Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,34,Mod(1,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.1");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.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: | \(110.372526210\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 65185566x - 173679864984 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{3}\cdot 7\cdot 11\cdot 29 \) |
Twist minimal: | no (minimal twist has level 4) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-6032.20\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.1 |
$q$-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 | ||||||||
\(3\) | 6.39317e7 | 0.857464 | 0.428732 | − | 0.903432i | \(-0.358960\pi\) | ||||
0.428732 | + | 0.903432i | \(0.358960\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.18954e11 | −0.641723 | −0.320861 | − | 0.947126i | \(-0.603972\pi\) | ||||
−0.320861 | + | 0.947126i | \(0.603972\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.92542e13 | 0.560178 | 0.280089 | − | 0.959974i | \(-0.409636\pi\) | ||||
0.280089 | + | 0.959974i | \(0.409636\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.47179e15 | −0.264756 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.23089e17 | 1.46386 | 0.731928 | − | 0.681382i | \(-0.238621\pi\) | ||||
0.731928 | + | 0.681382i | \(0.238621\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.57082e17 | 0.315557 | 0.157778 | − | 0.987475i | \(-0.449567\pi\) | ||||
0.157778 | + | 0.987475i | \(0.449567\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.39981e19 | −0.550254 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.49754e18 | −0.0323848 | −0.0161924 | − | 0.999869i | \(-0.505154\pi\) | ||||
−0.0161924 | + | 0.999869i | \(0.505154\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.92387e20 | 0.630236 | 0.315118 | − | 0.949053i | \(-0.397956\pi\) | ||||
0.315118 | + | 0.949053i | \(0.397956\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.14891e21 | 0.480332 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.99746e22 | −1.01916 | −0.509581 | − | 0.860423i | \(-0.670200\pi\) | ||||
−0.509581 | + | 0.860423i | \(0.670200\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.84746e22 | −0.588192 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.49495e23 | −1.08448 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.97632e24 | 1.46653 | 0.733263 | − | 0.679945i | \(-0.237996\pi\) | ||||
0.733263 | + | 0.679945i | \(0.237996\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.54327e24 | −1.12176 | −0.560881 | − | 0.827897i | \(-0.689537\pi\) | ||||
−0.560881 | + | 0.827897i | \(0.689537\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.42624e25 | 1.25520 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.07844e25 | −0.359479 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.28067e26 | 1.70651 | 0.853253 | − | 0.521498i | \(-0.174627\pi\) | ||||
0.853253 | + | 0.521498i | \(0.174627\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.84016e25 | 0.270579 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.19347e26 | −0.782221 | −0.391111 | − | 0.920344i | \(-0.627909\pi\) | ||||
−0.391111 | + | 0.920344i | \(0.627909\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.35211e27 | 1.50932 | 0.754662 | − | 0.656114i | \(-0.227801\pi\) | ||||
0.754662 | + | 0.656114i | \(0.227801\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.22255e26 | 0.169900 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.49210e27 | 0.898404 | 0.449202 | − | 0.893430i | \(-0.351708\pi\) | ||||
0.449202 | + | 0.893430i | \(0.351708\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.30502e27 | −0.686201 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.15399e26 | −0.0277688 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.47590e28 | 1.23173 | 0.615864 | − | 0.787852i | \(-0.288807\pi\) | ||||
0.615864 | + | 0.787852i | \(0.288807\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.88461e28 | −0.939389 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.06587e28 | 0.540404 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.26922e29 | −0.766443 | −0.383222 | − | 0.923656i | \(-0.625185\pi\) | ||||
−0.383222 | + | 0.923656i | \(0.625185\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.88135e29 | −1.35220 | −0.676099 | − | 0.736811i | \(-0.736331\pi\) | ||||
−0.676099 | + | 0.736811i | \(0.736331\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.24920e28 | −0.148310 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.65766e29 | −0.202500 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.28458e30 | 0.951758 | 0.475879 | − | 0.879511i | \(-0.342130\pi\) | ||||
0.475879 | + | 0.879511i | \(0.342130\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.91633e30 | −0.873895 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.52414e30 | 0.718373 | 0.359187 | − | 0.933266i | \(-0.383054\pi\) | ||||
0.359187 | + | 0.933266i | \(0.383054\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.98899e30 | 1.61765 | 0.808823 | − | 0.588052i | \(-0.200105\pi\) | ||||
0.808823 | + | 0.588052i | \(0.200105\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.37770e30 | −0.504353 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.09881e31 | 0.820019 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.32137e30 | −0.455651 | −0.227826 | − | 0.973702i | \(-0.573162\pi\) | ||||
−0.227826 | + | 0.973702i | \(0.573162\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.05552e31 | −0.665149 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.92342e31 | −0.416185 | −0.208093 | − | 0.978109i | \(-0.566726\pi\) | ||||
−0.208093 | + | 0.978109i | \(0.566726\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.42266e30 | 0.0207821 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.26349e32 | 1.25749 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.91532e31 | −0.473018 | −0.236509 | − | 0.971629i | \(-0.576003\pi\) | ||||
−0.236509 | + | 0.971629i | \(0.576003\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.72895e31 | 0.176768 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.90459e32 | −0.961870 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.73496e32 | −0.404436 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.57153e32 | 1.41685 | 0.708426 | − | 0.705785i | \(-0.249405\pi\) | ||||
0.708426 | + | 0.705785i | \(0.249405\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.28341e32 | −0.387564 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.67206e33 | 1.41889 | 0.709444 | − | 0.704761i | \(-0.248946\pi\) | ||||
0.709444 | + | 0.704761i | \(0.248946\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.55505e33 | 0.954842 | 0.477421 | − | 0.878675i | \(-0.341572\pi\) | ||||
