Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,9,Mod(7,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.7");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.f (of order \(4\), 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: | \(30.5533957546\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 192 x^{9} + 27713 x^{8} - 24384 x^{7} + 18432 x^{6} - 2072064 x^{5} + 128589064 x^{4} - 223046400 x^{3} + 184320000 x^{2} + 558720000 x + 846810000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{18}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.2 | ||
Root | \(-0.782794 + 0.782794i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.43 |
Dual form | 75.9.f.d.7.2 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −15.2792 | + | 15.2792i | −0.954951 | + | 0.954951i | −0.999028 | − | 0.0440768i | \(-0.985965\pi\) |
0.0440768 | + | 0.999028i | \(0.485965\pi\) | |||||||
\(3\) | 33.0681 | + | 33.0681i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 210.909i | − | 0.823864i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1010.51 | −0.779715 | ||||||||
\(7\) | 1776.62 | − | 1776.62i | 0.739952 | − | 0.739952i | −0.232617 | − | 0.972568i | \(-0.574729\pi\) |
0.972568 | + | 0.232617i | \(0.0747288\pi\) | |||||||
\(8\) | −688.952 | − | 688.952i | −0.168201 | − | 0.168201i | ||||
\(9\) | 2187.00i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4477.64 | 0.305829 | 0.152915 | − | 0.988239i | \(-0.451134\pi\) | ||||
0.152915 | + | 0.988239i | \(0.451134\pi\) | |||||||
\(12\) | 6974.37 | − | 6974.37i | 0.336341 | − | 0.336341i | ||||
\(13\) | −18402.3 | − | 18402.3i | −0.644314 | − | 0.644314i | 0.307299 | − | 0.951613i | \(-0.400575\pi\) |
−0.951613 | + | 0.307299i | \(0.900575\pi\) | |||||||
\(14\) | 54290.9i | 1.41324i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 75046.1 | 1.14511 | ||||||||
\(17\) | −40628.0 | + | 40628.0i | −0.486441 | + | 0.486441i | −0.907181 | − | 0.420740i | \(-0.861770\pi\) |
0.420740 | + | 0.907181i | \(0.361770\pi\) | |||||||
\(18\) | −33415.7 | − | 33415.7i | −0.318317 | − | 0.318317i | ||||
\(19\) | 161124.i | 1.23636i | 0.786036 | + | 0.618181i | \(0.212130\pi\) | ||||
−0.786036 | + | 0.618181i | \(0.787870\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 117499. | 0.604168 | ||||||||
\(22\) | −68414.9 | + | 68414.9i | −0.292052 | + | 0.292052i | ||||
\(23\) | 208665. | + | 208665.i | 0.745656 | + | 0.745656i | 0.973660 | − | 0.228004i | \(-0.0732199\pi\) |
−0.228004 | + | 0.973660i | \(0.573220\pi\) | |||||||
\(24\) | − | 45564.7i | − | 0.137336i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 562344. | 1.23058 | ||||||||
\(27\) | −72320.0 | + | 72320.0i | −0.136083 | + | 0.136083i | ||||
\(28\) | −374706. | − | 374706.i | −0.609620 | − | 0.609620i | ||||
\(29\) | 1.08625e6i | 1.53581i | 0.640561 | + | 0.767907i | \(0.278702\pi\) | ||||
−0.640561 | + | 0.767907i | \(0.721298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.33249e6 | 1.44284 | 0.721420 | − | 0.692498i | \(-0.243490\pi\) | ||||
0.721420 | + | 0.692498i | \(0.243490\pi\) | |||||||
\(32\) | −970274. | + | 970274.i | −0.925325 | + | 0.925325i | ||||
\(33\) | 148067. | + | 148067.i | 0.124854 | + | 0.124854i | ||||
\(34\) | − | 1.24153e6i | − | 0.929055i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 461259. | 0.274621 | ||||||||
\(37\) | −778701. | + | 778701.i | −0.415493 | + | 0.415493i | −0.883647 | − | 0.468154i | \(-0.844919\pi\) |
0.468154 | + | 0.883647i | \(0.344919\pi\) | |||||||
\(38\) | −2.46185e6 | − | 2.46185e6i | −1.18066 | − | 1.18066i | ||||
\(39\) | − | 1.21706e6i | − | 0.526080i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.79519e6 | −1.34307 | −0.671535 | − | 0.740973i | \(-0.734365\pi\) | ||||
−0.671535 | + | 0.740973i | \(0.734365\pi\) | |||||||
\(42\) | −1.79530e6 | + | 1.79530e6i | −0.576951 | + | 0.576951i | ||||
\(43\) | −3.70334e6 | − | 3.70334e6i | −1.08323 | − | 1.08323i | −0.996206 | − | 0.0870210i | \(-0.972265\pi\) |
−0.0870210 | − | 0.996206i | \(-0.527735\pi\) | |||||||
\(44\) | − | 944377.i | − | 0.251962i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.37648e6 | −1.42413 | ||||||||
\(47\) | −3.40201e6 | + | 3.40201e6i | −0.697179 | + | 0.697179i | −0.963801 | − | 0.266622i | \(-0.914092\pi\) |
0.266622 | + | 0.963801i | \(0.414092\pi\) | |||||||
\(48\) | 2.48163e6 | + | 2.48163e6i | 0.467490 | + | 0.467490i | ||||
\(49\) | − | 547985.i | − | 0.0950570i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.68698e6 | −0.397177 | ||||||||
\(52\) | −3.88121e6 | + | 3.88121e6i | −0.530827 | + | 0.530827i | ||||
\(53\) | 3.98610e6 | + | 3.98610e6i | 0.505178 | + | 0.505178i | 0.913042 | − | 0.407865i | \(-0.133726\pi\) |
−0.407865 | + | 0.913042i | \(0.633726\pi\) | |||||||
\(54\) | − | 2.20999e6i | − | 0.259905i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.44802e6 | −0.248921 | ||||||||
\(57\) | −5.32806e6 | + | 5.32806e6i | −0.504742 | + | 0.504742i | ||||
\(58\) | −1.65971e7 | − | 1.65971e7i | −1.46663 | − | 1.46663i | ||||
\(59\) | 4.53528e6i | 0.374279i | 0.982333 | + | 0.187140i | \(0.0599217\pi\) | ||||
−0.982333 | + | 0.187140i | \(0.940078\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.88819e6 | −0.353044 | −0.176522 | − | 0.984297i | \(-0.556485\pi\) | ||||
−0.176522 | + | 0.984297i | \(0.556485\pi\) | |||||||
\(62\) | −2.03595e7 | + | 2.03595e7i | −1.37784 | + | 1.37784i | ||||
\(63\) | 3.88548e6 | + | 3.88548e6i | 0.246651 | + | 0.246651i | ||||
\(64\) | − | 1.04383e7i | − | 0.622169i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.52471e6 | −0.238459 | ||||||||
\(67\) | 1.35112e7 | − | 1.35112e7i | 0.670492 | − | 0.670492i | −0.287337 | − | 0.957829i | \(-0.592770\pi\) |
0.957829 | + | 0.287337i | \(0.0927700\pi\) | |||||||
\(68\) | 8.56883e6 | + | 8.56883e6i | 0.400761 | + | 0.400761i | ||||
\(69\) | 1.38003e7i | 0.608826i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.27542e7 | 1.68246 | 0.841232 | − | 0.540675i | \(-0.181831\pi\) | ||||
0.841232 | + | 0.540675i | \(0.181831\pi\) | |||||||
\(72\) | 1.50674e6 | − | 1.50674e6i | 0.0560670 | − | 0.0560670i | ||||
\(73\) | −3.74805e7 | − | 3.74805e7i | −1.31982 | − | 1.31982i | −0.913917 | − | 0.405902i | \(-0.866957\pi\) |
−0.405902 | − | 0.913917i | \(-0.633043\pi\) | |||||||
\(74\) | − | 2.37959e7i | − | 0.793552i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.39825e7 | 1.01859 | ||||||||
\(77\) | 7.95509e6 | − | 7.95509e6i | 0.226299 | − | 0.226299i | ||||
\(78\) | 1.85957e7 | + | 1.85957e7i | 0.502381 | + | 0.502381i | ||||
\(79\) | 6.47257e7i | 1.66176i | 0.556451 | + | 0.830880i | \(0.312163\pi\) | ||||
−0.556451 | + | 0.830880i | \(0.687837\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.78297e6 | −0.111111 | ||||||||
\(82\) | 5.79876e7 | − | 5.79876e7i | 1.28257 | − | 1.28257i | ||||
\(83\) | 4.04525e7 | + | 4.04525e7i | 0.852379 | + | 0.852379i | 0.990426 | − | 0.138047i | \(-0.0440825\pi\) |
−0.138047 | + | 0.990426i | \(0.544083\pi\) | |||||||
\(84\) | − | 2.47817e7i | − | 0.497752i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.13168e8 | 2.06886 | ||||||||
\(87\) | −3.59203e7 | + | 3.59203e7i | −0.626993 | + | 0.626993i | ||||
\(88\) | −3.08488e6 | − | 3.08488e6i | −0.0514408 | − | 0.0514408i | ||||
\(89\) | 9.02203e7i | 1.43795i | 0.695035 | + | 0.718976i | \(0.255389\pi\) | ||||
−0.695035 | + | 0.718976i | \(0.744611\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.53878e7 | −0.953523 | ||||||||
\(92\) | 4.40094e7 | − | 4.40094e7i | 0.614320 | − | 0.614320i | ||||
\(93\) | 4.40630e7 | + | 4.40630e7i | 0.589037 | + | 0.589037i | ||||
\(94\) | − | 1.03960e8i | − | 1.33154i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −6.41702e7 | −0.755525 | ||||||||
\(97\) | 1.44242e7 | − | 1.44242e7i | 0.162932 | − | 0.162932i | −0.620932 | − | 0.783864i | \(-0.713246\pi\) |
0.783864 | + | 0.620932i | \(0.213246\pi\) | |||||||
\(98\) | 8.37278e6 | + | 8.37278e6i | 0.0907748 | + | 0.0907748i | ||||
\(99\) | 9.79261e6i | 0.101943i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.42466e8 | −1.36907 | −0.684535 | − | 0.728980i | \(-0.739995\pi\) | ||||
−0.684535 | + | 0.728980i | \(0.739995\pi\) | |||||||
\(102\) | 4.10550e7 | − | 4.10550e7i | 0.379285 | − | 0.379285i | ||||
\(103\) | 7.31307e7 | + | 7.31307e7i | 0.649756 | + | 0.649756i | 0.952934 | − | 0.303178i | \(-0.0980476\pi\) |
−0.303178 | + | 0.952934i | \(0.598048\pi\) | |||||||
\(104\) | 2.53565e7i | 0.216749i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.21809e8 | −0.964840 | ||||||||
\(107\) | 5.10438e7 | − | 5.10438e7i | 0.389411 | − | 0.389411i | −0.485067 | − | 0.874477i | \(-0.661205\pi\) |
0.874477 | + | 0.485067i | \(0.161205\pi\) | |||||||
\(108\) | 1.52529e7 | + | 1.52529e7i | 0.112114 | + | 0.112114i | ||||
