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 | 19.12 | ||
Character | \(\chi\) | \(=\) | 20.19 |
Dual form | 20.11.d.d.19.11 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.302723 | + | 31.9986i | −0.00946009 | + | 0.999955i | ||||
\(3\) | −375.794 | −1.54648 | −0.773240 | − | 0.634114i | \(-0.781365\pi\) | ||||
−0.773240 | + | 0.634114i | \(0.781365\pi\) | |||||||
\(4\) | −1023.82 | − | 19.3734i | −0.999821 | − | 0.0189193i | ||||
\(5\) | 2240.90 | − | 2178.07i | 0.717087 | − | 0.696984i | ||||
\(6\) | 113.762 | − | 12024.9i | 0.0146298 | − | 1.54641i | ||||
\(7\) | −19635.7 | −1.16831 | −0.584153 | − | 0.811644i | \(-0.698573\pi\) | ||||
−0.584153 | + | 0.811644i | \(0.698573\pi\) | |||||||
\(8\) | 929.854 | − | 32754.8i | 0.0283769 | − | 0.999597i | ||||
\(9\) | 82172.5 | 1.39160 | ||||||||
\(10\) | 69016.9 | + | 72364.8i | 0.690169 | + | 0.723648i | ||||
\(11\) | 163868.i | 1.01749i | 0.860917 | + | 0.508746i | \(0.169891\pi\) | ||||
−0.860917 | + | 0.508746i | \(0.830109\pi\) | |||||||
\(12\) | 384745. | + | 7280.42i | 1.54620 | + | 0.0292584i | ||||
\(13\) | − | 86535.9i | − | 0.233066i | −0.993187 | − | 0.116533i | \(-0.962822\pi\) | ||
0.993187 | − | 0.116533i | \(-0.0371781\pi\) | |||||||
\(14\) | 5944.18 | − | 628314.i | 0.0110523 | − | 1.16825i | ||||
\(15\) | −842116. | + | 818508.i | −1.10896 | + | 1.07787i | ||||
\(16\) | 1.04783e6 | + | 39669.6i | 0.999284 | + | 0.0378319i | ||||
\(17\) | 2.09541e6i | 1.47579i | 0.674914 | + | 0.737896i | \(0.264181\pi\) | ||||
−0.674914 | + | 0.737896i | \(0.735819\pi\) | |||||||
\(18\) | −24875.5 | + | 2.62940e6i | −0.0131646 | + | 1.39154i | ||||
\(19\) | − | 3.13936e6i | − | 1.26787i | −0.773388 | − | 0.633933i | \(-0.781440\pi\) | ||
0.773388 | − | 0.633933i | \(-0.218560\pi\) | |||||||
\(20\) | −2.33646e6 | + | 2.18654e6i | −0.730145 | + | 0.683292i | ||||
\(21\) | 7.37899e6 | 1.80676 | ||||||||
\(22\) | −5.24354e6 | − | 49606.6i | −1.01745 | − | 0.00962557i | ||||
\(23\) | 1.05386e7 | 1.63737 | 0.818683 | − | 0.574246i | \(-0.194705\pi\) | ||||
0.818683 | + | 0.574246i | \(0.194705\pi\) | |||||||
\(24\) | −349434. | + | 1.23091e7i | −0.0438843 | + | 1.54586i | ||||
\(25\) | 277605. | − | 9.76168e6i | 0.0284268 | − | 0.999596i | ||||
\(26\) | 2.76902e6 | + | 26196.4i | 0.233056 | + | 0.00220483i | ||||
\(27\) | −8.68968e6 | −0.605598 | ||||||||
\(28\) | 2.01034e7 | + | 380410.i | 1.16810 | + | 0.0221036i | ||||
\(29\) | 1.13219e7 | 0.551986 | 0.275993 | − | 0.961160i | \(-0.410993\pi\) | ||||
0.275993 | + | 0.961160i | \(0.410993\pi\) | |||||||
\(30\) | −2.59362e7 | − | 2.71943e7i | −1.06733 | − | 1.11911i | ||||
\(31\) | − | 1.21645e7i | − | 0.424898i | −0.977172 | − | 0.212449i | \(-0.931856\pi\) | ||
0.977172 | − | 0.212449i | \(-0.0681439\pi\) | |||||||
\(32\) | −1.58657e6 | + | 3.35169e7i | −0.0472835 | + | 0.998882i | ||||
\(33\) | − | 6.15807e7i | − | 1.57353i | ||||||
\(34\) | −6.70503e7 | − | 634330.i | −1.47573 | − | 0.0139611i | ||||
\(35\) | −4.40016e7 | + | 4.27680e7i | −0.837776 | + | 0.814290i | ||||
\(36\) | −8.41296e7 | − | 1.59196e6i | −1.39135 | − | 0.0263281i | ||||
\(37\) | − | 4.87589e7i | − | 0.703146i | −0.936160 | − | 0.351573i | \(-0.885647\pi\) | ||
0.936160 | − | 0.351573i | \(-0.114353\pi\) | |||||||
\(38\) | 1.00455e8 | + | 950356.i | 1.26781 | + | 0.0119941i | ||||
\(39\) | 3.25197e7i | 0.360432i | ||||||||
\(40\) | −6.92587e7 | − | 7.54254e7i | −0.676355 | − | 0.736576i | ||||
\(41\) | 4.55341e7 | 0.393022 | 0.196511 | − | 0.980502i | \(-0.437039\pi\) | ||||
0.196511 | + | 0.980502i | \(0.437039\pi\) | |||||||
\(42\) | −2.23379e6 | + | 2.36117e8i | −0.0170921 | + | 1.80668i | ||||
\(43\) | 7.47838e7 | 0.508704 | 0.254352 | − | 0.967112i | \(-0.418138\pi\) | ||||
0.254352 | + | 0.967112i | \(0.418138\pi\) | |||||||
\(44\) | 3.17468e6 | − | 1.67771e8i | 0.0192503 | − | 1.01731i | ||||
\(45\) | 1.84140e8 | − | 1.78978e8i | 0.997897 | − | 0.969922i | ||||
\(46\) | −3.19029e6 | + | 3.37222e8i | −0.0154896 | + | 1.63729i | ||||
\(47\) | 9.62539e6 | 0.0419690 | 0.0209845 | − | 0.999780i | \(-0.493320\pi\) | ||||
0.0209845 | + | 0.999780i | \(0.493320\pi\) | |||||||
\(48\) | −3.93767e8 | − | 1.49076e7i | −1.54537 | − | 0.0585062i | ||||
\(49\) | 1.03086e8 | 0.364937 | ||||||||
\(50\) | 3.12276e8 | + | 1.18380e7i | 0.999282 | + | 0.0378818i | ||||
\(51\) | − | 7.87445e8i | − | 2.28228i | ||||||
\(52\) | −1.67649e6 | + | 8.85969e7i | −0.00440946 | + | 0.233025i | ||||
\(53\) | − | 1.27224e8i | − | 0.304222i | −0.988363 | − | 0.152111i | \(-0.951393\pi\) | ||
0.988363 | − | 0.152111i | \(-0.0486071\pi\) | |||||||
\(54\) | 2.63056e6 | − | 2.78057e8i | 0.00572902 | − | 0.605571i | ||||
\(55\) | 3.56917e8 | + | 3.67211e8i | 0.709175 | + | 0.729630i | ||||
\(56\) | −1.82583e7 | + | 6.43164e8i | −0.0331529 | + | 1.16783i | ||||
\(57\) | 1.17975e9i | 1.96073i | ||||||||
\(58\) | −3.42739e6 | + | 3.62283e8i | −0.00522184 | + | 0.551961i | ||||
\(59\) | 1.18280e9i | 1.65444i | 0.561881 | + | 0.827218i | \(0.310078\pi\) | ||||
−0.561881 | + | 0.827218i | \(0.689922\pi\) | |||||||
\(60\) | 8.78030e8 | − | 8.21688e8i | 1.12915 | − | 1.05670i | ||||
\(61\) | 2.97404e8 | 0.352126 | 0.176063 | − | 0.984379i | \(-0.443664\pi\) | ||||
0.176063 | + | 0.984379i | \(0.443664\pi\) | |||||||
\(62\) | 3.89246e8 | + | 3.68246e6i | 0.424879 | + | 0.00401957i | ||||
\(63\) | −1.61351e9 | −1.62581 | ||||||||
\(64\) | −1.07201e9 | − | 6.09144e7i | −0.998390 | − | 0.0567309i | ||||
\(65\) | −1.88482e8 | − | 1.93918e8i | −0.162443 | − | 0.167129i | ||||
\(66\) | 1.97049e9 | + | 1.86419e7i | 1.57346 | + | 0.0148857i | ||||
\(67\) | 7.15670e8 | 0.530077 | 0.265039 | − | 0.964238i | \(-0.414615\pi\) | ||||
0.265039 | + | 0.964238i | \(0.414615\pi\) | |||||||
\(68\) | 4.05953e7 | − | 2.14532e9i | 0.0279210 | − | 1.47553i | ||||
\(69\) | −3.96036e9 | −2.53215 | ||||||||
\(70\) | −1.35520e9 | − | 1.42093e9i | −0.806328 | − | 0.845442i | ||||
\(71\) | − | 2.56419e9i | − | 1.42121i | −0.703589 | − | 0.710607i | \(-0.748421\pi\) | ||
0.703589 | − | 0.710607i | \(-0.251579\pi\) | |||||||
\(72\) | 7.64084e7 | − | 2.69154e9i | 0.0394892 | − | 1.39104i | ||||
\(73\) | 2.10771e9i | 1.01671i | 0.861148 | + | 0.508355i | \(0.169746\pi\) | ||||
−0.861148 | + | 0.508355i | \(0.830254\pi\) | |||||||
\(74\) | 1.56022e9 | + | 1.47604e7i | 0.703115 | + | 0.00665183i | ||||
\(75\) | −1.04322e8 | + | 3.66838e9i | −0.0439614 | + | 1.54585i | ||||
\(76\) | −6.08201e7 | + | 3.21413e9i | −0.0239872 | + | 1.26764i | ||||
\(77\) | − | 3.21766e9i | − | 1.18874i | ||||||
\(78\) | −1.04058e9 | − | 9.84446e6i | −0.360416 | − | 0.00340972i | ||||
\(79\) | − | 3.44771e9i | − | 1.12046i | −0.828338 | − | 0.560229i | \(-0.810713\pi\) | ||
0.828338 | − | 0.560229i | \(-0.189287\pi\) | |||||||
\(80\) | 2.43447e9 | − | 2.19335e9i | 0.742942 | − | 0.669356i | ||||
\(81\) | −1.58667e9 | −0.455053 | ||||||||
\(82\) | −1.37842e7 | + | 1.45702e9i | −0.00371803 | + | 0.393005i | ||||
\(83\) | 7.09842e9 | 1.80207 | 0.901034 | − | 0.433748i | \(-0.142809\pi\) | ||||
0.901034 | + | 0.433748i | \(0.142809\pi\) | |||||||
\(84\) | −7.55473e9 | − | 1.42956e8i | −1.80644 | − | 0.0341827i | ||||
\(85\) | 4.56397e9 | + | 4.69561e9i | 1.02860 | + | 1.05827i | ||||
\(86\) | −2.26388e7 | + | 2.39297e9i | −0.00481238 | + | 0.508681i | ||||
\(87\) | −4.25469e9 | −0.853634 | ||||||||
\(88\) | 5.36747e9 | + | 1.52373e8i | 1.01708 | + | 0.0288733i | ||||
\(89\) | −3.39502e9 | −0.607984 | −0.303992 | − | 0.952675i | \(-0.598320\pi\) | ||||
−0.303992 | + | 0.952675i | \(0.598320\pi\) | |||||||
\(90\) | 5.67129e9 | + | 5.94640e9i | 0.960438 | + | 1.00703i | ||||
\(91\) | 1.69919e9i | 0.272292i | ||||||||
\(92\) | −1.07896e10 | − | 2.04169e8i | −1.63707 | − | 0.0309779i | ||||
\(93\) | 4.57134e9i | 0.657096i | ||||||||
\(94\) | −2.91383e6 | + | 3.07999e8i | −0.000397031 | + | 0.0419671i | ||||
\(95\) | −6.83776e9 | − | 7.03498e9i | −0.883682 | − | 0.909170i | ||||
\(96\) | 5.96225e8 | − | 1.25955e10i | 0.0731230 | − | 1.54475i | ||||
\(97\) | − | 5.71771e9i | − | 0.665830i | −0.942957 | − | 0.332915i | \(-0.891968\pi\) | ||
0.942957 | − | 0.332915i | \(-0.108032\pi\) | |||||||
\(98\) | −3.12064e7 | + | 3.29859e9i | −0.00345233 | + | 0.364920i | ||||
\(99\) | 1.34654e10i | 1.41594i | ||||||||
\(100\) | −4.73334e8 | + | 9.98879e9i | −0.0473334 | + | 0.998879i | ||||
\(101\) | 1.71412e10 | 1.63093 | 0.815465 | − | 0.578807i | \(-0.196481\pi\) | ||||
0.815465 | + | 0.578807i | \(0.196481\pi\) | |||||||
\(102\) | 2.51971e10 | + | 2.38378e8i | 2.28218 | + | 0.0215906i | ||||
\(103\) | −7.45366e9 | −0.642960 | −0.321480 | − | 0.946916i | \(-0.604180\pi\) | ||||
−0.321480 | + | 0.946916i | \(0.604180\pi\) | |||||||
\(104\) | −2.83447e9 | − | 8.04657e7i | −0.232972 | − | 0.00661370i | ||||
\(105\) | 1.65355e10 | − | 1.60720e10i | 1.29560 | − | 1.25928i | ||||
\(106\) | 4.07099e9 | + | 3.85137e7i | 0.304208 | + | 0.00287797i | ||||
\(107\) | 7.26790e9 | 0.518191 | 0.259096 | − | 0.965852i | \(-0.416576\pi\) | ||||
0.259096 | + | 0.965852i | \(0.416576\pi\) | |||||||
\(108\) | 8.89664e9 | + | 1.68349e8i | 0.605490 | + | 0.0114575i | ||||
\(109\) | −9.09372e9 | −0.591029 | −0.295515 | − | 0.955338i | \(-0.595491\pi\) | ||||
−0.295515 | + | 0.955338i | \(0.595491\pi\) | |||||||
\(110\) | −1.18583e10 | + | 1.13097e10i | −0.736306 | + | 0.702241i | ||||
\(111\) | 1.83233e10i | 1.08740i | ||||||||
\(112\) | −2.05748e10 | − | 7.78941e8i | −1.16747 | − | 0.0441992i | ||||
\(113\) | − | 7.57770e9i | − | 0.411287i | −0.978627 | − | 0.205644i | \(-0.934071\pi\) | ||
0.978627 | − | 0.205644i | \(-0.0659288\pi\) | |||||||
\(114\) | −3.77504e10 | − | 3.57139e8i | −1.96064 | − | 0.0185487i | ||||
\(115\) | 2.36160e10 | − | 2.29540e10i | 1.17413 | − | 1.14122i | ||||
\(116\) | −1.15915e10 | − | 2.19343e8i | −0.551887 | − | 0.0104432i | ||||
\(117\) | − | 7.11087e9i | − | 0.324335i | ||||||
\(118\) | −3.78478e10 | − | 3.58060e8i | −1.65436 | − | 0.0156511i | ||||
