Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,8,Mod(32,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.32");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.d (of order \(2\), degree \(1\), 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: | \(10.3087058410\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 32.17 | ||
Character | \(\chi\) | \(=\) | 33.32 |
Dual form | 33.8.d.b.32.18 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.8692 | 0.960708 | 0.480354 | − | 0.877075i | \(-0.340508\pi\) | ||||
0.480354 | + | 0.877075i | \(0.340508\pi\) | |||||||
\(3\) | −0.0827838 | − | 46.7653i | −0.00177019 | − | 0.999998i | ||||
\(4\) | −9.86124 | −0.0770410 | ||||||||
\(5\) | − | 348.238i | − | 1.24589i | −0.782264 | − | 0.622947i | \(-0.785935\pi\) | ||
0.782264 | − | 0.622947i | \(-0.214065\pi\) | |||||||
\(6\) | −0.899791 | − | 508.300i | −0.00170064 | − | 0.960706i | ||||
\(7\) | 1046.71i | 1.15341i | 0.816954 | + | 0.576703i | \(0.195661\pi\) | ||||
−0.816954 | + | 0.576703i | \(0.804339\pi\) | |||||||
\(8\) | −1498.44 | −1.03472 | ||||||||
\(9\) | −2186.99 | + | 7.74282i | −0.999994 | + | 0.00354038i | ||||
\(10\) | − | 3785.06i | − | 1.19694i | ||||||
\(11\) | −2415.65 | − | 3694.83i | −0.547217 | − | 0.836990i | ||||
\(12\) | 0.816351 | + | 461.164i | 0.000136377 | + | 0.0770408i | ||||
\(13\) | − | 2640.65i | − | 0.333356i | −0.986011 | − | 0.166678i | \(-0.946696\pi\) | ||
0.986011 | − | 0.166678i | \(-0.0533041\pi\) | |||||||
\(14\) | 11376.8i | 1.10809i | ||||||||
\(15\) | −16285.5 | + | 28.8285i | −1.24589 | + | 0.00220547i | ||||
\(16\) | −15024.5 | −0.917024 | ||||||||
\(17\) | 30339.8 | 1.49776 | 0.748879 | − | 0.662707i | \(-0.230593\pi\) | ||||
0.748879 | + | 0.662707i | \(0.230593\pi\) | |||||||
\(18\) | −23770.7 | + | 84.1580i | −0.960702 | + | 0.00340127i | ||||
\(19\) | − | 36863.5i | − | 1.23299i | −0.787360 | − | 0.616494i | \(-0.788553\pi\) | ||
0.787360 | − | 0.616494i | \(-0.211447\pi\) | |||||||
\(20\) | 3434.06i | 0.0959849i | ||||||||
\(21\) | 48949.6 | − | 86.6504i | 1.15340 | − | 0.00204175i | ||||
\(22\) | −26256.1 | − | 40159.8i | −0.525716 | − | 0.804103i | ||||
\(23\) | − | 47795.0i | − | 0.819097i | −0.912288 | − | 0.409548i | \(-0.865686\pi\) | ||
0.912288 | − | 0.409548i | \(-0.134314\pi\) | |||||||
\(24\) | 124.046 | + | 70074.8i | 0.00183166 | + | 1.03472i | ||||
\(25\) | −43144.7 | −0.552252 | ||||||||
\(26\) | − | 28701.6i | − | 0.320258i | ||||||
\(27\) | 543.142 | + | 102274.i | 0.00531056 | + | 0.999986i | ||||
\(28\) | − | 10321.8i | − | 0.0888595i | ||||||
\(29\) | −189050. | −1.43940 | −0.719702 | − | 0.694283i | \(-0.755722\pi\) | ||||
−0.719702 | + | 0.694283i | \(0.755722\pi\) | |||||||
\(30\) | −177009. | + | 313.341i | −1.19694 | + | 0.00211882i | ||||
\(31\) | 269812. | 1.62665 | 0.813326 | − | 0.581808i | \(-0.197654\pi\) | ||||
0.813326 | + | 0.581808i | \(0.197654\pi\) | |||||||
\(32\) | 28495.9 | 0.153730 | ||||||||
\(33\) | −172590. | + | 113275.i | −0.836020 | + | 0.548698i | ||||
\(34\) | 329768. | 1.43891 | ||||||||
\(35\) | 364503. | 1.43702 | ||||||||
\(36\) | 21566.4 | − | 76.3538i | 0.0770405 | − | 0.000272755i | ||||
\(37\) | −90561.6 | −0.293926 | −0.146963 | − | 0.989142i | \(-0.546950\pi\) | ||||
−0.146963 | + | 0.989142i | \(0.546950\pi\) | |||||||
\(38\) | − | 400675.i | − | 1.18454i | ||||||
\(39\) | −123491. | + | 218.603i | −0.333356 | + | 0.000590106i | ||||
\(40\) | 521813.i | 1.28915i | ||||||||
\(41\) | 478887. | 1.08515 | 0.542575 | − | 0.840007i | \(-0.317449\pi\) | ||||
0.542575 | + | 0.840007i | \(0.317449\pi\) | |||||||
\(42\) | 532041. | − | 941.818i | 1.10808 | − | 0.00196153i | ||||
\(43\) | 167164.i | 0.320629i | 0.987066 | + | 0.160314i | \(0.0512508\pi\) | ||||
−0.987066 | + | 0.160314i | \(0.948749\pi\) | |||||||
\(44\) | 23821.3 | + | 36435.7i | 0.0421582 | + | 0.0644826i | ||||
\(45\) | 2696.34 | + | 761592.i | 0.00441094 | + | 1.24589i | ||||
\(46\) | − | 519492.i | − | 0.786912i | ||||||
\(47\) | − | 150168.i | − | 0.210977i | −0.994421 | − | 0.105488i | \(-0.966359\pi\) | ||
0.994421 | − | 0.105488i | \(-0.0336406\pi\) | |||||||
\(48\) | 1243.79 | + | 702626.i | 0.00162331 | + | 0.917022i | ||||
\(49\) | −272053. | −0.330345 | ||||||||
\(50\) | −468947. | −0.530553 | ||||||||
\(51\) | −2511.64 | − | 1.41885e6i | −0.00265132 | − | 1.49775i | ||||
\(52\) | 26040.1i | 0.0256821i | ||||||||
\(53\) | 8104.59i | 0.00747766i | 0.999993 | + | 0.00373883i | \(0.00119011\pi\) | ||||
−0.999993 | + | 0.00373883i | \(0.998810\pi\) | |||||||
\(54\) | 5903.50 | + | 1.11164e6i | 0.00510190 | + | 0.960694i | ||||
\(55\) | −1.28668e6 | + | 841222.i | −1.04280 | + | 0.681775i | ||||
\(56\) | − | 1.56842e6i | − | 1.19345i | ||||||
\(57\) | −1.72393e6 | + | 3051.70i | −1.23299 | + | 0.00218263i | ||||
\(58\) | −2.05481e6 | −1.38285 | ||||||||
\(59\) | − | 1.25309e6i | − | 0.794330i | −0.917747 | − | 0.397165i | \(-0.869994\pi\) | ||
0.917747 | − | 0.397165i | \(-0.130006\pi\) | |||||||
\(60\) | 160595. | − | 284.285i | 0.0959847 | − | 0.000169912i | ||||
\(61\) | − | 2.29402e6i | − | 1.29403i | −0.762478 | − | 0.647014i | \(-0.776018\pi\) | ||
0.762478 | − | 0.647014i | \(-0.223982\pi\) | |||||||
\(62\) | 2.93263e6 | 1.56274 | ||||||||
\(63\) | −8104.47 | − | 2.28913e6i | −0.00408350 | − | 1.15340i | ||||
\(64\) | 2.23287e6 | 1.06471 | ||||||||
\(65\) | −919574. | −0.415327 | ||||||||
\(66\) | −1.87591e6 | + | 1.23120e6i | −0.803171 | + | 0.527139i | ||||
\(67\) | −3.88969e6 | −1.57999 | −0.789993 | − | 0.613115i | \(-0.789916\pi\) | ||||
−0.789993 | + | 0.613115i | \(0.789916\pi\) | |||||||
\(68\) | −299188. | −0.115389 | ||||||||
\(69\) | −2.23515e6 | + | 3956.65i | −0.819095 | + | 0.00144996i | ||||
\(70\) | 3.96185e6 | 1.38056 | ||||||||
\(71\) | 605145.i | 0.200657i | 0.994954 | + | 0.100329i | \(0.0319894\pi\) | ||||
−0.994954 | + | 0.100329i | \(0.968011\pi\) | |||||||
\(72\) | 3.27706e6 | − | 11602.1i | 1.03471 | − | 0.00366331i | ||||
\(73\) | 6.02139e6i | 1.81162i | 0.423687 | + | 0.905809i | \(0.360736\pi\) | ||||
−0.423687 | + | 0.905809i | \(0.639264\pi\) | |||||||
\(74\) | −984329. | −0.282377 | ||||||||
\(75\) | 3571.68 | + | 2.01767e6i | 0.000977594 | + | 0.552251i | ||||
\(76\) | 363520.i | 0.0949905i | ||||||||
\(77\) | 3.86741e6 | − | 2.52848e6i | 0.965390 | − | 0.631164i | ||||
\(78\) | −1.34224e6 | + | 2376.03i | −0.320257 | + | 0.000566919i | ||||
\(79\) | − | 1.99704e6i | − | 0.455713i | −0.973695 | − | 0.227857i | \(-0.926828\pi\) | ||
0.973695 | − | 0.227857i | \(-0.0731718\pi\) | |||||||
\(80\) | 5.23211e6i | 1.14251i | ||||||||
\(81\) | 4.78285e6 | − | 33866.9i | 0.999975 | − | 0.00708072i | ||||
\(82\) | 5.20510e6 | 1.04251 | ||||||||
\(83\) | −2.68553e6 | −0.515533 | −0.257767 | − | 0.966207i | \(-0.582987\pi\) | ||||
−0.257767 | + | 0.966207i | \(0.582987\pi\) | |||||||
\(84\) | −482704. | + | 854.481i | −0.0888594 | + | 0.000157299i | ||||
\(85\) | − | 1.05655e7i | − | 1.86605i | ||||||
\(86\) | 1.81693e6i | 0.308031i | ||||||||
\(87\) | 15650.2 | + | 8.84096e6i | 0.00254803 | + | 1.43940i | ||||
\(88\) | 3.61970e6 | + | 5.53647e6i | 0.566218 | + | 0.866052i | ||||
\(89\) | − | 3.70801e6i | − | 0.557540i | −0.960358 | − | 0.278770i | \(-0.910073\pi\) | ||
0.960358 | − | 0.278770i | \(-0.0899267\pi\) | |||||||
\(90\) | 29307.0 | + | 8.27787e6i | 0.00423763 | + | 1.19693i | ||||
\(91\) | 2.76398e6 | 0.384495 | ||||||||
\(92\) | 471318.i | 0.0631040i | ||||||||
\(93\) | −22336.0 | − | 1.26178e7i | −0.00287949 | − | 1.62665i | ||||
\(94\) | − | 1.63220e6i | − | 0.202687i | ||||||
\(95\) | −1.28373e7 | −1.53617 | ||||||||
\(96\) | −2359.00 | − | 1.33262e6i | −0.000272132 | − | 0.153730i | ||||
\(97\) | −4.64760e6 | −0.517044 | −0.258522 | − | 0.966005i | \(-0.583235\pi\) | ||||
−0.258522 | + | 0.966005i | \(0.583235\pi\) | |||||||
\(98\) | −2.95699e6 | −0.317365 | ||||||||
\(99\) | 5.31161e6 | + | 8.06185e6i | 0.550177 | + | 0.835048i | ||||
\(100\) | 425460. | 0.0425460 | ||||||||
\(101\) | 1.34603e7 | 1.29996 | 0.649979 | − | 0.759953i | \(-0.274778\pi\) | ||||
0.649979 | + | 0.759953i | \(0.274778\pi\) | |||||||
\(102\) | −27299.5 | − | 1.54217e7i | −0.00254714 | − | 1.43890i | ||||
\(103\) | −94229.8 | −0.00849685 | −0.00424842 | − | 0.999991i | \(-0.501352\pi\) | ||||
−0.00424842 | + | 0.999991i | \(0.501352\pi\) | |||||||
\(104\) | 3.95684e6i | 0.344931i | ||||||||
\(105\) | −30175.0 | − | 1.70461e7i | −0.00254381 | − | 1.43702i | ||||
\(106\) | 88090.1i | 0.00718384i | ||||||||
\(107\) | −1.29347e6 | −0.102074 | −0.0510369 | − | 0.998697i | \(-0.516253\pi\) | ||||
−0.0510369 | + | 0.998697i | \(0.516253\pi\) | |||||||
\(108\) | −5356.06 | − | 1.00855e6i | −0.000409131 | − | 0.0770399i | ||||
\(109\) | 1.26898e7i | 0.938563i | 0.883049 | + | 0.469281i | \(0.155487\pi\) | ||||
−0.883049 | + | 0.469281i | \(0.844513\pi\) | |||||||
\(110\) | −1.39852e7 | + | 9.14338e6i | −1.00183 | + | 0.654986i | ||||
\(111\) | 7497.04 | + | 4.23514e6i | 0.000520306 | + | 0.293926i | ||||
\(112\) | − | 1.57263e7i | − | 1.05770i | ||||||
\(113\) | 1.82126e7i | 1.18740i | 0.804685 | + | 0.593702i | \(0.202334\pi\) | ||||
