Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,11,Mod(3,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(5.08285802139\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 51x^{5} + 30855x^{4} - 121569x^{3} + 12144527x^{2} + 279415575x + 3348211684 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{28}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.2 | ||
Root | \(16.5295 - 8.54130i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.11.d.b.3.1 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −27.0589 | + | 17.0826i | −0.845591 | + | 0.533831i | ||||
\(3\) | 203.867 | 0.838959 | 0.419480 | − | 0.907765i | \(-0.362213\pi\) | ||||
0.419480 | + | 0.907765i | \(0.362213\pi\) | |||||||
\(4\) | 440.370 | − | 924.473i | 0.430049 | − | 0.902806i | ||||
\(5\) | 2088.87i | 0.668438i | 0.942495 | + | 0.334219i | \(0.108473\pi\) | ||||
−0.942495 | + | 0.334219i | \(0.891527\pi\) | |||||||
\(6\) | −5516.42 | + | 3482.58i | −0.709417 | + | 0.447862i | ||||
\(7\) | 25367.2i | 1.50932i | 0.656115 | + | 0.754661i | \(0.272199\pi\) | ||||
−0.656115 | + | 0.754661i | \(0.727801\pi\) | |||||||
\(8\) | 3876.45 | + | 32537.9i | 0.118300 | + | 0.992978i | ||||
\(9\) | −17487.2 | −0.296147 | ||||||||
\(10\) | −35683.3 | − | 56522.5i | −0.356833 | − | 0.565225i | ||||
\(11\) | 132418. | 0.822211 | 0.411106 | − | 0.911588i | \(-0.365143\pi\) | ||||
0.411106 | + | 0.911588i | \(0.365143\pi\) | |||||||
\(12\) | 89777.0 | − | 188470.i | 0.360794 | − | 0.757417i | ||||
\(13\) | 304071.i | 0.818951i | 0.912321 | + | 0.409475i | \(0.134288\pi\) | ||||
−0.912321 | + | 0.409475i | \(0.865712\pi\) | |||||||
\(14\) | −433337. | − | 686408.i | −0.805723 | − | 1.27627i | ||||
\(15\) | 425852.i | 0.560792i | ||||||||
\(16\) | −660724. | − | 814221.i | −0.630116 | − | 0.776501i | ||||
\(17\) | 1.87886e6 | 1.32327 | 0.661635 | − | 0.749826i | \(-0.269863\pi\) | ||||
0.661635 | + | 0.749826i | \(0.269863\pi\) | |||||||
\(18\) | 473185. | − | 298727.i | 0.250420 | − | 0.158093i | ||||
\(19\) | −2.20249e6 | −0.889499 | −0.444750 | − | 0.895655i | \(-0.646707\pi\) | ||||
−0.444750 | + | 0.895655i | \(0.646707\pi\) | |||||||
\(20\) | 1.93110e6 | + | 919876.i | 0.603470 | + | 0.287461i | ||||
\(21\) | 5.17153e6i | 1.26626i | ||||||||
\(22\) | −3.58309e6 | + | 2.26204e6i | −0.695255 | + | 0.438922i | ||||
\(23\) | − | 4.83836e6i | − | 0.751724i | −0.926676 | − | 0.375862i | \(-0.877347\pi\) | ||
0.926676 | − | 0.375862i | \(-0.122653\pi\) | |||||||
\(24\) | 790281. | + | 6.63341e6i | 0.0992488 | + | 0.833068i | ||||
\(25\) | 5.40225e6 | 0.553190 | ||||||||
\(26\) | −5.19431e6 | − | 8.22782e6i | −0.437181 | − | 0.692497i | ||||
\(27\) | −1.56032e7 | −1.08741 | ||||||||
\(28\) | 2.34513e7 | + | 1.11709e7i | 1.36262 | + | 0.649082i | ||||
\(29\) | − | 2.08912e7i | − | 1.01853i | −0.860610 | − | 0.509265i | \(-0.829917\pi\) | ||
0.860610 | − | 0.509265i | \(-0.170083\pi\) | |||||||
\(30\) | −7.27465e6 | − | 1.15231e7i | −0.299368 | − | 0.474201i | ||||
\(31\) | − | 4.27897e7i | − | 1.49462i | −0.664476 | − | 0.747310i | \(-0.731345\pi\) | ||
0.664476 | − | 0.747310i | \(-0.268655\pi\) | |||||||
\(32\) | 3.17875e7 | + | 1.07450e7i | 0.947341 | + | 0.320227i | ||||
\(33\) | 2.69957e7 | 0.689802 | ||||||||
\(34\) | −5.08398e7 | + | 3.20957e7i | −1.11895 | + | 0.706403i | ||||
\(35\) | −5.29887e7 | −1.00889 | ||||||||
\(36\) | −7.70084e6 | + | 1.61664e7i | −0.127358 | + | 0.267363i | ||||
\(37\) | 1.24227e8i | 1.79146i | 0.444602 | + | 0.895728i | \(0.353345\pi\) | ||||
−0.444602 | + | 0.895728i | \(0.646655\pi\) | |||||||
\(38\) | 5.95970e7 | − | 3.76242e7i | 0.752153 | − | 0.474842i | ||||
\(39\) | 6.19900e7i | 0.687066i | ||||||||
\(40\) | −6.79674e7 | + | 8.09740e6i | −0.663744 | + | 0.0790761i | ||||
\(41\) | 1.24377e8 | 1.07355 | 0.536773 | − | 0.843727i | \(-0.319643\pi\) | ||||
0.536773 | + | 0.843727i | \(0.319643\pi\) | |||||||
\(42\) | −8.83432e7 | − | 1.39936e8i | −0.675969 | − | 1.07074i | ||||
\(43\) | 3.15891e7 | 0.214880 | 0.107440 | − | 0.994212i | \(-0.465735\pi\) | ||||
0.107440 | + | 0.994212i | \(0.465735\pi\) | |||||||
\(44\) | 5.83129e7 | − | 1.22417e8i | 0.353591 | − | 0.742297i | ||||
\(45\) | − | 3.65285e7i | − | 0.197956i | ||||||
\(46\) | 8.26517e7 | + | 1.30921e8i | 0.401294 | + | 0.635652i | ||||
\(47\) | 2.91858e7i | 0.127257i | 0.997974 | + | 0.0636286i | \(0.0202673\pi\) | ||||
−0.997974 | + | 0.0636286i | \(0.979733\pi\) | |||||||
\(48\) | −1.34700e8 | − | 1.65993e8i | −0.528641 | − | 0.651453i | ||||
\(49\) | −3.61018e8 | −1.27805 | ||||||||
\(50\) | −1.46179e8 | + | 9.22844e7i | −0.467773 | + | 0.295310i | ||||
\(51\) | 3.83037e8 | 1.11017 | ||||||||
\(52\) | 2.81105e8 | + | 1.33904e8i | 0.739353 | + | 0.352189i | ||||
\(53\) | − | 5.07012e8i | − | 1.21238i | −0.795320 | − | 0.606190i | \(-0.792697\pi\) | ||
0.795320 | − | 0.606190i | \(-0.207303\pi\) | |||||||
\(54\) | 4.22206e8 | − | 2.66543e8i | 0.919508 | − | 0.580496i | ||||
\(55\) | 2.76604e8i | 0.549597i | ||||||||
\(56\) | −8.25395e8 | + | 9.83346e7i | −1.49872 | + | 0.178553i | ||||
\(57\) | −4.49015e8 | −0.746254 | ||||||||
\(58\) | 3.56876e8 | + | 5.65293e8i | 0.543722 | + | 0.861259i | ||||
\(59\) | 1.64080e8 | 0.229506 | 0.114753 | − | 0.993394i | \(-0.463392\pi\) | ||||
0.114753 | + | 0.993394i | \(0.463392\pi\) | |||||||
\(60\) | 3.93688e8 | + | 1.87532e8i | 0.506287 | + | 0.241168i | ||||
\(61\) | 3.21644e7i | 0.0380826i | 0.999819 | + | 0.0190413i | \(0.00606140\pi\) | ||||
−0.999819 | + | 0.0190413i | \(0.993939\pi\) | |||||||
\(62\) | 7.30959e8 | + | 1.15784e9i | 0.797874 | + | 1.26384i | ||||
\(63\) | − | 4.43601e8i | − | 0.446982i | ||||||
\(64\) | −1.04369e9 | + | 2.52263e8i | −0.972010 | + | 0.234938i | ||||
\(65\) | −6.35164e8 | −0.547418 | ||||||||
\(66\) | −7.30473e8 | + | 4.61156e8i | −0.583290 | + | 0.368238i | ||||
\(67\) | −3.70351e8 | −0.274309 | −0.137154 | − | 0.990550i | \(-0.543796\pi\) | ||||
−0.137154 | + | 0.990550i | \(0.543796\pi\) | |||||||
\(68\) | 8.27392e8 | − | 1.73695e9i | 0.569071 | − | 1.19466i | ||||
\(69\) | − | 9.86382e8i | − | 0.630666i | ||||||
\(70\) | 1.43382e9 | − | 9.05184e8i | 0.853107 | − | 0.538576i | ||||
\(71\) | 3.20647e8i | 0.177719i | 0.996044 | + | 0.0888597i | \(0.0283223\pi\) | ||||
−0.996044 | + | 0.0888597i | \(0.971678\pi\) | |||||||
\(72\) | −6.77883e7 | − | 5.68997e8i | −0.0350342 | − | 0.294068i | ||||
\(73\) | 2.69897e9 | 1.30192 | 0.650959 | − | 0.759113i | \(-0.274367\pi\) | ||||
0.650959 | + | 0.759113i | \(0.274367\pi\) | |||||||
\(74\) | −2.12211e9 | − | 3.36144e9i | −0.956335 | − | 1.51484i | ||||
\(75\) | 1.10134e9 | 0.464104 | ||||||||
\(76\) | −9.69910e8 | + | 2.03614e9i | −0.382528 | + | 0.803045i | ||||
\(77\) | 3.35907e9i | 1.24098i | ||||||||
\(78\) | −1.05895e9 | − | 1.67738e9i | −0.366777 | − | 0.580977i | ||||
\(79\) | 1.89446e9i | 0.615673i | 0.951439 | + | 0.307837i | \(0.0996050\pi\) | ||||
−0.951439 | + | 0.307837i | \(0.900395\pi\) | |||||||
\(80\) | 1.70080e9 | − | 1.38017e9i | 0.519043 | − | 0.421193i | ||||
\(81\) | −2.14838e9 | −0.616150 | ||||||||
\(82\) | −3.36551e9 | + | 2.12468e9i | −0.907781 | + | 0.573092i | ||||
\(83\) | −2.20629e9 | −0.560108 | −0.280054 | − | 0.959984i | \(-0.590352\pi\) | ||||
−0.280054 | + | 0.959984i | \(0.590352\pi\) | |||||||
\(84\) | 4.78094e9 | + | 2.27739e9i | 1.14319 | + | 0.544554i | ||||
\(85\) | 3.92468e9i | 0.884525i | ||||||||
\(86\) | −8.54767e8 | + | 5.39624e8i | −0.181700 | + | 0.114709i | ||||
\(87\) | − | 4.25903e9i | − | 0.854504i | ||||||
\(88\) | 5.13312e8 | + | 4.30860e9i | 0.0972675 | + | 0.816438i | ||||
\(89\) | 9.12704e9 | 1.63448 | 0.817241 | − | 0.576296i | \(-0.195503\pi\) | ||||
0.817241 | + | 0.576296i | \(0.195503\pi\) | |||||||
\(90\) | 6.24001e8 | + | 9.88421e8i | 0.105675 | + | 0.167390i | ||||
\(91\) | −7.71341e9 | −1.23606 | ||||||||
\(92\) | −4.47293e9 | − | 2.13067e9i | −0.678661 | − | 0.323278i | ||||
\(93\) | − | 8.72341e9i | − | 1.25392i | ||||||
\(94\) | −4.98569e8 | − | 7.89736e8i | −0.0679338 | − | 0.107608i | ||||
\(95\) | − | 4.60071e9i | − | 0.594575i | ||||||
\(96\) | 6.48042e9 | + | 2.19056e9i | 0.794780 | + | 0.268658i | ||||
\(97\) | −1.89466e9 | −0.220634 | −0.110317 | − | 0.993896i | \(-0.535187\pi\) | ||||
−0.110317 | + | 0.993896i | \(0.535187\pi\) | |||||||
\(98\) | 9.76876e9 | − | 6.16713e9i | 1.08071 | − | 0.682264i | ||||
\(99\) | −2.31562e9 | −0.243496 | ||||||||
\(100\) | 2.37899e9 | − | 4.99423e9i | 0.237899 | − | 0.499423i | ||||
\(101\) | 5.17098e9i | 0.492001i | 0.969270 | + | 0.246000i | \(0.0791165\pi\) | ||||
−0.969270 | + | 0.246000i | \(0.920884\pi\) | |||||||
\(102\) | −1.03646e10 | + | 6.54326e9i | −0.938750 | + | 0.592643i | ||||
\(103\) | − | 9.68439e9i | − | 0.835384i | −0.908589 | − | 0.417692i | \(-0.862839\pi\) | ||
0.908589 | − | 0.417692i | \(-0.137161\pi\) | |||||||
\(104\) | −9.89382e9 | + | 1.17871e9i | −0.813200 | + | 0.0968817i | ||||
\(105\) | −1.08027e10 | −0.846416 | ||||||||
\(106\) | 8.66107e9 | + | 1.37192e10i | 0.647206 | + | 1.02518i | ||||
\(107\) | 1.63929e10 | 1.16879 | 0.584394 | − | 0.811470i | \(-0.301332\pi\) | ||||
0.584394 | + | 0.811470i | \(0.301332\pi\) | |||||||
\(108\) | −6.87119e9 | + | 1.44247e10i | −0.467642 | + | 0.981724i | ||||
\(109\) | − | 8.06193e9i | − | 0.523970i | −0.965072 | − | 0.261985i | \(-0.915623\pi\) | ||
0.965072 | − | 0.261985i | \(-0.0843771\pi\) | |||||||
\(110\) | −4.72511e9 | − | 7.48460e9i | −0.293392 | − | 0.464735i | ||||
\(111\) | 2.53257e10i | 1.50296i | ||||||||
\(112\) | 2.06545e10 | − | 1.67607e10i | 1.17199 | − | 0.951047i | ||||
\(113\) | −7.36232e9 | −0.399597 | −0.199799 | − | 0.979837i | \(-0.564029\pi\) | ||||
−0.199799 | + | 0.979837i | \(0.564029\pi\) | |||||||
