Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(1,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 97x^{2} + 7x + 294 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | no (minimal twist has level 21) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-9.22385\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.2239 | 1.80734 | 0.903669 | − | 0.428231i | \(-0.140863\pi\) | ||||
0.903669 | + | 0.428231i | \(0.140863\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 72.5272 | 2.26647 | ||||||||
\(5\) | 23.7528 | 0.424903 | 0.212452 | − | 0.977172i | \(-0.431855\pi\) | ||||
0.212452 | + | 0.977172i | \(0.431855\pi\) | |||||||
\(6\) | 92.0147 | 1.04347 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 414.344 | 2.28895 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 242.845 | 0.767944 | ||||||||
\(11\) | 465.526 | 1.16001 | 0.580006 | − | 0.814612i | \(-0.303050\pi\) | ||||
0.580006 | + | 0.814612i | \(0.303050\pi\) | |||||||
\(12\) | 652.744 | 1.30855 | ||||||||
\(13\) | −1019.30 | −1.67280 | −0.836399 | − | 0.548121i | \(-0.815343\pi\) | ||||
−0.836399 | + | 0.548121i | \(0.815343\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 213.775 | 0.245318 | ||||||||
\(16\) | 1915.32 | 1.87043 | ||||||||
\(17\) | 561.757 | 0.471440 | 0.235720 | − | 0.971821i | \(-0.424255\pi\) | ||||
0.235720 | + | 0.971821i | \(0.424255\pi\) | |||||||
\(18\) | 828.132 | 0.602446 | ||||||||
\(19\) | −1387.58 | −0.881807 | −0.440903 | − | 0.897555i | \(-0.645342\pi\) | ||||
−0.440903 | + | 0.897555i | \(0.645342\pi\) | |||||||
\(20\) | 1722.72 | 0.963032 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4759.47 | 2.09653 | ||||||||
\(23\) | 4113.62 | 1.62145 | 0.810727 | − | 0.585425i | \(-0.199072\pi\) | ||||
0.810727 | + | 0.585425i | \(0.199072\pi\) | |||||||
\(24\) | 3729.09 | 1.32152 | ||||||||
\(25\) | −2560.80 | −0.819457 | ||||||||
\(26\) | −10421.2 | −3.02331 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2381.37 | −0.525814 | −0.262907 | − | 0.964821i | \(-0.584681\pi\) | ||||
−0.262907 | + | 0.964821i | \(0.584681\pi\) | |||||||
\(30\) | 2185.61 | 0.443373 | ||||||||
\(31\) | 2950.66 | 0.551460 | 0.275730 | − | 0.961235i | \(-0.411080\pi\) | ||||
0.275730 | + | 0.961235i | \(0.411080\pi\) | |||||||
\(32\) | 6322.95 | 1.09155 | ||||||||
\(33\) | 4189.73 | 0.669733 | ||||||||
\(34\) | 5743.32 | 0.852051 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5874.70 | 0.755491 | ||||||||
\(37\) | −9908.95 | −1.18994 | −0.594968 | − | 0.803750i | \(-0.702835\pi\) | ||||
−0.594968 | + | 0.803750i | \(0.702835\pi\) | |||||||
\(38\) | −14186.4 | −1.59372 | ||||||||
\(39\) | −9173.70 | −0.965791 | ||||||||
\(40\) | 9841.83 | 0.972581 | ||||||||
\(41\) | −4477.13 | −0.415949 | −0.207974 | − | 0.978134i | \(-0.566687\pi\) | ||||
−0.207974 | + | 0.978134i | \(0.566687\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5181.48 | 0.427349 | 0.213675 | − | 0.976905i | \(-0.431457\pi\) | ||||
0.213675 | + | 0.976905i | \(0.431457\pi\) | |||||||
\(44\) | 33763.3 | 2.62914 | ||||||||
\(45\) | 1923.98 | 0.141634 | ||||||||
\(46\) | 42057.0 | 2.93052 | ||||||||
\(47\) | −3121.59 | −0.206125 | −0.103063 | − | 0.994675i | \(-0.532864\pi\) | ||||
−0.103063 | + | 0.994675i | \(0.532864\pi\) | |||||||
\(48\) | 17237.9 | 1.07989 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −26181.3 | −1.48104 | ||||||||
\(51\) | 5055.81 | 0.272186 | ||||||||
\(52\) | −73926.9 | −3.79135 | ||||||||
\(53\) | 1141.00 | 0.0557950 | 0.0278975 | − | 0.999611i | \(-0.491119\pi\) | ||||
0.0278975 | + | 0.999611i | \(0.491119\pi\) | |||||||
\(54\) | 7453.19 | 0.347823 | ||||||||
\(55\) | 11057.6 | 0.492893 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12488.2 | −0.509111 | ||||||||
\(58\) | −24346.8 | −0.950325 | ||||||||
\(59\) | 27497.1 | 1.02839 | 0.514194 | − | 0.857674i | \(-0.328091\pi\) | ||||
0.514194 | + | 0.857674i | \(0.328091\pi\) | |||||||
\(60\) | 15504.5 | 0.556007 | ||||||||
\(61\) | −21103.5 | −0.726157 | −0.363078 | − | 0.931759i | \(-0.618274\pi\) | ||||
−0.363078 | + | 0.931759i | \(0.618274\pi\) | |||||||
\(62\) | 30167.1 | 0.996676 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3354.67 | 0.102376 | ||||||||
\(65\) | −24211.2 | −0.710778 | ||||||||
\(66\) | 42835.2 | 1.21043 | ||||||||
\(67\) | −55588.4 | −1.51286 | −0.756428 | − | 0.654077i | \(-0.773057\pi\) | ||||
−0.756428 | + | 0.654077i | \(0.773057\pi\) | |||||||
\(68\) | 40742.6 | 1.06851 | ||||||||
\(69\) | 37022.6 | 0.936146 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6076.90 | −0.143066 | −0.0715330 | − | 0.997438i | \(-0.522789\pi\) | ||||
−0.0715330 | + | 0.997438i | \(0.522789\pi\) | |||||||
\(72\) | 33561.8 | 0.762982 | ||||||||
\(73\) | −16779.6 | −0.368532 | −0.184266 | − | 0.982876i | \(-0.558991\pi\) | ||||
−0.184266 | + | 0.982876i | \(0.558991\pi\) | |||||||
\(74\) | −101308. | −2.15062 | ||||||||
\(75\) | −23047.2 | −0.473114 | ||||||||
\(76\) | −100637. | −1.99859 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −93790.5 | −1.74551 | ||||||||
\(79\) | −4845.26 | −0.0873473 | −0.0436737 | − | 0.999046i | \(-0.513906\pi\) | ||||
−0.0436737 | + | 0.999046i | \(0.513906\pi\) | |||||||
\(80\) | 45494.2 | 0.794752 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −45773.5 | −0.751760 | ||||||||
\(83\) | 60145.4 | 0.958313 | 0.479156 | − | 0.877730i | \(-0.340943\pi\) | ||||
0.479156 | + | 0.877730i | \(0.340943\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13343.3 | 0.200316 | ||||||||
\(86\) | 52974.7 | 0.772365 | ||||||||
\(87\) | −21432.4 | −0.303579 | ||||||||
\(88\) | 192888. | 2.65520 | ||||||||
\(89\) | −62497.4 | −0.836348 | −0.418174 | − | 0.908367i | \(-0.637330\pi\) | ||||
−0.418174 | + | 0.908367i | \(0.637330\pi\) | |||||||
\(90\) | 19670.5 | 0.255981 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 298349. | 3.67498 | ||||||||
\(93\) | 26555.9 | 0.318386 | ||||||||
\(94\) | −31914.7 | −0.372539 | ||||||||
\(95\) | −32958.9 | −0.374683 | ||||||||
\(96\) | 56906.5 | 0.630208 | ||||||||
\(97\) | −63653.8 | −0.686903 | −0.343451 | − | 0.939170i | \(-0.611596\pi\) | ||||
−0.343451 | + | 0.939170i | \(0.611596\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 37707.6 | 0.386670 | ||||||||
\(100\) | −185728. | −1.85728 | ||||||||
\(101\) | 184623. | 1.80087 | 0.900434 | − | 0.434993i | \(-0.143249\pi\) | ||||
0.900434 | + | 0.434993i | \(0.143249\pi\) | |||||||
\(102\) | 51689.9 | 0.491932 | ||||||||
\(103\) | 52043.7 | 0.483365 | 0.241683 | − | 0.970355i | \(-0.422301\pi\) | ||||
0.241683 | + | 0.970355i | \(0.422301\pi\) | |||||||
\(104\) | −422341. | −3.82895 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11665.4 | 0.100840 | ||||||||
\(107\) | 48177.8 | 0.406806 | 0.203403 | − | 0.979095i | \(-0.434800\pi\) | ||||
0.203403 | + | 0.979095i | \(0.434800\pi\) | |||||||
\(108\) | 52872.3 | 0.436183 | ||||||||
\(109\) | −36435.6 | −0.293737 | −0.146869 | − | 0.989156i | \(-0.546919\pi\) | ||||
−0.146869 | + | 0.989156i | \(0.546919\pi\) | |||||||
\(110\) | 113051. | 0.890824 | ||||||||
\(111\) | −89180.6 | −0.687010 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −96711.1 | −0.712492 | −0.356246 | − | 0.934392i | \(-0.615944\pi\) | ||||
