Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,16,Mod(5,8)]
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([0, 1]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(11.4154804080\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 6354 x^{12} + 136110 x^{11} + 41390651 x^{10} - 1368564777 x^{9} - 361745089708 x^{8} + 52039630950804 x^{7} + \cdots + 24\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{91}\cdot 3^{6}\cdot 5^{4}\cdot 31^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.10 | ||
Root | \(-53.8860 - 74.8506i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.16.b.a.5.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 101.772 | + | 149.701i | 0.562216 | + | 0.826991i | ||||
\(3\) | 3583.46i | 0.946003i | 0.881062 | + | 0.473002i | \(0.156830\pi\) | ||||
−0.881062 | + | 0.473002i | \(0.843170\pi\) | |||||||
\(4\) | −12052.9 | + | 30470.8i | −0.367827 | + | 0.929894i | ||||
\(5\) | 82632.2i | 0.473014i | 0.971630 | + | 0.236507i | \(0.0760027\pi\) | ||||
−0.971630 | + | 0.236507i | \(0.923997\pi\) | |||||||
\(6\) | −536448. | + | 364695.i | −0.782336 | + | 0.531858i | ||||
\(7\) | −153730. | −0.0705543 | −0.0352772 | − | 0.999378i | \(-0.511231\pi\) | ||||
−0.0352772 | + | 0.999378i | \(0.511231\pi\) | |||||||
\(8\) | −5.78817e6 | + | 1.29673e6i | −0.975812 | + | 0.218612i | ||||
\(9\) | 1.50775e6 | 0.105078 | ||||||||
\(10\) | −1.23701e7 | + | 8.40964e6i | −0.391178 | + | 0.265936i | ||||
\(11\) | − | 2.04333e7i | − | 0.316150i | −0.987427 | − | 0.158075i | \(-0.949471\pi\) | ||
0.987427 | − | 0.158075i | \(-0.0505287\pi\) | |||||||
\(12\) | −1.09191e8 | − | 4.31912e7i | −0.879683 | − | 0.347965i | ||||
\(13\) | − | 7.09837e7i | − | 0.313750i | −0.987618 | − | 0.156875i | \(-0.949858\pi\) | ||
0.987618 | − | 0.156875i | \(-0.0501420\pi\) | |||||||
\(14\) | −1.56454e7 | − | 2.30136e7i | −0.0396668 | − | 0.0583478i | ||||
\(15\) | −2.96109e8 | −0.447473 | ||||||||
\(16\) | −7.83195e8 | − | 7.34525e8i | −0.729407 | − | 0.684080i | ||||
\(17\) | −2.71566e9 | −1.60513 | −0.802563 | − | 0.596567i | \(-0.796531\pi\) | ||||
−0.802563 | + | 0.596567i | \(0.796531\pi\) | |||||||
\(18\) | 1.53447e8 | + | 2.25712e8i | 0.0590763 | + | 0.0868982i | ||||
\(19\) | 4.09857e9i | 1.05191i | 0.850511 | + | 0.525957i | \(0.176293\pi\) | ||||
−0.850511 | + | 0.525957i | \(0.823707\pi\) | |||||||
\(20\) | −2.51787e9 | − | 9.95961e8i | −0.439853 | − | 0.173987i | ||||
\(21\) | − | 5.50885e8i | − | 0.0667446i | ||||||
\(22\) | 3.05889e9 | − | 2.07953e9i | 0.261453 | − | 0.177744i | ||||
\(23\) | 2.81564e10 | 1.72432 | 0.862160 | − | 0.506636i | \(-0.169111\pi\) | ||||
0.862160 | + | 0.506636i | \(0.169111\pi\) | |||||||
\(24\) | −4.64677e9 | − | 2.07416e10i | −0.206808 | − | 0.923121i | ||||
\(25\) | 2.36895e10 | 0.776257 | ||||||||
\(26\) | 1.06264e10 | − | 7.22415e9i | 0.259468 | − | 0.176395i | ||||
\(27\) | 5.68216e10i | 1.04541i | ||||||||
\(28\) | 1.85290e9 | − | 4.68428e9i | 0.0259518 | − | 0.0656081i | ||||
\(29\) | 1.54113e11i | 1.65903i | 0.558484 | + | 0.829515i | \(0.311383\pi\) | ||||
−0.558484 | + | 0.829515i | \(0.688617\pi\) | |||||||
\(30\) | −3.01356e10 | − | 4.43279e10i | −0.251577 | − | 0.370056i | ||||
\(31\) | −7.02050e10 | −0.458306 | −0.229153 | − | 0.973390i | \(-0.573596\pi\) | ||||
−0.229153 | + | 0.973390i | \(0.573596\pi\) | |||||||
\(32\) | 3.02521e10 | − | 1.91999e11i | 0.155643 | − | 0.987813i | ||||
\(33\) | 7.32217e10 | 0.299079 | ||||||||
\(34\) | −2.76378e11 | − | 4.06538e11i | −0.902427 | − | 1.32742i | ||||
\(35\) | − | 1.27031e10i | − | 0.0333732i | ||||||
\(36\) | −1.81728e10 | + | 4.59423e10i | −0.0386504 | + | 0.0977111i | ||||
\(37\) | 4.56880e11i | 0.791205i | 0.918422 | + | 0.395603i | \(0.129464\pi\) | ||||
−0.918422 | + | 0.395603i | \(0.870536\pi\) | |||||||
\(38\) | −6.13561e11 | + | 4.17119e11i | −0.869923 | + | 0.591403i | ||||
\(39\) | 2.54367e11 | 0.296808 | ||||||||
\(40\) | −1.07152e11 | − | 4.78289e11i | −0.103407 | − | 0.461573i | ||||
\(41\) | −4.22953e11 | −0.339166 | −0.169583 | − | 0.985516i | \(-0.554242\pi\) | ||||
−0.169583 | + | 0.985516i | \(0.554242\pi\) | |||||||
\(42\) | 8.24682e10 | − | 5.60646e10i | 0.0551972 | − | 0.0375249i | ||||
\(43\) | − | 9.06774e11i | − | 0.508728i | −0.967109 | − | 0.254364i | \(-0.918134\pi\) | ||
0.967109 | − | 0.254364i | \(-0.0818661\pi\) | |||||||
\(44\) | 6.22618e11 | + | 2.46281e11i | 0.293986 | + | 0.116288i | ||||
\(45\) | 1.24589e11i | 0.0497032i | ||||||||
\(46\) | 2.86553e12 | + | 4.21505e12i | 0.969440 | + | 1.42600i | ||||
\(47\) | 3.38491e12 | 0.974571 | 0.487286 | − | 0.873243i | \(-0.337987\pi\) | ||||
0.487286 | + | 0.873243i | \(0.337987\pi\) | |||||||
\(48\) | 2.63214e12 | − | 2.80654e12i | 0.647142 | − | 0.690022i | ||||
\(49\) | −4.72393e12 | −0.995022 | ||||||||
\(50\) | 2.41093e12 | + | 3.54635e12i | 0.436424 | + | 0.641958i | ||||
\(51\) | − | 9.73146e12i | − | 1.51845i | ||||||
\(52\) | 2.16293e12 | + | 8.55563e11i | 0.291754 | + | 0.115406i | ||||
\(53\) | − | 5.59117e11i | − | 0.0653783i | −0.999466 | − | 0.0326892i | \(-0.989593\pi\) | ||
0.999466 | − | 0.0326892i | \(-0.0104071\pi\) | |||||||
\(54\) | −8.50627e12 | + | 5.78285e12i | −0.864542 | + | 0.587745i | ||||
\(55\) | 1.68845e12 | 0.149543 | ||||||||
\(56\) | 8.89815e11 | − | 1.99346e11i | 0.0688477 | − | 0.0154240i | ||||
\(57\) | −1.46870e13 | −0.995114 | ||||||||
\(58\) | −2.30709e13 | + | 1.56844e13i | −1.37200 | + | 0.932733i | ||||
\(59\) | − | 2.62540e13i | − | 1.37343i | −0.726929 | − | 0.686713i | \(-0.759053\pi\) | ||
0.726929 | − | 0.686713i | \(-0.240947\pi\) | |||||||
\(60\) | 3.56898e12 | − | 9.02267e12i | 0.164593 | − | 0.416103i | ||||
\(61\) | 3.59071e13i | 1.46287i | 0.681910 | + | 0.731436i | \(0.261150\pi\) | ||||
−0.681910 | + | 0.731436i | \(0.738850\pi\) | |||||||
\(62\) | −7.14490e12 | − | 1.05098e13i | −0.257667 | − | 0.379014i | ||||
\(63\) | −2.31786e11 | −0.00741368 | ||||||||
\(64\) | 3.18214e13 | − | 1.50114e13i | 0.904417 | − | 0.426649i | ||||
\(65\) | 5.86554e12 | 0.148408 | ||||||||
\(66\) | 7.45192e12 | + | 1.09614e13i | 0.168147 | + | 0.247335i | ||||
\(67\) | − | 1.80671e13i | − | 0.364190i | −0.983281 | − | 0.182095i | \(-0.941712\pi\) | ||
0.983281 | − | 0.182095i | \(-0.0582879\pi\) | |||||||
\(68\) | 3.27317e13 | − | 8.27484e13i | 0.590408 | − | 1.49260i | ||||
\(69\) | 1.00897e14i | 1.63121i | ||||||||
\(70\) | 1.90166e12 | − | 1.29281e12i | 0.0275993 | − | 0.0187629i | ||||
\(71\) | 1.14816e14 | 1.49818 | 0.749091 | − | 0.662467i | \(-0.230490\pi\) | ||||
0.749091 | + | 0.662467i | \(0.230490\pi\) | |||||||
\(72\) | −8.72710e12 | + | 1.95514e12i | −0.102536 | + | 0.0229713i | ||||
\(73\) | −5.99884e12 | −0.0635545 | −0.0317772 | − | 0.999495i | \(-0.510117\pi\) | ||||
−0.0317772 | + | 0.999495i | \(0.510117\pi\) | |||||||
\(74\) | −6.83955e13 | + | 4.64975e13i | −0.654319 | + | 0.444828i | ||||
\(75\) | 8.48903e13i | 0.734342i | ||||||||
\(76\) | −1.24887e14 | − | 4.93998e13i | −0.978169 | − | 0.386922i | ||||
\(77\) | 3.14121e12i | 0.0223057i | ||||||||
\(78\) | 2.58874e13 | + | 3.80791e13i | 0.166870 | + | 0.245458i | ||||
\(79\) | 1.01573e14 | 0.595077 | 0.297538 | − | 0.954710i | \(-0.403834\pi\) | ||||
0.297538 | + | 0.954710i | \(0.403834\pi\) | |||||||
\(80\) | 6.06954e13 | − | 6.47171e13i | 0.323580 | − | 0.345020i | ||||
\(81\) | −1.81983e14 | −0.883881 | ||||||||
\(82\) | −4.30447e13 | − | 6.33165e13i | −0.190685 | − | 0.280487i | ||||
\(83\) | − | 1.34312e14i | − | 0.543286i | −0.962398 | − | 0.271643i | \(-0.912433\pi\) | ||
0.962398 | − | 0.271643i | \(-0.0875670\pi\) | |||||||
\(84\) | 1.67859e13 | + | 6.63979e12i | 0.0620654 | + | 0.0245504i | ||||
\(85\) | − | 2.24401e14i | − | 0.759248i | ||||||
\(86\) | 1.35745e14 | − | 9.22842e13i | 0.420713 | − | 0.286015i | ||||
\(87\) | −5.52257e14 | −1.56945 | ||||||||
\(88\) | 2.64964e13 | + | 1.18271e14i | 0.0691142 | + | 0.308503i | ||||
\(89\) | 8.80035e13 | 0.210899 | 0.105450 | − | 0.994425i | \(-0.466372\pi\) | ||||
0.105450 | + | 0.994425i | \(0.466372\pi\) | |||||||
\(90\) | −1.86511e13 | + | 1.26796e13i | −0.0411041 | + | 0.0279439i | ||||
\(91\) | 1.09123e13i | 0.0221364i | ||||||||
\(92\) | −3.39367e14 | + | 8.57947e14i | −0.634251 | + | 1.60344i | ||||
\(93\) | − | 2.51576e14i | − | 0.433559i | ||||||
\(94\) | 3.44489e14 | + | 5.06726e14i | 0.547920 | + | 0.805961i | ||||
\(95\) | −3.38674e14 | −0.497570 | ||||||||
\(96\) | 6.88021e14 | + | 1.08407e14i | 0.934475 | + | 0.147239i | ||||
\(97\) | 1.21693e15 | 1.52925 | 0.764624 | − | 0.644477i | \(-0.222925\pi\) | ||||
0.764624 | + | 0.644477i | \(0.222925\pi\) | |||||||
\(98\) | −4.80763e14 | − | 7.07178e14i | −0.559417 | − | 0.822874i | ||||
\(99\) | − | 3.08082e13i | − | 0.0332203i | ||||||
\(100\) | −2.85528e14 | + | 7.21837e14i | −0.285528 | + | 0.721837i | ||||
\(101\) | − | 1.49284e15i | − | 1.38549i | −0.721183 | − | 0.692745i | \(-0.756401\pi\) | ||
0.721183 | − | 0.692745i | \(-0.243599\pi\) | |||||||
\(102\) | 1.45681e15 | − | 9.90390e14i | 1.25575 | − | 0.853699i | ||||
\(103\) | 4.75271e14 | 0.380769 | 0.190385 | − | 0.981710i | \(-0.439026\pi\) | ||||
0.190385 | + | 0.981710i | \(0.439026\pi\) | |||||||
\(104\) | 9.20467e13 | + | 4.10865e14i | 0.0685896 | + | 0.306161i | ||||
\(105\) | 4.55208e13 | 0.0315712 | ||||||||
\(106\) | 8.37005e13 | − | 5.69024e13i | 0.0540672 | − | 0.0367567i | ||||
\(107\) | 2.70722e15i | 1.62984i | 0.579572 | + | 0.814921i | \(0.303220\pi\) | ||||
−0.579572 | + | 0.814921i | \(0.696780\pi\) | |||||||
\(108\) | −1.73140e15 | − | 6.84868e14i | −0.972118 | − | 0.384529i | ||||
\(109\) | 2.84661e14i | 0.149152i | 0.997215 | + | 0.0745760i | \(0.0237603\pi\) | ||||
