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 | 1.5 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −35.4923 | −1.56855 | −0.784276 | − | 0.620413i | \(-0.786965\pi\) | ||||
−0.784276 | + | 0.620413i | \(0.786965\pi\) | |||||||
\(3\) | 64.4314 | 0.459253 | 0.229627 | − | 0.973279i | \(-0.426250\pi\) | ||||
0.229627 | + | 0.973279i | \(0.426250\pi\) | |||||||
\(4\) | 747.701 | 1.46035 | ||||||||
\(5\) | 1779.33 | 1.27319 | 0.636594 | − | 0.771199i | \(-0.280343\pi\) | ||||
0.636594 | + | 0.771199i | \(0.280343\pi\) | |||||||
\(6\) | −2286.82 | −0.720362 | ||||||||
\(7\) | −1603.15 | −0.252367 | −0.126183 | − | 0.992007i | \(-0.540273\pi\) | ||||
−0.126183 | + | 0.992007i | \(0.540273\pi\) | |||||||
\(8\) | −8365.56 | −0.722088 | ||||||||
\(9\) | −15531.6 | −0.789087 | ||||||||
\(10\) | −63152.6 | −1.99706 | ||||||||
\(11\) | −38189.5 | −0.786461 | −0.393230 | − | 0.919440i | \(-0.628643\pi\) | ||||
−0.393230 | + | 0.919440i | \(0.628643\pi\) | |||||||
\(12\) | 48175.4 | 0.670672 | ||||||||
\(13\) | −116430. | −1.13063 | −0.565316 | − | 0.824875i | \(-0.691246\pi\) | ||||
−0.565316 | + | 0.824875i | \(0.691246\pi\) | |||||||
\(14\) | 56899.3 | 0.395850 | ||||||||
\(15\) | 114645. | 0.584715 | ||||||||
\(16\) | −85910.2 | −0.327722 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 551251. | 1.23772 | ||||||||
\(19\) | 850642. | 1.49746 | 0.748731 | − | 0.662874i | \(-0.230664\pi\) | ||||
0.748731 | + | 0.662874i | \(0.230664\pi\) | |||||||
\(20\) | 1.33041e6 | 1.85930 | ||||||||
\(21\) | −103293. | −0.115900 | ||||||||
\(22\) | 1.35543e6 | 1.23360 | ||||||||
\(23\) | 1.05393e6 | 0.785299 | 0.392649 | − | 0.919688i | \(-0.371559\pi\) | ||||
0.392649 | + | 0.919688i | \(0.371559\pi\) | |||||||
\(24\) | −539005. | −0.331621 | ||||||||
\(25\) | 1.21290e6 | 0.621006 | ||||||||
\(26\) | 4.13238e6 | 1.77345 | ||||||||
\(27\) | −2.26893e6 | −0.821644 | ||||||||
\(28\) | −1.19867e6 | −0.368545 | ||||||||
\(29\) | −1.44727e6 | −0.379979 | −0.189989 | − | 0.981786i | \(-0.560845\pi\) | ||||
−0.189989 | + | 0.981786i | \(0.560845\pi\) | |||||||
\(30\) | −4.06901e6 | −0.917156 | ||||||||
\(31\) | 5.24487e6 | 1.02002 | 0.510008 | − | 0.860170i | \(-0.329642\pi\) | ||||
0.510008 | + | 0.860170i | \(0.329642\pi\) | |||||||
\(32\) | 7.33231e6 | 1.23614 | ||||||||
\(33\) | −2.46061e6 | −0.361185 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.85253e6 | −0.321310 | ||||||||
\(36\) | −1.16130e7 | −1.15235 | ||||||||
\(37\) | −5.51006e6 | −0.483335 | −0.241667 | − | 0.970359i | \(-0.577694\pi\) | ||||
−0.241667 | + | 0.970359i | \(0.577694\pi\) | |||||||
\(38\) | −3.01912e7 | −2.34885 | ||||||||
\(39\) | −7.50177e6 | −0.519246 | ||||||||
\(40\) | −1.48851e7 | −0.919353 | ||||||||
\(41\) | 2.30276e7 | 1.27268 | 0.636342 | − | 0.771407i | \(-0.280447\pi\) | ||||
0.636342 | + | 0.771407i | \(0.280447\pi\) | |||||||
\(42\) | 3.66611e6 | 0.181796 | ||||||||
\(43\) | 1.73443e7 | 0.773659 | 0.386830 | − | 0.922151i | \(-0.373570\pi\) | ||||
0.386830 | + | 0.922151i | \(0.373570\pi\) | |||||||
\(44\) | −2.85543e7 | −1.14851 | ||||||||
\(45\) | −2.76359e7 | −1.00466 | ||||||||
\(46\) | −3.74062e7 | −1.23178 | ||||||||
\(47\) | 5.62789e7 | 1.68231 | 0.841154 | − | 0.540796i | \(-0.181877\pi\) | ||||
0.841154 | + | 0.540796i | \(0.181877\pi\) | |||||||
\(48\) | −5.53532e6 | −0.150507 | ||||||||
\(49\) | −3.77835e7 | −0.936311 | ||||||||
\(50\) | −4.30487e7 | −0.974080 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.70551e7 | −1.65112 | ||||||||
\(53\) | −7.72272e7 | −1.34440 | −0.672201 | − | 0.740369i | \(-0.734651\pi\) | ||||
−0.672201 | + | 0.740369i | \(0.734651\pi\) | |||||||
\(54\) | 8.05293e7 | 1.28879 | ||||||||
\(55\) | −6.79519e7 | −1.00131 | ||||||||
\(56\) | 1.34112e7 | 0.182231 | ||||||||
\(57\) | 5.48081e7 | 0.687714 | ||||||||
\(58\) | 5.13670e7 | 0.596016 | ||||||||
\(59\) | 9.35882e7 | 1.00551 | 0.502756 | − | 0.864428i | \(-0.332319\pi\) | ||||
0.502756 | + | 0.864428i | \(0.332319\pi\) | |||||||
\(60\) | 8.57202e7 | 0.853891 | ||||||||
\(61\) | −1.85319e8 | −1.71371 | −0.856853 | − | 0.515560i | \(-0.827584\pi\) | ||||
−0.856853 | + | 0.515560i | \(0.827584\pi\) | |||||||
\(62\) | −1.86152e8 | −1.59995 | ||||||||
\(63\) | 2.48994e7 | 0.199139 | ||||||||
\(64\) | −2.16254e8 | −1.61122 | ||||||||
\(65\) | −2.07168e8 | −1.43951 | ||||||||
\(66\) | 8.73325e7 | 0.566537 | ||||||||
\(67\) | −2.00683e8 | −1.21667 | −0.608337 | − | 0.793679i | \(-0.708163\pi\) | ||||
−0.608337 | + | 0.793679i | \(0.708163\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.79060e7 | 0.360651 | ||||||||
\(70\) | 1.01243e8 | 0.503992 | ||||||||
\(71\) | −7.05304e7 | −0.329392 | −0.164696 | − | 0.986344i | \(-0.552664\pi\) | ||||
−0.164696 | + | 0.986344i | \(0.552664\pi\) | |||||||
\(72\) | 1.29930e8 | 0.569790 | ||||||||
\(73\) | 2.21792e8 | 0.914099 | 0.457049 | − | 0.889441i | \(-0.348906\pi\) | ||||
0.457049 | + | 0.889441i | \(0.348906\pi\) | |||||||
\(74\) | 1.95564e8 | 0.758136 | ||||||||
\(75\) | 7.81491e7 | 0.285199 | ||||||||
\(76\) | 6.36026e8 | 2.18682 | ||||||||
\(77\) | 6.12234e7 | 0.198477 | ||||||||
\(78\) | 2.66255e8 | 0.814464 | ||||||||
\(79\) | 6.34329e8 | 1.83228 | 0.916141 | − | 0.400856i | \(-0.131287\pi\) | ||||
0.916141 | + | 0.400856i | \(0.131287\pi\) | |||||||
\(80\) | −1.52863e8 | −0.417251 | ||||||||
\(81\) | 1.59518e8 | 0.411744 | ||||||||
\(82\) | −8.17300e8 | −1.99627 | ||||||||
\(83\) | −5.88521e7 | −0.136116 | −0.0680582 | − | 0.997681i | \(-0.521680\pi\) | ||||
−0.0680582 | + | 0.997681i | \(0.521680\pi\) | |||||||
\(84\) | −7.72323e7 | −0.169255 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.15590e8 | −1.21352 | ||||||||
\(87\) | −9.32498e7 | −0.174506 | ||||||||
\(88\) | 3.19477e8 | 0.567894 | ||||||||
\(89\) | −7.76608e8 | −1.31204 | −0.656020 | − | 0.754743i | \(-0.727761\pi\) | ||||
−0.656020 | + | 0.754743i | \(0.727761\pi\) | |||||||
\(90\) | 9.80860e8 | 1.57585 | ||||||||
\(91\) | 1.86655e8 | 0.285334 | ||||||||
\(92\) | 7.88022e8 | 1.14681 | ||||||||
\(93\) | 3.37935e8 | 0.468446 | ||||||||
\(94\) | −1.99747e9 | −2.63879 | ||||||||
\(95\) | 1.51358e9 | 1.90655 | ||||||||
\(96\) | 4.72431e8 | 0.567699 | ||||||||
\(97\) | 6.87791e8 | 0.788831 | 0.394415 | − | 0.918932i | \(-0.370947\pi\) | ||||
0.394415 | + | 0.918932i | \(0.370947\pi\) | |||||||
\(98\) | 1.34102e9 | 1.46865 | ||||||||
\(99\) | 5.93144e8 | 0.620586 | ||||||||
\(100\) | 9.06889e8 | 0.906889 | ||||||||
\(101\) | −1.32312e9 | −1.26518 | −0.632590 | − | 0.774487i | \(-0.718008\pi\) | ||||
−0.632590 | + | 0.774487i | \(0.718008\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.63204e9 | −1.42877 | −0.714387 | − | 0.699751i | \(-0.753294\pi\) | ||||
−0.714387 | + | 0.699751i | \(0.753294\pi\) | |||||||
\(104\) | 9.74005e8 | 0.816415 | ||||||||
\(105\) | −1.83793e8 | −0.147563 | ||||||||
\(106\) | 2.74097e9 | 2.10876 | ||||||||
\(107\) | 9.81220e8 | 0.723668 | 0.361834 | − | 0.932243i | \(-0.382151\pi\) | ||||
0.361834 | + | 0.932243i | \(0.382151\pi\) | |||||||
\(108\) | −1.69648e9 | −1.19989 | ||||||||
\(109\) | −9.30599e8 | −0.631456 | −0.315728 | − | 0.948850i | \(-0.602249\pi\) | ||||
−0.315728 | + | 0.948850i | \(0.602249\pi\) | |||||||
\(110\) | 2.41177e9 | 1.57061 | ||||||||
\(111\) | −3.55021e8 | −0.221973 | ||||||||
\(112\) | 1.37727e8 | 0.0827061 | ||||||||
\(113\) | 2.85541e9 | 1.64746 | 0.823732 | − | 0.566979i | \(-0.191888\pi\) | ||||
