Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,10,Mod(5,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.b (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: | \(4.12028668931\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 59x^{6} - 313x^{5} - 315x^{4} - 92091x^{3} + 1261649x^{2} - 16074123x + 251007534 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{28}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.8 | ||
Root | \(-10.4846 - 6.16784i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.10.b.a.5.7 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 18.9692 | + | 12.3357i | 0.838329 | + | 0.545165i | ||||
\(3\) | 67.6316i | 0.482063i | 0.970517 | + | 0.241032i | \(0.0774858\pi\) | ||||
−0.970517 | + | 0.241032i | \(0.922514\pi\) | |||||||
\(4\) | 207.662 | + | 467.996i | 0.405591 | + | 0.914055i | ||||
\(5\) | 506.862i | 0.362681i | 0.983420 | + | 0.181340i | \(0.0580436\pi\) | ||||
−0.983420 | + | 0.181340i | \(0.941956\pi\) | |||||||
\(6\) | −834.282 | + | 1282.92i | −0.262804 | + | 0.404128i | ||||
\(7\) | 300.249 | 0.0472650 | 0.0236325 | − | 0.999721i | \(-0.492477\pi\) | ||||
0.0236325 | + | 0.999721i | \(0.492477\pi\) | |||||||
\(8\) | −1833.85 | + | 11439.2i | −0.158292 | + | 0.987392i | ||||
\(9\) | 15109.0 | 0.767615 | ||||||||
\(10\) | −6252.48 | + | 9614.77i | −0.197721 | + | 0.304046i | ||||
\(11\) | − | 55228.5i | − | 1.13736i | −0.822560 | − | 0.568678i | \(-0.807455\pi\) | ||
0.822560 | − | 0.568678i | \(-0.192545\pi\) | |||||||
\(12\) | −31651.3 | + | 14044.6i | −0.440632 | + | 0.195521i | ||||
\(13\) | − | 160140.i | − | 1.55508i | −0.628831 | − | 0.777542i | \(-0.716466\pi\) | ||
0.628831 | − | 0.777542i | \(-0.283534\pi\) | |||||||
\(14\) | 5695.48 | + | 3703.77i | 0.0396236 | + | 0.0257672i | ||||
\(15\) | −34279.9 | −0.174835 | ||||||||
\(16\) | −175897. | + | 194370.i | −0.670992 | + | 0.741464i | ||||
\(17\) | 305284. | 0.886510 | 0.443255 | − | 0.896396i | \(-0.353824\pi\) | ||||
0.443255 | + | 0.896396i | \(0.353824\pi\) | |||||||
\(18\) | 286605. | + | 186379.i | 0.643514 | + | 0.418477i | ||||
\(19\) | 634238.i | 1.11651i | 0.829671 | + | 0.558253i | \(0.188528\pi\) | ||||
−0.829671 | + | 0.558253i | \(0.811472\pi\) | |||||||
\(20\) | −237209. | + | 105256.i | −0.331510 | + | 0.147100i | ||||
\(21\) | 20306.3i | 0.0227847i | ||||||||
\(22\) | 681281. | − | 1.04764e6i | 0.620046 | − | 0.953479i | ||||
\(23\) | −2.25093e6 | −1.67721 | −0.838604 | − | 0.544741i | \(-0.816628\pi\) | ||||
−0.838604 | + | 0.544741i | \(0.816628\pi\) | |||||||
\(24\) | −773650. | − | 124026.i | −0.475986 | − | 0.0763068i | ||||
\(25\) | 1.69622e6 | 0.868463 | ||||||||
\(26\) | 1.97543e6 | − | 3.03773e6i | 0.847777 | − | 1.30367i | ||||
\(27\) | 2.35304e6i | 0.852103i | ||||||||
\(28\) | 62350.4 | + | 140515.i | 0.0191703 | + | 0.0432028i | ||||
\(29\) | − | 1.62728e6i | − | 0.427238i | −0.976917 | − | 0.213619i | \(-0.931475\pi\) | ||
0.976917 | − | 0.213619i | \(-0.0685252\pi\) | |||||||
\(30\) | −650263. | − | 422865.i | −0.146569 | − | 0.0953140i | ||||
\(31\) | −2.76752e6 | −0.538224 | −0.269112 | − | 0.963109i | \(-0.586730\pi\) | ||||
−0.269112 | + | 0.963109i | \(0.586730\pi\) | |||||||
\(32\) | −5.73431e6 | + | 1.51725e6i | −0.966732 | + | 0.255790i | ||||
\(33\) | 3.73520e6 | 0.548278 | ||||||||
\(34\) | 5.79099e6 | + | 3.76588e6i | 0.743187 | + | 0.483294i | ||||
\(35\) | 152185.i | 0.0171421i | ||||||||
\(36\) | 3.13756e6 | + | 7.07093e6i | 0.311337 | + | 0.701642i | ||||
\(37\) | − | 6.07614e6i | − | 0.532991i | −0.963836 | − | 0.266496i | \(-0.914134\pi\) | ||
0.963836 | − | 0.266496i | \(-0.0858658\pi\) | |||||||
\(38\) | −7.82375e6 | + | 1.20310e7i | −0.608680 | + | 0.935999i | ||||
\(39\) | 1.08305e7 | 0.749649 | ||||||||
\(40\) | −5.79808e6 | − | 929508.i | −0.358108 | − | 0.0574094i | ||||
\(41\) | −6.28260e6 | −0.347226 | −0.173613 | − | 0.984814i | \(-0.555544\pi\) | ||||
−0.173613 | + | 0.984814i | \(0.555544\pi\) | |||||||
\(42\) | −250492. | + | 385195.i | −0.0124214 | + | 0.0191011i | ||||
\(43\) | − | 2.76782e7i | − | 1.23461i | −0.786723 | − | 0.617306i | \(-0.788224\pi\) | ||
0.786723 | − | 0.617306i | \(-0.211776\pi\) | |||||||
\(44\) | 2.58467e7 | − | 1.14689e7i | 1.03961 | − | 0.461301i | ||||
\(45\) | 7.65816e6i | 0.278399i | ||||||||
\(46\) | −4.26984e7 | − | 2.77667e7i | −1.40605 | − | 0.914355i | ||||
\(47\) | 1.38355e7 | 0.413574 | 0.206787 | − | 0.978386i | \(-0.433699\pi\) | ||||
0.206787 | + | 0.978386i | \(0.433699\pi\) | |||||||
\(48\) | −1.31456e7 | − | 1.18962e7i | −0.357433 | − | 0.323461i | ||||
\(49\) | −4.02635e7 | −0.997766 | ||||||||
\(50\) | 3.21759e7 | + | 2.09240e7i | 0.728057 | + | 0.473455i | ||||
\(51\) | 2.06468e7i | 0.427354i | ||||||||
\(52\) | 7.49448e7 | − | 3.32550e7i | 1.42143 | − | 0.630728i | ||||
\(53\) | 1.04915e8i | 1.82641i | 0.407503 | + | 0.913204i | \(0.366400\pi\) | ||||
−0.407503 | + | 0.913204i | \(0.633600\pi\) | |||||||
\(54\) | −2.90263e7 | + | 4.46353e7i | −0.464536 | + | 0.714342i | ||||
\(55\) | 2.79932e7 | 0.412497 | ||||||||
\(56\) | −550611. | + | 3.43460e6i | −0.00748167 | + | 0.0466691i | ||||
\(57\) | −4.28946e7 | −0.538227 | ||||||||
\(58\) | 2.00735e7 | − | 3.08682e7i | 0.232915 | − | 0.358166i | ||||
\(59\) | 3.86522e7i | 0.415279i | 0.978205 | + | 0.207640i | \(0.0665782\pi\) | ||||
−0.978205 | + | 0.207640i | \(0.933422\pi\) | |||||||
\(60\) | −7.11865e6 | − | 1.60429e7i | −0.0709115 | − | 0.159809i | ||||
\(61\) | − | 1.10399e8i | − | 1.02089i | −0.859909 | − | 0.510447i | \(-0.829480\pi\) | ||
0.859909 | − | 0.510447i | \(-0.170520\pi\) | |||||||
\(62\) | −5.24977e7 | − | 3.41392e7i | −0.451209 | − | 0.293421i | ||||
\(63\) | 4.53644e6 | 0.0362813 | ||||||||
\(64\) | −1.27492e8 | − | 4.19555e7i | −0.949887 | − | 0.312593i | ||||
\(65\) | 8.11687e7 | 0.563999 | ||||||||
\(66\) | 7.08538e7 | + | 4.60762e7i | 0.459637 | + | 0.298902i | ||||
\(67\) | − | 1.57010e8i | − | 0.951901i | −0.879472 | − | 0.475950i | \(-0.842104\pi\) | ||
0.879472 | − | 0.475950i | \(-0.157896\pi\) | |||||||
\(68\) | 6.33960e7 | + | 1.42872e8i | 0.359560 | + | 0.810318i | ||||
\(69\) | − | 1.52234e8i | − | 0.808521i | ||||||
\(70\) | −1.87730e6 | + | 2.88682e6i | −0.00934528 | + | 0.0143707i | ||||
\(71\) | −1.55007e8 | −0.723919 | −0.361960 | − | 0.932194i | \(-0.617892\pi\) | ||||
−0.361960 | + | 0.932194i | \(0.617892\pi\) | |||||||
\(72\) | −2.77076e7 | + | 1.72834e8i | −0.121507 | + | 0.757937i | ||||
\(73\) | 2.67232e8 | 1.10138 | 0.550689 | − | 0.834711i | \(-0.314365\pi\) | ||||
0.550689 | + | 0.834711i | \(0.314365\pi\) | |||||||
\(74\) | 7.49533e7 | − | 1.15260e8i | 0.290568 | − | 0.446822i | ||||
\(75\) | 1.14718e8i | 0.418654i | ||||||||
\(76\) | −2.96821e8 | + | 1.31707e8i | −1.02055 | + | 0.452845i | ||||
\(77\) | − | 1.65823e7i | − | 0.0537572i | ||||||
\(78\) | 2.05446e8 | + | 1.33602e8i | 0.628453 | + | 0.408682i | ||||
\(79\) | −2.31067e8 | −0.667447 | −0.333723 | − | 0.942671i | \(-0.608305\pi\) | ||||
−0.333723 | + | 0.942671i | \(0.608305\pi\) | |||||||
\(80\) | −9.85190e7 | − | 8.91553e7i | −0.268915 | − | 0.243356i | ||||
\(81\) | 1.38250e8 | 0.356847 | ||||||||
\(82\) | −1.19176e8 | − | 7.75001e7i | −0.291090 | − | 0.189295i | ||||
\(83\) | 5.10130e8i | 1.17986i | 0.807455 | + | 0.589929i | \(0.200844\pi\) | ||||
−0.807455 | + | 0.589929i | \(0.799156\pi\) | |||||||
\(84\) | −9.50327e6 | + | 4.21686e6i | −0.0208265 | + | 0.00924128i | ||||
\(85\) | 1.54737e8i | 0.321520i | ||||||||
\(86\) | 3.41430e8 | − | 5.25035e8i | 0.673067 | − | 1.03501i | ||||
\(87\) | 1.10055e8 | 0.205956 | ||||||||
\(88\) | 6.31769e8 | + | 1.01281e8i | 1.12302 | + | 0.180034i | ||||
\(89\) | −3.91714e8 | −0.661781 | −0.330891 | − | 0.943669i | \(-0.607349\pi\) | ||||
−0.330891 | + | 0.943669i | \(0.607349\pi\) | |||||||
\(90\) | −9.44685e7 | + | 1.45269e8i | −0.151773 | + | 0.233390i | ||||
\(91\) | − | 4.80817e7i | − | 0.0735011i | ||||||
\(92\) | −4.67434e8 | − | 1.05343e9i | −0.680260 | − | 1.53306i | ||||
\(93\) | − | 1.87172e8i | − | 0.259458i | ||||||
\(94\) | 2.62448e8 | + | 1.70670e8i | 0.346711 | + | 0.225466i | ||||
\(95\) | −3.21471e8 | −0.404935 | ||||||||
\(96\) | −1.02614e8 | − | 3.87821e8i | −0.123307 | − | 0.466026i | ||||
\(97\) | −4.08584e8 | −0.468607 | −0.234303 | − | 0.972164i | \(-0.575281\pi\) | ||||
−0.234303 | + | 0.972164i | \(0.575281\pi\) | |||||||
\(98\) | −7.63766e8 | − | 4.96677e8i | −0.836456 | − | 0.543947i | ||||
\(99\) | − | 8.34446e8i | − | 0.873051i | ||||||
\(100\) | 3.52240e8 | + | 7.93822e8i | 0.352240 | + | 0.793822i | ||||
\(101\) | 9.53192e8i | 0.911452i | 0.890120 | + | 0.455726i | \(0.150620\pi\) | ||||
−0.890120 | + | 0.455726i | \(0.849380\pi\) | |||||||
\(102\) | −2.54693e8 | + | 3.91654e8i | −0.232978 | + | 0.358263i | ||||
\(103\) | 1.76824e9 | 1.54801 | 0.774005 | − | 0.633180i | \(-0.218251\pi\) | ||||
0.774005 | + | 0.633180i | \(0.218251\pi\) | |||||||
\(104\) | 1.83187e9 | + | 2.93672e8i | 1.53548 | + | 0.246157i | ||||
\(105\) | −1.02925e7 | −0.00826359 | ||||||||
\(106\) | −1.29420e9 | + | 1.99016e9i | −0.995693 | + | 1.53113i | ||||
\(107\) | − | 4.21493e8i | − | 0.310859i | −0.987847 | − | 0.155430i | \(-0.950324\pi\) | ||
0.987847 | − | 0.155430i | \(-0.0496762\pi\) | |||||||
\(108\) | −1.10121e9 | + | 4.88638e8i | −0.778868 | + | 0.345605i | ||||
\(109\) | 3.63239e8i | 0.246475i | 0.992377 | + | 0.123238i | \(0.0393278\pi\) | ||||
−0.992377 | + | 0.123238i | \(0.960672\pi\) | |||||||
\(110\) | 5.31010e8 | + | 3.45315e8i | 0.345808 | + | 0.224879i | ||||
\(111\) | 4.10939e8 | 0.256936 | ||||||||
\(112\) | −5.28127e7 | + | 5.83594e7i | −0.0317145 | + | 0.0350453i | ||||
\(113\) | −6.97516e8 | −0.402440 | −0.201220 | − | 0.979546i | \(-0.564491\pi\) | ||||
