Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,8,Mod(49,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.49");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.f (of order \(2\), degree \(1\), not 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: | \(187.431015290\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.49 |
Dual form | 600.8.f.a.49.1 |
$q$-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 \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 120.000i | − 0.132232i | −0.997812 | − | 0.0661162i | \(-0.978939\pi\) | ||||
0.997812 | − | 0.0661162i | \(-0.0210608\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −729.000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7196.00 | −1.63011 | −0.815055 | − | 0.579384i | \(-0.803293\pi\) | ||||
−0.815055 | + | 0.579384i | \(0.803293\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 9626.00i | − 1.21519i | −0.794247 | − | 0.607595i | \(-0.792134\pi\) | ||||
0.794247 | − | 0.607595i | \(-0.207866\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 18674.0i | − 0.921862i | −0.887436 | − | 0.460931i | \(-0.847515\pi\) | ||||
0.887436 | − | 0.460931i | \(-0.152485\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7004.00 | −0.234266 | −0.117133 | − | 0.993116i | \(-0.537370\pi\) | ||||
−0.117133 | + | 0.993116i | \(0.537370\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3240.00 | 0.0763445 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 63704.0i | − 1.09174i | −0.837870 | − | 0.545870i | \(-0.816199\pi\) | ||||
0.837870 | − | 0.545870i | \(-0.183801\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 19683.0i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29334.0 | −0.223346 | −0.111673 | − | 0.993745i | \(-0.535621\pi\) | ||||
−0.111673 | + | 0.993745i | \(0.535621\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 87968.0 | 0.530345 | 0.265173 | − | 0.964201i | \(-0.414571\pi\) | ||||
0.265173 | + | 0.964201i | \(0.414571\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 194292.i | − 0.941144i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 227982.i | − 0.739937i | −0.929044 | − | 0.369968i | \(-0.879369\pi\) | ||||
0.929044 | − | 0.369968i | \(-0.120631\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 259902. | 0.701590 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −160806. | −0.364384 | −0.182192 | − | 0.983263i | \(-0.558319\pi\) | ||||
−0.182192 | + | 0.983263i | \(0.558319\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 136132.i | 0.261108i | 0.991441 | + | 0.130554i | \(0.0416756\pi\) | ||||
−0.991441 | + | 0.130554i | \(0.958324\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.20696e6i | 1.69571i | 0.530232 | + | 0.847853i | \(0.322105\pi\) | ||||
−0.530232 | + | 0.847853i | \(0.677895\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 809143. | 0.982515 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 504198. | 0.532238 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 398786.i | − 0.367938i | −0.982932 | − | 0.183969i | \(-0.941105\pi\) | ||||
0.982932 | − | 0.183969i | \(-0.0588946\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 189108.i | − 0.135253i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.15244e6 | −0.730524 | −0.365262 | − | 0.930905i | \(-0.619021\pi\) | ||||
−0.365262 | + | 0.930905i | \(0.619021\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.07060e6 | −1.16800 | −0.583999 | − | 0.811754i | \(-0.698513\pi\) | ||||
−0.583999 | + | 0.811754i | \(0.698513\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 87480.0i | 0.0440775i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.07343e6i | 1.65462i | 0.561746 | + | 0.827310i | \(0.310130\pi\) | ||||
−0.561746 | + | 0.827310i | \(0.689870\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.72001e6 | 0.630316 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −383752. | −0.127247 | −0.0636233 | − | 0.997974i | \(-0.520266\pi\) | ||||
−0.0636233 | + | 0.997974i | \(0.520266\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.00601e6i | 0.904400i | 0.891917 | + | 0.452200i | \(0.149361\pi\) | ||||
−0.891917 | + | 0.452200i | \(0.850639\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 863520.i | 0.215553i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.94811e6 | 1.12913 | 0.564566 | − | 0.825388i | \(-0.309044\pi\) | ||||
0.564566 | + | 0.825388i | \(0.309044\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 9.16349e6i | − 1.75909i | −0.475817 | − | 0.879544i | \(-0.657848\pi\) | ||||
0.475817 | − | 0.879544i | \(-0.342152\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 792018.i | − 0.128949i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.30411e6 | −1.09825 | −0.549126 | − | 0.835740i | \(-0.685039\pi\) | ||||
−0.549126 | + | 0.835740i | \(0.685039\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.15512e6 | −0.160688 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.37514e6i | 0.306195i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 690526.i | 0.0768208i | 0.999262 | + | 0.0384104i | \(0.0122294\pi\) | ||||
−0.999262 | + | 0.0384104i | \(0.987771\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.24588e6 | 0.543370 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.32667e7 | 1.28126 | 0.640631 | − | 0.767849i | \(-0.278673\pi\) | ||||
0.640631 | + | 0.767849i | \(0.278673\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.86825e6i | 0.438978i | 0.975615 | + | 0.219489i | \(0.0704389\pi\) | ||||
−0.975615 | + | 0.219489i | \(0.929561\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 7.91860e6i | − 0.624892i | −0.949936 | − | 0.312446i | \(-0.898852\pi\) | ||||
0.949936 | − | 0.312446i | \(-0.101148\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.93030e6 | 0.364654 | 0.182327 | − | 0.983238i | \(-0.441637\pi\) | ||||
