Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,9,Mod(8,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.8");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.d (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.9992224717\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} + 427 x^{12} - 1362 x^{11} + 135762 x^{10} - 371244 x^{9} + 18261508 x^{8} + \cdots + 872385888256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{30} \) |
Twist minimal: | no (minimal twist has level 9) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 8.2 | ||
Root | \(-5.49482 - 9.51731i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.8 |
Dual form | 27.9.d.a.17.2 |
$q$-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 \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.4845 | − | 9.51731i | −1.03028 | − | 0.594832i | −0.113214 | − | 0.993571i | \(-0.536115\pi\) |
−0.917065 | + | 0.398739i | \(0.869448\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 53.1583 | + | 92.0729i | 0.207650 | + | 0.359660i | ||||
\(5\) | 46.9888 | − | 27.1290i | 0.0751821 | − | 0.0434064i | −0.461938 | − | 0.886912i | \(-0.652846\pi\) |
0.537120 | + | 0.843506i | \(0.319512\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −921.012 | + | 1595.24i | −0.383595 | + | 0.664406i | −0.991573 | − | 0.129548i | \(-0.958647\pi\) |
0.607978 | + | 0.793954i | \(0.291981\pi\) | |||||||
\(8\) | 2849.17i | 0.695597i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1032.78 | −0.103278 | ||||||||
\(11\) | 15872.1 | + | 9163.77i | 1.08409 | + | 0.625897i | 0.931996 | − | 0.362469i | \(-0.118066\pi\) |
0.152090 | + | 0.988367i | \(0.451399\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16240.1 | − | 28128.7i | −0.568611 | − | 0.984863i | −0.996704 | − | 0.0811279i | \(-0.974148\pi\) |
0.428093 | − | 0.903735i | \(-0.359186\pi\) | |||||||
\(14\) | 30364.8 | − | 17531.1i | 0.790420 | − | 0.456349i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 40724.9 | − | 70537.6i | 0.621413 | − | 1.07632i | ||||
\(17\) | − | 97572.1i | − | 1.16823i | −0.811670 | − | 0.584117i | \(-0.801441\pi\) | ||
0.811670 | − | 0.584117i | \(-0.198559\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 208951. | 1.60336 | 0.801680 | − | 0.597754i | \(-0.203940\pi\) | ||||
0.801680 | + | 0.597754i | \(0.203940\pi\) | |||||||
\(20\) | 4995.69 | + | 2884.26i | 0.0312231 | + | 0.0180266i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −174429. | − | 302119.i | −0.744607 | − | 1.28970i | ||||
\(23\) | 273878. | − | 158124.i | 0.978692 | − | 0.565048i | 0.0768167 | − | 0.997045i | \(-0.475524\pi\) |
0.901875 | + | 0.431997i | \(0.142191\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −193841. | + | 335742.i | −0.496232 | + | 0.859499i | ||||
\(26\) | 618248.i | 1.35291i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −195838. | −0.318614 | ||||||||
\(29\) | −96164.1 | − | 55520.4i | −0.135963 | − | 0.0784983i | 0.430476 | − | 0.902602i | \(-0.358346\pi\) |
−0.566439 | + | 0.824104i | \(0.691679\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 181257. | + | 313947.i | 0.196268 | + | 0.339945i | 0.947315 | − | 0.320303i | \(-0.103785\pi\) |
−0.751048 | + | 0.660248i | \(0.770451\pi\) | |||||||
\(32\) | −710990. | + | 410490.i | −0.678052 | + | 0.391474i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −928623. | + | 1.60842e6i | −0.694903 | + | 1.20361i | ||||
\(35\) | 99944.5i | 0.0666019i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.91887e6 | 1.02385 | 0.511927 | − | 0.859029i | \(-0.328932\pi\) | ||||
0.511927 | + | 0.859029i | \(0.328932\pi\) | |||||||
\(38\) | −3.44445e6 | − | 1.98865e6i | −1.65191 | − | 0.953729i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 77295.0 | + | 133879.i | 0.0301934 | + | 0.0522964i | ||||
\(41\) | 1.16149e6 | − | 670589.i | 0.411038 | − | 0.237313i | −0.280198 | − | 0.959942i | \(-0.590400\pi\) |
0.691235 | + | 0.722630i | \(0.257067\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.49489e6 | − | 2.58922e6i | 0.437254 | − | 0.757346i | −0.560222 | − | 0.828342i | \(-0.689284\pi\) |
0.997477 | + | 0.0709957i | \(0.0226177\pi\) | |||||||
\(44\) | 1.94852e6i | 0.519870i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.01964e6 | −1.34443 | ||||||||
\(47\) | 1.67689e6 | + | 968152.i | 0.343647 | + | 0.198405i | 0.661884 | − | 0.749607i | \(-0.269757\pi\) |
−0.318237 | + | 0.948011i | \(0.603091\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.18588e6 | + | 2.05400e6i | 0.205710 | + | 0.356300i | ||||
\(50\) | 6.39071e6 | − | 3.68968e6i | 1.02251 | − | 0.590349i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.72659e6 | − | 2.99054e6i | 0.236144 | − | 0.409013i | ||||
\(53\) | 1.03471e7i | 1.31134i | 0.755048 | + | 0.655669i | \(0.227613\pi\) | ||||
−0.755048 | + | 0.655669i | \(0.772387\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 994415. | 0.108672 | ||||||||
\(56\) | −4.54510e6 | − | 2.62411e6i | −0.462159 | − | 0.266828i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.05681e6 | + | 1.83045e6i | 0.0933866 | + | 0.161750i | ||||
\(59\) | 1.10364e7 | − | 6.37189e6i | 0.910796 | − | 0.525848i | 0.0301085 | − | 0.999547i | \(-0.490415\pi\) |
0.880687 | + | 0.473699i | \(0.157081\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.41822e6 | − | 1.11167e7i | 0.463549 | − | 0.802890i | −0.535586 | − | 0.844481i | \(-0.679909\pi\) |
0.999135 | + | 0.0415910i | \(0.0132426\pi\) | |||||||
\(62\) | − | 6.90032e6i | − | 0.466985i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.22412e6 | −0.311382 | ||||||||
\(65\) | −1.52620e6 | − | 881155.i | −0.0854987 | − | 0.0493627i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00252e6 | − | 1.21287e7i | −0.347500 | − | 0.601888i | 0.638304 | − | 0.769784i | \(-0.279636\pi\) |
−0.985805 | + | 0.167896i | \(0.946303\pi\) | |||||||
\(68\) | 8.98374e6 | − | 5.18677e6i | 0.420167 | − | 0.242583i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 951202. | − | 1.64753e6i | 0.0396169 | − | 0.0686185i | ||||
\(71\) | 1.72828e7i | 0.680112i | 0.940405 | + | 0.340056i | \(0.110446\pi\) | ||||
−0.940405 | + | 0.340056i | \(0.889554\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.32289e7 | 0.817970 | 0.408985 | − | 0.912541i | \(-0.365883\pi\) | ||||
0.408985 | + | 0.912541i | \(0.365883\pi\) | |||||||
\(74\) | −3.16315e7 | − | 1.82624e7i | −1.05485 | − | 0.609020i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.11075e7 | + | 1.92388e7i | 0.332937 | + | 0.576664i | ||||
\(77\) | −2.92368e7 | + | 1.68799e7i | −0.831700 | + | 0.480182i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.55263e7 | + | 6.15333e7i | −0.912097 | + | 1.57980i | −0.101001 | + | 0.994886i | \(0.532205\pi\) |
−0.811096 | + | 0.584913i | \(0.801129\pi\) | |||||||
\(80\) | − | 4.41930e6i | − | 0.107893i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.55288e7 | −0.564644 | ||||||||
\(83\) | 2.74593e7 | + | 1.58536e7i | 0.578597 | + | 0.334053i | 0.760576 | − | 0.649249i | \(-0.224917\pi\) |
−0.181978 | + | 0.983303i | \(0.558250\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.64703e6 | − | 4.58479e6i | −0.0507088 | − | 0.0878302i | ||||
\(86\) | −4.92848e7 | + | 2.84546e7i | −0.900988 | + | 0.520185i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.61091e7 | + | 4.52223e7i | −0.435372 | + | 0.754087i | ||||
\(89\) | − | 4.71037e6i | − | 0.0750749i | −0.999295 | − | 0.0375375i | \(-0.988049\pi\) | ||
0.999295 | − | 0.0375375i | \(-0.0119514\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.98292e7 | 0.872465 | ||||||||
\(92\) | 2.91178e7 | + | 1.68112e7i | 0.406450 | + | 0.234664i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.84284e7 | − | 3.19189e7i | −0.236035 | − | 0.408824i | ||||
\(95\) | 9.81837e6 | − | 5.66864e6i | 0.120544 | − | 0.0695960i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.45744e7 | − | 5.98847e7i | 0.390542 | − | 0.676439i | −0.601979 | − | 0.798512i | \(-0.705621\pi\) |
0.992521 | + | 0.122073i | \(0.0389542\pi\) | |||||||
\(98\) | − | 4.51454e7i | − | 0.489451i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.12169e7 | −0.412169 | ||||||||
\(101\) | 6.62937e7 | + | 3.82747e7i | 0.637069 | + | 0.367812i | 0.783485 | − | 0.621411i | \(-0.213440\pi\) |
−0.146416 | + | 0.989223i | \(0.546774\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.37265e7 | − | 9.30571e7i | −0.477353 | − | 0.826800i | 0.522310 | − | 0.852756i | \(-0.325070\pi\) |
−0.999663 | + | 0.0259558i | \(0.991737\pi\) | |||||||
\(104\) | 8.01432e7 | − | 4.62707e7i | 0.685067 | − | 0.395524i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.84765e7 | − | 1.70566e8i | 0.780026 | − | 1.35104i | ||||
\(107\) | − | 1.67910e8i | − | 1.28098i | −0.767968 | − | 0.640489i | \(-0.778732\pi\) | ||