−0.804685 | + | 0.593702i | \(0.797666\pi\) | |||||||
\(114\) | −1.87377e7 | + | 33169.4i | −1.18454 | + | 0.00209687i | ||||
\(115\) | −1.66440e7 | −1.02051 | ||||||||
\(116\) | 1.86426e6 | 0.110893 | ||||||||
\(117\) | 20446.1 | + | 5.77506e6i | 0.00118021 | + | 0.333354i | ||||
\(118\) | − | 1.36201e7i | − | 0.763119i | ||||||
\(119\) | 3.17569e7i | 1.72752i | ||||||||
\(120\) | 2.44027e7 | − | 43197.6i | 1.28915 | − | 0.00228205i | ||||
\(121\) | −7.81642e6 | + | 1.78509e7i | −0.401106 | + | 0.916032i | ||||
\(122\) | − | 2.49341e7i | − | 1.24318i | ||||||
\(123\) | −39644.1 | − | 2.23953e7i | −0.00192093 | − | 1.08515i | ||||
\(124\) | −2.66068e6 | −0.125319 | ||||||||
\(125\) | − | 1.21815e7i | − | 0.557847i | ||||||
\(126\) | −88088.8 | − | 2.48810e7i | −0.00392305 | − | 1.10808i | ||||
\(127\) | 1.91701e6i | 0.0830444i | 0.999138 | + | 0.0415222i | \(0.0132207\pi\) | ||||
−0.999138 | + | 0.0415222i | \(0.986779\pi\) | |||||||
\(128\) | 2.06219e7 | 0.869148 | ||||||||
\(129\) | 7.81746e6 | − | 13838.5i | 0.320628 | − | 0.000567575i | ||||
\(130\) | −9.99500e6 | −0.399007 | ||||||||
\(131\) | 2.35503e6 | 0.0915264 | 0.0457632 | − | 0.998952i | \(-0.485428\pi\) | ||||
0.0457632 | + | 0.998952i | \(0.485428\pi\) | |||||||
\(132\) | 1.70195e6 | − | 1.11703e6i | 0.0644078 | − | 0.0422722i | ||||
\(133\) | 3.85853e7 | 1.42213 | ||||||||
\(134\) | −4.22777e7 | −1.51791 | ||||||||
\(135\) | 3.56158e7 | − | 189143.i | 1.24588 | − | 0.00661640i | ||||
\(136\) | −4.54623e7 | −1.54976 | ||||||||
\(137\) | − | 3.66251e7i | − | 1.21690i | −0.793591 | − | 0.608452i | \(-0.791791\pi\) | ||
0.793591 | − | 0.608452i | \(-0.208209\pi\) | |||||||
\(138\) | −2.42942e7 | + | 43005.5i | −0.786911 | + | 0.00139299i | ||||
\(139\) | − | 1.41470e7i | − | 0.446800i | −0.974727 | − | 0.223400i | \(-0.928284\pi\) | ||
0.974727 | − | 0.223400i | \(-0.0717157\pi\) | |||||||
\(140\) | −3.59446e6 | −0.110710 | ||||||||
\(141\) | −7.02264e6 | + | 12431.5i | −0.210976 | + | 0.000373470i | ||||
\(142\) | 6.57742e6i | 0.192773i | ||||||||
\(143\) | −9.75675e6 | + | 6.37888e6i | −0.279016 | + | 0.182418i | ||||
\(144\) | 3.28584e7 | − | 116332.i | 0.917018 | − | 0.00324662i | ||||
\(145\) | 6.58343e7i | 1.79335i | ||||||||
\(146\) | 6.54474e7i | 1.74043i | ||||||||
\(147\) | 22521.6 | + | 1.27227e7i | 0.000584775 | + | 0.330344i | ||||
\(148\) | 893050. | 0.0226444 | ||||||||
\(149\) | 2.01010e7 | 0.497811 | 0.248906 | − | 0.968528i | \(-0.419929\pi\) | ||||
0.248906 | + | 0.968528i | \(0.419929\pi\) | |||||||
\(150\) | 38821.2 | + | 2.19304e7i | 0.000939181 | + | 0.530552i | ||||
\(151\) | 8.52532e6i | 0.201507i | 0.994911 | + | 0.100754i | \(0.0321254\pi\) | ||||
−0.994911 | + | 0.100754i | \(0.967875\pi\) | |||||||
\(152\) | 5.52376e7i | 1.27580i | ||||||||
\(153\) | −6.63527e7 | + | 234916.i | −1.49775 | + | 0.00530263i | ||||
\(154\) | 4.20355e7 | − | 2.74825e7i | 0.927457 | − | 0.606364i | ||||
\(155\) | − | 9.39587e7i | − | 2.02664i | ||||||
\(156\) | 1.21777e6 | − | 2155.70i | 0.0256821 | − | 4.54623e-5i | ||||
\(157\) | 8.15598e7 | 1.68201 | 0.841003 | − | 0.541031i | \(-0.181966\pi\) | ||||
0.841003 | + | 0.541031i | \(0.181966\pi\) | |||||||
\(158\) | − | 2.17062e7i | − | 0.437807i | ||||||
\(159\) | 379014. | − | 670.929i | 0.00747765 | − | 1.32369e-5i | ||||
\(160\) | − | 9.92337e6i | − | 0.191531i | ||||||
\(161\) | 5.00274e7 | 0.944751 | ||||||||
\(162\) | 5.19856e7 | − | 368105.i | 0.960683 | − | 0.00680250i | ||||
\(163\) | −2.43347e7 | −0.440119 | −0.220059 | − | 0.975487i | \(-0.570625\pi\) | ||||
−0.220059 | + | 0.975487i | \(0.570625\pi\) | |||||||
\(164\) | −4.72242e6 | −0.0836010 | ||||||||
\(165\) | 3.94465e7 | + | 6.01024e7i | 0.683620 | + | 1.04159i | ||||
\(166\) | −2.91895e7 | −0.495277 | ||||||||
\(167\) | 7.75661e7 | 1.28874 | 0.644369 | − | 0.764715i | \(-0.277120\pi\) | ||||
0.644369 | + | 0.764715i | \(0.277120\pi\) | |||||||
\(168\) | −7.33478e7 | + | 129840.i | −1.19345 | + | 0.00211265i | ||||
\(169\) | 5.57755e7 | 0.888874 | ||||||||
\(170\) | − | 1.14838e8i | − | 1.79273i | ||||||
\(171\) | 285427. | + | 8.06199e7i | 0.00436525 | + | 1.23298i | ||||
\(172\) | − | 1.64844e6i | − | 0.0247016i | ||||||
\(173\) | −8.86937e7 | −1.30236 | −0.651181 | − | 0.758923i | \(-0.725726\pi\) | ||||
−0.651181 | + | 0.758923i | \(0.725726\pi\) | |||||||
\(174\) | 170105. | + | 9.60939e7i | 0.00244791 | + | 1.38284i | ||||
\(175\) | − | 4.51599e7i | − | 0.636971i | ||||||
\(176\) | 3.62940e7 | + | 5.55131e7i | 0.501811 | + | 0.767540i | ||||
\(177\) | −5.86012e7 | + | 103736.i | −0.794328 | + | 0.00140612i | ||||
\(178\) | − | 4.03030e7i | − | 0.535633i | ||||||
\(179\) | − | 4.73183e7i | − | 0.616657i | −0.951280 | − | 0.308329i | \(-0.900230\pi\) | ||
0.951280 | − | 0.308329i | \(-0.0997696\pi\) | |||||||
\(180\) | −26589.3 | − | 7.51024e6i | −0.000339823 | − | 0.0959843i | ||||
\(181\) | 3.16949e7 | 0.397296 | 0.198648 | − | 0.980071i | \(-0.436345\pi\) | ||||
0.198648 | + | 0.980071i | \(0.436345\pi\) | |||||||
\(182\) | 3.00422e7 | 0.369387 | ||||||||
\(183\) | −1.07281e8 | + | 189908.i | −1.29403 | + | 0.00229068i | ||||
\(184\) | 7.16178e7i | 0.847537i | ||||||||
\(185\) | 3.15370e7i | 0.366201i | ||||||||
\(186\) | −242774. | − | 1.37145e8i | −0.00276635 | − | 1.56274i | ||||
\(187\) | −7.32904e7 | − | 1.12100e8i | −0.819599 | − | 1.25361i | ||||
\(188\) | 1.48084e6i | 0.0162538i | ||||||||
\(189\) | −1.07051e8 | + | 568511.i | −1.15339 | + | 0.00612523i | ||||
\(190\) | −1.39530e8 | −1.47581 | ||||||||
\(191\) | − | 1.31366e7i | − | 0.136417i | −0.997671 | − | 0.0682084i | \(-0.978272\pi\) | ||
0.997671 | − | 0.0682084i | \(-0.0217283\pi\) | |||||||
\(192\) | −184845. | − | 1.04421e8i | −0.00188475 | − | 1.06471i | ||||
\(193\) | − | 6.48665e6i | − | 0.0649486i | −0.999473 | − | 0.0324743i | \(-0.989661\pi\) | ||
0.999473 | − | 0.0324743i | \(-0.0103387\pi\) | |||||||
\(194\) | −5.05155e7 | −0.496728 | ||||||||
\(195\) | 76125.8 | + | 4.30041e7i | 0.000735209 | + | 0.415326i | ||||
\(196\) | 2.68278e6 | 0.0254501 | ||||||||
\(197\) | 4.70505e7 | 0.438463 | 0.219231 | − | 0.975673i | \(-0.429645\pi\) | ||||
0.219231 | + | 0.975673i | \(0.429645\pi\) | |||||||
\(198\) | 5.77327e7 | + | 8.76255e7i | 0.528560 | + | 0.802237i | ||||
\(199\) | −1.84450e8 | −1.65917 | −0.829587 | − | 0.558377i | \(-0.811424\pi\) | ||||
−0.829587 | + | 0.558377i | \(0.811424\pi\) | |||||||
\(200\) | 6.46496e7 | 0.571427 | ||||||||
\(201\) | 322004. | + | 1.81903e8i | 0.00279688 | + | 1.57998i | ||||
\(202\) | 1.46302e8 | 1.24888 | ||||||||
\(203\) | − | 1.97880e8i | − | 1.66022i | ||||||
\(204\) | 24767.9 | + | 1.39916e7i | 0.000204260 | + | 0.115388i | ||||
\(205\) | − | 1.66767e8i | − | 1.35198i | ||||||
\(206\) | −1.02420e6 | −0.00816299 | ||||||||
\(207\) | 370068. | + | 1.04527e8i | 0.00289992 | + | 0.819091i | ||||
\(208\) | 3.96745e7i | 0.305696i | ||||||||
\(209\) | −1.36204e8 | + | 8.90493e7i | −1.03200 | + | 0.674712i | ||||
\(210\) | −327977. | − | 1.85277e8i | −0.00244386 | − | 1.38056i | ||||
\(211\) | − | 2.44770e7i | − | 0.179378i | −0.995970 | − | 0.0896890i | \(-0.971413\pi\) | ||
0.995970 | − | 0.0896890i | \(-0.0285873\pi\) | |||||||
\(212\) | − | 79921.3i | − | 0.000576086i | ||||||
\(213\) | 2.82998e7 | − | 50096.2i | 0.200657 | − | 0.000355203i | ||||
\(214\) | −1.40590e7 | −0.0980631 | ||||||||
\(215\) | 5.82128e7 | 0.399470 | ||||||||
\(216\) | −813864. | − | 1.53252e8i | −0.00549495 | − | 1.03471i | ||||
\(217\) | 2.82414e8i | 1.87619i | ||||||||
\(218\) | 1.37928e8i | 0.901684i | ||||||||
\(219\) | 2.81592e8 | − | 498473.i | 1.81161 | − | 0.00320691i | ||||
\(220\) | 1.26883e7 | − | 8.29549e6i | 0.0803384 | − | 0.0525246i | ||||
\(221\) | − | 8.01167e7i | − | 0.499287i | ||||||
\(222\) | 81486.5 | + | 4.60325e7i | 0.000499862 | + | 0.282377i | ||||
\(223\) | 1.66161e6 | 0.0100337 | 0.00501686 | − | 0.999987i | \(-0.498403\pi\) | ||||
0.00501686 | + | 0.999987i | \(0.498403\pi\) | |||||||
\(224\) | 2.98269e7i | 0.177313i | ||||||||
\(225\) | 9.43568e7 | − | 334062.i | 0.552249 | − | 0.00195518i | ||||
\(226\) | 1.97956e8i | 1.14075i | ||||||||
\(227\) | 1.54743e8 | 0.878054 | 0.439027 | − | 0.898474i | \(-0.355323\pi\) | ||||
0.439027 | + | 0.898474i | \(0.355323\pi\) | |||||||
\(228\) | 1.70001e7 | − | 30093.5i | 0.0949904 | − | 0.000168152i | ||||
\(229\) | 1.90996e8 | 1.05099 | 0.525497 | − | 0.850796i | \(-0.323880\pi\) | ||||
0.525497 | + | 0.850796i | \(0.323880\pi\) | |||||||
\(230\) | −1.80907e8 | −0.980409 | ||||||||
\(231\) | −1.18565e8 | − | 1.80651e8i | −0.632872 | − | 0.964271i | ||||
\(232\) | 2.83279e8 | 1.48938 | ||||||||
\(233\) | 1.30980e8 | 0.678359 | 0.339179 | − | 0.940722i | \(-0.389851\pi\) | ||||
0.339179 | + | 0.940722i | \(0.389851\pi\) | |||||||
\(234\) | 222232. | + | 6.27701e7i | 0.00113384 | + | 0.320256i | ||||
\(235\) | −5.22941e7 | −0.262854 | ||||||||
\(236\) | 1.23570e7i | 0.0611959i | ||||||||
\(237\) | −9.33921e7 | + | 165323.i | −0.455713 | + | 0.000806701i | ||||
\(238\) | 3.45171e8i | 1.65964i | ||||||||
\(239\) | 7.59556e7 | 0.359888 | 0.179944 | − | 0.983677i | \(-0.442408\pi\) | ||||
