Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,8,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.a (trivial) |
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: | yes |
Analytic conductor: | \(165.876448532\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + \cdots + 24\!\cdots\!16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-3.88629\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.88629 | 0.343503 | 0.171751 | − | 0.985140i | \(-0.445057\pi\) | ||||
0.171751 | + | 0.985140i | \(0.445057\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −112.897 | −0.882006 | ||||||||
\(5\) | 26.2639 | 0.0939644 | 0.0469822 | − | 0.998896i | \(-0.485040\pi\) | ||||
0.0469822 | + | 0.998896i | \(0.485040\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −644.460 | −0.710155 | −0.355077 | − | 0.934837i | \(-0.615545\pi\) | ||||
−0.355077 | + | 0.934837i | \(0.615545\pi\) | |||||||
\(8\) | −936.194 | −0.646474 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 102.069 | 0.0322770 | ||||||||
\(11\) | 5692.26 | 1.28947 | 0.644734 | − | 0.764407i | \(-0.276968\pi\) | ||||
0.644734 | + | 0.764407i | \(0.276968\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −606.275 | −0.0765364 | −0.0382682 | − | 0.999268i | \(-0.512184\pi\) | ||||
−0.0382682 | + | 0.999268i | \(0.512184\pi\) | |||||||
\(14\) | −2504.56 | −0.243940 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 10812.5 | 0.659941 | ||||||||
\(17\) | 39283.3 | 1.93926 | 0.969632 | − | 0.244570i | \(-0.0786467\pi\) | ||||
0.969632 | + | 0.244570i | \(0.0786467\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −34062.8 | −1.13931 | −0.569656 | − | 0.821883i | \(-0.692923\pi\) | ||||
−0.569656 | + | 0.821883i | \(0.692923\pi\) | |||||||
\(20\) | −2965.10 | −0.0828772 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 22121.8 | 0.442935 | ||||||||
\(23\) | 21244.4 | 0.364081 | 0.182040 | − | 0.983291i | \(-0.441730\pi\) | ||||
0.182040 | + | 0.983291i | \(0.441730\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −77435.2 | −0.991171 | ||||||||
\(26\) | −2356.16 | −0.0262905 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 72757.5 | 0.626361 | ||||||||
\(29\) | −26193.7 | −0.199436 | −0.0997179 | − | 0.995016i | \(-0.531794\pi\) | ||||
−0.0997179 | + | 0.995016i | \(0.531794\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −310358. | −1.87110 | −0.935551 | − | 0.353193i | \(-0.885096\pi\) | ||||
−0.935551 | + | 0.353193i | \(0.885096\pi\) | |||||||
\(32\) | 161853. | 0.873165 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 152666. | 0.666142 | ||||||||
\(35\) | −16926.0 | −0.0667292 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −330264. | −1.07190 | −0.535951 | − | 0.844249i | \(-0.680047\pi\) | ||||
−0.535951 | + | 0.844249i | \(0.680047\pi\) | |||||||
\(38\) | −132378. | −0.391356 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −24588.1 | −0.0607455 | ||||||||
\(41\) | −318533. | −0.721790 | −0.360895 | − | 0.932607i | \(-0.617529\pi\) | ||||
−0.360895 | + | 0.932607i | \(0.617529\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16755.2 | 0.0321374 | 0.0160687 | − | 0.999871i | \(-0.494885\pi\) | ||||
0.0160687 | + | 0.999871i | \(0.494885\pi\) | |||||||
\(44\) | −642638. | −1.13732 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 82562.0 | 0.125063 | ||||||||
\(47\) | −764733. | −1.07440 | −0.537202 | − | 0.843454i | \(-0.680519\pi\) | ||||
−0.537202 | + | 0.843454i | \(0.680519\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −408214. | −0.495681 | ||||||||
\(50\) | −300935. | −0.340470 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 68446.5 | 0.0675056 | ||||||||
\(53\) | 1.38308e6 | 1.27609 | 0.638046 | − | 0.769998i | \(-0.279743\pi\) | ||||
0.638046 | + | 0.769998i | \(0.279743\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 149501. | 0.121164 | ||||||||
\(56\) | 603340. | 0.459096 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −101796. | −0.0685067 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −354332. | −0.199874 | −0.0999371 | − | 0.994994i | \(-0.531864\pi\) | ||||
−0.0999371 | + | 0.994994i | \(0.531864\pi\) | |||||||
\(62\) | −1.20614e6 | −0.642728 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −754988. | −0.360006 | ||||||||
\(65\) | −15923.1 | −0.00719170 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.54645e6 | 1.84676 | 0.923380 | − | 0.383887i | \(-0.125415\pi\) | ||||
0.923380 | + | 0.383887i | \(0.125415\pi\) | |||||||
\(68\) | −4.43496e6 | −1.71044 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −65779.3 | −0.0229217 | ||||||||
\(71\) | 367019. | 0.121698 | 0.0608491 | − | 0.998147i | \(-0.480619\pi\) | ||||
0.0608491 | + | 0.998147i | \(0.480619\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.13809e6 | −0.342411 | −0.171205 | − | 0.985235i | \(-0.554766\pi\) | ||||
−0.171205 | + | 0.985235i | \(0.554766\pi\) | |||||||
\(74\) | −1.28350e6 | −0.368201 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.84558e6 | 1.00488 | ||||||||
\(77\) | −3.66843e6 | −0.915721 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.04988e6 | 0.695967 | 0.347983 | − | 0.937501i | \(-0.386867\pi\) | ||||
0.347983 | + | 0.937501i | \(0.386867\pi\) | |||||||
\(80\) | 283977. | 0.0620109 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.23791e6 | −0.247937 | ||||||||
\(83\) | 8.39695e6 | 1.61194 | 0.805969 | − | 0.591958i | \(-0.201645\pi\) | ||||
0.805969 | + | 0.591958i | \(0.201645\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.03173e6 | 0.182222 | ||||||||
\(86\) | 65115.7 | 0.0110393 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.32906e6 | −0.833607 | ||||||||
\(89\) | 3.28661e6 | 0.494177 | 0.247089 | − | 0.968993i | \(-0.420526\pi\) | ||||
0.247089 | + | 0.968993i | \(0.420526\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 390720. | 0.0543527 | ||||||||
\(92\) | −2.39843e6 | −0.321121 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.97197e6 | −0.369060 | ||||||||
\(95\) | −894620. | −0.107055 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.46055e6 | 0.941234 | 0.470617 | − | 0.882338i | \(-0.344031\pi\) | ||||
0.470617 | + | 0.882338i | \(0.344031\pi\) | |||||||
\(98\) | −1.58644e6 | −0.170268 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.74219e6 | 0.874219 | ||||||||
\(101\) | −7.61349e6 | −0.735290 | −0.367645 | − | 0.929966i | \(-0.619836\pi\) | ||||
−0.367645 | + | 0.929966i | \(0.619836\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.15554e6 | 0.374712 | 0.187356 | − | 0.982292i | \(-0.440008\pi\) | ||||
0.187356 | + | 0.982292i | \(0.440008\pi\) | |||||||
\(104\) | 567591. | 0.0494788 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.37505e6 | 0.438341 | ||||||||
\(107\) | −1.11011e7 | −0.876038 | −0.438019 | − | 0.898966i | \(-0.644320\pi\) | ||||
