Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,22,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, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
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: | \(44.7163750859\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{2161}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 540 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8}\cdot 3\cdot 7 \) |
Twist minimal: | no (minimal twist has level 4) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-22.7433\) 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 | ||||||||
\(3\) | 92135.9 | 0.900856 | 0.450428 | − | 0.892813i | \(-0.351271\pi\) | ||||
0.450428 | + | 0.892813i | \(0.351271\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.86463e7 | −0.853903 | −0.426951 | − | 0.904275i | \(-0.640412\pi\) | ||||
−0.426951 | + | 0.904275i | \(0.640412\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.05236e8 | −0.809833 | −0.404916 | − | 0.914354i | \(-0.632699\pi\) | ||||
−0.404916 | + | 0.914354i | \(0.632699\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.97134e9 | −0.188458 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.12010e11 | −1.30206 | −0.651032 | − | 0.759050i | \(-0.725664\pi\) | ||||
−0.651032 | + | 0.759050i | \(0.725664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.55030e11 | 1.51901 | 0.759503 | − | 0.650504i | \(-0.225442\pi\) | ||||
0.759503 | + | 0.650504i | \(0.225442\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.71800e12 | −0.769244 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.15238e13 | 1.38638 | 0.693191 | − | 0.720754i | \(-0.256204\pi\) | ||||
0.693191 | + | 0.720754i | \(0.256204\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.15598e13 | 1.55511 | 0.777554 | − | 0.628816i | \(-0.216460\pi\) | ||||
0.777554 | + | 0.628816i | \(0.216460\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.57640e13 | −0.729543 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.14133e13 | 0.409782 | 0.204891 | − | 0.978785i | \(-0.434316\pi\) | ||||
0.204891 | + | 0.978785i | \(0.434316\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.29151e14 | −0.270850 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.14540e15 | −1.07063 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.46131e15 | 1.08639 | 0.543197 | − | 0.839605i | \(-0.317214\pi\) | ||||
0.543197 | + | 0.839605i | \(0.317214\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.30301e14 | −0.138118 | −0.0690590 | − | 0.997613i | \(-0.522000\pi\) | ||||
−0.0690590 | + | 0.997613i | \(0.522000\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.03201e16 | −1.17297 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.12854e16 | 0.691519 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.40093e16 | 0.478959 | 0.239480 | − | 0.970901i | \(-0.423023\pi\) | ||||
0.239480 | + | 0.970901i | \(0.423023\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.95654e16 | 1.36841 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.20777e17 | 1.40526 | 0.702628 | − | 0.711557i | \(-0.252010\pi\) | ||||
0.702628 | + | 0.711557i | \(0.252010\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.67373e17 | −1.18104 | −0.590522 | − | 0.807022i | \(-0.701078\pi\) | ||||
−0.590522 | + | 0.807022i | \(0.701078\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.67582e16 | 0.160925 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.73232e17 | 0.757712 | 0.378856 | − | 0.925456i | \(-0.376318\pi\) | ||||
0.378856 | + | 0.925456i | \(0.376318\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.92235e17 | −0.344171 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.06176e18 | 1.24893 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.24102e18 | 0.974726 | 0.487363 | − | 0.873199i | \(-0.337959\pi\) | ||||
0.487363 | + | 0.873199i | \(0.337959\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.08857e18 | 1.11184 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.82915e18 | 1.40093 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.96154e17 | 0.100906 | 0.0504531 | − | 0.998726i | \(-0.483933\pi\) | ||||
0.0504531 | + | 0.998726i | \(0.483933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.53713e18 | 1.53232 | 0.766158 | − | 0.642652i | \(-0.222166\pi\) | ||||
0.766158 | + | 0.642652i | \(0.222166\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.19312e18 | 0.152619 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.40785e19 | −1.29708 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.76971e19 | 1.18609 | 0.593043 | − | 0.805171i | \(-0.297926\pi\) | ||||
0.593043 | + | 0.805171i | \(0.297926\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.50108e18 | 0.369155 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.03284e19 | −0.376548 | −0.188274 | − | 0.982117i | \(-0.560289\pi\) | ||||
−0.188274 | + | 0.982117i | \(0.560289\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.55389e19 | −0.423185 | −0.211593 | − | 0.977358i | \(-0.567865\pi\) | ||||
−0.211593 | + | 0.977358i | \(0.567865\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.18995e19 | −0.243997 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.77923e19 | 1.05445 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.30491e19 | −0.868022 | −0.434011 | − | 0.900908i | \(-0.642902\pi\) | ||||
−0.434011 | + | 0.900908i | \(0.642902\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.49120e19 | −0.776026 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.17274e19 | −0.578160 | −0.289080 | − | 0.957305i | \(-0.593349\pi\) | ||||
−0.289080 | + | 0.957305i | \(0.593349\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.14877e20 | −1.18384 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.26775e20 | 0.978685 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.23635e20 | −0.760229 | −0.380114 | − | 0.924939i | \(-0.624115\pi\) | ||||
−0.380114 | + | 0.924939i | \(0.624115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.56972e20 | −1.23014 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.80733e19 | −0.124424 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.74938e20 | −1.32791 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.78850e20 | −0.383943 | −0.191972 | − | 0.981400i | \(-0.561488\pi\) | ||||
−0.191972 | + | 0.981400i | \(0.561488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.20809e20 | 0.245384 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.66280e21 | 1.49784 | 0.748920 | − | 0.662660i | \(-0.230573\pi\) | ||||
0.748920 | + | 0.662660i | \(0.230573\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.51135e21 | 1.10809 | 0.554046 | − | 0.832486i | \(-0.313083\pi\) | ||||
