Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,19,Mod(3,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 19, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 19);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 19 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.4308910168\) |
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: | \( x^{16} - 5 x^{15} + 56971 x^{14} - 14457953 x^{13} + 5222713963 x^{12} - 1887111404561 x^{11} + 551417417640415 x^{10} + \cdots + 32\!\cdots\!30 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{120}\cdot 3^{13}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.12 | ||
Root | \(135.604 + 208.454i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.19.d.b.3.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 297.207 | + | 416.907i | 0.580483 | + | 0.814272i | ||||
\(3\) | −25925.7 | −1.31716 | −0.658580 | − | 0.752510i | \(-0.728843\pi\) | ||||
−0.658580 | + | 0.752510i | \(0.728843\pi\) | |||||||
\(4\) | −85479.4 | + | 247816.i | −0.326078 | + | 0.945343i | ||||
\(5\) | − | 1.90314e6i | − | 0.974405i | −0.873289 | − | 0.487203i | \(-0.838017\pi\) | ||
0.873289 | − | 0.487203i | \(-0.161983\pi\) | |||||||
\(6\) | −7.70530e6 | − | 1.08086e7i | −0.764590 | − | 1.07253i | ||||
\(7\) | − | 9.33592e6i | − | 0.231353i | −0.993287 | − | 0.115676i | \(-0.963096\pi\) | ||
0.993287 | − | 0.115676i | \(-0.0369035\pi\) | |||||||
\(8\) | −1.28721e8 | + | 3.80157e7i | −0.959049 | + | 0.283239i | ||||
\(9\) | 2.84720e8 | 0.734912 | ||||||||
\(10\) | 7.93431e8 | − | 5.65626e8i | 0.793431 | − | 0.565626i | ||||
\(11\) | 2.94305e9 | 1.24814 | 0.624071 | − | 0.781367i | \(-0.285477\pi\) | ||||
0.624071 | + | 0.781367i | \(0.285477\pi\) | |||||||
\(12\) | 2.21611e9 | − | 6.42479e9i | 0.429497 | − | 1.24517i | ||||
\(13\) | 7.67712e9i | 0.723949i | 0.932188 | + | 0.361974i | \(0.117897\pi\) | ||||
−0.932188 | + | 0.361974i | \(0.882103\pi\) | |||||||
\(14\) | 3.89221e9 | − | 2.77470e9i | 0.188384 | − | 0.134296i | ||||
\(15\) | 4.93401e10i | 1.28345i | ||||||||
\(16\) | −5.41060e10 | − | 4.23663e10i | −0.787346 | − | 0.616511i | ||||
\(17\) | −1.40802e10 | −0.118732 | −0.0593662 | − | 0.998236i | \(-0.518908\pi\) | ||||
−0.0593662 | + | 0.998236i | \(0.518908\pi\) | |||||||
\(18\) | 8.46209e10 | + | 1.18702e11i | 0.426604 | + | 0.598418i | ||||
\(19\) | 5.59331e11 | 1.73335 | 0.866676 | − | 0.498871i | \(-0.166252\pi\) | ||||
0.866676 | + | 0.498871i | \(0.166252\pi\) | |||||||
\(20\) | 4.71627e11 | + | 1.62679e11i | 0.921147 | + | 0.317732i | ||||
\(21\) | 2.42040e11i | 0.304729i | ||||||||
\(22\) | 8.74698e11 | + | 1.22698e12i | 0.724526 | + | 1.01633i | ||||
\(23\) | − | 2.61543e12i | − | 1.45208i | −0.687650 | − | 0.726042i | \(-0.741358\pi\) | ||
0.687650 | − | 0.726042i | \(-0.258642\pi\) | |||||||
\(24\) | 3.33719e12 | − | 9.85583e11i | 1.26322 | − | 0.373072i | ||||
\(25\) | 1.92773e11 | 0.0505343 | ||||||||
\(26\) | −3.20065e12 | + | 2.28170e12i | −0.589491 | + | 0.420240i | ||||
\(27\) | 2.66258e12 | 0.349164 | ||||||||
\(28\) | 2.31359e12 | + | 7.98029e11i | 0.218708 | + | 0.0754391i | ||||
\(29\) | 1.91498e13i | 1.32003i | 0.751253 | + | 0.660014i | \(0.229450\pi\) | ||||
−0.751253 | + | 0.660014i | \(0.770550\pi\) | |||||||
\(30\) | −2.05702e13 | + | 1.46642e13i | −1.04508 | + | 0.745020i | ||||
\(31\) | − | 3.57176e13i | − | 1.35091i | −0.737401 | − | 0.675455i | \(-0.763947\pi\) | ||
0.737401 | − | 0.675455i | \(-0.236053\pi\) | |||||||
\(32\) | 1.58213e12 | − | 3.51488e13i | 0.0449668 | − | 0.998988i | ||||
\(33\) | −7.63007e13 | −1.64400 | ||||||||
\(34\) | −4.18475e12 | − | 5.87015e12i | −0.0689222 | − | 0.0966805i | ||||
\(35\) | −1.77675e13 | −0.225431 | ||||||||
\(36\) | −2.43377e13 | + | 7.05581e13i | −0.239639 | + | 0.694744i | ||||
\(37\) | − | 2.51975e14i | − | 1.93884i | −0.245414 | − | 0.969418i | \(-0.578924\pi\) | ||
0.245414 | − | 0.969418i | \(-0.421076\pi\) | |||||||
\(38\) | 1.66237e14 | + | 2.33189e14i | 1.00618 | + | 1.41142i | ||||
\(39\) | − | 1.99034e14i | − | 0.953557i | ||||||
\(40\) | 7.23491e13 | + | 2.44974e14i | 0.275990 | + | 0.934503i | ||||
\(41\) | 7.94564e13 | 0.242702 | 0.121351 | − | 0.992610i | \(-0.461277\pi\) | ||||
0.121351 | + | 0.992610i | \(0.461277\pi\) | |||||||
\(42\) | −1.00908e14 | + | 7.19361e13i | −0.248132 | + | 0.176890i | ||||
\(43\) | −3.62991e14 | −0.722236 | −0.361118 | − | 0.932520i | \(-0.617605\pi\) | ||||
−0.361118 | + | 0.932520i | \(0.617605\pi\) | |||||||
\(44\) | −2.51571e14 | + | 7.29336e14i | −0.406992 | + | 1.17992i | ||||
\(45\) | − | 5.41861e14i | − | 0.716102i | ||||||
\(46\) | 1.09039e15 | − | 7.77324e14i | 1.18239 | − | 0.842911i | ||||
\(47\) | 2.20997e14i | 0.197472i | 0.995114 | + | 0.0987361i | \(0.0314800\pi\) | ||||
−0.995114 | + | 0.0987361i | \(0.968520\pi\) | |||||||
\(48\) | 1.40273e15 | + | 1.09838e15i | 1.03706 | + | 0.812044i | ||||
\(49\) | 1.54125e15 | 0.946476 | ||||||||
\(50\) | 5.72935e13 | + | 8.03684e13i | 0.0293343 | + | 0.0411486i | ||||
\(51\) | 3.65039e14 | 0.156390 | ||||||||
\(52\) | −1.90251e15 | − | 6.56236e14i | −0.684380 | − | 0.236064i | ||||
\(53\) | − | 1.22228e15i | − | 0.370414i | −0.982700 | − | 0.185207i | \(-0.940704\pi\) | ||
0.982700 | − | 0.185207i | \(-0.0592956\pi\) | |||||||
\(54\) | 7.91339e14 | + | 1.11005e15i | 0.202684 | + | 0.284314i | ||||
\(55\) | − | 5.60103e15i | − | 1.21620i | ||||||
\(56\) | 3.54912e14 | + | 1.20173e15i | 0.0655282 | + | 0.221879i | ||||
\(57\) | −1.45010e16 | −2.28310 | ||||||||
\(58\) | −7.98371e15 | + | 5.69148e15i | −1.07486 | + | 0.766254i | ||||
\(59\) | 2.66374e15 | 0.307485 | 0.153742 | − | 0.988111i | \(-0.450867\pi\) | ||||
0.153742 | + | 0.988111i | \(0.450867\pi\) | |||||||
\(60\) | −1.22273e16 | − | 4.21756e15i | −1.21330 | − | 0.418505i | ||||
\(61\) | 2.02843e16i | 1.73457i | 0.497816 | + | 0.867283i | \(0.334135\pi\) | ||||
−0.497816 | + | 0.867283i | \(0.665865\pi\) | |||||||
\(62\) | 1.48909e16 | − | 1.06155e16i | 1.10001 | − | 0.784181i | ||||
\(63\) | − | 2.65812e15i | − | 0.170024i | ||||||
\(64\) | 1.51240e16 | − | 9.78688e15i | 0.839551 | − | 0.543281i | ||||
\(65\) | 1.46106e16 | 0.705420 | ||||||||
\(66\) | −2.26771e16 | − | 3.18103e16i | −0.954317 | − | 1.33867i | ||||
\(67\) | 3.97625e16 | 1.46151 | 0.730753 | − | 0.682642i | \(-0.239169\pi\) | ||||
0.730753 | + | 0.682642i | \(0.239169\pi\) | |||||||
\(68\) | 1.20357e15 | − | 3.48930e15i | 0.0387160 | − | 0.112243i | ||||
\(69\) | 6.78067e16i | 1.91263i | ||||||||
\(70\) | −5.28064e15 | − | 7.40741e15i | −0.130859 | − | 0.183562i | ||||
\(71\) | 1.25349e16i | 0.273398i | 0.990613 | + | 0.136699i | \(0.0436493\pi\) | ||||
−0.990613 | + | 0.136699i | \(0.956351\pi\) | |||||||
\(72\) | −3.66496e16 | + | 1.08238e16i | −0.704817 | + | 0.208156i | ||||
\(73\) | 6.29849e15 | 0.106987 | 0.0534934 | − | 0.998568i | \(-0.482964\pi\) | ||||
0.0534934 | + | 0.998568i | \(0.482964\pi\) | |||||||
\(74\) | 1.05050e17 | − | 7.48887e16i | 1.57874 | − | 1.12546i | ||||
\(75\) | −4.99777e15 | −0.0665617 | ||||||||
\(76\) | −4.78113e16 | + | 1.38611e17i | −0.565208 | + | 1.63861i | ||||
\(77\) | − | 2.74761e16i | − | 0.288761i | ||||||
\(78\) | 8.29789e16 | − | 5.91545e16i | 0.776455 | − | 0.553524i | ||||
\(79\) | − | 6.53764e16i | − | 0.545478i | −0.962088 | − | 0.272739i | \(-0.912070\pi\) | ||
0.962088 | − | 0.272739i | \(-0.0879295\pi\) | |||||||
\(80\) | −8.06289e16 | + | 1.02971e17i | −0.600732 | + | 0.767194i | ||||
\(81\) | −1.79336e17 | −1.19482 | ||||||||
\(82\) | 2.36150e16 | + | 3.31259e16i | 0.140885 | + | 0.197626i | ||||
\(83\) | 1.09064e17 | 0.583416 | 0.291708 | − | 0.956507i | \(-0.405776\pi\) | ||||
0.291708 | + | 0.956507i | \(0.405776\pi\) | |||||||
\(84\) | −5.99813e16 | − | 2.06894e16i | −0.288073 | − | 0.0993654i | ||||
\(85\) | 2.67966e16i | 0.115693i | ||||||||
\(86\) | −1.07883e17 | − | 1.51333e17i | −0.419246 | − | 0.588097i | ||||
\(87\) | − | 4.96472e17i | − | 1.73869i | ||||||
\(88\) | −3.78834e17 | + | 1.11882e17i | −1.19703 | + | 0.353523i | ||||
\(89\) | −3.14498e17 | −0.897652 | −0.448826 | − | 0.893619i | \(-0.648158\pi\) | ||||
−0.448826 | + | 0.893619i | \(0.648158\pi\) | |||||||
\(90\) | 2.25906e17 | − | 1.61045e17i | 0.583102 | − | 0.415685i | ||||
\(91\) | 7.16729e16 | 0.167488 | ||||||||
\(92\) | 6.48144e17 | + | 2.23565e17i | 1.37272 | + | 0.473493i | ||||
\(93\) | 9.26002e17i | 1.77937i | ||||||||
\(94\) | −9.21354e16 | + | 6.56820e16i | −0.160796 | + | 0.114629i | ||||
\(95\) | − | 1.06448e18i | − | 1.68899i | ||||||
\(96\) | −4.10178e16 | + | 9.11256e17i | −0.0592285 | + | 1.31583i | ||||
\(97\) | −5.54687e17 | −0.729629 | −0.364815 | − | 0.931080i | \(-0.618868\pi\) | ||||
−0.364815 | + | 0.931080i | \(0.618868\pi\) | |||||||
\(98\) | 4.58072e17 | + | 6.42560e17i | 0.549413 | + | 0.770689i | ||||
\(99\) | 8.37946e17 | 0.917275 | ||||||||
\(100\) | −1.64781e16 | + | 4.77722e16i | −0.0164781 | + | 0.0477722i | ||||
\(101\) | − | 3.73907e17i | − | 0.341878i | −0.985282 | − | 0.170939i | \(-0.945320\pi\) | ||
0.985282 | − | 0.170939i | \(-0.0546802\pi\) | |||||||
\(102\) | 1.08492e17 | + | 1.52188e17i | 0.0907816 | + | 0.127344i | ||||
\(103\) | − | 1.07694e18i | − | 0.825389i | −0.910870 | − | 0.412694i | \(-0.864588\pi\) | ||
0.910870 | − | 0.412694i | \(-0.135412\pi\) | |||||||
\(104\) | −2.91851e17 | − | 9.88209e17i | −0.205051 | − | 0.694303i | ||||
\(105\) | 4.60635e17 | 0.296929 | ||||||||
\(106\) | 5.09577e17 | − | 3.63270e17i | 0.301618 | − | 0.215019i | ||||
\(107\) | 1.24459e18 | 0.676972 | 0.338486 | − | 0.940971i | \(-0.390085\pi\) | ||||
0.338486 | + | 0.940971i | \(0.390085\pi\) | |||||||
\(108\) | −2.27596e17 | + | 6.59830e17i | −0.113855 | + | 0.330079i | ||||
