Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,11,Mod(19,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.19");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.7071450535\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.9 | ||
Character | \(\chi\) | \(=\) | 20.19 |
Dual form | 20.11.d.d.19.10 |
$q$-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 \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −17.2353 | − | 26.9619i | −0.538603 | − | 0.842560i | ||||
\(3\) | −146.443 | −0.602646 | −0.301323 | − | 0.953522i | \(-0.597428\pi\) | ||||
−0.301323 | + | 0.953522i | \(0.597428\pi\) | |||||||
\(4\) | −429.889 | + | 929.393i | −0.419813 | + | 0.907611i | ||||
\(5\) | −2538.13 | + | 1823.05i | −0.812202 | + | 0.583377i | ||||
\(6\) | 2523.99 | + | 3948.38i | 0.324587 | + | 0.507765i | ||||
\(7\) | 13979.7 | 0.831776 | 0.415888 | − | 0.909416i | \(-0.363471\pi\) | ||||
0.415888 | + | 0.909416i | \(0.363471\pi\) | |||||||
\(8\) | 32467.5 | − | 4427.76i | 0.990829 | − | 0.135124i | ||||
\(9\) | −37603.5 | −0.636818 | ||||||||
\(10\) | 92898.4 | + | 37012.0i | 0.928984 | + | 0.370120i | ||||
\(11\) | 88389.7i | 0.548830i | 0.961611 | + | 0.274415i | \(0.0884843\pi\) | ||||
−0.961611 | + | 0.274415i | \(0.911516\pi\) | |||||||
\(12\) | 62954.1 | − | 136103.i | 0.252999 | − | 0.546968i | ||||
\(13\) | − | 249490.i | − | 0.671948i | −0.941871 | − | 0.335974i | \(-0.890935\pi\) | ||
0.941871 | − | 0.335974i | \(-0.109065\pi\) | |||||||
\(14\) | −240944. | − | 376918.i | −0.447997 | − | 0.700821i | ||||
\(15\) | 371691. | − | 266973.i | 0.489470 | − | 0.351569i | ||||
\(16\) | −678968. | − | 799071.i | −0.647514 | − | 0.762054i | ||||
\(17\) | − | 410905.i | − | 0.289399i | −0.989476 | − | 0.144699i | \(-0.953779\pi\) | ||
0.989476 | − | 0.144699i | \(-0.0462215\pi\) | |||||||
\(18\) | 648107. | + | 1.01386e6i | 0.342992 | + | 0.536557i | ||||
\(19\) | − | 3.01950e6i | − | 1.21946i | −0.792610 | − | 0.609729i | \(-0.791278\pi\) | ||
0.792610 | − | 0.609729i | \(-0.208722\pi\) | |||||||
\(20\) | −603219. | − | 3.14263e6i | −0.188506 | − | 0.982072i | ||||
\(21\) | −2.04722e6 | −0.501266 | ||||||||
\(22\) | 2.38315e6 | − | 1.52342e6i | 0.462422 | − | 0.295602i | ||||
\(23\) | 4.53962e6 | 0.705311 | 0.352655 | − | 0.935753i | \(-0.385279\pi\) | ||||
0.352655 | + | 0.935753i | \(0.385279\pi\) | |||||||
\(24\) | −4.75463e6 | + | 648414.i | −0.597119 | + | 0.0814322i | ||||
\(25\) | 3.11858e6 | − | 9.25429e6i | 0.319343 | − | 0.947639i | ||||
\(26\) | −6.72671e6 | + | 4.30003e6i | −0.566156 | + | 0.361913i | ||||
\(27\) | 1.41541e7 | 0.986421 | ||||||||
\(28\) | −6.00970e6 | + | 1.29926e7i | −0.349191 | + | 0.754929i | ||||
\(29\) | 2.62491e7 | 1.27975 | 0.639874 | − | 0.768480i | \(-0.278987\pi\) | ||||
0.639874 | + | 0.768480i | \(0.278987\pi\) | |||||||
\(30\) | −1.36043e7 | − | 5.42014e6i | −0.559848 | − | 0.223051i | ||||
\(31\) | 3.62534e7i | 1.26631i | 0.774025 | + | 0.633155i | \(0.218240\pi\) | ||||
−0.774025 | + | 0.633155i | \(0.781760\pi\) | |||||||
\(32\) | −9.84227e6 | + | 3.20785e7i | −0.293323 | + | 0.956014i | ||||
\(33\) | − | 1.29440e7i | − | 0.330750i | ||||||
\(34\) | −1.10788e7 | + | 7.08207e6i | −0.243836 | + | 0.155871i | ||||
\(35\) | −3.54822e7 | + | 2.54857e7i | −0.675570 | + | 0.485239i | ||||
\(36\) | 1.61653e7 | − | 3.49484e7i | 0.267345 | − | 0.577983i | ||||
\(37\) | − | 8.29063e7i | − | 1.19558i | −0.801652 | − | 0.597791i | \(-0.796045\pi\) | ||
0.801652 | − | 0.597791i | \(-0.203955\pi\) | |||||||
\(38\) | −8.14114e7 | + | 5.20419e7i | −1.02747 | + | 0.656804i | ||||
\(39\) | 3.65360e7i | 0.404947i | ||||||||
\(40\) | −7.43346e7 | + | 7.04281e7i | −0.725924 | + | 0.687775i | ||||
\(41\) | 1.07285e8 | 0.926018 | 0.463009 | − | 0.886354i | \(-0.346770\pi\) | ||||
0.463009 | + | 0.886354i | \(0.346770\pi\) | |||||||
\(42\) | 3.52845e7 | + | 5.51970e7i | 0.269984 | + | 0.422347i | ||||
\(43\) | −1.58335e6 | −0.0107705 | −0.00538525 | − | 0.999985i | \(-0.501714\pi\) | ||||
−0.00538525 | + | 0.999985i | \(0.501714\pi\) | |||||||
\(44\) | −8.21488e7 | − | 3.79977e7i | −0.498124 | − | 0.230406i | ||||
\(45\) | 9.54425e7 | − | 6.85531e7i | 0.517225 | − | 0.371505i | ||||
\(46\) | −7.82418e7 | − | 1.22397e8i | −0.379883 | − | 0.594266i | ||||
\(47\) | 4.34667e8 | 1.89526 | 0.947628 | − | 0.319376i | \(-0.103473\pi\) | ||||
0.947628 | + | 0.319376i | \(0.103473\pi\) | |||||||
\(48\) | 9.94300e7 | + | 1.17018e8i | 0.390221 | + | 0.459248i | ||||
\(49\) | −8.70443e7 | −0.308148 | ||||||||
\(50\) | −3.03263e8 | + | 7.54175e7i | −0.970442 | + | 0.241336i | ||||
\(51\) | 6.01741e7i | 0.174405i | ||||||||
\(52\) | 2.31874e8 | + | 1.07253e8i | 0.609867 | + | 0.282093i | ||||
\(53\) | − | 3.42615e8i | − | 0.819269i | −0.912250 | − | 0.409635i | \(-0.865656\pi\) | ||
0.912250 | − | 0.409635i | \(-0.134344\pi\) | |||||||
\(54\) | −2.43950e8 | − | 3.81621e8i | −0.531290 | − | 0.831119i | ||||
\(55\) | −1.61139e8 | − | 2.24345e8i | −0.320175 | − | 0.445761i | ||||
\(56\) | 4.53884e8 | − | 6.18986e7i | 0.824148 | − | 0.112393i | ||||
\(57\) | 4.42184e8i | 0.734901i | ||||||||
\(58\) | −4.52411e8 | − | 7.07725e8i | −0.689276 | − | 1.07826i | ||||
\(59\) | − | 8.22725e8i | − | 1.15079i | −0.817877 | − | 0.575393i | \(-0.804849\pi\) | ||
0.817877 | − | 0.575393i | \(-0.195151\pi\) | |||||||
\(60\) | 8.83372e7 | + | 4.60216e8i | 0.113602 | + | 0.591841i | ||||
\(61\) | −9.43238e8 | −1.11679 | −0.558396 | − | 0.829575i | \(-0.688583\pi\) | ||||
−0.558396 | + | 0.829575i | \(0.688583\pi\) | |||||||
\(62\) | 9.77460e8 | − | 6.24838e8i | 1.06694 | − | 0.682039i | ||||
\(63\) | −5.25684e8 | −0.529690 | ||||||||
\(64\) | 1.03453e9 | − | 2.87516e8i | 0.963483 | − | 0.267770i | ||||
\(65\) | 4.54833e8 | + | 6.33237e8i | 0.391999 | + | 0.545757i | ||||
\(66\) | −3.48996e8 | + | 2.23094e8i | −0.278677 | + | 0.178143i | ||||
\(67\) | −1.13591e9 | −0.841333 | −0.420667 | − | 0.907215i | \(-0.638204\pi\) | ||||
−0.420667 | + | 0.907215i | \(0.638204\pi\) | |||||||
\(68\) | 3.81892e8 | + | 1.76643e8i | 0.262661 | + | 0.121493i | ||||
\(69\) | −6.64796e8 | −0.425053 | ||||||||
\(70\) | 1.29869e9 | + | 5.17415e8i | 0.772707 | + | 0.307857i | ||||
\(71\) | 2.91342e9i | 1.61477i | 0.590023 | + | 0.807386i | \(0.299118\pi\) | ||||
−0.590023 | + | 0.807386i | \(0.700882\pi\) | |||||||
\(72\) | −1.22089e9 | + | 1.66499e8i | −0.630978 | + | 0.0860497i | ||||
\(73\) | 2.08673e9i | 1.00659i | 0.864114 | + | 0.503295i | \(0.167879\pi\) | ||||
−0.864114 | + | 0.503295i | \(0.832121\pi\) | |||||||
\(74\) | −2.23531e9 | + | 1.42892e9i | −1.00735 | + | 0.643944i | ||||
\(75\) | −4.56695e8 | + | 1.35522e9i | −0.192451 | + | 0.571091i | ||||
\(76\) | 2.80630e9 | + | 1.29805e9i | 1.10679 | + | 0.511944i | ||||
\(77\) | 1.23566e9i | 0.456504i | ||||||||
\(78\) | 9.85080e8 | − | 6.29709e8i | 0.341192 | − | 0.218106i | ||||
\(79\) | − | 5.83812e9i | − | 1.89731i | −0.316318 | − | 0.948653i | \(-0.602447\pi\) | ||
0.316318 | − | 0.948653i | \(-0.397553\pi\) | |||||||
\(80\) | 3.18006e9 | + | 7.90353e8i | 0.970476 | + | 0.241197i | ||||
\(81\) | 1.47685e8 | 0.0423556 | ||||||||
\(82\) | −1.84909e9 | − | 2.89261e9i | −0.498756 | − | 0.780225i | ||||
\(83\) | 9.99337e8 | 0.253700 | 0.126850 | − | 0.991922i | \(-0.459513\pi\) | ||||
0.126850 | + | 0.991922i | \(0.459513\pi\) | |||||||
\(84\) | 8.80078e8 | − | 1.90267e9i | 0.210438 | − | 0.454955i | ||||
\(85\) | 7.49101e8 | + | 1.04293e9i | 0.168828 | + | 0.235050i | ||||
\(86\) | 2.72896e7 | + | 4.26902e7i | 0.00580102 | + | 0.00907478i | ||||
\(87\) | −3.84399e9 | −0.771234 | ||||||||
\(88\) | 3.91368e8 | + | 2.86979e9i | 0.0741604 | + | 0.543797i | ||||
\(89\) | −3.97301e9 | −0.711492 | −0.355746 | − | 0.934583i | \(-0.615773\pi\) | ||||
−0.355746 | + | 0.934583i | \(0.615773\pi\) | |||||||
\(90\) | −3.49330e9 | − | 1.39178e9i | −0.591594 | − | 0.235699i | ||||
\(91\) | − | 3.48778e9i | − | 0.558910i | ||||||
\(92\) | −1.95153e9 | + | 4.21910e9i | −0.296099 | + | 0.640148i | ||||
\(93\) | − | 5.30905e9i | − | 0.763136i | ||||||
\(94\) | −7.49163e9 | − | 1.17195e10i | −1.02079 | − | 1.59687i | ||||
\(95\) | 5.50470e9 | + | 7.66388e9i | 0.711403 | + | 0.990445i | ||||
\(96\) | 1.44133e9 | − | 4.69767e9i | 0.176770 | − | 0.576137i | ||||
\(97\) | − | 6.44299e9i | − | 0.750290i | −0.926966 | − | 0.375145i | \(-0.877593\pi\) | ||
0.926966 | − | 0.375145i | \(-0.122407\pi\) | |||||||
\(98\) | 1.50024e9 | + | 2.34688e9i | 0.165970 | + | 0.259633i | ||||
\(99\) | − | 3.32376e9i | − | 0.349505i | ||||||
\(100\) | 7.26023e9 | + | 6.87671e9i | 0.726023 | + | 0.687671i | ||||
\(101\) | 8.50355e9 | 0.809083 | 0.404542 | − | 0.914520i | \(-0.367431\pi\) | ||||
0.404542 | + | 0.914520i | \(0.367431\pi\) | |||||||
\(102\) | 1.62241e9 | − | 1.03712e9i | 0.146946 | − | 0.0939350i | ||||
\(103\) | 1.62785e10 | 1.40420 | 0.702100 | − | 0.712078i | \(-0.252246\pi\) | ||||
0.702100 | + | 0.712078i | \(0.252246\pi\) | |||||||
\(104\) | −1.10468e9 | − | 8.10030e9i | −0.0907966 | − | 0.665785i | ||||
\(105\) | 5.19612e9 | − | 3.73219e9i | 0.407129 | − | 0.292427i | ||||
\(106\) | −9.23755e9 | + | 5.90507e9i | −0.690283 | + | 0.441261i | ||||
\(107\) | 8.18368e8 | 0.0583485 | 0.0291743 | − | 0.999574i | \(-0.490712\pi\) | ||||
0.0291743 | + | 0.999574i | \(0.490712\pi\) | |||||||
\(108\) | −6.08467e9 | + | 1.31547e10i | −0.414113 | + | 0.895286i | ||||
\(109\) | −2.97062e9 | −0.193070 | −0.0965350 | − | 0.995330i | \(-0.530776\pi\) | ||||
−0.0965350 | + | 0.995330i | \(0.530776\pi\) | |||||||
\(110\) | −3.27148e9 | + | 8.21126e9i | −0.203133 | + | 0.509855i | ||||
\(111\) | 1.21410e10i | 0.720512i | ||||||||
\(112\) | −9.49174e9 | − | 1.11707e10i | −0.538587 | − | 0.633858i | ||||
\(113\) | − | 2.00487e10i | − | 1.08816i | −0.839033 | − | 0.544080i | \(-0.816879\pi\) | ||
0.839033 | − | 0.544080i | \(-0.183121\pi\) | |||||||
\(114\) | 1.19221e10 | − | 7.62117e9i | 0.619198 | − | 0.395820i | ||||
\(115\) | −1.15222e10 | + | 8.27597e9i | −0.572855 | + | 0.411462i | ||||
