Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,37,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 37, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 37);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 37 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.8365034637\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + \cdots + 51\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{240}\cdot 3^{24}\cdot 5^{6}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.10 | ||
Root | \(2.99676e7i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.37.b.b.3.9 |
$q$-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 \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 98385.8 | + | 242981.i | 0.375312 | + | 0.926899i | ||||
\(3\) | 4.79482e8i | 1.23763i | 0.785538 | + | 0.618813i | \(0.212386\pi\) | ||||
−0.785538 | + | 0.618813i | \(0.787614\pi\) | |||||||
\(4\) | −4.93600e10 | + | 4.78117e10i | −0.718282 | + | 0.695752i | ||||
\(5\) | 6.60636e12 | 1.73182 | 0.865909 | − | 0.500202i | \(-0.166741\pi\) | ||||
0.865909 | + | 0.500202i | \(0.166741\pi\) | |||||||
\(6\) | −1.16505e14 | + | 4.71742e13i | −1.14715 | + | 0.464496i | ||||
\(7\) | − | 2.27014e14i | − | 0.139408i | −0.997568 | − | 0.0697041i | \(-0.977794\pi\) | ||
0.997568 | − | 0.0697041i | \(-0.0222055\pi\) | |||||||
\(8\) | −1.64737e16 | − | 7.28954e15i | −0.914471 | − | 0.404650i | ||||
\(9\) | −7.98083e16 | −0.531720 | ||||||||
\(10\) | 6.49972e17 | + | 1.60522e18i | 0.649972 | + | 1.60522i | ||||
\(11\) | 8.91010e18i | 1.60256i | 0.598289 | + | 0.801280i | \(0.295847\pi\) | ||||
−0.598289 | + | 0.801280i | \(0.704153\pi\) | |||||||
\(12\) | −2.29249e19 | − | 2.36672e19i | −0.861081 | − | 0.888965i | ||||
\(13\) | −1.69290e20 | −1.50539 | −0.752696 | − | 0.658368i | \(-0.771247\pi\) | ||||
−0.752696 | + | 0.658368i | \(0.771247\pi\) | |||||||
\(14\) | 5.51601e19 | − | 2.23350e19i | 0.129217 | − | 0.0523216i | ||||
\(15\) | 3.16763e21i | 2.14334i | ||||||||
\(16\) | 1.50445e20 | − | 4.71997e21i | 0.0318580 | − | 0.999492i | ||||
\(17\) | −1.04222e22 | −0.741101 | −0.370551 | − | 0.928812i | \(-0.620831\pi\) | ||||
−0.370551 | + | 0.928812i | \(0.620831\pi\) | |||||||
\(18\) | −7.85200e21 | − | 1.93919e22i | −0.199561 | − | 0.492851i | ||||
\(19\) | − | 7.97251e21i | − | 0.0765649i | −0.999267 | − | 0.0382825i | \(-0.987811\pi\) | ||
0.999267 | − | 0.0382825i | \(-0.0121887\pi\) | |||||||
\(20\) | −3.26090e23 | + | 3.15861e23i | −1.24393 | + | 1.20492i | ||||
\(21\) | 1.08849e23 | 0.172535 | ||||||||
\(22\) | −2.16498e24 | + | 8.76627e23i | −1.48541 | + | 0.601460i | ||||
\(23\) | 1.29261e24i | 0.398443i | 0.979954 | + | 0.199222i | \(0.0638414\pi\) | ||||
−0.979954 | + | 0.199222i | \(0.936159\pi\) | |||||||
\(24\) | 3.49520e24 | − | 7.89882e24i | 0.500806 | − | 1.13177i | ||||
\(25\) | 2.90921e25 | 1.99919 | ||||||||
\(26\) | −1.66557e25 | − | 4.11341e25i | −0.564992 | − | 1.39535i | ||||
\(27\) | 3.37010e25i | 0.579556i | ||||||||
\(28\) | 1.08539e25 | + | 1.12054e25i | 0.0969936 | + | 0.100134i | ||||
\(29\) | 6.13174e25 | 0.291353 | 0.145677 | − | 0.989332i | \(-0.453464\pi\) | ||||
0.145677 | + | 0.989332i | \(0.453464\pi\) | |||||||
\(30\) | −7.69674e26 | + | 3.11650e26i | −1.98666 | + | 0.804423i | ||||
\(31\) | − | 7.63022e26i | − | 1.09151i | −0.837946 | − | 0.545754i | \(-0.816243\pi\) | ||
0.837946 | − | 0.545754i | \(-0.183757\pi\) | |||||||
\(32\) | 1.16166e27 | − | 4.27823e26i | 0.938385 | − | 0.345592i | ||||
\(33\) | −4.27223e27 | −1.98337 | ||||||||
\(34\) | −1.02539e27 | − | 2.53239e27i | −0.278144 | − | 0.686926i | ||||
\(35\) | − | 1.49974e27i | − | 0.241430i | ||||||
\(36\) | 3.93934e27 | − | 3.81577e27i | 0.381925 | − | 0.369945i | ||||
\(37\) | −1.94121e28 | −1.14932 | −0.574661 | − | 0.818392i | \(-0.694866\pi\) | ||||
−0.574661 | + | 0.818392i | \(0.694866\pi\) | |||||||
\(38\) | 1.93717e27 | − | 7.84381e26i | 0.0709679 | − | 0.0287357i | ||||
\(39\) | − | 8.11713e28i | − | 1.86311i | ||||||
\(40\) | −1.08831e29 | − | 4.81573e28i | −1.58370 | − | 0.700781i | ||||
\(41\) | 5.45164e28 | 0.508649 | 0.254324 | − | 0.967119i | \(-0.418147\pi\) | ||||
0.254324 | + | 0.967119i | \(0.418147\pi\) | |||||||
\(42\) | 1.07092e28 | + | 2.64483e28i | 0.0647546 | + | 0.159923i | ||||
\(43\) | 1.65794e29i | 0.656353i | 0.944616 | + | 0.328176i | \(0.106434\pi\) | ||||
−0.944616 | + | 0.328176i | \(0.893566\pi\) | |||||||
\(44\) | −4.26007e29 | − | 4.39802e29i | −1.11498 | − | 1.15109i | ||||
\(45\) | −5.27243e29 | −0.920842 | ||||||||
\(46\) | −3.14080e29 | + | 1.27174e29i | −0.369317 | + | 0.149541i | ||||
\(47\) | 5.00094e29i | 0.399292i | 0.979868 | + | 0.199646i | \(0.0639791\pi\) | ||||
−0.979868 | + | 0.199646i | \(0.936021\pi\) | |||||||
\(48\) | 2.26314e30 | + | 7.21357e28i | 1.23700 | + | 0.0394283i | ||||
\(49\) | 2.60020e30 | 0.980565 | ||||||||
\(50\) | 2.86225e30 | + | 7.06882e30i | 0.750321 | + | 1.85305i | ||||
\(51\) | − | 4.99724e30i | − | 0.917207i | ||||||
\(52\) | 8.35613e30 | − | 8.09403e30i | 1.08130 | − | 1.04738i | ||||
\(53\) | −2.38312e30 | −0.218867 | −0.109433 | − | 0.993994i | \(-0.534904\pi\) | ||||
−0.109433 | + | 0.993994i | \(0.534904\pi\) | |||||||
\(54\) | −8.18870e30 | + | 3.31570e30i | −0.537189 | + | 0.217514i | ||||
\(55\) | 5.88633e31i | 2.77534i | ||||||||
\(56\) | −1.65483e30 | + | 3.73975e30i | −0.0564116 | + | 0.127485i | ||||
\(57\) | 3.82267e30 | 0.0947588 | ||||||||
\(58\) | 6.03276e30 | + | 1.48990e31i | 0.109348 | + | 0.270055i | ||||
\(59\) | − | 7.57344e31i | − | 1.00915i | −0.863367 | − | 0.504576i | \(-0.831649\pi\) | ||
0.863367 | − | 0.504576i | \(-0.168351\pi\) | |||||||
\(60\) | −1.51450e32 | − | 1.56354e32i | −1.49124 | − | 1.53953i | ||||
\(61\) | 1.15248e32 | 0.842748 | 0.421374 | − | 0.906887i | \(-0.361548\pi\) | ||||
0.421374 | + | 0.906887i | \(0.361548\pi\) | |||||||
\(62\) | 1.85400e32 | − | 7.50705e31i | 1.01172 | − | 0.409656i | ||||
\(63\) | 1.81176e31i | 0.0741261i | ||||||||
\(64\) | 2.18244e32 | + | 2.40171e32i | 0.672516 | + | 0.740083i | ||||
\(65\) | −1.11839e33 | −2.60707 | ||||||||
\(66\) | −4.20327e32 | − | 1.03807e33i | −0.744383 | − | 1.83838i | ||||
\(67\) | 9.05989e32i | 1.22399i | 0.790863 | + | 0.611993i | \(0.209632\pi\) | ||||
−0.790863 | + | 0.611993i | \(0.790368\pi\) | |||||||
\(68\) | 5.14438e32 | − | 4.98302e32i | 0.532320 | − | 0.515623i | ||||
\(69\) | −6.19784e32 | −0.493124 | ||||||||
\(70\) | 3.64408e32 | − | 1.47553e32i | 0.223781 | − | 0.0906114i | ||||
\(71\) | 7.34519e32i | 0.349424i | 0.984620 | + | 0.174712i | \(0.0558995\pi\) | ||||
−0.984620 | + | 0.174712i | \(0.944101\pi\) | |||||||
\(72\) | 1.31473e33 | + | 5.81766e32i | 0.486243 | + | 0.215161i | ||||
\(73\) | 3.68724e33 | 1.06387 | 0.531937 | − | 0.846784i | \(-0.321464\pi\) | ||||
0.531937 | + | 0.846784i | \(0.321464\pi\) | |||||||
\(74\) | −1.90988e33 | − | 4.71677e33i | −0.431354 | − | 1.06531i | ||||
\(75\) | 1.39491e34i | 2.47426i | ||||||||
\(76\) | 3.81179e32 | + | 3.93523e32i | 0.0532702 | + | 0.0549952i | ||||
\(77\) | 2.02272e33 | 0.223410 | ||||||||
\(78\) | 1.97231e34 | − | 7.98610e33i | 1.72692 | − | 0.699249i | ||||
\(79\) | 2.27270e34i | 1.58217i | 0.611705 | + | 0.791086i | \(0.290484\pi\) | ||||
−0.611705 | + | 0.791086i | \(0.709516\pi\) | |||||||
\(80\) | 9.93894e32 | − | 3.11818e34i | 0.0551722 | − | 1.73094i | ||||
\(81\) | −2.81378e34 | −1.24899 | ||||||||
\(82\) | 5.36364e33 | + | 1.32465e34i | 0.190902 | + | 0.471466i | ||||
\(83\) | − | 1.22370e34i | − | 0.350163i | −0.984554 | − | 0.175082i | \(-0.943981\pi\) | ||
0.984554 | − | 0.175082i | \(-0.0560189\pi\) | |||||||
\(84\) | −5.37279e33 | + | 5.20427e33i | −0.123929 | + | 0.120042i | ||||
\(85\) | −6.88526e34 | −1.28345 | ||||||||
\(86\) | −4.02848e34 | + | 1.63118e34i | −0.608372 | + | 0.246337i | ||||
\(87\) | 2.94006e34i | 0.360586i | ||||||||
\(88\) | 6.49505e34 | − | 1.46782e35i | 0.648477 | − | 1.46550i | ||||
\(89\) | 8.48753e32 | 0.00691451 | 0.00345725 | − | 0.999994i | \(-0.498900\pi\) | ||||
0.00345725 | + | 0.999994i | \(0.498900\pi\) | |||||||
\(90\) | −5.18732e34 | − | 1.28110e35i | −0.345603 | − | 0.853527i | ||||
\(91\) | 3.84311e34i | 0.209864i | ||||||||
\(92\) | −6.18019e34 | − | 6.38032e34i | −0.277218 | − | 0.286195i | ||||
\(93\) | 3.65855e35 | 1.35088 | ||||||||
\(94\) | −1.21513e35 | + | 4.92021e34i | −0.370103 | + | 0.149859i | ||||
\(95\) | − | 5.26692e34i | − | 0.132597i | ||||||
\(96\) | 2.05133e35 | + | 5.56997e35i | 0.427714 | + | 1.16137i | ||||
\(97\) | −2.86871e35 | −0.496358 | −0.248179 | − | 0.968714i | \(-0.579832\pi\) | ||||
−0.248179 | + | 0.968714i | \(0.579832\pi\) | |||||||
\(98\) | 2.55822e35 | + | 6.31798e35i | 0.368018 | + | 0.908885i | ||||
\(99\) | − | 7.11100e35i | − | 0.852113i | ||||||
\(100\) | −1.43598e36 | + | 1.39094e36i | −1.43598 | + | 1.39094i | ||||
\(101\) | 5.18410e35 | 0.433400 | 0.216700 | − | 0.976238i | \(-0.430471\pi\) | ||||
0.216700 | + | 0.976238i | \(0.430471\pi\) | |||||||
\(102\) | 1.21423e36 | − | 4.91657e35i | 0.850158 | − | 0.344239i | ||||
\(103\) | − | 5.22189e35i | − | 0.306731i | −0.988170 | − | 0.153366i | \(-0.950989\pi\) | ||
0.988170 | − | 0.153366i | \(-0.0490112\pi\) | |||||||
\(104\) | 2.78882e36 | + | 1.23404e36i | 1.37664 | + | 0.609158i | ||||
\(105\) | 7.19097e35 | 0.298800 | ||||||||
\(106\) | −2.34465e35 | − | 5.79052e35i | −0.0821433 | − | 0.202867i | ||||
\(107\) | − | 3.32310e36i | − | 0.983184i | −0.870826 | − | 0.491592i | \(-0.836415\pi\) | ||
0.870826 | − | 0.491592i | \(-0.163585\pi\) | |||||||
\(108\) | −1.61130e36 | − | 1.66348e36i | −0.403227 | − | 0.416285i | ||||
