Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,2,Mod(31,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("980.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.o (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: | \(7.82533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.31 |
Dual form | 980.2.o.c.411.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.707107 | + | 0.707107i | ||||
\(3\) | −0.866025 | + | 1.50000i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | −0.866025 | + | 0.500000i | −0.387298 | + | 0.223607i | ||||
\(6\) | −2.36603 | + | 0.633975i | −0.965926 | + | 0.258819i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.00000 | + | 2.00000i | −0.707107 | + | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.36603 | − | 0.366025i | −0.431975 | − | 0.115747i | ||||
\(11\) | 3.23205 | + | 1.86603i | 0.974500 | + | 0.562628i | 0.900605 | − | 0.434638i | \(-0.143124\pi\) |
0.0738948 | + | 0.997266i | \(0.476457\pi\) | |||||||
\(12\) | −3.00000 | − | 1.73205i | −0.866025 | − | 0.500000i | ||||
\(13\) | 6.46410i | 1.79282i | 0.443227 | + | 0.896410i | \(0.353834\pi\) | ||||
−0.443227 | + | 0.896410i | \(0.646166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.73205i | − | 0.447214i | ||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | −0.401924 | − | 0.232051i | −0.0974808 | − | 0.0562806i | 0.450467 | − | 0.892793i | \(-0.351257\pi\) |
−0.547948 | + | 0.836512i | \(0.684591\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | − | 5.19615i | −0.688247 | − | 1.19208i | −0.972404 | − | 0.233301i | \(-0.925047\pi\) |
0.284157 | − | 0.958778i | \(-0.408286\pi\) | |||||||
\(20\) | −1.00000 | − | 1.73205i | −0.223607 | − | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.36603 | + | 5.09808i | 0.291238 | + | 1.08691i | ||||
\(23\) | 4.73205 | − | 2.73205i | 0.986701 | − | 0.569672i | 0.0824143 | − | 0.996598i | \(-0.473737\pi\) |
0.904286 | + | 0.426926i | \(0.140404\pi\) | |||||||
\(24\) | −1.26795 | − | 4.73205i | −0.258819 | − | 0.965926i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −6.46410 | + | 6.46410i | −1.26771 | + | 1.26771i | ||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.92820 | −1.10084 | −0.550420 | − | 0.834888i | \(-0.685532\pi\) | ||||
−0.550420 | + | 0.834888i | \(0.685532\pi\) | |||||||
\(30\) | 1.73205 | − | 1.73205i | 0.316228 | − | 0.316228i | ||||
\(31\) | 3.00000 | − | 5.19615i | 0.538816 | − | 0.933257i | −0.460152 | − | 0.887840i | \(-0.652205\pi\) |
0.998968 | − | 0.0454165i | \(-0.0144615\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.707107 | − | 0.707107i | ||||
\(33\) | −5.59808 | + | 3.23205i | −0.974500 | + | 0.562628i | ||||
\(34\) | −0.169873 | − | 0.633975i | −0.0291330 | − | 0.108726i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.26795 | + | 2.19615i | 0.208450 | + | 0.361045i | 0.951226 | − | 0.308494i | \(-0.0998250\pi\) |
−0.742777 | + | 0.669539i | \(0.766492\pi\) | |||||||
\(38\) | 2.19615 | − | 8.19615i | 0.356263 | − | 1.32959i | ||||
\(39\) | −9.69615 | − | 5.59808i | −1.55263 | − | 0.896410i | ||||
\(40\) | 0.732051 | − | 2.73205i | 0.115747 | − | 0.431975i | ||||
\(41\) | 3.46410i | 0.541002i | 0.962720 | + | 0.270501i | \(0.0871893\pi\) | ||||
−0.962720 | + | 0.270501i | \(0.912811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.00000i | − | 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | −3.73205 | + | 6.46410i | −0.562628 | + | 0.974500i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.46410 | + | 2.00000i | 1.10052 | + | 0.294884i | ||||
\(47\) | 0.866025 | + | 1.50000i | 0.126323 | + | 0.218797i | 0.922249 | − | 0.386596i | \(-0.126349\pi\) |
−0.795926 | + | 0.605393i | \(0.793016\pi\) | |||||||
\(48\) | 3.46410 | − | 6.00000i | 0.500000 | − | 0.866025i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.36603 | − | 0.366025i | 0.193185 | − | 0.0517638i | ||||
\(51\) | 0.696152 | − | 0.401924i | 0.0974808 | − | 0.0562806i | ||||
\(52\) | −12.9282 | −1.79282 | ||||||||
\(53\) | −1.00000 | + | 1.73205i | −0.137361 | + | 0.237915i | −0.926497 | − | 0.376303i | \(-0.877195\pi\) |
0.789136 | + | 0.614218i | \(0.210529\pi\) | |||||||
\(54\) | −5.19615 | − | 5.19615i | −0.707107 | − | 0.707107i | ||||
\(55\) | −3.73205 | −0.503230 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.3923 | 1.37649 | ||||||||
\(58\) | −5.92820 | − | 5.92820i | −0.778411 | − | 0.778411i | ||||
\(59\) | −1.73205 | + | 3.00000i | −0.225494 | + | 0.390567i | −0.956467 | − | 0.291839i | \(-0.905733\pi\) |
0.730974 | + | 0.682406i | \(0.239066\pi\) | |||||||
\(60\) | 3.46410 | 0.447214 | ||||||||
\(61\) | 2.19615 | − | 1.26795i | 0.281189 | − | 0.162344i | −0.352773 | − | 0.935709i | \(-0.614761\pi\) |
0.633961 | + | 0.773365i | \(0.281428\pi\) | |||||||
\(62\) | 8.19615 | − | 2.19615i | 1.04091 | − | 0.278912i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | −3.23205 | − | 5.59808i | −0.400887 | − | 0.694356i | ||||
\(66\) | −8.83013 | − | 2.36603i | −1.08691 | − | 0.291238i | ||||
\(67\) | 3.00000 | + | 1.73205i | 0.366508 | + | 0.211604i | 0.671932 | − | 0.740613i | \(-0.265465\pi\) |
−0.305424 | + | 0.952217i | \(0.598798\pi\) | |||||||
\(68\) | 0.464102 | − | 0.803848i | 0.0562806 | − | 0.0974808i | ||||
\(69\) | 9.46410i | 1.13934i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.535898i | − | 0.0635994i | −0.999494 | − | 0.0317997i | \(-0.989876\pi\) | ||
0.999494 | − | 0.0317997i | \(-0.0101239\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.803848 | + | 0.464102i | 0.0940832 | + | 0.0543190i | 0.546303 | − | 0.837587i | \(-0.316035\pi\) |
−0.452220 | + | 0.891906i | \(0.649368\pi\) | |||||||
\(74\) | −0.928203 | + | 3.46410i | −0.107901 | + | 0.402694i | ||||
\(75\) | 0.866025 | + | 1.50000i | 0.100000 | + | 0.173205i | ||||
\(76\) | 10.3923 | − | 6.00000i | 1.19208 | − | 0.688247i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.09808 | − | 15.2942i | −0.464016 | − | 1.73173i | ||||
\(79\) | 2.30385 | − | 1.33013i | 0.259203 | − | 0.149651i | −0.364768 | − | 0.931098i | \(-0.618852\pi\) |
0.623971 | + | 0.781448i | \(0.285518\pi\) | |||||||
\(80\) | 3.46410 | − | 2.00000i | 0.387298 | − | 0.223607i | ||||
\(81\) | 4.50000 | − | 7.79423i | 0.500000 | − | 0.866025i | ||||
\(82\) | −3.46410 | + | 3.46410i | −0.382546 | + | 0.382546i | ||||
\(83\) | 8.53590 | 0.936937 | 0.468468 | − | 0.883480i | \(-0.344806\pi\) | ||||
0.468468 | + | 0.883480i | \(0.344806\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.464102 | 0.0503389 | ||||||||
\(86\) | 2.00000 | − | 2.00000i | 0.215666 | − | 0.215666i | ||||
\(87\) | 5.13397 | − | 8.89230i | 0.550420 | − | 0.953355i | ||||
\(88\) | −10.1962 | + | 2.73205i | −1.08691 | + | 0.291238i | ||||
\(89\) | 8.19615 | − | 4.73205i | 0.868790 | − | 0.501596i | 0.00184433 | − | 0.999998i | \(-0.499413\pi\) |
0.866946 | + | 0.498402i | \(0.166080\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.46410 | + | 9.46410i | 0.569672 | + | 0.986701i | ||||
\(93\) | 5.19615 | + | 9.00000i | 0.538816 | + | 0.933257i | ||||
\(94\) | −0.633975 | + | 2.36603i | −0.0653895 | + | 0.244037i | ||||
\(95\) | 5.19615 | + | 3.00000i | 0.533114 | + | 0.307794i | ||||
\(96\) | 9.46410 | − | 2.53590i | 0.965926 | − | 0.258819i | ||||
\(97\) | 7.39230i | 0.750575i | 0.926908 | + | 0.375287i | \(0.122456\pi\) | ||||
−0.926908 | + | 0.375287i | \(0.877544\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.73205 | + | 1.00000i | 0.173205 | + | 0.100000i | ||||
\(101\) | 7.39230 | + | 4.26795i | 0.735562 | + | 0.424677i | 0.820453 | − | 0.571713i | \(-0.193721\pi\) |
−0.0848916 | + | 0.996390i | \(0.527054\pi\) | |||||||
\(102\) | 1.09808 | + | 0.294229i | 0.108726 | + | 0.0291330i | ||||
\(103\) | 8.59808 | + | 14.8923i | 0.847194 | + | 1.46738i | 0.883702 | + | 0.468049i | \(0.155043\pi\) |
−0.0365089 | + | 0.999333i | \(0.511624\pi\) | |||||||
\(104\) | −12.9282 | − | 12.9282i | −1.26771 | − | 1.26771i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.73205 | + | 0.732051i | −0.265360 | + | 0.0711031i | ||||
\(107\) | −15.9282 | + | 9.19615i | −1.53984 | + | 0.889026i | −0.540990 | + | 0.841029i | \(0.681950\pi\) |
−0.998847 | + | 0.0479966i | \(0.984716\pi\) | |||||||
\(108\) | − | 10.3923i | − | 1.00000i | ||||||
\(109\) | −7.96410 | + | 13.7942i | −0.762823 | + | 1.32125i | 0.178568 | + | 0.983928i | \(0.442854\pi\) |
−0.941390 | + | 0.337320i | \(0.890480\pi\) | |||||||
\(110\) | −3.73205 | − | 3.73205i | −0.355837 | − | 0.355837i | ||||
\(111\) | −4.39230 | −0.416899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.46410 | −0.137731 | −0.0688655 | − | 0.997626i | \(-0.521938\pi\) | ||||
−0.0688655 | + | 0.997626i | \(0.521938\pi\) | |||||||
\(114\) | 10.3923 | + | 10.3923i | 0.973329 | + | 0.973329i | ||||
\(115\) | −2.73205 | + | 4.73205i | −0.254765 | + | 0.441266i | ||||
