Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,27,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 27, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 27);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 27 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.b (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: | \(12.8487876219\) |
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: | \( x^{8} + 2728193x^{6} + 2071419806976x^{4} + 503906274711956480x^{2} + 26754716118873014272000 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{33}\cdot 3^{38}\cdot 5^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.3 | ||
Root | \(-575.513i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.27.b.a.2.6 |
$q$-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 \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 6906.16i | − | 0.843037i | −0.906820 | − | 0.421518i | \(-0.861497\pi\) | ||
0.906820 | − | 0.421518i | \(-0.138503\pi\) | |||||||
\(3\) | 618315. | + | 1.46954e6i | 0.387823 | + | 0.921734i | ||||
\(4\) | 1.94139e7 | 0.289289 | ||||||||
\(5\) | 1.04255e9i | 0.854054i | 0.904239 | + | 0.427027i | \(0.140439\pi\) | ||||
−0.904239 | + | 0.427027i | \(0.859561\pi\) | |||||||
\(6\) | 1.01489e10 | − | 4.27018e9i | 0.777055 | − | 0.326949i | ||||
\(7\) | −1.82788e11 | −1.88657 | −0.943284 | − | 0.331986i | \(-0.892281\pi\) | ||||
−0.943284 | + | 0.331986i | \(0.892281\pi\) | |||||||
\(8\) | − | 5.97540e11i | − | 1.08692i | ||||||
\(9\) | −1.77724e12 | + | 1.81728e12i | −0.699187 | + | 0.714939i | ||||
\(10\) | 7.19999e12 | 0.719999 | ||||||||
\(11\) | 2.00553e13i | 0.580929i | 0.956886 | + | 0.290465i | \(0.0938099\pi\) | ||||
−0.956886 | + | 0.290465i | \(0.906190\pi\) | |||||||
\(12\) | 1.20039e13 | + | 2.85295e13i | 0.112193 | + | 0.266648i | ||||
\(13\) | −1.77823e14 | −0.587118 | −0.293559 | − | 0.955941i | \(-0.594840\pi\) | ||||
−0.293559 | + | 0.955941i | \(0.594840\pi\) | |||||||
\(14\) | 1.26236e15i | 1.59045i | ||||||||
\(15\) | −1.53207e15 | + | 6.44622e14i | −0.787211 | + | 0.331222i | ||||
\(16\) | −2.82386e15 | −0.627022 | ||||||||
\(17\) | 1.19613e16i | 1.20766i | 0.797115 | + | 0.603828i | \(0.206359\pi\) | ||||
−0.797115 | + | 0.603828i | \(0.793641\pi\) | |||||||
\(18\) | 1.25504e16 | + | 1.22739e16i | 0.602719 | + | 0.589440i | ||||
\(19\) | −3.24857e15 | −0.0772494 | −0.0386247 | − | 0.999254i | \(-0.512298\pi\) | ||||
−0.0386247 | + | 0.999254i | \(0.512298\pi\) | |||||||
\(20\) | 2.02399e16i | 0.247069i | ||||||||
\(21\) | −1.13020e17 | − | 2.68614e17i | −0.731654 | − | 1.73891i | ||||
\(22\) | 1.38505e17 | 0.489745 | ||||||||
\(23\) | − | 1.64173e17i | − | 0.325716i | −0.986650 | − | 0.162858i | \(-0.947929\pi\) | ||
0.986650 | − | 0.162858i | \(-0.0520712\pi\) | |||||||
\(24\) | 8.78109e17 | − | 3.69467e17i | 1.00185 | − | 0.421532i | ||||
\(25\) | 4.03212e17 | 0.270591 | ||||||||
\(26\) | 1.22808e18i | 0.494962i | ||||||||
\(27\) | −3.76946e18 | − | 1.48808e18i | −0.930144 | − | 0.367195i | ||||
\(28\) | −3.54862e18 | −0.545764 | ||||||||
\(29\) | 1.21188e19i | 1.18110i | 0.807002 | + | 0.590549i | \(0.201089\pi\) | ||||
−0.807002 | + | 0.590549i | \(0.798911\pi\) | |||||||
\(30\) | 4.45186e18 | + | 1.05807e19i | 0.279232 | + | 0.663648i | ||||
\(31\) | 2.60244e18 | 0.106581 | 0.0532904 | − | 0.998579i | \(-0.483029\pi\) | ||||
0.0532904 | + | 0.998579i | \(0.483029\pi\) | |||||||
\(32\) | − | 2.05982e19i | − | 0.558315i | ||||||
\(33\) | −2.94720e19 | + | 1.24005e19i | −0.535462 | + | 0.225298i | ||||
\(34\) | 8.26067e19 | 1.01810 | ||||||||
\(35\) | − | 1.90565e20i | − | 1.61123i | ||||||
\(36\) | −3.45031e19 | + | 3.52804e19i | −0.202267 | + | 0.206824i | ||||
\(37\) | −2.51577e19 | −0.103288 | −0.0516438 | − | 0.998666i | \(-0.516446\pi\) | ||||
−0.0516438 | + | 0.998666i | \(0.516446\pi\) | |||||||
\(38\) | 2.24351e19i | 0.0651240i | ||||||||
\(39\) | −1.09951e20 | − | 2.61319e20i | −0.227698 | − | 0.541167i | ||||
\(40\) | 6.22963e20 | 0.928287 | ||||||||
\(41\) | 1.30238e21i | 1.40782i | 0.710290 | + | 0.703909i | \(0.248564\pi\) | ||||
−0.710290 | + | 0.703909i | \(0.751436\pi\) | |||||||
\(42\) | −1.85509e21 | + | 7.80536e20i | −1.46597 | + | 0.616811i | ||||
\(43\) | 1.35087e21 | 0.786183 | 0.393091 | − | 0.919499i | \(-0.371406\pi\) | ||||
0.393091 | + | 0.919499i | \(0.371406\pi\) | |||||||
\(44\) | 3.89350e20i | 0.168057i | ||||||||
\(45\) | −1.89460e21 | − | 1.85286e21i | −0.610597 | − | 0.597144i | ||||
\(46\) | −1.13380e21 | −0.274590 | ||||||||
\(47\) | − | 1.28484e21i | − | 0.235276i | −0.993057 | − | 0.117638i | \(-0.962468\pi\) | ||
0.993057 | − | 0.117638i | \(-0.0375323\pi\) | |||||||
\(48\) | −1.74603e21 | − | 4.14978e21i | −0.243173 | − | 0.577948i | ||||
\(49\) | 2.40239e22 | 2.55914 | ||||||||
\(50\) | − | 2.78465e21i | − | 0.228118i | ||||||
\(51\) | −1.75777e22 | + | 7.39586e21i | −1.11314 | + | 0.468356i | ||||
\(52\) | −3.45224e21 | −0.169847 | ||||||||
\(53\) | − | 4.21845e22i | − | 1.62019i | −0.586298 | − | 0.810096i | \(-0.699415\pi\) | ||
0.586298 | − | 0.810096i | \(-0.300585\pi\) | |||||||
\(54\) | −1.02769e22 | + | 2.60325e22i | −0.309559 | + | 0.784145i | ||||
\(55\) | −2.09085e22 | −0.496145 | ||||||||
\(56\) | 1.09223e23i | 2.05055i | ||||||||
\(57\) | −2.00864e21 | − | 4.77390e21i | −0.0299591 | − | 0.0712034i | ||||
\(58\) | 8.36943e22 | 0.995708 | ||||||||
\(59\) | − | 3.86894e22i | − | 0.368567i | −0.982873 | − | 0.184283i | \(-0.941004\pi\) | ||
0.982873 | − | 0.184283i | \(-0.0589964\pi\) | |||||||
\(60\) | −2.97434e22 | + | 1.25146e22i | −0.227732 | + | 0.0958189i | ||||
\(61\) | −1.13641e23 | −0.701856 | −0.350928 | − | 0.936402i | \(-0.614134\pi\) | ||||
−0.350928 | + | 0.936402i | \(0.614134\pi\) | |||||||
\(62\) | − | 1.79729e22i | − | 0.0898516i | ||||||
\(63\) | 3.24858e23 | − | 3.32176e23i | 1.31906 | − | 1.34878i | ||||
\(64\) | −3.31760e23 | −1.09770 | ||||||||
\(65\) | − | 1.85389e23i | − | 0.501431i | ||||||
\(66\) | 8.56395e22 | + | 2.03538e23i | 0.189934 | + | 0.451414i | ||||
\(67\) | 4.68597e23 | 0.854726 | 0.427363 | − | 0.904080i | \(-0.359443\pi\) | ||||
0.427363 | + | 0.904080i | \(0.359443\pi\) | |||||||
\(68\) | 2.32216e23i | 0.349362i | ||||||||
\(69\) | 2.41258e23 | − | 1.01510e23i | 0.300223 | − | 0.126320i | ||||
\(70\) | −1.31607e24 | −1.35833 | ||||||||
\(71\) | 5.64254e23i | 0.484302i | 0.970239 | + | 0.242151i | \(0.0778529\pi\) | ||||
−0.970239 | + | 0.242151i | \(0.922147\pi\) | |||||||
\(72\) | 1.08590e24 | + | 1.06197e24i | 0.777080 | + | 0.759959i | ||||
\(73\) | −1.49767e24 | −0.895814 | −0.447907 | − | 0.894080i | \(-0.647831\pi\) | ||||
−0.447907 | + | 0.894080i | \(0.647831\pi\) | |||||||
\(74\) | 1.73743e23i | 0.0870753i | ||||||||
\(75\) | 2.49312e23 | + | 5.92537e23i | 0.104941 | + | 0.249413i | ||||
\(76\) | −6.30673e22 | −0.0223474 | ||||||||
\(77\) | − | 3.66586e24i | − | 1.09596i | ||||||
\(78\) | −1.80471e24 | + | 7.59338e23i | −0.456223 | + | 0.191958i | ||||
\(79\) | 4.28960e24 | 0.918892 | 0.459446 | − | 0.888206i | \(-0.348048\pi\) | ||||
0.459446 | + | 0.888206i | \(0.348048\pi\) | |||||||
\(80\) | − | 2.94400e24i | − | 0.535511i | ||||||
\(81\) | −1.43920e23 | − | 6.45948e24i | −0.0222748 | − | 0.999752i | ||||
\(82\) | 8.99442e24 | 1.18684 | ||||||||
\(83\) | 1.38291e25i | 1.55876i | 0.626550 | + | 0.779381i | \(0.284466\pi\) | ||||
−0.626550 | + | 0.779381i | \(0.715534\pi\) | |||||||
\(84\) | −2.19416e24 | − | 5.21485e24i | −0.211660 | − | 0.503049i | ||||
\(85\) | −1.24702e25 | −1.03140 | ||||||||
\(86\) | − | 9.32932e24i | − | 0.662781i | ||||||
\(87\) | −1.78091e25 | + | 7.49323e24i | −1.08866 | + | 0.458056i | ||||
\(88\) | 1.19838e25 | 0.631423 | ||||||||
\(89\) | 2.05341e25i | 0.934126i | 0.884224 | + | 0.467063i | \(0.154688\pi\) | ||||
−0.884224 | + | 0.467063i | \(0.845312\pi\) | |||||||
\(90\) | −1.27961e25 | + | 1.30844e25i | −0.503414 | + | 0.514755i | ||||
\(91\) | 3.25040e25 | 1.10764 | ||||||||
\(92\) | − | 3.18723e24i | − | 0.0942261i | ||||||
\(93\) | 1.60913e24 | + | 3.82440e24i | 0.0413345 | + | 0.0982392i | ||||
\(94\) | −8.87333e24 | −0.198347 | ||||||||
\(95\) | − | 3.38678e24i | − | 0.0659752i | ||||||
\(96\) | 3.02699e25 | − | 1.27362e25i | 0.514618 | − | 0.216527i | ||||
\(97\) | −3.14676e25 | −0.467554 | −0.233777 | − | 0.972290i | \(-0.575109\pi\) | ||||
−0.233777 | + | 0.972290i | \(0.575109\pi\) | |||||||
\(98\) | − | 1.65913e26i | − | 2.15745i | ||||||
\(99\) | −3.64460e25 | − | 3.56430e25i | −0.415329 | − | 0.406178i | ||||
\(100\) | 7.82791e24 | 0.0782791 | ||||||||
\(101\) | 8.23542e25i | 0.723615i | 0.932253 | + | 0.361808i | \(0.117840\pi\) | ||||
−0.932253 | + | 0.361808i | \(0.882160\pi\) | |||||||
\(102\) | 5.10769e25 | + | 1.21394e26i | 0.394841 | + | 0.938415i | ||||
\(103\) | 3.23565e25 | 0.220332 | 0.110166 | − | 0.993913i | \(-0.464862\pi\) | ||||
0.110166 | + | 0.993913i | \(0.464862\pi\) | |||||||
\(104\) | 1.06257e26i | 0.638149i | ||||||||
\(105\) | 2.80043e26 | − | 1.17829e26i | 1.48513 | − | 0.624872i | ||||
\(106\) | −2.91332e26 | −1.36588 | ||||||||