0.179944 | + | 0.983677i | \(0.442408\pi\) | |||||||
\(240\) | 2.44681e8 | − | 433134.i | 1.14251 | − | 0.00202247i | ||||
\(241\) | − | 1.64421e8i | − | 0.756655i | −0.925672 | − | 0.378327i | \(-0.876499\pi\) | ||
0.925672 | − | 0.378327i | \(-0.123501\pi\) | |||||||
\(242\) | −8.49580e7 | + | 1.94024e8i | −0.385346 | + | 0.880039i | ||||
\(243\) | −1.97974e6 | − | 2.23669e8i | −0.00885086 | − | 0.999961i | ||||
\(244\) | 2.26219e7i | 0.0996932i | ||||||||
\(245\) | 9.47393e7i | 0.411575i | ||||||||
\(246\) | −430898. | − | 2.43418e8i | −0.00184545 | − | 1.04251i | ||||
\(247\) | −9.73434e7 | −0.411024 | ||||||||
\(248\) | −4.04296e8 | −1.68313 | ||||||||
\(249\) | 222318. | + | 1.25590e8i | 0.000912594 | + | 0.515532i | ||||
\(250\) | − | 1.32402e8i | − | 0.535927i | ||||||
\(251\) | 3.01031e8i | 1.20158i | 0.799407 | + | 0.600791i | \(0.205147\pi\) | ||||
−0.799407 | + | 0.600791i | \(0.794853\pi\) | |||||||
\(252\) | 79920.1 | + | 2.25737e7i | 0.000314597 | + | 0.0888589i | ||||
\(253\) | −1.76595e8 | + | 1.15456e8i | −0.685576 | + | 0.448224i | ||||
\(254\) | 2.08362e7i | 0.0797814i | ||||||||
\(255\) | −4.94097e8 | + | 874650.i | −1.86604 | + | 0.00330327i | ||||
\(256\) | −6.16639e7 | −0.229716 | ||||||||
\(257\) | − | 4.99179e7i | − | 0.183438i | −0.995785 | − | 0.0917192i | \(-0.970764\pi\) | ||
0.995785 | − | 0.0917192i | \(-0.0292362\pi\) | |||||||
\(258\) | 8.49693e7 | − | 150412.i | 0.308030 | − | 0.000545274i | ||||
\(259\) | − | 9.47915e7i | − | 0.339016i | ||||||
\(260\) | 9.06814e6 | 0.0319972 | ||||||||
\(261\) | 4.13449e8 | − | 1.46378e6i | 1.43940 | − | 0.00509604i | ||||
\(262\) | 2.55972e7 | 0.0879301 | ||||||||
\(263\) | −3.52864e8 | −1.19609 | −0.598043 | − | 0.801464i | \(-0.704055\pi\) | ||||
−0.598043 | + | 0.801464i | \(0.704055\pi\) | |||||||
\(264\) | 2.58615e8 | − | 1.69735e8i | 0.865048 | − | 0.567750i | ||||
\(265\) | 2.82233e6 | 0.00931637 | ||||||||
\(266\) | 4.19390e8 | 1.36626 | ||||||||
\(267\) | −1.73406e8 | + | 306963.i | −0.557539 | + | 0.000986955i | ||||
\(268\) | 3.83572e7 | 0.121724 | ||||||||
\(269\) | − | 5.56088e8i | − | 1.74185i | −0.491416 | − | 0.870925i | \(-0.663520\pi\) | ||
0.491416 | − | 0.870925i | \(-0.336480\pi\) | |||||||
\(270\) | 3.87114e8 | − | 2.05582e6i | 1.19692 | − | 0.00635642i | ||||
\(271\) | − | 4.26918e8i | − | 1.30302i | −0.758638 | − | 0.651512i | \(-0.774135\pi\) | ||
0.758638 | − | 0.651512i | \(-0.225865\pi\) | |||||||
\(272\) | −4.55841e8 | −1.37348 | ||||||||
\(273\) | −228813. | − | 1.29259e8i | −0.000680631 | − | 0.384494i | ||||
\(274\) | − | 3.98084e8i | − | 1.16909i | ||||||
\(275\) | 1.04223e8 | + | 1.59412e8i | 0.302202 | + | 0.462230i | ||||
\(276\) | 2.20413e7 | − | 39017.5i | 0.0631039 | − | 0.000111706i | ||||
\(277\) | 2.91367e8i | 0.823685i | 0.911255 | + | 0.411842i | \(0.135115\pi\) | ||||
−0.911255 | + | 0.411842i | \(0.864885\pi\) | |||||||
\(278\) | − | 1.53766e8i | − | 0.429244i | ||||||
\(279\) | −5.90075e8 | + | 2.08910e6i | −1.62664 | + | 0.00575897i | ||||
\(280\) | −5.46185e8 | −1.48692 | ||||||||
\(281\) | 1.38541e8 | 0.372483 | 0.186241 | − | 0.982504i | \(-0.440369\pi\) | ||||
0.186241 | + | 0.982504i | \(0.440369\pi\) | |||||||
\(282\) | −7.63302e7 | + | 135120.i | −0.202686 | + | 0.000358795i | ||||
\(283\) | − | 6.73305e8i | − | 1.76587i | −0.469493 | − | 0.882936i | \(-0.655563\pi\) | ||
0.469493 | − | 0.882936i | \(-0.344437\pi\) | |||||||
\(284\) | − | 5.96748e6i | − | 0.0154588i | ||||||
\(285\) | 1.06272e6 | + | 6.00338e8i | 0.00271932 | + | 1.53617i | ||||
\(286\) | −1.06048e8 | + | 6.93332e7i | −0.268053 | + | 0.175251i | ||||
\(287\) | 5.01255e8i | 1.25162i | ||||||||
\(288\) | −6.23202e7 | + | 220639.i | −0.153729 | + | 0.000544262i | ||||
\(289\) | 5.10164e8 | 1.24328 | ||||||||
\(290\) | 7.15564e8i | 1.72288i | ||||||||
\(291\) | 384746. | + | 2.17346e8i | 0.000915269 | + | 0.517043i | ||||
\(292\) | − | 5.93783e7i | − | 0.139569i | ||||||
\(293\) | 4.54303e8 | 1.05514 | 0.527569 | − | 0.849512i | \(-0.323104\pi\) | ||||
0.527569 | + | 0.849512i | \(0.323104\pi\) | |||||||
\(294\) | 244791. | + | 1.38285e8i | 0.000561797 | + | 0.317364i | ||||
\(295\) | −4.36374e8 | −0.989651 | ||||||||
\(296\) | 1.35701e8 | 0.304132 | ||||||||
\(297\) | 3.76575e8 | − | 2.49066e8i | 0.834073 | − | 0.551655i | ||||
\(298\) | 2.18481e8 | 0.478251 | ||||||||
\(299\) | −1.26210e8 | −0.273051 | ||||||||
\(300\) | −35221.2 | − | 1.98968e7i | −7.53147e−5 | − | 0.0425460i | ||||
\(301\) | −1.74972e8 | −0.369815 | ||||||||
\(302\) | 9.26631e7i | 0.193590i | ||||||||
\(303\) | −1.11429e6 | − | 6.29474e8i | −0.00230118 | − | 1.29995i | ||||
\(304\) | 5.53856e8i | 1.13068i | ||||||||
\(305\) | −7.98866e8 | −1.61222 | ||||||||
\(306\) | −7.21199e8 | + | 2.55334e6i | −1.43890 | + | 0.00509428i | ||||
\(307\) | 7.72881e8i | 1.52450i | 0.647281 | + | 0.762252i | \(0.275906\pi\) | ||||
−0.647281 | + | 0.762252i | \(0.724094\pi\) | |||||||
\(308\) | −3.81375e7 | + | 2.49340e7i | −0.0743745 | + | 0.0486255i | ||||
\(309\) | 7800.70 | + | 4.40668e6i | 1.50411e−5 | + | 0.00849684i | ||||
\(310\) | − | 1.02125e9i | − | 1.94701i | ||||||
\(311\) | − | 6.00287e7i | − | 0.113161i | −0.998398 | − | 0.0565806i | \(-0.981980\pi\) | ||
0.998398 | − | 0.0565806i | \(-0.0180198\pi\) | |||||||
\(312\) | 1.85043e8 | − | 327563.i | 0.344930 | − | 0.000610595i | ||||
\(313\) | 8.72612e8 | 1.60848 | 0.804240 | − | 0.594304i | \(-0.202572\pi\) | ||||
0.804240 | + | 0.594304i | \(0.202572\pi\) | |||||||
\(314\) | 8.86487e8 | 1.61592 | ||||||||
\(315\) | −7.97164e8 | + | 2.82228e6i | −1.43701 | + | 0.00508761i | ||||
\(316\) | 1.96933e7i | 0.0351086i | ||||||||
\(317\) | − | 5.10125e8i | − | 0.899434i | −0.893171 | − | 0.449717i | \(-0.851525\pi\) | ||
0.893171 | − | 0.449717i | \(-0.148475\pi\) | |||||||
\(318\) | 4.11956e6 | − | 7292.44i | 0.00718383 | − | 1.27168e-5i | ||||
\(319\) | 4.56678e8 | + | 6.98507e8i | 0.787667 | + | 1.20477i | ||||
\(320\) | − | 7.77568e8i | − | 1.32652i | ||||||
\(321\) | 107079. | + | 6.04897e7i | 0.000180691 | + | 0.102074i | ||||
\(322\) | 5.43756e8 | 0.907629 | ||||||||
\(323\) | − | 1.11843e9i | − | 1.84672i | ||||||
\(324\) | −4.71648e7 | + | 333970.i | −0.0770390 | + | 0.000545506i | ||||
\(325\) | 1.13930e8i | 0.184097i | ||||||||
\(326\) | −2.64498e8 | −0.422825 | ||||||||
\(327\) | 5.93444e8 | − | 1.05051e6i | 0.938561 | − | 0.00166144i | ||||
\(328\) | −7.17582e8 | −1.12283 | ||||||||
\(329\) | 1.57182e8 | 0.243342 | ||||||||
\(330\) | 4.28751e8 | + | 6.53263e8i | 0.656759 | + | 1.00067i | ||||
\(331\) | −5.05329e8 | −0.765907 | −0.382953 | − | 0.923768i | \(-0.625093\pi\) | ||||
−0.382953 | + | 0.923768i | \(0.625093\pi\) | |||||||
\(332\) | 2.64827e7 | 0.0397172 | ||||||||
\(333\) | 1.98057e8 | − | 701202.i | 0.293924 | − | 0.00104061i | ||||
\(334\) | 8.43079e8 | 1.23810 | ||||||||
\(335\) | 1.35454e9i | 1.96850i | ||||||||
\(336\) | −7.35444e8 | + | 1.30188e6i | −1.05770 | + | 0.00187234i | ||||
\(337\) | 1.44876e8i | 0.206201i | 0.994671 | + | 0.103101i | \(0.0328764\pi\) | ||||
−0.994671 | + | 0.103101i | \(0.967124\pi\) | |||||||
\(338\) | 6.06233e8 | 0.853948 | ||||||||
\(339\) | 8.51720e8 | − | 1.50771e6i | 1.18740 | − | 0.00210194i | ||||
\(340\) | 1.04189e8i | 0.143762i | ||||||||
\(341\) | −6.51771e8 | − | 9.96909e8i | −0.890133 | − | 1.36149i | ||||
\(342\) | 3.10235e6 | + | 8.76271e8i | 0.00419373 | + | 1.18453i | ||||
\(343\) | 5.77248e8i | 0.772384i | ||||||||
\(344\) | − | 2.50484e8i | − | 0.331762i | ||||||
\(345\) | 1.37786e6 | + | 7.78363e8i | 0.00180650 | + | 1.02051i | ||||
\(346\) | −9.64027e8 | −1.25119 | ||||||||
\(347\) | −6.59572e8 | −0.847440 | −0.423720 | − | 0.905793i | \(-0.639276\pi\) | ||||
−0.423720 | + | 0.905793i | \(0.639276\pi\) | |||||||
\(348\) | −154331. | − | 8.71829e7i | −0.000196302 | − | 0.110893i | ||||
\(349\) | − | 3.52913e8i | − | 0.444405i | −0.975001 | − | 0.222202i | \(-0.928675\pi\) | ||
0.975001 | − | 0.222202i | \(-0.0713245\pi\) | |||||||
\(350\) | − | 4.90850e8i | − | 0.611943i | ||||||
\(351\) | 2.70071e8 | − | 1.43425e6i | 0.333352 | − | 0.00177031i | ||||
\(352\) | −6.88363e7 | − | 1.05288e8i | −0.0841236 | − | 0.128670i | ||||
\(353\) | 8.35795e8i | 1.01132i | 0.862733 | + | 0.505660i | \(0.168751\pi\) | ||||
−0.862733 | + | 0.505660i | \(0.831249\pi\) | |||||||
\(354\) | −6.36946e8 | + | 1.12752e6i | −0.763117 | + | 0.00135087i | ||||
\(355\) | 2.10734e8 | 0.249998 | ||||||||
\(356\) | 3.65656e7i | 0.0429534i | ||||||||
\(357\) | 1.48512e9 | − | 2.62896e6i | 1.72752 | − | 0.00305805i | ||||
\(358\) | − | 5.14311e8i | − | 0.592427i | ||||||
\(359\) | 7.94097e8 | 0.905823 | 0.452911 | − | 0.891556i | \(-0.350385\pi\) | ||||
0.452911 | + | 0.891556i | \(0.350385\pi\) | |||||||
\(360\) | −4.04030e6 | − | 1.14120e9i | −0.00456410 | − | 1.28915i | ||||
\(361\) | −4.65043e8 | −0.520257 | ||||||||
\(362\) | 3.44497e8 | 0.381685 | ||||||||
\(363\) | 8.35448e8 | + | 3.64060e8i | 0.916740 | + | 0.399484i | ||||
\(364\) | −2.72563e7 | −0.0296219 | ||||||||
\(365\) | 2.09688e9 | 2.25708 | ||||||||
\(366\) | −1.16605e9 | + | 2.06414e6i | −1.24318 | + | 0.00220067i | ||||