\(116\) | − | 11.8564i | − | 1.10084i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.73205 | + | 1.26795i | −0.435621 | + | 0.116724i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.46410 | + | 3.46410i | 0.316228 | + | 0.316228i | ||||
\(121\) | 1.46410 | + | 2.53590i | 0.133100 | + | 0.230536i | ||||
\(122\) | 3.46410 | + | 0.928203i | 0.313625 | + | 0.0840356i | ||||
\(123\) | −5.19615 | − | 3.00000i | −0.468521 | − | 0.270501i | ||||
\(124\) | 10.3923 | + | 6.00000i | 0.933257 | + | 0.538816i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.53590i | 0.757438i | 0.925512 | + | 0.378719i | \(0.123635\pi\) | ||||
−0.925512 | + | 0.378719i | \(0.876365\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.707107 | − | 0.707107i | ||||
\(129\) | 3.00000 | + | 1.73205i | 0.264135 | + | 0.152499i | ||||
\(130\) | 2.36603 | − | 8.83013i | 0.207514 | − | 0.774453i | ||||
\(131\) | −4.73205 | − | 8.19615i | −0.413441 | − | 0.716101i | 0.581822 | − | 0.813316i | \(-0.302340\pi\) |
−0.995263 | + | 0.0972148i | \(0.969007\pi\) | |||||||
\(132\) | −6.46410 | − | 11.1962i | −0.562628 | − | 0.974500i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.26795 | + | 4.73205i | 0.109534 | + | 0.408787i | ||||
\(135\) | 4.50000 | − | 2.59808i | 0.387298 | − | 0.223607i | ||||
\(136\) | 1.26795 | − | 0.339746i | 0.108726 | − | 0.0291330i | ||||
\(137\) | 0.196152 | − | 0.339746i | 0.0167584 | − | 0.0290265i | −0.857525 | − | 0.514443i | \(-0.827999\pi\) |
0.874283 | + | 0.485417i | \(0.161332\pi\) | |||||||
\(138\) | −9.46410 | + | 9.46410i | −0.805638 | + | 0.805638i | ||||
\(139\) | −6.92820 | −0.587643 | −0.293821 | − | 0.955860i | \(-0.594927\pi\) | ||||
−0.293821 | + | 0.955860i | \(0.594927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.00000 | −0.252646 | ||||||||
\(142\) | 0.535898 | − | 0.535898i | 0.0449716 | − | 0.0449716i | ||||
\(143\) | −12.0622 | + | 20.8923i | −1.00869 | + | 1.74710i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.13397 | − | 2.96410i | 0.426353 | − | 0.246155i | ||||
\(146\) | 0.339746 | + | 1.26795i | 0.0281176 | + | 0.104936i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.39230 | + | 2.53590i | −0.361045 | + | 0.208450i | ||||
\(149\) | −8.46410 | − | 14.6603i | −0.693406 | − | 1.20101i | −0.970715 | − | 0.240234i | \(-0.922776\pi\) |
0.277309 | − | 0.960781i | \(-0.410557\pi\) | |||||||
\(150\) | −0.633975 | + | 2.36603i | −0.0517638 | + | 0.193185i | ||||
\(151\) | 4.16025 | + | 2.40192i | 0.338557 | + | 0.195466i | 0.659634 | − | 0.751587i | \(-0.270711\pi\) |
−0.321077 | + | 0.947053i | \(0.604045\pi\) | |||||||
\(152\) | 16.3923 | + | 4.39230i | 1.32959 | + | 0.356263i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000i | 0.481932i | ||||||||
\(156\) | 11.1962 | − | 19.3923i | 0.896410 | − | 1.55263i | ||||
\(157\) | 17.1962 | + | 9.92820i | 1.37240 | + | 0.792357i | 0.991230 | − | 0.132147i | \(-0.0421871\pi\) |
0.381172 | + | 0.924504i | \(0.375520\pi\) | |||||||
\(158\) | 3.63397 | + | 0.973721i | 0.289103 | + | 0.0774650i | ||||
\(159\) | −1.73205 | − | 3.00000i | −0.137361 | − | 0.237915i | ||||
\(160\) | 5.46410 | + | 1.46410i | 0.431975 | + | 0.115747i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 12.2942 | − | 3.29423i | 0.965926 | − | 0.258819i | ||||
\(163\) | −18.0000 | + | 10.3923i | −1.40987 | + | 0.813988i | −0.995375 | − | 0.0960641i | \(-0.969375\pi\) |
−0.414494 | + | 0.910052i | \(0.636041\pi\) | |||||||
\(164\) | −6.92820 | −0.541002 | ||||||||
\(165\) | 3.23205 | − | 5.59808i | 0.251615 | − | 0.435810i | ||||
\(166\) | 8.53590 | + | 8.53590i | 0.662514 | + | 0.662514i | ||||
\(167\) | 5.19615 | 0.402090 | 0.201045 | − | 0.979582i | \(-0.435566\pi\) | ||||
0.201045 | + | 0.979582i | \(0.435566\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −28.7846 | −2.21420 | ||||||||
\(170\) | 0.464102 | + | 0.464102i | 0.0355950 | + | 0.0355950i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.00000 | 0.304997 | ||||||||
\(173\) | 17.5981 | − | 10.1603i | 1.33796 | − | 0.772470i | 0.351453 | − | 0.936206i | \(-0.385688\pi\) |
0.986504 | + | 0.163736i | \(0.0523545\pi\) | |||||||
\(174\) | 14.0263 | − | 3.75833i | 1.06333 | − | 0.284918i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.9282 | − | 7.46410i | −0.974500 | − | 0.562628i | ||||
\(177\) | −3.00000 | − | 5.19615i | −0.225494 | − | 0.390567i | ||||
\(178\) | 12.9282 | + | 3.46410i | 0.969010 | + | 0.259645i | ||||
\(179\) | 12.4641 | + | 7.19615i | 0.931611 | + | 0.537866i | 0.887321 | − | 0.461153i | \(-0.152564\pi\) |
0.0442901 | + | 0.999019i | \(0.485897\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.9282i | 0.960946i | 0.877010 | + | 0.480473i | \(0.159535\pi\) | ||||
−0.877010 | + | 0.480473i | \(0.840465\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.39230i | 0.324689i | ||||||||
\(184\) | −4.00000 | + | 14.9282i | −0.294884 | + | 1.10052i | ||||
\(185\) | −2.19615 | − | 1.26795i | −0.161464 | − | 0.0932215i | ||||
\(186\) | −3.80385 | + | 14.1962i | −0.278912 | + | 1.04091i | ||||
\(187\) | −0.866025 | − | 1.50000i | −0.0633300 | − | 0.109691i | ||||
\(188\) | −3.00000 | + | 1.73205i | −0.218797 | + | 0.126323i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.19615 | + | 8.19615i | 0.159326 | + | 0.594611i | ||||
\(191\) | 2.76795 | − | 1.59808i | 0.200282 | − | 0.115633i | −0.396505 | − | 0.918033i | \(-0.629777\pi\) |
0.596787 | + | 0.802400i | \(0.296444\pi\) | |||||||
\(192\) | 12.0000 | + | 6.92820i | 0.866025 | + | 0.500000i | ||||
\(193\) | 1.26795 | − | 2.19615i | 0.0912690 | − | 0.158083i | −0.816776 | − | 0.576954i | \(-0.804241\pi\) |
0.908045 | + | 0.418872i | \(0.137574\pi\) | |||||||
\(194\) | −7.39230 | + | 7.39230i | −0.530737 | + | 0.530737i | ||||
\(195\) | 11.1962 | 0.801773 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.3205 | 1.51902 | 0.759512 | − | 0.650494i | \(-0.225438\pi\) | ||||
0.759512 | + | 0.650494i | \(0.225438\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.73205 | − | 3.00000i | 0.122782 | − | 0.212664i | −0.798082 | − | 0.602549i | \(-0.794152\pi\) |
0.920864 | + | 0.389885i | \(0.127485\pi\) | |||||||
\(200\) | 0.732051 | + | 2.73205i | 0.0517638 | + | 0.193185i | ||||
\(201\) | −5.19615 | + | 3.00000i | −0.366508 | + | 0.211604i | ||||
\(202\) | 3.12436 | + | 11.6603i | 0.219829 | + | 0.820413i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.803848 | + | 1.39230i | 0.0562806 | + | 0.0974808i | ||||
\(205\) | −1.73205 | − | 3.00000i | −0.120972 | − | 0.209529i | ||||
\(206\) | −6.29423 | + | 23.4904i | −0.438540 | + | 1.63665i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 25.8564i | − | 1.79282i | ||||||
\(209\) | − | 22.3923i | − | 1.54891i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.19615i | 0.495404i | 0.968836 | + | 0.247702i | \(0.0796753\pi\) | ||||
−0.968836 | + | 0.247702i | \(0.920325\pi\) | |||||||
\(212\) | −3.46410 | − | 2.00000i | −0.237915 | − | 0.137361i | ||||
\(213\) | 0.803848 | + | 0.464102i | 0.0550787 | + | 0.0317997i | ||||
\(214\) | −25.1244 | − | 6.73205i | −1.71747 | − | 0.460194i | ||||
\(215\) | 1.00000 | + | 1.73205i | 0.0681994 | + | 0.118125i | ||||
\(216\) | 10.3923 | − | 10.3923i | 0.707107 | − | 0.707107i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −21.7583 | + | 5.83013i | −1.47366 | + | 0.394866i | ||||
\(219\) | −1.39230 | + | 0.803848i | −0.0940832 | + | 0.0543190i | ||||
\(220\) | − | 7.46410i | − | 0.503230i | ||||||
\(221\) | 1.50000 | − | 2.59808i | 0.100901 | − | 0.174766i | ||||
\(222\) | −4.39230 | − | 4.39230i | −0.294792 | − | 0.294792i | ||||
\(223\) | −10.2679 | −0.687593 | −0.343796 | − | 0.939044i | \(-0.611713\pi\) | ||||
−0.343796 | + | 0.939044i | \(0.611713\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.46410 | − | 1.46410i | −0.0973906 | − | 0.0973906i | ||||
\(227\) | −1.66987 | + | 2.89230i | −0.110833 | + | 0.191969i | −0.916107 | − | 0.400935i | \(-0.868685\pi\) |
0.805273 | + | 0.592904i | \(0.202019\pi\) | |||||||
\(228\) | 20.7846i | 1.37649i | ||||||||
\(229\) | −13.3923 | + | 7.73205i | −0.884988 | + | 0.510948i | −0.872300 | − | 0.488971i | \(-0.837372\pi\) |
−0.0126885 | + | 0.999919i | \(0.504039\pi\) | |||||||
\(230\) | −7.46410 | + | 2.00000i | −0.492168 | + | 0.131876i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.8564 | − | 11.8564i | 0.778411 | − | 0.778411i | ||||
\(233\) | 11.4641 | + | 19.8564i | 0.751038 | + | 1.30084i | 0.947320 | + | 0.320289i | \(0.103780\pi\) |
−0.196282 | + | 0.980548i | \(0.562887\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.50000 | − | 0.866025i | −0.0978492 | − | 0.0564933i | ||||
\(236\) | −6.00000 | − | 3.46410i | −0.390567 | − | 0.225494i | ||||
\(237\) | 4.60770i | 0.299302i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 27.9808i | − | 1.80993i | −0.425491 | − | 0.904963i | \(-0.639899\pi\) | ||