0.767968 | − | 0.640489i | \(-0.221268\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.20746e8 | 0.855395 | 0.427697 | − | 0.903922i | \(-0.359325\pi\) | ||||
0.427697 | + | 0.903922i | \(0.359325\pi\) | |||||||
\(110\) | −1.63924e7 | − | 9.46415e6i | −0.111962 | − | 0.0646414i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.50162e7 | + | 1.29932e8i | 0.476742 | + | 0.825741i | ||||
\(113\) | −4.56007e7 | + | 2.63276e7i | −0.279678 | + | 0.161472i | −0.633278 | − | 0.773925i | \(-0.718291\pi\) |
0.353600 | + | 0.935397i | \(0.384957\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.57947e6 | − | 1.48601e7i | 0.0490534 | − | 0.0849629i | ||||
\(116\) | − | 1.18055e7i | − | 0.0652006i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.42573e8 | −1.25116 | ||||||||
\(119\) | 1.55651e8 | + | 8.98650e7i | 0.776182 | + | 0.448129i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.07697e7 | + | 1.05256e8i | 0.283495 | + | 0.491028i | ||||
\(122\) | −2.11602e8 | + | 1.22168e8i | −0.955169 | + | 0.551467i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.92707e7 | + | 3.33777e7i | −0.0815098 | + | 0.141179i | ||||
\(125\) | 4.22293e7i | 0.172971i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.60681e8 | −1.00206 | −0.501032 | − | 0.865429i | \(-0.667046\pi\) | ||||
−0.501032 | + | 0.865429i | \(0.667046\pi\) | |||||||
\(128\) | 2.68130e8 | + | 1.54805e8i | 0.998862 | + | 0.576693i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.67724e7 | + | 2.90507e7i | 0.0587250 | + | 0.101715i | ||||
\(131\) | −8.71036e7 | + | 5.02893e7i | −0.295768 | + | 0.170762i | −0.640540 | − | 0.767925i | \(-0.721289\pi\) |
0.344772 | + | 0.938686i | \(0.387956\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.92447e8 | + | 3.33327e8i | −0.615041 | + | 1.06528i | ||||
\(134\) | 2.66581e8i | 0.826817i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.77999e8 | 0.812620 | ||||||||
\(137\) | −5.57700e8 | − | 3.21988e8i | −1.58314 | − | 0.914024i | −0.994398 | − | 0.105701i | \(-0.966291\pi\) |
−0.588739 | − | 0.808323i | \(-0.700375\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.55562e7 | + | 4.42647e7i | 0.0684601 | + | 0.118576i | 0.898224 | − | 0.439539i | \(-0.144858\pi\) |
−0.829764 | + | 0.558115i | \(0.811525\pi\) | |||||||
\(140\) | −9.20218e6 | + | 5.31288e6i | −0.0239540 | + | 0.0138299i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.64486e8 | − | 2.84897e8i | 0.404552 | − | 0.700705i | ||||
\(143\) | − | 5.95281e8i | − | 1.42357i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.02485e6 | −0.0136293 | ||||||||
\(146\) | −3.82916e8 | − | 2.21077e8i | −0.842737 | − | 0.486555i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.02004e8 | + | 1.76676e8i | 0.212603 | + | 0.368239i | ||||
\(149\) | −8.81724e7 | + | 5.09063e7i | −0.178891 | + | 0.103282i | −0.586771 | − | 0.809753i | \(-0.699601\pi\) |
0.407881 | + | 0.913035i | \(0.366268\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.38856e8 | + | 2.40506e8i | −0.267090 | + | 0.462613i | −0.968109 | − | 0.250529i | \(-0.919395\pi\) |
0.701019 | + | 0.713142i | \(0.252729\pi\) | |||||||
\(152\) | 5.95337e8i | 1.11529i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.42604e8 | 1.14251 | ||||||||
\(155\) | 1.70341e7 | + | 9.83465e6i | 0.0295116 | + | 0.0170385i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.32160e8 | − | 5.75317e8i | −0.546699 | − | 0.946910i | −0.998498 | − | 0.0547905i | \(-0.982551\pi\) |
0.451799 | − | 0.892120i | \(-0.350782\pi\) | |||||||
\(158\) | 1.17126e9 | − | 6.76229e8i | 1.87943 | − | 1.08509i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.22724e7 | + | 3.85769e7i | −0.0339849 | + | 0.0588636i | ||||
\(161\) | 5.82535e8i | 0.866998i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.76238e8 | −0.532981 | −0.266491 | − | 0.963838i | \(-0.585864\pi\) | ||||
−0.266491 | + | 0.963838i | \(0.585864\pi\) | |||||||
\(164\) | 1.23486e8 | + | 7.12947e7i | 0.170704 | + | 0.0985558i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.01767e8 | − | 5.22676e8i | −0.397411 | − | 0.688336i | ||||
\(167\) | −4.60947e8 | + | 2.66128e8i | −0.592632 | + | 0.342156i | −0.766137 | − | 0.642677i | \(-0.777824\pi\) |
0.173506 | + | 0.984833i | \(0.444490\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.19616e8 | + | 2.07180e8i | −0.146636 | + | 0.253981i | ||||
\(170\) | 1.00770e8i | 0.120653i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.17862e8 | 0.363183 | ||||||||
\(173\) | 9.67319e8 | + | 5.58482e8i | 1.07990 | + | 0.623483i | 0.930870 | − | 0.365349i | \(-0.119050\pi\) |
0.149033 | + | 0.988832i | \(0.452384\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.57059e8 | − | 6.18444e8i | −0.380704 | − | 0.659399i | ||||
\(176\) | 1.29278e9 | − | 7.46387e8i | 1.34733 | − | 0.777882i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.48300e7 | + | 7.76479e7i | −0.0446570 | + | 0.0773481i | ||||
\(179\) | 1.48500e8i | 0.144648i | 0.997381 | + | 0.0723242i | \(0.0230416\pi\) | ||||
−0.997381 | + | 0.0723242i | \(0.976958\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.87611e7 | −0.0361146 | −0.0180573 | − | 0.999837i | \(-0.505748\pi\) | ||||
−0.0180573 | + | 0.999837i | \(0.505748\pi\) | |||||||
\(182\) | −9.86253e8 | − | 5.69413e8i | −0.898882 | − | 0.518970i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.50520e8 | + | 7.80324e8i | 0.393046 | + | 0.680775i | ||||
\(185\) | 9.01652e7 | − | 5.20569e7i | 0.0769754 | − | 0.0444418i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.94127e8 | − | 1.54867e9i | 0.731195 | − | 1.26647i | ||||
\(188\) | 2.05861e8i | 0.164795i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.15801e8 | −0.165592 | ||||||||
\(191\) | −1.34933e9 | − | 7.79034e8i | −1.01387 | − | 0.585360i | −0.101550 | − | 0.994830i | \(-0.532380\pi\) |
−0.912323 | + | 0.409470i | \(0.865714\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.07571e9 | + | 1.86319e9i | 0.775295 | + | 1.34285i | 0.934629 | + | 0.355625i | \(0.115732\pi\) |
−0.159334 | + | 0.987225i | \(0.550935\pi\) | |||||||
\(194\) | −1.13988e9 | + | 6.58111e8i | −0.804735 | + | 0.464614i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.26078e8 | + | 2.18374e8i | −0.0854311 | + | 0.147971i | ||||
\(197\) | − | 1.66896e9i | − | 1.10810i | −0.832483 | − | 0.554051i | \(-0.813081\pi\) | ||
0.832483 | − | 0.554051i | \(-0.186919\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.47037e8 | 0.285057 | 0.142528 | − | 0.989791i | \(-0.454477\pi\) | ||||
0.142528 | + | 0.989791i | \(0.454477\pi\) | |||||||
\(200\) | −9.56584e8 | − | 5.52284e8i | −0.597865 | − | 0.345177i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.28544e8 | − | 1.26187e9i | −0.437572 | − | 0.757898i | ||||
\(203\) | 1.77137e8 | − | 1.02270e8i | 0.104310 | − | 0.0602231i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.63848e7 | − | 6.30203e7i | 0.0206018 | − | 0.0356833i | ||||
\(206\) | 2.04533e9i | 1.13578i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.64551e9 | −1.41337 | ||||||||
\(209\) | 3.31650e9 | + | 1.91478e9i | 1.73818 | + | 1.00354i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.23373e8 | + | 1.25292e9i | 0.364949 | + | 0.632111i | 0.988768 | − | 0.149458i | \(-0.0477530\pi\) |
−0.623819 | + | 0.781569i | \(0.714420\pi\) | |||||||
\(212\) | −9.52687e8 | + | 5.50034e8i | −0.471636 | + | 0.272299i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.59805e9 | + | 2.76791e9i | −0.761966 | + | 1.31976i | ||||
\(215\) | − | 1.62219e8i | − | 0.0759185i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.67760e8 | −0.301149 | ||||||||
\(218\) | −1.99043e9 | − | 1.14918e9i | −0.881295 | − | 0.508816i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.28614e7 | + | 9.15587e7i | 0.0225657 | + | 0.0390849i | ||||
\(221\) | −2.74457e9 | + | 1.58458e9i | −1.15055 | + | 0.664270i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.71529e8 | − | 1.16312e9i | 0.271547 | − | 0.470333i | −0.697711 | − | 0.716379i | \(-0.745798\pi\) |
0.969258 | + | 0.246046i | \(0.0791314\pi\) | |||||||
\(224\) | − | 1.51226e9i | − | 0.600670i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.00227e9 | 0.384195 | ||||||||
\(227\) | 1.83609e9 | + | 1.06007e9i | 0.691498 | + | 0.399237i | 0.804173 | − | 0.594395i | \(-0.202609\pi\) |
−0.112675 | + | 0.993632i | \(0.535942\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.89310e9 | + | 3.27894e9i | 0.688385 | + | 1.19232i | 0.972360 | + | 0.233486i | \(0.0750132\pi\) |
−0.283976 | + | 0.958831i | \(0.591654\pi\) | |||||||
\(230\) | −2.82856e8 | + | 1.63307e8i | −0.101077 | + | 0.0583570i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.58187e8 | − | 2.73988e8i | 0.0546032 | − | 0.0945755i | ||||
\(233\) | 7.71302e8i | 0.261698i | 0.991402 | + | 0.130849i | \(0.0417703\pi\) | ||||
−0.991402 | + | 0.130849i | \(0.958230\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.05060e8 | 0.0344481 | ||||||||
