Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,8,Mod(67,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.67");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.c (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: | \(30.6137324974\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{1969})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 493x^{2} + 492x + 242064 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.1 | ||
Root | \(11.3434 + 19.6473i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.79 |
Dual form | 98.8.c.k.67.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | + | 6.92820i | −0.353553 | + | 0.612372i | ||||
\(3\) | −4.68671 | − | 8.11762i | −0.100217 | − | 0.173582i | 0.811557 | − | 0.584274i | \(-0.198621\pi\) |
−0.911774 | + | 0.410692i | \(0.865287\pi\) | |||||||
\(4\) | −32.0000 | − | 55.4256i | −0.250000 | − | 0.433013i | ||||
\(5\) | 231.180 | − | 400.416i | 0.827096 | − | 1.43257i | −0.0732108 | − | 0.997316i | \(-0.523325\pi\) |
0.900307 | − | 0.435256i | \(-0.143342\pi\) | |||||||
\(6\) | 74.9873 | 0.141729 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 1049.57 | − | 1817.91i | 0.479913 | − | 0.831234i | ||||
\(10\) | 1849.44 | + | 3203.33i | 0.584845 | + | 1.01298i | ||||
\(11\) | −1940.53 | − | 3361.09i | −0.439587 | − | 0.761387i | 0.558070 | − | 0.829794i | \(-0.311542\pi\) |
−0.997658 | + | 0.0684065i | \(0.978209\pi\) | |||||||
\(12\) | −299.949 | + | 519.527i | −0.0501087 | + | 0.0867909i | ||||
\(13\) | 11585.6 | 1.46257 | 0.731284 | − | 0.682073i | \(-0.238922\pi\) | ||||
0.731284 | + | 0.682073i | \(0.238922\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4333.90 | −0.331558 | ||||||||
\(16\) | −2048.00 | + | 3547.24i | −0.125000 | + | 0.216506i | ||||
\(17\) | −7621.20 | − | 13200.3i | −0.376229 | − | 0.651647i | 0.614281 | − | 0.789087i | \(-0.289446\pi\) |
−0.990510 | + | 0.137440i | \(0.956113\pi\) | |||||||
\(18\) | 8396.56 | + | 14543.3i | 0.339350 | + | 0.587771i | ||||
\(19\) | −16230.9 | + | 28112.7i | −0.542880 | + | 0.940297i | 0.455857 | + | 0.890053i | \(0.349333\pi\) |
−0.998737 | + | 0.0502433i | \(0.984000\pi\) | |||||||
\(20\) | −29591.1 | −0.827096 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 31048.4 | 0.621670 | ||||||||
\(23\) | −28073.1 | + | 48623.9i | −0.481108 | + | 0.833303i | −0.999765 | − | 0.0216794i | \(-0.993099\pi\) |
0.518657 | + | 0.854982i | \(0.326432\pi\) | |||||||
\(24\) | −2399.59 | − | 4156.22i | −0.0354322 | − | 0.0613704i | ||||
\(25\) | −67826.2 | − | 117478.i | −0.868176 | − | 1.50372i | ||||
\(26\) | −46342.3 | + | 80267.2i | −0.517096 | + | 0.895636i | ||||
\(27\) | −40175.8 | −0.392818 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −26442.0 | −0.201326 | −0.100663 | − | 0.994921i | \(-0.532096\pi\) | ||||
−0.100663 | + | 0.994921i | \(0.532096\pi\) | |||||||
\(30\) | 17335.6 | − | 30026.1i | 0.117223 | − | 0.203037i | ||||
\(31\) | −22724.1 | − | 39359.3i | −0.137000 | − | 0.237291i | 0.789360 | − | 0.613931i | \(-0.210413\pi\) |
−0.926360 | + | 0.376640i | \(0.877079\pi\) | |||||||
\(32\) | −16384.0 | − | 28377.9i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −18189.3 | + | 31504.9i | −0.0881086 | + | 0.152609i | ||||
\(34\) | 121939. | 0.532068 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −134345. | −0.479913 | ||||||||
\(37\) | 277622. | − | 480856.i | 0.901049 | − | 1.56066i | 0.0749145 | − | 0.997190i | \(-0.476132\pi\) |
0.826135 | − | 0.563473i | \(-0.190535\pi\) | |||||||
\(38\) | −129847. | − | 224902.i | −0.383874 | − | 0.664890i | ||||
\(39\) | −54298.2 | − | 94047.3i | −0.146575 | − | 0.253875i | ||||
\(40\) | 118364. | − | 205013.i | 0.292423 | − | 0.506491i | ||||
\(41\) | −306385. | −0.694264 | −0.347132 | − | 0.937816i | \(-0.612844\pi\) | ||||
−0.347132 | + | 0.937816i | \(0.612844\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 780755. | 1.49753 | 0.748765 | − | 0.662836i | \(-0.230647\pi\) | ||||
0.748765 | + | 0.662836i | \(0.230647\pi\) | |||||||
\(44\) | −124194. | + | 215110.i | −0.219794 | + | 0.380694i | ||||
\(45\) | −485280. | − | 840529.i | −0.793868 | − | 1.37502i | ||||
\(46\) | −224584. | − | 388992.i | −0.340194 | − | 0.589234i | ||||
\(47\) | −265622. | + | 460070.i | −0.373182 | + | 0.646370i | −0.990053 | − | 0.140694i | \(-0.955067\pi\) |
0.616871 | + | 0.787064i | \(0.288400\pi\) | |||||||
\(48\) | 38393.5 | 0.0501087 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.08522e6 | 1.22779 | ||||||||
\(51\) | −71436.6 | + | 123732.i | −0.0754094 | + | 0.130613i | ||||
\(52\) | −370738. | − | 642138.i | −0.365642 | − | 0.633310i | ||||
\(53\) | 181796. | + | 314880.i | 0.167733 | + | 0.290523i | 0.937623 | − | 0.347655i | \(-0.113022\pi\) |
−0.769889 | + | 0.638178i | \(0.779689\pi\) | |||||||
\(54\) | 160703. | − | 278346.i | 0.138882 | − | 0.240551i | ||||
\(55\) | −1.79445e6 | −1.45432 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 304277. | 0.217624 | ||||||||
\(58\) | 105768. | − | 183195.i | 0.0711796 | − | 0.123287i | ||||
\(59\) | −1.07048e6 | − | 1.85412e6i | −0.678570 | − | 1.17532i | −0.975411 | − | 0.220392i | \(-0.929266\pi\) |
0.296841 | − | 0.954927i | \(-0.404067\pi\) | |||||||
\(60\) | 138685. | + | 240209.i | 0.0828895 | + | 0.143569i | ||||
\(61\) | 444412. | − | 769744.i | 0.250687 | − | 0.434202i | −0.713028 | − | 0.701135i | \(-0.752677\pi\) |
0.963715 | + | 0.266933i | \(0.0860103\pi\) | |||||||
\(62\) | 363586. | 0.193747 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 2.67836e6 | − | 4.63905e6i | 1.20968 | − | 2.09523i | ||||
\(66\) | −145515. | − | 252039.i | −0.0623022 | − | 0.107911i | ||||
\(67\) | −2.17270e6 | − | 3.76323e6i | −0.882549 | − | 1.52862i | −0.848498 | − | 0.529199i | \(-0.822492\pi\) |
−0.0340512 | − | 0.999420i | \(-0.510841\pi\) | |||||||
\(68\) | −487757. | + | 844819.i | −0.188114 | + | 0.325824i | ||||
\(69\) | 526281. | 0.192862 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 663207. | 0.219910 | 0.109955 | − | 0.993937i | \(-0.464929\pi\) | ||||
0.109955 | + | 0.993937i | \(0.464929\pi\) | |||||||
\(72\) | 537380. | − | 930769.i | 0.169675 | − | 0.293885i | ||||
\(73\) | 671009. | + | 1.16222e6i | 0.201882 | + | 0.349671i | 0.949135 | − | 0.314870i | \(-0.101961\pi\) |
−0.747252 | + | 0.664540i | \(0.768627\pi\) | |||||||
\(74\) | 2.22098e6 | + | 3.84685e6i | 0.637138 | + | 1.10356i | ||||
\(75\) | −635763. | + | 1.10117e6i | −0.174013 | + | 0.301399i | ||||
\(76\) | 2.07755e6 | 0.542880 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 868771. | 0.207288 | ||||||||
\(79\) | −3.52917e6 | + | 6.11270e6i | −0.805337 | + | 1.39488i | 0.110727 | + | 0.993851i | \(0.464682\pi\) |
−0.916063 | + | 0.401033i | \(0.868651\pi\) | |||||||
\(80\) | 946915. | + | 1.64010e6i | 0.206774 | + | 0.358143i | ||||
\(81\) | −2.10712e6 | − | 3.64963e6i | −0.440546 | − | 0.763048i | ||||
\(82\) | 1.22554e6 | − | 2.12270e6i | 0.245459 | − | 0.425148i | ||||
\(83\) | −6.60874e6 | −1.26866 | −0.634330 | − | 0.773063i | \(-0.718724\pi\) | ||||
−0.634330 | + | 0.773063i | \(0.718724\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.04748e6 | −1.24471 | ||||||||
\(86\) | −3.12302e6 | + | 5.40923e6i | −0.529456 | + | 0.917046i | ||||
\(87\) | 123926. | + | 214646.i | 0.0201764 | + | 0.0349466i | ||||
\(88\) | −993549. | − | 1.72088e6i | −0.155417 | − | 0.269191i | ||||
\(89\) | −2.66499e6 | + | 4.61590e6i | −0.400710 | + | 0.694050i | −0.993812 | − | 0.111077i | \(-0.964570\pi\) |
0.593102 | + | 0.805128i | \(0.297903\pi\) | |||||||
\(90\) | 7.76448e6 | 1.12270 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.59335e6 | 0.481108 | ||||||||
\(93\) | −213002. | + | 368931.i | −0.0274596 | + | 0.0475614i | ||||
\(94\) | −2.12497e6 | − | 3.68056e6i | −0.263880 | − | 0.457053i | ||||
\(95\) | 7.50452e6 | + | 1.29982e7i | 0.898029 | + | 1.55543i | ||||
\(96\) | −153574. | + | 265998.i | −0.0177161 | + | 0.0306852i | ||||
\(97\) | 2.09810e6 | 0.233413 | 0.116707 | − | 0.993166i | \(-0.462766\pi\) | ||||
0.116707 | + | 0.993166i | \(0.462766\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.14686e6 | −0.843854 | ||||||||
\(100\) | −4.34088e6 | + | 7.51862e6i | −0.434088 | + | 0.751862i | ||||
\(101\) | 9.77690e6 | + | 1.69341e7i | 0.944227 | + | 1.63545i | 0.757291 | + | 0.653078i | \(0.226522\pi\) |
0.186936 | + | 0.982372i | \(0.440144\pi\) | |||||||
\(102\) | −571493. | − | 989855.i | −0.0533225 | − | 0.0923573i | ||||
\(103\) | −4.47546e6 | + | 7.75173e6i | −0.403560 | + | 0.698986i | −0.994153 | − | 0.107984i | \(-0.965561\pi\) |
0.590593 | + | 0.806970i | \(0.298894\pi\) | |||||||
\(104\) | 5.93181e6 | 0.517096 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.90874e6 | −0.237211 | ||||||||
\(107\) | 6.97547e6 | − | 1.20819e7i | 0.550466 | − | 0.953435i | −0.447775 | − | 0.894146i | \(-0.647783\pi\) |
0.998241 | − | 0.0592886i | \(-0.0188832\pi\) | |||||||
\(108\) | 1.28562e6 | + | 2.22677e6i | 0.0982044 | + | 0.170095i | ||||
\(109\) | −2.92147e6 | − | 5.06014e6i | −0.216077 | − | 0.374257i | 0.737528 | − | 0.675317i | \(-0.235993\pi\) |
−0.953605 | + | 0.301060i | \(0.902660\pi\) | |||||||
\(110\) | 7.17778e6 | − | 1.24323e7i | 0.514181 | − | 0.890587i | ||||
\(111\) | −5.20454e6 | −0.361203 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.20951e7 | −0.788562 | −0.394281 | − | 0.918990i | \(-0.629006\pi\) | ||||
−0.394281 | + | 0.918990i | \(0.629006\pi\) | |||||||