0.425491 | − | 0.904963i | \(-0.360101\pi\) | |||||||
\(240\) | 6.92820i | 0.447214i | ||||||||
\(241\) | 3.80385 | + | 2.19615i | 0.245027 | + | 0.141467i | 0.617485 | − | 0.786583i | \(-0.288152\pi\) |
−0.372458 | + | 0.928049i | \(0.621485\pi\) | |||||||
\(242\) | −1.07180 | + | 4.00000i | −0.0688977 | + | 0.257130i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.53590 | + | 4.39230i | 0.162344 | + | 0.281189i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.19615 | − | 8.19615i | −0.140022 | − | 0.522568i | ||||
\(247\) | 33.5885 | − | 19.3923i | 2.13718 | − | 1.23390i | ||||
\(248\) | 4.39230 | + | 16.3923i | 0.278912 | + | 1.04091i | ||||
\(249\) | −7.39230 | + | 12.8038i | −0.468468 | + | 0.811411i | ||||
\(250\) | −1.00000 | + | 1.00000i | −0.0632456 | + | 0.0632456i | ||||
\(251\) | 1.85641 | 0.117175 | 0.0585877 | − | 0.998282i | \(-0.481340\pi\) | ||||
0.0585877 | + | 0.998282i | \(0.481340\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.3923 | 1.28205 | ||||||||
\(254\) | −8.53590 | + | 8.53590i | −0.535590 | + | 0.535590i | ||||
\(255\) | −0.401924 | + | 0.696152i | −0.0251694 | + | 0.0435948i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 5.19615 | − | 3.00000i | 0.324127 | − | 0.187135i | −0.329104 | − | 0.944294i | \(-0.606747\pi\) |
0.653231 | + | 0.757159i | \(0.273413\pi\) | |||||||
\(258\) | 1.26795 | + | 4.73205i | 0.0789391 | + | 0.294605i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 11.1962 | − | 6.46410i | 0.694356 | − | 0.400887i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.46410 | − | 12.9282i | 0.214013 | − | 0.798707i | ||||
\(263\) | −3.92820 | − | 2.26795i | −0.242223 | − | 0.139848i | 0.373975 | − | 0.927439i | \(-0.377995\pi\) |
−0.616198 | + | 0.787591i | \(0.711328\pi\) | |||||||
\(264\) | 4.73205 | − | 17.6603i | 0.291238 | − | 1.08691i | ||||
\(265\) | − | 2.00000i | − | 0.122859i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.3923i | 1.00319i | ||||||||
\(268\) | −3.46410 | + | 6.00000i | −0.211604 | + | 0.366508i | ||||
\(269\) | 10.3923 | + | 6.00000i | 0.633630 | + | 0.365826i | 0.782157 | − | 0.623082i | \(-0.214120\pi\) |
−0.148527 | + | 0.988908i | \(0.547453\pi\) | |||||||
\(270\) | 7.09808 | + | 1.90192i | 0.431975 | + | 0.115747i | ||||
\(271\) | −1.26795 | − | 2.19615i | −0.0770224 | − | 0.133407i | 0.824942 | − | 0.565218i | \(-0.191208\pi\) |
−0.901964 | + | 0.431811i | \(0.857875\pi\) | |||||||
\(272\) | 1.60770 | + | 0.928203i | 0.0974808 | + | 0.0562806i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.535898 | − | 0.143594i | 0.0323748 | − | 0.00867480i | ||||
\(275\) | 3.23205 | − | 1.86603i | 0.194900 | − | 0.112526i | ||||
\(276\) | −18.9282 | −1.13934 | ||||||||
\(277\) | 12.3923 | − | 21.4641i | 0.744581 | − | 1.28965i | −0.205809 | − | 0.978592i | \(-0.565982\pi\) |
0.950390 | − | 0.311061i | \(-0.100684\pi\) | |||||||
\(278\) | −6.92820 | − | 6.92820i | −0.415526 | − | 0.415526i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.92820 | 0.353647 | 0.176823 | − | 0.984243i | \(-0.443418\pi\) | ||||
0.176823 | + | 0.984243i | \(0.443418\pi\) | |||||||
\(282\) | −3.00000 | − | 3.00000i | −0.178647 | − | 0.178647i | ||||
\(283\) | 6.06218 | − | 10.5000i | 0.360359 | − | 0.624160i | −0.627661 | − | 0.778487i | \(-0.715988\pi\) |
0.988020 | + | 0.154327i | \(0.0493208\pi\) | |||||||
\(284\) | 1.07180 | 0.0635994 | ||||||||
\(285\) | −9.00000 | + | 5.19615i | −0.533114 | + | 0.307794i | ||||
\(286\) | −32.9545 | + | 8.83013i | −1.94864 | + | 0.522136i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.39230 | − | 14.5359i | −0.493665 | − | 0.855053i | ||||
\(290\) | 8.09808 | + | 2.16987i | 0.475535 | + | 0.127419i | ||||
\(291\) | −11.0885 | − | 6.40192i | −0.650017 | − | 0.375287i | ||||
\(292\) | −0.928203 | + | 1.60770i | −0.0543190 | + | 0.0940832i | ||||
\(293\) | − | 14.3205i | − | 0.836613i | −0.908306 | − | 0.418307i | \(-0.862624\pi\) | ||
0.908306 | − | 0.418307i | \(-0.137376\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3.46410i | − | 0.201688i | ||||||
\(296\) | −6.92820 | − | 1.85641i | −0.402694 | − | 0.107901i | ||||
\(297\) | −16.7942 | − | 9.69615i | −0.974500 | − | 0.562628i | ||||
\(298\) | 6.19615 | − | 23.1244i | 0.358933 | − | 1.33956i | ||||
\(299\) | 17.6603 | + | 30.5885i | 1.02132 | + | 1.76898i | ||||
\(300\) | −3.00000 | + | 1.73205i | −0.173205 | + | 0.100000i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.75833 | + | 6.56218i | 0.101181 | + | 0.377611i | ||||
\(303\) | −12.8038 | + | 7.39230i | −0.735562 | + | 0.424677i | ||||
\(304\) | 12.0000 | + | 20.7846i | 0.688247 | + | 1.19208i | ||||
\(305\) | −1.26795 | + | 2.19615i | −0.0726026 | + | 0.125751i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.73205 | −0.0988534 | −0.0494267 | − | 0.998778i | \(-0.515739\pi\) | ||||
−0.0494267 | + | 0.998778i | \(0.515739\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −29.7846 | −1.69439 | ||||||||
\(310\) | −6.00000 | + | 6.00000i | −0.340777 | + | 0.340777i | ||||
\(311\) | 9.92820 | − | 17.1962i | 0.562977 | − | 0.975104i | −0.434258 | − | 0.900789i | \(-0.642989\pi\) |
0.997235 | − | 0.0743158i | \(-0.0236773\pi\) | |||||||
\(312\) | 30.5885 | − | 8.19615i | 1.73173 | − | 0.464016i | ||||
\(313\) | −21.1865 | + | 12.2321i | −1.19753 | + | 0.691396i | −0.960005 | − | 0.279984i | \(-0.909671\pi\) |
−0.237529 | + | 0.971380i | \(0.576337\pi\) | |||||||
\(314\) | 7.26795 | + | 27.1244i | 0.410154 | + | 1.53072i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.66025 | + | 4.60770i | 0.149651 | + | 0.259203i | ||||
\(317\) | 8.46410 | + | 14.6603i | 0.475391 | + | 0.823402i | 0.999603 | − | 0.0281863i | \(-0.00897316\pi\) |
−0.524211 | + | 0.851588i | \(0.675640\pi\) | |||||||
\(318\) | 1.26795 | − | 4.73205i | 0.0711031 | − | 0.265360i | ||||
\(319\) | −19.1603 | − | 11.0622i | −1.07277 | − | 0.619363i | ||||
\(320\) | 4.00000 | + | 6.92820i | 0.223607 | + | 0.387298i | ||||
\(321\) | − | 31.8564i | − | 1.77805i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.78461i | 0.154940i | ||||||||
\(324\) | 15.5885 | + | 9.00000i | 0.866025 | + | 0.500000i | ||||
\(325\) | 5.59808 | + | 3.23205i | 0.310525 | + | 0.179282i | ||||
\(326\) | −28.3923 | − | 7.60770i | −1.57250 | − | 0.421351i | ||||
\(327\) | −13.7942 | − | 23.8923i | −0.762823 | − | 1.32125i | ||||
\(328\) | −6.92820 | − | 6.92820i | −0.382546 | − | 0.382546i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 8.83013 | − | 2.36603i | 0.486082 | − | 0.130245i | ||||
\(331\) | 4.85641 | − | 2.80385i | 0.266932 | − | 0.154113i | −0.360560 | − | 0.932736i | \(-0.617415\pi\) |
0.627493 | + | 0.778622i | \(0.284081\pi\) | |||||||
\(332\) | 17.0718i | 0.936937i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.19615 | + | 5.19615i | 0.284321 | + | 0.284321i | ||||
\(335\) | −3.46410 | −0.189264 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | −28.7846 | − | 28.7846i | −1.56568 | − | 1.56568i | ||||
\(339\) | 1.26795 | − | 2.19615i | 0.0688655 | − | 0.119279i | ||||
\(340\) | 0.928203i | 0.0503389i | ||||||||
\(341\) | 19.3923 | − | 11.1962i | 1.05015 | − | 0.606306i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.00000 | + | 4.00000i | 0.215666 | + | 0.215666i | ||||
\(345\) | −4.73205 | − | 8.19615i | −0.254765 | − | 0.441266i | ||||
\(346\) | 27.7583 | + | 7.43782i | 1.49230 | + | 0.399860i | ||||
\(347\) | −12.3397 | − | 7.12436i | −0.662432 | − | 0.382455i | 0.130771 | − | 0.991413i | \(-0.458255\pi\) |
−0.793203 | + | 0.608957i | \(0.791588\pi\) | |||||||
\(348\) | 17.7846 | + | 10.2679i | 0.953355 | + | 0.550420i | ||||
\(349\) | 29.3205i | 1.56949i | 0.619818 | + | 0.784745i | \(0.287206\pi\) | ||||
−0.619818 | + | 0.784745i | \(0.712794\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 33.5885i | − | 1.79282i | ||||||
\(352\) | −5.46410 | − | 20.3923i | −0.291238 | − | 1.08691i | ||||
\(353\) | −11.5981 | − | 6.69615i | −0.617303 | − | 0.356400i | 0.158515 | − | 0.987357i | \(-0.449329\pi\) |
−0.775818 | + | 0.630956i | \(0.782663\pi\) | |||||||
\(354\) | 2.19615 | − | 8.19615i | 0.116724 | − | 0.435621i | ||||
\(355\) | 0.267949 | + | 0.464102i | 0.0142213 | + | 0.0246320i | ||||
\(356\) | 9.46410 | + | 16.3923i | 0.501596 | + | 0.868790i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.26795 | + | 19.6603i | 0.278420 | + | 1.03908i | ||||
\(359\) | 8.07180 | − | 4.66025i | 0.426013 | − | 0.245959i | −0.271634 | − | 0.962401i | \(-0.587564\pi\) |
0.697647 | + | 0.716442i | \(0.254231\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | + | 14.7224i | −0.447368 | + | 0.774865i | ||||
\(362\) | −12.9282 | + | 12.9282i | −0.679491 | + | 0.679491i | ||||
\(363\) | −5.07180 | −0.266200 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.928203 | −0.0485844 | ||||||||