0.477421 | + | 0.878675i | \(0.341572\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.89465e32 | −0.308240 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.58097e32 | 0.117265 | 0.0586325 | − | 0.998280i | \(-0.481326\pi\) | ||||
0.0586325 | + | 0.998280i | \(0.481326\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.52686e33 | 0.850847 | 0.425423 | − | 0.904995i | \(-0.360125\pi\) | ||||
0.425423 | + | 0.904995i | \(0.360125\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.18752e33 | 1.46327 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.01423e33 | −0.534328 | −0.267164 | − | 0.963651i | \(-0.586087\pi\) | ||||
−0.267164 | + | 0.963651i | \(0.586087\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.56304e33 | 0.654020 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.11427e33 | −0.0835455 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.20031e32 | −0.0181413 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.65434e34 | 1.14287 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.04164e34 | −0.670726 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.04823e34 | 1.01918 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.61417e34 | 0.700241 | 0.350121 | − | 0.936705i | \(-0.386141\pi\) | ||||
0.350121 | + | 0.936705i | \(0.386141\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.64428e34 | 1.29419 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.50991e35 | 1.75377 | 0.876887 | − | 0.480696i | \(-0.159616\pi\) | ||||
0.876887 | + | 0.480696i | \(0.159616\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.90284e34 | 0.353044 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.84186e34 | 0.695937 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.42195e34 | 0.189838 | 0.0949192 | − | 0.995485i | \(-0.469741\pi\) | ||||
0.0949192 | + | 0.995485i | \(0.469741\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.08655e35 | 1.34812 | 0.674060 | − | 0.738677i | \(-0.264549\pi\) | ||||
0.674060 | + | 0.738677i | \(0.264549\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.23256e35 | 0.770349 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.68896e35 | 0.461930 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.32722e35 | −0.941103 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.39159e35 | −0.588393 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.12808e36 | 1.56591 | 0.782955 | − | 0.622078i | \(-0.213711\pi\) | ||||
0.782955 | + | 0.622078i | \(0.213711\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.27117e36 | −1.41607 | −0.708033 | − | 0.706179i | \(-0.750417\pi\) | ||||
−0.708033 | + | 0.706179i | \(0.750417\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.56304e33 | 0.00857407 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.94766e35 | 0.719860 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.68303e35 | 0.449975 | 0.224987 | − | 0.974362i | \(-0.427766\pi\) | ||||
0.224987 | + | 0.974362i | \(0.427766\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.22220e36 | 1.05616 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.47637e36 | −0.570912 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.17206e36 | −0.369704 | −0.184852 | − | 0.982766i | \(-0.559181\pi\) | ||||
−0.184852 | + | 0.982766i | \(0.559181\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.12282e36 | −0.805492 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.02289e35 | −0.106202 | −0.0531009 | − | 0.998589i | \(-0.516911\pi\) | ||||
−0.0531009 | + | 0.998589i | \(0.516911\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.18296e36 | −0.900424 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.16623e36 | −0.166859 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.22082e36 | 0.616564 | 0.308282 | − | 0.951295i | \(-0.400246\pi\) | ||||
0.308282 | + | 0.951295i | \(0.400246\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.37266e36 | −0.329492 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.11437e36 | −0.657197 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.47756e37 | −1.66705 | −0.833527 | − | 0.552479i | \(-0.813682\pi\) | ||||
−0.833527 | + | 0.552479i | \(0.813682\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.26307e36 | 0.462855 | 0.231427 | − | 0.972852i | \(-0.425660\pi\) | ||||
0.231427 | + | 0.972852i | \(0.425660\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.48141e37 | −1.15946 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.80407e37 | −1.09510 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.44953e36 | −0.0474067 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.21395e37 | −0.607503 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.54554e37 | 0.587125 | 0.293562 | − | 0.955940i | \(-0.405159\pi\) | ||||
0.293562 | + | 0.955940i | \(0.405159\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.64000e37 | −1.48388 | −0.741938 | − | 0.670469i | \(-0.766093\pi\) | ||||
−0.741938 | + | 0.670469i | \(0.766093\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.05977e37 | −0.173636 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00607e37 | 0.277749 | 0.138875 | − | 0.990310i | \(-0.455651\pi\) | ||||
0.138875 | + | 0.990310i | \(0.455651\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.98496e36 | −0.0349835 | −0.0174918 | − | 0.999847i | \(-0.505568\pi\) | ||||
−0.0174918 | + | 0.999847i | \(0.505568\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.21253e37 | 0.816098 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.73419e37 | 0.821515 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.99223e37 | 0.501969 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.41164e37 | 0.269829 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.76773e38 | 0.922574 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.29116e38 | −0.575863 | −0.287931 | − | 0.957651i | \(-0.592968\pi\) | ||||
−0.287931 | + | 0.957651i | \(0.592968\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.61372e38 | 0.615979 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.96050e38 | −0.968568 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.23775e38 | −0.628386 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.74681e38 | 1.38707 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.91917e36 | −0.0102193 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.28250e38 | 0.945822 | 0.472911 | − | 0.881110i | \(-0.343203\pi\) | ||||
0.472911 | + | 0.881110i | \(0.343203\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00780e38 | 0.155727 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.73287e38 | 0.631972 | 0.315986 | − | 0.948764i | \(-0.397665\pi\) | ||||
