Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.33 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 38.8851 | 1.71849 | 0.859247 | − | 0.511561i | \(-0.170933\pi\) | ||||
0.859247 | + | 0.511561i | \(0.170933\pi\) | |||||||
\(3\) | 39.5980 | 0.282246 | 0.141123 | − | 0.989992i | \(-0.454929\pi\) | ||||
0.141123 | + | 0.989992i | \(0.454929\pi\) | |||||||
\(4\) | 1000.05 | 1.95322 | ||||||||
\(5\) | 1326.61 | 0.949246 | 0.474623 | − | 0.880189i | \(-0.342584\pi\) | ||||
0.474623 | + | 0.880189i | \(0.342584\pi\) | |||||||
\(6\) | 1539.77 | 0.485038 | ||||||||
\(7\) | −2031.17 | −0.319745 | −0.159873 | − | 0.987138i | \(-0.551108\pi\) | ||||
−0.159873 | + | 0.987138i | \(0.551108\pi\) | |||||||
\(8\) | 18977.8 | 1.63810 | ||||||||
\(9\) | −18115.0 | −0.920337 | ||||||||
\(10\) | 51585.4 | 1.63127 | ||||||||
\(11\) | −79765.4 | −1.64266 | −0.821330 | − | 0.570453i | \(-0.806767\pi\) | ||||
−0.821330 | + | 0.570453i | \(0.806767\pi\) | |||||||
\(12\) | 39600.0 | 0.551289 | ||||||||
\(13\) | 19866.3 | 0.192917 | 0.0964586 | − | 0.995337i | \(-0.469248\pi\) | ||||
0.0964586 | + | 0.995337i | \(0.469248\pi\) | |||||||
\(14\) | −78982.0 | −0.549480 | ||||||||
\(15\) | 52531.2 | 0.267921 | ||||||||
\(16\) | 225928. | 0.861848 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −704403. | −1.58159 | ||||||||
\(19\) | −430239. | −0.757388 | −0.378694 | − | 0.925522i | \(-0.623627\pi\) | ||||
−0.378694 | + | 0.925522i | \(0.623627\pi\) | |||||||
\(20\) | 1.32668e6 | 1.85409 | ||||||||
\(21\) | −80430.2 | −0.0902469 | ||||||||
\(22\) | −3.10168e6 | −2.82290 | ||||||||
\(23\) | −1.47745e6 | −1.10088 | −0.550438 | − | 0.834876i | \(-0.685539\pi\) | ||||
−0.550438 | + | 0.834876i | \(0.685539\pi\) | |||||||
\(24\) | 751484. | 0.462348 | ||||||||
\(25\) | −193226. | −0.0989319 | ||||||||
\(26\) | 772501. | 0.331527 | ||||||||
\(27\) | −1.49673e6 | −0.542008 | ||||||||
\(28\) | −2.03126e6 | −0.624533 | ||||||||
\(29\) | 5.01398e6 | 1.31641 | 0.658206 | − | 0.752838i | \(-0.271316\pi\) | ||||
0.658206 | + | 0.752838i | \(0.271316\pi\) | |||||||
\(30\) | 2.04268e6 | 0.460421 | ||||||||
\(31\) | −8.00000e6 | −1.55583 | −0.777915 | − | 0.628369i | \(-0.783723\pi\) | ||||
−0.777915 | + | 0.628369i | \(0.783723\pi\) | |||||||
\(32\) | −931397. | −0.157022 | ||||||||
\(33\) | −3.15856e6 | −0.463635 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.69457e6 | −0.303517 | ||||||||
\(36\) | −1.81159e7 | −1.79762 | ||||||||
\(37\) | −688170. | −0.0603653 | −0.0301827 | − | 0.999544i | \(-0.509609\pi\) | ||||
−0.0301827 | + | 0.999544i | \(0.509609\pi\) | |||||||
\(38\) | −1.67299e7 | −1.30157 | ||||||||
\(39\) | 786665. | 0.0544501 | ||||||||
\(40\) | 2.51762e7 | 1.55496 | ||||||||
\(41\) | −8.23001e6 | −0.454855 | −0.227427 | − | 0.973795i | \(-0.573031\pi\) | ||||
−0.227427 | + | 0.973795i | \(0.573031\pi\) | |||||||
\(42\) | −3.12753e6 | −0.155089 | ||||||||
\(43\) | 4.37889e7 | 1.95324 | 0.976621 | − | 0.214967i | \(-0.0689644\pi\) | ||||
0.976621 | + | 0.214967i | \(0.0689644\pi\) | |||||||
\(44\) | −7.97693e7 | −3.20848 | ||||||||
\(45\) | −2.40316e7 | −0.873626 | ||||||||
\(46\) | −5.74509e7 | −1.89185 | ||||||||
\(47\) | −3.64741e7 | −1.09030 | −0.545148 | − | 0.838340i | \(-0.683526\pi\) | ||||
−0.545148 | + | 0.838340i | \(0.683526\pi\) | |||||||
\(48\) | 8.94632e6 | 0.243253 | ||||||||
\(49\) | −3.62280e7 | −0.897763 | ||||||||
\(50\) | −7.51362e6 | −0.170014 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.98672e7 | 0.376810 | ||||||||
\(53\) | 5.12196e7 | 0.891651 | 0.445826 | − | 0.895120i | \(-0.352910\pi\) | ||||
0.445826 | + | 0.895120i | \(0.352910\pi\) | |||||||
\(54\) | −5.82003e7 | −0.931437 | ||||||||
\(55\) | −1.05818e8 | −1.55929 | ||||||||
\(56\) | −3.85471e7 | −0.523775 | ||||||||
\(57\) | −1.70366e7 | −0.213770 | ||||||||
\(58\) | 1.94969e8 | 2.26225 | ||||||||
\(59\) | 1.34598e8 | 1.44612 | 0.723060 | − | 0.690785i | \(-0.242735\pi\) | ||||
0.723060 | + | 0.690785i | \(0.242735\pi\) | |||||||
\(60\) | 5.25338e7 | 0.523309 | ||||||||
\(61\) | −9.39211e7 | −0.868518 | −0.434259 | − | 0.900788i | \(-0.642990\pi\) | ||||
−0.434259 | + | 0.900788i | \(0.642990\pi\) | |||||||
\(62\) | −3.11081e8 | −2.67369 | ||||||||
\(63\) | 3.67946e7 | 0.294273 | ||||||||
\(64\) | −1.51893e8 | −1.13169 | ||||||||
\(65\) | 2.63548e7 | 0.183126 | ||||||||
\(66\) | −1.22821e8 | −0.796753 | ||||||||
\(67\) | 1.29800e8 | 0.786934 | 0.393467 | − | 0.919339i | \(-0.371276\pi\) | ||||
0.393467 | + | 0.919339i | \(0.371276\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.85043e7 | −0.310718 | ||||||||
\(70\) | −1.04778e8 | −0.521592 | ||||||||
\(71\) | −2.39269e7 | −0.111744 | −0.0558720 | − | 0.998438i | \(-0.517794\pi\) | ||||
−0.0558720 | + | 0.998438i | \(0.517794\pi\) | |||||||
\(72\) | −3.43783e8 | −1.50761 | ||||||||
\(73\) | −4.14566e8 | −1.70860 | −0.854301 | − | 0.519779i | \(-0.826014\pi\) | ||||
−0.854301 | + | 0.519779i | \(0.826014\pi\) | |||||||
\(74\) | −2.67595e7 | −0.103737 | ||||||||
\(75\) | −7.65139e6 | −0.0279232 | ||||||||
\(76\) | −4.30260e8 | −1.47935 | ||||||||
\(77\) | 1.62017e8 | 0.525233 | ||||||||
\(78\) | 3.05895e7 | 0.0935722 | ||||||||
\(79\) | −3.87393e8 | −1.11900 | −0.559500 | − | 0.828830i | \(-0.689007\pi\) | ||||
−0.559500 | + | 0.828830i | \(0.689007\pi\) | |||||||
\(80\) | 2.99719e8 | 0.818106 | ||||||||
\(81\) | 2.97290e8 | 0.767357 | ||||||||
\(82\) | −3.20024e8 | −0.781665 | ||||||||
\(83\) | 2.80744e8 | 0.649319 | 0.324660 | − | 0.945831i | \(-0.394750\pi\) | ||||
0.324660 | + | 0.945831i | \(0.394750\pi\) | |||||||
\(84\) | −8.04341e7 | −0.176272 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.70274e9 | 3.35663 | ||||||||
\(87\) | 1.98544e8 | 0.371552 | ||||||||
\(88\) | −1.51377e9 | −2.69084 | ||||||||
\(89\) | 9.07508e8 | 1.53319 | 0.766594 | − | 0.642132i | \(-0.221950\pi\) | ||||
0.766594 | + | 0.642132i | \(0.221950\pi\) | |||||||
\(90\) | −9.34469e8 | −1.50132 | ||||||||
\(91\) | −4.03516e7 | −0.0616843 | ||||||||
\(92\) | −1.47753e9 | −2.15025 | ||||||||
\(93\) | −3.16784e8 | −0.439127 | ||||||||
\(94\) | −1.41830e9 | −1.87367 | ||||||||
\(95\) | −5.70760e8 | −0.718948 | ||||||||
\(96\) | −3.68815e7 | −0.0443188 | ||||||||
\(97\) | 1.62096e9 | 1.85908 | 0.929542 | − | 0.368716i | \(-0.120202\pi\) | ||||
0.929542 | + | 0.368716i | \(0.120202\pi\) | |||||||
\(98\) | −1.40873e9 | −1.54280 | ||||||||
\(99\) | 1.44495e9 | 1.51180 | ||||||||
\(100\) | −1.93236e8 | −0.193236 | ||||||||
\(101\) | 1.25201e9 | 1.19719 | 0.598593 | − | 0.801053i | \(-0.295727\pi\) | ||||
0.598593 | + | 0.801053i | \(0.295727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.74839e8 | −0.153063 | −0.0765315 | − | 0.997067i | \(-0.524385\pi\) | ||||
−0.0765315 | + | 0.997067i | \(0.524385\pi\) | |||||||
\(104\) | 3.77018e8 | 0.316018 | ||||||||
\(105\) | −1.06700e8 | −0.0856665 | ||||||||
\(106\) | 1.99168e9 | 1.53230 | ||||||||
\(107\) | 1.01435e9 | 0.748105 | 0.374053 | − | 0.927407i | \(-0.377968\pi\) | ||||
0.374053 | + | 0.927407i | \(0.377968\pi\) | |||||||
\(108\) | −1.49680e9 | −1.05866 | ||||||||
\(109\) | −6.13770e8 | −0.416472 | −0.208236 | − | 0.978079i | \(-0.566772\pi\) | ||||
−0.208236 | + | 0.978079i | \(0.566772\pi\) | |||||||
\(110\) | −4.11473e9 | −2.67963 | ||||||||
\(111\) | −2.72502e7 | −0.0170379 | ||||||||
\(112\) | −4.58898e8 | −0.275572 | ||||||||
\(113\) | 5.73250e7 | 0.0330743 | 0.0165372 | − | 0.999863i | \(-0.494736\pi\) | ||||
