Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,22,Mod(1,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(134.149125258\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 6) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 48.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 59049.0 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.29542e7 | 0.593232 | 0.296616 | − | 0.954997i | \(-0.404142\pi\) | ||||
0.296616 | + | 0.954997i | \(0.404142\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.79513e8 | 0.641610 | 0.320805 | − | 0.947145i | \(-0.396047\pi\) | ||||
0.320805 | + | 0.947145i | \(0.396047\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.15658e11 | −1.34447 | −0.672236 | − | 0.740337i | \(-0.734666\pi\) | ||||
−0.672236 | + | 0.740337i | \(0.734666\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.95658e11 | 0.594819 | 0.297409 | − | 0.954750i | \(-0.403877\pi\) | ||||
0.297409 | + | 0.954750i | \(0.403877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.64931e11 | 0.342503 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.62698e12 | 0.797264 | 0.398632 | − | 0.917111i | \(-0.369485\pi\) | ||||
0.398632 | + | 0.917111i | \(0.369485\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.85762e13 | −1.06928 | −0.534640 | − | 0.845080i | \(-0.679553\pi\) | ||||
−0.534640 | + | 0.845080i | \(0.679553\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.83148e13 | 0.370434 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.35385e14 | −1.68811 | −0.844057 | − | 0.536254i | \(-0.819839\pi\) | ||||
−0.844057 | + | 0.536254i | \(0.819839\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.09027e14 | −0.648076 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.05891e14 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.99224e14 | −0.308630 | −0.154315 | − | 0.988022i | \(-0.549317\pi\) | ||||
−0.154315 | + | 0.988022i | \(0.549317\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.48496e15 | 0.763659 | 0.381830 | − | 0.924233i | \(-0.375294\pi\) | ||||
0.381830 | + | 0.924233i | \(0.375294\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.82948e15 | −0.776231 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.21170e15 | 0.380624 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.51815e16 | −1.20281 | −0.601404 | − | 0.798945i | \(-0.705392\pi\) | ||||
−0.601404 | + | 0.798945i | \(0.705392\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.74583e16 | 0.343419 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.13206e15 | 0.0713470 | 0.0356735 | − | 0.999363i | \(-0.488642\pi\) | ||||
0.0356735 | + | 0.999363i | \(0.488642\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.33261e17 | −1.64597 | −0.822987 | − | 0.568060i | \(-0.807694\pi\) | ||||
−0.822987 | + | 0.568060i | \(0.807694\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.51684e16 | 0.197744 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.80206e17 | 1.60899 | 0.804497 | − | 0.593957i | \(-0.202435\pi\) | ||||
0.804497 | + | 0.593957i | \(0.202435\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.28613e17 | −0.588337 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.91317e17 | 0.460301 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.39447e18 | −1.09525 | −0.547625 | − | 0.836724i | \(-0.684468\pi\) | ||||
−0.547625 | + | 0.836724i | \(0.684468\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.49825e18 | −0.797584 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.68740e18 | −0.617349 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.35248e18 | −0.599210 | −0.299605 | − | 0.954063i | \(-0.596855\pi\) | ||||
−0.299605 | + | 0.954063i | \(0.596855\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.92063e18 | 1.78064 | 0.890320 | − | 0.455336i | \(-0.150481\pi\) | ||||
0.890320 | + | 0.455336i | \(0.150481\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.67196e18 | 0.213870 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.83001e18 | 0.352866 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.60690e19 | −1.74718 | −0.873592 | − | 0.486659i | \(-0.838215\pi\) | ||||
−0.873592 | + | 0.486659i | \(0.838215\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.98042e19 | −0.974633 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.33370e19 | 0.486233 | 0.243116 | − | 0.969997i | \(-0.421830\pi\) | ||||
0.243116 | + | 0.969997i | \(0.421830\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.03753e18 | 0.246127 | 0.123064 | − | 0.992399i | \(-0.460728\pi\) | ||||
0.123064 | + | 0.992399i | \(0.460728\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.82477e19 | −0.374167 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.54594e19 | −0.862626 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.72839e19 | 0.918342 | 0.459171 | − | 0.888348i | \(-0.348147\pi\) | ||||
0.459171 | + | 0.888348i | \(0.348147\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.55698e20 | 1.10145 | 0.550724 | − | 0.834687i | \(-0.314352\pi\) | ||||
0.550724 | + | 0.834687i | \(0.314352\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.58471e19 | 0.472963 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.12885e19 | −0.178187 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.53837e20 | 0.862900 | 0.431450 | − | 0.902137i | \(-0.358002\pi\) | ||||
0.431450 | + | 0.902137i | \(0.358002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.41772e20 | 0.381642 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.05783e20 | 0.440899 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.70181e20 | −0.634331 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.03072e21 | −1.41918 | −0.709591 | − | 0.704613i | \(-0.751120\pi\) | ||||
−0.709591 | + | 0.704613i | \(0.751120\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.03274e20 | −0.448157 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.65513e20 | −0.689570 | −0.344785 | − | 0.938682i | \(-0.612048\pi\) | ||||
−0.344785 | + | 0.938682i | \(0.612048\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.97524e20 | 0.658044 | 0.329022 | − | 0.944322i | \(-0.393281\pi\) | ||||
0.329022 | + | 0.944322i | \(0.393281\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.66794e20 | 0.219753 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.71774e21 | −0.844166 | −0.422083 | − | 0.906557i | \(-0.638701\pi\) | ||||
−0.422083 | + | 0.906557i | \(0.638701\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.99848e21 | 1.21317 | 0.606586 | − | 0.795018i | \(-0.292539\pi\) | ||||
