Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,12,Mod(5,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.5");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.k (of order \(6\), 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: | \(64.5408271670\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 5.5 | ||
Character | \(\chi\) | \(=\) | 84.5 |
Dual form | 84.12.k.b.17.5 |
$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −377.843 | − | 185.422i | −0.897728 | − | 0.440550i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2528.83 | − | 4380.06i | 0.361896 | − | 0.626823i | −0.626377 | − | 0.779520i | \(-0.715463\pi\) |
0.988273 | + | 0.152698i | \(0.0487962\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −41471.0 | + | 16046.3i | −0.932621 | + | 0.360856i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 108384. | + | 140121.i | 0.611832 | + | 0.790988i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −456316. | + | 263454.i | −0.854292 | + | 0.493225i | −0.862097 | − | 0.506744i | \(-0.830849\pi\) |
0.00780495 | + | 0.999970i | \(0.497516\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.07826e6i | − | 1.55243i | −0.630469 | − | 0.776214i | \(-0.717137\pi\) | ||
0.630469 | − | 0.776214i | \(-0.282863\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.76766e6 | + | 1.18607e6i | −0.601031 | + | 0.403283i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.35427e6 | + | 5.80977e6i | 0.572967 | + | 0.992407i | 0.996259 | + | 0.0864144i | \(0.0275409\pi\) |
−0.423293 | + | 0.905993i | \(0.639126\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.56480e7 | + | 9.03437e6i | 1.44982 | + | 0.837053i | 0.998470 | − | 0.0552953i | \(-0.0176100\pi\) |
0.451348 | + | 0.892348i | \(0.350943\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.86449e7 | + | 1.62667e6i | 0.996216 | + | 0.0869149i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.17125e7 | − | 1.83092e7i | −1.02737 | − | 0.593153i | −0.111140 | − | 0.993805i | \(-0.535450\pi\) |
−0.916230 | + | 0.400652i | \(0.868784\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.16241e7 | + | 2.01336e7i | 0.238062 | + | 0.412336i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.49707e7 | − | 7.30407e7i | −0.200790 | − | 0.979634i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.82965e8i | 1.65646i | 0.560391 | + | 0.828228i | \(0.310651\pi\) | ||||
−0.560391 | + | 0.828228i | \(0.689349\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.05444e8 | + | 6.08780e7i | −0.661503 | + | 0.381919i | −0.792849 | − | 0.609418i | \(-0.791403\pi\) |
0.131346 | + | 0.991337i | \(0.458070\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.21266e8 | − | 1.49333e7i | 0.984212 | − | 0.0664246i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.45895e7 | + | 2.22224e8i | −0.111319 | + | 0.715181i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.41836e7 | − | 4.18872e7i | 0.0573338 | − | 0.0993051i | −0.835934 | − | 0.548830i | \(-0.815073\pi\) |
0.893268 | + | 0.449525i | \(0.148407\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.85356e8 | + | 7.85257e8i | −0.683922 | + | 1.39366i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.29202e7 | −0.0848162 | −0.0424081 | − | 0.999100i | \(-0.513503\pi\) | ||||
−0.0424081 | + | 0.999100i | \(0.513503\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.04363e9 | −1.08260 | −0.541301 | − | 0.840829i | \(-0.682068\pi\) | ||||
−0.541301 | + | 0.840829i | \(0.682068\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.87823e8 | − | 1.20387e8i | 0.717229 | − | 0.0972548i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.32425e9 | − | 2.29366e9i | 0.842230 | − | 1.45879i | −0.0457747 | − | 0.998952i | \(-0.514576\pi\) |
0.888005 | − | 0.459834i | \(-0.152091\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.46236e9 | − | 1.33091e9i | 0.739565 | − | 0.673085i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.90129e8 | − | 2.81714e9i | −0.0771637 | − | 1.14333i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.42170e9 | − | 1.39817e9i | 0.795433 | − | 0.459243i | −0.0464390 | − | 0.998921i | \(-0.514787\pi\) |
0.841872 | + | 0.539678i | \(0.181454\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.66492e9i | 0.713986i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.23731e9 | − | 6.31506e9i | −0.932779 | − | 1.39016i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.18937e9 | + | 2.06005e9i | 0.216587 | + | 0.375139i | 0.953762 | − | 0.300562i | \(-0.0971743\pi\) |
−0.737176 | + | 0.675701i | \(0.763841\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.69101e9 | + | 2.13101e9i | 0.559540 | + | 0.323051i | 0.752961 | − | 0.658065i | \(-0.228625\pi\) |
−0.193421 | + | 0.981116i | \(0.561958\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.74322e9 | − | 4.07180e9i | −0.856041 | − | 0.516908i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.10290e9 | − | 5.25556e9i | −0.973097 | − | 0.561818i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.51703e9 | − | 4.35962e9i | −0.227760 | − | 0.394491i | 0.729384 | − | 0.684104i | \(-0.239807\pi\) |
−0.957144 | + | 0.289613i | \(0.906473\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.58742e9 | + | 1.27982e10i | 0.660986 | + | 0.985097i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.63164e10i | − | 1.07326i | −0.843818 | − | 0.536629i | \(-0.819697\pi\) | ||
0.843818 | − | 0.536629i | \(-0.180303\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.87306e10 | − | 1.08141e10i | 1.05749 | − | 0.610541i | 0.132751 | − | 0.991149i | \(-0.457619\pi\) |
0.924736 | + | 0.380609i | \(0.124286\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.58888e8 | − | 9.76272e9i | −0.0320608 | − | 0.475044i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.46964e10 | − | 1.82479e10i | 0.618747 | − | 0.768269i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.31030e10 | − | 2.26950e10i | 0.479094 | − | 0.829815i | −0.520619 | − | 0.853789i | \(-0.674299\pi\) |
0.999713 | + | 0.0239743i | \(0.00763198\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.88678e9 | + | 3.03738e10i | −0.251323 | + | 0.967903i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.02431e10 | −1.40006 | −0.700031 | − | 0.714113i | \(-0.746830\pi\) | ||||
−0.700031 | + | 0.714113i | \(0.746830\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.39295e10 | 0.829418 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.39259e10 | − | 6.91323e10i | 0.729751 | − | 1.48705i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.52449e10 | + | 2.64050e10i | −0.289388 | + | 0.501234i | −0.973664 | − | 0.227989i | \(-0.926785\pi\) |
0.684276 | + | 0.729223i | \(0.260118\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.33483e10 | + | 8.61876e10i | 0.560204 | + | 1.44783i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.11294e10 | − | 3.45073e9i | 0.762104 | − | 0.0514346i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.91420e10 | − | 4.56927e10i | 1.04937 | − | 0.605852i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.24537e11i | − | 1.47249i | −0.676714 | − | 0.736246i | \(-0.736597\pi\) | ||
0.676714 | − | 0.736246i | \(-0.263403\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.63730e10 | − | 3.53852e10i | −0.912818 | − | 0.373963i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.08856e10 | − | 1.40098e11i | −0.765780 | − | 1.32637i | −0.939833 | − | 0.341633i | \(-0.889020\pi\) |
0.174054 | − | 0.984736i | \(-0.444313\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.55052e10 | + | 5.51399e10i | 0.811750 | + | 0.468664i | 0.847563 | − | 0.530694i | \(-0.178069\pi\) |
−0.0358133 | + | 0.999358i | \(0.511402\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.42746e10 | − | 7.75520e10i | 0.415007 | − | 0.592996i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.09178e11 | − | 6.30340e10i | −0.752532 | − | 0.434475i | 0.0740760 | − | 0.997253i | \(-0.476399\pi\) |
−0.826608 | + | 0.562778i | \(0.809733\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.16744e10 | − | 7.21822e10i | −0.259432 | − | 0.449350i | 0.706658 | − | 0.707556i | \(-0.250202\pi\) |
−0.966090 | + | 0.258206i | \(0.916869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.69044e10 | + | 1.13426e10i | −0.0952190 | + | 0.0638906i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.11618e11i | − | 1.59107i | −0.605905 | − | 0.795537i | \(-0.707189\pi\) | ||
