Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [81,9,Mod(8,81)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(81, base_ring=CyclotomicField(18))
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("81.8");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.f (of order \(18\), degree \(6\), 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: | \(32.9976674150\) |
Analytic rank: | \(0\) |
Dimension: | \(138\) |
Relative dimension: | \(23\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 8.9 | ||
Character | \(\chi\) | \(=\) | 81.8 |
Dual form | 81.9.f.a.71.9 |
$q$-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 \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −13.3375 | − | 2.35175i | −0.833591 | − | 0.146985i | −0.259466 | − | 0.965752i | \(-0.583547\pi\) |
−0.574125 | + | 0.818768i | \(0.694658\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −68.2042 | − | 24.8243i | −0.266423 | − | 0.0969699i | ||||
\(5\) | 636.805 | + | 758.914i | 1.01889 | + | 1.21426i | 0.976579 | + | 0.215158i | \(0.0690267\pi\) |
0.0423083 | + | 0.999105i | \(0.486529\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2502.00 | + | 910.653i | −1.04207 | + | 0.379281i | −0.805663 | − | 0.592375i | \(-0.798191\pi\) |
−0.236402 | + | 0.971655i | \(0.575968\pi\) | |||||||
\(8\) | 3853.85 | + | 2225.02i | 0.940882 | + | 0.543219i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6708.58 | − | 11619.6i | −0.670858 | − | 1.16196i | ||||
\(11\) | −15349.9 | + | 18293.3i | −1.04842 | + | 1.24946i | −0.0808814 | + | 0.996724i | \(0.525773\pi\) |
−0.967536 | + | 0.252732i | \(0.918671\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4780.28 | + | 27110.3i | 0.167371 | + | 0.949208i | 0.946586 | + | 0.322451i | \(0.104507\pi\) |
−0.779215 | + | 0.626757i | \(0.784382\pi\) | |||||||
\(14\) | 35511.9 | − | 6261.71i | 0.924405 | − | 0.162997i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −31934.2 | − | 26796.0i | −0.487277 | − | 0.408874i | ||||
\(17\) | 105956. | − | 61173.5i | 1.26861 | − | 0.732432i | 0.293885 | − | 0.955841i | \(-0.405052\pi\) |
0.974725 | + | 0.223409i | \(0.0717185\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −547.495 | + | 948.289i | −0.00420113 | + | 0.00727656i | −0.868118 | − | 0.496357i | \(-0.834671\pi\) |
0.863917 | + | 0.503634i | \(0.168004\pi\) | |||||||
\(20\) | −24593.2 | − | 67569.4i | −0.153708 | − | 0.422309i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 247750. | − | 207887.i | 1.05760 | − | 0.887434i | ||||
\(23\) | −50471.0 | + | 138668.i | −0.180356 | + | 0.495524i | −0.996619 | − | 0.0821558i | \(-0.973819\pi\) |
0.816264 | + | 0.577680i | \(0.196042\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −102599. | + | 581870.i | −0.262654 | + | 1.48959i | ||||
\(26\) | − | 372825.i | − | 0.815853i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 193253. | 0.314409 | ||||||||
\(29\) | 924074. | + | 162939.i | 1.30652 | + | 0.230374i | 0.783203 | − | 0.621766i | \(-0.213585\pi\) |
0.523313 | + | 0.852140i | \(0.324696\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 131238. | + | 47766.6i | 0.142106 | + | 0.0517223i | 0.412094 | − | 0.911141i | \(-0.364798\pi\) |
−0.269988 | + | 0.962864i | \(0.587020\pi\) | |||||||
\(32\) | −369368. | − | 440196.i | −0.352257 | − | 0.419804i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.55704e6 | + | 566717.i | −1.16516 | + | 0.424083i | ||||
\(35\) | −2.28439e6 | − | 1.31889e6i | −1.52229 | − | 0.878897i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −379045. | − | 656525.i | −0.202248 | − | 0.350303i | 0.747005 | − | 0.664819i | \(-0.231491\pi\) |
−0.949252 | + | 0.314515i | \(0.898158\pi\) | |||||||
\(38\) | 9532.34 | − | 11360.2i | 0.00457157 | − | 0.00544818i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 765550. | + | 4.34165e6i | 0.299043 | + | 1.69596i | ||||
\(41\) | −4.60079e6 | + | 811243.i | −1.62816 | + | 0.287088i | −0.911797 | − | 0.410641i | \(-0.865305\pi\) |
−0.716361 | + | 0.697730i | \(0.754194\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.82392e6 | − | 1.53045e6i | −0.533498 | − | 0.447658i | 0.335810 | − | 0.941930i | \(-0.390990\pi\) |
−0.869307 | + | 0.494272i | \(0.835435\pi\) | |||||||
\(44\) | 1.50104e6 | − | 866629.i | 0.400482 | − | 0.231218i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 999268. | − | 1.73078e6i | 0.223178 | − | 0.386555i | ||||
\(47\) | −425686. | − | 1.16956e6i | −0.0872365 | − | 0.239680i | 0.888401 | − | 0.459068i | \(-0.151816\pi\) |
−0.975638 | + | 0.219387i | \(0.929594\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.01461e6 | − | 851361.i | 0.176001 | − | 0.147683i | ||||
\(50\) | 2.73683e6 | − | 7.51938e6i | 0.437893 | − | 1.20310i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 346960. | − | 1.96771e6i | 0.0474532 | − | 0.269121i | ||||
\(53\) | 6.96711e6i | 0.882977i | 0.897267 | + | 0.441489i | \(0.145549\pi\) | ||||
−0.897267 | + | 0.441489i | \(0.854451\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.36579e7 | −2.58539 | ||||||||
\(56\) | −1.16686e7 | − | 2.05748e6i | −1.18649 | − | 0.209211i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.19416e7 | − | 4.34639e6i | −1.05524 | − | 0.384076i | ||||
\(59\) | −4.48304e6 | − | 5.34268e6i | −0.369968 | − | 0.440911i | 0.548653 | − | 0.836050i | \(-0.315141\pi\) |
−0.918621 | + | 0.395139i | \(0.870696\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.36882e7 | + | 8.62179e6i | −1.71085 | + | 0.622699i | −0.996986 | − | 0.0775852i | \(-0.975279\pi\) |
−0.713865 | + | 0.700284i | \(0.753057\pi\) | |||||||
\(62\) | −1.63804e6 | − | 945725.i | −0.110856 | − | 0.0640026i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 9.22715e6 | + | 1.59819e7i | 0.549981 | + | 0.952595i | ||||
\(65\) | −1.75303e7 | + | 2.08918e7i | −0.982056 | + | 1.17037i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.60777e6 | − | 2.04607e7i | −0.179036 | − | 1.01536i | −0.933382 | − | 0.358885i | \(-0.883157\pi\) |
0.754346 | − | 0.656477i | \(-0.227954\pi\) | |||||||
\(68\) | −8.74520e6 | + | 1.54201e6i | −0.409010 | + | 0.0721195i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.73663e7 | + | 2.29630e7i | 1.13979 | + | 0.956394i | ||||
\(71\) | 1.06620e7 | − | 6.15572e6i | 0.419571 | − | 0.242240i | −0.275323 | − | 0.961352i | \(-0.588785\pi\) |
0.694894 | + | 0.719112i | \(0.255451\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.50114e6 | − | 6.06416e6i | 0.123287 | − | 0.213540i | −0.797775 | − | 0.602956i | \(-0.793990\pi\) |
0.921062 | + | 0.389415i | \(0.127323\pi\) | |||||||
\(74\) | 3.51151e6 | + | 9.64780e6i | 0.117103 | + | 0.321737i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 60882.1 | − | 51086.1i | 0.00182488 | − | 0.00153126i | ||||
\(77\) | 2.17466e7 | − | 5.97482e7i | 0.618625 | − | 1.69966i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.79249e6 | − | 1.58370e7i | 0.0716941 | − | 0.406598i | −0.927748 | − | 0.373207i | \(-0.878258\pi\) |
0.999442 | − | 0.0333910i | \(-0.0106306\pi\) | |||||||
\(80\) | − | 4.12991e7i | − | 1.00828i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.32706e7 | 1.39942 | ||||||||
\(83\) | −4.48356e6 | − | 790573.i | −0.0944737 | − | 0.0166583i | 0.126211 | − | 0.992003i | \(-0.459718\pi\) |
−0.220685 | + | 0.975345i | \(0.570829\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.13898e8 | + | 4.14556e7i | 2.18194 | + | 0.794159i | ||||
\(86\) | 2.07272e7 | + | 2.47018e7i | 0.378920 | + | 0.451579i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.98592e7 | + | 3.63458e7i | −1.66517 | + | 0.606071i | ||||
\(89\) | 3.86601e7 | + | 2.23204e7i | 0.616174 | + | 0.355748i | 0.775378 | − | 0.631497i | \(-0.217559\pi\) |
−0.159204 | + | 0.987246i | \(0.550893\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.66484e7 | − | 6.34768e7i | −0.534428 | − | 0.925656i | ||||
\(92\) | 6.88467e6 | − | 8.20483e6i | 0.0961018 | − | 0.114530i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.92705e6 | + | 1.66001e7i | 0.0374903 | + | 0.212618i | ||||
\(95\) | −1.06832e6 | + | 188373.i | −0.0131161 | + | 0.00231273i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.19186e7 | + | 1.00009e7i | 0.134629 | + | 0.112967i | 0.707616 | − | 0.706598i | \(-0.249771\pi\) |
−0.572987 | + | 0.819565i | \(0.694215\pi\) | |||||||
\(98\) | −1.55345e7 | + | 8.96887e6i | −0.168420 | + | 0.0972374i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.14422e7 | − | 3.71390e7i | 0.214422 | − | 0.371390i | ||||
\(101\) | 5.97338e7 | + | 1.64117e8i | 0.574030 | + | 1.57714i | 0.798076 | + | 0.602557i | \(0.205851\pi\) |
−0.224046 | + | 0.974579i | \(0.571927\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.03092e7 | − | 5.06054e7i | 0.535839 | − | 0.449623i | −0.334273 | − | 0.942476i | \(-0.608491\pi\) |
0.870112 | + | 0.492854i | \(0.164046\pi\) | |||||||
\(104\) | −4.18986e7 | + | 1.15116e8i | −0.358151 | + | 0.984012i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.63849e7 | − | 9.29236e7i | 0.129784 | − | 0.736042i | ||||
\(107\) | − | 6.15134e7i | − | 0.469283i | −0.972082 | − | 0.234641i | \(-0.924608\pi\) | ||
0.972082 | − | 0.234641i | \(-0.0753916\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.02005e7 | −0.143105 | −0.0715526 | − | 0.997437i | \(-0.522795\pi\) | ||||
