Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [104,2,Mod(53,104)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(104, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("104.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 104 = 2^{3} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 104.b (of order \(2\), degree \(1\), 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: | \(0.830444181021\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 53.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 104.53 |
Dual form | 104.2.b.b.53.1 |
$q$-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 \(\left(\mathbb{Z}/104\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(53\) | \(79\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.366025 | + | 1.36603i | −0.258819 | + | 0.965926i | ||||
\(3\) | − | 2.00000i | − | 1.15470i | −0.816497 | − | 0.577350i | \(-0.804087\pi\) | ||
0.816497 | − | 0.577350i | \(-0.195913\pi\) | |||||||
\(4\) | −1.73205 | − | 1.00000i | −0.866025 | − | 0.500000i | ||||
\(5\) | − | 3.46410i | − | 1.54919i | −0.632456 | − | 0.774597i | \(-0.717953\pi\) | ||
0.632456 | − | 0.774597i | \(-0.282047\pi\) | |||||||
\(6\) | 2.73205 | + | 0.732051i | 1.11536 | + | 0.298858i | ||||
\(7\) | −1.26795 | −0.479240 | −0.239620 | − | 0.970867i | \(-0.577023\pi\) | ||||
−0.239620 | + | 0.970867i | \(0.577023\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 4.73205 | + | 1.26795i | 1.49641 | + | 0.400961i | ||||
\(11\) | 4.73205i | 1.42677i | 0.700774 | + | 0.713384i | \(0.252838\pi\) | ||||
−0.700774 | + | 0.713384i | \(0.747162\pi\) | |||||||
\(12\) | −2.00000 | + | 3.46410i | −0.577350 | + | 1.00000i | ||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | 0.464102 | − | 1.73205i | 0.124036 | − | 0.462910i | ||||
\(15\) | −6.92820 | −1.78885 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 5.46410 | 1.32524 | 0.662620 | − | 0.748956i | \(-0.269445\pi\) | ||||
0.662620 | + | 0.748956i | \(0.269445\pi\) | |||||||
\(18\) | 0.366025 | − | 1.36603i | 0.0862730 | − | 0.321975i | ||||
\(19\) | − | 0.732051i | − | 0.167944i | −0.996468 | − | 0.0839720i | \(-0.973239\pi\) | ||
0.996468 | − | 0.0839720i | \(-0.0267606\pi\) | |||||||
\(20\) | −3.46410 | + | 6.00000i | −0.774597 | + | 1.34164i | ||||
\(21\) | 2.53590i | 0.553378i | ||||||||
\(22\) | −6.46410 | − | 1.73205i | −1.37815 | − | 0.369274i | ||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | −4.00000 | − | 4.00000i | −0.816497 | − | 0.816497i | ||||
\(25\) | −7.00000 | −1.40000 | ||||||||
\(26\) | 1.36603 | + | 0.366025i | 0.267900 | + | 0.0717835i | ||||
\(27\) | − | 4.00000i | − | 0.769800i | ||||||
\(28\) | 2.19615 | + | 1.26795i | 0.415034 | + | 0.239620i | ||||
\(29\) | − | 2.00000i | − | 0.371391i | −0.982607 | − | 0.185695i | \(-0.940546\pi\) | ||
0.982607 | − | 0.185695i | \(-0.0594537\pi\) | |||||||
\(30\) | 2.53590 | − | 9.46410i | 0.462990 | − | 1.72790i | ||||
\(31\) | −6.73205 | −1.20911 | −0.604556 | − | 0.796563i | \(-0.706649\pi\) | ||||
−0.604556 | + | 0.796563i | \(0.706649\pi\) | |||||||
\(32\) | −5.46410 | + | 1.46410i | −0.965926 | + | 0.258819i | ||||
\(33\) | 9.46410 | 1.64749 | ||||||||
\(34\) | −2.00000 | + | 7.46410i | −0.342997 | + | 1.28008i | ||||
\(35\) | 4.39230i | 0.742435i | ||||||||
\(36\) | 1.73205 | + | 1.00000i | 0.288675 | + | 0.166667i | ||||
\(37\) | 8.92820i | 1.46779i | 0.679264 | + | 0.733894i | \(0.262299\pi\) | ||||
−0.679264 | + | 0.733894i | \(0.737701\pi\) | |||||||
\(38\) | 1.00000 | + | 0.267949i | 0.162221 | + | 0.0434671i | ||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | −6.92820 | − | 6.92820i | −1.09545 | − | 1.09545i | ||||
\(41\) | 8.92820 | 1.39435 | 0.697176 | − | 0.716900i | \(-0.254440\pi\) | ||||
0.697176 | + | 0.716900i | \(0.254440\pi\) | |||||||
\(42\) | −3.46410 | − | 0.928203i | −0.534522 | − | 0.143225i | ||||
\(43\) | 0.535898i | 0.0817237i | 0.999165 | + | 0.0408619i | \(0.0130104\pi\) | ||||
−0.999165 | + | 0.0408619i | \(0.986990\pi\) | |||||||
\(44\) | 4.73205 | − | 8.19615i | 0.713384 | − | 1.23562i | ||||
\(45\) | 3.46410i | 0.516398i | ||||||||
\(46\) | −1.46410 | + | 5.46410i | −0.215870 | + | 0.805638i | ||||
\(47\) | 6.73205 | 0.981971 | 0.490985 | − | 0.871168i | \(-0.336637\pi\) | ||||
0.490985 | + | 0.871168i | \(0.336637\pi\) | |||||||
\(48\) | 6.92820 | − | 4.00000i | 1.00000 | − | 0.577350i | ||||
\(49\) | −5.39230 | −0.770329 | ||||||||
\(50\) | 2.56218 | − | 9.56218i | 0.362347 | − | 1.35230i | ||||
\(51\) | − | 10.9282i | − | 1.53025i | ||||||
\(52\) | −1.00000 | + | 1.73205i | −0.138675 | + | 0.240192i | ||||
\(53\) | 2.92820i | 0.402220i | 0.979569 | + | 0.201110i | \(0.0644548\pi\) | ||||
−0.979569 | + | 0.201110i | \(0.935545\pi\) | |||||||
\(54\) | 5.46410 | + | 1.46410i | 0.743570 | + | 0.199239i | ||||
\(55\) | 16.3923 | 2.21034 | ||||||||
\(56\) | −2.53590 | + | 2.53590i | −0.338874 | + | 0.338874i | ||||
\(57\) | −1.46410 | −0.193925 | ||||||||
\(58\) | 2.73205 | + | 0.732051i | 0.358736 | + | 0.0961230i | ||||
\(59\) | 10.1962i | 1.32743i | 0.747987 | + | 0.663713i | \(0.231020\pi\) | ||||
−0.747987 | + | 0.663713i | \(0.768980\pi\) | |||||||
\(60\) | 12.0000 | + | 6.92820i | 1.54919 | + | 0.894427i | ||||
\(61\) | − | 2.92820i | − | 0.374918i | −0.982272 | − | 0.187459i | \(-0.939975\pi\) | ||
0.982272 | − | 0.187459i | \(-0.0600252\pi\) | |||||||
\(62\) | 2.46410 | − | 9.19615i | 0.312941 | − | 1.16791i | ||||
\(63\) | 1.26795 | 0.159747 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | −3.46410 | −0.429669 | ||||||||
\(66\) | −3.46410 | + | 12.9282i | −0.426401 | + | 1.59135i | ||||
\(67\) | − | 0.732051i | − | 0.0894342i | −0.999000 | − | 0.0447171i | \(-0.985761\pi\) | ||
0.999000 | − | 0.0447171i | \(-0.0142386\pi\) | |||||||
\(68\) | −9.46410 | − | 5.46410i | −1.14769 | − | 0.662620i | ||||
\(69\) | − | 8.00000i | − | 0.963087i | ||||||
\(70\) | −6.00000 | − | 1.60770i | −0.717137 | − | 0.192156i | ||||
\(71\) | −8.19615 | −0.972704 | −0.486352 | − | 0.873763i | \(-0.661673\pi\) | ||||
−0.486352 | + | 0.873763i | \(0.661673\pi\) | |||||||
\(72\) | −2.00000 | + | 2.00000i | −0.235702 | + | 0.235702i | ||||
\(73\) | −7.46410 | −0.873607 | −0.436804 | − | 0.899557i | \(-0.643889\pi\) | ||||
−0.436804 | + | 0.899557i | \(0.643889\pi\) | |||||||
\(74\) | −12.1962 | − | 3.26795i | −1.41777 | − | 0.379891i | ||||
\(75\) | 14.0000i | 1.61658i | ||||||||
\(76\) | −0.732051 | + | 1.26795i | −0.0839720 | + | 0.145444i | ||||