0.315986 | + | 0.948764i | \(0.397665\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.97730e38 | −0.575054 | −0.287527 | − | 0.957773i | \(-0.592833\pi\) | ||||
−0.287527 | + | 0.957773i | \(0.592833\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.02486e38 | 0.703137 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.20413e39 | 1.91366 | 0.956831 | − | 0.290644i | \(-0.0938696\pi\) | ||||
0.956831 | + | 0.290644i | \(0.0938696\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.64608e38 | −0.576526 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.95931e38 | −0.390704 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.24449e38 | −0.128101 | −0.0640504 | − | 0.997947i | \(-0.520402\pi\) | ||||
−0.0640504 | + | 0.997947i | \(0.520402\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.40422e39 | 1.19590 | 0.597949 | − | 0.801534i | \(-0.295983\pi\) | ||||
0.597949 | + | 0.801534i | \(0.295983\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.18464e39 | 0.514142 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.16155e39 | 0.440351 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.99902e38 | 0.198875 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.22968e39 | −0.356864 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.59890e39 | −1.93257 | −0.966283 | − | 0.257481i | \(-0.917107\pi\) | ||||
−0.966283 | + | 0.257481i | \(0.917107\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.68698e39 | −1.49191 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.09531e37 | 0.0178199 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.53622e39 | −1.29795 | −0.648974 | − | 0.760811i | \(-0.724802\pi\) | ||||
−0.648974 | + | 0.760811i | \(0.724802\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.30782e39 | 0.955946 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.90873e39 | −0.388271 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.45996e39 | −0.524882 | −0.262441 | − | 0.964948i | \(-0.584527\pi\) | ||||
−0.262441 | + | 0.964948i | \(0.584527\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.61060e39 | −0.790428 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.42109e39 | −0.405596 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.47220e40 | 1.19414 | 0.597069 | − | 0.802190i | \(-0.296332\pi\) | ||||
0.597069 | + | 0.802190i | \(0.296332\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.39791e40 | −1.00343 | −0.501714 | − | 0.865034i | \(-0.667297\pi\) | ||||
−0.501714 | + | 0.865034i | \(0.667297\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.38398e39 | 0.151572 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.52759e40 | −0.861028 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.35630e40 | −1.17846 | −0.589228 | − | 0.807967i | \(-0.700568\pi\) | ||||
−0.589228 | + | 0.807967i | \(0.700568\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.68676e39 | 0.296993 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.71685e40 | 1.46731 | 0.733654 | − | 0.679523i | \(-0.237813\pi\) | ||||
0.733654 | + | 0.679523i | \(0.237813\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.67224e39 | 0.339665 | 0.169833 | − | 0.985473i | \(-0.445677\pi\) | ||||
0.169833 | + | 0.985473i | \(0.445677\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.10919e40 | −0.346790 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.57292e40 | −0.438183 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.02123e40 | −0.998951 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.47993e40 | 1.21490 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.46285e40 | 1.08169 | 0.540845 | − | 0.841122i | \(-0.318104\pi\) | ||||
0.540845 | + | 0.841122i | \(0.318104\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.77901e40 | 0.491844 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00277e41 | −1.58753 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.26932e40 | −0.321604 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.65971e40 | 0.845490 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.06897e41 | 1.21665 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.49836e40 | 0.867736 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.30064e40 | −0.119227 | −0.0596135 | − | 0.998222i | \(-0.518987\pi\) | ||||
−0.0596135 | + | 0.998222i | \(0.518987\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.94173e40 | 0.818742 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.40564e41 | −1.78108 | −0.890542 | − | 0.454901i | \(-0.849675\pi\) | ||||
−0.890542 | + | 0.454901i | \(0.849675\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.63493e40 | 0.242111 | 0.121055 | − | 0.992646i | \(-0.461372\pi\) | ||||
0.121055 | + | 0.992646i | \(0.461372\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.58724e40 | 0.0951740 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.26788e41 | 0.684859 | 0.342429 | − | 0.939544i | \(-0.388750\pi\) | ||||
0.342429 | + | 0.939544i | \(0.388750\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.40894e41 | 2.14678 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.28938e40 | 0.100550 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.14856e39 | −0.0204101 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.18409e40 | −0.185608 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.25478e41 | 0.729570 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.72001e41 | 0.503266 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.46365e41 | 0.652254 | 0.326127 | − | 0.945326i | \(-0.394256\pi\) | ||||
0.326127 | + | 0.945326i | \(0.394256\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.88488e41 | −0.451807 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.81263e41 | −0.610764 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.62980e41 | −0.714478 | −0.357239 | − | 0.934013i | \(-0.616282\pi\) | ||||
−0.357239 | + | 0.934013i | \(0.616282\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.56637e41 | −0.458167 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.01355e42 | −1.64210 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.42078e41 | −0.944572 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.19587e41 | 0.560798 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.21611e42 | −1.47754 | −0.738768 | − | 0.673960i | \(-0.764592\pi\) | ||||
−0.738768 | + | 0.673960i | \(0.764592\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.93880e41 | 0.214246 | 0.107123 | − | 0.994246i | \(-0.465836\pi\) | ||||
0.107123 | + | 0.994246i | \(0.465836\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.40304e41 | −0.342216 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.41824e41 | 0.221420 | 0.110710 | − | 0.993853i | \(-0.464688\pi\) | ||||