\(116\) | −1.12842e10 | + | 2.43957e10i | −0.537255 | + | 1.16151i | ||||
\(117\) | 9.38168e9i | 0.427909i | ||||||||
\(118\) | −2.21822e10 | + | 1.41799e10i | −0.969605 | + | 0.619817i | ||||
\(119\) | − | 5.74431e9i | − | 0.240715i | ||||||
\(120\) | 1.08858e10 | − | 1.03137e10i | 0.437475 | − | 0.414484i | ||||
\(121\) | 1.81247e10 | 0.698785 | ||||||||
\(122\) | 1.62570e10 | + | 2.54315e10i | 0.601507 | + | 0.940963i | ||||
\(123\) | −1.57111e10 | −0.558061 | ||||||||
\(124\) | −3.36936e10 | − | 1.55849e10i | −1.14932 | − | 0.531614i | ||||
\(125\) | 8.95568e9 | + | 2.91739e10i | 0.293460 | + | 0.955971i | ||||
\(126\) | 9.06032e9 | + | 1.41734e10i | 0.285293 | + | 0.446296i | ||||
\(127\) | 1.68474e10 | 0.509936 | 0.254968 | − | 0.966950i | \(-0.417935\pi\) | ||||
0.254968 | + | 0.966950i | \(0.417935\pi\) | |||||||
\(128\) | −2.55825e10 | − | 2.29375e10i | −0.744547 | − | 0.667570i | ||||
\(129\) | 2.31871e8 | 0.00649079 | ||||||||
\(130\) | 9.23410e9 | − | 2.31772e10i | 0.248701 | − | 0.624229i | ||||
\(131\) | − | 6.87972e9i | − | 0.178326i | −0.996017 | − | 0.0891629i | \(-0.971581\pi\) | ||
0.996017 | − | 0.0891629i | \(-0.0284192\pi\) | |||||||
\(132\) | 1.20301e10 | + | 5.56450e9i | 0.300192 | + | 0.138853i | ||||
\(133\) | − | 4.22115e10i | − | 1.01432i | ||||||
\(134\) | 1.95777e10 | + | 3.06262e10i | 0.453145 | + | 0.708873i | ||||
\(135\) | −3.59249e10 | + | 2.58036e10i | −0.801173 | + | 0.575455i | ||||
\(136\) | −1.81939e9 | − | 1.33410e10i | −0.0391048 | − | 0.286745i | ||||
\(137\) | 3.80906e10i | 0.789251i | 0.918842 | + | 0.394626i | \(0.129126\pi\) | ||||
−0.918842 | + | 0.394626i | \(0.870874\pi\) | |||||||
\(138\) | 1.14580e10 | + | 1.79242e10i | 0.228935 | + | 0.358132i | ||||
\(139\) | − | 1.89688e10i | − | 0.365566i | −0.983153 | − | 0.182783i | \(-0.941489\pi\) | ||
0.983153 | − | 0.182783i | \(-0.0585107\pi\) | |||||||
\(140\) | −8.43280e9 | − | 4.39329e10i | −0.156795 | − | 0.816864i | ||||
\(141\) | −6.36540e10 | −1.14217 | ||||||||
\(142\) | 7.85513e10 | − | 5.02137e10i | 1.36054 | − | 0.869722i | ||||
\(143\) | 2.20523e10 | 0.368785 | ||||||||
\(144\) | 2.55315e10 | + | 3.00479e10i | 0.412349 | + | 0.485290i | ||||
\(145\) | −6.66236e10 | + | 4.78535e10i | −1.03941 | + | 0.746575i | ||||
\(146\) | 5.62623e10 | − | 3.59655e10i | 0.848112 | − | 0.542153i | ||||
\(147\) | 1.27470e10 | 0.185704 | ||||||||
\(148\) | 7.70526e10 | + | 3.56405e10i | 1.08512 | + | 0.501921i | ||||
\(149\) | −2.46526e10 | −0.335685 | −0.167842 | − | 0.985814i | \(-0.553680\pi\) | ||||
−0.167842 | + | 0.985814i | \(0.553680\pi\) | |||||||
\(150\) | 4.44107e10 | − | 1.10444e10i | 0.584832 | − | 0.145440i | ||||
\(151\) | − | 9.59561e10i | − | 1.22233i | −0.791504 | − | 0.611164i | \(-0.790701\pi\) | ||
0.791504 | − | 0.611164i | \(-0.209299\pi\) | |||||||
\(152\) | −1.33696e10 | − | 9.80354e10i | −0.164778 | − | 1.20827i | ||||
\(153\) | 1.54514e10i | 0.184294i | ||||||||
\(154\) | 3.33157e10 | − | 2.12969e10i | 0.384632 | − | 0.245875i | ||||
\(155\) | −6.60918e10 | − | 9.20158e10i | −0.738736 | − | 1.02850i | ||||
\(156\) | −3.39563e10 | − | 1.57064e10i | −0.367534 | − | 0.170002i | ||||
\(157\) | 4.22802e10i | 0.443240i | 0.975133 | + | 0.221620i | \(0.0711344\pi\) | ||||
−0.975133 | + | 0.221620i | \(0.928866\pi\) | |||||||
\(158\) | −1.57407e11 | + | 1.00622e11i | −1.59859 | + | 1.02190i | ||||
\(159\) | 5.01735e10i | 0.493729i | ||||||||
\(160\) | −3.34998e10 | − | 9.93624e10i | −0.319479 | − | 0.947593i | ||||
\(161\) | 6.34624e10 | 0.586661 | ||||||||
\(162\) | −2.54539e9 | − | 3.98186e9i | −0.0228129 | − | 0.0356871i | ||||
\(163\) | 1.44588e11 | 1.25659 | 0.628297 | − | 0.777974i | \(-0.283752\pi\) | ||||
0.628297 | + | 0.777974i | \(0.283752\pi\) | |||||||
\(164\) | −4.61206e10 | + | 9.97099e10i | −0.388754 | + | 0.840464i | ||||
\(165\) | 2.35977e10 | + | 3.28537e10i | 0.192952 | + | 0.268636i | ||||
\(166\) | −1.72239e10 | − | 2.69440e10i | −0.136644 | − | 0.213758i | ||||
\(167\) | −2.16899e11 | −1.66984 | −0.834922 | − | 0.550368i | \(-0.814487\pi\) | ||||
−0.834922 | + | 0.550368i | \(0.814487\pi\) | |||||||
\(168\) | −6.64681e10 | + | 9.06460e9i | −0.496669 | + | 0.0677333i | ||||
\(169\) | 7.56134e10 | 0.548486 | ||||||||
\(170\) | 1.52084e10 | − | 3.81724e10i | 0.107112 | − | 0.268847i | ||||
\(171\) | 1.13544e11i | 0.776573i | ||||||||
\(172\) | 6.80666e8 | − | 1.47156e9i | 0.00452159 | − | 0.00977541i | ||||
\(173\) | − | 2.64712e11i | − | 1.70821i | −0.520097 | − | 0.854107i | \(-0.674104\pi\) | ||
0.520097 | − | 0.854107i | \(-0.325896\pi\) | |||||||
\(174\) | 6.62524e10 | + | 1.03641e11i | 0.415389 | + | 0.649811i | ||||
\(175\) | 4.35968e10 | − | 1.29372e11i | 0.265622 | − | 0.788224i | ||||
\(176\) | 7.06296e10 | − | 6.00137e10i | 0.418238 | − | 0.355375i | ||||
\(177\) | 1.20482e11i | 0.693516i | ||||||||
\(178\) | 6.84761e10 | + | 1.07120e11i | 0.383212 | + | 0.599474i | ||||
\(179\) | 3.53056e11i | 1.92122i | 0.277892 | + | 0.960612i | \(0.410364\pi\) | ||||
−0.277892 | + | 0.960612i | \(0.589636\pi\) | |||||||
\(180\) | 2.26831e10 | + | 1.18174e11i | 0.120044 | + | 0.625401i | ||||
\(181\) | −1.89345e11 | −0.974678 | −0.487339 | − | 0.873213i | \(-0.662032\pi\) | ||||
−0.487339 | + | 0.873213i | \(0.662032\pi\) | |||||||
\(182\) | −9.40372e10 | + | 6.01129e10i | −0.470915 | + | 0.301031i | ||||
\(183\) | 1.38130e11 | 0.673030 | ||||||||
\(184\) | 1.47390e11 | − | 2.01004e10i | 0.698842 | − | 0.0953047i | ||||
\(185\) | 1.51143e11 | + | 2.10427e11i | 0.697474 | + | 0.971053i | ||||
\(186\) | −1.43142e11 | + | 9.15031e10i | −0.642988 | + | 0.411028i | ||||
\(187\) | 3.63197e10 | 0.158831 | ||||||||
\(188\) | −1.86859e11 | + | 4.03977e11i | −0.795653 | + | 1.72015i | ||||
\(189\) | 1.97869e11 | 0.820482 | ||||||||
\(190\) | 1.11758e11 | − | 2.80506e11i | 0.451345 | − | 1.13286i | ||||
\(191\) | 1.77750e11i | 0.699266i | 0.936887 | + | 0.349633i | \(0.113694\pi\) | ||||
−0.936887 | + | 0.349633i | \(0.886306\pi\) | |||||||
\(192\) | −1.51500e11 | + | 4.21047e10i | −0.580639 | + | 0.161371i | ||||
\(193\) | − | 4.76572e11i | − | 1.77968i | −0.456271 | − | 0.889841i | \(-0.650815\pi\) | ||
0.456271 | − | 0.889841i | \(-0.349185\pi\) | |||||||
\(194\) | −1.73715e11 | + | 1.11047e11i | −0.632164 | + | 0.404108i | ||||
\(195\) | −6.66070e10 | − | 9.27331e10i | −0.236236 | − | 0.328898i | ||||
\(196\) | 3.74194e10 | − | 8.08984e10i | 0.129365 | − | 0.279679i | ||||
\(197\) | − | 3.11485e11i | − | 1.04980i | −0.851164 | − | 0.524900i | \(-0.824103\pi\) | ||
0.851164 | − | 0.524900i | \(-0.175897\pi\) | |||||||
\(198\) | −8.96149e10 | + | 5.72860e10i | −0.294479 | + | 0.188245i | ||||
\(199\) | − | 8.32510e10i | − | 0.266762i | −0.991065 | − | 0.133381i | \(-0.957417\pi\) | ||
0.991065 | − | 0.133381i | \(-0.0425834\pi\) | |||||||
\(200\) | 6.02768e10 | − | 3.14272e11i | 0.188365 | − | 0.982099i | ||||
\(201\) | 1.66345e11 | 0.507026 | ||||||||
\(202\) | −1.46561e11 | − | 2.29272e11i | −0.435775 | − | 0.681701i | ||||
\(203\) | 3.66953e11 | 1.06446 | ||||||||
\(204\) | −5.59254e10 | − | 2.58682e10i | −0.158292 | − | 0.0732175i | ||||
\(205\) | −2.72303e11 | + | 1.95586e11i | −0.752113 | + | 0.540217i | ||||
\(206\) | −2.80565e11 | − | 4.38900e11i | −0.756307 | − | 1.18312i | ||||
\(207\) | −1.70706e11 | −0.449155 | ||||||||
\(208\) | −1.99360e11 | + | 1.69395e11i | −0.512060 | + | 0.435096i | ||||
\(209\) | 2.66892e11 | 0.669275 | ||||||||
\(210\) | −1.90184e11 | − | 7.57717e10i | −0.465668 | − | 0.185529i | ||||
\(211\) | − | 4.08040e11i | − | 0.975641i | −0.872944 | − | 0.487820i | \(-0.837792\pi\) | ||
0.872944 | − | 0.487820i | \(-0.162208\pi\) | |||||||
\(212\) | 3.18424e11 | + | 1.47286e11i | 0.743578 | + | 0.343940i | ||||
\(213\) | − | 4.26650e11i | − | 0.973136i | ||||||
\(214\) | −1.41048e10 | − | 2.20648e10i | −0.0314267 | − | 0.0491621i | ||||
\(215\) | 4.01876e9 | − | 2.88654e9i | 0.00874781 | − | 0.00628325i | ||||
\(216\) | 4.59547e11 | − | 6.26708e10i | 0.977375 | − | 0.133290i | ||||
\(217\) | 5.06810e11i | 1.05329i | ||||||||
\(218\) | 5.11996e10 | + | 8.00936e10i | 0.103988 | + | 0.162673i | ||||
\(219\) | − | 3.05587e11i | − | 0.606617i | ||||||
\(220\) | 2.77776e11 | − | 5.33184e10i | 0.538991 | − | 0.103458i | ||||
\(221\) | −1.02516e11 | −0.194461 | ||||||||
\(222\) | 3.27346e11 | − | 2.09255e11i | 0.607074 | − | 0.388070i | ||||
\(223\) | 3.09347e11 | 0.560947 | 0.280473 | − | 0.959862i | \(-0.409509\pi\) | ||||
0.280473 | + | 0.959862i | \(0.409509\pi\) | |||||||
\(224\) | −1.37592e11 | + | 4.48446e11i | −0.243979 | + | 0.795189i | ||||
\(225\) | −1.17270e11 | + | 3.47993e11i | −0.203363 | + | 0.603474i | ||||
\(226\) | −5.40550e11 | + | 3.45545e11i | −0.916840 | + | 0.586087i | ||||
\(227\) | 4.36504e11 | 0.724200 | 0.362100 | − | 0.932139i | \(-0.382060\pi\) | ||||
0.362100 | + | 0.932139i | \(0.382060\pi\) | |||||||
\(228\) | −4.10963e11 | − | 1.90090e11i | −0.667004 | − | 0.308521i | ||||
\(229\) | −8.85513e11 | −1.40610 | −0.703052 | − | 0.711138i | \(-0.748180\pi\) | ||||
−0.703052 | + | 0.711138i | \(0.748180\pi\) | |||||||
\(230\) | 4.21724e11 | + | 1.68020e11i | 0.655223 | + | 0.261049i | ||||
\(231\) | − | 1.80953e11i | − | 0.275110i | ||||||
\(232\) | 8.52241e11 | − | 1.16225e11i | 1.26801 | − | 0.172925i | ||||
\(233\) | − | 3.44547e10i | − | 0.0501729i | −0.999685 | − | 0.0250864i | \(-0.992014\pi\) | ||
0.999685 | − | 0.0250864i | \(-0.00798610\pi\) | |||||||
\(234\) | 2.52948e11 | − | 1.61696e11i | 0.360539 | − | 0.230473i | ||||
\(235\) | −1.10324e12 | + | 7.92422e11i | −1.53933 | + | 1.10565i | ||||
\(236\) | 7.64635e11 | + | 3.53680e11i | 1.04447 | + | 0.483115i | ||||
\(237\) | 8.54951e11i | 1.14340i | ||||||||
\(238\) | −1.54878e11 | + | 9.90049e10i | −0.202817 | + | 0.129650i | ||||
\(239\) | 3.54744e11i | 0.454910i | 0.973789 | + | 0.227455i | \(0.0730404\pi\) | ||||
−0.973789 | + | 0.227455i | \(0.926960\pi\) | |||||||
\(240\) | −4.65697e11 | − | 1.15742e11i | −0.584853 | − | 0.145356i | ||||
