Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,22,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(58.6902423003\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.31 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.22.c.b.20.32 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 687.640i | − | 0.474839i | −0.971407 | − | 0.237419i | \(-0.923698\pi\) | ||
0.971407 | − | 0.237419i | \(-0.0763015\pi\) | |||||||
\(3\) | 100506. | − | 18946.7i | 0.982691 | − | 0.185251i | ||||
\(4\) | 1.62430e6 | 0.774528 | ||||||||
\(5\) | −6.28469e6 | −0.287805 | −0.143903 | − | 0.989592i | \(-0.545965\pi\) | ||||
−0.143903 | + | 0.989592i | \(0.545965\pi\) | |||||||
\(6\) | −1.30285e7 | − | 6.91116e7i | −0.0879645 | − | 0.466620i | ||||
\(7\) | 4.61336e8 | − | 5.87975e8i | 0.617289 | − | 0.786737i | ||||
\(8\) | − | 2.55902e9i | − | 0.842615i | ||||||
\(9\) | 9.74240e9 | − | 3.80851e9i | 0.931364 | − | 0.364090i | ||||
\(10\) | 4.32160e9i | 0.136661i | ||||||||
\(11\) | − | 6.92257e10i | − | 0.804719i | −0.915482 | − | 0.402360i | \(-0.868190\pi\) | ||
0.915482 | − | 0.402360i | \(-0.131810\pi\) | |||||||
\(12\) | 1.63252e11 | − | 3.07752e10i | 0.761122 | − | 0.143482i | ||||
\(13\) | 2.42034e11i | 0.486934i | 0.969909 | + | 0.243467i | \(0.0782848\pi\) | ||||
−0.969909 | + | 0.243467i | \(0.921715\pi\) | |||||||
\(14\) | −4.04315e11 | − | 3.17233e11i | −0.373573 | − | 0.293112i | ||||
\(15\) | −6.31646e11 | + | 1.19074e11i | −0.282824 | + | 0.0533163i | ||||
\(16\) | 1.64673e12 | 0.374422 | ||||||||
\(17\) | −6.97114e12 | −0.838668 | −0.419334 | − | 0.907832i | \(-0.637736\pi\) | ||||
−0.419334 | + | 0.907832i | \(0.637736\pi\) | |||||||
\(18\) | −2.61888e12 | − | 6.69926e12i | −0.172884 | − | 0.442248i | ||||
\(19\) | − | 3.12105e13i | − | 1.16785i | −0.811807 | − | 0.583925i | \(-0.801516\pi\) | ||
0.811807 | − | 0.583925i | \(-0.198484\pi\) | |||||||
\(20\) | −1.02082e13 | −0.222913 | ||||||||
\(21\) | 3.52267e13 | − | 6.78356e13i | 0.460860 | − | 0.887473i | ||||
\(22\) | −4.76024e13 | −0.382112 | ||||||||
\(23\) | − | 5.39902e13i | − | 0.271752i | −0.990726 | − | 0.135876i | \(-0.956615\pi\) | ||
0.990726 | − | 0.135876i | \(-0.0433849\pi\) | |||||||
\(24\) | −4.84851e13 | − | 2.57196e14i | −0.156095 | − | 0.828030i | ||||
\(25\) | −4.37340e14 | −0.917168 | ||||||||
\(26\) | 1.66432e14 | 0.231215 | ||||||||
\(27\) | 9.07007e14 | − | 5.67363e14i | 0.847795 | − | 0.530324i | ||||
\(28\) | 7.49350e14 | − | 9.55050e14i | 0.478107 | − | 0.609350i | ||||
\(29\) | 2.80226e15i | 1.23689i | 0.785830 | + | 0.618443i | \(0.212236\pi\) | ||||
−0.785830 | + | 0.618443i | \(0.787764\pi\) | |||||||
\(30\) | 8.18802e13 | + | 4.34345e14i | 0.0253166 | + | 0.134296i | ||||
\(31\) | 2.80728e15i | 0.615160i | 0.951522 | + | 0.307580i | \(0.0995192\pi\) | ||||
−0.951522 | + | 0.307580i | \(0.900481\pi\) | |||||||
\(32\) | − | 6.49901e15i | − | 1.02040i | ||||||
\(33\) | −1.31160e15 | − | 6.95757e15i | −0.149075 | − | 0.790790i | ||||
\(34\) | 4.79363e15i | 0.398232i | ||||||||
\(35\) | −2.89936e15 | + | 3.69524e15i | −0.177659 | + | 0.226427i | ||||
\(36\) | 1.58246e16 | − | 6.18617e15i | 0.721368 | − | 0.281998i | ||||
\(37\) | 3.19164e16 | 1.09118 | 0.545590 | − | 0.838053i | \(-0.316306\pi\) | ||||
0.545590 | + | 0.838053i | \(0.316306\pi\) | |||||||
\(38\) | −2.14616e16 | −0.554541 | ||||||||
\(39\) | 4.58575e15 | + | 2.43257e16i | 0.0902052 | + | 0.478506i | ||||
\(40\) | 1.60826e16i | 0.242509i | ||||||||
\(41\) | 1.94702e16 | 0.226537 | 0.113269 | − | 0.993564i | \(-0.463868\pi\) | ||||
0.113269 | + | 0.993564i | \(0.463868\pi\) | |||||||
\(42\) | −4.66465e16 | − | 2.42233e16i | −0.421406 | − | 0.218834i | ||||
\(43\) | 9.38339e16 | 0.662126 | 0.331063 | − | 0.943609i | \(-0.392593\pi\) | ||||
0.331063 | + | 0.943609i | \(0.392593\pi\) | |||||||
\(44\) | − | 1.12444e17i | − | 0.623278i | ||||||
\(45\) | −6.12279e16 | + | 2.39353e16i | −0.268051 | + | 0.104787i | ||||
\(46\) | −3.71258e16 | −0.129038 | ||||||||
\(47\) | 3.19152e16 | 0.0885055 | 0.0442528 | − | 0.999020i | \(-0.485909\pi\) | ||||
0.0442528 | + | 0.999020i | \(0.485909\pi\) | |||||||
\(48\) | 1.65505e17 | − | 3.12001e16i | 0.367942 | − | 0.0693622i | ||||
\(49\) | −1.32883e17 | − | 5.42509e17i | −0.237910 | − | 0.971287i | ||||
\(50\) | 3.00732e17i | 0.435507i | ||||||||
\(51\) | −7.00638e17 | + | 1.32080e17i | −0.824151 | + | 0.155364i | ||||
\(52\) | 3.93136e17i | 0.377144i | ||||||||
\(53\) | − | 1.47276e18i | − | 1.15674i | −0.815774 | − | 0.578370i | \(-0.803689\pi\) | ||
0.815774 | − | 0.578370i | \(-0.196311\pi\) | |||||||
\(54\) | −3.90141e17 | − | 6.23694e17i | −0.251818 | − | 0.402566i | ||||
\(55\) | 4.35062e17i | 0.231602i | ||||||||
\(56\) | −1.50464e18 | − | 1.18057e18i | −0.662916 | − | 0.520136i | ||||
\(57\) | −5.91336e17 | − | 3.13683e18i | −0.216346 | − | 1.14764i | ||||
\(58\) | 1.92695e18 | 0.587321 | ||||||||
\(59\) | −5.35304e18 | −1.36350 | −0.681749 | − | 0.731586i | \(-0.738780\pi\) | ||||
−0.681749 | + | 0.731586i | \(0.738780\pi\) | |||||||
\(60\) | −1.02599e18 | + | 1.93413e17i | −0.219055 | + | 0.0412950i | ||||
\(61\) | 9.25237e18i | 1.66069i | 0.557247 | + | 0.830347i | \(0.311858\pi\) | ||||
−0.557247 | + | 0.830347i | \(0.688142\pi\) | |||||||
\(62\) | 1.93040e18 | 0.292102 | ||||||||
\(63\) | 2.25522e18 | − | 7.48529e18i | 0.288478 | − | 0.957487i | ||||
\(64\) | −1.01554e18 | −0.110105 | ||||||||
\(65\) | − | 1.52111e18i | − | 0.140142i | ||||||
\(66\) | −4.78430e18 | + | 9.01909e17i | −0.375498 | + | 0.0707867i | ||||
\(67\) | 8.77935e18 | 0.588406 | 0.294203 | − | 0.955743i | \(-0.404946\pi\) | ||||
0.294203 | + | 0.955743i | \(0.404946\pi\) | |||||||
\(68\) | −1.13232e19 | −0.649572 | ||||||||
\(69\) | −1.02294e18 | − | 5.42632e18i | −0.0503424 | − | 0.267048i | ||||
\(70\) | 2.54099e18 | + | 1.99371e18i | 0.107516 | + | 0.0843593i | ||||
\(71\) | − | 4.46340e19i | − | 1.62724i | −0.581394 | − | 0.813622i | \(-0.697492\pi\) | ||
0.581394 | − | 0.813622i | \(-0.302508\pi\) | |||||||
\(72\) | −9.74605e18 | − | 2.49310e19i | −0.306787 | − | 0.784781i | ||||
\(73\) | − | 4.34206e19i | − | 1.18251i | −0.806484 | − | 0.591257i | \(-0.798632\pi\) | ||
0.806484 | − | 0.591257i | \(-0.201368\pi\) | |||||||
\(74\) | − | 2.19470e19i | − | 0.518134i | ||||||
\(75\) | −4.39551e19 | + | 8.28616e18i | −0.901293 | + | 0.169907i | ||||
\(76\) | − | 5.06953e19i | − | 0.904534i | ||||||
\(77\) | −4.07030e19 | − | 3.19363e19i | −0.633102 | − | 0.496744i | ||||
\(78\) | 1.67273e19 | − | 3.15334e18i | 0.227213 | − | 0.0428329i | ||||
\(79\) | 6.43691e18 | 0.0764879 | 0.0382439 | − | 0.999268i | \(-0.487824\pi\) | ||||
0.0382439 | + | 0.999268i | \(0.487824\pi\) | |||||||
\(80\) | −1.03492e19 | −0.107761 | ||||||||
\(81\) | 8.04096e19 | − | 7.42079e19i | 0.734878 | − | 0.678200i | ||||
\(82\) | − | 1.33885e19i | − | 0.107569i | ||||||
\(83\) | −2.21180e20 | −1.56468 | −0.782341 | − | 0.622850i | \(-0.785975\pi\) | ||||
−0.782341 | + | 0.622850i | \(0.785975\pi\) | |||||||
\(84\) | 5.72188e19 | − | 1.10186e20i | 0.356949 | − | 0.687373i | ||||
\(85\) | 4.38114e19 | 0.241373 | ||||||||
\(86\) | − | 6.45239e19i | − | 0.314403i | ||||||
\(87\) | 5.30937e19 | + | 2.81643e20i | 0.229135 | + | 1.21548i | ||||
\(88\) | −1.77150e20 | −0.678068 | ||||||||
\(89\) | −6.58942e19 | −0.224002 | −0.112001 | − | 0.993708i | \(-0.535726\pi\) | ||||
−0.112001 | + | 0.993708i | \(0.535726\pi\) | |||||||
\(90\) | 1.64588e19 | + | 4.21028e19i | 0.0497569 | + | 0.127281i | ||||
\(91\) | 1.42310e20 | + | 1.11659e20i | 0.383089 | + | 0.300579i | ||||
\(92\) | − | 8.76965e19i | − | 0.210480i | ||||||
\(93\) | 5.31888e19 | + | 2.82148e20i | 0.113959 | + | 0.604513i | ||||
\(94\) | − | 2.19462e19i | − | 0.0420258i | ||||||
\(95\) | 1.96148e20i | 0.336114i | ||||||||
\(96\) | −1.23135e20 | − | 6.53187e20i | −0.189031 | − | 1.00274i | ||||
\(97\) | 4.64245e20i | 0.639211i | 0.947551 | + | 0.319605i | \(0.103550\pi\) | ||||
−0.947551 | + | 0.319605i | \(0.896450\pi\) | |||||||
\(98\) | −3.73050e20 | + | 9.13759e19i | −0.461205 | + | 0.112969i | ||||
\(99\) | −2.63647e20 | − | 6.74424e20i | −0.292990 | − | 0.749486i | ||||
\(100\) | −7.10373e20 | −0.710373 | ||||||||
\(101\) | 8.74981e20 | 0.788178 | 0.394089 | − | 0.919072i | \(-0.371060\pi\) | ||||
0.394089 | + | 0.919072i | \(0.371060\pi\) | |||||||
\(102\) | 9.08236e19 | + | 4.81787e20i | 0.0737729 | + | 0.391339i | ||||
\(103\) | − | 3.36089e20i | − | 0.246413i | −0.992381 | − | 0.123206i | \(-0.960682\pi\) | ||
0.992381 | − | 0.123206i | \(-0.0393177\pi\) | |||||||
\(104\) | 6.19369e20 | 0.410298 | ||||||||
\(105\) | −2.21389e20 | + | 4.26326e20i | −0.132638 | + | 0.255419i | ||||
\(106\) | −1.01273e21 | −0.549265 | ||||||||
\(107\) | 1.57535e21i | 0.774188i | 0.922040 | + | 0.387094i | \(0.126521\pi\) | ||||
−0.922040 | + | 0.387094i | \(0.873479\pi\) | |||||||
\(108\) | 1.47325e21 | − | 9.21569e20i | 0.656641 | − | 0.410751i | ||||
\(109\) | 2.80464e21 | 1.13475 | 0.567374 | − | 0.823460i | \(-0.307959\pi\) | ||||
0.567374 | + | 0.823460i | \(0.307959\pi\) | |||||||
\(110\) | 2.99166e20 | 0.109974 | ||||||||
\(111\) | 3.20778e21 | − | 6.04712e20i | 1.07229 | − | 0.202142i | ||||
\(112\) | 7.59695e20 | − | 9.68234e20i | 0.231127 | − | 0.294572i | ||||
\(113\) | 5.14750e21i | 1.42650i | 0.700908 | + | 0.713252i | \(0.252779\pi\) | ||||
−0.700908 | + | 0.713252i | \(0.747221\pi\) | |||||||
