Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,22,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(58.6902423003\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.8 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.22.c.b.20.7 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 367.125i | 0.253512i | 0.991934 | + | 0.126756i | \(0.0404565\pi\) | ||||
−0.991934 | + | 0.126756i | \(0.959543\pi\) | |||||||
\(3\) | −91325.3 | + | 46043.9i | −0.892931 | + | 0.450193i | ||||
\(4\) | 1.96237e6 | 0.935732 | ||||||||
\(5\) | −3.23352e7 | −1.48078 | −0.740391 | − | 0.672177i | \(-0.765359\pi\) | ||||
−0.740391 | + | 0.672177i | \(0.765359\pi\) | |||||||
\(6\) | −1.69039e7 | − | 3.35278e7i | −0.114129 | − | 0.226369i | ||||
\(7\) | −4.79207e8 | + | 5.73504e8i | −0.641200 | + | 0.767374i | ||||
\(8\) | 1.49035e9i | 0.490731i | ||||||||
\(9\) | 6.22027e9 | − | 8.40995e9i | 0.594652 | − | 0.803983i | ||||
\(10\) | − | 1.18711e10i | − | 0.375396i | ||||||
\(11\) | 1.31196e11i | 1.52510i | 0.646932 | + | 0.762548i | \(0.276052\pi\) | ||||
−0.646932 | + | 0.762548i | \(0.723948\pi\) | |||||||
\(12\) | −1.79214e11 | + | 9.03553e10i | −0.835544 | + | 0.421260i | ||||
\(13\) | 6.69122e11i | 1.34617i | 0.739565 | + | 0.673085i | \(0.235031\pi\) | ||||
−0.739565 | + | 0.673085i | \(0.764969\pi\) | |||||||
\(14\) | −2.10547e11 | − | 1.75929e11i | −0.194538 | − | 0.162552i | ||||
\(15\) | 2.95302e12 | − | 1.48884e12i | 1.32224 | − | 0.666638i | ||||
\(16\) | 3.56825e12 | 0.811325 | ||||||||
\(17\) | −9.54655e12 | −1.14850 | −0.574252 | − | 0.818679i | \(-0.694707\pi\) | ||||
−0.574252 | + | 0.818679i | \(0.694707\pi\) | |||||||
\(18\) | 3.08750e12 | + | 2.28361e12i | 0.203819 | + | 0.150751i | ||||
\(19\) | 1.11389e13i | 0.416803i | 0.978043 | + | 0.208402i | \(0.0668261\pi\) | ||||
−0.978043 | + | 0.208402i | \(0.933174\pi\) | |||||||
\(20\) | −6.34537e13 | −1.38561 | ||||||||
\(21\) | 1.73574e13 | − | 7.44400e13i | 0.227081 | − | 0.973876i | ||||
\(22\) | −4.81652e13 | −0.386630 | ||||||||
\(23\) | 2.12594e14i | 1.07006i | 0.844832 | + | 0.535031i | \(0.179700\pi\) | ||||
−0.844832 | + | 0.535031i | \(0.820300\pi\) | |||||||
\(24\) | −6.86216e13 | − | 1.36107e14i | −0.220924 | − | 0.438189i | ||||
\(25\) | 5.68730e14 | 1.19271 | ||||||||
\(26\) | −2.45651e14 | −0.341270 | ||||||||
\(27\) | −1.80841e14 | + | 1.05445e15i | −0.169035 | + | 0.985610i | ||||
\(28\) | −9.40382e14 | + | 1.12543e15i | −0.599991 | + | 0.718056i | ||||
\(29\) | 1.26875e15i | 0.560012i | 0.959998 | + | 0.280006i | \(0.0903365\pi\) | ||||
−0.959998 | + | 0.280006i | \(0.909663\pi\) | |||||||
\(30\) | 5.46590e14 | + | 1.08413e15i | 0.169001 | + | 0.335203i | ||||
\(31\) | 5.66433e15i | 1.24123i | 0.784117 | + | 0.620613i | \(0.213116\pi\) | ||||
−0.784117 | + | 0.620613i | \(0.786884\pi\) | |||||||
\(32\) | 4.43548e15i | 0.696412i | ||||||||
\(33\) | −6.04077e15 | − | 1.19815e16i | −0.686588 | − | 1.36180i | ||||
\(34\) | − | 3.50477e15i | − | 0.291160i | ||||||
\(35\) | 1.54953e16 | − | 1.85444e16i | 0.949477 | − | 1.13631i | ||||
\(36\) | 1.22065e16 | − | 1.65034e16i | 0.556435 | − | 0.752313i | ||||
\(37\) | −4.08103e16 | −1.39525 | −0.697624 | − | 0.716464i | \(-0.745759\pi\) | ||||
−0.697624 | + | 0.716464i | \(0.745759\pi\) | |||||||
\(38\) | −4.08938e15 | −0.105665 | ||||||||
\(39\) | −3.08090e16 | − | 6.11077e16i | −0.606037 | − | 1.20204i | ||||
\(40\) | − | 4.81909e16i | − | 0.726666i | ||||||
\(41\) | 2.27791e16 | 0.265036 | 0.132518 | − | 0.991181i | \(-0.457694\pi\) | ||||
0.132518 | + | 0.991181i | \(0.457694\pi\) | |||||||
\(42\) | 2.73288e16 | + | 6.37231e15i | 0.246889 | + | 0.0575678i | ||||
\(43\) | 1.15256e17 | 0.813292 | 0.406646 | − | 0.913586i | \(-0.366698\pi\) | ||||
0.406646 | + | 0.913586i | \(0.366698\pi\) | |||||||
\(44\) | 2.57455e17i | 1.42708i | ||||||||
\(45\) | −2.01134e17 | + | 2.71938e17i | −0.880549 | + | 1.19052i | ||||
\(46\) | −7.80486e16 | −0.271274 | ||||||||
\(47\) | 1.81071e17 | 0.502136 | 0.251068 | − | 0.967969i | \(-0.419218\pi\) | ||||
0.251068 | + | 0.967969i | \(0.419218\pi\) | |||||||
\(48\) | −3.25871e17 | + | 1.64296e17i | −0.724458 | + | 0.365253i | ||||
\(49\) | −9.92673e16 | − | 5.49654e17i | −0.177725 | − | 0.984080i | ||||
\(50\) | 2.08795e17i | 0.302367i | ||||||||
\(51\) | 8.71841e17 | − | 4.39560e17i | 1.02554 | − | 0.517049i | ||||
\(52\) | 1.31307e18i | 1.25965i | ||||||||
\(53\) | − | 7.35468e17i | − | 0.577653i | −0.957381 | − | 0.288826i | \(-0.906735\pi\) | ||
0.957381 | − | 0.288826i | \(-0.0932650\pi\) | |||||||
\(54\) | −3.87113e17 | − | 6.63911e16i | −0.249864 | − | 0.0428524i | ||||
\(55\) | − | 4.24225e18i | − | 2.25833i | ||||||
\(56\) | −8.54722e17 | − | 7.14187e17i | −0.376574 | − | 0.314657i | ||||
\(57\) | −5.12881e17 | − | 1.01727e18i | −0.187642 | − | 0.372177i | ||||
\(58\) | −4.65790e17 | −0.141970 | ||||||||
\(59\) | −2.94154e18 | −0.749254 | −0.374627 | − | 0.927176i | \(-0.622229\pi\) | ||||
−0.374627 | + | 0.927176i | \(0.622229\pi\) | |||||||
\(60\) | 5.79493e18 | − | 2.92166e18i | 1.23726 | − | 0.623794i | ||||
\(61\) | − | 1.08357e18i | − | 0.194488i | −0.995261 | − | 0.0972441i | \(-0.968997\pi\) | ||
0.995261 | − | 0.0972441i | \(-0.0310028\pi\) | |||||||
\(62\) | −2.07951e18 | −0.314666 | ||||||||
\(63\) | 1.84234e18 | + | 7.59745e18i | 0.235665 | + | 0.971834i | ||||
\(64\) | 5.85478e18 | 0.634776 | ||||||||
\(65\) | − | 2.16362e19i | − | 1.99338i | ||||||
\(66\) | 4.39870e18 | − | 2.21772e18i | 0.345234 | − | 0.174058i | ||||
\(67\) | −6.78306e18 | −0.454611 | −0.227306 | − | 0.973823i | \(-0.572992\pi\) | ||||
−0.227306 | + | 0.973823i | \(0.572992\pi\) | |||||||
\(68\) | −1.87339e19 | −1.07469 | ||||||||
\(69\) | −9.78867e18 | − | 1.94152e19i | −0.481735 | − | 0.955492i | ||||
\(70\) | 6.80810e18 | + | 5.68869e18i | 0.288069 | + | 0.240704i | ||||
\(71\) | − | 2.06767e19i | − | 0.753822i | −0.926250 | − | 0.376911i | \(-0.876986\pi\) | ||
0.926250 | − | 0.376911i | \(-0.123014\pi\) | |||||||
\(72\) | 1.25338e19 | + | 9.27038e18i | 0.394540 | + | 0.291814i | ||||
\(73\) | − | 4.03443e19i | − | 1.09873i | −0.835582 | − | 0.549366i | \(-0.814869\pi\) | ||
0.835582 | − | 0.549366i | \(-0.185131\pi\) | |||||||
\(74\) | − | 1.49825e19i | − | 0.353712i | ||||||
\(75\) | −5.19394e19 | + | 2.61866e19i | −1.06501 | + | 0.536952i | ||||
\(76\) | 2.18587e19i | 0.390016i | ||||||||
\(77\) | −7.52413e19 | − | 6.28700e19i | −1.17032 | − | 0.977891i | ||||
\(78\) | 2.24342e19 | − | 1.13107e19i | 0.304731 | − | 0.153638i | ||||
\(79\) | 9.41640e19 | 1.11892 | 0.559462 | − | 0.828856i | \(-0.311008\pi\) | ||||
0.559462 | + | 0.828856i | \(0.311008\pi\) | |||||||
\(80\) | −1.15380e20 | −1.20140 | ||||||||
\(81\) | −3.20355e19 | − | 1.04624e20i | −0.292778 | − | 0.956180i | ||||
\(82\) | 8.36275e18i | 0.0671899i | ||||||||
\(83\) | −2.74031e19 | −0.193856 | −0.0969281 | − | 0.995291i | \(-0.530902\pi\) | ||||
−0.0969281 | + | 0.995291i | \(0.530902\pi\) | |||||||
\(84\) | 3.40616e19 | − | 1.46079e20i | 0.212487 | − | 0.911286i | ||||
\(85\) | 3.08690e20 | 1.70068 | ||||||||
\(86\) | 4.23135e19i | 0.206179i | ||||||||
\(87\) | −5.84183e19 | − | 1.15869e20i | −0.252114 | − | 0.500052i | ||||
\(88\) | −1.95528e20 | −0.748412 | ||||||||
\(89\) | 4.43565e20 | 1.50786 | 0.753932 | − | 0.656953i | \(-0.228155\pi\) | ||||
0.753932 | + | 0.656953i | \(0.228155\pi\) | |||||||
\(90\) | −9.98350e19 | − | 7.38412e19i | −0.301812 | − | 0.223230i | ||||
\(91\) | −3.83744e20 | − | 3.20648e20i | −1.03302 | − | 0.863165i | ||||
\(92\) | 4.17189e20i | 1.00129i | ||||||||
\(93\) | −2.60808e20 | − | 5.17296e20i | −0.558791 | − | 1.10833i | ||||
\(94\) | 6.64757e19i | 0.127298i | ||||||||
\(95\) | − | 3.60180e20i | − | 0.617195i | ||||||
\(96\) | −2.04227e20 | − | 4.05072e20i | −0.313520 | − | 0.621848i | ||||
\(97\) | 8.62831e20i | 1.18802i | 0.804459 | + | 0.594008i | \(0.202455\pi\) | ||||
−0.804459 | + | 0.594008i | \(0.797545\pi\) | |||||||
\(98\) | 2.01792e20 | − | 3.64435e19i | 0.249476 | − | 0.0450553i | ||||
\(99\) | 1.10335e21 | + | 8.16073e20i | 1.22615 | + | 0.906901i | ||||
\(100\) | 1.11606e21 | 1.11606 | ||||||||
\(101\) | −5.09810e20 | −0.459234 | −0.229617 | − | 0.973281i | \(-0.573747\pi\) | ||||
−0.229617 | + | 0.973281i | \(0.573747\pi\) | |||||||
\(102\) | 1.61373e20 | + | 3.20074e20i | 0.131078 | + | 0.259985i | ||||
\(103\) | − | 1.30498e20i | − | 0.0956782i | −0.998855 | − | 0.0478391i | \(-0.984767\pi\) | ||
0.998855 | − | 0.0478391i | \(-0.0152335\pi\) | |||||||
\(104\) | −9.97226e20 | −0.660608 | ||||||||
\(105\) | −5.61254e20 | + | 2.40703e21i | −0.336257 | + | 1.44210i | ||||
\(106\) | 2.70008e20 | 0.146442 | ||||||||
\(107\) | 2.46662e21i | 1.21220i | 0.795390 | + | 0.606098i | \(0.207266\pi\) | ||||
−0.795390 | + | 0.606098i | \(0.792734\pi\) | |||||||
\(108\) | −3.54877e20 | + | 2.06922e21i | −0.158172 | + | 0.922266i | ||||
\(109\) | −4.07891e21 | −1.65031 | −0.825155 | − | 0.564907i | \(-0.808912\pi\) | ||||
−0.825155 | + | 0.564907i | \(0.808912\pi\) | |||||||
\(110\) | 1.55743e21 | 0.572514 | ||||||||
\(111\) | 3.72701e21 | − | 1.87906e21i | 1.24586 | − | 0.628131i | ||||
\(112\) | −1.70993e21 | + | 2.04640e21i | −0.520222 | + | 0.622590i | ||||
\(113\) | 1.83094e21i | 0.507401i | 0.967283 | + | 0.253701i | \(0.0816478\pi\) | ||||
−0.967283 | + | 0.253701i | \(0.918352\pi\) | |||||||
