Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,11,Mod(19,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.19");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.7071450535\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.2 | ||
Character | \(\chi\) | \(=\) | 20.19 |
Dual form | 20.11.d.d.19.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −31.7400 | + | 4.07116i | −0.991874 | + | 0.127224i | ||||
\(3\) | 190.073 | 0.782194 | 0.391097 | − | 0.920349i | \(-0.372096\pi\) | ||||
0.391097 | + | 0.920349i | \(0.372096\pi\) | |||||||
\(4\) | 990.851 | − | 258.437i | 0.967628 | − | 0.252380i | ||||
\(5\) | 101.732 | − | 3123.34i | 0.0325543 | − | 0.999470i | ||||
\(6\) | −6032.92 | + | 773.819i | −0.775838 | + | 0.0995137i | ||||
\(7\) | 14056.7 | 0.836362 | 0.418181 | − | 0.908364i | \(-0.362668\pi\) | ||||
0.418181 | + | 0.908364i | \(0.362668\pi\) | |||||||
\(8\) | −30397.4 | + | 12236.7i | −0.927657 | + | 0.373434i | ||||
\(9\) | −22921.2 | −0.388173 | ||||||||
\(10\) | 9486.66 | + | 99549.0i | 0.0948666 | + | 0.995490i | ||||
\(11\) | 173205.i | 1.07547i | 0.843115 | + | 0.537733i | \(0.180719\pi\) | ||||
−0.843115 | + | 0.537733i | \(0.819281\pi\) | |||||||
\(12\) | 188334. | − | 49122.0i | 0.756873 | − | 0.197410i | ||||
\(13\) | − | 664258.i | − | 1.78904i | −0.447029 | − | 0.894519i | \(-0.647518\pi\) | ||
0.447029 | − | 0.894519i | \(-0.352482\pi\) | |||||||
\(14\) | −446160. | + | 57227.2i | −0.829566 | + | 0.106405i | ||||
\(15\) | 19336.6 | − | 593664.i | 0.0254638 | − | 0.781779i | ||||
\(16\) | 914997. | − | 512145.i | 0.872609 | − | 0.488420i | ||||
\(17\) | − | 1.08730e6i | − | 0.765782i | −0.923793 | − | 0.382891i | \(-0.874928\pi\) | ||
0.923793 | − | 0.382891i | \(-0.125072\pi\) | |||||||
\(18\) | 727518. | − | 93315.9i | 0.385018 | − | 0.0493848i | ||||
\(19\) | − | 2.14038e6i | − | 0.864417i | −0.901774 | − | 0.432209i | \(-0.857734\pi\) | ||
0.901774 | − | 0.432209i | \(-0.142266\pi\) | |||||||
\(20\) | −706386. | − | 3.12106e6i | −0.220746 | − | 0.975331i | ||||
\(21\) | 2.67181e6 | 0.654197 | ||||||||
\(22\) | −705145. | − | 5.49751e6i | −0.136825 | − | 1.06673i | ||||
\(23\) | 6.85374e6 | 1.06485 | 0.532425 | − | 0.846477i | \(-0.321281\pi\) | ||||
0.532425 | + | 0.846477i | \(0.321281\pi\) | |||||||
\(24\) | −5.77774e6 | + | 2.32587e6i | −0.725607 | + | 0.292098i | ||||
\(25\) | −9.74493e6 | − | 635490.i | −0.997880 | − | 0.0650742i | ||||
\(26\) | 2.70430e6 | + | 2.10835e7i | 0.227608 | + | 1.77450i | ||||
\(27\) | −1.55803e7 | −1.08582 | ||||||||
\(28\) | 1.39281e7 | − | 3.63278e6i | 0.809287 | − | 0.211081i | ||||
\(29\) | 1.60930e7 | 0.784595 | 0.392298 | − | 0.919838i | \(-0.371680\pi\) | ||||
0.392298 | + | 0.919838i | \(0.371680\pi\) | |||||||
\(30\) | 1.80316e6 | + | 1.89216e7i | 0.0742041 | + | 0.778666i | ||||
\(31\) | − | 3.87488e7i | − | 1.35347i | −0.736225 | − | 0.676737i | \(-0.763393\pi\) | ||
0.736225 | − | 0.676737i | \(-0.236607\pi\) | |||||||
\(32\) | −2.69569e7 | + | 1.99806e7i | −0.803379 | + | 0.595468i | ||||
\(33\) | 3.29216e7i | 0.841223i | ||||||||
\(34\) | 4.42658e6 | + | 3.45109e7i | 0.0974258 | + | 0.759560i | ||||
\(35\) | 1.43002e6 | − | 4.39040e7i | 0.0272272 | − | 0.835919i | ||||
\(36\) | −2.27115e7 | + | 5.92369e6i | −0.375607 | + | 0.0979670i | ||||
\(37\) | − | 1.29585e7i | − | 0.186873i | −0.995625 | − | 0.0934365i | \(-0.970215\pi\) | ||
0.995625 | − | 0.0934365i | \(-0.0297852\pi\) | |||||||
\(38\) | 8.71384e6 | + | 6.79357e7i | 0.109974 | + | 0.857393i | ||||
\(39\) | − | 1.26258e8i | − | 1.39938i | ||||||
\(40\) | 3.51270e7 | + | 9.61866e7i | 0.343037 | + | 0.939322i | ||||
\(41\) | 4.48926e7 | 0.387485 | 0.193743 | − | 0.981052i | \(-0.437937\pi\) | ||||
0.193743 | + | 0.981052i | \(0.437937\pi\) | |||||||
\(42\) | −8.48031e7 | + | 1.08774e7i | −0.648881 | + | 0.0832295i | ||||
\(43\) | 8.66330e7 | 0.589307 | 0.294653 | − | 0.955604i | \(-0.404796\pi\) | ||||
0.294653 | + | 0.955604i | \(0.404796\pi\) | |||||||
\(44\) | 4.47625e7 | + | 1.71620e8i | 0.271426 | + | 1.04065i | ||||
\(45\) | −2.33183e6 | + | 7.15908e7i | −0.0126367 | + | 0.387967i | ||||
\(46\) | −2.17538e8 | + | 2.79027e7i | −1.05620 | + | 0.135474i | ||||
\(47\) | −2.64135e8 | −1.15169 | −0.575845 | − | 0.817559i | \(-0.695327\pi\) | ||||
−0.575845 | + | 0.817559i | \(0.695327\pi\) | |||||||
\(48\) | 1.73916e8 | − | 9.73451e7i | 0.682549 | − | 0.382039i | ||||
\(49\) | −8.48835e7 | −0.300499 | ||||||||
\(50\) | 3.11891e8 | − | 1.95027e7i | 0.998051 | − | 0.0624088i | ||||
\(51\) | − | 2.06667e8i | − | 0.598990i | ||||||
\(52\) | −1.71669e8 | − | 6.58180e8i | −0.451518 | − | 1.73112i | ||||
\(53\) | − | 2.29181e8i | − | 0.548025i | −0.961726 | − | 0.274012i | \(-0.911649\pi\) | ||
0.961726 | − | 0.274012i | \(-0.0883509\pi\) | |||||||
\(54\) | 4.94519e8 | − | 6.34301e7i | 1.07700 | − | 0.138142i | ||||
\(55\) | 5.40978e8 | + | 1.76205e7i | 1.07490 | + | 0.0350111i | ||||
\(56\) | −4.27289e8 | + | 1.72008e8i | −0.775857 | + | 0.312326i | ||||
\(57\) | − | 4.06829e8i | − | 0.676142i | ||||||
\(58\) | −5.10790e8 | + | 6.55170e7i | −0.778220 | + | 0.0998192i | ||||
\(59\) | 5.54778e8i | 0.775996i | 0.921660 | + | 0.387998i | \(0.126833\pi\) | ||||
−0.921660 | + | 0.387998i | \(0.873167\pi\) | |||||||
\(60\) | −1.34265e8 | − | 5.93230e8i | −0.172666 | − | 0.762898i | ||||
\(61\) | 8.72720e8 | 1.03330 | 0.516649 | − | 0.856197i | \(-0.327179\pi\) | ||||
0.516649 | + | 0.856197i | \(0.327179\pi\) | |||||||
\(62\) | 1.57753e8 | + | 1.22989e9i | 0.172194 | + | 1.34248i | ||||
\(63\) | −3.22197e8 | −0.324653 | ||||||||
\(64\) | 7.74268e8 | − | 7.43929e8i | 0.721093 | − | 0.692838i | ||||
\(65\) | −2.07470e9 | − | 6.75765e7i | −1.78809 | − | 0.0582410i | ||||
\(66\) | −1.34029e8 | − | 1.04493e9i | −0.107024 | − | 0.834387i | ||||
\(67\) | 1.53061e8 | 0.113368 | 0.0566841 | − | 0.998392i | \(-0.481947\pi\) | ||||
0.0566841 | + | 0.998392i | \(0.481947\pi\) | |||||||
\(68\) | −2.80999e8 | − | 1.07735e9i | −0.193268 | − | 0.740993i | ||||
\(69\) | 1.30271e9 | 0.832920 | ||||||||
\(70\) | 1.33351e8 | + | 1.39933e9i | 0.0793428 | + | 0.832590i | ||||
\(71\) | 3.28433e9i | 1.82035i | 0.414221 | + | 0.910176i | \(0.364054\pi\) | ||||
−0.414221 | + | 0.910176i | \(0.635946\pi\) | |||||||
\(72\) | 6.96746e8 | − | 2.80480e8i | 0.360091 | − | 0.144957i | ||||
\(73\) | 1.61594e9i | 0.779493i | 0.920922 | + | 0.389747i | \(0.127437\pi\) | ||||
−0.920922 | + | 0.389747i | \(0.872563\pi\) | |||||||
\(74\) | 5.27562e7 | + | 4.11303e8i | 0.0237747 | + | 0.185355i | ||||
\(75\) | −1.85225e9 | − | 1.20790e8i | −0.780536 | − | 0.0509006i | ||||
\(76\) | −5.53154e8 | − | 2.12080e9i | −0.218162 | − | 0.836434i | ||||
\(77\) | 2.43469e9i | 0.899478i | ||||||||
\(78\) | 5.14015e8 | + | 4.00741e9i | 0.178034 | + | 1.38800i | ||||
\(79\) | 3.08746e9i | 1.00338i | 0.865047 | + | 0.501690i | \(0.167288\pi\) | ||||
−0.865047 | + | 0.501690i | \(0.832712\pi\) | |||||||
\(80\) | −1.50652e9 | − | 2.90995e9i | −0.459754 | − | 0.888046i | ||||
\(81\) | −1.60793e9 | −0.461150 | ||||||||
\(82\) | −1.42489e9 | + | 1.82765e8i | −0.384337 | + | 0.0492974i | ||||
\(83\) | 1.89093e9 | 0.480049 | 0.240024 | − | 0.970767i | \(-0.422845\pi\) | ||||
0.240024 | + | 0.970767i | \(0.422845\pi\) | |||||||
\(84\) | 2.64736e9 | − | 6.90494e8i | 0.633020 | − | 0.165106i | ||||
\(85\) | −3.39602e9 | − | 1.10614e8i | −0.765377 | − | 0.0249295i | ||||
\(86\) | −2.74973e9 | + | 3.52697e8i | −0.584518 | + | 0.0749738i | ||||
\(87\) | 3.05884e9 | 0.613706 | ||||||||
\(88\) | −2.11946e9 | − | 5.26498e9i | −0.401616 | − | 0.997663i | ||||
\(89\) | 8.69033e9 | 1.55627 | 0.778137 | − | 0.628095i | \(-0.216165\pi\) | ||||
0.778137 | + | 0.628095i | \(0.216165\pi\) | |||||||
\(90\) | −2.17446e8 | − | 2.28178e9i | −0.0368246 | − | 0.386422i | ||||
\(91\) | − | 9.33729e9i | − | 1.49628i | ||||||
\(92\) | 6.79104e9 | − | 1.77126e9i | 1.03038 | − | 0.268747i | ||||
\(93\) | − | 7.36511e9i | − | 1.05868i | ||||||
\(94\) | 8.38362e9 | − | 1.07533e9i | 1.14233 | − | 0.146523i | ||||
\(95\) | −6.68515e9 | − | 2.17746e8i | −0.863959 | − | 0.0281405i | ||||
\(96\) | −5.12379e9 | + | 3.79777e9i | −0.628398 | + | 0.465771i | ||||
\(97\) | − | 5.78965e9i | − | 0.674207i | −0.941468 | − | 0.337104i | \(-0.890553\pi\) | ||
0.941468 | − | 0.337104i | \(-0.109447\pi\) | |||||||
\(98\) | 2.69420e9 | − | 3.45574e8i | 0.298057 | − | 0.0382306i | ||||
\(99\) | − | 3.97006e9i | − | 0.417466i | ||||||
\(100\) | −9.82001e9 | + | 1.88877e9i | −0.982001 | + | 0.188877i | ||||
\(101\) | −1.07828e10 | −1.02594 | −0.512971 | − | 0.858406i | \(-0.671455\pi\) | ||||
−0.512971 | + | 0.858406i | \(0.671455\pi\) | |||||||
\(102\) | 8.41374e8 | + | 6.55960e9i | 0.0762058 | + | 0.594123i | ||||
\(103\) | 7.05867e9 | 0.608887 | 0.304444 | − | 0.952530i | \(-0.401529\pi\) | ||||
0.304444 | + | 0.952530i | \(0.401529\pi\) | |||||||
\(104\) | 8.12832e9 | + | 2.01917e10i | 0.668089 | + | 1.65961i | ||||
\(105\) | 2.71809e8 | − | 8.34497e9i | 0.0212970 | − | 0.653851i | ||||
\(106\) | 9.33035e8 | + | 7.27421e9i | 0.0697218 | + | 0.543571i | ||||
\(107\) | −1.81193e9 | −0.129188 | −0.0645942 | − | 0.997912i | \(-0.520575\pi\) | ||||
−0.0645942 | + | 0.997912i | \(0.520575\pi\) | |||||||
\(108\) | −1.54378e10 | + | 4.02654e9i | −1.05067 | + | 0.274039i | ||||
\(109\) | 1.33028e10 | 0.864588 | 0.432294 | − | 0.901733i | \(-0.357704\pi\) | ||||
0.432294 | + | 0.901733i | \(0.357704\pi\) | |||||||
\(110\) | −1.72424e10 | + | 1.64313e9i | −1.07062 | + | 0.102026i | ||||
\(111\) | − | 2.46307e9i | − | 0.146171i | ||||||
\(112\) | 1.28619e10 | − | 7.19909e9i | 0.729817 | − | 0.408496i | ||||
\(113\) | 2.35102e10i | 1.27604i | 0.770019 | + | 0.638020i | \(0.220246\pi\) | ||||
−0.770019 | + | 0.638020i | \(0.779754\pi\) | |||||||
\(114\) | 1.65627e9 | + | 1.29127e10i | 0.0860214 | + | 0.670648i | ||||
\(115\) | 6.97247e8 | − | 2.14066e10i | 0.0346655 | − | 1.06429i | ||||
\(116\) | 1.59457e10 | − | 4.15902e9i | 0.759197 | − | 0.198016i | ||||