−0.0715526 | + | 0.997437i | \(0.522795\pi\) | |||||||
\(110\) | 3.15536e8 | + | 5.56376e7i | 2.15516 | + | 0.380012i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.04301e8 | + | 3.79625e7i | 0.662852 | + | 0.241258i | ||||
\(113\) | −7.22019e7 | − | 8.60469e7i | −0.442828 | − | 0.527742i | 0.497750 | − | 0.867321i | \(-0.334160\pi\) |
−0.940578 | + | 0.339579i | \(0.889715\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.37377e8 | + | 5.00012e7i | −0.785459 | + | 0.285884i | ||||
\(116\) | −5.89809e7 | − | 3.40526e7i | −0.325746 | − | 0.188070i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.72277e7 | + | 8.18007e7i | 0.243595 | + | 0.421919i | ||||
\(119\) | −2.09393e8 | + | 2.49545e8i | −1.04418 | + | 1.24440i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.18021e7 | − | 3.50497e8i | −0.288311 | − | 1.63510i | ||||
\(122\) | 3.36216e8 | − | 5.92840e7i | 1.51768 | − | 0.267607i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.76519e6 | − | 6.51577e6i | −0.0328447 | − | 0.0275600i | ||||
\(125\) | −1.71783e8 | + | 9.91787e7i | −0.703622 | + | 0.406236i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.22668e8 | + | 2.12467e8i | −0.471536 | + | 0.816725i | −0.999470 | − | 0.0325610i | \(-0.989634\pi\) |
0.527934 | + | 0.849286i | \(0.322967\pi\) | |||||||
\(128\) | −3.51679e7 | − | 9.66229e7i | −0.131011 | − | 0.359948i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.82942e8 | − | 2.37417e8i | 0.990660 | − | 0.831262i | ||||
\(131\) | 1.43812e8 | − | 3.95121e8i | 0.488327 | − | 1.34167i | −0.413867 | − | 0.910337i | \(-0.635822\pi\) |
0.902194 | − | 0.431330i | \(-0.141955\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 506269. | − | 2.87120e6i | 0.00161799 | − | 0.00917606i | ||||
\(134\) | 2.81378e8i | 0.872713i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.44450e8 | 1.59148 | ||||||||
\(137\) | −3.65675e8 | − | 6.44783e7i | −1.03804 | − | 0.183034i | −0.371444 | − | 0.928456i | \(-0.621137\pi\) |
−0.666593 | + | 0.745422i | \(0.732248\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.96654e8 | − | 1.44370e8i | −1.06256 | − | 0.386739i | −0.249169 | − | 0.968460i | \(-0.580158\pi\) |
−0.813389 | + | 0.581721i | \(0.802380\pi\) | |||||||
\(140\) | 1.23064e8 | + | 1.46663e8i | 0.320347 | + | 0.381775i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.56681e8 | + | 5.70272e7i | −0.385357 | + | 0.140258i | ||||
\(143\) | −5.69314e8 | − | 3.28693e8i | −1.36147 | − | 0.786044i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.64798e8 | + | 8.05053e8i | 1.05146 | + | 1.82118i | ||||
\(146\) | −6.09578e7 | + | 7.26467e7i | −0.134158 | + | 0.159884i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.55468e6 | + | 5.41873e7i | 0.0199145 | + | 0.112941i | ||||
\(149\) | 4.73599e8 | − | 8.35083e7i | 0.960873 | − | 0.169428i | 0.328854 | − | 0.944381i | \(-0.393338\pi\) |
0.632019 | + | 0.774953i | \(0.282227\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.88229e8 | − | 3.25763e8i | −0.746758 | − | 0.626605i | 0.187885 | − | 0.982191i | \(-0.439837\pi\) |
−0.934643 | + | 0.355586i | \(0.884281\pi\) | |||||||
\(152\) | −4.21993e6 | + | 2.43638e6i | −0.00790553 | + | 0.00456426i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.30557e8 | + | 7.45746e8i | −0.765504 | + | 1.32589i | ||||
\(155\) | 4.73220e7 | + | 1.30016e8i | 0.0819854 | + | 0.225253i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.53896e8 | + | 2.96954e8i | −0.582475 | + | 0.488755i | −0.885759 | − | 0.464146i | \(-0.846361\pi\) |
0.303284 | + | 0.952900i | \(0.401917\pi\) | |||||||
\(158\) | −7.44895e7 | + | 2.04658e8i | −0.119527 | + | 0.328398i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.88555e7 | − | 5.60638e8i | 0.150842 | − | 0.855465i | ||||
\(161\) | − | 3.92908e8i | − | 0.584774i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.56114e8 | −0.646134 | −0.323067 | − | 0.946376i | \(-0.604714\pi\) | ||||
−0.323067 | + | 0.946376i | \(0.604714\pi\) | |||||||
\(164\) | 3.33932e8 | + | 5.88811e7i | 0.461617 | + | 0.0813956i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.79401e7 | + | 2.10885e7i | 0.0763040 | + | 0.0277724i | ||||
\(167\) | −1.61471e8 | − | 1.92434e8i | −0.207601 | − | 0.247409i | 0.652190 | − | 0.758056i | \(-0.273850\pi\) |
−0.859791 | + | 0.510647i | \(0.829406\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.44170e7 | − | 1.98062e7i | 0.0667095 | − | 0.0242803i | ||||
\(170\) | −1.42162e9 | − | 8.20774e8i | −1.70211 | − | 0.982715i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.64068e7 | + | 1.49661e8i | 0.0987265 | + | 0.170999i | ||||
\(173\) | 7.42345e8 | − | 8.84693e8i | 0.828746 | − | 0.987661i | −0.171251 | − | 0.985227i | \(-0.554781\pi\) |
0.999997 | − | 0.00243395i | \(-0.000774751\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.73178e8 | − | 1.54927e9i | −0.291269 | − | 1.65187i | ||||
\(176\) | 9.80372e8 | − | 1.72866e8i | 1.02174 | − | 0.180160i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.63136e8 | − | 3.88617e8i | −0.461348 | − | 0.387117i | ||||
\(179\) | −6.53835e8 | + | 3.77492e8i | −0.636878 | + | 0.367702i | −0.783411 | − | 0.621504i | \(-0.786522\pi\) |
0.146533 | + | 0.989206i | \(0.453189\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.14593e8 | − | 1.98480e8i | 0.106768 | − | 0.184928i | −0.807691 | − | 0.589606i | \(-0.799283\pi\) |
0.914459 | + | 0.404678i | \(0.132616\pi\) | |||||||
\(182\) | 3.39514e8 | + | 9.32808e8i | 0.309437 | + | 0.850171i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.03047e8 | + | 4.22107e8i | −0.438872 | + | 0.368257i | ||||
\(185\) | 2.56869e8 | − | 7.05741e8i | 0.219293 | − | 0.602502i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.07342e8 | + | 2.87728e9i | −0.414891 | + | 2.35297i | ||||
\(188\) | 9.03366e7i | 0.0723156i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.46916e7 | 0.0112734 | ||||||||
\(191\) | 9.71028e7 | + | 1.71218e7i | 0.0729623 | + | 0.0128652i | 0.210010 | − | 0.977699i | \(-0.432650\pi\) |
−0.137048 | + | 0.990564i | \(0.543761\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.38182e9 | + | 8.66911e8i | 1.71664 | + | 0.624806i | 0.997540 | − | 0.0700985i | \(-0.0223314\pi\) |
0.719102 | + | 0.694905i | \(0.244554\pi\) | |||||||
\(194\) | −1.35444e8 | − | 1.61416e8i | −0.0956211 | − | 0.113957i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.03352e7 | + | 3.28793e7i | −0.0612115 | + | 0.0222792i | ||||
\(197\) | −3.70754e8 | − | 2.14055e8i | −0.246162 | − | 0.142122i | 0.371843 | − | 0.928295i | \(-0.378726\pi\) |
−0.618006 | + | 0.786174i | \(0.712059\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.87197e8 | + | 8.43850e8i | 0.310665 | + | 0.538088i | 0.978507 | − | 0.206216i | \(-0.0661149\pi\) |
−0.667842 | + | 0.744303i | \(0.732782\pi\) | |||||||
\(200\) | −1.69008e9 | + | 2.01416e9i | −1.05630 | + | 1.25885i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.10734e8 | − | 2.32939e9i | −0.246692 | − | 1.39906i | ||||
\(203\) | −2.46041e9 | + | 4.33837e8i | −1.44885 | + | 0.255472i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.54547e9 | − | 2.97500e9i | −2.00751 | − | 1.68450i | ||||
\(206\) | −9.23383e8 | + | 5.33115e8i | −0.512759 | + | 0.296041i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.73793e8 | − | 9.93838e8i | 0.306550 | − | 0.530961i | ||||
\(209\) | −8.94333e6 | − | 2.45716e7i | −0.00468721 | − | 0.0128780i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.10978e9 | + | 9.31219e8i | −0.559897 | + | 0.469809i | −0.878276 | − | 0.478154i | \(-0.841306\pi\) |
0.318379 | + | 0.947964i | \(0.396862\pi\) | |||||||
\(212\) | 1.72954e8 | − | 4.75187e8i | 0.0856222 | − | 0.235245i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.44664e8 | + | 8.20432e8i | −0.0689773 | + | 0.391190i | ||||
\(215\) | − | 2.35880e9i | − | 1.10392i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.71855e8 | −0.167701 | ||||||||
\(218\) | 2.69423e8 | + | 4.75066e7i | 0.119291 | + | 0.0210343i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.61357e9 | + | 5.87291e8i | 0.688806 | + | 0.250705i | ||||
\(221\) | 2.16493e9 | + | 2.58006e9i | 0.907559 | + | 1.08159i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.28127e8 | − | 3.37811e8i | 0.375308 | − | 0.136601i | −0.147477 | − | 0.989065i | \(-0.547115\pi\) |
0.522785 | + | 0.852464i | \(0.324893\pi\) | |||||||
\(224\) | 1.32502e9 | + | 7.65003e8i | 0.526298 | + | 0.303858i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.60629e8 | + | 1.31745e9i | 0.291568 | + | 0.505010i | ||||
\(227\) | −4.10560e8 | + | 4.89286e8i | −0.154623 | + | 0.184272i | −0.837795 | − | 0.545985i | \(-0.816155\pi\) |
0.683172 | + | 0.730257i | \(0.260600\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.06279e8 | + | 6.02738e8i | 0.0386460 | + | 0.219173i | 0.998015 | − | 0.0629834i | \(-0.0200615\pi\) |
−0.959369 | + | 0.282156i | \(0.908950\pi\) | |||||||
\(230\) | 1.94985e9 | − | 3.43812e8i | 0.696772 | − | 0.122860i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.19870e9 | + | 2.68403e9i | 1.10413 | + | 0.926479i | ||||
\(233\) | 3.04859e9 | − | 1.76010e9i | 1.03437 | − | 0.597192i | 0.116134 | − | 0.993234i | \(-0.462950\pi\) |
0.918233 | + | 0.396041i | \(0.129616\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.16520e8 | − | 1.06784e9i | 0.202151 | − | 0.350135i | ||||