0.110710 | + | 0.993853i | \(0.464688\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.52669e41 | −0.460996 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.04601e40 | −0.0155555 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.31667e41 | 0.0912888 | 0.0456444 | − | 0.998958i | \(-0.485466\pi\) | ||||
0.0456444 | + | 0.998958i | \(0.485466\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.52894e41 | −0.602803 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.69697e42 | 0.979973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.96817e42 | −1.03808 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.81021e41 | −0.376420 | −0.188210 | − | 0.982129i | \(-0.560269\pi\) | ||||
−0.188210 | + | 0.982129i | \(0.560269\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.70013e41 | 0.207098 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.71202e42 | 0.689986 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.64138e41 | −0.355585 | −0.177793 | − | 0.984068i | \(-0.556896\pi\) | ||||
−0.177793 | + | 0.984068i | \(0.556896\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.58811e42 | 0.873909 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.49623e42 | 0.462772 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.62182e42 | −1.30998 | −0.654992 | − | 0.755636i | \(-0.727328\pi\) | ||||
−0.654992 | + | 0.755636i | \(0.727328\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.31060e42 | 0.600432 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.15063e41 | 0.0989313 | 0.0494657 | − | 0.998776i | \(-0.484248\pi\) | ||||
0.0494657 | + | 0.998776i | \(0.484248\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.40588e42 | −0.526225 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.99003e42 | −0.399602 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.10627e41 | −0.167947 | −0.0839735 | − | 0.996468i | \(-0.526761\pi\) | ||||
−0.0839735 | + | 0.996468i | \(0.526761\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.94761e41 | 0.0330054 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.65309e42 | 1.50380 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.04095e42 | 0.292402 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.34295e43 | 1.77018 | 0.885088 | − | 0.465423i | \(-0.154098\pi\) | ||||
0.885088 | + | 0.465423i | \(0.154098\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.49515e42 | 0.302722 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.37037e43 | −1.53093 | −0.765465 | − | 0.643477i | \(-0.777491\pi\) | ||||
−0.765465 | + | 0.643477i | \(0.777491\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.43963e42 | −0.353980 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.50064e42 | 0.426841 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.85702e43 | 2.49808 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.72611e42 | −0.461770 | −0.230885 | − | 0.972981i | \(-0.574162\pi\) | ||||
−0.230885 | + | 0.972981i | \(0.574162\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.18771e42 | 0.162780 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.25146e42 | −0.429344 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.21141e42 | 0.267075 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.97328e43 | 1.15596 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.34537e42 | 0.126964 | 0.0634818 | − | 0.997983i | \(-0.479780\pi\) | ||||
0.0634818 | + | 0.997983i | \(0.479780\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.43051e42 | 0.271760 | 0.135880 | − | 0.990725i | \(-0.456614\pi\) | ||||
0.135880 | + | 0.990725i | \(0.456614\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.13965e42 | −0.237858 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.44916e41 | 0.0190485 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.91173e43 | −0.757471 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.07978e43 | 0.396088 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.04863e43 | −0.695967 | −0.347983 | − | 0.937501i | \(-0.613133\pi\) | ||||
−0.347983 | + | 0.937501i | \(0.613133\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.78864e43 | −0.877691 | −0.438846 | − | 0.898562i | \(-0.644613\pi\) | ||||
−0.438846 | + | 0.898562i | \(0.644613\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.76647e43 | −0.806962 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.37514e43 | −0.642312 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.25782e43 | −0.566272 | −0.283136 | − | 0.959080i | \(-0.591375\pi\) | ||||
−0.283136 | + | 0.959080i | \(0.591375\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.80789e42 | 0.181676 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.19378e43 | −0.257789 | −0.128894 | − | 0.991658i | \(-0.541143\pi\) | ||||
−0.128894 | + | 0.991658i | \(0.541143\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.51414e43 | 0.303546 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.21202e43 | 1.34271 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.42445e43 | −1.11115 | −0.555573 | − | 0.831468i | \(-0.687501\pi\) | ||||
−0.555573 | + | 0.831468i | \(0.687501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.12428e43 | −1.14506 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.12680e43 | −1.21423 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.16467e42 | −0.113436 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.72354e43 | −0.868922 | −0.434461 | − | 0.900691i | \(-0.643061\pi\) | ||||
−0.434461 | + | 0.900691i | \(0.643061\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.92061e42 | 0.0351208 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.63019e43 | −0.294389 | −0.147195 | − | 0.989108i | \(-0.547024\pi\) | ||||
−0.147195 | + | 0.989108i | \(0.547024\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.76936e43 | 0.913864 | 0.456932 | − | 0.889502i | \(-0.348948\pi\) | ||||
0.456932 | + | 0.889502i | \(0.348948\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.35971e43 | 0.617254 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.35357e44 | −1.22392 | −0.611958 | − | 0.790890i | \(-0.709618\pi\) | ||||
−0.611958 | + | 0.790890i | \(0.709618\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.32709e43 | 0.533153 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.91190e43 | 0.385837 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.01641e44 | 2.20943 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.42584e43 | −0.370700 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.11580e43 | −0.326107 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.85163e43 | 0.467115 | 0.233558 | − | 0.972343i | \(-0.424963\pi\) | ||||