\(107\) | 2.11400e26i | 0.877235i | 0.898674 | + | 0.438617i | \(0.144532\pi\) | ||||
−0.898674 | + | 0.438617i | \(0.855468\pi\) | |||||||
\(108\) | −7.31798e25 | − | 2.88894e25i | −0.269081 | − | 0.106226i | ||||
\(109\) | −4.44000e26 | −1.44823 | −0.724116 | − | 0.689678i | \(-0.757752\pi\) | ||||
−0.724116 | + | 0.689678i | \(0.757752\pi\) | |||||||
\(110\) | 1.44398e26i | 0.418269i | ||||||||
\(111\) | −1.55554e25 | − | 3.69703e25i | −0.0400573 | − | 0.0952037i | ||||
\(112\) | 5.16167e26 | 1.18292 | ||||||||
\(113\) | − | 3.62279e26i | − | 0.739645i | −0.929103 | − | 0.369822i | \(-0.879419\pi\) | ||
0.929103 | − | 0.369822i | \(-0.120581\pi\) | |||||||
\(114\) | −3.29693e25 | + | 1.38720e25i | −0.0600270 | + | 0.0252566i | ||||
\(115\) | 1.71158e26 | 0.278179 | ||||||||
\(116\) | 2.35273e26i | 0.341679i | ||||||||
\(117\) | 3.16035e26 | − | 3.23155e26i | 0.410505 | − | 0.419753i | ||||
\(118\) | −2.67195e26 | −0.310715 | ||||||||
\(119\) | − | 2.18638e27i | − | 2.27832i | ||||||
\(120\) | 3.85187e26 | + | 9.15470e26i | 0.360011 | + | 0.855634i | ||||
\(121\) | 7.89604e26 | 0.662521 | ||||||||
\(122\) | 7.84824e26i | 0.591691i | ||||||||
\(123\) | −1.91390e27 | + | 8.05279e26i | −1.29763 | + | 0.545984i | ||||
\(124\) | 5.05235e25 | 0.0308327 | ||||||||
\(125\) | 1.97388e27i | 1.08515i | ||||||||
\(126\) | −2.29406e27 | − | 2.24352e27i | −1.13707 | − | 1.11202i | ||||
\(127\) | 2.03638e27 | 0.910775 | 0.455388 | − | 0.890293i | \(-0.349501\pi\) | ||||
0.455388 | + | 0.890293i | \(0.349501\pi\) | |||||||
\(128\) | 9.08866e26i | 0.367088i | ||||||||
\(129\) | 8.35263e26 | + | 1.98516e27i | 0.304900 | + | 0.724651i | ||||
\(130\) | −1.28033e27 | −0.422724 | ||||||||
\(131\) | 1.06949e27i | 0.319632i | 0.987147 | + | 0.159816i | \(0.0510901\pi\) | ||||
−0.987147 | + | 0.159816i | \(0.948910\pi\) | |||||||
\(132\) | −5.72167e26 | + | 2.40741e26i | −0.154904 | + | 0.0651762i | ||||
\(133\) | 5.93798e26 | 0.145736 | ||||||||
\(134\) | − | 3.23620e27i | − | 0.720565i | ||||||
\(135\) | 1.55139e27 | − | 3.92984e27i | 0.313605 | − | 0.794394i | ||||
\(136\) | 7.14736e27 | 1.31262 | ||||||||
\(137\) | 1.02973e27i | 0.171931i | 0.996298 | + | 0.0859657i | \(0.0273975\pi\) | ||||
−0.996298 | + | 0.0859657i | \(0.972602\pi\) | |||||||
\(138\) | −7.01046e26 | − | 1.66617e27i | −0.106492 | − | 0.253099i | ||||
\(139\) | −1.19179e28 | −1.64818 | −0.824092 | − | 0.566456i | \(-0.808314\pi\) | ||||
−0.824092 | + | 0.566456i | \(0.808314\pi\) | |||||||
\(140\) | − | 3.69960e27i | − | 0.466112i | ||||||
\(141\) | 1.88813e27 | − | 7.94438e26i | 0.216862 | − | 0.0912455i | ||||
\(142\) | 3.89682e27 | 0.408284 | ||||||||
\(143\) | − | 3.56630e27i | − | 0.341074i | ||||||
\(144\) | 5.01867e27 | − | 5.13173e27i | 0.438406 | − | 0.448283i | ||||
\(145\) | −1.26344e28 | −1.00872 | ||||||||
\(146\) | 1.03431e28i | 0.755204i | ||||||||
\(147\) | 1.48543e28 | + | 3.53041e28i | 0.992493 | + | 2.35885i | ||||
\(148\) | −4.88408e26 | −0.0298800 | ||||||||
\(149\) | − | 2.75606e27i | − | 0.154478i | −0.997013 | − | 0.0772390i | \(-0.975390\pi\) | ||
0.997013 | − | 0.0772390i | \(-0.0246104\pi\) | |||||||
\(150\) | 4.09215e27 | − | 1.72179e27i | 0.210264 | − | 0.0884694i | ||||
\(151\) | −6.47428e27 | −0.305134 | −0.152567 | − | 0.988293i | \(-0.548754\pi\) | ||||
−0.152567 | + | 0.988293i | \(0.548754\pi\) | |||||||
\(152\) | 1.94115e27i | 0.0839637i | ||||||||
\(153\) | −2.17370e28 | − | 2.12581e28i | −0.863400 | − | 0.844377i | ||||
\(154\) | −2.53170e28 | −0.923937 | ||||||||
\(155\) | 2.71317e27i | 0.0910259i | ||||||||
\(156\) | −2.13457e27 | − | 5.07322e27i | −0.0658705 | − | 0.156554i | ||||
\(157\) | 2.34823e28 | 0.666877 | 0.333438 | − | 0.942772i | \(-0.391791\pi\) | ||||
0.333438 | + | 0.942772i | \(0.391791\pi\) | |||||||
\(158\) | − | 2.96246e28i | − | 0.774659i | ||||||
\(159\) | 6.19918e28 | − | 2.60833e28i | 1.49339 | − | 0.628347i | ||||
\(160\) | 2.14746e28 | 0.476832 | ||||||||
\(161\) | 3.00087e28i | 0.614485i | ||||||||
\(162\) | −4.46102e28 | + | 9.93931e26i | −0.842827 | + | 0.0187785i | ||||
\(163\) | 1.16159e28 | 0.202589 | 0.101294 | − | 0.994856i | \(-0.467702\pi\) | ||||
0.101294 | + | 0.994856i | \(0.467702\pi\) | |||||||
\(164\) | 2.52842e28i | 0.407267i | ||||||||
\(165\) | −1.29281e28 | − | 3.07260e28i | −0.192416 | − | 0.457314i | ||||
\(166\) | 9.55062e28 | 1.31409 | ||||||||
\(167\) | − | 8.16140e28i | − | 1.03860i | −0.854591 | − | 0.519302i | \(-0.826192\pi\) | ||
0.854591 | − | 0.519302i | \(-0.173808\pi\) | |||||||
\(168\) | −1.60508e29 | + | 6.75341e28i | −1.89006 | + | 0.795248i | ||||
\(169\) | −6.01121e28 | −0.655292 | ||||||||
\(170\) | 8.61214e28i | 0.869511i | ||||||||
\(171\) | 5.77348e27 | − | 5.90355e27i | 0.0540118 | − | 0.0552286i | ||||
\(172\) | 2.62256e28 | 0.227434 | ||||||||
\(173\) | 6.03281e28i | 0.485199i | 0.970126 | + | 0.242600i | \(0.0780002\pi\) | ||||
−0.970126 | + | 0.242600i | \(0.922000\pi\) | |||||||
\(174\) | 5.17494e28 | + | 1.22992e29i | 0.386158 | + | 0.917778i | ||||
\(175\) | −7.37022e28 | −0.510489 | ||||||||
\(176\) | − | 5.66332e28i | − | 0.364256i | ||||||
\(177\) | 5.68557e28 | − | 2.39222e28i | 0.339721 | − | 0.142939i | ||||
\(178\) | 1.41812e29 | 0.787503 | ||||||||
\(179\) | − | 4.70459e28i | − | 0.242903i | −0.992597 | − | 0.121451i | \(-0.961245\pi\) | ||
0.992597 | − | 0.121451i | \(-0.0387549\pi\) | |||||||
\(180\) | −3.67815e28 | − | 3.59711e28i | −0.176639 | − | 0.172747i | ||||
\(181\) | 9.02584e28 | 0.403335 | 0.201668 | − | 0.979454i | \(-0.435364\pi\) | ||||
0.201668 | + | 0.979454i | \(0.435364\pi\) | |||||||
\(182\) | − | 2.24477e29i | − | 0.933780i | ||||||
\(183\) | −7.02661e28 | − | 1.67001e29i | −0.272196 | − | 0.646925i | ||||
\(184\) | −9.80996e28 | −0.354026 | ||||||||
\(185\) | − | 2.62281e28i | − | 0.0882133i | ||||||
\(186\) | 2.64119e28 | − | 1.11129e28i | 0.0828192 | − | 0.0348465i | ||||
\(187\) | −2.39887e29 | −0.701562 | ||||||||
\(188\) | − | 2.49438e28i | − | 0.0680629i | ||||||
\(189\) | 6.89011e29 | + | 2.72002e29i | 1.75478 | + | 0.692739i | ||||
\(190\) | −2.33896e28 | −0.0556195 | ||||||||
\(191\) | 3.87159e29i | 0.859916i | 0.902849 | + | 0.429958i | \(0.141472\pi\) | ||||
−0.902849 | + | 0.429958i | \(0.858528\pi\) | |||||||
\(192\) | −2.05132e29 | − | 4.87535e29i | −0.425714 | − | 1.01179i | ||||
\(193\) | −8.50418e29 | −1.64963 | −0.824817 | − | 0.565400i | \(-0.808722\pi\) | ||||
−0.824817 | + | 0.565400i | \(0.808722\pi\) | |||||||
\(194\) | 2.17320e29i | 0.394165i | ||||||||
\(195\) | 2.72437e29 | − | 1.14629e29i | 0.462186 | − | 0.194466i | ||||
\(196\) | 4.66397e29 | 0.740332 | ||||||||
\(197\) | 1.10042e30i | 1.63493i | 0.575977 | + | 0.817466i | \(0.304622\pi\) | ||||
−0.575977 | + | 0.817466i | \(0.695378\pi\) | |||||||
\(198\) | −2.46156e29 | + | 2.51702e29i | −0.342423 | + | 0.350137i | ||||
\(199\) | −1.76150e29 | −0.229505 | −0.114753 | − | 0.993394i | \(-0.536608\pi\) | ||||
−0.114753 | + | 0.993394i | \(0.536608\pi\) | |||||||
\(200\) | − | 2.40935e29i | − | 0.294110i | ||||||
\(201\) | 2.89740e29 | + | 6.88623e29i | 0.331482 | + | 0.787830i | ||||
\(202\) | 5.68751e29 | 0.610034 | ||||||||
\(203\) | − | 2.21517e30i | − | 2.22822i | ||||||
\(204\) | −3.41251e29 | + | 1.43582e29i | −0.322019 | + | 0.135490i | ||||
\(205\) | −1.35779e30 | −1.20235 | ||||||||
\(206\) | − | 2.23459e29i | − | 0.185748i | ||||||
\(207\) | 2.98347e29 | + | 2.91774e29i | 0.232867 | + | 0.227736i | ||||
\(208\) | 5.02148e29 | 0.368136 | ||||||||
\(209\) | − | 6.51508e28i | − | 0.0448764i | ||||||
\(210\) | −8.13746e29 | − | 1.93402e30i | −0.526790 | − | 1.25202i | ||||
\(211\) | 2.90897e30 | 1.77038 | 0.885191 | − | 0.465228i | \(-0.154028\pi\) | ||||
0.885191 | + | 0.465228i | \(0.154028\pi\) | |||||||
\(212\) | − | 8.18964e29i | − | 0.468704i | ||||||
\(213\) | −8.29194e29 | + | 3.48886e29i | −0.446397 | + | 0.187823i | ||||
\(214\) | 1.45996e30 | 0.739541 | ||||||||
\(215\) | 1.40835e30i | 0.671443i | ||||||||
\(216\) | −8.89185e29 | + | 2.25240e30i | −0.399111 | + | 1.01099i | ||||
\(217\) | −4.75695e29 | −0.201072 | ||||||||
\(218\) | 3.06633e30i | 1.22091i | ||||||||
\(219\) | −9.26029e29 | − | 2.20088e30i | −0.347417 | − | 0.825703i | ||||
\(220\) | −4.05916e29 | −0.143530 | ||||||||
\(221\) | − | 2.12700e30i | − | 0.709036i | ||||||
\(222\) | −2.55322e29 | + | 1.07428e29i | −0.0802602 | + | 0.0337698i | ||||
\(223\) | −2.33027e30 | −0.690944 | −0.345472 | − | 0.938429i | \(-0.612281\pi\) | ||||
−0.345472 | + | 0.938429i | \(0.612281\pi\) | |||||||
\(224\) | 3.76510e30i | 1.05330i | ||||||||
\(225\) | −7.16605e29 | + | 7.32749e29i | −0.189194 | + | 0.193456i | ||||
\(226\) | −2.50195e30 | −0.623547 | ||||||||
\(227\) | − | 6.02266e29i | − | 0.141727i | −0.997486 | − | 0.0708634i | \(-0.977425\pi\) | ||
0.997486 | − | 0.0708634i | \(-0.0225755\pi\) | |||||||
\(228\) | −3.89954e28 | − | 9.26800e28i | −0.00866684 | − | 0.0205984i | ||||
\(229\) | 2.90554e30 | 0.610050 | 0.305025 | − | 0.952344i | \(-0.401335\pi\) | ||||
0.305025 | + | 0.952344i | \(0.401335\pi\) | |||||||
\(230\) | − | 1.18204e30i | − | 0.234515i | ||||||