\(109\) | − | 5.91324e7i | − | 0.418909i | −0.977818 | − | 0.209454i | \(-0.932831\pi\) | ||
0.977818 | − | 0.209454i | \(-0.0671688\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.15004e7 | −0.339249 | ||||||||
\(112\) | 1.33329e8 | − | 1.33329e8i | 0.847328 | − | 0.847328i | ||||
\(113\) | 5.36434e7 | + | 5.36434e7i | 0.329005 | + | 0.329005i | 0.852208 | − | 0.523203i | \(-0.175263\pi\) |
−0.523203 | + | 0.852208i | \(0.675263\pi\) | |||||||
\(114\) | − | 1.62817e8i | − | 0.964009i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.29101e8 | 1.26530 | ||||||||
\(117\) | 4.02457e7 | − | 4.02457e7i | 0.214771 | − | 0.214771i | ||||
\(118\) | −6.92955e7 | − | 6.92955e7i | −0.357419 | − | 0.357419i | ||||
\(119\) | 1.44361e8i | 0.719886i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.94310e8 | −0.906469 | ||||||||
\(122\) | 7.46877e7 | − | 7.46877e7i | 0.337140 | − | 0.337140i | ||||
\(123\) | −1.25500e8 | − | 1.25500e8i | −0.548306 | − | 0.548306i | ||||
\(124\) | − | 2.81035e8i | − | 1.18870i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.18734e8 | −0.471079 | ||||||||
\(127\) | −1.38129e8 | + | 1.38129e8i | −0.530969 | + | 0.530969i | −0.920861 | − | 0.389892i | \(-0.872512\pi\) |
0.389892 | + | 0.920861i | \(0.372512\pi\) | |||||||
\(128\) | −8.89015e7 | − | 8.89015e7i | −0.331184 | − | 0.331184i | ||||
\(129\) | − | 2.44925e8i | − | 0.884452i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.43973e8 | 0.828432 | 0.414216 | − | 0.910179i | \(-0.364056\pi\) | ||||
0.414216 | + | 0.910179i | \(0.364056\pi\) | |||||||
\(132\) | 3.12288e7 | − | 3.12288e7i | 0.102863 | − | 0.102863i | ||||
\(133\) | 2.86256e8 | + | 2.86256e8i | 0.914848 | + | 0.914848i | ||||
\(134\) | 4.12880e8i | 1.28058i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.59815e7 | 0.163640 | ||||||||
\(137\) | −2.63122e8 | + | 2.63122e8i | −0.746920 | + | 0.746920i | −0.973900 | − | 0.226979i | \(-0.927115\pi\) |
0.226979 | + | 0.973900i | \(0.427115\pi\) | |||||||
\(138\) | −2.10858e8 | − | 2.10858e8i | −0.581399 | − | 0.581399i | ||||
\(139\) | 1.08062e8i | 0.289477i | 0.989470 | + | 0.144739i | \(0.0462341\pi\) | ||||
−0.989470 | + | 0.144739i | \(0.953766\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.24996e8 | −0.569244 | ||||||||
\(142\) | −6.53251e8 | + | 6.53251e8i | −1.60667 | + | 1.60667i | ||||
\(143\) | −8.23988e7 | − | 8.23988e7i | −0.197050 | − | 0.197050i | ||||
\(144\) | 1.64126e8i | 0.381704i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.14535e9 | 2.52073 | ||||||||
\(147\) | 1.81208e7 | − | 1.81208e7i | 0.0388069 | − | 0.0388069i | ||||
\(148\) | 1.64235e8 | + | 1.64235e8i | 0.342310 | + | 0.342310i | ||||
\(149\) | 2.55974e8i | 0.519340i | 0.965697 | + | 0.259670i | \(0.0836138\pi\) | ||||
−0.965697 | + | 0.259670i | \(0.916386\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.02108e8 | 0.581105 | 0.290553 | − | 0.956859i | \(-0.406161\pi\) | ||||
0.290553 | + | 0.956859i | \(0.406161\pi\) | |||||||
\(152\) | 1.11007e8 | − | 1.11007e8i | 0.207957 | − | 0.207957i | ||||
\(153\) | −8.88535e7 | − | 8.88535e7i | −0.162147 | − | 0.162147i | ||||
\(154\) | 2.43095e8i | 0.432209i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.56688e8 | −0.433419 | ||||||||
\(157\) | −1.07682e8 | + | 1.07682e8i | −0.177233 | + | 0.177233i | −0.790148 | − | 0.612916i | \(-0.789996\pi\) |
0.612916 | + | 0.790148i | \(0.289996\pi\) | |||||||
\(158\) | −9.88958e8 | − | 9.88958e8i | −1.58690 | − | 1.58690i | ||||
\(159\) | 2.63625e8i | 0.412476i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.41439e8 | 1.10350 | ||||||||
\(162\) | 7.30800e7 | − | 7.30800e7i | 0.106106 | − | 0.106106i | ||||
\(163\) | 7.20616e8 | + | 7.20616e8i | 1.02083 | + | 1.02083i | 0.999778 | + | 0.0210510i | \(0.00670125\pi\) |
0.0210510 | + | 0.999778i | \(0.493299\pi\) | |||||||
\(164\) | 8.00442e8i | 1.10651i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.23616e9 | −1.62796 | ||||||||
\(167\) | −4.94776e8 | + | 4.94776e8i | −0.636125 | + | 0.636125i | −0.949597 | − | 0.313472i | \(-0.898508\pi\) |
0.313472 | + | 0.949597i | \(0.398508\pi\) | |||||||
\(168\) | −8.09513e7 | − | 8.09513e7i | −0.101622 | − | 0.101622i | ||||
\(169\) | − | 1.38445e8i | − | 0.169718i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.52378e8 | −0.412120 | ||||||||
\(172\) | −7.81068e8 | + | 7.81068e8i | −0.892432 | + | 0.892432i | ||||
\(173\) | −3.67823e8 | − | 3.67823e8i | −0.410634 | − | 0.410634i | 0.471325 | − | 0.881959i | \(-0.343776\pi\) |
−0.881959 | + | 0.471325i | \(0.843776\pi\) | |||||||
\(174\) | − | 1.09767e9i | − | 1.19750i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.36030e8 | 0.350209 | ||||||||
\(177\) | −1.49973e8 | + | 1.49973e8i | −0.152799 | + | 0.152799i | ||||
\(178\) | −1.37850e9 | − | 1.37850e9i | −1.37317 | − | 1.37317i | ||||
\(179\) | − | 1.47156e9i | − | 1.43340i | −0.697383 | − | 0.716699i | \(-0.745652\pi\) | ||
0.697383 | − | 0.716699i | \(-0.254348\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.08757e9 | −1.01331 | −0.506654 | − | 0.862149i | \(-0.669118\pi\) | ||||
−0.506654 | + | 0.862149i | \(0.669118\pi\) | |||||||
\(182\) | 9.99074e8 | − | 9.99074e8i | 0.910568 | − | 0.910568i | ||||
\(183\) | −1.61643e8 | − | 1.61643e8i | −0.144130 | − | 0.144130i | ||||
\(184\) | − | 2.87521e8i | − | 0.250840i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.34650e9 | −1.12500 | ||||||||
\(187\) | −1.81918e8 | + | 1.81918e8i | −0.148768 | + | 0.148768i | ||||
\(188\) | 7.17516e8 | + | 7.17516e8i | 0.574381 | + | 0.574381i | ||||
\(189\) | 2.56971e8i | 0.201389i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.78708e8 | 0.359698 | 0.179849 | − | 0.983694i | \(-0.442439\pi\) | ||||
0.179849 | + | 0.983694i | \(0.442439\pi\) | |||||||
\(192\) | 3.45174e8 | − | 3.45174e8i | 0.253999 | − | 0.253999i | ||||
\(193\) | 1.58182e9 | + | 1.58182e9i | 1.14006 | + | 1.14006i | 0.988438 | + | 0.151624i | \(0.0484503\pi\) |
0.151624 | + | 0.988438i | \(0.451550\pi\) | |||||||
\(194\) | 4.40782e8i | 0.311184i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.15575e8 | −0.0783141 | ||||||||
\(197\) | −1.05458e9 | + | 1.05458e9i | −0.700185 | + | 0.700185i | −0.964450 | − | 0.264265i | \(-0.914871\pi\) |
0.264265 | + | 0.964450i | \(0.414871\pi\) | |||||||
\(198\) | −1.49623e8 | − | 1.49623e8i | −0.0973507 | − | 0.0973507i | ||||
\(199\) | − | 2.81932e9i | − | 1.79776i | −0.438190 | − | 0.898882i | \(-0.644380\pi\) | ||
0.438190 | − | 0.898882i | \(-0.355620\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.93578e8 | 0.547455 | ||||||||
\(202\) | 2.17677e9 | − | 2.17677e9i | 1.30740 | − | 1.30740i | ||||
\(203\) | 1.92986e9 | + | 1.92986e9i | 1.13643 | + | 1.13643i | ||||
\(204\) | 5.66710e8i | 0.327220i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.23476e9 | −1.24097 | ||||||||
\(207\) | −4.56351e8 | + | 4.56351e8i | −0.248552 | + | 0.248552i | ||||
\(208\) | −1.38102e9 | − | 1.38102e9i | −0.737812 | − | 0.737812i | ||||
\(209\) | 7.21455e8i | 0.378115i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.35002e9 | 0.681100 | 0.340550 | − | 0.940226i | \(-0.389387\pi\) | ||||
0.340550 | + | 0.940226i | \(0.389387\pi\) | |||||||
\(212\) | 8.40704e8 | − | 8.40704e8i | 0.416198 | − | 0.416198i | ||||
\(213\) | 1.41380e9 | + | 1.41380e9i | 0.686863 | + | 0.686863i | ||||
\(214\) | 1.55982e9i | 0.743737i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.96499e7 | 0.0457785 | ||||||||
\(217\) | 2.36734e9 | − | 2.36734e9i | 1.06763 | − | 1.06763i | ||||
\(218\) | 9.03497e8 | + | 9.03497e8i | 0.400038 | + | 0.400038i | ||||
\(219\) | − | 2.47882e9i | − | 1.07763i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.49530e9 | 0.626842 | ||||||||
\(222\) | 7.86885e8 | − | 7.86885e8i | 0.323966 | − | 0.323966i | ||||
\(223\) | −9.94179e8 | − | 9.94179e8i | −0.402018 | − | 0.402018i | 0.476926 | − | 0.878944i | \(-0.341751\pi\) |
−0.878944 | + | 0.476926i | \(0.841751\pi\) | |||||||
\(224\) | 3.44762e9i | 1.36939i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.63926e9 | −0.628367 | ||||||||
\(227\) | −8.75761e7 | + | 8.75761e7i | −0.0329824 | + | 0.0329824i | −0.723406 | − | 0.690423i | \(-0.757424\pi\) |
0.690423 | + | 0.723406i | \(0.257424\pi\) | |||||||
\(228\) | 1.12374e9 | + | 1.12374e9i | 0.415839 | + | 0.415839i | ||||
\(229\) | 2.09791e9i | 0.762859i | 0.924398 | + | 0.381430i | \(0.124568\pi\) | ||||
−0.924398 | + | 0.381430i | \(0.875432\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.26120e8 | 0.184772 | ||||||||
\(232\) | 7.48375e8 | − | 7.48375e8i | 0.258326 | − | 0.258326i | ||||
\(233\) | 2.74740e8 | + | 2.74740e8i | 0.0932178 | + | 0.0932178i | 0.752178 | − | 0.658960i | \(-0.229003\pi\) |
−0.658960 | + | 0.752178i | \(0.729003\pi\) | |||||||
\(234\) | 1.22985e9i | 0.410192i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.56532e8 | 0.308355 | ||||||||