\(109\) | 5.60436e36 | 1.18809 | 0.594044 | − | 0.804432i | \(-0.297530\pi\) | ||||
0.594044 | + | 0.804432i | \(0.297530\pi\) | |||||||
\(110\) | −1.43027e37 | + | 5.79132e36i | −2.57246 | + | 1.04162i | ||||
\(111\) | − | 9.30776e36i | − | 1.42243i | ||||||
\(112\) | −1.07150e36 | − | 3.41532e34i | −0.139337 | − | 0.00444126i | ||||
\(113\) | −1.35908e37 | −1.50603 | −0.753016 | − | 0.658003i | \(-0.771402\pi\) | ||||
−0.753016 | + | 0.658003i | \(0.771402\pi\) | |||||||
\(114\) | 3.76097e35 | + | 9.28836e35i | 0.0355641 | + | 0.0878318i | ||||
\(115\) | 8.53945e36i | 0.690032i | ||||||||
\(116\) | −3.02662e36 | + | 2.93169e36i | −0.209274 | + | 0.202710i | ||||
\(117\) | 1.35107e37 | 0.800448 | ||||||||
\(118\) | 1.84020e37 | − | 7.45119e36i | 0.935382 | − | 0.378747i | ||||
\(119\) | 2.36598e36i | 0.103316i | ||||||||
\(120\) | 2.30906e37 | − | 5.21825e37i | 0.867305 | − | 1.96003i | ||||
\(121\) | −4.84772e37 | −1.56820 | ||||||||
\(122\) | 1.13388e37 | + | 2.80031e37i | 0.316293 | + | 0.781142i | ||||
\(123\) | 2.61397e37i | 0.629517i | ||||||||
\(124\) | 3.64814e37 | + | 3.76627e37i | 0.759418 | + | 0.784010i | ||||
\(125\) | 9.60576e37 | 1.73042 | ||||||||
\(126\) | −4.40224e36 | + | 1.78252e36i | −0.0687074 | + | 0.0278204i | ||||
\(127\) | 1.31905e38i | 1.78564i | 0.450411 | + | 0.892822i | \(0.351278\pi\) | ||||
−0.450411 | + | 0.892822i | \(0.648722\pi\) | |||||||
\(128\) | −3.68848e37 | + | 7.66585e37i | −0.433578 | + | 0.901116i | ||||
\(129\) | −7.94953e37 | −0.812320 | ||||||||
\(130\) | −1.10033e38 | − | 2.71747e38i | −0.978463 | − | 2.41649i | ||||
\(131\) | − | 2.23577e36i | − | 0.0173198i | −0.999963 | − | 0.00865992i | \(-0.997243\pi\) | ||
0.999963 | − | 0.00865992i | \(-0.00275657\pi\) | |||||||
\(132\) | 2.10877e38 | − | 2.04263e38i | 1.42462 | − | 1.37993i | ||||
\(133\) | −1.80987e36 | −0.0106738 | ||||||||
\(134\) | −2.20138e38 | + | 8.91365e37i | −1.13451 | + | 0.459377i | ||||
\(135\) | 2.22641e38i | 1.00369i | ||||||||
\(136\) | 1.71691e38 | + | 7.59728e37i | 0.677716 | + | 0.299887i | ||||
\(137\) | −2.11161e38 | −0.730539 | −0.365270 | − | 0.930902i | \(-0.619023\pi\) | ||||
−0.365270 | + | 0.930902i | \(0.619023\pi\) | |||||||
\(138\) | −6.09779e37 | − | 1.50596e38i | −0.185075 | − | 0.457076i | ||||
\(139\) | − | 3.04795e38i | − | 0.812347i | −0.913796 | − | 0.406173i | \(-0.866863\pi\) | ||
0.913796 | − | 0.406173i | \(-0.133137\pi\) | |||||||
\(140\) | 7.17050e37 | + | 7.40270e37i | 0.167975 | + | 0.173415i | ||||
\(141\) | −2.39786e38 | −0.494174 | ||||||||
\(142\) | −1.78474e38 | + | 7.22662e37i | −0.323881 | + | 0.131143i | ||||
\(143\) | − | 1.50839e39i | − | 2.41248i | ||||||
\(144\) | −1.20068e37 | + | 3.76693e38i | −0.0169395 | + | 0.531450i | ||||
\(145\) | 4.05085e38 | 0.504570 | ||||||||
\(146\) | 3.62772e38 | + | 8.95930e38i | 0.399285 | + | 0.986103i | ||||
\(147\) | 1.24675e39i | 1.21357i | ||||||||
\(148\) | 9.58181e38 | − | 9.28127e38i | 0.825537 | − | 0.799643i | ||||
\(149\) | 1.09009e39 | 0.831976 | 0.415988 | − | 0.909370i | \(-0.363436\pi\) | ||||
0.415988 | + | 0.909370i | \(0.363436\pi\) | |||||||
\(150\) | −3.38937e39 | + | 1.37240e39i | −2.29338 | + | 0.928617i | ||||
\(151\) | 1.45223e39i | 0.871869i | 0.899978 | + | 0.435934i | \(0.143582\pi\) | ||||
−0.899978 | + | 0.435934i | \(0.856418\pi\) | |||||||
\(152\) | −5.81159e37 | + | 1.31336e38i | −0.0309820 | + | 0.0700165i | ||||
\(153\) | 8.31776e38 | 0.394058 | ||||||||
\(154\) | 1.99007e38 | + | 4.91482e38i | 0.0838484 | + | 0.207078i | ||||
\(155\) | − | 5.04080e39i | − | 1.89029i | ||||||
\(156\) | 3.88094e39 | + | 4.00661e39i | 1.29627 | + | 1.33824i | ||||
\(157\) | 3.77925e39 | 1.12515 | 0.562576 | − | 0.826745i | \(-0.309810\pi\) | ||||
0.562576 | + | 0.826745i | \(0.309810\pi\) | |||||||
\(158\) | −5.52222e39 | + | 2.23601e39i | −1.46651 | + | 0.593808i | ||||
\(159\) | − | 1.14266e39i | − | 0.270876i | ||||||
\(160\) | 7.67437e39 | − | 2.82635e39i | 1.62511 | − | 0.598503i | ||||
\(161\) | 2.93441e38 | 0.0555463 | ||||||||
\(162\) | −2.76836e39 | − | 6.83696e39i | −0.468762 | − | 1.15769i | ||||
\(163\) | − | 5.70992e39i | − | 0.865472i | −0.901521 | − | 0.432736i | \(-0.857548\pi\) | ||
0.901521 | − | 0.432736i | \(-0.142452\pi\) | |||||||
\(164\) | −2.69093e39 | + | 2.60653e39i | −0.365353 | + | 0.353894i | ||||
\(165\) | −2.82239e40 | −3.43484 | ||||||||
\(166\) | 2.97337e39 | − | 1.20395e39i | 0.324566 | − | 0.131420i | ||||
\(167\) | 2.00063e40i | 1.96006i | 0.198841 | + | 0.980032i | \(0.436282\pi\) | ||||
−0.198841 | + | 0.980032i | \(0.563718\pi\) | |||||||
\(168\) | −1.79314e39 | − | 7.93460e38i | −0.157779 | − | 0.0698165i | ||||
\(169\) | 1.60127e40 | 1.26621 | ||||||||
\(170\) | −6.77412e39 | − | 1.67299e40i | −0.481695 | − | 1.18963i | ||||
\(171\) | 6.36272e38i | 0.0407111i | ||||||||
\(172\) | −7.92691e39 | − | 8.18360e39i | −0.456659 | − | 0.471446i | ||||
\(173\) | −1.52851e39 | −0.0793301 | −0.0396651 | − | 0.999213i | \(-0.512629\pi\) | ||||
−0.0396651 | + | 0.999213i | \(0.512629\pi\) | |||||||
\(174\) | −7.14378e39 | + | 2.89260e39i | −0.334227 | + | 0.135332i | ||||
\(175\) | − | 6.60432e39i | − | 0.278704i | ||||||
\(176\) | 4.20554e40 | + | 1.34048e39i | 1.60175 | + | 0.0510543i | ||||
\(177\) | 3.63133e40 | 1.24895 | ||||||||
\(178\) | 8.35052e37 | + | 2.06231e38i | 0.00259510 | + | 0.00640905i | ||||
\(179\) | 5.96587e40i | 1.67617i | 0.545536 | + | 0.838087i | \(0.316326\pi\) | ||||
−0.545536 | + | 0.838087i | \(0.683674\pi\) | |||||||
\(180\) | 2.60247e40 | − | 2.52084e40i | 0.661424 | − | 0.640678i | ||||
\(181\) | 2.49321e39 | 0.0573515 | 0.0286758 | − | 0.999589i | \(-0.490871\pi\) | ||||
0.0286758 | + | 0.999589i | \(0.490871\pi\) | |||||||
\(182\) | −9.33803e39 | + | 3.78108e39i | −0.194523 | + | 0.0787645i | ||||
\(183\) | 5.52595e40i | 1.04301i | ||||||||
\(184\) | 9.42253e39 | − | 2.12940e40i | 0.161230 | − | 0.364365i | ||||
\(185\) | −1.28243e41 | −1.99042 | ||||||||
\(186\) | 3.59949e40 | + | 8.88958e40i | 0.507001 | + | 1.25213i | ||||
\(187\) | − | 9.28626e40i | − | 1.18766i | ||||||
\(188\) | −2.39103e40 | − | 2.46846e40i | −0.277808 | − | 0.286804i | ||||
\(189\) | 7.65061e39 | 0.0807948 | ||||||||
\(190\) | 1.27976e40 | − | 5.18190e39i | 0.122904 | − | 0.0497651i | ||||
\(191\) | 2.34835e40i | 0.205193i | 0.994723 | + | 0.102596i | \(0.0327150\pi\) | ||||
−0.994723 | + | 0.102596i | \(0.967285\pi\) | |||||||
\(192\) | −1.15157e41 | + | 1.04644e41i | −0.915946 | + | 0.832324i | ||||
\(193\) | 1.49860e41 | 1.08556 | 0.542781 | − | 0.839874i | \(-0.317371\pi\) | ||||
0.542781 | + | 0.839874i | \(0.317371\pi\) | |||||||
\(194\) | −2.82240e40 | − | 6.97041e40i | −0.186289 | − | 0.460073i | ||||
\(195\) | − | 5.36247e41i | − | 3.22658i | ||||||
\(196\) | −1.28346e41 | + | 1.24320e41i | −0.704322 | + | 0.682230i | ||||
\(197\) | 2.26156e41 | 1.13244 | 0.566222 | − | 0.824253i | \(-0.308404\pi\) | ||||
0.566222 | + | 0.824253i | \(0.308404\pi\) | |||||||
\(198\) | 1.72784e41 | − | 6.99621e40i | 0.789823 | − | 0.319808i | ||||
\(199\) | 2.93782e41i | 1.22650i | 0.789887 | + | 0.613252i | \(0.210139\pi\) | ||||
−0.789887 | + | 0.613252i | \(0.789861\pi\) | |||||||
\(200\) | −4.79253e41 | − | 2.12068e41i | −1.82821 | − | 0.808975i | ||||
\(201\) | −4.34406e41 | −1.51484 | ||||||||
\(202\) | 5.10041e40 | + | 1.25964e41i | 0.162660 | + | 0.401717i | ||||
\(203\) | − | 1.39199e40i | − | 0.0406170i | ||||||
\(204\) | 2.38927e41 | + | 2.46664e41i | 0.638149 | + | 0.658813i | ||||
\(205\) | 3.60155e41 | 0.880887 | ||||||||
\(206\) | 1.26882e41 | − | 5.13760e40i | 0.284309 | − | 0.115120i | ||||
\(207\) | − | 1.03161e41i | − | 0.211860i | ||||||
\(208\) | −2.54688e40 | + | 7.99042e41i | −0.0479588 | + | 1.50463i | ||||
\(209\) | 7.10358e40 | 0.122700 | ||||||||
\(210\) | 7.07489e40 | + | 1.74727e41i | 0.112143 | + | 0.276957i | ||||
\(211\) | − | 6.82410e41i | − | 0.993027i | −0.868029 | − | 0.496513i | \(-0.834613\pi\) | ||
0.868029 | − | 0.496513i | \(-0.165387\pi\) | |||||||
\(212\) | 1.17631e41 | − | 1.13941e41i | 0.157208 | − | 0.152277i | ||||
\(213\) | −3.52189e41 | −0.432457 | ||||||||
\(214\) | 8.07449e41 | − | 3.26945e41i | 0.911312 | − | 0.369001i | ||||
\(215\) | 1.09530e42i | 1.13668i | ||||||||
\(216\) | 2.45665e41 | − | 5.55179e41i | 0.234518 | − | 0.529987i | ||||
\(217\) | −1.73217e41 | −0.152165 | ||||||||
\(218\) | 5.51389e41 | + | 1.36175e42i | 0.445904 | + | 1.10124i | ||||
\(219\) | 1.76797e42i | 1.31668i | ||||||||
\(220\) | −2.81436e42 | − | 2.90549e42i | −1.93095 | − | 1.99348i | ||||
\(221\) | 1.76436e42 | 1.11565 | ||||||||
\(222\) | 2.26161e42 | − | 9.15751e41i | 1.31845 | − | 0.533856i | ||||
\(223\) | 2.30581e42i | 1.23976i | 0.784698 | + | 0.619878i | \(0.212818\pi\) | ||||
−0.784698 | + | 0.619878i | \(0.787182\pi\) | |||||||
\(224\) | −9.71218e40 | − | 2.63714e41i | −0.0481784 | − | 0.130819i | ||||
\(225\) | −2.32179e42 | −1.06301 | ||||||||
\(226\) | −1.33714e42 | − | 3.30231e42i | −0.565231 | − | 1.39594i | ||||
\(227\) | − | 4.50702e42i | − | 1.75964i | −0.475304 | − | 0.879821i | \(-0.657662\pi\) | ||
0.475304 | − | 0.879821i | \(-0.342338\pi\) | |||||||
\(228\) | −1.88687e41 | + | 1.82769e41i | −0.0680636 | + | 0.0659287i | ||||
\(229\) | −3.67329e42 | −1.22466 | −0.612331 | − | 0.790602i | \(-0.709768\pi\) | ||||
−0.612331 | + | 0.790602i | \(0.709768\pi\) | |||||||
\(230\) | −2.07492e42 | + | 8.40161e41i | −0.639589 | + | 0.258977i | ||||
\(231\) | 9.69858e41i | 0.276498i | ||||||||
\(232\) | −1.01012e42 | − | 4.46975e41i | −0.266434 | − | 0.117896i | ||||
\(233\) | 4.12814e42 | 1.00774 | 0.503869 | − | 0.863780i | \(-0.331910\pi\) | ||||
