Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,22,Mod(1,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(134.149125258\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 797544 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 12) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(893.553\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 59049.0 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.13060e7 | −0.517754 | −0.258877 | − | 0.965910i | \(-0.583352\pi\) | ||||
−0.258877 | + | 0.965910i | \(0.583352\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.09970e8 | 1.08378 | 0.541888 | − | 0.840451i | \(-0.317710\pi\) | ||||
0.541888 | + | 0.840451i | \(0.317710\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.57516e10 | 0.648088 | 0.324044 | − | 0.946042i | \(-0.394957\pi\) | ||||
0.324044 | + | 0.946042i | \(0.394957\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.33461e11 | −0.469687 | −0.234844 | − | 0.972033i | \(-0.575458\pi\) | ||||
−0.234844 | + | 0.972033i | \(0.575458\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.67607e11 | −0.298925 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −9.51155e12 | −1.14429 | −0.572147 | − | 0.820151i | \(-0.693889\pi\) | ||||
−0.572147 | + | 0.820151i | \(0.693889\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.41689e13 | −0.530179 | −0.265090 | − | 0.964224i | \(-0.585402\pi\) | ||||
−0.265090 | + | 0.964224i | \(0.585402\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.78279e13 | 0.625719 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.44892e14 | −0.729293 | −0.364646 | − | 0.931146i | \(-0.618810\pi\) | ||||
−0.364646 | + | 0.931146i | \(0.618810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.49012e14 | −0.731931 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.05891e14 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.75961e15 | 0.776669 | 0.388335 | − | 0.921518i | \(-0.373050\pi\) | ||||
0.388335 | + | 0.921518i | \(0.373050\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.79660e15 | −0.393690 | −0.196845 | − | 0.980435i | \(-0.563070\pi\) | ||||
−0.196845 | + | 0.980435i | \(0.563070\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.29208e15 | 0.374174 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.15751e15 | −0.561130 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.36600e16 | 1.83456 | 0.917281 | − | 0.398240i | \(-0.130379\pi\) | ||||
0.917281 | + | 0.398240i | \(0.130379\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.37856e16 | −0.271174 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.45090e16 | 0.750568 | 0.375284 | − | 0.926910i | \(-0.377545\pi\) | ||||
0.375284 | + | 0.926910i | \(0.377545\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.20122e17 | −0.847624 | −0.423812 | − | 0.905750i | \(-0.639308\pi\) | ||||
−0.423812 | + | 0.905750i | \(0.639308\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.94215e16 | −0.172585 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.12446e17 | −1.69840 | −0.849201 | − | 0.528070i | \(-0.822916\pi\) | ||||
−0.849201 | + | 0.528070i | \(0.822916\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.75063e16 | 0.174572 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.61648e17 | −0.660659 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.70894e17 | −0.291308 | −0.145654 | − | 0.989336i | \(-0.546529\pi\) | ||||
−0.145654 | + | 0.989336i | \(0.546529\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.30327e17 | −0.335550 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.36658e17 | −0.306099 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.74196e18 | 1.20785 | 0.603923 | − | 0.797043i | \(-0.293604\pi\) | ||||
0.603923 | + | 0.797043i | \(0.293604\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.07022e18 | −1.44851 | −0.724256 | − | 0.689532i | \(-0.757816\pi\) | ||||
−0.724256 | + | 0.689532i | \(0.757816\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.82419e18 | 0.361259 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.63950e18 | 0.243182 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.31777e17 | −0.0155340 | −0.00776702 | − | 0.999970i | \(-0.502472\pi\) | ||||
−0.00776702 | + | 0.999970i | \(0.502472\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.55572e18 | −0.421057 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.36832e19 | 0.863430 | 0.431715 | − | 0.902010i | \(-0.357909\pi\) | ||||
0.431715 | + | 0.902010i | \(0.357909\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.16445e19 | −0.589466 | −0.294733 | − | 0.955580i | \(-0.595231\pi\) | ||||
−0.294733 | + | 0.955580i | \(0.595231\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.06088e19 | −0.422580 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.51572e19 | 0.702383 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.92132e19 | −0.347133 | −0.173566 | − | 0.984822i | \(-0.555529\pi\) | ||||
−0.173566 | + | 0.984822i | \(0.555529\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.33727e20 | −0.946017 | −0.473008 | − | 0.881058i | \(-0.656832\pi\) | ||||
−0.473008 | + | 0.881058i | \(0.656832\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.07537e20 | 0.592463 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.03903e20 | 0.448410 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.98227e20 | 1.69368 | 0.846842 | − | 0.531845i | \(-0.178501\pi\) | ||||
0.846842 | + | 0.531845i | \(0.178501\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.89096e20 | −0.509036 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.06088e20 | −0.227297 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.60193e20 | 0.274502 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.53695e20 | −0.900061 | −0.450031 | − | 0.893013i | \(-0.648587\pi\) | ||||
−0.450031 | + | 0.893013i | \(0.648587\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.94394e20 | 0.216029 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.51751e20 | −0.587093 | −0.293547 | − | 0.955945i | \(-0.594836\pi\) | ||||
−0.293547 | + | 0.955945i | \(0.594836\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.29509e21 | 0.949531 | 0.474765 | − | 0.880112i | \(-0.342533\pi\) | ||||
0.474765 | + | 0.880112i | \(0.342533\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.40742e20 | −0.323968 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.07189e21 | −1.50965 | −0.754825 | − | 0.655927i | \(-0.772278\pi\) | ||||
−0.754825 | + | 0.655927i | \(0.772278\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.99895e21 | −1.21337 | −0.606683 | − | 0.794944i | \(-0.707500\pi\) | ||||
