Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,8,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, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
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: | \(119.955849786\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{366}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 366 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-19.1311\) 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 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −65.0490 | −0.232726 | −0.116363 | − | 0.993207i | \(-0.537124\pi\) | ||||
−0.116363 | + | 0.993207i | \(0.537124\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 275.245 | 0.303303 | 0.151651 | − | 0.988434i | \(-0.451541\pi\) | ||||
0.151651 | + | 0.988434i | \(0.451541\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5543.27 | −1.25572 | −0.627859 | − | 0.778327i | \(-0.716068\pi\) | ||||
−0.627859 | + | 0.778327i | \(0.716068\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4956.94 | 0.625766 | 0.312883 | − | 0.949792i | \(-0.398705\pi\) | ||||
0.312883 | + | 0.949792i | \(0.398705\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1756.32 | 0.134365 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −20343.4 | −1.00427 | −0.502136 | − | 0.864789i | \(-0.667452\pi\) | ||||
−0.502136 | + | 0.864789i | \(0.667452\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 49187.7 | 1.64520 | 0.822600 | − | 0.568621i | \(-0.192523\pi\) | ||||
0.822600 | + | 0.568621i | \(0.192523\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7431.62 | −0.175112 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 55150.9 | 0.945159 | 0.472580 | − | 0.881288i | \(-0.343323\pi\) | ||||
0.472580 | + | 0.881288i | \(0.343323\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −73893.6 | −0.945838 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 132595. | 1.00957 | 0.504783 | − | 0.863246i | \(-0.331572\pi\) | ||||
0.504783 | + | 0.863246i | \(0.331572\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −248716. | −1.49947 | −0.749736 | − | 0.661737i | \(-0.769820\pi\) | ||||
−0.749736 | + | 0.661737i | \(0.769820\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 149668. | 0.724989 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −17904.4 | −0.0705866 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −158346. | −0.513926 | −0.256963 | − | 0.966421i | \(-0.582722\pi\) | ||||
−0.256963 | + | 0.966421i | \(0.582722\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −133837. | −0.361286 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 411345. | 0.932100 | 0.466050 | − | 0.884759i | \(-0.345677\pi\) | ||||
0.466050 | + | 0.884759i | \(0.345677\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −165656. | −0.317736 | −0.158868 | − | 0.987300i | \(-0.550784\pi\) | ||||
−0.158868 | + | 0.987300i | \(0.550784\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −47420.7 | −0.0775755 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 881705. | 1.23874 | 0.619371 | − | 0.785099i | \(-0.287388\pi\) | ||||
0.619371 | + | 0.785099i | \(0.287388\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −747783. | −0.908007 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 549270. | 0.579817 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.06905e6 | 0.986351 | 0.493176 | − | 0.869930i | \(-0.335836\pi\) | ||||
0.493176 | + | 0.869930i | \(0.335836\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 360585. | 0.292239 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.32807e6 | −0.949856 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.20357e6 | 0.762936 | 0.381468 | − | 0.924382i | \(-0.375419\pi\) | ||||
0.381468 | + | 0.924382i | \(0.375419\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 723534. | 0.408136 | 0.204068 | − | 0.978957i | \(-0.434584\pi\) | ||||
0.204068 | + | 0.978957i | \(0.434584\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 200654. | 0.101101 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −322444. | −0.145632 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.51853e6 | 0.616826 | 0.308413 | − | 0.951253i | \(-0.400202\pi\) | ||||
0.308413 | + | 0.951253i | \(0.400202\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.48907e6 | −0.545688 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −524889. | −0.174046 | −0.0870229 | − | 0.996206i | \(-0.527735\pi\) | ||||
−0.0870229 | + | 0.996206i | \(0.527735\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −542977. | −0.163362 | −0.0816810 | − | 0.996659i | \(-0.526029\pi\) | ||||
−0.0816810 | + | 0.996659i | \(0.526029\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.99513e6 | 0.546080 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.52576e6 | −0.380863 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.24216e6 | 0.739842 | 0.369921 | − | 0.929063i | \(-0.379385\pi\) | ||||
0.369921 | + | 0.929063i | \(0.379385\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.79794e6 | −0.537113 | −0.268556 | − | 0.963264i | \(-0.586547\pi\) | ||||
−0.268556 | + | 0.963264i | \(0.586547\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.32331e6 | 0.233721 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.58007e6 | −0.582874 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.54242e6 | −0.231920 | −0.115960 | − | 0.993254i | \(-0.536994\pi\) | ||||
−0.115960 | + | 0.993254i | \(0.536994\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.36437e6 | 0.189797 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.71534e6 | 0.865721 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.19961e6 | −0.382881 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.01065e7 | −1.12435 | −0.562175 | − | 0.827018i | \(-0.690035\pi\) | ||||
−0.562175 | + | 0.827018i | \(0.690035\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.04105e6 | −0.418573 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.26941e6 | −0.895215 | −0.447607 | − | 0.894230i | \(-0.647724\pi\) | ||||
−0.447607 | + | 0.894230i | \(0.647724\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.69812e6 | −0.603980 | −0.301990 | − | 0.953311i | \(-0.597651\pi\) | ||||
−0.301990 | + | 0.953311i | \(0.597651\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 483419. | 0.0407532 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.52877e7 | 1.20642 | 0.603210 | − | 0.797583i | \(-0.293888\pi\) | ||||
0.603210 | + | 0.797583i | \(0.293888\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.32632e7 | −1.72058 | −0.860292 | − | 0.509802i | \(-0.829719\pi\) | ||||