0.233558 | + | 0.972343i | \(0.424963\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.69569e43 | 0.538499 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.43871e43 | −0.489536 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.87677e44 | −0.909226 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.82489e44 | 1.73138 | 0.865688 | − | 0.500584i | \(-0.166881\pi\) | ||||
0.865688 | + | 0.500584i | \(0.166881\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.49317e43 | −0.317007 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.02288e44 | −1.59108 | −0.795541 | − | 0.605900i | \(-0.792813\pi\) | ||||
−0.795541 | + | 0.605900i | \(0.792813\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.28412e43 | −0.0474932 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.18914e43 | 0.248709 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.24324e44 | 0.402416 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.25677e44 | 1.28950 | 0.644750 | − | 0.764393i | \(-0.276961\pi\) | ||||
0.644750 | + | 0.764393i | \(0.276961\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.21122e43 | −0.0910643 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.24439e44 | 1.39259 | 0.696295 | − | 0.717756i | \(-0.254830\pi\) | ||||
0.696295 | + | 0.717756i | \(0.254830\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.66103e44 | −0.910533 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.31355e44 | −0.772081 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.39856e44 | 1.83384 | 0.916920 | − | 0.399071i | \(-0.130667\pi\) | ||||
0.916920 | + | 0.399071i | \(0.130667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.42745e44 | 0.906169 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.56174e44 | −0.683479 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.40485e44 | −0.612744 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.79048e44 | 1.31513 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.33776e44 | 0.528681 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.55665e44 | 1.27198 | 0.635991 | − | 0.771696i | \(-0.280591\pi\) | ||||
0.635991 | + | 0.771696i | \(0.280591\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.81639e44 | −1.23030 | −0.615152 | − | 0.788408i | \(-0.710906\pi\) | ||||
−0.615152 | + | 0.788408i | \(0.710906\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.15620e44 | −0.282527 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.95201e43 | 0.0363281 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.34689e43 | 0.0386921 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.86804e44 | 0.202920 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.41772e44 | −0.246835 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.84067e43 | −0.0752516 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.58395e45 | −1.42944 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.18349e45 | −1.00450 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.37260e45 | −1.89439 | −0.947197 | − | 0.320651i | \(-0.896098\pi\) | ||||
−0.947197 | + | 0.320651i | \(0.896098\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.28272e44 | 0.396881 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.72220e44 | −0.546007 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.48406e45 | −0.987778 | −0.493889 | − | 0.869525i | \(-0.664425\pi\) | ||||
−0.493889 | + | 0.869525i | \(0.664425\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.71254e44 | 0.358002 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.56601e45 | 0.924257 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.59116e44 | −0.255246 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.79269e45 | −0.939011 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.92126e44 | 0.193560 | 0.0967799 | − | 0.995306i | \(-0.469146\pi\) | ||||
0.0967799 | + | 0.995306i | \(0.469146\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.02366e45 | 0.476278 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.26708e43 | −0.0406495 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.13519e45 | −0.469548 | −0.234774 | − | 0.972050i | \(-0.575435\pi\) | ||||
−0.234774 | + | 0.972050i | \(0.575435\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.78930e44 | 0.342890 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.01243e45 | −0.372601 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.83884e45 | −0.638544 | −0.319272 | − | 0.947663i | \(-0.603438\pi\) | ||||
−0.319272 | + | 0.947663i | \(0.603438\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.16473e45 | −1.03715 | −0.518574 | − | 0.855033i | \(-0.673537\pi\) | ||||
−0.518574 | + | 0.855033i | \(0.673537\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.62741e45 | 0.503438 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.05249e45 | 0.599463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.15172e45 | 1.69666 | 0.848332 | − | 0.529464i | \(-0.177607\pi\) | ||||
0.848332 | + | 0.529464i | \(0.177607\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.88438e45 | −1.27237 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.47367e44 | −0.233137 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.75433e45 | 1.80307 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.43973e44 | 0.0536130 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.28489e45 | 1.30548 | 0.652738 | − | 0.757584i | \(-0.273620\pi\) | ||||
0.652738 | + | 0.757584i | \(0.273620\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.60003e45 | −0.706974 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.28251e45 | 0.238160 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.26071e45 | −0.572677 | −0.286338 | − | 0.958129i | \(-0.592438\pi\) | ||||
−0.286338 | + | 0.958129i | \(0.592438\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.00720e43 | 0.0116417 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.90834e44 | −0.0299971 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.21811e45 | 0.924944 | 0.462472 | − | 0.886634i | \(-0.346963\pi\) | ||||
0.462472 | + | 0.886634i | \(0.346963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.29634e45 | 1.16804 | 0.584020 | − | 0.811739i | \(-0.301479\pi\) | ||||
0.584020 | + | 0.811739i | \(0.301479\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.89063e45 | −0.251983 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.81178e45 | −0.733408 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.16593e45 | −0.736861 | −0.368430 | − | 0.929655i | \(-0.620105\pi\) | ||||
