Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,10,Mod(1,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(197.773761087\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 14124x^{2} - 170336x + 18391464 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-103.810\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.1 |
$q$-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 | ||||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −397.737 | −0.284597 | −0.142299 | − | 0.989824i | \(-0.545449\pi\) | ||||
−0.142299 | + | 0.989824i | \(0.545449\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7340.72 | 1.15557 | 0.577787 | − | 0.816188i | \(-0.303917\pi\) | ||||
0.577787 | + | 0.816188i | \(0.303917\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 55385.5 | 1.14059 | 0.570294 | − | 0.821441i | \(-0.306829\pi\) | ||||
0.570294 | + | 0.821441i | \(0.306829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3409.79 | −0.0331118 | −0.0165559 | − | 0.999863i | \(-0.505270\pi\) | ||||
−0.0165559 | + | 0.999863i | \(0.505270\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 32216.7 | 0.164312 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −155165. | −0.450580 | −0.225290 | − | 0.974292i | \(-0.572333\pi\) | ||||
−0.225290 | + | 0.974292i | \(0.572333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −205264. | −0.361344 | −0.180672 | − | 0.983543i | \(-0.557827\pi\) | ||||
−0.180672 | + | 0.983543i | \(0.557827\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −594598. | −0.667171 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 158366. | 0.118001 | 0.0590006 | − | 0.998258i | \(-0.481209\pi\) | ||||
0.0590006 | + | 0.998258i | \(0.481209\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.79493e6 | −0.919004 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.82402e6 | −0.478893 | −0.239446 | − | 0.970910i | \(-0.576966\pi\) | ||||
−0.239446 | + | 0.970910i | \(0.576966\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.92219e6 | −0.373826 | −0.186913 | − | 0.982377i | \(-0.559848\pi\) | ||||
−0.186913 | + | 0.982377i | \(0.559848\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.48622e6 | −0.658519 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.91968e6 | −0.328873 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.17394e6 | −0.366132 | −0.183066 | − | 0.983101i | \(-0.558602\pi\) | ||||
−0.183066 | + | 0.983101i | \(0.558602\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 276193. | 0.0191171 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.70327e7 | −0.941361 | −0.470681 | − | 0.882304i | \(-0.655992\pi\) | ||||
−0.470681 | + | 0.882304i | \(0.655992\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.26916e7 | 1.45824 | 0.729119 | − | 0.684387i | \(-0.239930\pi\) | ||||
0.729119 | + | 0.684387i | \(0.239930\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.60955e6 | −0.0948658 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.89556e7 | −1.16447 | −0.582237 | − | 0.813019i | \(-0.697822\pi\) | ||||
−0.582237 | + | 0.813019i | \(0.697822\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.35326e7 | 0.335350 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.25683e7 | 0.260143 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.64592e7 | 0.808779 | 0.404390 | − | 0.914587i | \(-0.367484\pi\) | ||||
0.404390 | + | 0.914587i | \(0.367484\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.20288e7 | −0.324608 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.66264e7 | 0.208622 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.03738e8 | 1.11457 | 0.557283 | − | 0.830323i | \(-0.311844\pi\) | ||||
0.557283 | + | 0.830323i | \(0.311844\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.66289e7 | −0.431193 | −0.215596 | − | 0.976483i | \(-0.569170\pi\) | ||||
−0.215596 | + | 0.976483i | \(0.569170\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.81625e7 | 0.385191 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.35620e6 | 0.00942352 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.63363e7 | −0.402175 | −0.201087 | − | 0.979573i | \(-0.564448\pi\) | ||||
−0.201087 | + | 0.979573i | \(0.564448\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.28276e7 | −0.0681280 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.28975e7 | −0.293745 | −0.146873 | − | 0.989155i | \(-0.546921\pi\) | ||||
−0.146873 | + | 0.989155i | \(0.546921\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.04953e8 | 0.432557 | 0.216279 | − | 0.976332i | \(-0.430608\pi\) | ||||
0.216279 | + | 0.976332i | \(0.430608\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.45389e8 | 0.530587 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.06569e8 | 1.31803 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.63880e8 | 0.762227 | 0.381113 | − | 0.924528i | \(-0.375541\pi\) | ||||
0.381113 | + | 0.924528i | \(0.375541\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.37032e8 | −1.24208 | −0.621039 | − | 0.783780i | \(-0.713289\pi\) | ||||
−0.621039 | + | 0.783780i | \(0.713289\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.17146e7 | 0.128234 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.47746e8 | 0.276489 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.14261e8 | −0.361984 | −0.180992 | − | 0.983485i | \(-0.557931\pi\) | ||||
−0.180992 | + | 0.983485i | \(0.557931\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.50303e7 | −0.0382631 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.55698e8 | 0.215828 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.16410e7 | 0.102838 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.21818e9 | 1.39714 | 0.698570 | − | 0.715542i | \(-0.253820\pi\) | ||||
0.698570 | + | 0.715542i | \(0.253820\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.63384e8 | 0.380196 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.62080e8 | 0.728709 | 0.364355 | − | 0.931260i | \(-0.381290\pi\) | ||||
0.364355 | + | 0.931260i | \(0.381290\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.91478e9 | −1.67630 | −0.838148 | − | 0.545443i | \(-0.816361\pi\) | ||||
−0.838148 | + | 0.545443i | \(0.816361\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.36494e8 | 0.189875 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.38600e8 | 0.397228 | 0.198614 | − | 0.980078i | \(-0.436356\pi\) | ||||
0.198614 | + | 0.980078i | \(0.436356\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.78761e8 | −0.189153 | −0.0945765 | − | 0.995518i | \(-0.530150\pi\) | ||||
