Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,26,Mod(1,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(197.998389976\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2 x^{5} - 27590779188 x^{4} + 26487255863952 x^{3} + \cdots - 30\!\cdots\!08 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{4}\cdot 5^{18} \) |
Twist minimal: | no (minimal twist has level 10) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1691.05\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4096.00 | 0.707107 | ||||||||
\(3\) | −116655. | −0.126733 | −0.0633664 | − | 0.997990i | \(-0.520184\pi\) | ||||
−0.0633664 | + | 0.997990i | \(0.520184\pi\) | |||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.77821e8 | −0.0896137 | ||||||||
\(7\) | 1.34370e10 | 0.366926 | 0.183463 | − | 0.983027i | \(-0.441269\pi\) | ||||
0.183463 | + | 0.983027i | \(0.441269\pi\) | |||||||
\(8\) | 6.87195e10 | 0.353553 | ||||||||
\(9\) | −8.33680e11 | −0.983939 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.67882e11 | 0.0449498 | 0.0224749 | − | 0.999747i | \(-0.492845\pi\) | ||||
0.0224749 | + | 0.999747i | \(0.492845\pi\) | |||||||
\(12\) | −1.95715e12 | −0.0633664 | ||||||||
\(13\) | 9.38695e13 | 1.11746 | 0.558731 | − | 0.829349i | \(-0.311289\pi\) | ||||
0.558731 | + | 0.829349i | \(0.311289\pi\) | |||||||
\(14\) | 5.50381e13 | 0.259456 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | −6.14184e14 | −0.255674 | −0.127837 | − | 0.991795i | \(-0.540803\pi\) | ||||
−0.127837 | + | 0.991795i | \(0.540803\pi\) | |||||||
\(18\) | −3.41475e15 | −0.695750 | ||||||||
\(19\) | −1.66661e16 | −1.72748 | −0.863741 | − | 0.503936i | \(-0.831885\pi\) | ||||
−0.863741 | + | 0.503936i | \(0.831885\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.56750e15 | −0.0465016 | ||||||||
\(22\) | 1.91644e15 | 0.0317843 | ||||||||
\(23\) | 1.60865e17 | 1.53060 | 0.765301 | − | 0.643673i | \(-0.222590\pi\) | ||||
0.765301 | + | 0.643673i | \(0.222590\pi\) | |||||||
\(24\) | −8.01650e15 | −0.0448068 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.84489e17 | 0.790165 | ||||||||
\(27\) | 1.96094e17 | 0.251430 | ||||||||
\(28\) | 2.25436e17 | 0.183463 | ||||||||
\(29\) | −1.05009e18 | −0.551126 | −0.275563 | − | 0.961283i | \(-0.588864\pi\) | ||||
−0.275563 | + | 0.961283i | \(0.588864\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00725e18 | −0.685722 | −0.342861 | − | 0.939386i | \(-0.611396\pi\) | ||||
−0.342861 | + | 0.939386i | \(0.611396\pi\) | |||||||
\(32\) | 1.15292e18 | 0.176777 | ||||||||
\(33\) | −5.45810e16 | −0.00569662 | ||||||||
\(34\) | −2.51570e18 | −0.180789 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.39868e19 | −0.491969 | ||||||||
\(37\) | 3.36937e19 | 0.841449 | 0.420724 | − | 0.907189i | \(-0.361776\pi\) | ||||
0.420724 | + | 0.907189i | \(0.361776\pi\) | |||||||
\(38\) | −6.82643e19 | −1.22151 | ||||||||
\(39\) | −1.09504e19 | −0.141619 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.09874e19 | 0.352911 | 0.176455 | − | 0.984309i | \(-0.443537\pi\) | ||||
0.176455 | + | 0.984309i | \(0.443537\pi\) | |||||||
\(42\) | −6.42050e18 | −0.0328816 | ||||||||
\(43\) | −2.92822e20 | −1.11750 | −0.558751 | − | 0.829335i | \(-0.688719\pi\) | ||||
−0.558751 | + | 0.829335i | \(0.688719\pi\) | |||||||
\(44\) | 7.84976e18 | 0.0224749 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.58901e20 | 1.08230 | ||||||||
\(47\) | 9.77356e20 | 1.22696 | 0.613479 | − | 0.789711i | \(-0.289770\pi\) | ||||
0.613479 | + | 0.789711i | \(0.289770\pi\) | |||||||
\(48\) | −3.28356e19 | −0.0316832 | ||||||||
\(49\) | −1.16051e21 | −0.865365 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.16479e19 | 0.0324023 | ||||||||
\(52\) | 1.57487e21 | 0.558731 | ||||||||
\(53\) | −5.26216e21 | −1.47135 | −0.735675 | − | 0.677335i | \(-0.763135\pi\) | ||||
−0.735675 | + | 0.677335i | \(0.763135\pi\) | |||||||
\(54\) | 8.03202e20 | 0.177788 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.23387e20 | 0.129728 | ||||||||
\(57\) | 1.94419e21 | 0.218929 | ||||||||
\(58\) | −4.30117e21 | −0.389705 | ||||||||
\(59\) | 4.10935e20 | 0.0300693 | 0.0150346 | − | 0.999887i | \(-0.495214\pi\) | ||||
0.0150346 | + | 0.999887i | \(0.495214\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.44766e21 | −0.262777 | −0.131388 | − | 0.991331i | \(-0.541943\pi\) | ||||
−0.131388 | + | 0.991331i | \(0.541943\pi\) | |||||||
\(62\) | −1.23177e22 | −0.484879 | ||||||||
\(63\) | −1.12022e22 | −0.361032 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.23564e20 | −0.00402812 | ||||||||
\(67\) | −6.32396e22 | −0.944178 | −0.472089 | − | 0.881551i | \(-0.656500\pi\) | ||||
−0.472089 | + | 0.881551i | \(0.656500\pi\) | |||||||
\(68\) | −1.03043e22 | −0.127837 | ||||||||
\(69\) | −1.87657e22 | −0.193978 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.81308e22 | −0.131126 | −0.0655628 | − | 0.997848i | \(-0.520884\pi\) | ||||
−0.0655628 | + | 0.997848i | \(0.520884\pi\) | |||||||
\(72\) | −5.72901e22 | −0.347875 | ||||||||
\(73\) | 3.48574e23 | 1.78139 | 0.890694 | − | 0.454603i | \(-0.150219\pi\) | ||||
0.890694 | + | 0.454603i | \(0.150219\pi\) | |||||||
\(74\) | 1.38010e23 | 0.594994 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.79610e23 | −0.863741 | ||||||||
\(77\) | 6.28695e21 | 0.0164932 | ||||||||
\(78\) | −4.48528e22 | −0.100140 | ||||||||
\(79\) | 3.43193e23 | 0.653432 | 0.326716 | − | 0.945123i | \(-0.394058\pi\) | ||||
0.326716 | + | 0.945123i | \(0.394058\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.83492e23 | 0.952074 | ||||||||
\(82\) | 2.08844e23 | 0.249545 | ||||||||
\(83\) | −6.85739e23 | −0.704178 | −0.352089 | − | 0.935967i | \(-0.614529\pi\) | ||||
−0.352089 | + | 0.935967i | \(0.614529\pi\) | |||||||
\(84\) | −2.62984e22 | −0.0232508 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.19940e24 | −0.790194 | ||||||||
\(87\) | 1.22499e23 | 0.0698458 | ||||||||
\(88\) | 3.21526e22 | 0.0158922 | ||||||||
\(89\) | −4.29595e24 | −1.84367 | −0.921837 | − | 0.387579i | \(-0.873312\pi\) | ||||
−0.921837 | + | 0.387579i | \(0.873312\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.26133e24 | 0.410025 | ||||||||
\(92\) | 2.69886e24 | 0.765301 | ||||||||
\(93\) | 3.50812e23 | 0.0869035 | ||||||||
\(94\) | 4.00325e24 | 0.867590 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.34495e23 | −0.0224034 | ||||||||
\(97\) | 2.90151e24 | 0.424598 | 0.212299 | − | 0.977205i | \(-0.431905\pi\) | ||||
0.212299 | + | 0.977205i | \(0.431905\pi\) | |||||||
\(98\) | −4.75347e24 | −0.611906 | ||||||||
\(99\) | −3.90064e23 | −0.0442279 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.46099e24 | −0.747144 | −0.373572 | − | 0.927601i | \(-0.621867\pi\) | ||||
−0.373572 | + | 0.927601i | \(0.621867\pi\) | |||||||
\(102\) | 2.93470e23 | 0.0229119 | ||||||||
\(103\) | 1.06290e25 | 0.734562 | 0.367281 | − | 0.930110i | \(-0.380289\pi\) | ||||
0.367281 | + | 0.930110i | \(0.380289\pi\) | |||||||
\(104\) | 6.45066e24 | 0.395082 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.15538e25 | −1.04040 | ||||||||
\(107\) | −2.28121e25 | −0.979193 | −0.489597 | − | 0.871949i | \(-0.662856\pi\) | ||||
−0.489597 | + | 0.871949i | \(0.662856\pi\) | |||||||
\(108\) | 3.28991e24 | 0.125715 | ||||||||