\(77\) | − | 6.00000i | − | 0.683763i | ||||||
\(78\) | 0.732051 | − | 2.73205i | 0.0828884 | − | 0.309344i | ||||
\(79\) | 5.46410 | 0.614759 | 0.307380 | − | 0.951587i | \(-0.400548\pi\) | ||||
0.307380 | + | 0.951587i | \(0.400548\pi\) | |||||||
\(80\) | 12.0000 | − | 6.92820i | 1.34164 | − | 0.774597i | ||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | −3.26795 | + | 12.1962i | −0.360885 | + | 1.34684i | ||||
\(83\) | − | 3.26795i | − | 0.358704i | −0.983785 | − | 0.179352i | \(-0.942600\pi\) | ||
0.983785 | − | 0.179352i | \(-0.0574001\pi\) | |||||||
\(84\) | 2.53590 | − | 4.39230i | 0.276689 | − | 0.479240i | ||||
\(85\) | − | 18.9282i | − | 2.05305i | ||||||
\(86\) | −0.732051 | − | 0.196152i | −0.0789391 | − | 0.0211517i | ||||
\(87\) | −4.00000 | −0.428845 | ||||||||
\(88\) | 9.46410 | + | 9.46410i | 1.00888 | + | 1.00888i | ||||
\(89\) | −17.3205 | −1.83597 | −0.917985 | − | 0.396615i | \(-0.870185\pi\) | ||||
−0.917985 | + | 0.396615i | \(0.870185\pi\) | |||||||
\(90\) | −4.73205 | − | 1.26795i | −0.498802 | − | 0.133654i | ||||
\(91\) | 1.26795i | 0.132917i | ||||||||
\(92\) | −6.92820 | − | 4.00000i | −0.722315 | − | 0.417029i | ||||
\(93\) | 13.4641i | 1.39616i | ||||||||
\(94\) | −2.46410 | + | 9.19615i | −0.254153 | + | 0.948511i | ||||
\(95\) | −2.53590 | −0.260178 | ||||||||
\(96\) | 2.92820 | + | 10.9282i | 0.298858 | + | 1.11536i | ||||
\(97\) | 6.39230 | 0.649040 | 0.324520 | − | 0.945879i | \(-0.394797\pi\) | ||||
0.324520 | + | 0.945879i | \(0.394797\pi\) | |||||||
\(98\) | 1.97372 | − | 7.36603i | 0.199376 | − | 0.744081i | ||||
\(99\) | − | 4.73205i | − | 0.475589i | ||||||
\(100\) | 12.1244 | + | 7.00000i | 1.21244 | + | 0.700000i | ||||
\(101\) | 12.0000i | 1.19404i | 0.802225 | + | 0.597022i | \(0.203650\pi\) | ||||
−0.802225 | + | 0.597022i | \(0.796350\pi\) | |||||||
\(102\) | 14.9282 | + | 4.00000i | 1.47811 | + | 0.396059i | ||||
\(103\) | 6.92820 | 0.682656 | 0.341328 | − | 0.939944i | \(-0.389123\pi\) | ||||
0.341328 | + | 0.939944i | \(0.389123\pi\) | |||||||
\(104\) | −2.00000 | − | 2.00000i | −0.196116 | − | 0.196116i | ||||
\(105\) | 8.78461 | 0.857290 | ||||||||
\(106\) | −4.00000 | − | 1.07180i | −0.388514 | − | 0.104102i | ||||
\(107\) | − | 4.92820i | − | 0.476427i | −0.971213 | − | 0.238214i | \(-0.923438\pi\) | ||
0.971213 | − | 0.238214i | \(-0.0765619\pi\) | |||||||
\(108\) | −4.00000 | + | 6.92820i | −0.384900 | + | 0.666667i | ||||
\(109\) | 2.00000i | 0.191565i | 0.995402 | + | 0.0957826i | \(0.0305354\pi\) | ||||
−0.995402 | + | 0.0957826i | \(0.969465\pi\) | |||||||
\(110\) | −6.00000 | + | 22.3923i | −0.572078 | + | 2.13502i | ||||
\(111\) | 17.8564 | 1.69486 | ||||||||
\(112\) | −2.53590 | − | 4.39230i | −0.239620 | − | 0.415034i | ||||
\(113\) | 2.53590 | 0.238557 | 0.119279 | − | 0.992861i | \(-0.461942\pi\) | ||||
0.119279 | + | 0.992861i | \(0.461942\pi\) | |||||||
\(114\) | 0.535898 | − | 2.00000i | 0.0501915 | − | 0.187317i | ||||
\(115\) | − | 13.8564i | − | 1.29212i | ||||||
\(116\) | −2.00000 | + | 3.46410i | −0.185695 | + | 0.321634i | ||||
\(117\) | 1.00000i | 0.0924500i | ||||||||
\(118\) | −13.9282 | − | 3.73205i | −1.28220 | − | 0.343563i | ||||
\(119\) | −6.92820 | −0.635107 | ||||||||
\(120\) | −13.8564 | + | 13.8564i | −1.26491 | + | 1.26491i | ||||
\(121\) | −11.3923 | −1.03566 | ||||||||
\(122\) | 4.00000 | + | 1.07180i | 0.362143 | + | 0.0970359i | ||||
\(123\) | − | 17.8564i | − | 1.61006i | ||||||
\(124\) | 11.6603 | + | 6.73205i | 1.04712 | + | 0.604556i | ||||
\(125\) | 6.92820i | 0.619677i | ||||||||
\(126\) | −0.464102 | + | 1.73205i | −0.0413455 | + | 0.154303i | ||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | 10.9282 | + | 2.92820i | 0.965926 | + | 0.258819i | ||||
\(129\) | 1.07180 | 0.0943664 | ||||||||
\(130\) | 1.26795 | − | 4.73205i | 0.111207 | − | 0.415028i | ||||
\(131\) | − | 19.8564i | − | 1.73486i | −0.497557 | − | 0.867431i | \(-0.665770\pi\) | ||
0.497557 | − | 0.867431i | \(-0.334230\pi\) | |||||||
\(132\) | −16.3923 | − | 9.46410i | −1.42677 | − | 0.823744i | ||||
\(133\) | 0.928203i | 0.0804854i | ||||||||
\(134\) | 1.00000 | + | 0.267949i | 0.0863868 | + | 0.0231473i | ||||
\(135\) | −13.8564 | −1.19257 | ||||||||
\(136\) | 10.9282 | − | 10.9282i | 0.937086 | − | 0.937086i | ||||
\(137\) | 12.9282 | 1.10453 | 0.552265 | − | 0.833668i | \(-0.313763\pi\) | ||||
0.552265 | + | 0.833668i | \(0.313763\pi\) | |||||||
\(138\) | 10.9282 | + | 2.92820i | 0.930270 | + | 0.249265i | ||||
\(139\) | 10.0000i | 0.848189i | 0.905618 | + | 0.424094i | \(0.139408\pi\) | ||||
−0.905618 | + | 0.424094i | \(0.860592\pi\) | |||||||
\(140\) | 4.39230 | − | 7.60770i | 0.371218 | − | 0.642968i | ||||
\(141\) | − | 13.4641i | − | 1.13388i | ||||||
\(142\) | 3.00000 | − | 11.1962i | 0.251754 | − | 0.939560i | ||||
\(143\) | 4.73205 | 0.395714 | ||||||||
\(144\) | −2.00000 | − | 3.46410i | −0.166667 | − | 0.288675i | ||||
\(145\) | −6.92820 | −0.575356 | ||||||||
\(146\) | 2.73205 | − | 10.1962i | 0.226106 | − | 0.843840i | ||||
\(147\) | 10.7846i | 0.889500i | ||||||||
\(148\) | 8.92820 | − | 15.4641i | 0.733894 | − | 1.27114i | ||||
\(149\) | 12.9282i | 1.05912i | 0.848273 | + | 0.529560i | \(0.177643\pi\) | ||||
−0.848273 | + | 0.529560i | \(0.822357\pi\) | |||||||
\(150\) | −19.1244 | − | 5.12436i | −1.56150 | − | 0.418402i | ||||
\(151\) | −7.12436 | −0.579772 | −0.289886 | − | 0.957061i | \(-0.593617\pi\) | ||||
−0.289886 | + | 0.957061i | \(0.593617\pi\) | |||||||
\(152\) | −1.46410 | − | 1.46410i | −0.118754 | − | 0.118754i | ||||
\(153\) | −5.46410 | −0.441746 | ||||||||
\(154\) | 8.19615 | + | 2.19615i | 0.660465 | + | 0.176971i | ||||
\(155\) | 23.3205i | 1.87315i | ||||||||
\(156\) | 3.46410 | + | 2.00000i | 0.277350 | + | 0.160128i | ||||
\(157\) | 16.9282i | 1.35102i | 0.737352 | + | 0.675509i | \(0.236076\pi\) | ||||
−0.737352 | + | 0.675509i | \(0.763924\pi\) | |||||||
\(158\) | −2.00000 | + | 7.46410i | −0.159111 | + | 0.593812i | ||||
\(159\) | 5.85641 | 0.464443 | ||||||||
\(160\) | 5.07180 | + | 18.9282i | 0.400961 | + | 1.49641i | ||||
\(161\) | −5.07180 | −0.399714 | ||||||||
\(162\) | 4.02628 | − | 15.0263i | 0.316334 | − | 1.18058i | ||||
\(163\) | − | 16.7321i | − | 1.31056i | −0.755388 | − | 0.655278i | \(-0.772552\pi\) | ||
0.755388 | − | 0.655278i | \(-0.227448\pi\) | |||||||
\(164\) | −15.4641 | − | 8.92820i | −1.20754 | − | 0.697176i | ||||
\(165\) | − | 32.7846i | − | 2.55228i | ||||||