\(231\) | 5.38713e30 | − | 2.26665e30i | 1.01019 | − | 0.425039i | ||||
\(232\) | 7.24146e30 | 1.28376 | ||||||||
\(233\) | − | 8.98718e29i | − | 0.150659i | −0.997159 | − | 0.0753297i | \(-0.975999\pi\) | ||
0.997159 | − | 0.0753297i | \(-0.0240009\pi\) | |||||||
\(234\) | −2.23176e30 | − | 2.18259e30i | −0.353868 | − | 0.346071i | ||||
\(235\) | 1.33951e30 | 0.200939 | ||||||||
\(236\) | − | 7.51112e29i | − | 0.106622i | ||||||
\(237\) | 2.65232e30 | + | 6.30374e30i | 0.356367 | + | 0.846974i | ||||
\(238\) | −1.50995e31 | −1.92071 | ||||||||
\(239\) | − | 1.49139e31i | − | 1.79646i | −0.439524 | − | 0.898231i | \(-0.644853\pi\) | ||
0.439524 | − | 0.898231i | \(-0.355147\pi\) | |||||||
\(240\) | 4.32634e30 | − | 1.82032e30i | 0.493599 | − | 0.207683i | ||||
\(241\) | −9.48024e30 | −1.02470 | −0.512351 | − | 0.858776i | \(-0.671225\pi\) | ||||
−0.512351 | + | 0.858776i | \(0.671225\pi\) | |||||||
\(242\) | − | 5.45313e30i | − | 0.558529i | ||||||
\(243\) | 9.40349e30 | − | 4.20549e30i | 0.912867 | − | 0.408258i | ||||
\(244\) | −2.20622e30 | −0.203040 | ||||||||
\(245\) | 2.50460e31i | 2.18565i | ||||||||
\(246\) | 5.56138e30 | + | 1.32177e31i | 0.460284 | + | 1.09395i | ||||
\(247\) | 5.77671e29 | 0.0453545 | ||||||||
\(248\) | − | 1.55506e30i | − | 0.115845i | ||||||
\(249\) | −2.03225e31 | + | 8.55076e30i | −1.43676 | + | 0.604524i | ||||
\(250\) | 1.36319e31 | 0.914824 | ||||||||
\(251\) | 9.53997e30i | 0.607839i | 0.952698 | + | 0.303919i | \(0.0982954\pi\) | ||||
−0.952698 | + | 0.303919i | \(0.901705\pi\) | |||||||
\(252\) | 6.30675e30 | − | 6.44883e30i | 0.381591 | − | 0.390188i | ||||
\(253\) | 3.29252e30 | 0.189218 | ||||||||
\(254\) | − | 1.40636e31i | − | 0.767817i | ||||||
\(255\) | −7.71053e30 | − | 1.83255e31i | −0.400002 | − | 0.950680i | ||||
\(256\) | −1.59873e31 | −0.788234 | ||||||||
\(257\) | 2.95289e31i | 1.38394i | 0.721927 | + | 0.691970i | \(0.243257\pi\) | ||||
−0.721927 | + | 0.691970i | \(0.756743\pi\) | |||||||
\(258\) | 1.37098e31 | − | 5.76845e30i | 0.610908 | − | 0.257041i | ||||
\(259\) | 4.59852e30 | 0.194859 | ||||||||
\(260\) | − | 3.59913e30i | − | 0.145059i | ||||||
\(261\) | −2.20232e31 | − | 2.15380e31i | −0.844412 | − | 0.825808i | ||||
\(262\) | 7.38607e30 | 0.269462 | ||||||||
\(263\) | − | 4.55126e31i | − | 1.58018i | −0.612989 | − | 0.790092i | \(-0.710033\pi\) | ||
0.612989 | − | 0.790092i | \(-0.289967\pi\) | |||||||
\(264\) | 7.40976e30 | + | 1.76107e31i | 0.244880 | + | 0.582004i | ||||
\(265\) | 4.39793e31 | 1.38373 | ||||||||
\(266\) | − | 4.10086e30i | − | 0.122861i | ||||||
\(267\) | −3.01757e31 | + | 1.26965e31i | −0.861016 | + | 0.362275i | ||||
\(268\) | 9.09728e30 | 0.247263 | ||||||||
\(269\) | 1.57251e31i | 0.407206i | 0.979054 | + | 0.203603i | \(0.0652652\pi\) | ||||
−0.979054 | + | 0.203603i | \(0.934735\pi\) | |||||||
\(270\) | −2.71401e31 | − | 1.07141e31i | −0.669703 | − | 0.264380i | ||||
\(271\) | 1.74298e31 | 0.409913 | 0.204957 | − | 0.978771i | \(-0.434295\pi\) | ||||
0.204957 | + | 0.978771i | \(0.434295\pi\) | |||||||
\(272\) | − | 3.37771e31i | − | 0.757227i | ||||||
\(273\) | 2.00977e31 | + | 4.77659e31i | 0.429567 | + | 1.02095i | ||||
\(274\) | 7.11146e30 | 0.144944 | ||||||||
\(275\) | 8.08652e30i | 0.157194i | ||||||||
\(276\) | 4.68376e30 | − | 1.97071e30i | 0.0868514 | − | 0.0365430i | ||||
\(277\) | −3.68085e31 | −0.651195 | −0.325598 | − | 0.945508i | \(-0.605565\pi\) | ||||
−0.325598 | + | 0.945508i | \(0.605565\pi\) | |||||||
\(278\) | 8.23065e31i | 1.38948i | ||||||||
\(279\) | −4.62517e30 | + | 4.72936e30i | −0.0745200 | + | 0.0761988i | ||||
\(280\) | −1.13870e32 | −1.75128 | ||||||||
\(281\) | 3.00160e31i | 0.440728i | 0.975418 | + | 0.220364i | \(0.0707245\pi\) | ||||
−0.975418 | + | 0.220364i | \(0.929276\pi\) | |||||||
\(282\) | −5.48651e30 | − | 1.30397e31i | −0.0769233 | − | 0.182823i | ||||
\(283\) | 1.14970e32 | 1.53944 | 0.769719 | − | 0.638382i | \(-0.220396\pi\) | ||||
0.769719 | + | 0.638382i | \(0.220396\pi\) | |||||||
\(284\) | 1.09544e31i | 0.140103i | ||||||||
\(285\) | 4.97702e30 | − | 2.09410e30i | 0.0608115 | − | 0.0255867i | ||||
\(286\) | −2.46294e31 | −0.287538 | ||||||||
\(287\) | − | 2.38059e32i | − | 2.65595i | ||||||
\(288\) | 3.74327e31 | + | 3.66079e31i | 0.399161 | + | 0.390367i | ||||
\(289\) | −4.49724e31 | −0.458432 | ||||||||
\(290\) | 8.72553e31i | 0.850389i | ||||||||
\(291\) | −1.94569e31 | − | 4.62430e31i | −0.181328 | − | 0.430960i | ||||
\(292\) | −2.90755e31 | −0.259150 | ||||||||
\(293\) | 6.05334e31i | 0.516079i | 0.966134 | + | 0.258039i | \(0.0830764\pi\) | ||||
−0.966134 | + | 0.258039i | \(0.916924\pi\) | |||||||
\(294\) | 2.43816e32 | − | 1.02586e32i | 1.98859 | − | 0.836708i | ||||
\(295\) | 4.03355e31 | 0.314776 | ||||||||
\(296\) | 1.50327e31i | 0.112265i | ||||||||
\(297\) | 2.98438e31 | − | 7.55975e31i | 0.213314 | − | 0.540348i | ||||
\(298\) | −1.90338e31 | −0.130231 | ||||||||
\(299\) | 2.91937e31i | 0.191234i | ||||||||
\(300\) | 4.84011e30 | + | 1.15034e31i | 0.0303584 | + | 0.0721525i | ||||
\(301\) | −2.46922e32 | −1.48319 | ||||||||
\(302\) | 4.47124e31i | 0.257239i | ||||||||
\(303\) | −1.21023e32 | + | 5.09208e31i | −0.666981 | + | 0.280634i | ||||
\(304\) | 9.17349e30 | 0.0484371 | ||||||||
\(305\) | − | 1.18476e32i | − | 0.599424i | ||||||
\(306\) | −1.46812e32 | + | 1.50119e32i | −0.711841 | + | 0.727877i | ||||
\(307\) | 8.33385e31 | 0.387300 | 0.193650 | − | 0.981071i | \(-0.437967\pi\) | ||||
0.193650 | + | 0.981071i | \(0.437967\pi\) | |||||||
\(308\) | − | 7.11685e31i | − | 0.317050i | ||||||
\(309\) | 2.00065e31 | + | 4.75493e31i | 0.0854499 | + | 0.203088i | ||||
\(310\) | 1.87376e31 | 0.0767381 | ||||||||
\(311\) | 4.43574e32i | 1.74213i | 0.491165 | + | 0.871067i | \(0.336571\pi\) | ||||
−0.491165 | + | 0.871067i | \(0.663429\pi\) | |||||||
\(312\) | −1.56148e32 | + | 6.57000e31i | −0.588204 | + | 0.247489i | ||||
\(313\) | 3.26202e32 | 1.17872 | 0.589360 | − | 0.807871i | \(-0.299380\pi\) | ||||
0.589360 | + | 0.807871i | \(0.299380\pi\) | |||||||
\(314\) | − | 1.62173e32i | − | 0.562202i | ||||||
\(315\) | 3.46309e32 | + | 3.38679e32i | 1.15193 | + | 1.12655i | ||||
\(316\) | 8.32777e31 | 0.265826 | ||||||||
\(317\) | − | 2.02393e32i | − | 0.620047i | −0.950729 | − | 0.310023i | \(-0.899663\pi\) | ||
0.950729 | − | 0.310023i | \(-0.100337\pi\) | |||||||
\(318\) | −1.80135e32 | − | 4.28125e32i | −0.529719 | − | 1.25898i | ||||
\(319\) | −2.43046e32 | −0.686134 | ||||||||
\(320\) | − | 3.45876e32i | − | 0.937498i | ||||||
\(321\) | −3.10661e32 | + | 1.30712e32i | −0.808577 | + | 0.340212i | ||||
\(322\) | 2.07245e32 | 0.518033 | ||||||||
\(323\) | − | 3.88571e31i | − | 0.0932906i | ||||||
\(324\) | −2.79404e30 | − | 1.25404e32i | −0.00644388 | − | 0.289218i | ||||
\(325\) | −7.17006e31 | −0.158869 | ||||||||
\(326\) | − | 8.02215e31i | − | 0.170790i | ||||||
\(327\) | −2.74532e32 | − | 6.52476e32i | −0.561657 | − | 1.33488i | ||||
\(328\) | 7.78222e32 | 1.53018 | ||||||||
\(329\) | 2.34854e32i | 0.443865i | ||||||||
\(330\) | −2.12198e32 | + | 8.92832e31i | −0.385532 | + | 0.162214i | ||||
\(331\) | 1.37471e32 | 0.240131 | 0.120066 | − | 0.992766i | \(-0.461690\pi\) | ||||
0.120066 | + | 0.992766i | \(0.461690\pi\) | |||||||
\(332\) | 2.68477e32i | 0.450933i | ||||||||
\(333\) | 4.47112e31 | − | 4.57185e31i | 0.0722174 | − | 0.0738443i | ||||
\(334\) | −5.63639e32 | −0.875582 | ||||||||
\(335\) | 4.88534e32i | 0.729982i | ||||||||
\(336\) | 3.19153e32 | + | 7.58528e32i | 0.458763 | + | 1.09034i | ||||
\(337\) | 5.38851e32 | 0.745212 | 0.372606 | − | 0.927990i | \(-0.378464\pi\) | ||||
0.372606 | + | 0.927990i | \(0.378464\pi\) | |||||||
\(338\) | 4.15144e32i | 0.552435i | ||||||||
\(339\) | 5.32384e32 | − | 2.24002e32i | 0.681756 | − | 0.286851i | ||||
\(340\) | −2.42096e32 | −0.298374 | ||||||||
\(341\) | 5.21927e31i | 0.0619160i | ||||||||
\(342\) | −4.07708e31 | − | 3.98726e31i | −0.0465597 | − | 0.0455339i | ||||
\(343\) | −2.67536e33 | −2.94143 | ||||||||
\(344\) | − | 8.07198e32i | − | 0.854516i | ||||||
\(345\) | 1.05829e32 | + | 2.51523e32i | 0.107884 | + | 0.256407i | ||||
\(346\) | 4.16635e32 | 0.409041 | ||||||||
\(347\) | 4.22062e31i | 0.0399110i | 0.999801 | + | 0.0199555i | \(0.00635246\pi\) | ||||
−0.999801 | + | 0.0199555i | \(0.993648\pi\) | |||||||
\(348\) | −3.45744e32 | + | 1.45473e32i | −0.314937 | + | 0.132511i | ||||
\(349\) | 9.56464e32 | 0.839341 | 0.419670 | − | 0.907677i | \(-0.362146\pi\) | ||||
0.419670 | + | 0.907677i | \(0.362146\pi\) | |||||||
\(350\) | 5.08999e32i | 0.430361i | ||||||||
\(351\) | 6.70298e32 | + | 2.64615e32i | 0.546104 | + | 0.215587i | ||||
\(352\) | 4.13102e32 | 0.324342 | ||||||||
\(353\) | − | 1.63888e33i | − | 1.24016i | −0.784539 | − | 0.620079i | \(-0.787100\pi\) | ||
0.784539 | − | 0.620079i | \(-0.212900\pi\) | |||||||
\(354\) | −1.65211e32 | − | 3.92655e32i | −0.120502 | − | 0.286397i | ||||
\(355\) | −5.88261e32 | −0.413620 | ||||||||
\(356\) | 3.98647e32i | 0.270233i | ||||||||
\(357\) | 3.21298e33 | − | 1.35187e33i | 2.10001 | − | 0.883586i | ||||