\(109\) | −3.17871e25 | −1.08248 | −0.541240 | − | 0.840868i | \(-0.682045\pi\) | ||||
−0.541240 | + | 0.840868i | \(0.682045\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.93056e24 | −0.106639 | ||||||||
\(112\) | 3.78219e24 | 0.0917314 | ||||||||
\(113\) | −9.52597e24 | −0.206742 | −0.103371 | − | 0.994643i | \(-0.532963\pi\) | ||||
−0.103371 | + | 0.994643i | \(0.532963\pi\) | |||||||
\(114\) | 7.96340e24 | 0.154806 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.76176e25 | −0.275563 | ||||||||
\(117\) | −7.82571e25 | −1.09951 | ||||||||
\(118\) | 1.68319e24 | 0.0212622 | ||||||||
\(119\) | −8.25281e24 | −0.0938134 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.08128e26 | −0.997980 | ||||||||
\(122\) | −2.23136e25 | −0.185811 | ||||||||
\(123\) | −5.94796e24 | −0.0447254 | ||||||||
\(124\) | −5.04532e25 | −0.342861 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.58842e25 | −0.255289 | ||||||||
\(127\) | 2.95859e26 | 1.49121 | 0.745604 | − | 0.666390i | \(-0.232161\pi\) | ||||
0.745604 | + | 0.666390i | \(0.232161\pi\) | |||||||
\(128\) | 1.93428e25 | 0.0883883 | ||||||||
\(129\) | 3.41593e25 | 0.141624 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.19768e26 | −0.751749 | −0.375874 | − | 0.926671i | \(-0.622658\pi\) | ||||
−0.375874 | + | 0.926671i | \(0.622658\pi\) | |||||||
\(132\) | −9.15717e23 | −0.00284831 | ||||||||
\(133\) | −2.23943e26 | −0.633857 | ||||||||
\(134\) | −2.59029e26 | −0.667635 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.22064e25 | −0.0903945 | ||||||||
\(137\) | 3.42423e25 | 0.0669200 | 0.0334600 | − | 0.999440i | \(-0.489347\pi\) | ||||
0.0334600 | + | 0.999440i | \(0.489347\pi\) | |||||||
\(138\) | −7.68644e25 | −0.137163 | ||||||||
\(139\) | −2.79093e26 | −0.455055 | −0.227528 | − | 0.973772i | \(-0.573064\pi\) | ||||
−0.227528 | + | 0.973772i | \(0.573064\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.14014e26 | −0.155496 | ||||||||
\(142\) | −7.42638e25 | −0.0927199 | ||||||||
\(143\) | 4.39198e25 | 0.0502297 | ||||||||
\(144\) | −2.34660e26 | −0.245985 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.42776e27 | 1.25963 | ||||||||
\(147\) | 1.35380e26 | 0.109670 | ||||||||
\(148\) | 5.65287e26 | 0.420724 | ||||||||
\(149\) | 1.42906e27 | 0.977739 | 0.488870 | − | 0.872357i | \(-0.337409\pi\) | ||||
0.488870 | + | 0.872357i | \(0.337409\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.51226e27 | −1.45496 | −0.727482 | − | 0.686127i | \(-0.759310\pi\) | ||||
−0.727482 | + | 0.686127i | \(0.759310\pi\) | |||||||
\(152\) | −1.14528e27 | −0.610757 | ||||||||
\(153\) | 5.12033e26 | 0.251568 | ||||||||
\(154\) | 2.57513e25 | 0.0116625 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.83717e26 | −0.0708096 | ||||||||
\(157\) | −3.34741e27 | −1.19114 | −0.595571 | − | 0.803302i | \(-0.703074\pi\) | ||||
−0.595571 | + | 0.803302i | \(0.703074\pi\) | |||||||
\(158\) | 1.40572e27 | 0.462046 | ||||||||
\(159\) | 6.13860e26 | 0.186468 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.16154e27 | 0.561617 | ||||||||
\(162\) | 2.79958e27 | 0.673218 | ||||||||
\(163\) | −8.42668e26 | −0.187634 | −0.0938170 | − | 0.995589i | \(-0.529907\pi\) | ||||
−0.0938170 | + | 0.995589i | \(0.529907\pi\) | |||||||
\(164\) | 8.55426e26 | 0.176455 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.80879e27 | −0.497929 | ||||||||
\(167\) | −3.08789e27 | −0.507815 | −0.253907 | − | 0.967229i | \(-0.581716\pi\) | ||||
−0.253907 | + | 0.967229i | \(0.581716\pi\) | |||||||
\(168\) | −1.07718e26 | −0.0164408 | ||||||||
\(169\) | 1.75507e27 | 0.248720 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.38942e28 | 1.69974 | ||||||||
\(172\) | −4.91274e27 | −0.558751 | ||||||||
\(173\) | −9.76292e27 | −1.03277 | −0.516385 | − | 0.856357i | \(-0.672723\pi\) | ||||
−0.516385 | + | 0.856357i | \(0.672723\pi\) | |||||||
\(174\) | 5.01754e26 | 0.0493885 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.31697e26 | 0.0112375 | ||||||||
\(177\) | −4.79378e25 | −0.00381077 | ||||||||
\(178\) | −1.75962e28 | −1.30367 | ||||||||
\(179\) | −1.48035e28 | −1.02259 | −0.511294 | − | 0.859406i | \(-0.670834\pi\) | ||||
−0.511294 | + | 0.859406i | \(0.670834\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.20192e28 | 0.722591 | 0.361295 | − | 0.932451i | \(-0.382335\pi\) | ||||
0.361295 | + | 0.932451i | \(0.382335\pi\) | |||||||
\(182\) | 5.16640e27 | 0.289932 | ||||||||
\(183\) | 6.35499e26 | 0.0333025 | ||||||||
\(184\) | 1.10545e28 | 0.541150 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.43693e27 | 0.0614501 | ||||||||
\(187\) | −2.87366e26 | −0.0114925 | ||||||||
\(188\) | 1.63973e28 | 0.613479 | ||||||||
\(189\) | 2.63493e27 | 0.0922563 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.66884e27 | 0.266099 | 0.133050 | − | 0.991109i | \(-0.457523\pi\) | ||||
0.133050 | + | 0.991109i | \(0.457523\pi\) | |||||||
\(192\) | −5.50890e26 | −0.0158416 | ||||||||
\(193\) | 1.60225e28 | 0.431782 | 0.215891 | − | 0.976417i | \(-0.430734\pi\) | ||||
0.215891 | + | 0.976417i | \(0.430734\pi\) | |||||||
\(194\) | 1.18846e28 | 0.300236 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.94702e28 | −0.432683 | ||||||||
\(197\) | −6.69730e28 | −1.39660 | −0.698300 | − | 0.715805i | \(-0.746060\pi\) | ||||
−0.698300 | + | 0.715805i | \(0.746060\pi\) | |||||||
\(198\) | −1.59770e27 | −0.0312738 | ||||||||
\(199\) | 1.81836e28 | 0.334208 | 0.167104 | − | 0.985939i | \(-0.446558\pi\) | ||||
0.167104 | + | 0.985939i | \(0.446558\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.37724e27 | 0.119658 | ||||||||
\(202\) | −3.46562e28 | −0.528310 | ||||||||
\(203\) | −1.41101e28 | −0.202222 | ||||||||
\(204\) | 1.20205e27 | 0.0162012 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.35365e28 | 0.519414 | ||||||||
\(207\) | −1.34110e29 | −1.50602 | ||||||||
\(208\) | 2.64219e28 | 0.279365 | ||||||||
\(209\) | −7.79776e27 | −0.0776500 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.59042e29 | −1.40598 | −0.702992 | − | 0.711197i | \(-0.748153\pi\) | ||||
−0.702992 | + | 0.711197i | \(0.748153\pi\) | |||||||
\(212\) | −8.82844e28 | −0.735675 | ||||||||
\(213\) | 2.11506e27 | 0.0166179 | ||||||||
\(214\) | −9.34384e28 | −0.692394 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.34755e28 | 0.0888940 | ||||||||
\(217\) | −4.04085e28 | −0.251609 | ||||||||
\(218\) | −1.30200e29 | −0.765428 | ||||||||
\(219\) | −4.06630e28 | −0.225761 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.76531e28 | −0.285706 | ||||||||
\(222\) | −1.60996e28 | −0.0754053 | ||||||||
\(223\) | −3.74438e29 | −1.65794 | −0.828970 | − | 0.559293i | \(-0.811073\pi\) | ||||
−0.828970 | + | 0.559293i | \(0.811073\pi\) | |||||||
\(224\) | 1.54919e28 | 0.0648639 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.90184e28 | −0.146189 | ||||||||
\(227\) | −3.09492e29 | −1.09730 | −0.548651 | − | 0.836052i | \(-0.684858\pi\) | ||||
−0.548651 | + | 0.836052i | \(0.684858\pi\) | |||||||
\(228\) | 3.26181e28 | 0.109464 | ||||||||
\(229\) | 4.36225e29 | 1.38601 | 0.693006 | − | 0.720932i | \(-0.256286\pi\) | ||||
0.693006 | + | 0.720932i | \(0.256286\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.33407e26 | −0.00209024 | ||||||||
\(232\) | −7.21616e28 | −0.194853 | ||||||||