0.182327 | + | 0.983238i | \(0.441637\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.15551e6 | 0.427203 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.31707e6i | 0.151066i | 0.997143 | + | 0.0755328i | \(0.0240657\pi\) | ||||
−0.997143 | + | 0.0755328i | \(0.975934\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.01735e6i | 0.405063i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.24088e6 | −0.121900 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.22952e7 | 1.65726 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 4.34176e6i | − 0.210377i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.25119e7i | 0.975214i | 0.873063 | + | 0.487607i | \(0.162130\pi\) | ||||
−0.873063 | + | 0.487607i | \(0.837870\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.67556e6 | −0.150751 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.35895e7 | −0.528147 | −0.264073 | − | 0.964503i | \(-0.585066\pi\) | ||||
−0.264073 | + | 0.964503i | \(0.585066\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 840480.i | 0.0309775i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 714618.i | − 0.0237439i | −0.999930 | − | 0.0118719i | \(-0.996221\pi\) | ||||
0.999930 | − | 0.0118719i | \(-0.00377905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.78816e7 | −0.564747 | −0.282373 | − | 0.959305i | \(-0.591122\pi\) | ||||
−0.282373 | + | 0.959305i | \(0.591122\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.25879e7 | −0.979016 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.92687e7i | 1.98089i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.18469e7i | 0.567255i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.00391e7 | 0.496279 | 0.248139 | − | 0.968724i | \(-0.420181\pi\) | ||||
0.248139 | + | 0.968724i | \(0.420181\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.07634e7 | −0.963499 | −0.481749 | − | 0.876309i | \(-0.659998\pi\) | ||||
−0.481749 | + | 0.876309i | \(0.659998\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.36133e7i | 0.307287i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 5.54702e7i | − 1.14396i | −0.820268 | − | 0.571980i | \(-0.806176\pi\) | ||||
0.820268 | − | 0.571980i | \(-0.193824\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.07672e7 | 0.212429 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.64448e6 | −0.144363 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1.80344e6i | − 0.0326172i | −0.999867 | − | 0.0163086i | \(-0.994809\pi\) | ||||
0.999867 | − | 0.0163086i | \(-0.00519141\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 5.99273e6i | − 0.0995673i | −0.998760 | − | 0.0497837i | \(-0.984147\pi\) | ||||
0.998760 | − | 0.0497837i | \(-0.0158532\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.99114e7 | −0.476686 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.10592e6 | 0.0780885 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.25631e8i | 1.84474i | 0.386313 | + | 0.922368i | \(0.373748\pi\) | ||||
−0.386313 | + | 0.922368i | \(0.626252\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 3.11158e7i | − 0.421769i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.86498e7 | −0.634009 | −0.317004 | − | 0.948424i | \(-0.602677\pi\) | ||||
−0.317004 | + | 0.948424i | \(0.602677\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.97548e7 | −0.623677 | −0.311838 | − | 0.950135i | \(-0.600945\pi\) | ||||
−0.311838 | + | 0.950135i | \(0.600945\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 5.59063e7i | − 0.674344i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.34378e8i | 1.50274i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.36196e6 | −0.0254482 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.11324e8 | 1.15604 | 0.578021 | − | 0.816022i | \(-0.303825\pi\) | ||||
0.578021 | + | 0.816022i | \(0.303825\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 1.34786e8i | − 1.34957i | −0.738014 | − | 0.674786i | \(-0.764236\pi\) | ||||
0.738014 | − | 0.674786i | \(-0.235764\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 3.97557e7i | − 0.370482i | −0.982693 | − | 0.185241i | \(-0.940693\pi\) | ||||
0.982693 | − | 0.185241i | \(-0.0593066\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.03321e8 | 0.929398 | 0.464699 | − | 0.885469i | \(-0.346162\pi\) | ||||
0.464699 | + | 0.885469i | \(0.346162\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.09983e8 | −0.955295 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.52008e6i | 0.0295336i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.64402e7i | 0.363913i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.04008e7 | 0.381879 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.79475e8 | −1.31527 | −0.657634 | − | 0.753337i | \(-0.728443\pi\) | ||||
−0.657634 | + | 0.753337i | \(0.728443\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.03613e7i | − 0.0734659i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 1.05562e7i | − 0.0701289i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.11623e7 | −0.522155 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.79756e8 | −1.12024 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.85311e8i | 1.72286i | 0.507872 | + | 0.861432i | \(0.330432\pi\) | ||||
−0.507872 | + | 0.861432i | \(0.669568\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.74798e7i | 0.155928i | 0.996956 | + | 0.0779638i | \(0.0248419\pi\) | ||||
−0.996956 | + | 0.0779638i | \(0.975158\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.56562e7 | 0.471341 | 0.235670 | − | 0.971833i | \(-0.424271\pi\) | ||||
0.235670 | + | 0.971833i | \(0.424271\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.33150e7 | −0.124450 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.04907e8i | 0.543322i | 0.962393 | + | 0.271661i | \(0.0875729\pi\) | ||||
