Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,9,Mod(319,384)]
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([1, 1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.319");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.b (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: | \(156.433386263\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 200x^{6} - 586x^{5} + 10949x^{4} - 20926x^{3} + 78946x^{2} - 68580x + 222900 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.7 | ||
Root | \(-0.366025 - 9.69292i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.319 |
Dual form | 384.9.b.a.319.6 |
$q$-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 | ||||||||
\(3\) | 46.7654 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 402.176i | 0.643482i | 0.946828 | + | 0.321741i | \(0.104268\pi\) | ||||
−0.946828 | + | 0.321741i | \(0.895732\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1935.65i | 0.806184i | 0.915159 | + | 0.403092i | \(0.132065\pi\) | ||||
−0.915159 | + | 0.403092i | \(0.867935\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2187.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 20109.3 | 1.37350 | 0.686748 | − | 0.726896i | \(-0.259038\pi\) | ||||
0.686748 | + | 0.726896i | \(0.259038\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 43789.3i | − 1.53319i | −0.642134 | − | 0.766593i | \(-0.721951\pi\) | ||||
0.642134 | − | 0.766593i | \(-0.278049\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 18807.9i | 0.371514i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 101325. | 1.21317 | 0.606585 | − | 0.795018i | \(-0.292539\pi\) | ||||
0.606585 | + | 0.795018i | \(0.292539\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13935.8 | 0.106935 | 0.0534674 | − | 0.998570i | \(-0.482973\pi\) | ||||
0.0534674 | + | 0.998570i | \(0.482973\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 90521.3i | 0.465451i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 433050.i | 1.54749i | 0.633499 | + | 0.773743i | \(0.281618\pi\) | ||||
−0.633499 | + | 0.773743i | \(0.718382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 228879. | 0.585931 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 102276. | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 467978.i | − 0.661657i | −0.943691 | − | 0.330829i | \(-0.892672\pi\) | ||||
0.943691 | − | 0.330829i | \(-0.107328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1.48318e6i | − 1.60601i | −0.595975 | − | 0.803003i | \(-0.703234\pi\) | ||||
0.595975 | − | 0.803003i | \(-0.296766\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 940421. | 0.792988 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −778471. | −0.518765 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.57554e6i | − 1.37424i | −0.726545 | − | 0.687119i | \(-0.758875\pi\) | ||||
0.726545 | − | 0.687119i | \(-0.241125\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 2.04782e6i | − 0.885185i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.84335e6 | −1.36011 | −0.680057 | − | 0.733160i | \(-0.738045\pi\) | ||||
−0.680057 | + | 0.733160i | \(0.738045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.88197e6 | 0.550475 | 0.275238 | − | 0.961376i | \(-0.411243\pi\) | ||||
0.275238 | + | 0.961376i | \(0.411243\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 879559.i | 0.214494i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 5.93142e6i | − 1.21553i | −0.794115 | − | 0.607767i | \(-0.792065\pi\) | ||||
0.794115 | − | 0.607767i | \(-0.207935\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.01807e6 | 0.350067 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.73851e6 | 0.700425 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.07128e6i | 1.02291i | 0.859309 | + | 0.511457i | \(0.170894\pi\) | ||||
−0.859309 | + | 0.511457i | \(0.829106\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.08750e6i | 0.883819i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 651715. | 0.0617388 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.78704e7 | −1.47477 | −0.737386 | − | 0.675471i | \(-0.763940\pi\) | ||||
−0.737386 | + | 0.675471i | \(0.763940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 2.11682e7i | − 1.52885i | −0.644715 | − | 0.764423i | \(-0.723024\pi\) | ||||
0.644715 | − | 0.764423i | \(-0.276976\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.23326e6i | 0.268728i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.76110e7 | 0.986576 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.11867e6 | 0.353264 | 0.176632 | − | 0.984277i | \(-0.443480\pi\) | ||||
0.176632 | + | 0.984277i | \(0.443480\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.02518e7i | 0.893442i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 1.36430e7i | − 0.536879i | −0.963297 | − | 0.268439i | \(-0.913492\pi\) | ||||
0.963297 | − | 0.268439i | \(-0.0865079\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.97099e7 | 1.39832 | 0.699162 | − | 0.714963i | \(-0.253557\pi\) | ||||
0.699162 | + | 0.714963i | \(0.253557\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.07036e7 | 0.338288 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.89246e7i | 1.10729i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 829701.i | − 0.0213017i | −0.999943 | − | 0.0106508i | \(-0.996610\pi\) | ||||
0.999943 | − | 0.0106508i | \(-0.00339033\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.78297e6 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.45656e7 | −0.306914 | −0.153457 | − | 0.988155i | \(-0.549041\pi\) | ||||
−0.153457 | + | 0.988155i | \(0.549041\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.07506e7i | 0.780653i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 2.18851e7i | − 0.382008i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.77943e7 | 1.23990 | 0.619952 | − | 0.784640i | \(-0.287152\pi\) | ||||
0.619952 | + | 0.784640i | \(0.287152\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.47607e7 | 1.23603 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 6.93615e7i | − 0.927228i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.60466e6i | 0.0688105i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.95872e7 | −1.12491 | −0.562454 | − | 0.826829i | \(-0.690143\pi\) | ||||
−0.562454 | + | 0.826829i | \(0.690143\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.39791e7 | 0.457832 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 9.82839e7i | − 0.944489i | −0.881468 | − | 0.472244i | \(-0.843444\pi\) | ||||
0.881468 | − | 0.472244i | \(-0.156556\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.83029e8i | 1.62619i | 0.582130 | + | 0.813096i | \(0.302220\pi\) | ||||