−0.356246 | + | 0.934392i | \(0.615944\pi\) | |||||||
\(114\) | −127678. | −0.920137 | ||||||||
\(115\) | 97710.0 | 0.688961 | ||||||||
\(116\) | −172714. | −1.19174 | ||||||||
\(117\) | −82563.3 | −0.557599 | ||||||||
\(118\) | 281126. | 1.85864 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 88576.5 | 0.561520 | ||||||||
\(121\) | 55663.5 | 0.345626 | ||||||||
\(122\) | −215759. | −1.31241 | ||||||||
\(123\) | −40294.1 | −0.240148 | ||||||||
\(124\) | 214003. | 1.24987 | ||||||||
\(125\) | −135054. | −0.773093 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 23322.9 | 0.128314 | 0.0641568 | − | 0.997940i | \(-0.479564\pi\) | ||||
0.0641568 | + | 0.997940i | \(0.479564\pi\) | |||||||
\(128\) | −168037. | −0.906524 | ||||||||
\(129\) | 46633.4 | 0.246730 | ||||||||
\(130\) | −247532. | −1.28462 | ||||||||
\(131\) | −338758. | −1.72469 | −0.862345 | − | 0.506321i | \(-0.831005\pi\) | ||||
−0.862345 | + | 0.506321i | \(0.831005\pi\) | |||||||
\(132\) | 303870. | 1.51793 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −568328. | −2.73424 | ||||||||
\(135\) | 17315.8 | 0.0817727 | ||||||||
\(136\) | 232760. | 1.07910 | ||||||||
\(137\) | −62876.7 | −0.286213 | −0.143106 | − | 0.989707i | \(-0.545709\pi\) | ||||
−0.143106 | + | 0.989707i | \(0.545709\pi\) | |||||||
\(138\) | 378513. | 1.69193 | ||||||||
\(139\) | 211927. | 0.930356 | 0.465178 | − | 0.885217i | \(-0.345990\pi\) | ||||
0.465178 | + | 0.885217i | \(0.345990\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −28094.3 | −0.119007 | ||||||||
\(142\) | −62129.4 | −0.258569 | ||||||||
\(143\) | −474511. | −1.94047 | ||||||||
\(144\) | 155141. | 0.623477 | ||||||||
\(145\) | −56564.3 | −0.223420 | ||||||||
\(146\) | −171553. | −0.666062 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −718668. | −2.69696 | ||||||||
\(149\) | 140273. | 0.517616 | 0.258808 | − | 0.965929i | \(-0.416670\pi\) | ||||
0.258808 | + | 0.965929i | \(0.416670\pi\) | |||||||
\(150\) | −235632. | −0.855077 | ||||||||
\(151\) | −163991. | −0.585300 | −0.292650 | − | 0.956220i | \(-0.594537\pi\) | ||||
−0.292650 | + | 0.956220i | \(0.594537\pi\) | |||||||
\(152\) | −574934. | −2.01841 | ||||||||
\(153\) | 45502.3 | 0.157147 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 70086.4 | 0.234317 | ||||||||
\(156\) | −665342. | −2.18894 | ||||||||
\(157\) | 556543. | 1.80198 | 0.900990 | − | 0.433840i | \(-0.142842\pi\) | ||||
0.900990 | + | 0.433840i | \(0.142842\pi\) | |||||||
\(158\) | −49537.2 | −0.157866 | ||||||||
\(159\) | 10269.0 | 0.0322132 | ||||||||
\(160\) | 150188. | 0.463804 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 67078.7 | 0.200815 | ||||||||
\(163\) | −19726.6 | −0.0581546 | −0.0290773 | − | 0.999577i | \(-0.509257\pi\) | ||||
−0.0290773 | + | 0.999577i | \(0.509257\pi\) | |||||||
\(164\) | −324713. | −0.942736 | ||||||||
\(165\) | 99518.0 | 0.284572 | ||||||||
\(166\) | 614918. | 1.73200 | ||||||||
\(167\) | 94776.2 | 0.262971 | 0.131486 | − | 0.991318i | \(-0.458025\pi\) | ||||
0.131486 | + | 0.991318i | \(0.458025\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 667679. | 1.79825 | ||||||||
\(170\) | 136420. | 0.362039 | ||||||||
\(171\) | −112394. | −0.293936 | ||||||||
\(172\) | 375798. | 0.968576 | ||||||||
\(173\) | 338841. | 0.860757 | 0.430379 | − | 0.902649i | \(-0.358380\pi\) | ||||
0.430379 | + | 0.902649i | \(0.358380\pi\) | |||||||
\(174\) | −219121. | −0.548670 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 891631. | 2.16972 | ||||||||
\(177\) | 247474. | 0.593740 | ||||||||
\(178\) | −638965. | −1.51156 | ||||||||
\(179\) | 776193. | 1.81066 | 0.905330 | − | 0.424708i | \(-0.139623\pi\) | ||||
0.905330 | + | 0.424708i | \(0.139623\pi\) | |||||||
\(180\) | 139541. | 0.321011 | ||||||||
\(181\) | −132697. | −0.301067 | −0.150534 | − | 0.988605i | \(-0.548099\pi\) | ||||
−0.150534 | + | 0.988605i | \(0.548099\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −189932. | −0.419247 | ||||||||
\(184\) | 1.70445e6 | 3.71142 | ||||||||
\(185\) | −235366. | −0.505607 | ||||||||
\(186\) | 271504. | 0.575431 | ||||||||
\(187\) | 261512. | 0.546875 | ||||||||
\(188\) | −226400. | −0.467178 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −336967. | −0.677178 | ||||||||
\(191\) | 6637.41 | 0.0131648 | 0.00658242 | − | 0.999978i | \(-0.497905\pi\) | ||||
0.00658242 | + | 0.999978i | \(0.497905\pi\) | |||||||
\(192\) | 30192.0 | 0.0591070 | ||||||||
\(193\) | 452590. | 0.874604 | 0.437302 | − | 0.899315i | \(-0.355934\pi\) | ||||
0.437302 | + | 0.899315i | \(0.355934\pi\) | |||||||
\(194\) | −650787. | −1.24147 | ||||||||
\(195\) | −217901. | −0.410368 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 816952. | 1.49979 | 0.749896 | − | 0.661556i | \(-0.230104\pi\) | ||||
0.749896 | + | 0.661556i | \(0.230104\pi\) | |||||||
\(198\) | 385517. | 0.698845 | ||||||||
\(199\) | 806417. | 1.44353 | 0.721767 | − | 0.692136i | \(-0.243330\pi\) | ||||
0.721767 | + | 0.692136i | \(0.243330\pi\) | |||||||
\(200\) | −1.06105e6 | −1.87569 | ||||||||
\(201\) | −500296. | −0.873447 | ||||||||
\(202\) | 1.88756e6 | 3.25478 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 366684. | 0.616902 | ||||||||
\(205\) | −106344. | −0.176738 | ||||||||
\(206\) | 532087. | 0.873605 | ||||||||
\(207\) | 333203. | 0.540484 | ||||||||
\(208\) | −1.95229e6 | −3.12885 | ||||||||
\(209\) | −645954. | −1.02291 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 68773.9 | 0.106345 | 0.0531726 | − | 0.998585i | \(-0.483067\pi\) | ||||
0.0531726 | + | 0.998585i | \(0.483067\pi\) | |||||||
\(212\) | 82753.3 | 0.126458 | ||||||||
\(213\) | −54692.1 | −0.0825992 | ||||||||
\(214\) | 492563. | 0.735237 | ||||||||
\(215\) | 123075. | 0.181582 | ||||||||
\(216\) | 302057. | 0.440508 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −372512. | −0.530883 | ||||||||
\(219\) | −151017. | −0.212772 | ||||||||
\(220\) | 801973. | 1.11713 | ||||||||
\(221\) | −572599. | −0.788623 | ||||||||
\(222\) | −911769. | −1.24166 | ||||||||
\(223\) | −620227. | −0.835196 | −0.417598 | − | 0.908632i | \(-0.637128\pi\) | ||||
−0.417598 | + | 0.908632i | \(0.637128\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −207425. | −0.273152 | ||||||||
\(226\) | −988760. | −1.28771 | ||||||||
\(227\) | 1.00223e6 | 1.29093 | 0.645467 | − | 0.763788i | \(-0.276663\pi\) | ||||
0.645467 | + | 0.763788i | \(0.276663\pi\) | |||||||
\(228\) | −905734. | −1.15389 | ||||||||
\(229\) | 885861. | 1.11629 | 0.558145 | − | 0.829743i | \(-0.311513\pi\) | ||||
0.558145 | + | 0.829743i | \(0.311513\pi\) | |||||||
\(230\) | 998973. | 1.24519 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −986707. | −1.20356 | ||||||||
\(233\) | 596163. | 0.719408 | 0.359704 | − | 0.933066i | \(-0.382878\pi\) | ||||
0.359704 | + | 0.933066i | \(0.382878\pi\) | |||||||
\(234\) | −844115. | −1.00777 | ||||||||
\(235\) | −74146.6 | −0.0875834 | ||||||||
\(236\) | 1.99429e6 | 2.33081 | ||||||||
\(237\) | −43607.4 | −0.0504300 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 743111. | 0.841509 | 0.420754 | − | 0.907175i | \(-0.361765\pi\) | ||||
0.420754 | + | 0.907175i | \(0.361765\pi\) | |||||||