0.554046 | + | 0.832486i | \(0.313083\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.03979e21 | 0.622959 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.26434e21 | 1.11279 | 0.556393 | − | 0.830920i | \(-0.312185\pi\) | ||||
0.556393 | + | 0.830920i | \(0.312185\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.92748e21 | −1.58904 | −0.794522 | − | 0.607235i | \(-0.792279\pi\) | ||||
−0.794522 | + | 0.607235i | \(0.792279\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.29076e21 | 0.431474 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00234e21 | 1.66340 | 0.831701 | − | 0.555224i | \(-0.187367\pi\) | ||||
0.831701 | + | 0.555224i | \(0.187367\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.51806e21 | −0.349914 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.48842e21 | −0.286268 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.97464e21 | −1.12274 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.14593e21 | 0.695372 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.11279e22 | 1.26593 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.12995e22 | 1.08518 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.32453e22 | 1.07677 | 0.538385 | − | 0.842699i | \(-0.319035\pi\) | ||||
0.538385 | + | 0.842699i | \(0.319035\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.54210e22 | −1.06395 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.38495e22 | −1.40001 | −0.700004 | − | 0.714139i | \(-0.746818\pi\) | ||||
−0.700004 | + | 0.714139i | \(0.746818\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.51535e22 | −1.25938 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.13576e22 | 0.914214 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.16852e21 | −0.0795423 | −0.0397712 | − | 0.999209i | \(-0.512663\pi\) | ||||
−0.0397712 | + | 0.999209i | \(0.512663\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.92783e22 | −0.922337 | −0.461169 | − | 0.887313i | \(-0.652570\pi\) | ||||
−0.461169 | + | 0.887313i | \(0.652570\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.51745e22 | 0.682590 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.45707e22 | −1.97784 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.58944e22 | −0.927675 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.77117e22 | −0.310048 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.50216e22 | −0.380066 | −0.190033 | − | 0.981778i | \(-0.560860\pi\) | ||||
−0.190033 | + | 0.981778i | \(0.560860\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.09599e22 | 0.937033 | 0.468517 | − | 0.883455i | \(-0.344789\pi\) | ||||
0.468517 | + | 0.883455i | \(0.344789\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.27173e22 | −0.261275 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.17528e22 | 0.117939 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.23299e22 | 0.371280 | 0.185640 | − | 0.982618i | \(-0.440564\pi\) | ||||
0.185640 | + | 0.982618i | \(0.440564\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.14343e23 | 0.878088 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.92743e22 | −0.331855 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.03046e22 | 0.120123 | 0.0600614 | − | 0.998195i | \(-0.480870\pi\) | ||||
0.0600614 | + | 0.998195i | \(0.480870\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.92432e23 | 1.00161 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.47752e19 | 6.77660e−5 0 | 3.38830e−5 | − | 1.00000i | \(-0.499989\pi\) | ||||
3.38830e−5 | 1.00000i | \(0.499989\pi\) | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.23006e23 | 1.30738 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.19283e22 | −0.293072 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.87075e22 | 0.0592287 | 0.0296143 | − | 0.999561i | \(-0.490572\pi\) | ||||
0.0296143 | + | 0.999561i | \(0.490572\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.81671e22 | 0.219343 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.65000e22 | 0.0909020 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.14720e23 | 0.475244 | 0.237622 | − | 0.971358i | \(-0.423632\pi\) | ||||
0.237622 | + | 0.971358i | \(0.423632\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.51937e23 | −1.08709 | −0.543544 | − | 0.839381i | \(-0.682918\pi\) | ||||
−0.543544 | + | 0.839381i | \(0.682918\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.86576e23 | 1.38040 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.61222e23 | −0.408985 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.29078e24 | −1.80516 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.93240e23 | 0.867031 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.45180e24 | 1.62577 | 0.812883 | − | 0.582428i | \(-0.197897\pi\) | ||||
0.812883 | + | 0.582428i | \(0.197897\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.88032e23 | 0.590268 | 0.295134 | − | 0.955456i | \(-0.404636\pi\) | ||||
0.295134 | + | 0.955456i | \(0.404636\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.29714e24 | −1.16849 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.28721e24 | −1.04172 | −0.520862 | − | 0.853641i | \(-0.674390\pi\) | ||||
−0.520862 | + | 0.853641i | \(0.674390\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.02349e24 | −0.744948 | −0.372474 | − | 0.928043i | \(-0.621490\pi\) | ||||
−0.372474 | + | 0.928043i | \(0.621490\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.63054e24 | 1.06849 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.48967e24 | −0.879798 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.25206e24 | −1.19995 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.60493e23 | −0.0772267 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.65510e24 | −2.02485 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.95941e23 | −0.391984 | −0.195992 | − | 0.980606i | \(-0.562793\pi\) | ||||
−0.195992 | + | 0.980606i | \(0.562793\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.51616e23 | −0.339216 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.12089e24 | 1.00850 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.81481e23 | 0.111852 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.43169e24 | −0.381229 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.70084e24 | 2.10592 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.42854e24 | 0.975122 | 0.487561 | − | 0.873089i | \(-0.337887\pi\) | ||||
0.487561 | + | 0.873089i | \(0.337887\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.54601e23 | 0.0510438 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.23549e24 | −0.773806 | −0.386903 | − | 0.922120i | \(-0.626455\pi\) | ||||