−0.582130 | + | 0.813096i | \(0.697780\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.64055e7 | −0.299509 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.13285e7 | 0.315293 | 0.157647 | − | 0.987496i | \(-0.449609\pi\) | ||||
0.157647 | + | 0.987496i | \(0.449609\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 3.44974e7i | − 0.244388i | −0.992506 | − | 0.122194i | \(-0.961007\pi\) | ||||
0.992506 | − | 0.122194i | \(-0.0389930\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 1.20446e8i | − 0.793416i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.89315e7 | −0.116110 | −0.0580552 | − | 0.998313i | \(-0.518490\pi\) | ||||
−0.0580552 | + | 0.998313i | \(0.518490\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.74162e8 | −0.995779 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 9.57672e7i | − 0.511062i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.96130e8i | 0.978039i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.90027e8 | 0.886490 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.79736e8 | −0.785262 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.49150e8i | 1.02052i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.21326e8i | 0.850779i | 0.905010 | + | 0.425389i | \(0.139863\pi\) | ||||
−0.905010 | + | 0.425389i | \(0.860137\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.80108e7 | 0.317817 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.49555e8 | 1.86606 | 0.933030 | − | 0.359799i | \(-0.117155\pi\) | ||||
0.933030 | + | 0.359799i | \(0.117155\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.69749e7i | 0.0862091i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.11329e7i | 0.123838i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.68597e8 | −0.478595 | −0.239298 | − | 0.970946i | \(-0.576917\pi\) | ||||
−0.239298 | + | 0.970946i | \(0.576917\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.01732e8 | 1.07616 | 0.538080 | − | 0.842894i | \(-0.319150\pi\) | ||||
0.538080 | + | 0.842894i | \(0.319150\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 2.77385e8i | − 0.701789i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 8.80574e8i | − 2.10582i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.88209e8 | 0.425764 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.43756e7 | 0.202111 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.43104e7i | 0.0899002i | 0.998989 | + | 0.0449501i | \(0.0143129\pi\) | ||||
−0.998989 | + | 0.0449501i | \(0.985687\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 7.21307e8i | − 1.38743i | −0.720247 | − | 0.693717i | \(-0.755972\pi\) | ||||
0.720247 | − | 0.693717i | \(-0.244028\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.21598e8 | 0.404390 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.96499e8 | 1.03343 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.39344e8i | 0.393934i | 0.980410 | + | 0.196967i | \(0.0631091\pi\) | ||||
−0.980410 | + | 0.196967i | \(0.936891\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.77456e8i | 0.590579i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.38233e8 | −1.24756 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.87688e7 | 0.0549202 | 0.0274601 | − | 0.999623i | \(-0.491258\pi\) | ||||
0.0274601 | + | 0.999623i | \(0.491258\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.78215e8i | 0.510273i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.25595e7i | 0.0290044i | 0.999895 | + | 0.0145022i | \(0.00461635\pi\) | ||||
−0.999895 | + | 0.0145022i | \(0.995384\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.10177e9 | −1.35066 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.04777e7 | 0.0356449 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.04991e9i | 1.17210i | 0.810273 | + | 0.586052i | \(0.199319\pi\) | ||||
−0.810273 | + | 0.586052i | \(0.800681\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.43030e8i | 0.472369i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.35714e8 | −0.851460 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.39481e8 | 0.720302 | 0.360151 | − | 0.932894i | \(-0.382725\pi\) | ||||
0.360151 | + | 0.932894i | \(0.382725\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1.75347e9i | − 1.63374i | −0.576821 | − | 0.816870i | \(-0.695707\pi\) | ||||
0.576821 | − | 0.816870i | \(-0.304293\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 9.89937e8i | − 0.882680i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.03582e9 | 0.884296 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.03758e9 | 1.66628 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.97970e8i | 0.155150i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.91581e9i | 1.43953i | 0.694219 | + | 0.719764i | \(0.255750\pi\) | ||||
−0.694219 | + | 0.719764i | \(0.744250\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.58868e9 | −1.14501 | −0.572504 | − | 0.819902i | \(-0.694028\pi\) | ||||
−0.572504 | + | 0.819902i | \(0.694028\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.23585e8 | 0.569600 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.10608e9i | 1.39833i | 0.714961 | + | 0.699165i | \(0.246445\pi\) | ||||
−0.714961 | + | 0.699165i | \(0.753555\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 1.88646e8i | − 0.120291i | −0.998190 | − | 0.0601456i | \(-0.980843\pi\) | ||||
0.998190 | − | 0.0601456i | \(-0.0191565\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.32907e8 | 0.203957 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.05840e8 | 0.533418 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 1.54570e9i | − 0.875208i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.47081e8i | 0.515829i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.80241e8 | 0.146874 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.09009e9 | 1.55898 | 0.779490 | − | 0.626414i | \(-0.215478\pi\) | ||||
0.779490 | + | 0.626414i | \(0.215478\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 6.38019e8i | − 0.309967i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.56881e8i | 0.354221i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.87092e9 | 1.29474 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.85705e9 | 0.807323 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 4.43696e9i | − 1.86002i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3.32988e9i | − 1.34651i | −0.739411 | − | 0.673255i | \(-0.764896\pi\) | ||||
0.739411 | − | 0.673255i | \(-0.235104\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.00559e8 | 0.195310 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.70537e8 | −0.101888 | −0.0509439 | − | 0.998702i | \(-0.516223\pi\) | ||||
−0.0509439 | + | 0.998702i | \(0.516223\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.89958e8i | 0.287251i | 0.989632 | + | 0.143626i | \(0.0458762\pi\) | ||||