−0.606683 | + | 0.794944i | \(0.707500\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.16857e21 | 1.05919 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.29863e21 | 0.359884 | 0.179942 | − | 0.983677i | \(-0.442409\pi\) | ||||
0.179942 | + | 0.983677i | \(0.442409\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.63815e21 | 0.377594 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.14028e20 | −0.156562 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.70408e21 | −1.24016 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.29201e21 | −0.579982 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.80919e21 | 0.433340 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.33704e21 | 0.896714 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.95827e22 | −1.59197 | −0.795984 | − | 0.605318i | \(-0.793046\pi\) | ||||
−0.795984 | + | 0.605318i | \(0.793046\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.09307e21 | −0.489376 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.35956e22 | −1.97212 | −0.986062 | − | 0.166381i | \(-0.946792\pi\) | ||||
−0.986062 | + | 0.166381i | \(0.946792\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.14764e22 | −0.574596 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.32780e21 | −0.0996418 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.74398e22 | 1.37331 | 0.686653 | − | 0.726985i | \(-0.259079\pi\) | ||||
0.686653 | + | 0.726985i | \(0.259079\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.10058e22 | 1.60681 | 0.803405 | − | 0.595433i | \(-0.203020\pi\) | ||||
0.803405 | + | 0.595433i | \(0.203020\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.61643e22 | −0.980572 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.30158e22 | −0.304399 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.98941e22 | −0.402124 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.75765e21 | 0.100789 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.22264e22 | −0.641399 | −0.320699 | − | 0.947181i | \(-0.603918\pi\) | ||||
−0.320699 | + | 0.947181i | \(0.603918\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00887e22 | −0.133223 | −0.0666114 | − | 0.997779i | \(-0.521219\pi\) | ||||
−0.0666114 | + | 0.997779i | \(0.521219\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.31647e22 | −0.381432 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.03124e22 | 0.203835 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.38867e23 | −1.21802 | −0.609009 | − | 0.793163i | \(-0.708433\pi\) | ||||
−0.609009 | + | 0.793163i | \(0.708433\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.19009e22 | −0.168187 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.17358e23 | −0.790390 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.13956e23 | −1.26577 | −0.632885 | − | 0.774246i | \(-0.718129\pi\) | ||||
−0.632885 | + | 0.774246i | \(0.718129\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.72202e22 | −0.193730 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.67329e23 | −1.68474 | −0.842368 | − | 0.538902i | \(-0.818839\pi\) | ||||
−0.842368 | + | 0.538902i | \(0.818839\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.92561e23 | −0.779394 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.94038e22 | −0.176726 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.45906e23 | −1.09515 | −0.547576 | − | 0.836756i | \(-0.684449\pi\) | ||||
−0.547576 | + | 0.836756i | \(0.684449\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.82689e23 | −0.793250 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.80008e23 | 0.697350 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.89936e23 | −0.420388 | −0.210194 | − | 0.977660i | \(-0.567410\pi\) | ||||
−0.210194 | + | 0.977660i | \(0.567410\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.45122e23 | 1.46758 | 0.733791 | − | 0.679376i | \(-0.237749\pi\) | ||||
0.733791 | + | 0.679376i | \(0.237749\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.76538e23 | −0.836298 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.06679e23 | −0.949852 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.30284e23 | −0.741604 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.66766e23 | 0.208573 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.67578e23 | 0.859552 | 0.429776 | − | 0.902935i | \(-0.358592\pi\) | ||||
0.429776 | + | 0.902935i | \(0.358592\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.52907e23 | −0.755770 | −0.377885 | − | 0.925852i | \(-0.623349\pi\) | ||||
−0.377885 | + | 0.925852i | \(0.623349\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.55860e23 | 0.140401 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.80684e24 | −1.46226 | −0.731130 | − | 0.682238i | \(-0.761007\pi\) | ||||
−0.731130 | + | 0.682238i | \(0.761007\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.86235e23 | −0.281121 | −0.140561 | − | 0.990072i | \(-0.544891\pi\) | ||||
−0.140561 | + | 0.990072i | \(0.544891\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.36862e22 | −0.00896858 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.42523e24 | 0.841736 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.29338e23 | −0.388609 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.05207e23 | −0.243098 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.89938e23 | −0.343603 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.97752e23 | −0.0778315 | −0.0389158 | − | 0.999242i | \(-0.512390\pi\) | ||||
−0.0389158 | + | 0.999242i | \(0.512390\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.39847e24 | 0.498502 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.35810e24 | 0.438860 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.45520e24 | −0.426672 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.27809e24 | −0.340328 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.22058e24 | 0.537461 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.85195e24 | −0.848164 | −0.424082 | − | 0.905624i | \(-0.639403\pi\) | ||||
−0.424082 | + | 0.905624i | \(0.639403\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.21693e24 | −0.243977 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.39534e24 | 0.437619 | 0.218809 | − | 0.975768i | \(-0.429783\pi\) | ||||
0.218809 | + | 0.975768i | \(0.429783\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.70738e24 | 0.950964 | 0.475482 | − | 0.879726i | \(-0.342274\pi\) | ||||
0.475482 | + | 0.879726i | \(0.342274\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.66648e24 | 0.405521 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.29921e25 | 1.80486 | 0.902430 | − | 0.430836i | \(-0.141781\pi\) | ||||