0.605905 | − | 0.795537i | \(-0.292811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.60391e11 | + | 9.26016e10i | −0.743603 | + | 0.429319i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.91208e11 | − | 2.25251e11i | 1.22795 | − | 0.949826i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.32330e11 | − | 1.87114e11i | −0.892478 | − | 0.718782i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.83951e9 | + | 6.65023e9i | −0.0134572 | + | 0.0233086i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.37740e10 | + | 1.16668e10i | 0.0761419 | + | 0.0373658i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.64537e11 | 1.06841 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.70824e11 | 1.80172 | 0.900862 | − | 0.434106i | \(-0.142936\pi\) | ||||
0.900862 | + | 0.434106i | \(0.142936\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.94328e11 | + | 1.93512e11i | 0.971882 | + | 0.476940i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.25093e11 | + | 5.63077e11i | −0.736233 | + | 1.27519i | 0.217947 | + | 0.975961i | \(0.430064\pi\) |
−0.954180 | + | 0.299233i | \(0.903269\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.93905e11 | − | 1.23573e11i | −1.65419 | − | 0.257477i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.57780e11 | − | 1.19135e11i | −0.686722 | − | 0.228666i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.20519e11 | − | 6.95818e10i | 0.213350 | − | 0.123178i | −0.389517 | − | 0.921019i | \(-0.627358\pi\) |
0.602867 | + | 0.797841i | \(0.294025\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.47003e11i | − | 1.54800i | −0.633188 | − | 0.773998i | \(-0.718254\pi\) | ||
0.633188 | − | 0.773998i | \(-0.281746\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.25654e11 | + | 6.21101e11i | −1.39876 | + | 0.938549i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.47527e11 | + | 9.48344e11i | 0.765697 | + | 1.32623i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.01399e11 | + | 4.62688e11i | 1.03830 | + | 0.599465i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.99324e11 | + | 2.31721e11i | −0.960456 | + | 0.278432i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.15654e11 | + | 1.82243e11i | 0.352116 | + | 0.203294i | 0.665617 | − | 0.746294i | \(-0.268168\pi\) |
−0.313501 | + | 0.949588i | \(0.601502\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.52012e11 | + | 6.09703e11i | 0.364909 | + | 0.632041i | 0.988762 | − | 0.149501i | \(-0.0477668\pi\) |
−0.623853 | + | 0.781542i | \(0.714433\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.50521e11 | + | 1.09969e12i | −0.434423 | + | 1.06040i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.15800e11i | 0.552860i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.68725e11 | − | 5.59294e11i | 0.810499 | − | 0.467942i | −0.0366302 | − | 0.999329i | \(-0.511662\pi\) |
0.847129 | + | 0.531387i | \(0.178329\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.17428e12 | + | 7.92521e10i | −0.916402 | + | 0.0618481i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.60894e12 | + | 2.50435e11i | 1.17219 | + | 0.182453i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.28553e11 | + | 1.08869e12i | −0.427868 | + | 0.741090i | −0.996684 | − | 0.0813755i | \(-0.974069\pi\) |
0.568815 | + | 0.822465i | \(0.307402\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.94135e11 | − | 1.00692e12i | 0.314546 | − | 0.640965i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.33942e12 | −0.797951 | −0.398975 | − | 0.916962i | \(-0.630634\pi\) | ||||
−0.398975 | + | 0.916962i | \(0.630634\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.52701e12 | −1.41003 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.30089e11 | + | 3.17179e12i | 0.224947 | + | 1.65892i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.61920e11 | + | 1.49289e12i | −0.422876 | + | 0.732444i | −0.996219 | − | 0.0868719i | \(-0.972313\pi\) |
0.573343 | + | 0.819315i | \(0.305646\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.05134e11 | − | 6.48437e11i | −0.370816 | − | 0.298647i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.74168e10 | − | 9.98913e11i | −0.0291686 | − | 0.432190i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.88058e11 | − | 2.24046e11i | 0.157836 | − | 0.0911265i | −0.419002 | − | 0.907985i | \(-0.637620\pi\) |
0.576838 | + | 0.816859i | \(0.304287\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.81573e11i | − | 0.145998i | −0.997332 | − | 0.0729989i | \(-0.976743\pi\) | ||
0.997332 | − | 0.0729989i | \(-0.0232569\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.99488e11 | − | 1.48958e12i | −0.359995 | − | 0.536517i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.22312e11 | − | 2.11851e11i | −0.0414978 | − | 0.0718763i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.06122e12 | − | 1.76740e12i | −0.978961 | − | 0.565204i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.79288e12 | + | 2.78885e12i | 0.540768 | + | 0.841172i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.74749e12 | + | 2.74097e12i | 1.35139 | + | 0.780226i | 0.988444 | − | 0.151584i | \(-0.0484375\pi\) |
0.362946 | + | 0.931810i | \(0.381771\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.42187e11 | − | 1.28550e12i | −0.199502 | − | 0.345548i | 0.748865 | − | 0.662723i | \(-0.230599\pi\) |
−0.948367 | + | 0.317175i | \(0.897266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.46497e12 | + | 3.67366e12i | 0.626068 | + | 0.933057i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.36944e12i | 0.809084i | 0.914519 | + | 0.404542i | \(0.132569\pi\) | ||||
−0.914519 | + | 0.404542i | \(0.867431\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.04647e12 | − | 1.75888e12i | 0.691998 | − | 0.399525i | −0.112362 | − | 0.993667i | \(-0.535842\pi\) |
0.804360 | + | 0.594142i | \(0.202508\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.42672e11 | + | 2.11397e12i | 0.0306733 | + | 0.454485i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.93591e12 | − | 7.58776e12i | −0.597743 | − | 1.54485i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.59114e11 | + | 2.75594e11i | −0.0306947 | + | 0.0531647i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.71626e11 | − | 6.42802e12i | −0.159402 | − | 1.17555i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.52057e12 | −1.65142 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.92926e12 | 1.46981 | 0.734907 | − | 0.678168i | \(-0.237226\pi\) | ||||
0.734907 | + | 0.678168i | \(0.237226\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.02543e12 | + | 6.16506e12i | −0.472823 | + | 0.963494i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.63915e12 | + | 4.57114e12i | −0.391789 | + | 0.678599i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.39600e12 | − | 4.21665e12i | 0.479114 | − | 0.594894i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.08239e12 | + | 6.12972e11i | −1.21831 | + | 0.0822239i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.20742e13 | − | 6.97105e12i | 1.54064 | − | 0.889490i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.14685e12i | 0.867836i | 0.900952 | + | 0.433918i | \(0.142869\pi\) | ||||
−0.900952 | + | 0.433918i | \(0.857131\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.56127e12 | + | 3.81095e12i | −0.180499 | + | 0.440585i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.59923e12 | + | 7.96609e12i | 0.506457 | + | 0.877209i | 0.999972 | + | 0.00747206i | \(0.00237845\pi\) |
−0.493515 | + | 0.869737i | \(0.664288\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.73020e12 | + | 5.04038e12i | 0.916071 | + | 0.528894i | 0.882379 | − | 0.470539i | \(-0.155940\pi\) |
0.0336912 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.93651e12 | + | 4.16980e12i | −0.893927 | + | 0.417108i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.21726e13 | − | 7.02786e12i | −1.16125 | − | 0.670449i | −0.209648 | − | 0.977777i | \(-0.567232\pi\) |
−0.951604 | + | 0.307328i | \(0.900565\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.69758e12 | − | 1.16006e13i | −0.609600 | − | 1.05586i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.15903e12 | + | 6.14558e12i | −0.795671 | + | 0.533884i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.09354e12i | 0.0907083i | 0.998971 | + | 0.0453542i | \(0.0144416\pi\) | ||||
