Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,8,Mod(361,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.361");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.i (of order \(3\), degree \(2\), not 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: | \(183.682394985\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 373.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.373 |
Dual form | 588.8.i.f.361.1 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 13.5000 | + | 23.3827i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −50.0000 | + | 86.6025i | −0.178885 | + | 0.309839i | −0.941499 | − | 0.337016i | \(-0.890582\pi\) |
0.762614 | + | 0.646854i | \(0.223916\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −364.500 | + | 631.333i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1387.00 | − | 2402.35i | −0.314197 | − | 0.544205i | 0.665069 | − | 0.746782i | \(-0.268402\pi\) |
−0.979266 | + | 0.202576i | \(0.935069\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3294.00 | −0.415836 | −0.207918 | − | 0.978146i | \(-0.566669\pi\) | ||||
−0.207918 | + | 0.978146i | \(0.566669\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2700.00 | −0.206559 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2950.00 | − | 5109.55i | −0.145630 | − | 0.252239i | 0.783978 | − | 0.620789i | \(-0.213188\pi\) |
−0.929608 | + | 0.368550i | \(0.879854\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3322.00 | + | 5753.87i | −0.111112 | + | 0.192452i | −0.916219 | − | 0.400678i | \(-0.868775\pi\) |
0.805107 | + | 0.593130i | \(0.202108\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −991.000 | + | 1716.46i | −0.0169835 | + | 0.0294162i | −0.874392 | − | 0.485220i | \(-0.838740\pi\) |
0.857409 | + | 0.514636i | \(0.172073\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 34062.5 | + | 58998.0i | 0.436000 | + | 0.755174i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −208106. | −1.58450 | −0.792249 | − | 0.610198i | \(-0.791090\pi\) | ||||
−0.792249 | + | 0.610198i | \(0.791090\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 58896.0 | + | 102011.i | 0.355075 | + | 0.615008i | 0.987131 | − | 0.159915i | \(-0.0511221\pi\) |
−0.632056 | + | 0.774923i | \(0.717789\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 37449.0 | − | 64863.6i | 0.181402 | − | 0.314197i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 167843. | − | 290713.i | 0.544750 | − | 0.943535i | −0.453873 | − | 0.891067i | \(-0.649958\pi\) |
0.998623 | − | 0.0524680i | \(-0.0167088\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −44469.0 | − | 77022.6i | −0.120041 | − | 0.207918i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −265488. | −0.601591 | −0.300796 | − | 0.953689i | \(-0.597252\pi\) | ||||
−0.300796 | + | 0.953689i | \(0.597252\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −93292.0 | −0.178939 | −0.0894695 | − | 0.995990i | \(-0.528517\pi\) | ||||
−0.0894695 | + | 0.995990i | \(0.528517\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −36450.0 | − | 63133.3i | −0.0596285 | − | 0.103280i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 328758. | − | 569426.i | 0.461885 | − | 0.800008i | −0.537170 | − | 0.843474i | \(-0.680507\pi\) |
0.999055 | + | 0.0434658i | \(0.0138400\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 79650.0 | − | 137958.i | 0.0840795 | − | 0.145630i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 304359. | + | 527165.i | 0.280815 | + | 0.486386i | 0.971586 | − | 0.236688i | \(-0.0760619\pi\) |
−0.690771 | + | 0.723074i | \(0.742729\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 277400. | 0.224821 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −179388. | −0.128301 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 268060. | + | 464294.i | 0.169922 | + | 0.294314i | 0.938392 | − | 0.345572i | \(-0.112315\pi\) |
−0.768470 | + | 0.639886i | \(0.778982\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 898545. | − | 1.55633e6i | 0.506857 | − | 0.877902i | −0.493112 | − | 0.869966i | \(-0.664141\pi\) |
0.999969 | − | 0.00793591i | \(-0.00252610\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 164700. | − | 285269.i | 0.0743870 | − | 0.128842i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.06159e6 | − | 1.83872e6i | −0.431215 | − | 0.746887i | 0.565763 | − | 0.824568i | \(-0.308582\pi\) |
−0.996978 | + | 0.0776811i | \(0.975248\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −53514.0 | −0.0196108 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.19121e6 | −0.394990 | −0.197495 | − | 0.980304i | \(-0.563281\pi\) | ||||
−0.197495 | + | 0.980304i | \(0.563281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −528215. | − | 914895.i | −0.158921 | − | 0.275259i | 0.775559 | − | 0.631275i | \(-0.217468\pi\) |
−0.934480 | + | 0.356016i | \(0.884135\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −919688. | + | 1.59295e6i | −0.251725 | + | 0.436000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −499242. | + | 864713.i | −0.113924 | + | 0.197323i | −0.917349 | − | 0.398083i | \(-0.869675\pi\) |
0.803425 | + | 0.595406i | \(0.203009\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −265720. | − | 460241.i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.89800e6 | 0.748288 | 0.374144 | − | 0.927371i | \(-0.377937\pi\) | ||||