\(237\) | −2.14036e9 | + | 2.14036e9i | −0.678411 | + | 0.678411i | ||||
\(238\) | −2.20573e9 | − | 2.20573e9i | −0.687456 | − | 0.687456i | ||||
\(239\) | 5.48652e8i | 0.168153i | 0.996459 | + | 0.0840767i | \(0.0267941\pi\) | ||||
−0.996459 | + | 0.0840767i | \(0.973206\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.12166e9 | 1.51825 | 0.759123 | − | 0.650947i | \(-0.225628\pi\) | ||||
0.759123 | + | 0.650947i | \(0.225628\pi\) | |||||||
\(242\) | 2.96890e9 | − | 2.96890e9i | 0.865633 | − | 0.865633i | ||||
\(243\) | −1.58164e8 | − | 1.58164e8i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 1.03096e9i | 0.290860i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.83508e9 | 1.04721 | ||||||||
\(247\) | 2.96504e9 | − | 2.96504e9i | 0.796605 | − | 0.796605i | ||||
\(248\) | −9.18023e8 | − | 9.18023e8i | −0.242687 | − | 0.242687i | ||||
\(249\) | 2.67537e9i | 0.695964i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.04785e8 | −0.127178 | −0.0635889 | − | 0.997976i | \(-0.520255\pi\) | ||||
−0.0635889 | + | 0.997976i | \(0.520255\pi\) | |||||||
\(252\) | 8.19483e8 | − | 8.19483e8i | 0.203207 | − | 0.203207i | ||||
\(253\) | 9.34329e8 | + | 9.34329e8i | 0.228043 | + | 0.228043i | ||||
\(254\) | − | 4.22100e9i | − | 1.01410i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.38889e9 | 1.25470 | ||||||||
\(257\) | −1.17418e9 | + | 1.17418e9i | −0.269155 | + | 0.269155i | −0.828760 | − | 0.559605i | \(-0.810953\pi\) |
0.559605 | + | 0.828760i | \(0.310953\pi\) | |||||||
\(258\) | 3.74226e9 | + | 3.74226e9i | 0.844608 | + | 0.844608i | ||||
\(259\) | 2.76692e9i | 0.614890i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.37563e9 | −0.511938 | ||||||||
\(262\) | −3.72772e9 | + | 3.72772e9i | −0.791112 | + | 0.791112i | ||||
\(263\) | 3.37767e9 | + | 3.37767e9i | 0.705982 | + | 0.705982i | 0.965688 | − | 0.259706i | \(-0.0836255\pi\) |
−0.259706 | + | 0.965688i | \(0.583626\pi\) | |||||||
\(264\) | − | 2.04022e8i | − | 0.0420012i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.74755e9 | −1.74727 | ||||||||
\(267\) | −2.98341e9 | + | 2.98341e9i | −0.587041 | + | 0.587041i | ||||
\(268\) | −2.84963e9 | − | 2.84963e9i | −0.552395 | − | 0.552395i | ||||
\(269\) | − | 5.72780e9i | − | 1.09390i | −0.837165 | − | 0.546951i | \(-0.815788\pi\) | ||
0.837165 | − | 0.546951i | \(-0.184212\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.27185e9 | −1.16284 | −0.581418 | − | 0.813605i | \(-0.697502\pi\) | ||||
−0.581418 | + | 0.813605i | \(0.697502\pi\) | |||||||
\(272\) | −3.04897e9 | + | 3.04897e9i | −0.557029 | + | 0.557029i | ||||
\(273\) | −2.16225e9 | − | 2.16225e9i | −0.389274 | − | 0.389274i | ||||
\(274\) | − | 8.04059e9i | − | 1.42654i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.91062e9 | 0.501590 | ||||||||
\(277\) | 3.19244e8 | − | 3.19244e8i | 0.0542254 | − | 0.0542254i | −0.679474 | − | 0.733700i | \(-0.737792\pi\) |
0.733700 | + | 0.679474i | \(0.237792\pi\) | |||||||
\(278\) | −1.65111e9 | − | 1.65111e9i | −0.276437 | − | 0.276437i | ||||
\(279\) | 2.91416e9i | 0.480947i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.35532e9 | −1.34010 | −0.670051 | − | 0.742315i | \(-0.733728\pi\) | ||||
−0.670051 | + | 0.742315i | \(0.733728\pi\) | |||||||
\(282\) | 3.43777e9 | − | 3.43777e9i | 0.543601 | − | 0.543601i | ||||
\(283\) | 1.34940e7 | + | 1.34940e7i | 0.00210375 | + | 0.00210375i | 0.708158 | − | 0.706054i | \(-0.249526\pi\) |
−0.706054 | + | 0.708158i | \(0.749526\pi\) | |||||||
\(284\) | − | 9.01726e9i | − | 1.38612i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.51798e9 | 0.376346 | ||||||||
\(287\) | −6.74263e9 | + | 6.74263e9i | −0.993807 | + | 0.993807i | ||||
\(288\) | −2.12199e9 | − | 2.12199e9i | −0.308442 | − | 0.308442i | ||||
\(289\) | 3.67448e9i | 0.526750i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.53964e8 | 0.133033 | ||||||||
\(292\) | −7.90499e9 | + | 7.90499e9i | −1.08735 | + | 1.08735i | ||||
\(293\) | −5.13714e9 | − | 5.13714e9i | −0.697029 | − | 0.697029i | 0.266740 | − | 0.963769i | \(-0.414054\pi\) |
−0.963769 | + | 0.266740i | \(0.914054\pi\) | |||||||
\(294\) | 5.53744e8i | 0.0741173i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.07298e9 | 0.139773 | ||||||||
\(297\) | −3.23823e8 | + | 3.23823e8i | −0.0416181 | + | 0.0416181i | ||||
\(298\) | −3.91109e9 | − | 3.91109e9i | −0.495944 | − | 0.495944i | ||||
\(299\) | − | 7.67982e9i | − | 0.960874i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.31589e10 | −1.60307 | ||||||||
\(302\) | −4.61598e9 | + | 4.61598e9i | −0.554927 | + | 0.554927i | ||||
\(303\) | −4.71108e9 | − | 4.71108e9i | −0.558920 | − | 0.558920i | ||||
\(304\) | 1.20917e10i | 1.41577i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.71523e9 | 0.309685 | ||||||||
\(307\) | 2.16091e9 | − | 2.16091e9i | 0.243267 | − | 0.243267i | −0.574933 | − | 0.818200i | \(-0.694972\pi\) |
0.818200 | + | 0.574933i | \(0.194972\pi\) | |||||||
\(308\) | −1.67780e9 | − | 1.67780e9i | −0.186439 | − | 0.186439i | ||||
\(309\) | 4.83659e9i | 0.530524i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.44045e9 | −0.688454 | −0.344227 | − | 0.938887i | \(-0.611859\pi\) | ||||
−0.344227 | + | 0.938887i | \(0.611859\pi\) | |||||||
\(312\) | −8.38493e8 | + | 8.38493e8i | −0.0884873 | + | 0.0884873i | ||||
\(313\) | 1.04720e10 | + | 1.04720e10i | 1.09107 | + | 1.09107i | 0.995415 | + | 0.0956506i | \(0.0304931\pi\) |
0.0956506 | + | 0.995415i | \(0.469507\pi\) | |||||||
\(314\) | − | 3.29059e9i | − | 0.338497i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.36513e10 | 1.36907 | ||||||||
\(317\) | 1.01318e10 | − | 1.01318e10i | 1.00334 | − | 1.00334i | 0.00334628 | − | 0.999994i | \(-0.498935\pi\) |
0.999994 | − | 0.00334628i | \(-0.00106516\pi\) | |||||||
\(318\) | −4.02799e9 | − | 4.02799e9i | −0.393894 | − | 0.393894i | ||||
\(319\) | 4.86385e9i | 0.469697i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.37584e9 | 0.317953 | ||||||||
\(322\) | −1.13286e10 | + | 1.13286e10i | −1.05379 | + | 1.05379i | ||||
\(323\) | −6.54615e9 | − | 6.54615e9i | −0.601417 | − | 0.601417i | ||||
\(324\) | 1.00877e9i | 0.0915405i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.20209e10 | −1.94968 | ||||||||
\(327\) | 1.95540e9 | − | 1.95540e9i | 0.171019 | − | 0.171019i | ||||
\(328\) | 2.61471e9 | + | 2.61471e9i | 0.225906 | + | 0.225906i | ||||
\(329\) | 1.20882e10i | 1.03176i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.15436e10 | 1.79476 | 0.897378 | − | 0.441262i | \(-0.145469\pi\) | ||||
0.897378 | + | 0.441262i | \(0.145469\pi\) | |||||||
\(332\) | 8.53180e9 | − | 8.53180e9i | 0.702244 | − | 0.702244i | ||||
\(333\) | −1.70302e9 | − | 1.70302e9i | −0.138498 | − | 0.138498i | ||||
\(334\) | − | 1.51196e10i | − | 1.21494i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8.81785e9 | 0.691840 | ||||||||
\(337\) | −4.14231e9 | + | 4.14231e9i | −0.321161 | + | 0.321161i | −0.849213 | − | 0.528051i | \(-0.822923\pi\) |
0.528051 | + | 0.849213i | \(0.322923\pi\) | |||||||
\(338\) | 2.11533e9 | + | 2.11533e9i | 0.162073 | + | 0.162073i | ||||
\(339\) | 3.54777e9i | 0.268631i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.96643e9 | 0.441262 | ||||||||
\(342\) | 5.38406e9 | − | 5.38406e9i | 0.393555 | − | 0.393555i | ||||
\(343\) | 9.26832e9 | + | 9.26832e9i | 0.669614 | + | 0.669614i | ||||
\(344\) | 5.10284e9i | 0.364400i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.12401e10 | 0.784271 | ||||||||
\(347\) | −1.35085e10 | + | 1.35085e10i | −0.931730 | + | 0.931730i | −0.997814 | − | 0.0660836i | \(-0.978950\pi\) |
0.0660836 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(348\) | 7.57592e9 | + | 7.57592e9i | 0.516557 | + | 0.516557i | ||||
\(349\) | 7.36977e9i | 0.496766i | 0.968662 | + | 0.248383i | \(0.0798992\pi\) | ||||
−0.968662 | + | 0.248383i | \(0.920101\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.66170e9 | 0.175360 | ||||||||
\(352\) | −4.34454e9 | + | 4.34454e9i | −0.282991 | + | 0.282991i | ||||
\(353\) | −1.28656e10 | − | 1.28656e10i | −0.828576 | − | 0.828576i | 0.158743 | − | 0.987320i | \(-0.449256\pi\) |
−0.987320 | + | 0.158743i | \(0.949256\pi\) | |||||||
\(354\) | − | 4.58295e9i | − | 0.291831i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.90283e10 | 1.18468 | ||||||||
\(357\) | −4.77376e9 | + | 4.77376e9i | −0.293892 | + | 0.293892i | ||||
\(358\) | 2.24843e10 | + | 2.24843e10i | 1.36882 | + | 1.36882i | ||||
\(359\) | 2.68477e9i | 0.161633i | 0.996729 | + | 0.0808165i | \(0.0257528\pi\) | ||||
−0.996729 | + | 0.0808165i | \(0.974247\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.97733e9 | −0.528589 | ||||||||
\(362\) | 1.66172e10 | − | 1.66172e10i | 0.967660 | − | 0.967660i | ||||
\(363\) | −6.42545e9 | − | 6.42545e9i | −0.370064 | − | 0.370064i | ||||