\(114\) | 1.21499e10 | − | 7.67034e9i | 0.631026 | − | 0.398373i | ||||
\(115\) | 1.01067e10 | 0.502481 | ||||||||
\(116\) | −1.93133e10 | − | 9.19986e9i | −0.919534 | − | 0.438017i | ||||
\(117\) | − | 5.31734e9i | − | 0.242530i | ||||||
\(118\) | −4.43982e9 | + | 2.80291e9i | −0.194069 | + | 0.122518i | ||||
\(119\) | 4.76612e10i | 1.99724i | ||||||||
\(120\) | −1.38563e10 | + | 1.65079e9i | −0.556855 | + | 0.0663417i | ||||
\(121\) | −8.40292e9 | −0.323969 | ||||||||
\(122\) | −5.49452e8 | − | 8.70335e8i | −0.0203297 | − | 0.0322023i | ||||
\(123\) | 2.53564e10 | 0.900662 | ||||||||
\(124\) | −3.95579e10 | − | 1.88433e10i | −1.34935 | − | 0.642760i | ||||
\(125\) | 3.16837e10i | 1.03821i | ||||||||
\(126\) | 7.57785e9 | + | 1.20034e10i | 0.238613 | + | 0.377964i | ||||
\(127\) | − | 5.32119e10i | − | 1.61061i | −0.592861 | − | 0.805305i | \(-0.702002\pi\) | ||
0.592861 | − | 0.805305i | \(-0.297998\pi\) | |||||||
\(128\) | 2.39318e10 | − | 2.46549e10i | 0.696506 | − | 0.717551i | ||||
\(129\) | 6.43998e9 | 0.180275 | ||||||||
\(130\) | 1.71868e10 | − | 1.08502e10i | 0.462892 | − | 0.292229i | ||||
\(131\) | −1.66260e10 | −0.430955 | −0.215477 | − | 0.976509i | \(-0.569131\pi\) | ||||
−0.215477 | + | 0.976509i | \(0.569131\pi\) | |||||||
\(132\) | 1.18881e10 | − | 2.49568e10i | 0.296649 | − | 0.622757i | ||||
\(133\) | − | 5.58709e10i | − | 1.34254i | ||||||
\(134\) | 1.00213e10 | − | 6.32655e9i | 0.231953 | − | 0.146434i | ||||
\(135\) | − | 3.25931e10i | − | 0.726870i | ||||||
\(136\) | 7.28329e9 | + | 6.11340e10i | 0.156543 | + | 1.31398i | ||||
\(137\) | −8.03849e9 | −0.166560 | −0.0832802 | − | 0.996526i | \(-0.526540\pi\) | ||||
−0.0832802 | + | 0.996526i | \(0.526540\pi\) | |||||||
\(138\) | 1.68500e10 | + | 2.66904e10i | 0.336669 | + | 0.533286i | ||||
\(139\) | −2.95171e10 | −0.568852 | −0.284426 | − | 0.958698i | \(-0.591803\pi\) | ||||
−0.284426 | + | 0.958698i | \(0.591803\pi\) | |||||||
\(140\) | −2.33346e10 | + | 4.89866e10i | −0.433871 | + | 0.910830i | ||||
\(141\) | 5.95003e9i | 0.106764i | ||||||||
\(142\) | −5.47747e9 | − | 8.67635e9i | −0.0948721 | − | 0.150278i | ||||
\(143\) | 4.02644e10i | 0.673350i | ||||||||
\(144\) | 1.15542e10 | + | 1.42384e10i | 0.186607 | + | 0.229959i | ||||
\(145\) | 4.36390e10 | 0.680824 | ||||||||
\(146\) | −7.30312e10 | + | 4.61054e10i | −1.10089 | + | 0.695004i | ||||
\(147\) | −7.35998e10 | −1.07223 | ||||||||
\(148\) | 1.14844e11 | + | 5.47057e10i | 1.61734 | + | 0.770414i | ||||
\(149\) | 4.99611e10i | 0.680301i | 0.940371 | + | 0.340150i | \(0.110478\pi\) | ||||
−0.940371 | + | 0.340150i | \(0.889522\pi\) | |||||||
\(150\) | −2.98011e10 | + | 1.88138e10i | −0.392442 | + | 0.247753i | ||||
\(151\) | − | 2.89845e10i | − | 0.369217i | −0.982812 | − | 0.184608i | \(-0.940898\pi\) | ||
0.982812 | − | 0.184608i | \(-0.0591016\pi\) | |||||||
\(152\) | −8.53784e9 | − | 7.16644e10i | −0.105228 | − | 0.883253i | ||||
\(153\) | −3.28559e10 | −0.391883 | ||||||||
\(154\) | −5.73816e10 | − | 9.08928e10i | −0.662474 | − | 1.04936i | ||||
\(155\) | 8.93820e10 | 0.999061 | ||||||||
\(156\) | 5.73081e10 | + | 2.72985e10i | 0.620287 | + | 0.295472i | ||||
\(157\) | − | 7.19130e8i | − | 0.00753892i | −0.999993 | − | 0.00376946i | \(-0.998800\pi\) | ||
0.999993 | − | 0.00376946i | \(-0.00119986\pi\) | |||||||
\(158\) | −3.23623e10 | − | 5.12621e10i | −0.328665 | − | 0.520608i | ||||
\(159\) | − | 1.03363e11i | − | 1.01714i | ||||||
\(160\) | −2.24450e10 | + | 6.63999e10i | −0.214052 | + | 0.633239i | ||||
\(161\) | 1.22735e11 | 1.13459 | ||||||||
\(162\) | 5.81329e10 | − | 3.66999e10i | 0.521011 | − | 0.328920i | ||||
\(163\) | −1.44355e11 | −1.25456 | −0.627281 | − | 0.778793i | \(-0.715832\pi\) | ||||
−0.627281 | + | 0.778793i | \(0.715832\pi\) | |||||||
\(164\) | 5.47719e10 | − | 1.14983e11i | 0.461677 | − | 0.969203i | ||||
\(165\) | 5.63904e10i | 0.461090i | ||||||||
\(166\) | 5.96998e10 | − | 3.76891e10i | 0.473622 | − | 0.299003i | ||||
\(167\) | 6.02212e10i | 0.463625i | 0.972760 | + | 0.231813i | \(0.0744656\pi\) | ||||
−0.972760 | + | 0.231813i | \(0.925534\pi\) | |||||||
\(168\) | −1.68271e11 | + | 2.00472e10i | −1.25737 | + | 0.149798i | ||||
\(169\) | 4.53996e10 | 0.329320 | ||||||||
\(170\) | −6.70437e10 | − | 1.06198e11i | −0.472187 | − | 0.747946i | ||||
\(171\) | 3.85154e10 | 0.263423 | ||||||||
\(172\) | 1.39109e10 | − | 2.92033e10i | 0.0924087 | − | 0.193994i | ||||
\(173\) | 9.37427e9i | 0.0604932i | 0.999542 | + | 0.0302466i | \(0.00962926\pi\) | ||||
−0.999542 | + | 0.0302466i | \(0.990371\pi\) | |||||||
\(174\) | 7.27552e10 | + | 1.15245e11i | 0.456161 | + | 0.722561i | ||||
\(175\) | 1.37040e11i | 0.834942i | ||||||||
\(176\) | −8.74917e10 | − | 1.07817e11i | −0.518088 | − | 0.638448i | ||||
\(177\) | 3.34504e10 | 0.192546 | ||||||||
\(178\) | −2.46968e11 | + | 1.55914e11i | −1.38210 | + | 0.872537i | ||||
\(179\) | 4.54078e10 | 0.247096 | 0.123548 | − | 0.992339i | \(-0.460573\pi\) | ||||
0.123548 | + | 0.992339i | \(0.460573\pi\) | |||||||
\(180\) | −3.37696e10 | − | 1.60861e10i | −0.178716 | − | 0.0851308i | ||||
\(181\) | 2.09295e11i | 1.07737i | 0.842506 | + | 0.538686i | \(0.181079\pi\) | ||||
−0.842506 | + | 0.538686i | \(0.818921\pi\) | |||||||
\(182\) | 2.08717e11 | − | 1.31765e11i | 1.04520 | − | 0.659847i | ||||
\(183\) | 6.55727e9i | 0.0319498i | ||||||||
\(184\) | 1.57430e11 | − | 1.87556e10i | 0.746446 | − | 0.0889289i | ||||
\(185\) | −2.59493e11 | −1.19748 | ||||||||
\(186\) | 1.49018e11 | + | 2.36046e11i | 0.669384 | + | 1.06031i | ||||
\(187\) | 2.48794e11 | 1.08801 | ||||||||
\(188\) | 2.69815e10 | + | 1.28526e10i | 0.114889 | + | 0.0547268i | ||||
\(189\) | − | 3.95809e11i | − | 1.64126i | ||||||
\(190\) | 7.85921e10 | + | 1.24490e11i | 0.317403 | + | 0.502768i | ||||
\(191\) | 9.24953e10i | 0.363876i | 0.983310 | + | 0.181938i | \(0.0582370\pi\) | ||||
−0.983310 | + | 0.181938i | \(0.941763\pi\) | |||||||
\(192\) | −2.12774e11 | + | 5.14281e10i | −0.815477 | + | 0.197104i | ||||
\(193\) | −2.90187e11 | −1.08366 | −0.541828 | − | 0.840490i | \(-0.682268\pi\) | ||||
−0.541828 | + | 0.840490i | \(0.682268\pi\) | |||||||
\(194\) | 5.12675e10 | − | 3.23657e10i | 0.186566 | − | 0.117781i | ||||
\(195\) | −1.29489e11 | −0.459261 | ||||||||
\(196\) | −1.58982e11 | + | 3.33752e11i | −0.549625 | + | 1.15383i | ||||
\(197\) | − | 5.37709e11i | − | 1.81224i | −0.423019 | − | 0.906121i | \(-0.639030\pi\) | ||
0.423019 | − | 0.906121i | \(-0.360970\pi\) | |||||||
\(198\) | 6.26581e10 | − | 3.95568e10i | 0.205898 | − | 0.129985i | ||||
\(199\) | − | 2.72659e11i | − | 0.873683i | −0.899539 | − | 0.436841i | \(-0.856097\pi\) | ||
0.899539 | − | 0.436841i | \(-0.143903\pi\) | |||||||
\(200\) | 2.09416e10 | + | 1.75778e11i | 0.0654424 | + | 0.549306i | ||||
\(201\) | −7.55024e10 | −0.230134 | ||||||||
\(202\) | −8.83337e10 | − | 1.39921e11i | −0.262645 | − | 0.416032i | ||||
\(203\) | 5.29951e11 | 1.53729 | ||||||||
\(204\) | 1.68678e11 | − | 3.54107e11i | 0.477428 | − | 1.00227i | ||||
\(205\) | 2.59807e11i | 0.717599i | ||||||||
\(206\) | 1.65434e11 | + | 2.62049e11i | 0.445954 | + | 0.706393i | ||||
\(207\) | 8.46093e10i | 0.222621i | ||||||||
\(208\) | 2.47581e11 | − | 2.00907e11i | 0.635916 | − | 0.516034i | ||||
\(209\) | −2.91649e11 | −0.731356 | ||||||||
\(210\) | 2.92308e11 | − | 1.84537e11i | 0.715722 | − | 0.451843i | ||||
\(211\) | −6.55845e11 | −1.56815 | −0.784077 | − | 0.620664i | \(-0.786863\pi\) | ||||
−0.784077 | + | 0.620664i | \(0.786863\pi\) | |||||||
\(212\) | −4.68719e11 | − | 2.23273e11i | −1.09454 | − | 0.521383i | ||||
\(213\) | 6.53693e10i | 0.149099i | ||||||||
\(214\) | −4.43573e11 | + | 2.80033e11i | −0.988317 | + | 0.623935i | ||||
\(215\) | 6.59855e10i | 0.143634i | ||||||||
\(216\) | −6.04851e10 | − | 5.07696e11i | −0.128641 | − | 1.07978i | ||||
\(217\) | 1.08545e12 | 2.25586 | ||||||||
\(218\) | 1.37719e11 | + | 2.18147e11i | 0.279711 | + | 0.443064i | ||||
\(219\) | 5.50231e11 | 1.09226 | ||||||||
\(220\) | 2.55713e11 | + | 1.21808e11i | 0.496180 | + | 0.236354i | ||||
\(221\) | 5.71305e11i | 1.08369i | ||||||||
\(222\) | −4.32629e11 | − | 6.85287e11i | −0.802326 | − | 1.27089i | ||||
\(223\) | 1.20654e11i | 0.218784i | 0.993999 | + | 0.109392i | \(0.0348904\pi\) | ||||
−0.993999 | + | 0.109392i | \(0.965110\pi\) | |||||||
\(224\) | −2.72572e11 | + | 8.06359e11i | −0.483326 | + | 1.42984i | ||||
\(225\) | −9.44702e10 | −0.163826 | ||||||||
\(226\) | 1.99216e11 | − | 1.25767e11i | 0.337896 | − | 0.213317i | ||||
\(227\) | −1.01745e12 | −1.68805 | −0.844024 | − | 0.536305i | \(-0.819820\pi\) | ||||
−0.844024 | + | 0.536305i | \(0.819820\pi\) | |||||||
\(228\) | −1.97733e11 | + | 4.15102e11i | −0.320926 | + | 0.673722i | ||||
\(229\) | 4.00233e11i | 0.635529i | 0.948170 | + | 0.317764i | \(0.102932\pi\) | ||||
−0.948170 | + | 0.317764i | \(0.897068\pi\) | |||||||
\(230\) | −2.73476e11 | + | 1.72648e11i | −0.424894 | + | 0.268240i | ||||
\(231\) | 6.84804e11i | 1.04113i | ||||||||
\(232\) | 6.79756e11 | − | 8.09837e10i | 1.01138 | − | 0.120492i | ||||
\(233\) | −2.50256e8 | −0.000364422 | −0.000182211 | − | 1.00000i | \(-0.500058\pi\) | ||||
−0.000182211 | 1.00000i | \(0.500058\pi\) | ||||||||
\(234\) | 9.08340e10 | + | 1.43882e11i | 0.129470 | + | 0.205081i | ||||
\(235\) | −6.09653e10 | −0.0850636 | ||||||||
\(236\) | 7.22558e10 | − | 1.51687e11i | 0.0986990 | − | 0.207200i | ||||
\(237\) | 3.86218e11i | 0.516525i | ||||||||
\(238\) | −8.14178e11 | − | 1.28966e12i | −1.06619 | − | 1.68885i | ||||
\(239\) | − | 1.38040e12i | − | 1.77017i | −0.465427 | − | 0.885086i | \(-0.654099\pi\) | ||
0.465427 | − | 0.885086i | \(-0.345901\pi\) | |||||||