0.374144 | + | 0.927371i | \(0.377937\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 590000. | 0.104204 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.80943e6 | − | 4.86608e6i | −0.457405 | − | 0.792249i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.31118e6 | − | 4.00307e6i | 0.347511 | − | 0.601906i | −0.638296 | − | 0.769791i | \(-0.720360\pi\) |
0.985807 | + | 0.167885i | \(0.0536938\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.59019e6 | + | 2.75429e6i | −0.205003 | + | 0.355075i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −332200. | − | 575387.i | −0.0397527 | − | 0.0688538i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.52877e7 | 1.70075 | 0.850377 | − | 0.526174i | \(-0.176374\pi\) | ||||
0.850377 | + | 0.526174i | \(0.176374\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.02225e6 | 0.209465 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.11934e6 | − | 1.93876e6i | −0.108103 | − | 0.187240i | 0.806899 | − | 0.590690i | \(-0.201144\pi\) |
−0.915002 | + | 0.403450i | \(0.867811\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.22511e6 | + | 1.07822e7i | −0.561328 | + | 0.972249i | 0.436053 | + | 0.899921i | \(0.356376\pi\) |
−0.997381 | + | 0.0723279i | \(0.976957\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.79430e6 | − | 6.57192e6i | 0.299425 | − | 0.518620i | −0.676579 | − | 0.736370i | \(-0.736538\pi\) |
0.976005 | + | 0.217750i | \(0.0698717\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.58548e6 | − | 4.47819e6i | −0.191227 | − | 0.331215i | 0.754430 | − | 0.656380i | \(-0.227913\pi\) |
−0.945657 | + | 0.325166i | \(0.894580\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.06352e6 | 0.629023 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.63868e6 | −0.628410 | −0.314205 | − | 0.949355i | \(-0.601738\pi\) | ||||
−0.314205 | + | 0.949355i | \(0.601738\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −99100.0 | − | 171646.i | −0.00607619 | − | 0.0105243i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.20066e6 | − | 2.07961e6i | 0.0693060 | − | 0.120041i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.89605e6 | − | 1.02123e7i | 0.302560 | − | 0.524050i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.58409e6 | − | 6.20782e6i | −0.173664 | − | 0.300796i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.46250e7 | −0.669747 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.08309e6 | 0.350158 | 0.175079 | − | 0.984554i | \(-0.443982\pi\) | ||||
0.175079 | + | 0.984554i | \(0.443982\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.25944e6 | − | 2.18142e6i | −0.0516552 | − | 0.0894695i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.87927e6 | − | 1.71114e7i | 0.383951 | − | 0.665022i | −0.607672 | − | 0.794188i | \(-0.707897\pi\) |
0.991623 | + | 0.129166i | \(0.0412299\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 984150. | − | 1.70460e6i | 0.0344265 | − | 0.0596285i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.40448e7 | + | 4.16468e7i | 0.798913 | + | 1.38376i | 0.920325 | + | 0.391155i | \(0.127924\pi\) |
−0.121412 | + | 0.992602i | \(0.538742\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.37173e7 | 0.433229 | 0.216615 | − | 0.976257i | \(-0.430499\pi\) | ||||
0.216615 | + | 0.976257i | \(0.430499\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.77529e7 | 0.533339 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.56878e6 | + | 7.91336e6i | 0.130654 | + | 0.226300i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.04053e7 | − | 1.80225e7i | 0.283444 | − | 0.490939i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.53552e7 | − | 6.12370e7i | 0.875591 | − | 1.51657i | 0.0194598 | − | 0.999811i | \(-0.493805\pi\) |
0.856132 | − | 0.516758i | \(-0.172861\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.28485e7 | + | 2.22542e7i | 0.303691 | + | 0.526009i | 0.976969 | − | 0.213381i | \(-0.0684475\pi\) |
−0.673278 | + | 0.739390i | \(0.735114\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.30110e6 | 0.0970867 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.17792e7 | −0.254071 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.04590e7 | − | 1.81155e7i | −0.215695 | − | 0.373595i | 0.737792 | − | 0.675028i | \(-0.235868\pi\) |
−0.953487 | + | 0.301433i | \(0.902535\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.21769e6 | + | 1.42335e7i | −0.162129 | + | 0.280815i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.72080e7 | + | 4.71256e7i | −0.492084 | + | 0.852315i | −0.999958 | − | 0.00911613i | \(-0.997098\pi\) |
0.507874 | + | 0.861431i | \(0.330432\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.74490e6 | + | 6.48636e6i | 0.0649003 | + | 0.112411i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.41888e6 | 0.106648 | 0.0533238 | − | 0.998577i | \(-0.483018\pi\) | ||||
0.0533238 | + | 0.998577i | \(0.483018\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.18981e7 | −0.827081 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.42174e6 | − | 4.19457e6i | −0.0370374 | − | 0.0641507i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.73266e7 | − | 4.73311e7i | 0.401259 | − | 0.695000i | −0.592619 | − | 0.805483i | \(-0.701906\pi\) |
0.993878 | + | 0.110482i | \(0.0352395\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.23762e6 | + | 1.25359e7i | −0.0981046 | + | 0.169922i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.88329e7 | + | 3.26196e7i | 0.245433 | + | 0.425102i | 0.962253 | − | 0.272156i | \(-0.0877367\pi\) |
−0.716821 | + | 0.697258i | \(0.754403\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.76788e7 | 0.221604 | 0.110802 | − | 0.993842i | \(-0.464658\pi\) | ||||