0.0165372 | + | 0.999863i | \(0.494736\pi\) | |||||||
\(114\) | −6.62470e8 | −0.367362 | ||||||||
\(115\) | −1.96001e9 | −1.04500 | ||||||||
\(116\) | 5.01423e9 | 2.57124 | ||||||||
\(117\) | −3.59877e8 | −0.177549 | ||||||||
\(118\) | 5.23385e9 | 2.48515 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 9.96927e8 | 0.438882 | ||||||||
\(121\) | 4.00458e9 | 1.69833 | ||||||||
\(122\) | −3.65213e9 | −1.49254 | ||||||||
\(123\) | −3.25892e8 | −0.128381 | ||||||||
\(124\) | −8.00039e9 | −3.03888 | ||||||||
\(125\) | −2.84737e9 | −1.04316 | ||||||||
\(126\) | 1.43076e9 | 0.505707 | ||||||||
\(127\) | −5.54930e9 | −1.89287 | −0.946436 | − | 0.322892i | \(-0.895345\pi\) | ||||
−0.946436 | + | 0.322892i | \(0.895345\pi\) | |||||||
\(128\) | −5.42948e9 | −1.78778 | ||||||||
\(129\) | 1.73396e9 | 0.551295 | ||||||||
\(130\) | 1.02481e9 | 0.314701 | ||||||||
\(131\) | 1.26351e9 | 0.374851 | 0.187425 | − | 0.982279i | \(-0.439986\pi\) | ||||
0.187425 | + | 0.982279i | \(0.439986\pi\) | |||||||
\(132\) | −3.15871e9 | −0.905580 | ||||||||
\(133\) | 8.73886e8 | 0.242171 | ||||||||
\(134\) | 5.04728e9 | 1.35234 | ||||||||
\(135\) | −1.98558e9 | −0.514499 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.64045e9 | 0.882903 | 0.441452 | − | 0.897285i | \(-0.354464\pi\) | ||||
0.441452 | + | 0.897285i | \(0.354464\pi\) | |||||||
\(138\) | −2.27494e9 | −0.533967 | ||||||||
\(139\) | −2.14697e9 | −0.487820 | −0.243910 | − | 0.969798i | \(-0.578430\pi\) | ||||
−0.243910 | + | 0.969798i | \(0.578430\pi\) | |||||||
\(140\) | −2.69470e9 | −0.592835 | ||||||||
\(141\) | −1.44430e9 | −0.307732 | ||||||||
\(142\) | −9.30400e8 | −0.192031 | ||||||||
\(143\) | −1.58464e9 | −0.316897 | ||||||||
\(144\) | −4.09269e9 | −0.793191 | ||||||||
\(145\) | 6.65161e9 | 1.24960 | ||||||||
\(146\) | −1.61204e10 | −2.93622 | ||||||||
\(147\) | −1.43456e9 | −0.253390 | ||||||||
\(148\) | −6.88203e8 | −0.117907 | ||||||||
\(149\) | −2.29251e9 | −0.381041 | −0.190521 | − | 0.981683i | \(-0.561018\pi\) | ||||
−0.190521 | + | 0.981683i | \(0.561018\pi\) | |||||||
\(150\) | −2.97525e8 | −0.0479858 | ||||||||
\(151\) | −2.31951e9 | −0.363079 | −0.181539 | − | 0.983384i | \(-0.558108\pi\) | ||||
−0.181539 | + | 0.983384i | \(0.558108\pi\) | |||||||
\(152\) | −8.16499e9 | −1.24068 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.30003e9 | 0.902609 | ||||||||
\(155\) | −1.06129e10 | −1.47687 | ||||||||
\(156\) | 7.86703e8 | 0.106353 | ||||||||
\(157\) | −2.99512e9 | −0.393429 | −0.196714 | − | 0.980461i | \(-0.563027\pi\) | ||||
−0.196714 | + | 0.980461i | \(0.563027\pi\) | |||||||
\(158\) | −1.50638e10 | −1.92299 | ||||||||
\(159\) | 2.02820e9 | 0.251665 | ||||||||
\(160\) | −1.23560e9 | −0.149052 | ||||||||
\(161\) | 3.00095e9 | 0.352000 | ||||||||
\(162\) | 1.15601e10 | 1.31870 | ||||||||
\(163\) | −2.18156e9 | −0.242060 | −0.121030 | − | 0.992649i | \(-0.538620\pi\) | ||||
−0.121030 | + | 0.992649i | \(0.538620\pi\) | |||||||
\(164\) | −8.23041e9 | −0.888432 | ||||||||
\(165\) | −4.19018e9 | −0.440103 | ||||||||
\(166\) | 1.09167e10 | 1.11585 | ||||||||
\(167\) | −1.30714e10 | −1.30046 | −0.650232 | − | 0.759736i | \(-0.725328\pi\) | ||||
−0.650232 | + | 0.759736i | \(0.725328\pi\) | |||||||
\(168\) | −1.52639e9 | −0.147834 | ||||||||
\(169\) | −1.02098e10 | −0.962783 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.79378e9 | 0.697052 | ||||||||
\(172\) | 4.37911e10 | 3.81511 | ||||||||
\(173\) | −2.58955e9 | −0.219794 | −0.109897 | − | 0.993943i | \(-0.535052\pi\) | ||||
−0.109897 | + | 0.993943i | \(0.535052\pi\) | |||||||
\(174\) | 7.72039e9 | 0.638510 | ||||||||
\(175\) | 3.92475e8 | 0.0316330 | ||||||||
\(176\) | −1.80213e10 | −1.41572 | ||||||||
\(177\) | 5.32982e9 | 0.408162 | ||||||||
\(178\) | 3.52885e10 | 2.63477 | ||||||||
\(179\) | −6.20782e9 | −0.451960 | −0.225980 | − | 0.974132i | \(-0.572558\pi\) | ||||
−0.225980 | + | 0.974132i | \(0.572558\pi\) | |||||||
\(180\) | −2.40327e10 | −1.70638 | ||||||||
\(181\) | −1.12580e10 | −0.779664 | −0.389832 | − | 0.920886i | \(-0.627467\pi\) | ||||
−0.389832 | + | 0.920886i | \(0.627467\pi\) | |||||||
\(182\) | −1.56908e9 | −0.106004 | ||||||||
\(183\) | −3.71909e9 | −0.245136 | ||||||||
\(184\) | −2.80388e10 | −1.80335 | ||||||||
\(185\) | −9.12934e8 | −0.0573016 | ||||||||
\(186\) | −1.23182e10 | −0.754638 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −3.64759e10 | −2.12959 | ||||||||
\(189\) | 3.04010e9 | 0.173304 | ||||||||
\(190\) | −2.21940e10 | −1.23551 | ||||||||
\(191\) | −2.49016e10 | −1.35387 | −0.676936 | − | 0.736042i | \(-0.736693\pi\) | ||||
−0.676936 | + | 0.736042i | \(0.736693\pi\) | |||||||
\(192\) | −6.01466e9 | −0.319415 | ||||||||
\(193\) | 2.70015e9 | 0.140081 | 0.0700407 | − | 0.997544i | \(-0.477687\pi\) | ||||
0.0700407 | + | 0.997544i | \(0.477687\pi\) | |||||||
\(194\) | 6.30311e10 | 3.19482 | ||||||||
\(195\) | 1.04360e9 | 0.0516866 | ||||||||
\(196\) | −3.62297e10 | −1.75353 | ||||||||
\(197\) | −6.99326e8 | −0.0330813 | −0.0165406 | − | 0.999863i | \(-0.505265\pi\) | ||||
−0.0165406 | + | 0.999863i | \(0.505265\pi\) | |||||||
\(198\) | 5.61870e10 | 2.59802 | ||||||||
\(199\) | −1.79474e10 | −0.811267 | −0.405634 | − | 0.914036i | \(-0.632949\pi\) | ||||
−0.405634 | + | 0.914036i | \(0.632949\pi\) | |||||||
\(200\) | −3.66701e9 | −0.162061 | ||||||||
\(201\) | 5.13983e9 | 0.222109 | ||||||||
\(202\) | 4.86845e10 | 2.05736 | ||||||||
\(203\) | −1.01842e10 | −0.420916 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.09180e10 | −0.431769 | ||||||||
\(206\) | −6.79861e9 | −0.263038 | ||||||||
\(207\) | 2.67641e10 | 1.01318 | ||||||||
\(208\) | 4.48835e9 | 0.166265 | ||||||||
\(209\) | 3.43182e10 | 1.24413 | ||||||||
\(210\) | −4.14902e9 | −0.147217 | ||||||||
\(211\) | −1.27607e10 | −0.443202 | −0.221601 | − | 0.975137i | \(-0.571128\pi\) | ||||
−0.221601 | + | 0.975137i | \(0.571128\pi\) | |||||||
\(212\) | 5.12221e10 | 1.74159 | ||||||||
\(213\) | −9.47459e8 | −0.0315393 | ||||||||
\(214\) | 3.94432e10 | 1.28561 | ||||||||
\(215\) | 5.80909e10 | 1.85411 | ||||||||
\(216\) | −2.84046e10 | −0.887864 | ||||||||
\(217\) | 1.62493e10 | 0.497470 | ||||||||
\(218\) | −2.38665e10 | −0.715705 | ||||||||
\(219\) | −1.64160e10 | −0.482246 | ||||||||
\(220\) | −1.05823e11 | −3.04563 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.05962e9 | −0.0292795 | ||||||||
\(223\) | 4.40038e10 | 1.19157 | 0.595783 | − | 0.803145i | \(-0.296842\pi\) | ||||
0.595783 | + | 0.803145i | \(0.296842\pi\) | |||||||
\(224\) | 1.89182e9 | 0.0502070 | ||||||||
\(225\) | 3.50030e9 | 0.0910507 | ||||||||
\(226\) | 2.22909e9 | 0.0568381 | ||||||||
\(227\) | −5.01424e9 | −0.125340 | −0.0626698 | − | 0.998034i | \(-0.519962\pi\) | ||||
−0.0626698 | + | 0.998034i | \(0.519962\pi\) | |||||||
\(228\) | −1.70374e10 | −0.417540 | ||||||||
\(229\) | −4.24718e10 | −1.02057 | −0.510283 | − | 0.860007i | \(-0.670459\pi\) | ||||
−0.510283 | + | 0.860007i | \(0.670459\pi\) | |||||||
\(230\) | −7.62150e10 | −1.79583 | ||||||||
\(231\) | 6.41555e9 | 0.148245 | ||||||||
\(232\) | 9.51544e10 | 2.15642 | ||||||||
\(233\) | 7.54306e10 | 1.67666 | 0.838332 | − | 0.545160i | \(-0.183531\pi\) | ||||
0.838332 | + | 0.545160i | \(0.183531\pi\) | |||||||
\(234\) | −1.39938e10 | −0.305116 | ||||||||
\(235\) | −4.83870e10 | −1.03496 | ||||||||
\(236\) | 1.34605e11 | 2.82459 | ||||||||
