Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [200,6,Mod(49,200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("200.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 200.c (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(32.0767639626\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 8) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 200.49 |
Dual form | 200.6.c.a.49.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/200\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 20.0000i | 1.28300i | 0.767123 | + | 0.641500i | \(0.221688\pi\) | ||||
−0.767123 | + | 0.641500i | \(0.778312\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 24.0000i | 0.185125i | 0.995707 | + | 0.0925627i | \(0.0295059\pi\) | ||||
−0.995707 | + | 0.0925627i | \(0.970494\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −157.000 | −0.646091 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 124.000 | 0.308987 | 0.154493 | − | 0.987994i | \(-0.450625\pi\) | ||||
0.154493 | + | 0.987994i | \(0.450625\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 478.000i | 0.784458i | 0.919868 | + | 0.392229i | \(0.128296\pi\) | ||||
−0.919868 | + | 0.392229i | \(0.871704\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1198.00i | 1.00539i | 0.864464 | + | 0.502695i | \(0.167658\pi\) | ||||
−0.864464 | + | 0.502695i | \(0.832342\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3044.00 | −1.93446 | −0.967232 | − | 0.253894i | \(-0.918288\pi\) | ||||
−0.967232 | + | 0.253894i | \(0.918288\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −480.000 | −0.237516 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 184.000i | 0.0725268i | 0.999342 | + | 0.0362634i | \(0.0115455\pi\) | ||||
−0.999342 | + | 0.0362634i | \(0.988454\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1720.00i | 0.454066i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3282.00 | 0.724676 | 0.362338 | − | 0.932047i | \(-0.381979\pi\) | ||||
0.362338 | + | 0.932047i | \(0.381979\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5728.00 | −1.07053 | −0.535265 | − | 0.844684i | \(-0.679788\pi\) | ||||
−0.535265 | + | 0.844684i | \(0.679788\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2480.00i | 0.396430i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 10326.0i | − 1.24002i | −0.784595 | − | 0.620009i | \(-0.787129\pi\) | ||||
0.784595 | − | 0.620009i | \(-0.212871\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9560.00 | −1.00646 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8886.00 | −0.825556 | −0.412778 | − | 0.910832i | \(-0.635442\pi\) | ||||
−0.412778 | + | 0.910832i | \(0.635442\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 9188.00i | − 0.757792i | −0.925439 | − | 0.378896i | \(-0.876304\pi\) | ||||
0.925439 | − | 0.378896i | \(-0.123696\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 23664.0i | − 1.56258i | −0.624165 | − | 0.781292i | \(-0.714561\pi\) | ||||
0.624165 | − | 0.781292i | \(-0.285439\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16231.0 | 0.965729 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −23960.0 | −1.28992 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11686.0i | 0.571447i | 0.958312 | + | 0.285724i | \(0.0922339\pi\) | ||||
−0.958312 | + | 0.285724i | \(0.907766\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 60880.0i | − 2.48192i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −16876.0 | −0.631160 | −0.315580 | − | 0.948899i | \(-0.602199\pi\) | ||||
−0.315580 | + | 0.948899i | \(0.602199\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −18482.0 | −0.635952 | −0.317976 | − | 0.948099i | \(-0.603003\pi\) | ||||
−0.317976 | + | 0.948099i | \(0.603003\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 3768.00i | − 0.119608i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15532.0i | 0.422708i | 0.977410 | + | 0.211354i | \(0.0677873\pi\) | ||||
−0.977410 | + | 0.211354i | \(0.932213\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3680.00 | −0.0930519 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −31960.0 | −0.752421 | −0.376210 | − | 0.926534i | \(-0.622773\pi\) | ||||
−0.376210 | + | 0.926534i | \(0.622773\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 4886.00i | − 0.107312i | −0.998559 | − | 0.0536558i | \(-0.982913\pi\) | ||||
0.998559 | − | 0.0536558i | \(-0.0170874\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2976.00i | 0.0572013i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −44560.0 | −0.803299 | −0.401650 | − | 0.915793i | \(-0.631563\pi\) | ||||
−0.401650 | + | 0.915793i | \(0.631563\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −72551.0 | −1.22866 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 67364.0i | 1.07333i | 0.843796 | + | 0.536664i | \(0.180316\pi\) | ||||
−0.843796 | + | 0.536664i | \(0.819684\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 65640.0i | 0.929759i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −71994.0 | −0.963432 | −0.481716 | − | 0.876327i | \(-0.659986\pi\) | ||||
−0.481716 | + | 0.876327i | \(0.659986\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11472.0 | −0.145223 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 114560.i | − 1.37349i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 48866.0i | − 0.527324i | −0.964615 | − | 0.263662i | \(-0.915070\pi\) | ||||
0.964615 | − | 0.263662i | \(-0.0849303\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −19468.0 | −0.199633 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 51606.0 | 0.503381 | 0.251690 | − | 0.967808i | \(-0.419014\pi\) | ||||
0.251690 | + | 0.967808i | \(0.419014\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 180424.i | 1.67572i | 0.545886 | + | 0.837860i | \(0.316193\pi\) | ||||
−0.545886 | + | 0.837860i | \(0.683807\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 65700.0i | 0.554761i | 0.960760 | + | 0.277381i | \(0.0894663\pi\) | ||||
