Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,22,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(58.6902423003\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.20 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.22.c.b.20.19 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1077.74i | 0.744216i | 0.928189 | + | 0.372108i | \(0.121365\pi\) | ||||
−0.928189 | + | 0.372108i | \(0.878635\pi\) | |||||||
\(3\) | 64855.1 | + | 79083.3i | 0.634119 | + | 0.773235i | ||||
\(4\) | 935630. | 0.446143 | ||||||||
\(5\) | −7.14030e6 | −0.326988 | −0.163494 | − | 0.986544i | \(-0.552276\pi\) | ||||
−0.163494 | + | 0.986544i | \(0.552276\pi\) | |||||||
\(6\) | −8.52312e7 | + | 6.98969e7i | −0.575454 | + | 0.471921i | ||||
\(7\) | −3.76236e8 | − | 6.45749e8i | −0.503421 | − | 0.864041i | ||||
\(8\) | 3.26855e9i | 1.07624i | ||||||||
\(9\) | −2.04799e9 | + | 1.02579e10i | −0.195786 | + | 0.980647i | ||||
\(10\) | − | 7.69538e9i | − | 0.243349i | ||||||
\(11\) | 6.21657e8i | 0.00722649i | 0.999993 | + | 0.00361324i | \(0.00115013\pi\) | ||||
−0.999993 | + | 0.00361324i | \(0.998850\pi\) | |||||||
\(12\) | 6.06803e10 | + | 7.39927e10i | 0.282908 | + | 0.344974i | ||||
\(13\) | 3.37753e11i | 0.679508i | 0.940514 | + | 0.339754i | \(0.110344\pi\) | ||||
−0.940514 | + | 0.339754i | \(0.889656\pi\) | |||||||
\(14\) | 6.95949e11 | − | 4.05485e11i | 0.643033 | − | 0.374654i | ||||
\(15\) | −4.63085e11 | − | 5.64679e11i | −0.207349 | − | 0.252838i | ||||
\(16\) | −1.56049e12 | −0.354813 | ||||||||
\(17\) | −6.87345e12 | −0.826915 | −0.413458 | − | 0.910523i | \(-0.635679\pi\) | ||||
−0.413458 | + | 0.910523i | \(0.635679\pi\) | |||||||
\(18\) | −1.10554e13 | − | 2.20720e12i | −0.729813 | − | 0.145707i | ||||
\(19\) | − | 1.17334e13i | − | 0.439048i | −0.975607 | − | 0.219524i | \(-0.929550\pi\) | ||
0.975607 | − | 0.219524i | \(-0.0704504\pi\) | |||||||
\(20\) | −6.68068e12 | −0.145883 | ||||||||
\(21\) | 2.66672e13 | − | 7.16341e13i | 0.348878 | − | 0.937168i | ||||
\(22\) | −6.69984e11 | −0.00537807 | ||||||||
\(23\) | − | 8.43774e13i | − | 0.424701i | −0.977194 | − | 0.212351i | \(-0.931888\pi\) | ||
0.977194 | − | 0.212351i | \(-0.0681119\pi\) | |||||||
\(24\) | −2.58488e14 | + | 2.11982e14i | −0.832189 | + | 0.682466i | ||||
\(25\) | −4.25853e14 | −0.893079 | ||||||||
\(26\) | −3.64010e14 | −0.505700 | ||||||||
\(27\) | −9.44052e14 | + | 5.03316e14i | −0.882422 | + | 0.470458i | ||||
\(28\) | −3.52018e14 | − | 6.04182e14i | −0.224598 | − | 0.385486i | ||||
\(29\) | 6.05365e14i | 0.267201i | 0.991035 | + | 0.133601i | \(0.0426539\pi\) | ||||
−0.991035 | + | 0.133601i | \(0.957346\pi\) | |||||||
\(30\) | 6.08576e14 | − | 4.99085e14i | 0.188166 | − | 0.154312i | ||||
\(31\) | − | 1.22561e15i | − | 0.268568i | −0.990943 | − | 0.134284i | \(-0.957127\pi\) | ||
0.990943 | − | 0.134284i | \(-0.0428734\pi\) | |||||||
\(32\) | 5.17285e15i | 0.812185i | ||||||||
\(33\) | −4.91627e13 | + | 4.03176e13i | −0.00558778 | + | 0.00458245i | ||||
\(34\) | − | 7.40779e15i | − | 0.615403i | ||||||
\(35\) | 2.68644e15 | + | 4.61084e15i | 0.164612 | + | 0.282531i | ||||
\(36\) | −1.91616e15 | + | 9.59760e15i | −0.0873485 | + | 0.437509i | ||||
\(37\) | −3.62083e16 | −1.23791 | −0.618957 | − | 0.785425i | \(-0.712444\pi\) | ||||
−0.618957 | + | 0.785425i | \(0.712444\pi\) | |||||||
\(38\) | 1.26456e16 | 0.326746 | ||||||||
\(39\) | −2.67107e16 | + | 2.19050e16i | −0.525420 | + | 0.430889i | ||||
\(40\) | − | 2.33384e16i | − | 0.351918i | ||||||
\(41\) | −1.58503e16 | −0.184420 | −0.0922100 | − | 0.995740i | \(-0.529393\pi\) | ||||
−0.0922100 | + | 0.995740i | \(0.529393\pi\) | |||||||
\(42\) | 7.72029e16 | + | 2.87402e16i | 0.697455 | + | 0.259641i | ||||
\(43\) | −2.84588e16 | −0.200816 | −0.100408 | − | 0.994946i | \(-0.532015\pi\) | ||||
−0.100408 | + | 0.994946i | \(0.532015\pi\) | |||||||
\(44\) | 5.81640e14i | 0.00322405i | ||||||||
\(45\) | 1.46233e16 | − | 7.32446e16i | 0.0640196 | − | 0.320659i | ||||
\(46\) | 9.09368e16 | 0.316069 | ||||||||
\(47\) | −2.36994e17 | −0.657219 | −0.328609 | − | 0.944466i | \(-0.606580\pi\) | ||||
−0.328609 | + | 0.944466i | \(0.606580\pi\) | |||||||
\(48\) | −1.01205e17 | − | 1.23408e17i | −0.224994 | − | 0.274354i | ||||
\(49\) | −2.75438e17 | + | 4.85909e17i | −0.493134 | + | 0.869953i | ||||
\(50\) | − | 4.58959e17i | − | 0.664643i | ||||||
\(51\) | −4.45778e17 | − | 5.43575e17i | −0.524363 | − | 0.639400i | ||||
\(52\) | 3.16012e17i | 0.303158i | ||||||||
\(53\) | − | 6.88418e17i | − | 0.540699i | −0.962762 | − | 0.270350i | \(-0.912861\pi\) | ||
0.962762 | − | 0.270350i | \(-0.0871393\pi\) | |||||||
\(54\) | −5.42443e17 | − | 1.01744e18i | −0.350122 | − | 0.656713i | ||||
\(55\) | − | 4.43881e15i | − | 0.00236297i | ||||||
\(56\) | 2.11066e18 | − | 1.22975e18i | 0.929918 | − | 0.541803i | ||||
\(57\) | 9.27917e17 | − | 7.60972e17i | 0.339487 | − | 0.278408i | ||||
\(58\) | −6.52426e17 | −0.198855 | ||||||||
\(59\) | 4.19426e18 | 1.06834 | 0.534170 | − | 0.845377i | \(-0.320624\pi\) | ||||
0.534170 | + | 0.845377i | \(0.320624\pi\) | |||||||
\(60\) | −4.33276e17 | − | 5.28330e17i | −0.0925074 | − | 0.112802i | ||||
\(61\) | − | 5.56709e18i | − | 0.999229i | −0.866248 | − | 0.499615i | \(-0.833475\pi\) | ||
0.866248 | − | 0.499615i | \(-0.166525\pi\) | |||||||
\(62\) | 1.32089e18 | 0.199873 | ||||||||
\(63\) | 7.39457e18 | − | 2.53691e18i | 0.945882 | − | 0.324511i | ||||
\(64\) | −8.84756e18 | −0.959254 | ||||||||
\(65\) | − | 2.41166e18i | − | 0.222191i | ||||||
\(66\) | −4.34519e16 | − | 5.29845e16i | −0.00341033 | − | 0.00415851i | ||||
\(67\) | −1.57639e19 | −1.05652 | −0.528261 | − | 0.849082i | \(-0.677156\pi\) | ||||
−0.528261 | + | 0.849082i | \(0.677156\pi\) | |||||||
\(68\) | −6.43100e18 | −0.368922 | ||||||||
\(69\) | 6.67284e18 | − | 5.47230e18i | 0.328394 | − | 0.269311i | ||||
\(70\) | −4.96929e18 | + | 2.89528e18i | −0.210264 | + | 0.122507i | ||||
\(71\) | − | 7.43701e18i | − | 0.271135i | −0.990768 | − | 0.135567i | \(-0.956714\pi\) | ||
0.990768 | − | 0.135567i | \(-0.0432857\pi\) | |||||||
\(72\) | −3.35285e19 | − | 6.69396e18i | −1.05541 | − | 0.210713i | ||||
\(73\) | − | 4.27354e19i | − | 1.16385i | −0.813242 | − | 0.581926i | \(-0.802299\pi\) | ||
0.813242 | − | 0.581926i | \(-0.197701\pi\) | |||||||
\(74\) | − | 3.90231e19i | − | 0.921275i | ||||||
\(75\) | −2.76187e19 | − | 3.36779e19i | −0.566318 | − | 0.690560i | ||||
\(76\) | − | 1.09781e19i | − | 0.195878i | ||||||
\(77\) | 4.01434e17 | − | 2.33890e17i | 0.00624398 | − | 0.00363797i | ||||
\(78\) | −2.36079e19 | − | 2.87871e19i | −0.320674 | − | 0.391026i | ||||
\(79\) | −1.56226e20 | −1.85639 | −0.928196 | − | 0.372092i | \(-0.878641\pi\) | ||||
−0.928196 | + | 0.372092i | \(0.878641\pi\) | |||||||
\(80\) | 1.11423e19 | 0.116020 | ||||||||
\(81\) | −1.01030e20 | − | 4.20162e19i | −0.923336 | − | 0.383994i | ||||
\(82\) | − | 1.70825e19i | − | 0.137248i | ||||||
\(83\) | 1.29172e20 | 0.913793 | 0.456897 | − | 0.889520i | \(-0.348961\pi\) | ||||
0.456897 | + | 0.889520i | \(0.348961\pi\) | |||||||
\(84\) | 2.49506e19 | − | 6.70230e19i | 0.155650 | − | 0.418111i | ||||
\(85\) | 4.90785e19 | 0.270391 | ||||||||
\(86\) | − | 3.06712e19i | − | 0.149450i | ||||||
\(87\) | −4.78743e19 | + | 3.92610e19i | −0.206609 | + | 0.169437i | ||||
\(88\) | −2.03191e18 | −0.00777745 | ||||||||
\(89\) | 4.94133e20 | 1.67977 | 0.839883 | − | 0.542767i | \(-0.182623\pi\) | ||||
0.839883 | + | 0.542767i | \(0.182623\pi\) | |||||||
\(90\) | 7.89385e19 | + | 1.57601e19i | 0.238640 | + | 0.0476444i | ||||
\(91\) | 2.18104e20 | − | 1.27075e20i | 0.587123 | − | 0.342079i | ||||
\(92\) | − | 7.89460e19i | − | 0.189478i | ||||||
\(93\) | 9.69253e19 | − | 7.94870e19i | 0.207666 | − | 0.170304i | ||||
\(94\) | − | 2.55418e20i | − | 0.489112i | ||||||
\(95\) | 8.37801e19i | 0.143563i | ||||||||
\(96\) | −4.09086e20 | + | 3.35485e20i | −0.628010 | + | 0.515022i | ||||
\(97\) | 5.62341e19i | 0.0774277i | 0.999250 | + | 0.0387139i | \(0.0123261\pi\) | ||||
−0.999250 | + | 0.0387139i | \(0.987674\pi\) | |||||||
\(98\) | −5.23683e20 | − | 2.96851e20i | −0.647433 | − | 0.366998i | ||||
\(99\) | −6.37690e18 | − | 1.27315e18i | −0.00708663 | − | 0.00141485i | ||||
\(100\) | −3.98441e20 | −0.398441 | ||||||||
\(101\) | 7.78423e20 | 0.701199 | 0.350599 | − | 0.936526i | \(-0.385978\pi\) | ||||
0.350599 | + | 0.936526i | \(0.385978\pi\) | |||||||
\(102\) | 5.85832e20 | − | 4.80433e20i | 0.475852 | − | 0.390239i | ||||
\(103\) | 1.44000e21i | 1.05578i | 0.849314 | + | 0.527888i | \(0.177016\pi\) | ||||
−0.849314 | + | 0.527888i | \(0.822984\pi\) | |||||||
\(104\) | −1.10396e21 | −0.731315 | ||||||||
\(105\) | −1.90411e20 | + | 5.11489e20i | −0.114079 | + | 0.306442i | ||||
\(106\) | 7.41936e20 | 0.402397 | ||||||||
\(107\) | 2.60763e21i | 1.28149i | 0.767752 | + | 0.640747i | \(0.221375\pi\) | ||||
−0.767752 | + | 0.640747i | \(0.778625\pi\) | |||||||
\(108\) | −8.83283e20 | + | 4.70917e20i | −0.393687 | + | 0.209892i | ||||
\(109\) | 1.47050e21 | 0.594957 | 0.297479 | − | 0.954728i | \(-0.403854\pi\) | ||||
0.297479 | + | 0.954728i | \(0.403854\pi\) | |||||||
\(110\) | 4.78389e18 | 0.00175856 | ||||||||
\(111\) | −2.34829e21 | − | 2.86347e21i | −0.784985 | − | 0.957199i | ||||
\(112\) | 5.87112e20 | + | 1.00768e21i | 0.178621 | + | 0.306573i | ||||
\(113\) | 6.05155e21i | 1.67704i | 0.544873 | + | 0.838519i | \(0.316578\pi\) | ||||
