Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,9,Mod(53,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.53");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(34.2198032451\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.9 | ||
Character | \(\chi\) | \(=\) | 84.65 |
Dual form | 84.9.p.b.53.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −5.75427 | − | 80.7953i | −0.0710403 | − | 0.997473i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −701.327 | − | 404.911i | −1.12212 | − | 0.647858i | −0.180181 | − | 0.983634i | \(-0.557668\pi\) |
−0.941942 | + | 0.335776i | \(0.891002\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1952.36 | + | 1397.53i | 0.813144 | + | 0.582062i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6494.78 | + | 929.836i | −0.989907 | + | 0.141722i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1114.61 | + | 643.521i | −0.0761295 | + | 0.0439534i | −0.537582 | − | 0.843212i | \(-0.680662\pi\) |
0.461452 | + | 0.887165i | \(0.347329\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −24570.2 | −0.860272 | −0.430136 | − | 0.902764i | \(-0.641534\pi\) | ||||
−0.430136 | + | 0.902764i | \(0.641534\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −28679.3 | + | 58993.9i | −0.566505 | + | 1.16531i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −35201.9 | + | 20323.8i | −0.421474 | + | 0.243338i | −0.695708 | − | 0.718325i | \(-0.744909\pi\) |
0.274234 | + | 0.961663i | \(0.411576\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −39959.6 | + | 69212.1i | −0.306625 | + | 0.531090i | −0.977622 | − | 0.210370i | \(-0.932533\pi\) |
0.670997 | + | 0.741460i | \(0.265866\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 101680. | − | 165783.i | 0.522825 | − | 0.852440i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 293149. | + | 169249.i | 1.04755 | + | 0.604806i | 0.921964 | − | 0.387277i | \(-0.126584\pi\) |
0.125590 | + | 0.992082i | \(0.459917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 132594. | + | 229659.i | 0.339440 | + | 0.587927i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 112499. | + | 519397.i | 0.211687 | + | 0.977338i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.09251e6i | − | 1.54466i | −0.635221 | − | 0.772331i | \(-0.719091\pi\) | ||
0.635221 | − | 0.772331i | \(-0.280909\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 521266. | + | 902859.i | 0.564433 | + | 0.977627i | 0.997102 | + | 0.0760739i | \(0.0242385\pi\) |
−0.432669 | + | 0.901553i | \(0.642428\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 58407.3 | + | 86352.4i | 0.0492506 | + | 0.0728147i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −803366. | − | 1.77066e6i | −0.535354 | − | 1.17995i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −184949. | + | 320341.i | −0.0986837 | + | 0.170925i | −0.911140 | − | 0.412097i | \(-0.864797\pi\) |
0.812456 | + | 0.583022i | \(0.198130\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 141384. | + | 1.98516e6i | 0.0611140 | + | 0.858099i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.77625e6i | − | 0.982480i | −0.871024 | − | 0.491240i | \(-0.836544\pi\) | ||
0.871024 | − | 0.491240i | \(-0.163456\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.17741e6 | 1.22189 | 0.610946 | − | 0.791672i | \(-0.290789\pi\) | ||||
0.610946 | + | 0.791672i | \(0.290789\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.93146e6 | + | 1.97769e6i | 1.20261 | + | 0.482290i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.07575e6 | + | 4.08519e6i | 1.45004 | + | 0.837184i | 0.998483 | − | 0.0550566i | \(-0.0175339\pi\) |
0.451561 | + | 0.892240i | \(0.350867\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.85862e6 | + | 5.45697e6i | 0.322408 | + | 0.946601i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.84463e6 | + | 2.72720e6i | 0.272665 | + | 0.403122i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.31437e6 | − | 3.64560e6i | 0.800251 | − | 0.462025i | −0.0433076 | − | 0.999062i | \(-0.513790\pi\) |
0.843559 | + | 0.537036i | \(0.180456\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.04228e6 | 0.113902 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.82196e6 | + | 2.83029e6i | 0.551531 | + | 0.268121i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.54219e7 | + | 8.90382e6i | −1.27271 | + | 0.734799i | −0.975497 | − | 0.220013i | \(-0.929390\pi\) |
−0.297212 | + | 0.954812i | \(0.596057\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.05761e7 | + | 1.83184e7i | −0.763848 | + | 1.32302i | 0.177006 | + | 0.984210i | \(0.443359\pi\) |
−0.940854 | + | 0.338813i | \(0.889974\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.39796e7 | − | 7.26128e6i | −0.887428 | − | 0.460947i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.72318e7 | + | 9.94876e6i | 0.965331 | + | 0.557334i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.90653e6 | + | 1.02304e7i | 0.293112 | + | 0.507684i | 0.974544 | − | 0.224197i | \(-0.0719759\pi\) |
−0.681432 | + | 0.731881i | \(0.738643\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.19877e7 | − | 2.46589e7i | 0.528859 | − | 1.08787i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.35033e6i | − | 0.0924903i | −0.998930 | − | 0.0462451i | \(-0.985274\pi\) | ||
0.998930 | − | 0.0462451i | \(-0.0147255\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.95490e7 | + | 3.38599e7i | 0.688388 | + | 1.19232i | 0.972359 | + | 0.233490i | \(0.0750146\pi\) |
−0.283971 | + | 0.958833i | \(0.591652\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.77924e7 | − | 1.20345e7i | 0.562327 | − | 0.380348i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.07546e6 | − | 301319.i | −0.0874878 | − | 0.00857164i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.37450e6 | − | 1.62371e7i | 0.240680 | − | 0.416870i | −0.720228 | − | 0.693737i | \(-0.755963\pi\) |
0.960908 | + | 0.276867i | \(0.0892962\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.13175e7 | − | 1.20782e7i | 0.959830 | − | 0.280582i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.15449e7i | − | 0.664687i | −0.943158 | − | 0.332343i | \(-0.892161\pi\) | ||
0.943158 | − | 0.332343i | \(-0.107839\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.29174e7 | 0.630594 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.82697e7 | + | 6.28659e6i | −1.54076 | + | 0.109733i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.65369e6 | + | 4.41886e6i | 0.121986 | + | 0.0704287i | 0.559751 | − | 0.828661i | \(-0.310897\pi\) |
−0.437765 | + | 0.899089i | \(0.644230\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.79699e7 | − | 3.43377e7i | −0.699526 | − | 0.500732i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.99473e7 | − | 4.73111e7i | 0.935059 | − | 0.632458i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.60495e7 | − | 3.23602e7i | 0.688141 | − | 0.397299i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.17592e8 | −1.32828 | −0.664141 | − | 0.747607i | \(-0.731202\pi\) | ||||
−0.664141 | + | 0.747607i | \(0.731202\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.64078e6 | − | 5.21593e6i | 0.0691319 | − | 0.0542989i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.32453e8 | + | 7.64720e7i | −1.27285 | + | 0.734880i | −0.975523 | − | 0.219895i | \(-0.929428\pi\) |
−0.297327 | + | 0.954776i | \(0.596095\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.91745e7 | + | 6.78523e7i | −0.348061 | + | 0.602859i | −0.985905 | − | 0.167306i | \(-0.946493\pi\) |
0.637844 | + | 0.770165i | \(0.279826\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.38438e8 | + | 7.50971e7i | −1.13893 | + | 0.617826i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.92504e7 | − | 5.15288e7i | −0.680887 | − | 0.393110i | 0.119302 | − | 0.992858i | \(-0.461934\pi\) |
−0.800189 | + | 0.599748i | \(0.795268\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.43401e7 | − | 9.41198e7i | −0.384959 | − | 0.666768i | 0.606805 | − | 0.794851i | \(-0.292451\pi\) |
−0.991763 | + | 0.128083i | \(0.959118\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.69463e7 | + | 1.30997e7i | 0.177504 | + | 0.0862918i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.58454e7i | − | 0.158514i | −0.996854 | − | 0.0792572i | \(-0.974745\pi\) | ||
