Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [32,8,Mod(1,32)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("32.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.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: | \(9.99632081549\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{10}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.16228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 32.1 |
$q$-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 | ||||||||
\(3\) | −58.5964 | −1.25299 | −0.626494 | − | 0.779426i | \(-0.715511\pi\) | ||||
−0.626494 | + | 0.779426i | \(0.715511\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −494.772 | −1.77015 | −0.885074 | − | 0.465450i | \(-0.845893\pi\) | ||||
−0.885074 | + | 0.465450i | \(0.845893\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1332.35 | 1.46817 | 0.734083 | − | 0.679060i | \(-0.237612\pi\) | ||||
0.734083 | + | 0.679060i | \(0.237612\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1246.54 | 0.569979 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 725.267 | 0.164295 | 0.0821473 | − | 0.996620i | \(-0.473822\pi\) | ||||
0.0821473 | + | 0.996620i | \(0.473822\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4821.57 | 0.608677 | 0.304339 | − | 0.952564i | \(-0.401565\pi\) | ||||
0.304339 | + | 0.952564i | \(0.401565\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 28991.9 | 2.21797 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3533.15 | −0.174418 | −0.0872088 | − | 0.996190i | \(-0.527795\pi\) | ||||
−0.0872088 | + | 0.996190i | \(0.527795\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 44922.4 | 1.50254 | 0.751270 | − | 0.659995i | \(-0.229442\pi\) | ||||
0.751270 | + | 0.659995i | \(0.229442\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −78071.0 | −1.83959 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −56324.6 | −0.965274 | −0.482637 | − | 0.875821i | \(-0.660321\pi\) | ||||
−0.482637 | + | 0.875821i | \(0.660321\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 166674. | 2.13343 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 55107.4 | 0.538812 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −11201.8 | −0.0852896 | −0.0426448 | − | 0.999090i | \(-0.513578\pi\) | ||||
−0.0426448 | + | 0.999090i | \(0.513578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −14447.8 | −0.0871037 | −0.0435518 | − | 0.999051i | \(-0.513867\pi\) | ||||
−0.0435518 | + | 0.999051i | \(0.513867\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −42498.1 | −0.205859 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −659209. | −2.59887 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −380730. | −1.23569 | −0.617847 | − | 0.786298i | \(-0.711995\pi\) | ||||
−0.617847 | + | 0.786298i | \(0.711995\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −282527. | −0.762665 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 449262. | 1.01802 | 0.509009 | − | 0.860761i | \(-0.330012\pi\) | ||||
0.509009 | + | 0.860761i | \(0.330012\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 331342. | 0.635531 | 0.317765 | − | 0.948169i | \(-0.397068\pi\) | ||||
0.317765 | + | 0.948169i | \(0.397068\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −616754. | −1.00895 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 562571. | 0.790377 | 0.395189 | − | 0.918600i | \(-0.370679\pi\) | ||||
0.395189 | + | 0.918600i | \(0.370679\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 951614. | 1.15551 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 207030. | 0.218543 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.58053e6 | 1.45826 | 0.729132 | − | 0.684374i | \(-0.239924\pi\) | ||||
0.729132 | + | 0.684374i | \(0.239924\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −358841. | −0.290826 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.63230e6 | −1.88266 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.72292e6 | 1.72605 | 0.863023 | − | 0.505164i | \(-0.168568\pi\) | ||||
0.863023 | + | 0.505164i | \(0.168568\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −556745. | −0.314052 | −0.157026 | − | 0.987594i | \(-0.550191\pi\) | ||||
−0.157026 | + | 0.987594i | \(0.550191\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.66083e6 | 0.836823 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.38558e6 | −1.07745 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.11092e6 | 0.451252 | 0.225626 | − | 0.974214i | \(-0.427557\pi\) | ||||
0.225626 | + | 0.974214i | \(0.427557\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.30042e6 | 1.20948 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −299313. | −0.0992478 | −0.0496239 | − | 0.998768i | \(-0.515802\pi\) | ||||
−0.0496239 | + | 0.998768i | \(0.515802\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.93379e6 | 1.18354 | 0.591768 | − | 0.806108i | \(-0.298430\pi\) | ||||
0.591768 | + | 0.806108i | \(0.298430\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.76650e6 | −2.67316 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 966309. | 0.241212 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.15331e6 | −0.263178 | −0.131589 | − | 0.991304i | \(-0.542008\pi\) | ||||
−0.131589 | + | 0.991304i | \(0.542008\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.95529e6 | −1.24510 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.33540e6 | −0.256353 | −0.128177 | − | 0.991751i | \(-0.540912\pi\) | ||||
−0.128177 | + | 0.991751i | \(0.540912\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.74810e6 | 0.308745 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 656387. | 0.106867 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.58276e6 | −0.237985 | −0.118992 | − | 0.992895i | \(-0.537966\pi\) | ||||
−0.118992 | + | 0.992895i | \(0.537966\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.42402e6 | 0.893639 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 846591. | 0.109140 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.22263e7 | −2.65972 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.11303e7 | −1.23825 | −0.619123 | − | 0.785294i | \(-0.712512\pi\) | ||||
−0.619123 | + | 0.785294i | \(0.712512\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 904076. | 0.0936444 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.23576e6 | −0.505656 | −0.252828 | − | 0.967511i | \(-0.581361\pi\) | ||||
−0.252828 | + | 0.967511i | \(0.581361\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.86835e7 | 1.68472 | 0.842362 | − | 0.538912i | \(-0.181164\pi\) | ||||
0.842362 | + | 0.538912i | \(0.181164\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.86273e7 | 3.25636 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.09418e6 | 0.165261 | 0.0826306 | − | 0.996580i | \(-0.473668\pi\) | ||||