\(237\) | −1.53400e10 | −0.315834 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.07962e10 | −0.808778 | −0.404389 | − | 0.914587i | \(-0.632516\pi\) | ||||
−0.404389 | + | 0.914587i | \(0.632516\pi\) | |||||||
\(240\) | 1.18683e10 | 0.230907 | ||||||||
\(241\) | 5.72156e10 | 1.09254 | 0.546271 | − | 0.837609i | \(-0.316047\pi\) | ||||
0.546271 | + | 0.837609i | \(0.316047\pi\) | |||||||
\(242\) | 1.55718e11 | 2.91857 | ||||||||
\(243\) | 4.12322e10 | 0.758592 | ||||||||
\(244\) | −9.39257e10 | −1.69641 | ||||||||
\(245\) | −4.80605e10 | −0.852198 | ||||||||
\(246\) | −1.26723e10 | −0.220622 | ||||||||
\(247\) | −8.54723e9 | −0.146113 | ||||||||
\(248\) | −1.51822e11 | −2.54861 | ||||||||
\(249\) | 1.11169e10 | 0.183268 | ||||||||
\(250\) | −1.10720e11 | −1.79266 | ||||||||
\(251\) | −2.21629e10 | −0.352448 | −0.176224 | − | 0.984350i | \(-0.556388\pi\) | ||||
−0.176224 | + | 0.984350i | \(0.556388\pi\) | |||||||
\(252\) | 3.67963e10 | 0.574781 | ||||||||
\(253\) | 1.17850e11 | 1.80837 | ||||||||
\(254\) | −2.15785e11 | −3.25289 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.33357e11 | −1.94060 | ||||||||
\(257\) | −8.84957e10 | −1.26539 | −0.632693 | − | 0.774402i | \(-0.718051\pi\) | ||||
−0.632693 | + | 0.774402i | \(0.718051\pi\) | |||||||
\(258\) | 6.74250e10 | 0.947398 | ||||||||
\(259\) | 1.39779e9 | 0.0193015 | ||||||||
\(260\) | 2.63561e10 | 0.357685 | ||||||||
\(261\) | −9.08283e10 | −1.21154 | ||||||||
\(262\) | 4.91317e10 | 0.644179 | ||||||||
\(263\) | 6.15949e10 | 0.793860 | 0.396930 | − | 0.917849i | \(-0.370076\pi\) | ||||
0.396930 | + | 0.917849i | \(0.370076\pi\) | |||||||
\(264\) | −5.99424e10 | −0.759481 | ||||||||
\(265\) | 6.79485e10 | 0.846396 | ||||||||
\(266\) | 3.39811e10 | 0.416170 | ||||||||
\(267\) | 3.59355e10 | 0.432736 | ||||||||
\(268\) | 1.29806e11 | 1.53705 | ||||||||
\(269\) | 4.19152e10 | 0.488075 | 0.244037 | − | 0.969766i | \(-0.421528\pi\) | ||||
0.244037 | + | 0.969766i | \(0.421528\pi\) | |||||||
\(270\) | −7.72092e10 | −0.884163 | ||||||||
\(271\) | 1.56140e11 | 1.75854 | 0.879272 | − | 0.476319i | \(-0.158029\pi\) | ||||
0.879272 | + | 0.476319i | \(0.158029\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.59785e9 | −0.0174102 | ||||||||
\(274\) | 1.41559e11 | 1.51726 | ||||||||
\(275\) | 1.54128e10 | 0.162511 | ||||||||
\(276\) | −5.85071e10 | −0.606901 | ||||||||
\(277\) | −1.43796e11 | −1.46753 | −0.733765 | − | 0.679404i | \(-0.762238\pi\) | ||||
−0.733765 | + | 0.679404i | \(0.762238\pi\) | |||||||
\(278\) | −8.34851e10 | −0.838316 | ||||||||
\(279\) | 1.44920e11 | 1.43189 | ||||||||
\(280\) | −5.11370e10 | −0.497192 | ||||||||
\(281\) | 8.85329e10 | 0.847083 | 0.423542 | − | 0.905877i | \(-0.360787\pi\) | ||||
0.423542 | + | 0.905877i | \(0.360787\pi\) | |||||||
\(282\) | −5.61618e10 | −0.528835 | ||||||||
\(283\) | 1.83307e10 | 0.169879 | 0.0849394 | − | 0.996386i | \(-0.472930\pi\) | ||||
0.0849394 | + | 0.996386i | \(0.472930\pi\) | |||||||
\(284\) | −2.39281e10 | −0.218261 | ||||||||
\(285\) | −2.26010e10 | −0.202920 | ||||||||
\(286\) | −6.16188e10 | −0.544586 | ||||||||
\(287\) | 1.67165e10 | 0.145438 | ||||||||
\(288\) | 1.68722e10 | 0.144513 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 2.58648e11 | 2.14743 | ||||||||
\(291\) | 6.41868e10 | 0.524720 | ||||||||
\(292\) | −4.14586e11 | −3.33727 | ||||||||
\(293\) | −8.61025e10 | −0.682514 | −0.341257 | − | 0.939970i | \(-0.610853\pi\) | ||||
−0.341257 | + | 0.939970i | \(0.610853\pi\) | |||||||
\(294\) | −5.57829e10 | −0.435449 | ||||||||
\(295\) | 1.78559e11 | 1.37272 | ||||||||
\(296\) | −1.30599e10 | −0.0988846 | ||||||||
\(297\) | 1.19387e11 | 0.890335 | ||||||||
\(298\) | −8.91442e10 | −0.654817 | ||||||||
\(299\) | −2.93515e10 | −0.212378 | ||||||||
\(300\) | −7.65176e9 | −0.0545401 | ||||||||
\(301\) | −8.89426e10 | −0.624540 | ||||||||
\(302\) | −9.01945e10 | −0.623949 | ||||||||
\(303\) | 4.95772e10 | 0.337901 | ||||||||
\(304\) | −9.72032e10 | −0.652754 | ||||||||
\(305\) | −1.24597e11 | −0.824438 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.18874e11 | −0.763775 | −0.381887 | − | 0.924209i | \(-0.624726\pi\) | ||||
−0.381887 | + | 0.924209i | \(0.624726\pi\) | |||||||
\(308\) | 1.62025e11 | 1.02590 | ||||||||
\(309\) | −6.92327e9 | −0.0432014 | ||||||||
\(310\) | −4.12683e11 | −2.53798 | ||||||||
\(311\) | −2.72867e11 | −1.65397 | −0.826987 | − | 0.562220i | \(-0.809947\pi\) | ||||
−0.826987 | + | 0.562220i | \(0.809947\pi\) | |||||||
\(312\) | 1.49292e10 | 0.0891949 | ||||||||
\(313\) | 1.05123e11 | 0.619080 | 0.309540 | − | 0.950886i | \(-0.399825\pi\) | ||||
0.309540 | + | 0.950886i | \(0.399825\pi\) | |||||||
\(314\) | −1.16466e11 | −0.676105 | ||||||||
\(315\) | 4.88121e10 | 0.279338 | ||||||||
\(316\) | −3.87412e11 | −2.18565 | ||||||||
\(317\) | −1.75077e11 | −0.973781 | −0.486891 | − | 0.873463i | \(-0.661869\pi\) | ||||
−0.486891 | + | 0.873463i | \(0.661869\pi\) | |||||||
\(318\) | 7.88666e10 | 0.432485 | ||||||||
\(319\) | −3.99942e11 | −2.16242 | ||||||||
\(320\) | −2.01503e11 | −1.07425 | ||||||||
\(321\) | 4.01664e10 | 0.211150 | ||||||||
\(322\) | 1.16692e11 | 0.604910 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2.97304e11 | 1.49882 | ||||||||
\(325\) | −3.83868e9 | −0.0190857 | ||||||||
\(326\) | −8.48300e10 | −0.415978 | ||||||||
\(327\) | −2.43041e10 | −0.117548 | ||||||||
\(328\) | −1.56187e11 | −0.745099 | ||||||||
\(329\) | 7.40849e10 | 0.348617 | ||||||||
\(330\) | −1.62935e11 | −0.756315 | ||||||||
\(331\) | −1.62608e11 | −0.744588 | −0.372294 | − | 0.928115i | \(-0.621429\pi\) | ||||
−0.372294 | + | 0.928115i | \(0.621429\pi\) | |||||||
\(332\) | 2.80757e11 | 1.26826 | ||||||||
\(333\) | 1.24662e10 | 0.0555565 | ||||||||
\(334\) | −5.08282e11 | −2.23484 | ||||||||
\(335\) | 1.72194e11 | 0.746994 | ||||||||
\(336\) | −1.81715e10 | −0.0777791 | ||||||||
\(337\) | −5.36814e10 | −0.226720 | −0.113360 | − | 0.993554i | \(-0.536161\pi\) | ||||
−0.113360 | + | 0.993554i | \(0.536161\pi\) | |||||||
\(338\) | −3.97010e11 | −1.65454 | ||||||||
\(339\) | 2.26996e9 | 0.00933511 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.38123e11 | 2.55570 | ||||||||
\(342\) | 3.03061e11 | 1.19788 | ||||||||
\(343\) | 1.55550e11 | 0.606801 | ||||||||
\(344\) | 8.31018e11 | 3.19961 | ||||||||
\(345\) | −7.76124e10 | −0.294948 | ||||||||
\(346\) | −1.00695e11 | −0.377715 | ||||||||
\(347\) | −1.15461e11 | −0.427517 | −0.213758 | − | 0.976887i | \(-0.568570\pi\) | ||||
−0.213758 | + | 0.976887i | \(0.568570\pi\) | |||||||
\(348\) | 1.98554e11 | 0.725723 | ||||||||
\(349\) | 1.42013e11 | 0.512404 | 0.256202 | − | 0.966623i | \(-0.417529\pi\) | ||||
0.256202 | + | 0.966623i | \(0.417529\pi\) | |||||||
\(350\) | 1.52614e10 | 0.0543611 | ||||||||
\(351\) | −2.97344e10 | −0.104563 | ||||||||
\(352\) | 7.42933e10 | 0.257933 | ||||||||
\(353\) | 3.90958e11 | 1.34012 | 0.670060 | − | 0.742307i | \(-0.266268\pi\) | ||||
0.670060 | + | 0.742307i | \(0.266268\pi\) | |||||||
\(354\) | 2.07250e11 | 0.701424 | ||||||||
\(355\) | −3.17417e10 | −0.106073 | ||||||||
\(356\) | 9.07552e11 | 2.99465 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.41391e11 | −0.776691 | ||||||||
\(359\) | −4.03346e11 | −1.28160 | −0.640800 | − | 0.767708i | \(-0.721397\pi\) | ||||
−0.640800 | + | 0.767708i | \(0.721397\pi\) | |||||||
\(360\) | −4.56066e11 | −1.43109 | ||||||||
\(361\) | −1.37582e11 | −0.426363 | ||||||||
\(362\) | −4.37768e11 | −1.33985 | ||||||||