−0.438019 | + | 0.898966i | \(0.644320\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.22798e6 | 0.608556 | 0.304278 | − | 0.952583i | \(-0.401585\pi\) | ||||
0.304278 | + | 0.952583i | \(0.401585\pi\) | |||||||
\(110\) | 581002. | 0.0416201 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.96820e6 | −0.468660 | ||||||||
\(113\) | 1.87058e7 | 1.21956 | 0.609779 | − | 0.792571i | \(-0.291258\pi\) | ||||
0.609779 | + | 0.792571i | \(0.291258\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 557961. | 0.0342106 | ||||||||
\(116\) | 2.95718e6 | 0.175904 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 798162. | 0.0447202 | ||||||||
\(119\) | −2.53165e7 | −1.37718 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.29146e7 | 0.662725 | ||||||||
\(122\) | −1.37704e6 | −0.0686573 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.50384e7 | 1.65032 | ||||||||
\(125\) | −4.08561e6 | −0.187099 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.39760e7 | 0.605437 | 0.302718 | − | 0.953080i | \(-0.402106\pi\) | ||||
0.302718 | + | 0.953080i | \(0.402106\pi\) | |||||||
\(128\) | −2.36513e7 | −0.996828 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −61881.8 | −0.00247037 | ||||||||
\(131\) | −1.69407e7 | −0.658387 | −0.329193 | − | 0.944263i | \(-0.606777\pi\) | ||||
−0.329193 | + | 0.944263i | \(0.606777\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.19521e7 | 0.809087 | ||||||||
\(134\) | 1.76688e7 | 0.634367 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.67768e7 | −1.25368 | ||||||||
\(137\) | 2.48882e7 | 0.826935 | 0.413467 | − | 0.910519i | \(-0.364318\pi\) | ||||
0.413467 | + | 0.910519i | \(0.364318\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.91087e7 | −1.86681 | −0.933404 | − | 0.358826i | \(-0.883177\pi\) | ||||
−0.933404 | + | 0.358826i | \(0.883177\pi\) | |||||||
\(140\) | 1.91089e6 | 0.0588556 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.42634e6 | 0.0418036 | ||||||||
\(143\) | −3.45108e6 | −0.0986912 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −687946. | −0.0187399 | ||||||||
\(146\) | −4.42295e6 | −0.117619 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.72857e7 | 0.945424 | ||||||||
\(149\) | 4.77206e7 | 1.18183 | 0.590914 | − | 0.806735i | \(-0.298767\pi\) | ||||
0.590914 | + | 0.806735i | \(0.298767\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.71936e7 | 0.406393 | 0.203197 | − | 0.979138i | \(-0.434867\pi\) | ||||
0.203197 | + | 0.979138i | \(0.434867\pi\) | |||||||
\(152\) | 3.18894e7 | 0.736535 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.42566e7 | −0.314552 | ||||||||
\(155\) | −8.15120e6 | −0.175817 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.53780e7 | −0.523371 | −0.261685 | − | 0.965153i | \(-0.584278\pi\) | ||||
−0.261685 | + | 0.965153i | \(0.584278\pi\) | |||||||
\(158\) | 1.18527e7 | 0.239066 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.25089e6 | 0.0820464 | ||||||||
\(161\) | −1.36912e7 | −0.258554 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.34001e7 | 1.14666 | 0.573328 | − | 0.819326i | \(-0.305652\pi\) | ||||
0.573328 | + | 0.819326i | \(0.305652\pi\) | |||||||
\(164\) | 3.59613e7 | 0.636623 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.26330e7 | 0.553705 | ||||||||
\(167\) | 3.68194e7 | 0.611743 | 0.305872 | − | 0.952073i | \(-0.401052\pi\) | ||||
0.305872 | + | 0.952073i | \(0.401052\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.23809e7 | −0.994142 | ||||||||
\(170\) | 4.00960e6 | 0.0625936 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.89161e6 | −0.0283454 | ||||||||
\(173\) | 6.29918e7 | 0.924959 | 0.462480 | − | 0.886630i | \(-0.346960\pi\) | ||||
0.462480 | + | 0.886630i | \(0.346960\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.99039e7 | 0.703884 | ||||||||
\(176\) | 6.15474e7 | 0.850972 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.27727e7 | 0.169751 | ||||||||
\(179\) | 1.68796e7 | 0.219977 | 0.109989 | − | 0.993933i | \(-0.464919\pi\) | ||||
0.109989 | + | 0.993933i | \(0.464919\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.41326e7 | 0.678554 | 0.339277 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339277 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(182\) | 1.51845e6 | 0.0186703 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.98889e7 | −0.235369 | ||||||||
\(185\) | −8.67400e6 | −0.100721 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.23611e8 | 2.50062 | ||||||||
\(188\) | 8.63359e7 | 0.947630 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.47675e6 | −0.0367736 | ||||||||
\(191\) | 8.74794e7 | 0.908425 | 0.454213 | − | 0.890893i | \(-0.349921\pi\) | ||||
0.454213 | + | 0.890893i | \(0.349921\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.18019e7 | −0.819054 | −0.409527 | − | 0.912298i | \(-0.634306\pi\) | ||||
−0.409527 | + | 0.912298i | \(0.634306\pi\) | |||||||
\(194\) | 3.28801e7 | 0.323316 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.60861e7 | 0.437193 | ||||||||
\(197\) | 1.92295e8 | 1.79199 | 0.895996 | − | 0.444061i | \(-0.146463\pi\) | ||||
0.895996 | + | 0.444061i | \(0.146463\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.44937e6 | −0.0130375 | −0.00651873 | − | 0.999979i | \(-0.502075\pi\) | ||||
−0.00651873 | + | 0.999979i | \(0.502075\pi\) | |||||||
\(200\) | 7.24944e7 | 0.640766 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.95882e7 | −0.252574 | ||||||||
\(203\) | 1.68808e7 | 0.141630 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.36590e6 | −0.0678225 | ||||||||
\(206\) | 1.61496e7 | 0.128715 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.55533e6 | −0.0505095 | ||||||||
\(209\) | −1.93894e8 | −1.46910 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.14625e8 | −1.57286 | −0.786432 | − | 0.617676i | \(-0.788074\pi\) | ||||
−0.786432 | + | 0.617676i | \(0.788074\pi\) | |||||||
\(212\) | −1.56145e8 | −1.12552 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.31421e7 | −0.300921 | ||||||||
\(215\) | 440057. | 0.00301977 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00013e8 | 1.32877 | ||||||||
\(218\) | 3.19763e7 | 0.209041 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.68781e7 | −0.106867 | ||||||||
\(221\) | −2.38165e7 | −0.148424 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.05595e8 | −1.24150 | −0.620748 | − | 0.784011i | \(-0.713171\pi\) | ||||
−0.620748 | + | 0.784011i | \(0.713171\pi\) | |||||||
\(224\) | −1.04308e8 | −0.620082 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.26962e7 | 0.418921 | ||||||||
\(227\) | −1.87007e8 | −1.06113 | −0.530563 | − | 0.847646i | \(-0.678019\pi\) | ||||
−0.530563 | + | 0.847646i | \(0.678019\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.01441e8 | 0.558201 | 0.279100 | − | 0.960262i | \(-0.409964\pi\) | ||||
0.279100 | + | 0.960262i | \(0.409964\pi\) | |||||||
\(230\) | 2.16839e6 | 0.0117514 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.45223e7 | 0.128930 | ||||||||
