Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,13,Mod(19,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.19");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.d (of order \(6\), degree \(2\), not 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: | \(89.5713940931\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} - 2204556 x^{14} - 87623088 x^{13} + 1948666431190 x^{12} + 195028079162640 x^{11} + \cdots + 24\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{48}\cdot 3^{8}\cdot 7^{8} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.2 | ||
Root | \(468.905 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.19 |
Dual form | 98.13.d.a.31.2 |
$q$-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 \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −22.6274 | + | 39.1918i | −0.353553 | + | 0.612372i | ||||
\(3\) | −702.607 | + | 405.650i | −0.963796 | + | 0.556448i | −0.897339 | − | 0.441342i | \(-0.854503\pi\) |
−0.0664566 | + | 0.997789i | \(0.521169\pi\) | |||||||
\(4\) | −1024.00 | − | 1773.62i | −0.250000 | − | 0.433013i | ||||
\(5\) | 18305.2 | + | 10568.5i | 1.17153 | + | 0.676385i | 0.954041 | − | 0.299677i | \(-0.0968790\pi\) |
0.217492 | + | 0.976062i | \(0.430212\pi\) | |||||||
\(6\) | − | 36715.3i | − | 0.786936i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 92681.9 | 0.353553 | ||||||||
\(9\) | 63384.0 | − | 109784.i | 0.119268 | − | 0.206579i | ||||
\(10\) | −828399. | + | 478276.i | −0.828399 | + | 0.478276i | ||||
\(11\) | 651539. | + | 1.12850e6i | 0.367777 | + | 0.637008i | 0.989218 | − | 0.146453i | \(-0.0467857\pi\) |
−0.621441 | + | 0.783461i | \(0.713452\pi\) | |||||||
\(12\) | 1.43894e6 | + | 830772.i | 0.481898 | + | 0.278224i | ||||
\(13\) | − | 7.09849e6i | − | 1.47064i | −0.677720 | − | 0.735320i | \(-0.737032\pi\) | ||
0.677720 | − | 0.735320i | \(-0.262968\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.71485e7 | −1.50549 | ||||||||
\(16\) | −2.09715e6 | + | 3.63237e6i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.79240e7 | − | 1.61219e7i | 1.15687 | − | 0.667919i | 0.206318 | − | 0.978485i | \(-0.433852\pi\) |
0.950552 | + | 0.310566i | \(0.100519\pi\) | |||||||
\(18\) | 2.86843e6 | + | 4.96827e6i | 0.0843353 | + | 0.146073i | ||||
\(19\) | 2.32303e7 | + | 1.34120e7i | 0.493780 | + | 0.285084i | 0.726141 | − | 0.687545i | \(-0.241312\pi\) |
−0.232361 | + | 0.972630i | \(0.574645\pi\) | |||||||
\(20\) | − | 4.32886e7i | − | 0.676385i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.89706e7 | −0.520115 | ||||||||
\(23\) | 6.22412e7 | − | 1.07805e8i | 0.420447 | − | 0.728235i | −0.575536 | − | 0.817776i | \(-0.695207\pi\) |
0.995983 | + | 0.0895411i | \(0.0285400\pi\) | |||||||
\(24\) | −6.51190e7 | + | 3.75965e7i | −0.340753 | + | 0.196734i | ||||
\(25\) | 1.01317e8 | + | 1.75486e8i | 0.414993 | + | 0.718789i | ||||
\(26\) | 2.78203e8 | + | 1.60621e8i | 0.900579 | + | 0.519950i | ||||
\(27\) | − | 3.28312e8i | − | 0.847429i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.52793e8 | −1.26557 | −0.632787 | − | 0.774326i | \(-0.718089\pi\) | ||||
−0.632787 | + | 0.774326i | \(0.718089\pi\) | |||||||
\(30\) | 3.88026e8 | − | 6.72081e8i | 0.532272 | − | 0.921921i | ||||
\(31\) | −9.46508e8 | + | 5.46467e8i | −1.06648 | + | 0.615735i | −0.927219 | − | 0.374520i | \(-0.877807\pi\) |
−0.139265 | + | 0.990255i | \(0.544474\pi\) | |||||||
\(32\) | −9.49063e7 | − | 1.64382e8i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −9.15552e8 | − | 5.28594e8i | −0.708923 | − | 0.409297i | ||||
\(34\) | 1.45919e9i | 0.944580i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.59621e8 | −0.119268 | ||||||||
\(37\) | −1.93585e9 | + | 3.35299e9i | −0.754503 | + | 1.30684i | 0.191117 | + | 0.981567i | \(0.438789\pi\) |
−0.945621 | + | 0.325271i | \(0.894544\pi\) | |||||||
\(38\) | −1.05129e9 | + | 6.06960e8i | −0.349156 | + | 0.201585i | ||||
\(39\) | 2.87951e9 | + | 4.98745e9i | 0.818334 | + | 1.41740i | ||||
\(40\) | 1.69656e9 | + | 9.79510e8i | 0.414199 | + | 0.239138i | ||||
\(41\) | 2.55800e9i | 0.538516i | 0.963068 | + | 0.269258i | \(0.0867784\pi\) | ||||
−0.963068 | + | 0.269258i | \(0.913222\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.36133e9 | −0.689934 | −0.344967 | − | 0.938615i | \(-0.612110\pi\) | ||||
−0.344967 | + | 0.938615i | \(0.612110\pi\) | |||||||
\(44\) | 1.33435e9 | − | 2.31116e9i | 0.183888 | − | 0.318504i | ||||
\(45\) | 2.32051e9 | − | 1.33975e9i | 0.279453 | − | 0.161342i | ||||
\(46\) | 2.81672e9 | + | 4.87869e9i | 0.297301 | + | 0.514940i | ||||
\(47\) | −8.04169e9 | − | 4.64287e9i | −0.746037 | − | 0.430725i | 0.0782231 | − | 0.996936i | \(-0.475075\pi\) |
−0.824260 | + | 0.566211i | \(0.808409\pi\) | |||||||
\(48\) | − | 3.40284e9i | − | 0.278224i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −9.17013e9 | −0.586888 | ||||||||
\(51\) | −1.30797e10 | + | 2.26548e10i | −0.743324 | + | 1.28747i | ||||
\(52\) | −1.25900e10 | + | 7.26886e9i | −0.636805 | + | 0.367660i | ||||
\(53\) | −1.09179e8 | − | 1.89104e8i | −0.00492590 | − | 0.00853191i | 0.863552 | − | 0.504260i | \(-0.168235\pi\) |
−0.868478 | + | 0.495728i | \(0.834901\pi\) | |||||||
\(54\) | 1.28671e10 | + | 7.42884e9i | 0.518942 | + | 0.299612i | ||||
\(55\) | 2.75432e10i | 0.995034i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.17624e10 | −0.634538 | ||||||||
\(58\) | 1.70338e10 | − | 2.95033e10i | 0.447448 | − | 0.775003i | ||||
\(59\) | −5.45224e10 | + | 3.14785e10i | −1.29260 | + | 0.746280i | −0.979114 | − | 0.203314i | \(-0.934829\pi\) |
−0.313482 | + | 0.949594i | \(0.601495\pi\) | |||||||
\(60\) | 1.75600e10 | + | 3.04149e10i | 0.376373 | + | 0.651897i | ||||
\(61\) | −4.19753e10 | − | 2.42344e10i | −0.814732 | − | 0.470386i | 0.0338645 | − | 0.999426i | \(-0.489219\pi\) |
−0.848596 | + | 0.529041i | \(0.822552\pi\) | |||||||
\(62\) | − | 4.94605e10i | − | 0.870780i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.58993e9 | 0.125000 | ||||||||
\(65\) | 7.50205e10 | − | 1.29939e11i | 0.994718 | − | 1.72290i | ||||
\(66\) | 4.14331e10 | − | 2.39214e10i | 0.501284 | − | 0.289417i | ||||
\(67\) | −5.49220e10 | − | 9.51277e10i | −0.607152 | − | 1.05162i | −0.991707 | − | 0.128516i | \(-0.958979\pi\) |
0.384556 | − | 0.923102i | \(-0.374355\pi\) | |||||||
\(68\) | −5.71884e10 | − | 3.30177e10i | −0.578435 | − | 0.333959i | ||||
\(69\) | 1.00993e11i | 0.935826i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.43754e10 | −0.580603 | −0.290302 | − | 0.956935i | \(-0.593756\pi\) | ||||
−0.290302 | + | 0.956935i | \(0.593756\pi\) | |||||||
\(72\) | 5.87455e9 | − | 1.01750e10i | 0.0421677 | − | 0.0730366i | ||||
\(73\) | 2.26320e11 | − | 1.30666e11i | 1.49550 | − | 0.863427i | 0.495512 | − | 0.868601i | \(-0.334980\pi\) |
0.999987 | + | 0.00517437i | \(0.00164706\pi\) | |||||||
\(74\) | −8.76065e10 | − | 1.51739e11i | −0.533514 | − | 0.924074i | ||||
\(75\) | −1.42372e11 | − | 8.21982e10i | −0.799937 | − | 0.461844i | ||||
\(76\) | − | 5.49357e10i | − | 0.285084i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.60623e11 | −1.15730 | ||||||||
\(79\) | −1.20639e11 | + | 2.08953e11i | −0.496279 | + | 0.859580i | −0.999991 | − | 0.00429190i | \(-0.998634\pi\) |
0.503712 | + | 0.863871i | \(0.331967\pi\) | |||||||
\(80\) | −7.67776e10 | + | 4.43276e10i | −0.292883 | + | 0.169096i | ||||
\(81\) | 1.66865e11 | + | 2.89018e11i | 0.590818 | + | 1.02333i | ||||
\(82\) | −1.00253e11 | − | 5.78810e10i | −0.329772 | − | 0.190394i | ||||
\(83\) | 2.09983e11i | 0.642268i | 0.947034 | + | 0.321134i | \(0.104064\pi\) | ||||
−0.947034 | + | 0.321134i | \(0.895936\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.81540e11 | 1.80708 | ||||||||
\(86\) | 9.86855e10 | − | 1.70928e11i | 0.243929 | − | 0.422497i | ||||
\(87\) | 5.28918e11 | − | 3.05371e11i | 1.21975 | − | 0.704226i | ||||
\(88\) | 6.03859e10 | + | 1.04591e11i | 0.130029 | + | 0.225216i | ||||
\(89\) | −1.79050e10 | − | 1.03374e10i | −0.0360275 | − | 0.0208005i | 0.481878 | − | 0.876238i | \(-0.339955\pi\) |
−0.517906 | + | 0.855438i | \(0.673288\pi\) | |||||||
\(90\) | 1.21260e11i | 0.228173i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.54940e11 | −0.420447 | ||||||||
\(93\) | 4.43349e11 | − | 7.67903e11i | 0.685248 | − | 1.18689i | ||||
\(94\) | 3.63926e11 | − | 2.10113e11i | 0.527528 | − | 0.304568i | ||||
\(95\) | 2.83491e11 | + | 4.91020e11i | 0.385653 | + | 0.667971i | ||||
\(96\) | 1.33364e11 | + | 7.69975e10i | 0.170377 | + | 0.0983670i | ||||
\(97\) | − | 4.74911e11i | − | 0.570140i | −0.958507 | − | 0.285070i | \(-0.907983\pi\) | ||
0.958507 | − | 0.285070i | \(-0.0920169\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.65189e11 | 0.175456 | ||||||||
\(100\) | 2.07496e11 | − | 3.59394e11i | 0.207496 | − | 0.359394i | ||||
\(101\) | −9.97000e11 | + | 5.75618e11i | −0.939219 | + | 0.542259i | −0.889715 | − | 0.456515i | \(-0.849097\pi\) |
−0.0495038 | + | 0.998774i | \(0.515764\pi\) | |||||||
\(102\) | −5.91921e11 | − | 1.02524e12i | −0.525609 | − | 0.910382i | ||||
\(103\) | −8.21363e11 | − | 4.74214e11i | −0.687878 | − | 0.397147i | 0.114938 | − | 0.993373i | \(-0.463333\pi\) |
−0.802817 | + | 0.596226i | \(0.796666\pi\) | |||||||
\(104\) | − | 6.57902e11i | − | 0.519950i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.88179e9 | 0.00696628 | ||||||||
\(107\) | 1.66978e11 | − | 2.89214e11i | 0.111264 | − | 0.192715i | −0.805016 | − | 0.593253i | \(-0.797843\pi\) |
0.916280 | + | 0.400538i | \(0.131177\pi\) | |||||||
\(108\) | −5.82300e11 | + | 3.36191e11i | −0.366948 | + | 0.211857i | ||||
\(109\) | 3.67785e11 | + | 6.37022e11i | 0.219298 | + | 0.379835i | 0.954594 | − | 0.297911i | \(-0.0962899\pi\) |