−0.544873 | + | 0.838519i | \(0.683422\pi\) | |||||||
\(114\) | 8.20129e20 | + | 1.00005e21i | 0.207196 | + | 0.252652i | ||||
\(115\) | 6.02480e20i | 0.138872i | ||||||||
\(116\) | 5.66397e20i | 0.119210i | ||||||||
\(117\) | −3.46464e21 | − | 6.91716e20i | −0.666357 | − | 0.133038i | ||||
\(118\) | 4.52032e21i | 0.795076i | ||||||||
\(119\) | 2.58604e21 | + | 4.43852e21i | 0.416287 | + | 0.714489i | ||||
\(120\) | 1.84568e21 | − | 1.51361e21i | 0.272115 | − | 0.223158i | ||||
\(121\) | 7.39986e21 | 0.999948 | ||||||||
\(122\) | 5.99987e21 | 0.743642 | ||||||||
\(123\) | −1.02798e21 | − | 1.25350e21i | −0.116944 | − | 0.142600i | ||||
\(124\) | − | 1.14672e21i | − | 0.119820i | ||||||
\(125\) | 6.44548e21 | 0.619014 | ||||||||
\(126\) | 2.73413e21 | + | 7.96942e21i | 0.241506 | + | 0.703940i | ||||
\(127\) | −7.21609e21 | −0.586628 | −0.293314 | − | 0.956016i | \(-0.594758\pi\) | ||||
−0.293314 | + | 0.956016i | \(0.594758\pi\) | |||||||
\(128\) | 1.31288e21i | 0.0982926i | ||||||||
\(129\) | −1.84570e21 | − | 2.25062e21i | −0.127341 | − | 0.155278i | ||||
\(130\) | 2.59914e21 | 0.165358 | ||||||||
\(131\) | −1.65885e22 | −0.973778 | −0.486889 | − | 0.873464i | \(-0.661868\pi\) | ||||
−0.486889 | + | 0.873464i | \(0.661868\pi\) | |||||||
\(132\) | −4.59980e19 | + | 3.77223e19i | −0.00249295 | + | 0.00204443i | ||||
\(133\) | −7.57684e21 | + | 4.41454e21i | −0.379355 | + | 0.221026i | ||||
\(134\) | − | 1.69894e22i | − | 0.786281i | ||||||
\(135\) | 6.74082e21 | − | 3.59383e21i | 0.288541 | − | 0.153834i | ||||
\(136\) | − | 2.24662e22i | − | 0.889961i | ||||||
\(137\) | − | 4.04119e22i | − | 1.48232i | −0.671327 | − | 0.741161i | \(-0.734275\pi\) | ||
0.671327 | − | 0.741161i | \(-0.265725\pi\) | |||||||
\(138\) | 5.89771e21 | + | 7.19159e21i | 0.200426 | + | 0.244396i | ||||
\(139\) | 7.25523e21i | 0.228558i | 0.993449 | + | 0.114279i | \(0.0364557\pi\) | ||||
−0.993449 | + | 0.114279i | \(0.963544\pi\) | |||||||
\(140\) | 2.51351e21 | + | 4.31404e21i | 0.0734407 | + | 0.126049i | ||||
\(141\) | −1.53703e22 | − | 1.87423e22i | −0.416755 | − | 0.508185i | ||||
\(142\) | 8.01515e21 | 0.201783 | ||||||||
\(143\) | −2.09967e20 | −0.00491046 | ||||||||
\(144\) | 3.19586e21 | − | 1.60073e22i | 0.0694675 | − | 0.347947i | ||||
\(145\) | − | 4.32249e21i | − | 0.0873715i | ||||||
\(146\) | 4.60576e22 | 0.866157 | ||||||||
\(147\) | −5.62908e22 | + | 9.73108e21i | −0.985385 | + | 0.170345i | ||||
\(148\) | −3.38776e22 | −0.552286 | ||||||||
\(149\) | 5.74877e22i | 0.873210i | 0.899653 | + | 0.436605i | \(0.143819\pi\) | ||||
−0.899653 | + | 0.436605i | \(0.856181\pi\) | |||||||
\(150\) | 3.62960e22 | − | 2.97658e22i | 0.513926 | − | 0.421463i | ||||
\(151\) | −1.09733e23 | −1.44903 | −0.724515 | − | 0.689259i | \(-0.757936\pi\) | ||||
−0.724515 | + | 0.689259i | \(0.757936\pi\) | |||||||
\(152\) | 3.83512e22 | 0.472522 | ||||||||
\(153\) | 1.40768e22 | − | 7.05072e22i | 0.161898 | − | 0.810912i | ||||
\(154\) | 2.52072e20 | + | 4.32642e20i | 0.00270743 | + | 0.00464687i | ||||
\(155\) | 8.75122e21i | 0.0878184i | ||||||||
\(156\) | −2.49913e22 | + | 2.04950e22i | −0.234412 | + | 0.192238i | ||||
\(157\) | 7.99062e21i | 0.0700865i | 0.999386 | + | 0.0350432i | \(0.0111569\pi\) | ||||
−0.999386 | + | 0.0350432i | \(0.988843\pi\) | |||||||
\(158\) | − | 1.68371e23i | − | 1.38156i | ||||||
\(159\) | 5.44424e22 | − | 4.46474e22i | 0.418088 | − | 0.342868i | ||||
\(160\) | − | 3.69357e22i | − | 0.265574i | ||||||
\(161\) | −5.44866e22 | + | 3.17458e22i | −0.366959 | + | 0.213804i | ||||
\(162\) | 4.52825e22 | − | 1.08885e23i | 0.285774 | − | 0.687161i | ||||
\(163\) | −1.71233e23 | −1.01302 | −0.506510 | − | 0.862234i | \(-0.669065\pi\) | ||||
−0.506510 | + | 0.862234i | \(0.669065\pi\) | |||||||
\(164\) | −1.48300e22 | −0.0822777 | ||||||||
\(165\) | 3.51036e20 | − | 2.87880e20i | 0.00182713 | − | 0.00149841i | ||||
\(166\) | 1.39214e23i | 0.680059i | ||||||||
\(167\) | −3.54755e23 | −1.62707 | −0.813533 | − | 0.581519i | \(-0.802459\pi\) | ||||
−0.813533 | + | 0.581519i | \(0.802459\pi\) | |||||||
\(168\) | 2.34140e23 | + | 8.71629e22i | 1.00862 | + | 0.375478i | ||||
\(169\) | 1.32987e23 | 0.538269 | ||||||||
\(170\) | 5.28938e22i | 0.201229i | ||||||||
\(171\) | 1.20360e23 | + | 2.40299e22i | 0.430551 | + | 0.0859594i | ||||
\(172\) | −2.66269e22 | −0.0895926 | ||||||||
\(173\) | −1.34777e23 | −0.426709 | −0.213354 | − | 0.976975i | \(-0.568439\pi\) | ||||
−0.213354 | + | 0.976975i | \(0.568439\pi\) | |||||||
\(174\) | −4.23131e22 | − | 5.15960e22i | −0.126098 | − | 0.153762i | ||||
\(175\) | 1.60222e23 | + | 2.74994e23i | 0.449595 | + | 0.771657i | ||||
\(176\) | − | 9.70087e20i | − | 0.00256406i | ||||||
\(177\) | 2.72019e23 | + | 3.31696e23i | 0.677455 | + | 0.826079i | ||||
\(178\) | 5.32547e23i | 1.25011i | ||||||||
\(179\) | − | 6.29190e23i | − | 1.39260i | −0.717753 | − | 0.696298i | \(-0.754829\pi\) | ||
0.717753 | − | 0.696298i | \(-0.245171\pi\) | |||||||
\(180\) | 1.36820e22 | − | 6.85298e22i | 0.0285619 | − | 0.143060i | ||||
\(181\) | 8.74990e22i | 0.172337i | 0.996281 | + | 0.0861684i | \(0.0274623\pi\) | ||||
−0.996281 | + | 0.0861684i | \(0.972538\pi\) | |||||||
\(182\) | 1.36954e23 | + | 2.35059e23i | 0.254580 | + | 0.436946i | ||||
\(183\) | 4.40264e23 | − | 3.61054e23i | 0.772639 | − | 0.633630i | ||||
\(184\) | 2.75792e23 | 0.457082 | ||||||||
\(185\) | 2.58538e23 | 0.404783 | ||||||||
\(186\) | 8.56663e22 | + | 1.04460e23i | 0.126743 | + | 0.154549i | ||||
\(187\) | − | 4.27293e21i | − | 0.00597569i | ||||||
\(188\) | −2.21739e23 | −0.293213 | ||||||||
\(189\) | 6.80203e23 | + | 4.20255e23i | 0.850725 | + | 0.525611i | ||||
\(190\) | −9.02931e22 | −0.106842 | ||||||||
\(191\) | 1.61611e24i | 1.80976i | 0.425668 | + | 0.904879i | \(0.360039\pi\) | ||||
−0.425668 | + | 0.904879i | \(0.639961\pi\) | |||||||
\(192\) | −5.73809e23 | − | 6.99694e23i | −0.608281 | − | 0.741729i | ||||
\(193\) | 1.92008e23 | 0.192738 | 0.0963691 | − | 0.995346i | \(-0.469277\pi\) | ||||
0.0963691 | + | 0.995346i | \(0.469277\pi\) | |||||||
\(194\) | −6.06057e22 | −0.0576229 | ||||||||
\(195\) | 1.90722e23 | − | 1.56408e23i | 0.171806 | − | 0.140895i | ||||
\(196\) | −2.57708e23 | + | 4.54631e23i | −0.220008 | + | 0.388123i | ||||
\(197\) | 1.23814e24i | 1.00202i | 0.865443 | + | 0.501008i | \(0.167037\pi\) | ||||
−0.865443 | + | 0.501008i | \(0.832963\pi\) | |||||||
\(198\) | 1.37212e21 | − | 6.87263e21i | 0.00105295 | − | 0.00527398i | ||||
\(199\) | 1.90069e24i | 1.38342i | 0.722176 | + | 0.691710i | \(0.243142\pi\) | ||||
−0.722176 | + | 0.691710i | \(0.756858\pi\) | |||||||
\(200\) | − | 1.39192e24i | − | 0.961169i | ||||||
\(201\) | −1.02237e24 | − | 1.24666e24i | −0.669961 | − | 0.816941i | ||||
\(202\) | 8.38937e23i | 0.521843i | ||||||||
\(203\) | 3.90914e23 | − | 2.27760e23i | 0.230873 | − | 0.134515i | ||||
\(204\) | −4.17083e23 | − | 5.08585e23i | −0.233941 | − | 0.285264i | ||||
\(205\) | 1.13176e23 | 0.0603031 | ||||||||
\(206\) | −1.55195e24 | −0.785725 | ||||||||
\(207\) | 8.65535e23 | + | 1.72804e23i | 0.416482 | + | 0.0831506i | ||||
\(208\) | − | 5.27060e23i | − | 0.241099i | ||||||
\(209\) | 7.29415e21 | 0.00317277 | ||||||||
\(210\) | −5.51252e23 | − | 2.05214e23i | −0.228059 | − | 0.0848993i | ||||
\(211\) | −2.81290e24 | −1.10710 | −0.553552 | − | 0.832815i | \(-0.686728\pi\) | ||||
−0.553552 | + | 0.832815i | \(0.686728\pi\) | |||||||
\(212\) | − | 6.44105e23i | − | 0.241229i | ||||||
\(213\) | 5.88143e23 | − | 4.82328e23i | 0.209651 | − | 0.171932i | ||||
\(214\) | −2.81035e24 | −0.953708 | ||||||||
\(215\) | 2.03204e23 | 0.0656643 | ||||||||
\(216\) | −1.64511e24 | − | 3.08568e24i | −0.506327 | − | 0.949700i | ||||
\(217\) | −7.91436e23 | + | 4.61119e23i | −0.232054 | + | 0.135203i | ||||
\(218\) | 1.58481e24i | 0.442777i | ||||||||
\(219\) | 3.37966e24 | − | 2.77161e24i | 0.899931 | − | 0.738021i | ||||
\(220\) | − | 4.15309e21i | − | 0.00105422i | ||||||
\(221\) | − | 2.32153e24i | − | 0.561896i | ||||||
\(222\) | 3.08608e24 | − | 2.53085e24i | 0.712362 | − | 0.584198i | ||||
\(223\) | − | 2.45705e23i | − | 0.0541021i | −0.999634 | − | 0.0270510i | \(-0.991388\pi\) | ||
0.999634 | − | 0.0270510i | \(-0.00861166\pi\) | |||||||
\(224\) | 3.34036e24 | − | 1.94621e24i | 0.701761 | − | 0.408871i | ||||
\(225\) | 8.72143e23 | − | 4.36836e24i | 0.174852 | − | 0.875795i | ||||
\(226\) | −6.52199e24 | −1.24808 | ||||||||
\(227\) | 1.08437e25 | 1.98109 | 0.990545 | − | 0.137190i | \(-0.0438070\pi\) | ||||
0.990545 | + | 0.137190i | \(0.0438070\pi\) | |||||||
\(228\) | 8.68187e23 | − | 7.11988e23i | 0.151460 | − | 0.124210i | ||||
\(229\) | 7.03610e24i | 1.17236i | 0.810183 | + | 0.586178i | \(0.199368\pi\) | ||||
−0.810183 | + | 0.586178i | \(0.800632\pi\) | |||||||
\(230\) | −6.49316e23 | −0.103351 | ||||||||
\(231\) | 4.45318e22 | + | 1.65778e22i | 0.00677243 | + | 0.00252117i | ||||
\(232\) | −1.97866e24 | −0.287573 | ||||||||
\(233\) | − | 3.24912e24i | − | 0.451366i | −0.974201 | − | 0.225683i | \(-0.927539\pi\) | ||
0.974201 | − | 0.225683i | \(-0.0724613\pi\) | |||||||
\(234\) | 7.45489e23 | − | 3.73398e24i | 0.0990091 | − | 0.495913i | ||||
\(235\) | 1.69221e24 | 0.214902 | ||||||||
\(236\) | 3.92428e24 | 0.476633 | ||||||||
\(237\) | −1.01321e25 | − | 1.23549e25i | −1.17717 | − | 1.43543i | ||||
\(238\) | −4.78357e24 | + | 2.78708e24i | −0.531734 | + | 0.309807i | ||||