\(366\) | −4.39230 | + | 4.39230i | −0.229589 | + | 0.229589i | ||||
\(367\) | −18.0622 | + | 31.2846i | −0.942838 | + | 1.63304i | −0.182815 | + | 0.983147i | \(0.558521\pi\) |
−0.760023 | + | 0.649896i | \(0.774812\pi\) | |||||||
\(368\) | −18.9282 | + | 10.9282i | −0.986701 | + | 0.569672i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.928203 | − | 3.46410i | −0.0482550 | − | 0.180090i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −18.0000 | + | 10.3923i | −0.933257 | + | 0.538816i | ||||
\(373\) | 12.1962 | + | 21.1244i | 0.631493 | + | 1.09378i | 0.987247 | + | 0.159198i | \(0.0508908\pi\) |
−0.355754 | + | 0.934580i | \(0.615776\pi\) | |||||||
\(374\) | 0.633975 | − | 2.36603i | 0.0327820 | − | 0.122344i | ||||
\(375\) | −1.50000 | − | 0.866025i | −0.0774597 | − | 0.0447214i | ||||
\(376\) | −4.73205 | − | 1.26795i | −0.244037 | − | 0.0653895i | ||||
\(377\) | − | 38.3205i | − | 1.97361i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 26.3923i | − | 1.35568i | −0.735209 | − | 0.677841i | \(-0.762916\pi\) | ||
0.735209 | − | 0.677841i | \(-0.237084\pi\) | |||||||
\(380\) | −6.00000 | + | 10.3923i | −0.307794 | + | 0.533114i | ||||
\(381\) | −12.8038 | − | 7.39230i | −0.655961 | − | 0.378719i | ||||
\(382\) | 4.36603 | + | 1.16987i | 0.223385 | + | 0.0598559i | ||||
\(383\) | −10.2679 | − | 17.7846i | −0.524668 | − | 0.908751i | −0.999587 | − | 0.0287220i | \(-0.990856\pi\) |
0.474920 | − | 0.880029i | \(-0.342477\pi\) | |||||||
\(384\) | 5.07180 | + | 18.9282i | 0.258819 | + | 0.965926i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.46410 | − | 0.928203i | 0.176318 | − | 0.0472443i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.7846 | −0.750575 | ||||||||
\(389\) | −3.42820 | + | 5.93782i | −0.173817 | + | 0.301060i | −0.939751 | − | 0.341859i | \(-0.888943\pi\) |
0.765934 | + | 0.642919i | \(0.222277\pi\) | |||||||
\(390\) | 11.1962 | + | 11.1962i | 0.566939 | + | 0.566939i | ||||
\(391\) | −2.53590 | −0.128246 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.3923 | 0.826882 | ||||||||
\(394\) | 21.3205 | + | 21.3205i | 1.07411 | + | 1.07411i | ||||
\(395\) | −1.33013 | + | 2.30385i | −0.0669260 | + | 0.115919i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.79423 | − | 2.76795i | 0.240615 | − | 0.138919i | −0.374844 | − | 0.927088i | \(-0.622304\pi\) |
0.615460 | + | 0.788168i | \(0.288970\pi\) | |||||||
\(398\) | 4.73205 | − | 1.26795i | 0.237196 | − | 0.0635566i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | 11.9641 | + | 20.7224i | 0.597459 | + | 1.03483i | 0.993195 | + | 0.116465i | \(0.0371562\pi\) |
−0.395736 | + | 0.918364i | \(0.629511\pi\) | |||||||
\(402\) | −8.19615 | − | 2.19615i | −0.408787 | − | 0.109534i | ||||
\(403\) | 33.5885 | + | 19.3923i | 1.67316 | + | 0.966000i | ||||
\(404\) | −8.53590 | + | 14.7846i | −0.424677 | + | 0.735562i | ||||
\(405\) | 9.00000i | 0.447214i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.46410i | 0.469118i | ||||||||
\(408\) | −0.588457 | + | 2.19615i | −0.0291330 | + | 0.108726i | ||||
\(409\) | −27.5885 | − | 15.9282i | −1.36416 | − | 0.787599i | −0.373987 | − | 0.927434i | \(-0.622009\pi\) |
−0.990175 | + | 0.139835i | \(0.955343\pi\) | |||||||
\(410\) | 1.26795 | − | 4.73205i | 0.0626195 | − | 0.233699i | ||||
\(411\) | 0.339746 | + | 0.588457i | 0.0167584 | + | 0.0290265i | ||||
\(412\) | −29.7846 | + | 17.1962i | −1.46738 | + | 0.847194i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.39230 | + | 4.26795i | −0.362874 | + | 0.209505i | ||||
\(416\) | 25.8564 | − | 25.8564i | 1.26771 | − | 1.26771i | ||||
\(417\) | 6.00000 | − | 10.3923i | 0.293821 | − | 0.508913i | ||||
\(418\) | 22.3923 | − | 22.3923i | 1.09524 | − | 1.09524i | ||||
\(419\) | 24.2487 | 1.18463 | 0.592314 | − | 0.805708i | \(-0.298215\pi\) | ||||
0.592314 | + | 0.805708i | \(0.298215\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0000 | 0.926003 | 0.463002 | − | 0.886357i | \(-0.346772\pi\) | ||||
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(422\) | −7.19615 | + | 7.19615i | −0.350303 | + | 0.350303i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.46410 | − | 5.46410i | −0.0711031 | − | 0.265360i | ||||
\(425\) | −0.401924 | + | 0.232051i | −0.0194962 | + | 0.0112561i | ||||
\(426\) | 0.339746 | + | 1.26795i | 0.0164607 | + | 0.0614323i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −18.3923 | − | 31.8564i | −0.889026 | − | 1.53984i | ||||
\(429\) | −20.8923 | − | 36.1865i | −1.00869 | − | 1.74710i | ||||
\(430\) | −0.732051 | + | 2.73205i | −0.0353026 | + | 0.131751i | ||||
\(431\) | 15.2321 | + | 8.79423i | 0.733702 | + | 0.423603i | 0.819775 | − | 0.572686i | \(-0.194098\pi\) |
−0.0860729 | + | 0.996289i | \(0.527432\pi\) | |||||||
\(432\) | 20.7846 | 1.00000 | ||||||||
\(433\) | − | 4.14359i | − | 0.199128i | −0.995031 | − | 0.0995642i | \(-0.968255\pi\) | ||
0.995031 | − | 0.0995642i | \(-0.0317449\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.2679i | 0.492310i | ||||||||
\(436\) | −27.5885 | − | 15.9282i | −1.32125 | − | 0.762823i | ||||
\(437\) | −28.3923 | − | 16.3923i | −1.35819 | − | 0.784150i | ||||
\(438\) | −2.19615 | − | 0.588457i | −0.104936 | − | 0.0281176i | ||||
\(439\) | −7.85641 | − | 13.6077i | −0.374966 | − | 0.649460i | 0.615356 | − | 0.788249i | \(-0.289012\pi\) |
−0.990322 | + | 0.138789i | \(0.955679\pi\) | |||||||
\(440\) | 7.46410 | − | 7.46410i | 0.355837 | − | 0.355837i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.09808 | − | 1.09808i | 0.194926 | − | 0.0522302i | ||||
\(443\) | 22.5167 | − | 13.0000i | 1.06980 | − | 0.617649i | 0.141672 | − | 0.989914i | \(-0.454752\pi\) |
0.928126 | + | 0.372265i | \(0.121419\pi\) | |||||||
\(444\) | − | 8.78461i | − | 0.416899i | ||||||
\(445\) | −4.73205 | + | 8.19615i | −0.224321 | + | 0.388535i | ||||
\(446\) | −10.2679 | − | 10.2679i | −0.486201 | − | 0.486201i | ||||
\(447\) | 29.3205 | 1.38681 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.92820 | −0.0909975 | −0.0454988 | − | 0.998964i | \(-0.514488\pi\) | ||||
−0.0454988 | + | 0.998964i | \(0.514488\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.46410 | + | 11.1962i | −0.304383 | + | 0.527206i | ||||
\(452\) | − | 2.92820i | − | 0.137731i | ||||||
\(453\) | −7.20577 | + | 4.16025i | −0.338557 | + | 0.195466i | ||||
\(454\) | −4.56218 | + | 1.22243i | −0.214114 | + | 0.0573716i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −20.7846 | + | 20.7846i | −0.973329 | + | 0.973329i | ||||
\(457\) | −13.7321 | − | 23.7846i | −0.642358 | − | 1.11260i | −0.984905 | − | 0.173096i | \(-0.944623\pi\) |
0.342547 | − | 0.939501i | \(-0.388711\pi\) | |||||||
\(458\) | −21.1244 | − | 5.66025i | −0.987076 | − | 0.264486i | ||||
\(459\) | 2.08846 | + | 1.20577i | 0.0974808 | + | 0.0562806i | ||||
\(460\) | −9.46410 | − | 5.46410i | −0.441266 | − | 0.254765i | ||||
\(461\) | − | 27.7128i | − | 1.29071i | −0.763881 | − | 0.645357i | \(-0.776709\pi\) | ||
0.763881 | − | 0.645357i | \(-0.223291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.39230i | − | 0.204128i | −0.994778 | − | 0.102064i | \(-0.967455\pi\) | ||
0.994778 | − | 0.102064i | \(-0.0325446\pi\) | |||||||
\(464\) | 23.7128 | 1.10084 | ||||||||
\(465\) | −9.00000 | − | 5.19615i | −0.417365 | − | 0.240966i | ||||
\(466\) | −8.39230 | + | 31.3205i | −0.388766 | + | 1.45089i | ||||
\(467\) | 11.2583 | + | 19.5000i | 0.520973 | + | 0.902352i | 0.999703 | + | 0.0243897i | \(0.00776426\pi\) |
−0.478729 | + | 0.877963i | \(0.658902\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.633975 | − | 2.36603i | −0.0292431 | − | 0.109137i | ||||
\(471\) | −29.7846 | + | 17.1962i | −1.37240 | + | 0.792357i | ||||
\(472\) | −2.53590 | − | 9.46410i | −0.116724 | − | 0.435621i | ||||
\(473\) | 3.73205 | − | 6.46410i | 0.171600 | − | 0.297220i | ||||
\(474\) | −4.60770 | + | 4.60770i | −0.211638 | + | 0.211638i | ||||
\(475\) | −6.00000 | −0.275299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 27.9808 | − | 27.9808i | 1.27981 | − | 1.27981i | ||||
\(479\) | 18.5885 | − | 32.1962i | 0.849328 | − | 1.47108i | −0.0324804 | − | 0.999472i | \(-0.510341\pi\) |
0.881809 | − | 0.471607i | \(-0.156326\pi\) | |||||||
\(480\) | −6.92820 | + | 6.92820i | −0.316228 | + | 0.316228i | ||||
\(481\) | −14.1962 | + | 8.19615i | −0.647289 | + | 0.373712i | ||||
\(482\) | 1.60770 | + | 6.00000i | 0.0732285 | + | 0.273293i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.07180 | + | 2.92820i | −0.230536 | + | 0.133100i | ||||
\(485\) | −3.69615 | − | 6.40192i | −0.167834 | − | 0.290696i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.9282 | + | 14.3923i | 1.12960 | + | 0.652178i | 0.943835 | − | 0.330416i | \(-0.107189\pi\) |
0.185769 | + | 0.982593i | \(0.440522\pi\) | |||||||
\(488\) | −1.85641 | + | 6.92820i | −0.0840356 | + | 0.313625i | ||||