−0.962393 | + | 0.271661i | \(0.912427\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.33599e8i | 0.651905i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.77184e7 | 0.131333 | 0.0656667 | − | 0.997842i | \(-0.479083\pi\) | ||||
0.0656667 | + | 0.997842i | \(0.479083\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.95271e8 | −1.35882 | −0.679409 | − | 0.733760i | \(-0.737764\pi\) | ||||
−0.679409 | + | 0.733760i | \(0.737764\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.43489e7i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.74205e7i | 0.284677i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.47414e8 | 1.01561 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.02885e8 | −1.20898 | −0.604491 | − | 0.796612i | \(-0.706624\pi\) | ||||
−0.604491 | + | 0.796612i | \(0.706624\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.58414e8i | 1.77966i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 4.14636e7i | − 0.152370i | −0.997094 | − | 0.0761852i | \(-0.975726\pi\) | ||||
0.997094 | − | 0.0761852i | \(-0.0242740\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.73578e7 | −0.0978436 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.13845e7 | 0.0744487 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.20007e8i | 1.42368i | 0.702343 | + | 0.711839i | \(0.252137\pi\) | ||||
−0.702343 | + | 0.711839i | \(0.747863\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1.97211e8i | − 0.634076i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.56477e8 | −0.490138 | −0.245069 | − | 0.969506i | \(-0.578811\pi\) | ||||
−0.245069 | + | 0.969506i | \(0.578811\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.71491e8 | −0.828633 | −0.414316 | − | 0.910133i | \(-0.635979\pi\) | ||||
−0.414316 | + | 0.910133i | \(0.635979\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 3.11882e7i | − 0.0927730i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.80318e7i | 0.277133i | 0.990353 | + | 0.138566i | \(0.0442494\pi\) | ||||
−0.990353 | + | 0.138566i | \(0.955751\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.41287e7 | −0.176782 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.04839e8 | −1.08845 | −0.544227 | − | 0.838938i | \(-0.683177\pi\) | ||||
−0.544227 | + | 0.838938i | \(0.683177\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.41439e8i | 0.633220i | 0.948556 | + | 0.316610i | \(0.102545\pi\) | ||||
−0.948556 | + | 0.316610i | \(0.897455\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.92967e7i | 0.0481833i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.16204e7 | 0.150170 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.86442e7 | −0.0443525 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.95052e8i | − 0.453016i | −0.974009 | − | 0.226508i | \(-0.927269\pi\) | ||||
0.974009 | − | 0.226508i | \(-0.0727310\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.41639e8i | 0.313715i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.13215e8 | −1.32667 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.63358e7 | 0.0345270 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.58201e8i | 0.739737i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.02082e8i | 0.201356i | 0.994919 | + | 0.100678i | \(0.0321012\pi\) | ||||
−0.994919 | + | 0.100678i | \(0.967899\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.31443e8 | −0.253444 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.04913e8 | 0.574797 | 0.287398 | − | 0.957811i | \(-0.407210\pi\) | ||||
0.287398 | + | 0.957811i | \(0.407210\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.47441e8i | 1.19342i | 0.802455 | + | 0.596712i | \(0.203527\pi\) | ||||
−0.802455 | + | 0.596712i | \(0.796473\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.48935e8i | 0.262596i | 0.991343 | + | 0.131298i | \(0.0419145\pi\) | ||||
−0.991343 | + | 0.131298i | \(0.958086\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.11087e8 | 0.364079 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.13802e8 | 0.360782 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.30793e8i | 0.215961i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.33118e8i | 0.210533i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.44835e8 | 0.224227 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.68290e8 | 1.46760 | 0.733800 | − | 0.679366i | \(-0.237745\pi\) | ||||
0.733800 | + | 0.679366i | \(0.237745\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.66199e8i | 0.246646i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 1.65424e8i | − 0.235447i | −0.993046 | − | 0.117723i | \(-0.962440\pi\) | ||||
0.993046 | − | 0.117723i | \(-0.0375596\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.25610e7 | −0.0872177 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.33018e8 | −0.864521 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.95922e8i | − 0.262153i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.12455e9i | 1.44486i | 0.691443 | + | 0.722431i | \(0.256975\pi\) | ||||
−0.691443 | + | 0.722431i | \(0.743025\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.55383e8 | 0.321590 | 0.160795 | − | 0.986988i | \(-0.448594\pi\) | ||||
0.160795 | + | 0.986988i | \(0.448594\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.89469e8 | −0.233863 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.45151e8i | 0.417635i | 0.977955 | + | 0.208818i | \(0.0669615\pi\) | ||||
−0.977955 | + | 0.208818i | \(0.933038\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 6.05038e7i | − 0.0703791i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.11307e8 | 0.925453 | 0.462727 | − | 0.886501i | \(-0.346871\pi\) | ||||
