Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,9,Mod(28,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.28");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.g (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.3320374528\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} - 30x^{3} + 1089x^{2} - 3168x + 4608 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 5) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 37.2 | ||
Root | \(-4.23471 + 4.23471i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.37 |
Dual form | 45.9.g.a.28.2 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.39608 | + | 4.39608i | 0.274755 | + | 0.274755i | 0.831011 | − | 0.556256i | \(-0.187763\pi\) |
−0.556256 | + | 0.831011i | \(0.687763\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 217.349i | − | 0.849020i | ||||||
\(5\) | 14.1685 | − | 624.839i | 0.0226696 | − | 0.999743i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 730.992 | + | 730.992i | 0.304453 | + | 0.304453i | 0.842753 | − | 0.538300i | \(-0.180933\pi\) |
−0.538300 | + | 0.842753i | \(0.680933\pi\) | |||||||
\(8\) | 2080.88 | − | 2080.88i | 0.508027 | − | 0.508027i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2809.13 | − | 2684.56i | 0.280913 | − | 0.268456i | ||||
\(11\) | −19599.8 | −1.33869 | −0.669347 | − | 0.742950i | \(-0.733426\pi\) | ||||
−0.669347 | + | 0.742950i | \(0.733426\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −24915.1 | + | 24915.1i | −0.872347 | + | 0.872347i | −0.992728 | − | 0.120381i | \(-0.961588\pi\) |
0.120381 | + | 0.992728i | \(0.461588\pi\) | |||||||
\(14\) | 6426.99i | 0.167300i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −37346.0 | −0.569854 | ||||||||
\(17\) | 11288.6 | + | 11288.6i | 0.135159 | + | 0.135159i | 0.771450 | − | 0.636290i | \(-0.219532\pi\) |
−0.636290 | + | 0.771450i | \(0.719532\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 171525.i | − | 1.31617i | −0.752943 | − | 0.658086i | \(-0.771366\pi\) | ||
0.752943 | − | 0.658086i | \(-0.228634\pi\) | |||||||
\(20\) | −135808. | − | 3079.51i | −0.848802 | − | 0.0192469i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −86162.2 | − | 86162.2i | −0.367812 | − | 0.367812i | ||||
\(23\) | 132074. | − | 132074.i | 0.471961 | − | 0.471961i | −0.430587 | − | 0.902549i | \(-0.641694\pi\) |
0.902549 | + | 0.430587i | \(0.141694\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −390224. | − | 17706.1i | −0.998972 | − | 0.0453275i | ||||
\(26\) | −219057. | −0.479363 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 158880. | − | 158880.i | 0.258487 | − | 0.258487i | ||||
\(29\) | 127019.i | 0.179588i | 0.995960 | + | 0.0897939i | \(0.0286208\pi\) | ||||
−0.995960 | + | 0.0897939i | \(0.971379\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −960715. | −1.04027 | −0.520137 | − | 0.854083i | \(-0.674119\pi\) | ||||
−0.520137 | + | 0.854083i | \(0.674119\pi\) | |||||||
\(32\) | −696880. | − | 696880.i | −0.664597 | − | 0.664597i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 99251.5i | 0.0742713i | ||||||||
\(35\) | 467110. | − | 446396.i | 0.311277 | − | 0.297473i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −243873. | − | 243873.i | −0.130124 | − | 0.130124i | 0.639045 | − | 0.769169i | \(-0.279330\pi\) |
−0.769169 | + | 0.639045i | \(0.779330\pi\) | |||||||
\(38\) | 754036. | − | 754036.i | 0.361625 | − | 0.361625i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.27073e6 | − | 1.32970e6i | −0.496380 | − | 0.519413i | ||||
\(41\) | −2.50747e6 | −0.887360 | −0.443680 | − | 0.896185i | \(-0.646327\pi\) | ||||
−0.443680 | + | 0.896185i | \(0.646327\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6763.95 | + | 6763.95i | −0.00197846 | + | 0.00197846i | −0.708095 | − | 0.706117i | \(-0.750445\pi\) |
0.706117 | + | 0.708095i | \(0.250445\pi\) | |||||||
\(44\) | 4.26000e6i | 1.13658i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.16122e6 | 0.259347 | ||||||||
\(47\) | 1.79394e6 | + | 1.79394e6i | 0.367635 | + | 0.367635i | 0.866614 | − | 0.498979i | \(-0.166291\pi\) |
−0.498979 | + | 0.866614i | \(0.666291\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 4.69610e6i | − | 0.814617i | ||||||
\(50\) | −1.63761e6 | − | 1.79329e6i | −0.262018 | − | 0.286926i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.41527e6 | + | 5.41527e6i | 0.740640 | + | 0.740640i | ||||
\(53\) | 2.97161e6 | − | 2.97161e6i | 0.376608 | − | 0.376608i | −0.493269 | − | 0.869877i | \(-0.664198\pi\) |
0.869877 | + | 0.493269i | \(0.164198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −277700. | + | 1.22467e7i | −0.0303476 | + | 1.33835i | ||||
\(56\) | 3.04221e6 | 0.309341 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −558385. | + | 558385.i | −0.0493426 | + | 0.0493426i | ||||
\(59\) | − | 313805.i | − | 0.0258972i | −0.999916 | − | 0.0129486i | \(-0.995878\pi\) | ||
0.999916 | − | 0.0129486i | \(-0.00412178\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.76977e7 | 1.27820 | 0.639098 | − | 0.769125i | \(-0.279308\pi\) | ||||
0.639098 | + | 0.769125i | \(0.279308\pi\) | |||||||
\(62\) | −4.22338e6 | − | 4.22338e6i | −0.285820 | − | 0.285820i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.43349e6i | 0.204652i | ||||||||
\(65\) | 1.52149e7 | + | 1.59209e7i | 0.852347 | + | 0.891899i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.41349e6 | + | 4.41349e6i | 0.219020 | + | 0.219020i | 0.808085 | − | 0.589066i | \(-0.200504\pi\) |
−0.589066 | + | 0.808085i | \(0.700504\pi\) | |||||||
\(68\) | 2.45358e6 | − | 2.45358e6i | 0.114753 | − | 0.114753i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.01584e6 | + | 91060.8i | 0.167257 | + | 0.00379262i | ||||
\(71\) | 8.89315e6 | 0.349963 | 0.174982 | − | 0.984572i | \(-0.444013\pi\) | ||||
0.174982 | + | 0.984572i | \(0.444013\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.95076e7 | − | 1.95076e7i | 0.686928 | − | 0.686928i | −0.274624 | − | 0.961552i | \(-0.588553\pi\) |
0.961552 | + | 0.274624i | \(0.0885532\pi\) | |||||||
\(74\) | − | 2.14417e6i | − | 0.0715043i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.72808e7 | −1.11746 | ||||||||
\(77\) | −1.43273e7 | − | 1.43273e7i | −0.407569 | − | 0.407569i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.11272e7i | − | 0.285680i | −0.989746 | − | 0.142840i | \(-0.954377\pi\) | ||
0.989746 | − | 0.142840i | \(-0.0456234\pi\) | |||||||
\(80\) | −529136. | + | 2.33352e7i | −0.0129184 | + | 0.569708i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.10230e7 | − | 1.10230e7i | −0.243806 | − | 0.243806i | ||||
\(83\) | −1.58712e7 | + | 1.58712e7i | −0.334423 | + | 0.334423i | −0.854264 | − | 0.519840i | \(-0.825992\pi\) |
0.519840 | + | 0.854264i | \(0.325992\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.21353e6 | − | 6.89365e6i | 0.138189 | − | 0.132061i | ||||
\(86\) | −59469.7 | −0.00108718 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.07848e7 | + | 4.07848e7i | −0.680092 | + | 0.680092i | ||||
\(89\) | − | 4.85032e7i | − | 0.773056i | −0.922278 | − | 0.386528i | \(-0.873674\pi\) | ||
0.922278 | − | 0.386528i | \(-0.126326\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.64255e7 | −0.531178 | ||||||||
\(92\) | −2.87062e7 | − | 2.87062e7i | −0.400704 | − | 0.400704i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.57726e7i | 0.202019i | ||||||||
\(95\) | −1.07176e8 | − | 2.43025e6i | −1.31583 | − | 0.0298371i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.07411e8 | − | 1.07411e8i | −1.21329 | − | 1.21329i | −0.969939 | − | 0.243348i | \(-0.921754\pi\) |
−0.243348 | − | 0.969939i | \(-0.578246\pi\) | |||||||
\(98\) | 2.06444e7 | − | 2.06444e7i | 0.223820 | − | 0.223820i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.84840e6 | + | 8.48147e7i | −0.0384840 | + | 0.848147i | ||||
\(101\) | 7.16023e7 | 0.688084 | 0.344042 | − | 0.938954i | \(-0.388204\pi\) | ||||
0.344042 | + | 0.938954i | \(0.388204\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.89158e7 | − | 9.89158e7i | 0.878854 | − | 0.878854i | −0.114562 | − | 0.993416i | \(-0.536546\pi\) |
0.993416 | + | 0.114562i | \(0.0365464\pi\) | |||||||
\(104\) | 1.03691e8i | 0.886352i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.61269e7 | 0.206949 | ||||||||
\(107\) | −4.73497e7 | − | 4.73497e7i | −0.361228 | − | 0.361228i | 0.503037 | − | 0.864265i | \(-0.332216\pi\) |
−0.864265 | + | 0.503037i | \(0.832216\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.29072e7i | 0.162280i | 0.996703 | + | 0.0811401i | \(0.0258561\pi\) | ||||
−0.996703 | + | 0.0811401i | \(0.974144\pi\) | |||||||
