Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(53,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.53");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.bk (of order \(6\), degree \(2\), 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: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 233.17 | ||
Character | \(\chi\) | \(=\) | 252.233 |
Dual form | 252.9.bk.a.53.17 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 517.869 | + | 298.992i | 0.828591 | + | 0.478387i | 0.853370 | − | 0.521306i | \(-0.174555\pi\) |
−0.0247789 | + | 0.999693i | \(0.507888\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2338.25 | + | 545.349i | 0.973863 | + | 0.227134i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1572.34 | − | 907.792i | 0.107393 | − | 0.0620034i | −0.445341 | − | 0.895361i | \(-0.646918\pi\) |
0.552735 | + | 0.833357i | \(0.313584\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −35456.9 | −1.24144 | −0.620722 | − | 0.784031i | \(-0.713161\pi\) | ||||
−0.620722 | + | 0.784031i | \(0.713161\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 15328.2 | − | 8849.72i | 0.183525 | − | 0.105958i | −0.405423 | − | 0.914129i | \(-0.632876\pi\) |
0.588948 | + | 0.808171i | \(0.299542\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 61792.0 | − | 107027.i | 0.474153 | − | 0.821256i | −0.525409 | − | 0.850850i | \(-0.676088\pi\) |
0.999562 | + | 0.0295932i | \(0.00942118\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −351614. | − | 203005.i | −1.25648 | − | 0.725428i | −0.284091 | − | 0.958797i | \(-0.591692\pi\) |
−0.972388 | + | 0.233369i | \(0.925025\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −16520.0 | − | 28613.4i | −0.0422911 | − | 0.0732504i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.28998e6i | − | 1.82386i | −0.410348 | − | 0.911929i | \(-0.634593\pi\) | ||
0.410348 | − | 0.911929i | \(-0.365407\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −574013. | − | 994219.i | −0.621548 | − | 1.07655i | −0.989198 | − | 0.146589i | \(-0.953171\pi\) |
0.367649 | − | 0.929965i | \(-0.380163\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.04785e6 | + | 981537.i | 0.698277 | + | 0.654085i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −639192. | + | 1.10711e6i | −0.341055 | + | 0.590725i | −0.984629 | − | 0.174659i | \(-0.944118\pi\) |
0.643574 | + | 0.765384i | \(0.277451\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.15174e6i | 0.407584i | 0.979014 | + | 0.203792i | \(0.0653267\pi\) | ||||
−0.979014 | + | 0.203792i | \(0.934673\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.49924e6 | −1.31603 | −0.658014 | − | 0.753006i | \(-0.728603\pi\) | ||||
−0.658014 | + | 0.753006i | \(0.728603\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 588772. | + | 339928.i | 0.120658 | + | 0.0696619i | 0.559114 | − | 0.829091i | \(-0.311141\pi\) |
−0.438456 | + | 0.898752i | \(0.644475\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.16999e6 | + | 2.55032e6i | 0.896820 | + | 0.442395i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.08110e6 | − | 4.66562e6i | 1.02416 | − | 0.591298i | 0.108852 | − | 0.994058i | \(-0.465283\pi\) |
0.915305 | + | 0.402760i | \(0.131949\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.08569e6 | 0.118647 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.14373e7 | + | 6.60332e6i | −0.943876 | + | 0.544947i | −0.891173 | − | 0.453663i | \(-0.850117\pi\) |
−0.0527028 | + | 0.998610i | \(0.516784\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.72820e6 | − | 1.33856e7i | 0.558161 | − | 0.966763i | −0.439489 | − | 0.898248i | \(-0.644841\pi\) |
0.997650 | − | 0.0685150i | \(-0.0218261\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.83620e7 | − | 1.06013e7i | −1.02865 | − | 0.593891i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.52255e6 | + | 1.47615e7i | 0.422932 | + | 0.732540i | 0.996225 | − | 0.0868109i | \(-0.0276676\pi\) |
−0.573293 | + | 0.819351i | \(0.694334\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.31454e7i | 0.910817i | 0.890283 | + | 0.455409i | \(0.150507\pi\) | ||||
−0.890283 | + | 0.455409i | \(0.849493\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.04308e7 | + | 1.80667e7i | 0.367306 | + | 0.636192i | 0.989143 | − | 0.146954i | \(-0.0469470\pi\) |
−0.621838 | + | 0.783146i | \(0.713614\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.17159e6 | − | 1.26517e6i | 0.118669 | − | 0.0359902i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.77913e7 | − | 4.81360e7i | 0.713512 | − | 1.23584i | −0.250019 | − | 0.968241i | \(-0.580437\pi\) |
0.963531 | − | 0.267598i | \(-0.0862299\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 4.09134e7i | − | 0.862090i | −0.902330 | − | 0.431045i | \(-0.858145\pi\) | ||
0.902330 | − | 0.431045i | \(-0.141855\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.05840e7 | 0.202756 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.29143e7 | − | 4.78706e7i | −1.32151 | − | 0.762972i | −0.337538 | − | 0.941312i | \(-0.609594\pi\) |
−0.983969 | + | 0.178340i | \(0.942927\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.29069e7 | − | 1.93364e7i | −1.20900 | − | 0.281975i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.40004e7 | − | 3.69507e7i | 0.785757 | − | 0.453657i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.71573e7 | 0.645632 | 0.322816 | − | 0.946462i | \(-0.395371\pi\) | ||||
0.322816 | + | 0.946462i | \(0.395371\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.11673e7 | + | 6.44744e6i | −0.107316 | + | 0.0619586i | −0.552697 | − | 0.833382i | \(-0.686401\pi\) |
0.445382 | + | 0.895341i | \(0.353068\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.44198e7 | − | 4.22964e7i | 0.216967 | − | 0.375798i | −0.736912 | − | 0.675989i | \(-0.763717\pi\) |
0.953879 | + | 0.300190i | \(0.0970502\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.00639e7 | − | 3.46779e7i | −0.458225 | − | 0.264556i | 0.253073 | − | 0.967447i | \(-0.418559\pi\) |