−0.998971 | + | 0.0453542i | \(0.985558\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.69008e13 | − | 9.75768e12i | 1.33910 | − | 0.773131i | 0.352427 | − | 0.935839i | \(-0.385356\pi\) |
0.986674 | + | 0.162708i | \(0.0520230\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.61195e12 | − | 1.00142e13i | 0.652029 | − | 0.758194i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.13140e12 | − | 9.77086e12i | −0.154259 | − | 0.707163i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.87758e13 | − | 3.25206e13i | 1.29946 | − | 2.25074i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.89840e13 | + | 9.31619e12i | 1.25688 | + | 0.616797i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.20006e12 | −0.582888 | −0.291444 | − | 0.956588i | \(-0.594136\pi\) | ||||
−0.291444 | + | 0.956588i | \(0.594136\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.92946e13 | 1.17023 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.28200e13 | − | 6.29128e12i | −0.744592 | − | 0.365400i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.09065e13 | − | 1.88906e13i | 0.606809 | − | 1.05102i | −0.384954 | − | 0.922936i | \(-0.625783\pi\) |
0.991763 | − | 0.128088i | \(-0.0408841\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.30785e11 | + | 2.12516e12i | −0.0176359 | + | 0.113303i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.56373e13 | + | 1.98306e13i | −1.31024 | + | 1.01347i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.44069e13 | − | 8.31780e12i | 0.706013 | − | 0.407617i | −0.103570 | − | 0.994622i | \(-0.533027\pi\) |
0.809583 | + | 0.587005i | \(0.199693\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.41429e13i | − | 0.664793i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.06563e13 | − | 7.15020e12i | 0.480610 | − | 0.322483i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.62345e12 | − | 8.00806e12i | −0.200138 | − | 0.346649i | 0.748435 | − | 0.663208i | \(-0.230806\pi\) |
−0.948573 | + | 0.316559i | \(0.897472\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.19663e12 | − | 5.30968e12i | −0.382206 | − | 0.220667i | 0.296572 | − | 0.955011i | \(-0.404157\pi\) |
−0.678778 | + | 0.734344i | \(0.737490\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.38065e12 | − | 3.87489e13i | 0.134929 | − | 1.54655i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.06086e13 | − | 6.12486e12i | −0.406749 | − | 0.234837i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.05927e12 | + | 7.03086e12i | 0.149558 | + | 0.259042i | 0.931064 | − | 0.364856i | \(-0.118882\pi\) |
−0.781506 | + | 0.623897i | \(0.785548\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.99587e13 | − | 8.17669e12i | −0.706822 | − | 0.289571i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.55205e13i | − | 0.868970i | −0.900679 | − | 0.434485i | \(-0.856930\pi\) | ||
0.900679 | − | 0.434485i | \(-0.143070\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.15629e12 | − | 4.13169e12i | 0.234349 | − | 0.135301i | −0.378228 | − | 0.925713i | \(-0.623466\pi\) |
0.612577 | + | 0.790411i | \(0.290133\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.83757e13 | + | 2.58998e12i | −1.20895 | + | 0.0815925i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.60936e12 | − | 1.00963e12i | 0.0791014 | − | 0.0306065i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.36635e12 | + | 9.29479e12i | −0.156582 | + | 0.271207i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.30919e13 | + | 4.70554e13i | −0.648706 | + | 1.32190i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.18412e13 | 0.861424 | 0.430712 | − | 0.902489i | \(-0.358262\pi\) | ||||
0.430712 | + | 0.902489i | \(0.358262\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.20309e13 | 0.313527 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.60742e13 | + | 2.93855e13i | 0.654714 | + | 0.737859i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.80513e13 | + | 6.59068e13i | −0.920827 | + | 1.59492i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.32803e13 | − | 1.67463e13i | 1.00966 | − | 0.390664i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.58482e12 | + | 6.79331e13i | 0.103131 | + | 1.52808i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.86679e13 | − | 1.07779e13i | 0.404991 | − | 0.233822i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.39021e12i | 0.0500236i | 0.999687 | + | 0.0250118i | \(0.00796233\pi\) | ||||
−0.999687 | + | 0.0250118i | \(0.992038\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.58618e13 | − | 3.85430e13i | −0.522261 | − | 0.778349i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.15843e13 | − | 2.00646e13i | −0.225781 | − | 0.391064i | 0.730773 | − | 0.682621i | \(-0.239160\pi\) |
−0.956553 | + | 0.291557i | \(0.905827\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.97553e13 | + | 1.71793e13i | 0.559849 | + | 0.323229i | 0.753085 | − | 0.657923i | \(-0.228565\pi\) |
−0.193236 | + | 0.981152i | \(0.561898\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.48872e13 | + | 1.92388e13i | −0.633808 | + | 0.349518i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.46252e13 | + | 8.44384e12i | 0.256611 | + | 0.148154i | 0.622788 | − | 0.782391i | \(-0.286000\pi\) |
−0.366177 | + | 0.930545i | \(0.619333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.82030e13 | − | 8.34901e13i | −0.817007 | − | 1.41510i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.95643e13 | + | 4.40611e13i | 0.484162 | + | 0.721568i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.21215e14i | 1.91841i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.18429e13 | − | 2.41580e13i | 0.640122 | − | 0.369575i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.36222e12 | + | 3.50009e13i | 0.0349388 | + | 0.517687i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.81132e13 | + | 1.16370e14i | −0.259070 | + | 1.66442i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.99104e13 | − | 1.03768e14i | 0.828797 | − | 1.43552i | −0.0701849 | − | 0.997534i | \(-0.522359\pi\) |
0.898982 | − | 0.437985i | \(-0.144308\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.49039e12 | − | 1.15128e12i | 0.113628 | − | 0.0154077i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.54605e13 | −0.329701 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.40574e13 | −0.928120 | −0.464060 | − | 0.885804i | \(-0.653608\pi\) | ||||
−0.464060 | + | 0.885804i | \(0.653608\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.77808e13 | + | 1.17743e14i | −0.700947 | + | 1.42835i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.20772e13 | − | 5.55593e13i | 0.376744 | − | 0.652540i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.92895e13 | + | 7.86596e13i | −0.446847 | + | 0.894610i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.77729e13 | − | 5.24891e12i | 0.856690 | − | 0.0578181i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.26636e12 | + | 7.31136e11i | −0.0135128 | + | 0.00780164i | −0.506741 | − | 0.862098i | \(-0.669150\pi\) |
0.493228 | + | 0.869900i | \(0.335817\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.95539e13i | − | 0.202159i | −0.994878 | − | 0.101080i | \(-0.967770\pi\) | ||
0.994878 | − | 0.101080i | \(-0.0322297\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.51798e14 | + | 3.11130e13i | −1.52081 | + | 0.311712i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.60785e12 | + | 7.98102e12i | 0.0447442 | + | 0.0774993i | 0.887530 | − | 0.460750i | \(-0.152419\pi\) |
−0.842786 | + | 0.538249i | \(0.819086\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.14669e13 | − | 4.12614e13i | −0.672742 | − | 0.388408i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.30894e13 | + | 1.13779e14i | 0.484543 | + | 1.03845i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.73063e13 | − | 5.61798e13i | −0.861235 | − | 0.497234i | 0.00319073 | − | 0.999995i | \(-0.498984\pi\) |