\(114\) | −2.15701e21 | + | 4.06626e20i | −0.544942 | + | 0.102729i | ||||
\(115\) | 3.39312e20i | 0.0782117i | ||||||||
\(116\) | 4.55172e21i | 0.958003i | ||||||||
\(117\) | 9.21786e20 | + | 2.35799e21i | 0.177288 | + | 0.453513i | ||||
\(118\) | 3.68096e21i | 0.647442i | ||||||||
\(119\) | −3.21604e21 | + | 4.09885e21i | −0.517700 | + | 0.659811i | ||||
\(120\) | 3.04714e20 | + | 1.61640e21i | 0.0449251 | + | 0.238311i | ||||
\(121\) | 2.60805e21 | 0.352427 | ||||||||
\(122\) | 6.36230e21 | 0.788562 | ||||||||
\(123\) | 1.95686e21 | − | 3.68897e20i | 0.222616 | − | 0.0419663i | ||||
\(124\) | 4.55988e21i | 0.476459i | ||||||||
\(125\) | 5.74532e21 | 0.551771 | ||||||||
\(126\) | −5.14718e21 | − | 1.55078e21i | −0.454652 | − | 0.136980i | ||||
\(127\) | −2.26715e20 | −0.0184307 | −0.00921534 | − | 0.999958i | \(-0.502933\pi\) | ||||
−0.00921534 | + | 0.999958i | \(0.502933\pi\) | |||||||
\(128\) | − | 1.29311e22i | − | 0.968123i | ||||||
\(129\) | 9.43083e21 | − | 1.77785e21i | 0.650666 | − | 0.122660i | ||||
\(130\) | −1.04597e21 | −0.0665450 | ||||||||
\(131\) | −2.10295e22 | −1.23447 | −0.617234 | − | 0.786780i | \(-0.711747\pi\) | ||||
−0.617234 | + | 0.786780i | \(0.711747\pi\) | |||||||
\(132\) | −2.13044e21 | − | 1.13012e22i | −0.115463 | − | 0.612489i | ||||
\(133\) | −1.83510e22 | − | 1.43985e22i | −0.918791 | − | 0.720901i | ||||
\(134\) | − | 6.03703e21i | − | 0.279398i | ||||||
\(135\) | −5.70025e21 | + | 3.56570e21i | −0.244000 | + | 0.152630i | ||||
\(136\) | 1.78393e22i | 0.706674i | ||||||||
\(137\) | − | 3.53810e21i | − | 0.129779i | −0.997892 | − | 0.0648895i | \(-0.979331\pi\) | ||
0.997892 | − | 0.0648895i | \(-0.0206695\pi\) | |||||||
\(138\) | −3.73135e21 | + | 7.03413e20i | −0.126805 | + | 0.0239045i | ||||
\(139\) | − | 6.64239e21i | − | 0.209252i | −0.994512 | − | 0.104626i | \(-0.966636\pi\) | ||
0.994512 | − | 0.104626i | \(-0.0333645\pi\) | |||||||
\(140\) | −4.70943e21 | + | 6.00219e21i | −0.137602 | + | 0.175374i | ||||
\(141\) | 3.20766e21 | − | 6.04689e20i | 0.0869736 | − | 0.0163958i | ||||
\(142\) | −3.06921e22 | −0.772679 | ||||||||
\(143\) | 1.67550e22 | 0.391845 | ||||||||
\(144\) | 1.60431e22 | − | 6.27157e21i | 0.348723 | − | 0.136323i | ||||
\(145\) | − | 1.76113e22i | − | 0.355982i | ||||||
\(146\) | −2.98577e22 | −0.561503 | ||||||||
\(147\) | −2.36343e22 | − | 5.20074e22i | −0.413724 | − | 0.910402i | ||||
\(148\) | 5.18420e22 | 0.845149 | ||||||||
\(149\) | − | 9.63864e22i | − | 1.46406i | −0.681271 | − | 0.732031i | \(-0.738572\pi\) | ||
0.681271 | − | 0.732031i | \(-0.261428\pi\) | |||||||
\(150\) | 5.69789e21 | + | 3.02253e22i | 0.0806782 | + | 0.427969i | ||||
\(151\) | 1.48220e23 | 1.95727 | 0.978633 | − | 0.205617i | \(-0.0659201\pi\) | ||||
0.978633 | + | 0.205617i | \(0.0659201\pi\) | |||||||
\(152\) | −7.98682e22 | −0.984048 | ||||||||
\(153\) | −6.79156e22 | + | 2.65496e22i | −0.781105 | + | 0.305350i | ||||
\(154\) | −2.19607e22 | + | 2.79890e22i | −0.235873 | + | 0.300621i | ||||
\(155\) | − | 1.76429e22i | − | 0.177046i | ||||||
\(156\) | 7.44864e21 | + | 3.95124e22i | 0.0698665 | + | 0.370617i | ||||
\(157\) | − | 4.52599e22i | − | 0.396979i | −0.980103 | − | 0.198490i | \(-0.936396\pi\) | ||
0.980103 | − | 0.198490i | \(-0.0636036\pi\) | |||||||
\(158\) | − | 4.42627e21i | − | 0.0363194i | ||||||
\(159\) | −2.79040e22 | − | 1.48021e23i | −0.214288 | − | 1.13672i | ||||
\(160\) | 4.08443e22i | 0.293678i | ||||||||
\(161\) | −3.17449e22 | − | 2.49077e22i | −0.213797 | − | 0.167749i | ||||
\(162\) | −5.10283e22 | − | 5.52928e22i | −0.322035 | − | 0.348948i | ||||
\(163\) | −1.01747e23 | −0.601938 | −0.300969 | − | 0.953634i | \(-0.597310\pi\) | ||||
−0.300969 | + | 0.953634i | \(0.597310\pi\) | |||||||
\(164\) | 3.16255e22 | 0.175460 | ||||||||
\(165\) | 8.24301e21 | + | 4.37262e22i | 0.0429046 | + | 0.227594i | ||||
\(166\) | 1.52092e23i | 0.742972i | ||||||||
\(167\) | 1.17221e23 | 0.537630 | 0.268815 | − | 0.963192i | \(-0.413368\pi\) | ||||
0.268815 | + | 0.963192i | \(0.413368\pi\) | |||||||
\(168\) | −1.73593e23 | − | 9.01458e22i | −0.747798 | − | 0.388327i | ||||
\(169\) | 1.88484e23 | 0.762895 | ||||||||
\(170\) | − | 3.01265e22i | − | 0.114613i | ||||||
\(171\) | −1.18865e23 | − | 3.04065e23i | −0.425202 | − | 1.08769i | ||||
\(172\) | 1.52415e23 | 0.512836 | ||||||||
\(173\) | 4.68987e23 | 1.48483 | 0.742415 | − | 0.669940i | \(-0.233680\pi\) | ||||
0.742415 | + | 0.669940i | \(0.233680\pi\) | |||||||
\(174\) | 1.93669e23 | − | 3.65093e22i | 0.577155 | − | 0.108802i | ||||
\(175\) | −2.01761e23 | + | 2.57145e23i | −0.566157 | + | 0.721570i | ||||
\(176\) | − | 1.13996e23i | − | 0.301305i | ||||||
\(177\) | −5.38011e23 | + | 1.01423e23i | −1.33990 | + | 0.252590i | ||||
\(178\) | 4.53115e22i | 0.106365i | ||||||||
\(179\) | 6.57802e23i | 1.45592i | 0.685619 | + | 0.727961i | \(0.259532\pi\) | ||||
−0.685619 | + | 0.727961i | \(0.740468\pi\) | |||||||
\(180\) | −9.94527e22 | + | 3.88781e22i | −0.207613 | + | 0.0811604i | ||||
\(181\) | 5.16324e23i | 1.01695i | 0.861078 | + | 0.508473i | \(0.169790\pi\) | ||||
−0.861078 | + | 0.508473i | \(0.830210\pi\) | |||||||
\(182\) | 7.67811e22 | − | 9.78578e22i | 0.142727 | − | 0.181906i | ||||
\(183\) | 1.75302e23 | + | 9.29915e23i | 0.307646 | + | 1.63195i | ||||
\(184\) | −1.38162e23 | −0.228982 | ||||||||
\(185\) | −2.00585e23 | −0.314047 | ||||||||
\(186\) | 1.94016e23 | − | 3.65748e22i | 0.287046 | − | 0.0541123i | ||||
\(187\) | 4.82582e23i | 0.674892i | ||||||||
\(188\) | 5.18400e22 | 0.0685500 | ||||||||
\(189\) | 8.48400e22 | − | 7.95042e23i | 0.106109 | − | 0.994355i | ||||
\(190\) | 1.34879e23 | 0.159600 | ||||||||
\(191\) | 4.71277e23i | 0.527747i | 0.964557 | + | 0.263874i | \(0.0850002\pi\) | ||||
−0.964557 | + | 0.263874i | \(0.915000\pi\) | |||||||
\(192\) | −1.02068e23 | + | 1.92412e22i | −0.108199 | + | 0.0203971i | ||||
\(193\) | 1.57401e24 | 1.58000 | 0.789999 | − | 0.613108i | \(-0.210081\pi\) | ||||
0.789999 | + | 0.613108i | \(0.210081\pi\) | |||||||
\(194\) | 3.19233e23 | 0.303522 | ||||||||
\(195\) | −2.88200e22 | − | 1.52880e23i | −0.0259615 | − | 0.137717i | ||||
\(196\) | −2.15843e23 | − | 8.81198e23i | −0.184268 | − | 0.752289i | ||||
\(197\) | − | 6.17191e23i | − | 0.499487i | −0.968312 | − | 0.249744i | \(-0.919654\pi\) | ||
0.968312 | − | 0.249744i | \(-0.0803463\pi\) | |||||||
\(198\) | −4.63761e23 | + | 1.81294e23i | −0.355885 | + | 0.139123i | ||||
\(199\) | 1.18071e24i | 0.859380i | 0.902977 | + | 0.429690i | \(0.141377\pi\) | ||||
−0.902977 | + | 0.429690i | \(0.858623\pi\) | |||||||
\(200\) | 1.11916e24i | 0.772819i | ||||||||
\(201\) | 8.82374e23 | − | 1.66340e23i | 0.578221 | − | 0.109003i | ||||
\(202\) | − | 6.01672e23i | − | 0.374257i | ||||||
\(203\) | 1.64766e24 | + | 1.29279e24i | 0.973104 | + | 0.763516i | ||||
\(204\) | −1.13805e24 | + | 2.14538e23i | −0.638329 | + | 0.120334i | ||||
\(205\) | −1.22364e23 | −0.0651987 | ||||||||
\(206\) | −2.31108e23 | −0.117006 | ||||||||
\(207\) | −2.05622e23 | − | 5.25994e23i | −0.0989421 | − | 0.253100i | ||||
\(208\) | 3.98563e23i | 0.182319i | ||||||||
\(209\) | −2.16057e24 | −0.939792 | ||||||||
\(210\) | 2.93158e23 | + | 1.52236e23i | 0.121283 | + | 0.0629816i | ||||
\(211\) | 3.65042e23 | 0.143674 | 0.0718368 | − | 0.997416i | \(-0.477114\pi\) | ||||
0.0718368 | + | 0.997416i | \(0.477114\pi\) | |||||||
\(212\) | − | 2.39221e24i | − | 0.895928i | ||||||
\(213\) | −8.45668e23 | − | 4.48596e24i | −0.301449 | − | 1.59908i | ||||
\(214\) | 1.08327e24 | 0.367614 | ||||||||
\(215\) | −5.89717e23 | −0.190563 | ||||||||
\(216\) | −1.45189e24 | − | 2.32105e24i | −0.446859 | − | 0.714364i | ||||
\(217\) | 1.65061e24 | + | 1.29510e24i | 0.483969 | + | 0.379732i | ||||
\(218\) | − | 1.92858e24i | − | 0.538822i | ||||||
\(219\) | −8.22679e23 | − | 4.36401e24i | −0.219062 | − | 1.16205i | ||||
\(220\) | 7.06673e23i | 0.179383i | ||||||||
\(221\) | − | 1.68725e24i | − | 0.408376i | ||||||
\(222\) | −4.15824e23 | − | 2.20580e24i | −0.0959850 | − | 0.509166i | ||||
\(223\) | 8.80006e24i | 1.93769i | 0.247666 | + | 0.968846i | \(0.420337\pi\) | ||||
−0.247666 | + | 0.968846i | \(0.579663\pi\) | |||||||
\(224\) | −3.82126e24 | − | 2.99823e24i | −0.802790 | − | 0.629884i | ||||
\(225\) | −4.26074e24 | + | 1.66561e24i | −0.854217 | + | 0.333931i | ||||
\(226\) | 3.53963e24 | 0.677359 | ||||||||
\(227\) | −3.39805e24 | −0.620810 | −0.310405 | − | 0.950604i | \(-0.600465\pi\) | ||||
−0.310405 | + | 0.950604i | \(0.600465\pi\) | |||||||
\(228\) | −9.60510e23 | − | 5.09516e24i | −0.167566 | − | 0.888877i | ||||
\(229\) | 6.08362e24i | 1.01365i | 0.862048 | + | 0.506827i | \(0.169182\pi\) | ||||
−0.862048 | + | 0.506827i | \(0.830818\pi\) | |||||||
\(230\) | 2.33324e23 | 0.0371379 | ||||||||
\(231\) | −4.69597e24 | − | 2.43859e24i | −0.714166 | − | 0.370863i | ||||
\(232\) | 7.17105e24 | 1.04222 | ||||||||
\(233\) | 5.19101e24i | 0.721132i | 0.932734 | + | 0.360566i | \(0.117416\pi\) | ||||
−0.932734 | + | 0.360566i | \(0.882584\pi\) | |||||||
\(234\) | 1.62145e24 | − | 6.33857e23i | 0.215346 | − | 0.0841831i | ||||
\(235\) | −2.00577e23 | −0.0254724 | ||||||||
\(236\) | −8.69496e24 | −1.05607 | ||||||||
\(237\) | 6.46945e23 | − | 1.21958e23i | 0.0751640 | − | 0.0141695i | ||||
\(238\) | 2.81854e24 | + | 2.21148e24i | 0.313304 | + | 0.245824i | ||||
