Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,23,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 23, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 23);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 23 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(9.20122304526\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 126474x^{4} + 3861674040x^{2} + 9831214131200 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{22} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.4 | ||
Root | \(52.8797i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.23.b.a.2.3 |
$q$-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 \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 634.557i | 0.309842i | 0.987927 | + | 0.154921i | \(0.0495123\pi\) | ||||
−0.987927 | + | 0.154921i | \(0.950488\pi\) | |||||||
\(3\) | 48229.8 | + | 170455.i | 0.272259 | + | 0.962224i | ||||
\(4\) | 3.79164e6 | 0.903998 | ||||||||
\(5\) | 2.56634e6i | 0.0525586i | 0.999655 | + | 0.0262793i | \(0.00836593\pi\) | ||||
−0.999655 | + | 0.0262793i | \(0.991634\pi\) | |||||||
\(6\) | −1.08163e8 | + | 3.06045e7i | −0.298138 | + | 0.0843572i | ||||
\(7\) | 8.97619e8 | 0.453956 | 0.226978 | − | 0.973900i | \(-0.427115\pi\) | ||||
0.226978 | + | 0.973900i | \(0.427115\pi\) | |||||||
\(8\) | 5.06753e9i | 0.589939i | ||||||||
\(9\) | −2.67288e10 | + | 1.64420e10i | −0.851750 | + | 0.523948i | ||||
\(10\) | −1.62849e9 | −0.0162849 | ||||||||
\(11\) | 4.54805e11i | 1.59406i | 0.603937 | + | 0.797032i | \(0.293598\pi\) | ||||
−0.603937 | + | 0.797032i | \(0.706402\pi\) | |||||||
\(12\) | 1.82870e11 | + | 6.46305e11i | 0.246121 | + | 0.869849i | ||||
\(13\) | −1.52981e12 | −0.853615 | −0.426807 | − | 0.904343i | \(-0.640362\pi\) | ||||
−0.426807 | + | 0.904343i | \(0.640362\pi\) | |||||||
\(14\) | 5.69590e11i | 0.140655i | ||||||||
\(15\) | −4.37446e11 | + | 1.23774e11i | −0.0505732 | + | 0.0143095i | ||||
\(16\) | 1.26877e13 | 0.721210 | ||||||||
\(17\) | − | 5.06681e13i | − | 1.47842i | −0.673477 | − | 0.739208i | \(-0.735200\pi\) | ||
0.673477 | − | 0.739208i | \(-0.264800\pi\) | |||||||
\(18\) | −1.04334e13 | − | 1.69610e13i | −0.162341 | − | 0.263908i | ||||
\(19\) | 2.10259e13 | 0.180495 | 0.0902476 | − | 0.995919i | \(-0.471234\pi\) | ||||
0.0902476 | + | 0.995919i | \(0.471234\pi\) | |||||||
\(20\) | 9.73064e12i | 0.0475129i | ||||||||
\(21\) | 4.32920e13 | + | 1.53004e14i | 0.123593 | + | 0.436807i | ||||
\(22\) | −2.88599e14 | −0.493908 | ||||||||
\(23\) | 1.03543e15i | 1.08671i | 0.839503 | + | 0.543354i | \(0.182846\pi\) | ||||
−0.839503 | + | 0.543354i | \(0.817154\pi\) | |||||||
\(24\) | −8.63787e14 | + | 2.44406e14i | −0.567653 | + | 0.160616i | ||||
\(25\) | 2.37760e15 | 0.997238 | ||||||||
\(26\) | − | 9.70754e14i | − | 0.264486i | ||||||
\(27\) | −4.09175e15 | − | 3.76307e15i | −0.736051 | − | 0.676926i | ||||
\(28\) | 3.40345e15 | 0.410375 | ||||||||
\(29\) | − | 1.09681e16i | − | 0.898989i | −0.893283 | − | 0.449494i | \(-0.851604\pi\) | ||
0.893283 | − | 0.449494i | \(-0.148396\pi\) | |||||||
\(30\) | −7.85416e13 | − | 2.77584e14i | −0.00443370 | − | 0.0156697i | ||||
\(31\) | 2.32177e16 | 0.913779 | 0.456889 | − | 0.889523i | \(-0.348963\pi\) | ||||
0.456889 | + | 0.889523i | \(0.348963\pi\) | |||||||
\(32\) | 2.93058e16i | 0.813400i | ||||||||
\(33\) | −7.75238e16 | + | 2.19351e16i | −1.53385 | + | 0.433998i | ||||
\(34\) | 3.21518e16 | 0.458075 | ||||||||
\(35\) | 2.30359e15i | 0.0238593i | ||||||||
\(36\) | −1.01346e17 | + | 6.23423e16i | −0.769981 | + | 0.473648i | ||||
\(37\) | 2.29827e17 | 1.29176 | 0.645880 | − | 0.763439i | \(-0.276490\pi\) | ||||
0.645880 | + | 0.763439i | \(0.276490\pi\) | |||||||
\(38\) | 1.33421e16i | 0.0559250i | ||||||||
\(39\) | −7.37826e16 | − | 2.60765e17i | −0.232404 | − | 0.821369i | ||||
\(40\) | −1.30050e16 | −0.0310064 | ||||||||
\(41\) | − | 7.03825e17i | − | 1.27892i | −0.768825 | − | 0.639459i | \(-0.779159\pi\) | ||
0.768825 | − | 0.639459i | \(-0.220841\pi\) | |||||||
\(42\) | −9.70895e16 | + | 2.74712e16i | −0.135341 | + | 0.0382944i | ||||
\(43\) | 3.20294e17 | 0.344664 | 0.172332 | − | 0.985039i | \(-0.444870\pi\) | ||||
0.172332 | + | 0.985039i | \(0.444870\pi\) | |||||||
\(44\) | 1.72446e18i | 1.44103i | ||||||||
\(45\) | −4.21958e16 | − | 6.85952e16i | −0.0275380 | − | 0.0447668i | ||||
\(46\) | −6.57037e17 | −0.336708 | ||||||||
\(47\) | − | 3.71198e17i | − | 0.150151i | −0.997178 | − | 0.0750756i | \(-0.976080\pi\) | ||
0.997178 | − | 0.0750756i | \(-0.0239198\pi\) | |||||||
\(48\) | 6.11923e17 | + | 2.16268e18i | 0.196356 | + | 0.693966i | ||||
\(49\) | −3.10410e18 | −0.793924 | ||||||||
\(50\) | 1.50872e18i | 0.308986i | ||||||||
\(51\) | 8.63664e18 | − | 2.44371e18i | 1.42257 | − | 0.402511i | ||||
\(52\) | −5.80051e18 | −0.771666 | ||||||||
\(53\) | − | 1.31183e19i | − | 1.41528i | −0.706574 | − | 0.707639i | \(-0.749760\pi\) | ||
0.706574 | − | 0.707639i | \(-0.250240\pi\) | |||||||
\(54\) | 2.38788e18 | − | 2.59645e18i | 0.209740 | − | 0.228060i | ||||
\(55\) | −1.16718e18 | −0.0837818 | ||||||||
\(56\) | 4.54871e18i | 0.267806i | ||||||||
\(57\) | 1.01408e18 | + | 3.58398e18i | 0.0491414 | + | 0.173677i | ||||
\(58\) | 6.95989e18 | 0.278545 | ||||||||
\(59\) | 2.62199e19i | 0.869480i | 0.900556 | + | 0.434740i | \(0.143160\pi\) | ||||
−0.900556 | + | 0.434740i | \(0.856840\pi\) | |||||||
\(60\) | −1.65864e18 | + | 4.69307e17i | −0.0457180 | + | 0.0129358i | ||||
\(61\) | −3.33360e19 | −0.766099 | −0.383050 | − | 0.923728i | \(-0.625126\pi\) | ||||
−0.383050 | + | 0.923728i | \(0.625126\pi\) | |||||||
\(62\) | 1.47330e19i | 0.283127i | ||||||||
\(63\) | −2.39923e19 | + | 1.47587e19i | −0.386657 | + | 0.237849i | ||||
\(64\) | 3.46197e19 | 0.469185 | ||||||||
\(65\) | − | 3.92602e18i | − | 0.0448648i | ||||||
\(66\) | −1.39191e19 | − | 4.91933e19i | −0.134471 | − | 0.475250i | ||||
\(67\) | 1.84254e20 | 1.50867 | 0.754333 | − | 0.656492i | \(-0.227960\pi\) | ||||
0.754333 | + | 0.656492i | \(0.227960\pi\) | |||||||
\(68\) | − | 1.92115e20i | − | 1.33648i | ||||||
\(69\) | −1.76494e20 | + | 4.99384e19i | −1.04566 | + | 0.295866i | ||||
\(70\) | −1.46176e18 | −0.00739261 | ||||||||
\(71\) | 6.16084e19i | 0.266562i | 0.991078 | + | 0.133281i | \(0.0425513\pi\) | ||||
−0.991078 | + | 0.133281i | \(0.957449\pi\) | |||||||
\(72\) | −8.33206e19 | − | 1.35449e20i | −0.309097 | − | 0.502481i | ||||
\(73\) | 5.98508e19 | 0.190774 | 0.0953869 | − | 0.995440i | \(-0.469591\pi\) | ||||
0.0953869 | + | 0.995440i | \(0.469591\pi\) | |||||||
\(74\) | 1.45838e20i | 0.400242i | ||||||||
\(75\) | 1.14671e20 | + | 4.05274e20i | 0.271507 | + | 0.959566i | ||||
\(76\) | 7.97228e19 | 0.163167 | ||||||||
\(77\) | 4.08241e20i | 0.723634i | ||||||||
\(78\) | 1.65470e20 | − | 4.68193e19i | 0.254495 | − | 0.0720085i | ||||
\(79\) | −1.05786e21 | −1.41426 | −0.707132 | − | 0.707081i | \(-0.750011\pi\) | ||||
−0.707132 | + | 0.707081i | \(0.750011\pi\) | |||||||
\(80\) | 3.25608e19i | 0.0379058i | ||||||||
\(81\) | 4.44090e20 | − | 8.78953e20i | 0.450958 | − | 0.892545i | ||||
\(82\) | 4.46617e20 | 0.396262 | ||||||||
\(83\) | − | 1.35231e21i | − | 1.05007i | −0.851081 | − | 0.525035i | \(-0.824052\pi\) | ||
0.851081 | − | 0.525035i | \(-0.175948\pi\) | |||||||
\(84\) | 1.64148e20 | + | 5.80135e20i | 0.111728 | + | 0.394873i | ||||
\(85\) | 1.30032e20 | 0.0777035 | ||||||||
\(86\) | 2.03245e20i | 0.106791i | ||||||||
\(87\) | 1.86957e21 | − | 5.28990e20i | 0.865029 | − | 0.244757i | ||||
\(88\) | −2.30474e21 | −0.940400 | ||||||||
\(89\) | − | 7.46198e20i | − | 0.268883i | −0.990922 | − | 0.134442i | \(-0.957076\pi\) | ||
0.990922 | − | 0.134442i | \(-0.0429241\pi\) | |||||||
\(90\) | 4.35276e19 | − | 2.67756e19i | 0.0138706 | − | 0.00853242i | ||||
\(91\) | −1.37319e21 | −0.387503 | ||||||||
\(92\) | 3.92597e21i | 0.982383i | ||||||||
\(93\) | 1.11979e21 | + | 3.95758e21i | 0.248784 | + | 0.879260i | ||||
\(94\) | 2.35546e20 | 0.0465231 | ||||||||
\(95\) | 5.39597e19i | 0.00948658i | ||||||||
\(96\) | −4.99533e21 | + | 1.41341e21i | −0.782673 | + | 0.221455i | ||||
\(97\) | 5.46728e21 | 0.764332 | 0.382166 | − | 0.924094i | \(-0.375178\pi\) | ||||
0.382166 | + | 0.924094i | \(0.375178\pi\) | |||||||
\(98\) | − | 1.96973e21i | − | 0.245991i | ||||||
\(99\) | −7.47792e21 | − | 1.21564e22i | −0.835206 | − | 1.35774i | ||||
\(100\) | 9.01501e21 | 0.901501 | ||||||||
\(101\) | − | 3.76219e21i | − | 0.337214i | −0.985683 | − | 0.168607i | \(-0.946073\pi\) | ||
0.985683 | − | 0.168607i | \(-0.0539269\pi\) | |||||||
\(102\) | 1.55067e21 | + | 5.48044e21i | 0.124715 | + | 0.440771i | ||||
\(103\) | 1.62984e21 | 0.117743 | 0.0588716 | − | 0.998266i | \(-0.481250\pi\) | ||||
0.0588716 | + | 0.998266i | \(0.481250\pi\) | |||||||
\(104\) | − | 7.75239e21i | − | 0.503580i | ||||||
\(105\) | −3.92659e20 | + | 1.11102e20i | −0.0229580 | + | 0.00649590i | ||||
\(106\) | 8.32428e21 | 0.438513 | ||||||||
\(107\) | 1.32901e22i | 0.631403i | 0.948859 | + | 0.315701i | \(0.102240\pi\) | ||||
−0.948859 | + | 0.315701i | \(0.897760\pi\) | |||||||
\(108\) | −1.55145e22 | − | 1.42682e22i | −0.665389 | − | 0.611939i | ||||