\(233\) | −2.03884e29 | −0.521715 | −0.260858 | − | 0.965377i | \(-0.584005\pi\) | ||||
−0.260858 | + | 0.965377i | \(0.584005\pi\) | |||||||
\(234\) | −3.20541e29 | −0.777474 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.89435e27 | 0.0150346 | ||||||||
\(237\) | −4.00354e28 | −0.0828113 | ||||||||
\(238\) | −3.38035e28 | −0.0663361 | ||||||||
\(239\) | −7.19381e29 | −1.33963 | −0.669816 | − | 0.742527i | \(-0.733627\pi\) | ||||
−0.669816 | + | 0.742527i | \(0.733627\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.94932e28 | −0.0998285 | −0.0499142 | − | 0.998754i | \(-0.515895\pi\) | ||||
−0.0499142 | + | 0.998754i | \(0.515895\pi\) | |||||||
\(242\) | −4.42893e29 | −0.705678 | ||||||||
\(243\) | −2.45881e29 | −0.372089 | ||||||||
\(244\) | −9.13966e28 | −0.131388 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.43628e28 | −0.0316256 | ||||||||
\(247\) | −1.56444e30 | −1.93039 | ||||||||
\(248\) | −2.06656e29 | −0.242439 | ||||||||
\(249\) | 7.99951e28 | 0.0892425 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.11692e30 | −1.12745 | −0.563727 | − | 0.825961i | \(-0.690633\pi\) | ||||
−0.563727 | + | 0.825961i | \(0.690633\pi\) | |||||||
\(252\) | −1.87942e29 | −0.180516 | ||||||||
\(253\) | 7.52656e28 | 0.0688003 | ||||||||
\(254\) | 1.21184e30 | 1.05444 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | −2.23332e30 | −1.67798 | −0.838991 | − | 0.544146i | \(-0.816854\pi\) | ||||
−0.838991 | + | 0.544146i | \(0.816854\pi\) | |||||||
\(258\) | 1.39917e29 | 0.100144 | ||||||||
\(259\) | 4.52744e29 | 0.308749 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.75438e29 | 0.542275 | ||||||||
\(262\) | −9.00168e29 | −0.531566 | ||||||||
\(263\) | 1.67388e30 | 0.942489 | 0.471244 | − | 0.882003i | \(-0.343805\pi\) | ||||
0.471244 | + | 0.882003i | \(0.343805\pi\) | |||||||
\(264\) | −3.75078e27 | −0.00201406 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.17270e29 | −0.448205 | ||||||||
\(267\) | 5.01146e29 | 0.233654 | ||||||||
\(268\) | −1.06098e30 | −0.472089 | ||||||||
\(269\) | −1.51842e30 | −0.644895 | −0.322448 | − | 0.946587i | \(-0.604506\pi\) | ||||
−0.322448 | + | 0.946587i | \(0.604506\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.73589e30 | 1.44637 | 0.723183 | − | 0.690657i | \(-0.242678\pi\) | ||||
0.723183 | + | 0.690657i | \(0.242678\pi\) | |||||||
\(272\) | −1.72877e29 | −0.0639185 | ||||||||
\(273\) | −1.47141e29 | −0.0519637 | ||||||||
\(274\) | 1.40256e29 | 0.0473196 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.14837e29 | −0.0969888 | ||||||||
\(277\) | −4.88475e30 | −1.43829 | −0.719143 | − | 0.694863i | \(-0.755465\pi\) | ||||
−0.719143 | + | 0.694863i | \(0.755465\pi\) | |||||||
\(278\) | −1.14316e30 | −0.321772 | ||||||||
\(279\) | 2.50708e30 | 0.674708 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.07868e30 | 1.00390 | 0.501950 | − | 0.864896i | \(-0.332616\pi\) | ||||
0.501950 | + | 0.864896i | \(0.332616\pi\) | |||||||
\(282\) | −4.67001e29 | −0.109952 | ||||||||
\(283\) | −8.77909e30 | −1.97751 | −0.988756 | − | 0.149537i | \(-0.952222\pi\) | ||||
−0.988756 | + | 0.149537i | \(0.952222\pi\) | |||||||
\(284\) | −3.04184e29 | −0.0655628 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.79896e29 | 0.0355177 | ||||||||
\(287\) | 6.85120e29 | 0.129492 | ||||||||
\(288\) | −9.61168e29 | −0.173937 | ||||||||
\(289\) | −5.39341e30 | −0.934631 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.38477e29 | −0.0538105 | ||||||||
\(292\) | 5.84809e30 | 0.890694 | ||||||||
\(293\) | −4.02063e30 | −0.586744 | −0.293372 | − | 0.955998i | \(-0.594778\pi\) | ||||
−0.293372 | + | 0.955998i | \(0.594778\pi\) | |||||||
\(294\) | 5.54518e29 | 0.0775486 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.31542e30 | 0.297497 | ||||||||
\(297\) | 9.17489e28 | 0.0113017 | ||||||||
\(298\) | 5.85344e30 | 0.691366 | ||||||||
\(299\) | 1.51003e31 | 1.71039 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.93467e30 | −0.410040 | ||||||||
\(302\) | −1.02902e31 | −1.02882 | ||||||||
\(303\) | 9.87021e29 | 0.0946877 | ||||||||
\(304\) | −4.69108e30 | −0.431870 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.09729e30 | 0.177885 | ||||||||
\(307\) | −3.20834e29 | −0.0261247 | −0.0130623 | − | 0.999915i | \(-0.504158\pi\) | ||||
−0.0130623 | + | 0.999915i | \(0.504158\pi\) | |||||||
\(308\) | 1.05478e29 | 0.00824662 | ||||||||
\(309\) | −1.23993e30 | −0.0930932 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.26721e31 | −0.877692 | −0.438846 | − | 0.898562i | \(-0.644613\pi\) | ||||
−0.438846 | + | 0.898562i | \(0.644613\pi\) | |||||||
\(312\) | −7.52505e29 | −0.0500699 | ||||||||
\(313\) | 2.76579e31 | 1.76813 | 0.884066 | − | 0.467361i | \(-0.154795\pi\) | ||||
0.884066 | + | 0.467361i | \(0.154795\pi\) | |||||||
\(314\) | −1.37110e31 | −0.842265 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.75783e30 | 0.326716 | ||||||||
\(317\) | 8.12742e30 | 0.443315 | 0.221657 | − | 0.975125i | \(-0.428853\pi\) | ||||
0.221657 | + | 0.975125i | \(0.428853\pi\) | |||||||
\(318\) | 2.51437e30 | 0.131853 | ||||||||
\(319\) | −4.91318e29 | −0.0247730 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.66116e30 | 0.124096 | ||||||||
\(322\) | 8.85368e30 | 0.397123 | ||||||||
\(323\) | 1.02360e31 | 0.441672 | ||||||||
\(324\) | 1.14671e31 | 0.476037 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.45157e30 | −0.132677 | ||||||||
\(327\) | 3.70814e30 | 0.137186 | ||||||||
\(328\) | 3.50383e30 | 0.124773 | ||||||||
\(329\) | 1.31328e31 | 0.450203 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.24680e31 | −1.03182 | −0.515912 | − | 0.856642i | \(-0.672547\pi\) | ||||
−0.515912 | + | 0.856642i | \(0.672547\pi\) | |||||||
\(332\) | −1.15048e31 | −0.352089 | ||||||||
\(333\) | −2.80898e31 | −0.827934 | ||||||||
\(334\) | −1.26480e31 | −0.359079 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.41213e29 | −0.0116254 | ||||||||
\(337\) | 6.16105e31 | 1.56416 | 0.782080 | − | 0.623178i | \(-0.214159\pi\) | ||||
0.782080 | + | 0.623178i | \(0.214159\pi\) | |||||||
\(338\) | 7.18877e30 | 0.175872 | ||||||||
\(339\) | 1.11126e30 | 0.0262010 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.40704e30 | −0.0308231 | ||||||||
\(342\) | 5.69106e31 | 1.20189 | ||||||||
\(343\) | −3.36139e31 | −0.684451 | ||||||||
\(344\) | −2.01226e31 | −0.395097 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.99889e31 | −0.730279 | ||||||||
\(347\) | 8.34408e31 | 1.46981 | 0.734903 | − | 0.678172i | \(-0.237228\pi\) | ||||
0.734903 | + | 0.678172i | \(0.237228\pi\) | |||||||
\(348\) | 2.05519e30 | 0.0349229 | ||||||||
\(349\) | −1.07311e32 | −1.75924 | −0.879621 | − | 0.475676i | \(-0.842204\pi\) | ||||
−0.879621 | + | 0.475676i | \(0.842204\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.84073e31 | 0.280964 | ||||||||
\(352\) | 5.39431e29 | 0.00794608 | ||||||||
\(353\) | 1.05139e32 | 1.49479 | 0.747394 | − | 0.664381i | \(-0.231305\pi\) | ||||
0.747394 | + | 0.664381i | \(0.231305\pi\) | |||||||
\(354\) | −1.96353e29 | −0.00269462 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.20741e31 | −0.921837 | ||||||||
\(357\) | 9.62736e29 | 0.0118892 | ||||||||
\(358\) | −6.06350e31 | −0.723079 | ||||||||
\(359\) | 1.15543e32 | 1.33064 | 0.665321 | − | 0.746557i | \(-0.268295\pi\) | ||||