\(117\) | 1.52256e10i | 0.694456i | ||||||||
\(118\) | −2.25859e9 | − | 1.76086e10i | −0.0987251 | − | 0.769690i | ||||
\(119\) | − | 1.52839e10i | − | 0.640471i | ||||||
\(120\) | 6.67670e9 | + | 1.82825e10i | 0.268322 | + | 0.734732i | ||||
\(121\) | −4.06247e9 | −0.156626 | ||||||||
\(122\) | −2.77001e10 | + | 3.55298e9i | −1.02490 | + | 0.131460i | ||||
\(123\) | 8.53287e9 | 0.303089 | ||||||||
\(124\) | −1.00141e10 | − | 3.83943e10i | −0.341590 | − | 1.30966i | ||||
\(125\) | −2.97623e9 | + | 3.03721e10i | −0.0975250 | + | 0.995233i | ||||
\(126\) | 1.02265e10 | − | 1.31172e9i | 0.322015 | − | 0.0413036i | ||||
\(127\) | −4.14600e10 | −1.25490 | −0.627452 | − | 0.778655i | \(-0.715902\pi\) | ||||
−0.627452 | + | 0.778655i | \(0.715902\pi\) | |||||||
\(128\) | −2.15466e10 | + | 2.67645e10i | −0.627088 | + | 0.778948i | ||||
\(129\) | 1.64666e10 | 0.460952 | ||||||||
\(130\) | 6.61262e10 | − | 6.30158e9i | 1.78097 | − | 0.169720i | ||||
\(131\) | − | 1.38898e9i | − | 0.0360030i | −0.999838 | − | 0.0180015i | \(-0.994270\pi\) | ||
0.999838 | − | 0.0180015i | \(-0.00573037\pi\) | |||||||
\(132\) | 8.50816e9 | + | 3.26204e10i | 0.212308 | + | 0.813991i | ||||
\(133\) | − | 3.00868e10i | − | 0.722966i | ||||||
\(134\) | −4.85816e9 | + | 6.23137e8i | −0.112447 | + | 0.0144231i | ||||
\(135\) | −1.58502e9 | + | 4.86627e10i | −0.0353482 | + | 1.08524i | ||||
\(136\) | 1.33050e10 | + | 3.30512e10i | 0.285970 | + | 0.710383i | ||||
\(137\) | − | 4.15616e10i | − | 0.861170i | −0.902550 | − | 0.430585i | \(-0.858307\pi\) | ||
0.902550 | − | 0.430585i | \(-0.141693\pi\) | |||||||
\(138\) | −4.13481e10 | + | 5.30355e9i | −0.826152 | + | 0.105967i | ||||
\(139\) | 7.90047e10i | 1.52258i | 0.648414 | + | 0.761288i | \(0.275433\pi\) | ||||
−0.648414 | + | 0.761288i | \(0.724567\pi\) | |||||||
\(140\) | −9.92948e9 | − | 4.38719e10i | −0.184623 | − | 0.815730i | ||||
\(141\) | −5.02049e10 | −0.900846 | ||||||||
\(142\) | −1.33711e10 | − | 1.04245e11i | −0.231592 | − | 1.80556i | ||||
\(143\) | 1.15053e11 | 1.92405 | ||||||||
\(144\) | −2.09728e10 | + | 1.17390e10i | −0.338723 | + | 0.189591i | ||||
\(145\) | 1.63717e9 | − | 5.02638e10i | 0.0255420 | − | 0.784179i | ||||
\(146\) | −6.57877e9 | − | 5.12900e10i | −0.0991701 | − | 0.773159i | ||||
\(147\) | −1.61341e10 | −0.235048 | ||||||||
\(148\) | −3.34896e9 | − | 1.28400e10i | −0.0471630 | − | 0.180824i | ||||
\(149\) | −3.37967e9 | −0.0460197 | −0.0230098 | − | 0.999735i | \(-0.507325\pi\) | ||||
−0.0230098 | + | 0.999735i | \(0.507325\pi\) | |||||||
\(150\) | 5.92821e10 | − | 3.70695e9i | 0.780669 | − | 0.0488158i | ||||
\(151\) | 6.40458e10i | 0.815841i | 0.913017 | + | 0.407921i | \(0.133746\pi\) | ||||
−0.913017 | + | 0.407921i | \(0.866254\pi\) | |||||||
\(152\) | 2.61912e10 | + | 6.50622e10i | 0.322803 | + | 0.801882i | ||||
\(153\) | 2.49223e10i | 0.297256i | ||||||||
\(154\) | −9.91203e9 | − | 7.72771e10i | −0.114435 | − | 0.892169i | ||||
\(155\) | −1.21026e11 | − | 3.94201e9i | −1.35276 | − | 0.0440614i | ||||
\(156\) | −3.26296e10 | − | 1.25102e11i | −0.353174 | − | 1.35408i | ||||
\(157\) | − | 1.27096e10i | − | 0.133239i | −0.997778 | − | 0.0666197i | \(-0.978779\pi\) | ||
0.997778 | − | 0.0666197i | \(-0.0212214\pi\) | |||||||
\(158\) | −1.25695e10 | − | 9.79958e10i | −0.127654 | − | 0.995227i | ||||
\(159\) | − | 4.35612e10i | − | 0.428662i | ||||||
\(160\) | 5.96638e10 | + | 8.62284e10i | 0.568999 | + | 0.822339i | ||||
\(161\) | 9.63413e10 | 0.890601 | ||||||||
\(162\) | 5.10356e10 | − | 6.54614e9i | 0.457402 | − | 0.0586692i | ||||
\(163\) | 1.71627e11 | 1.49158 | 0.745790 | − | 0.666181i | \(-0.232072\pi\) | ||||
0.745790 | + | 0.666181i | \(0.232072\pi\) | |||||||
\(164\) | 4.44819e10 | − | 1.16019e10i | 0.374942 | − | 0.0977935i | ||||
\(165\) | 1.02825e11 | + | 3.34919e9i | 0.840777 | + | 0.0273855i | ||||
\(166\) | −6.00181e10 | + | 7.69829e9i | −0.476148 | + | 0.0610737i | ||||
\(167\) | −1.27551e11 | −0.981976 | −0.490988 | − | 0.871166i | \(-0.663364\pi\) | ||||
−0.490988 | + | 0.871166i | \(0.663364\pi\) | |||||||
\(168\) | −8.12161e10 | + | 3.26941e10i | −0.606870 | + | 0.244300i | ||||
\(169\) | −3.03380e11 | −2.20066 | ||||||||
\(170\) | 1.08240e11 | − | 1.03149e10i | 0.762329 | − | 0.0726471i | ||||
\(171\) | 4.90601e10i | 0.335543i | ||||||||
\(172\) | 8.58405e10 | − | 2.23892e10i | 0.570230 | − | 0.148729i | ||||
\(173\) | 1.87423e11i | 1.20946i | 0.796429 | + | 0.604732i | \(0.206720\pi\) | ||||
−0.796429 | + | 0.604732i | \(0.793280\pi\) | |||||||
\(174\) | −9.70874e10 | + | 1.24530e10i | −0.608719 | + | 0.0780780i | ||||
\(175\) | −1.36982e11 | − | 8.93291e9i | −0.834589 | − | 0.0544256i | ||||
\(176\) | 8.87060e10 | + | 1.58482e11i | 0.525279 | + | 0.938461i | ||||
\(177\) | 1.05448e11i | 0.606979i | ||||||||
\(178\) | −2.75831e11 | + | 3.53797e10i | −1.54363 | + | 0.197995i | ||||
\(179\) | − | 1.33805e11i | − | 0.728126i | −0.931374 | − | 0.364063i | \(-0.881389\pi\) | ||
0.931374 | − | 0.364063i | \(-0.118611\pi\) | |||||||
\(180\) | 1.61912e10 | + | 7.15384e10i | 0.0856874 | + | 0.378597i | ||||
\(181\) | 3.51003e11 | 1.80683 | 0.903417 | − | 0.428764i | \(-0.141051\pi\) | ||||
0.903417 | + | 0.428764i | \(0.141051\pi\) | |||||||
\(182\) | 3.80136e10 | + | 2.96365e11i | 0.190363 | + | 1.48413i | ||||
\(183\) | 1.65881e11 | 0.808239 | ||||||||
\(184\) | −2.08336e11 | + | 8.38672e10i | −0.987816 | + | 0.397652i | ||||
\(185\) | −4.04739e10 | − | 1.31830e9i | −0.186774 | − | 0.00608353i | ||||
\(186\) | 2.99845e10 | + | 2.33768e11i | 0.134689 | + | 1.05008i | ||||
\(187\) | 1.88326e11 | 0.823573 | ||||||||
\(188\) | −2.61718e11 | + | 6.82622e10i | −1.11441 | + | 0.290664i | ||||
\(189\) | −2.19009e11 | −0.908139 | ||||||||
\(190\) | 2.13073e11 | − | 2.03051e10i | 0.860519 | − | 0.0820043i | ||||
\(191\) | − | 3.35424e11i | − | 1.31956i | −0.751460 | − | 0.659778i | \(-0.770650\pi\) | ||
0.751460 | − | 0.659778i | \(-0.229350\pi\) | |||||||
\(192\) | 1.47168e11 | − | 1.41401e11i | 0.564035 | − | 0.541934i | ||||
\(193\) | − | 4.42274e11i | − | 1.65160i | −0.563964 | − | 0.825800i | \(-0.690724\pi\) | ||
0.563964 | − | 0.825800i | \(-0.309276\pi\) | |||||||
\(194\) | 2.35706e10 | + | 1.83763e11i | 0.0857752 | + | 0.668729i | ||||
\(195\) | −3.94346e11 | − | 1.28445e10i | −1.39863 | − | 0.0455557i | ||||
\(196\) | −8.41069e10 | + | 2.19370e10i | −0.290771 | + | 0.0758399i | ||||
\(197\) | 6.39016e10i | 0.215368i | 0.994185 | + | 0.107684i | \(0.0343434\pi\) | ||||
−0.994185 | + | 0.107684i | \(0.965657\pi\) | |||||||
\(198\) | 1.61628e10 | + | 1.26010e11i | 0.0531116 | + | 0.414074i | ||||
\(199\) | − | 2.95320e11i | − | 0.946298i | −0.880982 | − | 0.473149i | \(-0.843117\pi\) | ||
0.880982 | − | 0.473149i | \(-0.156883\pi\) | |||||||
\(200\) | 3.03997e11 | − | 9.99285e10i | 0.949991 | − | 0.312276i | ||||
\(201\) | 2.90928e10 | 0.0886759 | ||||||||
\(202\) | 3.42244e11 | − | 4.38983e10i | 1.01761 | − | 0.130524i | ||||
\(203\) | 2.26214e11 | 0.656206 | ||||||||
\(204\) | −5.34104e10 | − | 2.04776e11i | −0.151173 | − | 0.579600i | ||||
\(205\) | 4.56703e9 | − | 1.40215e11i | 0.0126143 | − | 0.387280i | ||||
\(206\) | −2.24042e11 | + | 2.87370e10i | −0.603939 | + | 0.0774649i | ||||
\(207\) | −1.57096e11 | −0.413346 | ||||||||
\(208\) | −3.40196e11 | − | 6.07793e11i | −0.873802 | − | 1.56113i | ||||
\(209\) | 3.70725e11 | 0.929651 | ||||||||
\(210\) | 2.53465e10 | + | 2.65976e11i | 0.0620614 | + | 0.651247i | ||||
\(211\) | 1.50649e11i | 0.360208i | 0.983648 | + | 0.180104i | \(0.0576435\pi\) | ||||
−0.983648 | + | 0.180104i | \(0.942356\pi\) | |||||||
\(212\) | −5.92290e10 | − | 2.27085e11i | −0.138310 | − | 0.530284i | ||||
\(213\) | 6.24264e11i | 1.42387i | ||||||||
\(214\) | 5.75107e10 | − | 7.37668e9i | 0.128139 | − | 0.0164358i | ||||
\(215\) | 8.81338e9 | − | 2.70585e11i | 0.0191845 | − | 0.588994i | ||||
\(216\) | 4.73602e11 | − | 1.90652e11i | 1.00727 | − | 0.405483i | ||||
\(217\) | − | 5.44682e11i | − | 1.13199i | ||||||
\(218\) | −4.22229e11 | + | 5.41577e10i | −0.857563 | + | 0.109996i | ||||
\(219\) | 3.07148e11i | 0.609715i | ||||||||
\(220\) | 5.40583e11 | − | 1.22349e11i | 1.04894 | − | 0.237404i | ||||
\(221\) | −7.22248e11 | −1.37001 | ||||||||
\(222\) | 1.00275e10 | + | 7.81776e10i | 0.0185964 | + | 0.144983i | ||||
\(223\) | 8.28926e11 | 1.50311 | 0.751556 | − | 0.659669i | \(-0.229304\pi\) | ||||
0.751556 | + | 0.659669i | \(0.229304\pi\) | |||||||
\(224\) | −3.78926e11 | + | 2.80862e11i | −0.671916 | + | 0.498027i | ||||
\(225\) | 2.23365e11 | + | 1.45662e10i | 0.387350 | + | 0.0252600i | ||||
\(226\) | −9.57139e10 | − | 7.46214e11i | −0.162343 | − | 1.26567i | ||||
\(227\) | −5.67893e11 | −0.942187 | −0.471093 | − | 0.882083i | \(-0.656140\pi\) | ||||
−0.471093 | + | 0.882083i | \(0.656140\pi\) | |||||||
\(228\) | −1.05140e11 | − | 4.03107e11i | −0.170645 | − | 0.654254i | ||||
\(229\) | 6.29580e10 | 0.0999708 | 0.0499854 | − | 0.998750i | \(-0.484083\pi\) | ||||
0.0499854 | + | 0.998750i | \(0.484083\pi\) | |||||||
\(230\) | 6.50191e10 | + | 6.82283e11i | 0.101019 | + | 1.06005i | ||||
\(231\) | 4.62770e11i | 0.703567i | ||||||||
\(232\) | −4.89185e11 | + | 1.96925e11i | −0.727835 | + | 0.292995i | ||||
\(233\) | − | 3.90579e11i | − | 0.568760i | −0.958712 | − | 0.284380i | \(-0.908212\pi\) | ||
0.958712 | − | 0.284380i | \(-0.0917877\pi\) | |||||||
\(234\) | −6.19858e10 | − | 4.83259e11i | −0.0883513 | − | 0.688813i | ||||
\(235\) | −2.68710e10 | + | 8.24983e11i | −0.0374925 | + | 1.15108i | ||||
\(236\) | 1.43375e11 | + | 5.49703e11i | 0.195846 | + | 0.750875i | ||||
\(237\) | 5.86843e11i | 0.784838i | ||||||||
\(238\) | 6.22233e10 | + | 4.85111e11i | 0.0814832 | + | 0.635267i | ||||
\(239\) | 8.56345e11i | 1.09814i | 0.835775 | + | 0.549072i | \(0.185019\pi\) | ||||
−0.835775 | + | 0.549072i | \(0.814981\pi\) | |||||||
\(240\) | −2.86349e11 | − | 5.53103e11i | −0.359617 | − | 0.694625i | ||||
\(241\) | −2.19603e11 | −0.270117 | −0.135059 | − | 0.990838i | \(-0.543122\pi\) | ||||