\(114\) | 3.73464e20 | − | 1.88291e20i | 0.0943513 | − | 0.0475695i | ||||
\(115\) | − | 6.87428e21i | − | 1.58453i | ||||||
\(116\) | 2.48976e21i | 0.524021i | ||||||||
\(117\) | 5.62728e21 | + | 4.16212e21i | 1.08230 | + | 0.800503i | ||||
\(118\) | − | 1.07991e21i | − | 0.189945i | ||||||
\(119\) | 4.57477e21 | − | 5.47498e21i | 0.736421 | − | 0.881332i | ||||
\(120\) | 2.21890e21 | + | 4.40104e21i | 0.327140 | + | 0.648862i | ||||
\(121\) | −9.81210e21 | −1.32591 | ||||||||
\(122\) | 3.97805e20 | 0.0493051 | ||||||||
\(123\) | −2.08030e21 | + | 1.04884e21i | −0.236659 | + | 0.119318i | ||||
\(124\) | 1.11155e22i | 1.16145i | ||||||||
\(125\) | −2.97138e21 | −0.285366 | ||||||||
\(126\) | −2.78921e21 | + | 6.76369e20i | −0.246372 | + | 0.0597438i | ||||
\(127\) | 1.75513e22 | 1.42683 | 0.713413 | − | 0.700744i | \(-0.247148\pi\) | ||||
0.713413 | + | 0.700744i | \(0.247148\pi\) | |||||||
\(128\) | 1.14513e22i | 0.857336i | ||||||||
\(129\) | −1.05258e22 | + | 5.30686e21i | −0.726213 | + | 0.366139i | ||||
\(130\) | 7.94319e21 | 0.505347 | ||||||||
\(131\) | 3.21780e21 | 0.188891 | 0.0944453 | − | 0.995530i | \(-0.469892\pi\) | ||||
0.0944453 | + | 0.995530i | \(0.469892\pi\) | |||||||
\(132\) | −1.18542e22 | − | 2.35122e22i | −0.642462 | − | 1.27428i | ||||
\(133\) | −6.38823e21 | − | 5.33786e21i | −0.319844 | − | 0.267254i | ||||
\(134\) | − | 2.49023e21i | − | 0.115249i | ||||||
\(135\) | 5.84753e21 | − | 3.40958e22i | 0.250304 | − | 1.45947i | ||||
\(136\) | − | 1.42277e22i | − | 0.563607i | ||||||
\(137\) | 3.65830e22i | 1.34188i | 0.741512 | + | 0.670940i | \(0.234109\pi\) | ||||
−0.741512 | + | 0.670940i | \(0.765891\pi\) | |||||||
\(138\) | 7.12781e21 | − | 3.59366e21i | 0.242229 | − | 0.122126i | ||||
\(139\) | 4.00599e22i | 1.26198i | 0.775789 | + | 0.630992i | \(0.217352\pi\) | ||||
−0.775789 | + | 0.630992i | \(0.782648\pi\) | |||||||
\(140\) | 3.04075e22 | − | 3.63910e22i | 0.888456 | − | 1.06328i | ||||
\(141\) | −1.65364e22 | + | 8.33722e21i | −0.448373 | + | 0.226058i | ||||
\(142\) | 7.59093e21 | 0.191103 | ||||||||
\(143\) | −8.77860e22 | −2.05304 | ||||||||
\(144\) | 2.21955e22 | − | 3.00088e22i | 0.482456 | − | 0.652292i | ||||
\(145\) | − | 4.10254e22i | − | 0.829256i | ||||||
\(146\) | 1.48114e22 | 0.278542 | ||||||||
\(147\) | 3.43738e22 | + | 4.56267e22i | 0.601722 | + | 0.798705i | ||||
\(148\) | −8.00849e22 | −1.30558 | ||||||||
\(149\) | − | 5.70779e22i | − | 0.866986i | −0.901157 | − | 0.433493i | \(-0.857281\pi\) | ||
0.901157 | − | 0.433493i | \(-0.142719\pi\) | |||||||
\(150\) | −9.61373e21 | − | 1.90683e22i | −0.136124 | − | 0.269993i | ||||
\(151\) | 1.37183e23 | 1.81151 | 0.905755 | − | 0.423801i | \(-0.139304\pi\) | ||||
0.905755 | + | 0.423801i | \(0.139304\pi\) | |||||||
\(152\) | −1.66009e22 | −0.204538 | ||||||||
\(153\) | −5.93821e22 | + | 8.02860e22i | −0.682960 | + | 0.923378i | ||||
\(154\) | 2.30811e22 | − | 2.76229e22i | 0.247907 | − | 0.296690i | ||||
\(155\) | − | 1.83157e23i | − | 1.83798i | ||||||
\(156\) | −6.04587e22 | − | 1.19916e23i | −0.567088 | − | 1.12478i | ||||
\(157\) | − | 8.48354e22i | − | 0.744099i | −0.928213 | − | 0.372050i | \(-0.878655\pi\) | ||
0.928213 | − | 0.372050i | \(-0.121345\pi\) | |||||||
\(158\) | 3.45699e22i | 0.283661i | ||||||||
\(159\) | 3.38638e22 | + | 6.71668e22i | 0.260055 | + | 0.515804i | ||||
\(160\) | − | 1.43422e23i | − | 1.03123i | ||||||
\(161\) | −1.21924e23 | − | 1.01877e23i | −0.821138 | − | 0.686124i | ||||
\(162\) | 3.84102e22 | − | 1.17610e22i | 0.242403 | − | 0.0742228i | ||||
\(163\) | −2.44238e23 | −1.44492 | −0.722461 | − | 0.691412i | \(-0.756989\pi\) | ||||
−0.722461 | + | 0.691412i | \(0.756989\pi\) | |||||||
\(164\) | 4.47010e22 | 0.248003 | ||||||||
\(165\) | 1.95330e23 | + | 3.87425e23i | 1.01669 | + | 2.01654i | ||||
\(166\) | − | 1.00604e22i | − | 0.0491449i | ||||||
\(167\) | −4.94570e22 | −0.226832 | −0.113416 | − | 0.993548i | \(-0.536179\pi\) | ||||
−0.113416 | + | 0.993548i | \(0.536179\pi\) | |||||||
\(168\) | 1.10942e23 | + | 2.58686e22i | 0.477911 | + | 0.111436i | ||||
\(169\) | −2.00659e23 | −0.812174 | ||||||||
\(170\) | 1.13328e23i | 0.431144i | ||||||||
\(171\) | 9.36780e22 | + | 6.92872e22i | 0.335103 | + | 0.247853i | ||||
\(172\) | 2.26176e23 | 0.761023 | ||||||||
\(173\) | 1.35934e23 | 0.430371 | 0.215185 | − | 0.976573i | \(-0.430964\pi\) | ||||
0.215185 | + | 0.976573i | \(0.430964\pi\) | |||||||
\(174\) | 4.25384e22 | − | 2.14468e22i | 0.126769 | − | 0.0639139i | ||||
\(175\) | −2.72539e23 | + | 3.26169e23i | −0.764768 | + | 0.915257i | ||||
\(176\) | 4.68139e23i | 1.23735i | ||||||||
\(177\) | 2.68637e23 | − | 1.35440e23i | 0.669032 | − | 0.337309i | ||||
\(178\) | 1.62844e23i | 0.382262i | ||||||||
\(179\) | 5.09904e23i | 1.12858i | 0.825578 | + | 0.564289i | \(0.190850\pi\) | ||||
−0.825578 | + | 0.564289i | \(0.809150\pi\) | |||||||
\(180\) | −3.94699e23 | + | 5.33643e23i | −0.823958 | + | 1.11401i | ||||
\(181\) | − | 2.55697e23i | − | 0.503617i | −0.967777 | − | 0.251809i | \(-0.918975\pi\) | ||
0.967777 | − | 0.251809i | \(-0.0810253\pi\) | |||||||
\(182\) | 1.17718e23 | − | 1.40882e23i | 0.218823 | − | 0.261882i | ||||
\(183\) | 4.98918e22 | + | 9.89573e22i | 0.0875573 | + | 0.173665i | ||||
\(184\) | −3.16840e23 | −0.525113 | ||||||||
\(185\) | 1.31961e24 | 2.06606 | ||||||||
\(186\) | 1.89912e23 | − | 9.57490e22i | 0.280975 | − | 0.141660i | ||||
\(187\) | − | 1.25247e24i | − | 1.75158i | ||||||
\(188\) | 3.55329e23 | 0.469865 | ||||||||
\(189\) | −5.18069e23 | − | 6.09011e23i | −0.647946 | − | 0.761686i | ||||
\(190\) | 1.32231e23 | 0.156466 | ||||||||
\(191\) | − | 9.41669e23i | − | 1.05450i | −0.849709 | − | 0.527252i | \(-0.823222\pi\) | ||
0.849709 | − | 0.527252i | \(-0.176778\pi\) | |||||||
\(192\) | −5.34690e23 | + | 2.69577e23i | −0.566812 | + | 0.285772i | ||||
\(193\) | −1.22581e24 | −1.23047 | −0.615236 | − | 0.788343i | \(-0.710939\pi\) | ||||
−0.615236 | + | 0.788343i | \(0.710939\pi\) | |||||||
\(194\) | −3.16767e23 | −0.301176 | ||||||||
\(195\) | 9.96216e23 | + | 1.97593e24i | 0.897408 | + | 1.77995i | ||||
\(196\) | −1.94799e23 | − | 1.07863e24i | −0.166302 | − | 0.920835i | ||||
\(197\) | 1.96576e24i | 1.59087i | 0.606040 | + | 0.795434i | \(0.292757\pi\) | ||||
−0.606040 | + | 0.795434i | \(0.707243\pi\) | |||||||
\(198\) | −2.99601e23 | + | 4.05067e23i | −0.229910 | + | 0.310844i | ||||
\(199\) | 9.29643e23i | 0.676642i | 0.941031 | + | 0.338321i | \(0.109859\pi\) | ||||
−0.941031 | + | 0.338321i | \(0.890141\pi\) | |||||||
\(200\) | 8.47608e23i | 0.585302i | ||||||||
\(201\) | 6.19465e23 | − | 3.12319e23i | 0.405937 | − | 0.204663i | ||||
\(202\) | − | 1.87164e23i | − | 0.116421i | ||||||
\(203\) | −7.27634e23 | − | 6.07994e23i | −0.429739 | − | 0.359080i | ||||
\(204\) | 1.71088e24 | − | 8.62581e23i | 0.959626 | − | 0.483819i | ||||
\(205\) | −7.36566e23 | −0.392461 | ||||||||
\(206\) | 4.79090e22 | 0.0242556 | ||||||||
\(207\) | 1.78791e24 | + | 1.32239e24i | 0.860312 | + | 0.636314i | ||||
\(208\) | 2.38759e24i | 1.09218i | ||||||||
\(209\) | −1.46138e24 | −0.635665 | ||||||||
\(210\) | −8.83681e23 | − | 2.06050e23i | −0.365589 | − | 0.0852453i | ||||
\(211\) | 2.16585e24 | 0.852436 | 0.426218 | − | 0.904621i | \(-0.359846\pi\) | ||||
0.426218 | + | 0.904621i | \(0.359846\pi\) | |||||||
\(212\) | − | 1.44326e24i | − | 0.540528i | ||||||
\(213\) | 9.52036e23 | + | 1.88831e24i | 0.339366 | + | 0.673111i | ||||
\(214\) | −9.05557e23 | −0.307306 | ||||||||
\(215\) | −3.72684e24 | −1.20431 | ||||||||
\(216\) | −1.57150e24 | − | 2.69516e23i | −0.483670 | − | 0.0829508i | ||||
\(217\) | −3.24851e24 | − | 2.71438e24i | −0.952483 | − | 0.795874i | ||||
\(218\) | − | 1.49747e24i | − | 0.418373i | ||||||
\(219\) | 1.85761e24 | + | 3.68445e24i | 0.494642 | + | 0.981093i | ||||
\(220\) | − | 8.32487e24i | − | 2.11319i | ||||||
\(221\) | − | 6.38780e24i | − | 1.54608i | ||||||
\(222\) | 6.89851e23 | + | 1.36828e24i | 0.159239 | + | 0.315840i | ||||
\(223\) | − | 1.09956e24i | − | 0.242113i | −0.992646 | − | 0.121056i | \(-0.961372\pi\) | ||
0.992646 | − | 0.121056i | \(-0.0386282\pi\) | |||||||
\(224\) | −2.54377e24 | − | 2.12551e24i | −0.534408 | − | 0.446540i | ||||
\(225\) | 3.53765e24 | − | 4.78299e24i | 0.709249 | − | 0.958922i | ||||
\(226\) | −6.72185e23 | −0.128632 | ||||||||
\(227\) | 3.04133e24 | 0.555638 | 0.277819 | − | 0.960633i | \(-0.410388\pi\) | ||||
0.277819 | + | 0.960633i | \(0.410388\pi\) | |||||||
\(228\) | −1.00646e24 | − | 1.99626e24i | −0.175583 | − | 0.348257i | ||||
\(229\) | − | 9.05432e24i | − | 1.50863i | −0.656511 | − | 0.754316i | \(-0.727969\pi\) | ||
0.656511 | − | 0.754316i | \(-0.272031\pi\) | |||||||
\(230\) | 2.52372e24 | 0.401697 | ||||||||
\(231\) | 9.76622e24 | + | 2.27721e24i | 1.48525 | + | 0.346320i | ||||
\(232\) | −1.89089e24 | −0.274816 | ||||||||
\(233\) | − | 8.39062e23i | − | 0.116562i | −0.998300 | − | 0.0582810i | \(-0.981438\pi\) | ||
0.998300 | − | 0.0582810i | \(-0.0185619\pi\) | |||||||
\(234\) | −1.52802e24 | + | 2.06591e24i | −0.202937 | + | 0.274376i | ||||
\(235\) | −5.85498e24 | −0.743554 | ||||||||
\(236\) | −5.77240e24 | −0.701100 | ||||||||
\(237\) | −8.59956e24 | + | 4.33568e24i | −0.999122 | + | 0.503732i | ||||
\(238\) | 2.01000e24 | + | 1.67951e24i | 0.223428 | + | 0.186692i | ||||