\(240\) | 409448. | 0.458850 | ||||||||
\(241\) | −1.17484e6 | −1.30297 | −0.651487 | − | 0.758660i | \(-0.725854\pi\) | ||||
−0.651487 | + | 0.758660i | \(0.725854\pi\) | |||||||
\(242\) | 569095. | 0.624664 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −1.53058e6 | −1.64582 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −411961. | −0.434029 | ||||||||
\(247\) | 1.41436e6 | 1.47508 | ||||||||
\(248\) | 1.22259e6 | 1.26226 | ||||||||
\(249\) | 541309. | 0.553282 | ||||||||
\(250\) | −1.38077e6 | −1.39724 | ||||||||
\(251\) | 352992. | 0.353655 | 0.176828 | − | 0.984242i | \(-0.443416\pi\) | ||||
0.176828 | + | 0.984242i | \(0.443416\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.91500e6 | 1.88090 | ||||||||
\(254\) | 238450. | 0.231906 | ||||||||
\(255\) | 120090. | 0.115653 | ||||||||
\(256\) | −1.82533e6 | −1.74077 | ||||||||
\(257\) | 10012.7 | 0.00945621 | 0.00472811 | − | 0.999989i | \(-0.498495\pi\) | ||||
0.00472811 | + | 0.999989i | \(0.498495\pi\) | |||||||
\(258\) | 476773. | 0.445925 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.75597e6 | −1.61096 | ||||||||
\(261\) | −192891. | −0.175271 | ||||||||
\(262\) | −3.46341e6 | −3.11710 | ||||||||
\(263\) | 1.68180e6 | 1.49929 | 0.749644 | − | 0.661841i | \(-0.230225\pi\) | ||||
0.749644 | + | 0.661841i | \(0.230225\pi\) | |||||||
\(264\) | 1.73599e6 | 1.53298 | ||||||||
\(265\) | 27101.9 | 0.0237075 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −562477. | −0.482866 | ||||||||
\(268\) | −4.03167e6 | −3.42885 | ||||||||
\(269\) | −1.91717e6 | −1.61540 | −0.807702 | − | 0.589591i | \(-0.799289\pi\) | ||||
−0.807702 | + | 0.589591i | \(0.799289\pi\) | |||||||
\(270\) | 177034. | 0.147791 | ||||||||
\(271\) | 2.29000e6 | 1.89414 | 0.947069 | − | 0.321029i | \(-0.104029\pi\) | ||||
0.947069 | + | 0.321029i | \(0.104029\pi\) | |||||||
\(272\) | 1.07594e6 | 0.881795 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −642843. | −0.517283 | ||||||||
\(275\) | −1.19212e6 | −0.950580 | ||||||||
\(276\) | 2.68514e6 | 2.12175 | ||||||||
\(277\) | −394802. | −0.309157 | −0.154579 | − | 0.987980i | \(-0.549402\pi\) | ||||
−0.154579 | + | 0.987980i | \(0.549402\pi\) | |||||||
\(278\) | 2.16671e6 | 1.68147 | ||||||||
\(279\) | 239003. | 0.183820 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.77699e6 | −1.34252 | −0.671259 | − | 0.741223i | \(-0.734246\pi\) | ||||
−0.671259 | + | 0.741223i | \(0.734246\pi\) | |||||||
\(282\) | −287232. | −0.215085 | ||||||||
\(283\) | 1.21524e6 | 0.901981 | 0.450991 | − | 0.892529i | \(-0.351071\pi\) | ||||
0.450991 | + | 0.892529i | \(0.351071\pi\) | |||||||
\(284\) | −440741. | −0.324255 | ||||||||
\(285\) | −296630. | −0.216323 | ||||||||
\(286\) | −4.85133e6 | −3.50708 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 512159. | 0.363851 | ||||||||
\(289\) | −1.10429e6 | −0.777745 | ||||||||
\(290\) | −578305. | −0.403796 | ||||||||
\(291\) | −572884. | −0.396583 | ||||||||
\(292\) | −1.21698e6 | −0.835268 | ||||||||
\(293\) | −1.48897e6 | −1.01325 | −0.506627 | − | 0.862165i | \(-0.669108\pi\) | ||||
−0.506627 | + | 0.862165i | \(0.669108\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 653133. | 0.436965 | ||||||||
\(296\) | −4.10571e6 | −2.72370 | ||||||||
\(297\) | 339368. | 0.223244 | ||||||||
\(298\) | 1.43413e6 | 0.935508 | ||||||||
\(299\) | −4.19301e6 | −2.71236 | ||||||||
\(300\) | −1.67155e6 | −1.07230 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.67662e6 | −1.05784 | ||||||||
\(303\) | 1.66161e6 | 1.03973 | ||||||||
\(304\) | −2.65766e6 | −1.64936 | ||||||||
\(305\) | −501268. | −0.308546 | ||||||||
\(306\) | 465209. | 0.284017 | ||||||||
\(307\) | 2.03109e6 | 1.22994 | 0.614968 | − | 0.788552i | \(-0.289169\pi\) | ||||
0.614968 | + | 0.788552i | \(0.289169\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 468394. | 0.279071 | ||||||||
\(310\) | 716553. | 0.423491 | ||||||||
\(311\) | 289785. | 0.169893 | 0.0849463 | − | 0.996386i | \(-0.472928\pi\) | ||||
0.0849463 | + | 0.996386i | \(0.472928\pi\) | |||||||
\(312\) | −3.80106e6 | −2.21064 | ||||||||
\(313\) | 218211. | 0.125897 | 0.0629484 | − | 0.998017i | \(-0.479950\pi\) | ||||
0.0629484 | + | 0.998017i | \(0.479950\pi\) | |||||||
\(314\) | 5.69002e6 | 3.25679 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −351413. | −0.197970 | ||||||||
\(317\) | 1.29063e6 | 0.721363 | 0.360681 | − | 0.932689i | \(-0.382544\pi\) | ||||
0.360681 | + | 0.932689i | \(0.382544\pi\) | |||||||
\(318\) | 104988. | 0.0582202 | ||||||||
\(319\) | −1.10859e6 | −0.609951 | ||||||||
\(320\) | 79682.8 | 0.0435000 | ||||||||
\(321\) | 433600. | 0.234870 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −779481. | −0.415719 | ||||||||
\(324\) | 475851. | 0.251830 | ||||||||
\(325\) | 2.61023e6 | 1.37079 | ||||||||
\(326\) | −201682. | −0.105105 | ||||||||
\(327\) | −327920. | −0.169589 | ||||||||
\(328\) | −1.85507e6 | −0.952084 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.01746e6 | 0.514318 | ||||||||
\(331\) | −3.48561e6 | −1.74867 | −0.874336 | − | 0.485321i | \(-0.838703\pi\) | ||||
−0.874336 | + | 0.485321i | \(0.838703\pi\) | |||||||
\(332\) | 4.36218e6 | 2.17199 | ||||||||
\(333\) | −802625. | −0.396645 | ||||||||
\(334\) | 968978. | 0.475278 | ||||||||
\(335\) | −1.32038e6 | −0.642817 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 249198. | 0.119528 | 0.0597641 | − | 0.998213i | \(-0.480965\pi\) | ||||
0.0597641 | + | 0.998213i | \(0.480965\pi\) | |||||||
\(338\) | 6.82625e6 | 3.25005 | ||||||||
\(339\) | −870400. | −0.411358 | ||||||||
\(340\) | 967752. | 0.454012 | ||||||||
\(341\) | 1.37361e6 | 0.639700 | ||||||||
\(342\) | −1.14910e6 | −0.531241 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.14692e6 | 0.978180 | ||||||||
\(345\) | 879390. | 0.397772 | ||||||||
\(346\) | 3.46426e6 | 1.55568 | ||||||||
\(347\) | −1.50601e6 | −0.671437 | −0.335719 | − | 0.941962i | \(-0.608979\pi\) | ||||
−0.335719 | + | 0.941962i | \(0.608979\pi\) | |||||||
\(348\) | −1.55443e6 | −0.688054 | ||||||||
\(349\) | 1.54370e6 | 0.678423 | 0.339212 | − | 0.940710i | \(-0.389840\pi\) | ||||
0.339212 | + | 0.940710i | \(0.389840\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −743070. | −0.321930 | ||||||||
\(352\) | 2.94350e6 | 1.26621 | ||||||||
\(353\) | −1.67796e6 | −0.716710 | −0.358355 | − | 0.933585i | \(-0.616662\pi\) | ||||
−0.358355 | + | 0.933585i | \(0.616662\pi\) | |||||||
\(354\) | 2.53014e6 | 1.07309 | ||||||||
\(355\) | −144344. | −0.0607892 | ||||||||
\(356\) | −4.53276e6 | −1.89556 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.93568e6 | 3.27248 | ||||||||
\(359\) | −2.49973e6 | −1.02366 | −0.511832 | − | 0.859086i | \(-0.671033\pi\) | ||||
−0.511832 | + | 0.859086i | \(0.671033\pi\) | |||||||
\(360\) | 797188. | 0.324194 | ||||||||
\(361\) | −550727. | −0.222417 | ||||||||
\(362\) | −1.35667e6 | −0.544130 | ||||||||
\(363\) | 500971. | 0.199547 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −398564. | −0.156591 | ||||||||
\(366\) | −1.94183e6 | −0.757721 | ||||||||
\(367\) | −2.10741e6 | −0.816740 | −0.408370 | − | 0.912816i | \(-0.633903\pi\) | ||||
−0.408370 | + | 0.912816i | \(0.633903\pi\) | |||||||
\(368\) | 7.87890e6 | 3.03281 | ||||||||