\(236\) | 1.73134e8 | + | 4.75681e8i | 0.0558128 | + | 0.153344i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.37963e9 | − | 2.83585e9i | 1.05332 | − | 0.883844i | ||||
\(239\) | 1.07538e9 | − | 2.95458e9i | 0.329587 | − | 0.905533i | −0.658629 | − | 0.752468i | \(-0.728863\pi\) |
0.988216 | − | 0.153065i | \(-0.0489144\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.25199e8 | − | 3.54568e9i | 0.185332 | − | 1.05107i | −0.740196 | − | 0.672391i | \(-0.765267\pi\) |
0.925528 | − | 0.378679i | \(-0.123622\pi\) | |||||||
\(242\) | 4.82009e9i | 1.40538i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.82966e9 | 0.516192 | ||||||||
\(245\) | 1.29222e9 | + | 2.27853e8i | 0.358651 | + | 0.0632398i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.83256e7 | − | 1.03097e7i | −0.00761012 | − | 0.00276986i | ||||
\(248\) | 3.99489e8 | + | 4.76093e8i | 0.105608 | + | 0.125859i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.52439e9 | − | 9.18802e8i | 0.646243 | − | 0.235213i | ||||
\(251\) | 1.40741e9 | + | 8.12567e8i | 0.354589 | + | 0.204722i | 0.666705 | − | 0.745322i | \(-0.267704\pi\) |
−0.312116 | + | 0.950044i | \(0.601038\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.76197e9 | − | 3.05182e9i | −0.430047 | − | 0.744863i | ||||
\(254\) | 2.13574e9 | − | 2.54528e9i | 0.513114 | − | 0.611506i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.78550e8 | − | 3.28112e9i | −0.134704 | − | 0.763945i | ||||
\(257\) | −5.64879e8 | + | 9.96034e7i | −0.129486 | + | 0.0228319i | −0.238016 | − | 0.971261i | \(-0.576497\pi\) |
0.108530 | + | 0.994093i | \(0.465386\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.54624e9 | + | 1.29745e9i | 0.343619 | + | 0.288330i | ||||
\(260\) | 1.71427e9 | − | 9.89732e8i | 0.375133 | − | 0.216583i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.84732e9 | + | 4.93170e9i | −0.604269 | + | 1.04663i | ||||
\(263\) | 2.40422e9 | + | 6.60554e9i | 0.502517 | + | 1.38065i | 0.888809 | + | 0.458278i | \(0.151534\pi\) |
−0.386292 | + | 0.922377i | \(0.626244\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.28744e9 | + | 4.43669e9i | −1.07217 | + | 0.899654i | ||||
\(266\) | −1.35047e7 | + | 3.71038e7i | −0.00269748 | + | 0.00741126i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.61857e8 | + | 1.48507e9i | −0.0507604 | + | 0.287877i | ||||
\(269\) | 8.50405e9i | 1.62411i | 0.583578 | + | 0.812057i | \(0.301652\pi\) | ||||
−0.583578 | + | 0.812057i | \(0.698348\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.66496e9 | 0.679504 | 0.339752 | − | 0.940515i | \(-0.389657\pi\) | ||||
0.339752 | + | 0.940515i | \(0.389657\pi\) | |||||||
\(272\) | −5.02280e9 | − | 8.85656e8i | −0.917636 | − | 0.161804i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.72554e9 | + | 1.71995e9i | 0.838395 | + | 0.305151i | ||||
\(275\) | −9.06942e9 | − | 1.08085e10i | −1.58580 | − | 1.88988i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.34026e9 | + | 2.67163e9i | −1.24679 | + | 0.453793i | −0.879315 | − | 0.476241i | \(-0.841999\pi\) |
−0.367472 | + | 0.930035i | \(0.619777\pi\) | |||||||
\(278\) | 4.95083e9 | + | 2.85836e9i | 0.828894 | + | 0.478562i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.86914e9 | − | 1.01657e10i | −0.954866 | − | 1.65388i | ||||
\(281\) | 1.00634e9 | − | 1.19931e9i | 0.161405 | − | 0.192356i | −0.679280 | − | 0.733879i | \(-0.737708\pi\) |
0.840686 | + | 0.541524i | \(0.182152\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.38681e9 | + | 7.86497e9i | 0.216207 | + | 1.22617i | 0.878799 | + | 0.477192i | \(0.158345\pi\) |
−0.662592 | + | 0.748980i | \(0.730544\pi\) | |||||||
\(284\) | −8.80006e8 | + | 1.55169e8i | −0.135273 | + | 0.0238523i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.82019e9 | + | 5.72282e9i | 1.01937 | + | 0.855354i | ||||
\(287\) | 1.07724e10 | − | 6.21945e9i | 1.58776 | − | 0.916693i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.99650e9 | − | 6.92215e9i | 0.572913 | − | 0.992315i | ||||
\(290\) | −4.30593e9 | − | 1.18305e10i | −0.608801 | − | 1.67267i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.89331e8 | + | 3.26688e8i | −0.0535535 | + | 0.0449367i | ||||
\(293\) | −3.64627e9 | + | 1.00180e10i | −0.494741 | + | 1.35929i | 0.401555 | + | 0.915835i | \(0.368470\pi\) |
−0.896296 | + | 0.443456i | \(0.853752\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.19981e9 | − | 6.80448e9i | 0.158426 | − | 0.898477i | ||||
\(296\) | − | 3.37354e9i | − | 0.439459i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.51300e9 | −0.825878 | ||||||||
\(299\) | −4.00060e9 | − | 7.05414e8i | −0.500542 | − | 0.0882590i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.95716e9 | + | 2.16823e9i | 0.725727 | + | 0.264143i | ||||
\(302\) | 4.41187e9 | + | 5.25787e9i | 0.530390 | + | 0.632094i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.28941e7 | − | 1.56122e7i | 0.00502231 | − | 0.00182797i | ||||
\(305\) | −2.16279e10 | − | 1.24869e10i | −2.49928 | − | 1.44296i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.42521e9 | − | 2.46854e9i | −0.160445 | − | 0.277899i | 0.774583 | − | 0.632472i | \(-0.217960\pi\) |
−0.935028 | + | 0.354573i | \(0.884626\pi\) | |||||||
\(308\) | −2.96641e9 | + | 3.53523e9i | −0.329632 | + | 0.392840i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.25390e8 | − | 1.84538e9i | −0.0352336 | − | 0.199820i | ||||
\(311\) | −1.12462e10 | + | 1.98300e9i | −1.20216 | + | 0.211974i | −0.738633 | − | 0.674108i | \(-0.764528\pi\) |
−0.463529 | + | 0.886082i | \(0.653417\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.45161e9 | + | 2.89625e9i | 0.359621 | + | 0.301758i | 0.804639 | − | 0.593764i | \(-0.202359\pi\) |
−0.445019 | + | 0.895521i | \(0.646803\pi\) | |||||||
\(314\) | 5.41844e9 | − | 3.12834e9i | 0.557386 | − | 0.321807i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.83602e8 | + | 1.01083e9i | −0.0585287 | + | 0.101375i | ||||
\(317\) | −1.83180e9 | − | 5.03284e9i | −0.181402 | − | 0.498398i | 0.815347 | − | 0.578973i | \(-0.196546\pi\) |
−0.996749 | + | 0.0805754i | \(0.974324\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.71651e10 | + | 1.44032e10i | −1.65762 | + | 1.39091i | ||||
\(320\) | −6.25299e9 | + | 1.71800e10i | −0.596332 | + | 1.63841i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.24024e8 | + | 5.24040e9i | −0.0859527 | + | 0.487462i | ||||
\(323\) | 1.33969e8i | 0.0123082i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.62651e10 | −1.45789 | ||||||||
\(326\) | 6.08340e9 | + | 1.07267e9i | 0.538612 | + | 0.0949718i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.95358e10 | − | 7.11045e9i | −1.68786 | − | 0.614330i | ||||
\(329\) | 2.13013e9 | + | 2.53859e9i | 0.181812 | + | 0.216675i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.90947e9 | + | 1.42293e9i | −0.325691 | + | 0.118542i | −0.499691 | − | 0.866204i | \(-0.666553\pi\) |
0.174000 | + | 0.984746i | \(0.444331\pi\) | |||||||
\(332\) | 2.86173e8 | + | 1.65222e8i | 0.0235546 | + | 0.0135992i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.70106e9 | + | 2.94632e9i | 0.136689 | + | 0.236752i | ||||
\(335\) | 1.32305e10 | − | 1.57675e10i | 1.05050 | − | 1.25194i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.67135e9 | − | 9.47871e9i | −0.129583 | − | 0.734902i | −0.978480 | − | 0.206343i | \(-0.933844\pi\) |
0.848897 | − | 0.528559i | \(-0.177267\pi\) | |||||||
\(338\) | −7.72364e8 | + | 1.36189e8i | −0.0591773 | + | 0.0104346i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.73924e9 | − | 5.65490e9i | −0.504307 | − | 0.423164i | ||||
\(341\) | −2.88829e9 | + | 1.66756e9i | −0.213611 | + | 0.123328i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.91133e9 | − | 1.02387e10i | 0.427080 | − | 0.739724i | ||||
\(344\) | −3.62384e9 | − | 9.95641e9i | −0.258782 | − | 0.710999i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.19816e10 | + | 1.00537e10i | −0.836007 | + | 0.701493i | ||||
\(347\) | 6.87957e7 | − | 1.89015e8i | 0.00474508 | − | 0.0130370i | −0.937297 | − | 0.348530i | \(-0.886681\pi\) |
0.942043 | + | 0.335493i | \(0.108903\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.82255e9 | − | 1.60075e10i | 0.190257 | − | 1.07900i | −0.728756 | − | 0.684773i | \(-0.759901\pi\) |
0.919013 | − | 0.394227i | \(-0.128988\pi\) | |||||||
\(350\) | 2.13058e10i | 1.41979i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.37224e10 | 0.893838 | ||||||||
\(353\) | −5.10574e9 | − | 9.00279e8i | −0.328821 | − | 0.0579800i | 0.00680064 | − | 0.999977i | \(-0.497835\pi\) |
−0.335622 | + | 0.941997i | \(0.608946\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.14613e10 | + | 4.17157e9i | 0.721639 | + | 0.262655i | ||||
\(356\) | −2.08270e9 | − | 2.48206e9i | −0.129666 | − | 0.154530i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.60827e9 | − | 3.49712e9i | 0.584942 | − | 0.212902i | ||||
\(359\) | 2.29627e10 | + | 1.32575e10i | 1.38244 | + | 0.798151i | 0.992448 | − | 0.122668i | \(-0.0391449\pi\) |
0.389991 | + | 0.920819i | \(0.372478\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.49118e9 | + | 1.47072e10i | 0.499965 | + | 0.865964i | ||||
\(362\) | −1.99515e9 | + | 2.37773e9i | −0.116183 | + | 0.138461i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.23805e8 | + | 5.23916e9i | 0.0526229 | + | 0.298439i | ||||