\(114\) | −1.21711e6 | + | 2.10810e6i | −0.0769419 | + | 0.133267i | ||||
\(115\) | 1.29799e7 | + | 2.24818e7i | 0.795844 | + | 1.37844i | ||||
\(116\) | 846143. | + | 1.46556e6i | 0.0503316 | + | 0.0871769i | ||||
\(117\) | 1.21599e7 | − | 2.10615e7i | 0.701905 | − | 1.21574i | ||||
\(118\) | 1.71276e7 | 0.959644 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.21896e6 | −0.117223 | ||||||||
\(121\) | 2.21231e6 | − | 3.83183e6i | 0.113526 | − | 0.196634i | ||||
\(122\) | 3.55529e6 | + | 6.15795e6i | 0.177262 | + | 0.307027i | ||||
\(123\) | 1.43594e6 | + | 2.48712e6i | 0.0695774 | + | 0.120512i | ||||
\(124\) | −1.45434e6 | + | 2.51899e6i | −0.0685000 | + | 0.118646i | ||||
\(125\) | −2.65984e7 | −1.21807 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −325760. | −0.0141119 | −0.00705594 | − | 0.999975i | \(-0.502246\pi\) | ||||
−0.00705594 | + | 0.999975i | \(0.502246\pi\) | |||||||
\(128\) | −1.04858e6 | + | 1.81619e6i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −3.65917e6 | − | 6.33787e6i | −0.150079 | − | 0.259944i | ||||
\(130\) | 2.14269e7 | + | 3.71124e7i | 0.855376 | + | 1.48155i | ||||
\(131\) | 3.19024e6 | − | 5.52566e6i | 0.123986 | − | 0.214751i | −0.797350 | − | 0.603517i | \(-0.793765\pi\) |
0.921336 | + | 0.388767i | \(0.127099\pi\) | |||||||
\(132\) | 2.32824e6 | 0.0881086 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.47633e7 | 1.24811 | ||||||||
\(135\) | −9.28785e6 | + | 1.60870e7i | −0.324898 | + | 0.562740i | ||||
\(136\) | −3.90205e6 | − | 6.75855e6i | −0.133017 | − | 0.230392i | ||||
\(137\) | −2.31162e6 | − | 4.00384e6i | −0.0768059 | − | 0.133032i | 0.825064 | − | 0.565039i | \(-0.191139\pi\) |
−0.901870 | + | 0.432007i | \(0.857806\pi\) | |||||||
\(138\) | −2.10512e6 | + | 3.64618e6i | −0.0681869 | + | 0.118103i | ||||
\(139\) | 3.55394e7 | 1.12243 | 0.561214 | − | 0.827671i | \(-0.310335\pi\) | ||||
0.561214 | + | 0.827671i | \(0.310335\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.97956e6 | 0.149597 | ||||||||
\(142\) | −2.65283e6 | + | 4.59483e6i | −0.0777499 | + | 0.134667i | ||||
\(143\) | −2.24821e7 | − | 3.89401e7i | −0.642926 | − | 1.11358i | ||||
\(144\) | 4.29904e6 | + | 7.44615e6i | 0.119978 | + | 0.207808i | ||||
\(145\) | −6.11286e6 | + | 1.05878e7i | −0.166516 | + | 0.288415i | ||||
\(146\) | −1.07362e7 | −0.285505 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.55357e7 | −0.901049 | ||||||||
\(149\) | −5.08540e6 | + | 8.80816e6i | −0.125943 | + | 0.218139i | −0.922101 | − | 0.386949i | \(-0.873529\pi\) |
0.796158 | + | 0.605088i | \(0.206862\pi\) | |||||||
\(150\) | −5.08611e6 | − | 8.80940e6i | −0.123046 | − | 0.213121i | ||||
\(151\) | −1.22636e7 | − | 2.12412e7i | −0.289867 | − | 0.502065i | 0.683911 | − | 0.729566i | \(-0.260278\pi\) |
−0.973778 | + | 0.227501i | \(0.926945\pi\) | |||||||
\(152\) | −8.31021e6 | + | 1.43937e7i | −0.191937 | + | 0.332445i | ||||
\(153\) | −3.19959e7 | −0.722228 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.10135e7 | −0.453249 | ||||||||
\(156\) | −3.47509e6 | + | 6.01902e6i | −0.0732874 | + | 0.126938i | ||||
\(157\) | −6.36893e6 | − | 1.10313e7i | −0.131346 | − | 0.227498i | 0.792849 | − | 0.609418i | \(-0.208597\pi\) |
−0.924196 | + | 0.381919i | \(0.875263\pi\) | |||||||
\(158\) | −2.82333e7 | − | 4.89016e7i | −0.569459 | − | 0.986332i | ||||
\(159\) | 1.70405e6 | − | 2.95151e6i | 0.0336196 | − | 0.0582309i | ||||
\(160\) | −1.51506e7 | −0.292423 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.37139e7 | 0.623026 | ||||||||
\(163\) | 4.25765e7 | − | 7.37447e7i | 0.770041 | − | 1.33375i | −0.167499 | − | 0.985872i | \(-0.553569\pi\) |
0.937540 | − | 0.347878i | \(-0.113098\pi\) | |||||||
\(164\) | 9.80433e6 | + | 1.69816e7i | 0.173566 | + | 0.300625i | ||||
\(165\) | 8.41004e6 | + | 1.45666e7i | 0.145749 | + | 0.252444i | ||||
\(166\) | 2.64349e7 | − | 4.57867e7i | 0.448539 | − | 0.776892i | ||||
\(167\) | 3.74260e6 | 0.0621822 | 0.0310911 | − | 0.999517i | \(-0.490102\pi\) | ||||
0.0310911 | + | 0.999517i | \(0.490102\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.14770e7 | 1.13910 | ||||||||
\(170\) | 2.81899e7 | − | 4.88264e7i | 0.440071 | − | 0.762226i | ||||
\(171\) | 3.40709e7 | + | 5.90124e7i | 0.521071 | + | 0.902521i | ||||
\(172\) | −2.49842e7 | − | 4.32738e7i | −0.374382 | − | 0.648449i | ||||
\(173\) | −3.63432e7 | + | 6.29483e7i | −0.533657 | + | 0.924321i | 0.465570 | + | 0.885011i | \(0.345849\pi\) |
−0.999227 | + | 0.0393101i | \(0.987484\pi\) | |||||||
\(174\) | −1.98281e6 | −0.0285338 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.58968e7 | 0.219794 | ||||||||
\(177\) | −1.00340e7 | + | 1.73794e7i | −0.136009 | + | 0.235575i | ||||
\(178\) | −2.13199e7 | − | 3.69272e7i | −0.283345 | − | 0.490768i | ||||
\(179\) | −5.12224e7 | − | 8.87198e7i | −0.667536 | − | 1.15621i | −0.978591 | − | 0.205814i | \(-0.934016\pi\) |
0.311056 | − | 0.950392i | \(-0.399317\pi\) | |||||||
\(180\) | −3.10579e7 | + | 5.37939e7i | −0.396934 | + | 0.687510i | ||||
\(181\) | −4.79161e6 | −0.0600630 | −0.0300315 | − | 0.999549i | \(-0.509561\pi\) | ||||
−0.0300315 | + | 0.999549i | \(0.509561\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.33131e6 | −0.100493 | ||||||||
\(184\) | −1.43734e7 | + | 2.48955e7i | −0.170097 | + | 0.294617i | ||||
\(185\) | −1.28362e8 | − | 2.22329e8i | −1.49051 | − | 2.58164i | ||||
\(186\) | −1.70402e6 | − | 2.95145e6i | −0.0194169 | − | 0.0336310i | ||||
\(187\) | −2.95782e7 | + | 5.12310e7i | −0.330771 | + | 0.572911i | ||||
\(188\) | 3.39996e7 | 0.373182 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.20072e8 | −1.27000 | ||||||||
\(191\) | −1.30086e7 | + | 2.25316e7i | −0.135087 | + | 0.233978i | −0.925631 | − | 0.378428i | \(-0.876465\pi\) |
0.790543 | + | 0.612406i | \(0.209798\pi\) | |||||||
\(192\) | −1.22859e6 | − | 2.12798e6i | −0.0125272 | − | 0.0216977i | ||||
\(193\) | 3.79163e7 | + | 6.56730e7i | 0.379643 | + | 0.657561i | 0.991010 | − | 0.133786i | \(-0.0427134\pi\) |
−0.611367 | + | 0.791347i | \(0.709380\pi\) | |||||||
\(194\) | −8.39241e6 | + | 1.45361e7i | −0.0825241 | + | 0.142936i | ||||
\(195\) | −5.02107e7 | −0.484926 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.19192e8 | 1.11075 | 0.555374 | − | 0.831601i | \(-0.312575\pi\) | ||||
0.555374 | + | 0.831601i | \(0.312575\pi\) | |||||||
\(198\) | 3.25875e7 | − | 5.64431e7i | 0.298347 | − | 0.516753i | ||||
\(199\) | 3.36331e7 | + | 5.82543e7i | 0.302539 | + | 0.524013i | 0.976710 | − | 0.214562i | \(-0.0688324\pi\) |
−0.674171 | + | 0.738575i | \(0.735499\pi\) | |||||||
\(200\) | −3.47270e7 | − | 6.01490e7i | −0.306946 | − | 0.531647i | ||||
\(201\) | −2.03657e7 | + | 3.52743e7i | −0.176894 | + | 0.306389i | ||||
\(202\) | −1.56430e8 | −1.33534 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 9.14389e6 | 0.0754094 | ||||||||
\(205\) | −7.08303e7 | + | 1.22682e8i | −0.574223 | + | 0.994583i | ||||
\(206\) | −3.58037e7 | − | 6.20139e7i | −0.285360 | − | 0.494258i | ||||
\(207\) | 5.89292e7 | + | 1.02068e8i | 0.461779 | + | 0.799825i | ||||
\(208\) | −2.37273e7 | + | 4.10968e7i | −0.182821 | + | 0.316655i | ||||
\(209\) | 1.25986e8 | 0.954573 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.32421e8 | 1.70328 | 0.851641 | − | 0.524126i | \(-0.175608\pi\) | ||||
0.851641 | + | 0.524126i | \(0.175608\pi\) | |||||||
\(212\) | 1.16350e7 | − | 2.01523e7i | 0.0838667 | − | 0.145261i | ||||
\(213\) | −3.10826e6 | − | 5.38366e6i | −0.0220388 | − | 0.0381723i | ||||
\(214\) | 5.58038e7 | + | 9.66550e7i | 0.389238 | + | 0.674180i | ||||
\(215\) | 1.80495e8 | − | 3.12627e8i | 1.23860 | − | 2.14532i | ||||
\(216\) | −2.05700e7 | −0.138882 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.67436e7 | 0.305580 | ||||||||
\(219\) | 6.28965e6 | − | 1.08940e7i | 0.0404643 | − | 0.0700862i | ||||
\(220\) | 5.74222e7 | + | 9.94583e7i | 0.363581 | + | 0.629740i | ||||
\(221\) | −8.82959e7 | − | 1.52933e8i | −0.550260 | − | 0.953078i | ||||
\(222\) | 2.08182e7 | − | 3.60581e7i | 0.127705 | − | 0.221191i | ||||
\(223\) | 2.53319e8 | 1.52968 | 0.764840 | − | 0.644221i | \(-0.222818\pi\) | ||||
0.764840 | + | 0.644221i | \(0.222818\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.84753e8 | −1.66659 | ||||||||
\(226\) | 4.83805e7 | − | 8.37975e7i | 0.278799 | − | 0.482894i | ||||
\(227\) | 2.25062e7 | + | 3.89819e7i | 0.127706 | + | 0.221194i | 0.922788 | − | 0.385309i | \(-0.125905\pi\) |
−0.795081 | + | 0.606503i | \(0.792572\pi\) | |||||||
\(228\) | −9.73688e6 | − | 1.68648e7i | −0.0544061 | − | 0.0942341i | ||||
\(229\) | 9.34866e7 | − | 1.61924e8i | 0.514429 | − | 0.891017i | −0.485431 | − | 0.874275i | \(-0.661337\pi\) |
0.999860 | − | 0.0167418i | \(-0.00532933\pi\) | |||||||
\(230\) | −2.07678e8 | −1.12549 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.35383e7 | −0.0711796 | ||||||||
\(233\) | 1.28794e8 | − | 2.23078e8i | 0.667038 | − | 1.15534i | −0.311691 | − | 0.950184i | \(-0.600895\pi\) |
0.978729 | − | 0.205159i | \(-0.0657713\pi\) | |||||||
\(234\) | 9.72789e7 | + | 1.68492e8i | 0.496322 | + | 0.859655i | ||||
\(235\) | 1.22813e8 | + | 2.12718e8i | 0.617315 | + | 1.06922i | ||||
\(236\) | −6.85105e7 | + | 1.18664e8i | −0.339285 | + | 0.587659i | ||||
\(237\) | 6.61607e7 | 0.322835 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.15071e8 | −1.49285 | −0.746425 | − | 0.665469i | \(-0.768231\pi\) | ||||
−0.746425 | + | 0.665469i | \(0.768231\pi\) | |||||||
