Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,8,Mod(1,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("336.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.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: | \(104.961368563\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 336.1 |
$q$-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 | ||||||||
\(5\) | 100.000 | 0.357771 | 0.178885 | − | 0.983870i | \(-0.442751\pi\) | ||||
0.178885 | + | 0.983870i | \(0.442751\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2774.00 | −0.628394 | −0.314197 | − | 0.949358i | \(-0.601735\pi\) | ||||
−0.314197 | + | 0.949358i | \(0.601735\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3294.00 | −0.415836 | −0.207918 | − | 0.978146i | \(-0.566669\pi\) | ||||
−0.207918 | + | 0.978146i | \(0.566669\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2700.00 | 0.206559 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5900.00 | 0.291260 | 0.145630 | − | 0.989339i | \(-0.453479\pi\) | ||||
0.145630 | + | 0.989339i | \(0.453479\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6644.00 | −0.222225 | −0.111112 | − | 0.993808i | \(-0.535441\pi\) | ||||
−0.111112 | + | 0.993808i | \(0.535441\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9261.00 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1982.00 | −0.0339669 | −0.0169835 | − | 0.999856i | \(-0.505406\pi\) | ||||
−0.0169835 | + | 0.999856i | \(0.505406\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −68125.0 | −0.872000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −208106. | −1.58450 | −0.792249 | − | 0.610198i | \(-0.791090\pi\) | ||||
−0.792249 | + | 0.610198i | \(0.791090\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 117792. | 0.710150 | 0.355075 | − | 0.934838i | \(-0.384455\pi\) | ||||
0.355075 | + | 0.934838i | \(0.384455\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −74898.0 | −0.362803 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 34300.0 | 0.135225 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −335686. | −1.08950 | −0.544750 | − | 0.838599i | \(-0.683375\pi\) | ||||
−0.544750 | + | 0.838599i | \(0.683375\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −88938.0 | −0.240083 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −265488. | −0.601591 | −0.300796 | − | 0.953689i | \(-0.597252\pi\) | ||||
−0.300796 | + | 0.953689i | \(0.597252\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 93292.0 | 0.178939 | 0.0894695 | − | 0.995990i | \(-0.471483\pi\) | ||||
0.0894695 | + | 0.995990i | \(0.471483\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 72900.0 | 0.119257 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 657516. | 0.923770 | 0.461885 | − | 0.886940i | \(-0.347173\pi\) | ||||
0.461885 | + | 0.886940i | \(0.347173\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 159300. | 0.168159 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −608718. | −0.561630 | −0.280815 | − | 0.959762i | \(-0.590605\pi\) | ||||
−0.280815 | + | 0.959762i | \(0.590605\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −277400. | −0.224821 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −179388. | −0.128301 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 536120. | 0.339844 | 0.169922 | − | 0.985457i | \(-0.445648\pi\) | ||||
0.169922 | + | 0.985457i | \(0.445648\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.79709e6 | −1.01371 | −0.506857 | − | 0.862030i | \(-0.669193\pi\) | ||||
−0.506857 | + | 0.862030i | \(0.669193\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 250047. | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −329400. | −0.148774 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.12318e6 | −0.862431 | −0.431215 | − | 0.902249i | \(-0.641915\pi\) | ||||
−0.431215 | + | 0.902249i | \(0.641915\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −53514.0 | −0.0196108 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.19121e6 | 0.394990 | 0.197495 | − | 0.980304i | \(-0.436719\pi\) | ||||
0.197495 | + | 0.980304i | \(0.436719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.05643e6 | 0.317842 | 0.158921 | − | 0.987291i | \(-0.449199\pi\) | ||||
0.158921 | + | 0.987291i | \(0.449199\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.83938e6 | −0.503449 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −951482. | −0.237511 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −998484. | −0.227849 | −0.113924 | − | 0.993489i | \(-0.536342\pi\) | ||||
−0.113924 | + | 0.993489i | \(0.536342\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.89800e6 | −0.748288 | −0.374144 | − | 0.927371i | \(-0.622063\pi\) | ||||
−0.374144 | + | 0.927371i | \(0.622063\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 590000. | 0.104204 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.61886e6 | −0.914810 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.62235e6 | −0.695021 | −0.347511 | − | 0.937676i | \(-0.612973\pi\) | ||||
−0.347511 | + | 0.937676i | \(0.612973\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.12984e6 | −0.157171 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.18038e6 | 0.410005 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −664400. | −0.0795055 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.52877e7 | 1.70075 | 0.850377 | − | 0.526174i | \(-0.176374\pi\) | ||||
0.850377 | + | 0.526174i | \(0.176374\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.02225e6 | −0.209465 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.23869e6 | 0.216207 | 0.108103 | − | 0.994140i | \(-0.465522\pi\) | ||||
0.108103 | + | 0.994140i | \(0.465522\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.24502e7 | −1.12266 | −0.561328 | − | 0.827593i | \(-0.689709\pi\) | ||||
−0.561328 | + | 0.827593i | \(0.689709\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 926100. | 0.0780720 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.58860e6 | 0.598851 | 0.299425 | − | 0.954120i | \(-0.403205\pi\) | ||||
0.299425 | + | 0.954120i | \(0.403205\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.17097e6 | 0.382454 | 0.191227 | − | 0.981546i | \(-0.438753\pi\) | ||||
0.191227 | + | 0.981546i | \(0.438753\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.06352e6 | −0.629023 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.63868e6 | −0.628410 | −0.314205 | − | 0.949355i | \(-0.601738\pi\) | ||||