0.823732 | + | 0.566979i | \(0.191888\pi\) | |||||||
\(114\) | −1.94526e9 | −1.07871 | ||||||||
\(115\) | 1.87529e9 | 0.999833 | ||||||||
\(116\) | −1.08213e9 | −0.554903 | ||||||||
\(117\) | 1.80835e9 | 0.892166 | ||||||||
\(118\) | −3.32166e9 | −1.57720 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −9.59069e8 | −0.422216 | ||||||||
\(121\) | −8.99508e8 | −0.381479 | ||||||||
\(122\) | 6.57740e9 | 2.68804 | ||||||||
\(123\) | 1.48370e9 | 0.584484 | ||||||||
\(124\) | 3.92159e9 | 1.48958 | ||||||||
\(125\) | −1.31710e9 | −0.482530 | ||||||||
\(126\) | −8.83737e8 | −0.312360 | ||||||||
\(127\) | −6.04257e8 | −0.206113 | −0.103056 | − | 0.994676i | \(-0.532862\pi\) | ||||
−0.103056 | + | 0.994676i | \(0.532862\pi\) | |||||||
\(128\) | 3.92121e9 | 1.29115 | ||||||||
\(129\) | 1.11752e9 | 0.355305 | ||||||||
\(130\) | 7.35288e9 | 2.25794 | ||||||||
\(131\) | −2.35573e9 | −0.698885 | −0.349442 | − | 0.936958i | \(-0.613629\pi\) | ||||
−0.349442 | + | 0.936958i | \(0.613629\pi\) | |||||||
\(132\) | −1.83980e9 | −0.527457 | ||||||||
\(133\) | −1.36371e9 | −0.377910 | ||||||||
\(134\) | 7.12270e9 | 1.90841 | ||||||||
\(135\) | −4.03718e9 | −1.04611 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.70241e9 | −0.897928 | −0.448964 | − | 0.893550i | \(-0.648207\pi\) | ||||
−0.448964 | + | 0.893550i | \(0.648207\pi\) | |||||||
\(138\) | −2.41014e9 | −0.565699 | ||||||||
\(139\) | 2.24358e9 | 0.509772 | 0.254886 | − | 0.966971i | \(-0.417962\pi\) | ||||
0.254886 | + | 0.966971i | \(0.417962\pi\) | |||||||
\(140\) | −2.13284e9 | −0.469227 | ||||||||
\(141\) | 3.62613e9 | 0.772605 | ||||||||
\(142\) | 2.50328e9 | 0.516669 | ||||||||
\(143\) | 4.44642e9 | 0.889197 | ||||||||
\(144\) | 1.33432e9 | 0.258601 | ||||||||
\(145\) | −2.57518e9 | −0.483784 | ||||||||
\(146\) | −7.87190e9 | −1.43381 | ||||||||
\(147\) | −2.43445e9 | −0.430004 | ||||||||
\(148\) | −4.11987e9 | −0.705840 | ||||||||
\(149\) | 2.50473e9 | 0.416316 | 0.208158 | − | 0.978095i | \(-0.433253\pi\) | ||||
0.208158 | + | 0.978095i | \(0.433253\pi\) | |||||||
\(150\) | −2.77369e9 | −0.447349 | ||||||||
\(151\) | −6.86721e9 | −1.07494 | −0.537470 | − | 0.843283i | \(-0.680620\pi\) | ||||
−0.537470 | + | 0.843283i | \(0.680620\pi\) | |||||||
\(152\) | −7.11610e9 | −1.08130 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.17296e9 | −0.311321 | ||||||||
\(155\) | 9.33237e9 | 1.29867 | ||||||||
\(156\) | −5.60908e9 | −0.758283 | ||||||||
\(157\) | −1.19135e10 | −1.56492 | −0.782461 | − | 0.622700i | \(-0.786036\pi\) | ||||
−0.782461 | + | 0.622700i | \(0.786036\pi\) | |||||||
\(158\) | −2.25138e10 | −2.87403 | ||||||||
\(159\) | −4.97586e9 | −0.617420 | ||||||||
\(160\) | 1.30466e10 | 1.57383 | ||||||||
\(161\) | −1.68960e9 | −0.198183 | ||||||||
\(162\) | −5.66166e9 | −0.645842 | ||||||||
\(163\) | −3.24459e9 | −0.360011 | −0.180005 | − | 0.983666i | \(-0.557612\pi\) | ||||
−0.180005 | + | 0.983666i | \(0.557612\pi\) | |||||||
\(164\) | 1.72177e10 | 1.85857 | ||||||||
\(165\) | −4.37824e9 | −0.459856 | ||||||||
\(166\) | 2.08879e9 | 0.213506 | ||||||||
\(167\) | −8.72685e9 | −0.868227 | −0.434114 | − | 0.900858i | \(-0.642938\pi\) | ||||
−0.434114 | + | 0.900858i | \(0.642938\pi\) | |||||||
\(168\) | 8.64104e8 | 0.0836902 | ||||||||
\(169\) | 2.95152e9 | 0.278327 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.32118e10 | −1.18163 | ||||||||
\(172\) | 1.29684e10 | 1.12982 | ||||||||
\(173\) | 5.55058e9 | 0.471119 | 0.235559 | − | 0.971860i | \(-0.424308\pi\) | ||||
0.235559 | + | 0.971860i | \(0.424308\pi\) | |||||||
\(174\) | 3.30965e9 | 0.273722 | ||||||||
\(175\) | −1.94446e9 | −0.156721 | ||||||||
\(176\) | 3.28087e9 | 0.257740 | ||||||||
\(177\) | 6.03002e9 | 0.461784 | ||||||||
\(178\) | 2.75636e10 | 2.05800 | ||||||||
\(179\) | 1.54065e10 | 1.12167 | 0.560834 | − | 0.827928i | \(-0.310480\pi\) | ||||
0.560834 | + | 0.827928i | \(0.310480\pi\) | |||||||
\(180\) | −2.06634e10 | −1.46715 | ||||||||
\(181\) | −2.46062e10 | −1.70409 | −0.852043 | − | 0.523472i | \(-0.824637\pi\) | ||||
−0.852043 | + | 0.523472i | \(0.824637\pi\) | |||||||
\(182\) | −6.62481e9 | −0.447561 | ||||||||
\(183\) | −1.19404e10 | −0.787025 | ||||||||
\(184\) | −8.81668e9 | −0.567055 | ||||||||
\(185\) | −9.80423e9 | −0.615376 | ||||||||
\(186\) | −1.19941e10 | −0.734781 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.20798e10 | 2.45676 | ||||||||
\(189\) | 3.63742e9 | 0.207356 | ||||||||
\(190\) | −5.37202e10 | −2.99052 | ||||||||
\(191\) | 1.53953e10 | 0.837025 | 0.418513 | − | 0.908211i | \(-0.362552\pi\) | ||||
0.418513 | + | 0.908211i | \(0.362552\pi\) | |||||||
\(192\) | −1.39336e10 | −0.739958 | ||||||||
\(193\) | −3.75476e10 | −1.94793 | −0.973967 | − | 0.226689i | \(-0.927210\pi\) | ||||
−0.973967 | + | 0.226689i | \(0.927210\pi\) | |||||||
\(194\) | −2.44113e10 | −1.23732 | ||||||||
\(195\) | −1.33482e10 | −0.661097 | ||||||||
\(196\) | −2.82508e10 | −1.36734 | ||||||||
\(197\) | −1.69699e10 | −0.802752 | −0.401376 | − | 0.915913i | \(-0.631468\pi\) | ||||
−0.401376 | + | 0.915913i | \(0.631468\pi\) | |||||||
\(198\) | −2.10520e10 | −0.973421 | ||||||||
\(199\) | 3.68433e10 | 1.66541 | 0.832703 | − | 0.553720i | \(-0.186792\pi\) | ||||
0.832703 | + | 0.553720i | \(0.186792\pi\) | |||||||
\(200\) | −1.01466e10 | −0.448421 | ||||||||
\(201\) | −1.29303e10 | −0.558761 | ||||||||
\(202\) | 4.69605e10 | 1.98450 | ||||||||
\(203\) | 2.32019e9 | 0.0958941 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.09737e10 | 1.62037 | ||||||||
\(206\) | 5.79248e10 | 2.24111 | ||||||||
\(207\) | −1.63692e10 | −0.619669 | ||||||||
\(208\) | 1.00026e10 | 0.370532 | ||||||||
\(209\) | −3.24856e10 | −1.17770 | ||||||||
\(210\) | 6.52322e9 | 0.231460 | ||||||||
\(211\) | 2.86188e9 | 0.0993988 | 0.0496994 | − | 0.998764i | \(-0.484174\pi\) | ||||
0.0496994 | + | 0.998764i | \(0.484174\pi\) | |||||||
\(212\) | −5.77428e10 | −1.96330 | ||||||||
\(213\) | −4.54437e9 | −0.151274 | ||||||||
\(214\) | −3.48257e10 | −1.13511 | ||||||||
\(215\) | 3.08614e10 | 0.985013 | ||||||||
\(216\) | 1.89808e10 | 0.593299 | ||||||||
\(217\) | −8.40830e9 | −0.257418 | ||||||||
\(218\) | 3.30290e10 | 0.990471 | ||||||||
\(219\) | 1.42904e10 | 0.419803 | ||||||||
\(220\) | −5.08077e10 | −1.46227 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.26005e10 | 0.348176 | ||||||||
\(223\) | −8.66212e9 | −0.234559 | −0.117279 | − | 0.993099i | \(-0.537417\pi\) | ||||
−0.117279 | + | 0.993099i | \(0.537417\pi\) | |||||||
\(224\) | −1.17548e10 | −0.311960 | ||||||||
\(225\) | −1.88383e10 | −0.490028 | ||||||||
\(226\) | −1.01345e11 | −2.58413 | ||||||||
\(227\) | −3.39293e10 | −0.848122 | −0.424061 | − | 0.905634i | \(-0.639396\pi\) | ||||
−0.424061 | + | 0.905634i | \(0.639396\pi\) | |||||||
\(228\) | 4.09801e10 | 1.00431 | ||||||||
\(229\) | −4.32441e10 | −1.03912 | −0.519561 | − | 0.854433i | \(-0.673905\pi\) | ||||
−0.519561 | + | 0.854433i | \(0.673905\pi\) | |||||||
\(230\) | −6.65582e10 | −1.56829 | ||||||||
\(231\) | 3.94471e9 | 0.0911510 | ||||||||
\(232\) | 1.21072e10 | 0.274378 | ||||||||
\(233\) | −2.83037e10 | −0.629131 | −0.314566 | − | 0.949236i | \(-0.601859\pi\) | ||||
−0.314566 | + | 0.949236i | \(0.601859\pi\) | |||||||
\(234\) | −6.41824e10 | −1.39941 | ||||||||
\(235\) | 1.00139e11 | 2.14189 | ||||||||
\(236\) | 6.99760e10 | 1.46840 | ||||||||