\(166\) | 4.46410 | + | 1.19615i | 0.346481 | + | 0.0928394i | ||||
\(167\) | −5.66025 | −0.438004 | −0.219002 | − | 0.975724i | \(-0.570280\pi\) | ||||
−0.219002 | + | 0.975724i | \(0.570280\pi\) | |||||||
\(168\) | 5.07180 | + | 5.07180i | 0.391298 | + | 0.391298i | ||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 25.8564 | + | 6.92820i | 1.98310 | + | 0.531369i | ||||
\(171\) | 0.732051i | 0.0559813i | ||||||||
\(172\) | 0.535898 | − | 0.928203i | 0.0408619 | − | 0.0707748i | ||||
\(173\) | − | 6.92820i | − | 0.526742i | −0.964695 | − | 0.263371i | \(-0.915166\pi\) | ||
0.964695 | − | 0.263371i | \(-0.0848343\pi\) | |||||||
\(174\) | 1.46410 | − | 5.46410i | 0.110993 | − | 0.414232i | ||||
\(175\) | 8.87564 | 0.670936 | ||||||||
\(176\) | −16.3923 | + | 9.46410i | −1.23562 | + | 0.713384i | ||||
\(177\) | 20.3923 | 1.53278 | ||||||||
\(178\) | 6.33975 | − | 23.6603i | 0.475184 | − | 1.77341i | ||||
\(179\) | 10.3923i | 0.776757i | 0.921500 | + | 0.388379i | \(0.126965\pi\) | ||||
−0.921500 | + | 0.388379i | \(0.873035\pi\) | |||||||
\(180\) | 3.46410 | − | 6.00000i | 0.258199 | − | 0.447214i | ||||
\(181\) | 8.92820i | 0.663628i | 0.943345 | + | 0.331814i | \(0.107661\pi\) | ||||
−0.943345 | + | 0.331814i | \(0.892339\pi\) | |||||||
\(182\) | −1.73205 | − | 0.464102i | −0.128388 | − | 0.0344015i | ||||
\(183\) | −5.85641 | −0.432918 | ||||||||
\(184\) | 8.00000 | − | 8.00000i | 0.589768 | − | 0.589768i | ||||
\(185\) | 30.9282 | 2.27389 | ||||||||
\(186\) | −18.3923 | − | 4.92820i | −1.34859 | − | 0.361353i | ||||
\(187\) | 25.8564i | 1.89081i | ||||||||
\(188\) | −11.6603 | − | 6.73205i | −0.850411 | − | 0.490985i | ||||
\(189\) | 5.07180i | 0.368919i | ||||||||
\(190\) | 0.928203 | − | 3.46410i | 0.0673389 | − | 0.251312i | ||||
\(191\) | −14.5359 | −1.05178 | −0.525890 | − | 0.850552i | \(-0.676268\pi\) | ||||
−0.525890 | + | 0.850552i | \(0.676268\pi\) | |||||||
\(192\) | −16.0000 | −1.15470 | ||||||||
\(193\) | −1.60770 | −0.115724 | −0.0578622 | − | 0.998325i | \(-0.518428\pi\) | ||||
−0.0578622 | + | 0.998325i | \(0.518428\pi\) | |||||||
\(194\) | −2.33975 | + | 8.73205i | −0.167984 | + | 0.626925i | ||||
\(195\) | 6.92820i | 0.496139i | ||||||||
\(196\) | 9.33975 | + | 5.39230i | 0.667125 | + | 0.385165i | ||||
\(197\) | 3.07180i | 0.218856i | 0.993995 | + | 0.109428i | \(0.0349020\pi\) | ||||
−0.993995 | + | 0.109428i | \(0.965098\pi\) | |||||||
\(198\) | 6.46410 | + | 1.73205i | 0.459384 | + | 0.123091i | ||||
\(199\) | 16.7846 | 1.18983 | 0.594915 | − | 0.803789i | \(-0.297186\pi\) | ||||
0.594915 | + | 0.803789i | \(0.297186\pi\) | |||||||
\(200\) | −14.0000 | + | 14.0000i | −0.989949 | + | 0.989949i | ||||
\(201\) | −1.46410 | −0.103270 | ||||||||
\(202\) | −16.3923 | − | 4.39230i | −1.15336 | − | 0.309041i | ||||
\(203\) | 2.53590i | 0.177985i | ||||||||
\(204\) | −10.9282 | + | 18.9282i | −0.765127 | + | 1.32524i | ||||
\(205\) | − | 30.9282i | − | 2.16012i | ||||||
\(206\) | −2.53590 | + | 9.46410i | −0.176684 | + | 0.659395i | ||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 3.46410 | − | 2.00000i | 0.240192 | − | 0.138675i | ||||
\(209\) | 3.46410 | 0.239617 | ||||||||
\(210\) | −3.21539 | + | 12.0000i | −0.221883 | + | 0.828079i | ||||
\(211\) | 7.85641i | 0.540857i | 0.962740 | + | 0.270429i | \(0.0871654\pi\) | ||||
−0.962740 | + | 0.270429i | \(0.912835\pi\) | |||||||
\(212\) | 2.92820 | − | 5.07180i | 0.201110 | − | 0.348332i | ||||
\(213\) | 16.3923i | 1.12318i | ||||||||
\(214\) | 6.73205 | + | 1.80385i | 0.460194 | + | 0.123308i | ||||
\(215\) | 1.85641 | 0.126606 | ||||||||
\(216\) | −8.00000 | − | 8.00000i | −0.544331 | − | 0.544331i | ||||
\(217\) | 8.53590 | 0.579455 | ||||||||
\(218\) | −2.73205 | − | 0.732051i | −0.185038 | − | 0.0495807i | ||||
\(219\) | 14.9282i | 1.00875i | ||||||||
\(220\) | −28.3923 | − | 16.3923i | −1.91421 | − | 1.10517i | ||||
\(221\) | − | 5.46410i | − | 0.367555i | ||||||
\(222\) | −6.53590 | + | 24.3923i | −0.438661 | + | 1.63710i | ||||
\(223\) | −0.196152 | −0.0131353 | −0.00656767 | − | 0.999978i | \(-0.502091\pi\) | ||||
−0.00656767 | + | 0.999978i | \(0.502091\pi\) | |||||||
\(224\) | 6.92820 | − | 1.85641i | 0.462910 | − | 0.124036i | ||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | −0.928203 | + | 3.46410i | −0.0617432 | + | 0.230429i | ||||
\(227\) | − | 2.87564i | − | 0.190863i | −0.995436 | − | 0.0954316i | \(-0.969577\pi\) | ||
0.995436 | − | 0.0954316i | \(-0.0304231\pi\) | |||||||
\(228\) | 2.53590 | + | 1.46410i | 0.167944 | + | 0.0969625i | ||||
\(229\) | 5.32051i | 0.351589i | 0.984427 | + | 0.175795i | \(0.0562494\pi\) | ||||
−0.984427 | + | 0.175795i | \(0.943751\pi\) | |||||||
\(230\) | 18.9282 | + | 5.07180i | 1.24809 | + | 0.334424i | ||||
\(231\) | −12.0000 | −0.789542 | ||||||||
\(232\) | −4.00000 | − | 4.00000i | −0.262613 | − | 0.262613i | ||||
\(233\) | 16.9282 | 1.10900 | 0.554502 | − | 0.832183i | \(-0.312909\pi\) | ||||
0.554502 | + | 0.832183i | \(0.312909\pi\) | |||||||
\(234\) | −1.36603 | − | 0.366025i | −0.0892999 | − | 0.0239278i | ||||
\(235\) | − | 23.3205i | − | 1.52126i | ||||||
\(236\) | 10.1962 | − | 17.6603i | 0.663713 | − | 1.14958i | ||||
\(237\) | − | 10.9282i | − | 0.709863i | ||||||
\(238\) | 2.53590 | − | 9.46410i | 0.164378 | − | 0.613467i | ||||
\(239\) | 18.7321 | 1.21168 | 0.605838 | − | 0.795588i | \(-0.292838\pi\) | ||||
0.605838 | + | 0.795588i | \(0.292838\pi\) | |||||||
\(240\) | −13.8564 | − | 24.0000i | −0.894427 | − | 1.54919i | ||||
\(241\) | −30.3923 | −1.95774 | −0.978870 | − | 0.204482i | \(-0.934449\pi\) | ||||
−0.978870 | + | 0.204482i | \(0.934449\pi\) | |||||||
\(242\) | 4.16987 | − | 15.5622i | 0.268050 | − | 1.00037i | ||||
\(243\) | 10.0000i | 0.641500i | ||||||||
\(244\) | −2.92820 | + | 5.07180i | −0.187459 | + | 0.324689i | ||||
\(245\) | 18.6795i | 1.19339i | ||||||||
\(246\) | 24.3923 | + | 6.53590i | 1.55520 | + | 0.416714i | ||||
\(247\) | −0.732051 | −0.0465793 | ||||||||
\(248\) | −13.4641 | + | 13.4641i | −0.854971 | + | 0.854971i | ||||
\(249\) | −6.53590 | −0.414196 | ||||||||
\(250\) | −9.46410 | − | 2.53590i | −0.598562 | − | 0.160384i | ||||
\(251\) | − | 6.39230i | − | 0.403479i | −0.979439 | − | 0.201739i | \(-0.935341\pi\) | ||
0.979439 | − | 0.201739i | \(-0.0646594\pi\) | |||||||
\(252\) | −2.19615 | − | 1.26795i | −0.138345 | − | 0.0798733i | ||||
\(253\) | 18.9282i | 1.19001i | ||||||||
\(254\) | 1.46410 | − | 5.46410i | 0.0918659 | − | 0.342848i | ||||