−0.314205 | + | 0.949355i | \(0.601738\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −198200. | −0.0121524 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.40133e6 | −0.138612 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.02370e6 | 0.110086 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.17921e7 | −0.605121 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.16818e6 | −0.347329 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.46250e7 | −0.669747 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.08309e6 | −0.350158 | −0.175079 | − | 0.984554i | \(-0.556018\pi\) | ||||
−0.175079 | + | 0.984554i | \(0.556018\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.51888e6 | 0.103310 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.97585e7 | 0.767901 | 0.383951 | − | 0.923354i | \(-0.374563\pi\) | ||||
0.383951 | + | 0.923354i | \(0.374563\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.27889e6 | −0.0839930 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.96830e6 | 0.0688530 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.80896e7 | −1.59783 | −0.798913 | − | 0.601447i | \(-0.794591\pi\) | ||||
−0.798913 | + | 0.601447i | \(0.794591\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.37173e7 | −0.433229 | −0.216615 | − | 0.976257i | \(-0.569501\pi\) | ||||
−0.216615 | + | 0.976257i | \(0.569501\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.77529e7 | 0.533339 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.13756e6 | 0.261309 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.08106e7 | −0.566887 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.17652e6 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.07104e7 | −1.75118 | −0.875591 | − | 0.483053i | \(-0.839528\pi\) | ||||
−0.875591 | + | 0.483053i | \(0.839528\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.56970e7 | 0.607383 | 0.303691 | − | 0.952770i | \(-0.401781\pi\) | ||||
0.303691 | + | 0.952770i | \(0.401781\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.30110e6 | 0.0970867 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.17792e7 | 0.254071 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.09180e7 | 0.431390 | 0.215695 | − | 0.976461i | \(-0.430798\pi\) | ||||
0.215695 | + | 0.976461i | \(0.430798\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.64354e7 | −0.324257 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −679826. | −0.0128383 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.44160e7 | −0.984169 | −0.492084 | − | 0.870547i | \(-0.663765\pi\) | ||||
−0.492084 | + | 0.870547i | \(0.663765\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.48980e6 | −0.129801 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.41888e6 | −0.106648 | −0.0533238 | − | 0.998577i | \(-0.516982\pi\) | ||||
−0.0533238 | + | 0.998577i | \(0.516982\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.18981e7 | −0.827081 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.84348e6 | −0.0740748 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.46532e7 | −0.802517 | −0.401259 | − | 0.915965i | \(-0.631427\pi\) | ||||
−0.401259 | + | 0.915965i | \(0.631427\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.33669e7 | −0.329585 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.44752e7 | 0.196209 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.76658e7 | 0.490865 | 0.245433 | − | 0.969414i | \(-0.421070\pi\) | ||||
0.245433 | + | 0.969414i | \(0.421070\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.76788e7 | 0.221604 | 0.110802 | − | 0.993842i | \(-0.464658\pi\) | ||||
0.110802 | + | 0.993842i | \(0.464658\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.85214e7 | −0.585268 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.35686e7 | −0.389791 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.63666e7 | −0.183026 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.75127e6 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.09177e7 | −0.424907 | −0.212454 | − | 0.977171i | \(-0.568145\pi\) | ||||
−0.212454 | + | 0.977171i | \(0.568145\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.63827e8 | −1.64034 | −0.820171 | − | 0.572118i | \(-0.806122\pi\) | ||||
−0.820171 | + | 0.572118i | \(0.806122\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.89380e6 | −0.0858947 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.02076e7 | 0.747453 | 0.373726 | − | 0.927539i | \(-0.378080\pi\) | ||||
0.373726 | + | 0.927539i | \(0.378080\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.83219e7 | −0.884432 | −0.442216 | − | 0.896908i | \(-0.645808\pi\) | ||||
−0.442216 | + | 0.896908i | \(0.645808\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.73258e7 | −0.497925 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.13804e7 | −0.598884 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.65488e7 | −0.215232 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.44488e6 | −0.0113223 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.84305e7 | 0.139645 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.36321e8 | −0.999021 | −0.499510 | − | 0.866308i | \(-0.666487\pi\) | ||||
−0.499510 | + | 0.866308i | \(0.666487\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.21628e7 | 0.228047 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.32920e6 | 0.0640191 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.04027e7 | 0.268411 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.85236e7 | 0.183506 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.94346e7 | −0.121116 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.26358e8 | −0.763019 | −0.381510 | − | 0.924365i | \(-0.624596\pi\) | ||||
−0.381510 | + | 0.924365i | \(0.624596\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.96631e7 | −0.290667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.34007e8 | −1.32782 | −0.663909 | − | 0.747814i | \(-0.731104\pi\) | ||||
−0.663909 | + | 0.747814i | \(0.731104\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.83606e7 | 0.376168 | 0.188084 | − | 0.982153i | \(-0.439772\pi\) | ||||
0.188084 | + | 0.982153i | \(0.439772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.56900e7 | −0.137127 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.80385e8 | 0.934230 | 0.467115 | − | 0.884197i | \(-0.345293\pi\) | ||||
0.467115 | + | 0.884197i | \(0.345293\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.57516e7 | 0.330498 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.69591e7 | −0.131548 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.61131e8 | −1.23727 | −0.618637 | − | 0.785677i | \(-0.712315\pi\) | ||||