\(367\) | 2.54522e8 | 0.268778 | 0.134389 | − | 0.990929i | \(-0.457093\pi\) | ||||
0.134389 | + | 0.990929i | \(0.457093\pi\) | |||||||
\(368\) | 7.18097e8i | 0.751131i | ||||||||
\(369\) | −1.04732e9 | + | 3.70794e6i | −1.08514 | + | 0.00384185i | ||||
\(370\) | 3.42781e8i | 0.351812i | ||||||||
\(371\) | −8.48313e6 | −0.00862477 | ||||||||
\(372\) | 220261. | + | 1.24427e8i | 0.000221839 | + | 0.125319i | ||||
\(373\) | 1.78663e9i | 1.78260i | 0.453418 | + | 0.891298i | \(0.350204\pi\) | ||||
−0.453418 | + | 0.891298i | \(0.649796\pi\) | |||||||
\(374\) | −7.96605e8 | − | 1.21844e9i | −0.787395 | − | 1.20435i | ||||
\(375\) | −5.69670e8 | + | 1.00843e6i | −0.557846 | + | 0.000987497i | ||||
\(376\) | 2.25017e8i | 0.218302i | ||||||||
\(377\) | 4.99213e8i | 0.479835i | ||||||||
\(378\) | −1.16356e9 | + | 6.17924e6i | −1.10807 | + | 0.00588456i | ||||
\(379\) | −1.31813e9 | −1.24371 | −0.621856 | − | 0.783131i | \(-0.713621\pi\) | ||||
−0.621856 | + | 0.783131i | \(0.713621\pi\) | |||||||
\(380\) | 1.26591e8 | 0.118348 | ||||||||
\(381\) | 8.96493e7 | − | 158697.i | 0.0830443 | − | 0.000147005i | ||||
\(382\) | − | 1.42784e8i | − | 0.131057i | ||||||
\(383\) | − | 1.97076e9i | − | 1.79241i | −0.443637 | − | 0.896206i | \(-0.646312\pi\) | ||
0.443637 | − | 0.896206i | \(-0.353688\pi\) | |||||||
\(384\) | −1.70716e6 | − | 9.64389e8i | −0.00153856 | − | 0.869147i | ||||
\(385\) | −8.80513e8 | − | 1.34678e9i | −0.786363 | − | 1.20277i | ||||
\(386\) | − | 7.05045e7i | − | 0.0623966i | ||||||
\(387\) | −1.29432e6 | − | 3.65585e8i | −0.00113515 | − | 0.320627i | ||||
\(388\) | 4.58311e7 | 0.0398336 | ||||||||
\(389\) | 7.80717e8i | 0.672466i | 0.941779 | + | 0.336233i | \(0.109153\pi\) | ||||
−0.941779 | + | 0.336233i | \(0.890847\pi\) | |||||||
\(390\) | 827424. | + | 4.67419e8i | 0.000706321 | + | 0.399007i | ||||
\(391\) | − | 1.45009e9i | − | 1.22681i | ||||||
\(392\) | 4.07655e8 | 0.341815 | ||||||||
\(393\) | −194958. | − | 1.10134e8i | −0.000162019 | − | 0.0915262i | ||||
\(394\) | 5.11400e8 | 0.421234 | ||||||||
\(395\) | −6.95445e8 | −0.567771 | ||||||||
\(396\) | −5.23790e7 | − | 7.94998e7i | −0.0423862 | − | 0.0643329i | ||||
\(397\) | 9.83480e8 | 0.788858 | 0.394429 | − | 0.918926i | \(-0.370942\pi\) | ||||
0.394429 | + | 0.918926i | \(0.370942\pi\) | |||||||
\(398\) | −2.00481e9 | −1.59398 | ||||||||
\(399\) | −3.19423e6 | − | 1.80445e9i | −0.00251745 | − | 1.42213i | ||||
\(400\) | 6.48228e8 | 0.506428 | ||||||||
\(401\) | 1.07636e9i | 0.833592i | 0.909000 | + | 0.416796i | \(0.136847\pi\) | ||||
−0.909000 | + | 0.416796i | \(0.863153\pi\) | |||||||
\(402\) | 3.49991e6 | + | 1.97713e9i | 0.00268699 | + | 1.51790i | ||||
\(403\) | − | 7.12478e8i | − | 0.542255i | ||||||
\(404\) | −1.32735e8 | −0.100150 | ||||||||
\(405\) | −1.17937e7 | − | 1.66557e9i | −0.00882183 | − | 1.24586i | ||||
\(406\) | − | 2.15079e9i | − | 1.59498i | ||||||
\(407\) | 2.18765e8 | + | 3.34610e8i | 0.160842 | + | 0.246013i | ||||
\(408\) | 3.76354e6 | + | 2.12606e9i | 0.00274338 | + | 1.54976i | ||||
\(409\) | 5.15625e8i | 0.372651i | 0.982488 | + | 0.186326i | \(0.0596579\pi\) | ||||
−0.982488 | + | 0.186326i | \(0.940342\pi\) | |||||||
\(410\) | − | 1.81261e9i | − | 1.29886i | ||||||
\(411\) | −1.71278e9 | + | 3.03196e6i | −1.21690 | + | 0.00215416i | ||||
\(412\) | 929223. | 0.000654605 | ||||||||
\(413\) | 1.31162e9 | 0.916184 | ||||||||
\(414\) | 4.02233e6 | + | 1.13612e9i | 0.00278597 | + | 0.786907i | ||||
\(415\) | 9.35204e8i | 0.642300i | ||||||||
\(416\) | − | 7.52477e7i | − | 0.0512468i | ||||||
\(417\) | −6.61590e8 | + | 1.17114e6i | −0.446800 | + | 0.000790923i | ||||
\(418\) | −1.48043e9 | + | 9.67891e8i | −0.991449 | + | 0.648201i | ||||
\(419\) | 1.11146e9i | 0.738153i | 0.929399 | + | 0.369076i | \(0.120326\pi\) | ||||
−0.929399 | + | 0.369076i | \(0.879674\pi\) | |||||||
\(420\) | 297563. | + | 1.68096e8i | 0.000195977 | + | 0.110709i | ||||
\(421\) | −1.11875e9 | −0.730711 | −0.365356 | − | 0.930868i | \(-0.619053\pi\) | ||||
−0.365356 | + | 0.930868i | \(0.619053\pi\) | |||||||
\(422\) | − | 2.66044e8i | − | 0.172330i | ||||||
\(423\) | 1.16272e6 | + | 3.28415e8i | 0.000746938 | + | 0.210975i | ||||
\(424\) | − | 1.21442e7i | − | 0.00773729i | ||||||
\(425\) | −1.30900e9 | −0.827139 | ||||||||
\(426\) | 3.07595e8 | − | 544504.i | 0.192773 | − | 0.000341246i | ||||
\(427\) | 2.40117e9 | 1.49254 | ||||||||
\(428\) | 1.27553e7 | 0.00786387 | ||||||||
\(429\) | 2.99118e8 | + | 4.55749e8i | 0.182912 | + | 0.278693i | ||||
\(430\) | 6.32724e8 | 0.383773 | ||||||||
\(431\) | −1.25877e9 | −0.757311 | −0.378656 | − | 0.925538i | \(-0.623614\pi\) | ||||
−0.378656 | + | 0.925538i | \(0.623614\pi\) | |||||||
\(432\) | −8.16045e6 | − | 1.53662e9i | −0.00486991 | − | 0.917011i | ||||
\(433\) | 2.01330e9 | 1.19179 | 0.595897 | − | 0.803061i | \(-0.296797\pi\) | ||||
0.595897 | + | 0.803061i | \(0.296797\pi\) | |||||||
\(434\) | 3.06960e9i | 1.80247i | ||||||||
\(435\) | 3.07876e9 | − | 5.45001e6i | 1.79334 | − | 0.00317457i | ||||
\(436\) | − | 1.25138e8i | − | 0.0723078i | ||||||
\(437\) | −1.76189e9 | −1.00994 | ||||||||
\(438\) | 3.06067e9 | − | 5.41799e6i | 1.74043 | − | 0.00308091i | ||||
\(439\) | − | 2.14252e8i | − | 0.120865i | −0.998172 | − | 0.0604324i | \(-0.980752\pi\) | ||
0.998172 | − | 0.0604324i | \(-0.0192480\pi\) | |||||||
\(440\) | 1.92801e9 | − | 1.26052e9i | 1.07901 | − | 0.705447i | ||||
\(441\) | 5.94977e8 | − | 2.10646e6i | 0.330343 | − | 0.00116955i | ||||
\(442\) | − | 8.70802e8i | − | 0.479669i | ||||||
\(443\) | 2.96139e9i | 1.61839i | 0.587542 | + | 0.809193i | \(0.300096\pi\) | ||||
−0.587542 | + | 0.809193i | \(0.699904\pi\) | |||||||
\(444\) | −73930.1 | − | 4.17638e7i | −4.00849e−5 | − | 0.0226443i | ||||
\(445\) | −1.29127e9 | −0.694636 | ||||||||
\(446\) | 1.80603e7 | 0.00963946 | ||||||||
\(447\) | −1.66403e6 | − | 9.40027e8i | −0.000881223 | − | 0.497811i | ||||
\(448\) | 2.33716e9i | 1.22805i | ||||||||
\(449\) | 8.63951e8i | 0.450430i | 0.974309 | + | 0.225215i | \(0.0723084\pi\) | ||||
−0.974309 | + | 0.225215i | \(0.927692\pi\) | |||||||
\(450\) | 1.02558e9 | − | 3.63097e6i | 0.530549 | − | 0.00187836i | ||||
\(451\) | −1.15682e9 | − | 1.76941e9i | −0.593813 | − | 0.908260i | ||||
\(452\) | − | 1.79599e8i | − | 0.0914787i | ||||||
\(453\) | 3.98689e8 | − | 705758.i | 0.201507 | − | 0.000356707i | ||||
\(454\) | 1.68193e9 | 0.843553 | ||||||||
\(455\) | − | 9.62525e8i | − | 0.479040i | ||||||
\(456\) | 2.58320e9 | − | 4.57278e6i | 1.27580 | − | 0.00225841i | ||||
\(457\) | 3.24917e9i | 1.59245i | 0.605002 | + | 0.796224i | \(0.293172\pi\) | ||||
−0.605002 | + | 0.796224i | \(0.706828\pi\) | |||||||
\(458\) | 2.07597e9 | 1.00970 | ||||||||
\(459\) | 1.64788e7 | + | 3.10298e9i | 0.00795393 | + | 1.49774i | ||||
\(460\) | 1.64131e8 | 0.0786209 | ||||||||
\(461\) | −1.26720e9 | −0.602410 | −0.301205 | − | 0.953559i | \(-0.597389\pi\) | ||||
−0.301205 | + | 0.953559i | \(0.597389\pi\) | |||||||
\(462\) | −1.28871e9 | − | 1.96353e9i | −0.608005 | − | 0.926382i | ||||
\(463\) | 8.55808e6 | 0.00400722 | 0.00200361 | − | 0.999998i | \(-0.499362\pi\) | ||||
0.00200361 | + | 0.999998i | \(0.499362\pi\) | |||||||
\(464\) | 2.84038e9 | 1.31997 | ||||||||
\(465\) | −4.39401e9 | + | 7.77826e6i | −2.02663 | + | 0.00358754i | ||||
\(466\) | 1.42364e9 | 0.651704 | ||||||||
\(467\) | 1.19556e8i | 0.0543204i | 0.999631 | + | 0.0271602i | \(0.00864643\pi\) | ||||
−0.999631 | + | 0.0271602i | \(0.991354\pi\) | |||||||
\(468\) | −201624. | − | 5.69493e7i | −9.09245e−5 | − | 0.0256819i | ||||
\(469\) | − | 4.07137e9i | − | 1.82237i | ||||||
\(470\) | −5.68393e8 | −0.252526 | ||||||||
\(471\) | −6.75183e6 | − | 3.81417e9i | −0.00297748 | − | 1.68200i | ||||
\(472\) | 1.87768e9i | 0.821910i | ||||||||
\(473\) | 6.17642e8 | − | 4.03810e8i | 0.268363 | − | 0.175454i | ||||
\(474\) | −1.01509e9 | + | 1.79692e6i | −0.437807 | + | 0.000775004i | ||||
\(475\) | 1.59046e9i | 0.680920i | ||||||||
\(476\) | − | 3.13162e8i | − | 0.133090i | ||||||
\(477\) | −62752.4 | − | 1.77246e7i | −2.64738e−5 | − | 0.00747761i | ||||
\(478\) | 8.25574e8 | 0.345747 | ||||||||
\(479\) | −3.84497e9 | −1.59852 | −0.799262 | − | 0.600983i | \(-0.794776\pi\) | ||||
−0.799262 | + | 0.600983i | \(0.794776\pi\) | |||||||
\(480\) | −4.64069e8 | + | 821494.i | −0.191531 | + | 0.000339047i | ||||
\(481\) | 2.39141e8i | 0.0979821i | ||||||||
\(482\) | − | 1.78712e9i | − | 0.726924i | ||||||
\(483\) | −4.14146e6 | − | 2.33955e9i | −0.00167239 | − | 0.944749i | ||||
\(484\) | 7.70796e7 | − | 1.76032e8i | 0.0309016 | − | 0.0705720i | ||||
\(485\) | 1.61847e9i | 0.644182i | ||||||||
\(486\) | −2.15181e7 | − | 2.43109e9i | −0.00850309 | − | 0.960670i | ||||
\(487\) | 2.47960e9 | 0.972815 | 0.486408 | − | 0.873732i | \(-0.338307\pi\) | ||||
0.486408 | + | 0.873732i | \(0.338307\pi\) | |||||||
\(488\) | 3.43745e9i | 1.33896i | ||||||||
\(489\) | 2.01452e6 | + | 1.13802e9i | 0.000779095 | + | 0.440118i | ||||
\(490\) | 1.02974e9i | 0.395403i | ||||||||
\(491\) | −4.35884e9 | −1.66183 | −0.830914 | − | 0.556401i | \(-0.812182\pi\) | ||||