\(237\) | 4.08707e10 | 0.841481 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.13610e10 | −0.819976 | −0.409988 | − | 0.912091i | \(-0.634467\pi\) | ||||
−0.409988 | + | 0.912091i | \(0.634467\pi\) | |||||||
\(240\) | −9.84918e9 | −0.191624 | ||||||||
\(241\) | −4.75351e10 | −0.907691 | −0.453846 | − | 0.891080i | \(-0.649948\pi\) | ||||
−0.453846 | + | 0.891080i | \(0.649948\pi\) | |||||||
\(242\) | 3.19256e10 | 0.598370 | ||||||||
\(243\) | 5.49373e10 | 1.01074 | ||||||||
\(244\) | −1.38563e11 | −2.50262 | ||||||||
\(245\) | −6.72295e10 | −1.19210 | ||||||||
\(246\) | −5.26598e10 | −0.916793 | ||||||||
\(247\) | −9.90406e10 | −1.69308 | ||||||||
\(248\) | −4.38763e10 | −0.736541 | ||||||||
\(249\) | −3.79192e9 | −0.0625119 | ||||||||
\(250\) | 4.67469e10 | 0.756873 | ||||||||
\(251\) | −1.97131e10 | −0.313490 | −0.156745 | − | 0.987639i | \(-0.550100\pi\) | ||||
−0.156745 | + | 0.987639i | \(0.550100\pi\) | |||||||
\(252\) | 1.86173e10 | 0.290814 | ||||||||
\(253\) | −4.02489e10 | −0.617607 | ||||||||
\(254\) | 2.14465e10 | 0.323299 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.84505e10 | −0.414009 | ||||||||
\(257\) | 1.37584e9 | 0.0196729 | 0.00983643 | − | 0.999952i | \(-0.496869\pi\) | ||||
0.00983643 | + | 0.999952i | \(0.496869\pi\) | |||||||
\(258\) | −3.96633e10 | −0.557315 | ||||||||
\(259\) | 8.83343e9 | 0.121978 | ||||||||
\(260\) | −1.54900e11 | −2.10219 | ||||||||
\(261\) | 2.24784e10 | 0.299836 | ||||||||
\(262\) | 8.36104e10 | 1.09624 | ||||||||
\(263\) | −6.61395e10 | −0.852432 | −0.426216 | − | 0.904621i | \(-0.640154\pi\) | ||||
−0.426216 | + | 0.904621i | \(0.640154\pi\) | |||||||
\(264\) | 2.05843e10 | 0.260807 | ||||||||
\(265\) | −1.37413e11 | −1.71167 | ||||||||
\(266\) | 4.84010e10 | 0.592771 | ||||||||
\(267\) | −5.00380e10 | −0.602558 | ||||||||
\(268\) | −1.50051e11 | −1.77677 | ||||||||
\(269\) | −1.71759e10 | −0.200002 | −0.100001 | − | 0.994987i | \(-0.531885\pi\) | ||||
−0.100001 | + | 0.994987i | \(0.531885\pi\) | |||||||
\(270\) | 1.43289e11 | 1.64087 | ||||||||
\(271\) | −3.72624e10 | −0.419671 | −0.209835 | − | 0.977737i | \(-0.567293\pi\) | ||||
−0.209835 | + | 0.977737i | \(0.567293\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.20264e10 | 0.131040 | ||||||||
\(274\) | 1.31407e11 | 1.40845 | ||||||||
\(275\) | −4.63202e10 | −0.488397 | ||||||||
\(276\) | 5.07734e10 | 0.526678 | ||||||||
\(277\) | 3.67272e10 | 0.374825 | 0.187413 | − | 0.982281i | \(-0.439990\pi\) | ||||
0.187413 | + | 0.982281i | \(0.439990\pi\) | |||||||
\(278\) | −7.96299e10 | −0.799603 | ||||||||
\(279\) | −8.14612e10 | −0.804881 | ||||||||
\(280\) | 2.38630e10 | 0.232014 | ||||||||
\(281\) | 1.47776e11 | 1.41392 | 0.706962 | − | 0.707252i | \(-0.250065\pi\) | ||||
0.706962 | + | 0.707252i | \(0.250065\pi\) | |||||||
\(282\) | −1.28700e11 | −1.21187 | ||||||||
\(283\) | 1.11330e11 | 1.03175 | 0.515873 | − | 0.856665i | \(-0.327468\pi\) | ||||
0.515873 | + | 0.856665i | \(0.327468\pi\) | |||||||
\(284\) | −5.27356e10 | −0.481029 | ||||||||
\(285\) | 9.75219e10 | 0.875589 | ||||||||
\(286\) | −1.57813e11 | −1.39475 | ||||||||
\(287\) | −3.69166e10 | −0.321183 | ||||||||
\(288\) | −1.13883e11 | −0.975418 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 9.13990e10 | 0.758840 | ||||||||
\(291\) | 4.43154e10 | 0.362273 | ||||||||
\(292\) | 1.65834e11 | 1.33491 | ||||||||
\(293\) | 1.00582e11 | 0.797290 | 0.398645 | − | 0.917105i | \(-0.369480\pi\) | ||||
0.398645 | + | 0.917105i | \(0.369480\pi\) | |||||||
\(294\) | 8.64040e10 | 0.674483 | ||||||||
\(295\) | 1.66525e11 | 1.28021 | ||||||||
\(296\) | 4.60947e10 | 0.349010 | ||||||||
\(297\) | 8.66492e10 | 0.646191 | ||||||||
\(298\) | −8.88987e10 | −0.653013 | ||||||||
\(299\) | −1.22709e11 | −0.887884 | ||||||||
\(300\) | 5.84321e10 | 0.416491 | ||||||||
\(301\) | −2.78055e10 | −0.195246 | ||||||||
\(302\) | 2.43733e11 | 1.68610 | ||||||||
\(303\) | −8.52504e10 | −0.581038 | ||||||||
\(304\) | −7.30789e10 | −0.490751 | ||||||||
\(305\) | −3.29745e11 | −2.18187 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.00813e11 | −0.647733 | −0.323866 | − | 0.946103i | \(-0.604983\pi\) | ||||
−0.323866 | + | 0.946103i | \(0.604983\pi\) | |||||||
\(308\) | 4.57768e10 | 0.289846 | ||||||||
\(309\) | −1.05155e11 | −0.656169 | ||||||||
\(310\) | −3.31227e11 | −2.03703 | ||||||||
\(311\) | −6.42046e10 | −0.389175 | −0.194587 | − | 0.980885i | \(-0.562337\pi\) | ||||
−0.194587 | + | 0.980885i | \(0.562337\pi\) | |||||||
\(312\) | 6.27565e10 | 0.374941 | ||||||||
\(313\) | 1.95618e11 | 1.15202 | 0.576008 | − | 0.817444i | \(-0.304610\pi\) | ||||
0.576008 | + | 0.817444i | \(0.304610\pi\) | |||||||
\(314\) | 4.22839e11 | 2.45466 | ||||||||
\(315\) | 4.43044e10 | 0.253542 | ||||||||
\(316\) | 4.74288e11 | 2.67578 | ||||||||
\(317\) | −2.98622e11 | −1.66095 | −0.830473 | − | 0.557059i | \(-0.811930\pi\) | ||||
−0.830473 | + | 0.557059i | \(0.811930\pi\) | |||||||
\(318\) | 1.76605e11 | 0.968456 | ||||||||
\(319\) | 5.52707e10 | 0.298838 | ||||||||
\(320\) | −3.84789e11 | −2.05139 | ||||||||
\(321\) | 6.32214e10 | 0.332347 | ||||||||
\(322\) | 5.99677e10 | 0.310861 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.19272e11 | 0.601292 | ||||||||
\(325\) | −1.41219e11 | −0.702129 | ||||||||
\(326\) | 1.15158e11 | 0.564695 | ||||||||
\(327\) | −5.99598e10 | −0.289998 | ||||||||
\(328\) | −1.92638e11 | −0.918990 | ||||||||
\(329\) | −9.02234e10 | −0.424559 | ||||||||
\(330\) | 1.55394e11 | 0.721307 | ||||||||
\(331\) | 2.80470e11 | 1.28428 | 0.642140 | − | 0.766587i | \(-0.278047\pi\) | ||||
0.642140 | + | 0.766587i | \(0.278047\pi\) | |||||||
\(332\) | −4.40037e10 | −0.198778 | ||||||||
\(333\) | 8.55799e10 | 0.381393 | ||||||||
\(334\) | 3.09736e11 | 1.36186 | ||||||||
\(335\) | −3.57082e11 | −1.54905 | ||||||||
\(336\) | 8.87393e9 | 0.0379830 | ||||||||
\(337\) | 1.33080e11 | 0.562053 | 0.281027 | − | 0.959700i | \(-0.409325\pi\) | ||||
0.281027 | + | 0.959700i | \(0.409325\pi\) | |||||||
\(338\) | −1.04756e11 | −0.436571 | ||||||||
\(339\) | 1.83978e11 | 0.756603 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.00299e11 | −0.802203 | ||||||||
\(342\) | 4.68918e11 | 1.85344 | ||||||||
\(343\) | 1.25265e11 | 0.488661 | ||||||||
\(344\) | −1.45095e11 | −0.558650 | ||||||||
\(345\) | 1.20827e11 | 0.459176 | ||||||||
\(346\) | −1.97002e11 | −0.738974 | ||||||||
\(347\) | 1.27576e10 | 0.0472373 | 0.0236187 | − | 0.999721i | \(-0.492481\pi\) | ||||
0.0236187 | + | 0.999721i | \(0.492481\pi\) | |||||||
\(348\) | −6.97230e10 | −0.254841 | ||||||||
\(349\) | 9.97908e10 | 0.360061 | 0.180030 | − | 0.983661i | \(-0.442380\pi\) | ||||
0.180030 | + | 0.983661i | \(0.442380\pi\) | |||||||
\(350\) | 6.90134e10 | 0.245826 | ||||||||
\(351\) | 2.64172e11 | 0.928976 | ||||||||
\(352\) | −2.80018e11 | −0.972173 | ||||||||
\(353\) | 2.18588e11 | 0.749272 | 0.374636 | − | 0.927172i | \(-0.377768\pi\) | ||||
0.374636 | + | 0.927172i | \(0.377768\pi\) | |||||||
\(354\) | −2.14019e11 | −0.724333 | ||||||||
\(355\) | −1.25497e11 | −0.419378 | ||||||||
\(356\) | −5.80671e11 | −1.91604 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.46811e11 | −1.75940 | ||||||||
\(359\) | −2.37311e11 | −0.754038 | −0.377019 | − | 0.926205i | \(-0.623051\pi\) | ||||
−0.377019 | + | 0.926205i | \(0.623051\pi\) | |||||||
\(360\) | 2.31190e11 | 0.725449 | ||||||||
\(361\) | 4.00904e11 | 1.24239 | ||||||||
\(362\) | 8.73331e11 | 2.67295 | ||||||||