\(358\) | −3.24907e32 | −0.204776 | ||||||||
\(359\) | − | 1.00603e33i | − | 0.611484i | −0.952114 | − | 0.305742i | \(-0.901095\pi\) | ||
0.952114 | − | 0.305742i | \(-0.0989045\pi\) | |||||||
\(360\) | −1.10715e33 | + | 1.13210e33i | −0.649046 | + | 0.663668i | ||||
\(361\) | −1.75790e33 | −0.994033 | ||||||||
\(362\) | − | 6.23339e32i | − | 0.340026i | ||||||
\(363\) | 4.88224e32 | + | 1.16036e33i | 0.256941 | + | 0.610668i | ||||
\(364\) | 6.31028e32 | 0.320428 | ||||||||
\(365\) | − | 1.56139e33i | − | 0.765074i | ||||||
\(366\) | −1.15333e33 | + | 4.85268e32i | −0.545381 | + | 0.229471i | ||||
\(367\) | 2.89094e33 | 1.31941 | 0.659706 | − | 0.751524i | \(-0.270681\pi\) | ||||
0.659706 | + | 0.751524i | \(0.270681\pi\) | |||||||
\(368\) | 4.63600e32i | 0.204231i | ||||||||
\(369\) | −2.36678e33 | − | 2.31464e33i | −1.00650 | − | 0.984328i | ||||
\(370\) | −1.81135e32 | −0.0743670 | ||||||||
\(371\) | 7.71080e33i | 3.05660i | ||||||||
\(372\) | 3.12394e31 | + | 7.42464e31i | 0.0119576 | + | 0.0284196i | ||||
\(373\) | −1.41727e33 | −0.523887 | −0.261943 | − | 0.965083i | \(-0.584363\pi\) | ||||
−0.261943 | + | 0.965083i | \(0.584363\pi\) | |||||||
\(374\) | 1.65670e33i | 0.591443i | ||||||||
\(375\) | −2.90070e33 | + | 1.22048e33i | −1.00022 | + | 0.420847i | ||||
\(376\) | −7.67745e32 | −0.255726 | ||||||||
\(377\) | − | 2.15501e33i | − | 0.693444i | ||||||
\(378\) | 1.87849e33 | − | 4.75842e33i | 0.584004 | − | 1.47934i | ||||
\(379\) | 7.08401e32 | 0.212799 | 0.106399 | − | 0.994323i | \(-0.466068\pi\) | ||||
0.106399 | + | 0.994323i | \(0.466068\pi\) | |||||||
\(380\) | − | 6.57506e31i | − | 0.0190859i | ||||||
\(381\) | 1.25913e33 | + | 2.99255e33i | 0.353219 | + | 0.839492i | ||||
\(382\) | 2.67378e33 | 0.724940 | ||||||||
\(383\) | − | 4.75619e33i | − | 1.24645i | −0.782042 | − | 0.623225i | \(-0.785822\pi\) | ||
0.782042 | − | 0.623225i | \(-0.214178\pi\) | |||||||
\(384\) | −1.33562e33 | + | 5.61965e32i | −0.338357 | + | 0.142365i | ||||
\(385\) | 3.82183e33 | 0.936012 | ||||||||
\(386\) | 5.87312e33i | 1.39070i | ||||||||
\(387\) | −2.40082e33 | + | 2.45491e33i | −0.549689 | + | 0.562073i | ||||
\(388\) | −6.10909e32 | −0.135258 | ||||||||
\(389\) | − | 3.55104e33i | − | 0.760345i | −0.924916 | − | 0.380172i | \(-0.875865\pi\) | ||
0.924916 | − | 0.380172i | \(-0.124135\pi\) | |||||||
\(390\) | −7.91645e32 | − | 1.88149e33i | −0.163942 | − | 0.389640i | ||||
\(391\) | 1.96372e33 | 0.393352 | ||||||||
\(392\) | − | 1.43552e34i | − | 2.78158i | ||||||
\(393\) | −1.57166e33 | + | 6.61282e32i | −0.294616 | + | 0.123961i | ||||
\(394\) | 7.59971e33 | 1.37831 | ||||||||
\(395\) | 4.47211e33i | 0.784783i | ||||||||
\(396\) | −7.07558e32 | − | 6.91969e32i | −0.120150 | − | 0.117503i | ||||
\(397\) | −1.15977e34 | −1.90588 | −0.952938 | − | 0.303164i | \(-0.901957\pi\) | ||||
−0.952938 | + | 0.303164i | \(0.901957\pi\) | |||||||
\(398\) | 1.21652e33i | 0.193481i | ||||||||
\(399\) | 3.67154e32 | + | 8.72611e32i | 0.0565198 | + | 0.134330i | ||||
\(400\) | −1.13861e33 | −0.169667 | ||||||||
\(401\) | 4.69837e33i | 0.677752i | 0.940831 | + | 0.338876i | \(0.110047\pi\) | ||||
−0.940831 | + | 0.338876i | \(0.889953\pi\) | |||||||
\(402\) | 4.75573e33 | − | 2.00099e33i | 0.664169 | − | 0.279452i | ||||
\(403\) | −4.62775e32 | −0.0625756 | ||||||||
\(404\) | 1.59881e33i | 0.209334i | ||||||||
\(405\) | 6.73431e33 | − | 1.50043e32i | 0.853842 | − | 0.0190239i | ||||
\(406\) | −1.52983e34 | −1.87847 | ||||||||
\(407\) | − | 5.04544e32i | − | 0.0600028i | ||||||
\(408\) | 4.41932e33 | + | 1.05033e34i | 0.509065 | + | 1.20989i | ||||
\(409\) | 1.30144e34 | 1.45218 | 0.726089 | − | 0.687601i | \(-0.241336\pi\) | ||||
0.726089 | + | 0.687601i | \(0.241336\pi\) | |||||||
\(410\) | 9.37710e33i | 1.01363i | ||||||||
\(411\) | −1.51323e33 | + | 6.36696e32i | −0.158475 | + | 0.0666789i | ||||
\(412\) | 6.28166e32 | 0.0637398 | ||||||||
\(413\) | 7.07196e33i | 0.695327i | ||||||||
\(414\) | 2.01504e33 | − | 2.06043e33i | 0.191990 | − | 0.196315i | ||||
\(415\) | −1.44175e34 | −1.33127 | ||||||||
\(416\) | 3.66284e33i | 0.327797i | ||||||||
\(417\) | −7.36898e33 | − | 1.75138e34i | −0.639203 | − | 1.51919i | ||||
\(418\) | −4.49942e32 | −0.0378325 | ||||||||
\(419\) | − | 1.08310e34i | − | 0.882848i | −0.897299 | − | 0.441424i | \(-0.854474\pi\) | ||
0.897299 | − | 0.441424i | \(-0.145526\pi\) | |||||||
\(420\) | 5.43672e33 | − | 2.28752e33i | 0.429632 | − | 0.180769i | ||||
\(421\) | 7.21830e33 | 0.553054 | 0.276527 | − | 0.961006i | \(-0.410816\pi\) | ||||
0.276527 | + | 0.961006i | \(0.410816\pi\) | |||||||
\(422\) | − | 2.00898e34i | − | 1.49250i | ||||||
\(423\) | 2.33492e33 | + | 2.28348e33i | 0.168208 | + | 0.164502i | ||||
\(424\) | −2.52069e34 | −1.76102 | ||||||||
\(425\) | 4.82295e33i | 0.326781i | ||||||||
\(426\) | 2.40946e33 | + | 5.72654e33i | 0.158342 | + | 0.376329i | ||||
\(427\) | 2.07722e34 | 1.32410 | ||||||||
\(428\) | 4.10409e33i | 0.253775i | ||||||||
\(429\) | 5.24082e33 | − | 2.20509e33i | 0.314380 | − | 0.132276i | ||||
\(430\) | 9.72625e33 | 0.566051 | ||||||||
\(431\) | − | 3.64644e33i | − | 0.205904i | −0.994686 | − | 0.102952i | \(-0.967171\pi\) | ||
0.994686 | − | 0.102952i | \(-0.0328288\pi\) | |||||||
\(432\) | 1.06444e34 | + | 4.20212e33i | 0.583221 | + | 0.230239i | ||||
\(433\) | 1.68552e34 | 0.896174 | 0.448087 | − | 0.893990i | \(-0.352105\pi\) | ||||
0.448087 | + | 0.893990i | \(0.352105\pi\) | |||||||
\(434\) | 3.28522e33i | 0.169511i | ||||||||
\(435\) | −7.81205e33 | − | 1.85668e34i | −0.391205 | − | 0.929773i | ||||
\(436\) | −8.61976e33 | −0.418958 | ||||||||
\(437\) | 5.33325e32i | 0.0251613i | ||||||||
\(438\) | −1.51996e34 | + | 6.39530e33i | −0.696097 | + | 0.292885i | ||||
\(439\) | 1.11671e34 | 0.496480 | 0.248240 | − | 0.968699i | \(-0.420148\pi\) | ||||
0.248240 | + | 0.968699i | \(0.420148\pi\) | |||||||
\(440\) | 1.24937e34i | 0.539269i | ||||||||
\(441\) | −4.26962e34 | + | 4.36581e34i | −1.78932 | + | 1.82963i | ||||
\(442\) | −1.46894e34 | −0.597744 | ||||||||
\(443\) | − | 3.64304e34i | − | 1.43951i | −0.694227 | − | 0.719756i | \(-0.744254\pi\) | ||
0.694227 | − | 0.719756i | \(-0.255746\pi\) | |||||||
\(444\) | −3.01990e32 | − | 7.17737e32i | −0.0115881 | − | 0.0275414i | ||||
\(445\) | −2.14078e34 | −0.797795 | ||||||||
\(446\) | 1.60932e34i | 0.582491i | ||||||||
\(447\) | 4.05014e33 | − | 1.70411e33i | 0.142388 | − | 0.0599101i | ||||
\(448\) | 6.06417e34 | 2.07089 | ||||||||
\(449\) | 1.73953e34i | 0.577072i | 0.957469 | + | 0.288536i | \(0.0931685\pi\) | ||||
−0.957469 | + | 0.288536i | \(0.906831\pi\) | |||||||
\(450\) | 5.06048e33 | + | 4.94898e33i | 0.163091 | + | 0.159497i | ||||
\(451\) | −2.61195e34 | −0.817843 | ||||||||
\(452\) | − | 7.03324e33i | − | 0.213971i | ||||||
\(453\) | −4.00314e33 | − | 9.51422e33i | −0.118338 | − | 0.281253i | ||||
\(454\) | −4.15934e33 | −0.119481 | ||||||||
\(455\) | 3.38869e34i | 0.945984i | ||||||||
\(456\) | −2.85260e33 | + | 1.20024e33i | −0.0773922 | + | 0.0325630i | ||||
\(457\) | 2.59048e34 | 0.683076 | 0.341538 | − | 0.939868i | \(-0.389052\pi\) | ||||
0.341538 | + | 0.939868i | \(0.389052\pi\) | |||||||
\(458\) | − | 2.00661e34i | − | 0.514294i | ||||||
\(459\) | 1.77994e34 | − | 4.50877e34i | 0.443445 | − | 1.12329i | ||||
\(460\) | 3.32283e33 | 0.0804742 | ||||||||
\(461\) | 1.24046e34i | 0.292060i | 0.989280 | + | 0.146030i | \(0.0466496\pi\) | ||||
−0.989280 | + | 0.146030i | \(0.953350\pi\) | |||||||
\(462\) | −1.56539e34 | − | 3.72043e34i | −0.358324 | − | 0.851624i | ||||
\(463\) | 5.33047e34 | 1.18635 | 0.593175 | − | 0.805073i | \(-0.297874\pi\) | ||||
0.593175 | + | 0.805073i | \(0.297874\pi\) | |||||||
\(464\) | − | 3.42218e34i | − | 0.740574i | ||||||
\(465\) | −3.98712e33 | + | 1.67759e33i | −0.0839016 | + | 0.0353019i | ||||
\(466\) | −6.20669e33 | −0.127011 | ||||||||
\(467\) | − | 8.65230e33i | − | 0.172192i | −0.996287 | − | 0.0860958i | \(-0.972561\pi\) | ||
0.996287 | − | 0.0860958i | \(-0.0274391\pi\) | |||||||
\(468\) | 6.13546e33 | − | 6.27369e33i | 0.118755 | − | 0.121430i | ||||
\(469\) | −8.56538e34 | −1.61250 | ||||||||
\(470\) | − | 9.25086e33i | − | 0.169399i | ||||||
\(471\) | 1.45195e34 | + | 3.45083e34i | 0.258630 | + | 0.614683i | ||||
\(472\) | −2.31185e34 | −0.400602 | ||||||||
\(473\) | 2.70920e34i | 0.456717i | ||||||||
\(474\) | 4.35346e34 | − | 1.83173e34i | 0.714030 | − | 0.300430i | ||||
\(475\) | −1.30986e33 | −0.0209030 | ||||||||
\(476\) | − | 4.24462e34i | − | 0.659095i | ||||||
\(477\) | 7.66609e34 | + | 7.49719e34i | 1.15834 | + | 1.13282i | ||||
\(478\) | −1.02998e35 | −1.51448 | ||||||||
\(479\) | 3.25576e34i | 0.465897i | 0.972489 | + | 0.232949i | \(0.0748374\pi\) | ||||
−0.972489 | + | 0.232949i | \(0.925163\pi\) | |||||||
\(480\) | 1.32781e34 | + | 3.15578e34i | 0.184926 | + | 0.439512i | ||||
\(481\) | 4.47363e33 | 0.0606420 | ||||||||
\(482\) | 6.54720e34i | 0.863861i | ||||||||
\(483\) | −4.40991e34 | + | 1.85548e34i | −0.566392 | + | 0.238311i | ||||
\(484\) | 1.53293e34 | 0.191660 | ||||||||
\(485\) | − | 3.28065e34i | − | 0.399316i | ||||||