\(109\) | 1.91158e17i | 0.0880146i | 0.999031 | + | 0.0440073i | \(0.0140125\pi\) | ||||
−0.999031 | + | 0.0440073i | \(0.985988\pi\) | |||||||
\(110\) | 2.33511e18 | − | 1.66467e18i | 0.990315 | − | 0.705982i | ||||
\(111\) | 6.53261e18i | 2.55376i | ||||||||
\(112\) | −3.95529e17 | + | 5.05129e17i | −0.142632 | + | 0.182155i | ||||
\(113\) | 4.88607e17 | 0.162650 | 0.0813249 | − | 0.996688i | \(-0.474085\pi\) | ||||
0.0813249 | + | 0.996688i | \(0.474085\pi\) | |||||||
\(114\) | −4.30982e18 | − | 6.04559e18i | −1.32530 | − | 1.85907i | ||||
\(115\) | −4.97751e18 | −1.41492 | ||||||||
\(116\) | −4.74564e18 | − | 1.63692e18i | −1.24788 | − | 0.430432i | ||||
\(117\) | 2.18583e18i | 0.532039i | ||||||||
\(118\) | 7.91683e17 | + | 1.11053e18i | 0.178490 | + | 0.250376i | ||||
\(119\) | 1.31452e17i | 0.0274691i | ||||||||
\(120\) | −1.87570e18 | − | 6.35112e18i | −0.363523 | − | 1.23089i | ||||
\(121\) | 3.10165e18 | 0.557860 | ||||||||
\(122\) | −8.45666e18 | + | 6.02863e18i | −1.41241 | + | 1.00689i | ||||
\(123\) | −2.05996e18 | −0.319678 | ||||||||
\(124\) | 8.85138e18 | + | 3.05312e18i | 1.27707 | + | 0.440502i | ||||
\(125\) | − | 7.62676e18i | − | 1.02365i | ||||||
\(126\) | 1.10819e18 | − | 7.90014e17i | 0.138446 | − | 0.0986960i | ||||
\(127\) | 4.06004e18i | 0.472386i | 0.971706 | + | 0.236193i | \(0.0758997\pi\) | ||||
−0.971706 | + | 0.236193i | \(0.924100\pi\) | |||||||
\(128\) | 8.57519e18 | + | 3.39658e18i | 0.929724 | + | 0.368257i | ||||
\(129\) | 9.41077e18 | 0.951301 | ||||||||
\(130\) | 4.34238e18 | + | 6.09126e18i | 0.409484 | + | 0.574404i | ||||
\(131\) | 4.83476e18 | 0.425533 | 0.212767 | − | 0.977103i | \(-0.431753\pi\) | ||||
0.212767 | + | 0.977103i | \(0.431753\pi\) | |||||||
\(132\) | 6.52214e18 | − | 1.89085e19i | 0.536074 | − | 1.55415i | ||||
\(133\) | − | 5.22187e18i | − | 0.401016i | ||||||
\(134\) | 1.18177e19 | + | 1.65773e19i | 0.848380 | + | 1.19006i | ||||
\(135\) | − | 5.06725e18i | − | 0.340227i | ||||||
\(136\) | 1.81243e18 | − | 5.35270e17i | 0.113870 | − | 0.0336297i | ||||
\(137\) | −2.02606e19 | −1.19170 | −0.595849 | − | 0.803096i | \(-0.703184\pi\) | ||||
−0.595849 | + | 0.803096i | \(0.703184\pi\) | |||||||
\(138\) | −2.82691e19 | + | 2.01526e19i | −1.55740 | + | 1.11025i | ||||
\(139\) | 1.28976e18 | 0.0665847 | 0.0332923 | − | 0.999446i | \(-0.489401\pi\) | ||||
0.0332923 | + | 0.999446i | \(0.489401\pi\) | |||||||
\(140\) | 1.51876e18 | − | 4.40307e18i | 0.0735082 | − | 0.213110i | ||||
\(141\) | − | 5.72950e18i | − | 0.260103i | ||||||
\(142\) | −5.22589e18 | + | 3.72546e18i | −0.222620 | + | 0.158703i | ||||
\(143\) | 2.25942e19i | 0.903591i | ||||||||
\(144\) | −1.54051e19 | − | 1.20625e19i | −0.578630 | − | 0.453082i | ||||
\(145\) | 3.64447e19 | 1.28624 | ||||||||
\(146\) | 1.87196e18 | + | 2.62589e18i | 0.0621041 | + | 0.0871164i | ||||
\(147\) | −3.99581e19 | −1.24666 | ||||||||
\(148\) | 6.24433e19 | + | 2.15386e19i | 1.83287 | + | 0.632212i | ||||
\(149\) | − | 6.12891e19i | − | 1.69319i | −0.532234 | − | 0.846597i | \(-0.678647\pi\) | ||
0.532234 | − | 0.846597i | \(-0.321353\pi\) | |||||||
\(150\) | −1.48537e18 | − | 2.08361e18i | −0.0386380 | − | 0.0541994i | ||||
\(151\) | − | 2.92476e19i | − | 0.716635i | −0.933600 | − | 0.358318i | \(-0.883350\pi\) | ||
0.933600 | − | 0.358318i | \(-0.116650\pi\) | |||||||
\(152\) | −7.19979e19 | + | 2.12634e19i | −1.66237 | + | 0.490953i | ||||
\(153\) | −4.00892e18 | −0.0872579 | ||||||||
\(154\) | 1.14550e19 | − | 8.16611e18i | 0.235130 | − | 0.167621i | ||||
\(155\) | −6.79754e19 | −1.31633 | ||||||||
\(156\) | 4.93239e19 | + | 1.70134e19i | 0.901438 | + | 0.310934i | ||||
\(157\) | − | 2.67899e19i | − | 0.462248i | −0.972924 | − | 0.231124i | \(-0.925760\pi\) | ||
0.972924 | − | 0.231124i | \(-0.0742403\pi\) | |||||||
\(158\) | 2.72559e19 | − | 1.94304e19i | 0.444168 | − | 0.316641i | ||||
\(159\) | 3.16884e19i | 0.487895i | ||||||||
\(160\) | −6.68929e19 | − | 3.01101e18i | −0.973420 | − | 0.0438159i | ||||
\(161\) | −2.44174e19 | −0.335944 | ||||||||
\(162\) | −5.32999e19 | − | 7.47663e19i | −0.693571 | − | 0.972906i | ||||
\(163\) | 1.09227e20 | 1.34475 | 0.672377 | − | 0.740209i | \(-0.265273\pi\) | ||||
0.672377 | + | 0.740209i | \(0.265273\pi\) | |||||||
\(164\) | −6.79189e18 | + | 1.96906e19i | −0.0791400 | + | 0.229437i | ||||
\(165\) | 1.45210e20i | 1.60193i | ||||||||
\(166\) | 3.24146e19 | + | 4.54696e19i | 0.338663 | + | 0.475060i | ||||
\(167\) | 6.47127e19i | 0.640533i | 0.947327 | + | 0.320267i | \(0.103772\pi\) | ||||
−0.947327 | + | 0.320267i | \(0.896228\pi\) | |||||||
\(168\) | −9.20132e18 | − | 3.11557e19i | −0.0863111 | − | 0.292250i | ||||
\(169\) | 5.35173e19 | 0.475898 | ||||||||
\(170\) | −1.11717e19 | + | 7.96414e18i | −0.0942060 | + | 0.0671581i | ||||
\(171\) | 1.59253e20 | 1.27386 | ||||||||
\(172\) | 3.10282e19 | − | 8.99548e19i | 0.235505 | − | 0.682761i | ||||
\(173\) | 1.74118e20i | 1.25438i | 0.778868 | + | 0.627188i | \(0.215794\pi\) | ||||
−0.778868 | + | 0.627188i | \(0.784206\pi\) | |||||||
\(174\) | 2.06983e20 | − | 1.47555e20i | 1.41577 | − | 1.00928i | ||||
\(175\) | − | 1.79971e18i | − | 0.0116912i | ||||||
\(176\) | −1.59237e20 | − | 1.24686e20i | −0.982720 | − | 0.769494i | ||||
\(177\) | −6.90592e19 | −0.405007 | ||||||||
\(178\) | −9.34711e19 | − | 1.31117e20i | −0.521072 | − | 0.730933i | ||||
\(179\) | 1.12492e20 | 0.596272 | 0.298136 | − | 0.954523i | \(-0.403635\pi\) | ||||
0.298136 | + | 0.954523i | \(0.403635\pi\) | |||||||
\(180\) | 1.34282e20 | + | 4.63179e19i | 0.676962 | + | 0.233505i | ||||
\(181\) | 2.48283e20i | 1.19080i | 0.803428 | + | 0.595402i | \(0.203007\pi\) | ||||
−0.803428 | + | 0.595402i | \(0.796993\pi\) | |||||||
\(182\) | 2.13017e19 | + | 2.98810e19i | 0.0972237 | + | 0.136380i | ||||
\(183\) | − | 5.25883e20i | − | 2.28470i | ||||||
\(184\) | 9.94273e19 | + | 3.36661e20i | 0.411287 | + | 1.39262i | ||||
\(185\) | −4.79542e20 | −1.88921 | ||||||||
\(186\) | −3.86057e20 | + | 2.75215e20i | −1.44889 | + | 1.03289i | ||||
\(187\) | −4.14389e19 | −0.148195 | ||||||||
\(188\) | −5.47666e19 | − | 1.88907e19i | −0.186679 | − | 0.0643914i | ||||
\(189\) | − | 2.48576e19i | − | 0.0807799i | ||||||
\(190\) | 4.43791e20 | − | 3.16372e20i | 1.37530 | − | 0.980429i | ||||
\(191\) | − | 3.36242e20i | − | 0.993922i | −0.867773 | − | 0.496961i | \(-0.834449\pi\) | ||
0.867773 | − | 0.496961i | \(-0.165551\pi\) | |||||||
\(192\) | −3.92100e20 | + | 2.53731e20i | −1.10582 | + | 0.715588i | ||||
\(193\) | 5.21758e20 | 1.40428 | 0.702139 | − | 0.712040i | \(-0.252228\pi\) | ||||
0.702139 | + | 0.712040i | \(0.252228\pi\) | |||||||
\(194\) | −1.64857e20 | − | 2.31253e20i | −0.423538 | − | 0.594117i | ||||
\(195\) | −3.78789e20 | −0.929151 | ||||||||
\(196\) | −1.31746e20 | + | 3.81947e20i | −0.308625 | + | 0.894744i | ||||
\(197\) | − | 5.19244e20i | − | 1.16192i | −0.813933 | − | 0.580959i | \(-0.802678\pi\) | ||
0.813933 | − | 0.580959i | \(-0.197322\pi\) | |||||||
\(198\) | 2.49044e20 | + | 3.49346e20i | 0.532463 | + | 0.746911i | ||||
\(199\) | 8.49305e20i | 1.73535i | 0.497135 | + | 0.867673i | \(0.334385\pi\) | ||||
−0.497135 | + | 0.867673i | \(0.665615\pi\) | |||||||
\(200\) | −2.48140e19 | + | 7.32840e18i | −0.0484648 | + | 0.0143133i | ||||
\(201\) | −1.03087e21 | −1.92504 | ||||||||
\(202\) | 1.55885e20 | − | 1.11128e20i | 0.278382 | − | 0.198455i | ||||
\(203\) | 1.78781e20 | 0.305392 | ||||||||
\(204\) | −3.12034e19 | + | 9.04625e19i | −0.0509953 | + | 0.147842i | ||||
\(205\) | − | 1.51216e20i | − | 0.236491i | ||||||
\(206\) | 4.48986e20 | − | 3.20076e20i | 0.672091 | − | 0.479124i | ||||
\(207\) | − | 7.44664e20i | − | 1.06715i | ||||||
\(208\) | 3.25251e20 | − | 4.15378e20i | 0.446323 | − | 0.569998i | ||||
\(209\) | 1.64614e21 | 2.16347 | ||||||||
\(210\) | 1.36904e20 | + | 1.92042e20i | 0.172362 | + | 0.241781i | ||||
\(211\) | 4.10455e20 | 0.495135 | 0.247567 | − | 0.968871i | \(-0.420369\pi\) | ||||
0.247567 | + | 0.968871i | \(0.420369\pi\) | |||||||
\(212\) | 3.02900e20 | + | 1.04480e20i | 0.350168 | + | 0.120784i | ||||
\(213\) | − | 3.24975e20i | − | 0.360109i | ||||||
\(214\) | 3.69900e20 | + | 5.18877e20i | 0.392971 | + | 0.551239i | ||||
\(215\) | 6.90820e20i | 0.703751i | ||||||||
\(216\) | −3.42731e20 | + | 1.01220e20i | −0.334865 | + | 0.0988969i | ||||
\(217\) | −3.33456e20 | −0.312537 | ||||||||
\(218\) | −7.96953e19 | + | 5.68137e19i | −0.0716678 | + | 0.0510910i | ||||
\(219\) | −1.63293e20 | −0.140919 | ||||||||
\(220\) | 1.38802e21 | + | 4.78773e20i | 1.14972 | + | 0.396575i | ||||
\(221\) | − | 1.08096e20i | − | 0.0859562i | ||||||
\(222\) | −2.72349e21 | + | 1.94154e21i | −2.07945 | + | 1.48241i | ||||
\(223\) | 2.13650e20i | 0.156660i | 0.996927 | + | 0.0783301i | \(0.0249588\pi\) | ||||
−0.996927 | + | 0.0783301i | \(0.975041\pi\) | |||||||
\(224\) | −3.28146e20 | − | 1.47706e19i | −0.231119 | − | 0.0104032i | ||||
\(225\) | 5.48863e19 | 0.0371382 | ||||||||
\(226\) | 1.45218e20 | + | 2.03704e20i | 0.0944155 | + | 0.132441i | ||||
\(227\) | −2.19788e21 | −1.37332 | −0.686660 | − | 0.726978i | \(-0.740924\pi\) | ||||
−0.686660 | + | 0.726978i | \(0.740924\pi\) | |||||||
\(228\) | 1.23954e21 | − | 3.59359e21i | 0.744470 | − | 2.15832i | ||||
\(229\) | 5.72813e20i | 0.330745i | 0.986231 | + | 0.165373i | \(0.0528827\pi\) | ||||
−0.986231 | + | 0.165373i | \(0.947117\pi\) | |||||||
\(230\) | −1.47935e21 | − | 2.07516e21i | −0.821337 | − | 1.15213i | ||||
\(231\) | 7.12337e20i | 0.380345i | ||||||||
\(232\) | −7.27995e20 | − | 2.46499e21i | −0.373884 | − | 1.26597i | ||||
\(233\) | −5.62737e20 | −0.278037 | −0.139018 | − | 0.990290i | \(-0.544395\pi\) | ||||