0.110802 | + | 0.993842i | \(0.464658\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.85214e7 | 0.585268 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.67843e7 | + | 2.90713e7i | 0.194896 | + | 0.337569i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.18330e6 | + | 1.41739e7i | −0.0915130 | + | 0.158505i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.04588e7 | + | 3.54357e7i | −0.212454 | + | 0.367980i | −0.952482 | − | 0.304595i | \(-0.901479\pi\) |
0.740028 | + | 0.672576i | \(0.234812\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.19134e7 | + | 1.41878e8i | 0.820171 | + | 1.42058i | 0.905554 | + | 0.424230i | \(0.139455\pi\) |
−0.0853830 | + | 0.996348i | \(0.527211\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.89380e6 | 0.0858947 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.02076e7 | 0.747453 | 0.373726 | − | 0.927539i | \(-0.378080\pi\) | ||||
0.373726 | + | 0.927539i | \(0.378080\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.91610e7 | − | 8.51493e7i | −0.442216 | − | 0.765941i | 0.555637 | − | 0.831425i | \(-0.312474\pi\) |
−0.997854 | + | 0.0654838i | \(0.979141\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.86629e7 | − | 4.96456e7i | 0.248962 | − | 0.431215i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.32744e7 | − | 2.29919e7i | 0.107616 | − | 0.186396i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −722439. | − | 1.25130e6i | −0.00566115 | − | 0.00980541i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.84305e7 | 0.139645 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.36321e8 | 0.999021 | 0.499510 | − | 0.866308i | \(-0.333513\pi\) | ||||
0.499510 | + | 0.866308i | \(0.333513\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.60814e7 | − | 2.78538e7i | −0.114024 | − | 0.197495i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.66460e6 | − | 8.07932e6i | 0.0320096 | − | 0.0554422i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.42618e7 | − | 2.47022e7i | 0.0917530 | − | 0.158921i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.71730e6 | + | 1.68309e7i | 0.0605582 | + | 0.104890i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.26358e8 | 0.763019 | 0.381510 | − | 0.924365i | \(-0.375404\pi\) | ||||
0.381510 | + | 0.924365i | \(0.375404\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.96631e7 | −0.290667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.17004e8 | − | 2.02656e8i | −0.663909 | − | 1.14992i | −0.979580 | − | 0.201055i | \(-0.935563\pi\) |
0.315671 | − | 0.948869i | \(-0.397770\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.41803e7 | + | 5.92020e7i | −0.188084 | + | 0.325771i | −0.944611 | − | 0.328191i | \(-0.893561\pi\) |
0.756527 | + | 0.653962i | \(0.226894\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.01923e7 | + | 1.56218e8i | −0.467115 | + | 0.809067i | −0.999294 | − | 0.0375648i | \(-0.988040\pi\) |
0.532179 | + | 0.846632i | \(0.321373\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.28758e7 | + | 5.69426e7i | 0.165249 | + | 0.286220i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.69591e7 | −0.131548 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.61131e8 | 1.23727 | 0.618637 | − | 0.785677i | \(-0.287685\pi\) | ||||
0.618637 | + | 0.785677i | \(0.287685\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.88781e6 | − | 1.71262e7i | −0.0455031 | − | 0.0788136i | 0.842377 | − | 0.538889i | \(-0.181156\pi\) |
−0.887880 | + | 0.460075i | \(0.847822\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.17445e6 | − | 1.24265e7i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.09427e7 | − | 1.89533e7i | 0.0462045 | − | 0.0800285i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.26231e7 | + | 9.11458e7i | 0.216012 | + | 0.374144i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.53770e8 | 0.613779 | 0.306890 | − | 0.951745i | \(-0.400712\pi\) | ||||
0.306890 | + | 0.951745i | \(0.400712\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.49807e6 | 0.0213446 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.96500e6 | + | 1.37958e7i | 0.0300812 | + | 0.0521022i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.16802e7 | − | 1.24154e8i | 0.263411 | − | 0.456241i | −0.703735 | − | 0.710462i | \(-0.748486\pi\) |
0.967146 | + | 0.254222i | \(0.0818192\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.58546e7 | − | 1.31384e8i | 0.264083 | − | 0.457405i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.53650e8 | + | 4.39336e8i | 0.859786 | + | 1.48919i | 0.872132 | + | 0.489270i | \(0.162737\pi\) |
−0.0123459 | + | 0.999924i | \(0.503930\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.08718e7 | −0.200935 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.24804e8 | 0.401271 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.63943e8 | − | 4.57163e8i | −0.826755 | − | 1.43198i | −0.900570 | − | 0.434710i | \(-0.856851\pi\) |
0.0738149 | − | 0.997272i | \(-0.476483\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.52918e8 | − | 4.38067e8i | 0.771947 | − | 1.33705i | −0.164548 | − | 0.986369i | \(-0.552616\pi\) |
0.936495 | − | 0.350682i | \(-0.114050\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.44894e7 | − | 1.63660e8i | 0.273980 | − | 0.474547i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.94293e8 | + | 5.09730e8i | 0.831956 | + | 1.44099i | 0.896485 | + | 0.443075i | \(0.146112\pi\) |