\(255\) | −37.8564 | −2.37066 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −23.8564 | −1.48812 | −0.744061 | − | 0.668112i | \(-0.767103\pi\) | ||||
−0.744061 | + | 0.668112i | \(0.767103\pi\) | |||||||
\(258\) | −0.392305 | + | 1.46410i | −0.0244238 | + | 0.0911510i | ||||
\(259\) | − | 11.3205i | − | 0.703422i | ||||||
\(260\) | 6.00000 | + | 3.46410i | 0.372104 | + | 0.214834i | ||||
\(261\) | 2.00000i | 0.123797i | ||||||||
\(262\) | 27.1244 | + | 7.26795i | 1.67575 | + | 0.449015i | ||||
\(263\) | −27.3205 | −1.68465 | −0.842327 | − | 0.538966i | \(-0.818815\pi\) | ||||
−0.842327 | + | 0.538966i | \(0.818815\pi\) | |||||||
\(264\) | 18.9282 | − | 18.9282i | 1.16495 | − | 1.16495i | ||||
\(265\) | 10.1436 | 0.623116 | ||||||||
\(266\) | −1.26795 | − | 0.339746i | −0.0777430 | − | 0.0208312i | ||||
\(267\) | 34.6410i | 2.12000i | ||||||||
\(268\) | −0.732051 | + | 1.26795i | −0.0447171 | + | 0.0774523i | ||||
\(269\) | 7.85641i | 0.479014i | 0.970895 | + | 0.239507i | \(0.0769857\pi\) | ||||
−0.970895 | + | 0.239507i | \(0.923014\pi\) | |||||||
\(270\) | 5.07180 | − | 18.9282i | 0.308660 | − | 1.15193i | ||||
\(271\) | −20.1962 | −1.22683 | −0.613414 | − | 0.789761i | \(-0.710204\pi\) | ||||
−0.613414 | + | 0.789761i | \(0.710204\pi\) | |||||||
\(272\) | 10.9282 | + | 18.9282i | 0.662620 | + | 1.14769i | ||||
\(273\) | 2.53590 | 0.153480 | ||||||||
\(274\) | −4.73205 | + | 17.6603i | −0.285874 | + | 1.06689i | ||||
\(275\) | − | 33.1244i | − | 1.99747i | ||||||
\(276\) | −8.00000 | + | 13.8564i | −0.481543 | + | 0.834058i | ||||
\(277\) | − | 1.85641i | − | 0.111541i | −0.998444 | − | 0.0557703i | \(-0.982239\pi\) | ||
0.998444 | − | 0.0557703i | \(-0.0177615\pi\) | |||||||
\(278\) | −13.6603 | − | 3.66025i | −0.819288 | − | 0.219527i | ||||
\(279\) | 6.73205 | 0.403037 | ||||||||
\(280\) | 8.78461 | + | 8.78461i | 0.524981 | + | 0.524981i | ||||
\(281\) | 9.32051 | 0.556015 | 0.278007 | − | 0.960579i | \(-0.410326\pi\) | ||||
0.278007 | + | 0.960579i | \(0.410326\pi\) | |||||||
\(282\) | 18.3923 | + | 4.92820i | 1.09525 | + | 0.293470i | ||||
\(283\) | − | 19.4641i | − | 1.15702i | −0.815675 | − | 0.578510i | \(-0.803634\pi\) | ||
0.815675 | − | 0.578510i | \(-0.196366\pi\) | |||||||
\(284\) | 14.1962 | + | 8.19615i | 0.842387 | + | 0.486352i | ||||
\(285\) | 5.07180i | 0.300427i | ||||||||
\(286\) | −1.73205 | + | 6.46410i | −0.102418 | + | 0.382230i | ||||
\(287\) | −11.3205 | −0.668228 | ||||||||
\(288\) | 5.46410 | − | 1.46410i | 0.321975 | − | 0.0862730i | ||||
\(289\) | 12.8564 | 0.756259 | ||||||||
\(290\) | 2.53590 | − | 9.46410i | 0.148913 | − | 0.555751i | ||||
\(291\) | − | 12.7846i | − | 0.749447i | ||||||
\(292\) | 12.9282 | + | 7.46410i | 0.756566 | + | 0.436804i | ||||
\(293\) | − | 32.9282i | − | 1.92369i | −0.273602 | − | 0.961843i | \(-0.588215\pi\) | ||
0.273602 | − | 0.961843i | \(-0.411785\pi\) | |||||||
\(294\) | −14.7321 | − | 3.94744i | −0.859191 | − | 0.230219i | ||||
\(295\) | 35.3205 | 2.05644 | ||||||||
\(296\) | 17.8564 | + | 17.8564i | 1.03788 | + | 1.03788i | ||||
\(297\) | 18.9282 | 1.09833 | ||||||||
\(298\) | −17.6603 | − | 4.73205i | −1.02303 | − | 0.274120i | ||||
\(299\) | − | 4.00000i | − | 0.231326i | ||||||
\(300\) | 14.0000 | − | 24.2487i | 0.808290 | − | 1.40000i | ||||
\(301\) | − | 0.679492i | − | 0.0391653i | ||||||
\(302\) | 2.60770 | − | 9.73205i | 0.150056 | − | 0.560017i | ||||
\(303\) | 24.0000 | 1.37876 | ||||||||
\(304\) | 2.53590 | − | 1.46410i | 0.145444 | − | 0.0839720i | ||||
\(305\) | −10.1436 | −0.580820 | ||||||||
\(306\) | 2.00000 | − | 7.46410i | 0.114332 | − | 0.426694i | ||||
\(307\) | − | 0.732051i | − | 0.0417803i | −0.999782 | − | 0.0208902i | \(-0.993350\pi\) | ||
0.999782 | − | 0.0208902i | \(-0.00665003\pi\) | |||||||
\(308\) | −6.00000 | + | 10.3923i | −0.341882 | + | 0.592157i | ||||
\(309\) | − | 13.8564i | − | 0.788263i | ||||||
\(310\) | −31.8564 | − | 8.53590i | −1.80932 | − | 0.484806i | ||||
\(311\) | 1.07180 | 0.0607760 | 0.0303880 | − | 0.999538i | \(-0.490326\pi\) | ||||
0.0303880 | + | 0.999538i | \(0.490326\pi\) | |||||||
\(312\) | −4.00000 | + | 4.00000i | −0.226455 | + | 0.226455i | ||||
\(313\) | 0.392305 | 0.0221744 | 0.0110872 | − | 0.999939i | \(-0.496471\pi\) | ||||
0.0110872 | + | 0.999939i | \(0.496471\pi\) | |||||||
\(314\) | −23.1244 | − | 6.19615i | −1.30498 | − | 0.349669i | ||||
\(315\) | − | 4.39230i | − | 0.247478i | ||||||
\(316\) | −9.46410 | − | 5.46410i | −0.532397 | − | 0.307380i | ||||
\(317\) | − | 3.46410i | − | 0.194563i | −0.995257 | − | 0.0972817i | \(-0.968985\pi\) | ||
0.995257 | − | 0.0972817i | \(-0.0310148\pi\) | |||||||
\(318\) | −2.14359 | + | 8.00000i | −0.120207 | + | 0.448618i | ||||
\(319\) | 9.46410 | 0.529888 | ||||||||
\(320\) | −27.7128 | −1.54919 | ||||||||
\(321\) | −9.85641 | −0.550131 | ||||||||
\(322\) | 1.85641 | − | 6.92820i | 0.103453 | − | 0.386094i | ||||
\(323\) | − | 4.00000i | − | 0.222566i | ||||||
\(324\) | 19.0526 | + | 11.0000i | 1.05848 | + | 0.611111i | ||||
\(325\) | 7.00000i | 0.388290i | ||||||||
\(326\) | 22.8564 | + | 6.12436i | 1.26590 | + | 0.339197i | ||||
\(327\) | 4.00000 | 0.221201 | ||||||||
\(328\) | 17.8564 | − | 17.8564i | 0.985955 | − | 0.985955i | ||||
\(329\) | −8.53590 | −0.470599 | ||||||||
\(330\) | 44.7846 | + | 12.0000i | 2.46531 | + | 0.660578i | ||||
\(331\) | − | 17.5167i | − | 0.962803i | −0.876500 | − | 0.481401i | \(-0.840128\pi\) | ||
0.876500 | − | 0.481401i | \(-0.159872\pi\) | |||||||
\(332\) | −3.26795 | + | 5.66025i | −0.179352 | + | 0.310647i | ||||
\(333\) | − | 8.92820i | − | 0.489263i | ||||||
\(334\) | 2.07180 | − | 7.73205i | 0.113364 | − | 0.423079i | ||||
\(335\) | −2.53590 | −0.138551 | ||||||||
\(336\) | −8.78461 | + | 5.07180i | −0.479240 | + | 0.276689i | ||||
\(337\) | 1.46410 | 0.0797547 | 0.0398773 | − | 0.999205i | \(-0.487303\pi\) | ||||
0.0398773 | + | 0.999205i | \(0.487303\pi\) | |||||||
\(338\) | 0.366025 | − | 1.36603i | 0.0199092 | − | 0.0743020i | ||||
\(339\) | − | 5.07180i | − | 0.275462i | ||||||
\(340\) | −18.9282 | + | 32.7846i | −1.02653 | + | 1.77800i | ||||
\(341\) | − | 31.8564i | − | 1.72512i | ||||||
\(342\) | −1.00000 | − | 0.267949i | −0.0540738 | − | 0.0144890i | ||||
\(343\) | 15.7128 | 0.848412 | ||||||||
\(344\) | 1.07180 | + | 1.07180i | 0.0577874 | + | 0.0577874i | ||||
\(345\) | −27.7128 | −1.49201 | ||||||||
\(346\) | 9.46410 | + | 2.53590i | 0.508793 | + | 0.136331i | ||||