0.606586 | + | 0.795018i | \(0.292539\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.07743e21 | −0.694442 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.11711e21 | −1.41808 | −0.709041 | − | 0.705168i | \(-0.750872\pi\) | ||||
−0.709041 | + | 0.705168i | \(0.750872\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.34464e21 | −1.00144 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.03090e21 | 0.198273 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.17773e21 | 0.511533 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.97647e21 | 0.807604 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.62092e20 | 0.0411922 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.01802e22 | −0.977691 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.05103e21 | −0.329326 | −0.164663 | − | 0.986350i | \(-0.552654\pi\) | ||||
−0.164663 | + | 0.986350i | \(0.552654\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.37738e22 | −0.950304 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.92867e22 | 1.13217 | 0.566083 | − | 0.824348i | \(-0.308458\pi\) | ||||
0.566083 | + | 0.824348i | \(0.308458\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.37027e22 | −0.686061 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.66715e21 | 0.114168 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.93536e22 | −1.07670 | −0.538351 | − | 0.842721i | \(-0.680953\pi\) | ||||
−0.538351 | + | 0.842721i | \(0.680953\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.24068e22 | −1.33592 | −0.667959 | − | 0.744198i | \(-0.732832\pi\) | ||||
−0.667959 | + | 0.744198i | \(0.732832\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.42606e22 | 0.928953 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.41952e22 | −0.799717 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.05787e21 | −0.183089 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.94043e22 | −0.339676 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.04492e22 | 0.766299 | 0.383150 | − | 0.923686i | \(-0.374839\pi\) | ||||
0.383150 | + | 0.923686i | \(0.374839\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.30789e22 | −1.09707 | −0.548533 | − | 0.836129i | \(-0.684814\pi\) | ||||
−0.548533 | + | 0.836129i | \(0.684814\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.31069e22 | 0.265755 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.51447e22 | 0.453027 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.66285e23 | −1.45850 | −0.729250 | − | 0.684247i | \(-0.760131\pi\) | ||||
−0.729250 | + | 0.684247i | \(0.760131\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.23422e22 | −0.632343 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.60822e23 | −1.08311 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.13921e23 | 0.673958 | 0.336979 | − | 0.941512i | \(-0.390595\pi\) | ||||
0.336979 | + | 0.941512i | \(0.390595\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.84702e22 | −0.460485 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.52378e23 | −1.61617 | −0.808084 | − | 0.589068i | \(-0.799495\pi\) | ||||
−0.808084 | + | 0.589068i | \(0.799495\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.59651e23 | −0.646190 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.96390e22 | −0.356427 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.43709e22 | −0.172140 | −0.0860702 | − | 0.996289i | \(-0.527431\pi\) | ||||
−0.0860702 | + | 0.996289i | \(0.527431\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.48182e23 | −0.415812 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.38911e23 | −0.345954 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.57843e23 | −1.23468 | −0.617341 | − | 0.786695i | \(-0.711790\pi\) | ||||
−0.617341 | + | 0.786695i | \(0.711790\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.29021e23 | −1.04195 | −0.520976 | − | 0.853571i | \(-0.674432\pi\) | ||||
−0.520976 | + | 0.853571i | \(0.674432\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.85803e23 | 1.02805 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.55748e23 | −0.713545 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.66462e23 | −1.07190 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.87275e22 | 0.123478 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.19262e22 | 0.0917429 | 0.0458715 | − | 0.998947i | \(-0.485394\pi\) | ||||
0.0458715 | + | 0.998947i | \(0.485394\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.60174e23 | 0.662684 | 0.331342 | − | 0.943511i | \(-0.392499\pi\) | ||||
0.331342 | + | 0.943511i | \(0.392499\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.26158e23 | 0.203727 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.79420e23 | −0.711707 | −0.355853 | − | 0.934542i | \(-0.615810\pi\) | ||||
−0.355853 | + | 0.934542i | \(0.615810\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.82376e23 | −0.642239 | −0.321119 | − | 0.947039i | \(-0.604059\pi\) | ||||
−0.321119 | + | 0.947039i | \(0.604059\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.53935e24 | −1.00874 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.35287e23 | −0.198020 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.94357e22 | 0.0423253 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.16942e24 | −0.562704 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.30506e24 | 1.43762 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.86260e24 | 1.12667 | 0.563333 | − | 0.826230i | \(-0.309519\pi\) | ||||
0.563333 | + | 0.826230i | \(0.309519\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.87534e23 | 0.280727 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.02170e24 | −0.976445 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.67108e24 | 0.489971 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.33657e23 | 0.142102 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.95932e24 | 0.474228 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.04892e24 | 0.230963 | 0.115481 | − | 0.993310i | \(-0.463159\pi\) | ||||
0.115481 | + | 0.993310i | \(0.463159\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.07751e24 | −0.216025 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.22561e24 | 0.772002 | 0.386001 | − | 0.922498i | \(-0.373856\pi\) | ||||
0.386001 | + | 0.922498i | \(0.373856\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.40000e24 | −1.56623 | −0.783115 | − | 0.621877i | \(-0.786370\pi\) | ||||
−0.783115 | + | 0.621877i | \(0.786370\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.27482e24 | −0.498038 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.59528e24 | −0.777293 | −0.388646 | − | 0.921387i | \(-0.627057\pi\) | ||||
