Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,8,Mod(193,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (of order \(2\), degree \(1\), 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: | \(119.955849786\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 7628 x^{10} + 22070097 x^{8} - 30593373916 x^{6} + 21405948373596 x^{4} + \cdots + 90\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{57}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.8 | ||
Root | \(31.5402 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.8.d.e.193.5 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 27.0000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 218.879i | − 0.783087i | −0.920160 | − | 0.391543i | \(-0.871941\pi\) | ||||
0.920160 | − | 0.391543i | \(-0.128059\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 904.541 | 0.996748 | 0.498374 | − | 0.866962i | \(-0.333931\pi\) | ||||
0.498374 | + | 0.866962i | \(0.333931\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −729.000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1956.99i | − 0.443318i | −0.975124 | − | 0.221659i | \(-0.928853\pi\) | ||||
0.975124 | − | 0.221659i | \(-0.0711471\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1492.92i | − 0.188467i | −0.995550 | − | 0.0942335i | \(-0.969960\pi\) | ||||
0.995550 | − | 0.0942335i | \(-0.0300400\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5909.75 | 0.452115 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14661.8 | 0.723797 | 0.361898 | − | 0.932218i | \(-0.382129\pi\) | ||||
0.361898 | + | 0.932218i | \(0.382129\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 32534.6i | − 1.08820i | −0.839021 | − | 0.544099i | \(-0.816872\pi\) | ||||
0.839021 | − | 0.544099i | \(-0.183128\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 24422.6i | 0.575473i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −24263.9 | −0.415827 | −0.207913 | − | 0.978147i | \(-0.566667\pi\) | ||||
−0.207913 | + | 0.978147i | \(0.566667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 30216.8 | 0.386775 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 19683.0i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 47760.3i | 0.363642i | 0.983332 | + | 0.181821i | \(0.0581991\pi\) | ||||
−0.983332 | + | 0.181821i | \(0.941801\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −38469.7 | −0.231928 | −0.115964 | − | 0.993253i | \(-0.536996\pi\) | ||||
−0.115964 | + | 0.993253i | \(0.536996\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 52838.8 | 0.255950 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 197986.i | − 0.780540i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 230575.i | − 0.748352i | −0.927358 | − | 0.374176i | \(-0.877926\pi\) | ||||
0.927358 | − | 0.374176i | \(-0.122074\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 40308.9 | 0.108812 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 503187. | 1.14021 | 0.570106 | − | 0.821571i | \(-0.306902\pi\) | ||||
0.570106 | + | 0.821571i | \(0.306902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 74103.4i | − 0.142134i | −0.997472 | − | 0.0710671i | \(-0.977360\pi\) | ||||
0.997472 | − | 0.0710671i | \(-0.0226404\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 159563.i | 0.261029i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −887487. | −1.24687 | −0.623433 | − | 0.781877i | \(-0.714263\pi\) | ||||
−0.623433 | + | 0.781877i | \(0.714263\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5347.93 | −0.00649381 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 395869.i | 0.417884i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 1.01950e6i | − 0.940633i | −0.882498 | − | 0.470317i | \(-0.844140\pi\) | ||||
0.882498 | − | 0.470317i | \(-0.155860\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −428346. | −0.347156 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 878434. | 0.628271 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 956905.i | 0.606578i | 0.952899 | + | 0.303289i | \(0.0980847\pi\) | ||||
−0.952899 | + | 0.303289i | \(0.901915\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.51951e6i | 0.857133i | 0.903510 | + | 0.428567i | \(0.140981\pi\) | ||||
−0.903510 | + | 0.428567i | \(0.859019\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −659411. | −0.332249 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −326770. | −0.147586 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.12707e6i | 0.864011i | 0.901871 | + | 0.432006i | \(0.142194\pi\) | ||||
−0.901871 | + | 0.432006i | \(0.857806\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 655124.i | − 0.240078i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.47131e6 | 0.487866 | 0.243933 | − | 0.969792i | \(-0.421562\pi\) | ||||
0.243933 | + | 0.969792i | \(0.421562\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.76425e6 | −1.43339 | −0.716695 | − | 0.697387i | \(-0.754346\pi\) | ||||
−0.716695 | + | 0.697387i | \(0.754346\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 815853.i | 0.223305i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.77018e6i | − 0.441876i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.66203e6 | −1.06385 | −0.531925 | − | 0.846791i | \(-0.678531\pi\) | ||||
−0.531925 | + | 0.846791i | \(0.678531\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 6.45883e6i | − 1.23988i | −0.784648 | − | 0.619941i | \(-0.787156\pi\) | ||||
0.784648 | − | 0.619941i | \(-0.212844\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 3.20917e6i | − 0.566796i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.28953e6 | −0.209949 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.18504e6 | 0.478906 | 0.239453 | − | 0.970908i | \(-0.423032\pi\) | ||||
0.239453 | + | 0.970908i | \(0.423032\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1.35041e6i | − 0.187854i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 1.03868e6i | − 0.133904i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.12115e6 | −0.852153 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.36353e7 | −1.51692 | −0.758462 | − | 0.651717i | \(-0.774049\pi\) | ||||
−0.758462 | + | 0.651717i | \(0.774049\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.42665e6i | 0.147773i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 695473.i | 0.0671670i | 0.999436 | + | 0.0335835i | \(0.0106920\pi\) | ||||
−0.999436 | + | 0.0335835i | \(0.989308\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.88699e6 | 0.260324 | 0.130162 | − | 0.991493i | \(-0.458450\pi\) | ||||
0.130162 | + | 0.991493i | \(0.458450\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.34561e6 | 0.450645 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1.47604e7i | − 1.16481i | −0.812898 | − | 0.582406i | \(-0.802112\pi\) | ||||