−0.830914 | + | 0.556401i | \(0.812182\pi\) | |||||||
\(492\) | 390940. | + | 2.20846e8i | 0.000147990 | + | 0.0836009i | ||||
\(493\) | −5.73573e9 | −2.15588 | ||||||||
\(494\) | −1.05804e9 | −0.394874 | ||||||||
\(495\) | 2.80744e9 | − | 1.84970e9i | 1.04038 | − | 0.685463i | ||||
\(496\) | −4.05379e9 | −1.49168 | ||||||||
\(497\) | −6.33410e8 | −0.231439 | ||||||||
\(498\) | 2.41642e6 | + | 1.36505e9i | 0.000876736 | + | 0.495276i | ||||
\(499\) | 3.11108e9 | 1.12088 | 0.560440 | − | 0.828195i | \(-0.310632\pi\) | ||||
0.560440 | + | 0.828195i | \(0.310632\pi\) | |||||||
\(500\) | 1.20124e8i | 0.0429770i | ||||||||
\(501\) | −6.42122e6 | − | 3.62740e9i | −0.00228132 | − | 1.28874i | ||||
\(502\) | 3.27195e9i | 1.15437i | ||||||||
\(503\) | 3.88319e9 | 1.36051 | 0.680254 | − | 0.732977i | \(-0.261870\pi\) | ||||
0.680254 | + | 0.732977i | \(0.261870\pi\) | |||||||
\(504\) | 1.21440e7 | + | 3.43012e9i | 0.00422528 | + | 1.19345i | ||||
\(505\) | − | 4.68738e9i | − | 1.61961i | ||||||
\(506\) | −1.91944e9 | + | 1.25491e9i | −0.658638 | + | 0.430612i | ||||
\(507\) | −4.61731e6 | − | 2.60836e9i | −0.00157348 | − | 0.888872i | ||||
\(508\) | − | 1.89041e7i | − | 0.00639782i | ||||||
\(509\) | − | 2.37980e9i | − | 0.799885i | −0.916540 | − | 0.399942i | \(-0.869030\pi\) | ||
0.916540 | − | 0.399942i | \(-0.130970\pi\) | |||||||
\(510\) | −5.37042e9 | + | 9.50671e6i | −1.79272 | + | 0.00317347i | ||||
\(511\) | −6.30263e9 | −2.08953 | ||||||||
\(512\) | −3.30984e9 | −1.08984 | ||||||||
\(513\) | 3.77019e9 | − | 2.00221e7i | 1.23297 | − | 0.00654785i | ||||
\(514\) | − | 5.42566e8i | − | 0.176231i | ||||||
\(515\) | 3.28144e7i | 0.0105862i | ||||||||
\(516\) | −7.70899e7 | + | 136464.i | −0.0247015 | + | 4.37266e-5i | ||||
\(517\) | −5.54845e8 | + | 3.62753e8i | −0.176585 | + | 0.115450i | ||||
\(518\) | − | 1.03030e9i | − | 0.325695i | ||||||
\(519\) | 7.34240e6 | + | 4.14779e9i | 0.00230543 | + | 1.30236i | ||||
\(520\) | 1.37792e9 | 0.429747 | ||||||||
\(521\) | − | 3.31948e9i | − | 1.02834i | −0.857687 | − | 0.514172i | \(-0.828099\pi\) | ||
0.857687 | − | 0.514172i | \(-0.171901\pi\) | |||||||
\(522\) | 4.49385e9 | − | 1.59100e7i | 1.38284 | − | 0.00489581i | ||||
\(523\) | 3.26086e9i | 0.996728i | 0.866968 | + | 0.498364i | \(0.166066\pi\) | ||||
−0.866968 | + | 0.498364i | \(0.833934\pi\) | |||||||
\(524\) | −2.32235e7 | −0.00705128 | ||||||||
\(525\) | −2.11191e9 | + | 3.73851e6i | −0.636970 | + | 0.00112756i | ||||
\(526\) | −3.83534e9 | −1.14909 | ||||||||
\(527\) | 8.18603e9 | 2.43633 | ||||||||
\(528\) | 2.59308e9 | − | 1.70190e9i | 0.766651 | − | 0.503169i | ||||
\(529\) | 1.12046e9 | 0.329081 | ||||||||
\(530\) | 3.06763e7 | 0.00895031 | ||||||||
\(531\) | 9.70246e6 | + | 2.74049e9i | 0.00281223 | + | 0.794325i | ||||
\(532\) | −3.80499e8 | −0.109563 | ||||||||
\(533\) | − | 1.26457e9i | − | 0.361742i | ||||||
\(534\) | −1.88478e9 | + | 3.33644e6i | −0.535632 | + | 0.000948175i | ||||
\(535\) | 4.50437e8i | 0.127173i | ||||||||
\(536\) | 5.82846e9 | 1.63485 | ||||||||
\(537\) | −2.21286e9 | + | 3.91719e6i | −0.616656 | + | 0.00109160i | ||||
\(538\) | − | 6.04422e9i | − | 1.67341i | ||||||
\(539\) | 6.57186e8 | + | 1.00519e9i | 0.180771 | + | 0.276496i | ||||
\(540\) | −3.51216e8 | + | 1.86518e6i | −0.0959835 | + | 0.000509734i | ||||
\(541\) | − | 2.72552e9i | − | 0.740046i | −0.929023 | − | 0.370023i | \(-0.879350\pi\) | ||
0.929023 | − | 0.370023i | \(-0.120650\pi\) | |||||||
\(542\) | − | 4.64025e9i | − | 1.25183i | ||||||
\(543\) | −2.62382e6 | − | 1.48222e9i | −0.000703291 | − | 0.397295i | ||||
\(544\) | 8.64561e8 | 0.230250 | ||||||||
\(545\) | 4.41908e9 | 1.16935 | ||||||||
\(546\) | −2.48701e6 | − | 1.40493e9i | −0.000653887 | − | 0.369387i | ||||
\(547\) | − | 2.17750e9i | − | 0.568856i | −0.958697 | − | 0.284428i | \(-0.908196\pi\) | ||
0.958697 | − | 0.284428i | \(-0.0918036\pi\) | |||||||
\(548\) | 3.61169e8i | 0.0937515i | ||||||||
\(549\) | 1.77622e7 | + | 5.01700e9i | 0.00458135 | + | 1.29402i | ||||
\(550\) | 1.13281e9 | + | 1.73268e9i | 0.290328 | + | 0.444068i | ||||
\(551\) | 6.96902e9i | 1.77477i | ||||||||
\(552\) | 3.34923e9 | − | 5.92879e6i | 0.847535 | − | 0.00150030i | ||||
\(553\) | 2.09032e9 | 0.525622 | ||||||||
\(554\) | 3.16691e9i | 0.791320i | ||||||||
\(555\) | 1.47484e9 | − | 2.61075e6i | 0.366200 | − | 0.000648247i | ||||
\(556\) | 1.39507e8i | 0.0344219i | ||||||||
\(557\) | 1.97313e9 | 0.483796 | 0.241898 | − | 0.970302i | \(-0.422230\pi\) | ||||
0.241898 | + | 0.970302i | \(0.422230\pi\) | |||||||
\(558\) | −6.41362e9 | + | 2.27068e7i | −1.56273 | + | 0.00553269i | ||||
\(559\) | 4.41421e8 | 0.106884 | ||||||||
\(560\) | −5.47649e9 | −1.31778 | ||||||||
\(561\) | −5.23635e9 | + | 3.43673e9i | −1.25216 | + | 0.821817i | ||||
\(562\) | 1.50582e9 | 0.357847 | ||||||||
\(563\) | −7.12172e9 | −1.68192 | −0.840960 | − | 0.541098i | \(-0.818009\pi\) | ||||
−0.840960 | + | 0.541098i | \(0.818009\pi\) | |||||||
\(564\) | 6.92520e7 | − | 122590.i | 0.0162538 | − | 2.87725e-5i | ||||
\(565\) | 6.34233e9 | 1.47938 | ||||||||
\(566\) | − | 7.31826e9i | − | 1.69649i | ||||||
\(567\) | 3.54487e7 | + | 5.00624e9i | 0.00816695 | + | 1.15338i | ||||
\(568\) | − | 9.06771e8i | − | 0.207625i | ||||||
\(569\) | −1.11338e9 | −0.253367 | −0.126684 | − | 0.991943i | \(-0.540433\pi\) | ||||
−0.126684 | + | 0.991943i | \(0.540433\pi\) | |||||||
\(570\) | 1.15508e7 | + | 6.52517e9i | 0.00261247 | + | 1.47581i | ||||
\(571\) | 7.76269e9i | 1.74496i | 0.488648 | + | 0.872481i | \(0.337490\pi\) | ||||
−0.488648 | + | 0.872481i | \(0.662510\pi\) | |||||||
\(572\) | 9.62137e7 | − | 6.29037e7i | 0.0214957 | − | 0.0140537i | ||||
\(573\) | −6.14339e8 | + | 1.08750e6i | −0.136416 | + | 0.000241484i | ||||
\(574\) | 5.44822e9i | 1.20244i | ||||||||
\(575\) | 2.06210e9i | 0.452348i | ||||||||
\(576\) | −4.88325e9 | + | 1.72887e7i | −1.06471 | + | 0.00376949i | ||||
\(577\) | −1.81821e8 | −0.0394029 | −0.0197014 | − | 0.999806i | \(-0.506272\pi\) | ||||
−0.0197014 | + | 0.999806i | \(0.506272\pi\) | |||||||
\(578\) | 5.54506e9 | 1.19442 | ||||||||
\(579\) | −3.03350e8 | + | 536990.i | −0.0649485 | + | 0.000114972i | ||||
\(580\) | − | 6.49208e8i | − | 0.138161i | ||||||
\(581\) | − | 2.81096e9i | − | 0.594619i | ||||||
\(582\) | 4.18187e6 | + | 2.36237e9i | 0.000879305 | + | 0.496727i | ||||
\(583\) | 2.99451e7 | − | 1.95779e7i | 0.00625873 | − | 0.00409190i | ||||
\(584\) | − | 9.02266e9i | − | 1.87452i | ||||||
\(585\) | 2.01110e9 | − | 7.12009e6i | 0.415324 | − | 0.00147042i | ||||
\(586\) | 4.93790e9 | 1.01368 | ||||||||
\(587\) | − | 1.01363e9i | − | 0.206846i | −0.994637 | − | 0.103423i | \(-0.967020\pi\) | ||
0.994637 | − | 0.103423i | \(-0.0329796\pi\) | |||||||
\(588\) | −222091. | − | 1.25461e8i | −4.50516e−5 | − | 0.0254500i | ||||
\(589\) | − | 9.94619e9i | − | 2.00564i | ||||||
\(590\) | −4.74302e9 | −0.950765 | ||||||||
\(591\) | −3.89502e6 | − | 2.20033e9i | −0.000776164 | − | 0.438462i | ||||
\(592\) | 1.36064e9 | 0.269537 | ||||||||
\(593\) | −2.01779e9 | −0.397361 | −0.198681 | − | 0.980064i | \(-0.563666\pi\) | ||||
−0.198681 | + | 0.980064i | \(0.563666\pi\) | |||||||
\(594\) | 4.09306e9 | − | 2.70714e9i | 0.801300 | − | 0.529979i | ||||
\(595\) | 1.10590e10 | 2.15231 | ||||||||
\(596\) | −1.98220e8 | −0.0383519 | ||||||||
\(597\) | 1.52694e7 | + | 8.62584e9i | 0.00293706 | + | 1.65917i | ||||
\(598\) | −1.37179e9 | −0.262322 | ||||||||
\(599\) | − | 7.03119e9i | − | 1.33670i | −0.743845 | − | 0.668352i | \(-0.767000\pi\) | ||
0.743845 | − | 0.668352i | \(-0.233000\pi\) | |||||||
\(600\) | −5.35194e6 | − | 3.02336e9i | −0.00101154 | − | 0.571426i | ||||
\(601\) | 7.33153e9i | 1.37763i | 0.724935 | + | 0.688817i | \(0.241870\pi\) | ||||
−0.724935 | + | 0.688817i | \(0.758130\pi\) | |||||||
\(602\) | −1.90179e9 | −0.355284 | ||||||||
\(603\) | 8.50671e9 | − | 3.01172e7i | 1.57998 | − | 0.00559376i | ||||
\(604\) | − | 8.40702e7i | − | 0.0155243i | ||||||
\(605\) | 6.21635e9 | + | 2.72198e9i | 1.14128 | + | 0.499736i | ||||
\(606\) | −1.21114e7 | − | 6.84185e9i | −0.00221076 | − | 1.24888i | ||||
\(607\) | − | 8.71379e9i | − | 1.58142i | −0.612193 | − | 0.790709i | \(-0.709712\pi\) | ||
0.612193 | − | 0.790709i | \(-0.290288\pi\) | |||||||
\(608\) | − | 1.05046e9i | − | 0.189547i | ||||||
\(609\) | −9.25390e9 | + | 1.63812e7i | −1.66021 | + | 0.00293891i | ||||
\(610\) | −8.68301e9 | −1.54887 | ||||||||
\(611\) | −3.96540e8 | −0.0703304 | ||||||||
\(612\) | 6.54320e8 | − | 2.31656e6i | 0.115388 | − | 0.000408520i | ||||
\(613\) | 6.11858e9i | 1.07285i | 0.843948 | + | 0.536425i | \(0.180226\pi\) | ||||
−0.843948 | + | 0.536425i | \(0.819774\pi\) | |||||||
\(614\) | 8.40057e9i | 1.46460i | ||||||||
\(615\) | −7.79890e9 | + | 1.38056e7i | −1.35198 | + | 0.00239327i | ||||
\(616\) | −5.79507e9 | + | 3.78877e9i | −0.998909 | + | 0.653079i | ||||
\(617\) | − | 3.41971e9i | − | 0.586126i | −0.956093 | − | 0.293063i | \(-0.905325\pi\) | ||
0.956093 | − | 0.293063i | \(-0.0946747\pi\) | |||||||
\(618\) | 84787.1 | + | 4.78970e7i | 1.44501e−5 | + | 0.00816297i | ||||
