Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,8,Mod(1,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(14.9944812232\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 24) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 48.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −530.000 | −1.89619 | −0.948093 | − | 0.317994i | \(-0.896991\pi\) | ||||
−0.948093 | + | 0.317994i | \(0.896991\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −120.000 | −0.132232 | −0.0661162 | − | 0.997812i | \(-0.521061\pi\) | ||||
−0.0661162 | + | 0.997812i | \(0.521061\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7196.00 | 1.63011 | 0.815055 | − | 0.579384i | \(-0.196707\pi\) | ||||
0.815055 | + | 0.579384i | \(0.196707\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9626.00 | −1.21519 | −0.607595 | − | 0.794247i | \(-0.707866\pi\) | ||||
−0.607595 | + | 0.794247i | \(0.707866\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 14310.0 | 1.09476 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18674.0 | 0.921862 | 0.460931 | − | 0.887436i | \(-0.347515\pi\) | ||||
0.460931 | + | 0.887436i | \(0.347515\pi\) | |||||||
\(18\) | 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 | ||||||||
\(23\) | 63704.0 | 1.09174 | 0.545870 | − | 0.837870i | \(-0.316199\pi\) | ||||
0.545870 | + | 0.837870i | \(0.316199\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 202775. | 2.59552 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29334.0 | 0.223346 | 0.111673 | − | 0.993745i | \(-0.464379\pi\) | ||||
0.111673 | + | 0.993745i | \(0.464379\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −87968.0 | −0.530345 | −0.265173 | − | 0.964201i | \(-0.585429\pi\) | ||||
−0.265173 | + | 0.964201i | \(0.585429\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −194292. | −0.941144 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 63600.0 | 0.250737 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 227982. | 0.739937 | 0.369968 | − | 0.929044i | \(-0.379369\pi\) | ||||
0.369968 | + | 0.929044i | \(0.379369\pi\) | |||||||
\(38\) | 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. | −0.261108 | −0.130554 | − | 0.991441i | \(-0.541676\pi\) | ||||
−0.130554 | + | 0.991441i | \(0.541676\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −386370. | −0.632062 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.20696e6 | 1.69571 | 0.847853 | − | 0.530232i | \(-0.177895\pi\) | ||||
0.847853 | + | 0.530232i | \(0.177895\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −809143. | −0.982515 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −504198. | −0.532238 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −398786. | −0.367938 | −0.183969 | − | 0.982932i | \(-0.558895\pi\) | ||||
−0.183969 | + | 0.982932i | \(0.558895\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.81388e6 | −3.09099 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 189108. | 0.135253 | ||||||||
\(58\) | 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 | ||||||||
\(63\) | −87480.0 | −0.0440775 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.10178e6 | 2.30423 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.07343e6 | 1.65462 | 0.827310 | − | 0.561746i | \(-0.189870\pi\) | ||||
0.827310 | + | 0.561746i | \(0.189870\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.72001e6 | −0.630316 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 383752. | 0.127247 | 0.0636233 | − | 0.997974i | \(-0.479734\pi\) | ||||
0.0636233 | + | 0.997974i | \(0.479734\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.00601e6 | 0.904400 | 0.452200 | − | 0.891917i | \(-0.350639\pi\) | ||||
0.452200 | + | 0.891917i | \(0.350639\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.47492e6 | −1.49852 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −863520. | −0.215553 | ||||||||
\(78\) | 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 | ||||||||
\(83\) | 9.16349e6 | 1.75909 | 0.879544 | − | 0.475817i | \(-0.157848\pi\) | ||||
0.879544 | + | 0.475817i | \(0.157848\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.89722e6 | −1.74802 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −792018. | −0.128949 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.30411e6 | 1.09825 | 0.549126 | − | 0.835740i | \(-0.314961\pi\) | ||||
0.549126 | + | 0.835740i | \(0.314961\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.15512e6 | 0.160688 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.37514e6 | 0.306195 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.71212e6 | 0.444211 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −690526. | −0.0768208 | −0.0384104 | − | 0.999262i | \(-0.512229\pi\) | ||||
−0.0384104 | + | 0.999262i | \(0.512229\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | −4.86825e6 | −0.438978 | −0.219489 | − | 0.975615i | \(-0.570439\pi\) | ||||
−0.219489 | + | 0.975615i | \(0.570439\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.71720e6 | −0.144763 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.91860e6 | −0.624892 | −0.312446 | − | 0.949936i | \(-0.601148\pi\) | ||||
−0.312446 | + | 0.949936i | \(0.601148\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.93030e6 | −0.364654 | −0.182327 | − | 0.983238i | \(-0.558363\pi\) | ||||
−0.182327 | + | 0.983238i | \(0.558363\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.15551e6 | −0.427203 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.31707e6 | 0.151066 | 0.0755328 | − | 0.997143i | \(-0.475934\pi\) | ||||