\(363\) | 1.58573e11 | 0.479348 | ||||||||
\(364\) | −4.03536e10 | −0.120483 | ||||||||
\(365\) | −5.49968e11 | −1.62188 | ||||||||
\(366\) | −1.44617e11 | −0.421265 | ||||||||
\(367\) | 1.76479e11 | 0.507803 | 0.253901 | − | 0.967230i | \(-0.418286\pi\) | ||||
0.253901 | + | 0.967230i | \(0.418286\pi\) | |||||||
\(368\) | −3.33799e11 | −0.948788 | ||||||||
\(369\) | 1.49087e11 | 0.418620 | ||||||||
\(370\) | −3.54995e10 | −0.0984724 | ||||||||
\(371\) | −1.04036e11 | −0.285101 | ||||||||
\(372\) | −3.16800e11 | −0.857712 | ||||||||
\(373\) | −1.09830e11 | −0.293786 | −0.146893 | − | 0.989152i | \(-0.546927\pi\) | ||||
−0.146893 | + | 0.989152i | \(0.546927\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.12750e11 | −0.294427 | ||||||||
\(376\) | −6.92198e11 | −1.78601 | ||||||||
\(377\) | 9.96090e10 | 0.253958 | ||||||||
\(378\) | 1.18215e11 | 0.297823 | ||||||||
\(379\) | −2.01826e11 | −0.502459 | −0.251230 | − | 0.967928i | \(-0.580835\pi\) | ||||
−0.251230 | + | 0.967928i | \(0.580835\pi\) | |||||||
\(380\) | −5.70788e11 | −1.40426 | ||||||||
\(381\) | −2.19741e11 | −0.534256 | ||||||||
\(382\) | −9.68302e11 | −2.32662 | ||||||||
\(383\) | −4.10697e11 | −0.975275 | −0.487638 | − | 0.873046i | \(-0.662141\pi\) | ||||
−0.487638 | + | 0.873046i | \(0.662141\pi\) | |||||||
\(384\) | −2.14997e11 | −0.504594 | ||||||||
\(385\) | 2.14933e11 | 0.498575 | ||||||||
\(386\) | 1.04996e11 | 0.240729 | ||||||||
\(387\) | −7.93236e11 | −1.79764 | ||||||||
\(388\) | 1.62104e12 | 3.63120 | ||||||||
\(389\) | 8.47825e11 | 1.87730 | 0.938649 | − | 0.344875i | \(-0.112079\pi\) | ||||
0.938649 | + | 0.344875i | \(0.112079\pi\) | |||||||
\(390\) | 4.05804e10 | 0.0888230 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −6.87527e11 | −1.47063 | ||||||||
\(393\) | 5.00326e10 | 0.105800 | ||||||||
\(394\) | −2.71934e10 | −0.0568499 | ||||||||
\(395\) | −5.13921e11 | −1.06221 | ||||||||
\(396\) | 1.44502e12 | 2.95288 | ||||||||
\(397\) | −1.38204e11 | −0.279231 | −0.139615 | − | 0.990206i | \(-0.544587\pi\) | ||||
−0.139615 | + | 0.990206i | \(0.544587\pi\) | |||||||
\(398\) | −6.97888e11 | −1.39416 | ||||||||
\(399\) | 3.46042e10 | 0.0683519 | ||||||||
\(400\) | −4.36553e10 | −0.0852643 | ||||||||
\(401\) | 8.10829e11 | 1.56596 | 0.782978 | − | 0.622050i | \(-0.213700\pi\) | ||||
0.782978 | + | 0.622050i | \(0.213700\pi\) | |||||||
\(402\) | 1.99863e11 | 0.381693 | ||||||||
\(403\) | −1.58930e11 | −0.300146 | ||||||||
\(404\) | 1.25207e12 | 2.33837 | ||||||||
\(405\) | 3.94388e11 | 0.728411 | ||||||||
\(406\) | −3.96014e11 | −0.723342 | ||||||||
\(407\) | 5.48921e10 | 0.0991597 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.60175e11 | 0.989849 | 0.494924 | − | 0.868936i | \(-0.335196\pi\) | ||||
0.494924 | + | 0.868936i | \(0.335196\pi\) | |||||||
\(410\) | −4.24548e11 | −0.741993 | ||||||||
\(411\) | 1.44155e11 | 0.249196 | ||||||||
\(412\) | −1.74847e11 | −0.298966 | ||||||||
\(413\) | −2.73391e11 | −0.462390 | ||||||||
\(414\) | 1.04072e12 | 1.74114 | ||||||||
\(415\) | 3.72438e11 | 0.616364 | ||||||||
\(416\) | −1.85034e10 | −0.0302922 | ||||||||
\(417\) | −8.50159e10 | −0.137685 | ||||||||
\(418\) | 1.33447e12 | 2.13803 | ||||||||
\(419\) | 9.94635e11 | 1.57652 | 0.788262 | − | 0.615340i | \(-0.210981\pi\) | ||||
0.788262 | + | 0.615340i | \(0.210981\pi\) | |||||||
\(420\) | −1.06705e11 | −0.167326 | ||||||||
\(421\) | −4.43656e11 | −0.688299 | −0.344149 | − | 0.938915i | \(-0.611833\pi\) | ||||
−0.344149 | + | 0.938915i | \(0.611833\pi\) | |||||||
\(422\) | −4.96199e11 | −0.761640 | ||||||||
\(423\) | 6.60728e11 | 1.00344 | ||||||||
\(424\) | 9.72036e11 | 1.46062 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.68420e10 | −0.0542001 | ||||||||
\(427\) | 1.90769e11 | 0.277705 | ||||||||
\(428\) | 1.01440e12 | 1.46121 | ||||||||
\(429\) | −6.27487e10 | −0.0894430 | ||||||||
\(430\) | 2.25887e12 | 3.18627 | ||||||||
\(431\) | 7.58706e11 | 1.05907 | 0.529536 | − | 0.848287i | \(-0.322366\pi\) | ||||
0.529536 | + | 0.848287i | \(0.322366\pi\) | |||||||
\(432\) | −3.38153e11 | −0.467129 | ||||||||
\(433\) | 1.31991e12 | 1.80447 | 0.902234 | − | 0.431246i | \(-0.141926\pi\) | ||||
0.902234 | + | 0.431246i | \(0.141926\pi\) | |||||||
\(434\) | 6.31856e11 | 0.854898 | ||||||||
\(435\) | 2.63391e11 | 0.352695 | ||||||||
\(436\) | −6.13800e11 | −0.813462 | ||||||||
\(437\) | 6.35658e11 | 0.833790 | ||||||||
\(438\) | −6.38337e11 | −0.828737 | ||||||||
\(439\) | 3.84672e11 | 0.494312 | 0.247156 | − | 0.968976i | \(-0.420504\pi\) | ||||
0.247156 | + | 0.968976i | \(0.420504\pi\) | |||||||
\(440\) | −2.00819e12 | −2.55427 | ||||||||
\(441\) | 6.56270e11 | 0.826245 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.34971e11 | 0.413228 | 0.206614 | − | 0.978423i | \(-0.433756\pi\) | ||||
0.206614 | + | 0.978423i | \(0.433756\pi\) | |||||||
\(444\) | −2.72515e10 | −0.0332788 | ||||||||
\(445\) | 1.20391e12 | 1.45537 | ||||||||
\(446\) | 1.71109e12 | 2.04770 | ||||||||
\(447\) | −9.07787e10 | −0.107547 | ||||||||
\(448\) | 3.08519e11 | 0.361852 | ||||||||
\(449\) | −1.09901e12 | −1.27612 | −0.638060 | − | 0.769986i | \(-0.720263\pi\) | ||||
−0.638060 | + | 0.769986i | \(0.720263\pi\) | |||||||
\(450\) | 1.36109e11 | 0.156470 | ||||||||
\(451\) | 6.56470e11 | 0.747172 | ||||||||
\(452\) | 5.73278e10 | 0.0646015 | ||||||||
\(453\) | −9.18483e10 | −0.102478 | ||||||||
\(454\) | −1.94979e11 | −0.215395 | ||||||||
\(455\) | −5.35310e10 | −0.0585536 | ||||||||
\(456\) | −3.23318e11 | −0.350177 | ||||||||
\(457\) | 1.31545e12 | 1.41075 | 0.705376 | − | 0.708833i | \(-0.250778\pi\) | ||||
0.705376 | + | 0.708833i | \(0.250778\pi\) | |||||||
\(458\) | −1.65152e12 | −1.75384 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.96010e12 | −2.04112 | ||||||||
\(461\) | −1.21831e12 | −1.25633 | −0.628163 | − | 0.778082i | \(-0.716193\pi\) | ||||
−0.628163 | + | 0.778082i | \(0.716193\pi\) | |||||||
\(462\) | 2.49469e11 | 0.254758 | ||||||||
\(463\) | −1.04671e12 | −1.05856 | −0.529278 | − | 0.848449i | \(-0.677537\pi\) | ||||
−0.529278 | + | 0.848449i | \(0.677537\pi\) | |||||||
\(464\) | 1.13280e12 | 1.13455 | ||||||||
\(465\) | −4.20250e11 | −0.416840 | ||||||||
\(466\) | 2.93312e12 | 2.88134 | ||||||||
\(467\) | 5.48990e11 | 0.534119 | 0.267060 | − | 0.963680i | \(-0.413948\pi\) | ||||
0.267060 | + | 0.963680i | \(0.413948\pi\) | |||||||
\(468\) | −3.59895e11 | −0.346792 | ||||||||
\(469\) | −2.63645e11 | −0.251618 | ||||||||
\(470\) | −1.88153e12 | −1.77857 | ||||||||
\(471\) | −1.18601e11 | −0.111044 | ||||||||
\(472\) | 2.55437e12 | 2.36889 | ||||||||
\(473\) | −3.49284e12 | −3.20851 | ||||||||
\(474\) | −5.96498e11 | −0.542758 | ||||||||
\(475\) | 8.31335e10 | 0.0749299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.27843e11 | −0.820619 | ||||||||
\(478\) | −1.58636e12 | −1.38988 | ||||||||
\(479\) | 8.94844e11 | 0.776672 | 0.388336 | − | 0.921518i | \(-0.373050\pi\) | ||||
0.388336 | + | 0.921518i | \(0.373050\pi\) | |||||||
\(480\) | −4.89274e10 | −0.0420694 | ||||||||
\(481\) | −1.36713e10 | −0.0116455 | ||||||||
\(482\) | 2.22483e12 | 1.87753 | ||||||||
\(483\) | 1.18832e11 | 0.0993507 | ||||||||
\(484\) | 4.00477e12 | 3.31721 | ||||||||
\(485\) | 2.15038e12 | 1.76473 | ||||||||
\(486\) | 1.60332e12 | 1.30363 | ||||||||
\(487\) | 4.43593e11 | 0.357359 | 0.178679 | − | 0.983907i | \(-0.442818\pi\) | ||||
0.178679 | + | 0.983907i | \(0.442818\pi\) | |||||||
