Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,18,Mod(1,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.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: | \(117.262135901\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{2146}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2146 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 8) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(46.3249\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 64.1 |
$q$-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 | ||||||||
\(3\) | 11383.2 | 1.00169 | 0.500845 | − | 0.865537i | \(-0.333023\pi\) | ||||
0.500845 | + | 0.865537i | \(0.333023\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −684741. | −0.783937 | −0.391969 | − | 0.919979i | \(-0.628206\pi\) | ||||
−0.391969 | + | 0.919979i | \(0.628206\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.14317e7 | −0.749510 | −0.374755 | − | 0.927124i | \(-0.622273\pi\) | ||||
−0.374755 | + | 0.927124i | \(0.622273\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 436725. | 0.00338179 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.71354e8 | −0.944309 | −0.472154 | − | 0.881516i | \(-0.656523\pi\) | ||||
−0.472154 | + | 0.881516i | \(0.656523\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.24288e9 | −1.78259 | −0.891295 | − | 0.453424i | \(-0.850202\pi\) | ||||
−0.891295 | + | 0.453424i | \(0.850202\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.79453e9 | −0.785262 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.10085e10 | 0.382746 | 0.191373 | − | 0.981517i | \(-0.438706\pi\) | ||||
0.191373 | + | 0.981517i | \(0.438706\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.02767e11 | 1.38819 | 0.694093 | − | 0.719885i | \(-0.255805\pi\) | ||||
0.694093 | + | 0.719885i | \(0.255805\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.30129e11 | −0.750776 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.80722e11 | −1.27999 | −0.639997 | − | 0.768378i | \(-0.721064\pi\) | ||||
−0.639997 | + | 0.768378i | \(0.721064\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.94069e11 | −0.385442 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.46505e12 | −0.998302 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.77099e12 | 1.02861 | 0.514306 | − | 0.857607i | \(-0.328050\pi\) | ||||
0.514306 | + | 0.857607i | \(0.328050\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.01908e12 | −0.214601 | −0.107301 | − | 0.994227i | \(-0.534221\pi\) | ||||
−0.107301 | + | 0.994227i | \(0.534221\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.64215e12 | −0.945904 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.82775e12 | 0.587569 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.01373e13 | 1.87860 | 0.939298 | − | 0.343102i | \(-0.111478\pi\) | ||||
0.939298 | + | 0.343102i | \(0.111478\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.96807e13 | −1.78560 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.54603e13 | 1.08472 | 0.542362 | − | 0.840145i | \(-0.317530\pi\) | ||||
0.542362 | + | 0.840145i | \(0.317530\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.56717e13 | 0.987305 | 0.493653 | − | 0.869659i | \(-0.335661\pi\) | ||||
0.493653 | + | 0.869659i | \(0.335661\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.99044e11 | −0.00265111 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.85390e13 | 0.603638 | 0.301819 | − | 0.953365i | \(-0.402406\pi\) | ||||
0.301819 | + | 0.953365i | \(0.402406\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.01947e14 | −0.438235 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.25311e14 | 0.383393 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.37330e14 | 1.40611 | 0.703056 | − | 0.711135i | \(-0.251819\pi\) | ||||
0.703056 | + | 0.711135i | \(0.251819\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.59704e14 | 0.740279 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.16982e15 | 1.39053 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.65484e15 | −1.46728 | −0.733640 | − | 0.679538i | \(-0.762180\pi\) | ||||
−0.733640 | + | 0.679538i | \(0.762180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.22251e14 | −0.148436 | −0.0742182 | − | 0.997242i | \(-0.523646\pi\) | ||||
−0.0742182 | + | 0.997242i | \(0.523646\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.99251e12 | −0.00253469 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.59002e15 | 1.39744 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.72692e15 | 0.519560 | 0.259780 | − | 0.965668i | \(-0.416350\pi\) | ||||
0.259780 | + | 0.965668i | \(0.416350\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.47215e15 | −1.28216 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.21864e15 | −0.223965 | −0.111983 | − | 0.993710i | \(-0.535720\pi\) | ||||
−0.111983 | + | 0.993710i | \(0.535720\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.87996e15 | −1.43387 | −0.716937 | − | 0.697138i | \(-0.754456\pi\) | ||||
−0.716937 | + | 0.697138i | \(0.754456\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.34744e15 | −0.386093 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.67472e15 | 0.707769 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.90668e15 | −0.215559 | −0.107780 | − | 0.994175i | \(-0.534374\pi\) | ||||
−0.107780 | + | 0.994175i | \(0.534374\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.67334e16 | −1.00337 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.24773e16 | 0.608075 | 0.304037 | − | 0.952660i | \(-0.401665\pi\) | ||||
0.304037 | + | 0.952660i | \(0.401665\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.53795e15 | −0.300049 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.15427e16 | 1.03035 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.06746e16 | −0.556701 | −0.278351 | − | 0.960480i | \(-0.589788\pi\) | ||||
−0.278351 | + | 0.960480i | \(0.589788\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.99350e16 | 1.33607 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.16003e16 | −0.214964 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.03688e16 | −1.08825 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.68657e16 | 0.736700 | 0.368350 | − | 0.929687i | \(-0.379923\pi\) | ||||
0.368350 | + | 0.929687i | \(0.379923\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.93197e14 | −0.00319346 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.05844e15 | 0.0189150 | 0.00945751 | − | 0.999955i | \(-0.496990\pi\) | ||||
0.00945751 | + | 0.999955i | \(0.496990\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.19881e16 | 0.715509 | 0.357754 | − | 0.933816i | \(-0.383542\pi\) | ||||
