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 | 20.5 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.22.c.b.20.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2329.72i | − | 1.60875i | −0.594119 | − | 0.804377i | \(-0.702499\pi\) | ||
0.594119 | − | 0.804377i | \(-0.297501\pi\) | |||||||
\(3\) | 52907.9 | − | 87527.8i | 0.517305 | − | 0.855801i | ||||
\(4\) | −3.33046e6 | −1.58809 | ||||||||
\(5\) | −3.45099e7 | −1.58037 | −0.790184 | − | 0.612869i | \(-0.790015\pi\) | ||||
−0.790184 | + | 0.612869i | \(0.790015\pi\) | |||||||
\(6\) | −2.03916e8 | − | 1.23261e8i | −1.37677 | − | 0.832217i | ||||
\(7\) | 4.88555e7 | − | 7.45761e8i | 0.0653709 | − | 0.997861i | ||||
\(8\) | 2.87327e9i | 0.946090i | ||||||||
\(9\) | −4.86187e9 | − | 9.26181e9i | −0.464790 | − | 0.885421i | ||||
\(10\) | 8.03985e10i | 2.54242i | ||||||||
\(11\) | 5.12942e9i | 0.0596273i | 0.999555 | + | 0.0298136i | \(0.00949138\pi\) | ||||
−0.999555 | + | 0.0298136i | \(0.990509\pi\) | |||||||
\(12\) | −1.76208e11 | + | 2.91508e11i | −0.821527 | + | 1.35909i | ||||
\(13\) | 3.88435e11i | 0.781471i | 0.920503 | + | 0.390736i | \(0.127779\pi\) | ||||
−0.920503 | + | 0.390736i | \(0.872221\pi\) | |||||||
\(14\) | −1.73742e12 | − | 1.13820e11i | −1.60531 | − | 0.105166i | ||||
\(15\) | −1.82584e12 | + | 3.02057e12i | −0.817533 | + | 1.35248i | ||||
\(16\) | −2.90549e11 | −0.0660633 | ||||||||
\(17\) | −4.11275e12 | −0.494787 | −0.247394 | − | 0.968915i | \(-0.579574\pi\) | ||||
−0.247394 | + | 0.968915i | \(0.579574\pi\) | |||||||
\(18\) | −2.15775e13 | + | 1.13268e13i | −1.42442 | + | 0.747733i | ||||
\(19\) | 7.35621e11i | 0.0275259i | 0.999905 | + | 0.0137629i | \(0.00438102\pi\) | ||||
−0.999905 | + | 0.0137629i | \(0.995619\pi\) | |||||||
\(20\) | 1.14934e14 | 2.50977 | ||||||||
\(21\) | −6.26899e13 | − | 4.37328e13i | −0.820154 | − | 0.572143i | ||||
\(22\) | 1.19501e13 | 0.0959256 | ||||||||
\(23\) | 2.80126e14i | 1.40997i | 0.709220 | + | 0.704987i | \(0.249047\pi\) | ||||
−0.709220 | + | 0.704987i | \(0.750953\pi\) | |||||||
\(24\) | 2.51491e14 | + | 1.52019e14i | 0.809664 | + | 0.489417i | ||||
\(25\) | 7.14095e14 | 1.49757 | ||||||||
\(26\) | 9.04946e14 | 1.25719 | ||||||||
\(27\) | −1.06790e15 | − | 6.44740e13i | −0.998182 | − | 0.0602649i | ||||
\(28\) | −1.62712e14 | + | 2.48373e15i | −0.103815 | + | 1.58469i | ||||
\(29\) | − | 2.85990e15i | − | 1.26233i | −0.775649 | − | 0.631164i | \(-0.782577\pi\) | ||
0.775649 | − | 0.631164i | \(-0.217423\pi\) | |||||||
\(30\) | 7.03710e15 | + | 4.25371e15i | 2.17581 | + | 1.31521i | ||||
\(31\) | − | 8.55595e15i | − | 1.87487i | −0.348163 | − | 0.937434i | \(-0.613194\pi\) | ||
0.348163 | − | 0.937434i | \(-0.386806\pi\) | |||||||
\(32\) | 6.70259e15i | 1.05237i | ||||||||
\(33\) | 4.48967e14 | + | 2.71387e14i | 0.0510291 | + | 0.0308455i | ||||
\(34\) | 9.58157e15i | 0.795991i | ||||||||
\(35\) | −1.68600e15 | + | 2.57361e16i | −0.103310 | + | 1.57699i | ||||
\(36\) | 1.61923e16 | + | 3.08461e16i | 0.738128 | + | 1.40613i | ||||
\(37\) | −2.16290e16 | −0.739465 | −0.369733 | − | 0.929138i | \(-0.620551\pi\) | ||||
−0.369733 | + | 0.929138i | \(0.620551\pi\) | |||||||
\(38\) | 1.71379e15 | 0.0442824 | ||||||||
\(39\) | 3.39988e16 | + | 2.05513e16i | 0.668784 | + | 0.404259i | ||||
\(40\) | − | 9.91564e16i | − | 1.49517i | ||||||
\(41\) | −8.87944e16 | −1.03313 | −0.516565 | − | 0.856248i | \(-0.672790\pi\) | ||||
−0.516565 | + | 0.856248i | \(0.672790\pi\) | |||||||
\(42\) | −1.01885e17 | + | 1.46050e17i | −0.920438 | + | 1.31943i | ||||
\(43\) | 2.16141e17 | 1.52517 | 0.762585 | − | 0.646888i | \(-0.223930\pi\) | ||||
0.762585 | + | 0.646888i | \(0.223930\pi\) | |||||||
\(44\) | − | 1.70833e16i | − | 0.0946934i | ||||||
\(45\) | 1.67783e17 | + | 3.19624e17i | 0.734540 | + | 1.39929i | ||||
\(46\) | 6.52616e17 | 2.26830 | ||||||||
\(47\) | 1.24937e17 | 0.346469 | 0.173235 | − | 0.984881i | \(-0.444578\pi\) | ||||
0.173235 | + | 0.984881i | \(0.444578\pi\) | |||||||
\(48\) | −1.53723e16 | + | 2.54311e16i | −0.0341749 | + | 0.0565370i | ||||
\(49\) | −5.53772e17 | − | 7.28691e16i | −0.991453 | − | 0.130462i | ||||
\(50\) | − | 1.66364e18i | − | 2.40921i | ||||||
\(51\) | −2.17597e17 | + | 3.59980e17i | −0.255956 | + | 0.423439i | ||||
\(52\) | − | 1.29367e18i | − | 1.24105i | ||||||
\(53\) | − | 1.11914e18i | − | 0.878997i | −0.898243 | − | 0.439499i | \(-0.855156\pi\) | ||
0.898243 | − | 0.439499i | \(-0.144844\pi\) | |||||||
\(54\) | −1.50207e17 | + | 2.48791e18i | −0.0969515 | + | 1.60583i | ||||
\(55\) | − | 1.77016e17i | − | 0.0942331i | ||||||
\(56\) | 2.14278e18 | + | 1.40375e17i | 0.944066 | + | 0.0618467i | ||||
\(57\) | 6.43872e16 | + | 3.89201e16i | 0.0235567 | + | 0.0142393i | ||||
\(58\) | −6.66279e18 | −2.03078 | ||||||||
\(59\) | 3.06749e18 | 0.781335 | 0.390667 | − | 0.920532i | \(-0.372244\pi\) | ||||
0.390667 | + | 0.920532i | \(0.372244\pi\) | |||||||
\(60\) | 6.08091e18 | − | 1.00599e19i | 1.29832 | − | 2.14786i | ||||
\(61\) | − | 8.59883e18i | − | 1.54339i | −0.635992 | − | 0.771696i | \(-0.719409\pi\) | ||
0.635992 | − | 0.771696i | \(-0.280591\pi\) | |||||||
\(62\) | −1.99330e19 | −3.01620 | ||||||||
\(63\) | −7.14463e18 | + | 3.17330e18i | −0.913911 | + | 0.405915i | ||||
\(64\) | 1.50059e19 | 1.62694 | ||||||||
\(65\) | − | 1.34048e19i | − | 1.23501i | ||||||
\(66\) | 6.32256e17 | − | 1.04597e18i | 0.0496228 | − | 0.0820932i | ||||
\(67\) | 9.86518e18 | 0.661180 | 0.330590 | − | 0.943774i | \(-0.392752\pi\) | ||||
0.330590 | + | 0.943774i | \(0.392752\pi\) | |||||||
\(68\) | 1.36974e19 | 0.785766 | ||||||||
\(69\) | 2.45188e19 | + | 1.48209e19i | 1.20666 | + | 0.729387i | ||||
\(70\) | 5.99581e19 | + | 3.92791e18i | 2.53699 | + | 0.166201i | ||||
\(71\) | 2.59864e19i | 0.947398i | 0.880687 | + | 0.473699i | \(0.157082\pi\) | ||||
−0.880687 | + | 0.473699i | \(0.842918\pi\) | |||||||
\(72\) | 2.66117e19 | − | 1.39695e19i | 0.837687 | − | 0.439733i | ||||
\(73\) | − | 2.69585e18i | − | 0.0734184i | −0.999326 | − | 0.0367092i | \(-0.988312\pi\) | ||
0.999326 | − | 0.0367092i | \(-0.0116875\pi\) | |||||||
\(74\) | 5.03895e19i | 1.18962i | ||||||||
\(75\) | 3.77812e19 | − | 6.25032e19i | 0.774699 | − | 1.28162i | ||||
\(76\) | − | 2.44996e18i | − | 0.0437135i | ||||||
\(77\) | 3.82532e18 | + | 2.50600e17i | 0.0594997 | + | 0.00389789i | ||||
\(78\) | 4.78788e19 | − | 7.92079e19i | 0.650354 | − | 1.07591i | ||||
\(79\) | 5.09894e19 | 0.605892 | 0.302946 | − | 0.953008i | \(-0.402030\pi\) | ||||
0.302946 | + | 0.953008i | \(0.402030\pi\) | |||||||
\(80\) | 1.00268e19 | 0.104404 | ||||||||
\(81\) | −6.21434e19 | + | 9.00595e19i | −0.567940 | + | 0.823070i | ||||
\(82\) | 2.06866e20i | 1.66205i | ||||||||
\(83\) | −1.71105e20 | −1.21044 | −0.605220 | − | 0.796058i | \(-0.706915\pi\) | ||||
−0.605220 | + | 0.796058i | \(0.706915\pi\) | |||||||
\(84\) | 2.08787e20 | + | 1.45651e20i | 1.30248 | + | 0.908614i | ||||
\(85\) | 1.41930e20 | 0.781946 | ||||||||
\(86\) | − | 5.03549e20i | − | 2.45362i | ||||||
\(87\) | −2.50321e20 | − | 1.51311e20i | −1.08030 | − | 0.653009i | ||||
\(88\) | −1.47382e19 | −0.0564127 | ||||||||
\(89\) | −3.53288e20 | −1.20098 | −0.600488 | − | 0.799634i | \(-0.705027\pi\) | ||||
−0.600488 | + | 0.799634i | \(0.705027\pi\) | |||||||
\(90\) | 7.44636e20 | − | 3.90887e20i | 2.25112 | − | 1.18169i | ||||
\(91\) | 2.89679e20 | + | 1.89772e19i | 0.779800 | + | 0.0510855i | ||||
\(92\) | − | 9.32949e20i | − | 2.23916i | ||||||
\(93\) | −7.48884e20 | − | 4.52677e20i | −1.60451 | − | 0.969879i | ||||
\(94\) | − | 2.91069e20i | − | 0.557384i | ||||||
\(95\) | − | 2.53862e19i | − | 0.0435010i | ||||||
\(96\) | 5.86663e20 | + | 3.54620e20i | 0.900618 | + | 0.544396i | ||||
\(97\) | 1.89705e20i | 0.261201i | 0.991435 | + | 0.130601i | \(0.0416905\pi\) | ||||
−0.991435 | + | 0.130601i | \(0.958309\pi\) | |||||||
\(98\) | −1.69765e20 | + | 1.29014e21i | −0.209881 | + | 1.59500i | ||||
\(99\) | 4.75077e19 | − | 2.49386e19i | 0.0527952 | − | 0.0277142i | ||||
\(100\) | −2.37827e21 | −2.37827 | ||||||||
\(101\) | −1.79298e21 | −1.61511 | −0.807555 | − | 0.589792i | \(-0.799210\pi\) | ||||
−0.807555 | + | 0.589792i | \(0.799210\pi\) | |||||||
\(102\) | 8.38653e20 | + | 5.06940e20i | 0.681209 | + | 0.411770i | ||||
\(103\) | 7.07965e20i | 0.519064i | 0.965734 | + | 0.259532i | \(0.0835684\pi\) | ||||
−0.965734 | + | 0.259532i | \(0.916432\pi\) | |||||||
\(104\) | −1.11608e21 | −0.739342 | ||||||||
\(105\) | 2.16342e21 | + | 1.50921e21i | 1.29615 | + | 0.904198i | ||||
\(106\) | −2.60729e21 | −1.41409 | ||||||||
\(107\) | 3.36740e21i | 1.65487i | 0.561559 | + | 0.827436i | \(0.310202\pi\) | ||||
−0.561559 | + | 0.827436i | \(0.689798\pi\) | |||||||
\(108\) | 3.55659e21 | + | 2.14728e20i | 1.58520 | + | 0.0957061i | ||||
\(109\) | 2.91696e21 | 1.18019 | 0.590096 | − | 0.807333i | \(-0.299090\pi\) | ||||
0.590096 | + | 0.807333i | \(0.299090\pi\) | |||||||
\(110\) | −4.12398e20 | −0.151598 | ||||||||
\(111\) | −1.14434e21 | + | 1.89314e21i | −0.382529 | + | 0.632835i | ||||
\(112\) | −1.41949e19 | + | 2.16680e20i | −0.00431861 | + | 0.0659220i | ||||
\(113\) | 1.25082e21i | 0.346635i | 0.984866 | + | 0.173318i | \(0.0554487\pi\) | ||||
−0.984866 | + | 0.173318i | \(0.944551\pi\) | |||||||
\(114\) | 9.06731e19 | − | 1.50005e20i | 0.0229075 | − | 0.0378969i | ||||