0.665321 | + | 0.746557i | \(0.268295\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.84682e32 | 1.98419 | ||||||||
\(362\) | 4.92305e31 | 0.510949 | ||||||||
\(363\) | 1.26137e31 | 0.126477 | ||||||||
\(364\) | 2.11616e31 | 0.205013 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.60300e30 | 0.0235484 | ||||||||
\(367\) | 5.65157e31 | 0.494133 | 0.247066 | − | 0.968999i | \(-0.420533\pi\) | ||||
0.247066 | + | 0.968999i | \(0.420533\pi\) | |||||||
\(368\) | 4.52793e31 | 0.382651 | ||||||||
\(369\) | −4.25072e31 | −0.347242 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.07079e31 | −0.539876 | ||||||||
\(372\) | 5.88565e30 | 0.0434518 | ||||||||
\(373\) | 1.41123e31 | 0.100748 | 0.0503741 | − | 0.998730i | \(-0.483959\pi\) | ||||
0.0503741 | + | 0.998730i | \(0.483959\pi\) | |||||||
\(374\) | −1.17705e30 | −0.00812643 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.71634e31 | 0.433795 | ||||||||
\(377\) | −9.85713e31 | −0.615862 | ||||||||
\(378\) | 1.07927e31 | 0.0652350 | ||||||||
\(379\) | 2.60316e32 | 1.52234 | 0.761169 | − | 0.648554i | \(-0.224626\pi\) | ||||
0.761169 | + | 0.648554i | \(0.224626\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.45135e31 | −0.188985 | ||||||||
\(382\) | 3.55076e31 | 0.188161 | ||||||||
\(383\) | 2.22460e32 | 1.14095 | 0.570475 | − | 0.821315i | \(-0.306759\pi\) | ||||
0.570475 | + | 0.821315i | \(0.306759\pi\) | |||||||
\(384\) | −2.25644e30 | −0.0112017 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.56283e31 | 0.305316 | ||||||||
\(387\) | 2.44120e32 | 1.09955 | ||||||||
\(388\) | 4.86793e31 | 0.212299 | ||||||||
\(389\) | 2.83579e31 | 0.119758 | 0.0598789 | − | 0.998206i | \(-0.480929\pi\) | ||||
0.0598789 | + | 0.998206i | \(0.480929\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.88004e31 | −0.391335 | ||||||||
\(392\) | −7.97499e31 | −0.305953 | ||||||||
\(393\) | 2.56371e31 | 0.0952713 | ||||||||
\(394\) | −2.74322e32 | −0.987545 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.54419e30 | −0.0221139 | ||||||||
\(397\) | 1.97865e32 | 0.647870 | 0.323935 | − | 0.946079i | \(-0.394994\pi\) | ||||
0.323935 | + | 0.946079i | \(0.394994\pi\) | |||||||
\(398\) | 7.44802e31 | 0.236321 | ||||||||
\(399\) | 2.61242e31 | 0.0803306 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.91837e32 | 1.70961 | 0.854806 | − | 0.518947i | \(-0.173676\pi\) | ||||
0.854806 | + | 0.518947i | \(0.173676\pi\) | |||||||
\(402\) | 3.02172e31 | 0.0846113 | ||||||||
\(403\) | −2.82289e32 | −0.766268 | ||||||||
\(404\) | −1.41952e32 | −0.373572 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.77949e31 | −0.142993 | ||||||||
\(407\) | 1.57647e31 | 0.0378229 | ||||||||
\(408\) | 4.92361e30 | 0.0114560 | ||||||||
\(409\) | 5.10098e32 | 1.15110 | 0.575549 | − | 0.817767i | \(-0.304788\pi\) | ||||
0.575549 | + | 0.817767i | \(0.304788\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.99455e30 | −0.00848097 | ||||||||
\(412\) | 1.78326e32 | 0.367281 | ||||||||
\(413\) | 5.52175e30 | 0.0110332 | ||||||||
\(414\) | −5.49313e32 | −1.06492 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.08224e32 | 0.197541 | ||||||||
\(417\) | 3.25577e31 | 0.0576704 | ||||||||
\(418\) | −3.19396e31 | −0.0549068 | ||||||||
\(419\) | 3.45646e32 | 0.576709 | 0.288354 | − | 0.957524i | \(-0.406892\pi\) | ||||
0.288354 | + | 0.957524i | \(0.406892\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.15256e31 | 0.0181191 | 0.00905955 | − | 0.999959i | \(-0.497116\pi\) | ||||
0.00905955 | + | 0.999959i | \(0.497116\pi\) | |||||||
\(422\) | −6.51435e32 | −0.994181 | ||||||||
\(423\) | −8.14803e32 | −1.20725 | ||||||||
\(424\) | −3.61613e32 | −0.520201 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.66328e30 | 0.0117507 | ||||||||
\(427\) | −7.32004e31 | −0.0964196 | ||||||||
\(428\) | −3.82724e32 | −0.489597 | ||||||||
\(429\) | −5.12349e30 | −0.00636575 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.12581e33 | −1.31978 | −0.659888 | − | 0.751364i | \(-0.729396\pi\) | ||||
−0.659888 | + | 0.751364i | \(0.729396\pi\) | |||||||
\(432\) | 5.51956e31 | 0.0628576 | ||||||||
\(433\) | −5.31109e32 | −0.587604 | −0.293802 | − | 0.955866i | \(-0.594921\pi\) | ||||
−0.293802 | + | 0.955866i | \(0.594921\pi\) | |||||||
\(434\) | −1.65513e32 | −0.177914 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.33299e32 | −0.541240 | ||||||||
\(437\) | −2.68098e33 | −2.64409 | ||||||||
\(438\) | −1.66556e32 | −0.159637 | ||||||||
\(439\) | 7.89847e32 | 0.735760 | 0.367880 | − | 0.929873i | \(-0.380084\pi\) | ||||
0.367880 | + | 0.929873i | \(0.380084\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.67498e32 | 0.851467 | ||||||||
\(442\) | −2.36147e32 | −0.202025 | ||||||||
\(443\) | 1.82758e33 | 1.51995 | 0.759974 | − | 0.649953i | \(-0.225212\pi\) | ||||
0.759974 | + | 0.649953i | \(0.225212\pi\) | |||||||
\(444\) | −6.59438e31 | −0.0533196 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.53370e33 | −1.17234 | ||||||||
\(447\) | −1.66708e32 | −0.123912 | ||||||||
\(448\) | 6.34546e31 | 0.0458657 | ||||||||
\(449\) | −8.32692e31 | −0.0585336 | −0.0292668 | − | 0.999572i | \(-0.509317\pi\) | ||||
−0.0292668 | + | 0.999572i | \(0.509317\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.38561e31 | 0.0158633 | ||||||||
\(452\) | −1.59819e32 | −0.103371 | ||||||||
\(453\) | 2.93069e32 | 0.184392 | ||||||||
\(454\) | −1.26768e33 | −0.775909 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.33604e32 | 0.0774030 | ||||||||
\(457\) | −2.02366e33 | −1.14074 | −0.570368 | − | 0.821389i | \(-0.693199\pi\) | ||||
−0.570368 | + | 0.821389i | \(0.693199\pi\) | |||||||
\(458\) | 1.78678e33 | 0.980058 | ||||||||
\(459\) | −1.20438e32 | −0.0642842 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.37646e32 | −0.423447 | −0.211724 | − | 0.977330i | \(-0.567908\pi\) | ||||
−0.211724 | + | 0.977330i | \(0.567908\pi\) | |||||||
\(462\) | −3.00404e30 | −0.00147802 | ||||||||
\(463\) | −3.37029e33 | −1.61401 | −0.807003 | − | 0.590547i | \(-0.798912\pi\) | ||||
−0.807003 | + | 0.590547i | \(0.798912\pi\) | |||||||
\(464\) | −2.95574e32 | −0.137782 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.35108e32 | −0.368909 | ||||||||
\(467\) | −2.79564e33 | −1.20232 | −0.601161 | − | 0.799128i | \(-0.705295\pi\) | ||||
−0.601161 | + | 0.799128i | \(0.705295\pi\) | |||||||
\(468\) | −1.31294e33 | −0.549757 | ||||||||
\(469\) | −8.49753e32 | −0.346443 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.90494e32 | 0.150957 | ||||||||
\(472\) | 2.82392e31 | 0.0106311 | ||||||||
\(473\) | −1.37006e32 | −0.0502315 | ||||||||
\(474\) | −1.63985e32 | −0.0585564 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.38459e32 | −0.0469067 | ||||||||
\(477\) | 4.38696e33 | 1.44772 | ||||||||
\(478\) | −2.94659e33 | −0.947263 | ||||||||
\(479\) | 6.03192e33 | 1.88913 | 0.944565 | − | 0.328324i | \(-0.106484\pi\) | ||||
0.944565 | + | 0.328324i | \(0.106484\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.16281e33 | 0.940286 | ||||||||
\(482\) | −2.43684e32 | −0.0705894 | ||||||||
\(483\) | −2.52156e32 | −0.0711754 | ||||||||
\(484\) | −1.81409e33 | −0.498990 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00713e33 | −0.263107 | ||||||||