0.357754 | + | 0.933816i | \(0.383542\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.91048e16 | 0.588562 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.56515e17 | −1.44328 | −0.721640 | − | 0.692268i | \(-0.756612\pi\) | ||||
−0.721640 | + | 0.692268i | \(0.756612\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.89834e16 | 0.187393 | 0.0936967 | − | 0.995601i | \(-0.470132\pi\) | ||||
0.0936967 | + | 0.995601i | \(0.470132\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.56890e17 | 1.88177 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.03583e17 | 0.366542 | 0.183271 | − | 0.983062i | \(-0.441331\pi\) | ||||
0.183271 | + | 0.983062i | \(0.441331\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.29170e17 | 1.00343 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.28970e15 | −0.00602835 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.25845e17 | −0.286872 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.47304e16 | −0.108281 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.31315e17 | 1.08656 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.23777e17 | 1.08610 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.46041e17 | 0.191488 | 0.0957441 | − | 0.995406i | \(-0.469477\pi\) | ||||
0.0957441 | + | 0.995406i | \(0.469477\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.61385e17 | 0.988973 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.43335e18 | 1.44393 | 0.721967 | − | 0.691928i | \(-0.243238\pi\) | ||||
0.721967 | + | 0.691928i | \(0.243238\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.17480e18 | −1.04046 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00318e18 | 0.782606 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.63665e18 | −1.81521 | −0.907606 | − | 0.419822i | \(-0.862092\pi\) | ||||
−0.907606 | + | 0.419822i | \(0.862092\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.11287e18 | 1.28602 | 0.643009 | − | 0.765858i | \(-0.277686\pi\) | ||||
0.643009 | + | 0.765858i | \(0.277686\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.12169e18 | 0.604657 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.51983e18 | 1.68332 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.89741e18 | −0.806367 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.16048e18 | −0.438975 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.47689e18 | −0.498041 | −0.249021 | − | 0.968498i | \(-0.580109\pi\) | ||||
−0.249021 | + | 0.968498i | \(0.580109\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.16874e18 | −0.652985 | −0.326492 | − | 0.945200i | \(-0.605867\pi\) | ||||
−0.326492 | + | 0.945200i | \(0.605867\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.80768e15 | 0.00129437 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.97803e17 | 0.168234 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.31830e18 | −1.36601 | −0.683004 | − | 0.730415i | \(-0.739327\pi\) | ||||
−0.683004 | + | 0.730415i | \(0.739327\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.25485e18 | 1.40849 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.49547e18 | 0.959368 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.04630e19 | 1.64461 | 0.822306 | − | 0.569046i | \(-0.192687\pi\) | ||||
0.822306 | + | 0.569046i | \(0.192687\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.23289e18 | 0.741529 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.20560e19 | 1.54210 | 0.771052 | − | 0.636773i | \(-0.219731\pi\) | ||||
0.771052 | + | 0.636773i | \(0.219731\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.88374e19 | 2.17763 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.48809e16 | 0.00469456 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.42778e18 | 0.324804 | 0.162402 | − | 0.986725i | \(-0.448076\pi\) | ||||
0.162402 | + | 0.986725i | \(0.448076\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.36171e18 | 0.288893 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.88373e19 | −1.46976 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.72370e19 | 1.22239 | 0.611197 | − | 0.791479i | \(-0.290688\pi\) | ||||
0.611197 | + | 0.791479i | \(0.290688\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.00941e19 | 0.651331 | 0.325665 | − | 0.945485i | \(-0.394412\pi\) | ||||
0.325665 | + | 0.945485i | \(0.394412\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.52992e18 | −0.148687 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.74837e19 | −1.47270 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.39058e18 | −0.361431 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.67481e19 | 0.748237 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.43562e19 | 0.995005 | 0.497503 | − | 0.867463i | \(-0.334251\pi\) | ||||
0.497503 | + | 0.867463i | \(0.334251\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.53853e19 | 1.32308 | 0.661539 | − | 0.749911i | \(-0.269904\pi\) | ||||
0.661539 | + | 0.749911i | \(0.269904\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.08658e19 | 1.39980 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.04294e18 | −0.252611 | −0.126305 | − | 0.991991i | \(-0.540312\pi\) | ||||
−0.126305 | + | 0.991991i | \(0.540312\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.98342e19 | −1.43640 | −0.718201 | − | 0.695835i | \(-0.755034\pi\) | ||||
−0.718201 | + | 0.695835i | \(0.755034\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.96578e19 | 0.520438 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.16771e19 | −0.770955 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.79759e19 | −0.850356 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.09944e17 | −0.00432867 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.89930e19 | −1.31088 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.14353e19 | −0.200376 | −0.100188 | − | 0.994969i | \(-0.531944\pi\) | ||||
−0.100188 | + | 0.994969i | \(0.531944\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.38720e19 | −0.224344 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.18155e19 | −0.773985 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.16498e19 | 0.160846 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.12465e20 | −1.43630 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.77161e19 | −0.682279 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.70378e19 | 1.06255 | 0.531275 | − | 0.847199i | \(-0.321713\pi\) | ||||
0.531275 | + | 0.847199i | \(0.321713\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.28427e17 | −0.00130349 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.56045e19 | −0.335186 | −0.167593 | − | 0.985856i | \(-0.553599\pi\) | ||||
−0.167593 | + | 0.985856i | \(0.553599\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.56164e19 | 0.223829 | 0.111914 | − | 0.993718i | \(-0.464302\pi\) | ||||
