Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,8,Mod(55,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, 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("162.55");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.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: | \(50.6063741284\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 518x^{5} + 53377x^{4} + 11940x^{3} + 3528x^{2} + 1563408x + 346406544 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{18} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.2 | ||
Root | \(-9.64382 - 9.64382i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.109 |
Dual form | 162.8.c.q.55.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −32.0000 | + | 55.4256i | −0.250000 | + | 0.433013i | ||||
\(5\) | −162.750 | + | 281.891i | −0.582272 | + | 1.00852i | 0.412938 | + | 0.910759i | \(0.364503\pi\) |
−0.995210 | + | 0.0977650i | \(0.968831\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 725.227 | + | 1256.13i | 0.799155 | + | 1.38418i | 0.920167 | + | 0.391525i | \(0.128052\pi\) |
−0.121013 | + | 0.992651i | \(0.538614\pi\) | |||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2604.00 | 0.823457 | ||||||||
\(11\) | 2777.90 | + | 4811.46i | 0.629277 | + | 1.08994i | 0.987697 | + | 0.156380i | \(0.0499823\pi\) |
−0.358420 | + | 0.933560i | \(0.616684\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6751.86 | + | 11694.6i | −0.852357 | + | 1.47633i | 0.0267188 | + | 0.999643i | \(0.491494\pi\) |
−0.879076 | + | 0.476682i | \(0.841839\pi\) | |||||||
\(14\) | 5801.82 | − | 10049.0i | 0.565088 | − | 0.978760i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2048.00 | − | 3547.24i | −0.125000 | − | 0.216506i | ||||
\(17\) | 11828.7 | 0.583937 | 0.291969 | − | 0.956428i | \(-0.405690\pi\) | ||||
0.291969 | + | 0.956428i | \(0.405690\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 44544.0 | 1.48988 | 0.744940 | − | 0.667131i | \(-0.232478\pi\) | ||||
0.744940 | + | 0.667131i | \(0.232478\pi\) | |||||||
\(20\) | −10416.0 | − | 18041.0i | −0.291136 | − | 0.504262i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 22223.2 | − | 38491.7i | 0.444966 | − | 0.770704i | ||||
\(23\) | −13403.3 | + | 23215.2i | −0.229702 | + | 0.397855i | −0.957720 | − | 0.287703i | \(-0.907108\pi\) |
0.728018 | + | 0.685558i | \(0.240442\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13912.6 | − | 24097.3i | −0.178081 | − | 0.308445i | ||||
\(26\) | 108030. | 1.20541 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −92829.0 | −0.799155 | ||||||||
\(29\) | −70432.1 | − | 121992.i | −0.536263 | − | 0.928834i | −0.999101 | − | 0.0423914i | \(-0.986502\pi\) |
0.462838 | − | 0.886443i | \(-0.346831\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −82846.2 | + | 143494.i | −0.499467 | + | 0.865102i | −1.00000 | 0.000615720i | \(-0.999804\pi\) | |
0.500533 | + | 0.865717i | \(0.333137\pi\) | |||||||
\(32\) | −16384.0 | + | 28377.9i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −47314.8 | − | 81951.7i | −0.206453 | − | 0.357587i | ||||
\(35\) | −472122. | −1.86130 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 36343.3 | 0.117956 | 0.0589778 | − | 0.998259i | \(-0.481216\pi\) | ||||
0.0589778 | + | 0.998259i | \(0.481216\pi\) | |||||||
\(38\) | −178176. | − | 308610.i | −0.526752 | − | 0.912362i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −83328.0 | + | 144328.i | −0.205864 | + | 0.356567i | ||||
\(41\) | 239035. | − | 414020.i | 0.541648 | − | 0.938163i | −0.457161 | − | 0.889384i | \(-0.651134\pi\) |
0.998810 | − | 0.0487788i | \(-0.0155329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 302108. | + | 523266.i | 0.579458 | + | 1.00365i | 0.995541 | + | 0.0943248i | \(0.0300692\pi\) |
−0.416083 | + | 0.909327i | \(0.636597\pi\) | |||||||
\(44\) | −355571. | −0.629277 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 214453. | 0.324848 | ||||||||
\(47\) | −251533. | − | 435667.i | −0.353388 | − | 0.612086i | 0.633453 | − | 0.773781i | \(-0.281637\pi\) |
−0.986841 | + | 0.161695i | \(0.948304\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −640137. | + | 1.10875e6i | −0.777296 | + | 1.34632i | ||||
\(50\) | −111301. | + | 192778.i | −0.125922 | + | 0.218104i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −432119. | − | 748452.i | −0.426178 | − | 0.738163i | ||||
\(53\) | 1.99651e6 | 1.84207 | 0.921036 | − | 0.389477i | \(-0.127344\pi\) | ||||
0.921036 | + | 0.389477i | \(0.127344\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.80841e6 | −1.46564 | ||||||||
\(56\) | 371316. | + | 643138.i | 0.282544 | + | 0.489380i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −563457. | + | 975935.i | −0.379195 | + | 0.656785i | ||||
\(59\) | −304536. | + | 527472.i | −0.193044 | + | 0.334362i | −0.946258 | − | 0.323414i | \(-0.895169\pi\) |
0.753214 | + | 0.657776i | \(0.228503\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −950933. | − | 1.64706e6i | −0.536408 | − | 0.929087i | −0.999094 | − | 0.0425640i | \(-0.986447\pi\) |
0.462685 | − | 0.886523i | \(-0.346886\pi\) | |||||||
\(62\) | 1.32554e6 | 0.706353 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −2.19773e6 | − | 3.80658e6i | −0.992607 | − | 1.71925i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −886834. | + | 1.53604e6i | −0.360231 | + | 0.623938i | −0.987999 | − | 0.154463i | \(-0.950635\pi\) |
0.627768 | + | 0.778401i | \(0.283969\pi\) | |||||||
\(68\) | −378519. | + | 655614.i | −0.145984 | + | 0.252852i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.88849e6 | + | 3.27096e6i | 0.658069 | + | 1.13981i | ||||
\(71\) | 1.00843e6 | 0.334380 | 0.167190 | − | 0.985925i | \(-0.446531\pi\) | ||||
0.167190 | + | 0.985925i | \(0.446531\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 146188. | 0.0439825 | 0.0219913 | − | 0.999758i | \(-0.492999\pi\) | ||||
0.0219913 | + | 0.999758i | \(0.492999\pi\) | |||||||
\(74\) | −145373. | − | 251794.i | −0.0417036 | − | 0.0722327i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.42541e6 | + | 2.46888e6i | −0.372470 | + | 0.645137i | ||||
\(77\) | −4.02921e6 | + | 6.97880e6i | −1.00578 | + | 1.74206i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.63689e6 | + | 6.29928e6i | 0.829919 | + | 1.43746i | 0.898101 | + | 0.439788i | \(0.144947\pi\) |
−0.0681828 | + | 0.997673i | \(0.521720\pi\) | |||||||
\(80\) | 1.33325e6 | 0.291136 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.82456e6 | −0.766007 | ||||||||
\(83\) | 2.68846e6 | + | 4.65655e6i | 0.516096 | + | 0.893905i | 0.999825 | + | 0.0186871i | \(0.00594865\pi\) |
−0.483729 | + | 0.875218i | \(0.660718\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.92512e6 | + | 3.33441e6i | −0.340010 | + | 0.588915i | ||||
\(86\) | 2.41686e6 | − | 4.18613e6i | 0.409739 | − | 0.709689i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.42228e6 | + | 2.46347e6i | 0.222483 | + | 0.385352i | ||||
\(89\) | −2.94159e6 | −0.442301 | −0.221150 | − | 0.975240i | \(-0.570981\pi\) | ||||
−0.221150 | + | 0.975240i | \(0.570981\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.95865e7 | −2.72466 | ||||||||
\(92\) | −857812. | − | 1.48577e6i | −0.114851 | − | 0.198928i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.01226e6 | + | 3.48534e6i | −0.249883 | + | 0.432810i | ||||
\(95\) | −7.24953e6 | + | 1.25566e7i | −0.867515 | + | 1.50258i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.95734e6 | + | 6.85431e6i | 0.440253 | + | 0.762540i | 0.997708 | − | 0.0676669i | \(-0.0215555\pi\) |
−0.557455 | + | 0.830207i | \(0.688222\pi\) | |||||||
\(98\) | 1.02422e7 | 1.09926 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.78081e6 | 0.178081 | ||||||||
\(101\) | −9.25788e6 | − | 1.60351e7i | −0.894101 | − | 1.54863i | −0.834913 | − | 0.550382i | \(-0.814482\pi\) |
−0.0591886 | − | 0.998247i | \(-0.518851\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.02032e6 | + | 8.69546e6i | −0.452691 | + | 0.784083i | −0.998552 | − | 0.0537923i | \(-0.982869\pi\) |
0.545862 | + | 0.837875i | \(0.316202\pi\) | |||||||
\(104\) | −3.45695e6 | + | 5.98761e6i | −0.301354 | + | 0.521960i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.98606e6 | − | 1.38323e7i | −0.651271 | − | 1.12803i | ||||
\(107\) | 1.26542e7 | 0.998601 | 0.499300 | − | 0.866429i | \(-0.333590\pi\) | ||||
0.499300 | + | 0.866429i | \(0.333590\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.26740e6 | −0.0937388 | −0.0468694 | − | 0.998901i | \(-0.514924\pi\) | ||||
−0.0468694 | + | 0.998901i | \(0.514924\pi\) | |||||||