−0.386903 | + | 0.922120i | \(0.626455\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.57364e24 | 1.09530 | 0.547650 | − | 0.836708i | \(-0.315523\pi\) | ||||
0.547650 | + | 0.836708i | \(0.315523\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.24611e24 | 0.949912 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.03875e24 | −0.144302 | −0.0721509 | − | 0.997394i | \(-0.522986\pi\) | ||||
−0.0721509 | + | 0.997394i | \(0.522986\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.09478e24 | −0.647012 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.73044e24 | −0.781963 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.83947e24 | 0.621149 | 0.310574 | − | 0.950549i | \(-0.399479\pi\) | ||||
0.310574 | + | 0.950549i | \(0.399479\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.84920e24 | 0.375138 | 0.187569 | − | 0.982251i | \(-0.439939\pi\) | ||||
0.187569 | + | 0.982251i | \(0.439939\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.15790e24 | 0.371542 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.58448e24 | 0.293888 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.13789e25 | 2.36222 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.53002e24 | −0.520839 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.86677e25 | −1.82313 | −0.911567 | − | 0.411151i | \(-0.865127\pi\) | ||||
−0.911567 | + | 0.411151i | \(0.865127\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.11908e24 | −0.533563 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.97979e25 | −1.06647 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.67250e25 | 1.82249 | 0.911243 | − | 0.411868i | \(-0.135124\pi\) | ||||
0.911243 | + | 0.411868i | \(0.135124\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.47894e24 | −0.387877 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.85207e24 | −0.204740 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.79474e25 | 0.698983 | 0.349492 | − | 0.936939i | \(-0.386354\pi\) | ||||
0.349492 | + | 0.936939i | \(0.386354\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.31405e25 | −0.832321 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.06048e25 | −0.684857 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.85890e24 | −0.210793 | −0.105396 | − | 0.994430i | \(-0.533611\pi\) | ||||
−0.105396 | + | 0.994430i | \(0.533611\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.95982e24 | −0.283187 | −0.141594 | − | 0.989925i | \(-0.545223\pi\) | ||||
−0.141594 | + | 0.989925i | \(0.545223\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.21035e25 | −1.10818 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.44662e25 | 0.352664 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.13250e25 | −0.255858 | −0.127929 | − | 0.991783i | \(-0.540833\pi\) | ||||
−0.127929 | + | 0.991783i | \(0.540833\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.24253e24 | 0.0260294 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.74755e23 | −0.00339636 | −0.00169818 | − | 0.999999i | \(-0.500541\pi\) | ||||
−0.00169818 | + | 0.999999i | \(0.500541\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.85617e23 | 0.00515260 | 0.00257630 | − | 0.999997i | \(-0.499180\pi\) | ||||
0.00257630 | + | 0.999997i | \(0.499180\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.13996e25 | −1.19626 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.30989e25 | −1.13802 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.37066e25 | 0.922055 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.56921e25 | −0.345878 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.21385e25 | 0.277357 | 0.138678 | − | 0.990337i | \(-0.455715\pi\) | ||||
0.138678 | + | 0.990337i | \(0.455715\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.38682e24 | −0.0861641 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.28296e26 | 1.39403 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.14695e25 | 0.622461 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.01300e26 | 0.956448 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.53204e26 | 1.34934 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.59186e26 | −1.30845 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.00481e26 | 0.771137 | 0.385569 | − | 0.922679i | \(-0.374005\pi\) | ||||
0.385569 | + | 0.922679i | \(0.374005\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.39250e26 | 0.998231 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.29128e26 | 0.865043 | 0.432521 | − | 0.901624i | \(-0.357624\pi\) | ||||
0.432521 | + | 0.901624i | \(0.357624\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.59492e26 | −0.998906 | −0.499453 | − | 0.866341i | \(-0.666466\pi\) | ||||
−0.499453 | + | 0.866341i | \(0.666466\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.22474e25 | −0.130322 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.73329e25 | 0.478692 | 0.239346 | − | 0.970934i | \(-0.423067\pi\) | ||||
0.239346 | + | 0.970934i | \(0.423067\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.75691e26 | −1.41456 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.08627e26 | 1.00246 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.78928e26 | 2.15598 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.75132e25 | −0.411423 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.61862e26 | −1.43150 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.65370e26 | −0.613620 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.50377e26 | −1.91631 | −0.958157 | − | 0.286245i | \(-0.907593\pi\) | ||||
−0.958157 | + | 0.286245i | \(0.907593\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.76170e25 | −0.0902636 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.29986e26 | −1.01280 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.51815e25 | 0.159103 | 0.0795517 | − | 0.996831i | \(-0.474651\pi\) | ||||
0.0795517 | + | 0.996831i | \(0.474651\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.53031e26 | 1.49849 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.05998e25 | 0.179838 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.54400e26 | 1.08855 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.39868e26 | −0.315222 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.14487e26 | 0.879126 | 0.439563 | − | 0.898212i | \(-0.355133\pi\) | ||||
0.439563 | + | 0.898212i | \(0.355133\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.30244e26 | −0.859108 | −0.429554 | − | 0.903041i | \(-0.641329\pi\) | ||||
−0.429554 | + | 0.903041i | \(0.641329\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.64815e26 | −1.62629 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.04943e26 | −0.717398 | −0.358699 | − | 0.933453i | \(-0.616780\pi\) | ||||