0.111914 | + | 0.993718i | \(0.464302\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.73628e19 | 0.708965 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.28548e19 | 0.0969483 | 0.0484741 | − | 0.998824i | \(-0.484564\pi\) | ||||
0.0484741 | + | 0.998824i | \(0.484564\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.74737e19 | −0.473214 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.30873e19 | −0.215924 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.31860e20 | −1.40878 | −0.704390 | − | 0.709813i | \(-0.748779\pi\) | ||||
−0.704390 | + | 0.709813i | \(0.748779\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.61676e17 | −0.00148122 | −0.000740609 | − | 1.00000i | \(-0.500236\pi\) | ||||
−0.000740609 | 1.00000i | \(0.500236\pi\) | ||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.28182e18 | −0.00676356 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.98072e19 | 0.343549 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.38795e20 | −2.47457 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.42031e20 | 0.609102 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.78336e19 | 0.311846 | 0.155923 | − | 0.987769i | \(-0.450165\pi\) | ||||
0.155923 | + | 0.987769i | \(0.450165\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.22735e20 | 1.20871 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.58058e19 | −0.300556 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.89910e19 | 0.258909 | 0.129454 | − | 0.991585i | \(-0.458677\pi\) | ||||
0.129454 | + | 0.991585i | \(0.458677\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.58837e20 | −1.40803 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.21016e18 | 0.00347855 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.40675e20 | −0.648348 | −0.324174 | − | 0.945998i | \(-0.605086\pi\) | ||||
−0.324174 | + | 0.945998i | \(0.605086\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.36406e20 | −1.10230 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.35343e20 | −0.557642 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.42480e20 | 1.20639 | 0.603197 | − | 0.797592i | \(-0.293893\pi\) | ||||
0.603197 | + | 0.797592i | \(0.293893\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.29207e20 | 0.896248 | 0.448124 | − | 0.893971i | \(-0.352092\pi\) | ||||
0.448124 | + | 0.893971i | \(0.352092\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.82251e20 | 1.33833 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.97425e20 | 0.363976 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.37181e20 | −1.10455 | −0.552275 | − | 0.833662i | \(-0.686240\pi\) | ||||
−0.552275 | + | 0.833662i | \(0.686240\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.45056e17 | −0.000725737 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.23193e20 | −0.802894 | −0.401447 | − | 0.915882i | \(-0.631493\pi\) | ||||
−0.401447 | + | 0.915882i | \(0.631493\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.19945e21 | −1.73300 | −0.866499 | − | 0.499180i | \(-0.833635\pi\) | ||||
−0.866499 | + | 0.499180i | \(0.833635\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.01021e20 | −1.09009 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.34005e20 | −0.813012 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.06054e20 | −0.853505 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.47312e20 | 0.737944 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.90842e20 | −0.743026 | −0.371513 | − | 0.928428i | \(-0.621161\pi\) | ||||
−0.371513 | + | 0.928428i | \(0.621161\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.13313e21 | 1.15026 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.83571e20 | 0.942705 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.52037e21 | 2.28170 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.65056e20 | −0.739995 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.34316e19 | 0.0189470 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.52184e20 | 0.116365 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.67762e21 | −1.21343 | −0.606717 | − | 0.794918i | \(-0.707514\pi\) | ||||
−0.606717 | + | 0.794918i | \(0.707514\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.04712e21 | 0.716718 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.35150e21 | 1.52364 | 0.761818 | − | 0.647791i | \(-0.224307\pi\) | ||||
0.761818 | + | 0.647791i | \(0.224307\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.33805e20 | 0.327533 | 0.163767 | − | 0.986499i | \(-0.447636\pi\) | ||||
0.163767 | + | 0.986499i | \(0.447636\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.41858e18 | 0.00198704 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.01032e21 | 1.10729 | 0.553645 | − | 0.832753i | \(-0.313237\pi\) | ||||
0.553645 | + | 0.832753i | \(0.313237\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.86031e21 | −0.971327 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.91996e21 | −1.44572 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.13131e21 | 0.531323 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.54177e21 | 0.687086 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.43755e20 | 0.187710 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.12647e21 | −0.452432 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.24927e21 | 1.23950 | 0.619752 | − | 0.784798i | \(-0.287233\pi\) | ||||
0.619752 | + | 0.784798i | \(0.287233\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.75290e19 | 0.00635303 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.18249e21 | −0.407303 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.35844e21 | 0.772272 | 0.386136 | − | 0.922442i | \(-0.373810\pi\) | ||||
0.386136 | + | 0.922442i | \(0.373810\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.17911e21 | 0.367161 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.84161e20 | 0.202650 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.82479e21 | 1.07797 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.74701e21 | 1.00513 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.44155e21 | 1.13431 | 0.567157 | − | 0.823609i | \(-0.308043\pi\) | ||||
0.567157 | + | 0.823609i | \(0.308043\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.88021e21 | −0.943711 | −0.471855 | − | 0.881676i | \(-0.656416\pi\) | ||||
−0.471855 | + | 0.881676i | \(0.656416\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.68111e21 | 1.77956 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.29170e20 | 0.0285152 | 0.0142576 | − | 0.999898i | \(-0.495462\pi\) | ||||
