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 | 73.1 | ||
Root | \(42.0992 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.73 |
Dual form | 126.9.n.d.19.1 |
$q$-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 | ||||
\(5\) | −565.865 | + | 326.703i | −0.905385 | + | 0.522724i | −0.878943 | − | 0.476926i | \(-0.841751\pi\) |
−0.0264413 | + | 0.999650i | \(0.508418\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2120.69 | + | 1125.82i | 0.883254 | + | 0.468895i | ||||
\(8\) | 1448.15 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6402.04 | + | 3696.22i | 0.640204 | + | 0.369622i | ||||
\(11\) | −13880.2 | + | 24041.2i | −0.948034 | + | 1.64204i | −0.198475 | + | 0.980106i | \(0.563599\pi\) |
−0.749559 | + | 0.661937i | \(0.769735\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6765.74i | − | 0.236887i | −0.992961 | − | 0.118444i | \(-0.962210\pi\) | ||
0.992961 | − | 0.118444i | \(-0.0377905\pi\) | |||||||
\(14\) | −965.728 | − | 27147.0i | −0.0251387 | − | 0.706660i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8192.00 | − | 14189.0i | −0.125000 | − | 0.216506i | ||||
\(17\) | 84547.9 | + | 48813.8i | 1.01230 | + | 0.584449i | 0.911863 | − | 0.410495i | \(-0.134644\pi\) |
0.100433 | + | 0.994944i | \(0.467977\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 67716.2 | − | 39095.9i | 0.519610 | − | 0.299997i | −0.217165 | − | 0.976135i | \(-0.569681\pi\) |
0.736775 | + | 0.676138i | \(0.236348\pi\) | |||||||
\(20\) | − | 83635.8i | − | 0.522724i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 314072. | 1.34072 | ||||||||
\(23\) | 46841.9 | + | 81132.5i | 0.167387 | + | 0.289924i | 0.937501 | − | 0.347984i | \(-0.113134\pi\) |
−0.770113 | + | 0.637907i | \(0.779800\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 18156.6 | − | 31448.1i | 0.0464808 | − | 0.0805072i | ||||
\(26\) | −66290.4 | + | 38272.8i | −0.145063 | + | 0.0837523i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −260523. | + | 163029.i | −0.423851 | + | 0.265236i | ||||
\(29\) | 305473. | 0.431897 | 0.215949 | − | 0.976405i | \(-0.430716\pi\) | ||||
0.215949 | + | 0.976405i | \(0.430716\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.10538e6 | − | 638191.i | −1.19692 | − | 0.691041i | −0.237051 | − | 0.971497i | \(-0.576181\pi\) |
−0.959867 | + | 0.280457i | \(0.909514\pi\) | |||||||
\(32\) | −92681.9 | + | 160530.i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.10453e6i | − | 0.826536i | ||||||
\(35\) | −1.56783e6 | + | 55774.1i | −1.04479 | + | 0.0371672i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.39624e6 | − | 2.41836e6i | −0.744994 | − | 1.29037i | −0.950197 | − | 0.311649i | \(-0.899119\pi\) |
0.205203 | − | 0.978719i | \(-0.434215\pi\) | |||||||
\(38\) | −766121. | − | 442320.i | −0.367420 | − | 0.212130i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −819461. | + | 473116.i | −0.320102 | + | 0.184811i | ||||
\(41\) | 2.12414e6i | 0.751707i | 0.926679 | + | 0.375853i | \(0.122650\pi\) | ||||
−0.926679 | + | 0.375853i | \(0.877350\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.96500e6 | 1.74477 | 0.872383 | − | 0.488824i | \(-0.162574\pi\) | ||||
0.872383 | + | 0.488824i | \(0.162574\pi\) | |||||||
\(44\) | −1.77666e6 | − | 3.07727e6i | −0.474017 | − | 0.821022i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 529955. | − | 917909.i | 0.118361 | − | 0.205007i | ||||
\(47\) | −3.70738e6 | + | 2.14046e6i | −0.759758 | + | 0.438647i | −0.829209 | − | 0.558939i | \(-0.811209\pi\) |
0.0694505 | + | 0.997585i | \(0.477875\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.22987e6 | + | 4.77503e6i | 0.560274 | + | 0.828307i | ||||
\(50\) | −410836. | −0.0657338 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 749990. | + | 433007.i | 0.102575 | + | 0.0592218i | ||||
\(53\) | −1.11299e6 | + | 1.92776e6i | −0.141055 | + | 0.244315i | −0.927894 | − | 0.372843i | \(-0.878383\pi\) |
0.786839 | + | 0.617158i | \(0.211716\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.81387e7i | − | 1.98224i | ||||||
\(56\) | 3.07109e6 | + | 1.63036e6i | 0.312277 | + | 0.165780i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.72802e6 | − | 2.99301e6i | −0.152699 | − | 0.264482i | ||||
\(59\) | −1.57427e7 | − | 9.08906e6i | −1.29919 | − | 0.750085i | −0.318923 | − | 0.947781i | \(-0.603321\pi\) |
−0.980264 | + | 0.197695i | \(0.936654\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.28000e6 | + | 2.47106e6i | −0.309118 | + | 0.178469i | −0.646532 | − | 0.762887i | \(-0.723781\pi\) |
0.337414 | + | 0.941356i | \(0.390448\pi\) | |||||||
\(62\) | 1.44406e7i | 0.977279i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.09715e6 | 0.125000 | ||||||||
\(65\) | 2.21038e6 | + | 3.82850e6i | 0.123827 | + | 0.214474i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.58826e7 | + | 2.75094e7i | −0.788173 | + | 1.36516i | 0.138911 | + | 0.990305i | \(0.455640\pi\) |
−0.927085 | + | 0.374852i | \(0.877694\pi\) | |||||||
\(68\) | −1.08221e7 | + | 6.24816e6i | −0.506148 | + | 0.292225i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 9.41548e6 | + | 1.50461e7i | 0.392148 | + | 0.626658i | ||||
\(71\) | −2.29883e7 | −0.904633 | −0.452317 | − | 0.891857i | \(-0.649402\pi\) | ||||
−0.452317 | + | 0.891857i | \(0.649402\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.88605e6 | − | 1.08891e6i | −0.0664143 | − | 0.0383443i | 0.466425 | − | 0.884561i | \(-0.345542\pi\) |
−0.532839 | + | 0.846216i | \(0.678875\pi\) | |||||||
\(74\) | −1.57966e7 | + | 2.73606e7i | −0.526791 | + | 0.912428i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00086e7i | 0.299997i | ||||||||
\(77\) | −5.65015e7 | + | 3.53573e7i | −1.60730 | + | 1.00581i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.82277e6 | − | 1.35494e7i | −0.200841 | − | 0.347867i | 0.747959 | − | 0.663745i | \(-0.231034\pi\) |
−0.948800 | + | 0.315879i | \(0.897701\pi\) | |||||||
\(80\) | 9.27114e6 | + | 5.35269e6i | 0.226346 | + | 0.130681i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.08123e7 | − | 1.20160e7i | 0.460324 | − | 0.265768i | ||||
\(83\) | − | 1.88638e7i | − | 0.397481i | −0.980052 | − | 0.198741i | \(-0.936315\pi\) | ||
0.980052 | − | 0.198741i | \(-0.0636851\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.37903e7 | −1.22202 | ||||||||
\(86\) | −3.37432e7 | − | 5.84449e7i | −0.616868 | − | 1.06845i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.01006e7 | + | 3.48153e7i | −0.335181 | + | 0.580550i | ||||
\(89\) | −6.59498e7 | + | 3.80762e7i | −1.05112 | + | 0.606866i | −0.922964 | − | 0.384887i | \(-0.874240\pi\) |
−0.128160 | + | 0.991754i | \(0.540907\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.61699e6 | − | 1.43480e7i | 0.111075 | − | 0.209232i | ||||
\(92\) | −1.19915e7 | −0.167387 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.19442e7 | + | 2.42165e7i | 0.537230 | + | 0.310170i | ||||
\(95\) | −2.55455e7 | + | 4.42461e7i | −0.313632 | + | 0.543226i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.44142e8i | 1.62818i | 0.580735 | + | 0.814092i | \(0.302765\pi\) | ||||
−0.580735 | + | 0.814092i | \(0.697235\pi\) | |||||||
\(98\) | 2.85146e7 | − | 5.86578e7i | 0.309146 | − | 0.635947i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.32404e6 | + | 4.02536e6i | 0.0232404 | + | 0.0402536i | ||||
\(101\) | −1.00997e8 | − | 5.83108e7i | −0.970564 | − | 0.560356i | −0.0711561 | − | 0.997465i | \(-0.522669\pi\) |
−0.899408 | + | 0.437110i | \(0.856002\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.72245e8 | − | 9.94459e7i | 1.53038 | − | 0.883564i | 0.531033 | − | 0.847351i | \(-0.321804\pi\) |
0.999344 | − | 0.0362123i | \(-0.0115292\pi\) | |||||||
\(104\) | − | 9.79783e6i | − | 0.0837523i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.51842e7 | 0.199482 | ||||||||
\(107\) | 7.65995e7 | + | 1.32674e8i | 0.584374 | + | 1.01216i | 0.994953 | + | 0.100340i | \(0.0319931\pi\) |
−0.410580 | + | 0.911825i | \(0.634674\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.41080e6 | + | 1.28359e7i | −0.0525000 | + | 0.0909327i | −0.891081 | − | 0.453844i | \(-0.850052\pi\) |
0.838581 | + | 0.544777i | \(0.183386\pi\) | |||||||
\(110\) | −1.77723e8 | + | 1.02608e8i | −1.21387 | + | 0.700828i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.39852e6 | − | 3.93131e7i | −0.00888787 | − | 0.249842i | ||||
\(113\) | −1.54533e8 | −0.947780 | −0.473890 | − | 0.880584i | \(-0.657151\pi\) | ||||
−0.473890 | + | 0.880584i | \(0.657151\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.30124e7 | − | 3.06067e7i | −0.303100 | − | 0.174995i | ||||
\(116\) | −1.95503e7 | + | 3.38620e7i | −0.107974 | + | 0.187017i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.05662e8i | 1.06078i | ||||||||