−0.989632 | + | 0.143626i | \(0.954124\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.82033e9i | 0.639295i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.01558e9 | 0.344579 | 0.172289 | − | 0.985046i | \(-0.444884\pi\) | ||||
0.172289 | + | 0.985046i | \(0.444884\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.38547e9 | 0.782174 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 3.88013e7i | − 0.0122985i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 1.85103e9i | − 0.567313i | −0.958926 | − | 0.283656i | \(-0.908452\pi\) | ||||
0.958926 | − | 0.283656i | \(-0.0915475\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.15721e8 | 0.271453 | 0.135727 | − | 0.990746i | \(-0.456663\pi\) | ||||
0.135727 | + | 0.990746i | \(0.456663\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.23677e8 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.11617e8i | 0.225261i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 6.10241e8i | − 0.163951i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.81166e8 | −0.177197 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.39220e9 | 1.61048 | 0.805240 | − | 0.592949i | \(-0.202036\pi\) | ||||
0.805240 | + | 0.592949i | \(0.202036\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.70836e9i | 2.12547i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.90572e9i | 0.450710i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.28995e8 | 0.144183 | 0.0720916 | − | 0.997398i | \(-0.477033\pi\) | ||||
0.0720916 | + | 0.997398i | \(0.477033\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.98535e9 | 1.10789 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 1.02347e9i | − 0.220552i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.04520e9i | 0.845507i | 0.906245 | + | 0.422753i | \(0.138936\pi\) | ||||
−0.906245 | + | 0.422753i | \(0.861064\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.24607e9 | −0.658226 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.63808e9 | 0.715859 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 5.27436e9i | − 1.00730i | −0.863907 | − | 0.503652i | \(-0.831989\pi\) | ||||
0.863907 | − | 0.503652i | \(-0.168011\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.68764e9i | 1.79614i | 0.439851 | + | 0.898071i | \(0.355031\pi\) | ||||
−0.439851 | + | 0.898071i | \(0.644969\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.96387e9 | 0.713622 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.60262e9 | 0.804774 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.41820e8i | − 0.0240889i | −0.999927 | − | 0.0120445i | \(-0.996166\pi\) | ||||
0.999927 | − | 0.0120445i | \(-0.00383397\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 3.24371e9i | − 0.535335i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.45914e9 | −0.875587 | −0.437793 | − | 0.899076i | \(-0.644240\pi\) | ||||
−0.437793 | + | 0.899076i | \(0.644240\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.18396e9 | 1.27590 | 0.637952 | − | 0.770077i | \(-0.279782\pi\) | ||||
0.637952 | + | 0.770077i | \(0.279782\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.62104e8i | 0.0397278i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 7.43938e9i | − 1.09650i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.29105e9 | 0.471783 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.65723e9 | −0.649466 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.39451e9i | 0.324897i | 0.986717 | + | 0.162448i | \(0.0519391\pi\) | ||||
−0.986717 | + | 0.162448i | \(0.948061\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 7.18703e9i | − 0.948989i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.05670e9 | 0.264329 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.89630e10 | 2.37258 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.64282e9i | 0.443785i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 4.59628e9i | − 0.545301i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.51333e9 | 0.983784 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.66896e8 | −0.108849 | −0.0544247 | − | 0.998518i | \(-0.517332\pi\) | ||||
−0.0544247 | + | 0.998518i | \(0.517332\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.55944e9i | 0.938882i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 2.31046e9i | − 0.246978i | −0.992346 | − | 0.123489i | \(-0.960592\pi\) | ||||
0.992346 | − | 0.123489i | \(-0.0394083\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.76591e8 | 0.0600745 | 0.0300373 | − | 0.999549i | \(-0.490437\pi\) | ||||
0.0300373 | + | 0.999549i | \(0.490437\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.70252e9 | −0.172922 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.90592e9i | 0.386800i | 0.981120 | + | 0.193400i | \(0.0619515\pi\) | ||||
−0.981120 | + | 0.193400i | \(0.938049\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 9.41072e9i | − 0.908783i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.93274e9 | 0.182035 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.41205e9 | 0.129730 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1.00225e10i | − 0.898341i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1.61328e9i | − 0.141098i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.14811e10 | 0.979944 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.78587e9 | −0.482011 | −0.241005 | − | 0.970524i | \(-0.577477\pi\) | ||||
−0.241005 | + | 0.970524i | \(0.577477\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 5.63271e9i | − 0.458079i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.86296e9i | 0.227319i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.20243e10 | −0.932267 | −0.466134 | − | 0.884714i | \(-0.654353\pi\) | ||||
−0.466134 | + | 0.884714i | \(0.654353\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.85339e8 | −0.0670364 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 2.98258e10i | − 2.20584i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.50649e10i | 1.08840i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.14477e9 | −0.574913 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.76753e9 | 0.466780 | 0.233390 | − | 0.972383i | \(-0.425018\pi\) | ||||
0.233390 | + | 0.972383i | \(0.425018\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 5.68848e9i | − 0.383438i | −0.981450 | − | 0.191719i | \(-0.938594\pi\) | ||||
0.981450 | − | 0.191719i | \(-0.0614062\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 4.47859e9i | − 0.295062i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.78794e9 | 0.115147 | 0.0575736 | − | 0.998341i | \(-0.481664\pi\) | ||||
0.0575736 | + | 0.998341i | \(0.481664\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.48688e9 | 0.345471 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.17210e9i | 0.564671i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.27395e9i | 0.317511i | 0.987318 | + | 0.158755i | \(0.0507481\pi\) | ||||