\(115\) | − | 9.66711e21i | − | 2.22828i | ||||||
\(116\) | 9.52480e21i | 2.00469i | ||||||||
\(117\) | 3.59761e21 | − | 1.88852e21i | 0.691931 | − | 0.363220i | ||||
\(118\) | − | 7.14641e21i | − | 1.25698i | ||||||
\(119\) | −2.00930e20 | + | 3.06713e21i | −0.0323447 | + | 0.493729i | ||||
\(120\) | −8.67894e21 | − | 5.24615e21i | −1.27957 | − | 0.773460i | ||||
\(121\) | 7.37394e21 | 0.996445 | ||||||||
\(122\) | −2.00329e22 | −2.48294 | ||||||||
\(123\) | −4.69792e21 | + | 7.77198e21i | −0.534444 | + | 0.884154i | ||||
\(124\) | 2.84953e22i | 2.97746i | ||||||||
\(125\) | −8.18774e21 | −0.786338 | ||||||||
\(126\) | 7.39292e21 | + | 1.66450e22i | 0.653018 | + | 1.47026i | ||||
\(127\) | −1.42120e22 | −1.15536 | −0.577680 | − | 0.816263i | \(-0.696042\pi\) | ||||
−0.577680 | + | 0.816263i | \(0.696042\pi\) | |||||||
\(128\) | − | 2.09032e22i | − | 1.56498i | ||||||
\(129\) | 1.14355e22 | − | 1.89183e22i | 0.788978 | − | 1.30524i | ||||
\(130\) | −3.12296e22 | −1.98683 | ||||||||
\(131\) | 1.04676e22 | 0.614470 | 0.307235 | − | 0.951634i | \(-0.400596\pi\) | ||||
0.307235 | + | 0.951634i | \(0.400596\pi\) | |||||||
\(132\) | −1.49527e21 | − | 9.03843e20i | −0.0810387 | − | 0.0489854i | ||||
\(133\) | 5.48597e20 | + | 3.59391e19i | 0.0274670 | + | 0.00179939i | ||||
\(134\) | − | 2.29831e22i | − | 1.06368i | ||||||
\(135\) | 3.68530e22 | + | 2.22499e21i | 1.57750 | + | 0.0952408i | ||||
\(136\) | − | 1.18171e22i | − | 0.468113i | ||||||
\(137\) | 1.22907e22i | 0.450829i | 0.974263 | + | 0.225414i | \(0.0723736\pi\) | ||||
−0.974263 | + | 0.225414i | \(0.927626\pi\) | |||||||
\(138\) | 3.45285e22 | − | 5.71220e22i | 1.17340 | − | 1.94121i | ||||
\(139\) | 1.09006e22i | 0.343397i | 0.985150 | + | 0.171699i | \(0.0549255\pi\) | ||||
−0.985150 | + | 0.171699i | \(0.945074\pi\) | |||||||
\(140\) | 5.61516e21 | − | 8.57132e22i | 0.164066 | − | 2.50440i | ||||
\(141\) | 6.61016e21 | − | 1.09355e22i | 0.179230 | − | 0.296509i | ||||
\(142\) | 6.05410e22 | 1.52413 | ||||||||
\(143\) | −1.99244e21 | −0.0465970 | ||||||||
\(144\) | 1.41261e21 | + | 2.69101e21i | 0.0307056 | + | 0.0584938i | ||||
\(145\) | 9.86950e22i | 1.99495i | ||||||||
\(146\) | −6.28058e21 | −0.118112 | ||||||||
\(147\) | −3.56770e22 | + | 4.46151e22i | −0.624534 | + | 0.780998i | ||||
\(148\) | 7.20345e22 | 1.17434 | ||||||||
\(149\) | 5.07250e22i | 0.770488i | 0.922815 | + | 0.385244i | \(0.125883\pi\) | ||||
−0.922815 | + | 0.385244i | \(0.874117\pi\) | |||||||
\(150\) | −1.45615e23 | − | 8.80199e22i | −2.06181 | − | 1.24630i | ||||
\(151\) | 1.27095e23 | 1.67831 | 0.839153 | − | 0.543896i | \(-0.183051\pi\) | ||||
0.839153 | + | 0.543896i | \(0.183051\pi\) | |||||||
\(152\) | −2.11364e21 | −0.0260419 | ||||||||
\(153\) | 1.99956e22 | + | 3.80915e22i | 0.229972 | + | 0.438095i | ||||
\(154\) | 5.83830e20 | − | 8.91194e21i | 0.00627074 | − | 0.0957204i | ||||
\(155\) | 2.95265e23i | 2.96298i | ||||||||
\(156\) | −1.13232e23 | − | 6.84452e22i | −1.06209 | − | 0.641999i | ||||
\(157\) | − | 6.04275e22i | − | 0.530015i | −0.964246 | − | 0.265008i | \(-0.914626\pi\) | ||
0.964246 | − | 0.265008i | \(-0.0853745\pi\) | |||||||
\(158\) | − | 1.18791e23i | − | 0.974731i | ||||||
\(159\) | −9.79558e22 | − | 5.92113e22i | −0.752247 | − | 0.454710i | ||||
\(160\) | − | 2.31306e23i | − | 1.66313i | ||||||
\(161\) | 2.08907e23 | + | 1.36857e22i | 1.40696 | + | 0.0921712i | ||||
\(162\) | 2.09814e23 | + | 1.44777e23i | 1.32412 | + | 0.913675i | ||||
\(163\) | 1.14916e22 | 0.0679844 | 0.0339922 | − | 0.999422i | \(-0.489178\pi\) | ||||
0.0339922 | + | 0.999422i | \(0.489178\pi\) | |||||||
\(164\) | 2.95727e23 | 1.64070 | ||||||||
\(165\) | −1.54938e22 | − | 9.36552e21i | −0.0806448 | − | 0.0487473i | ||||
\(166\) | 3.98628e23i | 1.94730i | ||||||||
\(167\) | −8.08026e21 | −0.0370597 | −0.0185299 | − | 0.999828i | \(-0.505899\pi\) | ||||
−0.0185299 | + | 0.999828i | \(0.505899\pi\) | |||||||
\(168\) | 1.25656e23 | − | 1.80125e23i | 0.541299 | − | 0.775939i | ||||
\(169\) | 9.61829e22 | 0.389303 | ||||||||
\(170\) | − | 3.30659e23i | − | 1.25796i | ||||||
\(171\) | 6.81318e21 | − | 3.57649e21i | 0.0243720 | − | 0.0127938i | ||||
\(172\) | −7.19849e23 | −2.42210 | ||||||||
\(173\) | 2.56010e22 | 0.0810536 | 0.0405268 | − | 0.999178i | \(-0.487096\pi\) | ||||
0.0405268 | + | 0.999178i | \(0.487096\pi\) | |||||||
\(174\) | −3.52514e23 | + | 5.83179e23i | −1.05053 | + | 1.73794i | ||||
\(175\) | 3.48875e22 | − | 5.32544e23i | 0.0978972 | − | 1.49436i | ||||
\(176\) | − | 1.49035e21i | − | 0.00393917i | ||||||
\(177\) | 1.62294e23 | − | 2.68491e23i | 0.404189 | − | 0.668667i | ||||
\(178\) | 8.23064e23i | 1.93207i | ||||||||
\(179\) | 3.91102e23i | 0.865632i | 0.901482 | + | 0.432816i | \(0.142480\pi\) | ||||
−0.901482 | + | 0.432816i | \(0.857520\pi\) | |||||||
\(180\) | −5.58794e23 | − | 1.06450e24i | −1.16651 | − | 2.22220i | ||||
\(181\) | 1.49908e23i | 0.295257i | 0.989043 | + | 0.147628i | \(0.0471640\pi\) | ||||
−0.989043 | + | 0.147628i | \(0.952836\pi\) | |||||||
\(182\) | 4.42116e22 | − | 6.74873e23i | 0.0821839 | − | 1.25451i | ||||
\(183\) | −7.52636e23 | − | 4.54946e23i | −1.32084 | − | 0.798405i | ||||
\(184\) | −8.04879e23 | −1.33396 | ||||||||
\(185\) | 7.46413e23 | 1.16863 | ||||||||
\(186\) | −1.05461e24 | + | 1.74469e24i | −1.56030 | + | 2.58127i | ||||
\(187\) | − | 2.10960e22i | − | 0.0295028i | ||||||
\(188\) | −4.16099e23 | −0.550224 | ||||||||
\(189\) | −1.00255e23 | + | 7.93246e23i | −0.125388 | + | 0.992108i | ||||
\(190\) | −5.91428e22 | −0.0699825 | ||||||||
\(191\) | − | 8.64251e23i | − | 0.967808i | −0.875121 | − | 0.483904i | \(-0.839218\pi\) | ||
0.875121 | − | 0.483904i | \(-0.160782\pi\) | |||||||
\(192\) | 7.93928e23 | − | 1.31343e24i | 0.841625 | − | 1.39234i | ||||
\(193\) | −9.50930e23 | −0.954546 | −0.477273 | − | 0.878755i | \(-0.658375\pi\) | ||||
−0.477273 | + | 0.878755i | \(0.658375\pi\) | |||||||
\(194\) | 4.41960e23 | 0.420208 | ||||||||
\(195\) | −1.17330e24 | − | 7.09221e23i | −1.05693 | − | 0.638879i | ||||
\(196\) | 1.84432e24 | + | 2.42688e23i | 1.57452 | + | 0.207185i | ||||
\(197\) | 1.85803e24i | 1.50368i | 0.659343 | + | 0.751842i | \(0.270834\pi\) | ||||
−0.659343 | + | 0.751842i | \(0.729166\pi\) | |||||||
\(198\) | −5.81000e22 | − | 1.10680e23i | −0.0445853 | − | 0.0849345i | ||||
\(199\) | 1.75406e24i | 1.27670i | 0.769747 | + | 0.638349i | \(0.220382\pi\) | ||||
−0.769747 | + | 0.638349i | \(0.779618\pi\) | |||||||
\(200\) | 2.05179e24i | 1.41683i | ||||||||
\(201\) | 5.21946e23 | − | 8.63477e23i | 0.342032 | − | 0.565838i | ||||
\(202\) | 4.17716e24i | 2.59831i | ||||||||
\(203\) | −2.13280e24 | − | 1.39722e23i | −1.25963 | − | 0.0825195i | ||||
\(204\) | 7.24698e23 | − | 1.19890e24i | 0.406481 | − | 0.672459i | ||||
\(205\) | 3.06429e24 | 1.63273 | ||||||||
\(206\) | 1.64936e24 | 0.835047 | ||||||||
\(207\) | 2.59447e24 | − | 1.36194e24i | 1.24842 | − | 0.655342i | ||||
\(208\) | − | 1.12859e23i | − | 0.0516265i | ||||||
\(209\) | −3.77331e21 | −0.00164129 | ||||||||
\(210\) | 3.51605e24 | − | 5.04018e24i | 1.45463 | − | 2.08518i | ||||
\(211\) | −4.91382e24 | −1.93399 | −0.966993 | − | 0.254802i | \(-0.917990\pi\) | ||||
−0.966993 | + | 0.254802i | \(0.917990\pi\) | |||||||
\(212\) | 3.72725e24i | 1.39593i | ||||||||
\(213\) | 2.27453e24 | + | 1.37488e24i | 0.810784 | + | 0.490094i | ||||
\(214\) | 7.84511e24 | 2.66228 | ||||||||
\(215\) | −7.45900e24 | −2.41033 | ||||||||
\(216\) | 1.85251e23 | − | 3.06836e24i | 0.0570160 | − | 0.944370i | ||||
\(217\) | −6.38069e24 | − | 4.18006e23i | −1.87086 | − | 0.122562i | ||||
\(218\) | − | 6.79571e24i | − | 1.89864i | ||||||
\(219\) | −2.35961e23 | − | 1.42631e23i | −0.0628316 | − | 0.0379798i | ||||
\(220\) | 5.89544e23i | 0.149650i | ||||||||
\(221\) | − | 1.59753e24i | − | 0.386662i | ||||||
\(222\) | 4.41048e24 | + | 2.66600e24i | 1.01808 | + | 0.615395i | ||||
\(223\) | 6.16436e24i | 1.35733i | 0.734446 | + | 0.678667i | \(0.237442\pi\) | ||||
−0.734446 | + | 0.678667i | \(0.762558\pi\) | |||||||
\(224\) | 4.99853e24 | + | 3.27459e23i | 1.05012 | + | 0.0687943i | ||||
\(225\) | −3.47184e24 | − | 6.61382e24i | −0.696054 | − | 1.32598i | ||||
\(226\) | 2.91408e24 | 0.557651 | ||||||||
\(227\) | 6.93449e24 | 1.26690 | 0.633451 | − | 0.773783i | \(-0.281638\pi\) | ||||
0.633451 | + | 0.773783i | \(0.281638\pi\) | |||||||
\(228\) | −2.14439e23 | − | 1.29622e23i | −0.0374101 | − | 0.0226132i | ||||
\(229\) | − | 3.15897e24i | − | 0.526349i | −0.964748 | − | 0.263174i | \(-0.915231\pi\) | ||
0.964748 | − | 0.263174i | \(-0.0847694\pi\) | |||||||
\(230\) | −2.25217e25 | −3.58475 | ||||||||
\(231\) | 2.24324e23 | − | 3.21563e23i | 0.0341153 | − | 0.0489035i | ||||
\(232\) | 8.21729e24 | 1.19428 | ||||||||
\(233\) | − | 9.88048e24i | − | 1.37259i | −0.727323 | − | 0.686295i | \(-0.759236\pi\) | ||
0.727323 | − | 0.686295i | \(-0.240764\pi\) | |||||||
\(234\) | −4.39973e24 | − | 8.38144e24i | −0.584332 | − | 1.11315i | ||||
\(235\) | −4.31157e24 | −0.547549 | ||||||||
\(236\) | −1.02162e25 | −1.24083 | ||||||||
\(237\) | 2.69774e24 | − | 4.46299e24i | 0.313431 | − | 0.518523i | ||||
\(238\) | 7.14556e24 | + | 4.68113e23i | 0.794288 | + | 0.0520346i | ||||
\(239\) | 2.66821e24i | 0.283820i | 0.989880 | + | 0.141910i | \(0.0453243\pi\) | ||||