−0.368430 | + | 0.929655i | \(0.620105\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.22324e45 | 0.704419 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.64380e45 | 0.283498 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.34569e45 | 0.543133 | 0.271566 | − | 0.962420i | \(-0.412458\pi\) | ||||
0.271566 | + | 0.962420i | \(0.412458\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.47025e45 | 0.430420 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.09959e45 | 0.191615 | 0.0958077 | − | 0.995400i | \(-0.469457\pi\) | ||||
0.0958077 | + | 0.995400i | \(0.469457\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.78373e45 | −0.586912 | −0.293456 | − | 0.955973i | \(-0.594805\pi\) | ||||
−0.293456 | + | 0.955973i | \(0.594805\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.34734e46 | 1.10526 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.40609e45 | −0.264974 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.92271e44 | −0.0658380 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.13014e46 | 0.791074 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.32118e44 | −0.0552649 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.16884e45 | −0.388794 | −0.194397 | − | 0.980923i | \(-0.562275\pi\) | ||||
−0.194397 | + | 0.980923i | \(0.562275\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.25460e45 | −0.493782 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.91337e45 | −0.449361 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.01633e45 | −0.216535 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.71501e45 | −0.190193 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.65757e45 | 0.420958 | 0.210479 | − | 0.977598i | \(-0.432498\pi\) | ||||
0.210479 | + | 0.977598i | \(0.432498\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.14944e46 | 1.45463 | 0.727314 | − | 0.686305i | \(-0.240769\pi\) | ||||
0.727314 | + | 0.686305i | \(0.240769\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.89270e46 | −0.830512 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.65528e46 | 0.690163 | 0.345081 | − | 0.938573i | \(-0.387851\pi\) | ||||
0.345081 | + | 0.938573i | \(0.387851\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.83149e46 | −1.12196 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.43063e46 | −0.538818 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.91669e46 | −0.686252 | −0.343126 | − | 0.939289i | \(-0.611486\pi\) | ||||
−0.343126 | + | 0.939289i | \(0.611486\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.30600e46 | −1.12544 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.32299e46 | −0.428281 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.47214e46 | −0.453251 | −0.226626 | − | 0.973982i | \(-0.572769\pi\) | ||||
−0.226626 | + | 0.973982i | \(0.572769\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.36391e46 | 0.692319 | 0.346160 | − | 0.938176i | \(-0.387486\pi\) | ||||
0.346160 | + | 0.938176i | \(0.387486\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.14491e44 | −0.00876264 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.54541e45 | −0.226556 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.92392e46 | −1.49463 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.37719e46 | 0.811008 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.65885e46 | −1.97942 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.32698e46 | −1.37704 | −0.688522 | − | 0.725216i | \(-0.741740\pi\) | ||||
−0.688522 | + | 0.725216i | \(0.741740\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.07790e46 | 0.637884 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.67075e44 | 0.0151400 | 0.00756998 | − | 0.999971i | \(-0.497590\pi\) | ||||
0.00756998 | + | 0.999971i | \(0.497590\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.22184e46 | 0.793689 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.02581e46 | 0.541893 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.85282e46 | 0.316148 | 0.158074 | − | 0.987427i | \(-0.449472\pi\) | ||||
0.158074 | + | 0.987427i | \(0.449472\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.49248e45 | −0.121824 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.18208e46 | −0.493088 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.63154e46 | 0.388680 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.06135e47 | 1.49441 | 0.747207 | − | 0.664591i | \(-0.231394\pi\) | ||||
0.747207 | + | 0.664591i | \(0.231394\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.61722e46 | −0.217105 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.75811e46 | −0.865119 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.07497e45 | 0.0253321 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.40914e47 | 1.64090 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.20778e46 | 0.911756 | 0.455878 | − | 0.890042i | \(-0.349325\pi\) | ||||
0.455878 | + | 0.890042i | \(0.349325\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.01478e47 | 1.07550 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.88827e46 | −0.494351 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.23558e46 | 0.794830 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.53905e45 | 0.0510238 | 0.0255119 | − | 0.999675i | \(-0.491878\pi\) | ||||
0.0255119 | + | 0.999675i | \(0.491878\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.37191e46 | 0.120636 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.36182e47 | 1.14326 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.69805e46 | −0.296431 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.43494e46 | −0.109842 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.50176e47 | −1.82902 | −0.914512 | − | 0.404559i | \(-0.867425\pi\) | ||||
−0.914512 | + | 0.404559i | \(0.867425\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.65930e46 | 0.534881 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.53706e47 | 1.02544 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.35327e47 | −0.862599 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.23979e47 | −1.97333 | −0.986664 | − | 0.162769i | \(-0.947958\pi\) | ||||
−0.986664 | + | 0.162769i | \(0.947958\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.90004e47 | 1.10601 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.78539e45 | −0.0488792 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.15065e47 | −0.611968 | −0.305984 | − | 0.952037i | \(-0.598985\pi\) | ||||
−0.305984 | + | 0.952037i | \(0.598985\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.42601e46 | 0.377585 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.86575e47 | 1.39324 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.15723e47 | 1.00291 | 0.501456 | − | 0.865183i | \(-0.332798\pi\) | ||||