\(369\) | −362647. | −0.138650 | ||||||||
\(370\) | −2.40634e6 | −0.913804 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.92602e6 | 0.721613 | ||||||||
\(373\) | 2.73225e6 | 1.01683 | 0.508414 | − | 0.861113i | \(-0.330232\pi\) | ||||
0.508414 | + | 0.861113i | \(0.330232\pi\) | |||||||
\(374\) | 2.67366e6 | 0.988389 | ||||||||
\(375\) | −1.21548e6 | −0.446346 | ||||||||
\(376\) | −1.29341e6 | −0.471810 | ||||||||
\(377\) | 2.42733e6 | 0.879581 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.04295e6 | −0.730567 | −0.365283 | − | 0.930896i | \(-0.619028\pi\) | ||||
−0.365283 | + | 0.930896i | \(0.619028\pi\) | |||||||
\(380\) | −2.39041e6 | −0.849208 | ||||||||
\(381\) | 209906. | 0.0740819 | ||||||||
\(382\) | 67859.9 | 0.0237933 | ||||||||
\(383\) | 1.50899e6 | 0.525643 | 0.262821 | − | 0.964845i | \(-0.415347\pi\) | ||||
0.262821 | + | 0.964845i | \(0.415347\pi\) | |||||||
\(384\) | −1.51233e6 | −0.523382 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.62721e6 | 1.58071 | ||||||||
\(387\) | 419700. | 0.142450 | ||||||||
\(388\) | −4.61663e6 | −1.55685 | ||||||||
\(389\) | 4.50065e6 | 1.50800 | 0.754000 | − | 0.656874i | \(-0.228122\pi\) | ||||
0.754000 | + | 0.656874i | \(0.228122\pi\) | |||||||
\(390\) | −2.22779e6 | −0.741673 | ||||||||
\(391\) | 2.31085e6 | 0.764417 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.04882e6 | −0.995751 | ||||||||
\(394\) | 8.35240e6 | 2.71063 | ||||||||
\(395\) | −115089. | −0.0371142 | ||||||||
\(396\) | 2.73483e6 | 0.876378 | ||||||||
\(397\) | −3.52136e6 | −1.12133 | −0.560665 | − | 0.828042i | \(-0.689455\pi\) | ||||
−0.560665 | + | 0.828042i | \(0.689455\pi\) | |||||||
\(398\) | 8.24469e6 | 2.60895 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.90476e6 | −1.53274 | ||||||||
\(401\) | −907107. | −0.281707 | −0.140853 | − | 0.990030i | \(-0.544985\pi\) | ||||
−0.140853 | + | 0.990030i | \(0.544985\pi\) | |||||||
\(402\) | −5.11495e6 | −1.57862 | ||||||||
\(403\) | −3.00760e6 | −0.922482 | ||||||||
\(404\) | 1.33902e7 | 4.08162 | ||||||||
\(405\) | 155842. | 0.0472115 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.61287e6 | −1.38034 | ||||||||
\(408\) | 2.09484e6 | 0.623019 | ||||||||
\(409\) | 4.31853e6 | 1.27652 | 0.638260 | − | 0.769821i | \(-0.279654\pi\) | ||||
0.638260 | + | 0.769821i | \(0.279654\pi\) | |||||||
\(410\) | −1.08725e6 | −0.319425 | ||||||||
\(411\) | −565891. | −0.165245 | ||||||||
\(412\) | 3.77458e6 | 1.09553 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.40662e6 | 0.976838 | ||||||||
\(415\) | 1.42862e6 | 0.407190 | ||||||||
\(416\) | −6.44498e6 | −1.82595 | ||||||||
\(417\) | 1.90734e6 | 0.537141 | ||||||||
\(418\) | −6.60413e6 | −1.84874 | ||||||||
\(419\) | −1.52041e6 | −0.423083 | −0.211541 | − | 0.977369i | \(-0.567848\pi\) | ||||
−0.211541 | + | 0.977369i | \(0.567848\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.42050e6 | −1.21553 | −0.607766 | − | 0.794116i | \(-0.707934\pi\) | ||||
−0.607766 | + | 0.794116i | \(0.707934\pi\) | |||||||
\(422\) | 703134. | 0.192202 | ||||||||
\(423\) | −252849. | −0.0687085 | ||||||||
\(424\) | 472765. | 0.127712 | ||||||||
\(425\) | −1.43855e6 | −0.386325 | ||||||||
\(426\) | −559164. | −0.149285 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.49420e6 | 0.922016 | ||||||||
\(429\) | −4.27060e6 | −1.12033 | ||||||||
\(430\) | 1.25830e6 | 0.328180 | ||||||||
\(431\) | −6.84785e6 | −1.77567 | −0.887833 | − | 0.460166i | \(-0.847790\pi\) | ||||
−0.887833 | + | 0.460166i | \(0.847790\pi\) | |||||||
\(432\) | 1.39627e6 | 0.359964 | ||||||||
\(433\) | −3.99328e6 | −1.02355 | −0.511777 | − | 0.859119i | \(-0.671012\pi\) | ||||
−0.511777 | + | 0.859119i | \(0.671012\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −509079. | −0.128992 | ||||||||
\(436\) | −2.64257e6 | −0.665748 | ||||||||
\(437\) | −5.70797e6 | −1.42981 | ||||||||
\(438\) | −1.54397e6 | −0.384551 | ||||||||
\(439\) | 1.48557e6 | 0.367901 | 0.183950 | − | 0.982936i | \(-0.441111\pi\) | ||||
0.183950 | + | 0.982936i | \(0.441111\pi\) | |||||||
\(440\) | 4.58163e6 | 1.12821 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.85416e6 | −1.42531 | ||||||||
\(443\) | −5.62193e6 | −1.36106 | −0.680528 | − | 0.732722i | \(-0.738250\pi\) | ||||
−0.680528 | + | 0.732722i | \(0.738250\pi\) | |||||||
\(444\) | −6.46801e6 | −1.55709 | ||||||||
\(445\) | −1.48449e6 | −0.355367 | ||||||||
\(446\) | −6.34111e6 | −1.50948 | ||||||||
\(447\) | 1.26246e6 | 0.298846 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.94883e6 | 0.456202 | 0.228101 | − | 0.973637i | \(-0.426748\pi\) | ||||
0.228101 | + | 0.973637i | \(0.426748\pi\) | |||||||
\(450\) | −2.12068e6 | −0.493679 | ||||||||
\(451\) | −2.08422e6 | −0.482505 | ||||||||
\(452\) | −7.01418e6 | −1.61484 | ||||||||
\(453\) | −1.47592e6 | −0.337923 | ||||||||
\(454\) | 1.02467e7 | 2.33315 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.17441e6 | −1.16533 | ||||||||
\(457\) | −2.67312e6 | −0.598726 | −0.299363 | − | 0.954139i | \(-0.596774\pi\) | ||||
−0.299363 | + | 0.954139i | \(0.596774\pi\) | |||||||
\(458\) | 9.05691e6 | 2.01751 | ||||||||
\(459\) | 409521. | 0.0907286 | ||||||||
\(460\) | 7.08663e6 | 1.56151 | ||||||||
\(461\) | −4.65262e6 | −1.01964 | −0.509819 | − | 0.860282i | \(-0.670287\pi\) | ||||
−0.509819 | + | 0.860282i | \(0.670287\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.18586e6 | −1.12426 | −0.562132 | − | 0.827047i | \(-0.690019\pi\) | ||||
−0.562132 | + | 0.827047i | \(0.690019\pi\) | |||||||
\(464\) | −4.56109e6 | −0.983499 | ||||||||
\(465\) | 630777. | 0.135283 | ||||||||
\(466\) | 6.09509e6 | 1.30021 | ||||||||
\(467\) | −5.05980e6 | −1.07360 | −0.536799 | − | 0.843710i | \(-0.680367\pi\) | ||||
−0.536799 | + | 0.843710i | \(0.680367\pi\) | |||||||
\(468\) | −5.98808e6 | −1.26378 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −758064. | −0.158293 | ||||||||
\(471\) | 5.00889e6 | 1.04037 | ||||||||
\(472\) | 1.13932e7 | 2.35392 | ||||||||
\(473\) | 2.41212e6 | 0.495730 | ||||||||
\(474\) | −445835. | −0.0911441 | ||||||||
\(475\) | 3.55331e6 | 0.722603 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 92420.8 | 0.0185983 | ||||||||
\(478\) | 7.59745e6 | 1.52089 | ||||||||
\(479\) | −5.55085e6 | −1.10540 | −0.552702 | − | 0.833379i | \(-0.686403\pi\) | ||||
−0.552702 | + | 0.833379i | \(0.686403\pi\) | |||||||
\(480\) | 1.35169e6 | 0.267778 | ||||||||
\(481\) | 1.01002e7 | 1.99052 | ||||||||
\(482\) | −1.20114e7 | −2.35491 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.03711e6 | 0.783353 | ||||||||
\(485\) | −1.51196e6 | −0.291867 | ||||||||
\(486\) | 603708. | 0.115941 | ||||||||
\(487\) | −6.87810e6 | −1.31415 | −0.657077 | − | 0.753824i | \(-0.728207\pi\) | ||||
−0.657077 | + | 0.753824i | \(0.728207\pi\) | |||||||
\(488\) | −8.74411e6 | −1.66213 | ||||||||
\(489\) | −177540. | −0.0335756 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.44459e6 | 1.39360 | 0.696798 | − | 0.717267i | \(-0.254607\pi\) | ||||
0.696798 | + | 0.717267i | \(0.254607\pi\) | |||||||
\(492\) | −2.92242e6 | −0.544289 | ||||||||
\(493\) | −1.33775e6 | −0.247890 | ||||||||
\(494\) | 1.44602e7 | 2.66598 | ||||||||
\(495\) | 895662. | 0.164298 | ||||||||