−0.358699 | + | 0.933453i | \(0.616780\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.92587e26 | 0.321535 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.42614e26 | −1.01143 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.27535e27 | −1.89294 | −0.946469 | − | 0.322794i | \(-0.895378\pi\) | ||||
−0.946469 | + | 0.322794i | \(0.895378\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.01301e27 | 1.41836 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.74125e26 | 0.626431 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.89744e26 | 0.361359 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.71084e26 | −0.554759 | −0.277380 | − | 0.960760i | \(-0.589466\pi\) | ||||
−0.277380 | + | 0.960760i | \(0.589466\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.38093e26 | −0.264832 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.51111e26 | −0.789365 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.52311e26 | −0.945880 | −0.472940 | − | 0.881095i | \(-0.656807\pi\) | ||||
−0.472940 | + | 0.881095i | \(0.656807\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.04109e27 | 0.977593 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.85836e27 | 1.65024 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.39167e26 | 0.536912 | 0.268456 | − | 0.963292i | \(-0.413487\pi\) | ||||
0.268456 | + | 0.963292i | \(0.413487\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.22037e27 | 0.970016 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.07948e27 | 1.56447 | 0.782237 | − | 0.622981i | \(-0.214078\pi\) | ||||
0.782237 | + | 0.622981i | \(0.214078\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.26408e27 | −0.900402 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.29948e26 | 0.222577 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.59448e26 | 0.613127 | 0.306564 | − | 0.951850i | \(-0.400821\pi\) | ||||
0.306564 | + | 0.951850i | \(0.400821\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.38193e26 | 0.568115 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.19739e27 | −1.26121 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.36210e27 | 0.741206 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.07265e27 | 0.553551 | 0.276776 | − | 0.960935i | \(-0.410734\pi\) | ||||
0.276776 | + | 0.960935i | \(0.410734\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.31754e27 | −1.13452 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.20976e27 | 1.49093 | 0.745464 | − | 0.666546i | \(-0.232228\pi\) | ||||
0.745464 | + | 0.666546i | \(0.232228\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.75896e26 | −0.209802 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.58330e27 | 0.662651 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.56918e27 | −0.623636 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.21280e27 | −0.457820 | −0.228910 | − | 0.973448i | \(-0.573516\pi\) | ||||
−0.228910 | + | 0.973448i | \(0.573516\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.99799e26 | −0.0716562 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.39767e26 | −0.0817172 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.52392e27 | 0.493692 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.69758e27 | −0.830893 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.87689e27 | −0.549784 | −0.274892 | − | 0.961475i | \(-0.588642\pi\) | ||||
−0.274892 | + | 0.961475i | \(0.588642\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.61930e27 | −0.451195 | −0.225598 | − | 0.974221i | \(-0.572433\pi\) | ||||
−0.225598 | + | 0.974221i | \(0.572433\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.38632e26 | −0.142797 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.48832e27 | −0.375502 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.16698e27 | −1.24092 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.79200e27 | −1.78175 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.51808e27 | 1.63718 | 0.818589 | − | 0.574380i | \(-0.194757\pi\) | ||||
0.818589 | + | 0.574380i | \(0.194757\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.53633e25 | −0.0114842 | −0.00574208 | − | 0.999984i | \(-0.501828\pi\) | ||||
−0.00574208 | + | 0.999984i | \(0.501828\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.22852e27 | −0.835702 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.38352e27 | 0.637256 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.79922e27 | −0.502527 | −0.251264 | − | 0.967919i | \(-0.580846\pi\) | ||||
−0.251264 | + | 0.967919i | \(0.580846\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.78960e26 | 0.0648616 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.75198e27 | 1.10203 | 0.551014 | − | 0.834496i | \(-0.314241\pi\) | ||||
0.551014 | + | 0.834496i | \(0.314241\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.16997e27 | 0.649162 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.30539e27 | −0.342385 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.45343e27 | 0.489400 | 0.244700 | − | 0.969599i | \(-0.421311\pi\) | ||||
0.244700 | + | 0.969599i | \(0.421311\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.35283e28 | −1.82973 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.53795e27 | 0.844132 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.52085e27 | 1.05042 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.82771e27 | −0.686085 | −0.343042 | − | 0.939320i | \(-0.611457\pi\) | ||||
−0.343042 | + | 0.939320i | \(0.611457\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.31994e28 | −1.48430 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.26600e27 | −0.995480 | −0.497740 | − | 0.867326i | \(-0.665837\pi\) | ||||
−0.497740 | + | 0.867326i | \(0.665837\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.43306e28 | 1.47117 | 0.735586 | − | 0.677431i | \(-0.236907\pi\) | ||||
0.735586 | + | 0.677431i | \(0.236907\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.08285e27 | 0.106246 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.24220e28 | 1.16510 | 0.582552 | − | 0.812794i | \(-0.302054\pi\) | ||||
0.582552 | + | 0.812794i | \(0.302054\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.07109e28 | −0.960532 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.90010e27 | 0.334470 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.87474e28 | 1.53780 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.36751e27 | −0.421201 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.44647e27 | −0.183695 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.55141e28 | 1.11482 | 0.557410 | − | 0.830237i | \(-0.311795\pi\) | ||||
