Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,12,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(22.2819522362\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 15790 x^{9} + 14666 x^{8} + 87206462 x^{7} - 14008334 x^{6} - 203974096304 x^{5} - 388180519304 x^{4} + 193065378004825 x^{3} + \cdots - 75\!\cdots\!58 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{13}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(33.9131\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 30.9131 | 0.683089 | 0.341545 | − | 0.939866i | \(-0.389050\pi\) | ||||
0.341545 | + | 0.939866i | \(0.389050\pi\) | |||||||
\(3\) | 543.939 | 1.29236 | 0.646179 | − | 0.763186i | \(-0.276366\pi\) | ||||
0.646179 | + | 0.763186i | \(0.276366\pi\) | |||||||
\(4\) | −1092.38 | −0.533389 | ||||||||
\(5\) | −6165.86 | −0.882386 | −0.441193 | − | 0.897412i | \(-0.645445\pi\) | ||||
−0.441193 | + | 0.897412i | \(0.645445\pi\) | |||||||
\(6\) | 16814.8 | 0.882796 | ||||||||
\(7\) | 8452.88 | 0.190093 | 0.0950464 | − | 0.995473i | \(-0.469700\pi\) | ||||
0.0950464 | + | 0.995473i | \(0.469700\pi\) | |||||||
\(8\) | −97078.9 | −1.04744 | ||||||||
\(9\) | 118722. | 0.670191 | ||||||||
\(10\) | −190606. | −0.602749 | ||||||||
\(11\) | −456924. | −0.855429 | −0.427714 | − | 0.903914i | \(-0.640681\pi\) | ||||
−0.427714 | + | 0.903914i | \(0.640681\pi\) | |||||||
\(12\) | −594188. | −0.689330 | ||||||||
\(13\) | −1.58605e6 | −1.18475 | −0.592376 | − | 0.805662i | \(-0.701810\pi\) | ||||
−0.592376 | + | 0.805662i | \(0.701810\pi\) | |||||||
\(14\) | 261305. | 0.129850 | ||||||||
\(15\) | −3.35385e6 | −1.14036 | ||||||||
\(16\) | −763810. | −0.182107 | ||||||||
\(17\) | −2.76267e6 | −0.471910 | −0.235955 | − | 0.971764i | \(-0.575822\pi\) | ||||
−0.235955 | + | 0.971764i | \(0.575822\pi\) | |||||||
\(18\) | 3.67007e6 | 0.457800 | ||||||||
\(19\) | 1.02298e7 | 0.947817 | 0.473908 | − | 0.880574i | \(-0.342843\pi\) | ||||
0.473908 | + | 0.880574i | \(0.342843\pi\) | |||||||
\(20\) | 6.73547e6 | 0.470656 | ||||||||
\(21\) | 4.59785e6 | 0.245668 | ||||||||
\(22\) | −1.41249e7 | −0.584334 | ||||||||
\(23\) | −4.57080e6 | −0.148078 | −0.0740388 | − | 0.997255i | \(-0.523589\pi\) | ||||
−0.0740388 | + | 0.997255i | \(0.523589\pi\) | |||||||
\(24\) | −5.28049e7 | −1.35367 | ||||||||
\(25\) | −1.08103e7 | −0.221394 | ||||||||
\(26\) | −4.90296e7 | −0.809291 | ||||||||
\(27\) | −3.17795e7 | −0.426232 | ||||||||
\(28\) | −9.23377e6 | −0.101393 | ||||||||
\(29\) | 2.05111e7 | 0.185695 | ||||||||
\(30\) | −1.03678e8 | −0.778967 | ||||||||
\(31\) | −1.86010e7 | −0.116694 | −0.0583469 | − | 0.998296i | \(-0.518583\pi\) | ||||
−0.0583469 | + | 0.998296i | \(0.518583\pi\) | |||||||
\(32\) | 1.75206e8 | 0.923047 | ||||||||
\(33\) | −2.48538e8 | −1.10552 | ||||||||
\(34\) | −8.54025e7 | −0.322357 | ||||||||
\(35\) | −5.21193e7 | −0.167735 | ||||||||
\(36\) | −1.29690e8 | −0.357472 | ||||||||
\(37\) | −3.49895e8 | −0.829524 | −0.414762 | − | 0.909930i | \(-0.636135\pi\) | ||||
−0.414762 | + | 0.909930i | \(0.636135\pi\) | |||||||
\(38\) | 3.16236e8 | 0.647443 | ||||||||
\(39\) | −8.62712e8 | −1.53112 | ||||||||
\(40\) | 5.98575e8 | 0.924248 | ||||||||
\(41\) | 4.05592e8 | 0.546737 | 0.273369 | − | 0.961909i | \(-0.411862\pi\) | ||||
0.273369 | + | 0.961909i | \(0.411862\pi\) | |||||||
\(42\) | 1.42134e8 | 0.167813 | ||||||||
\(43\) | −5.45192e8 | −0.565553 | −0.282777 | − | 0.959186i | \(-0.591255\pi\) | ||||
−0.282777 | + | 0.959186i | \(0.591255\pi\) | |||||||
\(44\) | 4.99135e8 | 0.456277 | ||||||||
\(45\) | −7.32025e8 | −0.591367 | ||||||||
\(46\) | −1.41298e8 | −0.101150 | ||||||||
\(47\) | 2.57186e8 | 0.163572 | 0.0817862 | − | 0.996650i | \(-0.473938\pi\) | ||||
0.0817862 | + | 0.996650i | \(0.473938\pi\) | |||||||
\(48\) | −4.15466e8 | −0.235347 | ||||||||
\(49\) | −1.90588e9 | −0.963865 | ||||||||
\(50\) | −3.34178e8 | −0.151232 | ||||||||
\(51\) | −1.50272e9 | −0.609877 | ||||||||
\(52\) | 1.73257e9 | 0.631934 | ||||||||
\(53\) | 2.86140e9 | 0.939857 | 0.469929 | − | 0.882704i | \(-0.344280\pi\) | ||||
0.469929 | + | 0.882704i | \(0.344280\pi\) | |||||||
\(54\) | −9.82402e8 | −0.291154 | ||||||||
\(55\) | 2.81733e9 | 0.754819 | ||||||||
\(56\) | −8.20596e8 | −0.199111 | ||||||||
\(57\) | 5.56441e9 | 1.22492 | ||||||||
\(58\) | 6.34063e8 | 0.126846 | ||||||||
\(59\) | 9.78675e8 | 0.178218 | 0.0891092 | − | 0.996022i | \(-0.471598\pi\) | ||||
0.0891092 | + | 0.996022i | \(0.471598\pi\) | |||||||
\(60\) | 3.66368e9 | 0.608256 | ||||||||
\(61\) | 6.10378e9 | 0.925305 | 0.462653 | − | 0.886540i | \(-0.346898\pi\) | ||||
0.462653 | + | 0.886540i | \(0.346898\pi\) | |||||||
\(62\) | −5.75015e8 | −0.0797123 | ||||||||
\(63\) | 1.00354e9 | 0.127398 | ||||||||
\(64\) | 6.98043e9 | 0.812630 | ||||||||
\(65\) | 9.77935e9 | 1.04541 | ||||||||
\(66\) | −7.68309e9 | −0.755169 | ||||||||
\(67\) | 2.11078e10 | 1.90999 | 0.954995 | − | 0.296622i | \(-0.0958602\pi\) | ||||
0.954995 | + | 0.296622i | \(0.0958602\pi\) | |||||||
\(68\) | 3.01788e9 | 0.251712 | ||||||||
\(69\) | −2.48623e9 | −0.191369 | ||||||||
\(70\) | −1.61117e9 | −0.114578 | ||||||||
\(71\) | −5.71117e9 | −0.375668 | −0.187834 | − | 0.982201i | \(-0.560147\pi\) | ||||
−0.187834 | + | 0.982201i | \(0.560147\pi\) | |||||||
\(72\) | −1.15254e10 | −0.701985 | ||||||||
\(73\) | −3.20418e10 | −1.80901 | −0.904504 | − | 0.426464i | \(-0.859759\pi\) | ||||
−0.904504 | + | 0.426464i | \(0.859759\pi\) | |||||||
\(74\) | −1.08163e10 | −0.566639 | ||||||||
\(75\) | −5.88012e9 | −0.286121 | ||||||||
\(76\) | −1.11749e10 | −0.505555 | ||||||||
\(77\) | −3.86232e9 | −0.162611 | ||||||||
\(78\) | −2.66691e10 | −1.04589 | ||||||||
\(79\) | 2.00645e9 | 0.0733634 | 0.0366817 | − | 0.999327i | \(-0.488321\pi\) | ||||
0.0366817 | + | 0.999327i | \(0.488321\pi\) | |||||||
\(80\) | 4.70955e9 | 0.160688 | ||||||||
\(81\) | −3.83174e10 | −1.22104 | ||||||||
\(82\) | 1.25381e10 | 0.373470 | ||||||||
\(83\) | 1.74717e10 | 0.486863 | 0.243431 | − | 0.969918i | \(-0.421727\pi\) | ||||
0.243431 | + | 0.969918i | \(0.421727\pi\) | |||||||
\(84\) | −5.02260e9 | −0.131037 | ||||||||
\(85\) | 1.70342e10 | 0.416407 | ||||||||
\(86\) | −1.68536e10 | −0.386323 | ||||||||
\(87\) | 1.11568e10 | 0.239985 | ||||||||
\(88\) | 4.43576e10 | 0.896012 | ||||||||
\(89\) | 2.66978e9 | 0.0506793 | 0.0253397 | − | 0.999679i | \(-0.491933\pi\) | ||||
0.0253397 | + | 0.999679i | \(0.491933\pi\) | |||||||
\(90\) | −2.26292e10 | −0.403956 | ||||||||
\(91\) | −1.34067e10 | −0.225213 | ||||||||
\(92\) | 4.99306e9 | 0.0789830 | ||||||||
\(93\) | −1.01178e10 | −0.150810 | ||||||||
\(94\) | 7.95043e9 | 0.111734 | ||||||||
\(95\) | −6.30758e10 | −0.836341 | ||||||||
\(96\) | 9.53012e10 | 1.19291 | ||||||||
\(97\) | −4.71279e10 | −0.557228 | −0.278614 | − | 0.960403i | \(-0.589875\pi\) | ||||
−0.278614 | + | 0.960403i | \(0.589875\pi\) | |||||||
\(98\) | −5.89165e10 | −0.658405 | ||||||||
\(99\) | −5.42470e10 | −0.573300 | ||||||||
\(100\) | 1.18089e10 | 0.118089 | ||||||||
\(101\) | −1.14953e11 | −1.08831 | −0.544157 | − | 0.838984i | \(-0.683150\pi\) | ||||
−0.544157 | + | 0.838984i | \(0.683150\pi\) | |||||||
\(102\) | −4.64537e10 | −0.416600 | ||||||||
\(103\) | 2.20861e11 | 1.87722 | 0.938608 | − | 0.344985i | \(-0.112116\pi\) | ||||
0.938608 | + | 0.344985i | \(0.112116\pi\) | |||||||
\(104\) | 1.53972e11 | 1.24096 | ||||||||
\(105\) | −2.83497e10 | −0.216774 | ||||||||
\(106\) | 8.84548e10 | 0.642006 | ||||||||
\(107\) | 1.25674e11 | 0.866233 | 0.433117 | − | 0.901338i | \(-0.357414\pi\) | ||||
0.433117 | + | 0.901338i | \(0.357414\pi\) | |||||||