\(110\) | −5.50583e7 | + | 5.26168e7i | −0.376056 | + | 0.359380i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.72996e7 | − | 2.72996e7i | −0.173494 | − | 0.173494i | ||||
\(113\) | 1.95361e8 | − | 1.95361e8i | 1.19819 | − | 1.19819i | 0.223480 | − | 0.974709i | \(-0.428258\pi\) |
0.974709 | − | 0.223480i | \(-0.0717416\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.06538e7 | − | 8.43964e7i | −0.461141 | − | 0.482539i | ||||
\(116\) | 2.76075e7 | 0.152474 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.37951e6 | − | 1.37951e6i | 0.00711537 | − | 0.00711537i | ||||
\(119\) | 1.65038e7i | 0.0822994i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.69794e8 | 0.792100 | ||||||||
\(122\) | 7.78004e7 | + | 7.78004e7i | 0.351190 | + | 0.351190i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.08811e8i | 0.883213i | ||||||||
\(125\) | −1.65923e7 | + | 2.43576e8i | −0.0679622 | + | 0.997688i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.84792e8 | + | 1.84792e8i | 0.710343 | + | 0.710343i | 0.966607 | − | 0.256264i | \(-0.0824917\pi\) |
−0.256264 | + | 0.966607i | \(0.582492\pi\) | |||||||
\(128\) | −1.93495e8 | + | 1.93495e8i | −0.720826 | + | 0.720826i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.10371e6 | + | 1.36876e8i | −0.0108670 | + | 0.479240i | ||||
\(131\) | 3.05076e8 | 1.03591 | 0.517956 | − | 0.855407i | \(-0.326693\pi\) | ||||
0.517956 | + | 0.855407i | \(0.326693\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.25383e8 | − | 1.25383e8i | 0.400713 | − | 0.400713i | ||||
\(134\) | 3.88041e7i | 0.120353i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.69806e7 | 0.137329 | ||||||||
\(137\) | −3.75735e8 | − | 3.75735e8i | −1.06659 | − | 1.06659i | −0.997618 | − | 0.0689766i | \(-0.978027\pi\) |
−0.0689766 | − | 0.997618i | \(-0.521973\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.10575e8i | 0.296208i | 0.988972 | + | 0.148104i | \(0.0473171\pi\) | ||||
−0.988972 | + | 0.148104i | \(0.952683\pi\) | |||||||
\(140\) | −9.70236e7 | − | 1.01526e8i | −0.252560 | − | 0.264280i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.90950e7 | + | 3.90950e7i | 0.0961540 | + | 0.0961540i | ||||
\(143\) | 4.88331e8 | − | 4.88331e8i | 1.16781 | − | 1.16781i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.93665e7 | + | 1.79967e6i | 0.179542 | + | 0.00407118i | ||||
\(146\) | 1.71513e8 | 0.377474 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.30056e7 | + | 5.30056e7i | −0.110478 | + | 0.110478i | ||||
\(149\) | 7.23744e8i | 1.46838i | 0.678942 | + | 0.734192i | \(0.262439\pi\) | ||||
−0.678942 | + | 0.734192i | \(0.737561\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.67246e8 | 1.47580 | 0.737899 | − | 0.674911i | \(-0.235818\pi\) | ||||
0.737899 | + | 0.674911i | \(0.235818\pi\) | |||||||
\(152\) | −3.56922e8 | − | 3.56922e8i | −0.668651 | − | 0.668651i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 1.25968e8i | − | 0.223963i | ||||||
\(155\) | −1.36119e7 | + | 6.00293e8i | −0.0235826 | + | 1.04001i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.03264e8 | − | 8.03264e8i | −1.32209 | − | 1.32209i | −0.912085 | − | 0.410001i | \(-0.865528\pi\) |
−0.410001 | − | 0.912085i | \(-0.634472\pi\) | |||||||
\(158\) | 4.89162e7 | − | 4.89162e7i | 0.0784918 | − | 0.0784918i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.45312e8 | + | 4.25565e8i | −0.679492 | + | 0.649360i | ||||
\(161\) | 1.93090e8 | 0.287380 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.34915e8 | + | 4.34915e8i | −0.616103 | + | 0.616103i | −0.944530 | − | 0.328426i | \(-0.893482\pi\) |
0.328426 | + | 0.944530i | \(0.393482\pi\) | |||||||
\(164\) | 5.44996e8i | 0.753386i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.39542e8 | −0.183769 | ||||||||
\(167\) | −7.16803e8 | − | 7.16803e8i | −0.921582 | − | 0.921582i | 0.0755590 | − | 0.997141i | \(-0.475926\pi\) |
−0.997141 | + | 0.0755590i | \(0.975926\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 4.25794e8i | − | 0.521979i | ||||||
\(170\) | 6.20162e7 | + | 1.40624e6i | 0.0742522 | + | 0.00168370i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.47014e6 | + | 1.47014e6i | 0.00167975 | + | 0.00167975i | ||||
\(173\) | −3.40359e8 | + | 3.40359e8i | −0.379973 | + | 0.379973i | −0.871092 | − | 0.491119i | \(-0.836588\pi\) |
0.491119 | + | 0.871092i | \(0.336588\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.72307e8 | − | 2.98193e8i | −0.290340 | − | 0.317940i | ||||
\(176\) | 7.31974e8 | 0.762860 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.13224e8 | − | 2.13224e8i | 0.212401 | − | 0.212401i | ||||
\(179\) | − | 1.29181e9i | − | 1.25830i | −0.777283 | − | 0.629151i | \(-0.783403\pi\) | ||
0.777283 | − | 0.629151i | \(-0.216597\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.92912e8 | 0.179740 | 0.0898700 | − | 0.995954i | \(-0.471355\pi\) | ||||
0.0898700 | + | 0.995954i | \(0.471355\pi\) | |||||||
\(182\) | −1.60129e8 | − | 1.60129e8i | −0.145944 | − | 0.145944i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 5.49660e8i | − | 0.479538i | ||||||
\(185\) | −1.55837e8 | + | 1.48926e8i | −0.133040 | + | 0.127141i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.21255e8 | − | 2.21255e8i | −0.180937 | − | 0.180937i | ||||
\(188\) | 3.89912e8 | − | 3.89912e8i | 0.312130 | − | 0.312130i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.60468e8 | − | 4.81835e8i | −0.353334 | − | 0.369729i | ||||
\(191\) | −7.64646e8 | −0.574549 | −0.287274 | − | 0.957848i | \(-0.592749\pi\) | ||||
−0.287274 | + | 0.957848i | \(0.592749\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.15389e8 | − | 1.15389e8i | 0.0831641 | − | 0.0831641i | −0.664301 | − | 0.747465i | \(-0.731271\pi\) |
0.747465 | + | 0.664301i | \(0.231271\pi\) | |||||||
\(194\) | − | 9.44378e8i | − | 0.666713i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.02069e9 | −0.691626 | ||||||||
\(197\) | 9.95415e7 | + | 9.95415e7i | 0.0660906 | + | 0.0660906i | 0.739379 | − | 0.673289i | \(-0.235119\pi\) |
−0.673289 | + | 0.739379i | \(0.735119\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.71187e9i | 1.09159i | 0.837919 | + | 0.545795i | \(0.183772\pi\) | ||||
−0.837919 | + | 0.545795i | \(0.816228\pi\) | |||||||
\(200\) | −8.48852e8 | + | 7.75163e8i | −0.530532 | + | 0.484477i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.14769e8 | + | 3.14769e8i | 0.189054 | + | 0.189054i | ||||
\(203\) | −9.28499e7 | + | 9.28499e7i | −0.0546761 | + | 0.0546761i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.55271e7 | + | 1.56676e9i | −0.0201161 | + | 0.887132i | ||||
\(206\) | 8.69683e8 | 0.482939 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.30479e8 | − | 9.30479e8i | 0.497111 | − | 0.497111i | ||||
\(209\) | 3.36185e9i | 1.76195i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.81230e8 | −0.343688 | −0.171844 | − | 0.985124i | \(-0.554972\pi\) | ||||
−0.171844 | + | 0.985124i | \(0.554972\pi\) | |||||||
\(212\) | −6.45878e8 | − | 6.45878e8i | −0.319747 | − | 0.319747i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 4.16305e8i | − | 0.198498i | ||||||
\(215\) | 4.13055e6 | + | 4.32222e6i | 0.00193310 | + | 0.00202280i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.02275e8 | − | 7.02275e8i | −0.316715 | − | 0.316715i | ||||
\(218\) | −1.00702e8 | + | 1.00702e8i | −0.0445872 | + | 0.0445872i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.66182e9 | + | 6.03578e7i | 1.13628 | + | 0.0257657i | ||||
\(221\) | −5.62515e8 | −0.235812 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.37608e8 | − | 9.37608e8i | 0.379142 | − | 0.379142i | −0.491651 | − | 0.870793i | \(-0.663606\pi\) |
0.870793 | + | 0.491651i | \(0.163606\pi\) | |||||||
\(224\) | − | 1.01883e9i | − | 0.404677i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.71765e9 | 0.658416 | ||||||||
\(227\) | 3.47956e9 | + | 3.47956e9i | 1.31045 | + | 1.31045i | 0.921082 | + | 0.389368i | \(0.127307\pi\) |
0.389368 | + | 0.921082i | \(0.372693\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.67273e9i | 1.33551i | 0.744382 | + | 0.667754i | \(0.232744\pi\) | ||||
−0.744382 | + | 0.667754i | \(0.767256\pi\) | |||||||
\(230\) | 1.64527e7 | − | 7.25573e8i | 0.00587930 | − | 0.259281i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.64311e8 | + | 2.64311e8i | 0.0912354 | + | 0.0912354i | ||||
\(233\) | 3.62893e9 | − | 3.62893e9i | 1.23128 | − | 1.23128i | 0.267801 | − | 0.963474i | \(-0.413703\pi\) |
0.963474 | − | 0.267801i | \(-0.0862970\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.14634e9 | − | 1.09551e9i | 0.375875 | − | 0.359207i | ||||