0.503869 | + | 0.863780i | \(0.331910\pi\) | |||||||
\(234\) | 1.32926e42 | + | 3.28285e42i | 0.300417 | + | 0.741934i | ||||
\(235\) | 3.30380e42i | 0.691500i | ||||||||
\(236\) | 3.62099e42 | + | 3.73825e42i | 0.702120 | + | 0.724856i | ||||
\(237\) | −1.08972e43 | −1.95814 | ||||||||
\(238\) | −5.74888e41 | + | 2.32779e41i | −0.0957631 | + | 0.0387756i | ||||
\(239\) | − | 2.53834e41i | − | 0.0392092i | −0.999808 | − | 0.0196046i | \(-0.993759\pi\) | ||
0.999808 | − | 0.0196046i | \(-0.00624074\pi\) | |||||||
\(240\) | 1.49511e43 | + | 4.76554e41i | 2.14226 | + | 0.0682826i | ||||
\(241\) | 1.11078e43 | 1.47680 | 0.738402 | − | 0.674360i | \(-0.235581\pi\) | ||||
0.738402 | + | 0.674360i | \(0.235581\pi\) | |||||||
\(242\) | −4.76947e42 | − | 1.17790e43i | −0.588564 | − | 1.45356i | ||||
\(243\) | − | 8.43324e42i | − | 0.966232i | ||||||
\(244\) | −5.68865e42 | + | 5.51022e42i | −0.605331 | + | 0.586344i | ||||
\(245\) | 1.71778e43 | 1.69816 | ||||||||
\(246\) | −6.35144e42 | + | 2.57177e42i | −0.583499 | + | 0.236265i | ||||
\(247\) | 1.34966e42i | 0.115260i | ||||||||
\(248\) | −5.56208e42 | + | 1.25698e43i | −0.441679 | + | 0.998152i | ||||
\(249\) | 5.86744e42 | 0.433371 | ||||||||
\(250\) | 9.45070e42 | + | 2.33402e43i | 0.649447 | + | 1.60392i | ||||
\(251\) | 7.49923e41i | 0.0479611i | 0.999712 | + | 0.0239806i | \(0.00763398\pi\) | ||||
−0.999712 | + | 0.0239806i | \(0.992366\pi\) | |||||||
\(252\) | −8.66235e41 | − | 8.94285e41i | −0.0515734 | − | 0.0532435i | ||||
\(253\) | −1.15173e43 | −0.638530 | ||||||||
\(254\) | −3.20504e43 | + | 1.29776e43i | −1.65511 | + | 0.670173i | ||||
\(255\) | − | 3.30136e43i | − | 1.58844i | ||||||
\(256\) | −2.22555e43 | − | 1.42019e42i | −0.997970 | − | 0.0636836i | ||||
\(257\) | −1.46734e43 | −0.613385 | −0.306692 | − | 0.951809i | \(-0.599222\pi\) | ||||
−0.306692 | + | 0.951809i | \(0.599222\pi\) | |||||||
\(258\) | −7.82121e42 | − | 1.93158e43i | −0.304873 | − | 0.752938i | ||||
\(259\) | 4.40683e42i | 0.160225i | ||||||||
\(260\) | 5.52036e43 | − | 5.34721e43i | 1.87261 | − | 1.81387i | ||||
\(261\) | −4.89364e42 | −0.154918 | ||||||||
\(262\) | 5.43249e41 | − | 2.19968e41i | 0.0160537 | − | 0.00650034i | ||||
\(263\) | 5.72464e42i | 0.157959i | 0.996876 | + | 0.0789796i | \(0.0251662\pi\) | ||||
−0.996876 | + | 0.0789796i | \(0.974834\pi\) | |||||||
\(264\) | 7.03793e43 | + | 3.11426e43i | 1.81374 | + | 0.802572i | ||||
\(265\) | −1.57437e43 | −0.379038 | ||||||||
\(266\) | −1.78066e41 | − | 4.39764e41i | −0.00400600 | − | 0.00989351i | ||||
\(267\) | 4.06962e41i | 0.00855758i | ||||||||
\(268\) | −4.33169e43 | − | 4.47196e43i | −0.851591 | − | 0.879167i | ||||
\(269\) | −4.65647e42 | −0.0856083 | −0.0428041 | − | 0.999083i | \(-0.513629\pi\) | ||||
−0.0428041 | + | 0.999083i | \(0.513629\pi\) | |||||||
\(270\) | −5.40975e43 | + | 2.19047e43i | −0.930314 | + | 0.376695i | ||||
\(271\) | − | 5.26399e43i | − | 0.846970i | −0.905903 | − | 0.423485i | \(-0.860807\pi\) | ||
0.905903 | − | 0.423485i | \(-0.139193\pi\) | |||||||
\(272\) | −1.56796e42 | + | 4.91923e43i | −0.0236100 | + | 0.740725i | ||||
\(273\) | −1.84270e43 | −0.259733 | ||||||||
\(274\) | −2.07752e43 | − | 5.13081e43i | −0.274180 | − | 0.677136i | ||||
\(275\) | 2.59213e44i | 3.20383i | ||||||||
\(276\) | 3.05925e43 | − | 2.96329e43i | 0.354202 | − | 0.343092i | ||||
\(277\) | 1.07450e44 | 1.16565 | 0.582827 | − | 0.812597i | \(-0.301947\pi\) | ||||
0.582827 | + | 0.812597i | \(0.301947\pi\) | |||||||
\(278\) | 7.40594e43 | − | 2.99875e43i | 0.752963 | − | 0.304883i | ||||
\(279\) | 6.08955e43i | 0.580376i | ||||||||
\(280\) | −1.09324e43 | + | 2.47062e43i | −0.0976946 | + | 0.220780i | ||||
\(281\) | −4.65870e43 | −0.390437 | −0.195219 | − | 0.980760i | \(-0.562542\pi\) | ||||
−0.195219 | + | 0.980760i | \(0.562542\pi\) | |||||||
\(282\) | −2.35915e43 | − | 5.82634e43i | −0.185469 | − | 0.458049i | ||||
\(283\) | − | 2.53833e42i | − | 0.0187237i | −0.999956 | − | 0.00936186i | \(-0.997020\pi\) | ||
0.999956 | − | 0.00936186i | \(-0.00298002\pi\) | |||||||
\(284\) | −3.51186e43 | − | 3.62558e43i | −0.243113 | − | 0.250985i | ||||
\(285\) | 2.52540e43 | 0.164105 | ||||||||
\(286\) | 3.66509e44 | − | 1.48404e44i | 2.23613 | − | 0.905433i | ||||
\(287\) | − | 1.23760e43i | − | 0.0709098i | ||||||
\(288\) | −9.27105e43 | + | 3.41438e43i | −0.498958 | + | 0.183758i | ||||
\(289\) | −8.91487e43 | −0.450769 | ||||||||
\(290\) | 3.98546e43 | + | 9.84278e43i | 0.189371 | + | 0.467686i | ||||
\(291\) | − | 1.37549e44i | − | 0.614306i | ||||||
\(292\) | −1.82002e44 | + | 1.76293e44i | −0.764162 | + | 0.740193i | ||||
\(293\) | −1.58940e43 | −0.0627504 | −0.0313752 | − | 0.999508i | \(-0.509989\pi\) | ||||
−0.0313752 | + | 0.999508i | \(0.509989\pi\) | |||||||
\(294\) | −3.02936e44 | + | 1.22662e44i | −1.12486 | + | 0.455469i | ||||
\(295\) | − | 5.00329e44i | − | 1.74767i | ||||||
\(296\) | 3.19788e44 | + | 1.41505e44i | 1.05102 | + | 0.465074i | ||||
\(297\) | −3.00280e44 | −0.928773 | ||||||||
\(298\) | 1.07250e44 | + | 2.64872e44i | 0.312251 | + | 0.771157i | ||||
\(299\) | − | 2.18826e44i | − | 0.599814i | ||||||
\(300\) | −6.66932e44 | − | 6.88529e44i | −1.72147 | − | 1.77721i | ||||
\(301\) | 3.76376e43 | 0.0915009 | ||||||||
\(302\) | −3.52865e44 | + | 1.42879e44i | −0.808134 | + | 0.327223i | ||||
\(303\) | 2.48568e44i | 0.536387i | ||||||||
\(304\) | −3.76300e43 | − | 1.19942e42i | −0.0765261 | − | 0.00243920i | ||||
\(305\) | 7.61372e44 | 1.45949 | ||||||||
\(306\) | 8.18349e43 | + | 2.02106e44i | 0.147895 | + | 0.365252i | ||||
\(307\) | 3.63013e44i | 0.618630i | 0.950960 | + | 0.309315i | \(0.100100\pi\) | ||||
−0.950960 | + | 0.309315i | \(0.899900\pi\) | |||||||
\(308\) | −9.98414e43 | + | 9.67097e43i | −0.160471 | + | 0.155438i | ||||
\(309\) | 2.50380e44 | 0.379619 | ||||||||
\(310\) | 1.22482e45 | − | 4.95943e44i | 1.75211 | − | 0.709449i | ||||
\(311\) | − | 9.78683e44i | − | 1.32116i | −0.750756 | − | 0.660580i | \(-0.770311\pi\) | ||
0.750756 | − | 0.660580i | \(-0.229689\pi\) | |||||||
\(312\) | −5.91701e44 | + | 1.33719e45i | −0.753910 | + | 1.70377i | ||||
\(313\) | 2.69011e44 | 0.323573 | 0.161786 | − | 0.986826i | \(-0.448274\pi\) | ||||
0.161786 | + | 0.986826i | \(0.448274\pi\) | |||||||
\(314\) | 3.71824e44 | + | 9.18284e44i | 0.422283 | + | 1.04290i | ||||
\(315\) | 1.19692e44i | 0.128373i | ||||||||
\(316\) | −1.08661e45 | − | 1.12180e45i | −1.10080 | − | 1.13645i | ||||
\(317\) | −3.60812e44 | −0.345314 | −0.172657 | − | 0.984982i | \(-0.555235\pi\) | ||||
−0.172657 | + | 0.984982i | \(0.555235\pi\) | |||||||
\(318\) | 2.77645e44 | − | 1.12422e44i | 0.251074 | − | 0.101663i | ||||
\(319\) | 5.46344e44i | 0.466911i | ||||||||
\(320\) | 1.44180e45 | + | 1.58665e45i | 1.16468 | + | 1.28169i | ||||
\(321\) | 1.59336e45 | 1.21681 | ||||||||
\(322\) | 2.88704e43 | + | 7.13006e43i | 0.0208472 | + | 0.0514858i | ||||
\(323\) | 8.30908e43i | 0.0567424i | ||||||||
\(324\) | 1.38888e45 | − | 1.34532e45i | 0.897130 | − | 0.868990i | ||||
\(325\) | −4.92499e45 | −3.00957 | ||||||||
\(326\) | 1.38740e45 | − | 5.61775e44i | 0.802205 | − | 0.324822i | ||||
\(327\) | 2.68719e45i | 1.47041i | ||||||||
\(328\) | −8.98085e44 | − | 3.97400e44i | −0.465145 | − | 0.205825i | ||||
\(329\) | 1.13528e44 | 0.0556645 | ||||||||
\(330\) | −2.77683e45 | − | 6.85787e45i | −1.28914 | − | 3.18375i | ||||
\(331\) | − | 1.74226e45i | − | 0.765963i | −0.923756 | − | 0.382982i | \(-0.874897\pi\) | ||
0.923756 | − | 0.382982i | \(-0.125103\pi\) | |||||||
\(332\) | 5.85074e44 | + | 6.04020e44i | 0.243627 | + | 0.251516i | ||||
\(333\) | 1.54925e45 | 0.611118 | ||||||||
\(334\) | −4.86115e45 | + | 1.96833e45i | −1.81678 | + | 0.735635i | ||||
\(335\) | 5.98529e45i | 2.11972i | ||||||||
\(336\) | 1.63758e43 | − | 5.13765e44i | 0.00549662 | − | 0.172448i | ||||
\(337\) | −2.28010e45 | −0.725464 | −0.362732 | − | 0.931894i | \(-0.618156\pi\) | ||||
−0.362732 | + | 0.931894i | \(0.618156\pi\) | |||||||
\(338\) | 1.57543e45 | + | 3.89079e45i | 0.475223 | + | 1.17365i | ||||
\(339\) | − | 6.51656e45i | − | 1.86390i | ||||||
\(340\) | 3.39856e45 | − | 3.29196e45i | 0.921881 | − | 0.892965i | ||||
\(341\) | 6.79860e45 | 1.74921 | ||||||||
\(342\) | −1.54602e44 | + | 6.26001e43i | −0.0377351 | + | 0.0152794i | ||||
\(343\) | − | 1.19226e45i | − | 0.276107i | ||||||
\(344\) | 1.20856e45 | − | 2.73124e45i | 0.265593 | − | 0.600216i | ||||
\(345\) | −4.09451e45 | −0.854001 | ||||||||
\(346\) | −1.50384e44 | − | 3.71399e44i | −0.0297735 | − | 0.0735310i | ||||
\(347\) | 6.07436e45i | 1.14175i | 0.821038 | + | 0.570873i | \(0.193395\pi\) | ||||
−0.821038 | + | 0.570873i | \(0.806605\pi\) | |||||||
\(348\) | −1.40569e45 | − | 1.45121e45i | −0.250879 | − | 0.259003i | ||||
\(349\) | 1.91350e44 | 0.0324317 | 0.0162159 | − | 0.999869i | \(-0.494838\pi\) | ||||
0.0162159 | + | 0.999869i | \(0.494838\pi\) | |||||||
\(350\) | 1.60472e45 | − | 6.49771e44i | 0.258330 | − | 0.104601i | ||||
\(351\) | − | 5.70523e45i | − | 0.872459i | ||||||
\(352\) | 3.81194e45 | + | 1.03505e46i | 0.553832 | + | 1.50382i | ||||
\(353\) | −4.83055e45 | −0.666887 | −0.333443 | − | 0.942770i | \(-0.608211\pi\) | ||||
−0.333443 | + | 0.942770i | \(0.608211\pi\) | |||||||
\(354\) | 3.57271e45 | + | 8.82343e45i | 0.468748 | + | 1.15765i | ||||
\(355\) | 4.85250e45i | 0.605139i | ||||||||
\(356\) | −4.18944e43 | + | 4.05804e43i | −0.00496657 | + | 0.00481078i | ||||
\(357\) | −1.13445e45 | −0.127866 | ||||||||
\(358\) | −1.44959e46 | + | 5.86957e45i | −1.55364 | + | 0.629088i | ||||
\(359\) | 4.78046e45i | 0.487270i | 0.969867 | + | 0.243635i | \(0.0783400\pi\) | ||||