0.462727 | + | 0.886501i | \(0.346871\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.44816e8 | −0.945120 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.71972e8i | 0.956818i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.76625e8i | 0.820125i | 0.912057 | + | 0.410062i | \(0.134493\pi\) | ||||
−0.912057 | + | 0.410062i | \(0.865507\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.17228e8 | 0.121461 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.78543e7 | −0.0486533 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.66790e9i | 1.66414i | 0.554669 | + | 0.832071i | \(0.312845\pi\) | ||||
−0.554669 | + | 0.832071i | \(0.687155\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.82369e8i | 0.271408i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.25007e9 | 1.17949 | 0.589747 | − | 0.807588i | \(-0.299228\pi\) | ||||
0.589747 | + | 0.807588i | \(0.299228\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.07822e8 | −0.563040 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.43374e9i | 1.30399i | 0.758223 | + | 0.651995i | \(0.226068\pi\) | ||||
−0.758223 | + | 0.651995i | \(0.773932\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 9.92402e7i | − 0.0870361i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.31613e8 | −0.630170 | −0.315085 | − | 0.949063i | \(-0.602033\pi\) | ||||
−0.315085 | + | 0.949063i | \(0.602033\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.18961e9 | −1.00643 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 3.66917e8i | − 0.304926i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1.19059e9i | − 0.954983i | −0.878636 | − | 0.477492i | \(-0.841546\pi\) | ||||
0.878636 | − | 0.477492i | \(-0.158454\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.26930e7 | −0.0178849 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.44638e9 | −1.89460 | −0.947302 | − | 0.320343i | \(-0.896202\pi\) | ||||
−0.947302 | + | 0.320343i | \(0.896202\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 8.46780e8i | − 0.644470i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.64056e9i | 1.20618i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.83663e9 | −1.32737 | −0.663684 | − | 0.748013i | \(-0.731008\pi\) | ||||
−0.663684 | + | 0.748013i | \(0.731008\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.92947e7 | 0.0137085 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.38292e8i | 0.0965991i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 4.82802e8i | − 0.326057i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.77854e9 | 1.84530 | 0.922651 | − | 0.385636i | \(-0.126018\pi\) | ||||
0.922651 | + | 0.385636i | \(0.126018\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.16625e9 | 0.761736 | 0.380868 | − | 0.924629i | \(-0.375625\pi\) | ||||
0.380868 | + | 0.924629i | \(0.375625\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 8.79874e8i | − 0.565235i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.48472e8i | 0.154447i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.87025e9 | −1.14367 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.90479e8 | −0.174761 | −0.0873806 | − | 0.996175i | \(-0.527850\pi\) | ||||
−0.0873806 | + | 0.996175i | \(0.527850\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.20651e9i | 1.30616i | 0.757288 | + | 0.653082i | \(0.226524\pi\) | ||||
−0.757288 | + | 0.653082i | \(0.773476\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.46183e8i | 0.255757i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.97564e7 | −0.0562749 | −0.0281375 | − | 0.999604i | \(-0.508958\pi\) | ||||
−0.0281375 | + | 0.999604i | \(0.508958\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.89865e8 | −0.327505 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 8.18948e8i | − 0.447552i | −0.974641 | − | 0.223776i | \(-0.928162\pi\) | ||||
0.974641 | − | 0.223776i | \(-0.0718383\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.41055e8i | 0.286527i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.46241e9 | 1.28380 | 0.641900 | − | 0.766788i | \(-0.278146\pi\) | ||||
0.641900 | + | 0.766788i | \(0.278146\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.15716e9 | 0.593985 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 1.10061e9i | − 0.556276i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.76135e9i | 1.35337i | 0.736274 | + | 0.676683i | \(0.236583\pi\) | ||||
−0.736274 | + | 0.676683i | \(0.763417\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.67560e8 | −0.177413 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.48308e9 | 0.705036 | 0.352518 | − | 0.935805i | \(-0.385326\pi\) | ||||
0.352518 | + | 0.935805i | \(0.385326\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 1.42591e9i | − 0.667666i | −0.942632 | − | 0.333833i | \(-0.891658\pi\) | ||||
0.942632 | − | 0.333833i | \(-0.108342\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 1.99579e9i | − 0.906788i | −0.891310 | − | 0.453394i | \(-0.850213\pi\) | ||||
0.891310 | − | 0.453394i | \(-0.149787\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.88811e8 | 0.218794 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.49769e9 | 0.660465 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 9.79606e8i | − 0.425635i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.90715e8i | 0.122646i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.66385e8 | −0.235471 | −0.117736 | − | 0.993045i | \(-0.537564\pi\) | ||||
−0.117736 | + | 0.993045i | \(0.537564\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.19455e9 | −0.899163 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 2.06401e8i | − 0.0833483i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.23609e9i | 0.484953i | 0.970157 | + | 0.242476i | \(0.0779597\pi\) | ||||
−0.970157 | + | 0.242476i | \(0.922040\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.86930e7 | 0.0188315 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.49612e8 | −0.285793 | −0.142896 | − | 0.989738i | \(-0.545642\pi\) | ||||
