Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,9,Mod(19,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.19");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.n (of order \(6\), degree \(2\), 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: | \(51.3297048677\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} - 26382 x^{18} + 177344 x^{17} + 298653216 x^{16} - 1823810808 x^{15} + \cdots + 42\!\cdots\!32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{40}\cdot 3^{18}\cdot 7^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 73.4 | ||
Root | \(-63.1006 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.73 |
Dual form | 126.9.n.d.19.4 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.65685 | − | 9.79796i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −64.0000 | + | 110.851i | −0.250000 | + | 0.433013i | ||||
\(5\) | 664.367 | − | 383.572i | 1.06299 | − | 0.613716i | 0.136730 | − | 0.990608i | \(-0.456341\pi\) |
0.926257 | + | 0.376893i | \(0.123008\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1667.57 | − | 1727.43i | 0.694531 | − | 0.719463i | ||||
\(8\) | 1448.15 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7516.45 | − | 4339.62i | −0.751645 | − | 0.433962i | ||||
\(11\) | 2523.72 | − | 4371.21i | 0.172374 | − | 0.298560i | −0.766876 | − | 0.641796i | \(-0.778190\pi\) |
0.939249 | + | 0.343236i | \(0.111523\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 28279.2i | − | 0.990133i | −0.868855 | − | 0.495066i | \(-0.835144\pi\) | ||
0.868855 | − | 0.495066i | \(-0.164856\pi\) | |||||||
\(14\) | −26358.5 | − | 6566.95i | −0.686133 | − | 0.170943i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8192.00 | − | 14189.0i | −0.125000 | − | 0.216506i | ||||
\(17\) | −13520.1 | − | 7805.85i | −0.161877 | − | 0.0934598i | 0.416873 | − | 0.908965i | \(-0.363126\pi\) |
−0.578750 | + | 0.815505i | \(0.696459\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 107562. | − | 62100.9i | 0.825361 | − | 0.476522i | −0.0269006 | − | 0.999638i | \(-0.508564\pi\) |
0.852262 | + | 0.523116i | \(0.175230\pi\) | |||||||
\(20\) | 98194.5i | 0.613716i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −57105.3 | −0.243773 | ||||||||
\(23\) | 89789.7 | + | 155520.i | 0.320860 | + | 0.555745i | 0.980666 | − | 0.195691i | \(-0.0626949\pi\) |
−0.659806 | + | 0.751436i | \(0.729362\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 98942.8 | − | 171374.i | 0.253293 | − | 0.438717i | ||||
\(26\) | −277078. | + | 159971.i | −0.606330 | + | 0.350065i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 84763.4 | + | 295408.i | 0.137904 | + | 0.480606i | ||||
\(29\) | 71160.2 | 0.100611 | 0.0503055 | − | 0.998734i | \(-0.483981\pi\) | ||||
0.0503055 | + | 0.998734i | \(0.483981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 845366. | + | 488072.i | 0.915372 | + | 0.528490i | 0.882156 | − | 0.470958i | \(-0.156092\pi\) |
0.0332165 | + | 0.999448i | \(0.489425\pi\) | |||||||
\(32\) | −92681.9 | + | 160530.i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 176626.i | 0.132172i | ||||||||
\(35\) | 445283. | − | 1.78728e6i | 0.296732 | − | 1.19102i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 704161. | + | 1.21964e6i | 0.375720 | + | 0.650767i | 0.990435 | − | 0.137983i | \(-0.0440620\pi\) |
−0.614714 | + | 0.788750i | \(0.710729\pi\) | |||||||
\(38\) | −1.21692e6 | − | 702591.i | −0.583618 | − | 0.336952i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 962105. | − | 555472.i | 0.375822 | − | 0.216981i | ||||
\(41\) | − | 3.98966e6i | − | 1.41189i | −0.708267 | − | 0.705945i | \(-0.750523\pi\) | ||
0.708267 | − | 0.705945i | \(-0.249477\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.21621e6 | 0.648243 | 0.324121 | − | 0.946016i | \(-0.394931\pi\) | ||||
0.324121 | + | 0.946016i | \(0.394931\pi\) | |||||||
\(44\) | 323036. | + | 559515.i | 0.0861868 | + | 0.149280i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.01585e6 | − | 1.75951e6i | 0.226882 | − | 0.392971i | ||||
\(47\) | 66978.0 | − | 38669.8i | 0.0137259 | − | 0.00792465i | −0.493121 | − | 0.869961i | \(-0.664144\pi\) |
0.506847 | + | 0.862036i | \(0.330811\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −203229. | − | 5.76122e6i | −0.0352535 | − | 0.999378i | ||||
\(50\) | −2.23882e6 | −0.358211 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.13478e6 | + | 1.80987e6i | 0.428740 | + | 0.247533i | ||||
\(53\) | −3.09571e6 | + | 5.36192e6i | −0.392334 | + | 0.679543i | −0.992757 | − | 0.120140i | \(-0.961666\pi\) |
0.600423 | + | 0.799683i | \(0.294999\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.87212e6i | − | 0.423153i | ||||||
\(56\) | 2.41490e6 | − | 2.50159e6i | 0.245554 | − | 0.254369i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −402543. | − | 697225.i | −0.0355714 | − | 0.0616114i | ||||
\(59\) | −1.27750e7 | − | 7.37564e6i | −1.05427 | − | 0.608684i | −0.130429 | − | 0.991458i | \(-0.541636\pi\) |
−0.923842 | + | 0.382774i | \(0.874969\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.14523e6 | + | 1.23855e6i | −0.154937 | + | 0.0894529i | −0.575464 | − | 0.817827i | \(-0.695179\pi\) |
0.420527 | + | 0.907280i | \(0.361845\pi\) | |||||||
\(62\) | − | 1.10438e7i | − | 0.747398i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.09715e6 | 0.125000 | ||||||||
\(65\) | −1.08471e7 | − | 1.87877e7i | −0.607660 | − | 1.05250i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.79499e6 | + | 3.10901e6i | −0.0890763 | + | 0.154285i | −0.907121 | − | 0.420870i | \(-0.861725\pi\) |
0.818045 | + | 0.575155i | \(0.195058\pi\) | |||||||
\(68\) | 1.73058e6 | − | 999149.i | 0.0809385 | − | 0.0467299i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00306e7 | + | 5.74752e6i | −0.834260 | + | 0.239380i | ||||
\(71\) | −3.51834e7 | −1.38454 | −0.692268 | − | 0.721641i | \(-0.743388\pi\) | ||||
−0.692268 | + | 0.721641i | \(0.743388\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 333640. | + | 192627.i | 0.0117486 | + | 0.00678307i | 0.505863 | − | 0.862614i | \(-0.331174\pi\) |
−0.494114 | + | 0.869397i | \(0.664508\pi\) | |||||||
\(74\) | 7.96667e6 | − | 1.37987e7i | 0.265674 | − | 0.460162i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.58978e7i | 0.476522i | ||||||||
\(77\) | −3.34249e6 | − | 1.16489e7i | −0.0950839 | − | 0.331375i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.68028e7 | + | 2.91034e7i | 0.431394 | + | 0.747197i | 0.996994 | − | 0.0774833i | \(-0.0246885\pi\) |
−0.565599 | + | 0.824680i | \(0.691355\pi\) | |||||||
\(80\) | −1.08850e7 | − | 6.28445e6i | −0.265747 | − | 0.153429i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.90906e7 | + | 2.25689e7i | −0.864603 | + | 0.499179i | ||||
\(83\) | − | 7.92564e7i | − | 1.67002i | −0.550233 | − | 0.835011i | \(-0.685461\pi\) | ||
0.550233 | − | 0.835011i | \(-0.314539\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.19764e7 | −0.229431 | ||||||||
\(86\) | −1.25368e7 | − | 2.17144e7i | −0.229188 | − | 0.396966i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.65474e6 | − | 6.33019e6i | 0.0609433 | − | 0.105557i | ||||
\(89\) | −4.51130e7 | + | 2.60460e7i | −0.719021 | + | 0.415127i | −0.814392 | − | 0.580315i | \(-0.802930\pi\) |
0.0953709 | + | 0.995442i | \(0.469596\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.88503e7 | − | 4.71575e7i | −0.712364 | − | 0.687678i | ||||
\(92\) | −2.29862e7 | −0.320860 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −757770. | − | 437499.i | −0.00970568 | − | 0.00560358i | ||||
\(95\) | 4.76403e7 | − | 8.25155e7i | 0.584898 | − | 1.01307i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.44662e8i | − | 1.63406i | −0.576598 | − | 0.817028i | \(-0.695620\pi\) | ||
0.576598 | − | 0.817028i | \(-0.304380\pi\) | |||||||
\(98\) | −5.52985e7 | + | 3.45816e7i | −0.599528 | + | 0.374922i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.26647e7 | + | 2.19359e7i | 0.126647 | + | 0.219359i | ||||
\(101\) | −8.12614e7 | − | 4.69163e7i | −0.780906 | − | 0.450857i | 0.0558450 | − | 0.998439i | \(-0.482215\pi\) |
−0.836751 | + | 0.547583i | \(0.815548\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.52669e8 | + | 8.81435e7i | −1.35645 | + | 0.783144i | −0.989143 | − | 0.146958i | \(-0.953052\pi\) |
−0.367302 | + | 0.930102i | \(0.619719\pi\) | |||||||
\(104\) | − | 4.09526e7i | − | 0.350065i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.00478e7 | 0.554844 | ||||||||
\(107\) | −8.92457e7 | − | 1.54578e8i | −0.680851 | − | 1.17927i | −0.974721 | − | 0.223424i | \(-0.928277\pi\) |
0.293870 | − | 0.955845i | \(-0.405057\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.18770e8 | − | 2.05716e8i | 0.841400 | − | 1.45735i | −0.0473118 | − | 0.998880i | \(-0.515065\pi\) |
0.888712 | − | 0.458467i | \(-0.151601\pi\) | |||||||