0.902430 | + | 0.430836i | \(0.141781\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.92431e24 | 0.879354 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.72501e24 | −0.200417 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.61680e25 | −1.71980 | −0.859901 | − | 0.510460i | \(-0.829475\pi\) | ||||
−0.859901 | + | 0.510460i | \(0.829475\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.12483e24 | 0.304542 | 0.152271 | − | 0.988339i | \(-0.451341\pi\) | ||||
0.152271 | + | 0.988339i | \(0.451341\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.17898e23 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.10241e24 | −0.0903852 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.30788e24 | 0.249019 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.89644e24 | −0.546183 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.13803e25 | 0.723736 | 0.361868 | − | 0.932229i | \(-0.382139\pi\) | ||||
0.361868 | + | 0.932229i | \(0.382139\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.07796e24 | −0.472646 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.34998e24 | 0.342059 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.24576e25 | 0.618211 | 0.309105 | − | 0.951028i | \(-0.399970\pi\) | ||||
0.309105 | + | 0.951028i | \(0.399970\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.34630e25 | 1.98826 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.13536e24 | 0.258890 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.40375e24 | −0.132563 | −0.0662814 | − | 0.997801i | \(-0.521114\pi\) | ||||
−0.0662814 | + | 0.997801i | \(0.521114\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.19332e24 | 0.150826 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.94198e25 | 0.977848 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.28652e25 | 0.395383 | 0.197691 | − | 0.980264i | \(-0.436656\pi\) | ||||
0.197691 | + | 0.980264i | \(0.436656\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.50882e25 | 1.28199 | 0.640996 | − | 0.767545i | \(-0.278522\pi\) | ||||
0.640996 | + | 0.767545i | \(0.278522\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.11660e25 | −0.293892 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.94580e25 | −0.474356 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.61059e25 | 1.04164 | 0.520821 | − | 0.853666i | \(-0.325626\pi\) | ||||
0.520821 | + | 0.853666i | \(0.325626\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.26437e24 | −0.131230 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.36154e25 | 1.04201 | 0.521006 | − | 0.853553i | \(-0.325557\pi\) | ||||
0.521006 | + | 0.853553i | \(0.325557\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.70275e25 | −1.02879 | −0.514395 | − | 0.857553i | \(-0.671983\pi\) | ||||
−0.514395 | + | 0.857553i | \(0.671983\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.45925e24 | 0.158484 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.22504e25 | 0.813448 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.13777e25 | 0.309410 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.86000e25 | −0.519651 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.56248e25 | −0.321033 | −0.160517 | − | 0.987033i | \(-0.551316\pi\) | ||||
−0.160517 | + | 0.987033i | \(0.551316\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.36125e25 | −0.625367 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.14788e25 | 0.124725 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.38266e25 | 0.342540 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.72951e25 | −0.918635 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.84852e25 | −0.338958 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.12417e25 | 0.749972 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.95148e26 | −1.49766 | −0.748828 | − | 0.662765i | \(-0.769383\pi\) | ||||
−0.748828 | + | 0.662765i | \(0.769383\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.64737e25 | 0.548212 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.09220e26 | 0.731677 | 0.365838 | − | 0.930678i | \(-0.380782\pi\) | ||||
0.365838 | + | 0.930678i | \(0.380782\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.63701e25 | −0.603569 | −0.301784 | − | 0.953376i | \(-0.597582\pi\) | ||||
−0.301784 | + | 0.953376i | \(0.597582\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.19303e25 | −0.187043 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.07372e26 | −1.68477 | −0.842387 | − | 0.538874i | \(-0.818850\pi\) | ||||
−0.842387 | + | 0.538874i | \(0.818850\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.81008e25 | 0.503350 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.81392e26 | −0.871596 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.34768e26 | 0.606681 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.14806e25 | 0.343779 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.77085e26 | −0.700537 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.96063e26 | −1.84069 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.07487e25 | −0.211516 | −0.105758 | − | 0.994392i | \(-0.533727\pi\) | ||||
−0.105758 | + | 0.994392i | \(0.533727\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.87101e26 | 0.611521 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.62046e24 | 0.00804281 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.45000e26 | −0.418075 | −0.209037 | − | 0.977908i | \(-0.567033\pi\) | ||||
−0.209037 | + | 0.977908i | \(0.567033\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.66829e25 | 0.207779 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.00164e26 | −0.255146 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.73428e26 | −0.894580 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.67309e25 | 0.218004 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.56465e26 | −0.543961 | −0.271981 | − | 0.962303i | \(-0.587679\pi\) | ||||
−0.271981 | + | 0.962303i | \(0.587679\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.11631e26 | 0.222903 | 0.111452 | − | 0.993770i | \(-0.464450\pi\) | ||||
0.111452 | + | 0.993770i | \(0.464450\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.80675e25 | −0.0903914 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.82297e26 | 1.74024 | 0.870118 | − | 0.492843i | \(-0.164042\pi\) | ||||
0.870118 | + | 0.492843i | \(0.164042\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.67762e26 | −0.447044 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.54918e26 | −0.716006 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.96503e26 | −0.736937 | −0.368468 | − | 0.929640i | \(-0.620118\pi\) | ||||