−0.860292 | + | 0.509802i | \(0.829719\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.27534e6 | 0.296715 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.81644e6 | −0.574803 | −0.287401 | − | 0.957810i | \(-0.592791\pi\) | ||||
−0.287401 | + | 0.957810i | \(0.592791\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.58751e6 | −0.219964 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.61361e6 | 0.208589 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.59941e6 | −0.304598 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.12407e7 | 0.576827 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.11063e7 | −0.538148 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.88866e6 | 0.452848 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.54448e7 | −0.669065 | −0.334533 | − | 0.942384i | \(-0.608578\pi\) | ||||
−0.334533 | + | 0.942384i | \(0.608578\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.47270e6 | 0.183445 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.58656e7 | 1.00525 | 0.502623 | − | 0.864506i | \(-0.332368\pi\) | ||||
0.502623 | + | 0.864506i | \(0.332368\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.35387e7 | 0.498994 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.28036e6 | 0.0447882 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.23006e7 | −0.740959 | −0.370479 | − | 0.928841i | \(-0.620807\pi\) | ||||
−0.370479 | + | 0.928841i | \(0.620807\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.43314e7 | 0.768451 | 0.384225 | − | 0.923239i | \(-0.374469\pi\) | ||||
0.384225 | + | 0.923239i | \(0.374469\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.38060e7 | −0.715188 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.74777e7 | −0.785785 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.62519e6 | −0.234953 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.01901e7 | 0.524238 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.33558e7 | −1.81670 | −0.908348 | − | 0.418215i | \(-0.862656\pi\) | ||||
−0.908348 | + | 0.418215i | \(0.862656\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.16331e7 | −0.984055 | −0.492028 | − | 0.870580i | \(-0.663744\pi\) | ||||
−0.492028 | + | 0.870580i | \(0.663744\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.48303e7 | −0.334757 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.61788e7 | 0.348967 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.76259e7 | −0.775958 | −0.387979 | − | 0.921668i | \(-0.626827\pi\) | ||||
−0.387979 | + | 0.921668i | \(0.626827\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.88643e7 | −0.569470 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.51800e7 | 0.286669 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.90955e7 | −0.707083 | −0.353541 | − | 0.935419i | \(-0.615023\pi\) | ||||
−0.353541 | + | 0.935419i | \(0.615023\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.73578e6 | −0.168724 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.38058e7 | −1.39241 | −0.696204 | − | 0.717844i | \(-0.745129\pi\) | ||||
−0.696204 | + | 0.717844i | \(0.745129\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.81773e7 | −0.608417 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.58578e7 | 0.548400 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.49967e7 | −1.39491 | −0.697457 | − | 0.716627i | \(-0.745685\pi\) | ||||
−0.697457 | + | 0.716627i | \(0.745685\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.03389e7 | −0.286875 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.24963e7 | −0.440481 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.62054e7 | −0.341511 | −0.170756 | − | 0.985313i | \(-0.554621\pi\) | ||||
−0.170756 | + | 0.985313i | \(0.554621\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.35606e7 | −0.546032 | −0.273016 | − | 0.962009i | \(-0.588021\pi\) | ||||
−0.273016 | + | 0.962009i | \(0.588021\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.95354e7 | −0.235637 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.03002e7 | 0.119604 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.12769e8 | 1.26108 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.41765e6 | −0.0583706 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.16280e8 | 1.20750 | 0.603749 | − | 0.797174i | \(-0.293673\pi\) | ||||
0.603749 | + | 0.797174i | \(0.293673\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.09584e8 | −1.09723 | −0.548615 | − | 0.836075i | \(-0.684845\pi\) | ||||
−0.548615 | + | 0.836075i | \(0.684845\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.70599e6 | 0.0840808 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.54530e8 | 1.44006 | 0.720029 | − | 0.693944i | \(-0.244129\pi\) | ||||
0.720029 | + | 0.693944i | \(0.244129\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.17206e8 | −1.05430 | −0.527151 | − | 0.849772i | \(-0.676740\pi\) | ||||
−0.527151 | + | 0.849772i | \(0.676740\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.10004e7 | −0.356124 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.64962e7 | 0.306204 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.67576e7 | −0.216924 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.02050e7 | 0.315053 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.72661e8 | −2.06591 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.34458e8 | 1.71821 | 0.859107 | − | 0.511796i | \(-0.171020\pi\) | ||||
0.859107 | + | 0.511796i | \(0.171020\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.41720e7 | 0.100485 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.07757e7 | 0.0739456 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.84579e7 | −0.454794 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.46604e7 | 0.0943171 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.00841e8 | −0.628439 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.36568e8 | −1.42853 | −0.714265 | − | 0.699876i | \(-0.753239\pi\) | ||||
−0.714265 | + | 0.699876i | \(0.753239\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.38685e7 | −0.315279 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.20042e8 | 1.24857 | 0.624287 | − | 0.781195i | \(-0.285390\pi\) | ||||
0.624287 | + | 0.781195i | \(0.285390\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.78074e8 | −1.53016 | −0.765079 | − | 0.643937i | \(-0.777300\pi\) | ||||
−0.765079 | + | 0.643937i | \(0.777300\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.11955e7 | 0.219891 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.21028e7 | 0.321637 | 0.160818 | − | 0.986984i | \(-0.448587\pi\) | ||||