−0.864426 | + | 0.502761i | \(0.832318\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.04994e14 | + | 1.81856e14i | 0.901315 | + | 1.56112i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.68383e12 | − | 1.80081e12i | 0.0223496 | − | 0.0149962i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.09388e14i | − | 0.883809i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.90508e13 | + | 1.09990e13i | −0.149365 | + | 0.0862361i | −0.572820 | − | 0.819681i | \(-0.694151\pi\) |
0.423455 | + | 0.905917i | \(0.360817\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.81956e12 | − | 8.81645e12i | −0.0518933 | − | 0.0670886i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.79950e13 | + | 9.68428e13i | −0.576116 | + | 0.715337i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.16570e13 | − | 2.01905e13i | 0.0835964 | − | 0.144793i | −0.821196 | − | 0.570646i | \(-0.806693\pi\) |
0.904792 | + | 0.425853i | \(0.140026\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.37738e14 | − | 6.75933e13i | −0.959140 | − | 0.470687i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.80250e14 | 2.57153 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.29279e12 | 0.0281984 | 0.0140992 | − | 0.999901i | \(-0.495512\pi\) | ||||
0.0140992 | + | 0.999901i | \(0.495512\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.53466e14 | − | 1.24386e14i | −1.61746 | − | 0.793749i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.48745e13 | + | 9.50455e13i | −0.340234 | + | 0.589302i | −0.984476 | − | 0.175519i | \(-0.943840\pi\) |
0.644242 | + | 0.764822i | \(0.277173\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.27620e13 | − | 1.10517e14i | −0.257646 | − | 0.665878i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.13113e14 | − | 1.46234e14i | −0.662371 | − | 0.856325i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.36280e13 | − | 1.94151e13i | 0.191416 | − | 0.110514i | −0.401229 | − | 0.915978i | \(-0.631417\pi\) |
0.592645 | + | 0.805464i | \(0.298084\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.45656e14i | − | 1.35943i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.27241e14 | − | 1.52476e14i | 1.22272 | − | 0.820430i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.62703e13 | − | 1.14783e14i | −0.346765 | − | 0.600614i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.33485e13 | − | 2.50273e13i | −0.220611 | − | 0.127370i | 0.385622 | − | 0.922657i | \(-0.373987\pi\) |
−0.606233 | + | 0.795287i | \(0.707320\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.77059e14 | + | 1.93899e14i | 1.37158 | + | 0.959896i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.97545e14 | + | 1.14053e14i | 0.951420 | + | 0.549303i | 0.893522 | − | 0.449020i | \(-0.148227\pi\) |
0.0578982 | + | 0.998322i | \(0.481560\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.26520e14 | + | 2.19140e14i | 0.592902 | + | 1.02694i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.13095e14 | + | 1.11355e14i | 0.515751 | + | 0.507815i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.54851e13i | 0.113114i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.73107e12 | + | 9.99435e11i | −0.00747889 | + | 0.00431794i | −0.503735 | − | 0.863858i | \(-0.668041\pi\) |
0.496256 | + | 0.868176i | \(0.334708\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.84394e13 | + | 3.94408e12i | −0.245796 | + | 0.0165888i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.23806e13 | − | 6.63475e13i | −0.337365 | − | 0.271706i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.27056e14 | + | 2.20068e14i | −0.506677 | + | 0.877590i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.75595e14 | + | 3.57819e14i | −0.681969 | + | 1.38968i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.63464e13 | −0.326638 | −0.163319 | − | 0.986573i | \(-0.552220\pi\) | ||||
−0.163319 | + | 0.986573i | \(0.552220\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.54049e14 | 0.936194 | 0.468097 | − | 0.883677i | \(-0.344940\pi\) | ||||
0.468097 | + | 0.883677i | \(0.344940\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.64918e14 | − | 6.30420e13i | 1.66918 | − | 0.226338i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.79811e13 | + | 1.35067e14i | −0.272804 | + | 0.472510i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.87265e14 | − | 2.91481e13i | −0.638414 | − | 0.0993702i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.10353e13 | − | 4.59849e14i | −0.103120 | − | 1.52792i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.58473e13 | + | 4.37905e13i | −0.245649 | + | 0.141826i | −0.617770 | − | 0.786359i | \(-0.711964\pi\) |
0.372121 | + | 0.928184i | \(0.378631\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.31081e13i | − | 0.0729594i | −0.999334 | − | 0.0364797i | \(-0.988386\pi\) | ||
0.999334 | − | 0.0364797i | \(-0.0116144\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.17011e14 | − | 3.23421e14i | −0.668021 | − | 0.995581i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.30824e14 | − | 5.73004e14i | −0.993000 | − | 1.71993i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.33538e13 | − | 5.38979e13i | −0.273261 | − | 0.157767i | 0.357108 | − | 0.934063i | \(-0.383763\pi\) |
−0.630369 | + | 0.776296i | \(0.717096\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.44985e14 | + | 6.06582e13i | 0.984892 | + | 0.173172i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.17079e14 | − | 6.75957e13i | −0.326031 | − | 0.188234i | 0.328047 | − | 0.944662i | \(-0.393610\pi\) |
−0.654078 | + | 0.756427i | \(0.726943\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.71035e13 | + | 1.33547e14i | 0.209457 | + | 0.362790i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.54758e13 | − | 1.27388e14i | −0.226544 | − | 0.337628i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.46184e14i | − | 0.895266i | −0.894217 | − | 0.447633i | \(-0.852267\pi\) | ||
0.894217 | − | 0.447633i | \(-0.147733\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.87115e13 | − | 1.65766e13i | 0.0724578 | − | 0.0418335i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.99530e13 | − | 2.95643e14i | −0.0491437 | − | 0.728161i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.61838e14 | + | 7.18859e13i | 1.11027 | + | 0.172815i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.58574e13 | + | 2.74658e13i | −0.0372128 | + | 0.0644545i | −0.884032 | − | 0.467426i | \(-0.845181\pi\) |
0.846819 | + | 0.531881i | \(0.178515\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.74134e14 | − | 3.31975e14i | 0.857151 | − | 0.760563i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.58396e14 | −1.02538 | −0.512692 | − | 0.858573i | \(-0.671352\pi\) | ||||
−0.512692 | + | 0.858573i | \(0.671352\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.80655e14 | 1.26830 | 0.634151 | − | 0.773210i | \(-0.281350\pi\) | ||||
0.634151 | + | 0.773210i | \(0.281350\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.14183e14 | − | 2.32676e14i | 0.243562 | − | 0.496318i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.58928e13 | − | 1.48771e14i | 0.178943 | − | 0.309938i | −0.762576 | − | 0.646899i | \(-0.776066\pi\) |
0.941519 | + | 0.336961i | \(0.109399\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.74339e14 | + | 1.40409e14i | 0.354768 | + | 0.285722i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.69732e14 | + | 3.17023e13i | −0.933759 | + | 0.0630196i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.76224e14 | − | 2.74948e14i | 0.924858 | − | 0.533967i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.20067e14i | 0.797083i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.58387e14 | + | 1.87792e14i | 0.849927 | + | 0.348198i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.77979e14 | − | 6.54679e14i | −0.684893 | − | 1.18627i | −0.973470 | − | 0.228813i | \(-0.926516\pi\) |
0.288578 | − | 0.957457i | \(-0.406818\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.70525e13 | − | 5.02598e13i | −0.154164 | − | 0.0890067i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.61492e14 | − | 3.92959e14i | −0.971929 | − | 0.680202i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.45478e14 | − | 3.14932e14i | −0.922991 | − | 0.532889i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.70058e14 | − | 2.94549e14i | −0.281312 | − | 0.487246i | 0.690396 | − | 0.723431i | \(-0.257436\pi\) |