\(119\) | − | 4.11449e10i | − | 1.72418i | ||||||
\(120\) | 2.60270e10 | + | 2.83444e10i | 1.04597 | + | 1.13910i | ||||
\(121\) | −9.15322e8 | −0.0352896 | ||||||||
\(122\) | −9.00312e7 | + | 9.51652e9i | −0.00333115 | + | 0.352110i | ||||
\(123\) | −1.71115e10 | −0.607801 | ||||||||
\(124\) | −2.35667e8 | + | 1.24542e10i | −0.00803879 | + | 0.424822i | ||||
\(125\) | −2.06396e10 | − | 2.24796e10i | −0.676318 | − | 0.736610i | ||||
\(126\) | 4.88448e8 | − | 5.16302e10i | 0.0153803 | − | 1.62574i | ||||
\(127\) | 6.24479e9 | 0.189016 | 0.0945081 | − | 0.995524i | \(-0.469872\pi\) | ||||
0.0945081 | + | 0.995524i | \(0.469872\pi\) | |||||||
\(128\) | 2.27370e9 | − | 3.42844e10i | 0.0661732 | − | 0.997808i | ||||
\(129\) | −2.81033e10 | −0.786700 | ||||||||
\(130\) | 6.26215e9 | − | 5.97244e9i | 0.168658 | − | 0.160855i | ||||
\(131\) | 5.72133e10i | 1.48300i | 0.670953 | + | 0.741499i | \(0.265885\pi\) | ||||
−0.670953 | + | 0.741499i | \(0.734115\pi\) | |||||||
\(132\) | −1.19303e9 | + | 6.30474e10i | −0.0297701 | + | 1.57325i | ||||
\(133\) | 6.16435e10i | 1.48125i | ||||||||
\(134\) | −2.16650e8 | + | 2.29004e10i | −0.00501458 | + | 0.530053i | ||||
\(135\) | −1.94727e10 | + | 1.89268e10i | −0.434267 | + | 0.422092i | ||||
\(136\) | 6.86349e10 | + | 1.94843e9i | 1.47520 | + | 0.0418784i | ||||
\(137\) | 1.24420e10i | 0.257803i | 0.991657 | + | 0.128902i | \(0.0411451\pi\) | ||||
−0.991657 | + | 0.128902i | \(0.958855\pi\) | |||||||
\(138\) | 1.19889e9 | − | 1.26726e11i | 0.0239544 | − | 2.53204i | ||||
\(139\) | 3.88376e9i | 0.0748477i | 0.999299 | + | 0.0374239i | \(0.0119152\pi\) | ||||
−0.999299 | + | 0.0374239i | \(0.988085\pi\) | |||||||
\(140\) | 4.58781e10 | − | 4.29342e10i | 0.853032 | − | 0.798294i | ||||
\(141\) | −3.61717e9 | −0.0649042 | ||||||||
\(142\) | 8.20506e10 | + | 7.76241e8i | 1.42115 | + | 0.0134448i | ||||
\(143\) | 1.41805e10 | 0.237143 | ||||||||
\(144\) | 8.61024e10 | + | 3.25975e9i | 1.39060 | + | 0.0526468i | ||||
\(145\) | 2.53711e10 | − | 2.46599e10i | 0.395822 | − | 0.384725i | ||||
\(146\) | −6.74438e10 | − | 6.38053e8i | −1.01666 | − | 0.00961817i | ||||
\(147\) | −3.87390e10 | −0.564367 | ||||||||
\(148\) | −9.44626e8 | + | 4.99202e10i | −0.0133031 | + | 0.703020i | ||||
\(149\) | 5.05127e10 | 0.687811 | 0.343905 | − | 0.939004i | \(-0.388250\pi\) | ||||
0.343905 | + | 0.939004i | \(0.388250\pi\) | |||||||
\(150\) | −1.17351e11 | − | 4.44867e9i | −1.54537 | − | 0.0585833i | ||||
\(151\) | − | 5.51200e10i | − | 0.702141i | −0.936349 | − | 0.351070i | \(-0.885818\pi\) | ||
0.936349 | − | 0.351070i | \(-0.114182\pi\) | |||||||
\(152\) | −1.02829e11 | − | 2.91915e9i | −1.26735 | − | 0.0359781i | ||||
\(153\) | 1.72185e11i | 2.05371i | ||||||||
\(154\) | 1.02961e11 | + | 9.74061e8i | 1.18869 | + | 0.0112456i | ||||
\(155\) | −2.64951e10 | − | 2.72593e10i | −0.296147 | − | 0.304689i | ||||
\(156\) | 6.30017e8 | − | 3.32942e10i | 0.00681914 | − | 0.360368i | ||||
\(157\) | 8.96109e10i | 0.939426i | 0.882819 | + | 0.469713i | \(0.155643\pi\) | ||||
−0.882819 | + | 0.469713i | \(0.844357\pi\) | |||||||
\(158\) | 1.10322e11 | + | 1.04370e9i | 1.12041 | + | 0.0105996i | ||||
\(159\) | 4.78101e10i | 0.470473i | ||||||||
\(160\) | 6.94470e10 | + | 7.85636e10i | 0.662298 | + | 0.749241i | ||||
\(161\) | −2.06934e11 | −1.91294 | ||||||||
\(162\) | 4.80322e8 | − | 5.07712e10i | 0.00430484 | − | 0.455032i | ||||
\(163\) | 1.16440e11 | 1.01197 | 0.505983 | − | 0.862543i | \(-0.331130\pi\) | ||||
0.505983 | + | 0.862543i | \(0.331130\pi\) | |||||||
\(164\) | −4.66185e10 | − | 8.82150e8i | −0.392952 | − | 0.00743572i | ||||
\(165\) | −1.34127e11 | − | 1.37996e11i | −1.09673 | − | 1.12836i | ||||
\(166\) | −2.14885e9 | + | 2.27139e11i | −0.0170477 | + | 1.80199i | ||||
\(167\) | 9.33076e10 | 0.718348 | 0.359174 | − | 0.933271i | \(-0.383058\pi\) | ||||
0.359174 | + | 0.933271i | \(0.383058\pi\) | |||||||
\(168\) | 6.86138e9 | − | 2.41697e11i | 0.0512702 | − | 1.80603i | ||||
\(169\) | 1.30370e11 | 0.945680 | ||||||||
\(170\) | −1.51634e11 | + | 1.44619e11i | −1.06795 | + | 1.01855i | ||||
\(171\) | − | 2.57969e11i | − | 1.76436i | ||||||
\(172\) | −7.65649e10 | − | 1.44882e9i | −0.508613 | − | 0.00962434i | ||||
\(173\) | 9.17264e10i | 0.591921i | 0.955200 | + | 0.295961i | \(0.0956397\pi\) | ||||
−0.955200 | + | 0.295961i | \(0.904360\pi\) | |||||||
\(174\) | 1.28799e9 | − | 1.36144e11i | 0.00807546 | − | 0.853596i | ||||
\(175\) | −5.45097e9 | + | 1.91677e11i | −0.0332111 | + | 1.16783i | ||||
\(176\) | −6.50058e9 | + | 1.71705e11i | −0.0384936 | + | 1.01676i | ||||
\(177\) | − | 4.44488e11i | − | 2.55855i | ||||||
\(178\) | 1.02775e9 | − | 1.08636e11i | 0.00575159 | − | 0.607957i | ||||
\(179\) | 1.07881e11i | 0.587059i | 0.955950 | + | 0.293529i | \(0.0948298\pi\) | ||||
−0.955950 | + | 0.293529i | \(0.905170\pi\) | |||||||
\(180\) | −1.91993e11 | + | 1.79673e11i | −1.01607 | + | 0.950868i | ||||
\(181\) | 3.43268e11 | 1.76702 | 0.883508 | − | 0.468417i | \(-0.155175\pi\) | ||||
0.883508 | + | 0.468417i | \(0.155175\pi\) | |||||||
\(182\) | −5.43717e10 | − | 5.14385e8i | −0.272280 | − | 0.00257591i | ||||
\(183\) | −1.11763e11 | −0.544556 | ||||||||
\(184\) | 9.79940e9 | − | 3.45191e11i | 0.0464633 | − | 1.63671i | ||||
\(185\) | −1.06201e11 | − | 1.09264e11i | −0.490082 | − | 0.504217i | ||||
\(186\) | −1.46276e11 | − | 1.38385e9i | −0.657066 | − | 0.00621619i | ||||
\(187\) | −3.43372e11 | −1.50161 | ||||||||
\(188\) | −9.85463e9 | − | 1.86476e8i | −0.0419615 | − | 0.000794026i | ||||
\(189\) | 1.70628e11 | 0.707524 | ||||||||
\(190\) | 2.27179e11 | − | 2.16669e11i | 0.917489 | − | 0.875042i | ||||
\(191\) | − | 2.33817e10i | − | 0.0919832i | −0.998942 | − | 0.0459916i | \(-0.985355\pi\) | ||
0.998942 | − | 0.0459916i | \(-0.0146447\pi\) | |||||||
\(192\) | 4.02856e11 | + | 2.28913e10i | 1.54399 | + | 0.0877332i | ||||
\(193\) | 2.97973e11i | 1.11273i | 0.830937 | + | 0.556366i | \(0.187805\pi\) | ||||
−0.830937 | + | 0.556366i | \(0.812195\pi\) | |||||||
\(194\) | 1.82958e11 | + | 1.73088e9i | 0.665800 | + | 0.00629881i | ||||
\(195\) | 7.08303e10 | + | 7.28733e10i | 0.251215 | + | 0.258461i | ||||
\(196\) | −1.05541e11 | − | 1.99712e9i | −0.364871 | − | 0.00690436i | ||||
\(197\) | − | 4.56567e11i | − | 1.53877i | −0.638785 | − | 0.769385i | \(-0.720563\pi\) | ||
0.638785 | − | 0.769385i | \(-0.279437\pi\) | |||||||
\(198\) | −4.30875e11 | − | 4.07630e9i | −1.41588 | − | 0.0133949i | ||||
\(199\) | 1.61572e11i | 0.517728i | 0.965914 | + | 0.258864i | \(0.0833481\pi\) | ||||
−0.965914 | + | 0.258864i | \(0.916652\pi\) | |||||||
\(200\) | −3.19484e11 | − | 1.81698e10i | −0.998387 | − | 0.0567807i | ||||
\(201\) | −2.68945e11 | −0.819753 | ||||||||
\(202\) | −5.18904e9 | + | 5.48495e11i | −0.0154287 | + | 1.63086i | ||||
\(203\) | −2.22313e11 | −0.644888 | ||||||||
\(204\) | −1.52555e10 | + | 8.06200e11i | −0.0431793 | + | 2.28187i | ||||
\(205\) | 1.02037e11 | − | 9.91766e10i | 0.281831 | − | 0.273930i | ||||
\(206\) | 2.25640e9 | − | 2.38507e11i | 0.00608246 | − | 0.642931i | ||||
\(207\) | 8.65987e11 | 2.27855 | ||||||||
\(208\) | 3.43285e9 | − | 9.06745e10i | 0.00881734 | − | 0.232899i | ||||
\(209\) | 5.14441e11 | 1.29004 | ||||||||
\(210\) | 5.09275e11 | + | 5.33979e11i | 1.24697 | + | 1.30746i | ||||
\(211\) | − | 1.81757e11i | − | 0.434588i | −0.976106 | − | 0.217294i | \(-0.930277\pi\) | ||
0.976106 | − | 0.217294i | \(-0.0697231\pi\) | |||||||
\(212\) | −2.46476e9 | + | 1.30254e11i | −0.00575567 | + | 0.304167i | ||||
\(213\) | 9.63610e11i | 2.19788i | ||||||||
\(214\) | −2.20016e9 | + | 2.32562e11i | −0.00490214 | + | 0.518168i | ||||
\(215\) | 1.67583e11 | − | 1.62885e11i | 0.364785 | − | 0.354558i | ||||
\(216\) | −8.08013e9 | + | 2.84629e11i | −0.0171850 | + | 0.605355i | ||||
\(217\) | 2.38858e11i | 0.496410i | ||||||||
\(218\) | 2.75288e9 | − | 2.90986e11i | 0.00559119 | − | 0.591003i | ||||
\(219\) | − | 7.92067e11i | − | 1.57232i | ||||||
\(220\) | −3.58303e11 | − | 3.82872e11i | −0.695244 | − | 0.742916i | ||||
\(221\) | 1.81329e11 | 0.343957 | ||||||||
\(222\) | −5.86321e11 | − | 5.54689e9i | −1.08735 | − | 0.0102869i | ||||
\(223\) | −1.11110e11 | −0.201479 | −0.100740 | − | 0.994913i | \(-0.532121\pi\) | ||||
−0.100740 | + | 0.994913i | \(0.532121\pi\) | |||||||
\(224\) | 3.11535e10 | − | 6.58128e11i | 0.0552416 | − | 1.16700i | ||||
\(225\) | 2.28115e10 | − | 8.02141e11i | 0.0395586 | − | 1.39104i | ||||
\(226\) | 2.42476e11 | + | 2.29394e9i | 0.411269 | + | 0.00389082i | ||||
\(227\) | −9.00145e11 | −1.49343 | −0.746713 | − | 0.665147i | \(-0.768369\pi\) | ||||
−0.746713 | + | 0.665147i | \(0.768369\pi\) | |||||||
\(228\) | 2.28559e10 | − | 1.20785e12i | 0.0370957 | − | 1.96038i | ||||
\(229\) | −5.43837e11 | −0.863558 | −0.431779 | − | 0.901979i | \(-0.642114\pi\) | ||||
−0.431779 | + | 0.901979i | \(0.642114\pi\) | |||||||
\(230\) | 7.27345e11 | + | 7.62627e11i | 1.13006 | + | 1.18488i | ||||
\(231\) | 1.20918e12i | 1.83836i | ||||||||
\(232\) | 1.05277e10 | − | 3.70845e11i | 0.0156636 | − | 0.551763i | ||||
\(233\) | − | 6.34760e11i | − | 0.924336i | −0.886792 | − | 0.462168i | \(-0.847072\pi\) | ||
0.886792 | − | 0.462168i | \(-0.152928\pi\) | |||||||
\(234\) | 2.27538e11 | + | 2.15262e9i | 0.324320 | + | 0.00306823i | ||||
\(235\) | 2.15695e10 | − | 2.09648e10i | 0.0300954 | − | 0.0292517i | ||||
\(236\) | 2.29148e10 | − | 1.21097e12i | 0.0313008 | − | 1.65414i | ||||
\(237\) | 1.29563e12i | 1.73277i | ||||||||
\(238\) | 1.31658e12 | + | 1.24555e10i | 1.72410 | + | 0.0163109i | ||||
\(239\) | 9.24284e10i | 0.118527i | 0.998242 | + | 0.0592633i | \(0.0188752\pi\) | ||||
−0.998242 | + | 0.0592633i | \(0.981125\pi\) | |||||||
\(240\) | −9.14861e11 | + | 8.24247e11i | −1.14894 | + | 1.03515i | ||||
\(241\) | −9.05993e11 | −1.11440 | −0.557198 | − | 0.830379i | \(-0.688124\pi\) | ||||
−0.557198 | + | 0.830379i | \(0.688124\pi\) | |||||||
\(242\) | 2.77089e8 | − | 2.92890e10i | 0.000333843 | − | 0.0352880i | ||||