\(236\) | −6.82053e7 | −0.0219872 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.25520e7 | + | 7.25520e7i | −0.0226121 | + | 0.0226121i | ||||
\(239\) | − | 2.64336e9i | − | 0.810148i | −0.914284 | − | 0.405074i | \(-0.867246\pi\) | ||
0.914284 | − | 0.405074i | \(-0.132754\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.20231e7 | −0.0213503 | −0.0106751 | − | 0.999943i | \(-0.503398\pi\) | ||||
−0.0106751 | + | 0.999943i | \(0.503398\pi\) | |||||||
\(242\) | 7.46425e8 | + | 7.46425e8i | 0.217633 | + | 0.217633i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 3.84658e9i | − | 1.08521i | ||||||
\(245\) | −2.93431e9 | − | 6.65367e7i | −0.814407 | − | 0.0184670i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.27356e9 | + | 4.27356e9i | 1.14816 | + | 1.14816i | ||||
\(248\) | −1.99913e9 | + | 1.99913e9i | −0.528487 | + | 0.528487i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.14372e9 | + | 9.97838e8i | −0.292792 | + | 0.255447i | ||||
\(251\) | −5.78911e7 | −0.0145854 | −0.00729268 | − | 0.999973i | \(-0.502321\pi\) | ||||
−0.00729268 | + | 0.999973i | \(0.502321\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.58863e9 | + | 2.58863e9i | −0.631811 | + | 0.631811i | ||||
\(254\) | 1.62472e9i | 0.390340i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.22267e8 | −0.191449 | ||||||||
\(257\) | 4.73425e8 | + | 4.73425e8i | 0.108522 | + | 0.108522i | 0.759283 | − | 0.650761i | \(-0.225550\pi\) |
−0.650761 | + | 0.759283i | \(0.725550\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.56539e8i | − | 0.0792333i | ||||||
\(260\) | 3.46040e9 | − | 3.30695e9i | 0.757240 | − | 0.723660i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.34114e9 | + | 1.34114e9i | 0.284622 | + | 0.284622i | ||||
\(263\) | −6.55957e9 | + | 6.55957e9i | −1.37105 | + | 1.37105i | −0.512155 | + | 0.858893i | \(0.671153\pi\) |
−0.858893 | + | 0.512155i | \(0.828847\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.81468e9 | − | 1.89889e9i | −0.367973 | − | 0.385048i | ||||
\(266\) | 1.10239e9 | 0.220195 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.59269e8 | − | 9.59269e8i | 0.185952 | − | 0.185952i | ||||
\(269\) | − | 5.38818e9i | − | 1.02904i | −0.857478 | − | 0.514521i | \(-0.827970\pi\) | ||
0.857478 | − | 0.514521i | \(-0.172030\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.79497e9 | −1.63064 | −0.815318 | − | 0.579013i | \(-0.803438\pi\) | ||||
−0.815318 | + | 0.579013i | \(0.803438\pi\) | |||||||
\(272\) | −4.21585e8 | − | 4.21585e8i | −0.0770211 | − | 0.0770211i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 3.30352e9i | − | 0.586104i | ||||||
\(275\) | 7.64831e9 | + | 3.47036e8i | 1.33732 | + | 0.0606797i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.78151e9 | − | 4.78151e9i | −0.812168 | − | 0.812168i | 0.172790 | − | 0.984959i | \(-0.444722\pi\) |
−0.984959 | + | 0.172790i | \(0.944722\pi\) | |||||||
\(278\) | −4.86096e8 | + | 4.86096e8i | −0.0813846 | + | 0.0813846i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.31035e7 | − | 1.90089e9i | 0.00701263 | − | 0.309261i | ||||
\(281\) | −1.22255e10 | −1.96083 | −0.980416 | − | 0.196936i | \(-0.936901\pi\) | ||||
−0.980416 | + | 0.196936i | \(0.936901\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.86857e8 | + | 2.86857e8i | −0.0447219 | + | 0.0447219i | −0.729114 | − | 0.684392i | \(-0.760068\pi\) |
0.684392 | + | 0.729114i | \(0.260068\pi\) | |||||||
\(284\) | − | 1.93292e9i | − | 0.297126i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.29348e9 | 0.641720 | ||||||||
\(287\) | −1.83294e9 | − | 1.83294e9i | −0.270160 | − | 0.270160i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 6.72089e9i | − | 0.963464i | ||||||
\(290\) | 3.40990e8 | + | 3.56813e8i | 0.0482113 | + | 0.0504485i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.23995e9 | − | 4.23995e9i | −0.583216 | − | 0.583216i | ||||
\(293\) | 1.02814e9 | − | 1.02814e9i | 0.139503 | − | 0.139503i | −0.633907 | − | 0.773410i | \(-0.718550\pi\) |
0.773410 | + | 0.633907i | \(0.218550\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.96078e8 | − | 4.44615e6i | −0.0258905 | − | 0.000587078i | ||||
\(296\) | −1.01494e9 | −0.132213 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.18163e9 | + | 3.18163e9i | −0.403445 | + | 0.403445i | ||||
\(299\) | 6.58128e9i | 0.823428i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.88879e6 | −0.00120469 | ||||||||
\(302\) | 3.37287e9 | + | 3.37287e9i | 0.405482 | + | 0.405482i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.40576e9i | 0.750026i | ||||||||
\(305\) | 2.50750e8 | − | 1.10582e10i | 0.0289762 | − | 1.27787i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.92159e9 | + | 7.92159e9i | 0.891783 | + | 0.891783i | 0.994691 | − | 0.102908i | \(-0.0328148\pi\) |
−0.102908 | + | 0.994691i | \(0.532815\pi\) | |||||||
\(308\) | −3.11403e9 | + | 3.11403e9i | −0.346034 | + | 0.346034i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.69877e9 | + | 2.57909e9i | −0.292226 | + | 0.279267i | ||||
\(311\) | −3.74059e9 | −0.399851 | −0.199926 | − | 0.979811i | \(-0.564070\pi\) | ||||
−0.199926 | + | 0.979811i | \(0.564070\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.79633e9 | + | 4.79633e9i | −0.499725 | + | 0.499725i | −0.911352 | − | 0.411627i | \(-0.864961\pi\) |
0.411627 | + | 0.911352i | \(0.364961\pi\) | |||||||
\(314\) | − | 7.06242e9i | − | 0.726499i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.41850e9 | −0.242548 | ||||||||
\(317\) | 5.54903e9 | + | 5.54903e9i | 0.549516 | + | 0.549516i | 0.926301 | − | 0.376785i | \(-0.122970\pi\) |
−0.376785 | + | 0.926301i | \(0.622970\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.48955e9i | − | 0.240413i | ||||||
\(320\) | 2.14538e9 | + | 4.86474e7i | 0.204599 | + | 0.00463937i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.48839e8 | + | 8.48839e8i | 0.0789591 | + | 0.0789591i | ||||
\(323\) | 1.93628e9 | − | 1.93628e9i | 0.177893 | − | 0.177893i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.01636e10 | − | 9.28131e9i | 0.910992 | − | 0.831909i | ||||
\(326\) | −3.82384e9 | −0.338555 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.21774e9 | + | 5.21774e9i | −0.450803 | + | 0.450803i | ||||
\(329\) | 2.62272e9i | 0.223855i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.49782e10 | 1.24780 | 0.623902 | − | 0.781503i | \(-0.285546\pi\) | ||||
0.623902 | + | 0.781503i | \(0.285546\pi\) | |||||||
\(332\) | 3.44958e9 | + | 3.44958e9i | 0.283932 | + | 0.283932i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 6.30224e9i | − | 0.506418i | ||||||
\(335\) | 2.82026e9 | − | 2.69519e9i | 0.223929 | − | 0.213998i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.29203e9 | + | 6.29203e9i | 0.487833 | + | 0.487833i | 0.907622 | − | 0.419789i | \(-0.137896\pi\) |
−0.419789 | + | 0.907622i | \(0.637896\pi\) | |||||||
\(338\) | 1.87182e9 | − | 1.87182e9i | 0.143416 | − | 0.143416i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.49833e9 | − | 1.56785e9i | −0.112122 | − | 0.117325i | ||||
\(341\) | 1.88298e10 | 1.39261 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.64684e9 | − | 7.64684e9i | 0.552466 | − | 0.552466i | ||||
\(344\) | 2.81499e7i | 0.00201022i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.99249e9 | −0.208799 | ||||||||
\(347\) | 8.28230e9 | + | 8.28230e9i | 0.571259 | + | 0.571259i | 0.932480 | − | 0.361221i | \(-0.117640\pi\) |
−0.361221 | + | 0.932480i | \(0.617640\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.11611e10i | 0.752328i | 0.926553 | + | 0.376164i | \(0.122757\pi\) | ||||
−0.926553 | + | 0.376164i | \(0.877243\pi\) | |||||||
\(350\) | 1.13797e8 | − | 2.50796e9i | 0.00758329 | − | 0.167128i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.36587e10 | + | 1.36587e10i | 0.889692 | + | 0.889692i | ||||
\(353\) | −1.05904e10 | + | 1.05904e10i | −0.682047 | + | 0.682047i | −0.960461 | − | 0.278414i | \(-0.910191\pi\) |
0.278414 | + | 0.960461i | \(0.410191\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.26003e8 | − | 5.55679e9i | 0.00793352 | − | 0.349873i | ||||
\(356\) | −1.05421e10 | −0.656339 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.67888e9 | − | 5.67888e9i | 0.345725 | − | 0.345725i | ||||
\(359\) | 9.48530e9i | 0.571049i | 0.958371 | + | 0.285524i | \(0.0921677\pi\) | ||||
−0.958371 | + | 0.285524i | \(0.907832\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.24372e10 | −0.732309 | ||||||||
\(362\) | 8.48055e8 | + | 8.48055e8i | 0.0493844 | + | 0.0493844i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.91704e9i | 0.450980i | ||||||||