0.996854 | − | 0.0792572i | \(-0.0252548\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.37062e8 | − | 2.37398e8i | −0.783656 | − | 1.35733i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.59578e8 | − | 2.28463e7i | 0.851589 | − | 0.121919i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.71300e7 | − | 9.51633e6i | −0.484357 | − | 0.0474550i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.06351e8 | + | 1.84206e8i | −0.496136 | + | 0.859333i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.24308e8 | + | 1.59753e7i | −0.979998 | + | 0.0697957i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.01582e8i | 0.416081i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.21235e7 | 0.315684 | 0.157842 | − | 0.987464i | \(-0.449546\pi\) | ||||
0.157842 | + | 0.987464i | \(0.449546\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.40379e7 | − | 3.37515e8i | −0.0868037 | − | 1.21881i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.76294e8 | + | 2.17254e8i | 1.27774 | + | 0.737703i | 0.976432 | − | 0.215824i | \(-0.0692437\pi\) |
0.301307 | + | 0.953527i | \(0.402577\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.74742e8 | + | 7.92821e7i | −0.558457 | + | 0.253378i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.31411e8 | − | 4.09819e8i | 0.395637 | − | 1.23384i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.54413e7 | + | 4.35561e7i | −0.214154 | + | 0.123642i | −0.603241 | − | 0.797559i | \(-0.706124\pi\) |
0.389086 | + | 0.921201i | \(0.372791\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.42039e8 | 0.648376 | 0.324188 | − | 0.945993i | \(-0.394909\pi\) | ||||
0.324188 | + | 0.945993i | \(0.394909\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.89348e8 | − | 5.95195e8i | 0.732057 | − | 1.50585i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.73863e7 | − | 1.58115e7i | 0.0654921 | − | 0.0378119i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.42369e8 | + | 7.66206e8i | −1.00072 | + | 1.73330i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.30203e8 | − | 1.81568e8i | 0.921305 | − | 0.388840i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.16102e8 | − | 2.97971e8i | −1.04711 | − | 0.604546i | −0.125268 | − | 0.992123i | \(-0.539979\pi\) |
−0.921838 | + | 0.387577i | \(0.873312\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.63368e8 | + | 6.29373e8i | 0.698939 | + | 1.21060i | 0.968835 | + | 0.247709i | \(0.0796776\pi\) |
−0.269895 | + | 0.962890i | \(0.586989\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.09731e8 | − | 1.64731e8i | 0.382733 | − | 0.300614i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.44265e8i | − | 1.46269i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.30584e8 | + | 3.99382e8i | 0.379516 | + | 0.657340i | 0.990992 | − | 0.133922i | \(-0.0427573\pi\) |
−0.611476 | + | 0.791263i | \(0.709424\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.30882e8 | − | 4.89194e8i | −0.517708 | − | 0.765407i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.35800e8 | + | 7.40120e8i | 0.499778 | + | 1.10154i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.48066e8 | + | 6.02868e8i | −0.493073 | + | 0.854028i | −0.999968 | − | 0.00798005i | \(-0.997460\pi\) |
0.506895 | + | 0.862008i | \(0.330793\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.99753e6 | − | 8.42110e7i | −0.00809165 | − | 0.113614i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.02172e9i | 1.31361i | 0.754060 | + | 0.656805i | \(0.228093\pi\) | ||||
−0.754060 | + | 0.656805i | \(0.771907\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.12034e8 | −0.259931 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.95173e8 | − | 4.86673e8i | 0.228263 | − | 0.569185i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.61654e8 | + | 3.24271e8i | 0.627024 | + | 0.362013i | 0.779599 | − | 0.626279i | \(-0.215423\pi\) |
−0.152575 | + | 0.988292i | \(0.548756\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.20850e7 | + | 6.33680e8i | −0.0661964 | + | 0.675644i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.08129e8 | + | 1.19478e9i | 0.823356 | + | 1.21729i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.17623e9 | − | 6.79096e8i | 1.14572 | − | 0.661483i | 0.197882 | − | 0.980226i | \(-0.436594\pi\) |
0.947841 | + | 0.318743i | \(0.103261\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.87644e8 | −0.454348 | −0.227174 | − | 0.973854i | \(-0.572949\pi\) | ||||
−0.227174 | + | 0.973854i | \(0.572949\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.54090e9 | + | 7.49092e8i | 1.37394 | + | 0.667930i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.59420e8 | − | 1.49776e8i | 0.221471 | − | 0.127866i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.61576e7 | − | 4.53064e7i | 0.0213911 | − | 0.0370504i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.06235e8 | + | 1.17127e9i | −0.396739 | + | 0.917931i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.52710e9 | − | 8.81672e8i | −1.14745 | − | 0.662481i | −0.199186 | − | 0.979962i | \(-0.563830\pi\) |
−0.948265 | + | 0.317481i | \(0.897163\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.13004e9 | + | 1.95729e9i | 0.814450 | + | 1.41067i | 0.909722 | + | 0.415218i | \(0.136295\pi\) |
−0.0952722 | + | 0.995451i | \(0.530372\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.04658e8 | − | 1.44949e9i | 0.487349 | − | 1.00249i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.26915e7i | 0.0283450i | 0.999900 | + | 0.0141725i | \(0.00451140\pi\) | ||||
−0.999900 | + | 0.0141725i | \(0.995489\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.76158e8 | − | 8.24730e8i | −0.303626 | − | 0.525895i | 0.673329 | − | 0.739343i | \(-0.264864\pi\) |
−0.976954 | + | 0.213448i | \(0.931531\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.92582e8 | − | 5.36089e8i | 0.485579 | − | 0.328437i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.52682e9 | − | 2.13297e9i | 0.899089 | − | 1.25603i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.12414e9 | + | 1.94706e9i | −0.636507 | + | 1.10246i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.06131e9 | − | 8.26657e8i | −1.12269 | − | 0.450240i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.02860e8i | − | 0.0539088i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.45001e9 | 0.731547 | 0.365774 | − | 0.930704i | \(-0.380804\pi\) | ||||
0.365774 | + | 0.930704i | \(0.380804\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.89896e8 | + | 1.35244e7i | −0.0922566 | + | 0.00657054i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.92973e9 | − | 1.69148e9i | −1.37111 | − | 0.791613i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.44075e8 | + | 2.49119e9i | −0.110074 | + | 1.12349i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.62323e9 | − | 1.77431e9i | 1.14041 | − | 0.771352i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.64919e8 | − | 4.99361e8i | 0.362582 | − | 0.209337i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.59542e9 | −0.645143 | −0.322572 | − | 0.946545i | \(-0.604547\pi\) | ||||
−0.322572 | + | 0.946545i | \(0.604547\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.07471e9 | − | 1.36829e9i | −0.419335 | − | 0.533886i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.60754e9 | + | 2.08281e9i | −1.35865 | + | 0.784417i | −0.989442 | − | 0.144930i | \(-0.953704\pi\) |
−0.369208 | + | 0.929347i | \(0.620371\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.61610e8 | − | 1.66556e9i | 0.349669 | − | 0.605644i | −0.636522 | − | 0.771259i | \(-0.719627\pi\) |
0.986191 | + | 0.165615i | \(0.0529608\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.64815e6 | + | 2.50217e8i | −0.00233482 | + | 0.0878757i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.38848e9 | + | 1.95634e9i | 1.14969 | + | 0.663774i | 0.948812 | − | 0.315842i | \(-0.102287\pi\) |
0.200878 | + | 0.979616i | \(0.435620\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.30828e9 | − | 5.73010e9i | −1.08475 | − | 1.87885i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.36583e9 | − | 6.63984e8i | −0.432915 | − | 0.210457i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.78953e9i | 1.46792i | 0.679194 | + | 0.733959i | \(0.262330\pi\) | ||||