−0.618637 | + | 0.785677i | \(0.712315\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.97756e7 | 0.0910061 | 0.0455031 | − | 0.998964i | \(-0.485511\pi\) | ||||
0.0455031 | + | 0.998964i | \(0.485511\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.17649e7 | 0.0511101 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.18853e7 | 0.0924089 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.05246e8 | −0.432024 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.53770e8 | −0.613779 | −0.306890 | − | 0.951745i | \(-0.599288\pi\) | ||||
−0.306890 | + | 0.951745i | \(0.599288\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.49807e6 | 0.0213446 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.59300e7 | 0.0601624 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.43360e8 | −0.526821 | −0.263411 | − | 0.964684i | \(-0.584847\pi\) | ||||
−0.263411 | + | 0.964684i | \(0.584847\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.15140e8 | −0.411792 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.51709e8 | −0.528166 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.07301e8 | 1.71957 | 0.859786 | − | 0.510654i | \(-0.170597\pi\) | ||||
0.859786 | + | 0.510654i | \(0.170597\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.08718e7 | −0.200935 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.24804e8 | −0.401271 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.27886e8 | 1.65351 | 0.826755 | − | 0.562562i | \(-0.190184\pi\) | ||||
0.826755 | + | 0.562562i | \(0.190184\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.05836e8 | 1.54389 | 0.771947 | − | 0.635687i | \(-0.219283\pi\) | ||||
0.771947 | + | 0.635687i | \(0.219283\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.05057e7 | −0.0907428 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.88979e8 | 0.547960 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.88586e8 | −1.66391 | −0.831956 | − | 0.554841i | \(-0.812779\pi\) | ||||
−0.831956 | + | 0.554841i | \(0.812779\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.58704e7 | 0.236717 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.65142e7 | 0.232603 | 0.116301 | − | 0.993214i | \(-0.462896\pi\) | ||||
0.116301 | + | 0.993214i | \(0.462896\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.57301e8 | 0.412552 | 0.206276 | − | 0.978494i | \(-0.433866\pi\) | ||||
0.206276 | + | 0.978494i | \(0.433866\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.79388e7 | −0.0459025 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.10624e7 | −0.227380 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.75529e8 | −0.915168 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.12768e8 | 0.981930 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.80964e8 | 1.58157 | 0.790783 | − | 0.612097i | \(-0.209674\pi\) | ||||
0.790783 | + | 0.612097i | \(0.209674\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.36120e7 | 0.121586 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.46006e7 | −0.120934 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.52871e6 | 0.0141247 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.19992e7 | 0.0676326 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.04446e7 | 0.124827 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.79709e8 | −0.362677 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.81734e8 | −0.555718 | −0.277859 | − | 0.960622i | \(-0.589625\pi\) | ||||
−0.277859 | + | 0.960622i | \(0.589625\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.36156e8 | −0.648166 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.19719e8 | 0.791220 | 0.395610 | − | 0.918419i | \(-0.370533\pi\) | ||||
0.395610 | + | 0.918419i | \(0.370533\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.28684e8 | −0.421532 | −0.210766 | − | 0.977537i | \(-0.567596\pi\) | ||||
−0.210766 | + | 0.977537i | \(0.567596\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.50047e7 | 0.0450749 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.66003e8 | 0.469006 | 0.234503 | − | 0.972115i | \(-0.424654\pi\) | ||||
0.234503 | + | 0.972115i | \(0.424654\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.77286e8 | 0.995689 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.04892e8 | 0.345747 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.91996e7 | −0.0647251 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.24404e8 | 0.362609 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.39616e8 | 0.220810 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.25528e8 | 0.349152 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.16107e8 | 1.08538 | 0.542688 | − | 0.839935i | \(-0.317407\pi\) | ||||
0.542688 | + | 0.839935i | \(0.317407\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.44715e8 | −0.363167 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.12318e8 | −0.308553 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.70266e8 | 0.811657 | 0.405829 | − | 0.913949i | \(-0.366983\pi\) | ||||
0.405829 | + | 0.913949i | \(0.366983\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.60244e8 | −0.362813 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.26755e8 | −0.446254 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.35140e6 | −0.00701618 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.64641e8 | 0.211536 | 0.105768 | − | 0.994391i | \(-0.466270\pi\) | ||||
0.105768 | + | 0.994391i | \(0.466270\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.31564e9 | 1.65671 | 0.828357 | − | 0.560200i | \(-0.189276\pi\) | ||||
0.828357 | + | 0.560200i | \(0.189276\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.48358e7 | −0.0800276 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.56118e9 | 1.88904 | 0.944518 | − | 0.328459i | \(-0.106529\pi\) | ||||
0.944518 | + | 0.328459i | \(0.106529\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.19121e8 | 0.141316 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.46399e7 | 0.0635581 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.60716e8 | 0.981814 | 0.490907 | − | 0.871212i | \(-0.336665\pi\) | ||||
0.490907 | + | 0.871212i | \(0.336665\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.49729e8 | −0.950616 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.18387e8 | −0.349367 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.05643e8 | 0.113714 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.12133e8 | −0.963223 | −0.481612 | − | 0.876385i | \(-0.659948\pi\) | ||||
