0.926809i | 0.464066 | + | 0.885801i | \(0.346390\pi\) |
−0.999159 | + | 0.0410078i | \(0.986943\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 5.39180e11i | − | 0.895015i | −0.894280 | − | 0.447507i | \(-0.852312\pi\) | ||
0.894280 | − | 0.447507i | \(-0.147688\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.39105e11 | −0.228823 | −0.114412 | − | 0.993433i | \(-0.536498\pi\) | ||||
−0.114412 | + | 0.993433i | \(0.536498\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.45611e11 | − | 2.57274e11i | −0.719882 | − | 0.415624i | 0.0948272 | − | 0.995494i | \(-0.469770\pi\) |
−0.814709 | + | 0.579870i | \(0.803103\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.98494e11 | + | 5.99992e11i | 1.11829 | + | 0.960592i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.23536e11 | + | 1.29059e11i | −0.351514 | + | 0.202946i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.03901e11 | −1.09703 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.23540e12 | + | 7.13261e11i | −1.89134 | + | 1.09197i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.24225e11 | − | 7.34779e11i | 0.643720 | − | 1.11496i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.66124e11 | + | 1.53647e11i | 0.396726 | + | 0.229050i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.91938e11 | + | 3.32447e11i | 0.283617 | + | 0.491239i | 0.972273 | − | 0.233849i | \(-0.0751322\pi\) |
−0.688656 | + | 0.725088i | \(0.741799\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.05117e12i | 1.52616i | 0.646306 | + | 0.763078i | \(0.276313\pi\) | ||||
−0.646306 | + | 0.763078i | \(0.723687\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.30439e11 | − | 3.99132e11i | −0.331644 | − | 0.574425i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.07569e11 | − | 3.06517e11i | −0.152129 | − | 0.433488i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.68948e10 | + | 1.50506e11i | −0.121824 | + | 0.211005i | −0.920487 | − | 0.390773i | \(-0.872208\pi\) |
0.798663 | + | 0.601778i | \(0.205541\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.93875e11i | 0.542689i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.63778e11 | 1.04328 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.06698e12 | + | 6.16020e11i | 1.43249 | + | 0.827050i | 0.997310 | − | 0.0732927i | \(-0.0233507\pi\) |
0.435182 | + | 0.900343i | \(0.356684\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.76965e11 | − | 1.47153e11i | −0.501767 | − | 0.195871i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.92735e11 | − | 3.99951e11i | 0.906402 | − | 0.523311i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.45315e11 | −0.318248 | −0.159124 | − | 0.987259i | \(-0.550867\pi\) | ||||
−0.159124 | + | 0.987259i | \(0.550867\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.40790e11 | + | 8.12850e10i | −0.179561 | + | 0.103670i | −0.587086 | − | 0.809524i | \(-0.699725\pi\) |
0.407525 | + | 0.913194i | \(0.366392\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.05661e11 | + | 1.83010e11i | −0.133619 | + | 0.231435i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.47524e11 | + | 4.31583e11i | 0.929448 | + | 0.536617i | 0.886637 | − | 0.462466i | \(-0.153035\pi\) |
0.0428111 | + | 0.999083i | \(0.486369\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.05413e9 | + | 3.55786e9i | 0.00253258 | + | 0.00438656i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4.03315e11i | − | 0.488960i | −0.969654 | − | 0.244480i | \(-0.921383\pi\) | ||
0.969654 | − | 0.244480i | \(-0.0786172\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.62701e11 | − | 6.28216e11i | −0.436049 | − | 0.755259i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.94049e11 | + | 5.53587e10i | 0.347652 | + | 0.0654502i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.10978e12 | + | 1.92220e12i | −1.30120 | + | 2.25374i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 3.21379e11i | − | 0.370602i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.52582e11 | 0.975058 | 0.487529 | − | 0.873107i | \(-0.337898\pi\) | ||||
0.487529 | + | 0.873107i | \(0.337898\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.21106e12 | + | 6.99203e11i | 1.36234 | + | 0.786550i | 0.989936 | − | 0.141518i | \(-0.0451984\pi\) |
0.372409 | + | 0.928069i | \(0.378532\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.78014e10 | − | 1.52910e10i | −0.0198610 | − | 0.0170602i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.30450e11 | − | 3.06255e11i | 0.582192 | − | 0.336129i | −0.179812 | − | 0.983701i | \(-0.557549\pi\) |
0.762004 | + | 0.647572i | \(0.224216\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.12969e12 | 1.22979 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.19275e10 | − | 5.30744e10i | 0.0984536 | − | 0.0568422i | −0.449965 | − | 0.893046i | \(-0.648563\pi\) |
0.548418 | + | 0.836204i | \(0.315230\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.03688e10 | + | 1.56523e11i | −0.0960005 | + | 0.166278i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.70476e11 | − | 2.13894e11i | −0.387235 | − | 0.223570i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.81982e11 | + | 1.18123e12i | 0.707096 | + | 1.22473i | 0.965930 | + | 0.258805i | \(0.0833286\pi\) |
−0.258833 | + | 0.965922i | \(0.583338\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.33754e11i | 0.646589i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.95115e11 | − | 1.20397e12i | −0.703519 | − | 1.21853i | −0.967223 | − | 0.253928i | \(-0.918278\pi\) |
0.263704 | − | 0.964604i | \(-0.415056\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.9.bk.a.233.7 | yes | 44 | |
3.2 | odd | 2 | inner | 252.9.bk.a.233.16 | yes | 44 | |
7.4 | even | 3 | inner | 252.9.bk.a.53.16 | yes | 44 | |
21.11 | odd | 6 | inner | 252.9.bk.a.53.7 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.bk.a.53.7 | ✓ | 44 | 21.11 | odd | 6 | inner | |
252.9.bk.a.53.16 | yes | 44 | 7.4 | even | 3 | inner | |
252.9.bk.a.233.7 | yes | 44 | 1.1 | even | 1 | trivial | |
252.9.bk.a.233.16 | yes | 44 | 3.2 | odd | 2 | inner |