\(363\) | −5.79566e10 | −0.175196 | ||||||||
\(364\) | 1.39562e11 | 0.416688 | ||||||||
\(365\) | 3.94642e11 | 1.16382 | ||||||||
\(366\) | 4.23792e11 | 1.23449 | ||||||||
\(367\) | 7.38520e10 | 0.212503 | 0.106251 | − | 0.994339i | \(-0.466115\pi\) | ||||
0.106251 | + | 0.994339i | \(0.466115\pi\) | |||||||
\(368\) | −9.05431e10 | −0.257359 | ||||||||
\(369\) | −3.57655e11 | −1.00426 | ||||||||
\(370\) | 3.47974e11 | 0.965249 | ||||||||
\(371\) | 1.23807e11 | 0.339282 | ||||||||
\(372\) | 2.52674e11 | 0.684096 | ||||||||
\(373\) | 1.63830e11 | 0.438232 | 0.219116 | − | 0.975699i | \(-0.429683\pi\) | ||||
0.219116 | + | 0.975699i | \(0.429683\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.48628e10 | −0.221603 | ||||||||
\(376\) | −4.70805e11 | −1.21477 | ||||||||
\(377\) | 1.68506e11 | 0.429616 | ||||||||
\(378\) | −1.29100e11 | −0.325248 | ||||||||
\(379\) | 5.52844e11 | 1.37634 | 0.688171 | − | 0.725548i | \(-0.258414\pi\) | ||||
0.688171 | + | 0.725548i | \(0.258414\pi\) | |||||||
\(380\) | 1.13170e12 | 2.78424 | ||||||||
\(381\) | −3.89332e10 | −0.0946580 | ||||||||
\(382\) | −5.46415e11 | −1.31292 | ||||||||
\(383\) | −4.45678e11 | −1.05834 | −0.529172 | − | 0.848515i | \(-0.677497\pi\) | ||||
−0.529172 | + | 0.848515i | \(0.677497\pi\) | |||||||
\(384\) | 2.52649e11 | 0.592963 | ||||||||
\(385\) | 1.08937e11 | 0.252698 | ||||||||
\(386\) | 1.33265e12 | 3.05543 | ||||||||
\(387\) | −2.69385e11 | −0.610484 | ||||||||
\(388\) | 5.14262e11 | 1.15197 | ||||||||
\(389\) | 1.27952e11 | 0.283317 | 0.141659 | − | 0.989916i | \(-0.454756\pi\) | ||||
0.141659 | + | 0.989916i | \(0.454756\pi\) | |||||||
\(390\) | 4.73756e11 | 1.03697 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.16080e11 | 0.676099 | ||||||||
\(393\) | −1.51783e11 | −0.320965 | ||||||||
\(394\) | 6.02300e11 | 1.25916 | ||||||||
\(395\) | 1.12868e12 | 2.33284 | ||||||||
\(396\) | 4.43494e11 | 0.906274 | ||||||||
\(397\) | −3.31658e11 | −0.670091 | −0.335045 | − | 0.942202i | \(-0.608752\pi\) | ||||
−0.335045 | + | 0.942202i | \(0.608752\pi\) | |||||||
\(398\) | −1.30765e12 | −2.61227 | ||||||||
\(399\) | −8.78655e10 | −0.173556 | ||||||||
\(400\) | −1.04201e11 | −0.203517 | ||||||||
\(401\) | −6.03112e11 | −1.16479 | −0.582396 | − | 0.812905i | \(-0.697885\pi\) | ||||
−0.582396 | + | 0.812905i | \(0.697885\pi\) | |||||||
\(402\) | 4.58925e11 | 0.876445 | ||||||||
\(403\) | −6.10662e11 | −1.15326 | ||||||||
\(404\) | −9.89297e11 | −1.84761 | ||||||||
\(405\) | 2.83836e11 | 0.524228 | ||||||||
\(406\) | −8.23489e10 | −0.150415 | ||||||||
\(407\) | 2.10426e11 | 0.380124 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.86595e11 | −0.859830 | −0.429915 | − | 0.902869i | \(-0.641456\pi\) | ||||
−0.429915 | + | 0.902869i | \(0.641456\pi\) | |||||||
\(410\) | −1.45425e12 | −2.54163 | ||||||||
\(411\) | −2.38551e11 | −0.412376 | ||||||||
\(412\) | −1.22028e12 | −2.08651 | ||||||||
\(413\) | −1.50036e11 | −0.253758 | ||||||||
\(414\) | 5.80978e11 | 0.971982 | ||||||||
\(415\) | −1.04717e11 | −0.173302 | ||||||||
\(416\) | −8.53704e11 | −1.39761 | ||||||||
\(417\) | 1.44557e11 | 0.234114 | ||||||||
\(418\) | 1.15299e12 | 1.84728 | ||||||||
\(419\) | −5.39425e11 | −0.855003 | −0.427502 | − | 0.904015i | \(-0.640606\pi\) | ||||
−0.427502 | + | 0.904015i | \(0.640606\pi\) | |||||||
\(420\) | −1.37422e11 | −0.215494 | ||||||||
\(421\) | 9.96515e11 | 1.54602 | 0.773008 | − | 0.634396i | \(-0.218751\pi\) | ||||
0.773008 | + | 0.634396i | \(0.218751\pi\) | |||||||
\(422\) | −1.01575e11 | −0.155912 | ||||||||
\(423\) | −8.74101e11 | −1.32749 | ||||||||
\(424\) | 6.46049e11 | 0.970776 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.61290e11 | 0.237282 | ||||||||
\(427\) | 2.97094e11 | 0.432483 | ||||||||
\(428\) | 7.33659e11 | 1.05681 | ||||||||
\(429\) | 2.86489e11 | 0.408367 | ||||||||
\(430\) | −1.09534e12 | −1.54504 | ||||||||
\(431\) | −1.04616e12 | −1.46033 | −0.730167 | − | 0.683268i | \(-0.760558\pi\) | ||||
−0.730167 | + | 0.683268i | \(0.760558\pi\) | |||||||
\(432\) | 1.94924e11 | 0.269270 | ||||||||
\(433\) | −4.38391e11 | −0.599330 | −0.299665 | − | 0.954044i | \(-0.596875\pi\) | ||||
−0.299665 | + | 0.954044i | \(0.596875\pi\) | |||||||
\(434\) | 2.98430e11 | 0.403774 | ||||||||
\(435\) | −1.65923e11 | −0.222179 | ||||||||
\(436\) | −6.95809e11 | −0.922149 | ||||||||
\(437\) | 8.96514e11 | 1.17595 | ||||||||
\(438\) | −5.07198e11 | −0.658482 | ||||||||
\(439\) | 1.24765e12 | 1.60325 | 0.801626 | − | 0.597825i | \(-0.203968\pi\) | ||||
0.801626 | + | 0.597825i | \(0.203968\pi\) | |||||||
\(440\) | 5.68456e11 | 0.723035 | ||||||||
\(441\) | 5.86838e11 | 0.738830 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.55140e11 | −0.561472 | −0.280736 | − | 0.959785i | \(-0.590578\pi\) | ||||
−0.280736 | + | 0.959785i | \(0.590578\pi\) | |||||||
\(444\) | −2.65449e11 | −0.324159 | ||||||||
\(445\) | −1.38185e12 | −1.67047 | ||||||||
\(446\) | 3.07438e11 | 0.367918 | ||||||||
\(447\) | 1.61384e11 | 0.191195 | ||||||||
\(448\) | 3.46688e11 | 0.406619 | ||||||||
\(449\) | −4.52274e11 | −0.525161 | −0.262581 | − | 0.964910i | \(-0.584574\pi\) | ||||
−0.262581 | + | 0.964910i | \(0.584574\pi\) | |||||||
\(450\) | 6.68614e11 | 0.768634 | ||||||||
\(451\) | −8.79412e11 | −1.00092 | ||||||||
\(452\) | 2.13500e12 | 2.40588 | ||||||||
\(453\) | −4.42464e11 | −0.493669 | ||||||||
\(454\) | 1.20423e12 | 1.33032 | ||||||||
\(455\) | 3.32122e11 | 0.363284 | ||||||||
\(456\) | −4.58500e11 | −0.496590 | ||||||||
\(457\) | −7.54079e11 | −0.808712 | −0.404356 | − | 0.914602i | \(-0.632504\pi\) | ||||
−0.404356 | + | 0.914602i | \(0.632504\pi\) | |||||||
\(458\) | 1.53483e12 | 1.62992 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.40215e12 | 1.46011 | ||||||||
\(461\) | −8.30299e11 | −0.856210 | −0.428105 | − | 0.903729i | \(-0.640819\pi\) | ||||
−0.428105 | + | 0.903729i | \(0.640819\pi\) | |||||||
\(462\) | −1.40007e11 | −0.142975 | ||||||||
\(463\) | −1.63965e12 | −1.65820 | −0.829098 | − | 0.559104i | \(-0.811145\pi\) | ||||
−0.829098 | + | 0.559104i | \(0.811145\pi\) | |||||||
\(464\) | 1.24336e11 | 0.124527 | ||||||||
\(465\) | 6.01298e11 | 0.596419 | ||||||||
\(466\) | 1.00456e12 | 0.986824 | ||||||||
\(467\) | 5.39940e10 | 0.0525314 | 0.0262657 | − | 0.999655i | \(-0.491638\pi\) | ||||
0.0262657 | + | 0.999655i | \(0.491638\pi\) | |||||||
\(468\) | 1.35210e12 | 1.30288 | ||||||||
\(469\) | 3.21725e11 | 0.307048 | ||||||||
\(470\) | −3.55416e12 | −3.35967 | ||||||||
\(471\) | −7.67607e11 | −0.718695 | ||||||||
\(472\) | −7.82918e11 | −0.726068 | ||||||||
\(473\) | −6.62372e11 | −0.608453 | ||||||||
\(474\) | −1.45059e12 | −1.31991 | ||||||||
\(475\) | 1.03175e12 | 0.929933 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.19946e12 | 1.06085 | ||||||||
\(478\) | 1.46800e12 | 1.28617 | ||||||||
\(479\) | −1.51563e12 | −1.31548 | −0.657740 | − | 0.753245i | \(-0.728487\pi\) | ||||
−0.657740 | + | 0.753245i | \(0.728487\pi\) | |||||||
\(480\) | 8.40613e11 | 0.722788 | ||||||||
\(481\) | 6.41538e11 | 0.546474 | ||||||||
\(482\) | 1.68713e12 | 1.42376 | ||||||||
\(483\) | −1.08863e11 | −0.0910163 | ||||||||
\(484\) | −6.72563e11 | −0.557094 | ||||||||
\(485\) | 1.22381e12 | 1.00433 | ||||||||
\(486\) | −1.94985e12 | −1.58540 | ||||||||
\(487\) | −1.37608e12 | −1.10857 | −0.554287 | − | 0.832326i | \(-0.687009\pi\) | ||||
−0.554287 | + | 0.832326i | \(0.687009\pi\) | |||||||