0.0142576 | + | 0.999898i | \(0.495462\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.34455e20 | 0.175575 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.43252e21 | −0.287357 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.74029e21 | −0.524197 | −0.262098 | − | 0.965041i | \(-0.584415\pi\) | ||||
−0.262098 | + | 0.965041i | \(0.584415\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.08066e21 | 0.927063 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.23006e20 | −0.108464 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.76521e21 | 1.12407 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.61315e21 | 0.414479 | 0.207239 | − | 0.978290i | \(-0.433552\pi\) | ||||
0.207239 | + | 0.978290i | \(0.433552\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.42209e19 | 0.00366831 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.28577e21 | −1.05389 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.19272e21 | −0.855768 | −0.427884 | − | 0.903834i | \(-0.640741\pi\) | ||||
−0.427884 | + | 0.903834i | \(0.640741\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.23889e21 | 1.08793 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.45280e22 | −1.83359 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.47374e21 | 0.177823 | 0.0889113 | − | 0.996040i | \(-0.471661\pi\) | ||||
0.0889113 | + | 0.996040i | \(0.471661\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.66241e21 | 0.191812 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.39392e21 | −0.374552 | −0.187276 | − | 0.982307i | \(-0.559966\pi\) | ||||
−0.187276 | + | 0.982307i | \(0.559966\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.25520e21 | −0.554846 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.30477e19 | 0.00333886 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.88689e21 | −0.569265 | −0.284632 | − | 0.958637i | \(-0.591872\pi\) | ||||
−0.284632 | + | 0.958637i | \(0.591872\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.29201e21 | −0.489913 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.63161e22 | 1.44637 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.99032e21 | 0.168985 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.80920e22 | −1.47153 | −0.735763 | − | 0.677239i | \(-0.763176\pi\) | ||||
−0.735763 | + | 0.677239i | \(0.763176\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.33730e22 | −1.04222 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.37678e22 | −1.77526 | −0.887629 | − | 0.460558i | \(-0.847649\pi\) | ||||
−0.887629 | + | 0.460558i | \(0.847649\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.34289e21 | 0.382546 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.14580e22 | 0.786579 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.69463e22 | −1.77397 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.01542e21 | 0.0641205 | 0.0320603 | − | 0.999486i | \(-0.489793\pi\) | ||||
0.0320603 | + | 0.999486i | \(0.489793\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.00135e22 | −1.81828 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.89176e22 | 1.09974 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.54373e21 | −0.476693 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.40512e22 | 1.28819 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.19062e22 | 0.612287 | 0.306144 | − | 0.951985i | \(-0.400961\pi\) | ||||
0.306144 | + | 0.951985i | \(0.400961\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.70081e21 | 0.281539 | 0.140770 | − | 0.990042i | \(-0.455042\pi\) | ||||
0.140770 | + | 0.990042i | \(0.455042\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.30345e19 | 0.00204138 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.23725e21 | −0.147527 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.54071e21 | 0.111255 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.00669e22 | 1.68616 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.33091e22 | 0.942906 | 0.471453 | − | 0.881891i | \(-0.343730\pi\) | ||||
0.471453 | + | 0.881891i | \(0.343730\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.82694e21 | −0.226618 | −0.113309 | − | 0.993560i | \(-0.536145\pi\) | ||||
−0.113309 | + | 0.993560i | \(0.536145\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.15986e22 | −0.807730 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.94024e22 | −1.77687 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.39338e22 | 0.482081 | 0.241041 | − | 0.970515i | \(-0.422511\pi\) | ||||
0.241041 | + | 0.970515i | \(0.422511\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.45228e19 | −0.00148202 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.73936e22 | −1.19775 | −0.598874 | − | 0.800843i | \(-0.704385\pi\) | ||||
−0.598874 | + | 0.800843i | \(0.704385\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.41568e22 | 0.436419 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.68117e22 | −0.498883 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.61756e22 | 1.03353 | 0.516764 | − | 0.856128i | \(-0.327137\pi\) | ||||
0.516764 | + | 0.856128i | \(0.327137\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.72335e22 | −1.02431 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.46871e22 | −0.654088 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.10400e22 | −1.04739 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.49241e22 | 1.10457 | 0.552283 | − | 0.833657i | \(-0.313757\pi\) | ||||
0.552283 | + | 0.833657i | \(0.313757\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.61280e22 | −0.382096 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.69974e20 | −0.0152968 | −0.00764839 | − | 0.999971i | \(-0.502435\pi\) | ||||
−0.00764839 | + | 0.999971i | \(0.502435\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.32337e22 | −0.291234 | −0.145617 | − | 0.989341i | \(-0.546517\pi\) | ||||
−0.145617 | + | 0.989341i | \(0.546517\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.94322e21 | 0.168518 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.65052e22 | 1.36039 | 0.680193 | − | 0.733033i | \(-0.261896\pi\) | ||||
0.680193 | + | 0.733033i | \(0.261896\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.97416e22 | −0.389416 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.19224e22 | −1.36832 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.08025e22 | −0.932321 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.02206e22 | −0.535066 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.78338e20 | 0.00475518 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.70928e22 | 0.941303 | 0.470651 | − | 0.882319i | \(-0.344019\pi\) | ||||