\(239\) | 1.00716e24i | 0.107132i | 0.998564 | + | 0.0535662i | \(0.0170588\pi\) | ||||
−0.998564 | + | 0.0535662i | \(0.982941\pi\) | |||||||
\(240\) | 7.22637e23 | + | 8.81173e23i | 0.0735703 | + | 0.0897105i | ||||
\(241\) | 1.65145e25i | 1.60949i | 0.593623 | + | 0.804743i | \(0.297697\pi\) | ||||
−0.593623 | + | 0.804743i | \(0.702303\pi\) | |||||||
\(242\) | 7.97513e24i | 0.744177i | ||||||||
\(243\) | −3.22956e24 | − | 1.07148e25i | −0.288587 | − | 0.957454i | ||||
\(244\) | − | 5.20874e24i | − | 0.445799i | ||||||
\(245\) | 1.96671e24 | − | 3.46953e24i | 0.161249 | − | 0.284464i | ||||
\(246\) | 1.35094e24 | − | 1.10789e24i | 0.106125 | − | 0.0870318i | ||||
\(247\) | 3.96300e24 | 0.298336 | ||||||||
\(248\) | 4.00596e24 | 0.289044 | ||||||||
\(249\) | 8.37745e24 | + | 1.02153e25i | 0.579454 | + | 0.706577i | ||||
\(250\) | 6.94655e24i | 0.460680i | ||||||||
\(251\) | −2.59270e25 | −1.64884 | −0.824418 | − | 0.565981i | \(-0.808498\pi\) | ||||
−0.824418 | + | 0.565981i | \(0.808498\pi\) | |||||||
\(252\) | 6.91857e24 | − | 2.37361e24i | 0.421999 | − | 0.144778i | ||||
\(253\) | 5.24537e22 | 0.00306910 | ||||||||
\(254\) | − | 7.77707e24i | − | 0.436578i | ||||||
\(255\) | 3.18299e24 | + | 3.88129e24i | 0.171460 | + | 0.209076i | ||||
\(256\) | −1.99696e25 | −1.03240 | ||||||||
\(257\) | −2.85855e25 | −1.41856 | −0.709279 | − | 0.704927i | \(-0.750980\pi\) | ||||
−0.709279 | + | 0.704927i | \(0.750980\pi\) | |||||||
\(258\) | 2.42558e24 | − | 1.98918e24i | 0.115560 | − | 0.0947693i | ||||
\(259\) | 1.36229e25 | + | 2.33815e25i | 0.623192 | + | 1.06961i | ||||
\(260\) | − | 2.25642e24i | − | 0.0991288i | ||||||
\(261\) | −6.20978e24 | − | 1.23978e24i | −0.262030 | − | 0.0523142i | ||||
\(262\) | − | 1.78781e25i | − | 0.724701i | ||||||
\(263\) | 4.87018e25i | 1.89675i | 0.317153 | + | 0.948374i | \(0.397273\pi\) | ||||
−0.317153 | + | 0.948374i | \(0.602727\pi\) | |||||||
\(264\) | −1.31780e23 | − | 1.60691e23i | −0.00493183 | − | 0.00601380i | ||||
\(265\) | 4.91551e24i | 0.176802i | ||||||||
\(266\) | −4.75772e24 | − | 8.16586e24i | −0.164491 | − | 0.282322i | ||||
\(267\) | 3.20471e25 | + | 3.90777e25i | 1.06517 | + | 1.29886i | ||||
\(268\) | −1.47492e25 | −0.471360 | ||||||||
\(269\) | 1.71594e25 | 0.527355 | 0.263678 | − | 0.964611i | \(-0.415064\pi\) | ||||
0.263678 | + | 0.964611i | \(0.415064\pi\) | |||||||
\(270\) | 3.87321e24 | + | 7.26484e24i | 0.114486 | + | 0.214737i | ||||
\(271\) | − | 5.72937e24i | − | 0.162903i | −0.996677 | − | 0.0814515i | \(-0.974044\pi\) | ||
0.996677 | − | 0.0814515i | \(-0.0259556\pi\) | |||||||
\(272\) | 1.07259e25 | 0.293401 | ||||||||
\(273\) | 2.41947e25 | + | 9.00692e24i | 0.636813 | + | 0.237066i | ||||
\(274\) | 4.35535e25 | 1.10317 | ||||||||
\(275\) | − | 2.64734e23i | − | 0.00645383i | ||||||
\(276\) | 6.24331e24 | − | 5.12005e24i | 0.146511 | − | 0.120151i | ||||
\(277\) | 6.39436e25 | 1.44464 | 0.722320 | − | 0.691559i | \(-0.243076\pi\) | ||||
0.722320 | + | 0.691559i | \(0.243076\pi\) | |||||||
\(278\) | −7.81925e24 | −0.170096 | ||||||||
\(279\) | 1.25722e25 | + | 2.51004e24i | 0.263370 | + | 0.0525819i | ||||
\(280\) | −1.50708e25 | + | 8.78076e24i | −0.304072 | + | 0.177163i | ||||
\(281\) | − | 5.72925e24i | − | 0.111348i | −0.998449 | − | 0.0556739i | \(-0.982269\pi\) | ||
0.998449 | − | 0.0556739i | \(-0.0177307\pi\) | |||||||
\(282\) | 2.01993e25 | − | 1.65651e25i | 0.378199 | − | 0.310155i | ||||
\(283\) | 5.34411e25i | 0.964090i | 0.876147 | + | 0.482045i | \(0.160106\pi\) | ||||
−0.876147 | + | 0.482045i | \(0.839894\pi\) | |||||||
\(284\) | − | 6.95828e24i | − | 0.120965i | ||||||
\(285\) | −6.62561e24 | + | 5.43357e24i | −0.111008 | + | 0.0910361i | ||||
\(286\) | − | 2.26289e23i | − | 0.00365444i | ||||||
\(287\) | 5.96348e24 | + | 1.02353e25i | 0.0928409 | + | 0.159347i | ||||
\(288\) | −5.30626e25 | − | 1.05939e25i | −0.796466 | − | 0.159014i | ||||
\(289\) | −2.18476e25 | −0.316211 | ||||||||
\(290\) | 4.65851e24 | 0.0650232 | ||||||||
\(291\) | −4.44718e24 | + | 3.64707e24i | −0.0598699 | + | 0.0490984i | ||||
\(292\) | − | 3.99845e25i | − | 0.519244i | ||||||
\(293\) | −1.11333e26 | −1.39480 | −0.697402 | − | 0.716680i | \(-0.745661\pi\) | ||||
−0.697402 | + | 0.716680i | \(0.745661\pi\) | |||||||
\(294\) | −1.04876e25 | − | 6.06669e25i | −0.126773 | − | 0.733339i | ||||
\(295\) | −2.99483e25 | −0.349334 | ||||||||
\(296\) | − | 1.18349e26i | − | 1.33230i | ||||||
\(297\) | −3.12890e23 | − | 5.86876e23i | −0.00339976 | − | 0.00637682i | ||||
\(298\) | −6.19567e25 | −0.649857 | ||||||||
\(299\) | 2.84987e25 | 0.288588 | ||||||||
\(300\) | −2.58409e25 | − | 3.15100e25i | −0.252659 | − | 0.308089i | ||||
\(301\) | 1.07072e25 | + | 1.83773e25i | 0.101095 | + | 0.173513i | ||||
\(302\) | − | 1.18263e26i | − | 1.07839i | ||||||
\(303\) | 5.04847e25 | + | 6.15602e25i | 0.444643 | + | 0.542192i | ||||
\(304\) | 1.83098e25i | 0.155780i | ||||||||
\(305\) | 3.97507e25i | 0.326736i | ||||||||
\(306\) | 7.59884e25 | + | 1.51711e25i | 0.603493 | + | 0.120487i | ||||
\(307\) | − | 2.15589e26i | − | 1.65452i | −0.561817 | − | 0.827261i | \(-0.689898\pi\) | ||
0.561817 | − | 0.827261i | \(-0.310102\pi\) | |||||||
\(308\) | 3.75594e23 | − | 2.18834e23i | 0.00278571 | − | 0.00162305i | ||||
\(309\) | −1.13880e26 | + | 9.33914e25i | −0.816364 | + | 0.669488i | ||||
\(310\) | −9.43154e24 | −0.0653559 | ||||||||
\(311\) | 1.36821e26 | 0.916576 | 0.458288 | − | 0.888804i | \(-0.348463\pi\) | ||||
0.458288 | + | 0.888804i | \(0.348463\pi\) | |||||||
\(312\) | −7.15976e25 | − | 8.73051e25i | −0.463741 | − | 0.565479i | ||||
\(313\) | − | 1.05616e26i | − | 0.661474i | −0.943723 | − | 0.330737i | \(-0.892703\pi\) | ||
0.943723 | − | 0.330737i | \(-0.107297\pi\) | |||||||
\(314\) | −8.61181e24 | −0.0521595 | ||||||||
\(315\) | −5.27994e25 | + | 1.81143e25i | −0.309292 | + | 0.106111i | ||||
\(316\) | −1.46170e26 | −0.828216 | ||||||||
\(317\) | 1.49928e26i | 0.821790i | 0.911683 | + | 0.410895i | \(0.134784\pi\) | ||||
−0.911683 | + | 0.410895i | \(0.865216\pi\) | |||||||
\(318\) | 4.81183e25 | + | 5.86747e25i | 0.255168 | + | 0.311148i | ||||
\(319\) | −3.76329e23 | −0.00193093 | ||||||||
\(320\) | 6.31742e25 | 0.313664 | ||||||||
\(321\) | −2.06220e26 | + | 1.69118e26i | −0.990897 | + | 0.812620i | ||||
\(322\) | −3.42137e25 | − | 5.87224e25i | −0.159116 | − | 0.273097i | ||||
\(323\) | 8.06490e25i | 0.363055i | ||||||||
\(324\) | −9.45271e25 | − | 3.93116e25i | −0.411940 | − | 0.171316i | ||||
\(325\) | − | 1.43833e26i | − | 0.606854i | ||||||
\(326\) | − | 1.84545e26i | − | 0.753905i | ||||||
\(327\) | 9.53692e25 | + | 1.16292e26i | 0.377274 | + | 0.460042i | ||||
\(328\) | − | 5.18076e25i | − | 0.198481i | ||||||
\(329\) | 8.91658e25 | + | 1.53039e26i | 0.330858 | + | 0.567864i | ||||
\(330\) | 3.10259e23 | + | 3.78326e23i | 0.00111514 | + | 0.00135978i | ||||
\(331\) | 1.65667e26 | 0.576822 | 0.288411 | − | 0.957507i | \(-0.406873\pi\) | ||||
0.288411 | + | 0.957507i | \(0.406873\pi\) | |||||||
\(332\) | 1.20857e26 | 0.407682 | ||||||||
\(333\) | 7.41543e25 | − | 3.71422e26i | 0.242366 | − | 1.21396i | ||||
\(334\) | − | 3.82333e26i | − | 1.21089i | ||||||
\(335\) | 1.12559e26 | 0.345470 | ||||||||
\(336\) | −4.16137e25 | + | 1.11784e26i | −0.123787 | + | 0.332520i | ||||
\(337\) | 3.84946e26 | 1.10991 | 0.554953 | − | 0.831882i | \(-0.312736\pi\) | ||||
0.554953 | + | 0.831882i | \(0.312736\pi\) | |||||||
\(338\) | 1.43326e26i | 0.400588i | ||||||||
\(339\) | −4.78576e26 | + | 3.92474e26i | −1.29674 | + | 1.06344i | ||||
\(340\) | 4.59193e25 | 0.120633 | ||||||||
\(341\) | 7.61908e23 | 0.00194080 | ||||||||
\(342\) | −2.58980e25 | + | 1.29717e26i | −0.0639723 | + | 0.320423i | ||||
\(343\) | 4.17405e26 | − | 4.95254e24i | 0.999930 | − | 0.0118642i | ||||
\(344\) | − | 9.30190e25i | − | 0.216126i | ||||||
\(345\) | −4.76461e25 | + | 3.90739e25i | −0.107381 | + | 0.0880615i | ||||
\(346\) | − | 1.45254e26i | − | 0.317563i | ||||||
\(347\) | − | 2.57009e26i | − | 0.545116i | −0.962139 | − | 0.272558i | \(-0.912130\pi\) | ||
0.962139 | − | 0.272558i | \(-0.0878697\pi\) | |||||||
\(348\) | −4.47926e25 | + | 3.67337e25i | −0.0921773 | + | 0.0755933i | ||||
\(349\) | 6.70849e26i | 1.33955i | 0.742565 | + | 0.669773i | \(0.233609\pi\) | ||||
−0.742565 | + | 0.669773i | \(0.766391\pi\) | |||||||
\(350\) | −2.96372e26 | + | 1.72677e26i | −0.574279 | + | 0.334596i | ||||
\(351\) | −1.69997e26 | − | 3.18857e26i | −0.319680 | − | 0.599613i | ||||
\(352\) | −3.21573e24 | −0.00586924 | ||||||||
\(353\) | −5.19858e26 | −0.920980 | −0.460490 | − | 0.887665i | \(-0.652326\pi\) | ||||
−0.460490 | + | 0.887665i | \(0.652326\pi\) | |||||||
\(354\) | −3.57482e26 | + | 2.93166e26i | −0.614781 | + | 0.504173i | ||||
\(355\) | 5.31024e25i | 0.0886578i | ||||||||
\(356\) | 4.62326e26 | 0.749416 | ||||||||
\(357\) | −1.83295e26 | + | 4.92374e26i | −0.288493 | + | 0.774959i | ||||
\(358\) | 6.78103e26 | 1.03639 | ||||||||
\(359\) | 6.53139e26i | 0.969424i | 0.874674 | + | 0.484712i | \(0.161076\pi\) | ||||
−0.874674 | + | 0.484712i | \(0.838924\pi\) | |||||||
\(360\) | 2.39403e26 | + | 4.77969e25i | 0.345107 | + | 0.0689006i | ||||
\(361\) | 5.76536e26 | 0.807237 | ||||||||
\(362\) | −9.43011e25 | −0.128256 | ||||||||
\(363\) | 4.79919e26 | + | 5.85206e26i | 0.634086 | + | 0.773195i | ||||