−0.0945765 | + | 0.995518i | \(0.530150\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.38089e8 | 0.211387 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.84040e8 | −0.106184 | −0.0530921 | − | 0.998590i | \(-0.516908\pi\) | ||||
−0.0530921 | + | 0.998590i | \(0.516908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.29880e7 | −0.0335828 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.23716e7 | −0.0110373 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.13902e9 | −0.520679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.09603e8 | 0.300941 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.37965e9 | 0.543495 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.49074e9 | 0.546143 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.29178e9 | −1.46393 | −0.731966 | − | 0.681341i | \(-0.761397\pi\) | ||||
−0.731966 | + | 0.681341i | \(0.761397\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.64802e9 | −0.841914 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.13152e9 | 0.632367 | 0.316184 | − | 0.948698i | \(-0.397598\pi\) | ||||
0.316184 | + | 0.948698i | \(0.397598\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.50678e9 | −0.417560 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.11374e8 | 0.0547708 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.67441e8 | −0.210377 | −0.105188 | − | 0.994452i | \(-0.533545\pi\) | ||||
−0.105188 | + | 0.994452i | \(0.533545\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.94615e9 | −0.442190 | −0.221095 | − | 0.975252i | \(-0.570963\pi\) | ||||
−0.221095 | + | 0.975252i | \(0.570963\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.15541e9 | 0.672310 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.88853e8 | −0.0377669 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.25480e8 | 0.136292 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.09614e9 | −0.193615 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.69461e9 | −0.780299 | −0.390149 | − | 0.920752i | \(-0.627577\pi\) | ||||
−0.390149 | + | 0.920752i | \(0.627577\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.44172e9 | 0.538741 | 0.269370 | − | 0.963037i | \(-0.413184\pi\) | ||||
0.269370 | + | 0.963037i | \(0.413184\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.01803e9 | −0.150193 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.64526e8 | 0.106390 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.02010e9 | −1.18485 | −0.592424 | − | 0.805626i | \(-0.701829\pi\) | ||||
−0.592424 | + | 0.805626i | \(0.701829\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.76319e9 | −0.466949 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.16252e9 | 0.136359 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.13021e10 | −1.25405 | −0.627026 | − | 0.778999i | \(-0.715728\pi\) | ||||
−0.627026 | + | 0.778999i | \(0.715728\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.78434e9 | 0.187413 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.59657e10 | 1.58841 | 0.794207 | − | 0.607647i | \(-0.207886\pi\) | ||||
0.794207 | + | 0.607647i | \(0.207886\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.05929e10 | −0.998904 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.34674e9 | −0.120448 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.95986e10 | 1.66348 | 0.831740 | − | 0.555166i | \(-0.187345\pi\) | ||||
0.831740 | + | 0.555166i | \(0.187345\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.31761e10 | −1.06198 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.40281e9 | −0.643495 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.19596e9 | −0.669512 | −0.334756 | − | 0.942305i | \(-0.608654\pi\) | ||||
−0.334756 | + | 0.942305i | \(0.608654\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.44145e10 | 1.69080 | 0.845402 | − | 0.534130i | \(-0.179361\pi\) | ||||
0.845402 | + | 0.534130i | \(0.179361\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.77694e9 | 0.248949 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.66013e9 | 0.104200 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.59386e9 | −0.513927 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.90116e9 | −0.222390 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.02163e10 | −0.555446 | −0.277723 | − | 0.960661i | \(-0.589580\pi\) | ||||
−0.277723 | + | 0.960661i | \(0.589580\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.80724e9 | −0.197516 | −0.0987581 | − | 0.995111i | \(-0.531487\pi\) | ||||
−0.0987581 | + | 0.995111i | \(0.531487\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.09852e8 | −0.00544067 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.21835e9 | −0.199547 | −0.0997734 | − | 0.995010i | \(-0.531812\pi\) | ||||
−0.0997734 | + | 0.995010i | \(0.531812\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.09330e9 | 0.0494198 | 0.0247099 | − | 0.999695i | \(-0.492134\pi\) | ||||
0.0247099 | + | 0.999695i | \(0.492134\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.37324e9 | 0.232196 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.33896e10 | −0.553396 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.77454e9 | 0.267909 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.03904e9 | 0.0393337 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.13686e10 | −0.412145 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.95404e9 | −0.0678677 | −0.0339339 | − | 0.999424i | \(-0.510804\pi\) | ||||
−0.0339339 | + | 0.999424i | \(0.510804\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.09470e9 | 0.169594 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.30027e10 | −0.415011 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.41103e10 | −0.431983 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.50123e9 | −0.249737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.29078e8 | 0.0149195 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.37625e8 | 0.00643457 | 0.00321729 | − | 0.999995i | \(-0.498976\pi\) | ||||
0.00321729 | + | 0.999995i | \(0.498976\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.17765e10 | −0.306335 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.44760e10 | −1.36172 | −0.680861 | − | 0.732412i | \(-0.738394\pi\) | ||||
−0.680861 | + | 0.732412i | \(0.738394\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.04329e8 | −0.0145216 | −0.00726078 | − | 0.999974i | \(-0.502311\pi\) | ||||
−0.00726078 | + | 0.999974i | \(0.502311\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.29321e10 | −0.760967 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.72907e10 | −1.71801 | −0.859004 | − | 0.511968i | \(-0.828917\pi\) | ||||