−0.0645284 | + | 0.997916i | \(0.520554\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.58704e7 | −0.236717 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.65142e7 | 0.232603 | 0.116301 | − | 0.993214i | \(-0.462896\pi\) | ||||
0.116301 | + | 0.993214i | \(0.462896\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.86504e7 | + | 1.36227e8i | 0.206276 | + | 0.357280i | 0.950538 | − | 0.310607i | \(-0.100532\pi\) |
−0.744263 | + | 0.667887i | \(0.767199\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.96940e6 | − | 1.55355e7i | 0.0229513 | − | 0.0397527i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.87764e8 | − | 3.25217e8i | 0.457584 | − | 0.792558i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.06384e8 | + | 3.57468e8i | 0.490965 | + | 0.850377i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.80964e8 | 1.58157 | 0.790783 | − | 0.612097i | \(-0.209674\pi\) | ||||
0.790783 | + | 0.612097i | \(0.209674\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.36120e7 | −0.121586 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.73003e7 | + | 4.72855e7i | 0.0604672 | + | 0.104732i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.26435e6 | − | 5.65403e6i | 0.00706233 | − | 0.0122323i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.02223e7 | − | 5.23465e7i | 0.0624134 | − | 0.108103i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.98545e7 | + | 1.55633e8i | 0.181339 | + | 0.314088i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.81734e8 | 0.555718 | 0.277859 | − | 0.960622i | \(-0.410375\pi\) | ||||
0.277859 | + | 0.960622i | \(0.410375\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.36156e8 | −0.648166 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.09860e8 | + | 3.63487e8i | 0.395610 | + | 0.685217i | 0.993179 | − | 0.116601i | \(-0.0371998\pi\) |
−0.597569 | + | 0.801818i | \(0.703866\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.14342e8 | − | 1.98046e8i | 0.210766 | − | 0.365057i | −0.741188 | − | 0.671297i | \(-0.765738\pi\) |
0.951954 | + | 0.306240i | \(0.0990709\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.33001e8 | + | 2.30365e8i | −0.234503 | + | 0.406171i | −0.959128 | − | 0.282972i | \(-0.908680\pi\) |
0.724625 | + | 0.689143i | \(0.242013\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.88643e8 | + | 4.99944e8i | 0.497844 | + | 0.862292i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.04892e8 | 0.345747 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.91996e7 | 0.0647251 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.12202e8 | − | 1.94339e8i | −0.181304 | − | 0.314028i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.98080e7 | − | 1.20911e8i | 0.110405 | − | 0.191227i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.58054e8 | − | 6.20167e8i | 0.542688 | − | 0.939963i | −0.456061 | − | 0.889949i | \(-0.650740\pi\) |
0.998749 | − | 0.0500141i | \(-0.0159266\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.22358e8 | + | 2.11929e8i | 0.181583 | + | 0.314512i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.12318e8 | 0.308553 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.70266e8 | 0.811657 | 0.405829 | − | 0.913949i | \(-0.366983\pi\) | ||||
0.405829 | + | 0.913949i | \(0.366983\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.30122e8 | − | 2.25378e8i | −0.181406 | − | 0.314205i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.63378e8 | − | 2.82978e8i | 0.223127 | − | 0.386467i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.67570e6 | − | 4.63445e6i | 0.00350809 | − | 0.00607619i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.23203e7 | + | 1.42583e8i | 0.105768 | + | 0.183195i | 0.914052 | − | 0.405598i | \(-0.132937\pi\) |
−0.808284 | + | 0.588793i | \(0.799603\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.31564e9 | 1.65671 | 0.828357 | − | 0.560200i | \(-0.189276\pi\) | ||||
0.828357 | + | 0.560200i | \(0.189276\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.48358e7 | 0.0800276 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.80588e8 | − | 1.35202e9i | −0.944518 | − | 1.63595i | −0.756713 | − | 0.653747i | \(-0.773196\pi\) |
−0.187805 | − | 0.982206i | \(-0.560137\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.95607e7 | − | 1.03162e8i | 0.0706579 | − | 0.122383i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.30358e8 | − | 7.45402e8i | 0.490907 | − | 0.850276i | −0.509038 | − | 0.860744i | \(-0.669999\pi\) |
0.999945 | + | 0.0104681i | \(0.00333215\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.24865e8 | + | 7.35887e8i | 0.475308 | + | 0.823258i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.18387e8 | 0.349367 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.05643e8 | 0.113714 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.56066e8 | − | 7.89930e8i | −0.481612 | − | 0.834176i | 0.518166 | − | 0.855280i | \(-0.326615\pi\) |
−0.999777 | + | 0.0211045i | \(0.993282\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.67704e7 | − | 1.67611e8i | 0.100265 | − | 0.173664i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.18002e8 | + | 2.04386e8i | −0.117736 | + | 0.203925i | −0.918870 | − | 0.394560i | \(-0.870897\pi\) |
0.801134 | + | 0.598485i | \(0.204230\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.97438e8 | − | 3.41972e8i | −0.193339 | − | 0.334874i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.85501e8 | 0.658891 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.29313e8 | 0.782495 | 0.391247 | − | 0.920286i | \(-0.372044\pi\) | ||||