\(239\) | − | 2.28072e24i | − | 0.242602i | −0.992616 | − | 0.121301i | \(-0.961293\pi\) | ||
0.992616 | − | 0.121301i | \(-0.0387066\pi\) | |||||||
\(240\) | −1.04015e24 | + | 1.96083e23i | −0.105896 | + | 0.0199628i | ||||
\(241\) | − | 1.01334e25i | − | 0.987586i | −0.869579 | − | 0.493793i | \(-0.835610\pi\) | ||
0.869579 | − | 0.493793i | \(-0.164390\pi\) | |||||||
\(242\) | − | 1.79340e24i | − | 0.167346i | ||||||
\(243\) | 6.67561e24 | − | 8.98181e24i | 0.596520 | − | 0.802598i | ||||
\(244\) | 1.50287e25i | 1.28625i | ||||||||
\(245\) | 8.35131e23 | + | 3.40950e24i | 0.0684716 | + | 0.279542i | ||||
\(246\) | −2.53668e23 | − | 1.34562e24i | −0.0199272 | − | 0.105707i | ||||
\(247\) | 7.55398e24 | 0.568667 | ||||||||
\(248\) | 7.18390e24 | 0.518343 | ||||||||
\(249\) | −2.22298e25 | + | 4.19064e24i | −1.53760 | + | 0.289859i | ||||
\(250\) | − | 3.95071e24i | − | 0.262002i | ||||||
\(251\) | 9.11602e24 | 0.579737 | 0.289869 | − | 0.957066i | \(-0.406388\pi\) | ||||
0.289869 | + | 0.957066i | \(0.406388\pi\) | |||||||
\(252\) | 3.66315e24 | − | 1.21584e25i | 0.223434 | − | 0.741600i | ||||
\(253\) | −3.73751e24 | −0.218684 | ||||||||
\(254\) | 1.55898e23i | 0.00875160i | ||||||||
\(255\) | 4.40329e24 | − | 8.30083e23i | 0.237195 | − | 0.0447147i | ||||
\(256\) | −1.10217e25 | −0.569807 | ||||||||
\(257\) | 1.05919e25 | 0.525623 | 0.262812 | − | 0.964847i | \(-0.415350\pi\) | ||||
0.262812 | + | 0.964847i | \(0.415350\pi\) | |||||||
\(258\) | −1.22252e24 | − | 6.48501e24i | −0.0582436 | − | 0.308961i | ||||
\(259\) | 1.47242e25 | − | 1.87661e25i | 0.673572 | − | 0.858471i | ||||
\(260\) | − | 2.47074e24i | − | 0.108544i | ||||||
\(261\) | 1.06724e25 | + | 2.73007e25i | 0.450337 | + | 1.15199i | ||||
\(262\) | 1.44607e25i | 0.586173i | ||||||||
\(263\) | 1.05737e25i | 0.411804i | 0.978573 | + | 0.205902i | \(0.0660128\pi\) | ||||
−0.978573 | + | 0.205902i | \(0.933987\pi\) | |||||||
\(264\) | −1.78046e25 | + | 3.35642e24i | −0.666331 | + | 0.125613i | ||||
\(265\) | 9.25585e24i | 0.332916i | ||||||||
\(266\) | −9.90100e24 | + | 1.26189e25i | −0.342312 | + | 0.436278i | ||||
\(267\) | −6.62274e24 | + | 1.24848e24i | −0.220125 | + | 0.0414967i | ||||
\(268\) | 1.42603e25 | 0.455737 | ||||||||
\(269\) | 6.26136e25 | 1.92429 | 0.962143 | − | 0.272546i | \(-0.0878658\pi\) | ||||
0.962143 | + | 0.272546i | \(0.0878658\pi\) | |||||||
\(270\) | 2.45192e24 | + | 3.91972e24i | 0.0724746 | + | 0.115861i | ||||
\(271\) | 4.94248e25i | 1.40529i | 0.711538 | + | 0.702647i | \(0.247999\pi\) | ||||
−0.711538 | + | 0.702647i | \(0.752001\pi\) | |||||||
\(272\) | −1.14796e25 | −0.314016 | ||||||||
\(273\) | 1.64185e25 | + | 8.52604e24i | 0.432141 | + | 0.224409i | ||||
\(274\) | −2.43294e24 | −0.0616241 | ||||||||
\(275\) | 3.02752e25i | 0.738063i | ||||||||
\(276\) | −1.66156e24 | − | 8.81399e24i | −0.0389916 | − | 0.206837i | ||||
\(277\) | −3.75420e25 | −0.848163 | −0.424082 | − | 0.905624i | \(-0.639403\pi\) | ||||
−0.424082 | + | 0.905624i | \(0.639403\pi\) | |||||||
\(278\) | −4.56757e24 | −0.0993608 | ||||||||
\(279\) | 1.06916e25 | + | 2.73497e25i | 0.223974 | + | 0.572938i | ||||
\(280\) | 9.45620e24 | + | 7.41951e24i | 0.190791 | + | 0.149698i | ||||
\(281\) | 7.95440e25i | 1.54594i | 0.634446 | + | 0.772968i | \(0.281228\pi\) | ||||
−0.634446 | + | 0.772968i | \(0.718772\pi\) | |||||||
\(282\) | −4.15808e23 | − | 2.20571e24i | −0.00778534 | − | 0.0412984i | ||||
\(283\) | − | 8.41458e24i | − | 0.151801i | −0.997115 | − | 0.0759006i | \(-0.975817\pi\) | ||
0.997115 | − | 0.0759006i | \(-0.0241832\pi\) | |||||||
\(284\) | − | 7.24991e25i | − | 1.26035i | ||||||
\(285\) | 3.71636e24 | + | 1.97140e25i | 0.0622655 | + | 0.330296i | ||||
\(286\) | − | 1.15214e25i | − | 0.186063i | ||||||
\(287\) | 8.98231e24 | − | 1.14480e25i | 0.139839 | − | 0.178225i | ||||
\(288\) | −2.47515e25 | − | 6.33159e25i | −0.371519 | − | 0.950368i | ||||
\(289\) | −2.04952e25 | −0.296637 | ||||||||
\(290\) | −1.21103e25 | −0.169034 | ||||||||
\(291\) | 8.79593e24 | + | 4.66592e25i | 0.118415 | + | 0.628147i | ||||
\(292\) | − | 7.05283e25i | − | 0.915890i | ||||||
\(293\) | −2.40398e25 | −0.301177 | −0.150588 | − | 0.988597i | \(-0.548117\pi\) | ||||
−0.150588 | + | 0.988597i | \(0.548117\pi\) | |||||||
\(294\) | −3.57624e25 | + | 1.62519e25i | −0.432294 | + | 0.196452i | ||||
\(295\) | 3.36422e25 | 0.392422 | ||||||||
\(296\) | − | 8.16748e25i | − | 0.919443i | ||||||
\(297\) | −3.92761e25 | − | 6.27882e25i | −0.426762 | − | 0.682237i | ||||
\(298\) | −6.62791e25 | −0.695194 | ||||||||
\(299\) | 1.30675e25 | 0.132325 | ||||||||
\(300\) | −7.13964e25 | + | 1.34592e25i | −0.698077 | + | 0.131597i | ||||
\(301\) | 4.32890e25 | − | 5.51720e25i | 0.408723 | − | 0.520919i | ||||
\(302\) | − | 1.01922e26i | − | 0.929385i | ||||||
\(303\) | 8.79405e25 | − | 1.65780e25i | 0.774536 | − | 0.146011i | ||||
\(304\) | − | 5.13951e25i | − | 0.437269i | ||||||
\(305\) | − | 5.81483e25i | − | 0.477956i | ||||||
\(306\) | 1.82566e25 | + | 4.67014e25i | 0.144992 | + | 0.370899i | ||||
\(307\) | 6.48510e25i | 0.497695i | 0.968543 | + | 0.248848i | \(0.0800518\pi\) | ||||
−0.968543 | + | 0.248848i | \(0.919948\pi\) | |||||||
\(308\) | −6.61140e25 | − | 5.18743e25i | −0.490355 | − | 0.384742i | ||||
\(309\) | −6.36778e24 | − | 3.37788e25i | −0.0456482 | − | 0.242147i | ||||
\(310\) | −1.21320e25 | −0.0840685 | ||||||||
\(311\) | −6.92031e25 | −0.463598 | −0.231799 | − | 0.972764i | \(-0.574461\pi\) | ||||
−0.231799 | + | 0.972764i | \(0.574461\pi\) | |||||||
\(312\) | 6.22501e25 | − | 1.17350e25i | 0.403196 | − | 0.0760082i | ||||
\(313\) | − | 3.85686e25i | − | 0.241556i | −0.992680 | − | 0.120778i | \(-0.961461\pi\) | ||
0.992680 | − | 0.120778i | \(-0.0385390\pi\) | |||||||
\(314\) | −3.11225e25 | −0.188501 | ||||||||
\(315\) | −1.41733e25 | + | 4.70427e25i | −0.0830254 | + | 0.275570i | ||||
\(316\) | 1.04555e25 | 0.0592420 | ||||||||
\(317\) | − | 1.86982e25i | − | 0.102489i | −0.998686 | − | 0.0512444i | \(-0.983681\pi\) | ||
0.998686 | − | 0.0512444i | \(-0.0163188\pi\) | |||||||
\(318\) | −1.01785e26 | + | 1.91879e25i | −0.539758 | + | 0.101752i | ||||
\(319\) | 1.93989e26 | 0.995346 | ||||||||
\(320\) | 6.38236e24 | 0.0316889 | ||||||||
\(321\) | 2.98477e25 | + | 1.58331e26i | 0.143419 | + | 0.760788i | ||||
\(322\) | −1.71275e25 | + | 2.18291e25i | −0.0796539 | + | 0.101519i | ||||
\(323\) | 2.17572e26i | 0.979439i | ||||||||
\(324\) | 1.30610e26 | − | 1.20536e26i | 0.569183 | − | 0.525285i | ||||
\(325\) | − | 1.05851e26i | − | 0.446601i | ||||||
\(326\) | 6.99653e25i | 0.285823i | ||||||||
\(327\) | 2.81882e26 | − | 5.31388e25i | 1.11511 | − | 0.210214i | ||||
\(328\) | − | 4.98246e25i | − | 0.190884i | ||||||
\(329\) | 1.47237e25 | − | 1.87654e25i | 0.0546335 | − | 0.0696306i | ||||
\(330\) | 3.00679e25 | − | 5.66822e24i | 0.108070 | − | 0.0203728i | ||||
\(331\) | −5.29120e26 | −1.84230 | −0.921149 | − | 0.389210i | \(-0.872748\pi\) | ||||
−0.921149 | + | 0.389210i | \(0.872748\pi\) | |||||||
\(332\) | −3.59264e26 | −1.21189 | ||||||||
\(333\) | 3.10942e26 | − | 1.21554e26i | 1.01628 | − | 0.397287i | ||||
\(334\) | − | 8.06060e25i | − | 0.255287i | ||||||
\(335\) | −5.51755e25 | −0.169346 | ||||||||
\(336\) | 5.80087e25 | − | 1.11707e26i | 0.172556 | − | 0.332290i | ||||
\(337\) | −2.44499e26 | −0.704959 | −0.352479 | − | 0.935820i | \(-0.614661\pi\) | ||||
−0.352479 | + | 0.935820i | \(0.614661\pi\) | |||||||
\(338\) | − | 1.29609e26i | − | 0.362252i | ||||||
\(339\) | 9.75284e25 | + | 5.17353e26i | 0.264262 | + | 1.40181i | ||||
\(340\) | 7.11630e25 | 0.186950 | ||||||||
\(341\) | 1.94336e26 | 0.495031 | ||||||||
\(342\) | −2.09087e26 | + | 8.17365e25i | −0.516479 | + | 0.201902i | ||||
\(343\) | −3.80285e26 | − | 1.72147e26i | −0.911006 | − | 0.412392i | ||||
\(344\) | − | 2.40123e26i | − | 0.557917i | ||||||
\(345\) | 6.42885e24 | + | 3.41027e25i | 0.0144888 | + | 0.0768579i | ||||
\(346\) | − | 3.22494e26i | − | 0.705055i | ||||||
\(347\) | 5.87259e26i | 1.24558i | 0.782391 | + | 0.622788i | \(0.214000\pi\) | ||||
−0.782391 | + | 0.622788i | \(0.786000\pi\) | |||||||
\(348\) | 8.62403e25 | + | 4.57474e26i | 0.177471 | + | 0.941421i | ||||
\(349\) | − | 9.24854e26i | − | 1.84674i | −0.383909 | − | 0.923371i | \(-0.625422\pi\) | ||
0.383909 | − | 0.923371i | \(-0.374578\pi\) | |||||||
\(350\) | 1.76823e26 | + | 1.38739e26i | 0.342629 | + | 0.268833i | ||||
\(351\) | 1.37321e26 | + | 2.19526e26i | 0.258233 | + | 0.412821i | ||||
\(352\) | −4.49899e26 | −0.821139 | ||||||||
\(353\) | 9.28342e26 | 1.64465 | 0.822326 | − | 0.569017i | \(-0.192676\pi\) | ||||
0.822326 | + | 0.569017i | \(0.192676\pi\) | |||||||
\(354\) | 6.97423e25 | + | 3.69958e26i | 0.119939 | + | 0.636235i | ||||
\(355\) | 2.80511e26i | 0.468330i | ||||||||
\(356\) | −1.07032e26 | −0.173496 | ||||||||
\(357\) | −2.45570e26 | + | 4.72891e26i | −0.386508 | + | 0.744295i | ||||
\(358\) | 4.52331e26 | 0.691328 | ||||||||
\(359\) | 9.86718e26i | 1.46454i | 0.681014 | + | 0.732270i | \(0.261539\pi\) | ||||
−0.681014 | + | 0.732270i | \(0.738461\pi\) | |||||||
\(360\) | 6.12509e25 | + | 1.56684e26i | 0.0882950 | + | 0.225864i | ||||
\(361\) | −2.59883e26 | −0.363876 | ||||||||
\(362\) | 3.55045e26 | 0.482885 | ||||||||
\(363\) | 2.62124e26 | − | 4.94140e25i | 0.346327 | − | 0.0652876i | ||||
\(364\) | 2.31154e26 | + | 1.81368e26i | 0.296713 | + | 0.232807i | ||||