−0.139018 | + | 0.990290i | \(0.544395\pi\) | |||||||
\(234\) | −9.11288e20 | + | 6.49644e20i | −0.433224 | + | 0.308840i | ||||
\(235\) | 4.20588e20 | 0.192418 | ||||||||
\(236\) | −2.27695e20 | + | 6.60117e20i | −0.100264 | + | 0.290679i | ||||
\(237\) | 1.69493e21i | 0.718482i | ||||||||
\(238\) | −5.48032e19 | + | 3.90685e19i | −0.0223673 | + | 0.0159453i | ||||
\(239\) | 2.59086e21i | 1.01827i | 0.860687 | + | 0.509135i | \(0.170035\pi\) | ||||
−0.860687 | + | 0.509135i | \(0.829965\pi\) | |||||||
\(240\) | 2.09036e21 | − | 2.66959e21i | 0.791260 | − | 1.01052i | ||||
\(241\) | 3.96324e21 | 1.44510 | 0.722549 | − | 0.691320i | \(-0.242970\pi\) | ||||
0.722549 | + | 0.691320i | \(0.242970\pi\) | |||||||
\(242\) | 9.21834e20 | + | 1.29310e21i | 0.323828 | + | 0.454250i | ||||
\(243\) | 3.61786e21 | 1.22460 | ||||||||
\(244\) | −5.02676e21 | − | 1.73389e21i | −1.63976 | − | 0.565604i | ||||
\(245\) | − | 2.93322e21i | − | 0.922251i | ||||||
\(246\) | −6.12235e20 | − | 8.58812e20i | −0.185568 | − | 0.260305i | ||||
\(247\) | 4.29405e21i | 1.25486i | ||||||||
\(248\) | 1.35783e21 | + | 4.59762e21i | 0.382631 | + | 1.29559i | ||||
\(249\) | −2.82756e21 | −0.768453 | ||||||||
\(250\) | 3.17965e21 | − | 2.26673e21i | 0.833527 | − | 0.594210i | ||||
\(251\) | −6.40834e21 | −1.62062 | −0.810312 | − | 0.585999i | \(-0.800702\pi\) | ||||
−0.810312 | + | 0.585999i | \(0.800702\pi\) | |||||||
\(252\) | 6.58725e20 | + | 2.27215e20i | 0.160731 | + | 0.0554411i | ||||
\(253\) | − | 7.69734e21i | − | 1.81241i | ||||||
\(254\) | −1.69266e21 | + | 1.20667e21i | −0.384651 | + | 0.274212i | ||||
\(255\) | − | 6.94719e20i | − | 0.152387i | ||||||
\(256\) | 1.13255e21 | + | 4.58455e21i | 0.239827 | + | 0.970816i | ||||
\(257\) | 4.82903e21 | 0.987329 | 0.493665 | − | 0.869652i | \(-0.335657\pi\) | ||||
0.493665 | + | 0.869652i | \(0.335657\pi\) | |||||||
\(258\) | 2.79695e21 | + | 3.92342e21i | 0.552214 | + | 0.774618i | ||||
\(259\) | −2.35241e21 | −0.448555 | ||||||||
\(260\) | −1.24891e21 | + | 3.62074e21i | −0.230022 | + | 0.666863i | ||||
\(261\) | 5.45234e21i | 0.970104i | ||||||||
\(262\) | 1.43693e21 | + | 2.01565e21i | 0.247015 | + | 0.346500i | ||||
\(263\) | − | 9.58434e21i | − | 1.59206i | −0.605255 | − | 0.796032i | \(-0.706929\pi\) | ||
0.605255 | − | 0.796032i | \(-0.293071\pi\) | |||||||
\(264\) | 9.82153e21 | − | 2.90063e21i | 1.57668 | − | 0.465647i | ||||
\(265\) | −2.32616e21 | −0.360933 | ||||||||
\(266\) | 2.17704e21 | − | 1.55198e21i | 0.326536 | − | 0.232783i | ||||
\(267\) | 8.15357e21 | 1.18235 | ||||||||
\(268\) | −3.39888e21 | + | 9.85379e21i | −0.476565 | + | 1.38162i | ||||
\(269\) | − | 1.09608e21i | − | 0.148618i | −0.997235 | − | 0.0743091i | \(-0.976325\pi\) | ||
0.997235 | − | 0.0743091i | \(-0.0236751\pi\) | |||||||
\(270\) | 2.11257e21 | − | 1.50603e21i | 0.277037 | − | 0.197496i | ||||
\(271\) | − | 4.44119e21i | − | 0.563346i | −0.959510 | − | 0.281673i | \(-0.909111\pi\) | ||
0.959510 | − | 0.281673i | \(-0.0908894\pi\) | |||||||
\(272\) | 7.61825e20 | + | 5.96528e20i | 0.0934835 | + | 0.0731999i | ||||
\(273\) | −1.85817e21 | −0.220608 | ||||||||
\(274\) | −6.02159e21 | − | 8.44677e21i | −0.691761 | − | 0.970367i | ||||
\(275\) | 5.67341e20 | 0.0630740 | ||||||||
\(276\) | −1.68036e22 | − | 5.79608e21i | −1.80809 | − | 0.623666i | ||||
\(277\) | 2.22727e21i | 0.231982i | 0.993250 | + | 0.115991i | \(0.0370044\pi\) | ||||
−0.993250 | + | 0.115991i | \(0.962996\pi\) | |||||||
\(278\) | 3.83325e20 | + | 5.37708e20i | 0.0386513 | + | 0.0542180i | ||||
\(279\) | − | 1.01695e22i | − | 0.992800i | ||||||
\(280\) | 2.28706e21 | − | 6.75445e20i | 0.216200 | − | 0.0638510i | ||||
\(281\) | −1.87209e22 | −1.71384 | −0.856919 | − | 0.515451i | \(-0.827624\pi\) | ||||
−0.856919 | + | 0.515451i | \(0.827624\pi\) | |||||||
\(282\) | 2.38867e21 | − | 1.70285e21i | 0.211794 | − | 0.150985i | ||||
\(283\) | −1.49875e21 | −0.128721 | −0.0643607 | − | 0.997927i | \(-0.520501\pi\) | ||||
−0.0643607 | + | 0.997927i | \(0.520501\pi\) | |||||||
\(284\) | −3.10635e21 | − | 1.07148e21i | −0.258455 | − | 0.0891491i | ||||
\(285\) | 2.75974e22i | 2.22467i | ||||||||
\(286\) | −9.41968e21 | + | 6.71516e21i | −0.735769 | + | 0.524520i | ||||
\(287\) | − | 7.41798e20i | − | 0.0561499i | ||||||
\(288\) | 4.50464e20 | − | 1.00076e22i | 0.0330467 | − | 0.734169i | ||||
\(289\) | −1.38648e22 | −0.985903 | ||||||||
\(290\) | 1.08316e22 | + | 1.51941e22i | 0.746642 | + | 1.04735i | ||||
\(291\) | 1.43806e22 | 0.961039 | ||||||||
\(292\) | −5.38391e20 | + | 1.56087e21i | −0.0348861 | + | 0.101139i | ||||
\(293\) | − | 9.73171e21i | − | 0.611478i | −0.952115 | − | 0.305739i | \(-0.901097\pi\) | ||
0.952115 | − | 0.305739i | \(-0.0989035\pi\) | |||||||
\(294\) | −1.18758e22 | − | 1.66588e22i | −0.723666 | − | 1.01512i | ||||
\(295\) | − | 5.06946e21i | − | 0.299615i | ||||||
\(296\) | 9.57900e21 | + | 3.24345e22i | 0.549155 | + | 1.85944i | ||||
\(297\) | 7.83612e21 | 0.435806 | ||||||||
\(298\) | 2.55519e22 | − | 1.82156e22i | 1.37872 | − | 0.982871i | ||||
\(299\) | 2.00789e22 | 1.05123 | ||||||||
\(300\) | 4.27206e20 | − | 1.23853e21i | 0.0217043 | − | 0.0629237i | ||||
\(301\) | 3.38885e21i | 0.167091i | ||||||||
\(302\) | 1.21936e22 | − | 8.69261e21i | 0.583536 | − | 0.415995i | ||||
\(303\) | 9.69380e21i | 0.450309i | ||||||||
\(304\) | −3.02632e22 | − | 2.36968e22i | −1.36475 | − | 1.06863i | ||||
\(305\) | 3.86037e22 | 1.69017 | ||||||||
\(306\) | −1.19148e21 | − | 1.67135e21i | −0.0506517 | − | 0.0710516i | ||||
\(307\) | −2.45469e22 | −1.01333 | −0.506665 | − | 0.862143i | \(-0.669122\pi\) | ||||
−0.506665 | + | 0.862143i | \(0.669122\pi\) | |||||||
\(308\) | 6.80902e21 | + | 2.34864e21i | 0.272978 | + | 0.0941587i | ||||
\(309\) | 2.79205e22i | 1.08717i | ||||||||
\(310\) | −2.02028e22 | − | 2.83394e22i | −0.764110 | − | 1.07185i | ||||
\(311\) | 1.32062e22i | 0.485216i | 0.970124 | + | 0.242608i | \(0.0780030\pi\) | ||||
−0.970124 | + | 0.242608i | \(0.921997\pi\) | |||||||
\(312\) | 7.56644e21 | + | 2.56200e22i | 0.270085 | + | 0.914508i | ||||
\(313\) | 2.13013e22 | 0.738766 | 0.369383 | − | 0.929277i | \(-0.379569\pi\) | ||||
0.369383 | + | 0.929277i | \(0.379569\pi\) | |||||||
\(314\) | 1.11689e22 | − | 7.96217e21i | 0.376396 | − | 0.268327i | ||||
\(315\) | −5.05876e21 | −0.165672 | ||||||||
\(316\) | 1.62013e22 | + | 5.58834e21i | 0.515664 | + | 0.177868i | ||||
\(317\) | − | 2.97371e22i | − | 0.919952i | −0.887931 | − | 0.459976i | \(-0.847858\pi\) | ||
0.887931 | − | 0.459976i | \(-0.152142\pi\) | |||||||
\(318\) | −1.32111e22 | + | 9.41803e21i | −0.397279 | + | 0.283215i | ||||
\(319\) | 5.63590e22i | 1.64758i | ||||||||
\(320\) | −1.86258e22 | − | 2.87830e22i | −0.529376 | − | 0.818063i | ||||
\(321\) | −3.22667e22 | −0.891681 | ||||||||
\(322\) | −7.25703e21 | − | 1.01798e22i | −0.195010 | − | 0.273550i | ||||
\(323\) | −7.87551e21 | −0.205805 | ||||||||
\(324\) | 1.53295e22 | − | 4.44422e22i | 0.389604 | − | 1.12951i | ||||
\(325\) | 1.47994e21i | 0.0365842i | ||||||||
\(326\) | 3.24632e22 | + | 4.55377e22i | 0.780608 | + | 1.09500i | ||||
\(327\) | − | 4.95591e21i | − | 0.115929i | ||||||
\(328\) | −1.02277e22 | + | 3.02059e21i | −0.232764 | + | 0.0687429i | ||||
\(329\) | 2.06321e21 | 0.0456857 | ||||||||
\(330\) | −6.05393e22 | + | 4.31576e22i | −1.30440 | + | 0.929891i | ||||
\(331\) | −2.58777e22 | −0.542593 | −0.271297 | − | 0.962496i | \(-0.587452\pi\) | ||||
−0.271297 | + | 0.962496i | \(0.587452\pi\) | |||||||
\(332\) | −9.32273e21 | + | 2.70278e22i | −0.190239 | + | 0.551528i | ||||
\(333\) | − | 7.17422e22i | − | 1.42487i | ||||||
\(334\) | −2.69792e22 | + | 1.92331e22i | −0.521568 | + | 0.371819i | ||||
\(335\) | − | 7.56735e22i | − | 1.42410i | ||||||
\(336\) | 1.02543e22 | − | 1.30958e22i | 0.187869 | − | 0.239927i | ||||
\(337\) | −7.84080e22 | −1.39859 | −0.699297 | − | 0.714832i | \(-0.746503\pi\) | ||||
−0.699297 | + | 0.714832i | \(0.746503\pi\) | |||||||
\(338\) | 1.59057e22 | + | 2.23118e22i | 0.276251 | + | 0.387510i | ||||
\(339\) | −1.26675e22 | −0.214236 | ||||||||
\(340\) | −6.64062e21 | − | 2.29056e21i | −0.109370 | − | 0.0377251i | ||||
\(341\) | − | 1.05119e23i | − | 1.68613i | ||||||
\(342\) | 4.73311e22 | + | 6.63937e22i | 0.739455 | + | 1.03727i | ||||
\(343\) | − | 2.95918e22i | − | 0.450322i | ||||||
\(344\) | 4.67247e22 | − | 1.37994e22i | 0.692660 | − | 0.204566i | ||||
\(345\) | 1.29045e23 | 1.86367 | ||||||||
\(346\) | −7.25909e22 | + | 5.17490e22i | −1.02140 | + | 0.728144i | ||||
\(347\) | −9.46254e21 | −0.129731 | −0.0648653 | − | 0.997894i | \(-0.520662\pi\) | ||||
−0.0648653 | + | 0.997894i | \(0.520662\pi\) | |||||||
\(348\) | 1.23034e23 | + | 4.24382e22i | 1.64366 | + | 0.566949i | ||||
\(349\) | 9.78658e22i | 1.27410i | 0.770824 | + | 0.637048i | \(0.219845\pi\) | ||||
−0.770824 | + | 0.637048i | \(0.780155\pi\) | |||||||
\(350\) | 7.50313e20 | − | 5.34888e20i | 0.00951985 | − | 0.00678657i | ||||
\(351\) | 2.04409e22i | 0.252777i | ||||||||
\(352\) | 4.65629e21 | − | 1.03445e23i | 0.0561250 | − | 1.24688i | ||||
\(353\) | −9.40912e22 | −1.10555 | −0.552773 | − | 0.833332i | \(-0.686430\pi\) | ||||
−0.552773 | + | 0.833332i | \(0.686430\pi\) | |||||||
\(354\) | −2.05249e22 | − | 2.87913e22i | −0.235100 | − | 0.329786i | ||||
\(355\) | 2.38556e22 | 0.266401 | ||||||||
\(356\) | 2.68831e22 | − | 7.79376e22i | 0.292705 | − | 0.848588i | ||||
\(357\) | − | 3.40798e21i | − | 0.0361812i | ||||||
\(358\) | 3.34335e22 | + | 4.68988e22i | 0.346126 | + | 0.485528i | ||||
\(359\) | 1.20975e23i | 1.22136i | 0.791877 | + | 0.610681i | \(0.209104\pi\) | ||||
−0.791877 | + | 0.610681i | \(0.790896\pi\) | |||||||