−0.859004 | + | 0.511968i | \(0.828917\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.54941e10 | 0.331406 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.13743e10 | −0.440072 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.71496e10 | −0.538235 | −0.269118 | − | 0.963107i | \(-0.586732\pi\) | ||||
−0.269118 | + | 0.963107i | \(0.586732\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.48987e10 | −1.81211 | −0.906053 | − | 0.423165i | \(-0.860919\pi\) | ||||
−0.906053 | + | 0.423165i | \(0.860919\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.38241e9 | −0.0954397 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.99906e8 | 0.0119647 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.34996e10 | 0.717114 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.17138e10 | −0.504333 | −0.252166 | − | 0.967684i | \(-0.581143\pi\) | ||||
−0.252166 | + | 0.967684i | \(0.581143\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.77117e9 | 0.134591 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.99889e9 | −0.0740359 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.11732e8 | 0.00159764 | 0.000798820 | − | 1.00000i | \(-0.499746\pi\) | ||||
0.000798820 | 1.00000i | \(0.499746\pi\) | ||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.06397e10 | −0.423093 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.19674e10 | −0.159631 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.46161e11 | −1.88378 | −0.941889 | − | 0.335924i | \(-0.890952\pi\) | ||||
−0.941889 | + | 0.335924i | \(0.890952\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.84785e10 | −0.230176 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.73552e10 | 0.208991 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.55093e11 | 1.80595 | 0.902977 | − | 0.429689i | \(-0.141377\pi\) | ||||
0.902977 | + | 0.429689i | \(0.141377\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.67924e10 | −0.414378 | −0.207189 | − | 0.978301i | \(-0.566431\pi\) | ||||
−0.207189 | + | 0.978301i | \(0.566431\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.02745e9 | 0.0220912 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.94131e10 | −1.04821 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.16867e11 | 1.19270 | 0.596352 | − | 0.802723i | \(-0.296616\pi\) | ||||
0.596352 | + | 0.802723i | \(0.296616\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.26115e10 | −0.124609 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.69078e10 | 0.257454 | 0.128727 | − | 0.991680i | \(-0.458911\pi\) | ||||
0.128727 | + | 0.991680i | \(0.458911\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.01819e10 | 0.0943603 | 0.0471801 | − | 0.998886i | \(-0.484977\pi\) | ||||
0.0471801 | + | 0.998886i | \(0.484977\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.61292e9 | −0.0593733 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.25032e11 | −1.08781 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.45119e10 | −0.796977 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.86729e10 | −0.806639 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.27162e10 | 0.497136 | 0.248568 | − | 0.968614i | \(-0.420040\pi\) | ||||
0.248568 | + | 0.968614i | \(0.420040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.12606e10 | −0.317202 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.94341e10 | −0.219506 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.39994e8 | −0.00390723 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.39980e11 | 1.68510 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.17285e10 | −0.420721 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.85460e10 | 0.122716 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.29318e10 | −0.532842 | −0.266421 | − | 0.963857i | \(-0.585841\pi\) | ||||
−0.266421 | + | 0.963857i | \(0.585841\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.55097e11 | 0.967810 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.17610e10 | 0.192518 | 0.0962592 | − | 0.995356i | \(-0.469312\pi\) | ||||
0.0962592 | + | 0.995356i | \(0.469312\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.68887e11 | 0.994598 | 0.497299 | − | 0.867579i | \(-0.334325\pi\) | ||||
0.497299 | + | 0.867579i | \(0.334325\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.91560e10 | −0.109624 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.52554e11 | 0.848509 | 0.424254 | − | 0.905543i | \(-0.360536\pi\) | ||||
0.424254 | + | 0.905543i | \(0.360536\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.01024e11 | −0.546220 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.36266e10 | −0.229339 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.18496e10 | 0.162815 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.12033e9 | 0.0304299 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.25797e10 | 0.109207 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.85962e11 | −1.34564 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.26946e11 | −1.49710 | −0.748548 | − | 0.663081i | \(-0.769249\pi\) | ||||
−0.748548 | + | 0.663081i | \(0.769249\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.73852e10 | −0.122044 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.63844e10 | 0.114458 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.21830e11 | −1.35923 | −0.679614 | − | 0.733570i | \(-0.737853\pi\) | ||||
−0.679614 | + | 0.733570i | \(0.737853\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.49073e10 | 0.0613055 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.06462e11 | −0.426381 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.96886e11 | −0.768052 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.10203e9 | 0.0193891 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.57562e10 | −0.354556 | −0.177278 | − | 0.984161i | \(-0.556729\pi\) | ||||
−0.177278 | + | 0.984161i | \(0.556729\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.34178e11 | 0.844950 | 0.422475 | − | 0.906375i | \(-0.361161\pi\) | ||||
0.422475 | + | 0.906375i | \(0.361161\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.81210e9 | 0.00637236 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.85742e9 | 0.0337891 | 0.0168946 | − | 0.999857i | \(-0.494622\pi\) | ||||
0.0168946 | + | 0.999857i | \(0.494622\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.50166e10 | 0.0835991 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.22606e10 | 0.300614 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.59435e11 | −0.506592 | −0.253296 | − | 0.967389i | \(-0.581515\pi\) | ||||
