Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,8,Mod(67,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.67");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.e (of order \(3\), 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: | \(45.9205987462\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 181x^{6} - 1656x^{5} - 6927x^{4} - 5022x^{3} - 974106x^{2} + 14431284x + 117021996 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{5}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.4 | ||
Root | \(0.634077 - 10.5628i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.79 |
Dual form | 147.8.e.m.67.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.8306 | − | 18.7592i | 0.957300 | − | 1.65809i | 0.228287 | − | 0.973594i | \(-0.426688\pi\) |
0.729014 | − | 0.684499i | \(-0.239979\pi\) | |||||||
\(3\) | 13.5000 | + | 23.3827i | 0.288675 | + | 0.500000i | ||||
\(4\) | −170.605 | − | 295.496i | −1.33285 | − | 2.30856i | ||||
\(5\) | 258.468 | − | 447.680i | 0.924725 | − | 1.60167i | 0.132721 | − | 0.991153i | \(-0.457628\pi\) |
0.792003 | − | 0.610517i | \(-0.209038\pi\) | |||||||
\(6\) | 584.853 | 1.10540 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4618.37 | −3.18914 | ||||||||
\(9\) | −364.500 | + | 631.333i | −0.166667 | + | 0.288675i | ||||
\(10\) | −5598.75 | − | 9697.31i | −1.77048 | − | 3.06656i | ||||
\(11\) | −331.291 | − | 573.812i | −0.0750473 | − | 0.129986i | 0.826060 | − | 0.563583i | \(-0.190577\pi\) |
−0.901107 | + | 0.433597i | \(0.857244\pi\) | |||||||
\(12\) | 4606.32 | − | 7978.39i | 0.769520 | − | 1.33285i | ||||
\(13\) | −7851.30 | −0.991151 | −0.495576 | − | 0.868565i | \(-0.665043\pi\) | ||||
−0.495576 | + | 0.868565i | \(0.665043\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13957.3 | 1.06778 | ||||||||
\(16\) | −28182.5 | + | 48813.5i | −1.72012 | + | 2.97934i | ||||
\(17\) | 5816.29 | + | 10074.1i | 0.287127 | + | 0.497319i | 0.973123 | − | 0.230287i | \(-0.0739664\pi\) |
−0.685996 | + | 0.727606i | \(0.740633\pi\) | |||||||
\(18\) | 7895.52 | + | 13675.4i | 0.319100 | + | 0.552698i | ||||
\(19\) | 7492.78 | − | 12977.9i | 0.250614 | − | 0.434076i | −0.713081 | − | 0.701082i | \(-0.752701\pi\) |
0.963695 | + | 0.267005i | \(0.0860341\pi\) | |||||||
\(20\) | −176384. | −4.93007 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −14352.3 | −0.287371 | ||||||||
\(23\) | 13092.5 | − | 22676.9i | 0.224375 | − | 0.388629i | −0.731757 | − | 0.681566i | \(-0.761299\pi\) |
0.956132 | + | 0.292937i | \(0.0946325\pi\) | |||||||
\(24\) | −62348.0 | − | 107990.i | −0.920627 | − | 1.59457i | ||||
\(25\) | −94549.3 | − | 163764.i | −1.21023 | − | 2.09618i | ||||
\(26\) | −85034.5 | + | 147284.i | −0.948830 | + | 1.64342i | ||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 108612. | 0.826959 | 0.413480 | − | 0.910513i | \(-0.364313\pi\) | ||||
0.413480 | + | 0.910513i | \(0.364313\pi\) | |||||||
\(30\) | 151166. | − | 261827.i | 1.02219 | − | 1.77048i | ||||
\(31\) | −97816.2 | − | 169423.i | −0.589719 | − | 1.02142i | −0.994269 | − | 0.106907i | \(-0.965905\pi\) |
0.404550 | − | 0.914516i | \(-0.367428\pi\) | |||||||
\(32\) | 314891. | + | 545407.i | 1.69877 | + | 2.94236i | ||||
\(33\) | 8944.85 | − | 15492.9i | 0.0433286 | − | 0.0750473i | ||||
\(34\) | 251976. | 1.09947 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 248741. | 0.888566 | ||||||||
\(37\) | −163284. | + | 282817.i | −0.529955 | + | 0.917908i | 0.469435 | + | 0.882967i | \(0.344458\pi\) |
−0.999389 | + | 0.0349412i | \(0.988876\pi\) | |||||||
\(38\) | −162303. | − | 281117.i | −0.479826 | − | 0.831083i | ||||
\(39\) | −105993. | − | 183585.i | −0.286121 | − | 0.495576i | ||||
\(40\) | −1.19370e6 | + | 2.06756e6i | −2.94908 | + | 5.10796i | ||||
\(41\) | 79193.0 | 0.179450 | 0.0897249 | − | 0.995967i | \(-0.471401\pi\) | ||||
0.0897249 | + | 0.995967i | \(0.471401\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 638173. | 1.22405 | 0.612025 | − | 0.790838i | \(-0.290355\pi\) | ||||
0.612025 | + | 0.790838i | \(0.290355\pi\) | |||||||
\(44\) | −113039. | + | 195790.i | −0.200053 | + | 0.346502i | ||||
\(45\) | 188423. | + | 326359.i | 0.308242 | + | 0.533890i | ||||
\(46\) | −283600. | − | 491209.i | −0.429589 | − | 0.744070i | ||||
\(47\) | −388420. | + | 672763.i | −0.545707 | + | 0.945191i | 0.452856 | + | 0.891584i | \(0.350405\pi\) |
−0.998562 | + | 0.0536075i | \(0.982928\pi\) | |||||||
\(48\) | −1.52185e6 | −1.98622 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.09611e6 | −4.63422 | ||||||||
\(51\) | −157040. | + | 272001.i | −0.165773 | + | 0.287127i | ||||
\(52\) | 1.33947e6 | + | 2.32003e6i | 1.32105 | + | 2.28813i | ||||
\(53\) | 464108. | + | 803859.i | 0.428207 | + | 0.741676i | 0.996714 | − | 0.0810022i | \(-0.0258121\pi\) |
−0.568507 | + | 0.822678i | \(0.692479\pi\) | |||||||
\(54\) | −213179. | + | 369237.i | −0.184233 | + | 0.319100i | ||||
\(55\) | −342513. | −0.277592 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 404610. | 0.289384 | ||||||||
\(58\) | 1.17633e6 | − | 2.03747e6i | 0.791648 | − | 1.37118i | ||||
\(59\) | −1.14747e6 | − | 1.98747e6i | −0.727374 | − | 1.25985i | −0.957989 | − | 0.286803i | \(-0.907407\pi\) |
0.230616 | − | 0.973045i | \(-0.425926\pi\) | |||||||
\(60\) | −2.38118e6 | − | 4.12432e6i | −1.42319 | − | 2.46504i | ||||
\(61\) | 1.21824e6 | − | 2.11006e6i | 0.687194 | − | 1.19026i | −0.285548 | − | 0.958365i | \(-0.592175\pi\) |
0.972742 | − | 0.231891i | \(-0.0744912\pi\) | |||||||
\(62\) | −4.23764e6 | −2.25815 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.42715e6 | 3.06470 | ||||||||
\(65\) | −2.02931e6 | + | 3.51487e6i | −0.916542 | + | 1.58750i | ||||
\(66\) | −193756. | − | 335596.i | −0.0829569 | − | 0.143686i | ||||
\(67\) | 875450. | + | 1.51632e6i | 0.355606 | + | 0.615928i | 0.987222 | − | 0.159354i | \(-0.0509410\pi\) |
−0.631615 | + | 0.775282i | \(0.717608\pi\) | |||||||
\(68\) | 1.98457e6 | − | 3.43738e6i | 0.765394 | − | 1.32570i | ||||
\(69\) | 706995. | 0.259086 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.22315e6 | −0.405581 | −0.202790 | − | 0.979222i | \(-0.565001\pi\) | ||||
−0.202790 | + | 0.979222i | \(0.565001\pi\) | |||||||
\(72\) | 1.68340e6 | − | 2.91573e6i | 0.531524 | − | 0.920627i | ||||
\(73\) | 232080. | + | 401974.i | 0.0698244 | + | 0.120939i | 0.898824 | − | 0.438310i | \(-0.144423\pi\) |
−0.829000 | + | 0.559249i | \(0.811089\pi\) | |||||||
\(74\) | 3.53694e6 | + | 6.12616e6i | 1.01465 | + | 1.75743i | ||||
\(75\) | 2.55283e6 | − | 4.42164e6i | 0.698728 | − | 1.21023i | ||||
\(76\) | −5.11321e6 | −1.33612 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.59186e6 | −1.09561 | ||||||||
\(79\) | −866218. | + | 1.50033e6i | −0.197666 | + | 0.342368i | −0.947771 | − | 0.318951i | \(-0.896670\pi\) |
0.750105 | + | 0.661319i | \(0.230003\pi\) | |||||||
\(80\) | 1.45686e7 | + | 2.52335e7i | 3.18128 | + | 5.51013i | ||||
\(81\) | −265720. | − | 460241.i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 857709. | − | 1.48560e6i | 0.171787 | − | 0.297545i | ||||
\(83\) | −3.98160e6 | −0.764337 | −0.382168 | − | 0.924093i | \(-0.624823\pi\) | ||||
−0.382168 | + | 0.924093i | \(0.624823\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.01330e6 | 1.06205 | ||||||||
\(86\) | 6.91181e6 | − | 1.19716e7i | 1.17178 | − | 2.02959i | ||||
\(87\) | 1.46626e6 | + | 2.53964e6i | 0.238723 | + | 0.413480i | ||||
\(88\) | 1.53002e6 | + | 2.65008e6i | 0.239337 | + | 0.414543i | ||||
\(89\) | −3.91627e6 | + | 6.78318e6i | −0.588854 | + | 1.01992i | 0.405529 | + | 0.914082i | \(0.367087\pi\) |
−0.994383 | + | 0.105842i | \(0.966246\pi\) | |||||||
\(90\) | 8.16297e6 | 1.18032 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.93456e6 | −1.19623 | ||||||||
\(93\) | 2.64104e6 | − | 4.57441e6i | 0.340474 | − | 0.589719i | ||||
\(94\) | 8.41366e6 | + | 1.45729e7i | 1.04481 | + | 1.80966i | ||||
\(95\) | −3.87330e6 | − | 6.70874e6i | −0.463498 | − | 0.802802i | ||||
\(96\) | −8.50206e6 | + | 1.47260e7i | −0.980787 | + | 1.69877i | ||||
\(97\) | 4.49108e6 | 0.499632 | 0.249816 | − | 0.968293i | \(-0.419630\pi\) | ||||
0.249816 | + | 0.968293i | \(0.419630\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 483022. | 0.0500315 | ||||||||
\(100\) | −3.22611e7 | + | 5.58779e7i | −3.22611 | + | 5.58779i | ||||
\(101\) | −6.21226e6 | − | 1.07600e7i | −0.599964 | − | 1.03917i | −0.992826 | − | 0.119570i | \(-0.961848\pi\) |
0.392862 | − | 0.919597i | \(-0.371485\pi\) | |||||||
\(102\) | 3.40167e6 | + | 5.89187e6i | 0.317389 | + | 0.549734i | ||||
\(103\) | 1.07147e7 | − | 1.85583e7i | 0.966157 | − | 1.67343i | 0.259683 | − | 0.965694i | \(-0.416382\pi\) |
0.706474 | − | 0.707739i | \(-0.250285\pi\) | |||||||
\(104\) | 3.62603e7 | 3.16092 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.01063e7 | 1.63969 | ||||||||
\(107\) | 1.11223e7 | − | 1.92644e7i | 0.877710 | − | 1.52024i | 0.0238619 | − | 0.999715i | \(-0.492404\pi\) |
0.853848 | − | 0.520523i | \(-0.174263\pi\) | |||||||
\(108\) | 3.35801e6 | + | 5.81624e6i | 0.256507 | + | 0.444283i | ||||
\(109\) | −4.95065e6 | − | 8.57478e6i | −0.366159 | − | 0.634206i | 0.622803 | − | 0.782379i | \(-0.285994\pi\) |
−0.988961 | + | 0.148173i | \(0.952661\pi\) | |||||||
\(110\) | −3.70962e6 | + | 6.42526e6i | −0.265739 | + | 0.460274i | ||||