\(108\) | 3.47153e10 | 0.227348 | ||||||||
\(109\) | −1.83444e11 | −1.14198 | −0.570988 | − | 0.820958i | \(-0.693440\pi\) | ||||
−0.570988 | + | 0.820958i | \(0.693440\pi\) | |||||||
\(110\) | 8.70923e10 | 0.515609 | ||||||||
\(111\) | −1.90322e11 | −1.07204 | ||||||||
\(112\) | −6.45640e9 | −0.0346171 | ||||||||
\(113\) | −2.20021e11 | −1.12340 | −0.561698 | − | 0.827342i | \(-0.689852\pi\) | ||||
−0.561698 | + | 0.827342i | \(0.689852\pi\) | |||||||
\(114\) | 1.72013e11 | 0.836729 | ||||||||
\(115\) | 2.81829e10 | 0.130662 | ||||||||
\(116\) | −2.24060e10 | −0.0990479 | ||||||||
\(117\) | −1.88299e11 | −0.794010 | ||||||||
\(118\) | 3.02539e10 | 0.121739 | ||||||||
\(119\) | −2.33525e10 | −0.0897067 | ||||||||
\(120\) | 3.25588e11 | 1.19446 | ||||||||
\(121\) | −7.65324e10 | −0.268241 | ||||||||
\(122\) | 1.88687e11 | 0.632066 | ||||||||
\(123\) | 2.20617e11 | 0.706580 | ||||||||
\(124\) | 2.03194e10 | 0.0622432 | ||||||||
\(125\) | 3.67722e11 | 1.07774 | ||||||||
\(126\) | 3.10227e10 | 0.0870244 | ||||||||
\(127\) | 2.27277e11 | 0.610430 | 0.305215 | − | 0.952284i | \(-0.401272\pi\) | ||||
0.305215 | + | 0.952284i | \(0.401272\pi\) | |||||||
\(128\) | −1.43035e11 | −0.367948 | ||||||||
\(129\) | −2.96551e11 | −0.730897 | ||||||||
\(130\) | 3.02310e11 | 0.714108 | ||||||||
\(131\) | −4.64818e11 | −1.05267 | −0.526333 | − | 0.850278i | \(-0.676434\pi\) | ||||
−0.526333 | + | 0.850278i | \(0.676434\pi\) | |||||||
\(132\) | 2.71499e11 | 0.589673 | ||||||||
\(133\) | 8.64717e10 | 0.180173 | ||||||||
\(134\) | 6.52506e11 | 1.30469 | ||||||||
\(135\) | 1.95948e11 | 0.376101 | ||||||||
\(136\) | 2.68197e11 | 0.494298 | ||||||||
\(137\) | −8.70791e11 | −1.54153 | −0.770763 | − | 0.637123i | \(-0.780125\pi\) | ||||
−0.770763 | + | 0.637123i | \(0.780125\pi\) | |||||||
\(138\) | −7.68572e10 | −0.130722 | ||||||||
\(139\) | −4.84555e11 | −0.792066 | −0.396033 | − | 0.918236i | \(-0.629613\pi\) | ||||
−0.396033 | + | 0.918236i | \(0.629613\pi\) | |||||||
\(140\) | 5.69341e10 | 0.0894682 | ||||||||
\(141\) | 1.39894e11 | 0.211394 | ||||||||
\(142\) | −1.76550e11 | −0.256615 | ||||||||
\(143\) | 7.24702e11 | 1.01347 | ||||||||
\(144\) | −9.06813e10 | −0.122046 | ||||||||
\(145\) | −1.26469e11 | −0.163855 | ||||||||
\(146\) | −9.90510e11 | −1.23571 | ||||||||
\(147\) | −1.03668e12 | −1.24566 | ||||||||
\(148\) | 3.82219e11 | 0.442459 | ||||||||
\(149\) | −2.65277e11 | −0.295920 | −0.147960 | − | 0.988993i | \(-0.547271\pi\) | ||||
−0.147960 | + | 0.988993i | \(0.547271\pi\) | |||||||
\(150\) | −1.81773e11 | −0.195446 | ||||||||
\(151\) | −4.88755e11 | −0.506661 | −0.253331 | − | 0.967380i | \(-0.581526\pi\) | ||||
−0.253331 | + | 0.967380i | \(0.581526\pi\) | |||||||
\(152\) | −9.93102e11 | −0.992783 | ||||||||
\(153\) | −3.27990e11 | −0.316270 | ||||||||
\(154\) | −1.19396e11 | −0.111078 | ||||||||
\(155\) | 1.14691e11 | 0.102969 | ||||||||
\(156\) | 9.42411e11 | 0.816686 | ||||||||
\(157\) | −1.40009e12 | −1.17141 | −0.585705 | − | 0.810524i | \(-0.699182\pi\) | ||||
−0.585705 | + | 0.810524i | \(0.699182\pi\) | |||||||
\(158\) | 6.20256e10 | 0.0501138 | ||||||||
\(159\) | 1.55643e12 | 1.21463 | ||||||||
\(160\) | −1.08029e12 | −0.814484 | ||||||||
\(161\) | −3.86364e10 | −0.0281485 | ||||||||
\(162\) | −1.18451e12 | −0.834076 | ||||||||
\(163\) | −5.97037e11 | −0.406414 | −0.203207 | − | 0.979136i | \(-0.565137\pi\) | ||||
−0.203207 | + | 0.979136i | \(0.565137\pi\) | |||||||
\(164\) | −4.43062e11 | −0.291624 | ||||||||
\(165\) | 1.53245e12 | 0.975497 | ||||||||
\(166\) | 5.40105e11 | 0.332571 | ||||||||
\(167\) | −8.57218e11 | −0.510682 | −0.255341 | − | 0.966851i | \(-0.582188\pi\) | ||||
−0.255341 | + | 0.966851i | \(0.582188\pi\) | |||||||
\(168\) | −4.46354e11 | −0.257323 | ||||||||
\(169\) | 7.23384e11 | 0.403638 | ||||||||
\(170\) | 5.26580e11 | 0.284443 | ||||||||
\(171\) | 1.21451e12 | 0.635218 | ||||||||
\(172\) | 5.95558e11 | 0.301660 | ||||||||
\(173\) | 1.77551e12 | 0.871104 | 0.435552 | − | 0.900164i | \(-0.356553\pi\) | ||||
0.435552 | + | 0.900164i | \(0.356553\pi\) | |||||||
\(174\) | 3.44891e11 | 0.163931 | ||||||||
\(175\) | −9.13778e10 | −0.0420854 | ||||||||
\(176\) | 3.49003e11 | 0.155779 | ||||||||
\(177\) | 5.32339e11 | 0.230322 | ||||||||
\(178\) | 8.25312e10 | 0.0346185 | ||||||||
\(179\) | −1.48356e12 | −0.603411 | −0.301706 | − | 0.953401i | \(-0.597556\pi\) | ||||
−0.301706 | + | 0.953401i | \(0.597556\pi\) | |||||||
\(180\) | 7.99651e11 | 0.315429 | ||||||||
\(181\) | −4.81102e12 | −1.84079 | −0.920396 | − | 0.390987i | \(-0.872134\pi\) | ||||
−0.920396 | + | 0.390987i | \(0.872134\pi\) | |||||||
\(182\) | −4.14441e11 | −0.153840 | ||||||||
\(183\) | 3.32008e12 | 1.19583 | ||||||||
\(184\) | 4.43728e11 | 0.155103 | ||||||||
\(185\) | 2.15741e12 | 0.731960 | ||||||||
\(186\) | −3.12773e11 | −0.103017 | ||||||||
\(187\) | 1.26233e12 | 0.403686 | ||||||||
\(188\) | −2.80946e11 | −0.0872478 | ||||||||
\(189\) | −2.68628e11 | −0.0810236 | ||||||||
\(190\) | −1.94987e12 | −0.571295 | ||||||||
\(191\) | 2.14249e12 | 0.609867 | 0.304933 | − | 0.952374i | \(-0.401366\pi\) | ||||
0.304933 | + | 0.952374i | \(0.401366\pi\) | |||||||
\(192\) | 3.79693e12 | 1.05021 | ||||||||
\(193\) | −3.06980e12 | −0.825172 | −0.412586 | − | 0.910919i | \(-0.635374\pi\) | ||||
−0.412586 | + | 0.910919i | \(0.635374\pi\) | |||||||
\(194\) | −1.45687e12 | −0.380637 | ||||||||
\(195\) | 5.31937e12 | 1.35104 | ||||||||
\(196\) | 2.08194e12 | 0.514115 | ||||||||
\(197\) | −6.87761e12 | −1.65148 | −0.825740 | − | 0.564052i | \(-0.809242\pi\) | ||||
−0.825740 | + | 0.564052i | \(0.809242\pi\) | |||||||
\(198\) | −1.67694e12 | −0.391615 | ||||||||
\(199\) | 2.80182e12 | 0.636427 | 0.318214 | − | 0.948019i | \(-0.396917\pi\) | ||||
0.318214 | + | 0.948019i | \(0.396917\pi\) | |||||||
\(200\) | 1.04945e12 | 0.231897 | ||||||||
\(201\) | 1.14813e13 | 2.46839 | ||||||||
\(202\) | −3.55356e12 | −0.743415 | ||||||||
\(203\) | 1.73378e11 | 0.0352993 | ||||||||
\(204\) | 1.64154e12 | 0.325302 | ||||||||
\(205\) | −2.50083e12 | −0.482433 | ||||||||
\(206\) | 6.82750e12 | 1.28231 | ||||||||
\(207\) | −5.42656e11 | −0.0992401 | ||||||||
\(208\) | 1.21144e12 | 0.215751 | ||||||||
\(209\) | −4.67426e12 | −0.810790 | ||||||||
\(210\) | −8.76377e11 | −0.148076 | ||||||||
\(211\) | 7.26139e12 | 1.19527 | 0.597635 | − | 0.801768i | \(-0.296107\pi\) | ||||
0.597635 | + | 0.801768i | \(0.296107\pi\) | |||||||
\(212\) | −3.12574e12 | −0.501310 | ||||||||
\(213\) | −3.10652e12 | −0.485497 | ||||||||
\(214\) | 3.88497e12 | 0.591714 | ||||||||
\(215\) | 3.36158e12 | 0.499036 | ||||||||
\(216\) | 3.08512e12 | 0.446453 | ||||||||
\(217\) | −1.57232e11 | −0.0221826 | ||||||||
\(218\) | −5.67081e12 | −0.780071 | ||||||||
\(219\) | −1.74288e13 | −2.33789 | ||||||||
\(220\) | −3.07760e12 | −0.402612 | ||||||||
\(221\) | 4.38172e12 | 0.559097 | ||||||||
\(222\) | −5.88343e12 | −0.732300 | ||||||||
\(223\) | −1.04017e12 | −0.126307 | −0.0631535 | − | 0.998004i | \(-0.520116\pi\) | ||||
−0.0631535 | + | 0.998004i | \(0.520116\pi\) | |||||||
\(224\) | 1.48099e12 | 0.175464 | ||||||||
\(225\) | −1.28342e12 | −0.148376 | ||||||||
\(226\) | −6.80153e12 | −0.767380 | ||||||||
\(227\) | −1.37568e13 | −1.51487 | −0.757435 | − | 0.652910i | \(-0.773548\pi\) | ||||
−0.757435 | + | 0.652910i | \(0.773548\pi\) | |||||||
\(228\) | −6.07846e12 | −0.653359 | ||||||||
\(229\) | −3.48055e12 | −0.365219 | −0.182609 | − | 0.983186i | \(-0.558454\pi\) | ||||
−0.182609 | + | 0.983186i | \(0.558454\pi\) | |||||||
\(230\) | 8.71221e11 | 0.0892535 | ||||||||
\(231\) | −2.10087e12 | −0.210151 | ||||||||