−0.679194 | + | 0.733959i | \(0.737670\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.04556e8 | + | 1.81097e8i | 0.0309943 | + | 0.0536836i | 0.881106 | − | 0.472918i | \(-0.156799\pi\) |
−0.850112 | + | 0.526602i | \(0.823466\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.21361e9 | − | 3.26876e9i | −0.348060 | − | 0.937472i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.06090e8 | − | 4.57969e9i | 0.251482 | − | 1.27108i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.81818e8 | − | 1.70056e9i | 0.263781 | − | 0.456882i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.54868e9 | + | 1.81518e8i | −0.663007 | + | 0.0472195i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.46779e9i | 1.12563i | 0.826581 | + | 0.562817i | \(0.190283\pi\) | ||||
−0.826581 | + | 0.562817i | \(0.809717\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.35662e8 | −0.106333 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.89415e8 | − | 2.65957e9i | −0.0447976 | − | 0.629001i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.03909e9 | + | 1.75462e9i | 0.696644 | + | 0.402208i | 0.806096 | − | 0.591784i | \(-0.201576\pi\) |
−0.109452 | + | 0.993992i | \(0.534910\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.08774e8 | + | 3.66949e8i | −0.179733 | + | 0.0815468i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.01585e9 | + | 7.09560e9i | 0.218912 | + | 1.52907i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.00484e9 | + | 3.46689e9i | −1.25510 | + | 0.724632i | −0.972118 | − | 0.234493i | \(-0.924657\pi\) |
−0.282982 | + | 0.959125i | \(0.591324\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.90458e9 | −1.19731 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.12982e8 | − | 6.43810e8i | 0.0615849 | − | 0.126681i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.76159e9 | + | 3.32645e9i | −1.10036 | + | 0.635291i | −0.936314 | − | 0.351163i | \(-0.885786\pi\) |
−0.164041 | + | 0.986453i | \(0.552453\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.62650e9 | − | 6.28128e9i | 0.672373 | − | 1.16458i | −0.304856 | − | 0.952399i | \(-0.598608\pi\) |
0.977229 | − | 0.212186i | \(-0.0680584\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.49829e9 | + | 4.07334e9i | −0.449772 | + | 0.733330i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.95581e8 | − | 1.70654e8i | −0.0516827 | − | 0.0298390i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.76342e9 | − | 4.78638e9i | −0.469383 | − | 0.812995i | 0.530004 | − | 0.847995i | \(-0.322190\pi\) |
−0.999387 | + | 0.0349995i | \(0.988857\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.22501e9 | − | 5.37917e9i | −0.697287 | − | 0.887767i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.02314e9i | − | 0.805656i | −0.915276 | − | 0.402828i | \(-0.868027\pi\) | ||
0.915276 | − | 0.402828i | \(-0.131973\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.01214e9 | − | 5.21718e9i | −0.469601 | − | 0.813373i | 0.529795 | − | 0.848126i | \(-0.322269\pi\) |
−0.999396 | + | 0.0347527i | \(0.988936\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.93708e9 | − | 4.34233e9i | −0.445181 | − | 0.658178i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.87990e9 | − | 5.42025e9i | 0.571864 | − | 0.798898i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.66176e9 | + | 4.61031e9i | −0.381573 | + | 0.660904i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.76655e8 | + | 9.50087e9i | 0.0943616 | + | 1.32493i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.65732e9i | 0.767609i | 0.923414 | + | 0.383805i | \(0.125386\pi\) | ||||
−0.923414 | + | 0.383805i | \(0.874614\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.44210e10 | 1.90418 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.59636e8 | − | 5.06531e8i | −0.0590729 | − | 0.0650998i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.20273e9 | − | 4.15850e9i | −0.901182 | − | 0.520298i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.15580e9 | + | 5.83806e9i | 0.993575 | + | 0.711217i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.94075e9 | + | 1.02616e10i | 0.823447 | + | 1.21743i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.48346e10 | − | 8.56477e9i | 1.71426 | − | 0.989730i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.08970e9 | 0.910708 | 0.455354 | − | 0.890311i | \(-0.349513\pi\) | ||||
0.455354 | + | 0.890311i | \(0.349513\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.70757e9 | + | 2.77468e9i | 0.626062 | + | 0.304354i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.38692e10 | − | 8.00737e9i | 1.48255 | − | 0.855949i | 0.482744 | − | 0.875761i | \(-0.339640\pi\) |
0.999804 | + | 0.0198119i | \(0.00630672\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.58737e9 | − | 7.94555e9i | 0.477954 | − | 0.827841i | −0.521727 | − | 0.853113i | \(-0.674712\pi\) |
0.999681 | + | 0.0252721i | \(0.00804520\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.86410e9 | + | 1.07530e10i | 0.697175 | + | 1.09217i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.21210e10 | − | 6.99804e9i | −1.20033 | − | 0.693010i | −0.239700 | − | 0.970847i | \(-0.577049\pi\) |
−0.960628 | + | 0.277837i | \(0.910382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.03053e8 | + | 1.21772e9i | 0.0678931 | + | 0.117594i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.64971e9 | + | 7.50753e9i | −0.343747 | + | 0.707094i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.24853e9i | − | 0.298454i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.25786e9 | − | 5.64277e9i | −0.292011 | − | 0.505777i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.29175e9 | + | 4.93201e9i | −0.637736 | + | 0.431354i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.10524e9 | + | 1.78643e10i | 0.691803 | + | 1.52477i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.48598e9 | + | 9.50200e9i | −0.457027 | + | 0.791595i | −0.998802 | − | 0.0489289i | \(-0.984419\pi\) |
0.541775 | + | 0.840524i | \(0.317753\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.03339e8 | − | 2.25252e9i | 0.0734639 | − | 0.183186i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 9.56648e9i | − | 0.759579i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.94045e10 | 1.50447 | 0.752233 | − | 0.658897i | \(-0.228977\pi\) | ||||
0.752233 | + | 0.658897i | \(0.228977\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.08819e9 | + | 1.48721e8i | −0.158114 | + | 0.0112609i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.16202e9 | − | 6.70891e8i | −0.0859400 | − | 0.0496175i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.99759e9 | + | 1.32514e10i | −0.288817 | + | 0.957384i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.83920e10 | + | 1.24400e10i | −1.29823 | + | 0.878101i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.31408e10 | + | 7.58685e9i | −0.906367 | + | 0.523291i | −0.879261 | − | 0.476341i | \(-0.841963\pi\) |
−0.0271067 | + | 0.999633i | \(0.508629\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.72031e9 | −0.115959 | −0.0579797 | − | 0.998318i | \(-0.518466\pi\) | ||||
−0.0579797 | + | 0.998318i | \(0.518466\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.76413e9 | − | 1.27617e10i | −0.182108 | − | 0.840776i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.34031e10 | + | 7.73830e9i | −0.863192 | + | 0.498364i | −0.865080 | − | 0.501634i | \(-0.832732\pi\) |
0.00188763 | + | 0.999998i | \(0.499399\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.51676e8 | + | 1.64835e9i | −0.0599205 | + | 0.103785i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.09963e8 | + | 7.90241e9i | −0.0129262 | + | 0.486504i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.65322e10 | + | 9.54488e9i | 0.995298 | + | 0.574636i | 0.906854 | − | 0.421445i | \(-0.138477\pi\) |
0.0884445 | + | 0.996081i | \(0.471810\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.29823e9 | + | 9.17681e9i | 0.311963 | + | 0.540335i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.54949e10 | + | 7.53271e9i | 0.892408 | + | 0.433835i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3.16624e10i | − | 1.78391i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.67235e10 | − | 2.89660e10i | −0.921856 | − | 1.59670i | −0.796540 | − | 0.604585i | \(-0.793339\pi\) |