\(365\) | −1.19127e10 | − | 1.24655e10i | −0.671179 | − | 0.702324i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.59996e9 | − | 9.59996e9i | −0.529182 | − | 0.529182i | 0.391146 | − | 0.920329i | \(-0.372079\pi\) |
−0.920329 | + | 0.391146i | \(0.872079\pi\) | |||||||
\(368\) | −4.93244e9 | + | 4.93244e9i | −0.268949 | + | 0.268949i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.33976e9 | − | 3.03797e7i | −0.0714860 | − | 0.00162097i | ||||
\(371\) | 4.34445e9 | 0.229319 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.48382e9 | − | 8.48382e9i | 0.438285 | − | 0.438285i | −0.453150 | − | 0.891434i | \(-0.649700\pi\) |
0.891434 | + | 0.453150i | \(0.149700\pi\) | |||||||
\(374\) | − | 1.94531e9i | − | 0.0994265i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.46595e9 | 0.373537 | ||||||||
\(377\) | −3.16469e9 | − | 3.16469e9i | −0.156663 | − | 0.156663i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.19075e10i | 1.06178i | 0.847440 | + | 0.530891i | \(0.178143\pi\) | ||||
−0.847440 | + | 0.530891i | \(0.821857\pi\) | |||||||
\(380\) | −5.28212e8 | + | 2.32945e10i | −0.0253323 | + | 1.11717i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.36144e9 | − | 3.36144e9i | −0.157860 | − | 0.157860i | ||||
\(383\) | 2.31285e10 | − | 2.31285e10i | 1.07486 | − | 1.07486i | 0.0778987 | − | 0.996961i | \(-0.475179\pi\) |
0.996961 | − | 0.0778987i | \(-0.0248211\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.15526e9 | + | 8.74927e9i | −0.416704 | + | 0.398225i | ||||
\(386\) | 1.01452e9 | 0.0456995 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.33458e10 | + | 2.33458e10i | −1.03010 | + | 1.03010i | ||||
\(389\) | − | 2.23175e10i | − | 0.974647i | −0.873221 | − | 0.487324i | \(-0.837973\pi\) | ||
0.873221 | − | 0.487324i | \(-0.162027\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.98188e9 | 0.127580 | ||||||||
\(392\) | −9.77202e9 | − | 9.77202e9i | −0.413847 | − | 0.413847i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.75184e8i | 0.0363174i | ||||||||
\(395\) | −6.95274e9 | − | 1.57656e8i | −0.285606 | − | 0.00647624i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.26036e10 | − | 2.26036e10i | −0.909947 | − | 0.909947i | 0.0863200 | − | 0.996267i | \(-0.472489\pi\) |
−0.996267 | + | 0.0863200i | \(0.972489\pi\) | |||||||
\(398\) | −7.52553e9 | + | 7.52553e9i | −0.299919 | + | 0.299919i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.45733e10 | + | 6.61250e8i | 0.569268 | + | 0.0258301i | ||||
\(401\) | −1.77913e10 | −0.688064 | −0.344032 | − | 0.938958i | \(-0.611793\pi\) | ||||
−0.344032 | + | 0.938958i | \(0.611793\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.39363e10 | − | 2.39363e10i | 0.907480 | − | 0.907480i | ||||
\(404\) | − | 1.55627e10i | − | 0.584197i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.16350e8 | −0.0300450 | ||||||||
\(407\) | 4.77987e9 | + | 4.77987e9i | 0.174196 | + | 0.174196i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.37112e10i | − | 1.56206i | −0.624490 | − | 0.781032i | \(-0.714693\pi\) | ||
0.624490 | − | 0.781032i | \(-0.285307\pi\) | |||||||
\(410\) | −7.04380e9 | + | 6.73144e9i | −0.249271 | + | 0.238217i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.14993e10 | − | 2.14993e10i | −0.746165 | − | 0.746165i | ||||
\(413\) | 2.29389e8 | − | 2.29389e8i | 0.00788447 | − | 0.00788447i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.69206e9 | + | 1.01418e10i | 0.326756 | + | 0.341919i | ||||
\(416\) | 3.47257e10 | 1.15952 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.47790e10 | + | 1.47790e10i | −0.484104 | + | 0.484104i | ||||
\(419\) | 2.98593e10i | 0.968776i | 0.874853 | + | 0.484388i | \(0.160958\pi\) | ||||
−0.874853 | + | 0.484388i | \(0.839042\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.33816e10 | −1.69927 | −0.849637 | − | 0.527368i | \(-0.823179\pi\) | ||||
−0.849637 | + | 0.527368i | \(0.823179\pi\) | |||||||
\(422\) | −2.99474e9 | − | 2.99474e9i | −0.0944298 | − | 0.0944298i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 1.23671e10i | − | 0.382654i | ||||||
\(425\) | −4.20522e9 | − | 4.60497e9i | −0.128894 | − | 0.141147i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.29369e10 | + | 1.29369e10i | 0.389151 | + | 0.389151i | ||||
\(428\) | −1.02914e10 | + | 1.02914e10i | −0.306690 | + | 0.306690i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −842596. | + | 3.71590e7i | −2.46459e−5 | + | 0.00108690i | ||||
\(431\) | −1.68739e10 | −0.488997 | −0.244499 | − | 0.969650i | \(-0.578623\pi\) | ||||
−0.244499 | + | 0.969650i | \(0.578623\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.15187e9 | − | 7.15187e9i | 0.203455 | − | 0.203455i | −0.598024 | − | 0.801478i | \(-0.704047\pi\) |
0.801478 | + | 0.598024i | \(0.204047\pi\) | |||||||
\(434\) | − | 6.17451e9i | − | 0.174038i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.97885e9 | 0.137779 | ||||||||
\(437\) | −2.26540e10 | − | 2.26540e10i | −0.621182 | − | 0.621182i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.62124e9i | 0.0705747i | 0.999377 | + | 0.0352873i | \(0.0112346\pi\) | ||||
−0.999377 | + | 0.0352873i | \(0.988765\pi\) | |||||||
\(440\) | 2.49061e10 | + | 2.60618e10i | 0.664500 | + | 0.695335i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.47286e9 | − | 2.47286e9i | −0.0647904 | − | 0.0647904i | ||||
\(443\) | 3.30317e10 | − | 3.30317e10i | 0.857663 | − | 0.857663i | −0.133400 | − | 0.991062i | \(-0.542589\pi\) |
0.991062 | + | 0.133400i | \(0.0425894\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.03067e10 | − | 6.87218e8i | −0.772857 | − | 0.0175249i | ||||
\(446\) | 8.24359e9 | 0.208342 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.50985e9 | + | 2.50985e9i | −0.0623069 | + | 0.0623069i | ||||
\(449\) | 2.56081e10i | 0.630074i | 0.949079 | + | 0.315037i | \(0.102017\pi\) | ||||
−0.949079 | + | 0.315037i | \(0.897983\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.91459e10 | 1.18790 | ||||||||
\(452\) | −4.24616e10 | − | 4.24616e10i | −1.01729 | − | 1.01729i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.05928e10i | 0.720105i | ||||||||
\(455\) | −5.16094e8 | + | 2.27601e10i | −0.0120416 | + | 0.531041i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.31162e10 | + | 1.31162e10i | 0.300707 | + | 0.300707i | 0.841290 | − | 0.540583i | \(-0.181796\pi\) |
−0.540583 | + | 0.841290i | \(0.681796\pi\) | |||||||
\(458\) | −1.61456e10 | + | 1.61456e10i | −0.366937 | + | 0.366937i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.83435e10 | + | 1.75300e10i | −0.409685 | + | 0.391518i | ||||
\(461\) | 3.99207e10 | 0.883883 | 0.441942 | − | 0.897044i | \(-0.354290\pi\) | ||||
0.441942 | + | 0.897044i | \(0.354290\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.43482e10 | − | 1.43482e10i | 0.312229 | − | 0.312229i | −0.533544 | − | 0.845772i | \(-0.679140\pi\) |
0.845772 | + | 0.533544i | \(0.179140\pi\) | |||||||
\(464\) | − | 4.74365e9i | − | 0.102339i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.19061e10 | 0.676597 | ||||||||
\(467\) | −2.44200e10 | − | 2.44200e10i | −0.513427 | − | 0.513427i | 0.402148 | − | 0.915575i | \(-0.368264\pi\) |
−0.915575 | + | 0.402148i | \(0.868264\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.45246e9i | 0.133363i | ||||||||
\(470\) | 9.85535e9 | + | 2.23474e8i | 0.201967 | + | 0.00457969i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.52990e8 | − | 6.52990e8i | −0.0131565 | − | 0.0131565i | ||||
\(473\) | 1.32572e8 | − | 1.32572e8i | 0.00264855 | − | 0.00264855i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.03703e9 | + | 6.69330e10i | −0.0596588 | + | 1.31482i | ||||
\(476\) | 3.58709e9 | 0.0698738 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.16204e10 | − | 1.16204e10i | 0.222592 | − | 0.222592i | ||||
\(479\) | 9.03857e9i | 0.171695i | 0.996308 | + | 0.0858475i | \(0.0273598\pi\) | ||||
−0.996308 | + | 0.0858475i | \(0.972640\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.21523e10 | 0.227026 | ||||||||
\(482\) | −3.16619e8 | − | 3.16619e8i | −0.00586609 | − | 0.00586609i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 3.69045e10i | − | 0.672508i | ||||||
\(485\) | −6.86368e10 | + | 6.55930e10i | −1.24048 | + | 1.18547i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.53950e10 | + | 3.53950e10i | 0.629255 | + | 0.629255i | 0.947881 | − | 0.318626i | \(-0.103221\pi\) |
−0.318626 | + | 0.947881i | \(0.603221\pi\) | |||||||
\(488\) | 3.68268e10 | − | 3.68268e10i | 0.649358 | − | 0.649358i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.26069e10 | − | 1.31919e10i | −0.218688 | − | 0.228836i | ||||
\(491\) | 5.87159e10 | 1.01025 | 0.505126 | − | 0.863045i | \(-0.331446\pi\) | ||||