−0.368468 | + | 0.929640i | \(0.620118\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.13452e26 | −0.718910 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.53439e26 | −0.334852 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.44713e26 | 0.305198 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.07854e26 | 0.362536 | 0.181268 | − | 0.983434i | \(-0.441980\pi\) | ||||
0.181268 | + | 0.983434i | \(0.441980\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.24929e26 | 0.250189 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.00413e26 | −0.315713 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.47938e26 | 0.246264 | 0.123132 | − | 0.992390i | \(-0.460706\pi\) | ||||
0.123132 | + | 0.992390i | \(0.460706\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.51343e26 | 0.517718 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.10799e26 | −0.364792 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.02616e26 | −0.170201 | −0.0851005 | − | 0.996372i | \(-0.527121\pi\) | ||||
−0.0851005 | + | 0.996372i | \(0.527121\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.15634e27 | −0.919123 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.73346e25 | −0.0280882 | −0.0140441 | − | 0.999901i | \(-0.504471\pi\) | ||||
−0.0140441 | + | 0.999901i | \(0.504471\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.10546e26 | −0.363662 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.18839e26 | −0.282541 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.25917e27 | 0.804664 | 0.402332 | − | 0.915494i | \(-0.368200\pi\) | ||||
0.402332 | + | 0.915494i | \(0.368200\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.37815e27 | 0.834526 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.98379e27 | −1.13861 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.30285e26 | 0.179729 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.27047e27 | −1.68776 | −0.843878 | − | 0.536536i | \(-0.819733\pi\) | ||||
−0.843878 | + | 0.536536i | \(0.819733\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.77669e26 | −0.331743 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.91653e27 | 1.35472 | 0.677362 | − | 0.735650i | \(-0.263123\pi\) | ||||
0.677362 | + | 0.735650i | \(0.263123\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.19437e26 | 0.184911 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.37454e26 | −0.0575282 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.99163e27 | 1.18896 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.31079e27 | 0.494808 | 0.247404 | − | 0.968912i | \(-0.420423\pi\) | ||||
0.247404 | + | 0.968912i | \(0.420423\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.21078e27 | 0.792879 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.84084e27 | 1.30903 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.51191e27 | 0.489804 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.01184e27 | 0.927692 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.30721e27 | 1.26168 | 0.630840 | − | 0.775913i | \(-0.282710\pi\) | ||||
0.630840 | + | 0.775913i | \(0.282710\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00292e27 | 0.558087 | 0.279044 | − | 0.960278i | \(-0.409983\pi\) | ||||
0.279044 | + | 0.960278i | \(0.409983\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.13547e27 | −0.566134 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.31965e27 | 0.837544 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.53664e27 | −1.56986 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.68571e26 | −0.175745 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.73790e26 | −0.146728 | −0.0733640 | − | 0.997305i | \(-0.523373\pi\) | ||||
−0.0733640 | + | 0.997305i | \(0.523373\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.69651e27 | 1.18164 | 0.590821 | − | 0.806802i | \(-0.298804\pi\) | ||||
0.590821 | + | 0.806802i | \(0.298804\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.17472e27 | −0.232166 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.05296e27 | 0.386656 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.20501e27 | −0.216328 | −0.108164 | − | 0.994133i | \(-0.534497\pi\) | ||||
−0.108164 | + | 0.994133i | \(0.534497\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.39984e26 | 0.0581906 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.12315e27 | 1.48904 | 0.744519 | − | 0.667602i | \(-0.232679\pi\) | ||||
0.744519 | + | 0.667602i | \(0.232679\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.63295e27 | −0.876911 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.49343e27 | −0.370312 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.91421e27 | −0.696414 | −0.348207 | − | 0.937418i | \(-0.613209\pi\) | ||||
−0.348207 | + | 0.937418i | \(0.613209\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.59648e27 | 0.486434 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.95730e26 | −0.0769162 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.13792e27 | 0.263555 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.25031e27 | 0.500380 | 0.250190 | − | 0.968197i | \(-0.419507\pi\) | ||||
0.250190 | + | 0.968197i | \(0.419507\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.95834e27 | −0.220220 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.47146e27 | −0.158084 | −0.0790421 | − | 0.996871i | \(-0.525186\pi\) | ||||
−0.0790421 | + | 0.996871i | \(0.525186\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.91401e27 | −0.196491 | −0.0982456 | − | 0.995162i | \(-0.531323\pi\) | ||||
−0.0982456 | + | 0.995162i | \(0.531323\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.19943e27 | 0.117684 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.92082e28 | 1.80161 | 0.900804 | − | 0.434225i | \(-0.142978\pi\) | ||||
0.900804 | + | 0.434225i | \(0.142978\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.87732e26 | −0.0168354 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.19998e27 | −0.703223 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.69698e27 | −0.549335 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.94511e27 | 0.388055 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.29323e27 | −0.0971028 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.32440e28 | 0.951692 | 0.475846 | − | 0.879529i | \(-0.342142\pi\) | ||||
0.475846 | + | 0.879529i | \(0.342142\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.25275e28 | −0.861671 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.92988e27 | −0.456332 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.39067e27 | 0.466010 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.28732e28 | −1.38125 | −0.690625 | − | 0.723213i | \(-0.742664\pi\) | ||||