−0.125316 | − | 0.992117i | \(-0.539994\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.58146e9 | + | 1.80311e10i | 0.139239 | + | 0.972563i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.74228e10 | + | 1.70700e9i | 0.919647 | + | 0.0901027i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.61432e9 | − | 1.31884e10i | 0.393365 | − | 0.681328i | −0.599526 | − | 0.800355i | \(-0.704644\pi\) |
0.992891 | + | 0.119027i | \(0.0379776\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.20738e9 | − | 5.84532e8i | 0.415030 | − | 0.0295585i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.68432e10i | 1.32883i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.26969e10 | 1.10004 | 0.550021 | − | 0.835151i | \(-0.314620\pi\) | ||||
0.550021 | + | 0.835151i | \(0.314620\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.72561e8 | − | 6.63520e9i | −0.0224263 | − | 0.314887i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.25381e9 | + | 4.76534e9i | 0.383583 | + | 0.221462i | 0.679376 | − | 0.733790i | \(-0.262251\pi\) |
−0.295793 | + | 0.955252i | \(0.595584\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.03490e9 | + | 1.45661e9i | 0.0926189 | + | 0.0662981i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.71313e10 | + | 3.88430e9i | −1.20956 | + | 0.173169i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.01606e9 | + | 4.05072e9i | −0.306404 | + | 0.176903i | −0.645316 | − | 0.763915i | \(-0.723274\pi\) |
0.338912 | + | 0.940818i | \(0.389941\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.37592e10 | −0.588689 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.53878e10 | − | 3.16530e10i | 0.645068 | − | 1.32692i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.31492e10 | + | 7.59168e9i | −0.540145 | + | 0.311853i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.37965e10 | − | 4.12167e10i | 0.957967 | − | 1.65925i | 0.230539 | − | 0.973063i | \(-0.425951\pi\) |
0.727428 | − | 0.686184i | \(-0.240716\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.41114e9 | + | 1.36621e10i | 0.292411 | + | 0.539046i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.59819e10 | + | 9.22713e9i | 0.618087 | + | 0.356853i | 0.776124 | − | 0.630580i | \(-0.217183\pi\) |
−0.158037 | + | 0.987433i | \(0.550516\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.28076e10 | − | 2.21835e10i | −0.485566 | − | 0.841025i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.38677e10 | − | 8.25920e9i | −1.25882 | − | 0.306985i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4.76075e8i | − | 0.0173499i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.50498e10 | − | 4.33876e10i | −0.895183 | − | 1.55050i | −0.833578 | − | 0.552402i | \(-0.813711\pi\) |
−0.0616053 | − | 0.998101i | \(-0.519622\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.95324e9 | + | 5.84467e9i | 0.138543 | + | 0.204830i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.25524e10 | − | 4.16908e9i | −1.46259 | − | 0.143298i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.27729e10 | + | 2.21233e10i | −0.430622 | + | 0.745860i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.39276e9 | − | 1.95557e10i | −0.0460609 | − | 0.646738i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 2.56571e10i | − | 0.832438i | −0.909264 | − | 0.416219i | \(-0.863355\pi\) | ||
0.909264 | − | 0.416219i | \(-0.136645\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.01551e10 | 1.91489 | 0.957446 | − | 0.288614i | \(-0.0931943\pi\) | ||||
0.957446 | + | 0.288614i | \(0.0931943\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.97540e10 | − | 1.99531e10i | −1.55406 | − | 0.623231i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.33510e9 | − | 5.38962e9i | −0.286130 | − | 0.165197i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.62489e10 | + | 2.09836e10i | −1.39120 | + | 0.631202i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.43508e9 | − | 2.12170e9i | −0.0423689 | − | 0.0626404i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.43030e10 | + | 8.25785e9i | −0.414494 | + | 0.239308i | −0.692719 | − | 0.721208i | \(-0.743587\pi\) |
0.278225 | + | 0.960516i | \(0.410254\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.28331e10 | −0.649550 | −0.324775 | − | 0.945791i | \(-0.605289\pi\) | ||||
−0.324775 | + | 0.945791i | \(0.605289\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.44514e10 | + | 3.13324e10i | 1.80001 | + | 0.875058i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.34282e10 | + | 1.35263e10i | −0.642412 | + | 0.370897i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.97887e10 | + | 3.42751e10i | −0.532794 | + | 0.922827i | 0.466472 | + | 0.884536i | \(0.345525\pi\) |
−0.999267 | + | 0.0382911i | \(0.987809\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.71454e10 | − | 3.37136e10i | −0.453307 | − | 0.891354i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.80223e10 | + | 1.04052e10i | 0.467945 | + | 0.270168i | 0.715379 | − | 0.698736i | \(-0.246254\pi\) |
−0.247434 | + | 0.968905i | \(0.579587\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.57849e9 | − | 6.19813e9i | −0.0912556 | − | 0.158059i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.11049e10 | + | 4.34132e10i | −0.528632 | + | 1.08741i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.22570e10i | − | 1.28576i | −0.765968 | − | 0.642878i | \(-0.777740\pi\) | ||
0.765968 | − | 0.642878i | \(-0.222260\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.78658e9 | + | 3.09444e9i | 0.0431833 | + | 0.0747957i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.87595e10 | − | 3.29801e10i | 1.15789 | − | 0.783175i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.97389e10 | + | 4.35055e10i | 0.460551 | + | 1.01508i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.38191e9 | − | 4.12560e9i | 0.0546086 | − | 0.0945849i | −0.837429 | − | 0.546546i | \(-0.815942\pi\) |
0.892037 | + | 0.451961i | \(0.149276\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.45163e10 | − | 1.59974e10i | −0.327044 | − | 0.360411i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.30654e10i | − | 0.732099i | −0.930595 | − | 0.366050i | \(-0.880710\pi\) | ||
0.930595 | − | 0.366050i | \(-0.119290\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.07220e10 | −0.886147 | −0.443073 | − | 0.896485i | \(-0.646112\pi\) | ||||
−0.443073 | + | 0.896485i | \(0.646112\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.82127e10 | + | 4.85813e9i | −1.45899 | + | 0.103910i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.85131e10 | + | 1.06885e10i | 0.389234 | + | 0.224724i | 0.681828 | − | 0.731512i | \(-0.261185\pi\) |
−0.292594 | + | 0.956237i | \(0.594518\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.76564e9 | + | 2.82280e10i | −0.0571617 | + | 0.583430i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.09414e10 | − | 2.09282e10i | 0.628719 | − | 0.425254i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.65619e9 | + | 2.68825e9i | −0.0930221 | + | 0.0537063i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.11936e10 | −0.416322 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.76206e10 | + | 2.95487e10i | −0.726695 | + | 0.570775i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.15918e10 | + | 2.40130e10i | −0.790069 | + | 0.456147i | −0.839987 | − | 0.542607i | \(-0.817437\pi\) |
0.0499177 | + | 0.998753i | \(0.484104\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.54425e9 | − | 7.87087e9i | 0.0848949 | − | 0.147042i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.78660e10 | − | 3.13899e10i | 1.06325 | − | 0.576769i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.24703e10 | + | 4.76142e10i | 1.49050 | + | 0.860538i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.00358e9 | − | 5.20235e9i | −0.0533977 | − | 0.0924876i | 0.838091 | − | 0.545530i | \(-0.183672\pi\) |
−0.891489 | + | 0.453043i | \(0.850338\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.07118e10 | + | 2.46531e10i | 0.886898 | + | 0.431157i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 1.85500e10i | − | 0.319167i | −0.987184 | − | 0.159583i | \(-0.948985\pi\) | ||