−0.201220 | + | 0.979546i | \(0.564491\pi\) | |||||||
\(114\) | −8.13676e8 | − | 5.29133e8i | −0.451211 | − | 0.293422i | ||||
\(115\) | − | 1.14091e9i | − | 0.608291i | ||||||
\(116\) | 7.61559e8 | − | 3.37924e8i | 0.390519 | − | 0.173284i | ||||
\(117\) | − | 2.41954e9i | − | 1.19371i | ||||||
\(118\) | −4.76801e8 | + | 7.33202e8i | −0.226396 | + | 0.348141i | ||||
\(119\) | 9.16610e7 | 0.0419009 | ||||||||
\(120\) | 6.28642e7 | − | 3.92134e8i | 0.0276750 | − | 0.172631i | ||||
\(121\) | −6.92244e8 | −0.293579 | ||||||||
\(122\) | 1.36184e9 | − | 2.09418e9i | 0.556555 | − | 0.855845i | ||||
\(123\) | − | 4.24903e8i | − | 0.167385i | ||||||
\(124\) | −5.74710e8 | − | 1.29519e9i | −0.218299 | − | 0.491967i | ||||
\(125\) | 1.84971e9i | 0.677656i | ||||||||
\(126\) | 8.60528e7 | + | 5.59601e7i | 0.0304157 | + | 0.0197793i | ||||
\(127\) | −1.71741e9 | −0.585809 | −0.292905 | − | 0.956142i | \(-0.594622\pi\) | ||||
−0.292905 | + | 0.956142i | \(0.594622\pi\) | |||||||
\(128\) | −1.90087e9 | − | 2.36856e9i | −0.625904 | − | 0.779900i | ||||
\(129\) | 1.87193e9 | 0.595161 | ||||||||
\(130\) | 1.53971e9 | + | 1.00127e9i | 0.472817 | + | 0.307473i | ||||
\(131\) | 6.19742e9i | 1.83861i | 0.393544 | + | 0.919306i | \(0.371249\pi\) | ||||
−0.393544 | + | 0.919306i | \(0.628751\pi\) | |||||||
\(132\) | 7.75660e8 | + | 1.74806e9i | 0.222376 | + | 0.501156i | ||||
\(133\) | 1.90429e8i | 0.0527717i | ||||||||
\(134\) | 1.93683e9 | − | 2.97836e9i | 0.518943 | − | 0.798006i | ||||
\(135\) | −1.19266e9 | −0.309041 | ||||||||
\(136\) | −5.59844e8 | + | 3.49219e9i | −0.140327 | + | 0.875333i | ||||
\(137\) | 2.20927e9 | 0.535805 | 0.267903 | − | 0.963446i | \(-0.413669\pi\) | ||||
0.267903 | + | 0.963446i | \(0.413669\pi\) | |||||||
\(138\) | 1.87791e9 | − | 2.88776e9i | 0.440777 | − | 0.677807i | ||||
\(139\) | 1.31612e9i | 0.299039i | 0.988759 | + | 0.149520i | \(0.0477727\pi\) | ||||
−0.988759 | + | 0.149520i | \(0.952227\pi\) | |||||||
\(140\) | −7.12218e7 | + | 3.16030e7i | −0.0156688 | + | 0.00695268i | ||||
\(141\) | 9.35715e8i | 0.199369i | ||||||||
\(142\) | −2.94037e9 | − | 1.91212e9i | −0.606882 | − | 0.394655i | ||||
\(143\) | −8.84428e9 | −1.76868 | ||||||||
\(144\) | −2.65761e9 | + | 2.93674e9i | −0.515064 | + | 0.569159i | ||||
\(145\) | 8.24804e8 | 0.154951 | ||||||||
\(146\) | 5.06919e9 | + | 3.29649e9i | 0.923317 | + | 0.600432i | ||||
\(147\) | − | 2.72308e9i | − | 0.480987i | ||||||
\(148\) | 2.84361e9 | − | 1.26179e9i | 0.487183 | − | 0.216176i | ||||
\(149\) | − | 4.24563e9i | − | 0.705673i | −0.935685 | − | 0.352837i | \(-0.885217\pi\) | ||
0.935685 | − | 0.352837i | \(-0.114783\pi\) | |||||||
\(150\) | −1.41512e9 | + | 2.17611e9i | −0.228235 | + | 0.350970i | ||||
\(151\) | 1.04571e10 | 1.63687 | 0.818434 | − | 0.574600i | \(-0.194843\pi\) | ||||
0.818434 | + | 0.574600i | \(0.194843\pi\) | |||||||
\(152\) | −7.25516e9 | − | 1.16310e9i | −1.10243 | − | 0.176734i | ||||
\(153\) | 4.61252e9 | 0.680498 | ||||||||
\(154\) | 2.04554e8 | − | 3.14553e8i | 0.0293065 | − | 0.0450662i | ||||
\(155\) | − | 1.40275e9i | − | 0.195204i | ||||||
\(156\) | 2.24909e9 | + | 5.06864e9i | 0.304051 | + | 0.685221i | ||||
\(157\) | − | 7.15069e9i | − | 0.939290i | −0.882855 | − | 0.469645i | \(-0.844382\pi\) | ||
0.882855 | − | 0.469645i | \(-0.155618\pi\) | |||||||
\(158\) | −4.38317e9 | − | 2.85037e9i | −0.559540 | − | 0.363869i | ||||
\(159\) | −7.09560e9 | −0.880445 | ||||||||
\(160\) | −7.69038e8 | − | 2.90650e9i | −0.0927700 | − | 0.350615i | ||||
\(161\) | −6.75839e8 | −0.0792733 | ||||||||
\(162\) | 2.62249e9 | + | 1.70541e9i | 0.299155 | + | 0.194541i | ||||
\(163\) | − | 1.05206e10i | − | 1.16734i | −0.811990 | − | 0.583671i | \(-0.801616\pi\) | ||
0.811990 | − | 0.583671i | \(-0.198384\pi\) | |||||||
\(164\) | −1.30466e9 | − | 2.94023e9i | −0.140832 | − | 0.317384i | ||||
\(165\) | 1.89323e9i | 0.198850i | ||||||||
\(166\) | −6.29279e9 | + | 9.67677e9i | −0.643216 | + | 0.989108i | ||||
\(167\) | 1.39991e10 | 1.39276 | 0.696382 | − | 0.717671i | \(-0.254792\pi\) | ||||
0.696382 | + | 0.717671i | \(0.254792\pi\) | |||||||
\(168\) | −2.32287e8 | − | 3.72387e7i | −0.0224975 | − | 0.00360664i | ||||
\(169\) | −1.50402e10 | −1.41829 | ||||||||
\(170\) | −1.90878e9 | + | 2.93523e9i | −0.175281 | + | 0.269540i | ||||
\(171\) | 9.58268e9i | 0.857047i | ||||||||
\(172\) | 1.29533e10 | − | 5.74773e9i | 1.12850 | − | 0.500747i | ||||
\(173\) | 8.80028e9i | 0.746946i | 0.927641 | + | 0.373473i | \(0.121833\pi\) | ||||
−0.927641 | + | 0.373473i | \(0.878167\pi\) | |||||||
\(174\) | 2.08766e9 | + | 1.35761e9i | 0.172659 | + | 0.112280i | ||||
\(175\) | 5.09286e8 | 0.0410479 | ||||||||
\(176\) | 1.07348e10 | + | 9.71451e9i | 0.843309 | + | 0.763157i | ||||
\(177\) | −2.61411e9 | −0.200191 | ||||||||
\(178\) | −7.43052e9 | − | 4.83206e9i | −0.554790 | − | 0.360780i | ||||
\(179\) | 4.93292e9i | 0.359141i | 0.983745 | + | 0.179571i | \(0.0574708\pi\) | ||||
−0.983745 | + | 0.179571i | \(0.942529\pi\) | |||||||
\(180\) | −3.58399e9 | + | 1.59031e9i | −0.254472 | + | 0.112916i | ||||
\(181\) | 2.32627e10i | 1.61104i | 0.592569 | + | 0.805520i | \(0.298114\pi\) | ||||
−0.592569 | + | 0.805520i | \(0.701886\pi\) | |||||||
\(182\) | 5.93120e8 | − | 9.12073e8i | 0.0400702 | − | 0.0616181i | ||||
\(183\) | 7.46646e9 | 0.492136 | ||||||||
\(184\) | 4.12787e9 | − | 2.57488e10i | 0.265489 | − | 1.65606i | ||||
\(185\) | 3.07976e9 | 0.193306 | ||||||||
\(186\) | 2.30889e9 | − | 3.55051e9i | 0.141448 | − | 0.217511i | ||||
\(187\) | − | 1.68604e10i | − | 1.00828i | ||||||
\(188\) | 2.87311e9 | + | 6.47494e9i | 0.167742 | + | 0.378029i | ||||
\(189\) | 7.06496e8i | 0.0402746i | ||||||||
\(190\) | −6.09806e9 | − | 3.96556e9i | −0.339469 | − | 0.220756i | ||||
\(191\) | −2.01231e10 | −1.09407 | −0.547034 | − | 0.837111i | \(-0.684243\pi\) | ||||
−0.547034 | + | 0.837111i | \(0.684243\pi\) | |||||||
\(192\) | 2.83752e9 | − | 8.62247e9i | 0.150689 | − | 0.457906i | ||||
\(193\) | −1.91524e10 | −0.993606 | −0.496803 | − | 0.867863i | \(-0.665493\pi\) | ||||
−0.496803 | + | 0.867863i | \(0.665493\pi\) | |||||||
\(194\) | −7.75052e9 | − | 5.04016e9i | −0.392847 | − | 0.255468i | ||||
\(195\) | 5.48957e9i | 0.271883i | ||||||||
\(196\) | −8.36121e9 | − | 1.88431e10i | −0.404685 | − | 0.912013i | ||||
\(197\) | − | 2.35449e10i | − | 1.11378i | −0.830586 | − | 0.556890i | \(-0.811995\pi\) | ||
0.830586 | − | 0.556890i | \(-0.188005\pi\) | |||||||
\(198\) | 1.02934e10 | − | 1.58288e10i | 0.475957 | − | 0.731904i | ||||
\(199\) | 2.87445e10 | 1.29932 | 0.649661 | − | 0.760224i | \(-0.274911\pi\) | ||||
0.649661 | + | 0.760224i | \(0.274911\pi\) | |||||||
\(200\) | −3.11061e9 | + | 1.94033e10i | −0.137471 | + | 0.857513i | ||||
\(201\) | 1.06189e10 | 0.458877 | ||||||||
\(202\) | −1.17583e10 | + | 1.80813e10i | −0.496892 | + | 0.764097i | ||||
\(203\) | − | 4.88587e8i | − | 0.0201934i | ||||||
\(204\) | −9.66264e9 | + | 4.28757e9i | −0.390625 | + | 0.173331i | ||||
\(205\) | − | 3.18441e9i | − | 0.125932i | ||||||
\(206\) | 3.35421e10 | + | 2.18124e10i | 1.29774 | + | 0.843920i | ||||
\(207\) | −3.40092e10 | −1.28745 | ||||||||
\(208\) | 3.11264e10 | + | 2.81680e10i | 1.15304 | + | 1.04345i | ||||
\(209\) | 3.50280e10 | 1.26987 | ||||||||
\(210\) | −1.95240e8 | − | 1.26965e8i | −0.00692760 | − | 0.00450502i | ||||
\(211\) | 1.31866e10i | 0.457996i | 0.973427 | + | 0.228998i | \(0.0735449\pi\) | ||||
−0.973427 | + | 0.228998i | \(0.926455\pi\) | |||||||
\(212\) | −4.91000e10 | + | 2.17870e10i | −1.66944 | + | 0.740774i | ||||
\(213\) | − | 1.04834e10i | − | 0.348975i | ||||||
\(214\) | 5.19940e9 | − | 7.99540e9i | 0.169469 | − | 0.260602i | ||||
\(215\) | 1.40290e10 | 0.447770 | ||||||||
\(216\) | −2.69168e10 | − | 4.31512e9i | −0.841360 | − | 0.134881i | ||||
\(217\) | −8.30944e8 | −0.0254392 | ||||||||
\(218\) | −4.48080e9 | + | 6.89036e9i | −0.134370 | + | 0.206627i | ||||
\(219\) | 1.80734e10i | 0.530934i | ||||||||
\(220\) | 5.81315e9 | + | 1.31007e10i | 0.167305 | + | 0.377045i | ||||
\(221\) | − | 4.88880e10i | − | 1.37860i | ||||||
\(222\) | 7.79520e9 | + | 5.06921e9i | 0.215397 | + | 0.140072i | ||||
\(223\) | −3.08477e10 | −0.835315 | −0.417658 | − | 0.908604i | \(-0.637149\pi\) | ||||
−0.417658 | + | 0.908604i | \(0.637149\pi\) | |||||||
\(224\) | −1.72172e9 | + | 4.55553e8i | −0.0456926 | + | 0.0120899i | ||||
\(225\) | 2.56281e10 | 0.666645 | ||||||||
\(226\) | −1.32313e10 | − | 8.60432e9i | −0.337377 | − | 0.219396i | ||||
\(227\) | − | 3.48742e10i | − | 0.871742i | −0.900009 | − | 0.435871i | \(-0.856440\pi\) | ||
0.900009 | − | 0.435871i | \(-0.143560\pi\) | |||||||
\(228\) | −8.90759e9 | − | 2.00745e10i | −0.218300 | − | 0.491969i | ||||
\(229\) | 5.73355e10i | 1.37773i | 0.724890 | + | 0.688864i | \(0.241890\pi\) | ||||
−0.724890 | + | 0.688864i | \(0.758110\pi\) | |||||||
\(230\) | 1.40739e10 | − | 2.16422e10i | 0.331619 | − | 0.509948i | ||||
\(231\) | 1.12149e9 | 0.0259144 | ||||||||
\(232\) | 1.86147e10 | + | 2.98418e9i | 0.421852 | + | 0.0676284i | ||||
\(233\) | 2.77681e10 | 0.617227 | 0.308613 | − | 0.951188i | \(-0.400135\pi\) | ||||
0.308613 | + | 0.951188i | \(0.400135\pi\) | |||||||
\(234\) | 2.98467e10 | − | 4.58969e10i | 0.650766 | − | 1.00072i | ||||
\(235\) | 7.01267e9i | 0.149995i | ||||||||
\(236\) | −1.80891e10 | + | 8.02662e9i | −0.379588 | + | 0.168433i | ||||
\(237\) | − | 1.56275e10i | − | 0.321752i | ||||||
\(238\) | 1.73874e9 | + | 1.13070e9i | 0.0351267 | + | 0.0228429i | ||||
\(239\) | −7.05276e10 | −1.39820 | −0.699099 | − | 0.715025i | \(-0.746415\pi\) | ||||
−0.699099 | + | 0.715025i | \(0.746415\pi\) | |||||||