\(110\) | 7.23364e6 | + | 1.25290e7i | 0.518182 | + | 0.897518i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.97053e6 | − | 5.14511e6i | 0.199789 | − | 0.346044i | ||||
\(113\) | 7.42101e6 | − | 1.28536e7i | 0.483825 | − | 0.838010i | −0.516002 | − | 0.856587i | \(-0.672580\pi\) |
0.999827 | + | 0.0185773i | \(0.00591367\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.36278e6 | − | 7.55655e6i | −0.267498 | − | 0.463320i | ||||
\(116\) | 9.01531e6 | 0.536263 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.87257e6 | 0.273005 | ||||||||
\(119\) | 8.57850e6 | + | 1.48584e7i | 0.466656 | + | 0.808272i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.68985e6 | + | 9.85512e6i | −0.291979 | + | 0.505723i | ||||
\(122\) | −7.60747e6 | + | 1.31765e7i | −0.379298 | + | 0.656963i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.30216e6 | − | 9.18360e6i | −0.249733 | − | 0.432551i | ||||
\(125\) | −1.63726e7 | −0.749778 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.71798e6 | −0.420982 | −0.210491 | − | 0.977596i | \(-0.567506\pi\) | ||||
−0.210491 | + | 0.977596i | \(0.567506\pi\) | |||||||
\(128\) | −1.04858e6 | − | 1.81619e6i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.75818e7 | + | 3.04526e7i | −0.701879 | + | 1.21569i | ||||
\(131\) | 9.15312e6 | − | 1.58537e7i | 0.355729 | − | 0.616141i | −0.631513 | − | 0.775365i | \(-0.717566\pi\) |
0.987242 | + | 0.159224i | \(0.0508992\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.23045e7 | + | 5.59530e7i | 1.19064 | + | 2.06226i | ||||
\(134\) | 1.41893e7 | 0.509443 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.05630e6 | 0.206453 | ||||||||
\(137\) | −2.42286e7 | − | 4.19652e7i | −0.805019 | − | 1.39433i | −0.916278 | − | 0.400543i | \(-0.868821\pi\) |
0.111258 | − | 0.993792i | \(-0.464512\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.89915e7 | − | 3.28943e7i | 0.599802 | − | 1.03889i | −0.393048 | − | 0.919518i | \(-0.628579\pi\) |
0.992850 | − | 0.119370i | \(-0.0380875\pi\) | |||||||
\(140\) | 1.51079e7 | − | 2.61677e7i | 0.465325 | − | 0.805967i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.03371e6 | − | 6.98658e6i | −0.118221 | − | 0.204765i | ||||
\(143\) | −7.50239e7 | −2.14547 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.58513e7 | 1.24900 | ||||||||
\(146\) | −584750. | − | 1.01282e6i | −0.0155502 | − | 0.0269337i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.16299e6 | + | 2.01435e6i | −0.0294889 | + | 0.0510762i | ||||
\(149\) | −1.79041e7 | + | 3.10108e7i | −0.443405 | + | 0.768000i | −0.997940 | − | 0.0641605i | \(-0.979563\pi\) |
0.554534 | + | 0.832161i | \(0.312896\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.40510e7 | − | 4.16575e7i | −0.568478 | − | 0.984632i | −0.996717 | − | 0.0809668i | \(-0.974199\pi\) |
0.428239 | − | 0.903665i | \(-0.359134\pi\) | |||||||
\(152\) | 2.28065e7 | 0.526752 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.44674e7 | 1.42239 | ||||||||
\(155\) | −2.69664e7 | − | 4.67072e7i | −0.581651 | − | 1.00745i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.97645e7 | − | 6.88742e7i | 0.820062 | − | 1.42039i | −0.0855727 | − | 0.996332i | \(-0.527272\pi\) |
0.905635 | − | 0.424058i | \(-0.139395\pi\) | |||||||
\(158\) | 2.90951e7 | − | 5.03942e7i | 0.586841 | − | 1.01644i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.33299e6 | − | 9.23701e6i | −0.102932 | − | 0.178284i | ||||
\(161\) | −3.88818e7 | −0.734269 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.46340e7 | −0.807252 | −0.403626 | − | 0.914924i | \(-0.632250\pi\) | ||||
−0.403626 | + | 0.914924i | \(0.632250\pi\) | |||||||
\(164\) | 1.52982e7 | + | 2.64973e7i | 0.270824 | + | 0.469081i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.15077e7 | − | 3.72524e7i | 0.364935 | − | 0.632086i | ||||
\(167\) | 3.54323e6 | − | 6.13706e6i | 0.0588697 | − | 0.101965i | −0.835089 | − | 0.550115i | \(-0.814584\pi\) |
0.893958 | + | 0.448150i | \(0.147917\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.98009e7 | − | 1.03578e8i | −0.953024 | − | 1.65069i | ||||
\(170\) | 3.08019e7 | 0.480847 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.86698e7 | −0.579458 | ||||||||
\(173\) | 3.44494e7 | + | 5.96681e7i | 0.505848 | + | 0.876154i | 0.999977 | + | 0.00676581i | \(0.00215364\pi\) |
−0.494129 | + | 0.869388i | \(0.664513\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.01795e7 | − | 3.49520e7i | 0.284628 | − | 0.492991i | ||||
\(176\) | 1.13783e7 | − | 1.97077e7i | 0.157319 | − | 0.272485i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.17664e7 | + | 2.03800e7i | 0.156377 | + | 0.270853i | ||||
\(179\) | −8.88821e7 | −1.15832 | −0.579161 | − | 0.815214i | \(-0.696620\pi\) | ||||
−0.579161 | + | 0.815214i | \(0.696620\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.42211e7 | 0.930363 | 0.465182 | − | 0.885215i | \(-0.345989\pi\) | ||||
0.465182 | + | 0.885215i | \(0.345989\pi\) | |||||||
\(182\) | 7.83460e7 | + | 1.35699e8i | 0.963313 | + | 1.66851i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.86250e6 | + | 1.18862e7i | −0.0812119 | + | 0.140663i | ||||
\(185\) | −5.91487e6 | + | 1.02449e7i | −0.0686822 | + | 0.118961i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.28589e7 | + | 5.69134e7i | 0.367458 | + | 0.636456i | ||||
\(188\) | 3.21962e7 | 0.353388 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.15992e8 | 1.22685 | ||||||||
\(191\) | −1.27812e7 | − | 2.21377e7i | −0.132726 | − | 0.229888i | 0.792001 | − | 0.610520i | \(-0.209040\pi\) |
−0.924726 | + | 0.380632i | \(0.875706\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.91854e7 | − | 8.51916e7i | 0.492477 | − | 0.852994i | −0.507486 | − | 0.861660i | \(-0.669425\pi\) |
0.999962 | + | 0.00866567i | \(0.00275840\pi\) | |||||||
\(194\) | 3.16587e7 | − | 5.48345e7i | 0.311306 | − | 0.539197i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.09687e7 | − | 7.09599e7i | −0.388648 | − | 0.673158i | ||||
\(197\) | 1.40581e7 | 0.131007 | 0.0655036 | − | 0.997852i | \(-0.479135\pi\) | ||||
0.0655036 | + | 0.997852i | \(0.479135\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.87427e7 | 0.258548 | 0.129274 | − | 0.991609i | \(-0.458735\pi\) | ||||
0.129274 | + | 0.991609i | \(0.458735\pi\) | |||||||
\(200\) | −7.12323e6 | − | 1.23378e7i | −0.0629611 | − | 0.109052i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.40630e7 | + | 1.28281e8i | −0.632225 | + | 1.09505i | ||||
\(203\) | 1.02158e8 | − | 1.76944e8i | 0.857113 | − | 1.48456i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.78058e7 | + | 1.34764e8i | 0.630773 | + | 1.09253i | ||||
\(206\) | 8.03252e7 | 0.640201 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.53112e7 | 0.426178 | ||||||||
\(209\) | 1.23739e8 | + | 2.14322e8i | 0.937548 | + | 1.62388i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.86546e7 | − | 1.70875e8i | 0.722984 | − | 1.25224i | −0.236815 | − | 0.971555i | \(-0.576103\pi\) |
0.959798 | − | 0.280690i | \(-0.0905633\pi\) | |||||||
\(212\) | −6.38884e7 | + | 1.10658e8i | −0.460518 | + | 0.797641i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.06169e7 | − | 8.76710e7i | −0.353059 | − | 0.611516i | ||||
\(215\) | −1.96672e8 | −1.34961 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.40329e8 | −1.59660 | ||||||||
\(218\) | 5.06958e6 | + | 8.78078e6i | 0.0331417 | + | 0.0574031i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.78691e7 | − | 1.00232e8i | 0.366410 | − | 0.634641i | ||||
\(221\) | −7.98657e7 | + | 1.38332e8i | −0.497723 | + | 0.862081i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.74143e7 | + | 6.48035e7i | 0.225928 | + | 0.391319i | 0.956598 | − | 0.291412i | \(-0.0941252\pi\) |
−0.730669 | + | 0.682732i | \(0.760792\pi\) | |||||||
\(224\) | −4.75285e7 | −0.282544 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.18736e8 | −0.684232 | ||||||||
\(227\) | −3.61741e7 | − | 6.26554e7i | −0.205261 | − | 0.355523i | 0.744955 | − | 0.667115i | \(-0.232471\pi\) |
−0.950216 | + | 0.311592i | \(0.899138\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.52392e8 | − | 2.63951e8i | 0.838567 | − | 1.45244i | −0.0525253 | − | 0.998620i | \(-0.516727\pi\) |
0.891093 | − | 0.453822i | \(-0.149940\pi\) | |||||||
\(230\) | −3.49022e7 | + | 6.04524e7i | −0.189150 | + | 0.327617i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.60612e7 | − | 6.24599e7i | −0.189597 | − | 0.328392i | ||||
\(233\) | −2.36334e7 | −0.122400 | −0.0612000 | − | 0.998126i | \(-0.519493\pi\) | ||||
−0.0612000 | + | 0.998126i | \(0.519493\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.63748e8 | 0.823072 | ||||||||