−0.971708 | + | 0.236185i | \(0.924103\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.39361e14 | − | 2.94805e14i | 0.710597 | − | 0.476800i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.84858e14i | 0.608628i | 0.952572 | + | 0.304314i | \(0.0984272\pi\) | ||||
−0.952572 | + | 0.304314i | \(0.901573\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.06299e15 | + | 6.13716e14i | −1.64388 | + | 0.949094i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.73412e14 | + | 2.88835e14i | −0.564754 | + | 0.436839i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.61818e14 | + | 6.76659e14i | 0.387292 | + | 1.00094i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.54888e14 | − | 7.87890e14i | 0.658191 | − | 1.14002i | −0.322893 | − | 0.946436i | \(-0.604655\pi\) |
0.981084 | − | 0.193585i | \(-0.0620114\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.06091e14 | + | 2.48358e14i | 0.716343 | + | 0.351537i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.36732e14 | 1.15868 | 0.579338 | − | 0.815087i | \(-0.303311\pi\) | ||||
0.579338 | + | 0.815087i | \(0.303311\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.18183e14 | −1.10853 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.54813e14 | + | 4.68563e14i | 1.26583 | + | 0.621190i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.82102e14 | + | 6.61820e14i | −0.495715 | + | 0.858603i | −0.999988 | − | 0.00494131i | \(-0.998427\pi\) |
0.504273 | + | 0.863544i | \(0.331760\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.03250e14 | + | 7.49027e14i | −0.765918 | + | 0.951004i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.25615e14 | − | 1.27819e15i | 0.528897 | − | 1.58836i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.83032e14 | − | 2.78879e14i | 0.587538 | − | 0.339215i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.39551e15i | 1.66164i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.02486e14 | − | 4.04259e14i | 0.702306 | − | 0.471237i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.18221e14 | + | 5.51176e14i | 0.363180 | + | 0.629046i | 0.988482 | − | 0.151336i | \(-0.0483576\pi\) |
−0.625302 | + | 0.780383i | \(0.715024\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.07555e15 | − | 6.20972e14i | −1.20191 | − | 0.693925i | −0.240933 | − | 0.970542i | \(-0.577453\pi\) |
−0.960980 | + | 0.276617i | \(0.910787\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.83980e14 | + | 3.94297e14i | 0.201323 | + | 0.431467i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.07375e14 | − | 4.08403e14i | −0.758039 | − | 0.437654i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.94049e14 | + | 3.36103e14i | 0.203660 | + | 0.352749i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.59748e14 | + | 3.89933e14i | −0.164216 | + | 0.400839i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.30765e14i | 0.131671i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.52185e14 | + | 3.18804e14i | −0.544677 | + | 0.314469i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.88168e14 | + | 1.26995e13i | −0.181839 | + | 0.0122724i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.16666e14 | + | 9.92581e14i | −0.299822 | + | 0.939783i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.54401e14 | − | 2.67431e14i | 0.143241 | − | 0.248100i | −0.785475 | − | 0.618894i | \(-0.787581\pi\) |
0.928715 | + | 0.370794i | \(0.120914\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.07522e13 | + | 1.44175e14i | −0.0643192 | + | 0.131066i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.21549e14 | −0.375550 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.43428e14 | −0.649096 | −0.324548 | − | 0.945869i | \(-0.605212\pi\) | ||||
−0.324548 | + | 0.945869i | \(0.605212\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.01448e14 | + | 7.48156e14i | 0.0868156 | + | 0.640242i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.65298e15 | + | 2.86304e15i | −1.38654 | + | 2.40156i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.79223e14 | + | 1.15144e15i | −0.147369 | + | 0.946787i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.93298e12 | + | 1.02726e14i | 0.00558867 | + | 0.0828072i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.60735e15 | − | 9.28006e14i | 1.27030 | − | 0.733411i | 0.295259 | − | 0.955417i | \(-0.404594\pi\) |
0.975045 | + | 0.222006i | \(0.0712606\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.16893e15i | 1.68066i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.28947e14 | + | 1.23542e15i | 0.629841 | + | 0.938680i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.25039e14 | + | 1.60221e15i | 0.689229 | + | 1.19378i | 0.972087 | + | 0.234619i | \(0.0753841\pi\) |
−0.282858 | + | 0.959162i | \(0.591283\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.36490e15 | − | 7.88027e14i | −0.997321 | − | 0.575804i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.60314e14 | − | 1.38619e15i | −0.114885 | − | 0.993379i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.92264e14 | + | 4.57414e14i | 0.556868 | + | 0.321508i | 0.751888 | − | 0.659291i | \(-0.229144\pi\) |
−0.195019 | + | 0.980799i | \(0.562477\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.35338e13 | − | 4.07618e13i | −0.0162253 | − | 0.0281031i | 0.857799 | − | 0.513986i | \(-0.171832\pi\) |
−0.874024 | + | 0.485883i | \(0.838498\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.28557e15 | − | 1.91595e15i | −0.869454 | − | 1.29579i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 8.51315e14i | − | 0.564829i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.95406e15 | − | 1.12818e15i | 1.27195 | − | 0.734363i | 0.296599 | − | 0.955002i | \(-0.404148\pi\) |
0.975355 | + | 0.220639i | \(0.0708143\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.20691e13 | + | 6.23337e14i | 0.0268678 | + | 0.398099i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.08363e15 | − | 8.06214e14i | 1.30573 | − | 0.505221i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.36708e14 | + | 1.27602e15i | −0.453021 | + | 0.784655i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.50196e14 | − | 1.84513e15i | −0.150981 | − | 1.11345i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.92840e14 | 0.291875 | 0.145937 | − | 0.989294i | \(-0.453380\pi\) | ||||
0.145937 | + | 0.989294i | \(0.453380\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.19998e15 | −1.27875 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.24769e14 | − | 1.27312e15i | 0.356442 | − | 0.726337i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.58000e15 | + | 2.73664e15i | −0.884821 | + | 1.53256i | −0.0389032 | + | 0.999243i | \(0.512386\pi\) |
−0.845918 | + | 0.533313i | \(0.820947\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.40709e15 | + | 5.44441e14i | −0.773533 | + | 0.299301i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.47722e15 | + | 9.96980e13i | −0.797237 | + | 0.0538056i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.85300e15 | − | 1.64718e15i | 1.51166 | − | 0.872758i | 0.511754 | − | 0.859132i | \(-0.328996\pi\) |
0.999907 | − | 0.0136257i | \(-0.00433731\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.34878e15i | − | 1.22189i | −0.791673 | − | 0.610945i | \(-0.790790\pi\) | ||
0.791673 | − | 0.610945i | \(-0.209210\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.38069e14 | − | 8.25203e14i | 0.172687 | − | 0.421517i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.94189e13 | + | 3.36345e13i | 0.00974025 | + | 0.0168706i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.32839e14 | + | 2.49900e14i | 0.213201 | + | 0.123092i | 0.602798 | − | 0.797894i | \(-0.294052\pi\) |
−0.389597 | + | 0.920985i | \(0.627386\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.97625e14 | + | 3.41137e15i | −0.143971 | + | 1.65019i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.76683e15 | − | 2.75213e15i | −2.26466 | − | 1.30750i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.24578e15 | + | 2.15776e15i | 0.581312 | + | 1.00686i | 0.995324 | + | 0.0965904i | \(0.0307937\pi\) |
−0.414012 | + | 0.910271i | \(0.635873\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.11222e14 | − | 7.46281e13i | 0.0509772 | − | 0.0342050i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 2.42597e15i | − | 1.09224i | −0.837708 | − | 0.546118i | \(-0.816105\pi\) | ||