−0.997215 | + | 0.0745760i | \(0.976240\pi\) | |||||||
\(110\) | 1.71836e14 | + | 2.52762e14i | 0.0840756 | + | 0.123671i | ||||
\(111\) | −1.63721e15 | −0.748483 | ||||||||
\(112\) | 1.20401e14 | + | 1.12919e14i | 0.0514628 | + | 0.0482648i | ||||
\(113\) | −2.09888e15 | −0.839267 | −0.419633 | − | 0.907694i | \(-0.637841\pi\) | ||||
−0.419633 | + | 0.907694i | \(0.637841\pi\) | |||||||
\(114\) | −1.49473e15 | − | 2.19867e15i | −0.559469 | − | 0.822950i | ||||
\(115\) | 2.32662e15i | 0.815628i | ||||||||
\(116\) | −4.69594e15 | − | 1.85752e15i | −1.54272 | − | 0.610236i | ||||
\(117\) | − | 1.07026e14i | − | 0.0329681i | ||||||
\(118\) | 3.93026e15 | − | 2.67192e15i | 1.13581 | − | 0.772162i | ||||
\(119\) | 4.17479e14 | 0.113249 | ||||||||
\(120\) | 1.71393e15 | − | 3.83973e14i | 0.436650 | − | 0.0978231i | ||||
\(121\) | 3.75973e15 | 0.900049 | ||||||||
\(122\) | −5.37534e15 | + | 3.65433e15i | −1.20978 | + | 0.822450i | ||||
\(123\) | − | 1.51563e15i | − | 0.320853i | ||||||
\(124\) | 8.46176e14 | − | 2.13920e15i | 0.168577 | − | 0.426176i | ||||
\(125\) | 4.47925e15i | 0.840195i | ||||||||
\(126\) | −2.35894e13 | − | 3.46987e13i | −0.00416809 | − | 0.00613104i | ||||
\(127\) | 5.68754e15 | 0.947102 | 0.473551 | − | 0.880766i | \(-0.342972\pi\) | ||||
0.473551 | + | 0.880766i | \(0.342972\pi\) | |||||||
\(128\) | 5.48574e15 | + | 3.23596e15i | 0.861312 | + | 0.508076i | ||||
\(129\) | 3.24939e15 | 0.481258 | ||||||||
\(130\) | 5.96948e14 | + | 8.78079e14i | 0.0834374 | + | 0.122732i | ||||
\(131\) | − | 6.69503e15i | − | 0.883523i | −0.897133 | − | 0.441761i | \(-0.854354\pi\) | ||
0.897133 | − | 0.441761i | \(-0.145646\pi\) | |||||||
\(132\) | −8.82537e14 | + | 2.23112e15i | −0.110009 | + | 0.278111i | ||||
\(133\) | − | 6.30073e14i | − | 0.0742171i | ||||||
\(134\) | 2.70467e15 | − | 1.83873e15i | 0.301182 | − | 0.204754i | ||||
\(135\) | −4.69530e15 | −0.494493 | ||||||||
\(136\) | 1.57187e16 | − | 3.52148e15i | 1.56630 | − | 0.350900i | ||||
\(137\) | −1.32688e16 | −1.25149 | −0.625743 | − | 0.780029i | \(-0.715204\pi\) | ||||
−0.625743 | + | 0.780029i | \(0.715204\pi\) | |||||||
\(138\) | −1.51044e16 | + | 1.02685e16i | −1.34900 | + | 0.917094i | ||||
\(139\) | − | 1.15579e16i | − | 0.977841i | −0.872328 | − | 0.488921i | \(-0.837391\pi\) | ||
0.872328 | − | 0.488921i | \(-0.162609\pi\) | |||||||
\(140\) | 3.87072e14 | + | 1.53109e14i | 0.0310336 | + | 0.0122756i | ||||
\(141\) | 1.21297e16i | 0.921948i | ||||||||
\(142\) | 1.16850e16 | + | 1.71881e16i | 0.842302 | + | 1.23898i | ||||
\(143\) | −1.45043e15 | −0.0991919 | ||||||||
\(144\) | −1.18086e15 | − | 1.10748e15i | −0.0766444 | − | 0.0718815i | ||||
\(145\) | −1.27347e16 | −0.784745 | ||||||||
\(146\) | −6.10514e14 | − | 8.98035e14i | −0.0357313 | − | 0.0525589i | ||||
\(147\) | − | 1.69280e16i | − | 0.941294i | ||||||
\(148\) | −1.39215e16 | − | 5.50675e15i | −0.735737 | − | 0.291026i | ||||
\(149\) | − | 2.44036e16i | − | 1.22619i | −0.790010 | − | 0.613094i | \(-0.789925\pi\) | ||
0.790010 | − | 0.613094i | \(-0.210075\pi\) | |||||||
\(150\) | −1.27082e16 | + | 8.63945e15i | −0.607294 | + | 0.412859i | ||||
\(151\) | 2.34346e16 | 1.06545 | 0.532723 | − | 0.846290i | \(-0.321169\pi\) | ||||
0.532723 | + | 0.846290i | \(0.321169\pi\) | |||||||
\(152\) | −5.31474e15 | − | 2.37232e16i | −0.229961 | − | 1.02647i | ||||
\(153\) | −4.09454e15 | −0.168663 | ||||||||
\(154\) | −4.70243e14 | + | 3.19687e14i | −0.0184466 | + | 0.0125406i | ||||
\(155\) | − | 5.80119e15i | − | 0.216785i | ||||||
\(156\) | −3.06587e15 | + | 7.75076e15i | −0.109174 | + | 0.276000i | ||||
\(157\) | 3.64533e16i | 1.23734i | 0.785651 | + | 0.618670i | \(0.212328\pi\) | ||||
−0.785651 | + | 0.618670i | \(0.787672\pi\) | |||||||
\(158\) | 1.03372e16 | + | 1.52055e16i | 0.334562 | + | 0.492123i | ||||
\(159\) | 2.00357e15 | 0.0618481 | ||||||||
\(160\) | 1.58653e16 | + | 2.49979e15i | 0.467250 | + | 0.0736215i | ||||
\(161\) | −4.32848e15 | −0.121658 | ||||||||
\(162\) | −1.85208e16 | − | 2.72431e16i | −0.496932 | − | 0.730961i | ||||
\(163\) | 6.21748e16i | 1.59297i | 0.604658 | + | 0.796485i | \(0.293310\pi\) | ||||
−0.604658 | + | 0.796485i | \(0.706690\pi\) | |||||||
\(164\) | 5.09782e15 | − | 1.28877e16i | 0.124754 | − | 0.315389i | ||||
\(165\) | 6.05047e15i | 0.141468i | ||||||||
\(166\) | 2.01066e16 | − | 1.36692e16i | 0.449292 | − | 0.305444i | ||||
\(167\) | −4.36211e15 | −0.0931801 | −0.0465901 | − | 0.998914i | \(-0.514835\pi\) | ||||
−0.0465901 | + | 0.998914i | \(0.514835\pi\) | |||||||
\(168\) | 7.14349e14 | + | 3.18861e15i | 0.0145912 | + | 0.0651302i | ||||
\(169\) | 4.61472e16 | 0.901561 | ||||||||
\(170\) | 3.35932e16 | − | 2.28378e16i | 0.627891 | − | 0.426861i | ||||
\(171\) | 6.17961e15i | 0.110533i | ||||||||
\(172\) | 2.76301e16 | + | 1.09293e16i | 0.473063 | + | 0.187124i | ||||
\(173\) | 2.78021e16i | 0.455755i | 0.973690 | + | 0.227877i | \(0.0731785\pi\) | ||||
−0.973690 | + | 0.227877i | \(0.926821\pi\) | |||||||
\(174\) | −5.62043e16 | − | 8.26736e16i | −0.882369 | − | 1.29792i | ||||
\(175\) | −3.64179e15 | −0.0547683 | ||||||||
\(176\) | −1.50087e16 | + | 1.60032e16i | −0.216272 | + | 0.230602i | ||||
\(177\) | 9.40800e16 | 1.29927 | ||||||||
\(178\) | 8.95629e15 | + | 1.31742e16i | 0.118571 | + | 0.174412i | ||||
\(179\) | 1.09589e16i | 0.139113i | 0.997578 | + | 0.0695566i | \(0.0221585\pi\) | ||||
−0.997578 | + | 0.0695566i | \(0.977842\pi\) | |||||||
\(180\) | −3.79631e15 | − | 1.50166e15i | −0.0462188 | − | 0.0182822i | ||||
\(181\) | − | 1.18530e17i | − | 1.38433i | −0.721739 | − | 0.692165i | \(-0.756657\pi\) | ||
0.721739 | − | 0.692165i | \(-0.243343\pi\) | |||||||
\(182\) | −1.63359e15 | + | 1.11057e15i | −0.0183066 | + | 0.0124454i | ||||
\(183\) | −1.28671e17 | −1.38388 | ||||||||
\(184\) | −1.62974e17 | + | 3.65112e16i | −1.68261 | + | 0.376958i | ||||
\(185\) | −3.77530e16 | −0.374251 | ||||||||
\(186\) | 3.76613e16 | − | 2.56034e16i | 0.358549 | − | 0.243754i | ||||
\(187\) | 5.54899e16i | 0.507460i | ||||||||
\(188\) | −4.07982e16 | + | 1.03141e17i | −0.358473 | + | 0.906249i | ||||
\(189\) | − | 8.73519e15i | − | 0.0737580i | ||||||
\(190\) | −3.44675e16 | − | 5.06999e16i | −0.279742 | − | 0.411486i | ||||
\(191\) | −3.98558e16 | −0.310986 | −0.155493 | − | 0.987837i | \(-0.549697\pi\) | ||||
−0.155493 | + | 0.987837i | \(0.549697\pi\) | |||||||
\(192\) | 5.37926e16 | + | 1.14030e17i | 0.403611 | + | 0.855582i | ||||
\(193\) | −1.28332e17 | −0.926094 | −0.463047 | − | 0.886334i | \(-0.653244\pi\) | ||||
−0.463047 | + | 0.886334i | \(0.653244\pi\) | |||||||
\(194\) | 1.23849e17 | + | 1.82176e17i | 0.859767 | + | 1.26467i | ||||
\(195\) | 2.10189e16i | 0.140395i | ||||||||
\(196\) | 5.69372e16 | − | 1.43942e17i | 0.365996 | − | 0.925265i | ||||
\(197\) | − | 2.94561e17i | − | 1.82255i | −0.411802 | − | 0.911273i | \(-0.635100\pi\) | ||
0.411802 | − | 0.911273i | \(-0.364900\pi\) | |||||||
\(198\) | 4.61203e15 | − | 3.13541e15i | 0.0274728 | − | 0.0186770i | ||||
\(199\) | 9.91123e16 | 0.568499 | 0.284249 | − | 0.958750i | \(-0.408256\pi\) | ||||
0.284249 | + | 0.958750i | \(0.408256\pi\) | |||||||
\(200\) | −1.37119e17 | + | 3.07189e16i | −0.757481 | + | 0.169699i | ||||
\(201\) | 6.47428e16 | 0.344525 | ||||||||
\(202\) | 2.23480e17 | − | 1.51929e17i | 1.14579 | − | 0.778945i | ||||
\(203\) | − | 2.36918e16i | − | 0.117052i | ||||||
\(204\) | 2.96525e17 | + | 1.17293e17i | 1.41200 | + | 0.558528i | ||||
\(205\) | − | 3.49495e16i | − | 0.160431i | ||||||
\(206\) | 4.83692e16 | + | 7.11487e16i | 0.214075 | + | 0.314893i | ||||
\(207\) | 4.24528e16 | 0.181188 | ||||||||
\(208\) | −5.21393e16 | + | 5.55941e16i | −0.214630 | + | 0.228851i | ||||
\(209\) | 8.37471e16 | 0.332562 | ||||||||
\(210\) | 4.63275e15 | + | 6.81453e15i | 0.0177498 | + | 0.0261091i | ||||
\(211\) | − | 8.69554e16i | − | 0.321498i | −0.986995 | − | 0.160749i | \(-0.948609\pi\) | ||
0.986995 | − | 0.160749i | \(-0.0513909\pi\) | |||||||
\(212\) | 1.70367e16 | + | 6.73901e15i | 0.0607949 | + | 0.0240479i | ||||
\(213\) | 4.11438e17i | 1.41729i | ||||||||
\(214\) | −4.05274e17 | + | 2.75519e17i | −1.34786 | + | 0.916323i | ||||
\(215\) | 7.49288e16 | 0.240636 | ||||||||
\(216\) | −7.36823e16 | − | 3.28893e17i | −0.228539 | − | 1.02012i | ||||
\(217\) | 1.07926e16 | 0.0323354 | ||||||||
\(218\) | −4.26141e16 | + | 2.89705e16i | −0.123347 | + | 0.0838556i | ||||
\(219\) | − | 2.14966e16i | − | 0.0601227i | ||||||
\(220\) | −2.03507e16 | + | 5.14483e16i | −0.0550060 | + | 0.139059i | ||||
\(221\) | 1.92768e17i | 0.503608i | ||||||||
\(222\) | −1.66622e17 | − | 2.45092e17i | −0.420809 | − | 0.618988i | ||||
\(223\) | −1.42111e17 | −0.347010 | −0.173505 | − | 0.984833i | \(-0.555509\pi\) | ||||
−0.173505 | + | 0.984833i | \(0.555509\pi\) | |||||||
\(224\) | −4.65065e15 | + | 2.95161e16i | −0.0109813 | + | 0.0696945i | ||||
\(225\) | 3.57178e16 | 0.0815673 | ||||||||
\(226\) | −2.13607e17 | − | 3.14206e17i | −0.471849 | − | 0.694066i | ||||
\(227\) | − | 4.43249e17i | − | 0.947227i | −0.880733 | − | 0.473613i | \(-0.842949\pi\) | ||
0.880733 | − | 0.473613i | \(-0.157051\pi\) | |||||||
\(228\) | 1.77022e17 | − | 4.47526e17i | 0.366029 | − | 0.925351i | ||||
\(229\) | 6.08062e17i | 1.21670i | 0.793671 | + | 0.608348i | \(0.208167\pi\) | ||||
−0.793671 | + | 0.608348i | \(0.791833\pi\) | |||||||
\(230\) | −3.48299e17 | + | 2.36785e17i | −0.674517 | + | 0.458559i | ||||
\(231\) | −1.12564e16 | −0.0211013 | ||||||||
\(232\) | −1.99843e17 | − | 8.92032e17i | −0.362685 | − | 1.61890i | ||||
\(233\) | −5.16263e17 | −0.907197 | −0.453599 | − | 0.891206i | \(-0.649860\pi\) | ||||
−0.453599 | + | 0.891206i | \(0.649860\pi\) | |||||||
\(234\) | 1.60219e16 | − | 1.08922e16i | 0.0272643 | − | 0.0185352i | ||||