\(119\) | 1.24345e8 | + | 1.98705e8i | 0.620068 | + | 0.990878i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.78139e8 | − | 4.81750e8i | −1.29754 | − | 2.24740i | ||||
\(122\) | 4.84227e7 | + | 2.79568e7i | 0.218579 | + | 0.126197i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.41488e8 | − | 8.16884e7i | 0.598459 | − | 0.345520i | ||||
\(125\) | − | 2.31509e8i | − | 0.948261i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.05583e8 | −1.55907 | −0.779534 | − | 0.626360i | \(-0.784544\pi\) | ||||
−0.779534 | + | 0.626360i | \(0.784544\pi\) | |||||||
\(128\) | −1.18633e7 | − | 2.05478e7i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.50076e7 | − | 4.33145e7i | 0.0875587 | − | 0.151656i | ||||
\(131\) | 2.62492e8 | − | 1.51550e8i | 0.891313 | − | 0.514600i | 0.0169415 | − | 0.999856i | \(-0.494607\pi\) |
0.874372 | + | 0.485256i | \(0.161274\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.87620e8 | − | 6.67439e6i | 0.599615 | − | 0.0213307i | ||||
\(134\) | 3.59382e8 | 1.11465 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.22439e8 | + | 7.06899e7i | 0.357901 | + | 0.206634i | ||||
\(137\) | 4.17078e7 | − | 7.22400e7i | 0.118395 | − | 0.205067i | −0.800736 | − | 0.599017i | \(-0.795558\pi\) |
0.919132 | + | 0.393950i | \(0.128892\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.40378e8i | − | 1.17969i | −0.807518 | − | 0.589843i | \(-0.799190\pi\) | ||
0.807518 | − | 0.589843i | \(-0.200810\pi\) | |||||||
\(140\) | 9.41587e7 | − | 1.77366e8i | 0.245103 | − | 0.461698i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.30041e8 | + | 2.25238e8i | 0.319836 | + | 0.553973i | ||||
\(143\) | 1.62656e8 | + | 9.39096e7i | 0.388979 | + | 0.224577i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.72856e8 | + | 9.97987e7i | −0.391033 | + | 0.225763i | ||||
\(146\) | 2.46392e7i | 0.0542270i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.57437e8 | 0.744994 | ||||||||
\(149\) | −2.24155e8 | − | 3.88248e8i | −0.454782 | − | 0.787705i | 0.543894 | − | 0.839154i | \(-0.316949\pi\) |
−0.998676 | + | 0.0514488i | \(0.983616\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.40664e7 | + | 1.10966e8i | −0.123232 | + | 0.213444i | −0.921040 | − | 0.389467i | \(-0.872659\pi\) |
0.797809 | + | 0.602911i | \(0.205992\pi\) | |||||||
\(152\) | 9.80635e7 | − | 5.66170e7i | 0.183710 | − | 0.106065i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.66051e8 | + | 3.53588e8i | 1.18420 | + | 0.628659i | ||||
\(155\) | 8.33994e8 | 1.44489 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.55619e8 | − | 3.20787e8i | −0.914489 | − | 0.527980i | −0.0326160 | − | 0.999468i | \(-0.510384\pi\) |
−0.881873 | + | 0.471488i | \(0.843717\pi\) | |||||||
\(158\) | −8.85045e7 | + | 1.53294e8i | −0.142016 | + | 0.245979i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 1.21118e8i | − | 0.184811i | ||||||
\(161\) | 7.99676e6 | + | 2.24792e8i | 0.0119017 | + | 0.334563i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.94108e8 | − | 3.36205e8i | −0.274975 | − | 0.476270i | 0.695154 | − | 0.718861i | \(-0.255336\pi\) |
−0.970129 | + | 0.242591i | \(0.922003\pi\) | |||||||
\(164\) | −2.35464e8 | − | 1.35945e8i | −0.325499 | − | 0.187927i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.84827e8 | + | 1.06710e8i | −0.243406 | + | 0.140531i | ||||
\(167\) | − | 8.17453e8i | − | 1.05099i | −0.850798 | − | 0.525493i | \(-0.823881\pi\) | ||
0.850798 | − | 0.525493i | \(-0.176119\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.69956e8 | 0.943884 | ||||||||
\(170\) | 3.60853e8 | + | 6.25015e8i | 0.432050 | + | 0.748333i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.81760e8 | + | 6.61228e8i | −0.436191 | + | 0.755505i | ||||
\(173\) | 2.71005e8 | − | 1.56465e8i | 0.302547 | − | 0.174676i | −0.341040 | − | 0.940049i | \(-0.610779\pi\) |
0.643586 | + | 0.765373i | \(0.277446\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.39094e7 | − | 4.62508e7i | 0.0788038 | − | 0.0493136i | ||||
\(176\) | 4.54825e8 | 0.474017 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.46137e8 | + | 4.30783e8i | 0.743256 | + | 0.429119i | ||||
\(179\) | 5.83564e8 | − | 1.01076e9i | 0.568429 | − | 0.984548i | −0.428293 | − | 0.903640i | \(-0.640885\pi\) |
0.996722 | − | 0.0809079i | \(-0.0257820\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.82102e7i | − | 0.0449184i | −0.999748 | − | 0.0224592i | \(-0.992850\pi\) | ||
0.999748 | − | 0.0224592i | \(-0.00714959\pi\) | |||||||
\(182\) | −1.83670e8 | + | 6.53386e6i | −0.167399 | + | 0.00595503i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.78343e7 | + | 1.17492e8i | 0.0591804 | + | 0.102503i | ||||
\(185\) | 1.58017e9 | + | 9.12310e8i | 1.34901 | + | 0.778853i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.34708e9 | + | 1.35509e9i | −1.91938 | + | 1.10816i | ||||
\(188\) | − | 5.47957e8i | − | 0.438647i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.78028e8 | 0.443542 | ||||||||
\(191\) | −1.84184e8 | − | 3.19017e8i | −0.138395 | − | 0.239706i | 0.788494 | − | 0.615042i | \(-0.210861\pi\) |
−0.926889 | + | 0.375335i | \(0.877528\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.07633e8 | + | 1.86426e8i | −0.0775742 | + | 0.134362i | −0.902203 | − | 0.431312i | \(-0.858051\pi\) |
0.824629 | + | 0.565674i | \(0.191384\pi\) | |||||||
\(194\) | 1.41230e9 | − | 8.15390e8i | 0.997055 | − | 0.575650i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.36029e8 | + | 5.24333e7i | −0.498736 | + | 0.0355290i | ||||
\(197\) | 1.24242e9 | 0.824901 | 0.412450 | − | 0.910980i | \(-0.364673\pi\) | ||||
0.412450 | + | 0.910980i | \(0.364673\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.63293e7 | + | 3.82952e7i | 0.0422954 | + | 0.0244193i | 0.520999 | − | 0.853558i | \(-0.325560\pi\) |
−0.478703 | + | 0.877977i | \(0.658893\pi\) | |||||||
\(200\) | 2.62935e7 | − | 4.55417e7i | 0.0164335 | − | 0.0284636i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.31942e9i | 0.792462i | ||||||||
\(203\) | 6.47814e8 | + | 3.43907e8i | 0.381475 | + | 0.202515i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.93963e8 | − | 1.20198e9i | −0.392935 | − | 0.680584i | ||||
\(206\) | −1.94873e9 | − | 1.12510e9i | −1.08214 | − | 0.624774i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9.59988e7 | + | 5.54249e7i | −0.0512876 | + | 0.0296109i | ||||
\(209\) | 2.17063e9i | 1.13763i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.38976e8 | −0.120566 | −0.0602829 | − | 0.998181i | \(-0.519200\pi\) | ||||
−0.0602829 | + | 0.998181i | \(0.519200\pi\) | |||||||
\(212\) | −1.42463e8 | − | 2.46753e8i | −0.0705276 | − | 0.122157i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.66624e8 | − | 1.50104e9i | 0.413215 | − | 0.715709i | ||||
\(215\) | −3.37539e9 | + | 1.94878e9i | −1.57968 | + | 0.912031i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.62568e9 | − | 2.59786e9i | −0.733156 | − | 1.17159i | ||||
\(218\) | 1.67687e8 | 0.0742462 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.01070e9 | + | 1.16088e9i | 0.858335 | + | 0.495560i | ||||
\(221\) | 3.30261e8 | − | 5.72029e8i | 0.138449 | − | 0.239800i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.46166e9i | 0.591055i | 0.955334 | + | 0.295527i | \(0.0954954\pi\) | ||||
−0.955334 | + | 0.295527i | \(0.904505\pi\) | |||||||
\(224\) | −3.77277e8 | + | 2.36091e8i | −0.149854 | + | 0.0937752i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.74171e8 | + | 1.51411e9i | 0.335091 | + | 0.580394i | ||||
\(227\) | 1.93853e9 | + | 1.11921e9i | 0.730079 | + | 0.421512i | 0.818451 | − | 0.574576i | \(-0.194833\pi\) |
−0.0883718 | + | 0.996088i | \(0.528166\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.57629e8 | − | 4.95153e8i | 0.311859 | − | 0.180052i | −0.335899 | − | 0.941898i | \(-0.609040\pi\) |
0.647758 | + | 0.761846i | \(0.275707\pi\) | |||||||
\(230\) | 6.92551e8i | 0.247480i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.42372e8 | 0.152699 | ||||||||
\(233\) | −1.52722e9 | − | 2.64522e9i | −0.518176 | − | 0.897507i | −0.999777 | − | 0.0211162i | \(-0.993278\pi\) |
0.481601 | − | 0.876390i | \(-0.340055\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.39858e9 | − | 2.42242e9i | 0.458582 | − | 0.794288i | ||||
\(236\) | 2.01507e9 | − | 1.16340e9i | 0.649593 | − | 0.375043i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.24350e9 | − | 2.34237e9i | 0.387559 | − | 0.730041i | ||||
\(239\) | −6.41304e9 | −1.96550 | −0.982748 | − | 0.184948i | \(-0.940788\pi\) | ||||
−0.982748 | + | 0.184948i | \(0.940788\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.46600e9 | + | 2.57845e9i | 1.32389 | + | 0.764346i | 0.984346 | − | 0.176245i | \(-0.0563952\pi\) |
0.339540 | + | 0.940592i | \(0.389729\pi\) | |||||||