\(243\) | 1.10938e12 | 1.30933 | ||||||||
\(244\) | −3.04488e11 | − | 5.76174e9i | −0.352063 | − | 0.00666199i | ||||
\(245\) | 2.31004e11 | − | 2.24528e11i | 0.261691 | − | 0.254355i | ||||
\(246\) | 5.18003e9 | − | 5.47542e11i | 0.00574985 | − | 0.607774i | ||||
\(247\) | −2.71667e11 | −0.295497 | ||||||||
\(248\) | −3.98445e11 | − | 1.13112e10i | −0.424727 | − | 0.0120573i | ||||
\(249\) | −2.66755e12 | −2.78686 | ||||||||
\(250\) | 7.25562e11 | − | 6.53632e11i | 0.742975 | − | 0.669319i | ||||
\(251\) | 1.13681e12i | 1.14109i | 0.821266 | + | 0.570546i | \(0.193268\pi\) | ||||
−0.821266 | + | 0.570546i | \(0.806732\pi\) | |||||||
\(252\) | 1.65194e12 | + | 3.12593e10i | 1.62552 | + | 0.0307593i | ||||
\(253\) | 1.72695e12i | 1.66601i | ||||||||
\(254\) | −1.89044e9 | + | 1.99824e11i | −0.00178811 | + | 0.189008i | ||||
\(255\) | −1.71511e12 | − | 1.76458e12i | −1.59071 | − | 1.63659i | ||||
\(256\) | 1.09636e12 | + | 8.31337e10i | 0.997137 | + | 0.0756096i | ||||
\(257\) | − | 6.98643e11i | − | 0.623146i | −0.950222 | − | 0.311573i | \(-0.899144\pi\) | ||
0.950222 | − | 0.311573i | \(-0.100856\pi\) | |||||||
\(258\) | 8.50752e9 | − | 8.99266e11i | 0.00744225 | − | 0.786665i | ||||
\(259\) | 9.57416e11i | 0.821489i | ||||||||
\(260\) | 1.89214e11 | + | 2.02188e11i | 0.159252 | + | 0.170172i | ||||
\(261\) | 9.30345e11 | 0.768142 | ||||||||
\(262\) | −1.83075e12 | − | 1.73198e10i | −1.48293 | − | 0.0140293i | ||||
\(263\) | −4.94717e10 | −0.0393168 | −0.0196584 | − | 0.999807i | \(-0.506258\pi\) | ||||
−0.0196584 | + | 0.999807i | \(0.506258\pi\) | |||||||
\(264\) | −2.01706e12 | − | 5.72611e10i | −1.57290 | − | 0.0446519i | ||||
\(265\) | −2.77104e11 | − | 2.85096e11i | −0.212038 | − | 0.218153i | ||||
\(266\) | −1.97251e12 | − | 1.86609e10i | −1.48119 | − | 0.0140128i | ||||
\(267\) | 1.27583e12 | 0.940235 | ||||||||
\(268\) | −7.32715e11 | − | 1.38650e10i | −0.529982 | − | 0.0100287i | ||||
\(269\) | 1.80389e12 | 1.28070 | 0.640351 | − | 0.768083i | \(-0.278789\pi\) | ||||
0.640351 | + | 0.768083i | \(0.278789\pi\) | |||||||
\(270\) | −5.99735e11 | − | 6.28827e11i | −0.417965 | − | 0.438240i | ||||
\(271\) | − | 2.03271e12i | − | 1.39069i | −0.718677 | − | 0.695344i | \(-0.755252\pi\) | ||
0.718677 | − | 0.695344i | \(-0.244748\pi\) | |||||||
\(272\) | −8.31243e10 | + | 2.19563e12i | −0.0558320 | + | 1.47474i | ||||
\(273\) | − | 6.38547e11i | − | 0.421095i | ||||||
\(274\) | −3.98127e11 | − | 3.76649e9i | −0.257792 | − | 0.00243884i | ||||
\(275\) | 1.59963e12 | + | 4.54906e10i | 1.01708 | + | 0.0289240i | ||||
\(276\) | 4.05469e12 | + | 7.67257e10i | 2.53170 | + | 0.0479066i | ||||
\(277\) | − | 9.87952e11i | − | 0.605811i | −0.953021 | − | 0.302905i | \(-0.902043\pi\) | ||
0.953021 | − | 0.302905i | \(-0.0979566\pi\) | |||||||
\(278\) | −1.24275e11 | − | 1.17570e9i | −0.0748444 | − | 0.000708066i | ||||
\(279\) | − | 9.99584e11i | − | 0.591287i | ||||||
\(280\) | 1.35994e12 | + | 1.48103e12i | 0.790188 | + | 0.860546i | ||||
\(281\) | 2.84398e12 | 1.62328 | 0.811642 | − | 0.584155i | \(-0.198574\pi\) | ||||
0.811642 | + | 0.584155i | \(0.198574\pi\) | |||||||
\(282\) | 1.09500e9 | − | 1.15744e11i | 0.000614000 | − | 0.0649013i | ||||
\(283\) | 9.25646e10 | 0.0509932 | 0.0254966 | − | 0.999675i | \(-0.491883\pi\) | ||||
0.0254966 | + | 0.999675i | \(0.491883\pi\) | |||||||
\(284\) | −4.96772e10 | + | 2.62527e12i | −0.0268884 | + | 1.42096i | ||||
\(285\) | 2.56959e12 | + | 2.64371e12i | 1.36660 | + | 1.40601i | ||||
\(286\) | −4.29275e9 | + | 4.53755e11i | −0.00224339 | + | 0.237132i | ||||
\(287\) | −8.94093e11 | −0.459170 | ||||||||
\(288\) | −1.30373e11 | + | 2.75417e12i | −0.0657997 | + | 1.39004i | ||||
\(289\) | −2.37477e12 | −1.17796 | ||||||||
\(290\) | 7.81400e11 | + | 8.19304e11i | 0.380963 | + | 0.399443i | ||||
\(291\) | 2.14868e12i | 1.02969i | ||||||||
\(292\) | 4.08336e10 | − | 2.15791e12i | 0.0192355 | − | 1.01653i | ||||
\(293\) | − | 2.24927e12i | − | 1.04161i | −0.853677 | − | 0.520803i | \(-0.825633\pi\) | ||
0.853677 | − | 0.520803i | \(-0.174367\pi\) | |||||||
\(294\) | 1.17272e10 | − | 1.23959e12i | 0.00533896 | − | 0.564342i | ||||
\(295\) | 2.57622e12 | + | 2.65052e12i | 1.15312 | + | 1.18637i | ||||
\(296\) | −1.59709e12 | − | 4.53387e10i | −0.702863 | − | 0.0199531i | ||||
\(297\) | − | 1.42396e12i | − | 0.616192i | ||||||
\(298\) | −1.52913e10 | + | 1.61633e12i | −0.00650675 | + | 0.687780i | ||||
\(299\) | − | 9.11971e11i | − | 0.381615i | ||||||
\(300\) | 1.77876e11 | − | 3.75373e12i | 0.0732001 | − | 1.54475i | ||||
\(301\) | −1.46843e12 | −0.594321 | ||||||||
\(302\) | 1.76376e12 | + | 1.66861e10i | 0.702110 | + | 0.00664232i | ||||
\(303\) | −6.44158e12 | −2.52220 | ||||||||
\(304\) | 1.24537e11 | − | 3.28950e12i | 0.0479658 | − | 1.26696i | ||||
\(305\) | 6.66453e11 | − | 6.47769e11i | 0.252505 | − | 0.245426i | ||||
\(306\) | −5.50969e12 | − | 5.21245e10i | −2.05362 | − | 0.0194283i | ||||
\(307\) | −2.31537e11 | −0.0849040 | −0.0424520 | − | 0.999099i | \(-0.513517\pi\) | ||||
−0.0424520 | + | 0.999099i | \(0.513517\pi\) | |||||||
\(308\) | −6.23371e10 | + | 3.29430e12i | −0.0224902 | + | 1.18853i | ||||
\(309\) | 2.80105e12 | 0.994324 | ||||||||
\(310\) | 8.80279e11 | − | 8.39554e11i | 0.307477 | − | 0.293251i | ||||
\(311\) | − | 3.78881e12i | − | 1.30227i | −0.758962 | − | 0.651135i | \(-0.774293\pi\) | ||
0.758962 | − | 0.651135i | \(-0.225707\pi\) | |||||||
\(312\) | 1.06518e12 | + | 3.02386e10i | 0.360287 | + | 0.0102279i | ||||
\(313\) | − | 2.24116e12i | − | 0.746022i | −0.927827 | − | 0.373011i | \(-0.878325\pi\) | ||
0.927827 | − | 0.373011i | \(-0.121675\pi\) | |||||||
\(314\) | −2.86742e12 | − | 2.71273e10i | −0.939384 | − | 0.00888705i | ||||
\(315\) | −3.61572e12 | + | 3.51436e12i | −1.16585 | + | 1.13316i | ||||
\(316\) | −6.67939e10 | + | 3.52983e12i | −0.0211983 | + | 1.12026i | ||||
\(317\) | 1.42968e12i | 0.446623i | 0.974747 | + | 0.223312i | \(0.0716868\pi\) | ||||
−0.974747 | + | 0.223312i | \(0.928313\pi\) | |||||||
\(318\) | −1.52986e12 | − | 1.44732e10i | −0.470452 | − | 0.00445071i | ||||
\(319\) | 1.85529e12i | 0.561641i | ||||||||
\(320\) | −2.53494e12 | + | 2.19842e12i | −0.755472 | + | 0.655180i | ||||
\(321\) | −2.73124e12 | −0.801372 | ||||||||
\(322\) | 6.26436e10 | − | 6.62158e12i | 0.0180966 | − | 1.91286i | ||||
\(323\) | 6.57826e12 | 1.87111 | ||||||||
\(324\) | 1.62446e12 | + | 3.07392e10i | 0.454971 | + | 0.00860929i | ||||
\(325\) | −8.44735e11 | − | 2.40228e10i | −0.232972 | − | 0.00662532i | ||||
\(326\) | −3.52492e10 | + | 3.72593e12i | −0.00957329 | + | 1.01192i | ||||
\(327\) | 3.41737e12 | 0.914015 | ||||||||
\(328\) | 4.23400e10 | − | 1.49146e12i | 0.0111527 | − | 0.392864i | ||||
\(329\) | −1.89001e11 | −0.0490326 | ||||||||
\(330\) | 4.45628e12 | − | 4.25011e12i | 1.13868 | − | 1.08600i | ||||
\(331\) | − | 6.11524e12i | − | 1.53912i | −0.638572 | − | 0.769562i | \(-0.720474\pi\) | ||
0.638572 | − | 0.769562i | \(-0.279526\pi\) | |||||||
\(332\) | −7.26748e12 | − | 1.37521e11i | −1.80175 | − | 0.0340939i | ||||
\(333\) | − | 4.00664e12i | − | 0.978497i | ||||||
\(334\) | −2.82464e10 | + | 2.98571e12i | −0.00679564 | + | 0.718316i | ||||
\(335\) | 1.60374e12 | − | 1.55878e12i | 0.380111 | − | 0.369455i | ||||
\(336\) | 7.73189e12 | + | 2.92722e11i | 1.80547 | + | 0.0683531i | ||||
\(337\) | − | 9.97821e11i | − | 0.229564i | −0.993391 | − | 0.114782i | \(-0.963383\pi\) | ||
0.993391 | − | 0.114782i | \(-0.0366169\pi\) | |||||||
\(338\) | −3.94660e10 | + | 4.17165e12i | −0.00894622 | + | 0.945638i | ||||
\(339\) | 2.84766e12i | 0.636047i | ||||||||
\(340\) | −4.58170e12 | − | 4.89586e12i | −1.00840 | − | 1.07754i | ||||
\(341\) | 1.99337e12 | 0.432330 | ||||||||
\(342\) | 8.25464e12 | + | 7.80931e10i | 1.76428 | + | 0.0166910i | ||||
\(343\) | 3.52244e12 | 0.741948 | ||||||||
\(344\) | 6.95380e10 | − | 2.44953e12i | 0.0144354 | − | 0.508499i | ||||
\(345\) | −8.87476e12 | + | 8.62597e12i | −1.81577 | + | 1.76487i | ||||
\(346\) | −2.93511e12 | − | 2.77677e10i | −0.591895 | − | 0.00559963i | ||||
\(347\) | −5.29192e12 | −1.05188 | −0.525940 | − | 0.850522i | \(-0.676286\pi\) | ||||
−0.525940 | + | 0.850522i | \(0.676286\pi\) | |||||||
\(348\) | 4.35603e12 | + | 8.24279e10i | 0.853482 | + | 0.0161502i | ||||
\(349\) | 3.21483e11 | 0.0620912 | 0.0310456 | − | 0.999518i | \(-0.490116\pi\) | ||||
0.0310456 | + | 0.999518i | \(0.490116\pi\) | |||||||
\(350\) | −6.13175e12 | − | 2.32448e11i | −1.16747 | − | 0.0442574i | ||||
\(351\) | 7.51969e11i | 0.141145i | ||||||||
\(352\) | −5.49235e12 | − | 2.59988e11i | −1.01635 | − | 0.0481106i | ||||
\(353\) | − | 6.41611e12i | − | 1.17057i | −0.810827 | − | 0.585286i | \(-0.800982\pi\) | ||
0.810827 | − | 0.585286i | \(-0.199018\pi\) | |||||||
\(354\) | 1.42230e13 | + | 1.34557e11i | 2.55844 | + | 0.0242041i | ||||
\(355\) | −5.58501e12 | − | 5.74609e12i | −0.990563 | − | 1.01913i | ||||
\(356\) | 3.47588e12 | + | 6.57731e10i | 0.607876 | + | 0.0115027i | ||||
\(357\) | 1.54620e13i | 2.66640i | ||||||||
\(358\) | −3.45205e12 | − | 3.26582e10i | −0.587032 | − | 0.00555363i | ||||
\(359\) | 4.19883e12i | 0.704136i | 0.935975 | + | 0.352068i | \(0.114521\pi\) | ||||
−0.935975 | + | 0.352068i | \(0.885479\pi\) | |||||||
\(360\) | −5.69116e12 | − | 6.19789e12i | −0.941214 | − | 1.02502i | ||||
\(361\) | −3.72452e12 | −0.607483 | ||||||||
\(362\) | −1.03915e11 | + | 1.09841e13i | −0.0167161 | + | 1.76694i | ||||
\(363\) | 3.43973e11 | 0.0545747 | ||||||||
\(364\) | 3.29191e10 | − | 1.73966e12i | 0.00515159 | − | 0.272244i | ||||
\(365\) | 4.59076e12 | + | 4.72317e12i | 0.708631 | + | 0.729069i | ||||
\(366\) | 3.38332e10 | − | 3.57625e12i | 0.00515155 | − | 0.544532i | ||||
\(367\) | −2.48261e12 | −0.372888 | −0.186444 | − | 0.982466i | \(-0.559696\pi\) | ||||
−0.186444 | + | 0.982466i | \(0.559696\pi\) | |||||||
\(368\) | 1.10427e13 | + | 4.18064e11i | 1.63619 | + | 0.0619446i | ||||
\(369\) | 3.74165e12 | 0.546929 | ||||||||