\(233\) | 1.98406e8 | 1.02757 | 0.513783 | − | 0.857920i | \(-0.328244\pi\) | ||||
0.513783 | + | 0.857920i | \(0.328244\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.00848e7 | −0.100956 | ||||||||
\(236\) | −2.31866e7 | −0.114827 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.83873e7 | −0.473064 | ||||||||
\(239\) | −9.06262e7 | −0.429399 | −0.214700 | − | 0.976680i | \(-0.568877\pi\) | ||||
−0.214700 | + | 0.976680i | \(0.568877\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.22377e8 | −1.02336 | −0.511681 | − | 0.859175i | \(-0.670977\pi\) | ||||
−0.511681 | + | 0.859175i | \(0.670977\pi\) | |||||||
\(242\) | 5.01900e7 | 0.227648 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.00030e7 | 0.176290 | ||||||||
\(245\) | −1.07213e7 | −0.0465763 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.06514e7 | 0.0871988 | ||||||||
\(248\) | 2.90555e8 | 1.20962 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.58779e7 | −0.0642690 | ||||||||
\(251\) | −4.71405e8 | −1.88164 | −0.940819 | − | 0.338909i | \(-0.889942\pi\) | ||||
−0.940819 | + | 0.338909i | \(0.889942\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.20929e8 | 0.469470 | ||||||||
\(254\) | 5.43146e7 | 0.207969 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.72267e6 | 0.0175933 | ||||||||
\(257\) | 6.85596e6 | 0.0251943 | 0.0125972 | − | 0.999921i | \(-0.495990\pi\) | ||||
0.0125972 | + | 0.999921i | \(0.495990\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.12842e8 | 0.761216 | ||||||||
\(260\) | 1.79767e6 | 0.00634312 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.58363e7 | −0.226158 | ||||||||
\(263\) | 4.52181e8 | 1.53273 | 0.766367 | − | 0.642403i | \(-0.222062\pi\) | ||||
0.766367 | + | 0.642403i | \(0.222062\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.63250e7 | 0.119907 | ||||||||
\(266\) | 8.53122e7 | 0.277924 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.13279e8 | −1.62885 | ||||||||
\(269\) | −6.31747e7 | −0.197884 | −0.0989419 | − | 0.995093i | \(-0.531546\pi\) | ||||
−0.0989419 | + | 0.995093i | \(0.531546\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.80213e8 | 1.77091 | 0.885453 | − | 0.464730i | \(-0.153849\pi\) | ||||
0.885453 | + | 0.464730i | \(0.153849\pi\) | |||||||
\(272\) | 4.24749e8 | 1.27980 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.67226e7 | 0.284054 | ||||||||
\(275\) | −4.40781e8 | −1.27808 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.08756e8 | 0.590146 | 0.295073 | − | 0.955475i | \(-0.404656\pi\) | ||||
0.295073 | + | 0.955475i | \(0.404656\pi\) | |||||||
\(278\) | −2.29714e8 | −0.641253 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.58460e7 | 0.0431387 | ||||||||
\(281\) | 6.75157e7 | 0.181523 | 0.0907617 | − | 0.995873i | \(-0.471070\pi\) | ||||
0.0907617 | + | 0.995873i | \(0.471070\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.48132e8 | 1.43758 | 0.718791 | − | 0.695226i | \(-0.244696\pi\) | ||||
0.718791 | + | 0.695226i | \(0.244696\pi\) | |||||||
\(284\) | −4.14352e7 | −0.107338 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.34119e7 | −0.0339007 | ||||||||
\(287\) | 2.05282e8 | 0.512582 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.13284e9 | 2.76074 | ||||||||
\(290\) | −2.67356e6 | −0.00643719 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.28487e8 | 0.302008 | ||||||||
\(293\) | −2.36630e8 | −0.549582 | −0.274791 | − | 0.961504i | \(-0.588609\pi\) | ||||
−0.274791 | + | 0.961504i | \(0.588609\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.39404e6 | 0.0122331 | ||||||||
\(296\) | 3.09191e8 | 0.692956 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.85456e8 | 0.405961 | ||||||||
\(299\) | −1.28800e7 | −0.0278654 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.07981e7 | −0.0228225 | ||||||||
\(302\) | 6.68191e7 | 0.139597 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.68303e8 | −0.751878 | ||||||||
\(305\) | −9.30614e6 | −0.0187811 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.84146e7 | −0.0560477 | −0.0280238 | − | 0.999607i | \(-0.508921\pi\) | ||||
−0.0280238 | + | 0.999607i | \(0.508921\pi\) | |||||||
\(308\) | 4.14154e8 | 0.807671 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.16779e7 | −0.0603936 | ||||||||
\(311\) | −3.86506e8 | −0.728609 | −0.364305 | − | 0.931280i | \(-0.618693\pi\) | ||||
−0.364305 | + | 0.931280i | \(0.618693\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.79214e8 | 1.43632 | 0.718160 | − | 0.695878i | \(-0.244984\pi\) | ||||
0.718160 | + | 0.695878i | \(0.244984\pi\) | |||||||
\(314\) | −9.86264e7 | −0.179779 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.44322e8 | −0.613847 | ||||||||
\(317\) | 4.02260e8 | 0.709251 | 0.354625 | − | 0.935008i | \(-0.384608\pi\) | ||||
0.354625 | + | 0.935008i | \(0.384608\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.49101e8 | −0.257166 | ||||||||
\(320\) | −1.98289e7 | −0.0338278 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.32079e7 | −0.0888138 | ||||||||
\(323\) | −1.33810e9 | −2.20943 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.69471e7 | 0.0758607 | ||||||||
\(326\) | 2.46391e8 | 0.393879 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.98209e8 | 0.466618 | ||||||||
\(329\) | 4.92840e8 | 0.762993 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.06425e8 | −0.919135 | −0.459568 | − | 0.888143i | \(-0.651996\pi\) | ||||
−0.459568 | + | 0.888143i | \(0.651996\pi\) | |||||||
\(332\) | −9.47989e8 | −1.42174 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.43091e8 | 0.210135 | ||||||||
\(335\) | 1.19407e8 | 0.173530 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.34722e8 | 1.04573 | 0.522864 | − | 0.852416i | \(-0.324864\pi\) | ||||
0.522864 | + | 0.852416i | \(0.324864\pi\) | |||||||
\(338\) | −2.42430e8 | −0.341490 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.16479e8 | −0.160721 | ||||||||
\(341\) | −1.76664e9 | −2.41272 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.93818e8 | 1.06216 | ||||||||
\(344\) | −1.56862e7 | −0.0207760 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.44804e8 | 0.317726 | ||||||||
\(347\) | 1.10182e9 | 1.41566 | 0.707830 | − | 0.706382i | \(-0.249674\pi\) | ||||
0.707830 | + | 0.706382i | \(0.249674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.38141e8 | −0.173953 | −0.0869766 | − | 0.996210i | \(-0.527721\pi\) | ||||
−0.0869766 | + | 0.996210i | \(0.527721\pi\) | |||||||
\(350\) | 1.93941e8 | 0.241786 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.21310e8 | 1.12592 | ||||||||
\(353\) | 2.28995e8 | 0.277086 | 0.138543 | − | 0.990356i | \(-0.455758\pi\) | ||||
0.138543 | + | 0.990356i | \(0.455758\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.63932e6 | 0.0114353 | ||||||||
\(356\) | −3.71047e8 | −0.435867 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.55991e7 | 0.0755627 | ||||||||