\(235\) | 2.79703e17i | 0.460986i | ||||||||
\(236\) | 7.99980e17 | + | 3.16438e17i | 1.27714 | + | 0.505183i | ||||
\(237\) | 3.63981e17i | 0.562945i | ||||||||
\(238\) | 4.24877e16 | + | 6.24972e16i | 0.0636701 | + | 0.0936555i | ||||
\(239\) | 8.09435e17 | 1.17543 | 0.587716 | − | 0.809067i | \(-0.300027\pi\) | ||||
0.587716 | + | 0.809067i | \(0.300027\pi\) | |||||||
\(240\) | 2.31911e17 | + | 2.17499e17i | 0.326390 | + | 0.306107i | ||||
\(241\) | −5.07196e17 | −0.691908 | −0.345954 | − | 0.938251i | \(-0.612445\pi\) | ||||
−0.345954 | + | 0.938251i | \(0.612445\pi\) | |||||||
\(242\) | 3.82635e17 | + | 5.62836e17i | 0.506022 | + | 0.744332i | ||||
\(243\) | 1.63199e17i | 0.209253i | ||||||||
\(244\) | −1.09412e18 | − | 4.32786e17i | −1.36032 | − | 0.538083i | ||||
\(245\) | − | 3.90349e17i | − | 0.470660i | ||||||
\(246\) | 2.26892e17 | − | 1.54249e17i | 0.265342 | − | 0.180388i | ||||
\(247\) | 2.90932e17 | 0.330038 | ||||||||
\(248\) | 4.06358e17 | − | 9.10369e16i | 0.447220 | − | 0.100191i | ||||
\(249\) | 4.81300e17 | 0.513950 | ||||||||
\(250\) | −6.70549e17 | + | 4.55862e17i | −0.694834 | + | 0.472371i | ||||
\(251\) | − | 9.30546e17i | − | 0.935804i | −0.883780 | − | 0.467902i | \(-0.845010\pi\) | ||
0.883780 | − | 0.467902i | \(-0.154990\pi\) | |||||||
\(252\) | 2.79371e15 | − | 7.06271e15i | 0.00272695 | − | 0.00689394i | ||||
\(253\) | − | 5.75327e17i | − | 0.545143i | ||||||
\(254\) | 5.78832e17 | + | 8.51432e17i | 0.532476 | + | 0.783244i | ||||
\(255\) | 8.04132e17 | 0.718251 | ||||||||
\(256\) | 7.38674e16 | + | 1.15055e18i | 0.0640697 | + | 0.997945i | ||||
\(257\) | 1.04519e17 | 0.0880433 | 0.0440217 | − | 0.999031i | \(-0.485983\pi\) | ||||
0.0440217 | + | 0.999031i | \(0.485983\pi\) | |||||||
\(258\) | 3.30696e17 | + | 4.86437e17i | 0.270571 | + | 0.397996i | ||||
\(259\) | − | 7.02362e16i | − | 0.0558229i | ||||||
\(260\) | −7.06970e16 | + | 1.78728e17i | −0.0545885 | + | 0.138004i | ||||
\(261\) | 2.32364e17i | 0.174327i | ||||||||
\(262\) | 1.00225e18 | − | 6.81366e17i | 0.730665 | − | 0.496730i | ||||
\(263\) | −1.81980e18 | −1.28930 | −0.644652 | − | 0.764476i | \(-0.722998\pi\) | ||||
−0.644652 | + | 0.764476i | \(0.722998\pi\) | |||||||
\(264\) | −4.23819e17 | + | 9.49488e16i | −0.291844 | + | 0.0653823i | ||||
\(265\) | 4.62011e16 | 0.0309249 | ||||||||
\(266\) | 9.43228e16 | − | 6.41238e16i | 0.0613768 | − | 0.0417260i | ||||
\(267\) | 3.15357e17i | 0.199511i | ||||||||
\(268\) | 5.50520e17 | + | 2.17762e17i | 0.338659 | + | 0.133959i | ||||
\(269\) | − | 3.24756e18i | − | 1.94274i | −0.237572 | − | 0.971370i | \(-0.576352\pi\) | ||
0.237572 | − | 0.971370i | \(-0.423648\pi\) | |||||||
\(270\) | −4.77850e17 | − | 7.02892e17i | −0.278012 | − | 0.408941i | ||||
\(271\) | −2.66200e18 | −1.50639 | −0.753197 | − | 0.657795i | \(-0.771489\pi\) | ||||
−0.753197 | + | 0.657795i | \(0.771489\pi\) | |||||||
\(272\) | 2.12689e18 | + | 1.99472e18i | 1.17079 | + | 1.09803i | ||||
\(273\) | −3.91039e16 | −0.0209411 | ||||||||
\(274\) | −1.35039e18 | − | 1.98635e18i | −0.703605 | − | 1.03497i | ||||
\(275\) | − | 4.84054e17i | − | 0.245413i | ||||||
\(276\) | −3.07441e18 | − | 1.21611e18i | −1.51686 | − | 0.600004i | ||||
\(277\) | 2.05102e18i | 0.984851i | 0.870354 | + | 0.492426i | \(0.163890\pi\) | ||||
−0.870354 | + | 0.492426i | \(0.836110\pi\) | |||||||
\(278\) | 1.73023e18 | − | 1.17627e18i | 0.808665 | − | 0.549758i | ||||
\(279\) | −1.05852e17 | −0.0481577 | ||||||||
\(280\) | 1.64724e16 | + | 7.35274e16i | 0.00729579 | + | 0.0325660i | ||||
\(281\) | −1.26318e16 | −0.00544713 | −0.00272357 | − | 0.999996i | \(-0.500867\pi\) | ||||
−0.00272357 | + | 0.999996i | \(0.500867\pi\) | |||||||
\(282\) | −1.81583e18 | + | 1.23446e18i | −0.762442 | + | 0.518334i | ||||
\(283\) | 2.69764e18i | 1.10302i | 0.834167 | + | 0.551512i | \(0.185949\pi\) | ||||
−0.834167 | + | 0.551512i | \(0.814051\pi\) | |||||||
\(284\) | −1.38387e18 | + | 3.49853e18i | −0.551071 | + | 1.39315i | ||||
\(285\) | − | 1.21362e18i | − | 0.470703i | ||||||
\(286\) | −1.47613e17 | − | 2.17131e17i | −0.0557673 | − | 0.0820308i | ||||
\(287\) | 6.50205e16 | 0.0239296 | ||||||||
\(288\) | 4.56125e16 | − | 2.89487e17i | 0.0163546 | − | 0.103797i | ||||
\(289\) | 4.51241e18 | 1.57643 | ||||||||
\(290\) | −1.29604e18 | − | 1.90640e18i | −0.441196 | − | 0.648977i | ||||
\(291\) | 4.36082e18i | 1.44667i | ||||||||
\(292\) | 7.23037e16 | − | 1.82789e17i | 0.0233770 | − | 0.0590989i | ||||
\(293\) | − | 2.63682e17i | − | 0.0830947i | −0.999137 | − | 0.0415474i | \(-0.986771\pi\) | ||
0.999137 | − | 0.0415474i | \(-0.0132287\pi\) | |||||||
\(294\) | 2.53414e18 | − | 1.72279e18i | 0.778441 | − | 0.529211i | ||||
\(295\) | 2.16943e18 | 0.649650 | ||||||||
\(296\) | −5.92450e17 | − | 2.64450e18i | −0.172967 | − | 0.772067i | ||||
\(297\) | 1.16105e18 | 0.330505 | ||||||||
\(298\) | 3.65325e18 | − | 2.48360e18i | 1.01405 | − | 0.689383i | ||||
\(299\) | − | 1.99864e18i | − | 0.541005i | ||||||
\(300\) | −2.58667e18 | − | 1.02318e18i | −0.682861 | − | 0.270111i | ||||
\(301\) | 1.39398e17i | 0.0358930i | ||||||||
\(302\) | 2.38499e18 | + | 3.50819e18i | 0.599010 | + | 0.881113i | ||||
\(303\) | 5.34953e18 | 1.31068 | ||||||||
\(304\) | 3.01050e18 | − | 3.20998e18i | 0.719593 | − | 0.767274i | ||||
\(305\) | −2.96708e18 | −0.691960 | ||||||||
\(306\) | −4.16709e17 | − | 6.12958e17i | −0.0948249 | − | 0.139483i | ||||
\(307\) | 3.96417e18i | 0.880268i | 0.897932 | + | 0.440134i | \(0.145069\pi\) | ||||
−0.897932 | + | 0.440134i | \(0.854931\pi\) | |||||||
\(308\) | −9.57151e16 | − | 3.78608e16i | −0.0207420 | − | 0.00820464i | ||||
\(309\) | 1.70311e18i | 0.360209i | ||||||||
\(310\) | 8.68446e17 | − | 5.90399e17i | 0.179279 | − | 0.121880i | ||||
\(311\) | −7.87147e18 | −1.58618 | −0.793091 | − | 0.609104i | \(-0.791529\pi\) | ||||
−0.793091 | + | 0.609104i | \(0.791529\pi\) | |||||||
\(312\) | −1.47232e18 | + | 3.29845e17i | −0.289629 | + | 0.0648860i | ||||
\(313\) | 8.70513e16 | 0.0167183 | 0.00835916 | − | 0.999965i | \(-0.497339\pi\) | ||||
0.00835916 | + | 0.999965i | \(0.497339\pi\) | |||||||
\(314\) | −5.45710e18 | + | 3.70992e18i | −1.02327 | + | 0.695652i | ||||
\(315\) | − | 1.91530e16i | − | 0.00350678i | ||||||
\(316\) | −1.22425e18 | + | 3.09499e18i | −0.218885 | + | 0.553359i | ||||
\(317\) | 1.70030e18i | 0.296880i | 0.988921 | + | 0.148440i | \(0.0474252\pi\) | ||||
−0.988921 | + | 0.148440i | \(0.952575\pi\) | |||||||
\(318\) | 2.03907e17 | + | 2.99937e17i | 0.0347720 | + | 0.0511478i | ||||
\(319\) | 3.14903e18 | 0.524502 | ||||||||
\(320\) | 1.24042e18 | + | 2.62947e18i | 0.201811 | + | 0.427802i | ||||
\(321\) | −9.70121e18 | −1.54184 | ||||||||
\(322\) | −4.40518e17 | − | 6.47979e17i | −0.0683982 | − | 0.100610i | ||||
\(323\) | − | 1.11303e19i | − | 1.68845i | ||||||
\(324\) | 2.19343e18 | − | 5.54517e18i | 0.325115 | − | 0.821916i | ||||
\(325\) | − | 1.68157e18i | − | 0.243551i | ||||||
\(326\) | −9.30765e18 | + | 6.32765e18i | −1.31737 | + | 0.895593i | ||||
\(327\) | −1.02007e18 | −0.141098 | ||||||||
\(328\) | 2.44812e18 | − | 5.48455e17i | 0.330963 | − | 0.0741459i | ||||
\(329\) | −5.20363e17 | −0.0687602 | ||||||||
\(330\) | −9.05763e17 | + | 6.15768e17i | −0.116993 | + | 0.0795358i | ||||
\(331\) | − | 9.05755e18i | − | 1.14367i | −0.820368 | − | 0.571835i | \(-0.806232\pi\) | ||
0.820368 | − | 0.571835i | \(-0.193768\pi\) | |||||||
\(332\) | 4.09259e18 | + | 1.61885e18i | 0.505199 | + | 0.199835i | ||||
\(333\) | 6.88860e17i | 0.0831380i | ||||||||
\(334\) | −4.43941e17 | − | 6.53014e17i | −0.0523873 | − | 0.0770591i | ||||
\(335\) | 1.49293e18 | 0.172267 | ||||||||
\(336\) | −4.04639e17 | + | 4.31450e17i | −0.0456586 | + | 0.0486840i | ||||
\(337\) | 1.06692e19 | 1.17736 | 0.588680 | − | 0.808366i | \(-0.299648\pi\) | ||||
0.588680 | + | 0.808366i | \(0.299648\pi\) | |||||||
\(338\) | 4.69649e18 | + | 6.90830e18i | 0.506872 | + | 0.745582i | ||||
\(339\) | − | 7.52126e18i | − | 0.793949i | ||||||
\(340\) | 6.83768e18 | + | 2.70470e18i | 0.706020 | + | 0.279271i | ||||
\(341\) | 1.43452e18i | 0.144893i | ||||||||
\(342\) | −9.25096e17 | + | 6.28911e17i | −0.0914094 | + | 0.0621432i | ||||
\(343\) | 1.45605e18 | 0.140757 | ||||||||
\(344\) | 1.17584e18 | + | 5.24856e18i | 0.111214 | + | 0.496423i | ||||
\(345\) | −8.33735e18 | −0.771587 | ||||||||
\(346\) | −4.16200e18 | + | 2.82947e18i | −0.376905 | + | 0.256233i | ||||
\(347\) | − | 2.62705e18i | − | 0.232808i | −0.993202 | − | 0.116404i | \(-0.962863\pi\) | ||
0.993202 | − | 0.116404i | \(-0.0371368\pi\) | |||||||
\(348\) | 6.65633e18 | − | 1.68277e19i | 0.577285 | − | 1.45942i | ||||
\(349\) | 1.30852e19i | 1.11068i | 0.831622 | + | 0.555342i | \(0.187413\pi\) | ||||
−0.831622 | + | 0.555342i | \(0.812587\pi\) | |||||||
\(350\) | −3.70632e17 | − | 5.45180e17i | −0.0307916 | − | 0.0452929i | ||||
\(351\) | 4.03341e18 | 0.327996 | ||||||||
\(352\) | −3.92317e18 | − | 6.18148e17i | −0.312297 | − | 0.0492065i | ||||
\(353\) | −3.44105e18 | −0.268152 | −0.134076 | − | 0.990971i | \(-0.542807\pi\) | ||||
−0.134076 | + | 0.990971i | \(0.542807\pi\) | |||||||
\(354\) | 9.57471e18 | + | 1.40839e19i | 0.730468 | + | 1.07448i | ||||
\(355\) | 9.48750e18i | 0.708662i | ||||||||
\(356\) | −1.06070e18 | + | 2.68154e18i | −0.0775743 | + | 0.196114i | ||||
\(357\) | 1.49602e18i | 0.107134i | ||||||||
\(358\) | −1.64056e18 | + | 1.11531e18i | −0.115045 | + | 0.0782117i | ||||
\(359\) | 8.79527e17 | 0.0604005 | 0.0302003 | − | 0.999544i | \(-0.490385\pi\) | ||||
0.0302003 | + | 0.999544i | \(0.490385\pi\) | |||||||
\(360\) | −1.61558e17 | − | 7.21140e17i | −0.0108657 | − | 0.0485010i | ||||
\(361\) | −1.61714e18 | −0.106523 | ||||||||