0.160818 | + | 0.986984i | \(0.448587\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.73540e7 | −0.288288 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.75382e7 | −0.427148 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.49575e8 | −1.65633 | −0.828166 | − | 0.560483i | \(-0.810615\pi\) | ||||
−0.828166 | + | 0.560483i | \(0.810615\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.47411e7 | 0.389973 | 0.194987 | − | 0.980806i | \(-0.437534\pi\) | ||||
0.194987 | + | 0.980806i | \(0.437534\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.86426e7 | 0.211317 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.43820e8 | 1.02951 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.55444e7 | 0.310102 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.31962e7 | 0.212335 | 0.106168 | − | 0.994348i | \(-0.466142\pi\) | ||||
0.106168 | + | 0.994348i | \(0.466142\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.05716e8 | −1.18685 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.57295e7 | −0.134939 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.31504e8 | −1.58569 | −0.792846 | − | 0.609422i | \(-0.791401\pi\) | ||||
−0.792846 | + | 0.609422i | \(0.791401\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.35839e7 | −0.155875 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.66620e7 | 0.336522 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.62847e7 | −0.190785 | −0.0953927 | − | 0.995440i | \(-0.530411\pi\) | ||||
−0.0953927 | + | 0.995440i | \(0.530411\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.95405e7 | −0.229550 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.16454e7 | 0.133899 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.57377e8 | −0.492957 | −0.246479 | − | 0.969148i | \(-0.579273\pi\) | ||||
−0.246479 | + | 0.969148i | \(0.579273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.61871e7 | 0.0799273 | 0.0399637 | − | 0.999201i | \(-0.487276\pi\) | ||||
0.0399637 | + | 0.999201i | \(0.487276\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.68381e7 | −0.109579 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.09613e8 | 1.18771 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.69358e8 | 1.60956 | 0.804779 | − | 0.593575i | \(-0.202284\pi\) | ||||
0.804779 | + | 0.593575i | \(0.202284\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.81314e8 | −0.499824 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.28150e7 | −0.168885 | −0.0844425 | − | 0.996428i | \(-0.526911\pi\) | ||||
−0.0844425 | + | 0.996428i | \(0.526911\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.59079e7 | −0.0417216 | −0.0208608 | − | 0.999782i | \(-0.506641\pi\) | ||||
−0.0208608 | + | 0.999782i | \(0.506641\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.63894e7 | 0.221057 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.13221e8 | 0.282708 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.51329e6 | 0.00856192 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.72877e8 | 0.649144 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.96493e8 | −0.688618 | −0.344309 | − | 0.938856i | \(-0.611887\pi\) | ||||
−0.344309 | + | 0.938856i | \(0.611887\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.82908e7 | −0.177555 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.09108e8 | 0.241663 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.73380e8 | 0.591449 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.55959e7 | −0.0963703 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.50274e8 | 0.516852 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.70652e7 | −0.0949840 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.44473e8 | −0.876721 | −0.438360 | − | 0.898799i | \(-0.644441\pi\) | ||||
−0.438360 | + | 0.898799i | \(0.644441\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.80849e8 | 0.348708 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.40599e8 | −0.453558 | −0.226779 | − | 0.973946i | \(-0.572820\pi\) | ||||
−0.226779 | + | 0.973946i | \(0.572820\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.75397e8 | 1.79794 | 0.898972 | − | 0.438005i | \(-0.144315\pi\) | ||||
0.898972 | + | 0.438005i | \(0.144315\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.30523e7 | −0.0235289 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.90517e8 | −0.335913 | −0.167956 | − | 0.985794i | \(-0.553717\pi\) | ||||
−0.167956 | + | 0.985794i | \(0.553717\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.35012e8 | −1.26773 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.12767e8 | −0.696527 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.00064e9 | −1.65223 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.66286e8 | −0.591874 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.28105e8 | 0.993380 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.42685e8 | 0.375714 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.18272e8 | −0.937091 | −0.468546 | − | 0.883439i | \(-0.655222\pi\) | ||||
−0.468546 | + | 0.883439i | \(0.655222\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.15434e8 | −0.171309 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.87791e7 | −0.143552 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.17191e9 | −1.66798 | −0.833990 | − | 0.551779i | \(-0.813949\pi\) | ||||
−0.833990 | + | 0.551779i | \(0.813949\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.38044e8 | 0.331862 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.37870e9 | 1.88291 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.32500e8 | −0.578704 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.68628e7 | 0.126996 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.14800e8 | −0.532949 | −0.266474 | − | 0.963842i | \(-0.585859\pi\) | ||||
−0.266474 | + | 0.963842i | \(0.585859\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.48010e9 | −1.86381 | −0.931905 | − | 0.362703i | \(-0.881854\pi\) | ||||
−0.931905 | + | 0.362703i | \(0.881854\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.75675e7 | −0.120429 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.02147e9 | 1.23599 | 0.617993 | − | 0.786183i | \(-0.287946\pi\) | ||||
0.617993 | + | 0.786183i | \(0.287946\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.41435e7 | 0.0405050 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.51184e8 | 0.175860 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.26250e9 | 1.44012 | 0.720062 | − | 0.693910i | \(-0.244113\pi\) | ||||