−0.142896 | + | 0.989738i | \(0.545642\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.47783e8i | 0.205894i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.60502e7i | 0.0168261i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.65642e9 | 1.31736 | 0.658680 | − | 0.752423i | \(-0.271115\pi\) | ||||
0.658680 | + | 0.752423i | \(0.271115\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.61804e8 | 0.0574852 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 2.19390e9i | − 0.768649i | −0.923198 | − | 0.384324i | \(-0.874434\pi\) | ||||
0.923198 | − | 0.384324i | \(-0.125566\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 8.07607e8i | − 0.275215i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.24865e9 | −1.42804 | −0.714018 | − | 0.700127i | \(-0.753127\pi\) | ||||
−0.714018 | + | 0.700127i | \(0.753127\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.60721e8 | 0.119591 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.37860e8i | 0.0450844i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 8.68528e9i | − 2.76419i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.39203e9 | −1.06506 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.70617e8 | −0.114814 | −0.0574068 | − | 0.998351i | \(-0.518283\pi\) | ||||
−0.0574068 | + | 0.998351i | \(0.518283\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.33645e9i | 1.93682i | 0.249356 | + | 0.968412i | \(0.419781\pi\) | ||||
−0.249356 | + | 0.968412i | \(0.580219\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.64271e9i | − 0.488905i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.53374e8 | −0.191897 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.40126e8 | 0.243508 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.54792e9i | 0.442795i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 1.31354e9i | − 0.366045i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.82259e9 | −1.60161 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.00792e9 | −1.08825 | −0.544125 | − | 0.839004i | \(-0.683138\pi\) | ||||
−0.544125 | + | 0.839004i | \(0.683138\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 1.34338e9i | − 0.360080i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.66046e9i | 0.956269i | 0.878287 | + | 0.478135i | \(0.158687\pi\) | ||||
−0.878287 | + | 0.478135i | \(0.841313\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.50947e9 | 0.389333 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.05455e8 | 0.0523223 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 5.93773e8i | − 0.149308i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 5.25630e9i | − 1.28880i | −0.764687 | − | 0.644402i | \(-0.777106\pi\) | ||||
0.764687 | − | 0.644402i | \(-0.222894\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.31041e9 | 0.317296 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.62821e9 | −0.867605 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 5.01985e9i | − 1.18553i | −0.805376 | − | 0.592764i | \(-0.798037\pi\) | ||||
0.805376 | − | 0.592764i | \(-0.201963\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 6.37729e7i | − 0.0146925i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.80495e9 | −0.638311 | −0.319155 | − | 0.947702i | \(-0.603399\pi\) | ||||
−0.319155 | + | 0.947702i | \(0.603399\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.10454e9 | 1.37223 | 0.686115 | − | 0.727493i | \(-0.259315\pi\) | ||||
0.686115 | + | 0.727493i | \(0.259315\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.00576e9i | 0.667442i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.02864e8i | 0.0656346i | 0.999461 | + | 0.0328173i | \(0.0104479\pi\) | ||||
−0.999461 | + | 0.0328173i | \(0.989552\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.63924e9 | 0.779175 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.09962e9 | −0.232609 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.86966e9i | 0.599779i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.42370e9i | 0.494590i | 0.968940 | + | 0.247295i | \(0.0795417\pi\) | ||||
−0.968940 | + | 0.247295i | \(0.920458\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.16128e8 | −0.124242 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.07340e9 | 0.213898 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 6.85538e9i | − 1.35002i | −0.737809 | − | 0.675010i | \(-0.764139\pi\) | ||||
0.737809 | − | 0.675010i | \(-0.235861\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.78966e9i | 0.536588i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.47203e8 | −0.0279847 | −0.0139924 | − | 0.999902i | \(-0.504454\pi\) | ||||
−0.0139924 | + | 0.999902i | \(0.504454\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.15884e9 | 1.34519 | 0.672593 | − | 0.740013i | \(-0.265181\pi\) | ||||
0.672593 | + | 0.740013i | \(0.265181\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 2.96953e9i | − 0.551540i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 4.08333e9i | − 0.741062i | −0.928820 | − | 0.370531i | \(-0.879176\pi\) | ||||
0.928820 | − | 0.370531i | \(-0.120824\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.50422e7 | −0.0170512 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.16182e10 | 2.06060 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 6.81081e9i | − 1.19423i | −0.802157 | − | 0.597113i | \(-0.796314\pi\) | ||||
0.802157 | − | 0.597113i | \(-0.203686\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 3.95161e9i | − 0.677292i | −0.940914 | − | 0.338646i | \(-0.890031\pi\) | ||||
0.940914 | − | 0.338646i | \(-0.109969\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.07835e10 | 1.82744 | 0.913722 | − | 0.406339i | \(-0.133195\pi\) | ||||