−0.987318 | + | 0.158755i | \(0.949252\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.67894e10 | −0.988565 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.88668e9 | 0.511815 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.59704e10i | 0.899796i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.40472e9i | 0.353050i | 0.984296 | + | 0.176525i | \(0.0564856\pi\) | ||||
−0.984296 | + | 0.176525i | \(0.943514\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.40542e9 | −0.453371 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.56232e10 | −0.824657 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 8.98900e9i | − 0.464383i | −0.972670 | − | 0.232191i | \(-0.925410\pi\) | ||||
0.972670 | − | 0.232191i | \(-0.0745895\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.16516e10i | 0.589196i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.04924e10 | −1.01444 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.67818e10 | 1.78269 | 0.891346 | − | 0.453324i | \(-0.149762\pi\) | ||||
0.891346 | + | 0.453324i | \(0.149762\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.03504e10i | 0.491197i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.51464e9i | 0.0703907i | 0.999380 | + | 0.0351953i | \(0.0112053\pi\) | ||||
−0.999380 | + | 0.0351953i | \(0.988795\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.56546e10 | −0.712521 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.11586e9 | 0.183492 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.35930e10i | 1.46707i | 0.679652 | + | 0.733534i | \(0.262131\pi\) | ||||
−0.679652 | + | 0.733534i | \(0.737869\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.38789e10i | 1.87737i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.57001e10 | 1.07737 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.33686e8 | 0.0137072 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 8.19714e9i | − 0.329990i | −0.986294 | − | 0.164995i | \(-0.947239\pi\) | ||||
0.986294 | − | 0.164995i | \(-0.0527608\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.26149e9i | 0.0497729i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.33618e10 | −0.516758 | −0.258379 | − | 0.966044i | \(-0.583188\pi\) | ||||
−0.258379 | + | 0.966044i | \(0.583188\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.49474e10 | −2.46230 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.92360e9i | 0.0714980i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 5.17925e10i | − 1.88751i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.12559e10 | −1.47432 | −0.737162 | − | 0.675716i | \(-0.763835\pi\) | ||||
−0.737162 | + | 0.675716i | \(0.763835\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.88451e9 | −0.276317 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 3.45907e10i | − 1.18894i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 5.85794e9i | − 0.197493i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.87871e10 | 0.621322 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.55204e10 | −1.80134 | −0.900671 | − | 0.434502i | \(-0.856924\pi\) | ||||
−0.900671 | + | 0.434502i | \(0.856924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.81918e10i | 1.21574i | 0.794036 | + | 0.607871i | \(0.207976\pi\) | ||||
−0.794036 | + | 0.607871i | \(0.792024\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 1.29720e10i | − 0.405178i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.31913e10 | 0.710835 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.09741e10 | 1.23253 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 4.11804e10i | − 1.21580i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.58425e10i | 1.32849i | 0.747514 | + | 0.664246i | \(0.231247\pi\) | ||||
−0.747514 | + | 0.664246i | \(0.768753\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.43662e10 | 1.54660 | 0.773299 | − | 0.634042i | \(-0.218605\pi\) | ||||
0.773299 | + | 0.634042i | \(0.218605\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.80168e9 | 0.245815 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.03492e9i | 0.165480i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 6.56595e10i | − 1.76783i | −0.467651 | − | 0.883913i | \(-0.654900\pi\) | ||||
0.467651 | − | 0.883913i | \(-0.345100\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.41351e9 | 0.116689 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.38733e10 | −0.879514 | −0.439757 | − | 0.898117i | \(-0.644936\pi\) | ||||
−0.439757 | + | 0.898117i | \(0.644936\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.12870e10i | 0.797855i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.07219e9i | 0.0519039i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.81346e10 | 0.446193 | 0.223097 | − | 0.974796i | \(-0.428383\pi\) | ||||
0.223097 | + | 0.974796i | \(0.428383\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.72874e10 | −1.86811 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 3.37322e10i | − 0.801036i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.40887e10i | 0.795362i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.66606e10 | −0.611231 | −0.305615 | − | 0.952155i | \(-0.598862\pi\) | ||||
−0.305615 | + | 0.952155i | \(0.598862\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.03631e10 | 0.233475 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.04638e10i | 1.56014i | 0.625695 | + | 0.780068i | \(0.284816\pi\) | ||||
−0.625695 | + | 0.780068i | \(0.715184\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 4.09104e10i | − 0.890245i | −0.895470 | − | 0.445123i | \(-0.853160\pi\) | ||||
0.895470 | − | 0.445123i | \(-0.146840\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.78955e10 | 0.596654 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.39912e10 | −1.13515 | −0.567577 | − | 0.823320i | \(-0.692119\pi\) | ||||
−0.567577 | + | 0.823320i | \(0.692119\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.37792e10i | 0.284796i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.11930e10i | 0.227438i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.78451e10 | 0.756075 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.18963e9 | 0.0626564 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.76519e10i | 0.340971i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.17582e10i | 0.793231i | 0.917985 | + | 0.396616i | \(0.129815\pi\) | ||||
−0.917985 | + | 0.396616i | \(0.870185\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.12781e11 | −2.10696 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.92003e10 | −0.720279 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 4.00516e10i | − 0.723857i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 5.40468e10i | − 0.960847i | −0.877037 | − | 0.480423i | \(-0.840483\pi\) | ||||