\(241\) | 5.46010e11 | 0.671608 | 0.335804 | − | 0.941932i | \(-0.390992\pi\) | ||||
0.335804 | + | 0.941932i | \(0.390992\pi\) | |||||||
\(242\) | −3.12385e11 | − | 4.88676e11i | −0.376368 | − | 0.588768i | ||||
\(243\) | −8.57411e11 | −1.01195 | ||||||||
\(244\) | 4.05487e11 | − | 8.76639e11i | 0.468844 | − | 1.01361i | ||||
\(245\) | 2.20930e11 | − | 1.58686e11i | 0.250279 | − | 0.179767i | ||||
\(246\) | 2.70786e11 | + | 4.23602e11i | 0.300573 | + | 0.470199i | ||||
\(247\) | −7.53333e11 | −0.819412 | ||||||||
\(248\) | 1.60521e11 | + | 1.17706e12i | 0.171109 | + | 1.25470i | ||||
\(249\) | −1.46346e11 | −0.152892 | ||||||||
\(250\) | 6.32231e11 | − | 7.44284e11i | 0.647405 | − | 0.762147i | ||||
\(251\) | 2.78449e11i | 0.279497i | 0.990187 | + | 0.139748i | \(0.0446293\pi\) | ||||
−0.990187 | + | 0.139748i | \(0.955371\pi\) | |||||||
\(252\) | 2.25986e11 | − | 4.88567e11i | 0.222371 | − | 0.480752i | ||||
\(253\) | 4.01256e11i | 0.387096i | ||||||||
\(254\) | −2.90371e11 | − | 4.54239e11i | −0.274653 | − | 0.429651i | ||||
\(255\) | −1.09701e11 | − | 1.52730e11i | −0.101744 | − | 0.141652i | ||||
\(256\) | −1.77518e11 | + | 1.08509e12i | −0.161452 | + | 0.986881i | ||||
\(257\) | − | 1.03896e11i | − | 0.0926688i | −0.998926 | − | 0.0463344i | \(-0.985246\pi\) | ||
0.998926 | − | 0.0463344i | \(-0.0147540\pi\) | |||||||
\(258\) | −3.99636e9 | − | 6.25168e9i | −0.00349596 | − | 0.00546888i | ||||
\(259\) | − | 1.15900e12i | − | 0.994456i | ||||||
\(260\) | −7.84054e11 | + | 1.50497e11i | −0.659901 | + | 0.126666i | ||||
\(261\) | −9.87057e11 | −0.814966 | ||||||||
\(262\) | −1.85490e11 | + | 1.18574e11i | −0.150250 | + | 0.0960469i | ||||
\(263\) | 3.81998e11 | 0.303586 | 0.151793 | − | 0.988412i | \(-0.451495\pi\) | ||||
0.151793 | + | 0.988412i | \(0.451495\pi\) | |||||||
\(264\) | −5.73131e10 | − | 4.20260e11i | −0.0446924 | − | 0.327717i | ||||
\(265\) | 6.24605e11 | + | 8.69601e11i | 0.477943 | + | 0.665412i | ||||
\(266\) | −1.13810e12 | + | 7.27529e11i | −0.854621 | + | 0.546314i | ||||
\(267\) | 5.81820e11 | 0.428778 | ||||||||
\(268\) | 4.88313e11 | − | 1.05570e12i | 0.353203 | − | 0.763603i | ||||
\(269\) | −9.64366e11 | −0.684668 | −0.342334 | − | 0.939578i | \(-0.611218\pi\) | ||||
−0.342334 | + | 0.939578i | \(0.611218\pi\) | |||||||
\(270\) | 1.31489e12 | + | 5.23870e11i | 0.916370 | + | 0.365094i | ||||
\(271\) | 5.71457e10i | 0.0390964i | 0.999809 | + | 0.0195482i | \(0.00622279\pi\) | ||||
−0.999809 | + | 0.0195482i | \(0.993777\pi\) | |||||||
\(272\) | −3.28342e11 | + | 2.78991e11i | −0.220537 | + | 0.187390i | ||||
\(273\) | 5.10761e11i | 0.336825i | ||||||||
\(274\) | 1.02700e12 | − | 6.56504e11i | 0.664991 | − | 0.425093i | ||||
\(275\) | 8.17984e11 | + | 2.75651e11i | 0.520093 | + | 0.175265i | ||||
\(276\) | 2.85788e11 | − | 6.17857e11i | 0.178443 | − | 0.385782i | ||||
\(277\) | − | 1.80699e12i | − | 1.10804i | −0.832503 | − | 0.554021i | \(-0.813093\pi\) | ||
0.832503 | − | 0.554021i | \(-0.186907\pi\) | |||||||
\(278\) | −5.11436e11 | + | 3.26933e11i | −0.308012 | + | 0.196895i | ||||
\(279\) | − | 1.36325e12i | − | 0.806409i | ||||||
\(280\) | −1.03917e12 | + | 9.84561e11i | −0.603806 | + | 0.572075i | ||||
\(281\) | 1.67597e12 | 0.956612 | 0.478306 | − | 0.878193i | \(-0.341251\pi\) | ||||
0.478306 | + | 0.878193i | \(0.341251\pi\) | |||||||
\(282\) | 1.09710e12 | + | 1.71623e12i | 0.615175 | + | 0.962344i | ||||
\(283\) | 1.29146e12 | 0.711459 | 0.355730 | − | 0.934589i | \(-0.384232\pi\) | ||||
0.355730 | + | 0.934589i | \(0.384232\pi\) | |||||||
\(284\) | −2.70771e12 | − | 1.25245e12i | −1.46558 | − | 0.677903i | ||||
\(285\) | −8.06124e11 | − | 1.12232e12i | −0.428724 | − | 0.596888i | ||||
\(286\) | −3.80078e11 | − | 5.94572e11i | −0.198629 | − | 0.310724i | ||||
\(287\) | 1.49981e12 | 0.770240 | ||||||||
\(288\) | 3.70104e11 | − | 1.20626e12i | 0.186793 | − | 0.608807i | ||||
\(289\) | 1.84715e12 | 0.916248 | ||||||||
\(290\) | 2.43850e12 | + | 9.71530e11i | 1.18886 | + | 0.473660i | ||||
\(291\) | 9.43530e11i | 0.452159i | ||||||||
\(292\) | −1.93940e12 | − | 8.97063e11i | −0.913592 | − | 0.422580i | ||||
\(293\) | − | 3.77568e12i | − | 1.74847i | −0.485507 | − | 0.874233i | \(-0.661365\pi\) | ||
0.485507 | − | 0.874233i | \(-0.338635\pi\) | |||||||
\(294\) | −2.19699e11 | − | 3.43684e11i | −0.100021 | − | 0.156467i | ||||
\(295\) | 1.49987e12 | + | 2.08818e12i | 0.671342 | + | 0.934670i | ||||
\(296\) | −3.67089e11 | − | 2.69176e12i | −0.161552 | − | 1.18462i | ||||
\(297\) | 1.25107e12i | 0.541378i | ||||||||
\(298\) | 4.24896e11 | + | 6.64682e11i | 0.180801 | + | 0.282835i | ||||
\(299\) | − | 1.13259e12i | − | 0.473932i | ||||||
\(300\) | −1.06321e12 | − | 1.00704e12i | −0.437535 | − | 0.414422i | ||||
\(301\) | −2.21347e10 | −0.00895864 | ||||||||
\(302\) | −2.58716e12 | + | 1.65383e12i | −1.02988 | + | 0.658350i | ||||
\(303\) | −1.24528e12 | −0.487591 | ||||||||
\(304\) | −2.41279e12 | + | 2.05014e12i | −0.929292 | + | 0.789615i | ||||
\(305\) | 2.39406e12 | − | 1.71957e12i | 0.907060 | − | 0.651510i | ||||
\(306\) | 4.16600e11 | − | 2.66310e11i | 0.155279 | − | 0.0992615i | ||||
\(307\) | −3.98468e12 | −1.46117 | −0.730587 | − | 0.682820i | \(-0.760754\pi\) | ||||
−0.730587 | + | 0.682820i | \(0.760754\pi\) | |||||||
\(308\) | −1.14841e12 | − | 5.31195e11i | −0.414328 | − | 0.191646i | ||||
\(309\) | −2.38388e12 | −0.846236 | ||||||||
\(310\) | −1.34181e12 | + | 3.36788e12i | −0.468686 | + | 1.17638i | ||||
\(311\) | 1.39871e12i | 0.480758i | 0.970679 | + | 0.240379i | \(0.0772717\pi\) | ||||
−0.970679 | + | 0.240379i | \(0.922728\pi\) | |||||||
\(312\) | 1.61772e11 | + | 1.18623e12i | 0.0547182 | + | 0.401233i | ||||
\(313\) | 5.82569e12i | 1.93921i | 0.244667 | + | 0.969607i | \(0.421321\pi\) | ||||
−0.244667 | + | 0.969607i | \(0.578679\pi\) | |||||||
\(314\) | 1.13995e12 | − | 7.28712e11i | 0.373456 | − | 0.238730i | ||||
\(315\) | 1.33425e12 | − | 9.58349e11i | 0.430215 | − | 0.309009i | ||||
\(316\) | 5.42591e12 | + | 2.50974e12i | 1.72202 | + | 0.796514i | ||||
\(317\) | − | 4.41493e12i | − | 1.37920i | −0.724190 | − | 0.689600i | \(-0.757786\pi\) | ||
0.724190 | − | 0.689600i | \(-0.242214\pi\) | |||||||
\(318\) | 1.35277e12 | − | 8.64756e11i | 0.415996 | − | 0.265924i | ||||
\(319\) | 2.32015e12i | 0.702364i | ||||||||
\(320\) | −2.10162e12 | + | 2.61576e12i | −0.626331 | + | 0.779557i | ||||
\(321\) | −1.19844e11 | −0.0351635 | ||||||||
\(322\) | −1.09379e12 | − | 1.71107e12i | −0.315977 | − | 0.494297i | ||||
\(323\) | −1.24073e12 | −0.352909 | ||||||||
\(324\) | −6.34880e10 | + | 1.37257e11i | −0.0177814 | + | 0.0384424i | ||||
\(325\) | −2.30885e12 | − | 7.78054e11i | −0.636764 | − | 0.214582i | ||||
\(326\) | −2.49202e12 | − | 3.89838e12i | −0.676806 | − | 1.05876i | ||||
\(327\) | 4.35027e11 | 0.116353 | ||||||||
\(328\) | 3.48327e12 | − | 4.75032e11i | 0.917525 | − | 0.125128i | ||||
\(329\) | 6.07650e12 | 1.57643 | ||||||||
\(330\) | 4.79084e11 | − | 1.20248e12i | 0.122417 | − | 0.307262i | ||||
\(331\) | 1.01492e12i | 0.255441i | 0.991810 | + | 0.127720i | \(0.0407660\pi\) | ||||
−0.991810 | + | 0.127720i | \(0.959234\pi\) | |||||||
\(332\) | −4.29603e11 | + | 9.28777e11i | −0.106507 | + | 0.230261i | ||||
\(333\) | 3.11757e12i | 0.761368i | ||||||||
\(334\) | 3.73833e12 | + | 5.84802e12i | 0.899383 | + | 1.40694i | ||||
\(335\) | 2.88308e12 | − | 2.07081e12i | 0.683332 | − | 0.490814i | ||||
\(336\) | 1.39000e12 | + | 1.63588e12i | 0.324577 | + | 0.381992i | ||||
\(337\) | 2.73619e12i | 0.629503i | 0.949174 | + | 0.314751i | \(0.101921\pi\) | ||||
−0.949174 | + | 0.314751i | \(0.898079\pi\) | |||||||
\(338\) | −1.30322e12 | − | 2.03868e12i | −0.295416 | − | 0.462132i | ||||
\(339\) | 2.93598e12i | 0.655775i | ||||||||
\(340\) | −1.29132e12 | + | 2.47866e11i | −0.284210 | + | 0.0545534i | ||||
\(341\) | −3.20442e12 | −0.694989 | ||||||||
\(342\) | 3.06135e12 | − | 1.95696e12i | 0.654309 | − | 0.418264i | ||||
\(343\) | −5.16576e12 | −1.08809 | ||||||||
\(344\) | −5.14075e10 | + | 7.01070e9i | −0.0106717 | + | 0.00145536i | ||||
\(345\) | 1.68734e12 | − | 1.21196e12i | 0.345228 | − | 0.247966i | ||||
\(346\) | −7.13713e12 | + | 4.56238e12i | −1.43927 | + | 0.920050i | ||||
\(347\) | 4.92030e12 | 0.978013 | 0.489006 | − | 0.872280i | \(-0.337359\pi\) | ||||
0.489006 | + | 0.872280i | \(0.337359\pi\) | |||||||
\(348\) | 1.65249e12 | − | 3.57258e12i | 0.323774 | − | 0.699980i | ||||
\(349\) | −4.17497e12 | −0.806355 | −0.403178 | − | 0.915122i | \(-0.632094\pi\) | ||||
−0.403178 | + | 0.915122i | \(0.632094\pi\) | |||||||
\(350\) | −4.23951e12 | + | 1.05431e12i | −0.807190 | + | 0.200737i | ||||
\(351\) | − | 3.53129e12i | − | 0.662824i | ||||||
\(352\) | −2.83541e12 | − | 8.69955e11i | −0.524689 | − | 0.160984i | ||||
\(353\) | 6.96972e12i | 1.27157i | 0.771864 | + | 0.635787i | \(0.219324\pi\) | ||||
−0.771864 | + | 0.635787i | \(0.780676\pi\) | |||||||
\(354\) | 3.24843e12 | − | 2.07655e12i | 0.584328 | − | 0.373530i | ||||
\(355\) | −5.31132e12 | − | 7.39464e12i | −0.942021 | − | 1.31152i | ||||
\(356\) | 1.70795e12 | − | 3.69249e12i | 0.298694 | − | 0.645758i | ||||
\(357\) | 8.41213e11i | 0.145066i | ||||||||
\(358\) | 9.51905e12 | − | 6.08502e12i | 1.61875 | − | 1.03478i | ||||
\(359\) | − | 6.96682e11i | − | 0.116832i | −0.998292 | − | 0.0584161i | \(-0.981395\pi\) | ||
0.998292 | − | 0.0584161i | \(-0.0186050\pi\) | |||||||
\(360\) | 2.79524e12 | − | 2.64834e12i | 0.462282 | − | 0.437987i | ||||
\(361\) | −2.98629e12 | −0.487076 | ||||||||
\(362\) | 3.26342e12 | + | 5.10510e12i | 0.524965 | + | 0.821224i | ||||
\(363\) | −2.65423e12 | −0.421120 | ||||||||
\(364\) | 3.24152e12 | + | 1.49936e12i | 0.507273 | + | 0.234638i | ||||
\(365\) | −3.80423e12 | − | 5.29640e12i | −0.587222 | − | 0.817555i | ||||
\(366\) | −2.38072e12 | − | 3.72426e12i | −0.362496 | − | 0.567067i | ||||
\(367\) | 3.80852e12 | 0.572039 | 0.286020 | − | 0.958224i | \(-0.407668\pi\) | ||||
0.286020 | + | 0.958224i | \(0.407668\pi\) | |||||||