\(365\) | 2.72885e26i | 0.340333i | ||||||||
\(366\) | 6.39446e26 | − | 1.20545e26i | 0.774913 | − | 0.146082i | ||||
\(367\) | 2.46775e26i | 0.290608i | 0.989387 | + | 0.145304i | \(0.0464161\pi\) | ||||
−0.989387 | + | 0.145304i | \(0.953584\pi\) | |||||||
\(368\) | − | 8.89072e25i | − | 0.101750i | ||||||
\(369\) | 1.89686e26 | − | 7.41524e25i | 0.210989 | − | 0.0824799i | ||||
\(370\) | 1.37930e26i | 0.149122i | ||||||||
\(371\) | −8.65947e26 | − | 6.79439e26i | −0.910050 | − | 0.714043i | ||||
\(372\) | 8.63948e25 | + | 4.58293e26i | 0.0882647 | + | 0.468212i | ||||
\(373\) | −9.39882e26 | −0.933535 | −0.466768 | − | 0.884380i | \(-0.654582\pi\) | ||||
−0.466768 | + | 0.884380i | \(0.654582\pi\) | |||||||
\(374\) | 3.31843e26 | 0.320465 | ||||||||
\(375\) | 5.77437e26 | − | 1.08855e26i | 0.542221 | − | 0.102216i | ||||
\(376\) | − | 8.16717e25i | − | 0.0745760i | ||||||
\(377\) | −6.78241e26 | −0.602282 | ||||||||
\(378\) | −5.46703e26 | − | 5.83393e25i | −0.472158 | − | 0.0503846i | ||||
\(379\) | 1.36756e27 | 1.14877 | 0.574387 | − | 0.818584i | \(-0.305240\pi\) | ||||
0.574387 | + | 0.818584i | \(0.305240\pi\) | |||||||
\(380\) | 3.18604e26i | 0.260330i | ||||||||
\(381\) | −2.27861e25 | + | 4.29551e24i | −0.0181117 | + | 0.00341431i | ||||
\(382\) | 3.24069e26 | 0.250595 | ||||||||
\(383\) | 6.34635e26 | 0.477460 | 0.238730 | − | 0.971086i | \(-0.423269\pi\) | ||||
0.238730 | + | 0.971086i | \(0.423269\pi\) | |||||||
\(384\) | −2.45002e26 | − | 1.29965e27i | −0.179346 | − | 0.951365i | ||||
\(385\) | 2.55806e26 | + | 2.00710e26i | 0.182210 | + | 0.142966i | ||||
\(386\) | − | 1.08235e27i | − | 0.750244i | ||||||
\(387\) | 9.14167e26 | − | 3.57367e26i | 0.616681 | − | 0.241073i | ||||
\(388\) | 7.54075e26i | 0.495087i | ||||||||
\(389\) | − | 7.80106e25i | − | 0.0498520i | −0.999689 | − | 0.0249260i | \(-0.992065\pi\) | ||
0.999689 | − | 0.0249260i | \(-0.00793502\pi\) | |||||||
\(390\) | −1.05126e26 | + | 1.98178e25i | −0.0653932 | + | 0.0123275i | ||||
\(391\) | 3.76373e26i | 0.227910i | ||||||||
\(392\) | −1.38829e27 | + | 3.40051e26i | −0.818421 | + | 0.200466i | ||||
\(393\) | −2.11358e27 | + | 3.98440e26i | −1.21310 | + | 0.228687i | ||||
\(394\) | −4.24405e26 | −0.237176 | ||||||||
\(395\) | −4.04539e25 | −0.0220136 | ||||||||
\(396\) | −4.28242e26 | − | 1.09547e27i | −0.226929 | − | 0.580498i | ||||
\(397\) | − | 2.38734e27i | − | 1.23201i | −0.787742 | − | 0.616005i | \(-0.788750\pi\) | ||
0.787742 | − | 0.616005i | \(-0.211250\pi\) | |||||||
\(398\) | 8.11902e26 | 0.408067 | ||||||||
\(399\) | −2.11718e27 | − | 1.09944e27i | −1.03644 | − | 0.538216i | ||||
\(400\) | −7.20179e26 | −0.343408 | ||||||||
\(401\) | − | 4.27170e27i | − | 1.98420i | −0.125460 | − | 0.992099i | \(-0.540041\pi\) | ||
0.125460 | − | 0.992099i | \(-0.459959\pi\) | |||||||
\(402\) | −1.14382e26 | − | 6.06755e26i | −0.0517588 | − | 0.274562i | ||||
\(403\) | −6.79457e26 | −0.299543 | ||||||||
\(404\) | 1.42124e27 | 0.610466 | ||||||||
\(405\) | −5.05349e26 | + | 4.66374e26i | −0.211502 | + | 0.195189i | ||||
\(406\) | 8.88970e26 | − | 1.13300e27i | 0.362547 | − | 0.462067i | ||||
\(407\) | − | 2.20944e27i | − | 0.878093i | ||||||
\(408\) | 3.37996e26 | + | 1.79295e27i | 0.130912 | + | 0.694442i | ||||
\(409\) | 2.55709e27i | 0.965276i | 0.875820 | + | 0.482638i | \(0.160321\pi\) | ||||
−0.875820 | + | 0.482638i | \(0.839679\pi\) | |||||||
\(410\) | 8.41424e25i | 0.0309588i | ||||||||
\(411\) | −6.70355e25 | − | 3.55599e26i | −0.0240417 | − | 0.127533i | ||||
\(412\) | − | 5.45910e26i | − | 0.190854i | ||||||
\(413\) | −2.46955e27 | + | 3.14745e27i | −0.841672 | + | 1.07271i | ||||
\(414\) | −3.61695e26 | + | 1.41394e26i | −0.120182 | + | 0.0469815i | ||||
\(415\) | 1.39005e27 | 0.450324 | ||||||||
\(416\) | 1.57298e27 | 0.496870 | ||||||||
\(417\) | −1.25852e26 | − | 6.67597e26i | −0.0387641 | − | 0.205630i | ||||
\(418\) | 1.48569e27i | 0.446249i | ||||||||
\(419\) | −5.10810e27 | −1.49628 | −0.748139 | − | 0.663542i | \(-0.769052\pi\) | ||||
−0.748139 | + | 0.663542i | \(0.769052\pi\) | |||||||
\(420\) | −3.59602e26 | + | 6.92482e26i | −0.102732 | + | 0.197830i | ||||
\(421\) | 1.00536e27 | 0.280129 | 0.140065 | − | 0.990142i | \(-0.455269\pi\) | ||||
0.140065 | + | 0.990142i | \(0.455269\pi\) | |||||||
\(422\) | − | 2.51017e26i | − | 0.0682217i | ||||||
\(423\) | 3.10931e26 | − | 1.21549e26i | 0.0824309 | − | 0.0322239i | ||||
\(424\) | −3.76883e27 | −0.974687 | ||||||||
\(425\) | 3.04876e27 | 0.769199 | ||||||||
\(426\) | −3.08473e27 | + | 5.81515e26i | −0.759304 | + | 0.143140i | ||||
\(427\) | 5.44016e27 | + | 4.26845e27i | 1.30653 | + | 1.02513i | ||||
\(428\) | 2.55884e27i | 0.599630i | ||||||||
\(429\) | 1.68397e27 | − | 3.17452e26i | 0.385063 | − | 0.0725899i | ||||
\(430\) | 4.05513e26i | 0.0904869i | ||||||||
\(431\) | − | 5.86068e27i | − | 1.27625i | −0.769932 | − | 0.638126i | \(-0.779710\pi\) | ||
0.769932 | − | 0.638126i | \(-0.220290\pi\) | |||||||
\(432\) | 1.49359e27 | − | 9.34291e26i | 0.317433 | − | 0.198565i | ||||
\(433\) | − | 5.82855e27i | − | 1.20903i | −0.796593 | − | 0.604516i | \(-0.793367\pi\) | ||
0.796593 | − | 0.604516i | \(-0.206633\pi\) | |||||||
\(434\) | 8.90563e26 | − | 1.13503e27i | 0.180311 | − | 0.229807i | ||||
\(435\) | −3.33677e26 | − | 1.77004e27i | −0.0659462 | − | 0.349821i | ||||
\(436\) | 4.55559e27 | 0.878894 | ||||||||
\(437\) | −1.68506e27 | −0.317366 | ||||||||
\(438\) | −3.00087e27 | + | 5.65707e26i | −0.551784 | + | 0.104019i | ||||
\(439\) | 1.00121e28i | 1.79742i | 0.438545 | + | 0.898709i | \(0.355494\pi\) | ||||
−0.438545 | + | 0.898709i | \(0.644506\pi\) | |||||||
\(440\) | 1.11333e27 | 0.195152 | ||||||||
\(441\) | −3.36075e27 | − | 4.77925e27i | −0.575216 | − | 0.818002i | ||||
\(442\) | −1.16022e27 | −0.193913 | ||||||||
\(443\) | 7.11611e27i | 1.16146i | 0.814097 | + | 0.580729i | \(0.197233\pi\) | ||||
−0.814097 | + | 0.580729i | \(0.802767\pi\) | |||||||
\(444\) | 5.21041e27 | − | 9.82236e26i | 0.830521 | − | 0.156565i | ||||
\(445\) | 4.14125e26 | 0.0644690 | ||||||||
\(446\) | 6.05127e27 | 0.920091 | ||||||||
\(447\) | −1.82621e27 | − | 9.68737e27i | −0.271220 | − | 1.43872i | ||||
\(448\) | −4.68506e26 | + | 5.97113e26i | −0.0679667 | + | 0.0866239i | ||||
\(449\) | 4.62514e27i | 0.655448i | 0.944774 | + | 0.327724i | \(0.106282\pi\) | ||||
−0.944774 | + | 0.327724i | \(0.893718\pi\) | |||||||
\(450\) | 1.14534e27 | + | 2.92985e27i | 0.158564 | + | 0.405615i | ||||
\(451\) | − | 1.34784e27i | − | 0.182299i | ||||||
\(452\) | 8.36111e27i | 1.10487i | ||||||||
\(453\) | 1.48970e28 | − | 2.80829e27i | 1.92339 | − | 0.362586i | ||||
\(454\) | 2.33664e27i | 0.294785i | ||||||||
\(455\) | −8.94372e26 | − | 7.01741e26i | −0.110255 | − | 0.0865082i | ||||
\(456\) | −8.02720e27 | + | 1.51324e27i | −0.967015 | + | 0.182296i | ||||
\(457\) | −5.65110e27 | −0.665293 | −0.332647 | − | 0.943052i | \(-0.607942\pi\) | ||||
−0.332647 | + | 0.943052i | \(0.607942\pi\) | |||||||
\(458\) | 4.18334e27 | 0.481322 | ||||||||
\(459\) | −6.32287e27 | + | 3.95516e27i | −0.711018 | + | 0.444766i | ||||
\(460\) | 5.51145e26i | 0.0605772i | ||||||||
\(461\) | −1.27891e28 | −1.37398 | −0.686990 | − | 0.726666i | \(-0.741069\pi\) | ||||
−0.686990 | + | 0.726666i | \(0.741069\pi\) | |||||||
\(462\) | −1.67687e27 | + | 3.22913e27i | −0.176100 | + | 0.339114i | ||||
\(463\) | 8.88393e27 | 0.912021 | 0.456010 | − | 0.889974i | \(-0.349278\pi\) | ||||
0.456010 | + | 0.889974i | \(0.349278\pi\) | |||||||
\(464\) | 4.61456e27i | 0.463118i | ||||||||
\(465\) | −3.34275e26 | − | 1.77321e27i | −0.0327981 | − | 0.173982i | ||||
\(466\) | 3.56955e27 | 0.342421 | ||||||||
\(467\) | 2.02160e28 | 1.89613 | 0.948066 | − | 0.318072i | \(-0.103035\pi\) | ||||
0.948066 | + | 0.318072i | \(0.103035\pi\) | |||||||
\(468\) | 1.49726e27 | + | 3.83009e27i | 0.137314 | + | 0.351259i | ||||
\(469\) | 4.05023e27 | − | 5.16204e27i | 0.363216 | − | 0.462920i | ||||
\(470\) | 1.37925e26i | 0.0120953i | ||||||||
\(471\) | −8.57528e26 | − | 4.54888e27i | −0.0735409 | − | 0.390108i | ||||
\(472\) | 1.36985e28i | 1.14890i | ||||||||
\(473\) | − | 6.49572e27i | − | 0.532826i | ||||||
\(474\) | −8.38634e25 | − | 4.44865e26i | −0.00672822 | − | 0.0356908i | ||||
\(475\) | 1.36496e28i | 1.07112i | ||||||||
\(476\) | −5.22382e27 | + | 6.65778e27i | −0.400973 | + | 0.511042i | ||||
\(477\) | −5.60902e27 | − | 1.43482e28i | −0.421157 | − | 1.07735i | ||||
\(478\) | −1.56832e27 | −0.115197 | ||||||||
\(479\) | −1.43805e28 | −1.03336 | −0.516680 | − | 0.856179i | \(-0.672832\pi\) | ||||
−0.516680 | + | 0.856179i | \(0.672832\pi\) | |||||||
\(480\) | 7.73865e26 | + | 4.10508e27i | 0.0544042 | + | 0.288595i | ||||
\(481\) | 7.72485e27i | 0.531333i | ||||||||
\(482\) | −6.96811e27 | −0.468944 | ||||||||
\(483\) | −3.66246e27 | − | 1.90190e27i | −0.241173 | − | 0.125240i | ||||
\(484\) | 4.23626e27 | 0.272965 | ||||||||
\(485\) | − | 2.91764e27i | − | 0.183968i | ||||||
\(486\) | −6.17625e27 | − | 4.59042e27i | −0.381105 | − | 0.283251i | ||||
\(487\) | 8.25040e26 | 0.0498219 | 0.0249110 | − | 0.999690i | \(-0.492070\pi\) | ||||
0.0249110 | + | 0.999690i | \(0.492070\pi\) | |||||||
\(488\) | 2.36770e28 | 1.39932 | ||||||||
\(489\) | −1.02261e28 | + | 1.92777e27i | −0.591519 | + | 0.111510i | ||||
\(490\) | 2.34451e27 | − | 5.74269e26i | 0.132737 | − | 0.0325130i | ||||