\(359\) | 1.59391e9 | 1.81817 | 0.909083 | − | 0.416615i | \(-0.136784\pi\) | ||||
0.909083 | + | 0.416615i | \(0.136784\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.66402e8 | 0.298031 | ||||||||
\(362\) | 2.10375e8 | 0.233085 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.41111e7 | −0.0479394 | ||||||||
\(365\) | −2.98907e7 | −0.0321744 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.97853e8 | −0.420137 | −0.210069 | − | 0.977687i | \(-0.567369\pi\) | ||||
−0.210069 | + | 0.977687i | \(0.567369\pi\) | |||||||
\(368\) | 2.29705e8 | 0.240272 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.37097e7 | −0.0345978 | ||||||||
\(371\) | −8.91340e8 | −0.906222 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.35221e9 | 1.34916 | 0.674582 | − | 0.738200i | \(-0.264324\pi\) | ||||
0.674582 | + | 0.738200i | \(0.264324\pi\) | |||||||
\(374\) | 8.69016e8 | 0.858968 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.15939e8 | 0.694574 | ||||||||
\(377\) | 1.58806e7 | 0.0152641 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.69493e9 | 1.59924 | 0.799621 | − | 0.600506i | \(-0.205034\pi\) | ||||
0.799621 | + | 0.600506i | \(0.205034\pi\) | |||||||
\(380\) | 1.01000e8 | 0.0944229 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.39970e8 | 0.312046 | ||||||||
\(383\) | 1.90311e9 | 1.73088 | 0.865442 | − | 0.501010i | \(-0.167038\pi\) | ||||
0.865442 | + | 0.501010i | \(0.167038\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.63472e7 | −0.0860452 | ||||||||
\(386\) | −3.17906e8 | −0.281347 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.55169e8 | −0.830174 | ||||||||
\(389\) | 1.65443e9 | 1.42503 | 0.712516 | − | 0.701655i | \(-0.247555\pi\) | ||||
0.712516 | + | 0.701655i | \(0.247555\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.34551e8 | 0.706048 | ||||||||
\(392\) | 3.82168e8 | 0.320445 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.47314e8 | 0.615554 | ||||||||
\(395\) | 8.01017e7 | 0.0653961 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.76432e9 | −1.41518 | −0.707590 | − | 0.706623i | \(-0.750218\pi\) | ||||
−0.707590 | + | 0.706623i | \(0.750218\pi\) | |||||||
\(398\) | −5.63266e6 | −0.00447840 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.37266e8 | −0.654114 | ||||||||
\(401\) | −9.40134e8 | −0.728089 | −0.364045 | − | 0.931381i | \(-0.618604\pi\) | ||||
−0.364045 | + | 0.931381i | \(0.618604\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.88163e8 | 0.143207 | ||||||||
\(404\) | 8.59538e8 | 0.648530 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.56035e7 | 0.0486503 | ||||||||
\(407\) | −1.87995e9 | −1.38218 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.46509e8 | −0.684059 | −0.342029 | − | 0.939689i | \(-0.611114\pi\) | ||||
−0.342029 | + | 0.939689i | \(0.611114\pi\) | |||||||
\(410\) | −3.25123e7 | −0.0232972 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.69148e8 | −0.330498 | ||||||||
\(413\) | −1.32359e8 | −0.0924542 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.20536e8 | 0.151465 | ||||||||
\(416\) | −9.81276e7 | −0.0668289 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.53528e8 | −0.504641 | ||||||||
\(419\) | 7.99568e8 | 0.531014 | 0.265507 | − | 0.964109i | \(-0.414461\pi\) | ||||
0.265507 | + | 0.964109i | \(0.414461\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.69924e9 | −1.10986 | −0.554930 | − | 0.831897i | \(-0.687255\pi\) | ||||
−0.554930 | + | 0.831897i | \(0.687255\pi\) | |||||||
\(422\) | −8.34094e8 | −0.540283 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.29483e9 | −0.824960 | ||||||||
\(425\) | −3.04191e9 | −1.92214 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.28353e8 | 0.141941 | ||||||||
\(428\) | 1.25328e9 | 0.772671 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.71019e6 | 0.00103730 | ||||||||
\(431\) | −1.67268e9 | −1.00634 | −0.503168 | − | 0.864188i | \(-0.667832\pi\) | ||||
−0.503168 | + | 0.864188i | \(0.667832\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.83377e9 | 1.08552 | 0.542759 | − | 0.839889i | \(-0.317380\pi\) | ||||
0.542759 | + | 0.839889i | \(0.317380\pi\) | |||||||
\(434\) | 7.77310e8 | 0.456436 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.28912e8 | −0.536750 | ||||||||
\(437\) | −7.23644e8 | −0.414801 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.26984e8 | −0.466521 | −0.233261 | − | 0.972414i | \(-0.574940\pi\) | ||||
−0.233261 | + | 0.972414i | \(0.574940\pi\) | |||||||
\(440\) | −1.39962e8 | −0.0783294 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.25578e7 | −0.0509841 | ||||||||
\(443\) | −4.49548e8 | −0.245676 | −0.122838 | − | 0.992427i | \(-0.539200\pi\) | ||||
−0.122838 | + | 0.992427i | \(0.539200\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.63190e7 | 0.0464351 | ||||||||
\(446\) | −7.99000e8 | −0.426457 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.86559e8 | 0.255660 | ||||||||
\(449\) | 1.26664e9 | 0.660377 | 0.330188 | − | 0.943915i | \(-0.392888\pi\) | ||||
0.330188 | + | 0.943915i | \(0.392888\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.81317e9 | −0.930724 | ||||||||
\(452\) | −2.11183e9 | −1.07566 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.26762e8 | −0.364499 | ||||||||
\(455\) | 1.02618e7 | 0.00510722 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.61328e8 | −0.128079 | −0.0640397 | − | 0.997947i | \(-0.520398\pi\) | ||||
−0.0640397 | + | 0.997947i | \(0.520398\pi\) | |||||||
\(458\) | 3.94230e8 | 0.191743 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.29919e7 | −0.0301740 | ||||||||
\(461\) | 2.60747e9 | 1.23956 | 0.619779 | − | 0.784777i | \(-0.287222\pi\) | ||||
0.619779 | + | 0.784777i | \(0.287222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.07005e9 | 1.43751 | 0.718757 | − | 0.695261i | \(-0.244711\pi\) | ||||
0.718757 | + | 0.695261i | \(0.244711\pi\) | |||||||
\(464\) | −2.83218e8 | −0.131616 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.71064e8 | 0.352971 | ||||||||
\(467\) | 2.89908e9 | 1.31720 | 0.658599 | − | 0.752494i | \(-0.271149\pi\) | ||||
0.658599 | + | 0.752494i | \(0.271149\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.93000e9 | −1.31149 | ||||||||
\(470\) | −7.80555e7 | −0.0346785 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.92275e8 | −0.0841637 | ||||||||
\(473\) | 9.53752e7 | 0.0414402 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.63766e9 | 1.12925 | ||||||||
\(476\) | 2.85815e9 | 1.21468 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.52199e8 | −0.147500 | ||||||||
\(479\) | 2.72155e9 | 1.13147 | 0.565733 | − | 0.824588i | \(-0.308593\pi\) | ||||
0.565733 | + | 0.824588i | \(0.308593\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00231e8 | 0.0820395 | ||||||||
\(482\) | −8.64220e8 | −0.351528 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.45802e9 | −0.584528 | ||||||||