−0.481612 | + | 0.876385i | \(0.659948\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.93541e8 | −0.200530 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.08790e8 | −0.212276 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.36004e8 | 0.235472 | 0.117736 | − | 0.993045i | \(-0.462436\pi\) | ||||
0.117736 | + | 0.993045i | \(0.462436\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.94875e8 | −0.386679 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.85501e8 | 0.658891 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.29313e8 | −0.782495 | −0.391247 | − | 0.920286i | \(-0.627956\pi\) | ||||
−0.391247 | + | 0.920286i | \(0.627956\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.18243e8 | −0.202164 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.21663e9 | 1.10653 | 0.553265 | − | 0.833005i | \(-0.313382\pi\) | ||||
0.553265 | + | 0.833005i | \(0.313382\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.51482e7 | −0.0849744 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.80099e7 | 0.0596463 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.18213e8 | −0.101822 | −0.0509109 | − | 0.998703i | \(-0.516212\pi\) | ||||
−0.0509109 | + | 0.998703i | \(0.516212\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.16938e7 | −0.00989321 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.33481e8 | 0.443348 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.98484e7 | −0.0815176 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.62565e7 | 0.0290817 | 0.0145408 | − | 0.999894i | \(-0.495371\pi\) | ||||
0.0145408 | + | 0.999894i | \(0.495371\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.15301e7 | −0.0484934 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.06850e8 | 0.392531 | 0.196265 | − | 0.980551i | \(-0.437119\pi\) | ||||
0.196265 | + | 0.980551i | \(0.437119\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.88007e8 | −0.295306 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.31441e7 | 0.0397523 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.31193e8 | 0.684635 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.68121e9 | 1.21504 | 0.607519 | − | 0.794305i | \(-0.292165\pi\) | ||||
0.607519 | + | 0.794305i | \(0.292165\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.29842e9 | −0.922505 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.83889e8 | 0.128449 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.89800e8 | −0.267716 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.70368e8 | −0.250125 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.94962e8 | −0.328718 | −0.164359 | − | 0.986401i | \(-0.552556\pi\) | ||||
−0.164359 | + | 0.986401i | \(0.552556\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.57487e7 | −0.0429437 | −0.0214719 | − | 0.999769i | \(-0.506835\pi\) | ||||
−0.0214719 | + | 0.999769i | \(0.506835\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.79329e8 | 0.307923 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.01938e8 | −0.253979 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.16402e8 | −0.383148 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.46714e8 | 0.150867 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.33418e9 | 0.802682 | 0.401341 | − | 0.915929i | \(-0.368544\pi\) | ||||
0.401341 | + | 0.915929i | \(0.368544\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.47903e7 | −0.0146749 | −0.00733745 | − | 0.999973i | \(-0.502336\pi\) | ||||
−0.00733745 | + | 0.999973i | \(0.502336\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.61886e8 | −0.327292 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.31684e7 | 0.00754828 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.89327e8 | 0.388866 | 0.194433 | − | 0.980916i | \(-0.437713\pi\) | ||||
0.194433 | + | 0.980916i | \(0.437713\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.57661e7 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.74617e8 | 0.314026 | 0.157013 | − | 0.987597i | \(-0.449814\pi\) | ||||
0.157013 | + | 0.987597i | \(0.449814\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.62235e8 | −0.248658 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.90918e9 | −1.01105 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.56884e7 | 0.0498881 | 0.0249440 | − | 0.999689i | \(-0.492059\pi\) | ||||
0.0249440 | + | 0.999689i | \(0.492059\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.36464e8 | 0.378036 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.93818e8 | 0.350672 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.12984e8 | −0.0562313 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.73089e7 | −0.0231866 | −0.0115933 | − | 0.999933i | \(-0.503690\pi\) | ||||
−0.0115933 | + | 0.999933i | \(0.503690\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.16130e8 | 0.0560530 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.13567e9 | −1.01527 | −0.507634 | − | 0.861573i | \(-0.669480\pi\) | ||||
−0.507634 | + | 0.861573i | \(0.669480\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.92675e8 | −0.137042 | −0.0685208 | − | 0.997650i | \(-0.521828\pi\) | ||||
−0.0685208 | + | 0.997650i | \(0.521828\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.18038e8 | 0.146688 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.53834e9 | 1.60765 | 0.803824 | − | 0.594868i | \(-0.202796\pi\) | ||||
0.803824 | + | 0.594868i | \(0.202796\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.28249e8 | −0.325968 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.64785e8 | 0.249063 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.58792e8 | −0.112444 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.52622e8 | 0.193780 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.43755e8 | −0.187210 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.15698e9 | 1.72824 | 0.864120 | − | 0.503286i | \(-0.167876\pi\) | ||||
0.864120 | + | 0.503286i | \(0.167876\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.10575e9 | 0.453053 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.83553e7 | −0.00741219 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.52877e9 | 0.608480 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.24092e8 | −0.0486847 | −0.0243423 | − | 0.999704i | \(-0.507749\pi\) | ||||
−0.0243423 | + | 0.999704i | \(0.507749\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.46923e9 | −0.568210 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.29218e9 | 1.25516 | 0.627578 | − | 0.778554i | \(-0.284046\pi\) | ||||