\(240\) | 6.02972e9 | − | 6.66300e9i | 0.117313 | − | 0.129634i | ||||
\(241\) | −6.27074e10 | −1.19741 | −0.598704 | − | 0.800970i | \(-0.704318\pi\) | ||||
−0.598704 | + | 0.800970i | \(0.704318\pi\) | |||||||
\(242\) | −1.31313e10 | − | 8.53929e9i | −0.246116 | − | 0.160049i | ||||
\(243\) | 5.56649e10i | 1.02413i | ||||||||
\(244\) | 5.16663e10 | − | 2.29257e10i | 0.933153 | − | 0.414065i | ||||
\(245\) | − | 2.04080e10i | − | 0.361871i | ||||||
\(246\) | 5.24146e9 | − | 8.06007e9i | 0.0912524 | − | 0.140324i | ||||
\(247\) | 1.01567e11 | 1.73626 | ||||||||
\(248\) | 5.07522e9 | − | 3.16582e10i | 0.0851966 | − | 0.531439i | ||||
\(249\) | −3.45009e10 | −0.568766 | ||||||||
\(250\) | −2.28174e10 | + | 3.50876e10i | −0.369434 | + | 0.568098i | ||||
\(251\) | − | 1.85039e10i | − | 0.294260i | −0.989117 | − | 0.147130i | \(-0.952996\pi\) | ||
0.989117 | − | 0.147130i | \(-0.0470036\pi\) | |||||||
\(252\) | 9.42049e8 | + | 2.12304e9i | 0.0147154 | + | 0.0331631i | ||||
\(253\) | 1.24316e11i | 1.90758i | ||||||||
\(254\) | −3.25778e10 | − | 2.11853e10i | −0.491101 | − | 0.319362i | ||||
\(255\) | −1.04651e10 | −0.154993 | ||||||||
\(256\) | −6.84026e9 | − | 6.83782e10i | −0.0995389 | − | 0.995034i | ||||
\(257\) | 5.36058e9 | 0.0766501 | 0.0383250 | − | 0.999265i | \(-0.487798\pi\) | ||||
0.0383250 | + | 0.999265i | \(0.487798\pi\) | |||||||
\(258\) | 3.55090e10 | + | 2.30915e10i | 0.498941 | + | 0.324461i | ||||
\(259\) | − | 1.82435e9i | − | 0.0251918i | ||||||
\(260\) | 1.68557e10 | + | 3.79866e10i | 0.228753 | + | 0.515526i | ||||
\(261\) | − | 2.45864e10i | − | 0.327954i | ||||||
\(262\) | −7.64493e10 | + | 1.17560e11i | −1.00235 | + | 1.54136i | ||||
\(263\) | 5.46057e10 | 0.703780 | 0.351890 | − | 0.936041i | \(-0.385539\pi\) | ||||
0.351890 | + | 0.936041i | \(0.385539\pi\) | |||||||
\(264\) | −6.84979e9 | + | 4.27276e10i | −0.0867880 | + | 0.541365i | ||||
\(265\) | −5.31776e10 | −0.662403 | ||||||||
\(266\) | −2.34907e9 | + | 3.61229e9i | −0.0287693 | + | 0.0442400i | ||||
\(267\) | − | 2.64923e10i | − | 0.319021i | ||||||
\(268\) | 7.34802e10 | − | 3.26052e10i | 0.870090 | − | 0.386082i | ||||
\(269\) | 4.00949e9i | 0.0466878i | 0.999727 | + | 0.0233439i | \(0.00743127\pi\) | ||||
−0.999727 | + | 0.0233439i | \(0.992569\pi\) | |||||||
\(270\) | −2.26239e10 | − | 1.47123e10i | −0.259078 | − | 0.168478i | ||||
\(271\) | 8.23746e10 | 0.927751 | 0.463875 | − | 0.885900i | \(-0.346459\pi\) | ||||
0.463875 | + | 0.885900i | \(0.346459\pi\) | |||||||
\(272\) | −5.36984e10 | + | 5.93381e10i | −0.594841 | + | 0.657315i | ||||
\(273\) | 3.25185e9 | 0.0354322 | ||||||||
\(274\) | 4.19082e10 | + | 2.72529e10i | 0.449181 | + | 0.292102i | ||||
\(275\) | − | 9.36795e10i | − | 0.987751i | ||||||
\(276\) | 7.12450e10 | − | 3.16133e10i | 0.739032 | − | 0.327929i | ||||
\(277\) | − | 9.10228e10i | − | 0.928948i | −0.885587 | − | 0.464474i | \(-0.846244\pi\) | ||
0.885587 | − | 0.464474i | \(-0.153756\pi\) | |||||||
\(278\) | −1.62352e10 | + | 2.49657e10i | −0.163026 | + | 0.250693i | ||||
\(279\) | −4.18144e10 | −0.413149 | ||||||||
\(280\) | −1.74087e9 | − | 2.79084e8i | −0.0169260 | − | 0.00271346i | ||||
\(281\) | −5.50847e8 | −0.00527051 | −0.00263525 | − | 0.999997i | \(-0.500839\pi\) | ||||
−0.00263525 | + | 0.999997i | \(0.500839\pi\) | |||||||
\(282\) | −1.15427e10 | + | 1.77498e10i | −0.108689 | + | 0.167137i | ||||
\(283\) | − | 1.29983e11i | − | 1.20461i | −0.798265 | − | 0.602306i | \(-0.794249\pi\) | ||
0.798265 | − | 0.602306i | \(-0.205751\pi\) | |||||||
\(284\) | −3.21892e10 | − | 7.25429e10i | −0.293615 | − | 0.661702i | ||||
\(285\) | − | 2.17416e10i | − | 0.195205i | ||||||
\(286\) | −1.67769e11 | − | 1.09100e11i | −1.48274 | − | 0.964225i | ||||
\(287\) | −1.88634e9 | −0.0164116 | ||||||||
\(288\) | −8.66395e10 | + | 2.29241e10i | −0.742078 | + | 0.196348i | ||||
\(289\) | −2.53898e10 | −0.214101 | ||||||||
\(290\) | 1.56459e10 | + | 1.01745e10i | 0.129900 | + | 0.0844739i | ||||
\(291\) | − | 2.76332e10i | − | 0.225898i | ||||||
\(292\) | 5.54942e10 | + | 1.25064e11i | 0.446709 | + | 1.00672i | ||||
\(293\) | 4.93910e10i | 0.391510i | 0.980653 | + | 0.195755i | \(0.0627158\pi\) | ||||
−0.980653 | + | 0.195755i | \(0.937284\pi\) | |||||||
\(294\) | 3.35911e10 | − | 5.16548e10i | 0.262217 | − | 0.403225i | ||||
\(295\) | −1.95913e10 | −0.150614 | ||||||||
\(296\) | 6.95060e10 | + | 1.11427e10i | 0.526272 | + | 0.0843682i | ||||
\(297\) | 1.29955e11 | 0.969144 | ||||||||
\(298\) | 5.23727e10 | − | 8.05362e10i | 0.384708 | − | 0.591586i | ||||
\(299\) | 3.60464e11i | 2.60820i | ||||||||
\(300\) | −5.36875e10 | + | 2.38226e10i | −0.382673 | + | 0.169802i | ||||
\(301\) | − | 8.31036e9i | − | 0.0583540i | ||||||
\(302\) | 1.98362e11 | + | 1.28995e11i | 1.37223 | + | 0.892363i | ||||
\(303\) | −6.44659e10 | −0.439378 | ||||||||
\(304\) | −1.23277e11 | − | 1.11560e11i | −0.827850 | − | 0.749167i | ||||
\(305\) | 5.59570e10 | 0.370259 | ||||||||
\(306\) | 8.74959e10 | + | 5.68985e10i | 0.570481 | + | 0.370983i | ||||
\(307\) | 3.94315e10i | 0.253350i | 0.991944 | + | 0.126675i | \(0.0404305\pi\) | ||||
−0.991944 | + | 0.126675i | \(0.959570\pi\) | |||||||
\(308\) | 7.76045e9 | − | 3.44352e9i | 0.0491370 | − | 0.0218034i | ||||
\(309\) | 1.19589e11i | 0.746239i | ||||||||
\(310\) | 1.73039e10 | − | 2.66091e10i | 0.106418 | − | 0.163645i | ||||
\(311\) | −1.46670e11 | −0.889036 | −0.444518 | − | 0.895770i | \(-0.646625\pi\) | ||||
−0.444518 | + | 0.895770i | \(0.646625\pi\) | |||||||
\(312\) | −1.98615e10 | + | 1.23892e11i | −0.118663 | + | 0.740198i | ||||
\(313\) | −4.50074e10 | −0.265054 | −0.132527 | − | 0.991179i | \(-0.542309\pi\) | ||||
−0.132527 | + | 0.991179i | \(0.542309\pi\) | |||||||
\(314\) | 8.82086e10 | − | 1.35643e11i | 0.512068 | − | 0.787434i | ||||
\(315\) | 2.29935e9i | 0.0131585i | ||||||||
\(316\) | −4.79840e10 | − | 1.08139e11i | −0.270710 | − | 0.610083i | ||||
\(317\) | − | 1.18290e10i | − | 0.0657932i | −0.999459 | − | 0.0328966i | \(-0.989527\pi\) | ||
0.999459 | − | 0.0328966i | \(-0.0104732\pi\) | |||||||
\(318\) | −1.34598e11 | − | 8.75290e10i | −0.738102 | − | 0.479987i | ||||
\(319\) | −8.98721e10 | −0.485922 | ||||||||
\(320\) | 2.12656e10 | − | 6.46207e10i | 0.113371 | − | 0.344506i | ||||
\(321\) | 2.85063e10 | 0.149854 | ||||||||
\(322\) | −1.28201e10 | − | 8.33693e9i | −0.0664571 | − | 0.0432170i | ||||
\(323\) | 1.93623e11i | 0.989793i | ||||||||
\(324\) | 2.87093e10 | + | 6.47004e10i | 0.144734 | + | 0.326178i | ||||
\(325\) | − | 2.71632e11i | − | 1.35053i | ||||||
\(326\) | 1.29779e11 | − | 1.99568e11i | 0.636394 | − | 0.978617i | ||||
\(327\) | −2.45665e10 | −0.118817 | ||||||||
\(328\) | 1.15213e10 | − | 7.18678e10i | 0.0549631 | − | 0.342848i | ||||
\(329\) | 4.15408e9 | 0.0195476 | ||||||||
\(330\) | −2.33542e10 | + | 3.59131e10i | −0.108406 | + | 0.166702i | ||||
\(331\) | − | 2.13896e11i | − | 0.979438i | −0.871880 | − | 0.489719i | \(-0.837099\pi\) | ||
0.871880 | − | 0.489719i | \(-0.162901\pi\) | |||||||
\(332\) | −2.38739e11 | + | 1.05935e11i | −1.07845 | + | 0.478539i | ||||
\(333\) | − | 9.18042e10i | − | 0.409132i | ||||||
\(334\) | 2.65553e11 | + | 1.72689e11i | 1.16759 | + | 0.759286i | ||||
\(335\) | 7.95826e10 | 0.345236 | ||||||||
\(336\) | −3.94695e9 | − | 3.57181e9i | −0.0168941 | − | 0.0152884i | ||||
\(337\) | 1.90045e11 | 0.802644 | 0.401322 | − | 0.915937i | \(-0.368551\pi\) | ||||
0.401322 | + | 0.915937i | \(0.368551\pi\) | |||||||
\(338\) | −2.85301e11 | − | 1.85531e11i | −1.18899 | − | 0.773200i | ||||
\(339\) | − | 4.71741e10i | − | 0.194002i | ||||||
\(340\) | −7.24161e10 | + | 3.21330e10i | −0.293887 | + | 0.130406i | ||||
\(341\) | 1.52846e11i | 0.612153i | ||||||||
\(342\) | −1.18209e11 | + | 1.81776e11i | −0.467232 | + | 0.718487i | ||||
\(343\) | −2.42052e10 | −0.0944244 | ||||||||
\(344\) | 3.16616e11 | + | 5.07578e10i | 1.21905 | + | 0.195429i | ||||
\(345\) | 7.71617e10 | 0.293235 | ||||||||
\(346\) | −1.08557e11 | + | 1.66935e11i | −0.407209 | + | 0.626186i | ||||
\(347\) | − | 2.51449e11i | − | 0.931039i | −0.885038 | − | 0.465519i | \(-0.845868\pi\) | ||
0.885038 | − | 0.465519i | \(-0.154132\pi\) | |||||||
\(348\) | 2.28544e10 | + | 5.15055e10i | 0.0835339 | + | 0.188255i | ||||
\(349\) | 2.95592e10i | 0.106654i | 0.998577 | + | 0.0533271i | \(0.0169826\pi\) | ||||
−0.998577 | + | 0.0533271i | \(0.983017\pi\) | |||||||
\(350\) | 9.66077e9 | + | 6.28239e9i | 0.0344116 | + | 0.0223779i | ||||
\(351\) | 3.76815e11 | 1.32509 | ||||||||
\(352\) | 8.37957e10 | + | 3.16698e11i | 0.290924 | + | 1.09952i | ||||
\(353\) | −3.46408e11 | −1.18741 | −0.593706 | − | 0.804682i | \(-0.702336\pi\) | ||||
−0.593706 | + | 0.804682i | \(0.702336\pi\) | |||||||
\(354\) | −4.95877e10 | − | 3.22468e10i | −0.167826 | − | 0.109137i | ||||
\(355\) | − | 7.85674e10i | − | 0.262552i | ||||||
\(356\) | −8.13444e10 | − | 1.83321e11i | −0.268412 | − | 0.604904i | ||||
\(357\) | 6.19918e9i | 0.0201989i | ||||||||
\(358\) | −6.08509e10 | + | 9.35736e10i | −0.195791 | + | 0.301079i | ||||
\(359\) | −2.46772e11 | −0.784100 | −0.392050 | − | 0.919944i | \(-0.628234\pi\) | ||||
−0.392050 | + | 0.919944i | \(0.628234\pi\) | |||||||
\(360\) | −8.76030e10 | − | 1.40439e10i | −0.274889 | − | 0.0440683i | ||||
\(361\) | −7.95703e10 | −0.246586 | ||||||||
\(362\) | −2.86961e11 | + | 4.41275e11i | −0.878282 | + | 1.35058i | ||||
\(363\) | − | 4.68176e10i | − | 0.141524i | ||||||
\(364\) | 2.25021e10 | − | 9.98477e9i | 0.0671840 | − | 0.0298114i | ||||
\(365\) | 1.35450e11i | 0.399449i | ||||||||
\(366\) | 1.41633e11 | + | 9.21038e10i | 0.412572 | + | 0.268295i | ||||
\(367\) | 4.79554e11 | 1.37988 | 0.689938 | − | 0.723868i | \(-0.257638\pi\) | ||||