\(111\) | −8.81736e6 | −0.611939 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.91928e7 | 1.25130 | 0.625652 | − | 0.780102i | \(-0.284833\pi\) | ||||
0.625652 | + | 0.780102i | \(0.284833\pi\) | |||||||
\(114\) | 4.38218e6 | − | 7.59016e6i | 0.277028 | − | 0.479826i | ||||
\(115\) | −6.76799e6 | − | 1.17225e7i | −0.414971 | − | 0.718750i | ||||
\(116\) | −1.85297e7 | − | 3.20943e7i | −1.10221 | − | 1.90909i | ||||
\(117\) | 2.86180e6 | − | 4.95678e6i | 0.165192 | − | 0.286121i | ||||
\(118\) | −4.97110e7 | −2.78526 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −6.44600e7 | −3.40530 | ||||||||
\(121\) | 9.52408e6 | − | 1.64962e7i | 0.488736 | − | 0.846515i | ||||
\(122\) | −2.63887e7 | − | 4.57065e7i | −1.31570 | − | 2.27886i | ||||
\(123\) | 1.06911e6 | + | 1.85174e6i | 0.0518027 | + | 0.0897249i | ||||
\(124\) | −3.33758e7 | + | 5.78086e7i | −1.57201 | + | 2.72280i | ||||
\(125\) | −5.73664e7 | −2.62707 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.43563e7 | −0.621912 | −0.310956 | − | 0.950424i | \(-0.600649\pi\) | ||||
−0.310956 | + | 0.950424i | \(0.600649\pi\) | |||||||
\(128\) | 2.93039e7 | − | 5.07559e7i | 1.23507 | − | 2.13920i | ||||
\(129\) | 8.61534e6 | + | 1.49222e7i | 0.353353 | + | 0.612025i | ||||
\(130\) | 4.39574e7 | + | 7.61365e7i | 1.75481 | + | 3.03942i | ||||
\(131\) | 9.10472e6 | − | 1.57698e7i | 0.353848 | − | 0.612883i | −0.633072 | − | 0.774093i | \(-0.718206\pi\) |
0.986920 | + | 0.161210i | \(0.0515396\pi\) | |||||||
\(132\) | −6.10413e6 | −0.231002 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.79267e7 | 1.36169 | ||||||||
\(135\) | −5.08743e6 | + | 8.81169e6i | −0.177963 | + | 0.308242i | ||||
\(136\) | −2.68618e7 | − | 4.65260e7i | −0.915690 | − | 1.58602i | ||||
\(137\) | −1.22635e7 | − | 2.12409e7i | −0.407466 | − | 0.705752i | 0.587139 | − | 0.809486i | \(-0.300254\pi\) |
−0.994605 | + | 0.103734i | \(0.966921\pi\) | |||||||
\(138\) | 7.65719e6 | − | 1.32626e7i | 0.248023 | − | 0.429589i | ||||
\(139\) | −1.18402e7 | −0.373946 | −0.186973 | − | 0.982365i | \(-0.559868\pi\) | ||||
−0.186973 | + | 0.982365i | \(0.559868\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.09747e7 | −0.630128 | ||||||||
\(142\) | −1.32475e7 | + | 2.29454e7i | −0.388263 | + | 0.672490i | ||||
\(143\) | 2.60106e6 | + | 4.50517e6i | 0.0743832 | + | 0.128835i | ||||
\(144\) | −2.05450e7 | − | 3.55850e7i | −0.573374 | − | 0.993112i | ||||
\(145\) | 2.80727e7 | − | 4.86234e7i | 0.764709 | − | 1.32452i | ||||
\(146\) | 1.00543e7 | 0.267372 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.11428e8 | 2.82540 | ||||||||
\(149\) | −2.81606e6 | + | 4.87755e6i | −0.0697412 | + | 0.120795i | −0.898787 | − | 0.438385i | \(-0.855551\pi\) |
0.829046 | + | 0.559180i | \(0.188884\pi\) | |||||||
\(150\) | −5.52975e7 | − | 9.57781e7i | −1.33778 | − | 2.31711i | ||||
\(151\) | 3.03979e7 | + | 5.26507e7i | 0.718495 | + | 1.24447i | 0.961596 | + | 0.274469i | \(0.0885022\pi\) |
−0.243101 | + | 0.970001i | \(0.578165\pi\) | |||||||
\(152\) | −3.46045e7 | + | 5.99367e7i | −0.799245 | + | 1.38433i | ||||
\(153\) | −8.48014e6 | −0.191418 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.01130e8 | −2.18131 | ||||||||
\(156\) | −3.61656e7 | + | 6.26407e7i | −0.762711 | + | 1.32105i | ||||
\(157\) | −2.81674e7 | − | 4.87873e7i | −0.580895 | − | 1.00614i | −0.995374 | − | 0.0960800i | \(-0.969370\pi\) |
0.414479 | − | 0.910059i | \(-0.363964\pi\) | |||||||
\(158\) | 1.87634e7 | + | 3.24991e7i | 0.378452 | + | 0.655498i | ||||
\(159\) | −1.25309e7 | + | 2.17042e7i | −0.247225 | + | 0.428207i | ||||
\(160\) | 3.25557e8 | 6.28359 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.15117e7 | −0.212733 | ||||||||
\(163\) | −2.63360e7 | + | 4.56152e7i | −0.476313 | + | 0.824999i | −0.999632 | − | 0.0271383i | \(-0.991361\pi\) |
0.523318 | + | 0.852137i | \(0.324694\pi\) | |||||||
\(164\) | −1.35107e7 | − | 2.34012e7i | −0.239179 | − | 0.414271i | ||||
\(165\) | −4.62392e6 | − | 8.00887e6i | −0.0801340 | − | 0.138796i | ||||
\(166\) | −4.31232e7 | + | 7.46916e7i | −0.731700 | + | 1.26734i | ||||
\(167\) | −2.07427e7 | −0.344634 | −0.172317 | − | 0.985042i | \(-0.555125\pi\) | ||||
−0.172317 | + | 0.985042i | \(0.555125\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.10556e6 | −0.0176189 | ||||||||
\(170\) | 6.51278e7 | − | 1.12805e8i | 1.01671 | − | 1.76099i | ||||
\(171\) | 5.46224e6 | + | 9.46088e6i | 0.0835380 | + | 0.144692i | ||||
\(172\) | −1.08875e8 | − | 1.88578e8i | −1.63147 | − | 2.82579i | ||||
\(173\) | 6.50263e7 | − | 1.12629e8i | 0.954834 | − | 1.65382i | 0.220087 | − | 0.975480i | \(-0.429366\pi\) |
0.734747 | − | 0.678341i | \(-0.237301\pi\) | |||||||
\(174\) | 6.35220e7 | 0.914117 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.73463e7 | 0.516361 | ||||||||
\(177\) | 3.09816e7 | − | 5.36616e7i | 0.419949 | − | 0.727374i | ||||
\(178\) | 8.48312e7 | + | 1.46932e8i | 1.12742 | + | 1.95275i | ||||
\(179\) | 7.67270e6 | + | 1.32895e7i | 0.0999914 | + | 0.173190i | 0.911681 | − | 0.410899i | \(-0.134785\pi\) |
−0.811689 | + | 0.584089i | \(0.801452\pi\) | |||||||
\(180\) | 6.42918e7 | − | 1.11357e8i | 0.821679 | − | 1.42319i | ||||
\(181\) | −7.02000e7 | −0.879959 | −0.439979 | − | 0.898008i | \(-0.645014\pi\) | ||||
−0.439979 | + | 0.898008i | \(0.645014\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.57851e7 | 0.793504 | ||||||||
\(184\) | −6.04660e7 | + | 1.04730e8i | −0.715565 | + | 1.23939i | ||||
\(185\) | 8.44077e7 | + | 1.46198e8i | 0.980124 | + | 1.69763i | ||||
\(186\) | −5.72082e7 | − | 9.90874e7i | −0.651873 | − | 1.12908i | ||||
\(187\) | 3.85376e6 | − | 6.67491e6i | 0.0430962 | − | 0.0746449i | ||||
\(188\) | 2.65065e8 | 2.90938 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.67801e8 | −1.77483 | ||||||||
\(191\) | −8.45556e7 | + | 1.46455e8i | −0.878063 | + | 1.52085i | −0.0245996 | + | 0.999697i | \(0.507831\pi\) |
−0.853464 | + | 0.521153i | \(0.825502\pi\) | |||||||
\(192\) | 8.67665e7 | + | 1.50284e8i | 0.884703 | + | 1.53235i | ||||
\(193\) | −4.98200e7 | − | 8.62907e7i | −0.498830 | − | 0.863999i | 0.501169 | − | 0.865349i | \(-0.332904\pi\) |
−0.999999 | + | 0.00135028i | \(0.999570\pi\) | |||||||
\(194\) | 4.86412e7 | − | 8.42490e7i | 0.478298 | − | 0.828436i | ||||
\(195\) | −1.09583e8 | −1.05833 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.73109e8 | 1.61319 | 0.806597 | − | 0.591101i | \(-0.201307\pi\) | ||||
0.806597 | + | 0.591101i | \(0.201307\pi\) | |||||||
\(198\) | 5.23143e6 | − | 9.06109e6i | 0.0478952 | − | 0.0829569i | ||||
\(199\) | −4.71759e7 | − | 8.17111e7i | −0.424360 | − | 0.735013i | 0.572000 | − | 0.820253i | \(-0.306168\pi\) |
−0.996360 | + | 0.0852402i | \(0.972834\pi\) | |||||||
\(200\) | 4.36664e8 | + | 7.56325e8i | 3.85960 | + | 6.68503i | ||||
\(201\) | −2.36371e7 | + | 4.09407e7i | −0.205309 | + | 0.355606i | ||||
\(202\) | −2.69131e8 | −2.29738 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.07167e8 | 0.883801 | ||||||||
\(205\) | 2.04689e7 | − | 3.54531e7i | 0.165942 | − | 0.287420i | ||||
\(206\) | −2.32093e8 | − | 4.01996e8i | −1.84981 | − | 3.20396i | ||||
\(207\) | 9.54443e6 | + | 1.65314e7i | 0.0747917 | + | 0.129543i | ||||
\(208\) | 2.21269e8 | − | 3.83249e8i | 1.70490 | − | 2.95297i | ||||
\(209\) | −9.92916e6 | −0.0752316 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.13471e6 | −0.0376294 | −0.0188147 | − | 0.999823i | \(-0.505989\pi\) | ||||
−0.0188147 | + | 0.999823i | \(0.505989\pi\) | |||||||
\(212\) | 1.58358e8 | − | 2.74284e8i | 1.14147 | − | 1.97708i | ||||
\(213\) | −1.65126e7 | − | 2.86006e7i | −0.117081 | − | 0.202790i | ||||
\(214\) | −2.40923e8 | − | 4.17290e8i | −1.68046 | − | 2.91065i | ||||
\(215\) | 1.64948e8 | − | 2.85698e8i | 1.13191 | − | 1.96052i | ||||
\(216\) | 9.09035e7 | 0.613751 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.14474e8 | −1.40210 | ||||||||
\(219\) | −6.26615e6 | + | 1.08533e7i | −0.0403131 | + | 0.0698244i | ||||
\(220\) | 5.84342e7 | + | 1.01211e8i | 0.369988 | + | 0.640839i | ||||
\(221\) | −4.56654e7 | − | 7.90948e7i | −0.284587 | − | 0.492919i | ||||
\(222\) | −9.54975e7 | + | 1.65406e8i | −0.585809 | + | 1.01465i | ||||
\(223\) | 1.73853e8 | 1.04982 | 0.524909 | − | 0.851158i | \(-0.324099\pi\) | ||||
0.524909 | + | 0.851158i | \(0.324099\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.37853e8 | 0.806821 | ||||||||
\(226\) | 2.07870e8 | − | 3.60041e8i | 1.19787 | − | 2.07478i | ||||
\(227\) | 8.51267e7 | + | 1.47444e8i | 0.483032 | + | 0.836635i | 0.999810 | − | 0.0194839i | \(-0.00620231\pi\) |
−0.516779 | + | 0.856119i | \(0.672869\pi\) | |||||||
\(228\) | −6.90284e7 | − | 1.19561e8i | −0.385705 | − | 0.668061i | ||||
\(229\) | 1.23849e8 | − | 2.14513e8i | 0.681504 | − | 1.18040i | −0.293018 | − | 0.956107i | \(-0.594659\pi\) |
0.974522 | − | 0.224293i | \(-0.0720072\pi\) | |||||||
\(230\) | −2.93206e8 | −1.58901 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.01610e8 | −2.63729 | ||||||||
\(233\) | 5.72057e7 | − | 9.90832e7i | 0.296274 | − | 0.513162i | −0.679006 | − | 0.734132i | \(-0.737589\pi\) |
0.975280 | + | 0.220971i | \(0.0709225\pi\) | |||||||
\(234\) | −6.19901e7 | − | 1.07370e8i | −0.316277 | − | 0.547807i | ||||
\(235\) | 2.00789e8 | + | 3.47776e8i | 1.00926 | + | 1.74808i | ||||
\(236\) | −3.91526e8 | + | 6.78142e8i | −1.93896 | + | 3.35837i | ||||