0.837708 | − | 0.546118i | \(-0.183895\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.68654e15 | − | 1.55107e15i | 1.18821 | − | 0.686015i | 0.230313 | − | 0.973117i | \(-0.426025\pi\) |
0.957900 | + | 0.287101i | \(0.0926916\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.62559e14 | + | 2.59040e15i | −0.374787 | + | 1.12555i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.08521e14 | − | 1.33967e15i | 0.0890156 | − | 0.571889i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.54267e14 | − | 6.13608e14i | 0.148590 | − | 0.257366i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.59728e15 | + | 1.76532e15i | 1.48253 | + | 0.727534i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.24473e14 | 0.131402 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.43683e15 | 0.969759 | 0.484880 | − | 0.874581i | \(-0.338863\pi\) | ||||
0.484880 | + | 0.874581i | \(0.338863\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.37386e15 | − | 1.65568e15i | −1.31949 | − | 0.647526i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.69640e15 | − | 2.93825e15i | 0.652037 | − | 1.12936i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.76598e15 | − | 3.03917e15i | −1.04492 | − | 1.14812i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.28628e15 | − | 1.76844e15i | 0.848934 | − | 0.656654i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.38245e15 | + | 7.98158e14i | −0.504580 | + | 0.291320i | −0.730603 | − | 0.682802i | \(-0.760761\pi\) |
0.226023 | + | 0.974122i | \(0.427428\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.81384e14i | 0.100958i | 0.998725 | + | 0.0504789i | \(0.0160748\pi\) | ||||
−0.998725 | + | 0.0504789i | \(0.983925\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.84478e15 | − | 1.23782e15i | 0.650677 | − | 0.436595i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.45457e15 | + | 4.25143e15i | 0.851140 | + | 1.47422i | 0.880180 | + | 0.474640i | \(0.157422\pi\) |
−0.0290395 | + | 0.999578i | \(0.509245\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.08546e15 | − | 6.26690e14i | −0.370056 | − | 0.213652i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.06502e15 | + | 9.63541e14i | −0.692194 | + | 0.322979i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.36912e15 | − | 2.52251e15i | −1.44003 | − | 0.831401i | −0.442179 | − | 0.896927i | \(-0.645794\pi\) |
−0.997851 | + | 0.0655255i | \(0.979128\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.64421e15 | + | 2.84785e15i | 0.532880 | + | 0.922975i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.54538e15 | + | 1.45247e15i | 1.12993 | + | 0.462911i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5.76865e14i | − | 0.180803i | −0.995905 | − | 0.0904013i | \(-0.971185\pi\) | ||
0.995905 | − | 0.0904013i | \(-0.0288150\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.65926e15 | + | 9.57974e14i | −0.511453 | + | 0.295288i | −0.733431 | − | 0.679764i | \(-0.762082\pi\) |
0.221977 | + | 0.975052i | \(0.428749\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.85475e15 | + | 3.95138e14i | −1.77494 | + | 0.119791i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.54890e15 | + | 3.16485e15i | −0.760036 | + | 0.943702i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.34995e15 | − | 5.80229e15i | 0.982531 | − | 1.70179i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.32518e15 | − | 2.70039e15i | 0.382325 | − | 0.779081i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.24569e15 | −0.637347 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.69954e15 | 1.31212 | 0.656058 | − | 0.754710i | \(-0.272223\pi\) | ||||
0.656058 | + | 0.754710i | \(0.272223\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.29655e15 | − | 1.15045e15i | 0.356138 | − | 0.316007i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.85106e15 | + | 4.93819e15i | −0.770494 | + | 1.33453i | 0.166799 | + | 0.985991i | \(0.446657\pi\) |
−0.937293 | + | 0.348544i | \(0.886676\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.99835e15 | + | 5.16467e15i | 0.531358 | + | 1.37328i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.60697e14 | − | 3.86273e15i | −0.0682066 | − | 1.01062i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.57744e15 | − | 2.64279e15i | 1.17844 | − | 0.680375i | 0.222790 | − | 0.974866i | \(-0.428484\pi\) |
0.955654 | + | 0.294491i | \(0.0951502\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 7.03841e14i | − | 0.178310i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.36405e15 | − | 3.52325e15i | −0.589379 | − | 0.878377i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.90576e15 | − | 5.03293e15i | −0.712942 | − | 1.23485i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.22946e15 | + | 1.28718e15i | 0.538356 | + | 0.310820i | 0.744412 | − | 0.667720i | \(-0.232730\pi\) |
−0.206056 | + | 0.978540i | \(0.566063\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.14978e15 | + | 8.14983e13i | 0.986261 | + | 0.0193694i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.14793e15 | − | 2.39481e15i | −0.970319 | − | 0.560214i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.11052e14 | − | 3.65552e14i | −0.0485969 | − | 0.0841723i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.29622e15 | + | 4.91250e15i | 0.747122 | + | 1.11347i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4.70196e15i | − | 1.04913i | −0.851370 | − | 0.524566i | \(-0.824228\pi\) | ||
0.851370 | − | 0.524566i | \(-0.175772\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.56848e14 | − | 4.36966e14i | 0.166247 | − | 0.0959829i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.79637e14 | + | 5.62507e15i | 0.0820972 | + | 1.21643i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.60246e15 | + | 4.51209e15i | 1.19281 | + | 0.960664i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.64468e15 | − | 4.58071e15i | 0.554394 | − | 0.960238i | −0.443557 | − | 0.896246i | \(-0.646284\pi\) |
0.997950 | − | 0.0639916i | \(-0.0203831\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.60020e15 | − | 6.23778e14i | 0.949499 | − | 0.128750i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.45851e15 | 0.906145 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.53840e15 | 1.10841 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.02767e14 | − | 4.13188e14i | 0.0399615 | − | 0.0814314i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.80696e15 | − | 8.32590e15i | 0.932957 | − | 1.61593i | 0.154719 | − | 0.987959i | \(-0.450553\pi\) |
0.778238 | − | 0.627970i | \(-0.216114\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.84549e15 | − | 7.54208e14i | −0.926176 | − | 0.144161i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.19515e15 | + | 5.53092e14i | −1.54275 | + | 0.104121i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.68375e15 | + | 2.12682e15i | −0.683017 | + | 0.394340i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 7.14214e15i | − | 1.30433i | −0.758075 | − | 0.652167i | \(-0.773860\pi\) | ||
0.758075 | − | 0.652167i | \(-0.226140\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.11082e15 | + | 2.18694e15i | −0.919367 | + | 0.393401i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.50061e15 | − | 6.06323e15i | −0.620295 | − | 1.07438i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.60636e15 | − | 3.23684e15i | −0.978610 | − | 0.565001i | −0.0767595 | − | 0.997050i | \(-0.524457\pi\) |
−0.901850 | + | 0.432049i | \(0.857791\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.00640e15 | + | 4.08706e15i | −0.173058 | + | 0.702799i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.29712e15 | + | 1.32624e15i | 0.389146 | + | 0.224674i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.41104e15 | − | 4.17604e15i | −0.402401 | − | 0.696979i | 0.591614 | − | 0.806221i | \(-0.298491\pi\) |
−0.994015 | + | 0.109242i | \(0.965158\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.31243e16 | + | 8.80624e15i | −2.15813 | + | 1.44807i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.11657e15i | 0.504938i | 0.967605 | + | 0.252469i | \(0.0812426\pi\) | ||||