\(109\) | −2.06868e22 | −0.801680 | −0.400840 | − | 0.916148i | \(-0.631282\pi\) | ||||
−0.400840 | + | 0.916148i | \(0.631282\pi\) | |||||||
\(110\) | − | 7.40644e20i | − | 0.0259591i | ||||||
\(111\) | 1.10845e22 | + | 3.91752e22i | 0.351693 | + | 1.24296i | ||||
\(112\) | 1.13887e22 | 0.327397 | ||||||||
\(113\) | 4.20738e22i | 1.09685i | 0.836198 | + | 0.548427i | \(0.184773\pi\) | ||||
−0.836198 | + | 0.548427i | \(0.815227\pi\) | |||||||
\(114\) | −2.27424e21 | + | 6.43489e20i | −0.0538124 | + | 0.0152261i | ||||
\(115\) | −2.65726e21 | −0.0571159 | ||||||||
\(116\) | − | 4.15872e22i | − | 0.812684i | ||||||
\(117\) | 4.08902e22 | − | 2.51533e22i | 0.727067 | − | 0.447249i | ||||
\(118\) | −1.66380e22 | −0.269402 | ||||||||
\(119\) | − | 4.54807e22i | − | 0.671135i | ||||||
\(120\) | −6.27229e20 | − | 2.21677e21i | −0.00844175 | − | 0.0298351i | ||||
\(121\) | −1.25445e23 | −1.54104 | ||||||||
\(122\) | − | 2.11536e22i | − | 0.237370i | ||||||
\(123\) | 1.19971e23 | − | 3.39454e22i | 1.23061 | − | 0.348196i | ||||
\(124\) | 8.80333e22 | 0.826054 | ||||||||
\(125\) | 1.22204e22i | 0.104972i | ||||||||
\(126\) | −9.36522e21 | − | 1.52245e22i | −0.0736956 | − | 0.119803i | ||||
\(127\) | −6.06941e22 | −0.437830 | −0.218915 | − | 0.975744i | \(-0.570252\pi\) | ||||
−0.218915 | + | 0.975744i | \(0.570252\pi\) | |||||||
\(128\) | 1.44886e23i | 0.958773i | ||||||||
\(129\) | 1.54477e22 | + | 5.45958e22i | 0.0938378 | + | 0.331644i | ||||
\(130\) | 2.49128e21 | 0.0139010 | ||||||||
\(131\) | − | 4.49359e21i | − | 0.0230467i | −0.999934 | − | 0.0115234i | \(-0.996332\pi\) | ||
0.999934 | − | 0.0115234i | \(-0.00366808\pi\) | |||||||
\(132\) | −2.93943e23 | + | 8.31702e22i | −1.38659 | + | 0.392333i | ||||
\(133\) | 1.88733e22 | 0.0819368 | ||||||||
\(134\) | 1.16919e23i | 0.467448i | ||||||||
\(135\) | 9.65731e21 | − | 1.05008e22i | 0.0355783 | − | 0.0386859i | ||||
\(136\) | 2.56762e23 | 0.872175 | ||||||||
\(137\) | − | 2.17085e23i | − | 0.680305i | −0.940370 | − | 0.340152i | \(-0.889521\pi\) | ||
0.940370 | − | 0.340152i | \(-0.110479\pi\) | |||||||
\(138\) | −3.16888e22 | − | 1.11995e23i | −0.0916717 | − | 0.323989i | ||||
\(139\) | 1.65363e23 | 0.441849 | 0.220925 | − | 0.975291i | \(-0.429092\pi\) | ||||
0.220925 | + | 0.975291i | \(0.429092\pi\) | |||||||
\(140\) | 8.73440e21i | 0.0215687i | ||||||||
\(141\) | 6.32725e22 | − | 1.79028e22i | 0.144479 | − | 0.0408799i | ||||
\(142\) | −3.90940e22 | −0.0825922 | ||||||||
\(143\) | − | 6.95767e23i | − | 1.36072i | ||||||
\(144\) | −3.39126e23 | + | 2.08611e23i | −0.614291 | + | 0.377876i | ||||
\(145\) | 2.81479e22 | 0.0472496 | ||||||||
\(146\) | 3.79787e22i | 0.0591097i | ||||||||
\(147\) | −1.49710e23 | − | 5.29110e23i | −0.216153 | − | 0.763933i | ||||
\(148\) | 8.71422e23 | 1.16775 | ||||||||
\(149\) | 1.29054e24i | 1.60592i | 0.596033 | + | 0.802960i | \(0.296743\pi\) | ||||
−0.596033 | + | 0.802960i | \(0.703257\pi\) | |||||||
\(150\) | −2.57169e23 | + | 7.27653e22i | −0.297314 | + | 0.0841242i | ||||
\(151\) | −1.02305e24 | −1.09938 | −0.549691 | − | 0.835368i | \(-0.685254\pi\) | ||||
−0.549691 | + | 0.835368i | \(0.685254\pi\) | |||||||
\(152\) | 1.06550e23i | 0.106481i | ||||||||
\(153\) | 8.33087e23 | + | 1.35430e24i | 0.774613 | + | 1.25924i | ||||
\(154\) | −2.59052e23 | −0.224212 | ||||||||
\(155\) | 5.95846e22i | 0.0480270i | ||||||||
\(156\) | −2.79757e23 | − | 9.88726e23i | −0.210093 | − | 0.742516i | ||||
\(157\) | −1.15645e24 | −0.809526 | −0.404763 | − | 0.914422i | \(-0.632646\pi\) | ||||
−0.404763 | + | 0.914422i | \(0.632646\pi\) | |||||||
\(158\) | − | 6.71273e23i | − | 0.438199i | ||||||
\(159\) | 2.23607e24 | − | 6.32691e23i | 1.36181 | − | 0.385322i | ||||
\(160\) | −7.52087e22 | −0.0427512 | ||||||||
\(161\) | 9.29419e23i | 0.493318i | ||||||||
\(162\) | 5.57745e23 | + | 2.81800e23i | 0.276548 | + | 0.139726i | ||||
\(163\) | −9.36187e23 | −0.433810 | −0.216905 | − | 0.976193i | \(-0.569596\pi\) | ||||
−0.216905 | + | 0.976193i | \(0.569596\pi\) | |||||||
\(164\) | − | 2.66865e24i | − | 1.15614i | ||||||
\(165\) | −5.62930e22 | − | 1.98952e23i | −0.0228103 | − | 0.0806168i | ||||
\(166\) | 8.58120e23 | 0.325356 | ||||||||
\(167\) | − | 1.70989e24i | − | 0.606859i | −0.952854 | − | 0.303429i | \(-0.901868\pi\) | ||
0.952854 | − | 0.303429i | \(-0.0981316\pi\) | |||||||
\(168\) | −7.75352e23 | + | 2.19384e23i | −0.257689 | + | 0.0729125i | ||||
\(169\) | −8.71507e23 | −0.271342 | ||||||||
\(170\) | 8.25124e22i | 0.0240758i | ||||||||
\(171\) | −5.61999e23 | + | 3.45709e23i | −0.153737 | + | 0.0945700i | ||||
\(172\) | 1.21444e24 | 0.311576 | ||||||||
\(173\) | 5.24499e24i | 1.26252i | 0.775572 | + | 0.631260i | \(0.217462\pi\) | ||||
−0.775572 | + | 0.631260i | \(0.782538\pi\) | |||||||
\(174\) | 3.35674e23 | + | 1.18635e24i | 0.0758362 | + | 0.268022i | ||||
\(175\) | 2.13418e24 | 0.452702 | ||||||||
\(176\) | 5.77041e24i | 1.14965i | ||||||||
\(177\) | −4.46932e24 | + | 1.26458e24i | −0.836635 | + | 0.236724i | ||||
\(178\) | 4.73505e23 | 0.0833114 | ||||||||
\(179\) | − | 6.85545e24i | − | 1.13410i | −0.823682 | − | 0.567052i | \(-0.808084\pi\) | ||
0.823682 | − | 0.567052i | \(-0.191916\pi\) | |||||||
\(180\) | −1.59991e23 | − | 2.60089e23i | −0.0248943 | − | 0.0404691i | ||||
\(181\) | 2.46571e23 | 0.0360976 | 0.0180488 | − | 0.999837i | \(-0.494255\pi\) | ||||
0.0180488 | + | 0.999837i | \(0.494255\pi\) | |||||||
\(182\) | − | 8.71367e23i | − | 0.120065i | ||||||
\(183\) | −1.60779e24 | − | 5.68229e24i | −0.208577 | − | 0.737159i | ||||
\(184\) | −5.24706e24 | −0.641092 | ||||||||
\(185\) | 5.89814e23i | 0.0678932i | ||||||||
\(186\) | −2.51131e24 | + | 7.10568e23i | −0.272432 | + | 0.0770838i | ||||
\(187\) | 2.30441e25 | 2.35669 | ||||||||
\(188\) | − | 1.40745e24i | − | 0.135736i | ||||||
\(189\) | −3.67284e24 | − | 3.37780e24i | −0.334135 | − | 0.307294i | ||||
\(190\) | −3.42405e22 | −0.00293934 | ||||||||
\(191\) | − | 1.19517e25i | − | 0.968414i | −0.874954 | − | 0.484207i | \(-0.839108\pi\) | ||
0.874954 | − | 0.484207i | \(-0.160892\pi\) | |||||||
\(192\) | 1.66970e24 | + | 5.90111e24i | 0.127740 | + | 0.451461i | ||||
\(193\) | −6.43828e24 | −0.465200 | −0.232600 | − | 0.972572i | \(-0.574723\pi\) | ||||
−0.232600 | + | 0.972572i | \(0.574723\pi\) | |||||||
\(194\) | 3.46930e24i | 0.236822i | ||||||||
\(195\) | 6.69211e23 | − | 1.89351e23i | 0.0431700 | − | 0.0122148i | ||||
\(196\) | −1.17696e25 | −0.717706 | ||||||||
\(197\) | 1.37996e25i | 0.795678i | 0.917455 | + | 0.397839i | \(0.130240\pi\) | ||||
−0.917455 | + | 0.397839i | \(0.869760\pi\) | |||||||
\(198\) | 7.71393e24 | − | 4.74516e24i | 0.420686 | − | 0.258782i | ||||
\(199\) | −2.34558e25 | −1.21023 | −0.605114 | − | 0.796139i | \(-0.706872\pi\) | ||||
−0.605114 | + | 0.796139i | \(0.706872\pi\) | |||||||
\(200\) | 1.20486e25i | 0.588309i | ||||||||
\(201\) | 8.88652e24 | + | 3.14070e25i | 0.410747 | + | 1.45168i | ||||
\(202\) | 2.38732e24 | 0.104483 | ||||||||
\(203\) | − | 9.84519e24i | − | 0.408101i | ||||||
\(204\) | 3.27470e25 | − | 9.26568e24i | 1.28600 | − | 0.363870i | ||||
\(205\) | 1.80625e24 | 0.0672181 | ||||||||
\(206\) | 1.03423e24i | 0.0364818i | ||||||||
\(207\) | −1.70245e25 | − | 2.76758e25i | −0.569379 | − | 0.925605i | ||||
\(208\) | −1.94098e25 | −0.615636 | ||||||||
\(209\) | 9.56270e24i | 0.287721i | ||||||||
\(210\) | −7.05004e22 | − | 2.49165e23i | −0.00201270 | − | 0.00711335i | ||||
\(211\) | 2.12594e25 | 0.576028 | 0.288014 | − | 0.957626i | \(-0.407005\pi\) | ||||
0.288014 | + | 0.957626i | \(0.407005\pi\) | |||||||
\(212\) | − | 4.97397e25i | − | 1.27941i | ||||||
\(213\) | −1.05015e25 | + | 2.97136e24i | −0.256492 | + | 0.0725738i | ||||
\(214\) | −8.43332e24 | −0.195635 | ||||||||
\(215\) | 8.21984e23i | 0.0181151i | ||||||||
\(216\) | 1.90695e25 | − | 2.07351e25i | 0.399345 | − | 0.434225i | ||||
\(217\) | 2.08407e25 | 0.414815 | ||||||||
\(218\) | − | 1.31269e25i | − | 0.248394i | ||||||
\(219\) | 2.88659e24 | + | 1.02019e25i | 0.0519398 | + | 0.183567i | ||||
\(220\) | −4.42554e24 | −0.0757386 | ||||||||
\(221\) | 7.75128e25i | 1.26200i | ||||||||
\(222\) | −2.48589e25 | + | 7.03375e24i | −0.385122 | + | 0.108969i | ||||
\(223\) | 1.45332e25 | 0.214293 | 0.107147 | − | 0.994243i | \(-0.465829\pi\) | ||||
0.107147 | + | 0.994243i | \(0.465829\pi\) | |||||||
\(224\) | 2.63055e25i | 0.369248i | ||||||||
\(225\) | −6.35505e25 | + | 3.90926e25i | −0.849398 | + | 0.522500i | ||||
\(226\) | −2.66982e25 | −0.339852 | ||||||||
\(227\) | − | 2.76745e25i | − | 0.335579i | −0.985823 | − | 0.167790i | \(-0.946337\pi\) | ||
0.985823 | − | 0.167790i | \(-0.0536629\pi\) | |||||||
\(228\) | 3.84501e24 | + | 1.35892e25i | 0.0444237 | + | 0.157003i | ||||
\(229\) | 8.87110e25 | 0.976759 | 0.488379 | − | 0.872631i | \(-0.337588\pi\) | ||||
0.488379 | + | 0.872631i | \(0.337588\pi\) | |||||||
\(230\) | − | 1.68618e24i | − | 0.0176969i | ||||||
\(231\) | −6.95868e25 | + | 1.96894e25i | −0.696298 | + | 0.197016i | ||||
\(232\) | 5.55813e25 | 0.530348 | ||||||||