−0.690625 | + | 0.723213i | \(0.742664\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.26339e28 | −0.730792 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.73094e28 | −0.959238 | −0.479619 | − | 0.877477i | \(-0.659225\pi\) | ||||
−0.479619 | + | 0.877477i | \(0.659225\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.67366e28 | −0.888739 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.19781e27 | −0.111850 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.91827e28 | 0.935766 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.15871e28 | −1.00958 | −0.504788 | − | 0.863243i | \(-0.668429\pi\) | ||||
−0.504788 | + | 0.863243i | \(0.668429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.16904e28 | −0.972683 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.63654e27 | 0.0703821 | 0.0351911 | − | 0.999381i | \(-0.488796\pi\) | ||||
0.0351911 | + | 0.999381i | \(0.488796\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.36868e27 | 0.303970 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.13705e28 | −0.449983 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.18700e28 | 0.830447 | 0.415223 | − | 0.909720i | \(-0.363703\pi\) | ||||
0.415223 | + | 0.909720i | \(0.363703\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.75314e28 | −0.638849 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.91725e27 | −0.102033 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.46423e28 | −0.491623 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.41448e28 | −1.10071 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.04254e28 | −0.632286 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.08574e28 | 1.80933 | 0.904664 | − | 0.426125i | \(-0.140122\pi\) | ||||
0.904664 | + | 0.426125i | \(0.140122\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.60789e27 | −0.245827 | −0.122913 | − | 0.992417i | \(-0.539224\pi\) | ||||
−0.122913 | + | 0.992417i | \(0.539224\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.66925e28 | −0.457983 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.70885e28 | 0.450498 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.84779e28 | −0.468132 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.65342e28 | 0.402615 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.50603e28 | −0.352532 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.47307e28 | 0.781627 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.12155e28 | −0.242711 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.43613e27 | 0.113138 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.28529e28 | −1.05803 | −0.529015 | − | 0.848613i | \(-0.677438\pi\) | ||||
−0.529015 | + | 0.848613i | \(0.677438\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.39987e28 | 0.847308 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.39061e28 | 0.628225 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.42072e27 | 0.0788181 | 0.0394091 | − | 0.999223i | \(-0.487452\pi\) | ||||
0.0394091 | + | 0.999223i | \(0.487452\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.81391e28 | −0.482837 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.49316e28 | −0.411774 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.36619e28 | −0.376214 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.58238e28 | −0.548397 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.85988e28 | −0.568976 | −0.284488 | − | 0.958680i | \(-0.591824\pi\) | ||||
−0.284488 | + | 0.958680i | \(0.591824\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.80437e28 | 0.398118 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.13128e28 | −0.428165 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.50679e28 | 0.593648 | 0.296824 | − | 0.954932i | \(-0.404072\pi\) | ||||
0.296824 | + | 0.954932i | \(0.404072\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.46823e28 | −0.186331 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.84735e27 | 0.120420 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.08302e29 | 1.27632 | 0.638160 | − | 0.769904i | \(-0.279696\pi\) | ||||
0.638160 | + | 0.769904i | \(0.279696\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.40701e29 | −1.59815 | −0.799076 | − | 0.601231i | \(-0.794677\pi\) | ||||
−0.799076 | + | 0.601231i | \(0.794677\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.53247e28 | 0.496263 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.05690e28 | 0.533792 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.38612e28 | 0.344633 | 0.172316 | − | 0.985042i | \(-0.444875\pi\) | ||||
0.172316 | + | 0.985042i | \(0.444875\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.44584e28 | −0.436344 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.08315e29 | −1.02527 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.06779e28 | −0.188794 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.20338e27 | 0.0810608 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.58705e28 | 0.559746 | 0.279873 | − | 0.960037i | \(-0.409708\pi\) | ||||
0.279873 | + | 0.960037i | \(0.409708\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.54559e28 | 0.208726 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.06692e29 | −0.844237 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.36861e29 | 1.80892 | 0.904459 | − | 0.426561i | \(-0.140275\pi\) | ||||
0.904459 | + | 0.426561i | \(0.140275\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.71022e28 | 0.642097 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.28068e28 | −0.162306 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.61602e29 | 1.11037 | 0.555183 | − | 0.831728i | \(-0.312648\pi\) | ||||
0.555183 | + | 0.831728i | \(0.312648\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.80624e29 | 1.19837 | 0.599187 | − | 0.800609i | \(-0.295490\pi\) | ||||
0.599187 | + | 0.800609i | \(0.295490\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.08156e26 | −0.00517801 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.85254e28 | 0.300288 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.81082e29 | −1.08242 | −0.541208 | − | 0.840888i | \(-0.682033\pi\) | ||||
−0.541208 | + | 0.840888i | \(0.682033\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.41583e28 | 0.485977 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.42982e29 | 0.797717 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.75920e27 | 0.0418295 | 0.0209147 | − | 0.999781i | \(-0.493342\pi\) | ||||