\(486\) | −2.90437e34 | − | 6.49419e34i | −0.344176 | − | 0.769580i | ||||
\(487\) | −1.32385e34 | −0.152744 | −0.0763718 | − | 0.997079i | \(-0.524334\pi\) | ||||
−0.0763718 | + | 0.997079i | \(0.524334\pi\) | |||||||
\(488\) | 6.79052e34i | 0.762860i | ||||||||
\(489\) | 7.18230e33 | + | 1.70701e34i | 0.0785685 | + | 0.186733i | ||||
\(490\) | 1.72972e35 | 1.84258 | ||||||||
\(491\) | − | 5.47725e34i | − | 0.568203i | −0.958794 | − | 0.284101i | \(-0.908305\pi\) | ||
0.958794 | − | 0.284101i | \(-0.0916952\pi\) | |||||||
\(492\) | −3.71562e34 | + | 1.56336e34i | −0.375392 | + | 0.157947i | ||||
\(493\) | −1.44957e35 | −1.42636 | ||||||||
\(494\) | − | 3.98949e33i | − | 0.0382355i | ||||||
\(495\) | 3.71595e34 | − | 3.79966e34i | 0.346898 | − | 0.354713i | ||||
\(496\) | −7.34893e33 | −0.0668286 | ||||||||
\(497\) | − | 1.03139e35i | − | 0.913668i | ||||||
\(498\) | 5.90529e34 | + | 1.40350e35i | 0.509635 | + | 1.21124i | ||||
\(499\) | −7.35107e33 | −0.0618079 | −0.0309039 | − | 0.999522i | \(-0.509839\pi\) | ||||
−0.0309039 | + | 0.999522i | \(0.509839\pi\) | |||||||
\(500\) | 3.83207e34i | 0.313924i | ||||||||
\(501\) | 1.19935e35 | − | 5.04631e34i | 0.957317 | − | 0.402794i | ||||
\(502\) | 6.58845e34 | 0.512430 | ||||||||
\(503\) | − | 2.09921e35i | − | 1.59101i | −0.605949 | − | 0.795503i | \(-0.707207\pi\) | ||
0.605949 | − | 0.795503i | \(-0.292793\pi\) | |||||||
\(504\) | −1.98488e35 | − | 1.94115e35i | −1.46601 | − | 1.43371i | ||||
\(505\) | −8.58581e34 | −0.618007 | ||||||||
\(506\) | − | 2.27387e34i | − | 0.159517i | ||||||
\(507\) | −3.71682e34 | − | 8.83373e34i | −0.254137 | − | 0.604005i | ||||
\(508\) | 3.95341e34 | 0.263478 | ||||||||
\(509\) | 2.02711e35i | 1.31688i | 0.752633 | + | 0.658441i | \(0.228784\pi\) | ||||
−0.752633 | + | 0.658441i | \(0.771216\pi\) | |||||||
\(510\) | −1.26559e35 | + | 5.32501e34i | −0.801458 | + | 0.337216i | ||||
\(511\) | 2.73755e35 | 1.69002 | ||||||||
\(512\) | 1.71404e35i | 1.03160i | ||||||||
\(513\) | 1.22453e34 | + | 4.83412e33i | 0.0718530 | + | 0.0283656i | ||||
\(514\) | 2.03931e35 | 1.16671 | ||||||||
\(515\) | 3.37332e34i | 0.188176i | ||||||||
\(516\) | 1.62157e34 | + | 3.85397e34i | 0.0882042 | + | 0.209634i | ||||
\(517\) | 2.57679e34 | 0.136679 | ||||||||
\(518\) | − | 3.17581e34i | − | 0.164273i | ||||||
\(519\) | −8.86547e34 | + | 3.73018e34i | −0.447225 | + | 0.188171i | ||||
\(520\) | −1.10777e35 | −0.545014 | ||||||||
\(521\) | 1.85639e35i | 0.890796i | 0.895333 | + | 0.445398i | \(0.146938\pi\) | ||||
−0.895333 | + | 0.445398i | \(0.853062\pi\) | |||||||
\(522\) | −1.48745e35 | + | 1.52096e35i | −0.696186 | + | 0.711871i | ||||
\(523\) | −1.31184e35 | −0.598906 | −0.299453 | − | 0.954111i | \(-0.596804\pi\) | ||||
−0.299453 | + | 0.954111i | \(0.596804\pi\) | |||||||
\(524\) | 2.07630e34i | 0.0924662i | ||||||||
\(525\) | −4.55712e34 | − | 1.08309e35i | −0.197979 | − | 0.470535i | ||||
\(526\) | −3.14317e35 | −1.33215 | ||||||||
\(527\) | 3.11286e34i | 0.128713i | ||||||||
\(528\) | 8.32248e34 | − | 3.50171e34i | 0.335747 | − | 0.141267i | ||||
\(529\) | 2.27100e35 | 0.893909 | ||||||||
\(530\) | − | 3.03728e35i | − | 1.16654i | ||||||
\(531\) | 7.03095e34 | + | 6.87604e34i | 0.263503 | + | 0.257697i | ||||
\(532\) | 1.15279e34 | 0.0421599 | ||||||||
\(533\) | − | 2.31593e35i | − | 0.826555i | ||||||
\(534\) | 8.76843e34 | + | 2.08398e35i | 0.305411 | + | 0.725868i | ||||
\(535\) | −2.20394e35 | −0.749206 | ||||||||
\(536\) | − | 2.80005e35i | − | 0.929017i | ||||||
\(537\) | 6.91360e34 | − | 2.90892e34i | 0.223892 | − | 0.0942033i | ||||
\(538\) | 1.08600e35 | 0.343290 | ||||||||
\(539\) | 4.81805e35i | 1.48668i | ||||||||
\(540\) | 3.01185e34 | − | 7.62934e34i | 0.0907225 | − | 0.229810i | ||||
\(541\) | 4.02730e35 | 1.18427 | 0.592134 | − | 0.805840i | \(-0.298286\pi\) | ||||
0.592134 | + | 0.805840i | \(0.298286\pi\) | |||||||
\(542\) | − | 1.20373e35i | − | 0.345572i | ||||||
\(543\) | 5.58081e34 | + | 1.32639e35i | 0.156423 | + | 0.371768i | ||||
\(544\) | 2.46382e35 | 0.674253 | ||||||||
\(545\) | − | 4.62891e35i | − | 1.23687i | ||||||
\(546\) | 3.29879e35 | − | 1.38798e35i | 0.860697 | − | 0.362141i | ||||
\(547\) | −6.57248e35 | −1.67453 | −0.837267 | − | 0.546795i | \(-0.815848\pi\) | ||||
−0.837267 | + | 0.546795i | \(0.815848\pi\) | |||||||
\(548\) | 1.99910e34i | 0.0497379i | ||||||||
\(549\) | 2.01968e35 | − | 2.06518e35i | 0.490729 | − | 0.501784i | ||||
\(550\) | 5.58468e34 | 0.132521 | ||||||||
\(551\) | − | 3.93687e34i | − | 0.0912390i | ||||||
\(552\) | −6.06564e34 | − | 1.44161e35i | −0.137299 | − | 0.326318i | ||||
\(553\) | −7.84086e35 | −1.73355 | ||||||||
\(554\) | 2.54205e35i | 0.548981i | ||||||||
\(555\) | 3.85432e34 | − | 1.62172e34i | 0.0813092 | − | 0.0342111i | ||||
\(556\) | −2.31372e35 | −0.476802 | ||||||||
\(557\) | 6.22563e35i | 1.25333i | 0.779288 | + | 0.626665i | \(0.215581\pi\) | ||||
−0.779288 | + | 0.626665i | \(0.784419\pi\) | |||||||
\(558\) | 3.26617e34 | + | 3.19421e34i | 0.0642384 | + | 0.0628231i | ||||
\(559\) | −2.40216e35 | −0.461582 | ||||||||
\(560\) | 5.38128e35i | 1.01028i | ||||||||
\(561\) | −1.48326e35 | − | 3.52524e35i | −0.272082 | − | 0.646654i | ||||
\(562\) | 2.07295e35 | 0.371550 | ||||||||
\(563\) | 2.87438e35i | 0.503426i | 0.967802 | + | 0.251713i | \(0.0809939\pi\) | ||||
−0.967802 | + | 0.251713i | \(0.919006\pi\) | |||||||
\(564\) | 3.66560e34 | − | 1.54231e34i | 0.0627359 | − | 0.0263964i | ||||
\(565\) | 3.77693e35 | 0.631697 | ||||||||
\(566\) | − | 7.94003e35i | − | 1.29780i | ||||||
\(567\) | 2.63067e34 | + | 1.18071e36i | 0.0420230 | + | 1.88610i | ||||
\(568\) | 3.37164e35 | 0.526396 | ||||||||
\(569\) | 3.47987e35i | 0.531011i | 0.964109 | + | 0.265506i | \(0.0855389\pi\) | ||||
−0.964109 | + | 0.265506i | \(0.914461\pi\) | |||||||
\(570\) | −1.44622e34 | − | 3.43721e34i | −0.0215705 | − | 0.0512664i | ||||
\(571\) | 1.25721e36 | 1.83289 | 0.916446 | − | 0.400159i | \(-0.131045\pi\) | ||||
0.916446 | + | 0.400159i | \(0.131045\pi\) | |||||||
\(572\) | − | 6.92356e34i | − | 0.0986691i | ||||||
\(573\) | −5.68947e35 | + | 2.39386e35i | −0.792613 | + | 0.333495i | ||||
\(574\) | −1.64407e36 | −2.23906 | ||||||||
\(575\) | − | 6.61963e34i | − | 0.0881357i | ||||||
\(576\) | 5.89617e35 | − | 6.02901e35i | 0.767499 | − | 0.784790i | ||||
\(577\) | 3.83337e35 | 0.487860 | 0.243930 | − | 0.969793i | \(-0.421563\pi\) | ||||
0.243930 | + | 0.969793i | \(0.421563\pi\) | |||||||
\(578\) | 3.10587e35i | 0.386475i | ||||||||
\(579\) | −5.25826e35 | − | 1.24972e36i | −0.639765 | − | 1.52052i | ||||
\(580\) | −2.45283e35 | −0.291812 | ||||||||
\(581\) | − | 2.52780e36i | − | 2.94071i | ||||||
\(582\) | −3.19361e35 | + | 1.34372e35i | −0.363315 | + | 0.152866i | ||||
\(583\) | 8.46020e35 | 0.941217 | ||||||||
\(584\) | 8.94915e35i | 0.973677i | ||||||||
\(585\) | 3.36904e35 | + | 3.29481e35i | 0.358492 | + | 0.350594i | ||||
\(586\) | 4.18053e35 | 0.435073 | ||||||||
\(587\) | 5.19443e35i | 0.528740i | 0.964421 | + | 0.264370i | \(0.0851641\pi\) | ||||
−0.964421 | + | 0.264370i | \(0.914836\pi\) | |||||||
\(588\) | 2.88380e35 | + | 6.85390e35i | 0.287118 | + | 0.682390i | ||||
\(589\) | −8.45421e33 | −0.00823330 | ||||||||
\(590\) | − | 2.78564e35i | − | 0.265368i | ||||||
\(591\) | −1.61712e36 | + | 6.80409e35i | −1.50697 | + | 0.634063i | ||||
\(592\) | 7.10417e34 | 0.0647636 | ||||||||
\(593\) | − | 1.58590e36i | − | 1.41437i | −0.707028 | − | 0.707186i | \(-0.749964\pi\) | ||
0.707028 | − | 0.707186i | \(-0.250036\pi\) | |||||||
\(594\) | −5.22088e35 | − | 2.06106e35i | −0.455533 | − | 0.179832i | ||||
\(595\) | 2.27941e36 | 1.94581 | ||||||||
\(596\) | − | 5.35058e34i | − | 0.0446888i | ||||||
\(597\) | −1.08916e35 | − | 2.58860e35i | −0.0890073 | − | 0.211543i | ||||
\(598\) | 2.01616e35 | 0.161217 | ||||||||
\(599\) | 1.07011e36i | 0.837294i | 0.908149 | + | 0.418647i | \(0.137496\pi\) | ||||
−0.908149 | + | 0.418647i | \(0.862504\pi\) | |||||||
\(600\) | 3.54064e35 | − | 1.48974e35i | 0.271091 | − | 0.114063i | ||||
\(601\) | −1.49432e36 | −1.11963 | −0.559815 | − | 0.828617i | \(-0.689128\pi\) | ||||
−0.559815 | + | 0.828617i | \(0.689128\pi\) | |||||||
\(602\) | 1.70529e36i | 1.25038i | ||||||||
\(603\) | −8.32809e35 | + | 8.51571e35i | −0.597613 | + | 0.611077i | ||||
\(604\) | −1.25691e35 | −0.0882721 | ||||||||
\(605\) | 8.23200e35i | 0.565829i | ||||||||
\(606\) | 3.51667e35 | + | 8.35803e35i | 0.236585 | + | 0.562289i | ||||
\(607\) | −1.90838e36 | −1.25664 | −0.628321 | − | 0.777954i | \(-0.716258\pi\) | ||||
−0.628321 | + | 0.777954i | \(0.716258\pi\) | |||||||
\(608\) | 6.69146e34i | 0.0431295i | ||||||||
\(609\) | 3.25528e36 | − | 1.36967e36i | 2.05383 | − | 0.864155i | ||||
\(610\) | −8.18216e35 | −0.505336 | ||||||||
\(611\) | 2.28475e35i | 0.138135i | ||||||||
\(612\) | −4.22000e35 | − | 4.12703e35i | −0.249772 | − | 0.244269i | ||||
\(613\) | 1.44907e36 | 0.839657 | 0.419828 | − | 0.907604i | \(-0.362090\pi\) | ||||
0.419828 | + | 0.907604i | \(0.362090\pi\) | |||||||
\(614\) | − | 5.75549e35i | − | 0.326508i | ||||||