\(240\) | 3.46737e11 | − | 2.81371e11i | 0.435456 | − | 0.353364i | ||||
\(241\) | 8.00760e11 | 0.984957 | 0.492479 | − | 0.870325i | \(-0.336091\pi\) | ||||
0.492479 | + | 0.870325i | \(0.336091\pi\) | |||||||
\(242\) | 2.27374e11 | − | 1.43544e11i | 0.273945 | − | 0.172945i | ||||
\(243\) | 4.83370e11 | 0.570490 | ||||||||
\(244\) | 2.97351e10 | + | 1.41643e10i | 0.0343812 | + | 0.0163774i | ||||
\(245\) | − | 7.54120e11i | − | 0.854299i | ||||||
\(246\) | −6.86116e11 | + | 4.33153e11i | −0.761591 | + | 0.480801i | ||||
\(247\) | − | 6.69712e11i | − | 0.728456i | ||||||
\(248\) | 1.39229e12 | − | 1.65872e11i | 1.48412 | − | 0.176813i | ||||
\(249\) | −4.49790e11 | −0.469908 | ||||||||
\(250\) | −5.41240e11 | − | 8.57327e11i | −0.554230 | − | 0.877903i | ||||
\(251\) | 4.85659e11 | 0.487486 | 0.243743 | − | 0.969840i | \(-0.421625\pi\) | ||||
0.243743 | + | 0.969840i | \(0.421625\pi\) | |||||||
\(252\) | −4.10097e11 | − | 1.95349e11i | −0.403537 | − | 0.192224i | ||||
\(253\) | − | 6.40685e11i | − | 0.618076i | ||||||
\(254\) | 9.08997e11 | + | 1.43986e12i | 0.859793 | + | 1.36192i | ||||
\(255\) | 8.00114e11i | 0.742080i | ||||||||
\(256\) | −2.26399e11 | + | 1.07595e12i | −0.205908 | + | 0.978571i | ||||
\(257\) | −5.41553e11 | −0.483031 | −0.241516 | − | 0.970397i | \(-0.577644\pi\) | ||||
−0.241516 | + | 0.970397i | \(0.577644\pi\) | |||||||
\(258\) | −1.74259e11 | + | 1.10012e11i | −0.152439 | + | 0.0962365i | ||||
\(259\) | −3.15128e12 | −2.70389 | ||||||||
\(260\) | −2.79707e11 | + | 5.87192e11i | −0.235416 | + | 0.494212i | ||||
\(261\) | 3.65329e11i | 0.301635i | ||||||||
\(262\) | 4.49882e11 | − | 2.84015e11i | 0.364411 | − | 0.230057i | ||||
\(263\) | 1.04908e11i | 0.0833736i | 0.999131 | + | 0.0416868i | \(0.0132732\pi\) | ||||
−0.999131 | + | 0.0416868i | \(0.986727\pi\) | |||||||
\(264\) | 1.04647e11 | + | 8.78382e11i | 0.0816035 | + | 0.684958i | ||||
\(265\) | 1.05908e12 | 0.810401 | ||||||||
\(266\) | 9.54420e11 | + | 1.51181e12i | 0.716690 | + | 1.13524i | ||||
\(267\) | 1.86070e12 | 1.37126 | ||||||||
\(268\) | −1.63092e11 | + | 3.42379e11i | −0.117966 | + | 0.247647i | ||||
\(269\) | − | 1.43692e12i | − | 1.02017i | −0.860125 | − | 0.510083i | \(-0.829615\pi\) | ||
0.860125 | − | 0.510083i | \(-0.170385\pi\) | |||||||
\(270\) | 5.56774e11 | + | 8.81933e11i | 0.388025 | + | 0.614635i | ||||
\(271\) | − | 1.21213e12i | − | 0.829280i | −0.909985 | − | 0.414640i | \(-0.863907\pi\) | ||
0.909985 | − | 0.414640i | \(-0.136093\pi\) | |||||||
\(272\) | −1.24140e12 | − | 1.52980e12i | −0.833814 | − | 1.02752i | ||||
\(273\) | −1.57251e12 | −1.03700 | ||||||||
\(274\) | 2.17513e11 | − | 1.37318e11i | 0.140842 | − | 0.0889151i | ||||
\(275\) | 7.15355e11 | 0.454839 | ||||||||
\(276\) | −9.11883e11 | − | 4.34373e11i | −0.569369 | − | 0.271217i | ||||
\(277\) | 2.87127e12i | 1.76066i | 0.474362 | + | 0.880330i | \(0.342679\pi\) | ||||
−0.474362 | + | 0.880330i | \(0.657321\pi\) | |||||||
\(278\) | 7.98700e11 | − | 5.04228e11i | 0.481016 | − | 0.303671i | ||||
\(279\) | 7.48272e11i | 0.442627i | ||||||||
\(280\) | −2.05408e11 | − | 1.72414e12i | −0.119351 | − | 1.00180i | ||||
\(281\) | −1.27196e12 | −0.726007 | −0.363004 | − | 0.931788i | \(-0.618249\pi\) | ||||
−0.363004 | + | 0.931788i | \(0.618249\pi\) | |||||||
\(282\) | −1.01642e11 | − | 1.61001e11i | −0.0569937 | − | 0.0902784i | ||||
\(283\) | 2.45158e12 | 1.35056 | 0.675279 | − | 0.737562i | \(-0.264023\pi\) | ||||
0.675279 | + | 0.737562i | \(0.264023\pi\) | |||||||
\(284\) | 2.96429e11 | + | 1.41203e11i | 0.160446 | + | 0.0764281i | ||||
\(285\) | − | 9.37934e11i | − | 0.498825i | ||||||
\(286\) | −6.87820e11 | − | 1.08951e12i | −0.359455 | − | 0.569379i | ||||
\(287\) | 3.15509e12i | 1.62033i | ||||||||
\(288\) | −5.55874e11 | − | 1.87901e11i | −0.280552 | − | 0.0948345i | ||||
\(289\) | 1.51410e12 | 0.751045 | ||||||||
\(290\) | −1.18082e12 | + | 7.45467e11i | −0.575699 | + | 0.363445i | ||||
\(291\) | −3.86259e11 | −0.185103 | ||||||||
\(292\) | 1.18855e12 | − | 2.49512e12i | 0.559888 | − | 1.17538i | ||||
\(293\) | − | 2.61648e12i | − | 1.21165i | −0.795596 | − | 0.605827i | \(-0.792842\pi\) | ||
0.795596 | − | 0.605827i | \(-0.207158\pi\) | |||||||
\(294\) | 1.99153e12 | − | 1.25727e12i | 0.906672 | − | 0.572392i | ||||
\(295\) | 3.42741e11i | 0.153411i | ||||||||
\(296\) | −4.04208e12 | + | 4.81559e11i | −1.77888 | + | 0.211929i | ||||
\(297\) | −2.06615e12 | −0.894085 | ||||||||
\(298\) | −8.53466e11 | − | 1.35189e12i | −0.363166 | − | 0.575256i | ||||
\(299\) | 1.47120e12 | 0.615625 | ||||||||
\(300\) | 4.84998e11 | − | 1.01816e12i | 0.199588 | − | 0.418996i | ||||
\(301\) | 8.01326e11i | 0.324322i | ||||||||
\(302\) | 4.95130e11 | + | 7.84289e11i | 0.197099 | + | 0.312206i | ||||
\(303\) | 1.05419e12i | 0.412769i | ||||||||
\(304\) | 1.45524e12 | + | 1.79331e12i | 0.560488 | + | 0.690697i | ||||
\(305\) | −6.71873e10 | −0.0254559 | ||||||||
\(306\) | 8.89046e11 | − | 5.61264e11i | 0.331373 | − | 0.209199i | ||||
\(307\) | −4.14347e11 | −0.151940 | −0.0759700 | − | 0.997110i | \(-0.524205\pi\) | ||||
−0.0759700 | + | 0.997110i | \(0.524205\pi\) | |||||||
\(308\) | 3.10537e12 | + | 1.47923e12i | 1.12036 | + | 0.533683i | ||||
\(309\) | − | 1.97433e12i | − | 0.700853i | ||||||
\(310\) | −2.41858e12 | + | 1.52688e12i | −0.844797 | + | 0.533329i | ||||
\(311\) | − | 1.73263e12i | − | 0.595530i | −0.954639 | − | 0.297765i | \(-0.903759\pi\) | ||
0.954639 | − | 0.297765i | \(-0.0962413\pi\) | |||||||
\(312\) | −2.01702e12 | + | 2.40301e11i | −0.682242 | + | 0.0812798i | ||||
\(313\) | −5.44579e11 | −0.181276 | −0.0906378 | − | 0.995884i | \(-0.528891\pi\) | ||||
−0.0906378 | + | 0.995884i | \(0.528891\pi\) | |||||||
\(314\) | 1.22846e10 | + | 1.94589e10i | 0.00402451 | + | 0.00637485i | ||||
\(315\) | 9.26624e11 | 0.298780 | ||||||||
\(316\) | 1.75138e12 | + | 8.34264e11i | 0.555833 | + | 0.264770i | ||||
\(317\) | 5.23802e12i | 1.63633i | 0.574985 | + | 0.818164i | \(0.305008\pi\) | ||||
−0.574985 | + | 0.818164i | \(0.694992\pi\) | |||||||
\(318\) | 1.76571e12 | + | 2.79689e12i | 0.542979 | + | 0.860082i | ||||
\(319\) | − | 2.76637e12i | − | 0.837446i | ||||||
\(320\) | −5.26945e11 | − | 2.18013e12i | −0.157042 | − | 0.649729i | ||||
\(321\) | 3.34197e12 | 0.980566 | ||||||||
\(322\) | −3.32109e12 | + | 2.09664e12i | −0.959403 | + | 0.605681i | ||||
\(323\) | −4.13816e12 | −1.17705 | ||||||||
\(324\) | −9.46083e11 | + | 1.98612e12i | −0.264975 | + | 0.556263i | ||||
\(325\) | 1.64267e12i | 0.453036i | ||||||||
\(326\) | 3.90608e12 | − | 2.46595e12i | 1.06085 | − | 0.669724i | ||||
\(327\) | − | 1.64356e12i | − | 0.439589i | ||||||
\(328\) | 4.82141e11 | + | 4.04697e12i | 0.127000 | + | 1.06601i | ||||
\(329\) | −7.40361e11 | −0.192072 | ||||||||
\(330\) | −9.63294e11 | − | 1.52586e12i | −0.246144 | − | 0.389893i | ||||
\(331\) | −6.72784e12 | −1.69331 | −0.846653 | − | 0.532145i | \(-0.821386\pi\) | ||||
−0.846653 | + | 0.532145i | \(0.821386\pi\) | |||||||
\(332\) | −9.71583e11 | + | 2.03965e12i | −0.240874 | + | 0.505669i | ||||
\(333\) | − | 2.17238e12i | − | 0.530535i | ||||||
\(334\) | −1.02873e12 | − | 1.62952e12i | −0.247497 | − | 0.392037i | ||||
\(335\) | − | 7.73615e11i | − | 0.183358i | ||||||
\(336\) | 4.21077e12 | − | 3.41696e12i | 0.983252 | − | 0.797890i | ||||
\(337\) | 5.42632e12 | 1.24841 | 0.624203 | − | 0.781262i | \(-0.285424\pi\) | ||||
0.624203 | + | 0.781262i | \(0.285424\pi\) | |||||||
\(338\) | −1.22846e12 | + | 7.75542e11i | −0.278470 | + | 0.175801i | ||||
\(339\) | −1.50093e12 | −0.335246 | ||||||||
\(340\) | 3.62826e12 | + | 1.72831e12i | 0.798554 | + | 0.380389i | ||||
\(341\) | − | 5.66612e12i | − | 1.22889i | ||||||
\(342\) | −1.04218e12 | + | 6.57942e11i | −0.222748 | + | 0.140623i | ||||
\(343\) | − | 1.99242e12i | − | 0.419671i | ||||||
\(344\) | 1.22454e11 | + | 1.02784e12i | 0.0254202 | + | 0.213371i | ||||
\(345\) | 2.06042e12 | 0.421561 | ||||||||
\(346\) | −1.60137e11 | − | 2.53657e11i | −0.0322932 | − | 0.0511525i | ||||
\(347\) | 5.28169e12 | 1.04985 | 0.524923 | − | 0.851149i | \(-0.324094\pi\) | ||||
0.524923 | + | 0.851149i | \(0.324094\pi\) | |||||||
\(348\) | −3.93736e12 | − | 1.87555e12i | −0.771451 | − | 0.367479i | ||||
\(349\) | − | 4.86322e11i | − | 0.0939283i | −0.998897 | − | 0.0469641i | \(-0.985045\pi\) | ||
0.998897 | − | 0.0469641i | \(-0.0149547\pi\) | |||||||
\(350\) | −2.34100e12 | − | 3.70815e12i | −0.445718 | − | 0.706020i | ||||
\(351\) | − | 4.74448e12i | − | 0.890539i | ||||||
\(352\) | 4.20923e12 | + | 1.42284e12i | 0.778914 | + | 0.263295i | ||||
\(353\) | −3.75886e12 | −0.685777 | −0.342888 | − | 0.939376i | \(-0.611405\pi\) | ||||
−0.342888 | + | 0.939376i | \(0.611405\pi\) | |||||||
\(354\) | −9.05133e11 | + | 5.71420e11i | −0.162816 | + | 0.102787i | ||||
\(355\) | −6.69789e11 | −0.118794 | ||||||||
\(356\) | 4.01928e12 | − | 8.43770e12i | 0.702907 | − | 1.47562i | ||||
\(357\) | 9.71656e12i | 1.67560i | ||||||||
\(358\) | −1.22869e12 | + | 7.75682e11i | −0.208942 | + | 0.131907i | ||||
\(359\) | 4.14060e12i | 0.694370i | 0.937797 | + | 0.347185i | \(0.112862\pi\) | ||||
−0.937797 | + | 0.347185i | \(0.887138\pi\) | |||||||
\(360\) | 1.18856e12 | − | 1.41601e11i | 0.196566 | − | 0.0234182i | ||||
\(361\) | −1.28011e12 | −0.208791 | ||||||||
\(362\) | −3.57530e12 | − | 5.66330e12i | −0.575135 | − | 0.911017i | ||||
\(363\) | −1.71308e12 | −0.271797 | ||||||||
\(364\) | −3.39676e12 | + | 7.13084e12i | −0.531566 | + | 1.11592i | ||||
\(365\) | 5.63779e12i | 0.870251i | ||||||||
\(366\) | −1.12015e11 | − | 1.77433e11i | −0.0170558 | − | 0.0270164i | ||||
\(367\) | 1.27382e13i | 1.91328i | 0.291272 | + | 0.956640i | \(0.405921\pi\) | ||||