−0.135059 | + | 0.990838i | \(0.543122\pi\) | |||||||
\(242\) | 1.28943e11 | − | 1.65390e10i | 0.155353 | − | 0.0199265i | ||||
\(243\) | 6.14379e11 | 0.725112 | ||||||||
\(244\) | 8.64735e11 | − | 2.25543e11i | 0.999848 | − | 0.260784i | ||||
\(245\) | −8.63539e9 | + | 2.65120e11i | −0.00978254 | + | 0.300339i | ||||
\(246\) | −2.70833e11 | + | 3.47387e10i | −0.300626 | + | 0.0385601i | ||||
\(247\) | −1.42177e12 | −1.54648 | ||||||||
\(248\) | 4.74158e11 | + | 1.17786e12i | 0.505434 | + | 1.25556i | ||||
\(249\) | 3.59415e11 | 0.375491 | ||||||||
\(250\) | −2.91844e10 | − | 9.76126e11i | −0.0298848 | − | 0.999553i | ||||
\(251\) | − | 3.77174e11i | − | 0.378593i | −0.981920 | − | 0.189297i | \(-0.939379\pi\) | ||
0.981920 | − | 0.189297i | \(-0.0606208\pi\) | |||||||
\(252\) | −3.19250e11 | + | 8.32677e10i | −0.314143 | + | 0.0819358i | ||||
\(253\) | 1.18710e12i | 1.14521i | ||||||||
\(254\) | 1.31594e12 | − | 1.68790e11i | 1.24471 | − | 0.159654i | ||||
\(255\) | −6.45492e11 | − | 2.10247e10i | −0.598673 | − | 0.0194997i | ||||
\(256\) | 5.74926e11 | − | 9.37223e11i | 0.522892 | − | 0.852399i | ||||
\(257\) | − | 8.23925e11i | − | 0.734889i | −0.930045 | − | 0.367445i | \(-0.880233\pi\) | ||
0.930045 | − | 0.367445i | \(-0.119767\pi\) | |||||||
\(258\) | −5.22650e11 | + | 6.70383e10i | −0.457206 | + | 0.0586441i | ||||
\(259\) | − | 1.82154e11i | − | 0.156293i | ||||||
\(260\) | −2.07319e12 | + | 4.69222e11i | −1.74491 | + | 0.394923i | ||||
\(261\) | −3.68870e11 | −0.304558 | ||||||||
\(262\) | 5.65476e9 | + | 4.40861e10i | 0.00458044 | + | 0.0357105i | ||||
\(263\) | 1.08787e12 | 0.864568 | 0.432284 | − | 0.901737i | \(-0.357708\pi\) | ||||
0.432284 | + | 0.901737i | \(0.357708\pi\) | |||||||
\(264\) | −4.02852e11 | − | 1.00073e12i | −0.314142 | − | 0.780366i | ||||
\(265\) | −7.15812e11 | − | 2.33152e10i | −0.547734 | − | 0.0178406i | ||||
\(266\) | 1.22488e11 | + | 9.54954e11i | 0.0919784 | + | 0.717091i | ||||
\(267\) | 1.65180e12 | 1.21731 | ||||||||
\(268\) | 1.51661e11 | − | 3.95567e10i | 0.109698 | − | 0.0286119i | ||||
\(269\) | 1.57558e12 | 1.11861 | 0.559305 | − | 0.828962i | \(-0.311068\pi\) | ||||
0.559305 | + | 0.828962i | \(0.311068\pi\) | |||||||
\(270\) | −1.47805e11 | − | 1.55101e12i | −0.103008 | − | 1.08092i | ||||
\(271\) | 7.48035e11i | 0.511771i | 0.966707 | + | 0.255885i | \(0.0823670\pi\) | ||||
−0.966707 | + | 0.255885i | \(0.917633\pi\) | |||||||
\(272\) | −5.56857e11 | − | 9.94877e11i | −0.374023 | − | 0.668228i | ||||
\(273\) | − | 1.77477e12i | − | 1.17038i | ||||||
\(274\) | 1.69204e11 | + | 1.31916e12i | 0.109561 | + | 0.854172i | ||||
\(275\) | 1.10070e11 | − | 1.68787e12i | 0.0699850 | − | 1.07319i | ||||
\(276\) | 1.29079e12 | − | 3.36669e11i | 0.805957 | − | 0.210212i | ||||
\(277\) | 1.35578e12i | 0.831360i | 0.909511 | + | 0.415680i | \(0.136456\pi\) | ||||
−0.909511 | + | 0.415680i | \(0.863544\pi\) | |||||||
\(278\) | −3.21641e11 | − | 2.50761e12i | −0.193708 | − | 1.51020i | ||||
\(279\) | 8.88169e11i | 0.525381i | ||||||||
\(280\) | 4.93771e11 | + | 1.35207e12i | 0.286903 | + | 0.785613i | ||||
\(281\) | −6.65579e11 | −0.379899 | −0.189949 | − | 0.981794i | \(-0.560832\pi\) | ||||
−0.189949 | + | 0.981794i | \(0.560832\pi\) | |||||||
\(282\) | 1.59350e12 | − | 2.04392e11i | 0.893526 | − | 0.114609i | ||||
\(283\) | −3.17294e12 | −1.74795 | −0.873977 | − | 0.485968i | \(-0.838467\pi\) | ||||
−0.873977 | + | 0.485968i | \(0.838467\pi\) | |||||||
\(284\) | 8.48794e11 | + | 3.25429e12i | 0.459421 | + | 1.76142i | ||||
\(285\) | −1.27067e12 | − | 4.13877e10i | −0.675784 | − | 0.0220114i | ||||
\(286\) | −3.65177e12 | + | 4.68398e11i | −1.90841 | + | 0.244785i | ||||
\(287\) | 6.31043e11 | 0.324078 | ||||||||
\(288\) | 6.17885e11 | − | 4.57979e11i | 0.311850 | − | 0.231144i | ||||
\(289\) | 8.33769e11 | 0.413577 | ||||||||
\(290\) | 1.52668e11 | + | 1.60204e12i | 0.0744319 | + | 0.781057i | ||||
\(291\) | − | 1.10046e12i | − | 0.527361i | ||||||
\(292\) | 4.17620e11 | + | 1.60116e12i | 0.196728 | + | 0.754259i | ||||
\(293\) | 3.22248e11i | 0.149229i | 0.997212 | + | 0.0746144i | \(0.0237726\pi\) | ||||
−0.997212 | + | 0.0746144i | \(0.976227\pi\) | |||||||
\(294\) | 5.12095e11 | − | 6.56844e10i | 0.233138 | − | 0.0299037i | ||||
\(295\) | 1.73276e12 | + | 5.64389e10i | 0.775584 | + | 0.0252620i | ||||
\(296\) | 1.58569e11 | + | 3.93906e11i | 0.0697848 | + | 0.173354i | ||||
\(297\) | − | 2.69859e12i | − | 1.16776i | ||||||
\(298\) | 1.07271e11 | − | 1.37592e10i | 0.0456457 | − | 0.00585480i | ||||
\(299\) | − | 4.55265e12i | − | 1.90506i | ||||||
\(300\) | −1.86652e12 | + | 3.59005e11i | −0.768115 | + | 0.147739i | ||||
\(301\) | 1.21778e12 | 0.492874 | ||||||||
\(302\) | −2.60741e11 | − | 2.03281e12i | −0.103794 | − | 0.809212i | ||||
\(303\) | −2.04951e12 | −0.802486 | ||||||||
\(304\) | −1.09619e12 | − | 1.95844e12i | −0.422199 | − | 0.754298i | ||||
\(305\) | 8.87838e10 | − | 2.72580e12i | 0.0336383 | − | 1.03275i | ||||
\(306\) | −1.01463e11 | − | 7.91032e11i | −0.0378180 | − | 0.294840i | ||||
\(307\) | 1.97279e12 | 0.723418 | 0.361709 | − | 0.932291i | \(-0.382193\pi\) | ||||
0.361709 | + | 0.932291i | \(0.382193\pi\) | |||||||
\(308\) | 6.29215e11 | + | 2.41242e12i | 0.227010 | + | 0.870361i | ||||
\(309\) | 1.34166e12 | 0.476268 | ||||||||
\(310\) | 3.85740e12 | − | 3.67597e11i | 1.34737 | − | 0.128399i | ||||
\(311\) | − | 5.13332e12i | − | 1.76440i | −0.470879 | − | 0.882198i | \(-0.656063\pi\) | ||
0.470879 | − | 0.882198i | \(-0.343937\pi\) | |||||||
\(312\) | 1.54498e12 | + | 3.83791e12i | 0.522575 | + | 1.29814i | ||||
\(313\) | 2.38086e10i | 0.00792523i | 0.999992 | + | 0.00396261i | \(0.00126134\pi\) | ||||
−0.999992 | + | 0.00396261i | \(0.998739\pi\) | |||||||
\(314\) | 5.17427e10 | + | 4.03401e11i | 0.0169512 | + | 0.132157i | ||||
\(315\) | −3.27779e10 | + | 1.00633e12i | −0.0105689 | + | 0.324481i | ||||
\(316\) | 7.97913e11 | + | 3.05921e12i | 0.253233 | + | 0.970899i | ||||
\(317\) | 5.06007e12i | 1.58074i | 0.612630 | + | 0.790370i | \(0.290111\pi\) | ||||
−0.612630 | + | 0.790370i | \(0.709889\pi\) | |||||||
\(318\) | 1.77345e11 | + | 1.38263e12i | 0.0545360 | + | 0.425178i | ||||
\(319\) | 2.78738e12i | 0.843805i | ||||||||
\(320\) | −2.24478e12 | − | 2.49399e12i | −0.668996 | − | 0.743266i | ||||
\(321\) | −3.44400e11 | −0.101050 | ||||||||
\(322\) | −3.05787e12 | + | 3.92221e11i | −0.883364 | + | 0.113306i | ||||
\(323\) | −2.32724e12 | −0.661956 | ||||||||
\(324\) | −1.59322e12 | + | 4.15549e11i | −0.446221 | + | 0.116385i | ||||
\(325\) | −4.22129e11 | + | 6.47314e12i | −0.116420 | + | 1.78525i | ||||
\(326\) | −5.44742e12 | + | 6.98720e11i | −1.47946 | + | 0.189764i | ||||
\(327\) | 2.52850e12 | 0.676276 | ||||||||
\(328\) | −1.36462e12 | + | 5.49337e11i | −0.359453 | + | 0.144700i | ||||
\(329\) | −3.71287e12 | −0.963230 | ||||||||
\(330\) | −3.27731e12 | + | 3.12316e11i | −0.837429 | + | 0.0798039i | ||||
\(331\) | 4.65034e12i | 1.17043i | 0.810879 | + | 0.585214i | \(0.198990\pi\) | ||||
−0.810879 | + | 0.585214i | \(0.801010\pi\) | |||||||
\(332\) | 1.87363e12 | − | 4.88687e11i | 0.464509 | − | 0.121155i | ||||
\(333\) | 2.97025e11i | 0.0725390i | ||||||||
\(334\) | 4.04846e12 | − | 5.19280e11i | 0.973996 | − | 0.124931i | ||||
\(335\) | 1.55713e10 | − | 4.78063e11i | 0.00369063 | − | 0.113308i | ||||
\(336\) | 2.44469e12 | − | 1.36835e12i | 0.570858 | − | 0.319523i | ||||
\(337\) | − | 2.23573e11i | − | 0.0514362i | −0.999669 | − | 0.0257181i | \(-0.991813\pi\) | ||
0.999669 | − | 0.0257181i | \(-0.00818723\pi\) | |||||||
\(338\) | 9.62926e12 | − | 1.23511e12i | 2.18278 | − | 0.279976i | ||||
\(339\) | 4.46866e12i | 0.998111i | ||||||||
\(340\) | −3.39353e12 | + | 7.68055e11i | −0.746892 | + | 0.169043i | ||||
\(341\) | 6.71148e12 | 1.45561 | ||||||||
\(342\) | −1.99732e11 | − | 1.55717e12i | −0.0426891 | − | 0.332816i | ||||
\(343\) | −5.16386e12 | −1.08769 | ||||||||
\(344\) | −2.63342e12 | + | 1.06010e12i | −0.546674 | + | 0.220067i | ||||
\(345\) | 1.32528e11 | − | 4.06882e12i | 0.0271152 | − | 0.832478i | ||||
\(346\) | −7.63031e11 | − | 5.94881e12i | −0.153873 | − | 1.19964i | ||||
\(347\) | −3.16769e12 | −0.629644 | −0.314822 | − | 0.949151i | \(-0.601945\pi\) | ||||
−0.314822 | + | 0.949151i | \(0.601945\pi\) | |||||||
\(348\) | 3.03085e12 | − | 7.90517e11i | 0.593839 | − | 0.154887i | ||||
\(349\) | −8.37634e12 | −1.61781 | −0.808904 | − | 0.587941i | \(-0.799939\pi\) | ||||
−0.808904 | + | 0.587941i | \(0.799939\pi\) | |||||||
\(350\) | 4.38417e12 | − | 2.74145e11i | 0.834732 | − | 0.0521963i | ||||
\(351\) | 1.03494e13i | 1.94257i | ||||||||
\(352\) | −3.46073e12 | − | 4.66907e12i | −0.640405 | − | 0.864007i | ||||
\(353\) | − | 2.56251e12i | − | 0.467512i | −0.972295 | − | 0.233756i | \(-0.924898\pi\) | ||
0.972295 | − | 0.233756i | \(-0.0751017\pi\) | |||||||
\(354\) | −4.29298e11 | − | 3.34693e12i | −0.0772222 | − | 0.602047i | ||||
\(355\) | 1.02581e13 | + | 3.34123e11i | 1.81939 | + | 0.0592604i | ||||
\(356\) | 8.61082e12 | − | 2.24590e12i | 1.50589 | − | 0.392772i | ||||
\(357\) | − | 2.90506e12i | − | 0.500973i | ||||||
\(358\) | 5.44741e11 | + | 4.24696e12i | 0.0926349 | + | 0.722209i | ||||
\(359\) | − | 9.99628e12i | − | 1.67636i | −0.545397 | − | 0.838178i | \(-0.683621\pi\) | ||
0.545397 | − | 0.838178i | \(-0.316379\pi\) | |||||||
\(360\) | −8.05153e11 | − | 2.20471e12i | −0.133158 | − | 0.364619i | ||||
\(361\) | 1.54983e12 | 0.252783 | ||||||||
\(362\) | −1.11408e13 | + | 1.42899e12i | −1.79215 | + | 0.229872i | ||||
\(363\) | −7.72167e11 | −0.122512 | ||||||||
\(364\) | −2.41310e12 | − | 9.25187e12i | −0.377632 | − | 1.44785i | ||||
\(365\) | 5.04715e12 | + | 1.64394e11i | 0.779080 | + | 0.0253759i | ||||
\(366\) | −5.26504e12 | + | 6.75327e11i | −0.801672 | + | 0.102827i | ||||
\(367\) | 2.30492e12 | 0.346199 | 0.173099 | − | 0.984904i | \(-0.444622\pi\) | ||||
0.173099 | + | 0.984904i | \(0.444622\pi\) | |||||||