−0.960760 | + | 0.277381i | \(0.910534\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 112706. | 0.908617 | 0.454308 | − | 0.890844i | \(-0.349886\pi\) | ||||
0.454308 | + | 0.890844i | \(0.349886\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 206520. | 1.59094 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 23502.0i | − 0.173145i | −0.996246 | − | 0.0865723i | \(-0.972409\pi\) | ||||
0.996246 | − | 0.0865723i | \(-0.0275913\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 75046.0i | − 0.506831i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −28752.0 | −0.186123 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −145675. | −0.904527 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 177720.i | − 1.05919i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 94592.0i | 0.520409i | 0.965553 | + | 0.260205i | \(0.0837900\pi\) | ||||
−0.965553 | + | 0.260205i | \(0.916210\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 183760. | 0.972247 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 70292.0 | 0.357872 | 0.178936 | − | 0.983861i | \(-0.442735\pi\) | ||||
0.178936 | + | 0.983861i | \(0.442735\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 73056.0i | − 0.358119i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 277290.i | − 1.26221i | −0.775696 | − | 0.631107i | \(-0.782601\pi\) | ||||
0.775696 | − | 0.631107i | \(-0.217399\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 130308. | 0.572050 | 0.286025 | − | 0.958222i | \(-0.407666\pi\) | ||||
0.286025 | + | 0.958222i | \(0.407666\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 473280. | 2.00480 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 59272.0i | 0.242387i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 324620.i | 1.23903i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 401530. | 1.48167 | 0.740836 | − | 0.671685i | \(-0.234429\pi\) | ||||
0.740836 | + | 0.671685i | \(0.234429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −75976.0 | −0.271165 | −0.135583 | − | 0.990766i | \(-0.543291\pi\) | ||||
−0.135583 | + | 0.990766i | \(0.543291\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 188086.i | − 0.649573i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 394322.i | 1.27674i | 0.769730 | + | 0.638369i | \(0.220391\pi\) | ||||
−0.769730 | + | 0.638369i | \(0.779609\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −233720. | −0.733167 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4416.00 | −0.0134265 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 11724.0i | − 0.0345626i | −0.999851 | − | 0.0172813i | \(-0.994499\pi\) | ||||
0.999851 | − | 0.0172813i | \(-0.00550109\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 551928.i | 1.53141i | 0.643192 | + | 0.765705i | \(0.277610\pi\) | ||||
−0.643192 | + | 0.765705i | \(0.722390\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 142809. | 0.384626 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 477908. | 1.24984 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 432894.i | 1.09968i | 0.835270 | + | 0.549840i | \(0.185311\pi\) | ||||
−0.835270 | + | 0.549840i | \(0.814689\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 337520.i | − 0.809779i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −559620. | −1.30545 | −0.652726 | − | 0.757594i | \(-0.726375\pi\) | ||||
−0.652726 | + | 0.757594i | \(0.726375\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 604710. | 1.37199 | 0.685995 | − | 0.727607i | \(-0.259367\pi\) | ||||
0.685995 | + | 0.727607i | \(0.259367\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 369640.i | − 0.815927i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 148552.i | 0.310652i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −41280.0 | −0.0840592 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −409152. | −0.811524 | −0.405762 | − | 0.913979i | \(-0.632994\pi\) | ||||
−0.405762 | + | 0.913979i | \(0.632994\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 540866.i | 1.04519i | 0.852580 | + | 0.522596i | \(0.175037\pi\) | ||||
−0.852580 | + | 0.522596i | \(0.824963\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 629898.i | 1.15639i | 0.815898 | + | 0.578195i | \(0.196243\pi\) | ||||
−0.815898 | + | 0.578195i | \(0.803757\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −283048. | −0.506673 | −0.253336 | − | 0.967378i | \(-0.581528\pi\) | ||||
−0.253336 | + | 0.967378i | \(0.581528\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −310640. | −0.542335 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 78768.0i | 0.134156i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 28888.0i | − 0.0468588i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −377456. | −0.597724 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 142756. | 0.220744 | 0.110372 | − | 0.993890i | \(-0.464796\pi\) | ||||
0.110372 | + | 0.993890i | \(0.464796\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 639200.i | − 0.965357i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 137472.i | − 0.198182i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 97720.0 | 0.137681 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −572644. | −0.788686 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 889696.i | 1.19806i | 0.800726 | + | 0.599031i | \(0.204447\pi\) | ||||
−0.800726 | + | 0.599031i | \(0.795553\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1.14316e6i | − 1.47245i | −0.676736 | − | 0.736226i | \(-0.736606\pi\) | ||||
0.676736 | − | 0.736226i | \(-0.263394\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 695786. | 0.876773 | 0.438386 | − | 0.898787i | \(-0.355550\pi\) | ||||
0.438386 | + | 0.898787i | \(0.355550\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −59520.0 | −0.0733893 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 347126.i | − 0.418887i | −0.977821 | − | 0.209444i | \(-0.932835\pi\) | ||||