−0.989880 | + | 0.141910i | \(0.954676\pi\) | |||||||
\(240\) | 5.30498e23 | − | 8.77626e23i | 0.0540089 | − | 0.0893493i | ||||
\(241\) | − | 1.85809e25i | − | 1.81087i | −0.424487 | − | 0.905434i | \(-0.639545\pi\) | ||
0.424487 | − | 0.905434i | \(-0.360455\pi\) | |||||||
\(242\) | − | 1.71792e25i | − | 1.60303i | ||||||
\(243\) | 4.59483e24 | + | 1.02041e25i | 0.410586 | + | 0.911822i | ||||
\(244\) | 2.86381e25i | 2.45104i | ||||||||
\(245\) | 1.91106e25 | + | 2.51470e24i | 1.56686 | + | 0.206178i | ||||
\(246\) | 1.81066e25 | + | 1.09449e25i | 1.42239 | + | 0.859789i | ||||
\(247\) | −2.85741e23 | −0.0215107 | ||||||||
\(248\) | 2.45836e25 | 1.77379 | ||||||||
\(249\) | −9.05281e24 | + | 1.49765e25i | −0.626167 | + | 1.03590i | ||||
\(250\) | 1.90752e25i | 1.26502i | ||||||||
\(251\) | −2.27896e25 | −1.44932 | −0.724658 | − | 0.689108i | \(-0.758002\pi\) | ||||
−0.724658 | + | 0.689108i | \(0.758002\pi\) | |||||||
\(252\) | 2.37949e25 | − | 1.05686e25i | 1.45137 | − | 0.644630i | ||||
\(253\) | −1.43688e24 | −0.0840729 | ||||||||
\(254\) | 3.31102e25i | 1.85869i | ||||||||
\(255\) | 7.50924e24 | − | 1.24229e25i | 0.404505 | − | 0.669190i | ||||
\(256\) | −1.72291e25 | −0.890721 | ||||||||
\(257\) | 6.00249e24 | 0.297875 | 0.148937 | − | 0.988847i | \(-0.452415\pi\) | ||||
0.148937 | + | 0.988847i | \(0.452415\pi\) | |||||||
\(258\) | −4.40745e25 | − | 2.66417e25i | −2.09981 | − | 1.26927i | ||||
\(259\) | −1.05669e24 | + | 1.61300e25i | −0.0483395 | + | 0.737883i | ||||
\(260\) | 4.46443e25i | 1.96131i | ||||||||
\(261\) | −2.64879e25 | + | 1.39045e25i | −1.11769 | + | 0.586718i | ||||
\(262\) | − | 2.43867e25i | − | 0.988531i | ||||||
\(263\) | − | 4.58439e23i | − | 0.0178545i | −0.999960 | − | 0.00892723i | \(-0.997158\pi\) | ||
0.999960 | − | 0.00892723i | \(-0.00284166\pi\) | |||||||
\(264\) | −7.79768e23 | + | 1.29000e24i | −0.0291826 | + | 0.0482781i | ||||
\(265\) | 3.86214e25i | 1.38914i | ||||||||
\(266\) | 8.37283e22 | − | 1.27808e24i | 0.00289478 | − | 0.0441876i | ||||
\(267\) | −1.86917e25 | + | 3.09225e25i | −0.621271 | + | 1.02780i | ||||
\(268\) | −3.28556e25 | −1.05001 | ||||||||
\(269\) | 2.23413e25 | 0.686610 | 0.343305 | − | 0.939224i | \(-0.388453\pi\) | ||||
0.343305 | + | 0.939224i | \(0.388453\pi\) | |||||||
\(270\) | 5.18361e24 | − | 8.58574e25i | 0.153219 | − | 2.53780i | ||||
\(271\) | 3.04586e25i | 0.866029i | 0.901387 | + | 0.433014i | \(0.142550\pi\) | ||||
−0.901387 | + | 0.433014i | \(0.857450\pi\) | |||||||
\(272\) | 1.19496e24 | 0.0326873 | ||||||||
\(273\) | 1.69873e25 | − | 2.43510e25i | 0.447114 | − | 0.640926i | ||||
\(274\) | 2.86340e25 | 0.725273 | ||||||||
\(275\) | 3.66289e24i | 0.0892958i | ||||||||
\(276\) | −8.16590e25 | − | 4.93603e25i | −1.91628 | − | 1.15833i | ||||
\(277\) | 2.91712e25 | 0.659048 | 0.329524 | − | 0.944147i | \(-0.393112\pi\) | ||||
0.329524 | + | 0.944147i | \(0.393112\pi\) | |||||||
\(278\) | 2.53955e25 | 0.552441 | ||||||||
\(279\) | −7.92437e25 | + | 4.15979e25i | −1.66005 | + | 0.871420i | ||||
\(280\) | −7.39469e25 | − | 4.84434e24i | −1.49197 | − | 0.0977406i | ||||
\(281\) | − | 3.04913e25i | − | 0.592598i | −0.955095 | − | 0.296299i | \(-0.904248\pi\) | ||
0.955095 | − | 0.296299i | \(-0.0957525\pi\) | |||||||
\(282\) | −2.54767e25 | − | 1.53999e25i | −0.477009 | − | 0.288338i | ||||
\(283\) | − | 2.91776e25i | − | 0.526370i | −0.964745 | − | 0.263185i | \(-0.915227\pi\) | ||
0.964745 | − | 0.263185i | \(-0.0847730\pi\) | |||||||
\(284\) | − | 8.65466e25i | − | 1.50455i | ||||||
\(285\) | −2.22200e24 | − | 1.34313e24i | −0.0372282 | − | 0.0225033i | ||||
\(286\) | 4.64185e24i | 0.0749631i | ||||||||
\(287\) | −4.33810e24 | + | 6.62194e25i | −0.0675366 | + | 1.03092i | ||||
\(288\) | 6.20782e25 | − | 3.25871e25i | 0.931790 | − | 0.489131i | ||||
\(289\) | −5.21772e25 | −0.755186 | ||||||||
\(290\) | 2.29932e26 | 3.20938 | ||||||||
\(291\) | 1.66044e25 | + | 1.00369e25i | 0.223536 | + | 0.135121i | ||||
\(292\) | 8.97842e24i | 0.116595i | ||||||||
\(293\) | −3.72338e25 | −0.466474 | −0.233237 | − | 0.972420i | \(-0.574932\pi\) | ||||
−0.233237 | + | 0.972420i | \(0.574932\pi\) | |||||||
\(294\) | 1.03941e26 | + | 8.31175e25i | 1.25643 | + | 1.00472i | ||||
\(295\) | −1.05859e26 | −1.23480 | ||||||||
\(296\) | − | 6.21460e25i | − | 0.699600i | ||||||
\(297\) | 3.30714e23 | − | 5.47769e24i | 0.00359343 | − | 0.0595189i | ||||
\(298\) | 1.18175e26 | 1.23953 | ||||||||
\(299\) | −1.08811e26 | −1.10185 | ||||||||
\(300\) | −1.25829e26 | + | 2.08164e26i | −1.23029 | + | 2.03532i | ||||
\(301\) | 1.05597e25 | − | 1.61189e26i | 0.0997017 | − | 1.52191i | ||||
\(302\) | − | 2.96097e26i | − | 2.69998i | ||||||
\(303\) | −9.48630e25 | + | 1.56936e26i | −0.835505 | + | 1.38221i | ||||
\(304\) | − | 2.13734e23i | − | 0.00181845i | ||||||
\(305\) | 2.96745e26i | 2.43913i | ||||||||
\(306\) | 8.87427e25 | − | 4.65843e25i | 0.704787 | − | 0.369969i | ||||
\(307\) | − | 2.05384e26i | − | 1.57621i | −0.615543 | − | 0.788104i | \(-0.711063\pi\) | ||
0.615543 | − | 0.788104i | \(-0.288937\pi\) | |||||||
\(308\) | −1.27401e25 | − | 8.34616e23i | −0.0944908 | − | 0.00619019i | ||||
\(309\) | 6.19666e25 | + | 3.74569e25i | 0.444216 | + | 0.268515i | ||||
\(310\) | 6.87886e26 | 4.76671 | ||||||||
\(311\) | 1.16711e26 | 0.781860 | 0.390930 | − | 0.920421i | \(-0.372154\pi\) | ||||
0.390930 | + | 0.920421i | \(0.372154\pi\) | |||||||
\(312\) | −5.90494e25 | + | 9.76880e25i | −0.382465 | + | 0.632729i | ||||
\(313\) | 1.15011e26i | 0.720315i | 0.932891 | + | 0.360158i | \(0.117277\pi\) | ||||
−0.932891 | + | 0.360158i | \(0.882723\pi\) | |||||||
\(314\) | −1.40779e26 | −0.852664 | ||||||||
\(315\) | 2.46560e26 | − | 1.09510e26i | 1.44432 | − | 0.641496i | ||||
\(316\) | −1.69818e26 | −0.962210 | ||||||||
\(317\) | 5.49826e25i | 0.301372i | 0.988582 | + | 0.150686i | \(0.0481483\pi\) | ||||
−0.988582 | + | 0.150686i | \(0.951852\pi\) | |||||||
\(318\) | −1.37946e26 | + | 2.28210e26i | −0.731516 | + | 1.21018i | ||||
\(319\) | 1.46696e25 | 0.0752692 | ||||||||
\(320\) | −5.17851e26 | −2.57116 | ||||||||
\(321\) | 2.94741e26 | + | 1.78162e26i | 1.41624 | + | 0.856075i | ||||
\(322\) | 3.18839e25 | − | 4.86695e26i | 0.148281 | − | 2.26345i | ||||
\(323\) | − | 3.02542e24i | − | 0.0136194i | ||||||
\(324\) | 2.06966e26 | − | 2.99940e26i | 0.901939 | − | 1.30711i | ||||
\(325\) | 2.77379e26i | 1.17030i | ||||||||
\(326\) | − | 2.67722e25i | − | 0.109370i | ||||||
\(327\) | 1.54330e26 | − | 2.55315e26i | 0.610519 | − | 1.01001i | ||||
\(328\) | − | 2.55131e26i | − | 0.977434i | ||||||
\(329\) | 6.10388e24 | − | 9.31733e25i | 0.0226490 | − | 0.345728i | ||||
\(330\) | −2.18191e25 | + | 3.60962e25i | −0.0784224 | + | 0.129738i | ||||
\(331\) | −2.90493e26 | −1.01145 | −0.505723 | − | 0.862696i | \(-0.668774\pi\) | ||||
−0.505723 | + | 0.862696i | \(0.668774\pi\) | |||||||
\(332\) | 5.69859e26 | 1.92229 | ||||||||
\(333\) | 1.05157e26 | + | 2.00323e26i | 0.343696 | + | 0.654738i | ||||
\(334\) | 1.88248e25i | 0.0596200i | ||||||||
\(335\) | −3.40446e26 | −1.04491 | ||||||||
\(336\) | 1.82145e25 | + | 1.27065e25i | 0.0541820 | + | 0.0377977i | ||||
\(337\) | −5.05078e26 | −1.45628 | −0.728139 | − | 0.685429i | \(-0.759615\pi\) | ||||
−0.728139 | + | 0.685429i | \(0.759615\pi\) | |||||||
\(338\) | − | 2.24080e26i | − | 0.626292i | ||||||
\(339\) | 1.09482e26 | + | 6.61785e25i | 0.296651 | + | 0.179316i | ||||
\(340\) | −4.72694e26 | −1.24180 | ||||||||
\(341\) | 4.38871e25 | 0.111793 | ||||||||
\(342\) | −8.33224e24 | − | 1.58728e25i | −0.0205820 | − | 0.0392085i | ||||
\(343\) | −8.13977e25 | + | 4.09421e26i | −0.194995 | + | 0.980804i | ||||
\(344\) | 6.21032e26i | 1.44295i | ||||||||
\(345\) | −8.46141e26 | − | 5.11466e26i | −1.90696 | − | 1.15270i | ||||
\(346\) | − | 5.96432e25i | − | 0.130395i | ||||||
\(347\) | 2.27772e26i | 0.483103i | 0.970388 | + | 0.241552i | \(0.0776563\pi\) | ||||
−0.970388 | + | 0.241552i | \(0.922344\pi\) | |||||||
\(348\) | 8.33685e26 | + | 5.03937e26i | 1.71562 | + | 1.03704i | ||||
\(349\) | 4.01953e26i | 0.802616i | 0.915943 | + | 0.401308i | \(0.131444\pi\) | ||||
−0.915943 | + | 0.401308i | \(0.868556\pi\) | |||||||
\(350\) | −1.24068e27 | − | 8.12782e25i | −2.40406 | − | 0.157492i | ||||
\(351\) | 2.50439e25 | − | 4.14808e26i | 0.0470953 | − | 0.780051i | ||||
\(352\) | −3.43804e25 | −0.0627499 | ||||||||
\(353\) | −7.95291e26 | −1.40894 | −0.704469 | − | 0.709735i | \(-0.748815\pi\) | ||||
−0.704469 | + | 0.709735i | \(0.748815\pi\) | |||||||
\(354\) | −6.25509e26 | − | 3.78101e26i | −1.07572 | − | 0.650240i | ||||
\(355\) | − | 8.96786e26i | − | 1.49724i | ||||||
\(356\) | 1.17661e27 | 1.90725 | ||||||||
\(357\) | 2.57828e26 | + | 1.79862e26i | 0.405801 | + | 0.283089i | ||||
\(358\) | 9.11160e26 | 1.39259 | ||||||||
\(359\) | − | 1.22948e26i | − | 0.182486i | −0.995829 | − | 0.0912429i | \(-0.970916\pi\) | ||
0.995829 | − | 0.0912429i | \(-0.0290840\pi\) | |||||||
\(360\) | −9.18368e26 | + | 4.82086e26i | −1.32386 | + | 0.694941i | ||||
\(361\) | 7.13668e26 | 0.999242 | ||||||||
\(362\) | 3.49245e26 | 0.474996 | ||||||||
\(363\) | 3.90139e26 | − | 6.45425e26i | 0.515466 | − | 0.852758i | ||||
\(364\) | −9.64767e26 | − | 6.32028e25i | −1.23839 | − | 0.0811282i | ||||
\(365\) | 9.30334e25i | 0.116028i | ||||||||