\(364\) | 2.04065e26 | − | 1.18895e26i | 0.261941 | − | 0.152616i | ||||
\(365\) | 3.05144e26i | 0.380565i | ||||||||
\(366\) | 3.89122e26 | + | 4.74490e26i | 0.471558 | + | 0.575010i | ||||
\(367\) | − | 1.07354e27i | − | 1.26423i | −0.774874 | − | 0.632115i | \(-0.782187\pi\) | ||
0.774874 | − | 0.632115i | \(-0.217813\pi\) | |||||||
\(368\) | 1.31670e26i | 0.150690i | ||||||||
\(369\) | 3.24613e25 | − | 1.62591e26i | 0.0361069 | − | 0.180851i | ||||
\(370\) | 2.78637e26i | 0.301246i | ||||||||
\(371\) | −4.44546e26 | + | 2.59008e26i | −0.467187 | + | 0.272199i | ||||
\(372\) | 9.06862e25 | − | 7.43704e25i | 0.0926489 | − | 0.0759800i | ||||
\(373\) | −2.84476e26 | −0.282555 | −0.141278 | − | 0.989970i | \(-0.545121\pi\) | ||||
−0.141278 | + | 0.989970i | \(0.545121\pi\) | |||||||
\(374\) | 4.60510e24 | 0.00444721 | ||||||||
\(375\) | 4.18022e26 | + | 5.09730e26i | 0.392528 | + | 0.478643i | ||||
\(376\) | − | 7.74626e26i | − | 0.707326i | ||||||
\(377\) | −2.04464e26 | −0.181565 | ||||||||
\(378\) | −4.52926e26 | + | 7.33081e26i | −0.391168 | + | 0.633123i | ||||
\(379\) | −1.97170e26 | −0.165626 | −0.0828129 | − | 0.996565i | \(-0.526390\pi\) | ||||
−0.0828129 | + | 0.996565i | \(0.526390\pi\) | |||||||
\(380\) | 7.83871e25i | 0.0640497i | ||||||||
\(381\) | −4.68000e26 | − | 5.70673e26i | −0.371992 | − | 0.453602i | ||||
\(382\) | −1.74175e27 | −1.34685 | ||||||||
\(383\) | 1.51088e27 | 1.13669 | 0.568347 | − | 0.822789i | \(-0.307583\pi\) | ||||
0.568347 | + | 0.822789i | \(0.307583\pi\) | |||||||
\(384\) | −1.03827e26 | + | 8.51471e25i | −0.0760034 | + | 0.0623292i | ||||
\(385\) | −2.86636e24 | + | 1.67004e24i | −0.00204171 | + | 0.00118957i | ||||
\(386\) | 2.06935e26i | 0.143439i | ||||||||
\(387\) | 5.82834e25 | − | 2.91928e26i | 0.0393169 | − | 0.196929i | ||||
\(388\) | 5.26143e25i | 0.0345438i | ||||||||
\(389\) | − | 1.62998e27i | − | 1.04163i | −0.853671 | − | 0.520813i | \(-0.825629\pi\) | ||
0.853671 | − | 0.520813i | \(-0.174371\pi\) | |||||||
\(390\) | 1.68568e26 | + | 2.05549e26i | 0.104857 | + | 0.127861i | ||||
\(391\) | 5.79964e26i | 0.351192i | ||||||||
\(392\) | −1.58822e27 | − | 9.00283e26i | −0.936280 | − | 0.530732i | ||||
\(393\) | −1.07585e27 | − | 1.31188e27i | −0.617491 | − | 0.752959i | ||||
\(394\) | −1.33439e27 | −0.745715 | ||||||||
\(395\) | 1.11550e27 | 0.607017 | ||||||||
\(396\) | −5.96641e24 | − | 1.19119e24i | −0.00316165 | − | 0.000631223i | ||||
\(397\) | 2.20610e26i | 0.113848i | 0.998379 | + | 0.0569239i | \(0.0181292\pi\) | ||||
−0.998379 | + | 0.0569239i | \(0.981871\pi\) | |||||||
\(398\) | −2.04845e27 | −1.02956 | ||||||||
\(399\) | −8.40513e26 | − | 3.12897e26i | −0.411461 | − | 0.153174i | ||||
\(400\) | 6.64538e26 | 0.316876 | ||||||||
\(401\) | − | 1.71853e27i | − | 0.798256i | −0.916895 | − | 0.399128i | \(-0.869313\pi\) | ||
0.916895 | − | 0.399128i | \(-0.130687\pi\) | |||||||
\(402\) | 1.34358e27 | − | 1.10185e27i | 0.607980 | − | 0.498596i | ||||
\(403\) | 4.13954e26 | 0.182494 | ||||||||
\(404\) | 7.28315e26 | 0.312835 | ||||||||
\(405\) | 7.21388e26 | + | 3.00008e26i | 0.301919 | + | 0.125561i | ||||
\(406\) | 2.45466e26 | + | 4.21303e26i | 0.100108 | + | 0.171819i | ||||
\(407\) | − | 2.25091e25i | − | 0.00894577i | ||||||
\(408\) | 1.77670e27 | − | 1.45705e27i | 0.688150 | − | 0.564341i | ||||
\(409\) | − | 1.01469e27i | − | 0.383037i | −0.981489 | − | 0.191518i | \(-0.938659\pi\) | ||
0.981489 | − | 0.191518i | \(-0.0613411\pi\) | |||||||
\(410\) | 1.21974e26i | 0.0448785i | ||||||||
\(411\) | 3.19590e27 | − | 2.62091e27i | 1.14618 | − | 0.939969i | ||||
\(412\) | 1.34731e27i | 0.471027i | ||||||||
\(413\) | −1.57803e27 | − | 2.70844e27i | −0.537825 | − | 0.923090i | ||||
\(414\) | −1.86238e26 | + | 9.32822e26i | −0.0618820 | + | 0.309952i | ||||
\(415\) | −9.22326e26 | −0.298799 | ||||||||
\(416\) | −1.74715e27 | −0.551886 | ||||||||
\(417\) | −5.73768e26 | + | 4.70539e26i | −0.176729 | + | 0.144933i | ||||
\(418\) | 7.86120e24i | 0.00236123i | ||||||||
\(419\) | 3.27068e27 | 0.958056 | 0.479028 | − | 0.877800i | \(-0.340989\pi\) | ||||
0.479028 | + | 0.877800i | \(0.340989\pi\) | |||||||
\(420\) | −1.78155e26 | + | 4.78564e26i | −0.0508955 | + | 0.136717i | ||||
\(421\) | −4.01568e27 | −1.11892 | −0.559458 | − | 0.828859i | \(-0.688991\pi\) | ||||
−0.559458 | + | 0.828859i | \(0.688991\pi\) | |||||||
\(422\) | − | 3.03157e27i | − | 0.823924i | ||||||
\(423\) | 4.85361e26 | − | 2.43106e27i | 0.128674 | − | 0.644499i | ||||
\(424\) | 2.25013e27 | 0.581923 | ||||||||
\(425\) | 2.92708e27 | 0.738501 | ||||||||
\(426\) | 5.19823e26 | + | 6.33865e26i | 0.127954 | + | 0.156026i | ||||
\(427\) | −3.59494e27 | + | 2.09454e27i | −0.863375 | + | 0.503033i | ||||
\(428\) | 2.43978e27i | 0.571730i | ||||||||
\(429\) | −1.36174e25 | − | 1.66049e25i | −0.00311381 | − | 0.00379694i | ||||
\(430\) | 2.19001e26i | 0.0488684i | ||||||||
\(431\) | 6.37440e27i | 1.38812i | 0.719916 | + | 0.694061i | \(0.244180\pi\) | ||||
−0.719916 | + | 0.694061i | \(0.755820\pi\) | |||||||
\(432\) | 1.47318e27 | − | 7.85417e26i | 0.313095 | − | 0.166925i | ||||
\(433\) | 6.23955e27i | 1.29429i | 0.762369 | + | 0.647143i | \(0.224036\pi\) | ||||
−0.762369 | + | 0.647143i | \(0.775964\pi\) | |||||||
\(434\) | −4.96966e26 | − | 8.52962e26i | −0.100620 | − | 0.172698i | ||||
\(435\) | 3.41837e26 | − | 2.80335e26i | 0.0675587 | − | 0.0554039i | ||||
\(436\) | 1.37584e27 | 0.265436 | ||||||||
\(437\) | −9.90035e26 | −0.186464 | ||||||||
\(438\) | 2.98707e27 | + | 3.64239e27i | 0.549247 | + | 0.669743i | ||||
\(439\) | − | 8.26648e27i | − | 1.48403i | −0.670383 | − | 0.742015i | \(-0.733870\pi\) | ||
0.670383 | − | 0.742015i | \(-0.266130\pi\) | |||||||
\(440\) | 1.45085e25 | 0.00254313 | ||||||||
\(441\) | −4.42031e27 | − | 3.82056e27i | −0.756568 | − | 0.653915i | ||||
\(442\) | 2.50201e27 | 0.418172 | ||||||||
\(443\) | 1.94582e27i | 0.317587i | 0.987312 | + | 0.158794i | \(0.0507604\pi\) | ||||
−0.987312 | + | 0.158794i | \(0.949240\pi\) | |||||||
\(444\) | −2.19713e27 | − | 2.67915e27i | −0.350215 | − | 0.427047i | ||||
\(445\) | −3.52826e27 | −0.549263 | ||||||||
\(446\) | 2.64806e26 | 0.0402636 | ||||||||
\(447\) | −4.54632e27 | + | 3.72837e27i | −0.675197 | + | 0.553719i | ||||
\(448\) | 3.32877e27 | + | 5.71330e27i | 0.482909 | + | 0.828835i | ||||
\(449\) | 1.69203e27i | 0.239785i | 0.992787 | + | 0.119893i | \(0.0382550\pi\) | ||||
−0.992787 | + | 0.119893i | \(0.961745\pi\) | |||||||
\(450\) | 4.70796e27 | + | 9.39943e26i | 0.651780 | + | 0.130128i | ||||
\(451\) | − | 9.85347e24i | − | 0.00133271i | ||||||
\(452\) | 5.66201e27i | 0.748198i | ||||||||
\(453\) | −7.11671e27 | − | 8.67801e27i | −0.918858 | − | 1.12044i | ||||
\(454\) | 1.16866e28i | 1.47436i | ||||||||
\(455\) | −1.55733e27 | + | 9.07354e26i | −0.191982 | + | 0.111855i | ||||
\(456\) | 2.48727e27 | + | 3.03294e27i | 0.299635 | + | 0.365370i | ||||
\(457\) | −7.92917e27 | −0.933486 | −0.466743 | − | 0.884393i | \(-0.654573\pi\) | ||||
−0.466743 | + | 0.884393i | \(0.654573\pi\) | |||||||
\(458\) | −7.58308e27 | −0.872485 | ||||||||
\(459\) | 6.48890e27 | − | 3.45952e27i | 0.729689 | − | 0.389029i | ||||
\(460\) | 5.63698e26i | 0.0619568i | ||||||||
\(461\) | −5.88926e27 | −0.632705 | −0.316352 | − | 0.948642i | \(-0.602458\pi\) | ||||
−0.316352 | + | 0.948642i | \(0.602458\pi\) | |||||||
\(462\) | −1.78666e25 | + | 4.79937e25i | −0.00187629 | + | 0.00504015i | ||||
\(463\) | 2.89487e27 | 0.297186 | 0.148593 | − | 0.988898i | \(-0.452526\pi\) | ||||
0.148593 | + | 0.988898i | \(0.452526\pi\) | |||||||
\(464\) | − | 9.44664e26i | − | 0.0948066i | ||||||
\(465\) | −6.92076e26 | + | 5.67561e26i | −0.0679043 | + | 0.0556874i | ||||
\(466\) | 3.50170e27 | 0.335913 | ||||||||
\(467\) | 1.50197e28 | 1.40875 | 0.704374 | − | 0.709829i | \(-0.251228\pi\) | ||||
0.704374 | + | 0.709829i | \(0.251228\pi\) | |||||||
\(468\) | −3.24162e27 | − | 6.47190e26i | −0.297291 | − | 0.0593540i | ||||
\(469\) | 5.93096e27 | + | 1.01795e28i | 0.531876 | + | 0.912879i | ||||
\(470\) | 1.82376e27i | 0.159934i | ||||||||
\(471\) | −6.31925e26 | + | 5.18233e26i | −0.0541934 | + | 0.0444432i | ||||
\(472\) | 1.37092e28i | 1.14979i | ||||||||
\(473\) | − | 1.76916e25i | − | 0.00145119i | ||||||
\(474\) | 1.33154e28 | − | 1.09197e28i | 1.06827 | − | 0.876071i | ||||
\(475\) | 4.99671e27i | 0.392104i | ||||||||
\(476\) | 2.41958e27 | + | 4.15282e27i | 0.185723 | + | 0.318764i | ||||
\(477\) | 7.06173e27 | + | 1.40987e27i | 0.530235 | + | 0.105861i | ||||
\(478\) | −1.08546e27 | −0.0797297 | ||||||||
\(479\) | 2.05235e28 | 1.47478 | 0.737391 | − | 0.675467i | \(-0.236058\pi\) | ||||
0.737391 | + | 0.675467i | \(0.236058\pi\) | |||||||
\(480\) | 2.92100e27 | − | 2.39547e27i | 0.205351 | − | 0.168406i | ||||
\(481\) | − | 1.22295e28i | − | 0.841172i | ||||||
\(482\) | −1.77984e28 | −1.19780 | ||||||||
\(483\) | −6.04430e27 | − | 2.25010e27i | −0.398017 | − | 0.148169i | ||||
\(484\) | 6.92353e27 | 0.446120 | ||||||||
\(485\) | − | 4.01528e26i | − | 0.0253179i | ||||||
\(486\) | 1.15478e28 | − | 3.48062e27i | 0.712552 | − | 0.214771i | ||||
\(487\) | −1.39386e28 | −0.841712 | −0.420856 | − | 0.907127i | \(-0.638270\pi\) | ||||
−0.420856 | + | 0.907127i | \(0.638270\pi\) | |||||||
\(488\) | 1.81963e28 | 1.07541 | ||||||||
\(489\) | −1.11053e28 | − | 1.35417e28i | −0.642375 | − | 0.783302i | ||||
\(490\) | 3.73925e27 | + | 2.11960e27i | 0.211703 | + | 0.120004i | ||||