\(368\) | −3.08226e12 | − | 3.62748e12i | −0.456699 | − | 0.537485i | ||||
\(369\) | −4.03429e12 | −0.589705 | ||||||||
\(370\) | 3.06853e12 | − | 7.70187e12i | 0.442508 | − | 1.11068i | ||||
\(371\) | − | 4.78964e12i | − | 0.681449i | ||||||
\(372\) | 4.93419e12 | + | 2.28230e12i | 0.692630 | + | 0.320375i | ||||
\(373\) | 9.60132e12i | 1.32980i | 0.746932 | + | 0.664901i | \(0.231526\pi\) | ||||
−0.746932 | + | 0.664901i | \(0.768474\pi\) | |||||||
\(374\) | −6.25982e11 | − | 9.79249e11i | −0.0855468 | − | 0.133824i | ||||
\(375\) | −1.31150e12 | − | 4.27232e12i | −0.176852 | − | 0.576112i | ||||
\(376\) | 1.41126e13 | − | 1.92460e12i | 1.87787 | − | 0.256095i | ||||
\(377\) | − | 6.54887e12i | − | 0.859924i | ||||||
\(378\) | −3.41033e12 | − | 5.33493e12i | −0.441914 | − | 0.691305i | ||||
\(379\) | 6.23848e12i | 0.797779i | 0.916999 | + | 0.398890i | \(0.130604\pi\) | ||||
−0.916999 | + | 0.398890i | \(0.869396\pi\) | |||||||
\(380\) | −9.48916e12 | + | 1.82142e12i | −1.19759 | + | 0.229875i | ||||
\(381\) | −2.46719e12 | −0.307311 | ||||||||
\(382\) | 4.79248e12 | − | 3.06357e12i | 0.589173 | − | 0.376627i | ||||
\(383\) | −8.64559e12 | −1.04906 | −0.524530 | − | 0.851392i | \(-0.675759\pi\) | ||||
−0.524530 | + | 0.851392i | \(0.675759\pi\) | |||||||
\(384\) | 3.74637e12 | + | 3.35904e12i | 0.448698 | + | 0.402308i | ||||
\(385\) | −2.25267e12 | − | 3.13626e12i | −0.266314 | − | 0.370773i | ||||
\(386\) | −1.28493e13 | + | 8.21387e12i | −1.49949 | + | 0.958542i | ||||
\(387\) | 5.95396e10 | 0.00685884 | ||||||||
\(388\) | 5.98807e12 | + | 2.76977e12i | 0.680971 | + | 0.314981i | ||||
\(389\) | 8.65443e12 | 0.971606 | 0.485803 | − | 0.874068i | \(-0.338527\pi\) | ||||
0.485803 | + | 0.874068i | \(0.338527\pi\) | |||||||
\(390\) | −1.35227e12 | + | 3.39413e12i | −0.149879 | + | 0.376189i | ||||
\(391\) | − | 1.86535e12i | − | 0.204116i | ||||||
\(392\) | −2.82611e12 | + | 3.85411e11i | −0.305322 | + | 0.0416384i | ||||
\(393\) | 1.00749e12i | 0.107467i | ||||||||
\(394\) | −8.39823e12 | + | 5.36854e12i | −0.884518 | + | 0.565425i | ||||
\(395\) | 1.06432e13 | + | 1.48179e13i | 1.10684 | + | 1.54100i | ||||
\(396\) | 3.08908e12 | + | 1.42885e12i | 0.317215 | + | 0.146727i | ||||
\(397\) | 5.71458e11i | 0.0579471i | 0.999580 | + | 0.0289736i | \(0.00922386\pi\) | ||||
−0.999580 | + | 0.0289736i | \(0.990776\pi\) | |||||||
\(398\) | −2.24461e12 | + | 1.43486e12i | −0.224763 | + | 0.143679i | ||||
\(399\) | 6.18158e12i | 0.611273i | ||||||||
\(400\) | −9.51225e12 | + | 3.79139e12i | −0.928931 | + | 0.370253i | ||||
\(401\) | 1.44767e13 | 1.39620 | 0.698098 | − | 0.716002i | \(-0.254030\pi\) | ||||
0.698098 | + | 0.716002i | \(0.254030\pi\) | |||||||
\(402\) | −2.86701e12 | − | 4.48499e12i | −0.273086 | − | 0.427200i | ||||
\(403\) | 9.04484e12 | 0.850894 | ||||||||
\(404\) | −3.65558e12 | + | 7.90314e12i | −0.339664 | + | 0.734333i | ||||
\(405\) | −3.74843e11 | + | 2.69237e11i | −0.0344013 | + | 0.0247093i | ||||
\(406\) | −6.32455e12 | − | 9.89376e12i | −0.573323 | − | 0.896874i | ||||
\(407\) | 7.32807e12 | 0.656171 | ||||||||
\(408\) | 2.66436e11 | + | 1.95370e12i | 0.0235664 | + | 0.172805i | ||||
\(409\) | 7.48900e12 | 0.654346 | 0.327173 | − | 0.944964i | \(-0.393904\pi\) | ||||
0.327173 | + | 0.944964i | \(0.393904\pi\) | |||||||
\(410\) | 9.96660e12 | + | 3.97083e12i | 0.860256 | + | 0.342737i | ||||
\(411\) | − | 5.57810e12i | − | 0.475639i | ||||||
\(412\) | −6.99796e12 | + | 1.51292e13i | −0.589502 | + | 1.27447i | ||||
\(413\) | − | 1.15014e13i | − | 0.957196i | ||||||
\(414\) | 2.94216e12 | + | 4.60255e12i | 0.241916 | + | 0.378440i | ||||
\(415\) | −2.53645e12 | + | 1.82184e12i | −0.206056 | + | 0.148003i | ||||
\(416\) | 8.00325e12 | + | 2.45554e12i | 0.642391 | + | 0.197097i | ||||
\(417\) | 2.77785e12i | 0.220307i | ||||||||
\(418\) | −4.59997e12 | − | 7.19593e12i | −0.360474 | − | 0.563904i | ||||
\(419\) | 6.35022e12i | 0.491721i | 0.969305 | + | 0.245861i | \(0.0790705\pi\) | ||||
−0.969305 | + | 0.245861i | \(0.920929\pi\) | |||||||
\(420\) | 1.23492e12 | + | 6.43366e12i | 0.0944917 | + | 0.492280i | ||||
\(421\) | 2.25594e12 | 0.170575 | 0.0852877 | − | 0.996356i | \(-0.472819\pi\) | ||||
0.0852877 | + | 0.996356i | \(0.472819\pi\) | |||||||
\(422\) | −1.10015e13 | + | 7.03269e12i | −0.822035 | + | 0.525483i | ||||
\(423\) | −1.63450e13 | −1.20693 | ||||||||
\(424\) | −1.51702e12 | − | 1.11238e13i | −0.110703 | − | 0.811756i | ||||
\(425\) | −3.80263e12 | − | 1.28144e12i | −0.274246 | − | 0.0924175i | ||||
\(426\) | −1.15033e13 | + | 7.35344e12i | −0.819925 | + | 0.524134i | ||||
\(427\) | −1.31861e13 | −0.928920 | ||||||||
\(428\) | −3.51807e11 | + | 7.60586e11i | −0.0244955 | + | 0.0529577i | ||||
\(429\) | −3.22940e12 | −0.222247 | ||||||||
\(430\) | −1.47091e11 | − | 5.86030e10i | −0.0100056 | − | 0.00398637i | ||||
\(431\) | 1.04502e13i | 0.702646i | 0.936254 | + | 0.351323i | \(0.114268\pi\) | ||||
−0.936254 | + | 0.351323i | \(0.885732\pi\) | |||||||
\(432\) | −9.61015e12 | − | 1.13101e13i | −0.638722 | − | 0.751706i | ||||
\(433\) | − | 6.36111e12i | − | 0.417920i | −0.977924 | − | 0.208960i | \(-0.932992\pi\) | ||
0.977924 | − | 0.208960i | \(-0.0670079\pi\) | |||||||
\(434\) | 1.36646e13 | − | 8.73502e12i | 0.887456 | − | 0.567303i | ||||
\(435\) | 9.75655e12 | − | 7.00780e12i | 0.626398 | − | 0.449920i | ||||
\(436\) | 1.27704e12 | − | 2.76088e12i | 0.0810533 | − | 0.175232i | ||||
\(437\) | − | 1.37074e13i | − | 0.860097i | ||||||
\(438\) | −8.23922e12 | + | 5.26689e12i | −0.511111 | + | 0.326726i | ||||
\(439\) | − | 1.91298e13i | − | 1.17324i | −0.809862 | − | 0.586620i | \(-0.800458\pi\) | ||
0.809862 | − | 0.586620i | \(-0.199542\pi\) | |||||||
\(440\) | −6.22512e12 | − | 6.57041e12i | −0.377472 | − | 0.398409i | ||||
\(441\) | 3.27317e12 | 0.196235 | ||||||||
\(442\) | 1.76690e12 | + | 2.76404e12i | 0.104737 | + | 0.163845i | ||||
\(443\) | 1.80726e13 | 1.05926 | 0.529629 | − | 0.848229i | \(-0.322331\pi\) | ||||
0.529629 | + | 0.848229i | \(0.322331\pi\) | |||||||
\(444\) | −1.12838e13 | − | 5.21930e12i | −0.653944 | − | 0.302480i | ||||
\(445\) | 1.00840e13 | − | 7.24301e12i | 0.577875 | − | 0.415068i | ||||
\(446\) | −5.33169e12 | − | 8.34058e12i | −0.302128 | − | 0.472631i | ||||
\(447\) | 3.61020e12 | 0.202299 | ||||||||
\(448\) | 1.44624e13 | − | 4.01938e12i | 0.801402 | − | 0.222725i | ||||
\(449\) | −7.71297e12 | −0.422659 | −0.211329 | − | 0.977415i | \(-0.567779\pi\) | ||||
−0.211329 | + | 0.977415i | \(0.567779\pi\) | |||||||
\(450\) | 1.14037e13 | − | 2.83596e12i | 0.617995 | − | 0.153687i | ||||
\(451\) | 9.48288e12i | 0.508227i | ||||||||
\(452\) | 1.86331e13 | + | 8.61869e12i | 0.987626 | + | 0.456824i | ||||
\(453\) | 1.40521e13i | 0.736631i | ||||||||
\(454\) | −7.52327e12 | − | 1.17690e13i | −0.390056 | − | 0.610182i | ||||
\(455\) | 6.35841e12 | + | 8.85244e12i | 0.326055 | + | 0.453948i | ||||
\(456\) | 1.95788e12 | + | 1.43566e13i | 0.0993030 | + | 0.728161i | ||||
\(457\) | − | 5.55477e12i | − | 0.278667i | −0.990246 | − | 0.139333i | \(-0.955504\pi\) | ||
0.990246 | − | 0.139333i | \(-0.0444959\pi\) | |||||||
\(458\) | 1.52621e13 | + | 2.38751e13i | 0.757332 | + | 1.18473i | ||||
\(459\) | − | 5.81597e12i | − | 0.285469i | ||||||
\(460\) | −2.73839e12 | − | 1.42664e13i | −0.132955 | − | 0.692666i | ||||
\(461\) | −1.48116e13 | −0.711372 | −0.355686 | − | 0.934605i | \(-0.615753\pi\) | ||||
−0.355686 | + | 0.934605i | \(0.615753\pi\) | |||||||
\(462\) | −4.87885e12 | + | 3.11879e12i | −0.231797 | + | 0.148175i | ||||
\(463\) | 2.87422e13 | 1.35087 | 0.675436 | − | 0.737418i | \(-0.263955\pi\) | ||||
0.675436 | + | 0.737418i | \(0.263955\pi\) | |||||||
\(464\) | −1.78223e13 | − | 2.09749e13i | −0.828654 | − | 0.975236i | ||||
\(465\) | 9.67868e12 | + | 1.34751e13i | 0.445196 | + | 0.619821i | ||||
\(466\) | −9.28965e11 | + | 5.93837e11i | −0.0422736 | + | 0.0270233i | ||||
\(467\) | −1.93804e13 | −0.872527 | −0.436264 | − | 0.899819i | \(-0.643698\pi\) | ||||
−0.436264 | + | 0.899819i | \(0.643698\pi\) | |||||||
\(468\) | −8.71927e12 | − | 4.03308e12i | −0.388374 | − | 0.179642i | ||||
\(469\) | −1.58796e13 | −0.699801 | ||||||||
\(470\) | 4.03799e13 | + | 1.60879e13i | 1.76066 | + | 0.701471i | ||||
\(471\) | − | 6.19163e12i | − | 0.267117i | ||||||
\(472\) | −3.64282e12 | − | 2.67118e13i | −0.155499 | − | 1.14023i | ||||
\(473\) | − | 1.39952e11i | − | 0.00591117i | ||||||
\(474\) | 2.30511e13 | − | 1.47353e13i | 0.963386 | − | 0.615841i | ||||
\(475\) | −2.79433e13 | − | 9.41656e12i | −1.15561 | − | 0.389425i | ||||
\(476\) | 5.33872e12 | + | 2.46941e12i | 0.218475 | + | 0.101055i | ||||
\(477\) | 1.28835e13i | 0.521726i | ||||||||
\(478\) | 9.56457e12 | − | 6.11412e12i | 0.383288 | − | 0.245016i | ||||
\(479\) | − | 1.28939e13i | − | 0.511335i | −0.966765 | − | 0.255667i | \(-0.917705\pi\) | ||
0.966765 | − | 0.255667i | \(-0.0822952\pi\) | |||||||
\(480\) | 4.90581e12 | + | 1.45509e13i | 0.192533 | + | 0.571063i | ||||
\(481\) | −2.06843e13 | −0.803369 | ||||||||
\(482\) | −9.41065e12 | − | 1.47215e13i | −0.361730 | − | 0.565869i | ||||
\(483\) | −9.29362e12 | −0.353549 | ||||||||
\(484\) | −7.79160e12 | + | 1.68450e13i | −0.293359 | + | 0.634225i | ||||
\(485\) | 1.17459e13 | + | 1.63532e13i | 0.437702 | + | 0.609386i | ||||
\(486\) | 1.47777e13 | + | 2.31174e13i | 0.545038 | + | 0.852625i | ||||
\(487\) | −1.59672e11 | −0.00582886 | −0.00291443 | − | 0.999996i | \(-0.500928\pi\) | ||||
−0.00291443 | + | 0.999996i | \(0.500928\pi\) | |||||||
\(488\) | −3.06246e13 | + | 4.17643e12i | −1.10655 | + | 0.150906i | ||||
\(489\) | −2.11739e13 | −0.757281 | ||||||||
\(490\) | −8.08628e12 | − | 3.22168e12i | −0.286265 | − | 0.114052i | ||||
\(491\) | 4.18477e12i | 0.146644i | 0.997308 | + | 0.0733219i | \(0.0233601\pi\) | ||||
−0.997308 | + | 0.0733219i | \(0.976640\pi\) | |||||||
\(492\) | 6.75403e12 | − | 1.46018e13i | 0.234281 | − | 0.506502i | ||||
\(493\) | − | 1.07859e13i | − | 0.370357i | ||||||