\(236\) | 1.17336e9 | + | 6.77438e8i | 0.378253 | + | 0.218384i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.71055e9 | − | 2.96275e9i | −0.533122 | − | 0.923395i | ||||
\(239\) | 4.44884e9 | − | 2.56854e9i | 1.36350 | − | 0.787217i | 0.373411 | − | 0.927666i | \(-0.378188\pi\) |
0.990088 | + | 0.140449i | \(0.0448547\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.52624e9 | − | 2.64352e9i | 0.452433 | − | 0.783636i | −0.546104 | − | 0.837717i | \(-0.683890\pi\) |
0.998537 | + | 0.0540811i | \(0.0172230\pi\) | |||||||
\(242\) | − | 2.31346e9i | − | 0.674528i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.36473e9 | 0.385023 | ||||||||
\(245\) | 1.11446e8 | + | 6.43432e7i | 0.0309314 | + | 0.0178582i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.39339e9 | − | 5.87752e9i | −0.911687 | − | 1.57909i | ||||
\(248\) | −8.94486e8 | + | 5.16432e8i | −0.236465 | + | 0.136523i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.01909e8 | − | 6.96128e8i | 0.102889 | − | 0.178209i | ||||
\(251\) | − | 7.81654e9i | − | 1.96934i | −0.174440 | − | 0.984668i | \(-0.555811\pi\) | ||
0.174440 | − | 0.984668i | \(-0.444189\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.79603e9 | 1.41465 | ||||||||
\(254\) | 4.29719e9 | + | 2.48099e9i | 1.03240 | + | 0.596059i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.27797e9 | − | 3.94555e9i | −0.530380 | − | 0.918646i | ||||
\(257\) | −4.91857e9 | + | 2.83974e9i | −1.12747 | + | 0.650947i | −0.943298 | − | 0.331946i | \(-0.892295\pi\) |
−0.184175 | + | 0.982893i | \(0.558961\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.76730e9 | + | 3.06105e9i | −0.392745 | + | 0.680254i | ||||
\(260\) | − | 1.87363e8i | − | 0.0410006i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.91447e9 | 0.406298 | ||||||||
\(263\) | 3.56245e9 | + | 2.05678e9i | 0.744606 | + | 0.429898i | 0.823742 | − | 0.566966i | \(-0.191883\pi\) |
−0.0791358 | + | 0.996864i | \(0.525216\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.80706e8 | + | 4.86197e8i | 0.0569205 | + | 0.0985892i | ||||
\(266\) | 6.34476e9 | − | 3.66315e9i | 1.26733 | − | 0.731691i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.44484e8 | − | 1.28948e9i | 0.144317 | − | 0.249964i | ||||
\(269\) | 7.56195e9i | 1.44419i | 0.691793 | + | 0.722096i | \(0.256821\pi\) | ||||
−0.691793 | + | 0.722096i | \(0.743179\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.29007e9 | −1.16621 | −0.583107 | − | 0.812395i | \(-0.698163\pi\) | ||||
−0.583107 | + | 0.812395i | \(0.698163\pi\) | |||||||
\(272\) | −6.88250e9 | − | 3.97361e9i | −1.25739 | − | 0.725956i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.12892e9 | + | 1.06156e10i | 1.08738 | + | 1.88340i | ||||
\(275\) | −6.15332e9 | + | 3.55262e9i | −1.07592 | + | 0.621180i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.49367e9 | + | 2.58711e9i | −0.253708 | + | 0.439436i | −0.964544 | − | 0.263923i | \(-0.914984\pi\) |
0.710836 | + | 0.703358i | \(0.248317\pi\) | |||||||
\(278\) | − | 9.72906e8i | − | 0.162889i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.84758e8 | −0.0463281 | ||||||||
\(281\) | −3.13118e8 | − | 1.80779e8i | −0.0502207 | − | 0.0289949i | 0.474679 | − | 0.880159i | \(-0.342564\pi\) |
−0.524900 | + | 0.851164i | \(0.675897\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.03882e9 | − | 3.53133e9i | −0.317858 | − | 0.550545i | 0.662183 | − | 0.749342i | \(-0.269630\pi\) |
−0.980041 | + | 0.198797i | \(0.936297\pi\) | |||||||
\(284\) | −1.59128e9 | + | 9.18724e8i | −0.244609 | + | 0.141225i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.66548e9 | + | 9.81289e9i | −0.846783 | + | 1.46667i | ||||
\(287\) | 2.47048e9i | 0.364128i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.54455e9 | −0.364770 | ||||||||
\(290\) | 9.93164e7 | + | 5.73403e7i | 0.0140420 | + | 0.00810715i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.23481e9 | + | 2.13875e9i | 0.169851 | + | 0.294191i | ||||
\(293\) | −1.95369e9 | + | 1.12796e9i | −0.265085 | + | 0.153047i | −0.626652 | − | 0.779299i | \(-0.715575\pi\) |
0.361567 | + | 0.932346i | \(0.382242\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.45726e8 | − | 5.98815e8i | 0.0456503 | − | 0.0790687i | ||||
\(296\) | 5.46717e9i | 0.712189i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.93797e9 | 0.245743 | ||||||||
\(299\) | −8.89561e9 | − | 5.13588e9i | −1.11299 | − | 0.642584i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.75361e9 | + | 4.76940e9i | 0.335457 | + | 0.581029i | ||||
\(302\) | 4.57793e9 | − | 2.64307e9i | 0.550354 | − | 0.317747i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.50953e9 | − | 1.47389e10i | 0.996348 | − | 1.72573i | ||||
\(305\) | − | 6.96479e8i | − | 0.0804839i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.57116e9 | −0.739756 | −0.369878 | − | 0.929080i | \(-0.620601\pi\) | ||||
−0.369878 | + | 0.929080i | \(0.620601\pi\) | |||||||
\(308\) | −3.10836e9 | − | 1.79461e9i | −0.345405 | − | 0.199419i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.87199e8 | − | 3.24238e8i | −0.0202701 | − | 0.0351089i | ||||
\(311\) | 1.13691e10 | − | 6.56393e9i | 1.21530 | − | 0.701653i | 0.251389 | − | 0.967886i | \(-0.419113\pi\) |
0.963909 | + | 0.266233i | \(0.0857792\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.29417e9 | + | 2.24157e9i | −0.134839 | + | 0.233547i | −0.925536 | − | 0.378660i | \(-0.876385\pi\) |
0.790697 | + | 0.612207i | \(0.209718\pi\) | |||||||
\(314\) | 1.26451e10i | 1.30078i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.55407e9 | −0.757587 | ||||||||
\(317\) | −4.30655e9 | − | 2.48639e9i | −0.426474 | − | 0.246225i | 0.271369 | − | 0.962475i | \(-0.412523\pi\) |
−0.697843 | + | 0.716250i | \(0.745857\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.01755e9 | − | 1.76245e9i | −0.0982638 | − | 0.170198i | ||||
\(320\) | −2.45475e8 | + | 1.41725e8i | −0.0234103 | + | 0.0135160i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.54416e9 | − | 9.60277e9i | 0.515718 | − | 0.893250i | ||||
\(323\) | − | 2.03878e10i | − | 1.87310i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.25920e10 | 1.12865 | ||||||||
\(326\) | 6.20208e9 | + | 3.58077e9i | 0.549119 | + | 0.317034i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.91062e9 | + | 3.30929e9i | 0.165074 | + | 0.285916i | ||||
\(329\) | −3.08887e9 | + | 1.78336e9i | −0.263643 | + | 0.152214i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.89585e8 | − | 3.28371e8i | 0.0157940 | − | 0.0273560i | −0.858020 | − | 0.513616i | \(-0.828306\pi\) |
0.873814 | + | 0.486260i | \(0.161639\pi\) | |||||||
\(332\) | 3.37100e9i | 0.277464i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.01313e10 | 0.814101 | ||||||||
\(335\) | −6.58080e8 | − | 3.79943e8i | −0.0522516 | − | 0.0301675i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.52936e8 | + | 1.30412e9i | 0.0583766 | + | 0.101111i | 0.893737 | − | 0.448592i | \(-0.148074\pi\) |
−0.835360 | + | 0.549703i | \(0.814741\pi\) | |||||||
\(338\) | 3.94360e9 | − | 2.27684e9i | 0.302152 | − | 0.174448i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.81423e8 | − | 4.87440e8i | 0.0210593 | − | 0.0364758i | ||||
\(341\) | 6.64399e9i | 0.491373i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.49877e10 | −1.08283 | ||||||||
\(344\) | 7.37711e9 | + | 4.25917e9i | 0.526808 | + | 0.304153i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.06305e10 | − | 1.84125e10i | −0.741735 | − | 1.28472i | ||||
\(347\) | 1.78865e10 | − | 1.03268e10i | 1.23369 | − | 0.712274i | 0.265897 | − | 0.964002i | \(-0.414332\pi\) |
0.967798 | + | 0.251728i | \(0.0809987\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.62214e9 | + | 9.73783e9i | −0.378966 | + | 0.656388i | −0.990912 | − | 0.134511i | \(-0.957054\pi\) |
0.611946 | + | 0.790899i | \(0.290387\pi\) | |||||||
\(350\) | 1.35930e10i | 0.905820i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.50465e10 | −0.980090 | ||||||||
\(353\) | 3.62138e9 | + | 2.09080e9i | 0.233225 | + | 0.134653i | 0.612059 | − | 0.790812i | \(-0.290342\pi\) |
−0.378834 | + | 0.925465i | \(0.623675\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.68865e8 | + | 8.12097e8i | 0.0295212 | + | 0.0511322i | ||||
\(356\) | 4.33697e8 | − | 2.50395e8i | 0.0270014 | − | 0.0155893i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.41332e9 | − | 2.44794e9i | 0.0860415 | − | 0.149028i | ||||
\(359\) | 1.61776e10i | 0.973950i | 0.873416 | + | 0.486975i | \(0.161900\pi\) | ||||
−0.873416 | + | 0.486975i | \(0.838100\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.66771e10 | 1.57076 | ||||||||
\(362\) | 6.38957e8 | + | 3.68902e8i | 0.0372081 | + | 0.0214821i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.18042e9 | + | 5.50865e9i | 0.181167 | + | 0.313791i | ||||