\(370\) | 3.52843e12 | − | 3.36519e12i | 0.508830 | − | 0.485290i | ||||
\(371\) | 2.49814e12i | 0.355424i | ||||||||
\(372\) | 8.85624e10 | − | 4.68021e12i | 0.0124318 | − | 0.656978i | ||||
\(373\) | 8.44089e12i | 1.16908i | 0.811365 | + | 0.584539i | \(0.198725\pi\) | ||||
−0.811365 | + | 0.584539i | \(0.801275\pi\) | |||||||
\(374\) | 1.03946e11 | − | 1.09874e13i | 0.0142053 | − | 1.50154i | ||||
\(375\) | 7.75624e12 | + | 8.44769e12i | 1.04591 | + | 1.13915i | ||||
\(376\) | 8.95020e9 | − | 3.15278e11i | 0.00119095 | − | 0.0419521i | ||||
\(377\) | − | 9.79747e11i | − | 0.128649i | ||||||
\(378\) | −5.16530e10 | + | 5.45985e12i | −0.00669324 | + | 0.707492i | ||||
\(379\) | − | 5.11317e12i | − | 0.653874i | −0.945046 | − | 0.326937i | \(-0.893984\pi\) | ||
0.945046 | − | 0.326937i | \(-0.106016\pi\) | |||||||
\(380\) | 6.86432e12 | + | 7.33500e12i | 0.866323 | + | 0.925725i | ||||
\(381\) | −2.34676e12 | −0.292310 | ||||||||
\(382\) | 7.48180e11 | + | 7.07816e9i | 0.0919791 | + | 0.000870169i | ||||
\(383\) | −8.87564e12 | −1.07698 | −0.538488 | − | 0.842633i | \(-0.681004\pi\) | ||||
−0.538488 | + | 0.842633i | \(0.681004\pi\) | |||||||
\(384\) | −8.54442e11 | + | 1.28839e13i | −0.102336 | + | 1.54309i | ||||
\(385\) | −7.00831e12 | − | 7.21045e12i | −0.828533 | − | 0.852430i | ||||
\(386\) | −9.53472e12 | − | 9.02033e10i | −1.11268 | − | 0.0105266i | ||||
\(387\) | 6.14517e12 | 0.707911 | ||||||||
\(388\) | −1.10771e11 | + | 5.85388e12i | −0.0125971 | + | 0.665710i | ||||
\(389\) | 1.08604e13 | 1.21927 | 0.609635 | − | 0.792683i | \(-0.291316\pi\) | ||||
0.609635 | + | 0.792683i | \(0.291316\pi\) | |||||||
\(390\) | −2.35328e12 | + | 2.24441e12i | −0.260826 | + | 0.248759i | ||||
\(391\) | 2.20828e13i | 2.41641i | ||||||||
\(392\) | 9.58545e10 | − | 3.37655e12i | 0.0103558 | − | 0.364790i | ||||
\(393\) | − | 2.15005e13i | − | 2.29343i | ||||||
\(394\) | 1.46095e13 | + | 1.38213e11i | 1.53870 | + | 0.0145569i | ||||
\(395\) | −7.50938e12 | − | 7.72597e12i | −0.780941 | − | 0.803466i | ||||
\(396\) | 2.60871e11 | − | 1.37861e13i | 0.0267886 | − | 1.41569i | ||||
\(397\) | 4.51332e12i | 0.457660i | 0.973466 | + | 0.228830i | \(0.0734900\pi\) | ||||
−0.973466 | + | 0.228830i | \(0.926510\pi\) | |||||||
\(398\) | −5.17008e12 | − | 4.89116e10i | −0.517705 | − | 0.00489775i | ||||
\(399\) | − | 2.31653e13i | − | 2.29073i | ||||||
\(400\) | 6.78124e11 | − | 1.02175e13i | 0.0662230 | − | 0.997805i | ||||
\(401\) | −4.32327e12 | −0.416956 | −0.208478 | − | 0.978027i | \(-0.566851\pi\) | ||||
−0.208478 | + | 0.978027i | \(0.566851\pi\) | |||||||
\(402\) | 8.14158e10 | − | 8.60585e12i | 0.00775494 | − | 0.819717i | ||||
\(403\) | −1.05266e12 | −0.0990294 | ||||||||
\(404\) | −1.75495e13 | − | 3.32084e11i | −1.63064 | − | 0.0308561i | ||||
\(405\) | −3.55556e12 | + | 3.45589e12i | −0.326312 | + | 0.317164i | ||||
\(406\) | 6.72991e10 | − | 7.11369e12i | 0.00610070 | − | 0.644859i | ||||
\(407\) | 7.99003e12 | 0.715446 | ||||||||
\(408\) | −2.57926e13 | − | 7.32209e11i | −2.28136 | − | 0.0647641i | ||||
\(409\) | 6.11557e11 | 0.0534343 | 0.0267172 | − | 0.999643i | \(-0.491495\pi\) | ||||
0.0267172 | + | 0.999643i | \(0.491495\pi\) | |||||||
\(410\) | 3.14262e12 | + | 3.29506e12i | 0.271252 | + | 0.284410i | ||||
\(411\) | − | 4.67564e12i | − | 0.398687i | ||||||
\(412\) | 7.63119e12 | + | 1.44403e11i | 0.642845 | + | 0.0121644i | ||||
\(413\) | − | 2.32250e13i | − | 1.93289i | ||||||
\(414\) | −2.62154e11 | + | 2.77103e13i | −0.0215553 | + | 2.27845i | ||||
\(415\) | 1.59068e13 | − | 1.54609e13i | 1.29224 | − | 1.25601i | ||||
\(416\) | 2.90041e12 | + | 1.37295e11i | 0.232806 | + | 0.0110202i | ||||
\(417\) | − | 1.45950e12i | − | 0.115750i | ||||||
\(418\) | −1.55733e11 | + | 1.64614e13i | −0.0122039 | + | 1.28999i | ||||
\(419\) | 1.05743e13i | 0.818808i | 0.912353 | + | 0.409404i | \(0.134263\pi\) | ||||
−0.912353 | + | 0.409404i | \(0.865737\pi\) | |||||||
\(420\) | −1.72407e13 | + | 1.61344e13i | −1.31920 | + | 1.23455i | ||||
\(421\) | 6.20493e12 | 0.469166 | 0.234583 | − | 0.972096i | \(-0.424628\pi\) | ||||
0.234583 | + | 0.972096i | \(0.424628\pi\) | |||||||
\(422\) | 5.81595e12 | + | 5.50219e10i | 0.434569 | + | 0.00411124i | ||||
\(423\) | 7.90942e11 | 0.0584040 | ||||||||
\(424\) | −4.16720e12 | − | 1.18300e11i | −0.304099 | − | 0.00863287i | ||||
\(425\) | 2.04548e13 | + | 5.81698e11i | 1.47520 | + | 0.0419520i | ||||
\(426\) | −3.08341e13 | − | 2.91707e11i | −2.19778 | − | 0.0207921i | ||||
\(427\) | −5.83975e12 | −0.411391 | ||||||||
\(428\) | −7.44100e12 | − | 1.40804e11i | −0.518098 | − | 0.00980383i | ||||
\(429\) | −5.32894e12 | −0.366737 | ||||||||
\(430\) | 5.16134e12 | + | 5.41171e12i | 0.351092 | + | 0.368123i | ||||
\(431\) | 3.75598e12i | 0.252544i | 0.991996 | + | 0.126272i | \(0.0403011\pi\) | ||||
−0.991996 | + | 0.126272i | \(0.959699\pi\) | |||||||
\(432\) | −9.10526e12 | − | 3.44716e11i | −0.605165 | − | 0.0229109i | ||||
\(433\) | 2.25078e13i | 1.47874i | 0.673297 | + | 0.739372i | \(0.264878\pi\) | ||||
−0.673297 | + | 0.739372i | \(0.735122\pi\) | |||||||
\(434\) | −7.64311e12 | − | 7.23078e10i | −0.496388 | − | 0.00469609i | ||||
\(435\) | −9.53432e12 | + | 9.26704e12i | −0.612130 | + | 0.594970i | ||||
\(436\) | 9.31030e12 | + | 1.76176e11i | 0.590924 | + | 0.0111819i | ||||
\(437\) | − | 3.30846e13i | − | 2.07596i | ||||||
\(438\) | 2.53450e13 | + | 2.39777e11i | 1.57225 | + | 0.0148743i | ||||
\(439\) | 1.93911e13i | 1.18927i | 0.803997 | + | 0.594633i | \(0.202703\pi\) | ||||
−0.803997 | + | 0.594633i | \(0.797297\pi\) | |||||||
\(440\) | 1.23598e13 | − | 1.13493e13i | 0.749460 | − | 0.688185i | ||||
\(441\) | 8.47080e12 | 0.507845 | ||||||||
\(442\) | −5.48923e10 | + | 5.80225e12i | −0.00325387 | + | 0.343942i | ||||
\(443\) | 3.53441e12 | 0.207157 | 0.103578 | − | 0.994621i | \(-0.466971\pi\) | ||||
0.103578 | + | 0.994621i | \(0.466971\pi\) | |||||||
\(444\) | 3.54985e11 | − | 1.87597e13i | 0.0205729 | − | 1.08721i | ||||
\(445\) | −7.60789e12 | + | 7.39461e12i | −0.435978 | + | 0.423755i | ||||
\(446\) | 3.36357e10 | − | 3.55537e12i | 0.00190601 | − | 0.201470i | ||||
\(447\) | −1.89824e13 | −1.06369 | ||||||||
\(448\) | 2.10497e13 | + | 1.19610e12i | 1.16642 | + | 0.0662790i | ||||
\(449\) | −3.48899e12 | −0.191192 | −0.0955958 | − | 0.995420i | \(-0.530476\pi\) | ||||
−0.0955958 | + | 0.995420i | \(0.530476\pi\) | |||||||
\(450\) | 2.56605e13 | + | 9.72762e11i | 1.39060 | + | 0.0527162i | ||||
\(451\) | 7.46158e12i | 0.399897i | ||||||||
\(452\) | −1.46806e11 | + | 7.75818e12i | −0.00778128 | + | 0.411214i | ||||
\(453\) | 2.07138e13i | 1.08585i | ||||||||
\(454\) | 2.72495e11 | − | 2.88034e13i | 0.0141279 | − | 1.49336i | ||||
\(455\) | 3.70097e12 | + | 3.80771e12i | 0.189783 | + | 0.195257i | ||||
\(456\) | 3.86426e13 | + | 1.09700e12i | 1.95994 | + | 0.0556394i | ||||
\(457\) | 3.56649e12i | 0.178921i | 0.995990 | + | 0.0894603i | \(0.0285142\pi\) | ||||
−0.995990 | + | 0.0894603i | \(0.971486\pi\) | |||||||
\(458\) | 1.64632e11 | − | 1.74020e13i | 0.00816934 | − | 0.863519i | ||||
\(459\) | − | 1.82085e13i | − | 0.893738i | ||||||
\(460\) | −2.46232e13 | + | 2.30431e13i | −1.19551 | + | 1.11880i | ||||
\(461\) | 2.11360e13 | 1.01512 | 0.507562 | − | 0.861615i | \(-0.330547\pi\) | ||||
0.507562 | + | 0.861615i | \(0.330547\pi\) | |||||||
\(462\) | −3.86920e13 | − | 3.66047e11i | −1.83828 | − | 0.0173911i | ||||
\(463\) | −2.00573e13 | −0.942686 | −0.471343 | − | 0.881950i | \(-0.656231\pi\) | ||||
−0.471343 | + | 0.881950i | \(0.656231\pi\) | |||||||
\(464\) | 1.18633e13 | + | 4.49134e11i | 0.551591 | + | 0.0208827i | ||||
\(465\) | 9.95672e12 | + | 1.02439e13i | 0.457985 | + | 0.471195i | ||||
\(466\) | 2.03114e13 | + | 1.92156e11i | 0.924295 | + | 0.00874431i | ||||
\(467\) | 1.63231e13 | 0.734884 | 0.367442 | − | 0.930046i | \(-0.380234\pi\) | ||||
0.367442 | + | 0.930046i | \(0.380234\pi\) | |||||||
\(468\) | −1.37762e11 | + | 7.28022e12i | −0.00613620 | + | 0.324277i | ||||
\(469\) | −1.40527e13 | −0.619292 | ||||||||
\(470\) | 6.64314e11 | + | 6.96539e11i | 0.0289657 | + | 0.0303708i | ||||
\(471\) | − | 3.36753e13i | − | 1.45280i | ||||||
\(472\) | 3.87423e13 | + | 1.09983e12i | 1.65377 | + | 0.0469478i | ||||
\(473\) | 1.22547e13i | 0.517602i | ||||||||
\(474\) | −4.14584e13 | − | 3.92217e11i | −1.73269 | − | 0.0163921i | ||||
\(475\) | −3.06454e13 | − | 8.71502e11i | −1.26735 | − | 0.0360413i | ||||
\(476\) | −7.97117e11 | + | 4.21249e13i | −0.0326203 | + | 1.72387i | ||||
\(477\) | − | 1.04543e13i | − | 0.423354i | ||||||
\(478\) | −2.95758e12 | − | 2.79802e10i | −0.118521 | − | 0.00112127i | ||||
\(479\) | 1.92868e13i | 0.764863i | 0.923984 | + | 0.382431i | \(0.124913\pi\) | ||||
−0.923984 | + | 0.382431i | \(0.875087\pi\) | |||||||
\(480\) | −2.60978e13 | − | 2.95238e13i | −1.02423 | − | 1.15868i | ||||
\(481\) | −4.21940e12 | −0.163880 | ||||||||
\(482\) | 2.74265e11 | − | 2.89905e13i | 0.0105423 | − | 1.11435i | ||||
\(483\) | 7.77645e13 | 2.95833 | ||||||||
\(484\) | 9.37122e11 | + | 1.77329e10i | 0.0352833 | + | 0.000667656i | ||||
\(485\) | −1.24536e13 | − | 1.28128e13i | −0.464073 | − | 0.477458i | ||||
\(486\) | −3.35834e11 | + | 3.54985e13i | −0.0123864 | + | 1.30927i | ||||
\(487\) | 1.78624e13 | 0.652071 | 0.326035 | − | 0.945358i | \(-0.394287\pi\) | ||||
0.326035 | + | 0.945358i | \(0.394287\pi\) | |||||||
\(488\) | 2.76543e11 | − | 9.74143e12i | 0.00999225 | − | 0.351984i | ||||
\(489\) | −4.37577e13 | −1.56498 | ||||||||
\(490\) | 7.11465e12 | + | 7.45977e12i | 0.251868 | + | 0.264086i | ||||
\(491\) | − | 3.49899e13i | − | 1.22613i | −0.790034 | − | 0.613063i | \(-0.789937\pi\) | ||
0.790034 | − | 0.613063i | \(-0.210063\pi\) | |||||||
\(492\) | 1.75190e13 | + | 3.31507e11i | 0.607692 | + | 0.0114992i | ||||
\(493\) | 2.37240e13i | 0.814616i | ||||||||
\(494\) | 8.22399e10 | − | 8.69296e12i | 0.00279543 | − | 0.295483i | ||||
\(495\) | 2.93287e13 | + | 3.01747e13i | 0.986887 | + | 1.01535i | ||||