\(368\) | 6.27115e12 | − | 3.51011e12i | 0.929198 | − | 0.520094i | ||||
\(369\) | −1.02899e12 | −0.150411 | ||||||||
\(370\) | 1.29001e12 | − | 1.22933e11i | 0.186030 | − | 0.0177280i | ||||
\(371\) | − | 3.22154e12i | − | 0.458347i | ||||||
\(372\) | −1.90342e12 | − | 7.29773e12i | −0.267189 | − | 1.02441i | ||||
\(373\) | 5.12634e11i | 0.0710008i | 0.999370 | + | 0.0355004i | \(0.0113025\pi\) | ||||
−0.999370 | + | 0.0355004i | \(0.988697\pi\) | |||||||
\(374\) | −5.97746e12 | + | 7.66705e11i | −0.816880 | + | 0.104778i | ||||
\(375\) | −5.65701e11 | + | 5.77292e12i | −0.0762835 | + | 0.778465i | ||||
\(376\) | 8.02902e12 | − | 3.23214e12i | 1.06837 | − | 0.430081i | ||||
\(377\) | − | 1.06899e13i | − | 1.40367i | ||||||
\(378\) | 6.95133e12 | − | 8.91620e11i | 0.900759 | − | 0.115537i | ||||
\(379\) | 1.30188e13i | 1.66485i | 0.554141 | + | 0.832423i | \(0.313047\pi\) | ||||
−0.554141 | + | 0.832423i | \(0.686953\pi\) | |||||||
\(380\) | −6.68026e12 | + | 1.51194e12i | −0.843093 | + | 0.190816i | ||||
\(381\) | −7.88043e12 | −0.981578 | ||||||||
\(382\) | 1.36557e12 | + | 1.06464e13i | 0.167879 | + | 1.30883i | ||||
\(383\) | −7.62061e10 | −0.00924689 | −0.00462345 | − | 0.999989i | \(-0.501472\pi\) | ||||
−0.00462345 | + | 0.999989i | \(0.501472\pi\) | |||||||
\(384\) | −4.09543e12 | + | 5.08720e12i | −0.490505 | + | 0.609289i | ||||
\(385\) | 7.60439e12 | + | 2.47687e11i | 0.899002 | + | 0.0292819i | ||||
\(386\) | 1.80057e12 | + | 1.40378e13i | 0.210123 | + | 1.63818i | ||||
\(387\) | −1.98573e12 | −0.228753 | ||||||||
\(388\) | −1.49626e12 | − | 5.73668e12i | −0.170156 | − | 0.652382i | ||||
\(389\) | −5.68167e12 | −0.637863 | −0.318932 | − | 0.947778i | \(-0.603324\pi\) | ||||
−0.318932 | + | 0.947778i | \(0.603324\pi\) | |||||||
\(390\) | 1.25688e13 | − | 1.19776e12i | 1.39306 | − | 0.132754i | ||||
\(391\) | − | 7.45209e12i | − | 0.815444i | ||||||
\(392\) | 2.58024e12 | − | 1.03869e12i | 0.278760 | − | 0.112217i | ||||
\(393\) | − | 2.64008e11i | − | 0.0281614i | ||||||
\(394\) | −2.60154e11 | − | 2.02823e12i | −0.0273999 | − | 0.213618i | ||||
\(395\) | 9.64319e12 | + | 3.14094e11i | 1.00285 | + | 0.0326644i | ||||
\(396\) | −1.02601e12 | − | 3.93374e12i | −0.105360 | − | 0.403952i | ||||
\(397\) | 1.23091e13i | 1.24818i | 0.781354 | + | 0.624088i | \(0.214529\pi\) | ||||
−0.781354 | + | 0.624088i | \(0.785471\pi\) | |||||||
\(398\) | 1.20230e12 | + | 9.37346e12i | 0.120392 | + | 0.938609i | ||||
\(399\) | − | 5.71869e12i | − | 0.565499i | ||||||
\(400\) | −9.24204e12 | + | 4.40935e12i | −0.902543 | + | 0.430600i | ||||
\(401\) | 3.21421e11 | 0.0309993 | 0.0154997 | − | 0.999880i | \(-0.495066\pi\) | ||||
0.0154997 | + | 0.999880i | \(0.495066\pi\) | |||||||
\(402\) | −9.23405e11 | + | 1.18442e11i | −0.0879553 | + | 0.0112817i | ||||
\(403\) | −2.57392e13 | −2.42142 | ||||||||
\(404\) | −1.06841e13 | + | 2.78666e12i | −0.992731 | + | 0.258927i | ||||
\(405\) | −1.63578e11 | + | 5.02212e12i | −0.0150124 | + | 0.460905i | ||||
\(406\) | −7.18004e12 | + | 9.20955e11i | −0.650873 | + | 0.0834850i | ||||
\(407\) | 2.24448e12 | 0.200976 | ||||||||
\(408\) | 2.52892e12 | + | 6.28214e12i | 0.223684 | + | 0.555657i | ||||
\(409\) | 1.03801e13 | 0.906952 | 0.453476 | − | 0.891268i | \(-0.350184\pi\) | ||||
0.453476 | + | 0.891268i | \(0.350184\pi\) | |||||||
\(410\) | 4.25880e11 | + | 4.46901e12i | 0.0367594 | + | 0.385738i | ||||
\(411\) | − | 7.89974e12i | − | 0.673602i | ||||||
\(412\) | 6.99409e12 | − | 1.82422e12i | 0.589176 | − | 0.153671i | ||||
\(413\) | 7.79837e12i | 0.649013i | ||||||||
\(414\) | 4.98622e12 | − | 6.39563e11i | 0.409987 | − | 0.0525874i | ||||
\(415\) | 1.92369e11 | − | 5.90603e12i | 0.0156277 | − | 0.479795i | ||||
\(416\) | 1.32723e13 | + | 1.79063e13i | 1.06531 | + | 1.43728i | ||||
\(417\) | 1.50167e13i | 1.19095i | ||||||||
\(418\) | −1.17668e13 | + | 1.50928e12i | −0.922097 | + | 0.118274i | ||||
\(419\) | − | 1.57632e13i | − | 1.22061i | −0.792168 | − | 0.610303i | \(-0.791048\pi\) | ||
0.792168 | − | 0.610303i | \(-0.208952\pi\) | |||||||
\(420\) | −1.88733e12 | − | 8.33887e12i | −0.144411 | − | 0.638059i | ||||
\(421\) | −1.50088e13 | −1.13484 | −0.567421 | − | 0.823428i | \(-0.692059\pi\) | ||||
−0.567421 | + | 0.823428i | \(0.692059\pi\) | |||||||
\(422\) | −6.13316e11 | − | 4.78159e12i | −0.0458271 | − | 0.357281i | ||||
\(423\) | 6.05428e12 | 0.447055 | ||||||||
\(424\) | 2.80443e12 | + | 6.96653e12i | 0.204651 | + | 0.508379i | ||||
\(425\) | −6.90969e11 | + | 1.05957e13i | −0.0498327 | + | 0.764159i | ||||
\(426\) | −2.54148e12 | − | 1.98141e13i | −0.181150 | − | 1.41230i | ||||
\(427\) | 1.22676e13 | 0.864211 | ||||||||
\(428\) | −1.79536e12 | + | 4.68271e11i | −0.125006 | + | 0.0326046i | ||||
\(429\) | 2.18684e13 | 1.50498 | ||||||||
\(430\) | 8.21858e11 | + | 8.62423e12i | 0.0559055 | + | 0.586649i | ||||
\(431\) | − | 5.91866e11i | − | 0.0397958i | −0.999802 | − | 0.0198979i | \(-0.993666\pi\) | ||
0.999802 | − | 0.0198979i | \(-0.00633411\pi\) | |||||||
\(432\) | −1.42560e13 | + | 7.97940e12i | −0.947496 | + | 0.530336i | ||||
\(433\) | − | 2.30044e13i | − | 1.51137i | −0.654933 | − | 0.755687i | \(-0.727303\pi\) | ||
0.654933 | − | 0.755687i | \(-0.272697\pi\) | |||||||
\(434\) | 2.21749e12 | + | 1.72882e13i | 0.144017 | + | 1.12280i | ||||
\(435\) | 3.11183e11 | − | 9.55380e12i | 0.0199788 | − | 0.613380i | ||||
\(436\) | 1.31811e13 | − | 3.43793e12i | 0.836600 | − | 0.218205i | ||||
\(437\) | − | 1.46696e13i | − | 0.920475i | ||||||
\(438\) | −1.25045e12 | − | 9.74886e12i | −0.0775702 | − | 0.604760i | ||||
\(439\) | − | 4.54425e12i | − | 0.278701i | −0.990243 | − | 0.139351i | \(-0.955498\pi\) | ||
0.990243 | − | 0.139351i | \(-0.0445015\pi\) | |||||||
\(440\) | −1.66600e13 | + | 6.08417e12i | −1.01021 | + | 0.368925i | ||||
\(441\) | 1.94563e12 | 0.116645 | ||||||||
\(442\) | 2.29241e13 | − | 2.94039e12i | 1.35888 | − | 0.174298i | ||||
\(443\) | 2.40350e12 | 0.140872 | 0.0704362 | − | 0.997516i | \(-0.477561\pi\) | ||||
0.0704362 | + | 0.997516i | \(0.477561\pi\) | |||||||
\(444\) | −6.36548e11 | − | 2.44053e12i | −0.0368906 | − | 0.141439i | ||||
\(445\) | 8.84087e11 | − | 2.71429e13i | 0.0506635 | − | 1.55545i | ||||
\(446\) | −2.63101e13 | + | 3.37469e12i | −1.49090 | + | 0.191232i | ||||
\(447\) | −6.42385e11 | −0.0359963 | ||||||||
\(448\) | 1.08837e13 | − | 1.04572e13i | 0.603095 | − | 0.579463i | ||||
\(449\) | −2.55386e13 | −1.39947 | −0.699737 | − | 0.714401i | \(-0.746699\pi\) | ||||
−0.699737 | + | 0.714401i | \(0.746699\pi\) | |||||||
\(450\) | −7.14891e12 | + | 4.47026e11i | −0.387416 | + | 0.0242254i | ||||
\(451\) | 7.77561e12i | 0.416727i | ||||||||
\(452\) | 6.07591e12 | + | 2.32951e13i | 0.322047 | + | 1.23473i | ||||
\(453\) | 1.21734e13i | 0.638146i | ||||||||
\(454\) | 1.80249e13 | − | 2.31198e12i | 0.934530 | − | 0.119869i | ||||
\(455\) | −2.91636e13 | − | 9.49904e11i | −1.49549 | − | 0.0487105i | ||||
\(456\) | 4.97825e12 | + | 1.23666e13i | 0.252495 | + | 0.627228i | ||||
\(457\) | − | 1.43833e13i | − | 0.721569i | −0.932649 | − | 0.360785i | \(-0.882509\pi\) | ||
0.932649 | − | 0.360785i | \(-0.117491\pi\) | |||||||
\(458\) | −1.99828e12 | + | 2.56312e11i | −0.0991585 | + | 0.0127187i | ||||
\(459\) | 1.69405e13i | 0.831502i | ||||||||
\(460\) | −4.84139e12 | − | 2.13910e13i | −0.235061 | − | 1.03858i | ||||
\(461\) | 3.07398e13 | 1.47638 | 0.738188 | − | 0.674595i | \(-0.235682\pi\) | ||||
0.738188 | + | 0.674595i | \(0.235682\pi\) | |||||||
\(462\) | −1.88401e12 | − | 1.46883e13i | −0.0895104 | − | 0.697849i | ||||
\(463\) | 1.66750e13 | 0.783718 | 0.391859 | − | 0.920025i | \(-0.371832\pi\) | ||||
0.391859 | + | 0.920025i | \(0.371832\pi\) | |||||||
\(464\) | 1.47250e13 | − | 8.24193e12i | 0.684645 | − | 0.383212i | ||||
\(465\) | −2.30038e13 | − | 7.49269e11i | −1.05812 | − | 0.0344646i | ||||
\(466\) | 1.59011e12 | + | 1.23970e13i | 0.0723598 | + | 0.564138i | ||||
\(467\) | 6.59007e12 | 0.296692 | 0.148346 | − | 0.988936i | \(-0.452605\pi\) | ||||
0.148346 | + | 0.988936i | \(0.452605\pi\) | |||||||
\(468\) | 3.93485e12 | + | 1.50863e13i | 0.175267 | + | 0.671975i | ||||
\(469\) | 2.15154e12 | 0.0948168 | ||||||||
\(470\) | −2.50575e12 | − | 2.62943e13i | −0.109257 | − | 1.14650i | ||||
\(471\) | − | 2.41575e12i | − | 0.104219i | ||||||
\(472\) | −6.78865e12 | − | 1.68638e13i | −0.289784 | − | 0.719857i | ||||
\(473\) | 1.50053e13i | 0.633779i | ||||||||
\(474\) | −2.38913e12 | − | 1.86264e13i | −0.0998500 | − | 0.778460i | ||||
\(475\) | −1.36019e12 | + | 2.08579e13i | −0.0562512 | + | 0.862585i | ||||
\(476\) | −3.94993e12 | − | 1.51441e13i | −0.161642 | − | 0.619738i | ||||
\(477\) | 5.25311e12i | 0.212728i | ||||||||
\(478\) | −3.48632e12 | − | 2.71804e13i | −0.139710 | − | 1.08922i | ||||
\(479\) | 3.32507e13i | 1.31863i | 0.751867 | + | 0.659315i | \(0.229154\pi\) | ||||
−0.751867 | + | 0.659315i | \(0.770846\pi\) | |||||||
\(480\) | 1.13405e13 | + | 1.63897e13i | 0.445067 | + | 0.643228i | ||||
\(481\) | −8.60779e12 | −0.334323 | ||||||||
\(482\) | 6.97018e12 | − | 8.94037e11i | 0.267922 | − | 0.0343653i | ||||
\(483\) | 1.83119e13 | 0.696622 | ||||||||
\(484\) | −4.02531e12 | + | 1.04989e12i | −0.151556 | + | 0.0395293i | ||||
\(485\) | −1.80831e13 | − | 5.88994e11i | −0.673850 | − | 0.0219484i | ||||
\(486\) | −1.95004e13 | + | 2.50124e12i | −0.719220 | + | 0.0922515i | ||||
\(487\) | −3.49858e12 | −0.127717 | −0.0638583 | − | 0.997959i | \(-0.520341\pi\) | ||||
−0.0638583 | + | 0.997959i | \(0.520341\pi\) | |||||||
\(488\) | −2.65285e13 | + | 1.06792e13i | −0.958546 | + | 0.385869i | ||||
\(489\) | 3.26216e13 | 1.16670 | ||||||||
\(490\) | −8.05260e11 | − | 8.45006e12i | −0.0285073 | − | 0.299143i | ||||
\(491\) | 1.49892e13i | 0.525254i | 0.964897 | + | 0.262627i | \(0.0845889\pi\) | ||||
−0.964897 | + | 0.262627i | \(0.915411\pi\) | |||||||
\(492\) | 8.45481e12 | − | 2.20521e12i | 0.293277 | − | 0.0764935i | ||||
\(493\) | − | 1.74979e13i | − | 0.600829i | ||||||