\(232\) | −1.99120e12 | −0.194505 | ||||||||
\(233\) | −2.14416e12 | −0.204550 | −0.102275 | − | 0.994756i | \(-0.532612\pi\) | ||||
−0.102275 | + | 0.994756i | \(0.532612\pi\) | |||||||
\(234\) | −5.82090e12 | −0.542379 | ||||||||
\(235\) | −1.58578e12 | −0.144334 | ||||||||
\(236\) | −1.06909e12 | −0.0950598 | ||||||||
\(237\) | 1.09139e12 | 0.0948119 | ||||||||
\(238\) | −7.21897e11 | −0.0612777 | ||||||||
\(239\) | 2.07449e13 | 1.72077 | 0.860387 | − | 0.509641i | \(-0.170222\pi\) | ||||
0.860387 | + | 0.509641i | \(0.170222\pi\) | |||||||
\(240\) | 2.56171e12 | 0.207667 | ||||||||
\(241\) | 3.85887e12 | 0.305750 | 0.152875 | − | 0.988246i | \(-0.451147\pi\) | ||||
0.152875 | + | 0.988246i | \(0.451147\pi\) | |||||||
\(242\) | −2.36585e12 | −0.183233 | ||||||||
\(243\) | −1.52127e13 | −1.15178 | ||||||||
\(244\) | −6.66766e12 | −0.493548 | ||||||||
\(245\) | 1.17514e13 | 0.850501 | ||||||||
\(246\) | 6.81996e12 | 0.482657 | ||||||||
\(247\) | −1.62250e13 | −1.12293 | ||||||||
\(248\) | 1.80577e12 | 0.122230 | ||||||||
\(249\) | 9.50356e12 | 0.629201 | ||||||||
\(250\) | 1.13674e13 | 0.736194 | ||||||||
\(251\) | 1.83565e13 | 1.16301 | 0.581506 | − | 0.813542i | \(-0.302464\pi\) | ||||
0.581506 | + | 0.813542i | \(0.302464\pi\) | |||||||
\(252\) | −1.09625e12 | −0.0679529 | ||||||||
\(253\) | 2.08851e12 | 0.126670 | ||||||||
\(254\) | 7.02584e12 | 0.416978 | ||||||||
\(255\) | 9.26557e12 | 0.538147 | ||||||||
\(256\) | −1.87176e13 | −1.06397 | ||||||||
\(257\) | 3.54585e13 | 1.97282 | 0.986412 | − | 0.164290i | \(-0.0525334\pi\) | ||||
0.986412 | + | 0.164290i | \(0.0525334\pi\) | |||||||
\(258\) | −9.16731e12 | −0.499268 | ||||||||
\(259\) | −2.95762e12 | −0.157686 | ||||||||
\(260\) | −1.06828e13 | −0.557610 | ||||||||
\(261\) | 2.43513e12 | 0.124451 | ||||||||
\(262\) | −1.43690e13 | −0.719065 | ||||||||
\(263\) | 2.92866e13 | 1.43520 | 0.717601 | − | 0.696455i | \(-0.245240\pi\) | ||||
0.717601 | + | 0.696455i | \(0.245240\pi\) | |||||||
\(264\) | 2.41278e13 | 1.15797 | ||||||||
\(265\) | −1.76430e13 | −0.829317 | ||||||||
\(266\) | 2.67311e12 | 0.123074 | ||||||||
\(267\) | 1.45220e12 | 0.0654959 | ||||||||
\(268\) | −2.30577e13 | −1.01877 | ||||||||
\(269\) | 3.25011e13 | 1.40689 | 0.703445 | − | 0.710749i | \(-0.251644\pi\) | ||||
0.703445 | + | 0.710749i | \(0.251644\pi\) | |||||||
\(270\) | 6.05735e12 | 0.256911 | ||||||||
\(271\) | −2.42500e13 | −1.00781 | −0.503907 | − | 0.863758i | \(-0.668104\pi\) | ||||
−0.503907 | + | 0.863758i | \(0.668104\pi\) | |||||||
\(272\) | 2.11015e12 | 0.0859379 | ||||||||
\(273\) | −7.29240e12 | −0.291056 | ||||||||
\(274\) | −2.69188e13 | −1.05300 | ||||||||
\(275\) | 4.93946e12 | 0.189387 | ||||||||
\(276\) | 2.71592e12 | 0.102074 | ||||||||
\(277\) | −3.35541e13 | −1.23625 | −0.618125 | − | 0.786079i | \(-0.712108\pi\) | ||||
−0.618125 | + | 0.786079i | \(0.712108\pi\) | |||||||
\(278\) | −1.49791e13 | −0.541052 | ||||||||
\(279\) | −2.20836e12 | −0.0782071 | ||||||||
\(280\) | 5.05968e12 | 0.175693 | ||||||||
\(281\) | 2.99054e13 | 1.01827 | 0.509137 | − | 0.860686i | \(-0.329965\pi\) | ||||
0.509137 | + | 0.860686i | \(0.329965\pi\) | |||||||
\(282\) | 4.32454e12 | 0.144401 | ||||||||
\(283\) | 5.38626e13 | 1.76385 | 0.881926 | − | 0.471389i | \(-0.156247\pi\) | ||||
0.881926 | + | 0.471389i | \(0.156247\pi\) | |||||||
\(284\) | 6.23877e12 | 0.200377 | ||||||||
\(285\) | −3.43094e13 | −1.08085 | ||||||||
\(286\) | 2.24028e13 | 0.692291 | ||||||||
\(287\) | 3.42842e12 | 0.103931 | ||||||||
\(288\) | 2.08008e13 | 0.618617 | ||||||||
\(289\) | −2.66396e13 | −0.777301 | ||||||||
\(290\) | −3.90954e12 | −0.111928 | ||||||||
\(291\) | −2.56347e13 | −0.720139 | ||||||||
\(292\) | 3.50018e13 | 0.964906 | ||||||||
\(293\) | 2.24694e13 | 0.607884 | 0.303942 | − | 0.952691i | \(-0.401697\pi\) | ||||
0.303942 | + | 0.952691i | \(0.401697\pi\) | |||||||
\(294\) | −3.20470e13 | −0.850896 | ||||||||
\(295\) | −6.03438e12 | −0.157258 | ||||||||
\(296\) | 3.39675e13 | 0.868878 | ||||||||
\(297\) | 1.45208e13 | 0.364611 | ||||||||
\(298\) | −8.20052e12 | −0.202140 | ||||||||
\(299\) | 7.24950e12 | 0.175435 | ||||||||
\(300\) | 6.42333e12 | 0.152614 | ||||||||
\(301\) | −4.60845e12 | −0.107508 | ||||||||
\(302\) | −1.51089e13 | −0.346095 | ||||||||
\(303\) | −6.25275e13 | −1.40649 | ||||||||
\(304\) | −7.81366e12 | −0.172604 | ||||||||
\(305\) | −3.76351e13 | −0.816477 | ||||||||
\(306\) | −1.01392e13 | −0.216040 | ||||||||
\(307\) | −1.53567e13 | −0.321394 | −0.160697 | − | 0.987004i | \(-0.551374\pi\) | ||||
−0.160697 | + | 0.987004i | \(0.551374\pi\) | |||||||
\(308\) | 4.21913e12 | 0.0867349 | ||||||||
\(309\) | 1.20135e14 | 2.42604 | ||||||||
\(310\) | 3.54547e12 | 0.0703370 | ||||||||
\(311\) | 3.86505e13 | 0.753308 | 0.376654 | − | 0.926354i | \(-0.377075\pi\) | ||||
0.376654 | + | 0.926354i | \(0.377075\pi\) | |||||||
\(312\) | 8.37511e13 | 1.60376 | ||||||||
\(313\) | −4.54140e13 | −0.854468 | −0.427234 | − | 0.904141i | \(-0.640512\pi\) | ||||
−0.427234 | + | 0.904141i | \(0.640512\pi\) | |||||||
\(314\) | −4.32812e13 | −0.800178 | ||||||||
\(315\) | −6.18772e12 | −0.112415 | ||||||||
\(316\) | −2.19181e12 | −0.0391313 | ||||||||
\(317\) | −7.27574e12 | −0.127659 | −0.0638295 | − | 0.997961i | \(-0.520331\pi\) | ||||
−0.0638295 | + | 0.997961i | \(0.520331\pi\) | |||||||
\(318\) | 4.81140e13 | 0.829702 | ||||||||
\(319\) | −9.37203e12 | −0.158849 | ||||||||
\(320\) | −4.30404e13 | −0.717053 | ||||||||
\(321\) | 6.83590e13 | 1.11948 | ||||||||
\(322\) | −1.19437e12 | −0.0192279 | ||||||||
\(323\) | −2.82617e13 | −0.447284 | ||||||||
\(324\) | 4.18572e13 | 0.651287 | ||||||||
\(325\) | 1.71456e13 | 0.262297 | ||||||||
\(326\) | −1.84562e13 | −0.277617 | ||||||||
\(327\) | −9.97821e13 | −1.47584 | ||||||||
\(328\) | −3.93745e13 | −0.572675 | ||||||||
\(329\) | 2.17397e12 | 0.0310939 | ||||||||
\(330\) | 4.73729e13 | 0.666351 | ||||||||
\(331\) | −9.00769e13 | −1.24612 | −0.623059 | − | 0.782175i | \(-0.714110\pi\) | ||||
−0.623059 | + | 0.782175i | \(0.714110\pi\) | |||||||
\(332\) | −1.90858e13 | −0.259687 | ||||||||
\(333\) | −4.15404e13 | −0.555939 | ||||||||
\(334\) | −2.64993e13 | −0.348842 | ||||||||
\(335\) | −1.30148e14 | −1.68535 | ||||||||
\(336\) | −3.51188e12 | −0.0447377 | ||||||||
\(337\) | −1.09026e14 | −1.36637 | −0.683183 | − | 0.730247i | \(-0.739405\pi\) | ||||
−0.683183 | + | 0.730247i | \(0.739405\pi\) | |||||||
\(338\) | 2.23620e13 | 0.275721 | ||||||||
\(339\) | −1.19678e14 | −1.45183 | ||||||||
\(340\) | −1.86079e13 | −0.222107 | ||||||||
\(341\) | 8.49925e12 | 0.0998233 | ||||||||
\(342\) | 3.75443e13 | 0.433910 | ||||||||
\(343\) | −3.28242e13 | −0.373316 | ||||||||
\(344\) | 5.29267e13 | 0.592384 | ||||||||
\(345\) | 1.53298e13 | 0.168862 | ||||||||
\(346\) | 5.48865e13 | 0.595042 | ||||||||
\(347\) | −9.88635e13 | −1.05493 | −0.527465 | − | 0.849576i | \(-0.676858\pi\) | ||||
−0.527465 | + | 0.849576i | \(0.676858\pi\) | |||||||
\(348\) | −1.21875e13 | −0.128005 | ||||||||
\(349\) | 4.39363e13 | 0.454238 | 0.227119 | − | 0.973867i | \(-0.427069\pi\) | ||||
0.227119 | + | 0.973867i | \(0.427069\pi\) | |||||||
\(350\) | −2.82477e12 | −0.0287481 | ||||||||
\(351\) | 5.04037e13 | 0.504979 | ||||||||
\(352\) | −8.00557e13 | −0.789601 | ||||||||
\(353\) | 1.89566e14 | 1.84077 | 0.920385 | − | 0.391013i | \(-0.127875\pi\) | ||||
0.920385 | + | 0.391013i | \(0.127875\pi\) | |||||||
\(354\) | 1.64562e13 | 0.157330 | ||||||||
\(355\) | 3.52143e13 | 0.331484 | ||||||||
\(356\) | −2.91642e12 | −0.0270318 | ||||||||
\(357\) | −1.27023e13 | −0.115933 | ||||||||