\(491\) | 4.28429e27i | 0.237423i | 0.992929 | + | 0.118712i | \(0.0378764\pi\) | ||||
−0.992929 | + | 0.118712i | \(0.962124\pi\) | |||||||
\(492\) | 3.17854e27 | − | 5.99200e26i | 0.172423 | − | 0.0325041i | ||||
\(493\) | − | 1.95349e28i | − | 1.03734i | ||||||
\(494\) | − | 5.19442e27i | − | 0.270025i | ||||||
\(495\) | 1.65694e27 | + | 4.23855e27i | 0.0843240 | + | 0.215706i | ||||
\(496\) | 4.62283e27i | 0.230330i | ||||||||
\(497\) | −2.62437e28 | − | 2.05913e28i | −1.28021 | − | 1.00448i | ||||
\(498\) | 2.88165e27 | + | 1.52861e28i | 0.137636 | + | 0.730112i | ||||
\(499\) | 6.11301e26 | 0.0285890 | 0.0142945 | − | 0.999898i | \(-0.495450\pi\) | ||||
0.0142945 | + | 0.999898i | \(0.495450\pi\) | |||||||
\(500\) | 9.33214e27 | 0.427362 | ||||||||
\(501\) | 1.17814e28 | − | 2.22096e27i | 0.528324 | − | 0.0995966i | ||||
\(502\) | − | 6.26854e27i | − | 0.275282i | ||||||
\(503\) | −3.59743e28 | −1.54713 | −0.773567 | − | 0.633714i | \(-0.781530\pi\) | ||||
−0.773567 | + | 0.633714i | \(0.781530\pi\) | |||||||
\(504\) | −1.91550e28 | − | 5.77114e27i | −0.806792 | − | 0.243075i | ||||
\(505\) | −5.49899e27 | −0.226842 | ||||||||
\(506\) | 2.57006e27i | 0.103840i | ||||||||
\(507\) | 1.89437e28 | − | 3.57116e27i | 0.749690 | − | 0.141327i | ||||
\(508\) | −3.68254e26 | −0.0142751 | ||||||||
\(509\) | 3.19042e28 | 1.21146 | 0.605732 | − | 0.795669i | \(-0.292880\pi\) | ||||
0.605732 | + | 0.795669i | \(0.292880\pi\) | |||||||
\(510\) | −5.70798e26 | − | 3.02788e27i | −0.0212322 | − | 0.112629i | ||||
\(511\) | −2.55302e28 | − | 2.00315e28i | −0.930327 | − | 0.729952i | ||||
\(512\) | − | 1.95395e28i | − | 0.697556i | ||||||
\(513\) | −1.77077e28 | − | 2.83081e28i | −0.619339 | − | 0.990098i | ||||
\(514\) | − | 7.28339e27i | − | 0.249586i | ||||||
\(515\) | 2.11221e27i | 0.0709188i | ||||||||
\(516\) | 1.53185e28 | − | 2.88776e27i | 0.503959 | − | 0.0950035i | ||||
\(517\) | − | 2.20935e27i | − | 0.0712221i | ||||||
\(518\) | −1.29043e28 | − | 1.01249e28i | −0.407635 | − | 0.319838i | ||||
\(519\) | 4.71358e28 | − | 8.88577e27i | 1.45913 | − | 0.275067i | ||||
\(520\) | −3.89254e27 | −0.118086 | ||||||||
\(521\) | 2.39651e28 | 0.712496 | 0.356248 | − | 0.934391i | \(-0.384056\pi\) | ||||
0.356248 | + | 0.934391i | \(0.384056\pi\) | |||||||
\(522\) | 1.87731e28 | − | 7.33879e27i | 0.547010 | − | 0.213838i | ||||
\(523\) | − | 9.11876e27i | − | 0.260416i | −0.991487 | − | 0.130208i | \(-0.958435\pi\) | ||
0.991487 | − | 0.130208i | \(-0.0415645\pi\) | |||||||
\(524\) | −3.41583e28 | −0.956130 | ||||||||
\(525\) | −1.54060e28 | + | 2.96672e28i | −0.422686 | + | 0.813962i | ||||
\(526\) | 7.27087e27 | 0.195540 | ||||||||
\(527\) | − | 1.95700e28i | − | 0.515915i | ||||||
\(528\) | −2.15985e27 | − | 1.14572e28i | −0.0558171 | − | 0.296090i | ||||
\(529\) | 3.65566e28 | 0.926151 | ||||||||
\(530\) | 6.36469e27 | 0.158081 | ||||||||
\(531\) | −5.21515e28 | + | 2.03871e28i | −1.26991 | + | 0.496435i | ||||
\(532\) | −2.98075e28 | − | 2.33876e28i | −0.711630 | − | 0.558358i | ||||
\(533\) | 4.71244e27i | 0.110309i | ||||||||
\(534\) | 8.58505e26 | + | 4.55406e27i | 0.0197042 | + | 0.104524i | ||||
\(535\) | − | 9.90056e27i | − | 0.222815i | ||||||
\(536\) | − | 2.24665e28i | − | 0.495799i | ||||||
\(537\) | 1.24632e28 | + | 6.61127e28i | 0.269711 | + | 1.43072i | ||||
\(538\) | − | 4.30556e28i | − | 0.913725i | ||||||
\(539\) | −3.75555e28 | + | 9.19895e27i | −0.781613 | + | 0.191450i | ||||
\(540\) | −9.25894e27 | + | 5.79178e27i | −0.188985 | + | 0.118216i | ||||
\(541\) | −3.18902e28 | −0.638389 | −0.319194 | − | 0.947689i | \(-0.603412\pi\) | ||||
−0.319194 | + | 0.947689i | \(0.603412\pi\) | |||||||
\(542\) | 3.39865e28 | 0.667288 | ||||||||
\(543\) | 9.78266e27 | + | 5.18935e28i | 0.188390 | + | 0.999343i | ||||
\(544\) | 4.53055e28i | 0.855780i | ||||||||
\(545\) | −1.76263e28 | −0.326586 | ||||||||
\(546\) | 5.86284e27 | − | 1.12900e28i | 0.106558 | − | 0.205197i | ||||
\(547\) | −4.10267e28 | −0.731475 | −0.365738 | − | 0.930718i | \(-0.619183\pi\) | ||||
−0.365738 | + | 0.930718i | \(0.619183\pi\) | |||||||
\(548\) | − | 5.74695e27i | − | 0.100517i | ||||||
\(549\) | 3.52377e28 | + | 9.01402e28i | 0.604641 | + | 1.54671i | ||||
\(550\) | 2.08184e28 | 0.350461 | ||||||||
\(551\) | 8.74599e28 | 1.44450 | ||||||||
\(552\) | −1.38861e28 | + | 2.61772e27i | −0.225019 | + | 0.0424193i | ||||
\(553\) | 2.96958e27 | − | 3.78474e27i | 0.0472151 | − | 0.0601758i | ||||
\(554\) | 2.58153e28i | 0.402741i | ||||||||
\(555\) | −2.01599e28 | + | 3.80043e27i | −0.308611 | + | 0.0581776i | ||||
\(556\) | − | 1.07893e28i | − | 0.162071i | ||||||
\(557\) | 4.59822e28i | 0.677813i | 0.940820 | + | 0.338906i | \(0.110057\pi\) | ||||
−0.940820 | + | 0.338906i | \(0.889943\pi\) | |||||||
\(558\) | 1.88067e28 | − | 7.35194e27i | 0.272053 | − | 0.106351i | ||||
\(559\) | 2.27110e28i | 0.322412i | ||||||||
\(560\) | −4.77445e27 | + | 6.08505e27i | −0.0665195 | + | 0.0847793i | ||||
\(561\) | 9.14335e27 | + | 4.85022e28i | 0.125025 | + | 0.663210i | ||||
\(562\) | 5.46976e28 | 0.734070 | ||||||||
\(563\) | 1.17978e29 | 1.55405 | 0.777023 | − | 0.629472i | \(-0.216729\pi\) | ||||
0.777023 | + | 0.629472i | \(0.216729\pi\) | |||||||
\(564\) | 5.21021e27 | − | 9.82199e26i | 0.0673635 | − | 0.0126990i | ||||
\(565\) | − | 3.23505e28i | − | 0.410555i | ||||||
\(566\) | −5.78620e27 | −0.0720810 | ||||||||
\(567\) | −6.53656e27 | − | 8.15136e28i | −0.0799332 | − | 0.996800i | ||||
\(568\) | −1.14219e29 | −1.37114 | ||||||||
\(569\) | 6.38010e28i | 0.751881i | 0.926644 | + | 0.375940i | \(0.122680\pi\) | ||||
−0.926644 | + | 0.375940i | \(0.877320\pi\) | |||||||
\(570\) | 1.35561e28 | − | 2.55552e27i | 0.156837 | − | 0.0295661i | ||||
\(571\) | −8.11711e28 | −0.921982 | −0.460991 | − | 0.887405i | \(-0.652506\pi\) | ||||
−0.460991 | + | 0.887405i | \(0.652506\pi\) | |||||||
\(572\) | 2.72151e28 | 0.303495 | ||||||||
\(573\) | 8.92916e27 | + | 4.73660e28i | 0.0977658 | + | 0.518613i | ||||
\(574\) | −7.87209e27 | − | 6.17659e27i | −0.0846283 | − | 0.0664009i | ||||
\(575\) | 2.36121e28i | 0.249242i | ||||||||
\(576\) | −9.89381e27 | + | 3.86770e27i | −0.102548 | + | 0.0400882i | ||||
\(577\) | − | 2.97701e28i | − | 0.302994i | −0.988458 | − | 0.151497i | \(-0.951591\pi\) | ||
0.988458 | − | 0.151497i | \(-0.0484095\pi\) | |||||||
\(578\) | 1.40933e28i | 0.140854i | ||||||||
\(579\) | 1.58197e29 | − | 2.98224e28i | 1.55265 | − | 0.292697i | ||||
\(580\) | − | 2.86062e28i | − | 0.275718i | ||||||
\(581\) | −1.02038e29 | + | 1.30048e29i | −0.965861 | + | 1.23099i | ||||
\(582\) | 3.20847e28 | − | 6.04843e27i | 0.298268 | − | 0.0562278i | ||||
\(583\) | −1.01953e29 | −0.930851 | ||||||||
\(584\) | −1.11114e29 | −0.996403 | ||||||||
\(585\) | −5.79314e27 | − | 1.48192e28i | −0.0510244 | − | 0.130523i | ||||
\(586\) | 1.65307e28i | 0.143010i | ||||||||
\(587\) | −1.40022e28 | −0.118986 | −0.0594932 | − | 0.998229i | \(-0.518948\pi\) | ||||
−0.0594932 | + | 0.998229i | \(0.518948\pi\) | |||||||
\(588\) | −3.83893e28 | − | 8.44759e28i | −0.320441 | − | 0.705132i | ||||
\(589\) | 8.76166e28 | 0.718416 | ||||||||
\(590\) | − | 2.31337e28i | − | 0.186337i | ||||||
\(591\) | −1.16938e28 | − | 6.20311e28i | −0.0925306 | − | 0.490842i | ||||
\(592\) | 5.25576e28 | 0.408562 | ||||||||
\(593\) | 1.86937e29 | 1.42765 | 0.713824 | − | 0.700325i | \(-0.246962\pi\) | ||||
0.713824 | + | 0.700325i | \(0.246962\pi\) | |||||||
\(594\) | −4.31756e28 | + | 2.70078e28i | −0.323952 | + | 0.202643i | ||||
\(595\) | 2.02118e28 | − | 2.57600e28i | 0.148997 | − | 0.189897i | ||||
\(596\) | − | 1.56561e29i | − | 1.13396i | ||||||
\(597\) | 2.23706e28 | + | 1.18668e29i | 0.159201 | + | 0.844505i | ||||
\(598\) | − | 8.98570e27i | − | 0.0628332i | ||||||
\(599\) | − | 3.47967e28i | − | 0.239087i | −0.992829 | − | 0.119544i | \(-0.961857\pi\) | ||
0.992829 | − | 0.119544i | \(-0.0381432\pi\) | |||||||
\(600\) | 2.12045e28 | + | 1.12482e29i | 0.143166 | + | 0.759443i | ||||
\(601\) | − | 9.77592e28i | − | 0.648598i | −0.945955 | − | 0.324299i | \(-0.894872\pi\) | ||
0.945955 | − | 0.324299i | \(-0.105128\pi\) | |||||||
\(602\) | −3.79385e28 | − | 2.97672e28i | −0.247353 | − | 0.194078i | ||||
\(603\) | 8.55319e28 | − | 3.34362e28i | 0.548020 | − | 0.214232i | ||||
\(604\) | 2.40755e29 | 1.51596 | ||||||||
\(605\) | −1.63908e28 | −0.101430 | ||||||||
\(606\) | −1.13997e28 | − | 6.04714e28i | −0.0693317 | − | 0.367779i | ||||
\(607\) | − | 6.18499e28i | − | 0.369707i | −0.982766 | − | 0.184854i | \(-0.940819\pi\) | ||
0.982766 | − | 0.184854i | \(-0.0591811\pi\) | |||||||
\(608\) | −2.02837e29 | −1.19168 | ||||||||
\(609\) | 1.90093e29 | + | 9.87144e28i | 1.09770 | + | 0.570031i | ||||
\(610\) | −3.99851e28 | −0.226952 | ||||||||
\(611\) | 7.72456e27i | 0.0430964i | ||||||||
\(612\) | −1.10315e29 | + | 4.31246e28i | −0.604988 | + | 0.236502i | ||||
\(613\) | −2.24650e29 | −1.21107 | −0.605537 | − | 0.795817i | \(-0.707042\pi\) | ||||
−0.605537 | + | 0.795817i | \(0.707042\pi\) | |||||||
\(614\) | 4.45941e28 | 0.236325 | ||||||||
\(615\) | −1.22983e28 | + | 2.31840e27i | −0.0640701 | + | 0.0120781i | ||||
\(616\) | −8.17258e28 | + | 1.04160e29i | −0.418564 | + | 0.533461i | ||||
\(617\) | − | 5.06622e27i | − | 0.0255088i | −0.999919 | − | 0.0127544i | \(-0.995940\pi\) | ||
0.999919 | − | 0.0127544i | \(-0.00405996\pi\) | |||||||