\(360\) | 2.05992e22 | + | 6.97491e22i | 0.202828 | + | 0.686777i | ||||
\(361\) | 2.08724e23 | 2.00451 | ||||||||
\(362\) | −1.03511e23 | + | 7.37916e22i | −0.969638 | + | 0.691242i | ||||
\(363\) | −8.04124e22 | −0.734791 | ||||||||
\(364\) | −6.12656e21 | + | 1.77617e22i | −0.0546140 | + | 0.158333i | ||||
\(365\) | − | 1.19869e22i | − | 0.104249i | ||||||
\(366\) | 2.19244e23 | − | 1.56296e23i | 1.86037 | − | 1.32623i | ||||
\(367\) | 4.06630e22i | 0.336670i | 0.985730 | + | 0.168335i | \(0.0538390\pi\) | ||||
−0.985730 | + | 0.168335i | \(0.946161\pi\) | |||||||
\(368\) | −1.10806e23 | + | 1.41510e23i | −0.895226 | + | 1.14329i | ||||
\(369\) | 2.26228e22 | 0.178365 | ||||||||
\(370\) | −1.42523e23 | − | 1.99924e23i | −1.09666 | − | 1.53833i | ||||
\(371\) | −1.14111e22 | −0.0856963 | ||||||||
\(372\) | −2.29478e23 | − | 7.91541e22i | −1.68211 | − | 0.580213i | ||||
\(373\) | 3.49817e21i | 0.0250300i | 0.999922 | + | 0.0125150i | \(0.00398376\pi\) | ||||
−0.999922 | + | 0.0125150i | \(0.996016\pi\) | |||||||
\(374\) | −1.23159e22 | − | 1.72762e22i | −0.0860247 | − | 0.120671i | ||||
\(375\) | 1.97729e23i | 1.34831i | ||||||||
\(376\) | −8.40137e21 | − | 2.84471e22i | −0.0559319 | − | 0.189386i | ||||
\(377\) | −1.47016e23 | −0.955633 | ||||||||
\(378\) | 1.03633e22 | − | 7.38787e21i | 0.0657769 | − | 0.0468914i | ||||
\(379\) | 2.17964e23 | 1.35092 | 0.675462 | − | 0.737395i | \(-0.263944\pi\) | ||||
0.675462 | + | 0.737395i | \(0.263944\pi\) | |||||||
\(380\) | 2.63796e23 | + | 9.09915e22i | 1.59667 | + | 0.550742i | ||||
\(381\) | − | 1.05259e23i | − | 0.622208i | ||||||
\(382\) | 1.40182e23 | − | 9.99338e22i | 0.809323 | − | 0.576955i | ||||
\(383\) | − | 3.16907e23i | − | 1.78707i | −0.448989 | − | 0.893537i | \(-0.648216\pi\) | ||
0.448989 | − | 0.893537i | \(-0.351784\pi\) | |||||||
\(384\) | −2.22318e23 | − | 8.80585e22i | −1.22460 | − | 0.485054i | ||||
\(385\) | −5.22908e22 | −0.281370 | ||||||||
\(386\) | 1.55070e23 | + | 2.17525e23i | 0.815160 | + | 1.14347i | ||||
\(387\) | −1.03351e23 | −0.530780 | ||||||||
\(388\) | 4.74143e22 | − | 1.37460e23i | 0.237916 | − | 0.689750i | ||||
\(389\) | 1.96504e23i | 0.963441i | 0.876325 | + | 0.481721i | \(0.159988\pi\) | ||||
−0.876325 | + | 0.481721i | \(0.840012\pi\) | |||||||
\(390\) | −1.12579e23 | − | 1.57920e23i | −0.539357 | − | 0.756582i | ||||
\(391\) | 3.68258e22i | 0.172409i | ||||||||
\(392\) | −1.98392e23 | + | 5.85919e22i | −0.907717 | + | 0.268079i | ||||
\(393\) | −1.25345e23 | −0.560496 | ||||||||
\(394\) | 2.16477e23 | − | 1.54323e23i | 0.946117 | − | 0.674474i | ||||
\(395\) | −1.24420e23 | −0.531517 | ||||||||
\(396\) | −7.16272e22 | + | 2.07656e23i | −0.299103 | + | 0.867139i | ||||
\(397\) | 3.12937e23i | 1.27745i | 0.769437 | + | 0.638723i | \(0.220537\pi\) | ||||
−0.769437 | + | 0.638723i | \(0.779463\pi\) | |||||||
\(398\) | −3.54082e23 | + | 2.52420e23i | −1.41304 | + | 1.00734i | ||||
\(399\) | 1.35381e23i | 0.528202i | ||||||||
\(400\) | −1.04302e22 | − | 8.16708e21i | −0.0397879 | − | 0.0311549i | ||||
\(401\) | −1.05642e23 | −0.394037 | −0.197018 | − | 0.980400i | \(-0.563126\pi\) | ||||
−0.197018 | + | 0.980400i | \(0.563126\pi\) | |||||||
\(402\) | −3.06382e23 | − | 4.29777e23i | −1.11745 | − | 1.56751i | ||||
\(403\) | 2.74208e23 | 0.977990 | ||||||||
\(404\) | 9.26602e22 | + | 3.19614e22i | 0.323192 | + | 0.111479i | ||||
\(405\) | 3.41300e23i | 1.16424i | ||||||||
\(406\) | 5.31351e22 | + | 7.45352e22i | 0.177275 | + | 0.248672i | ||||
\(407\) | − | 7.41575e23i | − | 2.41994i | ||||||
\(408\) | −4.69884e22 | + | 1.38772e22i | −0.149985 | + | 0.0442957i | ||||
\(409\) | 4.40895e22 | 0.137666 | 0.0688328 | − | 0.997628i | \(-0.478073\pi\) | ||||
0.0688328 | + | 0.997628i | \(0.478073\pi\) | |||||||
\(410\) | 6.30432e22 | − | 4.49426e22i | 0.192568 | − | 0.137279i | ||||
\(411\) | 5.25269e23 | 1.56966 | ||||||||
\(412\) | 2.66884e23 | + | 9.20566e22i | 0.780275 | + | 0.269141i | ||||
\(413\) | − | 2.48685e22i | − | 0.0711375i | ||||||
\(414\) | 3.10456e23 | − | 2.21320e23i | 0.868954 | − | 0.619465i | ||||
\(415\) | − | 2.07564e23i | − | 0.568484i | ||||||
\(416\) | 2.69841e23 | + | 1.21462e22i | 0.723217 | + | 0.0325537i | ||||
\(417\) | −3.34378e22 | −0.0877027 | ||||||||
\(418\) | 4.89246e23 | + | 6.86289e23i | 1.25586 | + | 1.76165i | ||||
\(419\) | −1.70150e23 | −0.427470 | −0.213735 | − | 0.976892i | \(-0.568563\pi\) | ||||
−0.213735 | + | 0.976892i | \(0.568563\pi\) | |||||||
\(420\) | −3.93748e22 | + | 1.14153e23i | −0.0968222 | + | 0.280700i | ||||
\(421\) | 6.33068e22i | 0.152374i | 0.997094 | + | 0.0761871i | \(0.0242746\pi\) | ||||
−0.997094 | + | 0.0761871i | \(0.975725\pi\) | |||||||
\(422\) | 1.21990e23 | + | 1.71122e23i | 0.287417 | + | 0.403174i | ||||
\(423\) | 6.29223e22i | 0.145125i | ||||||||
\(424\) | 4.64658e22 | + | 1.57333e23i | 0.104916 | + | 0.355245i | ||||
\(425\) | −2.71429e21 | −0.00600005 | ||||||||
\(426\) | 1.35485e23 | − | 9.65851e22i | 0.293227 | − | 0.209037i | ||||
\(427\) | 1.89372e23 | 0.401296 | ||||||||
\(428\) | −1.06386e23 | + | 3.08428e23i | −0.220746 | + | 0.639970i | ||||
\(429\) | − | 5.85769e23i | − | 1.19017i | ||||||
\(430\) | −2.88008e23 | + | 2.05317e23i | −0.573045 | + | 0.408516i | ||||
\(431\) | − | 2.34828e23i | − | 0.457567i | −0.973477 | − | 0.228783i | \(-0.926525\pi\) | ||
0.973477 | − | 0.228783i | \(-0.0734747\pi\) | |||||||
\(432\) | −1.44062e23 | − | 1.12804e23i | −0.274913 | − | 0.215263i | ||||
\(433\) | −5.71351e23 | −1.06785 | −0.533927 | − | 0.845531i | \(-0.679284\pi\) | ||||
−0.533927 | + | 0.845531i | \(0.679284\pi\) | |||||||
\(434\) | −9.91057e22 | − | 1.39020e23i | −0.181422 | − | 0.254490i | ||||
\(435\) | −9.44854e23 | −1.69419 | ||||||||
\(436\) | −4.73721e22 | − | 1.63401e22i | −0.0832039 | − | 0.0286996i | ||||
\(437\) | − | 1.46289e24i | − | 2.51697i | ||||||
\(438\) | −4.85318e22 | − | 6.80778e22i | −0.0818011 | − | 0.114746i | ||||
\(439\) | 1.88369e23i | 0.311050i | 0.987832 | + | 0.155525i | \(0.0497068\pi\) | ||||
−0.987832 | + | 0.155525i | \(0.950293\pi\) | |||||||
\(440\) | 2.12927e23 | + | 7.20973e23i | 0.344475 | + | 1.16639i | ||||
\(441\) | 4.38826e23 | 0.695576 | ||||||||
\(442\) | 4.50658e22 | − | 3.21268e22i | 0.0699917 | − | 0.0498961i | ||||
\(443\) | −4.33548e23 | −0.659787 | −0.329893 | − | 0.944018i | \(-0.607013\pi\) | ||||
−0.329893 | + | 0.944018i | \(0.607013\pi\) | |||||||
\(444\) | −1.61888e24 | − | 5.58404e23i | −2.41418 | − | 0.832725i | ||||
\(445\) | 5.98532e23i | 0.874676i | ||||||||
\(446\) | −8.90721e22 | + | 6.34983e22i | −0.127564 | + | 0.0909386i | ||||
\(447\) | 1.58896e24i | 2.23021i | ||||||||
\(448\) | −9.13695e22 | − | 1.41196e23i | −0.125690 | − | 0.194232i | ||||
\(449\) | 6.38051e23 | 0.860277 | 0.430139 | − | 0.902763i | \(-0.358465\pi\) | ||||
0.430139 | + | 0.902763i | \(0.358465\pi\) | |||||||
\(450\) | 1.63126e22 | + | 2.28825e22i | 0.0215581 | + | 0.0302406i | ||||
\(451\) | 2.33844e23 | 0.302927 | ||||||||
\(452\) | −4.17659e22 | + | 1.21085e23i | −0.0530366 | + | 0.153760i | ||||
\(453\) | 7.58264e23i | 0.943924i | ||||||||
\(454\) | −6.53227e23 | − | 9.16314e23i | −0.797190 | − | 1.11826i | ||||
\(455\) | − | 1.36403e23i | − | 0.163201i | ||||||
\(456\) | 1.86659e24 | − | 5.51268e23i | 2.18961 | − | 0.646665i | ||||
\(457\) | −2.32448e23 | −0.267350 | −0.133675 | − | 0.991025i | \(-0.542678\pi\) | ||||
−0.133675 | + | 0.991025i | \(0.542678\pi\) | |||||||
\(458\) | −2.38810e23 | + | 1.70244e23i | −0.269317 | + | 0.191992i | ||||
\(459\) | −3.74897e22 | −0.0414570 | ||||||||
\(460\) | 4.25475e23 | − | 1.23351e24i | 0.461374 | − | 1.33758i | ||||
\(461\) | 1.95601e22i | 0.0208000i | 0.999946 | + | 0.0104000i | \(0.00331048\pi\) | ||||
−0.999946 | + | 0.0104000i | \(0.996690\pi\) | |||||||
\(462\) | −2.96978e23 | + | 2.11712e23i | −0.309704 | + | 0.220784i | ||||
\(463\) | 3.50452e23i | 0.358426i | 0.983810 | + | 0.179213i | \(0.0573551\pi\) | ||||
−0.983810 | + | 0.179213i | \(0.942645\pi\) | |||||||
\(464\) | 8.11309e23 | − | 1.03612e24i | 0.813812 | − | 1.03932i | ||||
\(465\) | 1.76231e24 | 1.73382 | ||||||||
\(466\) | −1.67250e23 | − | 2.34609e23i | −0.161396 | − | 0.226397i | ||||
\(467\) | −2.45856e23 | −0.232717 | −0.116359 | − | 0.993207i | \(-0.537122\pi\) | ||||
−0.116359 | + | 0.993207i | \(0.537122\pi\) | |||||||
\(468\) | −5.41683e23 | − | 1.86843e23i | −0.502959 | − | 0.173486i | ||||
\(469\) | − | 3.71220e23i | − | 0.338123i | ||||||
\(470\) | 1.25002e23 | + | 1.75346e23i | 0.111695 | + | 0.156681i | ||||
\(471\) | 6.94547e23i | 0.608855i | ||||||||
\(472\) | −3.42880e23 | + | 1.01264e23i | −0.294893 | + | 0.0870918i | ||||
\(473\) | −1.06830e24 | −0.901453 | ||||||||
\(474\) | −7.06628e23 | + | 5.03745e23i | −0.585040 | + | 0.417067i | ||||
\(475\) | 1.07824e23 | 0.0875937 | ||||||||
\(476\) | −3.25758e22 | − | 1.12364e22i | −0.0259677 | − | 0.00895706i | ||||
\(477\) | − | 3.48007e23i | − | 0.272222i | ||||||
\(478\) | −1.08015e24 | + | 7.70023e23i | −0.829149 | + | 0.591089i | ||||
\(479\) | 4.93215e23i | 0.371549i | 0.982592 | + | 0.185775i | \(0.0594794\pi\) | ||||
−0.982592 | + | 0.185775i | \(0.940521\pi\) | |||||||
\(480\) | 1.73424e24 | + | 7.80624e22i | 1.28215 | + | 0.0577126i | ||||
\(481\) | 1.93444e24 | 1.40362 | ||||||||
\(482\) | 1.17791e24 | + | 1.65231e24i | 0.838855 | + | 1.17670i | ||||
\(483\) | 6.33037e23 | 0.442492 | ||||||||
\(484\) | −2.65128e23 | + | 7.68639e23i | −0.181906 | + | 0.527369i | ||||
\(485\) | 1.05564e24i | 0.710955i | ||||||||
\(486\) | 1.07525e24 | + | 1.50831e24i | 0.710861 | + | 0.997159i | ||||
\(487\) | − | 6.02753e23i | − | 0.391182i | −0.980686 | − | 0.195591i | \(-0.937338\pi\) | ||