\(489\) | − | 36.0000i | − | 1.62798i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.1244i | 1.54001i | 0.638037 | + | 0.770005i | \(0.279746\pi\) | ||||
−0.638037 | + | 0.770005i | \(0.720254\pi\) | |||||||
\(492\) | 6.00000 | − | 10.3923i | 0.270501 | − | 0.468521i | ||||
\(493\) | 2.38269 | + | 1.37564i | 0.107311 | + | 0.0619559i | ||||
\(494\) | 52.9808 | + | 14.1962i | 2.38372 | + | 0.638715i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.0000 | + | 20.7846i | −0.538816 | + | 0.933257i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −20.1962 | + | 5.41154i | −0.905011 | + | 0.242497i | ||||
\(499\) | 4.83975 | − | 2.79423i | 0.216657 | − | 0.125087i | −0.387745 | − | 0.921767i | \(-0.626746\pi\) |
0.604401 | + | 0.796680i | \(0.293412\pi\) | |||||||
\(500\) | −2.00000 | −0.0894427 | ||||||||
\(501\) | −4.50000 | + | 7.79423i | −0.201045 | + | 0.348220i | ||||
\(502\) | 1.85641 | + | 1.85641i | 0.0828555 | + | 0.0828555i | ||||
\(503\) | 15.5885 | 0.695055 | 0.347527 | − | 0.937670i | \(-0.387021\pi\) | ||||
0.347527 | + | 0.937670i | \(0.387021\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.53590 | −0.379842 | ||||||||
\(506\) | 20.3923 | + | 20.3923i | 0.906549 | + | 0.906549i | ||||
\(507\) | 24.9282 | − | 43.1769i | 1.10710 | − | 1.91755i | ||||
\(508\) | −17.0718 | −0.757438 | ||||||||
\(509\) | −1.60770 | + | 0.928203i | −0.0712598 | + | 0.0411419i | −0.535207 | − | 0.844721i | \(-0.679766\pi\) |
0.463947 | + | 0.885863i | \(0.346433\pi\) | |||||||
\(510\) | −1.09808 | + | 0.294229i | −0.0486236 | + | 0.0130287i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.707107 | + | 0.707107i | ||||
\(513\) | 15.5885 | + | 27.0000i | 0.688247 | + | 1.19208i | ||||
\(514\) | 8.19615 | + | 2.19615i | 0.361517 | + | 0.0968681i | ||||
\(515\) | −14.8923 | − | 8.59808i | −0.656233 | − | 0.378877i | ||||
\(516\) | −3.46410 | + | 6.00000i | −0.152499 | + | 0.264135i | ||||
\(517\) | 6.46410i | 0.284291i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 35.1962i | 1.54494i | ||||||||
\(520\) | 17.6603 | + | 4.73205i | 0.774453 | + | 0.207514i | ||||
\(521\) | −29.7846 | − | 17.1962i | −1.30489 | − | 0.753377i | −0.323649 | − | 0.946177i | \(-0.604910\pi\) |
−0.981238 | + | 0.192800i | \(0.938243\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.1244 | − | 21.0000i | −0.530161 | − | 0.918266i | −0.999381 | − | 0.0351845i | \(-0.988798\pi\) |
0.469220 | − | 0.883081i | \(-0.344535\pi\) | |||||||
\(524\) | 16.3923 | − | 9.46410i | 0.716101 | − | 0.413441i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.66025 | − | 6.19615i | −0.0723905 | − | 0.270165i | ||||
\(527\) | −2.41154 | + | 1.39230i | −0.105048 | + | 0.0606498i | ||||
\(528\) | 22.3923 | − | 12.9282i | 0.974500 | − | 0.562628i | ||||
\(529\) | 3.42820 | − | 5.93782i | 0.149052 | − | 0.258166i | ||||
\(530\) | 2.00000 | − | 2.00000i | 0.0868744 | − | 0.0868744i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.3923 | −0.969918 | ||||||||
\(534\) | −16.3923 | + | 16.3923i | −0.709364 | + | 0.709364i | ||||
\(535\) | 9.19615 | − | 15.9282i | 0.397584 | − | 0.688636i | ||||
\(536\) | −9.46410 | + | 2.53590i | −0.408787 | + | 0.109534i | ||||
\(537\) | −21.5885 | + | 12.4641i | −0.931611 | + | 0.537866i | ||||
\(538\) | 4.39230 | + | 16.3923i | 0.189366 | + | 0.706722i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.19615 | + | 9.00000i | 0.223607 | + | 0.387298i | ||||
\(541\) | 16.8923 | + | 29.2583i | 0.726257 | + | 1.25791i | 0.958455 | + | 0.285245i | \(0.0920750\pi\) |
−0.232198 | + | 0.972669i | \(0.574592\pi\) | |||||||
\(542\) | 0.928203 | − | 3.46410i | 0.0398697 | − | 0.148796i | ||||
\(543\) | −19.3923 | − | 11.1962i | −0.832203 | − | 0.480473i | ||||
\(544\) | 0.679492 | + | 2.53590i | 0.0291330 | + | 0.108726i | ||||
\(545\) | − | 15.9282i | − | 0.682289i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 14.5359i | − | 0.621510i | −0.950490 | − | 0.310755i | \(-0.899418\pi\) | ||
0.950490 | − | 0.310755i | \(-0.100582\pi\) | |||||||
\(548\) | 0.679492 | + | 0.392305i | 0.0290265 | + | 0.0167584i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.09808 | + | 1.36603i | 0.217383 | + | 0.0582475i | ||||
\(551\) | 17.7846 | + | 30.8038i | 0.757650 | + | 1.31229i | ||||
\(552\) | −18.9282 | − | 18.9282i | −0.805638 | − | 0.805638i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 33.8564 | − | 9.07180i | 1.43842 | − | 0.385424i | ||||
\(555\) | 3.80385 | − | 2.19615i | 0.161464 | − | 0.0932215i | ||||
\(556\) | − | 13.8564i | − | 0.587643i | ||||||
\(557\) | −2.92820 | + | 5.07180i | −0.124072 | + | 0.214899i | −0.921370 | − | 0.388687i | \(-0.872929\pi\) |
0.797298 | + | 0.603586i | \(0.206262\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.9282 | 0.546805 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.00000 | 0.126660 | ||||||||
\(562\) | 5.92820 | + | 5.92820i | 0.250066 | + | 0.250066i | ||||
\(563\) | 21.5885 | − | 37.3923i | 0.909845 | − | 1.57590i | 0.0955667 | − | 0.995423i | \(-0.469534\pi\) |
0.814278 | − | 0.580475i | \(-0.197133\pi\) | |||||||
\(564\) | − | 6.00000i | − | 0.252646i | ||||||
\(565\) | 1.26795 | − | 0.732051i | 0.0533430 | − | 0.0307976i | ||||
\(566\) | 16.5622 | − | 4.43782i | 0.696160 | − | 0.186536i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.07180 | + | 1.07180i | 0.0449716 | + | 0.0449716i | ||||
\(569\) | −10.4641 | − | 18.1244i | −0.438678 | − | 0.759813i | 0.558910 | − | 0.829228i | \(-0.311220\pi\) |
−0.997588 | + | 0.0694159i | \(0.977886\pi\) | |||||||
\(570\) | −14.1962 | − | 3.80385i | −0.594611 | − | 0.159326i | ||||
\(571\) | −35.7846 | − | 20.6603i | −1.49754 | − | 0.864605i | −0.497543 | − | 0.867439i | \(-0.665764\pi\) |
−0.999996 | + | 0.00283441i | \(0.999098\pi\) | |||||||
\(572\) | −41.7846 | − | 24.1244i | −1.74710 | − | 1.00869i | ||||
\(573\) | 5.53590i | 0.231265i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 5.46410i | − | 0.227869i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.20577 | + | 0.696152i | 0.0501969 | + | 0.0289812i | 0.524888 | − | 0.851171i | \(-0.324107\pi\) |
−0.474692 | + | 0.880152i | \(0.657440\pi\) | |||||||
\(578\) | 6.14359 | − | 22.9282i | 0.255540 | − | 0.953688i | ||||
\(579\) | 2.19615 | + | 3.80385i | 0.0912690 | + | 0.158083i | ||||
\(580\) | 5.92820 | + | 10.2679i | 0.246155 | + | 0.426353i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.68653 | − | 17.4904i | −0.194263 | − | 0.725000i | ||||
\(583\) | −6.46410 | + | 3.73205i | −0.267716 | + | 0.154566i | ||||
\(584\) | −2.53590 | + | 0.679492i | −0.104936 | + | 0.0281176i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.3205 | − | 14.3205i | 0.591575 | − | 0.591575i | ||||
\(587\) | −27.4641 | −1.13356 | −0.566782 | − | 0.823868i | \(-0.691812\pi\) | ||||
−0.566782 | + | 0.823868i | \(0.691812\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.0000 | −1.48335 | ||||||||
\(590\) | 3.46410 | − | 3.46410i | 0.142615 | − | 0.142615i | ||||
\(591\) | −18.4641 | + | 31.9808i | −0.759512 | + | 1.31551i | ||||
\(592\) | −5.07180 | − | 8.78461i | −0.208450 | − | 0.361045i | ||||
\(593\) | 20.3827 | − | 11.7679i | 0.837017 | − | 0.483252i | −0.0192324 | − | 0.999815i | \(-0.506122\pi\) |
0.856249 | + | 0.516563i | \(0.172789\pi\) | |||||||
\(594\) | −7.09808 | − | 26.4904i | −0.291238 | − | 1.08691i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 29.3205 | − | 16.9282i | 1.20101 | − | 0.693406i | ||||
\(597\) | 3.00000 | + | 5.19615i | 0.122782 | + | 0.212664i | ||||
\(598\) | −12.9282 | + | 48.2487i | −0.528674 | + | 1.97304i | ||||
\(599\) | 12.2321 | + | 7.06218i | 0.499788 | + | 0.288553i | 0.728626 | − | 0.684912i | \(-0.240159\pi\) |
−0.228838 | + | 0.973465i | \(0.573493\pi\) | |||||||
\(600\) | −4.73205 | − | 1.26795i | −0.193185 | − | 0.0517638i | ||||
\(601\) | 26.7846i | 1.09257i | 0.837600 | + | 0.546284i | \(0.183958\pi\) | ||||
−0.837600 | + | 0.546284i | \(0.816042\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.80385 | + | 8.32051i | −0.195466 | + | 0.338557i | ||||
\(605\) | −2.53590 | − | 1.46410i | −0.103099 | − | 0.0595242i | ||||
\(606\) | −20.1962 | − | 5.41154i | −0.820413 | − | 0.219829i | ||||
\(607\) | 9.40192 | + | 16.2846i | 0.381612 | + | 0.660972i | 0.991293 | − | 0.131675i | \(-0.0420356\pi\) |
−0.609681 | + | 0.792647i | \(0.708702\pi\) | |||||||
\(608\) | −8.78461 | + | 32.7846i | −0.356263 | + | 1.32959i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.46410 | + | 0.928203i | −0.140257 | + | 0.0375819i | ||||
\(611\) | −9.69615 | + | 5.59808i | −0.392264 | + | 0.226474i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.00000 | − | 8.66025i | 0.201948 | − | 0.349784i | −0.747208 | − | 0.664590i | \(-0.768606\pi\) |
0.949156 | + | 0.314806i | \(0.101939\pi\) | |||||||
\(614\) | −1.73205 | − | 1.73205i | −0.0698999 | − | 0.0698999i | ||||