0.812898 | − | 0.582406i | \(-0.197888\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1.87852e7i | − 1.38938i | −0.719307 | − | 0.694692i | \(-0.755541\pi\) | ||||
0.719307 | − | 0.694692i | \(-0.244459\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.22552e6 | 0.432061 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.76048e6 | −0.114778 | −0.0573888 | − | 0.998352i | \(-0.518277\pi\) | ||||
−0.0573888 | + | 0.998352i | \(0.518277\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.31086e6i | 0.325629i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.08834e6i | 0.0628224i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.32622e7 | 0.721443 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.56573e7 | 0.803469 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.35860e7i | 0.658302i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 2.37138e7i | − 1.08597i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.27489e7 | 0.985477 | 0.492738 | − | 0.870177i | \(-0.335996\pi\) | ||||
0.492738 | + | 0.870177i | \(0.335996\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.00079e6 | 0.0820612 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 5.07701e6i | − 0.197314i | −0.995121 | − | 0.0986572i | \(-0.968545\pi\) | ||||
0.995121 | − | 0.0986572i | \(-0.0314547\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.94289e7i | − 1.08466i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.30820e6 | −0.150705 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.02216e7 | 0.671882 | 0.335941 | − | 0.941883i | \(-0.390946\pi\) | ||||
0.335941 | + | 0.941883i | \(0.390946\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.10736e7i | 0.981384i | 0.871333 | + | 0.490692i | \(0.163256\pi\) | ||||
−0.871333 | + | 0.490692i | \(0.836744\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 2.39622e7i | − 0.719878i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.92164e6 | −0.0835508 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.04537e7 | 0.284763 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 144394.i | − 0.00374921i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 2.49409e7i | − 0.617676i | −0.951115 | − | 0.308838i | \(-0.900060\pi\) | ||||
0.951115 | − | 0.308838i | \(-0.0999401\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.24230e7 | −0.529999 | −0.264999 | − | 0.964249i | \(-0.585372\pi\) | ||||
−0.264999 | + | 0.964249i | \(0.585372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.06885e7 | −0.241266 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.42023e6i | 0.181620i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.43020e6i | 0.0501180i | 0.999686 | + | 0.0250590i | \(0.00797736\pi\) | ||||
−0.999686 | + | 0.0250590i | \(0.992023\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.75264e7 | 0.543075 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.19477e7 | −0.414474 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1.21622e7i | − 0.219966i | −0.993933 | − | 0.109983i | \(-0.964920\pi\) | ||||
0.993933 | − | 0.109983i | \(-0.0350797\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 1.15653e7i | − 0.200431i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.96319e7 | 0.824619 | 0.412310 | − | 0.911044i | \(-0.364722\pi\) | ||||
0.412310 | + | 0.911044i | \(0.364722\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.05197e7 | 0.964480 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.37177e7i | 0.362732i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.16889e8i | − 1.71638i | −0.513334 | − | 0.858189i | \(-0.671590\pi\) | ||||
0.513334 | − | 0.858189i | \(-0.328410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.73323e7 | 0.385517 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.58364e7 | −0.350208 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 6.32640e7i | − 0.824462i | −0.911079 | − | 0.412231i | \(-0.864750\pi\) | ||||
0.911079 | − | 0.412231i | \(-0.135250\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1.36460e8i | − 1.71053i | −0.518191 | − | 0.855265i | \(-0.673395\pi\) | ||||
0.518191 | − | 0.855265i | \(-0.326605\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.10267e7 | −0.494866 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.04681e7 | −0.586025 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.86931e7i | − 0.320872i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1.78041e7i | − 0.191824i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.55629e6 | 0.0473146 | 0.0236573 | − | 0.999720i | \(-0.492469\pi\) | ||||
0.0236573 | + | 0.999720i | \(0.492469\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.40685e7 | −0.140864 | −0.0704318 | − | 0.997517i | \(-0.522438\pi\) | ||||
−0.0704318 | + | 0.997517i | \(0.522438\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 8.82279e6i | − 0.0852089i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.95523e8i | − 1.82208i | −0.412321 | − | 0.911039i | \(-0.635282\pi\) | ||||
0.412321 | − | 0.911039i | \(-0.364718\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.17120e8 | −1.05352 | −0.526761 | − | 0.850013i | \(-0.676594\pi\) | ||||
−0.526761 | + | 0.850013i | \(0.676594\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.74308e7 | −0.498837 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.32011e7i | 0.362459i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 1.10137e8i | − 0.892885i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.76884e7 | 0.138609 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.36700e7 | −0.482417 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 9.76752e7i | − 0.715807i | −0.933759 | − | 0.357903i | \(-0.883492\pi\) | ||||
0.933759 | − | 0.357903i | \(-0.116508\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.97254e7i | 0.281669i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.62197e7 | −0.111303 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.47974e7 | −0.231174 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 1.28635e8i | − 0.827568i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 2.18890e7i | − 0.136412i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.49268e6 | −0.0573221 | −0.0286610 | − | 0.999589i | \(-0.509124\pi\) | ||||
−0.0286610 | + | 0.999589i | \(0.509124\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.20280e7 | −0.128925 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.45827e7i | 0.139489i | 0.997565 | + | 0.0697443i | \(0.0222183\pi\) | ||||
−0.997565 | + | 0.0697443i | \(0.977782\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 3.38153e8i | − 1.86076i | −0.366602 | − | 0.930378i | \(-0.619479\pi\) | ||||