−0.967605 | + | 0.252469i | \(0.918757\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.59647e15 | − | 9.21720e14i | 0.254859 | − | 0.147143i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.44556e15 | − | 7.04012e15i | −0.856603 | − | 1.10743i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.53919e15 | + | 8.62184e14i | 0.858611 | + | 0.133644i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.44104e14 | − | 5.96006e14i | 0.0525618 | − | 0.0910398i | −0.838547 | − | 0.544829i | \(-0.816595\pi\) |
0.891109 | + | 0.453789i | \(0.149928\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.47618e15 | + | 1.70590e15i | 0.523275 | + | 0.256791i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.56071e15 | 0.528236 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.38072e15 | −0.201874 | −0.100937 | − | 0.994893i | \(-0.532184\pi\) | ||||
−0.100937 | + | 0.994893i | \(0.532184\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.29032e15 | − | 3.57764e15i | −1.05055 | − | 0.515545i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.84283e15 | + | 1.18521e16i | −0.971897 | + | 1.68338i | −0.282082 | + | 0.959390i | \(0.591025\pi\) |
−0.689816 | + | 0.723985i | \(0.742308\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.88653e15 | + | 2.32475e15i | 0.404103 | + | 0.325455i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.67742e15 | + | 4.75424e15i | 0.507464 | + | 0.656059i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.28133e15 | − | 2.47182e15i | 0.582376 | − | 0.336235i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.76967e15i | 0.639577i | 0.947489 | + | 0.319789i | \(0.103612\pi\) | ||||
−0.947489 | + | 0.319789i | \(0.896388\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.62367e15 | + | 5.11537e15i | −1.00778 | + | 0.676205i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.51065e15 | + | 4.34858e15i | 0.327190 | + | 0.566709i | 0.981953 | − | 0.189125i | \(-0.0605651\pi\) |
−0.654763 | + | 0.755834i | \(0.727232\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.45139e15 | − | 1.41531e15i | −0.314958 | − | 0.181841i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.19036e14 | − | 7.41643e14i | 0.0657480 | − | 0.0939462i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.84574e14 | − | 5.68444e14i | −0.122968 | − | 0.0709957i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.29863e15 | + | 7.44545e15i | 0.529358 | + | 0.916876i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.33639e16 | − | 2.73912e15i | 1.62272 | − | 0.332599i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 5.65743e15i | − | 0.677385i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.48661e15 | − | 8.58292e14i | 0.175523 | − | 0.101338i | −0.409664 | − | 0.912236i | \(-0.634354\pi\) |
0.585188 | + | 0.810898i | \(0.301021\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.98584e15 | + | 4.71476e14i | −0.813383 | + | 0.0548954i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.00030e15 | + | 1.29231e16i | 0.574150 | + | 1.48387i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.42879e15 | − | 7.67088e15i | 0.501513 | − | 0.868646i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.62241e15 | + | 5.34381e15i | −0.292874 | + | 0.596804i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.09272e15 | 0.230511 | 0.115255 | − | 0.993336i | \(-0.463231\pi\) | ||||
0.115255 | + | 0.993336i | \(0.463231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.77675e16 | 1.93028 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.35220e15 | + | 7.25748e14i | −0.573527 | + | 0.0777691i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.69804e15 | + | 9.86930e15i | −0.602268 | + | 1.04316i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.16565e15 | − | 6.41395e15i | 0.538577 | − | 0.668726i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.62070e14 | + | 3.88308e15i | 0.0269534 | + | 0.399367i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.63793e16 | + | 9.45661e15i | −1.66180 | + | 0.959442i | −0.689948 | + | 0.723859i | \(0.742367\pi\) |
−0.971854 | + | 0.235584i | \(0.924300\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.88710e15i | 0.188878i | 0.995531 | + | 0.0944388i | \(0.0301057\pi\) | ||||
−0.995531 | + | 0.0944388i | \(0.969894\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.49035e15 | + | 3.71148e15i | 0.245902 | + | 0.366479i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.17900e15 | + | 5.50620e15i | 0.309688 | + | 0.536395i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.63307e16 | − | 9.42851e15i | −1.56958 | − | 0.906195i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.46227e15 | + | 1.40142e16i | −0.802463 | + | 1.32894i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.28090e15 | + | 7.39526e14i | 0.119847 | + | 0.0691937i | 0.558725 | − | 0.829353i | \(-0.311291\pi\) |
−0.438878 | + | 0.898547i | \(0.644624\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.50919e15 | + | 2.61399e15i | 0.139330 | + | 0.241326i | 0.927243 | − | 0.374460i | \(-0.122172\pi\) |
−0.787913 | + | 0.615786i | \(0.788839\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.87269e15 | + | 4.28130e15i | 0.261693 | + | 0.390013i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1.29098e16i | − | 1.16049i | −0.814443 | − | 0.580243i | \(-0.802958\pi\) | ||
0.814443 | − | 0.580243i | \(-0.197042\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.65564e14 | + | 1.53323e14i | −0.0235569 | + | 0.0136006i | −0.511732 | − | 0.859145i | \(-0.670996\pi\) |
0.488175 | + | 0.872746i | \(0.337663\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.30090e14 | − | 3.40924e15i | −0.0201415 | − | 0.298437i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.26374e16 | + | 4.03176e15i | 1.09172 | + | 0.348295i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.38716e15 | + | 5.86673e15i | −0.288775 | + | 0.500174i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.02514e15 | + | 6.79030e15i | 0.506964 | + | 0.571346i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.78378e15 | 0.812486 | 0.406243 | − | 0.913765i | \(-0.366839\pi\) | ||||
0.406243 | + | 0.913765i | \(0.366839\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.12758e16 | −1.74385 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.73207e15 | + | 9.64276e15i | −0.382825 | + | 0.780099i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.39036e15 | + | 1.10684e16i | −0.510286 | + | 0.883841i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.25171e13 | − | 3.37401e14i | 0.00413944 | − | 0.0265943i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.47006e15 | + | 2.34195e14i | −0.269988 | + | 0.0182216i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.53384e15 | + | 8.85564e14i | −0.117806 | + | 0.0680154i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.21089e16i | − | 0.918087i | −0.888414 | − | 0.459044i | \(-0.848192\pi\) | ||
0.888414 | − | 0.459044i | \(-0.151808\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.49803e16 | + | 6.13710e15i | 1.12126 | + | 0.459356i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.76637e15 | − | 9.98764e15i | −0.426096 | − | 0.738021i | 0.570426 | − | 0.821349i | \(-0.306778\pi\) |
−0.996522 | + | 0.0833285i | \(0.973445\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.25897e15 | + | 5.34567e15i | 0.675461 | + | 0.389978i | 0.798143 | − | 0.602469i | \(-0.205816\pi\) |
−0.122682 | + | 0.992446i | \(0.539149\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.17314e15 | − | 1.02351e14i | −0.0844953 | − | 0.00737179i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.50838e16 | − | 8.70865e15i | −1.07264 | − | 0.619286i | −0.143735 | − | 0.989616i | \(-0.545911\pi\) |
−0.928900 | + | 0.370330i | \(0.879245\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.35929e15 | + | 7.55052e15i | 0.306075 | + | 0.530137i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.75110e15 | − | 2.51693e15i | 0.260048 | − | 0.174489i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.38081e16i | 0.945205i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.06043e15 | + | 5.23104e15i | −0.612419 | + | 0.353580i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.74502e16 | − | 1.34978e16i | 1.16472 | − | 0.900918i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.51177e16 | + | 5.84946e15i | −0.996420 | + | 0.385542i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.44792e15 | − | 1.11681e16i | 0.419683 | − | 0.726913i | −0.576224 | − | 0.817292i | \(-0.695474\pi\) |