0.0826306 | + | 0.996580i | \(0.473668\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.79197e7 | −1.32537 | −0.662686 | − | 0.748897i | \(-0.730584\pi\) | ||||
−0.662686 | + | 0.748897i | \(0.730584\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.23094e7 | 1.54831 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.22948e7 | 0.801580 | 0.400790 | − | 0.916170i | \(-0.368736\pi\) | ||||
0.400790 | + | 0.916170i | \(0.368736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.78678e7 | 1.70868 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.01030e6 | 0.346933 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.70739e6 | −0.256074 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.89612e7 | −0.973007 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.63251e7 | −1.27557 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.38115e7 | −2.00633 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.55866e7 | 0.675208 | 0.337604 | − | 0.941288i | \(-0.390384\pi\) | ||||
0.337604 | + | 0.941288i | \(0.390384\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.94154e7 | −0.796312 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.26851e7 | −0.881638 | −0.440819 | − | 0.897596i | \(-0.645312\pi\) | ||||
−0.440819 | + | 0.897596i | \(0.645312\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.98524e7 | 2.20598 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.72656e7 | −0.953777 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.82819e7 | 1.27195 | 0.635977 | − | 0.771708i | \(-0.280597\pi\) | ||||
0.635977 | + | 0.771708i | \(0.280597\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.36838e7 | 1.06382 | 0.531911 | − | 0.846800i | \(-0.321474\pi\) | ||||
0.531911 | + | 0.846800i | \(0.321474\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.29646e7 | −0.990333 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.49693e6 | 0.100002 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.54234e6 | 0.150975 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.57612e7 | −1.44784 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.81432e7 | 0.449327 | 0.224663 | − | 0.974436i | \(-0.427872\pi\) | ||||
0.224663 | + | 0.974436i | \(0.427872\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.63250e7 | −1.33132 | −0.665659 | − | 0.746256i | \(-0.731849\pi\) | ||||
−0.665659 | + | 0.746256i | \(0.731849\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.40422e6 | −0.0994143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.14837e6 | 0.154186 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.45391e7 | 0.299839 | 0.149920 | − | 0.988698i | \(-0.452099\pi\) | ||||
0.149920 | + | 0.988698i | \(0.452099\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.26132e7 | −1.82719 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.50440e7 | −1.41718 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.20141e7 | 0.579008 | 0.289504 | − | 0.957177i | \(-0.406510\pi\) | ||||
0.289504 | + | 0.957177i | \(0.406510\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.10268e7 | 0.364401 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.97668e7 | 0.826860 | 0.413430 | − | 0.910536i | \(-0.364331\pi\) | ||||
0.413430 | + | 0.910536i | \(0.364331\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.95009e7 | −0.629512 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.59978e7 | 0.856415 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.05260e7 | 0.888752 | 0.444376 | − | 0.895840i | \(-0.353425\pi\) | ||||
0.444376 | + | 0.895840i | \(0.353425\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.22068e8 | 3.13222 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.59553e8 | −2.16272 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.70858e7 | −1.26523 | −0.632616 | − | 0.774466i | \(-0.718019\pi\) | ||||
−0.632616 | + | 0.774466i | \(0.718019\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.98470e7 | 0.624833 | 0.312417 | − | 0.949945i | \(-0.398862\pi\) | ||||
0.312417 | + | 0.949945i | \(0.398862\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.26233e7 | 0.393503 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.88374e8 | 2.18736 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.56247e6 | −0.0286559 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.34224e7 | 0.791065 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.03610e8 | −1.07594 | −0.537968 | − | 0.842965i | \(-0.680808\pi\) | ||||
−0.537968 | + | 0.842965i | \(0.680808\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.55867e7 | 0.756824 | 0.378412 | − | 0.925637i | \(-0.376470\pi\) | ||||
0.378412 | + | 0.925637i | \(0.376470\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.39786e8 | 1.35003 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.25368e8 | −1.16830 | −0.584150 | − | 0.811646i | \(-0.698572\pi\) | ||||
−0.584150 | + | 0.811646i | \(0.698572\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.05037e7 | 0.814105 | 0.407052 | − | 0.913405i | \(-0.366557\pi\) | ||||
0.407052 | + | 0.913405i | \(0.366557\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.50957e7 | −0.565414 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.49248e7 | −0.125219 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.22282e8 | −1.80204 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.02110e7 | −0.550185 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.25808e7 | 0.246859 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.60759e8 | 1.17811 | 0.589056 | − | 0.808092i | \(-0.299500\pi\) | ||||
0.589056 | + | 0.808092i | \(0.299500\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.75387e7 | 0.124356 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.63938e8 | −1.12498 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.92496e7 | −0.127883 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.30506e8 | −1.48296 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.70353e7 | −0.106164 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.59627e8 | −0.963915 | −0.481958 | − | 0.876195i | \(-0.660074\pi\) | ||||
−0.481958 | + | 0.876195i | \(0.660074\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.07766e8 | 1.21601 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.42550e8 | −0.808866 | −0.404433 | − | 0.914568i | \(-0.632531\pi\) | ||||
−0.404433 | + | 0.914568i | \(0.632531\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.20136e8 | 0.661070 | 0.330535 | − | 0.943794i | \(-0.392771\pi\) | ||||
0.330535 | + | 0.943794i | \(0.392771\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.66223e7 | −0.302236 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.21419e8 | −0.628841 | −0.314420 | − | 0.949284i | \(-0.601810\pi\) | ||||