−0.253296 | + | 0.967389i | \(0.581515\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.80554e11 | −0.869430 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.74779e10 | −0.173748 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.17438e10 | −0.123105 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.16207e11 | −0.909859 | −0.454930 | − | 0.890527i | \(-0.650336\pi\) | ||||
−0.454930 | + | 0.890527i | \(0.650336\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.11752e11 | −0.313787 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.41044e11 | 0.934604 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.44449e11 | −0.921372 | −0.460686 | − | 0.887563i | \(-0.652397\pi\) | ||||
−0.460686 | + | 0.887563i | \(0.652397\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.20750e11 | −0.315316 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.21952e9 | 0.0158570 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.90459e11 | −1.46999 | −0.734993 | − | 0.678075i | \(-0.762814\pi\) | ||||
−0.734993 | + | 0.678075i | \(0.762814\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.47634e11 | 0.845202 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.38731e11 | −0.329442 | −0.164721 | − | 0.986340i | \(-0.552672\pi\) | ||||
−0.164721 | + | 0.986340i | \(0.552672\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.61708e11 | −0.375109 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.14490e11 | 0.486079 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.35069e10 | 0.0520501 | 0.0260251 | − | 0.999661i | \(-0.491715\pi\) | ||||
0.0260251 | + | 0.999661i | \(0.491715\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.45728e10 | −0.0531690 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.72653e11 | −0.365097 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.04955e11 | −0.216928 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.02054e11 | −0.408234 | −0.204117 | − | 0.978946i | \(-0.565432\pi\) | ||||
−0.204117 | + | 0.978946i | \(0.565432\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.22050e11 | 0.241078 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.15838e11 | −1.57563 | −0.787815 | − | 0.615912i | \(-0.788788\pi\) | ||||
−0.787815 | + | 0.615912i | \(0.788788\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.55427e9 | 0.0123780 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.71213e10 | −0.0316219 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.31175e11 | −0.417606 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.04841e11 | 1.06877 | 0.534387 | − | 0.845240i | \(-0.320542\pi\) | ||||
0.534387 | + | 0.845240i | \(0.320542\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.02627e10 | 0.121461 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.61515e11 | 1.28796 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.13597e11 | 0.353492 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.57638e11 | 0.255298 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.44512e11 | −0.546061 | −0.273031 | − | 0.962005i | \(-0.588026\pi\) | ||||
−0.273031 | + | 0.962005i | \(0.588026\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.38031e11 | −0.679572 | −0.339786 | − | 0.940503i | \(-0.610355\pi\) | ||||
−0.339786 | + | 0.940503i | \(0.610355\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.55588e11 | −0.388158 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.78509e11 | 0.414085 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.42290e11 | −0.498275 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.52971e10 | 0.0218047 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.76492e11 | 0.385954 | 0.192977 | − | 0.981203i | \(-0.438186\pi\) | ||||
0.192977 | + | 0.981203i | \(0.438186\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.56798e10 | 0.103463 | 0.0517315 | − | 0.998661i | \(-0.483526\pi\) | ||||
0.0517315 | + | 0.998661i | \(0.483526\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.87639e10 | −0.0786880 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.25068e10 | −0.0426391 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.90618e11 | −0.373450 | −0.186725 | − | 0.982412i | \(-0.559787\pi\) | ||||
−0.186725 | + | 0.982412i | \(0.559787\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.87873e10 | 0.111783 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.10685e11 | −0.506632 | −0.253316 | − | 0.967384i | \(-0.581521\pi\) | ||||
−0.253316 | + | 0.967384i | \(0.581521\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.52197e10 | 0.103020 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.80263e11 | 0.450506 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.84583e11 | −1.02714 | −0.513571 | − | 0.858047i | \(-0.671678\pi\) | ||||
−0.513571 | + | 0.858047i | \(0.671678\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.43365e11 | −1.07371 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.78780e11 | −0.311042 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.95547e9 | 0.0108896 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.66348e11 | −0.500135 | −0.250068 | − | 0.968228i | \(-0.580453\pi\) | ||||
−0.250068 | + | 0.968228i | \(0.580453\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.24608e10 | 0.0867142 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.27386e11 | −0.131361 | −0.0656807 | − | 0.997841i | \(-0.520922\pi\) | ||||
−0.0656807 | + | 0.997841i | \(0.520922\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.67555e11 | 0.776238 | 0.388119 | − | 0.921609i | \(-0.373125\pi\) | ||||
0.388119 | + | 0.921609i | \(0.373125\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.19266e10 | −0.0614242 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.96670e11 | −0.677800 | −0.338900 | − | 0.940822i | \(-0.610055\pi\) | ||||
−0.338900 | + | 0.940822i | \(0.610055\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.86956e11 | −0.464742 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.30628e11 | 0.684072 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.81064e12 | 1.66325 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.68434e11 | 0.332077 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.04819e11 | 0.269593 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.51269e11 | 0.131292 | 0.0656462 | − | 0.997843i | \(-0.479089\pi\) | ||||
0.0656462 | + | 0.997843i | \(0.479089\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.42322e10 | 0.0121233 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.41641e10 | −0.0787270 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.84516e11 | −0.397622 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.04990e12 | 1.65140 | 0.825701 | − | 0.564108i | \(-0.190780\pi\) | ||||