\(364\) | 1.37909e10i | 0.785573i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.93957e9 | 0.275273 | ||||||||
\(367\) | 2.10778e10 | − | 2.10778e10i | 1.16188 | − | 1.16188i | 0.177817 | − | 0.984064i | \(-0.443096\pi\) |
0.984064 | − | 0.177817i | \(-0.0569036\pi\) | |||||||
\(368\) | 1.56595e10 | + | 1.56595e10i | 0.853860 | + | 0.853860i | ||||
\(369\) | − | 8.30009e9i | − | 0.447690i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.41636e10 | 0.747614 | ||||||||
\(372\) | 9.29330e9 | − | 9.29330e9i | 0.485286 | − | 0.485286i | ||||
\(373\) | −2.95974e9 | − | 2.95974e9i | −0.152904 | − | 0.152904i | 0.626510 | − | 0.779414i | \(-0.284483\pi\) |
−0.779414 | + | 0.626510i | \(0.784483\pi\) | |||||||
\(374\) | − | 5.55913e9i | − | 0.284132i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.68764e9 | 0.234532 | ||||||||
\(377\) | 1.99895e10 | − | 1.99895e10i | 0.989547 | − | 0.989547i | ||||
\(378\) | −3.92631e9 | − | 3.92631e9i | −0.192317 | − | 0.192317i | ||||
\(379\) | − | 8.01600e9i | − | 0.388509i | −0.980951 | − | 0.194254i | \(-0.937771\pi\) | ||
0.980951 | − | 0.194254i | \(-0.0622287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.13531e9 | −0.433534 | ||||||||
\(382\) | −7.31429e9 | + | 7.31429e9i | −0.343494 | + | 0.343494i | ||||
\(383\) | −1.37328e10 | − | 1.37328e10i | −0.638210 | − | 0.638210i | 0.311904 | − | 0.950114i | \(-0.399033\pi\) |
−0.950114 | + | 0.311904i | \(0.899033\pi\) | |||||||
\(384\) | − | 5.87961e9i | − | 0.270411i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.83380e10 | −2.17741 | ||||||||
\(387\) | 8.09920e9 | − | 8.09920e9i | 0.361076 | − | 0.361076i | ||||
\(388\) | −3.04220e9 | − | 3.04220e9i | −0.134234 | − | 0.134234i | ||||
\(389\) | − | 1.23902e10i | − | 0.541102i | −0.962706 | − | 0.270551i | \(-0.912794\pi\) | ||
0.962706 | − | 0.270551i | \(-0.0872059\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.69553e10 | −0.725436 | ||||||||
\(392\) | −3.77535e8 | + | 3.77535e8i | −0.0159887 | + | 0.0159887i | ||||
\(393\) | 8.06773e9 | + | 8.06773e9i | 0.338206 | + | 0.338206i | ||||
\(394\) | − | 3.22262e10i | − | 1.33729i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.06535e9 | 0.0839872 | ||||||||
\(397\) | 3.17968e10 | − | 3.17968e10i | 1.28003 | − | 1.28003i | 0.339385 | − | 0.940647i | \(-0.389781\pi\) |
0.940647 | − | 0.339385i | \(-0.110219\pi\) | |||||||
\(398\) | 4.30771e10 | + | 4.30771e10i | 1.71678 | + | 1.71678i | ||||
\(399\) | 1.89319e10i | 0.746970i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.45051e10 | −0.560976 | −0.280488 | − | 0.959857i | \(-0.590496\pi\) | ||||
−0.280488 | + | 0.959857i | \(0.590496\pi\) | |||||||
\(402\) | −1.36532e10 | + | 1.36532e10i | −0.522793 | + | 0.522793i | ||||
\(403\) | −2.45209e10 | − | 2.45209e10i | −0.929642 | − | 0.929642i | ||||
\(404\) | 3.00474e10i | 1.12793i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.89736e10 | −2.17047 | ||||||||
\(407\) | −3.48675e9 | + | 3.48675e9i | −0.127070 | + | 0.127070i | ||||
\(408\) | 1.85120e9 | + | 1.85120e9i | 0.0668057 | + | 0.0668057i | ||||
\(409\) | 4.43639e9i | 0.158539i | 0.996853 | + | 0.0792696i | \(0.0252588\pi\) | ||||
−0.996853 | + | 0.0792696i | \(0.974741\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.74019e10 | −0.609858 | ||||||||
\(412\) | 1.54239e10 | − | 1.54239e10i | 0.535311 | − | 0.535311i | ||||
\(413\) | 8.05749e9 | + | 8.05749e9i | 0.276949 | + | 0.276949i | ||||
\(414\) | − | 1.39454e10i | − | 0.474710i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.57105e10 | 1.19240 | ||||||||
\(417\) | −3.57341e9 | + | 3.57341e9i | −0.118179 | + | 0.118179i | ||||
\(418\) | −1.10233e10 | − | 1.10233e10i | −0.361082 | − | 0.361082i | ||||
\(419\) | − | 4.69093e10i | − | 1.52196i | −0.648777 | − | 0.760979i | \(-0.724719\pi\) | ||
0.648777 | − | 0.760979i | \(-0.275281\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.56171e10 | 0.815457 | 0.407728 | − | 0.913103i | \(-0.366321\pi\) | ||||
0.407728 | + | 0.913103i | \(0.366321\pi\) | |||||||
\(422\) | −2.06273e10 | + | 2.06273e10i | −0.650417 | + | 0.650417i | ||||
\(423\) | −7.44020e9 | − | 7.44020e9i | −0.232393 | − | 0.232393i | ||||
\(424\) | − | 5.49245e9i | − | 0.169943i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.32036e10 | −1.31184 | ||||||||
\(427\) | −8.68448e9 | + | 8.68448e9i | −0.261235 | + | 0.261235i | ||||
\(428\) | −1.07656e10 | − | 1.07656e10i | −0.320822 | − | 0.320822i | ||||
\(429\) | − | 5.44954e9i | − | 0.160891i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.60467e10 | 1.62420 | 0.812102 | − | 0.583515i | \(-0.198323\pi\) | ||||
0.812102 | + | 0.583515i | \(0.198323\pi\) | |||||||
\(432\) | −5.42733e9 | + | 5.42733e9i | −0.155830 | + | 0.155830i | ||||
\(433\) | −4.29249e9 | − | 4.29249e9i | −0.122112 | − | 0.122112i | 0.643410 | − | 0.765522i | \(-0.277519\pi\) |
−0.765522 | + | 0.643410i | \(0.777519\pi\) | |||||||
\(434\) | 7.23422e10i | 2.03907i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.24716e10 | −0.345124 | ||||||||
\(437\) | −3.36209e10 | + | 3.36209e10i | −0.921901 | + | 0.921901i | ||||
\(438\) | 3.78744e10 | + | 3.78744e10i | 1.02908 | + | 1.02908i | ||||
\(439\) | 3.37587e10i | 0.908925i | 0.890766 | + | 0.454463i | \(0.150169\pi\) | ||||
−0.890766 | + | 0.454463i | \(0.849831\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.19844e9 | 0.0316857 | ||||||||
\(442\) | −2.28469e10 | + | 2.28469e10i | −0.598603 | + | 0.598603i | ||||
\(443\) | 1.41248e10 | + | 1.41248e10i | 0.366749 | + | 0.366749i | 0.866290 | − | 0.499541i | \(-0.166498\pi\) |
−0.499541 | + | 0.866290i | \(0.666498\pi\) | |||||||
\(444\) | 1.08619e10i | 0.279495i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.03806e10 | 0.767815 | ||||||||
\(447\) | −8.46459e9 | + | 8.46459e9i | −0.212020 | + | 0.212020i | ||||
\(448\) | −1.85449e10 | − | 1.85449e10i | −0.460375 | − | 0.460375i | ||||
\(449\) | − | 7.48403e10i | − | 1.84141i | −0.390260 | − | 0.920705i | \(-0.627615\pi\) | ||
0.390260 | − | 0.920705i | \(-0.372385\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.69935e10 | −0.410750 | ||||||||
\(452\) | 1.13139e10 | − | 1.13139e10i | 0.271055 | − | 0.271055i | ||||
\(453\) | 9.99015e9 | + | 9.99015e9i | 0.237235 | + | 0.237235i | ||||
\(454\) | − | 2.67619e9i | − | 0.0629932i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.34155e9 | 0.169796 | ||||||||
\(457\) | 1.71094e10 | − | 1.71094e10i | 0.392256 | − | 0.392256i | −0.483235 | − | 0.875491i | \(-0.660538\pi\) |
0.875491 | + | 0.483235i | \(0.160538\pi\) | |||||||
\(458\) | −3.20544e10 | − | 3.20544e10i | −0.728493 | − | 0.728493i | ||||
\(459\) | − | 5.87644e9i | − | 0.132392i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.67176e10 | 1.92001 | 0.960006 | − | 0.279981i | \(-0.0903281\pi\) | ||||
0.960006 | + | 0.279981i | \(0.0903281\pi\) | |||||||
\(462\) | −8.03870e9 | + | 8.03870e9i | −0.176448 | + | 0.176448i | ||||
\(463\) | −5.15336e10 | − | 5.15336e10i | −1.12142 | − | 1.12142i | −0.991529 | − | 0.129888i | \(-0.958538\pi\) |
−0.129888 | − | 0.991529i | \(-0.541462\pi\) | |||||||
\(464\) | 8.15189e10i | 1.75868i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.39564e9 | −0.178037 | ||||||||
\(467\) | 6.73199e9 | − | 6.73199e9i | 0.141539 | − | 0.141539i | −0.632787 | − | 0.774326i | \(-0.718089\pi\) |
0.774326 | + | 0.632787i | \(0.218089\pi\) | |||||||
\(468\) | −8.48820e9 | − | 8.48820e9i | −0.176942 | − | 0.176942i | ||||
\(469\) | − | 4.80085e10i | − | 0.992264i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.12166e9 | −0.144710 | ||||||||
\(472\) | 3.12459e9 | − | 3.12459e9i | 0.0629542 | − | 0.0629542i | ||||
\(473\) | −1.65822e10 | − | 1.65822e10i | −0.331283 | − | 0.331283i | ||||
\(474\) | − | 6.54060e10i | − | 1.29570i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.04472e10 | 0.593088 | ||||||||
\(477\) | −8.71759e9 | + | 8.71759e9i | −0.168393 | + | 0.168393i | ||||
\(478\) | −8.38298e9 | − | 8.38298e9i | −0.160578 | − | 0.160578i | ||||
\(479\) | 2.02194e10i | 0.384084i | 0.981387 | + | 0.192042i | \(0.0615111\pi\) | ||||
−0.981387 | + | 0.192042i | \(0.938489\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.86597e10 | 0.535416 | ||||||||
\(482\) | −7.82549e10 | + | 7.82549e10i | −1.44985 | + | 1.44985i | ||||
\(483\) | 2.45180e10 | + | 2.45180e10i | 0.450502 | + | 0.450502i | ||||
\(484\) | 4.09817e10i | 0.746807i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.83324e9 | 0.0866349 | ||||||||
\(487\) | −5.31073e10 | + | 5.31073e10i | −0.944145 | + | 0.944145i | −0.998521 | − | 0.0543755i | \(-0.982683\pi\) |
0.0543755 | + | 0.998521i | \(0.482683\pi\) | |||||||
\(488\) | 3.36773e9 | + | 3.36773e9i | 0.0593824 | + | 0.0593824i | ||||