\(618\) | −2.32276e28 | + | 4.37874e27i | −0.114981 | + | 0.0216755i | ||||
\(619\) | 3.95071e28i | 0.192275i | 0.995368 | + | 0.0961376i | \(0.0306489\pi\) | ||||
−0.995368 | + | 0.0961376i | \(0.969351\pi\) | |||||||
\(620\) | − | 2.86574e28i | − | 0.137127i | ||||||
\(621\) | −3.06320e28 | − | 4.89695e28i | −0.144117 | − | 0.230390i | ||||
\(622\) | 4.75868e28i | 0.220134i | ||||||||
\(623\) | −3.03994e28 | + | 3.87442e28i | −0.138274 | + | 0.176231i | ||||
\(624\) | 7.55147e27 | + | 4.00578e28i | 0.0337749 | + | 0.179163i | ||||
\(625\) | 1.72432e29 | 0.758366 | ||||||||
\(626\) | −2.65213e28 | −0.114700 | ||||||||
\(627\) | −2.17149e29 | + | 4.09357e28i | −0.923525 | + | 0.174098i | ||||
\(628\) | − | 7.35159e28i | − | 0.307471i | ||||||
\(629\) | −2.22494e29 | −0.915137 | ||||||||
\(630\) | 3.23484e28 | + | 9.74614e27i | 0.130851 | + | 0.0394237i | ||||
\(631\) | −1.04298e29 | −0.414922 | −0.207461 | − | 0.978243i | \(-0.566520\pi\) | ||||
−0.207461 | + | 0.978243i | \(0.566520\pi\) | |||||||
\(632\) | − | 1.64722e28i | − | 0.0644498i | ||||||
\(633\) | 3.66887e28 | − | 6.91635e27i | 0.141187 | − | 0.0266157i | ||||
\(634\) | −1.28576e28 | −0.0486657 | ||||||||
\(635\) | 1.42483e27 | 0.00530445 | ||||||||
\(636\) | −4.53246e28 | − | 2.40431e29i | −0.165972 | − | 0.880421i | ||||
\(637\) | 1.31305e29 | − | 3.21622e28i | 0.472953 | − | 0.115846i | ||||
\(638\) | − | 1.33394e29i | − | 0.472629i | ||||||
\(639\) | −1.69989e29 | − | 4.34842e29i | −0.592463 | − | 1.51556i | ||||
\(640\) | 8.12679e28i | 0.278631i | ||||||||
\(641\) | − | 5.90673e29i | − | 1.99222i | −0.0881055 | − | 0.996111i | \(-0.528081\pi\) | ||
0.0881055 | − | 0.996111i | \(-0.471919\pi\) | |||||||
\(642\) | 1.08875e29 | − | 2.05244e28i | 0.361251 | − | 0.0681010i | ||||
\(643\) | − | 3.63466e29i | − | 1.18645i | −0.805038 | − | 0.593224i | \(-0.797855\pi\) | ||
0.805038 | − | 0.593224i | \(-0.202145\pi\) | |||||||
\(644\) | −5.15634e28 | − | 4.04576e28i | −0.165592 | − | 0.129927i | ||||
\(645\) | −5.92698e28 | + | 1.11732e28i | −0.187265 | + | 0.0353021i | ||||
\(646\) | 1.49611e29 | 0.465075 | ||||||||
\(647\) | −1.11731e29 | −0.341728 | −0.170864 | − | 0.985295i | \(-0.554656\pi\) | ||||
−0.170864 | + | 0.985295i | \(0.554656\pi\) | |||||||
\(648\) | −1.89900e29 | − | 2.05770e29i | −0.571461 | − | 0.619219i | ||||
\(649\) | 3.70568e29i | 1.09723i | ||||||||
\(650\) | −7.27873e28 | −0.212063 | ||||||||
\(651\) | 1.90434e29 | + | 9.88913e28i | 0.545938 | + | 0.283503i | ||||
\(652\) | −1.65268e29 | −0.466218 | ||||||||
\(653\) | 1.74296e29i | 0.483836i | 0.970297 | + | 0.241918i | \(0.0777765\pi\) | ||||
−0.970297 | + | 0.241918i | \(0.922223\pi\) | |||||||
\(654\) | −3.65404e28 | − | 1.93834e29i | −0.0998175 | − | 0.529496i | ||||
\(655\) | 1.32164e29 | 0.355286 | ||||||||
\(656\) | 3.20621e28 | 0.0848207 | ||||||||
\(657\) | −1.65368e29 | − | 4.23021e29i | −0.430541 | − | 1.10135i | ||||
\(658\) | −1.29038e28 | − | 1.01246e28i | −0.0330633 | − | 0.0259421i | ||||
\(659\) | 3.51653e29i | 0.886783i | 0.896328 | + | 0.443391i | \(0.146225\pi\) | ||||
−0.896328 | + | 0.443391i | \(0.853775\pi\) | |||||||
\(660\) | 1.33891e28 | + | 7.10246e28i | 0.0332309 | + | 0.176278i | ||||
\(661\) | 7.04382e29i | 1.72065i | 0.509744 | + | 0.860326i | \(0.329740\pi\) | ||||
−0.509744 | + | 0.860326i | \(0.670260\pi\) | |||||||
\(662\) | 3.63844e29i | 0.874794i | ||||||||
\(663\) | −3.19679e28 | − | 1.69578e29i | −0.0756522 | − | 0.401308i | ||||
\(664\) | 5.66005e29i | 1.31842i | ||||||||
\(665\) | 1.15330e29 | + | 9.04902e28i | 0.264433 | + | 0.207479i | ||||
\(666\) | −8.35853e28 | − | 2.13816e29i | −0.188647 | − | 0.482571i | ||||
\(667\) | 1.51295e29 | 0.336126 | ||||||||
\(668\) | 1.90403e29 | 0.416409 | ||||||||
\(669\) | 1.66732e29 | + | 8.84455e29i | 0.358960 | + | 1.90415i | ||||
\(670\) | 3.79409e28i | 0.0804121i | ||||||||
\(671\) | 6.40502e29 | 1.33639 | ||||||||
\(672\) | −4.40864e29 | − | 2.28939e29i | −0.905581 | − | 0.470264i | ||||
\(673\) | 4.00984e29 | 0.810902 | 0.405451 | − | 0.914117i | \(-0.367114\pi\) | ||||
0.405451 | + | 0.914117i | \(0.367114\pi\) | |||||||
\(674\) | 1.68128e29i | 0.334742i | ||||||||
\(675\) | −3.96670e29 | + | 2.48130e29i | −0.777571 | + | 0.486396i | ||||
\(676\) | 3.06156e29 | 0.590884 | ||||||||
\(677\) | 2.14790e29 | 0.408162 | 0.204081 | − | 0.978954i | \(-0.434579\pi\) | ||||
0.204081 | + | 0.978954i | \(0.434579\pi\) | |||||||
\(678\) | 3.55753e29 | − | 6.70644e28i | 0.665635 | − | 0.125482i | ||||
\(679\) | 2.72965e29 | + | 2.14173e29i | 0.502891 | + | 0.394578i | ||||
\(680\) | − | 1.12114e29i | − | 0.203384i | ||||||
\(681\) | −3.41523e29 | + | 6.43820e28i | −0.610064 | + | 0.115006i | ||||
\(682\) | − | 1.33633e29i | − | 0.235060i | ||||||
\(683\) | − | 5.53628e28i | − | 0.0958961i | −0.998850 | − | 0.0479480i | \(-0.984732\pi\) | ||
0.998850 | − | 0.0479480i | \(-0.0152682\pi\) | |||||||
\(684\) | −1.93073e29 | − | 4.93893e29i | −0.329331 | − | 0.842450i | ||||
\(685\) | 2.22359e28i | 0.0373511i | ||||||||
\(686\) | −1.18375e29 | + | 2.61499e29i | −0.195820 | + | 0.432581i | ||||
\(687\) | 1.15265e29 | + | 6.11438e29i | 0.187781 | + | 0.996108i | ||||
\(688\) | 1.54519e29 | 0.247915 | ||||||||
\(689\) | 3.56458e29 | 0.563257 | ||||||||
\(690\) | 2.34504e28 | − | 4.42073e27i | 0.0364951 | − | 0.00687985i | ||||
\(691\) | 2.55853e29i | 0.392168i | 0.980587 | + | 0.196084i | \(0.0628225\pi\) | ||||
−0.980587 | + | 0.196084i | \(0.937178\pi\) | |||||||
\(692\) | 7.61777e29 | 1.15004 | ||||||||
\(693\) | −5.18174e29 | − | 1.56119e29i | −0.770508 | − | 0.232143i | ||||
\(694\) | 4.03822e29 | 0.591447 | ||||||||
\(695\) | 4.17453e28i | 0.0602237i | ||||||||
\(696\) | 7.20730e29 | − | 1.35868e29i | 1.02418 | − | 0.193072i | ||||
\(697\) | −1.35729e29 | −0.189990 | ||||||||
\(698\) | −6.35966e29 | −0.876904 | ||||||||
\(699\) | 9.83527e28 | + | 5.21726e29i | 0.133591 | + | 0.708650i | ||||
\(700\) | −3.27721e29 | + | 4.17681e29i | −0.438505 | + | 0.558876i | ||||
\(701\) | 1.49094e29i | 0.196527i | 0.995160 | + | 0.0982633i | \(0.0313287\pi\) | ||||
−0.995160 | + | 0.0982633i | \(0.968671\pi\) | |||||||
\(702\) | 1.50955e29 | − | 9.44273e28i | 0.196023 | − | 0.122619i | ||||
\(703\) | − | 9.96126e29i | − | 1.27433i | ||||||
\(704\) | 7.03016e28i | 0.0886038i | ||||||||
\(705\) | −2.01591e28 | + | 3.80028e27i | −0.0250315 | + | 0.00471879i | ||||
\(706\) | − | 6.38365e29i | − | 0.780944i | ||||||
\(707\) | 4.03661e29 | − | 5.14467e29i | 0.486533 | − | 0.620089i | ||||
\(708\) | −8.73893e29 | + | 1.64741e29i | −1.03779 | + | 0.195638i | ||||
\(709\) | −1.33414e30 | −1.56104 | −0.780521 | − | 0.625130i | \(-0.785046\pi\) | ||||
−0.780521 | + | 0.625130i | \(0.785046\pi\) | |||||||
\(710\) | 1.92890e29 | 0.222381 | ||||||||
\(711\) | 6.27109e28 | − | 2.45150e28i | 0.0712381 | − | 0.0278484i | ||||
\(712\) | 1.68625e29i | 0.188747i | ||||||||
\(713\) | 1.51566e29 | 0.167171 | ||||||||
\(714\) | 3.25179e29 | + | 1.68864e29i | 0.353420 | + | 0.183529i | ||||
\(715\) | −1.05300e29 | −0.112775 | ||||||||
\(716\) | 1.06847e30i | 1.12765i | ||||||||
\(717\) | −4.32122e28 | − | 2.29225e29i | −0.0449423 | − | 0.238403i | ||||
\(718\) | 6.78507e29 | 0.695421 | ||||||||
\(719\) | −1.71233e30 | −1.72955 | −0.864775 | − | 0.502159i | \(-0.832539\pi\) | ||||
−0.864775 | + | 0.502159i | \(0.832539\pi\) | |||||||
\(720\) | −1.00826e29 | + | 3.94149e28i | −0.100364 | + | 0.0392346i | ||||
\(721\) | −1.97612e29 | − | 1.55050e29i | −0.193862 | − | 0.152108i | ||||
\(722\) | 1.78706e29i | 0.172782i | ||||||||
\(723\) | −1.91994e29 | − | 1.01846e30i | −0.182952 | − | 0.970492i | ||||
\(724\) | 8.38668e29i | 0.787653i | ||||||||
\(725\) | − | 1.22554e30i | − | 1.13443i | ||||||
\(726\) | −3.39791e28 | − | 1.80247e29i | −0.0310011 | − | 0.164450i | ||||
\(727\) | 1.15281e30i | 1.03668i | 0.855174 | + | 0.518341i | \(0.173450\pi\) | ||||
−0.855174 | + | 0.518341i | \(0.826550\pi\) | |||||||
\(728\) | 2.85737e29 | − | 3.64174e29i | 0.253272 | − | 0.322797i | ||||
\(729\) | 5.00760e29 | − | 1.02920e30i | 0.437513 | − | 0.899212i | ||||
\(730\) | 1.87647e29 | 0.161603 | ||||||||
\(731\) | −6.54129e29 | −0.555304 | ||||||||
\(732\) | 2.84744e29 | + | 1.51046e30i | 0.238280 | + | 1.26399i | ||||
\(733\) | − | 1.96769e30i | − | 1.62317i | −0.584233 | − | 0.811586i | \(-0.698605\pi\) | ||
0.584233 | − | 0.811586i | \(-0.301395\pi\) | |||||||
\(734\) | 1.69692e29 | 0.137992 | ||||||||
\(735\) | 1.48534e29 | + | 3.26851e29i | 0.119072 | + | 0.262019i | ||||
\(736\) | −3.50883e29 | −0.277297 | ||||||||
\(737\) | − | 6.07757e29i | − | 0.473501i | ||||||
\(738\) | −5.09901e28 | − | 1.30436e29i | −0.0391646 | − | 0.100186i | ||||
\(739\) | 1.29711e30 | 0.982226 | 0.491113 | − | 0.871096i | \(-0.336590\pi\) | ||||
0.491113 | + | 0.871096i | \(0.336590\pi\) | |||||||
\(740\) | −3.25811e29 | −0.243238 | ||||||||
\(741\) | 7.59217e29 | − | 1.43123e29i | 0.558824 | − | 0.105346i | ||||
\(742\) | −4.67209e29 | + | 5.95460e29i | −0.339055 | + | 0.432127i | ||||
\(743\) | − | 1.12719e30i | − | 0.806521i | −0.915085 | − | 0.403260i | \(-0.867877\pi\) | ||
0.915085 | − | 0.403260i | \(-0.132123\pi\) | |||||||
\(744\) | 7.22022e29 | − | 1.36111e29i | 0.509371 | − | 0.0960237i | ||||
\(745\) | 6.05758e29i | 0.421365i | ||||||||
\(746\) | 6.46300e29i | 0.443279i | ||||||||
\(747\) | −2.15483e30 | + | 8.42366e29i | −1.45729 | + | 0.569685i | ||||