\(366\) | −1.05990e27 | + | 1.75344e27i | −1.28444 | + | 2.12490i | ||||
\(367\) | − | 3.38582e26i | − | 0.398722i | −0.979926 | − | 0.199361i | \(-0.936113\pi\) | ||
0.979926 | − | 0.199361i | \(-0.0638866\pi\) | |||||||
\(368\) | − | 8.13904e25i | − | 0.0931475i | ||||||
\(369\) | 4.31707e26 | + | 8.22397e26i | 0.480189 | + | 0.914755i | ||||
\(370\) | − | 1.73894e27i | − | 1.88003i | ||||||
\(371\) | −8.34610e26 | − | 5.46761e25i | −0.877117 | − | 0.0574608i | ||||
\(372\) | 2.49413e27 | + | 1.50762e27i | 2.54811 | + | 1.54025i | ||||
\(373\) | 7.10009e26 | 0.705215 | 0.352607 | − | 0.935771i | \(-0.385295\pi\) | ||||
0.352607 | + | 0.935771i | \(0.385295\pi\) | |||||||
\(374\) | −4.91479e25 | −0.0474627 | ||||||||
\(375\) | −4.33196e26 | + | 7.16655e26i | −0.406777 | + | 0.672949i | ||||
\(376\) | 3.58979e26i | 0.327791i | ||||||||
\(377\) | 1.11089e27 | 0.986473 | ||||||||
\(378\) | 1.84804e27 | + | 2.33566e26i | 1.59606 | + | 0.201719i | ||||
\(379\) | −1.84776e27 | −1.55215 | −0.776073 | − | 0.630643i | \(-0.782791\pi\) | ||||
−0.776073 | + | 0.630643i | \(0.782791\pi\) | |||||||
\(380\) | 8.45478e25i | 0.0690835i | ||||||||
\(381\) | −7.51929e26 | + | 1.24395e27i | −0.597674 | + | 0.988759i | ||||
\(382\) | −2.01347e27 | −1.55697 | ||||||||
\(383\) | 8.45726e26 | 0.636272 | 0.318136 | − | 0.948045i | \(-0.396943\pi\) | ||||
0.318136 | + | 0.948045i | \(0.396943\pi\) | |||||||
\(384\) | −1.82961e27 | − | 1.10594e27i | −1.33931 | − | 0.809570i | ||||
\(385\) | −1.32011e26 | − | 8.64819e24i | −0.0940315 | − | 0.00616010i | ||||
\(386\) | 2.21540e27i | 1.53563i | ||||||||
\(387\) | −1.05085e27 | − | 2.00186e27i | −0.708884 | − | 1.35042i | ||||
\(388\) | − | 6.31805e26i | − | 0.414810i | ||||||
\(389\) | 1.41617e26i | 0.0904992i | 0.998976 | + | 0.0452496i | \(0.0144083\pi\) | ||||
−0.998976 | + | 0.0452496i | \(0.985592\pi\) | |||||||
\(390\) | −1.65229e27 | + | 2.73346e27i | −1.02780 | + | 1.70033i | ||||
\(391\) | − | 1.15209e27i | − | 0.697637i | ||||||
\(392\) | 2.09373e26 | − | 1.59114e27i | 0.123429 | − | 0.938004i | ||||
\(393\) | 5.53821e26 | − | 9.16210e26i | 0.317869 | − | 0.525864i | ||||
\(394\) | 4.32869e27 | 2.41906 | ||||||||
\(395\) | −1.75964e27 | −0.957533 | ||||||||
\(396\) | −1.58223e26 | + | 8.30570e25i | −0.0838435 | + | 0.0440126i | ||||
\(397\) | 2.27686e27i | 1.17500i | 0.809225 | + | 0.587498i | \(0.199887\pi\) | ||||
−0.809225 | + | 0.587498i | \(0.800113\pi\) | |||||||
\(398\) | 4.08648e27 | 2.05389 | ||||||||
\(399\) | 3.21708e25 | − | 4.61160e25i | 0.0157487 | − | 0.0225754i | ||||
\(400\) | −2.07480e26 | −0.0989341 | ||||||||
\(401\) | − | 1.94142e27i | − | 0.901784i | −0.892579 | − | 0.450892i | \(-0.851106\pi\) | ||
0.892579 | − | 0.450892i | \(-0.148894\pi\) | |||||||
\(402\) | −2.01166e27 | − | 1.21599e27i | −0.910294 | − | 0.550245i | ||||
\(403\) | 3.32343e27 | 1.46516 | ||||||||
\(404\) | 5.97147e27 | 2.56494 | ||||||||
\(405\) | 2.14456e27 | − | 3.10794e27i | 0.897555 | − | 1.30075i | ||||
\(406\) | −3.25514e26 | + | 4.96884e27i | −0.132754 | + | 2.02643i | ||||
\(407\) | − | 1.10944e26i | − | 0.0440923i | ||||||
\(408\) | −1.03432e27 | − | 6.25215e26i | −0.400611 | − | 0.242157i | ||||
\(409\) | − | 2.53930e27i | − | 0.958560i | −0.877662 | − | 0.479280i | \(-0.840898\pi\) | ||
0.877662 | − | 0.479280i | \(-0.159102\pi\) | |||||||
\(410\) | − | 7.13894e27i | − | 2.62666i | ||||||
\(411\) | 1.07578e27 | + | 6.50276e26i | 0.385820 | + | 0.233216i | ||||
\(412\) | − | 2.35785e27i | − | 0.824320i | ||||||
\(413\) | 1.49864e26 | − | 2.28761e27i | 0.0510765 | − | 0.779663i | ||||
\(414\) | −3.17294e27 | − | 6.04441e27i | −1.05428 | − | 2.00840i | ||||
\(415\) | 5.90482e27 | 1.91294 | ||||||||
\(416\) | −2.60352e27 | −0.822396 | ||||||||
\(417\) | 9.54109e26 | + | 5.76729e26i | 0.293880 | + | 0.177641i | ||||
\(418\) | 8.79076e24i | 0.00264044i | ||||||||
\(419\) | −4.21573e27 | −1.23488 | −0.617442 | − | 0.786617i | \(-0.711831\pi\) | ||||
−0.617442 | + | 0.786617i | \(0.711831\pi\) | |||||||
\(420\) | −7.20520e27 | − | 5.02638e27i | −2.05839 | − | 1.43595i | ||||
\(421\) | −4.62166e27 | −1.28776 | −0.643881 | − | 0.765126i | \(-0.722677\pi\) | ||||
−0.643881 | + | 0.765126i | \(0.722677\pi\) | |||||||
\(422\) | 1.14478e28i | 3.11131i | ||||||||
\(423\) | −6.07429e26 | − | 1.15715e27i | −0.161036 | − | 0.306771i | ||||
\(424\) | 3.21559e27 | 0.831610 | ||||||||
\(425\) | −2.93689e27 | −0.740976 | ||||||||
\(426\) | 3.20310e27 | − | 5.29902e27i | 0.788441 | − | 1.30435i | ||||
\(427\) | −6.41267e27 | − | 4.20100e26i | −1.54009 | − | 0.100893i | ||||
\(428\) | − | 1.12150e28i | − | 2.62808i | ||||||
\(429\) | −1.05416e26 | + | 1.74394e26i | −0.0241049 | + | 0.0398777i | ||||
\(430\) | 1.73774e28i | 3.87763i | ||||||||
\(431\) | 6.44524e27i | 1.40355i | 0.712399 | + | 0.701775i | \(0.247609\pi\) | ||||
−0.712399 | + | 0.701775i | \(0.752391\pi\) | |||||||
\(432\) | 3.10277e26 | + | 1.87329e25i | 0.0659432 | + | 0.00398130i | ||||
\(433\) | 2.69544e27i | 0.559122i | 0.960128 | + | 0.279561i | \(0.0901889\pi\) | ||||
−0.960128 | + | 0.279561i | \(0.909811\pi\) | |||||||
\(434\) | −9.73838e26 | + | 1.48653e28i | −0.197172 | + | 3.00975i | ||||
\(435\) | 8.63855e27 | + | 5.22174e27i | 1.70728 | + | 1.03200i | ||||
\(436\) | −9.71483e27 | −1.87425 | ||||||||
\(437\) | −2.06066e26 | −0.0388108 | ||||||||
\(438\) | −3.32292e26 | + | 5.49725e26i | −0.0611001 | + | 0.101081i | ||||
\(439\) | 3.86249e27i | 0.693409i | 0.937974 | + | 0.346704i | \(0.112699\pi\) | ||||
−0.937974 | + | 0.346704i | \(0.887301\pi\) | |||||||
\(440\) | 5.08615e26 | 0.0891529 | ||||||||
\(441\) | 2.01747e27 | + | 5.48321e27i | 0.345304 | + | 0.938491i | ||||
\(442\) | −3.72181e27 | −0.622044 | ||||||||
\(443\) | − | 7.13537e27i | − | 1.16460i | −0.812973 | − | 0.582301i | \(-0.802153\pi\) | ||
0.812973 | − | 0.582301i | \(-0.197847\pi\) | |||||||
\(444\) | 3.81119e27 | − | 6.30502e27i | 0.607490 | − | 1.00500i | ||||
\(445\) | 1.21919e28 | 1.89798 | ||||||||
\(446\) | 1.43613e28 | 2.18362 | ||||||||
\(447\) | 4.43984e27 | + | 2.68375e27i | 0.659384 | + | 0.398578i | ||||
\(448\) | 7.33120e26 | − | 1.11908e28i | 0.106354 | − | 1.62346i | ||||
\(449\) | 1.43840e27i | 0.203842i | 0.994792 | + | 0.101921i | \(0.0324989\pi\) | ||||
−0.994792 | + | 0.101921i | \(0.967501\pi\) | |||||||
\(450\) | −1.54084e28 | + | 8.08843e27i | −2.13317 | + | 1.11978i | ||||
\(451\) | − | 4.55464e26i | − | 0.0616027i | ||||||
\(452\) | − | 4.16583e27i | − | 0.550488i | ||||||
\(453\) | 6.72433e27 | − | 1.11244e28i | 0.868196 | − | 1.43630i | ||||
\(454\) | − | 1.61554e28i | − | 2.03813i | ||||||
\(455\) | −9.99680e27 | − | 6.54901e26i | −1.23237 | − | 0.0807339i | ||||
\(456\) | −1.11828e26 | + | 1.85002e26i | −0.0134716 | + | 0.0222867i | ||||
\(457\) | 4.29861e27 | 0.506067 | 0.253033 | − | 0.967458i | \(-0.418572\pi\) | ||||
0.253033 | + | 0.967458i | \(0.418572\pi\) | |||||||
\(458\) | −7.35954e27 | −0.846765 | ||||||||
\(459\) | 4.39199e27 | + | 2.65165e26i | 0.493888 | + | 0.0298183i | ||||
\(460\) | 3.21960e28i | 3.53870i | ||||||||
\(461\) | 5.09154e26 | 0.0547003 | 0.0273501 | − | 0.999626i | \(-0.491293\pi\) | ||||
0.0273501 | + | 0.999626i | \(0.491293\pi\) | |||||||
\(462\) | −7.49153e26 | − | 5.22613e26i | −0.0786737 | − | 0.0548832i | ||||
\(463\) | 6.80934e27 | 0.699044 | 0.349522 | − | 0.936928i | \(-0.386344\pi\) | ||||
0.349522 | + | 0.936928i | \(0.386344\pi\) | |||||||
\(464\) | 8.30943e26i | 0.0833936i | ||||||||
\(465\) | 2.58439e28 | + | 1.56218e28i | 2.53572 | + | 1.53277i | ||||
\(466\) | −2.30188e28 | −2.20816 | ||||||||
\(467\) | −1.41874e28 | −1.33068 | −0.665342 | − | 0.746539i | \(-0.731714\pi\) | ||||
−0.665342 | + | 0.746539i | \(0.731714\pi\) | |||||||
\(468\) | −1.19817e28 | + | 6.28965e27i | −1.09885 | + | 0.576826i | ||||
\(469\) | 4.81969e26 | − | 7.35706e27i | 0.0432219 | − | 0.659766i | ||||
\(470\) | 1.00448e28i | 0.880872i | ||||||||
\(471\) | −5.28909e27 | − | 3.19709e27i | −0.453588 | − | 0.274180i | ||||
\(472\) | 8.81374e27i | 0.739213i | ||||||||
\(473\) | 1.10868e27i | 0.0909417i | ||||||||
\(474\) | −1.03975e28 | − | 6.28498e27i | −0.834175 | − | 0.504233i | ||||
\(475\) | 5.25303e26i | 0.0412218i | ||||||||
\(476\) | 6.69192e26 | − | 1.02149e28i | 0.0513662 | − | 0.784085i | ||||
\(477\) | −1.03653e28 | + | 5.44111e27i | −0.778282 | + | 0.408549i | ||||
\(478\) | 6.21620e27 | 0.456596 | ||||||||
\(479\) | −5.73151e27 | −0.411857 | −0.205928 | − | 0.978567i | \(-0.566021\pi\) | ||||
−0.205928 | + | 0.978567i | \(0.566021\pi\) | |||||||
\(480\) | −2.02457e28 | − | 1.22379e28i | −1.42331 | − | 0.860347i | ||||
\(481\) | − | 8.40144e27i | − | 0.577871i | ||||||
\(482\) | −4.32883e28 | −2.91324 | ||||||||
\(483\) | 1.22507e28 | − | 1.75611e28i | 0.806707 | − | 1.15640i | ||||
\(484\) | −2.45586e28 | −1.58244 | ||||||||
\(485\) | − | 6.54669e27i | − | 0.412794i | ||||||
\(486\) | 2.37728e28 | − | 1.07047e28i | 1.46690 | − | 0.660531i | ||||
\(487\) | −1.45983e28 | −0.881554 | −0.440777 | − | 0.897617i | \(-0.645297\pi\) | ||||
−0.440777 | + | 0.897617i | \(0.645297\pi\) | |||||||
\(488\) | 2.47068e28 | 1.46019 | ||||||||
\(489\) | 6.07994e26 | − | 1.00583e27i | 0.0351687 | − | 0.0581811i | ||||
\(490\) | 5.85857e27 | − | 4.45225e28i | 0.331690 | − | 2.52070i | ||||