0.470651 | + | 0.882319i | \(0.344019\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.10435e23 | −3.34877 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.25560e22 | 0.960989 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.89383e22 | −0.577526 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.38038e22 | 0.770579 | 0.385289 | − | 0.922796i | \(-0.374102\pi\) | ||||
0.385289 | + | 0.922796i | \(0.374102\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.19103e23 | 1.64739 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.23196e22 | −1.09979 | −0.549896 | − | 0.835233i | \(-0.685333\pi\) | ||||
−0.549896 | + | 0.835233i | \(0.685333\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.05043e22 | 0.393697 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.00764e20 | 0.00250347 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.39312e22 | 0.167864 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.30825e22 | 0.152348 | 0.0761739 | − | 0.997095i | \(-0.475730\pi\) | ||||
0.0761739 | + | 0.997095i | \(0.475730\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.37236e23 | 1.54471 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.91572e22 | −0.317262 | −0.158631 | − | 0.987338i | \(-0.550708\pi\) | ||||
−0.158631 | + | 0.987338i | \(0.550708\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.40950e21 | −0.0148282 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.14429e23 | 2.18131 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.99375e22 | −0.294520 | −0.147260 | − | 0.989098i | \(-0.547045\pi\) | ||||
−0.147260 | + | 0.989098i | \(0.547045\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.12945e23 | 1.07470 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.50559e23 | −1.38583 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.29880e22 | −0.560914 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.61546e22 | −0.570020 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.90190e22 | 0.325352 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.35616e23 | 1.09444 | 0.547219 | − | 0.836989i | \(-0.315686\pi\) | ||||
0.547219 | + | 0.836989i | \(0.315686\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.21394e23 | 1.72942 | 0.864711 | − | 0.502271i | \(-0.167502\pi\) | ||||
0.864711 | + | 0.502271i | \(0.167502\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.82670e22 | 0.289381 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.12185e22 | −0.0821377 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.00439e22 | 0.638383 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.22709e20 | −0.00496204 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.90772e23 | −1.93362 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.75646e23 | 1.13144 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.96212e23 | 1.22446 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.84424e22 | 0.413829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.87467e23 | 1.09837 | 0.549186 | − | 0.835700i | \(-0.314938\pi\) | ||||
0.549186 | + | 0.835700i | \(0.314938\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.14904e23 | 0.652431 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.66935e22 | −0.146905 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.76202e22 | −0.467425 | −0.233713 | − | 0.972306i | \(-0.575087\pi\) | ||||
−0.233713 | + | 0.972306i | \(0.575087\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.70627e19 | −0.000501981 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.84766e23 | 1.42791 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.32283e22 | 0.161564 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.12852e23 | −1.47519 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.52062e23 | 1.15276 | 0.576378 | − | 0.817183i | \(-0.304465\pi\) | ||||
0.576378 | + | 0.817183i | \(0.304465\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.96738e23 | −1.75996 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.41283e22 | −0.362041 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.31530e22 | −0.138421 | −0.0692105 | − | 0.997602i | \(-0.522048\pi\) | ||||
−0.0692105 | + | 0.997602i | \(0.522048\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.09278e22 | −0.287346 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.91291e23 | 0.752036 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.02213e23 | 0.389990 | 0.194995 | − | 0.980804i | \(-0.437531\pi\) | ||||
0.194995 | + | 0.980804i | \(0.437531\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.69197e23 | 0.996928 | 0.498464 | − | 0.866910i | \(-0.333898\pi\) | ||||
0.498464 | + | 0.866910i | \(0.333898\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.77251e23 | 0.996686 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.41366e23 | 0.493364 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.40015e23 | −0.813286 | −0.406643 | − | 0.913587i | \(-0.633301\pi\) | ||||
−0.406643 | + | 0.913587i | \(0.633301\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.02797e23 | 1.32531 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.42637e23 | −0.455758 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.27874e23 | −1.32780 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.56785e21 | 0.00472585 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.35931e23 | 0.398011 | 0.199005 | − | 0.979998i | \(-0.436229\pi\) | ||||
0.199005 | + | 0.979998i | \(0.436229\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.04727e23 | −0.297906 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.15543e22 | −0.253038 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.20710e23 | −1.12984 | −0.564921 | − | 0.825145i | \(-0.691093\pi\) | ||||
−0.564921 | + | 0.825145i | \(0.691093\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.61715e22 | 0.224890 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.67272e23 | −1.43883 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.37249e23 | 0.831425 | 0.415712 | − | 0.909496i | \(-0.363532\pi\) | ||||
0.415712 | + | 0.909496i | \(0.363532\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.45318e22 | −0.178611 | −0.0893056 | − | 0.996004i | \(-0.528465\pi\) | ||||
−0.0893056 | + | 0.996004i | \(0.528465\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.54189e20 | 0.00175705 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.74761e22 | 0.0848856 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.68051e23 | −1.25108 | −0.625538 | − | 0.780194i | \(-0.715120\pi\) | ||||
−0.625538 | + | 0.780194i | \(0.715120\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.60586e23 | −0.772257 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.16628e23 | −1.07604 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.66099e23 | −1.14677 | −0.573387 | − | 0.819284i | \(-0.694371\pi\) | ||||