0.720062 | + | 0.693910i | \(0.244113\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.52555e9 | 1.70668 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.03499e8 | −0.333031 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.53201e7 | 0.0380187 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.24186e8 | 0.870350 | 0.435175 | − | 0.900346i | \(-0.356687\pi\) | ||||
0.435175 | + | 0.900346i | \(0.356687\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.99870e8 | 0.310700 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.94250e8 | 0.299163 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.68578e8 | 0.367746 | 0.183873 | − | 0.982950i | \(-0.441136\pi\) | ||||
0.183873 | + | 0.982950i | \(0.441136\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.66994e8 | −0.261452 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.57267e8 | 0.631753 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.53429e8 | −0.805248 | −0.402624 | − | 0.915365i | \(-0.631902\pi\) | ||||
−0.402624 | + | 0.915365i | \(0.631902\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.17009e8 | 0.386285 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.18529e9 | 1.07803 | 0.539013 | − | 0.842298i | \(-0.318797\pi\) | ||||
0.539013 | + | 0.842298i | \(0.318797\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.92491e7 | 0.0886368 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.20763e8 | −0.105912 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.11972e9 | 0.964461 | 0.482231 | − | 0.876044i | \(-0.339827\pi\) | ||||
0.482231 | + | 0.876044i | \(0.339827\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.12195e9 | −0.949197 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.98370e8 | −0.580379 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.10899e8 | −0.172181 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.33522e8 | −0.508153 | −0.254077 | − | 0.967184i | \(-0.581772\pi\) | ||||
−0.254077 | + | 0.967184i | \(0.581772\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.65544e8 | −0.288094 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.45494e9 | −1.12679 | −0.563393 | − | 0.826189i | \(-0.690504\pi\) | ||||
−0.563393 | + | 0.826189i | \(0.690504\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.23287e9 | −0.938319 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.45697e7 | −0.0258585 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.77754e8 | 0.645346 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.51094e9 | 1.09198 | 0.545990 | − | 0.837792i | \(-0.316154\pi\) | ||||
0.545990 | + | 0.837792i | \(0.316154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.02115e8 | 0.427793 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.31276e8 | 0.231401 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.82003e8 | 0.125000 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.56949e8 | −0.443665 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.43994e8 | 0.361281 | 0.180641 | − | 0.983549i | \(-0.442183\pi\) | ||||
0.180641 | + | 0.983549i | \(0.442183\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.01260e9 | 1.96768 | 0.983839 | − | 0.179055i | \(-0.0573039\pi\) | ||||
0.983839 | + | 0.179055i | \(0.0573039\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.42763e8 | 0.412914 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.50324e9 | 0.949879 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.99149e8 | 0.123789 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.41897e8 | 0.453673 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.03054e9 | 1.22164 | 0.610818 | − | 0.791771i | \(-0.290841\pi\) | ||||
0.610818 | + | 0.791771i | \(0.290841\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.89154e9 | 1.71168 | 0.855838 | − | 0.517244i | \(-0.173042\pi\) | ||||
0.855838 | + | 0.517244i | \(0.173042\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.32880e8 | 0.135650 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.71274e9 | 1.55498 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.66416e9 | 1.50291 | 0.751457 | − | 0.659782i | \(-0.229352\pi\) | ||||
0.751457 | + | 0.659782i | \(0.229352\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.45134e8 | −0.302669 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 875964. | 0.000478711 0 | 0.000239356 | − | 1.00000i | \(-0.499924\pi\) | ||||
0.000239356 | 1.00000i | \(0.499924\pi\) | ||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00333e8 | 0.0539739 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.98061e9 | 1.04887 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.61727e9 | −1.36454 | −0.682271 | − | 0.731099i | \(-0.739008\pi\) | ||||
−0.682271 | + | 0.731099i | \(0.739008\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.28020e9 | −1.17045 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.12409e9 | 0.568145 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.87511e7 | −0.0441707 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.90146e9 | 1.42203 | 0.711016 | − | 0.703176i | \(-0.248235\pi\) | ||||
0.711016 | + | 0.703176i | \(0.248235\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.00418e8 | 0.193272 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.10787e9 | −1.00205 | −0.501027 | − | 0.865432i | \(-0.667044\pi\) | ||||
−0.501027 | + | 0.865432i | \(0.667044\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.78584e9 | −0.836200 | −0.418100 | − | 0.908401i | \(-0.637304\pi\) | ||||
−0.418100 | + | 0.908401i | \(0.637304\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.36826e8 | −0.201476 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.88405e9 | −0.856021 | −0.428011 | − | 0.903774i | \(-0.640785\pi\) | ||||
−0.428011 | + | 0.903774i | \(0.640785\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.17969e8 | 0.187085 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.01590e9 | 0.448000 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.18275e8 | 0.398987 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.63466e9 | −1.55609 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.79336e8 | 0.328784 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.53861e8 | 0.396562 | 0.198281 | − | 0.980145i | \(-0.436464\pi\) | ||||
0.198281 | + | 0.980145i | \(0.436464\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.84910e8 | −0.321597 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.09860e8 | −0.165509 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.57421e8 | 0.261666 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.59346e9 | −1.01748 | −0.508742 | − | 0.860919i | \(-0.669889\pi\) | ||||