0.627578 | + | 0.778554i | \(0.284046\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.22783e9 | −0.461501 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.02225e8 | −0.0749404 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.08586e8 | 0.149292 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.60439e8 | 0.129861 | 0.0649306 | − | 0.997890i | \(-0.479317\pi\) | ||||
0.0649306 | + | 0.997890i | \(0.479317\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.73310e8 | −0.0615731 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.29760e9 | 1.50570 | 0.752849 | − | 0.658193i | \(-0.228679\pi\) | ||||
0.752849 | + | 0.658193i | \(0.228679\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.23869e8 | 0.0773524 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.40125e9 | −0.477515 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.42588e8 | −0.182372 | −0.0911860 | − | 0.995834i | \(-0.529066\pi\) | ||||
−0.0911860 | + | 0.995834i | \(0.529066\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.62355e8 | 0.120133 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.30774e8 | −0.0427671 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.24502e9 | −0.401654 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.82395e9 | −0.580492 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.47564e9 | −0.463334 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.36755e8 | −0.0733445 | −0.0366722 | − | 0.999327i | \(-0.511676\pi\) | ||||
−0.0366722 | + | 0.999327i | \(0.511676\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.48324e9 | −1.98169 | −0.990846 | − | 0.135000i | \(-0.956896\pi\) | ||||
−0.990846 | + | 0.135000i | \(0.956896\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.30906e8 | −0.190286 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.94973e8 | 0.206838 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.40090e9 | −0.998846 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.90831e8 | 0.113281 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.74517e8 | 0.250163 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.58860e8 | 0.214251 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.01698e9 | 0.283401 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.26358e8 | −0.0897706 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.50099e8 | −0.0407556 | −0.0203778 | − | 0.999792i | \(-0.506487\pi\) | ||||
−0.0203778 | + | 0.999792i | \(0.506487\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.77328e8 | 0.127943 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.17097e8 | 0.136831 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.32631e9 | −0.868974 | −0.434487 | − | 0.900678i | \(-0.643070\pi\) | ||||
−0.434487 | + | 0.900678i | \(0.643070\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.31008e9 | −0.337905 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.38266e9 | 0.352114 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.42480e8 | −0.0861187 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.06352e8 | −0.225046 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.72512e9 | 1.15856 | 0.579282 | − | 0.815127i | \(-0.303333\pi\) | ||||
0.579282 | + | 0.815127i | \(0.303333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.07304e8 | −0.0744092 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.41898e8 | −0.105670 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.11044e9 | −1.67926 | −0.839628 | − | 0.543162i | \(-0.817227\pi\) | ||||
−0.839628 | + | 0.543162i | \(0.817227\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.63868e8 | −0.224827 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.82284e8 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.55315e9 | 1.49127 | 0.745636 | − | 0.666353i | \(-0.232146\pi\) | ||||
0.745636 | + | 0.666353i | \(0.232146\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.29277e9 | −1.86412 | −0.932059 | − | 0.362306i | \(-0.881990\pi\) | ||||
−0.932059 | + | 0.362306i | \(0.881990\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.10478e9 | −0.245320 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.35024e8 | 0.0296192 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.88000e9 | −1.27427 | −0.637135 | − | 0.770752i | \(-0.719881\pi\) | ||||
−0.637135 | + | 0.770752i | \(0.719881\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.42333e9 | −0.947052 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.33702e9 | −0.282826 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.68858e9 | 0.352925 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.40133e8 | −0.0495913 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.43194e9 | 0.292207 | 0.146103 | − | 0.989269i | \(-0.453327\pi\) | ||||
0.146103 | + | 0.989269i | \(0.453327\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.82610e8 | −0.157813 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.16561e9 | 0.431542 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.48138e9 | 0.685584 | 0.342792 | − | 0.939411i | \(-0.388627\pi\) | ||||
0.342792 | + | 0.939411i | \(0.388627\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.02370e8 | 0.0393855 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.65469e9 | −0.510627 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.93597e9 | −1.50871 | −0.754356 | − | 0.656466i | \(-0.772051\pi\) | ||||
−0.754356 | + | 0.656466i | \(0.772051\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.05169e9 | −0.761335 | −0.380668 | − | 0.924712i | \(-0.624306\pi\) | ||||
−0.380668 | + | 0.924712i | \(0.624306\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.54780e9 | −0.287477 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.17921e9 | −0.216495 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.19159e9 | −0.942194 | −0.471097 | − | 0.882081i | \(-0.656142\pi\) | ||||
−0.471097 | + | 0.882081i | \(0.656142\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.92727e9 | −0.345766 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.16586e9 | −0.384137 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.69807e9 | 0.648430 | 0.324215 | − | 0.945983i | \(-0.394900\pi\) | ||||
0.324215 | + | 0.945983i | \(0.394900\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.16818e8 | −0.124264 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.19879e9 | −1.06245 | −0.531226 | − | 0.847230i | \(-0.678268\pi\) | ||||
−0.531226 | + | 0.847230i | \(0.678268\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.85137e9 | 0.483211 | 0.241605 | − | 0.970375i | \(-0.422326\pi\) | ||||