0.980686 | − | 0.195591i | \(-0.0626625\pi\) | |||||||
\(488\) | −7.71121e23 | − | 2.61102e24i | −0.491297 | − | 1.66353i | ||||
\(489\) | −2.83179e24 | −1.77126 | ||||||||
\(490\) | 1.22288e24 | − | 8.71774e23i | 0.750963 | − | 0.535351i | ||||
\(491\) | 2.08982e24 | 1.26001 | 0.630006 | − | 0.776590i | \(-0.283052\pi\) | ||||
0.630006 | + | 0.776590i | \(0.283052\pi\) | |||||||
\(492\) | 1.76084e23 | − | 5.10491e23i | 0.104240 | − | 0.302205i | ||||
\(493\) | − | 2.69634e23i | − | 0.156730i | ||||||
\(494\) | −1.79022e24 | + | 1.27622e24i | −1.02180 | + | 0.728424i | ||||
\(495\) | − | 1.59473e24i | − | 0.893797i | ||||||
\(496\) | −1.51322e24 | + | 1.93253e24i | −0.832852 | + | 1.06363i | ||||
\(497\) | 1.17025e23 | 0.0632514 | ||||||||
\(498\) | −8.40371e23 | − | 1.17883e24i | −0.446074 | − | 0.625730i | ||||
\(499\) | −2.80590e24 | −1.46274 | −0.731371 | − | 0.681980i | \(-0.761119\pi\) | ||||
−0.731371 | + | 0.681980i | \(0.761119\pi\) | |||||||
\(500\) | 1.89003e24 | + | 6.51931e23i | 0.967697 | + | 0.333789i | ||||
\(501\) | − | 1.67772e24i | − | 0.843685i | ||||||
\(502\) | −1.90461e24 | − | 2.67169e24i | −0.940745 | − | 1.31963i | ||||
\(503\) | 1.74591e24i | 0.847050i | 0.905884 | + | 0.423525i | \(0.139207\pi\) | ||||
−0.905884 | + | 0.423525i | \(0.860793\pi\) | |||||||
\(504\) | 1.01050e23 | + | 3.42157e23i | 0.0481574 | + | 0.163061i | ||||
\(505\) | −7.11596e23 | −0.333128 | ||||||||
\(506\) | 3.20908e24 | − | 2.28771e24i | 1.47579 | − | 1.05207i | ||||
\(507\) | −1.38747e24 | −0.626834 | ||||||||
\(508\) | −1.00614e24 | − | 3.47050e23i | −0.446567 | − | 0.154035i | ||||
\(509\) | − | 1.30535e24i | − | 0.569204i | −0.958646 | − | 0.284602i | \(-0.908139\pi\) | ||
0.958646 | − | 0.284602i | \(-0.0918615\pi\) | |||||||
\(510\) | 2.89633e23 | − | 2.06476e23i | 0.124084 | − | 0.0884580i | ||||
\(511\) | − | 5.88022e22i | − | 0.0247517i | ||||||
\(512\) | −1.57473e24 | + | 1.83473e24i | −0.651292 | + | 0.758827i | ||||
\(513\) | 1.48927e24 | 0.605223 | ||||||||
\(514\) | 1.43522e24 | + | 2.01326e24i | 0.573128 | + | 0.803955i | ||||
\(515\) | −2.04957e24 | −0.804263 | ||||||||
\(516\) | −8.04428e23 | + | 2.33214e24i | −0.310198 | + | 0.899305i | ||||
\(517\) | 6.50407e23i | 0.246474i | ||||||||
\(518\) | −6.99155e23 | − | 9.80738e23i | −0.260379 | − | 0.365246i | ||||
\(519\) | − | 4.51411e24i | − | 1.65221i | ||||||
\(520\) | −1.88070e24 | + | 5.55432e23i | −0.676532 | + | 0.199803i | ||||
\(521\) | 1.37668e24 | 0.486735 | 0.243368 | − | 0.969934i | \(-0.421748\pi\) | ||||
0.243368 | + | 0.969934i | \(0.421748\pi\) | |||||||
\(522\) | −2.27312e24 | + | 1.62048e24i | −0.789929 | + | 0.563129i | ||||
\(523\) | 2.71686e24 | 0.928009 | 0.464005 | − | 0.885833i | \(-0.346412\pi\) | ||||
0.464005 | + | 0.885833i | \(0.346412\pi\) | |||||||
\(524\) | −4.13273e23 | + | 1.19813e24i | −0.138757 | + | 0.402275i | ||||
\(525\) | 4.66587e22i | 0.0153992i | ||||||||
\(526\) | 3.99578e24 | − | 2.84854e24i | 1.29637 | − | 0.924166i | ||||
\(527\) | 5.02911e23i | 0.160397i | ||||||||
\(528\) | 4.12832e24 | + | 3.23258e24i | 1.29440 | + | 1.01355i | ||||
\(529\) | −3.59630e24 | −1.10855 | ||||||||
\(530\) | −6.91353e23 | − | 9.69794e23i | −0.209516 | − | 0.293898i | ||||
\(531\) | 7.58420e23 | 0.225974 | ||||||||
\(532\) | 1.29406e24 | + | 4.46363e23i | 0.379097 | + | 0.130762i | ||||
\(533\) | 6.09996e23i | 0.175704i | ||||||||
\(534\) | 2.42330e24 | + | 3.39928e24i | 0.686335 | + | 0.962756i | ||||
\(535\) | − | 2.36861e24i | − | 0.659645i | ||||||
\(536\) | −5.11829e24 | + | 1.51160e24i | −1.40166 | + | 0.413956i | ||||
\(537\) | −2.91643e24 | −0.785386 | ||||||||
\(538\) | 4.56964e23 | − | 3.25763e23i | 0.121016 | − | 0.0862703i | ||||
\(539\) | 4.53600e24 | 1.18134 | ||||||||
\(540\) | 1.25575e24 | + | 4.33146e23i | 0.321631 | + | 0.110941i | ||||
\(541\) | 4.31846e24i | 1.08781i | 0.839146 | + | 0.543906i | \(0.183055\pi\) | ||||
−0.839146 | + | 0.543906i | \(0.816945\pi\) | |||||||
\(542\) | 1.85156e24 | − | 1.31995e24i | 0.458717 | − | 0.327013i | ||||
\(543\) | − | 6.43691e24i | − | 1.56848i | ||||||
\(544\) | −2.22767e22 | + | 4.94903e23i | −0.00533902 | + | 0.118612i | ||||
\(545\) | 3.63800e23 | 0.0857619 | ||||||||
\(546\) | −5.52262e23 | − | 7.74684e23i | −0.128059 | − | 0.179635i | ||||
\(547\) | −2.16653e24 | −0.494172 | −0.247086 | − | 0.968994i | \(-0.579473\pi\) | ||||
−0.247086 | + | 0.968994i | \(0.579473\pi\) | |||||||
\(548\) | 1.73186e24 | − | 5.02089e24i | 0.388587 | − | 1.12656i | ||||
\(549\) | 5.77533e24i | 1.27475i | ||||||||
\(550\) | 1.68618e23 | + | 2.36529e23i | 0.0366134 | + | 0.0513594i | ||||
\(551\) | 1.07111e25i | 2.28807i | ||||||||
\(552\) | −2.57772e24 | − | 8.72817e24i | −0.541731 | − | 1.83430i | ||||
\(553\) | −6.10349e23 | −0.126198 | ||||||||
\(554\) | −9.28565e23 | + | 6.61961e23i | −0.188897 | + | 0.134662i | ||||
\(555\) | 1.24324e25 | 2.48840 | ||||||||
\(556\) | −1.10248e23 | + | 3.19622e23i | −0.0217118 | + | 0.0629453i | ||||
\(557\) | 1.39730e24i | 0.270765i | 0.990793 | + | 0.135382i | \(0.0432263\pi\) | ||||
−0.990793 | + | 0.135382i | \(0.956774\pi\) | |||||||
\(558\) | 4.23974e24 | − | 3.02245e24i | 0.808410 | − | 0.576304i | ||||
\(559\) | − | 2.78672e24i | − | 0.522862i | ||||||
\(560\) | 9.61329e23 | + | 7.52744e23i | 0.177492 | + | 0.138981i | ||||
\(561\) | 1.07433e24 | 0.195197 | ||||||||
\(562\) | −5.56399e24 | − | 7.80488e24i | −0.994854 | − | 1.39553i | ||||
\(563\) | −2.45279e24 | −0.431604 | −0.215802 | − | 0.976437i | \(-0.569237\pi\) | ||||
−0.215802 | + | 0.976437i | \(0.569237\pi\) | |||||||
\(564\) | 1.41986e24 | + | 4.89755e23i | 0.245886 | + | 0.0848138i | ||||
\(565\) | − | 9.29885e23i | − | 0.158487i | ||||||
\(566\) | −4.45439e23 | − | 6.24839e23i | −0.0747206 | − | 0.104814i | ||||
\(567\) | 1.67426e24i | 0.276424i | ||||||||
\(568\) | −4.76523e23 | − | 1.61351e24i | −0.0774371 | − | 0.262202i | ||||
\(569\) | 5.44844e24 | 0.871488 | 0.435744 | − | 0.900071i | \(-0.356485\pi\) | ||||
0.435744 | + | 0.900071i | \(0.356485\pi\) | |||||||
\(570\) | −1.15056e25 | + | 8.20217e24i | −1.81149 | + | 1.29138i | ||||
\(571\) | −2.77886e24 | −0.430667 | −0.215333 | − | 0.976541i | \(-0.569084\pi\) | ||||
−0.215333 | + | 0.976541i | \(0.569084\pi\) | |||||||
\(572\) | −5.59920e24 | − | 1.93134e24i | −0.854204 | − | 0.294641i | ||||
\(573\) | 8.71731e24i | 1.30915i | ||||||||
\(574\) | 3.09261e23 | − | 2.20468e23i | 0.0457213 | − | 0.0325941i | ||||
\(575\) | − | 5.04183e23i | − | 0.0733800i | ||||||
\(576\) | 4.30611e24 | − | 2.78652e24i | 0.616996 | − | 0.399264i | ||||
\(577\) | −1.00961e25 | −1.42421 | −0.712104 | − | 0.702074i | \(-0.752257\pi\) | ||||
−0.712104 | + | 0.702074i | \(0.752257\pi\) | |||||||
\(578\) | −4.12073e24 | − | 5.78035e24i | −0.572300 | − | 0.802793i | ||||
\(579\) | −1.35269e25 | −1.84966 | ||||||||
\(580\) | −3.11528e24 | + | 9.03159e24i | −0.419416 | + | 1.21594i | ||||
\(581\) | − | 1.01821e24i | − | 0.134975i | ||||||
\(582\) | 4.27403e24 | + | 5.99539e24i | 0.557867 | + | 0.782547i | ||||
\(583\) | − | 3.59723e24i | − | 0.462330i | ||||||
\(584\) | −8.10750e23 | + | 2.39442e23i | −0.102606 | + | 0.0303029i | ||||
\(585\) | 4.15993e24 | 0.518421 | ||||||||
\(586\) | 4.05722e24 | − | 2.89234e24i | 0.497909 | − | 0.354953i | ||||
\(587\) | −8.87476e24 | −1.07254 | −0.536270 | − | 0.844046i | \(-0.680167\pi\) | ||||
−0.536270 | + | 0.844046i | \(0.680167\pi\) | |||||||
\(588\) | 3.41559e24 | − | 9.90224e24i | 0.406509 | − | 1.17852i | ||||
\(589\) | − | 1.99780e25i | − | 2.34160i | ||||||
\(590\) | 2.11349e24 | − | 1.50668e24i | 0.243968 | − | 0.173921i | ||||
\(591\) | 1.34617e25i | 1.53043i | ||||||||
\(592\) | −1.06752e25 | + | 1.36333e25i | −1.19531 | + | 1.52654i | ||||
\(593\) | 5.60679e24 | 0.618333 | 0.309166 | − | 0.951008i | \(-0.399950\pi\) | ||||
0.309166 | + | 0.951008i | \(0.399950\pi\) | |||||||
\(594\) | 2.32895e24 | + | 3.26694e24i | 0.252978 | + | 0.354865i | ||||
\(595\) | 2.50171e23 | 0.0267660 | ||||||||
\(596\) | 1.51884e25 | + | 5.23896e24i | 1.60065 | + | 0.552114i | ||||
\(597\) | − | 2.20188e25i | − | 2.28573i | ||||||
\(598\) | 5.96761e24 | + | 8.37105e24i | 0.610224 | + | 0.855991i | ||||
\(599\) | 3.41193e24i | 0.343684i | 0.985125 | + | 0.171842i | \(0.0549718\pi\) | ||||
−0.985125 | + | 0.171842i | \(0.945028\pi\) | |||||||
\(600\) | 6.43320e23 | − | 1.89994e23i | 0.0638360 | − | 0.0188529i | ||||
\(601\) | 1.55289e25 | 1.51799 | 0.758996 | − | 0.651096i | \(-0.225690\pi\) | ||||
0.758996 | + | 0.651096i | \(0.225690\pi\) | |||||||
\(602\) | −1.41284e24 | + | 1.00719e24i | −0.136058 | + | 0.0969937i | ||||
\(603\) | 1.13212e25 | 1.07408 | ||||||||
\(604\) | 7.24803e24 | + | 2.50007e24i | 0.677466 | + | 0.233679i | ||||
\(605\) | − | 5.90287e24i | − | 0.543581i | ||||||
\(606\) | −4.04142e24 | + | 2.88107e24i | −0.366674 | + | 0.261397i | ||||
\(607\) | 1.87918e23i | 0.0167985i | 0.999965 | + | 0.00839926i | \(0.00267360\pi\) | ||||
−0.999965 | + | 0.00839926i | \(0.997326\pi\) | |||||||
\(608\) | 8.84935e23 | − | 1.96598e25i | 0.0779434 | − | 1.73160i | ||||
\(609\) | −4.63503e24 | −0.402250 | ||||||||
\(610\) | 1.14733e25 | + | 1.60942e25i | 0.981115 | + | 1.37626i | ||||
\(611\) | −1.69662e24 | −0.142960 | ||||||||
\(612\) | 3.42680e23 | − | 9.93474e23i | 0.0284529 | − | 0.0824886i | ||||
\(613\) | 1.63477e25i | 1.33756i | 0.743461 | + | 0.668779i | \(0.233183\pi\) | ||||
−0.743461 | + | 0.668779i | \(0.766817\pi\) | |||||||
\(614\) | −7.29552e24 | − | 1.02338e25i | −0.588221 | − | 0.825127i | ||||
\(615\) | 3.92038e24i | 0.311496i | ||||||||
\(616\) | 1.04452e24 | + | 3.53676e24i | 0.0817885 | + | 0.276936i | ||||