\(239\) | 1.16933e25i | 1.24383i | 0.783087 | + | 0.621913i | \(0.213644\pi\) | ||||
−0.783087 | + | 0.621913i | \(0.786356\pi\) | |||||||
\(240\) | 1.05371e25 | − | 5.31255e24i | 1.07276 | − | 0.540860i | ||||
\(241\) | − | 5.54789e24i | − | 0.540691i | −0.962763 | − | 0.270345i | \(-0.912862\pi\) | ||
0.962763 | − | 0.270345i | \(-0.0871379\pi\) | |||||||
\(242\) | − | 3.60226e24i | − | 0.336135i | ||||||
\(243\) | 7.74297e24 | + | 8.07980e24i | 0.691897 | + | 0.721996i | ||||
\(244\) | − | 2.12637e24i | − | 0.181989i | ||||||
\(245\) | 3.20983e24 | + | 1.77732e25i | 0.263171 | + | 1.45721i | ||||
\(246\) | −3.85054e23 | − | 7.63731e23i | −0.0302484 | − | 0.0599959i | ||||
\(247\) | −7.45331e24 | −0.561088 | ||||||||
\(248\) | −8.44184e24 | −0.609108 | ||||||||
\(249\) | 2.50260e24 | − | 1.26175e24i | 0.173100 | − | 0.0872728i | ||||
\(250\) | − | 1.09087e24i | − | 0.0723438i | ||||||
\(251\) | 8.18893e24 | 0.520779 | 0.260389 | − | 0.965504i | \(-0.416149\pi\) | ||||
0.260389 | + | 0.965504i | \(0.416149\pi\) | |||||||
\(252\) | 3.61536e24 | + | 1.49090e25i | 0.220519 | + | 0.909376i | ||||
\(253\) | −2.78915e25 | −1.63195 | ||||||||
\(254\) | 6.44353e24i | 0.361718i | ||||||||
\(255\) | −2.81912e25 | + | 1.42133e25i | −1.51859 | + | 0.765636i | ||||
\(256\) | 8.07430e24 | 0.417432 | ||||||||
\(257\) | 1.49657e25 | 0.742674 | 0.371337 | − | 0.928498i | \(-0.378900\pi\) | ||||
0.371337 | + | 0.928498i | \(0.378900\pi\) | |||||||
\(258\) | −1.94828e24 | − | 3.86429e24i | −0.0928205 | − | 0.184104i | ||||
\(259\) | 1.95566e25 | − | 2.34048e25i | 0.894633 | − | 1.07068i | ||||
\(260\) | − | 4.24583e25i | − | 1.86527i | ||||||
\(261\) | 1.06701e25 | + | 7.89197e24i | 0.450241 | + | 0.333012i | ||||
\(262\) | 1.18133e24i | 0.0478860i | ||||||||
\(263\) | 1.45078e25i | 0.565024i | 0.959264 | + | 0.282512i | \(0.0911678\pi\) | ||||
−0.959264 | + | 0.282512i | \(0.908832\pi\) | |||||||
\(264\) | 1.78566e25 | − | 9.00287e24i | 0.668280 | − | 0.336930i | ||||
\(265\) | 2.37815e25i | 0.855377i | ||||||||
\(266\) | 1.95966e24 | − | 2.34528e24i | 0.0677522 | − | 0.0810843i | ||||
\(267\) | −4.05087e25 | + | 2.04235e25i | −1.34642 | + | 0.678830i | ||||
\(268\) | −1.33109e25 | −0.425394 | ||||||||
\(269\) | 5.57484e25 | 1.71330 | 0.856650 | − | 0.515897i | \(-0.172541\pi\) | ||||
0.856650 | + | 0.515897i | \(0.172541\pi\) | |||||||
\(270\) | 1.25174e25 | + | 2.14677e24i | 0.369994 | + | 0.0634551i | ||||
\(271\) | 5.26405e25i | 1.49673i | 0.663290 | + | 0.748363i | \(0.269160\pi\) | ||||
−0.663290 | + | 0.748363i | \(0.730840\pi\) | |||||||
\(272\) | −3.40644e25 | −0.931810 | ||||||||
\(273\) | 4.98094e25 | + | 1.16142e25i | 1.31100 | + | 0.305690i | ||||
\(274\) | −1.34305e25 | −0.340183 | ||||||||
\(275\) | 7.46150e25i | 1.81900i | ||||||||
\(276\) | −1.92090e25 | − | 3.80999e25i | −0.450775 | − | 0.894084i | ||||
\(277\) | −4.98204e25 | −1.12556 | −0.562781 | − | 0.826606i | \(-0.690269\pi\) | ||||
−0.562781 | + | 0.826606i | \(0.690269\pi\) | |||||||
\(278\) | −1.47070e25 | −0.319928 | ||||||||
\(279\) | 4.76367e25 | + | 3.52336e25i | 0.997924 | + | 0.738097i | ||||
\(280\) | 2.76376e25 | + | 2.30934e25i | 0.557624 | + | 0.465938i | ||||
\(281\) | − | 2.53148e25i | − | 0.491992i | −0.969271 | − | 0.245996i | \(-0.920885\pi\) | ||
0.969271 | − | 0.245996i | \(-0.0791150\pi\) | |||||||
\(282\) | −3.06080e24 | − | 6.07091e24i | −0.0573085 | − | 0.113668i | ||||
\(283\) | − | 5.18238e25i | − | 0.934913i | −0.884016 | − | 0.467457i | \(-0.845170\pi\) | ||
0.884016 | − | 0.467457i | \(-0.154830\pi\) | |||||||
\(284\) | − | 4.05754e25i | − | 0.705375i | ||||||
\(285\) | 1.65841e25 | + | 3.28936e25i | 0.277857 | + | 0.551112i | ||||
\(286\) | − | 3.22284e25i | − | 0.520470i | ||||||
\(287\) | −1.09159e25 | + | 1.30639e25i | −0.169941 | + | 0.203382i | ||||
\(288\) | 3.73022e25 | + | 2.75899e25i | 0.559904 | + | 0.414123i | ||||
\(289\) | 2.20446e25 | 0.319062 | ||||||||
\(290\) | 1.50614e25 | 0.210226 | ||||||||
\(291\) | −3.97281e25 | − | 7.87983e25i | −0.534837 | − | 1.06082i | ||||
\(292\) | − | 7.91705e25i | − | 1.02812i | ||||||
\(293\) | 5.26755e25 | 0.659932 | 0.329966 | − | 0.943993i | \(-0.392963\pi\) | ||||
0.329966 | + | 0.943993i | \(0.392963\pi\) | |||||||
\(294\) | −1.67507e25 | + | 1.26195e25i | −0.202481 | + | 0.152544i | ||||
\(295\) | 9.51154e25 | 1.10948 | ||||||||
\(296\) | − | 6.08216e25i | − | 0.684692i | ||||||
\(297\) | −1.38339e26 | − | 2.37256e25i | −1.50315 | − | 0.257795i | ||||
\(298\) | 2.09547e25 | 0.219792 | ||||||||
\(299\) | −1.42251e26 | −1.44049 | ||||||||
\(300\) | −1.01924e26 | + | 5.13878e25i | −0.996564 | + | 0.502443i | ||||
\(301\) | −5.52317e25 | + | 6.61000e25i | −0.521483 | + | 0.624099i | ||||
\(302\) | 5.03631e25i | 0.459240i | ||||||||
\(303\) | 4.65586e25 | − | 2.34737e25i | 0.410064 | − | 0.206744i | ||||
\(304\) | 3.97465e25i | 0.338163i | ||||||||
\(305\) | 3.50375e25i | 0.287995i | ||||||||
\(306\) | −2.94750e25 | − | 2.18006e25i | −0.234087 | − | 0.173139i | ||||
\(307\) | 3.81010e25i | 0.292404i | 0.989255 | + | 0.146202i | \(0.0467050\pi\) | ||||
−0.989255 | + | 0.146202i | \(0.953295\pi\) | |||||||
\(308\) | −1.47651e26 | − | 1.23374e26i | −1.09510 | − | 0.915044i | ||||
\(309\) | 6.00864e24 | + | 1.19178e25i | 0.0430737 | + | 0.0854340i | ||||
\(310\) | 6.72416e25 | 0.465951 | ||||||||
\(311\) | 2.86439e26 | 1.91888 | 0.959440 | − | 0.281914i | \(-0.0909693\pi\) | ||||
0.959440 | + | 0.281914i | \(0.0909693\pi\) | |||||||
\(312\) | 9.10720e25 | − | 4.59162e25i | 0.589877 | − | 0.297401i | ||||
\(313\) | − | 7.04402e25i | − | 0.441169i | −0.975368 | − | 0.220585i | \(-0.929204\pi\) | ||
0.975368 | − | 0.220585i | \(-0.0707965\pi\) | |||||||
\(314\) | 3.11452e25 | 0.188638 | ||||||||
\(315\) | −5.95726e25 | − | 2.45665e26i | −0.348968 | − | 1.43907i | ||||
\(316\) | 1.84785e26 | 1.04701 | ||||||||
\(317\) | − | 1.14082e25i | − | 0.0625307i | −0.999511 | − | 0.0312653i | \(-0.990046\pi\) | ||
0.999511 | − | 0.0312653i | \(-0.00995369\pi\) | |||||||
\(318\) | −2.46586e25 | + | 1.24322e25i | −0.130763 | + | 0.0659272i | ||||
\(319\) | −1.66455e26 | −0.854072 | ||||||||
\(320\) | −1.89316e26 | −0.939965 | ||||||||
\(321\) | −1.13573e26 | − | 2.25265e26i | −0.545723 | − | 1.08241i | ||||
\(322\) | 3.74014e25 | − | 4.47611e25i | 0.173941 | − | 0.208168i | ||||
\(323\) | − | 1.06338e26i | − | 0.478700i | ||||||
\(324\) | −6.28656e25 | − | 2.05312e26i | −0.273962 | − | 0.894728i | ||||
\(325\) | 3.80550e26i | 1.60560i | ||||||||
\(326\) | − | 8.96659e25i | − | 0.366305i | ||||||
\(327\) | 3.72507e26 | − | 1.87809e26i | 1.47361 | − | 0.742958i | ||||
\(328\) | 3.39488e25i | 0.130062i | ||||||||
\(329\) | −8.67705e25 | + | 1.03845e26i | −0.321970 | + | 0.385326i | ||||
\(330\) | −1.42233e26 | + | 7.17104e25i | −0.511216 | + | 0.257742i | ||||
\(331\) | −2.67563e26 | −0.931605 | −0.465802 | − | 0.884889i | \(-0.654234\pi\) | ||||
−0.465802 | + | 0.884889i | \(0.654234\pi\) | |||||||
\(332\) | −5.37751e25 | −0.181397 | ||||||||
\(333\) | −2.53851e26 | + | 3.43212e26i | −0.829686 | + | 1.12176i | ||||
\(334\) | − | 1.81569e25i | − | 0.0575047i | ||||||
\(335\) | 2.19332e26 | 0.673180 | ||||||||
\(336\) | 6.19353e25 | − | 2.65620e26i | 0.184237 | − | 0.790130i | ||||
\(337\) | 5.06422e26 | 1.46015 | 0.730076 | − | 0.683366i | \(-0.239485\pi\) | ||||
0.730076 | + | 0.683366i | \(0.239485\pi\) | |||||||
\(338\) | − | 7.36670e25i | − | 0.205896i | ||||||
\(339\) | −8.43039e25 | − | 1.67212e26i | −0.228429 | − | 0.453074i | ||||
\(340\) | 6.05764e26 | 1.59138 | ||||||||
\(341\) | −7.43136e26 | −1.89299 | ||||||||
\(342\) | −2.54370e25 | + | 3.43915e25i | −0.0628337 | + | 0.0849526i | ||||
\(343\) | 3.62798e26 | + | 2.06468e26i | 0.869114 | + | 0.494611i | ||||
\(344\) | 1.71773e26i | 0.399108i | ||||||||
\(345\) | 3.16519e26 | + | 6.27796e26i | 0.713344 | + | 1.41487i | ||||
\(346\) | 4.99046e25i | 0.109104i | ||||||||
\(347\) | 5.76925e26i | 1.22366i | 0.790991 | + | 0.611828i | \(0.209566\pi\) | ||||
−0.790991 | + | 0.611828i | \(0.790434\pi\) | |||||||
\(348\) | −1.14638e26 | − | 2.27378e26i | −0.235911 | − | 0.467915i | ||||
\(349\) | 7.69223e26i | 1.53598i | 0.640463 | + | 0.767989i | \(0.278742\pi\) | ||||
−0.640463 | + | 0.767989i | \(0.721258\pi\) | |||||||
\(350\) | −1.19745e26 | − | 1.00056e26i | −0.232029 | − | 0.193878i | ||||
\(351\) | −7.05553e26 | − | 1.21005e26i | −1.32680 | − | 0.227550i | ||||
\(352\) | −5.81917e26 | −1.06209 | ||||||||
\(353\) | 7.28618e26 | 1.29082 | 0.645410 | − | 0.763837i | \(-0.276687\pi\) | ||||
0.645410 | + | 0.763837i | \(0.276687\pi\) | |||||||
\(354\) | 4.97234e25 | + | 9.86233e25i | 0.0855119 | + | 0.169608i | ||||
\(355\) | 6.68586e26i | 1.11625i | ||||||||
\(356\) | 8.70439e26 | 1.41096 | ||||||||
\(357\) | −1.65703e26 | + | 7.10645e26i | −0.260804 | + | 1.11850i | ||||
\(358\) | −1.87198e26 | −0.286108 | ||||||||
\(359\) | − | 8.02107e26i | − | 1.19053i | −0.803529 | − | 0.595265i | \(-0.797047\pi\) | ||
0.803529 | − | 0.595265i | \(-0.202953\pi\) | |||||||
\(360\) | −4.05283e26 | − | 2.99760e26i | −0.584227 | − | 0.432113i | ||||
\(361\) | 5.90133e26 | 0.826275 | ||||||||
\(362\) | 9.38726e25 | 0.127673 | ||||||||
\(363\) | 8.96093e26 | − | 4.51788e26i | 1.18395 | − | 0.596918i | ||||
\(364\) | −7.53048e26 | − | 6.29230e26i | −0.966625 | − | 0.807690i | ||||