\(485\) | 2.22207e8 | 0.0884425 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.18049e9 | −1.64012 | −0.820060 | − | 0.572278i | \(-0.806060\pi\) | ||||
−0.820060 | + | 0.572278i | \(0.806060\pi\) | |||||||
\(488\) | 3.31724e8 | 0.129213 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.16660e7 | −0.0159991 | ||||||||
\(491\) | −1.16233e9 | −0.443144 | −0.221572 | − | 0.975144i | \(-0.571119\pi\) | ||||
−0.221572 | + | 0.975144i | \(0.571119\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.02897e9 | −0.386758 | ||||||||
\(494\) | 8.02574e7 | 0.0299530 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.35574e9 | −1.23482 | ||||||||
\(497\) | −2.36529e8 | −0.0864245 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.46041e9 | −0.886453 | −0.443227 | − | 0.896410i | \(-0.646166\pi\) | ||||
−0.443227 | + | 0.896410i | \(0.646166\pi\) | |||||||
\(500\) | 4.61252e8 | 0.165023 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.83202e9 | −0.646347 | ||||||||
\(503\) | 3.44444e9 | 1.20679 | 0.603394 | − | 0.797443i | \(-0.293815\pi\) | ||||
0.603394 | + | 0.797443i | \(0.293815\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.99960e8 | −0.0690911 | ||||||||
\(506\) | 4.69964e8 | 0.161264 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.57784e9 | −0.533999 | ||||||||
\(509\) | 1.85883e9 | 0.624781 | 0.312391 | − | 0.949954i | \(-0.398870\pi\) | ||||
0.312391 | + | 0.949954i | \(0.398870\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.33455e8 | 0.243164 | ||||||||
\(512\) | 3.04572e9 | 1.00287 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.66442e7 | 0.00865431 | ||||||||
\(515\) | 1.09141e8 | 0.0352096 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.35306e9 | −1.38541 | ||||||||
\(518\) | 8.27164e8 | 0.261480 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.49071e7 | 0.00464925 | ||||||||
\(521\) | −1.66724e9 | −0.516496 | −0.258248 | − | 0.966079i | \(-0.583145\pi\) | ||||
−0.258248 | + | 0.966079i | \(0.583145\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.43856e8 | −0.166237 | −0.0831186 | − | 0.996540i | \(-0.526488\pi\) | ||||
−0.0831186 | + | 0.996540i | \(0.526488\pi\) | |||||||
\(524\) | 1.91255e9 | 0.580701 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.75730e9 | 0.526498 | ||||||||
\(527\) | −1.21919e10 | −3.62856 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.95350e9 | −0.867445 | ||||||||
\(530\) | 1.41169e8 | 0.0411884 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.47832e9 | −0.713620 | ||||||||
\(533\) | 1.93119e8 | 0.0552432 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.91558e8 | −0.0823164 | ||||||||
\(536\) | −4.25636e9 | −1.19388 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.45515e8 | −0.0679736 | ||||||||
\(539\) | −2.32366e9 | −0.639164 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.30286e8 | −0.0625283 | −0.0312642 | − | 0.999511i | \(-0.509953\pi\) | ||||
−0.0312642 | + | 0.999511i | \(0.509953\pi\) | |||||||
\(542\) | 2.25488e9 | 0.608310 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.35813e9 | 1.69330 | ||||||||
\(545\) | 2.16098e8 | 0.0571826 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.00304e9 | 1.04576 | 0.522882 | − | 0.852405i | \(-0.324857\pi\) | ||||
0.522882 | + | 0.852405i | \(0.324857\pi\) | |||||||
\(548\) | −2.80979e9 | −0.729361 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.71300e9 | −0.439024 | ||||||||
\(551\) | 8.92229e8 | 0.227219 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.96553e9 | −0.494244 | ||||||||
\(554\) | 8.11285e8 | 0.202717 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.67318e9 | 1.64654 | ||||||||
\(557\) | 3.49935e9 | 0.858014 | 0.429007 | − | 0.903301i | \(-0.358864\pi\) | ||||
0.429007 | + | 0.903301i | \(0.358864\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.01583e7 | −0.00245968 | ||||||||
\(560\) | −1.83012e8 | −0.0440373 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.62385e8 | 0.0623538 | ||||||||
\(563\) | −3.07572e9 | −0.726385 | −0.363193 | − | 0.931714i | \(-0.618313\pi\) | ||||
−0.363193 | + | 0.931714i | \(0.618313\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.91287e8 | 0.114595 | ||||||||
\(566\) | 2.13020e9 | 0.493813 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.43601e8 | −0.0786747 | ||||||||
\(569\) | 2.50567e9 | 0.570206 | 0.285103 | − | 0.958497i | \(-0.407972\pi\) | ||||
0.285103 | + | 0.958497i | \(0.407972\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.38840e9 | −1.43604 | −0.718019 | − | 0.696023i | \(-0.754951\pi\) | ||||
−0.718019 | + | 0.696023i | \(0.754951\pi\) | |||||||
\(572\) | 3.89615e8 | 0.0870462 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.97784e8 | 0.176073 | ||||||||
\(575\) | −1.64507e9 | −0.360866 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.86927e9 | −0.838520 | −0.419260 | − | 0.907866i | \(-0.637710\pi\) | ||||
−0.419260 | + | 0.907866i | \(0.637710\pi\) | |||||||
\(578\) | 4.40254e9 | 0.948322 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.76669e7 | 0.0165287 | ||||||||
\(581\) | −5.41150e9 | −1.14473 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.87285e9 | 1.64548 | ||||||||
\(584\) | 1.06547e9 | 0.221360 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.19611e8 | −0.188783 | ||||||||
\(587\) | 3.35794e9 | 0.685236 | 0.342618 | − | 0.939475i | \(-0.388686\pi\) | ||||
0.342618 | + | 0.939475i | \(0.388686\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.05717e10 | 2.13177 | ||||||||
\(590\) | 2.09628e7 | 0.00420211 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.57097e9 | −0.707391 | ||||||||
\(593\) | −9.52200e9 | −1.87515 | −0.937576 | − | 0.347780i | \(-0.886936\pi\) | ||||
−0.937576 | + | 0.347780i | \(0.886936\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.64909e8 | −0.129406 | ||||||||
\(596\) | −5.38750e9 | −1.04238 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.00553e7 | −0.00957185 | ||||||||
\(599\) | −4.99052e8 | −0.0948750 | −0.0474375 | − | 0.998874i | \(-0.515105\pi\) | ||||
−0.0474375 | + | 0.998874i | \(0.515105\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.14166e9 | −0.778241 | −0.389120 | − | 0.921187i | \(-0.627221\pi\) | ||||
−0.389120 | + | 0.921187i | \(0.627221\pi\) | |||||||
\(602\) | −4.19645e7 | −0.00783960 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.94110e9 | −0.358441 | ||||||||
\(605\) | 3.39188e8 | 0.0622726 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.83852e9 | −0.878117 | −0.439059 | − | 0.898458i | \(-0.644688\pi\) | ||||
−0.439059 | + | 0.898458i | \(0.644688\pi\) | |||||||
\(608\) | −5.51317e9 | −0.994807 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.61663e7 | −0.00645134 | ||||||||
\(611\) | 4.63639e8 | 0.0822310 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.78195e9 | 0.487795 | 0.243898 | − | 0.969801i | \(-0.421574\pi\) | ||||