0.913722 | + | 0.406339i | \(0.133195\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.25389e9 | −0.210105 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.76493e8i | 0.145225i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.36082e9i | 0.220478i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.25734e9 | −0.682120 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.10443e10 | 1.75000 | 0.874999 | − | 0.484125i | \(-0.160862\pi\) | ||||
0.874999 | + | 0.484125i | \(0.160862\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 4.84582e9i | − 0.759371i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 7.78881e9i | − 1.19394i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.79755e8 | 0.0424156 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.93797e9 | −0.890502 | −0.445251 | − | 0.895406i | \(-0.646886\pi\) | ||||
−0.445251 | + | 0.895406i | \(0.646886\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 8.24945e9i | − 1.22373i | −0.790961 | − | 0.611866i | \(-0.790419\pi\) | ||||
0.790961 | − | 0.611866i | \(-0.209581\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.49145e9i | 0.942272i | 0.882061 | + | 0.471136i | \(0.156156\pi\) | ||||
−0.882061 | + | 0.471136i | \(0.843844\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.29293e9 | 1.19083 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.85016e8 | 0.0404889 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1.04406e9i | − 0.146734i | −0.997305 | − | 0.0733668i | \(-0.976626\pi\) | ||||
0.997305 | − | 0.0733668i | \(-0.0233744\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 2.19138e9i | − 0.301467i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.11126e10 | −1.51257 | −0.756285 | − | 0.654243i | \(-0.772988\pi\) | ||||
−0.756285 | + | 0.654243i | \(0.772988\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.70105e9 | −0.229093 | −0.114547 | − | 0.993418i | \(-0.536541\pi\) | ||||
−0.114547 | + | 0.993418i | \(0.536541\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 4.85341e9i | − 0.646770i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.86869e9i | 0.243836i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.70339e9 | −0.994696 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.49001e10 | 1.90397 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 7.45938e9i | − 0.943301i | −0.881786 | − | 0.471650i | \(-0.843658\pi\) | ||||
0.881786 | − | 0.471650i | \(-0.156342\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.80473e9i | 0.718988i | 0.933147 | + | 0.359494i | \(0.117051\pi\) | ||||
−0.933147 | + | 0.359494i | \(0.882949\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.28631e7 | 0.0101582 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.41954e8 | −0.0900248 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 7.26903e9i | − 0.872979i | −0.899709 | − | 0.436490i | \(-0.856222\pi\) | ||||
0.899709 | − | 0.436490i | \(-0.143778\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.31272e9i | 0.272129i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.83871e9 | −0.447114 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.17298e10 | 1.35244 | 0.676219 | − | 0.736701i | \(-0.263617\pi\) | ||||
0.676219 | + | 0.736701i | \(0.263617\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 6.29506e8i | − 0.0718511i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.00289e9i | 0.335912i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.83248e9 | −0.313687 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.88743e9 | −1.08410 | −0.542051 | − | 0.840345i | \(-0.682352\pi\) | ||||
−0.542051 | + | 0.840345i | \(0.682352\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.59679e9i | 0.173342i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.59200e9i | − 0.169425i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.43284e10 | 1.50986 | 0.754931 | − | 0.655804i | \(-0.227670\pi\) | ||||
0.754931 | + | 0.655804i | \(0.227670\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.60717e9 | −0.376377 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 5.60391e9i | − 0.578999i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.48396e8i | 0.0758254i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.73607e10 | 1.74187 | 0.870936 | − | 0.491396i | \(-0.163513\pi\) | ||||
0.870936 | + | 0.491396i | \(0.163513\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.84190e8 | 0.0580471 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 7.97232e9i | − 0.784514i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.27740e10i | 1.23298i | 0.787364 | + | 0.616489i | \(0.211446\pi\) | ||||
−0.787364 | + | 0.616489i | \(0.788554\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.87420e8 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.54213e9 | 0.240706 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.12419e9i | 0.574361i | 0.957877 | + | 0.287180i | \(0.0927179\pi\) | ||||
−0.957877 | + | 0.287180i | \(0.907282\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 2.93124e10i | − 2.69721i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.05335e10 | −0.960104 | −0.480052 | − | 0.877240i | \(-0.659382\pi\) | ||||
−0.480052 | + | 0.877240i | \(0.659382\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.82035e9 | −0.164358 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.55392e9i | 0.675634i | 0.941212 | + | 0.337817i | \(0.109688\pi\) | ||||
−0.941212 | + | 0.337817i | \(0.890312\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.68019e9i | 0.586363i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.50232e8 | −0.0826310 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.31273e10 | −1.13093 | −0.565466 | − | 0.824772i | \(-0.691304\pi\) | ||||
−0.565466 | + | 0.824772i | \(0.691304\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 8.17790e9i | − 0.698007i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.72126e9i | 0.479353i | 0.970853 | + | 0.239677i | \(0.0770414\pi\) | ||||