\(491\) | − | 2.14939e28i | − | 1.19113i | −0.803308 | − | 0.595564i | \(-0.796929\pi\) | ||
0.803308 | − | 0.595564i | \(-0.203071\pi\) | |||||||
\(492\) | −9.61804e26 | − | 1.17281e27i | −0.0521739 | − | 0.0636200i | ||||
\(493\) | − | 4.16095e27i | − | 0.220953i | ||||||
\(494\) | 4.27108e27i | 0.222027i | ||||||||
\(495\) | 4.55330e25 | + | 9.09065e24i | 0.00231724 | + | 0.000462637i | ||||
\(496\) | 1.91255e27i | 0.0952916i | ||||||||
\(497\) | −4.80244e27 | + | 2.79807e27i | −0.234272 | + | 0.136495i | ||||
\(498\) | −1.10095e28 | + | 9.02871e27i | −0.525846 | + | 0.431239i | ||||
\(499\) | −4.87093e27 | −0.227801 | −0.113901 | − | 0.993492i | \(-0.536335\pi\) | ||||
−0.113901 | + | 0.993492i | \(0.536335\pi\) | |||||||
\(500\) | 6.03058e27 | 0.276169 | ||||||||
\(501\) | −2.30076e28 | − | 2.80552e28i | −1.03175 | − | 1.25811i | ||||
\(502\) | − | 2.79425e28i | − | 1.22709i | ||||||
\(503\) | −3.80145e28 | −1.63488 | −0.817439 | − | 0.576015i | \(-0.804607\pi\) | ||||
−0.817439 | + | 0.576015i | \(0.804607\pi\) | |||||||
\(504\) | 8.29202e27 | + | 2.41695e28i | 0.349253 | + | 1.01800i | ||||
\(505\) | −5.55817e27 | −0.229283 | ||||||||
\(506\) | 5.65315e25i | 0.00228407i | ||||||||
\(507\) | 8.62489e27 | + | 1.05171e28i | 0.341327 | + | 0.416209i | ||||
\(508\) | −6.75159e27 | −0.261720 | ||||||||
\(509\) | 3.14244e28 | 1.19325 | 0.596623 | − | 0.802521i | \(-0.296509\pi\) | ||||
0.596623 | + | 0.802521i | \(0.296509\pi\) | |||||||
\(510\) | −4.18302e27 | + | 3.43043e27i | −0.155598 | + | 0.127603i | ||||
\(511\) | −2.75963e28 | + | 1.60786e28i | −1.00562 | + | 0.585908i | ||||
\(512\) | − | 1.87687e28i | − | 0.670039i | ||||||
\(513\) | 5.90561e27 | + | 1.10770e28i | 0.206554 | + | 0.387425i | ||||
\(514\) | − | 3.08077e28i | − | 1.05571i | ||||||
\(515\) | − | 1.02820e28i | − | 0.345226i | ||||||
\(516\) | −1.72689e27 | − | 2.10574e27i | −0.0568124 | − | 0.0692761i | ||||
\(517\) | − | 1.47329e26i | − | 0.00474938i | ||||||
\(518\) | −2.51992e28 | + | 1.46819e28i | −0.796019 | + | 0.463789i | ||||
\(519\) | −8.74097e27 | − | 1.06586e28i | −0.270584 | − | 0.329946i | ||||
\(520\) | 7.88263e27 | 0.239131 | ||||||||
\(521\) | 1.29490e28 | 0.384982 | 0.192491 | − | 0.981299i | \(-0.438343\pi\) | ||||
0.192491 | + | 0.981299i | \(0.438343\pi\) | |||||||
\(522\) | 1.33616e27 | − | 6.69252e27i | 0.0389331 | − | 0.195007i | ||||
\(523\) | − | 5.98374e28i | − | 1.70885i | −0.519571 | − | 0.854427i | \(-0.673908\pi\) | ||
0.519571 | − | 0.854427i | \(-0.326092\pi\) | |||||||
\(524\) | −1.55207e28 | −0.434444 | ||||||||
\(525\) | −1.13563e28 | + | 3.05056e28i | −0.311576 | + | 0.836965i | ||||
\(526\) | −5.24879e28 | −1.41159 | ||||||||
\(527\) | 8.42417e27i | 0.222083i | ||||||||
\(528\) | 7.67177e25 | − | 6.29150e25i | 0.00198262 | − | 0.00162592i | ||||
\(529\) | 3.23520e28 | 0.819629 | ||||||||
\(530\) | −5.29764e27 | −0.131579 | ||||||||
\(531\) | −8.58981e27 | + | 4.30244e28i | −0.209166 | + | 1.04766i | ||||
\(532\) | −7.08912e27 | + | 4.13037e27i | −0.169247 | + | 0.0986091i | ||||
\(533\) | − | 5.35351e27i | − | 0.125315i | ||||||
\(534\) | −4.21156e28 | + | 3.45384e28i | −0.966629 | + | 0.792718i | ||||
\(535\) | − | 1.86193e28i | − | 0.419033i | ||||||
\(536\) | − | 5.15251e28i | − | 1.13707i | ||||||
\(537\) | 4.97584e28 | − | 4.08062e28i | 1.07680 | − | 0.883071i | ||||
\(538\) | 1.84934e28i | 0.392466i | ||||||||
\(539\) | −3.02068e26 | − | 1.71228e26i | −0.00628671 | − | 0.00356363i | ||||
\(540\) | 6.30691e27 | − | 3.36249e27i | 0.128731 | − | 0.0686320i | ||||
\(541\) | 7.37106e28 | 1.47557 | 0.737783 | − | 0.675038i | \(-0.235873\pi\) | ||||
0.737783 | + | 0.675038i | \(0.235873\pi\) | |||||||
\(542\) | 6.17476e27 | 0.121235 | ||||||||
\(543\) | −6.91971e27 | + | 5.67475e27i | −0.133257 | + | 0.109282i | ||||
\(544\) | − | 3.55553e28i | − | 0.671608i | ||||||
\(545\) | −1.04998e28 | −0.194544 | ||||||||
\(546\) | −9.70711e27 | + | 2.60756e28i | −0.176428 | + | 0.473926i | ||||
\(547\) | 6.40075e28 | 1.14121 | 0.570603 | − | 0.821226i | \(-0.306709\pi\) | ||||
0.570603 | + | 0.821226i | \(0.306709\pi\) | |||||||
\(548\) | − | 3.78105e28i | − | 0.661328i | ||||||
\(549\) | 5.71067e28 | + | 1.14013e28i | 0.979891 | + | 0.195635i | ||||
\(550\) | 2.85315e26 | 0.00480304 | ||||||||
\(551\) | 7.10300e27 | 0.117314 | ||||||||
\(552\) | 1.78865e28 | + | 2.18105e28i | 0.289844 | + | 0.353432i | ||||
\(553\) | 5.87780e28 | + | 1.00883e29i | 0.934547 | + | 1.60400i | ||||
\(554\) | 6.89145e28i | 1.07512i | ||||||||
\(555\) | 1.67675e28 | + | 2.04461e28i | 0.256680 | + | 0.312992i | ||||
\(556\) | 6.78821e27i | 0.101969i | ||||||||
\(557\) | 2.96472e28i | 0.437023i | 0.975834 | + | 0.218512i | \(0.0701202\pi\) | ||||
−0.975834 | + | 0.218512i | \(0.929880\pi\) | |||||||
\(558\) | −2.70517e27 | + | 1.35495e28i | −0.0391322 | + | 0.196004i | ||||
\(559\) | − | 9.61206e27i | − | 0.136456i | ||||||
\(560\) | −4.19215e27 | − | 7.19516e27i | −0.0584067 | − | 0.100246i | ||||
\(561\) | 3.37917e26 | − | 2.77121e26i | 0.00462062 | − | 0.00378930i | ||||
\(562\) | 6.17464e27 | 0.0828668 | ||||||||
\(563\) | −2.39088e28 | −0.314934 | −0.157467 | − | 0.987524i | \(-0.550333\pi\) | ||||
−0.157467 | + | 0.987524i | \(0.550333\pi\) | |||||||
\(564\) | −1.43809e28 | − | 1.75358e28i | −0.185932 | − | 0.226723i | ||||
\(565\) | − | 4.32099e28i | − | 0.548371i | ||||||
\(566\) | −5.75955e28 | −0.717491 | ||||||||
\(567\) | 1.08794e28 | + | 8.10484e28i | 0.133040 | + | 0.991111i | ||||
\(568\) | 2.43082e28 | 0.291807 | ||||||||
\(569\) | 9.30524e28i | 1.09660i | 0.836281 | + | 0.548300i | \(0.184725\pi\) | ||||
−0.836281 | + | 0.548300i | \(0.815275\pi\) | |||||||
\(570\) | −5.85597e27 | − | 7.14068e27i | −0.0677505 | − | 0.0826140i | ||||
\(571\) | 3.32995e28 | 0.378232 | 0.189116 | − | 0.981955i | \(-0.439438\pi\) | ||||
0.189116 | + | 0.981955i | \(0.439438\pi\) | |||||||
\(572\) | −1.96451e26 | −0.00219077 | ||||||||
\(573\) | −1.27807e29 | + | 1.04813e29i | −1.39937 | + | 1.14760i | ||||
\(574\) | −1.10310e28 | + | 6.42707e27i | −0.118588 | + | 0.0690937i | ||||
\(575\) | 3.59324e28i | 0.379292i | ||||||||
\(576\) | 1.81197e28 | − | 9.07574e28i | 0.187808 | − | 0.940689i | ||||
\(577\) | − | 5.75601e28i | − | 0.585835i | −0.956138 | − | 0.292917i | \(-0.905374\pi\) | ||
0.956138 | − | 0.292917i | \(-0.0946261\pi\) | |||||||
\(578\) | − | 2.35460e28i | − | 0.235329i | ||||||
\(579\) | 1.24527e28 | + | 1.51846e28i | 0.122219 | + | 0.149032i | ||||
\(580\) | − | 4.04425e27i | − | 0.0389802i | ||||||
\(581\) | −4.85991e28 | − | 8.34126e28i | −0.460023 | − | 0.789555i | ||||
\(582\) | −3.93059e27 | − | 4.79290e27i | −0.0365398 | − | 0.0445561i | ||||
\(583\) | 4.27960e26 | 0.00390736 | ||||||||
\(584\) | 1.39683e29 | 1.25259 | ||||||||
\(585\) | 2.47386e28 | + | 4.93906e27i | 0.217891 | + | 0.0435018i | ||||
\(586\) | − | 1.19988e29i | − | 1.03804i | ||||||
\(587\) | −1.17507e29 | −0.998540 | −0.499270 | − | 0.866447i | \(-0.666398\pi\) | ||||
−0.499270 | + | 0.866447i | \(0.666398\pi\) | |||||||
\(588\) | −5.26674e28 | + | 9.10469e27i | −0.439622 | + | 0.0759982i | ||||
\(589\) | −1.43806e28 | −0.117914 | ||||||||
\(590\) | − | 3.22765e28i | − | 0.259980i | ||||||
\(591\) | −9.79162e28 | + | 8.02996e28i | −0.774793 | + | 0.635397i | ||||
\(592\) | 5.65026e28 | 0.439228 | ||||||||
\(593\) | 1.36983e29 | 1.04614 | 0.523072 | − | 0.852289i | \(-0.324786\pi\) | ||||
0.523072 | + | 0.852289i | \(0.324786\pi\) | |||||||
\(594\) | 6.32500e26 | − | 3.37213e26i | 0.00474573 | − | 0.00253016i | ||||
\(595\) | −1.84651e28 | − | 3.16924e28i | −0.136121 | − | 0.233629i | ||||
\(596\) | 5.37872e28i | 0.389577i | ||||||||
\(597\) | −1.50313e29 | + | 1.23269e29i | −1.06971 | + | 0.877252i | ||||
\(598\) | 3.07142e28i | 0.214772i | ||||||||
\(599\) | 2.40682e29i | 1.65372i | 0.562410 | + | 0.826859i | \(0.309874\pi\) | ||||
−0.562410 | + | 0.826859i | \(0.690126\pi\) | |||||||
\(600\) | 1.10078e29 | − | 9.02732e28i | 0.743210 | − | 0.609496i | ||||
\(601\) | 3.96548e28i | 0.263096i | 0.991310 | + | 0.131548i | \(0.0419947\pi\) | ||||
−0.991310 | + | 0.131548i | \(0.958005\pi\) | |||||||
\(602\) | −1.98059e28 | + | 1.15396e28i | −0.129131 | + | 0.0752364i | ||||
\(603\) | 3.22844e28 | − | 1.61705e29i | 0.206852 | − | 1.03608i | ||||
\(604\) | −1.02669e29 | −0.646475 | ||||||||
\(605\) | −5.28372e28 | −0.326971 | ||||||||
\(606\) | −6.63459e28 | + | 5.44093e28i | −0.403507 | + | 0.330911i | ||||
\(607\) | − | 1.06491e29i | − | 0.636546i | −0.947999 | − | 0.318273i | \(-0.896897\pi\) | ||
0.947999 | − | 0.318273i | \(-0.103103\pi\) | |||||||
\(608\) | 6.06951e28 | 0.356588 | ||||||||
\(609\) | 4.33648e28 | + | 1.61434e28i | 0.250412 | + | 0.0932207i | ||||
\(610\) | −4.28409e28 | −0.243162 | ||||||||
\(611\) | − | 8.00455e28i | − | 0.446585i | ||||||
\(612\) | 1.31706e28 | − | 6.59687e28i | 0.0722298 | − | 0.361783i | ||||
\(613\) | −6.00070e28 | −0.323494 | −0.161747 | − | 0.986832i | \(-0.551713\pi\) | ||||
−0.161747 | + | 0.986832i | \(0.551713\pi\) | |||||||
\(614\) | 2.32348e29 | 1.23132 | ||||||||
\(615\) | 7.34005e27 | + | 8.95035e27i | 0.0382393 | + | 0.0466285i | ||||
\(616\) | 7.64480e26 | + | 1.31211e27i | 0.00391533 | + | 0.00672004i | ||||
\(617\) | 4.47628e28i | 0.225384i | 0.993630 | + | 0.112692i | \(0.0359473\pi\) | ||||
−0.993630 | + | 0.112692i | \(0.964053\pi\) | |||||||