0.366602 | − | 0.930378i | \(-0.380521\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.77949e7 | 0.255117 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00882e7 | −0.311203 | −0.155602 | − | 0.987820i | \(-0.549732\pi\) | ||||
−0.155602 | + | 0.987820i | \(0.549732\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.94253e8i | 0.976404i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.25875e8i | − 0.614215i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.80834e8 | −1.33063 | −0.665315 | − | 0.746563i | \(-0.731703\pi\) | ||||
−0.665315 | + | 0.746563i | \(0.731703\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.86107e8 | 0.856451 | 0.428225 | − | 0.903672i | \(-0.359139\pi\) | ||||
0.428225 | + | 0.903672i | \(0.359139\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.43489e7i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.17055e6i | 0.00508522i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.85716e7 | −0.205089 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.74388e8 | 0.715847 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.69957e8i | 1.87586i | 0.346828 | + | 0.937929i | \(0.387259\pi\) | ||||
−0.346828 | + | 0.937929i | \(0.612741\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.74842e7i | 0.184343i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.66476e7 | 0.327240 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.21615e8 | 0.814392 | 0.407196 | − | 0.913341i | \(-0.366507\pi\) | ||||
0.407196 | + | 0.913341i | \(0.366507\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2.08565e8i | − 0.745919i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 3.48172e7i | − 0.121214i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.13618e8 | 0.385125 | 0.192562 | − | 0.981285i | \(-0.438320\pi\) | ||||
0.192562 | + | 0.981285i | \(0.438320\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.23147e8 | −0.736598 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.59961e7i | 0.276496i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 5.81217e8i | − 1.82056i | −0.413991 | − | 0.910281i | \(-0.635866\pi\) | ||||
0.413991 | − | 0.910281i | \(-0.364134\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.49084e8 | −1.67589 | −0.837946 | − | 0.545753i | \(-0.816244\pi\) | ||||
−0.837946 | + | 0.545753i | \(0.816244\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.64611e7 | 0.108458 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 5.91341e7i | − 0.171464i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 8.37027e6i | − 0.0236625i | −0.999930 | − | 0.0118312i | \(-0.996234\pi\) | ||||
0.999930 | − | 0.0118312i | \(-0.00376609\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.80444e7 | 0.0773093 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.13256e8 | 0.842222 | 0.421111 | − | 0.907009i | \(-0.361640\pi\) | ||||
0.421111 | + | 0.907009i | \(0.361640\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.60420e8i | 0.420733i | 0.977623 | + | 0.210366i | \(0.0674657\pi\) | ||||
−0.977623 | + | 0.210366i | \(0.932534\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1.92271e8i | − 0.491991i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.55153e8 | 1.13650 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.95370e8 | −0.476118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 3.68153e8i | − 0.875797i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.18079e8i | 0.738751i | 0.929280 | + | 0.369376i | \(0.120428\pi\) | ||||
−0.929280 | + | 0.369376i | \(0.879572\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.09447e8 | 0.475003 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.85195e7 | −0.0853165 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.62241e7i | 0.0783697i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 6.70296e7i | − 0.141672i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.87778e7 | −0.0387789 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.32589e8 | 0.671210 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 7.12299e8i | − 1.40501i | −0.711681 | − | 0.702503i | \(-0.752066\pi\) | ||||
0.711681 | − | 0.702503i | \(-0.247934\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.79487e7i | 0.150298i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.23509e8 | 0.609853 | 0.304927 | − | 0.952376i | \(-0.401368\pi\) | ||||
0.304927 | + | 0.952376i | \(0.401368\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.33838e8 | −0.431033 | −0.215517 | − | 0.976500i | \(-0.569144\pi\) | ||||
−0.215517 | + | 0.976500i | \(0.569144\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.44331e8i | 0.260180i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.11496e8i | 0.372902i | 0.982464 | + | 0.186451i | \(0.0596985\pi\) | ||||
−0.982464 | + | 0.186451i | \(0.940301\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.34665e7 | 0.161209 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.98531e8 | 0.672504 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 4.77016e8i | − 0.787634i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 4.51113e7i | − 0.0728943i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.07199e8 | 0.802161 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.02769e8 | −1.24281 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.86427e8i | 0.585693i | 0.956160 | + | 0.292846i | \(0.0946025\pi\) | ||||
−0.956160 | + | 0.292846i | \(0.905398\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.68089e8i | 0.249451i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.65571e8 | 0.676596 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.02746e8 | −0.288568 | −0.144284 | − | 0.989536i | \(-0.546088\pi\) | ||||
−0.144284 | + | 0.989536i | \(0.546088\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 4.75331e7i | − 0.0662669i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.52850e7i | 0.102818i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.49766e8 | −1.00322 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.43393e8 | −0.188002 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.75722e8i | 0.739706i | 0.929090 | + | 0.369853i | \(0.120592\pi\) | ||||
−0.929090 | + | 0.369853i | \(0.879408\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.84660e8i | 0.610307i | 0.952303 | + | 0.305153i | \(0.0987077\pi\) | ||||
−0.952303 | + | 0.305153i | \(0.901292\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.93852e7 | −0.0362705 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.21228e7 | −0.0751691 | −0.0375846 | − | 0.999293i | \(-0.511966\pi\) | ||||