0.241605 | + | 0.970375i | \(0.422326\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.90117e7 | −0.00653694 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.58547e9 | −0.262693 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.85977e9 | 0.632384 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.97622e8 | 0.0806238 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.98055e9 | −0.317328 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.56414e9 | 1.19855 | 0.599276 | − | 0.800543i | \(-0.295455\pi\) | ||||
0.599276 | + | 0.800543i | \(0.295455\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.68067e9 | −0.576785 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.08309e8 | −0.125276 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.87536e8 | −0.0594051 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.68395e8 | 0.131663 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.12019e10 | 1.67991 | 0.839957 | − | 0.542653i | \(-0.182580\pi\) | ||||
0.839957 | + | 0.542653i | \(0.182580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.87742e9 | −1.16855 | −0.584273 | − | 0.811557i | \(-0.698620\pi\) | ||||
−0.584273 | + | 0.811557i | \(0.698620\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.51888e8 | 0.0369615 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.24945e9 | −0.181365 | −0.0906825 | − | 0.995880i | \(-0.528905\pi\) | ||||
−0.0906825 | + | 0.995880i | \(0.528905\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.48720e9 | −0.213556 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.09087e9 | 0.154967 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.52696e9 | 1.05785 | 0.528924 | − | 0.848669i | \(-0.322596\pi\) | ||||
0.528924 | + | 0.848669i | \(0.322596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.97585e9 | 0.274733 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.70137e8 | 0.105947 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.29417e9 | −0.312268 | −0.156134 | − | 0.987736i | \(-0.549903\pi\) | ||||
−0.156134 | + | 0.987736i | \(0.549903\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.08384e9 | −0.684679 | −0.342339 | − | 0.939576i | \(-0.611219\pi\) | ||||
−0.342339 | + | 0.939576i | \(0.611219\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.24734e8 | −0.0699265 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.27889e8 | −0.0300502 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.12466e8 | 0.0538205 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.41166e9 | −0.440529 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.98513e9 | 0.637012 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.62649e9 | −0.711516 | −0.355758 | − | 0.934578i | \(-0.615777\pi\) | ||||
−0.355758 | + | 0.934578i | \(0.615777\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.34090e9 | −0.167816 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.02745e10 | −1.27263 | −0.636314 | − | 0.771430i | \(-0.719542\pi\) | ||||
−0.636314 | + | 0.771430i | \(0.719542\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.24368e9 | 0.642824 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.31819e9 | −0.766616 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.55246e10 | −1.86443 | −0.932217 | − | 0.361901i | \(-0.882128\pi\) | ||||
−0.932217 | + | 0.361901i | \(0.882128\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.80896e9 | −0.571655 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.84574e9 | 0.217181 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.00512e9 | 0.233546 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.23449e9 | −0.949432 | −0.474716 | − | 0.880139i | \(-0.657449\pi\) | ||||
−0.474716 | + | 0.880139i | \(0.657449\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.93630e8 | −0.0791702 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.37173e9 | −0.154997 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.56638e9 | −0.175219 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.87039e9 | 0.539378 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.88820e9 | −0.535964 | −0.267982 | − | 0.963424i | \(-0.586357\pi\) | ||||
−0.267982 | + | 0.963424i | \(0.586357\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.23030e9 | 0.242114 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.77529e9 | 0.190813 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.67870e8 | 0.0817184 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.95106e9 | −0.837844 | −0.418922 | − | 0.908022i | \(-0.637592\pi\) | ||||
−0.418922 | + | 0.908022i | \(0.637592\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.27895e8 | −0.0759495 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.33464e8 | −0.0241216 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.13756e8 | 0.0934887 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.05053e9 | −0.714340 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.30035e10 | 1.30469 | 0.652346 | − | 0.757921i | \(-0.273785\pi\) | ||||
0.652346 | + | 0.757921i | \(0.273785\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.27043e9 | −0.424324 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.33942e8 | 0.0525424 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.41772e10 | 1.38168 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.73805e10 | 1.67761 | 0.838805 | − | 0.544431i | \(-0.183255\pi\) | ||||
0.838805 | + | 0.544431i | \(0.183255\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.50423e8 | 0.0521177 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.47114e9 | 0.888256 | 0.444128 | − | 0.895963i | \(-0.353513\pi\) | ||||
0.444128 | + | 0.895963i | \(0.353513\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.17652e8 | 0.0295084 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.88969e9 | 0.541946 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.52914e9 | −0.503967 | −0.251983 | − | 0.967732i | \(-0.581083\pi\) | ||||
−0.251983 | + | 0.967732i | \(0.581083\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.90904e8 | 0.0533523 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.53701e10 | 1.37472 | 0.687362 | − | 0.726315i | \(-0.258769\pi\) | ||||
0.687362 | + | 0.726315i | \(0.258769\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.07104e9 | −0.626522 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.84164e9 | −0.249429 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.60289e9 | 0.226344 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.51950e9 | 0.733964 | 0.366982 | − | 0.930228i | \(-0.380391\pi\) | ||||