0.243898 | + | 0.969801i | \(0.421574\pi\) | |||||||
\(614\) | −1.10427e8 | −0.0192525 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.43437e9 | 0.591990 | ||||||||
\(617\) | −6.18863e9 | −1.06071 | −0.530354 | − | 0.847776i | \(-0.677941\pi\) | ||||
−0.530354 | + | 0.847776i | \(0.677941\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.57626e9 | 0.606055 | 0.303027 | − | 0.952982i | \(-0.402003\pi\) | ||||
0.303027 | + | 0.952982i | \(0.402003\pi\) | |||||||
\(620\) | 9.20244e8 | 0.155072 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.50207e9 | −0.250279 | ||||||||
\(623\) | −2.11809e9 | −0.350942 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.94232e9 | 0.973590 | ||||||||
\(626\) | 3.02825e9 | 0.493380 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.86510e9 | 0.461616 | ||||||||
\(629\) | −1.29739e10 | −2.07870 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.06672e10 | 1.69024 | 0.845121 | − | 0.534574i | \(-0.179528\pi\) | ||||
0.845121 | + | 0.534574i | \(0.179528\pi\) | |||||||
\(632\) | −2.85528e9 | −0.449924 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.56330e9 | 0.243629 | ||||||||
\(635\) | 3.67063e8 | 0.0568895 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.47490e8 | 0.0379376 | ||||||||
\(638\) | −5.79449e8 | −0.0883371 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.21174e8 | −0.0936664 | ||||||||
\(641\) | 2.94407e9 | 0.441515 | 0.220757 | − | 0.975329i | \(-0.429147\pi\) | ||||
0.220757 | + | 0.975329i | \(0.429147\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.24967e10 | −1.85378 | −0.926889 | − | 0.375335i | \(-0.877528\pi\) | ||||
−0.926889 | + | 0.375335i | \(0.877528\pi\) | |||||||
\(644\) | 1.54569e9 | 0.228046 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.20024e9 | −0.758943 | ||||||||
\(647\) | 1.89232e9 | 0.274682 | 0.137341 | − | 0.990524i | \(-0.456144\pi\) | ||||
0.137341 | + | 0.990524i | \(0.456144\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.16907e9 | 0.167874 | ||||||||
\(650\) | 1.82450e8 | 0.0260583 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.15767e9 | −1.01136 | ||||||||
\(653\) | 1.18782e9 | 0.166937 | 0.0834687 | − | 0.996510i | \(-0.473400\pi\) | ||||
0.0834687 | + | 0.996510i | \(0.473400\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.44927e8 | −0.0618649 | ||||||||
\(656\) | −3.44413e9 | −0.476338 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.91532e9 | 0.262090 | ||||||||
\(659\) | 1.27625e10 | 1.73715 | 0.868574 | − | 0.495559i | \(-0.165037\pi\) | ||||
0.868574 | + | 0.495559i | \(0.165037\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.94189e9 | 0.800239 | 0.400120 | − | 0.916463i | \(-0.368969\pi\) | ||||
0.400120 | + | 0.916463i | \(0.368969\pi\) | |||||||
\(662\) | −2.35674e9 | −0.315725 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.86118e9 | −1.04208 | ||||||||
\(665\) | 5.76547e8 | 0.0760254 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.56469e8 | −0.0726107 | ||||||||
\(668\) | −4.15679e9 | −0.539561 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.64051e8 | 0.0596079 | ||||||||
\(671\) | −2.01695e9 | −0.257731 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.95302e9 | −0.626350 | −0.313175 | − | 0.949695i | \(-0.601393\pi\) | ||||
−0.313175 | + | 0.949695i | \(0.601393\pi\) | |||||||
\(674\) | 2.85534e9 | 0.359210 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.04261e9 | 0.876839 | ||||||||
\(677\) | −1.35131e9 | −0.167377 | −0.0836886 | − | 0.996492i | \(-0.526670\pi\) | ||||
−0.0836886 | + | 0.996492i | \(0.526670\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.45249e9 | −0.668421 | ||||||||
\(680\) | −9.65900e8 | −0.117802 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.86567e9 | −0.828777 | ||||||||
\(683\) | −1.43057e10 | −1.71806 | −0.859029 | − | 0.511927i | \(-0.828932\pi\) | ||||
−0.859029 | + | 0.511927i | \(0.828932\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.53659e8 | 0.0777024 | ||||||||
\(686\) | 3.08501e9 | 0.364856 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.81166e8 | 0.0212088 | ||||||||
\(689\) | −8.38527e8 | −0.0976675 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.07877e10 | −1.24382 | −0.621909 | − | 0.783089i | \(-0.713643\pi\) | ||||
−0.621909 | + | 0.783089i | \(0.713643\pi\) | |||||||
\(692\) | −7.11157e9 | −0.815820 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.28201e9 | 0.486283 | ||||||||
\(695\) | −1.55242e9 | −0.175414 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.25130e10 | −1.39974 | ||||||||
\(698\) | −5.36854e8 | −0.0597533 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.63399e9 | −0.620830 | ||||||||
\(701\) | 3.29304e9 | 0.361064 | 0.180532 | − | 0.983569i | \(-0.442218\pi\) | ||||
0.180532 | + | 0.983569i | \(0.442218\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.12497e10 | 1.22123 | ||||||||
\(704\) | −4.29759e9 | −0.464216 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.89939e8 | 0.0951796 | ||||||||
\(707\) | 4.90659e9 | 0.522170 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.66010e9 | 0.491059 | 0.245530 | − | 0.969389i | \(-0.421038\pi\) | ||||
0.245530 | + | 0.969389i | \(0.421038\pi\) | |||||||
\(710\) | 3.74612e7 | 0.00392805 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.07690e9 | −0.319473 | ||||||||
\(713\) | −6.59338e9 | −0.681232 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.06386e7 | −0.00927346 | ||||||||
\(716\) | −1.90566e9 | −0.194021 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.19440e9 | 0.624544 | ||||||||
\(719\) | 2.36164e9 | 0.236954 | 0.118477 | − | 0.992957i | \(-0.462199\pi\) | ||||
0.118477 | + | 0.992957i | \(0.462199\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.67808e9 | −0.266103 | ||||||||
\(722\) | 1.03531e9 | 0.102374 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.11140e9 | −0.598488 | ||||||||
\(725\) | 2.02831e9 | 0.197675 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.97525e9 | 0.287180 | 0.143590 | − | 0.989637i | \(-0.454135\pi\) | ||||
0.143590 | + | 0.989637i | \(0.454135\pi\) | |||||||
\(728\) | −3.65790e8 | −0.0351376 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.16164e8 | −0.0110520 | ||||||||
\(731\) | 6.58201e8 | 0.0623229 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.37632e10 | −1.29079 | −0.645397 | − | 0.763848i | \(-0.723308\pi\) | ||||
−0.645397 | + | 0.763848i | \(0.723308\pi\) | |||||||
\(734\) | −1.54617e9 | −0.144318 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.43848e9 | 0.317903 | ||||||||
\(737\) | 2.58796e10 | 2.38134 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.14115e10 | 1.04013 | 0.520064 | − | 0.854127i | \(-0.325908\pi\) | ||||
0.520064 | + | 0.854127i | \(0.325908\pi\) | |||||||
\(740\) | 9.79266e8 | 0.0888362 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.46400e9 | −0.311290 | ||||||||