0.505126 | + | 0.863045i | \(0.331446\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.43387e9 | + | 1.43387e9i | −0.0242730 | + | 0.0242730i | ||||
\(494\) | 3.75738e10i | 0.630924i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.58788e10 | 0.592805 | ||||||||
\(497\) | 6.50082e9 | + | 6.50082e9i | 0.106547 | + | 0.106547i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.57394e10i | 0.415141i | 0.978220 | + | 0.207571i | \(0.0665557\pi\) | ||||
−0.978220 | + | 0.207571i | \(0.933444\pi\) | |||||||
\(500\) | 5.29410e10 | + | 3.60633e9i | 0.847057 | + | 0.0577012i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.54494e8 | − | 2.54494e8i | −0.00400740 | − | 0.00400740i | ||||
\(503\) | 4.75499e10 | − | 4.75499e10i | 0.742810 | − | 0.742810i | −0.230308 | − | 0.973118i | \(-0.573973\pi\) |
0.973118 | + | 0.230308i | \(0.0739733\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.01450e9 | − | 4.47399e10i | 0.0155986 | − | 0.687907i | ||||
\(506\) | −2.27596e10 | −0.347186 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.01643e10 | − | 4.01643e10i | 0.603095 | − | 0.603095i | ||||
\(509\) | 8.69280e10i | 1.29506i | 0.762042 | + | 0.647528i | \(0.224197\pi\) | ||||
−0.762042 | + | 0.647528i | \(0.775803\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.85197e10 | 0.418275 | ||||||||
\(512\) | 4.59200e10 | + | 4.59200e10i | 0.668225 | + | 0.668225i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.16243e9i | 0.0596340i | ||||||||
\(515\) | −6.04050e10 | − | 6.32080e10i | −0.858705 | − | 0.898552i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.51609e10 | − | 3.51609e10i | −0.492151 | − | 0.492151i | ||||
\(518\) | 1.56737e9 | − | 1.56737e9i | 0.0217697 | − | 0.0217697i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.47900e10 | + | 1.46914e9i | 0.886124 | + | 0.0200932i | ||||
\(521\) | −6.44123e10 | −0.874214 | −0.437107 | − | 0.899409i | \(-0.643997\pi\) | ||||
−0.437107 | + | 0.899409i | \(0.643997\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.99903e10 | + | 5.99903e10i | −0.801815 | + | 0.801815i | −0.983379 | − | 0.181564i | \(-0.941884\pi\) |
0.181564 | + | 0.983379i | \(0.441884\pi\) | |||||||
\(524\) | − | 6.63079e10i | − | 0.879509i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.76728e10 | −0.753404 | ||||||||
\(527\) | −1.08452e10 | − | 1.08452e10i | −0.140603 | − | 0.140603i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.34238e10i | 0.554505i | ||||||||
\(530\) | 3.70179e8 | − | 1.63251e10i | 0.00469146 | − | 0.206896i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.72519e10 | − | 2.72519e10i | −0.340213 | − | 0.340213i | ||||
\(533\) | 6.24738e10 | − | 6.24738e10i | 0.774086 | − | 0.774086i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.02568e10 | + | 2.89151e10i | −0.369324 | + | 0.352947i | ||||
\(536\) | 1.83679e10 | 0.222536 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.36869e10 | − | 2.36869e10i | 0.282734 | − | 0.282734i | ||||
\(539\) | 9.20427e10i | 1.09052i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.38341e10 | −1.09540 | −0.547698 | − | 0.836676i | \(-0.684496\pi\) | ||||
−0.547698 | + | 0.836676i | \(0.684496\pi\) | |||||||
\(542\) | −3.86633e10 | − | 3.86633e10i | −0.448025 | − | 0.448025i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 1.57337e10i | − | 0.179653i | ||||||
\(545\) | 1.43133e10 | + | 3.24560e8i | 0.162238 | + | 0.00367883i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.86813e10 | + | 1.86813e10i | 0.208669 | + | 0.208669i | 0.803702 | − | 0.595032i | \(-0.202861\pi\) |
−0.595032 | + | 0.803702i | \(0.702861\pi\) | |||||||
\(548\) | −8.16657e10 | + | 8.16657e10i | −0.905560 | + | 0.905560i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.20969e10 | + | 3.51481e10i | 0.350762 | + | 0.384106i | ||||
\(551\) | 2.17869e10 | 0.236368 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.13393e9 | − | 8.13393e9i | 0.0869761 | − | 0.0869761i | ||||
\(554\) | − | 4.20398e10i | − | 0.446294i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.40333e10 | 0.251487 | ||||||||
\(557\) | 4.32331e9 | + | 4.32331e9i | 0.0449154 | + | 0.0449154i | 0.729208 | − | 0.684292i | \(-0.239889\pi\) |
−0.684292 | + | 0.729208i | \(0.739889\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.37049e8i | − | 0.00345180i | ||||||
\(560\) | −1.74447e10 | + | 1.66711e10i | −0.177382 | + | 0.169516i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.37441e10 | − | 5.37441e10i | −0.538748 | − | 0.538748i | ||||
\(563\) | −5.85471e10 | + | 5.85471e10i | −0.582736 | + | 0.582736i | −0.935654 | − | 0.352918i | \(-0.885189\pi\) |
0.352918 | + | 0.935654i | \(0.385189\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.19302e11 | − | 1.24837e11i | −1.17072 | − | 1.22504i | ||||
\(566\) | −2.52209e9 | −0.0245751 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.85056e10 | − | 1.85056e10i | 0.177791 | − | 0.177791i | ||||
\(569\) | − | 1.98793e11i | − | 1.89650i | −0.317524 | − | 0.948250i | \(-0.602851\pi\) | ||
0.317524 | − | 0.948250i | \(-0.397149\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.21842e10 | 0.584973 | 0.292487 | − | 0.956270i | \(-0.405517\pi\) | ||||
0.292487 | + | 0.956270i | \(0.405517\pi\) | |||||||
\(572\) | −1.06138e11 | − | 1.06138e11i | −0.991490 | − | 0.991490i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 1.61155e10i | − | 0.148455i | ||||||
\(575\) | −5.38769e10 | + | 4.91999e10i | −0.492869 | + | 0.450083i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.02056e11 | − | 1.02056e11i | −0.920739 | − | 0.920739i | 0.0763427 | − | 0.997082i | \(-0.475676\pi\) |
−0.997082 | + | 0.0763427i | \(0.975676\pi\) | |||||||
\(578\) | 2.95455e10 | − | 2.95455e10i | 0.264716 | − | 0.264716i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.91156e8 | − | 1.72502e10i | 0.00345651 | − | 0.152434i | ||||
\(581\) | −2.32034e10 | −0.203633 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.82431e10 | + | 5.82431e10i | −0.504162 | + | 0.504162i | ||||
\(584\) | − | 8.11857e10i | − | 0.697956i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.03959e9 | 0.0766581 | ||||||||
\(587\) | 1.52761e11 | + | 1.52761e11i | 1.28665 | + | 1.28665i | 0.936811 | + | 0.349837i | \(0.113763\pi\) |
0.349837 | + | 0.936811i | \(0.386237\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.64787e11i | 1.36918i | ||||||||
\(590\) | −8.42427e8 | − | 8.81518e8i | −0.00695223 | − | 0.00727484i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.10768e9 | + | 9.10768e9i | 0.0741517 | + | 0.0741517i | ||||
\(593\) | −9.35153e10 | + | 9.35153e10i | −0.756247 | + | 0.756247i | −0.975637 | − | 0.219390i | \(-0.929593\pi\) |
0.219390 | + | 0.975637i | \(0.429593\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.03122e10 | + | 2.33834e8i | 0.0822782 | + | 0.00186569i | ||||
\(596\) | 1.57305e11 | 1.24669 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.89318e10 | + | 2.89318e10i | −0.226241 | + | 0.226241i | ||||
\(599\) | 5.65120e10i | 0.438968i | 0.975616 | + | 0.219484i | \(0.0704374\pi\) | ||||
−0.975616 | + | 0.219484i | \(0.929563\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.99220e10 | −0.765884 | −0.382942 | − | 0.923772i | \(-0.625089\pi\) | ||||
−0.382942 | + | 0.923772i | \(0.625089\pi\) | |||||||
\(602\) | −4.34719e7 | − | 4.34719e7i | −0.000330996 | − | 0.000330996i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 1.66760e11i | − | 1.25298i | ||||||
\(605\) | 2.40572e9 | − | 1.06094e11i | 0.0179566 | − | 0.791896i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.27776e11 | + | 1.27776e11i | 0.941229 | + | 0.941229i | 0.998366 | − | 0.0571370i | \(-0.0181972\pi\) |
−0.0571370 | + | 0.998366i | \(0.518197\pi\) | |||||||
\(608\) | −1.19532e11 | + | 1.19532e11i | −0.874724 | + | 0.874724i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.97151e10 | − | 4.75105e10i | 0.359062 | − | 0.343139i | ||||
\(611\) | −8.93925e10 | −0.641411 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.34636e10 | − | 6.34636e10i | 0.449452 | − | 0.449452i | −0.445720 | − | 0.895172i | \(-0.647052\pi\) |
0.895172 | + | 0.445720i | \(0.147052\pi\) | |||||||
\(614\) | 6.96478e10i | 0.490043i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.96267e10 | −0.414112 | ||||||||
\(617\) | 6.39126e10 | + | 6.39126e10i | 0.441007 | + | 0.441007i | 0.892350 | − | 0.451343i | \(-0.149055\pi\) |
−0.451343 | + | 0.892350i | \(0.649055\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 5.76225e10i | − | 0.392491i | −0.980555 | − | 0.196245i | \(-0.937125\pi\) | ||