\(347\) | 7.07180i | 0.379634i | 0.981819 | + | 0.189817i | \(0.0607895\pi\) | ||||
−0.981819 | + | 0.189817i | \(0.939211\pi\) | |||||||
\(348\) | 6.92820 | + | 4.00000i | 0.371391 | + | 0.214423i | ||||
\(349\) | − | 9.60770i | − | 0.514288i | −0.966373 | − | 0.257144i | \(-0.917219\pi\) | ||
0.966373 | − | 0.257144i | \(-0.0827815\pi\) | |||||||
\(350\) | −3.24871 | + | 12.1244i | −0.173651 | + | 0.648074i | ||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | −6.92820 | − | 25.8564i | −0.369274 | − | 1.37815i | ||||
\(353\) | −11.0718 | −0.589292 | −0.294646 | − | 0.955606i | \(-0.595202\pi\) | ||||
−0.294646 | + | 0.955606i | \(0.595202\pi\) | |||||||
\(354\) | −7.46410 | + | 27.8564i | −0.396713 | + | 1.48055i | ||||
\(355\) | 28.3923i | 1.50691i | ||||||||
\(356\) | 30.0000 | + | 17.3205i | 1.59000 | + | 0.917985i | ||||
\(357\) | 13.8564i | 0.733359i | ||||||||
\(358\) | −14.1962 | − | 3.80385i | −0.750290 | − | 0.201040i | ||||
\(359\) | 31.5167 | 1.66339 | 0.831693 | − | 0.555236i | \(-0.187372\pi\) | ||||
0.831693 | + | 0.555236i | \(0.187372\pi\) | |||||||
\(360\) | 6.92820 | + | 6.92820i | 0.365148 | + | 0.365148i | ||||
\(361\) | 18.4641 | 0.971795 | ||||||||
\(362\) | −12.1962 | − | 3.26795i | −0.641016 | − | 0.171760i | ||||
\(363\) | 22.7846i | 1.19588i | ||||||||
\(364\) | 1.26795 | − | 2.19615i | 0.0664586 | − | 0.115110i | ||||
\(365\) | 25.8564i | 1.35339i | ||||||||
\(366\) | 2.14359 | − | 8.00000i | 0.112047 | − | 0.418167i | ||||
\(367\) | −22.2487 | −1.16137 | −0.580687 | − | 0.814127i | \(-0.697216\pi\) | ||||
−0.580687 | + | 0.814127i | \(0.697216\pi\) | |||||||
\(368\) | 8.00000 | + | 13.8564i | 0.417029 | + | 0.722315i | ||||
\(369\) | −8.92820 | −0.464784 | ||||||||
\(370\) | −11.3205 | + | 42.2487i | −0.588525 | + | 2.19641i | ||||
\(371\) | − | 3.71281i | − | 0.192760i | ||||||
\(372\) | 13.4641 | − | 23.3205i | 0.698081 | − | 1.20911i | ||||
\(373\) | 14.7846i | 0.765518i | 0.923848 | + | 0.382759i | \(0.125026\pi\) | ||||
−0.923848 | + | 0.382759i | \(0.874974\pi\) | |||||||
\(374\) | −35.3205 | − | 9.46410i | −1.82638 | − | 0.489377i | ||||
\(375\) | 13.8564 | 0.715542 | ||||||||
\(376\) | 13.4641 | − | 13.4641i | 0.694358 | − | 0.694358i | ||||
\(377\) | −2.00000 | −0.103005 | ||||||||
\(378\) | −6.92820 | − | 1.85641i | −0.356348 | − | 0.0954832i | ||||
\(379\) | − | 14.5885i | − | 0.749359i | −0.927154 | − | 0.374679i | \(-0.877753\pi\) | ||
0.927154 | − | 0.374679i | \(-0.122247\pi\) | |||||||
\(380\) | 4.39230 | + | 2.53590i | 0.225320 | + | 0.130089i | ||||
\(381\) | 8.00000i | 0.409852i | ||||||||
\(382\) | 5.32051 | − | 19.8564i | 0.272221 | − | 1.01594i | ||||
\(383\) | −10.3397 | −0.528336 | −0.264168 | − | 0.964477i | \(-0.585097\pi\) | ||||
−0.264168 | + | 0.964477i | \(0.585097\pi\) | |||||||
\(384\) | 5.85641 | − | 21.8564i | 0.298858 | − | 1.11536i | ||||
\(385\) | −20.7846 | −1.05928 | ||||||||
\(386\) | 0.588457 | − | 2.19615i | 0.0299517 | − | 0.111781i | ||||
\(387\) | − | 0.535898i | − | 0.0272412i | ||||||
\(388\) | −11.0718 | − | 6.39230i | −0.562085 | − | 0.324520i | ||||
\(389\) | − | 2.00000i | − | 0.101404i | −0.998714 | − | 0.0507020i | \(-0.983854\pi\) | ||
0.998714 | − | 0.0507020i | \(-0.0161459\pi\) | |||||||
\(390\) | −9.46410 | − | 2.53590i | −0.479233 | − | 0.128410i | ||||
\(391\) | 21.8564 | 1.10533 | ||||||||
\(392\) | −10.7846 | + | 10.7846i | −0.544705 | + | 0.544705i | ||||
\(393\) | −39.7128 | −2.00325 | ||||||||
\(394\) | −4.19615 | − | 1.12436i | −0.211399 | − | 0.0566442i | ||||
\(395\) | − | 18.9282i | − | 0.952381i | ||||||
\(396\) | −4.73205 | + | 8.19615i | −0.237795 | + | 0.411872i | ||||
\(397\) | 4.53590i | 0.227650i | 0.993501 | + | 0.113825i | \(0.0363104\pi\) | ||||
−0.993501 | + | 0.113825i | \(0.963690\pi\) | |||||||
\(398\) | −6.14359 | + | 22.9282i | −0.307951 | + | 1.14929i | ||||
\(399\) | 1.85641 | 0.0929366 | ||||||||
\(400\) | −14.0000 | − | 24.2487i | −0.700000 | − | 1.21244i | ||||
\(401\) | 4.53590 | 0.226512 | 0.113256 | − | 0.993566i | \(-0.463872\pi\) | ||||
0.113256 | + | 0.993566i | \(0.463872\pi\) | |||||||
\(402\) | 0.535898 | − | 2.00000i | 0.0267282 | − | 0.0997509i | ||||
\(403\) | 6.73205i | 0.335347i | ||||||||
\(404\) | 12.0000 | − | 20.7846i | 0.597022 | − | 1.03407i | ||||
\(405\) | 38.1051i | 1.89346i | ||||||||
\(406\) | −3.46410 | − | 0.928203i | −0.171920 | − | 0.0460660i | ||||
\(407\) | −42.2487 | −2.09419 | ||||||||
\(408\) | −21.8564 | − | 21.8564i | −1.08205 | − | 1.08205i | ||||
\(409\) | 12.9282 | 0.639259 | 0.319629 | − | 0.947543i | \(-0.396442\pi\) | ||||
0.319629 | + | 0.947543i | \(0.396442\pi\) | |||||||
\(410\) | 42.2487 | + | 11.3205i | 2.08652 | + | 0.559080i | ||||
\(411\) | − | 25.8564i | − | 1.27540i | ||||||
\(412\) | −12.0000 | − | 6.92820i | −0.591198 | − | 0.341328i | ||||
\(413\) | − | 12.9282i | − | 0.636155i | ||||||
\(414\) | 1.46410 | − | 5.46410i | 0.0719567 | − | 0.268546i | ||||
\(415\) | −11.3205 | −0.555702 | ||||||||
\(416\) | 1.46410 | + | 5.46410i | 0.0717835 | + | 0.267900i | ||||
\(417\) | 20.0000 | 0.979404 | ||||||||
\(418\) | −1.26795 | + | 4.73205i | −0.0620174 | + | 0.231452i | ||||
\(419\) | 30.7846i | 1.50393i | 0.659205 | + | 0.751963i | \(0.270893\pi\) | ||||
−0.659205 | + | 0.751963i | \(0.729107\pi\) | |||||||
\(420\) | −15.2154 | − | 8.78461i | −0.742435 | − | 0.428645i | ||||
\(421\) | − | 24.2487i | − | 1.18181i | −0.806741 | − | 0.590905i | \(-0.798771\pi\) | ||
0.806741 | − | 0.590905i | \(-0.201229\pi\) | |||||||
\(422\) | −10.7321 | − | 2.87564i | −0.522428 | − | 0.139984i | ||||
\(423\) | −6.73205 | −0.327324 | ||||||||
\(424\) | 5.85641 | + | 5.85641i | 0.284412 | + | 0.284412i | ||||
\(425\) | −38.2487 | −1.85534 | ||||||||
\(426\) | −22.3923 | − | 6.00000i | −1.08491 | − | 0.290701i | ||||
\(427\) | 3.71281i | 0.179676i | ||||||||
\(428\) | −4.92820 | + | 8.53590i | −0.238214 | + | 0.412598i | ||||
\(429\) | − | 9.46410i | − | 0.456931i | ||||||
\(430\) | −0.679492 | + | 2.53590i | −0.0327680 | + | 0.122292i | ||||
\(431\) | 39.1244 | 1.88455 | 0.942277 | − | 0.334835i | \(-0.108680\pi\) | ||||
0.942277 | + | 0.334835i | \(0.108680\pi\) | |||||||
\(432\) | 13.8564 | − | 8.00000i | 0.666667 | − | 0.384900i | ||||
\(433\) | −6.78461 | −0.326048 | −0.163024 | − | 0.986622i | \(-0.552125\pi\) | ||||
−0.163024 | + | 0.986622i | \(0.552125\pi\) | |||||||
\(434\) | −3.12436 | + | 11.6603i | −0.149974 | + | 0.559710i | ||||