0.977821 | − | 0.209444i | \(-0.0671653\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 891200.i | − 1.03063i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.64296e6 | 1.86051 | 0.930255 | − | 0.366912i | \(-0.119585\pi\) | ||||
0.930255 | + | 0.366912i | \(0.119585\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.16744e6 | −1.29477 | −0.647383 | − | 0.762165i | \(-0.724137\pi\) | ||||
−0.647383 | + | 0.762165i | \(0.724137\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.03306e6i | − 1.12230i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.45503e6i | − 1.51751i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.34728e6 | −1.37708 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −790612. | −0.792098 | −0.396049 | − | 0.918229i | \(-0.629619\pi\) | ||||
−0.396049 | + | 0.918229i | \(0.629619\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22816.0i | 0.0224098i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 129790.i | 0.122577i | 0.998120 | + | 0.0612884i | \(0.0195209\pi\) | ||||
−0.998120 | + | 0.0612884i | \(0.980479\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 247824. | 0.229559 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −515274. | −0.468206 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 70888.0i | 0.0631951i | 0.999501 | + | 0.0315975i | \(0.0100595\pi\) | ||||
−0.999501 | + | 0.0315975i | \(0.989941\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1.43988e6i | − 1.23608i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.79017e6 | −1.50839 | −0.754197 | − | 0.656649i | \(-0.771973\pi\) | ||||
−0.754197 | + | 0.656649i | \(0.771973\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.77362e6 | −1.46702 | −0.733511 | − | 0.679678i | \(-0.762120\pi\) | ||||
−0.733511 | + | 0.679678i | \(0.762120\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 229440.i | − 0.186321i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 275450.i | 0.215697i | 0.994167 | + | 0.107848i | \(0.0343961\pi\) | ||||
−0.994167 | + | 0.107848i | \(0.965604\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 899296. | 0.691659 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 594170. | 0.448895 | 0.224448 | − | 0.974486i | \(-0.427942\pi\) | ||||
0.224448 | + | 0.974486i | \(0.427942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.09243e6i | 0.810824i | 0.914134 | + | 0.405412i | \(0.132872\pi\) | ||||
−0.914134 | + | 0.405412i | \(0.867128\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 213264.i | − 0.152831i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15347.0 | −0.0108088 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 977320. | 0.676557 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 333654.i | 0.227053i | 0.993535 | + | 0.113527i | \(0.0362147\pi\) | ||||
−0.993535 | + | 0.113527i | \(0.963785\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 213280.i | 0.140300i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −87952.0 | −0.0568942 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 220512. | 0.140287 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.03212e6i | 0.645838i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.05997e6i | − 0.641872i | −0.947101 | − | 0.320936i | \(-0.896003\pi\) | ||||
0.947101 | − | 0.320936i | \(-0.103997\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.60848e6 | −2.14995 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.33649e6 | −0.783545 | −0.391773 | − | 0.920062i | \(-0.628138\pi\) | ||||
−0.391773 | + | 0.920062i | \(0.628138\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.64419e6i | 0.948615i | 0.880359 | + | 0.474308i | \(0.157302\pi\) | ||||
−0.880359 | + | 0.474308i | \(0.842698\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.72370e6i | 0.963414i | 0.876332 | + | 0.481707i | \(0.159983\pi\) | ||||
−0.876332 | + | 0.481707i | \(0.840017\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 406968. | 0.223915 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.31400e6 | −0.711759 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3.64671e6i | − 1.94489i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.25412e6i | 1.16576i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 567936. | 0.289274 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.74963e6 | 1.37944 | 0.689722 | − | 0.724074i | \(-0.257733\pi\) | ||||
0.689722 | + | 0.724074i | \(0.257733\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.62118e6i | 0.801164i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.41489e6i | 1.63796i | 0.573824 | + | 0.818978i | \(0.305459\pi\) | ||||
−0.573824 | + | 0.818978i | \(0.694541\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 470040. | 0.222145 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −710272. | −0.330780 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 792912.i | 0.363906i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 730764.i | − 0.325802i | −0.986642 | − | 0.162901i | \(-0.947915\pi\) | ||||
0.986642 | − | 0.162901i | \(-0.0520851\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.29749e6 | 1.00969 | 0.504847 | − | 0.863209i | \(-0.331549\pi\) | ||||
0.504847 | + | 0.863209i | \(0.331549\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −822160. | −0.356196 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 1.17072e6i | − 0.500052i | −0.968239 | − | 0.250026i | \(-0.919561\pi\) | ||||
0.968239 | − | 0.250026i | \(-0.0804392\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 575040.i | − 0.238796i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.88654e6 | −1.59157 | −0.795787 | − | 0.605577i | \(-0.792942\pi\) | ||||
−0.795787 | + | 0.605577i | \(0.792942\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.78984e6 | 2.74215 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2.91350e6i | − 1.16051i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 933040.i | − 0.361606i | −0.983519 | − | 0.180803i | \(-0.942130\pi\) | ||||