\(494\) | 4.51268e13 | − | 5.78824e12i | 1.53391 | − | 0.196749i | ||||
\(495\) | −1.23999e13 | − | 4.03884e11i | −0.417245 | − | 0.0135903i | ||||
\(496\) | −1.98450e13 | − | 3.54550e13i | −0.661064 | − | 1.18105i | ||||
\(497\) | 4.61670e13i | 1.52247i | ||||||||
\(498\) | −1.14078e13 | + | 1.46324e12i | −0.372440 | + | 0.0477714i | ||||
\(499\) | − | 2.01950e13i | − | 0.652741i | −0.945242 | − | 0.326370i | \(-0.894174\pi\) | ||
0.945242 | − | 0.326370i | \(-0.105826\pi\) | |||||||
\(500\) | 4.90028e12 | + | 3.08634e13i | 0.156809 | + | 0.987629i | ||||
\(501\) | −2.42440e13 | −0.768096 | ||||||||
\(502\) | 1.53553e12 | + | 1.19715e13i | 0.0481661 | + | 0.375517i | ||||
\(503\) | 3.87916e13 | 1.20475 | 0.602376 | − | 0.798213i | \(-0.294221\pi\) | ||||
0.602376 | + | 0.798213i | \(0.294221\pi\) | |||||||
\(504\) | 9.79397e12 | − | 3.94263e12i | 0.301166 | − | 0.121237i | ||||
\(505\) | −1.09695e12 | + | 3.36783e13i | −0.0333989 | + | 1.02540i | ||||
\(506\) | −4.83288e12 | − | 3.76786e13i | −0.145698 | − | 1.13590i | ||||
\(507\) | −5.76643e13 | −1.72134 | ||||||||
\(508\) | −4.10807e13 | + | 1.07148e13i | −1.21428 | + | 0.316713i | ||||
\(509\) | 2.53824e13 | 0.742923 | 0.371462 | − | 0.928448i | \(-0.378857\pi\) | ||||
0.371462 | + | 0.928448i | \(0.378857\pi\) | |||||||
\(510\) | 2.05735e13 | − | 1.96058e12i | 0.596289 | − | 0.0568242i | ||||
\(511\) | 2.27149e13i | 0.651938i | ||||||||
\(512\) | −1.44325e13 | + | 3.20880e13i | −0.410197 | + | 0.911997i | ||||
\(513\) | 3.33479e13i | 0.938602i | ||||||||
\(514\) | 3.35433e12 | + | 2.61513e13i | 0.0934954 | + | 0.728917i | ||||
\(515\) | 7.18095e11 | − | 2.20467e13i | 0.0198219 | − | 0.608564i | ||||
\(516\) | 1.63160e13 | − | 4.25558e12i | 0.446030 | − | 0.116335i | ||||
\(517\) | − | 4.57494e13i | − | 1.23860i | ||||||
\(518\) | 7.41580e11 | + | 5.78158e12i | 0.0198843 | + | 0.155023i | ||||
\(519\) | 3.56242e13i | 0.946036i | ||||||||
\(520\) | 6.38926e13 | − | 2.33334e13i | 1.68048 | − | 0.613707i | ||||
\(521\) | 9.37998e12 | 0.244351 | 0.122175 | − | 0.992509i | \(-0.461013\pi\) | ||||
0.122175 | + | 0.992509i | \(0.461013\pi\) | |||||||
\(522\) | 1.17079e13 | − | 1.50173e12i | 0.302084 | − | 0.0387471i | ||||
\(523\) | 1.03783e13 | 0.265227 | 0.132614 | − | 0.991168i | \(-0.457663\pi\) | ||||
0.132614 | + | 0.991168i | \(0.457663\pi\) | |||||||
\(524\) | −3.58964e11 | − | 1.37627e12i | −0.00908645 | − | 0.0348376i | ||||
\(525\) | −2.60366e13 | − | 1.69791e12i | −0.652811 | − | 0.0425713i | ||||
\(526\) | −3.45290e13 | + | 4.42890e12i | −0.857543 | + | 0.109994i | ||||
\(527\) | −4.21316e13 | −1.03647 | ||||||||
\(528\) | 1.68606e13 | + | 3.01231e13i | 0.410870 | + | 0.734058i | ||||
\(529\) | 5.54730e12 | 0.133907 | ||||||||
\(530\) | 2.28148e13 | − | 2.17417e12i | 0.545553 | − | 0.0519892i | ||||
\(531\) | − | 1.27162e13i | − | 0.301220i | ||||||
\(532\) | −7.77554e12 | − | 2.98115e13i | −0.182462 | − | 0.699562i | ||||
\(533\) | − | 2.98202e13i | − | 0.693226i | ||||||
\(534\) | −5.24280e13 | + | 6.72473e12i | −1.20742 | + | 0.154871i | ||||
\(535\) | −1.84332e11 | + | 5.65929e12i | −0.00420564 | + | 0.129120i | ||||
\(536\) | −4.65267e12 | + | 1.87296e12i | −0.105167 | + | 0.0423356i | ||||
\(537\) | − | 2.54327e13i | − | 0.569536i | ||||||
\(538\) | −5.00089e13 | + | 6.41444e12i | −1.10952 | + | 0.142314i | ||||
\(539\) | − | 1.47022e13i | − | 0.323176i | ||||||
\(540\) | 1.10057e13 | + | 4.86272e13i | 0.239690 | + | 1.05903i | ||||
\(541\) | −1.08616e13 | −0.234373 | −0.117187 | − | 0.993110i | \(-0.537388\pi\) | ||||
−0.117187 | + | 0.993110i | \(0.537388\pi\) | |||||||
\(542\) | −3.04537e12 | − | 2.37426e13i | −0.0651094 | − | 0.507612i | ||||
\(543\) | 6.67163e13 | 1.41329 | ||||||||
\(544\) | 2.17249e13 | + | 2.93103e13i | 0.455999 | + | 0.615214i | ||||
\(545\) | 1.35332e12 | − | 4.15491e13i | 0.0281461 | − | 0.864130i | ||||
\(546\) | 7.22537e12 | + | 5.63311e13i | 0.148901 | + | 1.16087i | ||||
\(547\) | 3.51242e13 | 0.717248 | 0.358624 | − | 0.933482i | \(-0.383246\pi\) | ||||
0.358624 | + | 0.933482i | \(0.383246\pi\) | |||||||
\(548\) | −1.07410e13 | − | 4.11813e13i | −0.217342 | − | 0.833293i | ||||
\(549\) | −2.00038e13 | −0.401098 | ||||||||
\(550\) | 3.37797e12 | + | 5.40210e13i | 0.0671185 | + | 1.07337i | ||||
\(551\) | − | 3.44451e13i | − | 0.678218i | ||||||
\(552\) | −3.95991e13 | + | 1.59409e13i | −0.772664 | + | 0.311041i | ||||
\(553\) | 4.33996e13i | 0.839189i | ||||||||
\(554\) | −5.51959e12 | − | 4.30323e13i | −0.105769 | − | 0.824605i | ||||
\(555\) | −7.69300e12 | − | 2.50573e11i | −0.146094 | − | 0.00475850i | ||||
\(556\) | 2.04178e13 | + | 7.82819e13i | 0.384268 | + | 1.47329i | ||||
\(557\) | − | 1.87712e13i | − | 0.350120i | −0.984558 | − | 0.175060i | \(-0.943988\pi\) | ||
0.984558 | − | 0.175060i | \(-0.0560119\pi\) | |||||||
\(558\) | −3.61588e12 | − | 2.81905e13i | −0.0668410 | − | 0.521112i | ||||
\(559\) | − | 5.75467e13i | − | 1.05429i | ||||||
\(560\) | −2.11768e13 | − | 4.09044e13i | −0.384521 | − | 0.742728i | ||||
\(561\) | 3.57957e13 | 0.644194 | ||||||||
\(562\) | 2.11255e13 | − | 2.70968e12i | 0.376812 | − | 0.0483322i | ||||
\(563\) | −7.50975e12 | −0.132765 | −0.0663825 | − | 0.997794i | \(-0.521146\pi\) | ||||
−0.0663825 | + | 0.997794i | \(0.521146\pi\) | |||||||
\(564\) | −4.97456e13 | + | 1.29748e13i | −0.871684 | + | 0.227355i | ||||
\(565\) | 7.34305e13 | + | 2.39175e12i | 1.27536 | + | 0.0415407i | ||||
\(566\) | 1.00709e14 | − | 1.29176e13i | 1.73375 | − | 0.222381i | ||||
\(567\) | −2.26022e13 | −0.385688 | ||||||||
\(568\) | −4.01894e13 | − | 9.98354e13i | −0.679783 | − | 1.68866i | ||||
\(569\) | −5.40193e13 | −0.905707 | −0.452853 | − | 0.891585i | \(-0.649594\pi\) | ||||
−0.452853 | + | 0.891585i | \(0.649594\pi\) | |||||||
\(570\) | 4.04994e13 | − | 3.85945e12i | 0.673093 | − | 0.0641433i | ||||
\(571\) | − | 7.48542e13i | − | 1.23321i | −0.787274 | − | 0.616603i | \(-0.788508\pi\) | ||
0.787274 | − | 0.616603i | \(-0.211492\pi\) | |||||||
\(572\) | 1.14000e14 | − | 2.97339e13i | 1.86176 | − | 0.485592i | ||||
\(573\) | − | 6.37552e13i | − | 1.03215i | ||||||
\(574\) | −2.00293e13 | + | 2.56908e12i | −0.321445 | + | 0.0412304i | ||||
\(575\) | −6.67892e13 | − | 4.35549e12i | −1.06259 | − | 0.0692943i | ||||
\(576\) | −1.77472e13 | + | 1.70517e13i | −0.279909 | + | 0.268941i | ||||
\(577\) | 7.48813e13i | 1.17083i | 0.810733 | + | 0.585416i | \(0.199069\pi\) | ||||
−0.810733 | + | 0.585416i | \(0.800931\pi\) | |||||||
\(578\) | −2.64638e13 | + | 3.39441e12i | −0.410217 | + | 0.0526169i | ||||
\(579\) | − | 8.40644e13i | − | 1.29187i | ||||||
\(580\) | −1.13678e13 | − | 5.02271e13i | −0.173196 | − | 0.765240i | ||||
\(581\) | 2.65803e13 | 0.401495 | ||||||||
\(582\) | 4.48014e12 | + | 3.49285e13i | 0.0670929 | + | 0.523076i | ||||
\(583\) | 3.96953e13 | 0.589382 | ||||||||
\(584\) | −1.97738e13 | − | 4.91206e13i | −0.291090 | − | 0.723102i | ||||
\(585\) | 4.75547e13 | + | 1.54893e12i | 0.694088 | + | 0.0226075i | ||||
\(586\) | −1.31193e12 | − | 1.02282e13i | −0.0189855 | − | 0.148016i | ||||
\(587\) | 4.76751e13 | 0.684071 | 0.342035 | − | 0.939687i | \(-0.388884\pi\) | ||||
0.342035 | + | 0.939687i | \(0.388884\pi\) | |||||||
\(588\) | −1.59865e13 | + | 4.16964e12i | −0.227439 | + | 0.0593215i | ||||
\(589\) | −8.29373e13 | −1.16997 | ||||||||
\(590\) | −5.52276e13 | + | 5.26299e12i | −0.772496 | + | 0.0736160i | ||||
\(591\) | 1.21460e13i | 0.168459i | ||||||||
\(592\) | −6.63665e12 | − | 1.18570e13i | −0.0912725 | − | 0.163067i | ||||
\(593\) | 8.03970e13i | 1.09639i | 0.836349 | + | 0.548197i | \(0.184686\pi\) | ||||
−0.836349 | + | 0.548197i | \(0.815314\pi\) | |||||||
\(594\) | 1.09864e13 | + | 8.56531e13i | 0.148567 | + | 1.15827i | ||||
\(595\) | −4.77369e13 | − | 1.55487e12i | −0.640132 | − | 0.0208501i | ||||
\(596\) | −3.34875e12 | + | 8.73433e11i | −0.0445299 | + | 0.0116144i | ||||
\(597\) | − | 5.61325e13i | − | 0.740189i | ||||||
\(598\) | 1.85346e13 | + | 1.44501e14i | 0.242369 | + | 1.88958i | ||||
\(599\) | 5.37083e13i | 0.696477i | 0.937406 | + | 0.348239i | \(0.113220\pi\) | ||||
−0.937406 | + | 0.348239i | \(0.886780\pi\) | |||||||
\(600\) | 5.77817e13 | − | 1.89937e13i | 0.743077 | − | 0.244261i | ||||
\(601\) | −3.12372e13 | −0.398382 | −0.199191 | − | 0.979961i | \(-0.563831\pi\) | ||||
−0.199191 | + | 0.979961i | \(0.563831\pi\) | |||||||
\(602\) | −3.86522e13 | + | 4.95777e12i | −0.488869 | + | 0.0627053i | ||||
\(603\) | −3.50835e12 | −0.0440064 | ||||||||
\(604\) | 1.65518e13 | + | 6.34598e13i | 0.205902 | + | 0.789431i | ||||
\(605\) | −4.13285e11 | + | 1.26885e13i | −0.00509885 | + | 0.156543i | ||||
\(606\) | 6.50515e13 | − | 8.34390e12i | 0.795965 | − | 0.102095i | ||||
\(607\) | −7.33861e13 | −0.890574 | −0.445287 | − | 0.895388i | \(-0.646898\pi\) | ||||
−0.445287 | + | 0.895388i | \(0.646898\pi\) | |||||||
\(608\) | 4.27661e13 | + | 5.76982e13i | 0.514733 | + | 0.694455i | ||||
\(609\) | 4.29973e13 | 0.513280 | ||||||||
\(610\) | 8.27919e12 | + | 8.68784e13i | 0.0980254 | + | 1.02864i | ||||
\(611\) | 1.75453e14i | 2.06042i | ||||||||
\(612\) | 6.44084e12 | + | 2.46942e13i | 0.0750214 | + | 0.287633i | ||||
\(613\) | − | 4.41534e13i | − | 0.510108i | −0.966927 | − | 0.255054i | \(-0.917907\pi\) | ||
0.966927 | − | 0.255054i | \(-0.0820933\pi\) | |||||||
\(614\) | −6.26164e13 | + | 8.03156e12i | −0.717540 | + | 0.0920360i | ||||
\(615\) | 8.68069e11 | − | 2.66511e13i | 0.00986685 | − | 0.302928i | ||||
\(616\) | −2.97926e13 | − | 7.40085e13i | −0.335896 | − | 0.834407i | ||||
\(617\) | 5.60294e13i | 0.626600i | 0.949654 | + | 0.313300i | \(0.101434\pi\) | ||||
−0.949654 | + | 0.313300i | \(0.898566\pi\) | |||||||
\(618\) | −4.25844e13 | + | 5.46213e12i | −0.472398 | + | 0.0605926i | ||||
\(619\) | 7.65763e13i | 0.842638i | 0.906913 | + | 0.421319i | \(0.138433\pi\) | ||||
−0.906913 | + | 0.421319i | \(0.861567\pi\) | |||||||
\(620\) | −1.20937e14 | + | 2.73716e13i | −1.32009 | + | 0.298774i | ||||
\(621\) | −1.06784e14 | −1.15624 | ||||||||