0.689938 | + | 0.723868i | \(0.257638\pi\) | |||||||
\(368\) | 3.95931e11 | − | 4.37515e11i | 1.12539 | − | 1.24359i | ||||
\(369\) | −9.49236e10 | −0.266536 | ||||||||
\(370\) | 5.84207e10 | + | 3.79910e10i | 0.162054 | + | 0.105383i | ||||
\(371\) | 3.15007e10i | 0.0863252i | ||||||||
\(372\) | 8.75958e10 | − | 3.88686e10i | 0.237159 | − | 0.105234i | ||||
\(373\) | 1.74705e11i | 0.467320i | 0.972318 | + | 0.233660i | \(0.0750703\pi\) | ||||
−0.972318 | + | 0.233660i | \(0.924930\pi\) | |||||||
\(374\) | 2.07984e11 | − | 3.19828e11i | 0.549677 | − | 0.845268i | ||||
\(375\) | −1.25099e11 | −0.326673 | ||||||||
\(376\) | −2.53722e10 | + | 1.58266e11i | −0.0654654 | + | 0.408360i | ||||
\(377\) | −2.60592e11 | −0.664392 | ||||||||
\(378\) | −8.71510e9 | + | 1.34017e10i | −0.0219563 | + | 0.0337634i | ||||
\(379\) | 4.64716e11i | 1.15694i | 0.815704 | + | 0.578470i | \(0.196350\pi\) | ||||
−0.815704 | + | 0.578470i | \(0.803650\pi\) | |||||||
\(380\) | −6.67575e10 | − | 1.50447e11i | −0.164238 | − | 0.370133i | ||||
\(381\) | − | 1.16151e11i | − | 0.282397i | ||||||
\(382\) | −3.81719e11 | − | 2.48232e11i | −0.917189 | − | 0.596447i | ||||
\(383\) | 5.58072e11 | 1.32524 | 0.662622 | − | 0.748954i | \(-0.269444\pi\) | ||||
0.662622 | + | 0.748954i | \(0.269444\pi\) | |||||||
\(384\) | 1.60189e11 | − | 1.28559e11i | 0.375962 | − | 0.301725i | ||||
\(385\) | 8.40493e9 | 0.0194967 | ||||||||
\(386\) | −3.63305e11 | − | 2.36257e11i | −0.832969 | − | 0.541679i | ||||
\(387\) | − | 4.18190e11i | − | 0.947707i | ||||||
\(388\) | −8.48476e10 | − | 1.91216e11i | −0.190063 | − | 0.428332i | ||||
\(389\) | 3.37004e11i | 0.746211i | 0.927789 | + | 0.373105i | \(0.121707\pi\) | ||||
−0.927789 | + | 0.373105i | \(0.878293\pi\) | |||||||
\(390\) | −6.77176e10 | + | 1.04133e11i | −0.148221 | + | 0.227928i | ||||
\(391\) | −6.87173e11 | −1.48686 | ||||||||
\(392\) | 7.38371e10 | − | 4.60581e11i | 0.157938 | − | 0.985187i | ||||
\(393\) | −4.19142e11 | −0.886328 | ||||||||
\(394\) | 2.90442e11 | − | 4.46629e11i | 0.607193 | − | 0.933714i | ||||
\(395\) | − | 1.17119e11i | − | 0.242070i | ||||||
\(396\) | 3.90517e11 | − | 1.73283e11i | 0.798017 | − | 0.354102i | ||||
\(397\) | − | 1.52291e11i | − | 0.307693i | −0.988095 | − | 0.153846i | \(-0.950834\pi\) | ||
0.988095 | − | 0.153846i | \(-0.0491661\pi\) | |||||||
\(398\) | 5.45261e11 | + | 3.54583e11i | 1.08926 | + | 0.708344i | ||||
\(399\) | −1.28790e10 | −0.0254393 | ||||||||
\(400\) | −2.98359e11 | + | 3.29694e11i | −0.582732 | + | 0.643934i | ||||
\(401\) | 2.43333e11 | 0.469949 | 0.234975 | − | 0.972001i | \(-0.424499\pi\) | ||||
0.234975 | + | 0.972001i | \(0.424499\pi\) | |||||||
\(402\) | 2.01432e11 | + | 1.30991e11i | 0.384690 | + | 0.250163i | ||||
\(403\) | 4.43190e11i | 0.836984i | ||||||||
\(404\) | −4.46090e11 | + | 1.97942e11i | −0.833117 | + | 0.369677i | ||||
\(405\) | 7.00736e10i | 0.129422i | ||||||||
\(406\) | 6.02705e9 | − | 9.26812e9i | 0.0110087 | − | 0.0169287i | ||||
\(407\) | −3.35576e11 | −0.606201 | ||||||||
\(408\) | −2.36183e11 | − | 3.78632e10i | −0.421966 | − | 0.0676467i | ||||
\(409\) | 9.06042e11 | 1.60101 | 0.800504 | − | 0.599327i | \(-0.204565\pi\) | ||||
0.800504 | + | 0.599327i | \(0.204565\pi\) | |||||||
\(410\) | 3.92818e10 | − | 6.04058e10i | 0.0686538 | − | 0.105573i | ||||
\(411\) | 1.49417e11i | 0.258292i | ||||||||
\(412\) | 3.67197e11 | + | 8.27529e11i | 0.627859 | + | 1.41497i | ||||
\(413\) | 1.16053e10i | 0.0196282i | ||||||||
\(414\) | −6.45129e11 | − | 4.19527e11i | −1.07931 | − | 0.701872i | ||||
\(415\) | −2.58565e11 | −0.427911 | ||||||||
\(416\) | 2.42972e11 | + | 9.18291e11i | 0.397775 | + | 1.50335i | ||||
\(417\) | −8.90112e10 | −0.144156 | ||||||||
\(418\) | 6.64455e11 | + | 4.32094e11i | 1.06456 | + | 0.692286i | ||||
\(419\) | − | 4.87495e10i | − | 0.0772693i | −0.999253 | − | 0.0386347i | \(-0.987699\pi\) | ||
0.999253 | − | 0.0386347i | \(-0.0123009\pi\) | |||||||
\(420\) | −2.13736e9 | − | 4.81684e9i | −0.00335163 | − | 0.00755337i | ||||
\(421\) | − | 1.21366e11i | − | 0.188290i | −0.995558 | − | 0.0941451i | \(-0.969988\pi\) | ||
0.995558 | − | 0.0941451i | \(-0.0300118\pi\) | |||||||
\(422\) | −1.62665e11 | + | 2.50139e11i | −0.249683 | + | 0.383951i | ||||
\(423\) | 2.09039e11 | 0.317466 | ||||||||
\(424\) | −1.20015e12 | − | 1.92399e11i | −1.80338 | − | 0.289106i | ||||
\(425\) | 5.17827e11 | 0.769900 | ||||||||
\(426\) | 1.29320e11 | − | 1.98862e11i | 0.190249 | − | 0.292556i | ||||
\(427\) | − | 3.31471e10i | − | 0.0482526i | ||||||
\(428\) | 1.97257e11 | − | 8.75283e10i | 0.284142 | − | 0.126082i | ||||
\(429\) | − | 5.98153e11i | − | 0.852618i | ||||||
\(430\) | 2.66120e11 | + | 1.73058e11i | 0.375379 | + | 0.244108i | ||||
\(431\) | 5.02186e11 | 0.700998 | 0.350499 | − | 0.936563i | \(-0.386012\pi\) | ||||
0.350499 | + | 0.936563i | \(0.386012\pi\) | |||||||
\(432\) | −4.57361e11 | − | 4.13891e11i | −0.631804 | − | 0.571754i | ||||
\(433\) | 5.10983e11 | 0.698572 | 0.349286 | − | 0.937016i | \(-0.386424\pi\) | ||||
0.349286 | + | 0.937016i | \(0.386424\pi\) | |||||||
\(434\) | −1.57624e10 | − | 1.02503e10i | −0.0213264 | − | 0.0138685i | ||||
\(435\) | 5.57828e10i | 0.0746963i | ||||||||
\(436\) | −1.69995e11 | + | 7.54312e10i | −0.225292 | + | 0.0999681i | ||||
\(437\) | − | 1.42763e12i | − | 1.87261i | ||||||
\(438\) | −2.22947e11 | + | 3.42838e11i | −0.289447 | + | 0.445097i | ||||
\(439\) | −1.29662e12 | −1.66618 | −0.833088 | − | 0.553140i | \(-0.813429\pi\) | ||||
−0.833088 | + | 0.553140i | \(0.813429\pi\) | |||||||
\(440\) | −5.13354e10 | + | 3.20220e11i | −0.0652950 | + | 0.407297i | ||||
\(441\) | −6.08339e11 | −0.765900 | ||||||||
\(442\) | 6.03067e11 | − | 9.27368e11i | 0.751563 | − | 1.15572i | ||||
\(443\) | − | 6.03046e11i | − | 0.743933i | −0.928246 | − | 0.371966i | \(-0.878684\pi\) | ||
0.928246 | − | 0.371966i | \(-0.121316\pi\) | |||||||
\(444\) | 8.53367e10 | + | 1.92318e11i | 0.104211 | + | 0.234853i | ||||
\(445\) | − | 1.98545e11i | − | 0.240015i | ||||||
\(446\) | −5.85156e11 | − | 3.80527e11i | −0.700269 | − | 0.455384i | ||||
\(447\) | 2.87139e11 | 0.340179 | ||||||||
\(448\) | −3.82792e10 | − | 1.25971e10i | −0.0448964 | − | 0.0147747i | ||||
\(449\) | −1.45512e11 | −0.168963 | −0.0844814 | − | 0.996425i | \(-0.526923\pi\) | ||||
−0.0844814 | + | 0.996425i | \(0.526923\pi\) | |||||||
\(450\) | 4.86144e11 | + | 3.16139e11i | 0.558868 | + | 0.363431i | ||||
\(451\) | 3.46979e11i | 0.394920i | ||||||||
\(452\) | −1.44848e11 | − | 3.26435e11i | −0.163226 | − | 0.367852i | ||||
\(453\) | 7.07229e11i | 0.789074i | ||||||||
\(454\) | 4.30197e11 | − | 6.61537e11i | 0.475243 | − | 0.730807i | ||||
\(455\) | 2.43708e10 | 0.0266574 | ||||||||
\(456\) | 7.86622e10 | − | 4.90678e11i | 0.0851970 | − | 0.531441i | ||||
\(457\) | 3.72554e11 | 0.399545 | 0.199773 | − | 0.979842i | \(-0.435980\pi\) | ||||
0.199773 | + | 0.979842i | \(0.435980\pi\) | |||||||
\(458\) | −7.07271e11 | + | 1.08761e12i | −0.751089 | + | 1.15499i | ||||
\(459\) | 7.18344e11i | 0.755397i | ||||||||
\(460\) | 5.33942e11 | − | 2.36924e11i | 0.556012 | − | 0.246717i | ||||
\(461\) | 1.61071e12i | 1.66097i | 0.557039 | + | 0.830486i | \(0.311937\pi\) | ||||
−0.557039 | + | 0.830486i | \(0.688063\pi\) | |||||||
\(462\) | 2.12737e10 | + | 1.38343e10i | 0.0217248 | + | 0.0141276i | ||||
\(463\) | 1.87693e11 | 0.189816 | 0.0949082 | − | 0.995486i | \(-0.469744\pi\) | ||||
0.0949082 | + | 0.995486i | \(0.469744\pi\) | |||||||
\(464\) | 3.16294e11 | + | 2.86232e11i | 0.316782 | + | 0.286674i | ||||
\(465\) | 9.48703e10 | 0.0941005 | ||||||||
\(466\) | 5.26740e11 | + | 3.42538e11i | 0.517439 | + | 0.336490i | ||||
\(467\) | − | 6.66110e11i | − | 0.648067i | −0.946046 | − | 0.324034i | \(-0.894961\pi\) | ||
0.946046 | − | 0.324034i | \(-0.105039\pi\) | |||||||
\(468\) | 1.13234e12 | − | 5.02449e11i | 1.09111 | − | 0.484156i | ||||
\(469\) | − | 4.71421e10i | − | 0.0449916i | ||||||
\(470\) | −8.65060e10 | + | 1.33025e11i | −0.0817722 | + | 0.125745i | ||||
\(471\) | 4.83613e11 | 0.452797 | ||||||||
\(472\) | −4.42149e11 | − | 7.08824e10i | −0.410044 | − | 0.0657354i | ||||
\(473\) | −1.52863e12 | −1.40419 | ||||||||
\(474\) | 1.92775e11 | − | 2.96441e11i | 0.175408 | − | 0.269734i | ||||
\(475\) | 1.07580e12i | 0.969644i | ||||||||
\(476\) | 1.90345e10 | + | 4.28970e10i | 0.0169946 | + | 0.0382997i | ||||
\(477\) | 1.58516e12i | 1.40198i | ||||||||
\(478\) | −1.33785e12 | − | 8.70005e11i | −1.17215 | − | 0.762248i | ||||
\(479\) | 5.09054e11 | 0.441829 | 0.220914 | − | 0.975293i | \(-0.429096\pi\) | ||||
0.220914 | + | 0.975293i | \(0.429096\pi\) | |||||||
\(480\) | 1.96572e11 | − | 5.20113e10i | 0.169019 | − | 0.0447210i | ||||
\(481\) | −9.73032e11 | −0.828846 | ||||||||
\(482\) | −1.18951e12 | − | 7.73538e11i | −1.00382 | − | 0.652785i | ||||
\(483\) | − | 4.57081e10i | − | 0.0382148i | ||||||
\(484\) | −1.43753e11 | − | 3.23967e11i | −0.119073 | − | 0.268347i | ||||
\(485\) | − | 2.07096e11i | − | 0.169955i | ||||||
\(486\) | −6.86664e11 | + | 1.05592e12i | −0.558317 | + | 0.858554i | ||||
\(487\) | −4.44777e11 | −0.358313 | −0.179156 | − | 0.983821i | \(-0.557337\pi\) | ||||
−0.179156 | + | 0.983821i | \(0.557337\pi\) | |||||||
\(488\) | 1.26287e12 | + | 2.02455e11i | 1.00802 | + | 0.161599i | ||||
\(489\) | 7.11529e11 | 0.562733 | ||||||||
\(490\) | 2.51746e11 | − | 3.87124e11i | 0.197279 | − | 0.303367i | ||||
\(491\) | − | 1.37326e12i | − | 1.06632i | −0.846015 | − | 0.533159i | \(-0.821005\pi\) | ||
0.846015 | − | 0.533159i | \(-0.178995\pi\) | |||||||
\(492\) | 1.98853e11 | − | 8.82363e10i | 0.152999 | − | 0.0678898i | ||||
\(493\) | − | 4.96781e11i | − | 0.378751i | ||||||