0.983519 | − | 0.180803i | \(-0.0578696\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.39510e6 | 0.533384 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −280464. | −0.105789 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 392218.i | − 0.145967i | −0.997333 | − | 0.0729836i | \(-0.976748\pi\) | ||||
0.997333 | − | 0.0729836i | \(-0.0232521\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.56880e6i | 0.568477i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.72930e6 | 1.69122 | 0.845608 | − | 0.533805i | \(-0.179238\pi\) | ||||
0.845608 | + | 0.533805i | \(0.179238\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.89184e6 | −0.667686 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.89734e6i | 0.660920i | 0.943820 | + | 0.330460i | \(0.107204\pi\) | ||||
−0.943820 | + | 0.330460i | \(0.892796\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.44252e6i | 0.489602i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.72295e6 | 1.24742 | 0.623711 | − | 0.781655i | \(-0.285624\pi\) | ||||
0.623711 | + | 0.781655i | \(0.285624\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −220432. | −0.0729177 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.40584e6i | 0.459150i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3.33808e6i | − 1.06297i | −0.847068 | − | 0.531484i | \(-0.821635\pi\) | ||||
0.847068 | − | 0.531484i | \(-0.178365\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.46112e6 | 0.459466 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.27490e6 | 1.32759 | 0.663796 | − | 0.747913i | \(-0.268944\pi\) | ||||
0.663796 | + | 0.747913i | \(0.268944\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 2.73798e6i | − 0.839785i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.28042e6i | − 0.383149i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.57319e6 | 0.760613 | 0.380306 | − | 0.924861i | \(-0.375819\pi\) | ||||
0.380306 | + | 0.924861i | \(0.375819\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.54580e6 | 1.61942 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 405024.i | − 0.116844i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.60616e6i | 0.733941i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.26828e6 | −1.46600 | −0.732999 | − | 0.680230i | \(-0.761880\pi\) | ||||
−0.732999 | + | 0.680230i | \(0.761880\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −973354. | −0.267649 | −0.133824 | − | 0.991005i | \(-0.542726\pi\) | ||||
−0.133824 | + | 0.991005i | \(0.542726\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.71525e6i | 1.00957i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 443568.i | − 0.117731i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.18544e6 | −0.310983 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.55736e6 | 0.922433 | 0.461216 | − | 0.887288i | \(-0.347413\pi\) | ||||
0.461216 | + | 0.887288i | \(0.347413\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 1.95496e6i | − 0.501092i | −0.968105 | − | 0.250546i | \(-0.919390\pi\) | ||||
0.968105 | − | 0.250546i | \(-0.0806102\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 560096.i | − 0.140300i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.29681e6 | 0.816455 | 0.408228 | − | 0.912880i | \(-0.366147\pi\) | ||||
0.408228 | + | 0.912880i | \(0.366147\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.54827e6 | −0.623948 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 5.05820e6i | − 1.22458i | −0.790634 | − | 0.612289i | \(-0.790249\pi\) | ||||
0.790634 | − | 0.612289i | \(-0.209751\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.03060e6i | 1.90099i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.12730e6 | −0.497981 | −0.248990 | − | 0.968506i | \(-0.580099\pi\) | ||||
−0.248990 | + | 0.968506i | \(0.580099\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.10186e6 | −0.255086 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 1.51952e6i | − 0.347905i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 289130.i | − 0.0647594i | −0.999476 | − | 0.0323797i | \(-0.989691\pi\) | ||||
0.999476 | − | 0.0323797i | \(-0.0103086\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.06056e6 | −0.456513 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.66870e6 | 0.584854 | 0.292427 | − | 0.956288i | \(-0.405537\pi\) | ||||
0.292427 | + | 0.956288i | \(0.405537\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.58619e6i | 1.64464i | 0.569024 | + | 0.822321i | \(0.307321\pi\) | ||||
−0.569024 | + | 0.822321i | \(0.692679\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.41961e6i | 0.301216i | 0.988594 | + | 0.150608i | \(0.0481231\pi\) | ||||
−0.988594 | + | 0.150608i | \(0.951877\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −372768. | −0.0782540 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.88644e6 | −1.63806 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 1.13931e6i | − 0.234148i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1.83470e6i | − 0.369207i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.88406e6 | 0.375195 | 0.187597 | − | 0.982246i | \(-0.439930\pi\) | ||||
0.187597 | + | 0.982246i | \(0.439930\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.93583e6 | 0.972741 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 88320.0i | − 0.0172263i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.01388e6i | 1.14903i | 0.818493 | + | 0.574516i | \(0.194810\pi\) | ||||
−0.818493 | + | 0.574516i | \(0.805190\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 234480. | 0.0443439 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.29232e6 | 0.803504 | 0.401752 | − | 0.915749i | \(-0.368401\pi\) | ||||
0.401752 | + | 0.915749i | \(0.368401\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.93184e6i | 0.728581i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 767040.i | − 0.139292i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.34509e6 | −0.241825 | −0.120912 | − | 0.992663i | \(-0.538582\pi\) | ||||