0.0755328 | + | 0.997143i | \(0.475934\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.37631e7 | −2.07014 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.01735e6 | −0.405063 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.24088e6 | −0.121900 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.22952e7 | 1.65726 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.34176e6 | 0.210377 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.60645e7 | −3.02540 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.25119e7 | 0.975214 | 0.487607 | − | 0.873063i | \(-0.337870\pi\) | ||||
0.487607 | + | 0.873063i | \(0.337870\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.67556e6 | 0.150751 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.35895e7 | 0.528147 | 0.264073 | − | 0.964503i | \(-0.414934\pi\) | ||||
0.264073 | + | 0.964503i | \(0.414934\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 840480. | 0.0309775 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.04320e7 | 0.364921 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 714618. | 0.0237439 | 0.0118719 | − | 0.999930i | \(-0.496221\pi\) | ||||
0.0118719 | + | 0.999930i | \(0.496221\pi\) | |||||||
\(138\) | 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 | ||||||||
\(143\) | −6.92687e7 | −1.98089 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.55470e7 | −0.423506 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.18469e7 | 0.567255 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.00391e7 | −0.496279 | −0.248139 | − | 0.968724i | \(-0.579819\pi\) | ||||
−0.248139 | + | 0.968724i | \(0.579819\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.07634e7 | 0.963499 | 0.481749 | − | 0.876309i | \(-0.340002\pi\) | ||||
0.481749 | + | 0.876309i | \(0.340002\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.36133e7 | 0.307287 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.66230e7 | 1.00563 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.54702e7 | 1.14396 | 0.571980 | − | 0.820268i | \(-0.306176\pi\) | ||||
0.571980 | + | 0.820268i | \(0.306176\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.07672e7 | 0.212429 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.64448e6 | −0.144363 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.80344e6 | 0.0326172 | 0.0163086 | − | 0.999867i | \(-0.494809\pi\) | ||||
0.0163086 | + | 0.999867i | \(0.494809\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.02975e8 | 1.78458 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.99273e6 | −0.0995673 | −0.0497837 | − | 0.998760i | \(-0.515853\pi\) | ||||
−0.0497837 | + | 0.998760i | \(0.515853\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.99114e7 | 0.476686 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.10592e6 | −0.0780885 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.25631e8 | 1.84474 | 0.922368 | − | 0.386313i | \(-0.126252\pi\) | ||||
0.922368 | + | 0.386313i | \(0.126252\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.43330e7 | −0.343212 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.11158e7 | 0.421769 | ||||||||
\(178\) | 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 | ||||||||
\(183\) | 5.59063e7 | 0.674344 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.20830e8 | −1.40306 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.34378e8 | 1.50274 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.36196e6 | 0.0254482 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.11324e8 | −1.15604 | −0.578021 | − | 0.816022i | \(-0.696175\pi\) | ||||
−0.578021 | + | 0.816022i | \(0.696175\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.34786e8 | −1.34957 | −0.674786 | − | 0.738014i | \(-0.735764\pi\) | ||||
−0.674786 | + | 0.738014i | \(0.735764\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.37748e8 | −1.33035 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.97557e7 | 0.370482 | 0.185241 | − | 0.982693i | \(-0.440693\pi\) | ||||
0.185241 | + | 0.982693i | \(0.440693\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | −3.52008e6 | −0.0295336 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.52272e7 | 0.690939 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.64402e7 | 0.363913 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.04008e7 | −0.381879 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.79475e8 | 1.31527 | 0.657634 | − | 0.753337i | \(-0.271557\pi\) | ||||
0.657634 | + | 0.753337i | \(0.271557\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.03613e7 | −0.0734659 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.21500e7 | 0.495110 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.05562e7 | 0.0701289 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.11623e7 | −0.522155 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.79756e8 | −1.12024 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.85311e8 | −1.72286 | −0.861432 | − | 0.507872i | \(-0.830432\pi\) | ||||
−0.861432 | + | 0.507872i | \(0.830432\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.47823e8 | 0.865173 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.74798e7 | 0.155928 | 0.0779638 | − | 0.996956i | \(-0.475158\pi\) | ||||
0.0779638 | + | 0.996956i | \(0.475158\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.56562e7 | −0.471341 | −0.235670 | − | 0.971833i | \(-0.575729\pi\) | ||||
−0.235670 | + | 0.971833i | \(0.575729\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.33150e7 | 0.124450 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.04907e8 | 0.543322 | 0.271661 | − | 0.962393i | \(-0.412427\pi\) | ||||
0.271661 | + | 0.962393i | \(0.412427\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.39689e8 | −3.21537 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.33599e8 | −0.651905 | ||||||||