\(491\) | 5.53228e27i | 0.306583i | 0.988181 | + | 0.153292i | \(0.0489874\pi\) | ||||
−0.988181 | + | 0.153292i | \(0.951013\pi\) | |||||||
\(492\) | 1.56463e28 | − | 2.58843e28i | 0.848744 | − | 1.40411i | ||||
\(493\) | 1.17621e28i | 0.624584i | ||||||||
\(494\) | 6.65697e26i | 0.0346054i | ||||||||
\(495\) | −1.63949e27 | + | 8.60627e26i | −0.0834359 | + | 0.0437986i | ||||
\(496\) | 2.48593e27i | 0.123860i | ||||||||
\(497\) | 1.93796e28 | + | 1.26958e27i | 0.945372 | + | 0.0619323i | ||||
\(498\) | 3.48910e28 | + | 2.10905e28i | 1.66650 | + | 1.00735i | ||||
\(499\) | −3.09444e27 | −0.144719 | −0.0723597 | − | 0.997379i | \(-0.523053\pi\) | ||||
−0.0723597 | + | 0.997379i | \(0.523053\pi\) | |||||||
\(500\) | 2.72690e28 | 1.24877 | ||||||||
\(501\) | −4.27509e26 | + | 7.07247e26i | −0.0191712 | + | 0.0317157i | ||||
\(502\) | 5.30936e28i | 2.33159i | ||||||||
\(503\) | −1.43502e28 | −0.617155 | −0.308577 | − | 0.951199i | \(-0.599853\pi\) | ||||
−0.308577 | + | 0.951199i | \(0.599853\pi\) | |||||||
\(504\) | −9.11777e27 | − | 2.05285e28i | −0.384032 | − | 0.864641i | ||||
\(505\) | 6.18757e28 | 2.55247 | ||||||||
\(506\) | 3.34754e27i | 0.135253i | ||||||||
\(507\) | 5.08883e27 | − | 8.41868e27i | 0.201388 | − | 0.333166i | ||||
\(508\) | 4.73327e28 | 1.83482 | ||||||||
\(509\) | 1.09072e28 | 0.414167 | 0.207084 | − | 0.978323i | \(-0.433603\pi\) | ||||
0.207084 | + | 0.978323i | \(0.433603\pi\) | |||||||
\(510\) | −2.89418e28 | − | 1.74944e28i | −1.07656 | − | 0.650749i | ||||
\(511\) | −2.01046e27 | − | 1.31707e26i | −0.0732614 | − | 0.00479943i | ||||
\(512\) | − | 3.69820e27i | − | 0.132025i | ||||||
\(513\) | 4.74284e25 | − | 7.85567e26i | 0.00165885 | − | 0.0274758i | ||||
\(514\) | − | 1.39841e28i | − | 0.479207i | ||||||
\(515\) | − | 2.44318e28i | − | 0.820313i | ||||||
\(516\) | −3.80857e28 | + | 6.30068e28i | −1.25297 | + | 2.07284i | ||||
\(517\) | 6.40856e26i | 0.0206590i | ||||||||
\(518\) | 3.75785e28 | + | 2.46181e27i | 1.18707 | + | 0.0777663i | ||||
\(519\) | 1.35449e27 | − | 2.24080e27i | 0.0419295 | − | 0.0693658i | ||||
\(520\) | 3.85158e28 | 1.16843 | ||||||||
\(521\) | −1.25296e28 | −0.372512 | −0.186256 | − | 0.982501i | \(-0.559635\pi\) | ||||
−0.186256 | + | 0.982501i | \(0.559635\pi\) | |||||||
\(522\) | 3.23936e28 | + | 6.17095e28i | 0.943885 | + | 1.79809i | ||||
\(523\) | 6.04609e28i | 1.72666i | 0.504639 | + | 0.863330i | \(0.331625\pi\) | ||||
−0.504639 | + | 0.863330i | \(0.668375\pi\) | |||||||
\(524\) | −3.48621e28 | −0.975832 | ||||||||
\(525\) | −4.47666e28 | − | 3.12294e28i | −1.22823 | − | 0.856822i | ||||
\(526\) | −1.06804e27 | −0.0287234 | ||||||||
\(527\) | 3.51885e28i | 0.927660i | ||||||||
\(528\) | −1.30447e26 | − | 7.88512e25i | −0.00337115 | − | 0.00203775i | ||||
\(529\) | −3.89989e28 | −0.988026 | ||||||||
\(530\) | 8.99771e28 | 2.23478 | ||||||||
\(531\) | −1.49137e28 | − | 2.84105e28i | −0.363157 | − | 0.691810i | ||||
\(532\) | −1.82708e27 | − | 1.19694e26i | −0.0436200 | − | 0.00285759i | ||||
\(533\) | − | 3.44908e28i | − | 0.807362i | ||||||
\(534\) | 7.20410e28 | + | 4.35466e28i | 1.65347 | + | 0.999472i | ||||
\(535\) | − | 1.16208e29i | − | 2.61531i | ||||||
\(536\) | 2.83454e28i | 0.625535i | ||||||||
\(537\) | 3.42323e28 | + | 2.06924e28i | 0.740809 | + | 0.447796i | ||||
\(538\) | − | 5.20492e28i | − | 1.10459i | ||||||
\(539\) | 3.73776e26 | − | 2.84053e27i | 0.00777910 | − | 0.0591177i | ||||
\(540\) | −1.22738e29 | − | 7.41024e27i | −2.50520 | − | 0.151251i | ||||
\(541\) | −6.04828e28 | −1.21077 | −0.605384 | − | 0.795934i | \(-0.706980\pi\) | ||||
−0.605384 | + | 0.795934i | \(0.706980\pi\) | |||||||
\(542\) | 7.09601e28 | 1.39323 | ||||||||
\(543\) | 1.31211e28 | + | 7.93132e27i | 0.252681 | + | 0.152738i | ||||
\(544\) | − | 2.75661e28i | − | 0.520699i | ||||||
\(545\) | −1.00664e29 | −1.86514 | ||||||||
\(546\) | −5.67310e28 | − | 3.95758e28i | −1.03109 | − | 0.719296i | ||||
\(547\) | −3.93098e28 | −0.700864 | −0.350432 | − | 0.936588i | \(-0.613965\pi\) | ||||
−0.350432 | + | 0.936588i | \(0.613965\pi\) | |||||||
\(548\) | − | 4.09338e28i | − | 0.715956i | ||||||
\(549\) | −7.96408e28 | + | 4.18064e28i | −1.36655 | + | 0.717353i | ||||
\(550\) | 8.53353e27 | 0.143655 | ||||||||
\(551\) | 2.10380e27 | 0.0347467 | ||||||||
\(552\) | −4.25844e28 | + | 7.04493e28i | −0.690065 | + | 1.14161i | ||||
\(553\) | 2.49111e27 | − | 3.80259e28i | 0.0396077 | − | 0.604596i | ||||
\(554\) | − | 6.79609e28i | − | 1.06025i | ||||||
\(555\) | 3.94911e28 | − | 6.53319e28i | 0.604537 | − | 1.00011i | ||||
\(556\) | − | 3.63042e28i | − | 0.545345i | ||||||
\(557\) | − | 4.25859e28i | − | 0.627750i | −0.949464 | − | 0.313875i | \(-0.898373\pi\) | ||
0.949464 | − | 0.313875i | \(-0.101627\pi\) | |||||||
\(558\) | 9.69117e28 | + | 1.84616e29i | 1.40190 | + | 2.67061i | ||||
\(559\) | 8.39566e28i | 1.19188i | ||||||||
\(560\) | 4.89866e26 | − | 7.47761e27i | 0.00682500 | − | 0.104181i | ||||
\(561\) | −1.84649e27 | − | 1.11614e27i | −0.0252485 | − | 0.0152620i | ||||
\(562\) | −7.10364e28 | −0.953344 | ||||||||
\(563\) | 7.91241e28 | 1.04225 | 0.521123 | − | 0.853481i | \(-0.325513\pi\) | ||||
0.521123 | + | 0.853481i | \(0.325513\pi\) | |||||||
\(564\) | −2.20149e28 | + | 3.64202e28i | −0.284634 | + | 0.470882i | ||||
\(565\) | − | 4.31658e28i | − | 0.547812i | ||||||
\(566\) | −6.79757e28 | −0.846800 | ||||||||
\(567\) | 6.41268e28 | + | 5.07440e28i | 0.784183 | + | 0.620530i | ||||
\(568\) | −7.46659e28 | −0.896324 | ||||||||
\(569\) | − | 3.77975e28i | − | 0.445435i | −0.974883 | − | 0.222718i | \(-0.928507\pi\) | ||
0.974883 | − | 0.222718i | \(-0.0714928\pi\) | |||||||
\(570\) | −3.12912e27 | + | 5.17664e27i | −0.0362023 | + | 0.0598911i | ||||
\(571\) | −1.16410e29 | −1.32224 | −0.661119 | − | 0.750281i | \(-0.729918\pi\) | ||||
−0.661119 | + | 0.750281i | \(0.729918\pi\) | |||||||
\(572\) | 6.63576e27 | 0.0740002 | ||||||||
\(573\) | −7.56459e28 | − | 4.57256e28i | −0.828251 | − | 0.500652i | ||||
\(574\) | 1.54273e29 | + | 1.01066e28i | 1.65850 | + | 0.108650i | ||||
\(575\) | 2.00037e29i | 2.11153i | ||||||||
\(576\) | −7.29566e28 | − | 1.38982e29i | −0.756186 | − | 1.44053i | ||||
\(577\) | − | 2.25293e28i | − | 0.229299i | −0.993406 | − | 0.114650i | \(-0.963425\pi\) | ||
0.993406 | − | 0.114650i | \(-0.0365745\pi\) | |||||||
\(578\) | 1.21559e29i | 1.21491i | ||||||||
\(579\) | −5.03117e28 | + | 8.32328e28i | −0.493792 | + | 0.816901i | ||||
\(580\) | − | 3.28700e29i | − | 3.16815i | ||||||
\(581\) | −8.35943e27 | + | 1.27603e29i | −0.0791275 | + | 1.20785i | ||||
\(582\) | 2.33831e28 | − | 3.86838e28i | 0.217376 | − | 0.359615i | ||||
\(583\) | 5.74053e27 | 0.0524122 | ||||||||
\(584\) | 7.74591e27 | 0.0694604 | ||||||||
\(585\) | −1.24153e29 | + | 6.51726e28i | −1.09351 | + | 0.574022i | ||||
\(586\) | 8.67446e28i | 0.750443i | ||||||||
\(587\) | 1.72478e29 | 1.46566 | 0.732830 | − | 0.680412i | \(-0.238199\pi\) | ||||
0.732830 | + | 0.680412i | \(0.238199\pi\) | |||||||
\(588\) | 1.18821e29 | − | 1.48589e29i | 0.991815 | − | 1.24029i | ||||
\(589\) | 6.29394e27 | 0.0516074 | ||||||||
\(590\) | 2.46622e29i | 1.98648i | ||||||||
\(591\) | 1.62629e29 | + | 9.83042e28i | 1.28685 | + | 0.777864i | ||||
\(592\) | 6.28428e27 | 0.0488515 | ||||||||
\(593\) | 1.84171e28 | 0.140652 | 0.0703261 | − | 0.997524i | \(-0.477596\pi\) | ||||
0.0703261 | + | 0.997524i | \(0.477596\pi\) | |||||||
\(594\) | −1.27615e28 | − | 7.70472e26i | −0.0957512 | − | 0.00578095i | ||||
\(595\) | 6.93409e27 | − | 1.05846e29i | 0.0511165 | − | 0.780274i | ||||
\(596\) | − | 1.68938e29i | − | 1.22360i | ||||||
\(597\) | 1.53529e29 | + | 9.28037e28i | 1.09260 | + | 0.660443i | ||||
\(598\) | 2.53499e29i | 1.77261i | ||||||||
\(599\) | − | 1.07610e29i | − | 0.739389i | −0.929153 | − | 0.369694i | \(-0.879462\pi\) | ||
0.929153 | − | 0.369694i | \(-0.120538\pi\) | |||||||
\(600\) | 1.79589e29 | + | 1.08556e29i | 1.21253 | + | 0.732935i | ||||
\(601\) | 1.62804e29i | 1.08015i | 0.841617 | + | 0.540075i | \(0.181604\pi\) | ||||
−0.841617 | + | 0.540075i | \(0.818396\pi\) | |||||||
\(602\) | −3.75527e29 | − | 2.46011e28i | −2.44837 | − | 0.160395i | ||||
\(603\) | −4.79632e28 | − | 9.13695e28i | −0.307310 | − | 0.585422i | ||||
\(604\) | −4.23286e29 | −2.66530 | ||||||||
\(605\) | −2.54474e29 | −1.57475 | ||||||||
\(606\) | 3.65617e29 | + | 2.21005e29i | 2.22364 | + | 1.34412i | ||||
\(607\) | 3.12917e27i | 0.0187046i | 0.999956 | + | 0.00935228i | \(0.00297697\pi\) | ||||
−0.999956 | + | 0.00935228i | \(0.997023\pi\) | |||||||
\(608\) | −4.93057e27 | −0.0289674 | ||||||||
\(609\) | −1.25072e29 | + | 1.79287e29i | −0.722233 | + | 1.03530i | ||||
\(610\) | 6.91333e29 | 3.92396 | ||||||||
\(611\) | 4.85300e28i | 0.270756i | ||||||||
\(612\) | −6.65948e28 | − | 1.26862e29i | −0.365216 | − | 0.695733i | ||||
\(613\) | 2.18203e29 | 1.17632 | 0.588161 | − | 0.808744i | \(-0.299852\pi\) | ||||
0.588161 | + | 0.808744i | \(0.299852\pi\) | |||||||
\(614\) | −4.78488e29 | −2.53573 | ||||||||
\(615\) | 1.62125e29 | − | 2.68210e29i | 0.844619 | − | 1.39729i | ||||
\(616\) | −7.20044e26 | + | 1.09912e28i | −0.00368775 | + | 0.0562921i | ||||
\(617\) | 6.39451e28i | 0.321968i | 0.986957 | + | 0.160984i | \(0.0514668\pi\) | ||||
−0.986957 | + | 0.160984i | \(0.948533\pi\) | |||||||
\(618\) | 8.72643e28 | − | 1.44365e29i | 0.431974 | − | 0.714634i | ||||