−0.0375846 | + | 0.999293i | \(0.511966\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 3.22040e8i | − 0.382041i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.58080e8i | 0.416525i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.14354e8 | −0.472651 | −0.236326 | − | 0.971674i | \(-0.575943\pi\) | ||||
−0.236326 | + | 0.971674i | \(0.575943\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.64627e8 | −0.184173 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.22748e8i | 0.463883i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.04280e9i | 1.12247i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.04021e8 | −0.743454 | −0.371727 | − | 0.928342i | \(-0.621234\pi\) | ||||
−0.371727 | + | 0.928342i | \(0.621234\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.66823e8 | −0.380071 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 9.22177e8i | − 0.937574i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.29622e8i | 0.328878i | 0.986387 | + | 0.164439i | \(0.0525814\pi\) | ||||
−0.986387 | + | 0.164439i | \(0.947419\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.40272e8 | 0.626982 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.13024e7 | 0.0685345 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.30902e9i | 1.23512i | 0.786525 | + | 0.617559i | \(0.211878\pi\) | ||||
−0.786525 | + | 0.617559i | \(0.788122\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.14219e8i | 0.568965i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.58491e9 | 1.44148 | 0.720739 | − | 0.693207i | \(-0.243803\pi\) | ||||
0.720739 | + | 0.693207i | \(0.243803\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.87456e8 | −0.346027 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.40214e7i | 0.0473781i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.62442e8i | 0.312187i | 0.987742 | + | 0.156094i | \(0.0498902\pi\) | ||||
−0.987742 | + | 0.156094i | \(0.950110\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.55752e8 | −0.300974 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.37079e8 | 0.113919 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.02042e9i | 0.833088i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.96171e9i | 1.57351i | 0.617268 | + | 0.786753i | \(0.288239\pi\) | ||||
−0.617268 | + | 0.786753i | \(0.711761\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.94580e8 | 0.626228 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.52413e8 | −0.427818 | −0.213909 | − | 0.976854i | \(-0.568620\pi\) | ||||
−0.213909 | + | 0.976854i | \(0.568620\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.74323e7i | 0.0437108i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1.16322e8i | − 0.0870097i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.51234e8 | −0.331758 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.13185e9 | 1.54072 | 0.770362 | − | 0.637607i | \(-0.220076\pi\) | ||||
0.770362 | + | 0.637607i | \(0.220076\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.45982e8i | 0.387911i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.65560e8i | 0.604605i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.41371e9 | −0.970936 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.38986e8 | −0.566603 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 2.74843e9i | − 1.82530i | −0.408737 | − | 0.912652i | \(-0.634031\pi\) | ||||
0.408737 | − | 0.912652i | \(-0.365969\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.34645e9i | 1.53258i | 0.642495 | + | 0.766290i | \(0.277899\pi\) | ||||
−0.642495 | + | 0.766290i | \(0.722101\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.46978e8 | 0.415622 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.43033e8 | 0.279946 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.37446e9i | 0.854345i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 7.88843e7i | − 0.0482381i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.81903e7 | 0.0169601 | 0.00848006 | − | 0.999964i | \(-0.497301\pi\) | ||||
0.00848006 | + | 0.999964i | \(0.497301\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.49955e9 | 0.887677 | 0.443838 | − | 0.896107i | \(-0.353616\pi\) | ||||
0.443838 | + | 0.896107i | \(0.353616\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.82251e8i | 0.164408i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.89414e8i | 0.452502i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.88664e9 | −1.62842 | −0.814211 | − | 0.580568i | \(-0.802830\pi\) | ||||
−0.814211 | + | 0.580568i | \(0.802830\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.89864e6 | 0.00216460 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.64909e8i | 0.144772i | 0.997377 | + | 0.0723860i | \(0.0230613\pi\) | ||||
−0.997377 | + | 0.0723860i | \(0.976939\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 6.97140e8i | − 0.375025i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.73405e8 | 0.356615 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.26551e8 | 0.0659787 | 0.0329893 | − | 0.999456i | \(-0.489497\pi\) | ||||
0.0329893 | + | 0.999456i | \(0.489497\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 9.84733e8i | − 0.505476i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 6.05422e8i | − 0.305995i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.95577e8 | −0.147106 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.87578e8 | 0.336989 | 0.168494 | − | 0.985703i | \(-0.446109\pi\) | ||||
0.168494 | + | 0.985703i | \(0.446109\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 2.88589e8i | − 0.139295i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.34169e9i | 1.11321i | 0.830779 | + | 0.556603i | \(0.187895\pi\) | ||||
−0.830779 | + | 0.556603i | \(0.812105\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.70455e9 | −1.26637 | −0.633187 | − | 0.773999i | \(-0.718253\pi\) | ||||
−0.633187 | + | 0.773999i | \(0.718253\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.27346e8 | −0.104858 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 1.92358e9i | − 0.873979i | −0.899467 | − | 0.436990i | \(-0.856045\pi\) | ||||
0.899467 | − | 0.436990i | \(-0.143955\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.92402e9i | 0.861201i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.56154e7 | −0.0289356 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.45020e8 | −0.0630106 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 9.83090e8i | − 0.420887i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.43213e8i | 0.313544i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.50399e9 | 0.625273 | 0.312637 | − | 0.949873i | \(-0.398788\pi\) | ||||
0.312637 | + | 0.949873i | \(0.398788\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.44231e8 | −0.141040 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 5.92587e8i | − 0.239297i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.98449e9i | 1.18788i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.17828e9 | −0.854598 | −0.427299 | − | 0.904110i | \(-0.640535\pi\) | ||||