\(238\) | 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 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.28846e8 | 1.86303 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.74205e7 | 0.284677 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.47414e8 | −1.01561 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.02885e8 | 1.20898 | 0.604491 | − | 0.796612i | \(-0.293376\pi\) | ||||
0.604491 | + | 0.796612i | \(0.293376\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.58414e8 | 1.77966 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.67225e8 | 1.00922 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.14636e7 | 0.152370 | 0.0761852 | − | 0.997094i | \(-0.475726\pi\) | ||||
0.0761852 | + | 0.997094i | \(0.475726\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.73578e7 | −0.0978436 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.13845e7 | 0.0744487 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.20007e8 | −1.42368 | −0.711839 | − | 0.702343i | \(-0.752137\pi\) | ||||
−0.711839 | + | 0.702343i | \(0.752137\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.11357e8 | 0.697678 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.97211e8 | −0.634076 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.56477e8 | 0.490138 | 0.245069 | − | 0.969506i | \(-0.421189\pi\) | ||||
0.245069 | + | 0.969506i | \(0.421189\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.71491e8 | 0.828633 | 0.414316 | − | 0.910133i | \(-0.364021\pi\) | ||||
0.414316 | + | 0.910133i | \(0.364021\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.11882e7 | −0.0927730 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.45917e9 | 4.23098 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.80318e7 | −0.277133 | −0.138566 | − | 0.990353i | \(-0.544249\pi\) | ||||
−0.138566 | + | 0.990353i | \(0.544249\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −2.41439e8 | −0.633220 | −0.316610 | − | 0.948556i | \(-0.602545\pi\) | ||||
−0.316610 | + | 0.948556i | \(0.602545\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00227e8 | −0.256465 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.92967e7 | 0.0481833 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.16204e7 | −0.150170 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.86442e7 | 0.0443525 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.95052e8 | −0.453016 | −0.226508 | − | 0.974009i | \(-0.572731\pi\) | ||||
−0.226508 | + | 0.974009i | \(0.572731\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.10791e8 | 1.38521 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.41639e8 | −0.313715 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.13215e8 | −1.32667 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.63358e7 | 0.0345270 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.58201e8 | −0.739737 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.09742e9 | 2.21474 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.02082e8 | 0.201356 | 0.100678 | − | 0.994919i | \(-0.467899\pi\) | ||||
0.100678 | + | 0.994919i | \(0.467899\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.31443e8 | 0.253444 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.04913e8 | −0.574797 | −0.287398 | − | 0.957811i | \(-0.592790\pi\) | ||||
−0.287398 | + | 0.957811i | \(0.592790\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.47441e8 | 1.19342 | 0.596712 | − | 0.802455i | \(-0.296473\pi\) | ||||
0.596712 | + | 0.802455i | \(0.296473\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.63644e7 | 0.0835791 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.48935e8 | −0.262596 | −0.131298 | − | 0.991343i | \(-0.541914\pi\) | ||||
−0.131298 | + | 0.991343i | \(0.541914\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.11087e8 | 0.364079 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.13802e8 | 0.360782 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.30793e8 | −0.215961 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.95191e9 | −3.15405 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.33118e8 | 0.210533 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.44835e8 | −0.224227 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.68290e8 | −1.46760 | −0.733800 | − | 0.679366i | \(-0.762255\pi\) | ||||
−0.733800 | + | 0.679366i | \(0.762255\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.66199e8 | 0.246646 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.15892e9 | −3.13747 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.65424e8 | 0.235447 | 0.117723 | − | 0.993046i | \(-0.462440\pi\) | ||||
0.117723 | + | 0.993046i | \(0.462440\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.25610e7 | −0.0872177 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.33018e8 | −0.864521 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.95922e8 | 0.262153 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.11604e8 | 1.19520 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.12455e9 | 1.44486 | 0.722431 | − | 0.691443i | \(-0.243025\pi\) | ||||
0.722431 | + | 0.691443i | \(0.243025\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.55383e8 | −0.321590 | −0.160795 | − | 0.986988i | \(-0.551406\pi\) | ||||
−0.160795 | + | 0.986988i | \(0.551406\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.89469e8 | 0.233863 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.45151e8 | 0.417635 | 0.208818 | − | 0.977955i | \(-0.433038\pi\) | ||||