0.366982 | + | 0.930228i | \(0.380391\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.15178e9 | −0.354366 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.56970e9 | 0.217304 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.72648e8 | −0.0396006 | −0.0198003 | − | 0.999804i | \(-0.506303\pi\) | ||||
−0.0198003 | + | 0.999804i | \(0.506303\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.48448e8 | 0.0123233 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.43465e10 | −1.18005 | −0.590025 | − | 0.807385i | \(-0.700882\pi\) | ||||
−0.590025 | + | 0.807385i | \(0.700882\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.77364e9 | 0.144554 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.30110e8 | 0.0347348 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.76598e9 | −0.141319 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.39480e10 | 1.10603 | 0.553017 | − | 0.833170i | \(-0.313476\pi\) | ||||
0.553017 | + | 0.833170i | \(0.313476\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.87073e9 | −0.304160 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.32337e9 | −0.336662 | −0.168331 | − | 0.985731i | \(-0.553838\pi\) | ||||
−0.168331 | + | 0.985731i | \(0.553838\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.02458e9 | −0.619250 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.10879e9 | −0.237748 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.76390e9 | 0.133688 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.30443e9 | −0.248209 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.09615e9 | −0.304937 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.09180e9 | 0.154339 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.71201e9 | −0.490842 | −0.245421 | − | 0.969417i | \(-0.578926\pi\) | ||||
−0.245421 | + | 0.969417i | \(0.578926\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.36971e10 | 0.992796 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.30607e9 | −0.237517 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.91961e9 | 0.421539 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.64354e9 | −0.116010 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.61333e9 | 0.392750 | 0.196375 | − | 0.980529i | \(-0.437083\pi\) | ||||
0.196375 | + | 0.980529i | \(0.437083\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.87934e9 | 0.269057 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.36969e9 | −0.231674 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.93054e9 | −0.199730 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.79826e7 | −0.00459317 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.42529e10 | 0.954655 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.15844e9 | 0.276128 | 0.138064 | − | 0.990423i | \(-0.455912\pi\) | ||||
0.138064 | + | 0.990423i | \(0.455912\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.11994e10 | 0.737259 | 0.368629 | − | 0.929576i | \(-0.379827\pi\) | ||||
0.368629 | + | 0.929576i | \(0.379827\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.36576e10 | 0.891367 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.44160e9 | −0.352107 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.19832e8 | −0.0397646 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.23655e8 | −0.0523904 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.32872e10 | 1.46864 | 0.734322 | − | 0.678801i | \(-0.237500\pi\) | ||||
0.734322 | + | 0.678801i | \(0.237500\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.31943e9 | −0.582761 | −0.291380 | − | 0.956607i | \(-0.594114\pi\) | ||||
−0.291380 | + | 0.956607i | \(0.594114\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.10243e9 | 0.316365 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.16608e10 | 0.716902 | 0.358451 | − | 0.933548i | \(-0.383305\pi\) | ||||
0.358451 | + | 0.933548i | \(0.383305\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.31007e8 | −0.0140826 | −0.00704132 | − | 0.999975i | \(-0.502241\pi\) | ||||
−0.00704132 | + | 0.999975i | \(0.502241\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.58918e10 | −0.960660 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.94129e8 | 0.0416086 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.41888e8 | −0.0381554 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.31850e9 | 0.136668 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.77032e10 | 1.61943 | 0.809716 | − | 0.586822i | \(-0.199621\pi\) | ||||
0.809716 | + | 0.586822i | \(0.199621\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.60582e10 | 1.51063 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.33588e9 | 0.134293 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.18981e9 | −0.295905 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.04469e9 | −0.228714 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.24712e9 | 0.238187 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.65330e8 | 0.0370070 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.87010e10 | 1.58335 | 0.791673 | − | 0.610944i | \(-0.209210\pi\) | ||||
0.791673 | + | 0.610944i | \(0.209210\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.84348e8 | −0.0265018 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.44528e9 | 0.0784366 | 0.0392183 | − | 0.999231i | \(-0.487513\pi\) | ||||
0.0392183 | + | 0.999231i | \(0.487513\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.94906e10 | −1.58748 | −0.793738 | − | 0.608260i | \(-0.791868\pi\) | ||||
−0.793738 | + | 0.608260i | \(0.791868\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.45868e9 | −0.131278 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.87258e9 | −0.469907 | −0.234954 | − | 0.972007i | \(-0.575494\pi\) | ||||
−0.234954 | + | 0.972007i | \(0.575494\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.46532e9 | −0.287117 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.01393e10 | −0.528372 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.76979e9 | 0.143179 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.99374e9 | 0.358630 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.11447e10 | 0.566918 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.01638e9 | −0.253141 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.57308e10 | 0.787504 | 0.393752 | − | 0.919217i | \(-0.371177\pi\) | ||||
0.393752 | + | 0.919217i | \(0.371177\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.83860e10 | 0.913117 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.12522e9 | −0.449602 | −0.224801 | − | 0.974405i | \(-0.572173\pi\) | ||||
−0.224801 | + | 0.974405i | \(0.572173\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.24538e10 | −1.09756 | −0.548778 | − | 0.835968i | \(-0.684907\pi\) | ||||