\(365\) | 6.83172e9 | − | 1.20462e9i | 0.384910 | − | 0.0678700i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.18128e10 | + | 1.83031e10i | 1.20239 | + | 1.00893i | 0.999558 | + | 0.0297143i | \(0.00945975\pi\) |
0.202834 | + | 0.979213i | \(0.434985\pi\) | |||||||
\(368\) | 5.32749e9 | − | 3.07583e9i | 0.290490 | − | 0.167714i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.08570e9 | + | 8.80870e9i | −0.271359 | + | 0.470007i | ||||
\(371\) | −6.34462e9 | − | 1.74317e10i | −0.334896 | − | 0.920120i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.43295e9 | − | 2.04149e9i | 0.125689 | − | 0.105466i | −0.577776 | − | 0.816195i | \(-0.696079\pi\) |
0.703465 | + | 0.710729i | \(0.251635\pi\) | |||||||
\(374\) | 1.35333e10 | − | 3.71825e10i | 0.691700 | − | 1.90043i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.61774e8 | − | 5.45449e9i | 0.0481196 | − | 0.272900i | ||||
\(377\) | 2.58308e10i | 1.27871i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.63613e10 | −1.27764 | −0.638822 | − | 0.769354i | \(-0.720578\pi\) | ||||
−0.638822 | + | 0.769354i | \(0.720578\pi\) | |||||||
\(380\) | 7.75400e7 | + | 1.36724e7i | 0.00371870 | + | 0.000655707i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.25484e9 | − | 4.56724e8i | −0.0589297 | − | 0.0214487i | ||||
\(383\) | −5.71089e9 | − | 6.80598e9i | −0.265405 | − | 0.316297i | 0.616839 | − | 0.787089i | \(-0.288413\pi\) |
−0.882244 | + | 0.470792i | \(0.843968\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.91920e10 | − | 2.15441e10i | 2.69414 | − | 0.980587i | ||||
\(386\) | −2.97287e10 | − | 1.71639e10i | −1.33914 | − | 0.773153i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.64634e8 | − | 9.77975e8i | −0.0249138 | − | 0.0431520i | ||||
\(389\) | −3.83291e9 | + | 4.56788e9i | −0.167390 | + | 0.199488i | −0.843218 | − | 0.537572i | \(-0.819342\pi\) |
0.675828 | + | 0.737059i | \(0.263786\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.13511e9 | + | 1.77801e10i | 0.134136 | + | 0.760725i | ||||
\(392\) | 5.80446e9 | − | 1.02348e9i | 0.245820 | − | 0.0433448i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.44152e9 | + | 3.72688e9i | 0.184309 | + | 0.154654i | ||||
\(395\) | 1.37972e10 | − | 7.96582e9i | 0.566765 | − | 0.327222i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.60190e9 | + | 2.77457e9i | −0.0644871 | + | 0.111695i | −0.896466 | − | 0.443112i | \(-0.853874\pi\) |
0.831979 | + | 0.554807i | \(0.187208\pi\) | |||||||
\(398\) | −4.51344e9 | − | 1.24006e10i | −0.179877 | − | 0.494208i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.88682e10 | − | 1.58323e10i | 0.737038 | − | 0.618449i | ||||
\(401\) | −1.33575e10 | + | 3.66996e10i | −0.516594 | + | 1.41933i | 0.357656 | + | 0.933853i | \(0.383576\pi\) |
−0.874250 | + | 0.485477i | \(0.838646\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.67616e8 | + | 3.78624e9i | −0.0253108 | + | 0.143545i | ||||
\(404\) | − | 1.26763e10i | − | 0.475848i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.38359e10 | 1.24530 | ||||||||
\(407\) | 1.78283e10 | + | 3.14361e9i | 0.649729 | + | 0.114565i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.94804e10 | − | 1.43697e10i | −1.41087 | − | 0.513516i | −0.479488 | − | 0.877548i | \(-0.659178\pi\) |
−0.931386 | + | 0.364032i | \(0.881400\pi\) | |||||||
\(410\) | 4.02910e10 | + | 4.80170e10i | 1.42585 | + | 1.69926i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.36959e9 | + | 1.95437e9i | −0.186360 | + | 0.0678294i | ||||
\(413\) | 1.60819e10 | + | 9.28487e9i | 0.552760 | + | 0.319136i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.25518e9 | − | 3.90608e9i | −0.0760306 | − | 0.131689i | ||||
\(416\) | 1.01682e10 | − | 1.21180e10i | 0.339523 | − | 0.404628i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.14950e7 | + | 3.48755e8i | 0.00201435 | + | 0.0114239i | ||||
\(419\) | −2.44273e10 | + | 4.30720e9i | −0.792538 | + | 0.139746i | −0.555239 | − | 0.831691i | \(-0.687373\pi\) |
−0.237299 | + | 0.971437i | \(0.576262\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.34557e10 | − | 3.64636e10i | −1.38331 | − | 1.16073i | −0.967971 | − | 0.251062i | \(-0.919220\pi\) |
−0.415335 | − | 0.909669i | \(-0.636335\pi\) | |||||||
\(422\) | 1.69917e10 | − | 9.81015e9i | 0.535780 | − | 0.309333i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.55020e10 | + | 2.68502e10i | −0.479650 | + | 0.830778i | ||||
\(425\) | 2.47240e10 | + | 6.79287e10i | 0.757815 | + | 2.08208i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.14163e10 | − | 4.31434e10i | 1.54664 | − | 1.29778i | ||||
\(428\) | −1.52703e9 | + | 4.19547e9i | −0.0455063 | + | 0.125028i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.54732e9 | + | 3.14604e10i | −0.162259 | + | 0.920217i | ||||
\(431\) | 6.46311e10i | 1.87298i | 0.350698 | + | 0.936489i | \(0.385945\pi\) | ||||
−0.350698 | + | 0.936489i | \(0.614055\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.65628e10 | 0.755653 | 0.377826 | − | 0.925876i | \(-0.376672\pi\) | ||||
0.377826 | + | 0.925876i | \(0.376672\pi\) | |||||||
\(434\) | 4.95961e9 | + | 8.74513e8i | 0.139794 | + | 0.0246494i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.37776e9 | + | 5.01463e8i | 0.0381265 | + | 0.0138769i | ||||
\(437\) | −1.03865e8 | − | 1.23781e8i | −0.00284801 | − | 0.00339413i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.28937e10 | + | 1.92517e10i | −1.42412 | + | 0.518337i | −0.935240 | − | 0.354015i | \(-0.884816\pi\) |
−0.488878 | + | 0.872352i | \(0.662594\pi\) | |||||||
\(440\) | −9.11741e10 | − | 5.26394e10i | −2.43255 | − | 1.40443i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.28070e10 | − | 3.95029e10i | −0.597557 | − | 1.03500i | ||||
\(443\) | −2.12742e10 | + | 2.53536e10i | −0.552381 | + | 0.658302i | −0.967916 | − | 0.251275i | \(-0.919150\pi\) |
0.415534 | + | 0.909577i | \(0.363595\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.67966e9 | + | 4.35535e10i | 0.195840 | + | 1.11066i | ||||
\(446\) | −1.31733e10 | + | 2.32281e9i | −0.332932 | + | 0.0587049i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.76403e10 | − | 3.15839e10i | −0.934417 | − | 0.784069i | ||||
\(449\) | 6.27975e10 | − | 3.62562e10i | 1.54510 | − | 0.892065i | 0.546597 | − | 0.837396i | \(-0.315923\pi\) |
0.998505 | − | 0.0546691i | \(-0.0174104\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.57812e10 | − | 9.66159e10i | 1.34829 | − | 2.33530i | ||||
\(452\) | 2.78842e9 | + | 7.66113e9i | 0.0668043 | + | 0.183543i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.62650e9 | − | 5.56030e9i | 0.155977 | − | 0.130880i | ||||
\(455\) | 2.48356e10 | − | 6.82353e10i | 0.579468 | − | 1.59208i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.23518e9 | + | 5.23753e10i | −0.211729 | + | 1.20078i | 0.674764 | + | 0.738033i | \(0.264245\pi\) |
−0.886493 | + | 0.462742i | \(0.846866\pi\) | |||||||
\(458\) | − | 8.28893e9i | − | 0.188381i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.06110e10 | 0.236986 | ||||||||
\(461\) | 3.01751e10 | + | 5.32068e9i | 0.668104 | + | 0.117805i | 0.497405 | − | 0.867518i | \(-0.334286\pi\) |
0.170699 | + | 0.985323i | \(0.445397\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.02920e10 | + | 1.10254e10i | 0.659181 | + | 0.239922i | 0.649883 | − | 0.760035i | \(-0.274818\pi\) |
0.00929829 | + | 0.999957i | \(0.497040\pi\) | |||||||
\(464\) | −2.51434e10 | − | 2.99648e10i | −0.542441 | − | 0.646456i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.47997e10 | + | 1.63058e10i | −0.950017 | + | 0.345778i | ||||
\(467\) | −4.49907e10 | − | 2.59754e10i | −0.945922 | − | 0.546129i | −0.0541106 | − | 0.998535i | \(-0.517232\pi\) |
−0.891812 | + | 0.452406i | \(0.850566\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.76592e10 | + | 4.79072e10i | 0.571674 | + | 0.990169i | ||||
\(470\) | −1.07341e10 | + | 1.27924e10i | −0.219976 | + | 0.262157i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.38939e9 | − | 3.05648e10i | −0.108585 | − | 0.615819i | ||||
\(473\) | 5.59940e10 | − | 9.87325e9i | 1.11866 | − | 0.197249i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.95608e8 | − | 4.15865e8i | −0.00973563 | − | 0.00816916i | ||||
\(476\) | 2.04762e10 | − | 1.18220e10i | 0.398862 | − | 0.230283i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.12913e10 | + | 3.68776e10i | −0.407840 | + | 0.706400i | ||||
\(479\) | 7.77313e9 | + | 2.13565e10i | 0.147657 | + | 0.405684i | 0.991367 | − | 0.131115i | \(-0.0418556\pi\) |
−0.843710 | + | 0.536799i | \(0.819633\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.59867e10 | − | 1.34144e10i | 0.298660 | − | 0.250606i | ||||
\(482\) | −1.66771e10 | + | 4.58201e10i | −0.308982 | + | 0.848922i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.48568e9 | + | 2.54396e10i | −0.0817424 | + | 0.463584i | ||||
\(485\) | 1.54138e10i | 0.278576i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.87683e10 | −1.22257 | −0.611283 | − | 0.791412i | \(-0.709346\pi\) | ||||
−0.611283 | + | 0.791412i | \(0.709346\pi\) | |||||||
\(488\) | −1.10474e11 | − | 1.94796e10i | −1.94797 | − | 0.343480i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.66991e10 | − | 6.07796e9i | −0.289673 | − | 0.105432i | ||||