0.987184 | − | 0.159583i | \(-0.0510151\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.22040e10 | + | 3.84584e10i | 0.375875 | + | 0.651034i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.76935e9 | + | 9.69146e8i | −0.112752 | + | 0.0161424i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.28466e9 | − | 4.58869e9i | 0.0538351 | − | 0.0752079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.61025e10 | + | 4.52108e10i | −0.420998 | + | 0.729189i | −0.996037 | − | 0.0889361i | \(-0.971653\pi\) |
0.575040 | + | 0.818126i | \(0.304987\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.25504e10 | − | 5.87926e9i | 1.31029 | − | 0.0933194i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 8.21977e10i | − | 1.28407i | −0.766676 | − | 0.642034i | \(-0.778091\pi\) | ||
0.766676 | − | 0.642034i | \(-0.221909\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.23857e11 | 1.90439 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.22010e9 | + | 1.71314e10i | 0.0184656 | + | 0.259275i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.85830e10 | − | 5.11434e10i | −1.31971 | − | 0.761937i | −0.336031 | − | 0.941851i | \(-0.609085\pi\) |
−0.983682 | + | 0.179915i | \(0.942418\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.15353e9 | + | 9.34270e10i | −0.134247 | + | 1.37022i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.04440e10 | − | 1.29686e10i | −0.583962 | − | 0.187251i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.49483e10 | − | 3.17244e10i | 0.781134 | − | 0.450988i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.05156e10 | −0.147188 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.29677e10 | − | 4.72450e10i | 0.316554 | − | 0.651157i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.31302e10 | − | 2.49012e10i | 0.585369 | − | 0.337963i | −0.177895 | − | 0.984049i | \(-0.556929\pi\) |
0.763264 | + | 0.646086i | \(0.223595\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.18682e10 | + | 2.05563e10i | −0.158627 | + | 0.274750i | −0.934374 | − | 0.356294i | \(-0.884040\pi\) |
0.775747 | + | 0.631044i | \(0.217373\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.15557e10 | + | 1.36981e9i | 0.678640 | + | 0.0180312i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.66991e10 | − | 2.11882e10i | −0.475787 | − | 0.274696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.81352e10 | + | 3.14111e10i | 0.231580 | + | 0.401107i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.18825e10 | − | 7.21682e10i | 1.15573 | − | 0.907753i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.82132e10i | 0.845200i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.17291e10 | + | 7.22770e10i | 0.509359 | + | 0.882236i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.16361e10 | − | 9.11261e10i | −0.741205 | − | 1.09584i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.58331e9 | − | 4.88634e9i | −0.0661510 | − | 0.0578933i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.17113e10 | + | 1.06887e11i | −0.720403 | + | 1.24777i | 0.240435 | + | 0.970665i | \(0.422710\pi\) |
−0.960838 | + | 0.277110i | \(0.910624\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.80603e9 | + | 3.93993e10i | 0.0322770 | + | 0.453200i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.80116e10i | 0.997594i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.02466e10 | −0.226153 | −0.113077 | − | 0.993586i | \(-0.536071\pi\) | ||||
−0.113077 | + | 0.993586i | \(0.536071\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.16564e10 | − | 1.28808e11i | 0.568637 | − | 1.41792i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.56149e10 | + | 4.36563e10i | 0.820354 | + | 0.473631i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.09943e10 | − | 1.85995e10i | 0.438352 | − | 0.198885i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.35940e10 | − | 2.00980e10i | −0.143276 | − | 0.211827i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.16565e10 | + | 4.71444e10i | −0.848340 | + | 0.489789i | −0.860090 | − | 0.510142i | \(-0.829593\pi\) |
0.0117506 | + | 0.999931i | \(0.496260\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.02640e11 | −1.05116 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.81106e9 | − | 1.85271e9i | −0.0384764 | − | 0.0187049i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.05062e11 | − | 6.06578e10i | 1.04572 | − | 0.603744i | 0.124269 | − | 0.992249i | \(-0.460342\pi\) |
0.921447 | + | 0.388505i | \(0.127008\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.04651e10 | + | 1.81260e10i | −0.102695 | + | 0.177873i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.75463e10 | + | 3.41616e10i | 0.943797 | + | 0.330527i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.12012e11 | + | 6.46699e10i | 1.06860 | + | 0.616955i | 0.927798 | − | 0.373083i | \(-0.121699\pi\) |
0.140799 | + | 0.990038i | \(0.455033\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.07167e10 | + | 1.85619e10i | 0.100813 | + | 0.174614i | 0.912020 | − | 0.410146i | \(-0.134522\pi\) |
−0.811207 | + | 0.584760i | \(0.801189\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.24476e10 | + | 1.28456e11i | −0.579292 | + | 1.19161i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.97655e10i | 0.821180i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.30017e10 | + | 5.71606e10i | 0.297737 | + | 0.515695i | 0.975618 | − | 0.219476i | \(-0.0704349\pi\) |
−0.677881 | + | 0.735172i | \(0.737102\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.51637e11 | − | 1.02565e11i | 1.34925 | − | 0.912607i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.40850e10 | − | 6.15870e10i | 0.386889 | − | 0.540486i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.69205e9 | + | 8.12686e9i | −0.0406151 | + | 0.0703475i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.21167e11 | − | 4.85923e10i | −1.03457 | − | 0.414900i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.82785e10i | 0.743537i | 0.928325 | + | 0.371769i | \(0.121248\pi\) | ||||
−0.928325 | + | 0.371769i | \(0.878752\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.33184e10 | −0.692277 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.44928e9 | − | 2.45658e8i | 0.0282734 | − | 0.00201364i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.64778e11 | − | 9.51345e10i | −1.33254 | − | 0.769342i | −0.346851 | − | 0.937920i | \(-0.612749\pi\) |
−0.985688 | + | 0.168579i | \(0.946082\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.42666e10 | + | 4.60031e10i | 0.512764 | + | 0.367045i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.38944e10 | + | 4.32171e10i | −0.502997 | + | 0.340218i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.55178e11 | + | 8.95923e10i | −1.20538 | + | 0.695927i | −0.961747 | − | 0.273941i | \(-0.911673\pi\) |
−0.243634 | + | 0.969867i | \(0.578339\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.68307e10 | −0.358949 | −0.179474 | − | 0.983763i | \(-0.557440\pi\) | ||||
−0.179474 | + | 0.983763i | \(0.557440\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.78742e10 | − | 6.09521e10i | −0.362103 | − | 0.461020i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.49174e11 | − | 8.61256e10i | 1.11345 | − | 0.642851i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.27939e10 | − | 2.21598e10i | 0.0942431 | − | 0.163234i | −0.815049 | − | 0.579392i | \(-0.803290\pi\) |
0.909292 | + | 0.416158i | \(0.136624\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.81120e11 | − | 1.11086e11i | −1.31673 | − | 0.807588i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.73853e11 | − | 1.00374e11i | −1.24743 | − | 0.720206i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.19833e8 | + | 1.41999e9i | 0.00580609 | + | 0.0100564i | 0.868914 | − | 0.494963i | \(-0.164819\pi\) |
−0.863108 | + | 0.505020i | \(0.831485\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.63782e11 | + | 7.96211e10i | 1.14490 | + | 0.556580i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.24163e11i | − | 0.856745i | −0.903602 | − | 0.428372i | \(-0.859087\pi\) | ||
0.903602 | − | 0.428372i | \(-0.140913\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.46997e10 | − | 7.74222e10i | −0.304468 | − | 0.527355i | 0.672674 | − | 0.739939i | \(-0.265145\pi\) |