\(622\) | 2.08986e13 | + | 1.62931e14i | 0.224473 | + | 1.75006i | ||||
\(623\) | 1.22158e14 | 1.30161 | ||||||||
\(624\) | −6.46622e13 | − | 1.15525e14i | −0.683483 | − | 1.22111i | ||||
\(625\) | 9.45597e13 | + | 1.23856e13i | 0.991531 | + | 0.129872i | ||||
\(626\) | −9.69285e10 | − | 7.55683e11i | −0.00100828 | − | 0.00786083i | ||||
\(627\) | 7.04648e13 | 0.727167 | ||||||||
\(628\) | −3.28462e12 | − | 1.25933e13i | −0.0336269 | − | 0.128926i | ||||
\(629\) | −1.40898e13 | −0.143104 | ||||||||
\(630\) | −3.05657e12 | − | 3.20744e13i | −0.0307987 | − | 0.323189i | ||||
\(631\) | − | 4.84894e13i | − | 0.484731i | −0.970185 | − | 0.242365i | \(-0.922077\pi\) | ||
0.970185 | − | 0.242365i | \(-0.0779232\pi\) | |||||||
\(632\) | −3.77803e13 | − | 9.38508e13i | −0.374697 | − | 0.930792i | ||||
\(633\) | 2.86343e13i | 0.281753i | ||||||||
\(634\) | −2.06004e13 | − | 1.60606e14i | −0.201108 | − | 1.56789i | ||||
\(635\) | −4.21782e12 | + | 1.29494e14i | −0.0408526 | + | 1.25424i | ||||
\(636\) | −1.12578e13 | − | 4.31627e13i | −0.108186 | − | 0.414785i | ||||
\(637\) | 5.63845e13i | 0.537604i | ||||||||
\(638\) | −1.13479e13 | − | 8.84712e13i | −0.107352 | − | 0.836948i | ||||
\(639\) | − | 7.52809e13i | − | 0.706611i | ||||||
\(640\) | 8.14026e13 | + | 7.00202e13i | 0.758121 | + | 0.652114i | ||||
\(641\) | 1.29283e13 | 0.119468 | 0.0597338 | − | 0.998214i | \(-0.480975\pi\) | ||||
0.0597338 | + | 0.998214i | \(0.480975\pi\) | |||||||
\(642\) | 1.09312e13 | − | 1.40211e12i | 0.100229 | − | 0.0128560i | ||||
\(643\) | −1.48437e14 | −1.35048 | −0.675238 | − | 0.737600i | \(-0.735959\pi\) | ||||
−0.675238 | + | 0.737600i | \(0.735959\pi\) | |||||||
\(644\) | 9.54599e13 | − | 2.48982e13i | 0.861770 | − | 0.224770i | ||||
\(645\) | 1.67519e12 | − | 5.14309e13i | 0.0150060 | − | 0.460708i | ||||
\(646\) | 7.38666e13 | − | 9.47458e12i | 0.656576 | − | 0.0842165i | ||||
\(647\) | 8.95550e12 | 0.0789894 | 0.0394947 | − | 0.999220i | \(-0.487425\pi\) | ||||
0.0394947 | + | 0.999220i | \(0.487425\pi\) | |||||||
\(648\) | 4.88769e13 | − | 1.96757e13i | 0.427788 | − | 0.172209i | ||||
\(649\) | −9.60902e13 | −0.834557 | ||||||||
\(650\) | −1.29548e13 | − | 2.07176e14i | −0.111652 | − | 1.78555i | ||||
\(651\) | − | 1.03529e14i | − | 0.885439i | ||||||
\(652\) | 1.70056e14 | − | 4.43547e13i | 1.44329 | − | 0.376445i | ||||
\(653\) | − | 7.28446e13i | − | 0.613524i | −0.951786 | − | 0.306762i | \(-0.900754\pi\) | ||
0.951786 | − | 0.306762i | \(-0.0992456\pi\) | |||||||
\(654\) | −8.02545e13 | + | 1.02939e13i | −0.670781 | + | 0.0860384i | ||||
\(655\) | −4.33826e12 | − | 1.41304e11i | −0.0359840 | − | 0.00117206i | ||||
\(656\) | 4.10766e13 | − | 2.29915e13i | 0.338123 | − | 0.189256i | ||||
\(657\) | − | 3.70394e13i | − | 0.302578i | ||||||
\(658\) | 1.17846e14 | − | 1.51157e13i | 0.955403 | − | 0.122546i | ||||
\(659\) | 2.12839e14i | 1.71247i | 0.516584 | + | 0.856237i | \(0.327203\pi\) | ||||
−0.516584 | + | 0.856237i | \(0.672797\pi\) | |||||||
\(660\) | 1.02750e14 | − | 2.32554e13i | 0.820471 | − | 0.185696i | ||||
\(661\) | 1.49053e14 | 1.18123 | 0.590613 | − | 0.806955i | \(-0.298886\pi\) | ||||
0.590613 | + | 0.806955i | \(0.298886\pi\) | |||||||
\(662\) | −1.89323e13 | − | 1.47602e14i | −0.148906 | − | 1.16092i | ||||
\(663\) | −1.37280e14 | −1.07162 | ||||||||
\(664\) | −5.74795e13 | + | 2.31388e13i | −0.445321 | + | 0.179267i | ||||
\(665\) | −9.39714e13 | − | 3.06080e12i | −0.722582 | − | 0.0235357i | ||||
\(666\) | −1.20924e12 | − | 9.42756e12i | −0.00922869 | − | 0.0719495i | ||||
\(667\) | 1.10297e14 | 0.835477 | ||||||||
\(668\) | −1.26384e14 | + | 3.29639e13i | −0.950187 | + | 0.247831i | ||||
\(669\) | 1.57557e14 | 1.17573 | ||||||||
\(670\) | 1.45204e12 | + | 1.52371e13i | 0.0107548 | + | 0.112857i | ||||
\(671\) | 1.51159e14i | 1.11128i | ||||||||
\(672\) | −7.20237e13 | + | 5.33843e13i | −0.525569 | + | 0.389553i | ||||
\(673\) | 9.10177e13i | 0.659251i | 0.944112 | + | 0.329625i | \(0.106922\pi\) | ||||
−0.944112 | + | 0.329625i | \(0.893078\pi\) | |||||||
\(674\) | 9.10200e11 | + | 7.09618e12i | 0.00654391 | + | 0.0510182i | ||||
\(675\) | 1.51829e14 | + | 9.90115e12i | 1.08352 | + | 0.0706589i | ||||
\(676\) | −3.00604e14 | + | 7.84045e13i | −2.12942 | + | 0.555402i | ||||
\(677\) | − | 1.25381e14i | − | 0.881636i | −0.897596 | − | 0.440818i | \(-0.854688\pi\) | ||
0.897596 | − | 0.440818i | \(-0.145312\pi\) | |||||||
\(678\) | −1.81926e13 | − | 1.41835e14i | −0.126984 | − | 0.990001i | ||||
\(679\) | − | 8.13835e13i | − | 0.563881i | ||||||
\(680\) | 1.04584e14 | − | 3.81937e13i | 0.719316 | − | 0.262692i | ||||
\(681\) | −1.07941e14 | −0.736973 | ||||||||
\(682\) | −2.13022e14 | + | 2.73235e13i | −1.44379 | + | 0.185189i | ||||
\(683\) | −1.14583e14 | −0.770931 | −0.385465 | − | 0.922722i | \(-0.625959\pi\) | ||||
−0.385465 | + | 0.922722i | \(0.625959\pi\) | |||||||
\(684\) | 1.26790e13 | + | 4.86113e13i | 0.0846843 | + | 0.324681i | ||||
\(685\) | −1.29811e14 | − | 4.22815e12i | −0.860714 | − | 0.0280348i | ||||
\(686\) | 1.63901e14 | − | 2.10229e13i | 1.07885 | − | 0.138380i | ||||
\(687\) | 1.19666e13 | 0.0781966 | ||||||||
\(688\) | 7.92689e13 | − | 4.43687e13i | 0.514234 | − | 0.287829i | ||||
\(689\) | −1.52236e14 | −0.980437 | ||||||||
\(690\) | 1.23584e13 | + | 1.29684e14i | 0.0790162 | + | 0.829163i | ||||
\(691\) | 3.74076e13i | 0.237449i | 0.992927 | + | 0.118724i | \(0.0378805\pi\) | ||||
−0.992927 | + | 0.118724i | \(0.962119\pi\) | |||||||
\(692\) | 4.84372e13 | + | 1.85709e14i | 0.305245 | + | 1.17031i | ||||
\(693\) | − | 5.58061e13i | − | 0.349153i | ||||||
\(694\) | 1.00542e14 | − | 1.28962e13i | 0.624528 | − | 0.0801057i | ||||
\(695\) | 2.46759e14 | + | 8.03734e12i | 1.52177 | + | 0.0495665i | ||||
\(696\) | −9.29809e13 | + | 3.74301e13i | −0.569308 | + | 0.229179i | ||||
\(697\) | − | 4.88118e13i | − | 0.296729i | ||||||
\(698\) | 2.65865e14 | − | 3.41014e13i | 1.60466 | − | 0.205824i | ||||
\(699\) | − | 7.42385e13i | − | 0.444881i | ||||||
\(700\) | −1.38037e14 | + | 2.65500e13i | −0.821308 | + | 0.157970i | ||||
\(701\) | 2.22503e14 | 1.31446 | 0.657229 | − | 0.753691i | \(-0.271729\pi\) | ||||
0.657229 | + | 0.753691i | \(0.271729\pi\) | |||||||
\(702\) | −4.21339e13 | − | 3.28488e14i | −0.247142 | − | 1.92679i | ||||
\(703\) | −2.77362e13 | −0.161536 | ||||||||
\(704\) | 1.28852e14 | + | 1.34107e14i | 0.745123 | + | 0.775511i | ||||
\(705\) | −5.10746e12 | + | 1.56807e14i | −0.0293264 | + | 0.900368i | ||||
\(706\) | 1.04324e13 | + | 8.13341e13i | 0.0594786 | + | 0.463713i | ||||
\(707\) | −1.51570e14 | −0.858059 | ||||||||
\(708\) | 2.72518e13 | + | 1.04484e14i | 0.153189 | + | 0.587330i | ||||
\(709\) | 9.78657e13 | 0.546260 | 0.273130 | − | 0.961977i | \(-0.411941\pi\) | ||||
0.273130 | + | 0.961977i | \(0.411941\pi\) | |||||||
\(710\) | −3.26952e14 | + | 3.11573e13i | −1.81214 | + | 0.172691i | ||||
\(711\) | − | 7.07682e13i | − | 0.389485i | ||||||
\(712\) | −2.64164e14 | + | 1.06341e14i | −1.44369 | + | 0.581166i | ||||
\(713\) | − | 2.65574e14i | − | 1.44125i | ||||||
\(714\) | 1.18270e13 | + | 9.22065e13i | 0.0637357 | + | 0.496902i | ||||
\(715\) | 1.17046e13 | − | 3.59349e14i | 0.0626362 | − | 1.92303i | ||||
\(716\) | −3.45801e13 | − | 1.32581e14i | −0.183764 | − | 0.704555i | ||||
\(717\) | 1.62768e14i | 0.858961i | ||||||||
\(718\) | 4.06965e13 | + | 3.17282e14i | 0.213272 | + | 1.66273i | ||||
\(719\) | − | 1.39680e14i | − | 0.726926i | −0.931609 | − | 0.363463i | \(-0.881594\pi\) | ||
0.931609 | − | 0.363463i | \(-0.118406\pi\) | |||||||
\(720\) | 3.45313e13 | + | 6.66996e13i | 0.178464 | + | 0.344715i | ||||
\(721\) | 9.92219e13 | 0.509250 | ||||||||
\(722\) | −4.91915e13 | + | 6.30960e12i | −0.250729 | + | 0.0321600i | ||||
\(723\) | −4.17405e13 | −0.211284 | ||||||||
\(724\) | 3.47792e14 | − | 9.07122e13i | 1.74834 | − | 0.456009i | ||||
\(725\) | −1.56825e14 | − | 1.02269e13i | −0.782932 | − | 0.0510569i | ||||
\(726\) | 2.45086e13 | − | 3.14362e12i | 0.121516 | − | 0.0155864i | ||||
\(727\) | −3.31152e13 | −0.163063 | −0.0815315 | − | 0.996671i | \(-0.525981\pi\) | ||||
−0.0815315 | + | 0.996671i | \(0.525981\pi\) | |||||||
\(728\) | 1.14258e14 | + | 2.83830e14i | 0.558764 | + | 1.38804i | ||||
\(729\) | 2.11724e14 | 1.02833 | ||||||||
\(730\) | −1.60866e14 | + | 1.53299e13i | −0.775978 | + | 0.0739478i | ||||
\(731\) | − | 9.41962e13i | − | 0.451281i | ||||||
\(732\) | 1.64363e14 | − | 4.28697e13i | 0.782075 | − | 0.203983i | ||||
\(733\) | 3.51027e14i | 1.65890i | 0.558580 | + | 0.829451i | \(0.311347\pi\) | ||||
−0.558580 | + | 0.829451i | \(0.688653\pi\) | |||||||
\(734\) | −7.31581e13 | + | 9.38370e12i | −0.343386 | + | 0.0440447i | ||||
\(735\) | −1.64136e12 | + | 5.03922e13i | −0.00765184 | + | 0.234924i | ||||
\(736\) | −1.84756e14 | + | 1.36942e14i | −0.855479 | + | 0.634084i | ||||
\(737\) | 2.65109e13i | 0.121924i | ||||||||
\(738\) | 3.26602e13 | − | 4.18919e12i | 0.149189 | − | 0.0191359i | ||||
\(739\) | − | 6.54869e13i | − | 0.297120i | −0.988903 | − | 0.148560i | \(-0.952536\pi\) | ||
0.988903 | − | 0.148560i | \(-0.0474639\pi\) | |||||||
\(740\) | −4.04443e13 | + | 9.15372e12i | −0.182263 | + | 0.0412514i | ||||
\(741\) | −2.70239e14 | −1.20964 | ||||||||
\(742\) | 1.31154e13 | + | 1.02252e14i | 0.0583126 | + | 0.454622i | ||||
\(743\) | −3.94592e14 | −1.74262 | −0.871312 | − | 0.490729i | \(-0.836731\pi\) | ||||
−0.871312 | + | 0.490729i | \(0.836731\pi\) | |||||||
\(744\) | 9.01246e13 | + | 2.23880e14i | 0.395347 | + | 0.982091i | ||||
\(745\) | −3.43822e11 | + | 1.05559e13i | −0.00149814 | + | 0.0459953i | ||||
\(746\) | −2.08702e12 | − | 1.62710e13i | −0.00903300 | − | 0.0704239i | ||||
\(747\) | −4.33424e13 | −0.186342 | ||||||||
\(748\) | 1.86603e14 | − | 4.86704e13i | 0.796912 | − | 0.207853i | ||||
\(749\) | −2.54699e13 | −0.108048 | ||||||||
\(750\) | −5.54717e12 | − | 1.85535e14i | −0.0233757 | − | 0.781845i | ||||
\(751\) | − | 2.64643e14i | − | 1.10780i | −0.832584 | − | 0.553899i | \(-0.813140\pi\) | ||