\(240\) | 8.87583e6 | − | 1.53734e7i | 0.0414447 | − | 0.0717844i | ||||
\(241\) | 4.19950e7 | + | 7.27374e7i | 0.193258 | + | 0.334733i | 0.946328 | − | 0.323208i | \(-0.104761\pi\) |
−0.753070 | + | 0.657940i | \(0.771428\pi\) | |||||||
\(242\) | 1.76985e7 | + | 3.06547e7i | 0.0802753 | + | 0.139041i | ||||
\(243\) | −6.36831e7 | + | 1.10302e8i | −0.284710 | + | 0.493131i | ||||
\(244\) | −5.68847e7 | −0.250687 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.29750e7 | −0.0983973 | ||||||||
\(247\) | −1.88044e8 | + | 3.25702e8i | −0.793999 | + | 1.37525i | ||||
\(248\) | −1.16347e7 | − | 2.01520e7i | −0.0484368 | − | 0.0838950i | ||||
\(249\) | 3.09732e7 | + | 5.36472e7i | 0.127142 | + | 0.220216i | ||||
\(250\) | 1.06394e8 | − | 1.84279e8i | 0.430652 | − | 0.745910i | ||||
\(251\) | 5.33130e6 | 0.0212802 | 0.0106401 | − | 0.999943i | \(-0.496613\pi\) | ||||
0.0106401 | + | 0.999943i | \(0.496613\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.17906e8 | 0.845955 | ||||||||
\(254\) | 1.30304e6 | − | 2.25693e6i | 0.00498930 | − | 0.00864173i | ||||
\(255\) | 3.30295e7 | + | 5.72088e7i | 0.124742 | + | 0.216059i | ||||
\(256\) | −8.38861e6 | − | 1.45295e7i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1.04971e8 | + | 1.81815e8i | −0.385747 | + | 0.668134i | −0.991873 | − | 0.127235i | \(-0.959390\pi\) |
0.606125 | + | 0.795369i | \(0.292723\pi\) | |||||||
\(258\) | 5.85467e7 | 0.212243 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.42830e8 | −1.20968 | ||||||||
\(261\) | −2.77527e7 | + | 4.80690e7i | −0.0966191 | + | 0.167349i | ||||
\(262\) | 2.55219e7 | + | 4.42053e7i | 0.0876717 | + | 0.151852i | ||||
\(263\) | 1.25403e8 | + | 2.17204e8i | 0.425071 | + | 0.736245i | 0.996427 | − | 0.0844572i | \(-0.0269156\pi\) |
−0.571356 | + | 0.820703i | \(0.693582\pi\) | |||||||
\(264\) | −9.31295e6 | + | 1.61305e7i | −0.0311511 | + | 0.0539553i | ||||
\(265\) | 1.68111e8 | 0.554926 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.99601e7 | 0.160633 | ||||||||
\(268\) | −1.39053e8 | + | 2.40847e8i | −0.441274 | + | 0.764310i | ||||
\(269\) | 1.69599e8 | + | 2.93753e8i | 0.531238 | + | 0.920131i | 0.999335 | + | 0.0364542i | \(0.0116063\pi\) |
−0.468097 | + | 0.883677i | \(0.655060\pi\) | |||||||
\(270\) | −7.43028e7 | − | 1.28696e8i | −0.229738 | − | 0.397917i | ||||
\(271\) | 3.79787e7 | − | 6.57810e7i | 0.115917 | − | 0.200774i | −0.802229 | − | 0.597017i | \(-0.796353\pi\) |
0.918146 | + | 0.396242i | \(0.129686\pi\) | |||||||
\(272\) | 6.24328e7 | 0.188114 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.69859e7 | 0.108620 | ||||||||
\(275\) | −2.63237e8 | + | 4.55940e8i | −0.763278 | + | 1.32204i | ||||
\(276\) | −1.68410e7 | − | 2.91694e7i | −0.0482154 | − | 0.0835115i | ||||
\(277\) | 2.50442e7 | + | 4.33778e7i | 0.0707990 | + | 0.122628i | 0.899252 | − | 0.437432i | \(-0.144112\pi\) |
−0.828453 | + | 0.560059i | \(0.810778\pi\) | |||||||
\(278\) | −1.42158e8 | + | 2.46224e8i | −0.396838 | + | 0.687344i | ||||
\(279\) | −9.54021e7 | −0.262992 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.41917e8 | 0.919283 | 0.459641 | − | 0.888105i | \(-0.347978\pi\) | ||||
0.459641 | + | 0.888105i | \(0.347978\pi\) | |||||||
\(282\) | −1.99182e7 | + | 3.44994e7i | −0.0528907 | + | 0.0916094i | ||||
\(283\) | 1.84539e8 | + | 3.19630e8i | 0.483988 | + | 0.838293i | 0.999831 | − | 0.0183909i | \(-0.00585435\pi\) |
−0.515842 | + | 0.856683i | \(0.672521\pi\) | |||||||
\(284\) | −2.12226e7 | − | 3.67586e7i | −0.0549775 | − | 0.0952238i | ||||
\(285\) | 7.03430e7 | − | 1.21838e8i | 0.179996 | − | 0.311763i | ||||
\(286\) | 3.59714e8 | 0.909234 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −6.87846e7 | −0.169675 | ||||||||
\(289\) | 8.90041e7 | − | 1.54160e8i | 0.216904 | − | 0.375689i | ||||
\(290\) | −4.89029e7 | − | 8.47023e7i | −0.117745 | − | 0.203940i | ||||
\(291\) | −9.83319e6 | − | 1.70316e7i | −0.0233921 | − | 0.0405163i | ||||
\(292\) | 4.29446e7 | − | 7.43822e7i | 0.100941 | − | 0.174835i | ||||
\(293\) | −5.92780e8 | −1.37676 | −0.688378 | − | 0.725352i | \(-0.741677\pi\) | ||||
−0.688378 | + | 0.725352i | \(0.741677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.89892e8 | −2.24497 | ||||||||
\(296\) | 1.42143e8 | − | 2.46198e8i | 0.318569 | − | 0.551778i | ||||
\(297\) | 7.79621e7 | + | 1.35034e8i | 0.172678 | + | 0.299086i | ||||
\(298\) | −4.06832e7 | − | 7.04653e7i | −0.0890549 | − | 0.154248i | ||||
\(299\) | −3.25242e8 | + | 5.63336e8i | −0.703652 | + | 1.21876i | ||||
\(300\) | 8.13777e7 | 0.174013 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.96218e8 | 0.409934 | ||||||||
\(303\) | 9.16430e7 | − | 1.58730e8i | 0.189256 | − | 0.327801i | ||||
\(304\) | −6.64816e7 | − | 1.15150e8i | −0.135720 | − | 0.235074i | ||||
\(305\) | −2.05479e8 | − | 3.55899e8i | −0.414684 | − | 0.718253i | ||||
\(306\) | 1.27984e8 | − | 2.21674e8i | 0.255346 | − | 0.442273i | ||||
\(307\) | 9.43846e8 | 1.86173 | 0.930865 | − | 0.365363i | \(-0.119055\pi\) | ||||
0.930865 | + | 0.365363i | \(0.119055\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.39008e7 | 0.161775 | ||||||||
\(310\) | 8.40538e7 | − | 1.45586e8i | 0.160248 | − | 0.277557i | ||||
\(311\) | −8.20325e7 | − | 1.42085e8i | −0.154641 | − | 0.267846i | 0.778287 | − | 0.627908i | \(-0.216089\pi\) |
−0.932928 | + | 0.360062i | \(0.882755\pi\) | |||||||
\(312\) | −2.78007e7 | − | 4.81522e7i | −0.0518220 | − | 0.0897584i | ||||
\(313\) | 1.73006e8 | − | 2.99655e8i | 0.318901 | − | 0.552352i | −0.661358 | − | 0.750070i | \(-0.730020\pi\) |
0.980259 | + | 0.197718i | \(0.0633530\pi\) | |||||||
\(314\) | 1.01903e8 | 0.185752 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.51734e8 | 0.805337 | ||||||||
\(317\) | 4.76620e8 | − | 8.25530e8i | 0.840359 | − | 1.45554i | −0.0492320 | − | 0.998787i | \(-0.515677\pi\) |
0.889591 | − | 0.456758i | \(-0.150989\pi\) | |||||||
\(318\) | 1.36324e7 | + | 2.36120e7i | 0.0237727 | + | 0.0411755i | ||||
\(319\) | 5.13113e7 | + | 8.88737e7i | 0.0885004 | + | 0.153287i | ||||
\(320\) | 6.06025e7 | − | 1.04967e8i | 0.103387 | − | 0.179072i | ||||
\(321\) | −1.30768e8 | −0.220665 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.94795e8 | 0.816989 | ||||||||
\(324\) | −1.34855e8 | + | 2.33577e8i | −0.220273 | + | 0.381524i | ||||
\(325\) | −7.85806e8 | − | 1.36106e9i | −1.26977 | − | 2.19930i | ||||
\(326\) | 3.40612e8 | + | 5.89958e8i | 0.544501 | + | 0.943104i | ||||
\(327\) | −2.73842e7 | + | 4.74308e7i | −0.0433095 | + | 0.0750142i | ||||
\(328\) | −1.56869e8 | −0.245459 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.34561e8 | −0.206120 | ||||||||
\(331\) | −1.12131e8 | + | 1.94217e8i | −0.169953 | + | 0.294367i | −0.938403 | − | 0.345542i | \(-0.887695\pi\) |
0.768450 | + | 0.639910i | \(0.221028\pi\) | |||||||
\(332\) | 2.11480e8 | + | 3.66293e8i | 0.317165 | + | 0.549346i | ||||
\(333\) | −5.82768e8 | − | 1.00938e9i | −0.864850 | − | 1.49796i | ||||
\(334\) | −1.49704e7 | + | 2.59295e7i | −0.0219847 | + | 0.0380787i | ||||
\(335\) | −2.00915e9 | −2.91981 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.56750e8 | 0.507761 | 0.253880 | − | 0.967236i | \(-0.418293\pi\) | ||||
0.253880 | + | 0.967236i | \(0.418293\pi\) | |||||||
\(338\) | −2.85908e8 | + | 4.95207e8i | −0.402734 | + | 0.697555i | ||||
\(339\) | 5.66863e7 | + | 9.81836e7i | 0.0790277 | + | 0.136880i | ||||
\(340\) | 2.25519e8 | + | 3.90611e8i | 0.311177 | + | 0.538975i | ||||
\(341\) | −8.81934e7 | + | 1.52755e8i | −0.120447 | + | 0.208620i | ||||
\(342\) | −5.45134e8 | −0.736905 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.99747e8 | 0.529456 | ||||||||
\(345\) | 1.21666e8 | − | 2.10731e8i | 0.159515 | − | 0.276288i | ||||
\(346\) | −2.90746e8 | − | 5.03587e8i | −0.377353 | − | 0.653594i | ||||
\(347\) | −8.09193e6 | − | 1.40156e7i | −0.0103968 | − | 0.0180077i | 0.860780 | − | 0.508977i | \(-0.169976\pi\) |
−0.871177 | + | 0.490969i | \(0.836643\pi\) | |||||||
\(348\) | 7.93125e6 | − | 1.37373e7i | 0.0100882 | − | 0.0174733i | ||||
\(349\) | −2.07780e8 | −0.261647 | −0.130823 | − | 0.991406i | \(-0.541762\pi\) | ||||
−0.130823 | + | 0.991406i | \(0.541762\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.65459e8 | −0.574522 | ||||||||
\(352\) | −6.35871e7 | + | 1.10136e8i | −0.0777087 | + | 0.134595i | ||||
\(353\) | −6.58118e8 | − | 1.13989e9i | −0.796328 | − | 1.37928i | −0.921992 | − | 0.387208i | \(-0.873440\pi\) |
0.125664 | − | 0.992073i | \(-0.459894\pi\) | |||||||
\(354\) | −8.02721e7 | − | 1.39035e8i | −0.0961731 | − | 0.166577i | ||||
\(355\) | 1.53320e8 | − | 2.65559e8i | 0.181887 | − | 0.315037i | ||||
\(356\) | 3.41119e8 | 0.400710 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.19559e8 | 0.944038 | ||||||||
\(359\) | 3.09636e8 | − | 5.36305e8i | 0.353200 | − | 0.611760i | −0.633608 | − | 0.773654i | \(-0.718427\pi\) |
0.986808 | + | 0.161894i | \(0.0517603\pi\) | |||||||
\(360\) | −2.48463e8 | − | 4.30351e8i | −0.280675 | − | 0.486143i | ||||
\(361\) | −7.99464e7 | − | 1.38471e8i | −0.0894383 | − | 0.154912i | ||||
\(362\) | 1.91665e7 | − | 3.31973e7i | 0.0212355 | − | 0.0367809i | ||||
\(363\) | −4.14738e7 | −0.0455093 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.20497e8 | 0.667905 | ||||||||
\(366\) | 3.33253e7 | − | 5.77210e7i | 0.0355295 | − | 0.0615390i | ||||
\(367\) | 1.39314e8 | + | 2.41299e8i | 0.147117 | + | 0.254815i | 0.930161 | − | 0.367152i | \(-0.119667\pi\) |