\(365\) | 1.30454e27i | 1.62698i | ||||||||
\(366\) | −3.63297e25 | + | 1.83165e25i | −0.0440261 | + | 0.0221968i | ||||
\(367\) | − | 1.07712e27i | − | 1.26844i | −0.773153 | − | 0.634219i | \(-0.781322\pi\) | ||
0.773153 | − | 0.634219i | \(-0.218678\pi\) | |||||||
\(368\) | 7.58588e26i | 0.868169i | ||||||||
\(369\) | 1.41692e26 | − | 1.91571e26i | 0.157604 | − | 0.213085i | ||||
\(370\) | 4.84461e26i | 0.523770i | ||||||||
\(371\) | 4.21793e26 | + | 3.52441e26i | 0.443276 | + | 0.370391i | ||||
\(372\) | −5.11802e26 | − | 1.01513e27i | −0.522879 | − | 1.03710i | ||||
\(373\) | −3.65727e26 | −0.363258 | −0.181629 | − | 0.983367i | \(-0.558137\pi\) | ||||
−0.181629 | + | 0.983367i | \(0.558137\pi\) | |||||||
\(374\) | 4.59812e26 | 0.444046 | ||||||||
\(375\) | 2.71362e26 | − | 1.36814e26i | 0.254813 | − | 0.128470i | ||||
\(376\) | 2.69860e26i | 0.246414i | ||||||||
\(377\) | −8.48949e26 | −0.753872 | ||||||||
\(378\) | 2.23583e26 | − | 1.90196e26i | 0.193097 | − | 0.164262i | ||||
\(379\) | −1.04194e27 | −0.875250 | −0.437625 | − | 0.899158i | \(-0.644180\pi\) | ||||
−0.437625 | + | 0.899158i | \(0.644180\pi\) | |||||||
\(380\) | − | 7.06808e26i | − | 0.577529i | ||||||
\(381\) | −1.60288e27 | + | 8.08132e26i | −1.27406 | + | 0.642347i | ||||
\(382\) | 3.45710e26 | 0.267329 | ||||||||
\(383\) | 2.53492e26 | 0.190711 | 0.0953557 | − | 0.995443i | \(-0.469601\pi\) | ||||
0.0953557 | + | 0.995443i | \(0.469601\pi\) | |||||||
\(384\) | −5.27264e26 | − | 1.04580e27i | −0.385967 | − | 0.765542i | ||||
\(385\) | 2.43295e27 | + | 2.03291e27i | 1.73298 | + | 1.44804i | ||||
\(386\) | − | 4.50025e26i | − | 0.311939i | ||||||
\(387\) | 7.16926e26 | − | 9.69301e26i | 0.483625 | − | 0.653873i | ||||
\(388\) | 1.69319e27i | 1.11166i | ||||||||
\(389\) | − | 1.49463e27i | − | 0.955132i | −0.878596 | − | 0.477566i | \(-0.841519\pi\) | ||
0.878596 | − | 0.477566i | \(-0.158481\pi\) | |||||||
\(390\) | −7.25414e26 | + | 3.65735e26i | −0.451240 | + | 0.227504i | ||||
\(391\) | − | 2.02954e27i | − | 1.22897i | ||||||
\(392\) | 8.19177e26 | − | 1.47943e26i | 0.482919 | − | 0.0872150i | ||||
\(393\) | −2.93866e26 | + | 1.48160e26i | −0.168666 | + | 0.0850373i | ||||
\(394\) | −7.21678e26 | −0.403304 | ||||||||
\(395\) | −3.04482e27 | −1.65688 | ||||||||
\(396\) | 2.16518e27 | + | 1.60144e27i | 1.14735 | + | 0.848616i | ||||
\(397\) | − | 3.24066e27i | − | 1.67237i | −0.548446 | − | 0.836186i | \(-0.684780\pi\) | ||
0.548446 | − | 0.836186i | \(-0.315220\pi\) | |||||||
\(398\) | −3.41295e26 | −0.171537 | ||||||||
\(399\) | 8.29183e26 | + | 1.93343e26i | 0.405915 | + | 0.0946482i | ||||
\(400\) | 2.02937e27 | 0.967679 | ||||||||
\(401\) | 2.32859e27i | 1.08163i | 0.841142 | + | 0.540814i | \(0.181884\pi\) | ||||
−0.841142 | + | 0.540814i | \(0.818116\pi\) | |||||||
\(402\) | 1.14660e26 | + | 2.27421e26i | 0.0518845 | + | 0.102910i | ||||
\(403\) | −3.79012e27 | −1.67090 | ||||||||
\(404\) | −1.00044e27 | −0.429720 | ||||||||
\(405\) | 1.03588e27 | + | 3.38305e27i | 0.433541 | + | 1.41589i | ||||
\(406\) | 2.23210e26 | − | 2.67132e26i | 0.0910311 | − | 0.108944i | ||||
\(407\) | − | 5.35414e27i | − | 2.12788i | ||||||
\(408\) | 6.55099e26 | + | 1.29935e27i | 0.253732 | + | 0.503262i | ||||
\(409\) | − | 2.01191e27i | − | 0.759476i | −0.925094 | − | 0.379738i | \(-0.876014\pi\) | ||
0.925094 | − | 0.379738i | \(-0.123986\pi\) | |||||||
\(410\) | − | 2.70412e26i | − | 0.0994935i | ||||||
\(411\) | −1.68443e27 | − | 3.34095e27i | −0.604105 | − | 1.19821i | ||||
\(412\) | − | 2.56085e26i | − | 0.0895291i | ||||||
\(413\) | 1.40961e27 | − | 1.68699e27i | 0.480422 | − | 0.574957i | ||||
\(414\) | −4.85483e26 | + | 6.56384e26i | −0.161313 | + | 0.218100i | ||||
\(415\) | 8.86086e26 | 0.287059 | ||||||||
\(416\) | −2.96788e27 | −0.937489 | ||||||||
\(417\) | −1.84451e27 | − | 3.65848e27i | −0.568137 | − | 1.12686i | ||||
\(418\) | − | 5.36510e26i | − | 0.161149i | ||||||
\(419\) | 4.70631e27 | 1.37858 | 0.689292 | − | 0.724483i | \(-0.257922\pi\) | ||||
0.689292 | + | 0.724483i | \(0.257922\pi\) | |||||||
\(420\) | −1.10139e27 | + | 4.72349e27i | −0.314647 | + | 1.34942i | ||||
\(421\) | 2.99709e27 | 0.835099 | 0.417550 | − | 0.908654i | \(-0.362889\pi\) | ||||
0.417550 | + | 0.908654i | \(0.362889\pi\) | |||||||
\(422\) | 7.95135e26i | 0.216103i | ||||||||
\(423\) | 1.12631e27 | − | 1.52280e27i | 0.298596 | − | 0.403709i | ||||
\(424\) | 1.09610e27 | 0.283472 | ||||||||
\(425\) | −5.42941e27 | −1.36984 | ||||||||
\(426\) | −6.93244e26 | + | 3.49516e26i | −0.170642 | + | 0.0860333i | ||||
\(427\) | 6.21431e26 | + | 5.19254e26i | 0.149245 | + | 0.124706i | ||||
\(428\) | 4.84043e27i | 1.13429i | ||||||||
\(429\) | 8.01708e27 | − | 4.04201e27i | 1.83322 | − | 0.924264i | ||||
\(430\) | − | 1.36822e27i | − | 0.305306i | ||||||
\(431\) | − | 7.88872e27i | − | 1.71789i | −0.512068 | − | 0.858945i | \(-0.671121\pi\) | ||
0.512068 | − | 0.858945i | \(-0.328879\pi\) | |||||||
\(432\) | −6.45285e26 | + | 3.76253e27i | −0.137142 | + | 0.799650i | ||||
\(433\) | − | 1.12507e27i | − | 0.233377i | −0.993169 | − | 0.116689i | \(-0.962772\pi\) | ||
0.993169 | − | 0.116689i | \(-0.0372279\pi\) | |||||||
\(434\) | 9.96518e26 | − | 1.19261e27i | 0.201764 | − | 0.241466i | ||||
\(435\) | 1.88897e27 | + | 3.74665e27i | 0.373325 | + | 0.740468i | ||||
\(436\) | −8.00433e27 | −1.54425 | ||||||||
\(437\) | −2.36807e27 | −0.446006 | ||||||||
\(438\) | −1.35265e27 | + | 6.81974e26i | −0.248719 | + | 0.125398i | ||||
\(439\) | 2.62451e26i | 0.0471163i | 0.999722 | + | 0.0235582i | \(0.00749949\pi\) | ||||
−0.999722 | + | 0.0235582i | \(0.992501\pi\) | |||||||
\(440\) | 6.32244e27 | 1.10823 | ||||||||
\(441\) | −5.24003e27 | − | 2.58416e27i | −0.896868 | − | 0.442298i | ||||
\(442\) | 2.34512e27 | 0.391950 | ||||||||
\(443\) | 8.58094e27i | 1.40054i | 0.713878 | + | 0.700270i | \(0.246937\pi\) | ||||
−0.713878 | + | 0.700270i | \(0.753063\pi\) | |||||||
\(444\) | 7.31378e27 | − | 3.68742e27i | 1.16579 | − | 0.587762i | ||||
\(445\) | −1.43428e28 | −2.23282 | ||||||||
\(446\) | 4.03676e26 | 0.0613786 | ||||||||
\(447\) | 2.62809e27 | + | 5.21266e27i | 0.390312 | + | 0.774159i | ||||
\(448\) | −2.80565e27 | + | 3.35774e27i | −0.407019 | + | 0.487111i | ||||
\(449\) | 4.40140e27i | 0.623741i | 0.950125 | + | 0.311871i | \(0.100956\pi\) | ||||
−0.950125 | + | 0.311871i | \(0.899044\pi\) | |||||||
\(450\) | 1.75595e27 | + | 1.29876e27i | 0.243098 | + | 0.179803i | ||||
\(451\) | 2.98852e27i | 0.404205i | ||||||||
\(452\) | 3.59299e27i | 0.474791i | ||||||||
\(453\) | −1.25282e28 | + | 6.31642e27i | −1.61755 | + | 0.815530i | ||||
\(454\) | 1.11655e27i | 0.140861i | ||||||||
\(455\) | 1.24084e28 | + | 1.03682e28i | 1.52967 | + | 1.27816i | ||||
\(456\) | 1.51609e27 | − | 7.64372e26i | 0.182639 | − | 0.0920819i | ||||
\(457\) | 3.77890e27 | 0.444883 | 0.222441 | − | 0.974946i | \(-0.428597\pi\) | ||||
0.222441 | + | 0.974946i | \(0.428597\pi\) | |||||||
\(458\) | 3.32406e27 | 0.382456 | ||||||||
\(459\) | 1.72641e27 | − | 1.00663e28i | 0.194138 | − | 1.13198i | ||||
\(460\) | − | 1.34899e28i | − | 1.48269i | ||||||
\(461\) | 3.80104e27 | 0.408359 | 0.204180 | − | 0.978933i | \(-0.434547\pi\) | ||||
0.204180 | + | 0.978933i | \(0.434547\pi\) | |||||||
\(462\) | −8.36021e26 | + | 3.58542e27i | −0.0877964 | + | 0.376530i | ||||
\(463\) | −4.97281e27 | −0.510507 | −0.255253 | − | 0.966874i | \(-0.582159\pi\) | ||||
−0.255253 | + | 0.966874i | \(0.582159\pi\) | |||||||
\(464\) | 4.52722e27i | 0.454352i | ||||||||
\(465\) | 8.43328e27 | + | 1.67269e28i | 0.827448 | + | 1.64119i | ||||
\(466\) | 3.08040e26 | 0.0295499 | ||||||||
\(467\) | −1.65815e28 | −1.55523 | −0.777617 | − | 0.628738i | \(-0.783572\pi\) | ||||
−0.777617 | + | 0.628738i | \(0.783572\pi\) | |||||||
\(468\) | 1.10428e28 | + | 8.16762e27i | 1.01274 | + | 0.749056i | ||||
\(469\) | 3.25049e27 | − | 3.89011e27i | 0.291497 | − | 0.348857i | ||||
\(470\) | − | 2.14951e27i | − | 0.188500i | ||||||
\(471\) | 3.90615e27 | + | 7.74762e27i | 0.334988 | + | 0.664429i | ||||
\(472\) | − | 4.38393e27i | − | 0.367682i | ||||||
\(473\) | 1.51212e28i | 1.24035i | ||||||||
\(474\) | −1.59174e27 | − | 3.15711e27i | −0.127702 | − | 0.253290i | ||||
\(475\) | 6.33505e27i | 0.497127i | ||||||||
\(476\) | 8.97740e27 | − | 1.07439e28i | 0.689093 | − | 0.824690i | ||||
\(477\) | −6.18524e27 | − | 4.57481e27i | −0.464423 | − | 0.343502i | ||||
\(478\) | −4.29290e27 | −0.315325 | ||||||||
\(479\) | −1.67048e28 | −1.20038 | −0.600188 | − | 0.799859i | \(-0.704908\pi\) | ||||
−0.600188 | + | 0.799859i | \(0.704908\pi\) | |||||||
\(480\) | 6.60373e27 | + | 1.30981e28i | 0.464255 | + | 0.920821i | ||||
\(481\) | − | 2.73070e28i | − | 1.87824i | ||||||
\(482\) | 2.03677e27 | 0.137072 | ||||||||
\(483\) | 1.58255e28 | + | 3.69007e27i | 1.04211 | + | 0.242991i | ||||
\(484\) | −1.92550e28 | −1.24070 | ||||||||
\(485\) | − | 2.78998e28i | − | 1.75919i | ||||||
\(486\) | −2.96630e27 | + | 2.84263e27i | −0.183035 | + | 0.175404i | ||||
\(487\) | 1.69052e28 | 1.02086 | 0.510429 | − | 0.859920i | \(-0.329487\pi\) | ||||
0.510429 | + | 0.859920i | \(0.329487\pi\) | |||||||
\(488\) | 1.61490e27 | 0.0954415 | ||||||||
\(489\) | 2.23051e28 | − | 1.12457e28i | 1.29021 | − | 0.650494i | ||||
\(490\) | −6.52498e27 | + | 1.17841e27i | −0.369420 | + | 0.0667171i | ||||