\(242\) | −3.14678e9 | + | 5.45038e9i | −0.917497 | + | 1.58915i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 6.32591e8i | − | 0.178469i | ||||||
\(245\) | −3.38768e9 | − | 1.64682e9i | −0.940240 | − | 0.457068i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.64513e8 | − | 4.58150e8i | −0.0710655 | − | 0.123089i | ||||
\(248\) | −1.60076e9 | − | 9.24199e8i | −0.423174 | − | 0.244320i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.26832e9 | + | 1.30961e9i | −0.580689 | + | 0.335261i | ||||
\(251\) | − | 5.54506e9i | − | 1.39705i | −0.715586 | − | 0.698524i | \(-0.753840\pi\) | ||
0.715586 | − | 0.698524i | \(-0.246160\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.60069e9 | −0.634756 | ||||||||
\(254\) | 2.29433e9 | + | 3.97389e9i | 0.551214 | + | 0.954730i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.34218e8 | + | 2.32472e8i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 4.04193e8 | − | 2.33361e8i | 0.0926522 | − | 0.0534928i | −0.452958 | − | 0.891532i | \(-0.649631\pi\) |
0.545610 | + | 0.838039i | \(0.316298\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.38363e8 | − | 6.70050e9i | −0.0529713 | − | 1.48905i | ||||
\(260\) | −5.65858e8 | −0.123827 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.96975e9 | − | 1.71459e9i | −0.630254 | − | 0.363877i | ||||
\(263\) | −3.52006e9 | + | 6.09692e9i | −0.735744 | + | 1.27435i | 0.218652 | + | 0.975803i | \(0.429834\pi\) |
−0.954396 | + | 0.298544i | \(0.903499\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.45447e9i | − | 0.294932i | ||||||
\(266\) | −1.12673e9 | − | 1.80054e9i | −0.225058 | − | 0.359646i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.03297e9 | − | 3.52121e9i | −0.394087 | − | 0.682578i | ||||
\(269\) | 1.82792e9 | + | 1.05535e9i | 0.349098 | + | 0.201552i | 0.664288 | − | 0.747477i | \(-0.268735\pi\) |
−0.315190 | + | 0.949029i | \(0.602068\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.02504e9 | + | 4.05591e9i | −1.30248 | + | 0.751988i | −0.980829 | − | 0.194869i | \(-0.937572\pi\) |
−0.321653 | + | 0.946858i | \(0.604238\pi\) | |||||||
\(272\) | − | 1.59953e9i | − | 0.292225i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.43740e8 | −0.167436 | ||||||||
\(275\) | 5.04033e8 | + | 8.73010e8i | 0.0881308 | + | 0.152647i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.53708e7 | + | 1.65187e8i | −0.0161993 | + | 0.0280580i | −0.874011 | − | 0.485905i | \(-0.838490\pi\) |
0.857812 | + | 0.513963i | \(0.171823\pi\) | |||||||
\(278\) | −4.31481e9 | + | 2.49116e9i | −0.722407 | + | 0.417082i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.27047e9 | + | 8.07695e7i | −0.369388 | + | 0.0131406i | ||||
\(281\) | −8.10613e9 | −1.30014 | −0.650068 | − | 0.759876i | \(-0.725259\pi\) | ||||
−0.650068 | + | 0.759876i | \(0.725259\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.32236e9 | + | 3.07287e9i | 0.829771 | + | 0.479069i | 0.853774 | − | 0.520643i | \(-0.174308\pi\) |
−0.0240029 | + | 0.999712i | \(0.507641\pi\) | |||||||
\(284\) | 1.47125e9 | − | 2.54828e9i | 0.226158 | − | 0.391718i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 2.12493e9i | − | 0.317600i | ||||||
\(287\) | −2.39140e9 | + | 4.50465e9i | −0.352472 | + | 0.663948i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.27769e9 | + | 2.21303e9i | 0.183162 | + | 0.317245i | ||||
\(290\) | 1.95565e9 | + | 1.12909e9i | 0.276502 | + | 0.159639i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.41414e8 | − | 1.39381e8i | 0.0332071 | − | 0.0191722i | ||||
\(293\) | 9.76338e9i | 1.32474i | 0.749178 | + | 0.662368i | \(0.230449\pi\) | ||||
−0.749178 | + | 0.662368i | \(0.769551\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.18777e10 | 1.56835 | ||||||||
\(296\) | −2.02197e9 | − | 3.50216e9i | −0.263395 | − | 0.456214i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.53602e9 | + | 4.39252e9i | −0.321579 | + | 0.556992i | ||||
\(299\) | 5.48921e8 | − | 3.16920e8i | 0.0686792 | − | 0.0396519i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.26499e10 | + | 6.71551e9i | 1.54107 | + | 0.818112i | ||||
\(302\) | 1.44966e9 | 0.174276 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.10946e9 | − | 6.40548e8i | −0.129903 | − | 0.0749993i | ||||
\(305\) | 1.61460e9 | − | 2.79657e9i | 0.186580 | − | 0.323167i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.84209e9i | 0.770257i | 0.922863 | + | 0.385128i | \(0.125843\pi\) | ||||
−0.922863 | + | 0.385128i | \(0.874157\pi\) | |||||||
\(308\) | −3.03308e8 | − | 8.52613e9i | −0.0337040 | − | 0.947435i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.71778e9 | − | 8.17144e9i | −0.510847 | − | 0.884813i | ||||
\(311\) | 3.27953e8 | + | 1.89344e8i | 0.0350566 | + | 0.0202399i | 0.517426 | − | 0.855728i | \(-0.326890\pi\) |
−0.482369 | + | 0.875968i | \(0.660224\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.00983e10 | + | 5.83026e9i | −1.05213 | + | 0.607450i | −0.923246 | − | 0.384209i | \(-0.874474\pi\) |
−0.128888 | + | 0.991659i | \(0.541141\pi\) | |||||||
\(314\) | 7.25857e9i | 0.746677i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00263e9 | 0.200841 | ||||||||
\(317\) | 1.50709e9 | + | 2.61035e9i | 0.149246 | + | 0.258501i | 0.930949 | − | 0.365150i | \(-0.118982\pi\) |
−0.781703 | + | 0.623651i | \(0.785649\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.24001e9 | + | 7.34392e9i | −0.409453 | + | 0.709194i | ||||
\(320\) | −1.18671e9 | + | 6.85145e8i | −0.113173 | + | 0.0653405i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.15727e9 | − | 1.34997e9i | 0.200669 | − | 0.125574i | ||||
\(323\) | 7.63368e9 | 0.701333 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.12770e8 | − | 1.22843e8i | −0.0190711 | − | 0.0110107i | ||||
\(326\) | −2.19608e9 | + | 3.80372e9i | −0.194436 | + | 0.336774i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.07609e9i | 0.265768i | ||||||||
\(329\) | −1.02720e10 | + | 3.65415e8i | −0.876739 | + | 0.0311891i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.73255e9 | − | 1.33932e10i | −0.644185 | − | 1.11576i | −0.984489 | − | 0.175446i | \(-0.943863\pi\) |
0.340304 | − | 0.940315i | \(-0.389470\pi\) | |||||||
\(332\) | 2.09107e9 | + | 1.20728e9i | 0.172114 | + | 0.0993703i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.00937e9 | + | 4.62421e9i | −0.643595 | + | 0.371580i | ||||
\(335\) | − | 2.07555e10i | − | 1.64799i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.53486e10 | 1.19001 | 0.595003 | − | 0.803723i | \(-0.297151\pi\) | ||||
0.595003 | + | 0.803723i | \(0.297151\pi\) | |||||||
\(338\) | −4.35553e9 | − | 7.54399e9i | −0.333714 | − | 0.578009i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.08258e9 | − | 7.07124e9i | 0.305506 | − | 0.529151i | ||||
\(341\) | 3.06857e10 | − | 1.77164e10i | 2.26944 | − | 1.31026i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.47375e9 | + | 1.37626e10i | 0.106475 | + | 0.994315i | ||||
\(344\) | 8.63825e9 | 0.616868 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.06607e9 | − | 1.77020e9i | −0.213933 | − | 0.123514i | ||||
\(347\) | −3.88941e9 | + | 6.73665e9i | −0.268266 | + | 0.464650i | −0.968414 | − | 0.249347i | \(-0.919784\pi\) |
0.700148 | + | 0.713998i | \(0.253117\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.49476e10i | 1.00756i | 0.863833 | + | 0.503778i | \(0.168057\pi\) | ||||
−0.863833 | + | 0.503778i | \(0.831943\pi\) | |||||||
\(350\) | −8.71258e8 | − | 4.62527e8i | −0.0580597 | − | 0.0308223i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.57288e9 | − | 4.45636e9i | −0.167590 | − | 0.290275i | ||||
\(353\) | 1.99572e10 | + | 1.15223e10i | 1.28529 | + | 0.742061i | 0.977810 | − | 0.209494i | \(-0.0671818\pi\) |
0.307478 | + | 0.951555i | \(0.400515\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.30083e10 | − | 7.51032e9i | 0.819041 | − | 0.472874i | ||||
\(356\) | − | 9.74750e9i | − | 0.606866i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.32045e10 | −0.803880 | ||||||||
\(359\) | −3.05292e9 | − | 5.28781e9i | −0.183796 | − | 0.318345i | 0.759374 | − | 0.650655i | \(-0.225505\pi\) |
−0.943170 | + | 0.332310i | \(0.892172\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.43480e9 | + | 9.41334e9i | −0.320003 | + | 0.554262i | ||||
\(362\) | −4.72362e8 | + | 2.72718e8i | −0.0275068 | + | 0.0158811i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.10301e9 | + | 1.76263e9i | 0.0628311 | + | 0.100405i | ||||
\(365\) | 1.42300e9 | 0.0801740 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.35256e10 | + | 7.80898e9i | 0.745574 | + | 0.430457i | 0.824092 | − | 0.566455i | \(-0.191686\pi\) |
−0.0785184 | + | 0.996913i | \(0.525019\pi\) | |||||||
\(368\) | 7.67457e8 | − | 1.32927e9i | 0.0418469 | − | 0.0724809i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 2.06432e10i | − | 1.10146i | ||||||