\(362\) | 1.77441e19 | − | 1.20631e19i | 1.14483 | − | 0.778293i | ||||
\(363\) | 1.34728e19i | 0.851450i | ||||||||
\(364\) | −3.32507e17 | − | 1.31526e17i | −0.0205845 | − | 0.00814236i | ||||
\(365\) | − | 4.95698e17i | − | 0.0300622i | ||||||
\(366\) | −1.30951e19 | − | 1.92623e19i | −0.778041 | − | 1.14446i | ||||
\(367\) | 1.68813e19 | 0.982676 | 0.491338 | − | 0.870969i | \(-0.336508\pi\) | ||||
0.491338 | + | 0.870969i | \(0.336508\pi\) | |||||||
\(368\) | −2.20519e19 | − | 2.06816e19i | −1.25773 | − | 1.17957i | ||||
\(369\) | −6.37706e17 | −0.0356388 | ||||||||
\(370\) | −3.84220e18 | − | 5.65167e18i | −0.210410 | − | 0.309502i | ||||
\(371\) | 8.59531e16i | 0.00461272i | ||||||||
\(372\) | 7.66573e18 | + | 3.03224e18i | 0.403164 | + | 0.159474i | ||||
\(373\) | − | 2.50203e19i | − | 1.28966i | −0.764325 | − | 0.644831i | \(-0.776928\pi\) | ||
0.764325 | − | 0.644831i | \(-0.223072\pi\) | |||||||
\(374\) | −8.30691e18 | + | 5.64731e18i | −0.419665 | + | 0.285302i | ||||
\(375\) | −1.60512e19 | −0.794828 | ||||||||
\(376\) | −1.95924e19 | + | 4.38932e18i | −0.950998 | + | 0.213053i | ||||
\(377\) | 1.09395e19 | 0.520521 | ||||||||
\(378\) | 1.30767e18 | − | 8.88998e17i | 0.0609972 | − | 0.0414679i | ||||
\(379\) | 2.47648e19i | 1.13251i | 0.824232 | + | 0.566253i | \(0.191607\pi\) | ||||
−0.824232 | + | 0.566253i | \(0.808393\pi\) | |||||||
\(380\) | 4.08202e18 | − | 1.03197e19i | 0.183020 | − | 0.462688i | ||||
\(381\) | 2.03811e19i | 0.895961i | ||||||||
\(382\) | −4.05620e18 | − | 5.96647e18i | −0.174842 | − | 0.257183i | ||||
\(383\) | 2.04166e19 | 0.862965 | 0.431483 | − | 0.902121i | \(-0.357991\pi\) | ||||
0.431483 | + | 0.902121i | \(0.357991\pi\) | |||||||
\(384\) | −1.15959e19 | + | 1.96579e19i | −0.480641 | + | 0.814804i | ||||
\(385\) | −2.59565e17 | −0.0105509 | ||||||||
\(386\) | −1.30606e19 | − | 1.92115e19i | −0.520665 | − | 0.765871i | ||||
\(387\) | − | 1.36719e18i | − | 0.0534559i | ||||||
\(388\) | −1.46676e19 | + | 3.70808e19i | −0.562498 | + | 1.42204i | ||||
\(389\) | − | 9.28297e18i | − | 0.349193i | −0.984640 | − | 0.174596i | \(-0.944138\pi\) | ||
0.984640 | − | 0.174596i | \(-0.0558620\pi\) | |||||||
\(390\) | −3.14656e18 | + | 2.13914e18i | −0.116105 | + | 0.0789321i | ||||
\(391\) | −7.64633e19 | −2.76775 | ||||||||
\(392\) | 2.73429e19 | − | 6.12566e18i | 0.970954 | − | 0.217524i | ||||
\(393\) | 2.39913e19 | 0.835815 | ||||||||
\(394\) | 4.40962e19 | − | 2.99781e19i | 1.50723 | − | 1.02466i | ||||
\(395\) | 8.39316e18i | 0.281480i | ||||||||
\(396\) | 9.38751e17 | + | 3.71330e17i | 0.0308913 | + | 0.0122193i | ||||
\(397\) | − | 2.03449e19i | − | 0.656942i | −0.944514 | − | 0.328471i | \(-0.893467\pi\) | ||
0.944514 | − | 0.328471i | \(-0.106533\pi\) | |||||||
\(398\) | 1.00869e19 | + | 1.48372e19i | 0.319619 | + | 0.470143i | ||||
\(399\) | 2.25784e18 | 0.0702096 | ||||||||
\(400\) | −1.85535e19 | − | 1.74005e19i | −0.566208 | − | 0.531022i | ||||
\(401\) | 1.23695e19 | 0.370483 | 0.185242 | − | 0.982693i | \(-0.440693\pi\) | ||||
0.185242 | + | 0.982693i | \(0.440693\pi\) | |||||||
\(402\) | 6.58900e18 | + | 9.69208e18i | 0.193698 | + | 0.284919i | ||||
\(403\) | 4.98341e18i | 0.143793i | ||||||||
\(404\) | 4.54881e19 | + | 1.79931e19i | 1.28836 | + | 0.509620i | ||||
\(405\) | − | 1.50377e19i | − | 0.418088i | ||||||
\(406\) | 3.54669e18 | − | 2.41116e18i | 0.0968007 | − | 0.0658084i | ||||
\(407\) | 9.33555e18 | 0.250139 | ||||||||
\(408\) | 1.26191e19 | + | 5.63273e19i | 0.331953 | + | 1.48173i | ||||
\(409\) | 1.53557e18 | 0.0396593 | 0.0198296 | − | 0.999803i | \(-0.493688\pi\) | ||||
0.0198296 | + | 0.999803i | \(0.493688\pi\) | |||||||
\(410\) | 5.23199e18 | − | 3.55688e18i | 0.132675 | − | 0.0901966i | ||||
\(411\) | − | 4.75480e19i | − | 1.18391i | ||||||
\(412\) | −5.72841e18 | + | 1.44819e19i | −0.140057 | + | 0.354075i | ||||
\(413\) | 4.03603e18i | 0.0969011i | ||||||||
\(414\) | 4.32050e18 | + | 6.35523e18i | 0.101867 | + | 0.149840i | ||||
\(415\) | 1.10985e19 | 0.256982 | ||||||||
\(416\) | −1.36288e19 | − | 2.14740e18i | −0.309926 | − | 0.0488330i | ||||
\(417\) | 4.14173e19 | 0.925041 | ||||||||
\(418\) | 8.52311e18 | + | 1.25371e19i | 0.186972 | + | 0.275026i | ||||
\(419\) | 3.07067e19i | 0.661649i | 0.943692 | + | 0.330825i | \(0.107327\pi\) | ||||
−0.943692 | + | 0.330825i | \(0.892673\pi\) | |||||||
\(420\) | −5.48660e17 | + | 1.38706e18i | −0.0116127 | + | 0.0293578i | ||||
\(421\) | − | 7.88348e19i | − | 1.63909i | −0.573016 | − | 0.819544i | \(-0.694227\pi\) | ||
0.573016 | − | 0.819544i | \(-0.305773\pi\) | |||||||
\(422\) | 1.30173e19 | − | 8.84962e18i | 0.265876 | − | 0.180751i | ||||
\(423\) | 5.10360e18 | 0.102406 | ||||||||
\(424\) | 7.25024e17 | + | 3.23626e18i | 0.0142925 | + | 0.0637969i | ||||
\(425\) | −6.43327e19 | −1.24599 | ||||||||
\(426\) | −6.15928e19 | + | 4.18728e19i | −1.17208 | + | 0.796821i | ||||
\(427\) | − | 5.52000e18i | − | 0.103212i | ||||||
\(428\) | −8.24911e19 | − | 3.26300e19i | −1.51558 | − | 0.599499i | ||||
\(429\) | − | 5.19755e18i | − | 0.0938359i | ||||||
\(430\) | 7.62564e18 | + | 1.12169e19i | 0.135289 | + | 0.199003i | ||||
\(431\) | 5.48780e19 | 0.956794 | 0.478397 | − | 0.878144i | \(-0.341218\pi\) | ||||
0.478397 | + | 0.878144i | \(0.341218\pi\) | |||||||
\(432\) | 4.17369e19 | − | 4.45024e19i | 0.715142 | − | 0.762528i | ||||
\(433\) | −9.01703e19 | −1.51846 | −0.759232 | − | 0.650821i | \(-0.774425\pi\) | ||||
−0.759232 | + | 0.650821i | \(0.774425\pi\) | |||||||
\(434\) | 1.09839e18 | + | 1.61567e18i | 0.0181795 | + | 0.0267411i | ||||
\(435\) | − | 4.56342e19i | − | 0.742372i | ||||||
\(436\) | −8.67384e18 | − | 3.43100e18i | −0.138696 | − | 0.0548621i | ||||
\(437\) | 1.15401e20i | 1.81384i | ||||||||
\(438\) | 3.21807e18 | − | 2.18775e18i | 0.0497209 | − | 0.0338020i | ||||
\(439\) | −9.88500e19 | −1.50139 | −0.750694 | − | 0.660650i | \(-0.770281\pi\) | ||||
−0.750694 | + | 0.660650i | \(0.770281\pi\) | |||||||
\(440\) | −9.77300e18 | + | 2.18946e18i | −0.145926 | + | 0.0326920i | ||||
\(441\) | −7.12250e18 | −0.104555 | ||||||||
\(442\) | −2.88576e19 | + | 1.96184e19i | −0.416479 | + | 0.283136i | ||||
\(443\) | 5.95210e19i | 0.844583i | 0.906460 | + | 0.422292i | \(0.138774\pi\) | ||||
−0.906460 | + | 0.422292i | \(0.861226\pi\) | |||||||
\(444\) | 1.97332e19 | − | 4.98870e19i | 0.275312 | − | 0.696010i | ||||
\(445\) | 7.27192e18i | 0.0997584i | ||||||||
\(446\) | −1.44629e19 | − | 2.12742e19i | −0.195095 | − | 0.286974i | ||||
\(447\) | 8.74493e19 | 1.15998 | ||||||||
\(448\) | −4.89190e18 | + | 2.30770e18i | −0.0638105 | + | 0.0301019i | ||||
\(449\) | 1.87833e18 | 0.0240949 | 0.0120474 | − | 0.999927i | \(-0.496165\pi\) | ||||
0.0120474 | + | 0.999927i | \(0.496165\pi\) | |||||||
\(450\) | 3.63507e18 | + | 5.34700e18i | 0.0458584 | + | 0.0674554i | ||||
\(451\) | 8.64230e18i | 0.107227i | ||||||||
\(452\) | 2.52977e19 | − | 6.39546e19i | 0.308705 | − | 0.780429i | ||||
\(453\) | 8.39770e19i | 1.00791i | ||||||||
\(454\) | 6.63550e19 | − | 4.51103e19i | 0.783348 | − | 0.532546i | ||||
\(455\) | −9.01710e17 | −0.0104708 | ||||||||
\(456\) | 8.50110e19 | − | 1.90451e19i | 0.971044 | − | 0.217544i | ||||
\(457\) | 1.02379e20 | 1.15038 | 0.575189 | − | 0.818020i | \(-0.304928\pi\) | ||||
0.575189 | + | 0.818020i | \(0.304928\pi\) | |||||||
\(458\) | −9.10277e19 | + | 6.18837e19i | −1.00620 | + | 0.684045i | ||||
\(459\) | − | 1.54308e20i | − | 1.67801i | ||||||
\(460\) | −7.08940e19 | − | 2.80427e19i | −0.758448 | − | 0.300010i | ||||
\(461\) | 1.09488e20i | 1.15242i | 0.817302 | + | 0.576209i | \(0.195469\pi\) | ||||
−0.817302 | + | 0.576209i | \(0.804531\pi\) | |||||||
\(462\) | −1.14558e18 | − | 1.68509e18i | −0.0118635 | − | 0.0174506i | ||||
\(463\) | 1.60836e20 | 1.63880 | 0.819398 | − | 0.573225i | \(-0.194308\pi\) | ||||
0.819398 | + | 0.573225i | \(0.194308\pi\) | |||||||
\(464\) | 1.13200e20 | − | 1.20701e20i | 1.13491 | − | 1.21011i | ||||
\(465\) | 2.07883e19 | 0.205079 | ||||||||
\(466\) | −5.25411e19 | − | 7.72853e19i | −0.510041 | − | 0.750244i | ||||
\(467\) | 4.70891e18i | 0.0449825i | 0.999747 | + | 0.0224913i | \(0.00715979\pi\) | ||||
−0.999747 | + | 0.0224913i | \(0.992840\pi\) | |||||||
\(468\) | 3.26115e18 | + | 1.28997e18i | 0.0306568 | + | 0.0121265i | ||||
\(469\) | 2.77746e18i | 0.0256952i | ||||||||
\(470\) | −4.18719e19 | + | 2.84659e19i | −0.381231 | + | 0.259174i | ||||
\(471\) | −1.30629e20 | −1.17053 | ||||||||
\(472\) | 3.40443e19 | + | 1.51962e20i | 0.300248 | + | 1.34021i | ||||
\(473\) | −1.85284e19 | −0.160834 | ||||||||
\(474\) | −5.44884e19 | + | 3.70430e19i | −0.465550 | + | 0.316496i | ||||
\(475\) | 9.70930e19i | 0.816556i | ||||||||
\(476\) | −5.03185e18 | + | 1.27209e19i | −0.0416558 | + | 0.105309i | ||||
\(477\) | − | 8.43008e17i | − | 0.00686980i | ||||||
\(478\) | 8.23778e19 | + | 1.21173e20i | 0.660847 | + | 0.972072i | ||||
\(479\) | 1.46825e20 | 1.15954 | 0.579768 | − | 0.814782i | \(-0.303143\pi\) | ||||
0.579768 | + | 0.814782i | \(0.303143\pi\) | |||||||
\(480\) | −8.95790e18 | + | 5.68527e19i | −0.0696461 | + | 0.442020i | ||||
\(481\) | 3.24310e19 | 0.248240 | ||||||||
\(482\) | −5.16184e19 | − | 7.59279e19i | −0.389002 | − | 0.572201i | ||||
\(483\) | − | 1.55109e19i | − | 0.115089i | ||||||
\(484\) | −4.53158e19 | + | 1.14562e20i | −0.331062 | + | 0.836951i | ||||
\(485\) | 1.00558e20i | 0.723356i | ||||||||
\(486\) | −2.44311e19 | + | 1.66091e19i | −0.173050 | + | 0.117645i | ||||
\(487\) | −1.93413e20 | −1.34902 | −0.674511 | − | 0.738265i | \(-0.735645\pi\) | ||||
−0.674511 | + | 0.738265i | \(0.735645\pi\) | |||||||
\(488\) | −4.65618e19 | − | 2.07836e20i | −0.319802 | − | 1.42749i | ||||