−0.314420 | + | 0.949284i | \(0.601810\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.78344e8 | −1.39909 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.75797e7 | 0.329759 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.73882e7 | 0.366676 | 0.183338 | − | 0.983050i | \(-0.441310\pi\) | ||||
0.183338 | + | 0.983050i | \(0.441310\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.93813e8 | 1.35211 | 0.676054 | − | 0.736852i | \(-0.263689\pi\) | ||||
0.676054 | + | 0.736852i | \(0.263689\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.28439e8 | 1.02129 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.70832e8 | −2.04543 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.16597e8 | 0.914561 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.82498e7 | 0.321207 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.76211e8 | 1.50167 | 0.750834 | − | 0.660491i | \(-0.229652\pi\) | ||||
0.750834 | + | 0.660491i | \(0.229652\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.08503e7 | −0.158589 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.02432e8 | −0.386854 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.31425e8 | 1.21792 | 0.608961 | − | 0.793200i | \(-0.291586\pi\) | ||||
0.608961 | + | 0.793200i | \(0.291586\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.07266e8 | −1.81420 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.39636e7 | −0.0486132 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.14878e8 | 1.74526 | 0.872628 | − | 0.488386i | \(-0.162414\pi\) | ||||
0.872628 | + | 0.488386i | \(0.162414\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.81999e8 | −2.58134 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.27440e7 | 0.298192 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.86030e7 | −0.0582708 | −0.0291354 | − | 0.999575i | \(-0.509275\pi\) | ||||
−0.0291354 | + | 0.999575i | \(0.509275\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.04683e7 | −0.245602 | −0.122801 | − | 0.992431i | \(-0.539188\pi\) | ||||
−0.122801 | + | 0.992431i | \(0.539188\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.76425e8 | −1.11972 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.20883e8 | 0.350510 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.67049e8 | 1.03764 | 0.518818 | − | 0.854885i | \(-0.326372\pi\) | ||||
0.518818 | + | 0.854885i | \(0.326372\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.80098e7 | −0.0496472 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.45888e8 | 0.929958 | 0.464979 | − | 0.885322i | \(-0.346062\pi\) | ||||
0.464979 | + | 0.885322i | \(0.346062\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.91779e8 | 1.81432 | 0.907162 | − | 0.420781i | \(-0.138244\pi\) | ||||
0.907162 | + | 0.420781i | \(0.138244\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.30238e9 | 3.33259 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.98574e8 | 1.49462 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.97856e8 | −0.969578 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.52198e8 | 1.55151 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.13809e8 | −1.19334 | −0.596671 | − | 0.802486i | \(-0.703510\pi\) | ||||
−0.596671 | + | 0.802486i | \(0.703510\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.34722e9 | −3.05536 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.99676e7 | 0.0885239 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.71573e8 | −0.587540 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.41463e8 | 0.933065 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.06797e8 | 0.633580 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.75461e8 | 0.555919 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.42633e8 | −1.66209 | −0.831044 | − | 0.556207i | \(-0.812256\pi\) | ||||
−0.831044 | + | 0.556207i | \(0.812256\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.09479e9 | −2.11094 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.43692e8 | −1.02492 | −0.512462 | − | 0.858710i | \(-0.671266\pi\) | ||||
−0.512462 | + | 0.858710i | \(0.671266\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.28626e8 | −1.71173 | −0.855866 | − | 0.517198i | \(-0.826975\pi\) | ||||
−0.855866 | + | 0.517198i | \(0.826975\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.21732e8 | −1.48130 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.28050e7 | −0.110735 | −0.0553677 | − | 0.998466i | \(-0.517633\pi\) | ||||
−0.0553677 | + | 0.998466i | \(0.517633\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.12431e6 | −0.0140126 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.22712e8 | −0.207070 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.58718e8 | −0.262069 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.03630e8 | 1.29857 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.05003e9 | 1.66067 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.49541e8 | 1.16041 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.87877e7 | 0.104259 | 0.0521294 | − | 0.998640i | \(-0.483399\pi\) | ||||
0.0521294 | + | 0.998640i | \(0.483399\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.74596e8 | −0.704319 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.49650e8 | −0.798784 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.32867e8 | 1.18542 | 0.592708 | − | 0.805417i | \(-0.298059\pi\) | ||||
0.592708 | + | 0.805417i | \(0.298059\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.20431e8 | −1.00437 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.04785e7 | −0.0143107 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.70635e8 | 0.228318 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.63295e9 | −2.14095 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.00233e8 | 0.514232 | 0.257116 | − | 0.966380i | \(-0.417228\pi\) | ||||
0.257116 | + | 0.966380i | \(0.417228\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.68178e8 | 0.967327 | 0.483663 | − | 0.875254i | \(-0.339306\pi\) | ||||
0.483663 | + | 0.875254i | \(0.339306\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.65705e8 | 0.327962 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.54035e8 | 1.15439 | 0.577195 | − | 0.816606i | \(-0.304147\pi\) | ||||
0.577195 | + | 0.816606i | \(0.304147\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.48091e8 | 0.175683 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.75836e8 | 0.320858 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.08981e9 | −1.24314 | −0.621570 | − | 0.783359i | \(-0.713505\pi\) | ||||