\(488\) | −1.78242e12 | −1.42272 | ||||||||
\(489\) | −8.63854e10 | −0.0683204 | ||||||||
\(490\) | −1.86883e12 | −1.46450 | ||||||||
\(491\) | −7.29563e11 | −0.566495 | −0.283247 | − | 0.959047i | \(-0.591412\pi\) | ||||
−0.283247 | + | 0.959047i | \(0.591412\pi\) | |||||||
\(492\) | −3.25908e11 | −0.250757 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −3.32360e11 | −0.251094 | ||||||||
\(495\) | 1.91689e12 | 1.43507 | ||||||||
\(496\) | −1.80743e12 | −1.34089 | ||||||||
\(497\) | 4.85995e10 | 0.0357296 | ||||||||
\(498\) | 4.32281e11 | 0.314945 | ||||||||
\(499\) | −3.28866e11 | −0.237447 | −0.118723 | − | 0.992927i | \(-0.537880\pi\) | ||||
−0.118723 | + | 0.992927i | \(0.537880\pi\) | |||||||
\(500\) | −2.84751e12 | −2.03751 | ||||||||
\(501\) | −5.17602e11 | −0.367051 | ||||||||
\(502\) | −8.61808e11 | −0.605680 | ||||||||
\(503\) | 1.15730e12 | 0.806099 | 0.403049 | − | 0.915178i | \(-0.367950\pi\) | ||||
0.403049 | + | 0.915178i | \(0.367950\pi\) | |||||||
\(504\) | 6.98280e11 | 0.482050 | ||||||||
\(505\) | 1.66093e12 | 1.13642 | ||||||||
\(506\) | 4.58259e12 | 3.10766 | ||||||||
\(507\) | −4.04289e11 | −0.271742 | ||||||||
\(508\) | −5.54957e12 | −3.69719 | ||||||||
\(509\) | −1.53067e12 | −1.01077 | −0.505384 | − | 0.862895i | \(-0.668649\pi\) | ||||
−0.505384 | + | 0.862895i | \(0.668649\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.42052e11 | 0.546317 | ||||||||
\(512\) | −2.40569e12 | −1.54712 | ||||||||
\(513\) | 6.43950e11 | 0.410510 | ||||||||
\(514\) | −3.44116e12 | −2.17456 | ||||||||
\(515\) | −2.31943e11 | −0.145294 | ||||||||
\(516\) | 1.73404e12 | 1.07680 | ||||||||
\(517\) | 2.90937e12 | 1.79098 | ||||||||
\(518\) | 5.43530e10 | 0.0331696 | ||||||||
\(519\) | −1.02541e11 | −0.0620361 | ||||||||
\(520\) | 5.00156e11 | 0.299979 | ||||||||
\(521\) | −8.28369e11 | −0.492554 | −0.246277 | − | 0.969199i | \(-0.579207\pi\) | ||||
−0.246277 | + | 0.969199i | \(0.579207\pi\) | |||||||
\(522\) | −3.53186e12 | −2.08203 | ||||||||
\(523\) | −1.93852e12 | −1.13295 | −0.566476 | − | 0.824078i | \(-0.691694\pi\) | ||||
−0.566476 | + | 0.824078i | \(0.691694\pi\) | |||||||
\(524\) | 1.26357e12 | 0.732166 | ||||||||
\(525\) | 1.55412e10 | 0.00892830 | ||||||||
\(526\) | 2.39512e12 | 1.36424 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −7.13607e11 | −0.399583 | ||||||||
\(529\) | 3.81715e11 | 0.211928 | ||||||||
\(530\) | 2.64218e12 | 1.45453 | ||||||||
\(531\) | −2.43824e12 | −1.33092 | ||||||||
\(532\) | 8.73929e11 | 0.473014 | ||||||||
\(533\) | −1.63499e11 | −0.0877493 | ||||||||
\(534\) | 1.39736e12 | 0.743655 | ||||||||
\(535\) | 1.34565e12 | 0.710136 | ||||||||
\(536\) | 2.46332e12 | 1.28908 | ||||||||
\(537\) | −2.45818e11 | −0.127564 | ||||||||
\(538\) | 1.62988e12 | 0.838753 | ||||||||
\(539\) | 2.88974e12 | 1.47472 | ||||||||
\(540\) | −1.98567e12 | −1.00493 | ||||||||
\(541\) | 8.12932e11 | 0.408006 | 0.204003 | − | 0.978970i | \(-0.434605\pi\) | ||||
0.204003 | + | 0.978970i | \(0.434605\pi\) | |||||||
\(542\) | 6.07153e12 | 3.02205 | ||||||||
\(543\) | −4.45795e11 | −0.220057 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.14234e11 | −0.395335 | ||||||||
\(546\) | −6.21324e10 | −0.0299193 | ||||||||
\(547\) | 1.04434e12 | 0.498768 | 0.249384 | − | 0.968405i | \(-0.419772\pi\) | ||||
0.249384 | + | 0.968405i | \(0.419772\pi\) | |||||||
\(548\) | 3.64063e12 | 1.72450 | ||||||||
\(549\) | 1.70138e12 | 0.799330 | ||||||||
\(550\) | 5.99327e11 | 0.279275 | ||||||||
\(551\) | −2.15721e12 | −0.997035 | ||||||||
\(552\) | −1.11028e12 | −0.508988 | ||||||||
\(553\) | 7.86860e11 | 0.357795 | ||||||||
\(554\) | −5.59150e12 | −2.52194 | ||||||||
\(555\) | −3.61504e10 | −0.0161732 | ||||||||
\(556\) | −2.14708e12 | −0.952820 | ||||||||
\(557\) | −3.24890e12 | −1.43017 | −0.715086 | − | 0.699036i | \(-0.753613\pi\) | ||||
−0.715086 | + | 0.699036i | \(0.753613\pi\) | |||||||
\(558\) | 5.63522e12 | 2.46069 | ||||||||
\(559\) | 8.69922e11 | 0.376814 | ||||||||
\(560\) | −6.08779e11 | −0.261586 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.44261e12 | 1.45571 | ||||||||
\(563\) | 4.37456e11 | 0.183504 | 0.0917522 | − | 0.995782i | \(-0.470753\pi\) | ||||
0.0917522 | + | 0.995782i | \(0.470753\pi\) | |||||||
\(564\) | −1.44437e12 | −0.601068 | ||||||||
\(565\) | 7.60481e10 | 0.0313957 | ||||||||
\(566\) | 7.12789e11 | 0.291936 | ||||||||
\(567\) | −6.03845e11 | −0.245359 | ||||||||
\(568\) | −4.54080e11 | −0.183048 | ||||||||
\(569\) | −2.44467e12 | −0.977720 | −0.488860 | − | 0.872362i | \(-0.662587\pi\) | ||||
−0.488860 | + | 0.872362i | \(0.662587\pi\) | |||||||
\(570\) | −8.78841e11 | −0.348717 | ||||||||
\(571\) | 4.30219e12 | 1.69366 | 0.846832 | − | 0.531860i | \(-0.178507\pi\) | ||||
0.846832 | + | 0.531860i | \(0.178507\pi\) | |||||||
\(572\) | −1.58472e12 | −0.618970 | ||||||||
\(573\) | −9.86056e11 | −0.382125 | ||||||||
\(574\) | 6.50023e11 | 0.249934 | ||||||||
\(575\) | 2.85483e11 | 0.108912 | ||||||||
\(576\) | 2.75154e12 | 1.04154 | ||||||||
\(577\) | 1.04390e12 | 0.392075 | 0.196037 | − | 0.980596i | \(-0.437193\pi\) | ||||
0.196037 | + | 0.980596i | \(0.437193\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.06921e11 | 0.0395374 | ||||||||
\(580\) | 6.65193e12 | 2.44074 | ||||||||
\(581\) | −5.70237e11 | −0.207617 | ||||||||
\(582\) | 2.49591e12 | 0.901727 | ||||||||
\(583\) | −4.08555e12 | −1.46468 | ||||||||
\(584\) | −7.86755e12 | −2.79886 | ||||||||
\(585\) | −4.77417e11 | −0.168537 | ||||||||
\(586\) | −3.34810e12 | −1.17290 | ||||||||
\(587\) | −2.53007e12 | −0.879552 | −0.439776 | − | 0.898107i | \(-0.644942\pi\) | ||||
−0.439776 | + | 0.898107i | \(0.644942\pi\) | |||||||
\(588\) | −1.43463e12 | −0.494927 | ||||||||
\(589\) | 3.44191e12 | 1.17837 | ||||||||
\(590\) | 6.94329e12 | 2.35902 | ||||||||
\(591\) | −2.76920e10 | −0.00933706 | ||||||||
\(592\) | −1.55477e11 | −0.0520258 | ||||||||
\(593\) | 2.29492e11 | 0.0762117 | 0.0381058 | − | 0.999274i | \(-0.487868\pi\) | ||||
0.0381058 | + | 0.999274i | \(0.487868\pi\) | |||||||
\(594\) | 4.64237e12 | 1.53003 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.29262e12 | −0.744258 | ||||||||
\(597\) | −7.10684e11 | −0.228977 | ||||||||
\(598\) | −1.14133e12 | −0.364970 | ||||||||
\(599\) | 2.96044e12 | 0.939583 | 0.469792 | − | 0.882777i | \(-0.344329\pi\) | ||||
0.469792 | + | 0.882777i | \(0.344329\pi\) | |||||||
\(600\) | −1.45207e11 | −0.0457410 | ||||||||
\(601\) | 2.71047e12 | 0.847443 | 0.423721 | − | 0.905793i | \(-0.360724\pi\) | ||||
0.423721 | + | 0.905793i | \(0.360724\pi\) | |||||||
\(602\) | −3.45854e12 | −1.07327 | ||||||||
\(603\) | −2.35133e12 | −0.724244 | ||||||||
\(604\) | −2.31963e12 | −0.709173 | ||||||||
\(605\) | 5.31252e12 | 1.61213 | ||||||||
\(606\) | 1.92781e12 | 0.580681 | ||||||||
\(607\) | −2.72636e12 | −0.815142 | −0.407571 | − | 0.913173i | \(-0.633624\pi\) | ||||
−0.407571 | + | 0.913173i | \(0.633624\pi\) | |||||||
\(608\) | 4.00723e11 | 0.118926 | ||||||||
\(609\) | −4.03276e11 | −0.118802 | ||||||||
\(610\) | −4.84496e12 | −1.41679 | ||||||||
\(611\) | −7.24603e11 | −0.210337 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.18239e12 | 0.910294 | 0.455147 | − | 0.890416i | \(-0.349587\pi\) | ||||
0.455147 | + | 0.890416i | \(0.349587\pi\) | |||||||
\(614\) | −4.62243e12 | −1.31254 | ||||||||
\(615\) | −4.32332e11 | −0.121865 | ||||||||
\(616\) | 3.07472e12 | 0.860385 | ||||||||