\(237\) | −4.67758e7 | −0.228245 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.83010e7 | −0.418382 | −0.209191 | − | 0.977875i | \(-0.567083\pi\) | ||||
−0.209191 | + | 0.977875i | \(0.567083\pi\) | |||||||
\(240\) | −3.93351e8 | + | 6.81304e8i | −1.83671 | + | 3.18128i | ||||
\(241\) | −7.78228e7 | − | 1.34793e8i | −0.358135 | − | 0.620308i | 0.629514 | − | 0.776989i | \(-0.283254\pi\) |
−0.987649 | + | 0.156681i | \(0.949921\pi\) | |||||||
\(242\) | −2.06303e8 | − | 3.57328e8i | −0.935734 | − | 1.62074i | ||||
\(243\) | 7.17445e6 | − | 1.24265e7i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −8.31351e8 | −3.66370 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.63163e7 | 0.198363 | ||||||||
\(247\) | −5.88281e7 | + | 1.01893e8i | −0.248397 | + | 0.430235i | ||||
\(248\) | 4.51752e8 | + | 7.82457e8i | 1.88070 | + | 3.25747i | ||||
\(249\) | −5.37516e7 | − | 9.31006e7i | −0.220645 | − | 0.382168i | ||||
\(250\) | −6.21313e8 | + | 1.07615e9i | −2.51490 | + | 4.35593i | ||||
\(251\) | 1.07520e8 | 0.429171 | 0.214585 | − | 0.976705i | \(-0.431160\pi\) | ||||
0.214585 | + | 0.976705i | \(0.431160\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.73497e7 | −0.0673550 | ||||||||
\(254\) | −1.55487e8 | + | 2.69312e8i | −0.595356 | + | 1.03119i | ||||
\(255\) | 8.11796e7 | + | 1.40607e8i | 0.306589 | + | 0.531027i | ||||
\(256\) | −2.23422e8 | − | 3.86978e8i | −0.832311 | − | 1.44160i | ||||
\(257\) | −2.01589e8 | + | 3.49162e8i | −0.740800 | + | 1.28310i | 0.211332 | + | 0.977414i | \(0.432220\pi\) |
−0.952132 | + | 0.305689i | \(0.901113\pi\) | |||||||
\(258\) | 3.73238e8 | 1.35306 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.38484e9 | 4.88645 | ||||||||
\(261\) | −3.95890e7 | + | 6.85702e7i | −0.137827 | + | 0.238723i | ||||
\(262\) | −1.97219e8 | − | 3.41594e8i | −0.677478 | − | 1.17343i | ||||
\(263\) | 1.36669e8 | + | 2.36718e8i | 0.463260 | + | 0.802390i | 0.999121 | − | 0.0419165i | \(-0.0133463\pi\) |
−0.535861 | + | 0.844306i | \(0.680013\pi\) | |||||||
\(264\) | −4.13107e7 | + | 7.15522e7i | −0.138181 | + | 0.239337i | ||||
\(265\) | 4.79829e8 | 1.58389 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.11478e8 | −0.679950 | ||||||||
\(268\) | 2.98712e8 | − | 5.17384e8i | 0.947939 | − | 1.64188i | ||||
\(269\) | 5.18206e7 | + | 8.97559e7i | 0.162319 | + | 0.281145i | 0.935700 | − | 0.352797i | \(-0.114769\pi\) |
−0.773381 | + | 0.633942i | \(0.781436\pi\) | |||||||
\(270\) | 1.10200e8 | + | 1.90872e8i | 0.340729 | + | 0.590160i | ||||
\(271\) | −9.90620e6 | + | 1.71580e7i | −0.0302353 | + | 0.0523691i | −0.880747 | − | 0.473587i | \(-0.842959\pi\) |
0.850512 | + | 0.525956i | \(0.176292\pi\) | |||||||
\(272\) | −6.55669e8 | −1.97557 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.31284e8 | −1.56027 | ||||||||
\(275\) | −6.26466e7 | + | 1.08507e8i | −0.181649 | + | 0.314626i | ||||
\(276\) | −1.20617e8 | − | 2.08914e8i | −0.345323 | − | 0.598116i | ||||
\(277\) | 1.78152e8 | + | 3.08569e8i | 0.503630 | + | 0.872314i | 0.999991 | + | 0.00419715i | \(0.00133600\pi\) |
−0.496361 | + | 0.868116i | \(0.665331\pi\) | |||||||
\(278\) | −1.28237e8 | + | 2.22113e8i | −0.357979 | + | 0.620037i | ||||
\(279\) | 1.42616e8 | 0.393146 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.59268e7 | −0.0428210 | −0.0214105 | − | 0.999771i | \(-0.506816\pi\) | ||||
−0.0214105 | + | 0.999771i | \(0.506816\pi\) | |||||||
\(282\) | −2.27169e8 | + | 3.93468e8i | −0.603221 | + | 1.04481i | ||||
\(283\) | 2.41180e8 | + | 4.17737e8i | 0.632542 | + | 1.09560i | 0.987030 | + | 0.160535i | \(0.0513218\pi\) |
−0.354488 | + | 0.935061i | \(0.615345\pi\) | |||||||
\(284\) | 2.08676e8 | + | 3.61437e8i | 0.540577 | + | 0.936308i | ||||
\(285\) | 1.04579e8 | − | 1.81136e8i | 0.267601 | − | 0.463498i | ||||
\(286\) | 1.12685e8 | 0.284828 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.59111e8 | −1.13252 | ||||||||
\(289\) | 1.37511e8 | − | 2.38176e8i | 0.335116 | − | 0.580438i | ||||
\(290\) | −6.08090e8 | − | 1.05324e9i | −1.46411 | − | 2.53592i | ||||
\(291\) | 6.06296e7 | + | 1.05014e8i | 0.144231 | + | 0.249816i | ||||
\(292\) | 7.91877e7 | − | 1.37157e8i | 0.186131 | − | 0.322388i | ||||
\(293\) | 4.43360e8 | 1.02972 | 0.514860 | − | 0.857274i | \(-0.327844\pi\) | ||||
0.514860 | + | 0.857274i | \(0.327844\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.18633e9 | −2.69048 | ||||||||
\(296\) | 7.54109e8 | − | 1.30615e9i | 1.69010 | − | 2.92734i | ||||
\(297\) | 6.52079e6 | + | 1.12943e7i | 0.0144429 | + | 0.0250158i | ||||
\(298\) | 6.09993e7 | + | 1.05654e8i | 0.133527 | + | 0.231275i | ||||
\(299\) | −1.02793e8 | + | 1.78043e8i | −0.222390 | + | 0.385190i | ||||
\(300\) | −1.74210e9 | −3.72519 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.31691e9 | 2.75126 | ||||||||
\(303\) | 1.67731e8 | − | 2.90519e8i | 0.346389 | − | 0.599964i | ||||
\(304\) | 4.22330e8 | + | 7.31497e8i | 0.862173 | + | 1.49333i | ||||
\(305\) | −6.29755e8 | − | 1.09077e9i | −1.27093 | − | 2.20132i | ||||
\(306\) | −9.18452e7 | + | 1.59081e8i | −0.183245 | + | 0.317389i | ||||
\(307\) | −7.75755e7 | −0.153017 | −0.0765086 | − | 0.997069i | \(-0.524377\pi\) | ||||
−0.0765086 | + | 0.997069i | \(0.524377\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.78591e8 | 1.11562 | ||||||||
\(310\) | −1.09530e9 | + | 1.89711e9i | −2.08817 | + | 3.61682i | ||||
\(311\) | −2.21318e8 | − | 3.83334e8i | −0.417211 | − | 0.722630i | 0.578447 | − | 0.815720i | \(-0.303659\pi\) |
−0.995658 | + | 0.0930898i | \(0.970326\pi\) | |||||||
\(312\) | 4.89513e8 | + | 8.47862e8i | 0.912480 | + | 1.58046i | ||||
\(313\) | 2.81513e8 | − | 4.87595e8i | 0.518912 | − | 0.898782i | −0.480847 | − | 0.876805i | \(-0.659671\pi\) |
0.999758 | − | 0.0219770i | \(-0.00699605\pi\) | |||||||
\(314\) | −1.22028e9 | −2.22436 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.91123e8 | 1.05384 | ||||||||
\(317\) | 3.81774e8 | − | 6.61252e8i | 0.673130 | − | 1.16590i | −0.303881 | − | 0.952710i | \(-0.598283\pi\) |
0.977012 | − | 0.213186i | \(-0.0683841\pi\) | |||||||
\(318\) | 2.71435e8 | + | 4.70140e8i | 0.473338 | + | 0.819845i | ||||
\(319\) | −3.59821e7 | − | 6.23228e7i | −0.0620610 | − | 0.107493i | ||||
\(320\) | 1.66121e9 | − | 2.87731e9i | 2.83401 | − | 4.90864i | ||||
\(321\) | 6.00604e8 | 1.01349 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.74321e8 | 0.287833 | ||||||||
\(324\) | −9.06663e7 | + | 1.57039e8i | −0.148094 | + | 0.256507i | ||||
\(325\) | 7.42336e8 | + | 1.28576e9i | 1.19952 | + | 2.07763i | ||||
\(326\) | 5.70470e8 | + | 9.88083e8i | 0.911950 | + | 1.57954i | ||||
\(327\) | 1.33668e8 | − | 2.31519e8i | 0.211402 | − | 0.366159i | ||||
\(328\) | −3.65743e8 | −0.572292 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.00320e8 | −0.306849 | ||||||||
\(331\) | −2.14344e8 | + | 3.71254e8i | −0.324872 | + | 0.562696i | −0.981487 | − | 0.191531i | \(-0.938655\pi\) |
0.656614 | + | 0.754227i | \(0.271988\pi\) | |||||||
\(332\) | 6.79280e8 | + | 1.17655e9i | 1.01874 | + | 1.76452i | ||||
\(333\) | −1.19034e8 | − | 2.06174e8i | −0.176652 | − | 0.305969i | ||||
\(334\) | −2.24656e8 | + | 3.89116e8i | −0.329918 | + | 0.571435i | ||||
\(335\) | 9.05105e8 | 1.31535 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.56118e8 | 1.07618 | 0.538090 | − | 0.842887i | \(-0.319146\pi\) | ||||
0.538090 | + | 0.842887i | \(0.319146\pi\) | |||||||
\(338\) | −1.19739e7 | + | 2.07394e7i | −0.0168665 | + | 0.0292137i | ||||
\(339\) | 2.59102e8 | + | 4.48779e8i | 0.361221 | + | 0.625652i | ||||
\(340\) | −1.02590e9 | − | 1.77691e9i | −1.41556 | − | 2.45182i | ||||
\(341\) | −6.48112e7 | + | 1.12256e8i | −0.0885136 | + | 0.153310i | ||||
\(342\) | 2.36638e8 | 0.319884 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.94732e9 | −3.90367 | ||||||||
\(345\) | 1.82736e8 | − | 3.16508e8i | 0.239583 | − | 0.414971i | ||||
\(346\) | −1.40855e9 | − | 2.43968e9i | −1.82813 | − | 3.16641i | ||||
\(347\) | −5.36282e8 | − | 9.28868e8i | −0.689033 | − | 1.19344i | −0.972151 | − | 0.234355i | \(-0.924702\pi\) |
0.283118 | − | 0.959085i | \(-0.408631\pi\) | |||||||
\(348\) | 5.00301e8 | − | 8.66547e8i | 0.636362 | − | 1.10221i | ||||
\(349\) | 8.07851e8 | 1.01728 | 0.508642 | − | 0.860978i | \(-0.330148\pi\) | ||||
0.508642 | + | 0.860978i | \(0.330148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.54537e8 | 0.190747 | ||||||||
\(352\) | 2.08641e8 | − | 3.61377e8i | 0.254976 | − | 0.441632i | ||||
\(353\) | 1.76320e8 | + | 3.05395e8i | 0.213349 | + | 0.369531i | 0.952760 | − | 0.303723i | \(-0.0982296\pi\) |
−0.739412 | + | 0.673253i | \(0.764896\pi\) | |||||||
\(354\) | −6.71099e8 | − | 1.16238e9i | −0.804035 | − | 1.39263i | ||||
\(355\) | −3.16147e8 | + | 5.47583e8i | −0.375050 | + | 0.649606i | ||||
\(356\) | 2.67253e9 | 3.13941 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.32400e8 | 0.382887 | ||||||||
\(359\) | −2.36734e8 | + | 4.10035e8i | −0.270041 | + | 0.467724i | −0.968872 | − | 0.247562i | \(-0.920371\pi\) |
0.698831 | + | 0.715287i | \(0.253704\pi\) | |||||||
\(360\) | −8.70210e8 | − | 1.50725e9i | −0.983027 | − | 1.70265i | ||||
\(361\) | 3.34652e8 | + | 5.79635e8i | 0.374385 | + | 0.648454i | ||||
\(362\) | −7.60310e8 | + | 1.31689e9i | −0.842385 | + | 1.45905i | ||||
\(363\) | 5.14300e8 | 0.564344 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.39941e8 | 0.258273 | ||||||||