\(489\) | −2.22801e20 | −1.50695 | ||||||||
\(490\) | 5.84357e19 | − | 3.97265e19i | 0.389231 | − | 0.264612i | ||||
\(491\) | − | 1.70816e20i | − | 1.12051i | −0.828320 | − | 0.560255i | \(-0.810703\pi\) | ||
0.828320 | − | 0.560255i | \(-0.189297\pi\) | |||||||
\(492\) | 4.61825e19 | + | 1.82678e19i | 0.298359 | + | 0.118018i | ||||
\(493\) | − | 4.18519e20i | − | 2.66295i | ||||||
\(494\) | 2.96087e19 | + | 4.35528e19i | 0.185553 | + | 0.272938i | ||||
\(495\) | 2.54575e18 | 0.0157137 | ||||||||
\(496\) | 5.49842e19 | + | 5.15673e19i | 0.334291 | + | 0.313518i | ||||
\(497\) | −1.76507e19 | −0.105703 | ||||||||
\(498\) | 4.89829e19 | + | 7.20513e19i | 0.288951 | + | 0.425032i | ||||
\(499\) | 6.57784e18i | 0.0382234i | 0.999817 | + | 0.0191117i | \(0.00608381\pi\) | ||||
−0.999817 | + | 0.0191117i | \(0.993916\pi\) | |||||||
\(500\) | −1.36486e20 | − | 5.39881e19i | −0.781293 | − | 0.309046i | ||||
\(501\) | − | 1.56314e19i | − | 0.0881487i | ||||||
\(502\) | 1.39304e20 | − | 9.47035e19i | 0.773901 | − | 0.526124i | ||||
\(503\) | −1.05517e20 | −0.577515 | −0.288758 | − | 0.957402i | \(-0.593242\pi\) | ||||
−0.288758 | + | 0.957402i | \(0.593242\pi\) | |||||||
\(504\) | 1.34162e18 | − | 3.00564e17i | 0.00723436 | − | 0.00162072i | ||||
\(505\) | 1.23357e20 | 0.655357 | ||||||||
\(506\) | 8.61271e19 | − | 5.85521e19i | 0.450828 | − | 0.306488i | ||||
\(507\) | 1.65366e20i | 0.852880i | ||||||||
\(508\) | −6.85516e19 | + | 1.73304e20i | −0.348369 | + | 0.880705i | ||||
\(509\) | − | 1.27123e20i | − | 0.636561i | −0.947997 | − | 0.318281i | \(-0.896895\pi\) | ||
0.947997 | − | 0.318281i | \(-0.103105\pi\) | |||||||
\(510\) | 8.18381e19 | + | 1.20380e20i | 0.403812 | + | 0.593987i | ||||
\(511\) | 9.22203e17 | 0.00448404 | ||||||||
\(512\) | −1.64722e20 | + | 1.28152e20i | −0.789270 | + | 0.614046i | ||||
\(513\) | −2.32887e20 | −1.09968 | ||||||||
\(514\) | 1.06371e19 | + | 1.56466e19i | 0.0494993 | + | 0.0728110i | ||||
\(515\) | 3.92727e19i | 0.180109i | ||||||||
\(516\) | −3.91647e19 | + | 9.90113e19i | −0.177020 | + | 0.447520i | ||||
\(517\) | − | 6.91648e19i | − | 0.308110i | ||||||
\(518\) | 1.05144e19 | − | 7.14807e18i | 0.0461650 | − | 0.0313845i | ||||
\(519\) | −9.96274e19 | −0.431145 | ||||||||
\(520\) | −3.39507e19 | + | 7.60602e18i | −0.144818 | + | 0.0324439i | ||||
\(521\) | 2.72339e20 | 1.14506 | 0.572529 | − | 0.819885i | \(-0.305963\pi\) | ||||
0.572529 | + | 0.819885i | \(0.305963\pi\) | |||||||
\(522\) | −3.47852e19 | + | 2.36481e19i | −0.144167 | + | 0.0980094i | ||||
\(523\) | 2.30971e20i | 0.943615i | 0.881702 | + | 0.471807i | \(0.156398\pi\) | ||||
−0.881702 | + | 0.471807i | \(0.843602\pi\) | |||||||
\(524\) | 2.04003e20 | + | 8.06948e19i | 0.821583 | + | 0.324983i | ||||
\(525\) | − | 1.30502e19i | − | 0.0518110i | ||||||
\(526\) | −1.85205e20 | − | 2.72426e20i | −0.724867 | − | 1.06624i | ||||
\(527\) | 1.90653e20 | 0.735638 | ||||||||
\(528\) | −5.73469e19 | − | 5.37832e19i | −0.218150 | − | 0.204594i | ||||
\(529\) | 5.26146e20 | 1.97328 | ||||||||
\(530\) | 4.70197e18 | + | 6.91636e18i | 0.0173865 | + | 0.0255746i | ||||
\(531\) | − | 3.95844e19i | − | 0.144316i | ||||||
\(532\) | 1.91988e19 | + | 7.59424e18i | 0.0690140 | + | 0.0272990i | ||||
\(533\) | 3.00227e19i | 0.106413i | ||||||||
\(534\) | −4.72093e19 | + | 3.20945e19i | −0.164994 | + | 0.112168i | ||||
\(535\) | −2.23704e20 | −0.770938 | ||||||||
\(536\) | 2.34282e19 | + | 1.04576e20i | 0.0796165 | + | 0.355381i | ||||
\(537\) | −3.92707e19 | −0.131602 | ||||||||
\(538\) | 4.86163e20 | − | 3.30510e20i | 1.60663 | − | 1.09224i | ||||
\(539\) | 9.65253e19i | 0.314576i | ||||||||
\(540\) | 5.65921e19 | − | 1.43069e20i | 0.181888 | − | 0.459826i | ||||
\(541\) | 6.21640e19i | 0.197042i | 0.995135 | + | 0.0985211i | \(0.0314112\pi\) | ||||
−0.995135 | + | 0.0985211i | \(0.968589\pi\) | |||||||
\(542\) | −2.70917e20 | − | 3.98505e20i | −0.846919 | − | 1.24577i | ||||
\(543\) | 4.24748e20 | 1.30958 | ||||||||
\(544\) | −8.21544e19 | + | 5.21406e20i | −0.249827 | + | 1.58556i | ||||
\(545\) | −2.35222e19 | −0.0705510 | ||||||||
\(546\) | −3.97968e18 | − | 5.85390e18i | −0.0117734 | − | 0.0173181i | ||||
\(547\) | 3.62211e20i | 1.05696i | 0.848947 | + | 0.528478i | \(0.177237\pi\) | ||||
−0.848947 | + | 0.528478i | \(0.822763\pi\) | |||||||
\(548\) | 1.59928e20 | − | 4.04309e20i | 0.460330 | − | 1.16375i | ||||
\(549\) | 5.41389e19i | 0.153715i | ||||||||
\(550\) | 7.24635e19 | − | 4.92631e19i | 0.202955 | − | 0.137975i | ||||
\(551\) | −6.31643e20 | −1.74516 | ||||||||
\(552\) | −1.30836e20 | − | 5.84009e20i | −0.356603 | − | 1.59176i | ||||
\(553\) | −1.56148e19 | −0.0419852 | ||||||||
\(554\) | −3.07040e20 | + | 2.08736e20i | −0.814463 | + | 0.553699i | ||||
\(555\) | − | 1.35286e20i | − | 0.354043i | ||||||
\(556\) | 3.52178e20 | + | 1.39307e20i | 0.909289 | + | 0.359676i | ||||
\(557\) | 5.86660e20i | 1.49442i | 0.664588 | + | 0.747210i | \(0.268607\pi\) | ||||
−0.664588 | + | 0.747210i | \(0.731393\pi\) | |||||||
\(558\) | −1.07727e19 | − | 1.58461e19i | −0.0270750 | − | 0.0398259i | ||||
\(559\) | −6.43662e19 | −0.159613 | ||||||||
\(560\) | −9.33071e18 | + | 9.94897e18i | −0.0228299 | + | 0.0243427i | ||||
\(561\) | −1.98846e20 | −0.480059 | ||||||||
\(562\) | −1.28556e18 | − | 1.89100e18i | −0.00306246 | − | 0.00450473i | ||||
\(563\) | − | 3.68047e20i | − | 0.865149i | −0.901598 | − | 0.432574i | \(-0.857605\pi\) | ||
0.901598 | − | 0.432574i | \(-0.142395\pi\) | |||||||
\(564\) | −3.69601e20 | − | 1.46198e20i | −0.857314 | − | 0.339117i | ||||
\(565\) | − | 1.73435e20i | − | 0.396985i | ||||||
\(566\) | −4.03840e20 | + | 2.74544e20i | −0.912191 | + | 0.620138i | ||||
\(567\) | 2.79763e19 | 0.0623616 | ||||||||
\(568\) | −6.64574e20 | + | 1.48885e20i | −1.46194 | + | 0.327521i | ||||
\(569\) | −4.30541e20 | −0.934700 | −0.467350 | − | 0.884072i | \(-0.654791\pi\) | ||||
−0.467350 | + | 0.884072i | \(0.654791\pi\) | |||||||
\(570\) | 1.81681e20 | − | 1.23513e20i | 0.389267 | − | 0.264637i | ||||
\(571\) | 4.02443e20i | 0.851009i | 0.904956 | + | 0.425504i | \(0.139903\pi\) | ||||
−0.904956 | + | 0.425504i | \(0.860097\pi\) | |||||||
\(572\) | 1.74819e19 | − | 4.41957e19i | 0.0364854 | − | 0.0922380i | ||||
\(573\) | − | 1.42822e20i | − | 0.294194i | ||||||
\(574\) | 6.61727e18 | + | 9.73366e18i | 0.0134536 | + | 0.0197896i | ||||
\(575\) | 6.67010e20 | 1.33852 | ||||||||
\(576\) | 4.79786e19 | − | 2.26334e19i | 0.0950340 | − | 0.0448313i | ||||
\(577\) | 1.05401e20 | 0.206076 | 0.103038 | − | 0.994677i | \(-0.467144\pi\) | ||||
0.103038 | + | 0.994677i | \(0.467144\pi\) | |||||||
\(578\) | 4.59236e20 | + | 6.75513e20i | 0.886293 | + | 1.30369i | ||||
\(579\) | − | 4.59872e20i | − | 0.876088i | ||||||
\(580\) | 1.53491e20 | − | 3.88036e20i | 0.288650 | − | 0.729730i | ||||
\(581\) | 2.06478e19i | 0.0383312i | ||||||||
\(582\) | −6.52820e20 | + | 4.43809e20i | −1.19639 | + | 0.813343i | ||||
\(583\) | −1.14246e19 | −0.0206693 | ||||||||
\(584\) | 3.47223e19 | − | 7.77888e18i | 0.0620172 | − | 0.0138938i | ||||
\(585\) | 8.84377e18 | 0.0155944 | ||||||||
\(586\) | 3.94735e19 | − | 2.68354e19i | 0.0687186 | − | 0.0467172i | ||||
\(587\) | − | 9.43833e20i | − | 1.62222i | −0.584895 | − | 0.811109i | \(-0.698864\pi\) | ||
0.584895 | − | 0.811109i | \(-0.301136\pi\) | |||||||
\(588\) | 5.15809e20 | + | 2.04032e20i | 0.875304 | + | 0.346233i | ||||
\(589\) | − | 2.87740e20i | − | 0.482098i | ||||||
\(590\) | 2.20787e20 | + | 3.24766e20i | 0.365244 | + | 0.537255i | ||||
\(591\) | 1.05555e21 | 1.72414 | ||||||||
\(592\) | 3.35590e20 | − | 3.57826e20i | 0.541247 | − | 0.577111i | ||||
\(593\) | −9.22953e20 | −1.46984 | −0.734919 | − | 0.678155i | \(-0.762780\pi\) | ||||
−0.734919 | + | 0.678155i | \(0.762780\pi\) | |||||||
\(594\) | 1.18162e20 | + | 1.73811e20i | 0.185815 | + | 0.273325i | ||||
\(595\) | 3.44972e19i | 0.0535682i | ||||||||
\(596\) | 7.43597e20 | + | 2.94135e20i | 1.14023 | + | 0.451025i | ||||
\(597\) | 3.55165e20i | 0.537802i | ||||||||
\(598\) | 2.99200e20 | − | 2.03406e20i | 0.447406 | − | 0.304162i | ||||
\(599\) | −1.14322e20 | −0.168822 | −0.0844109 | − | 0.996431i | \(-0.526901\pi\) | ||||
−0.0844109 | + | 0.996431i | \(0.526901\pi\) | |||||||
\(600\) | −1.10080e20 | − | 4.91359e20i | −0.160536 | − | 0.716580i | ||||
\(601\) | 3.40769e20 | 0.490797 | 0.245398 | − | 0.969422i | \(-0.421081\pi\) | ||||
0.245398 | + | 0.969422i | \(0.421081\pi\) | |||||||
\(602\) | −2.08681e19 | + | 1.41869e19i | −0.0296831 | + | 0.0201796i | ||||
\(603\) | − | 2.72407e19i | − | 0.0382683i | ||||||
\(604\) | −2.82456e20 | + | 7.14072e20i | −0.391899 | + | 0.990751i | ||||
\(605\) | 3.10675e20i | 0.425736i | ||||||||
\(606\) | 5.44432e20 | + | 8.00832e20i | 0.736884 | + | 1.08392i | ||||
\(607\) | −1.00534e21 | −1.34399 | −0.671995 | − | 0.740556i | \(-0.734562\pi\) | ||||
−0.671995 | + | 0.740556i | \(0.734562\pi\) | |||||||
\(608\) | 7.86922e20 | + | 1.23990e20i | 1.03909 | + | 0.163723i | ||||
\(609\) | 8.48986e19 | 0.110731 | ||||||||
\(610\) | −3.01966e20 | − | 4.44176e20i | −0.389031 | − | 0.572244i | ||||
\(611\) | − | 2.40274e20i | − | 0.305772i | ||||||
\(612\) | 4.93513e19 | − | 1.24764e20i | 0.0620387 | − | 0.156839i | ||||
\(613\) | − | 4.53810e20i | − | 0.563534i | −0.959483 | − | 0.281767i | \(-0.909079\pi\) | ||
0.959483 | − | 0.281767i | \(-0.0909206\pi\) | |||||||
\(614\) | −5.93442e20 | + | 4.03442e20i | −0.727973 | + | 0.494900i | ||||
\(615\) | 1.25240e20 | 0.151768 | ||||||||
\(616\) | −4.07330e18 | − | 1.81818e19i | −0.00487630 | − | 0.0217662i | ||||
\(617\) | −2.74187e20 | −0.324271 | −0.162136 | − | 0.986768i | \(-0.551838\pi\) | ||||
−0.162136 | + | 0.986768i | \(0.551838\pi\) | |||||||