\(618\) | −1.00652e29 | − | 1.22733e29i | −0.498243 | − | 0.607551i | ||||
\(619\) | − | 9.07018e28i | − | 0.441432i | −0.975338 | − | 0.220716i | \(-0.929161\pi\) | ||
0.975338 | − | 0.220716i | \(-0.0708394\pi\) | |||||||
\(620\) | 8.18790e27i | 0.0391796i | ||||||||
\(621\) | 4.24685e28 | + | 7.96566e28i | 0.199804 | + | 0.374766i | ||||
\(622\) | 1.47457e29i | 0.682130i | ||||||||
\(623\) | −1.85911e29 | − | 3.19086e29i | −0.845630 | − | 1.45139i | ||||
\(624\) | 4.16816e28 | − | 3.41825e28i | 0.186426 | − | 0.152885i | ||||
\(625\) | 1.57040e29 | 0.690669 | ||||||||
\(626\) | 1.13826e29 | 0.492280 | ||||||||
\(627\) | 4.73063e26 | + | 5.76846e26i | 0.00201192 | + | 0.00245330i | ||||
\(628\) | 7.47626e27i | 0.0312686i | ||||||||
\(629\) | 2.48876e29 | 1.02365 | ||||||||
\(630\) | −1.95225e28 | − | 5.69040e28i | −0.0789696 | − | 0.230180i | ||||
\(631\) | −6.30668e28 | −0.250895 | −0.125448 | − | 0.992100i | \(-0.540037\pi\) | ||||
−0.125448 | + | 0.992100i | \(0.540037\pi\) | |||||||
\(632\) | − | 5.10633e29i | − | 1.99793i | ||||||
\(633\) | −1.82431e29 | − | 2.22453e29i | −0.702036 | − | 0.856052i | ||||
\(634\) | −1.61583e29 | −0.611589 | ||||||||
\(635\) | 5.15251e28 | 0.191820 | ||||||||
\(636\) | 5.09379e28 | − | 4.17735e28i | 0.186527 | − | 0.152968i | ||||
\(637\) | −1.64117e29 | − | 9.30302e28i | −0.591140 | − | 0.335089i | ||||
\(638\) | − | 4.05585e26i | − | 0.00143703i | ||||||
\(639\) | 7.62881e28 | + | 1.52309e28i | 0.265888 | + | 0.0530844i | ||||
\(640\) | − | 9.37437e27i | − | 0.0321405i | ||||||
\(641\) | 2.58094e29i | 0.870501i | 0.900309 | + | 0.435250i | \(0.143340\pi\) | ||||
−0.900309 | + | 0.435250i | \(0.856660\pi\) | |||||||
\(642\) | −1.82265e29 | − | 2.22252e29i | −0.604765 | − | 0.737441i | ||||
\(643\) | 3.31180e29i | 1.08106i | 0.841325 | + | 0.540529i | \(0.181776\pi\) | ||||
−0.841325 | + | 0.540529i | \(0.818224\pi\) | |||||||
\(644\) | −5.09793e28 | + | 2.97023e28i | −0.163716 | + | 0.0953870i | ||||
\(645\) | 1.31788e28 | + | 1.60701e28i | 0.0416390 | + | 0.0507740i | ||||
\(646\) | −8.69187e28 | −0.270191 | ||||||||
\(647\) | −2.95666e29 | −0.904287 | −0.452143 | − | 0.891945i | \(-0.649340\pi\) | ||||
−0.452143 | + | 0.891945i | \(0.649340\pi\) | |||||||
\(648\) | 1.37332e29 | − | 3.30223e29i | 0.413270 | − | 0.993733i | ||||
\(649\) | 2.60739e27i | 0.00772035i | ||||||||
\(650\) | 1.55015e29 | 0.451631 | ||||||||
\(651\) | −8.77955e28 | − | 3.26835e28i | −0.251693 | − | 0.0936976i | ||||
\(652\) | −1.60211e29 | −0.451951 | ||||||||
\(653\) | − | 4.60468e28i | − | 0.127824i | −0.997956 | − | 0.0639118i | \(-0.979642\pi\) | ||
0.997956 | − | 0.0639118i | \(-0.0203576\pi\) | |||||||
\(654\) | −1.25332e29 | + | 1.02783e29i | −0.342371 | + | 0.280773i | ||||
\(655\) | 1.18447e29 | 0.318413 | ||||||||
\(656\) | 2.47342e28 | 0.0654347 | ||||||||
\(657\) | 4.38376e29 | + | 8.75217e28i | 1.14133 | + | 0.227866i | ||||
\(658\) | −1.64936e29 | + | 9.60975e28i | −0.422613 | + | 0.246229i | ||||
\(659\) | − | 5.55268e28i | − | 0.140025i | −0.997546 | − | 0.0700126i | \(-0.977696\pi\) | ||
0.997546 | − | 0.0700126i | \(-0.0223039\pi\) | |||||||
\(660\) | 3.28440e26 | − | 2.69349e26i | 0.000815163 | − | 0.000668503i | ||||
\(661\) | 3.21572e28i | 0.0785530i | 0.999228 | + | 0.0392765i | \(0.0125053\pi\) | ||||
−0.999228 | + | 0.0392765i | \(0.987495\pi\) | |||||||
\(662\) | 1.78546e29i | 0.429280i | ||||||||
\(663\) | 1.83594e29 | − | 1.50563e29i | 0.434478 | − | 0.356309i | ||||
\(664\) | 4.22204e29i | 0.983463i | ||||||||
\(665\) | 5.41009e28 | − | 3.15211e28i | 0.124044 | − | 0.0722727i | ||||
\(666\) | 4.00296e29 | + | 7.99190e28i | 0.903445 | + | 0.180373i | ||||
\(667\) | 5.10791e28 | 0.113481 | ||||||||
\(668\) | −3.31919e29 | −0.725904 | ||||||||
\(669\) | 1.94312e28 | − | 1.59352e28i | 0.0418336 | − | 0.0343071i | ||||
\(670\) | 1.21309e29i | 0.257104i | ||||||||
\(671\) | 3.46082e27 | 0.00722092 | ||||||||
\(672\) | 3.70552e29 | + | 1.37945e29i | 0.761153 | + | 0.283354i | ||||
\(673\) | −1.37267e29 | −0.277592 | −0.138796 | − | 0.990321i | \(-0.544323\pi\) | ||||
−0.138796 | + | 0.990321i | \(0.544323\pi\) | |||||||
\(674\) | 4.14872e29i | 0.826010i | ||||||||
\(675\) | 4.02028e29 | − | 2.14339e29i | 0.788073 | − | 0.420156i | ||||
\(676\) | 1.24427e29 | 0.240145 | ||||||||
\(677\) | −6.52328e29 | −1.23961 | −0.619805 | − | 0.784756i | \(-0.712788\pi\) | ||||
−0.619805 | + | 0.784756i | \(0.712788\pi\) | |||||||
\(678\) | −4.22984e29 | − | 5.15781e29i | −0.791430 | − | 0.965058i | ||||
\(679\) | 3.63131e28 | − | 2.11573e28i | 0.0669008 | − | 0.0389788i | ||||
\(680\) | 1.60415e29i | 0.291006i | ||||||||
\(681\) | 7.03266e29 | + | 8.57552e29i | 1.25625 | + | 1.53185i | ||||
\(682\) | 8.21139e26i | 0.00144438i | ||||||||
\(683\) | 3.61830e29i | 0.626740i | 0.949631 | + | 0.313370i | \(0.101458\pi\) | ||||
−0.949631 | + | 0.313370i | \(0.898542\pi\) | |||||||
\(684\) | 1.12613e29 | + | 2.24831e28i | 0.192087 | + | 0.0383502i | ||||
\(685\) | 2.88553e29i | 0.484701i | ||||||||
\(686\) | 5.33755e27 | + | 4.49854e29i | 0.00882955 | + | 0.744163i | ||||
\(687\) | −5.56438e29 | + | 4.56327e29i | −0.906506 | + | 0.743413i | ||||
\(688\) | 4.44096e28 | 0.0712522 | ||||||||
\(689\) | 2.32516e29 | 0.367409 | ||||||||
\(690\) | −4.21114e28 | − | 5.13501e28i | −0.0655367 | − | 0.0799145i | ||||
\(691\) | 6.57444e29i | 1.00772i | 0.863786 | + | 0.503859i | \(0.168087\pi\) | ||||
−0.863786 | + | 0.503859i | \(0.831913\pi\) | |||||||
\(692\) | −1.26101e29 | −0.190373 | ||||||||
\(693\) | 1.57709e27 | + | 4.59688e27i | 0.00234508 | + | 0.00683541i | ||||
\(694\) | 2.76989e29 | 0.405684 | ||||||||
\(695\) | − | 5.18045e28i | − | 0.0747356i | ||||||
\(696\) | −1.28326e29 | − | 1.56479e29i | −0.182356 | − | 0.222362i | ||||
\(697\) | 1.08947e29 | 0.152500 | ||||||||
\(698\) | −7.23001e29 | −0.996912 | ||||||||
\(699\) | 2.56951e29 | − | 2.10722e29i | 0.349012 | − | 0.286220i | ||||
\(700\) | 1.49908e29 | + | 2.57293e29i | 0.200584 | + | 0.344269i | ||||
\(701\) | − | 8.98314e29i | − | 1.18410i | −0.805901 | − | 0.592051i | \(-0.798318\pi\) | ||
0.805901 | − | 0.592051i | \(-0.201682\pi\) | |||||||
\(702\) | 3.43645e29 | − | 1.83212e29i | 0.446241 | − | 0.237911i | ||||
\(703\) | 4.24847e29i | 0.543503i | ||||||||
\(704\) | − | 5.50014e27i | − | 0.00693204i | ||||||
\(705\) | 1.09748e29 | + | 1.33825e29i | 0.136274 | + | 0.166170i | ||||
\(706\) | − | 5.60271e29i | − | 0.685408i | ||||||
\(707\) | −2.92871e29 | − | 5.02666e29i | −0.352998 | − | 0.605864i | ||||
\(708\) | 2.54509e29 | + | 3.10345e29i | 0.302242 | + | 0.368549i | ||||
\(709\) | −2.07195e29 | −0.242435 | −0.121217 | − | 0.992626i | \(-0.538680\pi\) | ||||
−0.121217 | + | 0.992626i | \(0.538680\pi\) | |||||||
\(710\) | −5.72306e28 | −0.0659805 | ||||||||
\(711\) | 3.19950e29 | − | 1.60256e30i | 0.363455 | − | 1.82046i | ||||
\(712\) | 1.61510e30i | 1.80784i | ||||||||
\(713\) | −1.03414e29 | −0.114061 | ||||||||
\(714\) | −5.30651e29 | − | 1.97545e29i | −0.576736 | − | 0.214701i | ||||
\(715\) | 1.49922e27 | 0.00160566 | ||||||||
\(716\) | − | 5.88689e29i | − | 0.621297i | ||||||
\(717\) | −7.96497e28 | + | 6.53195e28i | −0.0828386 | + | 0.0679347i | ||||
\(718\) | −7.03914e29 | −0.721461 | ||||||||
\(719\) | 4.91706e29 | 0.496651 | 0.248326 | − | 0.968677i | \(-0.420120\pi\) | ||||
0.248326 | + | 0.968677i | \(0.420120\pi\) | |||||||
\(720\) | −2.28194e28 | + | 1.14297e29i | −0.0227150 | + | 0.113774i | ||||
\(721\) | 9.29879e29 | − | 5.41781e29i | 0.912234 | − | 0.531500i | ||||
\(722\) | 6.21356e29i | 0.600759i | ||||||||
\(723\) | −1.30602e30 | + | 1.07105e30i | −1.24451 | + | 1.02061i | ||||
\(724\) | 8.18666e28i | 0.0768868i | ||||||||
\(725\) | − | 2.57797e29i | − | 0.238632i | ||||||
\(726\) | −6.30699e29 | + | 5.17227e29i | −0.575424 | + | 0.471897i | ||||
\(727\) | − | 1.76811e30i | − | 1.59000i | −0.606609 | − | 0.795001i | \(-0.707471\pi\) | ||
0.606609 | − | 0.795001i | \(-0.292529\pi\) | |||||||
\(728\) | 4.15351e29 | + | 7.12883e29i | 0.368159 | + | 0.631886i | ||||
\(729\) | 6.37908e29 | − | 9.50313e29i | 0.557338 | − | 0.830286i | ||||
\(730\) | −3.28865e29 | −0.283223 | ||||||||
\(731\) | 1.95610e29 | 0.166058 | ||||||||
\(732\) | 4.11924e29 | − | 3.37813e29i | 0.344708 | − | 0.282690i | ||||
\(733\) | − | 3.09927e29i | − | 0.255663i | −0.991796 | − | 0.127832i | \(-0.959198\pi\) | ||
0.991796 | − | 0.127832i | \(-0.0408017\pi\) | |||||||
\(734\) | 1.15700e30 | 0.940860 | ||||||||
\(735\) | 4.01933e29 | − | 6.94828e28i | 0.322209 | − | 0.0557007i | ||||
\(736\) | 4.36471e29 | 0.344936 | ||||||||
\(737\) | − | 9.79974e27i | − | 0.00763495i | ||||||
\(738\) | 1.75231e29 | + | 3.49849e28i | 0.134592 | + | 0.0268713i | ||||
\(739\) | −1.92783e29 | −0.145983 | −0.0729915 | − | 0.997333i | \(-0.523255\pi\) | ||||
−0.0729915 | + | 0.997333i | \(0.523255\pi\) | |||||||
\(740\) | 2.41896e29 | 0.180591 | ||||||||
\(741\) | 2.57021e29 | + | 3.13407e29i | 0.189181 | + | 0.230684i | ||||
\(742\) | −2.79143e29 | − | 4.79104e29i | −0.202575 | − | 0.347688i | ||||
\(743\) | − | 8.09967e29i | − | 0.579542i | −0.957096 | − | 0.289771i | \(-0.906421\pi\) | ||
0.957096 | − | 0.289771i | \(-0.0935791\pi\) | |||||||
\(744\) | 2.59807e29 | + | 3.16805e29i | 0.183289 | + | 0.223499i | ||||
\(745\) | − | 4.10479e29i | − | 0.285529i | ||||||
\(746\) | − | 3.06591e29i | − | 0.210282i | ||||||