−0.735295 | + | 0.677747i | \(0.762957\pi\) | |||||||
\(110\) | −1.07947e12 | − | 6.23231e11i | −0.609332 | − | 0.351798i | ||||
\(111\) | − | 3.14111e12i | − | 1.67937i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.66369e12 | −1.27942 | −0.639709 | − | 0.768617i | \(-0.720945\pi\) | ||||
−0.639709 | + | 0.768617i | \(0.720945\pi\) | |||||||
\(114\) | 4.92427e11 | − | 8.52908e11i | 0.224343 | − | 0.388574i | ||||
\(115\) | 2.27868e12 | − | 1.31559e12i | 0.985134 | − | 0.568768i | ||||
\(116\) | 7.70860e11 | + | 1.33517e12i | 0.316394 | + | 0.548010i | ||||
\(117\) | −7.79303e11 | − | 4.49931e11i | −0.303803 | − | 0.175400i | ||||
\(118\) | − | 2.84911e12i | − | 1.05540i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.58935e12 | −0.532272 | ||||||||
\(121\) | 7.20208e11 | − | 1.24744e12i | 0.229481 | − | 0.397472i | ||||
\(122\) | 1.89958e12 | − | 1.09673e12i | 0.576102 | − | 0.332613i | ||||
\(123\) | −1.03766e12 | − | 1.79727e12i | −0.299656 | − | 0.519019i | ||||
\(124\) | 1.93845e12 | + | 1.11916e12i | 0.533242 | + | 0.307867i | ||||
\(125\) | − | 8.77343e11i | − | 0.229990i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.69168e11 | −0.0641506 | −0.0320753 | − | 0.999485i | \(-0.510212\pi\) | ||||
−0.0320753 | + | 0.999485i | \(0.510212\pi\) | |||||||
\(128\) | −1.94368e11 | + | 3.36655e11i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 3.06430e12 | − | 1.76917e12i | 0.664956 | − | 0.383912i | ||||
\(130\) | 3.39504e12 | + | 5.88038e12i | 0.703372 | + | 1.21828i | ||||
\(131\) | −4.16356e12 | − | 2.40383e12i | −0.823829 | − | 0.475638i | 0.0279059 | − | 0.999611i | \(-0.491116\pi\) |
−0.851735 | + | 0.523972i | \(0.824449\pi\) | |||||||
\(132\) | 2.16512e12i | 0.409297i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.97097e12 | 0.858642 | ||||||||
\(135\) | 3.46976e12 | − | 6.00981e12i | 0.573188 | − | 0.992791i | ||||
\(136\) | 2.58805e12 | − | 1.49421e12i | 0.409015 | − | 0.236145i | ||||
\(137\) | −5.08937e12 | − | 8.81505e12i | −0.769734 | − | 1.33322i | −0.937707 | − | 0.347427i | \(-0.887056\pi\) |
0.167973 | − | 0.985792i | \(-0.446278\pi\) | |||||||
\(138\) | −3.95809e12 | − | 2.28520e12i | −0.573074 | − | 0.330865i | ||||
\(139\) | 3.81539e11i | 0.0528994i | 0.999650 | + | 0.0264497i | \(0.00842018\pi\) | ||||
−0.999650 | + | 0.0264497i | \(0.991580\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.53354e12 | 0.958703 | ||||||||
\(142\) | 1.68292e12 | − | 2.91491e12i | 0.205274 | − | 0.355545i | ||||
\(143\) | 8.01064e12 | − | 4.62495e12i | 0.936809 | − | 0.540867i | ||||
\(144\) | 2.65852e11 | + | 4.60469e11i | 0.0298170 | + | 0.0516446i | ||||
\(145\) | −1.37800e13 | − | 7.95590e12i | −1.48266 | − | 0.856015i | ||||
\(146\) | 1.18265e13i | 1.22107i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.92924e12 | 0.754503 | ||||||||
\(149\) | 1.01352e13 | − | 1.75546e13i | 0.926218 | − | 1.60426i | 0.136627 | − | 0.990623i | \(-0.456374\pi\) |
0.789591 | − | 0.613634i | \(-0.210293\pi\) | |||||||
\(150\) | 6.44300e12 | − | 3.71987e12i | 0.565641 | − | 0.326573i | ||||
\(151\) | 9.98191e12 | + | 1.72892e13i | 0.842077 | + | 1.45852i | 0.888136 | + | 0.459582i | \(0.152001\pi\) |
−0.0460585 | + | 0.998939i | \(0.514666\pi\) | |||||||
\(152\) | 2.15303e12 | + | 1.24305e12i | 0.174578 | + | 0.100793i | ||||
\(153\) | − | 4.08749e12i | − | 0.318646i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.31014e13 | −1.66589 | ||||||||
\(156\) | 5.89723e12 | − | 1.02143e13i | 0.409167 | − | 0.708698i | ||||
\(157\) | −6.85383e12 | + | 3.95706e12i | −0.457652 | + | 0.264226i | −0.711057 | − | 0.703135i | \(-0.751783\pi\) |
0.253404 | + | 0.967360i | \(0.418450\pi\) | |||||||
\(158\) | −5.45950e12 | − | 9.45613e12i | −0.350922 | − | 0.607815i | ||||
\(159\) | 1.53420e11 | + | 8.85774e10i | 0.00949512 | + | 0.00548201i | ||||
\(160\) | − | 4.01207e12i | − | 0.239138i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.51029e13 | −0.835543 | ||||||||
\(163\) | −1.22758e13 | + | 2.12623e13i | −0.654521 | + | 1.13366i | 0.327493 | + | 0.944854i | \(0.393796\pi\) |
−0.982014 | + | 0.188810i | \(0.939537\pi\) | |||||||
\(164\) | 4.53693e12 | − | 2.61940e12i | 0.233184 | − | 0.134629i | ||||
\(165\) | −1.11729e13 | − | 1.93520e13i | −0.553685 | − | 0.959010i | ||||
\(166\) | −8.22964e12 | − | 4.75138e12i | −0.393307 | − | 0.227076i | ||||
\(167\) | − | 2.03607e13i | − | 0.938629i | −0.883031 | − | 0.469315i | \(-0.844501\pi\) | ||
0.883031 | − | 0.469315i | \(-0.155499\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.70905e13 | −1.16278 | ||||||||
\(170\) | −1.54215e13 | + | 2.67108e13i | −0.638899 | + | 1.10661i | ||||
\(171\) | 2.94486e12 | − | 1.70022e12i | 0.117785 | − | 0.0680030i | ||||
\(172\) | 4.46600e12 | + | 7.73533e12i | 0.172484 | + | 0.298750i | ||||
\(173\) | −1.88719e13 | − | 1.08957e13i | −0.703945 | − | 0.406423i | 0.104870 | − | 0.994486i | \(-0.466557\pi\) |
−0.808815 | + | 0.588063i | \(0.799891\pi\) | |||||||
\(174\) | 2.76390e13i | 0.995926i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.46550e12 | −0.183888 | ||||||||
\(177\) | 2.55385e13 | − | 4.42340e13i | 0.830532 | − | 1.43852i | ||||
\(178\) | 8.10287e11 | − | 4.67819e11i | 0.0254753 | − | 0.0147081i | ||||
\(179\) | −5.29449e12 | − | 9.17033e12i | −0.160956 | − | 0.278783i | 0.774256 | − | 0.632872i | \(-0.218124\pi\) |
−0.935212 | + | 0.354089i | \(0.884791\pi\) | |||||||
\(180\) | −4.75241e12 | − | 2.74381e12i | −0.139727 | − | 0.0806712i | ||||
\(181\) | − | 5.35655e13i | − | 1.52340i | −0.647930 | − | 0.761700i | \(-0.724365\pi\) | ||
0.647930 | − | 0.761700i | \(-0.275635\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.93229e13 | 1.04698 | ||||||||
\(184\) | 5.76863e12 | − | 9.99156e12i | 0.148650 | − | 0.257470i | ||||
\(185\) | −7.08722e13 | + | 4.09181e13i | −1.76785 | + | 1.02067i | ||||
\(186\) | 2.00637e13 | + | 3.47513e13i | 0.484544 | + | 0.839255i | ||||
\(187\) | 3.63872e13 | + | 2.10081e13i | 0.850939 | + | 0.491290i | ||||
\(188\) | 1.90172e13i | 0.430725i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.56586e13 | −0.545396 | ||||||||
\(191\) | −3.11402e13 | + | 5.39365e13i | −0.641390 | + | 1.11092i | 0.343733 | + | 0.939067i | \(0.388308\pi\) |
−0.985123 | + | 0.171852i | \(0.945025\pi\) | |||||||
\(192\) | −6.03535e12 | + | 3.48451e12i | −0.120474 | + | 0.0695560i | ||||
\(193\) | 1.97810e13 | + | 3.42617e13i | 0.382740 | + | 0.662926i | 0.991453 | − | 0.130465i | \(-0.0416471\pi\) |
−0.608713 | + | 0.793391i | \(0.708314\pi\) | |||||||
\(194\) | 1.86126e13 | + | 1.07460e13i | 0.349138 | + | 0.201575i | ||||
\(195\) | 1.21728e14i | 2.21403i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.98938e12 | 0.0511427 | 0.0255713 | − | 0.999673i | \(-0.491860\pi\) | ||||
0.0255713 | + | 0.999673i | \(0.491860\pi\) | |||||||
\(198\) | −3.73779e12 | + | 6.47404e12i | −0.0620332 | + | 0.107445i | ||||
\(199\) | −5.16217e13 | + | 2.98038e13i | −0.831216 | + | 0.479903i | −0.854269 | − | 0.519831i | \(-0.825995\pi\) |
0.0230526 | + | 0.999734i | \(0.492661\pi\) | |||||||
\(200\) | 9.39022e12 | + | 1.62643e13i | 0.146722 | + | 0.254130i | ||||
\(201\) | 7.71771e13 | + | 4.45582e13i | 1.17034 | + | 0.675697i | ||||
\(202\) | − | 5.20990e13i | − | 0.766869i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.35746e13 | 0.743324 | ||||||||
\(205\) | −2.70343e13 | + | 4.68248e13i | −0.364244 | + | 0.630889i | ||||
\(206\) | 3.71706e13 | − | 2.14605e13i | 0.486403 | − | 0.280825i | ||||
\(207\) | −7.89019e12 | − | 1.36662e13i | −0.100292 | − | 0.173711i | ||||
\(208\) | 2.57844e13 | + | 1.48866e13i | 0.318403 | + | 0.183830i | ||||
\(209\) | 3.49539e13i | 0.419389i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.29666e14 | 1.46937 | 0.734684 | − | 0.678409i | \(-0.237330\pi\) | ||||
0.734684 | + | 0.678409i | \(0.237330\pi\) | |||||||
\(212\) | −2.23599e11 | + | 3.87286e11i | −0.00246295 | + | 0.00426595i | ||||
\(213\) | 5.22567e13 | − | 3.01704e13i | 0.559583 | − | 0.323075i | ||||
\(214\) | 7.55654e12 | + | 1.30883e13i | 0.0786756 | + | 0.136270i | ||||
\(215\) | −7.98349e13 | − | 4.60927e13i | −0.808281 | − | 0.466661i | ||||
\(216\) | − | 3.04285e13i | − | 0.299612i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.32881e13 | −0.310134 | ||||||||
\(219\) | −1.06009e14 | + | 1.83614e14i | −0.960904 | + | 1.66433i | ||||
\(220\) | 4.88512e13 | − | 2.82042e13i | 0.430863 | − | 0.248759i | ||||
\(221\) | −1.14441e14 | − | 1.98218e14i | −0.982268 | − | 1.70134i | ||||
\(222\) | 1.23106e14 | + | 7.10753e13i | 1.02840 | + | 0.593746i | ||||
\(223\) | − | 1.05020e14i | − | 0.853972i | −0.904258 | − | 0.426986i | \(-0.859575\pi\) | ||
0.904258 | − | 0.426986i | \(-0.140425\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.56874e13 | 0.197982 | ||||||||
\(226\) | 6.02724e13 | − | 1.04395e14i | 0.452343 | − | 0.783481i | ||||
\(227\) | −6.69859e13 | + | 3.86743e13i | −0.489585 | + | 0.282662i | −0.724402 | − | 0.689378i | \(-0.757884\pi\) |
0.234817 | + | 0.972040i | \(0.424551\pi\) | |||||||
\(228\) | 2.22847e13 | + | 3.85982e13i | 0.158635 | + | 0.274763i | ||||
\(229\) | 1.53002e14 | + | 8.83360e13i | 1.06093 | + | 0.612526i | 0.925688 | − | 0.378287i | \(-0.123487\pi\) |
0.135238 | + | 0.990813i | \(0.456820\pi\) | |||||||
\(230\) | 1.19074e14i | 0.804359i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.97703e13 | −0.447448 | ||||||||
\(233\) | −1.16414e14 | + | 2.01635e14i | −0.727562 | + | 1.26017i | 0.230349 | + | 0.973108i | \(0.426013\pi\) |
−0.957911 | + | 0.287066i | \(0.907320\pi\) | |||||||
\(234\) | 3.52672e13 | − | 2.03616e13i | 0.214821 | − | 0.124027i | ||||
\(235\) | −9.81366e13 | − | 1.69977e14i | −0.582671 | − | 1.00922i | ||||