−0.969867 | + | 0.243635i | \(0.921660\pi\) | |||||||
\(360\) | 8.68561e45 | + | 3.84335e45i | 0.842084 | + | 0.372619i | ||||
\(361\) | 1.07789e46 | 0.994138 | ||||||||
\(362\) | 2.45297e44 | + | 6.05803e44i | 0.0215247 | + | 0.0531591i | ||||
\(363\) | − | 2.32440e46i | − | 1.94085i | ||||||
\(364\) | −1.83746e45 | − | 1.89696e45i | −0.146013 | − | 0.150742i | ||||
\(365\) | 2.43593e46 | 1.84244 | ||||||||
\(366\) | −1.34270e46 | + | 5.43675e45i | −0.966762 | + | 0.391453i | ||||
\(367\) | − | 2.65158e46i | − | 1.81767i | −0.417153 | − | 0.908836i | \(-0.636972\pi\) | ||
0.417153 | − | 0.908836i | \(-0.363028\pi\) | |||||||
\(368\) | 6.10108e45 | + | 1.94467e44i | 0.398241 | + | 0.0126936i | ||||
\(369\) | −4.35087e45 | −0.270459 | ||||||||
\(370\) | −1.26173e46 | − | 3.11607e46i | −0.747027 | − | 1.84491i | ||||
\(371\) | 5.41002e44i | 0.0305118i | ||||||||
\(372\) | −1.80586e46 | + | 1.74922e46i | −0.970312 | + | 0.939876i | ||||
\(373\) | −1.20802e46 | −0.618466 | −0.309233 | − | 0.950986i | \(-0.600072\pi\) | ||||
−0.309233 | + | 0.950986i | \(0.600072\pi\) | |||||||
\(374\) | 2.25638e46 | − | 9.13636e45i | 1.10084 | − | 0.445743i | ||||
\(375\) | 4.60579e46i | 2.14161i | ||||||||
\(376\) | 3.64545e45 | − | 8.23837e45i | 0.161574 | − | 0.365141i | ||||
\(377\) | −1.03804e46 | −0.438601 | ||||||||
\(378\) | 7.52711e44 | + | 1.85895e45i | 0.0303233 | + | 0.0748886i | ||||
\(379\) | 1.04283e45i | 0.0400596i | 0.999799 | + | 0.0200298i | \(0.00637611\pi\) | ||||
−0.999799 | + | 0.0200298i | \(0.993624\pi\) | |||||||
\(380\) | 2.51821e45 | + | 2.59975e45i | 0.0922543 | + | 0.0952417i | ||||
\(381\) | −6.32461e46 | −2.20996 | ||||||||
\(382\) | −5.70604e45 | + | 2.31044e45i | −0.190193 | + | 0.0770113i | ||||
\(383\) | − | 7.05484e45i | − | 0.224341i | −0.993689 | − | 0.112171i | \(-0.964220\pi\) | ||
0.993689 | − | 0.112171i | \(-0.0357804\pi\) | |||||||
\(384\) | −3.67564e46 | − | 1.76856e46i | −1.11525 | − | 0.536608i | ||||
\(385\) | 1.33628e46 | 0.386905 | ||||||||
\(386\) | 1.47441e46 | + | 3.64132e46i | 0.407424 | + | 1.00621i | ||||
\(387\) | − | 1.32318e46i | − | 0.348996i | ||||||
\(388\) | 1.41599e46 | − | 1.37158e46i | 0.356525 | − | 0.345342i | ||||
\(389\) | 4.05550e46 | 0.974881 | 0.487440 | − | 0.873156i | \(-0.337931\pi\) | ||||
0.487440 | + | 0.873156i | \(0.337931\pi\) | |||||||
\(390\) | 1.30298e47 | − | 5.27591e46i | 2.99071 | − | 1.21097i | ||||
\(391\) | − | 1.34718e46i | − | 0.295287i | ||||||
\(392\) | −4.28347e46 | − | 1.89542e46i | −0.896699 | − | 0.396786i | ||||
\(393\) | 1.07201e45 | 0.0214355 | ||||||||
\(394\) | 2.22506e46 | + | 5.49517e46i | 0.425020 | + | 1.04966i | ||||
\(395\) | 1.50142e47i | 2.74003i | ||||||||
\(396\) | 3.39989e46 | + | 3.50999e46i | 0.592860 | + | 0.612058i | ||||
\(397\) | 5.04352e46 | 0.840436 | 0.420218 | − | 0.907423i | \(-0.361954\pi\) | ||||
0.420218 | + | 0.907423i | \(0.361954\pi\) | |||||||
\(398\) | −7.13833e46 | + | 2.89039e46i | −1.13685 | + | 0.460322i | ||||
\(399\) | − | 8.67801e44i | − | 0.0132102i | ||||||
\(400\) | 4.37676e45 | − | 1.37314e47i | 0.0636902 | − | 1.99818i | ||||
\(401\) | 6.66873e46 | 0.927779 | 0.463889 | − | 0.885893i | \(-0.346453\pi\) | ||||
0.463889 | + | 0.885893i | \(0.346453\pi\) | |||||||
\(402\) | −4.27393e46 | − | 1.05552e47i | −0.568537 | − | 1.40410i | ||||
\(403\) | 1.29172e47i | 1.64315i | ||||||||
\(404\) | −2.55887e46 | + | 2.47861e46i | −0.311303 | + | 0.301539i | ||||
\(405\) | −1.85889e47 | −2.16303 | ||||||||
\(406\) | 3.38227e45 | − | 1.36952e45i | 0.0376478 | − | 0.0152440i | ||||
\(407\) | − | 1.72964e47i | − | 1.84186i | ||||||
\(408\) | −3.64276e46 | + | 8.23228e46i | −0.371148 | + | 0.838759i | ||||
\(409\) | 2.73256e46 | 0.266410 | 0.133205 | − | 0.991089i | \(-0.457473\pi\) | ||||
0.133205 | + | 0.991089i | \(0.457473\pi\) | |||||||
\(410\) | 3.54342e46 | + | 8.75109e46i | 0.330607 | + | 0.816493i | ||||
\(411\) | − | 1.01248e47i | − | 0.904135i | ||||||
\(412\) | 2.49668e46 | + | 2.57752e46i | 0.213409 | + | 0.220319i | ||||
\(413\) | −1.71928e46 | −0.140684 | ||||||||
\(414\) | 2.50662e46 | − | 1.01496e46i | 0.196373 | − | 0.0795137i | ||||
\(415\) | − | 8.08423e46i | − | 0.606419i | ||||||
\(416\) | −1.96658e47 | + | 7.24259e46i | −1.41264 | + | 0.520252i | ||||
\(417\) | 1.46144e47 | 1.00538 | ||||||||
\(418\) | 6.98891e45 | + | 1.72604e46i | 0.0460507 | + | 0.113730i | ||||
\(419\) | − | 2.27184e47i | − | 1.43392i | −0.697113 | − | 0.716961i | \(-0.745532\pi\) | ||
0.697113 | − | 0.716961i | \(-0.254468\pi\) | |||||||
\(420\) | −3.54946e46 | + | 3.43813e46i | −0.214622 | + | 0.207891i | ||||
\(421\) | −1.97959e47 | −1.14683 | −0.573414 | − | 0.819266i | \(-0.694381\pi\) | ||||
−0.573414 | + | 0.819266i | \(0.694381\pi\) | |||||||
\(422\) | 1.65813e47 | − | 6.71394e46i | 0.920435 | − | 0.372695i | ||||
\(423\) | − | 3.99117e46i | − | 0.212311i | ||||||
\(424\) | 3.92587e46 | + | 1.73718e46i | 0.200148 | + | 0.0885646i | ||||
\(425\) | −3.03203e47 | −1.48160 | ||||||||
\(426\) | −3.46504e46 | − | 8.55752e46i | −0.162306 | − | 0.400844i | ||||
\(427\) | − | 2.61630e46i | − | 0.117486i | ||||||
\(428\) | 1.58883e47 | + | 1.64028e47i | 0.684052 | + | 0.706203i | ||||
\(429\) | 7.23245e47 | 2.98575 | ||||||||
\(430\) | −2.66136e47 | + | 1.07762e47i | −1.05359 | + | 0.426611i | ||||
\(431\) | 3.25686e47i | 1.23654i | 0.785965 | + | 0.618270i | \(0.212166\pi\) | ||||
−0.785965 | + | 0.618270i | \(0.787834\pi\) | |||||||
\(432\) | 1.59068e47 | + | 5.07015e45i | 0.579262 | + | 0.0184635i | ||||
\(433\) | 1.63248e47 | 0.570251 | 0.285126 | − | 0.958490i | \(-0.407965\pi\) | ||||
0.285126 | + | 0.958490i | \(0.407965\pi\) | |||||||
\(434\) | −1.70421e46 | − | 4.20884e46i | −0.0571093 | − | 0.141042i | ||||
\(435\) | 1.94231e47i | 0.624470i | ||||||||
\(436\) | −2.76631e47 | + | 2.67954e47i | −0.853382 | + | 0.826615i | ||||
\(437\) | 1.03053e46 | 0.0305068 | ||||||||
\(438\) | −4.29582e47 | + | 1.73943e47i | −1.22043 | + | 0.494165i | ||||
\(439\) | − | 2.84803e47i | − | 0.776574i | −0.921539 | − | 0.388287i | \(-0.873067\pi\) | ||
0.921539 | − | 0.388287i | \(-0.126933\pi\) | |||||||
\(440\) | 4.29086e47 | − | 9.69694e47i | 1.12304 | − | 2.53797i | ||||
\(441\) | −2.07517e47 | −0.521386 | ||||||||
\(442\) | 1.73588e47 | + | 4.28707e47i | 0.418716 | + | 1.03409i | ||||
\(443\) | − | 1.55992e47i | − | 0.361272i | −0.983550 | − | 0.180636i | \(-0.942184\pi\) | ||
0.983550 | − | 0.180636i | \(-0.0578157\pi\) | |||||||
\(444\) | 4.45020e47 | + | 4.59431e47i | 0.989660 | + | 1.02171i | ||||
\(445\) | 5.60717e45 | 0.0119747 | ||||||||
\(446\) | −5.60268e47 | + | 2.26859e47i | −1.14913 | + | 0.465295i | ||||
\(447\) | 5.22680e47i | 1.02968i | ||||||||
\(448\) | 5.45221e46 | − | 4.95445e46i | 0.103174 | − | 0.0937542i | ||||
\(449\) | −6.78002e46 | −0.123253 | −0.0616264 | − | 0.998099i | \(-0.519629\pi\) | ||||
−0.0616264 | + | 0.998099i | \(0.519629\pi\) | |||||||
\(450\) | −2.28431e47 | − | 5.64151e47i | −0.398961 | − | 0.985303i | ||||
\(451\) | 4.85747e47i | 0.815140i | ||||||||
\(452\) | 6.70843e47 | − | 6.49801e47i | 1.08176 | − | 1.04782i | ||||
\(453\) | −6.96319e47 | −1.07905 | ||||||||
\(454\) | 1.09512e48 | − | 4.43427e47i | 1.63101 | − | 0.660415i | ||||
\(455\) | 2.53890e47i | 0.363446i | ||||||||
\(456\) | −6.29734e46 | − | 2.78655e46i | −0.0866542 | − | 0.0383442i | ||||
\(457\) | −1.03943e48 | −1.37500 | −0.687498 | − | 0.726186i | \(-0.741291\pi\) | ||||
−0.687498 | + | 0.726186i | \(0.741291\pi\) | |||||||
\(458\) | −3.61399e47 | − | 8.92538e47i | −0.459630 | − | 1.13514i | ||||
\(459\) | − | 3.51238e47i | − | 0.429510i | ||||||
\(460\) | −4.08286e47 | − | 4.21507e47i | −0.480091 | − | 0.495637i | ||||
\(461\) | −5.48232e47 | −0.619937 | −0.309968 | − | 0.950747i | \(-0.600318\pi\) | ||||
−0.309968 | + | 0.950747i | \(0.600318\pi\) | |||||||
\(462\) | −2.35657e47 | + | 9.54202e46i | −0.256286 | + | 0.103773i | ||||
\(463\) | 6.58825e46i | 0.0689148i | 0.999406 | + | 0.0344574i | \(0.0109703\pi\) | ||||
−0.999406 | + | 0.0344574i | \(0.989030\pi\) | |||||||
\(464\) | 9.22489e45 | − | 2.89416e47i | 0.00928192 | − | 0.291205i | ||||
\(465\) | 2.41697e48 | 2.33948 | ||||||||
\(466\) | 4.06150e47 | + | 1.00306e48i | 0.378216 | + | 0.934070i | ||||
\(467\) | − | 1.28722e48i | − | 1.15332i | −0.816984 | − | 0.576660i | \(-0.804356\pi\) | ||
0.816984 | − | 0.576660i | \(-0.195644\pi\) | |||||||
\(468\) | −6.66888e47 | + | 6.45971e47i | −0.574947 | + | 0.556913i | ||||
\(469\) | 2.05672e47 | 0.170634 | ||||||||
\(470\) | −8.02760e47 | + | 3.25047e47i | −0.640951 | + | 0.259528i | ||||
\(471\) | 1.81208e48i | 1.39252i | ||||||||
\(472\) | −5.52069e47 | + | 1.24762e48i | −0.408354 | + | 0.922842i | ||||
\(473\) | −1.47724e48 | −1.05184 | ||||||||
\(474\) | −1.07213e48 | − | 2.64780e48i | −0.734912 | − | 1.81500i | ||||
\(475\) | − | 2.31937e47i | − | 0.153068i | ||||||
\(476\) | −1.13122e47 | − | 1.16785e47i | −0.0718820 | − | 0.0742097i | ||||
\(477\) | 1.90193e47 | 0.116376 | ||||||||
\(478\) | 6.16769e46 | − | 2.49737e46i | 0.0363430 | − | 0.0147157i | ||||
\(479\) | 1.18212e47i | 0.0670847i | 0.999437 | + | 0.0335423i | \(0.0106789\pi\) | ||||
−0.999437 | + | 0.0335423i | \(0.989321\pi\) | |||||||
\(480\) | 1.35518e48 | + | 3.67972e48i | 0.740723 | + | 2.01128i | ||||
\(481\) | 3.28627e48 | 1.73018 | ||||||||
\(482\) | 1.09285e48 | + | 2.69899e48i | 0.554262 | + | 1.36885i | ||||
\(483\) | 1.40700e47i | 0.0687456i | ||||||||
\(484\) | 2.39283e48 | − | 2.31778e48i | 1.12641 | − | 1.09108i | ||||
\(485\) | −1.89517e48 | −0.859601 | ||||||||
\(486\) | 2.04912e48 | − | 8.29711e47i | 0.895599 | − | 0.362639i | ||||