0.557410 | + | 0.830237i | \(0.311795\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.05775e28 | 0.727542 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.53993e27 | −0.298954 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.19953e27 | 0.327850 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.10212e26 | 0.00665542 | 0.00332771 | − | 0.999994i | \(-0.498941\pi\) | ||||
0.00332771 | + | 0.999994i | \(0.498941\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.87079e27 | 0.108213 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.45763e28 | 0.807779 | 0.403890 | − | 0.914808i | \(-0.367658\pi\) | ||||
0.403890 | + | 0.914808i | \(0.367658\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.83637e28 | 1.50616 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.11727e27 | −0.209534 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.25112e27 | 0.304941 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.13652e28 | −0.531522 | −0.265761 | − | 0.964039i | \(-0.585623\pi\) | ||||
−0.265761 | + | 0.964039i | \(0.585623\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.36133e24 | 6.10474e−5 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.78149e28 | −1.62630 | −0.813148 | − | 0.582057i | \(-0.802248\pi\) | ||||
−0.813148 | + | 0.582057i | \(0.802248\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.10051e28 | −1.27901 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.97605e28 | 1.17776 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.31841e27 | −0.353839 | −0.176919 | − | 0.984225i | \(-0.556613\pi\) | ||||
−0.176919 | + | 0.984225i | \(0.556613\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.40471e27 | 0.342710 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.76028e28 | −1.66495 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.81812e28 | −0.946202 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.06046e28 | −0.986590 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.72363e27 | 0.0533565 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.08795e25 | −0.000620762 0 | −0.000310381 | − | 1.00000i | \(-0.500099\pi\) | ||||
−0.000310381 | 1.00000i | \(0.500099\pi\) | ||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.53000e28 | −0.436941 | −0.218470 | − | 0.975844i | \(-0.570107\pi\) | ||||
−0.218470 | + | 0.975844i | \(0.570107\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.20199e27 | 0.197597 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.26347e27 | −0.191484 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.28435e28 | −0.832079 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.80952e26 | −0.0190166 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.11907e28 | 2.13459 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.22216e28 | −0.950210 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.97834e28 | 0.428126 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.15322e28 | 0.448132 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.80431e28 | −1.56230 | −0.781148 | − | 0.624346i | \(-0.785365\pi\) | ||||
−0.781148 | + | 0.624346i | \(0.785365\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.08532e28 | −0.979310 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.32332e28 | 1.35689 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.32938e28 | 0.771897 | 0.385948 | − | 0.922520i | \(-0.373874\pi\) | ||||
0.385948 | + | 0.922520i | \(0.373874\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.68295e28 | −0.288777 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.02292e29 | 1.68946 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.42120e28 | 0.702953 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.40679e28 | −0.368436 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.94436e28 | 0.286614 | 0.143307 | − | 0.989678i | \(-0.454226\pi\) | ||||
0.143307 | + | 0.989678i | \(0.454226\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.26372e29 | −1.79401 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.18927e29 | −1.62619 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.12608e29 | 1.48331 | 0.741655 | − | 0.670781i | \(-0.234041\pi\) | ||||
0.741655 | + | 0.670781i | \(0.234041\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.11922e29 | −1.42038 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.13918e28 | 0.628451 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.23100e28 | 0.734309 | 0.367154 | − | 0.930160i | \(-0.380332\pi\) | ||||
0.367154 | + | 0.930160i | \(0.380332\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.12398e29 | 1.27667 | 0.638334 | − | 0.769760i | \(-0.279624\pi\) | ||||
0.638334 | + | 0.769760i | \(0.279624\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.33763e29 | 1.46458 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.05146e28 | −0.110990 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.21433e29 | 1.23592 | 0.617960 | − | 0.786210i | \(-0.287960\pi\) | ||||
0.617960 | + | 0.786210i | \(0.287960\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.41788e28 | 0.531747 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.94644e28 | 0.468213 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.39006e29 | −1.26916 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.77535e28 | 0.244445 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.84042e28 | −0.581276 | −0.290638 | − | 0.956833i | \(-0.593868\pi\) | ||||
−0.290638 | + | 0.956833i | \(0.593868\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.61952e28 | −0.214788 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.18598e29 | −0.938444 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.52013e28 | −0.421575 | −0.210787 | − | 0.977532i | \(-0.567603\pi\) | ||||
−0.210787 | + | 0.977532i | \(0.567603\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.30051e29 | 0.958709 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.43001e28 | −0.671091 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.03055e29 | 0.708091 | 0.354046 | − | 0.935228i | \(-0.384806\pi\) | ||||
0.354046 | + | 0.935228i | \(0.384806\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.81265e29 | 1.20263 | 0.601314 | − | 0.799013i | \(-0.294644\pi\) | ||||
0.601314 | + | 0.799013i | \(0.294644\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.48869e28 | −0.223527 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.59527e28 | −0.593780 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.69189e28 | 0.220682 | 0.110341 | − | 0.993894i | \(-0.464806\pi\) | ||||
0.110341 | + | 0.993894i | \(0.464806\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.37252e29 | −0.792572 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.06298e29 | 1.15097 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.42961e29 | 0.770696 | 0.385348 | − | 0.922771i | \(-0.374081\pi\) | ||||