\(236\) | 1.11662e14 | + | 6.44680e13i | 0.646298 | + | 0.373140i | ||||
\(237\) | − | 1.95749e14i | − | 1.10461i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.20020e14 | 0.643971 | 0.321986 | − | 0.946745i | \(-0.395650\pi\) | ||||
0.321986 | + | 0.946745i | \(0.395650\pi\) | |||||||
\(240\) | 3.59630e13 | − | 6.22897e13i | 0.188186 | − | 0.325948i | ||||
\(241\) | −4.44336e13 | + | 2.56537e13i | −0.226782 | + | 0.130933i | −0.609087 | − | 0.793104i | \(-0.708464\pi\) |
0.382305 | + | 0.924036i | \(0.375131\pi\) | |||||||
\(242\) | 3.25929e13 | + | 5.64526e13i | 0.162267 | + | 0.281055i | ||||
\(243\) | −8.33779e13 | − | 4.81383e13i | −0.404961 | − | 0.233804i | ||||
\(244\) | 9.92643e13i | 0.470386i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.39179e13 | 0.423777 | ||||||||
\(247\) | 9.52053e13 | − | 1.64900e14i | 0.419256 | − | 0.726173i | ||||
\(248\) | −8.77242e13 | + | 5.06476e13i | −0.377059 | + | 0.217695i | ||||
\(249\) | −8.51799e13 | − | 1.47536e14i | −0.357389 | − | 0.619016i | ||||
\(250\) | 3.43847e13 | + | 1.98520e13i | 0.140840 | + | 0.0813138i | ||||
\(251\) | 1.04293e14i | 0.417073i | 0.978015 | + | 0.208537i | \(0.0668700\pi\) | ||||
−0.978015 | + | 0.208537i | \(0.933130\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.62210e14 | 0.618522 | ||||||||
\(254\) | 6.09057e12 | − | 1.05492e13i | 0.0226807 | − | 0.0392841i | ||||
\(255\) | −4.78855e14 | + | 2.76467e14i | −1.74166 | + | 1.00555i | ||||
\(256\) | −8.79609e12 | − | 1.52353e13i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −2.30306e14 | − | 1.32967e14i | −0.799295 | − | 0.461473i | 0.0439295 | − | 0.999035i | \(-0.486012\pi\) |
−0.843225 | + | 0.537561i | \(0.819346\pi\) | |||||||
\(258\) | 1.60127e14i | 0.542934i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.07284e14 | −0.994718 | ||||||||
\(261\) | −4.77150e13 | + | 8.26449e13i | −0.150943 | + | 0.261440i | ||||
\(262\) | 1.88421e14 | − | 1.08785e14i | 0.582535 | − | 0.336327i | ||||
\(263\) | 1.98352e14 | + | 3.43556e14i | 0.599380 | + | 1.03816i | 0.992913 | + | 0.118846i | \(0.0379195\pi\) |
−0.393533 | + | 0.919311i | \(0.628747\pi\) | |||||||
\(264\) | −8.48551e13 | − | 4.89911e13i | −0.250642 | − | 0.144708i | ||||
\(265\) | − | 4.61546e12i | − | 0.0133272i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.67735e13 | 0.0462975 | ||||||||
\(268\) | −1.12480e14 | + | 1.94821e14i | −0.303576 | + | 0.525809i | ||||
\(269\) | 5.98003e13 | − | 3.45257e13i | 0.157830 | − | 0.0911232i | −0.419005 | − | 0.907984i | \(-0.637621\pi\) |
0.576835 | + | 0.816861i | \(0.304288\pi\) | |||||||
\(270\) | 1.57024e14 | + | 2.71973e14i | 0.405305 | + | 0.702010i | ||||
\(271\) | 6.55851e14 | + | 3.78656e14i | 1.65573 | + | 0.955936i | 0.974652 | + | 0.223726i | \(0.0718221\pi\) |
0.681078 | + | 0.732211i | \(0.261511\pi\) | |||||||
\(272\) | 1.35241e14i | 0.333959i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.60637e14 | 1.08857 | ||||||||
\(275\) | −1.32023e14 | + | 2.28671e14i | −0.305249 | + | 0.528707i | ||||
\(276\) | 1.79123e14 | − | 1.03416e14i | 0.405225 | − | 0.233957i | ||||
\(277\) | −1.16361e14 | − | 2.01543e14i | −0.257590 | − | 0.446159i | 0.708006 | − | 0.706207i | \(-0.249595\pi\) |
−0.965596 | + | 0.260047i | \(0.916262\pi\) | |||||||
\(278\) | −1.49532e13 | − | 8.63325e12i | −0.0323941 | − | 0.0187028i | ||||
\(279\) | 1.38549e14i | 0.293750i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.05866e14 | −1.43379 | −0.716893 | − | 0.697183i | \(-0.754436\pi\) | ||||
−0.716893 | + | 0.697183i | \(0.754436\pi\) | |||||||
\(282\) | −1.70464e14 | + | 2.95253e14i | −0.338953 | + | 0.587083i | ||||
\(283\) | −6.72043e14 | + | 3.88004e14i | −1.30821 | + | 0.755297i | −0.981798 | − | 0.189930i | \(-0.939174\pi\) |
−0.326414 | + | 0.945227i | \(0.605841\pi\) | |||||||
\(284\) | 7.61604e13 | + | 1.31914e14i | 0.145151 | + | 0.251409i | ||||
\(285\) | −3.98365e14 | − | 2.29996e14i | −0.743382 | − | 0.429192i | ||||
\(286\) | 4.18602e14i | 0.764901i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.40622e13 | −0.0421677 | ||||||||
\(289\) | 2.28522e14 | − | 3.95813e14i | 0.392231 | − | 0.679364i | ||||
\(290\) | 6.23613e14 | − | 3.60043e14i | 1.04840 | − | 0.605294i | ||||
\(291\) | 1.92648e14 | + | 3.33676e14i | 0.317253 | + | 0.549499i | ||||
\(292\) | −4.63504e14 | − | 2.67604e14i | −0.747749 | − | 0.431713i | ||||
\(293\) | − | 6.68824e14i | − | 1.05708i | −0.848910 | − | 0.528538i | \(-0.822740\pi\) | ||
0.848910 | − | 0.528538i | \(-0.177260\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.33072e15 | −2.01909 | ||||||||
\(296\) | −1.79418e14 | + | 3.10761e14i | −0.266757 | + | 0.462037i | ||||
\(297\) | 3.70499e14 | − | 2.13908e14i | 0.539819 | − | 0.311665i | ||||
\(298\) | 4.58665e14 | + | 7.94431e14i | 0.654935 | + | 1.13438i | ||||
\(299\) | −7.65253e14 | − | 4.41819e14i | −1.07097 | − | 0.618325i | ||||
\(300\) | 3.36684e14i | 0.461844i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.03459e14 | −1.19088 | ||||||||
\(303\) | 4.67000e14 | − | 8.08867e14i | 0.603477 | − | 1.04525i | ||||
\(304\) | −9.74351e13 | + | 5.62542e13i | −0.123445 | + | 0.0712711i | ||||
\(305\) | −5.12244e14 | − | 8.87233e14i | −0.636323 | − | 1.10214i | ||||
\(306\) | 1.60196e14 | + | 9.24894e13i | 0.195130 | + | 0.112658i | ||||
\(307\) | − | 7.37934e14i | − | 0.881429i | −0.897647 | − | 0.440714i | \(-0.854725\pi\) | ||
0.897647 | − | 0.440714i | \(-0.145275\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.69460e14 | 0.883965 | ||||||||
\(310\) | 5.22724e14 | − | 9.05385e14i | 0.588983 | − | 1.02015i | ||||
\(311\) | −4.21657e14 | + | 2.43444e14i | −0.466012 | + | 0.269052i | −0.714569 | − | 0.699565i | \(-0.753377\pi\) |
0.248557 | + | 0.968617i | \(0.420044\pi\) | |||||||
\(312\) | 2.66878e14 | + | 4.62247e14i | 0.289325 | + | 0.501125i | ||||
\(313\) | −2.88228e14 | − | 1.66408e14i | −0.306528 | − | 0.176974i | 0.338844 | − | 0.940843i | \(-0.389964\pi\) |
−0.645372 | + | 0.763869i | \(0.723297\pi\) | |||||||
\(314\) | − | 3.58152e14i | − | 0.373671i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.94138e14 | 0.496279 | ||||||||
\(317\) | 7.44042e14 | − | 1.28872e15i | 0.733233 | − | 1.27000i | −0.222261 | − | 0.974987i | \(-0.571344\pi\) |
0.955494 | − | 0.295010i | \(-0.0953229\pi\) | |||||||
\(318\) | −6.94302e12 | + | 4.00855e12i | −0.00671407 | + | 0.00387637i | ||||
\(319\) | −4.90474e14 | − | 8.49526e14i | −0.465449 | − | 0.806181i | ||||
\(320\) | 1.57240e14 | + | 9.07828e13i | 0.146442 | + | 0.0845481i | ||||
\(321\) | 2.70938e14i | 0.247651i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.64912e14 | 0.761653 | ||||||||
\(324\) | 3.41739e14 | − | 5.91909e14i | 0.295409 | − | 0.511664i | ||||
\(325\) | 1.24568e15 | − | 7.19195e14i | 1.05708 | − | 0.610305i | ||||
\(326\) | −5.55538e14 | − | 9.62221e14i | −0.462816 | − | 0.801621i | ||||
\(327\) | −5.16817e14 | − | 2.98384e14i | −0.422717 | − | 0.244056i | ||||
\(328\) | 2.37081e14i | 0.190394i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.01126e15 | 0.783028 | ||||||||
\(331\) | −1.12300e14 | + | 1.94510e14i | −0.0853912 | + | 0.147902i | −0.905558 | − | 0.424223i | \(-0.860547\pi\) |
0.820167 | + | 0.572125i | \(0.193881\pi\) | |||||||
\(332\) | 3.72431e14 | − | 2.15023e14i | 0.278110 | − | 0.160567i | ||||
\(333\) | 2.45404e14 | + | 4.25052e14i | 0.179977 | + | 0.311728i | ||||
\(334\) | 7.97974e14 | + | 4.60710e14i | 0.574791 | + | 0.331856i | ||||
\(335\) | − | 2.32177e15i | − | 1.64267i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.02994e15 | 0.703124 | 0.351562 | − | 0.936165i | \(-0.385651\pi\) | ||||
0.351562 | + | 0.936165i | \(0.385651\pi\) | |||||||
\(338\) | 6.12989e14 | − | 1.06173e15i | 0.411105 | − | 0.712054i | ||||
\(339\) | 1.87153e15 | − | 1.08053e15i | 1.23310 | − | 0.711930i | ||||
\(340\) | −6.97896e14 | − | 1.20879e15i | −0.451770 | − | 0.782489i | ||||
\(341\) | −1.23337e15 | − | 7.12089e14i | −0.784456 | − | 0.452906i | ||||
\(342\) | 1.53886e14i | 0.0961707i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.04216e14 | −0.243929 | ||||||||
\(345\) | −1.06734e15 | + | 1.84869e15i | −0.632979 | + | 1.09635i | ||||
\(346\) | 8.54044e14 | − | 4.93083e14i | 0.497764 | − | 0.287384i | ||||
\(347\) | 4.36316e14 | + | 7.55722e14i | 0.249934 | + | 0.432898i | 0.963507 | − | 0.267683i | \(-0.0862579\pi\) |
−0.713574 | + | 0.700580i | \(0.752925\pi\) | |||||||
\(348\) | −1.08322e15 | − | 6.25399e14i | −0.609877 | − | 0.352113i | ||||
\(349\) | − | 2.50531e14i | − | 0.138647i | −0.997594 | − | 0.0693233i | \(-0.977916\pi\) | ||
0.997594 | − | 0.0693233i | \(-0.0220840\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.33052e15 | −1.24626 | ||||||||
\(352\) | 1.23670e14 | − | 2.14203e14i | 0.0650144 | − | 0.112608i | ||||
\(353\) | 2.45457e14 | − | 1.41714e14i | 0.126861 | − | 0.0732430i | −0.435227 | − | 0.900321i | \(-0.643332\pi\) |
0.562087 | + | 0.827078i | \(0.309998\pi\) | |||||||
\(354\) | 1.15574e15 | + | 2.00180e15i | 0.587275 | + | 1.01719i | ||||
\(355\) | −1.36146e15 | − | 7.86038e14i | −0.680196 | − | 0.392711i | ||||
\(356\) | 4.23422e13i | 0.0208005i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.79203e14 | 0.227626 | ||||||||
\(359\) | −2.96270e14 | + | 5.13154e14i | −0.138395 | + | 0.239707i | −0.926889 | − | 0.375335i | \(-0.877528\pi\) |
0.788494 | + | 0.615042i | \(0.210861\pi\) | |||||||
\(360\) | 2.15070e14 | − | 1.24171e14i | 0.0988016 | − | 0.0570431i | ||||
\(361\) | −7.46892e14 | − | 1.29365e15i | −0.337454 | − | 0.584487i | ||||
\(362\) | 2.09933e15 | + | 1.21205e15i | 0.932888 | + | 0.538603i | ||||