\(494\) | 1.29839e13 | + | 2.03113e13i | 0.441338 | + | 0.690403i | ||||
\(495\) | 6.05939e12 | + | 8.43613e12i | 0.203893 | + | 0.283869i | ||||
\(496\) | 2.89690e13 | − | 2.46149e13i | 0.964996 | − | 0.819953i | ||||
\(497\) | 4.07286e13i | 1.34313i | ||||||||
\(498\) | 2.52231e12 | + | 3.94576e12i | 0.0823479 | + | 0.128820i | ||||
\(499\) | − | 5.68728e13i | − | 1.83824i | −0.393978 | − | 0.919120i | \(-0.628902\pi\) | ||
0.393978 | − | 0.919120i | \(-0.371098\pi\) | |||||||
\(500\) | −3.09640e13 | − | 4.21820e12i | −0.990848 | − | 0.134982i | ||||
\(501\) | 3.17634e13 | 1.00632 | ||||||||
\(502\) | 7.50751e12 | − | 4.79915e12i | 0.235493 | − | 0.150538i | ||||
\(503\) | −4.10150e13 | −1.27380 | −0.636902 | − | 0.770945i | \(-0.719784\pi\) | ||||
−0.636902 | + | 0.770945i | \(0.719784\pi\) | |||||||
\(504\) | −1.70676e13 | + | 2.32760e12i | −0.524832 | + | 0.0715741i | ||||
\(505\) | −2.15831e13 | + | 1.55024e13i | −0.657139 | + | 0.472000i | ||||
\(506\) | 1.08186e13 | − | 6.91577e12i | 0.326151 | − | 0.208491i | ||||
\(507\) | −1.10731e13 | −0.330543 | ||||||||
\(508\) | −7.24252e12 | + | 1.56579e13i | −0.214078 | + | 0.462823i | ||||
\(509\) | 3.18969e13 | 0.933599 | 0.466799 | − | 0.884363i | \(-0.345407\pi\) | ||||
0.466799 | + | 0.884363i | \(0.345407\pi\) | |||||||
\(510\) | −2.22716e12 | + | 5.59008e12i | −0.0645507 | + | 0.162019i | ||||
\(511\) | 2.91718e13i | 0.837258i | ||||||||
\(512\) | 3.23156e13 | − | 1.39156e13i | 0.918464 | − | 0.395505i | ||||
\(513\) | − | 4.27382e13i | − | 1.20290i | ||||||
\(514\) | −2.80124e12 | + | 1.79068e12i | −0.0780790 | + | 0.0499117i | ||||
\(515\) | −4.13170e13 | + | 2.96766e13i | −1.14049 | + | 0.819178i | ||||
\(516\) | −9.96786e10 | + | 2.15499e11i | −0.00272492 | + | 0.00589111i | ||||
\(517\) | 3.84201e13i | 1.04017i | ||||||||
\(518\) | −3.12489e13 | + | 1.99758e13i | −0.837888 | + | 0.535617i | ||||
\(519\) | 3.87651e13i | 1.02945i | ||||||||
\(520\) | 1.75711e13 | + | 1.85457e13i | 0.462149 | + | 0.487783i | ||||
\(521\) | −1.50084e13 | −0.390972 | −0.195486 | − | 0.980707i | \(-0.562628\pi\) | ||||
−0.195486 | + | 0.980707i | \(0.562628\pi\) | |||||||
\(522\) | 1.70122e13 | + | 2.66129e13i | 0.438943 | + | 0.686658i | ||||
\(523\) | 4.78587e13 | 1.22307 | 0.611537 | − | 0.791216i | \(-0.290552\pi\) | ||||
0.611537 | + | 0.791216i | \(0.290552\pi\) | |||||||
\(524\) | 6.39397e12 | + | 2.95751e12i | 0.161850 | + | 0.0748635i | ||||
\(525\) | −6.38444e12 | + | 1.89456e13i | −0.160076 | + | 0.475020i | ||||
\(526\) | −6.58385e12 | − | 1.02994e13i | −0.163513 | − | 0.255790i | ||||
\(527\) | 1.48967e13 | 0.366468 | ||||||||
\(528\) | −1.03432e13 | + | 8.78858e12i | −0.252049 | + | 0.214165i | ||||
\(529\) | −2.08183e13 | −0.502536 | ||||||||
\(530\) | 1.26808e13 | − | 3.18284e13i | 0.303228 | − | 0.761088i | ||||
\(531\) | 3.09373e13i | 0.732841i | ||||||||
\(532\) | 3.92311e13 | + | 1.81463e13i | 0.920603 | + | 0.425823i | ||||
\(533\) | − | 2.67665e13i | − | 0.622236i | ||||||
\(534\) | −1.00278e13 | − | 1.56870e13i | −0.230941 | − | 0.361271i | ||||
\(535\) | −2.07713e12 | + | 1.49193e12i | −0.0473908 | + | 0.0340392i | ||||
\(536\) | −3.68800e13 | + | 5.02951e12i | −0.833617 | + | 0.113685i | ||||
\(537\) | − | 5.17025e13i | − | 1.15782i | ||||||
\(538\) | 1.66211e13 | + | 2.60011e13i | 0.368765 | + | 0.576874i | ||||
\(539\) | − | 7.69382e12i | − | 0.169121i | ||||||
\(540\) | −8.53801e12 | − | 4.44810e13i | −0.185946 | − | 0.968737i | ||||
\(541\) | 5.80418e12 | 0.125243 | 0.0626217 | − | 0.998037i | \(-0.480054\pi\) | ||||
0.0626217 | + | 0.998037i | \(0.480054\pi\) | |||||||
\(542\) | 1.54076e12 | − | 9.84924e11i | 0.0329411 | − | 0.0210575i | ||||
\(543\) | 2.77282e13 | 0.587385 | ||||||||
\(544\) | 1.31812e13 | + | 4.04424e12i | 0.276669 | + | 0.0848872i | ||||
\(545\) | 7.53983e12 | − | 5.41560e12i | 0.156812 | − | 0.112633i | ||||
\(546\) | 1.37711e13 | − | 8.80311e12i | 0.283795 | − | 0.181415i | ||||
\(547\) | 5.03600e13 | 1.02837 | 0.514185 | − | 0.857679i | \(-0.328094\pi\) | ||||
0.514185 | + | 0.857679i | \(0.328094\pi\) | |||||||
\(548\) | −3.54012e13 | − | 1.63747e13i | −0.716333 | − | 0.331338i | ||||
\(549\) | 3.54690e13 | 0.711193 | ||||||||
\(550\) | −6.66613e12 | − | 2.68053e13i | −0.132452 | − | 0.532608i | ||||
\(551\) | − | 7.92590e13i | − | 1.56060i | ||||||
\(552\) | −2.15842e13 | + | 2.94355e12i | −0.421154 | + | 0.0574350i | ||||
\(553\) | − | 8.16149e13i | − | 1.57813i | ||||||
\(554\) | −4.87198e13 | + | 3.11440e13i | −0.933591 | + | 0.596795i | ||||
\(555\) | −2.21338e13 | − | 3.08156e13i | −0.420330 | − | 0.585201i | ||||
\(556\) | 1.76295e13 | + | 8.15448e12i | 0.331792 | + | 0.153470i | ||||
\(557\) | 3.19874e13i | 0.596627i | 0.954468 | + | 0.298314i | \(0.0964242\pi\) | ||||
−0.954468 | + | 0.298314i | \(0.903576\pi\) | |||||||
\(558\) | −3.67559e13 | + | 2.34961e13i | −0.679448 | + | 0.434335i | ||||
\(559\) | 3.95030e11i | 0.00723721i | ||||||||
\(560\) | 4.44561e13 | + | 1.10489e13i | 0.807219 | + | 0.200622i | ||||
\(561\) | −5.31877e12 | −0.0957187 | ||||||||
\(562\) | −2.88859e13 | − | 4.51875e13i | −0.515234 | − | 0.806002i | ||||
\(563\) | 3.34105e13 | 0.590665 | 0.295332 | − | 0.955395i | \(-0.404570\pi\) | ||||
0.295332 | + | 0.955395i | \(0.404570\pi\) | |||||||
\(564\) | 2.73641e13 | − | 5.91596e13i | 0.479497 | − | 1.03664i | ||||
\(565\) | 3.65498e13 | + | 5.08861e13i | 0.634808 | + | 0.883806i | ||||
\(566\) | −2.22588e13 | − | 3.48203e13i | −0.383194 | − | 0.599447i | ||||
\(567\) | 2.06458e12 | 0.0352304 | ||||||||
\(568\) | 1.28999e13 | + | 9.45914e13i | 0.218195 | + | 1.59996i | ||||
\(569\) | −3.53976e13 | −0.593488 | −0.296744 | − | 0.954957i | \(-0.595901\pi\) | ||||
−0.296744 | + | 0.954957i | \(0.595901\pi\) | |||||||
\(570\) | −1.63661e13 | + | 4.10782e13i | −0.272001 | + | 0.682711i | ||||
\(571\) | − | 9.52378e12i | − | 0.156902i | −0.996918 | − | 0.0784511i | \(-0.975003\pi\) | ||
0.996918 | − | 0.0784511i | \(-0.0249974\pi\) | |||||||
\(572\) | −9.48003e12 | + | 2.04953e13i | −0.154821 | + | 0.334714i | ||||
\(573\) | − | 2.60302e13i | − | 0.421410i | ||||||
\(574\) | −2.58496e13 | − | 4.04377e13i | −0.414854 | − | 0.648973i | ||||
\(575\) | 1.41572e13 | − | 4.20110e13i | 0.225236 | − | 0.668380i | ||||
\(576\) | −3.89020e13 | + | 1.08116e13i | −0.613563 | + | 0.170521i | ||||
\(577\) | − | 7.27346e13i | − | 1.13727i | −0.822592 | − | 0.568633i | \(-0.807473\pi\) | ||
0.822592 | − | 0.568633i | \(-0.192527\pi\) | |||||||
\(578\) | −3.18362e13 | − | 4.98027e13i | −0.493494 | − | 0.771994i | ||||
\(579\) | 6.97906e13i | 1.07252i | ||||||||
\(580\) | −1.58340e13 | − | 8.24912e13i | −0.241240 | − | 1.25680i | ||||
\(581\) | 1.39704e13 | 0.211022 | ||||||||
\(582\) | 2.54394e13 | − | 1.62620e13i | 0.380971 | − | 0.243534i | ||||
\(583\) | 3.02836e13 | 0.449640 | ||||||||
\(584\) | 9.23955e12 | + | 6.77510e13i | 0.136015 | + | 0.997359i | ||||
\(585\) | −1.71033e13 | − | 2.38119e13i | −0.249632 | − | 0.347548i | ||||
\(586\) | −1.01800e14 | + | 6.50750e13i | −1.47319 | + | 0.941729i | ||||
\(587\) | −3.06508e13 | −0.439795 | −0.219898 | − | 0.975523i | \(-0.570572\pi\) | ||||
−0.219898 | + | 0.975523i | \(0.570572\pi\) | |||||||
\(588\) | −5.47980e12 | + | 1.18470e13i | −0.0779611 | + | 0.168547i | ||||
\(589\) | 1.09467e14 | 1.54421 | ||||||||
\(590\) | 3.04507e13 | − | 7.64298e13i | 0.425928 | − | 1.06906i | ||||
\(591\) | 4.56148e13i | 0.632657i | ||||||||
\(592\) | −6.62481e13 | + | 5.62907e13i | −0.911097 | + | 0.774156i | ||||
\(593\) | − | 1.36696e13i | − | 0.186416i | −0.995647 | − | 0.0932078i | \(-0.970288\pi\) | ||
0.995647 | − | 0.0932078i | \(-0.0297121\pi\) | |||||||
\(594\) | 3.37313e13 | − | 2.15626e13i | 0.456143 | − | 0.291588i | ||||
\(595\) | 1.04722e13 | + | 1.45798e13i | 0.140428 | + | 0.195509i | ||||
\(596\) | 1.05979e13 | − | 2.29120e13i | 0.140925 | − | 0.304671i | ||||
\(597\) | 1.21915e13i | 0.160763i | ||||||||
\(598\) | −3.05367e13 | + | 1.95205e13i | −0.399316 | + | 0.255261i | ||||
\(599\) | 9.08884e13i | 1.17862i | 0.807906 | + | 0.589311i | \(0.200601\pi\) | ||||
−0.807906 | + | 0.589311i | \(0.799399\pi\) | |||||||
\(600\) | −8.82711e12 | + | 4.60229e13i | −0.113517 | + | 0.591858i | ||||
\(601\) | 2.58195e13 | 0.329288 | 0.164644 | − | 0.986353i | \(-0.447352\pi\) | ||||
0.164644 | + | 0.986353i | \(0.447352\pi\) | |||||||
\(602\) | 3.81499e11 | + | 5.96795e11i | 0.00482515 | + | 0.00754819i | ||||
\(603\) | 4.27140e13 | 0.535776 | ||||||||
\(604\) | 8.91810e13 | + | 4.12505e13i | 1.10940 | + | 0.513150i | ||||
\(605\) | −4.60028e13 | + | 3.30423e13i | −0.567555 | + | 0.407655i | ||||
\(606\) | 2.14628e13 | + | 3.35752e13i | 0.262618 | + | 0.410824i | ||||
\(607\) | −1.20909e14 | −1.46729 | −0.733646 | − | 0.679532i | \(-0.762183\pi\) | ||||
−0.733646 | + | 0.679532i | \(0.762183\pi\) | |||||||
\(608\) | 9.68609e13 | + | 2.97187e13i | 1.16582 | + | 0.357694i | ||||
\(609\) | −5.37377e13 | −0.641494 | ||||||||
\(610\) | −8.76253e13 | − | 3.49111e13i | −1.03748 | − | 0.413346i | ||||
\(611\) | − | 1.08445e14i | − | 1.27351i | ||||||
\(612\) | −1.43605e13 | − | 6.64240e12i | −0.167268 | − | 0.0773692i | ||||
\(613\) | 4.75439e13i | 0.549278i | 0.961547 | + | 0.274639i | \(0.0885583\pi\) | ||||
−0.961547 | + | 0.274639i | \(0.911442\pi\) | |||||||
\(614\) | 6.86772e13 | + | 1.07435e14i | 0.786993 | + | 1.23113i | ||||
\(615\) | 3.98769e13 | − | 2.86422e13i | 0.453258 | − | 0.325560i | ||||
\(616\) | 5.47119e12 | + | 4.01187e13i | 0.0616848 | + | 0.452317i | ||||
\(617\) | 1.10787e14i | 1.23898i | 0.785006 | + | 0.619488i | \(0.212660\pi\) | ||||
−0.785006 | + | 0.619488i | \(0.787340\pi\) | |||||||
\(618\) | 4.10868e13 | + | 6.42738e13i | 0.455785 | + | 0.713004i | ||||
\(619\) | 1.29963e14i | 1.43010i | 0.699071 | + | 0.715052i | \(0.253597\pi\) | ||||
−0.699071 | + | 0.715052i | \(0.746403\pi\) | |||||||
\(620\) | 1.13931e14 | − | 2.18687e13i | 1.24361 | − | 0.238707i | ||||