0.825701 | + | 0.564108i | \(0.190780\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.15471e11 | 0.724027 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.38298e12 | 1.07387 | 0.536933 | − | 0.843625i | \(-0.319583\pi\) | ||||
0.536933 | + | 0.843625i | \(0.319583\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.83023e11 | 0.215780 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.44531e11 | −0.108203 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.61713e11 | −0.339444 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.12272e12 | 0.810626 | 0.405313 | − | 0.914178i | \(-0.367163\pi\) | ||||
0.405313 | + | 0.914178i | \(0.367163\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.29322e12 | −0.917072 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.76786e11 | −0.471407 | −0.235703 | − | 0.971825i | \(-0.575739\pi\) | ||||
−0.235703 | + | 0.971825i | \(0.575739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.03107e11 | −0.207389 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.58023e11 | 0.576717 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.27029e11 | 0.546124 | 0.273062 | − | 0.961996i | \(-0.411964\pi\) | ||||
0.273062 | + | 0.961996i | \(0.411964\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.70434e11 | 0.499852 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.09086e11 | 0.0695407 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.61577e11 | 0.477069 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.15758e12 | −1.32819 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.58749e12 | −0.960410 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.68612e12 | 1.59718 | 0.798592 | − | 0.601872i | \(-0.205578\pi\) | ||||
0.798592 | + | 0.601872i | \(0.205578\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.94122e12 | 1.13453 | 0.567267 | − | 0.823534i | \(-0.308001\pi\) | ||||
0.567267 | + | 0.823534i | \(0.308001\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.06726e12 | 0.613133 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.98256e11 | 0.168438 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.77607e12 | −0.986076 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.80628e11 | 0.371522 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.80779e10 | 0.0311701 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.14221e11 | −0.113050 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.44873e11 | 0.386543 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.49509e11 | 0.382496 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.54650e11 | 0.177997 | 0.0889983 | − | 0.996032i | \(-0.471633\pi\) | ||||
0.0889983 | + | 0.996032i | \(0.471633\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.97757e12 | −0.976187 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.10874e11 | 0.0538324 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.51666e11 | 0.215712 | 0.107856 | − | 0.994167i | \(-0.465601\pi\) | ||||
0.107856 | + | 0.994167i | \(0.465601\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.05933e11 | −0.143731 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.74405e11 | 0.173045 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.93707e12 | 0.880809 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.34470e11 | −0.0601601 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.52104e12 | −0.669563 | −0.334781 | − | 0.942296i | \(-0.608662\pi\) | ||||
−0.334781 | + | 0.942296i | \(0.608662\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.11472e11 | −0.0482848 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.96103e11 | 0.296716 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.30988e12 | 1.38843 | 0.694217 | − | 0.719766i | \(-0.255751\pi\) | ||||
0.694217 | + | 0.719766i | \(0.255751\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.31996e10 | 0.0302198 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.15994e11 | 0.128397 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.08233e12 | 1.23275 | 0.616374 | − | 0.787453i | \(-0.288601\pi\) | ||||
0.616374 | + | 0.787453i | \(0.288601\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.13710e12 | 0.447648 | 0.223824 | − | 0.974630i | \(-0.428146\pi\) | ||||
0.223824 | + | 0.974630i | \(0.428146\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.27518e11 | 0.320687 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.84256e11 | −0.108444 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.48044e12 | −0.931617 | −0.465808 | − | 0.884886i | \(-0.654236\pi\) | ||||
−0.465808 | + | 0.884886i | \(0.654236\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.08387e11 | 0.114036 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.94220e12 | −1.43531 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.57316e12 | 0.922484 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.89802e9 | 0.00314117 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.17038e12 | 0.406869 | 0.203435 | − | 0.979089i | \(-0.434790\pi\) | ||||
0.203435 | + | 0.979089i | \(0.434790\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.94556e11 | 0.135080 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.41687e11 | 0.115208 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.21383e12 | 0.403101 | 0.201550 | − | 0.979478i | \(-0.435402\pi\) | ||||
0.201550 | + | 0.979478i | \(0.435402\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.53030e11 | 0.148184 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.85574e10 | −0.0285325 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.28874e12 | 1.67854 | 0.839270 | − | 0.543716i | \(-0.182983\pi\) | ||||
0.839270 | + | 0.543716i | \(0.182983\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.10430e11 | −0.284650 | −0.142325 | − | 0.989820i | \(-0.545458\pi\) | ||||
−0.142325 | + | 0.989820i | \(0.545458\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.35233e11 | −0.134058 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.82235e11 | −0.0856470 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.57806e12 | 1.66776 | 0.833881 | − | 0.551945i | \(-0.186114\pi\) | ||||
0.833881 | + | 0.551945i | \(0.186114\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.08456e12 | 0.319503 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.32830e11 | 0.0385578 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.74576e12 | −1.64352 | −0.821761 | − | 0.569832i | \(-0.807008\pi\) | ||||
−0.821761 | + | 0.569832i | \(0.807008\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.48737e11 | −0.154677 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.31735e12 | 1.75490 | 0.877449 | − | 0.479670i | \(-0.159244\pi\) | ||||