0.385348 | + | 0.922771i | \(0.374081\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.07495e29 | −1.08098 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.41658e29 | −1.72027 | −0.860137 | − | 0.510063i | \(-0.829622\pi\) | ||||
−0.860137 | + | 0.510063i | \(0.829622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.26714e29 | −0.616700 | −0.308350 | − | 0.951273i | \(-0.599777\pi\) | ||||
−0.308350 | + | 0.951273i | \(0.599777\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.32511e28 | −0.438725 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.35352e29 | 0.615658 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.49109e29 | −0.655790 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.28902e29 | −1.82410 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.61441e29 | 0.664021 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.54527e28 | −0.339952 | −0.169976 | − | 0.985448i | \(-0.554369\pi\) | ||||
−0.169976 | + | 0.985448i | \(0.554369\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.17619e28 | −0.353121 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.46977e29 | −0.919457 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.45143e29 | −0.522797 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.03607e28 | 0.0709634 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.29678e29 | 1.11194 | 0.555969 | − | 0.831203i | \(-0.312347\pi\) | ||||
0.555969 | + | 0.831203i | \(0.312347\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.26473e29 | −0.739268 | −0.369634 | − | 0.929177i | \(-0.620517\pi\) | ||||
−0.369634 | + | 0.929177i | \(0.620517\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.87546e29 | 0.908511 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.40922e29 | 0.431005 | 0.215503 | − | 0.976503i | \(-0.430861\pi\) | ||||
0.215503 | + | 0.976503i | \(0.430861\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.43731e28 | −0.131386 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.51481e28 | 0.100763 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.00388e29 | −1.66665 | −0.833323 | − | 0.552786i | \(-0.813565\pi\) | ||||
−0.833323 | + | 0.552786i | \(0.813565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.44705e29 | 1.19547 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.06324e28 | 0.0797526 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.22410e29 | 1.31739 | 0.658695 | − | 0.752410i | \(-0.271109\pi\) | ||||
0.658695 | + | 0.752410i | \(0.271109\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.46063e29 | 1.08963 | 0.544817 | − | 0.838555i | \(-0.316599\pi\) | ||||
0.544817 | + | 0.838555i | \(0.316599\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.01659e29 | 1.89713 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.69021e29 | 1.07539 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.00383e29 | 0.445185 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.08027e29 | 0.878445 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.56241e29 | −1.99518 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.24333e29 | −1.46481 | −0.732403 | − | 0.680871i | \(-0.761601\pi\) | ||||
−0.732403 | + | 0.680871i | \(0.761601\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.47931e29 | 0.289980 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.20060e29 | 0.418176 | 0.209088 | − | 0.977897i | \(-0.432950\pi\) | ||||
0.209088 | + | 0.977897i | \(0.432950\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.68770e29 | 0.310930 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.90240e29 | −0.697088 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.92621e29 | −1.37293 | −0.686465 | − | 0.727163i | \(-0.740838\pi\) | ||||
−0.686465 | + | 0.727163i | \(0.740838\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.04350e28 | 0.0679214 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.05668e29 | 0.986708 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.37009e29 | 1.48061 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.05813e29 | −1.23514 | −0.617568 | − | 0.786517i | \(-0.711882\pi\) | ||||
−0.617568 | + | 0.786517i | \(0.711882\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.33641e29 | −0.198720 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.45932e29 | 0.787586 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.39182e30 | 1.94822 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.57057e28 | −0.129995 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.00523e29 | −1.05520 | −0.527600 | − | 0.849493i | \(-0.676908\pi\) | ||||
−0.527600 | + | 0.849493i | \(0.676908\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.82224e29 | 0.744834 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.69412e29 | −0.582865 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.00639e30 | −1.21300 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.20024e30 | −1.40437 | −0.702185 | − | 0.711994i | \(-0.747792\pi\) | ||||
−0.702185 | + | 0.711994i | \(0.747792\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.44004e29 | 0.163585 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.13149e28 | −0.0565983 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.57693e30 | 1.68889 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.38025e29 | 0.559566 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.17808e29 | 0.321004 | 0.160502 | − | 0.987035i | \(-0.448689\pi\) | ||||
0.160502 | + | 0.987035i | \(0.448689\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.14727e29 | −0.897369 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.54649e29 | 0.337946 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.17882e29 | −0.294250 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.42314e30 | −1.27978 | −0.639892 | − | 0.768465i | \(-0.721021\pi\) | ||||
−0.639892 | + | 0.768465i | \(0.721021\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.27130e30 | 1.11073 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.92877e30 | −1.63738 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.17834e30 | −0.972031 | −0.486016 | − | 0.873950i | \(-0.661550\pi\) | ||||
−0.486016 | + | 0.873950i | \(0.661550\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.30259e29 | 0.264751 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.98225e30 | −1.54436 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.73577e30 | −1.31440 | −0.657198 | − | 0.753718i | \(-0.728258\pi\) | ||||
−0.657198 | + | 0.753718i | \(0.728258\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.89112e30 | 2.12802 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.69683e29 | −0.336064 | −0.168032 | − | 0.985782i | \(-0.553741\pi\) | ||||