−0.388646 | + | 0.921387i | \(0.627057\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.51609e24 | 0.954507 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.56353e24 | 0.530205 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.79661e24 | 0.510219 | 0.255109 | − | 0.966912i | \(-0.417889\pi\) | ||||
0.255109 | + | 0.966912i | \(0.417889\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.30240e24 | 0.126930 | 0.0634649 | − | 0.997984i | \(-0.479785\pi\) | ||||
0.0634649 | + | 0.997984i | \(0.479785\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.17898e23 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.25691e24 | −0.349020 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.44878e24 | −0.636028 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.19384e24 | 0.635922 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.25489e25 | 0.798055 | 0.399027 | − | 0.916939i | \(-0.369348\pi\) | ||||
0.399027 | + | 0.916939i | \(0.369348\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.87899e25 | 2.26962 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.06919e24 | 0.273065 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.12478e25 | 1.55068 | 0.775339 | − | 0.631546i | \(-0.217579\pi\) | ||||
0.775339 | + | 0.631546i | \(0.217579\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.68700e25 | −0.771734 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.43804e24 | −0.102877 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.04345e25 | 0.795845 | 0.397923 | − | 0.917419i | \(-0.369731\pi\) | ||||
0.397923 | + | 0.917419i | \(0.369731\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.80642e25 | −0.649737 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.49888e25 | 0.498195 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.02651e24 | −0.185211 | −0.0926055 | − | 0.995703i | \(-0.529520\pi\) | ||||
−0.0926055 | + | 0.995703i | \(0.529520\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.13011e25 | 0.321324 | 0.160662 | − | 0.987009i | \(-0.448637\pi\) | ||||
0.160662 | + | 0.987009i | \(0.448637\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.37150e24 | 0.220341 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.57413e25 | 0.871319 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.51731e25 | 1.69834 | 0.849170 | − | 0.528119i | \(-0.177103\pi\) | ||||
0.849170 | + | 0.528119i | \(0.177103\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.21513e25 | 0.254553 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.24659e25 | −0.436623 | −0.218312 | − | 0.975879i | \(-0.570055\pi\) | ||||
−0.218312 | + | 0.975879i | \(0.570055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.02460e25 | 1.08685 | 0.543426 | − | 0.839457i | \(-0.317127\pi\) | ||||
0.543426 | + | 0.839457i | \(0.317127\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.18588e25 | −0.366231 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.94040e24 | 0.0457769 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.51750e25 | −0.364370 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.08631e25 | −0.819366 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.65033e24 | 0.0582604 | 0.0291302 | − | 0.999576i | \(-0.490726\pi\) | ||||
0.0291302 | + | 0.999576i | \(0.490726\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.04744e25 | −0.355471 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.38129e25 | −0.258744 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.91594e25 | −1.00412 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.11852e26 | −1.05607 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.52028e25 | −0.398123 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.28514e26 | 1.05633 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.89098e25 | 0.528844 | 0.264422 | − | 0.964407i | \(-0.414819\pi\) | ||||
0.264422 | + | 0.964407i | \(0.414819\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.29979e25 | 0.379922 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.75254e25 | 0.184395 | 0.0921976 | − | 0.995741i | \(-0.470611\pi\) | ||||
0.0921976 | + | 0.995741i | \(0.470611\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.51255e26 | −0.947316 | −0.473658 | − | 0.880709i | \(-0.657067\pi\) | ||||
−0.473658 | + | 0.880709i | \(0.657067\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.16588e25 | 0.126875 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.45958e25 | −0.299252 | −0.149626 | − | 0.988743i | \(-0.547807\pi\) | ||||
−0.149626 | + | 0.988743i | \(0.547807\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.08707e25 | 0.414944 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.01431e26 | −0.487379 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.89374e26 | −0.852499 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.13662e25 | −0.385488 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.77057e26 | 0.700425 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.78216e26 | 1.03235 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.57958e26 | −1.59453 | −0.797263 | − | 0.603632i | \(-0.793720\pi\) | ||||
−0.797263 | + | 0.603632i | \(0.793720\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.22670e26 | −0.400936 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.37702e26 | −1.03649 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.77477e26 | 0.511714 | 0.255857 | − | 0.966715i | \(-0.417642\pi\) | ||||
0.255857 | + | 0.966715i | \(0.417642\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.02160e26 | −0.818730 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.03062e26 | −1.02672 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.25404e26 | −1.01909 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.56547e26 | −0.578183 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.31317e26 | 0.702724 | 0.351362 | − | 0.936240i | \(-0.385719\pi\) | ||||
0.351362 | + | 0.936240i | \(0.385719\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.82866e26 | −0.365146 | −0.182573 | − | 0.983192i | \(-0.558443\pi\) | ||||
−0.182573 | + | 0.983192i | \(0.558443\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.08734e25 | 0.114473 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.58761e26 | −0.989900 | −0.494950 | − | 0.868921i | \(-0.664814\pi\) | ||||
−0.494950 | + | 0.868921i | \(0.664814\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.72769e26 | 0.288449 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.87642e26 | 0.295333 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.65986e26 | 1.28534 | 0.642671 | − | 0.766142i | \(-0.277826\pi\) | ||||