−0.783043 | + | 0.621967i | \(0.786334\pi\) | |||||||
\(368\) | −1.14987e8 | − | 1.99164e8i | −0.120277 | − | 0.208326i | ||||
\(369\) | −3.21573e8 | + | 5.56981e8i | −0.333186 | + | 0.577096i | ||||
\(370\) | 2.05379e9 | 2.10790 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.72643e7 | 0.0274596 | ||||||||
\(373\) | 8.25282e7 | − | 1.42943e8i | 0.0823420 | − | 0.142621i | −0.821913 | − | 0.569612i | \(-0.807093\pi\) |
0.904256 | + | 0.426992i | \(0.140427\pi\) | |||||||
\(374\) | −2.36626e8 | − | 4.09848e8i | −0.233890 | − | 0.405110i | ||||
\(375\) | 1.24659e8 | + | 2.15916e8i | 0.122072 | + | 0.211434i | ||||
\(376\) | −1.35998e8 | + | 2.35556e8i | −0.131940 | + | 0.228526i | ||||
\(377\) | −3.06345e8 | −0.294453 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.29433e8 | 0.405190 | 0.202595 | − | 0.979263i | \(-0.435063\pi\) | ||||
0.202595 | + | 0.979263i | \(0.435063\pi\) | |||||||
\(380\) | 4.80289e8 | − | 8.31885e8i | 0.449014 | − | 0.777716i | ||||
\(381\) | 1.52674e6 | + | 2.64440e6i | 0.00141426 | + | 0.00244957i | ||||
\(382\) | −1.04069e8 | − | 1.80253e8i | −0.0955213 | − | 0.165448i | ||||
\(383\) | 6.71888e8 | − | 1.16374e9i | 0.611084 | − | 1.05843i | −0.379974 | − | 0.924997i | \(-0.624067\pi\) |
0.991058 | − | 0.133432i | \(-0.0425997\pi\) | |||||||
\(384\) | 1.96575e7 | 0.0177161 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.06661e8 | −0.536897 | ||||||||
\(387\) | 8.19457e8 | − | 1.41934e9i | 0.718684 | − | 1.24480i | ||||
\(388\) | −6.71393e7 | − | 1.16289e8i | −0.0583533 | − | 0.101071i | ||||
\(389\) | 5.39354e7 | + | 9.34189e7i | 0.0464569 | + | 0.0804658i | 0.888319 | − | 0.459227i | \(-0.151874\pi\) |
−0.841862 | + | 0.539693i | \(0.818540\pi\) | |||||||
\(390\) | 2.00843e8 | − | 3.47870e8i | 0.171447 | − | 0.296955i | ||||
\(391\) | 8.55801e8 | 0.724026 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.98070e7 | −0.0497024 | ||||||||
\(394\) | −4.76768e8 | + | 8.25787e8i | −0.392709 | + | 0.680192i | ||||
\(395\) | 1.63175e9 | + | 2.82627e9i | 1.33218 | + | 2.30741i | ||||
\(396\) | 2.60700e8 | + | 4.51545e8i | 0.210963 | + | 0.365399i | ||||
\(397\) | −9.32624e8 | + | 1.61535e9i | −0.748066 | + | 1.29569i | 0.200683 | + | 0.979656i | \(0.435684\pi\) |
−0.948749 | + | 0.316031i | \(0.897650\pi\) | |||||||
\(398\) | −5.38130e8 | −0.427855 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.55632e8 | 0.434088 | ||||||||
\(401\) | −4.97362e6 | + | 8.61456e6i | −0.00385183 | + | 0.00667157i | −0.867945 | − | 0.496661i | \(-0.834559\pi\) |
0.864093 | + | 0.503332i | \(0.167893\pi\) | |||||||
\(402\) | −1.62925e8 | − | 2.82195e8i | −0.125083 | − | 0.216650i | ||||
\(403\) | −2.63272e8 | − | 4.56000e8i | −0.200372 | − | 0.347054i | ||||
\(404\) | 6.25722e8 | − | 1.08378e9i | 0.472114 | − | 0.817725i | ||||
\(405\) | −1.94850e9 | −1.45749 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.15493e9 | −1.58436 | ||||||||
\(408\) | −3.65756e7 | + | 6.33507e7i | −0.0266612 | + | 0.0461786i | ||||
\(409\) | −4.38188e8 | − | 7.58964e8i | −0.316686 | − | 0.548517i | 0.663108 | − | 0.748523i | \(-0.269237\pi\) |
−0.979794 | + | 0.200007i | \(0.935904\pi\) | |||||||
\(410\) | −5.66642e8 | − | 9.81454e8i | −0.406037 | − | 0.703277i | ||||
\(411\) | −2.16678e7 | + | 3.75297e7i | −0.0153946 | + | 0.0266642i | ||||
\(412\) | 5.72859e8 | 0.403560 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −9.42868e8 | −0.653055 | ||||||||
\(415\) | −1.52781e9 | + | 2.64624e9i | −1.04930 | + | 1.81745i | ||||
\(416\) | −1.89818e8 | − | 3.28775e8i | −0.129274 | − | 0.223909i | ||||
\(417\) | −1.66563e8 | − | 2.88495e8i | −0.112487 | − | 0.194833i | ||||
\(418\) | −5.03943e8 | + | 8.72854e8i | −0.337492 | + | 0.584554i | ||||
\(419\) | 2.01605e9 | 1.33891 | 0.669457 | − | 0.742851i | \(-0.266527\pi\) | ||||
0.669457 | + | 0.742851i | \(0.266527\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.69546e8 | 0.371999 | 0.186000 | − | 0.982550i | \(-0.440448\pi\) | ||||
0.186000 | + | 0.982550i | \(0.440448\pi\) | |||||||
\(422\) | −9.29683e8 | + | 1.61026e9i | −0.602201 | + | 1.04304i | ||||
\(423\) | 5.57577e8 | + | 9.65751e8i | 0.358190 | + | 0.620403i | ||||
\(424\) | 9.30797e7 | + | 1.61219e8i | 0.0593027 | + | 0.102715i | ||||
\(425\) | −1.03383e9 | + | 1.79065e9i | −0.653265 | + | 1.13149i | ||||
\(426\) | 4.97321e7 | 0.0311676 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −8.92860e8 | −0.550466 | ||||||||
\(429\) | −2.10734e8 | + | 3.65002e8i | −0.128865 | + | 0.223200i | ||||
\(430\) | 1.44396e9 | + | 2.50102e9i | 0.875823 | + | 1.51697i | ||||
\(431\) | 3.85970e8 | + | 6.68519e8i | 0.232211 | + | 0.402201i | 0.958459 | − | 0.285232i | \(-0.0920706\pi\) |
−0.726247 | + | 0.687433i | \(0.758737\pi\) | |||||||
\(432\) | 8.22800e7 | − | 1.42513e8i | 0.0491022 | − | 0.0850475i | ||||
\(433\) | −1.24002e9 | −0.734043 | −0.367021 | − | 0.930213i | \(-0.619622\pi\) | ||||
−0.367021 | + | 0.930213i | \(0.619622\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.14597e8 | 0.0667513 | ||||||||
\(436\) | −1.86974e8 | + | 3.23849e8i | −0.108039 | + | 0.187129i | ||||
\(437\) | −9.11300e8 | − | 1.57842e9i | −0.522368 | − | 0.904768i | ||||
\(438\) | 5.03172e7 | + | 8.71520e7i | 0.0286126 | + | 0.0495585i | ||||
\(439\) | 9.53106e8 | − | 1.65083e9i | 0.537669 | − | 0.931271i | −0.461360 | − | 0.887213i | \(-0.652638\pi\) |
0.999029 | − | 0.0440574i | \(-0.0140285\pi\) | |||||||
\(440\) | −9.18756e8 | −0.514181 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.41274e9 | 0.778185 | ||||||||
\(443\) | 2.52369e8 | − | 4.37116e8i | 0.137919 | − | 0.238882i | −0.788790 | − | 0.614663i | \(-0.789292\pi\) |
0.926709 | + | 0.375781i | \(0.122625\pi\) | |||||||
\(444\) | 1.66545e8 | + | 2.88465e8i | 0.0903009 | + | 0.156406i | ||||
\(445\) | 1.23219e9 | + | 2.13421e9i | 0.662852 | + | 1.14809i | ||||
\(446\) | −1.01328e9 | + | 1.75504e9i | −0.540823 | + | 0.936733i | ||||
\(447\) | 9.53351e7 | 0.0504866 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.02721e9 | −1.05691 | −0.528453 | − | 0.848962i | \(-0.677228\pi\) | ||||
−0.528453 | + | 0.848962i | \(0.677228\pi\) | |||||||
\(450\) | 1.13901e9 | − | 1.97283e9i | 0.589230 | − | 1.02058i | ||||
\(451\) | 5.94549e8 | + | 1.02979e9i | 0.305189 | + | 0.528604i | ||||
\(452\) | 3.87044e8 | + | 6.70380e8i | 0.197141 | + | 0.341457i | ||||
\(453\) | −1.14952e8 | + | 1.99103e8i | −0.0580995 | + | 0.100631i | ||||
\(454\) | −3.60100e8 | −0.180604 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.55790e8 | 0.0769419 | ||||||||
\(457\) | −1.01984e9 | + | 1.76642e9i | −0.499836 | + | 0.865741i | −1.00000 | 0.000189507i | \(-0.999940\pi\) | |
0.500164 | + | 0.865931i | \(0.333273\pi\) | |||||||
\(458\) | 7.47893e8 | + | 1.29539e9i | 0.363756 | + | 0.630044i | ||||
\(459\) | 3.06187e8 | + | 5.30332e8i | 0.147789 | + | 0.255979i | ||||
\(460\) | 8.30712e8 | − | 1.43884e9i | 0.397922 | − | 0.689221i | ||||
\(461\) | 3.41390e9 | 1.62292 | 0.811461 | − | 0.584406i | \(-0.198673\pi\) | ||||
0.811461 | + | 0.584406i | \(0.198673\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.97893e9 | −0.926608 | −0.463304 | − | 0.886199i | \(-0.653336\pi\) | ||||
−0.463304 | + | 0.886199i | \(0.653336\pi\) | |||||||
\(464\) | 5.41531e7 | − | 9.37960e7i | 0.0251658 | − | 0.0435884i | ||||
\(465\) | 9.84839e7 | + | 1.70579e8i | 0.0454234 | + | 0.0786757i | ||||
\(466\) | 1.03035e9 | + | 1.78462e9i | 0.471667 | + | 0.816951i | ||||
\(467\) | 9.32108e8 | − | 1.61446e9i | 0.423504 | − | 0.733530i | −0.572776 | − | 0.819712i | \(-0.694133\pi\) |
0.996279 | + | 0.0861822i | \(0.0274667\pi\) | |||||||
\(468\) | −1.55646e9 | −0.701905 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.96501e9 | −0.873015 | ||||||||
\(471\) | −5.96986e7 | + | 1.03401e8i | −0.0263264 | + | 0.0455986i | ||||
\(472\) | −5.48084e8 | − | 9.49309e8i | −0.239911 | − | 0.415538i | ||||
\(473\) | −1.51508e9 | − | 2.62419e9i | −0.658294 | − | 1.14020i | ||||
\(474\) | −2.64643e8 | + | 4.58375e8i | −0.114140 | + | 0.197695i | ||||
\(475\) | 4.40351e9 | 1.88526 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.63231e8 | 0.321990 | ||||||||
\(478\) | 1.26029e9 | − | 2.18288e9i | 0.527802 | − | 0.914181i | ||||
\(479\) | 1.85914e9 | + | 3.22013e9i | 0.772926 | + | 1.33875i | 0.935953 | + | 0.352125i | \(0.114541\pi\) |
−0.163027 | + | 0.986622i | \(0.552126\pi\) | |||||||
\(480\) | 7.10066e7 | + | 1.22987e8i | 0.0293059 | + | 0.0507592i | ||||
\(481\) | 3.21642e9 | − | 5.57099e9i | 1.31784 | − | 2.28257i | ||||
\(482\) | −6.71920e8 | −0.273308 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.83176e8 | −0.113526 | ||||||||
\(485\) | 4.85040e8 | − | 8.40114e8i | 0.193055 | − | 0.334381i | ||||
\(486\) | −5.09465e8 | − | 8.82419e8i | −0.201320 | − | 0.348697i | ||||
\(487\) | 1.08171e9 | + | 1.87357e9i | 0.424383 | + | 0.735053i | 0.996363 | − | 0.0852146i | \(-0.0271576\pi\) |
−0.571979 | + | 0.820268i | \(0.693824\pi\) | |||||||
\(488\) | 2.27539e8 | − | 3.94109e8i | 0.0886311 | − | 0.153514i | ||||
\(489\) | −7.98175e8 | −0.308686 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.37608e8 | 0.0905890 | 0.0452945 | − | 0.998974i | \(-0.485577\pi\) | ||||
0.0452945 | + | 0.998974i | \(0.485577\pi\) | |||||||
\(492\) | 9.19001e7 | − | 1.59176e8i | 0.0347887 | − | 0.0602558i | ||||
\(493\) | 2.01519e8 | + | 3.49042e8i | 0.0757447 | + | 0.131194i | ||||
\(494\) | −1.50435e9 | − | 2.60561e9i | −0.561442 | − | 0.972446i | ||||