0.501456 | + | 0.865183i | \(0.332798\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.83528e46 | 0.170528 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.13812e47 | 1.75990 | 0.879949 | − | 0.475069i | \(-0.157577\pi\) | ||||
0.879949 | + | 0.475069i | \(0.157577\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.46998e47 | −1.00488 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.83088e46 | 0.110187 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.76378e46 | 0.0656892 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.22086e47 | −1.14792 | −0.573962 | − | 0.818882i | \(-0.694594\pi\) | ||||
−0.573962 | + | 0.818882i | \(0.694594\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.85811e47 | −1.65711 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.78327e47 | 0.908722 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.08055e47 | 0.650274 | 0.325137 | − | 0.945667i | \(-0.394590\pi\) | ||||
0.325137 | + | 0.945667i | \(0.394590\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.27511e47 | −1.27926 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.02741e46 | −0.258652 | −0.129326 | − | 0.991602i | \(-0.541281\pi\) | ||||
−0.129326 | + | 0.991602i | \(0.541281\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.73713e47 | 0.476625 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.09386e45 | −0.00550218 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.60906e46 | −0.241856 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.05116e47 | −0.253444 | −0.126722 | − | 0.991938i | \(-0.540446\pi\) | ||||
−0.126722 | + | 0.991938i | \(0.540446\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.81804e47 | −1.11294 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.02385e47 | −1.33325 | −0.666627 | − | 0.745392i | \(-0.732262\pi\) | ||||
−0.666627 | + | 0.745392i | \(0.732262\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.11098e47 | 0.659811 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.03270e47 | 0.819689 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.53047e47 | −0.492984 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.63106e47 | 1.05159 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.88344e47 | −1.59042 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.68223e47 | −0.288759 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.16244e47 | −0.520523 | −0.260261 | − | 0.965538i | \(-0.583809\pi\) | ||||
−0.260261 | + | 0.965538i | \(0.583809\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.85133e47 | −0.450067 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.97718e47 | −0.299318 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.93850e47 | −0.426695 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.86559e47 | −0.677763 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.41105e47 | −0.589495 | −0.294747 | − | 0.955575i | \(-0.595235\pi\) | ||||
−0.294747 | + | 0.955575i | \(0.595235\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.26900e46 | −0.0290947 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.01779e47 | 0.125234 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.00534e48 | 2.36800 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.23257e47 | 0.366367 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.41204e47 | 1.02393 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.10768e48 | −1.15681 | −0.578406 | − | 0.815749i | \(-0.696325\pi\) | ||||
−0.578406 | + | 0.815749i | \(0.696325\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.46114e47 | −0.948635 | −0.474318 | − | 0.880354i | \(-0.657305\pi\) | ||||
−0.474318 | + | 0.880354i | \(0.657305\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.93709e47 | −0.860403 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.56627e47 | 0.237247 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.07139e48 | 0.951230 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.48824e46 | −0.0468003 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.23829e48 | 1.83338 | 0.916692 | − | 0.399594i | \(-0.130849\pi\) | ||||
0.916692 | + | 0.399594i | \(0.130849\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.31671e48 | 1.03608 | 0.518040 | − | 0.855356i | \(-0.326662\pi\) | ||||
0.518040 | + | 0.855356i | \(0.326662\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.76615e47 | −0.738301 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.96543e47 | 0.433312 | 0.216656 | − | 0.976248i | \(-0.430485\pi\) | ||||
0.216656 | + | 0.976248i | \(0.430485\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.00487e48 | 0.701392 | 0.350696 | − | 0.936489i | \(-0.385945\pi\) | ||||
0.350696 | + | 0.936489i | \(0.385945\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.50642e48 | −1.01048 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.44695e46 | 0.0222225 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.09978e47 | 0.0681521 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.04218e48 | 1.21653 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.96184e47 | 0.284165 | 0.142083 | − | 0.989855i | \(-0.454620\pi\) | ||||
0.142083 | + | 0.989855i | \(0.454620\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.08975e48 | 1.15070 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.37625e48 | 1.25816 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.13483e48 | 0.577822 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.30737e48 | 0.640212 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.18363e47 | 0.291251 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.83874e48 | −1.73921 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.70417e48 | −1.61448 | −0.807238 | − | 0.590226i | \(-0.799039\pi\) | ||||
−0.807238 | + | 0.590226i | \(0.799039\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.55350e47 | 0.107077 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.82096e47 | 0.194514 | 0.0972569 | − | 0.995259i | \(-0.468993\pi\) | ||||
0.0972569 | + | 0.995259i | \(0.468993\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.42649e48 | −0.942087 | −0.471043 | − | 0.882110i | \(-0.656122\pi\) | ||||
−0.471043 | + | 0.882110i | \(0.656122\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.00559e48 | −0.375726 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.96761e48 | 1.78636 | 0.893181 | − | 0.449698i | \(-0.148468\pi\) | ||||
0.893181 | + | 0.449698i | \(0.148468\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.14312e48 | −0.395663 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.57084e48 | −0.856565 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.07949e48 | −0.667008 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.72531e47 | 0.300334 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.26155e48 | −0.375120 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.99393e48 | 0.570921 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.66923e48 | −1.56326 | −0.781629 | − | 0.623743i | \(-0.785611\pi\) | ||||