\(233\) | − | 6.39561e25i | − | 0.582059i | −0.956714 | − | 0.291029i | \(-0.906002\pi\) | ||
0.956714 | − | 0.291029i | \(-0.0939978\pi\) | |||||||
\(234\) | 1.59612e25 | + | 2.59471e25i | 0.138577 | + | 0.225276i | ||||
\(235\) | 9.52619e23 | 0.00789174 | ||||||||
\(236\) | 9.94167e25i | 0.786008i | ||||||||
\(237\) | −5.10204e25 | − | 1.80318e26i | −0.385046 | − | 1.36084i | ||||
\(238\) | 2.88600e25 | 0.207946 | ||||||||
\(239\) | − | 1.54833e26i | − | 1.06534i | −0.846324 | − | 0.532669i | \(-0.821189\pi\) | ||
0.846324 | − | 0.532669i | \(-0.178811\pi\) | |||||||
\(240\) | −5.55016e24 | + | 1.57040e24i | −0.0364739 | + | 0.0103202i | ||||
\(241\) | −1.59574e25 | −0.100178 | −0.0500892 | − | 0.998745i | \(-0.515951\pi\) | ||||
−0.0500892 | + | 0.998745i | \(0.515951\pi\) | |||||||
\(242\) | − | 7.96018e25i | − | 0.477478i | ||||||
\(243\) | 1.71240e26 | + | 3.33057e25i | 0.981606 | + | 0.190919i | ||||
\(244\) | −1.26398e26 | −0.692552 | ||||||||
\(245\) | − | 7.96618e24i | − | 0.0417276i | ||||||
\(246\) | 2.15403e25 | + | 7.61282e25i | 0.107886 | + | 0.381293i | ||||
\(247\) | −3.21658e25 | −0.154073 | ||||||||
\(248\) | 1.17657e26i | 0.539074i | ||||||||
\(249\) | 2.30509e26 | − | 6.52218e25i | 1.01040 | − | 0.285891i | ||||
\(250\) | −7.75451e24 | −0.0325248 | ||||||||
\(251\) | 4.68439e26i | 1.88036i | 0.340674 | + | 0.940182i | \(0.389345\pi\) | ||||
−0.340674 | + | 0.940182i | \(0.610655\pi\) | |||||||
\(252\) | −9.09702e25 | + | 5.59596e25i | −0.349537 | + | 0.215015i | ||||
\(253\) | −4.70917e26 | −1.73228 | ||||||||
\(254\) | − | 3.85138e25i | − | 0.135658i | ||||||
\(255\) | 6.27140e24 | + | 2.21645e25i | 0.0211555 | + | 0.0747682i | ||||
\(256\) | 5.32674e25 | 0.172116 | ||||||||
\(257\) | − | 4.03799e26i | − | 1.24997i | −0.780635 | − | 0.624987i | \(-0.785104\pi\) | ||
0.780635 | − | 0.624987i | \(-0.214896\pi\) | |||||||
\(258\) | −3.46441e25 | + | 9.80246e24i | −0.102757 | + | 0.0290749i | ||||
\(259\) | 2.06297e26 | 0.586402 | ||||||||
\(260\) | − | 1.48861e25i | − | 0.0405577i | ||||||
\(261\) | 1.80338e26 | + | 2.93165e26i | 0.471023 | + | 0.765714i | ||||
\(262\) | 2.85144e24 | 0.00714085 | ||||||||
\(263\) | 1.08512e26i | 0.260593i | 0.991475 | + | 0.130296i | \(0.0415929\pi\) | ||||
−0.991475 | + | 0.130296i | \(0.958407\pi\) | |||||||
\(264\) | −1.11157e26 | − | 3.92855e26i | −0.256032 | − | 0.904875i | ||||
\(265\) | 3.36659e25 | 0.0743850 | ||||||||
\(266\) | 1.19762e25i | 0.0253875i | ||||||||
\(267\) | 1.27193e26 | − | 3.59890e25i | 0.258726 | − | 0.0732058i | ||||
\(268\) | 6.98624e26 | 1.36383 | ||||||||
\(269\) | − | 5.82469e26i | − | 1.09143i | −0.837970 | − | 0.545717i | \(-0.816257\pi\) | ||
0.837970 | − | 0.545717i | \(-0.183743\pi\) | |||||||
\(270\) | 6.66337e24 | + | 6.12811e24i | 0.0119865 | + | 0.0110236i | ||||
\(271\) | −1.12902e27 | −1.95003 | −0.975014 | − | 0.222144i | \(-0.928695\pi\) | ||||
−0.975014 | + | 0.222144i | \(0.928695\pi\) | |||||||
\(272\) | − | 6.42860e26i | − | 1.06625i | ||||||
\(273\) | −6.62287e25 | − | 2.34067e26i | −0.105501 | − | 0.372865i | ||||
\(274\) | 1.37753e26 | 0.210787 | ||||||||
\(275\) | 1.08134e27i | 1.58966i | ||||||||
\(276\) | −6.69201e26 | + | 1.89349e26i | −0.945272 | + | 0.267462i | ||||
\(277\) | 1.27014e27 | 1.72415 | 0.862073 | − | 0.506784i | \(-0.169166\pi\) | ||||
0.862073 | + | 0.506784i | \(0.169166\pi\) | |||||||
\(278\) | 1.04932e26i | 0.136904i | ||||||||
\(279\) | −6.20583e26 | + | 3.81747e26i | −0.778312 | + | 0.478772i | ||||
\(280\) | −1.16735e25 | −0.0140755 | ||||||||
\(281\) | 9.81868e26i | 1.13837i | 0.822209 | + | 0.569185i | \(0.192741\pi\) | ||||
−0.822209 | + | 0.569185i | \(0.807259\pi\) | |||||||
\(282\) | 1.13603e25 | + | 4.01500e25i | 0.0126663 | + | 0.0447657i | ||||
\(283\) | 4.86330e26 | 0.521531 | 0.260765 | − | 0.965402i | \(-0.416025\pi\) | ||||
0.260765 | + | 0.965402i | \(0.416025\pi\) | |||||||
\(284\) | 2.33597e26i | 0.240972i | ||||||||
\(285\) | −9.19770e24 | + | 2.60246e24i | −0.00912822 | + | 0.00258280i | ||||
\(286\) | 4.41504e26 | 0.421607 | ||||||||
\(287\) | − | 6.31767e26i | − | 0.580572i | ||||||
\(288\) | −4.81847e26 | − | 7.83310e26i | −0.426179 | − | 0.692814i | ||||
\(289\) | −1.39270e27 | −1.18571 | ||||||||
\(290\) | 1.78614e25i | 0.0146399i | ||||||||
\(291\) | 2.63686e26 | + | 9.31926e26i | 0.208096 | + | 0.735459i | ||||
\(292\) | 2.26933e26 | 0.172459 | ||||||||
\(293\) | − | 1.66808e27i | − | 1.22088i | −0.792063 | − | 0.610440i | \(-0.790993\pi\) | ||
0.792063 | − | 0.610440i | \(-0.209007\pi\) | |||||||
\(294\) | 3.35750e26 | − | 9.49996e25i | 0.236699 | − | 0.0669732i | ||||
\(295\) | −6.72893e25 | −0.0456987 | ||||||||
\(296\) | 1.16466e27i | 0.762060i | ||||||||
\(297\) | 1.71146e27 | − | 1.86095e27i | 1.07906 | − | 1.17331i | ||||
\(298\) | −8.18923e26 | −0.497582 | ||||||||
\(299\) | − | 1.58401e27i | − | 0.927631i | ||||||
\(300\) | 4.34792e26 | + | 1.53665e27i | 0.245441 | + | 0.867446i | ||||
\(301\) | 2.87502e26 | 0.156462 | ||||||||
\(302\) | − | 6.49180e26i | − | 0.340635i | ||||||
\(303\) | 6.41285e26 | − | 1.81450e26i | 0.324475 | − | 0.0918094i | ||||
\(304\) | 2.66770e26 | 0.130175 | ||||||||
\(305\) | − | 8.55514e25i | − | 0.0402651i | ||||||
\(306\) | −8.59380e26 | + | 5.28641e26i | −0.390166 | + | 0.240008i | ||||
\(307\) | −3.02980e27 | −1.32706 | −0.663532 | − | 0.748148i | \(-0.730943\pi\) | ||||
−0.663532 | + | 0.748148i | \(0.730943\pi\) | |||||||
\(308\) | 1.54791e27i | 0.654164i | ||||||||
\(309\) | 7.86069e25 | + | 2.77815e26i | 0.0320566 | + | 0.113295i | ||||
\(310\) | −3.78098e25 | −0.0148808 | ||||||||
\(311\) | 4.31241e27i | 1.63816i | 0.573681 | + | 0.819079i | \(0.305515\pi\) | ||||
−0.573681 | + | 0.819079i | \(0.694485\pi\) | |||||||
\(312\) | 1.32143e27 | − | 3.73896e26i | 0.484557 | − | 0.137104i | ||||
\(313\) | 1.34419e27 | 0.475855 | 0.237927 | − | 0.971283i | \(-0.423532\pi\) | ||||
0.237927 | + | 0.971283i | \(0.423532\pi\) | |||||||
\(314\) | − | 7.33833e26i | − | 0.250825i | ||||||
\(315\) | −3.78758e25 | − | 6.15724e25i | −0.0125010 | − | 0.0203222i | ||||
\(316\) | −4.01103e27 | −1.27849 | ||||||||
\(317\) | − | 1.59985e27i | − | 0.492523i | −0.969203 | − | 0.246261i | \(-0.920798\pi\) | ||
0.969203 | − | 0.246261i | \(-0.0792022\pi\) | |||||||
\(318\) | 4.01478e26 | + | 1.41892e27i | 0.119389 | + | 0.421947i | ||||
\(319\) | 4.98836e27 | 1.43305 | ||||||||
\(320\) | 8.88459e25i | 0.0246597i | ||||||||
\(321\) | −2.26536e27 | + | 6.40979e26i | −0.607551 | + | 0.171905i | ||||
\(322\) | −5.89769e26 | −0.152851 | ||||||||
\(323\) | − | 1.06534e27i | − | 0.266847i | ||||||
\(324\) | 1.68383e27 | − | 3.33267e27i | 0.407665 | − | 0.806859i | ||||
\(325\) | −3.63729e27 | −0.851257 | ||||||||
\(326\) | − | 5.94064e26i | − | 0.134412i | ||||||
\(327\) | −9.97718e26 | − | 3.52616e27i | −0.218264 | − | 0.771396i | ||||
\(328\) | 3.56666e27 | 0.754483 | ||||||||
\(329\) | − | 3.33194e26i | − | 0.0681620i | ||||||
\(330\) | 1.26247e26 | − | 3.57211e25i | 0.0249785 | − | 0.00706760i | ||||
\(331\) | 7.64020e27 | 1.46217 | 0.731083 | − | 0.682289i | \(-0.239015\pi\) | ||||
0.731083 | + | 0.682289i | \(0.239015\pi\) | |||||||
\(332\) | − | 5.12749e27i | − | 0.949261i | ||||||
\(333\) | −6.14301e27 | + | 3.77882e27i | −1.10026 | + | 0.676815i | ||||
\(334\) | 1.08502e27 | 0.188030 | ||||||||
\(335\) | 4.72857e26i | 0.0792934i | ||||||||
\(336\) | 5.49274e26 | + | 1.94126e27i | 0.0891368 | + | 0.315030i | ||||
\(337\) | 1.98642e27 | 0.311990 | 0.155995 | − | 0.987758i | \(-0.450142\pi\) | ||||
0.155995 | + | 0.987758i | \(0.450142\pi\) | |||||||
\(338\) | − | 5.53020e26i | − | 0.0840731i | ||||||
\(339\) | −7.17170e27 | + | 2.02921e27i | −1.05542 | + | 0.298628i | ||||
\(340\) | 4.93033e26 | 0.0702438 | ||||||||
\(341\) | 1.05595e28i | 1.45662i | ||||||||
\(342\) | −2.19372e26 | − | 3.56620e26i | −0.0293018 | − | 0.0476342i | ||||
\(343\) | −6.29583e27 | −0.814362 | ||||||||
\(344\) | 1.62310e27i | 0.203331i | ||||||||
\(345\) | −1.28159e26 | − | 4.52943e26i | −0.0155503 | − | 0.0549583i | ||||
\(346\) | −3.32825e27 | −0.391182 | ||||||||
\(347\) | − | 3.72382e27i | − | 0.423998i | −0.977270 | − | 0.211999i | \(-0.932003\pi\) | ||
0.977270 | − | 0.211999i | \(-0.0679974\pi\) | |||||||
\(348\) | 7.08875e27 | − | 2.00574e27i | 0.781984 | − | 0.221260i | ||||
\(349\) | 1.03630e28 | 1.10765 | 0.553827 | − | 0.832632i | \(-0.313167\pi\) | ||||
0.553827 | + | 0.832632i | \(0.313167\pi\) | |||||||
\(350\) | 1.35426e27i | 0.140266i | ||||||||
\(351\) | 6.25963e27 | + | 5.75680e27i | 0.628304 | + | 0.577834i | ||||
\(352\) | −1.33284e28 | −1.29661 | ||||||||
\(353\) | 4.70352e27i | 0.443508i | 0.975103 | + | 0.221754i | \(0.0711782\pi\) | ||||
−0.975103 | + | 0.221754i | \(0.928822\pi\) | |||||||
\(354\) | −8.02449e26 | − | 2.83604e27i | −0.0733469 | − | 0.259225i | ||||
\(355\) | −1.58108e26 | −0.0140101 | ||||||||
\(356\) | − | 2.82931e27i | − | 0.243070i | ||||||
\(357\) | 7.75241e27 | − | 2.19352e27i | 0.645783 | − | 0.182722i | ||||
\(358\) | 4.35017e27 | 0.351393 | ||||||||
\(359\) | − | 1.78774e28i | − | 1.40045i | −0.713924 | − | 0.700223i | \(-0.753084\pi\) | ||