\(236\) | −1.94903e7 | − | 3.37582e7i | −0.0965220 | − | 0.167181i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.86280e7 | − | 1.18867e8i | 0.329976 | − | 0.571535i | ||||
\(239\) | −1.15507e8 | + | 2.00064e8i | −0.547288 | + | 0.947931i | 0.451171 | + | 0.892438i | \(0.351007\pi\) |
−0.998459 | + | 0.0554937i | \(0.982327\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.96906e7 | + | 5.14256e7i | 0.136634 | + | 0.236657i | 0.926220 | − | 0.376982i | \(-0.123038\pi\) |
−0.789586 | + | 0.613639i | \(0.789705\pi\) | |||||||
\(242\) | 9.10377e7 | 0.412921 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.21719e8 | 0.536408 | ||||||||
\(245\) | −2.08364e8 | − | 3.60898e8i | −0.905195 | − | 1.56784i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.00755e8 | + | 5.20922e8i | −1.26991 | + | 2.19955i | ||||
\(248\) | −4.24172e7 | + | 7.34688e7i | −0.176588 | + | 0.305860i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.54904e7 | + | 1.13433e8i | 0.265086 | + | 0.459143i | ||||
\(251\) | 3.16166e8 | 1.26199 | 0.630997 | − | 0.775785i | \(-0.282646\pi\) | ||||
0.630997 | + | 0.775785i | \(0.282646\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.48932e8 | −0.578185 | ||||||||
\(254\) | 3.88719e7 | + | 6.73282e7i | 0.148839 | + | 0.257798i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.38861e6 | + | 1.45295e7i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 2.83155e7 | − | 4.90438e7i | 0.104054 | − | 0.180226i | −0.809297 | − | 0.587399i | \(-0.800152\pi\) |
0.913351 | + | 0.407173i | \(0.133485\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.63571e7 | + | 4.56519e7i | 0.0942647 | + | 0.163271i | ||||
\(260\) | 2.81309e8 | 0.992607 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.46450e8 | −0.503077 | ||||||||
\(263\) | −1.20320e7 | − | 2.08400e7i | −0.0407842 | − | 0.0706404i | 0.844913 | − | 0.534904i | \(-0.179652\pi\) |
−0.885697 | + | 0.464264i | \(0.846319\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.24932e8 | + | 5.62799e8i | −1.07259 | + | 1.85778i | ||||
\(266\) | 2.58436e8 | − | 4.47624e8i | 0.841913 | − | 1.45824i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.67574e7 | − | 9.83067e7i | −0.180115 | − | 0.311969i | ||||
\(269\) | −4.42132e8 | −1.38490 | −0.692451 | − | 0.721465i | \(-0.743469\pi\) | ||||
−0.692451 | + | 0.721465i | \(0.743469\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.81928e8 | 0.555272 | 0.277636 | − | 0.960686i | \(-0.410449\pi\) | ||||
0.277636 | + | 0.960686i | \(0.410449\pi\) | |||||||
\(272\) | −2.42252e7 | − | 4.19593e7i | −0.0729921 | − | 0.126426i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.93829e8 | + | 3.35721e8i | −0.569235 | + | 0.985943i | ||||
\(275\) | 7.72954e7 | − | 1.33880e8i | 0.224124 | − | 0.388195i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.30393e8 | − | 2.25847e8i | −0.368617 | − | 0.638463i | 0.620733 | − | 0.784022i | \(-0.286835\pi\) |
−0.989350 | + | 0.145559i | \(0.953502\pi\) | |||||||
\(278\) | −3.03864e8 | −0.848249 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.41727e8 | −0.658069 | ||||||||
\(281\) | 1.77884e8 | + | 3.08105e8i | 0.478261 | + | 0.828373i | 0.999689 | − | 0.0249221i | \(-0.00793379\pi\) |
−0.521428 | + | 0.853295i | \(0.674600\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.52802e7 | − | 1.30389e8i | 0.197437 | − | 0.341971i | −0.750260 | − | 0.661143i | \(-0.770072\pi\) |
0.947697 | + | 0.319172i | \(0.103405\pi\) | |||||||
\(284\) | −3.22697e7 | + | 5.58927e7i | −0.0835950 | + | 0.144791i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.00096e8 | + | 5.19781e8i | 0.758540 | + | 1.31383i | ||||
\(287\) | 6.93418e8 | 1.73144 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.70420e8 | −0.659017 | ||||||||
\(290\) | −1.83405e8 | − | 3.17667e8i | −0.441589 | − | 0.764855i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.67800e6 | + | 8.10254e6i | −0.0109956 | + | 0.0190450i | ||||
\(293\) | −1.09451e8 | + | 1.89574e8i | −0.254204 | + | 0.440294i | −0.964679 | − | 0.263429i | \(-0.915147\pi\) |
0.710475 | + | 0.703722i | \(0.248480\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.91264e7 | − | 1.71692e8i | −0.224808 | − | 0.389379i | ||||
\(296\) | 1.86078e7 | 0.0417036 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.86466e8 | 0.627070 | ||||||||
\(299\) | −1.80994e8 | − | 3.13492e8i | −0.391576 | − | 0.678230i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.38193e8 | + | 7.58973e8i | −0.926154 | + | 1.60415i | ||||
\(302\) | −1.92408e8 | + | 3.33260e8i | −0.401974 | + | 0.696240i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.12261e7 | − | 1.58008e8i | −0.186235 | − | 0.322569i | ||||
\(305\) | 6.19057e8 | 1.24934 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.49207e8 | −1.08331 | −0.541654 | − | 0.840602i | \(-0.682202\pi\) | ||||
−0.541654 | + | 0.840602i | \(0.682202\pi\) | |||||||
\(308\) | −2.57870e8 | − | 4.46643e8i | −0.502890 | − | 0.871030i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.15731e8 | + | 3.73658e8i | −0.411289 | + | 0.712374i | ||||
\(311\) | −2.54600e8 | + | 4.40980e8i | −0.479951 | + | 0.831299i | −0.999736 | − | 0.0229982i | \(-0.992679\pi\) |
0.519785 | + | 0.854297i | \(0.326012\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.80921e8 | − | 4.86569e8i | −0.517819 | − | 0.896889i | −0.999786 | − | 0.0206997i | \(-0.993411\pi\) |
0.481966 | − | 0.876190i | \(-0.339923\pi\) | |||||||
\(314\) | −6.36232e8 | −1.15974 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.65522e8 | −0.829919 | ||||||||
\(317\) | −4.47978e8 | − | 7.75921e8i | −0.789859 | − | 1.36808i | −0.926053 | − | 0.377394i | \(-0.876820\pi\) |
0.136194 | − | 0.990682i | \(-0.456513\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.91306e8 | − | 6.77762e8i | 0.674916 | − | 1.16899i | ||||
\(320\) | −4.26639e7 | + | 7.38961e7i | −0.0727840 | + | 0.126066i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.55527e8 | + | 2.69381e8i | 0.259603 | + | 0.449646i | ||||
\(323\) | 5.26898e8 | 0.869997 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.75743e8 | 0.607154 | ||||||||
\(326\) | 1.78536e8 | + | 3.09233e8i | 0.285407 | + | 0.494339i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.22386e8 | − | 2.11978e8i | 0.191502 | − | 0.331691i | ||||
\(329\) | 3.64836e8 | − | 6.31915e8i | 0.564823 | − | 0.978303i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.52581e8 | + | 6.10688e8i | 0.534393 | + | 0.925595i | 0.999192 | + | 0.0401795i | \(0.0127930\pi\) |
−0.464800 | + | 0.885416i | \(0.653874\pi\) | |||||||
\(332\) | −3.44123e8 | −0.516096 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.66917e7 | −0.0832543 | ||||||||
\(335\) | −2.88664e8 | − | 4.99981e8i | −0.419504 | − | 0.726603i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.97208e8 | + | 8.61189e8i | −0.707674 | + | 1.22573i | 0.258044 | + | 0.966133i | \(0.416922\pi\) |
−0.965718 | + | 0.259594i | \(0.916411\pi\) | |||||||
\(338\) | −4.78407e8 | + | 8.28625e8i | −0.673890 | + | 1.16721i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.23208e8 | − | 2.13402e8i | −0.170005 | − | 0.294457i | ||||
\(341\) | −9.20553e8 | −1.25721 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.62466e8 | −0.886409 | ||||||||
\(344\) | 1.54679e8 | + | 2.67912e8i | 0.204869 | + | 0.354844i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.75595e8 | − | 4.77345e8i | 0.357688 | − | 0.619535i | ||||
\(347\) | −8.19608e6 | + | 1.41960e7i | −0.0105306 | + | 0.0182395i | −0.871243 | − | 0.490853i | \(-0.836685\pi\) |
0.860712 | + | 0.509092i | \(0.170019\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.13389e8 | + | 3.69600e8i | 0.268709 | + | 0.465418i | 0.968529 | − | 0.248902i | \(-0.0800695\pi\) |
−0.699819 | + | 0.714320i | \(0.746736\pi\) | |||||||
\(350\) | −3.22873e8 | −0.402525 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.82052e8 | −0.222483 | ||||||||
\(353\) | 8.02765e8 | + | 1.39043e9i | 0.971353 | + | 1.68243i | 0.691480 | + | 0.722396i | \(0.256959\pi\) |
0.279873 | + | 0.960037i | \(0.409708\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.64121e8 | + | 2.84267e8i | −0.194700 | + | 0.337230i | ||||
\(356\) | 9.41310e7 | − | 1.63040e8i | 0.110575 | − | 0.191522i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.55529e8 | + | 6.15794e8i | 0.409528 | + | 0.709324i | ||||
\(359\) | 1.39612e9 | 1.59255 | 0.796276 | − | 0.604934i | \(-0.206801\pi\) | ||||
0.796276 | + | 0.604934i | \(0.206801\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.09029e9 | 1.21974 | ||||||||