\(363\) | 1.16861e15i | 0.510776i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.52378e15 | 2.33603 | ||||||||
\(366\) | −8.89775e14 | + | 1.54113e15i | −0.370163 | + | 0.641142i | ||||
\(367\) | 4.05423e14 | − | 2.34071e14i | 0.165925 | − | 0.0957969i | −0.414738 | − | 0.909941i | \(-0.636127\pi\) |
0.580663 | + | 0.814144i | \(0.302793\pi\) | |||||||
\(368\) | 2.61059e14 | + | 4.52167e14i | 0.105112 | + | 0.182059i | ||||
\(369\) | 2.80829e14 | + | 1.62137e14i | 0.111246 | + | 0.0642278i | ||||
\(370\) | − | 3.70348e15i | − | 1.44344i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.81596e15 | −0.685248 | ||||||||
\(373\) | 1.17094e15 | − | 2.02812e15i | 0.434791 | − | 0.753081i | −0.562487 | − | 0.826806i | \(-0.690155\pi\) |
0.997279 | + | 0.0737253i | \(0.0234888\pi\) | |||||||
\(374\) | −1.64669e15 | + | 9.50720e14i | −0.601705 | + | 0.347394i | ||||
\(375\) | 3.55895e14 | + | 6.16428e14i | 0.127978 | + | 0.221664i | ||||
\(376\) | −7.45320e14 | − | 4.30310e14i | −0.263764 | − | 0.152284i | ||||
\(377\) | 5.34370e15i | 1.86120i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.89878e15 | −1.65292 | −0.826461 | − | 0.562994i | \(-0.809649\pi\) | ||||
−0.826461 | + | 0.562994i | \(0.809649\pi\) | |||||||
\(380\) | 5.80589e14 | − | 1.00561e15i | 0.192827 | − | 0.333986i | ||||
\(381\) | 1.89119e14 | − | 1.09188e14i | 0.0618281 | − | 0.0356965i | ||||
\(382\) | −1.40925e15 | − | 2.44089e15i | −0.453531 | − | 0.785539i | ||||
\(383\) | 4.07029e15 | + | 2.34998e15i | 1.28953 | + | 0.744513i | 0.978571 | − | 0.205909i | \(-0.0660150\pi\) |
0.310963 | + | 0.950422i | \(0.399348\pi\) | |||||||
\(384\) | − | 3.15382e14i | − | 0.0983670i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.79037e15 | −0.541276 | ||||||||
\(387\) | −2.76438e14 | + | 4.78805e14i | −0.0822872 | + | 0.142526i | ||||
\(388\) | −8.42311e14 | + | 4.86309e14i | −0.246878 | + | 0.142535i | ||||
\(389\) | 1.04054e15 | + | 1.80226e15i | 0.300303 | + | 0.520140i | 0.976205 | − | 0.216852i | \(-0.0695788\pi\) |
−0.675901 | + | 0.736992i | \(0.736246\pi\) | |||||||
\(390\) | −4.77076e15 | − | 2.75440e15i | −1.35581 | − | 0.782779i | ||||
\(391\) | − | 4.01379e15i | − | 1.12330i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.90046e15 | 1.05867 | ||||||||
\(394\) | −6.76419e13 | + | 1.17159e14i | −0.0180817 | + | 0.0313184i | ||||
\(395\) | −4.41665e15 | + | 2.54995e15i | −1.16281 | + | 0.671350i | ||||
\(396\) | −1.69153e14 | − | 2.92982e14i | −0.0438641 | − | 0.0759748i | ||||
\(397\) | −5.98851e14 | − | 3.45747e14i | −0.152959 | − | 0.0883110i | 0.421567 | − | 0.906797i | \(-0.361480\pi\) |
−0.574526 | + | 0.818486i | \(0.694814\pi\) | |||||||
\(398\) | − | 2.69753e15i | − | 0.678685i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.49905e14 | −0.207496 | ||||||||
\(401\) | 2.13958e15 | − | 3.70586e15i | 0.514592 | − | 0.891299i | −0.485265 | − | 0.874367i | \(-0.661277\pi\) |
0.999857 | − | 0.0169316i | \(-0.00538977\pi\) | |||||||
\(402\) | −3.49264e15 | + | 2.01648e15i | −0.827556 | + | 0.477790i | ||||
\(403\) | 3.87909e15 | + | 6.71878e15i | 0.905524 | + | 1.56841i | ||||
\(404\) | 2.04186e15 | + | 1.17887e15i | 0.469610 | + | 0.271129i | ||||
\(405\) | 7.05404e15i | 1.59848i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.04512e15 | −1.10996 | ||||||||
\(408\) | −1.21226e15 | + | 2.09969e15i | −0.262805 | + | 0.455191i | ||||
\(409\) | 5.93554e13 | − | 3.42689e13i | 0.0126800 | − | 0.00732082i | −0.493647 | − | 0.869663i | \(-0.664336\pi\) |
0.506327 | + | 0.862342i | \(0.331003\pi\) | |||||||
\(410\) | −1.22343e15 | − | 2.11905e15i | −0.257559 | − | 0.446106i | ||||
\(411\) | 7.15166e15 | + | 4.12901e15i | 1.48373 | + | 0.856633i | ||||
\(412\) | 1.94238e15i | 0.397147i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.14139e14 | 0.141834 | ||||||||
\(415\) | −2.21921e15 | + | 3.84379e15i | −0.434421 | + | 0.752439i | ||||
\(416\) | −1.16687e15 | + | 6.73692e14i | −0.225145 | + | 0.129987i | ||||
\(417\) | −1.54772e14 | − | 2.68072e14i | −0.0294357 | − | 0.0509842i | ||||
\(418\) | −1.36991e15 | − | 7.90916e14i | −0.256823 | − | 0.148277i | ||||
\(419\) | − | 2.03797e15i | − | 0.376628i | −0.982109 | − | 0.188314i | \(-0.939698\pi\) | ||
0.982109 | − | 0.188314i | \(-0.0603023\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.75234e15 | −1.39232 | −0.696162 | − | 0.717885i | \(-0.745110\pi\) | ||||
−0.696162 | + | 0.717885i | \(0.745110\pi\) | |||||||
\(422\) | −2.93400e15 | + | 5.08184e15i | −0.519500 | + | 0.899801i | ||||
\(423\) | −1.01943e15 | + | 5.88568e14i | −0.177957 | + | 0.102744i | ||||
\(424\) | −1.01190e13 | − | 1.75265e13i | −0.00174157 | − | 0.00301649i | ||||
\(425\) | 5.65833e15 | + | 3.26684e15i | 0.960185 | + | 0.554363i | ||||
\(426\) | 2.73071e15i | 0.456897i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.83940e14 | −0.111264 | ||||||||
\(429\) | −3.75222e15 | + | 6.49904e15i | −0.601928 | + | 1.04257i | ||||
\(430\) | 3.61292e15 | − | 2.08592e15i | 0.571541 | − | 0.329979i | ||||
\(431\) | −3.20180e13 | − | 5.54569e13i | −0.00499495 | − | 0.00865151i | 0.863517 | − | 0.504320i | \(-0.168257\pi\) |
−0.868512 | + | 0.495668i | \(0.834923\pi\) | |||||||
\(432\) | 1.19255e15 | + | 6.88519e14i | 0.183474 | + | 0.105929i | ||||
\(433\) | − | 3.93012e14i | − | 0.0596319i | −0.999555 | − | 0.0298159i | \(-0.990508\pi\) | ||
0.999555 | − | 0.0298159i | \(-0.00949211\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.29093e16 | 1.90531 | ||||||||
\(436\) | 7.53223e14 | − | 1.30462e15i | 0.109649 | − | 0.189918i | ||||
\(437\) | 2.89177e15 | − | 1.66956e15i | 0.415217 | − | 0.239725i | ||||
\(438\) | −4.79744e15 | − | 8.30941e15i | −0.679461 | − | 1.17686i | ||||
\(439\) | −6.94942e15 | − | 4.01225e15i | −0.970871 | − | 0.560533i | −0.0713694 | − | 0.997450i | \(-0.522737\pi\) |
−0.899502 | + | 0.436917i | \(0.856070\pi\) | |||||||
\(440\) | 2.55276e15i | 0.351798i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.03581e16 | 1.38914 | ||||||||
\(443\) | −7.81118e14 | + | 1.35294e15i | −0.103346 | + | 0.179001i | −0.913061 | − | 0.407822i | \(-0.866288\pi\) |
0.809715 | + | 0.586823i | \(0.199622\pi\) | |||||||
\(444\) | −5.57114e15 | + | 3.21650e15i | −0.727187 | + | 0.419842i | ||||
\(445\) | −2.18503e14 | − | 3.78458e14i | −0.0281382 | − | 0.0487369i | ||||
\(446\) | 4.11593e15 | + | 2.37633e15i | 0.522949 | + | 0.301925i | ||||
\(447\) | 1.64453e16i | 2.06157i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.29552e15 | −0.280158 | −0.140079 | − | 0.990140i | \(-0.544736\pi\) | ||||
−0.140079 | + | 0.990140i | \(0.544736\pi\) | |||||||
\(450\) | −5.81240e14 | + | 1.00674e15i | −0.0699971 | + | 0.121239i | ||||
\(451\) | −2.88670e15 | + | 1.66664e15i | −0.343039 | + | 0.198053i | ||||
\(452\) | 2.72762e15 | + | 4.72437e15i | 0.319855 | + | 0.554005i | ||||
\(453\) | −1.40267e16 | − | 8.09833e15i | −1.62318 | − | 0.937144i | ||||
\(454\) | − | 3.50040e15i | − | 0.399744i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.01698e15 | −0.224343 | ||||||||
\(457\) | −3.78307e15 | + | 6.55247e15i | −0.415286 | + | 0.719296i | −0.995458 | − | 0.0951976i | \(-0.969652\pi\) |
0.580173 | + | 0.814493i | \(0.302985\pi\) | |||||||
\(458\) | −6.92410e15 | + | 3.99763e15i | −0.750188 | + | 0.433121i | ||||
\(459\) | −5.29302e15 | − | 9.16777e15i | −0.566014 | − | 0.980365i | ||||
\(460\) | −4.66673e15 | − | 2.69434e15i | −0.492567 | − | 0.284384i | ||||
\(461\) | − | 3.83644e15i | − | 0.399690i | −0.979828 | − | 0.199845i | \(-0.935956\pi\) | ||
0.979828 | − | 0.199845i | \(-0.0640439\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.62714e15 | 0.469707 | 0.234853 | − | 0.972031i | \(-0.424539\pi\) | ||||
0.234853 | + | 0.972031i | \(0.424539\pi\) | |||||||
\(464\) | 1.57872e15 | − | 2.73443e15i | 0.158197 | − | 0.274005i | ||||
\(465\) | 1.62312e16 | − | 9.37108e15i | 1.60558 | − | 0.926983i | ||||
\(466\) | −5.26830e15 | − | 9.12496e15i | −0.514464 | − | 0.891078i | ||||
\(467\) | 1.22742e16 | + | 7.08650e15i | 1.18329 | + | 0.683173i | 0.956773 | − | 0.290834i | \(-0.0939328\pi\) |
0.226517 | + | 0.974007i | \(0.427266\pi\) | |||||||
\(468\) | 1.84292e15i | 0.175400i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.88231e15 | 0.824022 | ||||||||
\(471\) | 3.21037e15 | − | 5.56052e15i | 0.294056 | − | 0.509319i | ||||
\(472\) | −5.05324e15 | + | 2.91749e15i | −0.457001 | + | 0.263850i | ||||
\(473\) | −2.84157e15 | − | 4.92175e15i | −0.253742 | − | 0.439494i | ||||
\(474\) | 7.67177e15 | + | 4.42930e15i | 0.676434 | + | 0.390539i | ||||
\(475\) | 5.43545e15i | 0.473232i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.76809e13 | −0.00235001 | ||||||||
\(478\) | −2.71575e15 | + | 4.70381e15i | −0.227678 | + | 0.394350i | ||||
\(479\) | −3.20508e15 | + | 1.85045e15i | −0.265354 | + | 0.153202i | −0.626774 | − | 0.779201i | \(-0.715625\pi\) |
0.361421 | + | 0.932403i | \(0.382292\pi\) | |||||||
\(480\) | 1.62750e15 | + | 2.81891e15i | 0.133068 | + | 0.230480i | ||||
\(481\) | 2.38012e16 | + | 1.37416e16i | 1.92189 | + | 1.10960i | ||||
\(482\) | − | 2.32191e15i | − | 0.185167i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.94997e15 | −0.229481 | ||||||||
\(485\) | 5.01910e15 | − | 8.69334e15i | 0.385634 | − | 0.667938i | ||||
\(486\) | 3.77325e15 | − | 2.17849e15i | 0.286351 | − | 0.165325i | ||||
\(487\) | 8.57581e15 | + | 1.48537e16i | 0.642838 | + | 1.11343i | 0.984796 | + | 0.173713i | \(0.0555764\pi\) |
−0.341959 | + | 0.939715i | \(0.611090\pi\) | |||||||
\(488\) | −3.89035e15 | − | 2.24609e15i | −0.288051 | − | 0.166306i | ||||
\(489\) | − | 1.99187e16i | − | 1.45683i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.18747e16 | −0.847487 | −0.423744 | − | 0.905782i | \(-0.639284\pi\) | ||||