0.642671 | + | 0.766142i | \(0.277826\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.02389e26 | 0.143360 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.52905e26 | 0.466270 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.17074e26 | 0.146011 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.31813e26 | 0.155227 | 0.0776133 | − | 0.996984i | \(-0.475270\pi\) | ||||
0.0776133 | + | 0.996984i | \(0.475270\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.13812e25 | 0.0237823 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.68667e26 | −0.702723 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.80048e26 | −0.476806 | −0.238403 | − | 0.971166i | \(-0.576624\pi\) | ||||
−0.238403 | + | 0.971166i | \(0.576624\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.01132e26 | −0.564470 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.06731e26 | −0.183579 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.61041e26 | −0.303281 | −0.151640 | − | 0.988436i | \(-0.548456\pi\) | ||||
−0.151640 | + | 0.988436i | \(0.548456\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.39209e26 | −0.190136 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.45743e26 | 0.335349 | 0.167675 | − | 0.985842i | \(-0.446374\pi\) | ||||
0.167675 | + | 0.985842i | \(0.446374\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.18431e26 | −0.511738 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.13330e26 | −0.548658 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.63616e27 | 1.68461 | 0.842307 | − | 0.538998i | \(-0.181197\pi\) | ||||
0.842307 | + | 0.538998i | \(0.181197\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.22259e27 | −1.34587 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.13886e27 | 0.653657 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.00115e27 | 0.544790 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.91276e27 | −0.987100 | −0.493550 | − | 0.869717i | \(-0.664301\pi\) | ||||
−0.493550 | + | 0.869717i | \(0.664301\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.09128e26 | −0.396097 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.31621e27 | 1.07588 | 0.537939 | − | 0.842984i | \(-0.319203\pi\) | ||||
0.537939 | + | 0.842984i | \(0.319203\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.03036e27 | 0.454239 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.57493e26 | 0.0659147 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.06902e27 | 1.61714 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.77500e27 | 0.670045 | 0.335022 | − | 0.942210i | \(-0.391256\pi\) | ||||
0.335022 | + | 0.942210i | \(0.391256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.73330e27 | −0.621634 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.12804e27 | −0.384459 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.01694e27 | 0.653415 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.50408e27 | −0.771293 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.22580e27 | 0.651988 | 0.325994 | − | 0.945372i | \(-0.394301\pi\) | ||||
0.325994 | + | 0.945372i | \(0.394301\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.26274e27 | 0.630482 | 0.315241 | − | 0.949012i | \(-0.397915\pi\) | ||||
0.315241 | + | 0.949012i | \(0.397915\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.02305e27 | 0.536331 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.04791e27 | −0.516687 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.75707e27 | 1.14248 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.01919e27 | −0.461717 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.80751e27 | 0.393612 | 0.196806 | − | 0.980442i | \(-0.436943\pi\) | ||||
0.196806 | + | 0.980442i | \(0.436943\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.12467e27 | 1.47789 | 0.738945 | − | 0.673766i | \(-0.235324\pi\) | ||||
0.738945 | + | 0.673766i | \(0.235324\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.34858e26 | −0.105706 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.58403e27 | 1.80507 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.58875e27 | −0.285218 | −0.142609 | − | 0.989779i | \(-0.545549\pi\) | ||||
−0.142609 | + | 0.989779i | \(0.545549\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.14580e27 | −0.196112 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.52672e26 | −0.0575614 | −0.0287807 | − | 0.999586i | \(-0.509162\pi\) | ||||
−0.0287807 | + | 0.999586i | \(0.509162\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.28825e27 | 0.511900 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.97897e27 | 0.442423 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.74724e27 | 1.09789 | 0.548947 | − | 0.835857i | \(-0.315029\pi\) | ||||
0.548947 | + | 0.835857i | \(0.315029\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.09220e26 | −0.0959240 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.90573e27 | −0.633391 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.83654e27 | 0.226402 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.41977e28 | −1.67147 | −0.835735 | − | 0.549132i | \(-0.814958\pi\) | ||||
−0.835735 | + | 0.549132i | \(0.814958\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.36444e27 | 0.153434 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.10321e27 | −0.225956 | −0.112978 | − | 0.993598i | \(-0.536039\pi\) | ||||
−0.112978 | + | 0.993598i | \(0.536039\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.66348e28 | −1.70772 | −0.853860 | − | 0.520503i | \(-0.825744\pi\) | ||||
−0.853860 | + | 0.520503i | \(0.825744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.66575e27 | 0.261555 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.92552e28 | 1.80601 | 0.903006 | − | 0.429629i | \(-0.141356\pi\) | ||||
0.903006 | + | 0.429629i | \(0.141356\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.25004e28 | −1.12101 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.81896e27 | −0.842065 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.69784e28 | 2.21297 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.83080e27 | 0.692974 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.86222e27 | −0.365083 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.98417e28 | −1.42579 | −0.712894 | − | 0.701272i | \(-0.752616\pi\) | ||||
−0.712894 | + | 0.701272i | \(0.752616\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.04017e28 | −0.715454 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.49635e27 | −0.625334 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.33522e28 | −0.841905 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.91036e26 | 0.0115361 | 0.00576807 | − | 0.999983i | \(-0.498164\pi\) | ||||