\(494\) | 1.92664e12 | + | 1.25289e12i | 1.45556 | + | 0.946549i | ||||
\(495\) | 4.22949e11 | 0.316639 | ||||||||
\(496\) | 4.86798e11 | − | 5.37924e11i | 0.361144 | − | 0.399074i | ||||
\(497\) | −4.65408e10 | −0.0342160 | ||||||||
\(498\) | −6.54456e11 | − | 4.25592e11i | −0.476813 | − | 0.310071i | ||||
\(499\) | − | 7.60506e11i | − | 0.549099i | −0.961573 | − | 0.274549i | \(-0.911471\pi\) | ||
0.961573 | − | 0.274549i | \(-0.0885287\pi\) | |||||||
\(500\) | −8.65658e11 | + | 3.84116e11i | −0.619414 | + | 0.274851i | ||||
\(501\) | 9.46785e11i | 0.671401i | ||||||||
\(502\) | 2.28258e11 | − | 3.51004e11i | 0.160420 | − | 0.246687i | ||||
\(503\) | 1.79142e12 | 1.24779 | 0.623895 | − | 0.781508i | \(-0.285549\pi\) | ||||
0.623895 | + | 0.781508i | \(0.285549\pi\) | |||||||
\(504\) | −8.31916e9 | + | 5.18932e10i | −0.00574304 | + | 0.0358239i | ||||
\(505\) | −4.83136e11 | −0.330566 | ||||||||
\(506\) | −1.53352e12 | + | 2.35817e12i | −1.03995 | + | 1.59918i | ||||
\(507\) | − | 1.01720e12i | − | 0.683705i | ||||||
\(508\) | −3.56641e11 | − | 8.03739e11i | −0.237599 | − | 0.535462i | ||||
\(509\) | − | 2.67944e12i | − | 1.76935i | −0.466209 | − | 0.884674i | \(-0.654381\pi\) | ||
0.466209 | − | 0.884674i | \(-0.345619\pi\) | |||||||
\(510\) | −1.98515e11 | − | 1.29094e11i | −0.129935 | − | 0.0844967i | ||||
\(511\) | 8.02362e10 | 0.0520566 | ||||||||
\(512\) | 7.13736e11 | − | 1.38146e12i | 0.459011 | − | 0.888431i | ||||
\(513\) | −1.49239e12 | −0.951378 | ||||||||
\(514\) | 1.01686e11 | + | 6.61263e10i | 0.0642580 | + | 0.0417869i | ||||
\(515\) | 8.96253e11i | 0.561433i | ||||||||
\(516\) | 3.88729e11 | + | 8.76054e11i | 0.241392 | + | 0.544010i | ||||
\(517\) | − | 7.64112e11i | − | 0.470381i | ||||||
\(518\) | 2.25046e10 | − | 3.46065e10i | 0.0137337 | − | 0.0211190i | ||||
\(519\) | −5.95178e11 | −0.360075 | ||||||||
\(520\) | −1.48851e11 | + | 9.28503e11i | −0.0892765 | + | 0.556889i | ||||
\(521\) | 9.97197e11 | 0.592941 | 0.296470 | − | 0.955042i | \(-0.404190\pi\) | ||||
0.296470 | + | 0.955042i | \(0.404190\pi\) | |||||||
\(522\) | 3.03290e11 | − | 4.66386e11i | 0.178789 | − | 0.274934i | ||||
\(523\) | − | 1.46266e12i | − | 0.854840i | −0.904053 | − | 0.427420i | \(-0.859423\pi\) | ||
0.904053 | − | 0.427420i | \(-0.140577\pi\) | |||||||
\(524\) | −2.90037e12 | + | 1.28697e12i | −1.68059 | + | 0.745724i | ||||
\(525\) | 3.44439e10i | 0.0197877i | ||||||||
\(526\) | 1.03583e12 | + | 6.73598e11i | 0.589999 | + | 0.383676i | ||||
\(527\) | −8.44879e11 | −0.477141 | ||||||||
\(528\) | −6.57008e11 | + | 7.26012e11i | −0.367890 | + | 0.406529i | ||||
\(529\) | 3.26554e12 | 1.81303 | ||||||||
\(530\) | −1.00874e12 | − | 6.55981e11i | −0.555312 | − | 0.361119i | ||||
\(531\) | 5.83995e11i | 0.318775i | ||||||||
\(532\) | −8.91201e10 | + | 3.95450e10i | −0.0482362 | + | 0.0214037i | ||||
\(533\) | 1.00609e12i | 0.539966i | ||||||||
\(534\) | 3.26800e11 | − | 5.02538e11i | 0.173919 | − | 0.267444i | ||||
\(535\) | 2.13639e11 | 0.112743 | ||||||||
\(536\) | 1.79607e12 | + | 2.87933e11i | 0.939900 | + | 0.150678i | ||||
\(537\) | −3.33621e11 | −0.173129 | ||||||||
\(538\) | −4.94597e10 | + | 7.60568e10i | −0.0254525 | + | 0.0391397i | ||||
\(539\) | 2.22369e12i | 1.13482i | ||||||||
\(540\) | −2.47672e11 | − | 5.58162e11i | −0.125344 | − | 0.282481i | ||||
\(541\) | 5.74239e11i | 0.288207i | 0.989563 | + | 0.144104i | \(0.0460299\pi\) | ||||
−0.989563 | + | 0.144104i | \(0.953970\pi\) | |||||||
\(542\) | 1.56258e12 | + | 1.01615e12i | 0.777760 | + | 0.505777i | ||||
\(543\) | −1.57329e12 | −0.776624 | ||||||||
\(544\) | −1.75059e12 | + | 4.63193e11i | −0.857018 | + | 0.226760i | ||||
\(545\) | −1.84112e11 | −0.0893919 | ||||||||
\(546\) | 6.16850e10 | + | 4.01137e10i | 0.0297038 | + | 0.0193164i | ||||
\(547\) | 2.55692e12i | 1.22117i | 0.791952 | + | 0.610583i | \(0.209065\pi\) | ||||
−0.791952 | + | 0.610583i | \(0.790935\pi\) | |||||||
\(548\) | 4.58783e11 | + | 1.03393e12i | 0.217318 | + | 0.489756i | ||||
\(549\) | − | 1.66801e12i | − | 0.783653i | ||||||
\(550\) | 1.15560e12 | − | 1.77703e12i | 0.538487 | − | 0.828061i | ||||
\(551\) | 1.03208e12 | 0.477014 | ||||||||
\(552\) | 1.74143e12 | + | 2.79175e11i | 0.798327 | + | 0.127982i | ||||
\(553\) | −6.93777e10 | −0.0315469 | ||||||||
\(554\) | 1.12283e12 | − | 1.72663e12i | 0.506429 | − | 0.778764i | ||||
\(555\) | 2.08289e11i | 0.0931856i | ||||||||
\(556\) | −6.15938e11 | + | 2.73308e11i | −0.273338 | + | 0.121288i | ||||
\(557\) | 2.10146e12i | 0.925065i | 0.886602 | + | 0.462533i | \(0.153059\pi\) | ||||
−0.886602 | + | 0.462533i | \(0.846941\pi\) | |||||||
\(558\) | −7.93186e11 | − | 5.15808e11i | −0.346355 | − | 0.225234i | ||||
\(559\) | −4.43239e12 | −1.91993 | ||||||||
\(560\) | −2.95802e10 | − | 2.67687e10i | −0.0127103 | − | 0.0115022i | ||||
\(561\) | 1.14029e12 | 0.486054 | ||||||||
\(562\) | −1.04491e10 | − | 6.79506e9i | −0.00441842 | − | 0.00287329i | ||||
\(563\) | − | 2.42568e12i | − | 1.01753i | −0.860906 | − | 0.508764i | \(-0.830103\pi\) | ||
0.860906 | − | 0.508764i | \(-0.169897\pi\) | |||||||
\(564\) | −4.37911e11 | + | 1.94313e11i | −0.182234 | + | 0.0808622i | ||||
\(565\) | − | 3.53544e11i | − | 0.145957i | ||||||
\(566\) | 1.60343e12 | − | 2.46567e12i | 0.656712 | − | 1.00986i | ||||
\(567\) | 4.15093e10 | 0.0168664 | ||||||||
\(568\) | 2.84260e11 | − | 1.77316e12i | 0.114591 | − | 0.714792i | ||||
\(569\) | 1.74418e12 | 0.697567 | 0.348784 | − | 0.937203i | \(-0.386595\pi\) | ||||
0.348784 | + | 0.937203i | \(0.386595\pi\) | |||||||
\(570\) | 2.68197e11 | − | 4.12421e11i | 0.106419 | − | 0.163646i | ||||
\(571\) | 1.57621e12i | 0.620515i | 0.950653 | + | 0.310258i | \(0.100415\pi\) | ||||
−0.950653 | + | 0.310258i | \(0.899585\pi\) | |||||||
\(572\) | −1.83663e12 | − | 4.13909e12i | −0.717362 | − | 1.61667i | ||||
\(573\) | − | 1.36096e12i | − | 0.527410i | ||||||
\(574\) | −3.57824e10 | − | 2.32693e10i | −0.0137584 | − | 0.00894705i | ||||
\(575\) | −3.81807e12 | −1.45659 | ||||||||
\(576\) | −1.92627e12 | − | 6.33903e11i | −0.729148 | − | 0.239951i | ||||
\(577\) | −2.85422e12 | −1.07200 | −0.536001 | − | 0.844217i | \(-0.680066\pi\) | ||||
−0.536001 | + | 0.844217i | \(0.680066\pi\) | |||||||
\(578\) | −4.81624e11 | − | 3.13200e11i | −0.179487 | − | 0.116720i | ||||
\(579\) | − | 1.29531e12i | − | 0.478981i | ||||||
\(580\) | 1.71281e11 | + | 3.86005e11i | 0.0628468 | + | 0.141634i | ||||
\(581\) | 1.53166e11i | 0.0557660i | ||||||||
\(582\) | 3.40874e11 | − | 5.24180e11i | 0.123152 | − | 0.189377i | ||||
\(583\) | 5.79432e12 | 2.07728 | ||||||||
\(584\) | −4.90064e11 | + | 3.05692e12i | −0.174339 | + | 1.08749i | ||||
\(585\) | 1.22637e12 | 0.432934 | ||||||||
\(586\) | −6.09271e11 | + | 9.36908e11i | −0.213438 | + | 0.328214i | ||||
\(587\) | 3.12539e12i | 1.08651i | 0.839569 | + | 0.543254i | \(0.182808\pi\) | ||||
−0.839569 | + | 0.543254i | \(0.817192\pi\) | |||||||
\(588\) | 1.27439e12 | − | 5.65482e11i | 0.439648 | − | 0.195084i | ||||
\(589\) | − | 1.75527e12i | − | 0.600931i | ||||||
\(590\) | −3.71632e11 | − | 2.41672e11i | −0.126264 | − | 0.0821094i | ||||
\(591\) | 1.59238e12 | 0.536912 | ||||||||
\(592\) | 1.18102e12 | + | 1.06877e12i | 0.395194 | + | 0.357633i | ||||
\(593\) | 3.82893e11 | 0.127155 | 0.0635773 | − | 0.997977i | \(-0.479749\pi\) | ||||
0.0635773 | + | 0.997977i | \(0.479749\pi\) | |||||||
\(594\) | 2.46514e12 | + | 1.60308e12i | 0.812462 | + | 0.528343i | ||||
\(595\) | 4.64595e10i | 0.0151966i | ||||||||
\(596\) | 1.98694e12 | − | 8.81657e11i | 0.645024 | − | 0.286215i | ||||
\(597\) | 1.94404e12i | 0.626355i | ||||||||
\(598\) | −4.44656e12 | + | 6.83771e12i | −1.42190 | + | 2.18653i | ||||
\(599\) | −7.48723e10 | −0.0237629 | −0.0118815 | − | 0.999929i | \(-0.503782\pi\) | ||||
−0.0118815 | + | 0.999929i | \(0.503782\pi\) | |||||||
\(600\) | −1.31228e12 | − | 2.10375e11i | −0.413376 | − | 0.0662696i | ||||
\(601\) | −2.78892e12 | −0.871969 | −0.435984 | − | 0.899954i | \(-0.643600\pi\) | ||||
−0.435984 | + | 0.899954i | \(0.643600\pi\) | |||||||
\(602\) | 1.02514e11 | − | 1.57641e11i | 0.0318125 | − | 0.0489198i | ||||
\(603\) | − | 2.37226e12i | − | 0.730693i | ||||||
\(604\) | 2.17154e12 | + | 4.89387e12i | 0.663899 | + | 1.49619i | ||||
\(605\) | − | 3.50872e11i | − | 0.106475i | ||||||
\(606\) | −1.22287e12 | − | 7.95230e11i | −0.368343 | − | 0.239533i | ||||
\(607\) | 2.12944e12 | 0.636673 | 0.318337 | − | 0.947978i | \(-0.396876\pi\) | ||||
0.318337 | + | 0.947978i | \(0.396876\pi\) | |||||||
\(608\) | −9.62300e11 | − | 3.63692e12i | −0.285591 | − | 1.07936i | ||||
\(609\) | 3.30440e10 | 0.00973451 | ||||||||
\(610\) | 1.06146e12 | + | 6.90267e11i | 0.310399 | + | 0.201852i | ||||
\(611\) | − | 2.21561e12i | − | 0.643143i | ||||||
\(612\) | 9.57847e11 | + | 2.15864e12i | 0.276004 | + | 0.622012i | ||||
\(613\) | 4.30691e12i | 1.23195i | 0.787765 | + | 0.615976i | \(0.211238\pi\) | ||||
−0.787765 | + | 0.615976i | \(0.788762\pi\) | |||||||
\(614\) | −4.86414e11 | + | 7.47984e11i | −0.138117 | + | 0.212390i | ||||
\(615\) | 2.15367e11 | 0.0607073 | ||||||||
\(616\) | 1.89688e11 | + | 3.04094e10i | 0.0530794 | + | 0.00850932i | ||||
\(617\) | −2.30493e12 | −0.640286 | −0.320143 | − | 0.947369i | \(-0.603731\pi\) | ||||
−0.320143 | + | 0.947369i | \(0.603731\pi\) | |||||||
\(618\) | −1.47521e12 | + | 2.26851e12i | −0.406823 | + | 0.625594i | ||||
\(619\) | − | 5.14701e12i | − | 1.40912i | −0.709646 | − | 0.704559i | \(-0.751145\pi\) | ||
0.709646 | − | 0.704559i | \(-0.248855\pi\) | |||||||
\(620\) | 6.56482e11 | − | 2.91299e11i | 0.178427 | − | 0.0791728i | ||||
\(621\) | − | 5.29653e12i | − | 1.42915i | ||||||
\(622\) | −2.78221e12 | − | 1.80927e12i | −0.745304 | − | 0.484671i | ||||