−0.711298 | + | 0.702891i | \(0.751892\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.45824e7 | + | 2.52574e7i | 0.103305 | + | 0.178930i | 0.913045 | − | 0.407860i | \(-0.133725\pi\) |
−0.809739 | + | 0.586790i | \(0.800391\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.09275e8i | − | 0.670205i | −0.942182 | − | 0.335103i | \(-0.891229\pi\) | ||
0.942182 | − | 0.335103i | \(-0.108771\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.21394e8 | − | 2.10260e8i | −0.694072 | − | 1.20217i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.06672e7 | − | 1.23336e7i | 0.202795 | − | 0.0615039i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.05531e8 | + | 1.82786e8i | −0.492311 | + | 0.852708i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2.53345e8i | − | 1.03770i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.52517e8 | 0.970681 | 0.485340 | − | 0.874325i | \(-0.338696\pi\) | ||||
0.485340 | + | 0.874325i | \(0.338696\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.70826e8 | − | 2.14096e8i | −1.25917 | − | 0.726983i | −0.286258 | − | 0.958153i | \(-0.592412\pi\) |
−0.972914 | + | 0.231169i | \(0.925745\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.02852e8 | − | 2.16557e8i | 0.648295 | − | 0.692095i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.74792e8 | + | 1.58651e8i | −0.780050 | + | 0.450362i | −0.836448 | − | 0.548046i | \(-0.815372\pi\) |
0.0563980 | + | 0.998408i | \(0.482038\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.61026e8 | 1.77076 | 0.885380 | − | 0.464868i | \(-0.153898\pi\) | ||||
0.885380 | + | 0.464868i | \(0.153898\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.57504e7 | + | 3.21875e7i | −0.133323 | + | 0.0769738i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.85694e8 | − | 6.68041e8i | 0.872511 | − | 1.51123i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.25970e8 | − | 4.76874e8i | −1.67579 | − | 0.967517i | −0.964297 | − | 0.264822i | \(-0.914687\pi\) |
−0.711491 | − | 0.702695i | \(-0.751980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.02229e8 | − | 5.23477e8i | −0.581338 | − | 1.00691i | −0.995321 | − | 0.0966229i | \(-0.969196\pi\) |
0.413983 | − | 0.910285i | \(-0.364137\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 6.86501e8i | − | 1.18936i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.56925e8 | + | 9.64623e8i | 0.916639 | + | 1.58767i | 0.804484 | + | 0.593975i | \(0.202442\pi\) |
0.112155 | + | 0.993691i | \(0.464225\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.11452e8 | − | 6.66427e8i | −1.05887 | − | 0.991858i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.77579e8 | − | 4.80780e8i | 0.393220 | − | 0.681077i | −0.599652 | − | 0.800261i | \(-0.704694\pi\) |
0.992872 | + | 0.119184i | \(0.0380277\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.08481e8i | 0.139473i | 0.997565 | + | 0.0697364i | \(0.0222158\pi\) | ||||
−0.997565 | + | 0.0697364i | \(0.977784\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.41461e8 | 0.541184 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.77710e8 | + | 4.49011e8i | 0.868227 | + | 0.501271i | 0.866759 | − | 0.498728i | \(-0.166199\pi\) |
0.00146854 | + | 0.999999i | \(0.499533\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.30234e7 | − | 7.59144e7i | −0.0245481 | − | 0.0809416i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.60713e8 | − | 2.65993e8i | 0.448764 | − | 0.259094i | −0.258544 | − | 0.965999i | \(-0.583243\pi\) |
0.707308 | + | 0.706905i | \(0.249909\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.05192e7 | −0.0843386 | −0.0421693 | − | 0.999110i | \(-0.513427\pi\) | ||||
−0.0421693 | + | 0.999110i | \(0.513427\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.62036e8 | + | 3.82227e8i | −0.565191 | + | 0.326313i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.60674e7 | − | 2.78296e7i | 0.0131395 | − | 0.0227583i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.57013e9 | − | 9.06517e8i | −1.17979 | − | 0.681150i | −0.223821 | − | 0.974630i | \(-0.571853\pi\) |
−0.955965 | + | 0.293481i | \(0.905186\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.96214e8 | − | 1.37908e9i | −0.573853 | − | 0.993942i | −0.996165 | − | 0.0874919i | \(-0.972115\pi\) |
0.422312 | − | 0.906450i | \(-0.361219\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.10470e9i | − | 0.733466i | −0.930326 | − | 0.366733i | \(-0.880476\pi\) | ||
0.930326 | − | 0.366733i | \(-0.119524\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.02682e8 | − | 6.97466e8i | −0.256774 | − | 0.444745i | 0.708602 | − | 0.705608i | \(-0.249326\pi\) |
−0.965376 | + | 0.260863i | \(0.915993\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.03490e8 | − | 3.01629e9i | 0.414261 | − | 1.77619i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.44360e8 | + | 5.96449e8i | −0.194983 | + | 0.337721i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2.24377e8i | − | 0.117596i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.98359e9 | 1.00074 | 0.500371 | − | 0.865811i | \(-0.333197\pi\) | ||||
0.500371 | + | 0.865811i | \(0.333197\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.33002e9 | − | 1.34524e9i | −1.09045 | − | 0.629571i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.99987e8 | − | 2.63777e9i | −0.360781 | − | 1.18959i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.43489e8 | + | 3.13784e8i | −0.227836 | + | 0.131541i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.73592e9 | 1.51070 | 0.755351 | − | 0.655321i | \(-0.227467\pi\) | ||||
0.755351 | + | 0.655321i | \(0.227467\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.02521e8 | + | 3.47865e8i | −0.226918 | + | 0.131011i | −0.609149 | − | 0.793056i | \(-0.708489\pi\) |
0.382232 | + | 0.924067i | \(0.375156\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.15791e8 | − | 3.73761e8i | 0.0784678 | − | 0.135910i | −0.824121 | − | 0.566413i | \(-0.808331\pi\) |
0.902589 | + | 0.430503i | \(0.141664\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.32117e9 | − | 7.62775e8i | −0.448264 | − | 0.258805i | 0.258833 | − | 0.965922i | \(-0.416662\pi\) |