\(617\) | −5.80402e12 | −1.61230 | −0.806150 | − | 0.591712i | \(-0.798452\pi\) | ||||
−0.806150 | + | 0.591712i | \(0.798452\pi\) | |||||||
\(618\) | −2.69212e11 | −0.0742414 | ||||||||
\(619\) | −2.54189e12 | −0.695903 | −0.347952 | − | 0.937512i | \(-0.613123\pi\) | ||||
−0.347952 | + | 0.937512i | \(0.613123\pi\) | |||||||
\(620\) | −1.06134e13 | −2.88464 | ||||||||
\(621\) | 2.21134e12 | 0.596684 | ||||||||
\(622\) | −1.06104e13 | −2.84234 | ||||||||
\(623\) | −1.84330e12 | −0.490230 | ||||||||
\(624\) | 1.77730e11 | 0.0469278 | ||||||||
\(625\) | −3.39997e12 | −0.891281 | ||||||||
\(626\) | 4.08770e12 | 1.06388 | ||||||||
\(627\) | 1.35893e12 | 0.351151 | ||||||||
\(628\) | −2.99527e12 | −0.768453 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1.89806e12 | 0.480040 | ||||||||
\(631\) | −6.29472e12 | −1.58068 | −0.790340 | − | 0.612668i | \(-0.790096\pi\) | ||||
−0.790340 | + | 0.612668i | \(0.790096\pi\) | |||||||
\(632\) | −7.35187e12 | −1.83304 | ||||||||
\(633\) | −5.05297e11 | −0.125092 | ||||||||
\(634\) | −6.80787e12 | −1.67344 | ||||||||
\(635\) | −7.36176e12 | −1.79680 | ||||||||
\(636\) | 2.02830e12 | 0.491557 | ||||||||
\(637\) | −7.19714e11 | −0.173194 | ||||||||
\(638\) | −1.55518e13 | −3.71610 | ||||||||
\(639\) | 4.33436e11 | 0.102842 | ||||||||
\(640\) | −7.20282e12 | −1.69704 | ||||||||
\(641\) | 4.27476e12 | 1.00012 | 0.500058 | − | 0.865992i | \(-0.333312\pi\) | ||||
0.500058 | + | 0.865992i | \(0.333312\pi\) | |||||||
\(642\) | 1.56188e12 | 0.362860 | ||||||||
\(643\) | 3.30486e12 | 0.762437 | 0.381218 | − | 0.924485i | \(-0.375505\pi\) | ||||
0.381218 | + | 0.924485i | \(0.375505\pi\) | |||||||
\(644\) | 3.00110e12 | 0.687533 | ||||||||
\(645\) | 2.30029e12 | 0.523315 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.81390e12 | 0.406952 | 0.203476 | − | 0.979080i | \(-0.434776\pi\) | ||||
0.203476 | + | 0.979080i | \(0.434776\pi\) | |||||||
\(648\) | 5.64191e12 | 1.25701 | ||||||||
\(649\) | −1.07363e13 | −2.37548 | ||||||||
\(650\) | −1.49268e11 | −0.0327986 | ||||||||
\(651\) | 6.43442e11 | 0.140409 | ||||||||
\(652\) | −2.18166e12 | −0.472796 | ||||||||
\(653\) | −1.96397e12 | −0.422694 | −0.211347 | − | 0.977411i | \(-0.567785\pi\) | ||||
−0.211347 | + | 0.977411i | \(0.567785\pi\) | |||||||
\(654\) | −9.45066e11 | −0.202005 | ||||||||
\(655\) | 1.67619e12 | 0.355826 | ||||||||
\(656\) | −1.85939e12 | −0.392016 | ||||||||
\(657\) | 7.50986e12 | 1.57249 | ||||||||
\(658\) | 2.88080e12 | 0.599096 | ||||||||
\(659\) | 1.93103e11 | 0.0398845 | 0.0199422 | − | 0.999801i | \(-0.493652\pi\) | ||||
0.0199422 | + | 0.999801i | \(0.493652\pi\) | |||||||
\(660\) | −4.19038e12 | −0.859618 | ||||||||
\(661\) | 1.01510e10 | 0.00206825 | 0.00103413 | − | 0.999999i | \(-0.499671\pi\) | ||||
0.00103413 | + | 0.999999i | \(0.499671\pi\) | |||||||
\(662\) | −6.32302e12 | −1.27957 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.32790e12 | 1.06365 | ||||||||
\(665\) | 1.15931e12 | 0.229880 | ||||||||
\(666\) | 4.84749e11 | 0.0954734 | ||||||||
\(667\) | −7.40792e12 | −1.44921 | ||||||||
\(668\) | −1.30720e13 | −2.54009 | ||||||||
\(669\) | 1.74246e12 | 0.336315 | ||||||||
\(670\) | 6.69578e12 | 1.28370 | ||||||||
\(671\) | 7.49166e12 | 1.42668 | ||||||||
\(672\) | 7.49124e10 | 0.0141707 | ||||||||
\(673\) | −6.50508e12 | −1.22232 | −0.611160 | − | 0.791507i | \(-0.709297\pi\) | ||||
−0.611160 | + | 0.791507i | \(0.709297\pi\) | |||||||
\(674\) | −2.08741e12 | −0.389617 | ||||||||
\(675\) | 2.89207e11 | 0.0536219 | ||||||||
\(676\) | −1.02103e13 | −1.88053 | ||||||||
\(677\) | −9.60958e12 | −1.75815 | −0.879074 | − | 0.476685i | \(-0.841838\pi\) | ||||
−0.879074 | + | 0.476685i | \(0.841838\pi\) | |||||||
\(678\) | 8.82675e10 | 0.0160423 | ||||||||
\(679\) | −3.29244e12 | −0.594433 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.98554e11 | −0.0353766 | ||||||||
\(682\) | 2.48135e13 | 4.39196 | ||||||||
\(683\) | −5.49684e11 | −0.0966541 | −0.0483271 | − | 0.998832i | \(-0.515389\pi\) | ||||
−0.0483271 | + | 0.998832i | \(0.515389\pi\) | |||||||
\(684\) | 7.79415e12 | 1.36150 | ||||||||
\(685\) | 4.82947e12 | 0.838092 | ||||||||
\(686\) | 6.04857e12 | 1.04278 | ||||||||
\(687\) | −1.68180e12 | −0.288051 | ||||||||
\(688\) | 9.89316e12 | 1.68340 | ||||||||
\(689\) | 1.01754e12 | 0.172015 | ||||||||
\(690\) | −3.01797e12 | −0.506866 | ||||||||
\(691\) | −1.00783e13 | −1.68166 | −0.840828 | − | 0.541302i | \(-0.817932\pi\) | ||||
−0.840828 | + | 0.541302i | \(0.817932\pi\) | |||||||
\(692\) | −2.58967e12 | −0.429306 | ||||||||
\(693\) | −2.93493e12 | −0.483391 | ||||||||
\(694\) | −4.48971e12 | −0.734684 | ||||||||
\(695\) | −2.84820e12 | −0.463061 | ||||||||
\(696\) | 3.76793e12 | 0.608641 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 5.52217e12 | 0.880562 | ||||||||
\(699\) | 2.98691e12 | 0.473232 | ||||||||
\(700\) | 3.92494e11 | 0.0617862 | ||||||||
\(701\) | −9.77792e11 | −0.152938 | −0.0764690 | − | 0.997072i | \(-0.524365\pi\) | ||||
−0.0764690 | + | 0.997072i | \(0.524365\pi\) | |||||||
\(702\) | −1.15622e12 | −0.179690 | ||||||||
\(703\) | 2.96077e11 | 0.0457200 | ||||||||
\(704\) | 1.21158e13 | 1.85898 | ||||||||
\(705\) | −1.91603e12 | −0.292113 | ||||||||
\(706\) | 1.52024e13 | 2.30299 | ||||||||
\(707\) | −2.54304e12 | −0.382795 | ||||||||
\(708\) | 5.33008e12 | 0.797230 | ||||||||
\(709\) | −1.08153e13 | −1.60743 | −0.803714 | − | 0.595016i | \(-0.797146\pi\) | ||||
−0.803714 | + | 0.595016i | \(0.797146\pi\) | |||||||
\(710\) | −1.23428e12 | −0.182285 | ||||||||
\(711\) | 7.01763e12 | 1.02986 | ||||||||
\(712\) | 1.72225e13 | 2.51152 | ||||||||
\(713\) | 1.18196e13 | 1.71278 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.10220e12 | −0.300813 | ||||||||
\(716\) | −6.20812e12 | −0.882778 | ||||||||
\(717\) | −1.61545e12 | −0.228274 | ||||||||
\(718\) | −1.56841e13 | −2.20242 | ||||||||
\(719\) | 1.62784e12 | 0.227161 | 0.113580 | − | 0.993529i | \(-0.463768\pi\) | ||||
0.113580 | + | 0.993529i | \(0.463768\pi\) | |||||||
\(720\) | −5.42941e12 | −0.752933 | ||||||||
\(721\) | 3.55126e11 | 0.0489411 | ||||||||
\(722\) | −5.34989e12 | −0.732703 | ||||||||
\(723\) | 2.26563e12 | 0.308366 | ||||||||
\(724\) | −1.12585e13 | −1.52286 | ||||||||
\(725\) | −9.68834e11 | −0.130235 | ||||||||
\(726\) | 6.16614e12 | 0.823756 | ||||||||
\(727\) | 2.04920e12 | 0.272069 | 0.136035 | − | 0.990704i | \(-0.456564\pi\) | ||||
0.136035 | + | 0.990704i | \(0.456564\pi\) | |||||||
\(728\) | −7.65786e11 | −0.101045 | ||||||||
\(729\) | −4.21884e12 | −0.553248 | ||||||||
\(730\) | −2.13855e13 | −2.78720 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −3.71927e12 | −0.478805 | ||||||||
\(733\) | −2.62355e12 | −0.335677 | −0.167839 | − | 0.985814i | \(-0.553679\pi\) | ||||
−0.167839 | + | 0.985814i | \(0.553679\pi\) | |||||||
\(734\) | 6.86239e12 | 0.872656 | ||||||||
\(735\) | −1.90310e12 | −0.240530 | ||||||||
\(736\) | 1.37610e12 | 0.172862 | ||||||||
\(737\) | −1.03536e13 | −1.29266 | ||||||||
\(738\) | 5.79724e12 | 0.719396 | ||||||||
\(739\) | 1.33151e13 | 1.64227 | 0.821133 | − | 0.570737i | \(-0.193342\pi\) | ||||
0.821133 | + | 0.570737i | \(0.193342\pi\) | |||||||
\(740\) | −9.12978e11 | −0.111923 | ||||||||
\(741\) | −3.38454e11 | −0.0412399 | ||||||||
\(742\) | −4.04543e12 | −0.489945 | ||||||||
\(743\) | −6.67750e11 | −0.0803830 | −0.0401915 | − | 0.999192i | \(-0.512797\pi\) | ||||