\(747\) | −2.64543e29 | + | 1.32503e30i | −0.178908 | + | 0.896108i | ||||
\(748\) | − | 3.99788e27i | − | 0.00266601i | ||||||
\(749\) | 1.68388e30 | − | 9.81086e29i | 1.10726 | − | 0.645131i | ||||
\(750\) | −5.49356e29 | + | 4.50519e29i | −0.356214 | + | 0.292126i | ||||
\(751\) | −9.79340e29 | −0.626201 | −0.313101 | − | 0.949720i | \(-0.601368\pi\) | ||||
−0.313101 | + | 0.949720i | \(0.601368\pi\) | |||||||
\(752\) | 3.69826e29 | 0.233190 | ||||||||
\(753\) | −1.68150e30 | − | 2.05039e30i | −1.04556 | − | 1.27494i | ||||
\(754\) | − | 2.20359e29i | − | 0.135124i | ||||||
\(755\) | 7.83523e29 | 0.473815 | ||||||||
\(756\) | 6.36418e29 | + | 3.93203e29i | 0.379545 | + | 0.234498i | ||||
\(757\) | −1.72229e30 | −1.01298 | −0.506489 | − | 0.862246i | \(-0.669057\pi\) | ||||
−0.506489 | + | 0.862246i | \(0.669057\pi\) | |||||||
\(758\) | − | 2.12497e29i | − | 0.123261i | ||||||
\(759\) | 3.40189e27 | + | 4.14822e27i | 0.00194617 | + | 0.00237314i | ||||
\(760\) | −2.73839e29 | −0.154509 | ||||||||
\(761\) | −2.24991e30 | −1.25206 | −0.626032 | − | 0.779797i | \(-0.715322\pi\) | ||||
−0.626032 | + | 0.779797i | \(0.715322\pi\) | |||||||
\(762\) | 6.15036e29 | − | 5.04382e29i | 0.337578 | − | 0.276842i | ||||
\(763\) | −5.53254e29 | − | 9.49572e29i | −0.299514 | − | 0.514068i | ||||
\(764\) | 1.51208e30i | 0.807411i | ||||||||
\(765\) | −1.00512e29 | + | 5.03443e29i | −0.0529388 | + | 0.265158i | ||||
\(766\) | 1.62834e30i | 0.845945i | ||||||||
\(767\) | 1.41663e30i | 0.725946i | ||||||||
\(768\) | −1.29513e30 | − | 1.57926e30i | −0.654668 | − | 0.798292i | ||||
\(769\) | − | 3.91252e30i | − | 1.95088i | −0.220271 | − | 0.975439i | \(-0.570694\pi\) | ||
0.220271 | − | 0.975439i | \(-0.429306\pi\) | |||||||
\(770\) | −1.79987e27 | − | 3.08919e27i | −0.000885297 | − | 0.00151947i | ||||
\(771\) | −1.85391e30 | − | 2.26063e30i | −0.899535 | − | 1.09688i | ||||
\(772\) | 1.79648e29 | 0.0859888 | ||||||||
\(773\) | −9.37932e29 | −0.442881 | −0.221440 | − | 0.975174i | \(-0.571076\pi\) | ||||
−0.221440 | + | 0.975174i | \(0.571076\pi\) | |||||||
\(774\) | 3.14622e29 | + | 6.28143e28i | 0.146558 | + | 0.0292603i | ||||
\(775\) | 5.21930e29i | 0.239853i | ||||||||
\(776\) | −1.83804e29 | −0.0833310 | ||||||||
\(777\) | −9.65573e29 | + | 2.59375e30i | −0.431881 | + | 1.16013i | ||||
\(778\) | 1.75670e30 | 0.775195 | ||||||||
\(779\) | 1.85979e29i | 0.0809692i | ||||||||
\(780\) | 1.78445e29 | − | 1.46340e29i | 0.0766499 | − | 0.0628595i | ||||
\(781\) | 4.62326e27 | 0.00195935 | ||||||||
\(782\) | −6.25050e29 | −0.261363 | ||||||||
\(783\) | −3.04690e29 | − | 5.71496e29i | −0.125707 | − | 0.235784i | ||||
\(784\) | 4.29818e29 | − | 7.58254e29i | 0.174971 | − | 0.308671i | ||||
\(785\) | − | 5.70555e28i | − | 0.0229174i | ||||||
\(786\) | 1.41386e30 | − | 1.15949e30i | 0.560364 | − | 0.459546i | ||||
\(787\) | − | 5.38816e29i | − | 0.210720i | −0.994434 | − | 0.105360i | \(-0.966400\pi\) | ||
0.994434 | − | 0.105360i | \(-0.0335995\pi\) | |||||||
\(788\) | 1.15844e30i | 0.447042i | ||||||||
\(789\) | −3.85150e30 | + | 3.15856e30i | −1.46663 | + | 1.20276i | ||||
\(790\) | 1.20222e30i | 0.451752i | ||||||||
\(791\) | 3.90778e30 | − | 2.27681e30i | 1.44903 | − | 0.844256i | ||||
\(792\) | 4.16134e27 | − | 2.08432e28i | 0.00152272 | − | 0.00762693i | ||||
\(793\) | 1.88030e30 | 0.678984 | ||||||||
\(794\) | −2.37760e29 | −0.0847273 | ||||||||
\(795\) | −3.88735e29 | + | 3.18796e29i | −0.136710 | + | 0.112114i | ||||
\(796\) | 1.77834e30i | 0.617203i | ||||||||
\(797\) | −1.93642e30 | −0.663264 | −0.331632 | − | 0.943409i | \(-0.607599\pi\) | ||||
−0.331632 | + | 0.943409i | \(0.607599\pi\) | |||||||
\(798\) | 3.37221e29 | − | 9.05854e29i | 0.113995 | − | 0.306216i | ||||
\(799\) | 1.62897e30 | 0.543464 | ||||||||
\(800\) | − | 2.20287e30i | − | 0.725345i | ||||||
\(801\) | −1.01198e30 | + | 5.06877e30i | −0.328875 | + | 1.64726i | ||||
\(802\) | 1.85213e30 | 0.594075 | ||||||||
\(803\) | 2.65667e28 | 0.00841056 | ||||||||
\(804\) | −9.56560e29 | − | 1.16641e30i | −0.298898 | − | 0.364472i | ||||
\(805\) | 3.89051e29 | − | 2.26675e29i | 0.119991 | − | 0.0699112i | ||||
\(806\) | 4.46134e29i | 0.135815i | ||||||||
\(807\) | 1.11287e30 | + | 1.35702e30i | 0.334406 | + | 0.407770i | ||||
\(808\) | 2.54431e30i | 0.754660i | ||||||||
\(809\) | 5.89657e30i | 1.72639i | 0.504867 | + | 0.863197i | \(0.331542\pi\) | ||||
−0.504867 | + | 0.863197i | \(0.668458\pi\) | |||||||
\(810\) | −3.23331e29 | + | 7.77468e29i | −0.0934446 | + | 0.224693i | ||||
\(811\) | − | 5.40534e30i | − | 1.54207i | −0.636793 | − | 0.771035i | \(-0.719739\pi\) | ||
0.636793 | − | 0.771035i | \(-0.280261\pi\) | |||||||
\(812\) | 3.65751e29 | − | 2.13099e29i | 0.103002 | − | 0.0600128i | ||||
\(813\) | 4.53097e29 | − | 3.71578e29i | 0.125962 | − | 0.103300i | ||||
\(814\) | 2.42590e28 | 0.00665758 | ||||||||
\(815\) | 1.22265e30 | 0.331245 | ||||||||
\(816\) | 6.95631e29 | + | 8.48242e29i | 0.186051 | + | 0.226868i | ||||
\(817\) | 3.33919e29i | 0.0881677i | ||||||||
\(818\) | 1.09358e30 | 0.285062 | ||||||||
\(819\) | 8.56850e29 | + | 2.49754e30i | 0.220508 | + | 0.642734i | ||||
\(820\) | 1.05891e29 | 0.0269038 | ||||||||
\(821\) | − | 2.36026e30i | − | 0.592047i | −0.955181 | − | 0.296024i | \(-0.904339\pi\) | ||
0.955181 | − | 0.296024i | \(-0.0956607\pi\) | |||||||
\(822\) | 2.82466e30 | + | 3.44435e30i | 0.699540 | + | 0.853009i | ||||
\(823\) | 4.60455e30 | 1.12587 | 0.562936 | − | 0.826501i | \(-0.309672\pi\) | ||||
0.562936 | + | 0.826501i | \(0.309672\pi\) | |||||||
\(824\) | −4.70671e30 | −1.13627 | ||||||||
\(825\) | 2.09361e28 | − | 1.71694e28i | 0.00499033 | − | 0.00409249i | ||||
\(826\) | 2.91900e30 | − | 1.70071e30i | 0.686978 | − | 0.400258i | ||||
\(827\) | 5.99819e30i | 1.39384i | 0.717150 | + | 0.696919i | \(0.245446\pi\) | ||||
−0.717150 | + | 0.696919i | \(0.754554\pi\) | |||||||
\(828\) | 8.09821e29 | + | 1.61681e29i | 0.185811 | + | 0.0370970i | ||||
\(829\) | − | 2.77814e30i | − | 0.629406i | −0.949190 | − | 0.314703i | \(-0.898095\pi\) | ||
0.949190 | − | 0.314703i | \(-0.101905\pi\) | |||||||
\(830\) | − | 9.94027e29i | − | 0.222371i | ||||||
\(831\) | 4.14707e30 | + | 5.05687e30i | 0.916073 | + | 1.11705i | ||||
\(832\) | − | 2.98829e30i | − | 0.651821i | ||||||
\(833\) | 1.89321e30 | − | 3.33987e30i | 0.407780 | − | 0.719378i | ||||
\(834\) | −5.07118e29 | − | 6.18372e29i | −0.107861 | − | 0.131524i | ||||
\(835\) | 2.53305e30 | 0.532031 | ||||||||
\(836\) | 6.82463e27 | 0.00141551 | ||||||||
\(837\) | 6.16869e29 | + | 1.15704e30i | 0.126350 | + | 0.236990i | ||||
\(838\) | 3.52494e30i | 0.713000i | ||||||||
\(839\) | −1.52551e30 | −0.304730 | −0.152365 | − | 0.988324i | \(-0.548689\pi\) | ||||
−0.152365 | + | 0.988324i | \(0.548689\pi\) | |||||||
\(840\) | −1.67183e30 | − | 6.22369e29i | −0.329806 | − | 0.122777i | ||||
\(841\) | 4.76638e30 | 0.928604 | ||||||||
\(842\) | − | 4.32786e30i | − | 0.832714i | ||||||
\(843\) | 4.53088e29 | − | 3.71571e29i | 0.0860981 | − | 0.0706078i | ||||
\(844\) | −2.63183e30 | −0.493927 | ||||||||
\(845\) | −9.49568e29 | −0.176007 | ||||||||
\(846\) | 2.62005e30 | + | 5.23093e29i | 0.479646 | + | 0.0957613i | ||||
\(847\) | −2.78410e30 | − | 4.77846e30i | −0.503395 | − | 0.863996i | ||||
\(848\) | 1.07427e30i | 0.191847i | ||||||||
\(849\) | −4.22630e30 | + | 3.46592e30i | −0.745468 | + | 0.611348i | ||||
\(850\) | 3.15463e30i | 0.549604i | ||||||||
\(851\) | 3.05516e30i | 0.525744i | ||||||||
\(852\) | 5.50284e29 | − | 4.51280e29i | 0.0935344 | − | 0.0767062i | ||||
\(853\) | 1.94054e30i | 0.325806i | 0.986642 | + | 0.162903i | \(0.0520857\pi\) | ||||
−0.986642 | + | 0.162903i | \(0.947914\pi\) | |||||||
\(854\) | −2.25737e30 | − | 3.87441e30i | −0.374365 | − | 0.642537i | ||||
\(855\) | −8.59409e29 | − | 1.71581e29i | −0.140785 | − | 0.0281077i | ||||
\(856\) | −8.52317e30 | −1.37920 | ||||||||
\(857\) | −1.03943e31 | −1.66149 | −0.830744 | − | 0.556655i | \(-0.812085\pi\) | ||||
−0.830744 | + | 0.556655i | \(0.812085\pi\) | |||||||
\(858\) | 1.78957e28 | − | 1.46760e28i | 0.00282574 | − | 0.00231735i | ||||
\(859\) | 3.88737e30i | 0.606356i | 0.952934 | + | 0.303178i | \(0.0980476\pi\) | ||||
−0.952934 | + | 0.303178i | \(0.901952\pi\) | |||||||
\(860\) | 1.90124e29 | 0.0292957 | ||||||||
\(861\) | −4.22683e29 | + | 1.13543e30i | −0.0643402 | + | 0.172833i | ||||
\(862\) | −6.86994e30 | −1.03306 | ||||||||
\(863\) | − | 5.66899e29i | − | 0.0842155i | −0.999113 | − | 0.0421078i | \(-0.986593\pi\) | ||
0.999113 | − | 0.0421078i | \(-0.0134073\pi\) | |||||||
\(864\) | −2.60357e30 | − | 4.88344e30i | −0.382099 | − | 0.716690i | ||||
\(865\) | 9.62347e29 | 0.139528 | ||||||||
\(866\) | −6.72461e30 | −0.963228 | ||||||||
\(867\) | −1.41693e30 | − | 1.72778e30i | −0.200515 | − | 0.244505i | ||||
\(868\) | −7.40491e29 | + | 4.31437e29i | −0.103529 | + | 0.0603198i | ||||
\(869\) | − | 9.71191e28i | − | 0.0134152i | ||||||
\(870\) | 3.02128e29 | + | 3.68411e29i | 0.0412325 | + | 0.0502783i | ||||
\(871\) | − | 5.32432e30i | − | 0.717915i | ||||||
\(872\) | 4.80639e30i | 0.640318i | ||||||||
\(873\) | −5.76844e29 | − | 1.15167e29i | −0.0759293 | − | 0.0151593i | ||||
\(874\) | − | 1.06700e30i | − | 0.138770i | ||||||
\(875\) | −2.42502e30 | − | 4.16216e30i | −0.311624 | − | 0.534853i | ||||
\(876\) | 3.16211e30 | − | 2.59320e30i | 0.401498 | − | 0.329263i | ||||