−0.707097 | + | 0.707117i | \(0.749995\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.03271e8 | + | 3.52076e8i | 0.0666507 | + | 0.115442i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.62327e8i | − | 0.0803990i | −0.999192 | − | 0.0401995i | \(-0.987201\pi\) | ||
0.999192 | − | 0.0401995i | \(-0.0127994\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.27912e8 | − | 3.94755e8i | −0.0675615 | − | 0.117020i | 0.830266 | − | 0.557368i | \(-0.188189\pi\) |
−0.897827 | + | 0.440348i | \(0.854855\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.91485e9 | + | 2.86652e9i | 0.531461 | + | 0.795592i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.19095e9 | + | 3.79484e9i | −0.588634 | + | 1.01954i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.71873e9i | 1.44080i | 0.693556 | + | 0.720402i | \(0.256043\pi\) | ||||
−0.693556 | + | 0.720402i | \(0.743957\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.37144e8 | −0.179916 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.14707e8 | − | 2.39431e8i | −0.0950623 | − | 0.0548843i | 0.451715 | − | 0.892162i | \(-0.350812\pi\) |
−0.546778 | + | 0.837278i | \(0.684146\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.09835e9 | + | 2.24012e9i | −0.466315 | + | 0.497820i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.27146e9 | − | 1.88878e9i | 0.683784 | − | 0.394783i | −0.117495 | − | 0.993073i | \(-0.537486\pi\) |
0.801279 | + | 0.598290i | \(0.204153\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.57994e9 | 1.13148 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.07652e9 | − | 1.19888e9i | 0.396577 | − | 0.228964i | −0.288429 | − | 0.957501i | \(-0.593133\pi\) |
0.685006 | + | 0.728537i | \(0.259800\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.35974e9 | − | 2.35513e9i | 0.252103 | − | 0.436655i | −0.712002 | − | 0.702178i | \(-0.752211\pi\) |
0.964105 | + | 0.265523i | \(0.0855445\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.19501e7 | − | 2.99934e7i | −0.00908355 | − | 0.00524439i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.64025e8 | − | 6.30509e8i | −0.0618318 | − | 0.107096i | 0.833452 | − | 0.552591i | \(-0.186361\pi\) |
−0.895284 | + | 0.445495i | \(0.853028\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.18211e10i | 1.89598i | 0.318299 | + | 0.947990i | \(0.396888\pi\) | ||||
−0.318299 | + | 0.947990i | \(0.603112\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.44075e9 | + | 5.95956e9i | 0.536423 | + | 0.929113i | 0.999093 | + | 0.0425819i | \(0.0135583\pi\) |
−0.462670 | + | 0.886531i | \(0.653108\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.28099e8 | + | 2.69304e9i | −0.0925764 | + | 0.396932i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.33124e9 | + | 5.76988e9i | −0.477546 | + | 0.827134i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.35666e9i | − | 1.13387i | −0.823764 | − | 0.566933i | \(-0.808130\pi\) | ||
0.823764 | − | 0.566933i | \(-0.191870\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.89736e9 | −1.04278 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.24672e10 | + | 7.19791e9i | 1.55985 | + | 0.900579i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.05203e10 | − | 2.45366e9i | −1.28163 | − | 0.298915i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.00440e9 | − | 4.62134e9i | 0.924974 | − | 0.534034i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.15726e10 | −1.30280 | −0.651400 | − | 0.758735i | \(-0.725818\pi\) | ||||
−0.651400 | + | 0.758735i | \(0.725818\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.04592e10 | + | 6.03861e9i | −1.11804 | + | 0.645499i | −0.940899 | − | 0.338687i | \(-0.890017\pi\) |
−0.177138 | + | 0.984186i | \(0.556684\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.14939e8 | − | 1.23831e9i | 0.0744889 | − | 0.129019i | −0.826375 | − | 0.563120i | \(-0.809601\pi\) |
0.900864 | + | 0.434102i | \(0.142934\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.17505e10 | + | 6.78415e9i | 1.16364 | + | 0.671828i | 0.952174 | − | 0.305557i | \(-0.0988426\pi\) |
0.211467 | + | 0.977385i | \(0.432176\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.17103e9 | − | 2.02829e9i | −0.113085 | − | 0.195870i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.18737e9i | − | 0.200961i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.85747e8 | + | 1.01454e9i | 0.0525021 | + | 0.0909362i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.19132e9 | + | 1.11592e9i | 0.101682 | + | 0.0952467i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.46041e9 | + | 4.26156e9i | −0.204972 | + | 0.355023i | −0.950124 | − | 0.311872i | \(-0.899044\pi\) |
0.745151 | + | 0.666895i | \(0.232377\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.01927e10i | 0.809301i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.63479e9 | −0.514408 | −0.257204 | − | 0.966357i | \(-0.582801\pi\) | ||||
−0.257204 | + | 0.966357i | \(0.582801\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.80509e9 | − | 1.04217e9i | −0.133500 | − | 0.0770763i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.06979e10 | + | 8.78273e9i | 0.772897 | + | 0.634531i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.51787e9 | − | 2.03104e9i | 0.242639 | − | 0.140088i | −0.373750 | − | 0.927530i | \(-0.621928\pi\) |
0.616389 | + | 0.787442i | \(0.288595\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.59026e9 | −0.309411 | −0.154705 | − | 0.987961i | \(-0.549443\pi\) | ||||
−0.154705 | + | 0.987961i | \(0.549443\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.26530e9 | − | 3.03992e9i | 0.339097 | − | 0.195778i | −0.320775 | − | 0.947155i | \(-0.603943\pi\) |
0.659873 | + | 0.751377i | \(0.270610\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.92029e9 | + | 1.19863e10i | −0.435723 | + | 0.754695i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.76858e9 | − | 2.17579e9i | −0.226882 | − | 0.130990i | 0.382251 | − | 0.924059i | \(-0.375149\pi\) |