\(488\) | 1.55030e12 | 1.23745 | ||||||||
\(489\) | −2.09053e11 | −0.165336 | ||||||||
\(490\) | 2.38613e12 | 1.86987 | ||||||||
\(491\) | −1.98919e12 | −1.54457 | −0.772287 | − | 0.635273i | \(-0.780887\pi\) | ||||
−0.772287 | + | 0.635273i | \(0.780887\pi\) | |||||||
\(492\) | 1.10936e12 | 0.853553 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 3.51517e12 | 2.65568 | ||||||||
\(495\) | 1.05540e12 | 0.790122 | ||||||||
\(496\) | −4.50588e11 | −0.334281 | ||||||||
\(497\) | 1.13071e11 | 0.0831277 | ||||||||
\(498\) | 1.34584e11 | 0.0980531 | ||||||||
\(499\) | 6.52474e11 | 0.471098 | 0.235549 | − | 0.971863i | \(-0.424311\pi\) | ||||
0.235549 | + | 0.971863i | \(0.424311\pi\) | |||||||
\(500\) | −9.84798e11 | −0.704664 | ||||||||
\(501\) | −5.62283e11 | −0.398736 | ||||||||
\(502\) | 6.99663e11 | 0.491725 | ||||||||
\(503\) | −1.99625e12 | −1.39046 | −0.695229 | − | 0.718788i | \(-0.744697\pi\) | ||||
−0.695229 | + | 0.718788i | \(0.744697\pi\) | |||||||
\(504\) | −2.08298e11 | −0.143796 | ||||||||
\(505\) | −2.35427e12 | −1.61081 | ||||||||
\(506\) | 1.42853e12 | 0.968748 | ||||||||
\(507\) | 1.90171e11 | 0.127823 | ||||||||
\(508\) | −4.51804e11 | −0.300998 | ||||||||
\(509\) | −1.28730e12 | −0.850063 | −0.425032 | − | 0.905179i | \(-0.639737\pi\) | ||||
−0.425032 | + | 0.905179i | \(0.639737\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.55565e11 | −0.230688 | ||||||||
\(512\) | −9.97889e11 | −0.641752 | ||||||||
\(513\) | −1.93004e12 | −1.23038 | ||||||||
\(514\) | −4.88315e10 | −0.0308579 | ||||||||
\(515\) | −2.90395e12 | −1.81910 | ||||||||
\(516\) | 8.35571e11 | 0.518871 | ||||||||
\(517\) | −2.14927e12 | −1.32307 | ||||||||
\(518\) | −3.13519e11 | −0.191328 | ||||||||
\(519\) | 3.57631e11 | 0.216363 | ||||||||
\(520\) | 1.73308e12 | 1.03945 | ||||||||
\(521\) | 8.54672e11 | 0.508194 | 0.254097 | − | 0.967179i | \(-0.418222\pi\) | ||||
0.254097 | + | 0.967179i | \(0.418222\pi\) | |||||||
\(522\) | −7.97811e11 | −0.470308 | ||||||||
\(523\) | −4.36274e11 | −0.254978 | −0.127489 | − | 0.991840i | \(-0.540692\pi\) | ||||
−0.127489 | + | 0.991840i | \(0.540692\pi\) | |||||||
\(524\) | −1.76138e12 | −1.02062 | ||||||||
\(525\) | −1.25284e11 | −0.0719748 | ||||||||
\(526\) | 2.34744e12 | 1.33708 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2.11391e11 | 0.118368 | ||||||||
\(529\) | −6.90392e11 | −0.383306 | ||||||||
\(530\) | 4.87710e12 | 2.68485 | ||||||||
\(531\) | −1.45357e12 | −0.793436 | ||||||||
\(532\) | −1.01964e12 | −0.551882 | ||||||||
\(533\) | −2.68111e12 | −1.43894 | ||||||||
\(534\) | 1.77596e12 | 0.945144 | ||||||||
\(535\) | 1.74592e12 | 0.921365 | ||||||||
\(536\) | 1.67883e12 | 0.878545 | ||||||||
\(537\) | 9.92661e11 | 0.515130 | ||||||||
\(538\) | 6.09612e11 | 0.313714 | ||||||||
\(539\) | 1.44293e12 | 0.736372 | ||||||||
\(540\) | −3.01860e12 | −1.52768 | ||||||||
\(541\) | −2.18108e12 | −1.09467 | −0.547337 | − | 0.836913i | \(-0.684358\pi\) | ||||
−0.547337 | + | 0.836913i | \(0.684358\pi\) | |||||||
\(542\) | 1.32253e12 | 0.658275 | ||||||||
\(543\) | −1.58541e12 | −0.782607 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.65585e12 | −0.803962 | ||||||||
\(546\) | −4.26846e11 | −0.205544 | ||||||||
\(547\) | −2.19466e12 | −1.04815 | −0.524077 | − | 0.851671i | \(-0.675589\pi\) | ||||
−0.524077 | + | 0.851671i | \(0.675589\pi\) | |||||||
\(548\) | −2.76829e12 | −1.31129 | ||||||||
\(549\) | 2.87830e12 | 1.35226 | ||||||||
\(550\) | 1.64401e12 | 0.766076 | ||||||||
\(551\) | −1.23111e12 | −0.569004 | ||||||||
\(552\) | −5.68071e11 | −0.260422 | ||||||||
\(553\) | −1.01692e12 | −0.462407 | ||||||||
\(554\) | −1.30353e12 | −0.587932 | ||||||||
\(555\) | −6.31700e11 | −0.282613 | ||||||||
\(556\) | 1.67753e12 | 0.744447 | ||||||||
\(557\) | 2.19414e12 | 0.965864 | 0.482932 | − | 0.875658i | \(-0.339572\pi\) | ||||
0.482932 | + | 0.875658i | \(0.339572\pi\) | |||||||
\(558\) | 2.89124e12 | 1.26250 | ||||||||
\(559\) | −2.01941e12 | −0.874723 | ||||||||
\(560\) | 2.45062e11 | 0.105300 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.24491e12 | −2.21781 | ||||||||
\(563\) | −2.03940e12 | −0.855489 | −0.427745 | − | 0.903900i | \(-0.640692\pi\) | ||||
−0.427745 | + | 0.903900i | \(0.640692\pi\) | |||||||
\(564\) | 2.71126e12 | 1.12828 | ||||||||
\(565\) | 5.08073e12 | 2.09753 | ||||||||
\(566\) | −3.95135e12 | −1.61835 | ||||||||
\(567\) | −2.55731e11 | −0.103911 | ||||||||
\(568\) | 5.90026e11 | 0.237850 | ||||||||
\(569\) | −3.56626e12 | −1.42629 | −0.713144 | − | 0.701017i | \(-0.752730\pi\) | ||||
−0.713144 | + | 0.701017i | \(0.752730\pi\) | |||||||
\(570\) | −3.46127e12 | −1.37341 | ||||||||
\(571\) | 2.49685e12 | 0.982945 | 0.491473 | − | 0.870893i | \(-0.336459\pi\) | ||||
0.491473 | + | 0.870893i | \(0.336459\pi\) | |||||||
\(572\) | 3.32459e12 | 1.29854 | ||||||||
\(573\) | 9.91942e11 | 0.384406 | ||||||||
\(574\) | 1.31025e12 | 0.503792 | ||||||||
\(575\) | 1.27831e12 | 0.487675 | ||||||||
\(576\) | 3.35878e12 | 1.27139 | ||||||||
\(577\) | 3.19650e12 | 1.20056 | 0.600279 | − | 0.799791i | \(-0.295056\pi\) | ||||
0.600279 | + | 0.799791i | \(0.295056\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.41925e12 | −0.894595 | ||||||||
\(580\) | −1.92547e12 | −0.706496 | ||||||||
\(581\) | 9.43486e10 | 0.0343513 | ||||||||
\(582\) | −1.57285e12 | −0.568244 | ||||||||
\(583\) | 2.94927e12 | 1.05732 | ||||||||
\(584\) | −1.85541e12 | −0.660059 | ||||||||
\(585\) | 3.21765e12 | 1.13589 | ||||||||
\(586\) | −3.56989e12 | −1.25059 | ||||||||
\(587\) | 4.21874e12 | 1.46660 | 0.733299 | − | 0.679906i | \(-0.237979\pi\) | ||||
0.733299 | + | 0.679906i | \(0.237979\pi\) | |||||||
\(588\) | −1.82024e12 | −0.627957 | ||||||||
\(589\) | 4.46151e12 | 1.52744 | ||||||||
\(590\) | −5.91034e12 | −2.00807 | ||||||||
\(591\) | −1.09340e12 | −0.368666 | ||||||||
\(592\) | 4.73370e11 | 0.158399 | ||||||||
\(593\) | −1.41657e12 | −0.470427 | −0.235214 | − | 0.971944i | \(-0.575579\pi\) | ||||
−0.235214 | + | 0.971944i | \(0.575579\pi\) | |||||||
\(594\) | −3.07538e12 | −1.01358 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.87279e12 | 0.607969 | ||||||||
\(597\) | 2.37387e12 | 0.764843 | ||||||||
\(598\) | 4.35522e12 | 1.39269 | ||||||||
\(599\) | 4.20552e12 | 1.33475 | 0.667374 | − | 0.744722i | \(-0.267418\pi\) | ||||
0.667374 | + | 0.744722i | \(0.267418\pi\) | |||||||
\(600\) | −6.53760e11 | −0.205939 | ||||||||
\(601\) | −4.21313e12 | −1.31725 | −0.658627 | − | 0.752469i | \(-0.728863\pi\) | ||||
−0.658627 | + | 0.752469i | \(0.728863\pi\) | |||||||
\(602\) | 9.86882e11 | 0.306253 | ||||||||
\(603\) | 3.11693e12 | 0.960061 | ||||||||
\(604\) | −5.13462e12 | −1.56979 | ||||||||
\(605\) | −1.60052e12 | −0.485695 | ||||||||
\(606\) | 3.02573e12 | 0.911388 | ||||||||
\(607\) | −5.49794e11 | −0.164381 | −0.0821904 | − | 0.996617i | \(-0.526192\pi\) | ||||
−0.0821904 | + | 0.996617i | \(0.526192\pi\) | |||||||
\(608\) | 6.23718e12 | 1.85107 | ||||||||
\(609\) | 1.49493e11 | 0.0440396 | ||||||||
\(610\) | 1.17034e13 | 3.42238 | ||||||||
\(611\) | −6.55257e12 | −1.90207 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.73227e11 | 0.135362 | 0.0676810 | − | 0.997707i | \(-0.478440\pi\) | ||||
0.0676810 | + | 0.997707i | \(0.478440\pi\) | |||||||
\(614\) | 3.57810e12 | 1.01600 | ||||||||
\(615\) | 2.63999e12 | 0.744158 | ||||||||
\(616\) | −5.12168e11 | −0.143318 | ||||||||