0.391247 | + | 0.920286i | \(0.372044\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.09122e8 | + | 1.89004e8i | 0.101082 | + | 0.175079i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.08316e8 | − | 1.05363e9i | 0.553265 | − | 0.958284i | −0.444771 | − | 0.895644i | \(-0.646715\pi\) |
0.998036 | − | 0.0626393i | \(-0.0199518\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.40049e7 | − | 5.88983e7i | 0.0298232 | − | 0.0516552i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.91064e7 | + | 1.02375e8i | 0.0509109 | + | 0.0881803i | 0.890358 | − | 0.455261i | \(-0.150454\pi\) |
−0.839447 | + | 0.543442i | \(0.817121\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.16938e7 | 0.00989321 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.33481e8 | 0.443348 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.99242e7 | − | 8.64713e7i | −0.0407588 | − | 0.0705963i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.81283e7 | + | 3.13991e7i | −0.0145408 | + | 0.0251855i | −0.873204 | − | 0.487354i | \(-0.837962\pi\) |
0.858663 | + | 0.512540i | \(0.171295\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.53425e8 | + | 4.38945e8i | −0.196265 | + | 0.339942i | −0.947315 | − | 0.320305i | \(-0.896215\pi\) |
0.751049 | + | 0.660246i | \(0.229548\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.94003e8 | − | 3.36024e8i | −0.147653 | − | 0.255742i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.31441e7 | 0.0397523 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.31193e8 | −0.684635 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.40605e8 | − | 1.45597e9i | −0.607519 | − | 1.05225i | −0.991648 | − | 0.128975i | \(-0.958831\pi\) |
0.384128 | − | 0.923280i | \(-0.374502\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.49210e8 | + | 1.12446e9i | −0.461252 | + | 0.798913i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.94900e8 | + | 3.37577e8i | −0.133858 | + | 0.231849i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.85184e8 | + | 3.20748e8i | 0.125062 | + | 0.216615i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.94962e8 | 0.328718 | 0.164359 | − | 0.986401i | \(-0.447444\pi\) | ||||
0.164359 | + | 0.986401i | \(0.447444\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.57487e7 | −0.0429437 | −0.0214719 | − | 0.999769i | \(-0.506835\pi\) | ||||
−0.0214719 | + | 0.999769i | \(0.506835\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.39665e8 | + | 4.15111e8i | 0.153962 | + | 0.266669i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00969e8 | − | 3.48088e8i | 0.126989 | − | 0.219952i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.23357e8 | + | 2.13661e8i | −0.0754333 | + | 0.130654i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.67089e8 | + | 1.15543e9i | 0.401341 | + | 0.695143i | 0.993888 | − | 0.110393i | \(-0.0352109\pi\) |
−0.592547 | + | 0.805536i | \(0.701878\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.47903e7 | −0.0146749 | −0.00733745 | − | 0.999973i | \(-0.502336\pi\) | ||||
−0.00733745 | + | 0.999973i | \(0.502336\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.61886e8 | 0.327292 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.58420e6 | − | 1.14042e7i | −0.00377414 | − | 0.00653701i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.44664e8 | − | 5.96975e8i | 0.194433 | − | 0.336768i | −0.752282 | − | 0.658842i | \(-0.771047\pi\) |
0.946714 | + | 0.322074i | \(0.104380\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.87308e8 | − | 4.97633e8i | 0.157013 | − | 0.271954i | −0.776777 | − | 0.629775i | \(-0.783147\pi\) |
0.933790 | + | 0.357821i | \(0.116480\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.31118e8 | + | 4.00307e8i | 0.124329 | + | 0.215344i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.90918e9 | 1.01105 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.56884e7 | 0.0498881 | 0.0249440 | − | 0.999689i | \(-0.492059\pi\) | ||||
0.0249440 | + | 0.999689i | \(0.492059\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.68232e8 | + | 6.37796e8i | 0.189018 | + | 0.327389i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.46909e8 | + | 6.00864e8i | −0.175336 | + | 0.303691i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.36545e7 | − | 4.09707e7i | 0.0115933 | − | 0.0200802i | −0.860171 | − | 0.510006i | \(-0.829643\pi\) |
0.871764 | + | 0.489926i | \(0.162976\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.80648e7 | + | 1.00571e8i | 0.0280265 | + | 0.0485433i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.13567e9 | −1.01527 | −0.507634 | − | 0.861573i | \(-0.669480\pi\) | ||||
−0.507634 | + | 0.861573i | \(0.669480\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.92675e8 | 0.137042 | 0.0685208 | − | 0.997650i | \(-0.478172\pi\) | ||||
0.0685208 | + | 0.997650i | \(0.478172\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.59019e8 | − | 2.75429e8i | −0.0733439 | − | 0.127035i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.76917e9 | − | 3.06429e9i | 0.803824 | − | 1.39226i | −0.113259 | − | 0.993566i | \(-0.536129\pi\) |
0.917082 | − | 0.398698i | \(-0.130538\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.82392e8 | − | 4.89118e8i | 0.124532 | − | 0.215695i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.29396e8 | + | 2.24120e8i | 0.0562221 | + | 0.0973795i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.52622e8 | −0.193780 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.43755e8 | −0.187210 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.07849e9 | + | 3.60005e9i | 0.864120 | + | 1.49670i | 0.867919 | + | 0.496707i | \(0.165457\pi\) |