−0.427299 | + | 0.904110i | \(0.640535\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.28380e8 | 0.126998 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.21725e9i | 0.845337i | 0.906284 | + | 0.422669i | \(0.138907\pi\) | ||||
−0.906284 | + | 0.422669i | \(0.861093\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.00252e8i | 0.263203i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.12264e8 | 0.115719 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.33086e9 | 0.486279 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 3.34308e9i | − 1.20447i | −0.798320 | − | 0.602234i | \(-0.794277\pi\) | ||||
0.798320 | − | 0.602234i | \(-0.205723\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.34006e9i | 0.476094i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.18036e9 | 1.81498 | 0.907490 | − | 0.420073i | \(-0.137996\pi\) | ||||
0.907490 | + | 0.420073i | \(0.137996\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.52225e8 | 0.0525976 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.63403e9i | 0.556843i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.12633e8i | 0.105081i | 0.998619 | + | 0.0525403i | \(0.0167318\pi\) | ||||
−0.998619 | + | 0.0525403i | \(0.983268\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.30946e9 | −1.42873 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.40378e8 | −0.209424 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 6.31902e8i | − 0.203857i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.73681e9i | 0.552758i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.15601e9 | 0.990951 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.44796e9 | −0.758355 | −0.379177 | − | 0.925324i | \(-0.623793\pi\) | ||||
−0.379177 | + | 0.925324i | \(0.623793\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.27503e9i | 1.61239i | 0.591652 | + | 0.806194i | \(0.298476\pi\) | ||||
−0.591652 | + | 0.806194i | \(0.701524\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.37973e8i | 0.222578i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.64036e8 | −0.167869 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.81609e9 | −0.827088 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 6.97583e8i | − 0.202193i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 7.51219e8i | − 0.214892i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.23075e9 | −0.912149 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.70813e9 | 0.476003 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.04659e7i | 0.00287882i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 5.50854e9i | − 1.49571i | −0.663864 | − | 0.747853i | \(-0.731085\pi\) | ||||
0.663864 | − | 0.747853i | \(-0.268915\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.68442e9 | 0.987575 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.11169e9 | −1.08801 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 9.96556e8i | − 0.260343i | −0.991491 | − | 0.130172i | \(-0.958447\pi\) | ||||
0.991491 | − | 0.130172i | \(-0.0415528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 1.10772e9i | − 0.285711i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.55386e9 | 0.395714 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.21700e9 | −1.06039 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 1.36264e9i | − 0.338342i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.27851e8i | 0.227502i | 0.993509 | + | 0.113751i | \(0.0362866\pi\) | ||||
−0.993509 | + | 0.113751i | \(0.963713\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.10631e8 | −0.0267876 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.74713e8 | 0.185255 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.01459e9i | 1.42045i | 0.703974 | + | 0.710226i | \(0.251407\pi\) | ||||
−0.703974 | + | 0.710226i | \(0.748593\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.85334e8i | 0.0898809i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.80710e8 | 0.110750 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.33955e9 | 0.987533 | 0.493766 | − | 0.869595i | \(-0.335620\pi\) | ||||
0.493766 | + | 0.869595i | \(0.335620\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.36325e9i | 0.531232i | 0.964079 | + | 0.265616i | \(0.0855753\pi\) | ||||
−0.964079 | + | 0.265616i | \(0.914425\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.23020e8i | 0.0273171i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.33176e8 | −0.160831 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.66330e9 | −0.577171 | −0.288586 | − | 0.957454i | \(-0.593185\pi\) | ||||
−0.288586 | + | 0.957454i | \(0.593185\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 3.79851e8i | − 0.0813276i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 5.84228e9i | − 1.23585i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.99515e9 | −0.416999 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.38215e8 | 0.0491954 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.21780e9i | 0.656638i | 0.944567 | + | 0.328319i | \(0.106482\pi\) | ||||
−0.944567 | + | 0.328319i | \(0.893518\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.25160e9i | 0.252383i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.27913e9 | 1.05198 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.62179e9 | 1.69788 | 0.848938 | − | 0.528492i | \(-0.177242\pi\) | ||||
0.848938 | + | 0.528492i | \(0.177242\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 2.90283e9i | − 0.564952i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 3.16223e9i | − 0.608251i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.04802e10 | 1.99240 | 0.996201 | − | 0.0870868i | \(-0.0277558\pi\) | ||||
0.996201 | + | 0.0870868i | \(0.0277558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.98735e9 | 0.373433 | 0.186717 | − | 0.982414i | \(-0.440215\pi\) | ||||
0.186717 | + | 0.982414i | \(0.440215\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.55063e9i | − 0.288004i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 3.42707e9i | − 0.629186i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.29420e9 | −1.14230 | −0.571150 | − | 0.820846i | \(-0.693503\pi\) | ||||
−0.571150 | + | 0.820846i | \(0.693503\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.16643e9 | −0.209266 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.32495e9i | 0.234993i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.40995e8i | − 0.0247225i | −0.999924 | − | 0.0123612i | \(-0.996065\pi\) | ||||