−0.609133 | + | 0.793068i | \(0.708482\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.55270e8 | + | 1.48137e9i | 0.0503587 | + | 0.0872238i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.24749e10i | 0.702857i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.24771e9 | − | 1.60175e10i | −0.509765 | − | 0.882939i | −0.999936 | − | 0.0113124i | \(-0.996399\pi\) |
0.490171 | − | 0.871626i | \(-0.336934\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.14400e10 | − | 6.50236e9i | 1.13169 | − | 0.343222i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.96707e9 | + | 6.87116e9i | −0.204943 | + | 0.354973i | −0.950115 | − | 0.311901i | \(-0.899034\pi\) |
0.745171 | + | 0.666873i | \(0.232368\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.57387e10i | 2.26422i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.63069e10 | 0.790342 | 0.395171 | − | 0.918608i | \(-0.370685\pi\) | ||||
0.395171 | + | 0.918608i | \(0.370685\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.96738e10 | + | 1.13587e10i | 0.914309 | + | 0.527876i | 0.881815 | − | 0.471595i | \(-0.156322\pi\) |
0.0324938 | + | 0.999472i | \(0.489655\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.53861e9 | + | 5.92081e8i | 0.115546 | + | 0.0269487i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.88603e10 | + | 2.24360e10i | −1.69710 | + | 0.979821i | −0.748610 | + | 0.663010i | \(0.769279\pi\) |
−0.948489 | + | 0.316810i | \(0.897388\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.18614e9 | −0.307460 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.87846e10 | − | 1.66188e10i | 1.18242 | − | 0.682670i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.24361e10 | + | 3.88605e10i | −0.903204 | + | 1.56439i | −0.0798931 | + | 0.996803i | \(0.525458\pi\) |
−0.823311 | + | 0.567591i | \(0.807875\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.60799e10 | + | 2.08307e10i | 1.39536 | + | 0.805614i | 0.993903 | − | 0.110261i | \(-0.0351688\pi\) |
0.401462 | + | 0.915876i | \(0.368502\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.03527e10 | + | 3.52519e10i | 0.771618 | + | 1.33648i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.32102e9i | 0.0845864i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.72902e8 | − | 2.99476e8i | −0.00617885 | − | 0.0107021i | 0.862919 | − | 0.505341i | \(-0.168633\pi\) |
−0.869098 | + | 0.494639i | \(0.835300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.03443e10 | + | 9.20287e9i | −1.04298 | + | 0.316317i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.22328e10 | − | 2.11878e10i | 0.412413 | − | 0.714321i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 5.40269e10i | − | 1.75289i | −0.481503 | − | 0.876444i | \(-0.659909\pi\) | ||
0.481503 | − | 0.876444i | \(-0.340091\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.75550e10 | −0.558820 | −0.279410 | − | 0.960172i | \(-0.590139\pi\) | ||||
−0.279410 | + | 0.960172i | \(0.590139\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.06442e8 | − | 2.92394e8i | −0.0155229 | − | 0.00896217i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.53703e10 | − | 2.70844e10i | 0.763157 | − | 0.814718i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.28336e10 | − | 7.40949e9i | 0.371912 | − | 0.214723i | −0.302382 | − | 0.953187i | \(-0.597782\pi\) |
0.674293 | + | 0.738464i | \(0.264448\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.02897e10 | −0.292720 | −0.146360 | − | 0.989231i | \(-0.546756\pi\) | ||||
−0.146360 | + | 0.989231i | \(0.546756\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.34539e10 | + | 2.50881e10i | −1.19153 | + | 0.687927i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.12804e10 | − | 1.95382e10i | 0.303715 | − | 0.526049i | −0.673260 | − | 0.739406i | \(-0.735106\pi\) |
0.976974 | + | 0.213357i | \(0.0684397\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.71575e9 | − | 5.60939e9i | −0.252268 | − | 0.145647i | 0.368535 | − | 0.929614i | \(-0.379860\pi\) |
−0.620802 | + | 0.783967i | \(0.713193\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.86259e10 | − | 4.95814e10i | −0.729993 | − | 1.26438i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 4.44507e10i | − | 1.09369i | −0.837235 | − | 0.546844i | \(-0.815829\pi\) | ||
0.837235 | − | 0.546844i | \(-0.184171\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.04554e9 | + | 1.81092e9i | 0.0252716 | + | 0.0437718i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.71535e10 | − | 3.48022e10i | −0.866871 | − | 0.812011i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.66755e10 | − | 2.88828e10i | 0.382308 | − | 0.662178i | −0.609083 | − | 0.793106i | \(-0.708463\pi\) |
0.991392 | + | 0.130929i | \(0.0417958\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 6.58638e10i | − | 1.45829i | −0.684361 | − | 0.729144i | \(-0.739919\pi\) | ||
0.684361 | − | 0.729144i | \(-0.260081\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.17003e9 | −0.112504 | −0.0562521 | − | 0.998417i | \(-0.517915\pi\) | ||||
−0.0562521 | + | 0.998417i | \(0.517915\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.75868e10 | − | 2.17008e10i | −0.790256 | − | 0.456255i | 0.0497964 | − | 0.998759i | \(-0.484143\pi\) |
−0.840053 | + | 0.542505i | \(0.817476\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.18777e10 | + | 3.91638e10i | 0.245493 | + | 0.809456i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.07434e9 | + | 4.08437e9i | −0.141332 | + | 0.0815982i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.08321e9 | −0.0802098 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.31609e10 | − | 1.33719e10i | 0.439959 | − | 0.254011i | −0.263621 | − | 0.964626i | \(-0.584917\pi\) |
0.703580 | + | 0.710616i | \(0.251584\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.26638e10 | − | 3.92548e10i | 0.423401 | − | 0.733352i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.96000e10 | + | 1.70896e10i | 0.534965 | + | 0.308862i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.02541e10 | + | 1.77606e10i | 0.182298 | + | 0.315749i | 0.942663 | − | 0.333747i | \(-0.108313\pi\) |