\(496\) | 5.65145e6 | 1.03147 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.53426e6 | 0.999968 | ||||||||
\(499\) | 2.15329e6 | 0.387126 | 0.193563 | − | 0.981088i | \(-0.437996\pi\) | ||||
0.193563 | + | 0.981088i | \(0.437996\pi\) | |||||||
\(500\) | −9.79507e6 | −1.75220 | ||||||||
\(501\) | 852986. | 0.151826 | ||||||||
\(502\) | 3.60894e6 | 0.639175 | ||||||||
\(503\) | 8.61012e6 | 1.51736 | 0.758681 | − | 0.651463i | \(-0.225844\pi\) | ||||
0.758681 | + | 0.651463i | \(0.225844\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.38531e6 | 0.765195 | ||||||||
\(506\) | 1.95786e7 | 3.39943 | ||||||||
\(507\) | 6.00911e6 | 1.03822 | ||||||||
\(508\) | 1.69154e6 | 0.290820 | ||||||||
\(509\) | 3.34201e6 | 0.571759 | 0.285879 | − | 0.958266i | \(-0.407714\pi\) | ||||
0.285879 | + | 0.958266i | \(0.407714\pi\) | |||||||
\(510\) | 1.22778e6 | 0.209024 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.32848e7 | −2.23964 | ||||||||
\(513\) | −1.01154e6 | −0.169704 | ||||||||
\(514\) | 102368. | 0.0170906 | ||||||||
\(515\) | 1.23619e6 | 0.205383 | ||||||||
\(516\) | 3.38219e6 | 0.559208 | ||||||||
\(517\) | −1.45318e6 | −0.239108 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.04957e6 | 0.496958 | ||||||||
\(520\) | −1.00318e7 | −1.62693 | ||||||||
\(521\) | −2.68305e6 | −0.433046 | −0.216523 | − | 0.976278i | \(-0.569472\pi\) | ||||
−0.216523 | + | 0.976278i | \(0.569472\pi\) | |||||||
\(522\) | −1.97209e6 | −0.316775 | ||||||||
\(523\) | −5.42355e6 | −0.867021 | −0.433511 | − | 0.901148i | \(-0.642725\pi\) | ||||
−0.433511 | + | 0.901148i | \(0.642725\pi\) | |||||||
\(524\) | −2.45692e7 | −3.90897 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.71945e7 | 2.70972 | ||||||||
\(527\) | 1.65755e6 | 0.259980 | ||||||||
\(528\) | 8.02468e6 | 1.25269 | ||||||||
\(529\) | 1.04855e7 | 1.62911 | ||||||||
\(530\) | 277086. | 0.0428474 | ||||||||
\(531\) | 2.22726e6 | 0.342796 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.56353e6 | 0.695798 | ||||||||
\(534\) | −5.75068e6 | −0.872702 | ||||||||
\(535\) | 1.14436e6 | 0.172853 | ||||||||
\(536\) | −2.30327e7 | −3.46285 | ||||||||
\(537\) | 6.98574e6 | 1.04539 | ||||||||
\(538\) | −1.96009e7 | −2.91958 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.25587e6 | 0.185336 | ||||||||
\(541\) | 2.18456e6 | 0.320900 | 0.160450 | − | 0.987044i | \(-0.448705\pi\) | ||||
0.160450 | + | 0.987044i | \(0.448705\pi\) | |||||||
\(542\) | 2.34126e7 | 3.42335 | ||||||||
\(543\) | −1.19427e6 | −0.173821 | ||||||||
\(544\) | 3.55196e6 | 0.514601 | ||||||||
\(545\) | −865447. | −0.124810 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −691437. | −0.0988062 | −0.0494031 | − | 0.998779i | \(-0.515732\pi\) | ||||
−0.0494031 | + | 0.998779i | \(0.515732\pi\) | |||||||
\(548\) | −4.56027e6 | −0.648693 | ||||||||
\(549\) | −1.70939e6 | −0.242052 | ||||||||
\(550\) | −1.21881e7 | −1.71802 | ||||||||
\(551\) | 3.30434e6 | 0.463667 | ||||||||
\(552\) | 1.53401e7 | 2.14279 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.03639e6 | −0.558752 | ||||||||
\(555\) | −2.11829e6 | −0.291913 | ||||||||
\(556\) | 1.53705e7 | 2.10863 | ||||||||
\(557\) | 5.47656e6 | 0.747946 | 0.373973 | − | 0.927440i | \(-0.377995\pi\) | ||||
0.373973 | + | 0.927440i | \(0.377995\pi\) | |||||||
\(558\) | 2.44353e6 | 0.332225 | ||||||||
\(559\) | −5.28149e6 | −0.714869 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.35361e6 | 0.315739 | ||||||||
\(562\) | −1.81677e7 | −2.42638 | ||||||||
\(563\) | 398976. | 0.0530488 | 0.0265244 | − | 0.999648i | \(-0.491556\pi\) | ||||
0.0265244 | + | 0.999648i | \(0.491556\pi\) | |||||||
\(564\) | −2.03760e6 | −0.269725 | ||||||||
\(565\) | −2.29716e6 | −0.302740 | ||||||||
\(566\) | 1.24245e7 | 1.63019 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.51793e6 | −0.327471 | ||||||||
\(569\) | −4.23113e6 | −0.547868 | −0.273934 | − | 0.961749i | \(-0.588325\pi\) | ||||
−0.273934 | + | 0.961749i | \(0.588325\pi\) | |||||||
\(570\) | −3.03270e6 | −0.390969 | ||||||||
\(571\) | 8.75102e6 | 1.12323 | 0.561615 | − | 0.827399i | \(-0.310180\pi\) | ||||
0.561615 | + | 0.827399i | \(0.310180\pi\) | |||||||
\(572\) | −3.44149e7 | −4.39801 | ||||||||
\(573\) | 59736.7 | 0.00760072 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.05342e7 | −1.32871 | ||||||||
\(576\) | 271728. | 0.0341254 | ||||||||
\(577\) | −1.76712e6 | −0.220966 | −0.110483 | − | 0.993878i | \(-0.535240\pi\) | ||||
−0.110483 | + | 0.993878i | \(0.535240\pi\) | |||||||
\(578\) | −1.12901e7 | −1.40565 | ||||||||
\(579\) | 4.07331e6 | 0.504953 | ||||||||
\(580\) | −4.10245e6 | −0.506376 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5.85709e6 | −0.716761 | ||||||||
\(583\) | 531164. | 0.0647228 | ||||||||
\(584\) | −6.95254e6 | −0.843551 | ||||||||
\(585\) | −1.96111e6 | −0.236926 | ||||||||
\(586\) | −1.52231e7 | −1.83129 | ||||||||
\(587\) | −8.65009e6 | −1.03616 | −0.518078 | − | 0.855333i | \(-0.673352\pi\) | ||||
−0.518078 | + | 0.855333i | \(0.673352\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.09426e6 | −0.486281 | ||||||||
\(590\) | 6.67754e6 | 0.789744 | ||||||||
\(591\) | 7.35257e6 | 0.865905 | ||||||||
\(592\) | −1.89788e7 | −2.22569 | ||||||||
\(593\) | 1.54514e7 | 1.80439 | 0.902194 | − | 0.431329i | \(-0.141955\pi\) | ||||
0.902194 | + | 0.431329i | \(0.141955\pi\) | |||||||
\(594\) | 3.46965e6 | 0.403478 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.01736e7 | 1.17316 | ||||||||
\(597\) | 7.25775e6 | 0.833425 | ||||||||
\(598\) | −4.28687e7 | −4.90216 | ||||||||
\(599\) | −3.84801e6 | −0.438196 | −0.219098 | − | 0.975703i | \(-0.570312\pi\) | ||||
−0.219098 | + | 0.975703i | \(0.570312\pi\) | |||||||
\(600\) | −9.54948e6 | −1.08293 | ||||||||
\(601\) | 1.27578e7 | 1.44075 | 0.720376 | − | 0.693583i | \(-0.243969\pi\) | ||||
0.720376 | + | 0.693583i | \(0.243969\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.50266e6 | −0.504285 | ||||||||
\(604\) | −1.18938e7 | −1.32657 | ||||||||
\(605\) | 1.32216e6 | 0.146858 | ||||||||
\(606\) | 1.69880e7 | 1.87915 | ||||||||
\(607\) | −1.36207e7 | −1.50047 | −0.750233 | − | 0.661173i | \(-0.770059\pi\) | ||||
−0.750233 | + | 0.661173i | \(0.770059\pi\) | |||||||
\(608\) | −8.77359e6 | −0.962539 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.12489e6 | −0.557648 | ||||||||
\(611\) | 3.18184e6 | 0.344806 | ||||||||
\(612\) | 3.30015e6 | 0.356168 | ||||||||
\(613\) | 1.53474e7 | 1.64962 | 0.824812 | − | 0.565407i | \(-0.191281\pi\) | ||||
0.824812 | + | 0.565407i | \(0.191281\pi\) | |||||||
\(614\) | 2.07655e7 | 2.22291 | ||||||||
\(615\) | −957099. | −0.102040 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.18485e7 | 1.25300 | 0.626500 | − | 0.779421i | \(-0.284487\pi\) | ||||
0.626500 | + | 0.779421i | \(0.284487\pi\) | |||||||
\(618\) | 4.78879e6 | 0.504376 | ||||||||
\(619\) | −874460. | −0.0917304 | −0.0458652 | − | 0.998948i | \(-0.514604\pi\) | ||||
−0.0458652 | + | 0.998948i | \(0.514604\pi\) | |||||||
\(620\) | 5.08317e6 | 0.531074 | ||||||||
\(621\) | 2.99883e6 | 0.312049 | ||||||||
\(622\) | 2.96272e6 | 0.307054 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.75706e7 | −1.80644 | ||||||||