\(366\) | 7.12494e8 | − | 1.23408e9i | 0.759621 | − | 1.31570i | ||||
\(367\) | 4.87256e8 | + | 8.43952e8i | 0.514548 | + | 0.891223i | 0.999858 | + | 0.0168807i | \(0.00537355\pi\) |
−0.485310 | + | 0.874342i | \(0.661293\pi\) | |||||||
\(368\) | 7.37957e8 | + | 1.27818e9i | 0.771905 | + | 1.33698i | ||||
\(369\) | −2.88658e7 | + | 4.99971e7i | −0.0299083 | + | 0.0518027i | ||||
\(370\) | 3.65675e9 | 3.75309 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.80229e9 | −1.81520 | ||||||||
\(373\) | −2.90067e8 | + | 5.02410e8i | −0.289412 | + | 0.501276i | −0.973670 | − | 0.227964i | \(-0.926793\pi\) |
0.684257 | + | 0.729241i | \(0.260126\pi\) | |||||||
\(374\) | −8.34773e7 | − | 1.44587e8i | −0.0825121 | − | 0.142915i | ||||
\(375\) | −7.74446e8 | − | 1.34138e9i | −0.758371 | − | 1.31354i | ||||
\(376\) | 1.79387e9 | − | 3.10707e9i | 1.74034 | − | 3.01435i | ||||
\(377\) | −8.52744e8 | −0.819642 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.10991e8 | −0.482143 | −0.241072 | − | 0.970507i | \(-0.577499\pi\) | ||||
−0.241072 | + | 0.970507i | \(0.577499\pi\) | |||||||
\(380\) | −1.32160e9 | + | 2.28909e9i | −1.23555 | + | 2.14003i | ||||
\(381\) | −1.93810e8 | − | 3.35688e8i | −0.179530 | − | 0.310956i | ||||
\(382\) | 1.83158e9 | + | 3.17239e9i | 1.68114 | + | 2.91182i | ||||
\(383\) | −1.18441e6 | + | 2.05145e6i | −0.00107722 | + | 0.00186580i | −0.866564 | − | 0.499067i | \(-0.833676\pi\) |
0.865486 | + | 0.500933i | \(0.167010\pi\) | |||||||
\(384\) | 1.58241e9 | 1.42613 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.15832e9 | −1.91012 | ||||||||
\(387\) | −2.32614e8 | + | 4.02900e8i | −0.204008 | + | 0.353353i | ||||
\(388\) | −7.66199e8 | − | 1.32710e9i | −0.665933 | − | 1.15343i | ||||
\(389\) | 6.71810e8 | + | 1.16361e9i | 0.578660 | + | 1.00227i | 0.995633 | + | 0.0933494i | \(0.0297573\pi\) |
−0.416974 | + | 0.908919i | \(0.636909\pi\) | |||||||
\(390\) | −1.18685e9 | + | 2.05569e9i | −1.01314 | + | 1.75481i | ||||
\(391\) | 3.04599e8 | 0.257697 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.91655e8 | 0.408589 | ||||||||
\(394\) | 1.87487e9 | − | 3.24738e9i | 1.54431 | − | 2.67483i | ||||
\(395\) | 4.47780e8 | + | 7.75578e8i | 0.365574 | + | 0.633192i | ||||
\(396\) | −8.24057e7 | − | 1.42731e8i | −0.0666844 | − | 0.115501i | ||||
\(397\) | −4.18044e8 | + | 7.24073e8i | −0.335317 | + | 0.580785i | −0.983546 | − | 0.180660i | \(-0.942177\pi\) |
0.648229 | + | 0.761445i | \(0.275510\pi\) | |||||||
\(398\) | −2.04378e9 | −1.62496 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.06585e10 | 8.32698 | ||||||||
\(401\) | 1.20855e8 | − | 2.09327e8i | 0.0935962 | − | 0.162113i | −0.815426 | − | 0.578862i | \(-0.803497\pi\) |
0.909022 | + | 0.416748i | \(0.136830\pi\) | |||||||
\(402\) | 5.12010e8 | + | 8.86827e8i | 0.393086 | + | 0.680844i | ||||
\(403\) | 7.67985e8 | + | 1.33019e9i | 0.584501 | + | 1.01238i | ||||
\(404\) | −2.11968e9 | + | 3.67140e9i | −1.59932 | + | 2.77011i | ||||
\(405\) | −2.74721e8 | −0.205494 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.16378e8 | 0.159087 | ||||||||
\(408\) | 7.25268e8 | − | 1.25620e9i | 0.528674 | − | 0.915690i | ||||
\(409\) | 1.33700e8 | + | 2.31575e8i | 0.0966273 | + | 0.167363i | 0.910287 | − | 0.413979i | \(-0.135861\pi\) |
−0.813659 | + | 0.581342i | \(0.802528\pi\) | |||||||
\(410\) | −4.43381e8 | − | 7.67959e8i | −0.317712 | − | 0.550294i | ||||
\(411\) | 3.31114e8 | − | 5.73505e8i | 0.235251 | − | 0.407466i | ||||
\(412\) | −7.31187e9 | −5.15096 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.13488e8 | 0.286393 | ||||||||
\(415\) | −1.02912e9 | + | 1.78249e9i | −0.706801 | + | 1.22422i | ||||
\(416\) | −2.47230e9 | − | 4.28216e9i | −1.68374 | − | 2.91633i | ||||
\(417\) | −1.59843e8 | − | 2.76857e8i | −0.107949 | − | 0.186973i | ||||
\(418\) | −1.07539e8 | + | 1.86263e8i | −0.0720193 | + | 0.124741i | ||||
\(419\) | 1.59619e9 | 1.06007 | 0.530036 | − | 0.847975i | \(-0.322178\pi\) | ||||
0.530036 | + | 0.847975i | \(0.322178\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.89643e9 | −1.23865 | −0.619327 | − | 0.785133i | \(-0.712595\pi\) | ||||
−0.619327 | + | 0.785133i | \(0.712595\pi\) | |||||||
\(422\) | −5.56121e7 | + | 9.63230e7i | −0.0360227 | + | 0.0623931i | ||||
\(423\) | −2.83158e8 | − | 4.90444e8i | −0.181902 | − | 0.315064i | ||||
\(424\) | −2.14343e9 | − | 3.71252e9i | −1.36561 | − | 2.36531i | ||||
\(425\) | 1.09985e9 | − | 1.90500e9i | 0.694981 | − | 1.20374i | ||||
\(426\) | −7.15366e8 | −0.448327 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.59005e9 | −4.67942 | ||||||||
\(429\) | −7.02287e7 | + | 1.21640e8i | −0.0429452 | + | 0.0743832i | ||||
\(430\) | −3.57297e9 | − | 6.18857e9i | −2.16715 | − | 3.75362i | ||||
\(431\) | 2.09961e8 | + | 3.63663e8i | 0.126319 | + | 0.218790i | 0.922248 | − | 0.386600i | \(-0.126350\pi\) |
−0.795929 | + | 0.605390i | \(0.793017\pi\) | |||||||
\(432\) | 5.54715e8 | − | 9.60795e8i | 0.331037 | − | 0.573374i | ||||
\(433\) | −2.39286e9 | −1.41648 | −0.708238 | − | 0.705974i | \(-0.750509\pi\) | ||||
−0.708238 | + | 0.705974i | \(0.750509\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.51593e9 | 0.883010 | ||||||||
\(436\) | −1.68921e9 | + | 2.92579e9i | −0.976068 | + | 1.69060i | ||||
\(437\) | −1.96198e8 | − | 3.39826e8i | −0.112463 | − | 0.194792i | ||||
\(438\) | 1.35733e8 | + | 2.35096e8i | 0.0771835 | + | 0.133686i | ||||
\(439\) | −2.84003e8 | + | 4.91908e8i | −0.160213 | + | 0.277497i | −0.934945 | − | 0.354793i | \(-0.884551\pi\) |
0.774732 | + | 0.632290i | \(0.217885\pi\) | |||||||
\(440\) | 1.58185e9 | 0.885282 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.97834e9 | −1.08974 | ||||||||
\(443\) | 1.13170e9 | − | 1.96015e9i | 0.618467 | − | 1.07122i | −0.371299 | − | 0.928514i | \(-0.621087\pi\) |
0.989766 | − | 0.142703i | \(-0.0455793\pi\) | |||||||
\(444\) | 1.50428e9 | + | 2.60549e9i | 0.815622 | + | 1.41270i | ||||
\(445\) | 2.02446e9 | + | 3.50647e9i | 1.08906 | + | 1.88630i | ||||
\(446\) | 1.88293e9 | − | 3.26133e9i | 1.00499 | − | 1.74070i | ||||
\(447\) | −1.52067e8 | −0.0805302 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.86592e8 | 0.410098 | 0.205049 | − | 0.978752i | \(-0.434265\pi\) | ||||
0.205049 | + | 0.978752i | \(0.434265\pi\) | |||||||
\(450\) | 1.49303e9 | − | 2.58601e9i | 0.772370 | − | 1.33778i | ||||
\(451\) | −2.62359e7 | − | 4.54419e7i | −0.0134672 | − | 0.0233259i | ||||
\(452\) | −3.27437e9 | − | 5.67138e9i | −1.66780 | − | 2.88871i | ||||
\(453\) | −8.20743e8 | + | 1.42157e9i | −0.414823 | + | 0.718495i | ||||
\(454\) | 3.68790e9 | 1.84963 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.86864e9 | −0.922888 | ||||||||
\(457\) | −5.74677e8 | + | 9.95370e8i | −0.281655 | + | 0.487841i | −0.971792 | − | 0.235838i | \(-0.924217\pi\) |
0.690138 | + | 0.723678i | \(0.257550\pi\) | |||||||
\(458\) | −2.68272e9 | − | 4.64661e9i | −1.30481 | − | 2.25999i | ||||
\(459\) | −1.14482e8 | − | 1.98289e8i | −0.0552577 | − | 0.0957091i | ||||
\(460\) | −2.30930e9 | + | 3.99983e9i | −1.10619 | + | 1.91597i | ||||
\(461\) | 7.67125e8 | 0.364681 | 0.182340 | − | 0.983235i | \(-0.441633\pi\) | ||||
0.182340 | + | 0.983235i | \(0.441633\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.43312e9 | 1.13928 | 0.569640 | − | 0.821894i | \(-0.307082\pi\) | ||||
0.569640 | + | 0.821894i | \(0.307082\pi\) | |||||||
\(464\) | −3.06095e9 | + | 5.30172e9i | −1.42247 | + | 2.46379i | ||||
\(465\) | −1.36525e9 | − | 2.36468e9i | −0.629690 | − | 1.09066i | ||||
\(466\) | −1.23915e9 | − | 2.14626e9i | −0.567247 | − | 0.982500i | ||||
\(467\) | 1.19466e9 | − | 2.06921e9i | 0.542794 | − | 0.940146i | −0.455948 | − | 0.890006i | \(-0.650700\pi\) |
0.998742 | − | 0.0501403i | \(-0.0159668\pi\) | |||||||
\(468\) | −1.95294e9 | −0.880703 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.69866e9 | 3.86465 | ||||||||
\(471\) | 7.60519e8 | − | 1.31726e9i | 0.335380 | − | 0.580895i | ||||
\(472\) | 5.29942e9 | + | 9.17887e9i | 2.31970 | + | 4.01784i | ||||
\(473\) | −2.11421e8 | − | 3.66192e8i | −0.0918616 | − | 0.159109i | ||||
\(474\) | −5.06611e8 | + | 8.77475e8i | −0.218499 | + | 0.378452i | ||||
\(475\) | −2.83375e9 | −1.21320 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.76670e8 | −0.285471 | ||||||||
\(478\) | −9.56354e8 | + | 1.65645e9i | −0.400517 | + | 0.693716i | ||||
\(479\) | 1.11598e9 | + | 1.93294e9i | 0.463964 | + | 0.803609i | 0.999154 | − | 0.0411228i | \(-0.0130935\pi\) |
−0.535190 | + | 0.844731i | \(0.679760\pi\) | |||||||
\(480\) | 4.39503e9 | + | 7.61241e9i | 1.81392 | + | 3.14179i | ||||
\(481\) | 1.28200e9 | − | 2.22048e9i | 0.525265 | − | 0.909786i | ||||
\(482\) | −3.37148e9 | −1.37137 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.49941e9 | −2.60564 | ||||||||
\(485\) | 1.16080e9 | − | 2.01057e9i | 0.462022 | − | 0.800245i | ||||
\(486\) | −1.55408e8 | − | 2.69174e8i | −0.0614109 | − | 0.106367i | ||||
\(487\) | −1.03913e8 | − | 1.79983e8i | −0.0407681 | − | 0.0706124i | 0.844921 | − | 0.534891i | \(-0.179647\pi\) |
−0.885689 | + | 0.464278i | \(0.846314\pi\) | |||||||
\(488\) | −5.62630e9 | + | 9.74504e9i | −2.19156 | + | 3.79590i | ||||
\(489\) | −1.42214e9 | −0.549999 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.49013e9 | 0.568119 | 0.284060 | − | 0.958807i | \(-0.408319\pi\) | ||||