−0.760365 | + | 0.649496i | \(0.774980\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.23018e9i | 0.0555777i | 0.999614 | + | 0.0277888i | \(0.00884660\pi\) | ||||
−0.999614 | + | 0.0277888i | \(0.991153\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.14160e10 | − | 1.97730e10i | −0.193252 | − | 0.334723i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.26223e10 | + | 5.41196e10i | −0.206878 | + | 0.887012i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.67911e10 | − | 4.64035e10i | 0.432104 | − | 0.748426i | −0.564950 | − | 0.825125i | \(-0.691105\pi\) |
0.997054 | + | 0.0766989i | \(0.0244380\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 7.69019e10i | − | 1.20134i | −0.799498 | − | 0.600669i | \(-0.794901\pi\) | ||
0.799498 | − | 0.600669i | \(-0.205099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.71094e9 | −0.118561 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.01771e10 | − | 2.31963e10i | −0.598560 | − | 0.345579i | 0.169915 | − | 0.985459i | \(-0.445651\pi\) |
−0.768475 | + | 0.639880i | \(0.778984\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.45372e10 | + | 4.79329e10i | 0.213205 | + | 0.702992i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.52926e10 | − | 1.46027e10i | 0.359554 | − | 0.207589i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.23434e9 | 0.0172771 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.23241e10 | + | 3.59828e10i | −0.845872 | + | 0.488365i | −0.859256 | − | 0.511546i | \(-0.829073\pi\) |
0.0133836 | + | 0.999910i | \(0.495740\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.22903e10 | − | 3.86079e10i | 0.297926 | − | 0.516023i | −0.677735 | − | 0.735306i | \(-0.737038\pi\) |
0.975661 | + | 0.219283i | \(0.0703717\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.75971e10 | − | 1.01597e10i | −0.228139 | − | 0.131716i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.32663e10 | + | 7.49394e10i | 0.552493 | + | 0.956946i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4.08370e10i | − | 0.505993i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.07369e10 | − | 3.59173e10i | −0.253121 | − | 0.438418i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.04442e10 | − | 6.83298e8i | 0.123742 | − | 0.00809571i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.21947e9 | + | 9.04039e9i | −0.0609309 | + | 0.105535i | −0.894882 | − | 0.446303i | \(-0.852740\pi\) |
0.833951 | + | 0.551839i | \(0.186074\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.74401e10i | 0.197680i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.16157e10 | 1.02334 | 0.511671 | − | 0.859182i | \(-0.329027\pi\) | ||||
0.511671 | + | 0.859182i | \(0.329027\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.38063e11 | − | 7.97105e10i | −1.49785 | − | 0.864787i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.12340e10 | − | 9.73979e10i | 0.975565 | − | 1.04148i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.47004e10 | + | 2.58078e10i | −0.464398 | + | 0.268120i | −0.713892 | − | 0.700256i | \(-0.753069\pi\) |
0.249494 | + | 0.968376i | \(0.419736\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.59529e11 | 1.63377 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.38401e9 | + | 3.68581e9i | −0.0635419 | + | 0.0366859i | −0.531434 | − | 0.847099i | \(-0.678347\pi\) |
0.467892 | + | 0.883785i | \(0.345013\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.26724e10 | − | 5.65903e10i | 0.320618 | − | 0.555326i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.48763e10 | − | 4.90033e10i | −0.809724 | − | 0.467495i | 0.0371359 | − | 0.999310i | \(-0.488177\pi\) |
−0.846860 | + | 0.531816i | \(0.821510\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.08919e10 | + | 1.05468e11i | 0.572816 | + | 0.992147i | 0.996275 | + | 0.0862317i | \(0.0274825\pi\) |
−0.423459 | + | 0.905915i | \(0.639184\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.34145e10i | 0.122717i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.81452e10 | − | 1.69993e11i | −0.885454 | − | 1.53365i | −0.845192 | − | 0.534462i | \(-0.820514\pi\) |
−0.0402615 | − | 0.999189i | \(-0.512819\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.23121e10 | − | 9.56655e10i | 0.195810 | − | 0.839558i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.47083e9 | − | 1.46719e10i | 0.0733250 | − | 0.127003i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.26503e11i | − | 1.06549i | −0.846277 | − | 0.532743i | \(-0.821161\pi\) | ||
0.846277 | − | 0.532743i | \(-0.178839\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.41878e11 | −1.17883 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.65960e10 | + | 2.11287e10i | 0.295947 | + | 0.170865i | 0.640621 | − | 0.767857i | \(-0.278677\pi\) |
−0.344674 | + | 0.938723i | \(0.612010\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.47480e10 | + | 5.77197e9i | 0.197457 | + | 0.0460528i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.48720e11 | − | 8.58634e10i | 1.15521 | − | 0.666962i | 0.205060 | − | 0.978749i | \(-0.434261\pi\) |
0.950152 | + | 0.311788i | \(0.100928\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.98855e10 | −0.305715 | −0.152857 | − | 0.988248i | \(-0.548848\pi\) | ||||
−0.152857 | + | 0.988248i | \(0.548848\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.09303e11 | + | 6.31060e10i | −0.815849 | + | 0.471031i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.14485e11 | + | 1.98293e11i | −0.843320 | + | 1.46067i | 0.0437514 | + | 0.999042i | \(0.486069\pi\) |
−0.887072 | + | 0.461631i | \(0.847264\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.08760e10 | − | 1.20528e10i | −0.149790 | − | 0.0864814i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.39859e10 | − | 5.88654e10i | −0.240690 | − | 0.416887i | 0.720221 | − | 0.693744i | \(-0.244040\pi\) |
−0.960911 | + | 0.276858i | \(0.910707\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.24449e11i | 1.54874i | 0.632735 | + | 0.774368i | \(0.281932\pi\) | ||||