\(110\) | −3.79389e7 | + | 2.19040e7i | −0.259127 | + | 0.149607i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.81712e7 | − | 9.50996e6i | −0.242585 | − | 0.0604375i | ||||
\(113\) | 2.19712e8 | 1.34753 | 0.673766 | − | 0.738945i | \(-0.264675\pi\) | ||||
0.673766 | + | 0.738945i | \(0.264675\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.19307e8 | + | 6.88817e7i | 0.682139 | + | 0.393833i | ||||
\(116\) | −4.55425e6 | + | 7.88820e6i | −0.0251527 | + | 0.0435658i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.66892e8i | 0.860809i | ||||||||
\(119\) | −3.60298e7 | + | 1.03383e7i | −0.179669 | + | 0.0515538i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.44411e7 | + | 1.63577e8i | 0.440575 | + | 0.763098i | ||||
\(122\) | 2.42705e7 | + | 1.40126e7i | 0.109557 | + | 0.0632527i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.08207e8 | + | 6.24732e7i | −0.457686 | + | 0.264245i | ||||
\(125\) | 1.47859e8i | 0.605631i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.52796e8 | 1.35615 | 0.678076 | − | 0.734992i | \(-0.262814\pi\) | ||||
0.678076 | + | 0.734992i | \(0.262814\pi\) | |||||||
\(128\) | −1.18633e7 | − | 2.05478e7i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.22721e8 | + | 2.12559e8i | −0.429680 | + | 0.744228i | ||||
\(131\) | 1.90353e7 | − | 1.09900e7i | 0.0646360 | − | 0.0373176i | −0.467334 | − | 0.884081i | \(-0.654785\pi\) |
0.531970 | + | 0.846763i | \(0.321452\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.20919e7 | − | 2.89363e8i | 0.230399 | − | 0.924776i | ||||
\(134\) | 4.06159e7 | 0.125973 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.95792e7 | − | 1.13041e7i | −0.0572322 | − | 0.0330430i | ||||
\(137\) | −3.05741e8 | + | 5.29559e8i | −0.867903 | + | 1.50325i | −0.00376775 | + | 0.999993i | \(0.501199\pi\) |
−0.864135 | + | 0.503259i | \(0.832134\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.49082e8i | − | 0.399360i | −0.979861 | − | 0.199680i | \(-0.936010\pi\) | ||
0.979861 | − | 0.199680i | \(-0.0639903\pi\) | |||||||
\(140\) | 1.69624e8 | + | 1.63746e8i | 0.441545 | + | 0.426244i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.99027e8 | + | 3.44725e8i | 0.489507 | + | 0.847851i | ||||
\(143\) | −1.23614e8 | − | 7.13688e7i | −0.295614 | − | 0.170673i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.72765e7 | − | 2.72951e7i | 0.106948 | − | 0.0617465i | ||||
\(146\) | − | 4.35866e6i | − | 0.00959270i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.80265e8 | −0.375720 | ||||||||
\(149\) | 3.50024e8 | + | 6.06260e8i | 0.710155 | + | 1.23002i | 0.964799 | + | 0.262990i | \(0.0847085\pi\) |
−0.254644 | + | 0.967035i | \(0.581958\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.86258e8 | − | 8.42224e8i | 0.935318 | − | 1.62002i | 0.161252 | − | 0.986913i | \(-0.448447\pi\) |
0.774066 | − | 0.633105i | \(-0.218220\pi\) | |||||||
\(152\) | 1.55766e8 | − | 8.99317e7i | 0.291809 | − | 0.168476i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.52270e7 | + | 9.86454e7i | −0.169308 | + | 0.175386i | ||||
\(155\) | 7.48843e8 | 1.29737 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.55513e7 | − | 8.97854e6i | −0.0255957 | − | 0.0147777i | 0.487148 | − | 0.873320i | \(-0.338037\pi\) |
−0.512743 | + | 0.858542i | \(0.671371\pi\) | |||||||
\(158\) | 1.90102e8 | − | 3.29267e8i | 0.305042 | − | 0.528348i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.42201e8i | 0.216981i | ||||||||
\(161\) | 4.18381e8 | + | 1.04235e8i | 0.622685 | + | 0.155136i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.50185e8 | − | 7.79744e8i | −0.637736 | − | 1.10459i | −0.985928 | − | 0.167168i | \(-0.946538\pi\) |
0.348192 | − | 0.937423i | \(-0.386796\pi\) | |||||||
\(164\) | 4.42259e8 | + | 2.55339e8i | 0.611366 | + | 0.352973i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.76551e8 | + | 4.48342e8i | −1.02268 | + | 0.590442i | ||||
\(167\) | − | 2.27161e8i | − | 0.292057i | −0.989280 | − | 0.146029i | \(-0.953351\pi\) | ||
0.989280 | − | 0.146029i | \(-0.0466492\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.60184e7 | 0.0196369 | ||||||||
\(170\) | 6.77489e7 | + | 1.17345e8i | 0.0811160 | + | 0.140497i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.41838e8 | + | 2.45670e8i | −0.162061 | + | 0.280697i | ||||
\(173\) | −2.34309e8 | + | 1.35278e8i | −0.261580 | + | 0.151023i | −0.625055 | − | 0.780581i | \(-0.714924\pi\) |
0.363475 | + | 0.931604i | \(0.381590\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.31043e8 | − | 4.56694e8i | −0.139721 | − | 0.486938i | ||||
\(176\) | −8.26973e7 | −0.0861868 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.10396e8 | + | 2.94677e8i | 0.508425 | + | 0.293539i | ||||
\(179\) | −4.41046e8 | + | 7.63914e8i | −0.429608 | + | 0.744102i | −0.996838 | − | 0.0794568i | \(-0.974681\pi\) |
0.567231 | + | 0.823559i | \(0.308015\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.95902e8i | 0.462042i | 0.972949 | + | 0.231021i | \(0.0742067\pi\) | ||||
−0.972949 | + | 0.231021i | \(0.925793\pi\) | |||||||
\(182\) | −1.85708e8 | + | 7.45396e8i | −0.169256 | + | 0.679363i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.30029e8 | + | 2.25218e8i | 0.113441 | + | 0.196486i | ||||
\(185\) | 9.35641e8 | + | 5.40193e8i | 0.798771 | + | 0.461171i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.82421e7 | + | 3.93996e7i | −0.0558067 | + | 0.0322200i | ||||
\(188\) | 9.89946e6i | 0.00792465i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.07798e9 | −0.827171 | ||||||||
\(191\) | 7.89952e8 | + | 1.36824e9i | 0.593564 | + | 1.02808i | 0.993748 | + | 0.111648i | \(0.0356129\pi\) |
−0.400184 | + | 0.916435i | \(0.631054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.26070e8 | + | 1.43079e9i | −0.595371 | + | 1.03121i | 0.398124 | + | 0.917332i | \(0.369661\pi\) |
−0.993494 | + | 0.113881i | \(0.963672\pi\) | |||||||
\(194\) | −1.41739e9 | + | 8.18331e8i | −1.00065 | + | 0.577726i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.51645e8 | + | 3.46190e8i | 0.441557 | + | 0.234579i | ||||
\(197\) | 5.40965e8 | 0.359174 | 0.179587 | − | 0.983742i | \(-0.442524\pi\) | ||||
0.179587 | + | 0.983742i | \(0.442524\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.18428e8 | − | 6.83742e7i | −0.0755163 | − | 0.0435994i | 0.461766 | − | 0.887002i | \(-0.347216\pi\) |
−0.537283 | + | 0.843402i | \(0.680549\pi\) | |||||||
\(200\) | 1.43284e8 | − | 2.48176e8i | 0.0895528 | − | 0.155110i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.06159e9i | 0.637607i | ||||||||
\(203\) | 1.18665e8 | − | 1.22924e8i | 0.0698774 | − | 0.0723859i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.53032e9 | − | 2.65060e9i | −0.866499 | − | 1.50082i | ||||
\(206\) | 1.72725e9 | + | 9.97230e8i | 0.959151 | + | 0.553766i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.01252e8 | + | 2.31663e8i | −0.214370 | + | 0.123767i | ||||
\(209\) | − | 6.26901e8i | − | 0.328560i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.90323e8 | 0.449177 | 0.224589 | − | 0.974454i | \(-0.427896\pi\) | ||||
0.224589 | + | 0.974454i | \(0.427896\pi\) | |||||||
\(212\) | −3.96250e8 | − | 6.86326e8i | −0.196167 | − | 0.339771i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.00970e9 | + | 1.74885e9i | −0.481435 | + | 0.833869i | ||||
\(215\) | 1.47238e9 | − | 8.50077e8i | 0.689073 | − | 0.397837i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.25282e9 | − | 6.46416e8i | 1.01598 | − | 0.291523i | ||||
\(218\) | −2.68747e9 | −1.18992 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.29229e8 | + | 2.47816e8i | 0.183231 | + | 0.105788i | ||||
\(221\) | −2.20743e8 | + | 3.82338e8i | −0.0925376 | + | 0.160280i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 9.24549e8i | − | 0.373861i | −0.982373 | − | 0.186931i | \(-0.940146\pi\) | ||
0.982373 | − | 0.186931i | \(-0.0598540\pi\) | |||||||
\(224\) | 1.22751e8 | + | 4.27796e8i | 0.0487564 | + | 0.169920i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.24288e9 | − | 2.15273e9i | −0.476425 | − | 0.825192i | ||||
\(227\) | −3.04346e9 | − | 1.75714e9i | −1.14621 | − | 0.661765i | −0.198249 | − | 0.980152i | \(-0.563526\pi\) |
−0.947961 | + | 0.318387i | \(0.896859\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.54322e9 | − | 1.46833e9i | 0.924789 | − | 0.533927i | 0.0396290 | − | 0.999214i | \(-0.487382\pi\) |
0.885160 | + | 0.465288i | \(0.154049\pi\) | |||||||
\(230\) | − | 1.55861e9i | − | 0.556964i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.03051e8 | 0.0355714 | ||||||||
\(233\) | −1.94715e9 | − | 3.37256e9i | −0.660657 | − | 1.14429i | −0.980443 | − | 0.196801i | \(-0.936945\pi\) |
0.319787 | − | 0.947490i | \(-0.396389\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.96653e7 | − | 5.13818e7i | 0.00972697 | − | 0.0168476i | ||||
\(236\) | 1.63520e9 | − | 9.44082e8i | 0.527136 | − | 0.304342i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.05110e8 | + | 2.94536e8i | 0.0950929 | + | 0.0917976i | ||||