0.284060 | + | 0.958807i | \(0.408319\pi\) | |||||||
\(492\) | 3.64789e8 | − | 6.31832e8i | 0.138090 | − | 0.239179i | ||||
\(493\) | 6.31717e8 | + | 1.09417e9i | 0.237443 | + | 0.411263i | ||||
\(494\) | 1.27429e9 | + | 2.20713e9i | 0.475580 | + | 0.823729i | ||||
\(495\) | 1.24846e8 | − | 2.16239e8i | 0.0462654 | − | 0.0801340i | ||||
\(496\) | 1.10268e10 | 4.05755 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.32865e9 | −0.844894 | ||||||||
\(499\) | −8.85786e8 | + | 1.53423e9i | −0.319137 | + | 0.552761i | −0.980308 | − | 0.197474i | \(-0.936726\pi\) |
0.661171 | + | 0.750235i | \(0.270060\pi\) | |||||||
\(500\) | 9.78697e9 | + | 1.69515e10i | 3.50149 | + | 6.06476i | ||||
\(501\) | −2.80027e8 | − | 4.85020e8i | −0.0994872 | − | 0.172317i | ||||
\(502\) | 1.16450e9 | − | 2.01698e9i | 0.410845 | − | 0.711605i | ||||
\(503\) | 2.60286e8 | 0.0911933 | 0.0455966 | − | 0.998960i | \(-0.485481\pi\) | ||||
0.0455966 | + | 0.998960i | \(0.485481\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.42270e9 | −2.21921 | ||||||||
\(506\) | −1.87908e8 | + | 3.25466e8i | −0.0644790 | + | 0.111681i | ||||
\(507\) | −1.49250e7 | − | 2.58509e7i | −0.00508613 | − | 0.00880943i | ||||
\(508\) | 2.44925e9 | + | 4.24222e9i | 0.828914 | + | 1.43572i | ||||
\(509\) | 6.06242e8 | − | 1.05004e9i | 0.203767 | − | 0.352935i | −0.745972 | − | 0.665977i | \(-0.768015\pi\) |
0.949739 | + | 0.313042i | \(0.101348\pi\) | |||||||
\(510\) | 3.51690e9 | 1.17399 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2.17738e9 | −0.716951 | ||||||||
\(513\) | −1.47480e8 | + | 2.55444e8i | −0.0482307 | + | 0.0835380i | ||||
\(514\) | 4.36667e9 | + | 7.56329e9i | 1.41834 | + | 2.45663i | ||||
\(515\) | −5.53880e9 | − | 9.59348e9i | −1.78686 | − | 3.09493i | ||||
\(516\) | 2.93963e9 | − | 5.09159e9i | 0.941931 | − | 1.63147i | ||||
\(517\) | 5.14720e8 | 0.163815 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.51142e9 | 1.10255 | ||||||||
\(520\) | 9.37213e9 | − | 1.62330e10i | 2.92299 | − | 5.06276i | ||||
\(521\) | −1.28716e9 | − | 2.22942e9i | −0.398749 | − | 0.690654i | 0.594823 | − | 0.803857i | \(-0.297222\pi\) |
−0.993572 | + | 0.113203i | \(0.963889\pi\) | |||||||
\(522\) | 8.57547e8 | + | 1.48531e9i | 0.263883 | + | 0.457058i | ||||
\(523\) | −1.36134e9 | + | 2.35791e9i | −0.416113 | + | 0.720729i | −0.995545 | − | 0.0942920i | \(-0.969941\pi\) |
0.579432 | + | 0.815021i | \(0.303275\pi\) | |||||||
\(524\) | −6.21323e9 | −1.88650 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.92084e9 | 1.77392 | ||||||||
\(527\) | 1.13785e9 | − | 1.97082e9i | 0.338649 | − | 0.586557i | ||||
\(528\) | 5.04176e8 | + | 8.73258e8i | 0.149061 | + | 0.258181i | ||||
\(529\) | 1.35959e9 | + | 2.35487e9i | 0.399312 | + | 0.691628i | ||||
\(530\) | 5.19685e9 | − | 9.00120e9i | 1.51626 | − | 2.62624i | ||||
\(531\) | 1.67300e9 | 0.484916 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.21768e8 | −0.177862 | ||||||||
\(534\) | −2.29044e9 | + | 3.96716e9i | −0.650916 | + | 1.12742i | ||||
\(535\) | −5.74952e9 | − | 9.95846e9i | −1.62328 | − | 2.81160i | ||||
\(536\) | −4.04316e9 | − | 7.00295e9i | −1.13408 | − | 1.96428i | ||||
\(537\) | −2.07163e8 | + | 3.58817e8i | −0.0577301 | + | 0.0999914i | ||||
\(538\) | 2.24500e9 | 0.621552 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.47176e9 | 0.948793 | ||||||||
\(541\) | 7.70981e8 | − | 1.33538e9i | 0.209340 | − | 0.362588i | −0.742167 | − | 0.670216i | \(-0.766202\pi\) |
0.951507 | + | 0.307627i | \(0.0995350\pi\) | |||||||
\(542\) | 2.14580e8 | + | 3.71664e8i | 0.0578885 | + | 0.100266i | ||||
\(543\) | −9.47700e8 | − | 1.64146e9i | −0.254022 | − | 0.439979i | ||||
\(544\) | −3.66299e9 | + | 6.34449e9i | −0.975528 | + | 1.68966i | ||||
\(545\) | −5.11835e9 | −1.35438 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.49200e9 | −1.43475 | −0.717373 | − | 0.696689i | \(-0.754656\pi\) | ||||
−0.717373 | + | 0.696689i | \(0.754656\pi\) | |||||||
\(548\) | −4.18441e9 | + | 7.24760e9i | −1.08618 | + | 1.88132i | ||||
\(549\) | 8.88099e8 | + | 1.53823e9i | 0.229065 | + | 0.396752i | ||||
\(550\) | 1.35700e9 | + | 2.35040e9i | 0.347786 | + | 0.602382i | ||||
\(551\) | 8.13805e8 | − | 1.40955e9i | 0.207248 | − | 0.358963i | ||||
\(552\) | −3.26517e9 | −0.826263 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.71799e9 | 1.92850 | ||||||||
\(555\) | −2.27901e9 | + | 3.94736e9i | −0.565875 | + | 0.980124i | ||||
\(556\) | 2.02000e9 | + | 3.49874e9i | 0.498413 | + | 0.863277i | ||||
\(557\) | 3.07010e9 | + | 5.31756e9i | 0.752764 | + | 1.30382i | 0.946478 | + | 0.322767i | \(0.104613\pi\) |
−0.193715 | + | 0.981058i | \(0.562054\pi\) | |||||||
\(558\) | 1.54462e9 | − | 2.67536e9i | 0.376359 | − | 0.651873i | ||||
\(559\) | −5.01049e9 | −1.21322 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.08103e8 | 0.0497632 | ||||||||
\(562\) | −1.72497e8 | + | 2.98774e8i | −0.0409925 | + | 0.0710012i | ||||
\(563\) | −1.62383e9 | − | 2.81256e9i | −0.383497 | − | 0.664236i | 0.608063 | − | 0.793889i | \(-0.291947\pi\) |
−0.991559 | + | 0.129653i | \(0.958614\pi\) | |||||||
\(564\) | 3.57838e9 | + | 6.19793e9i | 0.839865 | + | 1.45469i | ||||
\(565\) | 4.96072e9 | − | 8.59223e9i | 1.15711 | − | 2.00418i | ||||
\(566\) | 1.04485e10 | 2.42213 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.64899e9 | 1.29346 | ||||||||
\(569\) | −1.00581e9 | + | 1.74211e9i | −0.228887 | + | 0.396444i | −0.957479 | − | 0.288504i | \(-0.906842\pi\) |
0.728591 | + | 0.684949i | \(0.240175\pi\) | |||||||
\(570\) | −2.26531e9 | − | 3.92363e9i | −0.512349 | − | 0.887414i | ||||
\(571\) | 1.83448e9 | + | 3.17741e9i | 0.412369 | + | 0.714244i | 0.995148 | − | 0.0983863i | \(-0.0313681\pi\) |
−0.582779 | + | 0.812631i | \(0.698035\pi\) | |||||||
\(572\) | 8.87507e8 | − | 1.53721e9i | 0.198283 | − | 0.343436i | ||||
\(573\) | −4.56600e9 | −1.01390 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.95155e9 | −1.08618 | ||||||||
\(576\) | −2.34269e9 | + | 4.05767e9i | −0.510784 | + | 0.884703i | ||||
\(577\) | 1.71811e9 | + | 2.97585e9i | 0.372337 | + | 0.644906i | 0.989925 | − | 0.141596i | \(-0.0452234\pi\) |
−0.617588 | + | 0.786502i | \(0.711890\pi\) | |||||||
\(578\) | −2.97866e9 | − | 5.15919e9i | −0.641613 | − | 1.11131i | ||||
\(579\) | 1.34514e9 | − | 2.32985e9i | 0.288000 | − | 0.498830i | ||||
\(580\) | −1.91573e10 | −4.07697 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.62662e9 | 0.552290 | ||||||||
\(583\) | 3.07509e8 | − | 5.32622e8i | 0.0642715 | − | 0.111322i | ||||
\(584\) | −1.07183e9 | − | 1.85646e9i | −0.222680 | − | 0.385693i | ||||
\(585\) | −1.47937e9 | − | 2.56234e9i | −0.305514 | − | 0.529166i | ||||
\(586\) | 4.80186e9 | − | 8.31707e9i | 0.985752 | − | 1.70737i | ||||
\(587\) | −8.47232e9 | −1.72890 | −0.864449 | − | 0.502721i | \(-0.832332\pi\) | ||||
−0.864449 | + | 0.502721i | \(0.832332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.93166e9 | −0.591168 | ||||||||
\(590\) | −1.28487e10 | + | 2.22547e10i | −2.57560 | + | 4.46107i | ||||
\(591\) | 2.33697e9 | + | 4.04774e9i | 0.465689 | + | 0.806597i | ||||
\(592\) | −9.20351e9 | − | 1.59410e10i | −1.82317 | − | 3.15783i | ||||
\(593\) | −4.79464e9 | + | 8.30457e9i | −0.944202 | + | 1.63541i | −0.186861 | + | 0.982386i | \(0.559831\pi\) |
−0.757341 | + | 0.653019i | \(0.773502\pi\) | |||||||
\(594\) | 2.82497e8 | 0.0553046 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.92173e9 | 0.371818 | ||||||||
\(597\) | 1.27375e9 | − | 2.20620e9i | 0.245004 | − | 0.424360i | ||||
\(598\) | 2.22663e9 | + | 3.85663e9i | 0.425788 | + | 0.737486i | ||||
\(599\) | 1.58317e9 | + | 2.74213e9i | 0.300978 | + | 0.521308i | 0.976358 | − | 0.216161i | \(-0.0693538\pi\) |
−0.675380 | + | 0.737470i | \(0.736020\pi\) | |||||||
\(600\) | −1.17899e10 | + | 2.04208e10i | −2.22834 | + | 3.85960i | ||||
\(601\) | 5.32513e9 | 1.00062 | 0.500310 | − | 0.865846i | \(-0.333219\pi\) | ||||
0.500310 | + | 0.865846i | \(0.333219\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.27641e9 | −0.237071 | ||||||||
\(604\) | 1.03720e10 | − | 1.79649e10i | 1.91529 | − | 3.31738i | ||||
\(605\) | −4.92335e9 | − | 8.52749e9i | −0.903892 | − | 1.56559i | ||||
\(606\) | −3.63326e9 | − | 6.29300e9i | −0.663197 | − | 1.14869i | ||||
\(607\) | −2.66020e9 | + | 4.60760e9i | −0.482785 | + | 0.836207i | −0.999805 | − | 0.0197659i | \(-0.993708\pi\) |
0.517020 | + | 0.855973i | \(0.327041\pi\) | |||||||
\(608\) | 9.43764e9 | 1.70295 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.72825e10 | −4.86665 | ||||||||
\(611\) | 3.04960e9 | − | 5.28207e9i | 0.540878 | − | 0.936828i | ||||
\(612\) | 1.44675e9 | + | 2.50585e9i | 0.255131 | + | 0.441901i | ||||
\(613\) | 3.07598e9 | + | 5.32775e9i | 0.539351 | + | 0.934183i | 0.998939 | + | 0.0460509i | \(0.0146636\pi\) |
−0.459588 | + | 0.888132i | \(0.652003\pi\) | |||||||
\(614\) | −8.40191e8 | + | 1.45525e9i | −0.146484 | + | 0.253717i | ||||
\(615\) | 1.10532e9 | 0.191613 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.29619e9 | −0.736352 | −0.368176 | − | 0.929756i | \(-0.620018\pi\) | ||||
−0.368176 | + | 0.929756i | \(0.620018\pi\) | |||||||
\(618\) | 6.26650e9 | − | 1.08539e10i | 1.06799 | − | 1.84981i | ||||
\(619\) | −1.95075e9 | − | 3.37881e9i | −0.330587 | − | 0.572593i | 0.652040 | − | 0.758184i | \(-0.273913\pi\) |
−0.982627 | + | 0.185591i | \(0.940580\pi\) | |||||||