−0.00379880 | + | 0.999993i | \(0.501209\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.52875e8 | + | 9.57607e8i | −0.226527 | + | 0.392355i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.64386e8 | + | 1.32395e9i | −0.304240 | + | 0.526959i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.20460e7 | − | 1.07467e8i | −0.0243423 | − | 0.0421622i | 0.853598 | − | 0.520933i | \(-0.174416\pi\) |
−0.877940 | + | 0.478771i | \(0.841083\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.46923e9 | −0.568210 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.29218e9 | −1.25516 | −0.627578 | − | 0.778554i | \(-0.715954\pi\) | ||||
−0.627578 | + | 0.778554i | \(0.715954\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.13913e8 | + | 1.06333e9i | 0.230750 | + | 0.399671i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.01112e8 | + | 1.75132e8i | −0.0374702 | + | 0.0649003i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.80219e8 | − | 3.12149e8i | 0.0649306 | − | 0.112463i | −0.831733 | − | 0.555176i | \(-0.812651\pi\) |
0.896663 | + | 0.442713i | \(0.145984\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.66548e7 | + | 1.50091e8i | 0.0307865 | + | 0.0533238i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.29760e9 | −1.50570 | −0.752849 | − | 0.658193i | \(-0.771321\pi\) | ||||
−0.752849 | + | 0.658193i | \(0.771321\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.23869e8 | 0.0773524 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.00624e8 | − | 1.21352e9i | −0.238758 | − | 0.413540i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.71294e8 | − | 4.69895e8i | 0.0911860 | − | 0.157939i | −0.816824 | − | 0.576886i | \(-0.804268\pi\) |
0.908010 | + | 0.418948i | \(0.137601\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.53869e7 | − | 1.13253e8i | 0.0213836 | − | 0.0370374i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.22511e8 | − | 1.07822e9i | −0.200827 | − | 0.347842i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.82395e9 | −0.580492 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.47564e9 | 0.463334 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.18378e8 | + | 2.05036e8i | 0.0366722 | + | 0.0635182i | 0.883779 | − | 0.467905i | \(-0.154991\pi\) |
−0.847107 | + | 0.531423i | \(0.821658\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.24162e9 | + | 5.61465e9i | −0.990846 | + | 1.71619i | −0.378509 | + | 0.925598i | \(0.623563\pi\) |
−0.612337 | + | 0.790597i | \(0.709770\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.47486e8 | − | 6.01864e8i | 0.103419 | − | 0.179127i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.70045e9 | + | 2.94526e9i | 0.499423 | + | 0.865026i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.90831e8 | −0.113281 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.74517e8 | 0.250163 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.79430e8 | + | 6.57192e8i | 0.107126 | + | 0.185547i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.08489e8 | + | 8.80729e8i | −0.141701 | + | 0.245433i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.50494e7 | − | 1.29989e8i | 0.0203778 | − | 0.0352954i | −0.855657 | − | 0.517544i | \(-0.826846\pi\) |
0.876034 | + | 0.482248i | \(0.160180\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.38664e8 | + | 4.13378e8i | 0.0639716 | + | 0.110802i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.17097e8 | 0.136831 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.32631e9 | 0.868974 | 0.434487 | − | 0.900678i | \(-0.356930\pi\) | ||||
0.434487 | + | 0.900678i | \(0.356930\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.55039e8 | + | 1.13456e9i | 0.168952 | + | 0.292634i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.91328e8 | − | 1.19742e9i | 0.176057 | − | 0.304940i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.53176e8 | + | 7.84924e8i | −0.112523 | + | 0.194896i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.36256e9 | − | 4.09208e9i | −0.579282 | − | 1.00335i | −0.995562 | − | 0.0941092i | \(-0.970000\pi\) |
0.416280 | − | 0.909236i | \(-0.363334\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.07304e8 | 0.0744092 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.41898e8 | −0.105670 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.55522e9 | − | 6.15782e9i | −0.839628 | − | 1.45428i | −0.890206 | − | 0.455558i | \(-0.849440\pi\) |
0.0505779 | − | 0.998720i | \(-0.483894\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.81934e8 | − | 8.34734e8i | 0.112413 | − | 0.194706i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.27657e9 | + | 5.67519e9i | −0.745636 | + | 1.29148i | 0.204260 | + | 0.978917i | \(0.434521\pi\) |
−0.949897 | + | 0.312564i | \(0.898812\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.14639e9 | − | 7.18175e9i | −0.932059 | − | 1.61437i | −0.779796 | − | 0.626034i | \(-0.784677\pi\) |
−0.152263 | − | 0.988340i | \(-0.548656\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.10478e9 | −0.245320 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.35024e8 | −0.0296192 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.94000e9 | + | 5.09223e9i | 0.637135 | + | 1.10355i | 0.986058 | + | 0.166400i | \(0.0532141\pi\) |