\(487\) | − | 6.47797e47i | − | 0.272846i | −0.990651 | − | 0.136423i | \(-0.956439\pi\) | ||
0.990651 | − | 0.136423i | \(-0.0435606\pi\) | |||||||
\(488\) | −1.89856e48 | − | 8.40107e47i | −0.770669 | − | 0.341018i | ||||
\(489\) | 2.73780e48 | 1.07113 | ||||||||
\(490\) | 1.69005e48 | + | 4.17388e48i | 0.637340 | + | 1.57402i | ||||
\(491\) | − | 4.44317e48i | − | 1.61520i | −0.589731 | − | 0.807600i | \(-0.700766\pi\) | ||
0.589731 | − | 0.807600i | \(-0.299234\pi\) | |||||||
\(492\) | −1.24978e48 | − | 1.29025e48i | −0.437988 | − | 0.452171i | ||||
\(493\) | −6.39060e47 | −0.215922 | ||||||||
\(494\) | −3.27942e47 | + | 1.32788e47i | −0.106835 | + | 0.0432586i | ||||
\(495\) | − | 4.69779e48i | − | 1.47571i | ||||||
\(496\) | −3.60144e48 | − | 1.14793e47i | −1.09095 | − | 0.0347732i | ||||
\(497\) | 1.66746e47 | 0.0487126 | ||||||||
\(498\) | 5.77272e47 | + | 1.42568e48i | 0.162649 | + | 0.401691i | ||||
\(499\) | 9.00710e47i | 0.244779i | 0.992482 | + | 0.122390i | \(0.0390558\pi\) | ||||
−0.992482 | + | 0.122390i | \(0.960944\pi\) | |||||||
\(500\) | −4.74140e48 | + | 4.59268e48i | −1.24293 | + | 1.20394i | ||||
\(501\) | −9.59266e48 | −2.42583 | ||||||||
\(502\) | −1.82217e47 | + | 7.37817e46i | −0.0444551 | + | 0.0180004i | ||||
\(503\) | 2.54884e48i | 0.599954i | 0.953946 | + | 0.299977i | \(0.0969791\pi\) | ||||
−0.953946 | + | 0.299977i | \(0.903021\pi\) | |||||||
\(504\) | 1.32069e47 | − | 2.98463e47i | 0.0299952 | − | 0.0677862i | ||||
\(505\) | 3.42480e48 | 0.750569 | ||||||||
\(506\) | −1.13314e48 | − | 2.79848e48i | −0.239648 | − | 0.591852i | ||||
\(507\) | 7.67782e48i | 1.56709i | ||||||||
\(508\) | −6.30661e48 | − | 6.51083e48i | −1.24236 | − | 1.28260i | ||||
\(509\) | 6.81591e48 | 1.29600 | 0.647998 | − | 0.761642i | \(-0.275606\pi\) | ||||
0.647998 | + | 0.761642i | \(0.275606\pi\) | |||||||
\(510\) | 8.02167e48 | − | 3.24807e48i | 1.47232 | − | 0.596159i | ||||
\(511\) | − | 8.37057e47i | − | 0.148313i | ||||||
\(512\) | −1.84454e48 | − | 5.54738e48i | −0.315522 | − | 0.948918i | ||||
\(513\) | 2.68682e47 | 0.0443737 | ||||||||
\(514\) | −1.44365e48 | − | 3.56534e48i | −0.230211 | − | 0.568546i | ||||
\(515\) | − | 3.44977e48i | − | 0.531203i | ||||||
\(516\) | 3.92389e48 | − | 3.80081e48i | 0.583474 | − | 0.565173i | ||||
\(517\) | −4.45589e48 | −0.639889 | ||||||||
\(518\) | −1.07077e48 | + | 4.33569e47i | −0.148512 | + | 0.0601343i | ||||
\(519\) | − | 7.32893e47i | − | 0.0981811i | ||||||
\(520\) | 1.84239e49 | + | 8.15253e48i | 2.38409 | + | 1.05495i | ||||
\(521\) | −5.58419e48 | −0.698041 | −0.349020 | − | 0.937115i | \(-0.613486\pi\) | ||||
−0.349020 | + | 0.937115i | \(0.613486\pi\) | |||||||
\(522\) | −4.81464e47 | − | 1.18906e48i | −0.0581427 | − | 0.143594i | ||||
\(523\) | 1.22870e49i | 1.43356i | 0.697298 | + | 0.716781i | \(0.254385\pi\) | ||||
−0.697298 | + | 0.716781i | \(0.745615\pi\) | |||||||
\(524\) | 1.06896e47 | + | 1.10357e47i | 0.0120503 | + | 0.0124405i | ||||
\(525\) | 3.16665e48 | 0.344931 | ||||||||
\(526\) | −1.39098e48 | + | 5.63223e47i | −0.146412 | + | 0.0592839i | ||||
\(527\) | 7.95234e48i | 0.808917i | ||||||||
\(528\) | −6.42736e47 | + | 2.01648e49i | −0.0631862 | + | 1.98236i | ||||
\(529\) | 8.85367e48 | 0.841243 | ||||||||
\(530\) | −1.54896e48 | − | 3.82543e48i | −0.142257 | − | 0.351329i | ||||
\(531\) | 6.04424e48i | 0.536587i | ||||||||
\(532\) | 8.93352e46 | − | 8.65331e46i | 0.00766679 | − | 0.00742631i | ||||
\(533\) | −9.22907e48 | −0.765716 | ||||||||
\(534\) | −9.88840e46 | + | 4.00393e46i | −0.00793201 | + | 0.00321176i | ||||
\(535\) | − | 2.19536e49i | − | 1.70270i | ||||||
\(536\) | 6.60424e48 | − | 1.49250e49i | 0.495287 | − | 1.11930i | ||||
\(537\) | −2.86053e49 | −2.07448 | ||||||||
\(538\) | −4.58130e47 | − | 1.13143e48i | −0.0321298 | − | 0.0793502i | ||||
\(539\) | 2.31680e49i | 1.57141i | ||||||||
\(540\) | −1.06449e49 | − | 1.09896e49i | −0.698316 | − | 0.720929i | ||||
\(541\) | 2.08018e49 | 1.31993 | 0.659964 | − | 0.751297i | \(-0.270572\pi\) | ||||
0.659964 | + | 0.751297i | \(0.270572\pi\) | |||||||
\(542\) | 1.27905e49 | − | 5.17902e48i | 0.785055 | − | 0.317878i | ||||
\(543\) | 1.19545e48i | 0.0709798i | ||||||||
\(544\) | −1.21071e49 | + | 4.45884e48i | −0.695438 | + | 0.256119i | ||||
\(545\) | 3.70244e49 | 2.05755 | ||||||||
\(546\) | −1.81296e48 | − | 4.47742e48i | −0.0974811 | − | 0.240747i | ||||
\(547\) | − | 2.21627e49i | − | 1.15305i | −0.817078 | − | 0.576527i | \(-0.804407\pi\) | ||
0.817078 | − | 0.576527i | \(-0.195593\pi\) | |||||||
\(548\) | 1.04229e49 | − | 1.00960e49i | 0.524733 | − | 0.508274i | ||||
\(549\) | −9.19778e48 | −0.448106 | ||||||||
\(550\) | −6.29839e49 | + | 2.55029e49i | −2.96962 | + | 1.20243i | ||||
\(551\) | − | 4.88853e47i | − | 0.0223074i | ||||||
\(552\) | 1.02101e49 | + | 4.51793e48i | 0.450948 | + | 0.199543i | ||||
\(553\) | 5.15934e48 | 0.220568 | ||||||||
\(554\) | 1.05715e49 | + | 2.61082e49i | 0.437484 | + | 1.08044i | ||||
\(555\) | − | 6.14904e49i | − | 2.46339i | ||||||
\(556\) | 1.45728e49 | + | 1.50447e49i | 0.565192 | + | 0.583494i | ||||
\(557\) | −3.43445e49 | −1.28962 | −0.644812 | − | 0.764341i | \(-0.723065\pi\) | ||||
−0.644812 | + | 0.764341i | \(0.723065\pi\) | |||||||
\(558\) | −1.47964e49 | + | 5.99125e48i | −0.537950 | + | 0.217822i | ||||
\(559\) | − | 2.80672e49i | − | 0.988069i | ||||||
\(560\) | −7.07872e48 | − | 2.25628e47i | −0.241307 | − | 0.00769146i | ||||
\(561\) | 4.45259e49 | 1.46988 | ||||||||
\(562\) | −4.58350e48 | − | 1.13198e49i | −0.146536 | − | 0.361896i | ||||
\(563\) | 3.38206e49i | 1.04720i | 0.851964 | + | 0.523601i | \(0.175412\pi\) | ||||
−0.851964 | + | 0.523601i | \(0.824588\pi\) | |||||||
\(564\) | 1.18358e49 | − | 1.14646e49i | 0.354956 | − | 0.343823i | ||||
\(565\) | −8.97859e49 | −2.60817 | ||||||||
\(566\) | 6.16766e47 | − | 2.49735e47i | 0.0173550 | − | 0.00702724i | ||||
\(567\) | 6.38769e48i | 0.174120i | ||||||||
\(568\) | 5.35431e48 | − | 1.21002e49i | 0.141395 | − | 0.319538i | ||||
\(569\) | 6.96348e49 | 1.78158 | 0.890791 | − | 0.454414i | \(-0.150151\pi\) | ||||
0.890791 | + | 0.454414i | \(0.150151\pi\) | |||||||
\(570\) | 2.48463e48 | + | 6.13623e48i | 0.0615906 | + | 0.152109i | ||||
\(571\) | − | 1.13276e48i | − | 0.0272076i | −0.999907 | − | 0.0136038i | \(-0.995670\pi\) | ||
0.999907 | − | 0.0136038i | \(-0.00433035\pi\) | |||||||
\(572\) | 7.21186e49 | + | 7.44539e49i | 1.67849 | + | 1.73284i | ||||
\(573\) | −1.12599e49 | −0.253952 | ||||||||
\(574\) | 3.00713e48 | − | 1.21762e48i | 0.0657262 | − | 0.0266133i | ||||
\(575\) | 3.76047e49i | 0.796565i | ||||||||
\(576\) | −1.74177e49 | − | 1.91676e49i | −0.357590 | − | 0.393517i | ||||
\(577\) | 3.94515e48 | 0.0785052 | 0.0392526 | − | 0.999229i | \(-0.487502\pi\) | ||||
0.0392526 | + | 0.999229i | \(0.487502\pi\) | |||||||
\(578\) | −8.77097e48 | − | 2.16614e49i | −0.169179 | − | 0.417817i | ||||
\(579\) | 7.18553e49i | 1.34352i | ||||||||
\(580\) | −1.99950e49 | + | 1.93678e49i | −0.362424 | + | 0.351056i | ||||
\(581\) | −2.77798e48 | −0.0488156 | ||||||||
\(582\) | 3.34219e49 | − | 1.35329e49i | 0.569399 | − | 0.230556i | ||||
\(583\) | − | 2.12338e49i | − | 0.350747i | ||||||
\(584\) | −6.07424e49 | − | 2.68783e49i | −0.972882 | − | 0.430497i | ||||
\(585\) | 8.92567e49 | 1.38623 | ||||||||
\(586\) | −1.56374e48 | − | 3.86194e48i | −0.0235510 | − | 0.0581633i | ||||
\(587\) | − | 7.75747e49i | − | 1.13301i | −0.824058 | − | 0.566506i | \(-0.808295\pi\) | ||
0.824058 | − | 0.566506i | \(-0.191705\pi\) | |||||||
\(588\) | −5.96091e49 | − | 6.15394e49i | −0.844347 | − | 0.871688i | ||||
\(589\) | −6.08320e48 | −0.0835712 | ||||||||
\(590\) | 1.21570e50 | − | 4.92252e49i | 1.61991 | − | 0.655921i | ||||
\(591\) | 1.08438e50i | 1.40154i | ||||||||
\(592\) | −2.92046e48 | + | 9.16246e49i | −0.0366151 | + | 1.14874i | ||||
\(593\) | 3.70508e49 | 0.450623 | 0.225311 | − | 0.974287i | \(-0.427660\pi\) | ||||
0.225311 | + | 0.974287i | \(0.427660\pi\) | |||||||
\(594\) | −2.95432e49 | − | 7.29622e49i | −0.348580 | − | 0.860878i | ||||
\(595\) | 1.56305e49i | 0.178924i | ||||||||
\(596\) | −5.38070e49 | + | 5.21192e49i | −0.597593 | + | 0.578849i | ||||
\(597\) | −1.40863e50 | −1.51796 | ||||||||
\(598\) | 5.31704e49 | − | 2.15293e49i | 0.555967 | − | 0.225117i | ||||
\(599\) | 1.01866e50i | 1.03359i | 0.856109 | + | 0.516795i | \(0.172875\pi\) | ||||
−0.856109 | + | 0.516795i | \(0.827125\pi\) | |||||||
\(600\) | 1.01683e50 | − | 2.29793e50i | 1.00121 | − | 2.26264i | ||||
\(601\) | −6.84375e49 | −0.653963 | −0.326982 | − | 0.945031i | \(-0.606032\pi\) | ||||
−0.326982 | + | 0.945031i | \(0.606032\pi\) | |||||||
\(602\) | 3.70301e48 | + | 9.14523e48i | 0.0343414 | + | 0.0848121i | ||||
\(603\) | − | 7.23055e49i | − | 0.650818i | ||||||
\(604\) | −6.94337e49 | − | 7.16821e49i | −0.606605 | − | 0.626248i | ||||
\(605\) | −3.20258e50 | −2.71584 | ||||||||
\(606\) | −6.03973e49 | + | 2.44556e49i | −0.497176 | + | 0.201312i | ||||
\(607\) | − | 4.26011e49i | − | 0.340428i | −0.985407 | − | 0.170214i | \(-0.945554\pi\) | ||
0.985407 | − | 0.170214i | \(-0.0544458\pi\) | |||||||
\(608\) | −3.41082e48 | − | 9.26137e48i | −0.0264603 | − | 0.0718474i | ||||
\(609\) | 6.67435e48 | 0.0502687 | ||||||||
\(610\) | 7.49082e49 | + | 1.84999e50i | 0.547762 | + | 1.35280i | ||||
\(611\) | − | 8.46607e49i | − | 0.601091i | ||||||
\(612\) | −4.10564e49 | + | 3.97686e49i | −0.283045 | + | 0.274167i | ||||
\(613\) | 2.84023e50 | 1.90137 | 0.950683 | − | 0.310165i | \(-0.100384\pi\) | ||||
0.950683 | + | 0.310165i | \(0.100384\pi\) | |||||||