\(620\) | 1.72532e10 | + | 2.98834e10i | 2.90736 | + | 5.03569i | ||||
\(621\) | −2.57700e8 | + | 4.46349e8i | −0.0431810 | + | 0.0747917i | ||||
\(622\) | −9.58804e9 | −1.59758 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.19485e10 | 1.96865 | ||||||||
\(625\) | −7.44073e9 | + | 1.28877e10i | −1.21909 | + | 2.11152i | ||||
\(626\) | −6.09792e9 | − | 1.05619e10i | −0.993509 | − | 1.72081i | ||||
\(627\) | −1.34044e8 | − | 2.32170e8i | −0.0217175 | − | 0.0376158i | ||||
\(628\) | −9.61096e9 | + | 1.66467e10i | −1.54849 | + | 2.68206i | ||||
\(629\) | −3.79884e9 | −0.608658 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.79183e9 | 0.917726 | 0.458863 | − | 0.888507i | \(-0.348257\pi\) | ||||
0.458863 | + | 0.888507i | \(0.348257\pi\) | |||||||
\(632\) | 4.00052e9 | − | 6.92910e9i | 0.630386 | − | 1.09186i | ||||
\(633\) | −6.93186e7 | − | 1.20063e8i | −0.0108627 | − | 0.0188147i | ||||
\(634\) | −8.26970e9 | − | 1.43235e10i | −1.28878 | − | 2.23223i | ||||
\(635\) | −3.71064e9 | + | 6.42702e9i | −0.575097 | + | 0.996097i | ||||
\(636\) | 8.55133e9 | 1.31806 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.55883e9 | −0.237644 | ||||||||
\(639\) | 4.45840e8 | − | 7.72217e8i | 0.0675968 | − | 0.117081i | ||||
\(640\) | −1.51483e10 | − | 2.62376e10i | −2.28420 | − | 3.95634i | ||||
\(641\) | −1.65946e9 | − | 2.87426e9i | −0.248864 | − | 0.431046i | 0.714347 | − | 0.699792i | \(-0.246724\pi\) |
−0.963211 | + | 0.268746i | \(0.913391\pi\) | |||||||
\(642\) | 6.50491e9 | − | 1.12668e10i | 0.970216 | − | 1.68046i | ||||
\(643\) | 1.23513e10 | 1.83220 | 0.916100 | − | 0.400949i | \(-0.131319\pi\) | ||||
0.916100 | + | 0.400949i | \(0.131319\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.90718e9 | 1.30702 | ||||||||
\(646\) | 1.88800e9 | − | 3.27011e9i | 0.275542 | − | 0.477253i | ||||
\(647\) | 4.33840e9 | + | 7.51432e9i | 0.629744 | + | 1.09075i | 0.987603 | + | 0.156973i | \(0.0501737\pi\) |
−0.357858 | + | 0.933776i | \(0.616493\pi\) | |||||||
\(648\) | 1.22720e9 | + | 2.12557e9i | 0.177175 | + | 0.306876i | ||||
\(649\) | −7.60289e8 | + | 1.31686e9i | −0.109175 | + | 0.189096i | ||||
\(650\) | 3.21598e10 | 4.59321 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.79722e10 | 2.53941 | ||||||||
\(653\) | 2.54107e9 | − | 4.40127e9i | 0.357126 | − | 0.618560i | −0.630354 | − | 0.776308i | \(-0.717090\pi\) |
0.987479 | + | 0.157748i | \(0.0504234\pi\) | |||||||
\(654\) | −2.89540e9 | − | 5.01499e9i | −0.404750 | − | 0.701048i | ||||
\(655\) | −4.70656e9 | − | 8.15201e9i | −0.654424 | − | 1.13350i | ||||
\(656\) | −2.23185e9 | + | 3.86568e9i | −0.308675 | + | 0.534642i | ||||
\(657\) | −3.38372e8 | −0.0465496 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.83208e9 | 1.06605 | 0.533026 | − | 0.846099i | \(-0.321055\pi\) | ||||
0.533026 | + | 0.846099i | \(0.321055\pi\) | |||||||
\(660\) | −1.57772e9 | + | 2.73270e9i | −0.213613 | + | 0.369988i | ||||
\(661\) | −3.18338e9 | − | 5.51377e9i | −0.428729 | − | 0.742581i | 0.568031 | − | 0.823007i | \(-0.307705\pi\) |
−0.996761 | + | 0.0804261i | \(0.974372\pi\) | |||||||
\(662\) | 4.64295e9 | + | 8.04183e9i | 0.622001 | + | 1.07734i | ||||
\(663\) | 1.23297e9 | − | 2.13556e9i | 0.164306 | − | 0.284587i | ||||
\(664\) | 1.83885e10 | 2.43758 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.15686e9 | −0.676434 | ||||||||
\(667\) | 1.42200e9 | − | 2.46297e9i | 0.185549 | − | 0.321381i | ||||
\(668\) | 3.53880e9 | + | 6.12938e9i | 0.459345 | + | 0.795608i | ||||
\(669\) | 2.34701e9 | + | 4.06514e9i | 0.303056 | + | 0.524909i | ||||
\(670\) | 9.80284e9 | − | 1.69790e10i | 1.25919 | − | 2.18098i | ||||
\(671\) | −1.61437e9 | −0.206288 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.11438e10 | 1.40923 | 0.704615 | − | 0.709590i | \(-0.251120\pi\) | ||||
0.704615 | + | 0.709590i | \(0.251120\pi\) | |||||||
\(674\) | 8.18923e9 | − | 1.41842e10i | 1.03023 | − | 1.78441i | ||||
\(675\) | 1.86101e9 | + | 3.22337e9i | 0.232909 | + | 0.403411i | ||||
\(676\) | 1.88613e8 | + | 3.26688e8i | 0.0234833 | + | 0.0406742i | ||||
\(677\) | −3.86595e9 | + | 6.69603e9i | −0.478846 | + | 0.829386i | −0.999706 | − | 0.0242563i | \(-0.992278\pi\) |
0.520859 | + | 0.853642i | \(0.325612\pi\) | |||||||
\(678\) | 1.12250e10 | 1.38319 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.77717e10 | −3.38705 | ||||||||
\(681\) | −2.29842e9 | + | 3.98098e9i | −0.278878 | + | 0.483032i | ||||
\(682\) | 1.40389e9 | + | 2.43161e9i | 0.169468 | + | 0.293527i | ||||
\(683\) | −1.63295e9 | − | 2.82835e9i | −0.196110 | − | 0.339673i | 0.751154 | − | 0.660127i | \(-0.229498\pi\) |
−0.947264 | + | 0.320455i | \(0.896164\pi\) | |||||||
\(684\) | 1.86377e9 | − | 3.22814e9i | 0.222687 | − | 0.385705i | ||||
\(685\) | −1.26789e10 | −1.50717 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.68785e9 | 0.786933 | ||||||||
\(688\) | −1.79853e10 | + | 3.11514e10i | −2.10551 | + | 3.64686i | ||||
\(689\) | −3.64385e9 | − | 6.31134e9i | −0.424418 | − | 0.735113i | ||||
\(690\) | −3.95828e9 | − | 6.85595e9i | −0.458707 | − | 0.794503i | ||||
\(691\) | −7.20996e9 | + | 1.24880e10i | −0.831303 | + | 1.43986i | 0.0657020 | + | 0.997839i | \(0.479071\pi\) |
−0.897005 | + | 0.442020i | \(0.854262\pi\) | |||||||
\(692\) | −4.43752e10 | −5.09060 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.32331e10 | −2.63845 | ||||||||
\(695\) | −3.06033e9 | + | 5.30065e9i | −0.345797 | + | 0.598938i | ||||
\(696\) | −6.77173e9 | − | 1.17290e10i | −0.761321 | − | 1.31865i | ||||
\(697\) | 4.60609e8 | + | 7.97798e8i | 0.0515250 | + | 0.0892439i | ||||
\(698\) | 8.74952e9 | − | 1.51546e10i | 0.973846 | − | 1.68675i | ||||
\(699\) | 3.08911e9 | 0.342108 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.37465e9 | 0.150723 | 0.0753615 | − | 0.997156i | \(-0.475989\pi\) | ||||
0.0753615 | + | 0.997156i | \(0.475989\pi\) | |||||||
\(702\) | 1.67373e9 | − | 2.89899e9i | 0.182602 | − | 0.316277i | ||||
\(703\) | 2.44691e9 | + | 4.23817e9i | 0.265628 | + | 0.460082i | ||||
\(704\) | −2.12925e9 | − | 3.68798e9i | −0.229997 | − | 0.398367i | ||||
\(705\) | −5.42129e9 | + | 9.38996e9i | −0.582695 | + | 1.00926i | ||||
\(706\) | 7.63862e9 | 0.816955 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.11424e10 | −2.23892 | ||||||||
\(709\) | 7.07713e9 | − | 1.22579e10i | 0.745753 | − | 1.29168i | −0.204089 | − | 0.978952i | \(-0.565423\pi\) |
0.949842 | − | 0.312730i | \(-0.101244\pi\) | |||||||
\(710\) | 6.84813e9 | + | 1.18613e10i | 0.718072 | + | 1.24374i | ||||
\(711\) | −6.31473e8 | − | 1.09374e9i | −0.0658887 | − | 0.114123i | ||||
\(712\) | 1.80868e10 | − | 3.13272e10i | 1.87794 | − | 3.25269i | ||||
\(713\) | −5.12263e9 | −0.529273 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.68917e9 | 0.275136 | ||||||||
\(716\) | 2.61800e9 | − | 4.53450e9i | 0.266547 | − | 0.461673i | ||||
\(717\) | −1.19206e9 | − | 2.06471e9i | −0.120776 | − | 0.209191i | ||||
\(718\) | 5.12794e9 | + | 8.88186e9i | 0.517020 | + | 0.895505i | ||||
\(719\) | −3.32111e9 | + | 5.75234e9i | −0.333221 | + | 0.577156i | −0.983141 | − | 0.182846i | \(-0.941469\pi\) |
0.649920 | + | 0.760002i | \(0.274802\pi\) | |||||||
\(720\) | −2.12409e10 | −2.12085 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.44980e10 | 1.43360 | ||||||||
\(723\) | 2.10122e9 | − | 3.63941e9i | 0.206769 | − | 0.358135i | ||||
\(724\) | 1.19764e10 | + | 2.07438e10i | 1.17285 | + | 2.03144i | ||||
\(725\) | −1.02692e10 | − | 1.77867e10i | −1.00081 | − | 1.73346i | ||||
\(726\) | 5.57019e9 | − | 9.64785e9i | 0.540246 | − | 0.935734i | ||||
\(727\) | 7.79081e9 | 0.751990 | 0.375995 | − | 0.926622i | \(-0.377301\pi\) | ||||
0.375995 | + | 0.926622i | \(0.377301\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 2.59871e9 | − | 4.50110e9i | 0.247245 | − | 0.428241i | ||||
\(731\) | 3.71180e9 | + | 6.42902e9i | 0.351458 | + | 0.608743i | ||||
\(732\) | −1.12232e10 | − | 1.94392e10i | −1.05762 | − | 1.83185i | ||||
\(733\) | 9.60758e9 | − | 1.66408e10i | 0.901052 | − | 1.56067i | 0.0749215 | − | 0.997189i | \(-0.476129\pi\) |
0.826131 | − | 0.563479i | \(-0.190537\pi\) | |||||||
\(734\) | 2.11091e10 | 1.97031 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.64908e10 | 1.52465 | ||||||||
\(737\) | 5.80057e8 | − | 1.00469e9i | 0.0533746 | − | 0.0924475i | ||||
\(738\) | 6.25270e8 | + | 1.08300e9i | 0.0572625 | + | 0.0991815i | ||||
\(739\) | 5.66298e9 | + | 9.80857e9i | 0.516166 | + | 0.894026i | 0.999824 | + | 0.0187685i | \(0.00597455\pi\) |
−0.483658 | + | 0.875257i | \(0.660692\pi\) | |||||||
\(740\) | 2.88007e10 | − | 4.98843e10i | 2.61271 | − | 4.52535i | ||||
\(741\) | −3.17672e9 | −0.286824 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.10743e9 | −0.814582 | −0.407291 | − | 0.913298i | \(-0.633527\pi\) | ||||
−0.407291 | + | 0.913298i | \(0.633527\pi\) | |||||||
\(744\) | −1.21973e10 | + | 2.11263e10i | −1.08582 | + | 1.88070i | ||||
\(745\) | 1.45572e9 | + | 2.52139e9i | 0.128983 | + | 0.223405i | ||||
\(746\) | 6.28320e9 | + | 1.08828e10i | 0.554109 | + | 0.959744i | ||||
\(747\) | 1.45129e9 | − | 2.51372e9i | 0.127389 | − | 0.220645i | ||||
\(748\) | −2.62988e9 | −0.229763 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3.35509e10 | −2.90396 | ||||||||
\(751\) | −8.26880e8 | + | 1.43220e9i | −0.0712365 | + | 0.123385i | −0.899443 | − | 0.437037i | \(-0.856028\pi\) |