\(615\) | 6.00000 | 0.241943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.07180 | −0.365217 | −0.182608 | − | 0.983186i | \(-0.558454\pi\) | ||||
−0.182608 | + | 0.983186i | \(0.558454\pi\) | |||||||
\(618\) | −29.7846 | − | 29.7846i | −1.19811 | − | 1.19811i | ||||
\(619\) | −17.6603 | + | 30.5885i | −0.709826 | + | 1.22945i | 0.255096 | + | 0.966916i | \(0.417893\pi\) |
−0.964922 | + | 0.262538i | \(0.915440\pi\) | |||||||
\(620\) | −12.0000 | −0.481932 | ||||||||
\(621\) | −24.5885 | + | 14.1962i | −0.986701 | + | 0.569672i | ||||
\(622\) | 27.1244 | − | 7.26795i | 1.08759 | − | 0.291418i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 38.7846 | + | 22.3923i | 1.55263 | + | 0.896410i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −33.4186 | − | 8.95448i | −1.33568 | − | 0.357893i | ||||
\(627\) | 33.5885 | + | 19.3923i | 1.34139 | + | 0.774454i | ||||
\(628\) | −19.8564 | + | 34.3923i | −0.792357 | + | 1.37240i | ||||
\(629\) | − | 1.17691i | − | 0.0469267i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.9090i | 1.07123i | 0.844463 | + | 0.535614i | \(0.179920\pi\) | ||||
−0.844463 | + | 0.535614i | \(0.820080\pi\) | |||||||
\(632\) | −1.94744 | + | 7.26795i | −0.0774650 | + | 0.289103i | ||||
\(633\) | −10.7942 | − | 6.23205i | −0.429032 | − | 0.247702i | ||||
\(634\) | −6.19615 | + | 23.1244i | −0.246081 | + | 0.918385i | ||||
\(635\) | −4.26795 | − | 7.39230i | −0.169368 | − | 0.293355i | ||||
\(636\) | 6.00000 | − | 3.46410i | 0.237915 | − | 0.137361i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.09808 | − | 30.2224i | −0.320606 | − | 1.19652i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.92820 | + | 10.9282i | −0.115747 | + | 0.431975i | ||||
\(641\) | 2.46410 | − | 4.26795i | 0.0973262 | − | 0.168574i | −0.813251 | − | 0.581913i | \(-0.802304\pi\) |
0.910577 | + | 0.413339i | \(0.135638\pi\) | |||||||
\(642\) | 31.8564 | − | 31.8564i | 1.25727 | − | 1.25727i | ||||
\(643\) | −31.0526 | −1.22459 | −0.612297 | − | 0.790628i | \(-0.709754\pi\) | ||||
−0.612297 | + | 0.790628i | \(0.709754\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.46410 | −0.136399 | ||||||||
\(646\) | −2.78461 | + | 2.78461i | −0.109559 | + | 0.109559i | ||||
\(647\) | −5.19615 | + | 9.00000i | −0.204282 | + | 0.353827i | −0.949904 | − | 0.312543i | \(-0.898819\pi\) |
0.745622 | + | 0.666369i | \(0.232153\pi\) | |||||||
\(648\) | 6.58846 | + | 24.5885i | 0.258819 | + | 0.965926i | ||||
\(649\) | −11.1962 | + | 6.46410i | −0.439487 | + | 0.253738i | ||||
\(650\) | 2.36603 | + | 8.83013i | 0.0928032 | + | 0.346346i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.7846 | − | 36.0000i | −0.813988 | − | 1.40987i | ||||
\(653\) | −19.1962 | − | 33.2487i | −0.751203 | − | 1.30112i | −0.947240 | − | 0.320526i | \(-0.896140\pi\) |
0.196036 | − | 0.980597i | \(-0.437193\pi\) | |||||||
\(654\) | 10.0981 | − | 37.6865i | 0.394866 | − | 1.47366i | ||||
\(655\) | 8.19615 | + | 4.73205i | 0.320250 | + | 0.184897i | ||||
\(656\) | − | 13.8564i | − | 0.541002i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.8038i | 0.810403i | 0.914227 | + | 0.405201i | \(0.132799\pi\) | ||||
−0.914227 | + | 0.405201i | \(0.867201\pi\) | |||||||
\(660\) | 11.1962 | + | 6.46410i | 0.435810 | + | 0.251615i | ||||
\(661\) | 13.6077 | + | 7.85641i | 0.529278 | + | 0.305579i | 0.740722 | − | 0.671811i | \(-0.234483\pi\) |
−0.211444 | + | 0.977390i | \(0.567817\pi\) | |||||||
\(662\) | 7.66025 | + | 2.05256i | 0.297724 | + | 0.0797750i | ||||
\(663\) | 2.59808 | + | 4.50000i | 0.100901 | + | 0.174766i | ||||
\(664\) | −17.0718 | + | 17.0718i | −0.662514 | + | 0.662514i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.0526 | + | 16.1962i | −1.08620 | + | 0.627118i | ||||
\(668\) | 10.3923i | 0.402090i | ||||||||
\(669\) | 8.89230 | − | 15.4019i | 0.343796 | − | 0.595473i | ||||
\(670\) | −3.46410 | − | 3.46410i | −0.133830 | − | 0.133830i | ||||
\(671\) | 9.46410 | 0.365358 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 49.1769 | 1.89563 | 0.947815 | − | 0.318820i | \(-0.103286\pi\) | ||||
0.947815 | + | 0.318820i | \(0.103286\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.59808 | + | 4.50000i | −0.100000 | + | 0.173205i | ||||
\(676\) | − | 57.5692i | − | 2.21420i | ||||||
\(677\) | −3.99038 | + | 2.30385i | −0.153363 | + | 0.0885441i | −0.574718 | − | 0.818352i | \(-0.694888\pi\) |
0.421355 | + | 0.906896i | \(0.361555\pi\) | |||||||
\(678\) | 3.46410 | − | 0.928203i | 0.133038 | − | 0.0356474i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.928203 | + | 0.928203i | −0.0355950 | + | 0.0355950i | ||||
\(681\) | −2.89230 | − | 5.00962i | −0.110833 | − | 0.191969i | ||||
\(682\) | 30.5885 | + | 8.19615i | 1.17129 | + | 0.313847i | ||||
\(683\) | −23.6603 | − | 13.6603i | −0.905334 | − | 0.522695i | −0.0264074 | − | 0.999651i | \(-0.508407\pi\) |
−0.878927 | + | 0.476956i | \(0.841740\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.392305i | 0.0149892i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 26.7846i | − | 1.02190i | ||||||
\(688\) | 8.00000i | 0.304997i | ||||||||
\(689\) | −11.1962 | − | 6.46410i | −0.426539 | − | 0.246263i | ||||
\(690\) | 3.46410 | − | 12.9282i | 0.131876 | − | 0.492168i | ||||
\(691\) | −23.3205 | − | 40.3923i | −0.887154 | − | 1.53660i | −0.843225 | − | 0.537561i | \(-0.819346\pi\) |
−0.0439291 | − | 0.999035i | \(-0.513988\pi\) | |||||||
\(692\) | 20.3205 | + | 35.1962i | 0.772470 | + | 1.33796i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.21539 | − | 19.4641i | −0.197974 | − | 0.738847i | ||||
\(695\) | 6.00000 | − | 3.46410i | 0.227593 | − | 0.131401i | ||||
\(696\) | 7.51666 | + | 28.0526i | 0.284918 | + | 1.06333i | ||||
\(697\) | 0.803848 | − | 1.39230i | 0.0304479 | − | 0.0527373i | ||||
\(698\) | −29.3205 | + | 29.3205i | −1.10980 | + | 1.10980i | ||||
\(699\) | −39.7128 | −1.50208 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.78461 | 0.142943 | 0.0714714 | − | 0.997443i | \(-0.477231\pi\) | ||||
0.0714714 | + | 0.997443i | \(0.477231\pi\) | |||||||
\(702\) | 33.5885 | − | 33.5885i | 1.26771 | − | 1.26771i | ||||
\(703\) | 7.60770 | − | 13.1769i | 0.286930 | − | 0.496977i | ||||
\(704\) | 14.9282 | − | 25.8564i | 0.562628 | − | 0.974500i | ||||
\(705\) | 2.59808 | − | 1.50000i | 0.0978492 | − | 0.0564933i | ||||
\(706\) | −4.90192 | − | 18.2942i | −0.184486 | − | 0.688512i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.3923 | − | 6.00000i | 0.390567 | − | 0.225494i | ||||
\(709\) | −10.5000 | − | 18.1865i | −0.394336 | − | 0.683010i | 0.598680 | − | 0.800988i | \(-0.295692\pi\) |
−0.993016 | + | 0.117978i | \(0.962359\pi\) | |||||||
\(710\) | −0.196152 | + | 0.732051i | −0.00736147 | + | 0.0274734i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.92820 | + | 25.8564i | −0.259645 | + | 0.969010i | ||||
\(713\) | − | 32.7846i | − | 1.22779i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 24.1244i | − | 0.902200i | ||||||
\(716\) | −14.3923 | + | 24.9282i | −0.537866 | + | 0.931611i | ||||
\(717\) | 41.9711 | + | 24.2321i | 1.56744 | + | 0.904963i | ||||
\(718\) | 12.7321 | + | 3.41154i | 0.475156 | + | 0.127318i | ||||
\(719\) | −22.7321 | − | 39.3731i | −0.847762 | − | 1.46837i | −0.883200 | − | 0.468996i | \(-0.844616\pi\) |
0.0354380 | − | 0.999372i | \(-0.488717\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −23.2224 | + | 6.22243i | −0.864249 | + | 0.231575i | ||||
\(723\) | −6.58846 | + | 3.80385i | −0.245027 | + | 0.141467i | ||||
\(724\) | −25.8564 | −0.960946 | ||||||||
\(725\) | −2.96410 | + | 5.13397i | −0.110084 | + | 0.190671i | ||||
\(726\) | −5.07180 | − | 5.07180i | −0.188232 | − | 0.188232i | ||||
\(727\) | −34.3923 | −1.27554 | −0.637770 | − | 0.770227i | \(-0.720143\pi\) | ||||
−0.637770 | + | 0.770227i | \(0.720143\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −0.928203 | − | 0.928203i | −0.0343543 | − | 0.0343543i | ||||
\(731\) | −0.464102 | + | 0.803848i | −0.0171654 | + | 0.0297314i | ||||
\(732\) | −8.78461 | −0.324689 | ||||||||
\(733\) | 15.9904 | − | 9.23205i | 0.590618 | − | 0.340994i | −0.174724 | − | 0.984618i | \(-0.555903\pi\) |
0.765342 | + | 0.643624i | \(0.222570\pi\) | |||||||
\(734\) | −49.3468 | + | 13.2224i | −1.82142 | + | 0.488049i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29.8564 | − | 8.00000i | −1.10052 | − | 0.294884i | ||||
\(737\) | 6.46410 | + | 11.1962i | 0.238108 | + | 0.412416i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.69615 | − | 3.86603i | −0.246322 | − | 0.142214i | 0.371757 | − | 0.928330i | \(-0.378755\pi\) |
−0.618079 | + | 0.786116i | \(0.712089\pi\) | |||||||
\(740\) | 2.53590 | − | 4.39230i | 0.0932215 | − | 0.161464i | ||||
\(741\) | 67.1769i | 2.46781i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 9.60770i | − | 0.352472i | −0.984348 | − | 0.176236i | \(-0.943608\pi\) | ||