0.713924 | − | 0.700223i | \(-0.246916\pi\) | |||||||
\(360\) | 3.47609e26 | − | 2.13829e26i | 0.0264097 | − | 0.0162457i | ||||
\(361\) | −1.31279e28 | −0.967421 | ||||||||
\(362\) | 1.56463e26i | 0.0111845i | ||||||||
\(363\) | −6.05017e27 | − | 2.13827e28i | −0.419561 | − | 1.48282i | ||||
\(364\) | −5.20665e27 | −0.350302 | ||||||||
\(365\) | 1.53597e26i | 0.0100268i | ||||||||
\(366\) | 3.60573e27 | − | 1.02023e27i | 0.228403 | − | 0.0646260i | ||||
\(367\) | 1.37751e28 | 0.846777 | 0.423388 | − | 0.905948i | \(-0.360841\pi\) | ||||
0.423388 | + | 0.905948i | \(0.360841\pi\) | |||||||
\(368\) | 1.31371e28i | 0.783745i | ||||||||
\(369\) | 1.15723e28 | + | 1.88124e28i | 0.670086 | + | 1.08932i | ||||
\(370\) | −3.74270e26 | −0.0210362 | ||||||||
\(371\) | − | 1.17752e28i | − | 0.642473i | ||||||
\(372\) | 4.24583e27 | + | 1.50057e28i | 0.224900 | + | 0.794849i | ||||
\(373\) | −1.54597e28 | −0.795065 | −0.397532 | − | 0.917588i | \(-0.630133\pi\) | ||||
−0.397532 | + | 0.917588i | \(0.630133\pi\) | |||||||
\(374\) | 1.46228e28i | 0.730201i | ||||||||
\(375\) | −2.08302e27 | + | 5.89385e26i | −0.101007 | + | 0.0285796i | ||||
\(376\) | 1.88106e27 | 0.0885800 | ||||||||
\(377\) | 1.67792e28i | 0.767390i | ||||||||
\(378\) | 2.14341e27 | − | 2.33062e27i | 0.0952127 | − | 0.103529i | ||||
\(379\) | −1.43985e28 | −0.621277 | −0.310639 | − | 0.950528i | \(-0.600543\pi\) | ||||
−0.310639 | + | 0.950528i | \(0.600543\pi\) | |||||||
\(380\) | 2.04596e26i | 0.00857585i | ||||||||
\(381\) | −2.92726e27 | − | 1.03456e28i | −0.119203 | − | 0.421291i | ||||
\(382\) | 7.58400e27 | 0.300055 | ||||||||
\(383\) | − | 1.66071e28i | − | 0.638423i | −0.947684 | − | 0.319211i | \(-0.896582\pi\) | ||
0.947684 | − | 0.319211i | \(-0.103418\pi\) | |||||||
\(384\) | −2.46965e28 | + | 6.98781e27i | −0.922555 | + | 0.261034i | ||||
\(385\) | −1.04769e27 | −0.0380332 | ||||||||
\(386\) | − | 4.08546e27i | − | 0.144139i | ||||||
\(387\) | −8.56109e27 | + | 5.26629e27i | −0.293568 | + | 0.180586i | ||||
\(388\) | 2.07300e28 | 0.690955 | ||||||||
\(389\) | 3.87537e27i | 0.125565i | 0.998027 | + | 0.0627823i | \(0.0199974\pi\) | ||||
−0.998027 | + | 0.0627823i | \(0.980003\pi\) | |||||||
\(390\) | 1.20154e26 | + | 4.24652e26i | 0.00378467 | + | 0.0133759i | ||||
\(391\) | 5.24631e28 | 1.60661 | ||||||||
\(392\) | − | 1.57301e28i | − | 0.468367i | ||||||
\(393\) | 7.65956e26 | − | 2.16725e26i | 0.0221761 | − | 0.00627467i | ||||
\(394\) | −8.75662e27 | −0.246535 | ||||||||
\(395\) | − | 2.71483e27i | − | 0.0743318i | ||||||
\(396\) | −2.83536e28 | − | 4.60927e28i | −0.755024 | − | 1.22740i | ||||
\(397\) | 1.40537e28 | 0.363994 | 0.181997 | − | 0.983299i | \(-0.441744\pi\) | ||||
0.181997 | + | 0.983299i | \(0.441744\pi\) | |||||||
\(398\) | − | 1.48841e28i | − | 0.374979i | ||||||
\(399\) | 9.10254e26 | + | 3.21705e27i | 0.0223080 | + | 0.0788416i | ||||
\(400\) | 3.01662e28 | 0.719218 | ||||||||
\(401\) | − | 1.32647e28i | − | 0.307687i | −0.988095 | − | 0.153844i | \(-0.950835\pi\) | ||
0.988095 | − | 0.153844i | \(-0.0491652\pi\) | |||||||
\(402\) | −1.99295e28 | + | 5.63900e27i | −0.449790 | + | 0.127267i | ||||
\(403\) | −3.55188e28 | −0.780015 | ||||||||
\(404\) | − | 1.42649e28i | − | 0.304841i | ||||||
\(405\) | 2.25569e27 | + | 1.13969e27i | 0.0469110 | + | 0.0237017i | ||||
\(406\) | 6.24733e27 | 0.126447 | ||||||||
\(407\) | 1.04526e29i | 2.05915i | ||||||||
\(408\) | 1.23836e28 | + | 4.37665e28i | 0.237457 | + | 0.839228i | ||||
\(409\) | −6.25768e28 | −1.16804 | −0.584019 | − | 0.811740i | \(-0.698520\pi\) | ||||
−0.584019 | + | 0.811740i | \(0.698520\pi\) | |||||||
\(410\) | 1.14617e27i | 0.0208270i | ||||||||
\(411\) | 3.70032e28 | − | 1.04700e28i | 0.654606 | − | 0.185219i | ||||
\(412\) | 6.17977e27 | 0.106440 | ||||||||
\(413\) | 2.35355e28i | 0.394706i | ||||||||
\(414\) | 1.75618e28 | − | 1.08030e28i | 0.286791 | − | 0.176417i | ||||
\(415\) | 3.47050e27 | 0.0551903 | ||||||||
\(416\) | − | 4.48325e28i | − | 0.694330i | ||||||
\(417\) | 7.97540e27 | + | 2.81869e28i | 0.120297 | + | 0.425158i | ||||
\(418\) | −6.06807e27 | −0.0891480 | ||||||||
\(419\) | 8.86074e27i | 0.126799i | 0.997988 | + | 0.0633995i | \(0.0201942\pi\) | ||||
−0.997988 | + | 0.0633995i | \(0.979806\pi\) | |||||||
\(420\) | −1.48882e27 | + | 4.21259e26i | −0.0207540 | + | 0.00587228i | ||||
\(421\) | −9.59743e28 | −1.30332 | −0.651661 | − | 0.758510i | \(-0.725928\pi\) | ||||
−0.651661 | + | 0.758510i | \(0.725928\pi\) | |||||||
\(422\) | 1.34903e28i | 0.178478i | ||||||||
\(423\) | 6.10324e27 | + | 9.92168e27i | 0.0786713 | + | 0.127891i | ||||
\(424\) | 6.64772e28 | 0.834927 | ||||||||
\(425\) | − | 1.20468e29i | − | 1.47433i | ||||||
\(426\) | −1.88550e27 | − | 6.66378e27i | −0.0224864 | − | 0.0794722i | ||||
\(427\) | −2.99230e28 | −0.347775 | ||||||||
\(428\) | 5.03913e28i | 0.570787i | ||||||||
\(429\) | 1.18597e29 | − | 3.35567e28i | 1.30931 | − | 0.370467i | ||||
\(430\) | −5.21595e26 | −0.00561281 | ||||||||
\(431\) | − | 8.10825e28i | − | 0.850505i | −0.905075 | − | 0.425253i | \(-0.860185\pi\) | ||
0.905075 | − | 0.425253i | \(-0.139815\pi\) | |||||||
\(432\) | −5.19148e28 | − | 4.77446e28i | −0.530848 | − | 0.488206i | ||||
\(433\) | 8.99261e28 | 0.896435 | 0.448217 | − | 0.893925i | \(-0.352059\pi\) | ||||
0.448217 | + | 0.893925i | \(0.352059\pi\) | |||||||
\(434\) | 1.32246e28i | 0.128527i | ||||||||
\(435\) | 1.35757e27 | + | 4.79796e27i | 0.0128641 | + | 0.0454647i | ||||
\(436\) | −7.84368e28 | −0.724717 | ||||||||
\(437\) | 2.17708e28i | 0.196146i | ||||||||
\(438\) | −6.47367e27 | + | 1.83171e27i | −0.0568768 | + | 0.0160931i | ||||
\(439\) | −8.56774e28 | −0.734102 | −0.367051 | − | 0.930201i | \(-0.619633\pi\) | ||||
−0.367051 | + | 0.930201i | \(0.619633\pi\) | |||||||
\(440\) | − | 5.91474e27i | − | 0.0494261i | ||||||
\(441\) | 8.29690e28 | − | 5.10377e28i | 0.676225 | − | 0.415975i | ||||
\(442\) | −4.91863e28 | −0.391020 | ||||||||
\(443\) | 8.02193e28i | 0.622068i | 0.950399 | + | 0.311034i | \(0.100675\pi\) | ||||
−0.950399 | + | 0.311034i | \(0.899325\pi\) | |||||||
\(444\) | 4.20285e28 | + | 1.48538e29i | 0.317930 | + | 1.12364i | ||||
\(445\) | 1.91500e27 | 0.0141321 | ||||||||
\(446\) | 9.22215e27i | 0.0663970i | ||||||||
\(447\) | −2.19980e29 | + | 6.22427e28i | −1.54526 | + | 0.437226i | ||||
\(448\) | 3.10753e28 | 0.212989 | ||||||||
\(449\) | 6.61838e28i | 0.442631i | 0.975202 | + | 0.221316i | \(0.0710351\pi\) | ||||
−0.975202 | + | 0.221316i | \(0.928965\pi\) | |||||||
\(450\) | −2.48064e28 | − | 4.03264e28i | −0.161893 | − | 0.263179i | ||||
\(451\) | 3.20103e29 | 2.03868 | ||||||||
\(452\) | 1.59529e29i | 0.991555i | ||||||||
\(453\) | −4.93413e28 | − | 1.74383e29i | −0.299316 | − | 1.05785i | ||||
\(454\) | 1.75610e28 | 0.103977 | ||||||||
\(455\) | − | 3.52407e27i | − | 0.0203666i | ||||||
\(456\) | −1.81619e28 | + | 5.13887e27i | −0.102459 | + | 0.0289904i | ||||
\(457\) | 1.17663e28 | 0.0647981 | 0.0323991 | − | 0.999475i | \(-0.489685\pi\) | ||||
0.0323991 | + | 0.999475i | \(0.489685\pi\) | |||||||
\(458\) | 5.62922e28i | 0.302641i | ||||||||
\(459\) | −1.90668e29 | + | 2.07322e29i | −1.00078 | + | 1.08819i | ||||
\(460\) | −1.00754e28 | −0.0516327 | ||||||||
\(461\) | − | 3.81875e29i | − | 1.91078i | −0.295346 | − | 0.955390i | \(-0.595435\pi\) | ||
0.295346 | − | 0.955390i | \(-0.404565\pi\) | |||||||
\(462\) | −1.24940e28 | − | 4.41568e28i | −0.0610437 | − | 0.215743i | ||||
\(463\) | −3.90433e28 | −0.186276 | −0.0931378 | − | 0.995653i | \(-0.529690\pi\) | ||||
−0.0931378 | + | 0.995653i | \(0.529690\pi\) | |||||||
\(464\) | − | 1.39160e29i | − | 0.648360i | ||||||
\(465\) | −1.01565e28 | + | 2.87375e27i | −0.0462127 | + | 0.0130758i | ||||
\(466\) | 4.05838e28 | 0.180346 | ||||||||
\(467\) | − | 4.96399e28i | − | 0.215449i | −0.994181 | − | 0.107725i | \(-0.965643\pi\) | ||
0.994181 | − | 0.107725i | \(-0.0343565\pi\) | |||||||
\(468\) | 1.55041e29 | − | 9.53722e28i | 0.657267 | − | 0.404313i | ||||
\(469\) | 1.65390e29 | 0.684868 | ||||||||
\(470\) | 6.04491e26i | 0.00244519i | ||||||||
\(471\) | −5.57754e28 | − | 1.97123e29i | −0.220401 | − | 0.778946i | ||||
\(472\) | −1.32871e29 | −0.512940 | ||||||||
\(473\) | 1.45671e29i | 0.549417i | ||||||||
\(474\) | 1.14422e29 | − | 3.23753e28i | 0.421645 | − | 0.119303i | ||||
\(475\) | 4.99912e28 | 0.179997 | ||||||||
\(476\) | − | 1.72446e29i | − | 0.606705i | ||||||
\(477\) | 2.15691e29 | + | 3.50636e29i | 0.741531 | + | 1.20546i | ||||
\(478\) | 9.82504e28 | 0.330086 | ||||||||
\(479\) | 3.94959e29i | 1.29677i | 0.761314 | + | 0.648383i | \(0.224555\pi\) | ||||
−0.761314 | + | 0.648383i | \(0.775445\pi\) | |||||||
\(480\) | −3.62730e27 | − | 1.28197e28i | −0.0116394 | − | 0.0411362i | ||||
\(481\) | −3.51593e29 | −1.10267 | ||||||||
\(482\) | − | 1.01259e28i | − | 0.0310395i | ||||||
\(483\) | −1.58424e29 | + | 4.48257e28i | −0.474682 | + | 0.134310i | ||||
\(484\) | −4.75642e29 | −1.39310 | ||||||||
\(485\) | 1.40309e28i | 0.0401723i | ||||||||
\(486\) | −2.11344e28 | + | 1.08662e29i | −0.0591548 | + | 0.304143i | ||||