\(617\) | 6.13226e12 | 1.70348 | 0.851740 | − | 0.523964i | \(-0.175547\pi\) | ||||
0.851740 | + | 0.523964i | \(0.175547\pi\) | |||||||
\(618\) | 3.73218e12 | 1.02923 | ||||||||
\(619\) | −2.20706e12 | −0.604237 | −0.302118 | − | 0.953270i | \(-0.597694\pi\) | ||||
−0.302118 | + | 0.953270i | \(0.597694\pi\) | |||||||
\(620\) | 6.97782e12 | 1.89652 | ||||||||
\(621\) | −2.39128e12 | −0.645236 | ||||||||
\(622\) | 2.27877e12 | 0.610440 | ||||||||
\(623\) | 1.24502e12 | 0.331115 | ||||||||
\(624\) | 6.44479e11 | 0.170168 | ||||||||
\(625\) | −4.71251e12 | −1.23536 | ||||||||
\(626\) | −6.94292e12 | −1.80700 | ||||||||
\(627\) | −2.09309e12 | −0.540860 | ||||||||
\(628\) | −8.90777e12 | −2.28534 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1.57246e12 | −0.397693 | ||||||||
\(631\) | 5.73681e12 | 1.44058 | 0.720291 | − | 0.693672i | \(-0.244008\pi\) | ||||
0.720291 | + | 0.693672i | \(0.244008\pi\) | |||||||
\(632\) | −5.30651e12 | −1.32307 | ||||||||
\(633\) | 1.84395e11 | 0.0456492 | ||||||||
\(634\) | 1.05988e13 | 2.60528 | ||||||||
\(635\) | −1.07518e12 | −0.262420 | ||||||||
\(636\) | −3.72045e12 | −0.901652 | ||||||||
\(637\) | 4.39915e12 | 1.05862 | ||||||||
\(638\) | −1.96168e12 | −0.468744 | ||||||||
\(639\) | 1.09545e12 | 0.259919 | ||||||||
\(640\) | 6.97715e12 | 1.64387 | ||||||||
\(641\) | −3.02882e12 | −0.708618 | −0.354309 | − | 0.935128i | \(-0.615284\pi\) | ||||
−0.354309 | + | 0.935128i | \(0.615284\pi\) | |||||||
\(642\) | −2.24387e12 | −0.521303 | ||||||||
\(643\) | 3.56039e12 | 0.821389 | 0.410694 | − | 0.911773i | \(-0.365286\pi\) | ||||
0.410694 | + | 0.911773i | \(0.365286\pi\) | |||||||
\(644\) | −1.26331e12 | −0.289418 | ||||||||
\(645\) | 1.98844e12 | 0.452370 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.12696e12 | −0.252835 | −0.126418 | − | 0.991977i | \(-0.540348\pi\) | ||||
−0.126418 | + | 0.991977i | \(0.540348\pi\) | |||||||
\(648\) | −1.33446e12 | −0.297315 | ||||||||
\(649\) | −3.57409e12 | −0.790796 | ||||||||
\(650\) | 5.01217e12 | 1.10133 | ||||||||
\(651\) | −5.41759e11 | −0.118220 | ||||||||
\(652\) | −2.42598e12 | −0.525743 | ||||||||
\(653\) | 5.96043e11 | 0.128283 | 0.0641413 | − | 0.997941i | \(-0.479569\pi\) | ||||
0.0641413 | + | 0.997941i | \(0.479569\pi\) | |||||||
\(654\) | 2.12811e12 | 0.454877 | ||||||||
\(655\) | −4.19164e12 | −0.889811 | ||||||||
\(656\) | −1.97830e12 | −0.417086 | ||||||||
\(657\) | −3.44478e12 | −0.721303 | ||||||||
\(658\) | 3.20223e12 | 0.665942 | ||||||||
\(659\) | 3.31591e12 | 0.684887 | 0.342443 | − | 0.939538i | \(-0.388745\pi\) | ||||
0.342443 | + | 0.939538i | \(0.388745\pi\) | |||||||
\(660\) | −3.27361e12 | −0.671552 | ||||||||
\(661\) | 7.15298e12 | 1.45740 | 0.728702 | − | 0.684831i | \(-0.240124\pi\) | ||||
0.728702 | + | 0.684831i | \(0.240124\pi\) | |||||||
\(662\) | −9.95450e12 | −2.01446 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.92330e11 | 0.0982880 | ||||||||
\(665\) | −2.42649e12 | −0.481150 | ||||||||
\(666\) | −3.03743e12 | −0.598235 | ||||||||
\(667\) | −1.52532e12 | −0.298397 | ||||||||
\(668\) | −6.52507e12 | −1.26792 | ||||||||
\(669\) | −5.58112e11 | −0.107722 | ||||||||
\(670\) | 1.26737e13 | 2.42977 | ||||||||
\(671\) | 7.07726e12 | 1.34776 | ||||||||
\(672\) | −7.57377e11 | −0.143268 | ||||||||
\(673\) | 1.72634e12 | 0.324384 | 0.162192 | − | 0.986759i | \(-0.448144\pi\) | ||||
0.162192 | + | 0.986759i | \(0.448144\pi\) | |||||||
\(674\) | −4.72330e12 | −0.881609 | ||||||||
\(675\) | −2.75199e12 | −0.510246 | ||||||||
\(676\) | 2.20686e12 | 0.406456 | ||||||||
\(677\) | −9.74400e12 | −1.78274 | −0.891370 | − | 0.453276i | \(-0.850255\pi\) | ||||
−0.891370 | + | 0.453276i | \(0.850255\pi\) | |||||||
\(678\) | −6.52981e12 | −1.18677 | ||||||||
\(679\) | −1.10263e12 | −0.199075 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.18611e12 | −0.389503 | ||||||||
\(682\) | 7.10907e12 | 1.25830 | ||||||||
\(683\) | 5.73218e12 | 1.00792 | 0.503961 | − | 0.863726i | \(-0.331876\pi\) | ||||
0.503961 | + | 0.863726i | \(0.331876\pi\) | |||||||
\(684\) | −9.87850e12 | −1.72559 | ||||||||
\(685\) | −6.58781e12 | −1.14323 | ||||||||
\(686\) | −4.44595e12 | −0.766489 | ||||||||
\(687\) | −2.78628e12 | −0.477220 | ||||||||
\(688\) | −1.49006e12 | −0.253545 | ||||||||
\(689\) | 8.99159e12 | 1.52002 | ||||||||
\(690\) | −4.28844e12 | −0.720241 | ||||||||
\(691\) | 1.94747e12 | 0.324952 | 0.162476 | − | 0.986712i | \(-0.448052\pi\) | ||||
0.162476 | + | 0.986712i | \(0.448052\pi\) | |||||||
\(692\) | 4.15017e12 | 0.688000 | ||||||||
\(693\) | −9.50898e11 | −0.156615 | ||||||||
\(694\) | −4.52795e11 | −0.0740942 | ||||||||
\(695\) | 3.99208e12 | 0.649035 | ||||||||
\(696\) | 7.80087e11 | 0.126009 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −3.54180e12 | −0.564774 | ||||||||
\(699\) | −1.82365e12 | −0.288930 | ||||||||
\(700\) | −1.45388e12 | −0.228869 | ||||||||
\(701\) | −4.61502e12 | −0.721842 | −0.360921 | − | 0.932596i | \(-0.617538\pi\) | ||||
−0.360921 | + | 0.932596i | \(0.617538\pi\) | |||||||
\(702\) | −9.37606e12 | −1.45715 | ||||||||
\(703\) | −4.68709e12 | −0.723776 | ||||||||
\(704\) | 8.25865e12 | 1.26716 | ||||||||
\(705\) | 6.45210e12 | 0.983671 | ||||||||
\(706\) | −7.75817e12 | −1.17527 | ||||||||
\(707\) | 2.12115e12 | 0.319290 | ||||||||
\(708\) | 4.50865e12 | 0.674368 | ||||||||
\(709\) | 2.50294e12 | 0.372000 | 0.186000 | − | 0.982550i | \(-0.440448\pi\) | ||||
0.186000 | + | 0.982550i | \(0.440448\pi\) | |||||||
\(710\) | 4.45417e12 | 0.657816 | ||||||||
\(711\) | −9.85213e12 | −1.44583 | ||||||||
\(712\) | 6.49676e12 | 0.947408 | ||||||||
\(713\) | 5.52771e12 | 0.801018 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.91166e12 | 1.13211 | ||||||||
\(716\) | 1.15194e13 | 1.63803 | ||||||||
\(717\) | −2.66495e12 | −0.376576 | ||||||||
\(718\) | 8.42272e12 | 1.18275 | ||||||||
\(719\) | −1.15159e13 | −1.60701 | −0.803504 | − | 0.595300i | \(-0.797033\pi\) | ||||
−0.803504 | + | 0.595300i | \(0.797033\pi\) | |||||||
\(720\) | 2.37421e12 | 0.329247 | ||||||||
\(721\) | 2.61640e12 | 0.360575 | ||||||||
\(722\) | −1.42290e13 | −1.94875 | ||||||||
\(723\) | −3.06276e12 | −0.416860 | ||||||||
\(724\) | −1.83981e13 | −2.48857 | ||||||||
\(725\) | −1.75540e12 | −0.235969 | ||||||||
\(726\) | 2.05701e12 | 0.274803 | ||||||||
\(727\) | −4.59761e12 | −0.610418 | −0.305209 | − | 0.952285i | \(-0.598726\pi\) | ||||
−0.305209 | + | 0.952285i | \(0.598726\pi\) | |||||||
\(728\) | −1.56147e12 | −0.206036 | ||||||||
\(729\) | 3.99890e11 | 0.0524405 | ||||||||
\(730\) | −1.40067e13 | −1.82551 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −8.92784e12 | −1.14933 | ||||||||
\(733\) | −5.97894e12 | −0.764991 | −0.382495 | − | 0.923957i | \(-0.624935\pi\) | ||||
−0.382495 | + | 0.923957i | \(0.624935\pi\) | |||||||
\(734\) | −2.62118e12 | −0.333322 | ||||||||
\(735\) | −4.33169e12 | −0.547475 | ||||||||
\(736\) | 7.72772e12 | 0.970736 | ||||||||
\(737\) | 7.66399e12 | 0.956866 | ||||||||
\(738\) | 1.26940e13 | 1.57523 | ||||||||
\(739\) | 6.24601e12 | 0.770376 | 0.385188 | − | 0.922838i | \(-0.374137\pi\) | ||||
0.385188 | + | 0.922838i | \(0.374137\pi\) | |||||||
\(740\) | −7.33063e12 | −0.898666 | ||||||||
\(741\) | −6.38132e12 | −0.777551 | ||||||||
\(742\) | −4.39418e12 | −0.532182 | ||||||||
\(743\) | −7.10024e12 | −0.854719 | −0.427360 | − | 0.904082i | \(-0.640556\pi\) | ||||