\(362\) | −2.96885e8 | − | 5.14219e8i | −0.328933 | − | 0.569729i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.26768e8 | − | 1.08559e9i | 0.681165 | − | 1.17981i | ||||
\(365\) | −2.37920e7 | + | 4.12090e7i | −0.0256098 | + | 0.0443575i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.53807e8 | + | 1.30563e9i | 0.796029 | + | 1.37876i | 0.922184 | + | 0.386752i | \(0.126403\pi\) |
−0.126154 | + | 0.992011i | \(0.540264\pi\) | |||||||
\(368\) | 1.09800e8 | 0.114851 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.46379e7 | 0.0971313 | ||||||||
\(371\) | 1.44793e9 | + | 2.50788e9i | 1.47210 | + | 2.54975i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.86590e8 | − | 6.69593e8i | 0.385718 | − | 0.668083i | −0.606151 | − | 0.795350i | \(-0.707287\pi\) |
0.991868 | + | 0.127267i | \(0.0406206\pi\) | |||||||
\(374\) | 2.62872e8 | − | 4.55307e8i | 0.259832 | − | 0.450043i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.28785e8 | − | 2.23062e8i | −0.124942 | − | 0.216405i | ||||
\(377\) | 1.90219e9 | 1.82835 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.65039e9 | 1.55722 | 0.778610 | − | 0.627508i | \(-0.215925\pi\) | ||||
0.778610 | + | 0.627508i | \(0.215925\pi\) | |||||||
\(380\) | −4.63970e8 | − | 8.03619e8i | −0.433758 | − | 0.751290i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.02250e8 | + | 1.77102e8i | −0.0938514 | + | 0.162555i | ||||
\(383\) | 3.25719e8 | − | 5.64162e8i | 0.296242 | − | 0.513107i | −0.679031 | − | 0.734110i | \(-0.737600\pi\) |
0.975273 | + | 0.221003i | \(0.0709331\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.31151e9 | − | 2.27160e9i | −1.17127 | − | 2.02871i | ||||
\(386\) | −7.86966e8 | −0.696467 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.06539e8 | −0.440253 | ||||||||
\(389\) | 4.36384e8 | + | 7.55840e8i | 0.375877 | + | 0.651038i | 0.990458 | − | 0.137816i | \(-0.0440082\pi\) |
−0.614581 | + | 0.788854i | \(0.710675\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.58544e8 | + | 2.74606e8i | −0.134131 | + | 0.232323i | ||||
\(392\) | −3.27750e8 | + | 5.67680e8i | −0.274816 | + | 0.475995i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.62324e7 | − | 9.73974e7i | −0.0463180 | − | 0.0802252i | ||||
\(395\) | −2.36761e9 | −1.93295 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.62633e8 | 0.290871 | 0.145436 | − | 0.989368i | \(-0.453542\pi\) | ||||
0.145436 | + | 0.989368i | \(0.453542\pi\) | |||||||
\(398\) | −1.14971e8 | − | 1.99135e8i | −0.0914107 | − | 0.158328i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.69859e7 | + | 9.87024e7i | −0.0445202 | + | 0.0771113i | ||||
\(401\) | −3.49199e8 | + | 6.04830e8i | −0.270438 | + | 0.468412i | −0.968974 | − | 0.247163i | \(-0.920502\pi\) |
0.698536 | + | 0.715575i | \(0.253835\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.11873e9 | − | 1.93770e9i | −0.851448 | − | 1.47475i | ||||
\(404\) | 1.18501e9 | 0.894101 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.63454e9 | −1.21214 | ||||||||
\(407\) | 1.00958e8 | + | 1.74864e8i | 0.0742267 | + | 0.128564i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.15434e8 | − | 1.06596e9i | 0.444785 | − | 0.770390i | −0.553252 | − | 0.833014i | \(-0.686613\pi\) |
0.998037 | + | 0.0626235i | \(0.0199467\pi\) | |||||||
\(410\) | 6.22446e8 | − | 1.07811e9i | 0.446024 | − | 0.772536i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.21301e8 | − | 5.56509e8i | −0.226345 | − | 0.392042i | ||||
\(413\) | −8.83430e8 | −0.617088 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.75019e9 | −1.20203 | ||||||||
\(416\) | −2.21245e8 | − | 3.83207e8i | −0.150677 | − | 0.260980i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.89909e8 | − | 1.71457e9i | 0.662946 | − | 1.14826i | ||||
\(419\) | 7.98065e8 | − | 1.38229e9i | 0.530016 | − | 0.918015i | −0.469371 | − | 0.883001i | \(-0.655519\pi\) |
0.999387 | − | 0.0350135i | \(-0.0111474\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.86456e8 | + | 6.69362e8i | 0.252414 | + | 0.437194i | 0.964190 | − | 0.265213i | \(-0.0854422\pi\) |
−0.711776 | + | 0.702407i | \(0.752109\pi\) | |||||||
\(422\) | −1.57847e9 | −1.02245 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.02222e9 | 0.651271 | ||||||||
\(425\) | −1.64568e8 | − | 2.85040e8i | −0.103988 | − | 0.180113i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.37928e9 | − | 2.38899e9i | 0.857346 | − | 1.48497i | ||||
\(428\) | −4.04935e8 | + | 7.01368e8i | −0.249650 | + | 0.432407i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.86688e8 | + | 1.36258e9i | 0.477159 | + | 0.826463i | ||||
\(431\) | 2.41483e8 | 0.145284 | 0.0726418 | − | 0.997358i | \(-0.476857\pi\) | ||||
0.0726418 | + | 0.997358i | \(0.476857\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.85764e9 | 1.69161 | 0.845805 | − | 0.533493i | \(-0.179121\pi\) | ||||
0.845805 | + | 0.533493i | \(0.179121\pi\) | |||||||
\(434\) | 9.61316e8 | + | 1.66505e9i | 0.564485 | + | 0.977716i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.05567e7 | − | 7.02462e7i | 0.0234347 | − | 0.0405901i | ||||
\(437\) | −5.97037e8 | + | 1.03410e9i | −0.342228 | + | 0.592757i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.63501e8 | − | 2.83192e8i | −0.0922347 | − | 0.159755i | 0.816216 | − | 0.577746i | \(-0.196068\pi\) |
−0.908451 | + | 0.417991i | \(0.862734\pi\) | |||||||
\(440\) | −9.25906e8 | −0.518182 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.27785e9 | 0.703886 | ||||||||
\(443\) | −3.98605e8 | − | 6.90404e8i | −0.217836 | − | 0.377303i | 0.736310 | − | 0.676644i | \(-0.236566\pi\) |
−0.954146 | + | 0.299341i | \(0.903233\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.78744e8 | − | 8.29209e8i | 0.257539 | − | 0.446071i | ||||
\(446\) | 2.99314e8 | − | 5.18428e8i | 0.159755 | − | 0.276704i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.90114e8 | + | 3.29287e8i | 0.0998943 | + | 0.173022i | ||||
\(449\) | −1.41817e9 | −0.739378 | −0.369689 | − | 0.929155i | \(-0.620536\pi\) | ||||
−0.369689 | + | 0.929155i | \(0.620536\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.65606e9 | 1.36339 | ||||||||
\(452\) | 4.74945e8 | + | 8.22628e8i | 0.241913 | + | 0.419005i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.89393e8 | + | 5.01243e8i | −0.145142 | + | 0.251393i | ||||
\(455\) | 3.18770e9 | − | 5.52126e9i | 1.58649 | − | 2.74789i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.87453e8 | + | 8.44293e8i | 0.238905 | + | 0.413796i | 0.960400 | − | 0.278623i | \(-0.0898781\pi\) |
−0.721495 | + | 0.692420i | \(0.756545\pi\) | |||||||
\(458\) | −2.43827e9 | −1.18591 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.58435e8 | 0.267498 | ||||||||
\(461\) | −6.86431e8 | − | 1.18893e9i | −0.326320 | − | 0.565203i | 0.655459 | − | 0.755231i | \(-0.272475\pi\) |
−0.981779 | + | 0.190028i | \(0.939142\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.93573e8 | + | 1.54771e9i | −0.418405 | + | 0.724698i | −0.995779 | − | 0.0917813i | \(-0.970744\pi\) |
0.577375 | + | 0.816479i | \(0.304077\pi\) | |||||||
\(464\) | −2.88490e8 | + | 4.99679e8i | −0.134066 | + | 0.232209i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.45338e7 | + | 1.63737e8i | 0.0432749 | + | 0.0749544i | ||||
\(467\) | 2.25768e9 | 1.02578 | 0.512889 | − | 0.858455i | \(-0.328575\pi\) | ||||
0.512889 | + | 0.858455i | \(0.328575\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.57262e9 | −1.15152 | ||||||||
\(470\) | −6.54991e8 | − | 1.13448e9i | −0.291000 | − | 0.504026i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.55922e8 | + | 2.70065e8i | −0.0682514 | + | 0.118215i | ||||
\(473\) | −1.67845e9 | + | 2.90716e9i | −0.729280 | + | 1.26315i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.19721e8 | − | 1.07339e9i | −0.265319 | − | 0.459546i | ||||
\(476\) | −1.09805e9 | −0.466656 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.84811e9 | 0.773983 | ||||||||
\(479\) | −8.71334e8 | − | 1.50919e9i | −0.362252 | − | 0.627438i | 0.626080 | − | 0.779759i | \(-0.284659\pi\) |
−0.988331 | + | 0.152321i | \(0.951325\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.45385e8 | + | 4.25019e8i | −0.100540 | + | 0.174141i | ||||
\(482\) | 2.37525e8 | − | 4.11405e8i | 0.0966149 | − | 0.167342i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.64151e8 | − | 6.30727e8i | −0.145990 | − | 0.252862i | ||||
\(485\) | −2.57623e9 | −1.02539 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.68849e9 | −1.05477 | −0.527384 | − | 0.849627i | \(-0.676827\pi\) | ||||
−0.527384 | + | 0.849627i | \(0.676827\pi\) | |||||||
\(488\) | −4.86878e8 | − | 8.43297e8i | −0.189649 | − | 0.328482i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.66691e9 | + | 2.88718e9i | −0.640070 | + | 1.10863i | ||||