0.877037 | − | 0.480423i | \(-0.159517\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.81304e9 | 0.0317082 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.85347e10 | 0.663019 | 0.331510 | − | 0.943452i | \(-0.392442\pi\) | ||||
0.331510 | + | 0.943452i | \(0.392442\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4.74179e10i | − 0.802703i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.76874e10i | 0.294606i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.64080e10 | 0.432823 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.84419e10 | −0.942588 | −0.471294 | − | 0.881976i | \(-0.656213\pi\) | ||||
−0.471294 | + | 0.881976i | \(0.656213\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.05500e9i | 0.0167457i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 1.70744e10i | − 0.266731i | −0.991067 | − | 0.133365i | \(-0.957422\pi\) | ||||
0.991067 | − | 0.133365i | \(-0.0425783\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.95274e10 | 0.607761 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.15248e10 | −0.779802 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 1.01105e11i | − 1.50627i | −0.657867 | − | 0.753134i | \(-0.728541\pi\) | ||||
0.657867 | − | 0.753134i | \(-0.271459\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.68645e10i | 1.12731i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.42530e9 | 0.0205796 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.36100e10 | −1.04642 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1.19277e11i | − 1.66953i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.90993e10i | 0.676715i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.85240e10 | 0.930019 | 0.465010 | − | 0.885306i | \(-0.346051\pi\) | ||||
0.465010 | + | 0.885306i | \(0.346051\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.17769e11 | −1.57407 | −0.787036 | − | 0.616907i | \(-0.788385\pi\) | ||||
−0.787036 | + | 0.616907i | \(0.788385\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.07185e10i | 0.272722i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.50284e11i | − 1.94836i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.09221e11 | −1.39471 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.90825e10 | −0.491591 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.68298e11i | 2.08531i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.66213e10i | 0.202885i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.45821e10 | 0.415867 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.05820e10 | 0.480815 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.06808e10i | 0.124685i | 0.998055 | + | 0.0623424i | \(0.0198571\pi\) | ||||
−0.998055 | + | 0.0623424i | \(0.980143\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 8.20015e10i | − 0.943240i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.38740e10 | 0.157259 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.66204e11 | −1.85649 | −0.928245 | − | 0.371971i | \(-0.878682\pi\) | ||||
−0.928245 | + | 0.371971i | \(0.878682\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 4.62948e10i | − 0.509615i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 6.52166e9i | − 0.0707541i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.60601e9 | 0.0171731 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.84406e10 | 0.510549 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.12167e10i | 0.739880i | 0.929056 | + | 0.369940i | \(0.120622\pi\) | ||||
−0.929056 | + | 0.369940i | \(0.879378\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 8.24099e10i | − 0.843980i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.52884e10 | 0.962030 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.48999e10 | −0.546435 | −0.273217 | − | 0.961952i | \(-0.588088\pi\) | ||||
−0.273217 | + | 0.961952i | \(0.588088\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 7.61380e9i | − 0.0747149i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.25815e9i | 0.0895760i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.65851e11 | 1.58222 | 0.791112 | − | 0.611671i | \(-0.209502\pi\) | ||||
0.791112 | + | 0.611671i | \(0.209502\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.77889e11 | 1.67342 | 0.836709 | − | 0.547648i | \(-0.184477\pi\) | ||||
0.836709 | + | 0.547648i | \(0.184477\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.95938e10i | 0.831112i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.91163e10i | 0.906721i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.39402e11 | −1.25767 | −0.628834 | − | 0.777540i | \(-0.716468\pi\) | ||||
−0.628834 | + | 0.777540i | \(0.716468\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.42954e10 | −0.661070 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 2.81939e10i | − 0.247429i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.62308e11i | 1.40497i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.85153e10 | 0.328859 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.09518e10 | 0.681827 | 0.340914 | − | 0.940095i | \(-0.389264\pi\) | ||||
0.340914 | + | 0.940095i | \(0.389264\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 2.06694e10i | − 0.171738i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.84915e10i | 0.807326i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.00987e11 | 0.816674 | 0.408337 | − | 0.912831i | \(-0.366109\pi\) | ||||
0.408337 | + | 0.912831i | \(0.366109\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.88788e10 | −0.629350 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 8.82208e9i | − 0.0694502i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.02923e11i | 0.799474i | 0.916630 | + | 0.399737i | \(0.130898\pi\) | ||||
−0.916630 | + | 0.399737i | \(0.869102\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.21864e11 | −1.70055 | −0.850273 | − | 0.526342i | \(-0.823563\pi\) | ||||
−0.850273 | + | 0.526342i | \(0.823563\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.55685e10 | 0.117755 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.64243e10i | 0.570440i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 5.54725e10i | − 0.408623i | −0.978906 | − | 0.204311i | \(-0.934504\pi\) | ||||
0.978906 | − | 0.204311i | \(-0.0654955\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.23619e10 | 0.307969 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.59733e11 | −1.86364 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.49374e11i | 1.05787i | 0.848662 | + | 0.528935i | \(0.177409\pi\) | ||||