−0.427360 | + | 0.904082i | \(0.640556\pi\) | |||||||
\(744\) | −2.82701e12 | −0.338259 | ||||||||
\(745\) | 4.45676e12 | 0.530049 | ||||||||
\(746\) | −5.81470e12 | −0.687390 | ||||||||
\(747\) | 9.14066e11 | 0.107408 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.57304e12 | −0.182630 | ||||||||
\(750\) | 3.01197e12 | 0.347596 | ||||||||
\(751\) | −1.86664e12 | −0.214132 | −0.107066 | − | 0.994252i | \(-0.534146\pi\) | ||||
−0.107066 | + | 0.994252i | \(0.534146\pi\) | |||||||
\(752\) | −4.83494e12 | −0.551329 | ||||||||
\(753\) | −1.27014e12 | −0.143971 | ||||||||
\(754\) | −5.98068e12 | −0.673875 | ||||||||
\(755\) | −1.22191e13 | −1.36860 | ||||||||
\(756\) | 2.71971e12 | 0.302812 | ||||||||
\(757\) | 1.50795e13 | 1.66900 | 0.834498 | − | 0.551012i | \(-0.185758\pi\) | ||||
0.834498 | + | 0.551012i | \(0.185758\pi\) | |||||||
\(758\) | −1.96217e13 | −2.15886 | ||||||||
\(759\) | −2.59330e12 | −0.283638 | ||||||||
\(760\) | −1.26619e13 | −1.37670 | ||||||||
\(761\) | −1.49680e13 | −1.61782 | −0.808912 | − | 0.587929i | \(-0.799943\pi\) | ||||
−0.808912 | + | 0.587929i | \(0.799943\pi\) | |||||||
\(762\) | 1.38183e12 | 0.148476 | ||||||||
\(763\) | 1.49189e12 | 0.159359 | ||||||||
\(764\) | 1.15111e13 | 1.22235 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.58181e13 | 1.66007 | ||||||||
\(767\) | −1.08965e13 | −1.13686 | ||||||||
\(768\) | −1.83311e12 | −0.190135 | ||||||||
\(769\) | 4.90137e12 | 0.505416 | 0.252708 | − | 0.967543i | \(-0.418679\pi\) | ||||
0.252708 | + | 0.967543i | \(0.418679\pi\) | |||||||
\(770\) | −3.86642e12 | −0.396370 | ||||||||
\(771\) | 8.86470e10 | 0.00903482 | ||||||||
\(772\) | −2.80744e13 | −2.84467 | ||||||||
\(773\) | −1.28051e13 | −1.28996 | −0.644978 | − | 0.764201i | \(-0.723133\pi\) | ||||
−0.644978 | + | 0.764201i | \(0.723133\pi\) | |||||||
\(774\) | 9.56109e12 | 0.957576 | ||||||||
\(775\) | 6.36152e12 | 0.633437 | ||||||||
\(776\) | −5.75376e12 | −0.569605 | ||||||||
\(777\) | 5.69151e11 | 0.0560186 | ||||||||
\(778\) | −4.54130e12 | −0.444398 | ||||||||
\(779\) | 1.95882e13 | 1.90580 | ||||||||
\(780\) | −9.98043e12 | −0.965436 | ||||||||
\(781\) | 2.69352e12 | 0.259054 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.28376e12 | 0.312207 | ||||||||
\(784\) | 3.24599e12 | 0.306849 | ||||||||
\(785\) | −2.11982e13 | −1.99244 | ||||||||
\(786\) | 5.38713e12 | 0.503450 | ||||||||
\(787\) | −7.79210e12 | −0.724050 | −0.362025 | − | 0.932168i | \(-0.617914\pi\) | ||||
−0.362025 | + | 0.932168i | \(0.617914\pi\) | |||||||
\(788\) | −1.26884e13 | −1.17230 | ||||||||
\(789\) | −4.26146e12 | −0.391482 | ||||||||
\(790\) | −4.00595e13 | −3.65918 | ||||||||
\(791\) | −4.57765e12 | −0.415766 | ||||||||
\(792\) | −4.96198e12 | −0.448117 | ||||||||
\(793\) | 2.15768e13 | 1.93757 | ||||||||
\(794\) | 1.17713e13 | 1.05107 | ||||||||
\(795\) | −8.85371e12 | −0.786092 | ||||||||
\(796\) | 2.75478e13 | 2.43208 | ||||||||
\(797\) | 1.20701e13 | 1.05961 | 0.529807 | − | 0.848118i | \(-0.322264\pi\) | ||||
0.529807 | + | 0.848118i | \(0.322264\pi\) | |||||||
\(798\) | 3.11854e12 | 0.272232 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 8.89339e12 | 0.767648 | ||||||||
\(801\) | 1.20620e13 | 1.03531 | ||||||||
\(802\) | 2.14058e13 | 1.82704 | ||||||||
\(803\) | −8.47013e12 | −0.718903 | ||||||||
\(804\) | −9.66799e12 | −0.815989 | ||||||||
\(805\) | −3.00636e12 | −0.252325 | ||||||||
\(806\) | 2.16738e13 | 1.80895 | ||||||||
\(807\) | −1.10667e12 | −0.0918516 | ||||||||
\(808\) | 1.10686e13 | 0.913572 | ||||||||
\(809\) | 1.04899e13 | 0.860999 | 0.430500 | − | 0.902591i | \(-0.358337\pi\) | ||||
0.430500 | + | 0.902591i | \(0.358337\pi\) | |||||||
\(810\) | −1.00740e13 | −0.822278 | ||||||||
\(811\) | 4.24679e12 | 0.344721 | 0.172360 | − | 0.985034i | \(-0.444861\pi\) | ||||
0.172360 | + | 0.985034i | \(0.444861\pi\) | |||||||
\(812\) | 1.73481e12 | 0.140039 | ||||||||
\(813\) | −2.40087e12 | −0.192735 | ||||||||
\(814\) | −7.46851e12 | −0.596244 | ||||||||
\(815\) | −5.77321e12 | −0.458361 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.47538e13 | 1.15853 | ||||||||
\(818\) | 1.72703e13 | 1.34869 | ||||||||
\(819\) | −2.89905e12 | −0.225153 | ||||||||
\(820\) | 3.06361e13 | 2.36631 | ||||||||
\(821\) | −8.29736e12 | −0.637376 | −0.318688 | − | 0.947860i | \(-0.603242\pi\) | ||||
−0.318688 | + | 0.947860i | \(0.603242\pi\) | |||||||
\(822\) | 8.46673e12 | 0.646833 | ||||||||
\(823\) | −1.69218e13 | −1.28572 | −0.642860 | − | 0.765984i | \(-0.722252\pi\) | ||||
−0.642860 | + | 0.765984i | \(0.722252\pi\) | |||||||
\(824\) | 1.36529e13 | 1.03170 | ||||||||
\(825\) | −2.98448e12 | −0.224298 | ||||||||
\(826\) | 5.32511e12 | 0.398032 | ||||||||
\(827\) | −5.01967e12 | −0.373165 | −0.186582 | − | 0.982439i | \(-0.559741\pi\) | ||||
−0.186582 | + | 0.982439i | \(0.559741\pi\) | |||||||
\(828\) | −1.22392e13 | −0.904935 | ||||||||
\(829\) | 8.26746e12 | 0.607963 | 0.303981 | − | 0.952678i | \(-0.401684\pi\) | ||||
0.303981 | + | 0.952678i | \(0.401684\pi\) | |||||||
\(830\) | 3.71666e12 | 0.271833 | ||||||||
\(831\) | 2.36638e12 | 0.172140 | ||||||||
\(832\) | 2.51786e13 | 1.82170 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5.13067e12 | −0.367220 | ||||||||
\(835\) | −1.55280e13 | −1.10542 | ||||||||
\(836\) | −2.42895e13 | −1.71985 | ||||||||
\(837\) | −1.19002e13 | −0.838090 | ||||||||
\(838\) | 1.91454e13 | 1.34112 | ||||||||
\(839\) | −1.09618e13 | −0.763751 | −0.381875 | − | 0.924214i | \(-0.624722\pi\) | ||||
−0.381875 | + | 0.924214i | \(0.624722\pi\) | |||||||
\(840\) | 1.53753e12 | 0.106553 | ||||||||
\(841\) | −1.24125e13 | −0.855616 | ||||||||
\(842\) | −3.53686e13 | −2.42501 | ||||||||
\(843\) | 9.52143e12 | 0.649349 | ||||||||
\(844\) | 2.13983e12 | 0.145157 | ||||||||
\(845\) | 5.25174e12 | 0.354363 | ||||||||
\(846\) | 3.10238e13 | 2.08223 | ||||||||
\(847\) | 1.44204e12 | 0.0962727 | ||||||||
\(848\) | 6.63461e12 | 0.440589 | ||||||||
\(849\) | 7.17315e12 | 0.473833 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.80719e12 | −0.379562 | ||||||||
\(852\) | −3.39783e12 | −0.220914 | ||||||||
\(853\) | 5.66078e12 | 0.366105 | 0.183052 | − | 0.983103i | \(-0.441402\pi\) | ||||
0.183052 | + | 0.983103i | \(0.441402\pi\) | |||||||
\(854\) | −1.05446e13 | −0.678372 | ||||||||
\(855\) | −2.35082e13 | −1.50443 | ||||||||
\(856\) | −8.20845e12 | −0.522552 | ||||||||
\(857\) | 2.86169e13 | 1.81221 | 0.906106 | − | 0.423050i | \(-0.139041\pi\) | ||||
0.906106 | + | 0.423050i | \(0.139041\pi\) | |||||||
\(858\) | −1.01681e13 | −0.640544 | ||||||||
\(859\) | −2.17190e13 | −1.36104 | −0.680521 | − | 0.732729i | \(-0.738246\pi\) | ||||
−0.680521 | + | 0.732729i | \(0.738246\pi\) | |||||||
\(860\) | 2.30751e13 | 1.43847 | ||||||||
\(861\) | −2.37859e12 | −0.147504 | ||||||||
\(862\) | 3.71308e13 | 2.29061 | ||||||||
\(863\) | −2.05248e13 | −1.25959 | −0.629796 | − | 0.776761i | \(-0.716861\pi\) | ||||
−0.629796 | + | 0.776761i | \(0.716861\pi\) | |||||||
\(864\) | −1.66365e13 | −1.01566 | ||||||||
\(865\) | 9.87632e12 | 0.599823 | ||||||||
\(866\) | 1.55595e13 | 0.940080 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.28690e12 | −0.375922 | ||||||||
\(869\) | −2.42247e13 | −1.44102 | ||||||||
\(870\) | 5.88897e12 | 0.348500 | ||||||||
\(871\) | 2.33656e13 | 1.37561 | ||||||||
\(872\) | 7.78498e12 | 0.455967 | ||||||||
\(873\) | −1.06825e13 | −0.622456 | ||||||||