\(496\) | 4.82560e11 | − | 1.27462e13i | 0.0160747 | − | 0.424594i | ||||
\(497\) | 5.03498e13i | 1.66041i | ||||||||
\(498\) | 8.07528e11 | − | 8.53577e13i | 0.0263640 | − | 2.78674i | ||||
\(499\) | 2.40650e13i | 0.777828i | 0.921274 | + | 0.388914i | \(0.127150\pi\) | ||||
−0.921274 | + | 0.388914i | \(0.872850\pi\) | |||||||
\(500\) | 2.06956e13 | + | 2.34148e13i | 0.662261 | + | 0.749274i | ||||
\(501\) | −3.50645e13 | −1.11091 | ||||||||
\(502\) | −3.63764e13 | − | 3.44139e11i | −1.14104 | − | 0.0107948i | ||||
\(503\) | −5.61224e13 | −1.74299 | −0.871497 | − | 0.490401i | \(-0.836850\pi\) | ||||
−0.871497 | + | 0.490401i | \(0.836850\pi\) | |||||||
\(504\) | −1.50033e12 | + | 5.28503e13i | −0.0461355 | + | 1.62516i | ||||
\(505\) | 3.84117e13 | − | 3.73349e13i | 1.16952 | − | 1.13673i | ||||
\(506\) | −5.52598e13 | − | 5.22787e11i | −1.66593 | − | 0.0157606i | ||||
\(507\) | −4.89923e13 | −1.46247 | ||||||||
\(508\) | −6.39352e12 | − | 1.20983e11i | −0.188982 | − | 0.00357606i | ||||
\(509\) | −5.17336e13 | −1.51420 | −0.757100 | − | 0.653298i | \(-0.773385\pi\) | ||||
−0.757100 | + | 0.653298i | \(0.773385\pi\) | |||||||
\(510\) | 5.69833e13 | − | 5.43470e13i | 1.65157 | − | 1.57516i | ||||
\(511\) | − | 4.13864e13i | − | 1.18783i | ||||||
\(512\) | −2.99205e12 | + | 3.50569e13i | −0.0850393 | + | 0.996378i | ||||
\(513\) | 2.72800e13i | 0.767817i | ||||||||
\(514\) | 2.23556e13 | + | 2.11495e11i | 0.623118 | + | 0.00589502i | ||||
\(515\) | −1.67029e13 | + | 1.62346e13i | −0.461058 | + | 0.448133i | ||||
\(516\) | 2.87727e13 | + | 5.44457e11i | 0.786559 | + | 0.0148838i | ||||
\(517\) | 1.57729e12i | 0.0427031i | ||||||||
\(518\) | −3.06359e13 | − | 2.89832e11i | −0.821452 | − | 0.00777136i | ||||
\(519\) | − | 3.44703e13i | − | 0.915394i | ||||||
\(520\) | −6.52700e12 | + | 5.99336e12i | −0.171671 | + | 0.157635i | ||||
\(521\) | −4.68852e13 | −1.22137 | −0.610684 | − | 0.791874i | \(-0.709106\pi\) | ||||
−0.610684 | + | 0.791874i | \(0.709106\pi\) | |||||||
\(522\) | −2.81637e11 | + | 2.97697e13i | −0.00726670 | + | 0.768108i | ||||
\(523\) | 2.65731e13 | 0.679100 | 0.339550 | − | 0.940588i | \(-0.389725\pi\) | ||||
0.339550 | + | 0.940588i | \(0.389725\pi\) | |||||||
\(524\) | 1.10842e12 | − | 5.85760e13i | 0.0280574 | − | 1.48273i | ||||
\(525\) | 2.04844e12 | − | 7.20313e13i | 0.0513603 | − | 1.80603i | ||||
\(526\) | 1.49762e10 | − | 1.58302e12i | 0.000371941 | − | 0.0393151i | ||||
\(527\) | 2.54896e13 | 0.627061 | ||||||||
\(528\) | 2.44288e12 | − | 6.45258e13i | 0.0595296 | − | 1.57240i | ||||
\(529\) | 6.96365e13 | 1.68097 | ||||||||
\(530\) | 9.20655e12 | − | 8.78062e12i | 0.220149 | − | 0.209964i | ||||
\(531\) | 9.71933e13i | 2.30231i | ||||||||
\(532\) | 1.19425e12 | − | 6.31117e13i | 0.0280243 | − | 1.48099i | ||||
\(533\) | − | 3.94033e12i | − | 0.0916002i | ||||||
\(534\) | −3.86223e11 | + | 4.08247e13i | −0.00889471 | + | 0.940193i | ||||
\(535\) | 1.62866e13 | − | 1.58300e13i | 0.371588 | − | 0.361171i | ||||
\(536\) | 6.65469e11 | − | 2.34416e13i | 0.0150419 | − | 0.529864i | ||||
\(537\) | − | 4.05412e13i | − | 0.907874i | ||||||
\(538\) | −5.46078e11 | + | 5.77218e13i | −0.0121156 | + | 1.28064i | ||||
\(539\) | 1.68924e13i | 0.371320i | ||||||||
\(540\) | 2.03031e13 | − | 1.90003e13i | 0.442175 | − | 0.413801i | ||||
\(541\) | 6.66188e13 | 1.43751 | 0.718755 | − | 0.695264i | \(-0.244712\pi\) | ||||
0.718755 | + | 0.695264i | \(0.244712\pi\) | |||||||
\(542\) | 6.50440e13 | + | 6.15349e11i | 1.39063 | + | 0.0131560i | ||||
\(543\) | −1.28998e14 | −2.73265 | ||||||||
\(544\) | −7.02318e13 | − | 3.32453e12i | −1.47414 | − | 0.0697807i | ||||
\(545\) | −2.03781e13 | + | 1.98068e13i | −0.423819 | + | 0.411938i | ||||
\(546\) | 2.04326e13 | + | 1.93303e11i | 0.421076 | + | 0.00398359i | ||||
\(547\) | 2.28605e13 | 0.466819 | 0.233410 | − | 0.972378i | \(-0.425012\pi\) | ||||
0.233410 | + | 0.972378i | \(0.425012\pi\) | |||||||
\(548\) | 2.41044e11 | − | 1.27384e13i | 0.00487746 | − | 0.257757i | ||||
\(549\) | 2.44385e13 | 0.490018 | ||||||||
\(550\) | −1.93988e12 | + | 5.11720e13i | −0.0385444 | + | 1.01676i | ||||
\(551\) | − | 3.55434e13i | − | 0.699844i | ||||||
\(552\) | −3.68256e12 | + | 1.29721e14i | −0.0718546 | + | 2.53113i | ||||
\(553\) | 6.76983e13i | 1.30904i | ||||||||
\(554\) | 3.16130e13 | + | 2.99076e11i | 0.605784 | + | 0.00573103i | ||||
\(555\) | 3.99096e13 | + | 4.10607e13i | 0.757901 | + | 0.779761i | ||||
\(556\) | 7.52417e10 | − | 3.97626e12i | 0.00141607 | − | 0.0748343i | ||||
\(557\) | − | 1.22463e12i | − | 0.0228417i | −0.999935 | − | 0.0114208i | \(-0.996365\pi\) | ||
0.999935 | − | 0.0114208i | \(-0.00363545\pi\) | |||||||
\(558\) | 3.19853e13 | + | 3.02597e11i | 0.591261 | + | 0.00559363i | ||||
\(559\) | − | 6.47148e12i | − | 0.118562i | ||||||
\(560\) | −4.78025e13 | + | 4.30679e13i | −0.867982 | + | 0.782012i | ||||
\(561\) | 1.29037e14 | 2.32220 | ||||||||
\(562\) | −8.60937e11 | + | 9.10032e13i | −0.0153564 | + | 1.62321i | ||||
\(563\) | 7.79602e13 | 1.37826 | 0.689130 | − | 0.724638i | \(-0.257993\pi\) | ||||
0.689130 | + | 0.724638i | \(0.257993\pi\) | |||||||
\(564\) | 3.70332e12 | + | 7.00768e10i | 0.0648926 | + | 0.00122794i | ||||
\(565\) | −1.65048e13 | − | 1.69808e13i | −0.286661 | − | 0.294929i | ||||
\(566\) | −2.80214e10 | + | 2.96193e12i | −0.000482401 | + | 0.0509910i | ||||
\(567\) | 3.11554e13 | 0.531640 | ||||||||
\(568\) | −8.39897e13 | − | 2.38433e12i | −1.42064 | − | 0.0403296i | ||||
\(569\) | 7.32445e13 | 1.22804 | 0.614021 | − | 0.789290i | \(-0.289551\pi\) | ||||
0.614021 | + | 0.789290i | \(0.289551\pi\) | |||||||
\(570\) | −8.53727e13 | + | 8.14230e13i | −1.41888 | + | 1.35323i | ||||
\(571\) | − | 2.41704e13i | − | 0.398202i | −0.979979 | − | 0.199101i | \(-0.936198\pi\) | ||
0.979979 | − | 0.199101i | \(-0.0638021\pi\) | |||||||
\(572\) | −1.45182e13 | − | 2.74724e11i | −0.237101 | − | 0.00448659i | ||||
\(573\) | 8.78670e12i | 0.142250i | ||||||||
\(574\) | 2.70663e11 | − | 2.86097e13i | 0.00434379 | − | 0.459149i | ||||
\(575\) | 2.92558e12 | − | 1.02875e14i | 0.0465450 | − | 1.63670i | ||||
\(576\) | −8.80899e13 | − | 5.00548e12i | −1.38936 | − | 0.0789466i | ||||
\(577\) | − | 8.99224e13i | − | 1.40601i | −0.711184 | − | 0.703006i | \(-0.751841\pi\) | ||
0.711184 | − | 0.703006i | \(-0.248159\pi\) | |||||||
\(578\) | 7.18897e11 | − | 7.59892e13i | 0.0111436 | − | 1.17791i | ||||
\(579\) | − | 1.11977e14i | − | 1.72082i | ||||||
\(580\) | −2.64531e13 | + | 2.47557e13i | −0.403030 | + | 0.377168i | ||||
\(581\) | −1.39382e14 | −2.10537 | ||||||||
\(582\) | −6.87547e13 | − | 6.50455e11i | −1.02965 | − | 0.00974098i | ||||
\(583\) | 2.08480e13 | 0.309543 | ||||||||
\(584\) | 6.90377e13 | + | 1.95987e12i | 1.01630 | + | 0.0288511i | ||||
\(585\) | −1.54880e13 | − | 1.59347e13i | −0.226056 | − | 0.232576i | ||||
\(586\) | 7.19734e13 | + | 6.80906e11i | 1.04156 | + | 0.00985369i | ||||
\(587\) | −6.12391e13 | −0.878695 | −0.439347 | − | 0.898317i | \(-0.644790\pi\) | ||||
−0.439347 | + | 0.898317i | \(0.644790\pi\) | |||||||
\(588\) | 3.96616e13 | + | 7.50506e11i | 0.564266 | + | 0.0106774i | ||||
\(589\) | −3.81886e13 | −0.538713 | ||||||||
\(590\) | −8.55929e13 | + | 8.16330e13i | −1.19723 | + | 1.14184i | ||||
\(591\) | 1.71576e14i | 2.37968i | ||||||||
\(592\) | 1.93425e12 | − | 5.10909e13i | 0.0266014 | − | 0.702643i | ||||
\(593\) | 6.82796e13i | 0.931145i | 0.885010 | + | 0.465573i | \(0.154152\pi\) | ||||
−0.885010 | + | 0.465573i | \(0.845848\pi\) | |||||||
\(594\) | 4.55647e13 | + | 4.31065e11i | 0.616164 | + | 0.00582923i | ||||
\(595\) | −8.96168e13 | − | 9.22015e13i | −1.20172 | − | 1.23638i | ||||
\(596\) | −5.17157e13 | − | 9.78602e11i | −0.687688 | − | 0.0130129i | ||||
\(597\) | − | 6.07180e13i | − | 0.800655i | ||||||
\(598\) | 2.91818e13 | + | 2.76074e11i | 0.381598 | + | 0.00361011i | ||||
\(599\) | 1.28055e14i | 1.66059i | 0.557320 | + | 0.830297i | \(0.311829\pi\) | ||||
−0.557320 | + | 0.830297i | \(0.688171\pi\) | |||||||
\(600\) | 1.20060e14 | + | 6.82812e12i | 1.54398 | + | 0.0878102i | ||||
\(601\) | 2.79462e13 | 0.356410 | 0.178205 | − | 0.983993i | \(-0.442971\pi\) | ||||
0.178205 | + | 0.983993i | \(0.442971\pi\) | |||||||
\(602\) | 4.44528e11 | − | 4.69877e13i | 0.00562233 | − | 0.594295i | ||||
\(603\) | 5.88084e13 | 0.737654 | ||||||||
\(604\) | −1.06786e12 | + | 5.64328e13i | −0.0132840 | + | 0.702015i | ||||
\(605\) | −2.05114e12 | + | 1.99364e12i | −0.0253057 | + | 0.0245963i | ||||
\(606\) | 1.95001e12 | − | 2.06121e14i | 0.0238602 | − | 2.52209i | ||||
\(607\) | 3.52260e13 | 0.427484 | 0.213742 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213742 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(608\) | 1.05222e14 | + | 4.98082e12i | 1.26645 | + | 0.0599492i | ||||
\(609\) | 8.35439e13 | 0.997305 | ||||||||
\(610\) | 2.05259e13 | + | 2.15216e13i | 0.243027 | + | 0.254815i | ||||
\(611\) | − | 8.32941e11i | − | 0.00978156i | ||||||
\(612\) | 3.33582e12 | − | 1.76286e14i | 0.0388548 | − | 2.05334i | ||||
\(613\) | − | 1.16497e14i | − | 1.34590i | −0.739688 | − | 0.672950i | \(-0.765027\pi\) | ||
0.739688 | − | 0.672950i | \(-0.234973\pi\) | |||||||
\(614\) | 7.00915e10 | − | 7.40885e12i | 0.000803200 | − | 0.0849002i | ||||
\(615\) | −3.83450e13 | + | 3.72700e13i | −0.435846 | + | 0.423627i | ||||
\(616\) | −1.05394e14 | − | 2.99196e12i | −1.18826 | − | 0.0337328i | ||||
\(617\) | 6.43868e13i | 0.720064i | 0.932940 | + | 0.360032i | \(0.117234\pi\) | ||||
−0.932940 | + | 0.360032i | \(0.882766\pi\) | |||||||
\(618\) | −8.47941e11 | + | 8.96295e13i | −0.00940639 | + | 0.994279i | ||||
\(619\) | 9.70473e13i | 1.06790i | 0.845516 | + | 0.533950i | \(0.179293\pi\) | ||||
−0.845516 | + | 0.533950i | \(0.820707\pi\) | |||||||
\(620\) | 2.65980e13 | + | 2.84218e13i | 0.290330 | + | 0.310237i | ||||
\(621\) | −9.15774e13 | −0.991586 | ||||||||
\(622\) | 1.21237e14 | + | 1.14696e12i | 1.30221 | + | 0.0123196i | ||||
\(623\) | 6.66636e13 | 0.710311 | ||||||||