0.980555 | − | 0.196245i | \(-0.0628749\pi\) | |||||||
\(620\) | 1.30473e11 | + | 2.95853e9i | 0.882986 | + | 0.0200221i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.64439e10 | − | 1.64439e10i | −0.109861 | − | 0.109861i | ||||
\(623\) | 3.54555e10 | − | 3.54555e10i | 0.235359 | − | 0.235359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.51961e11 | + | 1.38186e10i | 0.995891 | + | 0.0905619i | ||||
\(626\) | −4.21700e10 | −0.274604 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.74589e11 | + | 1.74589e11i | −1.12248 | + | 1.12248i | ||||
\(629\) | − | 5.50600e9i | − | 0.0351749i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.53061e11 | 0.965486 | 0.482743 | − | 0.875762i | \(-0.339641\pi\) | ||||
0.482743 | + | 0.875762i | \(0.339641\pi\) | |||||||
\(632\) | −2.31544e10 | − | 2.31544e10i | −0.145133 | − | 0.145133i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.87880e10i | 0.301964i | ||||||||
\(635\) | 1.18083e11 | − | 1.12847e11i | 0.726263 | − | 0.694057i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.17004e11 | + | 1.17004e11i | 0.710628 | + | 0.710628i | ||||
\(638\) | 1.09442e10 | − | 1.09442e10i | 0.0660546 | − | 0.0660546i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.18162e11 | + | 1.23645e11i | 0.704300 | + | 0.736982i | ||||
\(641\) | −1.10388e11 | −0.653867 | −0.326934 | − | 0.945047i | \(-0.606015\pi\) | ||||
−0.326934 | + | 0.945047i | \(0.606015\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.62452e10 | − | 4.62452e10i | 0.270535 | − | 0.270535i | −0.558781 | − | 0.829315i | \(-0.688731\pi\) |
0.829315 | + | 0.558781i | \(0.188731\pi\) | |||||||
\(644\) | − | 4.19680e10i | − | 0.243991i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.70241e10 | 0.0977539 | ||||||||
\(647\) | 9.64071e10 | + | 9.64071e10i | 0.550164 | + | 0.550164i | 0.926488 | − | 0.376324i | \(-0.122812\pi\) |
−0.376324 | + | 0.926488i | \(0.622812\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.15052e9i | 0.0346683i | ||||||||
\(650\) | 8.54813e10 | + | 3.87864e9i | 0.478870 | + | 0.0217283i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.45283e10 | + | 9.45283e10i | 0.523084 | + | 0.523084i | ||||
\(653\) | 2.02786e11 | − | 2.02786e11i | 1.11528 | − | 1.11528i | 0.122857 | − | 0.992424i | \(-0.460794\pi\) |
0.992424 | − | 0.122857i | \(-0.0392057\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.32247e9 | − | 1.90623e11i | 0.0234837 | − | 1.03565i | ||||
\(656\) | 9.36438e10 | 0.505666 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.15297e10 | + | 1.15297e10i | −0.0615053 | + | 0.0615053i | ||||
\(659\) | − | 5.78139e10i | − | 0.306542i | −0.988184 | − | 0.153271i | \(-0.951019\pi\) | ||
0.988184 | − | 0.153271i | \(-0.0489808\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.80376e10 | 0.199254 | 0.0996271 | − | 0.995025i | \(-0.468235\pi\) | ||||
0.0996271 | + | 0.995025i | \(0.468235\pi\) | |||||||
\(662\) | 6.58451e10 | + | 6.58451e10i | 0.342840 | + | 0.342840i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.60520e10i | 0.339792i | ||||||||
\(665\) | −7.65679e10 | − | 8.01209e10i | −0.391526 | − | 0.409694i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.67759e10 | + | 1.67759e10i | 0.0847585 | + | 0.0847585i | ||||
\(668\) | −1.55797e11 | + | 1.55797e11i | −0.782442 | + | 0.782442i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.42463e10 | + | 5.49796e8i | 0.120323 | + | 0.00272836i | ||||
\(671\) | −3.46872e11 | −1.71111 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.23735e11 | − | 1.23735e11i | 0.603158 | − | 0.603158i | −0.337991 | − | 0.941149i | \(-0.609747\pi\) |
0.941149 | + | 0.337991i | \(0.109747\pi\) | |||||||
\(674\) | 5.53205e10i | 0.268069i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.25460e10 | −0.443170 | ||||||||
\(677\) | 8.44279e10 | + | 8.44279e10i | 0.401912 | + | 0.401912i | 0.878906 | − | 0.476994i | \(-0.158274\pi\) |
−0.476994 | + | 0.878906i | \(0.658274\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.57034e11i | − | 0.738778i | ||||||
\(680\) | 6.65644e8 | − | 2.93553e10i | 0.00311320 | − | 0.137294i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.27774e10 | + | 8.27774e10i | 0.382626 | + | 0.382626i | ||||
\(683\) | 2.87370e10 | − | 2.87370e10i | 0.132056 | − | 0.132056i | −0.637989 | − | 0.770045i | \(-0.720234\pi\) |
0.770045 | + | 0.637989i | \(0.220234\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.40098e11 | + | 2.29450e11i | −1.09050 | + | 1.04214i | ||||
\(686\) | 6.72321e10 | 0.303585 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.52606e8 | − | 2.52606e8i | 0.00112743 | − | 0.00112743i | ||||
\(689\) | 1.48076e11i | 0.657065i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.87703e10 | −0.389364 | −0.194682 | − | 0.980866i | \(-0.562367\pi\) | ||||
−0.194682 | + | 0.980866i | \(0.562367\pi\) | |||||||
\(692\) | 7.39768e10 | + | 7.39768e10i | 0.322605 | + | 0.322605i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.28192e10i | 0.313912i | ||||||||
\(695\) | 6.90915e10 | + | 1.56668e9i | 0.296132 | + | 0.00671492i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.83059e10 | − | 2.83059e10i | −0.119935 | − | 0.119935i | ||||
\(698\) | −4.90652e10 | + | 4.90652e10i | −0.206706 | + | 0.206706i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.48120e10 | + | 5.91857e10i | −0.269938 | + | 0.246504i | ||||
\(701\) | −1.22790e11 | −0.508499 | −0.254249 | − | 0.967139i | \(-0.581828\pi\) | ||||
−0.254249 | + | 0.967139i | \(0.581828\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.18303e10 | + | 4.18303e10i | −0.171266 | + | 0.171266i | ||||
\(704\) | − | 6.72957e10i | − | 0.273966i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.31125e10 | −0.374791 | ||||||||
\(707\) | 5.23407e10 | + | 5.23407e10i | 0.209489 | + | 0.209489i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 2.07670e11i | − | 0.821842i | −0.911671 | − | 0.410921i | \(-0.865207\pi\) | ||
0.911671 | − | 0.410921i | \(-0.134793\pi\) | |||||||
\(710\) | 2.49820e10 | − | 2.38742e10i | 0.0983091 | − | 0.0939495i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.00929e11 | − | 1.00929e11i | −0.392733 | − | 0.392733i | ||||
\(713\) | −1.26886e11 | + | 1.26886e11i | −0.490969 | + | 0.490969i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.98210e11 | − | 3.12048e11i | −1.14103 | − | 1.19398i | ||||
\(716\) | −2.80773e11 | −1.06832 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.16981e10 | + | 4.16981e10i | −0.156898 | + | 0.156898i | ||||
\(719\) | − | 1.66571e11i | − | 0.623281i | −0.950200 | − | 0.311640i | \(-0.899122\pi\) | ||
0.950200 | − | 0.311640i | \(-0.100878\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.44613e11 | 0.535140 | ||||||||
\(722\) | −5.46750e10 | − | 5.46750e10i | −0.201205 | − | 0.201205i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 4.19292e10i | − | 0.152603i | ||||||
\(725\) | 2.24901e9 | − | 4.95658e10i | 0.00814027 | − | 0.179403i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.61369e11 | + | 1.61369e11i | 0.577673 | + | 0.577673i | 0.934262 | − | 0.356588i | \(-0.116060\pi\) |
−0.356588 | + | 0.934262i | \(0.616060\pi\) | |||||||
\(728\) | −7.57970e10 | + | 7.57970e10i | −0.269853 | + | 0.269853i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.43009e9 | − | 1.07168e11i | 0.00855717 | − | 0.377377i | ||||
\(731\) | −1.52712e8 | −0.000534814 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.72057e10 | − | 4.72057e10i | 0.163523 | − | 0.163523i | −0.620603 | − | 0.784125i | \(-0.713112\pi\) |
0.784125 | + | 0.620603i | \(0.213112\pi\) | |||||||
\(734\) | − | 8.44043e10i | − | 0.290791i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.84080e11 | −0.627328 | ||||||||
\(737\) | −8.65036e10 | − | 8.65036e10i | −0.293200 | − | 0.293200i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 2.13693e11i | − | 0.716494i | −0.933627 | − | 0.358247i | \(-0.883375\pi\) | ||
0.933627 | − | 0.358247i | \(-0.116625\pi\) | |||||||
\(740\) | 3.23690e10 | + | 3.38710e10i | 0.107945 | + | 0.112954i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.90985e10 | + | 1.90985e10i | 0.0630064 | + | 0.0630064i | ||||
\(743\) | 3.10741e11 | − | 3.10741e11i | 1.01963 | − | 1.01963i | 0.0198284 | − | 0.999803i | \(-0.493688\pi\) |
0.999803 | − | 0.0198284i | \(-0.00631198\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.52224e11 | + | 1.02544e10i | 1.46801 | + | 0.0332877i | ||||
\(746\) | 7.45910e10 | 0.240841 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.80896e10 | + | 4.80896e10i | −0.153619 | + | 0.153619i | ||||