\(487\) | 2.85794e29 | 0.782051 | 0.391026 | − | 0.920380i | \(-0.372120\pi\) | ||||
0.391026 | + | 0.920380i | \(0.372120\pi\) | |||||||
\(488\) | − | 1.68931e29i | − | 0.451952i | ||||||
\(489\) | −4.51521e28 | − | 1.59578e29i | −0.118108 | − | 0.417422i | ||||
\(490\) | 5.05499e27 | 0.0129290 | ||||||||
\(491\) | 5.21641e29i | 1.30459i | 0.757963 | + | 0.652297i | \(0.226195\pi\) | ||||
−0.757963 | + | 0.652297i | \(0.773805\pi\) | |||||||
\(492\) | 4.54886e29 | − | 1.28709e29i | 1.11246 | − | 0.314769i | ||||
\(493\) | −5.55734e29 | −1.32908 | ||||||||
\(494\) | − | 2.04110e28i | − | 0.0477384i | ||||||
\(495\) | 3.11975e28 | − | 1.91909e28i | 0.0713612 | − | 0.0438973i | ||||
\(496\) | 2.94579e29 | 0.659027 | ||||||||
\(497\) | 5.53009e28i | 0.121007i | ||||||||
\(498\) | 4.13869e28 | + | 1.46271e29i | 0.0885810 | + | 0.313065i | ||||
\(499\) | 3.17671e29 | 0.665076 | 0.332538 | − | 0.943090i | \(-0.392095\pi\) | ||||
0.332538 | + | 0.943090i | \(0.392095\pi\) | |||||||
\(500\) | 4.63352e28i | 0.0948945i | ||||||||
\(501\) | 2.91460e29 | − | 8.24678e28i | 0.583934 | − | 0.165223i | ||||
\(502\) | −2.97251e29 | −0.582616 | ||||||||
\(503\) | − | 6.15651e29i | − | 1.18056i | −0.807200 | − | 0.590278i | \(-0.799018\pi\) | ||
0.807200 | − | 0.590278i | \(-0.200982\pi\) | |||||||
\(504\) | −7.47901e28 | − | 1.21582e29i | −0.140316 | − | 0.228104i | ||||
\(505\) | 9.65506e27 | 0.0177235 | ||||||||
\(506\) | − | 2.98824e29i | − | 0.536734i | ||||||
\(507\) | −4.20326e28 | − | 1.48553e29i | −0.0738752 | − | 0.261092i | ||||
\(508\) | −2.30130e29 | −0.395797 | ||||||||
\(509\) | − | 8.72791e29i | − | 1.46898i | −0.678622 | − | 0.734488i | \(-0.737423\pi\) | ||
0.678622 | − | 0.734488i | \(-0.262577\pi\) | |||||||
\(510\) | −1.40647e28 | + | 3.97956e27i | −0.0231663 | + | 0.00655485i | ||||
\(511\) | 5.37232e28 | 0.0866028 | ||||||||
\(512\) | 6.41496e29i | 1.01210i | ||||||||
\(513\) | −8.60330e28 | − | 7.91221e28i | −0.132854 | − | 0.122182i | ||||
\(514\) | 2.56233e29 | 0.387295 | ||||||||
\(515\) | 4.18272e27i | 0.00618842i | ||||||||
\(516\) | 5.85723e28 | + | 2.07008e29i | 0.0848292 | + | 0.299806i | ||||
\(517\) | 1.68822e29 | 0.239350 | ||||||||
\(518\) | 1.30907e29i | 0.181692i | ||||||||
\(519\) | −8.94036e29 | + | 2.52965e29i | −1.21483 | + | 0.343732i | ||||
\(520\) | 1.98953e28 | 0.0264675 | ||||||||
\(521\) | 1.40880e30i | 1.83500i | 0.397741 | + | 0.917498i | \(0.369794\pi\) | ||||
−0.397741 | + | 0.917498i | \(0.630206\pi\) | |||||||
\(522\) | −1.86030e29 | + | 1.14435e29i | −0.237250 | + | 0.145943i | ||||
\(523\) | 1.27849e30 | 1.59654 | 0.798271 | − | 0.602299i | \(-0.205748\pi\) | ||||
0.798271 | + | 0.602299i | \(0.205748\pi\) | |||||||
\(524\) | − | 1.70381e28i | − | 0.0208342i | ||||||
\(525\) | 1.02931e29 | + | 3.63782e29i | 0.123252 | + | 0.435600i | ||||
\(526\) | −6.88567e28 | −0.0807427 | ||||||||
\(527\) | − | 1.17640e30i | − | 1.35095i | ||||||
\(528\) | −9.83596e29 | + | 2.78306e29i | −1.10623 | + | 0.313003i | ||||
\(529\) | −1.64262e29 | −0.180936 | ||||||||
\(530\) | 2.13629e28i | 0.0230476i | ||||||||
\(531\) | −4.31109e29 | − | 7.00829e29i | −0.455562 | − | 0.740580i | ||||
\(532\) | 7.15607e28 | 0.0740707 | ||||||||
\(533\) | 1.07672e30i | 1.09170i | ||||||||
\(534\) | 2.28370e28 | + | 8.07113e28i | 0.0226822 | + | 0.0801642i | ||||
\(535\) | −3.41069e28 | −0.0331857 | ||||||||
\(536\) | 9.33712e29i | 0.890021i | ||||||||
\(537\) | 1.16855e30 | − | 3.30637e29i | 1.09126 | − | 0.308770i | ||||
\(538\) | 3.69609e29 | 0.338172 | ||||||||
\(539\) | − | 1.41176e30i | − | 1.26557i | ||||||
\(540\) | 3.66171e28 | − | 3.98154e28i | 0.0321627 | − | 0.0349719i | ||||
\(541\) | −1.57318e30 | −1.35396 | −0.676982 | − | 0.735999i | \(-0.736713\pi\) | ||||
−0.676982 | + | 0.735999i | \(0.736713\pi\) | |||||||
\(542\) | − | 7.16429e29i | − | 0.604201i | ||||||
\(543\) | 1.18921e28 | + | 4.20293e28i | 0.00982787 | + | 0.0347339i | ||||
\(544\) | 1.48487e30 | 1.20254 | ||||||||
\(545\) | − | 5.30892e28i | − | 0.0421352i | ||||||
\(546\) | 1.48529e29 | − | 4.20259e28i | 0.115529 | − | 0.0326887i | ||||
\(547\) | −9.42184e28 | −0.0718249 | −0.0359125 | − | 0.999355i | \(-0.511434\pi\) | ||||
−0.0359125 | + | 0.999355i | \(0.511434\pi\) | |||||||
\(548\) | − | 8.23109e29i | − | 0.614994i | ||||||
\(549\) | 8.91032e29 | − | 5.48111e29i | 0.652525 | − | 0.401396i | ||||
\(550\) | −6.86174e29 | −0.492544 | ||||||||
\(551\) | − | 2.30615e29i | − | 0.162263i | ||||||
\(552\) | −2.53065e29 | − | 8.94389e29i | −0.174543 | − | 0.616874i | ||||
\(553\) | −9.49556e29 | −0.642013 | ||||||||
\(554\) | 8.05976e29i | 0.534213i | ||||||||
\(555\) | −1.00537e29 | + | 2.84466e28i | −0.0653284 | + | 0.0184845i | ||||
\(556\) | 6.26995e29 | 0.399431 | ||||||||
\(557\) | 1.89002e29i | 0.118048i | 0.998257 | + | 0.0590242i | \(0.0187989\pi\) | ||||
−0.998257 | + | 0.0590242i | \(0.981201\pi\) | |||||||
\(558\) | −2.42240e29 | − | 3.93795e29i | −0.148344 | − | 0.241154i | ||||
\(559\) | −4.89991e29 | −0.294210 | ||||||||
\(560\) | 2.92272e28i | 0.0172076i | ||||||||
\(561\) | 1.11141e30 | + | 3.92799e30i | 0.641629 | + | 2.26766i | ||||
\(562\) | −6.23051e29 | −0.352715 | ||||||||
\(563\) | 9.85747e29i | 0.547234i | 0.961839 | + | 0.273617i | \(0.0882201\pi\) | ||||
−0.961839 | + | 0.273617i | \(0.911780\pi\) | |||||||
\(564\) | 2.39907e29 | − | 6.78809e28i | 0.130609 | − | 0.0369554i | ||||
\(565\) | −1.07976e29 | −0.0576492 | ||||||||
\(566\) | 3.08604e29i | 0.161592i | ||||||||
\(567\) | 3.98624e29 | − | 7.88964e29i | 0.204715 | − | 0.405176i | ||||
\(568\) | −3.12203e29 | −0.157255 | ||||||||
\(569\) | 1.47077e30i | 0.726623i | 0.931668 | + | 0.363311i | \(0.118354\pi\) | ||||
−0.931668 | + | 0.363311i | \(0.881646\pi\) | |||||||
\(570\) | −1.65141e27 | − | 5.83646e27i | −0.000800261 | − | 0.00282831i | ||||
\(571\) | −1.14696e30 | −0.545194 | −0.272597 | − | 0.962128i | \(-0.587883\pi\) | ||||
−0.272597 | + | 0.962128i | \(0.587883\pi\) | |||||||
\(572\) | − | 2.63810e30i | − | 1.23008i | ||||||
\(573\) | 2.03722e30 | − | 5.76426e29i | 0.931831 | − | 0.263659i | ||||
\(574\) | 4.00892e29 | 0.179886 | ||||||||
\(575\) | 2.46183e30i | 1.08371i | ||||||||
\(576\) | −9.25344e29 | + | 5.69218e29i | −0.399628 | + | 0.245828i | ||||
\(577\) | −4.46369e30 | −1.89130 | −0.945650 | − | 0.325187i | \(-0.894573\pi\) | ||||
−0.945650 | + | 0.325187i | \(0.894573\pi\) | |||||||
\(578\) | − | 8.83744e29i | − | 0.367384i | ||||||
\(579\) | −3.10517e29 | − | 1.09744e30i | −0.126655 | − | 0.447627i | ||||
\(580\) | 1.06727e29 | 0.0427136 | ||||||||
\(581\) | − | 1.21386e30i | − | 0.476685i | ||||||
\(582\) | −5.91360e29 | + | 1.67324e29i | −0.227876 | + | 0.0644769i | ||||
\(583\) | 5.96625e30 | 2.25604 | ||||||||
\(584\) | 3.03296e29i | 0.112545i | ||||||||
\(585\) | 6.45518e28 | + | 1.04938e29i | 0.0235068 | + | 0.0382136i | ||||
\(586\) | 1.05849e30 | 0.378280 | ||||||||
\(587\) | − | 3.37868e30i | − | 1.18503i | −0.805560 | − | 0.592514i | \(-0.798136\pi\) | ||
0.805560 | − | 0.592514i | \(-0.201864\pi\) | |||||||
\(588\) | −5.67647e29 | − | 2.00620e30i | −0.195402 | − | 0.690594i | ||||
\(589\) | 4.88174e29 | 0.164933 | ||||||||
\(590\) | − | 4.26989e28i | − | 0.0141594i | ||||||
\(591\) | −2.35221e30 | + | 6.65551e29i | −0.765621 | + | 0.216630i | ||||
\(592\) | 2.91597e30 | 0.931631 | ||||||||
\(593\) | − | 2.00698e30i | − | 0.629420i | −0.949188 | − | 0.314710i | \(-0.898093\pi\) | ||
0.949188 | − | 0.314710i | \(-0.101907\pi\) | |||||||
\(594\) | 1.18088e30 | + | 1.08602e30i | 0.363542 | + | 0.334339i | ||||
\(595\) | 1.16719e29 | 0.0352740 | ||||||||
\(596\) | 4.89328e30i | 1.45175i | ||||||||
\(597\) | −1.13127e30 | − | 3.99817e30i | −0.329495 | − | 1.16451i | ||||
\(598\) | 1.00514e30 | 0.287419 | ||||||||
\(599\) | 1.49421e30i | 0.419485i | 0.977757 | + | 0.209743i | \(0.0672626\pi\) | ||||
−0.977757 | + | 0.209743i | \(0.932737\pi\) | |||||||
\(600\) | −2.05374e30 | + | 5.81100e29i | −0.566085 | + | 0.160172i | ||||
\(601\) | −2.18938e30 | −0.592518 | −0.296259 | − | 0.955108i | \(-0.595739\pi\) | ||||
−0.296259 | + | 0.955108i | \(0.595739\pi\) | |||||||
\(602\) | 1.82436e29i | 0.0484786i | ||||||||
\(603\) | −4.92488e30 | + | 3.02950e30i | −1.28501 | + | 0.790462i | ||||
\(604\) | −3.87902e30 | −0.993839 | ||||||||
\(605\) | − | 3.21934e29i | − | 0.0809948i | ||||||
\(606\) | 1.15140e29 | + | 4.06931e29i | 0.0284464 | + | 0.100536i | ||||
\(607\) | 6.64897e30 | 1.61316 | 0.806582 | − | 0.591122i | \(-0.201315\pi\) | ||||
0.806582 | + | 0.591122i | \(0.201315\pi\) | |||||||
\(608\) | 6.16182e29i | 0.146815i | ||||||||
\(609\) | 1.67816e30 | − | 4.74832e29i | 0.392685 | − | 0.111109i | ||||
\(610\) | 5.42872e28 | 0.0124758 | ||||||||
\(611\) | 5.67863e29i | 0.128171i | ||||||||
\(612\) | 3.15877e30 | + | 5.13502e30i | 0.700248 | + | 1.13835i | ||||
\(613\) | −1.47531e30 | −0.321231 | −0.160615 | − | 0.987017i | \(-0.551348\pi\) | ||||
−0.160615 | + | 0.987017i | \(0.551348\pi\) | |||||||
\(614\) | − | 1.92258e30i | − | 0.411180i | ||||||
\(615\) | 8.71153e28 | + | 3.07885e29i | 0.0183007 | + | 0.0646789i | ||||