−0.848662 | + | 0.528935i | \(0.822591\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 7.22855e10i | − 0.505301i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.45992e11 | −1.00737 | −0.503686 | − | 0.863887i | \(-0.668023\pi\) | ||||
−0.503686 | + | 0.863887i | \(0.668023\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.29296e11 | −1.56183 | −0.780915 | − | 0.624637i | \(-0.785247\pi\) | ||||
−0.780915 | + | 0.624637i | \(0.785247\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.42906e10i | 0.297814i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.50582e11i | 0.999591i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.07960e10 | −0.0707528 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.31056e10 | 0.0847980 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 2.60967e11i | − 1.66718i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.64365e10i | 0.292915i | 0.989217 | + | 0.146458i | \(0.0467872\pi\) | ||||
−0.989217 | + | 0.146458i | \(0.953213\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.44509e11 | 0.900078 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.90118e10 | −0.547460 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 8.83697e10i | − 0.536717i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 2.98372e10i | − 0.178960i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.85844e11 | −1.69316 | −0.846578 | − | 0.532264i | \(-0.821341\pi\) | ||||
−0.846578 | + | 0.532264i | \(0.821341\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.95497e11 | 1.72866 | 0.864328 | − | 0.502928i | \(-0.167744\pi\) | ||||
0.864328 | + | 0.502928i | \(0.167744\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.53958e10i | 0.204509i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 8.99469e10i | − 0.513297i | −0.966505 | − | 0.256649i | \(-0.917382\pi\) | ||||
0.966505 | − | 0.256649i | \(-0.0826183\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.59361e11 | −2.02559 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.34259e11 | 0.747517 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 2.81927e10i | − 0.155055i | −0.996990 | − | 0.0775273i | \(-0.975298\pi\) | ||||
0.996990 | − | 0.0775273i | \(-0.0247025\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.21018e11i | 1.20078i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.68456e10 | 0.466108 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.19224e11 | −0.632152 | −0.316076 | − | 0.948734i | \(-0.602365\pi\) | ||||
−0.316076 | + | 0.948734i | \(0.602365\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.48610e11i | 1.30230i | 0.758947 | + | 0.651152i | \(0.225714\pi\) | ||||
−0.758947 | + | 0.651152i | \(0.774286\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 2.07496e11i | − 1.07388i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.08487e10 | −0.0554740 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.02658e11 | 1.02391 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 1.55723e11i | − 0.777408i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 4.25678e11i | − 2.09986i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.89295e10 | −0.336004 | −0.168002 | − | 0.985787i | \(-0.553732\pi\) | ||||
−0.168002 | + | 0.985787i | \(0.553732\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.34088e10 | 0.112763 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.65608e11i | − 0.788365i | −0.919032 | − | 0.394182i | \(-0.871028\pi\) | ||||
0.919032 | − | 0.394182i | \(-0.128972\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 1.92766e11i | − 0.906883i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.26517e10 | −0.0588250 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.44222e11 | 1.12228 | 0.561141 | − | 0.827720i | \(-0.310362\pi\) | ||||
0.561141 | + | 0.827720i | \(0.310362\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 6.78058e10i | − 0.307967i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.69427e10i | 0.165845i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.53436e11 | 1.56831 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.38454e10 | −0.323900 | −0.161950 | − | 0.986799i | \(-0.551778\pi\) | ||||
−0.161950 | + | 0.986799i | \(0.551778\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.51282e10i | 0.369097i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.61567e11i | 0.692490i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.89429e11 | −1.65005 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.74937e10 | 0.198943 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 2.12728e11i | − 0.880953i | −0.897764 | − | 0.440476i | \(-0.854810\pi\) | ||||
0.897764 | − | 0.440476i | \(-0.145190\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 3.58923e10i | − 0.146954i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.11558e11 | 0.451588 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.90243e11 | 0.761432 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.44756e11i | 0.572863i | 0.958101 | + | 0.286432i | \(0.0924691\pi\) | ||||
−0.958101 | + | 0.286432i | \(0.907531\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 1.81456e9i | − 0.00710055i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.42291e11 | 2.48527 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.54146e11 | 1.35506 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 8.65642e10i | − 0.327538i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 4.70245e11i | − 1.75958i | −0.475363 | − | 0.879790i | \(-0.657683\pi\) | ||||
0.475363 | − | 0.879790i | \(-0.342317\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.54281e11 | −1.31101 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.28240e10 | 0.156724 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 1.07110e11i | − 0.387686i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.92240e10i | 0.319407i | 0.987165 | + | 0.159703i | \(0.0510537\pi\) | ||||
−0.987165 | + | 0.159703i | \(0.948946\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.04604e10 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.90691e11 | 0.667820 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.06258e11i | 0.714487i | 0.934011 | + | 0.357244i | \(0.116283\pi\) | ||||
−0.934011 | + | 0.357244i | \(0.883717\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.79556e10i | 0.130055i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.43152e11 | 0.485207 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.46428e10 | 0.116154 | 0.0580772 | − | 0.998312i | \(-0.481503\pi\) | ||||
0.0580772 | + | 0.998312i | \(0.481503\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 2.85381e10i | − 0.0946570i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.92994e9i | 0.0128953i | 0.999979 | + | 0.00644764i | \(0.00205236\pi\) | ||||