\(239\) | −2.17474e8 | −0.0666525 | −0.0333262 | − | 0.999445i | \(-0.510610\pi\) | ||||
−0.0333262 | + | 0.999445i | \(0.510610\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.28371e9 | + | 1.31850e9i | 0.676977 | + | 0.390853i | 0.798715 | − | 0.601710i | \(-0.205514\pi\) |
−0.121738 | + | 0.992562i | \(0.538847\pi\) | |||||||
\(242\) | 1.06848e9 | − | 1.85066e9i | 0.311533 | − | 0.539592i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 3.17069e8i | − | 0.0894529i | ||||||
\(245\) | −2.34486e9 | − | 3.74961e9i | −0.650808 | − | 1.04069i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.75616e9 | − | 3.04176e9i | −0.471821 | − | 0.817217i | ||||
\(248\) | 1.22422e9 | + | 7.06804e8i | 0.323633 | + | 0.186850i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.44872e9 | − | 8.36417e8i | 0.370871 | − | 0.214123i | ||||
\(251\) | 1.72673e9i | 0.435041i | 0.976056 | + | 0.217520i | \(0.0697969\pi\) | ||||
−0.976056 | + | 0.217520i | \(0.930203\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.06417e8 | 0.221231 | ||||||||
\(254\) | −1.99571e9 | − | 3.45668e9i | −0.479472 | − | 0.830470i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.34218e8 | + | 2.32472e8i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 9.30785e8 | − | 5.37389e8i | 0.213362 | − | 0.123185i | −0.389511 | − | 0.921022i | \(-0.627356\pi\) |
0.602873 | + | 0.797837i | \(0.294023\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.28108e9 | + | 8.17449e8i | 0.729152 | + | 0.181661i | ||||
\(260\) | 2.77686e9 | 0.607660 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.15360e8 | − | 1.24338e8i | −0.0457046 | − | 0.0263876i | ||||
\(263\) | −2.60739e9 | + | 4.51614e9i | −0.544984 | + | 0.943939i | 0.453624 | + | 0.891193i | \(0.350131\pi\) |
−0.998608 | + | 0.0527463i | \(0.983203\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.74971e9i | 0.963127i | ||||||||
\(266\) | −3.24298e9 | + | 9.30532e8i | −0.647766 | + | 0.185868i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.29758e8 | − | 3.97953e8i | −0.0445381 | − | 0.0771423i | ||||
\(269\) | −6.32340e9 | − | 3.65082e9i | −1.20765 | − | 0.697237i | −0.245405 | − | 0.969421i | \(-0.578921\pi\) |
−0.962245 | + | 0.272183i | \(0.912254\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.76676e9 | + | 3.32944e9i | −1.06919 | + | 0.617296i | −0.927960 | − | 0.372681i | \(-0.878439\pi\) |
−0.141229 | + | 0.989977i | \(0.545105\pi\) | |||||||
\(272\) | 2.55782e8i | 0.0467299i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.91813e9 | 1.22740 | ||||||||
\(275\) | −4.99408e8 | − | 8.65000e8i | −0.0873222 | − | 0.151247i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.54607e9 | + | 6.14198e9i | −0.602322 | + | 1.04325i | 0.390147 | + | 0.920753i | \(0.372424\pi\) |
−0.992469 | + | 0.122499i | \(0.960909\pi\) | |||||||
\(278\) | −1.46070e9 | + | 8.43333e8i | −0.244557 | + | 0.141195i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.44838e8 | − | 2.58826e9i | 0.104910 | − | 0.421090i | ||||
\(281\) | 1.26746e9 | 0.203287 | 0.101643 | − | 0.994821i | \(-0.467590\pi\) | ||||
0.101643 | + | 0.994821i | \(0.467590\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.86397e9 | + | 4.54027e9i | 1.22602 | + | 0.707841i | 0.966194 | − | 0.257816i | \(-0.0830027\pi\) |
0.259822 | + | 0.965656i | \(0.416336\pi\) | |||||||
\(284\) | 2.25174e9 | − | 3.90012e9i | 0.346134 | − | 0.599521i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.61489e9i | 0.241368i | ||||||||
\(287\) | −6.89187e9 | − | 6.65304e9i | −1.01580 | − | 0.980601i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.36602e9 | − | 5.83011e9i | −0.482531 | − | 0.835767i | ||||
\(290\) | −5.34872e8 | − | 3.08809e8i | −0.0756237 | − | 0.0436614i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.27059e7 | + | 2.46563e7i | −0.00587431 | + | 0.00339153i | ||||
\(293\) | − | 7.62166e9i | − | 1.03414i | −0.855943 | − | 0.517070i | \(-0.827023\pi\) | ||
0.855943 | − | 0.517070i | \(-0.172977\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.13164e10 | −1.49424 | ||||||||
\(296\) | 1.01973e9 | + | 1.76623e9i | 0.132837 | + | 0.230081i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.96007e9 | − | 6.85905e9i | 0.502155 | − | 0.869759i | ||||
\(299\) | 4.39799e9 | − | 2.53918e9i | 0.550262 | − | 0.317694i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.69569e9 | − | 3.82835e9i | 0.450225 | − | 0.466386i | ||||
\(302\) | −1.10028e10 | −1.32274 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.76229e9 | − | 1.01746e9i | −0.206340 | − | 0.119131i | ||||
\(305\) | −9.50147e8 | + | 1.64570e9i | −0.109797 | + | 0.190174i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.77342e9i | 0.312221i | 0.987740 | + | 0.156110i | \(0.0498956\pi\) | ||||
−0.987740 | + | 0.156110i | \(0.950104\pi\) | |||||||
\(308\) | 1.50521e9 | + | 3.75008e8i | 0.167261 | + | 0.0416713i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.23610e9 | − | 7.33714e9i | −0.458690 | − | 0.794474i | ||||
\(311\) | 1.30379e10 | + | 7.52746e9i | 1.39369 | + | 0.804650i | 0.993722 | − | 0.111877i | \(-0.0356863\pi\) |
0.399973 | + | 0.916527i | \(0.369020\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.14520e10 | + | 6.61182e9i | −1.19318 | + | 0.688880i | −0.959025 | − | 0.283320i | \(-0.908564\pi\) |
−0.234150 | + | 0.972200i | \(0.575231\pi\) | |||||||
\(314\) | 2.03161e8i | 0.0208988i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.30153e9 | −0.431394 | ||||||||
\(317\) | 1.47764e9 | + | 2.55935e9i | 0.146329 | + | 0.253450i | 0.929868 | − | 0.367893i | \(-0.119921\pi\) |
−0.783539 | + | 0.621343i | \(0.786587\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.79589e8 | − | 3.11057e8i | 0.0173427 | − | 0.0300384i | ||||
\(320\) | 1.39328e9 | − | 8.04409e8i | 0.132873 | − | 0.0767144i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.34543e9 | − | 4.68892e9i | −0.125152 | − | 0.436164i | ||||
\(323\) | −1.93900e9 | −0.178143 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.84631e9 | − | 2.79802e9i | −0.434388 | − | 0.250794i | ||||
\(326\) | −5.09327e9 | + | 8.82179e9i | −0.450947 | + | 0.781064i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 5.77765e9i | − | 0.499179i | ||||||
\(329\) | 4.48911e7 | − | 1.80184e8i | 0.00383157 | − | 0.0153792i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.86192e9 | + | 6.68905e9i | 0.321730 | + | 0.557253i | 0.980845 | − | 0.194789i | \(-0.0624023\pi\) |
−0.659115 | + | 0.752042i | \(0.729069\pi\) | |||||||
\(332\) | 8.78568e9 | + | 5.07241e9i | 0.723141 | + | 0.417505i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.22572e9 | + | 1.28502e9i | −0.178848 | + | 0.103258i | ||||
\(335\) | 2.75403e9i | 0.218670i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.36239e10 | 1.05629 | 0.528145 | − | 0.849154i | \(-0.322888\pi\) | ||||
0.528145 | + | 0.849154i | \(0.322888\pi\) | |||||||
\(338\) | −9.06140e7 | − | 1.56948e8i | −0.00694270 | − | 0.0120251i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.66492e8 | − | 1.32760e9i | 0.0573577 | − | 0.0993465i | ||||
\(341\) | 4.26694e9 | − | 2.46352e9i | 0.315572 | − | 0.182196i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.02910e10 | − | 9.25616e9i | −0.743500 | − | 0.668736i | ||||
\(344\) | 3.20942e9 | 0.229188 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.65091e9 | + | 1.53050e9i | 0.184965 | + | 0.106790i | ||||
\(347\) | −4.20981e9 | + | 7.29161e9i | −0.290365 | + | 0.502927i | −0.973896 | − | 0.226994i | \(-0.927110\pi\) |
0.683531 | + | 0.729922i | \(0.260443\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.69363e10i | 1.14161i | 0.821087 | + | 0.570803i | \(0.193368\pi\) | ||||
−0.821087 | + | 0.570803i | \(0.806632\pi\) | |||||||
\(350\) | −3.73338e9 | + | 3.86740e9i | −0.248789 | + | 0.257720i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.67807e8 | + | 8.10265e8i | 0.0304716 | + | 0.0527784i | ||||
\(353\) | 2.53285e10 | + | 1.46234e10i | 1.63121 | + | 0.941780i | 0.983720 | + | 0.179707i | \(0.0575150\pi\) |
0.647491 | + | 0.762073i | \(0.275818\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.33747e10 | + | 1.34954e10i | −1.47174 | + | 0.849711i | ||||
\(356\) | − | 6.66778e9i | − | 0.415127i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.97973e9 | 0.607557 | ||||||||
\(359\) | −2.55730e9 | − | 4.42937e9i | −0.153959 | − | 0.266664i | 0.778721 | − | 0.627371i | \(-0.215869\pi\) |
−0.932679 | + | 0.360707i | \(0.882536\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.78741e8 | + | 1.34882e9i | −0.0458527 | + | 0.0794191i | ||||
\(362\) | 4.85883e9 | − | 2.80525e9i | 0.282942 | − | 0.163357i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.35389e9 | − | 2.39704e9i | 0.475864 | − | 0.136543i | ||||