0.832584 | − | 0.553899i | \(-0.186860\pi\) | |||||||
\(752\) | −2.41682e14 | + | 1.35275e14i | −1.00498 | + | 0.562509i | ||||
\(753\) | − | 7.16906e13i | − | 0.296133i | ||||||
\(754\) | 4.35202e13 | + | 3.39296e14i | 0.178580 | + | 1.39227i | ||||
\(755\) | 2.00037e14 | + | 6.51552e12i | 0.815409 | + | 0.0265592i | ||||
\(756\) | −2.17005e14 | + | 5.66000e13i | −0.878741 | + | 0.229196i | ||||
\(757\) | 2.99343e13i | 0.120418i | 0.998186 | + | 0.0602089i | \(0.0191767\pi\) | ||||
−0.998186 | + | 0.0602089i | \(0.980823\pi\) | |||||||
\(758\) | −5.30015e13 | − | 4.13215e14i | −0.211808 | − | 1.65132i | ||||
\(759\) | 2.25636e14i | 0.895777i | ||||||||
\(760\) | 2.05876e14 | − | 7.51853e13i | 0.811966 | − | 0.296527i | ||||
\(761\) | 1.89021e14 | 0.740605 | 0.370302 | − | 0.928911i | \(-0.379254\pi\) | ||||
0.370302 | + | 0.928911i | \(0.379254\pi\) | |||||||
\(762\) | 2.50125e14 | − | 3.20825e13i | 0.973602 | − | 0.124880i | ||||
\(763\) | 1.86993e14 | 0.723109 | ||||||||
\(764\) | −8.66861e13 | − | 3.32356e14i | −0.333030 | − | 1.27684i | ||||
\(765\) | 7.78408e13 | + | 2.53540e12i | 0.297098 | + | 0.00967696i | ||||
\(766\) | 2.41878e12 | − | 3.10247e11i | 0.00917176 | − | 0.00117643i | ||||
\(767\) | 3.68516e14 | 1.38829 | ||||||||
\(768\) | 1.09278e14 | − | 1.78141e14i | 0.409003 | − | 0.666741i | ||||
\(769\) | 1.99563e14 | 0.742076 | 0.371038 | − | 0.928618i | \(-0.379002\pi\) | ||||
0.371038 | + | 0.928618i | \(0.379002\pi\) | |||||||
\(770\) | −2.42371e14 | + | 2.30971e13i | −0.895422 | + | 0.0853304i | ||||
\(771\) | − | 1.56606e14i | − | 0.574826i | ||||||
\(772\) | −1.14300e14 | − | 4.38228e14i | −0.416831 | − | 1.59813i | ||||
\(773\) | 1.95460e14i | 0.708208i | 0.935206 | + | 0.354104i | \(0.115214\pi\) | ||||
−0.935206 | + | 0.354104i | \(0.884786\pi\) | |||||||
\(774\) | 6.30271e13 | − | 8.08424e12i | 0.226894 | − | 0.0291028i | ||||
\(775\) | −2.46245e13 | + | 3.77604e14i | −0.0880762 | + | 1.35060i | ||||
\(776\) | 7.08462e13 | + | 1.75990e14i | 0.251772 | + | 0.625433i | ||||
\(777\) | − | 3.46227e13i | − | 0.122252i | ||||||
\(778\) | 1.80336e14 | − | 2.31310e13i | 0.632680 | − | 0.0811514i | ||||
\(779\) | − | 9.60873e13i | − | 0.334949i | ||||||
\(780\) | −3.94057e14 | + | 8.91866e13i | −1.36485 | + | 0.308906i | ||||
\(781\) | −5.68862e14 | −1.95773 | ||||||||
\(782\) | 3.03387e13 | + | 2.36529e14i | 0.103744 | + | 0.808818i | ||||
\(783\) | −2.50734e14 | −0.851929 | ||||||||
\(784\) | −7.76681e13 | + | 4.34727e13i | −0.262218 | + | 0.146770i | ||||
\(785\) | −3.96964e13 | − | 1.29297e12i | −0.133169 | − | 0.00433752i | ||||
\(786\) | 1.07482e12 | + | 8.37959e12i | 0.00358280 | + | 0.0279325i | ||||
\(787\) | 1.04188e14 | 0.345100 | 0.172550 | − | 0.985001i | \(-0.444799\pi\) | ||||
0.172550 | + | 0.985001i | \(0.444799\pi\) | |||||||
\(788\) | 1.65145e13 | + | 6.33169e13i | 0.0543545 | + | 0.208396i | ||||
\(789\) | 2.06775e14 | 0.676260 | ||||||||
\(790\) | −3.07353e14 | + | 2.92896e13i | −0.998855 | + | 0.0951872i | ||||
\(791\) | 3.30477e14i | 1.06723i | ||||||||
\(792\) | 4.85805e13 | + | 1.20680e14i | 0.155896 | + | 0.387265i | ||||
\(793\) | − | 5.79711e14i | − | 1.84861i | ||||||
\(794\) | −5.01125e13 | − | 3.90692e14i | −0.158798 | − | 1.23803i | ||||
\(795\) | −1.36057e14 | − | 4.43159e12i | −0.428434 | − | 0.0139548i | ||||
\(796\) | −7.63217e13 | − | 2.92619e14i | −0.238827 | − | 0.915665i | ||||
\(797\) | − | 1.43104e14i | − | 0.445000i | −0.974933 | − | 0.222500i | \(-0.928578\pi\) | ||
0.974933 | − | 0.222500i | \(-0.0714217\pi\) | |||||||
\(798\) | 2.32817e13 | + | 1.81511e14i | 0.0719450 | + | 0.560904i | ||||
\(799\) | 2.87194e14i | 0.881945i | ||||||||
\(800\) | 2.75391e14 | − | 1.77578e14i | 0.840426 | − | 0.541926i | ||||
\(801\) | −1.99193e14 | −0.604103 | ||||||||
\(802\) | −1.02019e13 | + | 1.30856e12i | −0.0307474 | + | 0.00394385i | ||||
\(803\) | −2.79889e14 | −0.838318 | ||||||||
\(804\) | 2.88267e13 | − | 7.51867e12i | 0.0858053 | − | 0.0223800i | ||||
\(805\) | 9.80102e12 | − | 3.00907e14i | 0.0289929 | − | 0.890129i | ||||
\(806\) | 8.16961e14 | − | 1.04788e14i | 2.40174 | − | 0.308062i | ||||
\(807\) | 2.99475e14 | 0.874971 | ||||||||
\(808\) | 3.27768e14 | − | 1.31945e14i | 0.951722 | − | 0.383122i | ||||
\(809\) | −4.37170e13 | −0.126156 | −0.0630780 | − | 0.998009i | \(-0.520092\pi\) | ||||
−0.0630780 | + | 0.998009i | \(0.520092\pi\) | |||||||
\(810\) | −1.52539e13 | − | 1.60068e14i | −0.0437477 | − | 0.459070i | ||||
\(811\) | 3.48250e14i | 0.992629i | 0.868143 | + | 0.496314i | \(0.165314\pi\) | ||||
−0.868143 | + | 0.496314i | \(0.834686\pi\) | |||||||
\(812\) | 2.24145e14 | − | 5.84622e13i | 0.634963 | − | 0.165613i | ||||
\(813\) | 1.42181e14i | 0.400304i | ||||||||
\(814\) | −7.12396e13 | + | 9.13763e12i | −0.199342 | + | 0.0255689i | ||||
\(815\) | 1.74600e13 | − | 5.36049e14i | 0.0485574 | − | 1.49079i | ||||
\(816\) | −1.05843e14 | − | 1.89099e14i | −0.292559 | − | 0.522684i | ||||
\(817\) | − | 1.85428e14i | − | 0.509407i | ||||||
\(818\) | −3.29464e14 | + | 4.22590e13i | −0.899583 | + | 0.115386i | ||||
\(819\) | 2.14022e14i | 0.580816i | ||||||||
\(820\) | −3.17115e13 | − | 1.40112e14i | −0.0855357 | − | 0.377927i | ||||
\(821\) | 3.27880e14 | 0.879021 | 0.439511 | − | 0.898237i | \(-0.355152\pi\) | ||||
0.439511 | + | 0.898237i | \(0.355152\pi\) | |||||||
\(822\) | 3.21611e13 | + | 2.50737e14i | 0.0856982 | + | 0.668129i | ||||
\(823\) | 1.64425e14 | 0.435481 | 0.217740 | − | 0.976007i | \(-0.430131\pi\) | ||||
0.217740 | + | 0.976007i | \(0.430131\pi\) | |||||||
\(824\) | −2.14566e14 | + | 8.63749e13i | −0.564838 | + | 0.227379i | ||||
\(825\) | 2.09213e13 | − | 3.20818e14i | 0.0547419 | − | 0.839440i | ||||
\(826\) | −3.17484e13 | − | 2.47520e14i | −0.0825699 | − | 0.643739i | ||||
\(827\) | −8.72181e13 | −0.225465 | −0.112732 | − | 0.993625i | \(-0.535960\pi\) | ||||
−0.112732 | + | 0.993625i | \(0.535960\pi\) | |||||||
\(828\) | −1.55659e14 | + | 4.05994e13i | −0.399965 | + | 0.104320i | ||||
\(829\) | 2.12343e14 | 0.542333 | 0.271166 | − | 0.962532i | \(-0.412591\pi\) | ||||
0.271166 | + | 0.962532i | \(0.412591\pi\) | |||||||
\(830\) | 1.79386e13 | + | 1.88240e14i | 0.0455406 | + | 0.477884i | ||||
\(831\) | 2.57697e14i | 0.650285i | ||||||||
\(832\) | −4.94160e14 | − | 5.14313e14i | −1.23951 | − | 1.29006i | ||||
\(833\) | 9.22939e13i | 0.230117i | ||||||||
\(834\) | −6.11353e13 | − | 4.76629e14i | −0.151517 | − | 1.18127i | ||||
\(835\) | −1.29760e13 | + | 3.98385e14i | −0.0319676 | + | 0.981455i | ||||
\(836\) | 3.67333e14 | − | 9.58090e13i | 0.899556 | − | 0.234625i | ||||
\(837\) | 6.03719e14i | 1.46963i | ||||||||
\(838\) | 6.41747e13 | + | 5.00325e14i | 0.155290 | + | 1.21069i | ||||
\(839\) | − | 7.14552e12i | − | 0.0171879i | −0.999963 | − | 0.00859397i | \(-0.997264\pi\) | ||
0.999963 | − | 0.00859397i | \(-0.00273558\pi\) | |||||||
\(840\) | 9.38526e13 | + | 2.56992e14i | 0.224414 | + | 0.614502i | ||||
\(841\) | −1.61724e14 | −0.384410 | ||||||||
\(842\) | 4.76379e14 | − | 6.11033e13i | 1.12562 | − | 0.144379i | ||||
\(843\) | −1.26509e14 | −0.297155 | ||||||||
\(844\) | 3.89333e13 | + | 1.49271e14i | 0.0909094 | + | 0.348548i | ||||
\(845\) | −3.08635e13 | + | 9.47559e14i | −0.0716410 | + | 2.19949i | ||||
\(846\) | −1.92163e14 | + | 2.46480e13i | −0.443422 | + | 0.0568760i | ||||
\(847\) | −5.71051e13 | −0.130996 | ||||||||
\(848\) | −1.17374e14 | − | 2.09700e14i | −0.267666 | − | 0.478211i | ||||
\(849\) | −6.03091e14 | −1.36724 | ||||||||
\(850\) | −2.12054e13 | − | 3.39119e14i | −0.0477915 | − | 0.764290i | ||||
\(851\) | − | 8.88144e13i | − | 0.198992i | ||||||
\(852\) | 1.61333e14 | + | 6.18552e14i | 0.359356 | + | 1.37778i | ||||
\(853\) | − | 1.73226e14i | − | 0.383591i | −0.981435 | − | 0.191795i | \(-0.938569\pi\) | ||
0.981435 | − | 0.191795i | \(-0.0614310\pi\) | |||||||
\(854\) | −3.89373e14 | + | 4.99433e13i | −0.857189 | + | 0.109948i | ||||
\(855\) | 1.53232e14 | + | 4.99100e12i | 0.335365 | + | 0.0109234i | ||||
\(856\) | 5.50782e13 | − | 2.21721e13i | 0.119842 | − | 0.0482434i | ||||
\(857\) | 1.24930e14i | 0.270248i | 0.990829 | + | 0.135124i | \(0.0431432\pi\) | ||||
−0.990829 | + | 0.135124i | \(0.956857\pi\) | |||||||
\(858\) | −6.94103e14 | + | 8.90298e13i | −1.49275 | + | 0.191469i | ||||
\(859\) | − | 3.15975e14i | − | 0.675596i | −0.941219 | − | 0.337798i | \(-0.890318\pi\) | ||
0.941219 | − | 0.337798i | \(-0.109682\pi\) | |||||||
\(860\) | −6.11964e13 | − | 2.70387e14i | −0.130087 | − | 0.574769i | ||||
\(861\) | 1.19944e14 | 0.253492 | ||||||||
\(862\) | 2.40958e12 | + | 1.87858e13i | 0.00506297 | + | 0.0394724i | ||||
\(863\) | −1.53961e14 | −0.321631 | −0.160816 | − | 0.986984i | \(-0.551412\pi\) | ||||
−0.160816 | + | 0.986984i | \(0.551412\pi\) | |||||||
\(864\) | 4.19998e14 | − | 3.11304e14i | 0.872325 | − | 0.646571i | ||||
\(865\) | 5.85388e14 | + | 1.90670e13i | 1.20882 | + | 0.0393733i | ||||
\(866\) | 9.36547e13 | + | 7.30160e14i | 0.192283 | + | 1.49909i | ||||
\(867\) | 1.58477e14 | 0.323498 | ||||||||
\(868\) | −1.40766e14 | − | 5.39699e14i | −0.285693 | − | 1.09535i | ||||
\(869\) | −5.34762e14 | −1.07910 | ||||||||
\(870\) | 2.90181e13 | + | 3.04504e14i | 0.0582202 | + | 0.610938i | ||||
\(871\) | − | 1.01672e14i | − | 0.202820i | ||||||
\(872\) | −4.04370e14 | + | 1.62782e14i | −0.802041 | + | 0.322867i | ||||
\(873\) | 1.32706e14i | 0.261709i | ||||||||
\(874\) | 5.97225e13 | + | 4.65614e14i | 0.117106 | + | 0.912996i | ||||
\(875\) | −4.18360e13 | + | 4.26933e14i | −0.0815662 | + | 0.832375i | ||||
\(876\) | 7.93784e13 | + | 3.04338e14i | 0.153880 | + | 0.589977i | ||||
\(877\) | 1.51963e14i | 0.292913i | 0.989217 | + | 0.146457i | \(0.0467869\pi\) | ||||
−0.989217 | + | 0.146457i | \(0.953213\pi\) | |||||||
\(878\) | 1.85004e13 | + | 1.44234e14i | 0.0354575 | + | 0.276437i | ||||
\(879\) | 6.12508e13i | 0.116726i | ||||||||
\(880\) | 5.04017e14 | − | 2.60937e14i | 0.955063 | − | 0.494449i | ||||