0.208818 | + | 0.977955i | \(0.433038\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.03389e8 | −0.241283 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.05038e7 | 0.0703791 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | −8.71972e8 | −0.956818 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.59319e9 | −1.71491 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.76625e8 | 0.820125 | 0.410062 | − | 0.912057i | \(-0.365507\pi\) | ||||
0.410062 | + | 0.912057i | \(0.365507\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.17228e8 | −0.121461 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.78543e7 | 0.0486533 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.66790e9 | 1.66414 | 0.832071 | − | 0.554669i | \(-0.187155\pi\) | ||||
0.832071 | + | 0.554669i | \(0.187155\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.78374e9 | 1.74672 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.82369e8 | −0.271408 | ||||||||
\(378\) | 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 | ||||||||
\(383\) | −1.43374e9 | −1.30399 | −0.651995 | − | 0.758223i | \(-0.726068\pi\) | ||||
−0.651995 | + | 0.758223i | \(0.726068\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.57666e8 | 0.408729 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.92402e7 | −0.0870361 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.31613e8 | 0.630170 | 0.315085 | − | 0.949063i | \(-0.397967\pi\) | ||||
0.315085 | + | 0.949063i | \(0.397967\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.18961e9 | 1.00643 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.66917e8 | −0.304926 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.62250e9 | −2.14104 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.19059e9 | 0.954983 | 0.477492 | − | 0.878636i | \(-0.341546\pi\) | ||||
0.477492 | + | 0.878636i | \(0.341546\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 8.46780e8 | 0.644470 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.81664e8 | −0.210687 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.64056e9 | 1.20618 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.83663e9 | 1.32737 | 0.663684 | − | 0.748013i | \(-0.268992\pi\) | ||||
0.663684 | + | 0.748013i | \(0.268992\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.92947e7 | −0.0137085 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.38292e8 | 0.0965991 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.85665e9 | −3.33556 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.82802e8 | 0.326057 | ||||||||
\(418\) | 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 | ||||||||
\(423\) | 8.79874e8 | 0.565235 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.78662e9 | 2.39271 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.48472e8 | 0.154447 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.87025e9 | 1.14367 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.90479e8 | 0.174761 | 0.0873806 | − | 0.996175i | \(-0.472150\pi\) | ||||
0.0873806 | + | 0.996175i | \(0.472150\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.20651e9 | 1.30616 | 0.653082 | − | 0.757288i | \(-0.273476\pi\) | ||||
0.653082 | + | 0.757288i | \(0.273476\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.19770e8 | 0.244511 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.46183e8 | −0.255757 | ||||||||
\(438\) | 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 | ||||||||
\(443\) | 8.18948e8 | 0.447552 | 0.223776 | − | 0.974641i | \(-0.428162\pi\) | ||||
0.223776 | + | 0.974641i | \(0.428162\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.87118e9 | −2.08249 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.41055e8 | 0.286527 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.46241e9 | −1.28380 | −0.641900 | − | 0.766788i | \(-0.721854\pi\) | ||||
−0.641900 | + | 0.766788i | \(0.721854\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.15716e9 | −0.593985 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.10061e9 | −0.556276 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.12214e8 | −0.304693 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.76135e9 | −1.35337 | −0.676683 | − | 0.736274i | \(-0.736583\pi\) | ||||
−0.676683 | + | 0.736274i | \(0.736583\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 1.42591e9 | 0.667666 | 0.333833 | − | 0.942632i | \(-0.391658\pi\) | ||||
0.333833 | + | 0.942632i | \(0.391658\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.25882e9 | −0.580603 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.99579e9 | −0.906788 | −0.453394 | − | 0.891310i | \(-0.649787\pi\) | ||||
−0.453394 | + | 0.891310i | \(0.649787\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.88811e8 | −0.218794 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.49769e9 | −0.660465 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.79606e8 | −0.425635 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.42024e9 | −0.608041 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.90715e8 | −0.122646 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 2.06401e8 | 0.0833483 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.65979e8 | 0.145667 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.23609e9 | 0.484953 | 0.242476 | − | 0.970157i | \(-0.422040\pi\) | ||||
0.242476 | + | 0.970157i | \(0.422040\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.86930e7 | −0.0188315 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.49612e8 | 0.285793 | 0.142896 | − | 0.989738i | \(-0.454358\pi\) | ||||
0.142896 | + | 0.989738i | \(0.454358\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.47783e8 | 0.205894 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.78032e9 | −1.03033 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.60502e7 | −0.0168261 | ||||||||