\(489\) | 4.76588e10i | 0.833504i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.28584e10 | 0.393296 | 0.196648 | − | 0.980474i | \(-0.436994\pi\) | ||||
0.196648 | + | 0.980474i | \(0.436994\pi\) | |||||||
\(492\) | −2.64691e10 | + | 2.64691e10i | −0.451730 | + | 0.451730i | ||||
\(493\) | −4.41323e10 | − | 4.41323e10i | −0.747083 | − | 0.747083i | ||||
\(494\) | 9.06071e10i | 1.52144i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.99983e10 | 1.65221 | ||||||||
\(497\) | 7.59582e10 | − | 7.59582e10i | 1.24494 | − | 1.24494i | ||||
\(498\) | −4.08776e10 | − | 4.08776e10i | −0.664612 | − | 0.664612i | ||||
\(499\) | − | 5.00108e10i | − | 0.806606i | −0.915066 | − | 0.403303i | \(-0.867862\pi\) | ||
0.915066 | − | 0.403303i | \(-0.132138\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.27226e10 | −0.519394 | ||||||||
\(502\) | 7.71272e9 | − | 7.71272e9i | 0.121449 | − | 0.121449i | ||||
\(503\) | 1.48953e10 | + | 1.48953e10i | 0.232689 | + | 0.232689i | 0.813814 | − | 0.581125i | \(-0.197387\pi\) |
−0.581125 | + | 0.813814i | \(0.697387\pi\) | |||||||
\(504\) | − | 5.35381e9i | − | 0.0829738i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.85516e10 | −0.435541 | ||||||||
\(507\) | 4.57810e9 | − | 4.57810e9i | 0.0692873 | − | 0.0692873i | ||||
\(508\) | 2.91326e10 | + | 2.91326e10i | 0.437446 | + | 0.437446i | ||||
\(509\) | 5.21786e10i | 0.777358i | 0.921373 | + | 0.388679i | \(0.127068\pi\) | ||||
−0.921373 | + | 0.388679i | \(0.872932\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.33178e11 | −1.95320 | ||||||||
\(512\) | −5.95792e10 | + | 5.95792e10i | −0.866992 | + | 0.866992i | ||||
\(513\) | −1.16525e10 | − | 1.16525e10i | −0.168247 | − | 0.168247i | ||||
\(514\) | − | 3.58812e10i | − | 0.514060i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.16569e10 | −0.728668 | ||||||||
\(517\) | −1.52330e10 | + | 1.52330e10i | −0.213218 | + | 0.213218i | ||||
\(518\) | −4.22764e10 | − | 4.22764e10i | −0.587190 | − | 0.587190i | ||||
\(519\) | − | 2.43264e10i | − | 0.335281i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.76185e9 | 0.132489 | 0.0662447 | − | 0.997803i | \(-0.478898\pi\) | ||||
0.0662447 | + | 0.997803i | \(0.478898\pi\) | |||||||
\(522\) | 3.62978e10 | − | 3.62978e10i | 0.488876 | − | 0.488876i | ||||
\(523\) | 3.56960e10 | + | 3.56960e10i | 0.477104 | + | 0.477104i | 0.904204 | − | 0.427100i | \(-0.140465\pi\) |
−0.427100 | + | 0.904204i | \(0.640465\pi\) | |||||||
\(524\) | − | 5.14562e10i | − | 0.682515i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.03216e11 | −1.34836 | ||||||||
\(527\) | −5.41366e10 | + | 5.41366e10i | −0.701856 | + | 0.701856i | ||||
\(528\) | 1.11119e10 | + | 1.11119e10i | 0.142972 | + | 0.142972i | ||||
\(529\) | 8.77137e9i | 0.112007i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.91866e9 | −0.124760 | ||||||||
\(532\) | 6.03741e10 | − | 6.03741e10i | 0.753710 | − | 0.753710i | ||||
\(533\) | 6.98402e10 | + | 6.98402e10i | 0.865359 | + | 0.865359i | ||||
\(534\) | − | 9.11685e10i | − | 1.12119i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.86171e10 | −0.225555 | ||||||||
\(537\) | 4.86618e10 | − | 4.86618e10i | 0.585182 | − | 0.585182i | ||||
\(538\) | 8.75163e10 | + | 8.75163e10i | 1.04462 | + | 1.04462i | ||||
\(539\) | − | 2.45368e9i | − | 0.0290712i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.06153e10 | −0.590871 | −0.295436 | − | 0.955363i | \(-0.595465\pi\) | ||||
−0.295436 | + | 0.955363i | \(0.595465\pi\) | |||||||
\(542\) | 9.58290e10 | − | 9.58290e10i | 1.11045 | − | 1.11045i | ||||
\(543\) | −3.59638e10 | − | 3.59638e10i | −0.413681 | − | 0.413681i | ||||
\(544\) | − | 7.88406e10i | − | 0.900232i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.60750e10 | 0.743476 | ||||||||
\(547\) | −1.06937e11 | + | 1.06937e11i | −1.19448 | + | 1.19448i | −0.218683 | + | 0.975796i | \(0.570176\pi\) |
−0.975796 | + | 0.218683i | \(0.929824\pi\) | |||||||
\(548\) | 5.54948e10 | + | 5.54948e10i | 0.615361 | + | 0.615361i | ||||
\(549\) | − | 1.06905e10i | − | 0.117681i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.75021e11 | −1.89882 | ||||||||
\(552\) | 9.50776e9 | − | 9.50776e9i | 0.102405 | − | 0.102405i | ||||
\(553\) | 1.14993e11 | + | 1.14993e11i | 1.22962 | + | 1.22962i | ||||
\(554\) | 9.75559e9i | 0.103565i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.27913e10 | 0.238490 | ||||||||
\(557\) | 9.95647e10 | − | 9.95647e10i | 1.03439 | − | 1.03439i | 0.0350030 | − | 0.999387i | \(-0.488856\pi\) |
0.999387 | − | 0.0350030i | \(-0.0111441\pi\) | |||||||
\(558\) | −4.45261e10 | − | 4.45261e10i | −0.459281 | − | 0.459281i | ||||
\(559\) | 1.36300e11i | 1.39588i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.20314e10 | −0.121468 | ||||||||
\(562\) | 1.27663e11 | − | 1.27663e11i | 1.27973 | − | 1.27973i | ||||
\(563\) | −1.21355e11 | − | 1.21355e11i | −1.20788 | − | 1.20788i | −0.971713 | − | 0.236166i | \(-0.924109\pi\) |
−0.236166 | − | 0.971713i | \(-0.575891\pi\) | |||||||
\(564\) | 4.74538e10i | 0.468980i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.12355e8 | −0.00401796 | ||||||||
\(567\) | −8.49754e9 | + | 8.49754e9i | −0.0822169 | + | 0.0822169i | ||||
\(568\) | −2.94556e10 | − | 2.94556e10i | −0.282992 | − | 0.282992i | ||||
\(569\) | − | 1.62563e11i | − | 1.55086i | −0.631436 | − | 0.775428i | \(-0.717534\pi\) | ||
0.631436 | − | 0.775428i | \(-0.282466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.54958e10 | 0.710197 | 0.355098 | − | 0.934829i | \(-0.384447\pi\) | ||||
0.355098 | + | 0.934829i | \(0.384447\pi\) | |||||||
\(572\) | −1.73787e10 | + | 1.73787e10i | −0.162343 | + | 0.162343i | ||||
\(573\) | 1.58300e10 | + | 1.58300e10i | 0.146846 | + | 0.146846i | ||||
\(574\) | − | 2.06044e11i | − | 1.89807i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.28285e10 | 0.207390 | ||||||||
\(577\) | −1.95276e10 | + | 1.95276e10i | −0.176175 | + | 0.176175i | −0.789686 | − | 0.613511i | \(-0.789757\pi\) |
0.613511 | + | 0.789686i | \(0.289757\pi\) | |||||||
\(578\) | −5.61432e10 | − | 5.61432e10i | −0.503021 | − | 0.503021i | ||||
\(579\) | 1.04616e11i | 0.930857i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.43738e11 | 1.26144 | ||||||||
\(582\) | −1.45758e10 | + | 1.45758e10i | −0.127040 | + | 0.127040i | ||||
\(583\) | 1.78483e10 | + | 1.78483e10i | 0.154498 | + | 0.154498i | ||||
\(584\) | 5.16445e10i | 0.443990i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.56983e11 | 1.33126 | ||||||||
\(587\) | 1.15917e11 | − | 1.15917e11i | 0.976322 | − | 0.976322i | −0.0234041 | − | 0.999726i | \(-0.507450\pi\) |
0.999726 | + | 0.0234041i | \(0.00745043\pi\) | |||||||
\(588\) | −3.82185e9 | − | 3.82185e9i | −0.0319716 | − | 0.0319716i | ||||
\(589\) | 2.14696e11i | 1.78387i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.97457e10 | −0.571699 | ||||||||
\(592\) | −5.84385e10 | + | 5.84385e10i | −0.475786 | + | 0.475786i | ||||
\(593\) | 8.32677e10 | + | 8.32677e10i | 0.673377 | + | 0.673377i | 0.958493 | − | 0.285116i | \(-0.0920322\pi\) |
−0.285116 | + | 0.958493i | \(0.592032\pi\) | |||||||
\(594\) | − | 9.89553e9i | − | 0.0794865i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.39874e10 | 0.427866 | ||||||||
\(597\) | 9.32297e10 | − | 9.32297e10i | 0.733934 | − | 0.733934i | ||||
\(598\) | 1.17342e11 | + | 1.17342e11i | 0.917588 | + | 0.917588i | ||||
\(599\) | − | 1.05049e11i | − | 0.815991i | −0.912984 | − | 0.407995i | \(-0.866228\pi\) | ||
0.912984 | − | 0.407995i | \(-0.133772\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.20830e10 | −0.475855 | −0.237928 | − | 0.971283i | \(-0.576468\pi\) | ||||
−0.237928 | + | 0.971283i | \(0.576468\pi\) | |||||||
\(602\) | 2.01057e11 | − | 2.01057e11i | 1.53086 | − | 1.53086i | ||||
\(603\) | 2.95489e10 | + | 2.95489e10i | 0.223497 | + | 0.223497i | ||||
\(604\) | − | 6.37174e10i | − | 0.478752i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.43963e11 | 1.06748 | ||||||||
\(607\) | −8.59912e10 | + | 8.59912e10i | −0.633431 | + | 0.633431i | −0.948927 | − | 0.315496i | \(-0.897829\pi\) |
0.315496 | + | 0.948927i | \(0.397829\pi\) | |||||||
\(608\) | −1.56334e11 | − | 1.56334e11i | −1.14404 | − | 1.14404i | ||||
\(609\) | 1.27634e11i | 0.927890i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.25209e11 | 0.898405 | ||||||||
\(612\) | −1.87400e10 | + | 1.87400e10i | −0.133587 | + | 0.133587i | ||||
\(613\) | 9.83687e10 | + | 9.83687e10i | 0.696651 | + | 0.696651i | 0.963687 | − | 0.267036i | \(-0.0860442\pi\) |
−0.267036 | + | 0.963687i | \(0.586044\pi\) | |||||||
\(614\) | 6.60340e10i | 0.464616i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.09613e10 | −0.0761274 | ||||||||
\(617\) | −2.02120e11 | + | 2.02120e11i | −1.39466 | + | 1.39466i | −0.580166 | + | 0.814498i | \(0.697012\pi\) |
−0.814498 | + | 0.580166i | \(0.802988\pi\) | |||||||