\(491\) | −4.69265e10 | − | 5.59248e10i | −0.807406 | − | 0.962229i | 0.192412 | − | 0.981314i | \(-0.438369\pi\) |
−0.999818 | + | 0.0190855i | \(0.993925\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.07878e11 | − | 3.92645e10i | 1.82619 | − | 0.664679i | ||||
\(494\) | 3.53546e8 | + | 2.04120e8i | 0.00593660 | + | 0.00342750i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.91102e9 | − | 5.04203e9i | −0.0480970 | − | 0.0833064i | ||||
\(497\) | −2.10706e10 | + | 2.51110e10i | −0.345344 | + | 0.411565i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.66714e9 | + | 3.78112e10i | 0.107532 | + | 0.609844i | 0.990179 | + | 0.139807i | \(0.0446482\pi\) |
−0.882647 | + | 0.470037i | \(0.844241\pi\) | |||||||
\(500\) | 1.41783e10 | − | 2.50002e9i | 0.226853 | − | 0.0400004i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.68603e10 | − | 1.41475e10i | −0.265491 | − | 0.222774i | ||||
\(503\) | −1.37684e9 | + | 7.94918e8i | −0.0215085 | + | 0.0124180i | −0.510716 | − | 0.859750i | \(-0.670620\pi\) |
0.489207 | + | 0.872168i | \(0.337286\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.65122e10 | + | 1.49844e11i | −1.33018 | + | 2.30395i | ||||
\(506\) | 1.63230e10 | + | 4.48472e10i | 0.249000 | + | 0.684121i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.36408e10 | − | 1.14460e10i | 0.204826 | − | 0.171869i | ||||
\(509\) | 2.97231e10 | − | 8.16637e10i | 0.442816 | − | 1.21663i | −0.494816 | − | 0.868998i | \(-0.664764\pi\) |
0.937632 | − | 0.347630i | \(-0.113013\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.23751e9 | + | 1.83608e10i | −0.0474819 | + | 0.269283i | ||||
\(512\) | 7.14453e10i | 1.03967i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.76829e9 | 0.111294 | ||||||||
\(515\) | 7.68104e10 | + | 1.35437e10i | 1.09192 | + | 0.192535i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.79294e10 | + | 1.01655e10i | 0.390930 | + | 0.142287i | ||||
\(518\) | −1.75716e10 | − | 2.09410e10i | −0.244057 | − | 0.290856i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.14044e11 | + | 4.15086e10i | −1.55977 | + | 0.567708i | ||||
\(521\) | −1.18023e11 | − | 6.81406e10i | −1.60183 | − | 0.924815i | −0.991122 | − | 0.132956i | \(-0.957553\pi\) |
−0.610704 | − | 0.791859i | \(-0.709114\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.68568e10 | − | 2.91969e10i | −0.225304 | − | 0.390238i | 0.731107 | − | 0.682263i | \(-0.239004\pi\) |
−0.956411 | + | 0.292025i | \(0.905671\pi\) | |||||||
\(524\) | −1.96172e10 | + | 2.33789e10i | −0.260203 | + | 0.310098i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.65316e10 | − | 9.37552e10i | −0.215959 | − | 1.22476i | ||||
\(527\) | 1.68274e10 | − | 2.96713e9i | 0.218160 | − | 0.0384675i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.33082e10 | + | 3.63399e10i | 0.553029 | + | 0.464046i | ||||
\(530\) | 8.09551e10 | − | 4.67394e10i | 1.02598 | − | 0.592352i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.05805e8 | + | 1.83260e8i | −0.00132087 | + | 0.00228781i | ||||
\(533\) | −4.39861e10 | − | 1.20851e11i | −0.545013 | − | 1.49741i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.66834e10 | − | 3.91720e10i | 0.569832 | − | 0.478146i | ||||
\(536\) | 3.16217e10 | − | 8.68799e10i | 0.383112 | − | 1.05259i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.99994e10 | − | 1.13422e11i | 0.238720 | − | 1.35385i | ||||
\(539\) | 3.16289e10i | 0.374739i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.02849e11 | 1.20064 | 0.600319 | − | 0.799760i | \(-0.295040\pi\) | ||||
0.600319 | + | 0.799760i | \(0.295040\pi\) | |||||||
\(542\) | −4.88813e10 | − | 8.61908e9i | −0.566429 | − | 0.0998767i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.60649e10 | − | 2.40457e10i | −0.754354 | − | 0.274562i | ||||
\(545\) | −1.28638e10 | − | 1.53304e10i | −0.145808 | − | 0.173767i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.29316e11 | + | 4.70673e10i | −1.44446 | + | 0.525739i | −0.941037 | − | 0.338304i | \(-0.890147\pi\) |
−0.503418 | + | 0.864043i | \(0.667925\pi\) | |||||||
\(548\) | 2.33399e10 | + | 1.34753e10i | 0.258808 | + | 0.149423i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.55441e10 | + | 1.65487e11i | 1.04413 | + | 1.80848i | ||||
\(551\) | −6.60439e8 | + | 7.87081e8i | −0.00716517 | + | 0.00853912i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.43521e9 | + | 4.21672e10i | 0.0795047 | + | 0.450893i | ||||
\(554\) | 1.04183e11 | − | 1.83703e10i | 1.10601 | − | 0.195020i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.34696e10 | + | 1.96933e10i | 0.245587 | + | 0.206072i | ||||
\(557\) | −1.34913e11 | + | 7.78922e10i | −1.40163 | + | 0.809232i | −0.994560 | − | 0.104165i | \(-0.966783\pi\) |
−0.407071 | + | 0.913397i | \(0.633450\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.27722e10 | − | 5.67631e10i | 0.335628 | − | 0.581325i | ||||
\(560\) | 3.76091e10 | + | 1.03330e11i | 0.382421 | + | 1.05069i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.62425e10 | + | 1.36290e10i | −0.162820 | + | 0.136622i | ||||
\(563\) | −3.49849e10 | + | 9.61202e10i | −0.348214 | + | 0.956711i | 0.634718 | + | 0.772744i | \(0.281116\pi\) |
−0.982932 | + | 0.183967i | \(0.941106\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.93237e10 | − | 1.09590e11i | 0.189625 | − | 1.07542i | ||||
\(566\) | − | 1.08160e11i | − | 1.05391i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.47865e10 | 0.526356 | ||||||||
\(569\) | 8.94456e10 | + | 1.57717e10i | 0.853316 | + | 0.150463i | 0.583163 | − | 0.812355i | \(-0.301815\pi\) |
0.270152 | + | 0.962818i | \(0.412926\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.14927e11 | − | 4.18298e10i | −1.08113 | − | 0.393497i | −0.260799 | − | 0.965393i | \(-0.583986\pi\) |
−0.820326 | + | 0.571896i | \(0.806208\pi\) | |||||||
\(572\) | 3.06700e10 | + | 3.65511e10i | 0.286503 | + | 0.341441i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.58303e11 | + | 5.76176e10i | −1.45828 | + | 0.530771i | ||||
\(575\) | −7.55084e10 | − | 4.35948e10i | −0.690755 | − | 0.398807i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.35572e9 | − | 2.34817e9i | −0.0122311 | − | 0.0211849i | 0.859845 | − | 0.510555i | \(-0.170560\pi\) |
−0.872076 | + | 0.489370i | \(0.837227\pi\) | |||||||
\(578\) | −6.95824e10 | + | 8.29251e10i | −0.623431 | + | 0.742976i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.17163e10 | − | 6.64463e10i | −0.103533 | − | 0.587163i | ||||
\(581\) | 1.19378e10 | − | 2.10496e9i | 0.104766 | − | 0.0184731i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.27451e11 | − | 1.06944e11i | −1.10324 | − | 0.925729i | ||||
\(584\) | 2.69858e10 | − | 1.55803e10i | 0.231998 | − | 0.133944i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.21919e10 | − | 1.25040e11i | 0.612207 | − | 1.06037i | ||||
\(587\) | 4.01800e10 | + | 1.10394e11i | 0.338421 | + | 0.929805i | 0.985843 | + | 0.167673i | \(0.0536253\pi\) |
−0.647421 | + | 0.762132i | \(0.724153\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.17149e8 | + | 9.82993e7i | −0.000973365 | + | 0.000816751i | ||||
\(590\) | −3.20049e10 | + | 8.79328e10i | −0.264125 | + | 0.725677i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.48773e9 | + | 3.11224e10i | −0.0446792 | + | 0.253389i | ||||
\(593\) | 1.69673e11i | 1.37212i | 0.727544 | + | 0.686061i | \(0.240662\pi\) | ||||
−0.727544 | + | 0.686061i | \(0.759338\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.22725e11 | −2.57493 | ||||||||
\(596\) | −3.43745e10 | − | 6.06115e9i | −0.272428 | − | 0.0480364i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.16989e10 | + | 1.88168e10i | 0.404274 | + | 0.147144i | ||||
\(599\) | 1.03440e11 | + | 1.23275e11i | 0.803493 | + | 0.957566i | 0.999736 | − | 0.0229897i | \(-0.00731850\pi\) |
−0.196243 | + | 0.980555i | \(0.562874\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.59242e11 | − | 5.79593e10i | 1.22056 | − | 0.444248i | 0.350206 | − | 0.936673i | \(-0.386112\pi\) |
0.870355 | + | 0.492425i | \(0.163889\pi\) | |||||||
\(602\) | −7.43542e10 | − | 4.29284e10i | −0.566135 | − | 0.326858i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.83920e10 | + | 3.18559e10i | 0.138192 | + | 0.239355i | ||||
\(605\) | 2.26641e11 | − | 2.70101e11i | 1.69168 | − | 2.01606i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.08833e10 | + | 1.75148e11i | 0.227494 | + | 1.29018i | 0.857860 | + | 0.513883i | \(0.171794\pi\) |
−0.630366 | + | 0.776298i | \(0.717095\pi\) | |||||||
\(608\) | 6.19660e8 | − | 1.09263e8i | 0.00453460 | − | 0.000799573i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.59096e11 | + | 2.17407e11i | 1.87129 | + | 1.57020i | ||||
\(611\) | 2.96724e10 | − | 1.71314e10i | 0.212906 | − | 0.122921i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.91010e10 | + | 5.04044e10i | −0.206094 | + | 0.356966i | −0.950481 | − | 0.310783i | \(-0.899409\pi\) |
0.744387 | + | 0.667749i | \(0.232742\pi\) | |||||||
\(614\) | 1.32033e10 | + | 3.62758e10i | 0.0928987 | + | 0.255237i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.16749e11 | − | 1.81874e11i | 1.50534 | − | 1.26313i | ||||
\(617\) | −4.57298e10 | + | 1.25641e11i | −0.315543 | + | 0.866947i | 0.675969 | + | 0.736930i | \(0.263725\pi\) |