\(358\) | −4.58614e13 | −0.412184 | ||||||||
\(359\) | 9.61153e13 | 0.850694 | 0.425347 | − | 0.905030i | \(-0.360152\pi\) | ||||
0.425347 | + | 0.905030i | \(0.360152\pi\) | |||||||
\(360\) | 7.10642e13 | 0.619422 | ||||||||
\(361\) | −1.18405e13 | −0.101644 | ||||||||
\(362\) | −1.48723e14 | −1.25743 | ||||||||
\(363\) | −4.16289e13 | −0.346664 | ||||||||
\(364\) | 1.46452e13 | 0.120126 | ||||||||
\(365\) | 1.97565e14 | 1.59624 | ||||||||
\(366\) | 1.02634e14 | 0.816856 | ||||||||
\(367\) | 6.15690e13 | 0.482724 | 0.241362 | − | 0.970435i | \(-0.422406\pi\) | ||||
0.241362 | + | 0.970435i | \(0.422406\pi\) | |||||||
\(368\) | 3.49122e12 | 0.0269659 | ||||||||
\(369\) | 4.81528e13 | 0.366418 | ||||||||
\(370\) | 6.66921e13 | 0.499994 | ||||||||
\(371\) | 2.41871e13 | 0.178660 | ||||||||
\(372\) | 1.10525e13 | 0.0804406 | ||||||||
\(373\) | 1.67703e14 | 1.20266 | 0.601330 | − | 0.799001i | \(-0.294638\pi\) | ||||
0.601330 | + | 0.799001i | \(0.294638\pi\) | |||||||
\(374\) | 3.90224e13 | 0.275753 | ||||||||
\(375\) | 2.00018e14 | 1.39283 | ||||||||
\(376\) | −2.49674e13 | −0.171332 | ||||||||
\(377\) | −3.25316e13 | −0.220003 | ||||||||
\(378\) | −8.30412e12 | −0.0553463 | ||||||||
\(379\) | −3.55256e13 | −0.233360 | −0.116680 | − | 0.993170i | \(-0.537225\pi\) | ||||
−0.116680 | + | 0.993170i | \(0.537225\pi\) | |||||||
\(380\) | 6.89029e13 | 0.446095 | ||||||||
\(381\) | 1.23625e14 | 0.788894 | ||||||||
\(382\) | 6.62309e13 | 0.416593 | ||||||||
\(383\) | −2.93299e14 | −1.81851 | −0.909257 | − | 0.416235i | \(-0.863349\pi\) | ||||
−0.909257 | + | 0.416235i | \(0.863349\pi\) | |||||||
\(384\) | −7.78021e13 | −0.475521 | ||||||||
\(385\) | 2.38145e13 | 0.143486 | ||||||||
\(386\) | −9.48968e13 | −0.563666 | ||||||||
\(387\) | −6.47265e13 | −0.379028 | ||||||||
\(388\) | 5.14816e13 | 0.297220 | ||||||||
\(389\) | −2.33407e14 | −1.32859 | −0.664294 | − | 0.747471i | \(-0.731268\pi\) | ||||
−0.664294 | + | 0.747471i | \(0.731268\pi\) | |||||||
\(390\) | 1.64438e14 | 0.922883 | ||||||||
\(391\) | 1.26276e13 | 0.0698793 | ||||||||
\(392\) | 1.85020e14 | 1.00959 | ||||||||
\(393\) | −2.52832e14 | −1.36042 | ||||||||
\(394\) | −2.12608e14 | −1.12811 | ||||||||
\(395\) | −1.23715e13 | −0.0647349 | ||||||||
\(396\) | 5.92584e13 | 0.305792 | ||||||||
\(397\) | 3.29462e12 | 0.0167671 | 0.00838354 | − | 0.999965i | \(-0.497331\pi\) | ||||
0.00838354 | + | 0.999965i | \(0.497331\pi\) | |||||||
\(398\) | 8.66130e13 | 0.434736 | ||||||||
\(399\) | 4.70353e13 | 0.232848 | ||||||||
\(400\) | 8.25699e12 | 0.0403173 | ||||||||
\(401\) | −1.82842e14 | −0.880606 | −0.440303 | − | 0.897849i | \(-0.645129\pi\) | ||||
−0.440303 | + | 0.897849i | \(0.645129\pi\) | |||||||
\(402\) | 3.54923e14 | 1.68613 | ||||||||
\(403\) | 2.95021e13 | 0.138253 | ||||||||
\(404\) | 1.25573e14 | 0.580495 | ||||||||
\(405\) | 2.36260e14 | 1.07742 | ||||||||
\(406\) | 5.35966e12 | 0.0241126 | ||||||||
\(407\) | 1.59876e14 | 0.709599 | ||||||||
\(408\) | 1.45882e14 | 0.638811 | ||||||||
\(409\) | 2.44493e14 | 1.05630 | 0.528152 | − | 0.849150i | \(-0.322885\pi\) | ||||
0.528152 | + | 0.849150i | \(0.322885\pi\) | |||||||
\(410\) | −7.73083e13 | −0.329545 | ||||||||
\(411\) | −4.73657e14 | −1.99220 | ||||||||
\(412\) | −2.41264e14 | −1.00129 | ||||||||
\(413\) | 8.27262e12 | 0.0338780 | ||||||||
\(414\) | −1.67752e13 | −0.0677899 | ||||||||
\(415\) | −1.07728e14 | −0.429601 | ||||||||
\(416\) | −2.77885e14 | −1.09358 | ||||||||
\(417\) | −2.63568e14 | −1.02363 | ||||||||
\(418\) | −1.44496e14 | −0.553842 | ||||||||
\(419\) | −1.80116e13 | −0.0681358 | −0.0340679 | − | 0.999420i | \(-0.510846\pi\) | ||||
−0.0340679 | + | 0.999420i | \(0.510846\pi\) | |||||||
\(420\) | 3.09687e13 | 0.115625 | ||||||||
\(421\) | −3.46365e14 | −1.27639 | −0.638193 | − | 0.769877i | \(-0.720318\pi\) | ||||
−0.638193 | + | 0.769877i | \(0.720318\pi\) | |||||||
\(422\) | 2.24472e14 | 0.816476 | ||||||||
\(423\) | 3.05338e13 | 0.109625 | ||||||||
\(424\) | −2.77782e14 | −0.984445 | ||||||||
\(425\) | 2.98651e13 | 0.104478 | ||||||||
\(426\) | −9.60322e13 | −0.331638 | ||||||||
\(427\) | 5.15946e13 | 0.175894 | ||||||||
\(428\) | −1.37284e14 | −0.462039 | ||||||||
\(429\) | 3.94194e14 | 1.30977 | ||||||||
\(430\) | 1.03917e14 | 0.340886 | ||||||||
\(431\) | −2.61420e14 | −0.846670 | −0.423335 | − | 0.905973i | \(-0.639141\pi\) | ||||
−0.423335 | + | 0.905973i | \(0.639141\pi\) | |||||||
\(432\) | 2.42735e13 | 0.0776196 | ||||||||
\(433\) | 1.18456e14 | 0.374001 | 0.187001 | − | 0.982360i | \(-0.440123\pi\) | ||||
0.187001 | + | 0.982360i | \(0.440123\pi\) | |||||||
\(434\) | −4.86053e12 | −0.0151527 | ||||||||
\(435\) | −6.87913e13 | −0.211759 | ||||||||
\(436\) | 2.00390e14 | 0.609118 | ||||||||
\(437\) | −4.67586e13 | −0.140350 | ||||||||
\(438\) | −5.38776e14 | −1.59699 | ||||||||
\(439\) | 2.73272e14 | 0.799910 | 0.399955 | − | 0.916535i | \(-0.369026\pi\) | ||||
0.399955 | + | 0.916535i | \(0.369026\pi\) | |||||||
\(440\) | −2.73503e14 | −0.790629 | ||||||||
\(441\) | −2.26270e14 | −0.645973 | ||||||||
\(442\) | 1.35452e14 | 0.381913 | ||||||||
\(443\) | −2.68138e13 | −0.0746686 | −0.0373343 | − | 0.999303i | \(-0.511887\pi\) | ||||
−0.0373343 | + | 0.999303i | \(0.511887\pi\) | |||||||
\(444\) | 2.07904e14 | 0.571816 | ||||||||
\(445\) | −1.64615e13 | −0.0447187 | ||||||||
\(446\) | −3.21548e13 | −0.0862789 | ||||||||
\(447\) | −1.44294e14 | −0.382435 | ||||||||
\(448\) | 5.90048e13 | 0.154475 | ||||||||
\(449\) | 4.98402e14 | 1.28892 | 0.644458 | − | 0.764639i | \(-0.277083\pi\) | ||||
0.644458 | + | 0.764639i | \(0.277083\pi\) | |||||||
\(450\) | −3.96744e13 | −0.101354 | ||||||||
\(451\) | −1.85325e14 | −0.467695 | ||||||||
\(452\) | 2.40347e14 | 0.599208 | ||||||||
\(453\) | −2.65853e14 | −0.654788 | ||||||||
\(454\) | −4.25265e14 | −1.03479 | ||||||||
\(455\) | 8.26636e13 | 0.198725 | ||||||||
\(456\) | −5.40187e14 | −1.28303 | ||||||||
\(457\) | 4.40553e13 | 0.103385 | 0.0516927 | − | 0.998663i | \(-0.483538\pi\) | ||||
0.0516927 | + | 0.998663i | \(0.483538\pi\) | |||||||
\(458\) | −1.07595e14 | −0.249477 | ||||||||
\(459\) | 8.77961e13 | 0.201143 | ||||||||
\(460\) | −3.07865e13 | −0.0696935 | ||||||||
\(461\) | 4.19399e14 | 0.938150 | 0.469075 | − | 0.883158i | \(-0.344587\pi\) | ||||
0.469075 | + | 0.883158i | \(0.344587\pi\) | |||||||
\(462\) | −6.49442e13 | −0.143552 | ||||||||
\(463\) | 7.77752e14 | 1.69881 | 0.849407 | − | 0.527738i | \(-0.176960\pi\) | ||||
0.849407 | + | 0.527738i | \(0.176960\pi\) | |||||||
\(464\) | −1.56666e13 | −0.0338163 | ||||||||
\(465\) | 6.23851e13 | 0.133073 | ||||||||
\(466\) | −6.62824e13 | −0.139726 | ||||||||
\(467\) | 2.21898e14 | 0.462285 | 0.231143 | − | 0.972920i | \(-0.425754\pi\) | ||||
0.231143 | + | 0.972920i | \(0.425754\pi\) | |||||||
\(468\) | 2.05694e14 | 0.423516 | ||||||||
\(469\) | 1.78421e14 | 0.363075 | ||||||||
\(470\) | −4.90212e13 | −0.0985930 | ||||||||
\(471\) | −7.61566e14 | −1.51388 | ||||||||
\(472\) | −9.50087e13 | −0.186673 | ||||||||
\(473\) | 2.49111e14 | 0.483790 | ||||||||
\(474\) | 3.37381e13 | 0.0647649 | ||||||||
\(475\) | −1.10587e14 | −0.209841 | ||||||||
\(476\) | 2.55098e13 | 0.0478486 | ||||||||
\(477\) | 3.39712e14 | 0.629883 | ||||||||
\(478\) | 6.41290e14 | 1.17544 | ||||||||
\(479\) | −8.63306e13 | −0.156430 | −0.0782149 | − | 0.996937i | \(-0.524922\pi\) | ||||
−0.0782149 | + | 0.996937i | \(0.524922\pi\) | |||||||
\(480\) | −5.87614e14 | −1.05261 | ||||||||
\(481\) | 5.54951e14 | 0.982780 | ||||||||
\(482\) | 1.19289e14 | 0.208854 | ||||||||
\(483\) | −2.10158e13 | −0.0363779 | ||||||||