−0.0401915 | + | 0.999192i | \(0.512797\pi\) | |||||||
\(744\) | −6.01187e12 | −0.719336 | ||||||||
\(745\) | −3.04126e12 | −0.361702 | ||||||||
\(746\) | −4.27074e12 | −0.504869 | ||||||||
\(747\) | −5.08567e12 | −0.597593 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.06032e12 | −0.239203 | ||||||||
\(750\) | −4.38431e12 | −0.505971 | ||||||||
\(751\) | 4.40301e12 | 0.505092 | 0.252546 | − | 0.967585i | \(-0.418732\pi\) | ||||
0.252546 | + | 0.967585i | \(0.418732\pi\) | |||||||
\(752\) | −8.24053e12 | −0.939669 | ||||||||
\(753\) | −8.77609e11 | −0.0994773 | ||||||||
\(754\) | 3.87330e12 | 0.436426 | ||||||||
\(755\) | −3.07710e12 | −0.344651 | ||||||||
\(756\) | 3.04025e12 | 0.338502 | ||||||||
\(757\) | 1.43998e12 | 0.159376 | 0.0796882 | − | 0.996820i | \(-0.474608\pi\) | ||||
0.0796882 | + | 0.996820i | \(0.474608\pi\) | |||||||
\(758\) | −7.84802e12 | −0.863473 | ||||||||
\(759\) | 4.66662e12 | 0.510404 | ||||||||
\(760\) | −1.08318e13 | −1.17771 | ||||||||
\(761\) | 1.23305e13 | 1.33276 | 0.666379 | − | 0.745613i | \(-0.267843\pi\) | ||||
0.666379 | + | 0.745613i | \(0.267843\pi\) | |||||||
\(762\) | −8.54465e12 | −0.918115 | ||||||||
\(763\) | 1.24667e12 | 0.133165 | ||||||||
\(764\) | −2.49028e13 | −2.64441 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.59700e13 | −1.67600 | ||||||||
\(767\) | 2.67396e12 | 0.278982 | ||||||||
\(768\) | −5.28067e12 | −0.547726 | ||||||||
\(769\) | 7.33617e12 | 0.756486 | 0.378243 | − | 0.925706i | \(-0.376528\pi\) | ||||
0.378243 | + | 0.925706i | \(0.376528\pi\) | |||||||
\(770\) | 8.35770e12 | 0.856798 | ||||||||
\(771\) | −3.50426e12 | −0.357151 | ||||||||
\(772\) | 2.70028e12 | 0.273610 | ||||||||
\(773\) | 1.30977e13 | 1.31944 | 0.659718 | − | 0.751513i | \(-0.270676\pi\) | ||||
0.659718 | + | 0.751513i | \(0.270676\pi\) | |||||||
\(774\) | −3.08450e13 | −3.08924 | ||||||||
\(775\) | 1.54581e12 | 0.153921 | ||||||||
\(776\) | 3.07622e13 | 3.04537 | ||||||||
\(777\) | 5.53496e10 | 0.00544779 | ||||||||
\(778\) | 3.29677e13 | 3.22612 | ||||||||
\(779\) | 3.54087e12 | 0.344502 | ||||||||
\(780\) | 1.04365e12 | 0.100955 | ||||||||
\(781\) | 1.90854e12 | 0.183557 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.50456e12 | −0.713506 | ||||||||
\(784\) | −8.18493e12 | −0.773735 | ||||||||
\(785\) | −3.97337e12 | −0.373461 | ||||||||
\(786\) | 1.94552e12 | 0.181817 | ||||||||
\(787\) | −1.90562e13 | −1.77072 | −0.885358 | − | 0.464910i | \(-0.846087\pi\) | ||||
−0.885358 | + | 0.464910i | \(0.846087\pi\) | |||||||
\(788\) | −6.99360e11 | −0.0646150 | ||||||||
\(789\) | 2.43904e12 | 0.224064 | ||||||||
\(790\) | −1.99838e13 | −1.82540 | ||||||||
\(791\) | −1.16437e11 | −0.0105754 | ||||||||
\(792\) | 2.74220e13 | 2.47648 | ||||||||
\(793\) | −1.86586e12 | −0.167552 | ||||||||
\(794\) | −5.37407e12 | −0.479856 | ||||||||
\(795\) | 2.69063e12 | 0.238892 | ||||||||
\(796\) | −1.79483e13 | −1.58458 | ||||||||
\(797\) | 1.05555e13 | 0.926652 | 0.463326 | − | 0.886188i | \(-0.346656\pi\) | ||||
0.463326 | + | 0.886188i | \(0.346656\pi\) | |||||||
\(798\) | 1.34559e12 | 0.117462 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1.79970e11 | 0.0155345 | ||||||||
\(801\) | −1.64395e13 | −1.41105 | ||||||||
\(802\) | 3.15291e13 | 2.69108 | ||||||||
\(803\) | 3.30680e13 | 2.80665 | ||||||||
\(804\) | 5.14008e12 | 0.433828 | ||||||||
\(805\) | 3.98110e12 | 0.334135 | ||||||||
\(806\) | −6.18000e12 | −0.515800 | ||||||||
\(807\) | 1.65976e12 | 0.137757 | ||||||||
\(808\) | 2.37604e13 | 1.96111 | ||||||||
\(809\) | 7.11754e12 | 0.584200 | 0.292100 | − | 0.956388i | \(-0.405646\pi\) | ||||
0.292100 | + | 0.956388i | \(0.405646\pi\) | |||||||
\(810\) | 1.53358e13 | 1.25177 | ||||||||
\(811\) | −1.96032e13 | −1.59123 | −0.795616 | − | 0.605802i | \(-0.792852\pi\) | ||||
−0.795616 | + | 0.605802i | \(0.792852\pi\) | |||||||
\(812\) | −1.01847e13 | −0.822142 | ||||||||
\(813\) | 6.18285e12 | 0.496343 | ||||||||
\(814\) | 2.13448e12 | 0.170405 | ||||||||
\(815\) | −2.89408e12 | −0.229774 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.88397e13 | −1.47936 | ||||||||
\(818\) | 2.17824e13 | 1.70105 | ||||||||
\(819\) | 7.30970e11 | 0.0567704 | ||||||||
\(820\) | −1.09186e13 | −0.843340 | ||||||||
\(821\) | 2.57782e13 | 1.98020 | 0.990099 | − | 0.140370i | \(-0.0448291\pi\) | ||||
0.990099 | + | 0.140370i | \(0.0448291\pi\) | |||||||
\(822\) | 5.60547e12 | 0.428242 | ||||||||
\(823\) | −1.81960e13 | −1.38254 | −0.691270 | − | 0.722597i | \(-0.742948\pi\) | ||||
−0.691270 | + | 0.722597i | \(0.742948\pi\) | |||||||
\(824\) | −3.31805e12 | −0.250733 | ||||||||
\(825\) | 6.10316e11 | 0.0458683 | ||||||||
\(826\) | −1.06308e13 | −0.794615 | ||||||||
\(827\) | 1.68619e13 | 1.25352 | 0.626760 | − | 0.779213i | \(-0.284381\pi\) | ||||
0.626760 | + | 0.779213i | \(0.284381\pi\) | |||||||
\(828\) | 2.67654e13 | 1.97896 | ||||||||
\(829\) | −2.04363e13 | −1.50282 | −0.751411 | − | 0.659834i | \(-0.770626\pi\) | ||||
−0.751411 | + | 0.659834i | \(0.770626\pi\) | |||||||
\(830\) | 1.44823e13 | 1.05922 | ||||||||
\(831\) | −5.69403e12 | −0.414205 | ||||||||
\(832\) | −3.01754e12 | −0.218322 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.30585e12 | −0.236611 | ||||||||
\(835\) | −1.73407e13 | −1.23446 | ||||||||
\(836\) | 3.43199e13 | 2.43006 | ||||||||
\(837\) | 1.19738e13 | 0.843273 | ||||||||
\(838\) | 3.86765e13 | 2.70925 | ||||||||
\(839\) | −1.01784e13 | −0.709167 | −0.354584 | − | 0.935024i | \(-0.615377\pi\) | ||||
−0.354584 | + | 0.935024i | \(0.615377\pi\) | |||||||
\(840\) | −2.02492e12 | −0.140331 | ||||||||
\(841\) | 1.06329e13 | 0.732940 | ||||||||
\(842\) | −1.72516e13 | −1.18284 | ||||||||
\(843\) | 3.50573e12 | 0.239086 | ||||||||
\(844\) | −1.27613e13 | −0.865671 | ||||||||
\(845\) | −1.35445e13 | −0.913918 | ||||||||
\(846\) | 2.56924e13 | 1.72440 | ||||||||
\(847\) | −8.13396e12 | −0.543033 | ||||||||
\(848\) | 1.15720e13 | 0.768468 | ||||||||
\(849\) | 7.25859e11 | 0.0479477 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.01674e12 | 0.0664548 | ||||||||
\(852\) | −9.47505e11 | −0.0616032 | ||||||||
\(853\) | −1.86820e13 | −1.20824 | −0.604119 | − | 0.796894i | \(-0.706475\pi\) | ||||
−0.604119 | + | 0.796894i | \(0.706475\pi\) | |||||||
\(854\) | 7.41808e12 | 0.477234 | ||||||||
\(855\) | 1.03393e13 | 0.661674 | ||||||||
\(856\) | 1.92502e13 | 1.22547 | ||||||||
\(857\) | 7.29110e12 | 0.461721 | 0.230860 | − | 0.972987i | \(-0.425846\pi\) | ||||
0.230860 | + | 0.972987i | \(0.425846\pi\) | |||||||
\(858\) | −2.43999e12 | −0.153707 | ||||||||
\(859\) | 4.02170e12 | 0.252023 | 0.126011 | − | 0.992029i | \(-0.459782\pi\) | ||||
0.126011 | + | 0.992029i | \(0.459782\pi\) | |||||||
\(860\) | 5.80937e13 | 3.62148 | ||||||||
\(861\) | 6.61941e11 | 0.0410492 | ||||||||
\(862\) | 2.95023e13 | 1.82001 | ||||||||
\(863\) | −1.68689e13 | −1.03523 | −0.517617 | − | 0.855613i | \(-0.673181\pi\) | ||||
−0.517617 | + | 0.855613i | \(0.673181\pi\) | |||||||
\(864\) | 1.39405e12 | 0.0851070 | ||||||||
\(865\) | −3.43532e12 | −0.208639 | ||||||||
\(866\) | 5.13249e13 | 3.10097 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.62501e13 | 0.971667 | ||||||||
\(869\) | 3.09006e13 | 1.83814 | ||||||||
\(870\) | 1.02420e13 | 0.606103 | ||||||||
\(871\) | 2.57864e12 | 0.151813 | ||||||||
\(872\) | −1.16480e13 | −0.682224 | ||||||||
\(873\) | −2.93637e13 | −1.71098 | ||||||||
\(874\) | 2.47176e13 | 1.43286 | ||||||||