−0.632735 | + | 0.774368i | \(0.718068\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.15809e10 | − | 2.00586e10i | −0.0788821 | − | 0.136628i | 0.823886 | − | 0.566756i | \(-0.191802\pi\) |
−0.902768 | + | 0.430128i | \(0.858468\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.67768e11 | − | 1.57150e11i | −1.11367 | − | 1.04319i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.92950e10 | − | 1.20022e11i | 0.454132 | − | 0.786579i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.26267e10i | 0.144550i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.69026e11 | 1.06619 | 0.533097 | − | 0.846054i | \(-0.321028\pi\) | ||||
0.533097 | + | 0.846054i | \(0.321028\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.30771e11 | + | 7.55007e10i | 0.804298 | + | 0.464361i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.83312e11 | − | 9.04265e10i | −1.11335 | − | 0.549209i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.06968e9 | + | 1.19493e9i | −0.0122595 | + | 0.00707800i | −0.506117 | − | 0.862465i | \(-0.668920\pi\) |
0.493858 | + | 0.869543i | \(0.335586\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.39269e10 | 0.0814723 | 0.0407361 | − | 0.999170i | \(-0.487030\pi\) | ||||
0.0407361 | + | 0.999170i | \(0.487030\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.77460e10 | − | 2.75662e10i | 0.272471 | − | 0.157311i | −0.357539 | − | 0.933898i | \(-0.616384\pi\) |
0.630010 | + | 0.776587i | \(0.283051\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.19889e10 | + | 2.07654e10i | −0.0675772 | + | 0.117047i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.01074e11 | + | 1.16090e11i | 1.10587 | + | 0.638472i | 0.937755 | − | 0.347296i | \(-0.112900\pi\) |
0.168110 | + | 0.985768i | \(0.446234\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.28026e11 | − | 2.21748e11i | −0.695559 | − | 1.20474i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 2.27443e11i | − | 1.20595i | −0.797759 | − | 0.602977i | \(-0.793981\pi\) | ||
0.797759 | − | 0.602977i | \(-0.206019\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.52803e11 | + | 2.64662e11i | 0.800434 | + | 1.38639i | 0.919331 | + | 0.393486i | \(0.128731\pi\) |
−0.118897 | + | 0.992907i | \(0.537936\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.69800e11 | − | 5.14972e10i | 0.868261 | − | 0.263328i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.61872e11 | + | 4.53575e11i | −1.32308 | + | 2.29164i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.80624e10i | − | 0.138432i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.36129e11 | −1.15104 | −0.575519 | − | 0.817788i | \(-0.695200\pi\) | ||||
−0.575519 | + | 0.817788i | \(0.695200\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.65227e11 | + | 9.53939e10i | 0.786551 | + | 0.454115i | 0.838747 | − | 0.544522i | \(-0.183289\pi\) |
−0.0521961 | + | 0.998637i | \(0.516622\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.33648e11 | + | 3.11707e10i | 0.628757 | + | 0.146645i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.09400e11 | + | 6.31623e10i | −0.502731 | + | 0.290252i | −0.729841 | − | 0.683617i | \(-0.760406\pi\) |
0.227109 | + | 0.973869i | \(0.427072\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.89742e11 | −0.861790 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.86531e11 | + | 1.65428e11i | −1.27143 | + | 0.734063i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.77438e11 | − | 3.07332e11i | 0.778278 | − | 1.34802i | −0.154656 | − | 0.987968i | \(-0.549427\pi\) |
0.932934 | − | 0.360048i | \(-0.117240\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.42325e11 | + | 1.97642e11i | 1.46724 | + | 0.847109i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.01925e10 | + | 1.76540e10i | 0.0431869 | + | 0.0748018i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.68942e11i | 1.11375i | 0.830597 | + | 0.556874i | \(0.187999\pi\) | ||||
−0.830597 | + | 0.556874i | \(0.812001\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.89940e10 | + | 1.36822e11i | 0.323424 | + | 0.560188i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.96280e10 | + | 8.98563e9i | −0.118584 | + | 0.0359642i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.85843e11 | + | 3.21890e11i | −0.735466 | + | 1.27386i | 0.219053 | + | 0.975713i | \(0.429703\pi\) |
−0.954519 | + | 0.298151i | \(0.903630\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.66109e11i | 1.80356i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.84952e10 | −0.147293 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.11727e11 | + | 2.37710e11i | 1.54061 | + | 0.889473i | 0.998800 | + | 0.0489736i | \(0.0155950\pi\) |
0.541812 | + | 0.840499i | \(0.317738\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.01659e10 | − | 8.55821e10i | 0.296653 | − | 0.316695i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.69107e10 | + | 2.13104e10i | −0.133598 | + | 0.0771330i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.14164e11 | 1.84062 | 0.920309 | − | 0.391192i | \(-0.127937\pi\) | ||||
0.920309 | + | 0.391192i | \(0.127937\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.89651e10 | + | 3.98170e10i | −0.241524 | + | 0.139444i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.15362e11 | + | 3.73017e11i | −0.746024 | + | 1.29215i | 0.203691 | + | 0.979035i | \(0.434706\pi\) |
−0.949715 | + | 0.313116i | \(0.898627\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.68007e10 | + | 1.54734e10i | 0.0908400 | + | 0.0524465i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.90588e10 | − | 3.30108e10i | −0.0639025 | − | 0.110682i | 0.832304 | − | 0.554319i | \(-0.187021\pi\) |
−0.896207 | + | 0.443637i | \(0.853688\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 5.19643e10i | − | 0.170510i | −0.996359 | − | 0.0852550i | \(-0.972830\pi\) | ||