\(484\) | 8.36025e13 | 0.143077 | ||||||||
\(485\) | 2.90584e14 | 0.491691 | ||||||||
\(486\) | −4.70270e14 | −0.786771 | ||||||||
\(487\) | 8.20942e14 | 1.35801 | 0.679005 | − | 0.734133i | \(-0.262411\pi\) | ||||
0.679005 | + | 0.734133i | \(0.262411\pi\) | |||||||
\(488\) | −5.92549e14 | −0.969203 | ||||||||
\(489\) | −3.24751e14 | −0.525233 | ||||||||
\(490\) | 3.63271e14 | 0.580968 | ||||||||
\(491\) | 1.43945e14 | 0.227640 | 0.113820 | − | 0.993501i | \(-0.463691\pi\) | ||||
0.113820 | + | 0.993501i | \(0.463691\pi\) | |||||||
\(492\) | −2.40998e14 | −0.376882 | ||||||||
\(493\) | −5.66655e13 | −0.0876315 | ||||||||
\(494\) | −5.01565e14 | −0.767060 | ||||||||
\(495\) | 3.34480e14 | 0.505873 | ||||||||
\(496\) | 1.42077e13 | 0.0212507 | ||||||||
\(497\) | −4.82758e13 | −0.0714117 | ||||||||
\(498\) | 2.93784e14 | 0.429801 | ||||||||
\(499\) | 4.42279e14 | 0.639945 | 0.319973 | − | 0.947427i | \(-0.396326\pi\) | ||||
0.319973 | + | 0.947427i | \(0.396326\pi\) | |||||||
\(500\) | −4.01693e14 | −0.574856 | ||||||||
\(501\) | −4.66274e14 | −0.659985 | ||||||||
\(502\) | 5.67456e14 | 0.794441 | ||||||||
\(503\) | 7.02029e14 | 0.972146 | 0.486073 | − | 0.873918i | \(-0.338429\pi\) | ||||
0.486073 | + | 0.873918i | \(0.338429\pi\) | |||||||
\(504\) | −9.74230e13 | −0.133442 | ||||||||
\(505\) | 7.08786e14 | 0.960313 | ||||||||
\(506\) | 6.45622e13 | 0.0865268 | ||||||||
\(507\) | 3.93477e14 | 0.521645 | ||||||||
\(508\) | −2.48274e14 | −0.325597 | ||||||||
\(509\) | 1.26187e15 | 1.63706 | 0.818532 | − | 0.574461i | \(-0.194788\pi\) | ||||
0.818532 | + | 0.574461i | \(0.194788\pi\) | |||||||
\(510\) | 2.86427e14 | 0.367603 | ||||||||
\(511\) | −2.70845e14 | −0.343879 | ||||||||
\(512\) | −2.85683e14 | −0.358839 | ||||||||
\(513\) | −3.25099e14 | −0.403990 | ||||||||
\(514\) | 1.09613e15 | 1.34761 | ||||||||
\(515\) | −1.36180e15 | −1.65643 | ||||||||
\(516\) | 3.23947e14 | 0.389853 | ||||||||
\(517\) | −1.17515e14 | −0.139925 | ||||||||
\(518\) | −9.14293e13 | −0.107714 | ||||||||
\(519\) | 9.65769e14 | 1.12578 | ||||||||
\(520\) | −9.49368e14 | −1.09501 | ||||||||
\(521\) | −1.05945e15 | −1.20913 | −0.604565 | − | 0.796555i | \(-0.706653\pi\) | ||||
−0.604565 | + | 0.796555i | \(0.706653\pi\) | |||||||
\(522\) | 7.52774e13 | 0.0850113 | ||||||||
\(523\) | −1.79848e14 | −0.200977 | −0.100488 | − | 0.994938i | \(-0.532041\pi\) | ||||
−0.100488 | + | 0.994938i | \(0.532041\pi\) | |||||||
\(524\) | 5.07758e14 | 0.561481 | ||||||||
\(525\) | −4.97039e13 | −0.0543894 | ||||||||
\(526\) | 9.05340e14 | 0.980371 | ||||||||
\(527\) | 5.13884e13 | 0.0550690 | ||||||||
\(528\) | 1.89836e14 | 0.201323 | ||||||||
\(529\) | −9.31918e14 | −0.978073 | ||||||||
\(530\) | −5.45400e14 | −0.566497 | ||||||||
\(531\) | 1.16191e14 | 0.119440 | ||||||||
\(532\) | −9.44600e13 | −0.0961024 | ||||||||
\(533\) | −6.43289e14 | −0.647748 | ||||||||
\(534\) | 4.48919e13 | 0.0447395 | ||||||||
\(535\) | −7.74889e14 | −0.764352 | ||||||||
\(536\) | −2.04912e15 | −2.00060 | ||||||||
\(537\) | −8.06966e14 | −0.779824 | ||||||||
\(538\) | 1.00471e15 | 0.961032 | ||||||||
\(539\) | 8.70840e14 | 0.824518 | ||||||||
\(540\) | −2.14050e14 | −0.200608 | ||||||||
\(541\) | −2.63503e14 | −0.244456 | −0.122228 | − | 0.992502i | \(-0.539004\pi\) | ||||
−0.122228 | + | 0.992502i | \(0.539004\pi\) | |||||||
\(542\) | −7.49641e14 | −0.688426 | ||||||||
\(543\) | −2.61690e15 | −2.37896 | ||||||||
\(544\) | −4.84035e14 | −0.435595 | ||||||||
\(545\) | 1.13109e15 | 1.00766 | ||||||||
\(546\) | −2.25431e14 | −0.198817 | ||||||||
\(547\) | −1.78221e15 | −1.55607 | −0.778036 | − | 0.628219i | \(-0.783784\pi\) | ||||
−0.778036 | + | 0.628219i | \(0.783784\pi\) | |||||||
\(548\) | 9.51235e14 | 0.822233 | ||||||||
\(549\) | 7.24655e14 | 0.620131 | ||||||||
\(550\) | 1.52694e14 | 0.129368 | ||||||||
\(551\) | 2.09826e14 | 0.176005 | ||||||||
\(552\) | 2.41361e14 | 0.200448 | ||||||||
\(553\) | 1.69603e13 | 0.0139459 | ||||||||
\(554\) | −1.03726e15 | −0.844469 | ||||||||
\(555\) | 1.17350e15 | 0.945955 | ||||||||
\(556\) | 5.29318e14 | 0.422480 | ||||||||
\(557\) | 4.27839e14 | 0.338125 | 0.169062 | − | 0.985605i | \(-0.445926\pi\) | ||||
0.169062 | + | 0.985605i | \(0.445926\pi\) | |||||||
\(558\) | −6.82671e13 | −0.0534224 | ||||||||
\(559\) | 8.64701e14 | 0.670040 | ||||||||
\(560\) | 3.98092e13 | 0.0305457 | ||||||||
\(561\) | 6.86629e14 | 0.521707 | ||||||||
\(562\) | 9.24467e14 | 0.695571 | ||||||||
\(563\) | 9.47616e14 | 0.706051 | 0.353026 | − | 0.935614i | \(-0.385153\pi\) | ||||
0.353026 | + | 0.935614i | \(0.385153\pi\) | |||||||
\(564\) | −1.52817e14 | −0.112755 | ||||||||
\(565\) | 1.35662e15 | 0.991270 | ||||||||
\(566\) | 1.66506e15 | 1.20487 | ||||||||
\(567\) | −3.23892e14 | −0.232110 | ||||||||
\(568\) | 5.54434e14 | 0.393490 | ||||||||
\(569\) | −1.54228e15 | −1.08404 | −0.542021 | − | 0.840365i | \(-0.682341\pi\) | ||||
−0.542021 | + | 0.840365i | \(0.682341\pi\) | |||||||
\(570\) | −1.06061e15 | −0.738318 | ||||||||
\(571\) | −2.54264e15 | −1.75302 | −0.876509 | − | 0.481386i | \(-0.840134\pi\) | ||||
−0.876509 | + | 0.481386i | \(0.840134\pi\) | |||||||
\(572\) | −7.91651e14 | −0.540575 | ||||||||
\(573\) | 1.16538e15 | 0.788166 | ||||||||
\(574\) | 1.05983e14 | 0.0709940 | ||||||||
\(575\) | 4.94115e13 | 0.0327835 | ||||||||
\(576\) | 8.28733e14 | 0.544617 | ||||||||
\(577\) | 5.19529e14 | 0.338176 | 0.169088 | − | 0.985601i | \(-0.445918\pi\) | ||||
0.169088 | + | 0.985601i | \(0.445918\pi\) | |||||||
\(578\) | −8.23511e14 | −0.530966 | ||||||||
\(579\) | −1.66978e15 | −1.06642 | ||||||||
\(580\) | 1.38152e14 | 0.0873985 | ||||||||
\(581\) | 1.47687e14 | 0.0925491 | ||||||||
\(582\) | −7.92447e14 | −0.491919 | ||||||||
\(583\) | −1.30744e15 | −0.803981 | ||||||||
\(584\) | 3.11058e15 | 1.89483 | ||||||||
\(585\) | 1.16103e15 | 0.700624 | ||||||||
\(586\) | 6.94600e14 | 0.415239 | ||||||||
\(587\) | −3.14123e15 | −1.86033 | −0.930165 | − | 0.367142i | \(-0.880336\pi\) | ||||
−0.930165 | + | 0.367142i | \(0.880336\pi\) | |||||||
\(588\) | 1.13245e15 | 0.664421 | ||||||||
\(589\) | −1.90286e14 | −0.110604 | ||||||||
\(590\) | −1.86541e14 | −0.107421 | ||||||||
\(591\) | −3.74100e15 | −2.13430 | ||||||||
\(592\) | 2.67254e14 | 0.151062 | ||||||||
\(593\) | −1.55824e15 | −0.872634 | −0.436317 | − | 0.899793i | \(-0.643717\pi\) | ||||
−0.436317 | + | 0.899793i | \(0.643717\pi\) | |||||||
\(594\) | 4.48883e14 | 0.249062 | ||||||||
\(595\) | 1.43988e14 | 0.0791560 | ||||||||
\(596\) | 2.89783e14 | 0.157841 | ||||||||
\(597\) | 1.52402e15 | 0.822492 | ||||||||
\(598\) | 2.24104e14 | 0.119838 | ||||||||
\(599\) | −1.68384e15 | −0.892181 | −0.446090 | − | 0.894988i | \(-0.647184\pi\) | ||||
−0.446090 | + | 0.894988i | \(0.647184\pi\) | |||||||
\(600\) | 5.70835e14 | 0.299695 | ||||||||
\(601\) | −5.99073e14 | −0.311652 | −0.155826 | − | 0.987785i | \(-0.549804\pi\) | ||||
−0.155826 | + | 0.987785i | \(0.549804\pi\) | |||||||
\(602\) | −1.42461e14 | −0.0734372 | ||||||||
\(603\) | 2.50596e15 | 1.28006 | ||||||||
\(604\) | 5.33907e14 | 0.270248 | ||||||||
\(605\) | 4.71888e14 | 0.236692 | ||||||||
\(606\) | −1.93292e15 | −0.960758 | ||||||||
\(607\) | −2.54207e15 | −1.25213 | −0.626064 | − | 0.779771i | \(-0.715335\pi\) | ||||
−0.626064 | + | 0.779771i | \(0.715335\pi\) | |||||||
\(608\) | 1.79233e15 | 0.874879 | ||||||||
\(609\) | 9.43071e13 | 0.0456194 | ||||||||
\(610\) | −1.16342e15 | −0.557727 | ||||||||
\(611\) | −4.07910e14 | −0.193793 | ||||||||
\(612\) | 3.58290e14 | 0.168695 | ||||||||
\(613\) | 1.94855e15 | 0.909240 | 0.454620 | − | 0.890686i | \(-0.349775\pi\) | ||||