\(365\) | 2.95546e8 | 0.0166515 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.72247e9 | + | 4.45857e9i | 0.425688 | + | 0.245771i | 0.697508 | − | 0.716577i | \(-0.254292\pi\) |
−0.271820 | + | 0.962348i | \(0.587625\pi\) | |||||||
\(368\) | 1.47111e9 | − | 2.54805e9i | 0.0802149 | − | 0.138936i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 1.22232e10i | − | 0.652194i | ||||||
\(371\) | 4.10004e9 | + | 1.42890e10i | 0.216418 | + | 0.754234i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.69622e10 | + | 2.93793e10i | 0.876286 | + | 1.51777i | 0.855386 | + | 0.517991i | \(0.173320\pi\) |
0.0209000 | + | 0.999782i | \(0.493347\pi\) | |||||||
\(374\) | 7.72071e8 | + | 4.45756e8i | 0.0394613 | + | 0.0227830i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.69945e7 | − | 5.59998e7i | 0.00485284 | − | 0.00280179i | ||||
\(377\) | − | 2.01235e9i | − | 0.0996182i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.48233e9 | 0.217244 | 0.108622 | − | 0.994083i | \(-0.465356\pi\) | ||||
0.108622 | + | 0.994083i | \(0.465356\pi\) | |||||||
\(380\) | 6.09796e9 | + | 1.05620e10i | 0.292449 | + | 0.506537i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.93729e9 | − | 1.54798e10i | 0.419713 | − | 0.726964i | ||||
\(383\) | −6.10111e8 | + | 3.52248e8i | −0.0283540 | + | 0.0163702i | −0.514110 | − | 0.857724i | \(-0.671878\pi\) |
0.485756 | + | 0.874094i | \(0.338544\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.68881e9 | − | 6.45702e9i | −0.304443 | − | 0.293893i | ||||
\(386\) | 1.86918e10 | 0.841981 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.60359e10 | + | 9.25836e9i | 0.707567 | + | 0.408514i | ||||
\(389\) | −2.05882e10 | + | 3.56598e10i | −0.899124 | + | 1.55733i | −0.0705080 | + | 0.997511i | \(0.522462\pi\) |
−0.828616 | + | 0.559817i | \(0.810871\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.80354e9i | − | 0.119950i | ||||||
\(392\) | −2.94307e8 | − | 8.34313e9i | −0.0124640 | − | 0.353334i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.06016e9 | − | 5.30035e9i | −0.126987 | − | 0.219948i | ||||
\(395\) | 2.23265e10 | + | 1.28902e10i | 0.917133 | + | 0.529507i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.35159e9 | + | 4.24444e9i | −0.295951 | + | 0.170867i | −0.640622 | − | 0.767856i | \(-0.721324\pi\) |
0.344672 | + | 0.938723i | \(0.387990\pi\) | |||||||
\(398\) | 1.54713e9i | 0.0616588i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.24216e9 | −0.126647 | ||||||||
\(401\) | 1.67749e10 | + | 2.90550e10i | 0.648757 | + | 1.12368i | 0.983420 | + | 0.181342i | \(0.0580442\pi\) |
−0.334663 | + | 0.942338i | \(0.608622\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.38023e10 | − | 2.39062e10i | 0.523276 | − | 0.906340i | ||||
\(404\) | 1.04015e10 | − | 6.00529e9i | 0.390453 | − | 0.225428i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.87568e9 | − | 4.67306e8i | −0.0690325 | − | 0.0171988i | ||||
\(407\) | 7.10842e9 | 0.259057 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.95983e10 | + | 1.13151e10i | 0.700367 | + | 0.404357i | 0.807484 | − | 0.589890i | \(-0.200829\pi\) |
−0.107117 | + | 0.994246i | \(0.534162\pi\) | |||||||
\(410\) | −1.73136e10 | + | 2.99881e10i | −0.612707 | + | 1.06124i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 2.25647e10i | − | 0.783144i | ||||||
\(413\) | −3.40441e10 | + | 9.76851e9i | −1.17015 | + | 0.335759i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.04006e10 | − | 5.26553e10i | −1.02492 | − | 1.77521i | ||||
\(416\) | 4.53965e9 | + | 2.62097e9i | 0.151583 | + | 0.0875162i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.14235e9 | + | 3.54629e9i | −0.201201 | + | 0.116163i | ||||
\(419\) | − | 3.35474e10i | − | 1.08844i | −0.838944 | − | 0.544218i | \(-0.816826\pi\) | ||
0.838944 | − | 0.544218i | \(-0.183174\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.27977e10 | 1.04403 | 0.522017 | − | 0.852935i | \(-0.325180\pi\) | ||||
0.522017 | + | 0.852935i | \(0.325180\pi\) | |||||||
\(422\) | −5.03643e9 | − | 8.72335e9i | −0.158808 | − | 0.275064i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.48306e9 | + | 7.76489e9i | −0.138711 | + | 0.240255i | ||||
\(425\) | −2.67544e9 | + | 1.54467e9i | −0.0820048 | + | 0.0473455i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.43781e9 | + | 5.77111e9i | −0.0432505 | + | 0.173599i | ||||
\(428\) | 2.28469e10 | 0.680851 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.66580e10 | − | 9.61753e9i | −0.487248 | − | 0.281313i | ||||
\(431\) | −6.60998e8 | + | 1.14488e9i | −0.0191554 | + | 0.0331781i | −0.875444 | − | 0.483319i | \(-0.839431\pi\) |
0.856289 | + | 0.516497i | \(0.172764\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.53701e9i | 0.0437246i | 0.999761 | + | 0.0218623i | \(0.00695954\pi\) | ||||
−0.999761 | + | 0.0218623i | \(0.993040\pi\) | |||||||
\(434\) | −1.90774e10 | − | 1.84163e10i | −0.537725 | − | 0.519091i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.52026e10 | + | 2.63317e10i | 0.420700 | + | 0.728674i | ||||
\(437\) | 1.93159e10 | + | 1.11520e10i | 0.529650 | + | 0.305794i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.05231e10 | − | 1.76225e10i | 0.821809 | − | 0.474472i | −0.0292309 | − | 0.999573i | \(-0.509306\pi\) |
0.851040 | + | 0.525101i | \(0.175972\pi\) | |||||||
\(440\) | − | 5.60743e9i | − | 0.149607i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.99485e9 | 0.130868 | ||||||||
\(443\) | −3.28022e10 | − | 5.68150e10i | −0.851702 | − | 1.47519i | −0.879671 | − | 0.475582i | \(-0.842238\pi\) |
0.0279697 | − | 0.999609i | \(-0.491096\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.99811e10 | + | 3.46082e10i | −0.509540 | + | 0.882549i | ||||
\(446\) | −9.05870e9 | + | 5.23004e9i | −0.228942 | + | 0.132180i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.49715e9 | − | 3.62268e9i | 0.0868164 | − | 0.0899329i | ||||
\(449\) | 5.51880e10 | 1.35787 | 0.678937 | − | 0.734196i | \(-0.262441\pi\) | ||||
0.678937 | + | 0.734196i | \(0.262441\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.74397e10 | − | 1.00688e10i | −0.421534 | − | 0.243373i | ||||
\(452\) | −1.40615e10 | + | 2.43553e10i | −0.336883 | + | 0.583499i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.97596e10i | 0.935877i | ||||||||
\(455\) | −5.05428e10 | − | 1.25922e10i | −1.17927 | − | 0.293804i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.09559e10 | + | 3.62968e10i | 0.480444 | + | 0.832153i | 0.999748 | − | 0.0224363i | \(-0.00714231\pi\) |
−0.519305 | + | 0.854589i | \(0.673809\pi\) | |||||||
\(458\) | −2.87733e10 | − | 1.66123e10i | −0.653924 | − | 0.377543i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.52712e10 | + | 8.81685e9i | −0.341070 | + | 0.196917i | ||||
\(461\) | − | 5.47469e10i | − | 1.21215i | −0.795408 | − | 0.606074i | \(-0.792743\pi\) | ||
0.795408 | − | 0.606074i | \(-0.207257\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.59007e10 | −1.21645 | −0.608223 | − | 0.793766i | \(-0.708117\pi\) | ||||
−0.608223 | + | 0.793766i | \(0.708117\pi\) | |||||||
\(464\) | −5.82945e8 | − | 1.00969e9i | −0.0125764 | − | 0.0217829i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.20295e10 | + | 3.81562e10i | −0.467155 | + | 0.809136i | ||||
\(467\) | 5.30982e10 | − | 3.06562e10i | 1.11638 | − | 0.644542i | 0.175906 | − | 0.984407i | \(-0.443715\pi\) |
0.940474 | + | 0.339865i | \(0.110381\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.37733e9 | + | 8.28520e9i | 0.0491358 | + | 0.171243i | ||||
\(470\) | −6.71249e8 | −0.0137560 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.85002e10 | − | 1.06811e10i | −0.372741 | − | 0.215202i | ||||
\(473\) | 5.59310e9 | − | 9.68754e9i | 0.111740 | − | 0.193539i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.45777e10i | − | 0.482800i | ||||||
\(476\) | 1.15990e9 | − | 4.65560e9i | 0.0225939 | − | 0.0906876i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.23022e9 | + | 2.13080e9i | 0.0235652 | + | 0.0408161i | ||||
\(479\) | 3.06068e10 | + | 1.76709e10i | 0.581402 | + | 0.335672i | 0.761690 | − | 0.647941i | \(-0.224370\pi\) |
−0.180288 | + | 0.983614i | \(0.557703\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.44905e10 | − | 1.99131e10i | 0.644346 | − | 0.372013i | ||||
\(482\) | − | 2.98343e10i | − | 0.552749i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.41769e10 | −0.440575 | ||||||||
\(485\) | −5.54883e10 | − | 9.61085e10i | −1.00285 | − | 1.73698i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.41762e10 | − | 2.45539e10i | 0.252026 | − | 0.436521i | −0.712058 | − | 0.702121i | \(-0.752237\pi\) |
0.964083 | + | 0.265600i | \(0.0855700\pi\) | |||||||
\(488\) | −3.10663e9 | + | 1.79361e9i | −0.0547785 | + | 0.0316264i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.34740e10 | + | 4.41858e10i | −0.407195 | + | 0.766476i | ||||