−0.573387 | + | 0.819284i | \(0.694371\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.32287e23 | −0.851793 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.70454e23 | 1.47680 | 0.738402 | − | 0.674361i | \(-0.235581\pi\) | ||||
0.738402 | + | 0.674361i | \(0.235581\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.95903e23 | −0.738275 | −0.369138 | − | 0.929375i | \(-0.620347\pi\) | ||||
−0.369138 | + | 0.929375i | \(0.620347\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.04285e23 | 1.27782 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.36346e23 | 0.417253 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.71243e23 | −0.465992 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.85361e23 | −1.31309 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.41850e23 | 0.719026 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.38852e23 | 0.378337 | 0.189168 | − | 0.981945i | \(-0.439421\pi\) | ||||
0.189168 | + | 0.981945i | \(0.439421\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.30170e23 | −0.200714 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.00000e23 | −0.150115 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.34495e23 | 0.781193 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.32212e20 | −0.000757404 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.88419e23 | 0.399697 | 0.199848 | − | 0.979827i | \(-0.435955\pi\) | ||||
0.199848 | + | 0.979827i | \(0.435955\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.78497e23 | −1.05066 | −0.525332 | − | 0.850897i | \(-0.676059\pi\) | ||||
−0.525332 | + | 0.850897i | \(0.676059\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.89825e23 | −0.775293 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.76233e23 | −0.481693 | −0.240847 | − | 0.970563i | \(-0.577425\pi\) | ||||
−0.240847 | + | 0.970563i | \(0.577425\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.11098e24 | 1.38557 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.32611e23 | 0.161117 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.76191e22 | 0.0563663 | 0.0281831 | − | 0.999603i | \(-0.491028\pi\) | ||||
0.0281831 | + | 0.999603i | \(0.491028\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.81476e23 | −1.13195 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.31483e21 | −0.00484906 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.28586e23 | −0.250336 | −0.125168 | − | 0.992136i | \(-0.539947\pi\) | ||||
−0.125168 | + | 0.992136i | \(0.539947\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.23156e24 | −1.31445 | −0.657224 | − | 0.753695i | \(-0.728269\pi\) | ||||
−0.657224 | + | 0.753695i | \(0.728269\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.56992e23 | −0.683432 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.04434e23 | 0.815655 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.33208e24 | −1.31662 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.10460e24 | 1.06435 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.49209e23 | 0.140170 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.22012e23 | 0.294947 | 0.147474 | − | 0.989066i | \(-0.452886\pi\) | ||||
0.147474 | + | 0.989066i | \(0.452886\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.30827e23 | 0.384788 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.06657e23 | −0.528371 | −0.264186 | − | 0.964472i | \(-0.585103\pi\) | ||||
−0.264186 | + | 0.964472i | \(0.585103\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.50071e23 | −0.552164 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.05293e23 | −0.335752 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.97688e23 | 0.644551 | 0.322276 | − | 0.946646i | \(-0.395552\pi\) | ||||
0.322276 | + | 0.946646i | \(0.395552\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.80542e24 | 1.42301 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.91596e23 | 0.224207 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.34145e24 | −2.50652 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.47998e24 | 1.81503 | 0.907516 | − | 0.420018i | \(-0.137976\pi\) | ||||
0.907516 | + | 0.420018i | \(0.137976\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.35175e21 | 0.00239353 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.44677e24 | −1.00816 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.10533e23 | 0.415174 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.46329e23 | 0.0971120 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.61477e23 | −0.428462 | −0.214231 | − | 0.976783i | \(-0.568724\pi\) | ||||
−0.214231 | + | 0.976783i | \(0.568724\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.12479e24 | 2.60784 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.68065e23 | −0.474013 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.35315e22 | −0.0141770 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.60176e24 | 1.53029 | 0.765147 | − | 0.643856i | \(-0.222666\pi\) | ||||
0.765147 | + | 0.643856i | \(0.222666\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.26942e21 | −0.000728978 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.89892e23 | 0.274688 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.41017e24 | −1.31961 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.63930e24 | −1.41116 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.59675e24 | −1.35592 | −0.677962 | − | 0.735097i | \(-0.737137\pi\) | ||||
−0.677962 | + | 0.735097i | \(0.737137\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.05158e24 | −0.536281 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.97871e21 | −0.00148372 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.14862e23 | −0.396471 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.73046e24 | 1.29776 | 0.648879 | − | 0.760892i | \(-0.275238\pi\) | ||||
0.648879 | + | 0.760892i | \(0.275238\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.14636e24 | 0.996595 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.33029e23 | 0.377887 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.56499e23 | −0.158006 | −0.0790031 | − | 0.996874i | \(-0.525174\pi\) | ||||
−0.0790031 | + | 0.996874i | \(0.525174\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.94628e23 | 0.344129 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.15937e24 | −0.490625 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.56674e24 | 1.06146 | 0.530730 | − | 0.847541i | \(-0.321918\pi\) | ||||
0.530730 | + | 0.847541i | \(0.321918\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.13320e24 | −2.47875 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.57755e24 | −0.623128 | −0.311564 | − | 0.950225i | \(-0.600853\pi\) | ||||