−0.423744 | + | 0.905782i | \(0.639284\pi\) | |||||||
\(492\) | −2.12512e15 | + | 3.68081e15i | −0.149828 | + | 0.259510i | ||||
\(493\) | −2.10210e16 | + | 1.21365e16i | −1.46410 | + | 0.845301i | ||||
\(494\) | 4.30850e15 | + | 7.46254e15i | 0.296459 | + | 0.513482i | ||||
\(495\) | 3.02381e15 | + | 1.74580e15i | 0.205553 | + | 0.118676i | ||||
\(496\) | − | 4.58410e15i | − | 0.307867i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.70960e15 | 0.505424 | ||||||||
\(499\) | 1.47725e15 | − | 2.55868e15i | 0.0956868 | − | 0.165734i | −0.814208 | − | 0.580573i | \(-0.802829\pi\) |
0.909895 | + | 0.414839i | \(0.136162\pi\) | |||||||
\(500\) | −1.55607e15 | + | 8.98399e14i | −0.0995887 | + | 0.0574976i | ||||
\(501\) | 8.25933e15 | + | 1.43056e16i | 0.522298 | + | 0.904647i | ||||
\(502\) | −4.08743e15 | − | 2.35988e15i | −0.255404 | − | 0.147458i | ||||
\(503\) | 3.88753e15i | 0.240030i | 0.992772 | + | 0.120015i | \(0.0382943\pi\) | ||||
−0.992772 | + | 0.120015i | \(0.961706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.43337e16 | −1.46710 | ||||||||
\(506\) | −3.67040e15 | + | 6.35732e15i | −0.218681 | + | 0.378766i | ||||
\(507\) | 1.90340e16 | − | 1.09893e16i | 1.12068 | − | 0.647026i | ||||
\(508\) | 2.75628e14 | + | 4.77402e14i | 0.0160377 | + | 0.0277780i | ||||
\(509\) | 2.28834e15 | + | 1.32117e15i | 0.131587 | + | 0.0759719i | 0.564349 | − | 0.825537i | \(-0.309127\pi\) |
−0.432761 | + | 0.901509i | \(0.642461\pi\) | |||||||
\(510\) | − | 2.50229e16i | − | 1.42206i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 7.96131e14 | 0.0441942 | ||||||||
\(513\) | 4.40333e15 | − | 7.62679e15i | 0.241589 | − | 0.418444i | ||||
\(514\) | 1.04225e16 | − | 6.01742e15i | 0.565187 | − | 0.326311i | ||||
\(515\) | −1.00235e16 | − | 1.73612e16i | −0.537248 | − | 0.930541i | ||||
\(516\) | −6.27568e15 | − | 3.62327e15i | −0.332478 | − | 0.191956i | ||||
\(517\) | − | 1.21001e16i | − | 0.633642i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.76794e16 | 0.904613 | ||||||||
\(520\) | 6.95305e15 | − | 1.20430e16i | 0.351686 | − | 0.609138i | ||||
\(521\) | 8.74947e15 | − | 5.05151e15i | 0.437477 | − | 0.252578i | −0.265050 | − | 0.964235i | \(-0.585388\pi\) |
0.702527 | + | 0.711657i | \(0.252055\pi\) | |||||||
\(522\) | −2.15934e15 | − | 3.74008e15i | −0.106733 | − | 0.184866i | ||||
\(523\) | −2.00319e16 | − | 1.15654e16i | −0.978843 | − | 0.565135i | −0.0769222 | − | 0.997037i | \(-0.524509\pi\) |
−0.901921 | + | 0.431902i | \(0.857843\pi\) | |||||||
\(524\) | 9.84610e15i | 0.475638i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.79528e16 | −0.847651 | ||||||||
\(527\) | −1.76202e16 | + | 3.05191e16i | −0.822522 | + | 1.42465i | ||||
\(528\) | 3.84010e15 | − | 2.21708e15i | 0.177231 | − | 0.102324i | ||||
\(529\) | 3.20938e15 | + | 5.55881e15i | 0.146449 | + | 0.253657i | ||||
\(530\) | 1.80888e14 | + | 1.04436e14i | 0.00816122 | + | 0.00471188i | ||||
\(531\) | 7.98093e15i | 0.356030i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.81580e16 | 0.791962 | ||||||||
\(534\) | −3.79542e14 | + | 6.57386e14i | −0.0163686 | + | 0.0283513i | ||||
\(535\) | 6.11311e15 | − | 3.52941e15i | 0.260699 | − | 0.150515i | ||||
\(536\) | −5.09027e15 | − | 8.81661e15i | −0.214661 | − | 0.371803i | ||||
\(537\) | 7.43989e15 | + | 4.29542e15i | 0.310257 | + | 0.179127i | ||||
\(538\) | 3.12491e15i | 0.128868i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.42122e16 | −0.573188 | ||||||||
\(541\) | 1.20154e16 | − | 2.08113e16i | 0.479243 | − | 0.830073i | −0.520474 | − | 0.853878i | \(-0.674245\pi\) |
0.999717 | + | 0.0238046i | \(0.00757796\pi\) | |||||||
\(542\) | −2.96804e16 | + | 1.71360e16i | −1.17078 | + | 0.675949i | ||||
\(543\) | 2.17289e16 | + | 3.76355e16i | 0.847692 | + | 1.46825i | ||||
\(544\) | −5.30033e15 | − | 3.06015e15i | −0.204508 | − | 0.118072i | ||||
\(545\) | 1.55478e16i | 0.593320i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.61473e16 | 0.976119 | 0.488060 | − | 0.872810i | \(-0.337705\pi\) | ||||
0.488060 | + | 0.872810i | \(0.337705\pi\) | |||||||
\(548\) | −1.04230e16 | + | 1.80532e16i | −0.384867 | + | 0.666609i | ||||
\(549\) | −5.32112e15 | + | 3.07215e15i | −0.194343 | + | 0.112204i | ||||
\(550\) | −5.97470e15 | − | 1.03485e16i | −0.215844 | − | 0.373853i | ||||
\(551\) | −1.74876e16 | − | 1.00965e16i | −0.624916 | − | 0.360795i | ||||
\(552\) | 9.36019e15i | 0.330865i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.05318e16 | 0.364288 | ||||||||
\(555\) | 3.31969e16 | − | 5.74987e16i | 1.13590 | − | 1.96743i | ||||
\(556\) | 6.76706e14 | − | 3.90696e14i | 0.0229061 | − | 0.0132248i | ||||
\(557\) | 9.52588e15 | + | 1.64993e16i | 0.318988 | + | 0.552503i | 0.980277 | − | 0.197628i | \(-0.0633238\pi\) |
−0.661289 | + | 0.750131i | \(0.729990\pi\) | |||||||
\(558\) | −5.42999e15 | − | 3.13501e15i | −0.179885 | − | 0.103856i | ||||
\(559\) | 3.09588e16i | 1.01464i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.40878e16 | −1.09351 | ||||||||
\(562\) | 1.59719e16 | − | 2.76642e16i | 0.506920 | − | 0.878011i | ||||
\(563\) | 1.49006e16 | − | 8.60286e15i | 0.467900 | − | 0.270142i | −0.247460 | − | 0.968898i | \(-0.579596\pi\) |
0.715360 | + | 0.698756i | \(0.246263\pi\) | |||||||
\(564\) | −7.71434e15 | − | 1.33616e16i | −0.239676 | − | 0.415131i | ||||
\(565\) | −4.87593e16 | − | 2.81512e16i | −1.49888 | − | 0.865379i | ||||
\(566\) | − | 3.51181e16i | − | 1.06815i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.89326e15 | −0.205274 | ||||||||
\(569\) | −1.64180e16 | + | 2.84368e16i | −0.483779 | + | 0.837930i | −0.999826 | − | 0.0186304i | \(-0.994069\pi\) |
0.516048 | + | 0.856560i | \(0.327403\pi\) | |||||||
\(570\) | 1.80279e16 | − | 1.04084e16i | 0.525651 | − | 0.303484i | ||||
\(571\) | −2.21946e16 | − | 3.84422e16i | −0.640369 | − | 1.10915i | −0.985350 | − | 0.170543i | \(-0.945448\pi\) |
0.344981 | − | 0.938610i | \(-0.387885\pi\) | |||||||
\(572\) | −1.64058e16 | − | 9.47189e15i | −0.468404 | − | 0.270433i | ||||
\(573\) | − | 5.05282e16i | − | 1.42760i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.52243e16 | 0.697929 | ||||||||
\(576\) | 5.44464e14 | − | 9.43040e14i | 0.0149085 | − | 0.0258223i | ||||
\(577\) | 1.53625e16 | − | 8.86954e15i | 0.416300 | − | 0.240351i | −0.277193 | − | 0.960814i | \(-0.589404\pi\) |
0.693493 | + | 0.720463i | \(0.256071\pi\) | |||||||
\(578\) | 1.03417e16 | + | 1.79124e16i | 0.277349 | + | 0.480383i | ||||
\(579\) | −2.77965e16 | − | 1.60483e16i | −0.737767 | − | 0.425950i | ||||
\(580\) | 3.25874e16i | 0.856015i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.74365e16 | −0.448664 | ||||||||
\(583\) | 1.42269e14 | − | 2.46418e14i | 0.00362326 | − | 0.00627568i | ||||
\(584\) | 2.09758e16 | − | 1.21104e16i | 0.528739 | − | 0.305267i | ||||
\(585\) | −9.51020e15 | − | 1.64722e16i | −0.237276 | − | 0.410975i | ||||
\(586\) | 2.62124e16 | + | 1.51338e16i | 0.647324 | + | 0.373733i | ||||
\(587\) | − | 1.42997e16i | − | 0.349542i | −0.984609 | − | 0.174771i | \(-0.944081\pi\) | ||
0.984609 | − | 0.174771i | \(-0.0559185\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.93169e16 | −0.702145 | ||||||||
\(590\) | 3.01108e16 | − | 5.21535e16i | 0.713856 | − | 1.23644i | ||||
\(591\) | −2.10036e15 | + | 1.21264e15i | −0.0492911 | + | 0.0284582i | ||||
\(592\) | −8.11954e15 | − | 1.40635e16i | −0.188626 | − | 0.326710i | ||||
\(593\) | −6.69933e15 | − | 3.86786e15i | −0.154065 | − | 0.0889493i | 0.420986 | − | 0.907067i | \(-0.361684\pi\) |
−0.575050 | + | 0.818118i | \(0.695018\pi\) | |||||||
\(594\) | 1.93607e16i | 0.440761i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.15136e16 | −0.926218 | ||||||||
\(597\) | 2.41799e16 | − | 4.18807e16i | 0.534082 | − | 0.925057i | ||||
\(598\) | 3.46314e16 | − | 1.99944e16i | 0.757291 | − | 0.437222i | ||||
\(599\) | −1.42448e16 | − | 2.46727e16i | −0.308387 | − | 0.534141i | 0.669623 | − | 0.742701i | \(-0.266456\pi\) |
−0.978010 | + | 0.208560i | \(0.933122\pi\) | |||||||
\(600\) | −1.31953e16 | − | 7.61829e15i | −0.282820 | − | 0.163286i | ||||
\(601\) | − | 1.25771e16i | − | 0.266892i | −0.991056 | − | 0.133446i | \(-0.957396\pi\) | ||
0.991056 | − | 0.133446i | \(-0.0426042\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.39247e16 | −0.289656 | ||||||||
\(604\) | 2.04429e16 | − | 3.54082e16i | 0.421039 | − | 0.729260i | ||||
\(605\) | 2.63671e16 | − | 1.52231e16i | 0.537688 | − | 0.310434i | ||||
\(606\) | 2.11340e16 | + | 3.66051e16i | 0.426723 | + | 0.739105i | ||||
\(607\) | 3.41643e16 | + | 1.97248e16i | 0.683030 | + | 0.394348i | 0.800996 | − | 0.598670i | \(-0.204304\pi\) |
−0.117965 | + | 0.993018i | \(0.537637\pi\) | |||||||
\(608\) | − | 5.09155e15i | − | 0.100793i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.63630e16 | 0.899897 | ||||||||
\(611\) | −3.29574e16 | + | 5.70839e16i | −0.633441 | + | 1.09715i | ||||
\(612\) | −7.24966e15 | + | 4.18559e15i | −0.137978 | + | 0.0796615i | ||||
\(613\) | 1.23442e16 | + | 2.13807e16i | 0.232648 | + | 0.402958i | 0.958586 | − | 0.284802i | \(-0.0919277\pi\) |
−0.725939 | + | 0.687759i | \(0.758594\pi\) | |||||||
\(614\) | 2.89210e16 | + | 1.66975e16i | 0.539763 | + | 0.311632i | ||||
\(615\) | − | 4.38659e16i | − | 0.810730i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.97598e16 | −0.901919 | −0.450959 | − | 0.892545i | \(-0.648918\pi\) | ||||
−0.450959 | + | 0.892545i | \(0.648918\pi\) | |||||||
\(618\) | −1.74109e16 | + | 3.01566e16i | −0.312529 | + | 0.541316i | ||||
\(619\) | 1.68034e16 | − | 9.70147e15i | 0.298713 | − | 0.172462i | −0.343152 | − | 0.939280i | \(-0.611494\pi\) |