\(618\) | −2.54958e20 | + | 1.73329e20i | −0.297890 | + | 0.202515i | ||||
\(619\) | − | 8.27168e20i | − | 0.954803i | −0.878685 | − | 0.477402i | \(-0.841579\pi\) | ||
0.878685 | − | 0.477402i | \(-0.158421\pi\) | |||||||
\(620\) | 1.76767e20 | + | 6.99214e19i | 0.201587 | + | 0.0797393i | ||||
\(621\) | 1.59989e21i | 1.80262i | ||||||||
\(622\) | −8.01095e20 | − | 1.17837e21i | −0.891776 | − | 1.31176i | ||||
\(623\) | −1.35288e19 | −0.0148798 | ||||||||
\(624\) | −1.99219e20 | − | 1.86839e20i | −0.216494 | − | 0.203041i | ||||
\(625\) | 3.52816e20 | 0.378833 | ||||||||
\(626\) | 8.85938e18 | + | 1.30317e19i | 0.00939931 | + | 0.0138259i | ||||
\(627\) | 3.00104e20i | 0.314605i | ||||||||
\(628\) | −1.11076e21 | − | 4.39369e20i | −1.15060 | − | 0.455127i | ||||
\(629\) | − | 1.24073e21i | − | 1.26998i | ||||||
\(630\) | 2.86723e18 | − | 1.94924e18i | 0.00290007 | − | 0.00197157i | ||||
\(631\) | −8.71825e20 | −0.871383 | −0.435691 | − | 0.900096i | \(-0.643496\pi\) | ||||
−0.435691 | + | 0.900096i | \(0.643496\pi\) | |||||||
\(632\) | −5.87919e20 | + | 1.31712e20i | −0.580683 | + | 0.130091i | ||||
\(633\) | 3.11601e20 | 0.304138 | ||||||||
\(634\) | −2.54537e20 | + | 1.73043e20i | −0.245517 | + | 0.166911i | ||||
\(635\) | 4.69974e20i | 0.447993i | ||||||||
\(636\) | −2.41489e19 | + | 6.10504e19i | −0.0227494 | + | 0.0575122i | ||||
\(637\) | 3.35322e20i | 0.312188i | ||||||||
\(638\) | 3.20483e20 | + | 4.71414e20i | 0.294883 | + | 0.433758i | ||||
\(639\) | 1.73114e20 | 0.157425 | ||||||||
\(640\) | −2.67395e20 | + | 4.53299e20i | −0.240327 | + | 0.407413i | ||||
\(641\) | 1.06761e21 | 0.948367 | 0.474184 | − | 0.880426i | \(-0.342743\pi\) | ||||
0.474184 | + | 0.880426i | \(0.342743\pi\) | |||||||
\(642\) | −9.87311e20 | − | 1.45228e21i | −0.866844 | − | 1.27508i | ||||
\(643\) | 1.92026e21i | 1.66640i | 0.552974 | + | 0.833199i | \(0.313493\pi\) | ||||
−0.552974 | + | 0.833199i | \(0.686507\pi\) | |||||||
\(644\) | 5.21709e19 | − | 1.31892e20i | 0.0447491 | − | 0.113129i | ||||
\(645\) | 2.68504e20i | 0.227642i | ||||||||
\(646\) | 1.66623e21 | − | 1.13276e21i | 1.39634 | − | 0.949276i | ||||
\(647\) | 4.75461e20 | 0.393852 | 0.196926 | − | 0.980418i | \(-0.436904\pi\) | ||||
0.196926 | + | 0.980418i | \(0.436904\pi\) | |||||||
\(648\) | 1.05335e21 | − | 2.35983e20i | 0.862502 | − | 0.193227i | ||||
\(649\) | −5.36455e20 | −0.434208 | ||||||||
\(650\) | 2.51733e20 | − | 1.71136e20i | 0.201414 | − | 0.136928i | ||||
\(651\) | 3.86749e19i | 0.0305894i | ||||||||
\(652\) | −1.89452e21 | − | 7.49389e20i | −1.48129 | − | 0.585937i | ||||
\(653\) | − | 6.30709e20i | − | 0.487507i | −0.969837 | − | 0.243753i | \(-0.921621\pi\) | ||
0.969837 | − | 0.243753i | \(-0.0783787\pi\) | |||||||
\(654\) | −1.03815e20 | − | 1.52706e20i | −0.0793277 | − | 0.116687i | ||||
\(655\) | 5.53225e20 | 0.417919 | ||||||||
\(656\) | 3.31254e20 | + | 3.10669e20i | 0.247390 | + | 0.232017i | ||||
\(657\) | −9.04475e18 | −0.00667815 | ||||||||
\(658\) | −5.29584e19 | − | 7.78990e19i | −0.0386581 | − | 0.0568641i | ||||
\(659\) | − | 6.82905e20i | − | 0.492855i | −0.969161 | − | 0.246428i | \(-0.920743\pi\) | ||
0.969161 | − | 0.246428i | \(-0.0792568\pi\) | |||||||
\(660\) | −1.84363e20 | − | 7.29260e19i | −0.131551 | − | 0.0520359i | ||||
\(661\) | − | 9.29821e20i | − | 0.655977i | −0.944682 | − | 0.327988i | \(-0.893629\pi\) | ||
0.944682 | − | 0.327988i | \(-0.106371\pi\) | |||||||
\(662\) | 1.35593e21 | − | 9.21805e20i | 0.945805 | − | 0.642990i | ||||
\(663\) | −6.90775e20 | −0.476415 | ||||||||
\(664\) | 1.74166e20 | + | 7.77419e20i | 0.118769 | + | 0.530145i | ||||
\(665\) | 5.20644e19 | 0.0351057 | ||||||||
\(666\) | −1.03123e20 | + | 7.01067e19i | −0.0687543 | + | 0.0467415i | ||||
\(667\) | 4.33926e21i | 2.86070i | ||||||||
\(668\) | 5.25763e19 | − | 1.32917e20i | 0.0342741 | − | 0.0866477i | ||||
\(669\) | − | 5.09250e20i | − | 0.328273i | ||||||
\(670\) | 1.51938e20 | + | 2.23493e20i | 0.0968514 | + | 0.142463i | ||||
\(671\) | 7.33699e20 | 0.462487 | ||||||||
\(672\) | −1.05770e20 | − | 1.66654e19i | −0.0659312 | − | 0.0103883i | ||||
\(673\) | −2.08455e20 | −0.128499 | −0.0642494 | − | 0.997934i | \(-0.520465\pi\) | ||||
−0.0642494 | + | 0.997934i | \(0.520465\pi\) | |||||||
\(674\) | 1.08583e21 | + | 1.59720e21i | 0.661930 | + | 0.973665i | ||||
\(675\) | 1.34608e21i | 0.811505i | ||||||||
\(676\) | −5.56210e20 | + | 1.40614e21i | −0.331618 | + | 0.838357i | ||||
\(677\) | − | 1.08759e18i | − | 0.000641285i | −1.00000 | 0.000320642i | \(-0.999898\pi\) | |||
1.00000 | 0.000320642i | \(-0.000102064\pi\) | ||||||||
\(678\) | 1.12594e21 | − | 7.65453e20i | 0.656588 | − | 0.446371i | ||||
\(679\) | −1.87079e20 | −0.107895 | ||||||||
\(680\) | 2.90988e20 | + | 1.29887e21i | 0.165981 | + | 0.740883i | ||||
\(681\) | 1.58836e21 | 0.896080 | ||||||||
\(682\) | −2.14749e20 | + | 1.45994e20i | −0.119825 | + | 0.0814612i | ||||
\(683\) | − | 3.05497e21i | − | 1.68598i | −0.537933 | − | 0.842988i | \(-0.680794\pi\) | ||
0.537933 | − | 0.842988i | \(-0.319206\pi\) | |||||||
\(684\) | −1.88298e20 | − | 7.44825e19i | −0.102784 | − | 0.0406568i | ||||
\(685\) | − | 1.09643e21i | − | 0.591971i | ||||||
\(686\) | 1.48185e20 | + | 2.17973e20i | 0.0791361 | + | 0.116405i | ||||
\(687\) | −2.17896e21 | −1.15100 | ||||||||
\(688\) | −6.66048e20 | + | 7.10181e20i | −0.348011 | + | 0.371070i | ||||
\(689\) | −3.96882e19 | −0.0205124 | ||||||||
\(690\) | −8.48509e20 | − | 1.24811e21i | −0.433799 | − | 0.638095i | ||||
\(691\) | − | 2.17146e21i | − | 1.09816i | −0.835768 | − | 0.549082i | \(-0.814977\pi\) | ||
0.835768 | − | 0.549082i | \(-0.185023\pi\) | |||||||
\(692\) | −8.47150e20 | − | 3.35097e20i | −0.423804 | − | 0.167639i | ||||
\(693\) | 4.73615e18i | 0.00234383i | ||||||||
\(694\) | 3.93273e20 | − | 2.67360e20i | 0.192530 | − | 0.130888i | ||||
\(695\) | 9.55056e20 | 0.462533 | ||||||||
\(696\) | 3.19656e21 | − | 7.16129e20i | 1.53149 | − | 0.343101i | ||||
\(697\) | 1.14860e21 | 0.544405 | ||||||||
\(698\) | −1.95888e21 | + | 1.33171e21i | −0.918525 | + | 0.624444i | ||||
\(699\) | − | 1.85001e21i | − | 0.858212i | ||||||
\(700\) | 4.38943e19 | − | 1.10968e20i | 0.0201452 | − | 0.0509287i | ||||
\(701\) | − | 2.23982e21i | − | 1.01702i | −0.861056 | − | 0.508509i | \(-0.830197\pi\) | ||
0.861056 | − | 0.508509i | \(-0.169803\pi\) | |||||||
\(702\) | 4.10488e20 | + | 6.03807e20i | 0.184405 | + | 0.271250i | ||||
\(703\) | −1.87255e21 | −0.832280 | ||||||||
\(704\) | −3.06731e20 | − | 6.50214e20i | −0.134885 | − | 0.285931i | ||||
\(705\) | −1.00230e21 | −0.436095 | ||||||||
\(706\) | −3.50202e20 | − | 5.15130e20i | −0.150759 | − | 0.221759i | ||||
\(707\) | 2.29495e20i | 0.0977523i | ||||||||
\(708\) | −1.13394e21 | + | 2.86669e21i | −0.477904 | + | 1.20818i | ||||
\(709\) | − | 2.31658e20i | − | 0.0966052i | −0.998833 | − | 0.0483026i | \(-0.984619\pi\) | ||
0.998833 | − | 0.0483026i | \(-0.0153812\pi\) | |||||||
\(710\) | −1.42029e21 | + | 9.65561e20i | −0.586057 | + | 0.398421i | ||||
\(711\) | 1.53146e20 | 0.0625293 | ||||||||
\(712\) | −5.09379e20 | + | 1.14117e20i | −0.205798 | + | 0.0461052i | ||||
\(713\) | −1.97672e21 | −0.790266 | ||||||||
\(714\) | −2.23956e20 | + | 1.52253e20i | −0.0885984 | + | 0.0602322i | ||||
\(715\) | − | 1.19852e20i | − | 0.0469192i | ||||||
\(716\) | −3.33926e20 | − | 1.32087e20i | −0.129361 | − | 0.0511696i | ||||
\(717\) | 2.90057e21i | 1.11196i | ||||||||
\(718\) | 8.95112e19 | + | 1.31666e20i | 0.0339581 | + | 0.0499507i | ||||
\(719\) | −3.78747e21 | −1.42195 | −0.710973 | − | 0.703220i | \(-0.751745\pi\) | ||||
−0.710973 | + | 0.703220i | \(0.751745\pi\) | |||||||
\(720\) | 9.15135e19 | − | 9.75772e19i | 0.0340010 | − | 0.0362539i | ||||
\(721\) | −7.30634e19 | −0.0268649 | ||||||||
\(722\) | −1.64579e20 | − | 2.42087e20i | −0.0598888 | − | 0.0880934i | ||||
\(723\) | − | 1.81752e21i | − | 0.654547i | ||||||
\(724\) | 3.61171e21 | + | 1.42864e21i | 1.28728 | + | 0.509194i | ||||
\(725\) | 3.65086e21i | 1.28783i | ||||||||
\(726\) | −2.01690e21 | + | 1.37116e21i | −0.704141 | + | 0.478699i | ||||
\(727\) | 4.78780e21 | 1.65435 | 0.827176 | − | 0.561943i | \(-0.189946\pi\) | ||||
0.827176 | + | 0.561943i | \(0.189946\pi\) | |||||||
\(728\) | −1.41503e19 | − | 6.31624e19i | −0.00483929 | − | 0.0216010i | ||||
\(729\) | −3.19608e21 | −1.08183 | ||||||||
\(730\) | 7.42066e19 | − | 5.04481e19i | 0.0248611 | − | 0.0169014i | ||||
\(731\) | 2.46249e21i | 0.816573i | ||||||||
\(732\) | 1.55087e21 | − | 3.92072e21i | 0.509029 | − | 1.28686i | ||||
\(733\) | − | 8.55865e20i | − | 0.278051i | −0.990289 | − | 0.139026i | \(-0.955603\pi\) | ||
0.990289 | − | 0.139026i | \(-0.0443971\pi\) | |||||||
\(734\) | 1.71804e21 | + | 2.52715e21i | 0.552476 | + | 0.812664i | ||||
\(735\) | 1.39880e21 | 0.445246 | ||||||||
\(736\) | 8.51788e20 | − | 5.40601e21i | 0.268379 | − | 1.70331i | ||||
\(737\) | −3.69171e20 | −0.115139 | ||||||||
\(738\) | −6.49006e19 | − | 9.54655e19i | −0.0200367 | − | 0.0294730i | ||||
\(739\) | − | 2.01440e21i | − | 0.615620i | −0.951448 | − | 0.307810i | \(-0.900404\pi\) | ||
0.951448 | − | 0.307810i | \(-0.0995961\pi\) | |||||||
\(740\) | 4.55035e20 | − | 1.15036e21i | 0.137660 | − | 0.348014i | ||||
\(741\) | 1.04254e21i | 0.312217i | ||||||||
\(742\) | −1.28673e19 | + | 8.74762e18i | −0.00381468 | + | 0.00259335i | ||||
\(743\) | 2.89435e21 | 0.849445 | 0.424722 | − | 0.905324i | \(-0.360372\pi\) | ||||
0.424722 | + | 0.905324i | \(0.360372\pi\) | |||||||
\(744\) | 3.26227e20 | + | 1.45617e21i | 0.0947813 | + | 0.423072i | ||||
\(745\) | 2.01653e21 | 0.580005 | ||||||||
\(746\) | 3.74557e21 | − | 2.54636e21i | 1.06654 | − | 0.725068i | ||||