\(491\) | −5.07023e10 | −0.872372 | −0.436186 | − | 0.899857i | \(-0.643671\pi\) | ||||
−0.436186 | + | 0.899857i | \(0.643671\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.62096e8 | − | 5.55466e8i | −0.0162866 | − | 0.00940308i | ||||
\(494\) | −1.98687e10 | + | 3.44136e10i | −0.333628 | + | 0.577860i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 1.59931e10i | − | 0.264245i | ||||||
\(497\) | −5.86707e10 | + | 6.07768e10i | −0.961603 | + | 0.996122i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.08989e10 | − | 5.35184e10i | −0.498357 | − | 0.863179i | 0.501642 | − | 0.865076i | \(-0.332730\pi\) |
−0.999998 | + | 0.00189664i | \(0.999396\pi\) | |||||||
\(500\) | −1.63904e10 | − | 9.46298e9i | −0.262246 | − | 0.151408i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.69185e10 | − | 9.76787e9i | 0.266407 | − | 0.153810i | ||||
\(503\) | − | 1.17222e11i | − | 1.83121i | −0.402082 | − | 0.915604i | \(-0.631713\pi\) | ||
0.402082 | − | 0.915604i | \(-0.368287\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.19832e10 | −1.10679 | ||||||||
\(506\) | −5.12747e9 | − | 8.88104e9i | −0.0782170 | − | 0.135476i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.25789e10 | + | 3.91078e10i | −0.339038 | + | 0.587231i | ||||
\(509\) | −4.30042e10 | + | 2.48285e10i | −0.640677 | + | 0.369895i | −0.784875 | − | 0.619654i | \(-0.787273\pi\) |
0.144198 | + | 0.989549i | \(0.453940\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.89118e8 | − | 2.55121e8i | 0.0130399 | − | 0.00374164i | ||||
\(512\) | 3.03700e9 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.05306e10 | − | 6.07986e9i | −0.150870 | − | 0.0871047i | ||||
\(515\) | −6.76188e10 | + | 1.17119e11i | −0.961255 | + | 1.66494i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3.90367e8i | − | 0.00546400i | ||||||
\(518\) | −1.05513e10 | − | 3.67721e10i | −0.146550 | − | 0.510739i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.57083e10 | − | 2.72076e10i | −0.214840 | − | 0.372114i | ||||
\(521\) | 8.97396e10 | + | 5.18112e10i | 1.21796 | + | 0.703190i | 0.964481 | − | 0.264151i | \(-0.0850918\pi\) |
0.253479 | + | 0.967341i | \(0.418425\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.08458e11 | − | 6.26180e10i | 1.44962 | − | 0.836936i | 0.451158 | − | 0.892444i | \(-0.351011\pi\) |
0.998458 | + | 0.0555075i | \(0.0176777\pi\) | |||||||
\(524\) | 2.81345e9i | 0.0373176i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.89986e10 | 0.770723 | ||||||||
\(527\) | −7.61964e9 | − | 1.31976e10i | −0.0987852 | − | 0.171101i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.30311e10 | − | 3.98911e10i | 0.294098 | − | 0.509393i | ||||
\(530\) | 4.65374e10 | − | 2.68684e10i | 0.589792 | − | 0.340517i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.74624e10 | + | 2.65107e10i | 0.342840 | + | 0.330960i | ||||
\(533\) | −1.12824e11 | −1.39796 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.18584e11 | − | 6.84643e10i | −1.44747 | − | 0.835698i | ||||
\(536\) | −2.59942e9 | + | 4.50232e9i | −0.0314932 | + | 0.0545479i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.26085e10i | 0.986043i | ||||||||
\(539\) | −2.56964e10 | − | 1.36514e10i | −0.304451 | − | 0.161741i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.14145e10 | + | 3.70910e10i | 0.249988 | + | 0.432992i | 0.963522 | − | 0.267629i | \(-0.0862401\pi\) |
−0.713534 | + | 0.700620i | \(0.752907\pi\) | |||||||
\(542\) | 6.52434e10 | + | 3.76683e10i | 0.756031 | + | 0.436494i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.50614e9 | − | 1.44692e9i | 0.0286161 | − | 0.0165215i | ||||
\(545\) | − | 1.82228e11i | − | 2.06552i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.63137e10 | −0.517321 | −0.258660 | − | 0.965968i | \(-0.583281\pi\) | ||||
−0.258660 | + | 0.965968i | \(0.583281\pi\) | |||||||
\(548\) | −3.91348e10 | − | 6.77835e10i | −0.433952 | − | 0.751626i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.65016e9 | + | 9.78636e9i | −0.0617461 | + | 0.106947i | ||||
\(551\) | 7.65413e9 | − | 4.41911e9i | 0.0830404 | − | 0.0479434i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.82940e10 | + | 1.95061e10i | 0.837197 | + | 0.208579i | ||||
\(554\) | 8.02384e10 | 0.851811 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.65259e10 | + | 9.54122e9i | 0.172928 | + | 0.0998401i | ||||
\(557\) | 6.61578e9 | − | 1.14589e10i | 0.0687322 | − | 0.119048i | −0.829611 | − | 0.558341i | \(-0.811438\pi\) |
0.898343 | + | 0.439294i | \(0.144771\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.26727e10i | − | 0.641846i | ||||||
\(560\) | −2.90074e10 | + | 8.32330e9i | −0.294956 | + | 0.0846337i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.16984e9 | − | 1.24185e10i | −0.0718727 | − | 0.124487i | ||||
\(563\) | 1.09939e11 | + | 6.34731e10i | 1.09425 | + | 0.631765i | 0.934705 | − | 0.355425i | \(-0.115664\pi\) |
0.159545 | + | 0.987191i | \(0.448997\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.45969e11 | − | 8.42753e10i | 1.43241 | − | 0.827002i | ||||
\(566\) | − | 1.02735e11i | − | 1.00104i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.09510e10 | −0.489507 | ||||||||
\(569\) | 3.80836e10 | + | 6.59628e10i | 0.363320 | + | 0.629289i | 0.988505 | − | 0.151188i | \(-0.0483098\pi\) |
−0.625185 | + | 0.780477i | \(0.714976\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.57055e10 | + | 2.72028e10i | −0.147743 | + | 0.255899i | −0.930393 | − | 0.366563i | \(-0.880534\pi\) |
0.782650 | + | 0.622462i | \(0.213868\pi\) | |||||||
\(572\) | 1.58226e10 | − | 9.13521e9i | 0.147807 | − | 0.0853364i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.61999e10 | + | 1.05162e11i | −0.241353 | + | 0.968744i | ||||
\(575\) | 3.55362e10 | 0.325087 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.21942e11 | + | 7.04032e10i | 1.10014 | + | 0.635168i | 0.936259 | − | 0.351311i | \(-0.114264\pi\) |
0.163885 | + | 0.986479i | \(0.447597\pi\) | |||||||
\(578\) | −3.80821e10 | + | 6.59602e10i | −0.341201 | + | 0.590977i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.98754e9i | 0.0617465i | ||||||||
\(581\) | −1.36910e11 | − | 1.32166e11i | −1.20152 | − | 1.15988i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.56254e10 | + | 2.70640e10i | 0.135256 | + | 0.234271i | ||||
\(584\) | 4.83162e8 | + | 2.78954e8i | 0.00415376 | + | 0.00239818i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.46767e10 | + | 4.31146e10i | −0.633278 | + | 0.365623i | ||||
\(587\) | 1.27088e11i | 1.07041i | 0.844722 | + | 0.535205i | \(0.179766\pi\) | ||||
−0.844722 | + | 0.535205i | \(0.820234\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.21239e11 | 1.00735 | ||||||||
\(590\) | 6.40150e10 | + | 1.10877e11i | 0.528292 | + | 0.915028i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.15370e10 | − | 1.99826e10i | 0.0939301 | − | 0.162692i | ||||
\(593\) | 9.49497e10 | − | 5.48192e10i | 0.767847 | − | 0.443317i | −0.0642590 | − | 0.997933i | \(-0.520468\pi\) |
0.832106 | + | 0.554617i | \(0.187135\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.99715e10 | + | 2.06884e10i | −0.159347 | + | 0.165067i | ||||
\(596\) | −8.96062e10 | −0.710155 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.97576e10 | − | 2.87275e10i | −0.389094 | − | 0.224643i | ||||
\(599\) | −9.86732e10 | + | 1.70907e11i | −0.766464 | + | 1.32755i | 0.173005 | + | 0.984921i | \(0.444652\pi\) |
−0.939469 | + | 0.342634i | \(0.888681\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.14321e10i | 0.470866i | 0.971891 | + | 0.235433i | \(0.0756508\pi\) | ||||
−0.971891 | + | 0.235433i | \(0.924349\pi\) | |||||||
\(602\) | −5.84160e10 | − | 1.45538e10i | −0.444781 | − | 0.110813i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.22411e10 | + | 1.07805e11i | 0.467659 | + | 0.810009i | ||||
\(605\) | 1.25487e11 | + | 7.24500e10i | 0.936650 | + | 0.540775i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.44988e10 | − | 4.30119e10i | 0.548775 | − | 0.316836i | −0.199853 | − | 0.979826i | \(-0.564046\pi\) |
0.748628 | + | 0.662990i | \(0.230713\pi\) | |||||||
\(608\) | 2.30225e10i | 0.168476i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.14994e10 | 0.155277 | ||||||||
\(611\) | −1.09355e9 | − | 1.89408e9i | −0.00784646 | − | 0.0135905i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.44561e10 | − | 7.70002e10i | 0.314839 | − | 0.545318i | −0.664564 | − | 0.747231i | \(-0.731383\pi\) |
0.979403 | + | 0.201914i | \(0.0647160\pi\) | |||||||
\(614\) | 2.71738e10 | − | 1.56888e10i | 0.191195 | − | 0.110387i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.84044e9 | − | 1.68693e10i | −0.0336172 | − | 0.117159i | ||||
\(617\) | 2.75927e11 | 1.90394 | 0.951971 | − | 0.306189i | \(-0.0990539\pi\) | ||||
0.951971 | + | 0.306189i | \(0.0990539\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.88747e11 | − | 1.08973e11i | −1.28564 | − | 0.742262i | −0.307763 | − | 0.951463i | \(-0.599580\pi\) |