\(491\) | 1.17441e9 | − | 2.03413e9i | 0.447747 | − | 0.775521i | −0.550492 | − | 0.834841i | \(-0.685560\pi\) |
0.998239 | + | 0.0593196i | \(0.0188931\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.33120e8 | − | 1.44301e9i | −0.313144 | − | 0.542381i | ||||
\(494\) | 4.81207e9 | 1.79592 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.78676e8 | 0.249733 | ||||||||
\(497\) | 7.31338e8 | + | 1.26671e9i | 0.267221 | + | 0.462841i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.33712e8 | − | 1.44403e9i | 0.300375 | − | 0.520265i | −0.675846 | − | 0.737043i | \(-0.736221\pi\) |
0.976221 | + | 0.216778i | \(0.0695547\pi\) | |||||||
\(500\) | 5.23923e8 | − | 9.07461e8i | 0.187444 | − | 0.324663i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.26467e9 | − | 2.19046e9i | −0.446182 | − | 0.772811i | ||||
\(503\) | 3.41605e9 | 1.19684 | 0.598419 | − | 0.801183i | \(-0.295796\pi\) | ||||
0.598419 | + | 0.801183i | \(0.295796\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.02688e9 | 2.08244 | ||||||||
\(506\) | 5.95729e8 | + | 1.03183e9i | 0.204419 | + | 0.354064i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.10975e8 | − | 5.38625e8i | 0.105245 | − | 0.182290i | ||||
\(509\) | −2.52319e9 | + | 4.37030e9i | −0.848083 | + | 1.46892i | 0.0348342 | + | 0.999393i | \(0.488910\pi\) |
−0.882917 | + | 0.469529i | \(0.844424\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.06019e8 | + | 1.83631e8i | 0.0351489 | + | 0.0608796i | ||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.53047e8 | −0.147154 | ||||||||
\(515\) | −1.63411e9 | − | 2.83037e9i | −0.527178 | − | 0.913099i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.39746e9 | − | 2.42048e9i | 0.444758 | − | 0.770344i | ||||
\(518\) | 2.10857e8 | − | 3.65215e8i | 0.0666552 | − | 0.115450i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.12524e9 | − | 1.94897e9i | −0.350939 | − | 0.607845i | ||||
\(521\) | 2.07610e9 | 0.643156 | 0.321578 | − | 0.946883i | \(-0.395787\pi\) | ||||
0.321578 | + | 0.946883i | \(0.395787\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.82869e9 | −0.864627 | −0.432314 | − | 0.901723i | \(-0.642303\pi\) | ||||
−0.432314 | + | 0.901723i | \(0.642303\pi\) | |||||||
\(524\) | 5.85800e8 | + | 1.01463e9i | 0.177865 | + | 0.308071i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.62559e7 | + | 1.66720e8i | −0.0288388 | + | 0.0499503i | ||||
\(527\) | −9.79963e8 | + | 1.69735e9i | −0.291657 | + | 0.505165i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.34312e9 | + | 2.32634e9i | 0.394474 | + | 0.683249i | ||||
\(530\) | 5.19892e9 | 1.51687 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.13498e9 | −1.19064 | ||||||||
\(533\) | 3.22786e9 | + | 5.59081e9i | 0.923356 | + | 1.59930i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.05947e9 | + | 3.56711e9i | −0.581457 | + | 1.00711i | ||||
\(536\) | −4.54059e8 | + | 7.86454e8i | −0.127361 | + | 0.220595i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.76853e9 | + | 3.06318e9i | 0.489637 | + | 0.848076i | ||||
\(539\) | −7.11294e9 | −1.95654 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.38888e9 | −0.920166 | −0.460083 | − | 0.887876i | \(-0.652180\pi\) | ||||
−0.460083 | + | 0.887876i | \(0.652180\pi\) | |||||||
\(542\) | −7.27710e8 | − | 1.26043e9i | −0.196318 | − | 0.340033i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.93802e8 | + | 3.35674e8i | −0.0516132 | + | 0.0893967i | ||||
\(545\) | 2.06269e8 | − | 3.57268e8i | 0.0545815 | − | 0.0945379i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.30774e8 | + | 1.43894e9i | 0.217034 | + | 0.375913i | 0.953900 | − | 0.300125i | \(-0.0970285\pi\) |
−0.736866 | + | 0.676039i | \(0.763695\pi\) | |||||||
\(548\) | 3.10126e9 | 0.805019 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.23673e9 | −0.316960 | ||||||||
\(551\) | −3.13733e9 | − | 5.43401e9i | −0.798967 | − | 1.38385i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.27514e9 | + | 9.13682e9i | −1.32647 | + | 2.29751i | ||||
\(554\) | −1.04314e9 | + | 1.80678e9i | −0.260651 | + | 0.451462i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.21546e9 | + | 2.10523e9i | 0.299901 | + | 0.519444i | ||||
\(557\) | −6.21412e9 | −1.52365 | −0.761827 | − | 0.647780i | \(-0.775697\pi\) | ||||
−0.761827 | + | 0.647780i | \(0.775697\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.15915e9 | −1.97562 | ||||||||
\(560\) | 9.66907e8 | + | 1.67473e9i | 0.232663 | + | 0.402983i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.42307e9 | − | 2.46484e9i | 0.338182 | − | 0.585748i | ||||
\(563\) | 3.04740e8 | − | 5.27825e8i | 0.0719697 | − | 0.124655i | −0.827795 | − | 0.561031i | \(-0.810405\pi\) |
0.899765 | + | 0.436376i | \(0.143738\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.41554e9 | + | 4.18383e9i | 0.563436 | + | 0.975899i | ||||
\(566\) | −1.20448e9 | −0.279218 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.16314e8 | 0.118221 | ||||||||
\(569\) | −2.27558e9 | − | 3.94141e9i | −0.517844 | − | 0.896931i | −0.999785 | − | 0.0207280i | \(-0.993402\pi\) |
0.481942 | − | 0.876203i | \(-0.339932\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.66501e9 | − | 2.88388e9i | 0.374275 | − | 0.648262i | −0.615944 | − | 0.787790i | \(-0.711225\pi\) |
0.990218 | + | 0.139528i | \(0.0445584\pi\) | |||||||
\(572\) | 2.40076e9 | − | 4.15825e9i | 0.536369 | − | 0.929018i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.77367e9 | − | 4.80414e9i | −0.612158 | − | 1.06029i | ||||
\(575\) | 7.45898e8 | 0.163622 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.26141e9 | −0.273363 | −0.136682 | − | 0.990615i | \(-0.543644\pi\) | ||||
−0.136682 | + | 0.990615i | \(0.543644\pi\) | |||||||
\(578\) | 1.08168e9 | + | 1.87353e9i | 0.232998 | + | 0.403564i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.46724e9 | + | 2.54133e9i | −0.312251 | + | 0.540834i | ||||
\(581\) | −3.89949e9 | + | 6.75412e9i | −0.824881 | + | 1.42874i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.54611e9 | + | 9.60615e9i | 1.15917 | + | 2.00775i | ||||
\(584\) | 7.48480e7 | 0.0155502 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.75121e9 | 0.359498 | ||||||||
\(587\) | 2.15884e9 | + | 3.73921e9i | 0.440541 | + | 0.763039i | 0.997730 | − | 0.0673465i | \(-0.0214533\pi\) |
−0.557189 | + | 0.830386i | \(0.688120\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.69030e9 | + | 6.39178e9i | −0.744146 | + | 1.28890i | ||||
\(590\) | −7.93011e8 | + | 1.37354e9i | −0.158963 | + | 0.275333i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.44311e7 | − | 1.28918e8i | −0.0147444 | − | 0.0255381i | ||||
\(593\) | 2.64830e9 | 0.521525 | 0.260762 | − | 0.965403i | \(-0.416026\pi\) | ||||
0.260762 | + | 0.965403i | \(0.416026\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.58460e9 | −1.08688 | ||||||||
\(596\) | −1.14586e9 | − | 1.98469e9i | −0.221703 | − | 0.384000i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.44796e9 | + | 2.50793e9i | −0.276886 | + | 0.479581i | ||||
\(599\) | −3.56231e9 | + | 6.17011e9i | −0.677233 | + | 1.17300i | 0.298577 | + | 0.954385i | \(0.403488\pi\) |
−0.975811 | + | 0.218617i | \(0.929845\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.04714e8 | − | 1.81369e8i | −0.0196762 | − | 0.0340803i | 0.856020 | − | 0.516943i | \(-0.172930\pi\) |
−0.875696 | + | 0.482863i | \(0.839597\pi\) | |||||||
\(602\) | 7.01109e9 | 1.30978 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.07853e9 | 0.568478 | ||||||||
\(605\) | −1.85205e9 | − | 3.20784e9i | −0.340023 | − | 0.588937i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.89744e9 | − | 6.75057e9i | 0.707326 | − | 1.22512i | −0.258520 | − | 0.966006i | \(-0.583235\pi\) |
0.965846 | − | 0.259118i | \(-0.0834319\pi\) | |||||||
\(608\) | −7.29809e8 | + | 1.26407e9i | −0.131688 | + | 0.228090i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.47623e9 | − | 4.28895e9i | −0.441709 | − | 0.765063i | ||||
\(611\) | 6.79325e9 | 1.20485 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.11476e8 | −0.159821 | −0.0799105 | − | 0.996802i | \(-0.525463\pi\) | ||||
−0.0799105 | + | 0.996802i | \(0.525463\pi\) | |||||||
\(614\) | 2.19683e9 | + | 3.80502e9i | 0.383007 | + | 0.663388i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.06296e9 | + | 3.57315e9i | −0.355597 | + | 0.615912i | ||||
\(617\) | −1.17581e9 | + | 2.03657e9i | −0.201530 | + | 0.349061i | −0.949022 | − | 0.315211i | \(-0.897925\pi\) |