−0.999979 | + | 0.00644764i | \(0.997948\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.78206e10 | −0.0578491 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.18550e10 | −0.102305 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.99975e10i | 0.254184i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.31276e11i | 1.04143i | 0.853730 | + | 0.520716i | \(0.174335\pi\) | ||||
−0.853730 | + | 0.520716i | \(0.825665\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.98934e11 | 0.929811 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.90092e11 | 0.892789 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 6.32528e10i | − 0.192618i | −0.995351 | − | 0.0963089i | \(-0.969296\pi\) | ||||
0.995351 | − | 0.0963089i | \(-0.0307037\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.07250e11i | 1.22714i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.86012e11 | 0.852797 | 0.426399 | − | 0.904535i | \(-0.359782\pi\) | ||||
0.426399 | + | 0.904535i | \(0.359782\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.67748e10 | 0.197022 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.91215e10i | 0.260218i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.82530e11i | 2.26110i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.53604e11 | −0.439235 | −0.219617 | − | 0.975586i | \(-0.570481\pi\) | ||||
−0.219617 | + | 0.975586i | \(0.570481\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.94152e10 | 0.0832443 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.38819e11i | 0.668883i | 0.942416 | + | 0.334442i | \(0.108548\pi\) | ||||
−0.942416 | + | 0.334442i | \(0.891452\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 3.39469e11i | − 0.941009i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.33142e11 | 0.639640 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.35604e10 | −0.145443 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 2.74352e11i | − 0.737400i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 4.78628e10i | − 0.127336i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.62582e10 | −0.253489 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.90235e11 | 0.756572 | 0.378286 | − | 0.925689i | \(-0.376514\pi\) | ||||
0.378286 | + | 0.925689i | \(0.376514\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.89175e11i | 0.488153i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 3.66447e10i | − 0.0936064i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.26939e11 | −2.34400 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.51804e11 | −0.380027 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.71943e11i | 1.41749i | 0.705465 | + | 0.708744i | \(0.250738\pi\) | ||||
−0.705465 | + | 0.708744i | \(0.749262\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 6.01002e11i | − 1.47465i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.70136e11 | 0.413301 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.98541e11 | 1.92059 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 3.37117e11i | − 0.802781i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 2.46657e11i | − 0.581567i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.26381e10 | −0.122887 | −0.0614435 | − | 0.998111i | \(-0.519570\pi\) | ||||
−0.0614435 | + | 0.998111i | \(0.519570\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.17986e11 | 0.272739 | 0.136369 | − | 0.990658i | \(-0.456457\pi\) | ||||
0.136369 | + | 0.990658i | \(0.456457\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.53046e11i | 1.03700i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.55919e10i | 0.0353402i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.62268e10 | 0.0588649 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.85372e11 | 0.412010 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.94904e11i | 0.428992i | 0.976725 | + | 0.214496i | \(0.0688109\pi\) | ||||
−0.976725 | + | 0.214496i | \(0.931189\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1.25481e11i | − 0.273513i | −0.990605 | − | 0.136756i | \(-0.956332\pi\) | ||||
0.990605 | − | 0.136756i | \(-0.0436678\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.15243e11 | 0.464637 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.47785e11 | 1.17108 | 0.585542 | − | 0.810642i | \(-0.300882\pi\) | ||||
0.585542 | + | 0.810642i | \(0.300882\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1.15721e11i | − 0.245015i | −0.992468 | − | 0.122507i | \(-0.960906\pi\) | ||||
0.992468 | − | 0.122507i | \(-0.0390935\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 6.63225e9i | − 0.0139078i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.04481e11 | 0.424691 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.07289e9 | −0.0186638 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1.51694e11i | − 0.309076i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.81036e11i | 0.567172i | 0.958947 | + | 0.283586i | \(0.0915241\pi\) | ||||
−0.958947 | + | 0.283586i | \(0.908476\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.81243e11 | 0.562210 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.55299e11 | −0.505520 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 4.43106e11i | − 0.869123i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.67826e11i | 0.714674i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.82726e11 | 0.736643 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.11534e12 | 2.12661 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 8.36511e11i | − 1.58007i | −0.613063 | − | 0.790034i | \(-0.710063\pi\) | ||||
0.613063 | − | 0.790034i | \(-0.289937\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.22574e10i | 0.0229368i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.69801e9 | 0.0161249 | 0.00806244 | − | 0.999967i | \(-0.497434\pi\) | ||||
0.00806244 | + | 0.999967i | \(0.497434\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.46238e11 | 0.452254 | 0.226127 | − | 0.974098i | \(-0.427394\pi\) | ||||
0.226127 | + | 0.974098i | \(0.427394\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 3.47906e11i | − 0.633066i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.52034e11i | 1.53608i | 0.640402 | + | 0.768040i | \(0.278768\pi\) | ||||
−0.640402 | + | 0.768040i | \(0.721232\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.22247e11 | −0.754228 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.53907e11 | 0.272384 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.66848e10i | − 0.0292577i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 3.11722e11i | − 0.541620i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.17797e11 | −0.374969 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.82267e11 | −0.822725 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.14656e11i | 1.54618i | 0.634298 | + | 0.773089i | \(0.281289\pi\) | ||||