−0.508742 | + | 0.860919i | \(0.669889\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.05558e9 | 0.408234 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.95226e9 | 1.12556 | 0.562780 | − | 0.826606i | \(-0.309732\pi\) | ||||
0.562780 | + | 0.826606i | \(0.309732\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.69743e9 | −1.01388 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.62866e8 | 0.0974129 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.44473e8 | −0.0527886 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.13817e8 | −0.149093 | −0.0745463 | − | 0.997218i | \(-0.523751\pi\) | ||||
−0.0745463 | + | 0.997218i | \(0.523751\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.26276e9 | 0.803907 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.99193e9 | −1.39860 | −0.699302 | − | 0.714827i | \(-0.746506\pi\) | ||||
−0.699302 | + | 0.714827i | \(0.746506\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.02966e8 | 0.208340 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.03079e9 | 0.351270 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.11683e9 | 1.04761 | 0.523807 | − | 0.851837i | \(-0.324511\pi\) | ||||
0.523807 | + | 0.851837i | \(0.324511\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.49452e8 | −0.0495482 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.68161e8 | −0.316619 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.35706e8 | 0.140562 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.88753e9 | −1.55551 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.56491e9 | 0.805354 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.65025e8 | 0.144060 | 0.0720301 | − | 0.997402i | \(-0.477052\pi\) | ||||
0.0720301 | + | 0.997402i | \(0.477052\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.35138e9 | −0.413070 | −0.206535 | − | 0.978439i | \(-0.566219\pi\) | ||||
−0.206535 | + | 0.978439i | \(0.566219\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.49149e8 | 0.165628 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.05972e9 | 1.50588 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.63206e8 | −0.106674 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.77400e8 | 0.254312 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.03901e9 | 0.583276 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.94448e8 | −0.280766 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.07546e8 | 0.197172 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.14517e9 | 1.14020 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.89823e9 | 0.786941 | 0.393470 | − | 0.919337i | \(-0.371274\pi\) | ||||
0.393470 | + | 0.919337i | \(0.371274\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.17614e9 | 0.315252 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.51325e9 | 0.400425 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.18287e9 | −0.570259 | −0.285129 | − | 0.958489i | \(-0.592037\pi\) | ||||
−0.285129 | + | 0.958489i | \(0.592037\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.27456e8 | 0.136045 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.52205e9 | 1.66094 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.92387e8 | 0.224396 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.78106e8 | −0.0690535 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.04284e8 | −0.221723 | −0.110862 | − | 0.993836i | \(-0.535361\pi\) | ||||
−0.110862 | + | 0.993836i | \(0.535361\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.21145e8 | −0.198828 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.04476e9 | −0.728086 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.09873e9 | −0.731820 | −0.365910 | − | 0.930650i | \(-0.619242\pi\) | ||||
−0.365910 | + | 0.930650i | \(0.619242\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.73501e8 | 0.133772 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.46277e8 | 0.0337003 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.33477e9 | −0.758880 | −0.379440 | − | 0.925216i | \(-0.623883\pi\) | ||||
−0.379440 | + | 0.925216i | \(0.623883\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.76279e9 | −0.396255 | −0.198128 | − | 0.980176i | \(-0.563486\pi\) | ||||
−0.198128 | + | 0.980176i | \(0.563486\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.13955e9 | −0.697149 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.07530e9 | −0.893968 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.31922e9 | 0.936030 | 0.468015 | − | 0.883720i | \(-0.344969\pi\) | ||||
0.468015 | + | 0.883720i | \(0.344969\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.95878e9 | 0.633486 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.70120e8 | −0.162908 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.92603e9 | −1.23858 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.35062e8 | −0.0485441 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.62609e9 | −0.739955 | −0.369978 | − | 0.929041i | \(-0.620635\pi\) | ||||
−0.369978 | + | 0.929041i | \(0.620635\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.22338e10 | −2.46693 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.17230e9 | −0.831418 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.25587e9 | −1.23196 | −0.615980 | − | 0.787762i | \(-0.711240\pi\) | ||||
−0.615980 | + | 0.787762i | \(0.711240\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.64236e8 | 0.0708881 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.16457e9 | 0.608701 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.87712e8 | −0.0356860 | −0.0178430 | − | 0.999841i | \(-0.505680\pi\) | ||||
−0.0178430 | + | 0.999841i | \(0.505680\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.67744e9 | 1.63054 | 0.815269 | − | 0.579082i | \(-0.196589\pi\) | ||||
0.815269 | + | 0.579082i | \(0.196589\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.10701e9 | 0.205609 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.31198e8 | −0.134243 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.47758e9 | −1.72003 | −0.860017 | − | 0.510265i | \(-0.829547\pi\) | ||||
−0.860017 | + | 0.510265i | \(0.829547\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.85397e8 | −0.176787 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.37056e9 | 0.775162 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.39813e9 | −1.64790 | −0.823948 | − | 0.566665i | \(-0.808233\pi\) | ||||
−0.823948 | + | 0.566665i | \(0.808233\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.22454e8 | 0.125241 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.02430e8 | 0.154673 | 0.0773367 | − | 0.997005i | \(-0.475358\pi\) | ||||