0.747491 | + | 0.664271i | \(0.231258\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.76271e8 | + | 1.51775e9i | 0.148498 | + | 0.257206i | 0.930673 | − | 0.365853i | \(-0.119223\pi\) |
−0.782174 | + | 0.623060i | \(0.785889\pi\) | |||||||
\(620\) | 3.45170e9 | 0.581651 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.07360e9 | 0.678753 | ||||||||
\(623\) | −2.13332e9 | − | 3.69502e9i | −0.353467 | − | 0.612222i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.75156e9 | − | 6.49789e9i | 0.614655 | − | 1.06461i | ||||
\(626\) | −2.24736e9 | + | 3.89255e9i | −0.366154 | + | 0.634197i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.54493e9 | + | 4.40795e9i | 0.410031 | + | 0.710195i | ||||
\(629\) | 4.29894e8 | 0.0688786 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.95065e9 | 0.309084 | 0.154542 | − | 0.987986i | \(-0.450610\pi\) | ||||
0.154542 | + | 0.987986i | \(0.450610\pi\) | |||||||
\(632\) | 1.86209e9 | + | 3.22523e9i | 0.293421 | + | 0.508219i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.58383e9 | + | 6.20737e9i | −0.558515 | + | 0.967376i | ||||
\(635\) | 1.58160e9 | − | 2.73941e9i | 0.245126 | − | 0.424570i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.64422e9 | − | 1.49722e10i | −1.32507 | − | 2.29508i | ||||
\(638\) | −6.26090e9 | −0.954475 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.82623e8 | 0.102932 | ||||||||
\(641\) | 6.82635e8 | + | 1.18236e9i | 0.102373 | + | 0.177315i | 0.912662 | − | 0.408715i | \(-0.134023\pi\) |
−0.810289 | + | 0.586031i | \(0.800690\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.85524e9 | − | 6.67747e9i | 0.571891 | − | 0.990544i | −0.424481 | − | 0.905437i | \(-0.639543\pi\) |
0.996372 | − | 0.0851072i | \(-0.0271233\pi\) | |||||||
\(644\) | 1.24422e9 | − | 2.15505e9i | 0.183567 | − | 0.317948i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.10759e9 | − | 3.65045e9i | −0.307590 | − | 0.532762i | ||||
\(647\) | 1.07543e10 | 1.56106 | 0.780529 | − | 0.625120i | \(-0.214950\pi\) | ||||
0.780529 | + | 0.625120i | \(0.214950\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.38388e9 | −0.485913 | ||||||||
\(650\) | −1.50297e9 | − | 2.60322e9i | −0.214661 | − | 0.371804i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.42829e9 | − | 2.47387e9i | 0.201813 | − | 0.349550i | ||||
\(653\) | 6.41419e9 | − | 1.11097e10i | 0.901458 | − | 1.56137i | 0.0758554 | − | 0.997119i | \(-0.475831\pi\) |
0.825603 | − | 0.564252i | \(-0.190835\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.97934e9 | + | 5.16037e9i | 0.414262 | + | 0.717523i | ||||
\(656\) | −1.95817e9 | −0.270824 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.83738e9 | −0.798781 | ||||||||
\(659\) | −4.04554e9 | − | 7.00708e9i | −0.550652 | − | 0.953758i | −0.998228 | − | 0.0595117i | \(-0.981046\pi\) |
0.447575 | − | 0.894246i | \(-0.352288\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.42598e9 | + | 9.39806e9i | −0.730756 | + | 1.26571i | 0.225804 | + | 0.974173i | \(0.427499\pi\) |
−0.956560 | + | 0.291535i | \(0.905834\pi\) | |||||||
\(662\) | 2.82065e9 | − | 4.88550e9i | 0.377873 | − | 0.654495i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.37649e9 | + | 2.38416e9i | 0.182468 | + | 0.316043i | ||||
\(665\) | −2.10302e10 | −2.77312 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.77609e9 | 0.492722 | ||||||||
\(668\) | 2.26767e8 | + | 3.92772e8i | 0.0294348 | + | 0.0509827i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.30932e9 | + | 3.99985e9i | −0.296634 | + | 0.513786i | ||||
\(671\) | 5.28319e9 | − | 9.15076e9i | 0.675099 | − | 1.16931i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.23340e9 | − | 7.33246e9i | −0.535348 | − | 0.927250i | −0.999146 | − | 0.0413095i | \(-0.986847\pi\) |
0.463798 | − | 0.885941i | \(-0.346486\pi\) | |||||||
\(674\) | 7.95532e9 | 1.00080 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.65451e9 | 0.953024 | ||||||||
\(677\) | −3.69685e9 | − | 6.40313e9i | −0.457901 | − | 0.793108i | 0.540949 | − | 0.841056i | \(-0.318065\pi\) |
−0.998850 | + | 0.0479477i | \(0.984732\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.73994e9 | + | 9.94186e9i | −0.703660 | + | 1.21877i | ||||
\(680\) | −9.85662e8 | + | 1.70722e9i | −0.120212 | + | 0.208213i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.68221e9 | + | 6.37778e9i | 0.444492 | + | 0.769882i | ||||
\(683\) | 4.64936e9 | 0.558368 | 0.279184 | − | 0.960238i | \(-0.409936\pi\) | ||||
0.279184 | + | 0.960238i | \(0.409936\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.57728e10 | 1.87496 | ||||||||
\(686\) | 2.64986e9 | + | 4.58970e9i | 0.313393 | + | 0.542813i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.23743e9 | − | 2.14330e9i | 0.144865 | − | 0.250913i | ||||
\(689\) | −1.34802e10 | + | 2.33483e10i | −1.57010 | + | 2.71950i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.83835e9 | + | 1.01123e10i | 0.673158 | + | 1.16594i | 0.977004 | + | 0.213223i | \(0.0683959\pi\) |
−0.303846 | + | 0.952721i | \(0.598271\pi\) | |||||||
\(692\) | −4.40952e9 | −0.505848 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.31137e8 | 0.0148925 | ||||||||
\(695\) | 6.18174e9 | + | 1.07071e10i | 0.698496 | + | 1.20983i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.82747e9 | − | 4.89733e9i | 0.316289 | − | 0.547828i | ||||
\(698\) | 1.70711e9 | − | 2.95680e9i | 0.190006 | − | 0.329100i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.29149e9 | + | 2.23693e9i | 0.142314 | + | 0.246495i | ||||
\(701\) | −1.48274e10 | −1.62575 | −0.812873 | − | 0.582441i | \(-0.802098\pi\) | ||||
−0.812873 | + | 0.582441i | \(0.802098\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.61888e9 | 0.175740 | ||||||||
\(704\) | 7.28209e8 | + | 1.26130e9i | 0.0786596 | + | 0.136242i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.42212e9 | − | 1.11234e10i | 0.686850 | − | 1.18966i | ||||
\(707\) | 1.34281e10 | − | 2.32582e10i | 1.42905 | − | 2.47519i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.08325e9 | − | 5.34034e9i | −0.324898 | − | 0.562739i | 0.656594 | − | 0.754244i | \(-0.271996\pi\) |
−0.981492 | + | 0.191505i | \(0.938663\pi\) | |||||||
\(710\) | 2.62594e9 | 0.275347 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.50610e9 | −0.156377 | ||||||||
\(713\) | −2.22083e9 | − | 3.84658e9i | −0.229457 | − | 0.397431i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.22101e10 | − | 2.11486e10i | 1.24925 | − | 2.16376i | ||||
\(716\) | 2.84423e9 | − | 4.92635e9i | 0.289580 | − | 0.501568i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.58450e9 | − | 9.67263e9i | −0.563052 | − | 0.975234i | ||||
\(719\) | −1.31343e10 | −1.31782 | −0.658912 | − | 0.752220i | \(-0.728983\pi\) | ||||
−0.658912 | + | 0.752220i | \(0.728983\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.45635e10 | −1.44708 | ||||||||
\(722\) | −4.36118e9 | − | 7.55378e9i | −0.431245 | − | 0.746938i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.37508e9 | + | 4.11375e9i | −0.232591 | + | 0.402859i | ||||
\(725\) | −1.95978e9 | + | 3.39444e9i | −0.190996 | + | 0.330815i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.22778e9 | − | 3.85863e9i | −0.215031 | − | 0.372445i | 0.738251 | − | 0.674526i | \(-0.235652\pi\) |
−0.953282 | + | 0.302081i | \(0.902319\pi\) | |||||||
\(728\) | −1.00283e10 | −0.963313 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.80672e8 | 0.0362177 | ||||||||
\(731\) | 3.57354e9 | + | 6.18956e9i | 0.338367 | + | 0.586069i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.49868e9 | + | 2.59579e9i | −0.140555 | + | 0.243448i | −0.927706 | − | 0.373313i | \(-0.878222\pi\) |
0.787151 | + | 0.616760i | \(0.211555\pi\) | |||||||
\(734\) | 6.03046e9 | − | 1.04451e10i | 0.562878 | − | 0.974933i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.39200e8 | − | 7.60716e8i | −0.0406060 | − | 0.0703316i | ||||
\(737\) | −9.85414e9 | −0.906740 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.82559e9 | 0.804429 | 0.402215 | − | 0.915545i | \(-0.368241\pi\) | ||||
0.402215 | + | 0.915545i | \(0.368241\pi\) | |||||||
\(740\) | −3.78552e8 | − | 6.55671e8i | −0.0343411 | − | 0.0594805i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.15834e10 | − | 2.00630e10i | 1.04093 | − | 1.80295i | ||||
\(743\) | −1.00349e10 | + | 1.73809e10i | −0.897534 | + | 1.55457i | −0.0668969 | + | 0.997760i | \(0.521310\pi\) |
−0.830637 | + | 0.556814i | \(0.812023\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.82778e9 | − | 1.00940e10i | −0.516365 | − | 0.894370i | ||||
\(746\) | −6.18544e9 | −0.545487 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.20595e9 | −0.367458 | ||||||||