0.877449 | + | 0.479670i | \(0.159244\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.23867e12 | −1.16044 | −0.580218 | − | 0.814461i | \(-0.697033\pi\) | ||||
−0.580218 | + | 0.814461i | \(0.697033\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.41622e10 | −0.0227093 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.57283e12 | −0.418299 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.91280e12 | 0.763573 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.20859e11 | 0.237952 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.47647e11 | 0.164972 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.74768e12 | 0.438864 | 0.219432 | − | 0.975628i | \(-0.429580\pi\) | ||||
0.219432 | + | 0.975628i | \(0.429580\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.58278e11 | 0.0391834 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.70700e12 | 0.416631 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.61433e10 | −0.0111040 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.12670e11 | −0.0979151 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.99186e11 | −0.0699971 | −0.0349986 | − | 0.999387i | \(-0.511143\pi\) | ||||
−0.0349986 | + | 0.999387i | \(0.511143\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.75869e12 | 0.405732 | 0.202866 | − | 0.979207i | \(-0.434974\pi\) | ||||
0.202866 | + | 0.979207i | \(0.434974\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.05322e12 | 0.239606 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.30030e12 | 0.291726 | 0.145863 | − | 0.989305i | \(-0.453404\pi\) | ||||
0.145863 | + | 0.989305i | \(0.453404\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.74560e12 | 1.27126 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.14293e12 | 0.249406 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.41572e12 | 1.59604 | 0.798021 | − | 0.602630i | \(-0.205881\pi\) | ||||
0.798021 | + | 0.602630i | \(0.205881\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.47786e11 | −0.179970 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.88599e11 | 0.144186 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.67183e12 | −0.551855 | −0.275927 | − | 0.961178i | \(-0.588985\pi\) | ||||
−0.275927 | + | 0.961178i | \(0.588985\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.73151e12 | −1.77903 | −0.889514 | − | 0.456908i | \(-0.848957\pi\) | ||||
−0.889514 | + | 0.456908i | \(0.848957\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.28553e10 | −0.00861378 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.99303e11 | 0.118836 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.88863e11 | −0.0565100 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.92476e10 | −0.00371500 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.58257e12 | −0.491813 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.22078e12 | −1.16890 | −0.584449 | − | 0.811430i | \(-0.698689\pi\) | ||||
−0.584449 | + | 0.811430i | \(0.698689\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.53900e11 | 0.176862 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.30526e12 | −1.33655 | −0.668277 | − | 0.743912i | \(-0.732968\pi\) | ||||
−0.668277 | + | 0.743912i | \(0.732968\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.94235e12 | 1.61450 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.41255e12 | 0.786191 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.82808e12 | 1.55229 | 0.776145 | − | 0.630554i | \(-0.217172\pi\) | ||||
0.776145 | + | 0.630554i | \(0.217172\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.45013e11 | 0.0598726 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.89506e10 | 0.00838403 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.58416e11 | −0.0267801 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.73949e12 | −1.45826 | −0.729130 | − | 0.684375i | \(-0.760075\pi\) | ||||
−0.729130 | + | 0.684375i | \(0.760075\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.66750e12 | 0.439344 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.74054e11 | 0.125846 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.64287e12 | 0.424159 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.26054e12 | 0.991893 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.40844e12 | 0.376708 | 0.188354 | − | 0.982101i | \(-0.439685\pi\) | ||||
0.188354 | + | 0.982101i | \(0.439685\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.56758e11 | 0.132300 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.25502e12 | −0.191337 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.59422e12 | 0.842077 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.05935e13 | −1.57446 | −0.787230 | − | 0.616660i | \(-0.788485\pi\) | ||||
−0.787230 | + | 0.616660i | \(0.788485\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.73131e12 | 0.254076 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.04410e11 | −0.0441119 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.51137e10 | 0.0107484 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.19911e12 | 0.310750 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.20874e11 | 0.128505 | 0.0642525 | − | 0.997934i | \(-0.479534\pi\) | ||||
0.0642525 | + | 0.997934i | \(0.479534\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.40558e13 | −1.93708 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.68679e12 | 1.04622 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.27399e12 | 0.440105 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.54020e12 | −1.00110 | −0.500551 | − | 0.865707i | \(-0.666869\pi\) | ||||
−0.500551 | + | 0.865707i | \(0.666869\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.07258e12 | −0.657053 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.26906e12 | −1.05801 | −0.529003 | − | 0.848620i | \(-0.677434\pi\) | ||||
−0.529003 | + | 0.848620i | \(0.677434\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.35975e11 | 0.0551022 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.67407e12 | −0.458716 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.43637e13 | −1.77160 | −0.885802 | − | 0.464064i | \(-0.846391\pi\) | ||||
−0.885802 | + | 0.464064i | \(0.846391\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.66924e10 | −0.00690785 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.12328e13 | −1.35220 | −0.676099 | − | 0.736811i | \(-0.736331\pi\) | ||||