\(487\) | −2.63729e33 | −0.671500 | −0.335750 | − | 0.941951i | \(-0.608990\pi\) | ||||
−0.335750 | + | 0.941951i | \(0.608990\pi\) | |||||||
\(488\) | −3.74360e32 | −0.0929056 | ||||||||
\(489\) | 9.83018e31 | 0.0237794 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.59365e33 | 1.05594 | 0.527970 | − | 0.849263i | \(-0.322953\pi\) | ||||
0.527970 | + | 0.849263i | \(0.322953\pi\) | |||||||
\(492\) | −9.97902e31 | −0.0223627 | ||||||||
\(493\) | 6.44948e32 | 0.140909 | ||||||||
\(494\) | −6.40793e33 | −1.36499 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.46465e32 | −0.171430 | ||||||||
\(497\) | −2.43624e32 | −0.0481134 | ||||||||
\(498\) | 3.27660e32 | 0.0631040 | ||||||||
\(499\) | 4.28804e33 | 0.805382 | 0.402691 | − | 0.915336i | \(-0.368075\pi\) | ||||
0.402691 | + | 0.915336i | \(0.368075\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.60219e32 | 0.0643569 | ||||||||
\(502\) | −4.57488e33 | −0.797230 | ||||||||
\(503\) | 1.27163e33 | 0.216152 | 0.108076 | − | 0.994143i | \(-0.465531\pi\) | ||||
0.108076 | + | 0.994143i | \(0.465531\pi\) | |||||||
\(504\) | −7.69809e32 | −0.127644 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.08288e32 | 0.0486491 | ||||||||
\(507\) | −2.04739e32 | −0.0315210 | ||||||||
\(508\) | 4.96369e33 | 0.745604 | ||||||||
\(509\) | 8.49642e33 | 1.24527 | 0.622635 | − | 0.782512i | \(-0.286062\pi\) | ||||
0.622635 | + | 0.782512i | \(0.286062\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.68380e33 | 0.653637 | ||||||||
\(512\) | 3.24519e32 | 0.0441942 | ||||||||
\(513\) | −3.26812e33 | −0.434341 | ||||||||
\(514\) | −9.14768e33 | −1.18651 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.73098e32 | 0.0708122 | ||||||||
\(517\) | 4.57287e32 | 0.0551515 | ||||||||
\(518\) | 1.85444e33 | 0.218319 | ||||||||
\(519\) | 1.13890e33 | 0.130886 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.16997e34 | −1.28146 | −0.640730 | − | 0.767767i | \(-0.721368\pi\) | ||||
−0.640730 | + | 0.767767i | \(0.721368\pi\) | |||||||
\(522\) | 3.58580e33 | 0.383446 | ||||||||
\(523\) | 2.58251e33 | 0.269631 | 0.134816 | − | 0.990871i | \(-0.456956\pi\) | ||||
0.134816 | + | 0.990871i | \(0.456956\pi\) | |||||||
\(524\) | −3.68709e33 | −0.375874 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.85619e33 | 0.666440 | ||||||||
\(527\) | 1.84700e33 | 0.175321 | ||||||||
\(528\) | −1.53632e31 | −0.00142415 | ||||||||
\(529\) | 1.48316e34 | 1.34274 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.42588e32 | −0.0295863 | ||||||||
\(532\) | −3.75714e33 | −0.316929 | ||||||||
\(533\) | 4.78616e33 | 0.394364 | ||||||||
\(534\) | 2.05269e33 | 0.165218 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.34579e33 | −0.333817 | ||||||||
\(537\) | 1.72691e33 | 0.129596 | ||||||||
\(538\) | −6.21946e33 | −0.456010 | ||||||||
\(539\) | −5.42984e32 | −0.0388980 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.08434e33 | 0.552941 | 0.276470 | − | 0.961022i | \(-0.410835\pi\) | ||||
0.276470 | + | 0.961022i | \(0.410835\pi\) | |||||||
\(542\) | 1.53022e34 | 1.02274 | ||||||||
\(543\) | −1.40210e33 | −0.0915760 | ||||||||
\(544\) | −7.08106e32 | −0.0451972 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6.02689e32 | −0.0367439 | ||||||||
\(547\) | 3.07411e34 | 1.83180 | 0.915900 | − | 0.401408i | \(-0.131479\pi\) | ||||
0.915900 | + | 0.401408i | \(0.131479\pi\) | |||||||
\(548\) | 5.74491e32 | 0.0334600 | ||||||||
\(549\) | 4.54160e33 | 0.258556 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.75009e34 | 0.952061 | ||||||||
\(552\) | −1.28957e33 | −0.0685814 | ||||||||
\(553\) | 4.61150e33 | 0.239761 | ||||||||
\(554\) | −2.00079e34 | −1.01702 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.68240e33 | −0.227528 | ||||||||
\(557\) | 2.42852e34 | 1.15385 | 0.576927 | − | 0.816796i | \(-0.304252\pi\) | ||||
0.576927 | + | 0.816796i | \(0.304252\pi\) | |||||||
\(558\) | 1.02690e34 | 0.477091 | ||||||||
\(559\) | −2.74871e34 | −1.24877 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.35228e31 | 0.00145648 | ||||||||
\(562\) | 1.67063e34 | 0.709865 | ||||||||
\(563\) | 2.54352e34 | 1.05701 | 0.528507 | − | 0.848929i | \(-0.322752\pi\) | ||||
0.528507 | + | 0.848929i | \(0.322752\pi\) | |||||||
\(564\) | −1.91284e33 | −0.0777480 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.59592e34 | −1.39831 | ||||||||
\(567\) | 9.18411e33 | 0.349341 | ||||||||
\(568\) | −1.24594e33 | −0.0463599 | ||||||||
\(569\) | 9.11823e33 | 0.331900 | 0.165950 | − | 0.986134i | \(-0.446931\pi\) | ||||
0.165950 | + | 0.986134i | \(0.446931\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.94351e33 | −0.276733 | −0.138366 | − | 0.990381i | \(-0.544185\pi\) | ||||
−0.138366 | + | 0.990381i | \(0.544185\pi\) | |||||||
\(572\) | 7.36853e32 | 0.0251148 | ||||||||
\(573\) | −1.01127e33 | −0.0337236 | ||||||||
\(574\) | 2.80625e33 | 0.0915646 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.93694e33 | −0.122992 | ||||||||
\(577\) | −3.99407e33 | −0.122101 | −0.0610503 | − | 0.998135i | \(-0.519445\pi\) | ||||
−0.0610503 | + | 0.998135i | \(0.519445\pi\) | |||||||
\(578\) | −2.20914e34 | −0.660884 | ||||||||
\(579\) | −1.86912e33 | −0.0547210 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.21430e33 | −0.258381 | ||||||||
\(582\) | −1.38640e33 | −0.0380498 | ||||||||
\(583\) | −2.46207e33 | −0.0661369 | ||||||||
\(584\) | 2.39538e34 | 0.629816 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.64685e34 | −0.414891 | ||||||||
\(587\) | 1.28546e34 | 0.317017 | 0.158508 | − | 0.987358i | \(-0.449332\pi\) | ||||
0.158508 | + | 0.987358i | \(0.449332\pi\) | |||||||
\(588\) | 2.27131e33 | 0.0548351 | ||||||||
\(589\) | 5.01190e34 | 1.18457 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.81277e33 | 0.176995 | ||||||||
\(592\) | 9.48394e33 | 0.210362 | ||||||||
\(593\) | −1.35249e34 | −0.293732 | −0.146866 | − | 0.989156i | \(-0.546919\pi\) | ||||
−0.146866 | + | 0.989156i | \(0.546919\pi\) | |||||||
\(594\) | 3.75804e32 | 0.00799154 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.39757e34 | 0.488870 | ||||||||
\(597\) | −2.12122e33 | −0.0423552 | ||||||||
\(598\) | 6.18507e34 | 1.20943 | ||||||||
\(599\) | −4.11263e34 | −0.787561 | −0.393781 | − | 0.919204i | \(-0.628833\pi\) | ||||
−0.393781 | + | 0.919204i | \(0.628833\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.66879e34 | −1.59231 | −0.796155 | − | 0.605092i | \(-0.793136\pi\) | ||||
−0.796155 | + | 0.605092i | \(0.793136\pi\) | |||||||
\(602\) | −1.61164e34 | −0.289942 | ||||||||
\(603\) | 5.27216e34 | 0.929013 | ||||||||
\(604\) | −4.21487e34 | −0.727482 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.04284e33 | 0.0669543 | ||||||||
\(607\) | −1.06263e35 | −1.72394 | −0.861972 | − | 0.506956i | \(-0.830771\pi\) | ||||
−0.861972 | + | 0.506956i | \(0.830771\pi\) | |||||||
\(608\) | −1.92147e34 | −0.305378 | ||||||||
\(609\) | 1.64602e33 | 0.0256282 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.17439e34 | 1.37108 | ||||||||
\(612\) | 8.59049e33 | 0.125784 | ||||||||
\(613\) | −3.14879e34 | −0.451740 | −0.225870 | − | 0.974157i | \(-0.572522\pi\) | ||||
−0.225870 | + | 0.974157i | \(0.572522\pi\) | |||||||