\(435\) | 13.8564i | 0.664364i | ||||||||
\(436\) | 2.00000 | − | 3.46410i | 0.0957826 | − | 0.165900i | ||||
\(437\) | − | 2.92820i | − | 0.140075i | ||||||
\(438\) | −20.3923 | − | 5.46410i | −0.974382 | − | 0.261085i | ||||
\(439\) | 2.92820 | 0.139756 | 0.0698778 | − | 0.997556i | \(-0.477739\pi\) | ||||
0.0698778 | + | 0.997556i | \(0.477739\pi\) | |||||||
\(440\) | 32.7846 | − | 32.7846i | 1.56294 | − | 1.56294i | ||||
\(441\) | 5.39230 | 0.256776 | ||||||||
\(442\) | 7.46410 | + | 2.00000i | 0.355031 | + | 0.0951303i | ||||
\(443\) | 30.0000i | 1.42534i | 0.701498 | + | 0.712672i | \(0.252515\pi\) | ||||
−0.701498 | + | 0.712672i | \(0.747485\pi\) | |||||||
\(444\) | −30.9282 | − | 17.8564i | −1.46779 | − | 0.847428i | ||||
\(445\) | 60.0000i | 2.84427i | ||||||||
\(446\) | 0.0717968 | − | 0.267949i | 0.00339968 | − | 0.0126878i | ||||
\(447\) | 25.8564 | 1.22297 | ||||||||
\(448\) | 10.1436i | 0.479240i | ||||||||
\(449\) | 17.6077 | 0.830959 | 0.415479 | − | 0.909603i | \(-0.363614\pi\) | ||||
0.415479 | + | 0.909603i | \(0.363614\pi\) | |||||||
\(450\) | −2.56218 | + | 9.56218i | −0.120782 | + | 0.450765i | ||||
\(451\) | 42.2487i | 1.98941i | ||||||||
\(452\) | −4.39230 | − | 2.53590i | −0.206597 | − | 0.119279i | ||||
\(453\) | 14.2487i | 0.669463i | ||||||||
\(454\) | 3.92820 | + | 1.05256i | 0.184360 | + | 0.0493990i | ||||
\(455\) | 4.39230 | 0.205914 | ||||||||
\(456\) | −2.92820 | + | 2.92820i | −0.137126 | + | 0.137126i | ||||
\(457\) | −14.0000 | −0.654892 | −0.327446 | − | 0.944870i | \(-0.606188\pi\) | ||||
−0.327446 | + | 0.944870i | \(0.606188\pi\) | |||||||
\(458\) | −7.26795 | − | 1.94744i | −0.339609 | − | 0.0909979i | ||||
\(459\) | − | 21.8564i | − | 1.02017i | ||||||
\(460\) | −13.8564 | + | 24.0000i | −0.646058 | + | 1.11901i | ||||
\(461\) | − | 20.9282i | − | 0.974724i | −0.873200 | − | 0.487362i | \(-0.837959\pi\) | ||
0.873200 | − | 0.487362i | \(-0.162041\pi\) | |||||||
\(462\) | 4.39230 | − | 16.3923i | 0.204349 | − | 0.762639i | ||||
\(463\) | 1.66025 | 0.0771585 | 0.0385793 | − | 0.999256i | \(-0.487717\pi\) | ||||
0.0385793 | + | 0.999256i | \(0.487717\pi\) | |||||||
\(464\) | 6.92820 | − | 4.00000i | 0.321634 | − | 0.185695i | ||||
\(465\) | 46.6410 | 2.16293 | ||||||||
\(466\) | −6.19615 | + | 23.1244i | −0.287031 | + | 1.07122i | ||||
\(467\) | − | 36.2487i | − | 1.67739i | −0.544601 | − | 0.838695i | \(-0.683319\pi\) | ||
0.544601 | − | 0.838695i | \(-0.316681\pi\) | |||||||
\(468\) | 1.00000 | − | 1.73205i | 0.0462250 | − | 0.0800641i | ||||
\(469\) | 0.928203i | 0.0428604i | ||||||||
\(470\) | 31.8564 | + | 8.53590i | 1.46943 | + | 0.393732i | ||||
\(471\) | 33.8564 | 1.56002 | ||||||||
\(472\) | 20.3923 | + | 20.3923i | 0.938632 | + | 0.938632i | ||||
\(473\) | −2.53590 | −0.116601 | ||||||||
\(474\) | 14.9282 | + | 4.00000i | 0.685675 | + | 0.183726i | ||||
\(475\) | 5.12436i | 0.235122i | ||||||||
\(476\) | 12.0000 | + | 6.92820i | 0.550019 | + | 0.317554i | ||||
\(477\) | − | 2.92820i | − | 0.134073i | ||||||
\(478\) | −6.85641 | + | 25.5885i | −0.313605 | + | 1.17039i | ||||
\(479\) | 21.2679 | 0.971757 | 0.485879 | − | 0.874026i | \(-0.338500\pi\) | ||||
0.485879 | + | 0.874026i | \(0.338500\pi\) | |||||||
\(480\) | 37.8564 | − | 10.1436i | 1.72790 | − | 0.462990i | ||||
\(481\) | 8.92820 | 0.407091 | ||||||||
\(482\) | 11.1244 | − | 41.5167i | 0.506701 | − | 1.89103i | ||||
\(483\) | 10.1436i | 0.461549i | ||||||||
\(484\) | 19.7321 | + | 11.3923i | 0.896911 | + | 0.517832i | ||||
\(485\) | − | 22.1436i | − | 1.00549i | ||||||
\(486\) | −13.6603 | − | 3.66025i | −0.619642 | − | 0.166032i | ||||
\(487\) | −42.4449 | −1.92336 | −0.961680 | − | 0.274174i | \(-0.911596\pi\) | ||||
−0.961680 | + | 0.274174i | \(0.911596\pi\) | |||||||
\(488\) | −5.85641 | − | 5.85641i | −0.265107 | − | 0.265107i | ||||
\(489\) | −33.4641 | −1.51330 | ||||||||
\(490\) | −25.5167 | − | 6.83717i | −1.15273 | − | 0.308872i | ||||
\(491\) | 24.2487i | 1.09433i | 0.837025 | + | 0.547165i | \(0.184293\pi\) | ||||
−0.837025 | + | 0.547165i | \(0.815707\pi\) | |||||||
\(492\) | −17.8564 | + | 30.9282i | −0.805029 | + | 1.39435i | ||||
\(493\) | − | 10.9282i | − | 0.492182i | ||||||
\(494\) | 0.267949 | − | 1.00000i | 0.0120556 | − | 0.0449921i | ||||
\(495\) | −16.3923 | −0.736779 | ||||||||
\(496\) | −13.4641 | − | 23.3205i | −0.604556 | − | 1.04712i | ||||
\(497\) | 10.3923 | 0.466159 | ||||||||
\(498\) | 2.39230 | − | 8.92820i | 0.107202 | − | 0.400082i | ||||
\(499\) | 7.26795i | 0.325358i | 0.986679 | + | 0.162679i | \(0.0520135\pi\) | ||||
−0.986679 | + | 0.162679i | \(0.947986\pi\) | |||||||
\(500\) | 6.92820 | − | 12.0000i | 0.309839 | − | 0.536656i | ||||
\(501\) | 11.3205i | 0.505763i | ||||||||
\(502\) | 8.73205 | + | 2.33975i | 0.389731 | + | 0.104428i | ||||
\(503\) | 30.5359 | 1.36153 | 0.680764 | − | 0.732503i | \(-0.261648\pi\) | ||||
0.680764 | + | 0.732503i | \(0.261648\pi\) | |||||||
\(504\) | 2.53590 | − | 2.53590i | 0.112958 | − | 0.112958i | ||||
\(505\) | 41.5692 | 1.84981 | ||||||||
\(506\) | −25.8564 | − | 6.92820i | −1.14946 | − | 0.307996i | ||||
\(507\) | 2.00000i | 0.0888231i | ||||||||
\(508\) | 6.92820 | + | 4.00000i | 0.307389 | + | 0.177471i | ||||
\(509\) | − | 14.3923i | − | 0.637928i | −0.947767 | − | 0.318964i | \(-0.896665\pi\) | ||
0.947767 | − | 0.318964i | \(-0.103335\pi\) | |||||||
\(510\) | 13.8564 | − | 51.7128i | 0.613572 | − | 2.28988i | ||||
\(511\) | 9.46410 | 0.418667 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | −2.92820 | −0.129283 | ||||||||
\(514\) | 8.73205 | − | 32.5885i | 0.385154 | − | 1.43742i | ||||
\(515\) | − | 24.0000i | − | 1.05757i | ||||||
\(516\) | −1.85641 | − | 1.07180i | −0.0817237 | − | 0.0471832i | ||||
\(517\) | 31.8564i | 1.40104i | ||||||||
\(518\) | 15.4641 | + | 4.14359i | 0.679454 | + | 0.182059i | ||||
\(519\) | −13.8564 | −0.608229 | ||||||||
\(520\) | −6.92820 | + | 6.92820i | −0.303822 | + | 0.303822i | ||||
\(521\) | −25.1769 | −1.10302 | −0.551510 | − | 0.834168i | \(-0.685948\pi\) | ||||
−0.551510 | + | 0.834168i | \(0.685948\pi\) | |||||||
\(522\) | −2.73205 | − | 0.732051i | −0.119579 | − | 0.0320410i | ||||
\(523\) | − | 14.0000i | − | 0.612177i | −0.952003 | − | 0.306089i | \(-0.900980\pi\) | ||
0.952003 | − | 0.306089i | \(-0.0990204\pi\) | |||||||
\(524\) | −19.8564 | + | 34.3923i | −0.867431 | + | 1.50243i | ||||
\(525\) | − | 17.7513i | − | 0.774730i | ||||||