0.0773367 | + | 0.997005i | \(0.475358\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.94894e9 | −1.68601 | −0.843004 | − | 0.537908i | \(-0.819215\pi\) | ||||
−0.843004 | + | 0.537908i | \(0.819215\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.08553e9 | −0.181896 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.24544e8 | −0.0703419 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.12969e9 | 0.840449 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.36184e9 | 1.19275 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.22128e9 | 0.516121 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.16471e8 | −0.0818358 | −0.0409179 | − | 0.999163i | \(-0.513028\pi\) | ||||
−0.0409179 | + | 0.999163i | \(0.513028\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.33038e9 | −0.992011 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.00467e9 | 0.155709 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.70672e9 | −0.568200 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.82644e8 | −0.0580152 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.32326e9 | −0.948283 | −0.474141 | − | 0.880449i | \(-0.657241\pi\) | ||||
−0.474141 | + | 0.880449i | \(0.657241\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.34254e9 | 0.199153 | 0.0995766 | − | 0.995030i | \(-0.468251\pi\) | ||||
0.0995766 | + | 0.995030i | \(0.468251\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.90945e8 | −0.0426925 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.15547e9 | −0.893504 | −0.446752 | − | 0.894658i | \(-0.647419\pi\) | ||||
−0.446752 | + | 0.894658i | \(0.647419\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.67170e9 | −0.958032 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.84836e9 | 0.262575 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.94403e9 | 1.39755 | 0.698773 | − | 0.715343i | \(-0.253730\pi\) | ||||
0.698773 | + | 0.715343i | \(0.253730\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.68253e9 | −0.233947 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.95830e8 | −0.0544540 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.58150e9 | 0.759718 | 0.379859 | − | 0.925044i | \(-0.375973\pi\) | ||||
0.379859 | + | 0.925044i | \(0.375973\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.82898e9 | −0.650354 | −0.325177 | − | 0.945653i | \(-0.605424\pi\) | ||||
−0.325177 | + | 0.945653i | \(0.605424\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.72270e9 | 0.362830 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.80677e8 | −0.116129 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.31275e9 | 0.954201 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.38734e9 | 0.824762 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.01075e9 | −0.512503 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.20000e9 | −0.404666 | −0.202333 | − | 0.979317i | \(-0.564852\pi\) | ||||
−0.202333 | + | 0.979317i | \(0.564852\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.45445e9 | 0.182027 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.97836e9 | −0.616632 | −0.308316 | − | 0.951284i | \(-0.599765\pi\) | ||||
−0.308316 | + | 0.951284i | \(0.599765\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.78178e9 | −0.341018 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.94112e9 | −0.720865 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.56314e10 | 1.87726 | 0.938630 | − | 0.344926i | \(-0.112096\pi\) | ||||
0.938630 | + | 0.344926i | \(0.112096\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.45063e9 | 0.172441 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.50800e9 | 0.883437 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.29921e9 | 0.617225 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.62162e8 | 0.0878768 | 0.0439384 | − | 0.999034i | \(-0.486009\pi\) | ||||
0.0439384 | + | 0.999034i | \(0.486009\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.11228e9 | −0.126954 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.58274e9 | −0.178839 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.36813e9 | −0.936081 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.67678e9 | −0.185697 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.20366e10 | −1.31974 | −0.659872 | − | 0.751378i | \(-0.729390\pi\) | ||||
−0.659872 | + | 0.751378i | \(0.729390\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.78866e9 | −0.845510 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.54856e9 | 0.166443 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.55136e9 | −0.271521 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.95168e9 | −0.311034 | −0.155517 | − | 0.987833i | \(-0.549704\pi\) | ||||
−0.155517 | + | 0.987833i | \(0.549704\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.36353e9 | 0.246614 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.37169e10 | −1.41724 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.78740e9 | 0.182873 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.43852e9 | 0.956283 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.15653e10 | 1.16040 | 0.580198 | − | 0.814476i | \(-0.302975\pi\) | ||||
0.580198 | + | 0.814476i | \(0.302975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.84362e9 | −0.183189 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.28801e9 | −0.225151 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.79795e9 | −0.954887 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.35771e10 | −1.31050 | −0.655249 | − | 0.755413i | \(-0.727436\pi\) | ||||
−0.655249 | + | 0.755413i | \(0.727436\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.36999e9 | 0.319093 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.68831e9 | −0.721053 | −0.360527 | − | 0.932749i | \(-0.617403\pi\) | ||||
−0.360527 | + | 0.932749i | \(0.617403\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.31335e9 | −0.122004 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.41764e9 | −0.774559 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.20836e9 | 0.565876 | 0.282938 | − | 0.959138i | \(-0.408691\pi\) | ||||
0.282938 | + | 0.959138i | \(0.408691\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.58315e9 | −0.594388 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.70406e9 | −0.420738 | −0.210369 | − | 0.977622i | \(-0.567467\pi\) | ||||