\(365\) | 1.09150e9 | − | 6.30177e8i | 0.0614967 | − | 0.0355051i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.41622e9 | + | 7.64912e9i | −0.243437 | + | 0.421646i | −0.961691 | − | 0.274136i | \(-0.911608\pi\) |
0.718254 | + | 0.695781i | \(0.244942\pi\) | |||||||
\(368\) | − | 2.57583e10i | − | 1.40451i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.98177e9 | −0.105742 | ||||||||
\(371\) | −1.65061e10 | − | 9.52979e9i | −0.871261 | − | 0.503023i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.14224e10 | − | 1.97841e10i | −0.590094 | − | 1.02207i | −0.994219 | − | 0.107369i | \(-0.965757\pi\) |
0.404125 | − | 0.914704i | \(-0.367576\pi\) | |||||||
\(374\) | −2.94784e10 | + | 1.70194e10i | −1.50667 | + | 0.869876i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.75842e9 | + | 4.77773e9i | −0.138010 | + | 0.239040i | ||||
\(377\) | 3.60662e9i | 0.178540i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.47178e10 | 1.19799 | 0.598995 | − | 0.800753i | \(-0.295567\pi\) | ||||
0.598995 | + | 0.800753i | \(0.295567\pi\) | |||||||
\(380\) | 1.04386e9 | + | 6.02671e8i | 0.0500618 | + | 0.0289032i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.48286e10 | + | 2.56839e10i | 0.696382 | + | 1.20617i | ||||
\(383\) | −3.94315e9 | + | 2.27658e9i | −0.183252 | + | 0.105800i | −0.588819 | − | 0.808265i | \(-0.700407\pi\) |
0.405568 | + | 0.914065i | \(0.367074\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.15868e8 | + | 1.58633e9i | −0.0416860 | + | 0.0722022i | ||||
\(386\) | − | 4.09515e10i | − | 1.84468i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.35167e9 | 0.324384 | ||||||||
\(389\) | −6.97457e9 | − | 4.02677e9i | −0.304592 | − | 0.175856i | 0.339912 | − | 0.940457i | \(-0.389603\pi\) |
−0.644504 | + | 0.764601i | \(0.722936\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.54284e10 | − | 2.67228e10i | −0.660108 | − | 1.14334i | ||||
\(392\) | −5.85218e9 | + | 3.37876e9i | −0.247841 | + | 0.143091i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.58840e10 | + | 2.75118e10i | −0.659134 | + | 1.14165i | ||||
\(395\) | 3.85517e9i | 0.158363i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.77691e10 | −1.11789 | −0.558946 | − | 0.829204i | \(-0.688794\pi\) | ||||
−0.558946 | + | 0.829204i | \(0.688794\pi\) | |||||||
\(398\) | −7.36917e9 | − | 4.25459e9i | −0.293688 | − | 0.169561i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.57883e10 | + | 2.73461e10i | 0.616730 | + | 1.06821i | ||||
\(401\) | −2.11169e10 | + | 1.21919e10i | −0.816682 | + | 0.471512i | −0.849271 | − | 0.527957i | \(-0.822958\pi\) |
0.0325886 | + | 0.999469i | \(0.489625\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.88726e9 | − | 1.01970e10i | 0.223200 | − | 0.386593i | ||||
\(404\) | 8.13847e9i | 0.305504i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.89333e9 | −0.143291 | ||||||||
\(407\) | 3.04564e10 | + | 1.75840e10i | 1.10995 | + | 0.640827i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.41854e10 | + | 4.18904e10i | 0.864292 | + | 1.49700i | 0.867748 | + | 0.497004i | \(0.165567\pi\) |
−0.00345597 | + | 0.999994i | \(0.501100\pi\) | |||||||
\(410\) | −1.19957e9 | + | 6.92571e8i | −0.0424511 | + | 0.0245092i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.71202e9 | − | 9.89351e9i | 0.198244 | − | 0.343370i | ||||
\(413\) | 2.34743e10i | 0.806851i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.72037e9 | 0.0580002 | ||||||||
\(416\) | 2.30931e10 | + | 1.33328e10i | 0.771096 | + | 0.445192i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.64471e10 | − | 6.31283e10i | −1.19387 | − | 2.06785i | ||||
\(419\) | −2.62485e10 | + | 1.51546e10i | −0.851624 | + | 0.491685i | −0.861198 | − | 0.508269i | \(-0.830286\pi\) |
0.00957454 | + | 0.999954i | \(0.496952\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.37935e8 | + | 5.85321e8i | −0.0107573 | + | 0.0186323i | −0.871354 | − | 0.490655i | \(-0.836758\pi\) |
0.860597 | + | 0.509287i | \(0.170091\pi\) | |||||||
\(422\) | − | 2.75383e10i | − | 0.868334i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.94806e10 | −0.912163 | ||||||||
\(425\) | 3.27590e10 | + | 1.89134e10i | 1.00410 | + | 0.579715i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.18225e10 | + | 2.04772e10i | 0.355630 | + | 0.615969i | ||||
\(428\) | 1.54600e10 | − | 8.92581e9i | 0.460716 | − | 0.265995i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.54389e9 | + | 2.67409e9i | −0.0451587 | + | 0.0782172i | ||||
\(431\) | − | 3.59140e9i | − | 0.104077i | −0.998645 | − | 0.0520384i | \(-0.983428\pi\) | ||
0.998645 | − | 0.0520384i | \(-0.0165718\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.82741e10 | −1.37329 | −0.686646 | − | 0.726992i | \(-0.740918\pi\) | ||||
−0.686646 | + | 0.726992i | \(0.740918\pi\) | |||||||
\(434\) | 1.10077e10 | + | 6.35528e9i | 0.310267 | + | 0.179133i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.41865e9 | + | 1.11174e10i | 0.177622 | + | 0.307651i | ||||
\(437\) | 5.72272e10 | − | 3.30401e10i | 1.56919 | − | 0.905975i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.41050e10 | − | 5.90716e10i | 0.918248 | − | 1.59045i | 0.116173 | − | 0.993229i | \(-0.462937\pi\) |
0.802075 | − | 0.597223i | \(-0.203729\pi\) | |||||||
\(440\) | 2.83325e9i | 0.0755918i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.03237e10 | 1.58052 | ||||||||
\(443\) | −3.44012e10 | − | 1.98615e10i | −0.893220 | − | 0.515701i | −0.0182258 | − | 0.999834i | \(-0.505802\pi\) |
−0.874994 | + | 0.484133i | \(0.839135\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.27788e8 | − | 2.21335e8i | −0.00325873 | − | 0.00564429i | ||||
\(446\) | −2.21396e10 | + | 1.27823e10i | −0.559539 | + | 0.323050i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.81147e9 | − | 8.33372e9i | 0.119444 | − | 0.206884i | ||||
\(449\) | − | 4.02929e10i | − | 0.991386i | −0.868498 | − | 0.495693i | \(-0.834914\pi\) | ||
0.868498 | − | 0.495693i | \(-0.165086\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.45805e10 | 0.594133 | ||||||||
\(452\) | −4.84812e9 | − | 2.79906e9i | −0.116150 | − | 0.0670592i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.01780e10 | − | 3.49493e10i | −0.474957 | − | 0.822650i | ||||
\(455\) | 2.81130e9 | − | 1.62311e9i | 0.0655937 | − | 0.0378705i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.25809e10 | − | 3.91113e10i | 0.517698 | − | 0.896680i | −0.482090 | − | 0.876121i | \(-0.660122\pi\) |
0.999789 | − | 0.0205582i | \(-0.00654433\pi\) | |||||||
\(458\) | − | 7.20688e10i | − | 1.63789i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.82428e9 | 0.0407437 | ||||||||
\(461\) | −4.07475e9 | − | 2.35256e9i | −0.0902190 | − | 0.0520879i | 0.454212 | − | 0.890894i | \(-0.349921\pi\) |
−0.544431 | + | 0.838806i | \(0.683254\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.74222e10 | + | 3.01762e10i | 0.379122 | + | 0.656659i | 0.990935 | − | 0.134344i | \(-0.0428926\pi\) |
−0.611812 | + | 0.791003i | \(0.709559\pi\) | |||||||
\(464\) | −7.83255e9 | + | 4.52213e9i | −0.168978 | + | 0.0975598i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.34072e9 | − | 1.27145e10i | 0.155666 | − | 0.269622i | ||||
\(467\) | 9.27082e10i | 1.94917i | 0.224011 | + | 0.974587i | \(0.428085\pi\) | ||||
−0.224011 | + | 0.974587i | \(0.571915\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.57976e10 | 0.533198 | ||||||||
\(470\) | −1.73186e9 | − | 9.99888e8i | −0.0354912 | − | 0.0204908i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.81546e10 | + | 3.14446e10i | 0.365778 | + | 0.633547i | ||||
\(473\) | 4.74540e10 | − | 2.73976e10i | 0.948043 | − | 0.547353i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.05033e10 | + | 7.01537e10i | −0.795638 | + | 1.37809i | ||||
\(476\) | 1.91083e10i | 0.372215i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.77822e10 | −1.87305 | ||||||||
\(479\) | −2.82374e10 | − | 1.63029e10i | −0.536392 | − | 0.309686i | 0.207224 | − | 0.978294i | \(-0.433557\pi\) |
−0.743615 | + | 0.668608i | \(0.766891\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.11626e10 | − | 5.39751e10i | −0.582174 | − | 1.00835i | ||||
\(482\) | −5.03184e10 | + | 2.90513e10i | −0.932264 | + | 0.538243i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.46083e9 | + | 1.11905e10i | −0.117735 | + | 0.203924i | ||||
\(485\) | − | 3.75188e9i | − | 0.0678081i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.98358e8 | 0.0141932 | 0.00709662 | − | 0.999975i | \(-0.497741\pi\) | ||||
0.00709662 | + | 0.999975i | \(0.497741\pi\) | |||||||
\(488\) | 3.16733e10 | + | 1.82866e10i | 0.558488 | + | 0.322443i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.22475e9 | − | 2.12133e9i | −0.0212453 | − | 0.0367979i | ||||
\(491\) | 4.32216e10 | − | 2.49540e10i | 0.743660 | − | 0.429353i | −0.0797382 | − | 0.996816i | \(-0.525408\pi\) |