\(498\) | 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 | ||||||||
\(503\) | 2.19390e9 | 0.768649 | 0.384324 | − | 0.923198i | \(-0.374434\pi\) | ||||
0.384324 | + | 0.923198i | \(0.374434\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.03135e9 | −2.42951 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.07607e8 | −0.275215 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.24865e9 | 1.42804 | 0.714018 | − | 0.700127i | \(-0.246873\pi\) | ||||
0.714018 | + | 0.700127i | \(0.246873\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.60721e8 | −0.119591 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.37860e8 | 0.0450844 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.58017e9 | 0.832383 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.68528e9 | 2.76419 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | −6.33645e9 | −1.93682 | −0.968412 | − | 0.249356i | \(-0.919781\pi\) | ||||
−0.968412 | + | 0.249356i | \(0.919781\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.56991e8 | 0.198154 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.64271e9 | −0.488905 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.53374e8 | 0.191897 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.40126e8 | −0.243508 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.54792e9 | 0.442795 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.19686e9 | 1.18491 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.31354e9 | 0.366045 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 1.34338e9 | 0.360080 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.61306e9 | 0.691451 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.66046e9 | 0.956269 | 0.478135 | − | 0.878287i | \(-0.341313\pi\) | ||||
0.478135 | + | 0.878287i | \(0.341313\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.50947e9 | −0.389333 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.05455e8 | −0.0523223 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.93773e8 | −0.149308 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.26242e9 | 0.810055 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.25630e9 | 1.28880 | 0.644402 | − | 0.764687i | \(-0.277106\pi\) | ||||
0.644402 | + | 0.764687i | \(0.277106\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.31041e9 | 0.317296 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.62821e9 | −0.867605 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.01985e9 | 1.18553 | 0.592764 | − | 0.805376i | \(-0.298037\pi\) | ||||
0.592764 | + | 0.805376i | \(0.298037\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.22805e9 | −0.286448 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.37729e7 | −0.0146925 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.80495e9 | 0.638311 | 0.319155 | − | 0.947702i | \(-0.396601\pi\) | ||||
0.319155 | + | 0.947702i | \(0.396601\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.10454e9 | −1.37223 | −0.686115 | − | 0.727493i | \(-0.740685\pi\) | ||||
−0.686115 | + | 0.727493i | \(0.740685\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.00576e9 | 0.667442 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.29176e10 | 2.83363 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.02864e8 | −0.0656346 | −0.0328173 | − | 0.999461i | \(-0.510448\pi\) | ||||
−0.0328173 | + | 0.999461i | \(0.510448\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.63924e9 | 0.779175 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.09962e9 | −0.232609 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.86966e9 | −0.599779 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.71920e9 | 0.768075 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.42370e9 | 0.494590 | 0.247295 | − | 0.968940i | \(-0.420458\pi\) | ||||
0.247295 | + | 0.968940i | \(0.420458\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.16128e8 | 0.124242 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.07340e9 | −0.213898 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.85538e9 | −1.35002 | −0.675010 | − | 0.737809i | \(-0.735861\pi\) | ||||
−0.675010 | + | 0.737809i | \(0.735861\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.18767e9 | 0.231145 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.78966e9 | −0.536588 | ||||||||
\(598\) | 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 | ||||||||
\(603\) | 2.96953e9 | 0.551540 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.71165e10 | −3.14247 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.08333e9 | −0.741062 | −0.370531 | − | 0.928820i | \(-0.620824\pi\) | ||||
−0.370531 | + | 0.928820i | \(0.620824\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.50422e7 | 0.0170512 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.16182e10 | −2.06060 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.81081e9 | −1.19423 | −0.597113 | − | 0.802157i | \(-0.703686\pi\) | ||||
−0.597113 | + | 0.802157i | \(0.703686\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.30113e9 | −0.398914 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.95161e9 | 0.677292 | 0.338646 | − | 0.940914i | \(-0.390031\pi\) | ||||
0.338646 | + | 0.940914i | \(0.390031\pi\) | |||||||
\(618\) | 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 | ||||||||
\(623\) | −8.76493e8 | −0.145225 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.91724e10 | 3.14120 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.36082e9 | 0.220478 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.25734e9 | 0.682120 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.10443e10 | −1.75000 | −0.874999 | − | 0.484125i | \(-0.839138\pi\) | ||||