\(615\) | −8.39541e35 | − | 1.99533e36i | −0.466300 | − | 1.10825i | ||||
\(616\) | −2.19049e36 | −1.19122 | ||||||||
\(617\) | 2.71381e36i | 1.44501i | 0.691364 | + | 0.722506i | \(0.257010\pi\) | ||||
−0.691364 | + | 0.722506i | \(0.742990\pi\) | |||||||
\(618\) | 3.28383e35 | − | 1.38168e35i | 0.171210 | − | 0.0720374i | ||||
\(619\) | −1.00442e36 | −0.512787 | −0.256394 | − | 0.966572i | \(-0.582534\pi\) | ||||
−0.256394 | + | 0.966572i | \(0.582534\pi\) | |||||||
\(620\) | 5.26731e34i | 0.0263328i | ||||||||
\(621\) | −2.44302e35 | + | 6.18842e35i | −0.119601 | + | 0.302962i | ||||
\(622\) | 3.06339e36 | 1.46868 | ||||||||
\(623\) | − | 3.75338e36i | − | 1.76229i | ||||||
\(624\) | 3.10486e35 | + | 7.37927e35i | 0.142772 | + | 0.339324i | ||||
\(625\) | −1.45703e36 | −0.656189 | ||||||||
\(626\) | − | 2.25280e36i | − | 0.993704i | ||||||
\(627\) | 9.57419e34 | − | 4.02837e34i | 0.0413641 | − | 0.0174041i | ||||
\(628\) | 4.55883e35 | 0.192920 | ||||||||
\(629\) | − | 3.00919e35i | − | 0.124736i | ||||||
\(630\) | 2.33897e36 | − | 2.39167e36i | 0.949725 | − | 0.971121i | ||||
\(631\) | 2.02638e36 | 0.806010 | 0.403005 | − | 0.915198i | \(-0.367966\pi\) | ||||
0.403005 | + | 0.915198i | \(0.367966\pi\) | |||||||
\(632\) | − | 2.56320e36i | − | 0.998760i | ||||||
\(633\) | 1.79866e36 | + | 4.27485e36i | 0.686594 | + | 1.63182i | ||||
\(634\) | −1.39776e36 | −0.522722 | ||||||||
\(635\) | 2.12302e36i | 0.777851i | ||||||||
\(636\) | 1.20350e36 | − | 5.06378e35i | 0.432021 | − | 0.181774i | ||||
\(637\) | −4.27201e36 | −1.50252 | ||||||||
\(638\) | 1.67851e36i | 0.578436i | ||||||||
\(639\) | −1.02541e36 | − | 1.00281e36i | −0.346246 | − | 0.338617i | ||||
\(640\) | −9.47535e35 | −0.313513 | ||||||||
\(641\) | 1.44958e36i | 0.469989i | 0.971997 | + | 0.234994i | \(0.0755072\pi\) | ||||
−0.971997 | + | 0.234994i | \(0.924493\pi\) | |||||||
\(642\) | 9.02715e35 | + | 2.14547e36i | 0.286811 | + | 0.681660i | ||||
\(643\) | 2.15306e36 | 0.670368 | 0.335184 | − | 0.942153i | \(-0.391202\pi\) | ||||
0.335184 | + | 0.942153i | \(0.391202\pi\) | |||||||
\(644\) | 5.82586e35i | 0.177764i | ||||||||
\(645\) | −2.06962e36 | + | 8.70800e35i | −0.618892 | + | 0.260401i | ||||
\(646\) | −2.68353e35 | −0.0786474 | ||||||||
\(647\) | − | 3.21045e36i | − | 0.922167i | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||
0.887357 | − | 0.461084i | \(-0.152539\pi\) | |||||||
\(648\) | −3.85979e36 | + | 8.59977e34i | −1.08665 | + | 0.0242109i | ||||
\(649\) | 7.75927e35 | 0.214111 | ||||||||
\(650\) | 4.95175e35i | 0.133932i | ||||||||
\(651\) | −2.94129e35 | − | 6.99053e35i | −0.0779803 | − | 0.185335i | ||||
\(652\) | 2.25510e35 | 0.0586068 | ||||||||
\(653\) | 4.55451e36i | 1.16030i | 0.814510 | + | 0.580150i | \(0.197006\pi\) | ||||
−0.814510 | + | 0.580150i | \(0.802994\pi\) | |||||||
\(654\) | −4.50610e36 | + | 1.89596e36i | −1.12536 | + | 0.473498i | ||||
\(655\) | −1.11499e36 | −0.272983 | ||||||||
\(656\) | − | 3.67773e36i | − | 0.882733i | ||||||
\(657\) | 2.66171e36 | − | 2.72168e36i | 0.626342 | − | 0.640452i | ||||
\(658\) | 1.62194e36 | 0.374194 | ||||||||
\(659\) | 6.29692e36i | 1.42435i | 0.702000 | + | 0.712177i | \(0.252291\pi\) | ||||
−0.702000 | + | 0.712177i | \(0.747709\pi\) | |||||||
\(660\) | −2.50984e35 | − | 5.96511e35i | −0.0556640 | − | 0.132296i | ||||
\(661\) | 1.81650e36 | 0.395018 | 0.197509 | − | 0.980301i | \(-0.436715\pi\) | ||||
0.197509 | + | 0.980301i | \(0.436715\pi\) | |||||||
\(662\) | − | 9.49399e35i | − | 0.202439i | ||||||
\(663\) | 3.12572e36 | − | 1.31516e36i | 0.653543 | − | 0.274980i | ||||
\(664\) | 8.26346e36 | 1.69425 | ||||||||
\(665\) | 6.19062e35i | 0.124467i | ||||||||
\(666\) | −3.15739e35 | − | 3.08783e35i | −0.0622535 | − | 0.0608819i | ||||
\(667\) | 1.98957e36 | 0.384702 | ||||||||
\(668\) | − | 1.58444e36i | − | 0.300457i | ||||||
\(669\) | −1.44084e36 | − | 3.42443e36i | −0.267964 | − | 0.636867i | ||||
\(670\) | 3.37389e36 | 0.615402 | ||||||||
\(671\) | − | 2.27911e36i | − | 0.407729i | ||||||
\(672\) | −5.53297e36 | + | 2.32802e36i | −0.970863 | + | 0.408494i | ||||
\(673\) | −9.54076e36 | −1.64205 | −0.821027 | − | 0.570890i | \(-0.806598\pi\) | ||||
−0.821027 | + | 0.570890i | \(0.806598\pi\) | |||||||
\(674\) | − | 3.72139e36i | − | 0.628241i | ||||||
\(675\) | −1.51989e36 | − | 6.00011e35i | −0.251689 | − | 0.0993597i | ||||
\(676\) | −1.16701e36 | −0.189569 | ||||||||
\(677\) | − | 1.04767e37i | − | 1.66945i | −0.550667 | − | 0.834725i | \(-0.685627\pi\) | ||
0.550667 | − | 0.834725i | \(-0.314373\pi\) | |||||||
\(678\) | −1.54699e36 | − | 3.67672e36i | −0.241826 | − | 0.574745i | ||||
\(679\) | 5.75190e36 | 0.882072 | ||||||||
\(680\) | 7.45146e36i | 1.12105i | ||||||||
\(681\) | 8.85055e35 | − | 3.72390e35i | 0.130634 | − | 0.0549649i | ||||
\(682\) | 3.60451e35 | 0.0521974 | ||||||||
\(683\) | − | 7.24061e36i | − | 1.02874i | −0.857568 | − | 0.514370i | \(-0.828026\pi\) | ||
0.857568 | − | 0.514370i | \(-0.171974\pi\) | |||||||
\(684\) | 1.12086e35 | − | 1.14611e35i | 0.0156250 | − | 0.0159770i | ||||
\(685\) | −1.07354e36 | −0.146839 | ||||||||
\(686\) | 1.84764e37i | 2.47973i | ||||||||
\(687\) | 1.79654e36 | + | 4.26981e36i | 0.236591 | + | 0.562304i | ||||
\(688\) | −3.81466e36 | −0.492954 | ||||||||
\(689\) | 7.50139e36i | 0.951244i | ||||||||
\(690\) | 1.73706e36 | − | 7.30873e35i | 0.216160 | − | 0.0909502i | ||||
\(691\) | 2.45929e36 | 0.300327 | 0.150164 | − | 0.988661i | \(-0.452020\pi\) | ||||
0.150164 | + | 0.988661i | \(0.452020\pi\) | |||||||
\(692\) | 1.17120e36i | 0.140363i | ||||||||
\(693\) | 6.66188e36 | + | 6.51510e36i | 0.783547 | + | 0.766283i | ||||
\(694\) | 2.91482e35 | 0.0336464 | ||||||||
\(695\) | − | 1.24249e37i | − | 1.40764i | ||||||
\(696\) | 4.47750e36 | + | 1.06416e37i | 0.497870 | + | 1.18328i | ||||
\(697\) | −1.55781e37 | −1.70016 | ||||||||
\(698\) | − | 6.60549e36i | − | 0.707595i | ||||||
\(699\) | 1.32070e36 | − | 5.55691e35i | 0.138868 | − | 0.0584292i | ||||
\(700\) | −1.43085e36 | −0.147679 | ||||||||
\(701\) | 1.29219e37i | 1.30915i | 0.755995 | + | 0.654577i | \(0.227153\pi\) | ||||
−0.755995 | + | 0.654577i | \(0.772847\pi\) | |||||||
\(702\) | 1.82747e36 | − | 4.62918e36i | 0.181748 | − | 0.460386i | ||||
\(703\) | 8.17264e34 | 0.00797890 | ||||||||
\(704\) | − | 6.65354e36i | − | 0.637688i | ||||||
\(705\) | 8.28239e35 | + | 1.96847e36i | 0.0779286 | + | 0.185212i | ||||
\(706\) | −1.13184e37 | −1.04550 | ||||||||
\(707\) | − | 1.50533e37i | − | 1.36515i | ||||||
\(708\) | 1.10379e36 | − | 4.64424e35i | 0.0982775 | − | 0.0413506i | ||||
\(709\) | 2.66702e36 | 0.233144 | 0.116572 | − | 0.993182i | \(-0.462809\pi\) | ||||
0.116572 | + | 0.993182i | \(0.462809\pi\) | |||||||
\(710\) | 4.06262e36i | 0.348697i | ||||||||
\(711\) | −7.62364e36 | + | 7.79539e36i | −0.642477 | + | 0.656951i | ||||
\(712\) | 1.22699e37 | 1.01532 | ||||||||
\(713\) | − | 4.27250e35i | − | 0.0347151i | ||||||
\(714\) | −9.33624e36 | − | 2.21893e37i | −0.744895 | − | 1.77038i | ||||
\(715\) | 3.71803e36 | 0.291296 | ||||||||
\(716\) | − | 9.13344e35i | − | 0.0702692i | ||||||
\(717\) | 2.19166e37 | − | 9.22147e36i | 1.65586 | − | 0.696709i | ||||
\(718\) | −6.94783e36 | −0.515503 | ||||||||
\(719\) | 6.85917e36i | 0.499800i | 0.968272 | + | 0.249900i | \(0.0803977\pi\) | ||||
−0.968272 | + | 0.249900i | \(0.919602\pi\) | |||||||
\(720\) | 5.35007e36 | + | 5.23220e36i | 0.382858 | + | 0.374422i | ||||
\(721\) | −5.91438e36 | −0.415672 | ||||||||
\(722\) | 1.21403e37i | 0.838006i | ||||||||
\(723\) | −5.86177e36 | − | 1.39316e37i | −0.397403 | − | 0.944503i | ||||
\(724\) | 1.75227e36 | 0.116681 | ||||||||
\(725\) | 4.88645e36i | 0.319594i | ||||||||
\(726\) | 8.01360e36 | − | 3.37175e36i | 0.514816 | − | 0.216610i | ||||
\(727\) | 1.97236e37 | 1.24463 | 0.622313 | − | 0.782768i | \(-0.286193\pi\) | ||||
0.622313 | + | 0.782768i | \(0.286193\pi\) | |||||||
\(728\) | − | 1.94224e37i | − | 1.20391i | ||||||
\(729\) | 1.19945e37 | + | 1.12185e37i | 0.730336 | + | 0.683088i | ||||
\(730\) | −1.07832e37 | −0.644986 | ||||||||
\(731\) | 1.61582e37i | 0.949438i | ||||||||
\(732\) | −1.36414e36 | − | 3.24213e36i | −0.0787434 | − | 0.187149i | ||||
\(733\) | −3.71159e36 | −0.210479 | −0.105239 | − | 0.994447i | \(-0.533561\pi\) | ||||
−0.105239 | + | 0.994447i | \(0.533561\pi\) | |||||||
\(734\) | − | 1.99653e37i | − | 1.11231i | ||||||
\(735\) | −3.68062e37 | + | 1.54863e37i | −2.01458 | + | 0.847643i | ||||
\(736\) | −3.38166e36 | −0.181852 | ||||||||
\(737\) | 9.39783e36i | 0.496535i | ||||||||
\(738\) | −1.59852e37 | + | 1.63454e37i | −0.829825 | + | 0.848519i | ||||
\(739\) | −2.02049e37 | −1.03057 | −0.515287 | − | 0.857018i | \(-0.672315\pi\) | ||||
−0.515287 | + | 0.857018i | \(0.672315\pi\) | |||||||
\(740\) | − | 5.09189e35i | − | 0.0255192i | ||||||
\(741\) | 3.57183e35 | + | 8.48912e35i | 0.0175895 | + | 0.0418048i | ||||
\(742\) | 5.32520e37 | 2.57683 | ||||||||
\(743\) | 3.45294e37i | 1.64185i | 0.571033 | + | 0.820927i | \(0.306543\pi\) | ||||
−0.571033 | + | 0.820927i | \(0.693457\pi\) | |||||||