−0.621570 | + | 0.783359i | \(0.713505\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.12415e9 | 1.25762 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.11106e9 | 1.21917 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.94633e9 | −2.09503 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.06975e9 | −1.12967 | −0.564833 | − | 0.825205i | \(-0.691060\pi\) | ||||
−0.564833 | + | 0.825205i | \(0.691060\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.60024e8 | 0.580249 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.10581e9 | 2.14097 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.08817e9 | −1.08572 | −0.542859 | − | 0.839824i | \(-0.682658\pi\) | ||||
−0.542859 | + | 0.839824i | \(0.682658\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.56720e9 | 2.51391 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.40104e7 | −0.0519138 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.02117e9 | −0.963523 | −0.481761 | − | 0.876302i | \(-0.660003\pi\) | ||||
−0.481761 | + | 0.876302i | \(0.660003\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.13318e8 | −0.846027 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.94316e9 | 1.76731 | 0.883657 | − | 0.468135i | \(-0.155074\pi\) | ||||
0.883657 | + | 0.468135i | \(0.155074\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.78102e8 | −0.426981 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.13032e8 | 0.362239 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.68612e7 | −0.0575904 | −0.0287952 | − | 0.999585i | \(-0.509167\pi\) | ||||
−0.0287952 | + | 0.999585i | \(0.509167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.99003e8 | 0.168361 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.32926e9 | 1.10468 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.70623e8 | 0.465865 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.78931e9 | −1.43522 | −0.717612 | − | 0.696443i | \(-0.754765\pi\) | ||||
−0.717612 | + | 0.696443i | \(0.754765\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.50714e9 | −2.76406 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.14443e7 | −0.0398411 | −0.0199206 | − | 0.999802i | \(-0.506341\pi\) | ||||
−0.0199206 | + | 0.999802i | \(0.506341\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.96613e7 | −0.0530180 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.94651e9 | 2.20402 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.76131e8 | −0.203018 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.71845e8 | 0.557826 | 0.278913 | − | 0.960316i | \(-0.410026\pi\) | ||||
0.278913 | + | 0.960316i | \(0.410026\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.24318e9 | −1.59374 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.62788e9 | 2.53412 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.60719e8 | 0.453783 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.97375e9 | −1.33296 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.35613e8 | −0.621366 | −0.310683 | − | 0.950514i | \(-0.600558\pi\) | ||||
−0.310683 | + | 0.950514i | \(0.600558\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.83597e8 | −0.381176 | −0.190588 | − | 0.981670i | \(-0.561039\pi\) | ||||
−0.190588 | + | 0.981670i | \(0.561039\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.01269e8 | 0.450498 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.88883e8 | −0.372107 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.41779e8 | −0.461081 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.04907e8 | −0.125302 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.70017e9 | 1.02287 | 0.511436 | − | 0.859322i | \(-0.329114\pi\) | ||||
0.511436 | + | 0.859322i | \(0.329114\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.79589e9 | −1.65506 | −0.827529 | − | 0.561423i | \(-0.810254\pi\) | ||||
−0.827529 | + | 0.561423i | \(0.810254\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.24762e8 | −0.189170 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.53024e9 | −1.45036 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.80716e9 | −1.01946 | −0.509729 | − | 0.860335i | \(-0.670254\pi\) | ||||
−0.509729 | + | 0.860335i | \(0.670254\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.18623e9 | 0.658617 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.29517e9 | −0.707807 | −0.353904 | − | 0.935282i | \(-0.615146\pi\) | ||||
−0.353904 | + | 0.935282i | \(0.615146\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.83103e8 | 0.421269 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.06313e9 | −0.563001 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.37411e9 | −0.716404 | −0.358202 | − | 0.933644i | \(-0.616610\pi\) | ||||
−0.358202 | + | 0.933644i | \(0.616610\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.25835e8 | 0.167255 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.30044e9 | 1.66813 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.17842e9 | −1.58187 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.53742e9 | 0.753504 | 0.376752 | − | 0.926314i | \(-0.377041\pi\) | ||||
0.376752 | + | 0.926314i | \(0.377041\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.94703e8 | −0.0939783 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.69895e9 | −1.75843 | −0.879214 | − | 0.476427i | \(-0.841932\pi\) | ||||
−0.879214 | + | 0.476427i | \(0.841932\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.76669e9 | 0.827232 | 0.413616 | − | 0.910451i | \(-0.364266\pi\) | ||||
0.413616 | + | 0.910451i | \(0.364266\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.18869e8 | −0.193194 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.53429e9 | −0.697103 | −0.348552 | − | 0.937290i | \(-0.613326\pi\) | ||||
−0.348552 | + | 0.937290i | \(0.613326\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.48013e9 | 0.662514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.51939e8 | −0.375695 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.40311e8 | 0.104414 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.48740e9 | 3.20556 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.97019e9 | 0.831179 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.94277e8 | −0.371790 | −0.185895 | − | 0.982570i | \(-0.559518\pi\) | ||||
−0.185895 | + | 0.982570i | \(0.559518\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.83572e9 | −0.752139 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.39731e9 | 1.77571 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.50697e9 | 2.19188 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.20006e9 | 1.64780 | 0.823899 | − | 0.566736i | \(-0.191794\pi\) | ||||
0.823899 | + | 0.566736i | \(0.191794\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.87591e9 | −0.725490 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.21508e8 | −0.236953 | −0.118476 | − | 0.992957i | \(-0.537801\pi\) | ||||