\(495\) | −1.88340e9 | + | 3.26214e9i | −0.697948 | + | 1.20888i | ||||
\(496\) | 1.86156e8 | 0.0685000 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.95571e8 | −0.179806 | ||||||||
\(499\) | −1.32583e9 | + | 2.29641e9i | −0.477679 | + | 0.827364i | −0.999673 | − | 0.0255852i | \(-0.991855\pi\) |
0.521994 | + | 0.852949i | \(0.325188\pi\) | |||||||
\(500\) | 8.51150e8 | + | 1.47423e9i | 0.304517 | + | 0.527438i | ||||
\(501\) | −1.75405e7 | − | 3.03810e7i | −0.00623174 | − | 0.0107937i | ||||
\(502\) | −2.13252e7 | + | 3.69363e7i | −0.00752368 | + | 0.0130314i | ||||
\(503\) | −2.15865e9 | −0.756300 | −0.378150 | − | 0.925744i | \(-0.623440\pi\) | ||||
−0.378150 | + | 0.925744i | \(0.623440\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.04091e9 | 3.12387 | ||||||||
\(506\) | −8.71623e8 | + | 1.50970e9i | −0.299090 | + | 0.518039i | ||||
\(507\) | −3.34992e8 | − | 5.80223e8i | −0.114158 | − | 0.197728i | ||||
\(508\) | 1.04243e7 | + | 1.80555e7i | 0.00352797 | + | 0.00611062i | ||||
\(509\) | 1.23916e9 | − | 2.14628e9i | 0.416499 | − | 0.721398i | −0.579085 | − | 0.815267i | \(-0.696590\pi\) |
0.995585 | + | 0.0938693i | \(0.0299236\pi\) | |||||||
\(510\) | −5.28472e8 | −0.176411 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | 6.52088e8 | − | 1.12945e9i | 0.213253 | − | 0.369365i | ||||
\(514\) | −8.39767e8 | − | 1.45452e9i | −0.272765 | − | 0.472442i | ||||
\(515\) | 2.06928e9 | + | 3.58410e9i | 0.667565 | + | 1.15626i | ||||
\(516\) | −2.34187e8 | + | 4.05624e8i | −0.0750393 | + | 0.129972i | ||||
\(517\) | 2.06178e9 | 0.656184 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.81321e8 | 0.213927 | ||||||||
\(520\) | 1.37132e9 | − | 2.37519e9i | 0.427688 | − | 0.740777i | ||||
\(521\) | −1.99867e9 | − | 3.46181e9i | −0.619170 | − | 1.07243i | −0.989637 | − | 0.143589i | \(-0.954136\pi\) |
0.370467 | − | 0.928846i | \(-0.379198\pi\) | |||||||
\(522\) | −2.22021e8 | − | 3.84552e8i | −0.0683200 | − | 0.118334i | ||||
\(523\) | −1.96566e9 | + | 3.40462e9i | −0.600831 | + | 1.04067i | 0.391865 | + | 0.920023i | \(0.371830\pi\) |
−0.992696 | + | 0.120647i | \(0.961503\pi\) | |||||||
\(524\) | −4.08351e8 | −0.123986 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.00644e9 | −0.601142 | ||||||||
\(527\) | −3.46370e8 | + | 5.99930e8i | −0.103087 | + | 0.178551i | ||||
\(528\) | −7.45036e7 | − | 1.29044e8i | −0.0220272 | − | 0.0381521i | ||||
\(529\) | 1.26220e8 | + | 2.18620e8i | 0.0370710 | + | 0.0642089i | ||||
\(530\) | −6.72444e8 | + | 1.16471e9i | −0.196196 | + | 0.339822i | ||||
\(531\) | −4.49416e9 | −1.30262 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.54965e9 | −1.01541 | ||||||||
\(534\) | −1.99840e8 | + | 3.46134e8i | −0.0567922 | + | 0.0983670i | ||||
\(535\) | −3.22518e9 | − | 5.58618e9i | −0.910576 | − | 1.57716i | ||||
\(536\) | −1.11242e9 | − | 1.92678e9i | −0.312028 | − | 0.540449i | ||||
\(537\) | −4.80129e8 | + | 8.31608e8i | −0.133797 | + | 0.231744i | ||||
\(538\) | −2.71358e9 | −0.751284 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.18884e9 | 0.324898 | ||||||||
\(541\) | 1.37383e9 | − | 2.37954e9i | 0.373028 | − | 0.646104i | −0.617001 | − | 0.786962i | \(-0.711653\pi\) |
0.990030 | + | 0.140858i | \(0.0449861\pi\) | |||||||
\(542\) | 3.03830e8 | + | 5.26248e8i | 0.0819658 | + | 0.141969i | ||||
\(543\) | 2.24569e7 | + | 3.88965e7i | 0.00601936 | + | 0.0104258i | ||||
\(544\) | −2.49731e8 | + | 4.32547e8i | −0.0665085 | + | 0.115196i | ||||
\(545\) | −2.70155e9 | −0.714867 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.40581e9 | −0.367258 | −0.183629 | − | 0.982996i | \(-0.558784\pi\) | ||||
−0.183629 | + | 0.982996i | \(0.558784\pi\) | |||||||
\(548\) | −1.47944e8 | + | 2.56246e8i | −0.0384029 | + | 0.0665159i | ||||
\(549\) | −9.32882e8 | − | 1.61580e9i | −0.240616 | − | 0.416758i | ||||
\(550\) | −2.10590e9 | − | 3.64752e9i | −0.539719 | − | 0.934820i | ||||
\(551\) | 4.29176e8 | − | 7.43355e8i | 0.109296 | − | 0.189306i | ||||
\(552\) | 2.69456e8 | 0.0681869 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.00707e8 | −0.100125 | ||||||||
\(555\) | −1.20319e9 | + | 2.08398e9i | −0.298750 | + | 0.517450i | ||||
\(556\) | −1.13726e9 | − | 1.96979e9i | −0.280607 | − | 0.486025i | ||||
\(557\) | −4.93902e8 | − | 8.55464e8i | −0.121101 | − | 0.209753i | 0.799101 | − | 0.601197i | \(-0.205309\pi\) |
−0.920202 | + | 0.391443i | \(0.871976\pi\) | |||||||
\(558\) | 3.81608e8 | − | 6.60965e8i | 0.0929818 | − | 0.161049i | ||||
\(559\) | 9.04550e9 | 2.19024 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.54498e8 | 0.132596 | ||||||||
\(562\) | −1.36767e9 | + | 2.36887e9i | −0.325016 | + | 0.562943i | ||||
\(563\) | 9.40576e8 | + | 1.62913e9i | 0.222134 | + | 0.384747i | 0.955456 | − | 0.295135i | \(-0.0953645\pi\) |
−0.733322 | + | 0.679882i | \(0.762031\pi\) | |||||||
\(564\) | −1.59346e8 | − | 2.75995e8i | −0.0373994 | − | 0.0647776i | ||||
\(565\) | −2.79616e9 | + | 4.84309e9i | −0.652217 | + | 1.12967i | ||||
\(566\) | −2.95262e9 | −0.684463 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.39562e8 | 0.0777499 | ||||||||
\(569\) | 1.94266e9 | − | 3.36478e9i | 0.442082 | − | 0.765708i | −0.555762 | − | 0.831342i | \(-0.687573\pi\) |
0.997844 | + | 0.0656331i | \(0.0209067\pi\) | |||||||
\(570\) | 5.62744e8 | + | 9.74701e8i | 0.127277 | + | 0.220450i | ||||
\(571\) | −1.22450e9 | − | 2.12089e9i | −0.275253 | − | 0.476752i | 0.694946 | − | 0.719062i | \(-0.255428\pi\) |
−0.970199 | + | 0.242310i | \(0.922095\pi\) | |||||||
\(572\) | −1.43885e9 | + | 2.49217e9i | −0.321463 | + | 0.556790i | ||||
\(573\) | 2.43871e8 | 0.0541525 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.61636e9 | 1.67074 | ||||||||
\(576\) | 2.75138e8 | − | 4.76554e8i | 0.0599891 | − | 0.103904i | ||||
\(577\) | 1.44109e9 | + | 2.49604e9i | 0.312303 | + | 0.540924i | 0.978860 | − | 0.204529i | \(-0.0655664\pi\) |
−0.666558 | + | 0.745453i | \(0.732233\pi\) | |||||||
\(578\) | 7.12033e8 | + | 1.23328e9i | 0.153374 | + | 0.265652i | ||||
\(579\) | 3.55405e8 | − | 6.15580e8i | 0.0760938 | − | 0.131798i | ||||
\(580\) | 7.82446e8 | 0.166516 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.57331e8 | 0.0330814 | ||||||||
\(583\) | 7.05561e8 | − | 1.22207e9i | 0.147467 | − | 0.255420i | ||||
\(584\) | 3.43557e8 | + | 5.95058e8i | 0.0713762 | + | 0.123627i | ||||
\(585\) | −5.62225e9 | − | 9.73801e9i | −1.16109 | − | 2.01106i | ||||
\(586\) | 2.37112e9 | − | 4.10690e9i | 0.486757 | − | 0.843087i | ||||
\(587\) | −4.72250e9 | −0.963692 | −0.481846 | − | 0.876256i | \(-0.660034\pi\) | ||||
−0.481846 | + | 0.876256i | \(0.660034\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.47533e9 | 0.297499 | ||||||||
\(590\) | 3.95957e9 | − | 6.85818e9i | 0.793717 | − | 1.37476i | ||||
\(591\) | −5.58618e8 | − | 9.67556e8i | −0.111316 | − | 0.192806i | ||||
\(592\) | 1.13714e9 | + | 1.96959e9i | 0.225262 | + | 0.390166i | ||||
\(593\) | 6.15833e7 | − | 1.06665e8i | 0.0121275 | − | 0.0210055i | −0.859898 | − | 0.510466i | \(-0.829473\pi\) |
0.872025 | + | 0.489460i | \(0.162806\pi\) | |||||||
\(594\) | −1.24739e9 | −0.244203 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.50931e8 | 0.125943 | ||||||||
\(597\) | 3.15257e8 | − | 5.46041e8i | 0.0606394 | − | 0.105031i | ||||
\(598\) | −2.60194e9 | − | 4.50669e9i | −0.497557 | − | 0.861794i | ||||
\(599\) | −6.77485e8 | − | 1.17344e9i | −0.128797 | − | 0.223083i | 0.794414 | − | 0.607377i | \(-0.207778\pi\) |
−0.923211 | + | 0.384294i | \(0.874445\pi\) | |||||||
\(600\) | −3.25511e8 | + | 5.63801e8i | −0.0615228 | + | 0.106561i | ||||
\(601\) | 5.25107e9 | 0.986704 | 0.493352 | − | 0.869830i | \(-0.335772\pi\) | ||||
0.493352 | + | 0.869830i | \(0.335772\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.12161e9 | −1.69419 | ||||||||
\(604\) | −7.84871e8 | + | 1.35944e9i | −0.144934 | + | 0.251032i | ||||
\(605\) | −1.02289e9 | − | 1.77169e9i | −0.187795 | − | 0.325270i | ||||
\(606\) | 7.33144e8 | + | 1.26984e9i | 0.133824 | + | 0.231791i | ||||
\(607\) | 2.49506e9 | − | 4.32157e9i | 0.452815 | − | 0.784298i | −0.545745 | − | 0.837951i | \(-0.683753\pi\) |
0.998560 | + | 0.0536532i | \(0.0170865\pi\) | |||||||
\(608\) | 1.06371e9 | 0.191937 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.28766e9 | 0.586452 | ||||||||
\(611\) | −3.07738e9 | + | 5.33018e9i | −0.545804 | + | 0.945360i | ||||
\(612\) | 1.02387e9 | + | 1.77339e9i | 0.180557 | + | 0.312734i | ||||
\(613\) | 1.23014e9 | + | 2.13067e9i | 0.215696 | + | 0.373597i | 0.953488 | − | 0.301432i | \(-0.0974645\pi\) |
−0.737791 | + | 0.675029i | \(0.764131\pi\) | |||||||
\(614\) | −3.77538e9 | + | 6.53916e9i | −0.658221 | + | 1.14007i | ||||
\(615\) | 1.32784e9 | 0.230189 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.93223e9 | −0.331178 | −0.165589 | − | 0.986195i | \(-0.552953\pi\) | ||||
−0.165589 | + | 0.986195i | \(0.552953\pi\) | |||||||
\(618\) | −3.35603e8 | + | 5.81282e8i | −0.0571961 | + | 0.0990665i | ||||
\(619\) | −4.06849e9 | − | 7.04684e9i | −0.689472 | − | 1.19420i | −0.972009 | − | 0.234943i | \(-0.924509\pi\) |
0.282538 | − | 0.959256i | \(-0.408824\pi\) | |||||||
\(620\) | 6.72431e8 | + | 1.16468e9i | 0.113312 | + | 0.196262i | ||||
\(621\) | 1.12786e9 | − | 1.95350e9i | 0.188988 | − | 0.327336i | ||||
\(622\) | 1.31252e9 | 0.218695 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.44811e8 | 0.0732874 | ||||||||