−0.210369 | + | 0.977622i | \(0.567467\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.77172e9 | 0.422793 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.03970e9 | −0.179038 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.20786e9 | 0.365910 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.36220e10 | −1.17355 | −0.586774 | − | 0.809750i | \(-0.699602\pi\) | ||||
−0.586774 | + | 0.809750i | \(0.699602\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.43630e9 | −0.122592 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.70819e9 | 0.229016 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.49409e9 | −0.544105 | −0.272052 | − | 0.962282i | \(-0.587702\pi\) | ||||
−0.272052 | + | 0.962282i | \(0.587702\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.25434e9 | 0.685230 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.76658e10 | −1.45307 | −0.726537 | − | 0.687128i | \(-0.758871\pi\) | ||||
−0.726537 | + | 0.687128i | \(0.758871\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.40307e9 | −0.521858 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.64697e8 | 0.0779069 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.96601e9 | 0.477420 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.98045e10 | 1.57044 | 0.785219 | − | 0.619218i | \(-0.212550\pi\) | ||||
0.785219 | + | 0.619218i | \(0.212550\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.16506e10 | 0.915500 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.80123e8 | 0.0218132 | 0.0109066 | − | 0.999941i | \(-0.496528\pi\) | ||||
0.0109066 | + | 0.999941i | \(0.496528\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.83786e10 | 1.41826 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.17676e9 | 0.0899945 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.02331e10 | 1.53349 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.90960e9 | 0.218552 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.60987e9 | −0.194291 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.44753e9 | 0.180586 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.73837e9 | −0.492769 | −0.246384 | − | 0.969172i | \(-0.579243\pi\) | ||||
−0.246384 | + | 0.969172i | \(0.579243\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.51969e9 | 0.110150 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.42668e9 | −0.174339 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.58652e9 | 0.255398 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.87759e9 | 0.132531 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.01524e10 | 0.710339 | 0.355169 | − | 0.934802i | \(-0.384423\pi\) | ||||
0.355169 | + | 0.934802i | \(0.384423\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.79368e10 | −1.24403 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.12442e9 | −0.0773066 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.00987e9 | 0.205137 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.87445e8 | −0.0667156 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.24919e9 | 0.284609 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.39524e10 | −0.926462 | −0.463231 | − | 0.886237i | \(-0.653310\pi\) | ||||
−0.463231 | + | 0.886237i | \(0.653310\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.65022e10 | −1.74466 | −0.872328 | − | 0.488921i | \(-0.837390\pi\) | ||||
−0.872328 | + | 0.488921i | \(0.837390\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.07053e8 | −0.0461461 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.54312e9 | 0.164557 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.14821e9 | −0.522739 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.94628e8 | 0.0632655 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.48371e9 | −0.282772 | −0.141386 | − | 0.989955i | \(-0.545156\pi\) | ||||
−0.141386 | + | 0.989955i | \(0.545156\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.00006e8 | −0.00625354 | −0.00312677 | − | 0.999995i | \(-0.500995\pi\) | ||||
−0.00312677 | + | 0.999995i | \(0.500995\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.10595e10 | −0.685722 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.16338e8 | 0.0563361 | 0.0281680 | − | 0.999603i | \(-0.491033\pi\) | ||||
0.0281680 | + | 0.999603i | \(0.491033\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.85040e8 | −0.0234728 | −0.0117364 | − | 0.999931i | \(-0.503736\pi\) | ||||
−0.0117364 | + | 0.999931i | \(0.503736\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.53727e10 | −0.929278 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.52124e10 | 0.911886 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.45148e9 | 0.324050 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.89548e9 | 0.288574 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.54534e10 | −0.903350 | −0.451675 | − | 0.892183i | \(-0.649173\pi\) | ||||
−0.451675 | + | 0.892183i | \(0.649173\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.31631e8 | 0.0192251 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.69601e9 | 0.0975058 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.48339e9 | 0.141595 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.09395e9 | 0.174953 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.29514e8 | 0.0240880 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.73291e9 | −0.485742 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.52946e10 | −0.843753 | −0.421876 | − | 0.906653i | \(-0.638628\pi\) | ||||
−0.421876 | + | 0.906653i | \(0.638628\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.33252e9 | −0.127627 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.34165e9 | 0.127084 | 0.0635419 | − | 0.997979i | \(-0.479760\pi\) | ||||
0.0635419 | + | 0.997979i | \(0.479760\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.11238e9 | −0.113709 | −0.0568546 | − | 0.998382i | \(-0.518107\pi\) | ||||
−0.0568546 | + | 0.998382i | \(0.518107\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.05696e9 | −0.163222 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.54620e10 | 1.87813 | 0.939065 | − | 0.343740i | \(-0.111694\pi\) | ||||
0.939065 | + | 0.343740i | \(0.111694\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.17944e9 | 0.324633 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.48588e7 | −0.00494323 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.79722e10 | −0.929033 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.52728e9 | 0.385988 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.36767e9 | −0.374783 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.72181e9 | 0.137350 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.20646e10 | 1.10458 | 0.552289 | − | 0.833652i | \(-0.313754\pi\) | ||||