−0.977873 | + | 0.209201i | \(0.932914\pi\) | |||||||
\(620\) | −4.79260e10 | + | 8.30102e10i | −0.324343 | + | 0.561778i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 1.70327e11i | − | 1.13795i | ||||||
\(623\) | −3.02364e10 | + | 1.21363e11i | −0.200714 | + | 0.805628i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.53641e10 | + | 1.65176e11i | 0.624978 | + | 1.08249i | ||||
\(626\) | 1.29565e11 | + | 7.48042e10i | 0.843703 | + | 0.487112i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.99056e9 | − | 1.14925e9i | 0.0127979 | − | 0.00738885i | ||||
\(629\) | − | 2.19863e10i | − | 0.140459i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.15606e11 | −0.729227 | −0.364614 | − | 0.931159i | \(-0.618799\pi\) | ||||
−0.364614 | + | 0.931159i | \(0.618799\pi\) | |||||||
\(632\) | 2.43331e10 | + | 4.21462e10i | 0.152521 | + | 0.264174i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.67176e10 | − | 2.89557e10i | 0.103471 | − | 0.179216i | ||||
\(635\) | 2.34386e11 | − | 1.35323e11i | 1.44157 | − | 0.832292i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.62923e11 | + | 5.74716e9i | −0.989517 | + | 0.0349056i | ||||
\(638\) | −4.06363e9 | −0.0245262 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.57631e10 | − | 9.10085e9i | −0.0939556 | − | 0.0542453i | ||||
\(641\) | −1.65141e11 | + | 2.86033e11i | −0.978191 | + | 1.69428i | −0.309215 | + | 0.950992i | \(0.600066\pi\) |
−0.668976 | + | 0.743284i | \(0.733267\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.72066e11i | − | 1.00659i | −0.864116 | − | 0.503293i | \(-0.832122\pi\) | ||
0.864116 | − | 0.503293i | \(-0.167878\pi\) | |||||||
\(644\) | −3.83310e10 | + | 3.97070e10i | −0.222847 | + | 0.230847i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.09686e10 | + | 1.89983e10i | 0.0629830 | + | 0.109090i | ||||
\(647\) | 1.78588e11 | + | 1.03108e11i | 1.01914 | + | 0.588402i | 0.913856 | − | 0.406039i | \(-0.133090\pi\) |
0.105287 | + | 0.994442i | \(0.466424\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.44810e10 | + | 3.72281e10i | −0.363457 | + | 0.209842i | ||||
\(650\) | 6.33120e10i | 0.354677i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.15247e11 | 0.637736 | ||||||||
\(653\) | 2.30745e10 | + | 3.99662e10i | 0.126905 | + | 0.219806i | 0.922476 | − | 0.386054i | \(-0.126162\pi\) |
−0.795571 | + | 0.605861i | \(0.792829\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.43095e9 | − | 1.46028e10i | 0.0458048 | − | 0.0793363i | ||||
\(656\) | −5.66092e10 | + | 3.26833e10i | −0.305683 | + | 0.176486i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.01938e9 | + | 5.79435e8i | −0.0107725 | + | 0.00309102i | ||||
\(659\) | 1.66601e10 | 0.0883357 | 0.0441679 | − | 0.999024i | \(-0.485936\pi\) | ||||
0.0441679 | + | 0.999024i | \(0.485936\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.05750e9 | − | 4.65200e9i | −0.0422080 | − | 0.0243688i | 0.478748 | − | 0.877953i | \(-0.341091\pi\) |
−0.520956 | + | 0.853584i | \(0.674424\pi\) | |||||||
\(662\) | 4.36927e10 | − | 7.56779e10i | 0.227498 | − | 0.394037i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 1.14776e11i | − | 0.590442i | ||||||
\(665\) | −6.30962e10 | − | 2.19896e11i | −0.322639 | − | 1.12442i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.38946e9 | + | 1.10669e10i | 0.0322820 | + | 0.0559141i | ||||
\(668\) | 2.51811e10 | + | 1.45383e10i | 0.126465 | + | 0.0730144i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.69839e10 | − | 1.55791e10i | 0.133907 | − | 0.0773115i | ||||
\(671\) | 1.25030e10i | 0.0616773i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.10631e11 | −0.539282 | −0.269641 | − | 0.962961i | \(-0.586905\pi\) | ||||
−0.269641 | + | 0.962961i | \(0.586905\pi\) | |||||||
\(674\) | −7.70687e10 | − | 1.33487e11i | −0.373455 | − | 0.646843i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.02518e9 | + | 1.77566e9i | −0.00490923 | + | 0.00850304i | ||||
\(677\) | −7.01094e10 | + | 4.04777e10i | −0.333750 | + | 0.192691i | −0.657505 | − | 0.753450i | \(-0.728388\pi\) |
0.323755 | + | 0.946141i | \(0.395055\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.49893e11 | − | 2.41234e11i | −1.17564 | − | 1.13490i | ||||
\(680\) | −1.73437e10 | −0.0811160 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.82749e10 | − | 2.78715e10i | −0.223143 | − | 0.128832i | ||||
\(683\) | −1.00435e11 | + | 1.73959e11i | −0.461534 | + | 0.799400i | −0.999038 | − | 0.0438612i | \(-0.986034\pi\) |
0.537504 | + | 0.843261i | \(0.319367\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.69095e11i | 2.13058i | ||||||||
\(686\) | −3.24768e10 | + | 1.53192e11i | −0.146648 | + | 0.691733i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.81552e10 | − | 3.14458e10i | −0.0810303 | − | 0.140349i | ||||
\(689\) | 1.51631e11 | + | 8.75440e10i | 0.672838 | + | 0.388463i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.77367e11 | + | 1.60138e11i | −1.21659 | + | 0.702397i | −0.964186 | − | 0.265226i | \(-0.914553\pi\) |
−0.252400 | + | 0.967623i | \(0.581220\pi\) | |||||||
\(692\) | − | 3.46313e10i | − | 0.151023i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.52571e10 | 0.410639 | ||||||||
\(695\) | −5.71836e10 | − | 9.90448e10i | −0.245094 | − | 0.424515i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.11427e10 | + | 5.39408e10i | −0.131955 | + | 0.228553i | ||||
\(698\) | 1.65941e11 | − | 9.58061e10i | 0.699088 | − | 0.403619i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.90119e10 | + | 1.47022e10i | 0.245780 | + | 0.0612337i | ||||
\(701\) | 5.65576e10 | 0.234217 | 0.117109 | − | 0.993119i | \(-0.462637\pi\) | ||||
0.117109 | + | 0.993119i | \(0.462637\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.51482e11 | + | 8.74580e10i | 0.620210 | + | 0.358078i | ||||
\(704\) | 5.29263e9 | − | 9.16710e9i | 0.0215467 | − | 0.0373200i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 3.30890e11i | − | 1.33188i | ||||||
\(707\) | −2.16554e11 | + | 6.21373e10i | −0.866738 | + | 0.248699i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.58821e11 | + | 2.75086e11i | 0.628525 | + | 1.08864i | 0.987848 | + | 0.155423i | \(0.0496742\pi\) |
−0.359323 | + | 0.933213i | \(0.616992\pi\) | |||||||
\(710\) | 2.64454e11 | + | 1.52683e11i | 1.04068 | + | 0.600836i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.53306e10 | + | 3.77187e10i | −0.254212 | + | 0.146770i | ||||
\(713\) | 1.75295e11i | 0.678285i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.09500e11 | −0.418978 | ||||||||
\(716\) | −5.64539e10 | − | 9.77810e10i | −0.214804 | − | 0.372051i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.89326e10 | + | 5.01126e10i | −0.108865 | + | 0.188560i | ||||
\(719\) | 2.58599e11 | − | 1.49302e11i | 0.967633 | − | 0.558663i | 0.0691194 | − | 0.997608i | \(-0.477981\pi\) |
0.898514 | + | 0.438945i | \(0.144648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.02324e11 | + | 4.10711e11i | −0.378650 | + | 1.51983i | ||||
\(722\) | 1.76209e10 | 0.0648454 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.49714e10 | − | 3.17377e10i | −0.200070 | − | 0.115511i | ||||
\(725\) | 7.04079e9 | − | 1.21950e10i | 0.0254841 | − | 0.0441398i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.15756e10i | − | 0.0772371i | −0.999254 | − | 0.0386185i | \(-0.987704\pi\) | ||
0.999254 | − | 0.0386185i | \(-0.0122957\pi\) | |||||||
\(728\) | −7.07428e10 | − | 6.82913e10i | −0.251859 | − | 0.243131i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.67186e9 | − | 2.89574e9i | −0.00588719 | − | 0.0101969i | ||||
\(731\) | −2.99635e10 | − | 1.72994e10i | −0.104936 | − | 0.0605846i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.03855e10 | + | 5.99605e9i | −0.0359758 | + | 0.0207706i | −0.517880 | − | 0.855453i | \(-0.673279\pi\) |
0.481904 | + | 0.876224i | \(0.339945\pi\) | |||||||
\(734\) | − | 1.00886e11i | − | 0.347573i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.32875e10 | −0.113441 | ||||||||
\(737\) | 9.06009e9 | + | 1.56925e10i | 0.0307088 | + | 0.0531892i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.03348e11 | − | 3.52209e11i | 0.681808 | − | 1.18093i | −0.292620 | − | 0.956229i | \(-0.594527\pi\) |
0.974429 | − | 0.224698i | \(-0.0721394\pi\) | |||||||
\(740\) | −1.19762e11 | + | 6.91447e10i | −0.399386 | + | 0.230585i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.16810e11 | − | 1.21003e11i | 0.385357 | − | 0.399190i | ||||
\(743\) | −1.32051e11 | −0.433299 | −0.216650 | − | 0.976249i | \(-0.569513\pi\) | ||||
−0.216650 | + | 0.976249i | \(0.569513\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.65089e11 | + | 2.68519e11i | 1.50977 | + | 0.871666i | ||||
\(746\) | 1.91905e11 | − | 3.32389e11i | 0.619628 | − | 1.07323i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1.00863e10i | − | 0.0322200i | ||||||