−0.676099 | + | 0.736811i | \(0.736331\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.86722e12 | 0.222071 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.52347e12 | −0.414026 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.95371e12 | 0.459026 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.15825e13 | 1.32869 | 0.664346 | − | 0.747425i | \(-0.268710\pi\) | ||||
0.664346 | + | 0.747425i | \(0.268710\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.56882e12 | 0.291177 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.36890e12 | −0.153324 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.19463e12 | −0.685621 | −0.342810 | − | 0.939405i | \(-0.611379\pi\) | ||||
−0.342810 | + | 0.939405i | \(0.611379\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.10465e11 | −0.0777060 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.57090e13 | −1.69793 | −0.848963 | − | 0.528453i | \(-0.822772\pi\) | ||||
−0.848963 | + | 0.528453i | \(0.822772\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.04631e12 | −0.218580 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.04910e11 | 0.0427446 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.53726e11 | −0.0369052 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.65088e12 | −0.479586 | −0.239793 | − | 0.970824i | \(-0.577080\pi\) | ||||
−0.239793 | + | 0.970824i | \(0.577080\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.05030e9 | −0.000922398 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.78167e12 | −0.380957 | −0.190478 | − | 0.981691i | \(-0.561004\pi\) | ||||
−0.190478 | + | 0.981691i | \(0.561004\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.45020e12 | 0.343547 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.48182e12 | 0.244273 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.49620e12 | 0.340155 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.48361e12 | −0.335042 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.69359e11 | 0.0921630 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.58762e12 | 0.337205 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.94623e12 | 0.366688 | 0.183344 | − | 0.983049i | \(-0.441308\pi\) | ||||
0.183344 | + | 0.983049i | \(0.441308\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.18390e13 | 1.08760 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.35099e12 | −0.122704 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.58995e11 | 0.0142775 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.49676e12 | 0.132892 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.76742e13 | 1.55159 | 0.775797 | − | 0.630982i | \(-0.217348\pi\) | ||||
0.775797 | + | 0.630982i | \(0.217348\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.04453e12 | 0.524689 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.40577e12 | −0.120661 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.81289e12 | 0.493370 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.62377e11 | −0.0388074 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.25625e13 | −1.04267 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.53289e12 | 0.700370 | 0.350185 | − | 0.936681i | \(-0.386119\pi\) | ||||
0.350185 | + | 0.936681i | \(0.386119\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.57738e13 | −1.28039 | −0.640197 | − | 0.768211i | \(-0.721147\pi\) | ||||
−0.640197 | + | 0.768211i | \(0.721147\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.98018e12 | 0.239241 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.49526e12 | 0.356900 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.71041e12 | −0.526926 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.64224e11 | −0.0127544 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.11176e12 | −0.315852 | −0.157926 | − | 0.987451i | \(-0.550481\pi\) | ||||
−0.157926 | + | 0.987451i | \(0.550481\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.47591e12 | −0.340081 | −0.170040 | − | 0.985437i | \(-0.554390\pi\) | ||||
−0.170040 | + | 0.985437i | \(0.554390\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.05246e12 | 0.605182 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.03686e12 | −0.597464 | −0.298732 | − | 0.954337i | \(-0.596564\pi\) | ||||
−0.298732 | + | 0.954337i | \(0.596564\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.67641e13 | 1.23277 | 0.616387 | − | 0.787443i | \(-0.288596\pi\) | ||||
0.616387 | + | 0.787443i | \(0.288596\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.46621e12 | −0.688607 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.09978e12 | −0.151102 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.35015e12 | −0.452058 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.02153e12 | 0.0719428 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.24921e13 | −0.870375 | −0.435187 | − | 0.900340i | \(-0.643318\pi\) | ||||
−0.435187 | + | 0.900340i | \(0.643318\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.11801e13 | −0.770662 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.17953e12 | −0.148641 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.21318e12 | 0.284285 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.20900e12 | 0.347760 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.24732e11 | −0.0544789 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.61009e11 | −0.0432041 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.63321e13 | 1.70300 | 0.851500 | − | 0.524355i | \(-0.175693\pi\) | ||||
0.851500 | + | 0.524355i | \(0.175693\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.35646e11 | 0.0342792 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.67767e13 | 1.69567 | 0.847837 | − | 0.530256i | \(-0.177904\pi\) | ||||
0.847837 | + | 0.530256i | \(0.177904\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.65495e13 | −1.03709 | −0.518544 | − | 0.855051i | \(-0.673526\pi\) | ||||
−0.518544 | + | 0.855051i | \(0.673526\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.01276e13 | 0.628049 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.48373e13 | −1.52425 | −0.762124 | − | 0.647432i | \(-0.775843\pi\) | ||||
−0.762124 | + | 0.647432i | \(0.775843\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.79508e12 | −0.473422 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.65546e12 | 0.460135 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.46151e13 | 0.869387 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.26193e11 | 0.0133167 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.99250e12 | 0.465713 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.09431e13 | 0.631109 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.75473e13 | −1.57247 | −0.786233 | − | 0.617930i | \(-0.787971\pi\) | ||||