0.984348 | − | 0.176236i | \(-0.0563922\pi\) | |||||||
\(744\) | −28.3923 | − | 7.60770i | −1.04091 | − | 0.278912i | ||||
\(745\) | 14.6603 | + | 8.46410i | 0.537110 | + | 0.310101i | ||||
\(746\) | −8.92820 | + | 33.3205i | −0.326885 | + | 1.21995i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.00000 | − | 1.73205i | 0.109691 | − | 0.0633300i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.633975 | − | 2.36603i | −0.0231495 | − | 0.0863950i | ||||
\(751\) | −4.83975 | + | 2.79423i | −0.176605 | + | 0.101963i | −0.585697 | − | 0.810530i | \(-0.699179\pi\) |
0.409092 | + | 0.912493i | \(0.365846\pi\) | |||||||
\(752\) | −3.46410 | − | 6.00000i | −0.126323 | − | 0.218797i | ||||
\(753\) | −1.60770 | + | 2.78461i | −0.0585877 | + | 0.101477i | ||||
\(754\) | 38.3205 | − | 38.3205i | 1.39555 | − | 1.39555i | ||||
\(755\) | −4.80385 | −0.174830 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.1436 | 0.368675 | 0.184338 | − | 0.982863i | \(-0.440986\pi\) | ||||
0.184338 | + | 0.982863i | \(0.440986\pi\) | |||||||
\(758\) | 26.3923 | − | 26.3923i | 0.958612 | − | 0.958612i | ||||
\(759\) | −17.6603 | + | 30.5885i | −0.641027 | + | 1.11029i | ||||
\(760\) | −16.3923 | + | 4.39230i | −0.594611 | + | 0.159326i | ||||
\(761\) | 5.41154 | − | 3.12436i | 0.196168 | − | 0.113258i | −0.398699 | − | 0.917082i | \(-0.630538\pi\) |
0.594867 | + | 0.803824i | \(0.297205\pi\) | |||||||
\(762\) | −5.41154 | − | 20.1962i | −0.196040 | − | 0.731629i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.19615 | + | 5.53590i | 0.115633 | + | 0.200282i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.51666 | − | 28.0526i | 0.271588 | − | 1.01358i | ||||
\(767\) | −19.3923 | − | 11.1962i | −0.700216 | − | 0.404270i | ||||
\(768\) | −13.8564 | + | 24.0000i | −0.500000 | + | 0.866025i | ||||
\(769\) | 18.0000i | 0.649097i | 0.945869 | + | 0.324548i | \(0.105212\pi\) | ||||
−0.945869 | + | 0.324548i | \(0.894788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.3923i | 0.374270i | ||||||||
\(772\) | 4.39230 | + | 2.53590i | 0.158083 | + | 0.0912690i | ||||
\(773\) | 10.7942 | + | 6.23205i | 0.388241 | + | 0.224151i | 0.681398 | − | 0.731913i | \(-0.261372\pi\) |
−0.293156 | + | 0.956064i | \(0.594706\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.00000 | − | 5.19615i | −0.107763 | − | 0.186651i | ||||
\(776\) | −14.7846 | − | 14.7846i | −0.530737 | − | 0.530737i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.36603 | + | 2.50962i | −0.335788 | + | 0.0899742i | ||||
\(779\) | 18.0000 | − | 10.3923i | 0.644917 | − | 0.372343i | ||||
\(780\) | 22.3923i | 0.801773i | ||||||||
\(781\) | 1.00000 | − | 1.73205i | 0.0357828 | − | 0.0619777i | ||||
\(782\) | −2.53590 | − | 2.53590i | −0.0906835 | − | 0.0906835i | ||||
\(783\) | 30.8038 | 1.10084 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.8564 | −0.708706 | ||||||||
\(786\) | 16.3923 | + | 16.3923i | 0.584694 | + | 0.584694i | ||||
\(787\) | −7.66987 | + | 13.2846i | −0.273401 | + | 0.473545i | −0.969731 | − | 0.244177i | \(-0.921482\pi\) |
0.696329 | + | 0.717723i | \(0.254815\pi\) | |||||||
\(788\) | 42.6410i | 1.51902i | ||||||||
\(789\) | 6.80385 | − | 3.92820i | 0.242223 | − | 0.139848i | ||||
\(790\) | −3.63397 | + | 0.973721i | −0.129291 | + | 0.0346434i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.19615 | + | 14.1962i | 0.291054 | + | 0.504120i | ||||
\(794\) | 7.56218 | + | 2.02628i | 0.268372 | + | 0.0719100i | ||||
\(795\) | 3.00000 | + | 1.73205i | 0.106399 | + | 0.0614295i | ||||
\(796\) | 6.00000 | + | 3.46410i | 0.212664 | + | 0.122782i | ||||
\(797\) | 40.1769i | 1.42314i | 0.702616 | + | 0.711570i | \(0.252015\pi\) | ||||
−0.702616 | + | 0.711570i | \(0.747985\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 0.803848i | − | 0.0284381i | ||||||
\(800\) | −5.46410 | + | 1.46410i | −0.193185 | + | 0.0517638i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.75833 | + | 32.6865i | −0.309267 | + | 1.15420i | ||||
\(803\) | 1.73205 | + | 3.00000i | 0.0611227 | + | 0.105868i | ||||
\(804\) | −6.00000 | − | 10.3923i | −0.211604 | − | 0.366508i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.1962 | + | 52.9808i | 0.500038 | + | 1.86617i | ||||
\(807\) | −18.0000 | + | 10.3923i | −0.633630 | + | 0.365826i | ||||
\(808\) | −23.3205 | + | 6.24871i | −0.820413 | + | 0.219829i | ||||
\(809\) | 2.96410 | − | 5.13397i | 0.104212 | − | 0.180501i | −0.809204 | − | 0.587528i | \(-0.800101\pi\) |
0.913416 | + | 0.407027i | \(0.133435\pi\) | |||||||
\(810\) | −9.00000 | + | 9.00000i | −0.316228 | + | 0.316228i | ||||
\(811\) | 42.9282 | 1.50741 | 0.753707 | − | 0.657211i | \(-0.228264\pi\) | ||||
0.753707 | + | 0.657211i | \(0.228264\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.39230 | 0.154045 | ||||||||
\(814\) | −9.46410 | + | 9.46410i | −0.331717 | + | 0.331717i | ||||
\(815\) | 10.3923 | − | 18.0000i | 0.364027 | − | 0.630512i | ||||
\(816\) | −2.78461 | + | 1.60770i | −0.0974808 | + | 0.0562806i | ||||
\(817\) | −10.3923 | + | 6.00000i | −0.363581 | + | 0.209913i | ||||
\(818\) | −11.6603 | − | 43.5167i | −0.407691 | − | 1.52152i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | − | 3.46410i | 0.209529 | − | 0.120972i | ||||
\(821\) | 6.89230 | + | 11.9378i | 0.240543 | + | 0.416633i | 0.960869 | − | 0.277003i | \(-0.0893411\pi\) |
−0.720326 | + | 0.693636i | \(0.756008\pi\) | |||||||
\(822\) | −0.248711 | + | 0.928203i | −0.00867480 | + | 0.0323748i | ||||
\(823\) | 21.5885 | + | 12.4641i | 0.752526 | + | 0.434471i | 0.826606 | − | 0.562781i | \(-0.190269\pi\) |
−0.0740797 | + | 0.997252i | \(0.523602\pi\) | |||||||
\(824\) | −46.9808 | − | 12.5885i | −1.63665 | − | 0.438540i | ||||
\(825\) | 6.46410i | 0.225051i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 41.8564i | − | 1.45549i | −0.685848 | − | 0.727745i | \(-0.740568\pi\) | ||
0.685848 | − | 0.727745i | \(-0.259432\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.7846 | + | 24.1244i | 1.45124 | + | 0.837874i | 0.998552 | − | 0.0537957i | \(-0.0171320\pi\) |
0.452688 | + | 0.891669i | \(0.350465\pi\) | |||||||
\(830\) | −11.6603 | − | 3.12436i | −0.404733 | − | 0.108448i | ||||
\(831\) | 21.4641 | + | 37.1769i | 0.744581 | + | 1.28965i | ||||
\(832\) | 51.7128 | 1.79282 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.3923 | − | 4.39230i | 0.567619 | − | 0.152093i | ||||
\(835\) | −4.50000 | + | 2.59808i | −0.155729 | + | 0.0899101i | ||||
\(836\) | 44.7846 | 1.54891 | ||||||||
\(837\) | −15.5885 | + | 27.0000i | −0.538816 | + | 0.933257i | ||||
\(838\) | 24.2487 | + | 24.2487i | 0.837658 | + | 0.837658i | ||||
\(839\) | −16.3923 | −0.565925 | −0.282963 | − | 0.959131i | \(-0.591317\pi\) | ||||
−0.282963 | + | 0.959131i | \(0.591317\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.14359 | 0.211848 | ||||||||
\(842\) | 19.0000 | + | 19.0000i | 0.654783 | + | 0.654783i | ||||
\(843\) | −5.13397 | + | 8.89230i | −0.176823 | + | 0.306267i | ||||
\(844\) | −14.3923 | −0.495404 | ||||||||
\(845\) | 24.9282 | − | 14.3923i | 0.857556 | − | 0.495110i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.00000 | − | 6.92820i | 0.137361 | − | 0.237915i | ||||
\(849\) | 10.5000 | + | 18.1865i | 0.360359 | + | 0.624160i | ||||
\(850\) | −0.633975 | − | 0.169873i | −0.0217451 | − | 0.00582660i | ||||
\(851\) | 12.0000 | + | 6.92820i | 0.411355 | + | 0.237496i | ||||
\(852\) | −0.928203 | + | 1.60770i | −0.0317997 | + | 0.0550787i | ||||
\(853\) | 38.7846i | 1.32796i | 0.747750 | + | 0.663980i | \(0.231134\pi\) | ||||
−0.747750 | + | 0.663980i | \(0.768866\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.4641 | − | 50.2487i | 0.460194 | − | 1.71747i | ||||
\(857\) | −1.98076 | − | 1.14359i | −0.0676615 | − | 0.0390644i | 0.465788 | − | 0.884897i | \(-0.345771\pi\) |
−0.533449 | + | 0.845832i | \(0.679104\pi\) | |||||||
\(858\) | 15.2942 | − | 57.0788i | 0.522136 | − | 1.94864i | ||||
\(859\) | 7.85641 | + | 13.6077i | 0.268057 | + | 0.464289i | 0.968360 | − | 0.249557i | \(-0.0802851\pi\) |
−0.700303 | + | 0.713846i | \(0.746952\pi\) | |||||||
\(860\) | −3.46410 | + | 2.00000i | −0.118125 | + | 0.0681994i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.43782 | + | 24.0263i | 0.219273 | + | 0.818338i | ||||
\(863\) | 10.5167 | − | 6.07180i | 0.357991 | − | 0.206686i | −0.310208 | − | 0.950669i | \(-0.600399\pi\) |
0.668199 | + | 0.743982i | \(0.267065\pi\) | |||||||
\(864\) | 20.7846 | + | 20.7846i | 0.707107 | + | 0.707107i | ||||
\(865\) | −10.1603 | + | 17.5981i | −0.345459 | + | 0.598353i | ||||
\(866\) | 4.14359 | − | 4.14359i | 0.140805 | − | 0.140805i | ||||
\(867\) | 29.0718 | 0.987330 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.92820 | 0.336791 | ||||||||
\(870\) | −10.2679 | + | 10.2679i | −0.348116 | + | 0.348116i | ||||
\(871\) | −11.1962 | + | 19.3923i | −0.379367 | + | 0.657083i | ||||