0.454620 | + | 0.890686i | \(0.349775\pi\) | |||||||
\(614\) | −4.74723e14 | −0.219540 | ||||||||
\(615\) | −1.36030e15 | −0.623477 | ||||||||
\(616\) | 3.74950e14 | 0.170325 | ||||||||
\(617\) | 2.66659e15 | 1.20057 | 0.600286 | − | 0.799785i | \(-0.295053\pi\) | ||||
0.600286 | + | 0.799785i | \(0.295053\pi\) | |||||||
\(618\) | 3.71374e15 | 1.65720 | ||||||||
\(619\) | −1.45237e15 | −0.642362 | −0.321181 | − | 0.947018i | \(-0.604080\pi\) | ||||
−0.321181 | + | 0.947018i | \(0.604080\pi\) | |||||||
\(620\) | −1.25287e14 | −0.0549226 | ||||||||
\(621\) | 1.45258e14 | 0.0631154 | ||||||||
\(622\) | 1.19481e15 | 0.514576 | ||||||||
\(623\) | 2.25673e13 | 0.00963377 | ||||||||
\(624\) | 6.58948e14 | 0.278828 | ||||||||
\(625\) | −1.73948e15 | −0.729591 | ||||||||
\(626\) | −1.40389e15 | −0.583678 | ||||||||
\(627\) | −2.54251e15 | −1.04783 | ||||||||
\(628\) | 1.52944e15 | 0.624818 | ||||||||
\(629\) | 9.66644e14 | 0.391461 | ||||||||
\(630\) | −1.91281e14 | −0.0767892 | ||||||||
\(631\) | 1.59115e15 | 0.633214 | 0.316607 | − | 0.948557i | \(-0.397456\pi\) | ||||
0.316607 | + | 0.948557i | \(0.397456\pi\) | |||||||
\(632\) | −1.94784e14 | −0.0768439 | ||||||||
\(633\) | 3.94975e15 | 1.54472 | ||||||||
\(634\) | −2.24916e14 | −0.0872025 | ||||||||
\(635\) | −1.40136e15 | −0.538635 | ||||||||
\(636\) | −1.70021e15 | −0.647872 | ||||||||
\(637\) | 3.02281e15 | 1.14194 | ||||||||
\(638\) | −2.89718e14 | −0.108508 | ||||||||
\(639\) | −6.78043e14 | −0.251769 | ||||||||
\(640\) | 8.81932e14 | 0.324672 | ||||||||
\(641\) | 4.39261e15 | 1.60326 | 0.801630 | − | 0.597820i | \(-0.203966\pi\) | ||||
0.801630 | + | 0.597820i | \(0.203966\pi\) | |||||||
\(642\) | 2.11319e15 | 0.764707 | ||||||||
\(643\) | 9.85800e14 | 0.353694 | 0.176847 | − | 0.984238i | \(-0.443410\pi\) | ||||
0.176847 | + | 0.984238i | \(0.443410\pi\) | |||||||
\(644\) | 4.22057e13 | 0.0150141 | ||||||||
\(645\) | 1.82849e15 | 0.644934 | ||||||||
\(646\) | −8.73655e14 | −0.305535 | ||||||||
\(647\) | 7.75343e13 | 0.0268856 | 0.0134428 | − | 0.999910i | \(-0.495721\pi\) | ||||
0.0134428 | + | 0.999910i | \(0.495721\pi\) | |||||||
\(648\) | 3.71981e15 | 1.27896 | ||||||||
\(649\) | −4.47180e14 | −0.152453 | ||||||||
\(650\) | 5.30023e14 | 0.179172 | ||||||||
\(651\) | −8.55247e13 | −0.0286679 | ||||||||
\(652\) | 6.52192e14 | 0.216777 | ||||||||
\(653\) | 5.07913e15 | 1.67405 | 0.837023 | − | 0.547168i | \(-0.184294\pi\) | ||||
0.837023 | + | 0.547168i | \(0.184294\pi\) | |||||||
\(654\) | −3.08457e15 | −1.00813 | ||||||||
\(655\) | 2.86600e15 | 0.928859 | ||||||||
\(656\) | −3.09796e14 | −0.0995644 | ||||||||
\(657\) | −3.80407e15 | −1.21238 | ||||||||
\(658\) | 6.72040e13 | 0.0212399 | ||||||||
\(659\) | 1.35108e15 | 0.423458 | 0.211729 | − | 0.977328i | \(-0.432091\pi\) | ||||
0.211729 | + | 0.977328i | \(0.432091\pi\) | |||||||
\(660\) | −1.67402e15 | −0.520320 | ||||||||
\(661\) | 4.07858e15 | 1.25719 | 0.628596 | − | 0.777732i | \(-0.283630\pi\) | ||||
0.628596 | + | 0.777732i | \(0.283630\pi\) | |||||||
\(662\) | −2.78455e15 | −0.851210 | ||||||||
\(663\) | 2.38339e15 | 0.722553 | ||||||||
\(664\) | −1.69614e15 | −0.509960 | ||||||||
\(665\) | −5.33172e14 | −0.158982 | ||||||||
\(666\) | −1.28414e15 | −0.379756 | ||||||||
\(667\) | −9.37524e13 | −0.0274973 | ||||||||
\(668\) | 9.36409e14 | 0.272393 | ||||||||
\(669\) | −5.65788e14 | −0.163234 | ||||||||
\(670\) | −4.02326e15 | −1.15124 | ||||||||
\(671\) | −2.78896e15 | −0.791533 | ||||||||
\(672\) | 8.05570e14 | 0.226763 | ||||||||
\(673\) | −5.20381e15 | −1.45291 | −0.726454 | − | 0.687215i | \(-0.758833\pi\) | ||||
−0.726454 | + | 0.687215i | \(0.758833\pi\) | |||||||
\(674\) | −3.37034e15 | −0.933350 | ||||||||
\(675\) | 3.43544e14 | 0.0943653 | ||||||||
\(676\) | −7.90211e14 | −0.215296 | ||||||||
\(677\) | −3.91496e15 | −1.05801 | −0.529005 | − | 0.848619i | \(-0.677435\pi\) | ||||
−0.529005 | + | 0.848619i | \(0.677435\pi\) | |||||||
\(678\) | −3.69962e15 | −0.991730 | ||||||||
\(679\) | −3.98366e14 | −0.105925 | ||||||||
\(680\) | −1.65366e15 | −0.436162 | ||||||||
\(681\) | −7.48286e15 | −1.95776 | ||||||||
\(682\) | 2.62738e14 | 0.0681882 | ||||||||
\(683\) | 1.55743e15 | 0.400954 | 0.200477 | − | 0.979698i | \(-0.435751\pi\) | ||||
0.200477 | + | 0.979698i | \(0.435751\pi\) | |||||||
\(684\) | −1.32671e15 | −0.338818 | ||||||||
\(685\) | 5.36918e15 | 1.36022 | ||||||||
\(686\) | −1.01470e15 | −0.255008 | ||||||||
\(687\) | −1.89321e15 | −0.471993 | ||||||||
\(688\) | 4.16424e14 | 0.102991 | ||||||||
\(689\) | −4.53832e15 | −1.11350 | ||||||||
\(690\) | 4.73891e14 | 0.115348 | ||||||||
\(691\) | 3.79974e15 | 0.917538 | 0.458769 | − | 0.888555i | \(-0.348290\pi\) | ||||
0.458769 | + | 0.888555i | \(0.348290\pi\) | |||||||
\(692\) | −1.93954e15 | −0.464637 | ||||||||
\(693\) | −4.58543e14 | −0.108980 | ||||||||
\(694\) | −3.05618e15 | −0.720612 | ||||||||
\(695\) | 2.98770e15 | 0.698908 | ||||||||
\(696\) | −1.08309e15 | −0.251370 | ||||||||
\(697\) | −1.12052e15 | −0.258011 | ||||||||
\(698\) | 1.35821e15 | 0.310285 | ||||||||
\(699\) | −1.16629e15 | −0.264351 | ||||||||
\(700\) | 9.98194e13 | 0.0224479 | ||||||||
\(701\) | −2.38592e15 | −0.532361 | −0.266181 | − | 0.963923i | \(-0.585762\pi\) | ||||
−0.266181 | + | 0.963923i | \(0.585762\pi\) | |||||||
\(702\) | 1.55814e15 | 0.344946 | ||||||||
\(703\) | −3.57938e15 | −0.786236 | ||||||||
\(704\) | −3.18953e15 | −0.695147 | ||||||||
\(705\) | −8.62565e14 | −0.186531 | ||||||||
\(706\) | 5.86007e15 | 1.25741 | ||||||||
\(707\) | −9.71686e14 | −0.206880 | ||||||||
\(708\) | −5.81518e14 | −0.122851 | ||||||||
\(709\) | −4.94373e15 | −1.03634 | −0.518168 | − | 0.855279i | \(-0.673386\pi\) | ||||
−0.518168 | + | 0.855279i | \(0.673386\pi\) | |||||||
\(710\) | 1.08858e15 | 0.226433 | ||||||||
\(711\) | 2.38210e14 | 0.0491675 | ||||||||
\(712\) | −2.59179e14 | −0.0530836 | ||||||||
\(713\) | 8.50216e13 | 0.0172797 | ||||||||
\(714\) | −3.92668e14 | −0.0791927 | ||||||||
\(715\) | −4.46842e15 | −0.894274 | ||||||||
\(716\) | 1.62061e15 | 0.321853 | ||||||||
\(717\) | 1.12840e16 | 2.22386 | ||||||||
\(718\) | 2.97122e15 | 0.581100 | ||||||||
\(719\) | 3.97715e15 | 0.771904 | 0.385952 | − | 0.922519i | \(-0.373873\pi\) | ||||
0.385952 | + | 0.922519i | \(0.373873\pi\) | |||||||
\(720\) | 5.59128e14 | 0.107692 | ||||||||
\(721\) | 1.86691e15 | 0.356845 | ||||||||
\(722\) | −3.66026e14 | −0.0694316 | ||||||||
\(723\) | 2.09899e15 | 0.395138 | ||||||||
\(724\) | 5.25547e15 | 0.981859 | ||||||||
\(725\) | −2.21731e14 | −0.0411119 | ||||||||
\(726\) | −1.28688e15 | −0.236802 | ||||||||
\(727\) | −1.01916e16 | −1.86125 | −0.930625 | − | 0.365974i | \(-0.880736\pi\) | ||||
−0.930625 | + | 0.365974i | \(0.880736\pi\) | |||||||
\(728\) | 1.30150e15 | 0.235897 | ||||||||
\(729\) | −1.48695e15 | −0.267482 | ||||||||
\(730\) | 6.10735e15 | 1.09038 | ||||||||
\(731\) | 1.50618e15 | 0.266890 | ||||||||
\(732\) | −3.62680e15 | −0.637841 | ||||||||
\(733\) | 6.33891e15 | 1.10648 | 0.553239 | − | 0.833022i | \(-0.313392\pi\) | ||||
0.553239 | + | 0.833022i | \(0.313392\pi\) | |||||||
\(734\) | 1.90329e15 | 0.329743 | ||||||||
\(735\) | 6.39202e15 | 1.09915 | ||||||||
\(736\) | −8.00831e14 | −0.136682 | ||||||||
\(737\) | −9.64464e15 | −1.63386 | ||||||||
\(738\) | 1.48855e15 | 0.250296 | ||||||||
\(739\) | −6.78577e15 | −1.13254 | −0.566271 | − | 0.824219i | \(-0.691615\pi\) | ||||
−0.566271 | + | 0.824219i | \(0.691615\pi\) | |||||||
\(740\) | −2.35671e15 | −0.390420 | ||||||||
\(741\) | −8.82541e15 | −1.45123 | ||||||||
\(742\) | 7.47698e14 | 0.122041 | ||||||||