\(624\) | −1.29004e12 | + | 3.40750e13i | −0.0136358 | + | 0.360174i | ||||
\(625\) | −9.52133e13 | − | 5.41978e12i | −0.998384 | − | 0.0568305i | ||||
\(626\) | 7.17140e13 | + | 6.78451e11i | 0.745989 | + | 0.00705744i | ||||
\(627\) | −1.93324e14 | −1.99502 | ||||||||
\(628\) | 1.73607e12 | − | 9.17451e13i | 0.0177733 | − | 0.939257i | ||||
\(629\) | 1.02170e14 | 1.03770 | ||||||||
\(630\) | −1.11360e14 | − | 1.16762e14i | −1.12208 | − | 1.17652i | ||||
\(631\) | 3.20145e13i | 0.320037i | 0.987114 | + | 0.160019i | \(0.0511554\pi\) | ||||
−0.987114 | + | 0.160019i | \(0.948845\pi\) | |||||||
\(632\) | −1.12929e14 | − | 3.20587e12i | −1.12001 | − | 0.0317951i | ||||
\(633\) | 6.83031e13i | 0.672082i | ||||||||
\(634\) | −4.57476e13 | − | 4.32796e11i | −0.446603 | − | 0.00422510i | ||||
\(635\) | 1.39939e13 | − | 1.36016e13i | 0.135541 | − | 0.131741i | ||||
\(636\) | 9.26245e11 | − | 4.89488e13i | 0.00890103 | − | 0.470388i | ||||
\(637\) | − | 8.92060e12i | − | 0.0850544i | ||||||
\(638\) | −5.93667e13 | − | 5.61639e11i | −0.561616 | − | 0.00531317i | ||||
\(639\) | − | 2.10706e14i | − | 1.97776i | ||||||
\(640\) | −6.95789e13 | − | 8.17801e13i | −0.648004 | − | 0.761637i | ||||
\(641\) | −1.25436e14 | −1.15913 | −0.579566 | − | 0.814926i | \(-0.696778\pi\) | ||||
−0.579566 | + | 0.814926i | \(0.696778\pi\) | |||||||
\(642\) | 8.26808e11 | − | 8.73957e13i | 0.00758105 | − | 0.801336i | ||||
\(643\) | −6.91453e13 | −0.629083 | −0.314542 | − | 0.949244i | \(-0.601851\pi\) | ||||
−0.314542 | + | 0.949244i | \(0.601851\pi\) | |||||||
\(644\) | 2.11862e14 | + | 4.00901e12i | 1.91260 | + | 0.0361916i | ||||
\(645\) | −6.29766e13 | + | 6.12111e13i | −0.564132 | + | 0.548317i | ||||
\(646\) | −1.99139e12 | + | 2.10495e14i | −0.0177008 | + | 1.87102i | ||||
\(647\) | 1.38085e14 | 1.21794 | 0.608971 | − | 0.793193i | \(-0.291583\pi\) | ||||
0.608971 | + | 0.793193i | \(0.291583\pi\) | |||||||
\(648\) | −1.47537e12 | + | 5.19711e13i | −0.0129130 | + | 0.454869i | ||||
\(649\) | −1.93823e14 | −1.68338 | ||||||||
\(650\) | 1.02442e12 | − | 2.70230e13i | 0.00882896 | − | 0.232899i | ||||
\(651\) | − | 8.97615e13i | − | 0.767688i | ||||||
\(652\) | −1.19214e14 | − | 2.25585e12i | −1.01179 | − | 0.0191457i | ||||
\(653\) | 1.70786e14i | 1.43842i | 0.694792 | + | 0.719211i | \(0.255497\pi\) | ||||
−0.694792 | + | 0.719211i | \(0.744503\pi\) | |||||||
\(654\) | −1.03452e12 | + | 1.09351e14i | −0.00864666 | + | 0.913974i | ||||
\(655\) | 1.24615e14 | + | 1.28209e14i | 1.03363 | + | 1.06344i | ||||
\(656\) | 4.77118e13 | + | 1.80632e12i | 0.392741 | + | 0.0148688i | ||||
\(657\) | 1.73196e14i | 1.41485i | ||||||||
\(658\) | 5.72150e10 | − | 6.04777e12i | 0.000463853 | − | 0.0490304i | ||||
\(659\) | − | 1.58743e14i | − | 1.27722i | −0.769530 | − | 0.638611i | \(-0.779509\pi\) | ||
0.769530 | − | 0.638611i | \(-0.220491\pi\) | |||||||
\(660\) | 1.34648e14 | + | 1.43881e14i | 1.07518 | + | 1.14890i | ||||
\(661\) | −4.27414e13 | −0.338720 | −0.169360 | − | 0.985554i | \(-0.554170\pi\) | ||||
−0.169360 | + | 0.985554i | \(0.554170\pi\) | |||||||
\(662\) | 1.95679e14 | + | 1.85122e12i | 1.53906 | + | 0.0145603i | ||||
\(663\) | −6.81423e13 | −0.531923 | ||||||||
\(664\) | 6.60049e12 | − | 2.32507e14i | 0.0511371 | − | 1.80134i | ||||
\(665\) | 1.34264e14 | + | 1.38137e14i | 1.03241 | + | 1.06219i | ||||
\(666\) | 1.28207e14 | + | 1.21290e12i | 0.978453 | + | 0.00925667i | ||||
\(667\) | 1.19317e14 | 0.903802 | ||||||||
\(668\) | −9.55299e13 | − | 1.80769e12i | −0.718219 | − | 0.0135907i | ||||
\(669\) | 4.17547e13 | 0.311584 | ||||||||
\(670\) | 4.93934e13 | + | 5.17894e13i | 0.365843 | + | 0.383589i | ||||
\(671\) | 4.87351e13i | 0.358286i | ||||||||
\(672\) | −1.17073e13 | + | 2.47321e14i | −0.0854300 | + | 1.80474i | ||||
\(673\) | − | 1.88489e14i | − | 1.36525i | −0.730770 | − | 0.682623i | \(-0.760839\pi\) | ||
0.730770 | − | 0.682623i | \(-0.239161\pi\) | |||||||
\(674\) | 3.19289e13 | + | 3.02063e11i | 0.229553 | + | 0.00217169i | ||||
\(675\) | −2.41230e12 | + | 8.48258e13i | −0.0172152 | + | 0.605354i | ||||
\(676\) | −1.33475e14 | − | 2.52571e12i | −0.945511 | − | 0.0178916i | ||||
\(677\) | − | 4.14436e13i | − | 0.291417i | −0.989328 | − | 0.145708i | \(-0.953454\pi\) | ||
0.989328 | − | 0.145708i | \(-0.0465461\pi\) | |||||||
\(678\) | −9.11210e13 | − | 8.62052e11i | −0.636019 | − | 0.00601707i | ||||
\(679\) | 1.12271e14i | 0.777892i | ||||||||
\(680\) | 1.58047e14 | − | 1.45126e14i | 1.08703 | − | 0.998159i | ||||
\(681\) | 3.38270e14 | 2.30955 | ||||||||
\(682\) | −6.03438e11 | + | 6.37849e13i | −0.00408988 | + | 0.432311i | ||||
\(683\) | −1.25711e14 | −0.845801 | −0.422901 | − | 0.906176i | \(-0.638988\pi\) | ||||
−0.422901 | + | 0.906176i | \(0.638988\pi\) | |||||||
\(684\) | −4.99774e12 | + | 2.64113e14i | −0.0333805 | + | 1.76404i | ||||
\(685\) | 2.70997e13 | + | 2.78813e13i | 0.179685 | + | 0.184867i | ||||
\(686\) | −1.06632e12 | + | 1.12713e14i | −0.00701889 | + | 0.741915i | ||||
\(687\) | 2.04371e14 | 1.33547 | ||||||||
\(688\) | 7.83603e13 | + | 2.96664e12i | 0.508340 | + | 0.0192452i | ||||
\(689\) | −1.10095e13 | −0.0709038 | ||||||||
\(690\) | −2.73332e14 | − | 2.86591e14i | −1.74761 | − | 1.83239i | ||||
\(691\) | − | 2.51924e14i | − | 1.59911i | −0.600592 | − | 0.799556i | \(-0.705068\pi\) | ||
0.600592 | − | 0.799556i | \(-0.294932\pi\) | |||||||
\(692\) | 1.77705e12 | − | 9.39110e13i | 0.0111988 | − | 0.591815i | ||||
\(693\) | − | 2.64403e14i | − | 1.65425i | ||||||
\(694\) | 1.60199e12 | − | 1.69334e14i | 0.00995087 | − | 1.05183i | ||||
\(695\) | 8.45912e12 | + | 8.70311e12i | 0.0521677 | + | 0.0536723i | ||||
\(696\) | −3.95624e12 | + | 1.39362e14i | −0.0242235 | + | 0.853291i | ||||
\(697\) | 9.54128e13i | 0.580019i | ||||||||
\(698\) | −9.73202e10 | + | 1.02870e13i | −0.000587389 | + | 0.0620885i | ||||
\(699\) | 2.38539e14i | 1.42947i | ||||||||
\(700\) | 9.29424e12 | − | 1.96137e14i | 0.0552998 | − | 1.16700i | ||||
\(701\) | −9.22547e13 | −0.545002 | −0.272501 | − | 0.962155i | \(-0.587851\pi\) | ||||
−0.272501 | + | 0.962155i | \(0.587851\pi\) | |||||||
\(702\) | −2.40619e13 | − | 2.27638e11i | −0.141138 | − | 0.00133524i | ||||
\(703\) | −1.53072e14 | −0.891495 | ||||||||
\(704\) | 9.98192e12 | − | 1.75669e14i | 0.0577232 | − | 1.01585i | ||||
\(705\) | −8.10570e12 | + | 7.87846e12i | −0.0465420 | + | 0.0452372i | ||||
\(706\) | 2.05306e14 | + | 1.94230e12i | 1.17052 | + | 0.0110737i | ||||
\(707\) | −3.36580e14 | −1.90542 | ||||||||
\(708\) | −8.61125e12 | + | 4.55075e14i | −0.0484061 | + | 2.55809i | ||||
\(709\) | 5.98699e13 | 0.334177 | 0.167089 | − | 0.985942i | \(-0.446563\pi\) | ||||
0.167089 | + | 0.985942i | \(0.446563\pi\) | |||||||
\(710\) | 1.85557e14 | − | 1.76973e14i | 1.02846 | − | 0.980877i | ||||
\(711\) | − | 2.83307e14i | − | 1.55923i | ||||||
\(712\) | −3.15687e12 | + | 1.11203e14i | −0.0172527 | + | 0.607740i | ||||
\(713\) | − | 1.28197e14i | − | 0.695713i | ||||||
\(714\) | −4.94763e14 | − | 4.68071e12i | −2.66628 | − | 0.0252244i | ||||
\(715\) | 3.17770e13 | − | 3.08861e13i | 0.170052 | − | 0.165285i | ||||
\(716\) | 2.09003e12 | − | 1.10451e14i | 0.0111068 | − | 0.586954i | ||||
\(717\) | − | 3.47341e13i | − | 0.183299i | ||||||
\(718\) | −1.34357e14 | − | 1.27108e12i | −0.704104 | − | 0.00666119i | ||||
\(719\) | 2.79087e14i | 1.45243i | 0.687469 | + | 0.726214i | \(0.258722\pi\) | ||||
−0.687469 | + | 0.726214i | \(0.741278\pi\) | |||||||
\(720\) | 2.00047e14 | − | 1.80233e14i | 1.03388 | − | 0.931475i | ||||
\(721\) | 1.46358e14 | 0.751173 | ||||||||
\(722\) | 1.12750e12 | − | 1.19179e14i | 0.00574684 | − | 0.607456i | ||||
\(723\) | 3.40467e14 | 1.72339 | ||||||||
\(724\) | −3.51443e14 | − | 6.65027e12i | −1.76670 | − | 0.0334308i | ||||
\(725\) | 3.14301e12 | − | 1.10520e14i | 0.0156912 | − | 0.551763i | ||||
\(726\) | −1.04128e11 | + | 1.10066e13i | −0.000516281 | + | 0.0545722i | ||||
\(727\) | −3.87651e14 | −1.90883 | −0.954417 | − | 0.298476i | \(-0.903522\pi\) | ||||
−0.954417 | + | 0.298476i | \(0.903522\pi\) | |||||||
\(728\) | 5.56567e13 | + | 1.58000e12i | 0.272183 | + | 0.00772681i | ||||
\(729\) | −3.23207e14 | −1.56980 | ||||||||
\(730\) | −1.52524e14 | + | 1.45468e14i | −0.735740 | + | 0.701702i | ||||
\(731\) | 1.56703e14i | 0.750741i | ||||||||
\(732\) | 1.14425e14 | + | 2.16523e12i | 0.544458 | + | 0.0103026i | ||||
\(733\) | − | 2.86598e14i | − | 1.35442i | −0.735790 | − | 0.677210i | \(-0.763189\pi\) | ||
0.735790 | − | 0.677210i | \(-0.236811\pi\) | |||||||
\(734\) | 7.51543e11 | − | 7.94400e13i | 0.00352755 | − | 0.372871i | ||||
\(735\) | −8.68100e13 | + | 8.43764e13i | −0.404700 | + | 0.393355i | ||||
\(736\) | −1.67203e13 | + | 3.53223e14i | −0.0774204 | + | 1.63553i | ||||
\(737\) | 1.17276e14i | 0.539349i | ||||||||
\(738\) | −1.13268e12 | + | 1.19727e14i | −0.00517400 | + | 0.546905i | ||||
\(739\) | 1.44810e14i | 0.657017i | 0.944501 | + | 0.328508i | \(0.106546\pi\) | ||||
−0.944501 | + | 0.328508i | \(0.893454\pi\) | |||||||
\(740\) | 1.06613e14 | + | 1.13923e14i | 0.480454 | + | 0.513399i | ||||
\(741\) | 1.02091e14 | 0.456979 | ||||||||
\(742\) | −7.99368e13 | − | 7.56243e11i | −0.355408 | − | 0.00336234i | ||||
\(743\) | 4.64148e13 | 0.204980 | 0.102490 | − | 0.994734i | \(-0.467319\pi\) | ||||
0.102490 | + | 0.994734i | \(0.467319\pi\) | |||||||
\(744\) | 1.49733e14 | + | 4.25068e12i | 0.656831 | + | 0.0186463i | ||||
\(745\) | 1.13194e14 | − | 1.10020e14i | 0.493220 | − | 0.479393i | ||||
\(746\) | −2.70096e14 | − | 2.55525e12i | −1.16903 | − | 0.0110596i | ||||
\(747\) | 5.83295e14 | 2.50776 | ||||||||
\(748\) | 3.51550e14 | + | 6.65227e12i | 1.50134 | + | 0.0284094i | ||||
\(749\) | −1.42710e14 | −0.605405 | ||||||||
\(750\) | −2.72662e14 | + | 2.45631e14i | −1.14900 | + | 1.03509i | ||||
\(751\) | − | 1.55194e14i | − | 0.649642i | −0.945775 | − | 0.324821i | \(-0.894696\pi\) | ||
0.945775 | − | 0.324821i | \(-0.105304\pi\) | |||||||