−0.977143 | + | 0.212584i | \(0.931812\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.49287e10 | + | 1.71301e11i | −0.369346 | + | 1.15184i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.76726e9 | + | 1.93235e10i | 0.0581985 | + | 0.128272i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.29262e10 | − | 1.60953e11i | 0.609001 | − | 1.05482i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.31057e9 | + | 5.91881e8i | −0.0537726 | + | 0.00382970i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.50355e10i | − | 0.0960540i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.02715e11 | −1.90949 | −0.954743 | − | 0.297431i | \(-0.903870\pi\) | ||||
−0.954743 | + | 0.297431i | \(0.903870\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.34377e9 | − | 1.17154e11i | −0.0519694 | − | 0.729699i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.75954e10 | − | 3.32527e10i | −0.354236 | − | 0.204518i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.56666e10 | − | 1.34079e11i | −0.277358 | − | 0.814335i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.18542e9 | + | 1.52649e10i | 0.0131079 | + | 0.0915567i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.94806e10 | − | 3.43411e10i | 0.352325 | − | 0.203415i | −0.313384 | − | 0.949627i | \(-0.601463\pi\) |
0.665709 | + | 0.746212i | \(0.268129\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.67422e11 | 0.979418 | 0.489709 | − | 0.871886i | \(-0.337103\pi\) | ||||
0.489709 | + | 0.871886i | \(0.337103\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.19805e11 | + | 2.46442e11i | −0.692208 | + | 1.42389i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.78175e10 | + | 5.07014e10i | −0.501145 | + | 0.289336i | −0.729186 | − | 0.684315i | \(-0.760101\pi\) |
0.228041 | + | 0.973652i | \(0.426768\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.14596e10 | − | 1.98486e10i | 0.0645938 | − | 0.111880i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.02681e11 | + | 5.38514e9i | 1.12847 | + | 0.0299829i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.24003e11 | − | 7.15934e10i | −0.681995 | − | 0.393750i | 0.118612 | − | 0.992941i | \(-0.462156\pi\) |
−0.800606 | + | 0.599191i | \(0.795489\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.75937e11 | − | 3.04731e11i | −0.955854 | − | 1.65559i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.58451e11 | − | 2.01735e11i | −0.850418 | − | 1.08273i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.49864e10i | 0.132484i | 0.997804 | + | 0.0662418i | \(0.0211009\pi\) | ||||
−0.997804 | + | 0.0662418i | \(0.978899\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.35081e11 | + | 2.33967e11i | 0.707599 | + | 1.22560i | 0.965745 | + | 0.259492i | \(0.0835552\pi\) |
−0.258146 | + | 0.966106i | \(0.583112\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.53231e10 | − | 6.70080e10i | −0.234566 | − | 0.346795i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.54653e11 | + | 1.51522e10i | 0.790811 | + | 0.0774798i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.84907e11 | − | 3.20268e11i | 0.934220 | − | 1.61812i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.18049e9 | + | 1.28903e11i | 0.0458312 | + | 0.643513i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.72238e10i | − | 0.134295i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.84302e10 | 0.284824 | 0.142412 | − | 0.989807i | \(-0.454514\pi\) | ||||
0.142412 | + | 0.989807i | \(0.454514\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.04368e11 | + | 9.47052e10i | −0.502748 | + | 0.456203i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.85501e11 | + | 1.07099e11i | 0.883063 | + | 0.509837i | 0.871667 | − | 0.490098i | \(-0.163039\pi\) |
0.0113962 | + | 0.999935i | \(0.496372\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.29582e11 | − | 1.64338e11i | −1.08008 | − | 0.773142i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.89040e11 | + | 2.79487e11i | 0.878954 | + | 1.29949i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.78222e11 | − | 1.02896e11i | 0.818988 | − | 0.472843i | −0.0310794 | − | 0.999517i | \(-0.509894\pi\) |
0.850067 | + | 0.526674i | \(0.176561\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.05453e10 | 0.320410 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.40103e11 | − | 6.81095e10i | −0.628955 | − | 0.305760i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.55146e11 | + | 8.95733e10i | −0.688434 | + | 0.397468i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.02069e11 | − | 1.76789e11i | 0.447696 | − | 0.775432i | −0.550540 | − | 0.834809i | \(-0.685578\pi\) |
0.998236 | + | 0.0593771i | \(0.0189114\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.02546e10 | − | 9.02676e8i | 0.0878196 | − | 0.00391380i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.69749e11 | − | 9.80045e10i | −0.727558 | − | 0.420056i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.64241e10 | + | 9.77294e10i | 0.239075 | + | 0.414090i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.38565e11 | − | 2.85030e11i | 0.580422 | − | 1.19394i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.92695e11i | 1.21211i | 0.795421 | + | 0.606057i | \(0.207250\pi\) | ||||
−0.795421 | + | 0.606057i | \(0.792750\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.47810e10 | − | 2.56015e10i | −0.0605178 | − | 0.104820i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.43929e11 | + | 3.00266e11i | −1.79704 | + | 1.21548i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.65468e11 | − | 3.58068e10i | −1.46276 | − | 0.143314i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.69687e10 | − | 1.67955e11i | 0.383749 | − | 0.664672i | −0.607846 | − | 0.794055i | \(-0.707966\pi\) |
0.991595 | + | 0.129383i | \(0.0412996\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.57875e10 | + | 1.14173e11i | −0.179171 | + | 0.446772i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.52896e11i | 1.36549i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.56090e10 | −0.0979869 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.86972e11 | − | 2.75603e10i | 1.46421 | − | 0.104281i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.62598e11 | + | 1.51611e11i | 0.982599 | + | 0.567304i | 0.903054 | − | 0.429527i | \(-0.141320\pi\) |
0.0795455 | + | 0.996831i | \(0.474653\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.71309e11 | + | 7.77245e10i | −0.633925 | + | 0.287618i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.40301e10 | − | 9.48973e9i | 0.0513462 | − | 0.0347297i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.50904e11 | − | 1.44860e11i | 0.908147 | − | 0.524319i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.93281e11 | −1.04990 | −0.524948 | − | 0.851135i | \(-0.675915\pi\) | ||||
−0.524948 | + | 0.851135i | \(0.675915\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.57117e11 | + | 1.16863e11i | −0.910377 | + | 0.413779i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.47053e11 | + | 8.49010e10i | −0.514996 | + | 0.297333i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.41246e10 | + | 4.17850e10i | −0.0835687 | + | 0.144745i | −0.904780 | − | 0.425878i | \(-0.859965\pi\) |
0.821212 | + | 0.570624i | \(0.193298\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.75232e11 | − | 4.68551e10i | −1.28573 | − | 0.160549i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.31670e10 | − | 7.60196e9i | −0.0446289 | − | 0.0257665i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.01824e11 | + | 3.49570e11i | 0.676700 | + | 1.17208i | 0.975969 | + | 0.217909i | \(0.0699237\pi\) |
−0.299270 | + | 0.954169i | \(0.596743\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.43047e11 | − | 6.95409e10i | −0.474467 | − | 0.230657i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.03948e11i | 0.997342i | 0.866791 | + | 0.498671i | \(0.166178\pi\) | ||||
−0.866791 | + | 0.498671i | \(0.833822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.41304e11 | + | 4.17951e11i | 0.783320 | + | 1.35675i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.93316e10 | + | 2.04877e11i | 0.0942005 | + | 0.657978i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.02236e11 | − | 2.25333e11i | −0.324845 | − | 0.715974i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.69823e11 | − | 2.94141e11i | 0.533870 | − | 0.924690i | −0.465347 | − | 0.885128i | \(-0.654070\pi\) |