\(616\) | −2.06878e30 | −0.426900 | ||||||||
\(617\) | 3.74802e30i | 0.759740i | 0.925040 | + | 0.379870i | \(0.124031\pi\) | ||||
−0.925040 | + | 0.379870i | \(0.875969\pi\) | |||||||
\(618\) | −1.76289e29 | + | 4.98805e28i | −0.0351036 | + | 0.00993248i | ||||
\(619\) | 1.70965e29 | 0.0334433 | 0.0167217 | − | 0.999860i | \(-0.494677\pi\) | ||||
0.0167217 | + | 0.999860i | \(0.494677\pi\) | |||||||
\(620\) | 2.25923e29i | 0.0434163i | ||||||||
\(621\) | 3.89638e30 | − | 4.23671e30i | 0.735621 | − | 0.799874i | ||||
\(622\) | −2.73647e30 | −0.507570 | ||||||||
\(623\) | − | 6.69801e29i | − | 0.122061i | ||||||
\(624\) | −9.36129e29 | − | 3.30849e30i | −0.167612 | − | 0.592379i | ||||
\(625\) | 5.63728e30 | 0.991720 | ||||||||
\(626\) | 8.52967e29i | 0.147440i | ||||||||
\(627\) | −1.63001e30 | + | 4.61207e29i | −0.276852 | + | 0.0783345i | ||||
\(628\) | −4.38485e30 | −0.731810 | ||||||||
\(629\) | − | 1.16449e31i | − | 1.90976i | ||||||
\(630\) | 3.90712e28 | − | 2.40343e28i | 0.00629666 | − | 0.00387334i | ||||
\(631\) | −6.59210e30 | −1.04400 | −0.522000 | − | 0.852945i | \(-0.674814\pi\) | ||||
−0.522000 | + | 0.852945i | \(0.674814\pi\) | |||||||
\(632\) | − | 5.36075e30i | − | 0.834329i | ||||||
\(633\) | 1.02534e30 | + | 3.62377e30i | 0.156829 | + | 0.554268i | ||||
\(634\) | 1.01519e30 | 0.152604 | ||||||||
\(635\) | − | 1.55762e29i | − | 0.0230117i | ||||||
\(636\) | 8.47839e30 | − | 2.39894e30i | 1.23108 | − | 0.348330i | ||||
\(637\) | 4.74870e30 | 0.677705 | ||||||||
\(638\) | 3.16539e30i | 0.444018i | ||||||||
\(639\) | −1.01297e30 | − | 1.64672e30i | −0.139665 | − | 0.227044i | ||||
\(640\) | −3.71826e29 | −0.0503918 | ||||||||
\(641\) | 6.27180e30i | 0.835514i | 0.908559 | + | 0.417757i | \(0.137184\pi\) | ||||
−0.908559 | + | 0.417757i | \(0.862816\pi\) | |||||||
\(642\) | −4.06737e29 | − | 1.43750e30i | −0.0532634 | − | 0.188245i | ||||
\(643\) | −2.53701e30 | −0.326589 | −0.163295 | − | 0.986577i | \(-0.552212\pi\) | ||||
−0.163295 | + | 0.986577i | \(0.552212\pi\) | |||||||
\(644\) | 3.52402e30i | 0.445958i | ||||||||
\(645\) | −1.40111e29 | + | 3.96441e28i | −0.0174308 | + | 0.00493199i | ||||
\(646\) | 6.76021e29 | 0.0826804 | ||||||||
\(647\) | 1.29877e31i | 1.56165i | 0.624750 | + | 0.780825i | \(0.285201\pi\) | ||||
−0.624750 | + | 0.780825i | \(0.714799\pi\) | |||||||
\(648\) | 4.45412e30 | + | 2.25044e30i | 0.526547 | + | 0.266037i | ||||
\(649\) | −1.19250e31 | −1.38601 | ||||||||
\(650\) | − | 2.30806e30i | − | 0.263755i | ||||||
\(651\) | 1.00514e30 | + | 3.55240e30i | 0.112937 | + | 0.399145i | ||||
\(652\) | −3.54969e30 | −0.392163 | ||||||||
\(653\) | − | 6.47158e30i | − | 0.703016i | −0.936185 | − | 0.351508i | \(-0.885669\pi\) | ||
0.936185 | − | 0.351508i | \(-0.114331\pi\) | |||||||
\(654\) | 2.23755e30 | − | 6.33109e29i | 0.239011 | − | 0.0676274i | ||||
\(655\) | 1.15321e28 | 0.00121130 | ||||||||
\(656\) | − | 8.92990e30i | − | 0.922368i | ||||||
\(657\) | −1.59974e30 | + | 9.84069e29i | −0.162492 | + | 0.0999554i | ||||
\(658\) | 2.11430e29 | 0.0211194 | ||||||||
\(659\) | 1.28556e31i | 1.26285i | 0.775437 | + | 0.631426i | \(0.217530\pi\) | ||||
−0.775437 | + | 0.631426i | \(0.782470\pi\) | |||||||
\(660\) | −2.13443e29 | − | 7.54356e29i | −0.0206205 | − | 0.0728775i | ||||
\(661\) | 5.17697e30 | 0.491880 | 0.245940 | − | 0.969285i | \(-0.420903\pi\) | ||||
0.245940 | + | 0.969285i | \(0.420903\pi\) | |||||||
\(662\) | 4.84814e30i | 0.453041i | ||||||||
\(663\) | −1.32125e31 | + | 3.73843e30i | −1.21432 | + | 0.343590i | ||||
\(664\) | 6.85290e30 | 0.619477 | ||||||||
\(665\) | 4.84352e28i | 0.00430649i | ||||||||
\(666\) | −2.39788e30 | − | 3.89809e30i | −0.209706 | − | 0.340906i | ||||
\(667\) | 1.13567e31 | 0.976939 | ||||||||
\(668\) | − | 6.48330e30i | − | 0.548599i | ||||||
\(669\) | 7.00934e29 | + | 2.47726e30i | 0.0583432 | + | 0.206198i | ||||
\(670\) | −3.00055e29 | −0.0245684 | ||||||||
\(671\) | − | 1.51614e31i | − | 1.22121i | ||||||
\(672\) | −4.48390e30 | + | 1.26871e30i | −0.355299 | + | 0.100531i | ||||
\(673\) | 1.47973e31 | 1.15350 | 0.576749 | − | 0.816921i | \(-0.304321\pi\) | ||||
0.576749 | + | 0.816921i | \(0.304321\pi\) | |||||||
\(674\) | 1.26049e30i | 0.0966677i | ||||||||
\(675\) | −9.72855e30 | − | 8.94707e30i | −0.734018 | − | 0.675056i | ||||
\(676\) | −3.30444e30 | −0.245293 | ||||||||
\(677\) | − | 1.40668e31i | − | 1.02735i | −0.857984 | − | 0.513677i | \(-0.828283\pi\) | ||
0.857984 | − | 0.513677i | \(-0.171717\pi\) | |||||||
\(678\) | −1.28765e30 | − | 4.55085e30i | −0.0925276 | − | 0.327014i | ||||
\(679\) | 4.90753e30 | 0.346973 | ||||||||
\(680\) | 6.58939e29i | 0.0458403i | ||||||||
\(681\) | 4.71726e30 | − | 1.33473e30i | 0.322902 | − | 0.0913644i | ||||
\(682\) | −6.70062e30 | −0.451323 | ||||||||
\(683\) | 7.69466e29i | 0.0509990i | 0.999675 | + | 0.0254995i | \(0.00811762\pi\) | ||||
−0.999675 | + | 0.0254995i | \(0.991882\pi\) | |||||||
\(684\) | −2.13090e30 | + | 1.31080e30i | −0.138978 | + | 0.0854911i | ||||
\(685\) | 5.57114e29 | 0.0357559 | ||||||||
\(686\) | − | 3.99506e30i | − | 0.252324i | ||||||
\(687\) | 4.27851e30 | + | 1.51212e31i | 0.265931 | + | 0.939861i | ||||
\(688\) | 4.06379e30 | 0.248575 | ||||||||
\(689\) | 2.00685e31i | 1.20810i | ||||||||
\(690\) | 2.87418e29 | − | 8.13241e28i | 0.0170284 | − | 0.00481814i | ||||
\(691\) | 4.11565e30 | 0.239982 | 0.119991 | − | 0.992775i | \(-0.461713\pi\) | ||||
0.119991 | + | 0.992775i | \(0.461713\pi\) | |||||||
\(692\) | 1.98871e31i | 1.14131i | ||||||||
\(693\) | −6.71232e30 | − | 1.09118e31i | −0.379146 | − | 0.616356i | ||||
\(694\) | 2.36297e30 | 0.131372 | ||||||||
\(695\) | 4.24376e29i | 0.0232230i | ||||||||
\(696\) | 2.68068e30 | + | 9.47412e30i | 0.144392 | + | 0.510314i | ||||
\(697\) | −3.56615e31 | −1.89077 | ||||||||
\(698\) | 6.57588e30i | 0.343198i | ||||||||
\(699\) | 1.09016e31 | − | 3.08459e30i | 0.560071 | − | 0.158471i | ||||
\(700\) | 8.09204e30 | 0.409241 | ||||||||
\(701\) | − | 2.27239e31i | − | 1.13132i | −0.824640 | − | 0.565658i | \(-0.808622\pi\) | ||
0.824640 | − | 0.565658i | \(-0.191378\pi\) | |||||||
\(702\) | −3.65302e30 | + | 3.97209e30i | −0.179037 | + | 0.194675i | ||||
\(703\) | 4.83233e30 | 0.233157 | ||||||||
\(704\) | 1.57452e31i | 0.747910i | ||||||||
\(705\) | 4.59446e28 | + | 1.62379e29i | 0.00214859 | + | 0.00759362i | ||||
\(706\) | −2.98465e30 | −0.137417 | ||||||||
\(707\) | − | 3.37701e30i | − | 0.153080i | ||||||
\(708\) | −1.69461e31 | + | 4.79485e30i | −0.756316 | + | 0.213998i | ||||
\(709\) | −1.72067e31 | −0.756117 | −0.378058 | − | 0.925782i | \(-0.623408\pi\) | ||||
−0.378058 | + | 0.925782i | \(0.623408\pi\) | |||||||
\(710\) | − | 1.00329e29i | − | 0.00434093i | ||||||
\(711\) | 2.82754e31 | − | 1.73934e31i | 1.20460 | − | 0.741000i | ||||
\(712\) | 3.78138e30 | 0.158625 | ||||||||
\(713\) | 2.40403e31i | 0.993012i | ||||||||
\(714\) | 1.39191e30 | + | 4.91934e30i | 0.0566151 | + | 0.200091i | ||||
\(715\) | 1.78557e30 | 0.0715174 | ||||||||
\(716\) | − | 2.59934e31i | − | 1.02523i | ||||||
\(717\) | 2.63921e31 | − | 7.46757e30i | 1.02509 | − | 0.290047i | ||||
\(718\) | 1.13442e31 | 0.433917 | ||||||||
\(719\) | − | 1.67074e31i | − | 0.629350i | −0.949199 | − | 0.314675i | \(-0.898104\pi\) | ||
0.949199 | − | 0.314675i | \(-0.101896\pi\) | |||||||
\(720\) | −5.35366e29 | − | 8.70313e29i | −0.0198607 | − | 0.0322863i | ||||
\(721\) | 1.46298e30 | 0.0534502 | ||||||||
\(722\) | − | 8.33039e30i | − | 0.299748i | ||||||
\(723\) | −7.69621e29 | − | 2.72002e30i | −0.0272744 | − | 0.0963940i | ||||
\(724\) | 9.34909e29 | 0.0326321 | ||||||||
\(725\) | − | 2.60778e31i | − | 0.896505i | ||||||
\(726\) | 1.35685e31 | − | 3.83918e30i | 0.459441 | − | 0.129998i | ||||
\(727\) | −5.89636e31 | −1.96655 | −0.983276 | − | 0.182121i | \(-0.941704\pi\) | ||||
−0.983276 | + | 0.182121i | \(0.941704\pi\) | |||||||
\(728\) | − | 6.95869e30i | − | 0.228603i | ||||||
\(729\) | 2.58176e30 | + | 3.07951e31i | 0.0835435 | + | 0.996504i | ||||
\(730\) | −9.74663e28 | −0.00310673 | ||||||||
\(731\) | − | 1.62287e31i | − | 0.509557i | ||||||
\(732\) | −6.09615e30 | − | 2.15452e31i | −0.188553 | − | 0.666390i | ||||
\(733\) | 2.16750e31 | 0.660411 | 0.330206 | − | 0.943909i | \(-0.392882\pi\) | ||||
0.330206 | + | 0.943909i | \(0.392882\pi\) | |||||||
\(734\) | 8.74110e30i | 0.262367i | ||||||||
\(735\) | 1.35788e30 | − | 3.84207e29i | 0.0401513 | − | 0.0113607i | ||||
\(736\) | −3.03440e31 | −0.883929 | ||||||||
\(737\) | 8.37995e31i | 2.40491i | ||||||||
\(738\) | −1.19376e31 | + | 7.34329e30i | −0.337517 | + | 0.207621i | ||||
\(739\) | 2.38405e31 | 0.664090 | 0.332045 | − | 0.943263i | \(-0.392261\pi\) | ||||
0.332045 | + | 0.943263i | \(0.392261\pi\) | |||||||
\(740\) | 2.23636e30i | 0.0613753i | ||||||||
\(741\) | −1.55135e30 | − | 5.48282e30i | −0.0419478 | − | 0.148253i | ||||
\(742\) | 7.47203e30 | 0.199065 | ||||||||
\(743\) | − | 3.19425e30i | − | 0.0838479i | −0.999121 | − | 0.0419239i | \(-0.986651\pi\) | ||
0.999121 | − | 0.0419239i | \(-0.0133487\pi\) | |||||||
\(744\) | −2.00552e31 | + | 5.67456e30i | −0.518710 | + | 0.146767i | ||||