\(623\) | −1.17612e11 | −0.0312791 | ||||||||
\(624\) | −1.90505e12 | + | 2.10513e12i | −0.503009 | + | 0.555838i | ||||
\(625\) | 2.37537e12 | 0.622690 | ||||||||
\(626\) | −8.53756e11 | − | 5.55197e11i | −0.222203 | − | 0.144498i | ||||
\(627\) | 2.36900e12i | 0.612156i | ||||||||
\(628\) | 3.34650e12 | − | 1.48493e12i | 0.858562 | − | 0.380967i | ||||
\(629\) | − | 1.85495e12i | − | 0.472502i | ||||||
\(630\) | −2.83640e10 | + | 4.36169e10i | −0.00717357 | + | 0.0110312i | ||||
\(631\) | 5.22883e12 | 1.31302 | 0.656512 | − | 0.754316i | \(-0.272031\pi\) | ||||
0.656512 | + | 0.754316i | \(0.272031\pi\) | |||||||
\(632\) | 4.23743e11 | − | 2.64322e12i | 0.105651 | − | 0.659032i | ||||
\(633\) | −8.91830e11 | −0.220783 | ||||||||
\(634\) | 1.45919e11 | − | 2.24387e11i | 0.0358681 | − | 0.0551563i | ||||
\(635\) | − | 8.70487e11i | − | 0.212462i | ||||||
\(636\) | −1.47349e12 | − | 3.32071e12i | −0.357100 | − | 0.804775i | ||||
\(637\) | 6.44778e12i | 1.55161i | ||||||||
\(638\) | −1.70480e12 | − | 1.10863e12i | −0.407363 | − | 0.264908i | ||||
\(639\) | −2.34200e12 | −0.555691 | ||||||||
\(640\) | 1.20053e12 | − | 9.63478e11i | 0.282855 | − | 0.227003i | ||||
\(641\) | −6.02644e12 | −1.40994 | −0.704969 | − | 0.709238i | \(-0.749039\pi\) | ||||
−0.704969 | + | 0.709238i | \(0.749039\pi\) | |||||||
\(642\) | 5.40742e11 | + | 3.51644e11i | 0.125627 | + | 0.0816950i | ||||
\(643\) | − | 5.00421e12i | − | 1.15448i | −0.816575 | − | 0.577240i | \(-0.804130\pi\) | ||
0.816575 | − | 0.577240i | \(-0.195870\pi\) | |||||||
\(644\) | −1.40346e11 | − | 3.16290e11i | −0.0321525 | − | 0.0724601i | ||||
\(645\) | 9.48807e11i | 0.215854i | ||||||||
\(646\) | −2.38846e12 | + | 3.67287e12i | −0.539600 | + | 0.829772i | ||||
\(647\) | 3.75255e11 | 0.0841893 | 0.0420946 | − | 0.999114i | \(-0.486597\pi\) | ||||
0.0420946 | + | 0.999114i | \(0.486597\pi\) | |||||||
\(648\) | −2.53530e11 | + | 1.58147e12i | −0.0564860 | + | 0.352348i | ||||
\(649\) | 2.13471e12 | 0.472321 | ||||||||
\(650\) | 3.35076e12 | − | 5.15264e12i | 0.736263 | − | 1.13219i | ||||
\(651\) | − | 5.61981e10i | − | 0.0122633i | ||||||
\(652\) | 4.92362e12 | − | 2.18474e12i | 1.06701 | − | 0.473463i | ||||
\(653\) | 3.69732e12i | 0.795753i | 0.917439 | + | 0.397877i | \(0.130253\pi\) | ||||
−0.917439 | + | 0.397877i | \(0.869747\pi\) | |||||||
\(654\) | −4.66007e11 | − | 3.03044e11i | −0.0996075 | − | 0.0647747i | ||||
\(655\) | −3.14124e12 | −0.666829 | ||||||||
\(656\) | 1.10509e12 | − | 1.22115e12i | 0.232986 | − | 0.257456i | ||||
\(657\) | 4.03761e12 | 0.845434 | ||||||||
\(658\) | 7.87996e10 | + | 5.12433e10i | 0.0163873 | + | 0.0106567i | ||||
\(659\) | 9.20538e12i | 1.90133i | 0.310220 | + | 0.950665i | \(0.399597\pi\) | ||||
−0.310220 | + | 0.950665i | \(0.600403\pi\) | |||||||
\(660\) | −8.86023e11 | + | 3.93153e11i | −0.181760 | + | 0.0806517i | ||||
\(661\) | − | 4.18896e12i | − | 0.853492i | −0.904371 | − | 0.426746i | \(-0.859660\pi\) | ||
0.904371 | − | 0.426746i | \(-0.140340\pi\) | |||||||
\(662\) | 2.63855e12 | − | 4.05744e12i | 0.533955 | − | 0.821091i | ||||
\(663\) | 3.30638e12 | 0.664571 | ||||||||
\(664\) | −5.83547e12 | − | 9.35502e11i | −1.16498 | − | 0.186762i | ||||
\(665\) | −9.65212e10 | −0.0191393 | ||||||||
\(666\) | 1.13247e12 | − | 1.74145e12i | 0.223044 | − | 0.342987i | ||||
\(667\) | 3.66289e12i | 0.716568i | ||||||||
\(668\) | 2.90710e12 | + | 6.55155e12i | 0.564892 | + | 1.27306i | ||||
\(669\) | − | 2.08628e12i | − | 0.402675i | ||||||
\(670\) | 1.50962e12 | + | 9.81704e11i | 0.289421 | + | 0.188211i | ||||
\(671\) | −6.09717e12 | −1.16112 | ||||||||
\(672\) | −3.08098e10 | − | 1.16443e11i | −0.00582810 | − | 0.0220267i | ||||
\(673\) | −9.82065e12 | −1.84532 | −0.922661 | − | 0.385611i | \(-0.873991\pi\) | ||||
−0.922661 | + | 0.385611i | \(0.873991\pi\) | |||||||
\(674\) | 3.60501e12 | + | 2.34434e12i | 0.672879 | + | 0.437573i | ||||
\(675\) | 3.99126e12i | 0.740019i | ||||||||
\(676\) | −3.12329e12 | − | 7.03877e12i | −0.575244 | − | 1.29639i | ||||
\(677\) | 1.20487e12i | 0.220440i | 0.993907 | + | 0.110220i | \(0.0351555\pi\) | ||||
−0.993907 | + | 0.110220i | \(0.964845\pi\) | |||||||
\(678\) | 5.81924e11 | − | 8.94856e11i | 0.105763 | − | 0.162637i | ||||
\(679\) | −1.22677e11 | −0.0221487 | ||||||||
\(680\) | −1.77006e12 | − | 2.83764e11i | −0.317466 | − | 0.0508940i | ||||
\(681\) | 2.35860e12 | 0.420235 | ||||||||
\(682\) | −1.88546e12 | + | 2.89937e12i | −0.333724 | + | 0.513185i | ||||
\(683\) | 3.83455e12i | 0.674251i | 0.941460 | + | 0.337125i | \(0.109455\pi\) | ||||
−0.941460 | + | 0.337125i | \(0.890545\pi\) | |||||||
\(684\) | −4.48466e12 | + | 1.98996e12i | −0.783388 | + | 0.347610i | ||||
\(685\) | 1.11980e12i | 0.194326i | ||||||||
\(686\) | −4.59153e11 | − | 2.98587e11i | −0.0791587 | − | 0.0514769i | ||||
\(687\) | −3.87769e12 | −0.664153 | ||||||||
\(688\) | 5.37983e12 | + | 4.86851e12i | 0.915421 | + | 0.828415i | ||||
\(689\) | 1.68011e13 | 2.84022 | ||||||||
\(690\) | 1.46370e12 | + | 9.51841e11i | 0.245827 | + | 0.159861i | ||||
\(691\) | − | 8.54150e12i | − | 1.42522i | −0.701559 | − | 0.712612i | \(-0.747512\pi\) | ||
0.701559 | − | 0.712612i | \(-0.252488\pi\) | |||||||
\(692\) | −4.11850e12 | + | 1.82749e12i | −0.682750 | + | 0.302954i | ||||
\(693\) | − | 2.50541e11i | − | 0.0412648i | ||||||
\(694\) | 3.10179e12 | − | 4.76980e12i | 0.507569 | − | 0.780517i | ||||
\(695\) | −6.67090e11 | −0.108456 | ||||||||
\(696\) | −2.01825e11 | + | 1.25894e12i | −0.0326012 | + | 0.203359i | ||||
\(697\) | −1.91798e12 | −0.307819 | ||||||||
\(698\) | −3.64632e11 | + | 5.60714e11i | −0.0581441 | + | 0.0894112i | ||||
\(699\) | 1.87800e12i | 0.297543i | ||||||||
\(700\) | 1.05760e11 | + | 2.38344e11i | 0.0166486 | + | 0.0375200i | ||||
\(701\) | 1.27661e11i | 0.0199676i | 0.999950 | + | 0.00998380i | \(0.00317799\pi\) | ||||
−0.999950 | + | 0.00998380i | \(0.996822\pi\) | |||||||
\(702\) | 7.14788e12 | + | 4.64826e12i | 1.11086 | + | 0.722393i | ||||
\(703\) | 3.85372e12 | 0.595088 | ||||||||
\(704\) | −2.31714e12 | + | 7.04118e12i | −0.355529 | + | 1.08036i | ||||
\(705\) | −4.74278e11 | −0.0723073 | ||||||||
\(706\) | −6.57109e12 | − | 4.27317e12i | −0.995442 | − | 0.647335i | ||||
\(707\) | 2.86194e11i | 0.0430798i | ||||||||
\(708\) | −5.42853e11 | − | 1.22339e12i | −0.0811956 | − | 0.182986i | ||||
\(709\) | − | 1.20824e13i | − | 1.79574i | −0.440258 | − | 0.897871i | \(-0.645113\pi\) | ||
0.440258 | − | 0.897871i | \(-0.354887\pi\) | |||||||
\(710\) | 9.69181e11 | − | 1.49036e12i | 0.143134 | − | 0.220105i | ||||
\(711\) | −3.49119e12 | −0.512342 | ||||||||
\(712\) | 7.18345e11 | − | 4.48089e12i | 0.104755 | − | 0.653438i | ||||
\(713\) | 6.22950e12 | 0.902714 | ||||||||
\(714\) | −7.64711e10 | + | 1.17594e11i | −0.0110117 | + | 0.0169333i | ||||
\(715\) | − | 4.48283e12i | − | 0.641468i | ||||||
\(716\) | −2.30859e12 | + | 1.02438e12i | −0.328275 | + | 0.145664i | ||||
\(717\) | − | 4.76990e12i | − | 0.674020i | ||||||
\(718\) | −4.68108e12 | − | 3.04410e12i | −0.657334 | − | 0.427464i | ||||
\(719\) | −3.46841e12 | −0.484005 | −0.242003 | − | 0.970276i | \(-0.577804\pi\) | ||||
−0.242003 | + | 0.970276i | \(0.577804\pi\) | |||||||
\(720\) | −1.48852e12 | − | 1.34704e12i | −0.206423 | − | 0.186804i | ||||
\(721\) | 5.30912e11 | 0.0731667 | ||||||||
\(722\) | −1.50939e12 | − | 9.81553e11i | −0.206720 | − | 0.134430i | ||||
\(723\) | − | 4.24101e12i | − | 0.577227i | ||||||
\(724\) | −1.08868e13 | + | 4.83079e12i | −1.47258 | + | 0.653423i | ||||
\(725\) | − | 2.76021e12i | − | 0.371041i | ||||||
\(726\) | 5.77526e11 | − | 8.88093e11i | 0.0771538 | − | 0.118643i | ||||
\(727\) | −2.83270e12 | −0.376093 | −0.188047 | − | 0.982160i | \(-0.560216\pi\) | ||||
−0.188047 | + | 0.982160i | \(0.560216\pi\) | |||||||
\(728\) | 5.50015e11 | + | 8.81747e10i | 0.0725744 | + | 0.0116346i | ||||
\(729\) | −1.04354e12 | −0.136846 | ||||||||
\(730\) | −1.67087e12 | + | 2.56938e12i | −0.217765 | + | 0.334869i | ||||
\(731\) | − | 8.44972e12i | − | 1.09450i | ||||||
\(732\) | 1.55050e12 | + | 3.49427e12i | 0.199606 | + | 0.449839i | ||||
\(733\) | 3.96035e12i | 0.506718i | 0.967372 | + | 0.253359i | \(0.0815353\pi\) | ||||
−0.967372 | + | 0.253359i | \(0.918465\pi\) | |||||||
\(734\) | 9.09677e12 | + | 5.91562e12i | 1.15679 | + | 0.752260i | ||||
\(735\) | 1.38023e12 | 0.174445 | ||||||||
\(736\) | 1.29075e13 | − | 3.41523e12i | 1.62141 | − | 0.429013i | ||||
\(737\) | −8.67145e12 | −1.08265 | ||||||||
\(738\) | −1.80063e12 | − | 1.17095e12i | −0.223445 | − | 0.145306i | ||||
\(739\) | 7.18973e12i | 0.886773i | 0.896330 | + | 0.443387i | \(0.146223\pi\) | ||||
−0.896330 | + | 0.443387i | \(0.853777\pi\) | |||||||
\(740\) | 6.39551e11 | + | 1.44132e12i | 0.0784030 | + | 0.176692i | ||||
\(741\) | 6.86912e12i | 0.836988i | ||||||||
\(742\) | −3.88582e11 | + | 5.97544e11i | −0.0470615 | + | 0.0723689i | ||||
\(743\) | 4.60214e12 | 0.554001 | 0.277000 | − | 0.960870i | \(-0.410660\pi\) | ||||
0.277000 | + | 0.960870i | \(0.410660\pi\) | |||||||
\(744\) | 2.14109e12 | + | 3.43245e11i | 0.256187 | + | 0.0410702i | ||||
\(745\) | 2.15195e12 | 0.255934 | ||||||||
\(746\) | −2.15510e12 | + | 3.31401e12i | −0.254767 | + | 0.391768i | ||||
\(747\) | 7.70753e12i | 0.905676i | ||||||||
\(748\) | 7.89059e12 | − | 3.50127e12i | 0.921620 | − | 0.408948i | ||||
\(749\) | − | 1.26553e11i | − | 0.0146928i | ||||||
\(750\) | −2.37303e12 | − | 1.54318e12i | −0.273859 | − | 0.178091i | ||||
\(751\) | 1.53501e13 | 1.76089 | 0.880446 | − | 0.474147i | \(-0.157244\pi\) | ||||
0.880446 | + | 0.474147i | \(0.157244\pi\) | |||||||
\(752\) | −2.43361e12 | + | 2.68920e12i | −0.277505 | + | 0.306650i | ||||