−0.120912 | + | 0.992663i | \(0.538582\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.10386e7 | −1.96480 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 202008.i | 0.0355999i | 0.999842 | + | 0.0177999i | \(0.00566620\pi\) | ||||
−0.999842 | + | 0.0177999i | \(0.994334\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.85618e6i | 0.493476i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.78344e6 | −1.67377 | −0.836887 | − | 0.547375i | \(-0.815627\pi\) | ||||
−0.836887 | + | 0.547375i | \(0.815627\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 117264. | 0.0198661 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 5.23568e6i | − 0.878374i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2.93434e6i | − 0.482818i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.65788e6 | −1.41089 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.04830e7 | −1.69197 | −0.845985 | − | 0.533207i | \(-0.820987\pi\) | ||||
−0.845985 | + | 0.533207i | \(0.820987\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.21017e6i | 0.992772i | 0.868102 | + | 0.496386i | \(0.165340\pi\) | ||||
−0.868102 | + | 0.496386i | \(0.834660\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 6.86214e6i | − 1.07630i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.40249e6 | 0.994740 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.64953e6 | 0.407787 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 4.24751e6i | − 0.647614i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 1.11924e7i | − 1.67489i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.01264e6 | 0.298397 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.08088e6 | 0.746355 | 0.373178 | − | 0.927760i | \(-0.378268\pi\) | ||||
0.373178 | + | 0.927760i | \(0.378268\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.20942e7i | 1.76026i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3.34687e6i | − 0.478267i | −0.970987 | − | 0.239133i | \(-0.923137\pi\) | ||||
0.970987 | − | 0.239133i | \(-0.0768633\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.90167e6 | 0.410883 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.99041e6 | −1.40186 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1.06944e6i | − 0.148711i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 7.00377e6i | − 0.956520i | −0.878218 | − | 0.478260i | \(-0.841268\pi\) | ||||
0.878218 | − | 0.478260i | \(-0.158732\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.39186e6 | 0.594456 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.97104e6 | −0.398567 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.29819e7i | − 1.72610i | −0.505116 | − | 0.863052i | \(-0.668550\pi\) | ||||
0.505116 | − | 0.863052i | \(-0.331450\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 1.74122e6i | − 0.227456i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.89942e6 | −0.245946 | −0.122973 | − | 0.992410i | \(-0.539243\pi\) | ||||
−0.122973 | + | 0.992410i | \(0.539243\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.66300e6 | −0.213452 | −0.106726 | − | 0.994288i | \(-0.534037\pi\) | ||||
−0.106726 | + | 0.994288i | \(0.534037\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 8.18304e6i | − 1.04119i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 8.77344e6i | − 1.09706i | −0.836131 | − | 0.548530i | \(-0.815188\pi\) | ||||
0.836131 | − | 0.548530i | \(-0.184812\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.08173e7 | −1.34098 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.61674e6 | −0.198700 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.44906e6i | 0.176570i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 5.18393e6i | − 0.620961i | −0.950580 | − | 0.310480i | \(-0.899510\pi\) | ||||
0.950580 | − | 0.310480i | \(-0.100490\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.74360e7 | 2.07090 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.25980e7 | −1.48365 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.49858e6i | 0.992452i | 0.868193 | + | 0.496226i | \(0.165281\pi\) | ||||
−0.868193 | + | 0.496226i | \(0.834719\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 5.66096e6i | − 0.650061i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.12471e7 | −1.28078 | −0.640388 | − | 0.768051i | \(-0.721227\pi\) | ||||
−0.640388 | + | 0.768051i | \(0.721227\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.46439e6 | −0.391238 | −0.195619 | − | 0.980680i | \(-0.562672\pi\) | ||||
−0.195619 | + | 0.980680i | \(0.562672\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 2.43852e6i | − 0.273108i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 999712.i | 0.110129i | 0.998483 | + | 0.0550647i | \(0.0175365\pi\) | ||||
−0.998483 | + | 0.0550647i | \(0.982463\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.57536e6 | −0.172122 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.13114e7 | 1.22578 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.81340e6i | 1.05480i | 0.849619 | + | 0.527398i | \(0.176832\pi\) | ||||
−0.849619 | + | 0.527398i | \(0.823168\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.34745e6i | 0.565501i | 0.959193 | + | 0.282751i | \(0.0912469\pi\) | ||||
−0.959193 | + | 0.282751i | \(0.908753\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.82768e6 | 0.716221 | 0.358110 | − | 0.933679i | \(-0.383421\pi\) | ||||
0.358110 | + | 0.933679i | \(0.383421\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −316480. | −0.0329319 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1.72786e6i | − 0.178356i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 7.54912e6i | − 0.766880i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.23705e7 | 1.24670 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.60970e6 | −0.360909 | −0.180455 | − | 0.983583i | \(-0.557757\pi\) | ||||
−0.180455 | + | 0.983583i | \(0.557757\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.85512e6i | 0.283214i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.75842e6i | 0.757573i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.01772e6 | 0.486132 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.33853e7 | −1.28672 | −0.643361 | − | 0.765563i | \(-0.722460\pi\) | ||||