\(618\) | −7.38993e10 | − | 7.38993e10i | −0.506625 | − | 0.506625i | ||||
\(619\) | 1.10074e11i | 0.749758i | 0.927074 | + | 0.374879i | \(0.122316\pi\) | ||||
−0.927074 | + | 0.374879i | \(0.877684\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.01813e10 | −0.202942 | ||||||||
\(622\) | 9.84051e10 | − | 9.84051e10i | 0.657440 | − | 0.657440i | ||||
\(623\) | 1.60288e11 | + | 1.60288e11i | 1.06401 | + | 1.06401i | ||||
\(624\) | − | 9.13352e10i | − | 0.602421i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.20007e11 | −2.08383 | ||||||||
\(627\) | −2.38572e10 | + | 2.38572e10i | −0.154365 | + | 0.154365i | ||||
\(628\) | 2.27111e10 | + | 2.27111e10i | 0.146016 | + | 0.146016i | ||||
\(629\) | − | 6.32742e10i | − | 0.404226i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.25703e11 | 1.42371 | 0.711854 | − | 0.702328i | \(-0.247856\pi\) | ||||
0.711854 | + | 0.702328i | \(0.247856\pi\) | |||||||
\(632\) | 4.45929e10 | − | 4.45929e10i | 0.279510 | − | 0.279510i | ||||
\(633\) | 4.46427e10 | + | 4.46427e10i | 0.278058 | + | 0.278058i | ||||
\(634\) | 3.09611e11i | 1.91628i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.56010e10 | 0.339824 | ||||||||
\(637\) | −1.00842e10 | + | 1.00842e10i | −0.0612466 | + | 0.0612466i | ||||
\(638\) | −7.43159e10 | − | 7.43159e10i | −0.448537 | − | 0.448537i | ||||
\(639\) | 9.35035e10i | 0.560821i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.36281e9 | −0.0495359 | −0.0247679 | − | 0.999693i | \(-0.507885\pi\) | ||||
−0.0247679 | + | 0.999693i | \(0.507885\pi\) | |||||||
\(642\) | −5.15803e10 | + | 5.15803e10i | −0.303629 | + | 0.303629i | ||||
\(643\) | −9.94984e10 | − | 9.94984e10i | −0.582066 | − | 0.582066i | 0.353405 | − | 0.935471i | \(-0.385024\pi\) |
−0.935471 | + | 0.353405i | \(0.885024\pi\) | |||||||
\(644\) | − | 1.56376e11i | − | 0.909134i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.00040e11 | 1.14865 | ||||||||
\(647\) | −1.64550e11 | + | 1.64550e11i | −0.939035 | + | 0.939035i | −0.998245 | − | 0.0592109i | \(-0.981142\pi\) |
0.0592109 | + | 0.998245i | \(0.481142\pi\) | |||||||
\(648\) | 3.29523e9 | + | 3.29523e9i | 0.0186890 | + | 0.0186890i | ||||
\(649\) | 2.03074e10i | 0.114466i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.56567e11 | 0.871718 | ||||||||
\(652\) | 1.51984e11 | − | 1.51984e11i | 0.841025 | − | 0.841025i | ||||
\(653\) | 6.64536e10 | + | 6.64536e10i | 0.365482 | + | 0.365482i | 0.865826 | − | 0.500344i | \(-0.166793\pi\) |
−0.500344 | + | 0.865826i | \(0.666793\pi\) | |||||||
\(654\) | 5.97539e10i | 0.326629i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.84814e11 | −1.53797 | ||||||||
\(657\) | 8.19699e10 | − | 8.19699e10i | 0.439940 | − | 0.439940i | ||||
\(658\) | −1.84698e11 | − | 1.84698e11i | −0.985278 | − | 0.985278i | ||||
\(659\) | 5.17280e10i | 0.274273i | 0.990552 | + | 0.137137i | \(0.0437900\pi\) | ||||
−0.990552 | + | 0.137137i | \(0.956210\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.89964e11 | −0.995095 | −0.497547 | − | 0.867437i | \(-0.665766\pi\) | ||||
−0.497547 | + | 0.867437i | \(0.665766\pi\) | |||||||
\(662\) | −3.29169e11 | + | 3.29169e11i | −1.71391 | + | 1.71391i | ||||
\(663\) | 4.94466e10 | + | 4.94466e10i | 0.255907 | + | 0.255907i | ||||
\(664\) | − | 5.57396e10i | − | 0.286742i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.20416e10 | 0.264517 | ||||||||
\(667\) | −2.26663e11 | + | 2.26663e11i | −1.14519 | + | 1.14519i | ||||
\(668\) | 1.04353e11 | + | 1.04353e11i | 0.524081 | + | 0.524081i | ||||
\(669\) | − | 6.57512e10i | − | 0.328246i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.18876e10 | −0.107971 | ||||||||
\(672\) | −1.14006e11 | + | 1.14006e11i | −0.559052 | + | 0.559052i | ||||
\(673\) | −1.70060e11 | − | 1.70060e11i | −0.828978 | − | 0.828978i | 0.158397 | − | 0.987375i | \(-0.449367\pi\) |
−0.987375 | + | 0.158397i | \(0.949367\pi\) | |||||||
\(674\) | − | 1.26583e11i | − | 0.613387i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.91992e10 | −0.139825 | ||||||||
\(677\) | 2.18049e11 | − | 2.18049e11i | 1.03801 | − | 1.03801i | 0.0387581 | − | 0.999249i | \(-0.487660\pi\) |
0.999249 | − | 0.0387581i | \(-0.0123402\pi\) | |||||||
\(678\) | −5.42072e10 | − | 5.42072e10i | −0.256530 | − | 0.256530i | ||||
\(679\) | − | 5.12529e10i | − | 0.241123i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.79195e9 | −0.0269300 | ||||||||
\(682\) | −9.11624e10 | + | 9.11624e10i | −0.421384 | + | 0.421384i | ||||
\(683\) | −1.05222e11 | − | 1.05222e11i | −0.483530 | − | 0.483530i | 0.422727 | − | 0.906257i | \(-0.361073\pi\) |
−0.906257 | + | 0.422727i | \(0.861073\pi\) | |||||||
\(684\) | 7.43197e10i | 0.339531i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.83225e11 | −1.27890 | ||||||||
\(687\) | −6.93738e10 | + | 6.93738e10i | −0.311436 | + | 0.311436i | ||||
\(688\) | −2.77921e11 | − | 2.77921e11i | −1.24042 | − | 1.24042i | ||||
\(689\) | − | 1.46706e11i | − | 0.650986i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.02900e11 | −1.32858 | −0.664290 | − | 0.747475i | \(-0.731266\pi\) | ||||
−0.664290 | + | 0.747475i | \(0.731266\pi\) | |||||||
\(692\) | −7.75773e10 | + | 7.75773e10i | −0.338307 | + | 0.338307i | ||||
\(693\) | 1.73978e10 | + | 1.73978e10i | 0.0754329 | + | 0.0754329i | ||||
\(694\) | − | 4.12800e11i | − | 1.77951i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.94947e10 | 0.210922 | ||||||||
\(697\) | 1.54191e11 | − | 1.54191e11i | 0.653324 | − | 0.653324i | ||||
\(698\) | −1.12604e11 | − | 1.12604e11i | −0.474388 | − | 0.474388i | ||||
\(699\) | 1.81703e10i | 0.0761120i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.79525e11 | −1.57170 | −0.785849 | − | 0.618419i | \(-0.787773\pi\) | ||||
−0.785849 | + | 0.618419i | \(0.787773\pi\) | |||||||
\(702\) | −4.06687e10 | + | 4.06687e10i | −0.167460 | + | 0.167460i | ||||
\(703\) | −1.25467e11 | − | 1.25467e11i | −0.513700 | − | 0.513700i | ||||
\(704\) | − | 4.67388e10i | − | 0.190277i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.93154e11 | 1.58250 | ||||||||
\(707\) | −2.53108e11 | + | 2.53108e11i | −1.01305 | + | 1.01305i | ||||
\(708\) | 3.16307e10 | + | 3.16307e10i | 0.125886 | + | 0.125886i | ||||
\(709\) | − | 2.85486e11i | − | 1.12980i | −0.825160 | − | 0.564899i | \(-0.808915\pi\) | ||
0.825160 | − | 0.564899i | \(-0.191085\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.41555e11 | −0.553920 | ||||||||
\(712\) | 6.21574e10 | − | 6.21574e10i | 0.241865 | − | 0.241865i | ||||
\(713\) | 2.78045e11 | + | 2.78045e11i | 1.07586 | + | 1.07586i | ||||
\(714\) | − | 1.45879e11i | − | 0.561305i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.10366e11 | −1.18092 | ||||||||
\(717\) | −1.81429e10 | + | 1.81429e10i | −0.0686483 | + | 0.0686483i | ||||
\(718\) | −4.10213e10 | − | 4.10213e10i | −0.154352 | − | 0.154352i | ||||
\(719\) | − | 2.09894e11i | − | 0.785389i | −0.919669 | − | 0.392695i | \(-0.871543\pi\) | ||
0.919669 | − | 0.392695i | \(-0.128457\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.59851e11 | 0.961577 | ||||||||
\(722\) | 1.37167e11 | − | 1.37167e11i | 0.504777 | − | 0.504777i | ||||
\(723\) | 1.69364e11 | + | 1.69364e11i | 0.619822 | + | 0.619822i | ||||
\(724\) | 2.29378e11i | 0.834829i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.96352e11 | 0.706787 | ||||||||
\(727\) | 7.80140e10 | − | 7.80140e10i | 0.279277 | − | 0.279277i | −0.553543 | − | 0.832820i | \(-0.686725\pi\) |
0.832820 | + | 0.553543i | \(0.186725\pi\) | |||||||
\(728\) | 4.50490e10 | + | 4.50490e10i | 0.160384 | + | 0.160384i | ||||
\(729\) | − | 1.04604e10i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.00919e11 | 1.05385 | ||||||||
\(732\) | −3.40921e10 | + | 3.40921e10i | −0.118743 | + | 0.118743i | ||||
\(733\) | 6.83172e10 | + | 6.83172e10i | 0.236654 | + | 0.236654i | 0.815463 | − | 0.578809i | \(-0.196482\pi\) |
−0.578809 | + | 0.815463i | \(0.696482\pi\) | |||||||
\(734\) | 6.44106e11i | 2.21908i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.04925e11 | −1.37995 | ||||||||
\(737\) | 6.04982e10 | − | 6.04982e10i | 0.205056 | − | 0.205056i | ||||
\(738\) | 1.26819e11 | + | 1.26819e11i | 0.427522 | + | 0.427522i | ||||
\(739\) | 1.68021e11i | 0.563358i | 0.959509 | + | 0.281679i | \(0.0908914\pi\) | ||||
−0.959509 | + | 0.281679i | \(0.909109\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.96097e11 | 0.650425 | ||||||||
\(742\) | −2.16409e11 | + | 2.16409e11i | −0.713935 | + | 0.713935i | ||||
\(743\) | −4.02895e11 | − | 4.02895e11i | −1.32201 | − | 1.32201i | −0.912143 | − | 0.409872i | \(-0.865573\pi\) |
−0.409872 | − | 0.912143i | \(-0.634427\pi\) | |||||||
\(744\) | − | 6.07146e10i | − | 0.198153i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.04450e10 | 0.292031 | ||||||||
\(747\) | −8.84695e10 | + | 8.84695e10i | −0.284126 | + | 0.284126i | ||||