−0.311564 | + | 0.950225i | \(0.600853\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.01129e24 | 0.390433 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.44916e21 | 0.00205638 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.93240e24 | 1.08175 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.71108e23 | −0.205958 | −0.102979 | − | 0.994684i | \(-0.532837\pi\) | ||||
−0.102979 | + | 0.994684i | \(0.532837\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.85994e23 | 0.312373 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.48502e24 | 0.511899 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.66627e23 | 0.224682 | 0.112341 | − | 0.993670i | \(-0.464165\pi\) | ||||
0.112341 | + | 0.993670i | \(0.464165\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.67375e24 | 1.21075 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.50345e24 | 1.12908 | 0.564542 | − | 0.825404i | \(-0.309053\pi\) | ||||
0.564542 | + | 0.825404i | \(0.309053\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.45646e23 | −0.140453 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.29201e21 | −0.00101470 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.67611e24 | 2.61556 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.55948e24 | −0.459840 | −0.229920 | − | 0.973210i | \(-0.573846\pi\) | ||||
−0.229920 | + | 0.973210i | \(0.573846\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.99170e23 | 0.259346 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.68122e24 | 1.32079 | 0.660394 | − | 0.750919i | \(-0.270389\pi\) | ||||
0.660394 | + | 0.750919i | \(0.270389\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.99679e23 | 0.0827163 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.22303e24 | −1.41041 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.69949e24 | 1.50580 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.18141e23 | 0.211492 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.05965e24 | −1.02687 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.32640e24 | 1.07086 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.84015e24 | −0.930172 | −0.465086 | − | 0.885265i | \(-0.653977\pi\) | ||||
−0.465086 | + | 0.885265i | \(0.653977\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.73965e24 | −0.649443 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.18413e24 | −0.274727 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.16524e24 | 0.264601 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.96769e24 | −1.10417 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.56582e24 | 1.64611 | 0.823057 | − | 0.567959i | \(-0.192267\pi\) | ||||
0.823057 | + | 0.567959i | \(0.192267\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.08476e24 | 0.231040 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.02913e21 | −0.00188265 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.63295e24 | 1.35402 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.76298e24 | −0.752084 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.17515e24 | 1.20843 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.52328e24 | −1.44160 | −0.720800 | − | 0.693143i | \(-0.756226\pi\) | ||||
−0.720800 | + | 0.693143i | \(0.756226\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.00203e25 | 1.88020 | 0.940102 | − | 0.340893i | \(-0.110729\pi\) | ||||
0.940102 | + | 0.340893i | \(0.110729\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.88574e24 | 0.897762 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.16447e24 | −1.28927 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.77655e24 | 1.37056 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.61751e22 | 0.00451831 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.21167e24 | 0.373941 | 0.186970 | − | 0.982366i | \(-0.440133\pi\) | ||||
0.186970 | + | 0.982366i | \(0.440133\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.54721e24 | −0.421858 | −0.210929 | − | 0.977501i | \(-0.567649\pi\) | ||||
−0.210929 | + | 0.977501i | \(0.567649\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.24732e24 | 0.364591 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.70056e24 | 0.429197 | 0.214599 | − | 0.976702i | \(-0.431156\pi\) | ||||
0.214599 | + | 0.976702i | \(0.431156\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.08133e24 | −0.946859 | −0.473430 | − | 0.880832i | \(-0.656984\pi\) | ||||
−0.473430 | + | 0.880832i | \(0.656984\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.25315e24 | −1.10642 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.12228e24 | −0.167733 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.25524e24 | −1.20891 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.49300e24 | 0.214237 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.18225e24 | −0.447464 | −0.223732 | − | 0.974651i | \(-0.571824\pi\) | ||||
−0.223732 | + | 0.974651i | \(0.571824\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.21223e23 | 0.0580425 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.95560e24 | −0.804251 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.28987e25 | −1.70712 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.25661e23 | 0.0811578 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.36536e25 | −1.73592 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.92949e25 | −2.40459 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.43556e24 | −0.297531 | −0.148766 | − | 0.988872i | \(-0.547530\pi\) | ||||
−0.148766 | + | 0.988872i | \(0.547530\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.07318e22 | −0.00368024 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.08693e23 | 0.0127604 | 0.00638022 | − | 0.999980i | \(-0.497969\pi\) | ||||
0.00638022 | + | 0.999980i | \(0.497969\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.41916e24 | −0.278435 | −0.139217 | − | 0.990262i | \(-0.544459\pi\) | ||||
−0.139217 | + | 0.990262i | \(0.544459\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.21700e24 | −0.814385 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.43640e25 | 1.58922 | 0.794608 | − | 0.607123i | \(-0.207677\pi\) | ||||
0.794608 | + | 0.607123i | \(0.207677\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.34714e24 | −0.254626 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.03714e24 | −0.854947 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.95141e24 | 0.203555 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.05402e24 | −0.926163 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.48347e22 | 0.00249137 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.27400e24 | −0.814043 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.42394e24 | −0.426887 | −0.213443 | − | 0.976955i | \(-0.568468\pi\) | ||||