\(752\) | 1.00857e13 | + | 3.81835e11i | 0.0419390 | + | 0.00158777i | ||||
\(753\) | − | 4.27208e14i | − | 1.76467i | ||||||
\(754\) | 3.13505e13 | + | 2.96592e11i | 0.128643 | + | 0.00121703i | ||||
\(755\) | −1.20055e14 | − | 1.23518e14i | −0.489381 | − | 0.503496i | ||||
\(756\) | −1.74692e14 | − | 3.30564e12i | −0.707397 | − | 0.0133859i | ||||
\(757\) | 2.71076e14i | 1.09046i | 0.838285 | + | 0.545232i | \(0.183558\pi\) | ||||
−0.838285 | + | 0.545232i | \(0.816442\pi\) | |||||||
\(758\) | 1.63614e14 | + | 1.54787e12i | 0.653845 | + | 0.00618571i | ||||
\(759\) | − | 6.48977e14i | − | 2.57644i | ||||||
\(760\) | −2.36788e14 | + | 2.17428e14i | −0.933880 | + | 0.857527i | ||||
\(761\) | −3.23023e14 | −1.26564 | −0.632819 | − | 0.774300i | \(-0.718102\pi\) | ||||
−0.632819 | + | 0.774300i | \(0.718102\pi\) | |||||||
\(762\) | 7.10417e11 | − | 7.50928e13i | 0.00276528 | − | 0.292297i | ||||
\(763\) | 1.78562e14 | 0.690503 | ||||||||
\(764\) | −4.52982e11 | + | 2.39385e13i | −0.00174026 | + | 0.0919667i | ||||
\(765\) | 3.75033e14 | + | 3.85850e14i | 1.43140 | + | 1.47269i | ||||
\(766\) | 2.68686e12 | − | 2.84008e14i | 0.0101883 | − | 1.07693i | ||||
\(767\) | 1.02354e14 | 0.385593 | ||||||||
\(768\) | −4.12008e14 | − | 3.12412e13i | −1.54205 | − | 0.116929i | ||||
\(769\) | 1.81547e14 | 0.675085 | 0.337542 | − | 0.941310i | \(-0.390404\pi\) | ||||
0.337542 | + | 0.941310i | \(0.390404\pi\) | |||||||
\(770\) | 2.32846e14 | − | 2.22073e14i | 0.860230 | − | 0.820432i | ||||
\(771\) | 2.62546e14i | 0.963683i | ||||||||
\(772\) | 5.77276e12 | − | 3.05070e14i | 0.0210522 | − | 1.11253i | ||||
\(773\) | 7.48801e13i | 0.271312i | 0.990756 | + | 0.135656i | \(0.0433142\pi\) | ||||
−0.990756 | + | 0.135656i | \(0.956686\pi\) | |||||||
\(774\) | −1.86028e12 | + | 1.96637e14i | −0.00669691 | + | 0.707880i | ||||
\(775\) | −1.18746e14 | − | 3.37692e12i | −0.424726 | − | 0.0120785i | ||||
\(776\) | −1.87282e14 | − | 5.31663e12i | −0.665561 | − | 0.0188942i | ||||
\(777\) | − | 3.59792e14i | − | 1.27042i | ||||||
\(778\) | −3.28771e12 | + | 3.47519e14i | −0.0115344 | + | 1.21921i | ||||
\(779\) | − | 1.42948e14i | − | 0.498299i | ||||||
\(780\) | −7.11055e13 | − | 7.59811e13i | −0.246281 | − | 0.263168i | ||||
\(781\) | 4.20190e14 | 1.44607 | ||||||||
\(782\) | −7.06619e14 | − | 6.68498e12i | −2.41630 | − | 0.0228595i | ||||
\(783\) | −9.83833e13 | −0.334282 | ||||||||
\(784\) | 1.08016e14 | + | 4.08937e12i | 0.364675 | + | 0.0138062i | ||||
\(785\) | 1.95179e14 | + | 2.00809e14i | 0.654765 | + | 0.673650i | ||||
\(786\) | 6.87984e14 | + | 6.50868e12i | 2.29332 | + | 0.0216960i | ||||
\(787\) | −1.15967e14 | −0.384116 | −0.192058 | − | 0.981384i | \(-0.561516\pi\) | ||||
−0.192058 | + | 0.981384i | \(0.561516\pi\) | |||||||
\(788\) | −8.84526e12 | + | 4.67441e14i | −0.0291125 | + | 1.53849i | ||||
\(789\) | 1.85912e13 | 0.0608026 | ||||||||
\(790\) | 2.49493e14 | − | 2.37950e14i | 0.810818 | − | 0.773306i | ||||
\(791\) | 1.48794e14i | 0.480509i | ||||||||
\(792\) | 4.41058e14 | + | 1.25209e13i | 1.41537 | + | 0.0401800i | ||||
\(793\) | − | 2.57362e13i | − | 0.0820687i | ||||||
\(794\) | −1.44420e14 | − | 1.36628e12i | −0.457640 | − | 0.00432951i | ||||
\(795\) | 1.04134e14 | + | 1.07138e14i | 0.327912 | + | 0.337370i | ||||
\(796\) | 3.13021e12 | − | 1.65420e14i | 0.00979507 | − | 0.517635i | ||||
\(797\) | 1.98139e14i | 0.616140i | 0.951364 | + | 0.308070i | \(0.0996830\pi\) | ||||
−0.951364 | + | 0.308070i | \(0.900317\pi\) | |||||||
\(798\) | 7.41257e14 | + | 7.01267e12i | 2.29063 | + | 0.0216705i | ||||
\(799\) | 2.01692e13i | 0.0619376i | ||||||||
\(800\) | 3.26741e14 | + | 2.47921e13i | 0.997134 | + | 0.0756594i | ||||
\(801\) | −2.78977e14 | −0.846070 | ||||||||
\(802\) | 1.30875e12 | − | 1.38338e14i | 0.00394444 | − | 0.416938i | ||||
\(803\) | −3.45387e14 | −1.03449 | ||||||||
\(804\) | 2.75350e14 | + | 5.21038e12i | 0.819607 | + | 0.0155092i | ||||
\(805\) | −4.63717e14 | + | 4.50717e14i | −1.37175 | + | 1.33329i | ||||
\(806\) | 3.18665e11 | − | 3.36837e13i | 0.000936827 | − | 0.0990249i | ||||
\(807\) | −6.77891e14 | −1.98058 | ||||||||
\(808\) | 1.59388e13 | − | 5.61458e14i | 0.0462807 | − | 1.63027i | ||||
\(809\) | −3.55439e14 | −1.02570 | −0.512852 | − | 0.858477i | \(-0.671411\pi\) | ||||
−0.512852 | + | 0.858477i | \(0.671411\pi\) | |||||||
\(810\) | −1.09507e14 | − | 1.14819e14i | −0.314063 | − | 0.329298i | ||||
\(811\) | 6.30302e14i | 1.79657i | 0.439413 | + | 0.898285i | \(0.355187\pi\) | ||||
−0.439413 | + | 0.898285i | \(0.644813\pi\) | |||||||
\(812\) | 2.27607e14 | + | 4.30695e12i | 0.644772 | + | 0.0122008i | ||||
\(813\) | 7.63883e14i | 2.15067i | ||||||||
\(814\) | −2.41877e12 | + | 2.55670e14i | −0.00676818 | + | 0.715413i | ||||
\(815\) | 2.60931e14 | − | 2.53616e14i | 0.725668 | − | 0.705324i | ||||
\(816\) | 3.12377e13 | − | 8.25105e14i | 0.0863431 | − | 2.28065i | ||||
\(817\) | − | 2.34773e14i | − | 0.644968i | ||||||
\(818\) | −1.85132e11 | + | 1.95689e13i | −0.000505494 | + | 0.0534319i | ||||
\(819\) | 1.39627e14i | 0.378922i | ||||||||
\(820\) | −1.06389e14 | + | 9.95619e13i | −0.286963 | + | 0.268549i | ||||
\(821\) | −4.02625e13 | −0.107941 | −0.0539703 | − | 0.998543i | \(-0.517188\pi\) | ||||
−0.0539703 | + | 0.998543i | \(0.517188\pi\) | |||||||
\(822\) | 1.49614e14 | + | 1.41542e12i | 0.398669 | + | 0.00377162i | ||||
\(823\) | 5.78856e14 | 1.53310 | 0.766551 | − | 0.642183i | \(-0.221971\pi\) | ||||
0.766551 | + | 0.642183i | \(0.221971\pi\) | |||||||
\(824\) | −6.93082e12 | + | 2.44143e14i | −0.0182452 | + | 0.642701i | ||||
\(825\) | −6.01131e14 | − | 1.70951e13i | −1.57289 | − | 0.0447304i | ||||
\(826\) | 7.43168e14 | + | 7.03075e12i | 1.93280 | + | 0.0182853i | ||||
\(827\) | 4.26504e14 | 1.10254 | 0.551271 | − | 0.834326i | \(-0.314143\pi\) | ||||
0.551271 | + | 0.834326i | \(0.314143\pi\) | |||||||
\(828\) | −8.86612e14 | − | 1.67771e13i | −2.27815 | − | 0.0431087i | ||||
\(829\) | 8.67325e13 | 0.221518 | 0.110759 | − | 0.993847i | \(-0.464672\pi\) | ||||
0.110759 | + | 0.993847i | \(0.464672\pi\) | |||||||
\(830\) | 4.89911e14 | + | 5.13676e14i | 1.24373 | + | 1.30406i | ||||
\(831\) | 3.71267e14i | 0.936874i | ||||||||
\(832\) | −5.27128e12 | + | 9.27675e13i | −0.0132221 | + | 0.232691i | ||||
\(833\) | 2.16007e14i | 0.538571i | ||||||||
\(834\) | 4.67018e13 | + | 4.41823e11i | 0.115745 | + | 0.00109501i | ||||
\(835\) | 2.09093e14 | − | 2.03231e14i | 0.515118 | − | 0.500677i | ||||
\(836\) | −5.26693e14 | − | 9.96647e12i | −1.28981 | − | 0.0244068i | ||||
\(837\) | 1.05705e14i | 0.257318i | ||||||||
\(838\) | −3.38363e14 | − | 3.20109e12i | −0.818771 | − | 0.00774600i | ||||
\(839\) | 6.16766e13i | 0.148358i | 0.997245 | + | 0.0741790i | \(0.0236336\pi\) | ||||
−0.997245 | + | 0.0741790i | \(0.976366\pi\) | |||||||
\(840\) | −5.11059e14 | − | 5.56563e14i | −1.22201 | − | 1.33082i | ||||
\(841\) | −2.92523e14 | −0.695312 | ||||||||
\(842\) | −1.87837e12 | + | 1.98549e14i | −0.00443835 | + | 0.469145i | ||||
\(843\) | −1.06875e15 | −2.51037 | ||||||||
\(844\) | −3.52124e12 | + | 1.86085e14i | −0.00822212 | + | 0.434510i | ||||
\(845\) | 2.92146e14 | − | 2.83956e14i | 0.678135 | − | 0.659124i | ||||
\(846\) | −2.39436e11 | + | 2.53090e13i | −0.000552507 | + | 0.0584014i | ||||
\(847\) | 1.79730e13 | 0.0412290 | ||||||||
\(848\) | 5.04693e12 | − | 1.33309e14i | 0.0115093 | − | 0.304004i | ||||
\(849\) | −3.47853e13 | −0.0788600 | ||||||||
\(850\) | −2.48056e13 | + | 6.54347e14i | −0.0559056 | + | 1.47473i | ||||
\(851\) | − | 5.13853e14i | − | 1.15131i | ||||||
\(852\) | 1.86684e13 | − | 9.86560e14i | 0.0415824 | − | 2.19748i | ||||
\(853\) | − | 5.00937e14i | − | 1.10927i | −0.832093 | − | 0.554636i | \(-0.812857\pi\) | ||
0.832093 | − | 0.554636i | \(-0.187143\pi\) | |||||||
\(854\) | 1.76782e12 | − | 1.86864e14i | 0.00389179 | − | 0.411372i | ||||
\(855\) | −5.61876e14 | − | 5.78082e14i | −1.22973 | − | 1.26520i | ||||
\(856\) | 6.75808e12 | − | 2.38059e14i | 0.0147047 | − | 0.517982i | ||||
\(857\) | − | 5.92500e14i | − | 1.28169i | −0.767668 | − | 0.640847i | \(-0.778583\pi\) | ||
0.767668 | − | 0.640847i | \(-0.221417\pi\) | |||||||
\(858\) | 1.61319e12 | − | 1.70518e14i | 0.00346936 | − | 0.366720i | ||||
\(859\) | − | 6.13470e14i | − | 1.31168i | −0.754901 | − | 0.655839i | \(-0.772315\pi\) | ||
0.754901 | − | 0.655839i | \(-0.227685\pi\) | |||||||
\(860\) | −1.74730e14 | + | 1.63517e14i | −0.371427 | + | 0.347593i | ||||
\(861\) | 3.35995e14 | 0.710097 | ||||||||
\(862\) | −1.20186e14 | − | 1.13702e12i | −0.252532 | − | 0.00238909i | ||||
\(863\) | 6.03721e14 | 1.26119 | 0.630597 | − | 0.776110i | \(-0.282810\pi\) | ||||
0.630597 | + | 0.776110i | \(0.282810\pi\) | |||||||
\(864\) | 1.37868e13 | − | 2.91251e14i | 0.0286348 | − | 0.604921i | ||||
\(865\) | 1.99787e14 | + | 2.05549e14i | 0.412560 | + | 0.424459i | ||||
\(866\) | −7.20217e14 | − | 6.81362e12i | −1.47868 | − | 0.0139891i | ||||
\(867\) | 8.92425e14 | 1.82170 | ||||||||
\(868\) | 4.62749e12 | − | 2.44547e14i | 0.00939176 | − | 0.496322i | ||||
\(869\) | 5.64970e14 | 1.14006 | ||||||||
\(870\) | −2.93646e14 | − | 3.07890e14i | −0.589152 | − | 0.617731i | ||||
\(871\) | − | 6.19312e13i | − | 0.123543i | ||||||
\(872\) | −8.45583e12 | + | 2.97863e14i | −0.0167716 | + | 0.590791i | ||||
\(873\) | − | 4.69838e14i | − | 0.926567i | ||||||
\(874\) | 1.05866e15 | + | 1.00155e13i | 2.07587 | + | 0.0196388i | ||||
\(875\) | 4.05273e14 | + | 4.41402e14i | 0.790146 | + | 0.860585i | ||||
\(876\) | −1.53450e13 | + | 8.10931e14i | −0.0297473 | + | 1.57204i | ||||
\(877\) | 9.12906e14i | 1.75966i | 0.475292 | + | 0.879828i | \(0.342343\pi\) | ||||
−0.475292 | + | 0.879828i | \(0.657657\pi\) | |||||||
\(878\) | −6.20486e14 | − | 5.87012e12i | −1.18921 | − | 0.0112506i | ||||
\(879\) | 8.45263e14i | 1.61082i | ||||||||
\(880\) | 3.59419e14 | + | 3.98932e14i | 0.681064 | + | 0.755937i | ||||
\(881\) | −5.56277e14 | −1.04812 | −0.524060 | − | 0.851681i | \(-0.675583\pi\) | ||||