\(748\) | 3.83682e10 | + | 3.83682e10i | 0.122564 | + | 0.122564i | ||||
\(749\) | − | 1.81371e11i | − | 0.576290i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.15049e11 | 0.361678 | 0.180839 | − | 0.983513i | \(-0.442119\pi\) | ||||
0.180839 | + | 0.983513i | \(0.442119\pi\) | |||||||
\(752\) | −2.55307e11 | + | 2.55307e11i | −0.798348 | + | 0.798348i | ||||
\(753\) | −1.66923e10 | − | 1.66923e10i | −0.0519201 | − | 0.0519201i | ||||
\(754\) | 6.10848e11i | 1.88994i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.41975e10 | 0.165917 | ||||||||
\(757\) | 1.32371e11 | − | 1.32371e11i | 0.403096 | − | 0.403096i | −0.476227 | − | 0.879323i | \(-0.657996\pi\) |
0.879323 | + | 0.476227i | \(0.157996\pi\) | |||||||
\(758\) | 1.22478e11 | + | 1.22478e11i | 0.371007 | + | 0.371007i | ||||
\(759\) | 6.17930e10i | 0.186197i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.75577e11 | 0.821683 | 0.410841 | − | 0.911707i | \(-0.365235\pi\) | ||||
0.410841 | + | 0.911707i | \(0.365235\pi\) | |||||||
\(762\) | 1.39580e11 | − | 1.39580e11i | 0.414004 | − | 0.414004i | ||||
\(763\) | −1.05056e11 | − | 1.05056e11i | −0.309972 | − | 0.309972i | ||||
\(764\) | − | 1.00964e11i | − | 0.296342i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.19652e11 | 1.21892 | ||||||||
\(767\) | 8.34594e10 | − | 8.34594e10i | 0.241154 | − | 0.241154i | ||||
\(768\) | 1.78200e11 | + | 1.78200e11i | 0.512228 | + | 0.512228i | ||||
\(769\) | 6.27339e10i | 0.179390i | 0.995969 | + | 0.0896948i | \(0.0285892\pi\) | ||||
−0.995969 | + | 0.0896948i | \(0.971411\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.76559e10 | −0.219764 | ||||||||
\(772\) | 3.33621e11 | − | 3.33621e11i | 0.939257 | − | 0.939257i | ||||
\(773\) | 2.75539e11 | + | 2.75539e11i | 0.771730 | + | 0.771730i | 0.978409 | − | 0.206679i | \(-0.0662655\pi\) |
−0.206679 | + | 0.978409i | \(0.566265\pi\) | |||||||
\(774\) | 2.47499e11i | 0.689620i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.98752e10 | −0.0548106 | ||||||||
\(777\) | −9.14968e10 | + | 9.14968e10i | −0.251028 | + | 0.251028i | ||||
\(778\) | 1.89312e11 | + | 1.89312e11i | 0.516726 | + | 0.516726i | ||||
\(779\) | − | 6.11496e11i | − | 1.66052i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.91438e11 | 0.514546 | ||||||||
\(782\) | 2.59064e11 | − | 2.59064e11i | 0.692756 | − | 0.692756i | ||||
\(783\) | −7.85577e10 | − | 7.85577e10i | −0.208998 | − | 0.208998i | ||||
\(784\) | − | 4.11241e10i | − | 0.108851i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.46537e11 | −0.645940 | ||||||||
\(787\) | −2.59480e11 | + | 2.59480e11i | −0.676402 | + | 0.676402i | −0.959184 | − | 0.282782i | \(-0.908743\pi\) |
0.282782 | + | 0.959184i | \(0.408743\pi\) | |||||||
\(788\) | 2.22420e11 | + | 2.22420e11i | 0.576858 | + | 0.576858i | ||||
\(789\) | 2.23386e11i | 0.576432i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.90608e11 | 0.486895 | ||||||||
\(792\) | 6.74663e9 | − | 6.74663e9i | 0.0171469 | − | 0.0171469i | ||||
\(793\) | 8.99537e10 | + | 8.99537e10i | 0.227471 | + | 0.227471i | ||||
\(794\) | 9.71660e11i | 2.44474i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.94622e11 | −1.48111 | ||||||||
\(797\) | 2.57815e11 | − | 2.57815e11i | 0.638961 | − | 0.638961i | −0.311338 | − | 0.950299i | \(-0.600777\pi\) |
0.950299 | + | 0.311338i | \(0.100777\pi\) | |||||||
\(798\) | −2.89265e11 | − | 2.89265e11i | −0.713320 | − | 0.713320i | ||||
\(799\) | − | 2.76434e11i | − | 0.678273i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.97312e11 | −0.479317 | ||||||||
\(802\) | 2.21627e11 | − | 2.21627e11i | 0.535705 | − | 0.535705i | ||||
\(803\) | −1.67824e11 | − | 1.67824e11i | −0.403639 | − | 0.403639i | ||||
\(804\) | − | 1.88464e11i | − | 0.451028i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.49320e11 | 1.77553 | ||||||||
\(807\) | 1.89407e11 | − | 1.89407e11i | 0.446584 | − | 0.446584i | ||||
\(808\) | 9.81522e10 | + | 9.81522e10i | 0.230279 | + | 0.230279i | ||||
\(809\) | 4.40964e11i | 1.02946i | 0.857353 | + | 0.514729i | \(0.172108\pi\) | ||||
−0.857353 | + | 0.514729i | \(0.827892\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.14945e11 | 0.728033 | 0.364016 | − | 0.931393i | \(-0.381405\pi\) | ||||
0.364016 | + | 0.931393i | \(0.381405\pi\) | |||||||
\(812\) | 4.07026e11 | − | 4.07026e11i | 0.936262 | − | 0.936262i | ||||
\(813\) | −2.07398e11 | − | 2.07398e11i | −0.474726 | − | 0.474726i | ||||
\(814\) | − | 1.06550e11i | − | 0.242691i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.01648e11 | −0.454813 | ||||||||
\(817\) | 5.96696e11 | − | 5.96696e11i | 1.33926 | − | 1.33926i | ||||
\(818\) | −6.77846e10 | − | 6.77846e10i | −0.151397 | − | 0.151397i | ||||
\(819\) | − | 1.43003e11i | − | 0.317841i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.96960e11 | 0.653621 | 0.326810 | − | 0.945090i | \(-0.394026\pi\) | ||||
0.326810 | + | 0.945090i | \(0.394026\pi\) | |||||||
\(822\) | 2.65887e11 | − | 2.65887e11i | 0.582385 | − | 0.582385i | ||||
\(823\) | 1.54849e11 | + | 1.54849e11i | 0.337526 | + | 0.337526i | 0.855436 | − | 0.517909i | \(-0.173289\pi\) |
−0.517909 | + | 0.855436i | \(0.673289\pi\) | |||||||
\(824\) | − | 1.00767e11i | − | 0.218579i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.46224e11 | −0.528945 | ||||||||
\(827\) | 4.19074e10 | − | 4.19074e10i | 0.0895919 | − | 0.0895919i | −0.660890 | − | 0.750482i | \(-0.729821\pi\) |
0.750482 | + | 0.660890i | \(0.229821\pi\) | |||||||
\(828\) | 9.62486e10 | + | 9.62486e10i | 0.204773 | + | 0.204773i | ||||
\(829\) | − | 6.56756e10i | − | 0.139055i | −0.997580 | − | 0.0695274i | \(-0.977851\pi\) | ||
0.997580 | − | 0.0695274i | \(-0.0221491\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.11136e10 | 0.0442749 | ||||||||
\(832\) | −1.92088e11 | + | 1.92088e11i | −0.400872 | + | 0.400872i | ||||
\(833\) | 2.22635e10 | + | 2.22635e10i | 0.0462396 | + | 0.0462396i | ||||
\(834\) | − | 1.09198e11i | − | 0.225710i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.52162e11 | 0.311516 | ||||||||
\(837\) | −9.63658e10 | + | 9.63658e10i | −0.196346 | + | 0.196346i | ||||
\(838\) | 7.16737e11 | + | 7.16737e11i | 1.45340 | + | 1.45340i | ||||
\(839\) | − | 7.98678e11i | − | 1.61185i | −0.592020 | − | 0.805924i | \(-0.701669\pi\) | ||
0.592020 | − | 0.805924i | \(-0.298331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.79697e11 | −1.35872 | ||||||||
\(842\) | −3.91409e11 | + | 3.91409e11i | −0.778721 | + | 0.778721i | ||||
\(843\) | −2.76295e11 | − | 2.76295e11i | −0.547094 | − | 0.547094i | ||||
\(844\) | − | 2.84732e11i | − | 0.561134i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.27361e11 | 0.443848 | ||||||||
\(847\) | −3.45215e11 | + | 3.45215e11i | −0.670743 | + | 0.670743i | ||||
\(848\) | 2.99141e11 | + | 2.99141e11i | 0.578485 | + | 0.578485i | ||||
\(849\) | 8.92440e8i | 0.00171770i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.24976e11 | −0.619630 | ||||||||
\(852\) | 2.98184e11 | − | 2.98184e11i | 0.565882 | − | 0.565882i | ||||
\(853\) | 1.87598e11 | + | 1.87598e11i | 0.354350 | + | 0.354350i | 0.861725 | − | 0.507375i | \(-0.169384\pi\) |
−0.507375 | + | 0.861725i | \(0.669384\pi\) | |||||||
\(854\) | − | 2.65384e11i | − | 0.498934i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.03334e10 | −0.130999 | ||||||||
\(857\) | 4.78106e11 | − | 4.78106e11i | 0.886342 | − | 0.886342i | −0.107828 | − | 0.994170i | \(-0.534390\pi\) |
0.994170 | + | 0.107828i | \(0.0343896\pi\) | |||||||
\(858\) | 8.32648e10 | + | 8.32648e10i | 0.153643 | + | 0.153643i | ||||
\(859\) | 2.92378e11i | 0.536996i | 0.963280 | + | 0.268498i | \(0.0865273\pi\) | ||||
−0.963280 | + | 0.268498i | \(0.913473\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.45932e11 | −0.811440 | ||||||||
\(862\) | −8.56349e11 | + | 8.56349e11i | −1.55104 | + | 1.55104i | ||||
\(863\) | −8.69978e10 | − | 8.69978e10i | −0.156843 | − | 0.156843i | 0.624323 | − | 0.781166i | \(-0.285375\pi\) |
−0.781166 | + | 0.624323i | \(0.785375\pi\) | |||||||
\(864\) | − | 1.40340e11i | − | 0.251842i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.31172e11 | 0.233222 | ||||||||
\(867\) | −1.21508e11 | + | 1.21508e11i | −0.215045 | + | 0.215045i | ||||
\(868\) | −4.99294e11 | − | 4.99294e11i | −0.879584 | − | 0.879584i | ||||
\(869\) | 2.89819e11i | 0.508215i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.97272e11 | −0.864015 | ||||||||
\(872\) | −4.07394e10 | + | 4.07394e10i | −0.0704609 | + | 0.0704609i | ||||
\(873\) | 3.15458e10 | + | 3.15458e10i | 0.0543106 | + | 0.0543106i | ||||
\(874\) | − | 1.02740e12i | − | 1.76074i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.22806e11 | −0.887819 | ||||||||
\(877\) | 3.39966e11 | − | 3.39966e11i | 0.574695 | − | 0.574695i | −0.358742 | − | 0.933437i | \(-0.616794\pi\) |