0.828207 | + | 0.560422i | \(0.189361\pi\) | |||||||
\(752\) | −2.18933e10 | − | 3.79202e10i | −1.87736 | − | 3.25169i | ||||
\(753\) | 1.45152e9 | + | 2.51410e9i | 0.123891 | + | 0.214585i | ||||
\(754\) | −9.23575e9 | + | 1.59968e10i | −0.784643 | + | 1.35904i | ||||
\(755\) | 3.14276e10 | 2.65764 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.48318e10 | 1.24268 | 0.621338 | − | 0.783543i | \(-0.286590\pi\) | ||||
0.621338 | + | 0.783543i | \(0.286590\pi\) | |||||||
\(758\) | −5.53435e9 | + | 9.58577e9i | −0.461556 | + | 0.799438i | ||||
\(759\) | −2.34221e8 | − | 4.05682e8i | −0.0194437 | − | 0.0336775i | ||||
\(760\) | 1.78883e10 | + | 3.09835e10i | 1.47816 | + | 2.56025i | ||||
\(761\) | 1.40318e9 | − | 2.43039e9i | 0.115417 | − | 0.199908i | −0.802530 | − | 0.596612i | \(-0.796513\pi\) |
0.917946 | + | 0.396705i | \(0.129846\pi\) | |||||||
\(762\) | −8.39631e9 | −0.687458 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.77023e10 | 4.68130 | ||||||||
\(765\) | −2.19185e9 | + | 3.79639e9i | −0.177009 | + | 0.306589i | ||||
\(766\) | 2.56557e7 | + | 4.44370e7i | 0.00206245 | + | 0.00357227i | ||||
\(767\) | 9.00910e9 | + | 1.56042e10i | 0.720937 | + | 1.24870i | ||||
\(768\) | 6.03239e9 | − | 1.04484e10i | 0.480535 | − | 0.832311i | ||||
\(769\) | 1.56499e10 | 1.24099 | 0.620496 | − | 0.784210i | \(-0.286932\pi\) | ||||
0.620496 | + | 0.784210i | \(0.286932\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.08858e10 | −0.855402 | ||||||||
\(772\) | −1.69990e10 | + | 2.94432e10i | −1.32973 | + | 2.30316i | ||||
\(773\) | 2.04453e9 | + | 3.54122e9i | 0.159208 | + | 0.275756i | 0.934583 | − | 0.355745i | \(-0.115773\pi\) |
−0.775375 | + | 0.631501i | \(0.782439\pi\) | |||||||
\(774\) | 5.03871e9 | + | 8.72730e9i | 0.390595 | + | 0.676530i | ||||
\(775\) | −1.84969e10 | + | 3.20376e10i | −1.42739 | + | 2.47232i | ||||
\(776\) | −2.07415e10 | −1.59340 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.91045e10 | 2.21580 | ||||||||
\(779\) | 5.93376e8 | − | 1.02776e9i | 0.0449727 | − | 0.0778950i | ||||
\(780\) | 1.86954e10 | + | 3.23813e10i | 1.41060 | + | 2.44322i | ||||
\(781\) | 4.05220e8 | + | 7.01861e8i | 0.0304377 | + | 0.0527197i | ||||
\(782\) | 3.29899e9 | − | 5.71402e9i | 0.246693 | − | 0.427286i | ||||
\(783\) | −2.13781e9 | −0.159148 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.91215e10 | −2.14867 | ||||||||
\(786\) | 5.32493e9 | − | 9.22304e9i | 0.391142 | − | 0.677478i | ||||
\(787\) | −1.26027e10 | − | 2.18286e10i | −0.921623 | − | 1.59630i | −0.796904 | − | 0.604106i | \(-0.793530\pi\) |
−0.124719 | − | 0.992192i | \(-0.539803\pi\) | |||||||
\(788\) | −2.95331e10 | − | 5.11529e10i | −2.15014 | − | 3.72416i | ||||
\(789\) | −3.69006e9 | + | 6.39137e9i | −0.267463 | + | 0.463260i | ||||
\(790\) | 1.93989e10 | 1.39986 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.23078e9 | −0.159558 | ||||||||
\(793\) | −9.56480e9 | + | 1.65667e10i | −0.681114 | + | 1.17972i | ||||
\(794\) | 9.05534e9 | + | 1.56843e10i | 0.641997 | + | 1.11197i | ||||
\(795\) | 6.47770e9 | + | 1.12197e10i | 0.457231 | + | 0.791947i | ||||
\(796\) | −1.60969e10 | + | 2.78806e10i | −1.13122 | + | 1.95932i | ||||
\(797\) | 6.07194e9 | 0.424838 | 0.212419 | − | 0.977179i | \(-0.431866\pi\) | ||||
0.212419 | + | 0.977179i | \(0.431866\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.03665e9 | −0.626749 | ||||||||
\(800\) | 5.95455e10 | − | 1.03136e11i | 4.11182 | − | 7.12188i | ||||
\(801\) | −2.85496e9 | − | 4.94494e9i | −0.196285 | − | 0.339975i | ||||
\(802\) | −2.61786e9 | − | 4.53427e9i | −0.179199 | − | 0.310383i | ||||
\(803\) | 1.53772e8 | − | 2.66340e8i | 0.0104803 | − | 0.0181523i | ||||
\(804\) | 1.61304e10 | 1.09459 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.32710e10 | 2.23817 | ||||||||
\(807\) | −1.39916e9 | + | 2.42341e9i | −0.0937149 | + | 0.162319i | ||||
\(808\) | 2.86906e10 | + | 4.96935e10i | 1.91337 | + | 3.31406i | ||||
\(809\) | −1.13125e10 | − | 1.95937e10i | −0.751168 | − | 1.30106i | −0.947257 | − | 0.320475i | \(-0.896158\pi\) |
0.196089 | − | 0.980586i | \(-0.437176\pi\) | |||||||
\(810\) | −2.97540e9 | + | 5.15355e9i | −0.196720 | + | 0.340729i | ||||
\(811\) | −1.70292e10 | −1.12104 | −0.560520 | − | 0.828141i | \(-0.689399\pi\) | ||||
−0.560520 | + | 0.828141i | \(0.689399\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.34935e8 | −0.0349127 | ||||||||
\(814\) | 2.34351e9 | − | 4.05908e9i | 0.152294 | − | 0.263780i | ||||
\(815\) | 1.36140e10 | + | 2.35802e10i | 0.880918 | + | 1.52579i | ||||
\(816\) | −8.85153e9 | − | 1.53313e10i | −0.570299 | − | 0.987787i | ||||
\(817\) | 4.78170e9 | − | 8.28214e9i | 0.306764 | − | 0.531331i | ||||
\(818\) | 5.79222e9 | 0.370006 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.39683e10 | −0.884701 | ||||||||
\(821\) | 1.49757e10 | − | 2.59386e10i | 0.944463 | − | 1.63586i | 0.187641 | − | 0.982238i | \(-0.439916\pi\) |
0.756822 | − | 0.653621i | \(-0.226751\pi\) | |||||||
\(822\) | −7.17233e9 | − | 1.24228e10i | −0.450411 | − | 0.780134i | ||||
\(823\) | 5.50746e9 | + | 9.53920e9i | 0.344391 | + | 0.596503i | 0.985243 | − | 0.171162i | \(-0.0547521\pi\) |
−0.640852 | + | 0.767665i | \(0.721419\pi\) | |||||||
\(824\) | −4.94843e10 | + | 8.57093e10i | −3.08121 | + | 5.33682i | ||||
\(825\) | −3.38292e9 | −0.209750 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.67625e10 | −1.03055 | −0.515276 | − | 0.857024i | \(-0.672311\pi\) | ||||
−0.515276 | + | 0.857024i | \(0.672311\pi\) | |||||||
\(828\) | 3.25665e9 | − | 5.64068e9i | 0.199372 | − | 0.345323i | ||||
\(829\) | 1.50012e10 | + | 2.59829e10i | 0.914504 | + | 1.58397i | 0.807626 | + | 0.589695i | \(0.200752\pi\) |
0.106878 | + | 0.994272i | \(0.465915\pi\) | |||||||
\(830\) | 2.22920e10 | + | 3.86108e10i | 1.35324 | + | 2.34388i | ||||
\(831\) | −4.81011e9 | + | 8.33135e9i | −0.290771 | + | 0.503630i | ||||
\(832\) | −5.04615e10 | −3.03758 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6.92481e9 | −0.413358 | ||||||||
\(835\) | −5.36134e9 | + | 9.28610e9i | −0.318691 | + | 0.551990i | ||||
\(836\) | 1.69396e9 | + | 2.93402e9i | 0.100272 | + | 0.173677i | ||||
\(837\) | 1.92532e9 | + | 3.33475e9i | 0.113491 | + | 0.196573i | ||||
\(838\) | 1.72877e10 | − | 2.99432e10i | 1.01481 | − | 1.75770i | ||||
\(839\) | 2.30538e10 | 1.34764 | 0.673821 | − | 0.738894i | \(-0.264652\pi\) | ||||
0.673821 | + | 0.738894i | \(0.264652\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.45335e9 | −0.316139 | ||||||||
\(842\) | −2.05395e10 | + | 3.55755e10i | −1.18576 | + | 2.05380i | ||||
\(843\) | −2.15012e8 | − | 3.72412e8i | −0.0123614 | − | 0.0214105i | ||||
\(844\) | 8.76006e8 | + | 1.51729e9i | 0.0501543 | + | 0.0868698i | ||||
\(845\) | −2.85752e8 | + | 4.94937e8i | −0.0162926 | + | 0.0282196i | ||||
\(846\) | −1.22671e10 | −0.696540 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.23188e10 | −2.94627 | ||||||||
\(849\) | −6.51187e9 | + | 1.12789e10i | −0.365198 | + | 0.632542i | ||||
\(850\) | −2.38242e10 | − | 4.12646e10i | −1.33061 | − | 2.30469i | ||||
\(851\) | 4.27560e9 | + | 7.40556e9i | 0.237817 | + | 0.411912i | ||||
\(852\) | −5.63425e9 | + | 9.75880e9i | −0.312103 | + | 0.540577i | ||||
\(853\) | 5.09026e9 | 0.280814 | 0.140407 | − | 0.990094i | \(-0.455159\pi\) | ||||
0.140407 | + | 0.990094i | \(0.455159\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.64726e9 | 0.308999 | ||||||||
\(856\) | −5.13669e10 | + | 8.89701e10i | −2.79914 | + | 4.84826i | ||||
\(857\) | −6.98397e9 | − | 1.20966e10i | −0.379026 | − | 0.656493i | 0.611895 | − | 0.790939i | \(-0.290408\pi\) |
−0.990921 | + | 0.134447i | \(0.957074\pi\) | |||||||
\(858\) | 1.52124e9 | + | 2.63487e9i | 0.0822228 | + | 0.142414i | ||||
\(859\) | −1.11721e10 | + | 1.93507e10i | −0.601396 | + | 1.04165i | 0.391214 | + | 0.920300i | \(0.372055\pi\) |
−0.992610 | + | 0.121348i | \(0.961278\pi\) | |||||||
\(860\) | −1.12563e11 | −6.03465 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.09602e9 | 0.483700 | ||||||||
\(863\) | 3.33117e9 | − | 5.76976e9i | 0.176425 | − | 0.305576i | −0.764229 | − | 0.644945i | \(-0.776880\pi\) |
0.940653 | + | 0.339369i | \(0.110213\pi\) | |||||||
\(864\) | −6.19800e9 | − | 1.07352e10i | −0.326929 | − | 0.566258i | ||||
\(865\) | −3.36145e10 | − | 5.82220e10i | −1.76592 | − | 3.05866i | ||||
\(866\) | −2.59161e10 | + | 4.48880e10i | −1.35599 | + | 2.34865i | ||||
\(867\) | 7.42559e9 | 0.386958 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.14788e9 | 0.0593372 | ||||||||
\(870\) | 1.64184e10 | − | 2.84375e10i | 0.845306 | − | 1.46411i | ||||
\(871\) | −6.87342e9 | − | 1.19051e10i | −0.352460 | − | 0.610478i | ||||
\(872\) | 2.28640e10 | + | 3.96015e10i | 1.16773 | + | 2.02257i | ||||
\(873\) | −1.63700e9 | + | 2.83537e9i | −0.0832719 | + | 0.144231i | ||||
\(874\) | −8.49980e9 | −0.430644 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.27614e9 | 0.214925 | ||||||||
\(877\) | 1.49491e10 | − | 2.58926e10i | 0.748370 | − | 1.29621i | −0.200234 | − | 0.979748i | \(-0.564170\pi\) |
0.948604 | − | 0.316467i | \(-0.102497\pi\) | |||||||
\(878\) | 6.15186e9 | + | 1.06553e10i | 0.306744 | + | 0.531296i | ||||
\(879\) | 5.98536e9 | + | 1.03669e10i | 0.297255 | + | 0.514860i | ||||
\(880\) | 9.65285e9 | − | 1.67192e10i | 0.477492 | − | 0.827041i | ||||