\(747\) | − | 2.02509e20i | − | 0.0570872i | ||||||
\(748\) | −1.69082e21 | − | 6.68816e20i | −0.471884 | − | 0.186657i | ||||
\(749\) | − | 4.16181e20i | − | 0.114992i | ||||||
\(750\) | −1.63356e21 | − | 2.40288e21i | −0.446865 | − | 0.657315i | ||||
\(751\) | 5.60310e21 | 1.51750 | 0.758750 | − | 0.651382i | \(-0.225811\pi\) | ||||
0.758750 | + | 0.651382i | \(0.225811\pi\) | |||||||
\(752\) | −2.65105e21 | − | 2.48630e21i | −0.710859 | − | 0.666685i | ||||
\(753\) | 3.33457e21 | 0.885274 | ||||||||
\(754\) | 1.11334e21 | + | 1.63766e21i | 0.292645 | + | 0.430466i | ||||
\(755\) | 1.93646e21i | 0.503971i | ||||||||
\(756\) | 2.66168e20 | + | 1.05285e20i | 0.0685871 | + | 0.0271301i | ||||
\(757\) | 5.61932e21i | 1.43372i | 0.697216 | + | 0.716861i | \(0.254422\pi\) | ||||
−0.697216 | + | 0.716861i | \(0.745578\pi\) | |||||||
\(758\) | −3.70732e21 | + | 2.52036e21i | −0.936571 | + | 0.636713i | ||||
\(759\) | 2.06166e21 | 0.515707 | ||||||||
\(760\) | 1.96030e21 | − | 4.39168e20i | 0.485535 | − | 0.108775i | ||||
\(761\) | −1.48465e21 | −0.364115 | −0.182057 | − | 0.983288i | \(-0.558276\pi\) | ||||
−0.182057 | + | 0.983288i | \(0.558276\pi\) | |||||||
\(762\) | −3.05107e21 | + | 2.07422e21i | −0.740952 | + | 0.503724i | ||||
\(763\) | − | 4.37610e19i | − | 0.0105233i | ||||||
\(764\) | 4.80380e20 | − | 1.21444e21i | 0.114389 | − | 0.289185i | ||||
\(765\) | − | 3.38341e20i | − | 0.0797799i | ||||||
\(766\) | 2.07784e21 | + | 3.05640e21i | 0.485173 | + | 0.713664i | ||||
\(767\) | −1.86361e21 | −0.430912 | ||||||||
\(768\) | −4.12296e21 | + | 2.64700e20i | −0.944060 | + | 0.0606102i | ||||
\(769\) | −3.53626e21 | −0.801855 | −0.400928 | − | 0.916110i | \(-0.631312\pi\) | ||||
−0.400928 | + | 0.916110i | \(0.631312\pi\) | |||||||
\(770\) | −2.64164e19 | − | 3.88572e19i | −0.00593190 | − | 0.00872552i | ||||
\(771\) | 3.74539e20i | 0.0832893i | ||||||||
\(772\) | 1.54678e21 | − | 3.91038e21i | 0.340642 | − | 0.861170i | ||||
\(773\) | 3.96702e21i | 0.865204i | 0.901585 | + | 0.432602i | \(0.142405\pi\) | ||||
−0.901585 | + | 0.432602i | \(0.857595\pi\) | |||||||
\(774\) | 2.04670e20 | − | 1.39141e20i | 0.0442076 | − | 0.0300538i | ||||
\(775\) | −1.66312e21 | −0.355763 | ||||||||
\(776\) | −7.04380e21 | + | 1.57803e21i | −1.49226 | + | 0.334312i | ||||
\(777\) | 2.51688e20 | 0.0528087 | ||||||||
\(778\) | 1.38967e21 | − | 9.44746e20i | 0.288779 | − | 0.196322i | ||||
\(779\) | − | 1.73350e21i | − | 0.356774i | ||||||
\(780\) | −6.40463e20 | − | 2.53340e20i | −0.130552 | − | 0.0516409i | ||||
\(781\) | − | 2.34607e21i | − | 0.473650i | ||||||
\(782\) | −7.78181e21 | − | 1.14466e22i | −1.55607 | − | 2.28890i | ||||
\(783\) | −8.75695e21 | −1.73436 | ||||||||
\(784\) | 3.69976e21 | + | 3.46984e21i | 0.725776 | + | 0.680674i | ||||
\(785\) | −3.01221e21 | −0.585280 | ||||||||
\(786\) | 2.44164e21 | + | 3.59153e21i | 0.469909 | + | 0.691211i | ||||
\(787\) | − | 5.35959e19i | − | 0.0102170i | −0.999987 | − | 0.00510848i | \(-0.998374\pi\) | ||
0.999987 | − | 0.00510848i | \(-0.00162609\pi\) | |||||||
\(788\) | 8.97551e21 | + | 3.55033e21i | 1.69478 | + | 0.670381i | ||||
\(789\) | − | 6.52117e21i | − | 1.21969i | ||||||
\(790\) | −1.25647e21 | + | 8.54189e20i | −0.232781 | + | 0.158252i | ||||
\(791\) | 3.22662e20 | 0.0592139 | ||||||||
\(792\) | 3.99500e19 | + | 1.78323e20i | 0.00726236 | + | 0.0324167i | ||||
\(793\) | 2.54882e21 | 0.458976 | ||||||||
\(794\) | 3.04566e21 | − | 2.07054e21i | 0.543285 | − | 0.369343i | ||||
\(795\) | 1.65560e20i | 0.0292550i | ||||||||
\(796\) | −1.19459e21 | + | 3.02003e21i | −0.209109 | + | 0.528644i | ||||
\(797\) | 8.79737e20i | 0.152551i | 0.997087 | + | 0.0762755i | \(0.0243029\pi\) | ||||
−0.997087 | + | 0.0762755i | \(0.975697\pi\) | |||||||
\(798\) | 2.29785e20 | + | 3.38002e20i | 0.0394729 | + | 0.0580627i | ||||
\(799\) | −9.19229e21 | −1.56431 | ||||||||
\(800\) | 7.16656e20 | − | 4.54837e21i | 0.120819 | − | 0.766797i | ||||
\(801\) | 1.32687e20 | 0.0221608 | ||||||||
\(802\) | 1.25887e21 | + | 1.85173e21i | 0.208292 | + | 0.306386i | ||||
\(803\) | 1.22576e20i | 0.0200927i | ||||||||
\(804\) | −7.80341e20 | + | 1.97276e21i | −0.126726 | + | 0.320372i | ||||
\(805\) | − | 3.57672e20i | − | 0.0575461i | ||||||
\(806\) | −7.46023e20 | + | 5.07171e20i | −0.118916 | + | 0.0808429i | ||||
\(807\) | 1.16375e22 | 1.83784 | ||||||||
\(808\) | 1.93581e21 | + | 8.64082e21i | 0.302885 | + | 1.35198i | ||||
\(809\) | 4.57183e21 | 0.708723 | 0.354361 | − | 0.935109i | \(-0.384698\pi\) | ||||
0.354361 | + | 0.935109i | \(0.384698\pi\) | |||||||
\(810\) | 2.25116e21 | − | 1.53041e21i | 0.345755 | − | 0.235056i | ||||
\(811\) | − | 4.73117e21i | − | 0.719967i | −0.932959 | − | 0.359984i | \(-0.882782\pi\) | ||
0.932959 | − | 0.359984i | \(-0.117218\pi\) | |||||||
\(812\) | 7.21908e20 | + | 2.85556e20i | 0.108846 | + | 0.0430548i | ||||
\(813\) | − | 9.53916e21i | − | 1.42505i | ||||||
\(814\) | 9.50097e20 | + | 1.39754e21i | 0.140632 | + | 0.206863i | ||||
\(815\) | −5.13764e21 | −0.753498 | ||||||||
\(816\) | −7.14800e21 | + | 7.62163e21i | −1.03874 | + | 1.10757i | ||||
\(817\) | 3.71648e21 | 0.535138 | ||||||||
\(818\) | 1.56278e20 | + | 2.29877e20i | 0.0222971 | + | 0.0327978i | ||||
\(819\) | 1.64531e19i | 0.00232604i | ||||||||
\(820\) | 1.06494e21 | + | 4.21244e20i | 0.149183 | + | 0.0590106i | ||||
\(821\) | − | 6.87046e21i | − | 0.953701i | −0.878984 | − | 0.476851i | \(-0.841778\pi\) | ||
0.878984 | − | 0.476851i | \(-0.158222\pi\) | |||||||
\(822\) | 7.11800e21 | − | 4.83905e21i | 0.979082 | − | 0.665613i | ||||
\(823\) | 2.19064e21 | 0.298588 | 0.149294 | − | 0.988793i | \(-0.452300\pi\) | ||||
0.149294 | + | 0.988793i | \(0.452300\pi\) | |||||||
\(824\) | −2.75095e21 | + | 6.16298e20i | −0.371559 | + | 0.0832409i | ||||
\(825\) | 1.73459e21 | 0.232162 | ||||||||
\(826\) | −6.04199e20 | + | 4.10754e20i | −0.0801363 | + | 0.0544794i | ||||
\(827\) | 1.22814e22i | 1.61420i | 0.590416 | + | 0.807099i | \(0.298964\pi\) | ||||
−0.590416 | + | 0.807099i | \(0.701036\pi\) | |||||||
\(828\) | −5.11681e20 | + | 1.29357e21i | −0.0666456 | + | 0.168485i | ||||
\(829\) | 1.90989e21i | 0.246518i | 0.992375 | + | 0.123259i | \(0.0393347\pi\) | ||||
−0.992375 | + | 0.123259i | \(0.960665\pi\) | |||||||
\(830\) | 1.12951e21 | + | 1.66146e21i | 0.144479 | + | 0.212522i | ||||
\(831\) | −7.34972e21 | −0.931673 | ||||||||
\(832\) | −1.06556e21 | − | 2.25880e21i | −0.133861 | − | 0.283761i | ||||
\(833\) | 1.28286e22 | 1.59714 | ||||||||
\(834\) | 4.21511e21 | + | 6.20022e21i | 0.520073 | + | 0.765000i | ||||
\(835\) | − | 3.60451e20i | − | 0.0440755i | ||||||
\(836\) | −1.00940e21 | + | 2.55184e21i | −0.122325 | + | 0.309248i | ||||
\(837\) | − | 3.98916e21i | − | 0.479116i | ||||||
\(838\) | −4.59683e21 | + | 3.12508e21i | −0.547178 | + | 0.371990i | ||||
\(839\) | 6.37998e21 | 0.752669 | 0.376335 | − | 0.926484i | \(-0.377184\pi\) | ||||
0.376335 | + | 0.926484i | \(0.377184\pi\) | |||||||
\(840\) | −2.63482e20 | + | 5.90282e19i | −0.0308075 | + | 0.00690185i | ||||
\(841\) | −1.51216e22 | −1.75238 | ||||||||
\(842\) | 1.18017e22 | − | 8.02317e21i | 1.35551 | − | 0.921521i | ||||
\(843\) | − | 4.52655e19i | − | 0.00515300i | ||||||
\(844\) | 2.64960e21 | + | 1.04807e21i | 0.298959 | + | 0.118255i | ||||
\(845\) | 3.81325e21i | 0.426451i | ||||||||
\(846\) | 5.19404e20 | + | 7.64016e20i | 0.0575741 | + | 0.0846885i | ||||
\(847\) | −5.77984e20 | −0.0635024 | ||||||||
\(848\) | −4.10685e20 | + | 4.37898e20i | −0.0447240 | + | 0.0476874i | ||||
\(849\) | −9.66686e21 | −1.04346 | ||||||||
\(850\) | −6.54726e21 | − | 9.63069e21i | −0.700516 | − | 1.03042i | ||||
\(851\) | 1.28641e22i | 1.36429i | ||||||||
\(852\) | −1.25368e22 | − | 4.95904e21i | −1.31793 | − | 0.521315i | ||||
\(853\) | − | 2.88561e20i | − | 0.0300690i | −0.999887 | − | 0.0150345i | \(-0.995214\pi\) | ||
0.999887 | − | 0.0150345i | \(-0.00478582\pi\) | |||||||
\(854\) | 8.26351e20 | − | 5.61781e20i | 0.0853553 | − | 0.0580274i | ||||
\(855\) | −5.10635e20 | −0.0522835 | ||||||||
\(856\) | −3.51053e21 | − | 1.56698e22i | −0.356303 | − | 1.59042i | ||||
\(857\) | 9.17156e21 | 0.922757 | 0.461378 | − | 0.887203i | \(-0.347355\pi\) | ||||
0.461378 | + | 0.887203i | \(0.347355\pi\) | |||||||
\(858\) | 7.78080e20 | − | 5.28965e20i | 0.0776014 | − | 0.0527560i | ||||
\(859\) | − | 1.00522e22i | − | 0.993834i | −0.867798 | − | 0.496917i | \(-0.834465\pi\) | ||
0.867798 | − | 0.496917i | \(-0.165535\pi\) | |||||||
\(860\) | −9.03112e20 | + | 2.28314e21i | −0.0885122 | + | 0.223766i | ||||
\(861\) | 2.32998e20i | 0.0226375i | ||||||||
\(862\) | 5.58504e21 | + | 8.21530e21i | 0.537925 | + | 0.791260i | ||||
\(863\) | −1.87741e21 | −0.179258 | −0.0896288 | − | 0.995975i | \(-0.528568\pi\) | ||||
−0.0896288 | + | 0.995975i | \(0.528568\pi\) | |||||||
\(864\) | 1.09097e22 | + | 1.71897e21i | 1.03267 | + | 0.162710i | ||||
\(865\) | −2.29735e21 | −0.215579 | ||||||||
\(866\) | −9.17681e21 | − | 1.34986e22i | −0.853704 | − | 1.25575i | ||||
\(867\) | 1.61700e22i | 1.49131i | ||||||||
\(868\) | −1.30083e20 | + | 3.28859e20i | −0.0118938 | + | 0.0300685i | ||||
\(869\) | − | 2.07546e21i | − | 0.188133i | ||||||
\(870\) | 6.83150e21 | − | 4.64429e21i | 0.613934 | − | 0.417373i | ||||
\(871\) | −1.28247e21 | −0.114265 | ||||||||
\(872\) | −3.69128e20 | − | 1.64766e21i | −0.0326065 | − | 0.145544i | ||||
\(873\) | 1.83483e21 | 0.160690 | ||||||||
\(874\) | −1.72757e22 | + | 1.17446e22i | −1.50003 | + | 1.01977i | ||||
\(875\) | − | 6.88596e20i | − | 0.0592794i | ||||||
\(876\) | 6.55018e20 | + | 2.59097e20i | 0.0559078 | + | 0.0221147i | ||||
\(877\) | 1.36577e22i | 1.15580i | 0.816109 | + | 0.577898i | \(0.196127\pi\) | ||||