\(749\) | 9.17718e9 | + | 1.58953e10i | 0.798036 | + | 1.38224i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.97123e9 | − | 3.41427e9i | 0.169824 | − | 0.294143i | −0.768534 | − | 0.639809i | \(-0.779014\pi\) |
0.938358 | + | 0.345666i | \(0.112347\pi\) | |||||||
\(752\) | −1.03028e9 | + | 1.78449e9i | −0.0883470 | + | 0.153022i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.60876e9 | − | 1.31788e10i | −0.646419 | − | 1.11963i | ||||
\(755\) | 1.56572e10 | 1.32403 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.54038e10 | 1.29060 | 0.645301 | − | 0.763928i | \(-0.276732\pi\) | ||||
0.645301 | + | 0.763928i | \(0.276732\pi\) | |||||||
\(758\) | −6.60157e9 | − | 1.14343e10i | −0.550561 | − | 0.953599i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.71176e9 | + | 6.42896e9i | −0.306713 | + | 0.531243i | ||||
\(761\) | 9.60848e9 | − | 1.66424e10i | 0.790330 | − | 1.36889i | −0.135433 | − | 0.990787i | \(-0.543243\pi\) |
0.925763 | − | 0.378105i | \(-0.123424\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.19149e8 | − | 1.59201e9i | −0.0749118 | − | 0.129751i | ||||
\(764\) | 1.63600e9 | 0.132726 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.21150e9 | −0.418950 | ||||||||
\(767\) | −4.11236e9 | − | 7.12282e9i | −0.329085 | − | 0.569992i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.02623e7 | − | 1.04377e8i | 0.00477863 | − | 0.00827683i | −0.863626 | − | 0.504133i | \(-0.831812\pi\) |
0.868405 | + | 0.495856i | \(0.165146\pi\) | |||||||
\(770\) | −1.04921e10 | + | 1.81728e10i | −0.828216 | + | 1.43451i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.14786e9 | + | 5.45226e9i | 0.246238 | + | 0.426497i | ||||
\(773\) | 2.06347e10 | 1.60683 | 0.803415 | − | 0.595420i | \(-0.203014\pi\) | ||||
0.803415 | + | 0.595420i | \(0.203014\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.61041e9 | 0.355782 | ||||||||
\(776\) | 2.02616e9 | + | 3.50941e9i | 0.155653 | + | 0.269599i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.49107e9 | − | 6.04672e9i | 0.265785 | − | 0.460353i | ||||
\(779\) | 1.06476e10 | − | 1.84421e10i | 0.806992 | − | 1.39775i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.80131e9 | + | 4.85201e9i | 0.210418 | + | 0.364454i | ||||
\(782\) | 2.53670e9 | 0.189691 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.24400e9 | 0.388648 | ||||||||
\(785\) | 1.29433e10 | + | 2.24185e10i | 0.954998 | + | 1.65411i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.45354e8 | + | 1.46420e9i | −0.0618197 | + | 0.107075i | −0.895279 | − | 0.445506i | \(-0.853024\pi\) |
0.833459 | + | 0.552581i | \(0.186357\pi\) | |||||||
\(788\) | −4.49859e8 | + | 7.79179e8i | −0.0327518 | + | 0.0567278i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 9.47046e9 | + | 1.64033e10i | 0.683402 | + | 1.18369i | ||||
\(791\) | 2.15277e10 | 1.54660 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.56823e10 | 1.82885 | ||||||||
\(794\) | −1.45053e9 | − | 2.51239e9i | −0.102838 | − | 0.178121i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.19767e8 | + | 1.59308e9i | −0.0646371 | + | 0.111955i | ||||
\(797\) | 6.79877e8 | − | 1.17758e9i | 0.0475692 | − | 0.0823923i | −0.841260 | − | 0.540630i | \(-0.818186\pi\) |
0.888830 | + | 0.458238i | \(0.151519\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.97531e9 | − | 5.15338e9i | −0.206356 | − | 0.357420i | ||||
\(800\) | 9.11774e8 | 0.0629611 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.58718e9 | 0.382457 | ||||||||
\(803\) | 4.06094e8 | + | 7.03376e8i | 0.0276772 | + | 0.0479383i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.32800e9 | − | 1.09604e10i | 0.427544 | − | 0.740529i | ||||
\(806\) | −8.94985e9 | + | 1.55016e10i | −0.602064 | + | 1.04281i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.74004e9 | − | 8.20998e9i | −0.316113 | − | 0.547523i | ||||
\(809\) | −1.53965e10 | −1.02235 | −0.511177 | − | 0.859475i | \(-0.670790\pi\) | ||||
−0.511177 | + | 0.859475i | \(0.670790\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.67476e9 | −0.636894 | −0.318447 | − | 0.947941i | \(-0.603161\pi\) | ||||
−0.318447 | + | 0.947941i | \(0.603161\pi\) | |||||||
\(812\) | 6.53814e9 | + | 1.13244e10i | 0.428557 | + | 0.742282i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.07664e8 | − | 1.39891e9i | 0.0524862 | − | 0.0909088i | ||||
\(815\) | 7.26417e9 | − | 1.25819e10i | 0.470040 | − | 0.814133i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.34571e10 | + | 2.33083e10i | 0.863324 | + | 1.49532i | ||||
\(818\) | −9.84695e9 | −0.629021 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.95914e9 | −0.630773 | ||||||||
\(821\) | 1.23171e10 | + | 2.13339e10i | 0.776799 | + | 1.34546i | 0.933778 | + | 0.357853i | \(0.116491\pi\) |
−0.156979 | + | 0.987602i | \(0.550176\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.07424e9 | − | 1.86064e9i | 0.0671743 | − | 0.116349i | −0.830482 | − | 0.557045i | \(-0.811935\pi\) |
0.897656 | + | 0.440696i | \(0.145268\pi\) | |||||||
\(824\) | −2.57041e9 | + | 4.45207e9i | −0.160050 | + | 0.277215i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.53372e9 | + | 6.12058e9i | 0.218174 | + | 0.377888i | ||||
\(827\) | −1.31873e10 | −0.810751 | −0.405375 | − | 0.914150i | \(-0.632859\pi\) | ||||
−0.405375 | + | 0.914150i | \(0.632859\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.41872e8 | 0.0391298 | 0.0195649 | − | 0.999809i | \(-0.493772\pi\) | ||||
0.0195649 | + | 0.999809i | \(0.493772\pi\) | |||||||
\(830\) | 7.00075e9 | + | 1.21257e10i | 0.424983 | + | 0.736092i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.76996e9 | + | 3.06566e9i | −0.106545 | + | 0.184541i | ||||
\(833\) | −7.57199e9 | + | 1.31151e10i | −0.453892 | + | 0.786164i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.15332e9 | + | 1.99761e9i | 0.0685563 | + | 0.118743i | ||||
\(836\) | −1.58385e10 | −0.937548 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.27690e10 | −0.749556 | ||||||||
\(839\) | −5.06722e9 | − | 8.77669e9i | −0.296212 | − | 0.513055i | 0.679054 | − | 0.734088i | \(-0.262390\pi\) |
−0.975266 | + | 0.221034i | \(0.929057\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.29642e9 | + | 2.24546e9i | −0.0751551 | + | 0.130173i | ||||
\(842\) | 3.09165e9 | − | 5.35490e9i | 0.178484 | − | 0.309143i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.31389e9 | + | 1.09360e10i | 0.361492 | + | 0.626122i | ||||
\(845\) | 3.89303e10 | 2.21968 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.65057e10 | −0.933347 | ||||||||
\(848\) | −4.08886e9 | − | 7.08211e9i | −0.230259 | − | 0.398820i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.31654e9 | + | 2.28032e9i | −0.0735306 | + | 0.127359i | ||||
\(851\) | −4.87121e8 | + | 8.43718e8i | −0.0270946 | + | 0.0469292i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.75163e9 | − | 1.16942e10i | −0.372467 | − | 0.645131i | 0.617478 | − | 0.786588i | \(-0.288155\pi\) |
−0.989944 | + | 0.141457i | \(0.954821\pi\) | |||||||
\(854\) | −2.20686e10 | −1.21247 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.47896e9 | 0.353059 | ||||||||
\(857\) | 2.75769e9 | + | 4.77646e9i | 0.149662 | + | 0.259223i | 0.931103 | − | 0.364757i | \(-0.118848\pi\) |
−0.781440 | + | 0.623980i | \(0.785515\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.06756e9 | + | 1.05093e10i | −0.326617 | + | 0.565717i | −0.981838 | − | 0.189720i | \(-0.939242\pi\) |
0.655222 | + | 0.755437i | \(0.272575\pi\) | |||||||
\(860\) | 6.29350e9 | − | 1.09007e10i | 0.337402 | − | 0.584398i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.65934e8 | − | 1.67305e9i | −0.0513655 | − | 0.0889677i | ||||
\(863\) | 2.09525e9 | 0.110968 | 0.0554839 | − | 0.998460i | \(-0.482330\pi\) | ||||
0.0554839 | + | 0.998460i | \(0.482330\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.24265e10 | −1.17816 | ||||||||
\(866\) | −1.14306e10 | − | 1.97983e10i | −0.598074 | − | 1.03589i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.69053e9 | − | 1.33204e10i | 0.399151 | − | 0.691350i | ||||
\(869\) | −2.02058e10 | + | 3.49975e10i | −1.04450 | + | 1.80912i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.19756e10 | − | 2.07423e10i | −0.614090 | − | 1.06364i | ||||
\(872\) | −6.48907e8 | −0.0331417 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.55259e9 | 0.483984 | ||||||||
\(875\) | −1.18738e10 | − | 2.05661e10i | −0.599188 | − | 1.03782i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.76793e10 | + | 3.06214e10i | −0.885045 | + | 1.53294i | −0.0393839 | + | 0.999224i | \(0.512540\pi\) |
−0.845662 | + | 0.533719i | \(0.820794\pi\) | |||||||