−0.168032 | + | 0.985782i | \(0.553741\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.66561e29 | 0.324540 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.61112e29 | 0.108959 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.37046e30 | −0.901170 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.47353e29 | 0.477866 | 0.238933 | − | 0.971036i | \(-0.423202\pi\) | ||||
0.238933 | + | 0.971036i | \(0.423202\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.64132e30 | −1.64238 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.32314e30 | −0.800135 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.10588e30 | 1.23859 | 0.619293 | − | 0.785160i | \(-0.287419\pi\) | ||||
0.619293 | + | 0.785160i | \(0.287419\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.40194e29 | −0.480664 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.10629e29 | −0.506760 | −0.253380 | − | 0.967367i | \(-0.581542\pi\) | ||||
−0.253380 | + | 0.967367i | \(0.581542\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.37706e30 | 1.28686 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.23595e29 | 0.223103 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.99108e29 | 0.153277 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.59434e30 | 1.29360 | 0.646801 | − | 0.762659i | \(-0.276106\pi\) | ||||
0.646801 | + | 0.762659i | \(0.276106\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.38369e30 | 1.64180 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.32692e30 | −0.626559 | −0.313279 | − | 0.949661i | \(-0.601428\pi\) | ||||
−0.313279 | + | 0.949661i | \(0.601428\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.14042e28 | 0.0374092 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.81215e29 | −0.349422 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.01949e30 | 2.18533 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.15688e30 | 0.490290 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.81920e30 | −1.16313 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.89298e29 | −0.317037 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.12807e29 | 0.200548 | 0.100274 | − | 0.994960i | \(-0.468028\pi\) | ||||
0.100274 | + | 0.994960i | \(0.468028\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.65360e30 | 0.629684 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.63284e30 | −1.34708 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.44579e30 | 2.32760 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.13207e30 | −0.749802 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.27653e30 | −0.437239 | −0.218620 | − | 0.975810i | \(-0.570155\pi\) | ||||
−0.218620 | + | 0.975810i | \(0.570155\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.14868e30 | 1.05048 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.40859e29 | 0.143271 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.74051e30 | 0.551015 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.18785e29 | 0.283372 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.31951e29 | −0.189894 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.38086e30 | 0.404287 | 0.202144 | − | 0.979356i | \(-0.435209\pi\) | ||||
0.202144 | + | 0.979356i | \(0.435209\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.03179e29 | −0.115021 | −0.0575107 | − | 0.998345i | \(-0.518316\pi\) | ||||
−0.0575107 | + | 0.998345i | \(0.518316\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.17657e29 | −0.255111 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.78607e29 | −0.102573 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.95598e30 | −1.83665 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.00845e29 | 0.231830 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.10056e29 | −0.0777745 | −0.0388873 | − | 0.999244i | \(-0.512381\pi\) | ||||
−0.0388873 | + | 0.999244i | \(0.512381\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.10242e30 | −0.269555 | −0.134777 | − | 0.990876i | \(-0.543032\pi\) | ||||
−0.134777 | + | 0.990876i | \(0.543032\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.33286e30 | 0.317700 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.82951e29 | 0.228415 | 0.114207 | − | 0.993457i | \(-0.463567\pi\) | ||||
0.114207 | + | 0.993457i | \(0.463567\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.60776e30 | −1.27048 | −0.635239 | − | 0.772316i | \(-0.719098\pi\) | ||||
−0.635239 | + | 0.772316i | \(0.719098\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.04344e30 | −0.230492 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.21528e30 | −0.477152 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.75504e26 | −5.78655e−5 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.21949e29 | 0.147873 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.92515e30 | −0.784071 | −0.392036 | − | 0.919950i | \(-0.628229\pi\) | ||||
−0.392036 | + | 0.919950i | \(0.628229\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.25212e29 | 0.180253 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.61012e28 | −0.00305963 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.02288e30 | −1.11637 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.11450e30 | −0.563135 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.63155e28 | 0.00464175 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.14054e30 | 0.196269 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.01715e30 | 1.51393 | 0.756963 | − | 0.653458i | \(-0.226683\pi\) | ||||
0.756963 | + | 0.653458i | \(0.226683\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.52766e30 | 0.250255 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.89609e30 | 1.26216 | 0.631079 | − | 0.775719i | \(-0.282612\pi\) | ||||
0.631079 | + | 0.775719i | \(0.282612\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.91414e30 | −0.610531 | −0.305266 | − | 0.952267i | \(-0.598745\pi\) | ||||
−0.305266 | + | 0.952267i | \(0.598745\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.73503e30 | −1.02520 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.32795e31 | −1.97273 | −0.986365 | − | 0.164572i | \(-0.947376\pi\) | ||||
−0.986365 | + | 0.164572i | \(0.947376\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.48826e29 | −0.0505755 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.86966e30 | 0.830639 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.18221e30 | 1.13022 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.33618e31 | 1.80167 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.49707e29 | 0.0723571 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.83884e30 | −0.878816 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.33474e31 | −1.67456 | −0.837278 | − | 0.546778i | \(-0.815854\pi\) | ||||