\(491\) | − | 2.73101e28i | − | 1.51345i | −0.653734 | − | 0.756725i | \(-0.726798\pi\) | ||
0.653734 | − | 0.756725i | \(-0.273202\pi\) | |||||||
\(492\) | −4.08233e27 | + | 2.05821e27i | −0.221449 | + | 0.111649i | ||||
\(493\) | − | 1.21122e28i | − | 0.643176i | ||||||
\(494\) | − | 2.73629e27i | − | 0.142243i | ||||||
\(495\) | −3.56771e28 | − | 2.63879e28i | −1.81566 | − | 1.34292i | ||||
\(496\) | 2.02117e28i | 1.00704i | ||||||||
\(497\) | 1.18582e28 | + | 9.90842e27i | 0.578463 | + | 0.483351i | ||||
\(498\) | 4.63218e26 | + | 9.18765e26i | 0.0221247 | + | 0.0438830i | ||||
\(499\) | −1.99149e28 | −0.931372 | −0.465686 | − | 0.884950i | \(-0.654192\pi\) | ||||
−0.465686 | + | 0.884950i | \(0.654192\pi\) | |||||||
\(500\) | −5.83095e27 | −0.267026 | ||||||||
\(501\) | 4.51668e27 | − | 2.27719e27i | 0.202546 | − | 0.102118i | ||||
\(502\) | 3.00636e27i | 0.132024i | ||||||||
\(503\) | −1.58196e27 | −0.0680350 | −0.0340175 | − | 0.999421i | \(-0.510830\pi\) | ||||
−0.0340175 | + | 0.999421i | \(0.510830\pi\) | |||||||
\(504\) | −1.13229e28 | + | 2.74574e27i | −0.476910 | + | 0.115648i | ||||
\(505\) | 1.64848e28 | 0.680025 | ||||||||
\(506\) | − | 1.02396e28i | − | 0.413718i | ||||||
\(507\) | 1.83253e28 | − | 9.23915e27i | 0.725216 | − | 0.365635i | ||||
\(508\) | 3.44422e28 | 1.33513 | ||||||||
\(509\) | −3.99452e28 | −1.51680 | −0.758400 | − | 0.651789i | \(-0.774019\pi\) | ||||
−0.758400 | + | 0.651789i | \(0.774019\pi\) | |||||||
\(510\) | −5.21805e27 | − | 1.03497e28i | −0.194098 | − | 0.384982i | ||||
\(511\) | 2.31376e28 | + | 1.93333e28i | 0.843138 | + | 0.704508i | ||||
\(512\) | 2.69794e28i | 0.963159i | ||||||||
\(513\) | −1.17454e28 | − | 2.01438e27i | −0.410806 | − | 0.0704544i | ||||
\(514\) | 5.49426e27i | 0.188277i | ||||||||
\(515\) | 4.21968e27i | 0.141678i | ||||||||
\(516\) | −2.06556e28 | + | 1.04140e28i | −0.679541 | + | 0.342607i | ||||
\(517\) | 2.37558e28i | 0.765806i | ||||||||
\(518\) | 8.59249e27 | + | 7.17969e27i | 0.271429 | + | 0.226800i | ||||
\(519\) | −1.24142e28 | + | 6.25891e27i | −0.384291 | + | 0.193750i | ||||
\(520\) | 3.22456e28 | 0.978216 | ||||||||
\(521\) | −4.15617e28 | −1.23565 | −0.617827 | − | 0.786314i | \(-0.711987\pi\) | ||||
−0.617827 | + | 0.786314i | \(0.711987\pi\) | |||||||
\(522\) | −2.89734e27 | + | 3.91727e27i | −0.0844226 | + | 0.114141i | ||||
\(523\) | 4.59294e28i | 1.31167i | 0.754906 | + | 0.655833i | \(0.227682\pi\) | ||||
−0.754906 | + | 0.655833i | \(0.772318\pi\) | |||||||
\(524\) | 6.31451e27 | 0.176751 | ||||||||
\(525\) | 9.87165e27 | − | 4.23362e28i | 0.270843 | − | 1.16155i | ||||
\(526\) | −5.32618e27 | −0.143240 | ||||||||
\(527\) | − | 5.40748e28i | − | 1.42555i | ||||||
\(528\) | −2.15550e28 | − | 4.27529e28i | −0.557046 | − | 1.10487i | ||||
\(529\) | −5.72469e27 | −0.145033 | ||||||||
\(530\) | −8.73078e27 | −0.216849 | ||||||||
\(531\) | −1.82972e28 | + | 2.47382e28i | −0.445545 | + | 0.602387i | ||||
\(532\) | −1.25361e28 | − | 1.04749e28i | −0.299288 | − | 0.250078i | ||||
\(533\) | 1.52420e28i | 0.356784i | ||||||||
\(534\) | −7.49796e27 | − | 1.48717e28i | −0.172092 | − | 0.341333i | ||||
\(535\) | − | 7.97588e28i | − | 1.79500i | ||||||
\(536\) | − | 1.01091e28i | − | 0.223092i | ||||||
\(537\) | −2.34780e28 | − | 4.65671e28i | −0.508078 | − | 1.00774i | ||||
\(538\) | 2.04666e28i | 0.434342i | ||||||||
\(539\) | 7.21123e28 | − | 1.30235e28i | 1.50082 | − | 0.271047i | ||||
\(540\) | 1.14750e28 | − | 6.69086e28i | 0.234217 | − | 1.36568i | ||||
\(541\) | 1.45892e28 | 0.292052 | 0.146026 | − | 0.989281i | \(-0.453352\pi\) | ||||
0.146026 | + | 0.989281i | \(0.453352\pi\) | |||||||
\(542\) | −1.93256e28 | −0.379438 | ||||||||
\(543\) | 1.17733e28 | + | 2.33516e28i | 0.226725 | + | 0.449695i | ||||
\(544\) | − | 4.23436e28i | − | 0.799832i | ||||||
\(545\) | 1.31892e29 | 2.44375 | ||||||||
\(546\) | −4.26385e27 | + | 1.82863e28i | −0.0774960 | + | 0.332355i | ||||
\(547\) | 2.78371e28 | 0.496314 | 0.248157 | − | 0.968720i | \(-0.420175\pi\) | ||||
0.248157 | + | 0.968720i | \(0.420175\pi\) | |||||||
\(548\) | 7.17895e28i | 1.25564i | ||||||||
\(549\) | −9.11276e27 | − | 6.74009e27i | −0.156365 | − | 0.115653i | ||||
\(550\) | −2.73930e28 | −0.461139 | ||||||||
\(551\) | −1.41326e28 | −0.233415 | ||||||||
\(552\) | 2.89355e28 | − | 1.45886e28i | 0.468890 | − | 0.236402i | ||||
\(553\) | −4.51241e28 | + | 5.40034e28i | −0.717454 | + | 0.858633i | ||||
\(554\) | − | 1.82903e28i | − | 0.285344i | ||||||
\(555\) | −1.20514e29 | + | 6.07600e28i | −1.84485 | + | 0.930125i | ||||
\(556\) | 7.86123e28i | 1.18088i | ||||||||
\(557\) | 8.40041e28i | 1.23829i | 0.785278 | + | 0.619143i | \(0.212520\pi\) | ||||
−0.785278 | + | 0.619143i | \(0.787480\pi\) | |||||||
\(558\) | −1.29351e28 | + | 1.74886e28i | −0.187116 | + | 0.252986i | ||||
\(559\) | 7.71206e28i | 1.09483i | ||||||||
\(560\) | 5.52909e28 | − | 6.61709e28i | 0.770335 | − | 0.921919i | ||||
\(561\) | 5.76685e28 | + | 1.14382e29i | 0.788549 | + | 1.56404i | ||||
\(562\) | 9.29368e27 | 0.124726 | ||||||||
\(563\) | −4.44784e28 | −0.585883 | −0.292941 | − | 0.956130i | \(-0.594634\pi\) | ||||
−0.292941 | + | 0.956130i | \(0.594634\pi\) | |||||||
\(564\) | −3.24505e28 | + | 1.63607e28i | −0.419557 | + | 0.211530i | ||||
\(565\) | − | 5.92040e28i | − | 0.751350i | ||||||
\(566\) | 1.90258e28 | 0.237012 | ||||||||
\(567\) | 7.53541e28 | + | 3.17642e28i | 0.921477 | + | 0.388433i | ||||
\(568\) | 3.08156e28 | 0.369924 | ||||||||
\(569\) | 3.84484e27i | 0.0453106i | 0.999743 | + | 0.0226553i | \(0.00721202\pi\) | ||||
−0.999743 | + | 0.0226553i | \(0.992788\pi\) | |||||||
\(570\) | −1.20760e28 | + | 6.08844e27i | −0.139714 | + | 0.0704401i | ||||
\(571\) | 7.58051e28 | 0.861032 | 0.430516 | − | 0.902583i | \(-0.358332\pi\) | ||||
0.430516 | + | 0.902583i | \(0.358332\pi\) | |||||||
\(572\) | −1.72269e29 | −1.92109 | ||||||||
\(573\) | 4.33581e28 | + | 8.59982e28i | 0.474731 | + | 0.941599i | ||||
\(574\) | −4.79607e27 | − | 4.00749e27i | −0.0515597 | − | 0.0430822i | ||||
\(575\) | 1.20909e29i | 1.27628i | ||||||||
\(576\) | 3.64183e28 | − | 4.92384e28i | 0.377471 | − | 0.510350i | ||||
\(577\) | 1.48691e29i | 1.51334i | 0.653795 | + | 0.756672i | \(0.273176\pi\) | ||||
−0.653795 | + | 0.756672i | \(0.726824\pi\) | |||||||
\(578\) | 8.09311e27i | 0.0808860i | ||||||||
\(579\) | 1.11947e29 | − | 5.64411e28i | 1.09873 | − | 0.553950i | ||||
\(580\) | − | 8.05070e28i | − | 0.775961i | ||||||
\(581\) | 1.31318e28 | − | 1.57158e28i | 0.124301 | − | 0.148760i | ||||
\(582\) | 2.89288e28 | − | 1.45852e28i | 0.268930 | − | 0.135588i | ||||
\(583\) | 9.64903e28 | 0.880975 | ||||||||
\(584\) | 6.01272e28 | 0.539183 | ||||||||
\(585\) | −1.81959e29 | − | 1.34583e29i | −1.60265 | − | 1.18537i | ||||
\(586\) | 1.93385e28i | 0.167301i | ||||||||
\(587\) | 9.38445e27 | 0.0797460 | 0.0398730 | − | 0.999205i | \(-0.487305\pi\) | ||||
0.0398730 | + | 0.999205i | \(0.487305\pi\) | |||||||
\(588\) | 6.74542e28 | + | 8.95365e28i | 0.563050 | + | 0.747374i | ||||
\(589\) | −6.30946e28 | −0.517347 | ||||||||
\(590\) | 3.49192e28i | 0.281267i | ||||||||
\(591\) | −9.05111e28 | − | 1.79523e29i | −0.716198 | − | 1.42054i | ||||
\(592\) | −1.45621e29 | −1.13200 | ||||||||
\(593\) | −1.65099e29 | −1.26087 | −0.630436 | − | 0.776241i | \(-0.717124\pi\) | ||||
−0.630436 | + | 0.776241i | \(0.717124\pi\) | |||||||
\(594\) | 8.71024e27 | − | 5.07877e28i | 0.0653541 | − | 0.381066i | ||||
\(595\) | −1.47926e29 | + | 1.77035e29i | −1.09048 | + | 1.30506i | ||||
\(596\) | − | 1.12008e29i | − | 0.811267i | ||||||
\(597\) | −4.28044e28 | − | 8.48999e28i | −0.304620 | − | 0.604194i | ||||
\(598\) | − | 5.22240e28i | − | 0.365181i | ||||||
\(599\) | − | 1.09948e29i | − | 0.755452i | −0.925917 | − | 0.377726i | \(-0.876706\pi\) | ||
0.925917 | − | 0.377726i | \(-0.123294\pi\) | |||||||
\(600\) | −3.90272e28 | − | 7.74080e28i | −0.263499 | − | 0.522634i | ||||
\(601\) | − | 1.93693e28i | − | 0.128508i | −0.997934 | − | 0.0642541i | \(-0.979533\pi\) | ||
0.997934 | − | 0.0642541i | \(-0.0204668\pi\) | |||||||
\(602\) | −2.42669e28 | − | 2.02769e28i | −0.158217 | − | 0.132202i | ||||
\(603\) | −4.21924e28 | + | 5.70452e28i | −0.270335 | + | 0.365500i | ||||
\(604\) | 2.69203e29 | 1.69509 | ||||||||
\(605\) | 3.17277e29 | 1.96339 | ||||||||
\(606\) | 8.61776e27 | + | 1.70928e28i | 0.0524121 | + | 0.103956i | ||||
\(607\) | 1.36592e28i | 0.0816474i | 0.999166 | + | 0.0408237i | \(0.0129982\pi\) | ||||
−0.999166 | + | 0.0408237i | \(0.987002\pi\) | |||||||
\(608\) | −4.94066e28 | −0.290267 | ||||||||
\(609\) | 9.44458e28 | + | 2.20222e28i | 0.545382 | + | 0.127168i | ||||
\(610\) | −1.28631e28 | −0.0730101 | ||||||||
\(611\) | 1.21159e29i | 0.675961i | ||||||||
\(612\) | −1.16530e29 | + | 1.57551e29i | −0.639067 | + | 0.864034i | ||||
\(613\) | 1.87515e29 | 1.01089 | 0.505443 | − | 0.862860i | \(-0.331329\pi\) | ||||
0.505443 | + | 0.862860i | \(0.331329\pi\) | |||||||
\(614\) | −1.39878e28 | −0.0741280 | ||||||||
\(615\) | 6.72671e28 | − | 3.39144e28i | 0.350440 | − | 0.176683i | ||||
\(616\) | 9.36983e28 | − | 1.12136e29i | 0.479882 | − | 0.574312i | ||||
\(617\) | − | 7.21390e28i | − | 0.363225i | −0.983370 | − | 0.181613i | \(-0.941868\pi\) | ||
0.983370 | − | 0.181613i | \(-0.0581317\pi\) | |||||||