−0.634298 | + | 0.773089i | \(0.718711\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.11980e11i | 0.187579i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.17443e11 | 1.02493 | 0.512464 | − | 0.858709i | \(-0.328733\pi\) | ||||
0.512464 | + | 0.858709i | \(0.328733\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.59286e11 | 1.08450 | 0.542252 | − | 0.840216i | \(-0.317572\pi\) | ||||
0.542252 | + | 0.840216i | \(0.317572\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 3.36104e11i | − 0.547899i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 9.49677e11i | − 1.53420i | −0.641529 | − | 0.767099i | \(-0.721700\pi\) | ||||
0.641529 | − | 0.767099i | \(-0.278300\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.28409e11 | −0.685885 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.61824e10 | 0.152611 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 8.26593e10i | − 0.129983i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.97401e11i | 0.463501i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.86810e11 | 1.36981 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.94095e11 | −1.06263 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.17824e11i | 1.24097i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.70358e11i | 0.256219i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.05202e11 | 1.05128 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.18987e11 | 0.471350 | 0.235675 | − | 0.971832i | \(-0.424270\pi\) | ||||
0.235675 | + | 0.971832i | \(0.424270\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 2.14947e11i | − 0.314830i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1.05774e12i | − 1.53570i | −0.640628 | − | 0.767852i | \(-0.721326\pi\) | ||||
0.640628 | − | 0.767852i | \(-0.278674\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.92905e11 | −0.421545 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.98129e11 | 0.567988 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.06374e12i | 1.50439i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.29009e12i | 1.80867i | 0.426828 | + | 0.904333i | \(0.359631\pi\) | ||||
−0.426828 | + | 0.904333i | \(0.640369\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.52173e10 | −0.0628443 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.97417e11 | −0.823134 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 5.89489e11i | − 0.805209i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.00285e11i | 0.542064i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.16906e11 | −0.693983 | −0.346991 | − | 0.937868i | \(-0.612797\pi\) | ||||
−0.346991 | + | 0.937868i | \(0.612797\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.81234e10 | 0.0374343 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1.08050e11i | − 0.142593i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.19468e11i | 1.07222i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.96069e11 | −1.03274 | −0.516371 | − | 0.856365i | \(-0.672718\pi\) | ||||
−0.516371 | + | 0.856365i | \(0.672718\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.69645e10 | 0.0346841 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 5.93891e11i | − 0.757440i | −0.925511 | − | 0.378720i | \(-0.876364\pi\) | ||||
0.925511 | − | 0.378720i | \(-0.123636\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.66437e12i | − 2.10476i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.96188e10 | −0.0998363 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.57641e10 | 0.0942028 | 0.0471014 | − | 0.998890i | \(-0.485002\pi\) | ||||
0.0471014 | + | 0.998890i | \(0.485002\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1.73887e12i | − 2.14389i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.82662e11i | 0.223319i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.44761e11 | 0.781676 | 0.390838 | − | 0.920459i | \(-0.372185\pi\) | ||||
0.390838 | + | 0.920459i | \(0.372185\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.70495e11 | −0.926309 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 4.40096e11i | − 0.524686i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 3.26345e11i | − 0.385836i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.34693e12 | −1.57925 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.03854e10 | 0.105098 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 6.38931e11i | − 0.736791i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.70360e11i | − 0.194833i | −0.995244 | − | 0.0974166i | \(-0.968942\pi\) | ||||
0.995244 | − | 0.0974166i | \(-0.0310579\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.60352e10 | 0.0748997 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.23154e11 | −0.476016 | −0.238008 | − | 0.971263i | \(-0.576495\pi\) | ||||
−0.238008 | + | 0.971263i | \(0.576495\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.77612e11i | 0.867584i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 4.68705e11i | − 0.518658i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.56737e12 | −1.72025 | −0.860127 | − | 0.510080i | \(-0.829616\pi\) | ||||
−0.860127 | + | 0.510080i | \(0.829616\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.56439e12 | 1.70300 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 7.54458e10i | − 0.0814627i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 9.58136e10i | − 0.102616i | −0.998683 | − | 0.0513078i | \(-0.983661\pi\) | ||||
0.998683 | − | 0.0513078i | \(-0.0163389\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.47014e11 | −0.899799 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.36920e11 | 0.565771 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.14985e11i | 0.851853i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 6.32891e11i | − 0.656198i | −0.944643 | − | 0.328099i | \(-0.893592\pi\) | ||||
0.944643 | − | 0.328099i | \(-0.106408\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.70578e11 | −0.278289 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.58687e10 | 0.0774052 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.96393e12i | 1.98767i | 0.110851 | + | 0.993837i | \(0.464642\pi\) | ||||
−0.110851 | + | 0.993837i | \(0.535358\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 2.63416e11i | − 0.264472i |
(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 | 384.9.b.a.319.7 | yes | 8 | |
4.3 | odd | 2 | inner | 384.9.b.a.319.3 | yes | 8 | |
8.3 | odd | 2 | inner | 384.9.b.a.319.6 | yes | 8 | |
8.5 | even | 2 | inner | 384.9.b.a.319.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.9.b.a.319.2 | ✓ | 8 | 8.5 | even | 2 | inner | |
384.9.b.a.319.3 | yes | 8 | 4.3 | odd | 2 | inner | |
384.9.b.a.319.6 | yes | 8 | 8.3 | odd | 2 | inner | |
384.9.b.a.319.7 | yes | 8 | 1.1 | even | 1 | trivial |