0.823399 | + | 0.567463i | \(0.192075\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.41724e9 | + | 9.38293e9i | −0.0917044 | + | 0.158837i | ||||
\(494\) | 1.29184e11i | 2.16920i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.95267e10 | 0.487853 | ||||||||
\(497\) | −2.75702e10 | − | 1.59177e10i | −0.451871 | − | 0.260888i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.26906e10 | + | 3.93012e10i | 0.365968 | + | 0.633875i | 0.988931 | − | 0.148376i | \(-0.0474046\pi\) |
−0.622963 | + | 0.782251i | \(0.714071\pi\) | |||||||
\(500\) | −3.88818e9 | + | 2.24484e9i | −0.0622108 | + | 0.0359174i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.43924e10 | + | 1.28851e11i | −1.17142 | + | 2.02896i | ||||
\(503\) | − | 2.21128e8i | − | 0.00345440i | −0.999999 | − | 0.00172720i | \(-0.999450\pi\) | ||
0.999999 | − | 0.00172720i | \(-0.000549785\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.15341e9 | 0.0638616 | ||||||||
\(506\) | −9.55444e10 | − | 5.51626e10i | −1.45748 | − | 0.841478i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.38574e10 | − | 2.40017e10i | −0.208078 | − | 0.360402i | ||||
\(509\) | −8.78597e10 | + | 5.07258e10i | −1.30894 | + | 0.755715i | −0.981919 | − | 0.189303i | \(-0.939377\pi\) |
−0.327018 | + | 0.945018i | \(0.606044\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.13941e10 | + | 3.70557e10i | −0.313769 | + | 0.543464i | ||||
\(512\) | 7.46028e9i | 0.108561i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.08107e11 | 1.54882 | ||||||||
\(515\) | −5.04909e9 | − | 2.91509e9i | −0.0717768 | − | 0.0414404i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.77438e10 | + | 3.07332e10i | 0.248362 | + | 0.430176i | ||||
\(518\) | 5.82659e10 | − | 3.36398e10i | 0.809274 | − | 0.467234i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.51056e9 | − | 4.34841e9i | 0.0343365 | − | 0.0594726i | ||||
\(521\) | − | 4.53217e10i | − | 0.615114i | −0.951530 | − | 0.307557i | \(-0.900489\pi\) | ||
0.951530 | − | 0.307557i | \(-0.0995114\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.59979e10 | 0.213824 | 0.106912 | − | 0.994268i | \(-0.465904\pi\) | ||||
0.106912 | + | 0.994268i | \(0.465904\pi\) | |||||||
\(524\) | −9.26056e9 | − | 5.34659e9i | −0.122832 | − | 0.0709172i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.91501e10 | − | 6.78100e10i | −0.511434 | − | 0.885830i | ||||
\(527\) | 3.06324e10 | − | 1.76856e10i | 0.397136 | − | 0.229286i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.08506e10 | − | 1.87938e10i | 0.138558 | − | 0.239990i | ||||
\(530\) | − | 1.06863e10i | − | 0.135432i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.09206e10 | −0.510852 | ||||||||
\(533\) | −3.77255e10 | − | 2.17808e10i | −0.467441 | − | 0.269877i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.55523e9 | − | 7.88989e9i | −0.0556026 | − | 0.0963065i | ||||
\(536\) | 3.45567e10 | − | 1.99513e10i | 0.418672 | − | 0.241720i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.19694e10 | − | 1.24655e11i | 0.859051 | − | 1.48792i | ||||
\(539\) | 4.34683e10i | 0.515013i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.28974e10 | −0.850987 | −0.425494 | − | 0.904961i | \(-0.639899\pi\) | ||||
−0.425494 | + | 0.904961i | \(0.639899\pi\) | |||||||
\(542\) | 1.03688e11 | + | 5.98646e10i | 1.20153 | + | 0.693701i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.00524e10 | + | 6.93727e10i | 0.457333 | + | 0.792124i | ||||
\(545\) | 5.67371e9 | − | 3.27572e9i | 0.0643104 | − | 0.0371296i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.24551e10 | − | 1.08175e11i | 0.697619 | − | 1.20831i | −0.271670 | − | 0.962390i | \(-0.587576\pi\) |
0.969290 | − | 0.245922i | \(-0.0790906\pi\) | |||||||
\(548\) | − | 6.84654e10i | − | 0.759187i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.35245e11 | 1.47799 | ||||||||
\(551\) | −2.00936e10 | − | 1.16011e10i | −0.217998 | − | 0.125861i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.54402e10 | − | 1.13346e11i | −0.699752 | − | 1.21201i | ||||
\(554\) | 4.92446e10 | − | 2.84314e10i | 0.522781 | − | 0.301828i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.71705e9 | + | 4.70607e9i | −0.0284314 | + | 0.0492447i | ||||
\(557\) | − | 9.05278e10i | − | 0.940505i | −0.882532 | − | 0.470253i | \(-0.844163\pi\) | ||
0.882532 | − | 0.470253i | \(-0.155837\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.71083e10 | −0.994510 | ||||||||
\(560\) | 7.04985e9 | + | 4.07023e9i | 0.0716849 | + | 0.0413873i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.44106e9 | + | 5.96008e9i | 0.0344942 | + | 0.0597457i | ||||
\(563\) | 3.91457e10 | − | 2.26008e10i | 0.389628 | − | 0.224952i | −0.292371 | − | 0.956305i | \(-0.594444\pi\) |
0.681999 | + | 0.731353i | \(0.261111\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.42848e9 | + | 2.47420e9i | −0.0140178 | + | 0.0242796i | ||||
\(566\) | 7.76162e10i | 0.756287i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.92415e10 | −0.473084 | ||||||||
\(569\) | 4.31087e10 | + | 2.48888e10i | 0.411259 | + | 0.237441i | 0.691331 | − | 0.722539i | \(-0.257025\pi\) |
−0.280071 | + | 0.959979i | \(0.590358\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.32484e10 | + | 2.29469e10i | 0.124629 | + | 0.215863i | 0.921588 | − | 0.388170i | \(-0.126893\pi\) |
−0.796959 | + | 0.604033i | \(0.793559\pi\) | |||||||
\(572\) | 5.48093e10 | − | 3.16442e10i | 0.512000 | − | 0.295603i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.35123e10 | − | 4.07245e10i | 0.216595 | − | 0.375153i | ||||
\(575\) | 1.22603e11i | 1.12158i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.02736e10 | −0.543780 | −0.271890 | − | 0.962328i | \(-0.587649\pi\) | ||||
−0.271890 | + | 0.962328i | \(0.587649\pi\) | |||||||
\(578\) | 4.19455e10 | + | 2.42173e10i | 0.375815 | + | 0.216977i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.20271e8 | − | 5.54725e8i | −0.00283012 | − | 0.00490192i | ||||
\(581\) | −5.05806e10 | + | 2.92027e10i | −0.443894 | + | 0.256282i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.48183e10 | + | 1.64230e11i | −0.820764 | + | 1.42160i | ||||
\(584\) | 6.61830e10i | 0.568978i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.29406e10 | 0.364148 | ||||||||
\(587\) | −1.04499e10 | − | 6.03326e9i | −0.0880157 | − | 0.0508159i | 0.455346 | − | 0.890314i | \(-0.349516\pi\) |
−0.543362 | + | 0.839499i | \(0.682849\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.78739e10 | + | 6.55996e10i | 0.314687 | + | 0.545054i | ||||
\(590\) | −1.13982e10 | + | 6.58076e9i | −0.0940651 | + | 0.0543085i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.81456e10 | − | 1.35352e11i | 0.636236 | − | 1.10199i | ||||
\(593\) | − | 1.37897e11i | − | 1.11515i | −0.830125 | − | 0.557577i | \(-0.811731\pi\) | ||
0.830125 | − | 0.557577i | \(-0.188269\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.75179e9 | 0.0778066 | ||||||||
\(596\) | −9.37419e9 | − | 5.41219e9i | −0.0742931 | − | 0.0428932i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.77595e10 | + | 1.69324e11i | 0.764459 | + | 1.32408i | ||||
\(599\) | −1.44514e11 | + | 8.34354e10i | −1.12255 | + | 0.648102i | −0.942049 | − | 0.335474i | \(-0.891104\pi\) |
−0.180496 | + | 0.983576i | \(0.557770\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.54667e10 | + | 4.41096e10i | −0.195198 | + | 0.338093i | −0.946965 | − | 0.321336i | \(-0.895868\pi\) |
0.751768 | + | 0.659428i | \(0.229202\pi\) | |||||||
\(602\) | − | 1.04828e11i | − | 0.798162i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.95254e10 | −0.221844 | ||||||||
\(605\) | 5.71099e9 | + | 3.29724e9i | 0.0426275 | + | 0.0246110i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.98453e10 | + | 3.43730e10i | 0.146185 | + | 0.253200i | 0.929814 | − | 0.368029i | \(-0.119967\pi\) |
−0.783629 | + | 0.621228i | \(0.786634\pi\) | |||||||
\(608\) | −1.48562e11 | + | 8.57725e10i | −1.08716 | + | 0.627673i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.62861e9 | + | 1.14811e10i | −0.0478744 | + | 0.0829208i | ||||
\(611\) | − | 6.28915e10i | − | 0.451260i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.75904e10 | −0.195396 | −0.0976982 | − | 0.995216i | \(-0.531148\pi\) | ||||
−0.0976982 | + | 0.995216i | \(0.531148\pi\) | |||||||
\(614\) | 1.08322e11 | + | 6.25398e10i | 0.762155 | + | 0.440030i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.80935e10 | − | 8.33005e10i | −0.334013 | − | 0.578528i | ||||
\(617\) | −7.51295e10 | + | 4.33761e10i | −0.518406 | + | 0.299302i | −0.736282 | − | 0.676675i | \(-0.763420\pi\) |
0.217876 | + | 0.975976i | \(0.430087\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.58249e10 | + | 2.74096e10i | −0.107790 | + | 0.186698i | −0.914875 | − | 0.403738i | \(-0.867711\pi\) |
0.807085 | + | 0.590436i | \(0.201044\pi\) | |||||||