−0.291272 | + | 0.956640i | \(0.594079\pi\) | |||||||
\(368\) | −3.93949e12 | + | 3.19682e12i | −0.583715 | + | 0.473673i | ||||
\(369\) | −2.17500e12 | −0.317928 | ||||||||
\(370\) | 7.02161e12 | − | 4.43282e12i | 1.01258 | − | 0.639251i | ||||
\(371\) | 1.28615e13 | 1.82987 | ||||||||
\(372\) | −8.06455e12 | − | 3.84153e12i | −1.13205 | − | 0.539249i | ||||
\(373\) | − | 1.97372e11i | − | 0.0273364i | −0.999907 | − | 0.0136682i | \(-0.995649\pi\) | ||
0.999907 | − | 0.0136682i | \(-0.00435085\pi\) | |||||||
\(374\) | −6.73210e12 | + | 4.25005e12i | −0.920010 | + | 0.580812i | ||||
\(375\) | 6.45927e12i | 0.871017i | ||||||||
\(376\) | −9.49645e11 | + | 1.13137e11i | −0.126364 | + | 0.0150545i | ||||
\(377\) | 6.35240e12 | 0.834125 | ||||||||
\(378\) | 6.76145e12 | + | 1.07102e13i | 0.876155 | + | 1.38783i | ||||
\(379\) | −4.09437e12 | −0.523590 | −0.261795 | − | 0.965124i | \(-0.584314\pi\) | ||||
−0.261795 | + | 0.965124i | \(0.584314\pi\) | |||||||
\(380\) | −4.25323e12 | − | 2.02602e12i | −0.536786 | − | 0.255697i | ||||
\(381\) | − | 1.08482e13i | − | 1.35124i | ||||||
\(382\) | −1.58006e12 | − | 2.50282e12i | −0.194248 | − | 0.307690i | ||||
\(383\) | − | 4.76814e12i | − | 0.578569i | −0.957243 | − | 0.289285i | \(-0.906583\pi\) | ||
0.957243 | − | 0.289285i | \(-0.0934174\pi\) | |||||||
\(384\) | 4.87890e12 | − | 5.02632e12i | 0.584340 | − | 0.601996i | ||||
\(385\) | −7.01666e12 | −0.829519 | ||||||||
\(386\) | 7.85214e12 | − | 4.95714e12i | 0.916330 | − | 0.578489i | ||||
\(387\) | −5.52405e11 | −0.0636360 | ||||||||
\(388\) | −8.34352e11 | + | 1.75156e12i | −0.0948835 | + | 0.199190i | ||||
\(389\) | 9.35450e11i | 0.105020i | 0.998620 | + | 0.0525101i | \(0.0167222\pi\) | ||||
−0.998620 | + | 0.0525101i | \(0.983278\pi\) | |||||||
\(390\) | 3.50383e12 | − | 2.21201e12i | 0.388347 | − | 0.245168i | ||||
\(391\) | − | 9.09057e12i | − | 0.994735i | ||||||
\(392\) | −1.39947e12 | − | 1.17468e13i | −0.151193 | − | 1.26908i | ||||
\(393\) | −3.38950e12 | −0.361553 | ||||||||
\(394\) | 9.18546e12 | + | 1.45498e13i | 0.967431 | + | 1.53242i | ||||
\(395\) | −3.95728e12 | −0.411540 | ||||||||
\(396\) | −1.01973e12 | + | 2.14073e12i | −0.104715 | + | 0.219829i | ||||
\(397\) | − | 1.13676e13i | − | 1.15270i | −0.817203 | − | 0.576351i | \(-0.804476\pi\) | ||
0.817203 | − | 0.576351i | \(-0.195524\pi\) | |||||||
\(398\) | 4.65771e12 | + | 7.37785e12i | 0.466399 | + | 0.738778i | ||||
\(399\) | − | 1.13902e13i | − | 1.12634i | ||||||
\(400\) | −3.56940e12 | − | 4.39862e12i | −0.348574 | − | 0.429553i | ||||
\(401\) | −6.60693e12 | −0.637203 | −0.318601 | − | 0.947889i | \(-0.603213\pi\) | ||||
−0.318601 | + | 0.947889i | \(0.603213\pi\) | |||||||
\(402\) | 2.04301e12 | − | 1.28978e12i | 0.194599 | − | 0.122853i | ||||
\(403\) | 1.30111e13 | 1.22402 | ||||||||
\(404\) | 4.78043e12 | + | 2.27714e12i | 0.444181 | + | 0.211584i | ||||
\(405\) | − | 4.48769e12i | − | 0.411858i | ||||||
\(406\) | −1.43399e13 | + | 9.05293e12i | −1.29992 | + | 0.820652i | ||||
\(407\) | 1.64498e13i | 1.47296i | ||||||||
\(408\) | 1.48482e12 | + | 1.24632e13i | 0.131333 | + | 1.10237i | ||||
\(409\) | −3.26755e12 | −0.285500 | −0.142750 | − | 0.989759i | \(-0.545594\pi\) | ||||
−0.142750 | + | 0.989759i | \(0.545594\pi\) | |||||||
\(410\) | −4.43818e12 | − | 7.03010e12i | −0.383077 | − | 0.606796i | ||||
\(411\) | −1.63878e12 | −0.139737 | ||||||||
\(412\) | −8.95295e12 | − | 4.26471e12i | −0.754189 | − | 0.359256i | ||||
\(413\) | 4.16224e12i | 0.346399i | ||||||||
\(414\) | −1.44535e12 | − | 2.28944e12i | −0.118842 | − | 0.188246i | ||||
\(415\) | − | 4.60865e12i | − | 0.374398i | ||||||
\(416\) | −3.26725e12 | + | 9.66564e12i | −0.262250 | + | 0.775825i | ||||
\(417\) | −6.01756e12 | −0.477244 | ||||||||
\(418\) | 7.89171e12 | − | 4.98212e12i | 0.618429 | − | 0.390421i | ||||
\(419\) | −2.06044e12 | −0.159548 | −0.0797738 | − | 0.996813i | \(-0.525420\pi\) | ||||
−0.0797738 | + | 0.996813i | \(0.525420\pi\) | |||||||
\(420\) | −4.75717e12 | + | 9.98676e12i | −0.364001 | + | 0.764149i | ||||
\(421\) | − | 5.83555e12i | − | 0.441237i | −0.975360 | − | 0.220618i | \(-0.929192\pi\) | ||
0.975360 | − | 0.220618i | \(-0.0708075\pi\) | |||||||
\(422\) | 1.77464e13 | − | 1.12035e13i | 1.32602 | − | 0.837129i | ||||
\(423\) | − | 5.10378e11i | − | 0.0376869i | ||||||
\(424\) | 1.64971e13 | − | 1.96541e12i | 1.20387 | − | 0.143424i | ||||
\(425\) | 1.01500e13 | 0.732021 | ||||||||
\(426\) | −1.11668e12 | − | 1.76882e12i | −0.0795939 | − | 0.126077i | ||||
\(427\) | −8.15921e11 | −0.0574789 | ||||||||
\(428\) | 7.21893e12 | − | 1.51548e13i | 0.502636 | − | 1.05519i | ||||
\(429\) | 8.20859e12i | 0.564914i | ||||||||
\(430\) | −1.12720e12 | − | 1.78550e12i | −0.0766761 | − | 0.121455i | ||||
\(431\) | 1.85492e13i | 1.24720i | 0.781742 | + | 0.623602i | \(0.214332\pi\) | ||||
−0.781742 | + | 0.623602i | \(0.785668\pi\) | |||||||
\(432\) | 1.03094e13 | + | 1.27045e13i | 0.685197 | + | 0.844379i | ||||
\(433\) | −4.60728e11 | −0.0302695 | −0.0151347 | − | 0.999885i | \(-0.504818\pi\) | ||||
−0.0151347 | + | 0.999885i | \(0.504818\pi\) | |||||||
\(434\) | −2.93712e13 | + | 1.85424e13i | −1.90754 | + | 1.20425i | ||||
\(435\) | 8.89655e12 | 0.571183 | ||||||||
\(436\) | −7.45303e12 | − | 3.55023e12i | −0.473043 | − | 0.225333i | ||||
\(437\) | 1.06564e13i | 0.668658i | ||||||||
\(438\) | −1.48887e13 | + | 9.39937e12i | −0.923602 | + | 0.583080i | ||||
\(439\) | − | 2.12657e13i | − | 1.30424i | −0.758115 | − | 0.652121i | \(-0.773879\pi\) | ||
0.758115 | − | 0.652121i | \(-0.226121\pi\) | |||||||
\(440\) | −9.00011e12 | + | 1.07224e12i | −0.545738 | + | 0.0650173i | ||||
\(441\) | 6.31320e12 | 0.378492 | ||||||||
\(442\) | −9.75936e12 | − | 1.54589e13i | −0.578509 | − | 0.916361i | ||||
\(443\) | −3.22811e13 | −1.89203 | −0.946017 | − | 0.324116i | \(-0.894933\pi\) | ||||
−0.946017 | + | 0.324116i | \(0.894933\pi\) | |||||||
\(444\) | 2.34130e13 | + | 1.11527e13i | 1.35688 | + | 0.646346i | ||||
\(445\) | 1.90652e13i | 1.09255i | ||||||||
\(446\) | −2.06108e12 | − | 3.26476e12i | −0.116794 | − | 0.185002i | ||||
\(447\) | 1.01854e13i | 0.570745i | ||||||||
\(448\) | −6.39920e12 | − | 2.64754e13i | −0.354598 | − | 1.46708i | ||||
\(449\) | 2.25683e13 | 1.23671 | 0.618353 | − | 0.785900i | \(-0.287800\pi\) | ||||
0.618353 | + | 0.785900i | \(0.287800\pi\) | |||||||
\(450\) | 2.55626e12 | − | 1.61380e12i | 0.138530 | − | 0.0874553i | ||||
\(451\) | 1.64697e13 | 0.882682 | ||||||||
\(452\) | −3.24215e12 | + | 6.80626e12i | −0.171846 | + | 0.360758i | ||||
\(453\) | − | 5.90899e12i | − | 0.309758i | ||||||
\(454\) | 2.75312e13 | − | 1.73807e13i | 1.42740 | − | 0.901133i | ||||
\(455\) | − | 1.61123e13i | − | 0.826230i | ||||||
\(456\) | −1.74058e12 | − | 1.46100e13i | −0.0882817 | − | 0.741014i | ||||
\(457\) | 1.06357e13 | 0.533563 | 0.266782 | − | 0.963757i | \(-0.414040\pi\) | ||||
0.266782 | + | 0.963757i | \(0.414040\pi\) | |||||||
\(458\) | −6.83701e12 | − | 1.08299e13i | −0.339265 | − | 0.537398i | ||||
\(459\) | −2.93162e13 | −1.43894 | ||||||||
\(460\) | 4.45069e12 | − | 9.34336e12i | 0.216092 | − | 0.453643i | ||||
\(461\) | 1.15452e13i | 0.554494i | 0.960799 | + | 0.277247i | \(0.0894221\pi\) | ||||
−0.960799 | + | 0.277247i | \(0.910578\pi\) | |||||||
\(462\) | −1.16982e13 | − | 1.85300e13i | −0.555789 | − | 0.880373i | ||||
\(463\) | 2.23021e12i | 0.104819i | 0.998626 | + | 0.0524097i | \(0.0166902\pi\) | ||||
−0.998626 | + | 0.0524097i | \(0.983310\pi\) | |||||||
\(464\) | −1.70100e13 | + | 1.38033e13i | −0.790889 | + | 0.641791i | ||||
\(465\) | 1.82221e13 | 0.838171 | ||||||||
\(466\) | 6.77166e9 | − | 4.27502e9i | 0.000308152 | − | 0.000194540i | ||||
\(467\) | 6.67938e12 | 0.300712 | 0.150356 | − | 0.988632i | \(-0.451958\pi\) | ||||
0.150356 | + | 0.988632i | \(0.451958\pi\) | |||||||
\(468\) | −4.91574e12 | − | 2.34160e12i | −0.218957 | − | 0.104300i | ||||
\(469\) | − | 9.39476e12i | − | 0.414020i | ||||||
\(470\) | 1.64966e12 | − | 1.04145e12i | 0.0719290 | − | 0.0454096i | ||||
\(471\) | − | 1.46607e11i | − | 0.00632485i | ||||||
\(472\) | 6.36047e11 | + | 5.33881e12i | 0.0271506 | + | 0.227895i | ||||
\(473\) | 4.18296e12 | 0.176676 | ||||||||
\(474\) | −6.59761e12 | − | 1.04507e13i | −0.275737 | − | 0.436769i | ||||
\(475\) | −1.18984e13 | −0.492063 | ||||||||
\(476\) | 4.40615e13 | + | 2.09886e13i | 1.80312 | + | 0.858912i | ||||
\(477\) | 8.86621e12i | 0.359043i | ||||||||
\(478\) | 2.35808e13 | + | 3.73521e13i | 0.944973 | + | 1.49684i | ||||
\(479\) | − | 3.25794e13i | − | 1.29201i | −0.763334 | − | 0.646004i | \(-0.776439\pi\) | ||
0.763334 | − | 0.646004i | \(-0.223561\pi\) | |||||||
\(480\) | −4.57580e12 | + | 1.35368e13i | −0.179581 | + | 0.531261i | ||||
\(481\) | −3.77737e13 | −1.46711 | ||||||||
\(482\) | −2.16677e13 | + | 1.36791e13i | −0.832871 | + | 0.525801i | ||||
\(483\) | 2.50217e13 | 0.951878 | ||||||||
\(484\) | −3.70039e12 | + | 7.76827e12i | −0.139322 | + | 0.292481i | ||||
\(485\) | − | 3.95770e12i | − | 0.147480i | ||||||
\(486\) | −1.30795e13 | + | 8.25721e12i | −0.482402 | + | 0.304545i | ||||
\(487\) | 3.47745e13i | 1.26945i | 0.772738 | + | 0.634726i | \(0.218887\pi\) | ||||
−0.772738 | + | 0.634726i | \(0.781113\pi\) | |||||||
\(488\) | −1.04656e12 | + | 1.24684e11i | −0.0378152 | + | 0.00450517i | ||||
\(489\) | −2.94291e13 | −1.05253 | ||||||||
\(490\) | 1.28823e13 | + | 2.04057e13i | 0.456051 | + | 0.722388i | ||||
\(491\) | −4.94642e12 | −0.173334 | −0.0866669 | − | 0.996237i | \(-0.527622\pi\) | ||||
−0.0866669 | + | 0.996237i | \(0.527622\pi\) | |||||||
\(492\) | 1.11662e13 | − | 2.34413e13i | 0.387329 | − | 0.813122i | ||||
\(493\) | − | 3.92515e13i | − | 1.34779i | ||||||