\(614\) | −8.82051e49 | + | 3.57153e49i | −0.573407 | + | 0.232179i | ||||
\(615\) | 1.72688e50i | 1.09021i | ||||||||
\(616\) | −3.33216e49 | − | 1.47447e49i | −0.204302 | − | 0.0904030i | ||||
\(617\) | 1.94103e50 | 1.15584 | 0.577921 | − | 0.816093i | \(-0.303864\pi\) | ||||
0.577921 | + | 0.816093i | \(0.303864\pi\) | |||||||
\(618\) | 2.46339e49 | + | 6.08376e49i | 0.142475 | + | 0.351868i | ||||
\(619\) | − | 2.91886e50i | − | 1.63976i | −0.572533 | − | 0.819882i | \(-0.694039\pi\) | ||
0.572533 | − | 0.819882i | \(-0.305961\pi\) | |||||||
\(620\) | 2.41009e50 | + | 2.48814e50i | 1.31517 | + | 1.35776i | ||||
\(621\) | −4.35623e49 | −0.230920 | ||||||||
\(622\) | 2.37801e50 | − | 9.62885e49i | 1.22458 | − | 0.495847i | ||||
\(623\) | − | 1.92679e47i | − | 0.000963939i | ||||||
\(624\) | −3.83126e50 | − | 1.22118e49i | −1.86217 | − | 0.0593550i | ||||
\(625\) | 2.11246e50 | 0.997580 | ||||||||
\(626\) | 2.64668e49 | + | 6.53645e49i | 0.121441 | + | 0.299919i | ||||
\(627\) | 3.40604e49i | 0.151857i | ||||||||
\(628\) | −1.86543e50 | + | 1.80692e50i | −0.808177 | + | 0.782827i | ||||
\(629\) | 2.02316e50 | 0.851764 | ||||||||
\(630\) | −2.90828e49 | + | 1.17759e49i | −0.118989 | + | 0.0481799i | ||||
\(631\) | − | 4.24994e50i | − | 1.68988i | −0.534864 | − | 0.844938i | \(-0.679637\pi\) | ||
0.534864 | − | 0.844938i | \(-0.320363\pi\) | |||||||
\(632\) | 1.65669e50 | − | 3.74396e50i | 0.640226 | − | 1.44685i | ||||
\(633\) | 3.27203e50 | 1.22900 | ||||||||
\(634\) | −3.54988e49 | − | 8.76704e49i | −0.129600 | − | 0.320071i | ||||
\(635\) | 8.71413e50i | 3.09241i | ||||||||
\(636\) | 5.46327e49 | + | 5.64018e49i | 0.188462 | + | 0.194565i | ||||
\(637\) | −4.40186e50 | −1.47614 | ||||||||
\(638\) | −1.32751e50 | + | 5.37525e49i | −0.432779 | + | 0.175237i | ||||
\(639\) | − | 5.86208e49i | − | 0.185796i | ||||||
\(640\) | −2.43674e50 | + | 5.06433e50i | −0.750879 | + | 1.56057i | ||||
\(641\) | −4.30618e50 | −1.29017 | −0.645085 | − | 0.764111i | \(-0.723178\pi\) | ||||
−0.645085 | + | 0.764111i | \(0.723178\pi\) | |||||||
\(642\) | 1.56764e50 | + | 3.87157e50i | 0.456685 | + | 1.12786i | ||||
\(643\) | − | 4.66172e50i | − | 1.32053i | −0.751032 | − | 0.660266i | \(-0.770444\pi\) | ||
0.751032 | − | 0.660266i | \(-0.229556\pi\) | |||||||
\(644\) | −1.44842e49 | + | 1.40299e49i | −0.0398979 | + | 0.0386464i | ||||
\(645\) | −5.25175e50 | −1.40679 | ||||||||
\(646\) | −2.01895e49 | + | 8.17495e48i | −0.0525944 | + | 0.0212961i | ||||
\(647\) | − | 7.15036e50i | − | 1.81155i | −0.423758 | − | 0.905776i | \(-0.639289\pi\) | ||
0.423758 | − | 0.905776i | \(-0.360711\pi\) | |||||||
\(648\) | 4.63533e50 | + | 2.05112e50i | 1.14217 | + | 0.505406i | ||||
\(649\) | 6.74801e50 | 1.61723 | ||||||||
\(650\) | −4.84549e50 | − | 1.19668e51i | −1.12953 | − | 2.78957i | ||||
\(651\) | − | 8.30543e49i | − | 0.188324i | ||||||
\(652\) | 2.73001e50 | + | 2.81841e50i | 0.602154 | + | 0.621653i | ||||
\(653\) | −9.56236e49 | −0.205177 | −0.102588 | − | 0.994724i | \(-0.532712\pi\) | ||||
−0.102588 | + | 0.994724i | \(0.532712\pi\) | |||||||
\(654\) | −6.52935e50 | + | 2.64381e50i | −1.36292 | + | 0.551862i | ||||
\(655\) | − | 1.47703e49i | − | 0.0299948i | ||||||
\(656\) | 8.20173e48 | − | 2.57316e50i | 0.0162045 | − | 0.508391i | ||||
\(657\) | −2.94273e50 | −0.565683 | ||||||||
\(658\) | 1.11696e49 | + | 2.75852e49i | 0.0208916 | + | 0.0515954i | ||||
\(659\) | 4.92362e50i | 0.896080i | 0.894014 | + | 0.448040i | \(0.147878\pi\) | ||||
−0.894014 | + | 0.448040i | \(0.852122\pi\) | |||||||
\(660\) | 1.39313e51 | − | 1.34943e51i | 2.46718 | − | 2.38980i | ||||
\(661\) | 3.31963e50 | 0.572088 | 0.286044 | − | 0.958216i | \(-0.407660\pi\) | ||||
0.286044 | + | 0.958216i | \(0.407660\pi\) | |||||||
\(662\) | 4.23335e50 | − | 1.71413e50i | 0.709970 | − | 0.287475i | ||||
\(663\) | 8.45981e50i | 1.38076i | ||||||||
\(664\) | −8.92023e49 | + | 2.01589e50i | −0.141694 | + | 0.320214i | ||||
\(665\) | −1.19567e49 | −0.0184850 | ||||||||
\(666\) | 1.52424e50 | + | 3.76438e50i | 0.229360 | + | 0.566444i | ||||
\(667\) | 7.92595e49i | 0.116088i | ||||||||
\(668\) | −9.56535e50 | − | 9.87510e50i | −1.36372 | − | 1.40788i | ||||
\(669\) | −1.10559e51 | −1.53436 | ||||||||
\(670\) | −1.45431e51 | + | 5.88868e50i | −1.96477 | + | 0.795557i | ||||
\(671\) | 1.02687e51i | 1.35055i | ||||||||
\(672\) | 1.26446e50 | − | 4.65681e49i | 0.161905 | − | 0.0596269i | ||||
\(673\) | 1.51276e51 | 1.88582 | 0.942908 | − | 0.333054i | \(-0.108079\pi\) | ||||
0.942908 | + | 0.333054i | \(0.108079\pi\) | |||||||
\(674\) | −2.24329e50 | − | 5.54021e50i | −0.272275 | − | 0.672431i | ||||
\(675\) | 9.80433e50i | 1.15864i | ||||||||
\(676\) | −7.90388e50 | + | 7.65597e50i | −0.909494 | + | 0.880967i | ||||
\(677\) | −1.31869e51 | −1.47757 | −0.738785 | − | 0.673942i | \(-0.764600\pi\) | ||||
−0.738785 | + | 0.673942i | \(0.764600\pi\) | |||||||
\(678\) | 1.58340e51 | − | 6.41137e50i | 1.72765 | − | 0.699546i | ||||
\(679\) | 6.51237e49i | 0.0691964i | ||||||||
\(680\) | 1.13425e51 | + | 5.01904e50i | 1.17368 | + | 0.519350i | ||||
\(681\) | 2.16104e51 | 2.17778 | ||||||||
\(682\) | 6.68886e50 | + | 1.65193e51i | 0.656498 | + | 1.62134i | ||||
\(683\) | − | 7.41047e50i | − | 0.708391i | −0.935171 | − | 0.354196i | \(-0.884755\pi\) | ||
0.935171 | − | 0.354196i | \(-0.115245\pi\) | |||||||
\(684\) | −3.04213e49 | − | 3.14064e49i | −0.0283248 | − | 0.0292421i | ||||
\(685\) | −1.39501e51 | −1.26516 | ||||||||
\(686\) | 2.89697e50 | − | 1.17302e50i | 0.255923 | − | 0.103626i | ||||
\(687\) | − | 1.76127e51i | − | 1.51567i | ||||||
\(688\) | 7.82544e50 | + | 2.49429e49i | 0.656019 | + | 0.0209101i | ||||
\(689\) | 4.03437e50 | 0.329481 | ||||||||
\(690\) | −4.02842e50 | − | 9.94889e50i | −0.320517 | − | 0.791573i | ||||
\(691\) | 3.66751e50i | 0.284293i | 0.989846 | + | 0.142147i | \(0.0454004\pi\) | ||||
−0.989846 | + | 0.142147i | \(0.954600\pi\) | |||||||
\(692\) | 7.54472e49 | − | 7.30807e49i | 0.0569814 | − | 0.0551941i | ||||
\(693\) | −1.61430e50 | −0.118792 | ||||||||
\(694\) | −1.47595e51 | + | 5.97630e50i | −1.05828 | + | 0.428511i | ||||
\(695\) | − | 2.01359e51i | − | 1.40684i | ||||||
\(696\) | 2.14317e50 | − | 4.84335e50i | 0.145911 | − | 0.329746i | ||||
\(697\) | −5.68180e50 | −0.376960 | ||||||||
\(698\) | 1.88261e49 | + | 4.64943e49i | 0.0121720 | + | 0.0300609i | ||||
\(699\) | 1.97937e51i | 1.24720i | ||||||||
\(700\) | 3.15764e50 | + | 3.25989e50i | 0.193909 | + | 0.200188i | ||||
\(701\) | 1.61915e49 | 0.00969085 | 0.00484542 | − | 0.999988i | \(-0.498458\pi\) | ||||
0.00484542 | + | 0.999988i | \(0.498458\pi\) | |||||||
\(702\) | 1.38626e51 | − | 5.61314e50i | 0.808681 | − | 0.327444i | ||||
\(703\) | 1.54763e50i | 0.0879978i | ||||||||
\(704\) | −2.13994e51 | + | 1.94458e51i | −1.18603 | + | 1.07775i | ||||
\(705\) | −1.58411e51 | −0.855819 | ||||||||
\(706\) | −4.75258e50 | − | 1.17373e51i | −0.250291 | − | 0.618136i | ||||
\(707\) | − | 1.17686e50i | − | 0.0604194i | ||||||
\(708\) | −1.79242e51 | + | 1.73620e51i | −0.897102 | + | 0.868963i | ||||
\(709\) | 2.41201e51 | 1.17692 | 0.588460 | − | 0.808527i | \(-0.299735\pi\) | ||||
0.588460 | + | 0.808527i | \(0.299735\pi\) | |||||||
\(710\) | −1.17906e51 | + | 4.77417e50i | −0.560903 | + | 0.227116i | ||||
\(711\) | − | 1.81380e51i | − | 0.841272i | ||||||
\(712\) | −1.39821e49 | − | 6.18702e48i | −0.00632312 | − | 0.00279796i | ||||
\(713\) | 9.86290e50 | 0.434904 | ||||||||
\(714\) | −1.11613e50 | − | 2.75648e50i | −0.0479897 | − | 0.118519i | ||||
\(715\) | − | 9.96495e51i | − | 4.17798i | ||||||
\(716\) | −2.85239e51 | − | 2.94475e51i | −1.16620 | − | 1.20397i | ||||
\(717\) | 1.21709e50 | 0.0485264 | ||||||||
\(718\) | −1.16156e51 | + | 4.70330e50i | −0.451650 | + | 0.182878i | ||||
\(719\) | 3.96171e51i | 1.50232i | 0.660120 | + | 0.751160i | \(0.270505\pi\) | ||||
−0.660120 | + | 0.751160i | \(0.729495\pi\) | |||||||
\(720\) | −7.93210e49 | + | 2.48857e51i | −0.0293362 | + | 0.920375i | ||||
\(721\) | −1.18544e50 | −0.0427608 | ||||||||
\(722\) | 1.06049e51 | + | 2.61908e51i | 0.373112 | + | 0.921465i | ||||
\(723\) | 5.32601e51i | 1.82773i | ||||||||
\(724\) | −1.23065e50 | + | 1.19205e50i | −0.0411946 | + | 0.0399025i | ||||
\(725\) | 1.78385e51 | 0.582471 | ||||||||
\(726\) | 5.64784e51 | − | 2.28687e51i | 1.79897 | − | 0.728422i | ||||
\(727\) | 1.85957e51i | 0.577821i | 0.957356 | + | 0.288910i | \(0.0932929\pi\) | ||||
−0.957356 | + | 0.288910i | \(0.906707\pi\) | |||||||
\(728\) | 2.80145e50 | − | 6.33101e50i | 0.0849216 | − | 0.191915i | ||||
\(729\) | −1.79751e50 | −0.0531588 | ||||||||
\(730\) | 2.39660e51 | + | 5.91883e51i | 0.691488 | + | 1.70775i | ||||
\(731\) | − | 1.72794e51i | − | 0.486424i | ||||||
\(732\) | −2.64205e51 | − | 2.72761e51i | −0.725675 | − | 0.749173i | ||||
\(733\) | 5.64939e50 | 0.151401 | 0.0757007 | − | 0.997131i | \(-0.475881\pi\) | ||||
0.0757007 | + | 0.997131i | \(0.475881\pi\) | |||||||
\(734\) | 6.44283e51 | − | 2.60878e51i | 1.68480 | − | 0.682194i | ||||
\(735\) | 8.23646e51i | 2.10169i | ||||||||
\(736\) | 5.53008e50 | + | 1.50158e51i | 0.137699 | + | 0.373893i | ||||
\(737\) | −8.07246e51 | −1.96151 | ||||||||
\(738\) | −4.28063e50 | − | 1.05718e51i | −0.101506 | − | 0.250688i | ||||
\(739\) | − | 3.16982e51i | − | 0.733558i | −0.930308 | − | 0.366779i | \(-0.880461\pi\) | ||
0.930308 | − | 0.366779i | \(-0.119539\pi\) | |||||||
\(740\) | 6.33009e51 | − | 6.13154e51i | 1.42968 | − | 1.38484i | ||||
\(741\) | −6.47139e50 | −0.142649 | ||||||||
\(742\) | −1.31453e50 | + | 5.32269e49i | −0.0282814 | + | 0.0114515i | ||||
\(743\) | 3.80186e50i | 0.0798358i | 0.999203 | + | 0.0399179i | \(0.0127096\pi\) | ||||