\(619\) | 7.74911e28i | 0.377138i | 0.982060 | + | 0.188569i | \(0.0603849\pi\) | ||||
−0.982060 | + | 0.188569i | \(0.939615\pi\) | |||||||
\(620\) | − | 9.83369e29i | − | 4.70548i | ||||||
\(621\) | 1.80608e28 | − | 2.99146e29i | 0.0849720 | − | 1.40741i | ||||
\(622\) | − | 2.71905e29i | − | 1.25782i | ||||||
\(623\) | −1.72601e28 | + | 2.63468e29i | −0.0785088 | + | 1.19841i | ||||
\(624\) | −9.87834e27 | − | 5.97115e27i | −0.0441820 | − | 0.0267067i | ||||
\(625\) | −5.79489e28 | −0.254862 | ||||||||
\(626\) | 2.67943e29 | 1.15881 | ||||||||
\(627\) | −1.99638e26 | + | 3.30269e26i | −0.000849050 | + | 0.00140462i | ||||
\(628\) | 2.01252e29i | 0.841711i | ||||||||
\(629\) | 8.89545e28 | 0.365878 | ||||||||
\(630\) | −2.55129e29 | − | 5.74417e29i | −1.03201 | − | 2.32355i | ||||
\(631\) | −6.62000e28 | −0.263360 | −0.131680 | − | 0.991292i | \(-0.542037\pi\) | ||||
−0.131680 | + | 0.991292i | \(0.542037\pi\) | |||||||
\(632\) | 1.46506e29i | 0.573228i | ||||||||
\(633\) | −2.59980e29 | + | 4.30096e29i | −1.00046 | + | 1.65511i | ||||
\(634\) | 1.28094e29 | 0.484834 | ||||||||
\(635\) | 4.90456e29 | 1.82590 | ||||||||
\(636\) | 3.26238e29 | + | 1.97201e29i | 1.19463 | + | 0.722120i | ||||
\(637\) | 2.83049e28 | − | 2.15104e29i | 0.101952 | − | 0.774792i | ||||
\(638\) | − | 3.41762e28i | − | 0.121090i | ||||||
\(639\) | 2.40681e29 | − | 1.26342e29i | 0.838846 | − | 0.440342i | ||||
\(640\) | 7.21366e29i | 2.47324i | ||||||||
\(641\) | − | 5.35790e29i | − | 1.80711i | −0.428469 | − | 0.903556i | \(-0.640947\pi\) | ||
0.428469 | − | 0.903556i | \(-0.359053\pi\) | |||||||
\(642\) | 4.15068e29 | − | 6.86665e29i | 1.37721 | − | 2.27838i | ||||
\(643\) | 7.02568e27i | 0.0229336i | 0.999934 | + | 0.0114668i | \(0.00365008\pi\) | ||||
−0.999934 | + | 0.0114668i | \(0.996350\pi\) | |||||||
\(644\) | −6.95757e29 | − | 4.55797e28i | −2.23437 | − | 0.146376i | ||||
\(645\) | −3.94639e29 | + | 6.52869e29i | −1.24688 | + | 2.06276i | ||||
\(646\) | −7.04840e27 | −0.0219103 | ||||||||
\(647\) | 1.86087e29 | 0.569141 | 0.284571 | − | 0.958655i | \(-0.408149\pi\) | ||||
0.284571 | + | 0.958655i | \(0.408149\pi\) | |||||||
\(648\) | −2.58766e29 | − | 1.78555e29i | −0.778698 | − | 0.537322i | ||||
\(649\) | 1.57344e28i | 0.0465889i | ||||||||
\(650\) | 6.46218e29 | 1.88273 | ||||||||
\(651\) | −3.74176e29 | + | 5.36372e29i | −1.07269 | + | 1.53768i | ||||
\(652\) | −3.82722e28 | −0.107965 | ||||||||
\(653\) | 1.68964e29i | 0.469037i | 0.972112 | + | 0.234518i | \(0.0753513\pi\) | ||||
−0.972112 | + | 0.234518i | \(0.924649\pi\) | |||||||
\(654\) | −5.94814e29 | − | 3.59547e29i | −1.62486 | − | 0.982175i | ||||
\(655\) | −3.61237e29 | −0.971089 | ||||||||
\(656\) | 2.57992e28 | 0.0682520 | ||||||||
\(657\) | −2.49684e28 | + | 1.31069e28i | −0.0650062 | + | 0.0341242i | ||||
\(658\) | −2.17068e29 | − | 1.42204e28i | −0.556191 | − | 0.0364367i | ||||
\(659\) | − | 1.52596e29i | − | 0.384809i | −0.981316 | − | 0.192405i | \(-0.938371\pi\) | ||
0.981316 | − | 0.192405i | \(-0.0616286\pi\) | |||||||
\(660\) | 5.16015e28 | + | 3.11915e28i | 0.128071 | + | 0.0774150i | ||||
\(661\) | − | 1.90403e29i | − | 0.465112i | −0.972583 | − | 0.232556i | \(-0.925291\pi\) | ||
0.972583 | − | 0.232556i | \(-0.0747090\pi\) | |||||||
\(662\) | 6.76770e29i | 1.62717i | ||||||||
\(663\) | −1.39829e29 | − | 8.45221e28i | −0.330906 | − | 0.200022i | ||||
\(664\) | − | 4.91632e29i | − | 1.14518i | ||||||
\(665\) | −1.89320e28 | − | 1.24026e27i | −0.0434080 | − | 0.00284370i | ||||
\(666\) | 4.66698e29 | − | 2.44987e29i | 1.05331 | − | 0.552923i | ||||
\(667\) | 8.01133e29 | 1.77985 | ||||||||
\(668\) | 2.69110e28 | 0.0588541 | ||||||||
\(669\) | 5.39552e29 | + | 3.26143e29i | 1.16161 | + | 0.702156i | ||||
\(670\) | 7.93146e29i | 1.68100i | ||||||||
\(671\) | 4.41070e28 | 0.0920282 | ||||||||
\(672\) | 2.93123e29 | − | 4.20185e29i | 0.602106 | − | 0.863104i | ||||
\(673\) | −9.33776e29 | −1.88836 | −0.944180 | − | 0.329431i | \(-0.893143\pi\) | ||||
−0.944180 | + | 0.329431i | \(0.893143\pi\) | |||||||
\(674\) | 1.17669e30i | 2.34279i | ||||||||
\(675\) | −7.62580e29 | − | 4.60405e28i | −1.49484 | − | 0.0902507i | ||||
\(676\) | −3.20334e29 | −0.618247 | ||||||||
\(677\) | −5.35876e29 | −1.01832 | −0.509159 | − | 0.860673i | \(-0.670043\pi\) | ||||
−0.509159 | + | 0.860673i | \(0.670043\pi\) | |||||||
\(678\) | 1.54178e29 | − | 2.55063e29i | 0.288476 | − | 0.477238i | ||||
\(679\) | 1.41474e29 | + | 9.26813e27i | 0.260642 | + | 0.0170749i | ||||
\(680\) | 4.07805e29i | 0.739791i | ||||||||
\(681\) | 3.66889e29 | − | 6.06960e29i | 0.655375 | − | 1.08422i | ||||
\(682\) | − | 1.02245e29i | − | 0.179848i | ||||||
\(683\) | 1.98799e29i | 0.344347i | 0.985067 | + | 0.172173i | \(0.0550789\pi\) | ||||
−0.985067 | + | 0.172173i | \(0.944921\pi\) | |||||||
\(684\) | −2.26911e28 | + | 1.19114e28i | −0.0387049 | + | 0.0203176i | ||||
\(685\) | − | 4.24152e29i | − | 0.712476i | ||||||
\(686\) | 9.53839e29 | + | 1.89634e29i | 1.57787 | + | 0.313699i | ||||
\(687\) | −2.76498e29 | − | 1.67135e29i | −0.450450 | − | 0.272283i | ||||
\(688\) | −6.27996e28 | −0.100758 | ||||||||
\(689\) | 4.34713e29 | 0.686911 | ||||||||
\(690\) | −1.19158e30 | + | 1.97128e30i | −1.85441 | + | 3.06783i | ||||
\(691\) | − | 1.59235e29i | − | 0.244073i | −0.992526 | − | 0.122036i | \(-0.961058\pi\) | ||
0.992526 | − | 0.122036i | \(-0.0389424\pi\) | |||||||
\(692\) | −8.52631e28 | −0.128720 | ||||||||
\(693\) | −1.62772e28 | − | 3.66478e28i | −0.0242036 | − | 0.0544940i | ||||
\(694\) | 5.30645e29 | 0.777194 | ||||||||
\(695\) | − | 3.76180e29i | − | 0.542694i | ||||||
\(696\) | 4.34759e29 | − | 7.19241e29i | 0.617805 | − | 1.02206i | ||||
\(697\) | 3.65189e29 | 0.511180 | ||||||||
\(698\) | 9.36439e29 | 1.29121 | ||||||||
\(699\) | −8.64816e29 | − | 5.22755e29i | −1.17466 | − | 0.710048i | ||||
\(700\) | −1.16192e29 | + | 1.77362e30i | −0.155469 | + | 2.37318i | ||||
\(701\) | − | 1.17219e30i | − | 1.54511i | −0.634947 | − | 0.772556i | \(-0.718978\pi\) | ||
0.634947 | − | 0.772556i | \(-0.281022\pi\) | |||||||
\(702\) | −9.66389e29 | − | 5.83454e28i | −1.25491 | − | 0.0757648i | ||||
\(703\) | − | 1.59107e28i | − | 0.0203544i | ||||||
\(704\) | 7.69714e28i | 0.0970100i | ||||||||
\(705\) | −2.28116e29 | + | 3.77382e29i | −0.283250 | + | 0.468593i | ||||
\(706\) | 1.85281e30i | 2.26663i | ||||||||
\(707\) | −8.75972e28 | + | 1.33714e30i | −0.105581 | + | 1.61166i | ||||
\(708\) | −5.40515e29 | + | 8.94198e29i | −0.641887 | + | 1.06190i | ||||
\(709\) | −1.06385e30 | −1.24479 | −0.622394 | − | 0.782704i | \(-0.713840\pi\) | ||||
−0.622394 | + | 0.782704i | \(0.713840\pi\) | |||||||
\(710\) | −2.08926e30 | −2.40869 | ||||||||
\(711\) | −2.47904e29 | − | 4.72254e29i | −0.281613 | − | 0.536469i | ||||
\(712\) | − | 1.01509e30i | − | 1.13623i | ||||||
\(713\) | 2.39674e30 | 2.64351 | ||||||||
\(714\) | 4.19029e29 | − | 6.00668e29i | 0.455421 | − | 0.652835i | ||||
\(715\) | 6.87590e28 | 0.0736404 | ||||||||
\(716\) | − | 1.30255e30i | − | 1.37470i | ||||||
\(717\) | 2.33543e29 | + | 1.41169e29i | 0.242893 | + | 0.146821i | ||||
\(718\) | −2.86434e29 | −0.293575 | ||||||||
\(719\) | 6.67357e29 | 0.674070 | 0.337035 | − | 0.941492i | \(-0.390576\pi\) | ||||
0.337035 | + | 0.941492i | \(0.390576\pi\) | |||||||
\(720\) | −4.87491e28 | − | 9.28666e28i | −0.0485261 | − | 0.0924418i | ||||
\(721\) | 5.27973e29 | + | 3.45880e28i | 0.517954 | + | 0.0339317i | ||||
\(722\) | − | 1.66265e30i | − | 1.60753i | ||||||
\(723\) | −1.62634e30 | − | 9.83073e29i | −1.54974 | − | 0.936772i | ||||
\(724\) | − | 4.99263e29i | − | 0.468894i | ||||||
\(725\) | − | 2.04224e30i | − | 1.89042i | ||||||
\(726\) | −1.50366e30 | − | 9.08917e29i | −1.37188 | − | 0.829258i | ||||
\(727\) | 6.90567e29i | 0.621004i | 0.950573 | + | 0.310502i | \(0.100497\pi\) | ||||
−0.950573 | + | 0.310502i | \(0.899503\pi\) | |||||||
\(728\) | −5.45267e28 | + | 8.32329e29i | −0.0483314 | + | 0.737760i | ||||
\(729\) | 1.13625e30 | + | 1.37703e29i | 0.992736 | + | 0.120311i | ||||
\(730\) | 2.16742e29 | 0.186661 | ||||||||
\(731\) | −8.88933e29 | −0.754634 | ||||||||
\(732\) | 2.50663e30 | + | 1.51518e30i | 2.09760 | + | 1.26794i | ||||
\(733\) | 4.20731e29i | 0.347066i | 0.984828 | + | 0.173533i | \(0.0555184\pi\) | ||||
−0.984828 | + | 0.173533i | \(0.944482\pi\) | |||||||
\(734\) | −7.88802e29 | −0.641445 | ||||||||
\(735\) | 1.23121e30 | − | 1.53966e30i | 0.986994 | − | 1.23426i | ||||
\(736\) | −1.87757e30 | −1.48381 | ||||||||
\(737\) | 5.06026e28i | 0.0394243i | ||||||||
\(738\) | 1.91596e30 | − | 1.00576e30i | 1.47162 | − | 0.772506i | ||||
\(739\) | 1.25107e30 | 0.947357 | 0.473678 | − | 0.880698i | \(-0.342926\pi\) | ||||
0.473678 | + | 0.880698i | \(0.342926\pi\) | |||||||
\(740\) | −2.48590e30 | −1.85588 | ||||||||
\(741\) | −1.51179e28 | + | 2.50102e28i | −0.0111276 | + | 0.0184089i | ||||
\(742\) | −1.27380e29 | + | 1.94441e30i | −0.0924403 | + | 1.41107i | ||||
\(743\) | − | 2.36025e29i | − | 0.168879i | −0.996429 | − | 0.0844395i | \(-0.973090\pi\) | ||
0.996429 | − | 0.0844395i | \(-0.0269100\pi\) | |||||||
\(744\) | 1.30067e30 | − | 2.15175e30i | 0.917593 | − | 1.51801i | ||||
\(745\) | − | 1.75051e30i | − | 1.21766i | ||||||
\(746\) | − | 1.65413e30i | − | 1.13452i | ||||||