\(748\) | 7.83860e29i | 0.522723i | ||||||||
\(749\) | 9.26264e29 | + | 7.26765e29i | 0.609082 | + | 0.477897i | ||||
\(750\) | −7.48530e28 | − | 3.97068e29i | −0.0485362 | − | 0.257467i | ||||
\(751\) | −2.62935e30 | −1.68124 | −0.840618 | − | 0.541629i | \(-0.817808\pi\) | ||||
−0.840618 | + | 0.541629i | \(0.817808\pi\) | |||||||
\(752\) | 5.25557e28 | 0.0331384 | ||||||||
\(753\) | 9.16211e29 | − | 1.72719e29i | 0.569703 | − | 0.107397i | ||||
\(754\) | 4.66386e29i | 0.285987i | ||||||||
\(755\) | −9.31518e29 | −0.563311 | ||||||||
\(756\) | 1.37806e29 | − | 1.29139e30i | 0.0821843 | − | 0.770156i | ||||
\(757\) | 1.02765e30 | 0.604422 | 0.302211 | − | 0.953241i | \(-0.402275\pi\) | ||||
0.302211 | + | 0.953241i | \(0.402275\pi\) | |||||||
\(758\) | − | 9.40389e29i | − | 0.545483i | ||||||
\(759\) | −3.75641e29 | + | 7.08137e28i | −0.214899 | + | 0.0405115i | ||||
\(760\) | 5.01947e29 | 0.283214 | ||||||||
\(761\) | −2.20358e30 | −1.22628 | −0.613141 | − | 0.789973i | \(-0.710094\pi\) | ||||
−0.613141 | + | 0.789973i | \(0.710094\pi\) | |||||||
\(762\) | 2.95376e27 | + | 1.56686e28i | 0.00162124 | + | 0.00860012i | ||||
\(763\) | 1.29388e30 | − | 1.64906e30i | 0.700467 | − | 0.892748i | ||||
\(764\) | 7.65497e29i | 0.408755i | ||||||||
\(765\) | 4.26828e29 | − | 1.66856e29i | 0.224806 | − | 0.0878814i | ||||
\(766\) | − | 4.36400e29i | − | 0.226716i | ||||||
\(767\) | − | 1.29562e30i | − | 0.663934i | ||||||
\(768\) | −1.10774e30 | + | 2.08825e29i | −0.559945 | + | 0.105558i | ||||
\(769\) | − | 1.92092e30i | − | 0.957818i | −0.877865 | − | 0.478909i | \(-0.841032\pi\) | ||
0.877865 | − | 0.478909i | \(-0.158968\pi\) | |||||||
\(770\) | 1.38016e29 | − | 1.75902e29i | 0.0678855 | − | 0.0865204i | ||||
\(771\) | 1.06454e30 | − | 2.00681e29i | 0.516525 | − | 0.0973724i | ||||
\(772\) | 2.55668e30 | 1.22375 | ||||||||
\(773\) | −2.61920e30 | −1.23675 | −0.618377 | − | 0.785881i | \(-0.712210\pi\) | ||||
−0.618377 | + | 0.785881i | \(0.712210\pi\) | |||||||
\(774\) | −2.45740e29 | − | 6.28618e29i | −0.114471 | − | 0.292824i | ||||
\(775\) | − | 1.22774e30i | − | 0.564206i | ||||||
\(776\) | 1.18801e30 | 0.538608 | ||||||||
\(777\) | 1.12431e30 | − | 2.16507e30i | 0.502881 | − | 0.968392i | ||||
\(778\) | −5.36432e28 | −0.0236717 | ||||||||
\(779\) | − | 6.07674e29i | − | 0.264562i | ||||||
\(780\) | −4.68124e28 | − | 2.48323e29i | −0.0201079 | − | 0.106665i | ||||
\(781\) | −3.08982e30 | −1.30947 | ||||||||
\(782\) | 2.58809e29 | 0.108220 | ||||||||
\(783\) | 1.58990e30 | + | 2.54167e30i | 0.655950 | + | 1.04863i | ||||
\(784\) | −2.18823e29 | − | 8.93363e29i | −0.0890786 | − | 0.363672i | ||||
\(785\) | 2.84445e29i | 0.114253i | ||||||||
\(786\) | 2.73983e29 | + | 1.45338e30i | 0.108589 | + | 0.576027i | ||||
\(787\) | − | 2.96658e30i | − | 1.16017i | −0.814556 | − | 0.580085i | \(-0.803019\pi\) | ||
0.814556 | − | 0.580085i | \(-0.196981\pi\) | |||||||
\(788\) | − | 1.00251e30i | − | 0.386867i | ||||||
\(789\) | 2.00336e29 | + | 1.06271e30i | 0.0762872 | + | 0.404676i | ||||
\(790\) | 2.78177e28i | 0.0104529i | ||||||||
\(791\) | 3.02660e30 | + | 2.37473e30i | 1.12228 | + | 0.880565i | ||||
\(792\) | −1.72587e30 | + | 6.74677e29i | −0.631528 | + | 0.246877i | ||||
\(793\) | −2.23938e30 | −0.808649 | ||||||||
\(794\) | −1.64163e30 | −0.585006 | ||||||||
\(795\) | 1.75368e29 | + | 9.30265e29i | 0.0616731 | + | 0.327154i | ||||
\(796\) | 1.91783e30i | 0.665614i | ||||||||
\(797\) | 3.88106e30 | 1.32934 | 0.664672 | − | 0.747135i | \(-0.268571\pi\) | ||||
0.664672 | + | 0.747135i | \(0.268571\pi\) | |||||||
\(798\) | −7.56019e29 | + | 1.45586e30i | −0.255566 | + | 0.492140i | ||||
\(799\) | −2.22485e29 | −0.0742267 | ||||||||
\(800\) | 2.84228e30i | 0.935883i | ||||||||
\(801\) | −6.41967e29 | + | 2.50958e29i | −0.208628 | + | 0.0815569i | ||||
\(802\) | −2.93739e30 | −0.942174 | ||||||||
\(803\) | −3.00582e30 | −0.951591 | ||||||||
\(804\) | 1.43324e30 | − | 2.70187e29i | 0.447849 | − | 0.0844258i | ||||
\(805\) | 1.99507e29 | + | 1.56537e29i | 0.0615320 | + | 0.0482792i | ||||
\(806\) | 4.67222e29i | 0.142234i | ||||||||
\(807\) | 6.29301e30 | − | 1.18632e30i | 1.89098 | − | 0.356476i | ||||
\(808\) | − | 2.23910e30i | − | 0.664130i | ||||||
\(809\) | 1.09132e30i | 0.319516i | 0.987156 | + | 0.159758i | \(0.0510714\pi\) | ||||
−0.987156 | + | 0.159758i | \(0.948929\pi\) | |||||||
\(810\) | 3.20697e29 | + | 3.47498e29i | 0.0926835 | + | 0.100429i | ||||
\(811\) | 4.87509e30i | 1.39080i | 0.718625 | + | 0.695398i | \(0.244772\pi\) | ||||
−0.718625 | + | 0.695398i | \(0.755228\pi\) | |||||||
\(812\) | 2.67630e30 | + | 2.09988e30i | 0.753696 | + | 0.591364i | ||||
\(813\) | 9.36439e29 | + | 4.96747e30i | 0.260333 | + | 1.38097i | ||||
\(814\) | −1.51930e30 | −0.416952 | ||||||||
\(815\) | 6.39448e29 | 0.173241 | ||||||||
\(816\) | −1.15376e30 | + | 2.17500e29i | −0.308581 | + | 0.0581718i | ||||
\(817\) | − | 2.92860e30i | − | 0.773265i | ||||||
\(818\) | 1.75836e30 | 0.458350 | ||||||||
\(819\) | 1.81169e30 | + | 5.45838e29i | 0.466233 | + | 0.140470i | ||||
\(820\) | −1.98756e29 | −0.0504982 | ||||||||
\(821\) | 1.09358e30i | 0.274313i | 0.990549 | + | 0.137156i | \(0.0437963\pi\) | ||||
−0.990549 | + | 0.137156i | \(0.956204\pi\) | |||||||
\(822\) | −2.44524e29 | + | 4.60963e28i | −0.0605574 | + | 0.0114159i | ||||
\(823\) | −2.79768e30 | −0.684068 | −0.342034 | − | 0.939688i | \(-0.611116\pi\) | ||||
−0.342034 | + | 0.939688i | \(0.611116\pi\) | |||||||
\(824\) | −8.60058e29 | −0.207631 | ||||||||
\(825\) | 5.73616e29 | + | 3.04282e30i | 0.136727 | + | 0.725288i | ||||
\(826\) | 2.16432e30 | + | 1.69816e30i | 0.509366 | + | 0.399658i | ||||
\(827\) | − | 3.42600e30i | − | 0.796121i | −0.917359 | − | 0.398060i | \(-0.869683\pi\) | ||
0.917359 | − | 0.398060i | \(-0.130317\pi\) | |||||||
\(828\) | −3.33993e29 | − | 8.54374e29i | −0.0766335 | − | 0.196033i | ||||
\(829\) | − | 2.00951e30i | − | 0.455269i | −0.973747 | − | 0.227635i | \(-0.926901\pi\) | ||
0.973747 | − | 0.227635i | \(-0.0730992\pi\) | |||||||
\(830\) | − | 9.55853e29i | − | 0.213831i | ||||||
\(831\) | −3.77318e30 | + | 7.11297e29i | −0.833482 | + | 0.157123i | ||||
\(832\) | − | 2.45795e29i | − | 0.0536140i | ||||||
\(833\) | 9.26348e29 | + | 3.78190e30i | 0.199527 | + | 0.814587i | ||||
\(834\) | −4.59066e29 | + | 8.65406e28i | −0.0976410 | + | 0.0184067i | ||||
\(835\) | −7.36699e29 | −0.154733 | ||||||||
\(836\) | −3.50942e30 | −0.727895 | ||||||||
\(837\) | 1.59275e30 | + | 2.54622e30i | 0.326234 | + | 0.521530i | ||||
\(838\) | 3.51253e30i | 0.710491i | ||||||||
\(839\) | 4.05300e30 | 0.809610 | 0.404805 | − | 0.914403i | \(-0.367339\pi\) | ||||
0.404805 | + | 0.914403i | \(0.367339\pi\) | |||||||
\(840\) | 1.09098e30 | + | 5.66538e29i | 0.215220 | + | 0.111763i | ||||
\(841\) | −2.71983e30 | −0.529887 | ||||||||
\(842\) | − | 6.91324e29i | − | 0.133016i | ||||||
\(843\) | 1.50710e30 | + | 7.99462e30i | 0.286386 | + | 1.51918i | ||||
\(844\) | 5.92939e29 | 0.111279 | ||||||||
\(845\) | −1.18456e30 | −0.219565 | ||||||||
\(846\) | −8.35821e28 | − | 2.13808e29i | −0.0153012 | − | 0.0391414i | ||||
\(847\) | 1.20319e30 | − | 1.53347e30i | 0.217549 | − | 0.277268i | ||||
\(848\) | − | 2.42524e30i | − | 0.433110i | ||||||
\(849\) | −1.59429e29 | − | 8.45712e29i | −0.0281213 | − | 0.149174i | ||||
\(850\) | − | 2.09645e30i | − | 0.365246i | ||||||
\(851\) | − | 1.72317e30i | − | 0.296530i | ||||||
\(852\) | −1.37362e30 | − | 7.28657e30i | −0.233481 | − | 1.23853i | ||||
\(853\) | − | 3.51211e30i | − | 0.589661i | −0.955550 | − | 0.294831i | \(-0.904737\pi\) | ||
0.955550 | − | 0.294831i | \(-0.0952632\pi\) | |||||||
\(854\) | 2.93516e30 | − | 3.74087e30i | 0.486770 | − | 0.620390i | ||||
\(855\) | 7.47031e29 | + | 1.91095e30i | 0.122375 | + | 0.313044i | ||||
\(856\) | 4.03134e30 | 0.652342 | ||||||||
\(857\) | 4.23459e30 | 0.676881 | 0.338441 | − | 0.940988i | \(-0.390101\pi\) | ||||
0.338441 | + | 0.940988i | \(0.390101\pi\) | |||||||
\(858\) | −2.18292e29 | − | 1.15796e30i | −0.0344685 | − | 0.182843i | ||||
\(859\) | − | 1.03728e31i | − | 1.61796i | −0.587836 | − | 0.808980i | \(-0.700020\pi\) | ||
0.587836 | − | 0.808980i | \(-0.299980\pi\) | |||||||
\(860\) | −9.57879e29 | −0.147597 | ||||||||
\(861\) | 6.85870e29 | − | 1.32077e30i | 0.104402 | − | 0.201046i | ||||
\(862\) | −4.03004e30 | −0.606014 | ||||||||
\(863\) | 9.08328e30i | 1.34936i | 0.738108 | + | 0.674682i | \(0.235719\pi\) | ||||
−0.738108 | + | 0.674682i | \(0.764281\pi\) | |||||||
\(864\) | −3.68730e30 | − | 5.89464e30i | −0.541145 | − | 0.865094i | ||||
\(865\) | −2.94744e30 | −0.427342 | ||||||||
\(866\) | −4.00794e30 | −0.574095 | ||||||||
\(867\) | −2.05988e30 | + | 3.88317e29i | −0.291502 | + | 0.0549523i | ||||
\(868\) | 2.68110e30 | + | 2.10364e30i | 0.374848 | + | 0.294113i | ||||
\(869\) | − | 4.45599e29i | − | 0.0615513i | ||||||
\(870\) | −1.21715e30 | + | 2.29450e29i | −0.166108 | + | 0.0313138i | ||||
\(871\) | 2.12490e30i | 0.286515i | ||||||||
\(872\) | − | 7.17714e30i | − | 0.956155i | ||||||
\(873\) | 1.76808e30 | + | 4.52286e30i | 0.232730 | + | 0.595338i | ||||
\(874\) | 1.15871e30i | 0.150698i | ||||||||
\(875\) | 2.65052e30 | − | 3.37810e30i | 0.340602 | − | 0.434099i | ||||
\(876\) | −1.33628e30 | − | 7.08848e30i | −0.169670 | − | 0.900037i | ||||
\(877\) | 3.36892e30 | 0.422663 | 0.211332 | − | 0.977414i | \(-0.432220\pi\) | ||||