\(371\) | −4.53063e9 | + | 2.83516e9i | −0.239146 | + | 0.149652i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.50571e9 | − | 9.53617e9i | −0.284432 | − | 0.492650i | 0.688040 | − | 0.725673i | \(-0.258472\pi\) |
−0.972471 | + | 0.233023i | \(0.925138\pi\) | |||||||
\(374\) | 2.65542e10 | + | 1.53311e10i | 1.35721 | + | 0.783584i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.36886e9 | + | 3.09971e9i | −0.268615 | + | 0.155085i | ||||
\(377\) | − | 2.06675e9i | − | 0.102311i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.66496e10 | −1.77629 | −0.888143 | − | 0.459567i | \(-0.848005\pi\) | ||||
−0.888143 | + | 0.459567i | \(0.848005\pi\) | |||||||
\(380\) | −3.26982e9 | − | 5.66350e9i | −0.156816 | − | 0.271613i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.08381e9 | + | 3.60926e9i | −0.0978598 | + | 0.169498i | ||||
\(383\) | 5.83120e9 | − | 3.36664e9i | 0.270996 | − | 0.156460i | −0.358344 | − | 0.933590i | \(-0.616659\pi\) |
0.629340 | + | 0.777130i | \(0.283325\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.04209e10 | − | 3.84667e10i | 0.929464 | − | 1.75082i | ||||
\(386\) | 2.43546e9 | 0.109706 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.59783e10 | − | 9.22509e9i | −0.705025 | − | 0.407046i | ||||
\(389\) | −1.84833e9 | + | 3.20140e9i | −0.0807199 | + | 0.139811i | −0.903559 | − | 0.428463i | \(-0.859055\pi\) |
0.822839 | + | 0.568274i | \(0.192389\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.14611e9i | 0.391318i | ||||||||
\(392\) | 4.67735e9 | + | 6.91498e9i | 0.198087 | + | 0.292851i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.02816e9 | − | 1.21731e10i | −0.291647 | − | 0.505147i | ||||
\(395\) | 8.85327e9 | + | 5.11144e9i | 0.363677 | + | 0.209969i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.27969e10 | − | 2.47088e10i | 1.72286 | − | 0.994694i | 0.809993 | − | 0.586439i | \(-0.199471\pi\) |
0.912868 | − | 0.408255i | \(-0.133863\pi\) | |||||||
\(398\) | − | 8.66522e8i | − | 0.0345340i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.94955e8 | −0.0232404 | ||||||||
\(401\) | 1.47061e9 | + | 2.54716e9i | 0.0568747 | + | 0.0985098i | 0.893061 | − | 0.449936i | \(-0.148553\pi\) |
−0.836186 | + | 0.548446i | \(0.815220\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.31783e9 | + | 7.47870e9i | −0.163699 | + | 0.283535i | ||||
\(404\) | 1.29277e10 | − | 7.46379e9i | 0.485282 | − | 0.280178i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.95004e8 | − | 8.29268e9i | −0.0108573 | − | 0.305205i | ||||
\(407\) | 7.75201e10 | 2.82512 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.16429e10 | + | 1.24956e10i | 0.773434 | + | 0.446542i | 0.834098 | − | 0.551616i | \(-0.185989\pi\) |
−0.0606645 | + | 0.998158i | \(0.519322\pi\) | |||||||
\(410\) | −7.85130e9 | + | 1.35988e10i | −0.277847 | + | 0.481245i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.54581e10i | 0.883564i | ||||||||
\(413\) | −2.31528e10 | − | 3.69985e10i | −0.795799 | − | 1.27170i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.16285e9 | + | 1.06744e10i | 0.207773 | + | 0.359873i | ||||
\(416\) | 1.08610e9 | + | 6.27061e8i | 0.0362658 | + | 0.0209381i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.12678e10 | − | 1.22790e10i | 0.696653 | − | 0.402213i | ||||
\(419\) | − | 5.50593e10i | − | 1.78638i | −0.449676 | − | 0.893192i | \(-0.648460\pi\) | ||
0.449676 | − | 0.893192i | \(-0.351540\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.98403e9 | 0.317817 | 0.158909 | − | 0.987293i | \(-0.449202\pi\) | ||||
0.158909 | + | 0.987293i | \(0.449202\pi\) | |||||||
\(422\) | 1.35185e9 | + | 2.34148e9i | 0.0426265 | + | 0.0738312i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.61179e9 | + | 2.79170e9i | −0.0498706 | + | 0.0863783i | ||||
\(425\) | 3.07020e9 | − | 1.77258e9i | 0.0941047 | − | 0.0543314i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.18585e10 | + | 4.21855e8i | −0.356713 | + | 0.0126897i | ||||
\(428\) | −1.96095e10 | −0.584374 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.81882e10 | + | 2.20480e10i | 1.11700 | + | 0.644903i | ||||
\(431\) | −2.10447e10 | + | 3.64504e10i | −0.609864 | + | 1.05631i | 0.381399 | + | 0.924411i | \(0.375443\pi\) |
−0.991262 | + | 0.131904i | \(0.957891\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.50235e9i | 0.0711863i | 0.999366 | + | 0.0355932i | \(0.0113321\pi\) | ||||
−0.999366 | + | 0.0355932i | \(0.988668\pi\) | |||||||
\(434\) | −1.62575e10 | + | 3.06241e10i | −0.458242 | + | 0.863185i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.48583e8 | − | 1.64299e9i | −0.0262500 | − | 0.0454663i | ||||
\(437\) | 6.34390e9 | + | 3.66265e9i | 0.173953 | + | 0.100432i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.15377e10 | + | 2.39818e10i | −1.11837 | + | 0.645689i | −0.940983 | − | 0.338453i | \(-0.890097\pi\) |
−0.177383 | + | 0.984142i | \(0.556763\pi\) | |||||||
\(440\) | − | 2.62677e10i | − | 0.700828i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.47296e9 | −0.195796 | ||||||||
\(443\) | 1.02730e10 | + | 1.77934e10i | 0.266737 | + | 0.462002i | 0.968017 | − | 0.250884i | \(-0.0807212\pi\) |
−0.701280 | + | 0.712886i | \(0.747388\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.48792e10 | − | 4.30920e10i | 0.634447 | − | 1.09889i | ||||
\(446\) | 1.43213e10 | − | 8.26842e9i | 0.361946 | − | 0.208969i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.44741e9 | + | 2.36101e9i | 0.110407 | + | 0.0586119i | ||||
\(449\) | −6.58561e10 | −1.62036 | −0.810178 | − | 0.586184i | \(-0.800630\pi\) | ||||
−0.810178 | + | 0.586184i | \(0.800630\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.10669e10 | − | 2.94835e10i | −1.23433 | − | 0.712644i | ||||
\(452\) | 9.89012e9 | − | 1.71302e10i | 0.236945 | − | 0.410401i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 2.53249e10i | − | 0.596107i | ||||||
\(455\) | 3.77353e8 | + | 1.06076e10i | 0.00880444 | + | 0.247497i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.45983e9 | − | 1.29208e10i | −0.171027 | − | 0.296227i | 0.767752 | − | 0.640747i | \(-0.221375\pi\) |
−0.938779 | + | 0.344520i | \(0.888042\pi\) | |||||||
\(458\) | −9.70297e9 | − | 5.60201e9i | −0.220517 | − | 0.127316i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.78558e9 | − | 3.91766e9i | 0.151550 | − | 0.0874974i | ||||
\(461\) | − | 1.31092e10i | − | 0.290251i | −0.989413 | − | 0.145125i | \(-0.953641\pi\) | ||
0.989413 | − | 0.145125i | \(-0.0463586\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.12775e10 | −0.680626 | −0.340313 | − | 0.940312i | \(-0.610533\pi\) | ||||
−0.340313 | + | 0.940312i | \(0.610533\pi\) | |||||||
\(464\) | −2.50243e9 | − | 4.33434e9i | −0.0539872 | − | 0.0935085i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.72785e10 | + | 2.99272e10i | −0.366406 | + | 0.634633i | ||||
\(467\) | −8.08128e10 | + | 4.66573e10i | −1.69908 | + | 0.980962i | −0.752438 | + | 0.658663i | \(0.771122\pi\) |
−0.946638 | + | 0.322299i | \(0.895544\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.46527e10 | + | 4.04581e10i | −1.33627 | + | 0.836208i | ||||
\(470\) | −3.16464e10 | −0.648533 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.27979e10 | − | 1.31624e10i | −0.459332 | − | 0.265195i | ||||
\(473\) | −8.27953e10 | + | 1.43406e11i | −1.65410 | + | 2.86498i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.83939e9i | − | 0.0557765i | ||||||
\(476\) | −2.99847e10 | + | 1.06668e9i | −0.584080 | + | 0.0207780i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.62776e10 | + | 6.28347e10i | 0.694908 | + | 1.20362i | ||||
\(479\) | 6.05959e10 | + | 3.49850e10i | 1.15107 | + | 0.664570i | 0.949147 | − | 0.314832i | \(-0.101948\pi\) |
0.201921 | + | 0.979402i | \(0.435282\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.63620e10 | + | 9.44659e9i | −0.305672 | + | 0.176480i | ||||
\(482\) | − | 5.83436e10i | − | 1.08095i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.12035e10 | 1.29754 | ||||||||
\(485\) | −4.70916e10 | − | 8.15650e10i | −0.851091 | − | 1.47413i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.00394e10 | + | 3.47092e10i | −0.356261 | + | 0.617062i | −0.987333 | − | 0.158662i | \(-0.949282\pi\) |
0.631072 | + | 0.775724i | \(0.282615\pi\) | |||||||
\(488\) | −6.19810e9 | + | 3.57848e9i | −0.109290 | + | 0.0630985i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.02820e9 | + | 4.25082e10i | 0.0525292 | + | 0.737375i | ||||
\(491\) | 6.13480e10 | 1.05554 | 0.527770 | − | 0.849387i | \(-0.323028\pi\) | ||||
0.527770 | + | 0.849387i | \(0.323028\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.58271e10 | + | 1.49113e10i | 0.437208 | + | 0.252422i | ||||
\(494\) | −2.99262e9 | + | 5.18337e9i | −0.0502509 | + | 0.0870371i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.09122e10i | 0.345520i | ||||||||