\(618\) | −4.37531e27 | + | 2.20592e27i | −0.0216586 | + | 0.0109197i | ||||
\(619\) | − | 9.03568e28i | − | 0.439753i | −0.975528 | − | 0.219877i | \(-0.929434\pi\) | ||
0.975528 | − | 0.219877i | \(-0.0705655\pi\) | |||||||
\(620\) | − | 3.59423e29i | − | 1.71986i | ||||||
\(621\) | −2.24169e29 | − | 3.84457e28i | −1.05466 | − | 0.180878i | ||||
\(622\) | 1.05159e29i | 0.486459i | ||||||||
\(623\) | −2.12559e29 | + | 2.54386e29i | −0.966843 | + | 1.15709i | ||||
\(624\) | −1.09934e29 | − | 2.18048e29i | −0.491693 | − | 0.975243i | ||||
\(625\) | −1.75111e29 | −0.770148 | ||||||||
\(626\) | 2.58603e28 | 0.111842 | ||||||||
\(627\) | 1.33461e29 | − | 6.72878e28i | 0.567605 | − | 0.286172i | ||||
\(628\) | − | 1.66479e29i | − | 0.696277i | ||||||
\(629\) | 3.89597e29 | 1.60245 | ||||||||
\(630\) | 9.01898e28 | − | 2.18706e28i | 0.364823 | − | 0.0884676i | ||||
\(631\) | −1.32905e29 | −0.528729 | −0.264364 | − | 0.964423i | \(-0.585162\pi\) | ||||
−0.264364 | + | 0.964423i | \(0.585162\pi\) | |||||||
\(632\) | 1.40337e29i | 0.549091i | ||||||||
\(633\) | −1.97796e29 | + | 9.97240e28i | −0.761166 | + | 0.383761i | ||||
\(634\) | 4.18822e27 | 0.0158523 | ||||||||
\(635\) | −5.67526e29 | −2.11282 | ||||||||
\(636\) | 6.64534e28 | + | 1.31806e29i | 0.243342 | + | 0.482654i | ||||
\(637\) | 3.67785e29 | − | 6.64219e28i | 1.32474 | − | 0.239247i | ||||
\(638\) | − | 6.11097e28i | − | 0.216518i | ||||||
\(639\) | −1.73890e29 | − | 1.28615e29i | −0.606060 | − | 0.448261i | ||||
\(640\) | − | 3.70281e29i | − | 1.26953i | ||||||
\(641\) | 4.35352e29i | 1.46836i | 0.678957 | + | 0.734178i | \(0.262432\pi\) | ||||
−0.678957 | + | 0.734178i | \(0.737568\pi\) | |||||||
\(642\) | 8.27003e28 | − | 4.16954e28i | 0.274403 | − | 0.138347i | ||||
\(643\) | 2.05844e29i | 0.671927i | 0.941875 | + | 0.335964i | \(0.109062\pi\) | ||||
−0.941875 | + | 0.335964i | \(0.890938\pi\) | |||||||
\(644\) | −2.39259e29 | − | 1.99920e29i | −0.768364 | − | 0.642028i | ||||
\(645\) | 3.40355e29 | − | 1.71598e29i | 1.07536 | − | 0.542171i | ||||
\(646\) | 3.90395e28 | 0.121356 | ||||||||
\(647\) | −2.25180e28 | −0.0688709 | −0.0344354 | − | 0.999407i | \(-0.510963\pi\) | ||||
−0.0344354 | + | 0.999407i | \(0.510963\pi\) | |||||||
\(648\) | 1.55927e29 | − | 4.77442e28i | 0.469228 | − | 0.143676i | ||||
\(649\) | − | 3.85918e29i | − | 1.14268i | ||||||
\(650\) | −1.39709e29 | −0.407038 | ||||||||
\(651\) | 4.21652e29 | + | 9.83177e28i | 1.20880 | + | 0.281859i | ||||
\(652\) | −4.79286e29 | −1.35206 | ||||||||
\(653\) | − | 4.78474e29i | − | 1.32822i | −0.747635 | − | 0.664110i | \(-0.768811\pi\) | ||
0.747635 | − | 0.664110i | \(-0.231189\pi\) | |||||||
\(654\) | 6.89492e28 | + | 1.36757e29i | 0.188349 | + | 0.373579i | ||||
\(655\) | −1.04048e29 | −0.279706 | ||||||||
\(656\) | 8.12813e28 | 0.215031 | ||||||||
\(657\) | −3.39293e29 | − | 2.50952e29i | −0.883363 | − | 0.653363i | ||||
\(658\) | −3.81240e28 | − | 3.18556e28i | −0.0976848 | − | 0.0816233i | ||||
\(659\) | − | 2.97678e29i | − | 0.750672i | −0.926889 | − | 0.375336i | \(-0.877527\pi\) | ||
0.926889 | − | 0.375336i | \(-0.122473\pi\) | |||||||
\(660\) | 3.83310e29 | + | 7.60271e29i | 0.951345 | + | 1.88694i | ||||
\(661\) | 5.59125e29i | 1.36582i | 0.730503 | + | 0.682910i | \(0.239286\pi\) | ||||
−0.730503 | + | 0.682910i | \(0.760714\pi\) | |||||||
\(662\) | − | 9.82289e28i | − | 0.236173i | ||||||
\(663\) | 2.94119e29 | + | 5.83368e29i | 0.696036 | + | 1.38054i | ||||
\(664\) | − | 4.08403e28i | − | 0.0951313i | ||||||
\(665\) | 2.06565e29 | + | 1.72601e29i | 0.473619 | + | 0.395745i | ||||
\(666\) | −1.26002e29 | − | 9.31949e28i | −0.284379 | − | 0.210336i | ||||
\(667\) | −2.69729e29 | −0.599248 | ||||||||
\(668\) | −9.70530e28 | −0.212254 | ||||||||
\(669\) | 5.06281e28 | + | 1.00418e29i | 0.108998 | + | 0.216190i | ||||
\(670\) | 8.05221e28i | 0.170659i | ||||||||
\(671\) | 1.42160e29 | 0.296613 | ||||||||
\(672\) | 3.30177e29 | + | 7.69883e28i | 0.678219 | + | 0.158142i | ||||
\(673\) | −2.43237e29 | −0.491893 | −0.245947 | − | 0.969283i | \(-0.579099\pi\) | ||||
−0.245947 | + | 0.969283i | \(0.579099\pi\) | |||||||
\(674\) | 1.85920e29i | 0.370166i | ||||||||
\(675\) | −1.02850e29 | + | 5.99696e29i | −0.201610 | + | 1.17555i | ||||
\(676\) | −3.93768e29 | −0.759977 | ||||||||
\(677\) | 9.11748e29 | 1.73258 | 0.866291 | − | 0.499540i | \(-0.166498\pi\) | ||||
0.866291 | + | 0.499540i | \(0.166498\pi\) | |||||||
\(678\) | 6.13875e28 | − | 3.09500e28i | 0.114860 | − | 0.0579094i | ||||
\(679\) | −4.94837e29 | − | 4.13475e29i | −0.911652 | − | 0.761756i | ||||
\(680\) | 4.60056e29i | 0.834579i | ||||||||
\(681\) | −2.77751e29 | + | 1.40035e29i | −0.496147 | + | 0.250145i | ||||
\(682\) | − | 2.72824e29i | − | 0.479895i | ||||||
\(683\) | 1.45654e29i | 0.252293i | 0.992012 | + | 0.126146i | \(0.0402609\pi\) | ||||
−0.992012 | + | 0.126146i | \(0.959739\pi\) | |||||||
\(684\) | 1.83831e29 | + | 1.35967e29i | 0.313566 | + | 0.231924i | ||||
\(685\) | − | 1.18292e30i | − | 1.98703i | ||||||
\(686\) | −7.57994e28 | + | 1.33192e29i | −0.125390 | + | 0.220331i | ||||
\(687\) | 4.16896e29 | + | 8.26889e29i | 0.679176 | + | 1.34710i | ||||
\(688\) | 4.11263e29 | 0.659844 | ||||||||
\(689\) | 4.92117e29 | 0.777619 | ||||||||
\(690\) | −2.30479e29 | + | 1.16202e29i | −0.358688 | + | 0.180841i | ||||
\(691\) | 2.38869e29i | 0.366135i | 0.983100 | + | 0.183067i | \(0.0586026\pi\) | ||||
−0.983100 | + | 0.183067i | \(0.941397\pi\) | |||||||
\(692\) | 2.66752e29 | 0.402711 | ||||||||
\(693\) | −9.96754e29 | + | 2.41708e29i | −1.48214 | + | 0.359411i | ||||
\(694\) | −2.11803e29 | −0.310212 | ||||||||
\(695\) | − | 1.29534e30i | − | 1.86872i | ||||||
\(696\) | 1.72686e29 | − | 8.70638e28i | 0.245391 | − | 0.123720i | ||||
\(697\) | −2.17461e29 | −0.304395 | ||||||||
\(698\) | −2.82401e29 | −0.389389 | ||||||||
\(699\) | 3.86337e28 | + | 7.66276e28i | 0.0524754 | + | 0.104082i | ||||
\(700\) | −5.34824e29 | + | 6.40064e29i | −0.715618 | + | 0.856435i | ||||
\(701\) | 1.08484e30i | 1.42996i | 0.699143 | + | 0.714981i | \(0.253565\pi\) | ||||
−0.699143 | + | 0.714981i | \(0.746435\pi\) | |||||||
\(702\) | 4.44238e28 | − | 2.59026e29i | 0.0576867 | − | 0.336360i | ||||
\(703\) | − | 4.54583e29i | − | 0.581544i | ||||||
\(704\) | 7.68123e29i | 0.968094i | ||||||||
\(705\) | 5.34707e29 | − | 2.69586e29i | 0.663943 | − | 0.334743i | ||||
\(706\) | 2.67494e29i | 0.327238i | ||||||||
\(707\) | 2.44305e29 | − | 2.92378e29i | 0.294461 | − | 0.352404i | ||||
\(708\) | 5.27166e29 | − | 2.65784e29i | 0.626034 | − | 0.315631i | ||||
\(709\) | −8.41126e29 | −0.984182 | −0.492091 | − | 0.870544i | \(-0.663767\pi\) | ||||
−0.492091 | + | 0.870544i | \(0.663767\pi\) | |||||||
\(710\) | −2.45454e29 | −0.282982 | ||||||||
\(711\) | 5.85726e29 | − | 7.91915e29i | 0.665370 | − | 0.899596i | ||||
\(712\) | 6.61067e29i | 0.739956i | ||||||||
\(713\) | −1.20420e30 | −1.32819 | ||||||||
\(714\) | −2.60895e29 | − | 6.08336e28i | −0.283553 | − | 0.0661168i | ||||
\(715\) | 2.83858e30 | 3.04010 | ||||||||
\(716\) | 1.00062e30i | 1.05605i | ||||||||
\(717\) | −5.38406e29 | − | 1.06789e30i | −0.559962 | − | 1.11065i | ||||
\(718\) | 2.94473e29 | 0.301814 | ||||||||
\(719\) | 4.13198e29 | 0.417354 | 0.208677 | − | 0.977985i | \(-0.433084\pi\) | ||||
0.208677 | + | 0.977985i | \(0.433084\pi\) | |||||||
\(720\) | −7.17695e29 | + | 9.70341e29i | −0.714412 | + | 0.965902i | ||||
\(721\) | 7.48411e28 | + | 6.25355e28i | 0.0734209 | + | 0.0613489i | ||||
\(722\) | 2.16653e29i | 0.209471i | ||||||||
\(723\) | 2.55447e29 | + | 5.06663e29i | 0.243416 | + | 0.482800i | ||||
\(724\) | − | 5.01772e29i | − | 0.471250i | ||||||
\(725\) | 7.21577e29i | 0.667934i | ||||||||
\(726\) | 1.65862e29 | + | 3.28978e29i | 0.151326 | + | 0.300146i | ||||
\(727\) | 3.45036e29i | 0.310279i | 0.987893 | + | 0.155140i | \(0.0495828\pi\) | ||||
−0.987893 | + | 0.155140i | \(0.950417\pi\) | |||||||
\(728\) | 4.77878e29 | − | 5.71913e29i | 0.423582 | − | 0.506933i | ||||
\(729\) | −1.07915e30 | − | 3.81374e29i | −0.942854 | − | 0.333205i | ||||
\(730\) | −4.78930e29 | −0.412460 | ||||||||
\(731\) | −1.10030e30 | −0.934069 | ||||||||
\(732\) | 9.79062e28 | + | 1.94191e29i | 0.0819302 | + | 0.162503i | ||||
\(733\) | 5.24361e28i | 0.0432553i | 0.999766 | + | 0.0216276i | \(0.00688482\pi\) | ||||
−0.999766 | + | 0.0216276i | \(0.993115\pi\) | |||||||
\(734\) | 3.95437e29 | 0.321565 | ||||||||
\(735\) | −1.11149e30 | − | 1.47535e30i | −0.891019 | − | 1.18271i | ||||
\(736\) | −9.42958e29 | −0.745204 | ||||||||
\(737\) | − | 8.89909e29i | − | 0.693325i | ||||||
\(738\) | 7.03303e28 | + | 5.20186e28i | 0.0540195 | + | 0.0399546i | ||||
\(739\) | 3.97690e29 | 0.301147 | 0.150573 | − | 0.988599i | \(-0.451888\pi\) | ||||
0.150573 | + | 0.988599i | \(0.451888\pi\) | |||||||
\(740\) | 2.58956e30 | 1.93327 | ||||||||
\(741\) | 6.80676e29 | − | 3.43180e29i | 0.501013 | − | 0.252598i | ||||
\(742\) | −1.29390e29 | + | 1.54851e29i | −0.0938986 | + | 0.112376i | ||||
\(743\) | − | 1.67451e30i | − | 1.19814i | −0.800698 | − | 0.599068i | \(-0.795538\pi\) | ||
0.800698 | − | 0.599068i | \(-0.204462\pi\) | |||||||
\(744\) | 7.70953e29 | − | 3.88695e29i | 0.543891 | − | 0.274216i | ||||
\(745\) | 1.84563e30i | 1.28382i | ||||||||
\(746\) | − | 1.34268e29i | − | 0.0920902i | ||||||