−0.548778 | + | 0.835968i | \(0.684907\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.44752e9 | 0.0701979 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.43569e10 | 1.65303 | 0.826516 | − | 0.562913i | \(-0.190320\pi\) | ||||
0.826516 | + | 0.562913i | \(0.190320\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.77250e9 | −0.132347 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.47422e9 | −0.0698216 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.36854e9 | −0.205284 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.76658e9 | 0.175617 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.76275e8 | 0.00815488 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.45132e10 | −1.12523 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.59144e9 | −0.163580 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.63977e8 | 0.0390477 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.76788e9 | 0.0792835 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.01062e10 | 1.78478 | 0.892392 | − | 0.451261i | \(-0.149026\pi\) | ||||
0.892392 | + | 0.451261i | \(0.149026\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.63200e9 | 0.0720688 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.70230e10 | 1.62240 | 0.811200 | − | 0.584769i | \(-0.198815\pi\) | ||||
0.811200 | + | 0.584769i | \(0.198815\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.08131e10 | 0.470220 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.85214e9 | −0.209392 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.77718e9 | 0.290239 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.37645e10 | 1.43501 | 0.717507 | − | 0.696551i | \(-0.245283\pi\) | ||||
0.717507 | + | 0.696551i | \(0.245283\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.60681e9 | −0.320844 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.92386e9 | −0.164251 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.28686e10 | 0.950044 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.07621e9 | −0.374219 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.77100e10 | −1.95233 | −0.976167 | − | 0.217019i | \(-0.930367\pi\) | ||||
−0.976167 | + | 0.217019i | \(0.930367\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.81660e8 | −0.0317464 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.13324e10 | 0.456811 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.63666e9 | −0.0654814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.86353e8 | 0.0153425 | 0.00767125 | − | 0.999971i | \(-0.497558\pi\) | ||||
0.00767125 | + | 0.999971i | \(0.497558\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.17447e9 | −0.243372 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.79446e10 | −1.09329 | −0.546643 | − | 0.837366i | \(-0.684095\pi\) | ||||
−0.546643 | + | 0.837366i | \(0.684095\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.26197e8 | 0.0204342 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.75127e8 | 0.0260240 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.50921e9 | 0.210797 | 0.105399 | − | 0.994430i | \(-0.466388\pi\) | ||||
0.105399 | + | 0.994430i | \(0.466388\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.47988e9 | −0.132170 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.18207e9 | 0.270781 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.40406e9 | −0.277105 | −0.138553 | − | 0.990355i | \(-0.544245\pi\) | ||||
−0.138553 | + | 0.990355i | \(0.544245\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.09177e9 | −0.152019 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.55867e10 | 0.574861 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.64947e10 | −0.603921 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.36377e10 | −0.495687 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.53209e9 | 0.199617 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.63827e10 | −0.586867 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.97731e10 | −0.703204 | −0.351602 | − | 0.936149i | \(-0.614363\pi\) | ||||
−0.351602 | + | 0.936149i | \(0.614363\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.05839e9 | −0.0373691 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.81294e10 | 0.986037 | 0.493018 | − | 0.870019i | \(-0.335894\pi\) | ||||
0.493018 | + | 0.870019i | \(0.335894\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.70504e9 | −0.163745 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.05890e9 | 0.209352 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.63337e8 | 0.0330482 | 0.0165241 | − | 0.999863i | \(-0.494740\pi\) | ||||
0.0165241 | + | 0.999863i | \(0.494740\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.28224e10 | 0.436747 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.76963e9 | 0.127485 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.20434e10 | −1.41176 | −0.705879 | − | 0.708332i | \(-0.749448\pi\) | ||||
−0.705879 | + | 0.708332i | \(0.749448\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.02076e9 | 0.267417 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.08926e9 | 0.201583 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.84905e8 | −0.00607800 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.87955e10 | 0.939869 | 0.469934 | − | 0.882701i | \(-0.344278\pi\) | ||||
0.469934 | + | 0.882701i | \(0.344278\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.93349e10 | 0.626642 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.83219e9 | −0.316424 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.54828e10 | −1.13393 | −0.566963 | − | 0.823743i | \(-0.691882\pi\) | ||||
−0.566963 | + | 0.823743i | \(0.691882\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.60731e9 | −0.209674 |
(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 | 336.8.a.j.1.1 | 1 | ||
4.3 | odd | 2 | 84.8.a.a.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 252.8.a.a.1.1 | 1 | |||
28.3 | even | 6 | 588.8.i.c.373.1 | 2 | |||
28.11 | odd | 6 | 588.8.i.f.373.1 | 2 | |||
28.19 | even | 6 | 588.8.i.c.361.1 | 2 | |||
28.23 | odd | 6 | 588.8.i.f.361.1 | 2 | |||
28.27 | even | 2 | 588.8.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.8.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
252.8.a.a.1.1 | 1 | 12.11 | even | 2 | |||
336.8.a.j.1.1 | 1 | 1.1 | even | 1 | trivial | ||
588.8.a.c.1.1 | 1 | 28.27 | even | 2 | |||
588.8.i.c.361.1 | 2 | 28.19 | even | 6 | |||
588.8.i.c.373.1 | 2 | 28.3 | even | 6 | |||
588.8.i.f.361.1 | 2 | 28.23 | odd | 6 | |||
588.8.i.f.373.1 | 2 | 28.11 | odd | 6 |