\(743\) | 9.85625e15 | 1.59688 | 0.798441 | − | 0.602073i | \(-0.205658\pi\) | ||||
0.798441 | + | 0.602073i | \(0.205658\pi\) | |||||||
\(744\) | 9.82227e14 | 0.157965 | ||||||||
\(745\) | 1.63566e15 | 0.261116 | ||||||||
\(746\) | 5.18423e15 | 0.821524 | ||||||||
\(747\) | 2.07428e15 | 0.326291 | ||||||||
\(748\) | −1.37894e15 | −0.215322 | ||||||||
\(749\) | 1.06231e15 | 0.164665 | ||||||||
\(750\) | 6.18318e15 | 0.951426 | ||||||||
\(751\) | 3.01620e14 | 0.0460723 | 0.0230362 | − | 0.999735i | \(-0.492667\pi\) | ||||
0.0230362 | + | 0.999735i | \(0.492667\pi\) | |||||||
\(752\) | −1.96442e14 | −0.0297876 | ||||||||
\(753\) | 9.98481e15 | 1.50303 | ||||||||
\(754\) | −1.00565e15 | −0.150282 | ||||||||
\(755\) | 3.01360e15 | 0.447071 | ||||||||
\(756\) | 2.93444e14 | 0.0432171 | ||||||||
\(757\) | −6.11741e14 | −0.0894417 | −0.0447209 | − | 0.999000i | \(-0.514240\pi\) | ||||
−0.0447209 | + | 0.999000i | \(0.514240\pi\) | |||||||
\(758\) | −1.09821e15 | −0.159405 | ||||||||
\(759\) | 1.13602e15 | 0.163703 | ||||||||
\(760\) | 6.12333e15 | 0.876018 | ||||||||
\(761\) | 1.15259e15 | 0.163704 | 0.0818520 | − | 0.996644i | \(-0.473917\pi\) | ||||
0.0818520 | + | 0.996644i | \(0.473917\pi\) | |||||||
\(762\) | 3.82163e15 | 0.538885 | ||||||||
\(763\) | −1.55063e15 | −0.217081 | ||||||||
\(764\) | −2.34041e15 | −0.325296 | ||||||||
\(765\) | 2.02234e15 | 0.279072 | ||||||||
\(766\) | −9.06676e15 | −1.24221 | ||||||||
\(767\) | −1.55222e15 | −0.211145 | ||||||||
\(768\) | −1.01812e16 | −1.37503 | ||||||||
\(769\) | −1.20278e16 | −1.61284 | −0.806418 | − | 0.591346i | \(-0.798597\pi\) | ||||
−0.806418 | + | 0.591346i | \(0.798597\pi\) | |||||||
\(770\) | 7.36181e14 | 0.0980134 | ||||||||
\(771\) | 1.92873e16 | 2.54960 | ||||||||
\(772\) | 3.35339e15 | 0.440138 | ||||||||
\(773\) | −1.67790e15 | −0.218665 | −0.109333 | − | 0.994005i | \(-0.534871\pi\) | ||||
−0.109333 | + | 0.994005i | \(0.534871\pi\) | |||||||
\(774\) | −2.00089e15 | −0.258910 | ||||||||
\(775\) | 2.01082e14 | 0.0258353 | ||||||||
\(776\) | 4.57512e15 | 0.583664 | ||||||||
\(777\) | −1.60877e15 | −0.203787 | ||||||||
\(778\) | −7.21532e15 | −0.907544 | ||||||||
\(779\) | 4.14915e15 | 0.518207 | ||||||||
\(780\) | −5.81077e15 | −0.720632 | ||||||||
\(781\) | 2.60957e15 | 0.321357 | ||||||||
\(782\) | 3.90358e14 | 0.0477338 | ||||||||
\(783\) | −6.51834e14 | −0.0791493 | ||||||||
\(784\) | 1.45573e15 | 0.175526 | ||||||||
\(785\) | 8.63279e15 | 1.03364 | ||||||||
\(786\) | −7.81583e15 | −0.929290 | ||||||||
\(787\) | −9.90983e15 | −1.17005 | −0.585026 | − | 0.811014i | \(-0.698916\pi\) | ||||
−0.585026 | + | 0.811014i | \(0.698916\pi\) | |||||||
\(788\) | 7.51297e15 | 0.880881 | ||||||||
\(789\) | 1.59301e16 | 1.85480 | ||||||||
\(790\) | −3.82441e14 | −0.0442197 | ||||||||
\(791\) | −1.85981e15 | −0.213549 | ||||||||
\(792\) | 5.26624e15 | 0.600499 | ||||||||
\(793\) | −9.68089e15 | −1.09626 | ||||||||
\(794\) | 1.01847e14 | 0.0114534 | ||||||||
\(795\) | −9.59672e15 | −1.07178 | ||||||||
\(796\) | −3.06066e15 | −0.339463 | ||||||||
\(797\) | −4.31203e15 | −0.474964 | −0.237482 | − | 0.971392i | \(-0.576322\pi\) | ||||
−0.237482 | + | 0.971392i | \(0.576322\pi\) | |||||||
\(798\) | 1.45401e15 | 0.159056 | ||||||||
\(799\) | −7.10520e14 | −0.0771915 | ||||||||
\(800\) | −1.89402e15 | −0.204357 | ||||||||
\(801\) | 3.16963e14 | 0.0339648 | ||||||||
\(802\) | −5.65220e15 | −0.601532 | ||||||||
\(803\) | 1.46406e16 | 1.54748 | ||||||||
\(804\) | −1.25420e16 | −1.31661 | ||||||||
\(805\) | 2.38227e14 | 0.0248378 | ||||||||
\(806\) | 9.12001e14 | 0.0944393 | ||||||||
\(807\) | 1.76786e16 | 1.81821 | ||||||||
\(808\) | 1.11595e16 | 1.13994 | ||||||||
\(809\) | −6.10637e15 | −0.619535 | −0.309768 | − | 0.950812i | \(-0.600251\pi\) | ||||
−0.309768 | + | 0.950812i | \(0.600251\pi\) | |||||||
\(810\) | 7.30352e15 | 0.735977 | ||||||||
\(811\) | −9.72944e15 | −0.973808 | −0.486904 | − | 0.873456i | \(-0.661874\pi\) | ||||
−0.486904 | + | 0.873456i | \(0.661874\pi\) | |||||||
\(812\) | −1.89395e14 | −0.0188283 | ||||||||
\(813\) | −1.31905e16 | −1.30246 | ||||||||
\(814\) | 4.94225e15 | 0.484719 | ||||||||
\(815\) | 3.68125e15 | 0.358615 | ||||||||
\(816\) | 1.14779e15 | 0.111063 | ||||||||
\(817\) | −5.57724e15 | −0.536041 | ||||||||
\(818\) | 7.55804e15 | 0.721549 | ||||||||
\(819\) | −1.59167e15 | −0.150935 | ||||||||
\(820\) | 2.73186e15 | 0.257325 | ||||||||
\(821\) | 1.94055e15 | 0.181567 | 0.0907834 | − | 0.995871i | \(-0.471063\pi\) | ||||
0.0907834 | + | 0.995871i | \(0.471063\pi\) | |||||||
\(822\) | −1.46422e16 | −1.36085 | ||||||||
\(823\) | 1.23186e16 | 1.13727 | 0.568634 | − | 0.822590i | \(-0.307472\pi\) | ||||
0.568634 | + | 0.822590i | \(0.307472\pi\) | |||||||
\(824\) | −2.14409e16 | −1.96627 | ||||||||
\(825\) | 2.68677e15 | 0.244756 | ||||||||
\(826\) | 2.55732e14 | 0.0231417 | ||||||||
\(827\) | 2.11773e16 | 1.90366 | 0.951831 | − | 0.306625i | \(-0.0991996\pi\) | ||||
0.951831 | + | 0.306625i | \(0.0991996\pi\) | |||||||
\(828\) | 5.92787e14 | 0.0529336 | ||||||||
\(829\) | −1.02746e16 | −0.911414 | −0.455707 | − | 0.890130i | \(-0.650614\pi\) | ||||
−0.455707 | + | 0.890130i | \(0.650614\pi\) | |||||||
\(830\) | −3.33022e15 | −0.293456 | ||||||||
\(831\) | −1.82514e16 | −1.59768 | ||||||||
\(832\) | −1.10713e16 | −0.962765 | ||||||||
\(833\) | 5.26530e15 | 0.454858 | ||||||||
\(834\) | −8.14770e15 | −0.699233 | ||||||||
\(835\) | 5.28549e15 | 0.450619 | ||||||||
\(836\) | 5.10607e15 | 0.432467 | ||||||||
\(837\) | 5.91131e14 | 0.0497386 | ||||||||
\(838\) | −5.56794e14 | −0.0465428 | ||||||||
\(839\) | 6.73136e15 | 0.559000 | 0.279500 | − | 0.960146i | \(-0.409831\pi\) | ||||
0.279500 | + | 0.960146i | \(0.409831\pi\) | |||||||
\(840\) | 2.75216e15 | 0.227058 | ||||||||
\(841\) | 4.20707e14 | 0.0344828 | ||||||||
\(842\) | −1.07072e16 | −0.871885 | ||||||||
\(843\) | 1.62667e16 | 1.31597 | ||||||||
\(844\) | −7.93220e15 | −0.637544 | ||||||||
\(845\) | −4.46029e15 | −0.356165 | ||||||||
\(846\) | 9.43893e14 | 0.0748834 | ||||||||
\(847\) | −6.46919e14 | −0.0509907 | ||||||||
\(848\) | −2.18557e15 | −0.171154 | ||||||||
\(849\) | 2.92980e16 | 2.27953 | ||||||||
\(850\) | 9.23224e14 | 0.0713679 | ||||||||
\(851\) | 1.59930e15 | 0.122834 | ||||||||
\(852\) | 3.39351e15 | 0.258959 | ||||||||
\(853\) | −2.02766e16 | −1.53736 | −0.768681 | − | 0.639633i | \(-0.779086\pi\) | ||||
−0.768681 | + | 0.639633i | \(0.779086\pi\) | |||||||
\(854\) | 1.59495e15 | 0.120151 | ||||||||
\(855\) | −7.48851e15 | −0.560508 | ||||||||
\(856\) | −1.22003e16 | −0.907329 | ||||||||
\(857\) | −2.50853e16 | −1.85364 | −0.926818 | − | 0.375512i | \(-0.877467\pi\) | ||||
−0.926818 | + | 0.375512i | \(0.877467\pi\) | |||||||
\(858\) | 1.21857e16 | 0.894689 | ||||||||
\(859\) | 6.88156e15 | 0.502024 | 0.251012 | − | 0.967984i | \(-0.419237\pi\) | ||||
0.251012 | + | 0.967984i | \(0.419237\pi\) | |||||||
\(860\) | −3.67213e15 | −0.266181 | ||||||||
\(861\) | 1.86485e15 | 0.134316 | ||||||||
\(862\) | −8.08130e15 | −0.578351 | ||||||||
\(863\) | 5.69018e13 | 0.00404638 | 0.00202319 | − | 0.999998i | \(-0.499356\pi\) | ||||
0.00202319 | + | 0.999998i | \(0.499356\pi\) | |||||||
\(864\) | −5.56795e15 | −0.393432 | ||||||||
\(865\) | −1.09476e16 | −0.768650 | ||||||||
\(866\) | 3.66184e15 | 0.255476 | ||||||||
\(867\) | −1.44903e16 | −1.00455 | ||||||||
\(868\) | 1.71758e14 | 0.0118320 | ||||||||
\(869\) | −9.16795e14 | −0.0627572 | ||||||||
\(870\) | −2.12655e15 | −0.144651 | ||||||||
\(871\) | −3.34779e16 | −2.26286 | ||||||||
\(872\) | 1.78085e16 | 1.19615 | ||||||||