\(749\) | − | 6.92245e10i | − | 0.219954i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.29510e11 | −1.66462 | −0.832308 | − | 0.554313i | \(-0.812981\pi\) | ||||
−0.832308 | + | 0.554313i | \(0.812981\pi\) | |||||||
\(752\) | −6.69965e10 | − | 6.69965e10i | −0.209498 | − | 0.209498i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 2.78245e10i | − | 0.0860877i | ||||||
\(755\) | 1.08707e10 | − | 4.79405e11i | 0.0334557 | − | 1.47542i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.66172e11 | − | 1.66172e11i | −0.506029 | − | 0.506029i | 0.407276 | − | 0.913305i | \(-0.366479\pi\) |
−0.913305 | + | 0.407276i | \(0.866479\pi\) | |||||||
\(758\) | −9.63068e10 | + | 9.63068e10i | −0.291729 | + | 0.291729i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.28076e11 | + | 2.17962e11i | −0.683637 | + | 0.653321i | ||||
\(761\) | 3.61095e11 | 1.07667 | 0.538335 | − | 0.842731i | \(-0.319054\pi\) | ||||
0.538335 | + | 0.842731i | \(0.319054\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.67450e10 | + | 1.67450e10i | −0.0494067 | + | 0.0494067i | ||||
\(764\) | 1.66195e11i | 0.487803i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.03349e11 | 0.590646 | ||||||||
\(767\) | 7.81849e9 | + | 7.81849e9i | 0.0225913 | + | 0.0225913i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.04700e11i | 0.585345i | 0.956213 | + | 0.292672i | \(0.0945446\pi\) | ||||
−0.956213 | + | 0.292672i | \(0.905455\pi\) | |||||||
\(770\) | −7.87096e10 | − | 1.78477e9i | −0.223906 | − | 0.00507716i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.50797e10 | − | 2.50797e10i | −0.0706080 | − | 0.0706080i | ||||
\(773\) | 8.07889e10 | − | 8.07889e10i | 0.226274 | − | 0.226274i | −0.584860 | − | 0.811134i | \(-0.698851\pi\) |
0.811134 | + | 0.584860i | \(0.198851\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.74894e11 | + | 1.70105e10i | 1.03921 | + | 0.0471531i | ||||
\(776\) | −4.47020e11 | −1.23276 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.81095e10 | − | 9.81095e10i | 0.267789 | − | 0.267789i | ||||
\(779\) | 4.30093e11i | 1.16792i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.74304e11 | −0.468493 | ||||||||
\(782\) | 1.31086e10 | + | 1.31086e10i | 0.0350532 | + | 0.0350532i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.75380e11i | 0.464213i | ||||||||
\(785\) | −5.13292e11 | + | 4.90530e11i | −1.35172 | + | 1.29177i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.41727e11 | − | 1.41727e11i | −0.369448 | − | 0.369448i | 0.497828 | − | 0.867276i | \(-0.334131\pi\) |
−0.867276 | + | 0.497828i | \(0.834131\pi\) | |||||||
\(788\) | 2.16353e10 | − | 2.16353e10i | 0.0561122 | − | 0.0561122i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.98717e10 | − | 3.12578e10i | −0.0766923 | − | 0.0802510i | ||||
\(791\) | 2.85615e11 | 0.729584 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.40940e11 | + | 4.40940e11i | −1.11503 | + | 1.11503i | ||||
\(794\) | − | 1.98735e11i | − | 0.500025i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.72074e11 | 0.926781 | ||||||||
\(797\) | 2.66505e11 | + | 2.66505e11i | 0.660499 | + | 0.660499i | 0.955498 | − | 0.294998i | \(-0.0953191\pi\) |
−0.294998 | + | 0.955498i | \(0.595319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.05024e10i | 0.0993787i | ||||||||
\(800\) | 2.59600e11 | + | 2.84278e11i | 0.633789 | + | 0.694038i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.82117e10 | − | 7.82117e10i | −0.189049 | − | 0.189049i | ||||
\(803\) | −3.82344e11 | + | 3.82344e11i | −0.919586 | + | 0.919586i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.73580e9 | − | 1.20650e11i | 0.00651479 | − | 0.287306i | ||||
\(806\) | 2.10452e11 | 0.498669 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.48996e11 | − | 1.48996e11i | 0.349565 | − | 0.349565i | ||||
\(809\) | − | 6.78011e11i | − | 1.58286i | −0.611259 | − | 0.791431i | \(-0.709337\pi\) | ||
0.611259 | − | 0.791431i | \(-0.290663\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.62623e11 | 1.06941 | 0.534704 | − | 0.845039i | \(-0.320423\pi\) | ||||
0.534704 | + | 0.845039i | \(0.320423\pi\) | |||||||
\(812\) | 2.01808e10 | + | 2.01808e10i | 0.0464211 | + | 0.0464211i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.20253e10i | 0.0957224i | ||||||||
\(815\) | 2.65590e11 | + | 2.77914e11i | 0.601978 | + | 0.629912i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.16019e9 | + | 1.16019e9i | 0.00260399 | + | 0.00260399i | ||||
\(818\) | 1.92158e11 | − | 1.92158e11i | 0.429185 | − | 0.429185i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.40535e11 | + | 7.72177e9i | 0.753193 | + | 0.0170790i | ||||
\(821\) | 2.02486e11 | 0.445678 | 0.222839 | − | 0.974855i | \(-0.428468\pi\) | ||||
0.222839 | + | 0.974855i | \(0.428468\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.67731e11 | − | 5.67731e11i | 1.23749 | − | 1.23749i | 0.276473 | − | 0.961022i | \(-0.410834\pi\) |
0.961022 | − | 0.276473i | \(-0.0891657\pi\) | |||||||
\(824\) | − | 4.11664e11i | − | 0.892963i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.01682e9 | 0.00433259 | ||||||||
\(827\) | −5.76065e11 | − | 5.76065e11i | −1.23154 | − | 1.23154i | −0.963371 | − | 0.268173i | \(-0.913580\pi\) |
−0.268173 | − | 0.963371i | \(-0.586420\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.12691e11i | 0.450330i | 0.974321 | + | 0.225165i | \(0.0722922\pi\) | ||||
−0.974321 | + | 0.225165i | \(0.927708\pi\) | |||||||
\(830\) | −1.97710e9 | + | 8.71912e10i | −0.00416596 | + | 0.183722i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.55457e10 | − | 8.55457e10i | −0.178527 | − | 0.178527i | ||||
\(833\) | 5.30126e10 | − | 5.30126e10i | 0.110103 | − | 0.110103i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.58043e11 | + | 4.37731e11i | −0.942237 | + | 0.900454i | ||||
\(836\) | 7.30696e11 | 1.49593 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.31264e11 | + | 1.31264e11i | −0.266176 | + | 0.266176i | ||||
\(839\) | 8.36816e11i | 1.68881i | 0.535701 | + | 0.844407i | \(0.320047\pi\) | ||||
−0.535701 | + | 0.844407i | \(0.679953\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.84113e11 | 0.967748 | ||||||||
\(842\) | −2.34670e11 | − | 2.34670e11i | −0.466883 | − | 0.466883i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.48065e11i | 0.291797i | ||||||||
\(845\) | −2.66053e11 | − | 6.03286e9i | −0.521845 | − | 0.0118331i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.24118e11 | + | 1.24118e11i | 0.241157 | + | 0.241157i | ||||
\(848\) | −1.10978e11 | + | 1.10978e11i | −0.214611 | + | 0.214611i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.75735e9 | − | 3.87303e10i | 0.00336654 | − | 0.0741950i | ||||
\(851\) | −6.44187e10 | −0.122827 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.74662e11 | − | 2.74662e11i | 0.518803 | − | 0.518803i | −0.398406 | − | 0.917209i | \(-0.630436\pi\) |
0.917209 | + | 0.398406i | \(0.130436\pi\) | |||||||
\(854\) | 1.13743e11i | 0.213842i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.97058e11 | −0.367027 | ||||||||
\(857\) | 9.65564e10 | + | 9.65564e10i | 0.179002 | + | 0.179002i | 0.790921 | − | 0.611919i | \(-0.209602\pi\) |
−0.611919 | + | 0.790921i | \(0.709602\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.22383e11i | 1.32677i | 0.748280 | + | 0.663383i | \(0.230880\pi\) | ||||
−0.748280 | + | 0.663383i | \(0.769120\pi\) | |||||||
\(860\) | 9.39430e8 | − | 8.97771e8i | 0.00171740 | − | 0.00164124i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.41790e10 | − | 7.41790e10i | −0.134354 | − | 0.134354i | ||||
\(863\) | 9.33124e10 | − | 9.33124e10i | 0.168227 | − | 0.168227i | −0.617973 | − | 0.786200i | \(-0.712046\pi\) |
0.786200 | + | 0.617973i | \(0.212046\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.07848e11 | + | 2.17492e11i | 0.371262 | + | 0.388490i | ||||
\(866\) | 6.28803e10 | 0.111800 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.52639e11 | + | 1.52639e11i | −0.268897 | + | 0.268897i | ||||
\(869\) | 2.18092e11i | 0.382437i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.19925e11 | −0.382123 | ||||||||
\(872\) | 4.76670e10 | + | 4.76670e10i | 0.0824427 | + | 0.0824427i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 1.99177e11i | − | 0.341346i | ||||||
\(875\) | −1.90181e11 | + | 1.65923e11i | −0.324441 | + | 0.283058i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.23388e11 | + | 5.23388e11i | 0.884760 | + | 0.884760i | 0.994014 | − | 0.109254i | \(-0.0348463\pi\) |
−0.109254 | + | 0.994014i | \(0.534846\pi\) | |||||||
\(878\) | −1.15232e10 | + | 1.15232e10i | −0.0193907 | + | 0.0193907i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.03710e10 | − | 4.57366e11i | 0.0172937 | − | 0.762664i | ||||