−0.837278 | + | 0.546778i | \(0.815854\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.03975e30 | 0.249859 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.47240e31 | −1.76108 | −0.880538 | − | 0.473976i | \(-0.842818\pi\) | ||||
−0.880538 | + | 0.473976i | \(0.842818\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.20820e29 | −0.0491484 | −0.0245742 | − | 0.999698i | \(-0.507823\pi\) | ||||
−0.0245742 | + | 0.999698i | \(0.507823\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.80591e29 | −0.0776215 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.56495e30 | −0.397060 | −0.198530 | − | 0.980095i | \(-0.563617\pi\) | ||||
−0.198530 | + | 0.980095i | \(0.563617\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.01654e30 | −0.872004 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.51097e30 | 1.01044 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.13555e31 | 1.17832 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.00375e30 | −0.405812 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.66355e30 | 0.560748 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.55137e30 | −0.150051 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.43013e31 | 1.35134 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.33337e30 | 0.861623 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.02916e31 | 0.928267 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.63550e30 | 0.761046 | 0.380523 | − | 0.924771i | \(-0.375744\pi\) | ||||
0.380523 | + | 0.924771i | \(0.375744\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.27794e30 | −0.282280 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.20841e31 | 1.85839 | 0.929197 | − | 0.369586i | \(-0.120500\pi\) | ||||
0.929197 | + | 0.369586i | \(0.120500\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.15426e30 | 0.752801 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.46668e31 | −1.17872 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.44346e31 | 1.13377 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.56943e30 | −0.197253 | −0.0986265 | − | 0.995125i | \(-0.531445\pi\) | ||||
−0.0986265 | + | 0.995125i | \(0.531445\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.25792e30 | 0.694684 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.79825e30 | −0.571978 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.80932e30 | −0.129726 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.97939e30 | −0.208828 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.85518e31 | −1.27122 | −0.635611 | − | 0.772010i | \(-0.719252\pi\) | ||||
−0.635611 | + | 0.772010i | \(0.719252\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.98925e30 | −0.535223 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.18974e31 | 0.779279 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.40683e31 | 1.54143 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.89731e30 | −0.369308 | −0.184654 | − | 0.982804i | \(-0.559116\pi\) | ||||
−0.184654 | + | 0.982804i | \(0.559116\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.46950e31 | −0.899871 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.82883e31 | −1.09517 | −0.547587 | − | 0.836749i | \(-0.684453\pi\) | ||||
−0.547587 | + | 0.836749i | \(0.684453\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.83289e30 | 0.575849 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.29264e31 | −0.740360 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.73590e30 | 0.321312 | 0.160656 | − | 0.987010i | \(-0.448639\pi\) | ||||
0.160656 | + | 0.987010i | \(0.448639\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.17324e31 | −0.642821 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.04649e30 | 0.431232 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.27548e31 | 0.668647 | 0.334324 | − | 0.942458i | \(-0.391492\pi\) | ||||
0.334324 | + | 0.942458i | \(0.391492\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.70708e31 | −1.38825 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.54010e31 | −1.27431 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.31247e30 | 0.0644160 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.04282e31 | −0.980923 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.46377e30 | −0.209713 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.09646e31 | −0.504031 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.48789e31 | −1.11906 | −0.559531 | − | 0.828810i | \(-0.689019\pi\) | ||||
−0.559531 | + | 0.828810i | \(0.689019\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.41264e31 | 1.94222 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.93374e31 | −1.26363 | −0.631814 | − | 0.775120i | \(-0.717689\pi\) | ||||
−0.631814 | + | 0.775120i | \(0.717689\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.77203e31 | 0.746939 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.98446e30 | −0.370633 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.41713e31 | −0.572159 | −0.286080 | − | 0.958206i | \(-0.592352\pi\) | ||||
−0.286080 | + | 0.958206i | \(0.592352\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.50493e31 | 0.989867 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.74239e30 | 0.299468 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.05921e31 | 1.15824 | 0.579119 | − | 0.815243i | \(-0.303397\pi\) | ||||
0.579119 | + | 0.815243i | \(0.303397\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.40017e31 | 0.889532 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.52365e31 | −0.552784 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.36264e31 | −0.483971 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.24783e31 | −1.47704 | −0.738522 | − | 0.674229i | \(-0.764476\pi\) | ||||
−0.738522 | + | 0.674229i | \(0.764476\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.07095e31 | −1.72632 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.90843e31 | 0.636113 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.55461e31 | −0.507369 | −0.253684 | − | 0.967287i | \(-0.581642\pi\) | ||||
−0.253684 | + | 0.967287i | \(0.581642\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.60463e31 | −0.512788 |
(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 | 16.22.a.d.1.2 | 2 | ||
4.3 | odd | 2 | 4.22.a.a.1.1 | ✓ | 2 | ||
8.3 | odd | 2 | 64.22.a.i.1.2 | 2 | |||
8.5 | even | 2 | 64.22.a.j.1.1 | 2 | |||
12.11 | even | 2 | 36.22.a.c.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.22.a.a.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
16.22.a.d.1.2 | 2 | 1.1 | even | 1 | trivial | ||
36.22.a.c.1.2 | 2 | 12.11 | even | 2 | |||
64.22.a.i.1.2 | 2 | 8.3 | odd | 2 | |||
64.22.a.j.1.1 | 2 | 8.5 | even | 2 |