\(497\) | −4.87510e10 | − | 2.58806e10i | −0.799021 | − | 0.424178i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.57072e10 | + | 2.72056e10i | 0.253335 | + | 0.438790i | 0.964442 | − | 0.264294i | \(-0.0851390\pi\) |
−0.711107 | + | 0.703084i | \(0.751806\pi\) | |||||||
\(500\) | 2.56631e10 | + | 1.48166e10i | 0.410609 | + | 0.237065i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.43303e10 | + | 3.13676e10i | −0.855514 | + | 0.493931i | ||||
\(503\) | − | 5.45243e10i | − | 0.851763i | −0.904779 | − | 0.425881i | \(-0.859964\pi\) | ||
0.904779 | − | 0.425881i | \(-0.140036\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.62012e10 | 1.17165 | ||||||||
\(506\) | 1.47117e10 | + | 2.54815e10i | 0.224420 | + | 0.388707i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.59573e10 | − | 4.49594e10i | 0.389767 | − | 0.675096i | ||||
\(509\) | 6.70138e10 | − | 3.86904e10i | 0.998373 | − | 0.576411i | 0.0906066 | − | 0.995887i | \(-0.471119\pi\) |
0.907767 | + | 0.419476i | \(0.137786\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.77381e9 | − | 4.43259e9i | −0.0406812 | − | 0.0650091i | ||||
\(512\) | 3.03700e9 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.57292e9 | − | 2.64018e9i | −0.0655150 | − | 0.0378251i | ||||
\(515\) | −6.49784e10 | + | 1.12546e11i | −0.923720 | + | 1.59993i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.18840e11i | − | 1.66341i | ||||||
\(518\) | −6.43029e10 | + | 4.02392e10i | −0.893123 | + | 0.558896i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.20098e9 | + | 5.54425e9i | 0.0437793 | + | 0.0758280i | ||||
\(521\) | 4.97137e10 | + | 2.87022e10i | 0.674722 | + | 0.389551i | 0.797864 | − | 0.602838i | \(-0.205963\pi\) |
−0.123141 | + | 0.992389i | \(0.539297\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.15576e10 | + | 1.24463e10i | −0.288133 | + | 0.166354i | −0.637100 | − | 0.770781i | \(-0.719866\pi\) |
0.348966 | + | 0.937135i | \(0.386533\pi\) | |||||||
\(524\) | 3.87967e10i | 0.514600i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.96498e10 | 1.04050 | ||||||||
\(527\) | −6.23050e10 | − | 1.07915e11i | −0.807756 | − | 1.39907i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.47672e10 | − | 6.02185e10i | 0.443963 | − | 0.768966i | ||||
\(530\) | −1.42509e10 | + | 8.22773e9i | −0.180608 | + | 0.104274i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.12678e10 | + | 2.12251e10i | −0.140667 | + | 0.264974i | ||||
\(533\) | 1.43714e10 | 0.178070 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.66900e10 | − | 5.00505e10i | −1.05817 | − | 0.610932i | ||||
\(536\) | −2.30004e10 | + | 3.98379e10i | −0.278661 | + | 0.482656i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 2.38798e10i | − | 0.285037i | ||||||
\(539\) | −1.59628e11 | + | 1.13716e10i | −1.89128 | + | 0.134731i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.51069e10 | + | 1.12768e11i | 0.760043 | + | 1.31643i | 0.942828 | + | 0.333280i | \(0.108155\pi\) |
−0.182785 | + | 0.983153i | \(0.558511\pi\) | |||||||
\(542\) | 7.94793e10 | + | 4.58874e10i | 0.920994 | + | 0.531736i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.56721e10 | + | 9.04831e9i | −0.178950 | + | 0.103317i | ||||
\(545\) | − | 9.68451e9i | − | 0.109772i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.36767e11 | −1.52768 | −0.763839 | − | 0.645407i | \(-0.776688\pi\) | ||||
−0.763839 | + | 0.645407i | \(0.776688\pi\) | |||||||
\(548\) | 5.33860e9 | + | 9.24673e9i | 0.0591977 | + | 0.102533i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.70248e9 | − | 9.87698e9i | 0.0623179 | − | 0.107938i | ||||
\(551\) | 2.06854e10 | − | 1.19427e10i | 0.224418 | − | 0.129568i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.33549e9 | − | 3.75412e10i | −0.0142804 | − | 0.401428i | ||||
\(554\) | 2.15799e9 | 0.0229093 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.88165e10 | + | 2.81842e10i | 0.510819 | + | 0.294922i | ||||
\(557\) | −1.82963e10 | + | 3.16901e10i | −0.190083 | + | 0.329233i | −0.945277 | − | 0.326268i | \(-0.894209\pi\) |
0.755195 | + | 0.655500i | \(0.227542\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.03577e10i | − | 0.413313i | ||||||
\(560\) | 1.36351e10 | + | 2.17890e10i | 0.138645 | + | 0.221557i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.58552e10 | + | 7.94236e10i | 0.459667 | + | 0.796167i | ||||
\(563\) | −7.96758e10 | − | 4.60008e10i | −0.793035 | − | 0.457859i | 0.0479946 | − | 0.998848i | \(-0.484717\pi\) |
−0.841030 | + | 0.540988i | \(0.818050\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.74449e10 | − | 5.04863e10i | 0.858106 | − | 0.495428i | ||||
\(566\) | − | 6.95310e10i | − | 0.677506i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.32905e10 | −0.319836 | ||||||||
\(569\) | 5.98155e10 | + | 1.03603e11i | 0.570643 | + | 0.988383i | 0.996500 | + | 0.0835923i | \(0.0266393\pi\) |
−0.425857 | + | 0.904790i | \(0.640027\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.22070e10 | − | 3.84636e10i | 0.208903 | − | 0.361831i | −0.742466 | − | 0.669883i | \(-0.766344\pi\) |
0.951369 | + | 0.308053i | \(0.0996774\pi\) | |||||||
\(572\) | −2.08200e10 | + | 1.20204e10i | −0.194490 | + | 0.112289i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.76642e10 | − | 2.05134e9i | 0.531201 | − | 0.0188969i | ||||
\(575\) | 3.40195e9 | 0.0311212 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.38340e11 | − | 7.98709e10i | −1.24809 | − | 0.720585i | −0.277362 | − | 0.960766i | \(-0.589460\pi\) |
−0.970728 | + | 0.240181i | \(0.922793\pi\) | |||||||
\(578\) | 1.44554e10 | − | 2.50375e10i | 0.129515 | − | 0.224326i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 2.55485e10i | − | 0.225763i | ||||||
\(581\) | 2.12372e10 | − | 4.00043e10i | 0.186377 | − | 0.351077i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.08971e10 | − | 5.35153e10i | −0.267450 | − | 0.463238i | ||||
\(584\) | −2.73129e9 | − | 1.57691e9i | −0.0234810 | − | 0.0135568i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.56612e10 | − | 5.52300e10i | 0.811232 | − | 0.468365i | ||||
\(587\) | − | 6.45369e10i | − | 0.543571i | −0.962358 | − | 0.271785i | \(-0.912386\pi\) | ||
0.962358 | − | 0.271785i | \(-0.0876141\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.98026e10 | −0.829241 | ||||||||
\(590\) | −6.71903e10 | − | 1.16377e11i | −0.554496 | − | 0.960415i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.28760e10 | + | 3.96224e10i | −0.186249 | + | 0.322592i | ||||
\(593\) | 1.42839e11 | − | 8.24683e10i | 1.15512 | − | 0.666912i | 0.204994 | − | 0.978763i | \(-0.434282\pi\) |
0.950131 | + | 0.311852i | \(0.100949\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.35280e11 | − | 7.18163e10i | −1.07936 | − | 0.573001i | ||||
\(596\) | 5.73836e10 | 0.454782 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.21033e9 | − | 3.58554e9i | −0.0485635 | − | 0.0280382i | ||||
\(599\) | 2.47750e10 | − | 4.29116e10i | 0.192445 | − | 0.333325i | −0.753615 | − | 0.657316i | \(-0.771692\pi\) |
0.946060 | + | 0.323992i | \(0.105025\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.98491e10i | 0.612029i | 0.952027 | + | 0.306014i | \(0.0989956\pi\) | ||||
−0.952027 | + | 0.306014i | \(0.901004\pi\) | |||||||
\(602\) | −5.76057e9 | − | 1.61932e11i | −0.0438611 | − | 1.23296i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.20050e9 | − | 1.42037e10i | −0.0616158 | − | 0.106722i | ||||
\(605\) | 3.14778e11 | + | 1.81737e11i | 2.34954 | + | 1.35651i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.48948e9 | − | 4.90140e9i | 0.0625355 | − | 0.0361049i | −0.468406 | − | 0.883513i | \(-0.655172\pi\) |
0.530942 | + | 0.847408i | \(0.321838\pi\) | |||||||
\(608\) | 1.44939e10i | 0.106065i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.65343e10 | −0.263865 | ||||||||
\(611\) | 1.44818e10 | + | 2.50832e10i | 0.103910 | + | 0.179977i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.89832e10 | − | 1.54123e11i | 0.630182 | − | 1.09151i | −0.357332 | − | 0.933977i | \(-0.616314\pi\) |
0.987514 | − | 0.157530i | \(-0.0503531\pi\) | |||||||
\(614\) | 6.70386e10 | − | 3.87047e10i | 0.471684 | − | 0.272327i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.18229e10 | + | 5.12029e10i | −0.568267 | + | 0.355608i | ||||
\(617\) | 2.41894e10 | 0.166911 | 0.0834553 | − | 0.996512i | \(-0.473404\pi\) | ||||
0.0834553 | + | 0.996512i | \(0.473404\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.35106e10 | + | 2.51209e10i | 0.296369 | + | 0.171109i | 0.640810 | − | 0.767699i | \(-0.278598\pi\) |
−0.344442 | + | 0.938808i | \(0.611932\pi\) | |||||||
\(620\) | −5.33756e10 | + | 9.24493e10i | −0.361224 | + | 0.625658i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 4.28436e9i | − | 0.0286236i | ||||||