\(619\) | 5.39566e9 | 0.914381 | 0.457191 | − | 0.889369i | \(-0.348856\pi\) | ||||
0.457191 | + | 0.889369i | \(0.348856\pi\) | |||||||
\(620\) | 9.26549e8i | 0.156134i | ||||||||
\(621\) | 4.88821e9 | − | 2.59595e7i | 0.819085 | − | 0.00434986i | ||||
\(622\) | − | 6.52461e8i | − | 0.108715i | ||||||
\(623\) | 3.88120e9 | 0.643070 | ||||||||
\(624\) | 1.85539e9 | − | 3.28440e6i | 0.305695 | − | 0.000541141i | ||||
\(625\) | −7.61273e9 | −1.24727 | ||||||||
\(626\) | 9.48456e9 | 1.54528 | ||||||||
\(627\) | 4.17569e9 | + | 6.36227e9i | 0.676538 | + | 1.03080i | ||||
\(628\) | −8.04281e8 | −0.129583 | ||||||||
\(629\) | −2.74762e9 | −0.440230 | ||||||||
\(630\) | −8.66450e9 | + | 3.06759e7i | −1.38055 | + | 0.00488770i | ||||
\(631\) | −1.09274e9 | −0.173147 | −0.0865734 | − | 0.996245i | \(-0.527592\pi\) | ||||
−0.0865734 | + | 0.996245i | \(0.527592\pi\) | |||||||
\(632\) | 2.99244e9i | 0.471536i | ||||||||
\(633\) | −1.14467e9 | + | 2.02630e6i | −0.179378 | + | 0.000317534i | ||||
\(634\) | − | 5.54463e9i | − | 0.864093i | ||||||
\(635\) | 6.67574e8 | 0.103465 | ||||||||
\(636\) | −3.73755e6 | + | 6616.19i | −0.000576085 | + | 1.01978e-6i | ||||
\(637\) | 7.18397e8i | 0.110123i | ||||||||
\(638\) | 4.96371e9 | + | 7.59219e9i | 0.756718 | + | 1.15743i | ||||
\(639\) | −4.68553e6 | − | 1.32344e9i | −0.000710404 | − | 0.200656i | ||||
\(640\) | − | 7.18133e9i | − | 1.08287i | ||||||
\(641\) | 4.97779e9i | 0.746506i | 0.927730 | + | 0.373253i | \(0.121758\pi\) | ||||
−0.927730 | + | 0.373253i | \(0.878242\pi\) | |||||||
\(642\) | 1.16386e6 | + | 6.57473e8i | 0.000173591 | + | 0.0980630i | ||||
\(643\) | −8.00751e9 | −1.18784 | −0.593922 | − | 0.804523i | \(-0.702421\pi\) | ||||
−0.593922 | + | 0.804523i | \(0.702421\pi\) | |||||||
\(644\) | −4.93332e8 | −0.0727845 | ||||||||
\(645\) | −4.81908e6 | − | 2.72234e9i | −0.000707139 | − | 0.399469i | ||||
\(646\) | − | 1.21564e10i | − | 1.77415i | ||||||
\(647\) | 7.57131e9i | 1.09902i | 0.835487 | + | 0.549510i | \(0.185186\pi\) | ||||
−0.835487 | + | 0.549510i | \(0.814814\pi\) | |||||||
\(648\) | −7.16680e9 | + | 5.07474e7i | −1.03470 | + | 0.00732658i | ||||
\(649\) | −4.62997e9 | + | 3.02703e9i | −0.664846 | + | 0.434671i | ||||
\(650\) | 1.23832e9i | 0.176863i | ||||||||
\(651\) | 1.32072e10 | − | 2.33793e7i | 1.87619 | − | 0.00332122i | ||||
\(652\) | 2.39971e8 | 0.0339072 | ||||||||
\(653\) | − | 1.10367e10i | − | 1.55111i | −0.631280 | − | 0.775555i | \(-0.717470\pi\) | ||
0.631280 | − | 0.775555i | \(-0.282530\pi\) | |||||||
\(654\) | 6.45024e9 | − | 1.14182e7i | 0.901683 | − | 0.00159616i | ||||
\(655\) | − | 8.20110e8i | − | 0.114032i | ||||||
\(656\) | −7.19505e9 | −0.995108 | ||||||||
\(657\) | −4.66225e7 | − | 1.31687e10i | −0.00641382 | − | 1.81161i | ||||
\(658\) | 1.70843e9 | 0.233780 | ||||||||
\(659\) | 4.27744e8 | 0.0582217 | 0.0291108 | − | 0.999576i | \(-0.490732\pi\) | ||||
0.0291108 | + | 0.999576i | \(0.490732\pi\) | |||||||
\(660\) | −3.88992e8 | − | 5.92684e8i | −0.0526667 | − | 0.0802453i | ||||
\(661\) | −6.06091e9 | −0.816268 | −0.408134 | − | 0.912922i | \(-0.633820\pi\) | ||||
−0.408134 | + | 0.912922i | \(0.633820\pi\) | |||||||
\(662\) | −5.49250e9 | −0.735812 | ||||||||
\(663\) | −3.74668e9 | + | 6.63236e6i | −0.499286 | + | 0.000883835i | ||||
\(664\) | 4.02410e9 | 0.533433 | ||||||||
\(665\) | − | 1.34369e10i | − | 1.77183i | ||||||
\(666\) | 2.15271e9 | − | 7.62148e6i | 0.282375 | − | 0.000999723i | ||||
\(667\) | 9.03563e9i | 1.17901i | ||||||||
\(668\) | −7.64898e8 | −0.0992856 | ||||||||
\(669\) | −137554. | − | 7.77056e7i | −1.77616e−5 | − | 0.0100337i | ||||
\(670\) | 1.47227e10i | 1.89115i | ||||||||
\(671\) | −8.47604e9 | + | 5.54156e9i | −1.08309 | + | 0.708115i | ||||
\(672\) | 1.39486e9 | − | 2.46918e6i | 0.177313 | − | 0.000313878i | ||||
\(673\) | 9.96057e9i | 1.25960i | 0.776759 | + | 0.629798i | \(0.216863\pi\) | ||||
−0.776759 | + | 0.629798i | \(0.783137\pi\) | |||||||
\(674\) | 1.57468e9i | 0.198099i | ||||||||
\(675\) | −2.34337e7 | − | 4.41260e9i | −0.00293277 | − | 0.552244i | ||||
\(676\) | −5.50016e8 | −0.0684797 | ||||||||
\(677\) | −9.03655e9 | −1.11929 | −0.559645 | − | 0.828733i | \(-0.689062\pi\) | ||||
−0.559645 | + | 0.828733i | \(0.689062\pi\) | |||||||
\(678\) | 9.25748e9 | − | 1.63876e7i | 1.14075 | − | 0.00201935i | ||||
\(679\) | − | 4.86468e9i | − | 0.596362i | ||||||
\(680\) | 1.58317e10i | 1.93084i | ||||||||
\(681\) | −1.28102e7 | − | 7.23662e9i | −0.00155433 | − | 0.878053i | ||||
\(682\) | −7.08421e9 | − | 1.08356e10i | −0.855157 | − | 1.30800i | ||||
\(683\) | − | 9.81205e9i | − | 1.17839i | −0.807992 | − | 0.589193i | \(-0.799446\pi\) | ||
0.807992 | − | 0.589193i | \(-0.200554\pi\) | |||||||
\(684\) | −2.81467e6 | − | 7.95012e8i | −0.000336303 | − | 0.0949899i | ||||
\(685\) | −1.27542e10 | −1.51613 | ||||||||
\(686\) | 6.27421e9i | 0.742035i | ||||||||
\(687\) | −1.58114e7 | − | 8.93198e9i | −0.00186046 | − | 1.05099i | ||||
\(688\) | − | 2.51156e9i | − | 0.294024i | ||||||
\(689\) | 2.14014e7 | 0.00249272 | ||||||||
\(690\) | 1.49762e7 | + | 8.46016e9i | 0.00173552 | + | 0.980408i | ||||
\(691\) | 1.48559e10 | 1.71287 | 0.856435 | − | 0.516255i | \(-0.172674\pi\) | ||||
0.856435 | + | 0.516255i | \(0.172674\pi\) | |||||||
\(692\) | 8.74630e8 | 0.100335 | ||||||||
\(693\) | −8.43839e9 | + | 5.55970e9i | −0.963149 | + | 0.634578i | ||||
\(694\) | −7.16900e9 | −0.814142 | ||||||||
\(695\) | −4.92653e9 | −0.556666 | ||||||||
\(696\) | −2.34509e7 | − | 1.32476e10i | −0.00263650 | − | 1.48938i | ||||
\(697\) | 1.45293e10 | 1.62529 | ||||||||
\(698\) | − | 3.83587e9i | − | 0.426943i | ||||||
\(699\) | −1.08430e7 | − | 6.12532e9i | −0.00120083 | − | 0.678358i | ||||
\(700\) | 4.45332e8i | 0.0490728i | ||||||||
\(701\) | 1.04249e10 | 1.14303 | 0.571517 | − | 0.820590i | \(-0.306355\pi\) | ||||
0.571517 | + | 0.820590i | \(0.306355\pi\) | |||||||
\(702\) | 2.93544e9 | − | 1.55891e7i | 0.320253 | − | 0.00170075i | ||||
\(703\) | 3.33841e9i | 0.362407i | ||||||||
\(704\) | −5.39383e9 | − | 8.25007e9i | −0.582630 | − | 0.891155i | ||||
\(705\) | 4.32911e6 | + | 2.44555e9i | 0.000465303 | + | 0.262854i | ||||
\(706\) | 9.08440e9i | 0.971583i | ||||||||
\(707\) | 1.40890e10i | 1.49938i | ||||||||
\(708\) | 5.77881e8 | − | 1.02296e6i | 0.0611958 | − | 0.000108329i | ||||
\(709\) | 9.80256e9 | 1.03295 | 0.516473 | − | 0.856303i | \(-0.327245\pi\) | ||||
0.516473 | + | 0.856303i | \(0.327245\pi\) | |||||||
\(710\) | 2.29051e9 | 0.240175 | ||||||||
\(711\) | 1.54627e7 | + | 4.36750e9i | 0.00161340 | + | 0.455711i | ||||
\(712\) | 5.55622e9i | 0.576899i | ||||||||
\(713\) | − | 1.28957e10i | − | 1.33239i | ||||||
\(714\) | 1.61420e10 | − | 2.85746e7i | 1.65964 | − | 0.00293789i | ||||
\(715\) | 2.22137e9 | + | 3.39767e9i | 0.227274 | + | 0.347624i | ||||
\(716\) | 4.66618e8i | 0.0475079i | ||||||||
\(717\) | −6.28789e6 | − | 3.55209e9i | −0.000637072 | − | 0.359887i | ||||
\(718\) | 8.63118e9 | 0.870231 | ||||||||
\(719\) | 8.94483e9i | 0.897472i | 0.893664 | + | 0.448736i | \(0.148126\pi\) | ||||
−0.893664 | + | 0.448736i | \(0.851874\pi\) | |||||||
\(720\) | −4.05113e7 | − | 1.14425e10i | −0.00404494 | − | 1.14251i | ||||
\(721\) | − | 9.86310e7i | − | 0.00980031i | ||||||
\(722\) | −5.05463e9 | −0.499815 | ||||||||
\(723\) | −7.68920e9 | + | 1.36114e7i | −0.756654 | + | 0.00133943i | ||||
\(724\) | −3.12551e8 | −0.0306081 | ||||||||
\(725\) | 8.15649e9 | 0.794914 | ||||||||
\(726\) | 9.08062e9 | + | 3.95702e9i | 0.880719 | + | 0.383787i | ||||
\(727\) | −1.03291e10 | −0.996989 | −0.498495 | − | 0.866893i | \(-0.666114\pi\) | ||||
−0.498495 | + | 0.866893i | \(0.666114\pi\) | |||||||
\(728\) | −4.14166e9 | −0.397845 | ||||||||
\(729\) | −1.04598e10 | + | 1.11099e8i | −0.999944 | + | 0.0106210i | ||||
\(730\) | 2.27913e10 | 2.16840 | ||||||||
\(731\) | 5.07171e9i | 0.480224i | ||||||||
\(732\) | 1.05792e9 | − | 1.87273e6i | 0.0996930 | − | 0.000176476i | ||||
\(733\) | − | 6.23025e9i | − | 0.584307i | −0.956371 | − | 0.292154i | \(-0.905628\pi\) | ||
0.956371 | − | 0.292154i | \(-0.0943719\pi\) | |||||||
\(734\) | 2.76644e9 | 0.258217 | ||||||||
\(735\) | 4.43051e9 | − | 7.84288e6i | 0.411574 | − | 0.000728567i | ||||
\(736\) | − | 1.36196e9i | − | 0.125920i | ||||||
\(737\) | 9.39614e9 | + | 1.43718e10i | 0.864597 | + | 1.32243i | ||||
\(738\) | −1.13835e10 | + | 4.03022e7i | −1.04251 | + | 0.00369089i | ||||
\(739\) | 2.69049e9i | 0.245231i | 0.992454 | + | 0.122616i | \(0.0391282\pi\) | ||||
−0.992454 | + | 0.122616i | \(0.960872\pi\) | |||||||
\(740\) | − | 3.10994e8i | − | 0.0282125i | ||||||
\(741\) | 8.05846e6 | + | 4.55229e9i | 0.000727592 | + | 0.411023i | ||||
\(742\) | −9.22046e7 | −0.00828588 | ||||||||
\(743\) | −5.08802e9 | −0.455080 | −0.227540 | − | 0.973769i | \(-0.573068\pi\) | ||||
−0.227540 | + | 0.973769i | \(0.573068\pi\) | |||||||
\(744\) | 3.34691e7 | + | 1.89070e10i | 0.00297947 | + | 1.68313i | ||||
\(745\) | − | 6.99992e9i | − | 0.620220i | ||||||
\(746\) | 1.94191e10i | 1.71255i | ||||||||
\(747\) | 5.87322e9 | − | 2.07936e7i | 0.515530 | − | 0.00182519i | ||||
\(748\) | 7.22734e8 | + | 1.10545e9i | 0.0631427 | + | 0.0965792i | ||||