\(749\) | −4.15846e11 | − | 1.03604e11i | −1.32131 | − | 0.329192i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.72943e10 | + | 2.99547e10i | 0.0543681 | + | 0.0941683i | 0.891929 | − | 0.452176i | \(-0.149352\pi\) |
−0.837560 | + | 0.546345i | \(0.816019\pi\) | |||||||
\(752\) | −1.09737e9 | − | 6.33566e8i | −0.00343148 | − | 0.00198116i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.97170e10 | + | 1.13836e10i | −0.0610035 | + | 0.0352204i | ||||
\(755\) | − | 7.46061e11i | − | 2.29608i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.94290e10 | −0.0896173 | −0.0448086 | − | 0.998996i | \(-0.514268\pi\) | ||||
−0.0448086 | + | 0.998996i | \(0.514268\pi\) | |||||||
\(758\) | −2.53559e10 | − | 4.39177e10i | −0.0768073 | − | 0.133034i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.89906e10 | − | 1.19495e11i | 0.206793 | − | 0.358176i | ||||
\(761\) | −1.88879e11 | + | 1.09050e11i | −0.563179 | + | 0.325151i | −0.754420 | − | 0.656392i | \(-0.772082\pi\) |
0.191242 | + | 0.981543i | \(0.438749\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.57303e11 | − | 5.48214e11i | −0.464129 | − | 1.61753i | ||||
\(764\) | −2.02228e11 | −0.593564 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.90262e9 | + | 3.98523e9i | 0.0200493 | + | 0.0115755i | ||||
\(767\) | −2.08577e11 | + | 3.61266e11i | −0.602678 | + | 1.04387i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.85675e11i | 0.530942i | 0.964119 | + | 0.265471i | \(0.0855275\pi\) | ||||
−0.964119 | + | 0.265471i | \(0.914473\pi\) | |||||||
\(770\) | −2.54280e10 | + | 1.02063e11i | −0.0723352 | + | 0.290340i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.05737e11 | − | 1.83142e11i | −0.297685 | − | 0.515606i | ||||
\(773\) | −6.54917e10 | − | 3.78116e10i | −0.183429 | − | 0.105903i | 0.405474 | − | 0.914107i | \(-0.367107\pi\) |
−0.588903 | + | 0.808204i | \(0.700440\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.67286e11 | − | 9.65824e10i | 0.463716 | − | 0.267726i | ||||
\(776\) | − | 2.09493e11i | − | 0.577726i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.65857e11 | 1.27155 | ||||||||
\(779\) | −2.47762e11 | − | 4.29136e11i | −0.672797 | − | 1.16532i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.87930e10 | + | 1.53794e11i | −0.238657 | + | 0.413367i | ||||
\(782\) | −2.74690e10 | + | 1.58592e10i | −0.0734540 | + | 0.0424087i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.00808e10 | + | 5.00795e10i | −0.211965 | + | 0.132555i | ||||
\(785\) | −1.37757e10 | −0.0362772 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.00701e11 | − | 2.89080e11i | −1.30521 | − | 0.753562i | −0.323915 | − | 0.946086i | \(-0.604999\pi\) |
−0.981292 | + | 0.192524i | \(0.938333\pi\) | |||||||
\(788\) | −3.46218e10 | + | 5.99667e10i | −0.0897934 | + | 0.155527i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 2.91672e11i | − | 0.748836i | ||||||
\(791\) | 3.66384e11 | − | 3.79537e11i | 0.935903 | − | 0.969500i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.50252e10 | + | 6.06654e10i | 0.0885702 | + | 0.153408i | ||||
\(794\) | 8.31738e10 | + | 4.80204e10i | 0.209269 | + | 0.120821i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.51587e10 | − | 8.75190e9i | 0.0377582 | − | 0.0217997i | ||||
\(797\) | − | 4.43180e11i | − | 1.09836i | −0.835703 | − | 0.549182i | \(-0.814939\pi\) | ||
0.835703 | − | 0.549182i | \(-0.185061\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.20740e9 | −0.00296254 | ||||||||
\(800\) | 1.83404e10 | + | 3.17665e10i | 0.0447764 | + | 0.0775550i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.89786e11 | − | 3.28719e11i | 0.458741 | − | 0.794562i | ||||
\(803\) | 1.68403e9 | − | 9.72275e8i | 0.00405030 | − | 0.00233844i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.17940e11 | − | 9.12288e10i | 0.757115 | − | 0.217244i | ||||
\(806\) | −3.12310e11 | −0.740024 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.17679e11 | − | 6.79421e10i | −0.276092 | − | 0.159402i | ||||
\(809\) | 1.23410e11 | − | 2.13752e11i | 0.288108 | − | 0.499017i | −0.685250 | − | 0.728308i | \(-0.740307\pi\) |
0.973358 | + | 0.229290i | \(0.0736406\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.79882e11i | 0.878143i | 0.898452 | + | 0.439071i | \(0.144693\pi\) | ||||
−0.898452 | + | 0.439071i | \(0.855307\pi\) | |||||||
\(812\) | 6.03178e9 | + | 2.10213e10i | 0.0138746 | + | 0.0483543i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.02113e10 | − | 6.96480e10i | −0.0915905 | − | 0.158639i | ||||
\(815\) | −5.98176e11 | − | 3.45357e11i | −1.35581 | − | 0.782777i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.38380e11 | − | 1.37629e11i | 0.535034 | − | 0.308902i | ||||
\(818\) | − | 2.56031e11i | − | 0.571847i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.91763e11 | 0.866499 | ||||||||
\(821\) | 3.79375e11 | + | 6.57097e11i | 0.835018 | + | 1.44629i | 0.894016 | + | 0.448036i | \(0.147876\pi\) |
−0.0589976 | + | 0.998258i | \(0.518790\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.26699e11 | + | 5.65860e11i | −0.712113 | + | 1.23342i | 0.251950 | + | 0.967740i | \(0.418928\pi\) |
−0.964063 | + | 0.265675i | \(0.914405\pi\) | |||||||
\(824\) | −2.21088e11 | + | 1.27645e11i | −0.479576 | + | 0.276883i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.88294e11 | + | 2.78304e11i | 0.619320 | + | 0.597859i | ||||
\(827\) | 1.50289e11 | 0.321296 | 0.160648 | − | 0.987012i | \(-0.448642\pi\) | ||||
0.160648 | + | 0.987012i | \(0.448642\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.29912e11 | + | 3.05945e11i | 1.12198 | + | 0.647776i | 0.941906 | − | 0.335877i | \(-0.109033\pi\) |
0.180075 | + | 0.983653i | \(0.442366\pi\) | |||||||
\(830\) | −3.43943e11 | + | 5.95727e11i | −0.724727 | + | 1.25526i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 5.93057e10i | − | 0.123767i | ||||||
\(833\) | −4.22235e10 | + | 7.94788e10i | −0.0876949 | + | 0.165071i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.71327e10 | − | 1.50918e11i | −0.179240 | − | 0.310453i | ||||
\(836\) | 6.94928e10 | + | 4.01217e10i | 0.142270 | + | 0.0821399i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.28696e11 | + | 1.89773e11i | −0.666529 | + | 0.384821i | ||||
\(839\) | 2.75074e11i | 0.555139i | 0.960706 | + | 0.277569i | \(0.0895288\pi\) | ||||
−0.960706 | + | 0.277569i | \(0.910471\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.95183e11 | −0.989877 | ||||||||
\(842\) | −1.85532e11 | − | 3.21350e11i | −0.369122 | − | 0.639338i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.69807e10 | + | 9.86934e10i | −0.112294 | + | 0.194499i | ||||
\(845\) | 1.06421e10 | − | 6.14423e9i | 0.0208738 | − | 0.0120515i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.40054e11 | + | 1.09635e11i | 0.855013 | + | 0.213018i | ||||
\(848\) | 1.01440e11 | 0.196167 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.02691e10 | + | 1.74759e10i | 0.0579861 | + | 0.0334783i | ||||
\(851\) | −1.26453e11 | + | 2.19023e11i | −0.241107 | + | 0.417610i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.75369e11i | 0.709026i | 0.935051 | + | 0.354513i | \(0.115353\pi\) | ||||
−0.935051 | + | 0.354513i | \(0.884647\pi\) | |||||||
\(854\) | 6.46786e10 | − | 1.85587e10i | 0.121599 | − | 0.0348912i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.29242e11 | − | 2.23853e11i | −0.240717 | − | 0.416935i | ||||
\(857\) | −2.12580e11 | − | 1.22733e11i | −0.394093 | − | 0.227530i | 0.289839 | − | 0.957075i | \(-0.406398\pi\) |
−0.683932 | + | 0.729546i | \(0.739731\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.67139e11 | + | 9.64979e10i | −0.306977 | + | 0.177233i | −0.645573 | − | 0.763699i | \(-0.723381\pi\) |
0.338596 | + | 0.940932i | \(0.390048\pi\) | |||||||
\(860\) | 2.17620e11i | 0.397837i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.49567e10 | 0.0270898 | ||||||||
\(863\) | −3.98230e11 | − | 6.89754e11i | −0.717944 | − | 1.24352i | −0.961813 | − | 0.273707i | \(-0.911750\pi\) |
0.243869 | − | 0.969808i | \(-0.421583\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.03778e11 | + | 1.79749e11i | −0.185371 | + | 0.321072i | ||||
\(866\) | 1.50596e10 | − | 8.69466e9i | 0.0267758 | − | 0.0154590i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.25241e10 | + | 2.91098e11i | −0.127763 | + | 0.512815i | ||||
\(869\) | 1.69623e11 | 0.297444 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.79202e10 | + | 5.07608e10i | 0.152762 | + | 0.0881973i | ||||
\(872\) | 1.71998e11 | − | 2.97909e11i | 0.297480 | − | 0.515250i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 2.52342e11i | − | 0.432458i | ||||||
\(875\) | 2.55416e11 | + | 2.46565e11i | 0.435729 | + | 0.420629i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.95942e11 | − | 6.85792e11i | −0.669319 | − | 1.15929i | −0.978095 | − | 0.208160i | \(-0.933253\pi\) |