−0.348923 | + | 0.937151i | \(0.613453\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.21166e9 | + | 3.83071e9i | −0.473526 | + | 0.820171i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.44292e8 | − | 1.46236e9i | 0.176463 | − | 0.305642i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.20066e8 | + | 2.07961e8i | 0.0247957 | + | 0.0429473i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.43194e9 | −0.292207 | −0.146103 | − | 0.989269i | \(-0.546673\pi\) | ||||
−0.146103 | + | 0.989269i | \(0.546673\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.82610e8 | −0.157813 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.08280e9 | + | 1.87547e9i | 0.215771 | + | 0.373726i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.74069e9 | + | 3.01497e9i | −0.342792 | + | 0.593733i | −0.984950 | − | 0.172839i | \(-0.944706\pi\) |
0.642158 | + | 0.766572i | \(0.278039\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.32735e9 | − | 2.29903e9i | 0.255314 | − | 0.442216i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.96799e9 | − | 6.87275e9i | −0.754356 | − | 1.30658i | −0.945694 | − | 0.325058i | \(-0.894616\pi\) |
0.191338 | − | 0.981524i | \(-0.438717\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.05169e9 | −0.761335 | −0.380668 | − | 0.924712i | \(-0.624306\pi\) | ||||
−0.380668 | + | 0.924712i | \(0.624306\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.54780e9 | 0.287477 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.89605e8 | + | 1.02123e9i | 0.108247 | + | 0.187490i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.59580e9 | + | 4.49605e9i | −0.471097 | + | 0.815964i | −0.999453 | − | 0.0330588i | \(-0.989475\pi\) |
0.528356 | + | 0.849023i | \(0.322808\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.08293e9 | + | 1.87569e9i | −0.192068 | + | 0.332672i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.84903e9 | − | 3.20262e9i | −0.324215 | − | 0.561557i | 0.657138 | − | 0.753770i | \(-0.271767\pi\) |
−0.981353 | + | 0.192213i | \(0.938434\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.16818e8 | 0.124264 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.19879e9 | −1.06245 | −0.531226 | − | 0.847230i | \(-0.678268\pi\) | ||||
−0.531226 | + | 0.847230i | \(0.678268\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.42569e9 | + | 2.46936e9i | 0.241605 | + | 0.418473i | 0.961172 | − | 0.275951i | \(-0.0889927\pi\) |
−0.719566 | + | 0.694424i | \(0.755659\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.95059e7 | − | 3.37851e7i | 0.00326847 | − | 0.00566115i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.92988e9 | + | 3.34266e9i | −0.316192 | + | 0.547661i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.48811e8 | + | 4.30954e8i | 0.0403119 | + | 0.0698223i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.98055e9 | −0.317328 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.56414e9 | −1.19855 | −0.599276 | − | 0.800543i | \(-0.704545\pi\) | ||||
−0.599276 | + | 0.800543i | \(0.704545\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.84033e9 | + | 3.18755e9i | 0.288392 | + | 0.499510i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.04155e8 | + | 7.00016e8i | −0.0626382 | + | 0.108493i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.34198e8 | − | 7.52052e8i | 0.0658316 | − | 0.114024i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.60093e9 | − | 9.70109e9i | −0.839957 | − | 1.45485i | −0.889930 | − | 0.456097i | \(-0.849247\pi\) |
0.0499734 | − | 0.998751i | \(-0.484086\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.87742e9 | 1.16855 | 0.584273 | − | 0.811557i | \(-0.301380\pi\) | ||||
0.584273 | + | 0.811557i | \(0.301380\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.51888e8 | 0.0369615 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.24724e8 | − | 1.08205e9i | −0.0906825 | − | 0.157067i | 0.817116 | − | 0.576473i | \(-0.195572\pi\) |
−0.907798 | + | 0.419407i | \(0.862238\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.43598e8 | − | 1.28795e9i | 0.106778 | − | 0.184945i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.76348e9 | + | 6.51854e9i | −0.528924 | + | 0.916124i | 0.470507 | + | 0.882396i | \(0.344071\pi\) |
−0.999431 | + | 0.0337275i | \(0.989262\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.87927e8 | + | 1.71114e9i | 0.137366 | + | 0.237926i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.70137e8 | 0.105947 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.29417e9 | 0.312268 | 0.156134 | − | 0.987736i | \(-0.450097\pi\) | ||||
0.156134 | + | 0.987736i | \(0.450097\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.54192e9 | + | 4.40274e9i | 0.342339 | + | 0.592949i | 0.984867 | − | 0.173314i | \(-0.0554474\pi\) |
−0.642527 | + | 0.766263i | \(0.722114\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.62367e8 | + | 4.54433e8i | −0.0349633 | + | 0.0605582i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.06233e8 | − | 3.57206e8i | 0.0269103 | − | 0.0466099i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.70583e9 | + | 2.95459e9i | 0.220265 | + | 0.381510i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.98513e9 | −0.637012 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.62649e9 | −0.711516 | −0.355758 | − | 0.934578i | \(-0.615777\pi\) | ||||
−0.355758 | + | 0.934578i | \(0.615777\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.70452e8 | − | 1.16126e9i | −0.0839082 | − | 0.145333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.13727e9 | − | 8.89801e9i | 0.636314 | − | 1.10213i | −0.349921 | − | 0.936779i | \(-0.613791\pi\) |