\(614\) | −1.31414e33 | −0.0184729 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.32036e32 | 0.00583124 | ||||||||
\(617\) | 1.34862e35 | 1.78371 | 0.891856 | − | 0.452320i | \(-0.149403\pi\) | ||||
0.891856 | + | 0.452320i | \(0.149403\pi\) | |||||||
\(618\) | −5.07877e33 | −0.0658268 | ||||||||
\(619\) | 2.48732e34 | 0.315936 | 0.157968 | − | 0.987444i | \(-0.449506\pi\) | ||||
0.157968 | + | 0.987444i | \(0.449506\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.15446e34 | 0.384840 | ||||||||
\(622\) | −5.19048e34 | −0.620622 | ||||||||
\(623\) | −5.77248e34 | −0.676491 | ||||||||
\(624\) | −3.08226e33 | −0.0354048 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.13287e35 | 1.25026 | ||||||||
\(627\) | 9.09651e32 | 0.00984080 | ||||||||
\(628\) | −5.61603e34 | −0.595571 | ||||||||
\(629\) | −2.06941e34 | −0.215137 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.95340e34 | −0.994499 | −0.497250 | − | 0.867607i | \(-0.665657\pi\) | ||||
−0.497250 | + | 0.867607i | \(0.665657\pi\) | |||||||
\(632\) | 2.35841e34 | 0.231023 | ||||||||
\(633\) | 1.85531e34 | 0.178184 | ||||||||
\(634\) | 3.32899e34 | 0.313471 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.02989e34 | 0.0932342 | ||||||||
\(637\) | −1.08937e35 | −0.967013 | ||||||||
\(638\) | −2.01244e33 | −0.0175172 | ||||||||
\(639\) | 1.51153e34 | 0.129020 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.11836e33 | 0.0173890 | 0.00869452 | − | 0.999962i | \(-0.497232\pi\) | ||||
0.00869452 | + | 0.999962i | \(0.497232\pi\) | |||||||
\(642\) | 1.09001e34 | 0.0877491 | ||||||||
\(643\) | −5.48861e34 | −0.433336 | −0.216668 | − | 0.976245i | \(-0.569519\pi\) | ||||
−0.216668 | + | 0.976245i | \(0.569519\pi\) | |||||||
\(644\) | 3.62647e34 | 0.280809 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.19268e34 | 0.312310 | ||||||||
\(647\) | 8.23657e34 | 0.601787 | 0.300894 | − | 0.953658i | \(-0.402715\pi\) | ||||
0.300894 | + | 0.953658i | \(0.402715\pi\) | |||||||
\(648\) | 4.69692e34 | 0.336609 | ||||||||
\(649\) | 1.92269e32 | 0.00135161 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.71387e33 | 0.0318871 | ||||||||
\(652\) | −1.41376e34 | −0.0938170 | ||||||||
\(653\) | −2.06557e35 | −1.34470 | −0.672349 | − | 0.740235i | \(-0.734714\pi\) | ||||
−0.672349 | + | 0.740235i | \(0.734714\pi\) | |||||||
\(654\) | 1.51885e34 | 0.0970050 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.43517e34 | 0.0882276 | ||||||||
\(657\) | −2.90599e35 | −1.75278 | ||||||||
\(658\) | 5.37919e34 | 0.318341 | ||||||||
\(659\) | −1.48751e35 | −0.863756 | −0.431878 | − | 0.901932i | \(-0.642149\pi\) | ||||
−0.431878 | + | 0.901932i | \(0.642149\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.93614e35 | 1.08248 | 0.541238 | − | 0.840869i | \(-0.317956\pi\) | ||||
0.541238 | + | 0.840869i | \(0.317956\pi\) | |||||||
\(662\) | −1.32989e35 | −0.729610 | ||||||||
\(663\) | 6.72555e33 | 0.0362084 | ||||||||
\(664\) | −4.71236e34 | −0.248965 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.15056e35 | −0.585438 | ||||||||
\(667\) | −1.68922e35 | −0.843555 | ||||||||
\(668\) | −5.18061e34 | −0.253907 | ||||||||
\(669\) | 4.36802e34 | 0.210116 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.54886e33 | −0.0118118 | ||||||||
\(672\) | −1.80721e33 | −0.00822039 | ||||||||
\(673\) | 2.68004e35 | 1.19661 | 0.598305 | − | 0.801268i | \(-0.295841\pi\) | ||||
0.598305 | + | 0.801268i | \(0.295841\pi\) | |||||||
\(674\) | 2.52357e35 | 1.10603 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.94452e34 | 0.124360 | ||||||||
\(677\) | −2.37470e35 | −0.984578 | −0.492289 | − | 0.870432i | \(-0.663840\pi\) | ||||
−0.492289 | + | 0.870432i | \(0.663840\pi\) | |||||||
\(678\) | 4.55170e33 | 0.0185269 | ||||||||
\(679\) | 3.89878e34 | 0.155796 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.61039e34 | 0.139064 | ||||||||
\(682\) | −5.76322e33 | −0.0217952 | ||||||||
\(683\) | 2.30743e35 | 0.856779 | 0.428390 | − | 0.903594i | \(-0.359081\pi\) | ||||
0.428390 | + | 0.903594i | \(0.359081\pi\) | |||||||
\(684\) | 2.33106e35 | 0.849868 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.37682e35 | −0.483980 | ||||||||
\(687\) | −5.08880e34 | −0.175653 | ||||||||
\(688\) | −8.24222e34 | −0.279376 | ||||||||
\(689\) | −4.93957e35 | −1.64418 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.65717e35 | −0.531974 | −0.265987 | − | 0.963977i | \(-0.585698\pi\) | ||||
−0.265987 | + | 0.963977i | \(0.585698\pi\) | |||||||
\(692\) | −1.63795e35 | −0.516385 | ||||||||
\(693\) | −5.24131e33 | −0.0162283 | ||||||||
\(694\) | 3.41774e35 | 1.03931 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.41804e33 | 0.0246942 | ||||||||
\(697\) | −3.13156e34 | −0.0902301 | ||||||||
\(698\) | −4.39545e35 | −1.24397 | ||||||||
\(699\) | 2.37842e34 | 0.0661185 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.91864e35 | −1.31938 | −0.659690 | − | 0.751538i | \(-0.729312\pi\) | ||||
−0.659690 | + | 0.751538i | \(0.729312\pi\) | |||||||
\(702\) | 7.53961e34 | 0.198671 | ||||||||
\(703\) | −5.61542e35 | −1.45359 | ||||||||
\(704\) | 2.20951e33 | 0.00561873 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.30649e35 | 1.05697 | ||||||||
\(707\) | −1.13691e35 | −0.274146 | ||||||||
\(708\) | −8.04263e32 | −0.00190538 | ||||||||
\(709\) | −7.85100e35 | −1.82746 | −0.913728 | − | 0.406326i | \(-0.866810\pi\) | ||||
−0.913728 | + | 0.406326i | \(0.866810\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.86114e35 | −0.642937 | ||||||||
\(712\) | −2.95215e35 | −0.651837 | ||||||||
\(713\) | −4.83759e35 | −1.04957 | ||||||||
\(714\) | 3.94337e33 | 0.00840697 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.48361e35 | −0.511294 | ||||||||
\(717\) | 8.39197e34 | 0.169775 | ||||||||
\(718\) | 4.73262e35 | 0.940906 | ||||||||
\(719\) | 2.69785e33 | 0.00527118 | 0.00263559 | − | 0.999997i | \(-0.499161\pi\) | ||||
0.00263559 | + | 0.999997i | \(0.499161\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.42823e35 | 0.269530 | ||||||||
\(722\) | 7.56456e35 | 1.40304 | ||||||||
\(723\) | 6.94021e33 | 0.0126516 | ||||||||
\(724\) | 2.01648e35 | 0.361295 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.16659e34 | 0.0894326 | ||||||||
\(727\) | 5.83647e35 | 0.993048 | 0.496524 | − | 0.868023i | \(-0.334609\pi\) | ||||
0.496524 | + | 0.868023i | \(0.334609\pi\) | |||||||
\(728\) | 8.66778e34 | 0.144966 | ||||||||
\(729\) | −5.50432e35 | −0.904918 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.79847e35 | 0.285717 | ||||||||
\(732\) | 1.06619e34 | 0.0166512 | ||||||||
\(733\) | 6.31572e35 | 0.969668 | 0.484834 | − | 0.874606i | \(-0.338880\pi\) | ||||
0.484834 | + | 0.874606i | \(0.338880\pi\) | |||||||
\(734\) | 2.31488e35 | 0.349405 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.85464e35 | 0.270575 | ||||||||
\(737\) | −2.95887e34 | −0.0424406 | ||||||||
\(738\) | −1.74109e35 | −0.245537 | ||||||||
\(739\) | 6.44973e35 | 0.894305 | 0.447153 | − | 0.894458i | \(-0.352438\pi\) | ||||
0.447153 | + | 0.894458i | \(0.352438\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.82500e35 | 0.244644 | ||||||||
\(742\) | −2.89620e35 | −0.381750 | ||||||||
\(743\) | 5.26299e35 | 0.682138 | 0.341069 | − | 0.940038i | \(-0.389211\pi\) | ||||
0.341069 | + | 0.940038i | \(0.389211\pi\) | |||||||