\(878\) | −1.30801e9 | + | 2.26554e9i | −0.0652198 | + | 0.112964i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.70363e9 | + | 6.41487e9i | 0.183205 | + | 0.317321i | ||||
\(881\) | −7.96497e8 | −0.0392436 | −0.0196218 | − | 0.999807i | \(-0.506246\pi\) | ||||
−0.0196218 | + | 0.999807i | \(0.506246\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.24897e9 | −0.207693 | −0.103846 | − | 0.994593i | \(-0.533115\pi\) | ||||
−0.103846 | + | 0.994593i | \(0.533115\pi\) | |||||||
\(884\) | −5.11141e9 | − | 8.85322e9i | −0.248861 | − | 0.431041i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.18884e9 | + | 5.52323e9i | −0.154033 | + | 0.266793i | ||||
\(887\) | 8.84899e9 | − | 1.53269e10i | 0.425756 | − | 0.737431i | −0.570735 | − | 0.821135i | \(-0.693341\pi\) |
0.996491 | + | 0.0837033i | \(0.0266748\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.04774e9 | − | 1.22070e10i | −0.336429 | − | 0.582713i | ||||
\(890\) | −7.65991e9 | −0.364215 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.78903e9 | −0.225928 | ||||||||
\(893\) | −1.12043e10 | − | 1.94064e10i | −0.526506 | − | 0.911935i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.44656e10 | − | 2.50551e10i | 0.674458 | − | 1.16819i | ||||
\(896\) | 1.52091e9 | − | 2.63430e9i | 0.0706359 | − | 0.122345i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.67269e9 | + | 9.82538e9i | 0.261410 | + | 0.452775i | ||||
\(899\) | 2.33401e10 | 1.07138 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.36162e10 | 1.07565 | ||||||||
\(902\) | −1.06242e10 | − | 1.84017e10i | −0.482030 | − | 0.834901i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.79956e9 | − | 6.58103e9i | 0.171058 | − | 0.296281i | ||||
\(905\) | −1.20795e10 | + | 2.09223e10i | −0.541724 | + | 0.938294i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.75478e8 | + | 9.96758e8i | 0.0256096 | + | 0.0443572i | 0.878546 | − | 0.477657i | \(-0.158514\pi\) |
−0.852937 | + | 0.522015i | \(0.825181\pi\) | |||||||
\(908\) | 4.63029e9 | 0.205261 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.10032e10 | −2.24364 | ||||||||
\(911\) | 5.73328e9 | + | 9.93034e9i | 0.251240 | + | 0.435161i | 0.963868 | − | 0.266382i | \(-0.0858283\pi\) |
−0.712627 | + | 0.701543i | \(0.752495\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.49366e10 | + | 2.58709e10i | −0.649535 | + | 1.12503i | ||||
\(914\) | 3.89962e9 | − | 6.75435e9i | 0.168932 | − | 0.292598i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.75309e9 | + | 1.68928e10i | 0.419284 | + | 0.726221i | ||||
\(917\) | 2.65524e10 | 1.13713 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.59560e10 | −1.52815 | −0.764076 | − | 0.645126i | \(-0.776805\pi\) | ||||
−0.764076 | + | 0.645126i | \(0.776805\pi\) | |||||||
\(920\) | −2.23374e9 | − | 3.86895e9i | −0.0945748 | − | 0.163808i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.49145e9 | + | 9.51147e9i | −0.230743 | + | 0.399659i | ||||
\(923\) | −6.80875e9 | + | 1.17931e10i | −0.285011 | + | 0.493653i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.05629e8 | − | 8.75774e8i | −0.0210056 | − | 0.0363828i | ||||
\(926\) | 1.42972e10 | 0.591714 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.61584e9 | 0.189597 | ||||||||
\(929\) | −2.86558e9 | − | 4.96333e9i | −0.117262 | − | 0.203104i | 0.801420 | − | 0.598102i | \(-0.204078\pi\) |
−0.918682 | + | 0.394999i | \(0.870745\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.85142e10 | + | 4.93881e10i | −1.15808 | + | 2.00585i | ||||
\(932\) | 7.56270e8 | − | 1.30990e9i | 0.0306000 | − | 0.0530008i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.03071e9 | − | 1.56417e10i | −0.362667 | − | 0.628158i | ||||
\(935\) | −2.13912e10 | −0.855842 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.02489e10 | −0.406995 | −0.203497 | − | 0.979076i | \(-0.565231\pi\) | ||||
−0.203497 | + | 0.979076i | \(0.565231\pi\) | |||||||
\(938\) | 1.02905e10 | + | 1.78237e10i | 0.407124 | + | 0.705159i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.23993e9 | + | 9.07582e9i | −0.205768 | + | 0.356400i | ||||
\(941\) | −5.69738e9 | + | 9.86815e9i | −0.222901 | + | 0.386075i | −0.955688 | − | 0.294383i | \(-0.904886\pi\) |
0.732787 | + | 0.680458i | \(0.238219\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.40771e9 | + | 1.10985e10i | 0.248835 | + | 0.430996i | ||||
\(944\) | 2.49476e9 | 0.0965220 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.68552e10 | 1.03136 | ||||||||
\(947\) | −1.20000e10 | − | 2.07846e10i | −0.459151 | − | 0.795273i | 0.539765 | − | 0.841816i | \(-0.318513\pi\) |
−0.998916 | + | 0.0465423i | \(0.985180\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.87037e8 | + | 1.70960e9i | −0.0374888 | + | 0.0649326i | ||||
\(950\) | −4.95777e9 | + | 8.58711e9i | −0.187609 | + | 0.324948i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.39219e9 | + | 7.60750e9i | 0.164988 | + | 0.285767i | ||||
\(953\) | −1.56339e10 | −0.585117 | −0.292558 | − | 0.956248i | \(-0.594507\pi\) | ||||
−0.292558 | + | 0.956248i | \(0.594507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.32058e9 | 0.309130 | ||||||||
\(956\) | −7.39246e9 | − | 1.28041e10i | −0.273644 | − | 0.473966i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.97067e9 | + | 1.20736e10i | −0.256150 | + | 0.443666i | ||||
\(959\) | 3.51425e10 | − | 6.08685e10i | 1.28667 | − | 2.22858i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.93306e7 | + | 5.08021e7i | 0.00106608 | + | 0.00184650i | ||||
\(962\) | 3.92616e9 | 0.142185 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.80039e9 | −0.136634 | ||||||||
\(965\) | 1.60098e10 | + | 2.77298e10i | 0.573510 | + | 0.993349i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.10964e10 | + | 3.65401e10i | −0.750268 | + | 1.29950i | 0.197425 | + | 0.980318i | \(0.436742\pi\) |
−0.947693 | + | 0.319184i | \(0.896591\pi\) | |||||||
\(968\) | −2.91320e9 | + | 5.04582e9i | −0.103230 | + | 0.178800i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.03049e10 | + | 1.78486e10i | 0.362529 | + | 0.627919i | ||||
\(971\) | 8.93754e9 | 0.313293 | 0.156646 | − | 0.987655i | \(-0.449932\pi\) | ||||
0.156646 | + | 0.987655i | \(0.449932\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.50927e10 | 1.91734 | ||||||||
\(974\) | 1.07540e10 | + | 1.86264e10i | 0.372917 | + | 0.645911i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.89502e9 | + | 6.74638e9i | −0.134102 | + | 0.232272i | ||||
\(977\) | 1.06289e10 | − | 1.84097e10i | 0.364633 | − | 0.631563i | −0.624084 | − | 0.781357i | \(-0.714528\pi\) |
0.988717 | + | 0.149794i | \(0.0478611\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.17145e9 | − | 1.41534e10i | −0.278330 | − | 0.482081i | ||||
\(980\) | 2.66706e10 | 0.905195 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.87905e10 | −0.633210 | ||||||||
\(983\) | 5.16755e9 | + | 8.95046e9i | 0.173519 | + | 0.300544i | 0.939648 | − | 0.342143i | \(-0.111153\pi\) |
−0.766129 | + | 0.642687i | \(0.777819\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.28796e9 | + | 3.96285e9i | −0.0762818 | + | 0.132124i | ||||
\(986\) | −6.66496e9 | + | 1.15441e10i | −0.221426 | + | 0.383521i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.92483e10 | − | 3.33390e10i | −0.634955 | − | 1.09977i | ||||
\(989\) | −1.61970e10 | −0.532411 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.00170e10 | 1.63253 | 0.816263 | − | 0.577681i | \(-0.196042\pi\) | ||||
0.816263 | + | 0.577681i | \(0.196042\pi\) | |||||||
\(992\) | −2.71470e9 | − | 4.70200e9i | −0.0882941 | − | 0.152930i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.85071e9 | − | 1.01337e10i | 0.188954 | − | 0.327278i | ||||
\(995\) | −4.67787e9 | + | 8.10231e9i | −0.150545 | + | 0.260752i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.69044e10 | + | 2.92792e10i | 0.540214 | + | 0.935678i | 0.998891 | + | 0.0470752i | \(0.0149901\pi\) |
−0.458677 | + | 0.888603i | \(0.651677\pi\) | |||||||
\(998\) | −1.33394e10 | −0.424795 | ||||||||
\(999\) | 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 | 162.8.c.q.109.2 | 8 | ||
3.2 | odd | 2 | 162.8.c.r.109.3 | 8 | |||
9.2 | odd | 6 | 162.8.c.r.55.3 | 8 | |||
9.4 | even | 3 | 162.8.a.j.1.3 | yes | 4 | ||
9.5 | odd | 6 | 162.8.a.g.1.2 | ✓ | 4 | ||
9.7 | even | 3 | inner | 162.8.c.q.55.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
162.8.a.g.1.2 | ✓ | 4 | 9.5 | odd | 6 | ||
162.8.a.j.1.3 | yes | 4 | 9.4 | even | 3 | ||
162.8.c.q.55.2 | 8 | 9.7 | even | 3 | inner | ||
162.8.c.q.109.2 | 8 | 1.1 | even | 1 | trivial | ||
162.8.c.r.55.3 | 8 | 9.2 | odd | 6 | |||
162.8.c.r.109.3 | 8 | 3.2 | odd | 2 |