\(494\) | 1.14404e13 | + | 1.81217e13i | 0.388872 | + | 0.615976i | ||||
\(495\) | − | 4.83702e12i | − | 0.162762i | ||||||
\(496\) | −3.48402e13 | + | 2.82722e13i | −1.16057 | + | 0.941783i | ||||
\(497\) | −8.13390e12 | −0.268236 | ||||||||
\(498\) | 1.21708e13 | − | 7.68357e12i | 0.397350 | − | 0.250851i | ||||
\(499\) | 6.33777e12 | 0.204849 | 0.102425 | − | 0.994741i | \(-0.467340\pi\) | ||||
0.102425 | + | 0.994741i | \(0.467340\pi\) | |||||||
\(500\) | 2.92907e13 | + | 1.39526e13i | 0.937303 | + | 0.446482i | ||||
\(501\) | 1.22771e13i | 0.388963i | ||||||||
\(502\) | −1.31414e13 | + | 8.29631e12i | −0.412214 | + | 0.260235i | ||||
\(503\) | − | 1.72088e13i | − | 0.534455i | −0.963633 | − | 0.267228i | \(-0.913892\pi\) | ||
0.963633 | − | 0.267228i | \(-0.0861075\pi\) | |||||||
\(504\) | 1.44338e13 | − | 1.71960e12i | 0.443843 | − | 0.0528779i | ||||
\(505\) | −1.08015e13 | −0.328872 | ||||||||
\(506\) | 1.09446e13 | + | 1.73362e13i | 0.329948 | + | 0.522640i | ||||
\(507\) | 9.25548e12 | 0.276286 | ||||||||
\(508\) | −4.91930e13 | − | 2.34329e13i | −1.45407 | − | 0.692641i | ||||
\(509\) | − | 5.81472e13i | − | 1.70192i | −0.525229 | − | 0.850961i | \(-0.676020\pi\) | ||
0.525229 | − | 0.850961i | \(-0.323980\pi\) | |||||||
\(510\) | −1.36680e13 | − | 2.16502e13i | −0.396145 | − | 0.627496i | ||||
\(511\) | 6.84652e13i | 1.96501i | ||||||||
\(512\) | −1.22539e13 | − | 3.29815e13i | −0.348277 | − | 0.937392i | ||||
\(513\) | 3.43659e13 | 0.967255 | ||||||||
\(514\) | 1.46538e13 | − | 9.25112e12i | 0.408447 | − | 0.257857i | ||||
\(515\) | 2.02294e13 | 0.558402 | ||||||||
\(516\) | 2.83598e12 | − | 5.95359e12i | 0.0775272 | − | 0.162753i | ||||
\(517\) | 3.86472e12i | 0.104632i | ||||||||
\(518\) | 8.52702e13 | − | 5.38320e13i | 2.28638 | − | 1.44342i | ||||
\(519\) | 1.91110e12i | 0.0507514i | ||||||||
\(520\) | −2.46218e12 | − | 2.06669e13i | −0.0647595 | − | 0.543574i | ||||
\(521\) | −5.26939e13 | −1.37269 | −0.686344 | − | 0.727277i | \(-0.740786\pi\) | ||||
−0.686344 | + | 0.727277i | \(0.740786\pi\) | |||||||
\(522\) | −6.24076e12 | − | 9.88540e12i | −0.161022 | − | 0.255060i | ||||
\(523\) | 4.02928e13 | 1.02972 | 0.514859 | − | 0.857275i | \(-0.327844\pi\) | ||||
0.514859 | + | 0.857275i | \(0.327844\pi\) | |||||||
\(524\) | −7.32160e12 | + | 1.53703e13i | −0.185332 | + | 0.389068i | ||||
\(525\) | 2.79379e13i | 0.700483i | ||||||||
\(526\) | −1.79209e12 | − | 2.83869e12i | −0.0445074 | − | 0.0705000i | ||||
\(527\) | − | 8.03956e13i | − | 1.97779i | ||||||
\(528\) | −1.78367e13 | − | 2.19804e13i | −0.434655 | − | 0.535632i | ||||
\(529\) | 1.80168e13 | 0.434910 | ||||||||
\(530\) | −2.86576e13 | + | 1.80918e13i | −0.685268 | + | 0.432617i | ||||
\(531\) | −2.86929e12 | −0.0679677 | ||||||||
\(532\) | −5.16511e13 | − | 2.46039e13i | −1.21205 | − | 0.577358i | ||||
\(533\) | 3.78194e13i | 0.879181i | ||||||||
\(534\) | −5.03486e13 | + | 3.17856e13i | −1.15953 | + | 0.732023i | ||||
\(535\) | 3.42425e13i | 0.781263i | ||||||||
\(536\) | −1.43565e12 | − | 1.20504e13i | −0.0324507 | − | 0.272382i | ||||
\(537\) | 9.25715e12 | 0.207303 | ||||||||
\(538\) | 2.45463e13 | + | 3.88815e13i | 0.544597 | + | 0.862644i | ||||
\(539\) | −4.78053e13 | −1.05083 | ||||||||
\(540\) | −3.01314e13 | − | 1.43530e13i | −0.656222 | − | 0.312590i | ||||
\(541\) | 2.22804e13i | 0.480769i | 0.970678 | + | 0.240385i | \(0.0772736\pi\) | ||||
−0.970678 | + | 0.240385i | \(0.922726\pi\) | |||||||
\(542\) | 2.07063e13 | + | 3.27988e13i | 0.442695 | + | 0.701232i | ||||
\(543\) | 4.26684e13i | 0.903872i | ||||||||
\(544\) | 5.97241e13 | + | 2.01884e13i | 1.25359 | + | 0.423748i | ||||
\(545\) | 1.68403e13 | 0.350241 | ||||||||
\(546\) | 4.25505e13 | − | 2.68626e13i | 0.876882 | − | 0.553585i | ||||
\(547\) | 6.41889e13 | 1.31076 | 0.655380 | − | 0.755299i | \(-0.272508\pi\) | ||||
0.655380 | + | 0.755299i | \(0.272508\pi\) | |||||||
\(548\) | −3.53991e12 | + | 7.43137e12i | −0.0716291 | + | 0.150372i | ||||
\(549\) | − | 5.62466e11i | − | 0.0112781i | ||||||
\(550\) | −1.93567e13 | + | 1.22201e13i | −0.384608 | + | 0.242807i | ||||
\(551\) | 4.60126e13i | 0.905981i | ||||||||
\(552\) | 3.20948e13 | − | 3.82366e12i | 0.626238 | − | 0.0746077i | ||||
\(553\) | −4.80571e13 | −0.929249 | ||||||||
\(554\) | −4.90487e13 | − | 7.76935e13i | −0.939894 | − | 1.48880i | ||||
\(555\) | −5.29022e13 | −1.00464 | ||||||||
\(556\) | −1.29984e13 | + | 2.72877e13i | −0.244634 | + | 0.513563i | ||||
\(557\) | − | 1.84305e13i | − | 0.343764i | −0.985118 | − | 0.171882i | \(-0.945015\pi\) | ||
0.985118 | − | 0.171882i | \(-0.0549849\pi\) | |||||||
\(558\) | −1.27824e13 | − | 2.02474e13i | −0.236288 | − | 0.374282i | ||||
\(559\) | 9.60532e12i | 0.175976i | ||||||||
\(560\) | 3.50109e13 | + | 4.31445e13i | 0.635716 | + | 0.783403i | ||||
\(561\) | 5.07209e13 | 0.912794 | ||||||||
\(562\) | 3.44178e13 | − | 2.17283e13i | 0.613905 | − | 0.387565i | ||||
\(563\) | −3.43128e13 | −0.606617 | −0.303309 | − | 0.952892i | \(-0.598091\pi\) | ||||
−0.303309 | + | 0.952892i | \(0.598091\pi\) | |||||||
\(564\) | 5.50064e12 | + | 2.62021e12i | 0.0963868 | + | 0.0459136i | ||||
\(565\) | − | 1.53789e13i | − | 0.267106i | ||||||
\(566\) | −6.63371e13 | + | 4.18793e13i | −1.14202 | + | 0.720970i | ||||
\(567\) | − | 5.44983e13i | − | 0.929968i | ||||||
\(568\) | −1.04332e13 | + | 1.24297e12i | −0.176471 | + | 0.0210242i | ||||
\(569\) | 9.76085e13 | 1.63654 | 0.818269 | − | 0.574835i | \(-0.194934\pi\) | ||||
0.818269 | + | 0.574835i | \(0.194934\pi\) | |||||||
\(570\) | 1.60223e13 | + | 2.53795e13i | 0.266288 | + | 0.421802i | ||||
\(571\) | 4.78352e13 | 0.788073 | 0.394037 | − | 0.919095i | \(-0.371078\pi\) | ||||
0.394037 | + | 0.919095i | \(0.371078\pi\) | |||||||
\(572\) | 3.72233e13 | + | 1.77312e13i | 0.607904 | + | 0.289574i | ||||
\(573\) | 1.88568e13i | 0.305277i | ||||||||
\(574\) | −5.38972e13 | − | 8.53734e13i | −0.864981 | − | 1.37013i | ||||
\(575\) | − | 2.61380e13i | − | 0.415847i | ||||||
\(576\) | 1.82512e13 | − | 4.41138e12i | 0.287858 | − | 0.0695763i | ||||
\(577\) | −9.82519e13 | −1.53625 | −0.768125 | − | 0.640300i | \(-0.778810\pi\) | ||||
−0.768125 | + | 0.640300i | \(0.778810\pi\) | |||||||
\(578\) | −4.09700e13 | + | 2.58648e13i | −0.635077 | + | 0.400931i | ||||
\(579\) | −5.91596e13 | −0.909143 | ||||||||
\(580\) | 1.92173e13 | − | 4.03431e13i | 0.292788 | − | 0.614651i | ||||
\(581\) | − | 5.59673e13i | − | 0.845383i | ||||||
\(582\) | 1.04517e13 | − | 6.59830e12i | 0.156522 | − | 0.0988137i | ||||
\(583\) | − | 6.71374e13i | − | 0.996832i | ||||||
\(584\) | 1.04624e13 | + | 8.78188e13i | 0.154017 | + | 1.29278i | ||||
\(585\) | 1.11072e13 | 0.162116 | ||||||||
\(586\) | 4.46962e13 | + | 7.07990e13i | 0.646819 | + | 1.02456i | ||||
\(587\) | −6.65454e12 | −0.0954834 | −0.0477417 | − | 0.998860i | \(-0.515202\pi\) | ||||
−0.0477417 | + | 0.998860i | \(0.515202\pi\) | |||||||
\(588\) | −3.24111e13 | + | 6.80410e13i | −0.461113 | + | 0.968019i | ||||
\(589\) | 9.42438e13i | 1.32946i | ||||||||
\(590\) | −5.85490e12 | − | 9.27420e12i | −0.0818954 | − | 0.129723i | ||||
\(591\) | − | 1.09621e14i | − | 1.52040i | ||||||
\(592\) | 1.01148e14 | − | 8.20796e13i | 1.39107 | − | 1.12883i | ||||
\(593\) | −5.14742e13 | −0.701967 | −0.350983 | − | 0.936382i | \(-0.614153\pi\) | ||||
−0.350983 | + | 0.936382i | \(0.614153\pi\) | |||||||
\(594\) | 5.59077e13 | − | 3.52951e13i | 0.756030 | − | 0.477290i | ||||
\(595\) | −9.95581e13 | −1.33503 | ||||||||
\(596\) | 4.61877e13 | + | 2.20014e13i | 0.614179 | + | 0.292563i | ||||
\(597\) | − | 5.55861e13i | − | 0.732984i | ||||||
\(598\) | −3.98091e13 | + | 2.51319e13i | −0.520567 | + | 0.328640i | ||||
\(599\) | − | 1.31771e13i | − | 0.170878i | −0.996343 | − | 0.0854390i | \(-0.972771\pi\) | ||
0.996343 | − | 0.0854390i | \(-0.0272293\pi\) | |||||||
\(600\) | 4.26929e12 | + | 3.58353e13i | 0.0549035 | + | 0.460845i | ||||
\(601\) | 9.02087e13 | 1.15047 | 0.575236 | − | 0.817988i | \(-0.304910\pi\) | ||||
0.575236 | + | 0.817988i | \(0.304910\pi\) | |||||||
\(602\) | −1.36887e13 | − | 2.16830e13i | −0.173133 | − | 0.274244i | ||||
\(603\) | 6.47640e12 | 0.0812357 | ||||||||
\(604\) | −2.67954e13 | − | 1.27639e13i | −0.333331 | − | 0.158781i | ||||
\(605\) | − | 1.75526e13i | − | 0.216553i | ||||||
\(606\) | −1.80083e13 | − | 2.85253e13i | −0.220349 | − | 0.349034i | ||||
\(607\) | − | 2.75800e12i | − | 0.0334696i | −0.999860 | − | 0.0167348i | \(-0.994673\pi\) | ||
0.999860 | − | 0.0167348i | \(-0.00532710\pi\) | |||||||
\(608\) | −7.00116e13 | − | 2.36658e13i | −0.842659 | − | 0.284842i | ||||
\(609\) | 1.08040e14 | 1.28972 | ||||||||
\(610\) | 1.81802e12 | − | 1.14773e12i | 0.0215253 | − | 0.0135891i | ||||
\(611\) | −8.87455e12 | −0.104217 | ||||||||
\(612\) | −1.44688e13 | + | 3.03744e13i | −0.168529 | + | 0.353794i | ||||
\(613\) | − | 4.06668e13i | − | 0.469826i | −0.972016 | − | 0.234913i | \(-0.924519\pi\) | ||
0.972016 | − | 0.234913i | \(-0.0754806\pi\) | |||||||
\(614\) | 1.12118e13 | − | 7.07812e12i | 0.128479 | − | 0.0811103i | ||||
\(615\) | 5.29662e13i | 0.602037i | ||||||||
\(616\) | −1.09297e14 | + | 1.30213e13i | −1.23227 | + | 0.146808i | ||||
\(617\) | 2.79773e13 | 0.312882 | 0.156441 | − | 0.987687i | \(-0.449998\pi\) | ||||
0.156441 | + | 0.987687i | \(0.449998\pi\) | |||||||
\(618\) | 3.37266e13 | + | 5.34232e13i | 0.374137 | + | 0.592635i | ||||
\(619\) | 3.72952e13 | 0.410393 | 0.205197 | − | 0.978721i | \(-0.434217\pi\) | ||||
0.205197 | + | 0.978721i | \(0.434217\pi\) | |||||||
\(620\) | 3.93612e13 | − | 8.26313e13i | 0.429645 | − | 0.901957i | ||||
\(621\) | 7.54939e13i | 0.817436i | ||||||||