0.996359 | − | 0.0852550i | \(-0.0271705\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.85163e11 | − | 4.93917e11i | −0.925696 | − | 1.60335i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.21533e11 | − | 1.13841e11i | −0.386159 | − | 0.361720i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.02878e11 | + | 3.51395e11i | −0.637787 | + | 1.10468i | 0.348131 | + | 0.937446i | \(0.386817\pi\) |
−0.985917 | + | 0.167233i | \(0.946517\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 3.61457e11i | − | 1.11242i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.05947e10 | −0.184523 | −0.0922616 | − | 0.995735i | \(-0.529410\pi\) | ||||
−0.0922616 | + | 0.995735i | \(0.529410\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.30256e9 | − | 3.63879e9i | −0.0187922 | − | 0.0108497i | 0.490574 | − | 0.871399i | \(-0.336787\pi\) |
−0.509367 | + | 0.860550i | \(0.670120\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.03231e10 | + | 6.70106e10i | 0.0599641 | + | 0.197718i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.05531e11 | − | 2.34133e11i | 1.17177 | − | 0.676521i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.64380e11 | 1.04196 | 0.520978 | − | 0.853570i | \(-0.325568\pi\) | ||||
0.520978 | + | 0.853570i | \(0.325568\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.13050e11 | + | 2.38475e11i | −1.15687 | + | 0.667920i | −0.950552 | − | 0.310565i | \(-0.899482\pi\) |
−0.206319 | + | 0.978485i | \(0.566148\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.89653e10 | + | 3.28489e10i | −0.0525719 | + | 0.0910573i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.23267e11 | + | 7.11681e10i | 0.334731 | + | 0.193257i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.10112e10 | + | 3.63925e10i | 0.0564738 | + | 0.0978155i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.66065e11i | 1.75403i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.68255e11 | − | 2.91425e11i | −0.438599 | − | 0.759676i | 0.558983 | − | 0.829179i | \(-0.311192\pi\) |
−0.997582 | + | 0.0695034i | \(0.977859\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.95932e10 | − | 2.55512e11i | 0.152227 | − | 0.652688i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.74018e11 | + | 4.74613e11i | −0.692926 | + | 1.20018i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.92820e11i | 0.973554i | 0.873526 | + | 0.486777i | \(0.161828\pi\) | ||||
−0.873526 | + | 0.486777i | \(0.838172\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.20331e10 | 0.0295250 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.28017e10 | + | 1.89381e10i | 0.0788922 | + | 0.0455484i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.69183e11 | − | 5.57841e11i | −0.402878 | − | 1.32839i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.36083e11 | − | 1.94038e11i | 0.784609 | − | 0.452994i | −0.0534525 | − | 0.998570i | \(-0.517023\pi\) |
0.838061 | + | 0.545576i | \(0.183689\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.05867e11 | −0.475886 | −0.237943 | − | 0.971279i | \(-0.576473\pi\) | ||||
−0.237943 | + | 0.971279i | \(0.576473\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.87499e11 | − | 1.65988e11i | 0.651637 | − | 0.376223i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.78017e11 | + | 4.81539e11i | −0.623998 | + | 1.08080i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.27601e11 | + | 1.89140e11i | 0.721061 | + | 0.416305i | 0.815143 | − | 0.579260i | \(-0.196658\pi\) |
−0.0940820 | + | 0.995564i | \(0.529992\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.94336e10 | + | 1.54904e11i | 0.194940 | + | 0.337646i | 0.946881 | − | 0.321584i | \(-0.104215\pi\) |
−0.751941 | + | 0.659231i | \(0.770882\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.35168e11i | 1.35790i | 0.734186 | + | 0.678948i | \(0.237564\pi\) | ||||
−0.734186 | + | 0.678948i | \(0.762436\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.61479e10 | + | 1.31892e11i | 0.161228 | + | 0.279255i | 0.935309 | − | 0.353831i | \(-0.115121\pi\) |
−0.774082 | + | 0.633086i | \(0.781788\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.01816e11 | − | 6.66121e9i | 0.211464 | − | 0.0138348i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.24351e10 | + | 5.61792e10i | −0.0667220 | + | 0.115566i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 4.77973e11i | − | 0.964618i | −0.876001 | − | 0.482309i | \(-0.839798\pi\) | ||
0.876001 | − | 0.482309i | \(-0.160202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.16380e12 | −2.32646 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.28619e11 | + | 1.31993e11i | 0.448420 | + | 0.258896i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.46440e11 | + | 3.69846e11i | −0.673123 | + | 0.718600i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.49498e11 | − | 2.59518e11i | 0.857057 | − | 0.494822i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.21672e10 | −0.174093 | −0.0870463 | − | 0.996204i | \(-0.527743\pi\) | ||||
−0.0870463 | + | 0.996204i | \(0.527743\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.00433e11 | + | 3.46660e11i | −1.11312 | + | 0.642659i | −0.939635 | − | 0.342178i | \(-0.888835\pi\) |
−0.173483 | + | 0.984837i | \(0.555502\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.47173e11 | − | 4.28116e11i | 0.453971 | − | 0.786300i | −0.544658 | − | 0.838659i | \(-0.683340\pi\) |
0.998628 | + | 0.0523580i | \(0.0166737\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.38014e11 | + | 7.96827e10i | 0.248818 | + | 0.143655i | 0.619223 | − | 0.785215i | \(-0.287448\pi\) |
−0.370405 | + | 0.928870i | \(0.620781\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.68502e11 | + | 4.65058e11i | 0.479604 | + | 0.830698i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.00915e11i | − | 0.176961i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.02183e11 | − | 5.23397e11i | −0.525047 | − | 0.909407i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.38161e11 | − | 5.92383e11i | 0.235697 | − | 1.01058i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.49820e11 | − | 9.52316e11i | 0.929441 | − | 1.60984i | 0.145183 | − | 0.989405i | \(-0.453623\pi\) |