0.211332 | + | 0.977414i | \(0.432220\pi\) | |||||||
\(878\) | 6.88474e30 | 0.853484 | ||||||||
\(879\) | −2.41614e30 | + | 4.55476e29i | −0.295964 | + | 0.0557934i | ||||
\(880\) | 7.16428e29i | 0.0867171i | ||||||||
\(881\) | −1.33016e30 | −0.159096 | −0.0795478 | − | 0.996831i | \(-0.525348\pi\) | ||||
−0.0795478 | + | 0.996831i | \(0.525348\pi\) | |||||||
\(882\) | −3.28640e30 | + | 2.31098e30i | −0.388419 | + | 0.273135i | ||||
\(883\) | 3.12329e30 | 0.364775 | 0.182387 | − | 0.983227i | \(-0.441617\pi\) | ||||
0.182387 | + | 0.983227i | \(0.441617\pi\) | |||||||
\(884\) | − | 2.74061e30i | − | 0.316299i | ||||||
\(885\) | 3.38123e30 | − | 6.37410e29i | 0.385630 | − | 0.0726967i | ||||
\(886\) | 4.89332e30 | 0.551505 | ||||||||
\(887\) | −1.51970e31 | −1.69263 | −0.846313 | − | 0.532686i | \(-0.821183\pi\) | ||||
−0.846313 | + | 0.532686i | \(0.821183\pi\) | |||||||
\(888\) | −1.54747e30 | − | 8.20877e30i | −0.170328 | − | 0.903529i | ||||
\(889\) | −1.04592e29 | + | 1.33303e29i | −0.0113770 | + | 0.0145001i | ||||
\(890\) | − | 2.84769e29i | − | 0.0306124i | ||||||
\(891\) | −5.13710e30 | − | 5.56641e30i | −0.545760 | − | 0.591370i | ||||
\(892\) | 1.42940e31i | 1.50080i | ||||||||
\(893\) | − | 9.96089e29i | − | 0.103361i | ||||||
\(894\) | −6.66142e30 | + | 1.25577e30i | −0.683161 | + | 0.128786i | ||||
\(895\) | − | 4.13408e30i | − | 0.419022i | ||||||
\(896\) | −7.60316e30 | − | 5.96558e30i | −0.761658 | − | 0.597611i | ||||
\(897\) | 1.31335e30 | − | 2.47586e29i | 0.130035 | − | 0.0245135i | ||||
\(898\) | 3.18043e30 | 0.311232 | ||||||||
\(899\) | −7.86674e30 | −0.760883 | ||||||||
\(900\) | −6.92073e30 | + | 2.70546e30i | −0.661615 | + | 0.258639i | ||||
\(901\) | 1.02668e31i | 0.970121i | ||||||||
\(902\) | −9.26827e29 | −0.0865626 | ||||||||
\(903\) | 3.30546e30 | − | 6.36528e30i | 0.305148 | − | 0.587619i | ||||
\(904\) | 1.31726e31 | 1.20199 | ||||||||
\(905\) | − | 3.24494e30i | − | 0.292682i | ||||||
\(906\) | −1.93109e30 | − | 1.02437e31i | −0.172170 | − | 0.913299i | ||||
\(907\) | 8.93602e30 | 0.787531 | 0.393765 | − | 0.919211i | \(-0.371172\pi\) | ||||
0.393765 | + | 0.919211i | \(0.371172\pi\) | |||||||
\(908\) | −5.51947e30 | −0.480835 | ||||||||
\(909\) | 8.52442e30 | − | 3.33237e30i | 0.734081 | − | 0.286967i | ||||
\(910\) | −4.82545e29 | + | 6.15006e29i | −0.0410775 | + | 0.0523534i | ||||
\(911\) | − | 8.17802e30i | − | 0.688185i | −0.938936 | − | 0.344092i | \(-0.888187\pi\) | ||
0.938936 | − | 0.344092i | \(-0.111813\pi\) | |||||||
\(912\) | −9.73769e29 | − | 5.16550e30i | −0.0810047 | − | 0.429701i | ||||
\(913\) | 1.53114e31i | 1.25913i | ||||||||
\(914\) | 3.88592e30i | 0.315907i | ||||||||
\(915\) | −1.10172e30 | − | 5.84422e30i | −0.0885420 | − | 0.469684i | ||||
\(916\) | 9.88164e30i | 0.785103i | ||||||||
\(917\) | −9.70166e30 | + | 1.23648e31i | −0.762023 | + | 0.971201i | ||||
\(918\) | 2.71973e30 | + | 4.34785e30i | 0.211192 | + | 0.337619i | ||||
\(919\) | −1.15778e31 | −0.888817 | −0.444409 | − | 0.895824i | \(-0.646586\pi\) | ||||
−0.444409 | + | 0.895824i | \(0.646586\pi\) | |||||||
\(920\) | 8.68306e29 | 0.0659023 | ||||||||
\(921\) | 1.22871e30 | + | 6.51788e30i | 0.0921987 | + | 0.489081i | ||||
\(922\) | 8.79430e30i | 0.652419i | ||||||||
\(923\) | 1.08029e31 | 0.792361 | ||||||||
\(924\) | −7.62768e30 | − | 3.96101e30i | −0.553142 | − | 0.287244i | ||||
\(925\) | −1.39583e31 | −1.00079 | ||||||||
\(926\) | − | 6.10894e30i | − | 0.433063i | ||||||
\(927\) | −1.28000e30 | − | 3.27431e30i | −0.0897163 | − | 0.229500i | ||||
\(928\) | 1.82119e31 | 1.26212 | ||||||||
\(929\) | 2.72594e31 | 1.86789 | 0.933945 | − | 0.357418i | \(-0.116343\pi\) | ||||
0.933945 | + | 0.357418i | \(0.116343\pi\) | |||||||
\(930\) | −1.21933e30 | + | 2.29861e29i | −0.0826134 | + | 0.0155738i | ||||
\(931\) | −1.69319e31 | + | 4.14735e30i | −1.13432 | + | 0.277843i | ||||
\(932\) | 8.43178e30i | 0.558537i | ||||||||
\(933\) | −6.95530e30 | + | 1.31117e30i | −0.455573 | + | 0.0858821i | ||||
\(934\) | − | 1.39014e31i | − | 0.900357i | ||||||
\(935\) | − | 3.03288e30i | − | 0.194237i | ||||||
\(936\) | 6.03414e30 | − | 2.35887e30i | 0.382137 | − | 0.149385i | ||||
\(937\) | − | 1.90472e31i | − | 1.19280i | −0.802689 | − | 0.596398i | \(-0.796598\pi\) | ||
0.802689 | − | 0.596398i | \(-0.203402\pi\) | |||||||
\(938\) | −3.54962e30 | − | 2.78510e30i | −0.219812 | − | 0.172469i | ||||
\(939\) | −7.30749e29 | − | 3.87636e30i | −0.0447486 | − | 0.237375i | ||||
\(940\) | −3.25798e29 | −0.0197291 | ||||||||
\(941\) | 7.71153e30 | 0.461795 | 0.230898 | − | 0.972978i | \(-0.425834\pi\) | ||||
0.230898 | + | 0.972978i | \(0.425834\pi\) | |||||||
\(942\) | −3.12799e30 | + | 5.89670e29i | −0.185238 | + | 0.0349200i | ||||
\(943\) | − | 1.05120e30i | − | 0.0615620i | ||||||
\(944\) | −8.81500e30 | −0.510524 | ||||||||
\(945\) | −5.33193e29 | + | 4.99659e30i | −0.0305387 | + | 0.286180i | ||||
\(946\) | −4.46671e30 | −0.253006 | ||||||||
\(947\) | 1.66253e31i | 0.931312i | 0.884966 | + | 0.465656i | \(0.154182\pi\) | ||||
−0.884966 | + | 0.465656i | \(0.845818\pi\) | |||||||
\(948\) | 1.05084e30 | − | 1.98097e29i | 0.0582166 | − | 0.0109747i | ||||
\(949\) | 1.05092e31 | 0.575806 | ||||||||
\(950\) | 9.38599e30 | 0.508607 | ||||||||
\(951\) | −3.54269e29 | − | 1.87927e30i | −0.0189862 | − | 0.100715i | ||||
\(952\) | 1.04891e31 | + | 8.22991e30i | 0.555966 | + | 0.436222i | ||||
\(953\) | 3.57000e31i | 1.87151i | 0.352648 | + | 0.935756i | \(0.385281\pi\) | ||||
−0.352648 | + | 0.935756i | \(0.614719\pi\) | |||||||
\(954\) | −9.86642e30 | + | 3.85699e30i | −0.511566 | + | 0.199982i | ||||
\(955\) | − | 2.96183e30i | − | 0.151888i | ||||||
\(956\) | − | 3.70458e30i | − | 0.187902i | ||||||
\(957\) | 1.94969e31 | − | 3.67545e30i | 0.978117 | − | 0.184389i | ||||
\(958\) | 9.88861e30i | 0.490679i | ||||||||
\(959\) | −2.08032e30 | − | 1.63225e30i | −0.102102 | − | 0.0801111i | ||||
\(960\) | 6.41463e29 | − | 1.20925e29i | 0.0311404 | − | 0.00587040i | ||||
\(961\) | 1.29447e31 | 0.621578 | ||||||||
\(962\) | 5.31191e30 | 0.252297 | ||||||||
\(963\) | 5.99972e30 | + | 1.53476e31i | 0.281874 | + | 0.721051i | ||||
\(964\) | − | 1.64597e31i | − | 0.764913i | ||||||
\(965\) | −9.89218e30 | −0.454732 | ||||||||
\(966\) | −1.30782e30 | + | 2.51845e30i | −0.0594686 | + | 0.114518i | ||||
\(967\) | 7.40714e29 | 0.0333175 | 0.0166588 | − | 0.999861i | \(-0.494697\pi\) | ||||
0.0166588 | + | 0.999861i | \(0.494697\pi\) | |||||||
\(968\) | − | 6.67405e30i | − | 0.296960i | ||||||
\(969\) | 4.12229e30 | + | 2.18672e31i | 0.181442 | + | 0.962486i | ||||
\(970\) | −2.00628e30 | −0.0873552 | ||||||||
\(971\) | 1.12383e31 | 0.484058 | 0.242029 | − | 0.970269i | \(-0.422187\pi\) | ||||
0.242029 | + | 0.970269i | \(0.422187\pi\) | |||||||
\(972\) | 1.08432e31 | − | 1.45892e31i | 0.462022 | − | 0.621635i | ||||
\(973\) | −3.90556e30 | − | 3.06438e30i | −0.164626 | − | 0.129169i | ||||
\(974\) | − | 5.67330e29i | − | 0.0236574i | ||||||
\(975\) | −2.00553e30 | − | 1.06386e31i | −0.0827334 | − | 0.438871i | ||||
\(976\) | 1.52361e31i | 0.621801i | ||||||||
\(977\) | 2.31274e31i | 0.933758i | 0.884321 | + | 0.466879i | \(0.154622\pi\) | ||||
−0.884321 | + | 0.466879i | \(0.845378\pi\) | |||||||
\(978\) | 1.32561e30 | + | 7.03190e30i | 0.0529492 | + | 0.280876i | ||||
\(979\) | 4.56157e30i | 0.180259i | ||||||||
\(980\) | 1.35651e30 | + | 5.53806e30i | 0.0530332 | + | 0.216513i | ||||
\(981\) | 2.73239e31 | − | 1.06815e31i | 1.05686 | − | 0.413150i | ||||
\(982\) | 2.94605e30 | 0.112738 | ||||||||
\(983\) | −1.23826e31 | −0.468812 | −0.234406 | − | 0.972139i | \(-0.575315\pi\) | ||||
−0.234406 | + | 0.972139i | \(0.575315\pi\) | |||||||
\(984\) | −9.44014e29 | − | 5.00766e30i | −0.0353614 | − | 0.187580i | ||||
\(985\) | 3.87885e30i | 0.143755i | ||||||||
\(986\) | −1.34330e31 | −0.492567 | ||||||||
\(987\) | 1.12427e30 | − | 2.16499e30i | 0.0407887 | − | 0.0785462i | ||||
\(988\) | 1.22700e31 | 0.440449 | ||||||||
\(989\) | − | 5.06611e30i | − | 0.179934i | ||||||
\(990\) | 2.91459e30 | − | 1.13938e30i | 0.102426 | − | 0.0400403i | ||||
\(991\) | −2.31578e30 | −0.0805237 | −0.0402619 | − | 0.999189i | \(-0.512819\pi\) | ||||
−0.0402619 | + | 0.999189i | \(0.512819\pi\) | |||||||
\(992\) | 1.82446e31 | 0.627713 | ||||||||
\(993\) | −5.31795e31 | + | 1.00251e31i | −1.81041 | + | 0.341288i | ||||
\(994\) | −1.41594e31 | + | 1.80462e31i | −0.476966 | + | 0.607895i | ||||
\(995\) | − | 7.42038e30i | − | 0.247334i | ||||||
\(996\) | −3.61080e31 | + | 6.80688e30i | −1.19091 | + | 0.224504i | ||||
\(997\) | 6.72524e30i | 0.219487i | 0.993960 | + | 0.109744i | \(0.0350030\pi\) | ||||
−0.993960 | + | 0.109744i | \(0.964997\pi\) | |||||||
\(998\) | − | 4.20355e29i | − | 0.0135752i | ||||||
\(999\) | 2.89484e31 | − | 1.81082e31i | 0.925096 | − | 0.578678i |
(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 | 21.22.c.b.20.31 | yes | 52 | |
3.2 | odd | 2 | inner | 21.22.c.b.20.22 | yes | 52 | |
7.6 | odd | 2 | inner | 21.22.c.b.20.21 | ✓ | 52 | |
21.20 | even | 2 | inner | 21.22.c.b.20.32 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.22.c.b.20.21 | ✓ | 52 | 7.6 | odd | 2 | inner | |
21.22.c.b.20.22 | yes | 52 | 3.2 | odd | 2 | inner | |
21.22.c.b.20.31 | yes | 52 | 1.1 | even | 1 | trivial | |
21.22.c.b.20.32 | yes | 52 | 21.20 | even | 2 | inner |