\(753\) | 1.25145e12 | 0.141852 | ||||||||
\(754\) | −4.94322e12 | − | 3.21457e12i | −0.556979 | − | 0.362203i | ||||
\(755\) | 5.30029e12i | 0.593661i | ||||||||
\(756\) | −3.30637e11 | + | 1.46713e11i | −0.0368132 | + | 0.0163350i | ||||
\(757\) | 1.45554e13i | 1.61099i | 0.592604 | + | 0.805494i | \(0.298100\pi\) | ||||
−0.592604 | + | 0.805494i | \(0.701900\pi\) | |||||||
\(758\) | −5.73258e12 | + | 8.81529e12i | −0.630723 | + | 0.969897i | ||||
\(759\) | −8.40767e12 | −0.919576 | ||||||||
\(760\) | 5.89530e11 | − | 3.67736e12i | 0.0640980 | − | 0.399830i | ||||
\(761\) | −9.75697e12 | −1.05459 | −0.527295 | − | 0.849682i | \(-0.676794\pi\) | ||||
−0.527295 | + | 0.849682i | \(0.676794\pi\) | |||||||
\(762\) | 1.43280e12 | − | 2.20329e12i | 0.153953 | − | 0.236742i | ||||
\(763\) | 1.09062e11i | 0.0116497i | ||||||||
\(764\) | −4.17881e12 | − | 9.41752e12i | −0.443744 | − | 1.00004i | ||||
\(765\) | 2.33791e12i | 0.246803i | ||||||||
\(766\) | 1.05862e13 | + | 6.88419e12i | 1.11099 | + | 0.722476i | ||||
\(767\) | 6.18976e12 | 0.645794 | ||||||||
\(768\) | 4.62453e12 | − | 4.62618e11i | 0.479669 | − | 0.0479841i | ||||
\(769\) | −7.29745e12 | −0.752494 | −0.376247 | − | 0.926519i | \(-0.622786\pi\) | ||||
−0.376247 | + | 0.926519i | \(0.622786\pi\) | |||||||
\(770\) | 1.59435e11 | + | 1.03680e11i | 0.0163446 | + | 0.0106289i | ||||
\(771\) | 3.62545e11i | 0.0369502i | ||||||||
\(772\) | −3.97723e12 | − | 8.96323e12i | −0.402997 | − | 0.908210i | ||||
\(773\) | − | 4.86326e12i | − | 0.489914i | −0.969534 | − | 0.244957i | \(-0.921226\pi\) | ||
0.969534 | − | 0.244957i | \(-0.0787739\pi\) | |||||||
\(774\) | 5.15865e12 | − | 7.93273e12i | 0.516656 | − | 0.794490i | ||||
\(775\) | −4.69431e12 | −0.467428 | ||||||||
\(776\) | 7.49282e11 | − | 4.67386e12i | 0.0741767 | − | 0.462699i | ||||
\(777\) | 1.23384e11 | 0.0121441 | ||||||||
\(778\) | −4.15717e12 | + | 6.39270e12i | −0.406808 | + | 0.625570i | ||||
\(779\) | − | 3.98467e12i | − | 0.387680i | ||||||
\(780\) | −2.56910e12 | + | 1.13998e12i | −0.248516 | + | 0.110273i | ||||
\(781\) | 8.56084e12i | 0.823354i | ||||||||
\(782\) | −1.30351e13 | − | 8.47674e12i | −1.24648 | − | 0.810584i | ||||
\(783\) | 3.82904e12 | 0.364051 | ||||||||
\(784\) | 7.08220e12 | − | 7.82603e12i | 0.669493 | − | 0.739808i | ||||
\(785\) | 3.62441e12 | 0.340662 | ||||||||
\(786\) | −7.95079e12 | − | 5.17039e12i | −0.743034 | − | 0.483195i | ||||
\(787\) | − | 9.38334e12i | − | 0.871909i | −0.899969 | − | 0.435955i | \(-0.856411\pi\) | ||
0.899969 | − | 0.435955i | \(-0.143589\pi\) | |||||||
\(788\) | 1.10189e13 | − | 4.88940e12i | 1.01806 | − | 0.451739i | ||||
\(789\) | 3.69307e12i | 0.339267i | ||||||||
\(790\) | 1.44474e12 | − | 2.22166e12i | 0.131968 | − | 0.202934i | ||||
\(791\) | −2.09428e11 | −0.0190213 | ||||||||
\(792\) | 9.54537e12 | + | 1.53025e12i | 0.862044 | + | 0.138197i | ||||
\(793\) | −1.76793e13 | −1.58758 | ||||||||
\(794\) | 1.87861e12 | − | 2.88884e12i | 0.167743 | − | 0.257948i | ||||
\(795\) | − | 3.59649e12i | − | 0.319320i | ||||||
\(796\) | 5.96916e12 | + | 1.34523e13i | 0.526993 | + | 1.18765i | ||||
\(797\) | − | 1.36323e13i | − | 1.19675i | −0.801214 | − | 0.598377i | \(-0.795812\pi\) | ||
0.801214 | − | 0.598377i | \(-0.204188\pi\) | |||||||
\(798\) | −2.44305e11 | − | 1.58871e11i | −0.0213265 | − | 0.0138686i | ||||
\(799\) | 4.22374e12 | 0.366637 | ||||||||
\(800\) | −9.72663e12 | + | 2.57359e12i | −0.839571 | + | 0.222144i | ||||
\(801\) | −5.91840e12 | −0.507993 | ||||||||
\(802\) | 4.61583e12 | + | 3.00167e12i | 0.393972 | + | 0.256200i | ||||
\(803\) | − | 1.47589e13i | − | 1.25266i | ||||||
\(804\) | 2.20514e12 | + | 4.96959e12i | 0.186116 | + | 0.419438i | ||||
\(805\) | − | 3.42557e11i | − | 0.0287509i | ||||||
\(806\) | −5.46705e12 | + | 8.40697e12i | −0.456294 | + | 0.701668i | ||||
\(807\) | −2.71168e11 | −0.0225065 | ||||||||
\(808\) | −1.09037e13 | − | 1.74801e12i | −0.899961 | − | 0.144276i | ||||
\(809\) | 1.51196e13 | 1.24100 | 0.620500 | − | 0.784207i | \(-0.286930\pi\) | ||||
0.620500 | + | 0.784207i | \(0.286930\pi\) | |||||||
\(810\) | −8.64405e11 | + | 1.32924e12i | −0.0705561 | + | 0.108498i | ||||
\(811\) | 2.17527e13i | 1.76571i | 0.469647 | + | 0.882855i | \(0.344381\pi\) | ||||
−0.469647 | + | 0.882855i | \(0.655619\pi\) | |||||||
\(812\) | 2.28657e11 | − | 1.01461e11i | 0.0184579 | − | 0.00819027i | ||||
\(813\) | 5.57113e12i | 0.447235i | ||||||||
\(814\) | −6.36562e12 | − | 4.13956e12i | −0.508196 | − | 0.330479i | ||||
\(815\) | 5.33251e12 | 0.423373 | ||||||||
\(816\) | −4.01313e12 | − | 3.63171e12i | −0.316868 | − | 0.286751i | ||||
\(817\) | 1.75546e13 | 1.37845 | ||||||||
\(818\) | 1.71869e13 | + | 1.11766e13i | 1.34217 | + | 0.872813i | ||||
\(819\) | − | 7.26465e11i | − | 0.0564205i | ||||||
\(820\) | 1.49029e12 | − | 6.61283e11i | 0.115109 | − | 0.0510769i | ||||
\(821\) | − | 4.58104e12i | − | 0.351900i | −0.984399 | − | 0.175950i | \(-0.943700\pi\) | ||
0.984399 | − | 0.175950i | \(-0.0562998\pi\) | |||||||
\(822\) | −1.84316e12 | + | 2.83432e12i | −0.140812 | + | 0.216534i | ||||
\(823\) | −9.64364e12 | −0.732727 | −0.366363 | − | 0.930472i | \(-0.619397\pi\) | ||||
−0.366363 | + | 0.930472i | \(0.619397\pi\) | |||||||
\(824\) | −3.24269e12 | + | 2.02272e13i | −0.245037 | + | 1.52849i | ||||
\(825\) | 6.33570e12 | 0.476159 | ||||||||
\(826\) | −1.43159e11 | + | 2.20143e11i | −0.0107006 | + | 0.0164549i | ||||
\(827\) | − | 1.45819e13i | − | 1.08403i | −0.840370 | − | 0.542014i | \(-0.817662\pi\) | ||
0.840370 | − | 0.542014i | \(-0.182338\pi\) | |||||||
\(828\) | −7.06244e12 | − | 1.59162e13i | −0.522178 | − | 1.17680i | ||||
\(829\) | − | 2.95768e12i | − | 0.217498i | −0.994069 | − | 0.108749i | \(-0.965315\pi\) | ||
0.994069 | − | 0.108749i | \(-0.0346845\pi\) | |||||||
\(830\) | −4.90478e12 | − | 3.18958e12i | −0.358731 | − | 0.233282i | ||||
\(831\) | 6.15602e12 | 0.447812 | ||||||||
\(832\) | −6.71873e12 | + | 2.04165e13i | −0.486108 | + | 1.47715i | ||||
\(833\) | −1.22918e13 | −0.884529 | ||||||||
\(834\) | −1.68847e12 | − | 1.09801e12i | −0.120850 | − | 0.0785887i | ||||
\(835\) | 7.09563e12i | 0.505129i | ||||||||
\(836\) | 7.27401e12 | + | 1.63930e13i | 0.515046 | + | 1.16073i | ||||
\(837\) | − | 6.51208e12i | − | 0.458622i | ||||||
\(838\) | 6.01358e11 | − | 9.24740e11i | 0.0421245 | − | 0.0647771i | ||||
\(839\) | −1.55381e13 | −1.08260 | −0.541302 | − | 0.840828i | \(-0.682069\pi\) | ||||
−0.541302 | + | 0.840828i | \(0.682069\pi\) | |||||||
\(840\) | 1.88749e10 | − | 1.17738e11i | 0.00130806 | − | 0.00815940i | ||||
\(841\) | 1.18591e13 | 0.817467 | ||||||||
\(842\) | 1.49713e12 | − | 2.30222e12i | 0.102649 | − | 0.157849i | ||||
\(843\) | − | 3.72547e10i | − | 0.00254072i | ||||||
\(844\) | −6.17127e12 | + | 2.73836e12i | −0.418633 | + | 0.185759i | ||||
\(845\) | − | 7.62332e12i | − | 0.514386i | ||||||
\(846\) | 3.96532e12 | + | 2.57864e12i | 0.266141 | + | 0.173071i | ||||
\(847\) | −2.07845e11 | −0.0138760 | ||||||||
\(848\) | −2.03925e13 | − | 1.84543e13i | −1.35422 | − | 1.22551i | ||||
\(849\) | 8.79095e12 | 0.580699 | ||||||||
\(850\) | 9.82277e12 | + | 6.38774e12i | 0.645430 | + | 0.419723i | ||||
\(851\) | 1.36770e13i | 0.893937i | ||||||||
\(852\) | 4.90619e12 | − | 2.17701e12i | 0.318982 | − | 0.141541i | ||||
\(853\) | − | 6.54122e12i | − | 0.423046i | −0.977373 | − | 0.211523i | \(-0.932158\pi\) | ||
0.977373 | − | 0.211523i | \(-0.0678424\pi\) | |||||||
\(854\) | 4.08892e11 | − | 6.28775e11i | 0.0263056 | − | 0.0404515i | ||||
\(855\) | −4.85709e12 | −0.310834 | ||||||||
\(856\) | 4.82154e12 | + | 7.72955e11i | 0.306940 | + | 0.0492065i | ||||
\(857\) | −2.99560e11 | −0.0189701 | −0.00948507 | − | 0.999955i | \(-0.503019\pi\) | ||||
−0.00948507 | + | 0.999955i | \(0.503019\pi\) | |||||||
\(858\) | 7.37862e12 | − | 1.13465e13i | 0.464818 | − | 0.714775i | ||||
\(859\) | 7.17624e12i | 0.449705i | 0.974393 | + | 0.224853i | \(0.0721900\pi\) | ||||
−0.974393 | + | 0.224853i | \(0.927810\pi\) | |||||||
\(860\) | 2.91331e12 | + | 6.56554e12i | 0.181611 | + | 0.409286i | ||||
\(861\) | − | 1.27576e11i | − | 0.00791145i | ||||||
\(862\) | 9.52607e12 | + | 6.19480e12i | 0.587667 | + | 0.382159i | ||||
\(863\) | 9.47202e12 | 0.581292 | 0.290646 | − | 0.956831i | \(-0.406130\pi\) | ||||
0.290646 | + | 0.956831i | \(0.406130\pi\) | |||||||
\(864\) | −3.57015e12 | − | 1.34930e13i | −0.217959 | − | 0.823755i | ||||
\(865\) | −4.46053e12 | −0.270903 | ||||||||
\(866\) | 9.69296e12 | + | 6.30332e12i | 0.585633 | + | 0.380837i | ||||
\(867\) | − | 1.71715e12i | − | 0.103210i | ||||||
\(868\) | −1.72556e11 | − | 3.88879e11i | −0.0103179 | − | 0.0232528i | ||||
\(869\) | 1.27615e13i | 0.759125i | ||||||||
\(870\) | −6.88119e11 | + | 1.05816e12i | −0.0407218 | + | 0.0626201i | ||||
\(871\) | −2.51436e13 | −1.48029 | ||||||||
\(872\) | −4.15516e12 | − | 6.66126e11i | −0.243368 | − | 0.0390151i | ||||
\(873\) | −6.17328e12 | −0.359709 | ||||||||
\(874\) | 1.76107e13 | − | 2.70810e13i | 1.02088 | − | 1.56987i | ||||
\(875\) | 5.55373e11i | 0.0320294i | ||||||||
\(876\) | −8.45827e12 | + | 3.75316e12i | −0.485303 | + | 0.215342i | ||||
\(877\) | − | 2.10319e13i | − | 1.20055i | −0.799793 | − | 0.600276i | \(-0.795057\pi\) | ||
0.799793 | − | 0.600276i | \(-0.204943\pi\) | |||||||
\(878\) | −2.45958e13 | − | 1.59946e13i | −1.39680 | − | 0.908340i | ||||
\(879\) | −3.34039e12 | −0.188733 | ||||||||
\(880\) | −4.92391e12 | + | 5.44106e12i | −0.276782 | + | 0.305852i | ||||
\(881\) | 2.22921e13 | 1.24669 | 0.623347 | − | 0.781946i | \(-0.285773\pi\) | ||||
0.623347 | + | 0.781946i | \(0.285773\pi\) | |||||||
\(882\) | −1.15397e13 | − | 7.50427e12i | −0.642076 | − | 0.417542i | ||||