0.641865 | + | 0.766818i | \(0.278161\pi\) | |||||||
\(620\) | 2.36558e16 | + | 4.09730e16i | 0.416474 | + | 0.721353i | ||||
\(621\) | −3.53936e16 | − | 2.04345e16i | −0.617128 | − | 0.356299i | ||||
\(622\) | − | 2.20340e16i | − | 0.380497i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.41551e16 | −0.409167 | ||||||||
\(625\) | 3.40077e16 | − | 5.89031e16i | 0.570555 | − | 0.988230i | ||||
\(626\) | 1.30437e16 | − | 7.53079e15i | 0.216748 | − | 0.125139i | ||||
\(627\) | −1.41791e16 | − | 2.45588e16i | −0.233368 | − | 0.404206i | ||||
\(628\) | 1.40366e16 | + | 8.10406e15i | 0.228826 | + | 0.132113i | ||||
\(629\) | 1.24839e17i | 2.01579i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.89698e16 | 0.300530 | 0.150265 | − | 0.988646i | \(-0.451987\pi\) | ||||
0.150265 | + | 0.988646i | \(0.451987\pi\) | |||||||
\(632\) | −1.11811e16 | + | 1.93662e16i | −0.175461 | + | 0.303907i | ||||
\(633\) | −9.11041e16 | + | 5.25990e16i | −1.41617 | + | 0.817627i | ||||
\(634\) | 3.36715e16 | + | 5.83208e16i | 0.518474 | + | 0.898024i | ||||
\(635\) | −4.92717e15 | − | 2.84470e15i | −0.0751546 | − | 0.0433905i | ||||
\(636\) | − | 3.62813e14i | − | 0.00548201i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.43926e16 | 0.658244 | ||||||||
\(639\) | −4.71421e15 | + | 8.16526e15i | −0.0692475 | + | 0.119940i | ||||
\(640\) | −7.11589e15 | + | 4.10836e15i | −0.103550 | + | 0.0597845i | ||||
\(641\) | −2.80509e16 | − | 4.85856e16i | −0.404389 | − | 0.700422i | 0.589861 | − | 0.807505i | \(-0.299182\pi\) |
−0.994250 | + | 0.107083i | \(0.965849\pi\) | |||||||
\(642\) | −1.06186e16 | − | 6.13063e15i | −0.151655 | − | 0.0875578i | ||||
\(643\) | 3.11805e15i | 0.0441182i | 0.999757 | + | 0.0220591i | \(0.00702220\pi\) | ||||
−0.999757 | + | 0.0220591i | \(0.992978\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.47901e16 | 1.03869 | ||||||||
\(646\) | −1.95707e16 | + | 3.38975e16i | −0.269285 | + | 0.466415i | ||||
\(647\) | −6.91898e16 | + | 3.99467e16i | −0.943227 | + | 0.544572i | −0.890970 | − | 0.454061i | \(-0.849975\pi\) |
−0.0522565 | + | 0.998634i | \(0.516641\pi\) | |||||||
\(648\) | 1.54653e16 | + | 2.67867e16i | 0.208886 | + | 0.361801i | ||||
\(649\) | −7.10469e16 | − | 4.10189e16i | −0.950773 | − | 0.548929i | ||||
\(650\) | 6.50941e16i | 0.863101i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.02816e16 | 0.654521 | ||||||||
\(653\) | −6.87264e16 | + | 1.19038e17i | −0.886430 | + | 1.53534i | −0.0423648 | + | 0.999102i | \(0.513489\pi\) |
−0.844066 | + | 0.536240i | \(0.819844\pi\) | |||||||
\(654\) | 2.33884e16 | − | 1.35033e16i | 0.298906 | − | 0.172574i | ||||
\(655\) | −5.08099e16 | − | 8.80053e16i | −0.643429 | − | 1.11445i | ||||
\(656\) | −9.29163e15 | − | 5.36453e15i | −0.116592 | − | 0.0673144i | ||||
\(657\) | − | 3.31285e16i | − | 0.411917i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.77636e15 | −0.0338972 | −0.0169486 | − | 0.999856i | \(-0.505395\pi\) | ||||
−0.0169486 | + | 0.999856i | \(0.505395\pi\) | |||||||
\(660\) | −2.28821e16 | + | 3.96330e16i | −0.276842 | + | 0.479505i | ||||
\(661\) | −1.34435e17 | + | 7.76164e16i | −1.61178 | + | 0.930560i | −0.622820 | + | 0.782365i | \(0.714013\pi\) |
−0.988958 | + | 0.148195i | \(0.952654\pi\) | |||||||
\(662\) | −5.08213e15 | − | 8.80251e15i | −0.0603807 | − | 0.104582i | ||||
\(663\) | 1.60815e17 | + | 9.28465e16i | 1.89341 | + | 1.09316i | ||||
\(664\) | 1.94617e16i | 0.227076i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.22114e16 | −0.254525 | ||||||||
\(667\) | −4.68547e16 | + | 8.11548e16i | −0.532106 | + | 0.921635i | ||||
\(668\) | −3.61122e16 | + | 2.08494e16i | −0.406438 | + | 0.234657i | ||||
\(669\) | 4.26015e16 | + | 7.37879e16i | 0.475191 | + | 0.823054i | ||||
\(670\) | 9.09946e16 | + | 5.25358e16i | 1.00593 | + | 0.580773i | ||||
\(671\) | − | 6.31587e16i | − | 0.691988i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.53293e15 | 0.0487852 | 0.0243926 | − | 0.999702i | \(-0.492235\pi\) | ||||
0.0243926 | + | 0.999702i | \(0.492235\pi\) | |||||||
\(674\) | −2.33048e16 | + | 4.03652e16i | −0.248592 | + | 0.430574i | ||||
\(675\) | 5.76139e16 | − | 3.32634e16i | 0.609123 | − | 0.351677i | ||||
\(676\) | 2.77407e16 | + | 4.80483e16i | 0.290695 | + | 0.503498i | ||||
\(677\) | 8.53907e16 | + | 4.93003e16i | 0.886908 | + | 0.512057i | 0.872930 | − | 0.487846i | \(-0.162217\pi\) |
0.0139781 | + | 0.999902i | \(0.495550\pi\) | |||||||
\(678\) | 9.77981e16i | 1.00682i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.31664e16 | 0.638899 | ||||||||
\(681\) | 3.13765e16 | − | 5.43457e16i | 0.314573 | − | 0.544857i | ||||
\(682\) | 5.58161e16 | − | 3.22255e16i | 0.554694 | − | 0.320253i | ||||
\(683\) | −3.01263e16 | − | 5.21802e16i | −0.296771 | − | 0.514022i | 0.678625 | − | 0.734485i | \(-0.262576\pi\) |
−0.975395 | + | 0.220463i | \(0.929243\pi\) | |||||||
\(684\) | −6.03108e15 | − | 3.48205e15i | −0.0588923 | − | 0.0340015i | ||||
\(685\) | − | 2.15148e17i | − | 2.08255i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.43334e17 | −1.36336 | ||||||||
\(688\) | 9.14636e15 | − | 1.58420e16i | 0.0862418 | − | 0.149375i | ||||
\(689\) | −1.34236e15 | + | 7.75010e14i | −0.0125474 | + | 0.00724422i | ||||
\(690\) | −4.83024e16 | − | 8.36622e16i | −0.447584 | − | 0.775238i | ||||
\(691\) | −1.24730e15 | − | 7.20129e14i | −0.0114578 | − | 0.00661518i | 0.494260 | − | 0.869314i | \(-0.335439\pi\) |
−0.505718 | + | 0.862699i | \(0.668772\pi\) | |||||||
\(692\) | 4.46288e16i | 0.406423i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.94909e16 | −0.353460 | ||||||||
\(695\) | −4.03230e15 | + | 6.98415e15i | −0.0357803 | + | 0.0619733i | ||||
\(696\) | 4.90211e16 | − | 2.83023e16i | 0.431248 | − | 0.248981i | ||||
\(697\) | 4.12400e16 | + | 7.14298e16i | 0.359685 | + | 0.622992i | ||||
\(698\) | 9.81877e15 | + | 5.66887e15i | 0.0849033 | + | 0.0490190i | ||||
\(699\) | − | 1.88894e17i | − | 1.61940i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.76004e17 | 1.48325 | 0.741623 | − | 0.670817i | \(-0.234056\pi\) | ||||
0.741623 | + | 0.670817i | \(0.234056\pi\) | |||||||
\(702\) | 5.27336e16 | − | 9.13373e16i | 0.440621 | − | 0.763177i | ||||
\(703\) | −8.99409e16 | + | 5.19274e16i | −0.745118 | + | 0.430194i | ||||
\(704\) | 5.59668e15 | + | 9.69373e15i | 0.0459721 | + | 0.0796260i | ||||
\(705\) | 1.37903e17 | + | 7.96183e16i | 1.12315 | + | 0.648452i | ||||
\(706\) | 1.28265e16i | 0.103581i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.04606e17 | −0.830532 | ||||||||
\(709\) | −7.39721e16 | + | 1.28123e17i | −0.582358 | + | 1.00867i | 0.412841 | + | 0.910803i | \(0.364537\pi\) |
−0.995199 | + | 0.0978712i | \(0.968797\pi\) | |||||||
\(710\) | 6.16125e16 | − | 3.55720e16i | 0.480971 | − | 0.277689i | ||||
\(711\) | 1.52932e16 | + | 2.64886e16i | 0.118380 | + | 0.205041i | ||||
\(712\) | −1.65947e15 | − | 9.58094e14i | −0.0127376 | − | 0.00735407i | ||||
\(713\) | 1.36051e17i | 1.03553i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.95515e17 | 1.46334 | ||||||||
\(716\) | −1.08431e16 | + | 1.87808e16i | −0.0804778 | + | 0.139392i | ||||
\(717\) | −8.43270e16 | + | 4.86862e16i | −0.620657 | + | 0.358336i | ||||
\(718\) | −1.34076e16 | − | 2.32227e16i | −0.0978601 | − | 0.169499i | ||||
\(719\) | 1.77523e16 | + | 1.02493e16i | 0.128493 | + | 0.0741857i | 0.562869 | − | 0.826546i | \(-0.309698\pi\) |
−0.434375 | + | 0.900732i | \(0.643031\pi\) | |||||||
\(720\) | 1.12386e16i | 0.0806712i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.76009e16 | 0.477232 | ||||||||
\(723\) | 2.08129e16 | − | 3.60490e16i | 0.145714 | − | 0.252385i | ||||
\(724\) | −9.50049e16 | + | 5.48511e16i | −0.659651 | + | 0.380850i | ||||
\(725\) | −7.62704e16 | − | 1.32104e17i | −0.525204 | − | 0.909680i | ||||
\(726\) | −4.58000e16 | − | 2.64427e16i | −0.312785 | − | 0.180586i | ||||
\(727\) | 9.52642e15i | 0.0645243i | 0.999479 | + | 0.0322621i | \(0.0102711\pi\) | ||||
−0.999479 | + | 0.0322621i | \(0.989729\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.92481e16 | −0.661237 | ||||||||
\(730\) | −1.24989e17 | + | 2.16487e17i | −0.825913 | + | 1.43052i | ||||
\(731\) | −1.21786e17 | + | 7.03130e16i | −0.798164 | + | 0.460820i | ||||
\(732\) | −4.02666e16 | − | 6.97438e16i | −0.261745 | − | 0.453356i | ||||
\(733\) | −8.31903e16 | − | 4.80299e16i | −0.536351 | − | 0.309662i | 0.207248 | − | 0.978288i | \(-0.433549\pi\) |
−0.743599 | + | 0.668626i | \(0.766883\pi\) | |||||||
\(734\) | 2.11857e16i | 0.135477i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.36283e16 | −0.148650 | ||||||||
\(737\) | 7.15676e16 | − | 1.23959e17i | 0.446593 | − | 0.773521i | ||||
\(738\) | −1.27089e16 | + | 7.33747e15i | −0.0786626 | + | 0.0454159i | ||||
\(739\) | −1.14442e17 | − | 1.98220e17i | −0.702618 | − | 1.21697i | −0.967544 | − | 0.252702i | \(-0.918681\pi\) |
0.264926 | − | 0.964269i | \(-0.414653\pi\) | |||||||
\(740\) | 1.45146e17 | + | 8.38003e16i | 0.883926 | + | 0.510335i | ||||
\(741\) | 1.54480e17i | 0.933177i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.73334e17 | −1.03027 | −0.515136 | − | 0.857109i | \(-0.672258\pi\) | ||||
−0.515136 | + | 0.857109i | \(0.672258\pi\) | |||||||
\(744\) | 4.10904e16 | − | 7.11707e16i | 0.242272 | − | 0.419627i | ||||
\(745\) | 3.71052e17 | − | 2.14227e17i | 2.17019 | − | 1.25296i | ||||
\(746\) | 5.29906e16 | + | 9.17824e16i | 0.307444 | + | 0.532508i | ||||
\(747\) | 2.30529e16 | + | 1.33096e16i | 0.132679 | + | 0.0766022i | ||||
\(748\) | − | 8.60493e16i | − | 0.491290i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3.22119e16 | −0.180988 | ||||||||
\(751\) | −5.91242e16 | + | 1.02406e17i | −0.329553 | + | 0.570803i | −0.982423 | − | 0.186667i | \(-0.940231\pi\) |