0.0209147 | + | 0.999781i | \(0.493342\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.30667e28 | −0.224364 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.97354e29 | 0.993692 | 0.496846 | − | 0.867839i | \(-0.334491\pi\) | ||||
0.496846 | + | 0.867839i | \(0.334491\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.26065e29 | 1.10022 | 0.550112 | − | 0.835091i | \(-0.314585\pi\) | ||||
0.550112 | + | 0.835091i | \(0.314585\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.98320e28 | −0.140352 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.03549e29 | 1.83557 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.08574e28 | 0.267654 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.66451e28 | −0.198379 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.10390e29 | −2.09928 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.50393e28 | −0.258742 | −0.129371 | − | 0.991596i | \(-0.541296\pi\) | ||||
−0.129371 | + | 0.991596i | \(0.541296\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.16771e28 | −0.0449360 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.21402e29 | 0.824248 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.27639e28 | −0.0819941 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.25781e28 | 0.287810 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.44790e29 | −0.488349 | −0.244175 | − | 0.969731i | \(-0.578517\pi\) | ||||
−0.244175 | + | 0.969731i | \(0.578517\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.95085e29 | 0.636809 | 0.318404 | − | 0.947955i | \(-0.396853\pi\) | ||||
0.318404 | + | 0.947955i | \(0.396853\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.01942e28 | 0.253376 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.01626e29 | −0.616667 | −0.308334 | − | 0.951278i | \(-0.599771\pi\) | ||||
−0.308334 | + | 0.951278i | \(0.599771\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.64372e29 | 0.782791 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.59279e28 | −0.246339 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.81684e29 | 0.781941 | 0.390971 | − | 0.920403i | \(-0.372139\pi\) | ||||
0.390971 | + | 0.920403i | \(0.372139\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.79832e29 | 1.02107 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.54699e28 | −0.196489 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.54764e29 | −1.39898 | −0.699489 | − | 0.714643i | \(-0.746589\pi\) | ||||
−0.699489 | + | 0.714643i | \(0.746589\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.76779e29 | −1.65322 | −0.826612 | − | 0.562772i | \(-0.809735\pi\) | ||||
−0.826612 | + | 0.562772i | \(0.809735\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.31123e29 | 0.310303 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.29752e29 | 0.297499 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.54953e29 | −0.566419 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.27454e29 | −0.489688 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.49927e29 | −0.938763 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.48648e29 | 1.51398 | 0.756989 | − | 0.653428i | \(-0.226670\pi\) | ||||
0.756989 | + | 0.653428i | \(0.226670\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.18584e28 | −0.140860 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.29954e28 | −0.138712 | −0.0693561 | − | 0.997592i | \(-0.522094\pi\) | ||||
−0.0693561 | + | 0.997592i | \(0.522094\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.29474e29 | −0.975465 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.41442e29 | 0.252659 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.79117e29 | −1.17632 | −0.588162 | − | 0.808743i | \(-0.700148\pi\) | ||||
−0.588162 | + | 0.808743i | \(0.700148\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.23294e29 | −0.711035 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.37015e29 | 0.549039 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.65892e28 | 0.136824 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.63963e28 | 0.132427 | 0.0662134 | − | 0.997805i | \(-0.478908\pi\) | ||||
0.0662134 | + | 0.997805i | \(0.478908\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.57453e29 | 0.234128 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.76671e29 | −0.831932 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.13581e29 | −0.858871 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.67173e29 | 1.04204 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.58498e29 | −0.736178 | −0.368089 | − | 0.929791i | \(-0.619988\pi\) | ||||
−0.368089 | + | 0.929791i | \(0.619988\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.60302e29 | −0.972647 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.08873e29 | 0.507695 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.27899e29 | −0.636278 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.18180e30 | −1.38279 | −0.691397 | − | 0.722475i | \(-0.743004\pi\) | ||||
−0.691397 | + | 0.722475i | \(0.743004\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.01860e29 | −0.115711 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.60313e29 | 0.287115 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.47157e29 | 0.157604 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.54705e29 | −0.992929 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.23046e29 | −0.831324 | −0.415662 | − | 0.909519i | \(-0.636450\pi\) | ||||
−0.415662 | + | 0.909519i | \(0.636450\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.04898e30 | 1.02908 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.84518e29 | 0.175827 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.14123e29 | −0.568468 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.96290e30 | 1.76518 | 0.882588 | − | 0.470148i | \(-0.155799\pi\) | ||||
0.882588 | + | 0.470148i | \(0.155799\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.14254e30 | 0.969931 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.34287e29 | −0.523232 | −0.261616 | − | 0.965172i | \(-0.584255\pi\) | ||||
−0.261616 | + | 0.965172i | \(0.584255\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.50959e28 | −0.0521839 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.29219e28 | −0.0100674 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.33383e30 | 1.01003 | 0.505013 | − | 0.863112i | \(-0.331488\pi\) | ||||
0.505013 | + | 0.863112i | \(0.331488\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.95327e29 | 0.143771 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.74142e29 | −0.339255 | −0.169627 | − | 0.985508i | \(-0.554256\pi\) | ||||