0.00576807 | + | 0.999983i | \(0.498164\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.72691e27 | 0.389110 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.06003e27 | −0.446664 | −0.223332 | − | 0.974742i | \(-0.571693\pi\) | ||||
−0.223332 | + | 0.974742i | \(0.571693\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.63375e27 | −0.246059 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.22408e27 | −0.265861 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.39525e27 | 0.311972 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.12631e28 | −1.46210 | −0.731048 | − | 0.682326i | \(-0.760968\pi\) | ||||
−0.731048 | + | 0.682326i | \(0.760968\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.08076e28 | −0.933095 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.14717e28 | 1.78356 | 0.891782 | − | 0.452466i | \(-0.149456\pi\) | ||||
0.891782 | + | 0.452466i | \(0.149456\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.91659e27 | −0.409075 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.42722e27 | −0.373078 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.54263e28 | 0.965488 | 0.482744 | − | 0.875762i | \(-0.339640\pi\) | ||||
0.482744 | + | 0.875762i | \(0.339640\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.33361e27 | 0.157918 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.88358e27 | −0.205783 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.16267e28 | 0.390373 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.71053e28 | −2.16325 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.21055e27 | −0.0993853 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.24742e28 | −0.965479 | −0.482739 | − | 0.875764i | \(-0.660358\pi\) | ||||
−0.482739 | + | 0.875764i | \(0.660358\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.45605e28 | −0.415822 | −0.207911 | − | 0.978148i | \(-0.566666\pi\) | ||||
−0.207911 | + | 0.978148i | \(0.566666\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.75002e27 | −0.240069 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.30948e28 | 0.608838 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.30116e28 | 1.84973 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.20258e27 | −0.199737 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.81299e27 | 0.0424385 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.22519e28 | −0.500786 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.29401e28 | −0.712844 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.80067e28 | 0.791002 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.59820e28 | 0.319933 | 0.159967 | − | 0.987122i | \(-0.448861\pi\) | ||||
0.159967 | + | 0.987122i | \(0.448861\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.12381e28 | −0.601571 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.88428e28 | 0.719692 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.03425e29 | −1.84399 | −0.921994 | − | 0.387203i | \(-0.873441\pi\) | ||||
−0.921994 | + | 0.387203i | \(0.873441\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.45911e28 | 0.593546 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.99812e28 | 0.330011 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.70586e28 | 0.589217 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.69114e28 | −0.411965 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.81350e28 | −1.44659 | −0.723293 | − | 0.690541i | \(-0.757372\pi\) | ||||
−0.723293 | + | 0.690541i | \(0.757372\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.89655e28 | −0.979057 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.52588e28 | −0.618861 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.10142e28 | −0.935421 | −0.467711 | − | 0.883882i | \(-0.654921\pi\) | ||||
−0.467711 | + | 0.883882i | \(0.654921\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.62879e28 | −0.841251 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.82976e27 | 0.0712900 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.47837e29 | 1.74222 | 0.871110 | − | 0.491087i | \(-0.163400\pi\) | ||||
0.871110 | + | 0.491087i | \(0.163400\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.30988e29 | 1.48783 | 0.743914 | − | 0.668275i | \(-0.232967\pi\) | ||||
0.743914 | + | 0.668275i | \(0.232967\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.83766e27 | 0.0529678 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.03643e29 | 1.09403 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.13007e29 | −1.15017 | −0.575083 | − | 0.818095i | \(-0.695030\pi\) | ||||
−0.575083 | + | 0.818095i | \(0.695030\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.89826e28 | 0.382601 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.46594e28 | 0.706700 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.61281e29 | 1.47253 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.33544e28 | 0.117622 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.05612e29 | 0.897455 | 0.448728 | − | 0.893669i | \(-0.351877\pi\) | ||||
0.448728 | + | 0.893669i | \(0.351877\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.95868e28 | −0.816566 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.19289e28 | −0.410904 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.22381e29 | 0.934630 | 0.467315 | − | 0.884091i | \(-0.345221\pi\) | ||||
0.467315 | + | 0.884091i | \(0.345221\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.11648e28 | 0.303458 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.21034e28 | −0.370797 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.37213e29 | −0.942789 | −0.471394 | − | 0.881922i | \(-0.656249\pi\) | ||||
−0.471394 | + | 0.881922i | \(0.656249\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.89598e29 | 1.25792 | 0.628958 | − | 0.777439i | \(-0.283482\pi\) | ||||
0.628958 | + | 0.777439i | \(0.283482\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.08969e28 | −0.582395 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.74203e28 | 0.479097 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.07832e29 | 0.644563 | 0.322281 | − | 0.946644i | \(-0.395550\pi\) | ||||
0.322281 | + | 0.946644i | \(0.395550\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.97984e28 | −0.114327 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.71543e29 | 0.957060 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.49900e28 | 0.242538 | 0.121269 | − | 0.992620i | \(-0.461304\pi\) | ||||