\(617\) | 6.58005e24 | 0.507765 | 0.253882 | − | 0.967235i | \(-0.418292\pi\) | ||||
0.253882 | + | 0.967235i | \(0.418292\pi\) | |||||||
\(618\) | −1.16403e25 | + | 8.29819e24i | −0.885252 | + | 0.631084i | ||||
\(619\) | 1.49523e25 | 1.12070 | 0.560352 | − | 0.828254i | \(-0.310666\pi\) | ||||
0.560352 | + | 0.828254i | \(0.310666\pi\) | |||||||
\(620\) | 5.81050e24 | − | 1.68454e25i | 0.429228 | − | 1.24439i | ||||
\(621\) | − | 6.96378e24i | − | 0.507015i | ||||||
\(622\) | −5.50578e24 | + | 3.92499e24i | −0.395098 | + | 0.281660i | ||||
\(623\) | 2.93613e24i | 0.207674i | ||||||||
\(624\) | −8.43236e24 | + | 1.07690e25i | −0.587879 | + | 0.750779i | ||||
\(625\) | −1.37794e25 | −0.946912 | ||||||||
\(626\) | 6.33090e24 | + | 8.88067e24i | 0.428841 | + | 0.601557i | ||||
\(627\) | −4.26774e25 | −2.84964 | ||||||||
\(628\) | 6.63897e24 | + | 2.28999e24i | 0.436983 | + | 0.150729i | ||||
\(629\) | 3.54786e24i | 0.230203i | ||||||||
\(630\) | −1.50350e24 | − | 2.10904e24i | −0.0961699 | − | 0.134902i | ||||
\(631\) | − | 2.04517e25i | − | 1.28963i | −0.764340 | − | 0.644814i | \(-0.776935\pi\) | ||
0.764340 | − | 0.644814i | \(-0.223065\pi\) | |||||||
\(632\) | 2.48533e24 | + | 8.41534e24i | 0.154501 | + | 0.523140i | ||||
\(633\) | −1.06413e25 | −0.652172 | ||||||||
\(634\) | 1.23976e25 | − | 8.83809e24i | 0.749091 | − | 0.534017i | ||||
\(635\) | 7.72681e24 | 0.460295 | ||||||||
\(636\) | −7.85289e24 | − | 2.70871e24i | −0.461228 | − | 0.159092i | ||||
\(637\) | 1.18324e25i | 0.685200i | ||||||||
\(638\) | −2.34965e25 | + | 1.67503e25i | −1.34158 | + | 0.956395i | ||||
\(639\) | 3.56893e24i | 0.200923i | ||||||||
\(640\) | 6.46414e24 | − | 1.63197e25i | 0.358832 | − | 0.905928i | ||||
\(641\) | 4.66244e24 | 0.255206 | 0.127603 | − | 0.991825i | \(-0.459272\pi\) | ||||
0.127603 | + | 0.991825i | \(0.459272\pi\) | |||||||
\(642\) | −9.58990e24 | − | 1.34522e25i | −0.517606 | − | 0.726071i | ||||
\(643\) | 2.00719e25 | 1.06829 | 0.534146 | − | 0.845392i | \(-0.320633\pi\) | ||||
0.534146 | + | 0.845392i | \(0.320633\pi\) | |||||||
\(644\) | 2.08719e24 | − | 6.05102e24i | 0.109544 | − | 0.317582i | ||||
\(645\) | − | 1.79100e25i | − | 0.926953i | ||||||
\(646\) | −2.34066e24 | − | 3.28336e24i | −0.119466 | − | 0.167581i | ||||
\(647\) | − | 1.11315e25i | − | 0.560291i | −0.959958 | − | 0.280146i | \(-0.909617\pi\) | ||
0.959958 | − | 0.280146i | \(-0.0903827\pi\) | |||||||
\(648\) | 2.30843e25 | − | 6.81757e24i | 1.14589 | − | 0.338419i | ||||
\(649\) | 7.83953e24 | 0.383785 | ||||||||
\(650\) | −6.16998e23 | + | 4.39849e23i | −0.0297895 | + | 0.0212365i | ||||
\(651\) | 8.64508e24 | 0.411661 | ||||||||
\(652\) | −9.33669e24 | + | 2.70683e25i | −0.438495 | + | 1.27125i | ||||
\(653\) | 3.18524e25i | 1.47545i | 0.675102 | + | 0.737724i | \(0.264100\pi\) | ||||
−0.675102 | + | 0.737724i | \(0.735900\pi\) | |||||||
\(654\) | 2.06615e24 | − | 1.47293e24i | 0.0943980 | − | 0.0672950i | ||||
\(655\) | − | 9.20121e24i | − | 0.414642i | ||||||
\(656\) | −4.29907e24 | − | 3.36628e24i | −0.191091 | − | 0.149629i | ||||
\(657\) | 1.79330e24 | 0.0786259 | ||||||||
\(658\) | 6.13202e23 | + | 8.60168e23i | 0.0265198 | + | 0.0372006i | ||||
\(659\) | −3.67144e25 | −1.56628 | −0.783138 | − | 0.621848i | \(-0.786382\pi\) | ||||
−0.783138 | + | 0.621848i | \(0.786382\pi\) | |||||||
\(660\) | −3.59855e25 | − | 1.24125e25i | −1.51437 | − | 0.522353i | ||||
\(661\) | 6.25876e24i | 0.259821i | 0.991526 | + | 0.129911i | \(0.0414691\pi\) | ||||
−0.991526 | + | 0.129911i | \(0.958531\pi\) | |||||||
\(662\) | −7.69105e24 | − | 1.07886e25i | −0.314966 | − | 0.441818i | ||||
\(663\) | 2.80245e24i | 0.113218i | ||||||||
\(664\) | −1.40389e25 | + | 4.14615e24i | −0.559525 | + | 0.165246i | ||||
\(665\) | −9.93793e24 | −0.390752 | ||||||||
\(666\) | 2.99098e25 | − | 2.13223e25i | 1.16024 | − | 0.827116i | ||||
\(667\) | 5.00850e25 | 1.91679 | ||||||||
\(668\) | −1.60368e25 | − | 5.53161e24i | −0.605523 | − | 0.208864i | ||||
\(669\) | − | 5.53901e24i | − | 0.206347i | ||||||
\(670\) | 3.15488e25 | − | 2.24907e25i | 1.15960 | − | 0.826666i | ||||
\(671\) | 5.96977e25i | 2.16498i | ||||||||
\(672\) | 8.50741e24 | + | 3.82939e23i | 0.304420 | + | 0.0137027i | ||||
\(673\) | −4.46463e25 | −1.57634 | −0.788170 | − | 0.615457i | \(-0.788971\pi\) | ||||
−0.788170 | + | 0.615457i | \(0.788971\pi\) | |||||||
\(674\) | −2.33035e25 | − | 3.26889e25i | −0.811860 | − | 1.13884i | ||||
\(675\) | 5.13273e23 | 0.0176447 | ||||||||
\(676\) | −4.57463e24 | + | 1.32624e25i | −0.155180 | + | 0.449887i | ||||
\(677\) | 2.43011e25i | 0.813444i | 0.913552 | + | 0.406722i | \(0.133328\pi\) | ||||
−0.913552 | + | 0.406722i | \(0.866672\pi\) | |||||||
\(678\) | −3.76486e24 | − | 5.28116e24i | −0.124360 | − | 0.174446i | ||||
\(679\) | 5.17851e24i | 0.168802i | ||||||||
\(680\) | −1.01869e24 | − | 3.44929e24i | −0.0327689 | − | 0.110956i | ||||
\(681\) | 5.69816e25 | 1.80888 | ||||||||
\(682\) | 4.38248e25 | − | 3.12421e25i | 1.37297 | − | 0.978770i | ||||
\(683\) | 4.85583e25 | 1.50133 | 0.750666 | − | 0.660682i | \(-0.229733\pi\) | ||||
0.750666 | + | 0.660682i | \(0.229733\pi\) | |||||||
\(684\) | −1.36128e25 | + | 3.94654e25i | −0.415378 | + | 1.20424i | ||||
\(685\) | 3.85586e25i | 1.16120i | ||||||||
\(686\) | 1.23370e25 | − | 8.79489e24i | 0.366685 | − | 0.261405i | ||||
\(687\) | − | 1.48506e25i | − | 0.435645i | ||||||
\(688\) | 1.96400e25 | + | 1.53786e25i | 0.568650 | + | 0.445267i | ||||
\(689\) | 9.38358e24 | 0.268161 | ||||||||
\(690\) | 3.83532e25 | + | 5.37999e25i | 1.08183 | + | 1.51754i | ||||
\(691\) | −5.60552e25 | −1.56068 | −0.780339 | − | 0.625356i | \(-0.784954\pi\) | ||||
−0.780339 | + | 0.625356i | \(0.784954\pi\) | |||||||
\(692\) | −4.31491e25 | − | 1.48835e25i | −1.18582 | − | 0.409025i | ||||
\(693\) | − | 7.82300e24i | − | 0.212214i | ||||||
\(694\) | −2.81234e24 | − | 3.94500e24i | −0.0753065 | − | 0.105636i | ||||
\(695\) | − | 2.45458e24i | − | 0.0648804i | ||||||
\(696\) | 1.88738e25 | + | 6.39066e25i | 0.492465 | + | 1.66749i | ||||
\(697\) | −1.11876e24 | −0.0288166 | ||||||||
\(698\) | −4.08010e25 | + | 2.90865e25i | −1.03746 | + | 0.739592i | ||||
\(699\) | 1.45893e25 | 0.366219 | ||||||||
\(700\) | 4.45997e23 | + | 1.53838e23i | 0.0110522 | + | 0.00381226i | ||||
\(701\) | − | 7.35112e25i | − | 1.79842i | −0.437516 | − | 0.899211i | \(-0.644142\pi\) | ||
0.437516 | − | 0.899211i | \(-0.355858\pi\) | |||||||
\(702\) | −8.52198e24 | + | 6.07520e24i | −0.205829 | + | 0.146733i | ||||
\(703\) | − | 1.40937e26i | − | 3.36069i | ||||||
\(704\) | 4.45108e25 | − | 2.88033e25i | 1.04788 | − | 0.678092i | ||||
\(705\) | −1.09040e25 | −0.253445 | ||||||||
\(706\) | −2.79646e25 | − | 3.92273e25i | −0.641751 | − | 0.900215i | ||||
\(707\) | −3.49077e24 | −0.0790945 | ||||||||
\(708\) | 5.90315e24 | − | 1.71140e25i | 0.132064 | − | 0.382870i | ||||
\(709\) | 6.76581e25i | 1.49453i | 0.664528 | + | 0.747263i | \(0.268633\pi\) | ||||
−0.664528 | + | 0.747263i | \(0.731367\pi\) | |||||||
\(710\) | 7.09006e24 | + | 9.94557e24i | 0.154641 | + | 0.216923i | ||||
\(711\) | − | 1.86140e25i | − | 0.400878i | ||||||
\(712\) | 4.04826e25 | − | 1.19559e25i | 0.860892 | − | 0.254250i | ||||
\(713\) | −9.34166e25 | −1.96164 | ||||||||
\(714\) | 1.42081e24 | − | 1.01288e24i | 0.0294613 | − | 0.0210026i | ||||
\(715\) | 4.29998e25 | 0.880464 | ||||||||
\(716\) | −9.61576e24 | + | 2.78773e25i | −0.194431 | + | 0.563682i | ||||
\(717\) | − | 6.71698e25i | − | 1.34123i | ||||||
\(718\) | −5.04352e25 | + | 3.59546e25i | −0.994521 | + | 0.708980i | ||||
\(719\) | 1.48792e24i | 0.0289747i | 0.999895 | + | 0.0144873i | \(0.00461162\pi\) | ||||
−0.999895 | + | 0.0144873i | \(0.995388\pi\) | |||||||
\(720\) | −2.29566e25 | + | 2.93179e25i | −0.441485 | + | 0.563820i | ||||
\(721\) | −1.00543e25 | −0.190956 | ||||||||
\(722\) | 6.20344e25 | + | 8.70187e25i | 1.16358 | + | 1.63222i | ||||
\(723\) | −1.02750e26 | −1.90343 | ||||||||
\(724\) | −6.15286e25 | − | 2.12231e25i | −1.12572 | − | 0.388295i | ||||
\(725\) | 3.69157e24i | 0.0667066i | ||||||||
\(726\) | −2.38992e25 | − | 3.35245e25i | −0.426534 | − | 0.598320i | ||||
\(727\) | 5.98201e24i | 0.105448i | 0.998609 | + | 0.0527239i | \(0.0167903\pi\) | ||||
−0.998609 | + | 0.0527239i | \(0.983210\pi\) | |||||||
\(728\) | −9.22584e24 | + | 2.72470e24i | −0.160629 | + | 0.0474391i | ||||
\(729\) | −2.43171e25 | −0.418180 | ||||||||
\(730\) | 4.99742e24 | − | 3.56259e24i | 0.0848867 | − | 0.0605146i | ||||
\(731\) | 5.11099e24 | 0.0857528 | ||||||||
\(732\) | 1.30322e26 | + | 4.49522e25i | 2.15983 | + | 0.744991i | ||||
\(733\) | 1.02391e26i | 1.67620i | 0.545520 | + | 0.838098i | \(0.316332\pi\) | ||||
−0.545520 | + | 0.838098i | \(0.683668\pi\) | |||||||
\(734\) | −1.69527e25 | + | 1.20853e25i | −0.274141 | + | 0.195431i | ||||
\(735\) | 7.60456e25i | 1.21475i | ||||||||
\(736\) | −9.19290e25 | − | 4.13794e24i | −1.45062 | − | 0.0652956i | ||||
\(737\) | 1.17023e26 | 1.82417 | ||||||||
\(738\) | 6.72367e24 | + | 9.43162e24i | 0.103538 | + | 0.145238i | ||||
\(739\) | 5.22864e25 | 0.795405 | 0.397703 | − | 0.917514i | \(-0.369808\pi\) | ||||
0.397703 | + | 0.917514i | \(0.369808\pi\) | |||||||
\(740\) | 4.09910e25 | − | 1.18838e26i | 0.616031 | − | 1.78595i | ||||
\(741\) | − | 1.11326e26i | − | 1.65285i | ||||||
\(742\) | −3.39146e24 | − | 4.75737e24i | −0.0497453 | − | 0.0697801i | ||||
\(743\) | − | 9.56206e23i | − | 0.0138564i | −0.999976 | − | 0.00692822i | \(-0.997795\pi\) | ||
0.999976 | − | 0.00692822i | \(-0.00220534\pi\) | |||||||
\(744\) | −3.52026e25 | − | 1.19196e26i | −0.503986 | − | 1.70650i | ||||
\(745\) | −1.16641e26 | −1.64986 | ||||||||
\(746\) | −1.45841e24 | + | 1.03968e24i | −0.0203813 | + | 0.0145295i | ||||