−0.874999 | + | 0.484125i | \(0.839138\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.84582e9 | −0.759371 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.19313e10 | −1.84919 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.78881e9 | 1.19394 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 8.24945e9 | 1.22373 | 0.611866 | − | 0.790961i | \(-0.290419\pi\) | ||||
0.611866 | + | 0.790961i | \(0.290419\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.94805e9 | −0.285852 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.49145e9 | 0.942272 | 0.471136 | − | 0.882061i | \(-0.343844\pi\) | ||||
0.471136 | + | 0.882061i | \(0.343844\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.29293e9 | −1.19083 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.85016e8 | −0.0404889 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.04406e9 | −0.146734 | −0.0733668 | − | 0.997305i | \(-0.523374\pi\) | ||||
−0.0733668 | + | 0.997305i | \(0.523374\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.20245e9 | −1.00146 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.19138e9 | 0.301467 | ||||||||
\(658\) | 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 | ||||||||
\(663\) | 4.85341e9 | 0.646770 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.45454e8 | −0.0587391 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.86869e9 | 0.243836 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.70339e9 | 0.994696 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.49001e10 | −1.90397 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.45938e9 | −0.943301 | −0.471650 | − | 0.881786i | \(-0.656342\pi\) | ||||
−0.471650 | + | 0.881786i | \(0.656342\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.99122e9 | −0.499508 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.80473e9 | −0.718988 | −0.359494 | − | 0.933147i | \(-0.617051\pi\) | ||||
−0.359494 | + | 0.933147i | \(0.617051\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.28631e7 | 0.0101582 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.41954e8 | −0.0900248 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.26903e9 | 0.872979 | 0.436490 | − | 0.899709i | \(-0.356222\pi\) | ||||
0.436490 | + | 0.899709i | \(0.356222\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.78748e8 | −0.0450228 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.31272e9 | 0.272129 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.83871e9 | 0.447114 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.17298e10 | −1.35244 | −0.676219 | − | 0.736701i | \(-0.736383\pi\) | ||||
−0.676219 | + | 0.736701i | \(0.736383\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.29506e8 | −0.0718511 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.47723e9 | 1.07087 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.00289e9 | −0.335912 | ||||||||
\(698\) | 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 | ||||||||
\(703\) | −1.59679e9 | −0.173342 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.72716e10 | 1.85640 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.59200e9 | −0.169425 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.43284e10 | −1.50986 | −0.754931 | − | 0.655804i | \(-0.772330\pi\) | ||||
−0.754931 | + | 0.655804i | \(0.772330\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.60717e9 | 0.376377 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.60391e9 | −0.578999 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.67124e10 | 3.75614 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.48396e8 | −0.0758254 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 7.97232e9 | 0.784514 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.94820e9 | 0.579699 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.27740e10 | 1.23298 | 0.616489 | − | 0.787364i | \(-0.288554\pi\) | ||||
0.616489 | + | 0.787364i | \(0.288554\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.54213e9 | −0.240706 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.12419e9 | 0.574361 | 0.287180 | − | 0.957877i | \(-0.407282\pi\) | ||||
0.287180 | + | 0.957877i | \(0.407282\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.15788e10 | −1.07562 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.93124e10 | 2.69721 | ||||||||
\(738\) | 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 | ||||||||
\(743\) | −7.55392e9 | −0.675634 | −0.337817 | − | 0.941212i | \(-0.609688\pi\) | ||||
−0.337817 | + | 0.941212i | \(0.609688\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.06207e10 | 0.941037 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.68019e9 | 0.586363 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.50232e8 | 0.0826310 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.31273e10 | 1.13093 | 0.565466 | − | 0.824772i | \(-0.308696\pi\) | ||||
0.565466 | + | 0.824772i | \(0.308696\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.17790e9 | −0.698007 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.16046e10 | −1.82697 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.72126e9 | −0.479353 | −0.239677 | − | 0.970853i | \(-0.577041\pi\) | ||||
−0.239677 | + | 0.970853i | \(0.577041\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 5.91636e8 | 0.0482190 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.21507e9 | −0.582674 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.10933e10 | 0.887726 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.59634e9 | −0.523071 | −0.261536 | − | 0.965194i | \(-0.584229\pi\) | ||||