\(749\) | − | 1.35389e9i | − | 0.117733i | ||||||
\(750\) | −6.19184e9 | + | 1.09608e7i | −0.535927 | + | 0.000948696i | ||||
\(751\) | 3.13996e9 | 0.270511 | 0.135255 | − | 0.990811i | \(-0.456815\pi\) | ||||
0.135255 | + | 0.990811i | \(0.456815\pi\) | |||||||
\(752\) | 2.25620e9i | 0.193471i | ||||||||
\(753\) | 1.40778e10 | − | 2.49205e7i | 1.20158 | − | 0.00212703i | ||||
\(754\) | 5.42603e9i | 0.460981i | ||||||||
\(755\) | 2.96884e9 | 0.251057 | ||||||||
\(756\) | 1.05566e9 | − | 5.60623e6i | 0.0888582 | − | 0.000471894i | ||||
\(757\) | −2.02487e10 | −1.69653 | −0.848264 | − | 0.529574i | \(-0.822352\pi\) | ||||
−0.848264 | + | 0.529574i | \(0.822352\pi\) | |||||||
\(758\) | −1.43269e10 | −1.19484 | ||||||||
\(759\) | 5.41396e9 | + | 8.24894e9i | 0.449437 | + | 0.684782i | ||||
\(760\) | 1.92358e10 | 1.58951 | ||||||||
\(761\) | 1.25541e10 | 1.03262 | 0.516311 | − | 0.856401i | \(-0.327305\pi\) | ||||
0.516311 | + | 0.856401i | \(0.327305\pi\) | |||||||
\(762\) | 9.74413e8 | − | 1.72490e6i | 0.0797812 | − | 0.000141229i | ||||
\(763\) | −1.32825e10 | −1.08254 | ||||||||
\(764\) | 1.29544e8i | 0.0105097i | ||||||||
\(765\) | 8.18065e7 | + | 2.31065e10i | 0.00660652 | + | 1.86603i | ||||
\(766\) | − | 2.14205e10i | − | 1.72198i | ||||||
\(767\) | −3.30897e9 | −0.264795 | ||||||||
\(768\) | 5.10477e6 | + | 2.88373e9i | 0.000406642 | + | 0.229716i | ||||
\(769\) | − | 2.12827e10i | − | 1.68765i | −0.536615 | − | 0.843827i | \(-0.680297\pi\) | ||
0.536615 | − | 0.843827i | \(-0.319703\pi\) | |||||||
\(770\) | −9.57044e9 | − | 1.46384e10i | −0.755465 | − | 1.15551i | ||||
\(771\) | −2.33443e9 | + | 4.13239e6i | −0.183438 | + | 0.000324722i | ||||
\(772\) | 6.39665e7i | 0.00500371i | ||||||||
\(773\) | 8.66823e9i | 0.674998i | 0.941326 | + | 0.337499i | \(0.109581\pi\) | ||||
−0.941326 | + | 0.337499i | \(0.890419\pi\) | |||||||
\(774\) | −1.40682e7 | − | 3.97360e9i | −0.00109055 | − | 0.308029i | ||||
\(775\) | −1.16409e10 | −0.898322 | ||||||||
\(776\) | 6.96413e9 | 0.534997 | ||||||||
\(777\) | −4.43295e9 | + | 7.84720e6i | −0.339016 | + | 0.000600124i | ||||
\(778\) | 8.48574e9i | 0.646043i | ||||||||
\(779\) | − | 1.76534e10i | − | 1.33798i | ||||||
\(780\) | −750695. | − | 4.24074e8i | −5.66412e−5 | − | 0.0319971i | ||||
\(781\) | 2.23591e9 | − | 1.46182e9i | 0.167948 | − | 0.109803i | ||||
\(782\) | − | 1.57613e10i | − | 1.17860i | ||||||
\(783\) | −1.02681e8 | − | 1.93349e10i | −0.00764405 | − | 1.43938i | ||||
\(784\) | 4.08747e9 | 0.302934 | ||||||||
\(785\) | − | 2.84022e10i | − | 2.09560i | ||||||
\(786\) | −2.11903e6 | − | 1.19706e9i | −0.000155653 | − | 0.0879299i | ||||
\(787\) | 2.85264e9i | 0.208610i | 0.994545 | + | 0.104305i | \(0.0332618\pi\) | ||||
−0.994545 | + | 0.104305i | \(0.966738\pi\) | |||||||
\(788\) | −4.63976e8 | −0.0337796 | ||||||||
\(789\) | 2.92114e7 | + | 1.65018e10i | 0.00211731 | + | 1.19608i | ||||
\(790\) | −7.55891e9 | −0.545462 | ||||||||
\(791\) | −1.90633e10 | −1.36956 | ||||||||
\(792\) | −7.95911e9 | − | 1.20802e10i | −0.569280 | − | 0.864042i | ||||
\(793\) | −6.05771e9 | −0.431372 | ||||||||
\(794\) | 1.06896e10 | 0.757862 | ||||||||
\(795\) | −233643. | − | 1.31987e8i | −1.64918e−5 | − | 0.00931635i | ||||
\(796\) | 1.81890e9 | 0.127824 | ||||||||
\(797\) | 1.80257e10i | 1.26121i | 0.776103 | + | 0.630606i | \(0.217194\pi\) | ||||
−0.776103 | + | 0.630606i | \(0.782806\pi\) | |||||||
\(798\) | −3.47187e7 | − | 1.96129e10i | −0.00241854 | − | 1.36625i | ||||
\(799\) | − | 4.55606e9i | − | 0.315992i | ||||||
\(800\) | −1.22945e9 | −0.0848976 | ||||||||
\(801\) | 2.87105e7 | + | 8.10937e9i | 0.00197391 | + | 0.557537i | ||||
\(802\) | 1.16992e10i | 0.800838i | ||||||||
\(803\) | 2.22480e10 | − | 1.45456e10i | 1.51631 | − | 0.991349i | ||||
\(804\) | −3.17536e6 | − | 1.79379e9i | −0.000215475 | − | 0.121724i | ||||
\(805\) | − | 1.74214e10i | − | 1.17706i | ||||||
\(806\) | − | 7.74404e9i | − | 0.520948i | ||||||
\(807\) | −2.60056e10 | + | 4.60351e7i | −1.74185 | + | 0.00308341i | ||||
\(808\) | −2.01694e10 | −1.34509 | ||||||||
\(809\) | 2.77447e9 | 0.184230 | 0.0921149 | − | 0.995748i | \(-0.470637\pi\) | ||||
0.0921149 | + | 0.995748i | \(0.470637\pi\) | |||||||
\(810\) | −1.28188e8 | − | 1.81034e10i | −0.00847520 | − | 1.19691i | ||||
\(811\) | 1.92521e10i | 1.26738i | 0.773588 | + | 0.633689i | \(0.218460\pi\) | ||||
−0.773588 | + | 0.633689i | \(0.781540\pi\) | |||||||
\(812\) | 1.95134e9i | 0.127905i | ||||||||
\(813\) | −1.99650e10 | + | 3.53419e7i | −1.30302 | + | 0.00230661i | ||||
\(814\) | 2.37780e9 | + | 3.63693e9i | 0.154522 | + | 0.236347i | ||||
\(815\) | 8.47427e9i | 0.548341i | ||||||||
\(816\) | 3.77362e7 | + | 2.13175e10i | 0.00243132 | + | 1.37348i | ||||
\(817\) | 6.16224e9 | 0.395331 | ||||||||
\(818\) | 5.60442e9i | 0.358009i | ||||||||
\(819\) | −6.04480e9 | + | 2.14010e7i | −0.384493 | + | 0.00136126i | ||||
\(820\) | 1.64453e9i | 0.104158i | ||||||||
\(821\) | −1.05163e10 | −0.663227 | −0.331614 | − | 0.943415i | \(-0.607593\pi\) | ||||
−0.331614 | + | 0.943415i | \(0.607593\pi\) | |||||||
\(822\) | −1.86165e10 | + | 3.29549e7i | −1.16909 | + | 0.00206951i | ||||
\(823\) | 1.00262e10 | 0.626956 | 0.313478 | − | 0.949595i | \(-0.398506\pi\) | ||||
0.313478 | + | 0.949595i | \(0.398506\pi\) | |||||||
\(824\) | 1.41197e8 | 0.00879187 | ||||||||
\(825\) | 7.44634e9 | − | 4.88720e9i | 0.461694 | − | 0.303020i | ||||
\(826\) | 1.42562e10 | 0.880185 | ||||||||
\(827\) | 4.87559e9 | 0.299749 | 0.149875 | − | 0.988705i | \(-0.452113\pi\) | ||||
0.149875 | + | 0.988705i | \(0.452113\pi\) | |||||||
\(828\) | −3.64933e6 | − | 1.03077e9i | −0.000223412 | − | 0.0631036i | ||||
\(829\) | −1.13229e10 | −0.690267 | −0.345133 | − | 0.938554i | \(-0.612166\pi\) | ||||
−0.345133 | + | 0.938554i | \(0.612166\pi\) | |||||||
\(830\) | 1.01649e10i | 0.617062i | ||||||||
\(831\) | 1.36259e10 | − | 2.41205e7i | 0.823683 | − | 0.00145808i | ||||
\(832\) | − | 5.89621e9i | − | 0.354929i | ||||||
\(833\) | −8.25404e9 | −0.494776 | ||||||||
\(834\) | −7.19093e9 | + | 1.27294e7i | −0.429244 | + | 0.000759846i | ||||
\(835\) | − | 2.70115e10i | − | 1.60563i | ||||||
\(836\) | 1.34314e9 | − | 8.78137e8i | 0.0795061 | − | 0.0519805i | ||||
\(837\) | 1.46546e8 | + | 2.75948e10i | 0.00863844 | + | 1.62663i | ||||
\(838\) | 1.20807e10i | 0.709149i | ||||||||
\(839\) | 6.78505e9i | 0.396630i | 0.980138 | + | 0.198315i | \(0.0635470\pi\) | ||||
−0.980138 | + | 0.198315i | \(0.936453\pi\) | |||||||
\(840\) | 4.52153e7 | + | 2.55425e10i | 0.00263213 | + | 1.48691i | ||||
\(841\) | 1.84899e10 | 1.07189 | ||||||||
\(842\) | −1.21599e10 | −0.702000 | ||||||||
\(843\) | −1.14689e7 | − | 6.47891e9i | −0.000659367 | − | 0.372482i | ||||
\(844\) | 2.41373e8i | 0.0138195i | ||||||||
\(845\) | − | 1.94231e10i | − | 1.10744i | ||||||
\(846\) | 1.26378e7 | + | 3.56960e9i | 0.000717589 | + | 0.202686i | ||||
\(847\) | −1.86846e10 | − | 8.18151e9i | −1.05656 | − | 0.462638i | ||||
\(848\) | − | 1.21768e8i | − | 0.00685719i | ||||||
\(849\) | −3.14873e10 | + | 5.57387e7i | −1.76587 | + | 0.00312594i | ||||
\(850\) | −1.42277e10 | −0.794639 | ||||||||
\(851\) | 4.32839e9i | 0.240754i | ||||||||
\(852\) | −2.79071e8 | + | 494011.i | −0.0154588 | + | 2.73652e-5i | ||||
\(853\) | 1.03168e10i | 0.569148i | 0.958654 | + | 0.284574i | \(0.0918522\pi\) | ||||
−0.958654 | + | 0.284574i | \(0.908148\pi\) | |||||||
\(854\) | 2.60987e10 | 1.43389 | ||||||||
\(855\) | 2.80749e10 | − | 9.93966e7i | 1.53616 | − | 0.00543864i | ||||
\(856\) | 1.93819e9 | 0.105618 | ||||||||
\(857\) | 3.39699e10 | 1.84358 | 0.921788 | − | 0.387694i | \(-0.126728\pi\) | ||||
0.921788 | + | 0.387694i | \(0.126728\pi\) | |||||||
\(858\) | 3.25116e9 | + | 4.95362e9i | 0.175725 | + | 0.267742i | ||||
\(859\) | 9.58191e9 | 0.515794 | 0.257897 | − | 0.966172i | \(-0.416971\pi\) | ||||
0.257897 | + | 0.966172i | \(0.416971\pi\) | |||||||
\(860\) | −5.74050e8 | −0.0307755 | ||||||||
\(861\) | 2.34413e10 | − | 4.14958e7i | 1.25162 | − | 0.00221561i | ||||
\(862\) | −1.36817e10 | −0.727555 | ||||||||
\(863\) | − | 1.46669e10i | − | 0.776784i | −0.921494 | − | 0.388392i | \(-0.873031\pi\) | ||
0.921494 | − | 0.388392i | \(-0.126969\pi\) | |||||||
\(864\) | 1.54773e7 | + | 2.91441e9i | 0.000816391 | + | 0.153728i | ||||
\(865\) | 3.08865e10i | 1.62260i | ||||||||
\(866\) | 2.18829e10 | 1.14496 | ||||||||
\(867\) | −4.22333e7 | − | 2.38580e10i | −0.00220084 | − | 1.24327i | ||||
\(868\) | − | 2.78495e9i | − | 0.144544i | ||||||
\(869\) | −7.37873e9 | + | 4.82415e9i | −0.381428 | + | 0.249374i | ||||
\(870\) | 3.34635e10 | − | 5.92371e7i | 1.72288 | − | 0.00304983i | ||||
\(871\) | 1.02713e10i | 0.526699i | ||||||||
\(872\) | − | 1.90149e10i | − | 0.971151i | ||||||
\(873\) | 1.01642e10 | − | 3.59855e7i | 0.517041 | − | 0.00183053i | ||||
\(874\) | −1.91503e10 | −0.970253 | ||||||||
\(875\) | 1.27504e10 | 0.643423 | ||||||||
\(876\) | −2.77685e9 | + | 4.91557e6i | −0.139569 | + | 0.000247064i | ||||
\(877\) | 1.90740e10i | 0.954870i | 0.878667 | + | 0.477435i | \(0.158433\pi\) | ||||
−0.878667 | + | 0.477435i | \(0.841567\pi\) | |||||||