\(623\) | −1.82726e11 | + | 6.50029e9i | −1.21297 | + | 0.0431500i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.27270e10 | + | 1.43287e11i | 0.542160 | + | 0.939049i | ||||
\(626\) | 1.14249e11 | + | 6.59618e10i | 0.743971 | + | 0.429532i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.11192e10 | − | 4.10607e10i | 0.457244 | − | 0.263990i | ||||
\(629\) | − | 2.72623e11i | − | 1.74165i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.14077e10 | −0.576587 | −0.288294 | − | 0.957542i | \(-0.593088\pi\) | ||||
−0.288294 | + | 0.957542i | \(0.593088\pi\) | |||||||
\(632\) | −1.13286e10 | − | 1.96217e10i | −0.0710080 | − | 0.122989i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.70508e10 | − | 2.95328e10i | 0.105533 | − | 0.182788i | ||||
\(635\) | 2.29506e11 | − | 1.32505e11i | 1.41156 | − | 0.814962i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.23066e10 | − | 2.18524e10i | 0.196215 | − | 0.132722i | ||||
\(638\) | 9.59406e10 | 0.579055 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.34260e10 | + | 7.75153e9i | 0.0800254 | + | 0.0462027i | ||||
\(641\) | −9.72074e10 | + | 1.68368e11i | −0.575794 | + | 0.997305i | 0.420161 | + | 0.907450i | \(0.361974\pi\) |
−0.995955 | + | 0.0898549i | \(0.971360\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.71299e11i | 1.58710i | 0.608506 | + | 0.793550i | \(0.291769\pi\) | ||||
−0.608506 | + | 0.793550i | \(0.708231\pi\) | |||||||
\(644\) | −2.54303e10 | − | 1.35003e10i | −0.147846 | − | 0.0784872i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.31826e10 | − | 7.47945e10i | −0.247958 | − | 0.429477i | ||||
\(647\) | 2.38580e11 | + | 1.37744e11i | 1.36150 | + | 0.786061i | 0.989823 | − | 0.142302i | \(-0.0454503\pi\) |
0.371675 | + | 0.928363i | \(0.378784\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.37023e11 | − | 2.52315e11i | 2.46335 | − | 1.42221i | ||||
\(650\) | 2.77961e9i | 0.0155715i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.96916e10 | 0.274975 | ||||||||
\(653\) | 7.33889e9 | + | 1.27113e10i | 0.0403624 | + | 0.0699098i | 0.885501 | − | 0.464638i | \(-0.153815\pi\) |
−0.845138 | + | 0.534547i | \(0.820482\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.90233e10 | + | 1.71513e11i | −0.537988 | + | 0.931822i | ||||
\(656\) | 3.01394e10 | − | 1.74010e10i | 0.162749 | − | 0.0939633i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.16874e10 | + | 9.85773e10i | 0.329073 | + | 0.525864i | ||||
\(659\) | 1.85183e11 | 0.981883 | 0.490941 | − | 0.871193i | \(-0.336653\pi\) | ||||
0.490941 | + | 0.871193i | \(0.336653\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.46702e11 | + | 1.42433e11i | 1.29231 | + | 0.746116i | 0.979063 | − | 0.203556i | \(-0.0652498\pi\) |
0.313247 | + | 0.949672i | \(0.398583\pi\) | |||||||
\(662\) | −8.74838e10 | + | 1.51526e11i | −0.455507 | + | 0.788962i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 2.73177e10i | − | 0.140531i | ||||||
\(665\) | −1.03987e11 | + | 6.50727e10i | −0.531732 | + | 0.332746i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.43089e10 | + | 2.47838e10i | 0.0722942 | + | 0.125217i | ||||
\(668\) | 9.06157e10 | + | 5.23170e10i | 0.455090 | + | 0.262747i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.03362e11 | + | 1.17411e11i | −1.00918 | + | 0.582652i | ||||
\(671\) | − | 1.37195e11i | − | 0.676780i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.03429e10 | −0.0991635 | −0.0495817 | − | 0.998770i | \(-0.515789\pi\) | ||||
−0.0495817 | + | 0.998770i | \(0.515789\pi\) | |||||||
\(674\) | −8.68248e10 | − | 1.50385e11i | −0.420731 | − | 0.728727i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.92772e10 | + | 8.53505e10i | −0.235971 | + | 0.408714i | ||||
\(677\) | 2.36996e11 | − | 1.36830e11i | 1.12820 | − | 0.651366i | 0.184718 | − | 0.982792i | \(-0.440863\pi\) |
0.943481 | + | 0.331425i | \(0.107529\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.62278e11 | + | 3.05681e11i | −0.763448 | + | 1.43810i | ||||
\(680\) | −9.23783e10 | −0.432050 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.47169e11 | − | 2.00438e11i | −1.60473 | − | 0.926494i | ||||
\(683\) | 8.12982e8 | − | 1.40813e9i | 0.00373592 | − | 0.00647081i | −0.864151 | − | 0.503232i | \(-0.832144\pi\) |
0.867887 | + | 0.496761i | \(0.165477\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.45042e10i | 0.247553i | ||||||||
\(686\) | 1.26509e11 | − | 9.22928e10i | 0.571247 | − | 0.416746i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.88653e10 | − | 8.46372e10i | −0.218096 | − | 0.377753i | ||||
\(689\) | 1.30427e10 | + | 7.53022e9i | 0.0578751 | + | 0.0334142i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.02262e10 | − | 1.16776e10i | 0.0887162 | − | 0.0512203i | −0.454986 | − | 0.890499i | \(-0.650356\pi\) |
0.543702 | + | 0.839278i | \(0.317022\pi\) | |||||||
\(692\) | 4.00550e10i | 0.174676i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.80072e10 | 0.379385 | ||||||||
\(695\) | 1.43873e11 | + | 2.49195e11i | 0.616650 | + | 1.06807i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.03687e11 | + | 1.79592e11i | −0.439334 | + | 0.760950i | ||||
\(698\) | 1.46456e11 | − | 8.45562e10i | 0.616999 | − | 0.356225i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.96756e8 | + | 1.11530e10i | 0.00165246 | + | 0.0464515i | ||||
\(701\) | −2.58500e11 | −1.07050 | −0.535252 | − | 0.844693i | \(-0.679783\pi\) | ||||
−0.535252 | + | 0.844693i | \(0.679783\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.89096e11 | − | 1.09175e11i | −0.774214 | − | 0.446992i | ||||
\(704\) | −2.91088e10 | + | 5.04180e10i | −0.118504 | + | 0.205255i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 2.60719e11i | − | 1.04943i | ||||||
\(707\) | −1.48537e11 | − | 2.37364e11i | −0.594506 | − | 0.950029i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.09246e11 | − | 1.89220e11i | −0.432336 | − | 0.748828i | 0.564738 | − | 0.825270i | \(-0.308977\pi\) |
−0.997074 | + | 0.0764424i | \(0.975644\pi\) | |||||||
\(710\) | −1.47172e11 | − | 8.49696e10i | −0.579149 | − | 0.334372i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.55056e10 | + | 5.51402e10i | −0.371628 | + | 0.214560i | ||||
\(713\) | − | 1.19576e11i | − | 0.462686i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.22722e11 | −0.469568 | ||||||||
\(716\) | 7.46962e10 | + | 1.29378e11i | 0.284215 | + | 0.492274i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.45398e10 | + | 5.98247e10i | −0.129964 | + | 0.225104i | ||||
\(719\) | −2.52373e11 | + | 1.45708e11i | −0.944337 | + | 0.545213i | −0.891317 | − | 0.453380i | \(-0.850218\pi\) |
−0.0530201 | + | 0.998593i | \(0.516885\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.77237e11 | − | 1.69772e10i | 1.76601 | − | 0.0628240i | ||||
\(722\) | 1.22975e11 | 0.452553 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.34416e9 | + | 3.08545e9i | 0.0194503 | + | 0.0112296i | ||||
\(725\) | 5.54634e9 | − | 9.60654e9i | 0.0200750 | − | 0.0347708i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 5.02509e10i | − | 0.179890i | −0.995947 | − | 0.0899448i | \(-0.971331\pi\) | ||
0.995947 | − | 0.0899448i | \(-0.0286691\pi\) | |||||||
\(728\) | 1.10306e10 | − | 2.07782e10i | 0.0392711 | − | 0.0739745i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.04970e9 | − | 1.39425e10i | −0.0283458 | − | 0.0490963i | ||||
\(731\) | 5.04329e11 | + | 2.91174e11i | 1.76622 | + | 1.01973i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.41107e10 | + | 8.14684e9i | −0.0488803 | + | 0.0282211i | −0.524241 | − | 0.851570i | \(-0.675651\pi\) |
0.475361 | + | 0.879791i | \(0.342318\pi\) | |||||||
\(734\) | − | 1.76697e11i | − | 0.608759i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.73656e10 | −0.0591804 | ||||||||
\(737\) | −4.40906e11 | − | 7.63671e11i | −1.49443 | − | 2.58843i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.84732e11 | + | 3.19966e11i | −0.619391 | + | 1.07282i | 0.370206 | + | 0.928950i | \(0.379287\pi\) |
−0.989597 | + | 0.143867i | \(0.954046\pi\) | |||||||
\(740\) | −2.02261e11 | + | 1.16776e11i | −0.674506 | + | 0.389426i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.34079e10 | + | 2.83528e10i | 0.176193 | + | 0.0935363i | ||||
\(743\) | −4.71388e11 | −1.54676 | −0.773380 | − | 0.633942i | \(-0.781436\pi\) | ||||
−0.773380 | + | 0.633942i | \(0.781436\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.53683e11 | + | 1.46464e11i | 0.823505 | + | 0.475451i | ||||
\(746\) | −6.22900e10 | + | 1.07889e11i | −0.201124 | + | 0.348356i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 3.46902e11i | − | 1.10816i | ||||||