\(625\) | 4.79460e6 | 0.490967 | ||||||||
\(626\) | 2.23095e6 | 0.227538 | ||||||||
\(627\) | −5.81358e6 | −0.590575 | ||||||||
\(628\) | 4.03645e7 | 4.08414 | ||||||||
\(629\) | −5.56642e6 | −0.560983 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.43859e6 | −0.443784 | −0.221892 | − | 0.975071i | \(-0.571223\pi\) | ||||
−0.221892 | + | 0.975071i | \(0.571223\pi\) | |||||||
\(632\) | −2.00760e6 | −0.199933 | ||||||||
\(633\) | 618965. | 0.0613984 | ||||||||
\(634\) | 1.31952e7 | 1.30375 | ||||||||
\(635\) | 553984. | 0.0545209 | ||||||||
\(636\) | 744780. | 0.0730104 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.13341e7 | −1.10239 | ||||||||
\(639\) | −492229. | −0.0476887 | ||||||||
\(640\) | −3.99135e6 | −0.385185 | ||||||||
\(641\) | 812551. | 0.0781098 | 0.0390549 | − | 0.999237i | \(-0.487565\pi\) | ||||
0.0390549 | + | 0.999237i | \(0.487565\pi\) | |||||||
\(642\) | 4.43306e6 | 0.424489 | ||||||||
\(643\) | −1.17941e7 | −1.12496 | −0.562481 | − | 0.826810i | \(-0.690153\pi\) | ||||
−0.562481 | + | 0.826810i | \(0.690153\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.10767e6 | 0.104837 | ||||||||
\(646\) | −7.96930e6 | −0.751344 | ||||||||
\(647\) | −2.43380e6 | −0.228573 | −0.114286 | − | 0.993448i | \(-0.536458\pi\) | ||||
−0.114286 | + | 0.993448i | \(0.536458\pi\) | |||||||
\(648\) | 2.71851e6 | 0.254327 | ||||||||
\(649\) | 1.28006e7 | 1.19294 | ||||||||
\(650\) | 2.66866e7 | 2.47748 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.43072e6 | −0.131806 | ||||||||
\(653\) | −9.46664e6 | −0.868786 | −0.434393 | − | 0.900723i | \(-0.643037\pi\) | ||||
−0.434393 | + | 0.900723i | \(0.643037\pi\) | |||||||
\(654\) | −3.35261e6 | −0.306506 | ||||||||
\(655\) | −8.04646e6 | −0.732827 | ||||||||
\(656\) | −8.57513e6 | −0.778003 | ||||||||
\(657\) | −1.35915e6 | −0.122844 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.40662e7 | 1.26172 | 0.630860 | − | 0.775896i | \(-0.282702\pi\) | ||||
0.630860 | + | 0.775896i | \(0.282702\pi\) | |||||||
\(660\) | 7.21776e6 | 0.644974 | ||||||||
\(661\) | −1.71606e7 | −1.52766 | −0.763832 | − | 0.645415i | \(-0.776685\pi\) | ||||
−0.763832 | + | 0.645415i | \(0.776685\pi\) | |||||||
\(662\) | −3.56363e7 | −3.16044 | ||||||||
\(663\) | −5.15339e6 | −0.455312 | ||||||||
\(664\) | 2.49209e7 | 2.19353 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.20592e6 | −0.716872 | ||||||||
\(667\) | −9.79606e6 | −0.852583 | ||||||||
\(668\) | 6.87385e6 | 0.596017 | ||||||||
\(669\) | −5.58204e6 | −0.482201 | ||||||||
\(670\) | −1.34994e7 | −1.16179 | ||||||||
\(671\) | −9.82424e6 | −0.842350 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.87113e6 | 0.499671 | 0.249836 | − | 0.968288i | \(-0.419623\pi\) | ||||
0.249836 | + | 0.968288i | \(0.419623\pi\) | |||||||
\(674\) | 2.54777e6 | 0.216028 | ||||||||
\(675\) | −1.86683e6 | −0.157705 | ||||||||
\(676\) | 4.84249e7 | 4.07570 | ||||||||
\(677\) | 1.39274e7 | 1.16788 | 0.583938 | − | 0.811798i | \(-0.301511\pi\) | ||||
0.583938 | + | 0.811798i | \(0.301511\pi\) | |||||||
\(678\) | −8.89884e6 | −0.743462 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.52872e6 | 0.458513 | ||||||||
\(681\) | 9.02009e6 | 0.745321 | ||||||||
\(682\) | 1.40436e7 | 1.15615 | ||||||||
\(683\) | 1.83101e7 | 1.50189 | 0.750945 | − | 0.660365i | \(-0.229598\pi\) | ||||
0.750945 | + | 0.660365i | \(0.229598\pi\) | |||||||
\(684\) | −8.15160e6 | −0.666197 | ||||||||
\(685\) | −1.49350e6 | −0.121613 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.97275e6 | 0.644490 | ||||||||
\(688\) | 9.92420e6 | 0.799327 | ||||||||
\(689\) | −1.16302e6 | −0.0933337 | ||||||||
\(690\) | 8.99076e6 | 0.718908 | ||||||||
\(691\) | −1.76717e7 | −1.40793 | −0.703967 | − | 0.710233i | \(-0.748590\pi\) | ||||
−0.703967 | + | 0.710233i | \(0.748590\pi\) | |||||||
\(692\) | 2.45752e7 | 1.95088 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.53973e7 | −1.21351 | ||||||||
\(695\) | 5.03386e6 | 0.395311 | ||||||||
\(696\) | −8.88036e6 | −0.694877 | ||||||||
\(697\) | −2.51506e6 | −0.196095 | ||||||||
\(698\) | 1.57826e7 | 1.22614 | ||||||||
\(699\) | 5.36547e6 | 0.415351 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.22993e6 | 0.632559 | 0.316279 | − | 0.948666i | \(-0.397566\pi\) | ||||
0.316279 | + | 0.948666i | \(0.397566\pi\) | |||||||
\(702\) | −7.59703e6 | −0.581837 | ||||||||
\(703\) | 1.37494e7 | 1.04929 | ||||||||
\(704\) | 1.56169e6 | 0.118758 | ||||||||
\(705\) | −667320. | −0.0505663 | ||||||||
\(706\) | −1.71552e7 | −1.29534 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.79486e7 | 1.34570 | ||||||||
\(709\) | 2.46367e7 | 1.84063 | 0.920314 | − | 0.391180i | \(-0.127933\pi\) | ||||
0.920314 | + | 0.391180i | \(0.127933\pi\) | |||||||
\(710\) | −1.47575e6 | −0.109867 | ||||||||
\(711\) | −392466. | −0.0291158 | ||||||||
\(712\) | −2.58954e7 | −1.91436 | ||||||||
\(713\) | 1.21379e7 | 0.894167 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.12710e7 | −0.824510 | ||||||||
\(716\) | 5.62951e7 | 4.10382 | ||||||||
\(717\) | 6.68800e6 | 0.485845 | ||||||||
\(718\) | −2.55569e7 | −1.85011 | ||||||||
\(719\) | −1.88254e7 | −1.35807 | −0.679034 | − | 0.734107i | \(-0.737601\pi\) | ||||
−0.679034 | + | 0.734107i | \(0.737601\pi\) | |||||||
\(720\) | 3.68503e6 | 0.264917 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.63055e6 | −0.401983 | ||||||||
\(723\) | −1.05735e7 | −0.752272 | ||||||||
\(724\) | −9.62411e6 | −0.682361 | ||||||||
\(725\) | 6.09823e6 | 0.430882 | ||||||||
\(726\) | 5.12186e6 | 0.360650 | ||||||||
\(727\) | 6.77607e6 | 0.475491 | 0.237745 | − | 0.971328i | \(-0.423592\pi\) | ||||
0.237745 | + | 0.971328i | \(0.423592\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −4.07486e6 | −0.283012 | ||||||||
\(731\) | 2.91073e6 | 0.201469 | ||||||||
\(732\) | −1.37752e7 | −0.950212 | ||||||||
\(733\) | −1.72227e7 | −1.18397 | −0.591986 | − | 0.805948i | \(-0.701656\pi\) | ||||
−0.591986 | + | 0.805948i | \(0.701656\pi\) | |||||||
\(734\) | −2.15459e7 | −1.47613 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.60102e7 | 1.76990 | ||||||||
\(737\) | −2.58779e7 | −1.75493 | ||||||||
\(738\) | −3.70765e6 | −0.250587 | ||||||||
\(739\) | −1.76534e7 | −1.18910 | −0.594548 | − | 0.804060i | \(-0.702669\pi\) | ||||
−0.594548 | + | 0.804060i | \(0.702669\pi\) | |||||||
\(740\) | −1.70704e7 | −1.14595 | ||||||||
\(741\) | 1.27292e7 | 0.851641 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.36977e7 | −0.910281 | −0.455141 | − | 0.890420i | \(-0.650411\pi\) | ||||
−0.455141 | + | 0.890420i | \(0.650411\pi\) | |||||||
\(744\) | 1.10033e7 | 0.728768 | ||||||||
\(745\) | 3.33188e6 | 0.219937 | ||||||||
\(746\) | 2.79341e7 | 1.83775 | ||||||||
\(747\) | 4.87178e6 | 0.319438 | ||||||||
\(748\) | 1.89668e7 | 1.23948 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.24269e7 | −0.806698 | ||||||||
\(751\) | 1.16089e7 | 0.751090 | 0.375545 | − | 0.926804i | \(-0.377456\pi\) | ||||
0.375545 | + | 0.926804i | \(0.377456\pi\) | |||||||
\(752\) | −5.97885e6 | −0.385543 | ||||||||
\(753\) | 3.17693e6 | 0.204183 | ||||||||
\(754\) | 2.48167e7 | 1.58970 | ||||||||
\(755\) | −3.89526e6 | −0.248696 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.25226e6 | 0.396550 | 0.198275 | − | 0.980146i | \(-0.436466\pi\) | ||||