\(620\) | 2.09117e9i | 0.0141522i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.49884e11 | −1.66946 | ||||||||
\(623\) | 7.51416e9 | + | 4.33830e9i | 0.0498802 | + | 0.0287984i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.45733e10 | − | 1.29165e11i | −0.488724 | − | 0.846494i | ||||
\(626\) | 4.26674e10 | − | 2.46341e10i | 0.277843 | − | 0.160413i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.53141e10 | − | 6.11658e10i | 0.227044 | − | 0.393251i | ||||
\(629\) | − | 1.87228e11i | − | 1.19610i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.47836e11 | 1.56332 | 0.781659 | − | 0.623706i | \(-0.214374\pi\) | ||||
0.781659 | + | 0.623706i | \(0.214374\pi\) | |||||||
\(632\) | −1.75319e11 | − | 1.01220e11i | −1.09890 | − | 0.634452i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.73274e10 | + | 8.19735e10i | 0.292925 | + | 0.507361i | ||||
\(635\) | −1.22491e10 | + | 7.07202e9i | −0.0753372 | + | 0.0434960i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.85175e10 | − | 6.67142e10i | 0.233937 | − | 0.405192i | ||||
\(638\) | 3.87374e10i | 0.233802i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.67988e10 | 0.100129 | ||||||||
\(641\) | 2.33521e11 | + | 1.34823e11i | 1.38323 | + | 0.798607i | 0.992540 | − | 0.121917i | \(-0.0389041\pi\) |
0.390687 | + | 0.920523i | \(0.372237\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.49218e10 | + | 2.58453e10i | 0.0872926 | + | 0.151195i | 0.906366 | − | 0.422494i | \(-0.138845\pi\) |
−0.819073 | + | 0.573689i | \(0.805512\pi\) | |||||||
\(644\) | −5.36357e10 | + | 3.09666e10i | −0.311824 | + | 0.180032i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.94037e11 | + | 3.36082e11i | −1.11418 | + | 1.92981i | ||||
\(647\) | 9.21631e10i | 0.525944i | 0.964803 | + | 0.262972i | \(0.0847028\pi\) | ||||
−0.964803 | + | 0.262972i | \(0.915297\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.33562e11 | 1.31651 | ||||||||
\(650\) | −2.07572e11 | − | 1.19841e11i | −1.16282 | − | 0.671357i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.00002e10 | − | 3.46413e10i | −0.110673 | − | 0.191692i | ||||
\(653\) | −1.50685e11 | + | 8.69982e10i | −0.828740 | + | 0.478473i | −0.853421 | − | 0.521222i | \(-0.825476\pi\) |
0.0246814 | + | 0.999695i | \(0.492143\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.72860e9 | + | 4.72607e9i | −0.0148243 | + | 0.0256764i | ||||
\(656\) | − | 1.09239e11i | − | 0.589876i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.78911e10 | 0.362167 | ||||||||
\(659\) | 1.25628e11 | + | 7.25316e10i | 0.666110 | + | 0.384579i | 0.794601 | − | 0.607132i | \(-0.207680\pi\) |
−0.128491 | + | 0.991711i | \(0.541013\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.24740e10 | − | 1.60170e11i | −0.484411 | − | 0.839024i | 0.515429 | − | 0.856932i | \(-0.327633\pi\) |
−0.999840 | + | 0.0179086i | \(0.994299\pi\) | |||||||
\(662\) | −6.25041e9 | + | 3.60867e9i | −0.0325444 | + | 0.0187895i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.51696e10 | + | 7.82360e10i | −0.232366 | + | 0.402471i | ||||
\(665\) | 2.08835e10i | 0.106787i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.51163e10 | −0.177421 | ||||||||
\(668\) | −4.90063e10 | − | 2.82938e10i | −0.246120 | − | 0.142097i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.23206e9 | + | 1.25263e10i | 0.0358891 | + | 0.0621618i | ||||
\(671\) | 2.03741e11 | − | 1.17630e11i | 1.00505 | − | 0.580268i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.33590e10 | − | 2.31384e10i | 0.0651198 | − | 0.112791i | −0.831627 | − | 0.555334i | \(-0.812590\pi\) |
0.896747 | + | 0.442543i | \(0.145924\pi\) | |||||||
\(674\) | − | 2.86637e10i | − | 0.138897i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.54343e10 | −0.121796 | ||||||||
\(677\) | 4.06009e10 | + | 2.34409e10i | 0.193277 | + | 0.111589i | 0.593516 | − | 0.804822i | \(-0.297739\pi\) |
−0.400239 | + | 0.916411i | \(0.631073\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.36869e10 | + | 1.10309e11i | 0.299620 | + | 0.518957i | ||||
\(680\) | 1.30628e10 | − | 7.54183e9i | 0.0610945 | − | 0.0352729i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.32329e10 | − | 1.09523e11i | 0.292284 | − | 0.506252i | ||||
\(683\) | 2.98469e11i | 1.37156i | 0.727807 | + | 0.685782i | \(0.240540\pi\) | ||||
−0.727807 | + | 0.685782i | \(0.759460\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.49409e10 | −0.158698 | ||||||||
\(686\) | 2.47064e11 | + | 1.42643e11i | 1.11561 | + | 0.644100i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.21758e11 | − | 2.10891e11i | −0.543431 | − | 0.941250i | ||||
\(689\) | 2.91050e11 | − | 1.68038e11i | 1.29149 | − | 0.745641i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.31099e10 | − | 9.19890e10i | 0.232950 | − | 0.403482i | −0.725725 | − | 0.687985i | \(-0.758495\pi\) |
0.958675 | + | 0.284503i | \(0.0918287\pi\) | |||||||
\(692\) | 1.18752e11i | 0.517864i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.93133e11 | −1.69473 | ||||||||
\(695\) | 2.40171e9 | + | 1.38663e9i | 0.0102939 | + | 0.00594321i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.54307e10 | − | 1.13329e11i | −0.277237 | − | 0.480188i | ||||
\(698\) | 1.85356e11 | − | 1.07015e11i | 0.780881 | − | 0.450842i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.79613e10 | − | 6.57509e10i | 0.158106 | − | 0.273848i | ||||
\(701\) | − | 1.76564e11i | − | 0.731191i | −0.930774 | − | 0.365595i | \(-0.880865\pi\) | ||
0.930774 | − | 0.365595i | \(-0.119135\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.00950e11 | 1.64160 | ||||||||
\(704\) | −8.29178e10 | − | 4.78726e10i | −0.337565 | − | 0.194893i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.97977e10 | − | 6.89316e10i | −0.160191 | − | 0.277459i | ||||
\(707\) | −1.22114e11 | + | 7.05028e10i | −0.488753 | + | 0.282182i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.90765e10 | + | 8.50029e10i | −0.194217 | + | 0.336394i | −0.946644 | − | 0.322282i | \(-0.895550\pi\) |
0.752426 | + | 0.658676i | \(0.228883\pi\) | |||||||
\(710\) | − | 1.78493e10i | − | 0.0702406i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.34206e10 | 0.0522219 | ||||||||
\(713\) | 9.92847e10 | + | 5.73221e10i | 0.384171 | + | 0.221801i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.61494e10 | − | 2.79716e10i | −0.0617919 | − | 0.107027i | ||||
\(716\) | −1.36728e10 | + | 7.89400e9i | −0.0520242 | + | 0.0300362i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.53967e11 | − | 2.66679e11i | 0.579337 | − | 1.00344i | ||||
\(719\) | − | 1.05784e11i | − | 0.395825i | −0.980220 | − | 0.197913i | \(-0.936584\pi\) | ||
0.980220 | − | 0.197913i | \(-0.0634162\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.97931e11 | 0.732441 | ||||||||
\(722\) | −4.39758e11 | − | 2.53894e11i | −1.61832 | − | 0.934339i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.06048e9 | − | 3.56885e9i | −0.00749918 | − | 0.0129890i | ||||
\(725\) | 3.72810e10 | − | 2.15242e10i | 0.134938 | − | 0.0779067i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.31053e11 | − | 2.26990e11i | 0.469147 | − | 0.812587i | −0.530231 | − | 0.847853i | \(-0.677895\pi\) |
0.999378 | + | 0.0352668i | \(0.0112281\pi\) | |||||||
\(728\) | 1.70463e11i | 0.606884i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.39904e10 | −0.0844783 | ||||||||
\(731\) | −2.52635e11 | − | 1.45859e11i | −0.884758 | − | 0.510815i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.24638e11 | + | 3.89084e11i | 0.778157 | + | 1.34781i | 0.933003 | + | 0.359869i | \(0.117179\pi\) |
−0.154846 | + | 0.987939i | \(0.549488\pi\) | |||||||
\(734\) | 1.45598e11 | − | 8.40611e10i | 0.501616 | − | 0.289608i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.29816e11 | + | 2.24848e11i | −0.442403 | + | 0.766264i | ||||
\(737\) | − | 2.56678e11i | − | 0.869998i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.69989e11 | −1.24054 | −0.620270 | − | 0.784388i | \(-0.712977\pi\) | ||||
−0.620270 | + | 0.784388i | \(0.712977\pi\) | |||||||
\(740\) | 9.58606e9 | + | 5.53451e9i | 0.0319678 | + | 0.0184566i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.81396e11 | + | 3.14187e11i | 0.598428 | + | 1.03651i | ||||
\(743\) | −1.31608e11 | + | 7.59837e10i | −0.431843 | + | 0.249325i | −0.700132 | − | 0.714014i | \(-0.746875\pi\) |
0.268288 | + | 0.963339i | \(0.413542\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.76208e9 | + | 4.78405e9i | −0.00896624 | + | 0.0155300i | ||||
\(746\) | 4.34841e11i | 1.40403i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.90121e11 | 0.607329 | ||||||||
\(749\) | 2.67857e11 | + | 1.54647e11i | 0.851089 | + | 0.491377i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.80268e10 | − | 3.12234e10i | −0.0566708 | − | 0.0981567i | 0.836298 | − | 0.548275i | \(-0.184715\pi\) |