−0.118476 | + | 0.992957i | \(0.537801\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.95777e7 | 0.0148760 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.47311e8 | −0.165765 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.98789e8 | −0.145712 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.24307e9 | −1.16844 | −0.584218 | − | 0.811597i | \(-0.698599\pi\) | ||||
−0.584218 | + | 0.811597i | \(0.698599\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.91616e9 | −1.03605 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.42333e9 | 1.19939 | 0.599696 | − | 0.800228i | \(-0.295288\pi\) | ||||
0.599696 | + | 0.800228i | \(0.295288\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.59050e9 | 0.895085 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.31462e9 | 0.788771 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.37250e9 | −0.797432 | −0.398716 | − | 0.917074i | \(-0.630544\pi\) | ||||
−0.398716 | + | 0.917074i | \(0.630544\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.24119e9 | 1.73763 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.47556e9 | 0.809586 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.24409e9 | −2.98221 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.08014e8 | 0.129855 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.54661e9 | −1.11360 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.79017e9 | −0.864367 | −0.432184 | − | 0.901786i | \(-0.642257\pi\) | ||||
−0.432184 | + | 0.901786i | \(0.642257\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.40390e8 | 0.165178 | 0.0825889 | − | 0.996584i | \(-0.473681\pi\) | ||||
0.0825889 | + | 0.996584i | \(0.473681\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.30124e10 | −3.92464 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.10463e7 | 0.0151924 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.32368e8 | −0.0682468 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.39423e9 | 0.983809 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.16615e9 | 0.619645 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.03614e9 | −0.292537 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.68888e9 | 1.58532 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.90174e8 | 0.189844 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.31485e9 | 1.17159 | 0.585794 | − | 0.810460i | \(-0.300783\pi\) | ||||
0.585794 | + | 0.810460i | \(0.300783\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.92086e9 | −0.782909 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.86615e9 | 2.34610 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.39068e9 | 1.14703 | 0.573516 | − | 0.819194i | \(-0.305579\pi\) | ||||
0.573516 | + | 0.819194i | \(0.305579\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.94006e8 | −0.179003 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.03213e8 | −0.128151 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.53661e9 | −0.386389 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.10381e10 | −2.74074 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.66990e9 | 0.409446 | 0.204723 | − | 0.978820i | \(-0.434371\pi\) | ||||
0.204723 | + | 0.978820i | \(0.434371\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.59759e9 | 0.386833 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.50152e8 | 0.0359055 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.74928e9 | 1.35780 | 0.678898 | − | 0.734233i | \(-0.262458\pi\) | ||||
0.678898 | + | 0.734233i | \(0.262458\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.08312e9 | −1.41892 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.93453e9 | −1.82802 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.80817e8 | −0.0411478 | −0.0205739 | − | 0.999788i | \(-0.506549\pi\) | ||||
−0.0205739 | + | 0.999788i | \(0.506549\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.36079e9 | −1.65462 | −0.827310 | − | 0.561746i | \(-0.810130\pi\) | ||||
−0.827310 | + | 0.561746i | \(0.810130\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.07120e9 | 1.34814 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.38783e9 | −2.05934 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.18503e9 | −0.906949 | −0.453474 | − | 0.891269i | \(-0.649816\pi\) | ||||
−0.453474 | + | 0.891269i | \(0.649816\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.42911e9 | −0.948291 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.77922e9 | −0.376369 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.14630e9 | 0.239585 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.97372e9 | −0.614123 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.28639e9 | 1.89502 | 0.947510 | − | 0.319727i | \(-0.103591\pi\) | ||||
0.947510 | + | 0.319727i | \(0.103591\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.49032e8 | −0.130877 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.34610e9 | 1.46386 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.05149e9 | −1.78250 | −0.891248 | − | 0.453516i | \(-0.850169\pi\) | ||||
−0.891248 | + | 0.453516i | \(0.850169\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.32908e9 | 0.453289 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.30319e9 | −1.02006 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.58913e9 | 1.06255 | 0.531276 | − | 0.847199i | \(-0.321713\pi\) | ||||
0.531276 | + | 0.847199i | \(0.321713\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.35393e9 | 1.75766 | 0.878828 | − | 0.477140i | \(-0.158326\pi\) | ||||
0.878828 | + | 0.477140i | \(0.158326\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.38481e9 | 0.257204 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.38144e9 | 1.72237 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.26278e9 | −1.13660 | −0.568299 | − | 0.822822i | \(-0.692398\pi\) | ||||
−0.568299 | + | 0.822822i | \(0.692398\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.74538e8 | 0.156898 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.71248e9 | 0.481085 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.08628e9 | −0.365815 | −0.182907 | − | 0.983130i | \(-0.558551\pi\) | ||||
−0.182907 | + | 0.983130i | \(0.558551\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.30249e10 | 2.25794 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.15947e9 | −0.712919 | −0.356459 | − | 0.934311i | \(-0.616016\pi\) | ||||
−0.356459 | + | 0.934311i | \(0.616016\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.59117e9 | 0.608581 | 0.304291 | − | 0.952579i | \(-0.401581\pi\) | ||||