0.198275 | + | 0.980146i | \(0.436466\pi\) | |||||||
\(758\) | −2.08868e7 | −1.32038 | ||||||||
\(759\) | 1.72350e7 | 1.08594 | ||||||||
\(760\) | −1.36563e7 | −0.857629 | ||||||||
\(761\) | −3.02125e7 | −1.89115 | −0.945574 | − | 0.325406i | \(-0.894499\pi\) | ||||
−0.945574 | + | 0.325406i | \(0.894499\pi\) | |||||||
\(762\) | 2.14605e6 | 0.133891 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 481393. | 0.0298378 | ||||||||
\(765\) | 1.08081e6 | 0.0667721 | ||||||||
\(766\) | 1.54277e7 | 0.950014 | ||||||||
\(767\) | −2.80278e7 | −1.72028 | ||||||||
\(768\) | −1.64280e7 | −1.00504 | ||||||||
\(769\) | −2.58756e7 | −1.57788 | −0.788940 | − | 0.614470i | \(-0.789370\pi\) | ||||
−0.788940 | + | 0.614470i | \(0.789370\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 90114.1 | 0.00545955 | ||||||||
\(772\) | 3.28251e7 | 1.98227 | ||||||||
\(773\) | 2.55409e7 | 1.53740 | 0.768701 | − | 0.639608i | \(-0.220903\pi\) | ||||
0.768701 | + | 0.639608i | \(0.220903\pi\) | |||||||
\(774\) | 4.29095e6 | 0.257455 | ||||||||
\(775\) | −7.55605e6 | −0.451898 | ||||||||
\(776\) | −2.63746e7 | −1.57228 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.60140e7 | 2.72547 | ||||||||
\(779\) | 6.21236e6 | 0.366786 | ||||||||
\(780\) | −1.58038e7 | −0.930087 | ||||||||
\(781\) | −2.82896e6 | −0.165958 | ||||||||
\(782\) | 2.36258e7 | 1.38156 | ||||||||
\(783\) | −1.73602e6 | −0.101193 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.32195e7 | 0.765667 | ||||||||
\(786\) | −3.11707e7 | −1.79966 | ||||||||
\(787\) | −8.81179e6 | −0.507139 | −0.253570 | − | 0.967317i | \(-0.581605\pi\) | ||||
−0.253570 | + | 0.967317i | \(0.581605\pi\) | |||||||
\(788\) | 5.92512e7 | 3.39924 | ||||||||
\(789\) | 1.51362e7 | 0.865614 | ||||||||
\(790\) | −1.17665e6 | −0.0670779 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.56239e7 | 0.885068 | ||||||||
\(793\) | 2.15108e7 | 1.21471 | ||||||||
\(794\) | −3.60018e7 | −2.02662 | ||||||||
\(795\) | 243917. | 0.0136875 | ||||||||
\(796\) | 5.84871e7 | 3.27173 | ||||||||
\(797\) | −2.07624e7 | −1.15780 | −0.578899 | − | 0.815399i | \(-0.696517\pi\) | ||||
−0.578899 | + | 0.815399i | \(0.696517\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.75358e6 | −0.0971757 | ||||||||
\(800\) | −1.61918e7 | −0.894481 | ||||||||
\(801\) | −5.06229e6 | −0.278783 | ||||||||
\(802\) | −9.27413e6 | −0.509140 | ||||||||
\(803\) | −7.81136e6 | −0.427501 | ||||||||
\(804\) | −3.62850e7 | −1.97965 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.07493e7 | −1.66724 | ||||||||
\(807\) | −1.72546e7 | −0.932653 | ||||||||
\(808\) | 7.64973e7 | 4.12209 | ||||||||
\(809\) | 1.37021e7 | 0.736067 | 0.368034 | − | 0.929813i | \(-0.380031\pi\) | ||||
0.368034 | + | 0.929813i | \(0.380031\pi\) | |||||||
\(810\) | 1.59331e6 | 0.0853271 | ||||||||
\(811\) | 3.30799e7 | 1.76609 | 0.883043 | − | 0.469292i | \(-0.155491\pi\) | ||||
0.883043 | + | 0.469292i | \(0.155491\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.06100e7 | 1.09358 | ||||||||
\(814\) | −4.71613e7 | −2.49474 | ||||||||
\(815\) | −468563. | −0.0247101 | ||||||||
\(816\) | 9.68350e6 | 0.509104 | ||||||||
\(817\) | −7.18971e6 | −0.376840 | ||||||||
\(818\) | 4.41520e7 | 2.30711 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.71285e6 | −0.400572 | ||||||||
\(821\) | 1.48323e7 | 0.767982 | 0.383991 | − | 0.923337i | \(-0.374549\pi\) | ||||
0.383991 | + | 0.923337i | \(0.374549\pi\) | |||||||
\(822\) | −5.78558e6 | −0.298653 | ||||||||
\(823\) | 1.08722e7 | 0.559525 | 0.279762 | − | 0.960069i | \(-0.409744\pi\) | ||||
0.279762 | + | 0.960069i | \(0.409744\pi\) | |||||||
\(824\) | 2.15640e7 | 1.10640 | ||||||||
\(825\) | −1.07291e7 | −0.548817 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.34267e7 | −0.682662 | −0.341331 | − | 0.939943i | \(-0.610878\pi\) | ||||
−0.341331 | + | 0.939943i | \(0.610878\pi\) | |||||||
\(828\) | 2.41663e7 | 1.22499 | ||||||||
\(829\) | −1.46754e7 | −0.741658 | −0.370829 | − | 0.928701i | \(-0.620926\pi\) | ||||
−0.370829 | + | 0.928701i | \(0.620926\pi\) | |||||||
\(830\) | 1.46060e7 | 0.735931 | ||||||||
\(831\) | −3.55322e6 | −0.178492 | ||||||||
\(832\) | −3.41941e6 | −0.171255 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.95004e7 | 0.970796 | ||||||||
\(835\) | 2.25120e6 | 0.111737 | ||||||||
\(836\) | −4.68492e7 | −2.31839 | ||||||||
\(837\) | 2.15103e6 | 0.106129 | ||||||||
\(838\) | −1.55444e7 | −0.764654 | ||||||||
\(839\) | 2.76635e7 | 1.35676 | 0.678379 | − | 0.734712i | \(-0.262683\pi\) | ||||
0.678379 | + | 0.734712i | \(0.262683\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.48402e7 | −0.723519 | ||||||||
\(842\) | −4.51946e7 | −2.19688 | ||||||||
\(843\) | −1.59929e7 | −0.775103 | ||||||||
\(844\) | 4.98798e6 | 0.241028 | ||||||||
\(845\) | 1.58593e7 | 0.764084 | ||||||||
\(846\) | −2.58509e6 | −0.124180 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.18537e6 | 0.104361 | ||||||||
\(849\) | 1.09372e7 | 0.520759 | ||||||||
\(850\) | −1.47075e7 | −0.698219 | ||||||||
\(851\) | −4.07616e7 | −1.92942 | ||||||||
\(852\) | −3.96667e6 | −0.187209 | ||||||||
\(853\) | 3.43515e6 | 0.161649 | 0.0808244 | − | 0.996728i | \(-0.474245\pi\) | ||||
0.0808244 | + | 0.996728i | \(0.474245\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.66967e6 | −0.124894 | ||||||||
\(856\) | 1.99622e7 | 0.931158 | ||||||||
\(857\) | −6.40626e6 | −0.297956 | −0.148978 | − | 0.988840i | \(-0.547598\pi\) | ||||
−0.148978 | + | 0.988840i | \(0.547598\pi\) | |||||||
\(858\) | −4.36619e7 | −2.02481 | ||||||||
\(859\) | 1.81739e7 | 0.840360 | 0.420180 | − | 0.907441i | \(-0.361967\pi\) | ||||
0.420180 | + | 0.907441i | \(0.361967\pi\) | |||||||
\(860\) | 8.92627e6 | 0.411551 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.00114e7 | −3.20923 | ||||||||
\(863\) | 818774. | 0.0374229 | 0.0187114 | − | 0.999825i | \(-0.494044\pi\) | ||||
0.0187114 | + | 0.999825i | \(0.494044\pi\) | |||||||
\(864\) | 4.60943e6 | 0.210069 | ||||||||
\(865\) | 8.04843e6 | 0.365739 | ||||||||
\(866\) | −4.08267e7 | −1.84991 | ||||||||
\(867\) | −9.93858e6 | −0.449031 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.25560e6 | −0.101324 | ||||||||
\(870\) | −5.20475e6 | −0.233132 | ||||||||
\(871\) | 5.66613e7 | 2.53070 | ||||||||
\(872\) | −1.50968e7 | −0.672350 | ||||||||
\(873\) | −5.15596e6 | −0.228968 | ||||||||
\(874\) | −5.83574e7 | −2.58415 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.09528e7 | −0.482242 | ||||||||
\(877\) | −3.33962e7 | −1.46622 | −0.733108 | − | 0.680113i | \(-0.761931\pi\) | ||||
−0.733108 | + | 0.680113i | \(0.761931\pi\) | |||||||
\(878\) | 1.51882e7 | 0.664921 | ||||||||
\(879\) | −1.34008e7 | −0.585002 | ||||||||
\(880\) | 2.11788e7 | 0.921921 | ||||||||
\(881\) | −1.24325e7 | −0.539658 | −0.269829 | − | 0.962908i | \(-0.586967\pi\) | ||||
−0.269829 | + | 0.962908i | \(0.586967\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.33298e7 | −1.00695 | −0.503476 | − | 0.864009i | \(-0.667946\pi\) | ||||
−0.503476 | + | 0.864009i | \(0.667946\pi\) | |||||||
\(884\) | −4.15290e7 | −1.78739 | ||||||||
\(885\) | 5.87820e6 | 0.252282 | ||||||||