\(881\) | 8.15621e10 | 0.135389 | 0.0676947 | − | 0.997706i | \(-0.478436\pi\) | ||||
0.0676947 | + | 0.997706i | \(0.478436\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.22895e11 | + | 3.22895e11i | −0.531151 | + | 0.531151i | −0.920915 | − | 0.389764i | \(-0.872557\pi\) |
0.389764 | + | 0.920915i | \(0.372557\pi\) | |||||||
\(884\) | 1.22262e11i | 0.200209i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.90420e11 | 0.471294 | ||||||||
\(887\) | −4.59932e11 | − | 4.59932e11i | −0.743018 | − | 0.743018i | 0.230140 | − | 0.973158i | \(-0.426082\pi\) |
−0.973158 | + | 0.230140i | \(0.926082\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.70163e11i | 0.432532i | ||||||||
\(890\) | −1.30210e11 | − | 1.36252e11i | −0.207531 | − | 0.217161i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.03788e11 | − | 2.03788e11i | −0.321899 | − | 0.321899i | ||||
\(893\) | 3.07706e11 | − | 3.07706e11i | 0.483871 | − | 0.483871i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.07171e11 | − | 1.83029e10i | −1.25798 | − | 0.0285252i | ||||
\(896\) | −2.82887e11 | −0.438915 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.12575e11 | + | 1.12575e11i | −0.173116 | + | 0.173116i | ||||
\(899\) | − | 1.22029e11i | − | 0.186821i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.70910e10 | 0.101804 | ||||||||
\(902\) | 2.16049e11 | + | 2.16049e11i | 0.326382 | + | 0.326382i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 8.13047e11i | − | 1.21742i | ||||||
\(905\) | 2.73327e9 | − | 1.20539e11i | 0.00407463 | − | 0.179694i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.98076e11 | − | 7.98076e11i | −1.17928 | − | 1.17928i | −0.979929 | − | 0.199347i | \(-0.936118\pi\) |
−0.199347 | − | 0.979929i | \(-0.563882\pi\) | |||||||
\(908\) | 7.56278e11 | − | 7.56278e11i | 1.11260 | − | 1.11260i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.02324e11 | + | 9.77862e10i | −0.149215 | + | 0.142598i | ||||
\(911\) | 1.50243e11 | 0.218132 | 0.109066 | − | 0.994034i | \(-0.465214\pi\) | ||||
0.109066 | + | 0.994034i | \(0.465214\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.11072e11 | − | 3.11072e11i | 0.447690 | − | 0.447690i | ||||
\(914\) | 1.15320e11i | 0.165241i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.98264e11 | 1.13387 | ||||||||
\(917\) | 2.23008e11 | + | 2.23008e11i | 0.315387 | + | 0.315387i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.02471e12i | − | 1.43662i | −0.695725 | − | 0.718308i | \(-0.744917\pi\) | ||
0.695725 | − | 0.718308i | \(-0.255083\pi\) | |||||||
\(920\) | −3.43449e11 | − | 7.78786e9i | −0.479415 | − | 0.0108709i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.75495e11 | + | 1.75495e11i | 0.242851 | + | 0.242851i | ||||
\(923\) | −2.21574e11 | + | 2.21574e11i | −0.305289 | + | 0.305289i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.08470e10 | + | 9.94831e10i | 0.124092 | + | 0.135888i | ||||
\(926\) | 1.26151e11 | 0.171573 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.85171e10 | − | 8.85171e10i | 0.119353 | − | 0.119353i | ||||
\(929\) | 1.38553e12i | 1.86017i | 0.367346 | + | 0.930084i | \(0.380266\pi\) | ||||
−0.367346 | + | 0.930084i | \(0.619734\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.05498e11 | −1.07218 | ||||||||
\(932\) | −7.88745e11 | − | 7.88745e11i | −1.04538 | − | 1.04538i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 2.14705e11i | − | 0.282133i | ||||||
\(935\) | −1.41384e11 | + | 1.35114e11i | −0.184992 | + | 0.176789i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.72786e11 | − | 7.72786e11i | −1.00254 | − | 1.00254i | −0.999997 | − | 0.00254091i | \(-0.999191\pi\) |
−0.00254091 | − | 0.999997i | \(-0.500809\pi\) | |||||||
\(938\) | −2.83655e10 | + | 2.83655e10i | −0.0366420 | + | 0.0366420i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.38108e11 | − | 2.49157e11i | −0.304973 | − | 0.319125i | ||||
\(941\) | 6.91185e11 | 0.881528 | 0.440764 | − | 0.897623i | \(-0.354708\pi\) | ||||
0.440764 | + | 0.897623i | \(0.354708\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.31172e11 | + | 3.31172e11i | −0.418800 | + | 0.418800i | ||||
\(944\) | 1.17194e10i | 0.0147576i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.16559e9 | 0.00145540 | ||||||||
\(947\) | −6.05426e11 | − | 6.05426e11i | −0.752768 | − | 0.752768i | 0.222227 | − | 0.974995i | \(-0.428667\pi\) |
−0.974995 | + | 0.222227i | \(0.928667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.72066e11i | 1.19848i | ||||||||
\(950\) | −3.07594e11 | + | 2.80892e11i | −0.377644 | + | 0.344861i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.43424e10 | + | 3.43424e10i | 0.0418103 | + | 0.0418103i | ||||
\(953\) | 3.45330e11 | − | 3.45330e11i | 0.418661 | − | 0.418661i | −0.466081 | − | 0.884742i | \(-0.654335\pi\) |
0.884742 | + | 0.466081i | \(0.154335\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.08339e10 | + | 4.77781e11i | −0.0130248 | + | 0.574401i | ||||
\(956\) | −5.74532e11 | −0.687832 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.97343e10 | + | 3.97343e10i | −0.0471740 | + | 0.0471740i | ||||
\(959\) | − | 5.49319e11i | − | 0.649456i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.00825e10 | 0.0821705 | ||||||||
\(962\) | 5.34222e10 | + | 5.34222e10i | 0.0623766 | + | 0.0623766i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.56542e10i | 0.0181268i | ||||||||
\(965\) | −7.04648e10 | − | 7.37346e10i | −0.0812575 | − | 0.0850281i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.77273e10 | − | 1.77273e10i | −0.0202739 | − | 0.0202739i | 0.696897 | − | 0.717171i | \(-0.254563\pi\) |
−0.717171 | + | 0.696897i | \(0.754563\pi\) | |||||||
\(968\) | 3.53320e11 | − | 3.53320e11i | 0.402408 | − | 0.402408i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.90084e11 | − | 1.33804e10i | −0.666541 | − | 0.0151141i | ||||
\(971\) | −1.52187e12 | −1.71199 | −0.855994 | − | 0.516986i | \(-0.827054\pi\) | ||||
−0.855994 | + | 0.516986i | \(0.827054\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.08294e10 | + | 8.08294e10i | −0.0901816 | + | 0.0901816i | ||||
\(974\) | 3.11199e11i | 0.345782i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.60938e11 | −0.728385 | ||||||||
\(977\) | −2.88131e11 | − | 2.88131e11i | −0.316237 | − | 0.316237i | 0.531083 | − | 0.847320i | \(-0.321785\pi\) |
−0.847320 | + | 0.531083i | \(0.821785\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.50654e11i | 1.03488i | ||||||||
\(980\) | −1.44617e10 | + | 6.37769e11i | −0.0156789 | + | 0.691448i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.58120e11 | + | 2.58120e11i | 0.277572 | + | 0.277572i | ||||
\(983\) | 2.15222e9 | − | 2.15222e9i | 0.00230501 | − | 0.00230501i | −0.705953 | − | 0.708258i | \(-0.749481\pi\) |
0.708258 | + | 0.705953i | \(0.249481\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.36078e10 | − | 6.07871e10i | 0.0675718 | − | 0.0645753i | ||||
\(986\) | −1.26068e10 | −0.0133382 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.28854e11 | − | 9.28854e11i | 0.974810 | − | 0.974810i | ||||
\(989\) | 1.78669e9i | 0.00186751i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.40286e10 | 0.0145452 | 0.00727261 | − | 0.999974i | \(-0.497685\pi\) | ||||
0.00727261 | + | 0.999974i | \(0.497685\pi\) | |||||||
\(992\) | 6.69504e11 | + | 6.69504e11i | 0.691363 | + | 0.691363i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.71562e10i | 0.0585488i | ||||||||
\(995\) | 1.06965e12 | + | 2.42547e10i | 1.09131 | + | 0.0247459i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.09850e11 | + | 7.09850e11i | 0.718433 | + | 0.718433i | 0.968284 | − | 0.249851i | \(-0.0803818\pi\) |
−0.249851 | + | 0.968284i | \(0.580382\pi\) | |||||||
\(998\) | −1.13152e11 | + | 1.13152e11i | −0.114062 | + | 0.114062i | ||||
\(999\) | 0 | 0 |
(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 | 45.9.g.a.37.2 | 6 | ||
3.2 | odd | 2 | 5.9.c.a.2.2 | ✓ | 6 | ||
5.3 | odd | 4 | inner | 45.9.g.a.28.2 | 6 | ||
12.11 | even | 2 | 80.9.p.c.17.1 | 6 | |||
15.2 | even | 4 | 25.9.c.b.18.2 | 6 | |||
15.8 | even | 4 | 5.9.c.a.3.2 | yes | 6 | ||
15.14 | odd | 2 | 25.9.c.b.7.2 | 6 | |||
60.23 | odd | 4 | 80.9.p.c.33.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.9.c.a.2.2 | ✓ | 6 | 3.2 | odd | 2 | ||
5.9.c.a.3.2 | yes | 6 | 15.8 | even | 4 | ||
25.9.c.b.7.2 | 6 | 15.14 | odd | 2 | |||
25.9.c.b.18.2 | 6 | 15.2 | even | 4 | |||
45.9.g.a.28.2 | 6 | 5.3 | odd | 4 | inner | ||
45.9.g.a.37.2 | 6 | 1.1 | even | 1 | trivial | ||
80.9.p.c.17.1 | 6 | 12.11 | even | 2 | |||
80.9.p.c.33.1 | 6 | 60.23 | odd | 4 |