\(622\) | 2.95978e13 | + | 4.68831e13i | 0.317913 | + | 0.503575i | ||||
\(623\) | 2.31527e14i | 2.46696i | ||||||||
\(624\) | 5.04735e13 | − | 4.09583e13i | 0.533508 | − | 0.432931i | ||||
\(625\) | −1.34268e13 | −0.140790 | ||||||||
\(626\) | 1.47357e13 | − | 9.30283e12i | 0.153285 | − | 0.0967706i | ||||
\(627\) | −5.94576e13 | −0.613578 | ||||||||
\(628\) | −6.64816e11 | − | 3.16684e11i | −0.00680618 | − | 0.00324211i | ||||
\(629\) | 2.33404e14i | 2.37058i | ||||||||
\(630\) | −2.50734e13 | + | 1.58291e13i | −0.252645 | + | 0.159498i | ||||
\(631\) | 2.81208e13i | 0.281113i | 0.990073 | + | 0.140557i | \(0.0448892\pi\) | ||||
−0.990073 | + | 0.140557i | \(0.955111\pi\) | |||||||
\(632\) | −6.16418e13 | + | 7.34379e12i | −0.611350 | + | 0.0728341i | ||||
\(633\) | −1.33705e14 | −1.31562 | ||||||||
\(634\) | −8.94789e13 | − | 1.41735e14i | −0.873523 | − | 1.38367i | ||||
\(635\) | 1.11153e14 | 1.07659 | ||||||||
\(636\) | −9.55563e13 | − | 4.55180e13i | −0.918277 | − | 0.437419i | ||||
\(637\) | − | 1.09775e14i | − | 1.04666i | ||||||
\(638\) | 4.72568e13 | + | 7.48550e13i | 0.447055 | + | 0.708137i | ||||
\(639\) | − | 5.60721e12i | − | 0.0526311i | ||||||
\(640\) | 5.15008e13 | + | 4.99903e13i | 0.479638 | + | 0.465571i | ||||
\(641\) | −1.42063e14 | −1.31278 | −0.656388 | − | 0.754423i | \(-0.727917\pi\) | ||||
−0.656388 | + | 0.754423i | \(0.727917\pi\) | |||||||
\(642\) | −9.04300e13 | + | 5.70894e13i | −0.829158 | + | 0.523456i | ||||
\(643\) | 1.42601e14 | 1.29738 | 0.648691 | − | 0.761052i | \(-0.275317\pi\) | ||||
0.648691 | + | 0.761052i | \(0.275317\pi\) | |||||||
\(644\) | 5.40490e13 | − | 1.13466e14i | 0.487931 | − | 1.02432i | ||||
\(645\) | 1.34523e13i | 0.120503i | ||||||||
\(646\) | 1.11974e14 | − | 7.06904e13i | 0.995302 | − | 0.628345i | ||||
\(647\) | − | 9.36509e13i | − | 0.826020i | −0.910727 | − | 0.413010i | \(-0.864478\pi\) | ||
0.910727 | − | 0.413010i | \(-0.135522\pi\) | |||||||
\(648\) | −8.32809e12 | − | 6.99038e13i | −0.0728904 | − | 0.611823i | ||||
\(649\) | 2.17271e13 | 0.188703 | ||||||||
\(650\) | −2.80610e13 | − | 4.44488e13i | −0.241844 | − | 0.383083i | ||||
\(651\) | 2.21288e14 | 1.89258 | ||||||||
\(652\) | −6.35694e13 | + | 1.33452e14i | −0.539523 | + | 1.13263i | ||||
\(653\) | − | 1.86286e14i | − | 1.56897i | −0.620147 | − | 0.784485i | \(-0.712927\pi\) | ||
0.620147 | − | 0.784485i | \(-0.287073\pi\) | |||||||
\(654\) | 2.80763e13 | + | 4.44730e13i | 0.234666 | + | 0.371713i | ||||
\(655\) | − | 3.47296e13i | − | 0.288067i | ||||||
\(656\) | −8.21789e13 | − | 1.01270e14i | −0.676458 | − | 0.833610i | ||||
\(657\) | −4.71974e13 | −0.385559 | ||||||||
\(658\) | 2.00334e13 | − | 1.26473e13i | 0.162414 | − | 0.102534i | ||||
\(659\) | −1.00559e14 | −0.809082 | −0.404541 | − | 0.914520i | \(-0.632569\pi\) | ||||
−0.404541 | + | 0.914520i | \(0.632569\pi\) | |||||||
\(660\) | 5.21314e13 | + | 2.48327e13i | 0.416274 | + | 0.198291i | ||||
\(661\) | − | 2.07976e14i | − | 1.64819i | −0.566454 | − | 0.824094i | \(-0.691685\pi\) | ||
0.566454 | − | 0.824094i | \(-0.308315\pi\) | |||||||
\(662\) | 1.82048e14 | − | 1.14929e14i | 1.43185 | − | 0.903940i | ||||
\(663\) | 1.16470e14i | 0.909175i | ||||||||
\(664\) | −8.55257e12 | − | 7.17880e13i | −0.0662607 | − | 0.556175i | ||||
\(665\) | 1.16707e14 | 0.897406 | ||||||||
\(666\) | 3.71098e13 | + | 5.87822e13i | 0.283216 | + | 0.448616i | ||||
\(667\) | −1.01079e14 | −0.765653 | ||||||||
\(668\) | 5.56728e13 | + | 2.65196e13i | 0.418563 | + | 0.199381i | ||||
\(669\) | 2.45973e13i | 0.183551i | ||||||||
\(670\) | 1.32153e13 | + | 2.09332e13i | 0.0978824 | + | 0.155046i | ||||
\(671\) | 4.25915e12i | 0.0313119i | ||||||||
\(672\) | −5.55684e13 | + | 1.64390e14i | −0.405491 | + | 1.19958i | ||||
\(673\) | −1.30742e14 | −0.946977 | −0.473488 | − | 0.880800i | \(-0.657005\pi\) | ||||
−0.473488 | + | 0.880800i | \(0.657005\pi\) | |||||||
\(674\) | −1.46830e14 | + | 9.26956e13i | −1.05564 | + | 0.666438i | ||||
\(675\) | −8.42925e13 | −0.601547 | ||||||||
\(676\) | 1.99926e13 | − | 4.19707e13i | 0.141624 | − | 0.297312i | ||||
\(677\) | 1.03511e14i | 0.727853i | 0.931428 | + | 0.363927i | \(0.118564\pi\) | ||||
−0.931428 | + | 0.363927i | \(0.881436\pi\) | |||||||
\(678\) | 4.06137e13 | − | 2.56398e13i | 0.283481 | − | 0.178965i | ||||
\(679\) | − | 4.80622e13i | − | 0.333008i | ||||||
\(680\) | −1.27701e14 | + | 1.52138e13i | −0.878313 | + | 0.104639i | ||||
\(681\) | −2.07425e14 | −1.41620 | ||||||||
\(682\) | 9.67920e13 | + | 1.53319e14i | 0.656021 | + | 1.03914i | ||||
\(683\) | 2.77817e14 | 1.86920 | 0.934600 | − | 0.355699i | \(-0.115757\pi\) | ||||
0.934600 | + | 0.355699i | \(0.115757\pi\) | |||||||
\(684\) | 1.69610e13 | − | 3.56064e13i | 0.113285 | − | 0.237820i | ||||
\(685\) | − | 1.67914e13i | − | 0.111335i | ||||||
\(686\) | 3.40356e13 | + | 5.39126e13i | 0.224034 | + | 0.354870i | ||||
\(687\) | 8.15943e13i | 0.533183i | ||||||||
\(688\) | −2.08717e13 | − | 2.57205e13i | −0.135399 | − | 0.166854i | ||||
\(689\) | 1.54167e14 | 0.992879 | ||||||||
\(690\) | −5.57528e13 | + | 3.51974e13i | −0.356469 | + | 0.225042i | ||||
\(691\) | −3.03259e14 | −1.92497 | −0.962483 | − | 0.271341i | \(-0.912533\pi\) | ||||
−0.962483 | + | 0.271341i | \(0.912533\pi\) | |||||||
\(692\) | 8.66625e12 | + | 4.12815e12i | 0.0546136 | + | 0.0260151i | ||||
\(693\) | − | 5.87407e13i | − | 0.367513i | ||||||
\(694\) | −1.42917e14 | + | 9.02250e13i | −0.887741 | + | 0.560441i | ||||
\(695\) | − | 6.16573e13i | − | 0.380242i | ||||||
\(696\) | 1.38580e14 | − | 1.65099e13i | 0.848504 | − | 0.101088i | ||||
\(697\) | 2.33686e14 | 1.42059 | ||||||||
\(698\) | 8.30763e12 | + | 1.31593e13i | 0.0501418 | + | 0.0794249i | ||||
\(699\) | −5.10190e10 | −0.000305736 | ||||||||
\(700\) | 1.26690e14 | + | 6.03483e13i | 0.753791 | + | 0.359066i | ||||
\(701\) | 1.61408e14i | 0.953533i | 0.879030 | + | 0.476766i | \(0.158191\pi\) | ||||
−0.879030 | + | 0.476766i | \(0.841809\pi\) | |||||||
\(702\) | 8.10480e13 | + | 1.28380e14i | 0.475397 | + | 0.753032i | ||||
\(703\) | − | 2.73608e14i | − | 1.59350i | ||||||
\(704\) | −1.38203e14 | + | 3.34042e13i | −0.799198 | + | 0.193169i | ||||
\(705\) | −1.24288e13 | −0.0713649 | ||||||||
\(706\) | 1.01711e14 | − | 6.42111e13i | 0.579887 | − | 0.366089i | ||||
\(707\) | −1.31173e14 | −0.742588 | ||||||||
\(708\) | 1.47306e13 | − | 3.09240e13i | 0.0828044 | − | 0.173832i | ||||
\(709\) | 2.45219e14i | 1.36874i | 0.729133 | + | 0.684372i | \(0.239924\pi\) | ||||
−0.729133 | + | 0.684372i | \(0.760076\pi\) | |||||||
\(710\) | 1.81238e13 | − | 1.14417e13i | 0.100452 | − | 0.0634162i | ||||
\(711\) | − | 3.31288e13i | − | 0.182330i | ||||||
\(712\) | 3.53805e13 | + | 2.96975e14i | 0.193359 | + | 1.62300i | ||||
\(713\) | −2.07032e14 | −1.12354 | ||||||||
\(714\) | −1.65984e14 | − | 2.62920e14i | −0.894489 | − | 1.41688i | ||||
\(715\) | −8.41071e13 | −0.450093 | ||||||||
\(716\) | 1.99962e13 | − | 4.19783e13i | 0.106263 | − | 0.223079i | ||||
\(717\) | − | 2.81418e14i | − | 1.48510i | ||||||
\(718\) | −7.07322e13 | − | 1.12040e14i | −0.370676 | − | 0.587153i | ||||
\(719\) | 5.06378e13i | 0.263530i | 0.991281 | + | 0.131765i | \(0.0420645\pi\) | ||||
−0.991281 | + | 0.131765i | \(0.957936\pi\) | |||||||
\(720\) | −2.97422e13 | + | 2.41352e13i | −0.153713 | + | 0.124735i | ||||
\(721\) | 2.45665e14 | 1.26086 | ||||||||
\(722\) | 3.46384e13 | − | 2.18676e13i | 0.176552 | − | 0.111459i | ||||
\(723\) | 1.63249e14 | 0.826339 | ||||||||
\(724\) | 1.93488e14 | + | 9.21673e13i | 0.972658 | + | 0.463323i | ||||
\(725\) | − | 1.12859e14i | − | 0.563440i | ||||||
\(726\) | 4.63540e13 | − | 2.92638e13i | 0.229829 | − | 0.145093i | ||||
\(727\) | 1.14938e14i | 0.565968i | 0.959125 | + | 0.282984i | \(0.0913243\pi\) | ||||
−0.959125 | + | 0.282984i | \(0.908676\pi\) | |||||||
\(728\) | −2.99007e13 | − | 2.50978e14i | −0.146226 | − | 1.22738i | ||||
\(729\) | 2.25403e14 | 1.09477 | ||||||||
\(730\) | −9.63081e13 | − | 1.52553e14i | −0.464567 | − | 0.735877i | ||||
\(731\) | 5.93514e13 | 0.284344 | ||||||||
\(732\) | 6.06202e12 | + | 2.88763e12i | 0.0288444 | + | 0.0137400i | ||||
\(733\) | 2.84996e14i | 1.34685i | 0.739256 | + | 0.673425i | \(0.235177\pi\) | ||||
−0.739256 | + | 0.673425i | \(0.764823\pi\) | |||||||
\(734\) | −2.17602e14 | − | 3.44683e14i | −1.02137 | − | 1.61785i | ||||
\(735\) | − | 1.53740e14i | − | 0.716722i | ||||||
\(736\) | 5.19884e13 | − | 1.53799e14i | 0.240723 | − | 0.712139i | ||||
\(737\) | −4.90411e13 | −0.225540 | ||||||||
\(738\) | 5.88533e13 | − | 3.71547e13i | 0.268837 | − | 0.169720i | ||||
\(739\) | −2.54337e14 | −1.15395 | −0.576976 | − | 0.816761i | \(-0.695767\pi\) | ||||
−0.576976 | + | 0.816761i | \(0.695767\pi\) | |||||||
\(740\) | −1.14273e14 | + | 2.39895e14i | −0.514974 | + | 1.08109i | ||||
\(741\) | − | 1.36532e14i | − | 0.611145i | ||||||
\(742\) | −3.48017e14 | + | 2.19707e14i | −1.54732 | + | 0.976842i | ||||
\(743\) | 3.38292e14i | 1.49399i | 0.664830 | + | 0.746995i | \(0.268504\pi\) | ||||
−0.664830 | + | 0.746995i | \(0.731496\pi\) | |||||||
\(744\) | 2.83841e14 | − | 3.38159e13i | 1.24512 | − | 0.148339i | ||||
\(745\) | −1.04362e14 | −0.454739 | ||||||||
\(746\) | 3.37162e12 | + | 5.34066e12i | 0.0145930 | + | 0.0231154i | ||||
\(747\) | 3.85818e13 | 0.165874 | ||||||||
\(748\) | 1.09562e14 | − | 2.30003e14i | 0.467897 | − | 0.982260i | ||||
\(749\) | 4.15841e14i | 1.76408i | ||||||||
\(750\) | −1.10341e14 | − | 1.74781e14i | −0.464976 | − | 0.736525i | ||||
\(751\) | − | 3.25526e13i | − | 0.136266i | −0.997676 | − | 0.0681329i | \(-0.978296\pi\) | ||
0.997676 | − | 0.0681329i | \(-0.0217042\pi\) | |||||||
\(752\) | 2.37637e13 | − | 1.92838e13i | 0.0988154 | − | 0.0801868i | ||||