\(745\) | −3.31197e30 | −0.0844050 | ||||||||
\(746\) | − | 9.81002e30i | − | 0.246345i | ||||||
\(747\) | 2.22348e31 | + | 3.61458e31i | 0.550182 | + | 0.894398i | ||||
\(748\) | 8.73750e31 | 2.13044 | ||||||||
\(749\) | 1.19294e31i | 0.286629i | ||||||||
\(750\) | −3.73998e29 | − | 1.32180e30i | −0.00885515 | − | 0.0312961i | ||||
\(751\) | −3.25961e31 | −0.760548 | −0.380274 | − | 0.924874i | \(-0.624170\pi\) | ||||
−0.380274 | + | 0.924874i | \(0.624170\pi\) | |||||||
\(752\) | − | 4.70963e30i | − | 0.108291i | ||||||
\(753\) | −7.98477e31 | + | 2.25927e31i | −1.80933 | + | 0.511945i | ||||
\(754\) | −1.06473e31 | −0.237770 | ||||||||
\(755\) | − | 2.62548e30i | − | 0.0577820i | ||||||
\(756\) | −1.39261e31 | − | 1.28074e31i | −0.302057 | − | 0.277793i | ||||
\(757\) | 4.87520e31 | 1.04217 | 0.521084 | − | 0.853506i | \(-0.325528\pi\) | ||||
0.521084 | + | 0.853506i | \(0.325528\pi\) | |||||||
\(758\) | − | 9.13665e30i | − | 0.192498i | ||||||
\(759\) | −2.27122e31 | − | 8.02702e31i | −0.471629 | − | 1.66684i | ||||
\(760\) | −2.73443e29 | −0.00559650 | ||||||||
\(761\) | 4.94746e31i | 0.998048i | 0.866588 | + | 0.499024i | \(0.166308\pi\) | ||||
−0.866588 | + | 0.499024i | \(0.833692\pi\) | |||||||
\(762\) | 6.56488e30 | − | 1.85751e30i | 0.130534 | − | 0.0369341i | ||||
\(763\) | −1.85688e31 | −0.363927 | ||||||||
\(764\) | − | 4.53164e31i | − | 0.875444i | ||||||
\(765\) | −3.47559e30 | + | 2.13798e30i | −0.0661840 | + | 0.0407126i | ||||
\(766\) | 1.05382e31 | 0.197810 | ||||||||
\(767\) | − | 4.01117e31i | − | 0.742201i | ||||||
\(768\) | 2.56908e30 | + | 9.07970e30i | 0.0468601 | + | 0.165614i | ||||
\(769\) | 2.18341e31 | 0.392596 | 0.196298 | − | 0.980544i | \(-0.437108\pi\) | ||||
0.196298 | + | 0.980544i | \(0.437108\pi\) | |||||||
\(770\) | − | 6.64816e29i | − | 0.0117843i | ||||||
\(771\) | 6.88296e31 | − | 1.94752e31i | 1.20276 | − | 0.340316i | ||||
\(772\) | −2.44117e31 | −0.420540 | ||||||||
\(773\) | − | 5.73569e31i | − | 0.974117i | −0.873369 | − | 0.487059i | \(-0.838070\pi\) | ||
0.873369 | − | 0.487059i | \(-0.161930\pi\) | |||||||
\(774\) | −3.34176e30 | − | 5.43250e30i | −0.0559531 | − | 0.0909597i | ||||
\(775\) | 5.52025e31 | 0.911255 | ||||||||
\(776\) | 2.77056e31i | 0.450909i | ||||||||
\(777\) | 9.94966e30 | + | 3.51644e31i | 0.159653 | + | 0.564250i | ||||
\(778\) | −2.45914e30 | −0.0389052 | ||||||||
\(779\) | − | 1.47986e31i | − | 0.230838i | ||||||
\(780\) | 2.53741e30 | − | 7.17952e29i | 0.0390256 | − | 0.0110422i | ||||
\(781\) | −2.80198e31 | −0.424917 | ||||||||
\(782\) | 3.32908e31i | 0.497795i | ||||||||
\(783\) | −4.12738e31 | + | 4.48789e31i | −0.608548 | + | 0.661702i | ||||
\(784\) | −3.93838e31 | −0.572586 | ||||||||
\(785\) | − | 2.96784e30i | − | 0.0425476i | ||||||
\(786\) | 1.37524e29 | + | 4.86042e29i | 0.00194416 | + | 0.00687110i | ||||
\(787\) | −5.02293e31 | −0.700221 | −0.350111 | − | 0.936708i | \(-0.613856\pi\) | ||||
−0.350111 | + | 0.936708i | \(0.613856\pi\) | |||||||
\(788\) | 5.23231e31i | 0.719291i | ||||||||
\(789\) | −1.84963e31 | + | 5.23349e30i | −0.250749 | + | 0.0709487i | ||||
\(790\) | 1.72271e30 | 0.0230311 | ||||||||
\(791\) | 3.77663e31i | 0.497924i | ||||||||
\(792\) | 6.16030e31 | − | 3.78946e31i | 0.800986 | − | 0.492720i | ||||
\(793\) | 5.09979e31 | 0.653954 | ||||||||
\(794\) | 8.91785e30i | 0.112781i | ||||||||
\(795\) | 1.62370e30 | + | 5.73852e30i | 0.0202520 | + | 0.0715751i | ||||
\(796\) | −8.89361e31 | −1.09404 | ||||||||
\(797\) | − | 6.01654e31i | − | 0.729971i | −0.931013 | − | 0.364985i | \(-0.881074\pi\) | ||
0.931013 | − | 0.364985i | \(-0.118926\pi\) | |||||||
\(798\) | −2.04140e30 | + | 5.77608e29i | −0.0244284 | + | 0.00691196i | ||||
\(799\) | −1.88079e31 | −0.221986 | ||||||||
\(800\) | 6.96775e31i | 0.811153i | ||||||||
\(801\) | 1.22690e31 | + | 1.99450e31i | 0.140881 | + | 0.229021i | ||||
\(802\) | 8.41720e30 | 0.0953344 | ||||||||
\(803\) | 2.72204e31i | 0.304105i | ||||||||
\(804\) | 3.36945e31 | + | 1.19084e32i | 0.371315 | + | 1.31231i | ||||
\(805\) | −2.38520e30 | −0.0259281 | ||||||||
\(806\) | − | 2.25387e31i | − | 0.241682i | ||||||
\(807\) | 9.92848e31 | − | 2.80923e31i | 1.05020 | − | 0.297152i | ||||
\(808\) | 1.90650e31 | 0.198936 | ||||||||
\(809\) | − | 7.06646e31i | − | 0.727391i | −0.931518 | − | 0.363696i | \(-0.881515\pi\) | ||
0.931518 | − | 0.363696i | \(-0.118485\pi\) | |||||||
\(810\) | −7.23195e29 | + | 1.43136e30i | −0.00734379 | + | 0.0145350i | ||||
\(811\) | −9.20570e31 | −0.922205 | −0.461102 | − | 0.887347i | \(-0.652546\pi\) | ||||
−0.461102 | + | 0.887347i | \(0.652546\pi\) | |||||||
\(812\) | − | 3.73294e31i | − | 0.368923i | ||||||
\(813\) | −5.44526e31 | − | 1.92448e32i | −0.530912 | − | 1.87636i | ||||
\(814\) | −6.63279e31 | −0.638011 | ||||||||
\(815\) | − | 2.40257e30i | − | 0.0228004i | ||||||
\(816\) | 1.09579e32 | − | 3.10050e31i | 1.02597 | − | 0.290295i | ||||
\(817\) | 6.73449e30 | 0.0622102 | ||||||||
\(818\) | − | 3.97085e31i | − | 0.361907i | ||||||
\(819\) | 3.67038e31 | − | 2.25780e31i | 0.330056 | − | 0.203031i | ||||
\(820\) | 6.84867e30 | 0.0607651 | ||||||||
\(821\) | 5.43653e30i | 0.0475934i | 0.999717 | + | 0.0237967i | \(0.00757544\pi\) | ||||
−0.999717 | + | 0.0237967i | \(0.992425\pi\) | |||||||
\(822\) | 6.64379e30 | + | 2.34807e31i | 0.0573886 | + | 0.202824i | ||||
\(823\) | 1.44520e32 | 1.23177 | 0.615885 | − | 0.787836i | \(-0.288799\pi\) | ||||
0.615885 | + | 0.787836i | \(0.288799\pi\) | |||||||
\(824\) | 8.25927e30i | 0.0694612i | ||||||||
\(825\) | −1.84321e32 | + | 5.21530e31i | −1.52961 | + | 0.432799i | ||||
\(826\) | −1.49346e31 | −0.122296 | ||||||||
\(827\) | − | 8.76228e31i | − | 0.708038i | −0.935238 | − | 0.354019i | \(-0.884815\pi\) | ||
0.935238 | − | 0.354019i | \(-0.115185\pi\) | |||||||
\(828\) | −6.45509e31 | − | 1.04937e32i | −0.514717 | − | 0.836745i | ||||
\(829\) | 1.45217e32 | 1.14266 | 0.571330 | − | 0.820720i | \(-0.306427\pi\) | ||||
0.571330 | + | 0.820720i | \(0.306427\pi\) | |||||||
\(830\) | 2.20223e30i | 0.0171003i | ||||||||
\(831\) | 6.12586e31 | + | 2.16502e32i | 0.469414 | + | 1.65902i | ||||
\(832\) | −5.29617e31 | −0.400503 | ||||||||
\(833\) | 1.57279e32i | 1.17375i | ||||||||
\(834\) | −1.78862e31 | + | 5.06084e30i | −0.131732 | + | 0.0372732i | ||||
\(835\) | 4.38816e30 | 0.0318957 | ||||||||
\(836\) | 3.62583e31i | 0.260099i | ||||||||
\(837\) | −9.50013e31 | − | 8.73700e31i | −0.672588 | − | 0.618560i | ||||
\(838\) | −5.62264e30 | −0.0392877 | ||||||||
\(839\) | 1.19979e32i | 0.827413i | 0.910410 | + | 0.413706i | \(0.135766\pi\) | ||||
−0.910410 | + | 0.413706i | \(0.864234\pi\) | |||||||
\(840\) | −5.63013e29 | − | 1.98982e30i | −0.00383218 | − | 0.0135438i | ||||
\(841\) | 2.85528e31 | 0.191819 | ||||||||
\(842\) | − | 6.09011e31i | − | 0.403824i | ||||||
\(843\) | −1.67364e32 | + | 4.73553e31i | −1.09537 | + | 0.309931i | ||||
\(844\) | 8.06080e31 | 0.520729 | ||||||||
\(845\) | − | 2.23658e30i | − | 0.0142614i | ||||||
\(846\) | −6.29587e30 | + | 3.87285e30i | −0.0396261 | + | 0.0243757i | ||||
\(847\) | −1.12602e32 | −0.699563 | ||||||||
\(848\) | − | 1.66440e32i | − | 1.02071i | ||||||
\(849\) | 2.34556e31 | + | 8.28974e31i | 0.141991 | + | 0.501829i | ||||
\(850\) | 7.64441e31 | 0.456810 | ||||||||
\(851\) | 2.37969e32i | 1.40377i | ||||||||
\(852\) | −3.98178e31 | + | 1.12663e31i | −0.231869 | + | 0.0656066i | ||||
\(853\) | 2.32758e32 | 1.33803 | 0.669013 | − | 0.743250i | \(-0.266717\pi\) | ||||
0.669013 | + | 0.743250i | \(0.266717\pi\) | |||||||
\(854\) | − | 1.89878e31i | − | 0.107755i | ||||||
\(855\) | −8.87207e29 | − | 1.44228e30i | −0.00497047 | − | 0.00808020i | ||||
\(856\) | −6.73480e31 | −0.372489 | ||||||||
\(857\) | − | 1.63518e32i | − | 0.892844i | −0.894823 | − | 0.446422i | \(-0.852698\pi\) | ||
0.894823 | − | 0.446422i | \(-0.147302\pi\) | |||||||
\(858\) | 2.12936e31 | + | 7.52565e31i | 0.114786 | + | 0.405680i | ||||
\(859\) | −1.18107e32 | −0.628565 | −0.314283 | − | 0.949329i | \(-0.601764\pi\) | ||||
−0.314283 | + | 0.949329i | \(0.601764\pi\) | |||||||
\(860\) | 3.11667e30i | 0.0163760i | ||||||||
\(861\) | 1.07688e32 | − | 3.04700e31i | 0.558640 | − | 0.158066i | ||||
\(862\) | 5.14514e31 | 0.263522 | ||||||||
\(863\) | 1.18236e32i | 0.597904i | 0.954268 | + | 0.298952i | \(0.0966371\pi\) | ||||
−0.954268 | + | 0.298952i | \(0.903363\pi\) | |||||||
\(864\) | 1.10280e32 | − | 1.19912e32i | 0.550611 | − | 0.598704i | ||||
\(865\) | −1.34604e31 | −0.0663563 | ||||||||
\(866\) | 5.70632e31i | 0.277753i | ||||||||
\(867\) | −6.71694e31 | − | 2.37392e32i | −0.322821 | − | 1.14092i | ||||
\(868\) | 7.90204e31 | 0.374992 | ||||||||
\(869\) | − | 4.81120e32i | − | 2.25443i | ||||||
\(870\) | −3.04458e30 | + | 8.61454e29i | −0.0140869 | + | 0.00398584i | ||||
\(871\) | −2.81874e32 | −1.28782 | ||||||||
\(872\) | − | 1.04831e32i | − | 0.472942i | ||||||
\(873\) | −1.46134e32 | + | 8.98932e31i | −0.651020 | + | 0.400470i | ||||
\(874\) | −1.38148e31 | −0.0607742 | ||||||||
\(875\) | 1.09692e31i | 0.0476527i | ||||||||