\(881\) | −1.24713e10 | −0.614466 | −0.307233 | − | 0.951634i | \(-0.599403\pi\) | ||||
−0.307233 | + | 0.951634i | \(0.599403\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.37548e10 | 0.672345 | 0.336173 | − | 0.941800i | \(-0.390867\pi\) | ||||
0.336173 | + | 0.941800i | \(0.390867\pi\) | |||||||
\(884\) | −1.55815e10 | + | 2.69879e10i | −0.758622 | + | 1.31397i | ||||
\(885\) | −1.60155e10 | − | 2.77397e10i | −0.776675 | − | 1.34524i | ||||
\(886\) | −2.45139e10 | − | 4.24594e10i | −1.18412 | − | 2.05095i | ||||
\(887\) | 1.56768e10 | − | 2.71530e10i | 0.754265 | − | 1.30643i | −0.191473 | − | 0.981498i | \(-0.561327\pi\) |
0.945739 | − | 0.324928i | \(-0.105340\pi\) | |||||||
\(888\) | 4.07219e10 | 1.95156 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.77048e10 | 4.17021 | ||||||||
\(891\) | −1.76061e8 | + | 3.04947e8i | −0.00833858 | + | 0.0144429i | ||||
\(892\) | −2.96600e10 | − | 5.13727e10i | −1.39925 | − | 2.42357i | ||||
\(893\) | 5.82069e9 | + | 1.00817e10i | 0.273524 | + | 0.473757i | ||||
\(894\) | −1.64698e9 | + | 2.85265e9i | −0.0770916 | + | 0.133527i | ||||
\(895\) | 7.93261e9 | 0.369858 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.55083e9 | −0.256794 | ||||||||
\(898\) | 8.51928e9 | − | 1.47558e10i | 0.392587 | − | 0.679980i | ||||
\(899\) | −1.06240e10 | − | 1.84013e10i | −0.487673 | − | 0.844675i | ||||
\(900\) | −2.35183e10 | − | 4.07350e10i | −1.07537 | − | 1.86260i | ||||
\(901\) | −5.39877e9 | + | 9.35095e9i | −0.245900 | + | 0.425911i | ||||
\(902\) | −1.13660e9 | −0.0515687 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.86394e10 | −3.99059 | ||||||||
\(905\) | −1.81445e10 | + | 3.14272e10i | −0.813719 | + | 1.40940i | ||||
\(906\) | 1.77783e10 | + | 3.07929e10i | 0.794221 | + | 1.37563i | ||||
\(907\) | 5.60311e8 | + | 9.70487e8i | 0.0249347 | + | 0.0431881i | 0.878223 | − | 0.478250i | \(-0.158729\pi\) |
−0.853289 | + | 0.521439i | \(0.825396\pi\) | |||||||
\(908\) | 2.90460e10 | − | 5.03092e10i | 1.28762 | − | 2.23022i | ||||
\(909\) | 9.05748e9 | 0.399976 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.97792e10 | −1.74318 | −0.871589 | − | 0.490238i | \(-0.836910\pi\) | ||||
−0.871589 | + | 0.490238i | \(0.836910\pi\) | |||||||
\(912\) | −1.14029e10 | + | 1.97504e10i | −0.497776 | + | 0.862173i | ||||
\(913\) | 1.31907e9 | + | 2.28469e9i | 0.0573614 | + | 0.0993528i | ||||
\(914\) | 1.24482e10 | + | 2.15609e10i | 0.539257 | + | 0.934020i | ||||
\(915\) | 1.70034e10 | − | 2.94507e10i | 0.733772 | − | 1.27093i | ||||
\(916\) | −8.45169e10 | −3.63337 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.95964e9 | −0.211593 | ||||||||
\(919\) | 7.21452e9 | − | 1.24959e10i | 0.306622 | − | 0.531085i | −0.670999 | − | 0.741458i | \(-0.734135\pi\) |
0.977621 | + | 0.210373i | \(0.0674680\pi\) | |||||||
\(920\) | 3.12571e10 | + | 5.41389e10i | 1.32340 | + | 2.29220i | ||||
\(921\) | −1.04727e9 | − | 1.81392e9i | −0.0441723 | − | 0.0765086i | ||||
\(922\) | 8.30844e9 | − | 1.43906e10i | 0.349109 | − | 0.604675i | ||||
\(923\) | 9.60336e9 | 0.401992 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.17537e10 | 2.56547 | ||||||||
\(926\) | 2.63522e10 | − | 4.56434e10i | 1.09063 | − | 1.88903i | ||||
\(927\) | 7.81098e9 | + | 1.35290e10i | 0.322052 | + | 0.557811i | ||||
\(928\) | 3.42009e10 | + | 5.92377e10i | 1.40482 | + | 2.43321i | ||||
\(929\) | 1.33031e10 | − | 2.30416e10i | 0.544374 | − | 0.942884i | −0.454272 | − | 0.890863i | \(-0.650101\pi\) |
0.998646 | − | 0.0520206i | \(-0.0165662\pi\) | |||||||
\(930\) | −5.91460e10 | −2.41121 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.90382e10 | −1.57955 | ||||||||
\(933\) | 5.97559e9 | − | 1.03500e10i | 0.240877 | − | 0.417211i | ||||
\(934\) | −2.58778e10 | − | 4.48217e10i | −1.03923 | − | 1.80001i | ||||
\(935\) | −1.99215e9 | − | 3.45051e9i | −0.0797043 | − | 0.138052i | ||||
\(936\) | −1.32169e10 | + | 2.28923e10i | −0.526821 | + | 0.912480i | ||||
\(937\) | −4.46208e10 | −1.77194 | −0.885970 | − | 0.463742i | \(-0.846506\pi\) | ||||
−0.885970 | + | 0.463742i | \(0.846506\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.52017e10 | 0.599188 | ||||||||
\(940\) | 6.85109e10 | − | 1.18664e11i | 2.69037 | − | 4.65986i | ||||
\(941\) | 2.14179e9 | + | 3.70970e9i | 0.0837942 | + | 0.145136i | 0.904877 | − | 0.425674i | \(-0.139963\pi\) |
−0.821083 | + | 0.570809i | \(0.806629\pi\) | |||||||
\(942\) | −1.64738e10 | − | 2.85334e10i | −0.642118 | − | 1.11218i | ||||
\(943\) | 1.03683e9 | − | 1.79585e9i | 0.0402641 | − | 0.0697395i | ||||
\(944\) | 1.29354e11 | 5.00468 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.15928e9 | −0.351757 | ||||||||
\(947\) | −8.93776e8 | + | 1.54807e9i | −0.0341982 | + | 0.0592331i | −0.882618 | − | 0.470091i | \(-0.844221\pi\) |
0.848420 | + | 0.529324i | \(0.177554\pi\) | |||||||
\(948\) | 7.98016e9 | + | 1.38220e10i | 0.304216 | + | 0.526918i | ||||
\(949\) | −1.82213e9 | − | 3.15602e9i | −0.0692065 | − | 0.119869i | ||||
\(950\) | −3.06913e10 | + | 5.31588e10i | −1.16140 | + | 2.01161i | ||||
\(951\) | 2.06158e10 | 0.777264 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.13652e10 | −0.425356 | −0.212678 | − | 0.977122i | \(-0.568219\pi\) | ||||
−0.212678 | + | 0.977122i | \(0.568219\pi\) | |||||||
\(954\) | −7.32875e9 | + | 1.26938e10i | −0.273282 | + | 0.473338i | ||||
\(955\) | 4.37099e10 | + | 7.57078e10i | 1.62393 | + | 2.81274i | ||||
\(956\) | 1.50645e10 | + | 2.60926e10i | 0.557639 | + | 0.965860i | ||||
\(957\) | 9.71516e8 | − | 1.68272e9i | 0.0358309 | − | 0.0620610i | ||||
\(958\) | 4.83472e10 | 1.77661 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.97056e10 | 3.27243 | ||||||||
\(961\) | −5.37973e9 | + | 9.31796e9i | −0.195537 | + | 0.338680i | ||||
\(962\) | −2.77696e10 | − | 4.80984e10i | −1.00567 | − | 1.74188i | ||||
\(963\) | 8.10815e9 | + | 1.40437e10i | 0.292570 | + | 0.506746i | ||||
\(964\) | −2.65538e10 | + | 4.59926e10i | −0.954680 | + | 1.65355i | ||||
\(965\) | −5.15075e10 | −1.84512 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.31418e10 | 1.53428 | 0.767141 | − | 0.641478i | \(-0.221678\pi\) | ||||
0.767141 | + | 0.641478i | \(0.221678\pi\) | |||||||
\(968\) | −4.39858e10 | + | 7.61856e10i | −1.55865 | + | 2.69966i | ||||
\(969\) | 2.35333e9 | + | 4.07609e9i | 0.0830901 | + | 0.143916i | ||||
\(970\) | −2.51444e10 | − | 4.35514e10i | −0.884587 | − | 1.53215i | ||||
\(971\) | −9.40111e9 | + | 1.62832e10i | −0.329543 | + | 0.570785i | −0.982421 | − | 0.186678i | \(-0.940228\pi\) |
0.652878 | + | 0.757463i | \(0.273561\pi\) | |||||||
\(972\) | −4.89598e9 | −0.171005 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.50179e9 | −0.156109 | ||||||||
\(975\) | −2.00431e10 | + | 3.47156e10i | −0.692545 | + | 1.19952i | ||||
\(976\) | 6.86662e10 | + | 1.18933e11i | 2.36411 | + | 4.09477i | ||||
\(977\) | 1.16023e9 | + | 2.00958e9i | 0.0398028 | + | 0.0689405i | 0.885241 | − | 0.465134i | \(-0.153994\pi\) |
−0.845438 | + | 0.534074i | \(0.820660\pi\) | |||||||
\(978\) | −1.54027e10 | + | 2.66782e10i | −0.526515 | + | 0.911950i | ||||
\(979\) | 5.18969e9 | 0.176767 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.21805e9 | 0.244106 | ||||||||
\(982\) | 1.61390e10 | − | 2.79536e10i | 0.543861 | − | 0.941994i | ||||
\(983\) | −1.21690e10 | − | 2.10772e10i | −0.408616 | − | 0.707744i | 0.586119 | − | 0.810225i | \(-0.300655\pi\) |
−0.994735 | + | 0.102481i | \(0.967322\pi\) | |||||||
\(984\) | −4.93753e9 | − | 8.55205e9i | −0.165206 | − | 0.286146i | ||||
\(985\) | 4.47431e10 | − | 7.74973e10i | 1.49176 | − | 2.58381i | ||||
\(986\) | 2.73676e10 | 0.909215 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.01454e10 | 1.32430 | ||||||||
\(989\) | 8.35528e9 | − | 1.44718e10i | 0.274646 | − | 0.475702i | ||||
\(990\) | −2.70432e9 | − | 4.68401e9i | −0.0885797 | − | 0.153425i | ||||
\(991\) | 1.36427e10 | + | 2.36299e10i | 0.445291 | + | 0.771267i | 0.998072 | − | 0.0620597i | \(-0.0197669\pi\) |
−0.552782 | + | 0.833326i | \(0.686434\pi\) | |||||||
\(992\) | 6.16029e10 | − | 1.06699e11i | 2.00360 | − | 3.47033i | ||||
\(993\) | −1.15746e10 | −0.375130 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.87739e10 | −1.56966 | ||||||||
\(996\) | −1.83406e10 | + | 3.17668e10i | −0.588173 | + | 1.01874i | ||||
\(997\) | −9.09819e8 | − | 1.57585e9i | −0.0290751 | − | 0.0503596i | 0.851122 | − | 0.524968i | \(-0.175923\pi\) |
−0.880197 | + | 0.474609i | \(0.842590\pi\) | |||||||
\(998\) | 1.91872e10 | + | 3.32332e10i | 0.611020 | + | 1.05832i | ||||
\(999\) | 3.21393e9 | − | 5.56669e9i | 0.101990 | − | 0.176652i |
(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 | 147.8.e.m.79.4 | 8 | ||
7.2 | even | 3 | 147.8.a.f.1.1 | ✓ | 4 | ||
7.3 | odd | 6 | 147.8.e.l.67.4 | 8 | |||
7.4 | even | 3 | inner | 147.8.e.m.67.4 | 8 | ||
7.5 | odd | 6 | 147.8.a.g.1.1 | yes | 4 | ||
7.6 | odd | 2 | 147.8.e.l.79.4 | 8 | |||
21.2 | odd | 6 | 441.8.a.v.1.4 | 4 | |||
21.5 | even | 6 | 441.8.a.u.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.8.a.f.1.1 | ✓ | 4 | 7.2 | even | 3 | ||
147.8.a.g.1.1 | yes | 4 | 7.5 | odd | 6 | ||
147.8.e.l.67.4 | 8 | 7.3 | odd | 6 | |||
147.8.e.l.79.4 | 8 | 7.6 | odd | 2 | |||
147.8.e.m.67.4 | 8 | 7.4 | even | 3 | inner | ||
147.8.e.m.79.4 | 8 | 1.1 | even | 1 | trivial | ||
441.8.a.u.1.4 | 4 | 21.5 | even | 6 | |||
441.8.a.v.1.4 | 4 | 21.2 | odd | 6 |