\(747\) | −1.70455e29 | + | 2.30459e29i | −0.115277 | + | 0.155857i | ||||
\(748\) | − | 2.45781e30i | − | 1.63901i | ||||||
\(749\) | −1.41462e30 | − | 1.18202e30i | −0.930207 | − | 0.777260i | ||||
\(750\) | 5.02278e28 | + | 9.96237e28i | 0.0325687 | + | 0.0645981i | ||||
\(751\) | 6.70899e28 | 0.0428981 | 0.0214490 | − | 0.999770i | \(-0.493172\pi\) | ||||
0.0214490 | + | 0.999770i | \(0.493172\pi\) | |||||||
\(752\) | 6.46106e29 | 0.407396 | ||||||||
\(753\) | −7.47856e29 | + | 3.77050e29i | −0.465019 | + | 0.234451i | ||||
\(754\) | − | 3.11670e29i | − | 0.191116i | ||||||
\(755\) | −4.43583e30 | −2.68245 | ||||||||
\(756\) | −1.01664e30 | − | 1.19511e30i | −0.606303 | − | 0.712734i | ||||
\(757\) | 3.15591e29 | 0.185617 | 0.0928084 | − | 0.995684i | \(-0.470416\pi\) | ||||
0.0928084 | + | 0.995684i | \(0.470416\pi\) | |||||||
\(758\) | − | 3.82523e29i | − | 0.221886i | ||||||
\(759\) | 2.54720e30 | − | 1.28423e30i | 1.45722 | − | 0.734692i | ||||
\(760\) | 5.36795e29 | 0.302877 | ||||||||
\(761\) | 1.60120e30 | 0.891062 | 0.445531 | − | 0.895267i | \(-0.353015\pi\) | ||||
0.445531 | + | 0.895267i | \(0.353015\pi\) | |||||||
\(762\) | −2.96685e29 | − | 5.88457e29i | −0.162843 | − | 0.322989i | ||||
\(763\) | 1.95464e30 | − | 2.33927e30i | 1.05818 | − | 1.26640i | ||||
\(764\) | − | 1.84790e30i | − | 0.986732i | ||||||
\(765\) | 1.92013e30 | − | 2.59607e30i | 1.01131 | − | 1.36732i | ||||
\(766\) | 9.30631e28i | 0.0483477i | ||||||||
\(767\) | − | 1.96825e30i | − | 1.00862i | ||||||
\(768\) | −7.37388e29 | + | 3.71772e29i | −0.372738 | + | 0.187925i | ||||
\(769\) | 2.32609e30i | 1.15985i | 0.814671 | + | 0.579923i | \(0.196917\pi\) | ||||
−0.814671 | + | 0.579923i | \(0.803083\pi\) | |||||||
\(770\) | −7.46333e29 | + | 8.93194e29i | −0.367096 | + | 0.439333i | ||||
\(771\) | −1.36674e30 | + | 6.89078e29i | −0.663156 | + | 0.334347i | ||||
\(772\) | −2.40549e30 | −1.15139 | ||||||||
\(773\) | −3.42342e30 | −1.61650 | −0.808251 | − | 0.588839i | \(-0.799585\pi\) | ||||
−0.808251 | + | 0.588839i | \(0.799585\pi\) | |||||||
\(774\) | 3.55854e29 | + | 2.63201e29i | 0.165765 | + | 0.122605i | ||||
\(775\) | 3.22147e30i | 1.48043i | ||||||||
\(776\) | −1.28592e30 | −0.582997 | ||||||||
\(777\) | −7.08358e29 | + | 3.03791e30i | −0.316834 | + | 1.35880i | ||||
\(778\) | 5.48716e29 | 0.242138 | ||||||||
\(779\) | 2.53735e29i | 0.110468i | ||||||||
\(780\) | 1.95495e30 | + | 3.87752e30i | 0.839733 | + | 1.66556i | ||||
\(781\) | 2.71270e30 | 1.14965 | ||||||||
\(782\) | 7.45094e29 | 0.311559 | ||||||||
\(783\) | −1.33783e30 | − | 2.29442e29i | −0.551954 | − | 0.0946618i | ||||
\(784\) | −3.54210e29 | − | 1.96130e30i | −0.144192 | − | 0.798409i | ||||
\(785\) | 2.74317e30i | 1.10185i | ||||||||
\(786\) | −5.43932e28 | − | 1.07886e29i | −0.0215580 | − | 0.0427589i | ||||
\(787\) | 5.34698e29i | 0.209110i | 0.994519 | + | 0.104555i | \(0.0333418\pi\) | ||||
−0.994519 | + | 0.104555i | \(0.966658\pi\) | |||||||
\(788\) | 3.85754e30i | 1.48863i | ||||||||
\(789\) | −6.67997e29 | − | 1.32493e30i | −0.254370 | − | 0.504528i | ||||
\(790\) | − | 1.11783e30i | − | 0.420040i | ||||||
\(791\) | −1.05005e30 | − | 8.77401e29i | −0.389366 | − | 0.325346i | ||||
\(792\) | −1.21624e30 | + | 1.64438e30i | −0.445045 | + | 0.601711i | ||||
\(793\) | 7.25040e29 | 0.261814 | ||||||||
\(794\) | 1.18973e30 | 0.423967 | ||||||||
\(795\) | −1.09499e30 | − | 2.17185e30i | −0.385085 | − | 0.763793i | ||||
\(796\) | 1.82430e30i | 0.633155i | ||||||||
\(797\) | 2.05810e30 | 0.704945 | 0.352472 | − | 0.935822i | \(-0.385341\pi\) | ||||
0.352472 | + | 0.935822i | \(0.385341\pi\) | |||||||
\(798\) | −7.09808e28 | + | 3.04413e29i | −0.0239944 | + | 0.102904i | ||||
\(799\) | −1.72860e30 | −0.576706 | ||||||||
\(800\) | 2.52259e30i | 0.830620i | ||||||||
\(801\) | 2.75909e30 | − | 3.73036e30i | 0.896654 | − | 1.21230i | ||||
\(802\) | −8.54884e29 | −0.274206 | ||||||||
\(803\) | 5.29300e30 | 1.67567 | ||||||||
\(804\) | 1.21562e30 | − | 6.12885e29i | 0.379848 | − | 0.191510i | ||||
\(805\) | 3.94243e30 | + | 3.29420e30i | 1.21593 | + | 1.01600i | ||||
\(806\) | − | 1.39145e30i | − | 0.423593i | ||||||
\(807\) | −5.09124e30 | + | 2.56688e30i | −1.52986 | + | 0.771317i | ||||
\(808\) | − | 7.59796e29i | − | 0.225361i | ||||||
\(809\) | 7.63848e29i | 0.223639i | 0.993729 | + | 0.111820i | \(0.0356679\pi\) | ||||
−0.993729 | + | 0.111820i | \(0.964332\pi\) | |||||||
\(810\) | −1.24200e30 | + | 3.80296e29i | −0.358946 | + | 0.109908i | ||||
\(811\) | 3.27107e29i | 0.0933190i | 0.998911 | + | 0.0466595i | \(0.0148576\pi\) | ||||
−0.998911 | + | 0.0466595i | \(0.985142\pi\) | |||||||
\(812\) | −1.42789e30 | − | 1.19311e30i | −0.402120 | − | 0.336003i | ||||
\(813\) | −2.42377e30 | − | 4.80741e30i | −0.673816 | − | 1.33647i | ||||
\(814\) | 1.96564e30 | 0.539444 | ||||||||
\(815\) | 7.89751e30 | 2.13961 | ||||||||
\(816\) | 3.11094e30 | − | 1.56846e30i | 0.832043 | − | 0.419495i | ||||
\(817\) | 1.28383e30i | 0.338983i | ||||||||
\(818\) | 7.38622e29 | 0.192536 | ||||||||
\(819\) | −5.08362e30 | + | 1.23275e30i | −1.30825 | + | 0.317245i | ||||
\(820\) | −1.44542e30 | −0.367238 | ||||||||
\(821\) | 2.21419e30i | 0.555408i | 0.960667 | + | 0.277704i | \(0.0895734\pi\) | ||||
−0.960667 | + | 0.277704i | \(0.910427\pi\) | |||||||
\(822\) | 1.22655e30 | − | 6.18394e29i | 0.303760 | − | 0.153148i | ||||
\(823\) | −6.59925e30 | −1.61360 | −0.806801 | − | 0.590823i | \(-0.798803\pi\) | ||||
−0.806801 | + | 0.590823i | \(0.798803\pi\) | |||||||
\(824\) | 1.94488e29 | 0.0469523 | ||||||||
\(825\) | −3.43557e30 | − | 6.81424e30i | −0.818902 | − | 1.62424i | ||||
\(826\) | 6.19334e29 | + | 5.17501e29i | 0.145759 | + | 0.121793i | ||||
\(827\) | 1.41248e30i | 0.328228i | 0.986441 | + | 0.164114i | \(0.0524764\pi\) | ||||
−0.986441 | + | 0.164114i | \(0.947524\pi\) | |||||||
\(828\) | 3.50854e30 | + | 2.59503e30i | 0.805021 | + | 0.595420i | ||||
\(829\) | 5.30162e30i | 1.20112i | 0.799580 | + | 0.600559i | \(0.205055\pi\) | ||||
−0.799580 | + | 0.600559i | \(0.794945\pi\) | |||||||
\(830\) | 3.25304e29i | 0.0727729i | ||||||||
\(831\) | 4.54986e30 | − | 2.29393e30i | 1.00505 | − | 0.506720i | ||||
\(832\) | 3.91756e30i | 0.854517i | ||||||||
\(833\) | 9.47660e29 | + | 5.24730e30i | 0.204117 | + | 1.13022i | ||||
\(834\) | 1.34312e30 | − | 6.77166e29i | 0.285674 | − | 0.144030i | ||||
\(835\) | 1.59920e30 | 0.335889 | ||||||||
\(836\) | −2.86778e30 | −0.594812 | ||||||||
\(837\) | −5.97273e30 | − | 1.02434e30i | −1.22336 | − | 0.209811i | ||||
\(838\) | 1.72780e30i | 0.349488i | ||||||||
\(839\) | −5.61455e30 | −1.12154 | −0.560769 | − | 0.827972i | \(-0.689495\pi\) | ||||
−0.560769 | + | 0.827972i | \(0.689495\pi\) | |||||||
\(840\) | −3.58733e30 | − | 8.36466e29i | −0.707682 | − | 0.165012i | ||||
\(841\) | 3.52311e30 | 0.686386 | ||||||||
\(842\) | 1.10031e30i | 0.211708i | ||||||||
\(843\) | 1.16559e30 | + | 2.31188e30i | 0.221491 | + | 0.439315i | ||||
\(844\) | 4.25019e30 | 0.797651 | ||||||||
\(845\) | 6.48837e30 | 1.20265 | ||||||||
\(846\) | 5.59057e29 | + | 4.13496e29i | 0.102345 | + | 0.0756978i | ||||
\(847\) | 4.70203e30 | − | 5.62728e30i | 0.850177 | − | 1.01747i | ||||
\(848\) | − | 2.62433e30i | − | 0.468664i | ||||||
\(849\) | 2.38617e30 | + | 4.73282e30i | 0.420892 | + | 0.834813i | ||||
\(850\) | − | 1.99327e30i | − | 0.347270i | ||||||
\(851\) | − | 8.67602e30i | − | 1.49300i | ||||||
\(852\) | 1.86825e30 | + | 3.70556e30i | 0.317555 | + | 0.629851i | ||||
\(853\) | 3.37502e30i | 0.566645i | 0.959025 | + | 0.283323i | \(0.0914367\pi\) | ||||
−0.959025 | + | 0.283323i | \(0.908563\pi\) | |||||||
\(854\) | −1.90631e29 | + | 2.28143e29i | −0.0316145 | + | 0.0378355i | ||||
\(855\) | −3.02910e30 | − | 2.24042e30i | −0.496214 | − | 0.367016i | ||||
\(856\) | −3.67613e30 | −0.594862 | ||||||||
\(857\) | −3.90662e30 | −0.624457 | −0.312228 | − | 0.950007i | \(-0.601075\pi\) | ||||
−0.312228 | + | 0.950007i | \(0.601075\pi\) | |||||||
\(858\) | 1.48392e30 | + | 2.94327e30i | 0.234312 | + | 0.464744i | ||||
\(859\) | 4.65168e30i | 0.725574i | 0.931872 | + | 0.362787i | \(0.118175\pi\) | ||||
−0.931872 | + | 0.362787i | \(0.881825\pi\) | |||||||
\(860\) | −7.31345e30 | −1.12691 | ||||||||
\(861\) | 3.95384e29 | − | 1.69567e30i | 0.0601847 | − | 0.258112i | ||||
\(862\) | 2.89614e30 | 0.435506 | ||||||||
\(863\) | − | 7.36536e30i | − | 1.09416i | −0.837080 | − | 0.547080i | \(-0.815739\pi\) | ||
0.837080 | − | 0.547080i | \(-0.184261\pi\) | |||||||
\(864\) | −4.67698e30 | − | 8.02117e29i | −0.686391 | − | 0.117718i | ||||
\(865\) | −4.39544e30 | −0.637285 | ||||||||
\(866\) | 4.13043e29 | 0.0591639 | ||||||||
\(867\) | −2.01323e30 | + | 1.01502e30i | −0.284900 | + | 0.143639i | ||||
\(868\) | −6.37479e30 | − | 5.32663e30i | −0.891269 | − | 0.744724i | ||||
\(869\) | 1.23539e31i | 1.70647i | ||||||||
\(870\) | −1.37549e30 | + | 6.93487e29i | −0.187718 | + | 0.0946425i | ||||
\(871\) | − | 4.53869e30i | − | 0.611984i | ||||||
\(872\) | − | 6.07900e30i | − | 0.809858i | ||||||
\(873\) | 7.25636e30 | + | 5.36704e30i | 0.955145 | + | 0.706456i | ||||
\(874\) | − | 8.69379e29i | − | 0.113068i | ||||||
\(875\) | 1.42391e30 | − | 1.70410e30i | 0.182977 | − | 0.218983i | ||||
\(876\) | 3.64532e30 | + | 7.23027e30i | 0.462852 | + | 0.918039i | ||||
\(877\) | 3.02934e30 | 0.380060 | 0.190030 | − | 0.981778i | \(-0.439141\pi\) | ||||