\(526\) | 10.0000 | − | 37.3205i | 0.436021 | − | 1.62725i | ||||
\(527\) | −36.7846 | −1.60236 | ||||||||
\(528\) | 18.9282 | + | 32.7846i | 0.823744 | + | 1.42677i | ||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −3.71281 | + | 13.8564i | −0.161274 | + | 0.601884i | ||||
\(531\) | − | 10.1962i | − | 0.442475i | ||||||
\(532\) | 0.928203 | − | 1.60770i | 0.0402427 | − | 0.0697024i | ||||
\(533\) | − | 8.92820i | − | 0.386723i | ||||||
\(534\) | −47.3205 | − | 12.6795i | −2.04776 | − | 0.548695i | ||||
\(535\) | −17.0718 | −0.738078 | ||||||||
\(536\) | −1.46410 | − | 1.46410i | −0.0632396 | − | 0.0632396i | ||||
\(537\) | 20.7846 | 0.896922 | ||||||||
\(538\) | −10.7321 | − | 2.87564i | −0.462692 | − | 0.123978i | ||||
\(539\) | − | 25.5167i | − | 1.09908i | ||||||
\(540\) | 24.0000 | + | 13.8564i | 1.03280 | + | 0.596285i | ||||
\(541\) | 3.07180i | 0.132067i | 0.997817 | + | 0.0660334i | \(0.0210344\pi\) | ||||
−0.997817 | + | 0.0660334i | \(0.978966\pi\) | |||||||
\(542\) | 7.39230 | − | 27.5885i | 0.317527 | − | 1.18503i | ||||
\(543\) | 17.8564 | 0.766292 | ||||||||
\(544\) | −29.8564 | + | 8.00000i | −1.28008 | + | 0.342997i | ||||
\(545\) | 6.92820 | 0.296772 | ||||||||
\(546\) | −0.928203 | + | 3.46410i | −0.0397234 | + | 0.148250i | ||||
\(547\) | 11.8564i | 0.506943i | 0.967343 | + | 0.253472i | \(0.0815725\pi\) | ||||
−0.967343 | + | 0.253472i | \(0.918428\pi\) | |||||||
\(548\) | −22.3923 | − | 12.9282i | −0.956552 | − | 0.552265i | ||||
\(549\) | 2.92820i | 0.124973i | ||||||||
\(550\) | 45.2487 | + | 12.1244i | 1.92941 | + | 0.516984i | ||||
\(551\) | −1.46410 | −0.0623728 | ||||||||
\(552\) | −16.0000 | − | 16.0000i | −0.681005 | − | 0.681005i | ||||
\(553\) | −6.92820 | −0.294617 | ||||||||
\(554\) | 2.53590 | + | 0.679492i | 0.107740 | + | 0.0288688i | ||||
\(555\) | − | 61.8564i | − | 2.62566i | ||||||
\(556\) | 10.0000 | − | 17.3205i | 0.424094 | − | 0.734553i | ||||
\(557\) | − | 34.7846i | − | 1.47387i | −0.675963 | − | 0.736936i | \(-0.736272\pi\) | ||
0.675963 | − | 0.736936i | \(-0.263728\pi\) | |||||||
\(558\) | −2.46410 | + | 9.19615i | −0.104314 | + | 0.389304i | ||||
\(559\) | 0.535898 | 0.0226661 | ||||||||
\(560\) | −15.2154 | + | 8.78461i | −0.642968 | + | 0.371218i | ||||
\(561\) | 51.7128 | 2.18332 | ||||||||
\(562\) | −3.41154 | + | 12.7321i | −0.143907 | + | 0.537069i | ||||
\(563\) | 7.46410i | 0.314574i | 0.987553 | + | 0.157287i | \(0.0502748\pi\) | ||||
−0.987553 | + | 0.157287i | \(0.949725\pi\) | |||||||
\(564\) | −13.4641 | + | 23.3205i | −0.566941 | + | 0.981971i | ||||
\(565\) | − | 8.78461i | − | 0.369571i | ||||||
\(566\) | 26.5885 | + | 7.12436i | 1.11760 | + | 0.299459i | ||||
\(567\) | 13.9474 | 0.585737 | ||||||||
\(568\) | −16.3923 | + | 16.3923i | −0.687806 | + | 0.687806i | ||||
\(569\) | −14.0000 | −0.586911 | −0.293455 | − | 0.955973i | \(-0.594805\pi\) | ||||
−0.293455 | + | 0.955973i | \(0.594805\pi\) | |||||||
\(570\) | −6.92820 | − | 1.85641i | −0.290191 | − | 0.0777563i | ||||
\(571\) | − | 2.67949i | − | 0.112133i | −0.998427 | − | 0.0560666i | \(-0.982144\pi\) | ||
0.998427 | − | 0.0560666i | \(-0.0178559\pi\) | |||||||
\(572\) | −8.19615 | − | 4.73205i | −0.342698 | − | 0.197857i | ||||
\(573\) | 29.0718i | 1.21449i | ||||||||
\(574\) | 4.14359 | − | 15.4641i | 0.172950 | − | 0.645459i | ||||
\(575\) | −28.0000 | −1.16768 | ||||||||
\(576\) | 8.00000i | 0.333333i | ||||||||
\(577\) | −7.07180 | −0.294403 | −0.147201 | − | 0.989107i | \(-0.547027\pi\) | ||||
−0.147201 | + | 0.989107i | \(0.547027\pi\) | |||||||
\(578\) | −4.70577 | + | 17.5622i | −0.195734 | + | 0.730490i | ||||
\(579\) | 3.21539i | 0.133627i | ||||||||
\(580\) | 12.0000 | + | 6.92820i | 0.498273 | + | 0.287678i | ||||
\(581\) | 4.14359i | 0.171905i | ||||||||
\(582\) | 17.4641 | + | 4.67949i | 0.723910 | + | 0.193971i | ||||
\(583\) | −13.8564 | −0.573874 | ||||||||
\(584\) | −14.9282 | + | 14.9282i | −0.617733 | + | 0.617733i | ||||
\(585\) | 3.46410 | 0.143223 | ||||||||
\(586\) | 44.9808 | + | 12.0526i | 1.85814 | + | 0.497887i | ||||
\(587\) | 4.33975i | 0.179120i | 0.995981 | + | 0.0895602i | \(0.0285462\pi\) | ||||
−0.995981 | + | 0.0895602i | \(0.971454\pi\) | |||||||
\(588\) | 10.7846 | − | 18.6795i | 0.444750 | − | 0.770329i | ||||
\(589\) | 4.92820i | 0.203063i | ||||||||
\(590\) | −12.9282 | + | 48.2487i | −0.532246 | + | 1.98637i | ||||
\(591\) | 6.14359 | 0.252714 | ||||||||
\(592\) | −30.9282 | + | 17.8564i | −1.27114 | + | 0.733894i | ||||
\(593\) | −7.85641 | −0.322624 | −0.161312 | − | 0.986903i | \(-0.551573\pi\) | ||||
−0.161312 | + | 0.986903i | \(0.551573\pi\) | |||||||
\(594\) | −6.92820 | + | 25.8564i | −0.284268 | + | 1.06090i | ||||
\(595\) | 24.0000i | 0.983904i | ||||||||
\(596\) | 12.9282 | − | 22.3923i | 0.529560 | − | 0.917225i | ||||
\(597\) | − | 33.5692i | − | 1.37390i | ||||||
\(598\) | 5.46410 | + | 1.46410i | 0.223444 | + | 0.0598716i | ||||
\(599\) | −45.1769 | −1.84588 | −0.922939 | − | 0.384945i | \(-0.874220\pi\) | ||||
−0.922939 | + | 0.384945i | \(0.874220\pi\) | |||||||
\(600\) | 28.0000 | + | 28.0000i | 1.14310 | + | 1.14310i | ||||
\(601\) | −4.39230 | −0.179166 | −0.0895829 | − | 0.995979i | \(-0.528553\pi\) | ||||
−0.0895829 | + | 0.995979i | \(0.528553\pi\) | |||||||
\(602\) | 0.928203 | + | 0.248711i | 0.0378307 | + | 0.0101367i | ||||
\(603\) | 0.732051i | 0.0298114i | ||||||||
\(604\) | 12.3397 | + | 7.12436i | 0.502097 | + | 0.289886i | ||||
\(605\) | 39.4641i | 1.60444i | ||||||||
\(606\) | −8.78461 | + | 32.7846i | −0.356850 | + | 1.33178i | ||||
\(607\) | 7.32051 | 0.297130 | 0.148565 | − | 0.988903i | \(-0.452535\pi\) | ||||
0.148565 | + | 0.988903i | \(0.452535\pi\) | |||||||
\(608\) | 1.07180 | + | 4.00000i | 0.0434671 | + | 0.162221i | ||||
\(609\) | 5.07180 | 0.205520 | ||||||||
\(610\) | 3.71281 | − | 13.8564i | 0.150327 | − | 0.561029i | ||||
\(611\) | − | 6.73205i | − | 0.272350i | ||||||
\(612\) | 9.46410 | + | 5.46410i | 0.382564 | + | 0.220873i | ||||
\(613\) | − | 24.6410i | − | 0.995241i | −0.867395 | − | 0.497621i | \(-0.834207\pi\) | ||
0.867395 | − | 0.497621i | \(-0.165793\pi\) | |||||||
\(614\) | 1.00000 | + | 0.267949i | 0.0403567 | + | 0.0108135i | ||||
\(615\) | −61.8564 | −2.49429 | ||||||||
\(616\) | −12.0000 | − | 12.0000i | −0.483494 | − | 0.483494i | ||||
\(617\) | 41.3205 | 1.66350 | 0.831751 | − | 0.555150i | \(-0.187339\pi\) | ||||
0.831751 | + | 0.555150i | \(0.187339\pi\) | |||||||
\(618\) | 18.9282 | + | 5.07180i | 0.761404 | + | 0.204018i | ||||