−0.213443 | + | 0.976955i | \(0.568468\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.86398e24 | −0.744281 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.22889e24 | 0.671084 | 0.335542 | − | 0.942025i | \(-0.391081\pi\) | ||||
0.335542 | + | 0.942025i | \(0.391081\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.56510e25 | 1.42520 | 0.712599 | − | 0.701572i | \(-0.247518\pi\) | ||||
0.712599 | + | 0.701572i | \(0.247518\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.28987e25 | 1.15220 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.58184e24 | 0.839650 | 0.419825 | − | 0.907605i | \(-0.362092\pi\) | ||||
0.419825 | + | 0.907605i | \(0.362092\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.66949e24 | −0.143522 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.12340e25 | 0.947491 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.01266e25 | 0.837962 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.18029e25 | −0.958280 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.86898e25 | 2.28556 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.82384e24 | −0.220741 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.01603e24 | 0.538184 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.84709e24 | −0.741245 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.91188e24 | −0.510603 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.51534e25 | −1.09863 | −0.549313 | − | 0.835617i | \(-0.685110\pi\) | ||||
−0.549313 | + | 0.835617i | \(0.685110\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.98973e20 | 6.39667e−5 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.15196e25 | −1.50289 | −0.751445 | − | 0.659795i | \(-0.770643\pi\) | ||||
−0.751445 | + | 0.659795i | \(0.770643\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.37669e24 | −0.574210 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.73234e24 | 0.116561 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.63857e25 | −1.08224 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.75945e24 | 0.373422 | 0.186711 | − | 0.982415i | \(-0.440217\pi\) | ||||
0.186711 | + | 0.982415i | \(0.440217\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.90966e25 | −1.21548 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.38920e24 | 0.399238 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.18031e25 | −0.724090 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.01735e22 | 0.00241970 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.80184e25 | 1.06557 | 0.532784 | − | 0.846251i | \(-0.321146\pi\) | ||||
0.532784 | + | 0.846251i | \(0.321146\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.04768e25 | −0.608352 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.67675e25 | 1.52621 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.06063e24 | 0.283339 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.21756e25 | 0.669428 | 0.334714 | − | 0.942320i | \(-0.391360\pi\) | ||||
0.334714 | + | 0.942320i | \(0.391360\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.07640e24 | 0.328087 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.16970e24 | 0.221102 | 0.110551 | − | 0.993870i | \(-0.464738\pi\) | ||||
0.110551 | + | 0.993870i | \(0.464738\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.66610e25 | −1.38844 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.14681e25 | −0.586571 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.68683e24 | 0.235453 | 0.117726 | − | 0.993046i | \(-0.462439\pi\) | ||||
0.117726 | + | 0.993046i | \(0.462439\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.17994e25 | 2.55601 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.28838e25 | 1.10916 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.40507e25 | −1.14509 | −0.572543 | − | 0.819875i | \(-0.694043\pi\) | ||||
−0.572543 | + | 0.819875i | \(0.694043\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.66777e25 | −0.780022 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.11763e25 | −0.972968 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.01414e25 | 1.36052 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.15116e25 | −0.953946 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.12027e23 | −0.00488088 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.42298e25 | −1.03721 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.05735e25 | −0.865331 | −0.432665 | − | 0.901555i | \(-0.642427\pi\) | ||||
−0.432665 | + | 0.901555i | \(0.642427\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.28779e25 | 0.532221 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.34864e25 | 0.547687 | 0.273844 | − | 0.961774i | \(-0.411705\pi\) | ||||
0.273844 | + | 0.961774i | \(0.411705\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.41537e25 | −0.963884 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.75502e25 | 0.688246 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.43897e25 | 1.71072 | 0.855359 | − | 0.518036i | \(-0.173337\pi\) | ||||
0.855359 | + | 0.518036i | \(0.173337\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.38800e25 | 0.525698 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.70250e22 | 0.000633726 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.03497e23 | 0.00744481 | 0.00372240 | − | 0.999993i | \(-0.498815\pi\) | ||||
0.00372240 | + | 0.999993i | \(0.498815\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.50733e24 | 0.198031 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.28228e25 | −0.453197 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.63771e25 | −1.26374 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.54664e25 | 1.89411 | 0.947053 | − | 0.321077i | \(-0.104045\pi\) | ||||
0.947053 | + | 0.321077i | \(0.104045\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.69870e25 | 1.24160 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.41235e25 | 1.12605 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.47645e25 | 0.478971 | 0.239485 | − | 0.970900i | \(-0.423021\pi\) | ||||
0.239485 | + | 0.970900i | \(0.423021\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.88033e25 | −1.87541 |
(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 | 64.18.a.h.1.2 | 2 | ||
4.3 | odd | 2 | 64.18.a.k.1.1 | 2 | |||
8.3 | odd | 2 | 8.18.a.a.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 16.18.a.d.1.1 | 2 | |||
24.11 | even | 2 | 72.18.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.18.a.a.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
16.18.a.d.1.1 | 2 | 8.5 | even | 2 | |||
64.18.a.h.1.2 | 2 | 1.1 | even | 1 | trivial | ||
64.18.a.k.1.1 | 2 | 4.3 | odd | 2 | |||
72.18.a.c.1.1 | 2 | 24.11 | even | 2 |