\(881\) | 5.87645e14 | 1.10722 | 0.553612 | − | 0.832774i | \(-0.313249\pi\) | ||||
0.553612 | + | 0.832774i | \(0.313249\pi\) | |||||||
\(882\) | −6.17543e13 | + | 7.92098e12i | −0.115697 | + | 0.0148401i | ||||
\(883\) | 4.47094e14 | 0.832904 | 0.416452 | − | 0.909158i | \(-0.363273\pi\) | ||||
0.416452 | + | 0.909158i | \(0.363273\pi\) | |||||||
\(884\) | −7.15641e14 | + | 1.86656e14i | −1.32566 | + | 0.345764i | ||||
\(885\) | 3.29352e14 | + | 1.07275e13i | 0.606657 | + | 0.0197598i | ||||
\(886\) | −7.62871e13 | + | 9.78504e12i | −0.139728 | + | 0.0179223i | ||||
\(887\) | −4.52899e14 | −0.824866 | −0.412433 | − | 0.910988i | \(-0.635321\pi\) | ||||
−0.412433 | + | 0.910988i | \(0.635321\pi\) | |||||||
\(888\) | 3.01398e13 | + | 7.48709e13i | 0.0545853 | + | 0.135596i | ||||
\(889\) | −5.82792e14 | −1.04955 | ||||||||
\(890\) | 8.24421e13 | + | 8.65113e14i | 0.147638 | + | 1.54926i | ||||
\(891\) | − | 2.78501e14i | − | 0.495950i | ||||||
\(892\) | 8.21342e14 | − | 2.14225e14i | 1.45445 | − | 0.379355i | ||||
\(893\) | 5.65349e14i | 0.995542i | ||||||||
\(894\) | 2.03893e13 | − | 2.61525e12i | 0.0357038 | − | 0.00457959i | ||||
\(895\) | −4.17918e14 | − | 1.36123e13i | −0.727740 | − | 0.0237037i | ||||
\(896\) | −3.02875e14 | + | 3.76221e14i | −0.524473 | + | 0.651483i | ||||
\(897\) | − | 8.65337e14i | − | 1.49013i | ||||||
\(898\) | 8.10593e14 | − | 1.03972e14i | 1.38810 | − | 0.178046i | ||||
\(899\) | − | 6.23583e14i | − | 1.06193i | ||||||
\(900\) | 2.25086e14 | − | 4.32930e13i | 0.381186 | − | 0.0733170i | ||||
\(901\) | −2.49189e14 | −0.419668 | ||||||||
\(902\) | −3.16558e13 | − | 2.46798e14i | −0.0530176 | − | 0.413341i | ||||
\(903\) | 2.31467e14 | 0.385523 | ||||||||
\(904\) | −2.87688e14 | − | 7.14651e14i | −0.476518 | − | 1.18373i | ||||
\(905\) | 3.57084e13 | − | 1.09630e15i | 0.0588203 | − | 1.80588i | ||||
\(906\) | −4.95598e13 | − | 3.86383e14i | −0.0811874 | − | 0.632961i | ||||
\(907\) | −9.97795e14 | −1.62557 | −0.812783 | − | 0.582566i | \(-0.802049\pi\) | ||||
−0.812783 | + | 0.582566i | \(0.802049\pi\) | |||||||
\(908\) | −5.62697e14 | + | 1.46765e14i | −0.911686 | + | 0.237789i | ||||
\(909\) | 2.47154e14 | 0.398243 | ||||||||
\(910\) | 9.29518e14 | − | 8.85797e13i | 1.48954 | − | 0.141947i | ||||
\(911\) | − | 1.01348e15i | − | 1.61518i | −0.589741 | − | 0.807592i | \(-0.700770\pi\) | ||
0.589741 | − | 0.807592i | \(-0.299230\pi\) | |||||||
\(912\) | −2.08356e14 | − | 3.72247e14i | −0.330241 | − | 0.590007i | ||||
\(913\) | 3.27519e14i | 0.516276i | ||||||||
\(914\) | 5.85568e13 | + | 4.56526e14i | 0.0918008 | + | 0.715706i | ||||
\(915\) | 1.68754e13 | − | 5.18102e14i | 0.0263117 | − | 0.807811i | ||||
\(916\) | 6.23820e13 | − | 1.62707e13i | 0.0967346 | − | 0.0252306i | ||||
\(917\) | − | 1.95245e13i | − | 0.0301116i | ||||||
\(918\) | −6.89676e13 | − | 5.37692e14i | −0.105787 | − | 0.824745i | ||||
\(919\) | − | 3.29429e14i | − | 0.502556i | −0.967915 | − | 0.251278i | \(-0.919149\pi\) | ||
0.967915 | − | 0.251278i | \(-0.0808508\pi\) | |||||||
\(920\) | 2.40752e14 | + | 6.59238e14i | 0.365284 | + | 1.00024i | ||||
\(921\) | 3.74975e14 | 0.565853 | ||||||||
\(922\) | −9.75681e14 | + | 1.25147e14i | −1.46438 | + | 0.187830i | ||||
\(923\) | 2.18164e15 | 3.25668 | ||||||||
\(924\) | 1.19597e14 | + | 4.58536e14i | 0.177566 | + | 0.680791i | ||||
\(925\) | −8.23501e12 | + | 1.26280e14i | −0.0121606 | + | 0.186477i | ||||
\(926\) | −5.29262e14 | + | 6.78864e13i | −0.777349 | + | 0.0997075i | ||||
\(927\) | −1.61793e14 | −0.236353 | ||||||||
\(928\) | −4.33817e14 | + | 3.21547e14i | −0.630328 | + | 0.467201i | ||||
\(929\) | −6.89030e14 | −0.995771 | −0.497886 | − | 0.867243i | \(-0.665890\pi\) | ||||
−0.497886 | + | 0.867243i | \(0.665890\pi\) | |||||||
\(930\) | 7.33189e14 | − | 6.98702e13i | 1.05390 | − | 0.100433i | ||||
\(931\) | 1.81683e14i | 0.259756i | ||||||||
\(932\) | −1.00940e14 | − | 3.87005e14i | −0.143544 | − | 0.550348i | ||||
\(933\) | − | 9.75705e14i | − | 1.38010i | ||||||
\(934\) | −2.09169e14 | + | 2.68292e13i | −0.294281 | + | 0.0377463i | ||||
\(935\) | 1.91588e13 | − | 5.88206e14i | 0.0268109 | − | 0.823136i | ||||
\(936\) | −1.86311e14 | − | 4.62819e14i | −0.259334 | − | 0.644216i | ||||
\(937\) | − | 1.02170e15i | − | 1.41458i | −0.706924 | − | 0.707289i | \(-0.749918\pi\) | ||
0.706924 | − | 0.707289i | \(-0.250082\pi\) | |||||||
\(938\) | −6.82898e13 | + | 8.75927e12i | −0.0940463 | + | 0.0120630i | ||||
\(939\) | 4.52537e12i | 0.00619906i | ||||||||
\(940\) | 1.86581e14 | + | 8.24380e14i | 0.254231 | + | 1.12328i | ||||
\(941\) | 7.35996e14 | 0.997532 | 0.498766 | − | 0.866737i | \(-0.333787\pi\) | ||||
0.498766 | + | 0.866737i | \(0.333787\pi\) | |||||||
\(942\) | 9.83490e12 | + | 7.66758e13i | 0.0132591 | + | 0.103372i | ||||
\(943\) | 3.07682e14 | 0.412614 | ||||||||
\(944\) | 2.84127e14 | + | 5.07620e14i | 0.379012 | + | 0.677141i | ||||
\(945\) | −2.22803e13 | + | 6.84039e14i | −0.0295639 | + | 0.907657i | ||||
\(946\) | −6.10888e13 | − | 4.76266e14i | −0.0806318 | − | 0.628629i | ||||
\(947\) | −7.17168e14 | −0.941609 | −0.470805 | − | 0.882237i | \(-0.656036\pi\) | ||||
−0.470805 | + | 0.882237i | \(0.656036\pi\) | |||||||
\(948\) | 1.51662e14 | + | 5.81474e14i | 0.198077 | + | 0.759431i | ||||
\(949\) | 1.07340e15 | 1.39454 | ||||||||
\(950\) | −4.17433e13 | − | 6.67566e14i | −0.0539472 | − | 0.862732i | ||||
\(951\) | 9.61783e14i | 1.23644i | ||||||||
\(952\) | 1.87025e14 | + | 4.64592e14i | 0.239174 | + | 0.594137i | ||||
\(953\) | − | 4.43899e14i | − | 0.564702i | −0.959311 | − | 0.282351i | \(-0.908886\pi\) | ||
0.959311 | − | 0.282351i | \(-0.0911143\pi\) | |||||||
\(954\) | −2.13863e13 | − | 1.66734e14i | −0.0270641 | − | 0.211000i | ||||
\(955\) | −1.04765e15 | − | 3.41235e13i | −1.31886 | − | 0.0429573i | ||||
\(956\) | 2.21311e14 | + | 8.48510e14i | 0.277149 | + | 1.06259i | ||||
\(957\) | 5.29805e14i | 0.660019i | ||||||||
\(958\) | −1.35369e14 | − | 1.05538e15i | −0.167761 | − | 1.30791i | ||||
\(959\) | − | 5.84220e14i | − | 0.720250i | ||||||
\(960\) | −4.26672e14 | − | 4.74040e14i | −0.523285 | − | 0.581378i | ||||
\(961\) | −6.81841e14 | −0.831891 | ||||||||
\(962\) | 2.73211e14 | − | 3.50437e13i | 0.331606 | − | 0.0425339i | ||||
\(963\) | 4.15317e13 | 0.0501474 | ||||||||
\(964\) | −2.17593e14 | + | 5.67534e13i | −0.261373 | + | 0.0681722i | ||||
\(965\) | −1.38137e15 | − | 4.49935e13i | −1.65072 | − | 0.0537667i | ||||
\(966\) | −5.81219e14 | + | 7.45507e13i | −0.690962 | + | 0.0886270i | ||||
\(967\) | 1.42458e15 | 1.68482 | 0.842410 | − | 0.538837i | \(-0.181136\pi\) | ||||
0.842410 | + | 0.538837i | \(0.181136\pi\) | |||||||
\(968\) | 1.23489e14 | − | 4.97113e13i | 0.145295 | − | 0.0584895i | ||||
\(969\) | −4.42346e14 | −0.517778 | ||||||||
\(970\) | 5.76354e14 | − | 5.49244e13i | 0.671167 | − | 0.0639597i | ||||
\(971\) | 4.62402e14i | 0.535702i | 0.963460 | + | 0.267851i | \(0.0863136\pi\) | ||||
−0.963460 | + | 0.267851i | \(0.913686\pi\) | |||||||
\(972\) | 6.08758e14 | − | 1.58778e14i | 0.701639 | − | 0.183004i | ||||
\(973\) | 1.11055e15i | 1.27343i | ||||||||
\(974\) | 1.11045e14 | − | 1.42433e13i | 0.126679 | − | 0.0162486i | ||||
\(975\) | −8.02354e13 | + | 1.23037e15i | −0.0910632 | + | 1.39641i | ||||
\(976\) | 7.98535e14 | − | 4.46959e14i | 0.901665 | − | 0.504683i | ||||
\(977\) | 1.24483e15i | 1.39842i | 0.714918 | + | 0.699209i | \(0.246464\pi\) | ||||
−0.714918 | + | 0.699209i | \(0.753536\pi\) | |||||||
\(978\) | −1.03541e15 | + | 1.32808e14i | −1.15722 | + | 0.148433i | ||||
\(979\) | 1.50521e15i | 1.67372i | ||||||||
\(980\) | 5.99605e13 | + | 2.64926e14i | 0.0663338 | + | 0.293086i | ||||
\(981\) | −3.04915e14 | −0.335609 | ||||||||
\(982\) | −6.10233e13 | − | 4.75755e14i | −0.0668249 | − | 0.520986i | ||||
\(983\) | −7.82351e14 | −0.852382 | −0.426191 | − | 0.904633i | \(-0.640145\pi\) | ||||
−0.426191 | + | 0.904633i | \(0.640145\pi\) | |||||||
\(984\) | −2.59378e14 | + | 1.04414e14i | −0.281162 | + | 0.113184i | ||||
\(985\) | 1.99587e14 | + | 6.50085e12i | 0.215253 | + | 0.00701115i | ||||
\(986\) | 7.12367e13 | + | 5.55383e14i | 0.0764398 | + | 0.595947i | ||||
\(987\) | −7.05717e14 | −0.753433 | ||||||||
\(988\) | −1.40876e15 | + | 3.67437e14i | −1.49641 | + | 0.390300i | ||||
\(989\) | 5.93761e14 | 0.627524 | ||||||||
\(990\) | 3.95216e14 | − | 3.76626e13i | 0.415583 | − | 0.0396036i | ||||
\(991\) | − | 5.07172e14i | − | 0.530624i | −0.964163 | − | 0.265312i | \(-0.914525\pi\) | ||
0.964163 | − | 0.265312i | \(-0.0854750\pi\) | |||||||
\(992\) | 7.74224e14 | + | 1.04455e15i | 0.805950 | + | 1.08735i | ||||
\(993\) | 8.83905e14i | 0.915502i | ||||||||
\(994\) | −1.87953e14 | − | 1.46534e15i | −0.193695 | − | 1.51010i | ||||
\(995\) | −9.22387e14 | − | 3.00436e13i | −0.945797 | − | 0.0308061i | ||||
\(996\) | 3.56127e14 | − | 9.28863e13i | 0.363336 | − | 0.0947665i | ||||
\(997\) | 5.76576e14i | 0.585303i | 0.956219 | + | 0.292652i | \(0.0945376\pi\) | ||||
−0.956219 | + | 0.292652i | \(0.905462\pi\) | |||||||
\(998\) | 8.22170e13 | + | 6.40988e14i | 0.0830442 | + | 0.647437i | ||||
\(999\) | 2.01898e14i | 0.202911i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 20.11.d.d.19.2 | yes | 24 | |
4.3 | odd | 2 | inner | 20.11.d.d.19.24 | yes | 24 | |
5.2 | odd | 4 | 100.11.b.h.51.11 | 24 | |||
5.3 | odd | 4 | 100.11.b.h.51.14 | 24 | |||
5.4 | even | 2 | inner | 20.11.d.d.19.23 | yes | 24 | |
20.3 | even | 4 | 100.11.b.h.51.13 | 24 | |||
20.7 | even | 4 | 100.11.b.h.51.12 | 24 | |||
20.19 | odd | 2 | inner | 20.11.d.d.19.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.11.d.d.19.1 | ✓ | 24 | 20.19 | odd | 2 | inner | |
20.11.d.d.19.2 | yes | 24 | 1.1 | even | 1 | trivial | |
20.11.d.d.19.23 | yes | 24 | 5.4 | even | 2 | inner | |
20.11.d.d.19.24 | yes | 24 | 4.3 | odd | 2 | inner | |
100.11.b.h.51.11 | 24 | 5.2 | odd | 4 | |||
100.11.b.h.51.12 | 24 | 20.7 | even | 4 | |||
100.11.b.h.51.13 | 24 | 20.3 | even | 4 | |||
100.11.b.h.51.14 | 24 | 5.3 | odd | 4 |