\(621\) | 6.42541e13 | 0.695734 | ||||||||
\(622\) | 3.77119e13 | − | 2.41072e13i | 0.405067 | − | 0.258938i | ||||
\(623\) | −5.55414e13 | −0.591802 | ||||||||
\(624\) | 2.91948e13 | − | 2.48067e13i | 0.308591 | − | 0.262209i | ||||
\(625\) | −7.59163e13 | − | 5.77206e13i | −0.796040 | − | 0.605244i | ||||
\(626\) | 1.57072e14 | − | 1.00408e14i | 1.63390 | − | 1.04447i | ||||
\(627\) | −3.90845e13 | −0.403336 | ||||||||
\(628\) | −3.92949e13 | − | 1.81758e13i | −0.402289 | − | 0.186078i | ||||
\(629\) | −3.40666e13 | −0.346000 | ||||||||
\(630\) | −4.88352e13 | − | 1.94566e13i | −0.492074 | − | 0.196049i | ||||
\(631\) | 1.72818e13i | 0.172760i | 0.996262 | + | 0.0863798i | \(0.0275299\pi\) | ||||
−0.996262 | + | 0.0863798i | \(0.972470\pi\) | |||||||
\(632\) | −2.58498e13 | − | 1.89549e14i | −0.256372 | − | 1.87991i | ||||
\(633\) | 5.97545e13i | 0.587966i | ||||||||
\(634\) | −1.19035e14 | + | 7.60926e13i | −1.16206 | + | 0.742842i | ||||
\(635\) | −4.27610e13 | + | 3.07138e13i | −0.414171 | + | 0.297485i | ||||
\(636\) | −4.66309e13 | − | 2.15690e13i | −0.448114 | − | 0.207274i | ||||
\(637\) | 2.17166e13i | 0.207060i | ||||||||
\(638\) | 6.25556e13 | − | 3.99885e13i | 0.591784 | − | 0.378296i | ||||
\(639\) | − | 1.09555e14i | − | 1.02832i | ||||||
\(640\) | 1.06748e14 | + | 1.15803e13i | 0.994167 | + | 0.107850i | ||||
\(641\) | −2.02056e14 | −1.86716 | −0.933580 | − | 0.358369i | \(-0.883333\pi\) | ||||
−0.933580 | + | 0.358369i | \(0.883333\pi\) | |||||||
\(642\) | 2.06555e12 | + | 3.23123e12i | 0.0189392 | + | 0.0296273i | ||||
\(643\) | −7.34393e13 | −0.668150 | −0.334075 | − | 0.942547i | \(-0.608424\pi\) | ||||
−0.334075 | + | 0.942547i | \(0.608424\pi\) | |||||||
\(644\) | −2.72818e13 | + | 5.89815e13i | −0.246288 | + | 0.532460i | ||||
\(645\) | −5.88518e11 | + | 4.22713e11i | −0.00527183 | + | 0.00378658i | ||||
\(646\) | 2.13843e13 | + | 3.34523e13i | 0.190078 | + | 0.297347i | ||||
\(647\) | −2.94516e13 | −0.259769 | −0.129885 | − | 0.991529i | \(-0.541461\pi\) | ||||
−0.129885 | + | 0.991529i | \(0.541461\pi\) | |||||||
\(648\) | 4.79495e12 | − | 6.53912e11i | 0.0419671 | − | 0.00572327i | ||||
\(649\) | 7.27204e13 | 0.631586 | ||||||||
\(650\) | 1.88159e13 | + | 7.56610e13i | 0.162165 | + | 0.652086i | ||||
\(651\) | − | 7.42187e13i | − | 0.634759i | ||||||
\(652\) | −6.21569e13 | + | 1.34379e14i | −0.527535 | + | 1.14050i | ||||
\(653\) | 9.08012e13i | 0.764761i | 0.924005 | + | 0.382381i | \(0.124896\pi\) | ||||
−0.924005 | + | 0.382381i | \(0.875104\pi\) | |||||||
\(654\) | −7.49781e12 | − | 1.17291e13i | −0.0626680 | − | 0.0980342i | ||||
\(655\) | 1.25421e13 | + | 1.74616e13i | 0.104031 | + | 0.144837i | ||||
\(656\) | −7.28430e13 | − | 8.57283e13i | −0.599609 | − | 0.705675i | ||||
\(657\) | − | 7.84685e13i | − | 0.641015i | ||||||
\(658\) | −1.04730e14 | − | 1.63834e14i | −0.849070 | − | 1.32823i | ||||
\(659\) | − | 1.09885e14i | − | 0.884119i | −0.896986 | − | 0.442060i | \(-0.854248\pi\) | ||
0.896986 | − | 0.442060i | \(-0.145752\pi\) | |||||||
\(660\) | −4.06783e13 | + | 7.80809e12i | −0.324821 | + | 0.0623484i | ||||
\(661\) | 9.98769e13 | 0.791512 | 0.395756 | − | 0.918356i | \(-0.370483\pi\) | ||||
0.395756 | + | 0.918356i | \(0.370483\pi\) | |||||||
\(662\) | 2.73640e13 | − | 1.74924e13i | 0.215224 | − | 0.137581i | ||||
\(663\) | 1.50128e13 | 0.117191 | ||||||||
\(664\) | 3.24459e13 | − | 4.42482e12i | 0.251374 | − | 0.0342811i | ||||
\(665\) | 7.69539e13 | + | 1.07138e14i | 0.591728 | + | 0.823829i | ||||
\(666\) | 8.40555e13 | − | 5.37322e13i | 0.641498 | − | 0.410075i | ||||
\(667\) | 1.19161e14 | 0.902620 | ||||||||
\(668\) | 9.32426e13 | − | 2.01585e14i | 0.701022 | − | 1.51557i | ||||
\(669\) | −4.53017e13 | −0.338052 | ||||||||
\(670\) | −1.05524e14 | − | 4.20421e13i | −0.781585 | − | 0.311394i | ||||
\(671\) | − | 8.33725e13i | − | 0.612929i | ||||||
\(672\) | 2.01493e13 | − | 6.56718e13i | 0.147033 | − | 0.479217i | ||||
\(673\) | 3.19718e13i | 0.231575i | 0.993274 | + | 0.115787i | \(0.0369392\pi\) | ||||
−0.993274 | + | 0.115787i | \(0.963061\pi\) | |||||||
\(674\) | 7.37730e13 | − | 4.71591e13i | 0.530393 | − | 0.339052i | ||||
\(675\) | 4.41407e13 | − | 1.30986e14i | 0.315007 | − | 0.934772i | ||||
\(676\) | −3.25054e13 | + | 7.02746e13i | −0.230262 | + | 0.497812i | ||||
\(677\) | − | 1.90887e13i | − | 0.134225i | −0.997745 | − | 0.0671123i | \(-0.978621\pi\) | ||
0.997745 | − | 0.0671123i | \(-0.0213786\pi\) | |||||||
\(678\) | 7.91597e13 | − | 5.06026e13i | 0.552530 | − | 0.353203i | ||||
\(679\) | − | 9.00708e13i | − | 0.624073i | ||||||
\(680\) | 2.89393e13 | + | 3.05445e13i | 0.199041 | + | 0.210082i | ||||
\(681\) | −6.39229e13 | −0.436436 | ||||||||
\(682\) | 5.52292e13 | + | 8.63974e13i | 0.374323 | + | 0.585570i | ||||
\(683\) | 9.20549e12 | 0.0619360 | 0.0309680 | − | 0.999520i | \(-0.490141\pi\) | ||||
0.0309680 | + | 0.999520i | \(0.490141\pi\) | |||||||
\(684\) | −1.05527e14 | − | 4.88111e13i | −0.704825 | − | 0.326015i | ||||
\(685\) | −6.94412e13 | − | 9.66790e13i | −0.460431 | − | 0.641031i | ||||
\(686\) | 8.90334e13 | + | 1.39279e14i | 0.586047 | + | 0.916778i | ||||
\(687\) | 1.29677e14 | 0.847383 | ||||||||
\(688\) | 1.07505e12 | + | 1.26521e12i | 0.00697404 | + | 0.00820769i | ||||
\(689\) | −8.54788e13 | −0.550506 | ||||||||
\(690\) | −6.17585e13 | − | 2.46054e13i | −0.394867 | − | 0.157320i | ||||
\(691\) | 2.89506e14i | 1.83767i | 0.394645 | + | 0.918834i | \(0.370868\pi\) | ||||
−0.394645 | + | 0.918834i | \(0.629132\pi\) | |||||||
\(692\) | 2.46021e14 | + | 1.13796e14i | 1.55039 | + | 0.717131i | ||||
\(693\) | − | 4.64650e13i | − | 0.290710i | ||||||
\(694\) | −8.48029e13 | − | 1.32661e14i | −0.526761 | − | 0.824034i | ||||
\(695\) | 3.45812e13 | + | 4.81453e13i | 0.213263 | + | 0.296914i | ||||
\(696\) | −1.24805e14 | + | 1.70203e13i | −0.764161 | + | 0.104213i | ||||
\(697\) | − | 4.40839e13i | − | 0.267988i | ||||||
\(698\) | 7.19569e13 | + | 1.12565e14i | 0.434306 | + | 0.679402i | ||||
\(699\) | 5.04565e12i | 0.0302365i | ||||||||
\(700\) | 1.01496e14 | + | 9.61340e13i | 0.603889 | + | 0.571988i | ||||
\(701\) | −1.50130e14 | −0.886903 | −0.443451 | − | 0.896298i | \(-0.646246\pi\) | ||||
−0.443451 | + | 0.896298i | \(0.646246\pi\) | |||||||
\(702\) | −9.52104e13 | + | 6.08629e13i | −0.558469 | + | 0.356999i | ||||
\(703\) | −2.50335e14 | −1.45796 | ||||||||
\(704\) | 2.54135e13 | + | 9.14419e13i | 0.146960 | + | 0.528789i | ||||
\(705\) | 1.61562e14 | − | 1.16045e14i | 0.927671 | − | 0.666314i | ||||
\(706\) | 1.87917e14 | − | 1.20125e14i | 1.07138 | − | 0.684874i | ||||
\(707\) | 1.18877e14 | 0.672976 | ||||||||
\(708\) | −1.11975e14 | − | 5.17939e13i | −0.629442 | − | 0.291147i | ||||
\(709\) | 5.68854e13 | 0.317519 | 0.158760 | − | 0.987317i | \(-0.449251\pi\) | ||||
0.158760 | + | 0.987317i | \(0.449251\pi\) | |||||||
\(710\) | −1.07831e14 | + | 2.70652e14i | −0.597659 | + | 1.50010i | ||||
\(711\) | 2.19534e14i | 1.20824i | ||||||||
\(712\) | −1.28994e14 | + | 1.75915e13i | −0.704967 | + | 0.0961400i | ||||
\(713\) | 1.64577e14i | 0.893142i | ||||||||
\(714\) | 2.26807e13 | − | 1.44986e13i | 0.122227 | − | 0.0781329i | ||||
\(715\) | −5.59716e13 | + | 4.02025e13i | −0.299528 | + | 0.215141i | ||||
\(716\) | −3.28128e14 | − | 1.51775e14i | −1.74372 | − | 0.806555i | ||||
\(717\) | − | 5.19497e13i | − | 0.274149i | ||||||
\(718\) | −1.87839e13 | + | 1.20075e13i | −0.0984381 | + | 0.0629262i | ||||
\(719\) | 4.60962e13i | 0.239895i | 0.992780 | + | 0.119947i | \(0.0382725\pi\) | ||||
−0.992780 | + | 0.119947i | \(0.961727\pi\) | |||||||
\(720\) | −1.19581e14 | − | 2.97200e13i | −0.618017 | − | 0.153598i | ||||
\(721\) | 2.27568e14 | 1.16798 | ||||||||
\(722\) | 5.14697e13 | + | 8.05162e13i | 0.262341 | + | 0.410390i | ||||
\(723\) | −7.99593e13 | −0.404741 | ||||||||
\(724\) | 8.13973e13 | − | 1.75976e14i | 0.409183 | − | 0.884628i | ||||
\(725\) | 8.18600e13 | − | 2.42917e14i | 0.408678 | − | 1.21274i | ||||
\(726\) | 4.57465e13 | + | 7.15632e13i | 0.226817 | + | 0.354819i | ||||
\(727\) | 1.49821e14 | 0.737736 | 0.368868 | − | 0.929482i | \(-0.379746\pi\) | ||||
0.368868 | + | 0.929482i | \(0.379746\pi\) | |||||||
\(728\) | −1.54430e13 | − | 1.13239e14i | −0.0755224 | − | 0.553784i | ||||
\(729\) | 1.16841e14 | 0.567490 | ||||||||
\(730\) | −7.72341e13 | + | 1.93854e14i | −0.372559 | + | 0.935107i | ||||
\(731\) | 6.50607e11i | 0.00311697i | ||||||||
\(732\) | −5.93807e13 | + | 1.28378e14i | −0.282547 | + | 0.610849i | ||||
\(733\) | 9.25379e13i | 0.437320i | 0.975801 | + | 0.218660i | \(0.0701686\pi\) | ||||
−0.975801 | + | 0.218660i | \(0.929831\pi\) | |||||||
\(734\) | −6.56410e13 | − | 1.02685e14i | −0.308102 | − | 0.481977i | ||||
\(735\) | −3.23536e13 | + | 2.32385e13i | −0.150829 | + | 0.108336i | ||||
\(736\) | −4.46802e13 | + | 1.45624e14i | −0.206884 | + | 0.674287i | ||||
\(737\) | − | 1.00402e14i | − | 0.461749i | ||||||
\(738\) | 6.95321e13 | + | 1.08772e14i | 0.317617 | + | 0.496862i | ||||
\(739\) | − | 4.85434e13i | − | 0.220246i | −0.993918 | − | 0.110123i | \(-0.964876\pi\) | ||
0.993918 | − | 0.110123i | \(-0.0351245\pi\) | |||||||
\(740\) | −2.60544e14 | + | 5.00107e13i | −1.17415 | + | 0.225374i | ||||
\(741\) | 1.10320e14 | 0.493815 | ||||||||
\(742\) | −1.29138e14 | + | 8.25509e13i | −0.574161 | + | 0.367031i | ||||
\(743\) | −4.13114e13 | −0.182442 | −0.0912211 | − | 0.995831i | \(-0.529077\pi\) | ||||
−0.0912211 | + | 0.995831i | \(0.529077\pi\) | |||||||
\(744\) | −2.35072e13 | − | 1.72371e14i | −0.103118 | − | 0.756137i | ||||
\(745\) | 6.25716e13 | − | 4.49430e13i | 0.272644 | − | 0.195831i | ||||
\(746\) | 2.58870e14 | − | 1.65482e14i | 1.12044 | − | 0.716235i | ||||
\(747\) | −3.75785e13 | −0.161561 | ||||||||
\(748\) | −1.56134e13 | + | 3.37553e13i | −0.0666792 | + | 0.144157i | ||||
\(749\) | 1.14405e13 | 0.0485329 | ||||||||
\(750\) | −9.25857e13 | + | 1.08995e14i | −0.390156 | + | 0.459304i | ||||
\(751\) | − | 8.29433e13i | − | 0.347202i | −0.984816 | − | 0.173601i | \(-0.944460\pi\) | ||