0.999217 | − | 0.0395617i | \(-0.0125962\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.60976e11 | − | 2.57088e10i | 1.12279 | − | 0.0799655i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 5.88528e11i | − | 1.81125i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.49280e11 | 1.36815 | 0.684074 | − | 0.729412i | \(-0.260206\pi\) | ||||
0.684074 | + | 0.729412i | \(0.260206\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.50692e9 | + | 3.51995e10i | 0.00755393 | + | 0.106064i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.71405e11 | + | 2.14431e11i | 1.10741 | + | 0.639364i | 0.938158 | − | 0.346208i | \(-0.112531\pi\) |
0.169254 | + | 0.985573i | \(0.445864\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.54439e10 | − | 2.59698e11i | 0.0750734 | − | 0.766249i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.13791e11 | + | 3.06078e10i | −0.624229 | + | 0.0893688i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.78919e11 | − | 2.18769e11i | 1.09488 | − | 0.632127i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.84679e11 | 1.10000 | 0.550001 | − | 0.835164i | \(-0.314627\pi\) | ||||
0.550001 | + | 0.835164i | \(0.314627\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.24277e11 | − | 2.55641e11i | 0.351702 | − | 0.723457i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.61563e11 | + | 1.51013e11i | −0.732585 | + | 0.422958i | −0.819367 | − | 0.573269i | \(-0.805675\pi\) |
0.0867823 | + | 0.996227i | \(0.472342\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.38233e11 | + | 2.39427e11i | −0.383182 | + | 0.663690i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.43017e10 | + | 6.32337e10i | 0.0941091 | + | 0.173486i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.92150e11 | + | 1.10938e11i | 0.521785 | + | 0.301253i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.51249e9 | + | 2.61971e9i | 0.00406526 | + | 0.00704123i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.67446e11 | − | 1.22906e11i | 1.50966 | − | 0.326985i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 3.73463e11i | − | 0.983489i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.59141e11 | + | 6.22051e11i | 0.936195 | + | 1.62154i | 0.772489 | + | 0.635029i | \(0.219012\pi\) |
0.163706 | + | 0.986509i | \(0.447655\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.14662e11 | + | 4.65213e11i | 0.811964 | + | 1.20045i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.61197e10 | − | 5.04595e10i | 0.0922653 | − | 0.128895i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.59858e11 | − | 4.50087e11i | 0.657117 | − | 1.13816i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.39765e10 | + | 4.77063e11i | 0.0850571 | + | 1.19428i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.04056e11i | − | 0.505727i | −0.967502 | − | 0.252864i | \(-0.918628\pi\) | ||
0.967502 | − | 0.252864i | \(-0.0813724\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.32107e11 | −0.814874 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.38178e10 | − | 2.15828e10i | −0.130736 | − | 0.0524298i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.35791e10 | − | 2.51604e10i | −0.104813 | − | 0.0605139i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.41772e10 | − | 6.55035e11i | 0.152826 | − | 1.55984i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.01916e11 | + | 4.46368e11i | 0.711855 | + | 1.05244i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.51905e10 | + | 5.49583e10i | −0.222228 | + | 0.128304i | −0.606982 | − | 0.794716i | \(-0.707620\pi\) |
0.384753 | + | 0.923019i | \(0.374287\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.33734e11 | 0.540305 | 0.270152 | − | 0.962818i | \(-0.412926\pi\) | ||||
0.270152 | + | 0.962818i | \(0.412926\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.28366e11 | − | 2.56860e11i | −1.20941 | − | 0.587942i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.88216e11 | − | 2.81872e11i | 1.10658 | − | 0.638883i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.66928e11 | + | 2.89127e11i | −0.374663 | + | 0.648935i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.43482e11 | + | 1.78411e11i | 0.763430 | + | 0.396540i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.20573e11 | − | 3.00553e11i | −1.14580 | − | 0.661528i | −0.197940 | − | 0.980214i | \(-0.563425\pi\) |
−0.947860 | + | 0.318686i | \(0.896759\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.79738e11 | − | 3.11316e11i | −0.391779 | − | 0.678581i | 0.600905 | − | 0.799320i | \(-0.294807\pi\) |
−0.992684 | + | 0.120739i | \(0.961474\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.20872e10 | + | 2.48635e10i | −0.0260921 | + | 0.0536719i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.43642e10i | 0.116223i | 0.998310 | + | 0.0581113i | \(0.0185078\pi\) | ||||
−0.998310 | + | 0.0581113i | \(0.981492\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.74898e11 | + | 4.76138e11i | 0.582041 | + | 1.00813i | 0.995237 | + | 0.0974831i | \(0.0310792\pi\) |
−0.413196 | + | 0.910642i | \(0.635587\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.70816e11 | + | 2.50813e11i | −0.777596 | + | 0.525953i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.76333e11 | − | 1.54321e11i | −0.366230 | − | 0.320513i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.13707e11 | − | 7.16561e11i | 0.851033 | − | 1.47403i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.10300e11 | + | 3.72315e11i | −0.835988 | + | 0.758592i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.91290e11i | 0.789679i | 0.918750 | + | 0.394840i | \(0.129200\pi\) | ||||
−0.918750 | + | 0.394840i | \(0.870800\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.93330e11 | −1.38598 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.05846e11 | + | 2.89045e10i | −0.803620 | + | 0.0572341i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.48705e11 | + | 8.58550e10i | 0.291675 | + | 0.168399i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.65069e11 | + | 2.11007e11i | −0.903616 | + | 0.409980i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.04191e11 | + | 2.73388e11i | −0.777957 | + | 0.526197i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.08435e11 | + | 6.26051e10i | −0.206753 | + | 0.119369i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.62938e11 | −0.496658 | −0.248329 | − | 0.968676i | \(-0.579881\pi\) | ||||
−0.248329 | + | 0.968676i | \(0.579881\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.33940e11 | + | 2.62289e11i | −0.624890 | + | 0.490813i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.71064e11 | − | 9.87636e10i | 0.317128 | − | 0.183094i | −0.332984 | − | 0.942933i | \(-0.608055\pi\) |
0.650112 | + | 0.759839i | \(0.274722\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.96947e10 | + | 1.03394e11i | −0.109638 | + | 0.189899i | −0.915624 | − | 0.402036i | \(-0.868303\pi\) |
0.805985 | + | 0.591935i | \(0.201636\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.60257e11 | − | 2.82288e11i | −0.837505 | − | 0.513666i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.81431e11 | − | 4.51160e11i | −1.40879 | − | 0.813368i | −0.413522 | − | 0.910494i | \(-0.635702\pi\) |
−0.995272 | + | 0.0971260i | \(0.969035\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.62602e11 | − | 4.54840e11i | −0.469065 | − | 0.812445i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.87808e11 | + | 1.88529e11i | 0.686341 | + | 0.333658i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.41308e10i | 0.0423148i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.45125e11 | − | 2.51364e11i | −0.252156 | − | 0.436747i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.63733e11 | − | 1.09341e11i | 1.31487 | − | 0.188246i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.41964e11 | + | 1.98325e11i | −0.242185 | + | 0.338334i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.13531e11 | − | 5.43052e11i | 0.530008 | − | 0.918001i | −0.469379 | − | 0.882997i | \(-0.655522\pi\) |