−0.991512 | + | 0.130017i | \(0.958497\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.33487e10 | − | 1.32417e11i | 0.159038 | − | 0.901948i | −0.795963 | − | 0.605345i | \(-0.793035\pi\) |
0.955001 | − | 0.296603i | \(-0.0958538\pi\) | |||||||
\(620\) | − | 1.00424e10i | − | 0.0679627i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.54659e11 | 1.03327 | ||||||||
\(623\) | −1.17054e11 | − | 2.06397e10i | −0.777022 | − | 0.137010i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.22202e10 | + | 1.17272e10i | 0.211158 | + | 0.0768554i | ||||
\(626\) | −3.92245e10 | − | 4.67459e10i | −0.255423 | − | 0.304401i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.15089e10 | − | 1.14683e10i | 0.202579 | − | 0.0737328i | ||||
\(629\) | −8.03238e10 | − | 4.63750e10i | −0.513147 | − | 0.296265i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.52481e10 | − | 2.64105e10i | −0.0961831 | − | 0.166594i | 0.813919 | − | 0.580979i | \(-0.197330\pi\) |
−0.910102 | + | 0.414385i | \(0.863997\pi\) | |||||||
\(632\) | 4.59996e10 | − | 5.48202e10i | 0.288327 | − | 0.343615i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.25956e10 | + | 7.14333e10i | 0.0779583 | + | 0.442123i | ||||
\(635\) | −2.39359e11 | + | 4.22055e10i | −1.47216 | + | 0.259582i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.79308e10 | + | 2.34367e10i | 0.169639 | + | 0.142344i | ||||
\(638\) | 2.62812e11 | − | 1.51735e11i | 1.58622 | − | 0.915802i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.09334e10 | − | 8.82193e10i | 0.303587 | − | 0.525828i | ||||
\(641\) | −7.45477e10 | − | 2.04818e11i | −0.441572 | − | 1.21321i | −0.938458 | − | 0.345394i | \(-0.887745\pi\) |
0.496885 | − | 0.867816i | \(-0.334477\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.17314e11 | + | 9.84380e10i | −0.686286 | + | 0.575863i | −0.917836 | − | 0.396961i | \(-0.870065\pi\) |
0.231549 | + | 0.972823i | \(0.425621\pi\) | |||||||
\(644\) | −9.75368e9 | + | 2.67980e10i | −0.0567055 | + | 0.155797i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.15061e8 | − | 1.78680e9i | 0.00180911 | − | 0.0102600i | ||||
\(647\) | 1.23404e11i | 0.704226i | 0.935957 | + | 0.352113i | \(0.114537\pi\) | ||||
−0.935957 | + | 0.352113i | \(0.885463\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.66549e11 | 0.938780 | ||||||||
\(650\) | 2.16936e11 | + | 3.82516e10i | 1.21528 | + | 0.214287i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.11089e10 | + | 1.13227e10i | 0.172145 | + | 0.0626556i | ||||
\(653\) | 4.83237e10 | + | 5.75899e10i | 0.265771 | + | 0.316733i | 0.882381 | − | 0.470535i | \(-0.155939\pi\) |
−0.616610 | + | 0.787268i | \(0.711495\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.91443e11 | − | 1.42474e11i | 2.12669 | − | 0.774051i | ||||
\(656\) | 1.68660e11 | + | 9.73761e10i | 0.910747 | + | 0.525820i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.24404e10 | − | 3.88680e10i | −0.119709 | − | 0.207342i | ||||
\(659\) | −4.53931e10 | + | 5.40973e10i | −0.240684 | + | 0.286836i | −0.872842 | − | 0.488004i | \(-0.837725\pi\) |
0.632157 | + | 0.774840i | \(0.282170\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.47641e10 | − | 1.40444e11i | −0.129723 | − | 0.735696i | −0.978390 | − | 0.206768i | \(-0.933705\pi\) |
0.848667 | − | 0.528928i | \(-0.177406\pi\) | |||||||
\(662\) | 5.54888e10 | − | 9.78418e9i | 0.288917 | − | 0.0509439i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.55200e10 | − | 1.30228e10i | −0.0798396 | − | 0.0669934i | ||||
\(665\) | 2.50139e9 | − | 1.44418e9i | 0.0127907 | − | 0.00738471i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.92334e10 | + | 1.19916e11i | −0.349794 | + | 0.605861i | ||||
\(668\) | 6.23597e9 | + | 1.71332e10i | 0.0313183 | + | 0.0860464i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.13542e11 | + | 1.79183e11i | −1.05970 | + | 0.889196i | ||||
\(671\) | 2.05890e11 | − | 5.65678e11i | 1.01565 | − | 2.79048i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.33595e10 | + | 7.57657e10i | −0.0651225 | + | 0.369328i | 0.934778 | + | 0.355232i | \(0.115598\pi\) |
−0.999901 | + | 0.0140960i | \(0.995513\pi\) | |||||||
\(674\) | 1.30353e11i | 0.631655i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.20314e9 | −0.0201274 | ||||||||
\(677\) | 2.24167e11 | + | 3.95267e10i | 1.06713 | + | 0.188164i | 0.679518 | − | 0.733659i | \(-0.262189\pi\) |
0.387612 | + | 0.921823i | \(0.373300\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.89277e10 | − | 1.41685e10i | −0.183138 | − | 0.0666569i | ||||
\(680\) | 3.46708e11 | + | 4.13191e11i | 1.62154 | + | 1.93248i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.24442e10 | − | 1.54484e10i | 0.196192 | − | 0.0714079i | ||||
\(683\) | 6.00315e10 | + | 3.46592e10i | 0.275865 | + | 0.159271i | 0.631550 | − | 0.775335i | \(-0.282419\pi\) |
−0.355685 | + | 0.934606i | \(0.615752\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.83930e11 | − | 3.18576e11i | −0.835392 | − | 1.44694i | ||||
\(686\) | −1.02921e11 | + | 1.22657e11i | −0.464738 | + | 0.553853i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.72355e10 | + | 9.77475e10i | 0.0769255 | + | 0.436266i | ||||
\(689\) | −1.88881e11 | + | 3.33048e10i | −0.838129 | + | 0.147785i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.29010e10 | − | 5.27802e10i | −0.275896 | − | 0.231504i | 0.494331 | − | 0.869274i | \(-0.335413\pi\) |
−0.770228 | + | 0.637769i | \(0.779857\pi\) | |||||||
\(692\) | −7.25930e10 | + | 4.19116e10i | −0.316570 | + | 0.182772i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.36208e9 | + | 2.35919e9i | −0.00587170 | + | 0.0101701i | ||||
\(695\) | −1.43026e11 | − | 3.92962e11i | −0.613024 | − | 1.68427i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.37852e11 | + | 3.67402e11i | −1.85522 | + | 1.55672i | ||||
\(698\) | −7.52914e10 | + | 2.06861e11i | −0.317193 | + | 0.871480i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.98276e10 | + | 1.12448e11i | −0.0825808 | + | 0.468339i | ||||
\(701\) | 3.67111e11i | 1.52029i | 0.649755 | + | 0.760144i | \(0.274871\pi\) | ||||
−0.649755 | + | 0.760144i | \(0.725129\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.30101e8 | 0.00339867 | ||||||||
\(704\) | −4.33997e11 | − | 7.65254e10i | −1.76684 | − | 0.311541i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.59803e10 | + | 2.40149e10i | 0.265580 | + | 0.0966633i | ||||
\(707\) | −2.98908e11 | − | 3.56224e11i | −1.19635 | − | 1.42576i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.03327e10 | + | 7.40048e9i | −0.0804654 | + | 0.0292870i | −0.381939 | − | 0.924187i | \(-0.624744\pi\) |
0.301474 | + | 0.953474i | \(0.402521\pi\) | |||||||
\(710\) | −1.43054e11 | − | 8.25922e10i | −0.562945 | − | 0.325017i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.93270e10 | + | 1.72039e11i | 0.386498 | + | 0.669435i | ||||
\(713\) | −1.32474e10 | + | 1.57876e10i | −0.0512593 | + | 0.0610884i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.13092e11 | − | 6.41374e11i | −0.432719 | − | 2.45407i | ||||
\(716\) | 5.39653e10 | − | 9.51553e9i | 0.205335 | − | 0.0362060i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.75086e11 | − | 2.30825e11i | −1.03507 | − | 0.868529i | ||||
\(719\) | 2.85002e11 | − | 1.64546e11i | 1.06643 | − | 0.615703i | 0.139226 | − | 0.990261i | \(-0.455539\pi\) |
0.927204 | + | 0.374557i | \(0.122205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.04810e11 | + | 1.81535e11i | −0.387846 | + | 0.671770i | ||||
\(722\) | −7.86632e10 | − | 2.16125e11i | −0.289483 | − | 0.795347i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.27428e10 | + | 1.06925e10i | −0.0463780 | + | 0.0389158i | ||||
\(725\) | −1.89619e11 | + | 5.20973e11i | −0.686324 | + | 1.88566i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.75215e10 | + | 3.82933e11i | −0.241715 | + | 1.37084i | 0.586283 | + | 0.810106i | \(0.300590\pi\) |
−0.827999 | + | 0.560730i | \(0.810521\pi\) | |||||||
\(728\) | − | 3.26174e11i | − | 1.16124i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9.39508e10 | −0.330833 | ||||||||
\(731\) | −2.86878e11 | − | 5.05843e10i | −1.00468 | − | 0.177152i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.34914e11 | + | 8.55016e10i | 0.813753 | + | 0.296182i | 0.715173 | − | 0.698947i | \(-0.246348\pi\) |
0.0985795 | + | 0.995129i | \(0.468570\pi\) | |||||||
\(734\) | −2.47882e11 | − | 2.95415e11i | −0.854007 | − | 1.01777i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.96834e10 | − | 2.90024e10i | 0.271554 | − | 0.0988377i | ||||
\(737\) | 4.29672e11 | + | 2.48071e11i | 1.45635 | + | 0.840827i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.59650e11 | − | 4.49726e11i | −0.870582 | − | 1.50789i | −0.861395 | − | 0.507935i | \(-0.830409\pi\) |
−0.00918707 | − | 0.999958i | \(-0.502924\pi\) | |||||||
\(740\) | −3.50390e10 | + | 4.17579e10i | −0.116849 | + | 0.139255i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.36261e10 | + | 2.47416e11i | 0.143923 | + | 0.816228i | ||||
\(743\) | 1.13404e11 | − | 1.99962e10i | 0.372112 | − | 0.0656133i | 0.0155348 | − | 0.999879i | \(-0.495055\pi\) |
0.356577 | + | 0.934266i | \(0.383944\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.64966e11 | + | 3.06243e11i | 1.18475 | + | 0.994124i | ||||