−0.643361 | + | 0.765563i | \(0.722460\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 9.91115e6i | − 0.945358i | −0.881235 | − | 0.472679i | \(-0.843287\pi\) | ||||
0.881235 | − | 0.472679i | \(-0.156713\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.78359e7i | 1.67508i | 0.546378 | + | 0.837539i | \(0.316006\pi\) | ||||
−0.546378 | + | 0.837539i | \(0.683994\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.09262e6 | −0.195020 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.74944e6 | 0.254268 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 4.32323e6i | − 0.396758i | −0.980125 | − | 0.198379i | \(-0.936432\pi\) | ||||
0.980125 | − | 0.198379i | \(-0.0635677\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 767102.i | 0.0693330i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.97858e7 | −1.77476 | −0.887382 | − | 0.461035i | \(-0.847478\pi\) | ||||
−0.887382 | + | 0.461035i | \(0.847478\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.57772e7 | 1.40451 | 0.702255 | − | 0.711925i | \(-0.252176\pi\) | ||||
0.702255 | + | 0.711925i | \(0.252176\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 1.14529e7i | − 1.01188i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 603888.i | 0.0525584i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.77939e7 | −1.53711 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.29177e6 | −0.196501 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.78762e6i | 0.577670i | 0.957379 | + | 0.288835i | \(0.0932679\pi\) | ||||
−0.957379 | + | 0.288835i | \(0.906732\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.49942e7i | 1.25734i | 0.777673 | + | 0.628669i | \(0.216400\pi\) | ||||
−0.777673 | + | 0.628669i | \(0.783600\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.17278e6 | 0.0976211 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.28631e7 | 1.88916 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.15580e7i | 0.948053i | 0.880511 | + | 0.474026i | \(0.157200\pi\) | ||||
−0.880511 | + | 0.474026i | \(0.842800\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.39157e7i | 1.12490i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.58591e6 | −0.448276 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −220156. | −0.0175402 | −0.00877012 | − | 0.999962i | \(-0.502792\pi\) | ||||
−0.00877012 | + | 0.999962i | \(0.502792\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 467232.i | − 0.0369572i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 1.06454e7i | − 0.830006i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.94252e6 | 0.537433 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.78933e6 | 0.368111 | 0.184056 | − | 0.982916i | \(-0.441077\pi\) | ||||
0.184056 | + | 0.982916i | \(0.441077\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.14323e7i | 2.39877i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.23854e6i | 0.0931886i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.26892e6 | −0.318935 | −0.159468 | − | 0.987203i | \(-0.550978\pi\) | ||||
−0.159468 | + | 0.987203i | \(0.550978\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.99592e6 | 0.519004 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1.05395e6i | − 0.0776421i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.28592e7i | 2.38704i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.61960e7 | 1.16838 | 0.584190 | − | 0.811617i | \(-0.301412\pi\) | ||||
0.584190 | + | 0.811617i | \(0.301412\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.33018e6 | −0.310218 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 2.33488e7i | − 1.66119i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 6.53426e6i | − 0.458522i | −0.973365 | − | 0.229261i | \(-0.926369\pi\) | ||||
0.973365 | − | 0.229261i | \(-0.0736310\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.03131e6 | 0.211257 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.10072e7 | 0.761876 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.31617e7i | 0.904800i | 0.891815 | + | 0.452400i | \(0.149432\pi\) | ||||
−0.891815 | + | 0.452400i | \(0.850568\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.92597e6i | 0.130611i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.42348e7 | 0.958825 | 0.479412 | − | 0.877590i | \(-0.340850\pi\) | ||||
0.479412 | + | 0.877590i | \(0.340850\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.91006e7 | 1.94696 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 2.15835e7i | − 1.43434i | −0.696901 | − | 0.717168i | \(-0.745438\pi\) | ||||
0.696901 | − | 0.717168i | \(-0.254562\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.05761e7i | − 0.693467i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.57680e6 | −0.102700 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.86594e7 | 1.20725 | 0.603625 | − | 0.797268i | \(-0.293722\pi\) | ||||
0.603625 | + | 0.797268i | \(0.293722\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 1.58122e7i | − 1.01626i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.56681e6i | 0.162800i | 0.996682 | + | 0.0813999i | \(0.0259391\pi\) | ||||
−0.996682 | + | 0.0813999i | \(0.974061\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −456320. | −0.0287518 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.59586e7 | −1.62487 | −0.812436 | − | 0.583051i | \(-0.801859\pi\) | ||||
−0.812436 | + | 0.583051i | \(0.801859\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.70494e6i | 0.168208i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 8.06673e6i | − 0.495118i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.53267e6 | −0.337380 | −0.168690 | − | 0.985669i | \(-0.553954\pi\) | ||||
−0.168690 | + | 0.985669i | \(0.553954\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.59580e6 | −0.157266 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.32940e6i | 0.501378i | 0.968068 | + | 0.250689i | \(0.0806571\pi\) | ||||