0.552289 | + | 0.833652i | \(0.313754\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.00532e9 | 0.397574 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.74750e10 | 1.35370 | 0.676850 | − | 0.736121i | \(-0.263345\pi\) | ||||
0.676850 | + | 0.736121i | \(0.263345\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.14560e9 | 0.104878 | 0.0524392 | − | 0.998624i | \(-0.483300\pi\) | ||||
0.0524392 | + | 0.998624i | \(0.483300\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.11385e9 | 0.102512 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.01285e10 | −0.487317 | −0.243658 | − | 0.969861i | \(-0.578348\pi\) | ||||
−0.243658 | + | 0.969861i | \(0.578348\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.25110e9 | −0.202929 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.94592e9 | −0.139524 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.33690e10 | 2.03798 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.70464e9 | 0.0794787 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.38125e9 | −0.341473 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.29786e10 | −1.51382 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.17480e10 | −0.990565 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.23109e9 | 0.0556394 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.83357e9 | 0.127076 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.37970e10 | 1.50402 | 0.752008 | − | 0.659154i | \(-0.229086\pi\) | ||||
0.752008 | + | 0.659154i | \(0.229086\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.75740e9 | −0.298405 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.02764e10 | 0.450325 | 0.225163 | − | 0.974321i | \(-0.427709\pi\) | ||||
0.225163 | + | 0.974321i | \(0.427709\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.55098e10 | 0.674462 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.27076e9 | 0.0548390 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.11937e9 | 0.304894 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.82318e10 | −1.19987 | −0.599935 | − | 0.800049i | \(-0.704807\pi\) | ||||
−0.599935 | + | 0.800049i | \(0.704807\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.20008e10 | 0.506175 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.60184e9 | −0.108912 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.17007e10 | 0.486091 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.88293e9 | −0.201327 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.51907e10 | 0.621617 | 0.310808 | − | 0.950473i | \(-0.399400\pi\) | ||||
0.310808 | + | 0.950473i | \(0.399400\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.67817e10 | −1.49385 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.49619e9 | 0.261862 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.33550e9 | −0.293487 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.14565e9 | −0.363183 | −0.181592 | − | 0.983374i | \(-0.558125\pi\) | ||||
−0.181592 | + | 0.983374i | \(0.558125\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.63357e10 | −1.03804 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.70181e9 | −0.183951 | −0.0919754 | − | 0.995761i | \(-0.529318\pi\) | ||||
−0.0919754 | + | 0.995761i | \(0.529318\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.26860e10 | 0.880983 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.52413e8 | 0.0135844 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.28407e10 | −1.63920 | −0.819600 | − | 0.572936i | \(-0.805804\pi\) | ||||
−0.819600 | + | 0.572936i | \(0.805804\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.69150e9 | −0.102226 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.14396e9 | 0.193939 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.14045e10 | 1.54961 | 0.774804 | − | 0.632201i | \(-0.217848\pi\) | ||||
0.774804 | + | 0.632201i | \(0.217848\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.56387e9 | −0.281017 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.98453e10 | 0.731925 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.13812e9 | −0.224735 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.43472e10 | 1.24842 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.11447e10 | 0.402140 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.12835e9 | 0.255354 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.22566e10 | 1.50280 | 0.751402 | − | 0.659845i | \(-0.229378\pi\) | ||||
0.751402 | + | 0.659845i | \(0.229378\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.70173e10 | 0.953914 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.50043e10 | −0.876491 | −0.438245 | − | 0.898855i | \(-0.644400\pi\) | ||||
−0.438245 | + | 0.898855i | \(0.644400\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.69711e9 | 0.233073 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.88973e9 | 0.341718 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.67463e10 | 0.574498 | 0.287249 | − | 0.957856i | \(-0.407259\pi\) | ||||
0.287249 | + | 0.957856i | \(0.407259\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.55006e9 | 0.291226 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.69588e10 | −0.573528 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.79707e9 | −0.127500 | −0.0637502 | − | 0.997966i | \(-0.520306\pi\) | ||||
−0.0637502 | + | 0.997966i | \(0.520306\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.00520e10 | −0.335139 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.55249e9 | −0.216918 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.13605e9 | −0.300311 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.52745e9 | −0.245692 | −0.122846 | − | 0.992426i | \(-0.539202\pi\) | ||||
−0.122846 | + | 0.992426i | \(0.539202\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.66934e10 | 0.541030 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.62415e9 | 0.245364 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.29435e9 | 0.0413637 | 0.0206819 | − | 0.999786i | \(-0.493416\pi\) | ||||
0.0206819 | + | 0.999786i | \(0.493416\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.11672e9 | 0.0989051 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 384.8.a.f.1.1 | yes | 2 | |
4.3 | odd | 2 | 384.8.a.h.1.1 | yes | 2 | ||
8.3 | odd | 2 | 384.8.a.e.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 384.8.a.g.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.a.e.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
384.8.a.f.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
384.8.a.g.1.2 | yes | 2 | 8.5 | even | 2 | ||
384.8.a.h.1.1 | yes | 2 | 4.3 | odd | 2 |