0.984816 | − | 0.173601i | \(-0.0555403\pi\) | |||||||
\(752\) | −2.95125e14 | − | 3.47330e14i | −1.22720 | − | 1.44429i | ||||
\(753\) | − | 4.07768e13i | − | 0.168437i | ||||||
\(754\) | −1.76570e14 | + | 1.12872e14i | −0.724537 | + | 0.463158i | ||||
\(755\) | 1.74933e14 | + | 2.43549e14i | 0.713078 | + | 0.992777i | ||||
\(756\) | −8.50617e13 | + | 1.83898e14i | −0.344449 | + | 0.744678i | ||||
\(757\) | − | 1.93514e14i | − | 0.778455i | −0.921142 | − | 0.389228i | \(-0.872742\pi\) | ||
0.921142 | − | 0.389228i | \(-0.127258\pi\) | |||||||
\(758\) | 1.68201e14 | − | 1.07522e14i | 0.672176 | − | 0.429686i | ||||
\(759\) | − | 5.87611e13i | − | 0.233282i | ||||||
\(760\) | 2.12658e14 | + | 2.24453e14i | 0.838712 | + | 0.885234i | ||||
\(761\) | 1.66032e14 | 0.650531 | 0.325265 | − | 0.945623i | \(-0.394546\pi\) | ||||
0.325265 | + | 0.945623i | \(0.394546\pi\) | |||||||
\(762\) | 4.25227e13 | + | 6.65201e13i | 0.165518 | + | 0.258927i | ||||
\(763\) | −4.15283e13 | −0.160591 | ||||||||
\(764\) | −1.65200e14 | − | 7.64127e13i | −0.634661 | − | 0.293561i | ||||
\(765\) | −2.81688e13 | − | 3.92178e13i | −0.107513 | − | 0.149684i | ||||
\(766\) | 1.49009e14 | + | 2.33102e14i | 0.565028 | + | 0.883896i | ||||
\(767\) | −2.05261e14 | −0.773268 | ||||||||
\(768\) | 2.59962e13 | − | 1.58903e14i | 0.0972981 | − | 0.594739i | ||||
\(769\) | −4.26640e14 | −1.58646 | −0.793232 | − | 0.608919i | \(-0.791603\pi\) | ||||
−0.793232 | + | 0.608919i | \(0.791603\pi\) | |||||||
\(770\) | −4.57341e13 | + | 1.14791e14i | −0.168961 | + | 0.424085i | ||||
\(771\) | 1.52148e13i | 0.0558464i | ||||||||
\(772\) | 4.42923e14 | + | 2.04873e14i | 1.61526 | + | 0.747134i | ||||
\(773\) | 4.17310e14i | 1.51203i | 0.654552 | + | 0.756017i | \(0.272857\pi\) | ||||
−0.654552 | + | 0.756017i | \(0.727143\pi\) | |||||||
\(774\) | −1.02618e12 | − | 1.60530e12i | −0.00369420 | − | 0.00577898i | ||||
\(775\) | 3.35499e14 | + | 1.13059e14i | 1.20000 | + | 0.404387i | ||||
\(776\) | −2.85280e13 | − | 2.09188e14i | −0.101382 | − | 0.743408i | ||||
\(777\) | 1.69728e14i | 0.599305i | ||||||||
\(778\) | −1.49162e14 | − | 2.33340e14i | −0.523310 | − | 0.818636i | ||||
\(779\) | − | 3.23946e14i | − | 1.12924i | ||||||
\(780\) | 1.14819e14 | − | 2.20392e13i | 0.397687 | − | 0.0763349i | ||||
\(781\) | −2.57516e14 | −0.886236 | ||||||||
\(782\) | −5.02935e13 | + | 3.21499e13i | −0.171980 | + | 0.109938i | ||||
\(783\) | 3.71531e14 | 1.26237 | ||||||||
\(784\) | 5.91003e13 | + | 6.95546e13i | 0.199530 | + | 0.234826i | ||||
\(785\) | −7.70790e13 | − | 1.07313e14i | −0.258576 | − | 0.360000i | ||||
\(786\) | 2.71637e13 | − | 1.73643e13i | 0.0905476 | − | 0.0578822i | ||||
\(787\) | −1.87778e13 | −0.0621974 | −0.0310987 | − | 0.999516i | \(-0.509901\pi\) | ||||
−0.0310987 | + | 0.999516i | \(0.509901\pi\) | |||||||
\(788\) | 2.89492e14 | + | 1.33904e14i | 0.952809 | + | 0.440719i | ||||
\(789\) | −5.59409e13 | −0.182955 | ||||||||
\(790\) | 2.16080e14 | − | 5.42352e14i | 0.702230 | − | 1.76257i | ||||
\(791\) | − | 2.80273e14i | − | 0.905106i | ||||||
\(792\) | −1.47168e13 | − | 1.07914e14i | −0.0472267 | − | 0.346300i | ||||
\(793\) | 2.35328e14i | 0.750426i | ||||||||
\(794\) | 1.54076e13 | − | 9.84926e12i | 0.0488239 | − | 0.0312105i | ||||
\(795\) | −9.14689e13 | − | 1.27347e14i | −0.288030 | − | 0.401008i | ||||
\(796\) | 7.73729e13 | + | 3.57887e13i | 0.242116 | + | 0.111990i | ||||
\(797\) | − | 2.33356e14i | − | 0.725649i | −0.931857 | − | 0.362825i | \(-0.881812\pi\) | ||
0.931857 | − | 0.362825i | \(-0.118188\pi\) | |||||||
\(798\) | 1.66667e14 | − | 1.06541e14i | 0.515034 | − | 0.329234i | ||||
\(799\) | − | 1.78607e14i | − | 0.548485i | ||||||
\(800\) | 2.66170e14 | + | 1.91123e14i | 0.812285 | + | 0.583260i | ||||
\(801\) | 1.49399e14 | 0.453091 | ||||||||
\(802\) | −2.49510e14 | − | 3.90318e14i | −0.751996 | − | 1.17638i | ||||
\(803\) | −1.84446e14 | −0.552447 | ||||||||
\(804\) | −7.15099e13 | + | 1.54600e14i | −0.212856 | + | 0.460182i | ||||
\(805\) | −1.61076e14 | + | 1.15695e14i | −0.476487 | + | 0.342244i | ||||
\(806\) | −1.55891e14 | − | 2.43866e14i | −0.458294 | − | 0.716929i | ||||
\(807\) | 1.41224e14 | 0.412612 | ||||||||
\(808\) | 2.76089e14 | − | 3.76516e13i | 0.801663 | − | 0.109327i | ||||
\(809\) | 3.46851e14 | 1.00092 | 0.500461 | − | 0.865759i | \(-0.333164\pi\) | ||||
0.500461 | + | 0.865759i | \(0.333164\pi\) | |||||||
\(810\) | 1.37197e13 | + | 5.46610e12i | 0.0393477 | + | 0.0156766i | ||||
\(811\) | − | 1.48396e14i | − | 0.422978i | −0.977380 | − | 0.211489i | \(-0.932169\pi\) | ||
0.977380 | − | 0.211489i | \(-0.0678313\pi\) | |||||||
\(812\) | −1.57749e14 | + | 3.41044e14i | −0.446876 | + | 0.966118i | ||||
\(813\) | − | 8.36859e12i | − | 0.0235613i | ||||||
\(814\) | −1.26301e14 | − | 1.97579e14i | −0.353416 | − | 0.552863i | ||||
\(815\) | −3.66984e14 | + | 2.63592e14i | −1.02061 | + | 0.733068i | ||||
\(816\) | 4.80834e13 | − | 4.08562e13i | 0.132906 | − | 0.112930i | ||||
\(817\) | 4.78093e12i | 0.0131342i | ||||||||
\(818\) | −1.29075e14 | − | 2.01918e14i | −0.352433 | − | 0.551325i | ||||
\(819\) | 1.31153e14i | 0.355924i | ||||||||
\(820\) | −6.47163e13 | − | 3.37157e14i | −0.174560 | − | 0.909416i | ||||
\(821\) | −4.15425e14 | −1.11372 | −0.556861 | − | 0.830605i | \(-0.687995\pi\) | ||||
−0.556861 | + | 0.830605i | \(0.687995\pi\) | |||||||
\(822\) | −1.50396e14 | + | 9.61403e13i | −0.400754 | + | 0.256181i | ||||
\(823\) | −4.98563e14 | −1.32045 | −0.660224 | − | 0.751069i | \(-0.729539\pi\) | ||||
−0.660224 | + | 0.751069i | \(0.729539\pi\) | |||||||
\(824\) | 5.28523e14 | − | 7.20774e13i | 1.39132 | − | 0.189742i | ||||
\(825\) | −1.19788e14 | − | 4.03671e13i | −0.313432 | − | 0.105623i | ||||
\(826\) | −3.10100e14 | + | 1.98230e14i | −0.806495 | + | 0.515549i | ||||
\(827\) | −6.46871e14 | −1.67221 | −0.836104 | − | 0.548571i | \(-0.815172\pi\) | ||||
−0.836104 | + | 0.548571i | \(0.815172\pi\) | |||||||
\(828\) | 7.33844e13 | − | 1.58653e14i | 0.188561 | − | 0.407658i | ||||
\(829\) | −1.71726e14 | −0.438596 | −0.219298 | − | 0.975658i | \(-0.570377\pi\) | ||||
−0.219298 | + | 0.975658i | \(0.570377\pi\) | |||||||
\(830\) | 9.28368e13 | + | 3.69874e13i | 0.235684 | + | 0.0938995i | ||||
\(831\) | 2.64620e14i | 0.667756i | ||||||||
\(832\) | −7.17323e13 | − | 2.58105e14i | −0.179928 | − | 0.647410i | ||||
\(833\) | 3.57669e13i | 0.0891778i | ||||||||
\(834\) | 7.48961e13 | − | 4.78771e13i | 0.185622 | − | 0.118658i | ||||
\(835\) | 5.50519e14 | − | 3.95419e14i | 1.35625 | − | 0.974148i | ||||
\(836\) | −1.14734e14 | + | 2.48048e14i | −0.280970 | + | 0.607441i | ||||
\(837\) | 5.13133e14i | 1.24912i | ||||||||
\(838\) | 1.71214e14 | − | 1.09448e14i | 0.414304 | − | 0.264843i | ||||
\(839\) | 3.56109e14i | 0.856591i | 0.903639 | + | 0.428295i | \(0.140886\pi\) | ||||
−0.903639 | + | 0.428295i | \(0.859114\pi\) | |||||||
\(840\) | 1.52180e14 | − | 1.44182e14i | 0.363881 | − | 0.344758i | ||||
\(841\) | 2.68307e14 | 0.637753 | ||||||||
\(842\) | −3.88818e13 | − | 6.08244e13i | −0.0918725 | − | 0.143720i | ||||
\(843\) | −2.45435e14 | −0.576498 | ||||||||
\(844\) | 3.79229e14 | + | 1.75412e14i | 0.885502 | + | 0.409587i | ||||
\(845\) | −1.91917e14 | + | 1.37847e14i | −0.445481 | + | 0.319974i | ||||
\(846\) | 2.81711e14 | + | 4.40693e14i | 0.650058 | + | 1.01691i | ||||
\(847\) | 2.53377e14 | 0.581233 | ||||||||
\(848\) | −2.73774e14 | + | 2.32624e14i | −0.624327 | + | 0.530488i | ||||
\(849\) | −1.89126e14 | −0.428758 | ||||||||
\(850\) | 3.09894e13 | + | 1.24612e14i | 0.0698423 | + | 0.280845i | ||||
\(851\) | − | 3.76364e14i | − | 0.843257i | ||||||
\(852\) | 3.96525e14 | + | 1.83412e14i | 0.883228 | + | 0.408535i | ||||
\(853\) | − | 3.78193e14i | − | 0.837468i | −0.908109 | − | 0.418734i | \(-0.862474\pi\) | ||
0.908109 | − | 0.418734i | \(-0.137526\pi\) | |||||||
\(854\) | 2.27267e14 | + | 3.55524e14i | 0.500320 | + | 0.782671i | ||||
\(855\) | −2.06996e14 | − | 2.88188e14i | −0.453034 | − | 0.630734i | ||||
\(856\) | 2.65703e13 | − | 3.62354e12i | 0.0578134 | − | 0.00788431i | ||||
\(857\) | 3.25573e14i | 0.704278i | 0.935948 | + | 0.352139i | \(0.114546\pi\) | ||||
−0.935948 | + | 0.352139i | \(0.885454\pi\) | |||||||
\(858\) | 5.56597e13 | + | 8.70709e13i | 0.119703 | + | 0.187256i | ||||
\(859\) | 1.71426e14i | 0.366531i | 0.983063 | + | 0.183266i | \(0.0586668\pi\) | ||||
−0.983063 | + | 0.183266i | \(0.941333\pi\) | |||||||
\(860\) | 9.55109e11 | + | 4.97589e12i | 0.00203030 | + | 0.0105774i | ||||
\(861\) | −2.19636e14 | −0.464182 | ||||||||
\(862\) | 2.81756e14 | − | 1.80112e14i | 0.592021 | − | 0.378447i | ||||
\(863\) | 7.32951e14 | 1.53116 | 0.765581 | − | 0.643340i | \(-0.222452\pi\) | ||||
0.765581 | + | 0.643340i | \(0.222452\pi\) | |||||||
\(864\) | −1.39308e14 | + | 4.54041e14i | −0.289340 | + | 0.943032i | ||||
\(865\) | 4.82583e14 | + | 6.71872e14i | 0.996533 | + | 1.38741i | ||||
\(866\) | −1.71508e14 | + | 1.09636e14i | −0.352123 | + | 0.225093i | ||||
\(867\) | −2.70502e14 | −0.552173 | ||||||||
\(868\) | −4.71026e14 | − | 2.17872e14i | −0.955974 | − | 0.442183i | ||||
\(869\) | 5.16029e14 | 1.04130 | ||||||||
\(870\) | −3.57101e14 | − | 1.42274e14i | −0.716464 | − | 0.285449i | ||||
\(871\) | 2.83397e14i | 0.565332i | ||||||||
\(872\) | −9.64486e13 | + | 1.31532e13i | −0.191299 | + | 0.0260885i | ||||
\(873\) | 2.42279e14i | 0.477798i | ||||||||
\(874\) | −3.69577e14 | + | 2.36251e14i | −0.724683 | + | 0.463251i | ||||
\(875\) | 1.25197e14 | + | 4.07842e14i | 0.244093 | + | 0.795154i | ||||
\(876\) | 2.84011e14 | + | 1.31369e14i | 0.550572 | + | 0.254666i | ||||
\(877\) | − | 6.25010e14i | − | 1.20473i | −0.798222 | − | 0.602364i | \(-0.794226\pi\) | ||
0.798222 | − | 0.602364i | \(-0.205774\pi\) | |||||||
\(878\) | −5.15775e14 | + | 3.29707e14i | −0.988524 | + | 0.631911i | ||||
\(879\) | 5.52922e14i | 1.05371i | ||||||||
\(880\) | −6.98591e13 | + | 2.81084e14i | −0.132376 | + | 0.532627i | ||||