−0.169627 | + | 0.985508i | \(0.554256\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.77411e29 | 0.332087 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.66277e29 | −0.315339 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.48814e30 | −1.63612 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.47957e30 | −0.946056 | −0.473028 | − | 0.881047i | \(-0.656839\pi\) | ||||
−0.473028 | + | 0.881047i | \(0.656839\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.71996e29 | 0.417849 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.14063e29 | 0.0689766 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.39255e29 | 0.258351 | 0.129175 | − | 0.991622i | \(-0.458767\pi\) | ||||
0.129175 | + | 0.991622i | \(0.458767\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.76995e29 | −0.272882 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.00062e30 | −0.556838 | −0.278419 | − | 0.960460i | \(-0.589810\pi\) | ||||
−0.278419 | + | 0.960460i | \(0.589810\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.42906e30 | −1.31502 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.74960e29 | 0.197488 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.10706e30 | −0.567310 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.87704e30 | 1.43456 | 0.717280 | − | 0.696785i | \(-0.245387\pi\) | ||||
0.717280 | + | 0.696785i | \(0.245387\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.35609e29 | 0.356924 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.54616e29 | −0.450759 | −0.225379 | − | 0.974271i | \(-0.572362\pi\) | ||||
−0.225379 | + | 0.974271i | \(0.572362\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.27036e29 | 0.288154 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.56645e30 | 1.14792 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.14021e29 | −0.397936 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.32038e30 | 0.559579 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.62287e29 | 0.149470 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.57003e30 | 0.630634 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.94377e29 | −0.310665 | −0.155332 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155332 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.00988e29 | −0.0765352 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.05185e30 | 0.390034 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.88408e30 | 0.680347 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.47611e29 | 0.0870795 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.52810e30 | −1.20845 | −0.604225 | − | 0.796814i | \(-0.706517\pi\) | ||||
−0.604225 | + | 0.796814i | \(0.706517\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.82531e30 | 1.94347 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.73721e30 | 0.564561 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.20672e30 | −0.382026 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.32685e30 | 0.409228 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.59677e29 | 0.228274 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.39629e30 | −1.28714 | −0.643572 | − | 0.765385i | \(-0.722548\pi\) | ||||
−0.643572 | + | 0.765385i | \(0.722548\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.09120e29 | 0.202302 | 0.101151 | − | 0.994871i | \(-0.467747\pi\) | ||||
0.101151 | + | 0.994871i | \(0.467747\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.66241e30 | 0.740158 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.41898e30 | 0.655357 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.70199e30 | 0.449392 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.59338e29 | −0.169679 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.18582e30 | 0.297451 | 0.148725 | − | 0.988879i | \(-0.452483\pi\) | ||||
0.148725 | + | 0.988879i | \(0.452483\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.11669e30 | 0.517559 | 0.258780 | − | 0.965936i | \(-0.416680\pi\) | ||||
0.258780 | + | 0.965936i | \(0.416680\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.14897e30 | −0.273869 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.22718e29 | −0.0517544 | −0.0258772 | − | 0.999665i | \(-0.508238\pi\) | ||||
−0.0258772 | + | 0.999665i | \(0.508238\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.55590e29 | 0.216495 | 0.108248 | − | 0.994124i | \(-0.465476\pi\) | ||||
0.108248 | + | 0.994124i | \(0.465476\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.72251e30 | 0.601392 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.27437e29 | −0.199761 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.15301e30 | 0.872279 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.69905e29 | −0.0757657 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.20883e30 | 0.840738 | 0.420369 | − | 0.907353i | \(-0.361901\pi\) | ||||
0.420369 | + | 0.907353i | \(0.361901\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.03663e30 | −0.396785 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.16593e30 | 0.601606 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.17709e30 | 0.403534 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.47640e30 | −0.628570 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.36742e30 | −0.593972 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.77490e30 | −1.33793 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.44490e30 | −0.914166 | −0.457083 | − | 0.889424i | \(-0.651106\pi\) | ||||
−0.457083 | + | 0.889424i | \(0.651106\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.58559e29 | 0.0915008 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.17339e30 | 1.30648 | 0.653242 | − | 0.757150i | \(-0.273409\pi\) | ||||
0.653242 | + | 0.757150i | \(0.273409\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.15256e30 | 0.647721 | 0.323861 | − | 0.946105i | \(-0.395019\pi\) | ||||
0.323861 | + | 0.946105i | \(0.395019\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.08533e30 | 0.469644 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.90281e30 | −1.32256 | −0.661278 | − | 0.750141i | \(-0.729986\pi\) | ||||
−0.661278 | + | 0.750141i | \(0.729986\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.91081e30 | 0.567019 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.26233e30 | 0.178638 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.62869e30 | −0.224973 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.41108e28 | 0.00729614 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.27929e30 | −0.300020 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.56272e30 | 0.971838 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.40744e30 | 0.803876 | 0.401938 | − | 0.915667i | \(-0.368337\pi\) | ||||