0.121269 | + | 0.992620i | \(0.461304\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.69060e27 | 0.0244365 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.83973e29 | 1.42982 | 0.714911 | − | 0.699215i | \(-0.246467\pi\) | ||||
0.714911 | + | 0.699215i | \(0.246467\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.17452e29 | −0.571624 | −0.285812 | − | 0.958286i | \(-0.592263\pi\) | ||||
−0.285812 | + | 0.958286i | \(0.592263\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.90528e28 | −0.324878 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.21718e29 | 0.553645 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.54791e28 | 0.0680776 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.95160e29 | 0.830008 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.33147e29 | −0.958956 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.11858e29 | −0.444999 | −0.222500 | − | 0.974933i | \(-0.571422\pi\) | ||||
−0.222500 | + | 0.974933i | \(0.571422\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.69034e29 | 0.650481 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.24777e28 | −0.195367 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.71572e28 | −0.349954 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.65031e28 | 0.162078 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.02292e29 | 1.69413 | 0.847066 | − | 0.531488i | \(-0.178367\pi\) | ||||
0.847066 | + | 0.531488i | \(0.178367\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.27106e29 | −1.39419 | −0.697093 | − | 0.716980i | \(-0.745524\pi\) | ||||
−0.697093 | + | 0.716980i | \(0.745524\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.78428e29 | −0.563751 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.32869e29 | 1.32392 | 0.661960 | − | 0.749539i | \(-0.269725\pi\) | ||||
0.661960 | + | 0.749539i | \(0.269725\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.72082e29 | 0.805621 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.86758e28 | 0.282885 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.73969e29 | −0.760525 | −0.380263 | − | 0.924879i | \(-0.624166\pi\) | ||||
−0.380263 | + | 0.924879i | \(0.624166\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.49844e29 | 0.671637 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.15119e28 | 0.0820424 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.07743e28 | −0.0776053 | −0.0388026 | − | 0.999247i | \(-0.512354\pi\) | ||||
−0.0388026 | + | 0.999247i | \(0.512354\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.06325e29 | −0.748286 | −0.374143 | − | 0.927371i | \(-0.622063\pi\) | ||||
−0.374143 | + | 0.927371i | \(0.622063\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.15696e29 | 0.273796 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.77507e29 | −0.406993 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.34509e29 | 0.521002 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.19378e28 | 0.133346 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.14740e30 | −2.39402 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.09843e29 | 1.03105 | 0.515523 | − | 0.856876i | \(-0.327598\pi\) | ||||
0.515523 | + | 0.856876i | \(0.327598\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.36258e28 | −0.124722 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.38047e29 | −1.40250 | −0.701250 | − | 0.712915i | \(-0.747374\pi\) | ||||
−0.701250 | + | 0.712915i | \(0.747374\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.94245e29 | −0.910562 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.49518e29 | 0.445716 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.68059e29 | 0.810743 | 0.405372 | − | 0.914152i | \(-0.367142\pi\) | ||||
0.405372 | + | 0.914152i | \(0.367142\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.80252e29 | −0.638734 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.55061e29 | −0.904263 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.12287e29 | −0.651475 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.77475e29 | 0.731865 | 0.365932 | − | 0.930641i | \(-0.380750\pi\) | ||||
0.365932 | + | 0.930641i | \(0.380750\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.93375e29 | −0.287542 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.49345e29 | −0.792510 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.06370e28 | 0.0568824 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.30396e29 | −0.448770 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.76926e29 | −1.28772 | −0.643862 | − | 0.765142i | \(-0.722669\pi\) | ||||
−0.643862 | + | 0.765142i | \(0.722669\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.00535e30 | 1.28614 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.43817e29 | 0.551085 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.67073e29 | −0.442435 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.06956e29 | −0.944201 | −0.472101 | − | 0.881545i | \(-0.656504\pi\) | ||||
−0.472101 | + | 0.881545i | \(0.656504\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.69472e29 | 0.306114 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.16880e30 | −1.28914 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.42970e29 | −0.474418 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.83235e29 | 0.294575 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.20303e29 | −0.222519 | −0.111259 | − | 0.993791i | \(-0.535488\pi\) | ||||
−0.111259 | + | 0.993791i | \(0.535488\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.30374e29 | 0.422208 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.69051e28 | 0.0732830 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.16079e29 | 0.200015 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.52128e30 | −1.36804 | −0.684020 | − | 0.729463i | \(-0.739770\pi\) | ||||
−0.684020 | + | 0.729463i | \(0.739770\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.54582e30 | −1.31228 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.36651e29 | 0.277708 | 0.138854 | − | 0.990313i | \(-0.455658\pi\) | ||||
0.138854 | + | 0.990313i | \(0.455658\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.51366e29 | −0.201507 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.01508e30 | 2.34904 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.59622e29 | 0.196596 | 0.0982982 | − | 0.995157i | \(-0.468660\pi\) | ||||
0.0982982 | + | 0.995157i | \(0.468660\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.98892e29 | −0.367211 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.31717e30 | 0.942455 | 0.471227 | − | 0.882012i | \(-0.343811\pi\) | ||||