0.999924 | − | 0.0123612i | \(-0.00393481\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.97370e9 | 0.515507 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.20227e9 | −1.40584 | −0.702920 | − | 0.711269i | \(-0.748121\pi\) | ||||
−0.702920 | + | 0.711269i | \(0.748121\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 9.32340e9i | − 1.58000i | −0.613107 | − | 0.790000i | \(-0.710081\pi\) | ||||
0.613107 | − | 0.790000i | \(-0.289919\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.77586e8i | 0.0800259i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.88100e9 | 0.477348 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.82978e9 | −0.463630 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1.71909e9i | − 0.278524i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 3.38065e9i | − 0.541655i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.15522e9 | −1.29221 | −0.646104 | − | 0.763249i | \(-0.723603\pi\) | ||||
−0.646104 | + | 0.763249i | \(0.723603\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.63723e9 | 0.413271 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 4.97926e9i | − 0.771714i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.98405e6i | 0.00122387i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.07259e9 | −0.162622 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.02076e10 | 1.53081 | 0.765404 | − | 0.643550i | \(-0.222539\pi\) | ||||
0.765404 | + | 0.643550i | \(0.222539\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.61713e9i | 0.388229i | 0.980979 | + | 0.194114i | \(0.0621833\pi\) | ||||
−0.980979 | + | 0.194114i | \(0.937817\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 4.37932e8i | − 0.0642611i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.19935e9 | −0.174093 | −0.0870464 | − | 0.996204i | \(-0.527743\pi\) | ||||
−0.0870464 | + | 0.996204i | \(0.527743\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.87266e9 | 0.268907 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 9.39531e8i | − 0.133468i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 9.90994e9i | − 1.39276i | −0.717675 | − | 0.696378i | \(-0.754794\pi\) | ||||
0.717675 | − | 0.696378i | \(-0.245206\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.11125e9 | −0.154514 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.47314e9 | 0.477796 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 3.18930e9i | − 0.434107i | −0.976160 | − | 0.217054i | \(-0.930355\pi\) | ||||
0.976160 | − | 0.217054i | \(-0.0696446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 1.35933e10i | − 1.83071i | −0.402648 | − | 0.915355i | \(-0.631910\pi\) | ||||
0.402648 | − | 0.915355i | \(-0.368090\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.91002e8 | 0.0787574 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.44138e9 | −0.849382 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.15885e9i | − 0.151212i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 2.56302e8i | − 0.0330949i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.97367e9 | 0.379982 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.29616e9 | 0.543285 | 0.271643 | − | 0.962398i | \(-0.412433\pi\) | ||||
0.271643 | + | 0.962398i | \(0.412433\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 5.94757e8i | − 0.0744348i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 5.90012e9i | − 0.730803i | −0.930850 | − | 0.365402i | \(-0.880932\pi\) | ||||
0.930850 | − | 0.365402i | \(-0.119068\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.23337e10 | −1.51199 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.63732e8 | −0.0805337 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.16844e9i | 0.740803i | 0.928872 | + | 0.370401i | \(0.120780\pi\) | ||||
−0.928872 | + | 0.370401i | \(0.879220\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 4.42608e9i | − 0.526142i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.13014e9 | 1.07431 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.52203e9 | −0.177278 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.57866e9i | 0.643216i | 0.946873 | + | 0.321608i | \(0.104223\pi\) | ||||
−0.946873 | + | 0.321608i | \(0.895777\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.29046e9i | 0.147292i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.80136e9 | 0.768509 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.37763e9 | 0.825282 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 1.62238e9i | − 0.179673i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.02296e9i | 0.660385i | 0.943914 | + | 0.330192i | \(0.107114\pi\) | ||||
−0.943914 | + | 0.330192i | \(0.892886\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.50166e9 | −0.814355 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.24483e9 | −0.563727 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.29084e8i | 0.0669485i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 9.08400e9i | − 0.957228i | −0.878025 | − | 0.478614i | \(-0.841139\pi\) | ||||
0.878025 | − | 0.478614i | \(-0.158861\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.39862e9 | 0.354617 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.33423e8 | 0.0964418 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.39487e8i | 0.0654275i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 7.58252e9i | − 0.768239i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.64006e9 | 0.967227 | 0.483614 | − | 0.875282i | \(-0.339324\pi\) | ||||
0.483614 | + | 0.875282i | \(0.339324\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.61140e9 | 0.259478 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.02488e9i | 0.494472i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.44316e9i | 0.140647i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.07015e10 | −1.03293 | −0.516467 | − | 0.856307i | \(-0.672753\pi\) | ||||
−0.516467 | + | 0.856307i | \(0.672753\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.87420e8 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1.08649e9i | − 0.102876i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.40489e10i | − 1.31758i | −0.752326 | − | 0.658791i | \(-0.771068\pi\) | ||||
0.752326 | − | 0.658791i | \(-0.228932\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.16049e7 | −0.00293595 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.16266e9 | 0.383031 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.03116e9i | 0.732020i | 0.930611 | + | 0.366010i | \(0.119276\pi\) | ||||
−0.930611 | + | 0.366010i | \(0.880724\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 1.31143e9i | − 0.118408i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.30525e10 | −1.16744 | −0.583718 | − | 0.811957i | \(-0.698403\pi\) | ||||