\(744\) | 2.28523e36 | − | 9.61518e35i | 0.106778 | − | 0.0449272i | ||||
\(745\) | 2.87332e36 | 0.131933 | ||||||||
\(746\) | 9.78788e36i | 0.441656i | ||||||||
\(747\) | −2.51314e37 | − | 2.45777e37i | −1.11442 | − | 1.08987i | ||||
\(748\) | −4.65714e36 | −0.202955 | ||||||||
\(749\) | − | 3.86413e37i | − | 1.65496i | ||||||
\(750\) | 8.42883e36 | + | 2.00327e37i | 0.354790 | + | 0.843225i | ||||
\(751\) | 2.44251e37 | 1.01046 | 0.505229 | − | 0.862986i | \(-0.331408\pi\) | ||||
0.505229 | + | 0.862986i | \(0.331408\pi\) | |||||||
\(752\) | 3.62822e36i | 0.147523i | ||||||||
\(753\) | −1.40194e37 | + | 5.89870e36i | −0.560266 | + | 0.235734i | ||||
\(754\) | −1.48828e37 | −0.584598 | ||||||||
\(755\) | − | 6.74974e36i | − | 0.260601i | ||||||
\(756\) | 1.33764e37 | + | 5.28062e36i | 0.507639 | + | 0.200402i | ||||
\(757\) | −3.68388e37 | −1.37423 | −0.687114 | − | 0.726550i | \(-0.741123\pi\) | ||||
−0.687114 | + | 0.726550i | \(0.741123\pi\) | |||||||
\(758\) | − | 4.89233e36i | − | 0.179397i | ||||||
\(759\) | 2.03581e36 | + | 4.83850e36i | 0.0733829 | + | 0.174408i | ||||
\(760\) | −2.02374e36 | −0.0717096 | ||||||||
\(761\) | − | 3.62230e37i | − | 1.26178i | −0.775872 | − | 0.630891i | \(-0.782690\pi\) | ||
0.775872 | − | 0.630891i | \(-0.217310\pi\) | |||||||
\(762\) | 2.06670e37 | − | 8.69572e36i | 0.707723 | − | 0.297777i | ||||
\(763\) | 8.11577e37 | 2.73219 | ||||||||
\(764\) | 7.51626e36i | 0.248764i | ||||||||
\(765\) | 2.21626e37 | − | 2.26619e37i | 0.721144 | − | 0.737390i | ||||
\(766\) | −3.28470e37 | −1.05080 | ||||||||
\(767\) | 6.87989e36i | 0.216392i | ||||||||
\(768\) | −9.88517e36 | − | 2.34940e37i | −0.305695 | − | 0.726542i | ||||
\(769\) | 2.47123e37 | 0.751399 | 0.375699 | − | 0.926742i | \(-0.377403\pi\) | ||||
0.375699 | + | 0.926742i | \(0.377403\pi\) | |||||||
\(770\) | − | 2.63941e37i | − | 0.789092i | ||||||
\(771\) | −4.33940e37 | + | 1.82582e37i | −1.27562 | + | 0.536723i | ||||
\(772\) | −1.65099e37 | −0.477221 | ||||||||
\(773\) | 2.44726e37i | 0.695579i | 0.937573 | + | 0.347789i | \(0.113068\pi\) | ||||
−0.937573 | + | 0.347789i | \(0.886932\pi\) | |||||||
\(774\) | 1.69540e37 | + | 1.65804e37i | 0.473848 | + | 0.463408i | ||||
\(775\) | 1.04934e36 | 0.0288398 | ||||||||
\(776\) | 1.88032e37i | 0.508193i | ||||||||
\(777\) | 2.84333e36 | + | 6.75771e36i | 0.0755708 | + | 0.179608i | ||||
\(778\) | −2.45240e37 | −0.640998 | ||||||||
\(779\) | − | 4.23086e36i | − | 0.108753i | ||||||
\(780\) | 5.28907e36 | − | 2.22539e36i | 0.133705 | − | 0.0562570i | ||||
\(781\) | −1.13163e37 | −0.281345 | ||||||||
\(782\) | − | 1.35618e37i | − | 0.331610i | ||||||
\(783\) | 1.80337e37 | − | 4.56813e37i | 0.433693 | − | 1.09859i | ||||
\(784\) | −6.78400e37 | −1.60464 | ||||||||
\(785\) | 2.44814e37i | 0.569549i | ||||||||
\(786\) | 4.56692e36 | + | 1.08541e37i | 0.104503 | + | 0.248372i | ||||
\(787\) | −5.75180e37 | −1.29459 | −0.647295 | − | 0.762240i | \(-0.724100\pi\) | ||||
−0.647295 | + | 0.762240i | \(0.724100\pi\) | |||||||
\(788\) | 2.13635e37i | 0.472968i | ||||||||
\(789\) | 6.68827e37 | − | 2.81411e37i | 1.45651 | − | 0.612831i | ||||
\(790\) | 3.08851e37 | 0.661601 | ||||||||
\(791\) | 6.62201e37i | 1.39539i | ||||||||
\(792\) | −2.12981e37 | + | 2.17779e37i | −0.441483 | + | 0.451428i | ||||
\(793\) | 2.02081e37 | 0.412073 | ||||||||
\(794\) | 8.00954e37i | 1.60672i | ||||||||
\(795\) | 2.71930e37 | + | 6.46294e37i | 0.536642 | + | 1.27543i | ||||
\(796\) | −3.41975e36 | −0.0663934 | ||||||||
\(797\) | − | 9.65724e37i | − | 1.84457i | −0.386512 | − | 0.922285i | \(-0.626320\pi\) | ||
0.386512 | − | 0.922285i | \(-0.373680\pi\) | |||||||
\(798\) | 6.02639e36 | − | 2.53562e36i | 0.113245 | − | 0.0476483i | ||||
\(799\) | 1.53684e37 | 0.284133 | ||||||||
\(800\) | − | 8.30544e36i | − | 0.151075i | ||||||
\(801\) | −3.73162e37 | − | 3.64940e37i | −0.667843 | − | 0.653129i | ||||
\(802\) | 3.24477e37 | 0.571369 | ||||||||
\(803\) | − | 3.00361e37i | − | 0.520405i | ||||||
\(804\) | 5.62498e36 | + | 1.33688e37i | 0.0958943 | + | 0.227911i | ||||
\(805\) | −3.12855e37 | −0.524803 | ||||||||
\(806\) | 3.19600e36i | 0.0527535i | ||||||||
\(807\) | −2.31087e37 | + | 9.72307e36i | −0.375336 | + | 0.157924i | ||||
\(808\) | 4.92099e37 | 0.786511 | ||||||||
\(809\) | − | 4.97913e37i | − | 0.783110i | −0.920155 | − | 0.391555i | \(-0.871937\pi\) | ||
0.920155 | − | 0.391555i | \(-0.128063\pi\) | |||||||
\(810\) | −1.03622e36 | − | 4.65082e37i | −0.0160379 | − | 0.719820i | ||||
\(811\) | −7.39902e37 | −1.12695 | −0.563473 | − | 0.826134i | \(-0.690535\pi\) | ||||
−0.563473 | + | 0.826134i | \(0.690535\pi\) | |||||||
\(812\) | − | 4.30050e37i | − | 0.644601i | ||||||
\(813\) | 1.07771e37 | + | 2.56138e37i | 0.158974 | + | 0.377831i | ||||
\(814\) | −3.48446e36 | −0.0505846 | ||||||||
\(815\) | 1.21102e37i | 0.173022i | ||||||||
\(816\) | 4.96368e37 | − | 2.08848e37i | 0.697962 | − | 0.293670i | ||||
\(817\) | −4.38839e36 | −0.0607321 | ||||||||
\(818\) | − | 8.98792e37i | − | 1.22424i | ||||||
\(819\) | −5.77673e37 | + | 5.90687e37i | −0.774447 | + | 0.791894i | ||||
\(820\) | −2.63600e37 | −0.347828 | ||||||||
\(821\) | − | 9.98209e37i | − | 1.29646i | −0.761443 | − | 0.648232i | \(-0.775509\pi\) | ||
0.761443 | − | 0.648232i | \(-0.224491\pi\) | |||||||
\(822\) | 4.39712e36 | + | 1.04506e37i | 0.0562127 | + | 0.133600i | ||||
\(823\) | 1.13685e38 | 1.43056 | 0.715282 | − | 0.698836i | \(-0.246298\pi\) | ||||
0.715282 | + | 0.698836i | \(0.246298\pi\) | |||||||
\(824\) | − | 1.93343e37i | − | 0.239483i | ||||||
\(825\) | −1.18835e37 | + | 5.00002e36i | −0.144891 | + | 0.0609635i | ||||
\(826\) | 4.88400e37 | 0.586186 | ||||||||
\(827\) | 9.88322e37i | 1.16769i | 0.811866 | + | 0.583844i | \(0.198452\pi\) | ||||
−0.811866 | + | 0.583844i | \(0.801548\pi\) | |||||||
\(828\) | 5.79208e36 | + | 5.66446e36i | 0.0673659 | + | 0.0658816i | ||||
\(829\) | 2.48526e37 | 0.284553 | 0.142276 | − | 0.989827i | \(-0.454558\pi\) | ||||
0.142276 | + | 0.989827i | \(0.454558\pi\) | |||||||
\(830\) | 9.95697e37i | 1.12231i | ||||||||
\(831\) | −2.27592e37 | − | 5.40916e37i | −0.252548 | − | 0.600229i | ||||
\(832\) | 5.89948e37 | 0.644481 | ||||||||
\(833\) | 2.87357e38i | 3.09056i | ||||||||
\(834\) | −1.20953e38 | + | 5.08913e37i | −1.28073 | + | 0.538872i | ||||
\(835\) | 8.50864e37 | 0.887025 | ||||||||
\(836\) | − | 1.26483e36i | − | 0.0129823i | ||||||
\(837\) | −9.80981e36 | − | 3.87264e36i | −0.0991356 | − | 0.0391360i | ||||
\(838\) | −7.48005e37 | −0.744273 | ||||||||
\(839\) | − | 9.09390e37i | − | 0.890932i | −0.895299 | − | 0.445466i | \(-0.853038\pi\) | ||
0.895299 | − | 0.445466i | \(-0.146962\pi\) | |||||||
\(840\) | −7.04075e37 | − | 1.67337e38i | −0.679185 | − | 1.61421i | ||||
\(841\) | −4.15849e37 | −0.394992 | ||||||||
\(842\) | − | 4.98507e37i | − | 0.466245i | ||||||
\(843\) | −4.41097e37 | + | 1.85593e37i | −0.406234 | + | 0.170924i | ||||
\(844\) | 5.64744e37 | 0.512153 | ||||||||
\(845\) | − | 6.26697e37i | − | 0.559655i | ||||||
\(846\) | 1.57700e37 | − | 1.61253e37i | 0.138681 | − | 0.141806i | ||||
\(847\) | −1.44330e38 | −1.24989 | ||||||||
\(848\) | 1.19123e38i | 1.01590i | ||||||||
\(849\) | 7.10879e37 | + | 1.68954e38i | 0.597029 | + | 1.41895i | ||||
\(850\) | 3.33080e37 | 0.275488 | ||||||||
\(851\) | 4.13020e36i | 0.0336424i | ||||||||
\(852\) | −1.60979e37 | + | 6.77324e36i | −0.129138 | + | 0.0543352i | ||||
\(853\) | −1.98067e38 | −1.56486 | −0.782430 | − | 0.622738i | \(-0.786020\pi\) | ||||
−0.782430 | + | 0.622738i | \(0.786020\pi\) | |||||||
\(854\) | − | 1.43456e38i | − | 1.11626i | ||||||
\(855\) | 6.15473e36 | + | 6.01912e36i | 0.0471682 | + | 0.0461290i | ||||
\(856\) | 1.26320e38 | 0.953482 | ||||||||
\(857\) | 8.03880e37i | 0.597641i | 0.954309 | + | 0.298821i | \(0.0965933\pi\) | ||||
−0.954309 | + | 0.298821i | \(0.903407\pi\) | |||||||
\(858\) | −1.52287e37 | − | 3.61939e37i | −0.111514 | − | 0.265034i | ||||
\(859\) | 2.25210e38 | 1.62434 | 0.812168 | − | 0.583423i | \(-0.198287\pi\) | ||||
0.812168 | + | 0.583423i | \(0.198287\pi\) | |||||||
\(860\) | 2.73414e37i | 0.194241i | ||||||||
\(861\) | 3.49837e38 | − | 1.47195e38i | 2.44808 | − | 1.03004i | ||||
\(862\) | −2.51829e37 | −0.173584 | ||||||||
\(863\) | − | 2.03964e38i | − | 1.38488i | −0.721473 | − | 0.692442i | \(-0.756535\pi\) | ||
0.721473 | − | 0.692442i | \(-0.243465\pi\) | |||||||
\(864\) | −3.06517e37 | + | 7.76441e37i | −0.205011 | + | 0.519314i | ||||
\(865\) | −6.28949e37 | −0.414387 | ||||||||
\(866\) | − | 1.16405e38i | − | 0.755507i | ||||||
\(867\) | −2.78071e37 | − | 6.60889e37i | −0.177790 | − | 0.422552i | ||||
\(868\) | −9.23508e36 | −0.0581680 | ||||||||
\(869\) | 8.60290e37i | 0.533811i | ||||||||
\(870\) | −1.28225e38 | + | 5.39512e37i | −0.783833 | + | 0.329800i | ||||
\(871\) | −8.33275e37 | −0.501825 | ||||||||
\(872\) | 2.65307e38i | 1.57411i | ||||||||
\(873\) | 5.59255e37 | − | 5.71854e37i | 0.326907 | − | 0.334272i | ||||
\(874\) | 3.68323e36 | 0.0212119 | ||||||||
\(875\) | − | 3.60802e38i | − | 2.04722i | ||||||