\(753\) | 9.90098e13 | 0.408981 | ||||||||
\(754\) | −1.71889e14 | + | 1.08515e14i | −0.705329 | + | 0.445282i | ||||
\(755\) | 6.05448e13 | 0.246798 | ||||||||
\(756\) | −3.65915e14 | − | 1.74303e14i | −1.48174 | − | 0.705822i | ||||
\(757\) | 1.45864e14i | 0.586772i | 0.955994 | + | 0.293386i | \(0.0947821\pi\) | ||||
−0.955994 | + | 0.293386i | \(0.905218\pi\) | |||||||
\(758\) | 1.10789e14 | − | 6.99425e13i | 0.442743 | − | 0.279508i | ||||
\(759\) | − | 1.30615e14i | − | 0.518541i | ||||||
\(760\) | 1.49697e14 | − | 1.78344e13i | 0.590400 | − | 0.0703382i | ||||
\(761\) | 1.60409e14 | 0.628500 | 0.314250 | − | 0.949340i | \(-0.398247\pi\) | ||||
0.314250 | + | 0.949340i | \(0.398247\pi\) | |||||||
\(762\) | 1.85315e14 | + | 2.93539e14i | 0.721331 | + | 1.14259i | ||||
\(763\) | 2.04508e14 | 0.790839 | ||||||||
\(764\) | 8.55094e13 | + | 4.07322e13i | 0.328509 | + | 0.156484i | ||||
\(765\) | − | 6.86317e13i | − | 0.261950i | ||||||
\(766\) | 8.14522e13 | + | 1.29021e14i | 0.308858 | + | 0.489233i | ||||
\(767\) | 4.98918e13i | 0.187954i | ||||||||
\(768\) | −4.61553e13 | + | 2.19351e14i | −0.172749 | + | 0.820981i | ||||
\(769\) | 2.82478e14 | 1.05040 | 0.525199 | − | 0.850980i | \(-0.323991\pi\) | ||||
0.525199 | + | 0.850980i | \(0.323991\pi\) | |||||||
\(770\) | 1.89863e14 | − | 1.19863e14i | 0.701434 | − | 0.442823i | ||||
\(771\) | −1.10405e14 | −0.405243 | ||||||||
\(772\) | −1.27790e14 | + | 2.68270e14i | −0.466025 | + | 0.978330i | ||||
\(773\) | − | 3.90458e14i | − | 1.41474i | −0.706843 | − | 0.707370i | \(-0.749881\pi\) | ||
0.706843 | − | 0.707370i | \(-0.250119\pi\) | |||||||
\(774\) | 1.49475e13 | − | 9.43651e12i | 0.0538100 | − | 0.0339709i | ||||
\(775\) | − | 2.31161e14i | − | 0.826809i | ||||||
\(776\) | −7.34456e12 | − | 6.16483e13i | −0.0261010 | − | 0.219085i | ||||
\(777\) | −6.42442e14 | −2.26845 | ||||||||
\(778\) | −1.59799e13 | − | 2.53123e13i | −0.0560630 | − | 0.0888041i | ||||
\(779\) | −2.73939e14 | −0.954919 | ||||||||
\(780\) | −5.70231e13 | + | 1.19709e14i | −0.197505 | + | 0.414624i | ||||
\(781\) | 4.24594e13i | 0.146123i | ||||||||
\(782\) | 1.55290e14 | + | 2.45981e14i | 0.531020 | + | 0.841139i | ||||
\(783\) | 3.25970e14i | 1.10756i | ||||||||
\(784\) | 2.38534e14 | + | 2.93949e14i | 0.805321 | + | 0.992410i | ||||
\(785\) | 1.50217e12 | 0.00503930 | ||||||||
\(786\) | 9.17161e13 | − | 5.79014e13i | 0.305726 | − | 0.193008i | ||||
\(787\) | −1.96267e14 | −0.650089 | −0.325045 | − | 0.945699i | \(-0.605379\pi\) | ||||
−0.325045 | + | 0.945699i | \(0.605379\pi\) | |||||||
\(788\) | −4.97097e14 | − | 2.36791e14i | −1.63610 | − | 0.779353i | ||||
\(789\) | 2.13872e13i | 0.0699470i | ||||||||
\(790\) | 1.07080e14 | − | 6.76006e13i | 0.347994 | − | 0.219693i | ||||
\(791\) | − | 1.86761e14i | − | 0.603121i | ||||||
\(792\) | −8.97638e12 | − | 7.53454e13i | −0.0288055 | − | 0.241786i | ||||
\(793\) | −9.78026e12 | −0.0311878 | ||||||||
\(794\) | 1.94188e14 | + | 3.07595e14i | 0.615348 | + | 0.974714i | ||||
\(795\) | 2.15912e14 | 0.679893 | ||||||||
\(796\) | −2.52065e14 | − | 1.20071e14i | −0.788766 | − | 0.375726i | ||||
\(797\) | − | 4.02234e14i | − | 1.25080i | −0.780306 | − | 0.625398i | \(-0.784937\pi\) | ||
0.780306 | − | 0.625398i | \(-0.215063\pi\) | |||||||
\(798\) | 1.94575e14 | + | 3.08208e14i | 0.601274 | + | 0.952421i | ||||
\(799\) | 5.48359e13i | 0.168396i | ||||||||
\(800\) | 1.71724e14 | + | 5.80474e13i | 0.524060 | + | 0.177147i | ||||
\(801\) | −1.59606e14 | −0.484047 | ||||||||
\(802\) | 1.78776e14 | − | 1.12863e14i | 0.538813 | − | 0.340159i | ||||
\(803\) | 3.57392e14 | 1.07045 | ||||||||
\(804\) | −3.32490e13 | + | 6.97999e13i | −0.0989688 | + | 0.207766i | ||||
\(805\) | 2.56378e14i | 0.758406i | ||||||||
\(806\) | −3.52066e14 | + | 2.22263e14i | −1.03502 | + | 0.653419i | ||||
\(807\) | − | 2.92941e14i | − | 0.855879i | ||||||
\(808\) | −1.68253e14 | + | 2.00450e13i | −0.488546 | + | 0.0582036i | ||||
\(809\) | −2.08977e14 | −0.603053 | −0.301527 | − | 0.953458i | \(-0.597496\pi\) | ||||
−0.301527 | + | 0.953458i | \(0.597496\pi\) | |||||||
\(810\) | 7.66613e13 | + | 1.21432e14i | 0.219862 | + | 0.348263i | ||||
\(811\) | 2.46451e14 | 0.702468 | 0.351234 | − | 0.936288i | \(-0.385762\pi\) | ||||
0.351234 | + | 0.936288i | \(0.385762\pi\) | |||||||
\(812\) | 2.33375e14 | − | 4.89925e14i | 0.661109 | − | 1.38787i | ||||
\(813\) | − | 2.47113e14i | − | 0.695732i | ||||||
\(814\) | −2.81006e14 | − | 4.45115e14i | −0.786309 | − | 1.24552i | ||||
\(815\) | − | 3.01538e14i | − | 0.838598i | ||||||
\(816\) | −2.53082e14 | − | 3.11876e14i | −0.699536 | − | 0.862049i | ||||
\(817\) | −6.95747e13 | −0.191135 | ||||||||
\(818\) | 8.84163e13 | − | 5.58182e13i | 0.241416 | − | 0.152409i | ||||
\(819\) | 1.34886e14 | 0.366056 | ||||||||
\(820\) | 2.40185e14 | + | 1.14411e14i | 0.647853 | + | 0.308603i | ||||
\(821\) | − | 4.81499e14i | − | 1.29086i | −0.763819 | − | 0.645431i | \(-0.776678\pi\) | ||
0.763819 | − | 0.645431i | \(-0.223322\pi\) | |||||||
\(822\) | 4.43437e13 | − | 2.79947e13i | 0.118161 | − | 0.0745961i | ||||
\(823\) | 4.66519e14i | 1.23558i | 0.786344 | + | 0.617789i | \(0.211971\pi\) | ||||
−0.786344 | + | 0.617789i | \(0.788029\pi\) | |||||||
\(824\) | 3.15110e14 | − | 3.75410e13i | 0.829517 | − | 0.0988258i | ||||
\(825\) | 1.45837e14 | 0.381592 | ||||||||
\(826\) | −7.11018e13 | − | 1.12626e14i | −0.184918 | − | 0.292912i | ||||
\(827\) | 2.28021e14 | 0.589450 | 0.294725 | − | 0.955582i | \(-0.404772\pi\) | ||||
0.294725 | + | 0.955582i | \(0.404772\pi\) | |||||||
\(828\) | 7.82190e13 | + | 3.72594e13i | 0.200984 | + | 0.0957380i | ||||
\(829\) | − | 4.42704e14i | − | 1.13068i | −0.824857 | − | 0.565342i | \(-0.808744\pi\) | ||
0.824857 | − | 0.565342i | \(-0.191256\pi\) | |||||||
\(830\) | 7.87276e13 | + | 1.24705e14i | 0.199865 | + | 0.316587i | ||||
\(831\) | 5.85358e14i | 1.47712i | ||||||||
\(832\) | −7.67058e13 | − | 3.17355e14i | −0.192403 | − | 0.796028i | ||||
\(833\) | −6.78301e14 | −1.69121 | ||||||||
\(834\) | 1.62829e14 | − | 1.02795e14i | 0.403553 | − | 0.254767i | ||||
\(835\) | −1.25794e14 | −0.309905 | ||||||||
\(836\) | −1.28434e14 | + | 2.69622e14i | −0.314519 | + | 0.660273i | ||||
\(837\) | 6.67657e14i | 1.62527i | ||||||||
\(838\) | 5.57533e13 | − | 3.51977e13i | 0.134912 | − | 0.0851715i | ||||
\(839\) | 2.87447e14i | 0.691429i | 0.938340 | + | 0.345715i | \(0.112363\pi\) | ||||
−0.938340 | + | 0.345715i | \(0.887637\pi\) | |||||||
\(840\) | −4.18760e13 | − | 3.51496e14i | −0.100131 | − | 0.840473i | ||||
\(841\) | −1.57350e13 | −0.0374014 | ||||||||
\(842\) | 9.96864e13 | + | 1.57904e14i | 0.235546 | + | 0.373106i | ||||
\(843\) | −2.59310e14 | −0.609090 | ||||||||
\(844\) | −2.88814e14 | + | 6.06311e14i | −0.674383 | + | 1.41574i | ||||
\(845\) | 9.48337e13i | 0.220130i | ||||||||
\(846\) | 8.71858e12 | + | 1.38103e13i | 0.0201184 | + | 0.0318677i | ||||
\(847\) | − | 2.13158e14i | − | 0.488973i | ||||||
\(848\) | −4.12819e14 | + | 3.34995e14i | −0.941414 | + | 0.763939i | ||||
\(849\) | 4.99796e14 | 1.13306 | ||||||||
\(850\) | −2.74649e14 | + | 1.73389e14i | −0.618990 | + | 0.390775i | ||||
\(851\) | 6.01053e14 | 1.34668 | ||||||||
\(852\) | 6.04321e13 | + | 2.87867e13i | 0.134608 | + | 0.0641200i | ||||
\(853\) | 3.23468e14i | 0.716286i | 0.933667 | + | 0.358143i | \(0.116590\pi\) | ||||
−0.933667 | + | 0.358143i | \(0.883410\pi\) | |||||||
\(854\) | 2.20779e13 | − | 1.39380e13i | 0.0486037 | − | 0.0306840i | ||||
\(855\) | 8.04536e13i | 0.176082i | ||||||||
\(856\) | 6.35461e13 | + | 5.33389e14i | 0.138268 | + | 1.16058i | ||||
\(857\) | 5.02722e14 | 1.08749 | 0.543743 | − | 0.839252i | \(-0.317007\pi\) | ||||
0.543743 | + | 0.839252i | \(0.317007\pi\) | |||||||
\(858\) | −1.40224e14 | − | 2.22115e14i | −0.301568 | − | 0.477686i | ||||
\(859\) | −6.31840e14 | −1.35096 | −0.675478 | − | 0.737380i | \(-0.736063\pi\) | ||||
−0.675478 | + | 0.737380i | \(0.736063\pi\) | |||||||
\(860\) | 6.10018e13 | + | 2.90581e13i | 0.129673 | + | 0.0617695i | ||||
\(861\) | 6.43220e14i | 1.35939i | ||||||||
\(862\) | −3.16868e14 | − | 5.01920e14i | −0.665796 | − | 1.05463i | ||||
\(863\) | 1.69445e14i | 0.353976i | 0.984213 | + | 0.176988i | \(0.0566353\pi\) | ||||
−0.984213 | + | 0.176988i | \(0.943365\pi\) | |||||||
\(864\) | −4.95987e14 | − | 1.67657e14i | −1.03015 | − | 0.348220i | ||||
\(865\) | −1.95816e13 | −0.0404360 | ||||||||
\(866\) | 1.24668e13 | − | 7.87043e12i | 0.0255956 | − | 0.0161588i | ||||
\(867\) | 3.08676e14 | 0.630096 | ||||||||
\(868\) | 4.78001e14 | − | 1.00347e15i | 0.970131 | − | 2.03660i | ||||
\(869\) | 2.50861e14i | 0.506214i | ||||||||
\(870\) | −2.40731e14 | + | 1.51976e14i | −0.482988 | + | 0.304915i | ||||
\(871\) | − | 1.12613e14i | − | 0.224645i | ||||||
\(872\) | 2.62318e14 | − | 3.12517e13i | 0.520291 | − | 0.0619856i | ||||
\(873\) | 3.31323e13 | 0.0653402 | ||||||||
\(874\) | −1.82039e14 | − | 2.88351e14i | −0.356951 | − | 0.565412i | ||||
\(875\) | −8.03726e14 | −1.56700 | ||||||||
\(876\) | 2.42305e14 | − | 5.08673e14i | 0.469724 | − | 0.986095i | ||||
\(877\) | − | 7.57672e13i | − | 0.146044i | −0.997330 | − | 0.0730219i | \(-0.976736\pi\) | ||
0.997330 | − | 0.0730219i | \(-0.0232643\pi\) | |||||||
\(878\) | 3.63274e14 | + | 5.75428e14i | 0.696245 | + | 1.10286i | ||||
\(879\) | − | 5.33414e14i | − | 1.01653i | ||||||
\(880\) | 2.25216e14 | − | 1.82759e14i | 0.426763 | − | 0.346310i | ||||
\(881\) | −3.19549e14 | −0.602085 | −0.301042 | − | 0.953611i | \(-0.597335\pi\) | ||||
−0.301042 | + | 0.953611i | \(0.597335\pi\) | |||||||
\(882\) | −1.70828e14 | + | 1.07846e14i | −0.320049 | + | 0.202051i | ||||
\(883\) | 4.13607e14 | 0.770522 | 0.385261 | − | 0.922808i | \(-0.374112\pi\) | ||||