0.652870 | + | 0.757470i | \(0.273565\pi\) | |||||||
\(752\) | 3.37293e16 | − | 1.94736e16i | 0.186509 | − | 0.107681i | ||||
\(753\) | −4.23064e16 | − | 7.32769e16i | −0.232079 | − | 0.401973i | ||||
\(754\) | −2.09429e17 | − | 1.20914e17i | −1.13975 | − | 0.658035i | ||||
\(755\) | 4.21976e17i | 2.27827i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.23980e17 | 1.19024 | 0.595118 | − | 0.803638i | \(-0.297105\pi\) | ||||
0.595118 | + | 0.803638i | \(0.297105\pi\) | |||||||
\(758\) | 1.10847e17 | − | 1.91992e17i | 0.584396 | − | 1.01220i | ||||
\(759\) | −1.13970e17 | + | 6.58007e16i | −0.596129 | + | 0.344175i | ||||
\(760\) | 2.62745e16 | + | 4.55087e16i | 0.136349 | + | 0.236163i | ||||
\(761\) | −7.69944e16 | − | 4.44527e16i | −0.396416 | − | 0.228871i | 0.288521 | − | 0.957474i | \(-0.406837\pi\) |
−0.684936 | + | 0.728603i | \(0.740170\pi\) | |||||||
\(762\) | 9.88258e15i | 0.0504824i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.27550e17 | 0.641390 | ||||||||
\(765\) | 4.31987e16 | − | 7.48224e16i | 0.215527 | − | 0.373304i | ||||
\(766\) | −1.84200e17 | + | 1.06348e17i | −0.911839 | + | 0.526450i | ||||
\(767\) | 2.23450e17 | + | 3.87027e17i | 1.09751 | + | 1.90094i | ||||
\(768\) | 1.23604e16 | + | 7.13628e15i | 0.0602372 | + | 0.0347780i | ||||
\(769\) | 6.79519e16i | 0.328582i | 0.986412 | + | 0.164291i | \(0.0525336\pi\) | ||||
−0.986412 | + | 0.164291i | \(0.947466\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.15753e17 | 1.02714 | ||||||||
\(772\) | 4.05115e16 | − | 7.01679e16i | 0.191370 | − | 0.331463i | ||||
\(773\) | 1.75550e17 | − | 1.01354e17i | 0.822856 | − | 0.475076i | −0.0285441 | − | 0.999593i | \(-0.509087\pi\) |
0.851400 | + | 0.524516i | \(0.175754\pi\) | |||||||
\(774\) | −1.25102e16 | − | 2.16682e16i | −0.0581859 | − | 0.100781i | ||||
\(775\) | −1.91794e17 | − | 1.10732e17i | −0.885166 | − | 0.511051i | ||||
\(776\) | − | 4.40156e16i | − | 0.201575i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.41786e16 | −0.424693 | ||||||||
\(779\) | −3.43081e16 | + | 5.94233e16i | −0.153522 | + | 0.265908i | ||||
\(780\) | 2.15900e17 | − | 1.24650e17i | 0.958705 | − | 0.553509i | ||||
\(781\) | −4.84585e16 | − | 8.39326e16i | −0.213532 | − | 0.369849i | ||||
\(782\) | 1.57308e17 | + | 9.08218e16i | 0.687876 | + | 0.397145i | ||||
\(783\) | 2.47151e17i | 1.07248i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.67281e17 | −0.714873 | ||||||||
\(786\) | −8.82574e16 | + | 1.52866e17i | −0.374297 | + | 0.648301i | ||||
\(787\) | −5.94097e15 | + | 3.43002e15i | −0.0250040 | + | 0.0144361i | −0.512450 | − | 0.858717i | \(-0.671262\pi\) |
0.487446 | + | 0.873153i | \(0.337929\pi\) | |||||||
\(788\) | −3.06112e15 | − | 5.30202e15i | −0.0127857 | − | 0.0221454i | ||||
\(789\) | −2.78727e17 | − | 1.60923e17i | −1.15536 | − | 0.667047i | ||||
\(790\) | − | 2.30795e17i | − | 0.949433i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.53100e16 | 0.0620332 | ||||||||
\(793\) | −1.72028e17 | + | 2.97961e17i | −0.691768 | + | 1.19818i | ||||
\(794\) | 2.71009e16 | − | 1.56467e16i | 0.108158 | − | 0.0624453i | ||||
\(795\) | 1.87226e15 | + | 3.24285e15i | 0.00741590 | + | 0.0128447i | ||||
\(796\) | 1.05721e17 | + | 6.10382e16i | 0.415608 | + | 0.239951i | ||||
\(797\) | − | 3.49871e17i | − | 1.36508i | −0.730848 | − | 0.682540i | \(-0.760875\pi\) | ||
0.730848 | − | 0.682540i | \(-0.239125\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.99408e17 | −1.15076 | ||||||||
\(800\) | 1.92312e16 | − | 3.33093e16i | 0.0733611 | − | 0.127065i | ||||
\(801\) | −2.26978e15 | + | 1.31046e15i | −0.00859386 | + | 0.00496167i | ||||
\(802\) | 9.68264e16 | + | 1.67708e17i | 0.363871 | + | 0.630243i | ||||
\(803\) | 2.94913e17 | + | 1.70268e17i | 1.10002 | + | 0.635096i | ||||
\(804\) | − | 1.82511e17i | − | 0.675697i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.51095e17 | −1.28060 | ||||||||
\(807\) | −2.80107e16 | + | 4.85160e16i | −0.101411 | + | 0.175648i | ||||
\(808\) | −9.24039e16 | + | 5.33494e16i | −0.332064 | + | 0.191717i | ||||
\(809\) | 2.06423e17 | + | 3.57535e17i | 0.736320 | + | 1.27534i | 0.954142 | + | 0.299355i | \(0.0967714\pi\) |
−0.217822 | + | 0.975989i | \(0.569895\pi\) | |||||||
\(810\) | −2.76461e17 | − | 1.59615e17i | −0.978867 | − | 0.565149i | ||||
\(811\) | 1.30953e17i | 0.460246i | 0.973162 | + | 0.230123i | \(0.0739129\pi\) | ||||
−0.973162 | + | 0.230123i | \(0.926087\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.14408e17 | −2.12771 | ||||||||
\(814\) | 1.14158e17 | − | 1.97728e17i | 0.392428 | − | 0.679706i | ||||
\(815\) | −4.49421e17 | + | 2.59473e17i | −1.53359 | + | 0.885416i | ||||
\(816\) | −5.48604e16 | − | 9.50210e16i | −0.185831 | − | 0.321869i | ||||
\(817\) | −1.01315e17 | − | 5.84943e16i | −0.340676 | − | 0.196689i | ||||
\(818\) | 3.10166e15i | 0.0103532i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.10733e17 | 0.364244 | ||||||||
\(821\) | 2.28661e17 | − | 3.96053e17i | 0.746679 | − | 1.29329i | −0.202728 | − | 0.979235i | \(-0.564981\pi\) |
0.949406 | − | 0.314050i | \(-0.101686\pi\) | |||||||
\(822\) | −3.23647e17 | + | 1.86858e17i | −1.04916 | + | 0.605731i | ||||
\(823\) | −1.34881e17 | − | 2.33620e17i | −0.434061 | − | 0.751816i | 0.563157 | − | 0.826350i | \(-0.309586\pi\) |
−0.997218 | + | 0.0745339i | \(0.976253\pi\) | |||||||
\(824\) | −7.61254e16 | − | 4.39510e16i | −0.243202 | − | 0.140413i | ||||
\(825\) | − | 2.14221e17i | − | 0.679421i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.09486e17 | 0.967403 | 0.483702 | − | 0.875233i | \(-0.339292\pi\) | ||||
0.483702 | + | 0.875233i | \(0.339292\pi\) | |||||||
\(828\) | −1.61591e16 | + | 2.79884e16i | −0.0501459 | + | 0.0868553i | ||||
\(829\) | 3.48271e17 | − | 2.01074e17i | 1.07298 | − | 0.619482i | 0.143982 | − | 0.989580i | \(-0.454009\pi\) |
0.928993 | + | 0.370098i | \(0.120676\pi\) | |||||||
\(830\) | −1.00430e17 | − | 1.73950e17i | −0.307182 | − | 0.532054i | ||||
\(831\) | 1.63512e17 | + | 9.44039e16i | 0.496529 | + | 0.286671i | ||||
\(832\) | − | 6.09756e16i | − | 0.183830i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.40083e16 | 0.0416284 | ||||||||
\(835\) | 2.15182e17 | − | 3.72707e17i | 0.634875 | − | 1.09964i | ||||
\(836\) | 6.19949e16 | − | 3.57928e16i | 0.181601 | − | 0.104847i | ||||
\(837\) | 1.79411e17 | + | 3.10750e17i | 0.521792 | + | 0.903770i | ||||
\(838\) | 7.98716e16 | + | 4.61139e16i | 0.230637 | + | 0.133158i | ||||
\(839\) | − | 6.07001e17i | − | 1.74027i | −0.492810 | − | 0.870137i | \(-0.664030\pi\) | ||
0.492810 | − | 0.870137i | \(-0.335970\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.12882e17 | 0.601678 | ||||||||
\(842\) | 1.75415e17 | − | 3.03828e17i | 0.492261 | − | 0.852620i | ||||
\(843\) | 4.95947e17 | − | 2.86335e17i | 1.38188 | − | 0.797827i | ||||
\(844\) | −1.32778e17 | − | 2.29978e17i | −0.367342 | − | 0.636255i | ||||
\(845\) | −4.95898e17 | − | 2.86307e17i | −1.36223 | − | 0.786487i | ||||
\(846\) | − | 5.32711e16i | − | 0.145301i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.15863e14 | 0.00246295 | ||||||||
\(849\) | 3.14788e17 | − | 5.45229e17i | 0.840566 | − | 1.45590i | ||||
\(850\) | −2.56067e17 | + | 1.47840e17i | −0.678953 | + | 0.391994i | ||||
\(851\) | 2.40979e17 | + | 4.17388e17i | 0.634457 | + | 1.09891i | ||||
\(852\) | −1.07022e17 | − | 6.17890e16i | −0.279791 | − | 0.161538i | ||||
\(853\) | 9.20133e16i | 0.238867i | 0.992842 | + | 0.119434i | \(0.0381078\pi\) | ||||
−0.992842 | + | 0.119434i | \(0.961892\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.18751e16 | 0.183985 | ||||||||
\(856\) | 1.54758e16 | − | 2.68049e16i | 0.0393378 | − | 0.0681351i | ||||
\(857\) | 4.68450e17 | − | 2.70460e17i | 1.18244 | − | 0.682681i | 0.225860 | − | 0.974160i | \(-0.427481\pi\) |
0.956577 | + | 0.291479i | \(0.0941473\pi\) | |||||||
\(858\) | −1.69806e17 | − | 2.94113e17i | −0.425628 | − | 0.737209i | ||||
\(859\) | 1.73078e16 | + | 9.99268e15i | 0.0430808 | + | 0.0248727i | 0.521386 | − | 0.853321i | \(-0.325415\pi\) |
−0.478305 | + | 0.878194i | \(0.658749\pi\) | |||||||
\(860\) | 1.88796e17i | 0.466661i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.89794e15 | 0.00706393 | ||||||||
\(863\) | −2.56860e17 | + | 4.44894e17i | −0.621772 | + | 1.07694i | 0.367384 | + | 0.930069i | \(0.380254\pi\) |
−0.989156 | + | 0.146871i | \(0.953080\pi\) | |||||||
\(864\) | −5.39687e16 | + | 3.11588e16i | −0.129736 | + | 0.0749029i | ||||
\(865\) | −2.30303e17 | − | 3.98896e17i | −0.549797 | − | 0.952276i | ||||
\(866\) | 1.54029e16 | + | 8.89285e15i | 0.0365169 | + | 0.0210831i | ||||
\(867\) | 3.70801e17i | 0.873024i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.14404e17 | −0.730079 | ||||||||
\(870\) | −2.92103e17 | + | 5.05938e17i | −0.673629 | + | 1.16676i | ||||
\(871\) | −6.75263e17 | + | 3.89863e17i | −1.54655 | + | 0.892901i | ||||
\(872\) | 3.40870e16 | + | 5.90404e16i | 0.0775336 | + | 0.134292i | ||||
\(873\) | −5.21378e16 | − | 3.01017e16i | −0.117779 | − | 0.0679996i | ||||
\(874\) | 1.51112e17i | 0.339023i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.34215e17 | 0.960904 | ||||||||
\(877\) | 2.23428e17 | − | 3.86989e17i | 0.491066 | − | 0.850551i | −0.508881 | − | 0.860837i | \(-0.669941\pi\) |
0.999947 | + | 0.0102854i | \(0.00327400\pi\) | |||||||
\(878\) | 3.14495e17 | − | 1.81574e17i | 0.686510 | − | 0.396356i | ||||
\(879\) | 2.71309e17 | + | 4.69920e17i | 0.588207 | + | 1.01880i | ||||
\(880\) | −1.00047e17 | − | 5.77623e16i | −0.215431 | − | 0.124379i | ||||
\(881\) | − | 1.15011e17i | − | 0.245971i | −0.992408 | − | 0.122985i | \(-0.960753\pi\) | ||