\(744\) | 2.41076e34 | 0.0307250 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.78040e34 | 0.0712398 | ||||||||
\(747\) | 5.71687e35 | 0.692868 | ||||||||
\(748\) | −4.82119e33 | −0.00574625 | ||||||||
\(749\) | −3.06527e35 | −0.359291 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.61425e36 | −1.83009 | −0.915044 | − | 0.403355i | \(-0.867844\pi\) | ||||
−0.915044 | + | 0.403355i | \(0.867844\pi\) | |||||||
\(752\) | 2.75101e35 | 0.306740 | ||||||||
\(753\) | 1.30294e35 | 0.142885 | ||||||||
\(754\) | −4.03748e35 | −0.435481 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.42067e34 | 0.0461281 | ||||||||
\(757\) | 6.23656e35 | 0.640098 | 0.320049 | − | 0.947401i | \(-0.396301\pi\) | ||||
0.320049 | + | 0.947401i | \(0.396301\pi\) | |||||||
\(758\) | 1.06625e36 | 1.07645 | ||||||||
\(759\) | −8.78014e33 | −0.00871926 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.69451e35 | 0.451110 | 0.225555 | − | 0.974230i | \(-0.427580\pi\) | ||||
0.225555 | + | 0.974230i | \(0.427580\pi\) | |||||||
\(762\) | −1.41367e35 | −0.133633 | ||||||||
\(763\) | −4.27125e35 | −0.397190 | ||||||||
\(764\) | 1.45439e35 | 0.133050 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.11195e35 | 0.806774 | ||||||||
\(767\) | 3.85743e34 | 0.0336013 | ||||||||
\(768\) | −9.24240e33 | −0.00792081 | ||||||||
\(769\) | 1.07024e36 | 0.902402 | 0.451201 | − | 0.892422i | \(-0.350996\pi\) | ||||
0.451201 | + | 0.892422i | \(0.350996\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.60529e35 | 0.212655 | ||||||||
\(772\) | 2.68814e35 | 0.215891 | ||||||||
\(773\) | 1.40143e36 | 1.10746 | 0.553732 | − | 0.832695i | \(-0.313203\pi\) | ||||
0.553732 | + | 0.832695i | \(0.313203\pi\) | |||||||
\(774\) | 9.99916e35 | 0.777502 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.99390e35 | 0.150118 | ||||||||
\(777\) | −5.28151e34 | −0.0391287 | ||||||||
\(778\) | 1.16154e35 | 0.0846816 | ||||||||
\(779\) | −8.49760e35 | −0.609646 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.48308e33 | −0.00589407 | ||||||||
\(782\) | −4.04686e35 | −0.276716 | ||||||||
\(783\) | −2.05916e35 | −0.138570 | ||||||||
\(784\) | −3.26656e35 | −0.216341 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.05010e35 | 0.0673670 | ||||||||
\(787\) | 2.04262e36 | 1.28974 | 0.644870 | − | 0.764292i | \(-0.276911\pi\) | ||||
0.644870 | + | 0.764292i | \(0.276911\pi\) | |||||||
\(788\) | −1.12362e36 | −0.698300 | ||||||||
\(789\) | −1.95267e35 | −0.119444 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.28001e35 | −0.0758589 | ||||||||
\(792\) | −2.68050e34 | −0.0156369 | ||||||||
\(793\) | −5.11369e35 | −0.293643 | ||||||||
\(794\) | 8.10456e35 | 0.458114 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.05071e35 | 0.167104 | ||||||||
\(797\) | 4.60347e35 | 0.248231 | 0.124115 | − | 0.992268i | \(-0.460391\pi\) | ||||
0.124115 | + | 0.992268i | \(0.460391\pi\) | |||||||
\(798\) | 1.07005e35 | 0.0568023 | ||||||||
\(799\) | −6.00276e35 | −0.313701 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.58145e36 | 1.81406 | ||||||||
\(802\) | 2.42417e36 | 1.20888 | ||||||||
\(803\) | 1.63091e35 | 0.0800731 | ||||||||
\(804\) | 1.23770e35 | 0.0598292 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.15625e36 | −0.541833 | ||||||||
\(807\) | 1.77132e35 | 0.0817294 | ||||||||
\(808\) | −5.81435e35 | −0.264155 | ||||||||
\(809\) | 2.81919e35 | 0.126115 | 0.0630576 | − | 0.998010i | \(-0.479915\pi\) | ||||
0.0630576 | + | 0.998010i | \(0.479915\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.66756e35 | 0.375955 | 0.187978 | − | 0.982173i | \(-0.439807\pi\) | ||||
0.187978 | + | 0.982173i | \(0.439807\pi\) | |||||||
\(812\) | −2.36728e35 | −0.101111 | ||||||||
\(813\) | −4.35812e35 | −0.183302 | ||||||||
\(814\) | 6.45722e34 | 0.0267449 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.01671e34 | 0.00810058 | ||||||||
\(817\) | 4.88020e36 | 1.93047 | ||||||||
\(818\) | 2.08936e36 | 0.813950 | ||||||||
\(819\) | −1.05154e36 | −0.403440 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.61490e36 | −0.973120 | −0.486560 | − | 0.873647i | \(-0.661748\pi\) | ||||
−0.486560 | + | 0.873647i | \(0.661748\pi\) | |||||||
\(822\) | −1.63617e34 | −0.00599695 | ||||||||
\(823\) | −3.63703e35 | −0.131295 | −0.0656477 | − | 0.997843i | \(-0.520911\pi\) | ||||
−0.0656477 | + | 0.997843i | \(0.520911\pi\) | |||||||
\(824\) | 7.30422e35 | 0.259707 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.26171e34 | 0.00780165 | ||||||||
\(827\) | −3.87599e36 | −1.31693 | −0.658467 | − | 0.752610i | \(-0.728795\pi\) | ||||
−0.658467 | + | 0.752610i | \(0.728795\pi\) | |||||||
\(828\) | −2.24998e36 | −0.753009 | ||||||||
\(829\) | 1.44009e36 | 0.474743 | 0.237371 | − | 0.971419i | \(-0.423714\pi\) | ||||
0.237371 | + | 0.971419i | \(0.423714\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.69832e35 | 0.182278 | ||||||||
\(832\) | 4.43286e35 | 0.139683 | ||||||||
\(833\) | 7.12769e35 | 0.221252 | ||||||||
\(834\) | 1.33356e35 | 0.0407792 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.30825e35 | −0.0388250 | ||||||||
\(837\) | −5.89704e35 | −0.172411 | ||||||||
\(838\) | 1.41577e36 | 0.407795 | ||||||||
\(839\) | −2.94352e36 | −0.835300 | −0.417650 | − | 0.908608i | \(-0.637146\pi\) | ||||
−0.417650 | + | 0.908608i | \(0.637146\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.52767e36 | −0.696260 | ||||||||
\(842\) | 4.72088e34 | 0.0128121 | ||||||||
\(843\) | −4.75800e35 | −0.127227 | ||||||||
\(844\) | −2.66828e36 | −0.702992 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.33743e36 | −0.853656 | ||||||||
\(847\) | −1.45292e36 | −0.366184 | ||||||||
\(848\) | −1.48117e36 | −0.367837 | ||||||||
\(849\) | 1.02413e36 | 0.250616 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.42013e36 | 1.28792 | ||||||||
\(852\) | 3.54848e34 | 0.00830897 | ||||||||
\(853\) | 1.60861e36 | 0.371183 | 0.185591 | − | 0.982627i | \(-0.440580\pi\) | ||||
0.185591 | + | 0.982627i | \(0.440580\pi\) | |||||||
\(854\) | −2.99829e35 | −0.0681789 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.56764e36 | −0.346197 | ||||||||
\(857\) | −7.04998e36 | −1.53436 | −0.767180 | − | 0.641432i | \(-0.778341\pi\) | ||||
−0.767180 | + | 0.641432i | \(0.778341\pi\) | |||||||
\(858\) | −2.09858e34 | −0.00450127 | ||||||||
\(859\) | 6.59563e36 | 1.39425 | 0.697126 | − | 0.716948i | \(-0.254462\pi\) | ||||
0.697126 | + | 0.716948i | \(0.254462\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.99230e34 | −0.0164109 | ||||||||
\(862\) | −4.61133e36 | −0.933222 | ||||||||
\(863\) | 9.41312e36 | 1.87758 | 0.938791 | − | 0.344487i | \(-0.111947\pi\) | ||||
0.938791 | + | 0.344487i | \(0.111947\pi\) | |||||||
\(864\) | 2.26081e35 | 0.0444470 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.17542e36 | −0.415499 | ||||||||
\(867\) | 6.29170e35 | 0.118448 | ||||||||
\(868\) | −6.77942e35 | −0.125805 | ||||||||
\(869\) | 1.60574e35 | 0.0293716 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.93627e36 | −1.05508 | ||||||||
\(872\) | −2.18439e36 | −0.382714 | ||||||||
\(873\) | −2.41893e36 | −0.417778 | ||||||||
\(874\) | −1.09813e37 | −1.86965 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.82212e35 | −0.112880 | ||||||||