0.304291 | + | 0.952579i | \(0.401581\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.10390e9 | −0.520101 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.10879e9 | −0.349401 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.65527e9 | 1.41808 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.90912e9 | −0.309312 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.34517e9 | 0.215527 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.31712e9 | 0.208700 | 0.104350 | − | 0.994541i | \(-0.466724\pi\) | ||||
0.104350 | + | 0.994541i | \(0.466724\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.41991e9 | −1.47616 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.71179e9 | −1.19522 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.58828e9 | 0.703334 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.73106e8 | −0.0565691 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.66349e8 | −0.0549404 | −0.0274702 | − | 0.999623i | \(-0.508745\pi\) | ||||
−0.0274702 | + | 0.999623i | \(0.508745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.40404e9 | 0.653301 | 0.326650 | − | 0.945145i | \(-0.394080\pi\) | ||||
0.326650 | + | 0.945145i | \(0.394080\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.60621e9 | 1.40959 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.85799e9 | 0.705166 | 0.352583 | − | 0.935781i | \(-0.385303\pi\) | ||||
0.352583 | + | 0.935781i | \(0.385303\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.97484e9 | 0.283580 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.12796e9 | 0.160235 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.96158e9 | 1.40001 | 0.700007 | − | 0.714136i | \(-0.253180\pi\) | ||||
0.700007 | + | 0.714136i | \(0.253180\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.12239e10 | 1.56063 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.90364e9 | 0.674590 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.58699e9 | −0.760464 | −0.380232 | − | 0.924891i | \(-0.624156\pi\) | ||||
−0.380232 | + | 0.924891i | \(0.624156\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.09996e9 | −0.686849 | −0.343425 | − | 0.939180i | \(-0.611587\pi\) | ||||
−0.343425 | + | 0.939180i | \(0.611587\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.98209e8 | 0.133022 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.96133e10 | −3.90491 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.30938e8 | 0.0823278 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.35356e9 | 1.20777 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.03788e8 | −0.0515971 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.00616e10 | −1.27238 | −0.636188 | − | 0.771534i | \(-0.719490\pi\) | ||||
−0.636188 | + | 0.771534i | \(0.719490\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.18497e9 | 1.14951 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.91470e9 | −0.484885 | −0.242442 | − | 0.970166i | \(-0.577949\pi\) | ||||
−0.242442 | + | 0.970166i | \(0.577949\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.48295e10 | −1.81795 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.35292e9 | 1.01350 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.62271e9 | 0.314977 | 0.157488 | − | 0.987521i | \(-0.449660\pi\) | ||||
0.157488 | + | 0.987521i | \(0.449660\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.89408e10 | −2.25155 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.03952e9 | −0.828313 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.62062e9 | 0.887611 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.80668e9 | −1.13070 | −0.565352 | − | 0.824850i | \(-0.691260\pi\) | ||||
−0.565352 | + | 0.824850i | \(0.691260\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.20455e9 | 0.137486 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.66658e10 | −1.88312 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.58731e9 | −0.177560 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.11472e9 | 0.787930 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.29229e9 | 1.01885 | 0.509424 | − | 0.860515i | \(-0.329858\pi\) | ||||
0.509424 | + | 0.860515i | \(0.329858\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.71033e10 | −1.85668 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.63100e10 | 1.75304 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.97586e9 | −0.742386 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.37224e9 | −0.355350 | −0.177675 | − | 0.984089i | \(-0.556858\pi\) | ||||
−0.177675 | + | 0.984089i | \(0.556858\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.43765e9 | −0.150006 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.13768e8 | 0.0840789 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.73018e9 | −0.177019 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.53467e9 | −0.459440 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.58951e10 | 1.59482 | 0.797410 | − | 0.603438i | \(-0.206203\pi\) | ||||
0.797410 | + | 0.603438i | \(0.206203\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.48930e10 | 2.47346 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.72164e10 | −1.69418 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.86705e9 | −0.181959 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.57648e8 | −0.0248689 | −0.0124344 | − | 0.999923i | \(-0.503958\pi\) | ||||
−0.0124344 | + | 0.999923i | \(0.503958\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.61484e8 | −0.0345575 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.17068e9 | −0.110848 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.80778e9 | −0.544686 | −0.272343 | − | 0.962200i | \(-0.587799\pi\) | ||||
−0.272343 | + | 0.962200i | \(0.587799\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.75891e10 | 2.56290 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.05711e8 | 0.0741384 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.85330e9 | 0.624661 | 0.312330 | − | 0.949974i | \(-0.398890\pi\) | ||||
0.312330 | + | 0.949974i | \(0.398890\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.26918e10 | −1.14593 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.61728e9 | 0.144652 | 0.0723261 | − | 0.997381i | \(-0.476958\pi\) | ||||
0.0723261 | + | 0.997381i | \(0.476958\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.97675e9 | −0.795375 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.66464e9 | −0.146116 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.79018e9 | 0.242631 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.22343e10 | −1.05400 | −0.526999 | − | 0.849866i | \(-0.676683\pi\) | ||||
−0.526999 | + | 0.849866i | \(0.676683\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.20446e10 | −1.88157 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.78680e10 | 2.35663 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.82416e9 | 0.320406 | 0.160203 | − | 0.987084i | \(-0.448785\pi\) | ||||