0.992408 | − | 0.122985i | \(-0.0392469\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.25816e16 | 0.0476421 | 0.0238210 | − | 0.999716i | \(-0.492417\pi\) | ||||
0.0238210 | + | 0.999716i | \(0.492417\pi\) | |||||||
\(884\) | −2.34376e17 | + | 4.05951e17i | −0.491134 | + | 0.850669i | ||||
\(885\) | 9.34976e17 | − | 5.39809e17i | 1.94599 | − | 1.12352i | ||||
\(886\) | −3.53494e16 | − | 6.12269e16i | −0.0730767 | − | 0.126573i | ||||
\(887\) | 3.28689e17 | + | 1.89769e17i | 0.674907 | + | 0.389658i | 0.797933 | − | 0.602746i | \(-0.205927\pi\) |
−0.123026 | + | 0.992403i | \(0.539260\pi\) | |||||||
\(888\) | − | 2.91124e17i | − | 0.593746i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.97766e16 | 0.0397935 | ||||||||
\(891\) | −2.17438e17 | + | 3.76613e17i | −0.434579 | + | 0.752712i | ||||
\(892\) | −1.86266e17 | + | 1.07541e17i | −0.369781 | + | 0.213493i | ||||
\(893\) | −1.24541e17 | − | 2.15711e17i | −0.245586 | − | 0.425367i | ||||
\(894\) | −6.44523e17 | − | 3.72115e17i | −1.26245 | − | 0.728874i | ||||
\(895\) | − | 2.23820e17i | − | 0.435472i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.16896e17 | 1.37626 | ||||||||
\(898\) | 5.19417e16 | − | 8.99656e16i | 0.0990508 | − | 0.171561i | ||||
\(899\) | 7.12525e17 | − | 4.11376e17i | 1.34971 | − | 0.779258i | ||||
\(900\) | −2.63039e16 | − | 4.55597e16i | −0.0494954 | − | 0.0857286i | ||||
\(901\) | −6.09746e15 | − | 3.52037e15i | −0.0113972 | − | 0.00658020i | ||||
\(902\) | − | 1.50847e17i | − | 0.280090i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.46876e17 | −0.452343 | ||||||||
\(905\) | 5.66108e17 | − | 9.80527e17i | 1.03040 | − | 1.78471i | ||||
\(906\) | 6.34777e17 | − | 3.66489e17i | 1.14776 | − | 0.662661i | ||||
\(907\) | −2.02438e17 | − | 3.50632e17i | −0.363620 | − | 0.629808i | 0.624934 | − | 0.780678i | \(-0.285126\pi\) |
−0.988554 | + | 0.150870i | \(0.951793\pi\) | |||||||
\(908\) | 1.37187e17 | + | 7.92050e16i | 0.244792 | + | 0.141331i | ||||
\(909\) | 1.45940e17i | 0.258697i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.61744e17 | 0.282956 | 0.141478 | − | 0.989941i | \(-0.454815\pi\) | ||||
0.141478 | + | 0.989941i | \(0.454815\pi\) | |||||||
\(912\) | 4.56391e16 | − | 7.90492e16i | 0.0793173 | − | 0.137382i | ||||
\(913\) | −2.36966e17 | + | 1.36812e17i | −0.409130 | + | 0.236211i | ||||
\(914\) | −1.71202e17 | − | 2.96531e17i | −0.293651 | − | 0.508619i | ||||
\(915\) | 7.19813e17 | + | 4.15584e17i | 1.22657 | + | 0.708161i | ||||
\(916\) | − | 3.61824e17i | − | 0.612526i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.79069e17 | 0.800465 | ||||||||
\(919\) | −2.48909e17 | + | 4.31123e17i | −0.413188 | + | 0.715662i | −0.995236 | − | 0.0974921i | \(-0.968918\pi\) |
0.582049 | + | 0.813154i | \(0.302251\pi\) | |||||||
\(920\) | 2.11192e17 | − | 1.21932e17i | 0.348298 | − | 0.201090i | ||||
\(921\) | 2.99343e17 | + | 5.18478e17i | 0.490469 | + | 0.849517i | ||||
\(922\) | 1.50357e17 | + | 8.68088e16i | 0.244759 | + | 0.141312i | ||||
\(923\) | 5.27954e17i | 0.853858i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.84535e17 | −1.25245 | ||||||||
\(926\) | −1.04700e17 | + | 1.81346e17i | −0.166066 | + | 0.287636i | ||||
\(927\) | −1.04122e17 | + | 6.01151e16i | −0.164084 | + | 0.0947339i | ||||
\(928\) | 7.14448e16 | + | 1.23746e17i | 0.111862 | + | 0.193751i | ||||
\(929\) | −2.35012e17 | − | 1.35684e17i | −0.365591 | − | 0.211074i | 0.305939 | − | 0.952051i | \(-0.401030\pi\) |
−0.671531 | + | 0.740977i | \(0.734363\pi\) | |||||||
\(930\) | 8.48173e17i | 1.31095i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.76832e17 | 0.727562 | ||||||||
\(933\) | 1.97506e17 | − | 3.42091e17i | 0.299427 | − | 0.518623i | ||||
\(934\) | −5.55466e17 | + | 3.20699e17i | −0.836713 | + | 0.483076i | ||||
\(935\) | 4.44050e17 | + | 7.69116e17i | 0.664602 | + | 1.15112i | ||||
\(936\) | −7.22273e16 | − | 4.17005e16i | −0.107410 | − | 0.0620134i | ||||
\(937\) | − | 1.19374e18i | − | 1.76389i | −0.471356 | − | 0.881943i | \(-0.656235\pi\) | ||
0.471356 | − | 0.881943i | \(-0.343765\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.70015e17 | 0.393907 | ||||||||
\(940\) | −2.00984e17 | + | 3.48114e17i | −0.291336 | + | 0.504608i | ||||
\(941\) | 2.05289e17 | − | 1.18523e17i | 0.295684 | − | 0.170713i | −0.344819 | − | 0.938669i | \(-0.612060\pi\) |
0.640502 | + | 0.767956i | \(0.278726\pi\) | |||||||
\(942\) | 1.45285e17 | + | 2.51640e17i | 0.207929 | + | 0.360143i | ||||
\(943\) | 2.75766e17 | + | 1.59213e17i | 0.392166 | + | 0.226417i | ||||
\(944\) | − | 2.64061e17i | − | 0.373140i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.57190e17 | 0.358845 | ||||||||
\(947\) | −1.20199e17 | + | 2.08191e17i | −0.166648 | + | 0.288643i | −0.937239 | − | 0.348687i | \(-0.886628\pi\) |
0.770591 | + | 0.637330i | \(0.219961\pi\) | |||||||
\(948\) | −3.47185e17 | + | 2.00447e17i | −0.478311 | + | 0.276153i | ||||
\(949\) | −9.27532e17 | − | 1.60653e18i | −1.26979 | − | 2.19934i | ||||
\(950\) | −2.13025e17 | − | 1.22990e17i | −0.289794 | − | 0.167313i | ||||
\(951\) | 1.20728e18i | 1.63202i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.51022e17 | 0.201596 | 0.100798 | − | 0.994907i | \(-0.467860\pi\) | ||||
0.100798 | + | 0.994907i | \(0.467860\pi\) | |||||||
\(954\) | 6.26348e14 | − | 1.08487e15i | 0.000830855 | − | 0.00143908i | ||||
\(955\) | −1.14006e18 | + | 6.58212e17i | −1.50282 | + | 0.867652i | ||||
\(956\) | −1.22901e17 | − | 2.12870e17i | −0.160993 | − | 0.278848i | ||||
\(957\) | 6.89221e17 | + | 3.97922e17i | 0.897195 | + | 0.517996i | ||||
\(958\) | − | 1.67484e17i | − | 0.216660i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.47304e17 | −0.188186 | ||||||||
\(961\) | 2.03421e17 | − | 3.52335e17i | 0.258259 | − | 0.447317i | ||||
\(962\) | −1.07712e18 | + | 6.21875e17i | −1.35898 | + | 0.784607i | ||||
\(963\) | −2.11674e16 | − | 3.66630e16i | −0.0265406 | − | 0.0459696i | ||||
\(964\) | 9.09999e16 | + | 5.25388e16i | 0.113391 | + | 0.0654664i | ||||
\(965\) | 8.36223e17i | 1.03552i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.07464e18 | −1.31433 | −0.657166 | − | 0.753746i | \(-0.728245\pi\) | ||||
−0.657166 | + | 0.753746i | \(0.728245\pi\) | |||||||
\(968\) | 6.67503e16 | − | 1.15615e17i | 0.0811336 | − | 0.140528i | ||||
\(969\) | −6.07694e17 | + | 3.50852e17i | −0.734078 | + | 0.423820i | ||||
\(970\) | 2.27139e17 | + | 3.93416e17i | 0.272685 | + | 0.472303i | ||||
\(971\) | −1.29510e18 | − | 7.47725e17i | −1.54521 | − | 0.892127i | −0.998497 | − | 0.0548066i | \(-0.982546\pi\) |
−0.546712 | − | 0.837320i | \(-0.684121\pi\) | |||||||
\(972\) | 1.97174e17i | 0.233804i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −7.76194e17 | −0.909110 | ||||||||
\(975\) | −5.83484e17 | + | 1.01062e18i | −0.679205 | + | 1.17642i | ||||
\(976\) | 1.76057e17 | − | 1.01647e17i | 0.203683 | − | 0.117596i | ||||
\(977\) | −4.73033e16 | − | 8.19317e16i | −0.0543906 | − | 0.0942073i | 0.837548 | − | 0.546364i | \(-0.183988\pi\) |
−0.891939 | + | 0.452156i | \(0.850655\pi\) | |||||||
\(978\) | 7.80650e17 | + | 4.50709e17i | 0.892120 | + | 0.515066i | ||||
\(979\) | − | 2.69410e16i | − | 0.0305997i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.32467e16 | 0.104621 | ||||||||
\(982\) | 2.68693e17 | − | 4.65391e17i | 0.299632 | − | 0.518978i | ||||
\(983\) | 1.78182e17 | − | 1.02873e17i | 0.197488 | − | 0.114020i | −0.397995 | − | 0.917388i | \(-0.630294\pi\) |
0.595483 | + | 0.803368i | \(0.296961\pi\) | |||||||
\(984\) | −9.61719e16 | − | 1.66575e17i | −0.105944 | − | 0.183501i | ||||
\(985\) | 5.47212e16 | + | 3.15933e16i | 0.0599153 | + | 0.0345921i | ||||
\(986\) | − | 1.09847e18i | − | 1.19544i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.89961e17 | −0.419256 | ||||||||
\(989\) | −2.71454e17 | + | 4.70172e17i | −0.290081 | + | 0.502434i | ||||
\(990\) | −1.36842e17 | + | 7.90058e16i | −0.145348 | + | 0.0839166i | ||||
\(991\) | −4.00321e16 | − | 6.93377e16i | −0.0422636 | − | 0.0732027i | 0.844120 | − | 0.536155i | \(-0.180124\pi\) |
−0.886383 | + | 0.462952i | \(0.846790\pi\) | |||||||
\(992\) | 1.79659e17 | + | 1.03726e17i | 0.188529 | + | 0.108848i | ||||
\(993\) | − | 1.82219e17i | − | 0.190063i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.25993e18 | −1.29840 | ||||||||
\(996\) | −1.74448e17 | + | 3.02153e17i | −0.178694 | + | 0.309508i | ||||
\(997\) | −9.46237e17 | + | 5.46310e17i | −0.963449 | + | 0.556248i | −0.897233 | − | 0.441558i | \(-0.854426\pi\) |
−0.0662163 | + | 0.997805i | \(0.521093\pi\) | |||||||
\(998\) | 6.68529e16 | + | 1.15793e17i | 0.0676608 | + | 0.117192i | ||||
\(999\) | 1.10083e18 | + | 6.35562e17i | 1.10745 | + | 0.639388i |
(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 | 98.13.d.a.19.2 | 16 | ||
7.2 | even | 3 | 98.13.b.c.97.11 | 16 | |||
7.3 | odd | 6 | inner | 98.13.d.a.31.2 | 16 | ||
7.4 | even | 3 | 14.13.d.a.3.3 | ✓ | 16 | ||
7.5 | odd | 6 | 98.13.b.c.97.14 | 16 | |||
7.6 | odd | 2 | 14.13.d.a.5.3 | yes | 16 | ||
21.11 | odd | 6 | 126.13.n.a.73.8 | 16 | |||
21.20 | even | 2 | 126.13.n.a.19.8 | 16 | |||
28.11 | odd | 6 | 112.13.s.c.17.3 | 16 | |||
28.27 | even | 2 | 112.13.s.c.33.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.13.d.a.3.3 | ✓ | 16 | 7.4 | even | 3 | ||
14.13.d.a.5.3 | yes | 16 | 7.6 | odd | 2 | ||
98.13.b.c.97.11 | 16 | 7.2 | even | 3 | |||
98.13.b.c.97.14 | 16 | 7.5 | odd | 6 | |||
98.13.d.a.19.2 | 16 | 1.1 | even | 1 | trivial | ||
98.13.d.a.31.2 | 16 | 7.3 | odd | 6 | inner | ||
112.13.s.c.17.3 | 16 | 28.11 | odd | 6 | |||
112.13.s.c.33.3 | 16 | 28.27 | even | 2 | |||
126.13.n.a.19.8 | 16 | 21.20 | even | 2 | |||
126.13.n.a.73.8 | 16 | 21.11 | odd | 6 |