−0.892969 | + | 0.450118i | \(0.851382\pi\) | |||||||
\(752\) | 1.36582e11 | − | 7.88558e10i | 0.427093 | − | 0.246583i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.43254e10 | − | 5.94533e10i | 0.106201 | − | 0.183946i | ||||
\(755\) | 1.50681e10i | 0.0463736i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.49675e11 | −1.97839 | −0.989197 | − | 0.146590i | \(-0.953170\pi\) | ||||
−0.989197 | + | 0.146590i | \(0.953170\pi\) | |||||||
\(758\) | −4.07460e11 | − | 2.35247e11i | −1.23426 | − | 0.712602i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.61509e10 | + | 2.79742e10i | 0.0484108 | + | 0.0838500i | ||||
\(761\) | −4.58208e11 | + | 2.64546e11i | −1.36623 | + | 0.788794i | −0.990444 | − | 0.137913i | \(-0.955961\pi\) |
−0.375786 | + | 0.926706i | \(0.622627\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.11208e11 | + | 1.92619e11i | −0.328125 | + | 0.568329i | ||||
\(764\) | − | 1.65649e11i | − | 0.486199i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.66675e10 | 0.251734 | ||||||||
\(767\) | −3.58465e11 | − | 2.06960e11i | −1.03578 | − | 0.598006i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.38751e11 | + | 2.40323e11i | 0.396761 | + | 0.687211i | 0.993324 | − | 0.115355i | \(-0.0368007\pi\) |
−0.596563 | + | 0.802566i | \(0.703467\pi\) | |||||||
\(770\) | 3.01952e10 | − | 1.74332e10i | 0.0858963 | − | 0.0495923i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.14366e11 | + | 1.98088e11i | −0.321979 | + | 0.557685i | ||||
\(773\) | 6.48893e11i | 1.81742i | 0.417430 | + | 0.908709i | \(0.362931\pi\) | ||||
−0.417430 | + | 0.908709i | \(0.637069\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.40540e11 | −0.389577 | ||||||||
\(776\) | 1.70621e11 | + | 9.85083e10i | 0.470529 | + | 0.271660i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.66480e10 | + | 1.32758e11i | 0.209210 | + | 0.362362i | ||||
\(779\) | 2.42696e11 | − | 1.40120e11i | 0.659041 | − | 0.380497i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.58375e11 | + | 2.74314e11i | −0.425680 | + | 0.737300i | ||||
\(782\) | 5.87349e11i | 1.57061i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.93179e11 | 0.511323 | ||||||||
\(785\) | −3.12156e10 | − | 1.80223e10i | −0.0822039 | − | 0.0474605i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.24484e11 | − | 3.88818e11i | −0.585177 | − | 1.01356i | −0.994853 | − | 0.101325i | \(-0.967692\pi\) |
0.409677 | − | 0.912231i | \(-0.365641\pi\) | |||||||
\(788\) | 1.53666e11 | − | 8.87189e10i | 0.398540 | − | 0.230097i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.66908e10 | − | 6.35504e10i | 0.0941996 | − | 0.163158i | ||||
\(791\) | − | 9.69921e10i | − | 0.247759i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.16930e11 | −1.05431 | ||||||||
\(794\) | 4.57759e11 | + | 2.64287e11i | 1.15174 | + | 0.664957i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.37637e10 | + | 4.11600e10i | 0.0591919 | + | 0.102523i | ||||
\(797\) | −1.23670e11 | + | 7.14010e10i | −0.306501 | + | 0.176958i | −0.645360 | − | 0.763879i | \(-0.723292\pi\) |
0.338859 | + | 0.940837i | \(0.389959\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.44646e10 | − | 1.63617e11i | 0.231783 | − | 0.401460i | ||||
\(800\) | − | 3.18278e11i | − | 0.777047i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.64135e11 | 1.12188 | ||||||||
\(803\) | 3.68692e11 | + | 2.12864e11i | 0.886750 | + | 0.511965i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.58036e10 | + | 2.73726e10i | 0.0376333 | + | 0.0651827i | ||||
\(806\) | −1.94097e11 | + | 1.12062e11i | −0.459916 | + | 0.265532i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.09051e11 | + | 1.88882e11i | −0.255849 | + | 0.443143i | ||||
\(809\) | − | 4.15227e11i | − | 0.969374i | −0.874688 | − | 0.484687i | \(-0.838934\pi\) | ||
0.874688 | − | 0.484687i | \(-0.161066\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.13963e11 | 0.263440 | 0.131720 | − | 0.991287i | \(-0.457950\pi\) | ||||
0.131720 | + | 0.991287i | \(0.457950\pi\) | |||||||
\(812\) | 1.88326e10 | + | 1.08730e10i | 0.0433197 | + | 0.0250106i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.34705e11 | − | 5.79727e11i | −0.762369 | − | 1.32046i | ||||
\(815\) | −1.76790e10 | + | 1.02069e10i | −0.0400706 | + | 0.0231348i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.12358e11 | − | 5.41020e11i | 0.701076 | − | 1.21430i | ||||
\(818\) | − | 9.20721e11i | − | 2.05643i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.73662e9 | 0.0171118 | ||||||||
\(821\) | −6.17284e11 | − | 3.56389e11i | −1.35867 | − | 0.784426i | −0.369221 | − | 0.929342i | \(-0.620376\pi\) |
−0.989444 | + | 0.144916i | \(0.953709\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.17917e11 | + | 2.04238e11i | 0.257026 | + | 0.445182i | 0.965444 | − | 0.260611i | \(-0.0839241\pi\) |
−0.708418 | + | 0.705793i | \(0.750591\pi\) | |||||||
\(824\) | 2.65135e11 | − | 1.53076e11i | 0.575120 | − | 0.332045i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.23413e11 | − | 3.86962e11i | 0.479941 | − | 0.831281i | ||||
\(827\) | − | 5.38659e9i | − | 0.0115157i | −0.999983 | − | 0.00575787i | \(-0.998167\pi\) | ||
0.999983 | − | 0.00575787i | \(-0.00183280\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.01700e11 | 1.27398 | 0.636989 | − | 0.770873i | \(-0.280180\pi\) | ||||
0.636989 | + | 0.770873i | \(0.280180\pi\) | |||||||
\(830\) | −2.83594e10 | − | 1.63733e10i | −0.0597564 | − | 0.0345004i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.48401e10 | + | 1.46947e11i | 0.177055 | + | 0.306668i | ||||
\(833\) | 2.00413e11 | − | 1.15708e11i | 0.416241 | − | 0.240317i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.44396e10 | + | 2.50100e10i | −0.0297035 | + | 0.0514480i | ||||
\(836\) | 4.07146e11i | 0.833538i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.76922e11 | 1.16988 | ||||||||
\(839\) | −5.25649e11 | − | 3.03483e11i | −1.06083 | − | 0.612473i | −0.135172 | − | 0.990822i | \(-0.543159\pi\) |
−0.925663 | + | 0.378349i | \(0.876492\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.43958e11 | − | 4.22548e11i | −0.487676 | − | 0.844680i | ||||
\(842\) | 1.11414e10 | − | 6.43247e9i | 0.0221661 | − | 0.0127976i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.69066e10 | + | 1.33206e11i | −0.151563 | + | 0.262515i | ||||
\(845\) | 1.29802e10i | 0.0254598i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.23879e11 | −0.434990 | ||||||||
\(848\) | 7.29859e11 | + | 4.21384e11i | 1.41142 | + | 0.814883i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.60010e11 | − | 6.23555e11i | −0.689665 | − | 1.19454i | ||||
\(851\) | 5.25535e11 | − | 3.03418e11i | 1.00204 | − | 0.578526i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.19576e11 | + | 3.80317e11i | −0.414752 | + | 0.718372i | −0.995402 | − | 0.0957811i | \(-0.969465\pi\) |
0.580650 | + | 0.814153i | \(0.302798\pi\) | |||||||
\(854\) | − | 4.50074e11i | − | 0.846160i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.78403e11 | 0.891044 | ||||||||
\(857\) | 8.21446e11 | + | 4.74262e11i | 1.52285 | + | 0.879216i | 0.999635 | + | 0.0270123i | \(0.00859934\pi\) |
0.523211 | + | 0.852203i | \(0.324734\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.63139e11 | − | 4.55769e11i | −0.483294 | − | 0.837091i | 0.516521 | − | 0.856274i | \(-0.327227\pi\) |
−0.999816 | + | 0.0191836i | \(0.993893\pi\) | |||||||
\(860\) | 1.49360e10 | − | 8.62328e9i | 0.0273048 | − | 0.0157645i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.41804e10 | + | 5.92022e10i | −0.0619082 | + | 0.107228i | ||||
\(863\) | − | 1.08602e11i | − | 0.195792i | −0.995197 | − | 0.0978961i | \(-0.968789\pi\) | ||
0.995197 | − | 0.0978961i | \(-0.0312113\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.06042e10 | 0.108253 | ||||||||
\(866\) | 7.95773e11 | + | 4.59440e11i | 1.41487 | + | 0.816877i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.54970e10 | − | 6.14826e10i | −0.0625335 | − | 0.108311i | ||||
\(869\) | −1.12775e12 | + | 6.51109e11i | −1.97758 | + | 1.14176i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.27443e11 | + | 3.93943e11i | −0.395185 | + | 0.684480i | ||||
\(872\) | 3.44025e11i | 0.595010i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.25781e12 | −2.15561 | ||||||||
\(875\) | −6.73659e10 | − | 3.88937e10i | −0.114923 | − | 0.0663509i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.18494e11 | + | 8.98059e11i | 0.876487 | + | 1.51812i | 0.855170 | + | 0.518348i | \(0.173453\pi\) |
0.0213175 | + | 0.999773i | \(0.493214\pi\) | |||||||
\(878\) | −1.12441e12 | + | 6.49176e11i | −1.89210 | + | 1.09241i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.04975e10 | − | 7.01437e10i | 0.0675301 | − | 0.116965i | ||||
\(881\) | − | 2.08222e11i | − | 0.345640i | −0.984953 | − | 0.172820i | \(-0.944712\pi\) | ||