\(746\) | −3.72504e10 | + | 2.15065e10i | −0.120275 | + | 0.0694409i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.06029e11 | − | 1.83648e11i | 0.338703 | − | 0.586652i | ||||
\(749\) | 5.60173e10 | + | 1.53906e11i | 0.177990 | + | 0.489023i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.06886e11 | + | 1.73598e11i | −0.650387 | + | 0.545740i | −0.907188 | − | 0.420725i | \(-0.861776\pi\) |
0.256801 | + | 0.966464i | \(0.417331\pi\) | |||||||
\(752\) | −1.77456e10 | + | 4.87557e10i | −0.0554907 | + | 0.152459i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.07478e10 | − | 3.44518e11i | 0.187951 | − | 1.06592i | ||||
\(755\) | − | 5.02080e11i | − | 1.54520i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.18441e11 | −0.969719 | −0.484859 | − | 0.874592i | \(-0.661129\pi\) | ||||
−0.484859 | + | 0.874592i | \(0.661129\pi\) | |||||||
\(758\) | 3.51593e11 | + | 6.19953e10i | 1.06503 | + | 0.187794i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.53627e9 | − | 1.65107e9i | −0.0135971 | − | 0.00494892i | ||||
\(761\) | −2.11330e11 | − | 2.51853e11i | −0.630118 | − | 0.750946i | 0.352656 | − | 0.935753i | \(-0.385278\pi\) |
−0.982775 | + | 0.184807i | \(0.940834\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.05416e10 | − | 1.83956e10i | 0.149125 | − | 0.0542771i | ||||
\(764\) | −6.19778e9 | − | 3.57829e9i | −0.0181913 | − | 0.0105027i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.01628e10 | + | 1.04205e11i | 0.174748 | + | 0.302673i | ||||
\(767\) | 1.23412e11 | − | 1.47076e11i | 0.356594 | − | 0.424972i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.37175e10 | + | 3.04647e11i | 0.153607 | + | 0.871148i | 0.960048 | + | 0.279834i | \(0.0902794\pi\) |
−0.806442 | + | 0.591314i | \(0.798609\pi\) | |||||||
\(770\) | −8.40138e11 | + | 1.48139e11i | −2.38994 | + | 0.421412i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.40930e11 | − | 1.18254e11i | −0.396765 | − | 0.332925i | ||||
\(773\) | −4.97453e11 | + | 2.87205e11i | −1.39327 | + | 0.804403i | −0.993675 | − | 0.112291i | \(-0.964181\pi\) |
−0.399591 | + | 0.916694i | \(0.630848\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.12589e10 | + | 7.14625e10i | −0.114370 | + | 0.198094i | ||||
\(776\) | 2.36803e10 | + | 6.50612e10i | 0.0653042 | + | 0.179422i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.18638e10 | − | 5.19099e10i | 0.168857 | − | 0.141688i | ||||
\(779\) | 1.74961e9 | − | 4.80703e9i | 0.00475108 | − | 0.0130535i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.10524e10 | + | 2.89533e11i | −0.137218 | + | 0.778204i | ||||
\(782\) | − | 2.44515e11i | − | 0.653849i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.52138e10 | −0.146145 | ||||||||
\(785\) | −4.50726e11 | − | 7.94751e10i | −1.18695 | − | 0.209292i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.88907e11 | + | 1.77948e11i | 1.27446 | + | 0.463867i | 0.888598 | − | 0.458687i | \(-0.151680\pi\) |
0.385867 | + | 0.922555i | \(0.373902\pi\) | |||||||
\(788\) | 1.99732e10 | + | 2.38032e10i | 0.0518017 | + | 0.0617348i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.02753e11 | + | 7.37962e10i | −0.520547 | + | 0.189463i | ||||
\(791\) | 2.59008e11 | + | 1.49538e11i | 0.661618 | + | 0.381985i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.46976e11 | − | 6.00979e11i | −0.877417 | − | 1.51973i | ||||
\(794\) | 2.78904e10 | − | 3.32384e10i | 0.0701733 | − | 0.0836293i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.22809e10 | − | 6.96484e10i | −0.0305899 | − | 0.173484i | ||||
\(797\) | 2.25157e11 | − | 3.97012e10i | 0.558023 | − | 0.0983945i | 0.112478 | − | 0.993654i | \(-0.464121\pi\) |
0.445545 | + | 0.895260i | \(0.353010\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.16650e11 | − | 9.78811e10i | −0.286219 | − | 0.240166i | ||||
\(800\) | 2.94034e11 | − | 1.69760e11i | 0.717856 | − | 0.414454i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.64464e11 | − | 4.58065e11i | 0.639248 | − | 1.10721i | ||||
\(803\) | 5.71912e10 | + | 1.57132e11i | 0.137552 | + | 0.377921i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.98184e11 | − | 2.50206e11i | 0.710069 | − | 0.595819i | ||||
\(806\) | 1.78086e10 | − | 4.89287e10i | 0.0421978 | − | 0.115937i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.34960e11 | + | 7.65393e11i | −0.316634 | + | 1.79572i | ||||
\(809\) | 2.80231e11i | 0.654218i | 0.944987 | + | 0.327109i | \(0.106074\pi\) | ||||
−0.944987 | + | 0.327109i | \(0.893926\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.94464e11 | −1.60534 | −0.802668 | − | 0.596426i | \(-0.796587\pi\) | ||||
−0.802668 | + | 0.596426i | \(0.796587\pi\) | |||||||
\(812\) | 1.78580e11 | + | 3.14885e10i | 0.410780 | + | 0.0724316i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.30391e11 | − | 8.38555e10i | −0.524769 | − | 0.191000i | ||||
\(815\) | −2.90455e11 | − | 3.46151e11i | −0.658338 | − | 0.784577i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.44990e9 | − | 8.91690e8i | 0.00549870 | − | 0.00200136i | ||||
\(818\) | 4.92774e11 | + | 2.84503e11i | 1.10061 | + | 0.635440i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.67963e11 | + | 2.90921e11i | 0.371500 | + | 0.643458i | ||||
\(821\) | −9.00287e10 | + | 1.07292e11i | −0.198157 | + | 0.236154i | −0.855968 | − | 0.517029i | \(-0.827038\pi\) |
0.657811 | + | 0.753183i | \(0.271482\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.32353e11 | + | 7.50609e11i | 0.288492 | + | 1.63612i | 0.692540 | + | 0.721379i | \(0.256492\pi\) |
−0.404048 | + | 0.914738i | \(0.632397\pi\) | |||||||
\(824\) | 3.45021e11 | − | 6.08365e10i | 0.748405 | − | 0.131964i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.92656e11 | − | 1.61657e11i | −0.413868 | − | 0.347276i | ||||
\(827\) | −1.73429e11 | + | 1.00129e11i | −0.370765 | + | 0.214061i | −0.673793 | − | 0.738921i | \(-0.735336\pi\) |
0.303028 | + | 0.952982i | \(0.402003\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.02214e11 | − | 5.23449e11i | 0.639876 | − | 1.10830i | −0.345584 | − | 0.938388i | \(-0.612319\pi\) |
0.985460 | − | 0.169910i | \(-0.0543476\pi\) | |||||||
\(830\) | 2.08922e10 | + | 5.74008e10i | 0.0440222 | + | 0.120950i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.89166e11 | + | 3.26549e11i | −0.812160 | + | 0.681483i | ||||
\(833\) | 5.54231e10 | − | 1.52274e11i | 0.115109 | − | 0.316260i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.32152e10 | − | 2.45085e11i | 0.0888976 | − | 0.504164i | ||||
\(836\) | 1.89790e9i | 0.00388551i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.35928e11 | 0.681193 | ||||||||
\(839\) | 8.98602e11 | + | 1.58448e11i | 1.81351 | + | 0.319771i | 0.974507 | − | 0.224358i | \(-0.0720285\pi\) |
0.839002 | + | 0.544129i | \(0.183140\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.57286e11 | + | 1.30041e11i | 0.714219 | + | 0.259955i | ||||
\(842\) | 4.93835e11 | + | 5.88529e11i | 0.982502 | + | 1.17090i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.88087e10 | − | 3.59634e10i | 0.194727 | − | 0.0708747i | ||||
\(845\) | 4.96842e10 | + | 2.86852e10i | 0.0974521 | + | 0.0562640i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.73810e11 | + | 8.20663e11i | 0.920599 | + | 1.59452i | ||||
\(848\) | 1.86690e11 | − | 2.22489e11i | 0.361026 | − | 0.430254i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.70004e11 | − | 9.64141e11i | −0.325674 | − | 1.84699i | ||||
\(851\) | 1.10170e11 | − | 1.94259e10i | 0.210060 | − | 0.0370393i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.59900e10 | + | 3.85902e10i | 0.0868695 | + | 0.0728922i | 0.685188 | − | 0.728366i | \(-0.259720\pi\) |
−0.598319 | + | 0.801258i | \(0.704164\pi\) | |||||||
\(854\) | −7.87225e11 | + | 4.54505e11i | −1.48002 | + | 0.854490i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.36869e11 | − | 2.37064e11i | 0.254923 | − | 0.441540i | ||||
\(857\) | 1.56719e11 | + | 4.30581e11i | 0.290535 | + | 0.798237i | 0.995988 | + | 0.0894815i | \(0.0285210\pi\) |
−0.705454 | + | 0.708756i | \(0.749257\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.76176e11 | − | 2.31740e11i | 0.507241 | − | 0.425625i | −0.352916 | − | 0.935655i | \(-0.614810\pi\) |
0.860157 | + | 0.510030i | \(0.170366\pi\) | |||||||
\(860\) | −5.85556e10 | + | 1.60880e11i | −0.107047 | + | 0.294109i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.51996e11 | − | 8.62015e11i | 0.275299 | − | 1.56130i | ||||
\(863\) | − | 8.65609e11i | − | 1.56055i | −0.625435 | − | 0.780276i | \(-0.715078\pi\) | ||
0.625435 | − | 0.780276i | \(-0.284922\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.14414e12 | 2.04368 | ||||||||
\(866\) | −3.54280e11 | − | 6.24692e10i | −0.629906 | − | 0.111069i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.53621e10 | + | 9.23105e9i | 0.0446793 | + | 0.0162619i | ||||
\(869\) | 2.46846e11 | + | 2.94180e11i | 0.432860 | + | 0.515863i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.37450e11 | − | 1.95616e11i | 0.933825 | − | 0.339885i | ||||
\(872\) | −7.78497e10 | − | 4.49465e10i | −0.134645 | − | 0.0777375i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.09419e9 | + | 1.89519e9i | 0.00187519 | + | 0.00324793i | ||||
\(875\) | 3.39482e11 | − | 4.04579e11i | 0.579142 | − | 0.690195i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.54872e10 | − | 3.14683e11i | −0.0937981 | − | 0.531956i | −0.995109 | − | 0.0987829i | \(-0.968505\pi\) |