\(749\) | 1.30769e10 | + | 3.67598e11i | 0.0415507 | + | 1.16801i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.80229e10 | + | 8.31780e10i | 0.150969 | + | 0.261486i | 0.931584 | − | 0.363526i | \(-0.118427\pi\) |
−0.780615 | + | 0.625012i | \(0.785094\pi\) | |||||||
\(752\) | 6.07417e10 | + | 3.50692e10i | 0.189940 | + | 0.109662i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.02499e10 | + | 1.16913e10i | −0.0626524 | + | 0.0361724i | ||||
\(755\) | − | 8.37226e10i | − | 0.257665i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.08191e11 | 1.54754 | 0.773772 | − | 0.633464i | \(-0.218367\pi\) | ||||
0.773772 | + | 0.633464i | \(0.218367\pi\) | |||||||
\(758\) | 2.07322e11 | + | 3.59092e11i | 0.628012 | + | 1.08775i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.69938e10 | + | 6.40752e10i | −0.110885 | + | 0.192059i | ||||
\(761\) | −3.00390e11 | + | 1.73430e11i | −0.895667 | + | 0.517113i | −0.875792 | − | 0.482689i | \(-0.839660\pi\) |
−0.0198748 | + | 0.999802i | \(0.506327\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.01669e10 | + | 1.88777e10i | −0.0890087 | + | 0.0556996i | ||||
\(764\) | 4.71512e10 | 0.138395 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.59725e10 | − | 3.80892e10i | −0.191623 | − | 0.110634i | ||||
\(767\) | −6.14942e10 | + | 1.06511e11i | −0.177686 | + | 0.307761i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.21968e11i | − | 0.634724i | −0.948304 | − | 0.317362i | \(-0.897203\pi\) | ||
0.948304 | − | 0.317362i | \(-0.102797\pi\) | |||||||
\(770\) | −4.92413e11 | + | 1.75171e10i | −1.40077 | + | 0.0498309i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.37771e10 | − | 2.38626e10i | −0.0387871 | − | 0.0671812i | ||||
\(773\) | −3.27357e11 | − | 1.88999e11i | −0.916860 | − | 0.529349i | −0.0342281 | − | 0.999414i | \(-0.510897\pi\) |
−0.882632 | + | 0.470065i | \(0.844231\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.01398e10 | + | 2.31747e10i | −0.111267 | + | 0.0642403i | ||||
\(776\) | 2.08740e11i | 0.575650i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.18229e10 | 0.114155 | ||||||||
\(779\) | 8.30454e10 | + | 1.43839e11i | 0.225510 | + | 0.390595i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.19081e11 | − | 5.52664e11i | 0.857623 | − | 1.48545i | ||||
\(782\) | 8.96132e10 | − | 5.17382e10i | 0.239632 | − | 0.138352i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.12936e10 | − | 8.49455e10i | 0.109300 | − | 0.224841i | ||||
\(785\) | 4.19207e11 | 1.10395 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.86479e8 | − | 1.65399e8i | −0.000746783 | − | 0.000431156i | 0.499627 | − | 0.866241i | \(-0.333471\pi\) |
−0.500373 | + | 0.865810i | \(0.666804\pi\) | |||||||
\(788\) | −7.95146e10 | + | 1.37723e11i | −0.206225 | + | 0.357193i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 1.15659e11i | − | 0.296941i | ||||||
\(791\) | −3.27717e11 | − | 1.73976e11i | −0.837130 | − | 0.444410i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.67185e10 | + | 2.89574e10i | 0.0422771 | + | 0.0732261i | ||||
\(794\) | −4.84192e11 | − | 2.79548e11i | −1.21825 | − | 0.703355i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.49015e9 | + | 4.90179e9i | −0.0211477 | + | 0.0122096i | ||||
\(797\) | 4.05700e11i | 1.00548i | 0.864439 | + | 0.502738i | \(0.167674\pi\) | ||||
−0.864439 | + | 0.502738i | \(0.832326\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.17935e11 | −1.02547 | ||||||||
\(800\) | 3.36557e9 | + | 5.82934e9i | 0.00821673 | + | 0.0142318i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.66380e10 | − | 2.88179e10i | 0.0402165 | − | 0.0696569i | ||||
\(803\) | 5.23573e10 | − | 3.02285e10i | 0.125926 | − | 0.0727034i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.79653e10 | − | 1.24590e11i | −0.185660 | − | 0.296687i | ||||
\(806\) | 9.77013e10 | 0.231505 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.46260e11 | − | 8.44431e10i | −0.343146 | − | 0.198116i | ||||
\(809\) | −3.98666e11 | + | 6.90510e11i | −0.930712 | + | 1.61204i | −0.148605 | + | 0.988897i | \(0.547478\pi\) |
−0.782107 | + | 0.623144i | \(0.785855\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.69434e11i | 1.54748i | 0.633504 | + | 0.773739i | \(0.281616\pi\) | ||||
−0.633504 | + | 0.773739i | \(0.718384\pi\) | |||||||
\(812\) | −7.95826e10 | + | 4.98009e10i | −0.183060 | + | 0.114555i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.38520e11 | − | 7.59539e11i | −0.998831 | − | 1.73003i | ||||
\(815\) | 2.19678e11 | + | 1.26831e11i | 0.497916 | + | 0.287472i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.03927e11 | − | 2.33207e11i | 0.906598 | − | 0.523425i | ||||
\(818\) | − | 2.82742e11i | − | 0.631506i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.77655e11 | 0.392935 | ||||||||
\(821\) | −2.05956e11 | − | 3.56727e11i | −0.453318 | − | 0.785169i | 0.545272 | − | 0.838259i | \(-0.316426\pi\) |
−0.998590 | + | 0.0530899i | \(0.983093\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.43752e11 | − | 4.22191e11i | 0.531311 | − | 0.920258i | −0.468021 | − | 0.883717i | \(-0.655033\pi\) |
0.999332 | − | 0.0365405i | \(-0.0116338\pi\) | |||||||
\(824\) | 2.49438e11 | − | 1.44013e11i | 0.541070 | − | 0.312387i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.31538e11 | + | 4.36146e11i | −0.497395 | + | 0.936939i | ||||
\(827\) | −2.20022e11 | −0.470376 | −0.235188 | − | 0.971950i | \(-0.575571\pi\) | ||||
−0.235188 | + | 0.971950i | \(0.575571\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.08634e11 | + | 2.93660e11i | 1.07693 | + | 0.621766i | 0.930067 | − | 0.367391i | \(-0.119749\pi\) |
0.146863 | + | 0.989157i | \(0.453082\pi\) | |||||||
\(830\) | 6.97247e10 | − | 1.20767e11i | 0.146918 | − | 0.254469i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 1.41888e10i | − | 0.0296109i | ||||||
\(833\) | 3.99917e10 | + | 5.61381e11i | 0.0830596 | + | 1.16594i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.67064e11 | + | 4.62569e11i | 0.549376 | + | 0.951547i | ||||
\(836\) | −2.40617e11 | − | 1.38920e11i | −0.492608 | − | 0.284408i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.39469e11 | + | 3.11463e11i | −1.09393 | + | 0.631582i | ||||
\(839\) | 2.54607e11i | 0.513834i | 0.966433 | + | 0.256917i | \(0.0827067\pi\) | ||||
−0.966433 | + | 0.256917i | \(0.917293\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.06933e11 | −0.813465 | ||||||||
\(842\) | −5.64782e10 | − | 9.78231e10i | −0.112365 | − | 0.194623i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.52945e10 | − | 2.64908e10i | 0.0301415 | − | 0.0522066i | ||||
\(845\) | −4.35691e11 | + | 2.51546e11i | −0.854578 | + | 0.493391i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.74833e10 | − | 1.33478e12i | −0.0922587 | − | 2.59343i | ||||
\(848\) | 3.64706e10 | 0.0705276 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.47354e10 | − | 2.00545e10i | −0.0665421 | − | 0.0384181i | ||||
\(851\) | 1.30805e11 | − | 2.26561e11i | 0.249405 | − | 0.431983i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.69174e11i | 1.64176i | 0.571099 | + | 0.820881i | \(0.306517\pi\) | ||||
−0.571099 | + | 0.820881i | \(0.693483\pi\) | |||||||
\(854\) | 7.12153e10 | + | 1.13803e11i | 0.133888 | + | 0.213955i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.10928e11 | + | 1.92133e11i | 0.206607 | + | 0.357854i | ||||
\(857\) | 2.04031e11 | + | 1.17797e11i | 0.378245 | + | 0.218380i | 0.677054 | − | 0.735933i | \(-0.263256\pi\) |
−0.298810 | + | 0.954313i | \(0.596590\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.48368e11 | + | 3.16600e11i | −1.00716 | + | 0.581485i | −0.910359 | − | 0.413819i | \(-0.864195\pi\) |
−0.0968021 | + | 0.995304i | \(0.530861\pi\) | |||||||
\(860\) | − | 4.98888e11i | − | 0.912031i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.76186e11 | 0.862478 | ||||||||
\(863\) | −1.38463e11 | − | 2.39825e11i | −0.249626 | − | 0.432365i | 0.713796 | − | 0.700354i | \(-0.246974\pi\) |
−0.963422 | + | 0.267989i | \(0.913641\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.02235e11 | + | 1.77076e11i | −0.182614 | + | 0.316297i | ||||
\(866\) | 2.45179e10 | − | 1.41554e10i | 0.0435925 | − | 0.0251682i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.92020e11 | − | 1.39457e10i | 0.690604 | − | 0.0245675i | ||||
\(869\) | 4.34325e11 | 0.761616 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.86122e11 | + | 1.07457e11i | 0.323388 | + | 0.186708i | ||||
\(872\) | −1.07320e10 | + | 1.85883e10i | −0.0185616 | + | 0.0321495i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 8.28764e10i | − | 0.142032i | ||||||
\(875\) | 2.60637e11 | − | 4.90960e11i | 0.444635 | − | 0.837555i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.05639e11 | − | 3.56178e11i | −0.347623 | − | 0.602100i | 0.638204 | − | 0.769867i | \(-0.279678\pi\) |