\(747\) | 8.31891e29 | + | 1.58474e30i | 0.562601 | + | 1.07175i | ||||
\(748\) | 7.02595e28i | 0.0468531i | ||||||||
\(749\) | 2.51127e30 | + | 1.64516e29i | 1.65133 | + | 0.108180i | ||||
\(750\) | 1.66961e30 | + | 1.00923e30i | 1.08261 | + | 0.654404i | ||||
\(751\) | 1.54560e30 | 0.988273 | 0.494137 | − | 0.869384i | \(-0.335484\pi\) | ||||
0.494137 | + | 0.869384i | \(0.335484\pi\) | |||||||
\(752\) | −3.63004e28 | −0.0228889 | ||||||||
\(753\) | −1.20575e30 | + | 1.99473e30i | −0.749739 | + | 1.24033i | ||||
\(754\) | − | 2.58806e30i | − | 1.58699i | ||||||
\(755\) | −4.38604e30 | −2.65234 | ||||||||
\(756\) | 3.33895e29 | − | 2.64188e30i | 0.199127 | − | 1.57556i | ||||
\(757\) | 1.15022e30 | 0.676510 | 0.338255 | − | 0.941055i | \(-0.390163\pi\) | ||||
0.338255 | + | 0.941055i | \(0.390163\pi\) | |||||||
\(758\) | 4.30476e30i | 2.49702i | ||||||||
\(759\) | −7.60224e28 | + | 1.25767e29i | −0.0434914 | + | 0.0719496i | ||||
\(760\) | 7.29415e28 | 0.0411559 | ||||||||
\(761\) | 8.64030e28 | 0.0480828 | 0.0240414 | − | 0.999711i | \(-0.492347\pi\) | ||||
0.0240414 | + | 0.999711i | \(0.492347\pi\) | |||||||
\(762\) | 2.89806e30 | + | 1.75179e30i | 1.59067 | + | 0.961511i | ||||
\(763\) | 1.42510e29 | − | 2.17535e30i | 0.0771501 | − | 1.17767i | ||||
\(764\) | 2.87835e30i | 1.53697i | ||||||||
\(765\) | −6.90048e29 | − | 1.31453e30i | −0.363441 | − | 0.692351i | ||||
\(766\) | − | 1.97031e30i | − | 1.02360i | ||||||
\(767\) | 1.19152e30i | 0.610591i | ||||||||
\(768\) | −9.11552e29 | + | 1.50802e30i | −0.460775 | + | 0.762280i | ||||
\(769\) | 2.41996e30i | 1.20665i | 0.797494 | + | 0.603326i | \(0.206158\pi\) | ||||
−0.797494 | + | 0.603326i | \(0.793842\pi\) | |||||||
\(770\) | −2.01479e28 | + | 3.07550e29i | −0.00991008 | + | 0.151274i | ||||
\(771\) | 3.17579e29 | − | 5.25384e29i | 0.154092 | − | 0.254921i | ||||
\(772\) | 3.16704e30 | 1.51590 | ||||||||
\(773\) | −1.59678e29 | −0.0753983 | −0.0376991 | − | 0.999289i | \(-0.512003\pi\) | ||||
−0.0376991 | + | 0.999289i | \(0.512003\pi\) | |||||||
\(774\) | −4.66377e30 | + | 2.44819e30i | −2.17249 | + | 1.14042i | ||||
\(775\) | − | 6.10977e30i | − | 2.80774i | ||||||
\(776\) | −5.45074e29 | −0.247120 | ||||||||
\(777\) | 1.35592e30 | + | 9.45896e29i | 0.606475 | + | 0.423080i | ||||
\(778\) | 3.29929e29 | 0.145591 | ||||||||
\(779\) | − | 6.53190e28i | − | 0.0284378i | ||||||
\(780\) | 3.90762e30 | + | 2.36204e30i | 1.67849 | + | 1.01460i | ||||
\(781\) | −1.33295e29 | −0.0564908 | ||||||||
\(782\) | −2.68405e30 | −1.12233 | ||||||||
\(783\) | −1.84389e29 | + | 3.05408e30i | −0.0760742 | + | 1.26003i | ||||
\(784\) | 1.60898e29 | + | 2.11721e28i | 0.0654986 | + | 0.00861875i | ||||
\(785\) | 2.08535e30i | 0.837620i | ||||||||
\(786\) | −2.13452e30 | − | 1.29025e30i | −0.845985 | − | 0.511372i | ||||
\(787\) | 3.10288e30i | 1.21347i | 0.794903 | + | 0.606736i | \(0.207522\pi\) | ||||
−0.794903 | + | 0.606736i | \(0.792478\pi\) | |||||||
\(788\) | − | 6.18809e30i | − | 2.38798i | ||||||
\(789\) | −4.01262e28 | − | 2.42550e28i | −0.0152799 | − | 0.00923621i | ||||
\(790\) | 4.09947e30i | 1.54043i | ||||||||
\(791\) | 9.32816e29 | + | 6.11097e28i | 0.345894 | + | 0.0226599i | ||||
\(792\) | 7.16554e28 | + | 1.36503e29i | 0.0262201 | + | 0.0499490i | ||||
\(793\) | 3.34008e30 | 1.20612 | ||||||||
\(794\) | 5.30446e30 | 1.89028 | ||||||||
\(795\) | 3.38044e30 | + | 2.04337e30i | 1.18883 | + | 0.718609i | ||||
\(796\) | − | 5.84184e30i | − | 2.02751i | ||||||
\(797\) | −2.95812e30 | −1.01322 | −0.506610 | − | 0.862175i | \(-0.669102\pi\) | ||||
−0.506610 | + | 0.862175i | \(0.669102\pi\) | |||||||
\(798\) | −1.07438e29 | − | 7.49490e28i | −0.0363183 | − | 0.0253359i | ||||
\(799\) | −5.13836e29 | −0.171428 | ||||||||
\(800\) | 4.78629e30i | 1.57599i | ||||||||
\(801\) | 1.71764e30 | + | 3.27209e30i | 0.558202 | + | 1.06337i | ||||
\(802\) | −4.52296e30 | −1.45075 | ||||||||
\(803\) | 1.38281e28 | 0.00437774 | ||||||||
\(804\) | −1.73832e30 | + | 2.87578e30i | −0.543177 | + | 0.898601i | ||||
\(805\) | −7.20935e30 | − | 4.72292e29i | −2.22351 | − | 0.145665i | ||||
\(806\) | − | 7.74268e30i | − | 2.35707i | ||||||
\(807\) | 1.18203e30 | − | 1.95549e30i | 0.355187 | − | 0.587602i | ||||
\(808\) | − | 5.15174e30i | − | 1.52804i | ||||||
\(809\) | − | 2.66423e30i | − | 0.780033i | −0.920808 | − | 0.390017i | \(-0.872469\pi\) | ||
0.920808 | − | 0.390017i | \(-0.127531\pi\) | |||||||
\(810\) | −7.24065e30 | − | 4.99624e30i | −2.09259 | − | 1.44394i | ||||
\(811\) | 6.24009e29i | 0.178021i | 0.996031 | + | 0.0890107i | \(0.0283705\pi\) | ||||
−0.996031 | + | 0.0890107i | \(0.971629\pi\) | |||||||
\(812\) | 7.10322e30 | + | 4.65339e29i | 2.00040 | + | 0.131048i | ||||
\(813\) | 2.66597e30 | + | 1.61150e30i | 0.741148 | + | 0.448001i | ||||
\(814\) | −2.58469e29 | −0.0709336 | ||||||||
\(815\) | −3.96573e29 | −0.107440 | ||||||||
\(816\) | 6.32226e28 | − | 1.04592e29i | 0.0169093 | − | 0.0279738i | ||||
\(817\) | 1.58998e29i | 0.0419816i | ||||||||
\(818\) | −5.91587e30 | −1.54209 | ||||||||
\(819\) | −1.23262e30 | − | 2.77522e30i | −0.317211 | − | 0.714195i | ||||
\(820\) | −1.02055e31 | −2.59292 | ||||||||
\(821\) | 2.05593e30i | 0.515711i | 0.966184 | + | 0.257855i | \(0.0830158\pi\) | ||||
−0.966184 | + | 0.257855i | \(0.916984\pi\) | |||||||
\(822\) | 1.51496e30 | − | 2.50627e30i | 0.375187 | − | 0.620689i | ||||
\(823\) | 1.84157e30 | 0.450286 | 0.225143 | − | 0.974326i | \(-0.427715\pi\) | ||||
0.225143 | + | 0.974326i | \(0.427715\pi\) | |||||||
\(824\) | −2.03418e30 | −0.491081 | ||||||||
\(825\) | 3.20605e29 | + | 1.93796e29i | 0.0764194 | + | 0.0461932i | ||||
\(826\) | −5.32951e30 | − | 3.49142e29i | −1.25429 | − | 0.0821696i | ||||
\(827\) | 6.46545e30i | 1.50242i | 0.660065 | + | 0.751209i | \(0.270529\pi\) | ||||
−0.660065 | + | 0.751209i | \(0.729471\pi\) | |||||||
\(828\) | −8.64080e30 | + | 4.53588e30i | −1.98260 | + | 1.04074i | ||||
\(829\) | − | 2.82216e30i | − | 0.639380i | −0.947522 | − | 0.319690i | \(-0.896421\pi\) | ||
0.947522 | − | 0.319690i | \(-0.103579\pi\) | |||||||
\(830\) | − | 1.37566e31i | − | 3.07745i | ||||||
\(831\) | 1.54339e30 | − | 2.55329e30i | 0.340929 | − | 0.564014i | ||||
\(832\) | 5.82880e30i | 1.27141i | ||||||||
\(833\) | 2.27752e30 | + | 2.99692e29i | 0.490558 | + | 0.0645510i | ||||
\(834\) | 1.34362e30 | − | 2.22281e30i | 0.285781 | − | 0.472780i | ||||
\(835\) | 2.78849e29 | 0.0585680 | ||||||||
\(836\) | 1.25669e28 | 0.00260652 | ||||||||
\(837\) | −5.51636e29 | + | 9.13688e30i | −0.112989 | + | 1.87146i | ||||
\(838\) | 9.82150e30i | 1.98662i | ||||||||
\(839\) | 6.87817e30 | 1.37395 | 0.686977 | − | 0.726679i | \(-0.258937\pi\) | ||||
0.686977 | + | 0.726679i | \(0.258937\pi\) | |||||||
\(840\) | −4.33639e30 | + | 6.21611e30i | −0.855452 | + | 1.22627i | ||||
\(841\) | −3.04621e30 | −0.593474 | ||||||||
\(842\) | 1.07672e31i | 2.07169i | ||||||||
\(843\) | −2.66884e30 | − | 1.61323e30i | −0.507146 | − | 0.306554i | ||||
\(844\) | 1.63653e31 | 3.07134 | ||||||||
\(845\) | −3.31926e30 | −0.615242 | ||||||||
\(846\) | −2.69583e30 | + | 1.41514e30i | −0.493519 | + | 0.259066i | ||||
\(847\) | 3.60258e29 | − | 5.49919e30i | 0.0651385 | − | 0.994313i | ||||
\(848\) | 3.25165e29i | 0.0580694i | ||||||||
\(849\) | −2.55385e30 | − | 1.54372e30i | −0.450468 | − | 0.272294i | ||||
\(850\) | 6.84215e30i | 1.19205i | ||||||||
\(851\) | − | 6.05883e30i | − | 1.04263i | ||||||
\(852\) | −7.57523e30 | − | 4.57899e30i | −1.28760 | − | 0.778313i | ||||
\(853\) | − | 9.66484e30i | − | 1.62267i | −0.584583 | − | 0.811334i | \(-0.698742\pi\) | ||
0.584583 | − | 0.811334i | \(-0.301258\pi\) | |||||||
\(854\) | −9.78718e29 | + | 1.49398e31i | −0.162312 | + | 2.47763i | ||||
\(855\) | −2.35122e29 | + | 1.23424e29i | −0.0385167 | + | 0.0202189i | ||||
\(856\) | −9.67546e30 | −1.56566 | ||||||||
\(857\) | −9.77331e30 | −1.56222 | −0.781111 | − | 0.624392i | \(-0.785347\pi\) | ||||
−0.781111 | + | 0.624392i | \(0.785347\pi\) | |||||||
\(858\) | 4.06291e29 | + | 2.45590e29i | 0.0641535 | + | 0.0387788i | ||||
\(859\) | − | 1.74488e30i | − | 0.272168i | −0.990697 | − | 0.136084i | \(-0.956548\pi\) | ||
0.990697 | − | 0.136084i | \(-0.0434517\pi\) | |||||||
\(860\) | 2.48419e31 | 3.82782 | ||||||||
\(861\) | 5.56652e30 | + | 3.88323e30i | 0.847326 | + | 0.591099i | ||||
\(862\) | 1.50156e31 | 2.25797 | ||||||||
\(863\) | − | 5.51035e30i | − | 0.818589i | −0.912402 | − | 0.409295i | \(-0.865775\pi\) | ||
0.912402 | − | 0.409295i | \(-0.134225\pi\) | |||||||
\(864\) | 4.32143e29 | − | 7.15768e30i | 0.0634210 | − | 1.05046i | ||||
\(865\) | −8.83487e29 | −0.128095 | ||||||||
\(866\) | 6.27963e30 | 0.899489 | ||||||||
\(867\) | −2.76059e30 | + | 4.56696e30i | −0.390662 | + | 0.646289i | ||||
\(868\) | 2.12507e31 | + | 1.39215e30i | 2.97109 | + | 0.194639i | ||||
\(869\) | 2.61546e29i | 0.0361277i | ||||||||
\(870\) | 1.21652e31 | − | 2.01254e31i | 1.66023 | − | 2.74659i | ||||
\(871\) | 3.83198e30i | 0.516693i | ||||||||
\(872\) | 8.38123e30i | 1.11657i | ||||||||
\(873\) | 1.75701e30 | − | 9.22320e29i | 0.231273 | − | 0.121404i | ||||
\(874\) | 4.80078e29i | 0.0624370i | ||||||||
\(875\) | −4.00017e29 | + | 6.10610e30i | −0.0514036 | + | 0.784656i | ||||
\(876\) | 7.85861e29 | + | 4.75029e29i | 0.0997821 | + | 0.0603152i | ||||