\(877\) | 3.63806e29 | 0.0456430 | 0.0228215 | − | 0.999740i | \(-0.492735\pi\) | ||||
0.0228215 | + | 0.999740i | \(0.492735\pi\) | |||||||
\(878\) | 8.90911e30 | 1.10444 | ||||||||
\(879\) | −7.22050e30 | − | 8.80457e30i | −0.884472 | − | 1.07851i | ||||
\(880\) | 6.92671e27i | 0.000838415i | ||||||||
\(881\) | 1.48754e31 | 1.77918 | 0.889591 | − | 0.456758i | \(-0.150990\pi\) | ||||
0.889591 | + | 0.456758i | \(0.150990\pi\) | |||||||
\(882\) | 4.11756e30 | − | 4.76395e30i | 0.486654 | − | 0.563050i | ||||
\(883\) | 8.98766e29 | 0.104969 | 0.0524843 | − | 0.998622i | \(-0.483286\pi\) | ||||
0.0524843 | + | 0.998622i | \(0.483286\pi\) | |||||||
\(884\) | − | 2.17209e30i | − | 0.250686i | ||||||
\(885\) | −1.94230e30 | − | 2.36841e30i | −0.221519 | − | 0.270118i | ||||
\(886\) | −2.09708e30 | −0.236353 | ||||||||
\(887\) | 1.04913e30 | 0.116851 | 0.0584253 | − | 0.998292i | \(-0.481392\pi\) | ||||
0.0584253 | + | 0.998292i | \(0.481392\pi\) | |||||||
\(888\) | 9.35941e30 | − | 7.67551e30i | 1.03018 | − | 0.844834i | ||||
\(889\) | 2.71496e30 | + | 4.65979e30i | 0.295321 | + | 0.506871i | ||||
\(890\) | − | 3.80254e30i | − | 0.408770i | ||||||
\(891\) | 2.61196e28 | − | 6.28063e28i | 0.00277493 | − | 0.00667248i | ||||
\(892\) | − | 2.29889e29i | − | 0.0241373i | ||||||
\(893\) | 2.78075e30i | 0.288550i | ||||||||
\(894\) | −4.01821e30 | − | 4.89974e30i | −0.412087 | − | 0.502492i | ||||
\(895\) | 4.49260e30i | 0.455362i | ||||||||
\(896\) | 8.47793e29 | − | 4.93954e29i | 0.0849289 | − | 0.0494826i | ||||
\(897\) | 1.84829e30 | + | 2.25378e30i | 0.182999 | + | 0.223146i | ||||
\(898\) | −1.82357e30 | −0.178452 | ||||||||
\(899\) | 7.41941e29 | 0.0717617 | ||||||||
\(900\) | 8.16003e29 | − | 4.08717e30i | 0.0780091 | − | 0.390730i | ||||
\(901\) | 4.73181e30i | 0.447113i | ||||||||
\(902\) | 1.06195e28 | 0.000991823 | ||||||||
\(903\) | −7.58915e29 | + | 2.03862e30i | −0.0700603 | + | 0.188198i | ||||
\(904\) | −1.97798e31 | −1.80490 | ||||||||
\(905\) | − | 6.24769e29i | − | 0.0563520i | ||||||
\(906\) | 9.35264e30 | − | 7.66996e30i | 0.833850 | − | 0.683828i | ||||
\(907\) | −8.65904e30 | −0.763120 | −0.381560 | − | 0.924344i | \(-0.624613\pi\) | ||||
−0.381560 | + | 0.924344i | \(0.624613\pi\) | |||||||
\(908\) | 1.01456e31 | 0.883849 | ||||||||
\(909\) | −1.59420e30 | + | 7.98499e30i | −0.137285 | + | 0.687628i | ||||
\(910\) | −9.77892e29 | − | 1.67839e30i | −0.0832446 | − | 0.142876i | ||||
\(911\) | − | 1.30878e31i | − | 1.10135i | −0.834720 | − | 0.550674i | \(-0.814371\pi\) | ||
0.834720 | − | 0.550674i | \(-0.185629\pi\) | |||||||
\(912\) | −1.44800e30 | + | 1.18749e30i | −0.120455 | + | 0.0987831i | ||||
\(913\) | 8.03005e28i | 0.00660352i | ||||||||
\(914\) | − | 8.54558e30i | − | 0.694715i | ||||||
\(915\) | −3.14362e30 | + | 2.57803e30i | −0.252644 | + | 0.207189i | ||||
\(916\) | 6.58318e30i | 0.523038i | ||||||||
\(917\) | 6.24122e30 | + | 1.07120e31i | 0.490220 | + | 0.841384i | ||||
\(918\) | 3.72846e30 | + | 6.99334e30i | 0.289522 | + | 0.543046i | ||||
\(919\) | −6.25718e29 | −0.0480359 | −0.0240179 | − | 0.999712i | \(-0.507646\pi\) | ||||
−0.0240179 | + | 0.999712i | \(0.507646\pi\) | |||||||
\(920\) | −1.96923e30 | −0.149460 | ||||||||
\(921\) | 1.70495e31 | − | 1.39820e31i | 1.27934 | − | 1.04916i | ||||
\(922\) | − | 6.34709e30i | − | 0.470869i | ||||||
\(923\) | 2.51187e30 | 0.184238 | ||||||||
\(924\) | 4.16653e28 | + | 1.55107e28i | 0.00302147 | + | 0.00112480i | ||||
\(925\) | 1.54194e31 | 1.10555 | ||||||||
\(926\) | 3.11992e30i | 0.221171i | ||||||||
\(927\) | −1.47714e31 | − | 2.94911e30i | −1.03534 | − | 0.206706i | ||||
\(928\) | −3.13146e30 | −0.217017 | ||||||||
\(929\) | −3.76917e30 | −0.258274 | −0.129137 | − | 0.991627i | \(-0.541221\pi\) | ||||
−0.129137 | + | 0.991627i | \(0.541221\pi\) | |||||||
\(930\) | −6.11683e29 | − | 7.45877e29i | −0.0414434 | − | 0.0505355i | ||||
\(931\) | 5.70137e30 | + | 3.23183e30i | 0.381951 | + | 0.216510i | ||||
\(932\) | − | 3.03997e30i | − | 0.201374i | ||||||
\(933\) | 8.87353e30 | + | 1.08202e31i | 0.581218 | + | 0.708729i | ||||
\(934\) | 1.61873e31i | 1.04841i | ||||||||
\(935\) | 3.05100e28i | 0.00195398i | ||||||||
\(936\) | 2.26091e30 | − | 1.13244e31i | 0.143181 | − | 0.717162i | ||||
\(937\) | 5.44084e30i | 0.340722i | 0.985382 | + | 0.170361i | \(0.0544934\pi\) | ||||
−0.985382 | + | 0.170361i | \(0.945507\pi\) | |||||||
\(938\) | −1.09709e31 | + | 6.39203e30i | −0.679379 | + | 0.395830i | ||||
\(939\) | 8.35244e30 | − | 6.84971e30i | 0.511475 | − | 0.419453i | ||||
\(940\) | 1.58328e30 | 0.0958772 | ||||||||
\(941\) | −1.75096e29 | −0.0104854 | −0.00524270 | − | 0.999986i | \(-0.501669\pi\) | ||||
−0.00524270 | + | 0.999986i | \(0.501669\pi\) | |||||||
\(942\) | −5.58520e29 | − | 6.81051e29i | −0.0330753 | − | 0.0403316i | ||||
\(943\) | 1.33741e30i | 0.0783234i | ||||||||
\(944\) | −6.54509e30 | −0.379062 | ||||||||
\(945\) | −4.85685e30 | − | 3.00075e30i | −0.278177 | − | 0.171868i | ||||
\(946\) | 1.90669e28 | 0.00108000 | ||||||||
\(947\) | − | 1.67680e30i | − | 0.0939305i | −0.998897 | − | 0.0469652i | \(-0.985045\pi\) | ||
0.998897 | − | 0.0469652i | \(-0.0149550\pi\) | |||||||
\(948\) | −9.47986e30 | − | 1.15596e31i | −0.525188 | − | 0.640406i | ||||
\(949\) | 1.44340e31 | 0.790847 | ||||||||
\(950\) | −5.38516e30 | −0.291810 | ||||||||
\(951\) | −1.18568e31 | + | 9.72360e30i | −0.635437 | + | 0.521113i | ||||
\(952\) | −1.45075e31 | + | 8.45260e30i | −0.768963 | + | 0.448025i | ||||
\(953\) | 2.58264e31i | 1.35390i | 0.736027 | + | 0.676952i | \(0.236700\pi\) | ||||
−0.736027 | + | 0.676952i | \(0.763300\pi\) | |||||||
\(954\) | −1.51948e30 | + | 7.61071e30i | −0.0787837 | + | 0.394609i | ||||
\(955\) | − | 1.15395e31i | − | 0.591769i | ||||||
\(956\) | 9.42330e29i | 0.0477964i | ||||||||
\(957\) | −2.44069e28 | − | 2.97614e28i | −0.00122444 | − | 0.00149306i | ||||
\(958\) | 2.21189e31i | 1.09756i | ||||||||
\(959\) | −2.60959e31 | + | 1.52044e31i | −1.28079 | + | 0.746233i | ||||
\(960\) | 4.09717e30 | + | 4.99603e30i | 0.198900 | + | 0.242536i | ||||
\(961\) | 1.93234e31 | 0.927871 | ||||||||
\(962\) | 1.31802e31 | 0.626014 | ||||||||
\(963\) | −2.67489e31 | − | 5.34041e30i | −1.25669 | − | 0.250899i | ||||
\(964\) | 1.54515e31i | 0.718061i | ||||||||
\(965\) | −1.37100e30 | −0.0630230 | ||||||||
\(966\) | 2.42503e30 | − | 6.51418e30i | 0.110270 | − | 0.296210i | ||||
\(967\) | −2.54600e31 | −1.14520 | −0.572599 | − | 0.819836i | \(-0.694065\pi\) | ||||
−0.572599 | + | 0.819836i | \(0.694065\pi\) | |||||||
\(968\) | 2.41868e31i | 1.07619i | ||||||||
\(969\) | −6.37799e30 | + | 5.23050e30i | −0.280727 | + | 0.230220i | ||||
\(970\) | 4.32743e29 | 0.0188420 | ||||||||
\(971\) | 4.36527e31 | 1.88022 | 0.940111 | − | 0.340868i | \(-0.110721\pi\) | ||||
0.940111 | + | 0.340868i | \(0.110721\pi\) | |||||||
\(972\) | −3.02167e30 | − | 1.00251e31i | −0.128751 | − | 0.427161i | ||||
\(973\) | 4.68506e30 | − | 2.72968e30i | 0.197483 | − | 0.115061i | ||||
\(974\) | − | 1.50221e31i | − | 0.626415i | ||||||
\(975\) | 1.13748e31 | − | 9.32833e30i | 0.469241 | − | 0.384818i | ||||
\(976\) | 8.68737e30i | 0.354540i | ||||||||
\(977\) | 2.05782e31i | 0.830833i | 0.909631 | + | 0.415416i | \(0.136364\pi\) | ||||
−0.909631 | + | 0.415416i | \(0.863636\pi\) | |||||||
\(978\) | 1.45944e31 | − | 1.19687e31i | 0.582946 | − | 0.478065i | ||||
\(979\) | 3.07181e29i | 0.0121388i | ||||||||
\(980\) | 1.84011e30 | − | 3.24620e30i | 0.0719401 | − | 0.126912i | ||||
\(981\) | −3.01156e30 | + | 1.50842e31i | −0.116484 | + | 0.583443i | ||||
\(982\) | 2.31648e31 | 0.886457 | ||||||||
\(983\) | −1.33127e31 | −0.504027 | −0.252013 | − | 0.967724i | \(-0.581093\pi\) | ||||
−0.252013 | + | 0.967724i | \(0.581093\pi\) | |||||||
\(984\) | 4.09712e30 | − | 3.35999e30i | 0.153472 | − | 0.125860i | ||||
\(985\) | − | 8.84069e30i | − | 0.327647i | ||||||
\(986\) | 4.48441e30 | 0.164436 | ||||||||
\(987\) | −6.31995e30 | + | 1.69769e31i | −0.229289 | + | 0.615924i | ||||
\(988\) | 3.70790e30 | 0.133101 | ||||||||
\(989\) | 2.40128e30i | 0.0852868i | ||||||||
\(990\) | −9.79735e27 | + | 4.90727e28i | −0.000344302 | + | 0.00172453i | ||||
\(991\) | 1.15424e31 | 0.401350 | 0.200675 | − | 0.979658i | \(-0.435686\pi\) | ||||
0.200675 | + | 0.979658i | \(0.435686\pi\) | |||||||
\(992\) | 6.33989e30 | 0.218127 | ||||||||
\(993\) | 1.07443e31 | + | 1.31015e31i | 0.365774 | + | 0.446019i | ||||
\(994\) | −3.01559e30 | − | 5.17578e30i | −0.101582 | − | 0.174349i | ||||
\(995\) | − | 1.35715e31i | − | 0.452361i | ||||||
\(996\) | 7.83819e30 | + | 9.55777e30i | 0.258519 | + | 0.315234i | ||||
\(997\) | − | 3.21188e31i | − | 1.04824i | −0.851645 | − | 0.524119i | \(-0.824395\pi\) | ||
0.851645 | − | 0.524119i | \(-0.175605\pi\) | |||||||
\(998\) | − | 5.24959e30i | − | 0.169533i | ||||||
\(999\) | 3.41825e31 | − | 1.82242e31i | 1.09236 | − | 0.582387i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 21.22.c.b.20.20 | yes | 52 | |
3.2 | odd | 2 | inner | 21.22.c.b.20.33 | yes | 52 | |
7.6 | odd | 2 | inner | 21.22.c.b.20.34 | yes | 52 | |
21.20 | even | 2 | inner | 21.22.c.b.20.19 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.22.c.b.20.19 | ✓ | 52 | 21.20 | even | 2 | inner | |
21.22.c.b.20.20 | yes | 52 | 1.1 | even | 1 | trivial | |
21.22.c.b.20.33 | yes | 52 | 3.2 | odd | 2 | inner | |
21.22.c.b.20.34 | yes | 52 | 7.6 | odd | 2 | inner |