\(872\) | −11.6603 | − | 43.5167i | −0.394866 | − | 1.47366i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12.0000 | − | 44.7846i | −0.405906 | − | 1.51486i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.60770 | − | 2.78461i | −0.0543190 | − | 0.0940832i | ||||
\(877\) | −1.19615 | − | 2.07180i | −0.0403912 | − | 0.0699596i | 0.845123 | − | 0.534572i | \(-0.179527\pi\) |
−0.885514 | + | 0.464612i | \(0.846194\pi\) | |||||||
\(878\) | 5.75129 | − | 21.4641i | 0.194097 | − | 0.724378i | ||||
\(879\) | 21.4808 | + | 12.4019i | 0.724528 | + | 0.418307i | ||||
\(880\) | 14.9282 | 0.503230 | ||||||||
\(881\) | − | 42.9282i | − | 1.44629i | −0.690697 | − | 0.723144i | \(-0.742696\pi\) | ||
0.690697 | − | 0.723144i | \(-0.257304\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.3923i | 1.49392i | 0.664869 | + | 0.746960i | \(0.268487\pi\) | ||||
−0.664869 | + | 0.746960i | \(0.731513\pi\) | |||||||
\(884\) | 5.19615 | + | 3.00000i | 0.174766 | + | 0.100901i | ||||
\(885\) | 5.19615 | + | 3.00000i | 0.174667 | + | 0.100844i | ||||
\(886\) | 35.5167 | + | 9.51666i | 1.19321 | + | 0.319718i | ||||
\(887\) | 7.73205 | + | 13.3923i | 0.259617 | + | 0.449670i | 0.966139 | − | 0.258021i | \(-0.0830704\pi\) |
−0.706522 | + | 0.707691i | \(0.749737\pi\) | |||||||
\(888\) | 8.78461 | − | 8.78461i | 0.294792 | − | 0.294792i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.9282 | + | 3.46410i | −0.433354 | + | 0.116117i | ||||
\(891\) | 29.0885 | − | 16.7942i | 0.974500 | − | 0.562628i | ||||
\(892\) | − | 20.5359i | − | 0.687593i | ||||||
\(893\) | 5.19615 | − | 9.00000i | 0.173883 | − | 0.301174i | ||||
\(894\) | 29.3205 | + | 29.3205i | 0.980624 | + | 0.980624i | ||||
\(895\) | −14.3923 | −0.481082 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −61.1769 | −2.04264 | ||||||||
\(898\) | −1.92820 | − | 1.92820i | −0.0643450 | − | 0.0643450i | ||||
\(899\) | −17.7846 | + | 30.8038i | −0.593150 | + | 1.02737i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.803848 | − | 0.464102i | 0.0267800 | − | 0.0154615i | ||||
\(902\) | −17.6603 | + | 4.73205i | −0.588022 | + | 0.157560i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.92820 | − | 2.92820i | 0.0973906 | − | 0.0973906i | ||||
\(905\) | −6.46410 | − | 11.1962i | −0.214874 | − | 0.372173i | ||||
\(906\) | −11.3660 | − | 3.04552i | −0.377611 | − | 0.101181i | ||||
\(907\) | −10.0526 | − | 5.80385i | −0.333790 | − | 0.192714i | 0.323733 | − | 0.946149i | \(-0.395062\pi\) |
−0.657522 | + | 0.753435i | \(0.728395\pi\) | |||||||
\(908\) | −5.78461 | − | 3.33975i | −0.191969 | − | 0.110833i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 28.2487i | − | 0.935922i | −0.883749 | − | 0.467961i | \(-0.844989\pi\) | ||
0.883749 | − | 0.467961i | \(-0.155011\pi\) | |||||||
\(912\) | −41.5692 | −1.37649 | ||||||||
\(913\) | 27.5885 | + | 15.9282i | 0.913045 | + | 0.527147i | ||||
\(914\) | 10.0526 | − | 37.5167i | 0.332509 | − | 1.24094i | ||||
\(915\) | −2.19615 | − | 3.80385i | −0.0726026 | − | 0.125751i | ||||
\(916\) | −15.4641 | − | 26.7846i | −0.510948 | − | 0.884988i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.882686 | + | 3.29423i | 0.0291330 | + | 0.108726i | ||||
\(919\) | 32.5526 | − | 18.7942i | 1.07381 | − | 0.619964i | 0.144590 | − | 0.989492i | \(-0.453814\pi\) |
0.929220 | + | 0.369527i | \(0.120480\pi\) | |||||||
\(920\) | −4.00000 | − | 14.9282i | −0.131876 | − | 0.492168i | ||||
\(921\) | 1.50000 | − | 2.59808i | 0.0494267 | − | 0.0856095i | ||||
\(922\) | 27.7128 | − | 27.7128i | 0.912673 | − | 0.912673i | ||||
\(923\) | 3.46410 | 0.114022 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.53590 | 0.0833798 | ||||||||
\(926\) | 4.39230 | − | 4.39230i | 0.144340 | − | 0.144340i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 23.7128 | + | 23.7128i | 0.778411 | + | 0.778411i | ||||
\(929\) | 36.8038 | − | 21.2487i | 1.20750 | − | 0.697148i | 0.245284 | − | 0.969451i | \(-0.421119\pi\) |
0.962211 | + | 0.272304i | \(0.0877855\pi\) | |||||||
\(930\) | −3.80385 | − | 14.1962i | −0.124733 | − | 0.465510i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −39.7128 | + | 22.9282i | −1.30084 | + | 0.751038i | ||||
\(933\) | 17.1962 | + | 29.7846i | 0.562977 | + | 0.975104i | ||||
\(934\) | −8.24167 | + | 30.7583i | −0.269676 | + | 1.00644i | ||||
\(935\) | 1.50000 | + | 0.866025i | 0.0490552 | + | 0.0283221i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 4.60770i | − | 0.150527i | −0.997164 | − | 0.0752634i | \(-0.976020\pi\) | ||
0.997164 | − | 0.0752634i | \(-0.0239798\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 42.3731i | − | 1.38279i | ||||||
\(940\) | 1.73205 | − | 3.00000i | 0.0564933 | − | 0.0978492i | ||||
\(941\) | 44.1962 | + | 25.5167i | 1.44075 | + | 0.831819i | 0.997900 | − | 0.0647746i | \(-0.0206329\pi\) |
0.442853 | + | 0.896594i | \(0.353966\pi\) | |||||||
\(942\) | −46.9808 | − | 12.5885i | −1.53072 | − | 0.410154i | ||||
\(943\) | 9.46410 | + | 16.3923i | 0.308194 | + | 0.533807i | ||||
\(944\) | 6.92820 | − | 12.0000i | 0.225494 | − | 0.390567i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.1962 | − | 2.73205i | 0.331506 | − | 0.0888266i | ||||
\(947\) | 16.2679 | − | 9.39230i | 0.528637 | − | 0.305209i | −0.211824 | − | 0.977308i | \(-0.567940\pi\) |
0.740461 | + | 0.672099i | \(0.234607\pi\) | |||||||
\(948\) | −9.21539 | −0.299302 | ||||||||
\(949\) | −3.00000 | + | 5.19615i | −0.0973841 | + | 0.168674i | ||||
\(950\) | −6.00000 | − | 6.00000i | −0.194666 | − | 0.194666i | ||||
\(951\) | −29.3205 | −0.950783 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.3205 | −0.431494 | −0.215747 | − | 0.976449i | \(-0.569219\pi\) | ||||
−0.215747 | + | 0.976449i | \(0.569219\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.59808 | + | 2.76795i | −0.0517125 | + | 0.0895687i | ||||
\(956\) | 55.9615 | 1.80993 | ||||||||
\(957\) | 33.1865 | − | 19.1603i | 1.07277 | − | 0.619363i | ||||
\(958\) | 50.7846 | − | 13.6077i | 1.64078 | − | 0.439645i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −13.8564 | −0.447214 | ||||||||
\(961\) | −2.50000 | − | 4.33013i | −0.0806452 | − | 0.139682i | ||||
\(962\) | −22.3923 | − | 6.00000i | −0.721957 | − | 0.193448i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.39230 | + | 7.60770i | −0.141467 | + | 0.245027i | ||||
\(965\) | 2.53590i | 0.0816335i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.1769i | 1.00258i | 0.865279 | + | 0.501291i | \(0.167141\pi\) | ||||
−0.865279 | + | 0.501291i | \(0.832859\pi\) | |||||||
\(968\) | −8.00000 | − | 2.14359i | −0.257130 | − | 0.0688977i | ||||
\(969\) | −4.17691 | − | 2.41154i | −0.134182 | − | 0.0774699i | ||||
\(970\) | 2.70577 | − | 10.0981i | 0.0868771 | − | 0.324230i | ||||
\(971\) | 13.3923 | + | 23.1962i | 0.429780 | + | 0.744400i | 0.996853 | − | 0.0792670i | \(-0.0252580\pi\) |
−0.567074 | + | 0.823667i | \(0.691925\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 10.5359 | + | 39.3205i | 0.337592 | + | 1.25991i | ||||
\(975\) | −9.69615 | + | 5.59808i | −0.310525 | + | 0.179282i | ||||
\(976\) | −8.78461 | + | 5.07180i | −0.281189 | + | 0.162344i | ||||
\(977\) | −22.1244 | + | 38.3205i | −0.707821 | + | 1.22598i | 0.257843 | + | 0.966187i | \(0.416988\pi\) |
−0.965664 | + | 0.259795i | \(0.916345\pi\) | |||||||
\(978\) | 36.0000 | − | 36.0000i | 1.15115 | − | 1.15115i | ||||
\(979\) | 35.3205 | 1.12885 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −34.1244 | + | 34.1244i | −1.08895 | + | 1.08895i | ||||
\(983\) | −1.79423 | + | 3.10770i | −0.0572270 | + | 0.0991201i | −0.893220 | − | 0.449621i | \(-0.851559\pi\) |
0.835993 | + | 0.548741i | \(0.184893\pi\) | |||||||
\(984\) | 16.3923 | − | 4.39230i | 0.522568 | − | 0.140022i | ||||
\(985\) | −18.4641 | + | 10.6603i | −0.588315 | + | 0.339664i | ||||
\(986\) | 1.00704 | + | 3.75833i | 0.0320707 | + | 0.119690i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 38.7846 | + | 67.1769i | 1.23390 | + | 2.13718i | ||||
\(989\) | −5.46410 | − | 9.46410i | −0.173748 | − | 0.300941i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.1436 | − | 7.58846i | −0.417520 | − | 0.241055i | 0.276496 | − | 0.961015i | \(-0.410827\pi\) |
−0.694016 | + | 0.719960i | \(0.744160\pi\) | |||||||
\(992\) | −32.7846 | + | 8.78461i | −1.04091 | + | 0.278912i | ||||
\(993\) | 9.71281i | 0.308227i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.46410i | 0.109819i | ||||||||
\(996\) | −25.6077 | − | 14.7846i | −0.811411 | − | 0.468468i | ||||
\(997\) | −10.7942 | − | 6.23205i | −0.341857 | − | 0.197371i | 0.319236 | − | 0.947675i | \(-0.396574\pi\) |
−0.661093 | + | 0.750304i | \(0.729907\pi\) | |||||||
\(998\) | 7.63397 | + | 2.04552i | 0.241649 | + | 0.0647497i | ||||
\(999\) | −6.58846 | − | 11.4115i | −0.208450 | − | 0.361045i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))