0.308776 | − | 0.951135i | \(-0.400081\pi\) | |||||||
\(878\) | −3.45330e11 | − | 1.99376e11i | −0.581107 | − | 0.335502i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.49413e10 | + | 3.17204e10i | −0.0916154 | + | 0.0528942i | ||||
\(881\) | − | 5.78522e11i | − | 0.960320i | −0.877181 | − | 0.480160i | \(-0.840579\pi\) | ||
0.877181 | − | 0.480160i | \(-0.159421\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.90230e11 | −1.46440 | −0.732199 | − | 0.681090i | \(-0.761506\pi\) | ||||
−0.732199 | + | 0.681090i | \(0.761506\pi\) | |||||||
\(884\) | −2.82551e10 | − | 4.89393e10i | −0.0462688 | − | 0.0801399i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.71114e11 | + | 6.42788e11i | −0.602244 | + | 1.04312i | ||||
\(887\) | 5.27870e11 | − | 3.04766e11i | 0.852771 | − | 0.492347i | −0.00881401 | − | 0.999961i | \(-0.502806\pi\) |
0.861585 | + | 0.507614i | \(0.169472\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.88311e11 | − | 6.09430e11i | 0.941890 | − | 0.975701i | ||||
\(890\) | 4.52120e11 | 0.720598 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.02487e11 | + | 5.91712e10i | 0.161887 | + | 0.0934654i | ||||
\(893\) | 4.80286e9 | − | 8.31879e9i | 0.00755255 | − | 0.0130814i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.76692e11i | 1.05463i | ||||||||
\(896\) | −5.52777e10 | − | 1.37719e10i | −0.0857666 | − | 0.0213679i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.12191e11 | − | 5.40730e11i | −0.480081 | − | 0.831525i | ||||
\(899\) | 6.01564e10 | + | 3.47313e10i | 0.0920965 | + | 0.0531719i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.37087e10 | − | 4.83293e10i | 0.127020 | − | 0.0733349i | ||||
\(902\) | 2.27831e11i | 0.344181i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.18176e11 | 0.476425 | ||||||||
\(905\) | 1.90214e11 | + | 3.29461e11i | 0.283563 | + | 0.491145i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.03801e11 | − | 3.52994e11i | 0.301147 | − | 0.521601i | −0.675249 | − | 0.737590i | \(-0.735964\pi\) |
0.976396 | + | 0.215988i | \(0.0692973\pi\) | |||||||
\(908\) | 3.89563e11 | − | 2.24914e11i | 0.573105 | − | 0.330882i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.62535e11 | + | 5.66449e11i | 0.237018 | + | 0.826029i | ||||
\(911\) | 2.27629e11 | 0.330487 | 0.165243 | − | 0.986253i | \(-0.447159\pi\) | ||||
0.165243 | + | 0.986253i | \(0.447159\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.46447e11 | − | 2.00021e11i | −0.498601 | − | 0.287868i | ||||
\(914\) | 2.37089e11 | − | 4.10651e11i | 0.339725 | − | 0.588421i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.75893e11i | 0.533927i | ||||||||
\(917\) | 1.27582e10 | − | 5.12088e10i | 0.0180431 | − | 0.0724215i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.31609e11 | − | 1.09398e12i | −0.885496 | − | 1.53372i | −0.845144 | − | 0.534538i | \(-0.820486\pi\) |
−0.0403516 | − | 0.999186i | \(-0.512848\pi\) | |||||||
\(920\) | 1.72774e11 | + | 9.97513e10i | 0.241173 | + | 0.139241i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.36408e11 | + | 3.09695e11i | −0.742287 | + | 0.428559i | ||||
\(923\) | 9.94957e11i | 1.37087i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.78686e11 | 0.380670 | ||||||||
\(926\) | 3.16222e11 | + | 5.47712e11i | 0.430079 | + | 0.744918i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.59527e9 | + | 1.14233e10i | −0.00889284 | + | 0.0154028i | ||||
\(929\) | −1.22952e12 | + | 7.09863e11i | −1.65072 | + | 0.953041i | −0.673938 | + | 0.738788i | \(0.735398\pi\) |
−0.976778 | + | 0.214253i | \(0.931268\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.79636e11 | − | 6.07067e11i | −0.505323 | − | 0.808049i | ||||
\(932\) | 4.98471e11 | 0.660657 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.00737e11 | − | 3.46836e11i | −0.789400 | − | 0.455760i | ||||
\(935\) | −3.02252e10 | + | 5.23516e10i | −0.0395478 | + | 0.0684988i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 4.06177e11i | − | 0.526935i | −0.964668 | − | 0.263467i | \(-0.915134\pi\) | ||
0.964668 | − | 0.263467i | \(-0.0848661\pi\) | |||||||
\(938\) | 6.77298e10 | − | 7.01612e10i | 0.0874921 | − | 0.0906328i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.79716e9 | + | 6.57687e9i | 0.00486348 | + | 0.00842380i | ||||
\(941\) | 8.54334e11 | + | 4.93250e11i | 1.08961 | + | 0.629084i | 0.933471 | − | 0.358652i | \(-0.116764\pi\) |
0.156134 | + | 0.987736i | \(0.450097\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.20474e11 | − | 3.58231e11i | 0.784651 | − | 0.453019i | ||||
\(944\) | 2.41685e11i | 0.304342i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.26557e11 | −0.158024 | ||||||||
\(947\) | 2.02568e11 | + | 3.50858e11i | 0.251867 | + | 0.436246i | 0.964040 | − | 0.265758i | \(-0.0856222\pi\) |
−0.712173 | + | 0.702004i | \(0.752289\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.44734e9 | − | 9.43507e9i | 0.00671614 | − | 0.0116327i | ||||
\(950\) | −2.40812e11 | + | 1.39033e11i | −0.295653 | + | 0.170696i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.21767e10 | + | 1.49714e10i | −0.0635227 | + | 0.0182270i | ||||
\(953\) | 8.59856e9 | 0.0104245 | 0.00521224 | − | 0.999986i | \(-0.498341\pi\) | ||||
0.00521224 | + | 0.999986i | \(0.498341\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.04964e12 | + | 6.06007e11i | 1.26190 | + | 0.728559i | ||||
\(956\) | 1.39184e10 | − | 2.41073e10i | 0.0166631 | − | 0.0288614i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 3.99846e11i | − | 0.474713i | ||||||
\(959\) | 4.04932e11 | + | 1.41122e12i | 0.478749 | + | 1.66848i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.99831e10 | + | 8.65732e10i | 0.0586043 | + | 0.101506i | ||||
\(962\) | −3.90215e11 | − | 2.25291e11i | −0.455621 | − | 0.263053i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.92315e11 | + | 1.68768e11i | −0.338488 | + | 0.195426i | ||||
\(965\) | 1.26743e12i | 1.46155i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.57902e10 | −0.0866777 | −0.0433388 | − | 0.999060i | \(-0.513800\pi\) | ||||
−0.0433388 | + | 0.999060i | \(0.513800\pi\) | |||||||
\(968\) | 1.36765e11 | + | 2.36884e11i | 0.155767 | + | 0.269796i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.27778e11 | + | 1.08734e12i | −0.709119 | + | 1.22823i | ||||
\(971\) | −6.05255e11 | + | 3.49444e11i | −0.680866 | + | 0.393098i | −0.800181 | − | 0.599758i | \(-0.795263\pi\) |
0.119315 | + | 0.992856i | \(0.461930\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.57528e11 | − | 2.48604e11i | −0.287325 | − | 0.277368i | ||||
\(974\) | −3.20771e11 | −0.356418 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.51475e10 | + | 2.02924e10i | 0.0387342 | + | 0.0223632i | ||||
\(977\) | 8.73103e11 | − | 1.51226e12i | 0.958269 | − | 1.65977i | 0.231565 | − | 0.972819i | \(-0.425615\pi\) |
0.726704 | − | 0.686951i | \(-0.241051\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.62932e11i | 0.286228i | ||||||||
\(980\) | 5.65720e11 | − | 1.99560e10i | 0.613334 | − | 0.0216356i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.86815e11 | + | 4.96779e11i | 0.308430 | + | 0.534216i | ||||
\(983\) | 4.86285e11 | + | 2.80757e11i | 0.520807 | + | 0.300688i | 0.737265 | − | 0.675604i | \(-0.236117\pi\) |
−0.216458 | + | 0.976292i | \(0.569450\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.59399e11 | − | 2.07499e11i | 0.381797 | − | 0.220430i | ||||
\(986\) | 1.25688e10i | 0.0132980i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.49578e11 | 0.471821 | ||||||||
\(989\) | 1.98993e11 | + | 3.44666e11i | 0.207995 | + | 0.360258i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.22767e11 | − | 7.32253e11i | 0.438335 | − | 0.759218i | −0.559226 | − | 0.829015i | \(-0.688902\pi\) |
0.997561 | + | 0.0697966i | \(0.0222350\pi\) | |||||||
\(992\) | −1.56700e11 | + | 9.04709e10i | −0.161816 | + | 0.0934248i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.27380e11 | + | 2.31047e11i | 0.949975 | + | 0.236677i | ||||
\(995\) | −1.04906e11 | −0.107030 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.57819e11 | + | 4.95262e11i | 0.868190 | + | 0.501250i | 0.866746 | − | 0.498749i | \(-0.166207\pi\) |
0.00144368 | + | 0.999999i | \(0.499540\pi\) | |||||||
\(998\) | −3.49581e11 | + | 6.05491e11i | −0.352391 | + | 0.610360i | ||||
\(999\) | 0 | 0 |
(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 | 126.9.n.d.73.4 | yes | 20 | |
3.2 | odd | 2 | inner | 126.9.n.d.73.7 | yes | 20 | |
7.5 | odd | 6 | inner | 126.9.n.d.19.4 | ✓ | 20 | |
21.5 | even | 6 | inner | 126.9.n.d.19.7 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.9.n.d.19.4 | ✓ | 20 | 7.5 | odd | 6 | inner | |
126.9.n.d.19.7 | yes | 20 | 21.5 | even | 6 | inner | |
126.9.n.d.73.4 | yes | 20 | 1.1 | even | 1 | trivial | |
126.9.n.d.73.7 | yes | 20 | 3.2 | odd | 2 | inner |