\(876\) | 1.09449e31 | + | 3.86819e31i | 0.0469535 | + | 0.165944i | ||||
\(877\) | 2.05585e32 | 0.870955 | 0.435477 | − | 0.900200i | \(-0.356580\pi\) | ||||
0.435477 | + | 0.900200i | \(0.356580\pi\) | |||||||
\(878\) | − | 5.43671e31i | − | 0.227456i | ||||||
\(879\) | 2.84333e32 | − | 8.04511e31i | 1.17476 | − | 0.332395i | ||||
\(880\) | −1.48088e31 | −0.0604243 | ||||||||
\(881\) | 3.13678e32i | 1.26401i | 0.774966 | + | 0.632003i | \(0.217767\pi\) | ||||
−0.774966 | + | 0.632003i | \(0.782233\pi\) | |||||||
\(882\) | 3.23863e31 | + | 5.26485e31i | 0.128886 | + | 0.209523i | ||||
\(883\) | −1.81247e32 | −0.712365 | −0.356182 | − | 0.934416i | \(-0.615922\pi\) | ||||
−0.356182 | + | 0.934416i | \(0.615922\pi\) | |||||||
\(884\) | 2.93901e32i | 1.14084i | ||||||||
\(885\) | −3.24535e30 | − | 1.14698e31i | −0.0124419 | − | 0.0439724i | ||||
\(886\) | −5.09037e31 | −0.192743 | ||||||||
\(887\) | 1.06780e32i | 0.399327i | 0.979865 | + | 0.199664i | \(0.0639849\pi\) | ||||
−0.979865 | + | 0.199664i | \(0.936015\pi\) | |||||||
\(888\) | −1.98522e32 | + | 5.61711e31i | −0.733272 | + | 0.207477i | ||||
\(889\) | −5.44802e31 | −0.198755 | ||||||||
\(890\) | 1.21517e30i | 0.00437873i | ||||||||
\(891\) | 3.99752e32 | + | 2.01974e32i | 1.42277 | + | 0.718855i | ||||
\(892\) | 5.51048e31 | 0.193721 | ||||||||
\(893\) | − | 7.80477e30i | − | 0.0271016i | ||||||
\(894\) | −3.94965e31 | − | 1.39590e32i | −0.135471 | − | 0.478785i | ||||
\(895\) | 1.75934e31 | 0.0596070 | ||||||||
\(896\) | 1.30052e32i | 0.435240i | ||||||||
\(897\) | 2.70003e32 | − | 7.63965e31i | 0.892589 | − | 0.252555i | ||||
\(898\) | −4.19974e31 | −0.137146 | ||||||||
\(899\) | − | 2.54655e32i | − | 0.821477i | ||||||
\(900\) | −2.40961e32 | + | 1.48225e32i | −0.767854 | + | 0.472339i | ||||
\(901\) | −6.64677e32 | −2.09237 | ||||||||
\(902\) | 2.03124e32i | 0.631667i | ||||||||
\(903\) | 1.38662e31 | + | 4.90062e31i | 0.0425982 | + | 0.150552i | ||||
\(904\) | −2.13211e32 | −0.647077 | ||||||||
\(905\) | 6.32785e29i | 0.00189724i | ||||||||
\(906\) | 1.10656e32 | − | 3.13098e31i | 0.327767 | − | 0.0927408i | ||||
\(907\) | 2.64776e31 | 0.0774815 | 0.0387407 | − | 0.999249i | \(-0.487665\pi\) | ||||
0.0387407 | + | 0.999249i | \(0.487665\pi\) | |||||||
\(908\) | − | 1.04932e32i | − | 0.303363i | ||||||
\(909\) | 6.18580e31 | + | 1.00559e32i | 0.176682 | + | 0.287222i | ||||
\(910\) | 2.23622e30 | 0.00631044 | ||||||||
\(911\) | − | 4.05859e32i | − | 1.13155i | −0.824560 | − | 0.565774i | \(-0.808577\pi\) | ||
0.824560 | − | 0.565774i | \(-0.191423\pi\) | |||||||
\(912\) | 1.28663e31 | + | 4.54723e31i | 0.0354413 | + | 0.125257i | ||||
\(913\) | 6.15039e32 | 1.67388 | ||||||||
\(914\) | 7.46640e30i | 0.0200772i | ||||||||
\(915\) | 1.45827e31 | − | 4.12613e30i | 0.0387441 | − | 0.0109625i | ||||
\(916\) | 3.36360e32 | 0.882988 | ||||||||
\(917\) | − | 4.03353e30i | − | 0.0104622i | ||||||
\(918\) | −1.31557e32 | − | 1.20989e32i | −0.337167 | − | 0.310083i | ||||
\(919\) | −2.56221e32 | −0.648851 | −0.324425 | − | 0.945911i | \(-0.605171\pi\) | ||||
−0.324425 | + | 0.945911i | \(0.605171\pi\) | |||||||
\(920\) | − | 1.34657e31i | − | 0.0336949i | ||||||
\(921\) | −1.46127e32 | − | 5.16445e32i | −0.361304 | − | 1.27693i | ||||
\(922\) | 2.42321e32 | 0.592040 | ||||||||
\(923\) | − | 9.42495e31i | − | 0.227541i | ||||||
\(924\) | −2.63848e32 | + | 7.46552e31i | −0.629452 | + | 0.178102i | ||||
\(925\) | 5.46437e32 | 1.28819 | ||||||||
\(926\) | − | 2.47752e31i | − | 0.0577160i | ||||||
\(927\) | −4.35637e31 | + | 2.67979e31i | −0.100288 | + | 0.0616912i | ||||
\(928\) | 3.21430e32 | 0.731237 | ||||||||
\(929\) | − | 7.36318e31i | − | 0.165536i | −0.996569 | − | 0.0827680i | \(-0.973624\pi\) | ||
0.996569 | − | 0.0827680i | \(-0.0263760\pi\) | |||||||
\(930\) | −1.82356e30 | − | 6.44487e30i | −0.00405142 | − | 0.0143186i | ||||
\(931\) | −6.52666e31 | −0.143300 | ||||||||
\(932\) | − | 2.42499e32i | − | 0.526180i | ||||||
\(933\) | −7.35072e32 | + | 2.07987e32i | −1.57628 | + | 0.446003i | ||||
\(934\) | 3.14993e31 | 0.0667553 | ||||||||
\(935\) | 5.91390e31i | 0.123864i | ||||||||
\(936\) | 1.27465e32 | + | 2.07212e32i | 0.263850 | + | 0.428925i | ||||
\(937\) | −9.63908e32 | −1.97197 | −0.985984 | − | 0.166838i | \(-0.946644\pi\) | ||||
−0.985984 | + | 0.166838i | \(0.946644\pi\) | |||||||
\(938\) | 1.04949e32i | 0.212201i | ||||||||
\(939\) | 6.48302e31 | + | 2.29125e32i | 0.129556 | + | 0.457879i | ||||
\(940\) | 3.61199e30 | 0.00713411 | ||||||||
\(941\) | 3.17400e32i | 0.619614i | 0.950800 | + | 0.309807i | \(0.100264\pi\) | ||||
−0.950800 | + | 0.309807i | \(0.899736\pi\) | |||||||
\(942\) | 1.25086e32 | − | 3.53926e31i | 0.241350 | − | 0.0682894i | ||||
\(943\) | 7.28760e32 | 1.38981 | ||||||||
\(944\) | 3.32670e32i | 0.627078i | ||||||||
\(945\) | 8.66859e30 | − | 9.42574e30i | 0.0161510 | − | 0.0175617i | ||||
\(946\) | −9.24368e31 | −0.170232 | ||||||||
\(947\) | 5.32754e32i | 0.969788i | 0.874573 | + | 0.484894i | \(0.161142\pi\) | ||||
−0.874573 | + | 0.484894i | \(0.838858\pi\) | |||||||
\(948\) | −1.93451e32 | − | 6.83701e32i | −0.348080 | − | 1.23020i | ||||
\(949\) | −9.15606e31 | −0.162847 | ||||||||
\(950\) | 3.17223e31i | 0.0557705i | ||||||||
\(951\) | 2.72702e32 | − | 7.71603e31i | 0.473917 | − | 0.134094i | ||||
\(952\) | 2.30475e32 | 0.395929 | ||||||||
\(953\) | 6.69580e32i | 1.13705i | 0.822665 | + | 0.568526i | \(0.192486\pi\) | ||||
−0.822665 | + | 0.568526i | \(0.807514\pi\) | |||||||
\(954\) | −2.22498e32 | + | 1.36868e32i | −0.373503 | + | 0.229758i | ||||
\(955\) | 3.06720e31 | 0.0508985 | ||||||||
\(956\) | − | 5.87072e32i | − | 0.963062i | ||||||
\(957\) | 2.40587e32 | + | 8.50291e32i | 0.390159 | + | 1.37891i | ||||
\(958\) | −2.50624e32 | −0.401793 | ||||||||
\(959\) | − | 1.94860e32i | − | 0.308828i | ||||||
\(960\) | −1.51442e31 | + | 4.28502e30i | −0.0237282 | + | 0.00671381i | ||||
\(961\) | −1.06528e32 | −0.165008 | ||||||||
\(962\) | − | 2.23105e32i | − | 0.341652i | ||||||
\(963\) | −2.18516e32 | − | 3.55229e32i | −0.330822 | − | 0.537798i | ||||
\(964\) | −6.05047e31 | −0.0905610 | ||||||||
\(965\) | − | 1.65228e31i | − | 0.0244503i | ||||||
\(966\) | −2.84444e31 | − | 1.00529e32i | −0.0416149 | − | 0.147077i | ||||
\(967\) | −6.62071e31 | −0.0957664 | −0.0478832 | − | 0.998853i | \(-0.515248\pi\) | ||||
−0.0478832 | + | 0.998853i | \(0.515248\pi\) | |||||||
\(968\) | − | 6.35696e32i | − | 0.909118i | ||||||
\(969\) | 1.81593e32 | − | 5.13813e31i | 0.256767 | − | 0.0726514i | ||||
\(970\) | −8.90340e30 | −0.0124471 | ||||||||
\(971\) | − | 8.07920e32i | − | 1.11675i | −0.829588 | − | 0.558376i | \(-0.811425\pi\) | ||
0.829588 | − | 0.558376i | \(-0.188575\pi\) | |||||||
\(972\) | 6.49282e32 | + | 1.26283e32i | 0.887370 | + | 0.172591i | ||||
\(973\) | 1.48433e32 | 0.200580 | ||||||||
\(974\) | 1.81353e32i | 0.242312i | ||||||||
\(975\) | −1.75426e32 | − | 6.19994e32i | −0.231762 | − | 0.819100i | ||||
\(976\) | −4.22956e32 | −0.552518 | ||||||||
\(977\) | 2.37096e32i | 0.306255i | 0.988206 | + | 0.153128i | \(0.0489345\pi\) | ||||
−0.988206 | + | 0.153128i | \(0.951065\pi\) | |||||||
\(978\) | 1.01261e32 | − | 2.86516e31i | 0.129335 | − | 0.0365950i | ||||
\(979\) | 3.39374e32 | 0.428617 | ||||||||
\(980\) | − | 3.02049e31i | − | 0.0377216i | ||||||
\(981\) | 5.52933e32 | − | 3.40132e32i | 0.682831 | − | 0.420038i | ||||
\(982\) | −3.31011e32 | −0.404218 | ||||||||
\(983\) | − | 4.35578e31i | − | 0.0525990i | −0.999654 | − | 0.0262995i | \(-0.991628\pi\) | ||
0.999654 | − | 0.0262995i | \(-0.00837235\pi\) | |||||||
\(984\) | 1.72019e32 | + | 6.07955e32i | 0.205414 | + | 0.725982i | ||||
\(985\) | −3.54144e31 | −0.0418197 | ||||||||
\(986\) | − | 3.52645e32i | − | 0.411805i | ||||||
\(987\) | 5.67946e31 | − | 1.60699e31i | 0.0655871 | − | 0.0185577i | ||||
\(988\) | −1.21961e32 | −0.139282 | ||||||||
\(989\) | 3.31641e32i | 0.374550i | ||||||||
\(990\) | 1.21777e31 | + | 1.97966e31i | 0.0136012 | + | 0.0221107i | ||||
\(991\) | −1.04870e33 | −1.15836 | −0.579178 | − | 0.815201i | \(-0.696626\pi\) | ||||
−0.579178 | + | 0.815201i | \(0.696626\pi\) | |||||||
\(992\) | 6.80415e32i | 0.743268i | ||||||||
\(993\) | 3.68485e32 | + | 1.30231e33i | 0.398087 | + | 1.40693i | ||||
\(994\) | −3.50915e31 | −0.0374932 | ||||||||
\(995\) | − | 6.01956e31i | − | 0.0636079i | ||||||
\(996\) | 8.74007e32 | − | 2.47298e32i | 0.913402 | − | 0.258445i | ||||
\(997\) | −1.34722e33 | −1.39249 | −0.696243 | − | 0.717807i | \(-0.745146\pi\) | ||||
−0.696243 | + | 0.717807i | \(0.745146\pi\) | |||||||
\(998\) | 2.01580e32i | 0.206069i | ||||||||
\(999\) | −9.40396e32 | − | 8.64855e32i | −0.950802 | − | 0.874426i |
(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 | 3.23.b.a.2.4 | yes | 6 | |
3.2 | odd | 2 | inner | 3.23.b.a.2.3 | ✓ | 6 | |
4.3 | odd | 2 | 48.23.e.b.17.3 | 6 | |||
12.11 | even | 2 | 48.23.e.b.17.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.23.b.a.2.3 | ✓ | 6 | 3.2 | odd | 2 | inner | |
3.23.b.a.2.4 | yes | 6 | 1.1 | even | 1 | trivial | |
48.23.e.b.17.3 | 6 | 4.3 | odd | 2 | |||
48.23.e.b.17.4 | 6 | 12.11 | even | 2 |