\(874\) | −3.18193e13 | −1.84455 | ||||||||
\(875\) | 2.11151e12 | 0.121775 | ||||||||
\(876\) | 1.06849e13 | 0.613060 | ||||||||
\(877\) | 3.10724e13 | 1.77369 | 0.886843 | − | 0.462072i | \(-0.152894\pi\) | ||||
0.886843 | + | 0.462072i | \(0.152894\pi\) | |||||||
\(878\) | −4.42819e13 | −2.51478 | ||||||||
\(879\) | 6.48065e12 | 0.366158 | ||||||||
\(880\) | 5.83776e12 | 0.328152 | ||||||||
\(881\) | 4.35667e12 | 0.243648 | 0.121824 | − | 0.992552i | \(-0.461126\pi\) | ||||
0.121824 | + | 0.992552i | \(0.461126\pi\) | |||||||
\(882\) | −2.08282e13 | −1.15889 | ||||||||
\(883\) | 1.30562e13 | 0.722758 | 0.361379 | − | 0.932419i | \(-0.382306\pi\) | ||||
0.361379 | + | 0.932419i | \(0.382306\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.07294e13 | 0.587938 | ||||||||
\(886\) | 1.61539e13 | 0.880697 | ||||||||
\(887\) | 3.11601e13 | 1.69022 | 0.845108 | − | 0.534596i | \(-0.179536\pi\) | ||||
0.845108 | + | 0.534596i | \(0.179536\pi\) | |||||||
\(888\) | 2.96995e12 | 0.160284 | ||||||||
\(889\) | 9.68714e11 | 0.0520161 | ||||||||
\(890\) | 4.90448e13 | 2.62022 | ||||||||
\(891\) | −6.09192e12 | −0.323821 | ||||||||
\(892\) | −6.47667e12 | −0.342539 | ||||||||
\(893\) | 4.78732e13 | 2.51919 | ||||||||
\(894\) | −5.72787e12 | −0.299898 | ||||||||
\(895\) | 2.74133e13 | 1.42809 | ||||||||
\(896\) | −6.28628e12 | −0.325843 | ||||||||
\(897\) | −7.90631e12 | −0.407763 | ||||||||
\(898\) | 1.60522e13 | 0.823742 | ||||||||
\(899\) | −7.59076e12 | −0.387585 | ||||||||
\(900\) | −1.40854e13 | −0.715614 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 3.12123e13 | 1.56999 | ||||||||
\(903\) | −1.79155e12 | −0.0896673 | ||||||||
\(904\) | −2.38871e13 | −1.18961 | ||||||||
\(905\) | −4.37827e13 | −2.16962 | ||||||||
\(906\) | 1.57041e13 | 0.774346 | ||||||||
\(907\) | 1.75730e13 | 0.862208 | 0.431104 | − | 0.902302i | \(-0.358124\pi\) | ||||
0.431104 | + | 0.902302i | \(0.358124\pi\) | |||||||
\(908\) | −2.53689e13 | −1.23856 | ||||||||
\(909\) | 2.05501e13 | 0.998337 | ||||||||
\(910\) | −1.17877e13 | −0.569829 | ||||||||
\(911\) | −3.26951e12 | −0.157272 | −0.0786358 | − | 0.996903i | \(-0.525056\pi\) | ||||
−0.0786358 | + | 0.996903i | \(0.525056\pi\) | |||||||
\(912\) | −4.70858e12 | −0.225379 | ||||||||
\(913\) | 2.24753e12 | 0.107050 | ||||||||
\(914\) | 2.67640e13 | 1.26851 | ||||||||
\(915\) | −2.12459e13 | −1.00203 | ||||||||
\(916\) | −3.23336e13 | −1.51749 | ||||||||
\(917\) | 3.77659e12 | 0.176375 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.28770e13 | −0.595517 | −0.297759 | − | 0.954641i | \(-0.596239\pi\) | ||||
−0.297759 | + | 0.954641i | \(0.596239\pi\) | |||||||
\(920\) | −1.56878e13 | −0.721967 | ||||||||
\(921\) | −6.49556e12 | −0.297473 | ||||||||
\(922\) | 2.94692e13 | 1.34301 | ||||||||
\(923\) | 8.21187e12 | 0.372421 | ||||||||
\(924\) | 2.94947e12 | 0.133113 | ||||||||
\(925\) | −6.68316e12 | −0.300154 | ||||||||
\(926\) | 5.81947e13 | 2.60096 | ||||||||
\(927\) | 2.53482e13 | 1.12743 | ||||||||
\(928\) | −1.06119e13 | −0.469705 | ||||||||
\(929\) | −8.08221e12 | −0.356008 | −0.178004 | − | 0.984030i | \(-0.556964\pi\) | ||||
−0.178004 | + | 0.984030i | \(0.556964\pi\) | |||||||
\(930\) | −2.13414e13 | −0.935514 | ||||||||
\(931\) | −3.21403e13 | −1.40209 | ||||||||
\(932\) | −2.11627e13 | −0.918754 | ||||||||
\(933\) | −4.13679e12 | −0.178730 | ||||||||
\(934\) | −1.91637e12 | −0.0823983 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.51278e13 | −0.644222 | ||||||||
\(937\) | 6.49112e12 | 0.275101 | 0.137550 | − | 0.990495i | \(-0.456077\pi\) | ||||
0.137550 | + | 0.990495i | \(0.456077\pi\) | |||||||
\(938\) | −1.14187e13 | −0.481621 | ||||||||
\(939\) | 1.26039e13 | 0.529067 | ||||||||
\(940\) | 7.48740e13 | 3.12792 | ||||||||
\(941\) | −1.21565e11 | −0.00505423 | −0.00252711 | − | 0.999997i | \(-0.500804\pi\) | ||||
−0.00252711 | + | 0.999997i | \(0.500804\pi\) | |||||||
\(942\) | 2.72441e13 | 1.12731 | ||||||||
\(943\) | 2.42694e13 | 0.999437 | ||||||||
\(944\) | −8.04019e12 | −0.329528 | ||||||||
\(945\) | 6.47219e12 | 0.264003 | ||||||||
\(946\) | 2.35091e13 | 0.954389 | ||||||||
\(947\) | 4.00324e12 | 0.161747 | 0.0808735 | − | 0.996724i | \(-0.474229\pi\) | ||||
0.0808735 | + | 0.996724i | \(0.474229\pi\) | |||||||
\(948\) | 3.05591e13 | 1.22886 | ||||||||
\(949\) | −2.58233e13 | −1.03351 | ||||||||
\(950\) | −3.66190e13 | −1.45865 | ||||||||
\(951\) | −1.92407e13 | −0.762795 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.60121e13 | −1.41426 | −0.707131 | − | 0.707082i | \(-0.750011\pi\) | ||||
−0.707131 | + | 0.707082i | \(0.750011\pi\) | |||||||
\(954\) | −4.25716e13 | −1.66400 | ||||||||
\(955\) | 2.73934e13 | 1.06569 | ||||||||
\(956\) | −3.09257e13 | −1.19745 | ||||||||
\(957\) | 3.56117e12 | 0.137242 | ||||||||
\(958\) | 5.37932e13 | 2.06340 | ||||||||
\(959\) | 5.93550e12 | 0.226607 | ||||||||
\(960\) | −2.47925e13 | −0.942105 | ||||||||
\(961\) | 1.06905e12 | 0.0404336 | ||||||||
\(962\) | −2.27696e13 | −0.857172 | ||||||||
\(963\) | −1.52399e13 | −0.571037 | ||||||||
\(964\) | −3.55421e13 | −1.32555 | ||||||||
\(965\) | −6.68097e13 | −2.48009 | ||||||||
\(966\) | 3.86380e12 | 0.142764 | ||||||||
\(967\) | 4.03493e13 | 1.48394 | 0.741972 | − | 0.670431i | \(-0.233891\pi\) | ||||
0.741972 | + | 0.670431i | \(0.233891\pi\) | |||||||
\(968\) | 7.52489e12 | 0.275461 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.34358e13 | −1.57534 | ||||||||
\(971\) | 1.94578e13 | 0.702435 | 0.351218 | − | 0.936294i | \(-0.385768\pi\) | ||||
0.351218 | + | 0.936294i | \(0.385768\pi\) | |||||||
\(972\) | 4.10766e13 | 1.47604 | ||||||||
\(973\) | −3.59680e12 | −0.128649 | ||||||||
\(974\) | 4.88404e13 | 1.73886 | ||||||||
\(975\) | −9.09892e12 | −0.322455 | ||||||||
\(976\) | 1.59208e13 | 0.561619 | ||||||||
\(977\) | 4.00163e13 | 1.40511 | 0.702557 | − | 0.711627i | \(-0.252042\pi\) | ||||
0.702557 | + | 0.711627i | \(0.252042\pi\) | |||||||
\(978\) | 7.41978e12 | 0.259338 | ||||||||
\(979\) | 2.96583e13 | 1.03187 | ||||||||
\(980\) | −5.02676e13 | −1.74089 | ||||||||
\(981\) | 1.44537e13 | 0.498273 | ||||||||
\(982\) | 7.06007e13 | 2.42274 | ||||||||
\(983\) | 1.03796e13 | 0.354559 | 0.177280 | − | 0.984161i | \(-0.443270\pi\) | ||||
0.177280 | + | 0.984161i | \(0.443270\pi\) | |||||||
\(984\) | −1.24120e13 | −0.422049 | ||||||||
\(985\) | −3.01951e13 | −1.02205 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.81322e12 | −0.194980 | ||||||||
\(988\) | −7.40527e13 | −2.47249 | ||||||||
\(989\) | 1.82797e13 | 0.607554 | ||||||||
\(990\) | −3.74586e13 | −1.23935 | ||||||||
\(991\) | −1.11004e13 | −0.365601 | −0.182800 | − | 0.983150i | \(-0.558516\pi\) | ||||
−0.182800 | + | 0.983150i | \(0.558516\pi\) | |||||||
\(992\) | 3.84570e13 | 1.26088 | ||||||||
\(993\) | 1.80711e13 | 0.589810 | ||||||||
\(994\) | −4.01313e12 | −0.130390 | ||||||||
\(995\) | 6.55566e13 | 2.12037 | ||||||||
\(996\) | −2.83522e12 | −0.0912894 | ||||||||
\(997\) | 5.51871e12 | 0.176892 | 0.0884462 | − | 0.996081i | \(-0.471810\pi\) | ||||
0.0884462 | + | 0.996081i | \(0.471810\pi\) | |||||||
\(998\) | −2.31578e13 | −0.738941 | ||||||||
\(999\) | 1.25019e13 | 0.397129 |
(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.1.5 | ✓ | 36 | |
17.16 | even | 2 | 289.10.a.h.1.5 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.g.1.5 | ✓ | 36 | 1.1 | even | 1 | trivial | |
289.10.a.h.1.5 | yes | 36 | 17.16 | even | 2 |