−0.968068 | + | 0.250689i | \(0.919343\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.95648e6i | 0.294524i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.70490e7 | 1.59701 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.96304e6 | −0.232488 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.64504e6i | 0.329051i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.36523e7i | 0.785719i | 0.919598 | + | 0.392860i | \(0.128514\pi\) | ||||
−0.919598 | + | 0.392860i | \(0.871486\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.41776e6 | −0.0810793 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 564048. | 0.0320535 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 8.83440e6i | − 0.498877i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.54626e6i | 0.476574i | 0.971195 | + | 0.238287i | \(0.0765859\pi\) | ||||
−0.971195 | + | 0.238287i | \(0.923414\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.83495e7 | 1.57101 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.13031e7 | 0.622465 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 605864.i | − 0.0331578i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 3.58035e7i | − 1.93527i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.58484e6 | −0.407451 | −0.203725 | − | 0.979028i | \(-0.565305\pi\) | ||||
−0.203725 | + | 0.979028i | \(0.565305\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.18473e6 | 0.330194 | 0.165097 | − | 0.986277i | \(-0.447206\pi\) | ||||
0.165097 | + | 0.986277i | \(0.447206\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 3.54723e7i | − 1.88219i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.79683e7i | 1.46592i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.80110e6 | 0.0938273 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.78102e6 | −0.143995 | −0.0719973 | − | 0.997405i | \(-0.522937\pi\) | ||||
−0.0719973 | + | 0.997405i | \(0.522937\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.63895e7i | 0.843461i | 0.906721 | + | 0.421731i | \(0.138577\pi\) | ||||
−0.906721 | + | 0.421731i | \(0.861423\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 2.29511e7i | − 1.16692i | −0.812142 | − | 0.583459i | \(-0.801699\pi\) | ||||
0.812142 | − | 0.583459i | \(-0.198301\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.50136e6 | 0.176950 | 0.0884750 | − | 0.996078i | \(-0.471801\pi\) | ||||
0.0884750 | + | 0.996078i | \(0.471801\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.50900e6 | −0.276739 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.94447e7i | 0.970934i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 9.85216e6i | − 0.486091i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.29668e6 | −0.259776 | −0.129888 | − | 0.991529i | \(-0.541462\pi\) | ||||
−0.129888 | + | 0.991529i | \(0.541462\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.73962e6 | −0.474845 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.18834e7i | 0.575933i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 3.49620e6i | − 0.167451i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.18486e7 | −1.04029 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.89998e6 | 0.0899344 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.02948e7i | − 0.955021i | −0.878626 | − | 0.477511i | \(-0.841539\pi\) | ||||
0.878626 | − | 0.477511i | \(-0.158461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.82785e6i | 0.224544i | 0.993678 | + | 0.112272i | \(0.0358128\pi\) | ||||
−0.993678 | + | 0.112272i | \(0.964187\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.30210e7 | 0.602092 | 0.301046 | − | 0.953610i | \(-0.402664\pi\) | ||||
0.301046 | + | 0.953610i | \(0.402664\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.26528e6 | 0.196083 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 3.92387e7i | − 1.79344i | −0.442596 | − | 0.896721i | \(-0.645942\pi\) | ||||
0.442596 | − | 0.896721i | \(-0.354058\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 306940.i | − 0.0138677i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.52544e6 | −0.248209 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.42430e6 | −0.331596 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.67196e6i | 0.340699i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.34622e7i | − 0.591041i | −0.955336 | − | 0.295520i | \(-0.904507\pi\) | ||||
0.955336 | − | 0.295520i | \(-0.0954930\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.67308e6 | −0.291309 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −917710. | −0.0398351 | −0.0199175 | − | 0.999802i | \(-0.506340\pi\) | ||||
−0.0199175 | + | 0.999802i | \(0.506340\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.45488e7i | 1.05957i | 0.848133 | + | 0.529784i | \(0.177727\pi\) | ||||
−0.848133 | + | 0.529784i | \(0.822273\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.61463e7i | 0.689070i | 0.938773 | + | 0.344535i | \(0.111963\pi\) | ||||
−0.938773 | + | 0.344535i | \(0.888037\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.27021e6 | −0.0963410 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.99632e6 | −0.379639 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.20332e7i | 3.02276i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 1.75904e6i | − 0.0729953i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.87993e7 | −0.775787 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.39998e7 | −0.574527 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.41024e6i | 0.179988i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.03361e7i | 0.820824i | 0.911900 | + | 0.410412i | \(0.134615\pi\) | ||||
−0.911900 | + | 0.410412i | \(0.865385\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.10214e6 | −0.325230 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.07726e7 | 0.430054 | 0.215027 | − | 0.976608i | \(-0.431016\pi\) | ||||