0.986235 | − | 0.165349i | \(-0.0528752\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.15909e9 | − | 5.47171e9i | 0.383308 | − | 0.663909i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.76228e9 | − | 1.34447e10i | −0.932217 | − | 1.61465i | −0.779524 | − | 0.626373i | \(-0.784539\pi\) |
−0.152693 | − | 0.988274i | \(-0.548795\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.80896e9 | −0.571655 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.84574e9 | −0.217181 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.00256e9 | − | 1.73648e9i | −0.116773 | − | 0.202257i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.11725e9 | + | 7.13128e9i | −0.474716 | + | 0.822232i | −0.999581 | − | 0.0289536i | \(-0.990782\pi\) |
0.524865 | + | 0.851186i | \(0.324116\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.85866e8 | + | 1.18796e9i | −0.0774984 | + | 0.134231i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.83190e8 | + | 1.35652e9i | 0.0876097 | + | 0.151744i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.87039e9 | −0.539378 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.88820e9 | −0.535964 | −0.267982 | − | 0.963424i | \(-0.586357\pi\) | ||||
−0.267982 | + | 0.963424i | \(0.586357\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.11515e9 | + | 1.93149e9i | 0.121057 | + | 0.209677i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.87647e8 | + | 1.53745e9i | −0.0954065 | + | 0.165249i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.97553e9 | − | 6.88582e9i | 0.418922 | − | 0.725594i | −0.576909 | − | 0.816808i | \(-0.695741\pi\) |
0.995831 | + | 0.0912141i | \(0.0290748\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.63947e8 | − | 6.30375e8i | −0.0379748 | − | 0.0657742i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.33464e8 | −0.0241216 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.13756e8 | −0.0934887 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.52527e9 | + | 6.10594e9i | 0.357170 | + | 0.618637i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.50173e9 | − | 1.12613e10i | 0.652346 | − | 1.12990i | −0.330206 | − | 0.943909i | \(-0.607118\pi\) |
0.982552 | − | 0.185987i | \(-0.0595484\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.66971e8 | − | 4.62407e8i | 0.0262712 | − | 0.0455031i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.08861e9 | − | 1.22778e10i | −0.690841 | − | 1.19657i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.73805e10 | −1.67761 | −0.838805 | − | 0.544431i | \(-0.816745\pi\) | ||||
−0.838805 | + | 0.544431i | \(0.816745\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.75211e8 | + | 4.76680e8i | 0.0260589 | + | 0.0451353i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.73557e9 | + | 8.20225e9i | −0.444128 | + | 0.769253i | −0.997991 | − | 0.0633553i | \(-0.979820\pi\) |
0.553863 | + | 0.832608i | \(0.313153\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.94485e9 | + | 5.10062e9i | −0.270973 | + | 0.469339i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.76457e9 | − | 4.78837e9i | −0.251983 | − | 0.436448i | 0.712088 | − | 0.702090i | \(-0.247749\pi\) |
−0.964072 | + | 0.265642i | \(0.914416\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.90904e8 | 0.0533523 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.53701e10 | −1.37472 | −0.687362 | − | 0.726315i | \(-0.741231\pi\) | ||||
−0.687362 | + | 0.726315i | \(0.741231\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.53552e9 | + | 6.12370e9i | 0.313261 | + | 0.542584i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.42082e9 | + | 2.46094e9i | −0.124715 | + | 0.216012i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.25975e9 | − | 7.37811e9i | 0.366982 | − | 0.635631i | −0.622110 | − | 0.782930i | \(-0.713724\pi\) |
0.989092 | + | 0.147299i | \(0.0470578\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.07589e9 | + | 3.59555e9i | 0.177183 | + | 0.306890i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.56970e9 | −0.217304 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.72648e8 | −0.0396006 | −0.0198003 | − | 0.999804i | \(-0.506303\pi\) | ||||
−0.0198003 | + | 0.999804i | \(0.506303\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.42239e7 | + | 1.28560e8i | 0.00616166 | + | 0.0106723i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.17326e9 | − | 1.24245e10i | 0.590025 | − | 1.02195i | −0.404203 | − | 0.914669i | \(-0.632451\pi\) |
0.994228 | − | 0.107284i | \(-0.0342154\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.15055e8 | + | 3.72486e8i | −0.0173674 | + | 0.0300812i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.82990e8 | − | 1.52938e9i | −0.0706597 | − | 0.122386i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.39480e10 | 1.10603 | 0.553017 | − | 0.833170i | \(-0.313476\pi\) | ||||
0.553017 | + | 0.833170i | \(0.313476\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.87073e9 | 0.304160 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.16169e9 | + | 3.74415e9i | 0.168331 | + | 0.291558i | 0.937833 | − | 0.347086i | \(-0.112829\pi\) |
−0.769502 | + | 0.638644i | \(0.779496\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.01229e9 | + | 6.94949e9i | −0.309625 | + | 0.536287i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.81951e8 | − | 1.52758e9i | 0.0668442 | − | 0.115777i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.65221e9 | + | 2.86172e9i | 0.124105 | + | 0.214955i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.09615e9 | 0.304937 | ||||||||