\(625\) | −8.50112e8 | + | 1.47244e9i | −0.139282 | + | 0.241244i | ||||
\(626\) | 1.38405e9 | + | 2.39724e9i | 0.225497 | + | 0.390572i | ||||
\(627\) | −5.90458e8 | − | 1.02270e9i | −0.0956649 | − | 0.165696i | ||||
\(628\) | −4.07612e8 | + | 7.06004e8i | −0.0656731 | + | 0.113749i | ||||
\(629\) | −8.46326e9 | −1.35600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.83737e9 | 1.40030 | 0.700149 | − | 0.713997i | \(-0.253117\pi\) | ||||
0.700149 | + | 0.713997i | \(0.253117\pi\) | |||||||
\(632\) | −1.80693e9 | + | 3.12970e9i | −0.284730 | + | 0.493166i | ||||
\(633\) | −1.08929e9 | − | 1.88670e9i | −0.170699 | − | 0.295659i | ||||
\(634\) | 3.81296e9 | + | 6.60424e9i | 0.594224 | + | 1.02923i | ||||
\(635\) | −7.53093e7 | + | 1.30440e8i | −0.0116719 | + | 0.0202163i | ||||
\(636\) | −2.18119e8 | −0.0336196 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.20981e8 | −0.125159 | ||||||||
\(639\) | 6.96082e8 | − | 1.20565e9i | 0.105538 | − | 0.182796i | ||||
\(640\) | 4.84820e8 | + | 8.39734e8i | 0.0731057 | + | 0.126623i | ||||
\(641\) | 6.29527e9 | + | 1.09037e10i | 0.944086 | + | 1.63520i | 0.757572 | + | 0.652752i | \(0.226386\pi\) |
0.186514 | + | 0.982452i | \(0.440281\pi\) | |||||||
\(642\) | 5.23072e8 | − | 9.05987e8i | 0.0780169 | − | 0.135129i | ||||
\(643\) | −6.47578e9 | −0.960625 | −0.480312 | − | 0.877098i | \(-0.659477\pi\) | ||||
−0.480312 | + | 0.877098i | \(0.659477\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.38371e9 | −0.496518 | ||||||||
\(646\) | −1.97918e9 | + | 3.42804e9i | −0.288849 | + | 0.500301i | ||||
\(647\) | 4.34760e9 | + | 7.53027e9i | 0.631081 | + | 1.09306i | 0.987331 | + | 0.158673i | \(0.0507216\pi\) |
−0.356251 | + | 0.934390i | \(0.615945\pi\) | |||||||
\(648\) | −1.07884e9 | − | 1.86861e9i | −0.155756 | − | 0.269778i | ||||
\(649\) | −4.15457e9 | + | 7.19593e9i | −0.596582 | + | 1.03331i | ||||
\(650\) | 1.25729e10 | 1.79572 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.44980e9 | −0.770041 | ||||||||
\(653\) | 1.93949e9 | − | 3.35929e9i | 0.272578 | − | 0.472119i | −0.696943 | − | 0.717126i | \(-0.745457\pi\) |
0.969521 | + | 0.245007i | \(0.0787904\pi\) | |||||||
\(654\) | −2.19074e8 | − | 3.79447e8i | −0.0306244 | − | 0.0530430i | ||||
\(655\) | −1.47504e9 | − | 2.55485e9i | −0.205097 | − | 0.355239i | ||||
\(656\) | 6.27477e8 | − | 1.08682e9i | 0.0867830 | − | 0.150313i | ||||
\(657\) | 2.81708e9 | 0.387544 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.30333e9 | −0.177400 | −0.0887000 | − | 0.996058i | \(-0.528271\pi\) | ||||
−0.0887000 | + | 0.996058i | \(0.528271\pi\) | |||||||
\(660\) | 5.38243e8 | − | 9.32264e8i | 0.0728743 | − | 0.126222i | ||||
\(661\) | 3.42944e9 | + | 5.93996e9i | 0.461868 | + | 0.799979i | 0.999054 | − | 0.0434848i | \(-0.0138460\pi\) |
−0.537186 | + | 0.843464i | \(0.680513\pi\) | |||||||
\(662\) | −8.97051e8 | − | 1.55374e9i | −0.120175 | − | 0.208149i | ||||
\(663\) | −8.27635e8 | + | 1.43351e9i | −0.110291 | + | 0.191030i | ||||
\(664\) | −3.38367e9 | −0.448539 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.32429e9 | 1.22308 | ||||||||
\(667\) | 7.42306e8 | − | 1.28571e9i | 0.0968596 | − | 0.167766i | ||||
\(668\) | −1.19763e8 | − | 2.07436e8i | −0.0155455 | − | 0.0269257i | ||||
\(669\) | −1.18723e9 | − | 2.05634e9i | −0.153301 | − | 0.265524i | ||||
\(670\) | 8.03658e9 | − | 1.39198e10i | 1.03231 | − | 1.78801i | ||||
\(671\) | −3.44957e9 | −0.440794 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.44953e9 | −0.815596 | −0.407798 | − | 0.913072i | \(-0.633703\pi\) | ||||
−0.407798 | + | 0.913072i | \(0.633703\pi\) | |||||||
\(674\) | −1.42700e9 | + | 2.47163e9i | −0.179520 | + | 0.310939i | ||||
\(675\) | 2.72497e9 | + | 4.71979e9i | 0.341035 | + | 0.590689i | ||||
\(676\) | −2.28727e9 | − | 3.96166e9i | −0.284776 | − | 0.493246i | ||||
\(677\) | 1.91513e9 | − | 3.31711e9i | 0.237213 | − | 0.410865i | −0.722700 | − | 0.691161i | \(-0.757099\pi\) |
0.959914 | + | 0.280296i | \(0.0904327\pi\) | |||||||
\(678\) | −9.06981e8 | −0.111762 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.60831e9 | −0.440071 | ||||||||
\(681\) | 2.10960e8 | − | 3.65394e8i | 0.0255968 | − | 0.0443349i | ||||
\(682\) | −7.05547e8 | − | 1.22204e9i | −0.0851688 | − | 0.147517i | ||||
\(683\) | 9.89178e8 | + | 1.71331e9i | 0.118796 | + | 0.205761i | 0.919291 | − | 0.393579i | \(-0.128763\pi\) |
−0.800495 | + | 0.599340i | \(0.795430\pi\) | |||||||
\(684\) | 2.18053e9 | − | 3.77680e9i | 0.260535 | − | 0.451260i | ||||
\(685\) | −2.13761e9 | −0.254103 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.75258e9 | −0.206219 | ||||||||
\(688\) | −1.59899e9 | + | 2.76953e9i | −0.187191 | + | 0.324225i | ||||
\(689\) | 2.10621e9 | + | 3.64807e9i | 0.245321 | + | 0.424909i | ||||
\(690\) | 9.73326e8 | + | 1.68585e9i | 0.112794 | + | 0.195365i | ||||
\(691\) | 5.01275e9 | − | 8.68233e9i | 0.577967 | − | 1.00107i | −0.417746 | − | 0.908564i | \(-0.637180\pi\) |
0.995712 | − | 0.0925035i | \(-0.0294869\pi\) | |||||||
\(692\) | 4.65193e9 | 0.533657 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.29471e8 | 0.0147033 | ||||||||
\(695\) | 8.21601e9 | − | 1.42305e10i | 0.928355 | − | 1.60796i | ||||
\(696\) | 6.34500e7 | + | 1.09899e8i | 0.00713344 | + | 0.0123555i | ||||
\(697\) | 2.33502e9 | + | 4.04438e9i | 0.261202 | + | 0.452415i | ||||
\(698\) | 8.31122e8 | − | 1.43955e9i | 0.0925062 | − | 0.160225i | ||||
\(699\) | −2.41448e9 | −0.267395 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.21616e9 | 0.133345 | 0.0666727 | − | 0.997775i | \(-0.478762\pi\) | ||||
0.0666727 | + | 0.997775i | \(0.478762\pi\) | |||||||
\(702\) | 1.86184e9 | − | 3.22480e9i | 0.203124 | − | 0.351822i | ||||
\(703\) | 9.01211e9 | + | 1.56094e10i | 0.978324 | + | 1.69451i | ||||
\(704\) | −5.08697e8 | − | 8.81089e8i | −0.0549484 | − | 0.0951734i | ||||
\(705\) | 1.15118e9 | − | 1.99390e9i | 0.123731 | − | 0.214309i | ||||
\(706\) | 1.05299e10 | 1.12618 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.28435e9 | 0.136009 | ||||||||
\(709\) | −5.23530e9 | + | 9.06781e9i | −0.551671 | + | 0.955522i | 0.446483 | + | 0.894792i | \(0.352676\pi\) |
−0.998154 | + | 0.0607300i | \(0.980657\pi\) | |||||||
\(710\) | 1.22656e9 | + | 2.12447e9i | 0.128613 | + | 0.222765i | ||||
\(711\) | 7.40822e9 | + | 1.28314e10i | 0.772983 | + | 1.33885i | ||||
\(712\) | −1.36447e9 | + | 2.36334e9i | −0.141672 | + | 0.245384i | ||||
\(713\) | 2.55174e9 | 0.263647 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.07897e10 | −2.12705 | ||||||||
\(716\) | −3.27823e9 | + | 5.67807e9i | −0.333768 | + | 0.578103i | ||||
\(717\) | 1.47665e9 | + | 2.55763e9i | 0.149610 | + | 0.259132i | ||||
\(718\) | 2.47709e9 | + | 4.29044e9i | 0.249750 | + | 0.432580i | ||||
\(719\) | −1.49793e9 | + | 2.59449e9i | −0.150294 | + | 0.260316i | −0.931335 | − | 0.364163i | \(-0.881355\pi\) |
0.781042 | + | 0.624479i | \(0.214689\pi\) | |||||||
\(720\) | 3.97541e9 | 0.396934 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.27914e9 | 0.126485 | ||||||||
\(723\) | 3.93636e8 | − | 6.81798e8i | 0.0387357 | − | 0.0670922i | ||||
\(724\) | 1.53332e8 | + | 2.65578e8i | 0.0150157 | + | 0.0260080i | ||||
\(725\) | 1.79346e9 | + | 3.10636e9i | 0.174787 | + | 0.302739i | ||||
\(726\) | 1.65895e8 | − | 2.87339e8i | 0.0160900 | − | 0.0278687i | ||||
\(727\) | 6.52469e9 | 0.629781 | 0.314890 | − | 0.949128i | \(-0.398032\pi\) | ||||
0.314890 | + | 0.949128i | \(0.398032\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.02267e9 | −0.766960 | ||||||||
\(730\) | −2.48199e9 | + | 4.29893e9i | −0.236140 | + | 0.409006i | ||||
\(731\) | −5.95029e9 | − | 1.03062e10i | −0.563413 | − | 0.975861i | ||||
\(732\) | 2.66602e8 | + | 4.61768e8i | 0.0251232 | + | 0.0435146i | ||||
\(733\) | −5.99282e9 | + | 1.03799e10i | −0.562040 | + | 0.973482i | 0.435278 | + | 0.900296i | \(0.356650\pi\) |
−0.997318 | + | 0.0731862i | \(0.976683\pi\) | |||||||
\(734\) | −2.22903e9 | −0.208056 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.83980e9 | 0.170097 | ||||||||
\(737\) | −8.43237e9 | + | 1.46053e10i | −0.775914 | + | 1.34392i | ||||
\(738\) | −2.57258e9 | − | 4.45584e9i | −0.235598 | − | 0.408068i | ||||
\(739\) | −9.09217e9 | − | 1.57481e10i | −0.828728 | − | 1.43540i | −0.899036 | − | 0.437874i | \(-0.855732\pi\) |
0.0703080 | − | 0.997525i | \(-0.477602\pi\) | |||||||
\(740\) | −8.21515e9 | + | 1.42291e10i | −0.745254 | + | 1.29082i | ||||
\(741\) | 3.52523e9 | 0.318290 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.10111e9 | 0.545692 | 0.272846 | − | 0.962058i | \(-0.412035\pi\) | ||||
0.272846 | + | 0.962058i | \(0.412035\pi\) | |||||||
\(744\) | −1.09057e8 | + | 1.88893e8i | −0.00970843 | + | 0.0168155i | ||||
\(745\) | 2.35129e9 | + | 4.07255e9i | 0.208333 | + | 0.360844i | ||||
\(746\) | 6.60226e8 | + | 1.14354e9i | 0.0582246 | + | 0.100848i | ||||
\(747\) | −6.93633e9 | + | 1.20141e10i | −0.608846 | + | 1.05455i | ||||
\(748\) | 3.78602e9 | 0.330771 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.99455e9 | −0.172635 | ||||||||
\(751\) | 1.84692e9 | − | 3.19896e9i | 0.159114 | − | 0.275594i | −0.775435 | − | 0.631427i | \(-0.782470\pi\) |
0.934549 | + | 0.355833i | \(0.115803\pi\) | |||||||
\(752\) | −1.08799e9 | − | 1.88445e9i | −0.0932955 | − | 0.161593i | ||||
\(753\) | −2.49862e7 | − | 4.32775e7i | −0.00213265 | − | 0.00369385i | ||||
\(754\) | 1.22538e9 | − | 2.12242e9i | 0.104105 | − | 0.180315i | ||||