\(878\) | − | 2.32875e9i | − | 0.116116i | ||||||
\(879\) | −3.76089e7 | − | 2.12456e10i | −0.00186780 | − | 1.05514i | ||||
\(880\) | 1.93318e10 | − | 1.26390e10i | 0.956274 | − | 0.625204i | ||||
\(881\) | − | 1.76902e9i | − | 0.0871599i | −0.999050 | − | 0.0435799i | \(-0.986124\pi\) | ||
0.999050 | − | 0.0435799i | \(-0.0138763\pi\) | |||||||
\(882\) | 6.46690e9 | − | 2.28954e7i | 0.317363 | − | 0.00112359i | ||||
\(883\) | 3.28663e10 | 1.60653 | 0.803264 | − | 0.595623i | \(-0.203095\pi\) | ||||
0.803264 | + | 0.595623i | \(0.203095\pi\) | |||||||
\(884\) | 7.90050e8i | 0.0384655i | ||||||||
\(885\) | 3.61247e7 | + | 2.04072e10i | 0.00175187 | + | 0.989649i | ||||
\(886\) | 3.21878e10i | 1.55480i | ||||||||
\(887\) | 6.93021e9 | 0.333437 | 0.166719 | − | 0.986005i | \(-0.446683\pi\) | ||||
0.166719 | + | 0.986005i | \(0.446683\pi\) | |||||||
\(888\) | −1.12338e7 | − | 6.34609e9i | −0.000538372 | − | 0.304131i | ||||
\(889\) | −2.00654e9 | −0.0957839 | ||||||||
\(890\) | −1.40350e10 | −0.667342 | ||||||||
\(891\) | −1.16788e10 | − | 1.75900e10i | −0.553130 | − | 0.833095i | ||||
\(892\) | −1.63855e7 | −0.000773007 | ||||||||
\(893\) | −5.53570e9 | −0.260131 | ||||||||
\(894\) | −1.80867e7 | − | 1.02173e10i | −0.000846597 | − | 0.478250i | ||||
\(895\) | −1.64780e10 | −0.768289 | ||||||||
\(896\) | 2.15851e10i | 1.00248i | ||||||||
\(897\) | 1.04481e7 | + | 5.90224e9i | 0.000483353 | + | 0.273051i | ||||
\(898\) | 9.39043e9i | 0.432731i | ||||||||
\(899\) | −5.10078e10 | −2.34141 | ||||||||
\(900\) | −9.30476e8 | + | 3.29426e6i | −0.0425458 | + | 0.000150629i | ||||
\(901\) | 2.45892e8i | 0.0111997i | ||||||||
\(902\) | −1.25737e10 | − | 1.92320e10i | −0.570481 | − | 0.872572i | ||||
\(903\) | 1.44848e7 | + | 8.18260e9i | 0.000654645 | + | 0.369815i | ||||
\(904\) | − | 2.72905e10i | − | 1.22863i | ||||||
\(905\) | − | 1.10374e10i | − | 0.494989i | ||||||
\(906\) | 4.33342e9 | − | 7.67100e6i | 0.193589 | − | 0.000342692i | ||||
\(907\) | 2.22914e10 | 0.992002 | 0.496001 | − | 0.868322i | \(-0.334801\pi\) | ||||
0.496001 | + | 0.868322i | \(0.334801\pi\) | |||||||
\(908\) | −1.52596e9 | −0.0676462 | ||||||||
\(909\) | −2.94374e10 | + | 1.04220e8i | −1.29995 | + | 0.00460235i | ||||
\(910\) | − | 1.04618e10i | − | 0.460217i | ||||||
\(911\) | − | 3.24874e10i | − | 1.42364i | −0.702362 | − | 0.711820i | \(-0.747871\pi\) | ||
0.702362 | − | 0.711820i | \(-0.252129\pi\) | |||||||
\(912\) | 2.59012e10 | − | 4.58503e7i | 1.13068 | − | 0.00200152i | ||||
\(913\) | 6.48731e9 | + | 9.92259e9i | 0.282109 | + | 0.431496i | ||||
\(914\) | 3.53157e10i | 1.52988i | ||||||||
\(915\) | 6.61332e7 | + | 3.73592e10i | 0.00285395 | + | 1.61222i | ||||
\(916\) | −1.88346e9 | −0.0809695 | ||||||||
\(917\) | 2.46502e9i | 0.105567i | ||||||||
\(918\) | 1.79111e8 | + | 3.37269e10i | 0.00764140 | + | 1.43889i | ||||
\(919\) | − | 2.67382e9i | − | 0.113639i | −0.998384 | − | 0.0568196i | \(-0.981904\pi\) | ||
0.998384 | − | 0.0568196i | \(-0.0180960\pi\) | |||||||
\(920\) | 2.49400e10 | 1.05594 | ||||||||
\(921\) | 3.61440e10 | − | 6.39820e7i | 1.52450 | − | 0.00269867i | ||||
\(922\) | −1.37734e10 | −0.578739 | ||||||||
\(923\) | 1.59797e9 | 0.0668904 | ||||||||
\(924\) | 1.16920e9 | + | 1.78145e9i | 0.0487571 | + | 0.0742884i | ||||
\(925\) | 3.90725e9 | 0.162321 | ||||||||
\(926\) | 9.30192e7 | 0.00384977 | ||||||||
\(927\) | 2.06079e8 | − | 729604.i | 0.00849680 | − | 3.00821e-5i | ||||
\(928\) | −5.38715e9 | −0.221279 | ||||||||
\(929\) | 4.20467e9i | 0.172059i | 0.996293 | + | 0.0860293i | \(0.0274179\pi\) | ||||
−0.996293 | + | 0.0860293i | \(0.972582\pi\) | |||||||
\(930\) | −4.77592e10 | + | 8.45432e7i | −1.94700 | + | 0.00344658i | ||||
\(931\) | 1.00288e10i | 0.407311i | ||||||||
\(932\) | −1.29163e9 | −0.0522614 | ||||||||
\(933\) | −2.80726e9 | + | 4.96940e6i | −0.113161 | + | 0.000200317i | ||||
\(934\) | 1.29948e9i | 0.0521860i | ||||||||
\(935\) | −3.90376e10 | + | 2.55225e10i | −1.56186 | + | 1.02113i | ||||
\(936\) | −3.06371e7 | − | 8.65356e9i | −0.00122119 | − | 0.344929i | ||||
\(937\) | − | 4.34501e9i | − | 0.172545i | −0.996272 | − | 0.0862725i | \(-0.972504\pi\) | ||
0.996272 | − | 0.0862725i | \(-0.0274956\pi\) | |||||||
\(938\) | − | 4.42524e10i | − | 1.75076i | ||||||
\(939\) | −7.22381e7 | − | 4.08079e10i | −0.00284732 | − | 1.60848i | ||||
\(940\) | 5.15685e8 | 0.0202506 | ||||||||
\(941\) | −1.18732e10 | −0.464520 | −0.232260 | − | 0.972654i | \(-0.574612\pi\) | ||||
−0.232260 | + | 0.972654i | \(0.574612\pi\) | |||||||
\(942\) | −7.33868e7 | − | 4.14568e10i | −0.00286048 | − | 1.61591i | ||||
\(943\) | − | 2.28884e10i | − | 0.888843i | ||||||
\(944\) | 1.88271e10i | 0.728419i | ||||||||
\(945\) | 1.97977e8 | + | 3.72794e10i | 0.00763139 | + | 1.43700i | ||||
\(946\) | 6.71326e9 | − | 4.38907e9i | 0.257819 | − | 0.168560i | ||||
\(947\) | 2.98586e10i | 1.14247i | 0.820786 | + | 0.571236i | \(0.193536\pi\) | ||||
−0.820786 | + | 0.571236i | \(0.806464\pi\) | |||||||
\(948\) | 9.20963e8 | − | 1.63029e6i | 0.0351085 | − | 6.21491e-5i | ||||
\(949\) | 1.59004e10 | 0.603914 | ||||||||
\(950\) | 1.72870e10i | 0.654165i | ||||||||
\(951\) | −2.38561e10 | + | 4.22301e7i | −0.899432 | + | 0.00159217i | ||||
\(952\) | − | 4.75857e10i | − | 1.78750i | ||||||
\(953\) | 4.53039e9 | 0.169555 | 0.0847776 | − | 0.996400i | \(-0.472982\pi\) | ||||
0.0847776 | + | 0.996400i | \(0.472982\pi\) | |||||||
\(954\) | −682066. | − | 1.92652e8i | −2.54336e−5 | − | 0.00718380i | ||||
\(955\) | −4.57468e9 | −0.169961 | ||||||||
\(956\) | −7.49017e8 | −0.0277261 | ||||||||
\(957\) | 3.26281e10 | − | 2.14145e10i | 1.20337 | − | 0.789799i | ||||
\(958\) | −4.17916e10 | −1.53571 | ||||||||
\(959\) | 3.83357e10 | 1.40358 | ||||||||
\(960\) | −3.63632e10 | + | 6.43701e7i | −1.32652 | + | 0.00234820i | ||||
\(961\) | 4.52857e10 | 1.64600 | ||||||||
\(962\) | 2.59927e9i | 0.0941322i | ||||||||
\(963\) | 2.82881e9 | − | 1.00151e7i | 0.102073 | − | 0.000361381i | ||||
\(964\) | 1.62140e9i | 0.0582934i | ||||||||
\(965\) | −2.25890e9 | −0.0809191 | ||||||||
\(966\) | −4.50142e7 | − | 2.54289e10i | −0.00160668 | − | 0.907628i | ||||
\(967\) | − | 2.30257e10i | − | 0.818878i | −0.912337 | − | 0.409439i | \(-0.865724\pi\) | ||
0.912337 | − | 0.409439i | \(-0.134276\pi\) | |||||||
\(968\) | 1.17124e10 | − | 2.67484e10i | 0.415033 | − | 0.947838i | ||||
\(969\) | −5.23037e10 | + | 9.25879e7i | −1.84671 | + | 0.00326904i | ||||
\(970\) | 1.75914e10i | 0.618871i | ||||||||
\(971\) | 4.49193e10i | 1.57458i | 0.616580 | + | 0.787292i | \(0.288518\pi\) | ||||
−0.616580 | + | 0.787292i | \(0.711482\pi\) | |||||||
\(972\) | 1.95227e7 | + | 2.20565e9i | 0.000681879 | + | 0.0770379i | ||||
\(973\) | 1.48078e10 | 0.515342 | ||||||||
\(974\) | 2.69512e10 | 0.934591 | ||||||||
\(975\) | 5.32797e9 | − | 9.43155e6i | 0.184096 | − | 0.000325887i | ||||
\(976\) | 3.44666e10i | 1.18665i | ||||||||
\(977\) | − | 1.50720e10i | − | 0.517059i | −0.966003 | − | 0.258530i | \(-0.916762\pi\) | ||
0.966003 | − | 0.258530i | \(-0.0832380\pi\) | |||||||
\(978\) | 2.18962e7 | + | 1.23693e10i | 0.000748483 | + | 0.422825i | ||||
\(979\) | −1.37005e10 | + | 8.95727e9i | −0.466656 | + | 0.305096i | ||||
\(980\) | − | 9.34247e8i | − | 0.0317081i | ||||||
\(981\) | −9.82551e7 | − | 2.77525e10i | −0.00332287 | − | 0.938557i | ||||
\(982\) | −4.73770e10 | −1.59653 | ||||||||
\(983\) | 1.59581e10i | 0.535851i | 0.963440 | + | 0.267925i | \(0.0863380\pi\) | ||||
−0.963440 | + | 0.267925i | \(0.913662\pi\) | |||||||
\(984\) | 5.94042e7 | + | 3.35579e10i | 0.00198762 | + | 1.12283i | ||||
\(985\) | − | 1.63848e10i | − | 0.546278i | ||||||
\(986\) | −6.23426e10 | −2.07117 | ||||||||
\(987\) | −1.30121e7 | − | 7.35065e9i | −0.000430762 | − | 0.243341i | ||||
\(988\) | 9.59927e8 | 0.0316657 | ||||||||
\(989\) | 7.98959e9 | 0.262626 | ||||||||
\(990\) | 3.05145e10 | − | 2.01047e10i | 0.999502 | − | 0.658529i | ||||
\(991\) | −3.50853e9 | −0.114516 | −0.0572582 | − | 0.998359i | \(-0.518236\pi\) | ||||
−0.0572582 | + | 0.998359i | \(0.518236\pi\) | |||||||
\(992\) | 7.68854e9 | 0.250065 | ||||||||
\(993\) | 4.18330e7 | + | 2.36318e10i | 0.00135580 | + | 0.765906i | ||||
\(994\) | −6.88463e9 | −0.222346 | ||||||||
\(995\) | 6.42324e10i | 2.06716i | ||||||||
\(996\) | −2.19234e6 | − | 1.23847e9i | −7.03071e−5 | − | 0.0397171i | ||||
\(997\) | − | 8.84561e9i | − | 0.282680i | −0.989961 | − | 0.141340i | \(-0.954859\pi\) | ||
0.989961 | − | 0.141340i | \(-0.0451411\pi\) | |||||||
\(998\) | 3.38148e10 | 1.07684 | ||||||||
\(999\) | −4.91878e7 | − | 9.26214e9i | −0.00156091 | − | 0.293922i |
(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 | 33.8.d.b.32.17 | yes | 24 | |
3.2 | odd | 2 | inner | 33.8.d.b.32.8 | yes | 24 | |
11.10 | odd | 2 | inner | 33.8.d.b.32.7 | ✓ | 24 | |
33.32 | even | 2 | inner | 33.8.d.b.32.18 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.8.d.b.32.7 | ✓ | 24 | 11.10 | odd | 2 | inner | |
33.8.d.b.32.8 | yes | 24 | 3.2 | odd | 2 | inner | |
33.8.d.b.32.17 | yes | 24 | 1.1 | even | 1 | trivial | |
33.8.d.b.32.18 | yes | 24 | 33.32 | even | 2 | inner |