\(743\) | −5.94931e9 | −0.532115 | −0.266057 | − | 0.963957i | \(-0.585721\pi\) | ||||
−0.266057 | + | 0.963957i | \(0.585721\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.25333e9 | 0.111050 | ||||||||
\(746\) | 5.25509e9 | 0.463441 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.52449e10 | −2.20556 | ||||||||
\(749\) | 7.15422e9 | 0.622123 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.58856e9 | −0.653762 | −0.326881 | − | 0.945066i | \(-0.605998\pi\) | ||||
−0.326881 | + | 0.945066i | \(0.605998\pi\) | |||||||
\(752\) | −8.26865e9 | −0.709043 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.17164e7 | 0.00524326 | ||||||||
\(755\) | 4.51569e8 | 0.0381865 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.43522e10 | −1.20250 | −0.601248 | − | 0.799063i | \(-0.705329\pi\) | ||||
−0.601248 | + | 0.799063i | \(0.705329\pi\) | |||||||
\(758\) | 6.58698e9 | 0.549343 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.37538e8 | 0.0692081 | ||||||||
\(761\) | 5.32785e9 | 0.438233 | 0.219117 | − | 0.975699i | \(-0.429682\pi\) | ||||
0.219117 | + | 0.975699i | \(0.429682\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.30260e9 | −0.432169 | ||||||||
\(764\) | −9.87614e9 | −0.801236 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.39602e9 | 0.594563 | ||||||||
\(767\) | −1.24516e8 | −0.00996419 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.89088e9 | 0.705022 | 0.352511 | − | 0.935808i | \(-0.385328\pi\) | ||||
0.352511 | + | 0.935808i | \(0.385328\pi\) | |||||||
\(770\) | −3.74433e8 | −0.0295567 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.23517e9 | 0.722411 | ||||||||
\(773\) | 2.40093e10 | 1.86961 | 0.934807 | − | 0.355155i | \(-0.115572\pi\) | ||||
0.934807 | + | 0.355155i | \(0.115572\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.40327e10 | 1.85458 | ||||||||
\(776\) | −7.92071e9 | −0.608483 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.42959e9 | 0.489502 | ||||||||
\(779\) | 1.08501e10 | 0.822343 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.08917e9 | 0.156926 | ||||||||
\(782\) | 3.24331e9 | 0.242529 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.41380e9 | −0.327120 | ||||||||
\(785\) | −6.66525e8 | −0.0491782 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.74554e10 | 1.27649 | 0.638246 | − | 0.769833i | \(-0.279660\pi\) | ||||
0.638246 | + | 0.769833i | \(0.279660\pi\) | |||||||
\(788\) | −2.17095e10 | −1.58055 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.11298e8 | 0.0224637 | ||||||||
\(791\) | −1.20552e10 | −0.866075 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.14823e8 | 0.0152976 | ||||||||
\(794\) | −6.85667e9 | −0.486118 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.63629e8 | 0.0114991 | ||||||||
\(797\) | 2.13622e10 | 1.49466 | 0.747329 | − | 0.664454i | \(-0.231336\pi\) | ||||
0.747329 | + | 0.664454i | \(0.231336\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.00413e10 | −2.08355 | ||||||||
\(800\) | −1.25331e10 | −0.865456 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.65363e9 | −0.250101 | ||||||||
\(803\) | −6.47831e9 | −0.441527 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.59583e8 | −0.0242948 | ||||||||
\(806\) | 7.31254e8 | 0.0491921 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.12770e9 | 0.475346 | ||||||||
\(809\) | 8.12776e9 | 0.539698 | 0.269849 | − | 0.962903i | \(-0.413026\pi\) | ||||
0.269849 | + | 0.962903i | \(0.413026\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.71482e9 | −0.310379 | −0.155190 | − | 0.987885i | \(-0.549599\pi\) | ||||
−0.155190 | + | 0.987885i | \(0.549599\pi\) | |||||||
\(812\) | −1.90578e9 | −0.124919 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.30601e9 | −0.474783 | ||||||||
\(815\) | 1.66513e9 | 0.107745 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.70730e8 | −0.0366145 | ||||||||
\(818\) | −3.67841e9 | −0.234976 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.44483e8 | 0.0598199 | ||||||||
\(821\) | 1.97226e10 | 1.24383 | 0.621917 | − | 0.783083i | \(-0.286354\pi\) | ||||
0.621917 | + | 0.783083i | \(0.286354\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.20133e9 | 0.0751215 | 0.0375608 | − | 0.999294i | \(-0.488041\pi\) | ||||
0.0375608 | + | 0.999294i | \(0.488041\pi\) | |||||||
\(824\) | −3.89040e9 | −0.242242 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.14383e8 | −0.0317583 | ||||||||
\(827\) | −8.23556e9 | −0.506319 | −0.253159 | − | 0.967425i | \(-0.581470\pi\) | ||||
−0.253159 | + | 0.967425i | \(0.581470\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.37482e9 | 0.205736 | 0.102868 | − | 0.994695i | \(-0.467198\pi\) | ||||
0.102868 | + | 0.994695i | \(0.467198\pi\) | |||||||
\(830\) | 8.57067e8 | 0.0520285 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.57731e8 | 0.0275536 | ||||||||
\(833\) | −1.60360e10 | −0.961255 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.67020e8 | 0.0574821 | ||||||||
\(836\) | 2.18900e10 | 1.29576 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.10735e9 | 0.182405 | ||||||||
\(839\) | −2.19151e10 | −1.28108 | −0.640540 | − | 0.767925i | \(-0.721289\pi\) | ||||
−0.640540 | + | 0.767925i | \(0.721289\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.65638e10 | −0.960225 | ||||||||
\(842\) | −6.60375e9 | −0.381240 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.42305e10 | 1.38728 | ||||||||
\(845\) | −1.63836e9 | −0.0934140 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.32297e9 | −0.470637 | ||||||||
\(848\) | 1.49545e10 | 0.842145 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.18217e10 | −0.660260 | ||||||||
\(851\) | −7.01627e9 | −0.390259 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.68331e10 | −1.48030 | −0.740148 | − | 0.672444i | \(-0.765245\pi\) | ||||
−0.740148 | + | 0.672444i | \(0.765245\pi\) | |||||||
\(854\) | 8.87446e8 | 0.0487573 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.03928e10 | 0.566336 | ||||||||
\(857\) | 3.79081e9 | 0.205731 | 0.102865 | − | 0.994695i | \(-0.467199\pi\) | ||||
0.102865 | + | 0.994695i | \(0.467199\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.08182e10 | −0.582342 | −0.291171 | − | 0.956671i | \(-0.594045\pi\) | ||||
−0.291171 | + | 0.956671i | \(0.594045\pi\) | |||||||
\(860\) | −4.96810e7 | −0.00266346 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.50053e9 | −0.345679 | ||||||||
\(863\) | 2.34587e10 | 1.24241 | 0.621206 | − | 0.783647i | \(-0.286643\pi\) | ||||
0.621206 | + | 0.783647i | \(0.286643\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.65441e9 | 0.0869133 | ||||||||
\(866\) | 7.12655e9 | 0.372878 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.25809e10 | −1.17198 | ||||||||
\(869\) | 1.73607e10 | 0.897426 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.75640e9 | −0.141344 | ||||||||