0.999387 | − | 0.0350045i | \(-0.0111446\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.57085e11 | − | 3.25537e10i | 0.765670 | − | 0.0545312i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.66629e11i | 1.43857i | 0.694718 | + | 0.719283i | \(0.255529\pi\) | ||||
−0.694718 | + | 0.719283i | \(0.744471\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.10650e11 | 0.675506 | 0.337753 | − | 0.941235i | \(-0.390333\pi\) | ||||
0.337753 | + | 0.941235i | \(0.390333\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.29825e10 | − | 1.16515e12i | −0.135274 | − | 1.89937i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.80385e11 | + | 1.04145e11i | 0.291410 | + | 0.168246i | 0.638578 | − | 0.769557i | \(-0.279523\pi\) |
−0.347167 | + | 0.937803i | \(0.612856\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.60335e11 | + | 1.14770e11i | 0.256697 | + | 0.183748i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.82804e10 | + | 4.00512e10i | −0.0607388 | + | 0.0635484i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.65489e11 | + | 3.26485e11i | −0.889239 | + | 0.513402i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.09989e12 | −1.71419 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.94541e11 | + | 6.05876e11i | −0.454963 | + | 0.935867i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.86382e11 | − | 5.69488e11i | 1.51010 | − | 0.871858i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.48185e11 | + | 2.56664e11i | −0.224857 | + | 0.389463i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.24757e11 | − | 6.92545e11i | 0.638837 | − | 1.04159i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.41998e11 | + | 1.97452e11i | 0.509834 | + | 0.294353i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.53863e11 | + | 2.66498e11i | 0.227355 | + | 0.393791i | 0.957023 | − | 0.290011i | \(-0.0936588\pi\) |
−0.729668 | + | 0.683801i | \(0.760326\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.89148e11 | − | 6.19828e11i | 1.15585 | − | 0.907853i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.45404e11i | 1.37260i | 0.727318 | + | 0.686300i | \(0.240766\pi\) | ||||
−0.727318 | + | 0.686300i | \(0.759234\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.02998e10 | + | 3.51603e10i | 0.0292152 | + | 0.0506022i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.77356e11 | − | 1.14928e12i | −1.10901 | − | 1.63962i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.31043e11 | + | 9.50040e11i | 0.609598 | + | 1.34358i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.01341e11 | + | 8.68347e11i | −0.702863 | + | 1.21739i | 0.264594 | + | 0.964360i | \(0.414762\pi\) |
−0.967457 | + | 0.253035i | \(0.918571\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.65503e10 | − | 6.53610e11i | −0.0646970 | − | 0.908407i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.77482e10i | 0.0795668i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.80923e10 | −0.133989 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.91338e11 | − | 4.77112e11i | 0.259109 | − | 0.646102i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.16648e12 | − | 6.73466e11i | −1.56608 | − | 0.904175i | −0.996620 | − | 0.0821543i | \(-0.973820\pi\) |
−0.569458 | − | 0.822021i | \(-0.692847\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.51958e11 | − | 8.94197e10i | −0.601588 | − | 0.119024i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.26765e11 | − | 1.07449e12i | −0.959108 | − | 1.41800i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.66901e10 | + | 2.11830e10i | −0.0480068 | + | 0.0277167i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.75433e11 | 0.227590 | 0.113795 | − | 0.993504i | \(-0.463699\pi\) | ||||
0.113795 | + | 0.993504i | \(0.463699\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.68361e11 | − | 3.24917e11i | −0.859703 | − | 0.417936i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.86868e11 | + | 3.96563e11i | −0.876021 | + | 0.505771i | −0.869344 | − | 0.494207i | \(-0.835459\pi\) |
−0.00667678 | + | 0.999978i | \(0.502125\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.69879e11 | − | 8.13855e11i | 0.594209 | − | 1.02920i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.29297e11 | − | 6.16464e11i | 1.03988 | − | 0.773001i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.71298e10 | + | 1.56634e10i | 0.0337323 | + | 0.0194754i | 0.516771 | − | 0.856123i | \(-0.327134\pi\) |
−0.483039 | + | 0.875599i | \(0.660467\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.80324e11 | − | 8.31945e11i | −0.592201 | − | 1.02572i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.95662e11 | + | 1.01959e12i | −0.605987 | + | 1.24653i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 7.84682e11i | − | 0.951310i | −0.879632 | − | 0.475655i | \(-0.842211\pi\) | ||
0.879632 | − | 0.475655i | \(-0.157789\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.13997e11 | + | 1.23668e12i | 0.858387 | + | 1.48677i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.43409e10 | − | 6.38105e10i | 0.112474 | − | 0.0760755i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.08159e11 | − | 2.03945e10i | −0.246106 | − | 0.0241123i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.16990e11 | + | 2.02633e11i | −0.137169 | + | 0.237584i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.27575e11 | + | 2.51680e11i | 0.729727 | + | 0.292646i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.83026e12i | − | 2.11059i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.43127e12 | −1.63687 | −0.818436 | − | 0.574597i | \(-0.805159\pi\) | ||||
−0.818436 | + | 0.574597i | \(0.805159\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.62466e11 | + | 1.86929e10i | −0.297700 | + | 0.0212023i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.46788e11 | − | 3.15688e11i | −0.615095 | − | 0.355125i | 0.159862 | − | 0.987139i | \(-0.448895\pi\) |
−0.774957 | + | 0.632014i | \(0.782228\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.72548e11 | + | 3.38258e11i | 0.527223 | + | 0.377395i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.37163e11 | + | 2.95690e11i | −0.483755 | + | 0.327203i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.05709e10 | − | 2.91971e10i | 0.0555037 | − | 0.0320451i | −0.471991 | − | 0.881603i | \(-0.656465\pi\) |
0.527495 | + | 0.849558i | \(0.323131\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.13745e10 | −0.0123823 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.40443e11 | + | 5.60759e11i | 0.475569 | + | 0.605481i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.30108e11 | + | 7.51179e10i | −0.139345 | + | 0.0804506i | −0.568052 | − | 0.822993i | \(-0.692303\pi\) |
0.428707 | + | 0.903444i | \(0.358969\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.72863e10 | − | 2.99407e10i | 0.0183635 | − | 0.0318066i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.39672e12 | − | 7.57662e11i | 1.47177 | − | 0.798375i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.22460e12 | + | 7.07024e11i | 1.28000 | + | 0.739008i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.95580e11 | + | 1.55119e12i | 0.928560 | + | 1.60831i | 0.785733 | + | 0.618566i | \(0.212286\pi\) |
0.142827 | + | 0.989748i | \(0.454381\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.99285e11 | + | 3.88565e11i | 0.822062 | + | 0.399638i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.71207e11i | 0.786825i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.35305e11 | + | 9.27175e11i | 0.541777 | + | 0.938385i | 0.998802 | + | 0.0489312i | \(0.0155815\pi\) |
−0.457025 | + | 0.889454i | \(0.651085\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.87191e11 | − | 6.00240e10i | −0.187942 | − | 0.0602647i |
(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 | 84.9.p.b.65.9 | yes | 40 | |
3.2 | odd | 2 | inner | 84.9.p.b.65.6 | yes | 40 | |
7.4 | even | 3 | inner | 84.9.p.b.53.6 | ✓ | 40 | |
21.11 | odd | 6 | inner | 84.9.p.b.53.9 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.9.p.b.53.6 | ✓ | 40 | 7.4 | even | 3 | inner | |
84.9.p.b.53.9 | yes | 40 | 21.11 | odd | 6 | inner | |
84.9.p.b.65.6 | yes | 40 | 3.2 | odd | 2 | inner | |
84.9.p.b.65.9 | yes | 40 | 1.1 | even | 1 | trivial |