−0.999203 | + | 0.0399179i | \(0.987290\pi\) | |||||||
\(744\) | −6.02697e51 | − | 2.66691e51i | −1.23534 | − | 0.546634i | ||||
\(745\) | 7.20155e51 | 1.44083 | ||||||||
\(746\) | −1.18852e51 | − | 2.93526e51i | −0.232118 | − | 0.573255i | ||||
\(747\) | 9.76617e50i | 0.186189i | ||||||||
\(748\) | 4.43992e51 | + | 4.58369e51i | 0.826316 | + | 0.853074i | ||||
\(749\) | −7.54390e50 | −0.137064 | ||||||||
\(750\) | −1.11912e52 | + | 4.53144e51i | −1.98506 | + | 0.803774i | ||||
\(751\) | − | 2.08756e51i | − | 0.361510i | −0.983528 | − | 0.180755i | \(-0.942146\pi\) | ||
0.983528 | − | 0.180755i | \(-0.0578540\pi\) | |||||||
\(752\) | 2.36043e51 | + | 7.52366e49i | 0.399089 | + | 0.0127206i | ||||
\(753\) | −3.59574e50 | −0.0593580 | ||||||||
\(754\) | −1.02128e51 | − | 2.52224e51i | −0.164612 | − | 0.406539i | ||||
\(755\) | 9.59397e51i | 1.50992i | ||||||||
\(756\) | −3.77634e50 | + | 3.65789e50i | −0.0580335 | + | 0.0562132i | ||||
\(757\) | −1.95547e51 | −0.293444 | −0.146722 | − | 0.989178i | \(-0.546872\pi\) | ||||
−0.146722 | + | 0.989178i | \(0.546872\pi\) | |||||||
\(758\) | −2.53387e50 | + | 1.02599e50i | −0.0371312 | + | 0.0150349i | ||||
\(759\) | − | 5.52233e51i | − | 0.790261i | ||||||
\(760\) | −3.83934e50 | + | 8.67655e50i | −0.0536553 | + | 0.121256i | ||||
\(761\) | −1.08898e52 | −1.48627 | −0.743135 | − | 0.669142i | \(-0.766662\pi\) | ||||
−0.743135 | + | 0.669142i | \(0.766662\pi\) | |||||||
\(762\) | −6.22252e51 | − | 1.53676e52i | −0.829424 | − | 2.04841i | ||||
\(763\) | − | 1.27227e51i | − | 0.165629i | ||||||
\(764\) | −1.12279e51 | − | 1.15914e51i | −0.142763 | − | 0.147386i | ||||
\(765\) | 5.49501e51 | 0.682437 | ||||||||
\(766\) | 1.71419e51 | − | 6.94096e50i | 0.207942 | − | 0.0841980i | ||||
\(767\) | 1.28210e52i | 1.51917i | ||||||||
\(768\) | 6.80956e50 | − | 1.06711e52i | 0.0788165 | − | 1.23511i | ||||
\(769\) | 3.33302e51 | 0.376846 | 0.188423 | − | 0.982088i | \(-0.439662\pi\) | ||||
0.188423 | + | 0.982088i | \(0.439662\pi\) | |||||||
\(770\) | 1.31471e51 | + | 3.24691e51i | 0.145210 | + | 0.358622i | ||||
\(771\) | − | 7.03561e51i | − | 0.759142i | ||||||
\(772\) | −7.39709e51 | + | 7.16507e51i | −0.779740 | + | 0.755282i | ||||
\(773\) | 1.13759e51 | 0.117153 | 0.0585766 | − | 0.998283i | \(-0.481344\pi\) | ||||
0.0585766 | + | 0.998283i | \(0.481344\pi\) | |||||||
\(774\) | 3.21506e51 | − | 1.30182e51i | 0.323484 | − | 0.130982i | ||||
\(775\) | − | 2.21979e52i | − | 2.18213i | ||||||
\(776\) | 4.72581e51 | + | 2.09115e51i | 0.453905 | + | 0.200851i | ||||
\(777\) | −2.11299e51 | −0.198299 | ||||||||
\(778\) | 3.99003e51 | + | 9.85409e51i | 0.365884 | + | 0.903615i | ||||
\(779\) | − | 4.34633e50i | − | 0.0389447i | ||||||
\(780\) | 2.56389e52 | + | 2.64691e52i | 2.24490 | + | 2.31759i | ||||
\(781\) | −6.54464e51 | −0.559973 | ||||||||
\(782\) | 3.27339e51 | − | 1.32543e51i | 0.273701 | − | 0.110825i | ||||
\(783\) | 2.06646e51i | 0.168855i | ||||||||
\(784\) | 3.91186e50 | − | 1.22728e52i | 0.0312388 | − | 0.980068i | ||||
\(785\) | 2.49671e52 | 1.94856 | ||||||||
\(786\) | 1.05471e50 | + | 2.60478e50i | 0.00804499 | + | 0.0198685i | ||||
\(787\) | − | 6.69833e51i | − | 0.499369i | −0.968327 | − | 0.249684i | \(-0.919673\pi\) | ||
0.968327 | − | 0.249684i | \(-0.0803268\pi\) | |||||||
\(788\) | −1.11631e52 | + | 1.08129e52i | −0.813414 | + | 0.787900i | ||||
\(789\) | −2.74486e51 | −0.195494 | ||||||||
\(790\) | −3.64817e52 | + | 1.47719e52i | −2.53973 | + | 1.02837i | ||||
\(791\) | 3.08531e51i | 0.209953i | ||||||||
\(792\) | −5.18359e51 | + | 1.17144e52i | −0.344808 | + | 0.779233i | ||||
\(793\) | −1.95103e52 | −1.26867 | ||||||||
\(794\) | 4.96210e51 | + | 1.22548e52i | 0.315426 | + | 0.778999i | ||||
\(795\) | − | 7.54884e51i | − | 0.469107i | ||||||
\(796\) | −1.40462e52 | − | 1.45011e52i | −0.853343 | − | 0.880976i | ||||
\(797\) | 2.43626e52 | 1.44702 | 0.723508 | − | 0.690316i | \(-0.242529\pi\) | ||||
0.723508 | + | 0.690316i | \(0.242529\pi\) | |||||||
\(798\) | 2.10859e50 | − | 8.53793e49i | 0.0122445 | − | 0.00495793i | ||||
\(799\) | − | 5.21206e51i | − | 0.295915i | ||||||
\(800\) | 3.37952e52 | − | 1.24463e52i | 1.87601 | − | 0.690906i | ||||
\(801\) | −6.77376e49 | −0.00367658 | ||||||||
\(802\) | 6.56108e51 | + | 1.62037e52i | 0.348206 | + | 0.859957i | ||||
\(803\) | 3.28537e52i | 1.70492i | ||||||||
\(804\) | 2.14422e52 | − | 2.07697e52i | 1.08808 | − | 1.05395i | ||||
\(805\) | 1.93858e51 | 0.0961961 | ||||||||
\(806\) | −3.13862e52 | + | 1.27087e52i | −1.52303 | + | 0.616693i | ||||
\(807\) | − | 2.23269e51i | − | 0.105951i | ||||||
\(808\) | −8.54010e51 | − | 3.77897e51i | −0.396331 | − | 0.175375i | ||||
\(809\) | −3.66483e51 | −0.166334 | −0.0831668 | − | 0.996536i | \(-0.526503\pi\) | ||||
−0.0831668 | + | 0.996536i | \(0.526503\pi\) | |||||||
\(810\) | −1.82888e52 | − | 4.51674e52i | −0.811811 | − | 2.00491i | ||||
\(811\) | 1.26501e52i | 0.549186i | 0.961561 | + | 0.274593i | \(0.0885431\pi\) | ||||
−0.961561 | + | 0.274593i | \(0.911457\pi\) | |||||||
\(812\) | 6.65535e50 | + | 6.87086e50i | 0.0282594 | + | 0.0291745i | ||||
\(813\) | 2.52399e52 | 1.04823 | ||||||||
\(814\) | 4.20269e52 | − | 1.70172e52i | 1.70722 | − | 0.691271i | ||||
\(815\) | − | 3.77218e52i | − | 1.49884i | ||||||
\(816\) | −2.35868e52 | − | 7.51810e50i | −0.916741 | − | 0.0292203i | ||||
\(817\) | 1.32180e51 | 0.0502536 | ||||||||
\(818\) | 2.68845e51 | + | 6.63959e51i | 0.0999867 | + | 0.246935i | ||||
\(819\) | − | 3.06712e51i | − | 0.111589i | ||||||
\(820\) | −1.77773e52 | + | 1.72196e52i | −0.632725 | + | 0.612879i | ||||
\(821\) | −1.21528e52 | −0.423155 | −0.211578 | − | 0.977361i | \(-0.567860\pi\) | ||||
−0.211578 | + | 0.977361i | \(0.567860\pi\) | |||||||
\(822\) | 2.46013e52 | − | 9.96135e51i | 0.838042 | − | 0.339333i | ||||
\(823\) | − | 1.18381e52i | − | 0.394535i | −0.980350 | − | 0.197268i | \(-0.936793\pi\) | ||
0.980350 | − | 0.197268i | \(-0.0632068\pi\) | |||||||
\(824\) | −3.80652e51 | + | 8.60237e51i | −0.124119 | + | 0.280497i | ||||
\(825\) | −1.24288e53 | −3.96514 | ||||||||
\(826\) | −1.69153e51 | − | 4.17752e51i | −0.0528005 | − | 0.130400i | ||||
\(827\) | − | 3.34744e52i | − | 1.02238i | −0.859467 | − | 0.511192i | \(-0.829204\pi\) | ||
0.859467 | − | 0.511192i | \(-0.170796\pi\) | |||||||
\(828\) | 4.93231e51 | + | 5.09203e51i | 0.147402 | + | 0.152175i | ||||
\(829\) | 4.02173e52 | 1.17607 | 0.588033 | − | 0.808837i | \(-0.299902\pi\) | ||||
0.588033 | + | 0.808837i | \(0.299902\pi\) | |||||||
\(830\) | 1.96431e52 | − | 7.95373e51i | 0.562089 | − | 0.227596i | ||||
\(831\) | 5.15202e52i | 1.44264i | ||||||||
\(832\) | −3.69464e52 | − | 4.06584e52i | −1.01240 | − | 1.11412i | ||||
\(833\) | −2.70997e52 | −0.726698 | ||||||||
\(834\) | 1.43785e52 | + | 3.55101e52i | 0.377332 | + | 0.931887i | ||||
\(835\) | 1.32169e53i | 3.39447i | ||||||||
\(836\) | −3.50633e51 | + | 3.39635e51i | −0.0881332 | + | 0.0853687i | ||||
\(837\) | 2.57146e52 | 0.632589 | ||||||||
\(838\) | 5.52014e52 | − | 2.23517e52i | 1.32910 | − | 0.538168i | ||||
\(839\) | − | 8.09034e51i | − | 0.190657i | −0.995446 | − | 0.0953283i | \(-0.969610\pi\) | ||
0.995446 | − | 0.0953283i | \(-0.0303901\pi\) | |||||||
\(840\) | −1.18462e52 | − | 5.24188e51i | −0.273244 | − | 0.120909i | ||||
\(841\) | −4.05324e52 | −0.915113 | ||||||||
\(842\) | −1.94764e52 | − | 4.81003e52i | −0.430418 | − | 1.06299i | ||||
\(843\) | − | 2.23376e52i | − | 0.483216i | ||||||
\(844\) | 3.26272e52 | + | 3.36837e52i | 0.690901 | + | 0.713273i | ||||
\(845\) | 1.05786e53 | 2.19284 | ||||||||
\(846\) | 9.69777e51 | − | 3.92674e51i | 0.196791 | − | 0.0796830i | ||||
\(847\) | 1.10050e52i | 0.218620i | ||||||||
\(848\) | −3.58528e50 | + | 1.12482e52i | −0.00697265 | + | 0.218756i | ||||
\(849\) | 1.21708e51 | 0.0231730 | ||||||||
\(850\) | −2.98308e52 | − | 7.36725e52i | −0.556064 | − | 1.37330i | ||||
\(851\) | − | 2.50923e52i | − | 0.457940i | ||||||
\(852\) | 1.73840e52 | − | 1.68388e52i | 0.310626 | − | 0.300883i | ||||
\(853\) | 4.99450e52 | 0.873794 | 0.436897 | − | 0.899511i | \(-0.356077\pi\) | ||||
0.436897 | + | 0.899511i | \(0.356077\pi\) | |||||||
\(854\) | 6.35711e51 | − | 2.57407e51i | 0.108898 | − | 0.0440939i | ||||
\(855\) | 4.20344e51i | 0.0705042i | ||||||||
\(856\) | −2.42238e52 | + | 5.47435e52i | −0.397846 | + | 0.899094i | ||||
\(857\) | 7.48536e52 | 1.20381 | 0.601905 | − | 0.798568i | \(-0.294409\pi\) | ||||
0.601905 | + | 0.798568i | \(0.294409\pi\) | |||||||
\(858\) | 7.11570e52 | + | 1.75735e53i | 1.12059 | + | 2.76749i | ||||
\(859\) | − | 1.11454e53i | − | 1.71877i | −0.511331 | − | 0.859384i | \(-0.670847\pi\) | ||
0.511331 | − | 0.859384i | \(-0.329153\pi\) | |||||||
\(860\) | −5.23680e52 | − | 5.40638e52i | −0.790850 | − | 0.816459i | ||||
\(861\) | 5.93407e51 | 0.0877599 | ||||||||
\(862\) | −7.91355e52 | + | 3.20429e52i | −1.14615 | + | 0.464089i | ||||
\(863\) | 1.10358e53i | 1.56534i | 0.622439 | + | 0.782669i | \(0.286142\pi\) | ||||
−0.622439 | + | 0.782669i | \(0.713858\pi\) | |||||||
\(864\) | 1.44181e52 | + | 3.91493e52i | 0.200290 | + | 0.543846i | ||||
\(865\) | −1.00979e52 | −0.137385 | ||||||||
\(866\) | 1.60613e52 | + | 3.96662e52i | 0.214022 | + | 0.528565i | ||||
\(867\) | − | 4.27452e52i | − | 0.557884i | ||||||
\(868\) | 8.54998e51 | − | 8.28179e51i | 0.109297 | − | 0.105869i | ||||
\(869\) | −2.02499e53 | −2.53553 | ||||||||
\(870\) | −4.71944e52 | + | 1.91095e52i | −0.578820 | + | 0.234371i | ||||
\(871\) | − | 1.53375e53i | − | 1.84258i | ||||||
\(872\) | −9.23242e52 | − | 4.08531e52i | −1.08647 | − | 0.480761i | ||||