\(747\) | 3.10527e25 | 0.428760 | ||||||||
\(748\) | 3.54217e24 | − | 1.02692e25i | 0.0483231 | − | 0.140095i | ||||
\(749\) | − | 1.16193e25i | − | 0.156619i | ||||||
\(750\) | −8.24346e25 | + | 5.87665e25i | −1.09789 | + | 0.782669i | ||||
\(751\) | 2.03300e25i | 0.267534i | 0.991013 | + | 0.133767i | \(0.0427074\pi\) | ||||
−0.991013 | + | 0.133767i | \(0.957293\pi\) | |||||||
\(752\) | 9.36285e24 | − | 1.19573e25i | 0.121744 | − | 0.155479i | ||||
\(753\) | 1.66141e26 | 2.13462 | ||||||||
\(754\) | −4.36941e25 | − | 6.12919e25i | −0.554729 | − | 0.778145i | ||||
\(755\) | −5.56622e25 | −0.698293 | ||||||||
\(756\) | 6.16012e24 | + | 2.12482e24i | 0.0763647 | + | 0.0263406i | ||||
\(757\) | − | 7.07010e25i | − | 0.866089i | −0.901372 | − | 0.433045i | \(-0.857439\pi\) | ||
0.901372 | − | 0.433045i | \(-0.142561\pi\) | |||||||
\(758\) | 6.47804e25 | + | 9.08706e25i | 0.784189 | + | 1.10002i | ||||
\(759\) | 1.99559e26i | 2.38723i | ||||||||
\(760\) | 4.04671e25 | + | 1.37022e26i | 0.478388 | + | 1.61982i | ||||
\(761\) | 5.11578e25 | 0.597654 | 0.298827 | − | 0.954307i | \(-0.403405\pi\) | ||||
0.298827 | + | 0.954307i | \(0.403405\pi\) | |||||||
\(762\) | 4.38834e25 | − | 3.12838e25i | 0.506647 | − | 0.361181i | ||||
\(763\) | 1.78464e24 | 0.0203624 | ||||||||
\(764\) | 8.33262e25 | + | 2.87418e25i | 0.939597 | + | 0.324096i | ||||
\(765\) | 7.62952e24i | 0.0850245i | ||||||||
\(766\) | 1.32121e26 | − | 9.41871e25i | 1.45516 | − | 1.03737i | ||||
\(767\) | 2.04498e25i | 0.222603i | ||||||||
\(768\) | −2.93622e25 | − | 1.18857e26i | −0.315891 | − | 1.27872i | ||||
\(769\) | 1.08358e26 | 1.15219 | 0.576094 | − | 0.817383i | \(-0.304576\pi\) | ||||
0.576094 | + | 0.817383i | \(0.304576\pi\) | |||||||
\(770\) | −1.55412e25 | − | 2.18004e25i | −0.163331 | − | 0.229112i | ||||
\(771\) | −1.25196e26 | −1.30047 | ||||||||
\(772\) | −4.45996e25 | + | 1.29300e26i | −0.457905 | + | 1.32752i | ||||
\(773\) | − | 1.02495e26i | − | 1.04013i | −0.854127 | − | 0.520064i | \(-0.825908\pi\) | ||
0.854127 | − | 0.520064i | \(-0.174092\pi\) | |||||||
\(774\) | −3.07166e25 | − | 4.30876e25i | −0.308109 | − | 0.432199i | ||||
\(775\) | − | 6.88538e24i | − | 0.0682673i | ||||||
\(776\) | 7.14001e25 | − | 2.10868e25i | 0.699750 | − | 0.206660i | ||||
\(777\) | 6.09879e25 | 0.590819 | ||||||||
\(778\) | −8.19240e25 | + | 5.84025e25i | −0.784503 | + | 0.559262i | ||||
\(779\) | 4.44425e25 | 0.420689 | ||||||||
\(780\) | 3.23787e25 | − | 9.38701e25i | 0.302976 | − | 0.878366i | ||||
\(781\) | 3.68909e25i | 0.341240i | ||||||||
\(782\) | −1.53529e25 | + | 1.09449e25i | −0.140388 | + | 0.100081i | ||||
\(783\) | 5.09880e25i | 0.460906i | ||||||||
\(784\) | −8.33911e25 | − | 6.52973e25i | −0.745204 | − | 0.583513i | ||||
\(785\) | −5.09849e25 | −0.450417 | ||||||||
\(786\) | −3.72533e25 | − | 5.22571e25i | −0.325358 | − | 0.456396i | ||||
\(787\) | −1.21477e26 | −1.04887 | −0.524436 | − | 0.851450i | \(-0.675724\pi\) | ||||
−0.524436 | + | 0.851450i | \(0.675724\pi\) | |||||||
\(788\) | 1.28677e26 | + | 4.43847e25i | 1.09841 | + | 0.378876i | ||||
\(789\) | 2.48480e26i | 2.09700i | ||||||||
\(790\) | −3.69786e25 | − | 5.18717e25i | −0.308537 | − | 0.432799i | ||||
\(791\) | − | 4.56159e24i | − | 0.0376295i | ||||||
\(792\) | −1.07862e26 | + | 3.18551e25i | −0.879712 | + | 0.259808i | ||||
\(793\) | −1.55725e26 | −1.25574 | ||||||||
\(794\) | −1.30466e26 | + | 9.30073e25i | −1.04019 | + | 0.741536i | ||||
\(795\) | 6.03073e25 | 0.475407 | ||||||||
\(796\) | −2.10471e26 | − | 7.25981e25i | −1.64050 | − | 0.565859i | ||||
\(797\) | − | 1.99141e26i | − | 1.53474i | −0.641204 | − | 0.767370i | \(-0.721565\pi\) | ||
0.641204 | − | 0.767370i | \(-0.278435\pi\) | |||||||
\(798\) | −5.64411e25 | + | 4.02361e25i | −0.430100 | + | 0.306613i | ||||
\(799\) | − | 3.11169e24i | − | 0.0234464i | ||||||
\(800\) | 3.04992e23 | − | 6.77573e24i | 0.00227237 | − | 0.0504831i | ||||
\(801\) | −8.95438e25 | −0.659695 | ||||||||
\(802\) | −3.13976e25 | − | 4.40429e25i | −0.228732 | − | 0.320853i | ||||
\(803\) | 1.85368e25 | 0.133535 | ||||||||
\(804\) | 8.81182e25 | − | 2.55466e26i | 0.627713 | − | 1.81982i | ||||
\(805\) | 4.64696e25i | 0.327345i | ||||||||
\(806\) | 8.14966e25 | + | 1.14319e26i | 0.567707 | + | 0.796350i | ||||
\(807\) | 2.84166e25i | 0.195754i | ||||||||
\(808\) | 1.42144e25 | + | 4.81299e25i | 0.0968334 | + | 0.327878i | ||||
\(809\) | 1.20488e26 | 0.811724 | 0.405862 | − | 0.913934i | \(-0.366971\pi\) | ||||
0.405862 | + | 0.913934i | \(0.366971\pi\) | |||||||
\(810\) | −1.42290e26 | + | 1.01437e26i | −0.948005 | + | 0.675819i | ||||
\(811\) | 2.18180e26 | 1.43756 | 0.718781 | − | 0.695237i | \(-0.244701\pi\) | ||||
0.718781 | + | 0.695237i | \(0.244701\pi\) | |||||||
\(812\) | −1.52821e25 | + | 4.43049e25i | −0.0995817 | + | 0.288700i | ||||
\(813\) | 1.15141e26i | 0.742018i | ||||||||
\(814\) | 3.09168e26 | − | 2.20402e26i | 1.97049 | − | 1.40474i | ||||
\(815\) | − | 2.07874e26i | − | 1.31034i | ||||||
\(816\) | −1.97508e25 | − | 1.54654e25i | −0.123133 | − | 0.0964160i | ||||
\(817\) | −2.03032e26 | −1.25189 | ||||||||
\(818\) | 1.31037e25 | + | 1.83812e25i | 0.0799125 | + | 0.112097i | ||||
\(819\) | 2.04067e25 | 0.123089 | ||||||||
\(820\) | 3.74738e25 | + | 1.29259e25i | 0.223565 | + | 0.0771144i | ||||
\(821\) | − | 9.20761e25i | − | 0.543324i | −0.962393 | − | 0.271662i | \(-0.912427\pi\) | ||
0.962393 | − | 0.271662i | \(-0.0875732\pi\) | |||||||
\(822\) | 1.56114e26 | + | 2.18988e26i | 0.911160 | + | 1.27813i | ||||
\(823\) | − | 3.23025e26i | − | 1.86482i | −0.361400 | − | 0.932411i | \(-0.617701\pi\) | ||
0.361400 | − | 0.932411i | \(-0.382299\pi\) | |||||||
\(824\) | 4.09408e25 | + | 1.38626e26i | 0.233782 | + | 0.791588i | ||||
\(825\) | −1.47087e25 | −0.0830785 | ||||||||
\(826\) | 1.03678e25 | − | 7.39109e24i | 0.0579252 | − | 0.0412941i | ||||
\(827\) | −1.80676e26 | −0.998509 | −0.499254 | − | 0.866455i | \(-0.666393\pi\) | ||||
−0.499254 | + | 0.866455i | \(0.666393\pi\) | |||||||
\(828\) | 1.84540e26 | + | 6.36534e25i | 1.00883 | + | 0.347976i | ||||
\(829\) | 1.13783e26i | 0.615301i | 0.951499 | + | 0.307651i | \(0.0995428\pi\) | ||||
−0.951499 | + | 0.307651i | \(0.900457\pi\) | |||||||
\(830\) | 8.65348e25 | − | 6.16894e25i | 0.462901 | − | 0.329995i | ||||
\(831\) | − | 5.77434e25i | − | 0.305558i | ||||||
\(832\) | 7.51350e25 | + | 1.16109e26i | 0.393308 | + | 0.607792i | ||||
\(833\) | −2.17012e25 | −0.112377 | ||||||||
\(834\) | −9.93796e24 | − | 1.39405e25i | −0.0509099 | − | 0.0714138i | ||||
\(835\) | 1.23157e26 | 0.624139 | ||||||||
\(836\) | −1.40711e26 | + | 4.07940e26i | −0.705461 | + | 2.04522i | ||||
\(837\) | − | 9.51009e25i | − | 0.471689i | ||||||
\(838\) | −5.05698e25 | − | 7.09367e25i | −0.248139 | − | 0.348077i | ||||
\(839\) | − | 3.30245e25i | − | 0.160317i | −0.996782 | − | 0.0801583i | \(-0.974457\pi\) | ||
0.996782 | − | 0.0801583i | \(-0.0255426\pi\) | |||||||
\(840\) | −5.92935e25 | + | 1.75114e25i | −0.284770 | + | 0.0841020i | ||||
\(841\) | −1.56259e26 | −0.742474 | ||||||||
\(842\) | −2.63931e25 | + | 1.88152e25i | −0.124074 | + | 0.0884506i | ||||
\(843\) | 4.85352e26 | 2.25740 | ||||||||
\(844\) | −3.50855e25 | + | 1.01717e26i | −0.161453 | + | 0.468072i | ||||
\(845\) | − | 1.01851e26i | − | 0.463717i | ||||||
\(846\) | −2.62328e25 | + | 1.87010e25i | −0.118171 | + | 0.0842425i | ||||
\(847\) | − | 2.89568e25i | − | 0.129062i | ||||||
\(848\) | −5.17835e25 | + | 6.61326e25i | −0.228365 | + | 0.291644i | ||||
\(849\) | 3.88560e25 | 0.169547 | ||||||||
\(850\) | −8.06706e23 | − | 1.13161e24i | −0.00348293 | − | 0.00488568i | ||||
\(851\) | −6.59021e26 | −2.81535 | ||||||||
\(852\) | 8.05341e25 | + | 2.77787e25i | 0.340427 | + | 0.117424i | ||||
\(853\) | 3.34899e26i | 1.40079i | 0.713755 | + | 0.700395i | \(0.246993\pi\) | ||||
−0.713755 | + | 0.700395i | \(0.753007\pi\) | |||||||
\(854\) | 5.62828e25 | + | 7.89506e25i | 0.232946 | + | 0.326764i | ||||
\(855\) | − | 3.03080e26i | − | 1.24126i | ||||||
\(856\) | −1.60205e26 | + | 4.73138e25i | −0.649249 | + | 0.191745i | ||||
\(857\) | 2.21197e26 | 0.887059 | 0.443530 | − | 0.896260i | \(-0.353726\pi\) | ||||
0.443530 | + | 0.896260i | \(0.353726\pi\) | |||||||
\(858\) | 2.44211e26 | − | 1.74095e26i | 0.969126 | − | 0.690877i | ||||
\(859\) | −1.39462e25 | −0.0547668 | −0.0273834 | − | 0.999625i | \(-0.508718\pi\) | ||||
−0.0273834 | + | 0.999625i | \(0.508718\pi\) | |||||||
\(860\) | −1.71196e26 | − | 5.90509e25i | −0.665286 | − | 0.229478i | ||||
\(861\) | 1.92316e25i | 0.0739584i | ||||||||
\(862\) | 9.79015e25 | − | 6.97926e25i | 0.372584 | − | 0.265610i | ||||
\(863\) | 4.01195e26i | 1.51098i | 0.655160 | + | 0.755490i | \(0.272601\pi\) | ||||
−0.655160 | + | 0.755490i | \(0.727399\pi\) | |||||||
\(864\) | 4.21255e24 | − | 9.35865e25i | 0.0157008 | − | 0.348810i | ||||
\(865\) | 3.31369e26 | 1.22227 | ||||||||
\(866\) | −1.69810e26 | − | 2.38200e26i | −0.619871 | − | 0.869523i | ||||
\(867\) | 3.59455e26 | 1.29859 | ||||||||
\(868\) | 2.85037e25 | − | 8.26358e25i | 0.101911 | − | 0.295454i | ||||
\(869\) | − | 1.92406e26i | − | 0.680834i | ||||||
\(870\) | −2.80818e26 | − | 3.93917e26i | −0.983448 | − | 1.37953i | ||||
\(871\) | 3.05261e26i | 1.05806i | ||||||||
\(872\) | −7.26702e24 | − | 2.46062e25i | −0.0249292 | − | 0.0844103i | ||||
\(873\) | −1.57930e26 | −0.536213 | ||||||||
\(874\) | 6.09889e26 | − | 4.34782e26i | 2.04950 | − | 1.46106i | ||||
\(875\) | −7.12028e25 | −0.236823 | ||||||||
\(876\) | 1.39582e25 | − | 4.04665e25i | 0.0459506 | − | 0.133217i | ||||
\(877\) | 1.63704e26i | 0.533411i | 0.963778 | + | 0.266705i | \(0.0859351\pi\) | ||||