−0.583718 | + | 0.811957i | \(0.698403\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.45906e9 | −0.483694 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.70849e9i | 0.413294i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1.33514e10i | − 1.16102i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.40425e10 | −1.20977 | −0.604887 | − | 0.796311i | \(-0.706782\pi\) | ||||
−0.604887 | + | 0.796311i | \(0.706782\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.26888e10 | −1.08303 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.90794e9i | 0.415035i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 9.68111e8i | − 0.0811129i | −0.999177 | − | 0.0405564i | \(-0.987087\pi\) | ||||
0.999177 | − | 0.0405564i | \(-0.0129131\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.28207e9 | −0.106431 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.11474e10 | −1.73944 | −0.869721 | − | 0.493544i | \(-0.835701\pi\) | ||||
−0.869721 | + | 0.493544i | \(0.835701\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.69920e10i | − 1.38487i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.33949e9i | 0.188932i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.42858e9 | 0.114320 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.98489e9 | 0.236694 | 0.118347 | − | 0.992972i | \(-0.462241\pi\) | ||||
0.118347 | + | 0.992972i | \(0.462241\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.98361e9i | 0.470189i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 4.76718e9i | − 0.371222i | −0.982623 | − | 0.185611i | \(-0.940574\pi\) | ||||
0.982623 | − | 0.185611i | \(-0.0594264\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.16243e9 | −0.0897038 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.63124e9 | 0.430656 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.63710e10i | − 1.24078i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 2.87935e9i | − 0.216279i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.40065e8 | 0.0699829 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.31921e8 | 0.0392467 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.70072e10i | 1.24371i | 0.783131 | + | 0.621857i | \(0.213622\pi\) | ||||
−0.783131 | + | 0.621857i | \(0.786378\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.06768e9i | 0.222352i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.59243e9 | −0.114404 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.26851e9 | 0.161541 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 6.02497e9i | − 0.425275i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 6.66070e9i | − 0.466032i | −0.972473 | − | 0.233016i | \(-0.925141\pi\) | ||||
0.972473 | − | 0.233016i | \(-0.0748594\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.30122e10 | −0.902477 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.32190e9 | −0.159635 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.32360e9i | 0.635447i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.80389e9i | 0.324570i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.56929e10 | 1.05110 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.80483e9 | −0.319050 | −0.159525 | − | 0.987194i | \(-0.550996\pi\) | ||||
−0.159525 | + | 0.987194i | \(0.550996\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.11907e10i | 0.736687i | 0.929690 | + | 0.368344i | \(0.120075\pi\) | ||||
−0.929690 | + | 0.368344i | \(0.879925\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1.48253e10i | − 0.967577i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.66206e9 | −0.172253 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.41092e9 | −0.154670 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.84449e8i | 0.0626181i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.88169e9i | 0.560137i | 0.959980 | + | 0.280069i | \(0.0903572\pi\) | ||||
−0.959980 | + | 0.280069i | \(0.909643\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.97962e9 | 0.373916 | 0.186958 | − | 0.982368i | \(-0.440137\pi\) | ||||
0.186958 | + | 0.982368i | \(0.440137\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.59662e9 | 0.0989948 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 2.78565e10i | − 1.71260i | −0.516477 | − | 0.856301i | \(-0.672757\pi\) | ||||
0.516477 | − | 0.856301i | \(-0.327243\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.53264e10i | 0.934325i | 0.884171 | + | 0.467163i | \(0.154724\pi\) | ||||
−0.884171 | + | 0.467163i | \(0.845276\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.25997e8 | 0.0136615 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.84105e7 | −0.00470020 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1.08634e10i | − 0.645748i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.57199e8i | 0.0446345i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.85999e9 | 0.225641 | 0.112821 | − | 0.993615i | \(-0.464011\pi\) | ||||
0.112821 | + | 0.993615i | \(0.464011\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.49688e10 | 0.867765 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.45790e9i | 0.486257i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.32465e10i | − 0.755272i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.41627e10 | 0.800856 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.33134e9 | −0.242910 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.59464e9i | 0.311185i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.15207e9i | − 0.118723i | −0.998237 | − | 0.0593614i | \(-0.981094\pi\) | ||||
0.998237 | − | 0.0593614i | \(-0.0189064\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.19132e9 | 0.284051 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.52606e10 | 0.828206 | 0.414103 | − | 0.910230i | \(-0.364095\pi\) | ||||
0.414103 | + | 0.910230i | \(0.364095\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 2.51735e10i | − 1.35509i | −0.735481 | − | 0.677545i | \(-0.763044\pi\) | ||||
0.735481 | − | 0.677545i | \(-0.236956\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.22891e10i | 0.656161i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.50441e10 | 0.796760 | 0.398380 | − | 0.917220i | \(-0.369572\pi\) | ||||
0.398380 | + | 0.917220i | \(0.369572\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.55846e10 | −1.34407 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 5.27498e9i | − 0.274887i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.12357e9i | 0.471624i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.17555e9 | 0.162838 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.94014e9 | 0.505642 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 2.14501e10i | − 1.08243i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.24650e10i | 1.62524i | 0.582797 | + | 0.812618i | \(0.301958\pi\) | ||||