\(883\) | 1.92369e13i | 1.06490i | 0.846460 | + | 0.532452i | \(0.178729\pi\) | ||||
−0.846460 | + | 0.532452i | \(0.821271\pi\) | |||||||
\(884\) | 2.28794e13 | − | 1.01522e13i | 1.26011 | − | 0.559146i | ||||
\(885\) | − | 1.32499e12i | − | 0.0726054i | ||||||
\(886\) | 7.43898e12 | − | 1.14393e13i | 0.405566 | − | 0.623661i | ||||
\(887\) | 4.86485e11 | 0.0263884 | 0.0131942 | − | 0.999913i | \(-0.495800\pi\) | ||||
0.0131942 | + | 0.999913i | \(0.495800\pi\) | |||||||
\(888\) | −7.53601e11 | + | 4.70081e12i | −0.0406708 | + | 0.253696i | ||||
\(889\) | −5.15649e11 | −0.0276883 | ||||||||
\(890\) | 2.44919e12 | − | 3.76624e12i | 0.130848 | − | 0.201212i | ||||
\(891\) | − | 7.63534e12i | − | 0.405862i | ||||||
\(892\) | −6.40590e12 | − | 1.44366e13i | −0.338796 | − | 0.763524i | ||||
\(893\) | 8.77498e12i | 0.461758i | ||||||||
\(894\) | 5.44680e12 | + | 3.54205e12i | 0.285182 | + | 0.185454i | ||||
\(895\) | −2.50031e12 | −0.130254 | ||||||||
\(896\) | −5.70733e11 | − | 7.11156e11i | −0.0295833 | − | 0.0368620i | ||||
\(897\) | −2.43787e13 | −1.25732 | ||||||||
\(898\) | −2.76025e12 | − | 1.79499e12i | −0.141646 | − | 0.0921125i | ||||
\(899\) | 4.50352e12i | 0.229950i | ||||||||
\(900\) | 5.32199e12 | + | 1.19938e13i | 0.270385 | + | 0.609350i | ||||
\(901\) | 3.20290e13i | 1.61913i | ||||||||
\(902\) | −4.28022e12 | + | 6.58192e12i | −0.215296 | + | 0.331073i | ||||
\(903\) | 5.62043e11 | 0.0281303 | ||||||||
\(904\) | 1.27914e12 | − | 7.97900e12i | 0.0637030 | − | 0.397366i | ||||
\(905\) | −1.17910e13 | −0.584293 | ||||||||
\(906\) | −8.72414e12 | + | 1.34156e13i | −0.430176 | + | 0.661504i | ||||
\(907\) | − | 2.40911e13i | − | 1.18202i | −0.806665 | − | 0.591009i | \(-0.798730\pi\) | ||
0.806665 | − | 0.591009i | \(-0.201270\pi\) | |||||||
\(908\) | 1.63210e13 | − | 7.24207e12i | 0.796820 | − | 0.353571i | ||||
\(909\) | 1.44017e13i | 0.699644i | ||||||||
\(910\) | 4.62295e11 | + | 3.00630e11i | 0.0223477 | + | 0.0145327i | ||||
\(911\) | 2.02201e13 | 0.972638 | 0.486319 | − | 0.873781i | \(-0.338339\pi\) | ||||
0.486319 | + | 0.873781i | \(0.338339\pi\) | |||||||
\(912\) | 7.54501e12 | − | 8.33743e12i | 0.361146 | − | 0.399076i | ||||
\(913\) | 2.81737e13 | 1.34192 | ||||||||
\(914\) | 7.06705e12 | + | 4.59570e12i | 0.334950 | + | 0.217818i | ||||
\(915\) | 3.78446e12i | 0.178488i | ||||||||
\(916\) | −2.68328e13 | + | 1.19064e13i | −1.25932 | + | 0.558794i | ||||
\(917\) | 1.86077e12i | 0.0869020i | ||||||||
\(918\) | −8.86125e12 | + | 1.36264e13i | −0.411816 | + | 0.633271i | ||||
\(919\) | −1.09691e13 | −0.507283 | −0.253641 | − | 0.967298i | \(-0.581628\pi\) | ||||
−0.253641 | + | 0.967298i | \(0.581628\pi\) | |||||||
\(920\) | 1.30511e13 | + | 2.09226e12i | 0.600622 | + | 0.0962876i | ||||
\(921\) | −2.66681e12 | −0.122131 | ||||||||
\(922\) | −1.98691e13 | + | 3.05538e13i | −0.905503 | + | 1.39244i | ||||
\(923\) | 2.48229e13i | 1.12576i | ||||||||
\(924\) | 2.32891e11 | + | 5.24852e11i | 0.0105106 | + | 0.0236871i | ||||
\(925\) | − | 1.03064e13i | − | 0.462883i | ||||||
\(926\) | 3.56039e12 | + | 2.31532e12i | 0.159129 | + | 0.103481i | ||||
\(927\) | 2.67163e13 | 1.18828 | ||||||||
\(928\) | 2.46899e12 | + | 9.33130e12i | 0.109283 | + | 0.413025i | ||||
\(929\) | −4.28913e13 | −1.88929 | −0.944644 | − | 0.328098i | \(-0.893592\pi\) | ||||
−0.944644 | + | 0.328098i | \(0.893592\pi\) | |||||||
\(930\) | 1.79962e12 | + | 1.17029e12i | 0.0788872 | + | 0.0513003i | ||||
\(931\) | − | 2.55366e13i | − | 1.11401i | ||||||
\(932\) | 5.76640e12 | + | 1.29954e13i | 0.250342 | + | 0.564179i | ||||
\(933\) | − | 9.91952e12i | − | 0.428572i | ||||||
\(934\) | 8.21691e12 | − | 1.26356e13i | 0.353303 | − | 0.543293i | ||||
\(935\) | 8.54588e12 | 0.365683 | ||||||||
\(936\) | 2.76776e13 | + | 4.43708e12i | 1.17866 | + | 0.188954i | ||||
\(937\) | 2.32900e13 | 0.987057 | 0.493528 | − | 0.869730i | \(-0.335707\pi\) | ||||
0.493528 | + | 0.869730i | \(0.335707\pi\) | |||||||
\(938\) | 5.81530e11 | − | 8.94250e11i | 0.0245278 | − | 0.0377178i | ||||
\(939\) | − | 3.04393e12i | − | 0.127773i | ||||||
\(940\) | −3.28190e12 | + | 1.45627e12i | −0.137104 | + | 0.0608367i | ||||
\(941\) | 2.17907e13i | 0.905979i | 0.891516 | + | 0.452990i | \(0.149643\pi\) | ||||
−0.891516 | + | 0.452990i | \(0.850357\pi\) | |||||||
\(942\) | 9.17376e12 | + | 5.96569e12i | 0.379593 | + | 0.246849i | ||||
\(943\) | 1.41417e13 | 0.582370 | ||||||||
\(944\) | −7.51285e12 | − | 6.79879e12i | −0.307915 | − | 0.278649i | ||||
\(945\) | −3.58096e11 | −0.0146068 | ||||||||
\(946\) | −2.89969e13 | − | 1.88567e13i | −1.17718 | − | 0.765517i | ||||
\(947\) | − | 4.13607e13i | − | 1.67114i | −0.549385 | − | 0.835570i | \(-0.685138\pi\) | ||
0.549385 | − | 0.835570i | \(-0.314862\pi\) | |||||||
\(948\) | 7.31359e12 | − | 3.24524e12i | 0.294099 | − | 0.130500i | ||||
\(949\) | − | 4.27945e13i | − | 1.71274i | ||||||
\(950\) | −1.32708e13 | + | 2.04072e13i | −0.528616 | + | 0.812881i | ||||
\(951\) | 8.00014e11 | 0.0317165 | ||||||||
\(952\) | −1.68092e11 | + | 1.04853e12i | −0.00663257 | + | 0.0413726i | ||||
\(953\) | −2.25956e13 | −0.887371 | −0.443685 | − | 0.896183i | \(-0.646329\pi\) | ||||
−0.443685 | + | 0.896183i | \(0.646329\pi\) | |||||||
\(954\) | −1.95540e13 | + | 3.00693e13i | −0.764309 | + | 1.17532i | ||||
\(955\) | − | 1.01996e13i | − | 0.396797i | ||||||
\(956\) | −1.46459e13 | − | 3.30066e13i | −0.567096 | − | 1.27803i | ||||
\(957\) | − | 6.07820e12i | − | 0.234245i | ||||||
\(958\) | 9.65636e12 | + | 6.27952e12i | 0.370398 | + | 0.240870i | ||||
\(959\) | 6.63332e11 | 0.0253249 | ||||||||
\(960\) | 4.37040e12 | + | 1.43823e12i | 0.166074 | + | 0.0546522i | ||||
\(961\) | −1.87804e13 | −0.710315 | ||||||||
\(962\) | −1.84576e13 | − | 1.20030e13i | −0.694846 | − | 0.451858i | ||||
\(963\) | − | 6.36833e12i | − | 0.238620i | ||||||
\(964\) | −1.30220e13 | − | 2.93468e13i | −0.485658 | − | 1.09450i | ||||
\(965\) | − | 9.70760e12i | − | 0.360362i | ||||||
\(966\) | 5.63840e11 | − | 8.67047e11i | 0.0208333 | − | 0.0320365i | ||||
\(967\) | 1.40461e13 | 0.516581 | 0.258290 | − | 0.966067i | \(-0.416841\pi\) | ||||
0.258290 | + | 0.966067i | \(0.416841\pi\) | |||||||
\(968\) | 1.26947e12 | − | 7.91870e12i | 0.0464712 | − | 0.289878i | ||||
\(969\) | −1.30950e13 | −0.477143 | ||||||||
\(970\) | 2.55466e12 | − | 3.92844e12i | 0.0926533 | − | 0.142478i | ||||
\(971\) | 8.14483e12i | 0.294032i | 0.989134 | + | 0.147016i | \(0.0469670\pi\) | ||||
−0.989134 | + | 0.147016i | \(0.953033\pi\) | |||||||
\(972\) | −2.60510e13 | + | 1.15595e13i | −0.936107 | + | 0.415376i | ||||
\(973\) | 3.95163e11i | 0.0141341i | ||||||||
\(974\) | −8.43708e12 | − | 5.48663e12i | −0.300384 | − | 0.195339i | ||||
\(975\) | 1.83709e13 | 0.651043 | ||||||||
\(976\) | 2.14583e13 | + | 1.94188e13i | 0.756956 | + | 0.685012i | ||||
\(977\) | 3.05508e13 | 1.07275 | 0.536373 | − | 0.843981i | \(-0.319794\pi\) | ||||
0.536373 | + | 0.843981i | \(0.319794\pi\) | |||||||
\(978\) | 1.34971e13 | + | 8.77718e12i | 0.471755 | + | 0.306782i | ||||
\(979\) | 2.16338e13i | 0.752681i | ||||||||
\(980\) | 9.55087e12 | − | 4.23798e12i | 0.330770 | − | 0.146771i | ||||
\(981\) | 5.48817e12i | 0.189198i | ||||||||
\(982\) | 1.69401e13 | − | 2.60497e13i | 0.581319 | − | 0.893925i | ||||
\(983\) | −1.56015e12 | −0.0532935 | −0.0266468 | − | 0.999645i | \(-0.508483\pi\) | ||||
−0.0266468 | + | 0.999645i | \(0.508483\pi\) | |||||||
\(984\) | 4.86054e12 | + | 7.79208e11i | 0.165275 | + | 0.0264957i | ||||
\(985\) | 1.19340e13 | 0.403946 | ||||||||
\(986\) | 6.12812e12 | − | 9.42354e12i | 0.206482 | − | 0.317518i | ||||
\(987\) | 2.80947e11i | 0.00942318i | ||||||||
\(988\) | 2.10916e13 | + | 4.75328e13i | 0.704212 | + | 1.58704i | ||||
\(989\) | 6.23018e13i | 2.07070i | ||||||||
\(990\) | 8.02301e12 | + | 5.21736e12i | 0.265448 | + | 0.172620i | ||||
\(991\) | −4.93667e13 | −1.62593 | −0.812967 | − | 0.582310i | \(-0.802149\pi\) | ||||
−0.812967 | + | 0.582310i | \(0.802149\pi\) | |||||||
\(992\) | 1.58698e13 | − | 4.19903e12i | 0.520319 | − | 0.137672i | ||||
\(993\) | 1.44661e13 | 0.472151 | ||||||||
\(994\) | −8.82842e11 | − | 5.74112e11i | −0.0286843 | − | 0.0186534i | ||||
\(995\) | 1.45695e13i | 0.471239i | ||||||||
\(996\) | −7.16455e12 | − | 1.61463e13i | −0.230686 | − | 0.519883i | ||||
\(997\) | − | 1.32312e13i | − | 0.424102i | −0.977259 | − | 0.212051i | \(-0.931986\pi\) | ||
0.977259 | − | 0.212051i | \(-0.0680142\pi\) | |||||||
\(998\) | 9.38136e12 | − | 1.44262e13i | 0.299349 | − | 0.460325i | ||||
\(999\) | 1.42974e13 | 0.454163 |
(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 | 8.10.b.a.5.8 | yes | 8 | |
3.2 | odd | 2 | 72.10.d.b.37.1 | 8 | |||
4.3 | odd | 2 | 32.10.b.a.17.4 | 8 | |||
8.3 | odd | 2 | 32.10.b.a.17.5 | 8 | |||
8.5 | even | 2 | inner | 8.10.b.a.5.7 | ✓ | 8 | |
12.11 | even | 2 | 288.10.d.b.145.3 | 8 | |||
16.3 | odd | 4 | 256.10.a.s.1.5 | 8 | |||
16.5 | even | 4 | 256.10.a.p.1.5 | 8 | |||
16.11 | odd | 4 | 256.10.a.s.1.4 | 8 | |||
16.13 | even | 4 | 256.10.a.p.1.4 | 8 | |||
24.5 | odd | 2 | 72.10.d.b.37.2 | 8 | |||
24.11 | even | 2 | 288.10.d.b.145.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.10.b.a.5.7 | ✓ | 8 | 8.5 | even | 2 | inner | |
8.10.b.a.5.8 | yes | 8 | 1.1 | even | 1 | trivial | |
32.10.b.a.17.4 | 8 | 4.3 | odd | 2 | |||
32.10.b.a.17.5 | 8 | 8.3 | odd | 2 | |||
72.10.d.b.37.1 | 8 | 3.2 | odd | 2 | |||
72.10.d.b.37.2 | 8 | 24.5 | odd | 2 | |||
256.10.a.p.1.4 | 8 | 16.13 | even | 4 | |||
256.10.a.p.1.5 | 8 | 16.5 | even | 4 | |||
256.10.a.s.1.4 | 8 | 16.11 | odd | 4 | |||
256.10.a.s.1.5 | 8 | 16.3 | odd | 4 | |||
288.10.d.b.145.3 | 8 | 12.11 | even | 2 | |||
288.10.d.b.145.6 | 8 | 24.11 | even | 2 |