\(755\) | −1.13404e10 | −0.958992 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.35894e10 | 1.13858 | 0.569292 | − | 0.822135i | \(-0.307217\pi\) | ||||
0.569292 | + | 0.822135i | \(0.307217\pi\) | |||||||
\(758\) | −1.71773e9 | + | 2.97520e9i | −0.143256 | + | 0.248127i | ||||
\(759\) | −1.02126e9 | − | 1.76888e9i | −0.0847794 | − | 0.146842i | ||||
\(760\) | 3.84231e9 | + | 6.65508e9i | 0.317501 | + | 0.549928i | ||||
\(761\) | 8.99970e9 | − | 1.55879e10i | 0.740255 | − | 1.28216i | −0.212123 | − | 0.977243i | \(-0.568038\pi\) |
0.952379 | − | 0.304917i | \(-0.0986288\pi\) | |||||||
\(762\) | −2.44279e7 | −0.00200006 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.66511e9 | 0.135087 | ||||||||
\(765\) | −7.39682e9 | + | 1.28117e10i | −0.597352 | + | 1.03464i | ||||
\(766\) | 5.37510e9 | + | 9.30995e9i | 0.432102 | + | 0.748422i | ||||
\(767\) | −1.24021e10 | − | 2.14810e10i | −0.992455 | − | 1.71898i | ||||
\(768\) | −7.86299e7 | + | 1.36191e8i | −0.00626359 | + | 0.0108489i | ||||
\(769\) | −1.41340e10 | −1.12079 | −0.560394 | − | 0.828226i | \(-0.689350\pi\) | ||||
−0.560394 | + | 0.828226i | \(0.689350\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.96787e9 | 0.154634 | ||||||||
\(772\) | 2.42664e9 | − | 4.20307e9i | 0.189822 | − | 0.328781i | ||||
\(773\) | −3.69742e9 | − | 6.40412e9i | −0.287919 | − | 0.498691i | 0.685394 | − | 0.728173i | \(-0.259630\pi\) |
−0.973313 | + | 0.229482i | \(0.926297\pi\) | |||||||
\(774\) | 6.55565e9 | + | 1.13547e10i | 0.508186 | + | 0.880204i | ||||
\(775\) | −3.08258e9 | + | 5.33918e9i | −0.237880 | + | 0.412021i | ||||
\(776\) | 1.07423e9 | 0.0825241 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.62967e8 | −0.0657000 | ||||||||
\(779\) | 4.97290e9 | − | 8.61332e9i | 0.376902 | − | 0.652814i | ||||
\(780\) | 1.60674e9 | + | 2.78296e9i | 0.121231 | + | 0.209979i | ||||
\(781\) | −1.28697e9 | − | 2.22910e9i | −0.0966695 | − | 0.167437i | ||||
\(782\) | −3.42320e9 | + | 5.92916e9i | −0.255982 | + | 0.443373i | ||||
\(783\) | 1.06233e9 | 0.0790845 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.88949e9 | −0.434544 | ||||||||
\(786\) | 2.39228e8 | − | 4.14355e8i | 0.0175725 | − | 0.0304364i | ||||
\(787\) | −4.74573e9 | − | 8.21985e9i | −0.347050 | − | 0.601107i | 0.638674 | − | 0.769477i | \(-0.279483\pi\) |
−0.985724 | + | 0.168370i | \(0.946150\pi\) | |||||||
\(788\) | −3.81415e9 | − | 6.60630e9i | −0.277687 | − | 0.480968i | ||||
\(789\) | 1.17545e9 | − | 2.03594e9i | 0.0851992 | − | 0.147569i | ||||
\(790\) | −2.61080e10 | −1.88399 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.17119e9 | −0.298347 | ||||||||
\(793\) | 5.14877e9 | − | 8.91793e9i | 0.366646 | − | 0.635050i | ||||
\(794\) | −7.46099e9 | − | 1.29228e10i | −0.528962 | − | 0.916189i | ||||
\(795\) | −7.87887e8 | − | 1.36466e9i | −0.0556133 | − | 0.0963251i | ||||
\(796\) | 2.15252e9 | − | 3.72827e9i | 0.151269 | − | 0.262006i | ||||
\(797\) | 8.83350e9 | 0.618057 | 0.309029 | − | 0.951053i | \(-0.399996\pi\) | ||||
0.309029 | + | 0.951053i | \(0.399996\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.09742e9 | 0.561607 | ||||||||
\(800\) | −2.22253e9 | + | 3.84953e9i | −0.153473 | + | 0.265823i | ||||
\(801\) | 5.59418e9 | + | 9.68941e9i | 0.384612 | + | 0.666167i | ||||
\(802\) | −3.97890e7 | − | 6.89165e7i | −0.00272366 | − | 0.00471751i | ||||
\(803\) | 2.60422e9 | − | 4.51064e9i | 0.177490 | − | 0.307421i | ||||
\(804\) | 2.60680e9 | 0.176894 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.21235e9 | 0.283368 | ||||||||
\(807\) | 1.58972e9 | − | 2.75347e9i | 0.106479 | − | 0.184426i | ||||
\(808\) | 5.00578e9 | + | 8.67026e9i | 0.333835 | + | 0.578219i | ||||
\(809\) | −3.07811e9 | − | 5.33144e9i | −0.204392 | − | 0.354018i | 0.745547 | − | 0.666453i | \(-0.232188\pi\) |
−0.949939 | + | 0.312436i | \(0.898855\pi\) | |||||||
\(810\) | 7.79398e9 | − | 1.34996e10i | 0.515302 | − | 0.892529i | ||||
\(811\) | 1.53945e10 | 1.01343 | 0.506715 | − | 0.862114i | \(-0.330860\pi\) | ||||
0.506715 | + | 0.862114i | \(0.330860\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.11980e8 | −0.0464677 | ||||||||
\(814\) | 8.61973e9 | − | 1.49298e10i | 0.560155 | − | 0.970217i | ||||
\(815\) | −1.96857e10 | − | 3.40967e10i | −1.27380 | − | 2.20628i | ||||
\(816\) | −2.92604e8 | − | 5.06806e8i | −0.0188523 | − | 0.0326532i | ||||
\(817\) | −1.26723e10 | + | 2.19491e10i | −0.812979 | + | 1.40812i | ||||
\(818\) | 7.01101e9 | 0.447862 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.06628e9 | 0.574223 | ||||||||
\(821\) | 1.37453e10 | − | 2.38076e10i | 0.866871 | − | 1.50146i | 0.00169374 | − | 0.999999i | \(-0.499461\pi\) |
0.865177 | − | 0.501466i | \(-0.167206\pi\) | |||||||
\(822\) | −1.73342e8 | − | 3.00238e8i | −0.0108856 | − | 0.0188544i | ||||
\(823\) | −8.06498e8 | − | 1.39690e9i | −0.0504318 | − | 0.0873504i | 0.839708 | − | 0.543039i | \(-0.182726\pi\) |
−0.890139 | + | 0.455689i | \(0.849393\pi\) | |||||||
\(824\) | −2.29144e9 | + | 3.96889e9i | −0.142680 | + | 0.247129i | ||||
\(825\) | 4.93486e9 | 0.305975 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.03950e9 | 0.555745 | 0.277872 | − | 0.960618i | \(-0.410371\pi\) | ||||
0.277872 | + | 0.960618i | \(0.410371\pi\) | |||||||
\(828\) | 3.77147e9 | − | 6.53238e9i | 0.230890 | − | 0.399913i | ||||
\(829\) | 1.23163e10 | + | 2.13324e10i | 0.750826 | + | 1.30047i | 0.947423 | + | 0.319984i | \(0.103677\pi\) |
−0.196597 | + | 0.980484i | \(0.562989\pi\) | |||||||
\(830\) | −1.22225e10 | − | 2.11700e10i | −0.741969 | − | 1.28513i | ||||
\(831\) | 2.34749e8 | − | 4.06598e8i | 0.0141906 | − | 0.0245788i | ||||
\(832\) | 3.03709e9 | 0.182821 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.66500e9 | 0.159080 | ||||||||
\(835\) | 8.65216e8 | − | 1.49860e9i | 0.0514306 | − | 0.0890805i | ||||
\(836\) | −4.03154e9 | − | 6.98283e9i | −0.238643 | − | 0.413342i | ||||
\(837\) | 9.12958e8 | + | 1.58129e9i | 0.0538160 | + | 0.0932121i | ||||
\(838\) | −8.06421e9 | + | 1.39676e10i | −0.473378 | + | 0.819914i | ||||
\(839\) | 6.84347e9 | 0.400046 | 0.200023 | − | 0.979791i | \(-0.435898\pi\) | ||||
0.200023 | + | 0.979791i | \(0.435898\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.65507e10 | −0.959468 | ||||||||
\(842\) | −2.27819e9 | + | 3.94593e9i | −0.131522 | + | 0.227802i | ||||
\(843\) | −1.60247e9 | − | 2.77555e9i | −0.0921282 | − | 0.159571i | ||||
\(844\) | −7.43747e9 | − | 1.28821e10i | −0.425820 | − | 0.737543i | ||||
\(845\) | 1.65241e10 | − | 2.86206e10i | 0.942148 | − | 1.63185i | ||||
\(846\) | −8.92123e9 | −0.506557 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.48928e9 | −0.0838667 | ||||||||
\(849\) | 1.72976e9 | − | 2.99603e9i | 0.0970082 | − | 0.168023i | ||||
\(850\) | −8.27067e9 | − | 1.43252e10i | −0.461928 | − | 0.800083i | ||||
\(851\) | 1.55874e10 | + | 2.69982e10i | 0.867003 | + | 1.50169i | ||||
\(852\) | −1.98928e8 | + | 3.44554e8i | −0.0110194 | + | 0.0190862i | ||||
\(853\) | −3.54072e10 | −1.95330 | −0.976652 | − | 0.214826i | \(-0.931081\pi\) | ||||
−0.976652 | + | 0.214826i | \(0.931081\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.15061e10 | 1.72390 | ||||||||
\(856\) | 3.57144e9 | − | 6.18592e9i | 0.194619 | − | 0.337090i | ||||
\(857\) | −9.36496e9 | − | 1.62206e10i | −0.508245 | − | 0.880306i | −0.999954 | − | 0.00954671i | \(-0.996961\pi\) |
0.491710 | − | 0.870759i | \(-0.336372\pi\) | |||||||
\(858\) | −1.68587e9 | − | 2.92002e9i | −0.0911212 | − | 0.157826i | ||||
\(859\) | −2.69136e9 | + | 4.66157e9i | −0.144876 | + | 0.250932i | −0.929327 | − | 0.369259i | \(-0.879612\pi\) |
0.784451 | + | 0.620191i | \(0.212945\pi\) | |||||||
\(860\) | −2.31034e10 | −1.23860 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.17552e9 | −0.328396 | ||||||||
\(863\) | −3.64722e9 | + | 6.31717e9i | −0.193163 | + | 0.334568i | −0.946297 | − | 0.323299i | \(-0.895208\pi\) |
0.753134 | + | 0.657868i | \(0.228541\pi\) | |||||||
\(864\) | 6.58240e8 | + | 1.14010e9i | 0.0347205 | + | 0.0601377i | ||||
\(865\) | 1.68037e10 | + | 2.91048e10i | 0.882771 | + | 1.52900i | ||||
\(866\) | 4.96008e9 | − | 8.59111e9i | 0.259523 | − | 0.449507i | ||||
\(867\) | −1.66854e9 | −0.0869503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.73938e10 | 1.41606 | ||||||||
\(870\) | −4.58387e8 | + | 7.93950e8i | −0.0236002 | + | 0.0408767i | ||||
\(871\) | −2.51720e10 | − | 4.35992e10i | −1.29079 | − | 2.23571i | ||||
\(872\) | −1.49579e9 | − | 2.59079e9i | −0.0763949 | − | 0.132320i | ||||
\(873\) | 2.20210e9 | − | 3.81416e9i | 0.112018 | − | 0.194021i | ||||
\(874\) | 1.45808e10 | 0.738740 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.05075e8 | −0.0404643 | ||||||||
\(877\) | −1.52811e10 | + | 2.64677e10i | −0.764992 | + | 1.32501i | 0.175258 | + | 0.984522i | \(0.443924\pi\) |
−0.940251 | + | 0.340483i | \(0.889409\pi\) | |||||||
\(878\) | 7.62485e9 | + | 1.32066e10i | 0.380190 | + | 0.658508i | ||||
\(879\) | 2.77819e9 | + | 4.81196e9i | 0.137975 | + | 0.238980i | ||||
\(880\) | 3.67502e9 | − | 6.36533e9i | 0.181790 | − | 0.314870i | ||||
\(881\) | 3.10736e10 | 1.53100 | 0.765500 | − | 0.643436i | \(-0.222492\pi\) | ||||
0.765500 | + | 0.643436i | \(0.222492\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.10432e9 | 0.445026 | 0.222513 | − | 0.974930i | \(-0.428574\pi\) | ||||
0.222513 | + | 0.974930i | \(0.428574\pi\) | |||||||
\(884\) | −5.65094e9 | + | 9.78772e9i | −0.275130 | + | 0.476539i | ||||