−0.582797 | + | 0.812618i | \(0.698042\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.58813e9 | −0.426518 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.20762e10 | 1.08770 | 0.543849 | − | 0.839183i | \(-0.316967\pi\) | ||||
0.543849 | + | 0.839183i | \(0.316967\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.48823e10i | 1.70507i | 0.522667 | + | 0.852537i | \(0.324937\pi\) | ||||
−0.522667 | + | 0.852537i | \(0.675063\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.65506e9i | 0.274243i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.90322e10 | 0.915705 | 0.457852 | − | 0.889028i | \(-0.348619\pi\) | ||||
0.457852 | + | 0.889028i | \(0.348619\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.05773e10 | 0.982272 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1.04003e9i | − 0.0492575i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.88740e10i | 1.35684i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.38472e10 | −0.645626 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.78050e8 | −0.0452467 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1.83732e9i | − 0.0843386i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.49477e10i | − 0.680827i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.80980e9 | 0.0817943 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.98683e10 | −1.33949 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 3.59008e9i | − 0.159764i | −0.996804 | − | 0.0798818i | \(-0.974546\pi\) | ||||
0.996804 | − | 0.0798818i | \(-0.0254543\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 5.07000e8i | − 0.0223890i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.18479e9 | 0.227205 | 0.113602 | − | 0.993526i | \(-0.463761\pi\) | ||||
0.113602 | + | 0.993526i | \(0.463761\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.26399e10 | −0.549662 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.97990e9i | 0.387523i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.59237e9i | − 0.196673i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.72664e9 | −0.370888 | −0.185444 | − | 0.982655i | \(-0.559372\pi\) | ||||
−0.185444 | + | 0.982655i | \(0.559372\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.92321e10 | 0.811180 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 2.19655e9i | − 0.0919466i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 6.96723e9i | − 0.289444i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.10461e9 | −0.0867748 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.57501e10 | 1.46293 | 0.731463 | − | 0.681882i | \(-0.238838\pi\) | ||||
0.731463 | + | 0.681882i | \(0.238838\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.73993e8i | 0.00706655i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.73475e9i | 0.352099i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.28033e9 | −0.251271 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.61665e10 | 0.641989 | 0.320995 | − | 0.947081i | \(-0.395983\pi\) | ||||
0.320995 | + | 0.947081i | \(0.395983\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 6.31364e9i | − 0.248857i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.67594e10i | 1.04692i | 0.852051 | + | 0.523459i | \(0.175359\pi\) | ||||
−0.852051 | + | 0.523459i | \(0.824641\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.22092e10 | −0.474131 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.89695e9 | −0.150215 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.63328e10i | 1.39019i | 0.718918 | + | 0.695095i | \(0.244637\pi\) | ||||
−0.718918 | + | 0.695095i | \(0.755363\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.11265e9i | 0.270147i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.71039e9 | −0.215295 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.03702e10 | −0.388115 | −0.194057 | − | 0.980990i | \(-0.562165\pi\) | ||||
−0.194057 | + | 0.980990i | \(0.562165\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 9.97279e8i | − 0.0370514i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.52360e9i | 0.0930740i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.82912e10 | 0.669697 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.60327e10 | −0.946209 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.07603e10i | 0.388270i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.07932e9i | 0.110308i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.82811e10 | 1.71706 | 0.858528 | − | 0.512766i | \(-0.171379\pi\) | ||||
0.858528 | + | 0.512766i | \(0.171379\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.28794e10 | 0.454740 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.54306e10i | 0.891433i | 0.895174 | + | 0.445716i | \(0.147051\pi\) | ||||
−0.895174 | + | 0.445716i | \(0.852949\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.81073e10i | 0.978193i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.21801e9 | 0.0420856 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.43404e10 | 0.491959 | 0.245980 | − | 0.969275i | \(-0.420890\pi\) | ||||
0.245980 | + | 0.969275i | \(0.420890\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 6.23311e9i | − 0.212307i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.36944e10i | 0.463128i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.57764e10 | −0.529750 | −0.264875 | − | 0.964283i | \(-0.585331\pi\) | ||||
−0.264875 | + | 0.964283i | \(0.585331\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.27961e10 | −1.42685 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2.16748e10i | − 0.717537i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.79803e9i | 0.0591032i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.15481e10 | 0.703318 | 0.351659 | − | 0.936128i | \(-0.385618\pi\) | ||||
0.351659 | + | 0.936128i | \(0.385618\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.04335e10 | −0.338150 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.56351e10i | 0.824999i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.08176e10i | 1.30441i | 0.758042 | + | 0.652205i | \(0.226156\pi\) | ||||
−0.758042 | + | 0.652205i | \(0.773844\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.53841e9 | −0.144020 |
(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 | 384.8.d.e.193.8 | yes | 12 | |
4.3 | odd | 2 | inner | 384.8.d.e.193.2 | ✓ | 12 | |
8.3 | odd | 2 | inner | 384.8.d.e.193.11 | yes | 12 | |
8.5 | even | 2 | inner | 384.8.d.e.193.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.d.e.193.2 | ✓ | 12 | 4.3 | odd | 2 | inner | |
384.8.d.e.193.5 | yes | 12 | 8.5 | even | 2 | inner | |
384.8.d.e.193.8 | yes | 12 | 1.1 | even | 1 | trivial | |
384.8.d.e.193.11 | yes | 12 | 8.3 | odd | 2 | inner |