\(872\) | −7.70299e9 | −0.393415 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.81229e9 | −0.142485 | ||||||||
\(875\) | 2.63301e9 | 0.132869 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.42071e10 | 1.71245 | 0.856224 | − | 0.516605i | \(-0.172805\pi\) | ||||
0.856224 | + | 0.516605i | \(0.172805\pi\) | |||||||
\(878\) | −3.21390e9 | −0.160251 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.61647e9 | 0.0799611 | ||||||||
\(881\) | 5.54512e9 | 0.273209 | 0.136605 | − | 0.990626i | \(-0.456381\pi\) | ||||
0.136605 | + | 0.990626i | \(0.456381\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.95899e10 | 0.957568 | 0.478784 | − | 0.877933i | \(-0.341078\pi\) | ||||
0.478784 | + | 0.877933i | \(0.341078\pi\) | |||||||
\(884\) | 2.68881e9 | 0.130911 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.74707e9 | −0.0843904 | ||||||||
\(887\) | −2.41962e10 | −1.16416 | −0.582081 | − | 0.813131i | \(-0.697762\pi\) | ||||
−0.582081 | + | 0.813131i | \(0.697762\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.00695e9 | −0.429954 | ||||||||
\(890\) | 3.35460e8 | 0.0159506 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.32110e10 | 1.09501 | ||||||||
\(893\) | 2.60489e10 | 1.22408 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.43324e8 | 0.0206700 | ||||||||
\(896\) | 1.52423e10 | 0.707902 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.92254e9 | 0.226841 | ||||||||
\(899\) | 8.12941e9 | 0.373164 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.43320e10 | 2.47468 | ||||||||
\(902\) | −7.04650e9 | −0.319706 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.75123e10 | −0.788412 | ||||||||
\(905\) | 1.42173e9 | 0.0637599 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.77861e10 | −0.791510 | −0.395755 | − | 0.918356i | \(-0.629517\pi\) | ||||
−0.395755 | + | 0.918356i | \(0.629517\pi\) | |||||||
\(908\) | 2.11125e10 | 0.935919 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.98804e7 | 0.00175434 | ||||||||
\(911\) | 3.79625e10 | 1.66357 | 0.831783 | − | 0.555101i | \(-0.187320\pi\) | ||||
0.831783 | + | 0.555101i | \(0.187320\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.77976e10 | 2.07854 | ||||||||
\(914\) | −1.01560e9 | −0.0439956 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.14524e10 | −0.492337 | ||||||||
\(917\) | 1.09176e10 | 0.467556 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.00064e10 | −1.70030 | −0.850149 | − | 0.526543i | \(-0.823488\pi\) | ||||
−0.850149 | + | 0.526543i | \(0.823488\pi\) | |||||||
\(920\) | −5.22359e8 | −0.0221163 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.01334e10 | 0.425791 | ||||||||
\(923\) | −2.22514e8 | −0.00931434 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.55740e10 | 1.06244 | ||||||||
\(926\) | 1.19311e10 | 0.493790 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.23953e9 | −0.174140 | ||||||||
\(929\) | 4.55114e10 | 1.86237 | 0.931183 | − | 0.364552i | \(-0.118778\pi\) | ||||
0.931183 | + | 0.364552i | \(0.118778\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.39049e10 | 0.564735 | ||||||||
\(932\) | −2.23994e10 | −0.906319 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.12667e10 | 0.452461 | ||||||||
\(935\) | 5.87288e9 | 0.234969 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.78655e9 | 0.150368 | 0.0751839 | − | 0.997170i | \(-0.476046\pi\) | ||||
0.0751839 | + | 0.997170i | \(0.476046\pi\) | |||||||
\(938\) | −1.13868e10 | −0.450498 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.26751e9 | 0.0890435 | ||||||||
\(941\) | 9.78869e9 | 0.382966 | 0.191483 | − | 0.981496i | \(-0.438670\pi\) | ||||
0.191483 | + | 0.981496i | \(0.438670\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.76705e9 | −0.262790 | ||||||||
\(944\) | 2.22065e9 | 0.0859170 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.70655e8 | 0.0142348 | ||||||||
\(947\) | −3.55199e10 | −1.35909 | −0.679543 | − | 0.733635i | \(-0.737822\pi\) | ||||
−0.679543 | + | 0.733635i | \(0.737822\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.89997e8 | 0.0262069 | ||||||||
\(950\) | 1.02507e10 | 0.387901 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.37012e10 | 0.890309 | ||||||||
\(953\) | 1.87406e9 | 0.0701389 | 0.0350695 | − | 0.999385i | \(-0.488835\pi\) | ||||
0.0350695 | + | 0.999385i | \(0.488835\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.29755e9 | 0.0853596 | ||||||||
\(956\) | 1.02314e10 | 0.378733 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.05767e10 | 0.388661 | ||||||||
\(959\) | −1.60394e10 | −0.587251 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.88096e10 | 2.50102 | ||||||||
\(962\) | 7.78154e8 | 0.0281808 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.51056e10 | 0.902612 | ||||||||
\(965\) | −2.14843e9 | −0.0769620 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.52830e10 | 0.899158 | 0.449579 | − | 0.893241i | \(-0.351574\pi\) | ||||
0.449579 | + | 0.893241i | \(0.351574\pi\) | |||||||
\(968\) | −1.20906e10 | −0.428434 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.63559e8 | 0.0303802 | ||||||||
\(971\) | −2.33470e10 | −0.818396 | −0.409198 | − | 0.912446i | \(-0.634192\pi\) | ||||
−0.409198 | + | 0.912446i | \(0.634192\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.80932e10 | 1.32572 | ||||||||
\(974\) | −1.62466e10 | −0.563385 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.83121e9 | −0.131905 | ||||||||
\(977\) | 3.73874e9 | 0.128261 | 0.0641304 | − | 0.997942i | \(-0.479573\pi\) | ||||
0.0641304 | + | 0.997942i | \(0.479573\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.87082e10 | 0.637225 | ||||||||
\(980\) | 1.21040e9 | 0.0410806 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.51716e9 | −0.152221 | ||||||||
\(983\) | 4.06366e10 | 1.36452 | 0.682261 | − | 0.731109i | \(-0.260997\pi\) | ||||
0.682261 | + | 0.731109i | \(0.260997\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.05041e9 | 0.168384 | ||||||||
\(986\) | −3.99889e9 | −0.132853 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.33148e9 | −0.0769099 | ||||||||
\(989\) | 3.55956e8 | 0.0117006 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.46369e10 | 0.804134 | 0.402067 | − | 0.915610i | \(-0.368292\pi\) | ||||
0.402067 | + | 0.915610i | \(0.368292\pi\) | |||||||
\(992\) | −5.02325e10 | −1.63378 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.19219e8 | −0.0296870 | ||||||||
\(995\) | −3.80660e7 | −0.00122506 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.08445e10 | −0.346558 | −0.173279 | − | 0.984873i | \(-0.555436\pi\) | ||||
−0.173279 | + | 0.984873i | \(0.555436\pi\) | |||||||
\(998\) | −9.56186e9 | −0.304499 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 531.8.a.c.1.10 | 17 | ||
3.2 | odd | 2 | 177.8.a.c.1.8 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.c.1.8 | ✓ | 17 | 3.2 | odd | 2 | ||
531.8.a.c.1.10 | 17 | 1.1 | even | 1 | trivial |