0.215027 | + | 0.976608i | \(0.431016\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.35314e6i | 0.331644i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.68701e6i | 0.0662512i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.18566e7 | −1.63484 | −0.817419 | − | 0.576043i | \(-0.804596\pi\) | ||||
−0.817419 | + | 0.576043i | \(0.804596\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.11994e7 | 0.823522 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1.52769e7i | − 0.590242i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 2.83266e7i | − 1.08267i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.99845e7 | −1.13988 | −0.569939 | − | 0.821687i | \(-0.693033\pi\) | ||||
−0.569939 | + | 0.821687i | \(0.693033\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.94072e7 | −1.86817 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 2.67298e7i | − 1.00529i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1.42402e7i | − 0.529867i | −0.964267 | − | 0.264934i | \(-0.914650\pi\) | ||||
0.964267 | − | 0.264934i | \(-0.0853501\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.28837e7 | −1.21707 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.14546e7 | −1.52615 | −0.763077 | − | 0.646307i | \(-0.776313\pi\) | ||||
−0.763077 | + | 0.646307i | \(0.776313\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.63502e6i | − 0.0598749i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.54079e7i | 0.558300i | 0.960248 | + | 0.279150i | \(0.0900527\pi\) | ||||
−0.960248 | + | 0.279150i | \(0.909947\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.33551e6 | 0.0841813 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.44740e7 | −1.23606 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 2.06328e7i | − 0.735912i | −0.929843 | − | 0.367956i | \(-0.880058\pi\) | ||||
0.929843 | − | 0.367956i | \(-0.119942\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.13936e6i | 0.287283i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.65496e6 | 0.233668 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.18083e6 | 0.146034 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1.03149e7i | − 0.358426i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.18724e7i | − 0.408294i | −0.978940 | − | 0.204147i | \(-0.934558\pi\) | ||||
0.978940 | − | 0.204147i | \(-0.0654421\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.29342e7 | 2.49530 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.53222e6 | 0.0521523 | 0.0260761 | − | 0.999660i | \(-0.491699\pi\) | ||||
0.0260761 | + | 0.999660i | \(0.491699\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.12739e6i | 0.105901i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 1.74321e7i | − 0.584269i | −0.956377 | − | 0.292135i | \(-0.905635\pi\) | ||||
0.956377 | − | 0.292135i | \(-0.0943655\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.92726e6 | −0.297688 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.76948e7 | −0.587049 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.23270e6i | 0.0736963i | 0.999321 | + | 0.0368482i | \(0.0117318\pi\) | ||||
−0.999321 | + | 0.0368482i | \(0.988268\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.13587e7i | 0.371139i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.69059e6 | 0.0549602 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.22501e7 | 0.719693 | 0.359847 | − | 0.933011i | \(-0.382829\pi\) | ||||
0.359847 | + | 0.933011i | \(0.382829\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.49926e7i | 1.76983i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 5.32662e7i | − 1.69712i | −0.529095 | − | 0.848562i | \(-0.677469\pi\) | ||||
0.529095 | − | 0.848562i | \(-0.322531\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.77607e7 | 0.563050 |
(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 | 200.6.c.a.49.2 | 2 | ||
4.3 | odd | 2 | 400.6.c.d.49.1 | 2 | |||
5.2 | odd | 4 | 8.6.a.a.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 200.6.a.a.1.1 | 1 | |||
5.4 | even | 2 | inner | 200.6.c.a.49.1 | 2 | ||
15.2 | even | 4 | 72.6.a.f.1.1 | 1 | |||
20.3 | even | 4 | 400.6.a.l.1.1 | 1 | |||
20.7 | even | 4 | 16.6.a.a.1.1 | 1 | |||
20.19 | odd | 2 | 400.6.c.d.49.2 | 2 | |||
35.2 | odd | 12 | 392.6.i.b.361.1 | 2 | |||
35.12 | even | 12 | 392.6.i.e.361.1 | 2 | |||
35.17 | even | 12 | 392.6.i.e.177.1 | 2 | |||
35.27 | even | 4 | 392.6.a.b.1.1 | 1 | |||
35.32 | odd | 12 | 392.6.i.b.177.1 | 2 | |||
40.27 | even | 4 | 64.6.a.g.1.1 | 1 | |||
40.37 | odd | 4 | 64.6.a.a.1.1 | 1 | |||
55.32 | even | 4 | 968.6.a.a.1.1 | 1 | |||
60.47 | odd | 4 | 144.6.a.k.1.1 | 1 | |||
80.27 | even | 4 | 256.6.b.d.129.2 | 2 | |||
80.37 | odd | 4 | 256.6.b.f.129.1 | 2 | |||
80.67 | even | 4 | 256.6.b.d.129.1 | 2 | |||
80.77 | odd | 4 | 256.6.b.f.129.2 | 2 | |||
120.77 | even | 4 | 576.6.a.g.1.1 | 1 | |||
120.107 | odd | 4 | 576.6.a.h.1.1 | 1 | |||
140.27 | odd | 4 | 784.6.a.l.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.6.a.a.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
16.6.a.a.1.1 | 1 | 20.7 | even | 4 | |||
64.6.a.a.1.1 | 1 | 40.37 | odd | 4 | |||
64.6.a.g.1.1 | 1 | 40.27 | even | 4 | |||
72.6.a.f.1.1 | 1 | 15.2 | even | 4 | |||
144.6.a.k.1.1 | 1 | 60.47 | odd | 4 | |||
200.6.a.a.1.1 | 1 | 5.3 | odd | 4 | |||
200.6.c.a.49.1 | 2 | 5.4 | even | 2 | inner | ||
200.6.c.a.49.2 | 2 | 1.1 | even | 1 | trivial | ||
256.6.b.d.129.1 | 2 | 80.67 | even | 4 | |||
256.6.b.d.129.2 | 2 | 80.27 | even | 4 | |||
256.6.b.f.129.1 | 2 | 80.37 | odd | 4 | |||
256.6.b.f.129.2 | 2 | 80.77 | odd | 4 | |||
392.6.a.b.1.1 | 1 | 35.27 | even | 4 | |||
392.6.i.b.177.1 | 2 | 35.32 | odd | 12 | |||
392.6.i.b.361.1 | 2 | 35.2 | odd | 12 | |||
392.6.i.e.177.1 | 2 | 35.17 | even | 12 | |||
392.6.i.e.361.1 | 2 | 35.12 | even | 12 | |||
400.6.a.l.1.1 | 1 | 20.3 | even | 4 | |||
400.6.c.d.49.1 | 2 | 4.3 | odd | 2 | |||
400.6.c.d.49.2 | 2 | 20.19 | odd | 2 | |||
576.6.a.g.1.1 | 1 | 120.77 | even | 4 | |||
576.6.a.h.1.1 | 1 | 120.107 | odd | 4 | |||
784.6.a.l.1.1 | 1 | 140.27 | odd | 4 | |||
968.6.a.a.1.1 | 1 | 55.32 | even | 4 |