\(877\) | −4.23262e36 | −0.690422 | −0.345211 | − | 0.938525i | \(-0.612193\pi\) | ||||
−0.345211 | + | 0.938525i | \(0.612193\pi\) | |||||||
\(878\) | 3.23521e36 | 0.520261 | ||||||||
\(879\) | 4.69029e35 | 0.0743598 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.23339e36 | −1.42286 | −0.711431 | − | 0.702756i | \(-0.751952\pi\) | ||||
−0.711431 | + | 0.702756i | \(0.751952\pi\) | |||||||
\(882\) | 3.96287e36 | 0.602078 | ||||||||
\(883\) | −9.76831e36 | −1.46322 | −0.731612 | − | 0.681721i | \(-0.761232\pi\) | ||||
−0.731612 | + | 0.681721i | \(0.761232\pi\) | |||||||
\(884\) | −9.67259e35 | −0.142853 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.48575e36 | 1.07477 | ||||||||
\(887\) | 1.62985e36 | 0.230729 | 0.115365 | − | 0.993323i | \(-0.463196\pi\) | ||||
0.115365 | + | 0.993323i | \(0.463196\pi\) | |||||||
\(888\) | −2.70106e35 | −0.0377027 | ||||||||
\(889\) | 3.97547e36 | 0.547162 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.19794e35 | 0.0427955 | ||||||||
\(892\) | −6.28202e36 | −0.828970 | ||||||||
\(893\) | −1.62887e37 | −2.11955 | ||||||||
\(894\) | −6.82836e35 | −0.0876188 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.59910e35 | 0.0324320 | ||||||||
\(897\) | −1.76153e36 | −0.216763 | ||||||||
\(898\) | −3.41071e35 | −0.0413895 | ||||||||
\(899\) | 3.15788e36 | 0.377919 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.23194e36 | 0.376186 | ||||||||
\(902\) | 9.77145e34 | 0.0112170 | ||||||||
\(903\) | 4.59000e35 | 0.0519656 | ||||||||
\(904\) | −6.54619e35 | −0.0730943 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.20041e36 | 0.130385 | ||||||||
\(907\) | −4.47773e36 | −0.479697 | −0.239848 | − | 0.970810i | \(-0.577098\pi\) | ||||
−0.239848 | + | 0.970810i | \(0.577098\pi\) | |||||||
\(908\) | −5.19241e36 | −0.548651 | ||||||||
\(909\) | 7.05376e36 | 0.735144 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.15716e36 | 0.928498 | 0.464249 | − | 0.885705i | \(-0.346324\pi\) | ||||
0.464249 | + | 0.885705i | \(0.346324\pi\) | |||||||
\(912\) | 5.47241e35 | 0.0547322 | ||||||||
\(913\) | −3.20845e35 | −0.0316527 | ||||||||
\(914\) | −8.28891e36 | −0.806622 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.31864e36 | 0.693006 | ||||||||
\(917\) | −2.95303e36 | −0.275836 | ||||||||
\(918\) | −4.93313e35 | −0.0454558 | ||||||||
\(919\) | 1.60416e36 | 0.145816 | 0.0729078 | − | 0.997339i | \(-0.476772\pi\) | ||||
0.0729078 | + | 0.997339i | \(0.476772\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.74270e34 | 0.00331085 | ||||||||
\(922\) | −3.43100e36 | −0.299422 | ||||||||
\(923\) | −1.70193e36 | −0.146528 | ||||||||
\(924\) | −1.23045e34 | −0.00104512 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.38047e37 | −1.14127 | ||||||||
\(927\) | −8.86121e36 | −0.722764 | ||||||||
\(928\) | −1.21067e36 | −0.0974263 | ||||||||
\(929\) | −8.64983e35 | −0.0686770 | −0.0343385 | − | 0.999410i | \(-0.510932\pi\) | ||||
−0.0343385 | + | 0.999410i | \(0.510932\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.93412e37 | 1.49490 | ||||||||
\(932\) | −3.42060e36 | −0.260858 | ||||||||
\(933\) | 1.47826e36 | 0.111232 | ||||||||
\(934\) | −1.14510e37 | −0.850170 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.37779e36 | −0.388737 | ||||||||
\(937\) | 7.42933e36 | 0.529913 | 0.264956 | − | 0.964260i | \(-0.414642\pi\) | ||||
0.264956 | + | 0.964260i | \(0.414642\pi\) | |||||||
\(938\) | −3.48059e36 | −0.244972 | ||||||||
\(939\) | −3.22644e36 | −0.224081 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.99775e36 | 0.473247 | 0.236623 | − | 0.971601i | \(-0.423959\pi\) | ||||
0.236623 | + | 0.971601i | \(0.423959\pi\) | |||||||
\(942\) | 1.59946e36 | 0.106743 | ||||||||
\(943\) | 8.20206e36 | 0.540166 | ||||||||
\(944\) | 1.15668e35 | 0.00751732 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.61178e35 | −0.0355190 | ||||||||
\(947\) | −9.94818e36 | −0.621397 | −0.310698 | − | 0.950509i | \(-0.600563\pi\) | ||||
−0.310698 | + | 0.950509i | \(0.600563\pi\) | |||||||
\(948\) | −6.71682e35 | −0.0414057 | ||||||||
\(949\) | 3.27204e37 | 1.99063 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.48108e35 | −0.0561825 | ||||||||
\(952\) | −5.67129e35 | −0.0331681 | ||||||||
\(953\) | 1.89836e37 | 1.09577 | 0.547883 | − | 0.836555i | \(-0.315434\pi\) | ||||
0.547883 | + | 0.836555i | \(0.315434\pi\) | |||||||
\(954\) | 1.79690e37 | 1.02369 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.20692e37 | −0.669816 | ||||||||
\(957\) | 5.73149e34 | 0.00313956 | ||||||||
\(958\) | 2.47068e37 | 1.33582 | ||||||||
\(959\) | 4.60115e35 | 0.0245547 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.01893e37 | −0.529785 | ||||||||
\(962\) | 1.29549e37 | 0.664883 | ||||||||
\(963\) | 1.90180e37 | 0.963466 | ||||||||
\(964\) | −9.98131e35 | −0.0499142 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.03283e36 | −0.0503286 | ||||||||
\(967\) | −1.99094e37 | −0.957693 | −0.478846 | − | 0.877899i | \(-0.658945\pi\) | ||||
−0.478846 | + | 0.877899i | \(0.658945\pi\) | |||||||
\(968\) | −7.43051e36 | −0.352839 | ||||||||
\(969\) | −1.19409e36 | −0.0559744 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.95878e37 | 0.894841 | 0.447421 | − | 0.894324i | \(-0.352343\pi\) | ||||
0.447421 | + | 0.894324i | \(0.352343\pi\) | |||||||
\(972\) | −4.12521e36 | −0.186045 | ||||||||
\(973\) | −3.75018e36 | −0.166971 | ||||||||
\(974\) | −1.08023e37 | −0.474822 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.53338e36 | −0.0656942 | ||||||||
\(977\) | 2.97587e37 | 1.25873 | 0.629365 | − | 0.777110i | \(-0.283315\pi\) | ||||
0.629365 | + | 0.777110i | \(0.283315\pi\) | |||||||
\(978\) | 4.02644e35 | 0.0168146 | ||||||||
\(979\) | −2.01000e36 | −0.0828727 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.65003e37 | 1.06509 | ||||||||
\(982\) | 1.88156e37 | 0.746663 | ||||||||
\(983\) | −4.05260e37 | −1.58787 | −0.793934 | − | 0.608004i | \(-0.791970\pi\) | ||||
−0.793934 | + | 0.608004i | \(0.791970\pi\) | |||||||
\(984\) | −4.08741e35 | −0.0158128 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.64171e36 | 0.0996376 | ||||||||
\(987\) | −1.53201e36 | −0.0570555 | ||||||||
\(988\) | −2.62469e37 | −0.965197 | ||||||||
\(989\) | −4.71047e37 | −1.71045 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.58276e37 | −1.26852 | −0.634260 | − | 0.773120i | \(-0.718695\pi\) | ||||
−0.634260 | + | 0.773120i | \(0.718695\pi\) | |||||||
\(992\) | −3.46712e36 | −0.121220 | ||||||||
\(993\) | 3.78757e36 | 0.130766 | ||||||||
\(994\) | −9.97886e35 | −0.0340213 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.34210e36 | 0.0446213 | ||||||||
\(997\) | 9.64459e36 | 0.316661 | 0.158330 | − | 0.987386i | \(-0.449389\pi\) | ||||
0.158330 | + | 0.987386i | \(0.449389\pi\) | |||||||
\(998\) | 1.75638e37 | 0.569491 | ||||||||
\(999\) | 6.60714e36 | 0.211566 |
(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 | 50.26.a.l.1.4 | 6 | ||
5.2 | odd | 4 | 10.26.b.a.9.9 | yes | 12 | ||
5.3 | odd | 4 | 10.26.b.a.9.4 | ✓ | 12 | ||
5.4 | even | 2 | 50.26.a.k.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.26.b.a.9.4 | ✓ | 12 | 5.3 | odd | 4 | ||
10.26.b.a.9.9 | yes | 12 | 5.2 | odd | 4 | ||
50.26.a.k.1.3 | 6 | 5.4 | even | 2 | |||
50.26.a.l.1.4 | 6 | 1.1 | even | 1 | trivial |