−0.985827 | + | 0.167767i | \(0.946344\pi\) | |||||||
\(878\) | 4.69945e11 | + | 2.71323e11i | 0.790805 | + | 0.456571i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.57370e11 | + | 1.48593e11i | −0.429168 | + | 0.247780i | ||||
\(881\) | − | 8.49897e11i | − | 1.41079i | −0.708814 | − | 0.705395i | \(-0.750769\pi\) | ||
0.708814 | − | 0.705395i | \(-0.249231\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.23996e11 | −0.368466 | −0.184233 | − | 0.982883i | \(-0.558980\pi\) | ||||
−0.184233 | + | 0.982883i | \(0.558980\pi\) | |||||||
\(884\) | 4.22734e10 | + | 7.32197e10i | 0.0692243 | + | 0.119900i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.16226e11 | − | 2.01309e11i | 0.188612 | − | 0.326685i | ||||
\(887\) | −4.79045e11 | + | 2.76577e11i | −0.773894 | + | 0.446808i | −0.834262 | − | 0.551368i | \(-0.814106\pi\) |
0.0603680 | + | 0.998176i | \(0.480773\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.60117e11 | − | 4.56613e11i | −1.37705 | − | 0.731040i | ||||
\(890\) | −5.62951e11 | −0.897244 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.62027e11 | − | 9.35464e10i | −0.255934 | − | 0.147764i | ||||
\(893\) | −1.67366e11 | + | 2.89887e11i | −0.263186 | + | 0.455851i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.62607e11i | 1.18853i | ||||||||
\(896\) | −2.02528e9 | − | 5.69315e10i | −0.00314234 | − | 0.0883325i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.72538e11 | + | 6.45255e11i | 0.572882 | + | 0.992261i | ||||
\(899\) | −3.37663e11 | − | 1.94950e11i | −0.516946 | − | 0.298459i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.88203e11 | + | 1.08659e11i | −0.285579 | + | 0.164879i | ||||
\(902\) | 6.67135e11i | 1.00783i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.23788e11 | −0.335091 | ||||||||
\(905\) | 1.57504e10 | + | 2.72805e10i | 0.0234800 | + | 0.0406685i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.49965e10 | − | 1.12577e11i | 0.0960420 | − | 0.166350i | −0.814001 | − | 0.580863i | \(-0.802715\pi\) |
0.910043 | + | 0.414514i | \(0.136048\pi\) | |||||||
\(908\) | −2.48132e11 | + | 1.43259e11i | −0.365040 | + | 0.210756i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.01798e11 | − | 6.37027e10i | 0.148447 | − | 0.0928949i | ||||
\(911\) | −1.39320e10 | −0.0202274 | −0.0101137 | − | 0.999949i | \(-0.503219\pi\) | ||||
−0.0101137 | + | 0.999949i | \(0.503219\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.53507e11 | + | 2.61833e11i | 0.652681 | + | 0.376826i | ||||
\(914\) | −8.43983e10 | + | 1.46182e11i | −0.120934 | + | 0.209464i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.26759e11i | 0.180052i | ||||||||
\(917\) | 7.27281e11 | − | 2.58723e10i | 1.02855 | − | 0.0365896i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.24911e11 | − | 3.89558e11i | −0.315318 | − | 0.546147i | 0.664187 | − | 0.747567i | \(-0.268778\pi\) |
−0.979505 | + | 0.201419i | \(0.935445\pi\) | |||||||
\(920\) | −7.67701e10 | − | 4.43233e10i | −0.107162 | − | 0.0618700i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.28444e11 | + | 7.41570e10i | −0.177742 | + | 0.102619i | ||||
\(923\) | 1.55532e11i | 0.214296i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.01404e11 | −0.138512 | ||||||||
\(926\) | 1.76932e11 | + | 3.06456e11i | 0.240638 | + | 0.416797i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.83118e10 | + | 4.90375e10i | −0.0381747 | + | 0.0661205i | ||||
\(929\) | 9.32448e11 | − | 5.38349e11i | 1.25188 | − | 0.722771i | 0.280395 | − | 0.959885i | \(-0.409535\pi\) |
0.971482 | + | 0.237113i | \(0.0762013\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.05398e11 | + | 1.97072e11i | 0.539614 | + | 0.262316i | ||||
\(932\) | 3.90968e11 | 0.518176 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.14293e11 | + | 5.27867e11i | 1.20143 | + | 0.693645i | ||||
\(935\) | 8.85421e11 | − | 1.53359e12i | 1.15852 | − | 2.00661i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.17387e11i | 0.152287i | 0.997097 | + | 0.0761433i | \(0.0242606\pi\) | ||||
−0.997097 | + | 0.0761433i | \(0.975739\pi\) | |||||||
\(938\) | 7.62138e11 | + | 4.04598e11i | 0.984515 | + | 0.522652i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.79019e11 | + | 3.10070e11i | 0.229291 | + | 0.397144i | ||||
\(941\) | −1.22577e12 | − | 7.07698e11i | −1.56333 | − | 0.902588i | −0.996917 | − | 0.0784643i | \(-0.974998\pi\) |
−0.566411 | − | 0.824123i | \(-0.691668\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.72337e11 | + | 9.94988e10i | −0.217937 | + | 0.125826i | ||||
\(944\) | 2.97830e11i | 0.375043i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.87344e12 | 2.33925 | ||||||||
\(947\) | 7.92418e11 | + | 1.37251e12i | 0.985268 | + | 1.70654i | 0.640737 | + | 0.767760i | \(0.278629\pi\) |
0.344531 | + | 0.938775i | \(0.388038\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.36728e9 | + | 1.27605e10i | −0.00908328 | + | 0.0157327i | ||||
\(950\) | −2.78203e10 | + | 1.60620e10i | −0.0341560 | + | 0.0197200i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.80070e11 | + | 2.87755e11i | 0.219227 | + | 0.350328i | ||||
\(953\) | 8.80951e11 | 1.06802 | 0.534011 | − | 0.845478i | \(-0.320684\pi\) | ||||
0.534011 | + | 0.845478i | \(0.320684\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.08447e11 | + | 1.20347e11i | 0.250601 | + | 0.144684i | ||||
\(956\) | 4.10435e11 | − | 7.10893e11i | 0.491374 | − | 0.851085i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 7.91621e11i | − | 0.939843i | ||||||
\(959\) | 1.69779e11 | − | 1.06243e11i | 0.200728 | − | 0.125611i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.88129e11 | + | 6.72259e11i | 0.455074 | + | 0.788212i | ||||
\(962\) | 1.85115e11 | + | 1.06876e11i | 0.216143 | + | 0.124790i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.71648e11 | + | 3.30041e11i | −0.661943 | + | 0.382173i | ||||
\(965\) | − | 1.40656e11i | − | 0.162200i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.07089e11 | −1.03739 | −0.518697 | − | 0.854958i | \(-0.673583\pi\) | ||||
−0.518697 | + | 0.854958i | \(0.673583\pi\) | |||||||
\(968\) | −4.02788e11 | − | 6.97649e11i | −0.458749 | − | 0.794576i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.32780e11 | + | 9.22802e11i | −0.601812 | + | 1.04237i | ||||
\(971\) | 8.42948e10 | − | 4.86676e10i | 0.0948252 | − | 0.0547474i | −0.451838 | − | 0.892100i | \(-0.649231\pi\) |
0.546663 | + | 0.837353i | \(0.315898\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.95786e11 | − | 9.33906e11i | 0.553150 | − | 1.04196i | ||||
\(974\) | 4.53439e11 | 0.503829 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.01235e10 | + | 4.04858e10i | 0.0772795 | + | 0.0446174i | ||||
\(977\) | 5.91684e11 | − | 1.02483e12i | 0.649398 | − | 1.12479i | −0.333868 | − | 0.942620i | \(-0.608354\pi\) |
0.983267 | − | 0.182171i | \(-0.0583126\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.11401e12i | − | 2.30132i | ||||||
\(980\) | 3.99363e11 | − | 2.70133e11i | 0.432976 | − | 0.292869i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.47037e11 | − | 6.01086e11i | −0.373190 | − | 0.646384i | ||||
\(983\) | 6.45965e11 | + | 3.72948e11i | 0.691823 | + | 0.399424i | 0.804295 | − | 0.594231i | \(-0.202543\pi\) |
−0.112471 | + | 0.993655i | \(0.535877\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.03040e11 | + | 4.05900e11i | −0.746853 | + | 0.431196i | ||||
\(986\) | − | 3.37404e11i | − | 0.356979i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.77153e10 | 0.0710655 | ||||||||
\(989\) | 2.79412e11 | + | 4.83956e11i | 0.292052 | + | 0.505848i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.51209e11 | + | 2.61902e11i | −0.156778 | + | 0.271547i | −0.933705 | − | 0.358044i | \(-0.883444\pi\) |
0.776927 | + | 0.629590i | \(0.216777\pi\) | |||||||
\(992\) | 2.04897e11 | − | 1.18297e11i | 0.211587 | − | 0.122160i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.22004e10 | + | 6.24063e11i | 0.0227413 | + | 0.639268i | ||||
\(995\) | −5.00446e10 | −0.0510581 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.35948e12 | − | 7.84897e11i | −1.37592 | − | 0.794387i | −0.384254 | − | 0.923228i | \(-0.625541\pi\) |
−0.991665 | + | 0.128840i | \(0.958875\pi\) | |||||||
\(998\) | 1.77706e11 | − | 3.07797e11i | 0.179135 | − | 0.310271i | ||||
\(999\) | 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.73.1 | yes | 20 | |
3.2 | odd | 2 | inner | 126.9.n.d.73.10 | yes | 20 | |
7.5 | odd | 6 | inner | 126.9.n.d.19.1 | ✓ | 20 | |
21.5 | even | 6 | inner | 126.9.n.d.19.10 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.9.n.d.19.1 | ✓ | 20 | 7.5 | odd | 6 | inner | |
126.9.n.d.19.10 | yes | 20 | 21.5 | even | 6 | inner | |
126.9.n.d.73.1 | yes | 20 | 1.1 | even | 1 | trivial | |
126.9.n.d.73.10 | yes | 20 | 3.2 | odd | 2 | inner |