\(881\) | 3.05476e14 | 0.575569 | 0.287784 | − | 0.957695i | \(-0.407081\pi\) | ||||
0.287784 | + | 0.957695i | \(0.407081\pi\) | |||||||
\(882\) | −5.64141e13 | − | 8.82509e13i | −0.105693 | − | 0.165339i | ||||
\(883\) | 3.59888e13 | 0.0670446 | 0.0335223 | − | 0.999438i | \(-0.489328\pi\) | ||||
0.0335223 | + | 0.999438i | \(0.489328\pi\) | |||||||
\(884\) | 4.40707e13 | − | 9.52781e13i | 0.0816372 | − | 0.176495i | ||||
\(885\) | −2.19645e14 | − | 3.05799e14i | −0.404581 | − | 0.563275i | ||||
\(886\) | −3.11487e14 | − | 4.87272e14i | −0.570520 | − | 0.892488i | ||||
\(887\) | 4.13812e14 | 0.753677 | 0.376839 | − | 0.926279i | \(-0.377011\pi\) | ||||
0.376839 | + | 0.926279i | \(0.377011\pi\) | |||||||
\(888\) | 5.37576e13 | + | 3.94189e14i | 0.0973588 | + | 0.713904i | ||||
\(889\) | 2.35522e14 | 0.424152 | ||||||||
\(890\) | −3.69087e14 | − | 1.47049e14i | −0.660965 | − | 0.263337i | ||||
\(891\) | 1.30538e13i | 0.0232460i | ||||||||
\(892\) | −1.32985e14 | + | 2.87505e14i | −0.235493 | + | 0.509121i | ||||
\(893\) | − | 1.31248e15i | − | 2.31118i | ||||||
\(894\) | −6.22229e13 | − | 9.73379e13i | −0.108959 | − | 0.170449i | ||||
\(895\) | −6.43639e14 | − | 8.96101e14i | −1.12080 | − | 1.56042i | ||||
\(896\) | −3.57634e14 | − | 3.20659e14i | −0.619297 | − | 0.555269i | ||||
\(897\) | 1.65860e14i | 0.285613i | ||||||||
\(898\) | 1.32935e14 | + | 2.07956e14i | 0.227645 | + | 0.356115i | ||||
\(899\) | 9.51618e14i | 1.62056i | ||||||||
\(900\) | −2.73010e14 | − | 2.58588e14i | −0.462345 | − | 0.437921i | ||||
\(901\) | −1.40782e14 | −0.237096 | ||||||||
\(902\) | 2.55676e14 | − | 1.63440e14i | 0.428211 | − | 0.273733i | ||||
\(903\) | 3.24148e12 | 0.00539888 | ||||||||
\(904\) | −8.87706e13 | − | 6.50929e14i | −0.147037 | − | 1.07818i | ||||
\(905\) | 4.80582e14 | − | 3.45186e14i | 0.791635 | − | 0.568604i | ||||
\(906\) | 3.78871e14 | − | 2.42192e14i | 0.620656 | − | 0.396752i | ||||
\(907\) | 8.06692e14 | 1.31423 | 0.657115 | − | 0.753791i | \(-0.271777\pi\) | ||||
0.657115 | + | 0.753791i | \(0.271777\pi\) | |||||||
\(908\) | −1.87648e14 | + | 4.05684e14i | −0.304029 | + | 0.657292i | ||||
\(909\) | −3.19763e14 | −0.515239 | ||||||||
\(910\) | 1.29090e14 | − | 3.24009e14i | 0.206864 | − | 0.519219i | ||||
\(911\) | − | 8.50991e14i | − | 1.35623i | −0.734956 | − | 0.678115i | \(-0.762797\pi\) | ||
0.734956 | − | 0.678115i | \(-0.237203\pi\) | |||||||
\(912\) | 3.53336e14 | − | 3.00228e14i | 0.560034 | − | 0.475858i | ||||
\(913\) | 8.83310e13i | 0.139239i | ||||||||
\(914\) | −1.49767e14 | + | 9.57381e13i | −0.234793 | + | 0.150091i | ||||
\(915\) | −3.50593e14 | + | 2.51819e14i | −0.546636 | + | 0.392630i | ||||
\(916\) | 3.80672e14 | − | 8.22990e14i | 0.590301 | − | 1.27620i | ||||
\(917\) | − | 9.61762e13i | − | 0.148327i | ||||||
\(918\) | −1.56810e14 | + | 1.00240e14i | −0.240525 | + | 0.153755i | ||||
\(919\) | − | 3.79956e14i | − | 0.579637i | −0.957082 | − | 0.289819i | \(-0.906405\pi\) | ||
0.957082 | − | 0.289819i | \(-0.0935950\pi\) | |||||||
\(920\) | −3.37451e14 | + | 3.19717e14i | −0.512002 | + | 0.485095i | ||||
\(921\) | 5.83529e14 | 0.880570 | ||||||||
\(922\) | 2.55282e14 | + | 3.99349e14i | 0.383147 | + | 0.599374i | ||||
\(923\) | 7.26868e14 | 1.08504 | ||||||||
\(924\) | 1.68177e14 | + | 7.77898e13i | 0.249693 | + | 0.115495i | ||||
\(925\) | −7.67239e14 | − | 2.58550e14i | −1.13298 | − | 0.381801i | ||||
\(926\) | −4.95380e14 | − | 7.74943e14i | −0.727584 | − | 1.13819i | ||||
\(927\) | −6.12130e14 | −0.894221 | ||||||||
\(928\) | −2.58351e14 | + | 8.42031e14i | −0.375379 | + | 1.22346i | ||||
\(929\) | 3.47287e14 | 0.501891 | 0.250946 | − | 0.968001i | \(-0.419258\pi\) | ||||
0.250946 | + | 0.968001i | \(0.419258\pi\) | |||||||
\(930\) | 1.96498e14 | − | 4.93202e14i | 0.282452 | − | 0.708941i | ||||
\(931\) | 2.62830e14i | 0.375774i | ||||||||
\(932\) | 3.20220e13 | + | 1.48117e13i | 0.0455374 | + | 0.0210632i | ||||
\(933\) | − | 2.04831e14i | − | 0.289726i | ||||||
\(934\) | 3.34027e14 | + | 5.22533e14i | 0.469946 | + | 0.735156i | ||||
\(935\) | −9.21842e13 | + | 6.62128e13i | −0.129003 | + | 0.0926582i | ||||
\(936\) | 4.15398e13 | + | 3.04599e14i | 0.0578209 | + | 0.423984i | ||||
\(937\) | 2.94468e14i | 0.407700i | 0.979002 | + | 0.203850i | \(0.0653455\pi\) | ||||
−0.979002 | + | 0.203850i | \(0.934654\pi\) | |||||||
\(938\) | 2.73689e14 | + | 4.28144e14i | 0.376915 | + | 0.589624i | ||||
\(939\) | − | 8.53131e14i | − | 1.16866i | ||||||
\(940\) | −2.62200e14 | − | 1.36600e15i | −0.357267 | − | 1.86128i | ||||
\(941\) | −6.35492e14 | −0.861315 | −0.430657 | − | 0.902515i | \(-0.641718\pi\) | ||||
−0.430657 | + | 0.902515i | \(0.641718\pi\) | |||||||
\(942\) | −1.66938e14 | + | 1.06715e14i | −0.225062 | + | 0.143870i | ||||
\(943\) | 4.87033e14 | 0.653131 | ||||||||
\(944\) | −6.57416e14 | + | 5.58603e14i | −0.876960 | + | 0.745150i | ||||
\(945\) | −5.02218e14 | + | 3.60726e14i | −0.666397 | + | 0.478650i | ||||
\(946\) | −3.77337e12 | + | 2.41212e12i | −0.00498051 | + | 0.00318378i | ||||
\(947\) | 1.19083e15 | 1.56351 | 0.781753 | − | 0.623589i | \(-0.214326\pi\) | ||||
0.781753 | + | 0.623589i | \(0.214326\pi\) | |||||||
\(948\) | −7.94586e14 | − | 3.67534e14i | −1.03777 | − | 0.480016i | ||||
\(949\) | 5.20618e14 | 0.676376 | ||||||||
\(950\) | 2.27723e14 | + | 9.15702e14i | 0.294299 | + | 1.18341i | ||||
\(951\) | 6.46535e14i | 0.831169i | ||||||||
\(952\) | −2.54344e13 | − | 1.86503e14i | −0.0325265 | − | 0.238507i | ||||
\(953\) | − | 8.93473e14i | − | 1.13662i | −0.822813 | − | 0.568312i | \(-0.807597\pi\) | ||
0.822813 | − | 0.568312i | \(-0.192403\pi\) | |||||||
\(954\) | 3.47364e14 | − | 2.22051e14i | 0.439585 | − | 0.281003i | ||||
\(955\) | −3.24047e14 | − | 4.51152e14i | −0.407936 | − | 0.567945i | ||||
\(956\) | −3.29696e14 | − | 1.52500e14i | −0.412881 | − | 0.190977i | ||||
\(957\) | − | 3.39769e14i | − | 0.423277i | ||||||
\(958\) | −3.47643e14 | + | 2.22229e14i | −0.430830 | + | 0.275406i | ||||
\(959\) | 5.32494e14i | 0.656480i | ||||||||
\(960\) | 3.07767e14 | − | 3.83059e14i | 0.377456 | − | 0.469797i | ||||
\(961\) | −4.94679e14 | −0.603541 | ||||||||
\(962\) | 3.56500e14 | + | 5.57687e14i | 0.432697 | + | 0.676886i | ||||
\(963\) | −3.07735e13 | −0.0371574 | ||||||||
\(964\) | −2.34724e14 | + | 5.07458e14i | −0.281950 | + | 0.609558i | ||||
\(965\) | 8.68816e14 | + | 1.20960e15i | 1.03822 | + | 1.44546i | ||||
\(966\) | 1.60178e14 | + | 2.50574e14i | 0.190422 | + | 0.297886i | ||||
\(967\) | −8.32138e14 | −0.984154 | −0.492077 | − | 0.870552i | \(-0.663762\pi\) | ||||
−0.492077 | + | 0.870552i | \(0.663762\pi\) | |||||||
\(968\) | 5.88463e14 | − | 8.02517e13i | 0.692376 | − | 0.0944230i | ||||
\(969\) | 1.81695e14 | 0.212679 | ||||||||
\(970\) | 2.38468e14 | − | 5.98544e14i | 0.277697 | − | 0.697007i | ||||
\(971\) | 7.63526e14i | 0.884561i | 0.896877 | + | 0.442281i | \(0.145830\pi\) | ||||
−0.896877 | + | 0.442281i | \(0.854170\pi\) | |||||||
\(972\) | 3.68591e14 | − | 7.96872e14i | 0.424829 | − | 0.918454i | ||||
\(973\) | − | 2.65178e14i | − | 0.304069i | ||||||
\(974\) | 2.75199e12 | + | 4.30506e12i | 0.00313944 | + | 0.00491116i | ||||
\(975\) | 3.38114e14 | + | 1.13941e14i | 0.383743 | + | 0.129317i | ||||
\(976\) | 6.40428e14 | + | 7.53714e14i | 0.723138 | + | 0.851055i | ||||
\(977\) | − | 1.34095e14i | − | 0.150640i | −0.997159 | − | 0.0753201i | \(-0.976002\pi\) | ||
0.997159 | − | 0.0753201i | \(-0.0239979\pi\) | |||||||
\(978\) | 3.64939e14 | + | 5.70889e14i | 0.407874 | + | 0.638054i | ||||
\(979\) | − | 3.51173e14i | − | 0.390488i | ||||||
\(980\) | 5.25068e13 | + | 2.73548e14i | 0.0580878 | + | 0.302624i | ||||
\(981\) | 1.11706e14 | 0.122951 | ||||||||
\(982\) | 1.12829e14 | − | 7.21257e13i | 0.123556 | − | 0.0789829i | ||||
\(983\) | 8.02271e13 | 0.0874084 | 0.0437042 | − | 0.999045i | \(-0.486084\pi\) | ||||
0.0437042 | + | 0.999045i | \(0.486084\pi\) | |||||||
\(984\) | −5.10100e14 | + | 6.95650e13i | −0.552943 | + | 0.0754076i | ||||
\(985\) | 5.67854e14 | + | 7.90590e14i | 0.612428 | + | 0.852649i | ||||
\(986\) | −2.90808e14 | + | 1.85898e14i | −0.312048 | + | 0.199476i | ||||
\(987\) | −8.89861e14 | −0.950028 | ||||||||
\(988\) | 3.23849e14 | − | 7.00143e14i | 0.344000 | − | 0.743707i | ||||
\(989\) | −7.18783e12 | −0.00759655 | ||||||||
\(990\) | 1.23019e14 | − | 3.08772e14i | 0.129359 | − | 0.324685i | ||||
\(991\) | 3.38502e14i | 0.354155i | 0.984197 | + | 0.177077i | \(0.0566643\pi\) | ||||
−0.984197 | + | 0.177077i | \(0.943336\pi\) | |||||||
\(992\) | −1.16295e15 | − | 3.56816e14i | −1.21061 | − | 0.371437i | ||||
\(993\) | − | 1.48627e14i | − | 0.153940i | ||||||
\(994\) | 1.09812e15 | − | 7.01970e14i | 1.13167 | − | 0.723414i | ||||
\(995\) | 1.51771e14 | + | 2.11302e14i | 0.155623 | + | 0.216665i | ||||
\(996\) | 6.29124e13 | − | 1.36013e14i | 0.0641859 | − | 0.138766i | ||||
\(997\) | 1.63118e15i | 1.65587i | 0.560825 | + | 0.827934i | \(0.310484\pi\) | ||||
−0.560825 | + | 0.827934i | \(0.689516\pi\) | |||||||
\(998\) | −1.53340e15 | + | 9.80220e14i | −1.54883 | + | 0.990082i | ||||
\(999\) | − | 1.17346e15i | − | 1.17935i |
(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 | 20.11.d.d.19.9 | ✓ | 24 | |
4.3 | odd | 2 | inner | 20.11.d.d.19.15 | yes | 24 | |
5.2 | odd | 4 | 100.11.b.h.51.21 | 24 | |||
5.3 | odd | 4 | 100.11.b.h.51.4 | 24 | |||
5.4 | even | 2 | inner | 20.11.d.d.19.16 | yes | 24 | |
20.3 | even | 4 | 100.11.b.h.51.3 | 24 | |||
20.7 | even | 4 | 100.11.b.h.51.22 | 24 | |||
20.19 | odd | 2 | inner | 20.11.d.d.19.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.11.d.d.19.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
20.11.d.d.19.10 | yes | 24 | 20.19 | odd | 2 | inner | |
20.11.d.d.19.15 | yes | 24 | 4.3 | odd | 2 | inner | |
20.11.d.d.19.16 | yes | 24 | 5.4 | even | 2 | inner | |
100.11.b.h.51.3 | 24 | 20.3 | even | 4 | |||
100.11.b.h.51.4 | 24 | 5.3 | odd | 4 | |||
100.11.b.h.51.21 | 24 | 5.2 | odd | 4 | |||
100.11.b.h.51.22 | 24 | 20.7 | even | 4 |