−0.261536 | + | 0.965194i | \(0.584229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.11952e9 | −0.0879711 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.24126e9 | −0.486009 | −0.243004 | − | 0.970025i | \(-0.578133\pi\) | ||||
−0.243004 | + | 0.970025i | \(0.578133\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.78377e10 | −1.37652 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.38662e8 | 0.0564901 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.12629e9 | 0.0853625 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.76148e9 | 0.207426 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.77381e8 | −0.0429830 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.93992e10 | −2.16916 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.69328e10 | −1.23827 | −0.619136 | − | 0.785284i | \(-0.712517\pi\) | ||||
−0.619136 | + | 0.785284i | \(0.712517\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.13402e10 | 0.821960 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.78049e8 | −0.0199758 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.99316e10 | 1.41934 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.70663e9 | −0.402805 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.25579e10 | 0.878641 | 0.439321 | − | 0.898330i | \(-0.355219\pi\) | ||||
0.439321 | + | 0.898330i | \(0.355219\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.25388e10 | 1.56321 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.32469e9 | 0.366084 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.16312e10 | 1.47427 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.05157e9 | 0.273740 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.22489e9 | −0.282981 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.51860e9 | −0.167239 | −0.0836197 | − | 0.996498i | \(-0.526648\pi\) | ||||
−0.0836197 | + | 0.996498i | \(0.526648\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.70760e10 | −1.78243 | −0.891213 | − | 0.453585i | \(-0.850145\pi\) | ||||
−0.891213 | + | 0.453585i | \(0.850145\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.33024e9 | −0.478411 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.55825e8 | −0.0618482 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.53469e8 | 0.0611687 | ||||||||
\(818\) | 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 | ||||||||
\(823\) | −1.23883e10 | −0.774662 | −0.387331 | − | 0.921941i | \(-0.626603\pi\) | ||||
−0.387331 | + | 0.921941i | \(0.626603\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.93976e10 | −2.44276 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.28562e10 | 1.40519 | 0.702596 | − | 0.711589i | \(-0.252024\pi\) | ||||
0.702596 | + | 0.711589i | \(0.252024\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.68742e9 | −0.529602 | −0.264801 | − | 0.964303i | \(-0.585306\pi\) | ||||
−0.264801 | + | 0.964303i | \(0.585306\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.64686e9 | 0.160003 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.51099e10 | −0.905743 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.17615e9 | 0.188798 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.73147e9 | 0.102065 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 1.09307e10 | 0.628419 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.58530e10 | −0.903886 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.87543e9 | −0.219143 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.51884e9 | 0.365589 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.45234e10 | 0.807819 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.25452e9 | 0.124375 | 0.0621875 | − | 0.998064i | \(-0.480192\pi\) | ||||
0.0621875 | + | 0.998064i | \(0.480192\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.70614e9 | 0.148070 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.96605e9 | −0.269512 | −0.134756 | − | 0.990879i | \(-0.543025\pi\) | ||||
−0.134756 | + | 0.990879i | \(0.543025\pi\) | |||||||
\(858\) | 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 | ||||||||
\(863\) | −4.61225e9 | −0.244273 | −0.122136 | − | 0.992513i | \(-0.538975\pi\) | ||||
−0.122136 | + | 0.992513i | \(0.538975\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.65842e10 | −3.49796 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.66375e9 | 0.0867005 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.56066e10 | 1.84061 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.92108e10 | −2.01068 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.03393e8 | −0.0256069 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.92774e9 | 0.400056 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.57505e10 | 1.78971 | 0.894856 | − | 0.446355i | \(-0.147278\pi\) | ||||
0.894856 | + | 0.446355i | \(0.147278\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | −9.37996e9 | −0.458499 | −0.229249 | − | 0.973368i | \(-0.573627\pi\) | ||||
−0.229249 | + | 0.973368i | \(0.573627\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.64914e10 | −0.799751 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.98940e9 | −0.288171 | −0.144086 | − | 0.989565i | \(-0.546024\pi\) | ||||