\(873\) | 2.28947e52 | 0.263923 | ||||||||
\(874\) | 1.01390e51 | + | 2.50400e51i | 0.0114496 | + | 0.0282767i | ||||
\(875\) | − | 2.18065e52i | − | 0.241235i | ||||||
\(876\) | −8.45295e52 | − | 8.72668e52i | −0.916082 | − | 0.945747i | ||||
\(877\) | −1.92716e52 | −0.204610 | −0.102305 | − | 0.994753i | \(-0.532622\pi\) | ||||
−0.102305 | + | 0.994753i | \(0.532622\pi\) | |||||||
\(878\) | 6.92016e52 | − | 2.80205e52i | 0.719805 | − | 0.291457i | ||||
\(879\) | − | 7.62089e51i | − | 0.0776616i | ||||||
\(880\) | 2.77833e53 | + | 8.85570e51i | 2.77393 | + | 0.0884168i | ||||
\(881\) | −1.86439e53 | −1.82377 | −0.911886 | − | 0.410444i | \(-0.865374\pi\) | ||||
−0.911886 | + | 0.410444i | \(0.865374\pi\) | |||||||
\(882\) | −2.04167e52 | − | 5.04227e52i | −0.195682 | − | 0.483272i | ||||
\(883\) | 2.64090e52i | 0.248004i | 0.992282 | + | 0.124002i | \(0.0395730\pi\) | ||||
−0.992282 | + | 0.124002i | \(0.960427\pi\) | |||||||
\(884\) | −8.70890e52 | + | 8.43573e52i | −0.801350 | + | 0.776215i | ||||
\(885\) | 2.39899e53 | 2.16296 | ||||||||
\(886\) | 3.79030e52 | − | 1.53474e52i | 0.334863 | − | 0.135590i | ||||
\(887\) | − | 9.02798e52i | − | 0.781565i | −0.920483 | − | 0.390783i | \(-0.872204\pi\) | ||
0.920483 | − | 0.390783i | \(-0.127796\pi\) | |||||||
\(888\) | −6.78492e52 | + | 1.53333e53i | −0.575588 | + | 1.30077i | ||||
\(889\) | 2.99443e52 | 0.248933 | ||||||||
\(890\) | 5.51666e50 | + | 1.36244e51i | 0.00449424 | + | 0.0110993i | ||||
\(891\) | − | 2.50711e53i | − | 2.00159i | ||||||
\(892\) | −1.10245e53 | − | 1.13815e53i | −0.862563 | − | 0.890494i | ||||
\(893\) | 3.98700e51 | 0.0305717 | ||||||||
\(894\) | −1.27001e53 | + | 5.14243e52i | −0.954405 | + | 0.386450i | ||||
\(895\) | 3.94127e53i | 2.90283i | ||||||||
\(896\) | 1.74026e52 | + | 8.37337e51i | 0.125623 | + | 0.0604444i | ||||
\(897\) | 1.04923e53 | 0.742346 | ||||||||
\(898\) | −6.67058e51 | − | 1.64742e52i | −0.0462583 | − | 0.114243i | ||||
\(899\) | − | 4.67865e52i | − | 0.318014i | ||||||
\(900\) | 1.14604e53 | − | 1.11009e53i | 0.763542 | − | 0.739592i | ||||
\(901\) | 2.48373e52 | 0.162203 | ||||||||
\(902\) | −1.18027e53 | + | 4.77906e52i | −0.755553 | + | 0.305932i | ||||
\(903\) | 1.80466e52i | 0.113244i | ||||||||
\(904\) | 2.23891e53 | + | 9.90708e52i | 1.37722 | + | 0.609416i | ||||
\(905\) | 1.64711e52 | 0.0993224 | ||||||||
\(906\) | −6.85079e52 | − | 1.69192e53i | −0.404980 | − | 1.00017i | ||||
\(907\) | 2.46300e53i | 1.42736i | 0.700471 | + | 0.713681i | \(0.252973\pi\) | ||||
−0.700471 | + | 0.713681i | \(0.747027\pi\) | |||||||
\(908\) | 2.15489e53 | + | 2.22467e53i | 1.22428 | + | 1.26392i | ||||
\(909\) | −4.13734e52 | −0.230447 | ||||||||
\(910\) | −6.16904e52 | + | 2.49792e52i | −0.336878 | + | 0.136406i | ||||
\(911\) | − | 7.65690e52i | − | 0.409942i | −0.978768 | − | 0.204971i | \(-0.934290\pi\) | ||
0.978768 | − | 0.204971i | \(-0.0657099\pi\) | |||||||
\(912\) | 5.75102e50 | − | 1.80429e52i | 0.00301882 | − | 0.0947107i | ||||
\(913\) | 1.09033e53 | 0.561158 | ||||||||
\(914\) | −1.02265e53 | − | 2.52560e53i | −0.516053 | − | 1.27448i | ||||
\(915\) | 3.65064e53i | 1.80630i | ||||||||
\(916\) | 1.81313e53 | − | 1.75626e53i | 0.879652 | − | 0.852061i | ||||
\(917\) | −5.07551e50 | −0.00241453 | ||||||||
\(918\) | 8.53441e52 | − | 3.45568e52i | 0.398112 | − | 0.161200i | ||||
\(919\) | 1.66167e53i | 0.760092i | 0.924968 | + | 0.380046i | \(0.124092\pi\) | ||||
−0.924968 | + | 0.380046i | \(0.875908\pi\) | |||||||
\(920\) | 6.22486e52 | − | 1.40676e53i | 0.279222 | − | 0.631014i | ||||
\(921\) | −1.74058e53 | −0.765633 | ||||||||
\(922\) | −5.39382e52 | − | 1.33210e53i | −0.232670 | − | 0.574619i | ||||
\(923\) | − | 1.24346e53i | − | 0.526021i | ||||||
\(924\) | −4.63706e52 | − | 4.78721e52i | −0.192374 | − | 0.198604i | ||||
\(925\) | −5.64739e53 | −2.29772 | ||||||||
\(926\) | −1.60082e52 | + | 6.48190e51i | −0.0638770 | + | 0.0258645i | ||||
\(927\) | 4.16751e52i | 0.163095i | ||||||||
\(928\) | 7.12302e52 | − | 2.62330e52i | 0.273401 | − | 0.100689i | ||||
\(929\) | −3.79141e53 | −1.42731 | −0.713654 | − | 0.700498i | \(-0.752961\pi\) | ||||
−0.713654 | + | 0.700498i | \(0.752961\pi\) | |||||||
\(930\) | 2.37796e53 | + | 5.87278e53i | 0.878033 | + | 2.16846i | ||||
\(931\) | − | 2.07301e52i | − | 0.0750769i | ||||||
\(932\) | −2.03765e53 | + | 1.97373e53i | −0.723840 | + | 0.701135i | ||||
\(933\) | 4.69261e53 | 1.63510 | ||||||||
\(934\) | 3.12770e53 | − | 1.26644e53i | 1.06901 | − | 0.432855i | ||||
\(935\) | − | 6.13484e53i | − | 2.05681i | ||||||
\(936\) | −2.22571e53 | − | 9.84869e52i | −0.731986 | − | 0.323902i | ||||
\(937\) | 1.11283e53 | 0.359018 | 0.179509 | − | 0.983756i | \(-0.442549\pi\) | ||||
0.179509 | + | 0.983756i | \(0.442549\pi\) | |||||||
\(938\) | 2.02352e52 | + | 4.99745e52i | 0.0640409 | + | 0.158160i | ||||
\(939\) | 1.28986e53i | 0.400462i | ||||||||
\(940\) | −1.57960e53 | − | 1.63075e53i | −0.481113 | − | 0.496692i | ||||
\(941\) | 5.75058e53 | 1.71830 | 0.859149 | − | 0.511725i | \(-0.170993\pi\) | ||||
0.859149 | + | 0.511725i | \(0.170993\pi\) | |||||||
\(942\) | −4.40301e53 | + | 1.78283e53i | −1.29072 | + | 0.522629i | ||||
\(943\) | 7.04685e52i | 0.202668i | ||||||||
\(944\) | −3.57464e53 | − | 1.13939e52i | −1.00864 | − | 0.0321496i | ||||
\(945\) | 5.05427e52 | 0.139922 | ||||||||
\(946\) | −1.45340e53 | − | 3.58942e53i | −0.394770 | − | 0.974953i | ||||
\(947\) | − | 3.74447e53i | − | 0.997909i | −0.866628 | − | 0.498955i | \(-0.833717\pi\) | ||
0.866628 | − | 0.498955i | \(-0.166283\pi\) | |||||||
\(948\) | 5.37884e53 | − | 5.21012e53i | 1.40650 | − | 1.36238i | ||||
\(949\) | −6.24212e53 | −1.60155 | ||||||||
\(950\) | 5.63562e52 | − | 2.28193e52i | 0.141879 | − | 0.0574483i | ||||
\(951\) | − | 1.73003e53i | − | 0.427370i | ||||||
\(952\) | 1.72469e52 | − | 3.89763e52i | 0.0418067 | − | 0.0944792i | ||||
\(953\) | 4.13944e53 | 0.984622 | 0.492311 | − | 0.870419i | \(-0.336152\pi\) | ||||
0.492311 | + | 0.870419i | \(0.336152\pi\) | |||||||
\(954\) | 1.87123e52 | + | 4.62132e52i | 0.0436773 | + | 0.107869i | ||||
\(955\) | 1.55140e53i | 0.355356i | ||||||||
\(956\) | 1.21363e52 | + | 1.25293e52i | 0.0272799 | + | 0.0281633i | ||||
\(957\) | −2.61962e53 | −0.577861 | ||||||||
\(958\) | −2.87233e52 | + | 1.16304e52i | −0.0621807 | + | 0.0251777i | ||||
\(959\) | 4.79366e52i | 0.101843i | ||||||||
\(960\) | −7.60772e53 | + | 6.91316e53i | −1.58625 | + | 1.44143i | ||||
\(961\) | −9.35266e52 | −0.191388 | ||||||||
\(962\) | 3.23322e53 | + | 7.98500e53i | 0.649358 | + | 1.60370i | ||||
\(963\) | 2.65211e53i | 0.522779i | ||||||||
\(964\) | −5.48283e53 | + | 5.31085e53i | −1.06076 | + | 1.02749i | ||||
\(965\) | 9.90031e53 | 1.88000 | ||||||||
\(966\) | −3.41873e52 | + | 1.38428e52i | −0.0637202 | + | 0.0258010i | ||||
\(967\) | 6.95431e53i | 1.27226i | 0.771580 | + | 0.636132i | \(0.219467\pi\) | ||||
−0.771580 | + | 0.636132i | \(0.780533\pi\) | |||||||
\(968\) | 7.98597e53 | + | 3.53377e53i | 1.43407 | + | 0.634573i | ||||
\(969\) | −3.98405e52 | −0.0702259 | ||||||||
\(970\) | −1.86458e53 | − | 4.60490e53i | −0.322619 | − | 0.796763i | ||||
\(971\) | − | 3.68158e53i | − | 0.625299i | −0.949869 | − | 0.312650i | \(-0.898783\pi\) | ||
0.949869 | − | 0.312650i | \(-0.101217\pi\) | |||||||
\(972\) | 4.03208e53 | + | 4.16264e53i | 0.672258 | + | 0.694027i | ||||
\(973\) | −6.91928e52 | −0.113248 | ||||||||
\(974\) | 1.57402e53 | − | 6.37340e52i | 0.252901 | − | 0.102402i | ||||
\(975\) | − | 2.36144e54i | − | 3.72473i | ||||||
\(976\) | 1.73385e52 | − | 5.43969e53i | 0.0268482 | − | 0.842320i | ||||
\(977\) | −6.57791e53 | −0.999968 | −0.499984 | − | 0.866035i | \(-0.666661\pi\) | ||||
−0.499984 | + | 0.866035i | \(0.666661\pi\) | |||||||
\(978\) | 2.69361e53 | + | 6.65234e53i | 0.402008 | + | 0.992830i | ||||
\(979\) | 7.56248e51i | 0.0110809i | ||||||||
\(980\) | −8.47897e53 | + | 8.21302e53i | −1.21976 | + | 1.18150i | ||||
\(981\) | −4.47274e53 | −0.631730 | ||||||||
\(982\) | 1.07961e54 | − | 4.37145e53i | 1.49713 | − | 0.606203i | ||||
\(983\) | 9.93199e53i | 1.35230i | 0.736764 | + | 0.676150i | \(0.236353\pi\) | ||||
−0.736764 | + | 0.676150i | \(0.763647\pi\) | |||||||
\(984\) | 1.90546e53 | − | 4.30616e53i | 0.254735 | − | 0.575676i | ||||
\(985\) | 1.49407e54 | 1.96119 | ||||||||
\(986\) | −6.28744e52 | − | 1.55279e53i | −0.0810381 | − | 0.200138i | ||||
\(987\) | 5.44348e52i | 0.0688919i | ||||||||
\(988\) | −6.45297e52 | − | 6.66193e52i | −0.0801926 | − | 0.0827894i | ||||
\(989\) | −2.14307e53 | −0.261519 | ||||||||
\(990\) | 1.14147e54 | − | 4.62195e53i | 1.36783 | − | 0.553850i | ||||
\(991\) | 2.96029e53i | 0.348344i | 0.984715 | + | 0.174172i | \(0.0557248\pi\) | ||||
−0.984715 | + | 0.174172i | \(0.944275\pi\) | |||||||
\(992\) | −3.26438e53 | − | 8.86375e53i | −0.377216 | − | 1.02425i | ||||
\(993\) | 8.35380e53 | 0.947977 | ||||||||
\(994\) | 1.64055e52 | + | 4.05162e52i | 0.0182824 | + | 0.0451516i | ||||
\(995\) | 1.94083e54i | 2.12408i | ||||||||
\(996\) | −2.89617e53 | + | 2.80532e53i | −0.311283 | + | 0.301519i | ||||
\(997\) | −1.49692e54 | −1.58011 | −0.790053 | − | 0.613039i | \(-0.789947\pi\) | ||||
−0.790053 | + | 0.613039i | \(0.789947\pi\) | |||||||
\(998\) | −2.18855e53 | + | 8.86170e52i | −0.226886 | + | 0.0918687i | ||||
\(999\) | − | 6.54208e53i | − | 0.666096i |
(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 | 4.37.b.b.3.10 | yes | 16 | |
4.3 | odd | 2 | inner | 4.37.b.b.3.9 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.37.b.b.3.9 | ✓ | 16 | 4.3 | odd | 2 | inner | |
4.37.b.b.3.10 | yes | 16 | 1.1 | even | 1 | trivial |