0.471227 | + | 0.882012i | \(0.343811\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.53528e29 | 0.454593 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.42887e29 | 0.367150 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.23679e29 | −0.541625 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.46730e29 | −0.0938209 | −0.0469104 | − | 0.998899i | \(-0.514938\pi\) | ||||
−0.0469104 | + | 0.998899i | \(0.514938\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.41002e29 | 0.460757 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.07622e30 | −0.650815 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.16010e29 | −0.185864 | −0.0929318 | − | 0.995672i | \(-0.529624\pi\) | ||||
−0.0929318 | + | 0.995672i | \(0.529624\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.29051e30 | 1.31037 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.02639e30 | −1.12767 | −0.563837 | − | 0.825886i | \(-0.690676\pi\) | ||||
−0.563837 | + | 0.825886i | \(0.690676\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.43781e30 | 0.778383 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.99330e29 | 0.157654 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.95529e29 | −0.356422 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.55510e30 | 0.775410 | 0.387705 | − | 0.921783i | \(-0.373268\pi\) | ||||
0.387705 | + | 0.921783i | \(0.373268\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.84515e30 | 0.895284 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.90527e30 | −1.84402 | −0.922012 | − | 0.387161i | \(-0.873456\pi\) | ||||
−0.922012 | + | 0.387161i | \(0.873456\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.07694e30 | −0.494909 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.96157e29 | −0.445561 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.75231e29 | −0.0762899 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.54252e30 | −0.653726 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.43964e29 | −0.0593958 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.15408e30 | −0.865229 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.91303e29 | 0.270355 | 0.135177 | − | 0.990821i | \(-0.456840\pi\) | ||||
0.135177 | + | 0.990821i | \(0.456840\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.20664e30 | 0.459481 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.45372e30 | −0.909855 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.93312e30 | 1.05916 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.06667e30 | −0.375126 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.05715e30 | 1.04714 | 0.523569 | − | 0.851983i | \(-0.324600\pi\) | ||||
0.523569 | + | 0.851983i | \(0.324600\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.84501e30 | 1.28279 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.85076e29 | 0.287633 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.04526e30 | −0.330911 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.08331e30 | −0.642536 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.55859e29 | −0.106932 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.62302e30 | 1.64630 | 0.823152 | − | 0.567821i | \(-0.192213\pi\) | ||||
0.823152 | + | 0.567821i | \(0.192213\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.35752e30 | 0.957854 | 0.478927 | − | 0.877855i | \(-0.341026\pi\) | ||||
0.478927 | + | 0.877855i | \(0.341026\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.67319e29 | 0.185517 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.47575e30 | 0.399814 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.66571e30 | 1.76001 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.94328e29 | 0.127214 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.66494e30 | 0.417634 | 0.208817 | − | 0.977955i | \(-0.433039\pi\) | ||||
0.208817 | + | 0.977955i | \(0.433039\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.79393e30 | 1.17218 | 0.586088 | − | 0.810247i | \(-0.300667\pi\) | ||||
0.586088 | + | 0.810247i | \(0.300667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.11049e30 | 0.503056 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.92737e30 | −1.60976 | −0.804879 | − | 0.593439i | \(-0.797770\pi\) | ||||
−0.804879 | + | 0.593439i | \(0.797770\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.55745e30 | −0.579408 | −0.289704 | − | 0.957116i | \(-0.593557\pi\) | ||||
−0.289704 | + | 0.957116i | \(0.593557\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.43890e30 | 0.980537 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.17771e30 | −0.469060 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.56477e30 | −0.958763 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.17522e29 | 0.146966 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.16860e29 | 0.0832702 | 0.0416351 | − | 0.999133i | \(-0.486743\pi\) | ||||
0.0416351 | + | 0.999133i | \(0.486743\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.64393e30 | −0.904748 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.32659e30 | −0.252085 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.06814e30 | −0.383341 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.86580e30 | 0.518167 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.55747e30 | 0.627495 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.17994e31 | 2.03048 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.40771e30 | 1.24371 | 0.621855 | − | 0.783132i | \(-0.286379\pi\) | ||||
0.621855 | + | 0.783132i | \(0.286379\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.29074e30 | −0.211444 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.64448e30 | −0.582555 | −0.291277 | − | 0.956639i | \(-0.594080\pi\) | ||||
−0.291277 | + | 0.956639i | \(0.594080\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.70416e30 | 0.577778 | 0.288889 | − | 0.957363i | \(-0.406714\pi\) | ||||
0.288889 | + | 0.957363i | \(0.406714\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.73628e29 | 0.0264293 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.86612e29 | −0.101999 | −0.0509997 | − | 0.998699i | \(-0.516241\pi\) | ||||
−0.0509997 | + | 0.998699i | \(0.516241\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.04330e29 | −0.102119 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.48656e30 | −0.210369 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.93848e30 | −1.23468 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.70751e30 | −1.03926 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.59391e30 | −0.473061 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.88155e30 | −0.627297 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.41886e31 | 1.78010 | 0.890049 | − | 0.455865i | \(-0.150670\pi\) | ||||