0.984953 | − | 0.172820i | \(-0.0552878\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.43243e11 | −1.38711 | −0.693554 | − | 0.720405i | \(-0.743956\pi\) | ||||
−0.693554 | + | 0.720405i | \(0.743956\pi\) | |||||||
\(884\) | −2.91794e11 | − | 1.68467e11i | −0.477823 | − | 0.275871i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.78057e11 | + | 6.54813e11i | 0.613511 | + | 1.06263i | ||||
\(887\) | 8.92264e11 | − | 5.15149e11i | 1.44145 | − | 0.832221i | 0.443502 | − | 0.896274i | \(-0.353736\pi\) |
0.997946 | + | 0.0640530i | \(0.0204027\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.40091e11 | − | 4.15849e11i | 0.384386 | − | 0.665777i | ||||
\(890\) | 4.86478e9i | 0.00775359i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.42789e11 | 0.225547 | ||||||||
\(893\) | 3.50388e11 | + | 2.02297e11i | 0.550990 | + | 0.318114i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.02865e9 | + | 6.97782e9i | 0.00627866 | + | 0.0108750i | ||||
\(896\) | −4.93902e11 | + | 2.85154e11i | −0.766317 | + | 0.442433i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.83480e11 | + | 6.64206e11i | −0.589708 | + | 1.02140i | ||||
\(899\) | − | 4.02539e10i | − | 0.0616267i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.00959e12 | 1.53195 | ||||||||
\(902\) | −4.05196e11 | − | 2.33940e11i | −0.612123 | − | 0.353409i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.50117e10 | − | 1.29924e11i | −0.112319 | − | 0.194543i | ||||
\(905\) | −1.82134e9 | + | 1.05155e9i | −0.00271517 | + | 0.00156760i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.65733e11 | − | 2.87057e11i | 0.244894 | − | 0.424170i | −0.717208 | − | 0.696860i | \(-0.754580\pi\) |
0.962102 | + | 0.272690i | \(0.0879134\pi\) | |||||||
\(908\) | 2.25406e11i | 0.331605i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.17904e10 | −0.0901064 | ||||||||
\(911\) | −7.58390e11 | − | 4.37857e11i | −1.10108 | − | 0.635709i | −0.164576 | − | 0.986364i | \(-0.552626\pi\) |
−0.936505 | + | 0.350655i | \(0.885959\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.90557e11 | + | 5.03260e11i | 0.418166 | + | 0.724285i | ||||
\(914\) | −7.44468e11 | + | 4.29819e11i | −1.06675 | + | 0.615887i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.01268e11 | + | 3.48606e11i | −0.285886 | + | 0.495169i | ||||
\(917\) | − | 1.85268e11i | − | 0.262013i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.62524e11 | −1.20923 | −0.604615 | − | 0.796518i | \(-0.706673\pi\) | ||||
−0.604615 | + | 0.796518i | \(0.706673\pi\) | |||||||
\(920\) | 4.23388e10 | + | 2.44443e10i | 0.0591000 | + | 0.0341214i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.47801e10 | + | 7.75614e10i | 0.0619671 | + | 0.107330i | ||||
\(923\) | 4.86142e11 | − | 2.80674e11i | 0.669817 | − | 0.386719i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.71954e11 | + | 6.44243e11i | −0.508069 | + | 0.880000i | ||||
\(926\) | − | 6.63251e11i | − | 0.902056i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.11623e10 | 0.122920 | ||||||||
\(929\) | 8.37182e10 | + | 4.83347e10i | 0.112398 | + | 0.0648928i | 0.555145 | − | 0.831754i | \(-0.312663\pi\) |
−0.442747 | + | 0.896646i | \(0.645996\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.47790e11 | + | 4.29186e11i | 0.329827 | + | 0.571276i | ||||
\(932\) | −7.10160e10 | + | 4.10011e10i | −0.0941223 | + | 0.0543415i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.82332e11 | − | 1.52824e12i | 1.15943 | − | 2.00819i | ||||
\(935\) | − | 9.70271e10i | − | 0.126954i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.92329e11 | 1.28735 | 0.643676 | − | 0.765298i | \(-0.277409\pi\) | ||||
0.643676 | + | 0.765298i | \(0.277409\pi\) | |||||||
\(938\) | −4.25260e11 | − | 2.45524e11i | −0.549342 | − | 0.317163i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.58481e9 | + | 9.67317e9i | 0.00715314 | + | 0.0123896i | ||||
\(941\) | −1.17412e12 | + | 6.77881e11i | −1.49746 | + | 0.864560i | −0.999996 | − | 0.00292364i | \(-0.999069\pi\) |
−0.497466 | + | 0.867484i | \(0.665736\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.12072e11 | − | 3.67319e11i | 0.268186 | − | 0.464512i | ||||
\(944\) | − | 1.03798e12i | − | 1.30708i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.04300e12 | −1.30233 | ||||||||
\(947\) | −4.88052e11 | − | 2.81777e11i | −0.606828 | − | 0.350352i | 0.164895 | − | 0.986311i | \(-0.447272\pi\) |
−0.771723 | + | 0.635959i | \(0.780605\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.77240e11 | − | 6.53398e11i | −0.465106 | − | 0.805588i | ||||
\(950\) | 1.33535e12 | − | 7.70964e11i | 1.63946 | − | 0.946541i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.56040e11 | + | 4.43475e11i | −0.311717 | + | 0.539910i | ||||
\(953\) | 1.39576e12i | 1.69216i | 0.533059 | + | 0.846078i | \(0.321042\pi\) | ||||
−0.533059 | + | 0.846078i | \(0.678958\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.45377e10 | −0.101633 | ||||||||
\(956\) | 4.72985e11 | + | 2.73078e11i | 0.566260 | + | 0.326931i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.10319e11 | + | 5.37488e11i | 0.368422 | + | 0.638126i | ||||
\(959\) | 1.02730e12 | − | 5.93110e11i | 1.21457 | − | 0.701230i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.60737e11 | − | 6.24815e11i | 0.422958 | − | 0.732585i | ||||
\(962\) | 1.18633e12i | 1.38518i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.24529e11 | 0.375790 | ||||||||
\(965\) | 1.01093e11 | + | 5.83660e10i | 0.116577 | + | 0.0673055i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.45600e10 | + | 4.25391e10i | 0.0280881 | + | 0.0486500i | 0.879728 | − | 0.475478i | \(-0.157725\pi\) |
−0.851640 | + | 0.524128i | \(0.824391\pi\) | |||||||
\(968\) | −2.99893e11 | + | 1.73143e11i | −0.341558 | + | 0.197199i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.57078e10 | + | 6.18477e10i | −0.0403344 | + | 0.0698613i | ||||
\(971\) | 7.05365e11i | 0.793482i | 0.917931 | + | 0.396741i | \(0.129859\pi\) | ||||
−0.917931 | + | 0.396741i | \(0.870141\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.41504e10 | −0.105044 | ||||||||
\(974\) | −1.31605e10 | − | 7.59822e9i | −0.0146230 | − | 0.00844260i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.22763e11 | − | 9.05452e11i | −0.576110 | − | 0.997852i | ||||
\(977\) | 1.00820e12 | − | 5.82086e11i | 1.10655 | − | 0.638864i | 0.168613 | − | 0.985682i | \(-0.446071\pi\) |
0.937933 | + | 0.346818i | \(0.112738\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.31647e10 | − | 7.47635e10i | 0.0469892 | − | 0.0813877i | ||||
\(980\) | 1.36815e10i | 0.0148330i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.49979e11 | −1.02157 | ||||||||
\(983\) | 2.64796e11 | + | 1.52880e11i | 0.283594 | + | 0.163733i | 0.635049 | − | 0.772471i | \(-0.280980\pi\) |
−0.351455 | + | 0.936205i | \(0.614313\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.52771e10 | − | 7.84222e10i | −0.0480987 | − | 0.0833094i | ||||
\(986\) | 1.78601e11 | − | 1.03115e11i | 0.188962 | − | 0.109097i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.60774e11 | − | 6.24878e11i | 0.378623 | − | 0.655794i | ||||
\(989\) | − | 9.45506e11i | − | 0.988278i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.71498e11 | 0.385179 | 0.192589 | − | 0.981279i | \(-0.438311\pi\) | ||||
0.192589 | + | 0.981279i | \(0.438311\pi\) | |||||||
\(992\) | −2.57744e11 | − | 1.48809e11i | −0.266159 | − | 0.153667i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.02986e11 | + | 5.24788e11i | 0.310368 | + | 0.537574i | ||||
\(995\) | 2.10057e10 | − | 1.21277e10i | 0.0214312 | − | 0.0123733i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.09939e11 | + | 8.83241e11i | −0.516105 | + | 0.893920i | 0.483720 | + | 0.875223i | \(0.339285\pi\) |
−0.999825 | + | 0.0186972i | \(0.994048\pi\) | |||||||
\(998\) | − | 8.63812e11i | − | 0.870757i | ||||||
\(999\) | 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 | 27.9.d.a.8.2 | 14 | ||
3.2 | odd | 2 | 9.9.d.a.2.6 | ✓ | 14 | ||
4.3 | odd | 2 | 432.9.q.a.305.5 | 14 | |||
9.2 | odd | 6 | 81.9.b.a.80.4 | 14 | |||
9.4 | even | 3 | 9.9.d.a.5.6 | yes | 14 | ||
9.5 | odd | 6 | inner | 27.9.d.a.17.2 | 14 | ||
9.7 | even | 3 | 81.9.b.a.80.11 | 14 | |||
12.11 | even | 2 | 144.9.q.a.65.1 | 14 | |||
36.23 | even | 6 | 432.9.q.a.17.5 | 14 | |||
36.31 | odd | 6 | 144.9.q.a.113.1 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.9.d.a.2.6 | ✓ | 14 | 3.2 | odd | 2 | ||
9.9.d.a.5.6 | yes | 14 | 9.4 | even | 3 | ||
27.9.d.a.8.2 | 14 | 1.1 | even | 1 | trivial | ||
27.9.d.a.17.2 | 14 | 9.5 | odd | 6 | inner | ||
81.9.b.a.80.4 | 14 | 9.2 | odd | 6 | |||
81.9.b.a.80.11 | 14 | 9.7 | even | 3 | |||
144.9.q.a.65.1 | 14 | 12.11 | even | 2 | |||
144.9.q.a.113.1 | 14 | 36.31 | odd | 6 | |||
432.9.q.a.17.5 | 14 | 36.23 | even | 6 | |||
432.9.q.a.305.5 | 14 | 4.3 | odd | 2 |