0.784258 | − | 0.620435i | \(-0.213044\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 6.13784e11i | − | 1.01885i | −0.860514 | − | 0.509427i | \(-0.829857\pi\) | ||
0.860514 | − | 0.509427i | \(-0.170143\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.78359e11 | 1.60937 | 0.804684 | − | 0.593704i | \(-0.202335\pi\) | ||||
0.804684 | + | 0.593704i | \(0.202335\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.31068e11 | − | 3.64347e11i | −1.01949 | − | 0.588601i | −0.105532 | − | 0.994416i | \(-0.533654\pi\) |
−0.913955 | + | 0.405815i | \(0.866988\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.90448e11 | + | 1.37710e11i | 0.945311 | + | 0.220475i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.27629e10 | − | 4.20097e10i | 0.114421 | − | 0.0660607i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.18119e11 | 0.495789 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.28252e12 | + | 7.40465e11i | −1.96348 | + | 1.13362i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.25790e10 | − | 1.43031e11i | 0.125306 | − | 0.217036i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.68771e10 | − | 2.70645e10i | −0.0698822 | − | 0.0403465i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.43764e11 | + | 2.49006e11i | 0.212432 | + | 0.367943i | 0.952475 | − | 0.304616i | \(-0.0985282\pi\) |
−0.740043 | + | 0.672560i | \(0.765195\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.16133e11i | 1.03973i | 0.854249 | + | 0.519864i | \(0.174017\pi\) | ||||
−0.854249 | + | 0.519864i | \(0.825983\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.71408e10 | − | 6.43298e10i | −0.0534526 | − | 0.0925826i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.50325e11 | − | 7.02840e11i | −1.06114 | − | 0.993983i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.55721e11 | + | 6.16127e11i | −0.498710 | + | 0.863791i | −0.999999 | − | 0.00148915i | \(-0.999526\pi\) |
0.501289 | + | 0.865280i | \(0.332859\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 8.20664e11i | − | 1.13073i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.22377e10 | 0.0576944 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.17850e11 | − | 1.25776e11i | −0.292479 | − | 0.168863i | 0.346580 | − | 0.938020i | \(-0.387343\pi\) |
−0.639059 | + | 0.769157i | \(0.720676\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.92417e11 | − | 3.95739e11i | 0.788550 | − | 0.526756i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.66417e10 | − | 9.60807e9i | 0.0217746 | − | 0.0125716i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.36704e12 | 1.77347 | 0.886735 | − | 0.462278i | \(-0.152968\pi\) | ||||
0.886735 | + | 0.462278i | \(0.152968\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.16618e11 | + | 4.71475e11i | −1.04150 | + | 0.601312i | −0.920259 | − | 0.391311i | \(-0.872022\pi\) |
−0.121244 | + | 0.992623i | \(0.538688\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.33808e11 | − | 4.04967e11i | 0.295673 | − | 0.512121i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.71459e11 | + | 3.87667e11i | 0.834872 | + | 0.482013i | 0.855518 | − | 0.517773i | \(-0.173239\pi\) |
−0.0206461 | + | 0.999787i | \(0.506572\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.69845e11 | − | 6.40590e11i | −0.455990 | − | 0.789797i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.55037e12i | − | 1.87959i | −0.341732 | − | 0.939797i | \(-0.611014\pi\) | ||
0.341732 | − | 0.939797i | \(-0.388986\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.42083e11 | − | 9.38915e11i | −0.651707 | − | 1.12879i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.29053e11 | + | 2.21108e11i | −0.861955 | + | 0.261415i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.32536e11 | + | 4.02764e11i | −0.272644 | + | 0.472234i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 9.52247e11i | − | 1.09810i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.12610e11 | −0.586248 | −0.293124 | − | 0.956074i | \(-0.594695\pi\) | ||||
−0.293124 | + | 0.956074i | \(0.594695\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.00319e10 | + | 1.15654e10i | 0.0225344 | + | 0.0130102i | 0.511225 | − | 0.859447i | \(-0.329192\pi\) |
−0.488691 | + | 0.872457i | \(0.662525\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.54564e12 | + | 3.60490e11i | 1.72448 | + | 0.402200i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.45252e11 | + | 1.99331e11i | −0.378929 | + | 0.218775i | −0.677352 | − | 0.735659i | \(-0.736873\pi\) |
0.298423 | + | 0.954434i | \(0.403539\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.73826e11 | −0.189228 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.29743e10 | + | 5.36787e10i | −0.0995747 | + | 0.0574895i | −0.548960 | − | 0.835848i | \(-0.684976\pi\) |
0.449386 | + | 0.893338i | \(0.351643\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.30297e11 | − | 5.72091e11i | 0.350881 | − | 0.607743i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.58200e12 | + | 9.13366e11i | 1.65356 | + | 0.954684i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.75960e11 | + | 1.51721e12i | 0.908217 | + | 1.57308i | 0.816540 | + | 0.577289i | \(0.195889\pi\) |
0.0916773 | + | 0.995789i | \(0.470777\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 4.81595e11i | − | 0.491349i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.08634e11 | − | 7.07775e11i | −0.413575 | − | 0.716332i | 0.581703 | − | 0.813401i | \(-0.302387\pi\) |
−0.995278 | + | 0.0970689i | \(0.969053\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 252.9.bk.a.233.17 | yes | 44 | |
3.2 | odd | 2 | inner | 252.9.bk.a.233.6 | yes | 44 | |
7.4 | even | 3 | inner | 252.9.bk.a.53.6 | ✓ | 44 | |
21.11 | odd | 6 | inner | 252.9.bk.a.53.17 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.bk.a.53.6 | ✓ | 44 | 7.4 | even | 3 | inner | |
252.9.bk.a.53.17 | yes | 44 | 21.11 | odd | 6 | inner | |
252.9.bk.a.233.6 | yes | 44 | 3.2 | odd | 2 | inner | |
252.9.bk.a.233.17 | yes | 44 | 1.1 | even | 1 | trivial |