−0.970853 | + | 0.239677i | \(0.922959\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.23772e10 | −1.02748 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.63771e10 | 1.34708 | 0.673538 | − | 0.739153i | \(-0.264774\pi\) | ||||
0.673538 | + | 0.739153i | \(0.264774\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 5.91636e8i | − 0.0482190i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.10933e10i | 0.887726i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.59634e9 | 0.523071 | 0.261536 | − | 0.965194i | \(-0.415771\pi\) | ||||
0.261536 | + | 0.965194i | \(0.415771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.11952e9 | 0.0879711 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 6.24126e9i | − 0.486009i | −0.970025 | − | 0.243004i | \(-0.921867\pi\) | ||||
0.970025 | − | 0.243004i | \(-0.0781329\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 7.38662e8i | − 0.0564901i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.12629e9 | 0.0853625 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.76148e9 | 0.207426 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.77381e8i | 0.0429830i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.69328e10i | − 1.23827i | −0.785284 | − | 0.619136i | \(-0.787483\pi\) | ||||
0.785284 | − | 0.619136i | \(-0.212517\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.13402e10 | −0.821960 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.78049e8 | 0.0199758 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.99316e10i | 1.41934i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.25579e10i | − 0.878641i | −0.898330 | − | 0.439321i | \(-0.855219\pi\) | ||||
0.898330 | − | 0.439321i | \(-0.144781\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.25388e10 | 1.56321 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.32469e9 | 0.366084 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.16312e10i | − 1.47427i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 4.22489e9i | − 0.282981i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.51860e9 | 0.167239 | 0.0836197 | − | 0.996498i | \(-0.473352\pi\) | ||||
0.0836197 | + | 0.996498i | \(0.473352\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.70760e10 | 1.78243 | 0.891213 | − | 0.453585i | \(-0.149855\pi\) | ||||
0.891213 | + | 0.453585i | \(0.149855\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 7.33024e9i | − 0.478411i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 9.53469e8i | − 0.0611687i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.42082e8 | 0.0535625 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.70089e10 | 1.70336 | 0.851678 | − | 0.524066i | \(-0.175585\pi\) | ||||
0.851678 | + | 0.524066i | \(0.175585\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.23883e10i | 0.774662i | 0.921941 | + | 0.387331i | \(0.126603\pi\) | ||||
−0.921941 | + | 0.387331i | \(0.873397\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.28562e10i | 1.40519i | 0.711589 | + | 0.702596i | \(0.247976\pi\) | ||||
−0.711589 | + | 0.702596i | \(0.752024\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.68742e9 | 0.529602 | 0.264801 | − | 0.964303i | \(-0.414694\pi\) | ||||
0.264801 | + | 0.964303i | \(0.414694\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.64686e9 | −0.160003 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1.51099e10i | − 0.905743i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1.73147e9i | − 0.102065i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.16792e10 | −0.682724 | −0.341362 | − | 0.939932i | \(-0.610888\pi\) | ||||
−0.341362 | + | 0.939932i | \(0.610888\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.63894e10 | −0.950117 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 1.09307e10i | − 0.628419i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 3.87543e9i | − 0.219143i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.51884e9 | −0.365589 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.45234e10 | −0.807819 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.25452e9i | 0.124375i | 0.998064 | + | 0.0621875i | \(0.0198077\pi\) | ||||
−0.998064 | + | 0.0621875i | \(0.980192\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.96605e9i | 0.269512i | 0.990879 | + | 0.134756i | \(0.0430250\pi\) | ||||
−0.990879 | + | 0.134756i | \(0.956975\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.54039e10 | −0.829192 | −0.414596 | − | 0.910006i | \(-0.636077\pi\) | ||||
−0.414596 | + | 0.910006i | \(0.636077\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.21011e8 | −0.0278187 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.61225e9i | 0.244273i | 0.992513 | + | 0.122136i | \(0.0389746\pi\) | ||||
−0.992513 | + | 0.122136i | \(0.961025\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.66375e9i | 0.0867005i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.56066e10 | −1.84061 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.92108e10 | 2.01068 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 5.03393e8i | − 0.0256069i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 3.57505e10i | − 1.78971i | −0.446355 | − | 0.894856i | \(-0.647278\pi\) | ||||
0.446355 | − | 0.894856i | \(-0.352722\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.26640e9 | 0.261549 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.48309e10 | −1.22342 | −0.611711 | − | 0.791082i | \(-0.709518\pi\) | ||||
−0.611711 | + | 0.791082i | \(0.709518\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.37996e9i | 0.458499i | 0.973368 | + | 0.229249i | \(0.0736272\pi\) | ||||
−0.973368 | + | 0.229249i | \(0.926373\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 5.98940e9i | − 0.288171i | −0.989565 | − | 0.144086i | \(-0.953976\pi\) | ||||