\(876\) | −1.79778e37 | − | 4.27277e37i | −0.100504 | − | 0.238867i | ||||
\(877\) | −1.20583e38 | −0.664187 | −0.332094 | − | 0.943246i | \(-0.607755\pi\) | ||||
−0.332094 | + | 0.943246i | \(0.607755\pi\) | |||||||
\(878\) | − | 7.71217e37i | − | 0.418550i | ||||||
\(879\) | −8.89563e37 | + | 3.74287e37i | −0.475687 | + | 0.200147i | ||||
\(880\) | 5.90427e37 | 0.311094 | ||||||||
\(881\) | 3.38133e37i | 0.175550i | 0.996140 | + | 0.0877751i | \(0.0279757\pi\) | ||||
−0.996140 | + | 0.0877751i | \(0.972024\pi\) | |||||||
\(882\) | 3.01510e38 | + | 2.94867e38i | 1.54244 | + | 1.50846i | ||||
\(883\) | 3.27626e37 | 0.165154 | 0.0825770 | − | 0.996585i | \(-0.473685\pi\) | ||||
0.0825770 | + | 0.996585i | \(0.473685\pi\) | |||||||
\(884\) | − | 4.12934e37i | − | 0.205117i | ||||||
\(885\) | 2.49401e37 | + | 5.92748e37i | 0.122077 | + | 0.290140i | ||||
\(886\) | −2.51594e38 | −1.21356 | ||||||||
\(887\) | 3.21541e38i | 1.52837i | 0.644997 | + | 0.764185i | \(0.276859\pi\) | ||||
−0.644997 | + | 0.764185i | \(0.723141\pi\) | |||||||
\(888\) | −2.20912e37 | + | 9.29495e36i | −0.103479 | + | 0.0435390i | ||||
\(889\) | −3.72226e38 | −1.71824 | ||||||||
\(890\) | 1.47845e38i | 0.672570i | ||||||||
\(891\) | 1.29547e38 | − | 2.88634e36i | 0.580785 | − | 0.0129401i | ||||
\(892\) | −4.52396e37 | −0.199883 | ||||||||
\(893\) | 4.17390e36i | 0.0181749i | ||||||||
\(894\) | −1.17688e37 | − | 2.79709e37i | −0.0505064 | − | 0.120038i | ||||
\(895\) | 4.90476e37 | 0.207452 | ||||||||
\(896\) | − | 1.66130e38i | − | 0.692537i | ||||||
\(897\) | −4.29014e37 | + | 1.80509e37i | −0.176266 | + | 0.0741647i | ||||
\(898\) | 1.20135e38 | 0.486493 | ||||||||
\(899\) | 3.15385e37i | 0.125882i | ||||||||
\(900\) | −1.39121e37 | + | 1.42255e37i | −0.0547318 | + | 0.0559648i | ||||
\(901\) | 5.04582e38 | 1.95663 | ||||||||
\(902\) | 1.80385e38i | 0.689471i | ||||||||
\(903\) | −1.52676e38 | − | 3.62863e38i | −0.575214 | − | 1.36710i | ||||
\(904\) | −2.16476e38 | −0.803933 | ||||||||
\(905\) | 9.40986e37i | 0.344470i | ||||||||
\(906\) | −6.57067e37 | + | 2.76463e37i | −0.237106 | + | 0.0997633i | ||||
\(907\) | 2.64704e38 | 0.941599 | 0.470800 | − | 0.882240i | \(-0.343965\pi\) | ||||
0.470800 | + | 0.882240i | \(0.343965\pi\) | |||||||
\(908\) | − | 1.16923e37i | − | 0.0410001i | ||||||
\(909\) | −1.49660e38 | − | 1.46363e38i | −0.517341 | − | 0.505942i | ||||
\(910\) | 2.34028e38 | 0.797499 | ||||||||
\(911\) | 5.19318e37i | 0.174459i | 0.996188 | + | 0.0872297i | \(0.0278014\pi\) | ||||
−0.996188 | + | 0.0872297i | \(0.972199\pi\) | |||||||
\(912\) | 5.67210e36 | + | 1.34808e37i | 0.0187850 | + | 0.0446461i | ||||
\(913\) | −2.77347e38 | −0.905531 | ||||||||
\(914\) | − | 1.78902e38i | − | 0.575858i | ||||||
\(915\) | 1.74106e38 | − | 7.32557e37i | 0.552509 | − | 0.232470i | ||||
\(916\) | 5.64078e37 | 0.176481 | ||||||||
\(917\) | − | 1.95490e38i | − | 0.603008i | ||||||
\(918\) | −3.11383e38 | − | 1.22925e38i | −0.946977 | − | 0.373840i | ||||
\(919\) | 9.37364e37 | 0.281065 | 0.140532 | − | 0.990076i | \(-0.455119\pi\) | ||||
0.140532 | + | 0.990076i | \(0.455119\pi\) | |||||||
\(920\) | − | 1.02273e38i | − | 0.302358i | ||||||
\(921\) | 5.15294e37 | + | 1.22469e38i | 0.150204 | + | 0.356987i | ||||
\(922\) | 8.56684e37 | 0.246217 | ||||||||
\(923\) | − | 1.00338e38i | − | 0.284342i | ||||||
\(924\) | 1.04585e38 | − | 4.40045e37i | 0.292236 | − | 0.122959i | ||||
\(925\) | −1.01439e37 | −0.0279487 | ||||||||
\(926\) | − | 3.68131e38i | − | 1.00014i | ||||||
\(927\) | −5.75053e37 | + | 5.88008e37i | −0.154053 | + | 0.157524i | ||||
\(928\) | 2.49626e38 | 0.659425 | ||||||||
\(929\) | 4.86704e38i | 1.26783i | 0.773403 | + | 0.633914i | \(0.218553\pi\) | ||||
−0.773403 | + | 0.633914i | \(0.781447\pi\) | |||||||
\(930\) | 1.15857e37 | + | 2.75356e37i | 0.0297608 | + | 0.0707321i | ||||
\(931\) | −7.80432e37 | −0.197692 | ||||||||
\(932\) | − | 1.74476e37i | − | 0.0435842i | ||||||
\(933\) | −6.51851e38 | + | 2.74268e38i | −1.60578 | + | 0.675639i | ||||
\(934\) | −5.97541e37 | −0.145164 | ||||||||
\(935\) | − | 2.50094e38i | − | 0.599173i | ||||||
\(936\) | −1.93098e38 | − | 1.88843e38i | −0.456238 | − | 0.446186i | ||||
\(937\) | 2.03446e38 | 0.474061 | 0.237031 | − | 0.971502i | \(-0.423826\pi\) | ||||
0.237031 | + | 0.971502i | \(0.423826\pi\) | |||||||
\(938\) | 5.91538e38i | 1.35940i | ||||||||
\(939\) | 2.01696e38 | + | 4.79368e38i | 0.457134 | + | 1.08647i | ||||
\(940\) | 2.60051e37 | 0.0581295 | ||||||||
\(941\) | − | 4.32737e38i | − | 0.954023i | −0.878897 | − | 0.477011i | \(-0.841720\pi\) | ||
0.878897 | − | 0.477011i | \(-0.158280\pi\) | |||||||
\(942\) | 2.38319e38 | − | 1.00274e38i | 0.518200 | − | 0.218035i | ||||
\(943\) | 2.13814e38 | 0.458548 | ||||||||
\(944\) | 1.09253e38i | 0.231100i | ||||||||
\(945\) | −2.83575e38 | + | 7.18326e38i | −0.591636 | + | 1.49868i | ||||
\(946\) | 1.87102e38 | 0.385029 | ||||||||
\(947\) | 1.52006e38i | 0.308540i | 0.988029 | + | 0.154270i | \(0.0493026\pi\) | ||||
−0.988029 | + | 0.154270i | \(0.950697\pi\) | |||||||
\(948\) | 5.14918e37 | + | 1.22380e38i | 0.103093 | + | 0.245020i | ||||
\(949\) | 2.66320e38 | 0.525949 | ||||||||
\(950\) | 9.04611e36i | 0.0176220i | ||||||||
\(951\) | 2.97425e38 | − | 1.25142e38i | 0.571518 | − | 0.240468i | ||||
\(952\) | −1.30645e39 | −2.47635 | ||||||||
\(953\) | 7.36063e38i | 1.37628i | 0.725577 | + | 0.688141i | \(0.241573\pi\) | ||||
−0.725577 | + | 0.688141i | \(0.758427\pi\) | |||||||
\(954\) | 5.17768e38 | − | 5.29432e38i | 0.955006 | − | 0.976521i | ||||
\(955\) | −4.03632e38 | −0.734415 | ||||||||
\(956\) | − | 2.89536e38i | − | 0.519697i | ||||||
\(957\) | −1.50279e38 | − | 3.57166e38i | −0.266098 | − | 0.632433i | ||||
\(958\) | 2.24848e38 | 0.392768 | ||||||||
\(959\) | − | 1.88222e38i | − | 0.324360i | ||||||
\(960\) | 5.08279e38 | − | 2.13860e38i | 0.864123 | − | 0.363583i | ||||
\(961\) | −5.89444e38 | −0.988641 | ||||||||
\(962\) | − | 3.08956e37i | − | 0.0511235i | ||||||
\(963\) | −3.84173e38 | − | 3.75708e38i | −0.627169 | − | 0.613351i | ||||
\(964\) | −1.84048e38 | −0.296435 | ||||||||
\(965\) | − | 8.86601e38i | − | 1.40888i | ||||||
\(966\) | 1.28143e38 | + | 3.04555e38i | 0.200905 | + | 0.477489i | ||||
\(967\) | −1.18571e38 | −0.183415 | −0.0917075 | − | 0.995786i | \(-0.529232\pi\) | ||||
−0.0917075 | + | 0.995786i | \(0.529232\pi\) | |||||||
\(968\) | − | 4.71820e38i | − | 0.720106i | ||||||
\(969\) | 5.71022e37 | − | 2.40259e37i | 0.0859891 | − | 0.0361802i | ||||
\(970\) | −2.26567e38 | −0.336638 | ||||||||
\(971\) | 8.77148e38i | 1.28595i | 0.765889 | + | 0.642973i | \(0.222299\pi\) | ||||
−0.765889 | + | 0.642973i | \(0.777701\pi\) | |||||||
\(972\) | 1.82558e38 | − | 8.16448e37i | 0.264083 | − | 0.118105i | ||||
\(973\) | 2.17844e39 | 3.10941 | ||||||||
\(974\) | 9.14272e37i | 0.128768i | ||||||||
\(975\) | −4.43335e37 | − | 1.05367e38i | −0.0616130 | − | 0.146435i | ||||
\(976\) | 3.20907e38 | 0.440080 | ||||||||
\(977\) | − | 3.71527e38i | − | 0.502760i | −0.967888 | − | 0.251380i | \(-0.919116\pi\) | ||
0.967888 | − | 0.251380i | \(-0.0808844\pi\) | |||||||
\(978\) | 1.17889e38 | − | 4.96021e37i | 0.157423 | − | 0.0662361i | ||||
\(979\) | −4.11817e38 | −0.542661 | ||||||||
\(980\) | 4.86241e38i | 0.632284i | ||||||||
\(981\) | 7.89094e38 | − | 8.06871e38i | 1.01259 | − | 1.03540i | ||||
\(982\) | −3.78267e38 | −0.479016 | ||||||||
\(983\) | − | 4.11799e38i | − | 0.514623i | −0.966329 | − | 0.257311i | \(-0.917163\pi\) | ||
0.966329 | − | 0.257311i | \(-0.0828366\pi\) | |||||||
\(984\) | 4.81186e38 | + | 1.14363e39i | 0.593440 | + | 1.41042i | ||||
\(985\) | −1.14724e39 | −1.39632 | ||||||||
\(986\) | 1.00109e39i | 1.20247i | ||||||||
\(987\) | −3.45127e38 | + | 1.45214e38i | −0.409125 | + | 0.172141i | ||||
\(988\) | 1.12148e37 | 0.0131206 | ||||||||
\(989\) | − | 2.21776e38i | − | 0.256072i | ||||||
\(990\) | −2.62411e38 | − | 2.56629e38i | −0.299036 | − | 0.292448i | ||||
\(991\) | −1.38403e39 | −1.55664 | −0.778318 | − | 0.627871i | \(-0.783927\pi\) | ||||
−0.778318 | + | 0.627871i | \(0.783927\pi\) | |||||||
\(992\) | − | 5.36057e37i | − | 0.0595057i | ||||||
\(993\) | 8.50006e37 | + | 2.02020e38i | 0.0931283 | + | 0.221337i | ||||
\(994\) | −7.12292e38 | −0.770256 | ||||||||
\(995\) | − | 1.83645e38i | − | 0.196010i | ||||||
\(996\) | −3.94539e38 | + | 1.66003e38i | −0.415641 | + | 0.174882i | ||||
\(997\) | 6.81486e38 | 0.708630 | 0.354315 | − | 0.935126i | \(-0.384714\pi\) | ||||
0.354315 | + | 0.935126i | \(0.384714\pi\) | |||||||
\(998\) | 5.07677e37i | 0.0521063i | ||||||||
\(999\) | 9.48309e37 | + | 3.74366e37i | 0.0960724 | + | 0.0379267i |
(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 | 3.27.b.a.2.3 | ✓ | 8 | |
3.2 | odd | 2 | inner | 3.27.b.a.2.6 | yes | 8 | |
4.3 | odd | 2 | 48.27.e.d.17.3 | 8 | |||
12.11 | even | 2 | 48.27.e.d.17.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.27.b.a.2.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
3.27.b.a.2.6 | yes | 8 | 3.2 | odd | 2 | inner | |
48.27.e.d.17.3 | 8 | 4.3 | odd | 2 | |||
48.27.e.d.17.4 | 8 | 12.11 | even | 2 |