−0.524060 | + | 0.851681i | \(0.675583\pi\) | |||||||
\(882\) | −2.56430e12 | + | 2.71053e14i | −0.00480426 | + | 0.507822i | ||||
\(883\) | −4.22428e14 | −0.786954 | −0.393477 | − | 0.919334i | \(-0.628728\pi\) | ||||
−0.393477 | + | 0.919334i | \(0.628728\pi\) | |||||||
\(884\) | −1.85647e14 | − | 3.51295e12i | −0.343896 | − | 0.00650745i | ||||
\(885\) | −9.68129e14 | − | 9.96052e14i | −1.78327 | − | 1.83470i | ||||
\(886\) | −1.06995e12 | + | 1.13096e14i | −0.00195972 | + | 0.207147i | ||||
\(887\) | −4.26239e14 | −0.776310 | −0.388155 | − | 0.921594i | \(-0.626888\pi\) | ||||
−0.388155 | + | 0.921594i | \(0.626888\pi\) | |||||||
\(888\) | 6.00177e14 | + | 1.70380e13i | 1.08696 | + | 0.0308571i | ||||
\(889\) | −1.22621e14 | −0.220829 | ||||||||
\(890\) | −2.34314e14 | − | 2.45680e14i | −0.419612 | − | 0.439967i | ||||
\(891\) | − | 2.60005e14i | − | 0.463012i | ||||||
\(892\) | 1.13757e14 | + | 2.15259e12i | 0.201443 | + | 0.00381186i | ||||
\(893\) | − | 3.02176e13i | − | 0.0532111i | ||||||
\(894\) | 5.74640e12 | − | 6.07409e14i | 0.0100626 | − | 1.06364i | ||||
\(895\) | 2.34974e14 | + | 2.41751e14i | 0.409170 | + | 0.420972i | ||||
\(896\) | −4.46456e13 | + | 6.73199e14i | −0.0773105 | + | 1.16574i | ||||
\(897\) | 3.42714e14i | 0.590159i | ||||||||
\(898\) | 1.05620e12 | − | 1.11643e14i | 0.00180869 | − | 0.191183i | ||||
\(899\) | − | 1.37724e14i | − | 0.234538i | ||||||
\(900\) | −3.88950e13 | + | 8.20804e14i | −0.0658690 | + | 1.39004i | ||||
\(901\) | 2.66587e14 | 0.448968 | ||||||||
\(902\) | −2.38760e14 | − | 2.25879e12i | −0.399879 | − | 0.00378306i | ||||
\(903\) | 5.51828e14 | 0.919105 | ||||||||
\(904\) | −2.48206e14 | − | 7.04616e12i | −0.411122 | − | 0.0116711i | ||||
\(905\) | 7.69228e14 | − | 7.47663e14i | 1.26710 | − | 1.23158i | ||||
\(906\) | −6.62811e14 | − | 6.27054e12i | −1.08580 | − | 0.0102722i | ||||
\(907\) | −3.83030e14 | −0.624017 | −0.312008 | − | 0.950079i | \(-0.601002\pi\) | ||||
−0.312008 | + | 0.950079i | \(0.601002\pi\) | |||||||
\(908\) | 9.21584e14 | + | 1.74389e13i | 1.49316 | + | 0.0282546i | ||||
\(909\) | 1.40854e15 | 2.26960 | ||||||||
\(910\) | −1.22962e14 | + | 1.17273e14i | −0.197044 | + | 0.187928i | ||||
\(911\) | − | 1.36122e14i | − | 0.216939i | −0.994100 | − | 0.108470i | \(-0.965405\pi\) | ||
0.994100 | − | 0.108470i | \(-0.0345950\pi\) | |||||||
\(912\) | −4.68004e13 | + | 1.23618e15i | −0.0741781 | + | 1.95932i | ||||
\(913\) | 1.16320e15i | 1.83359i | ||||||||
\(914\) | −1.14123e14 | − | 1.07966e12i | −0.178913 | − | 0.00169261i | ||||
\(915\) | −2.50449e14 | + | 2.43428e14i | −0.390494 | + | 0.379547i | ||||
\(916\) | 5.56789e14 | + | 1.05360e13i | 0.863403 | + | 0.0163379i | ||||
\(917\) | − | 1.12342e15i | − | 1.73260i | ||||||
\(918\) | 5.82645e14 | + | 5.51212e12i | 0.893698 | + | 0.00845484i | ||||
\(919\) | − | 1.45106e14i | − | 0.221365i | −0.993856 | − | 0.110682i | \(-0.964696\pi\) | ||
0.993856 | − | 0.110682i | \(-0.0353036\pi\) | |||||||
\(920\) | −7.29893e14 | − | 7.94881e14i | −1.10744 | − | 1.20604i | ||||
\(921\) | 8.70103e13 | 0.131302 | ||||||||
\(922\) | −6.39836e12 | + | 6.76323e14i | −0.00960316 | + | 1.01508i | ||||
\(923\) | −2.21895e14 | −0.331237 | ||||||||
\(924\) | 2.34259e13 | − | 1.23798e15i | 0.0347806 | − | 1.83803i | ||||
\(925\) | −4.75969e14 | − | 1.35357e13i | −0.702862 | − | 0.0199882i | ||||
\(926\) | 6.07180e12 | − | 6.41804e14i | 0.00891789 | − | 0.942643i | ||||
\(927\) | −6.12486e14 | −0.894742 | ||||||||
\(928\) | −1.79629e13 | + | 3.79474e14i | −0.0260998 | + | 0.551368i | ||||
\(929\) | 8.80611e14 | 1.27264 | 0.636320 | − | 0.771425i | \(-0.280456\pi\) | ||||
0.636320 | + | 0.771425i | \(0.280456\pi\) | |||||||
\(930\) | −3.30804e14 | + | 3.15500e14i | −0.475506 | + | 0.453507i | ||||
\(931\) | − | 3.23623e14i | − | 0.462691i | ||||||
\(932\) | −1.22975e13 | + | 6.49878e14i | −0.0174878 | + | 0.924171i | ||||
\(933\) | 1.42382e15i | 2.01394i | ||||||||
\(934\) | −4.94139e12 | + | 5.22317e14i | −0.00695207 | + | 0.734851i | ||||
\(935\) | −7.69460e14 | + | 7.47889e14i | −1.07678 | + | 1.04660i | ||||
\(936\) | −2.32915e14 | − | 6.61207e12i | −0.324204 | − | 0.00920361i | ||||
\(937\) | 4.17114e14i | 0.577506i | 0.957404 | + | 0.288753i | \(0.0932406\pi\) | ||||
−0.957404 | + | 0.288753i | \(0.906759\pi\) | |||||||
\(938\) | 4.25407e12 | − | 4.49666e14i | 0.00585856 | − | 0.619264i | ||||
\(939\) | 8.42216e14i | 1.15371i | ||||||||
\(940\) | −2.24894e13 | + | 2.10463e13i | −0.0306435 | + | 0.0286771i | ||||
\(941\) | −1.11785e14 | −0.151507 | −0.0757537 | − | 0.997127i | \(-0.524136\pi\) | ||||
−0.0757537 | + | 0.997127i | \(0.524136\pi\) | |||||||
\(942\) | 1.07756e15 | + | 1.01943e13i | 1.45274 | + | 0.0137436i | ||||
\(943\) | 4.79867e14 | 0.643521 | ||||||||
\(944\) | −4.69211e13 | + | 1.23936e15i | −0.0625905 | + | 1.65325i | ||||
\(945\) | 3.82359e14 | − | 3.71640e14i | 0.507356 | − | 0.493133i | ||||
\(946\) | −3.92132e14 | − | 3.70977e12i | −0.517579 | − | 0.00489656i | ||||
\(947\) | −5.17902e14 | −0.679982 | −0.339991 | − | 0.940429i | \(-0.610424\pi\) | ||||
−0.339991 | + | 0.940429i | \(0.610424\pi\) | |||||||
\(948\) | 2.51008e13 | − | 1.32649e15i | 0.0327828 | − | 1.73246i | ||||
\(949\) | 1.82393e14 | 0.236961 | ||||||||
\(950\) | 3.71639e13 | − | 9.80346e14i | 0.0480290 | − | 1.26696i | ||||
\(951\) | − | 5.37264e14i | − | 0.690694i | ||||||
\(952\) | −1.34769e15 | − | 3.82588e13i | −1.72348 | − | 0.0489267i | ||||
\(953\) | − | 1.16104e15i | − | 1.47701i | −0.674249 | − | 0.738504i | \(-0.735532\pi\) | ||
0.674249 | − | 0.738504i | \(-0.264468\pi\) | |||||||
\(954\) | 3.34523e14 | + | 3.16476e12i | 0.423335 | + | 0.00400497i | ||||
\(955\) | −5.09270e13 | − | 5.23959e13i | −0.0641108 | − | 0.0659599i | ||||
\(956\) | 1.79065e12 | − | 9.46298e13i | 0.00224245 | − | 0.118505i | ||||
\(957\) | − | 6.97208e14i | − | 0.868566i | ||||||
\(958\) | −6.17151e14 | − | 5.83857e12i | −0.764828 | − | 0.00723567i | ||||
\(959\) | − | 2.44308e14i | − | 0.301193i | ||||||
\(960\) | 9.52618e14 | − | 8.26154e14i | 1.16832 | − | 1.01322i | ||||
\(961\) | 6.71654e14 | 0.819462 | ||||||||
\(962\) | 1.27731e12 | − | 1.35015e14i | 0.00155032 | − | 0.163872i | ||||
\(963\) | 5.97221e14 | 0.721114 | ||||||||
\(964\) | 9.27571e14 | + | 1.75522e13i | 1.11420 | + | 0.0210836i | ||||
\(965\) | 6.49008e14 | + | 6.67727e14i | 0.775557 | + | 0.797926i | ||||
\(966\) | −2.35411e13 | + | 2.48835e15i | −0.0279860 | + | 2.95819i | ||||
\(967\) | 1.64367e15 | 1.94394 | 0.971972 | − | 0.235098i | \(-0.0755413\pi\) | ||||
0.971972 | + | 0.235098i | \(0.0755413\pi\) | |||||||
\(968\) | −8.51116e11 | + | 2.99812e13i | −0.00100141 | + | 0.0352754i | ||||
\(969\) | −2.47207e15 | −2.89363 | ||||||||
\(970\) | 4.13761e14 | − | 3.94618e14i | 0.481826 | − | 0.459535i | ||||
\(971\) | − | 1.09038e15i | − | 1.26323i | −0.775284 | − | 0.631613i | \(-0.782393\pi\) | ||
0.775284 | − | 0.631613i | \(-0.217607\pi\) | |||||||
\(972\) | −1.13580e15 | − | 2.14924e13i | −1.30909 | − | 0.0247716i | ||||
\(973\) | − | 7.62604e13i | − | 0.0874450i | ||||||
\(974\) | −5.40735e12 | + | 5.71571e14i | −0.00616865 | + | 0.652042i | ||||
\(975\) | 3.17447e14 | + | 9.02763e12i | 0.360286 | + | 0.0102459i | ||||
\(976\) | 3.11628e14 | + | 1.17979e13i | 0.351874 | + | 0.0133216i | ||||
\(977\) | − | 8.20193e14i | − | 0.921389i | −0.887559 | − | 0.460695i | \(-0.847600\pi\) | ||
0.887559 | − | 0.460695i | \(-0.152400\pi\) | |||||||
\(978\) | 1.32465e13 | − | 1.40018e15i | 0.0148049 | − | 1.56491i | ||||
\(979\) | − | 5.56336e14i | − | 0.618619i | ||||||
\(980\) | −2.40856e14 | + | 2.25400e14i | −0.266457 | + | 0.249358i | ||||
\(981\) | −7.47254e14 | −0.822475 | ||||||||
\(982\) | 1.11963e15 | + | 1.05922e13i | 1.22607 | + | 0.0115993i | ||||
\(983\) | 1.04826e15 | 1.14209 | 0.571047 | − | 0.820917i | \(-0.306537\pi\) | ||||
0.571047 | + | 0.820917i | \(0.306537\pi\) | |||||||
\(984\) | −1.59111e13 | + | 5.60482e14i | −0.0172475 | + | 0.607556i | ||||
\(985\) | −9.94438e14 | − | 1.02312e15i | −1.07250 | − | 1.10343i | ||||
\(986\) | −7.59134e14 | − | 7.18180e12i | −0.814580 | − | 0.00770635i | ||||
\(987\) | 7.10256e13 | 0.0758279 | ||||||||
\(988\) | 2.78138e14 | + | 5.26312e12i | 0.295444 | + | 0.00559060i | ||||
\(989\) | 7.88119e14 | 0.832934 | ||||||||
\(990\) | −9.74425e14 | + | 9.29343e14i | −1.02464 | + | 0.977238i | ||||
\(991\) | 3.12148e13i | 0.0326582i | 0.999867 | + | 0.0163291i | \(0.00519794\pi\) | ||||
−0.999867 | + | 0.0163291i | \(0.994802\pi\) | |||||||
\(992\) | 4.07715e14 | + | 1.92998e13i | 0.424423 | + | 0.0200907i | ||||
\(993\) | 2.29807e15i | 2.38022i | ||||||||
\(994\) | −1.61112e15 | − | 1.52420e13i | −1.66034 | − | 0.0157076i | ||||
\(995\) | 3.51917e14 | + | 3.62067e14i | 0.360848 | + | 0.371256i | ||||
\(996\) | 2.73108e15 | + | 5.16795e13i | 2.78636 | + | 0.0527256i | ||||
\(997\) | 4.10229e14i | 0.416438i | 0.978082 | + | 0.208219i | \(0.0667667\pi\) | ||||
−0.978082 | + | 0.208219i | \(0.933233\pi\) | |||||||
\(998\) | −7.70046e14 | − | 7.28503e12i | −0.777793 | − | 0.00735832i | ||||
\(999\) | 4.23699e14i | 0.425824i |
(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.19.12 | yes | 24 | |
4.3 | odd | 2 | inner | 20.11.d.d.19.14 | yes | 24 | |
5.2 | odd | 4 | 100.11.b.h.51.1 | 24 | |||
5.3 | odd | 4 | 100.11.b.h.51.24 | 24 | |||
5.4 | even | 2 | inner | 20.11.d.d.19.13 | yes | 24 | |
20.3 | even | 4 | 100.11.b.h.51.23 | 24 | |||
20.7 | even | 4 | 100.11.b.h.51.2 | 24 | |||
20.19 | odd | 2 | inner | 20.11.d.d.19.11 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.11.d.d.19.11 | ✓ | 24 | 20.19 | odd | 2 | inner | |
20.11.d.d.19.12 | yes | 24 | 1.1 | even | 1 | trivial | |
20.11.d.d.19.13 | yes | 24 | 5.4 | even | 2 | inner | |
20.11.d.d.19.14 | yes | 24 | 4.3 | odd | 2 | inner | |
100.11.b.h.51.1 | 24 | 5.2 | odd | 4 | |||
100.11.b.h.51.2 | 24 | 20.7 | even | 4 | |||
100.11.b.h.51.23 | 24 | 20.3 | even | 4 | |||
100.11.b.h.51.24 | 24 | 5.3 | odd | 4 |