0.989565 | − | 0.144086i | \(-0.0460241\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.70143e9 | 0.128955 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.82425e9 | −0.181123 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 8.45355e9i | − 0.397245i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 1.65568e10i | − 0.765954i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.58045e9 | −0.118451 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.44693e9 | −0.339188 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.41068e8i | 0.0199342i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.76568e9i | − 0.0785755i | −0.999228 | − | 0.0392878i | \(-0.987491\pi\) | ||||
0.999228 | − | 0.0392878i | \(-0.0125089\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.67143e9 | −0.427088 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.18232e10 | −1.83275 | −0.916373 | − | 0.400325i | \(-0.868897\pi\) | ||||
−0.916373 | + | 0.400325i | \(0.868897\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.59405e10i | 2.86751i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.63074e9i | 0.0698382i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.71658e10 | 1.57957 | 0.789785 | − | 0.613384i | \(-0.210192\pi\) | ||||
0.789785 | + | 0.613384i | \(0.210192\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.75622e9 | −0.116253 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.69400e9i | 0.154629i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 3.54895e9i | − 0.146326i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.56580e10 | −1.04995 | −0.524974 | − | 0.851118i | \(-0.675925\pi\) | ||||
−0.524974 | + | 0.851118i | \(0.675925\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.66724e9 | −0.230169 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.23264e9i | 0.331859i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.75353e9i | 0.228479i | 0.993453 | + | 0.114239i | \(0.0364431\pi\) | ||||
−0.993453 | + | 0.114239i | \(0.963557\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.74809e10 | −0.689024 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.60599e10 | −1.80202 | −0.901010 | − | 0.433799i | \(-0.857173\pi\) | ||||
−0.901010 | + | 0.433799i | \(0.857173\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.02440e10i | 0.397812i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.34709e7i | 0.00357645i | 0.999998 | + | 0.00178822i | \(0.000569209\pi\) | ||||
−0.999998 | + | 0.00178822i | \(0.999431\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.89359e10 | 1.09902 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.02123e9 | −0.151610 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.17289e10i | 0.438968i | 0.975616 | + | 0.219484i | \(0.0704373\pi\) | ||||
−0.975616 | + | 0.219484i | \(0.929563\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.69936e9i | 0.210201i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.57542e7 | −0.00313971 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.97742e10 | −0.718734 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.77266e9i | 0.208297i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.64786e10i | 0.586040i | 0.956106 | + | 0.293020i | \(0.0946602\pi\) | ||||
−0.956106 | + | 0.293020i | \(0.905340\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.53140e9 | −0.124685 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.88436e10 | −0.660536 | −0.330268 | − | 0.943887i | \(-0.607139\pi\) | ||||
−0.330268 | + | 0.943887i | \(0.607139\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.14579e9i | 0.0746779i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.26661e10i | 1.46370i | 0.681467 | + | 0.731849i | \(0.261343\pi\) | ||||
−0.681467 | + | 0.731849i | \(0.738657\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.25603e10 | 1.79027 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.59419e9 | −0.121551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.34527e9i | 0.145908i | 0.997335 | + | 0.0729541i | \(0.0232426\pi\) | ||||
−0.997335 | + | 0.0729541i | \(0.976757\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.91055e9i | 0.129458i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.67215e9 | 0.285062 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.36239e10 | 0.444675 | 0.222338 | − | 0.974970i | \(-0.428631\pi\) | ||||
0.222338 | + | 0.974970i | \(0.428631\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.61438e10i | 0.847319i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.32788e10i | 1.38306i | 0.722346 | + | 0.691531i | \(0.243064\pi\) | ||||
−0.722346 | + | 0.691531i | \(0.756936\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.48737e9 | −0.142401 |
(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 | 600.8.f.a.49.2 | 2 | ||
5.2 | odd | 4 | 24.8.a.b.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 600.8.a.b.1.1 | 1 | |||
5.4 | even | 2 | inner | 600.8.f.a.49.1 | 2 | ||
15.2 | even | 4 | 72.8.a.e.1.1 | 1 | |||
20.7 | even | 4 | 48.8.a.a.1.1 | 1 | |||
40.27 | even | 4 | 192.8.a.p.1.1 | 1 | |||
40.37 | odd | 4 | 192.8.a.h.1.1 | 1 | |||
60.47 | odd | 4 | 144.8.a.k.1.1 | 1 | |||
120.77 | even | 4 | 576.8.a.c.1.1 | 1 | |||
120.107 | odd | 4 | 576.8.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.8.a.b.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
48.8.a.a.1.1 | 1 | 20.7 | even | 4 | |||
72.8.a.e.1.1 | 1 | 15.2 | even | 4 | |||
144.8.a.k.1.1 | 1 | 60.47 | odd | 4 | |||
192.8.a.h.1.1 | 1 | 40.37 | odd | 4 | |||
192.8.a.p.1.1 | 1 | 40.27 | even | 4 | |||
576.8.a.b.1.1 | 1 | 120.107 | odd | 4 | |||
576.8.a.c.1.1 | 1 | 120.77 | even | 4 | |||
600.8.a.b.1.1 | 1 | 5.3 | odd | 4 | |||
600.8.f.a.49.1 | 2 | 5.4 | even | 2 | inner | ||
600.8.f.a.49.2 | 2 | 1.1 | even | 1 | trivial |