0.901311 | − | 0.433173i | \(-0.142606\pi\) | |||||||
\(878\) | 7.50743e11 | − | 1.32376e11i | 1.26332 | − | 0.222757i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.55496e11 | + | 6.33936e11i | 1.25980 | + | 1.05710i | ||||
\(881\) | 7.29538e11 | − | 4.21199e11i | 1.21100 | − | 0.699172i | 0.248024 | − | 0.968754i | \(-0.420219\pi\) |
0.962977 | + | 0.269582i | \(0.0868856\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.44619e11 | + | 9.43307e11i | −0.895880 | + | 1.55171i | −0.0631678 | + | 0.998003i | \(0.520120\pi\) |
−0.832712 | + | 0.553706i | \(0.813213\pi\) | |||||||
\(884\) | −8.36091e10 | − | 2.29714e11i | −0.136913 | − | 0.376165i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.43370e11 | − | 2.88121e11i | 0.557221 | − | 0.467564i | ||||
\(887\) | −1.25823e11 | + | 3.45697e11i | −0.203267 | + | 0.558471i | −0.998879 | − | 0.0473352i | \(-0.984927\pi\) |
0.795612 | + | 0.605806i | \(0.207149\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.13431e11 | − | 6.43299e11i | 0.181604 | − | 1.02992i | ||||
\(890\) | − | 5.98954e11i | − | 0.954626i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.16881e10 | −0.113237 | ||||||||
\(893\) | 1.34215e9 | + | 2.36657e8i | 0.00211054 | + | 0.000372145i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.02849e11 | − | 2.55816e11i | −1.09539 | − | 0.398690i | ||||
\(896\) | 1.75980e11 | + | 2.09725e11i | 0.273043 | + | 0.325400i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.22825e11 | + | 3.35881e11i | −1.41910 | + | 0.516511i | ||||
\(899\) | 1.13490e11 | + | 6.55237e10i | 0.173748 | + | 0.100314i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.26202e11 | + | 7.38204e11i | 0.646721 | + | 1.12015i | ||||
\(902\) | −9.71197e11 | + | 1.15743e12i | −1.46717 | + | 1.74851i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.67993e10 | − | 4.92263e11i | −0.129970 | − | 0.737096i | ||||
\(905\) | 2.23603e11 | − | 3.94272e10i | 0.333337 | − | 0.0587762i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.47819e11 | − | 1.24035e11i | −0.218425 | − | 0.183280i | 0.527009 | − | 0.849860i | \(-0.323313\pi\) |
−0.745434 | + | 0.666579i | \(0.767758\pi\) | |||||||
\(908\) | 4.01481e10 | − | 2.31795e10i | 0.0590638 | − | 0.0341005i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.91717e11 | + | 8.51678e11i | −0.717050 | + | 1.24197i | ||||
\(911\) | −3.85785e10 | − | 1.05994e11i | −0.0560109 | − | 0.153889i | 0.908532 | − | 0.417816i | \(-0.137204\pi\) |
−0.964543 | + | 0.263927i | \(0.914982\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.32844e10 | − | 6.98839e10i | 0.119862 | − | 0.100576i | ||||
\(914\) | 2.46348e11 | − | 6.76834e11i | 0.352991 | − | 0.969835i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.71387e9 | − | 4.37475e10i | 0.0109570 | − | 0.0621401i | ||||
\(917\) | 1.11955e12i | 1.58332i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.60073e11 | 0.504811 | 0.252405 | − | 0.967622i | \(-0.418778\pi\) | ||||
0.252405 | + | 0.967622i | \(0.418778\pi\) | |||||||
\(920\) | −6.40686e11 | − | 1.12970e11i | −0.894322 | − | 0.157693i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.89946e11 | − | 1.41929e11i | −0.539610 | − | 0.196402i | ||||
\(923\) | 2.17851e11 | + | 2.59625e11i | 0.300160 | + | 0.357717i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.20902e11 | − | 1.53196e11i | 0.574929 | − | 0.209257i | ||||
\(926\) | −3.78090e11 | − | 2.18290e11i | −0.514223 | − | 0.296887i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.69598e11 | − | 4.66958e11i | −0.363518 | − | 0.629631i | ||||
\(929\) | 4.96330e10 | − | 5.91503e10i | 0.0666358 | − | 0.0794135i | −0.731697 | − | 0.681630i | \(-0.761271\pi\) |
0.798333 | + | 0.602217i | \(0.205716\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.51841e8 | + | 1.42826e9i | 0.000335218 | + | 0.00190112i | ||||
\(932\) | −2.51620e11 | + | 4.43673e10i | −0.333489 | + | 0.0588030i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.38974e11 | + | 4.52253e11i | 0.708240 | + | 0.594284i | ||||
\(935\) | −2.50669e12 | + | 1.44724e12i | −3.27985 | + | 1.89362i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.46345e10 | + | 9.46298e10i | −0.0708776 | + | 0.122764i | −0.899286 | − | 0.437361i | \(-0.855913\pi\) |
0.828409 | + | 0.560124i | \(0.189247\pi\) | |||||||
\(938\) | −2.56238e11 | − | 7.04008e11i | −0.331003 | − | 0.909424i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.85577e10 | + | 5.75267e10i | −0.0878102 | + | 0.0736815i | ||||
\(941\) | 1.51783e11 | − | 4.17019e11i | 0.193581 | − | 0.531860i | −0.804488 | − | 0.593969i | \(-0.797560\pi\) |
0.998069 | + | 0.0621085i | \(0.0197825\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.19713e11 | − | 6.78926e11i | 0.151389 | − | 0.858569i | ||||
\(944\) | 2.90741e11i | 0.366116i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.70037e11 | −0.961495 | ||||||||
\(947\) | −5.80418e11 | − | 1.02343e11i | −0.721673 | − | 0.127250i | −0.199265 | − | 0.979946i | \(-0.563855\pi\) |
−0.522409 | + | 0.852695i | \(0.674966\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.81138e11 | + | 6.59288e10i | 0.223329 | + | 0.0812850i | ||||
\(950\) | 5.63214e9 | + | 6.71213e9i | 0.00691479 | + | 0.00824073i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.36221e12 | + | 4.95805e11i | −1.65843 | + | 0.603619i | ||||
\(953\) | −1.23865e10 | − | 7.15133e9i | −0.0150168 | − | 0.00866992i | 0.492473 | − | 0.870328i | \(-0.336093\pi\) |
−0.507490 | + | 0.861658i | \(0.669426\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.88415e10 | + | 8.45960e10i | 0.0587186 | + | 0.101704i | ||||
\(956\) | −1.46691e11 | + | 1.74819e11i | −0.175619 | + | 0.209294i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.34486e10 | − | 3.03122e11i | −0.0634562 | − | 0.359878i | ||||
\(959\) | 9.73635e11 | − | 1.71678e11i | 1.15112 | − | 0.202974i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.38411e11 | − | 5.35690e11i | −0.748526 | − | 0.628088i | ||||
\(962\) | −2.44769e11 | + | 1.41317e11i | −0.285796 | + | 0.165004i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.30660e11 | + | 2.26310e11i | −0.151299 | + | 0.262057i | ||||
\(965\) | 8.58842e11 | + | 2.35965e12i | 0.990385 | + | 2.72106i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.09840e11 | + | 9.21663e10i | −0.125618 | + | 0.105406i | −0.703433 | − | 0.710762i | \(-0.748350\pi\) |
0.577814 | + | 0.816168i | \(0.303906\pi\) | |||||||
\(968\) | 5.41688e11 | − | 1.48828e12i | 0.616947 | − | 1.69505i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.62495e10 | − | 2.05581e11i | 0.0409464 | − | 0.232218i | ||||
\(971\) | − | 1.68081e12i | − | 1.89078i | −0.325944 | − | 0.945389i | \(-0.605682\pi\) | ||
0.325944 | − | 0.945389i | \(-0.394318\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.12390e12 | 1.25394 | ||||||||
\(974\) | 9.17194e11 | + | 1.61726e11i | 1.01912 | + | 0.179698i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.87491e11 | + | 3.59417e11i | 1.08826 | + | 0.396095i | ||||
\(977\) | −3.78131e11 | − | 4.50639e11i | −0.415015 | − | 0.494596i | 0.517522 | − | 0.855670i | \(-0.326855\pi\) |
−0.932537 | + | 0.361074i | \(0.882410\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.00174e12 | + | 3.64605e11i | −1.09050 | + | 0.396909i | ||||
\(980\) | −8.24785e10 | − | 4.76190e10i | −0.0894204 | − | 0.0516269i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.94358e11 | + | 8.56254e11i | 0.531614 | + | 0.920782i | ||||
\(983\) | 5.44055e11 | − | 6.48380e11i | 0.582678 | − | 0.694409i | −0.391503 | − | 0.920177i | \(-0.628045\pi\) |
0.974181 | + | 0.225768i | \(0.0724891\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.36486e10 | − | 4.17682e11i | −0.0782384 | − | 0.443712i | ||||
\(986\) | −1.53116e12 | + | 2.69985e11i | −1.62000 | + | 0.285649i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.67600e9 | + | 1.40633e9i | 0.00175892 | + | 0.00147591i | ||||
\(989\) | 3.04280e11 | − | 1.75676e11i | 0.318045 | − | 0.183623i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.81519e11 | − | 8.34015e11i | 0.499251 | − | 0.864728i | −0.500749 | − | 0.865593i | \(-0.666942\pi\) |
1.00000 | 0.000864758i | \(0.000275261\pi\) | ||||||||
\(992\) | −2.74484e10 | − | 7.54138e10i | −0.0283446 | − | 0.0778761i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.40083e11 | − | 2.85364e11i | 0.348369 | − | 0.292317i | ||||
\(995\) | −3.30160e11 | + | 9.07108e11i | −0.336847 | + | 0.925480i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.22891e11 | + | 6.96951e11i | −0.124377 | + | 0.705378i | 0.857299 | + | 0.514819i | \(0.172141\pi\) |
−0.981676 | + | 0.190559i | \(0.938970\pi\) | |||||||
\(998\) | − | 5.19985e11i | − | 0.524166i | ||||||
\(999\) | 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 | 81.9.f.a.8.9 | 138 | ||
3.2 | odd | 2 | 27.9.f.a.2.15 | ✓ | 138 | ||
27.13 | even | 9 | 27.9.f.a.14.15 | yes | 138 | ||
27.14 | odd | 18 | inner | 81.9.f.a.71.9 | 138 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.9.f.a.2.15 | ✓ | 138 | 3.2 | odd | 2 | ||
27.9.f.a.14.15 | yes | 138 | 27.13 | even | 9 | ||
81.9.f.a.8.9 | 138 | 1.1 | even | 1 | trivial | ||
81.9.f.a.71.9 | 138 | 27.14 | odd | 18 | inner |