0.401938 | + | 0.915667i | \(0.368337\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.51312e30 | −0.185349 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.51950e31 | 1.81741 | 0.908704 | − | 0.417440i | \(-0.137073\pi\) | ||||
0.908704 | + | 0.417440i | \(0.137073\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.28784e31 | −1.50409 | −0.752046 | − | 0.659111i | \(-0.770933\pi\) | ||||
−0.752046 | + | 0.659111i | \(0.770933\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.16576e30 | −0.361056 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.05037e30 | −0.562503 | −0.281252 | − | 0.959634i | \(-0.590750\pi\) | ||||
−0.281252 | + | 0.959634i | \(0.590750\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.58614e31 | −1.72534 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.77809e29 | 0.0720098 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.67768e30 | 0.900457 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.14741e30 | 0.217657 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.99743e30 | 0.197765 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.16131e30 | −0.305767 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.52778e30 | 0.333343 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.74518e30 | −0.530374 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.42433e30 | −0.759846 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.07169e30 | 0.358838 | 0.179419 | − | 0.983773i | \(-0.442578\pi\) | ||||
0.179419 | + | 0.983773i | \(0.442578\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.27251e30 | −0.195698 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.43720e31 | −1.20941 | −0.604705 | − | 0.796450i | \(-0.706709\pi\) | ||||
−0.604705 | + | 0.796450i | \(0.706709\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.45549e30 | −0.613103 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.38773e30 | 0.432997 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.72115e31 | −2.13734 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.79023e30 | −0.290973 | −0.145487 | − | 0.989360i | \(-0.546475\pi\) | ||||
−0.145487 | + | 0.989360i | \(0.546475\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.15233e31 | −0.864672 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.52909e30 | −0.405542 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.87280e31 | −1.34277 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.51570e30 | 0.316510 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.28927e31 | −1.56867 | −0.784336 | − | 0.620337i | \(-0.786996\pi\) | ||||
−0.784336 | + | 0.620337i | \(0.786996\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.38156e30 | −0.0925543 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.44935e30 | 0.422434 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.99539e30 | 0.383968 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.72458e30 | 0.608983 | 0.304491 | − | 0.952515i | \(-0.401514\pi\) | ||||
0.304491 | + | 0.952515i | \(0.401514\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.69056e30 | −0.348471 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.55337e31 | 0.930217 | 0.465108 | − | 0.885254i | \(-0.346015\pi\) | ||||
0.465108 | + | 0.885254i | \(0.346015\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.34683e30 | −0.547384 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.88545e30 | −0.107989 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.82914e31 | 1.02464 | 0.512320 | − | 0.858794i | \(-0.328786\pi\) | ||||
0.512320 | + | 0.858794i | \(0.328786\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.05315e30 | 0.276865 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.81500e31 | −0.972704 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.25691e31 | −0.658915 | −0.329458 | − | 0.944170i | \(-0.606866\pi\) | ||||
−0.329458 | + | 0.944170i | \(0.606866\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.67823e30 | −0.445037 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.79275e30 | 0.290609 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.03251e31 | 1.48836 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.75977e31 | −0.845008 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.07110e31 | −0.503216 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.51236e30 | 0.391303 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.37160e30 | −0.151655 | −0.0758277 | − | 0.997121i | \(-0.524160\pi\) | ||||
−0.0758277 | + | 0.997121i | \(0.524160\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.95792e30 | 0.350268 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.40435e30 | 0.275850 | 0.137925 | − | 0.990443i | \(-0.455957\pi\) | ||||
0.137925 | + | 0.990443i | \(0.455957\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.13132e31 | 1.74142 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.81135e30 | 0.198481 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.82208e31 | 0.735657 | 0.367829 | − | 0.929894i | \(-0.380101\pi\) | ||||
0.367829 | + | 0.929894i | \(0.380101\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.77770e31 | 1.09766 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.04567e31 | −0.404455 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.86098e30 | 0.108319 | 0.0541594 | − | 0.998532i | \(-0.482752\pi\) | ||||
0.0541594 | + | 0.998532i | \(0.482752\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.04281e31 | 0.757091 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.92920e31 | −1.06272 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.74047e31 | 0.618166 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.44835e31 | −1.19905 | −0.599526 | − | 0.800356i | \(-0.704644\pi\) | ||||
−0.599526 | + | 0.800356i | \(0.704644\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.58715e30 | −0.122119 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.36676e30 | 0.145552 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.59375e31 | −0.520142 | −0.260071 | − | 0.965589i | \(-0.583746\pi\) | ||||
−0.260071 | + | 0.965589i | \(0.583746\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.10481e31 | 0.353062 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 48.22.a.i.1.1 | 2 | ||
4.3 | odd | 2 | 12.22.a.b.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 36.22.a.b.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.22.a.b.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
36.22.a.b.1.2 | 2 | 12.11 | even | 2 | |||
48.22.a.i.1.1 | 2 | 1.1 | even | 1 | trivial |