−0.786233 | + | 0.617930i | \(0.787971\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.08001e12 | −0.287022 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.65762e13 | 0.927029 | 0.463514 | − | 0.886089i | \(-0.346588\pi\) | ||||
0.463514 | + | 0.886089i | \(0.346588\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.97773e12 | −0.164840 | −0.0824198 | − | 0.996598i | \(-0.526265\pi\) | ||||
−0.0824198 | + | 0.996598i | \(0.526265\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.34211e12 | 0.183137 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.03383e12 | 0.273050 | 0.136525 | − | 0.990637i | \(-0.456407\pi\) | ||||
0.136525 | + | 0.990637i | \(0.456407\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.15048e13 | −1.69168 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.38416e12 | 0.126732 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.99618e12 | 0.420776 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.65757e12 | 0.190541 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.37395e10 | 0.00225584 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.50612e12 | 0.179022 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.20881e12 | −0.364420 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.94384e13 | −0.972894 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.71053e12 | −0.481198 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.38163e13 | −1.65918 | −0.829590 | − | 0.558373i | \(-0.811426\pi\) | ||||
−0.829590 | + | 0.558373i | \(0.811426\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.00001e12 | 0.242903 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.91391e13 | −1.88269 | −0.941344 | − | 0.337449i | \(-0.890436\pi\) | ||||
−0.941344 | + | 0.337449i | \(0.890436\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.97438e13 | −1.41670 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.50223e12 | −0.0708503 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.56469e13 | 0.730747 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.85085e12 | 0.455569 | 0.227784 | − | 0.973712i | \(-0.426852\pi\) | ||||
0.227784 | + | 0.973712i | \(0.426852\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.71748e12 | 0.307637 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.14467e11 | 0.00972642 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.49193e12 | 0.336477 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.25628e13 | −0.558765 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.01841e13 | 0.448593 | 0.224296 | − | 0.974521i | \(-0.427992\pi\) | ||||
0.224296 | + | 0.974521i | \(0.427992\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.77775e12 | −0.121177 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.57264e12 | −0.111151 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.41809e12 | 0.146262 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.02950e13 | −1.70775 | −0.853873 | − | 0.520481i | \(-0.825753\pi\) | ||||
−0.853873 | + | 0.520481i | \(0.825753\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.36799e13 | −0.574232 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.92352e12 | 0.204702 | 0.102351 | − | 0.994748i | \(-0.467363\pi\) | ||||
0.102351 | + | 0.994748i | \(0.467363\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.69740e12 | −0.111082 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.55164e12 | 0.0632917 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.44185e13 | −0.986606 | −0.493303 | − | 0.869858i | \(-0.664211\pi\) | ||||
−0.493303 | + | 0.869858i | \(0.664211\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.57869e11 | −0.0143227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.23569e13 | −0.489887 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.80434e13 | −0.708599 | −0.354299 | − | 0.935132i | \(-0.615281\pi\) | ||||
−0.354299 | + | 0.935132i | \(0.615281\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.06339e12 | 0.158079 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.18296e12 | 0.315360 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.36764e12 | −0.243106 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.27448e13 | −0.860254 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.53375e12 | 0.132409 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.51428e12 | 0.0562126 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.44115e13 | 0.530018 | 0.265009 | − | 0.964246i | \(-0.414625\pi\) | ||||
0.265009 | + | 0.964246i | \(0.414625\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.57982e12 | −0.0940010 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.58123e13 | 0.570831 | 0.285415 | − | 0.958404i | \(-0.407868\pi\) | ||||
0.285415 | + | 0.958404i | \(0.407868\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.42861e13 | −0.510983 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.95747e11 | −0.0175687 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.64628e13 | −1.63147 | −0.815737 | − | 0.578423i | \(-0.803668\pi\) | ||||
−0.815737 | + | 0.578423i | \(0.803668\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.18670e13 | −0.412874 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.82895e12 | −0.0630510 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.65220e13 | −1.58916 | −0.794580 | − | 0.607160i | \(-0.792309\pi\) | ||||
−0.794580 | + | 0.607160i | \(0.792309\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.67779e12 | 0.0567905 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.31630e13 | 0.776903 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.17724e12 | 0.172074 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.96520e12 | 0.130597 | 0.0652985 | − | 0.997866i | \(-0.479200\pi\) | ||||
0.0652985 | + | 0.997866i | \(0.479200\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.64826e13 | 0.864348 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.34846e11 | −0.0140647 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.82677e12 | −0.0585538 | −0.0292769 | − | 0.999571i | \(-0.509320\pi\) | ||||
−0.0292769 | + | 0.999571i | \(0.509320\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.21820e12 | 0.0704622 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 384.10.a.d.1.2 | yes | 4 | |
4.3 | odd | 2 | 384.10.a.h.1.2 | yes | 4 | ||
8.3 | odd | 2 | 384.10.a.a.1.3 | ✓ | 4 | ||
8.5 | even | 2 | 384.10.a.e.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.10.a.a.1.3 | ✓ | 4 | 8.3 | odd | 2 | ||
384.10.a.d.1.2 | yes | 4 | 1.1 | even | 1 | trivial | |
384.10.a.e.1.3 | yes | 4 | 8.5 | even | 2 | ||
384.10.a.h.1.2 | yes | 4 | 4.3 | odd | 2 |