\(885\) | 4.63934e9 | + | 8.03557e9i | 0.224985 | + | 0.389686i | ||||
\(886\) | 2.01895e9 | + | 3.49693e9i | 0.0975232 | + | 0.168915i | ||||
\(887\) | −2.51708e8 | + | 4.35972e8i | −0.0121106 | + | 0.0209761i | −0.872017 | − | 0.489475i | \(-0.837188\pi\) |
0.859907 | + | 0.510451i | \(0.170522\pi\) | |||||||
\(888\) | −2.66472e9 | −0.127705 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.97150e10 | −0.937414 | ||||||||
\(891\) | −8.17783e9 | + | 1.41644e10i | −0.387316 | + | 0.670852i | ||||
\(892\) | −8.10620e9 | − | 1.40404e10i | −0.382420 | − | 0.662370i | ||||
\(893\) | −8.62254e9 | − | 1.49347e10i | −0.405187 | − | 0.701804i | ||||
\(894\) | −3.81340e8 | + | 6.60501e8i | −0.0178497 | + | 0.0309166i | ||||
\(895\) | −4.73665e10 | −2.20846 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.09727e9 | 0.282073 | ||||||||
\(898\) | 8.10884e9 | − | 1.40449e10i | 0.373673 | − | 0.647221i | ||||
\(899\) | 6.00870e8 | + | 1.04074e9i | 0.0275817 | + | 0.0477729i | ||||
\(900\) | 9.11211e9 | + | 1.57826e10i | 0.416649 | + | 0.721657i | ||||
\(901\) | 2.77101e9 | − | 4.79953e9i | 0.126212 | − | 0.218606i | ||||
\(902\) | −9.51278e9 | −0.431603 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.19271e9 | −0.278799 | ||||||||
\(905\) | −1.10773e9 | + | 1.91864e9i | −0.0496778 | + | 0.0860445i | ||||
\(906\) | −9.19616e8 | − | 1.59282e9i | −0.0410826 | − | 0.0711571i | ||||
\(907\) | −1.77696e10 | − | 3.07779e10i | −0.790774 | − | 1.36966i | −0.925488 | − | 0.378776i | \(-0.876345\pi\) |
0.134715 | − | 0.990884i | \(-0.456988\pi\) | |||||||
\(908\) | 1.44040e9 | − | 2.49484e9i | 0.0638531 | − | 0.110597i | ||||
\(909\) | 4.10462e10 | 1.81259 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.60841e10 | 1.58125 | 0.790627 | − | 0.612299i | \(-0.209755\pi\) | ||||
0.790627 | + | 0.612299i | \(0.209755\pi\) | |||||||
\(912\) | −6.23160e8 | + | 1.07934e9i | −0.0272031 | + | 0.0471171i | ||||
\(913\) | 1.28244e10 | + | 2.22125e10i | 0.557686 | + | 0.965941i | ||||
\(914\) | −8.15876e9 | − | 1.41314e10i | −0.353437 | − | 0.612171i | ||||
\(915\) | −1.92604e9 | + | 3.33599e9i | −0.0831171 | + | 0.143963i | ||||
\(916\) | −1.19663e10 | −0.514429 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.89900e9 | −0.209006 | ||||||||
\(919\) | 3.53488e9 | − | 6.12259e9i | 0.150235 | − | 0.260214i | −0.781079 | − | 0.624432i | \(-0.785330\pi\) |
0.931314 | + | 0.364218i | \(0.118664\pi\) | |||||||
\(920\) | 6.64570e9 | + | 1.15107e10i | 0.281373 | + | 0.487353i | ||||
\(921\) | −4.42353e9 | − | 7.66178e9i | −0.186578 | − | 0.323162i | ||||
\(922\) | −1.36556e10 | + | 2.36522e10i | −0.573790 | + | 0.993833i | ||||
\(923\) | 7.68363e9 | 0.321633 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.53203e10 | −3.12908 | ||||||||
\(926\) | 7.91571e9 | − | 1.37104e10i | 0.327606 | − | 0.567429i | ||||
\(927\) | 9.39462e9 | + | 1.62720e10i | 0.387347 | + | 0.670905i | ||||
\(928\) | 4.33225e8 | + | 7.50368e8i | 0.0177949 | + | 0.0308217i | ||||
\(929\) | −7.75510e9 | + | 1.34322e10i | −0.317345 | + | 0.549659i | −0.979933 | − | 0.199326i | \(-0.936125\pi\) |
0.662588 | + | 0.748984i | \(0.269458\pi\) | |||||||
\(930\) | −1.57574e9 | −0.0642385 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.64856e10 | −0.667038 | ||||||||
\(933\) | −7.68925e8 | + | 1.33182e9i | −0.0309955 | + | 0.0536857i | ||||
\(934\) | 7.45687e9 | + | 1.29157e10i | 0.299462 | + | 0.518684i | ||||
\(935\) | 1.36758e10 | + | 2.36872e10i | 0.547158 | + | 0.947705i | ||||
\(936\) | 6.22585e9 | − | 1.07835e10i | 0.248161 | − | 0.429827i | ||||
\(937\) | 3.61814e10 | 1.43680 | 0.718400 | − | 0.695630i | \(-0.244875\pi\) | ||||
0.718400 | + | 0.695630i | \(0.244875\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.24331e9 | −0.127838 | ||||||||
\(940\) | 7.86003e9 | − | 1.36140e10i | 0.308657 | − | 0.534610i | ||||
\(941\) | 9.32588e9 | + | 1.61529e10i | 0.364860 | + | 0.631956i | 0.988754 | − | 0.149553i | \(-0.0477835\pi\) |
−0.623894 | + | 0.781509i | \(0.714450\pi\) | |||||||
\(942\) | −4.77589e8 | − | 8.27209e8i | −0.0186156 | − | 0.0322431i | ||||
\(943\) | 8.60117e9 | − | 1.48977e10i | 0.334016 | − | 0.578532i | ||||
\(944\) | 8.76934e9 | 0.339285 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.42412e10 | 0.930969 | ||||||||
\(947\) | −4.27815e9 | + | 7.40997e9i | −0.163693 | + | 0.283525i | −0.936190 | − | 0.351493i | \(-0.885674\pi\) |
0.772497 | + | 0.635018i | \(0.219007\pi\) | |||||||
\(948\) | −2.11714e9 | − | 3.66700e9i | −0.0807088 | − | 0.139792i | ||||
\(949\) | 7.77403e9 | + | 1.34650e10i | 0.295267 | + | 0.511417i | ||||
\(950\) | −1.76141e10 | + | 3.05084e10i | −0.666541 | + | 1.15448i | ||||
\(951\) | −8.93512e9 | −0.336875 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.92820e8 | −0.0221870 | −0.0110935 | − | 0.999938i | \(-0.503531\pi\) | ||||
−0.0110935 | + | 0.999938i | \(0.503531\pi\) | |||||||
\(954\) | −3.05293e9 | + | 5.28782e9i | −0.113841 | + | 0.197178i | ||||
\(955\) | 6.01468e9 | + | 1.04177e10i | 0.223461 | + | 0.387045i | ||||
\(956\) | 1.00823e10 | + | 1.74630e10i | 0.373213 | + | 0.646423i | ||||
\(957\) | 4.80962e8 | − | 8.33051e8i | 0.0177386 | − | 0.0307241i | ||||
\(958\) | −2.97462e10 | −1.09308 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.13611e9 | −0.0414447 | ||||||||
\(961\) | 1.27235e10 | − | 2.20378e10i | 0.462462 | − | 0.801008i | ||||
\(962\) | 2.57313e10 | + | 4.45680e10i | 0.931857 | + | 1.61402i | ||||
\(963\) | −1.46425e10 | − | 2.53615e10i | −0.528351 | − | 0.915131i | ||||
\(964\) | 2.68768e9 | − | 4.65520e9i | 0.0966291 | − | 0.167366i | ||||
\(965\) | 3.50620e10 | 1.25601 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.25393e10 | −1.86849 | −0.934247 | − | 0.356626i | \(-0.883927\pi\) | ||||
−0.934247 | + | 0.356626i | \(0.883927\pi\) | |||||||
\(968\) | 1.13270e9 | − | 1.96190e9i | 0.0401377 | − | 0.0695205i | ||||
\(969\) | −2.31896e9 | − | 4.01655e9i | −0.0818766 | − | 0.141814i | ||||
\(970\) | 3.88032e9 | + | 6.72091e9i | 0.136511 | + | 0.236443i | ||||
\(971\) | −4.58288e9 | + | 7.93778e9i | −0.160647 | + | 0.278248i | −0.935101 | − | 0.354382i | \(-0.884691\pi\) |
0.774454 | + | 0.632630i | \(0.218025\pi\) | |||||||
\(972\) | 8.15143e9 | 0.284710 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.73073e10 | −0.600169 | ||||||||
\(975\) | −7.36568e9 | + | 1.27577e10i | −0.254505 | + | 0.440816i | ||||
\(976\) | 1.82031e9 | + | 3.15287e9i | 0.0626717 | + | 0.108550i | ||||
\(977\) | 1.00802e10 | + | 1.74594e10i | 0.345809 | + | 0.598959i | 0.985500 | − | 0.169673i | \(-0.0542711\pi\) |
−0.639691 | + | 0.768632i | \(0.720938\pi\) | |||||||
\(978\) | 3.19270e9 | − | 5.52992e9i | 0.109137 | − | 0.189031i | ||||
\(979\) | 2.06859e10 | 0.704588 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.22652e10 | −0.414793 | ||||||||
\(982\) | −9.50432e8 | + | 1.64620e9i | −0.0320281 | + | 0.0554742i | ||||
\(983\) | −5.94946e8 | − | 1.03048e9i | −0.0199775 | − | 0.0346020i | 0.855864 | − | 0.517201i | \(-0.173026\pi\) |
−0.875841 | + | 0.482599i | \(0.839693\pi\) | |||||||
\(984\) | 7.35201e8 | + | 1.27341e9i | 0.0245993 | + | 0.0426073i | ||||
\(985\) | 2.75549e10 | − | 4.77264e10i | 0.918695 | − | 1.59123i | ||||
\(986\) | −3.22431e9 | −0.107119 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.40696e10 | 0.793999 | ||||||||
\(989\) | −2.19182e10 | + | 3.79634e10i | −0.720473 | + | 1.24790i | ||||
\(990\) | −1.50672e10 | − | 2.60971e10i | −0.493524 | − | 0.854809i | ||||
\(991\) | −1.04993e10 | − | 1.81853e10i | −0.342691 | − | 0.593558i | 0.642240 | − | 0.766503i | \(-0.278005\pi\) |
−0.984931 | + | 0.172945i | \(0.944672\pi\) | |||||||
\(992\) | −7.44623e8 | + | 1.28973e9i | −0.0242184 | + | 0.0419475i | ||||
\(993\) | 2.10211e9 | 0.0681291 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.11013e10 | 1.00092 | ||||||||
\(996\) | 1.98229e9 | − | 3.43342e9i | 0.0635709 | − | 0.110108i | ||||
\(997\) | 1.60829e10 | + | 2.78563e10i | 0.513961 | + | 0.890206i | 0.999869 | + | 0.0161963i | \(0.00515567\pi\) |
−0.485908 | + | 0.874010i | \(0.661511\pi\) | |||||||
\(998\) | −1.06066e10 | − | 1.83712e10i | −0.337770 | − | 0.585035i | ||||
\(999\) | −1.11537e10 | + | 1.93188e10i | −0.353948 | + | 0.613056i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 98.8.c.k.79.1 | 4 | ||
7.2 | even | 3 | 98.8.a.g.1.2 | 2 | |||
7.3 | odd | 6 | 98.8.c.g.67.2 | 4 | |||
7.4 | even | 3 | inner | 98.8.c.k.67.1 | 4 | ||
7.5 | odd | 6 | 14.8.a.c.1.1 | ✓ | 2 | ||
7.6 | odd | 2 | 98.8.c.g.79.2 | 4 | |||
21.5 | even | 6 | 126.8.a.i.1.1 | 2 | |||
28.19 | even | 6 | 112.8.a.g.1.2 | 2 | |||
35.12 | even | 12 | 350.8.c.k.99.4 | 4 | |||
35.19 | odd | 6 | 350.8.a.j.1.2 | 2 | |||
35.33 | even | 12 | 350.8.c.k.99.1 | 4 | |||
56.5 | odd | 6 | 448.8.a.l.1.2 | 2 | |||
56.19 | even | 6 | 448.8.a.s.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.8.a.c.1.1 | ✓ | 2 | 7.5 | odd | 6 | ||
98.8.a.g.1.2 | 2 | 7.2 | even | 3 | |||
98.8.c.g.67.2 | 4 | 7.3 | odd | 6 | |||
98.8.c.g.79.2 | 4 | 7.6 | odd | 2 | |||
98.8.c.k.67.1 | 4 | 7.4 | even | 3 | inner | ||
98.8.c.k.79.1 | 4 | 1.1 | even | 1 | trivial | ||
112.8.a.g.1.2 | 2 | 28.19 | even | 6 | |||
126.8.a.i.1.1 | 2 | 21.5 | even | 6 | |||
350.8.a.j.1.2 | 2 | 35.19 | odd | 6 | |||
350.8.c.k.99.1 | 4 | 35.33 | even | 12 | |||
350.8.c.k.99.4 | 4 | 35.12 | even | 12 | |||
448.8.a.l.1.2 | 2 | 56.5 | odd | 6 | |||
448.8.a.s.1.1 | 2 | 56.19 | even | 6 |