\(875\) | 5.78349e12 | 0.333544 | ||||||||
\(876\) | −1.64168e13 | −0.941933 | ||||||||
\(877\) | −9.39568e12 | −0.536328 | −0.268164 | − | 0.963373i | \(-0.586417\pi\) | ||||
−0.268164 | + | 0.963373i | \(0.586417\pi\) | |||||||
\(878\) | 1.49580e13 | 0.849471 | ||||||||
\(879\) | −3.40949e12 | −0.192637 | ||||||||
\(880\) | −2.39072e13 | −1.34387 | ||||||||
\(881\) | 2.49688e13 | 1.39639 | 0.698194 | − | 0.715909i | \(-0.253987\pi\) | ||||
0.698194 | + | 0.715909i | \(0.253987\pi\) | |||||||
\(882\) | 2.55191e13 | 1.41990 | ||||||||
\(883\) | −1.24749e13 | −0.690578 | −0.345289 | − | 0.938496i | \(-0.612219\pi\) | ||||
−0.345289 | + | 0.938496i | \(0.612219\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.07060e12 | 0.387446 | ||||||||
\(886\) | 1.30254e13 | 0.710130 | ||||||||
\(887\) | −2.86371e13 | −1.55336 | −0.776682 | − | 0.629893i | \(-0.783099\pi\) | ||||
−0.776682 | + | 0.629893i | \(0.783099\pi\) | |||||||
\(888\) | −5.17148e11 | −0.0279098 | ||||||||
\(889\) | 1.12715e13 | 0.605237 | ||||||||
\(890\) | 4.68141e13 | 2.50105 | ||||||||
\(891\) | −2.37135e13 | −1.26051 | ||||||||
\(892\) | 4.40059e13 | 2.32739 | ||||||||
\(893\) | 1.56926e13 | 0.825777 | ||||||||
\(894\) | −3.52994e12 | −0.184820 | ||||||||
\(895\) | −8.23537e12 | −0.429022 | ||||||||
\(896\) | 1.10282e13 | 0.571634 | ||||||||
\(897\) | −1.16226e12 | −0.0599429 | ||||||||
\(898\) | −4.27349e13 | −2.19301 | ||||||||
\(899\) | −4.01119e13 | −2.04811 | ||||||||
\(900\) | 3.50047e12 | 0.177842 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 2.55269e13 | 1.28401 | ||||||||
\(903\) | −3.52195e12 | −0.176274 | ||||||||
\(904\) | 1.08790e12 | 0.0541792 | ||||||||
\(905\) | −1.49350e13 | −0.740093 | ||||||||
\(906\) | −3.57153e12 | −0.176107 | ||||||||
\(907\) | 1.51352e13 | 0.742599 | 0.371300 | − | 0.928513i | \(-0.378912\pi\) | ||||
0.371300 | + | 0.928513i | \(0.378912\pi\) | |||||||
\(908\) | −5.01448e12 | −0.244816 | ||||||||
\(909\) | −2.26802e13 | −1.10182 | ||||||||
\(910\) | −2.08156e12 | −0.100624 | ||||||||
\(911\) | 7.50977e12 | 0.361238 | 0.180619 | − | 0.983553i | \(-0.442190\pi\) | ||||
0.180619 | + | 0.983553i | \(0.442190\pi\) | |||||||
\(912\) | −3.84906e12 | −0.184237 | ||||||||
\(913\) | −2.23936e13 | −1.06661 | ||||||||
\(914\) | 5.11513e13 | 2.42437 | ||||||||
\(915\) | −4.93379e12 | −0.232694 | ||||||||
\(916\) | −4.24739e13 | −1.99339 | ||||||||
\(917\) | −2.56640e12 | −0.119857 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.29909e13 | −1.06325 | −0.531626 | − | 0.846979i | \(-0.678419\pi\) | ||||
−0.531626 | + | 0.846979i | \(0.678419\pi\) | |||||||
\(920\) | −3.71966e13 | −1.71182 | ||||||||
\(921\) | −4.70719e12 | −0.215572 | ||||||||
\(922\) | −4.73739e13 | −2.15899 | ||||||||
\(923\) | −4.75338e11 | −0.0215573 | ||||||||
\(924\) | 6.41586e12 | 0.289555 | ||||||||
\(925\) | 1.32973e11 | 0.00597206 | ||||||||
\(926\) | −4.07016e13 | −1.81912 | ||||||||
\(927\) | 3.16720e12 | 0.140869 | ||||||||
\(928\) | −4.67001e12 | −0.206705 | ||||||||
\(929\) | −4.46802e12 | −0.196809 | −0.0984044 | − | 0.995147i | \(-0.531374\pi\) | ||||
−0.0984044 | + | 0.995147i | \(0.531374\pi\) | |||||||
\(930\) | −1.63414e13 | −0.716337 | ||||||||
\(931\) | 1.55867e13 | 0.679955 | ||||||||
\(932\) | 7.54343e13 | 3.27489 | ||||||||
\(933\) | −1.08050e13 | −0.466828 | ||||||||
\(934\) | 2.13475e13 | 0.917881 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.82968e12 | −0.290843 | ||||||||
\(937\) | −3.69266e13 | −1.56499 | −0.782494 | − | 0.622658i | \(-0.786053\pi\) | ||||
−0.782494 | + | 0.622658i | \(0.786053\pi\) | |||||||
\(938\) | −1.02519e13 | −0.432404 | ||||||||
\(939\) | 4.16265e12 | 0.174733 | ||||||||
\(940\) | −4.83893e13 | −2.02150 | ||||||||
\(941\) | −2.73922e13 | −1.13887 | −0.569434 | − | 0.822037i | \(-0.692838\pi\) | ||||
−0.569434 | + | 0.822037i | \(0.692838\pi\) | |||||||
\(942\) | −4.61181e12 | −0.190828 | ||||||||
\(943\) | 1.21595e13 | 0.500739 | ||||||||
\(944\) | 3.04095e13 | 1.24634 | ||||||||
\(945\) | 4.03303e12 | 0.164509 | ||||||||
\(946\) | −1.35819e14 | −5.51381 | ||||||||
\(947\) | 4.08999e12 | 0.165252 | 0.0826261 | − | 0.996581i | \(-0.473669\pi\) | ||||
0.0826261 | + | 0.996581i | \(0.473669\pi\) | |||||||
\(948\) | −1.53408e13 | −0.616893 | ||||||||
\(949\) | −8.23587e12 | −0.329618 | ||||||||
\(950\) | 3.23265e12 | 0.128766 | ||||||||
\(951\) | −6.93269e12 | −0.274846 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.68559e13 | −0.661964 | −0.330982 | − | 0.943637i | \(-0.607380\pi\) | ||||
−0.330982 | + | 0.943637i | \(0.607380\pi\) | |||||||
\(954\) | −3.60792e13 | −1.41023 | ||||||||
\(955\) | −3.30348e13 | −1.28516 | ||||||||
\(956\) | −4.07982e13 | −1.57972 | ||||||||
\(957\) | −1.58369e13 | −0.610334 | ||||||||
\(958\) | 3.47961e13 | 1.33471 | ||||||||
\(959\) | −7.39437e12 | −0.282304 | ||||||||
\(960\) | −7.97911e12 | −0.303203 | ||||||||
\(961\) | 3.75604e13 | 1.42061 | ||||||||
\(962\) | −5.31611e11 | −0.0200127 | ||||||||
\(963\) | −1.83750e13 | −0.688509 | ||||||||
\(964\) | 5.72184e13 | 2.13397 | ||||||||
\(965\) | 3.58205e12 | 0.132972 | ||||||||
\(966\) | 4.62078e12 | 0.170733 | ||||||||
\(967\) | −3.07043e13 | −1.12922 | −0.564611 | − | 0.825357i | \(-0.690974\pi\) | ||||
−0.564611 | + | 0.825357i | \(0.690974\pi\) | |||||||
\(968\) | 7.59981e13 | 2.78204 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.36178e13 | 3.03267 | ||||||||
\(971\) | −6.39625e12 | −0.230908 | −0.115454 | − | 0.993313i | \(-0.536832\pi\) | ||||
−0.115454 | + | 0.993313i | \(0.536832\pi\) | |||||||
\(972\) | 4.12342e13 | 1.48170 | ||||||||
\(973\) | 4.36086e12 | 0.155978 | ||||||||
\(974\) | 1.72492e13 | 0.614119 | ||||||||
\(975\) | −1.52004e11 | −0.00538686 | ||||||||
\(976\) | −2.12194e13 | −0.748531 | ||||||||
\(977\) | −1.10943e13 | −0.389559 | −0.194780 | − | 0.980847i | \(-0.562399\pi\) | ||||
−0.194780 | + | 0.980847i | \(0.562399\pi\) | |||||||
\(978\) | −3.35910e12 | −0.117408 | ||||||||
\(979\) | −7.23877e13 | −2.51851 | ||||||||
\(980\) | −4.80628e13 | −1.66453 | ||||||||
\(981\) | 1.11184e13 | 0.383295 | ||||||||
\(982\) | −2.83691e13 | −0.973518 | ||||||||
\(983\) | −1.58231e13 | −0.540506 | −0.270253 | − | 0.962789i | \(-0.587107\pi\) | ||||
−0.270253 | + | 0.962789i | \(0.587107\pi\) | |||||||
\(984\) | −6.18472e12 | −0.210301 | ||||||||
\(985\) | −9.27735e11 | −0.0314022 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.93362e12 | 0.0983958 | ||||||||
\(988\) | −8.54765e12 | −0.285391 | ||||||||
\(989\) | −6.46961e13 | −2.15028 | ||||||||
\(990\) | 7.45383e13 | 2.46616 | ||||||||
\(991\) | −2.00594e13 | −0.660672 | −0.330336 | − | 0.943863i | \(-0.607162\pi\) | ||||
−0.330336 | + | 0.943863i | \(0.607162\pi\) | |||||||
\(992\) | 7.45117e12 | 0.244299 | ||||||||
\(993\) | −6.43896e12 | −0.210157 | ||||||||
\(994\) | 1.88980e12 | 0.0614011 | ||||||||
\(995\) | −2.38093e13 | −0.770092 | ||||||||
\(996\) | 1.11174e13 | 0.357963 | ||||||||
\(997\) | 2.94028e12 | 0.0942455 | 0.0471228 | − | 0.998889i | \(-0.484995\pi\) | ||||
0.0471228 | + | 0.998889i | \(0.484995\pi\) | |||||||
\(998\) | −1.27880e13 | −0.408051 | ||||||||
\(999\) | 1.03000e12 | 0.0327185 |
(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 | 289.10.a.g.1.33 | ✓ | 36 | |
17.16 | even | 2 | 289.10.a.h.1.33 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.g.1.33 | ✓ | 36 | 1.1 | even | 1 | trivial | |
289.10.a.h.1.33 | yes | 36 | 17.16 | even | 2 |