−0.816109 | + | 0.577898i | \(0.803873\pi\) | |||||||
\(878\) | −1.00602e22 | − | 1.47980e22i | −0.844104 | − | 1.24163i | ||||
\(879\) | 9.44893e20 | 0.0786079 | ||||||||
\(880\) | −1.32238e21 | − | 1.24021e21i | −0.109078 | − | 0.102300i | ||||
\(881\) | −3.72174e21 | −0.304387 | −0.152194 | − | 0.988351i | \(-0.548634\pi\) | ||||
−0.152194 | + | 0.988351i | \(0.548634\pi\) | |||||||
\(882\) | −7.24871e20 | − | 1.06625e21i | −0.0587822 | − | 0.0864656i | ||||
\(883\) | − | 2.07606e22i | − | 1.66930i | −0.550780 | − | 0.834651i | \(-0.685670\pi\) | ||
0.550780 | − | 0.834651i | \(-0.314330\pi\) | |||||||
\(884\) | −5.87379e21 | − | 2.32342e21i | −0.468302 | − | 0.185240i | ||||
\(885\) | 7.77404e21i | 0.614571i | ||||||||
\(886\) | −8.91037e21 | + | 6.05757e21i | −0.698462 | + | 0.474838i | ||||
\(887\) | 1.13338e22 | 0.880944 | 0.440472 | − | 0.897766i | \(-0.354811\pi\) | ||||
0.440472 | + | 0.897766i | \(0.354811\pi\) | |||||||
\(888\) | 9.47644e21 | − | 2.12302e21i | 0.730378 | − | 0.163628i | ||||
\(889\) | −8.74346e20 | −0.0668221 | ||||||||
\(890\) | −1.08862e21 | + | 7.40078e20i | −0.0824992 | + | 0.0560857i | ||||
\(891\) | 3.71851e21i | 0.279439i | ||||||||
\(892\) | 1.71286e21 | − | 4.33024e21i | 0.127640 | − | 0.322683i | ||||
\(893\) | 1.38733e22i | 1.02517i | ||||||||
\(894\) | 8.89989e21 | + | 1.30913e22i | 0.652158 | + | 0.959291i | ||||
\(895\) | −9.05557e20 | −0.0658026 | ||||||||
\(896\) | −8.43324e20 | − | 4.97465e20i | −0.0607693 | − | 0.0358469i | ||||
\(897\) | 7.16205e21 | 0.511793 | ||||||||
\(898\) | 1.91162e20 | + | 2.81189e20i | 0.0135465 | + | 0.0199262i | ||||
\(899\) | − | 1.08195e22i | − | 0.760343i | ||||||
\(900\) | −4.30505e20 | + | 1.08835e21i | −0.0300026 | + | 0.0758490i | ||||
\(901\) | 1.51837e21i | 0.104940i | ||||||||
\(902\) | −1.29376e21 | + | 8.79544e20i | −0.0886760 | + | 0.0602849i | ||||
\(903\) | −4.99528e20 | −0.0339549 | ||||||||
\(904\) | 1.21487e22 | − | 2.72168e21i | 0.818966 | − | 0.183474i | ||||
\(905\) | 9.79442e21 | 0.654808 | ||||||||
\(906\) | −1.25715e22 | + | 8.54650e21i | −0.833536 | + | 0.566666i | ||||
\(907\) | − | 1.97341e21i | − | 0.129766i | −0.997893 | − | 0.0648832i | \(-0.979333\pi\) | ||
0.997893 | − | 0.0648832i | \(-0.0206675\pi\) | |||||||
\(908\) | 1.35061e22 | + | 5.34246e21i | 0.880821 | + | 0.348415i | ||||
\(909\) | − | 2.25083e21i | − | 0.145584i | ||||||
\(910\) | −9.17688e19 | − | 1.34987e20i | −0.00588687 | − | 0.00865928i | ||||
\(911\) | −1.04284e22 | −0.663484 | −0.331742 | − | 0.943370i | \(-0.607636\pi\) | ||||
−0.331742 | + | 0.943370i | \(0.607636\pi\) | |||||||
\(912\) | 1.15028e22 | + | 1.07880e22i | 0.725843 | + | 0.680737i | ||||
\(913\) | −2.74443e21 | −0.171760 | ||||||||
\(914\) | 1.04193e22 | + | 1.53263e22i | 0.646761 | + | 0.951352i | ||||
\(915\) | − | 1.06324e22i | − | 0.654596i | ||||||
\(916\) | −1.85281e22 | − | 7.32894e21i | −1.13140 | − | 0.447533i | ||||
\(917\) | 1.02923e21i | 0.0623363i | ||||||||
\(918\) | 2.31002e22 | − | 1.57043e22i | 1.38770 | − | 0.943404i | ||||
\(919\) | 2.97590e22 | 1.77318 | 0.886589 | − | 0.462559i | \(-0.153069\pi\) | ||||
0.886589 | + | 0.462559i | \(0.153069\pi\) | |||||||
\(920\) | −3.01700e21 | − | 1.34669e22i | −0.178306 | − | 0.795900i | ||||
\(921\) | −1.42054e22 | −0.832736 | ||||||||
\(922\) | −1.63905e22 | + | 1.11428e22i | −0.953039 | + | 0.647908i | ||||
\(923\) | − | 8.15006e21i | − | 0.470055i | ||||||
\(924\) | 1.35672e20 | − | 3.42991e20i | 0.00776161 | − | 0.0196220i | ||||
\(925\) | 1.08233e22i | 0.614179i | ||||||||
\(926\) | 1.63686e22 | + | 2.40773e22i | 0.921357 | + | 1.35527i | ||||
\(927\) | 7.16589e20 | 0.0400103 | ||||||||
\(928\) | 2.95896e22 | + | 4.66224e21i | 1.63881 | + | 0.258217i | ||||
\(929\) | −1.15495e22 | −0.634521 | −0.317261 | − | 0.948338i | \(-0.602763\pi\) | ||||
−0.317261 | + | 0.948338i | \(0.602763\pi\) | |||||||
\(930\) | 2.11567e21 | + | 3.11204e21i | 0.115299 | + | 0.169599i | ||||
\(931\) | − | 1.93613e22i | − | 1.04668i | ||||||
\(932\) | 6.22249e21 | − | 1.57309e22i | 0.333691 | − | 0.843598i | ||||
\(933\) | − | 2.82071e22i | − | 1.50053i | ||||||
\(934\) | −7.04930e20 | + | 4.79235e20i | −0.0372001 | + | 0.0252899i | ||||
\(935\) | −4.58525e21 | −0.240036 | ||||||||
\(936\) | 1.38783e20 | + | 6.19482e20i | 0.00720723 | + | 0.0321707i | ||||
\(937\) | −2.26316e22 | −1.16592 | −0.582958 | − | 0.812502i | \(-0.698105\pi\) | ||||
−0.582958 | + | 0.812502i | \(0.698105\pi\) | |||||||
\(938\) | −4.15790e20 | + | 2.82668e20i | −0.0212497 | + | 0.0144462i | ||||
\(939\) | 3.11944e20i | 0.0158156i | ||||||||
\(940\) | −8.52277e21 | − | 3.37124e21i | −0.428669 | − | 0.169563i | ||||
\(941\) | − | 1.06350e22i | − | 0.530656i | −0.964158 | − | 0.265328i | \(-0.914520\pi\) | ||
0.964158 | − | 0.265328i | \(-0.0854803\pi\) | |||||||
\(942\) | −1.32943e22 | − | 1.95553e22i | −0.658089 | − | 0.968015i | ||||
\(943\) | −1.19088e22 | −0.584831 | ||||||||
\(944\) | −1.92842e22 | + | 2.05620e22i | −0.939533 | + | 1.00179i | ||||
\(945\) | 7.21808e20 | 0.0348886 | ||||||||
\(946\) | −1.88567e21 | − | 2.77372e21i | −0.0904235 | − | 0.133008i | ||||
\(947\) | 2.15212e22i | 1.02386i | 0.859026 | + | 0.511932i | \(0.171070\pi\) | ||||
−0.859026 | + | 0.511932i | \(0.828930\pi\) | |||||||
\(948\) | −1.10908e22 | − | 4.38704e21i | −0.523479 | − | 0.207066i | ||||
\(949\) | 4.25820e20i | 0.0199402i | ||||||||
\(950\) | −1.45349e22 | + | 9.88135e21i | −0.675284 | + | 0.459081i | ||||
\(951\) | −6.09295e21 | −0.280850 | ||||||||
\(952\) | −2.41644e21 | + | 5.41358e20i | −0.110509 | + | 0.0247575i | ||||
\(953\) | −9.29601e21 | −0.421794 | −0.210897 | − | 0.977508i | \(-0.567638\pi\) | ||||
−0.210897 | + | 0.977508i | \(0.567638\pi\) | |||||||
\(954\) | 1.26199e20 | − | 8.57946e19i | 0.00568126 | − | 0.00386231i | ||||
\(955\) | − | 3.29337e21i | − | 0.147101i | ||||||
\(956\) | −9.75607e21 | + | 2.46641e22i | −0.432355 | + | 1.09303i | ||||
\(957\) | 1.12844e22i | 0.496181i | ||||||||
\(958\) | 1.49427e22 | + | 2.19799e22i | 0.651909 | + | 0.958925i | ||||
\(959\) | 2.03981e21 | 0.0882977 | ||||||||
\(960\) | −9.42259e21 | + | 4.44500e21i | −0.404702 | + | 0.190914i | ||||
\(961\) | −1.85365e22 | −0.789956 | ||||||||
\(962\) | 3.30057e21 | + | 4.85497e21i | 0.139565 | + | 0.205293i | ||||
\(963\) | 4.08181e21i | 0.171260i | ||||||||
\(964\) | 6.11321e21 | − | 1.54547e22i | 0.254502 | − | 0.643401i | ||||
\(965\) | − | 1.06044e22i | − | 0.438056i | ||||||
\(966\) | 2.32201e21 | − | 1.57858e21i | 0.0951776 | − | 0.0647049i | ||||
\(967\) | 1.70383e22 | 0.692992 | 0.346496 | − | 0.938051i | \(-0.387371\pi\) | ||||
0.346496 | + | 0.938051i | \(0.387371\pi\) | |||||||
\(968\) | −2.17619e22 | + | 4.87535e21i | −0.878279 | + | 0.196762i | ||||
\(969\) | 3.98851e22 | 1.59728 | ||||||||
\(970\) | −1.50536e22 | + | 1.02339e22i | −0.598209 | + | 0.406682i | ||||
\(971\) | 1.90042e22i | 0.749386i | 0.927149 | + | 0.374693i | \(0.122252\pi\) | ||||
−0.927149 | + | 0.374693i | \(0.877748\pi\) | |||||||
\(972\) | −4.97281e21 | − | 1.96703e21i | −0.194583 | − | 0.0769687i | ||||
\(973\) | 1.77680e21i | 0.0689909i | ||||||||
\(974\) | −1.96840e22 | − | 2.89542e22i | −0.758441 | − | 1.11563i | ||||
\(975\) | 6.02583e21 | 0.230400 | ||||||||
\(976\) | 2.63747e22 | − | 2.81223e22i | 1.00072 | − | 1.06703i | ||||
\(977\) | 2.36787e22 | 0.891556 | 0.445778 | − | 0.895144i | \(-0.352927\pi\) | ||||
0.445778 | + | 0.895144i | \(0.352927\pi\) | |||||||
\(978\) | −2.26749e22 | − | 3.33536e22i | −0.847234 | − | 1.24624i | ||||
\(979\) | − | 1.79820e21i | − | 0.0666757i | ||||||
\(980\) | 1.18942e22 | + | 4.70485e21i | 0.437664 | + | 0.173121i | ||||
\(981\) | 4.29197e20i | 0.0156725i | ||||||||
\(982\) | 2.55713e22 | − | 1.73842e22i | 0.926652 | − | 0.629969i | ||||
\(983\) | −4.28171e22 | −1.53981 | −0.769903 | − | 0.638161i | \(-0.779695\pi\) | ||||
−0.769903 | + | 0.638161i | \(0.779695\pi\) | |||||||
\(984\) | 1.96537e21 | + | 8.77273e21i | 0.0701423 | + | 0.313092i | ||||
\(985\) | 2.43402e22 | 0.862091 | ||||||||
\(986\) | 6.26529e22 | − | 4.25935e22i | 2.20224 | − | 1.49715i | ||||
\(987\) | − | 1.86470e21i | − | 0.0650474i | ||||||
\(988\) | −3.50658e21 | + | 8.86491e21i | −0.121397 | + | 0.306900i | ||||
\(989\) | − | 2.55315e22i | − | 0.877210i | ||||||
\(990\) | 2.59086e20 | + | 3.81102e20i | 0.00883447 | + | 0.0129950i | ||||
\(991\) | 1.02666e22 | 0.347435 | 0.173718 | − | 0.984795i | \(-0.444422\pi\) | ||||
0.173718 | + | 0.984795i | \(0.444422\pi\) | |||||||
\(992\) | −2.12384e21 | + | 1.34793e22i | −0.0713321 | + | 0.452720i | ||||
\(993\) | 3.24573e22 | 1.08192 | ||||||||
\(994\) | −1.79634e21 | − | 2.64233e21i | −0.0594280 | − | 0.0874156i | ||||
\(995\) | 8.18987e21i | 0.268908i | ||||||||
\(996\) | −5.80109e21 | + | 1.46656e22i | −0.189045 | + | 0.477920i | ||||
\(997\) | 5.17267e22i | 1.67302i | 0.547951 | + | 0.836511i | \(0.315408\pi\) | ||||
−0.547951 | + | 0.836511i | \(0.684592\pi\) | |||||||
\(998\) | −9.84711e20 | + | 6.69440e20i | −0.0316104 | + | 0.0214898i | ||||
\(999\) | −2.59607e22 | −0.827131 |
(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 | 8.16.b.a.5.10 | yes | 14 | |
3.2 | odd | 2 | 72.16.d.b.37.5 | 14 | |||
4.3 | odd | 2 | 32.16.b.a.17.4 | 14 | |||
8.3 | odd | 2 | 32.16.b.a.17.11 | 14 | |||
8.5 | even | 2 | inner | 8.16.b.a.5.9 | ✓ | 14 | |
24.5 | odd | 2 | 72.16.d.b.37.6 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.16.b.a.5.9 | ✓ | 14 | 8.5 | even | 2 | inner | |
8.16.b.a.5.10 | yes | 14 | 1.1 | even | 1 | trivial | |
32.16.b.a.17.4 | 14 | 4.3 | odd | 2 | |||
32.16.b.a.17.11 | 14 | 8.3 | odd | 2 | |||
72.16.d.b.37.5 | 14 | 3.2 | odd | 2 | |||
72.16.d.b.37.6 | 14 | 24.5 | odd | 2 |