0.933437 | + | 0.358742i | \(0.116794\pi\) | |||||||
\(878\) | −5.15807e11 | − | 5.15807e11i | −0.867979 | − | 0.867979i | ||||
\(879\) | − | 3.39751e11i | − | 0.569122i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.22272e11 | 0.368961 | 0.184480 | − | 0.982836i | \(-0.440940\pi\) | ||||
0.184480 | + | 0.982836i | \(0.440940\pi\) | |||||||
\(882\) | −1.83113e10 | + | 1.83113e10i | −0.0302583 | + | 0.0302583i | ||||
\(883\) | 2.34413e11 | + | 2.34413e11i | 0.385602 | + | 0.385602i | 0.873116 | − | 0.487513i | \(-0.162096\pi\) |
−0.487513 | + | 0.873116i | \(0.662096\pi\) | |||||||
\(884\) | − | 3.15372e11i | − | 0.516432i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.31633e11 | −0.700454 | ||||||||
\(887\) | −7.39337e11 | + | 7.39337e11i | −1.19439 | + | 1.19439i | −0.218574 | + | 0.975820i | \(0.570140\pi\) |
−0.975820 | + | 0.218574i | \(0.929860\pi\) | |||||||
\(888\) | 3.54813e10 | + | 3.54813e10i | 0.0570620 | + | 0.0570620i | ||||
\(889\) | 4.90806e11i | 0.785783i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.14164e10 | −0.0339810 | ||||||||
\(892\) | −2.09682e11 | + | 2.09682e11i | −0.331208 | + | 0.331208i | ||||
\(893\) | −5.48145e11 | − | 5.48145e11i | −0.861965 | − | 0.861965i | ||||
\(894\) | − | 2.58665e11i | − | 0.404937i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.15889e11 | −0.490120 | ||||||||
\(897\) | 2.53957e11 | − | 2.53957e11i | 0.392275 | − | 0.392275i | ||||
\(898\) | 1.14350e12 | + | 1.14350e12i | 1.75846 | + | 1.75846i | ||||
\(899\) | 1.44742e12i | 2.21593i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.23894e11 | −0.491478 | ||||||||
\(902\) | 2.59648e11 | − | 2.59648e11i | 0.392246 | − | 0.392246i | ||||
\(903\) | −4.35139e11 | − | 4.35139e11i | −0.654451 | − | 0.654451i | ||||
\(904\) | − | 7.39154e10i | − | 0.110678i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.05284e11 | −0.453096 | ||||||||
\(907\) | 9.79482e10 | − | 9.79482e10i | 0.144733 | − | 0.144733i | −0.631027 | − | 0.775760i | \(-0.717367\pi\) |
0.775760 | + | 0.631027i | \(0.217367\pi\) | |||||||
\(908\) | 1.84706e10 | + | 1.84706e10i | 0.0271730 | + | 0.0271730i | ||||
\(909\) | − | 3.11573e11i | − | 0.456357i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.30284e10 | −0.0915088 | −0.0457544 | − | 0.998953i | \(-0.514569\pi\) | ||||
−0.0457544 | + | 0.998953i | \(0.514569\pi\) | |||||||
\(912\) | −3.99850e11 | + | 3.99850e11i | −0.577987 | + | 0.577987i | ||||
\(913\) | 1.81132e11 | + | 1.81132e11i | 0.260682 | + | 0.260682i | ||||
\(914\) | 5.22836e11i | 0.749171i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.42468e11 | 0.628492 | ||||||||
\(917\) | 4.33449e11 | − | 4.33449e11i | 0.613000 | − | 0.613000i | ||||
\(918\) | 8.97874e10 | + | 8.97874e10i | 0.126428 | + | 0.126428i | ||||
\(919\) | − | 1.20904e12i | − | 1.69503i | −0.530772 | − | 0.847515i | \(-0.678098\pi\) | ||
0.530772 | − | 0.847515i | \(-0.321902\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.42914e11 | 0.198626 | ||||||||
\(922\) | −1.32498e12 | + | 1.32498e12i | −1.83352 | + | 1.83352i | ||||
\(923\) | −7.86774e11 | − | 7.86774e11i | −1.08403 | − | 1.08403i | ||||
\(924\) | − | 1.10964e11i | − | 0.152227i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.57479e12 | 2.14180 | ||||||||
\(927\) | −1.59937e11 | + | 1.59937e11i | −0.216585 | + | 0.216585i | ||||
\(928\) | −1.05396e12 | − | 1.05396e12i | −1.42113 | − | 1.42113i | ||||
\(929\) | 1.37970e12i | 1.85234i | 0.377106 | + | 0.926170i | \(0.376919\pi\) | ||||
−0.377106 | + | 0.926170i | \(0.623081\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.82934e10 | 0.117525 | ||||||||
\(932\) | 5.79453e10 | − | 5.79453e10i | 0.0767988 | − | 0.0767988i | ||||
\(933\) | −2.12974e11 | − | 2.12974e11i | −0.281060 | − | 0.281060i | ||||
\(934\) | 2.05719e11i | 0.270325i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.54547e10 | −0.0722496 | ||||||||
\(937\) | 1.57203e11 | − | 1.57203e11i | 0.203940 | − | 0.203940i | −0.597746 | − | 0.801686i | \(-0.703937\pi\) |
0.801686 | + | 0.597746i | \(0.203937\pi\) | |||||||
\(938\) | 7.33533e11 | + | 7.33533e11i | 0.947564 | + | 0.947564i | ||||
\(939\) | 6.92576e11i | 0.890851i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.08269e11 | 0.648239 | 0.324120 | − | 0.946016i | \(-0.394932\pi\) | ||||
0.324120 | + | 0.946016i | \(0.394932\pi\) | |||||||
\(942\) | 1.08813e11 | − | 1.08813e11i | 0.138191 | − | 0.138191i | ||||
\(943\) | −7.91925e11 | − | 7.91925e11i | −1.00147 | − | 1.00147i | ||||
\(944\) | 3.40355e11i | 0.428592i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.06727e11 | 0.632717 | ||||||||
\(947\) | −4.22518e11 | + | 4.22518e11i | −0.525346 | + | 0.525346i | −0.919181 | − | 0.393835i | \(-0.871148\pi\) |
0.393835 | + | 0.919181i | \(0.371148\pi\) | |||||||
\(948\) | 4.51421e11 | + | 4.51421e11i | 0.558918 | + | 0.558918i | ||||
\(949\) | 1.37945e12i | 1.70076i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.70077e11 | 0.819224 | ||||||||
\(952\) | 9.94581e10 | − | 9.94581e10i | 0.121086 | − | 0.121086i | ||||
\(953\) | −5.77256e11 | − | 5.77256e11i | −0.699837 | − | 0.699837i | 0.264538 | − | 0.964375i | \(-0.414781\pi\) |
−0.964375 | + | 0.264538i | \(0.914781\pi\) | |||||||
\(954\) | − | 2.66396e11i | − | 0.321613i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.15716e11 | 0.138536 | ||||||||
\(957\) | −1.60838e11 | + | 1.60838e11i | −0.191753 | + | 0.191753i | ||||
\(958\) | −3.08937e11 | − | 3.08937e11i | −0.366782 | − | 0.366782i | ||||
\(959\) | 9.34936e11i | 1.10537i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.22646e11 | 1.08179 | ||||||||
\(962\) | −4.37898e11 | + | 4.37898e11i | −0.511297 | + | 0.511297i | ||||
\(963\) | 1.11633e11 | + | 1.11633e11i | 0.129804 | + | 0.129804i | ||||
\(964\) | − | 1.08020e12i | − | 1.25083i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7.49232e11 | −0.860415 | ||||||||
\(967\) | 6.14848e11 | − | 6.14848e11i | 0.703173 | − | 0.703173i | −0.261918 | − | 0.965090i | \(-0.584355\pi\) |
0.965090 | + | 0.261918i | \(0.0843549\pi\) | |||||||
\(968\) | 1.33870e11 | + | 1.33870e11i | 0.152469 | + | 0.152469i | ||||
\(969\) | − | 4.32937e11i | − | 0.491055i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.74017e11 | −0.420741 | −0.210370 | − | 0.977622i | \(-0.567467\pi\) | ||||
−0.210370 | + | 0.977622i | \(0.567467\pi\) | |||||||
\(972\) | −3.33582e10 | + | 3.33582e10i | −0.0373712 | + | 0.0373712i | ||||
\(973\) | 1.91986e11 | + | 1.91986e11i | 0.214199 | + | 0.214199i | ||||
\(974\) | − | 1.62288e12i | − | 1.80323i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.66839e11 | −0.404275 | ||||||||
\(977\) | −5.84649e11 | + | 5.84649e11i | −0.641678 | + | 0.641678i | −0.950968 | − | 0.309290i | \(-0.899909\pi\) |
0.309290 | + | 0.950968i | \(0.399909\pi\) | |||||||
\(978\) | −7.28189e11 | − | 7.28189e11i | −0.795956 | − | 0.795956i | ||||
\(979\) | 4.03974e11i | 0.439767i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.29323e11 | 0.139636 | ||||||||
\(982\) | −3.49259e11 | + | 3.49259e11i | −0.375579 | + | 0.375579i | ||||
\(983\) | 1.87740e11 | + | 1.87740e11i | 0.201068 | + | 0.201068i | 0.800457 | − | 0.599390i | \(-0.204590\pi\) |
−0.599390 | + | 0.800457i | \(0.704590\pi\) | |||||||
\(984\) | 1.72927e11i | 0.184451i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.34861e12 | 1.42686 | ||||||||
\(987\) | −3.99734e11 | + | 3.99734e11i | −0.421213 | + | 0.421213i | ||||
\(988\) | −6.25355e11 | − | 6.25355e11i | −0.656295 | − | 0.656295i | ||||
\(989\) | − | 1.54552e12i | − | 1.61543i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.37718e11 | −0.350155 | −0.175077 | − | 0.984555i | \(-0.556018\pi\) | ||||
−0.175077 | + | 0.984555i | \(0.556018\pi\) | |||||||
\(992\) | −1.29288e12 | + | 1.29288e12i | −1.33510 | + | 1.33510i | ||||
\(993\) | 7.12405e11 | + | 7.12405e11i | 0.732706 | + | 0.732706i | ||||
\(994\) | 2.32116e12i | 2.37772i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.64261e11 | 0.573380 | ||||||||
\(997\) | 5.07145e11 | − | 5.07145e11i | 0.513277 | − | 0.513277i | −0.402252 | − | 0.915529i | \(-0.631772\pi\) |
0.915529 | + | 0.402252i | \(0.131772\pi\) | |||||||
\(998\) | 7.64126e11 | + | 7.64126e11i | 0.770270 | + | 0.770270i | ||||
\(999\) | − | 1.12631e11i | − | 0.113083i |
(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 | 75.9.f.d.43.2 | yes | 12 | |
5.2 | odd | 4 | inner | 75.9.f.d.7.2 | ✓ | 12 | |
5.3 | odd | 4 | inner | 75.9.f.d.7.5 | yes | 12 | |
5.4 | even | 2 | inner | 75.9.f.d.43.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.9.f.d.7.2 | ✓ | 12 | 5.2 | odd | 4 | inner | |
75.9.f.d.7.5 | yes | 12 | 5.3 | odd | 4 | inner | |
75.9.f.d.43.2 | yes | 12 | 1.1 | even | 1 | trivial | |
75.9.f.d.43.5 | yes | 12 | 5.4 | even | 2 | inner |