−0.781629 | + | 0.623743i | \(0.785611\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.49249e48 | 0.927511 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.15832e48 | 1.06369 | 0.531845 | − | 0.846842i | \(-0.321499\pi\) | ||||
0.531845 | + | 0.846842i | \(0.321499\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.01243e48 | −0.495870 | −0.247935 | − | 0.968777i | \(-0.579752\pi\) | ||||
−0.247935 | + | 0.968777i | \(0.579752\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.77667e48 | 0.421738 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.27157e48 | −1.66299 | −0.831493 | − | 0.555535i | \(-0.812513\pi\) | ||||
−0.831493 | + | 0.555535i | \(0.812513\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.78013e48 | 0.392259 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.58563e48 | −0.973681 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.76709e48 | 0.566206 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.42472e48 | 1.06979 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.45082e48 | −0.275763 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.97894e48 | −1.64509 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.25848e47 | −0.0398893 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.25767e48 | 0.724977 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.80923e48 | −0.297024 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.77548e48 | −1.23085 | −0.615427 | − | 0.788194i | \(-0.711017\pi\) | ||||
−0.615427 | + | 0.788194i | \(0.711017\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.46092e48 | −0.375659 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.43513e48 | 0.358484 | 0.179242 | − | 0.983805i | \(-0.442636\pi\) | ||||
0.179242 | + | 0.983805i | \(0.442636\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.29094e48 | −0.609235 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.43315e48 | 0.744052 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.43692e48 | 0.982425 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.51449e48 | −0.320438 | −0.160219 | − | 0.987081i | \(-0.551220\pi\) | ||||
−0.160219 | + | 0.987081i | \(0.551220\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.31524e47 | −0.102233 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.91098e48 | 0.226687 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.76931e48 | −1.00375 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.28872e48 | −0.252800 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.90806e48 | −0.416584 | −0.208292 | − | 0.978067i | \(-0.566790\pi\) | ||||
−0.208292 | + | 0.978067i | \(0.566790\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.20363e48 | −0.432468 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.53797e49 | −1.52721 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.17379e47 | 0.0304220 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.90657e48 | −0.639086 | −0.319543 | − | 0.947572i | \(-0.603529\pi\) | ||||
−0.319543 | + | 0.947572i | \(0.603529\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.32387e48 | 0.207601 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.15202e49 | 0.993646 | 0.496823 | − | 0.867852i | \(-0.334500\pi\) | ||||
0.496823 | + | 0.867852i | \(0.334500\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.57229e48 | 0.797210 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.84753e48 | 0.389848 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.25510e48 | 0.175142 | 0.0875711 | − | 0.996158i | \(-0.472090\pi\) | ||||
0.0875711 | + | 0.996158i | \(0.472090\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.80540e48 | 0.510459 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.10579e48 | 0.587242 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.18218e49 | 0.827277 | 0.413638 | − | 0.910441i | \(-0.364258\pi\) | ||||
0.413638 | + | 0.910441i | \(0.364258\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.57357e48 | −0.376771 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.81871e49 | 1.84079 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.68545e48 | 0.106343 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.23783e48 | 0.258349 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.27045e47 | −0.0310466 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.67281e49 | 0.952237 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.25640e48 | −0.179144 | −0.0895718 | − | 0.995980i | \(-0.528550\pi\) | ||||
−0.0895718 | + | 0.995980i | \(0.528550\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.29157e47 | −0.0175009 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.66132e49 | 1.36767 | 0.683833 | − | 0.729639i | \(-0.260312\pi\) | ||||
0.683833 | + | 0.729639i | \(0.260312\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.52025e49 | 0.755187 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.31428e48 | −0.159152 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.77551e49 | −0.824256 | −0.412128 | − | 0.911126i | \(-0.635214\pi\) | ||||
−0.412128 | + | 0.911126i | \(0.635214\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.54273e49 | −0.692430 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.19081e48 | −0.225267 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.83065e49 | 1.18782 | 0.593912 | − | 0.804530i | \(-0.297583\pi\) | ||||
0.593912 | + | 0.804530i | \(0.297583\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.39236e48 | −0.178238 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.09963e49 | 0.431532 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.05289e49 | −1.53825 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.61657e49 | 0.593442 | 0.296721 | − | 0.954964i | \(-0.404107\pi\) | ||||
0.296721 | + | 0.954964i | \(0.404107\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.57505e49 | 0.559284 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.53569e47 | 0.0224497 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.74014e48 | −0.290434 | −0.145217 | − | 0.989400i | \(-0.546388\pi\) | ||||
−0.145217 | + | 0.989400i | \(0.546388\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.75653e49 | −1.85067 |
(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 | 16.34.a.d.1.3 | 3 | ||
4.3 | odd | 2 | 4.34.a.a.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.34.a.a.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
16.34.a.d.1.3 | 3 | 1.1 | even | 1 | trivial |