0.890049 | + | 0.455865i | \(0.150670\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.74597e29 | 0.0336367 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.83090e30 | 1.17583 | 0.587917 | − | 0.808921i | \(-0.299948\pi\) | ||||
0.587917 | + | 0.808921i | \(0.299948\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.06031e30 | −0.123835 | −0.0619176 | − | 0.998081i | \(-0.519722\pi\) | ||||
−0.0619176 | + | 0.998081i | \(0.519722\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.79948e30 | −0.205231 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.96894e30 | 0.998949 | 0.499474 | − | 0.866329i | \(-0.333527\pi\) | ||||
0.499474 | + | 0.866329i | \(0.333527\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.94252e30 | −0.211299 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.40613e30 | −0.149386 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.65801e31 | −1.72047 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.22640e30 | −0.732453 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.85526e30 | −0.579730 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.43677e30 | −0.235688 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.24114e30 | −0.873203 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.60473e30 | −0.609724 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.85303e30 | −0.618119 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.04599e30 | −0.268443 | −0.134221 | − | 0.990951i | \(-0.542853\pi\) | ||||
−0.134221 | + | 0.990951i | \(0.542853\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.66918e30 | −0.229857 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.54796e30 | −0.803466 | −0.401733 | − | 0.915757i | \(-0.631592\pi\) | ||||
−0.401733 | + | 0.915757i | \(0.631592\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.80077e31 | −1.48087 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.58860e30 | 0.609874 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.24824e30 | 0.726409 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.56370e31 | −1.20044 | −0.600219 | − | 0.799835i | \(-0.704920\pi\) | ||||
−0.600219 | + | 0.799835i | \(0.704920\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.06905e30 | 0.305328 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.94318e30 | 0.289220 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.08720e31 | 0.779511 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.12947e30 | 0.219348 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.04044e30 | −0.276862 | −0.138431 | − | 0.990372i | \(-0.544206\pi\) | ||||
−0.138431 | + | 0.990372i | \(0.544206\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.39051e30 | 0.629097 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.62535e30 | 0.106461 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.92888e30 | −0.635885 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.09838e31 | −1.31407 | −0.657035 | − | 0.753860i | \(-0.728190\pi\) | ||||
−0.657035 | + | 0.753860i | \(0.728190\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.93147e30 | −0.546933 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.17744e31 | 1.30393 | 0.651967 | − | 0.758247i | \(-0.273944\pi\) | ||||
0.651967 | + | 0.758247i | \(0.273944\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.05660e30 | −0.120442 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.27893e30 | 0.0732511 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.21468e31 | −0.680435 | −0.340218 | − | 0.940347i | \(-0.610501\pi\) | ||||
−0.340218 | + | 0.940347i | \(0.610501\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.67202e30 | 0.146401 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.22383e30 | −0.172773 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.95212e30 | 0.364453 | 0.182227 | − | 0.983257i | \(-0.441670\pi\) | ||||
0.182227 | + | 0.983257i | \(0.441670\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.06129e30 | 0.0544248 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.77534e30 | 0.239568 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.40754e31 | −0.690823 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.68058e30 | −0.416824 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.98939e30 | −0.281389 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.55201e30 | 0.393126 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.85795e30 | 0.398433 | 0.199216 | − | 0.979956i | \(-0.436160\pi\) | ||||
0.199216 | + | 0.979956i | \(0.436160\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.11823e31 | −0.492190 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.05382e31 | 1.31535 | 0.657676 | − | 0.753301i | \(-0.271540\pi\) | ||||
0.657676 | + | 0.753301i | \(0.271540\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.03346e31 | −0.857138 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.39509e30 | −0.222561 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.38019e31 | −0.960989 | −0.480495 | − | 0.876998i | \(-0.659543\pi\) | ||||
−0.480495 | + | 0.876998i | \(0.659543\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.93583e31 | −1.16014 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.04550e31 | 0.404391 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.40761e31 | 1.29014 | 0.645072 | − | 0.764122i | \(-0.276827\pi\) | ||||
0.645072 | + | 0.764122i | \(0.276827\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.13922e31 | −0.422207 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.64284e31 | 0.596026 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.82322e31 | 2.77859 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.53546e31 | 1.22934 | 0.614671 | − | 0.788784i | \(-0.289289\pi\) | ||||
0.614671 | + | 0.788784i | \(0.289289\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.70420e31 | −0.920600 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.14305e31 | −0.380997 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.23577e31 | −1.38240 | −0.691199 | − | 0.722664i | \(-0.742917\pi\) | ||||
−0.691199 | + | 0.722664i | \(0.742917\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.24357e30 | −0.231481 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 48.22.a.f.1.1 | 1 | ||
4.3 | odd | 2 | 6.22.a.b.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 18.22.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.22.a.b.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
18.22.a.a.1.1 | 1 | 12.11 | even | 2 | |||
48.22.a.f.1.1 | 1 | 1.1 | even | 1 | trivial |