\(873\) | −5.59513e15 | −0.373449 | ||||||||
\(874\) | −1.44545e15 | −0.0958718 | ||||||||
\(875\) | 3.10831e15 | 0.204871 | ||||||||
\(876\) | 1.90388e16 | 1.24700 | ||||||||
\(877\) | 2.00469e15 | 0.130482 | 0.0652408 | − | 0.997870i | \(-0.479218\pi\) | ||||
0.0652408 | + | 0.997870i | \(0.479218\pi\) | |||||||
\(878\) | 8.44769e15 | 0.546410 | ||||||||
\(879\) | 1.22220e16 | 0.785603 | ||||||||
\(880\) | −2.15190e15 | −0.137457 | ||||||||
\(881\) | −2.62684e16 | −1.66750 | −0.833751 | − | 0.552140i | \(-0.813811\pi\) | ||||
−0.833751 | + | 0.552140i | \(0.813811\pi\) | |||||||
\(882\) | −6.99470e15 | −0.441257 | ||||||||
\(883\) | 1.53593e16 | 0.962916 | 0.481458 | − | 0.876469i | \(-0.340107\pi\) | ||||
0.481458 | + | 0.876469i | \(0.340107\pi\) | |||||||
\(884\) | −4.78651e15 | −0.298216 | ||||||||
\(885\) | −3.28233e15 | −0.203233 | ||||||||
\(886\) | −8.28897e14 | −0.0510053 | ||||||||
\(887\) | 2.06637e15 | 0.126365 | 0.0631826 | − | 0.998002i | \(-0.479875\pi\) | ||||
0.0631826 | + | 0.998002i | \(0.479875\pi\) | |||||||
\(888\) | 1.84762e16 | 1.12290 | ||||||||
\(889\) | 1.92115e15 | 0.116038 | ||||||||
\(890\) | −5.08876e14 | −0.0305469 | ||||||||
\(891\) | 1.75081e16 | 1.04451 | ||||||||
\(892\) | 1.13626e15 | 0.0673708 | ||||||||
\(893\) | 2.63098e15 | 0.155037 | ||||||||
\(894\) | −4.46058e15 | −0.261237 | ||||||||
\(895\) | 9.14743e15 | 0.532442 | ||||||||
\(896\) | −1.20906e15 | −0.0699443 | ||||||||
\(897\) | 3.94328e15 | 0.226725 | ||||||||
\(898\) | 1.54071e16 | 0.880445 | ||||||||
\(899\) | −3.81529e14 | −0.0216695 | ||||||||
\(900\) | 1.40198e15 | 0.0791423 | ||||||||
\(901\) | −7.90510e15 | −0.443528 | ||||||||
\(902\) | −5.72896e15 | −0.319477 | ||||||||
\(903\) | −2.50671e15 | −0.138938 | ||||||||
\(904\) | 2.13594e16 | 1.17669 | ||||||||
\(905\) | 2.96641e16 | 1.62429 | ||||||||
\(906\) | −8.21832e15 | −0.447279 | ||||||||
\(907\) | 3.60909e16 | 1.95235 | 0.976175 | − | 0.216986i | \(-0.0696227\pi\) | ||||
0.976175 | + | 0.216986i | \(0.0696227\pi\) | |||||||
\(908\) | 1.50277e16 | 0.808016 | ||||||||
\(909\) | −1.36475e16 | −0.729377 | ||||||||
\(910\) | 2.55539e15 | 0.135747 | ||||||||
\(911\) | −2.96381e16 | −1.56495 | −0.782473 | − | 0.622685i | \(-0.786042\pi\) | ||||
−0.782473 | + | 0.622685i | \(0.786042\pi\) | |||||||
\(912\) | −4.25015e15 | −0.223066 | ||||||||
\(913\) | −7.98325e15 | −0.416477 | ||||||||
\(914\) | 1.36189e15 | 0.0706215 | ||||||||
\(915\) | −2.04712e16 | −1.05518 | ||||||||
\(916\) | 3.80209e15 | 0.194804 | ||||||||
\(917\) | −3.92905e15 | −0.200104 | ||||||||
\(918\) | 2.71405e15 | 0.137399 | ||||||||
\(919\) | −9.30854e15 | −0.468431 | −0.234216 | − | 0.972185i | \(-0.575252\pi\) | ||||
−0.234216 | + | 0.972185i | \(0.575252\pi\) | |||||||
\(920\) | −2.73597e15 | −0.136860 | ||||||||
\(921\) | −8.35311e15 | −0.415356 | ||||||||
\(922\) | 1.29649e16 | 0.640840 | ||||||||
\(923\) | 9.05818e15 | 0.445073 | ||||||||
\(924\) | 2.29495e15 | 0.112093 | ||||||||
\(925\) | 3.78246e15 | 0.183652 | ||||||||
\(926\) | 2.40427e16 | 1.16044 | ||||||||
\(927\) | 2.62211e16 | 1.25809 | ||||||||
\(928\) | 3.59367e15 | 0.171405 | ||||||||
\(929\) | −1.29838e16 | −0.615624 | −0.307812 | − | 0.951447i | \(-0.599597\pi\) | ||||
−0.307812 | + | 0.951447i | \(0.599597\pi\) | |||||||
\(930\) | 1.92852e15 | 0.0909006 | ||||||||
\(931\) | −1.94968e16 | −0.913567 | ||||||||
\(932\) | 2.34224e15 | 0.109105 | ||||||||
\(933\) | 2.10235e16 | 0.973544 | ||||||||
\(934\) | 6.85954e15 | 0.315782 | ||||||||
\(935\) | −7.78334e15 | −0.356207 | ||||||||
\(936\) | 1.82799e16 | 0.831679 | ||||||||
\(937\) | −2.39113e16 | −1.08152 | −0.540761 | − | 0.841176i | \(-0.681864\pi\) | ||||
−0.540761 | + | 0.841176i | \(0.681864\pi\) | |||||||
\(938\) | 5.51556e15 | 0.248013 | ||||||||
\(939\) | −2.47024e16 | −1.10428 | ||||||||
\(940\) | 1.73227e15 | 0.0769862 | ||||||||
\(941\) | 2.73040e15 | 0.120638 | 0.0603189 | − | 0.998179i | \(-0.480788\pi\) | ||||
0.0603189 | + | 0.998179i | \(0.480788\pi\) | |||||||
\(942\) | −2.35423e16 | −1.03412 | ||||||||
\(943\) | −1.85388e15 | −0.0809595 | ||||||||
\(944\) | −7.47522e14 | −0.0324547 | ||||||||
\(945\) | 1.65632e15 | 0.0714941 | ||||||||
\(946\) | 7.70080e15 | 0.330472 | ||||||||
\(947\) | −2.61239e16 | −1.11458 | −0.557292 | − | 0.830317i | \(-0.688159\pi\) | ||||
−0.557292 | + | 0.830317i | \(0.688159\pi\) | |||||||
\(948\) | −1.19221e15 | −0.0505716 | ||||||||
\(949\) | 5.08197e16 | 2.14323 | ||||||||
\(950\) | −3.41859e15 | −0.143340 | ||||||||
\(951\) | −3.95756e15 | −0.164981 | ||||||||
\(952\) | 2.26703e15 | 0.0939625 | ||||||||
\(953\) | 1.02664e16 | 0.423066 | 0.211533 | − | 0.977371i | \(-0.432154\pi\) | ||||
0.211533 | + | 0.977371i | \(0.432154\pi\) | |||||||
\(954\) | 1.05016e16 | 0.430266 | ||||||||
\(955\) | −1.32103e16 | −0.538138 | ||||||||
\(956\) | −2.26614e16 | −0.917842 | ||||||||
\(957\) | −5.09781e15 | −0.205290 | ||||||||
\(958\) | −2.66874e15 | −0.106855 | ||||||||
\(959\) | −7.36069e15 | −0.293033 | ||||||||
\(960\) | −2.34113e16 | −0.926690 | ||||||||
\(961\) | −2.50625e16 | −0.986383 | ||||||||
\(962\) | 1.71552e16 | 0.671326 | ||||||||
\(963\) | 1.49203e16 | 0.580541 | ||||||||
\(964\) | −4.21535e15 | −0.163084 | ||||||||
\(965\) | 1.89279e16 | 0.728120 | ||||||||
\(966\) | −6.49664e14 | −0.0248493 | ||||||||
\(967\) | 3.75814e16 | 1.42931 | 0.714656 | − | 0.699476i | \(-0.246583\pi\) | ||||
0.714656 | + | 0.699476i | \(0.246583\pi\) | |||||||
\(968\) | 7.42968e15 | 0.280967 | ||||||||
\(969\) | −1.53726e16 | −0.578052 | ||||||||
\(970\) | 8.98285e15 | 0.335869 | ||||||||
\(971\) | 2.34840e15 | 0.0873107 | 0.0436553 | − | 0.999047i | \(-0.486100\pi\) | ||||
0.0436553 | + | 0.999047i | \(0.486100\pi\) | |||||||
\(972\) | 1.66180e16 | 0.614349 | ||||||||
\(973\) | −4.09588e15 | −0.150566 | ||||||||
\(974\) | 2.53779e16 | 0.927642 | ||||||||
\(975\) | 9.32614e15 | 0.338982 | ||||||||
\(976\) | −4.66213e15 | −0.168504 | ||||||||
\(977\) | 6.37431e15 | 0.229094 | 0.114547 | − | 0.993418i | \(-0.463458\pi\) | ||||
0.114547 | + | 0.993418i | \(0.463458\pi\) | |||||||
\(978\) | −1.00391e16 | −0.358781 | ||||||||
\(979\) | −1.21989e15 | −0.0433526 | ||||||||
\(980\) | −1.28370e16 | −0.453648 | ||||||||
\(981\) | −2.17788e16 | −0.765342 | ||||||||
\(982\) | 4.44978e15 | 0.155498 | ||||||||
\(983\) | 3.13081e16 | 1.08796 | 0.543980 | − | 0.839098i | \(-0.316917\pi\) | ||||
0.543980 | + | 0.839098i | \(0.316917\pi\) | |||||||
\(984\) | −2.14173e16 | −0.740102 | ||||||||
\(985\) | 4.24064e16 | 1.45724 | ||||||||
\(986\) | −1.75170e15 | −0.0598601 | ||||||||
\(987\) | 1.18250e15 | 0.0401845 | ||||||||
\(988\) | 1.77239e16 | 0.598958 | ||||||||
\(989\) | 2.49197e15 | 0.0837457 | ||||||||
\(990\) | 1.03398e16 | 0.345556 | ||||||||
\(991\) | −1.05224e16 | −0.349713 | −0.174856 | − | 0.984594i | \(-0.555946\pi\) | ||||
−0.174856 | + | 0.984594i | \(0.555946\pi\) | |||||||
\(992\) | −3.25901e15 | −0.107714 | ||||||||
\(993\) | −4.89963e16 | −1.61043 | ||||||||
\(994\) | −1.49235e15 | −0.0487806 | ||||||||
\(995\) | −1.72757e16 | −0.561575 | ||||||||
\(996\) | −1.03815e16 | −0.335609 | ||||||||
\(997\) | −3.58375e16 | −1.15216 | −0.576082 | − | 0.817392i | \(-0.695419\pi\) | ||||
−0.576082 | + | 0.817392i | \(0.695419\pi\) | |||||||
\(998\) | 1.36722e16 | 0.437140 | ||||||||
\(999\) | 1.11195e16 | 0.353570 |
(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 | 29.12.a.a.1.8 | ✓ | 11 | |
3.2 | odd | 2 | 261.12.a.a.1.4 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.12.a.a.1.8 | ✓ | 11 | 1.1 | even | 1 | trivial | |
261.12.a.a.1.4 | 11 | 3.2 | odd | 2 |