\(877\) | −1.28183e30 | −0.160818 | −0.0804090 | − | 0.996762i | \(-0.525623\pi\) | ||||
−0.0804090 | + | 0.996762i | \(0.525623\pi\) | |||||||
\(878\) | 8.99853e30 | 1.11552 | ||||||||
\(879\) | −1.96996e30 | + | 3.25900e30i | −0.241310 | + | 0.399209i | ||||
\(880\) | 5.14318e28i | 0.00622535i | ||||||||
\(881\) | −5.77654e30 | −0.690909 | −0.345455 | − | 0.938435i | \(-0.612275\pi\) | ||||
−0.345455 | + | 0.938435i | \(0.612275\pi\) | |||||||
\(882\) | 1.27744e31 | − | 4.70015e30i | 1.50980 | − | 0.555509i | ||||
\(883\) | 4.13098e30 | 0.482465 | 0.241232 | − | 0.970467i | \(-0.422448\pi\) | ||||
0.241232 | + | 0.970467i | \(0.422448\pi\) | |||||||
\(884\) | 5.32053e30i | 0.614053i | ||||||||
\(885\) | −5.60076e30 | + | 9.26558e30i | −0.638767 | + | 1.05674i | ||||
\(886\) | −1.66234e31 | −1.87356 | ||||||||
\(887\) | 1.32995e31 | 1.48128 | 0.740641 | − | 0.671900i | \(-0.234522\pi\) | ||||
0.740641 | + | 0.671900i | \(0.234522\pi\) | |||||||
\(888\) | −5.43950e30 | − | 3.28801e30i | −0.598719 | − | 0.361907i | ||||
\(889\) | −6.94337e29 | + | 1.05988e31i | −0.0755269 | + | 1.15289i | ||||
\(890\) | − | 2.84038e31i | − | 3.05339i | ||||||
\(891\) | −4.61953e29 | − | 3.18760e29i | −0.0490774 | − | 0.0338647i | ||||
\(892\) | − | 2.05302e31i | − | 2.15557i | ||||||
\(893\) | 9.19065e28i | 0.00953687i | ||||||||
\(894\) | 6.25239e30 | − | 1.03436e31i | 0.641213 | − | 1.06079i | ||||
\(895\) | − | 1.34969e31i | − | 1.36802i | ||||||
\(896\) | −1.55888e31 | − | 1.02124e30i | −1.56163 | − | 0.102304i | ||||
\(897\) | −5.75694e30 | + | 9.52396e30i | −0.569995 | + | 0.942967i | ||||
\(898\) | 3.35109e30 | 0.327932 | ||||||||
\(899\) | −2.44692e31 | −2.36670 | ||||||||
\(900\) | 1.15628e31 | + | 2.20271e31i | 1.10540 | + | 2.10577i | ||||
\(901\) | 4.60274e30i | 0.434916i | ||||||||
\(902\) | −1.06110e30 | −0.0991036 | ||||||||
\(903\) | −1.35499e31 | − | 9.45245e30i | −1.25087 | − | 0.872615i | ||||
\(904\) | −3.59396e30 | −0.327948 | ||||||||
\(905\) | − | 5.17331e30i | − | 0.466615i | ||||||
\(906\) | −2.59167e31 | − | 1.56658e31i | −2.31065 | − | 1.39671i | ||||
\(907\) | −7.06118e30 | −0.622302 | −0.311151 | − | 0.950361i | \(-0.600714\pi\) | ||||
−0.311151 | + | 0.950361i | \(0.600714\pi\) | |||||||
\(908\) | −2.30951e31 | −2.01195 | ||||||||
\(909\) | 8.71726e30 | + | 1.66063e31i | 0.750687 | + | 1.43005i | ||||
\(910\) | −1.52574e30 | + | 2.32898e31i | −0.129881 | + | 1.98258i | ||||
\(911\) | − | 9.76514e30i | − | 0.821742i | −0.911693 | − | 0.410871i | \(-0.865225\pi\) | ||
0.911693 | − | 0.410871i | \(-0.134775\pi\) | |||||||
\(912\) | −1.87077e28 | − | 1.13082e28i | −0.00155623 | − | 0.000940694i | ||||
\(913\) | − | 8.77670e29i | − | 0.0721752i | ||||||
\(914\) | − | 1.00146e31i | − | 0.814137i | ||||||
\(915\) | 2.59734e31 | + | 1.57001e31i | 2.08741 | + | 1.26177i | ||||
\(916\) | 1.05208e31i | 0.835888i | ||||||||
\(917\) | 5.11403e29 | − | 7.80636e30i | 0.0401684 | − | 0.613155i | ||||
\(918\) | 6.17762e29 | − | 1.02321e31i | 0.0479703 | − | 0.794544i | ||||
\(919\) | 1.61670e30 | 0.124113 | 0.0620565 | − | 0.998073i | \(-0.480234\pi\) | ||||
0.0620565 | + | 0.998073i | \(0.480234\pi\) | |||||||
\(920\) | 2.77763e31 | 2.10815 | ||||||||
\(921\) | −1.79768e31 | − | 1.08664e31i | −1.34892 | − | 0.815380i | ||||
\(922\) | − | 1.18619e30i | − | 0.0879993i | ||||||
\(923\) | −1.00940e31 | −0.740365 | ||||||||
\(924\) | −7.47102e29 | + | 1.07095e30i | −0.0541782 | + | 0.0776631i | ||||
\(925\) | −1.54451e31 | −1.10740 | ||||||||
\(926\) | − | 1.58639e31i | − | 1.12459i | ||||||
\(927\) | 6.55704e30 | − | 3.44204e30i | 0.459590 | − | 0.241256i | ||||
\(928\) | 1.91688e31 | 1.32844 | ||||||||
\(929\) | 4.32143e30 | 0.296116 | 0.148058 | − | 0.988979i | \(-0.452698\pi\) | ||||
0.148058 | + | 0.988979i | \(0.452698\pi\) | |||||||
\(930\) | 3.63946e31 | − | 6.02091e31i | 2.46584 | − | 4.07935i | ||||
\(931\) | 5.36040e28 | − | 4.07366e29i | 0.00359108 | − | 0.0272906i | ||||
\(932\) | 3.29066e31i | 2.17979i | ||||||||
\(933\) | 6.17494e30 | − | 1.02155e31i | 0.404460 | − | 0.669116i | ||||
\(934\) | 3.30527e31i | 2.14074i | ||||||||
\(935\) | 7.28021e29i | 0.0466253i | ||||||||
\(936\) | 5.42624e30 | + | 1.03369e31i | 0.343639 | + | 0.654629i | ||||
\(937\) | − | 5.99725e30i | − | 0.375566i | −0.982210 | − | 0.187783i | \(-0.939870\pi\) | ||
0.982210 | − | 0.187783i | \(-0.0601302\pi\) | |||||||
\(938\) | −1.71399e31 | − | 1.12285e30i | −1.06140 | − | 0.0695334i | ||||
\(939\) | 1.00666e31 | + | 6.08497e30i | 0.616446 | + | 0.372623i | ||||
\(940\) | 1.43595e31 | 0.869556 | ||||||||
\(941\) | −7.31941e30 | −0.438314 | −0.219157 | − | 0.975690i | \(-0.570331\pi\) | ||||
−0.219157 | + | 0.975690i | \(0.570331\pi\) | |||||||
\(942\) | −7.44834e30 | + | 1.23221e31i | −0.441088 | + | 0.729711i | ||||
\(943\) | − | 2.48736e31i | − | 1.45669i | ||||||
\(944\) | −8.91257e29 | −0.0516175 | ||||||||
\(945\) | 3.45978e30 | − | 2.73748e31i | 0.198159 | − | 1.56790i | ||||
\(946\) | 2.58291e30 | 0.146303 | ||||||||
\(947\) | 1.89558e31i | 1.06186i | 0.847416 | + | 0.530929i | \(0.178157\pi\) | ||||
−0.847416 | + | 0.530929i | \(0.821843\pi\) | |||||||
\(948\) | −8.98472e30 | + | 1.48638e31i | −0.497756 | + | 0.823460i | ||||
\(949\) | 1.04716e30 | 0.0573744 | ||||||||
\(950\) | 1.22381e30 | 0.0663157 | ||||||||
\(951\) | 4.81251e30 | + | 2.90901e30i | 0.257915 | + | 0.155901i | ||||
\(952\) | −8.81269e30 | − | 5.77328e29i | −0.467112 | − | 0.0306010i | ||||
\(953\) | 9.15410e30i | 0.479888i | 0.970787 | + | 0.239944i | \(0.0771291\pi\) | ||||
−0.970787 | + | 0.239944i | \(0.922871\pi\) | |||||||
\(954\) | 1.26763e31 | + | 2.41482e31i | 0.657255 | + | 1.25206i | ||||
\(955\) | 2.98252e31i | 1.52949i | ||||||||
\(956\) | − | 8.88638e30i | − | 0.450731i | ||||||
\(957\) | 7.76139e29 | − | 1.28400e30i | 0.0389372 | − | 0.0644155i | ||||
\(958\) | 1.33528e31i | 0.662576i | ||||||||
\(959\) | 9.16594e30 | + | 6.00470e29i | 0.449865 | + | 0.0294711i | ||||
\(960\) | −2.73984e31 | + | 4.53263e31i | −1.33008 | + | 2.20041i | ||||
\(961\) | −5.23789e31 | −2.51513 | ||||||||
\(962\) | −1.95730e31 | −0.929652 | ||||||||
\(963\) | 3.11882e31 | − | 1.63718e31i | 1.46526 | − | 0.769169i | ||||
\(964\) | 6.18829e31i | 2.87582i | ||||||||
\(965\) | 3.28165e31 | 1.50853 | ||||||||
\(966\) | −4.09125e31 | − | 2.85407e31i | −1.86035 | − | 1.29779i | ||||
\(967\) | 2.08330e31 | 0.937074 | 0.468537 | − | 0.883444i | \(-0.344781\pi\) | ||||
0.468537 | + | 0.883444i | \(0.344781\pi\) | |||||||
\(968\) | 2.11874e31i | 0.942726i | ||||||||
\(969\) | −2.64808e29 | − | 1.60069e29i | −0.0116555 | − | 0.00704541i | ||||
\(970\) | −1.52520e31 | −0.664084 | ||||||||
\(971\) | −3.78036e31 | −1.62829 | −0.814144 | − | 0.580663i | \(-0.802793\pi\) | ||||
−0.814144 | + | 0.580663i | \(0.802793\pi\) | |||||||
\(972\) | −1.53029e31 | − | 3.39845e31i | −0.652046 | − | 1.44805i | ||||
\(973\) | 8.12927e30 | + | 5.32557e29i | 0.342663 | + | 0.0224482i | ||||
\(974\) | 3.40101e31i | 1.41820i | ||||||||
\(975\) | 2.42784e31 | + | 1.46755e31i | 1.00155 | + | 0.605405i | ||||
\(976\) | 2.49838e30i | 0.101961i | ||||||||
\(977\) | 4.51470e31i | 1.82279i | 0.411535 | + | 0.911394i | \(0.364993\pi\) | ||||
−0.411535 | + | 0.911394i | \(0.635007\pi\) | |||||||
\(978\) | −2.34331e30 | − | 1.41646e30i | −0.0935991 | − | 0.0565778i | ||||
\(979\) | − | 1.81216e30i | − | 0.0716109i | ||||||
\(980\) | −6.36472e31 | − | 8.37513e30i | −2.48832 | − | 0.327429i | ||||
\(981\) | −1.41819e31 | − | 2.70163e31i | −0.548541 | − | 1.04497i | ||||
\(982\) | 1.28887e31 | 0.493217 | ||||||||
\(983\) | 6.86801e30 | 0.260027 | 0.130014 | − | 0.991512i | \(-0.458498\pi\) | ||||
0.130014 | + | 0.991512i | \(0.458498\pi\) | |||||||
\(984\) | −2.23310e31 | − | 1.34984e31i | −0.836489 | − | 0.505632i | ||||
\(985\) | − | 6.41203e31i | − | 2.37638i | ||||||
\(986\) | 2.74024e31 | 1.00480 | ||||||||
\(987\) | −7.83231e30 | − | 5.46386e30i | −0.284158 | − | 0.198230i | ||||
\(988\) | 9.51649e29 | 0.0341609 | ||||||||
\(989\) | 6.05467e31i | 2.15045i | ||||||||
\(990\) | 2.00502e30 | + | 3.81955e30i | 0.0704612 | + | 0.134228i | ||||
\(991\) | −3.29436e31 | −1.14551 | −0.572754 | − | 0.819727i | \(-0.694125\pi\) | ||||
−0.572754 | + | 0.819727i | \(0.694125\pi\) | |||||||
\(992\) | 5.73471e31 | 1.97305 | ||||||||
\(993\) | −1.53694e31 | + | 2.54262e31i | −0.523226 | + | 0.865596i | ||||
\(994\) | 2.95776e30 | − | 4.51491e31i | 0.0996338 | − | 1.52087i | ||||
\(995\) | − | 6.05325e31i | − | 2.01765i | ||||||
\(996\) | 3.01500e31 | − | 4.98785e31i | 0.994408 | − | 1.64509i | ||||
\(997\) | 1.34350e31i | 0.438467i | 0.975672 | + | 0.219234i | \(0.0703557\pi\) | ||||
−0.975672 | + | 0.219234i | \(0.929644\pi\) | |||||||
\(998\) | 7.20920e30i | 0.232818i | ||||||||
\(999\) | 2.30975e31 | + | 1.39450e30i | 0.738121 | + | 0.0445638i |
(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.20.5 | ✓ | 52 | |
3.2 | odd | 2 | inner | 21.22.c.b.20.48 | yes | 52 | |
7.6 | odd | 2 | inner | 21.22.c.b.20.47 | yes | 52 | |
21.20 | even | 2 | inner | 21.22.c.b.20.6 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.22.c.b.20.5 | ✓ | 52 | 1.1 | even | 1 | trivial | |
21.22.c.b.20.6 | yes | 52 | 21.20 | even | 2 | inner | |
21.22.c.b.20.47 | yes | 52 | 7.6 | odd | 2 | inner | |
21.22.c.b.20.48 | yes | 52 | 3.2 | odd | 2 | inner |