0.160203 | + | 0.987084i | \(0.448785\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.39368e9 | 0.198710 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.74562e9 | 0.801610 | 0.400805 | − | 0.916163i | \(-0.368731\pi\) | ||||
0.400805 | + | 0.916163i | \(0.368731\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.38753e10 | −1.94587 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.17908e9 | 0.175978 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.31287e10 | 1.05061 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.69708e9 | −0.531059 | −0.265530 | − | 0.964103i | \(-0.585547\pi\) | ||||
−0.265530 | + | 0.964103i | \(0.585547\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.94203e10 | −1.52604 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.84770e9 | −0.299621 | −0.149811 | − | 0.988715i | \(-0.547866\pi\) | ||||
−0.149811 | + | 0.988715i | \(0.547866\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.40808e9 | −0.185829 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.97240e10 | 2.27318 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.01819e10 | 1.52961 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.17082e8 | −0.0163059 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.17304e8 | −0.0459550 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.19353e9 | −0.530760 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.08120e9 | 0.0790666 | 0.0395333 | − | 0.999218i | \(-0.487413\pi\) | ||||
0.0395333 | + | 0.999218i | \(0.487413\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.01700e10 | −2.18678 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.63810e10 | 1.17685 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.68438e9 | −0.191156 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.58224e10 | 3.23439 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.35998e9 | −0.235089 | −0.117545 | − | 0.993068i | \(-0.537502\pi\) | ||||
−0.117545 | + | 0.993068i | \(0.537502\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.98764e9 | −0.137856 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.97298e9 | −0.135646 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.85305e9 | 0.194449 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.71297e10 | 2.50862 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.09007e9 | 0.0730125 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.79911e10 | 1.19465 | 0.597323 | − | 0.802001i | \(-0.296231\pi\) | ||||
0.597323 | + | 0.802001i | \(0.296231\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.03707e9 | −0.397423 | −0.198711 | − | 0.980058i | \(-0.563676\pi\) | ||||
−0.198711 | + | 0.980058i | \(0.563676\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.71515e9 | 0.307736 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.58397e10 | −1.02493 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.48847e10 | 0.954910 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.00782e9 | 0.509355 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.62254e10 | −1.02328 | −0.511641 | − | 0.859200i | \(-0.670962\pi\) | ||||
−0.511641 | + | 0.859200i | \(0.670962\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.87177e10 | 1.17045 | 0.585225 | − | 0.810871i | \(-0.301006\pi\) | ||||
0.585225 | + | 0.810871i | \(0.301006\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.08332e9 | −0.439185 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.09971e10 | −1.29089 | −0.645445 | − | 0.763806i | \(-0.723328\pi\) | ||||
−0.645445 | + | 0.763806i | \(0.723328\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.77963e9 | 0.413300 | 0.206650 | − | 0.978415i | \(-0.433744\pi\) | ||||
0.206650 | + | 0.978415i | \(0.433744\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.15078e10 | −1.30015 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.36219e9 | −0.201542 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.46232e10 | −1.46367 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.96183e8 | −0.0469325 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.76720e8 | 0.0512500 | 0.0256250 | − | 0.999672i | \(-0.491842\pi\) | ||||
0.0256250 | + | 0.999672i | \(0.491842\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.71244e10 | −0.992726 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.02678e10 | −1.16523 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.95439e10 | 1.11433 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.52629e10 | −1.42854 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.05358e10 | −2.27333 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.14444e10 | 1.19278 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.48352e10 | 1.92175 | 0.960875 | − | 0.276984i | \(-0.0893348\pi\) | ||||
0.960875 | + | 0.276984i | \(0.0893348\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.77061e10 | −1.51598 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.85212e9 | −0.263329 | −0.131665 | − | 0.991294i | \(-0.542032\pi\) | ||||
−0.131665 | + | 0.991294i | \(0.542032\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.09083e10 | 0.587191 | 0.293596 | − | 0.955930i | \(-0.405148\pi\) | ||||
0.293596 | + | 0.955930i | \(0.405148\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.50743e10 | −1.87274 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.92478e9 | −0.472672 | −0.236336 | − | 0.971671i | \(-0.575947\pi\) | ||||
−0.236336 | + | 0.971671i | \(0.575947\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.99465e10 | −1.57322 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.33129e10 | 1.21487 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.36455e8 | −0.0432388 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.35636e9 | 0.274667 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.38744e10 | −0.705774 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.83722e10 | −2.94563 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.64337e10 | −1.32331 | −0.661653 | − | 0.749810i | \(-0.730145\pi\) | ||||
−0.661653 | + | 0.749810i | \(0.730145\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.01074e10 | 1.49524 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.62164e10 | 0.798984 | 0.399492 | − | 0.916737i | \(-0.369186\pi\) | ||||
0.399492 | + | 0.916737i | \(0.369186\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.95689e9 | −0.486700 | −0.243350 | − | 0.969939i | \(-0.578246\pi\) | ||||
−0.243350 | + | 0.969939i | \(0.578246\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.89424e10 | 3.82833 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.18915e10 | 0.572143 | 0.286072 | − | 0.958208i | \(-0.407650\pi\) | ||||