−0.963778 | + | 0.266705i | \(0.914065\pi\) | |||||||
\(878\) | −7.85326e25 | + | 5.59848e25i | −0.253279 | + | 0.180559i | ||||
\(879\) | 2.52301e26i | 0.805414i | ||||||||
\(880\) | −2.37295e26 | + | 3.03049e26i | −0.749799 | + | 0.957568i | ||||
\(881\) | −4.63397e26 | −1.44934 | −0.724670 | − | 0.689096i | \(-0.758008\pi\) | ||||
−0.724670 | + | 0.689096i | \(0.758008\pi\) | |||||||
\(882\) | 1.30422e26 | + | 1.82950e26i | 0.403771 | + | 0.566388i | ||||
\(883\) | 1.38157e26 | 0.423375 | 0.211688 | − | 0.977337i | \(-0.432104\pi\) | ||||
0.211688 | + | 0.977337i | \(0.432104\pi\) | |||||||
\(884\) | 2.67878e25 | + | 9.23994e24i | 0.0812581 | + | 0.0280284i | ||||
\(885\) | 1.31429e26i | 0.394641i | ||||||||
\(886\) | −1.28854e26 | − | 1.80749e26i | −0.382995 | − | 0.537246i | ||||
\(887\) | − | 2.16587e26i | − | 0.637266i | −0.947878 | − | 0.318633i | \(-0.896776\pi\) | ||
0.947878 | − | 0.318633i | \(-0.103224\pi\) | |||||||
\(888\) | −2.48342e26 | − | 8.40887e26i | −0.723325 | − | 2.44918i | ||||
\(889\) | 3.79042e25 | 0.109288 | ||||||||
\(890\) | −2.49532e26 | + | 1.77888e26i | −0.712225 | + | 0.507735i | ||||
\(891\) | −5.27794e26 | −1.49130 | ||||||||
\(892\) | −5.29458e25 | − | 1.82627e25i | −0.148098 | − | 0.0510835i | ||||
\(893\) | 1.23611e26i | 0.342289i | ||||||||
\(894\) | −6.62450e26 | + | 4.72251e26i | −1.81600 | + | 1.29460i | ||||
\(895\) | − | 2.14088e26i | − | 0.581011i | ||||||
\(896\) | 3.17101e25 | − | 8.00572e25i | 0.0851974 | − | 0.215094i | ||||
\(897\) | −5.20560e26 | −1.38465 | ||||||||
\(898\) | 1.89634e26 | + | 2.66008e26i | 0.499377 | + | 0.700500i | ||||
\(899\) | 6.83986e26 | 1.78324 | ||||||||
\(900\) | −4.69165e24 | + | 1.36017e25i | −0.0121100 | + | 0.0351084i | ||||
\(901\) | 1.72100e25i | 0.0439802i | ||||||||
\(902\) | 6.95003e25 | + | 9.74915e25i | 0.175844 | + | 0.246665i | ||||
\(903\) | − | 8.78582e25i | − | 0.220086i | ||||||
\(904\) | −6.28942e25 | + | 1.85748e25i | −0.155989 | + | 0.0460688i | ||||
\(905\) | 4.72517e26 | 1.16033 | ||||||||
\(906\) | −3.16126e26 | + | 2.25362e26i | −0.768611 | + | 0.547932i | ||||
\(907\) | 2.92584e26 | 0.704344 | 0.352172 | − | 0.935935i | \(-0.385443\pi\) | ||||
0.352172 | + | 0.935935i | \(0.385443\pi\) | |||||||
\(908\) | 1.87874e26 | − | 5.44671e26i | 0.447810 | − | 1.29826i | ||||
\(909\) | − | 1.06459e26i | − | 0.251250i | ||||||
\(910\) | 5.68675e25 | − | 4.05401e25i | 0.132890 | − | 0.0947353i | ||||
\(911\) | 2.29099e26i | 0.530101i | 0.964235 | + | 0.265050i | \(0.0853886\pi\) | ||||
−0.964235 | + | 0.265050i | \(0.914611\pi\) | |||||||
\(912\) | 7.84593e26 | + | 6.14356e26i | 1.79759 | + | 1.40756i | ||||
\(913\) | 3.20981e26 | 0.728187 | ||||||||
\(914\) | −6.90854e25 | − | 9.69095e25i | −0.155192 | − | 0.217696i | ||||
\(915\) | −1.00083e27 | −2.22622 | ||||||||
\(916\) | −1.41952e26 | − | 4.89638e25i | −0.312668 | − | 0.107849i | ||||
\(917\) | − | 4.51370e25i | − | 0.0984483i | ||||||
\(918\) | −1.11422e25 | − | 1.56297e25i | −0.0240651 | − | 0.0337573i | ||||
\(919\) | 5.13378e26i | 1.09799i | 0.835827 | + | 0.548994i | \(0.184989\pi\) | ||||
−0.835827 | + | 0.548994i | \(0.815011\pi\) | |||||||
\(920\) | 6.40712e26 | − | 1.89224e26i | 1.35698 | − | 0.400761i | ||||
\(921\) | 6.36394e26 | 1.33472 | ||||||||
\(922\) | −8.15476e24 | + | 5.81341e24i | −0.0169369 | + | 0.0120741i | ||||
\(923\) | −9.62318e25 | −0.197926 | ||||||||
\(924\) | −1.76528e26 | − | 6.08901e25i | −0.359556 | − | 0.124022i | ||||
\(925\) | − | 4.85739e25i | − | 0.0979777i | ||||||
\(926\) | −1.46106e26 | + | 1.04157e26i | −0.291856 | + | 0.208060i | ||||
\(927\) | − | 3.06628e26i | − | 0.606588i | ||||||
\(928\) | 6.73094e26 | + | 3.02975e25i | 1.31869 | + | 0.0593575i | ||||
\(929\) | −2.51419e26 | −0.487817 | −0.243909 | − | 0.969798i | \(-0.578430\pi\) | ||||
−0.243909 | + | 0.969798i | \(0.578430\pi\) | |||||||
\(930\) | 5.23771e26 | + | 7.34719e26i | 1.00646 | + | 1.41180i | ||||
\(931\) | 8.62072e26 | 1.64058 | ||||||||
\(932\) | 4.81024e25 | − | 1.39455e26i | 0.0906617 | − | 0.262840i | ||||
\(933\) | − | 3.42381e26i | − | 0.639108i | ||||||
\(934\) | −7.30702e25 | − | 1.02499e26i | −0.135089 | − | 0.189495i | ||||
\(935\) | 7.88638e25i | 0.144402i | ||||||||
\(936\) | −8.30959e25 | − | 2.81363e26i | −0.150694 | − | 0.510251i | ||||
\(937\) | 3.73439e26 | 0.670754 | 0.335377 | − | 0.942084i | \(-0.391136\pi\) | ||||
0.335377 | + | 0.942084i | \(0.391136\pi\) | |||||||
\(938\) | 1.54764e26 | − | 1.10329e26i | 0.275324 | − | 0.196275i | ||||
\(939\) | −5.52250e26 | −0.973074 | ||||||||
\(940\) | −3.59516e25 | + | 1.04228e26i | −0.0627433 | + | 0.181901i | ||||
\(941\) | − | 1.37271e26i | − | 0.237285i | −0.992937 | − | 0.118643i | \(-0.962146\pi\) | ||
0.992937 | − | 0.118643i | \(-0.0378543\pi\) | |||||||
\(942\) | −2.89562e26 | + | 2.06425e26i | −0.495773 | + | 0.353430i | ||||
\(943\) | − | 2.07812e26i | − | 0.352424i | ||||||
\(944\) | −1.44124e26 | − | 1.12853e26i | −0.242097 | − | 0.189568i | ||||
\(945\) | −4.73074e25 | −0.0787124 | ||||||||
\(946\) | −3.17507e26 | − | 4.45382e26i | −0.523279 | − | 0.734028i | ||||
\(947\) | −3.55248e26 | −0.579938 | −0.289969 | − | 0.957036i | \(-0.593645\pi\) | ||||
−0.289969 | + | 0.957036i | \(0.593645\pi\) | |||||||
\(948\) | −4.20030e26 | − | 1.44881e26i | −0.679212 | − | 0.234281i | ||||
\(949\) | 4.83542e25i | 0.0774530i | ||||||||
\(950\) | 3.20461e25 | + | 4.49526e25i | 0.0508467 | + | 0.0713251i | ||||
\(951\) | 7.70954e26i | 1.21172i | ||||||||
\(952\) | −4.99724e24 | − | 1.69207e25i | −0.00778032 | − | 0.0263442i | ||||
\(953\) | 1.26477e26 | 0.195063 | 0.0975315 | − | 0.995232i | \(-0.468905\pi\) | ||||
0.0975315 | + | 0.995232i | \(0.468905\pi\) | |||||||
\(954\) | 1.45087e26 | − | 1.03430e26i | 0.221663 | − | 0.158020i | ||||
\(955\) | −6.39915e26 | −0.968483 | ||||||||
\(956\) | −6.42057e26 | − | 2.21465e26i | −0.962614 | − | 0.332036i | ||||
\(957\) | − | 1.46115e27i | − | 2.17013i | ||||||
\(958\) | −2.05625e26 | + | 1.46587e26i | −0.302542 | + | 0.215678i | ||||
\(959\) | 1.89151e26i | 0.275703i | ||||||||
\(960\) | 4.82885e26 | + | 7.46219e26i | 0.697273 | + | 1.07752i | ||||
\(961\) | −5.76691e26 | −0.824959 | ||||||||
\(962\) | 5.74929e26 | + | 8.06481e26i | 0.814777 | + | 1.14293i | ||||
\(963\) | 3.54358e26 | 0.497515 | ||||||||
\(964\) | −3.38776e26 | + | 9.82155e26i | −0.471215 | + | 1.36611i | ||||
\(965\) | − | 9.92976e26i | − | 1.36834i | ||||||
\(966\) | 1.88143e26 | + | 2.63918e26i | 0.256859 | + | 0.360309i | ||||
\(967\) | − | 3.93340e26i | − | 0.532022i | −0.963970 | − | 0.266011i | \(-0.914294\pi\) | ||
0.963970 | − | 0.266011i | \(-0.0857058\pi\) | |||||||
\(968\) | −3.99249e26 | + | 1.17912e26i | −0.535015 | + | 0.158008i | ||||
\(969\) | 2.04178e26 | 0.271078 | ||||||||
\(970\) | −4.40106e26 | + | 3.13745e26i | −0.578911 | + | 0.412697i | ||||
\(971\) | −3.37169e26 | −0.439414 | −0.219707 | − | 0.975566i | \(-0.570510\pi\) | ||||
−0.219707 | + | 0.975566i | \(0.570510\pi\) | |||||||
\(972\) | −3.09252e26 | + | 8.96562e26i | −0.399316 | + | 1.15767i | ||||
\(973\) | − | 1.20410e25i | − | 0.0154045i | ||||||
\(974\) | 2.51292e26 | − | 1.79143e26i | 0.318528 | − | 0.227075i | ||||
\(975\) | − | 3.83684e25i | − | 0.0481873i | ||||||
\(976\) | 8.59370e26 | − | 1.09750e27i | 1.06938 | − | 1.36570i | ||||
\(977\) | −1.57789e26 | −0.194547 | −0.0972737 | − | 0.995258i | \(-0.531012\pi\) | ||||
−0.0972737 | + | 0.995258i | \(0.531012\pi\) | |||||||
\(978\) | −8.41630e26 | − | 1.18060e27i | −1.02819 | − | 1.44229i | ||||
\(979\) | −9.25585e26 | −1.12040 | ||||||||
\(980\) | 7.26898e26 | + | 2.50730e26i | 0.871844 | + | 0.300726i | ||||
\(981\) | 5.44266e25i | 0.0646830i | ||||||||
\(982\) | 6.21109e26 | + | 8.71260e26i | 0.731416 | + | 1.02599i | ||||
\(983\) | 9.44218e26i | 1.10177i | 0.834582 | + | 0.550884i | \(0.185709\pi\) | ||||
−0.834582 | + | 0.550884i | \(0.814291\pi\) | |||||||
\(984\) | 2.65161e26 | − | 7.83109e25i | 0.306587 | − | 0.0905454i | ||||
\(985\) | −9.88192e26 | −1.13218 | ||||||||
\(986\) | 1.12412e26 | − | 8.01372e25i | 0.127621 | − | 0.0909792i | ||||
\(987\) | −5.34902e25 | −0.0601755 | ||||||||
\(988\) | −1.06413e27 | − | 3.67053e26i | −1.18627 | − | 0.409182i | ||||
\(989\) | 9.49375e26i | 1.04875i | ||||||||
\(990\) | 6.64853e26 | − | 4.73964e26i | 0.727794 | − | 0.518834i | ||||
\(991\) | − | 1.51912e27i | − | 1.64790i | −0.566665 | − | 0.823948i | \(-0.691767\pi\) | ||
0.566665 | − | 0.823948i | \(-0.308233\pi\) | |||||||
\(992\) | −1.25543e27 | − | 5.65098e25i | −1.34954 | − | 0.0607462i | ||||
\(993\) | 6.70897e26 | 0.714682 | ||||||||
\(994\) | 3.47806e25 | + | 4.87885e25i | 0.0367164 | + | 0.0515038i | ||||
\(995\) | 1.61634e27 | 1.69093 | ||||||||
\(996\) | 2.41698e26 | − | 7.00714e26i | 0.250576 | − | 0.726451i | ||||
\(997\) | 7.65044e26i | 0.786013i | 0.919536 | + | 0.393007i | \(0.128565\pi\) | ||||
−0.919536 | + | 0.393007i | \(0.871435\pi\) | |||||||
\(998\) | −8.33935e26 | − | 1.16980e27i | −0.849097 | − | 1.19107i | ||||
\(999\) | − | 6.70903e26i | − | 0.676971i |
(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 | 8.19.d.b.3.12 | yes | 16 | |
3.2 | odd | 2 | 72.19.b.b.19.5 | 16 | |||
4.3 | odd | 2 | 32.19.d.b.15.13 | 16 | |||
8.3 | odd | 2 | inner | 8.19.d.b.3.11 | ✓ | 16 | |
8.5 | even | 2 | 32.19.d.b.15.14 | 16 | |||
24.11 | even | 2 | 72.19.b.b.19.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.19.d.b.3.11 | ✓ | 16 | 8.3 | odd | 2 | inner | |
8.19.d.b.3.12 | yes | 16 | 1.1 | even | 1 | trivial | |
32.19.d.b.15.13 | 16 | 4.3 | odd | 2 | |||
32.19.d.b.15.14 | 16 | 8.5 | even | 2 | |||
72.19.b.b.19.5 | 16 | 3.2 | odd | 2 | |||
72.19.b.b.19.6 | 16 | 24.11 | even | 2 |