0.385261 | + | 0.922808i | \(0.374112\pi\) | |||||||
\(884\) | 5.28156e14 | + | 2.51586e14i | 0.978364 | + | 0.466041i | ||||
\(885\) | 6.98736e13i | 0.128705i | ||||||||
\(886\) | 8.73490e14 | − | 5.51444e14i | 1.59989 | − | 1.01003i | ||||
\(887\) | − | 7.76606e14i | − | 1.41443i | −0.706997 | − | 0.707217i | \(-0.749950\pi\) | ||
0.706997 | − | 0.707217i | \(-0.250050\pi\) | |||||||
\(888\) | −8.24046e14 | + | 9.81740e13i | −1.49241 | + | 0.177800i | ||||
\(889\) | 1.34984e15 | 2.43093 | ||||||||
\(890\) | −3.25683e14 | − | 5.15884e14i | −0.583237 | − | 0.923851i | ||||
\(891\) | −2.84484e14 | −0.506605 | ||||||||
\(892\) | 1.11541e14 | + | 5.31322e13i | 0.197520 | + | 0.0940879i | ||||
\(893\) | − | 6.42814e13i | − | 0.113195i | ||||||
\(894\) | −1.73994e14 | − | 2.75607e14i | −0.304681 | − | 0.482617i | ||||
\(895\) | 9.48509e13i | 0.165168i | ||||||||
\(896\) | 6.25424e14 | + | 6.07081e14i | 1.08302 | + | 1.05125i | ||||
\(897\) | 2.99930e14 | 0.516484 | ||||||||
\(898\) | −6.10673e14 | + | 3.85524e14i | −1.04575 | + | 0.660192i | ||||
\(899\) | −8.93928e14 | −1.52231 | ||||||||
\(900\) | −4.16019e13 | + | 8.73352e13i | −0.0704531 | + | 0.147903i | ||||
\(901\) | − | 9.52601e14i | − | 1.60431i | ||||||
\(902\) | −4.45653e14 | + | 2.81346e14i | −0.746388 | + | 0.471203i | ||||
\(903\) | 1.63364e14i | 0.272093i | ||||||||
\(904\) | −2.85397e13 | − | 2.39554e14i | −0.0472723 | − | 0.396791i | ||||
\(905\) | −4.37190e14 | −0.720157 | ||||||||
\(906\) | 1.00941e14 | + | 1.59891e14i | 0.165358 | + | 0.261928i | ||||
\(907\) | −2.38403e14 | −0.388396 | −0.194198 | − | 0.980962i | \(-0.562210\pi\) | ||||
−0.194198 | + | 0.980962i | \(0.562210\pi\) | |||||||
\(908\) | −4.48056e14 | + | 9.40607e14i | −0.725944 | + | 1.52398i | ||||
\(909\) | − | 9.04259e13i | − | 0.145705i | ||||||
\(910\) | 2.75240e14 | + | 4.35982e14i | 0.441067 | + | 0.698653i | ||||
\(911\) | − | 1.97185e14i | − | 0.314255i | −0.987578 | − | 0.157128i | \(-0.949777\pi\) | ||
0.987578 | − | 0.157128i | \(-0.0502234\pi\) | |||||||
\(912\) | 2.96675e14 | + | 3.65597e14i | 0.470226 | + | 0.579467i | ||||
\(913\) | −2.92152e14 | −0.460527 | ||||||||
\(914\) | −2.87791e14 | + | 1.81686e14i | −0.451176 | + | 0.284833i | ||||
\(915\) | −1.36973e13 | −0.0213564 | ||||||||
\(916\) | 3.70004e14 | + | 1.76251e14i | 0.573759 | + | 0.273309i | ||||
\(917\) | − | 4.21755e14i | − | 0.650449i | ||||||
\(918\) | 7.93264e14 | − | 5.00796e14i | 1.21676 | − | 0.768153i | ||||
\(919\) | − | 6.18802e14i | − | 0.944005i | −0.881597 | − | 0.472003i | \(-0.843531\pi\) | ||
0.881597 | − | 0.472003i | \(-0.156469\pi\) | |||||||
\(920\) | 3.91781e13 | + | 3.28851e14i | 0.0594435 | + | 0.498953i | ||||
\(921\) | −8.44717e13 | −0.127471 | ||||||||
\(922\) | −1.97222e14 | − | 3.12401e14i | −0.296006 | − | 0.468875i | ||||
\(923\) | −9.74992e13 | −0.145543 | ||||||||
\(924\) | 6.33082e14 | + | 3.01567e14i | 0.939941 | + | 0.447738i | ||||
\(925\) | 6.71104e14i | 0.991017i | ||||||||
\(926\) | −3.80978e13 | − | 6.03472e13i | −0.0559558 | − | 0.0886344i | ||||
\(927\) | 1.69353e14i | 0.247397i | ||||||||
\(928\) | 2.24477e14 | − | 6.64079e14i | 0.326161 | − | 0.964894i | ||||
\(929\) | −3.05402e14 | −0.441360 | −0.220680 | − | 0.975346i | \(-0.570828\pi\) | ||||
−0.220680 | + | 0.975346i | \(0.570828\pi\) | |||||||
\(930\) | −4.93069e14 | + | 3.11280e14i | −0.708750 | + | 0.447442i | ||||
\(931\) | 7.95139e14 | 1.13683 | ||||||||
\(932\) | −1.10205e11 | + | 2.31355e11i | −0.000156719 | + | 0.000329003i | ||||
\(933\) | − | 3.53226e14i | − | 0.499626i | ||||||
\(934\) | −1.80737e14 | + | 1.14101e14i | −0.254280 | + | 0.160530i | ||||
\(935\) | 5.19698e14i | 0.727266i | ||||||||
\(936\) | 1.73015e14 | − | 2.06124e13i | 0.240827 | − | 0.0286913i | ||||
\(937\) | −1.24962e15 | −1.73013 | −0.865066 | − | 0.501658i | \(-0.832724\pi\) | ||||
−0.865066 | + | 0.501658i | \(0.832724\pi\) | |||||||
\(938\) | 1.60487e14 | + | 2.54212e14i | 0.221017 | + | 0.350092i | ||||
\(939\) | −1.11022e14 | −0.152083 | ||||||||
\(940\) | −2.68473e13 | + | 5.63608e13i | −0.0365815 | + | 0.0767959i | ||||
\(941\) | 8.67444e14i | 1.17569i | 0.808973 | + | 0.587846i | \(0.200024\pi\) | ||||
−0.808973 | + | 0.587846i | \(0.799976\pi\) | |||||||
\(942\) | 2.50443e12 | + | 3.96703e12i | 0.00337640 | + | 0.00534824i | ||||
\(943\) | − | 6.01780e14i | − | 0.807011i | ||||||
\(944\) | −1.08411e14 | − | 1.33597e14i | −0.144616 | − | 0.178212i | ||||
\(945\) | 8.26794e14 | 1.09708 | ||||||||
\(946\) | −1.13187e14 | + | 7.14559e13i | −0.149396 | + | 0.0943153i | ||||
\(947\) | 1.24423e15 | 1.63362 | 0.816812 | − | 0.576904i | \(-0.195739\pi\) | ||||
0.816812 | + | 0.576904i | \(0.195739\pi\) | |||||||
\(948\) | 3.57048e14 | + | 1.70079e14i | 0.466322 | + | 0.222131i | ||||
\(949\) | 8.20677e14i | 1.06621i | ||||||||
\(950\) | 3.21958e14 | − | 2.03255e14i | 0.416084 | − | 0.262678i | ||||
\(951\) | 1.06786e15i | 1.37281i | ||||||||
\(952\) | −1.55080e15 | + | 1.84756e14i | −1.98322 | + | 0.236273i | ||||
\(953\) | 1.19147e15 | 1.51572 | 0.757860 | − | 0.652417i | \(-0.226245\pi\) | ||||
0.757860 | + | 0.652417i | \(0.226245\pi\) | |||||||
\(954\) | −1.51458e14 | − | 2.39910e14i | −0.191668 | − | 0.303604i | ||||
\(955\) | −1.93211e14 | −0.243228 | ||||||||
\(956\) | −1.27614e15 | − | 6.07887e14i | −1.59812 | − | 0.761261i | ||||
\(957\) | − | 5.63972e14i | − | 0.702583i | ||||||
\(958\) | 5.56541e14 | + | 8.81563e14i | 0.689714 | + | 1.09251i | ||||
\(959\) | − | 2.03914e14i | − | 0.251393i | ||||||
\(960\) | −1.07427e14 | − | 4.44456e14i | −0.131752 | − | 0.545096i | ||||
\(961\) | −1.01133e15 | −1.23389 | ||||||||
\(962\) | 1.02212e15 | − | 6.45272e14i | 1.24058 | − | 0.783191i | ||||
\(963\) | −2.86665e14 | −0.346134 | ||||||||
\(964\) | 3.52631e14 | − | 7.40281e14i | 0.423580 | − | 0.889225i | ||||
\(965\) | − | 6.06163e14i | − | 0.724357i | ||||||
\(966\) | −6.77061e14 | + | 4.27436e14i | −0.804900 | + | 0.508142i | ||||
\(967\) | 1.37316e15i | 1.62401i | 0.583652 | + | 0.812004i | \(0.301623\pi\) | ||||
−0.583652 | + | 0.812004i | \(0.698377\pi\) | |||||||
\(968\) | −3.25735e13 | − | 2.73413e14i | −0.0383255 | − | 0.321694i | ||||
\(969\) | −8.43634e14 | −0.987496 | ||||||||
\(970\) | 6.76077e13 | + | 1.07091e14i | 0.0787295 | + | 0.124708i | ||||
\(971\) | −7.44459e14 | −0.862471 | −0.431235 | − | 0.902239i | \(-0.641922\pi\) | ||||
−0.431235 | + | 0.902239i | \(0.641922\pi\) | |||||||
\(972\) | 2.12862e14 | − | 4.46862e14i | 0.245339 | − | 0.515042i | ||||
\(973\) | − | 7.48765e14i | − | 0.858581i | ||||||
\(974\) | −5.94038e14 | − | 9.40960e14i | −0.677672 | − | 1.07344i | ||||
\(975\) | 3.34885e14i | 0.380078i | ||||||||
\(976\) | 2.61889e13 | − | 2.12518e13i | 0.0295712 | − | 0.0239964i | ||||
\(977\) | 8.44024e14 | 0.948161 | 0.474081 | − | 0.880482i | \(-0.342781\pi\) | ||||
0.474081 | + | 0.880482i | \(0.342781\pi\) | |||||||
\(978\) | 7.96321e14 | − | 5.02726e14i | 0.890008 | − | 0.561872i | ||||
\(979\) | 1.20858e15 | 1.34389 | ||||||||
\(980\) | −6.97164e14 | − | 3.32092e14i | −0.771266 | − | 0.367391i | ||||
\(981\) | 1.40981e14i | 0.155172i | ||||||||
\(982\) | 1.33845e14 | − | 8.44976e13i | 0.146569 | − | 0.0925309i | ||||
\(983\) | − | 6.75786e14i | − | 0.736277i | −0.929771 | − | 0.368139i | \(-0.879995\pi\) | ||
0.929771 | − | 0.368139i | \(-0.120005\pi\) | |||||||
\(984\) | 9.82927e13 | + | 8.25043e14i | 0.106548 | + | 0.894337i | ||||
\(985\) | 1.12320e15 | 1.21137 | ||||||||
\(986\) | 6.70518e14 | + | 1.06210e15i | 0.719492 | + | 1.13968i | ||||
\(987\) | −1.50935e14 | −0.161141 | ||||||||
\(988\) | −6.19131e14 | − | 2.94921e14i | −0.657654 | − | 0.313272i | ||||
\(989\) | − | 1.52839e14i | − | 0.161530i | ||||||
\(990\) | 8.26289e13 | + | 1.30885e14i | 0.0868873 | + | 0.137630i | ||||
\(991\) | 5.73477e14i | 0.599995i | 0.953940 | + | 0.299998i | \(0.0969859\pi\) | ||||
−0.953940 | + | 0.299998i | \(0.903014\pi\) | |||||||
\(992\) | 4.59777e14 | − | 1.36018e15i | 0.478618 | − | 1.41591i | ||||
\(993\) | −1.37159e15 | −1.42062 | ||||||||
\(994\) | 2.20094e14 | − | 1.38948e14i | 0.226818 | − | 0.143193i | ||||
\(995\) | 5.69548e14 | 0.584003 | ||||||||
\(996\) | −1.98074e14 | + | 4.15818e14i | −0.202083 | + | 0.424235i | ||||
\(997\) | 4.15346e14i | 0.421633i | 0.977526 | + | 0.210816i | \(0.0676122\pi\) | ||||
−0.977526 | + | 0.210816i | \(0.932388\pi\) | |||||||
\(998\) | −1.71493e14 | + | 1.08266e14i | −0.173219 | + | 0.109355i | ||||
\(999\) | − | 1.93834e15i | − | 1.94806i |
(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 | 8.11.d.b.3.2 | yes | 8 | |
3.2 | odd | 2 | 72.11.b.b.19.7 | 8 | |||
4.3 | odd | 2 | 32.11.d.b.15.4 | 8 | |||
8.3 | odd | 2 | inner | 8.11.d.b.3.1 | ✓ | 8 | |
8.5 | even | 2 | 32.11.d.b.15.3 | 8 | |||
12.11 | even | 2 | 288.11.b.b.271.3 | 8 | |||
16.3 | odd | 4 | 256.11.c.m.255.4 | 16 | |||
16.5 | even | 4 | 256.11.c.m.255.3 | 16 | |||
16.11 | odd | 4 | 256.11.c.m.255.13 | 16 | |||
16.13 | even | 4 | 256.11.c.m.255.14 | 16 | |||
24.5 | odd | 2 | 288.11.b.b.271.6 | 8 | |||
24.11 | even | 2 | 72.11.b.b.19.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.11.d.b.3.1 | ✓ | 8 | 8.3 | odd | 2 | inner | |
8.11.d.b.3.2 | yes | 8 | 1.1 | even | 1 | trivial | |
32.11.d.b.15.3 | 8 | 8.5 | even | 2 | |||
32.11.d.b.15.4 | 8 | 4.3 | odd | 2 | |||
72.11.b.b.19.7 | 8 | 3.2 | odd | 2 | |||
72.11.b.b.19.8 | 8 | 24.11 | even | 2 | |||
256.11.c.m.255.3 | 16 | 16.5 | even | 4 | |||
256.11.c.m.255.4 | 16 | 16.3 | odd | 4 | |||
256.11.c.m.255.13 | 16 | 16.11 | odd | 4 | |||
256.11.c.m.255.14 | 16 | 16.13 | even | 4 | |||
288.11.b.b.271.3 | 8 | 12.11 | even | 2 | |||
288.11.b.b.271.6 | 8 | 24.5 | odd | 2 |