0.286072 | + | 0.958208i | \(0.407650\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.07668e10 | 0.991317 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.31917e9 | −0.204564 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.52721e10 | 1.18757 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.80353e10 | 2.23965 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.59132e10 | 0.736181 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.61842e8 | 0.00742904 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.58423e9 | −0.254347 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.58682e10 | −1.16912 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.46629e10 | −1.10605 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.98425e9 | −0.355311 | −0.177655 | − | 0.984093i | \(-0.556851\pi\) | ||||
−0.177655 | + | 0.984093i | \(0.556851\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.52660e9 | −0.288213 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.41995e10 | −1.93688 | −0.968441 | − | 0.249242i | \(-0.919818\pi\) | ||||
−0.968441 | + | 0.249242i | \(0.919818\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.68522e8 | −0.0421174 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.61411e10 | −0.696559 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.02244e10 | −1.29439 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.34655e10 | 0.997299 | 0.498650 | − | 0.866804i | \(-0.333829\pi\) | ||||
0.498650 | + | 0.866804i | \(0.333829\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.93753e10 | 2.08258 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.44316e9 | −0.0604099 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.34577e10 | −2.63626 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.32898e10 | 0.960257 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.61342e10 | 1.06944 | 0.534718 | − | 0.845031i | \(-0.320418\pi\) | ||||
0.534718 | + | 0.845031i | \(0.320418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.27488e10 | 1.73620 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.18584e10 | 1.28422 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.26784e9 | 0.0507252 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.03666e10 | −0.808779 | −0.404389 | − | 0.914587i | \(-0.632516\pi\) | ||||
−0.404389 | + | 0.914587i | \(0.632516\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.44142e10 | 2.14478 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.75644e10 | −0.687180 | −0.343590 | − | 0.939120i | \(-0.611643\pi\) | ||||
−0.343590 | + | 0.939120i | \(0.611643\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.53045e10 | −0.982667 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.63273e10 | −1.40030 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.43195e10 | −0.547903 | −0.273951 | − | 0.961744i | \(-0.588331\pi\) | ||||
−0.273951 | + | 0.961744i | \(0.588331\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.89671e10 | 0.720391 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.68015e9 | 0.138750 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.93399e10 | 0.723817 | 0.361908 | − | 0.932214i | \(-0.382125\pi\) | ||||
0.361908 | + | 0.932214i | \(0.382125\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.12635e10 | 1.90457 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.76056e8 | 0.0175576 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.10049e10 | 1.86744 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.73039e10 | −0.992413 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.61049e9 | 0.0941954 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.73981e10 | −1.33969 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.23800e10 | 0.440280 | 0.220140 | − | 0.975468i | \(-0.429349\pi\) | ||||
0.220140 | + | 0.975468i | \(0.429349\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.30029e9 | 0.328370 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.53075e10 | 1.58819 | 0.794096 | − | 0.607792i | \(-0.207945\pi\) | ||||
0.794096 | + | 0.607792i | \(0.207945\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.48786e10 | 1.56187 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.70899e10 | −1.62709 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.32784e10 | −0.798587 | −0.399293 | − | 0.916823i | \(-0.630744\pi\) | ||||
−0.399293 | + | 0.916823i | \(0.630744\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.14792e9 | −0.0390996 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.23377e10 | −0.755433 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.09683e10 | −0.368300 | −0.184150 | − | 0.982898i | \(-0.558953\pi\) | ||||
−0.184150 | + | 0.982898i | \(0.558953\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.20284e10 | 2.06806 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.39204e10 | −1.45397 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.86627e10 | −0.613461 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.57317e10 | −0.839868 | −0.419934 | − | 0.907555i | \(-0.637947\pi\) | ||||
−0.419934 | + | 0.907555i | \(0.637947\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.03071e9 | −0.130635 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.47786e10 | −1.44109 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.67530e10 | −0.854948 | −0.427474 | − | 0.904028i | \(-0.640596\pi\) | ||||
−0.427474 | + | 0.904028i | \(0.640596\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.09810e10 | −0.665806 |
(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 | 32.8.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 288.8.a.o.1.2 | 2 | |||
4.3 | odd | 2 | 32.8.a.d.1.2 | yes | 2 | ||
8.3 | odd | 2 | 64.8.a.h.1.1 | 2 | |||
8.5 | even | 2 | 64.8.a.j.1.2 | 2 | |||
12.11 | even | 2 | 288.8.a.n.1.2 | 2 | |||
16.3 | odd | 4 | 256.8.b.j.129.4 | 4 | |||
16.5 | even | 4 | 256.8.b.h.129.4 | 4 | |||
16.11 | odd | 4 | 256.8.b.j.129.1 | 4 | |||
16.13 | even | 4 | 256.8.b.h.129.1 | 4 | |||
24.5 | odd | 2 | 576.8.a.bf.1.1 | 2 | |||
24.11 | even | 2 | 576.8.a.be.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.8.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
32.8.a.d.1.2 | yes | 2 | 4.3 | odd | 2 | ||
64.8.a.h.1.1 | 2 | 8.3 | odd | 2 | |||
64.8.a.j.1.2 | 2 | 8.5 | even | 2 | |||
256.8.b.h.129.1 | 4 | 16.13 | even | 4 | |||
256.8.b.h.129.4 | 4 | 16.5 | even | 4 | |||
256.8.b.j.129.1 | 4 | 16.11 | odd | 4 | |||
256.8.b.j.129.4 | 4 | 16.3 | odd | 4 | |||
288.8.a.n.1.2 | 2 | 12.11 | even | 2 | |||
288.8.a.o.1.2 | 2 | 3.2 | odd | 2 | |||
576.8.a.be.1.1 | 2 | 24.11 | even | 2 | |||
576.8.a.bf.1.1 | 2 | 24.5 | odd | 2 |