0.995907 | + | 0.0903788i | \(0.0288078\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.20310e16 | − | 5.90406e15i | −0.773325 | − | 0.379500i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.53304e15 | 0.287754 | 0.143877 | − | 0.989596i | \(-0.454043\pi\) | ||||
0.143877 | + | 0.989596i | \(0.454043\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.27808e16 | −0.801264 | −0.400632 | − | 0.916239i | \(-0.631209\pi\) | ||||
−0.400632 | + | 0.916239i | \(0.631209\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.54578e15 | − | 2.23079e15i | −0.281462 | − | 0.138124i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.11265e15 | − | 1.05874e16i | 0.373809 | − | 0.647456i | −0.616339 | − | 0.787481i | \(-0.711385\pi\) |
0.990148 | + | 0.140025i | \(0.0447182\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.78198e16 | + | 1.07642e16i | −1.68033 | + | 0.650164i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.40325e15 | − | 1.59379e16i | −0.262691 | − | 0.950831i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.14436e16 | − | 2.39275e16i | 2.44216 | − | 1.40998i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2.26629e15i | − | 0.131913i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.65980e16 | − | 1.78469e16i | 1.52929 | − | 1.02613i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.11386e16 | − | 1.92926e16i | −0.632632 | − | 1.09575i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.62461e16 | + | 9.37969e15i | 0.911513 | + | 0.526262i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.94583e16 | − | 1.69764e15i | −1.07851 | − | 0.0940942i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.67131e15 | − | 9.64933e14i | −0.0915146 | − | 0.0528360i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.28559e15 | + | 9.15491e15i | 0.285926 | + | 0.495238i | 0.972833 | − | 0.231507i | \(-0.0743656\pi\) |
−0.686908 | + | 0.726745i | \(0.741032\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.08640e16 | − | 2.65182e16i | 0.580613 | − | 1.41724i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.63984e15i | 0.244992i | 0.992469 | + | 0.122496i | \(0.0390899\pi\) | ||||
−0.992469 | + | 0.122496i | \(0.960910\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.29268e16 | − | 1.32368e16i | 1.19606 | − | 0.690546i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.05198e15 | + | 6.10920e14i | −0.466582 | + | 0.0314897i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.44665e15 | − | 2.85679e16i | 0.226465 | − | 1.45495i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.88230e15 | − | 8.45640e15i | 0.245691 | − | 0.425550i | −0.716635 | − | 0.697449i | \(-0.754318\pi\) |
0.962326 | + | 0.271899i | \(0.0876518\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.43198e14 | − | 9.03125e14i | 0.0220379 | − | 0.0449076i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.39098e16 | −1.66616 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.12445e15 | 0.0545961 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.62499e15 | + | 1.93586e16i | 0.125947 | + | 0.928828i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.10412e16 | − | 1.91239e16i | 0.523517 | − | 0.906757i | −0.476109 | − | 0.879386i | \(-0.657953\pi\) |
0.999625 | − | 0.0273709i | \(-0.00871352\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.49069e16 | − | 7.61452e15i | 1.63564 | − | 0.356796i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.56629e14 | + | 9.72925e15i | 0.0304068 | + | 0.450537i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.54826e16 | + | 8.93887e15i | −0.708565 | + | 0.409090i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.35109e16i | 1.51572i | 0.652418 | + | 0.757859i | \(0.273755\pi\) | ||||
−0.652418 | + | 0.757859i | \(0.726245\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.05744e15 | − | 1.20084e16i | −0.360194 | − | 0.536813i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.69651e14 | + | 1.50628e15i | 0.0384239 | + | 0.0665522i | 0.884598 | − | 0.466355i | \(-0.154433\pi\) |
−0.846174 | + | 0.532907i | \(0.821100\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.99536e15 | + | 1.15202e15i | 0.0871377 | + | 0.0503090i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.67492e16 | − | 8.00403e14i | 0.722967 | − | 0.0345489i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.40621e16 | + | 8.11878e15i | 0.599966 | + | 0.346390i | 0.769028 | − | 0.639215i | \(-0.220741\pi\) |
−0.169062 | + | 0.985605i | \(0.554074\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.24745e16 | − | 3.89270e16i | −0.947821 | − | 1.64167i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.96035e15 | − | 5.90228e15i | −0.165097 | − | 0.246052i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.58666e16i | − | 0.653842i | −0.945052 | − | 0.326921i | \(-0.893989\pi\) | ||
0.945052 | − | 0.326921i | \(-0.106011\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.40112e16 | − | 1.38629e16i | 0.978126 | − | 0.564721i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.73228e15 | + | 4.04841e16i | 0.110030 | + | 1.63030i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.88152e15 | + | 4.81951e15i | −0.154525 | + | 0.191867i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.29197e15 | + | 9.16596e15i | −0.208276 | + | 0.360744i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.00079e15 | − | 2.21301e16i | −0.116759 | − | 0.861069i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.50744e15 | −0.288796 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.19955e16 | −1.21687 | −0.608433 | − | 0.793605i | \(-0.708202\pi\) | ||||
−0.608433 | + | 0.793605i | \(0.708202\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.24759e16 | − | 4.58003e16i | 0.845156 | − | 1.72221i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.64085e16 | + | 2.84204e16i | −0.610048 | + | 1.05663i | 0.381184 | + | 0.924499i | \(0.375516\pi\) |
−0.991232 | + | 0.132135i | \(0.957817\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.51959e16 | + | 3.92732e16i | 0.558605 | + | 1.44369i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.02895e16 | + | 1.36934e15i | −0.737472 | + | 0.0497721i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.62593e16 | + | 9.38730e15i | −0.584361 | + | 0.337381i | −0.762865 | − | 0.646558i | \(-0.776208\pi\) |
0.178504 | + | 0.983939i | \(0.442874\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.60654e16i | − | 0.570934i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.59740e15 | − | 1.36629e16i | 0.196701 | − | 0.480134i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.42416e16 | + | 2.46671e16i | 0.494895 | + | 0.857183i | 0.999983 | − | 0.00588469i | \(-0.00187317\pi\) |
−0.505088 | + | 0.863068i | \(0.668540\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.47583e16 | + | 8.52073e15i | 0.507152 | + | 0.292804i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.84215e16 | − | 4.06110e16i | 0.965833 | − | 1.38006i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.30960e16 | + | 1.91080e16i | 1.11223 | + | 0.642148i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.73725e16 | + | 3.00900e16i | 0.577373 | + | 1.00004i | 0.995779 | + | 0.0917800i | \(0.0292556\pi\) |
−0.418406 | + | 0.908260i | \(0.637411\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.18776e16 | + | 2.80993e16i | −1.37645 | + | 0.923580i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1.77916e16i | − | 0.578346i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.29010e16 | + | 2.47689e16i | −1.37925 | + | 0.796313i | −0.992070 | − | 0.125689i | \(-0.959886\pi\) |
−0.387185 | + | 0.922002i | \(0.626552\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.42151e15 | − | 1.13930e15i | −0.108795 | − | 0.0362268i |
(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 | 84.12.k.b.5.5 | ✓ | 56 | |
3.2 | odd | 2 | inner | 84.12.k.b.5.14 | yes | 56 | |
7.3 | odd | 6 | inner | 84.12.k.b.17.14 | yes | 56 | |
21.17 | even | 6 | inner | 84.12.k.b.17.5 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.12.k.b.5.5 | ✓ | 56 | 1.1 | even | 1 | trivial | |
84.12.k.b.5.14 | yes | 56 | 3.2 | odd | 2 | inner | |
84.12.k.b.17.5 | yes | 56 | 21.17 | even | 6 | inner | |
84.12.k.b.17.14 | yes | 56 | 7.3 | odd | 6 | inner |