−0.144086 | + | 0.989565i | \(0.546024\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.70143e9 | −0.128955 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.82425e9 | 0.181123 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.45355e9 | −0.397245 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.57844e10 | 1.20220 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.65568e10 | 0.765954 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.58045e9 | −0.118451 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.44693e9 | −0.339188 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.41068e8 | −0.0199342 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.63700e10 | 1.18261 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.76568e9 | −0.0785755 | −0.0392878 | − | 0.999228i | \(-0.512509\pi\) | ||||
−0.0392878 | + | 0.999228i | \(0.512509\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.67143e9 | 0.427088 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.18232e10 | 1.83275 | 0.916373 | − | 0.400325i | \(-0.131103\pi\) | ||||
0.916373 | + | 0.400325i | \(0.131103\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.59405e10 | 2.86751 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.96303e10 | −1.27868 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.63074e9 | −0.0698382 | ||||||||
\(918\) | 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 | ||||||||
\(923\) | −3.69400e9 | −0.154629 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.62291e10 | 1.92052 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.54895e9 | −0.146326 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.56580e10 | 1.04995 | 0.524974 | − | 0.851118i | \(-0.324075\pi\) | ||||
0.524974 | + | 0.851118i | \(0.324075\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.66724e9 | 0.230169 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.23264e9 | 0.331859 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.12204e10 | −2.84947 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.75353e9 | −0.228479 | −0.114239 | − | 0.993453i | \(-0.536443\pi\) | ||||
−0.114239 | + | 0.993453i | \(0.536443\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | −1.02440e10 | −0.397812 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.25184e9 | −0.0482544 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.34709e7 | 0.00357645 | 0.00178822 | − | 0.999998i | \(-0.499431\pi\) | ||||
0.00178822 | + | 0.999998i | \(0.499431\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.89359e10 | −1.09902 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.02123e9 | 0.151610 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.17289e10 | 0.438968 | 0.219484 | − | 0.975616i | \(-0.429563\pi\) | ||||
0.219484 | + | 0.975616i | \(0.429563\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.90020e10 | 2.19207 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.69936e9 | −0.210201 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.57542e7 | −0.00313971 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.97742e10 | −0.718734 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.77266e9 | −0.208297 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.14368e10 | 2.55904 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.64786e10 | 0.586040 | 0.293020 | − | 0.956106i | \(-0.405340\pi\) | ||||
0.293020 | + | 0.956106i | \(0.405340\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.53140e9 | 0.124685 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.88436e10 | 0.660536 | 0.330268 | − | 0.943887i | \(-0.392861\pi\) | ||||
0.330268 | + | 0.943887i | \(0.392861\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.14579e9 | 0.0746779 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.27016e10 | 1.82099 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.26661e10 | −1.46370 | −0.731849 | − | 0.681467i | \(-0.761343\pi\) | ||||
−0.731849 | + | 0.681467i | \(0.761343\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.25603e10 | 1.79027 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.59419e9 | −0.121551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.34527e9 | −0.145908 | −0.0729541 | − | 0.997335i | \(-0.523243\pi\) | ||||
−0.0729541 | + | 0.997335i | \(0.523243\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.10705e10 | −0.702503 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.91055e9 | 0.129458 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.67215e9 | −0.285062 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.36239e10 | −0.444675 | −0.222338 | − | 0.974970i | \(-0.571369\pi\) | ||||
−0.222338 | + | 0.974970i | \(0.571369\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.61438e10 | 0.847319 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.47600e10 | −1.76231 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.32788e10 | −1.38306 | −0.691531 | − | 0.722346i | \(-0.743064\pi\) | ||||
−0.691531 | + | 0.722346i | \(0.743064\pi\) | |||||||
\(998\) | 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 | 48.8.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 144.8.a.k.1.1 | 1 | |||
4.3 | odd | 2 | 24.8.a.b.1.1 | ✓ | 1 | ||
8.3 | odd | 2 | 192.8.a.h.1.1 | 1 | |||
8.5 | even | 2 | 192.8.a.p.1.1 | 1 | |||
12.11 | even | 2 | 72.8.a.e.1.1 | 1 | |||
20.3 | even | 4 | 600.8.f.a.49.2 | 2 | |||
20.7 | even | 4 | 600.8.f.a.49.1 | 2 | |||
20.19 | odd | 2 | 600.8.a.b.1.1 | 1 | |||
24.5 | odd | 2 | 576.8.a.b.1.1 | 1 | |||
24.11 | even | 2 | 576.8.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.8.a.b.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
48.8.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
72.8.a.e.1.1 | 1 | 12.11 | even | 2 | |||
144.8.a.k.1.1 | 1 | 3.2 | odd | 2 | |||
192.8.a.h.1.1 | 1 | 8.3 | odd | 2 | |||
192.8.a.p.1.1 | 1 | 8.5 | even | 2 | |||
576.8.a.b.1.1 | 1 | 24.5 | odd | 2 | |||
576.8.a.c.1.1 | 1 | 24.11 | even | 2 | |||
600.8.a.b.1.1 | 1 | 20.19 | odd | 2 | |||
600.8.f.a.49.1 | 2 | 20.7 | even | 4 | |||
600.8.f.a.49.2 | 2 | 20.3 | even | 4 |