\(886\) | −5.74778e7 | −2.45989 | ||||||||
\(887\) | −4.75528e6 | −0.202940 | −0.101470 | − | 0.994839i | \(-0.532355\pi\) | ||||
−0.101470 | + | 0.994839i | \(0.532355\pi\) | |||||||
\(888\) | −3.69514e7 | −1.57253 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.51772e7 | −0.642269 | ||||||||
\(891\) | 3.05432e6 | 0.128890 | ||||||||
\(892\) | −4.49833e7 | −1.89295 | ||||||||
\(893\) | 4.33145e6 | 0.181763 | ||||||||
\(894\) | 1.29072e7 | 0.540116 | ||||||||
\(895\) | 1.84368e7 | 0.769356 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.77371e7 | −1.56598 | ||||||||
\(898\) | 1.99245e7 | 0.824512 | ||||||||
\(899\) | −7.02661e6 | −0.289966 | ||||||||
\(900\) | −1.50440e7 | −0.619093 | ||||||||
\(901\) | 640963. | 0.0263040 | ||||||||
\(902\) | −2.13087e7 | −0.872050 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.00716e7 | −1.63086 | ||||||||
\(905\) | −3.15192e6 | −0.127924 | ||||||||
\(906\) | −1.50896e7 | −0.610742 | ||||||||
\(907\) | −1.90902e7 | −0.770537 | −0.385268 | − | 0.922805i | \(-0.625891\pi\) | ||||
−0.385268 | + | 0.922805i | \(0.625891\pi\) | |||||||
\(908\) | 7.26891e7 | 2.92587 | ||||||||
\(909\) | 1.49544e7 | 0.600289 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.22591e6 | −0.0489399 | −0.0244700 | − | 0.999701i | \(-0.507790\pi\) | ||||
−0.0244700 | + | 0.999701i | \(0.507790\pi\) | |||||||
\(912\) | −2.39189e7 | −0.952257 | ||||||||
\(913\) | 2.79993e7 | 1.11165 | ||||||||
\(914\) | −2.73296e7 | −1.08210 | ||||||||
\(915\) | −4.51141e6 | −0.178139 | ||||||||
\(916\) | 6.42490e7 | 2.53004 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.18688e6 | 0.163977 | ||||||||
\(919\) | −1.69227e7 | −0.660970 | −0.330485 | − | 0.943811i | \(-0.607212\pi\) | ||||
−0.330485 | + | 0.943811i | \(0.607212\pi\) | |||||||
\(920\) | 4.04855e7 | 1.57699 | ||||||||
\(921\) | 1.82798e7 | 0.710103 | ||||||||
\(922\) | −4.75677e7 | −1.84283 | ||||||||
\(923\) | 6.19419e6 | 0.239321 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.53749e7 | 0.975101 | ||||||||
\(926\) | −5.30195e7 | −2.03193 | ||||||||
\(927\) | 4.21554e6 | 0.161122 | ||||||||
\(928\) | −1.50573e7 | −0.573954 | ||||||||
\(929\) | 6.77240e6 | 0.257456 | 0.128728 | − | 0.991680i | \(-0.458911\pi\) | ||||
0.128728 | + | 0.991680i | \(0.458911\pi\) | |||||||
\(930\) | 6.44897e6 | 0.244502 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.32380e7 | 1.63052 | ||||||||
\(933\) | 2.60806e6 | 0.0980875 | ||||||||
\(934\) | −5.17307e7 | −1.94035 | ||||||||
\(935\) | 6.21166e6 | 0.232369 | ||||||||
\(936\) | −3.42096e7 | −1.27632 | ||||||||
\(937\) | −1.41035e7 | −0.524779 | −0.262389 | − | 0.964962i | \(-0.584511\pi\) | ||||
−0.262389 | + | 0.964962i | \(0.584511\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.96389e6 | 0.0726866 | ||||||||
\(940\) | −5.37765e6 | −0.198505 | ||||||||
\(941\) | −5.62524e6 | −0.207094 | −0.103547 | − | 0.994625i | \(-0.533019\pi\) | ||||
−0.103547 | + | 0.994625i | \(0.533019\pi\) | |||||||
\(942\) | 5.12102e7 | 1.88031 | ||||||||
\(943\) | −1.84172e7 | −0.674441 | ||||||||
\(944\) | 5.26657e7 | 1.92353 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.46611e7 | 0.895952 | ||||||||
\(947\) | 2.64126e7 | 0.957052 | 0.478526 | − | 0.878073i | \(-0.341171\pi\) | ||||
0.478526 | + | 0.878073i | \(0.341171\pi\) | |||||||
\(948\) | −3.16272e6 | −0.114298 | ||||||||
\(949\) | 1.71035e7 | 0.616480 | ||||||||
\(950\) | 3.63286e7 | 1.30599 | ||||||||
\(951\) | 1.16157e7 | 0.416479 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.21824e7 | 1.50452 | 0.752262 | − | 0.658864i | \(-0.228963\pi\) | ||||
0.752262 | + | 0.658864i | \(0.228963\pi\) | |||||||
\(954\) | 944896. | 0.0336135 | ||||||||
\(955\) | 157657. | 0.00559378 | ||||||||
\(956\) | 5.38957e7 | 1.90726 | ||||||||
\(957\) | −9.97732e6 | −0.352155 | ||||||||
\(958\) | −5.67511e7 | −1.99784 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 717145. | 0.0251148 | ||||||||
\(961\) | −1.99228e7 | −0.695892 | ||||||||
\(962\) | 1.03263e8 | 3.59755 | ||||||||
\(963\) | 3.90240e6 | 0.135602 | ||||||||
\(964\) | −8.52077e7 | −2.95315 | ||||||||
\(965\) | 1.07503e7 | 0.371622 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.01501e7 | 1.38077 | 0.690384 | − | 0.723443i | \(-0.257441\pi\) | ||||
0.690384 | + | 0.723443i | \(0.257441\pi\) | |||||||
\(968\) | 2.30638e7 | 0.791120 | ||||||||
\(969\) | −7.01533e6 | −0.240015 | ||||||||
\(970\) | −1.54580e7 | −0.527503 | ||||||||
\(971\) | 1.64551e7 | 0.560084 | 0.280042 | − | 0.959988i | \(-0.409652\pi\) | ||||
0.280042 | + | 0.959988i | \(0.409652\pi\) | |||||||
\(972\) | 4.28266e6 | 0.145394 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −7.03207e7 | −2.37512 | ||||||||
\(975\) | 2.34920e7 | 0.791424 | ||||||||
\(976\) | −4.04200e7 | −1.35823 | ||||||||
\(977\) | 1.71176e7 | 0.573729 | 0.286865 | − | 0.957971i | \(-0.407387\pi\) | ||||
0.286865 | + | 0.957971i | \(0.407387\pi\) | |||||||
\(978\) | −1.81514e6 | −0.0606825 | ||||||||
\(979\) | −2.90942e7 | −0.970174 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.95128e6 | −0.0979125 | ||||||||
\(982\) | 7.61124e7 | 2.51870 | ||||||||
\(983\) | −2.33803e7 | −0.771730 | −0.385865 | − | 0.922555i | \(-0.626097\pi\) | ||||
−0.385865 | + | 0.922555i | \(0.626097\pi\) | |||||||
\(984\) | −1.66956e7 | −0.549686 | ||||||||
\(985\) | 1.94049e7 | 0.637266 | ||||||||
\(986\) | −1.36770e7 | −0.448021 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.02579e8 | 3.34324 | ||||||||
\(989\) | 2.13146e7 | 0.692927 | ||||||||
\(990\) | 9.15712e6 | 0.296941 | ||||||||
\(991\) | −4.70955e6 | −0.152333 | −0.0761667 | − | 0.997095i | \(-0.524268\pi\) | ||||
−0.0761667 | + | 0.997095i | \(0.524268\pi\) | |||||||
\(992\) | 1.86568e7 | 0.601948 | ||||||||
\(993\) | −3.13705e7 | −1.00960 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.91547e7 | 0.613362 | ||||||||
\(996\) | 3.92596e7 | 1.25400 | ||||||||
\(997\) | −4.55428e7 | −1.45105 | −0.725524 | − | 0.688197i | \(-0.758403\pi\) | ||||
−0.725524 | + | 0.688197i | \(0.758403\pi\) | |||||||
\(998\) | 2.20150e7 | 0.699667 | ||||||||
\(999\) | −7.22363e6 | −0.229003 |
(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 | 147.6.a.m.1.4 | 4 | ||
3.2 | odd | 2 | 441.6.a.w.1.1 | 4 | |||
7.2 | even | 3 | 21.6.e.c.4.1 | ✓ | 8 | ||
7.3 | odd | 6 | 147.6.e.o.79.1 | 8 | |||
7.4 | even | 3 | 21.6.e.c.16.1 | yes | 8 | ||
7.5 | odd | 6 | 147.6.e.o.67.1 | 8 | |||
7.6 | odd | 2 | 147.6.a.l.1.4 | 4 | |||
21.2 | odd | 6 | 63.6.e.e.46.4 | 8 | |||
21.11 | odd | 6 | 63.6.e.e.37.4 | 8 | |||
21.20 | even | 2 | 441.6.a.v.1.1 | 4 | |||
28.11 | odd | 6 | 336.6.q.j.289.2 | 8 | |||
28.23 | odd | 6 | 336.6.q.j.193.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.e.c.4.1 | ✓ | 8 | 7.2 | even | 3 | ||
21.6.e.c.16.1 | yes | 8 | 7.4 | even | 3 | ||
63.6.e.e.37.4 | 8 | 21.11 | odd | 6 | |||
63.6.e.e.46.4 | 8 | 21.2 | odd | 6 | |||
147.6.a.l.1.4 | 4 | 7.6 | odd | 2 | |||
147.6.a.m.1.4 | 4 | 1.1 | even | 1 | trivial | ||
147.6.e.o.67.1 | 8 | 7.5 | odd | 6 | |||
147.6.e.o.79.1 | 8 | 7.3 | odd | 6 | |||
336.6.q.j.193.2 | 8 | 28.23 | odd | 6 | |||
336.6.q.j.289.2 | 8 | 28.11 | odd | 6 | |||
441.6.a.v.1.1 | 4 | 21.20 | even | 2 | |||
441.6.a.w.1.1 | 4 | 3.2 | odd | 2 |