0.190030 | + | 0.981778i | \(0.439141\pi\) | |||||||
\(878\) | −9.63524e28 | −0.0119446 | ||||||||
\(879\) | −4.81061e30 | + | 2.42539e30i | −0.589273 | + | 0.297097i | ||||
\(880\) | − | 1.51374e31i | − | 1.83224i | ||||||
\(881\) | 3.23996e30 | 0.387519 | 0.193759 | − | 0.981049i | \(-0.437932\pi\) | ||||
0.193759 | + | 0.981049i | \(0.437932\pi\) | |||||||
\(882\) | 9.48710e29 | − | 1.92374e30i | 0.112128 | − | 0.227367i | ||||
\(883\) | 6.38595e30 | 0.745827 | 0.372913 | − | 0.927866i | \(-0.378359\pi\) | ||||
0.372913 | + | 0.927866i | \(0.378359\pi\) | |||||||
\(884\) | − | 1.25352e31i | − | 1.44672i | ||||||
\(885\) | −8.68644e30 | + | 4.37949e30i | −0.990690 | + | 0.499481i | ||||
\(886\) | −3.15027e30 | −0.355054 | ||||||||
\(887\) | −8.04598e30 | −0.896150 | −0.448075 | − | 0.893996i | \(-0.647890\pi\) | ||||
−0.448075 | + | 0.893996i | \(0.647890\pi\) | |||||||
\(888\) | 2.80047e30 | + | 5.55455e30i | 0.308244 | + | 0.611382i | ||||
\(889\) | −8.41072e30 | + | 1.00658e31i | −0.914881 | + | 1.09491i | ||||
\(890\) | − | 5.26559e30i | − | 0.566046i | ||||||
\(891\) | 1.37263e31 | − | 4.20293e30i | 1.45827 | − | 0.446515i | ||||
\(892\) | − | 2.15775e30i | − | 0.226553i | ||||||
\(893\) | 2.01694e30i | 0.209292i | ||||||||
\(894\) | −1.91370e30 | + | 9.64837e29i | −0.196259 | + | 0.0989487i | ||||
\(895\) | − | 1.64879e31i | − | 1.67118i | ||||||
\(896\) | −6.56737e30 | − | 5.48755e30i | −0.657897 | − | 0.549724i | ||||
\(897\) | 1.29911e31 | − | 6.54981e30i | 1.28625 | − | 0.648497i | ||||
\(898\) | −1.61586e30 | −0.158126 | ||||||||
\(899\) | −7.18662e30 | −0.695101 | ||||||||
\(900\) | 6.94219e30 | − | 9.38601e30i | 0.663667 | − | 0.897293i | ||||
\(901\) | 7.02117e30i | 0.663437i | ||||||||
\(902\) | −1.09716e30 | −0.102471 | ||||||||
\(903\) | 2.00055e30 | − | 8.57968e30i | 0.184683 | − | 0.792045i | ||||
\(904\) | −2.72875e30 | −0.248998 | ||||||||
\(905\) | 8.26802e30i | 0.745747i | ||||||||
\(906\) | −2.31891e30 | − | 4.59942e30i | −0.206747 | − | 0.410069i | ||||
\(907\) | 7.97062e30 | 0.702450 | 0.351225 | − | 0.936291i | \(-0.385765\pi\) | ||||
0.351225 | + | 0.936291i | \(0.385765\pi\) | |||||||
\(908\) | 5.96822e30 | 0.519928 | ||||||||
\(909\) | −3.17116e30 | + | 4.28748e30i | −0.273084 | + | 0.369217i | ||||
\(910\) | −3.80643e30 | + | 4.55545e30i | −0.324028 | + | 0.387790i | ||||
\(911\) | − | 4.16999e29i | − | 0.0350907i | −0.999846 | − | 0.0175453i | \(-0.994415\pi\) | ||
0.999846 | − | 0.0175453i | \(-0.00558514\pi\) | |||||||
\(912\) | −1.83008e30 | − | 3.62986e30i | −0.152239 | − | 0.301956i | ||||
\(913\) | − | 3.59517e30i | − | 0.295649i | ||||||
\(914\) | 1.38733e30i | 0.112783i | ||||||||
\(915\) | −1.61326e30 | − | 3.19981e30i | −0.129653 | − | 0.257159i | ||||
\(916\) | − | 1.77679e31i | − | 1.41167i | ||||||
\(917\) | −1.54199e30 | + | 1.84542e30i | −0.121117 | + | 0.144950i | ||||
\(918\) | 3.69560e30 | + | 6.33806e29i | 0.286970 | + | 0.0492162i | ||||
\(919\) | 4.12496e30 | 0.316670 | 0.158335 | − | 0.987385i | \(-0.449387\pi\) | ||||
0.158335 | + | 0.987385i | \(0.449387\pi\) | |||||||
\(920\) | 1.02451e31 | 0.777578 | ||||||||
\(921\) | −1.75432e30 | − | 3.47959e30i | −0.131639 | − | 0.261097i | ||||
\(922\) | 1.39546e30i | 0.103524i | ||||||||
\(923\) | 1.38352e31 | 1.01477 | ||||||||
\(924\) | 1.91649e31 | + | 4.46874e30i | 1.38980 | + | 0.324063i | ||||
\(925\) | −2.32100e31 | −1.66413 | ||||||||
\(926\) | − | 1.82564e30i | − | 0.129420i | ||||||
\(927\) | −1.09748e30 | − | 8.11732e29i | −0.0769237 | − | 0.0568952i | ||||
\(928\) | −5.62753e30 | −0.389999 | ||||||||
\(929\) | −3.85340e30 | −0.264046 | −0.132023 | − | 0.991247i | \(-0.542147\pi\) | ||||
−0.132023 | + | 0.991247i | \(0.542147\pi\) | |||||||
\(930\) | −6.14086e30 | + | 3.09607e30i | −0.416062 | + | 0.209768i | ||||
\(931\) | 6.12256e30 | − | 1.10573e30i | 0.410168 | − | 0.0740762i | ||||
\(932\) | − | 1.64655e30i | − | 0.109071i | ||||||
\(933\) | −2.61591e31 | + | 1.31888e31i | −1.71343 | + | 0.863867i | ||||
\(934\) | − | 6.08747e30i | − | 0.394271i | ||||||
\(935\) | 4.04988e31i | 2.59370i | ||||||||
\(936\) | −6.20302e30 | + | 8.38662e30i | −0.392832 | + | 0.531118i | ||||
\(937\) | − | 1.95142e30i | − | 0.122204i | −0.998132 | − | 0.0611020i | \(-0.980539\pi\) | ||
0.998132 | − | 0.0611020i | \(-0.0194615\pi\) | |||||||
\(938\) | 1.42816e30 | + | 1.19333e30i | 0.0884394 | + | 0.0738980i | ||||
\(939\) | 3.24334e30 | + | 6.43297e30i | 0.198611 | + | 0.393934i | ||||
\(940\) | −1.14896e31 | −0.695767 | ||||||||
\(941\) | 1.60469e31 | 0.960947 | 0.480474 | − | 0.877009i | \(-0.340465\pi\) | ||||
0.480474 | + | 0.877009i | \(0.340465\pi\) | |||||||
\(942\) | −2.84434e30 | + | 1.43405e30i | −0.168441 | + | 0.0849236i | ||||
\(943\) | 4.84269e30i | 0.283605i | ||||||||
\(944\) | −1.04961e31 | −0.607888 | ||||||||
\(945\) | 1.67519e31 | + | 1.96925e31i | 0.959466 | + | 1.12789i | ||||
\(946\) | −5.55135e30 | −0.314443 | ||||||||
\(947\) | 4.95459e30i | 0.277544i | 0.990324 | + | 0.138772i | \(0.0443156\pi\) | ||||
−0.990324 | + | 0.138772i | \(0.955684\pi\) | |||||||
\(948\) | −1.68755e31 | + | 8.50822e30i | −0.934910 | + | 0.471358i | ||||
\(949\) | 2.69952e31 | 1.47908 | ||||||||
\(950\) | −2.32575e30 | −0.126028 | ||||||||
\(951\) | 5.25276e29 | + | 1.04185e30i | 0.0281509 | + | 0.0558356i | ||||
\(952\) | 8.15964e30 | + | 6.81801e30i | 0.432497 | + | 0.361385i | ||||
\(953\) | − | 1.14242e31i | − | 0.598895i | −0.954113 | − | 0.299447i | \(-0.903198\pi\) | ||
0.954113 | − | 0.299447i | \(-0.0968023\pi\) | |||||||
\(954\) | 1.67952e30 | − | 2.27076e30i | 0.0870820 | − | 0.117737i | ||||
\(955\) | 3.04491e31i | 1.56149i | ||||||||
\(956\) | 2.29466e31i | 1.16389i | ||||||||
\(957\) | 1.52015e31 | − | 7.66424e30i | 0.762627 | − | 0.384498i | ||||
\(958\) | − | 6.13273e30i | − | 0.304310i | ||||||
\(959\) | −2.09805e31 | − | 1.75308e31i | −1.02972 | − | 0.860413i | ||||
\(960\) | 1.72893e31 | − | 8.71683e30i | 0.839324 | − | 0.423166i | ||||
\(961\) | −1.12591e31 | −0.540640 | ||||||||
\(962\) | 1.00251e31 | 0.476157 | ||||||||
\(963\) | 2.07442e31 | + | 1.53430e31i | 0.974585 | + | 0.720834i | ||||
\(964\) | − | 1.08870e31i | − | 0.505942i | ||||||
\(965\) | 3.96369e31 | 1.82206 | ||||||||
\(966\) | −1.35472e30 | + | 5.80993e30i | −0.0616011 | + | 0.264187i | ||||
\(967\) | −3.41790e31 | −1.53738 | −0.768690 | − | 0.639622i | \(-0.779091\pi\) | ||||
−0.768690 | + | 0.639622i | \(0.779091\pi\) | |||||||
\(968\) | − | 1.46235e31i | − | 0.650668i | ||||||
\(969\) | 4.89624e30 | + | 9.71139e30i | 0.215508 | + | 0.427446i | ||||
\(970\) | 1.02427e31 | 0.445977 | ||||||||
\(971\) | −3.79278e31 | −1.63364 | −0.816818 | − | 0.576896i | \(-0.804264\pi\) | ||||
−0.816818 | + | 0.576896i | \(0.804264\pi\) | |||||||
\(972\) | 1.51946e31 | + | 1.58556e31i | 0.647430 | + | 0.675595i | ||||
\(973\) | −2.29745e31 | − | 1.91970e31i | −0.968413 | − | 0.809185i | ||||
\(974\) | 6.20631e30i | 0.258800i | ||||||||
\(975\) | −1.75220e31 | − | 3.47538e31i | −0.722828 | − | 1.43369i | ||||
\(976\) | − | 3.86644e30i | − | 0.157793i | ||||||
\(977\) | − | 2.50257e31i | − | 1.01040i | −0.863003 | − | 0.505200i | \(-0.831419\pi\) | ||
0.863003 | − | 0.505200i | \(-0.168581\pi\) | |||||||
\(978\) | 4.12857e30 | + | 8.18877e30i | 0.164908 | + | 0.327085i | ||||
\(979\) | 5.81939e31i | 2.29964i | ||||||||
\(980\) | 6.29888e30 | + | 3.48776e31i | 0.246258 | + | 1.36356i | ||||
\(981\) | −2.53719e31 | + | 3.43034e31i | −0.981360 | + | 1.32682i | ||||
\(982\) | 1.00262e31 | 0.383678 | ||||||||
\(983\) | −3.40644e30 | −0.128970 | −0.0644851 | − | 0.997919i | \(-0.520540\pi\) | ||||
−0.0644851 | + | 0.997919i | \(0.520540\pi\) | |||||||
\(984\) | −1.56314e30 | − | 3.10038e30i | −0.0585529 | − | 0.116136i | ||||
\(985\) | − | 6.35632e31i | − | 2.35573i | ||||||
\(986\) | 4.44668e30 | 0.163053 | ||||||||
\(987\) | 3.14292e30 | − | 1.34789e31i | 0.114026 | − | 0.489018i | ||||
\(988\) | −1.46262e31 | −0.525028 | ||||||||
\(989\) | 2.45028e31i | 0.870273i | ||||||||
\(990\) | 9.68766e30 | − | 1.30979e31i | 0.340447 | − | 0.460292i | ||||
\(991\) | 1.23866e31 | 0.430702 | 0.215351 | − | 0.976537i | \(-0.430910\pi\) | ||||
0.215351 | + | 0.976537i | \(0.430910\pi\) | |||||||
\(992\) | −2.51240e31 | −0.864404 | ||||||||
\(993\) | 2.44352e31 | − | 1.23196e31i | 0.831859 | − | 0.419402i | ||||
\(994\) | −3.63763e30 | + | 4.35343e30i | −0.122535 | + | 0.146647i | ||||
\(995\) | − | 3.00602e31i | − | 1.00196i | ||||||
\(996\) | 4.91103e30 | − | 2.47602e30i | 0.161975 | − | 0.0816639i | ||||
\(997\) | − | 1.86025e31i | − | 0.607116i | −0.952813 | − | 0.303558i | \(-0.901825\pi\) | ||
0.952813 | − | 0.303558i | \(-0.0981745\pi\) | |||||||
\(998\) | − | 7.31126e30i | − | 0.236114i | ||||||
\(999\) | 7.38016e30 | − | 4.30322e31i | 0.235846 | − | 1.37517i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 21.22.c.b.20.8 | yes | 52 | |
3.2 | odd | 2 | inner | 21.22.c.b.20.45 | yes | 52 | |
7.6 | odd | 2 | inner | 21.22.c.b.20.46 | yes | 52 | |
21.20 | even | 2 | inner | 21.22.c.b.20.7 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.22.c.b.20.7 | ✓ | 52 | 21.20 | even | 2 | inner | |
21.22.c.b.20.8 | yes | 52 | 1.1 | even | 1 | trivial | |
21.22.c.b.20.45 | yes | 52 | 3.2 | odd | 2 | inner | |
21.22.c.b.20.46 | yes | 52 | 7.6 | odd | 2 | inner |