\(619\) | 18.5885i | 0.747133i | 0.927603 | + | 0.373567i | \(0.121865\pi\) | ||||
−0.927603 | + | 0.373567i | \(0.878135\pi\) | |||||||
\(620\) | 23.3205 | − | 40.3923i | 0.936574 | − | 1.62219i | ||||
\(621\) | − | 16.0000i | − | 0.642058i | ||||||
\(622\) | −0.392305 | + | 1.46410i | −0.0157300 | + | 0.0587051i | ||||
\(623\) | 21.9615 | 0.879870 | ||||||||
\(624\) | −4.00000 | − | 6.92820i | −0.160128 | − | 0.277350i | ||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −0.143594 | + | 0.535898i | −0.00573915 | + | 0.0214188i | ||||
\(627\) | − | 6.92820i | − | 0.276686i | ||||||
\(628\) | 16.9282 | − | 29.3205i | 0.675509 | − | 1.17002i | ||||
\(629\) | 48.7846i | 1.94517i | ||||||||
\(630\) | 6.00000 | + | 1.60770i | 0.239046 | + | 0.0640521i | ||||
\(631\) | −42.0526 | −1.67409 | −0.837043 | − | 0.547137i | \(-0.815718\pi\) | ||||
−0.837043 | + | 0.547137i | \(0.815718\pi\) | |||||||
\(632\) | 10.9282 | − | 10.9282i | 0.434701 | − | 0.434701i | ||||
\(633\) | 15.7128 | 0.624528 | ||||||||
\(634\) | 4.73205 | + | 1.26795i | 0.187934 | + | 0.0503567i | ||||
\(635\) | 13.8564i | 0.549875i | ||||||||
\(636\) | −10.1436 | − | 5.85641i | −0.402220 | − | 0.232222i | ||||
\(637\) | 5.39230i | 0.213651i | ||||||||
\(638\) | −3.46410 | + | 12.9282i | −0.137145 | + | 0.511832i | ||||
\(639\) | 8.19615 | 0.324235 | ||||||||
\(640\) | 10.1436 | − | 37.8564i | 0.400961 | − | 1.49641i | ||||
\(641\) | −22.2487 | −0.878771 | −0.439386 | − | 0.898299i | \(-0.644804\pi\) | ||||
−0.439386 | + | 0.898299i | \(0.644804\pi\) | |||||||
\(642\) | 3.60770 | − | 13.4641i | 0.142384 | − | 0.531386i | ||||
\(643\) | 12.7321i | 0.502103i | 0.967974 | + | 0.251052i | \(0.0807764\pi\) | ||||
−0.967974 | + | 0.251052i | \(0.919224\pi\) | |||||||
\(644\) | 8.78461 | + | 5.07180i | 0.346162 | + | 0.199857i | ||||
\(645\) | − | 3.71281i | − | 0.146192i | ||||||
\(646\) | 5.46410 | + | 1.46410i | 0.214982 | + | 0.0576043i | ||||
\(647\) | 37.8564 | 1.48829 | 0.744144 | − | 0.668019i | \(-0.232857\pi\) | ||||
0.744144 | + | 0.668019i | \(0.232857\pi\) | |||||||
\(648\) | −22.0000 | + | 22.0000i | −0.864242 | + | 0.864242i | ||||
\(649\) | −48.2487 | −1.89393 | ||||||||
\(650\) | −9.56218 | − | 2.56218i | −0.375059 | − | 0.100497i | ||||
\(651\) | − | 17.0718i | − | 0.669096i | ||||||
\(652\) | −16.7321 | + | 28.9808i | −0.655278 | + | 1.13497i | ||||
\(653\) | 3.07180i | 0.120209i | 0.998192 | + | 0.0601043i | \(0.0191433\pi\) | ||||
−0.998192 | + | 0.0601043i | \(0.980857\pi\) | |||||||
\(654\) | −1.46410 | + | 5.46410i | −0.0572509 | + | 0.213663i | ||||
\(655\) | −68.7846 | −2.68764 | ||||||||
\(656\) | 17.8564 | + | 30.9282i | 0.697176 | + | 1.20754i | ||||
\(657\) | 7.46410 | 0.291202 | ||||||||
\(658\) | 3.12436 | − | 11.6603i | 0.121800 | − | 0.454564i | ||||
\(659\) | − | 14.0000i | − | 0.545363i | −0.962104 | − | 0.272681i | \(-0.912090\pi\) | ||
0.962104 | − | 0.272681i | \(-0.0879105\pi\) | |||||||
\(660\) | −32.7846 | + | 56.7846i | −1.27614 | + | 2.21034i | ||||
\(661\) | − | 17.3205i | − | 0.673690i | −0.941560 | − | 0.336845i | \(-0.890640\pi\) | ||
0.941560 | − | 0.336845i | \(-0.109360\pi\) | |||||||
\(662\) | 23.9282 | + | 6.41154i | 0.929996 | + | 0.249192i | ||||
\(663\) | −10.9282 | −0.424416 | ||||||||
\(664\) | −6.53590 | − | 6.53590i | −0.253642 | − | 0.253642i | ||||
\(665\) | 3.21539 | 0.124687 | ||||||||
\(666\) | 12.1962 | + | 3.26795i | 0.472591 | + | 0.126630i | ||||
\(667\) | − | 8.00000i | − | 0.309761i | ||||||
\(668\) | 9.80385 | + | 5.66025i | 0.379322 | + | 0.219002i | ||||
\(669\) | 0.392305i | 0.0151674i | ||||||||
\(670\) | 0.928203 | − | 3.46410i | 0.0358596 | − | 0.133830i | ||||
\(671\) | 13.8564 | 0.534921 | ||||||||
\(672\) | −3.71281 | − | 13.8564i | −0.143225 | − | 0.534522i | ||||
\(673\) | 33.1769 | 1.27888 | 0.639438 | − | 0.768843i | \(-0.279167\pi\) | ||||
0.639438 | + | 0.768843i | \(0.279167\pi\) | |||||||
\(674\) | −0.535898 | + | 2.00000i | −0.0206420 | + | 0.0770371i | ||||
\(675\) | 28.0000i | 1.07772i | ||||||||
\(676\) | 1.73205 | + | 1.00000i | 0.0666173 | + | 0.0384615i | ||||
\(677\) | − | 21.0718i | − | 0.809855i | −0.914349 | − | 0.404927i | \(-0.867297\pi\) | ||
0.914349 | − | 0.404927i | \(-0.132703\pi\) | |||||||
\(678\) | 6.92820 | + | 1.85641i | 0.266076 | + | 0.0712949i | ||||
\(679\) | −8.10512 | −0.311046 | ||||||||
\(680\) | −37.8564 | − | 37.8564i | −1.45173 | − | 1.45173i | ||||
\(681\) | −5.75129 | −0.220390 | ||||||||
\(682\) | 43.5167 | + | 11.6603i | 1.66634 | + | 0.446494i | ||||
\(683\) | 17.8038i | 0.681245i | 0.940200 | + | 0.340623i | \(0.110638\pi\) | ||||
−0.940200 | + | 0.340623i | \(0.889362\pi\) | |||||||
\(684\) | 0.732051 | − | 1.26795i | 0.0279907 | − | 0.0484812i | ||||
\(685\) | − | 44.7846i | − | 1.71113i | ||||||
\(686\) | −5.75129 | + | 21.4641i | −0.219585 | + | 0.819503i | ||||
\(687\) | 10.6410 | 0.405980 | ||||||||
\(688\) | −1.85641 | + | 1.07180i | −0.0707748 | + | 0.0408619i | ||||
\(689\) | 2.92820 | 0.111556 | ||||||||
\(690\) | 10.1436 | − | 37.8564i | 0.386160 | − | 1.44117i | ||||
\(691\) | 32.8372i | 1.24918i | 0.780951 | + | 0.624592i | \(0.214735\pi\) | ||||
−0.780951 | + | 0.624592i | \(0.785265\pi\) | |||||||
\(692\) | −6.92820 | + | 12.0000i | −0.263371 | + | 0.456172i | ||||
\(693\) | 6.00000i | 0.227921i | ||||||||
\(694\) | −9.66025 | − | 2.58846i | −0.366698 | − | 0.0982565i | ||||
\(695\) | 34.6410 | 1.31401 | ||||||||
\(696\) | −8.00000 | + | 8.00000i | −0.303239 | + | 0.303239i | ||||
\(697\) | 48.7846 | 1.84785 | ||||||||
\(698\) | 13.1244 | + | 3.51666i | 0.496764 | + | 0.133108i | ||||
\(699\) | − | 33.8564i | − | 1.28057i | ||||||
\(700\) | −15.3731 | − | 8.87564i | −0.581047 | − | 0.335468i | ||||
\(701\) | 40.6410i | 1.53499i | 0.641055 | + | 0.767495i | \(0.278497\pi\) | ||||
−0.641055 | + | 0.767495i | \(0.721503\pi\) | |||||||
\(702\) | 1.46410 | − | 5.46410i | 0.0552590 | − | 0.206229i | ||||
\(703\) | 6.53590 | 0.246506 | ||||||||
\(704\) | 37.8564 | 1.42677 | ||||||||
\(705\) | −46.6410 | −1.75660 | ||||||||
\(706\) | 4.05256 | − | 15.1244i | 0.152520 | − | 0.569213i | ||||
\(707\) | − | 15.2154i | − | 0.572234i | ||||||
\(708\) | −35.3205 | − | 20.3923i | −1.32743 | − | 0.766390i | ||||
\(709\) | − | 29.3205i | − | 1.10115i | −0.834784 | − | 0.550577i | \(-0.814408\pi\) | ||
0.834784 | − | 0.550577i | \(-0.185592\pi\) | |||||||
\(710\) | −38.7846 | − | 10.3923i | −1.45556 | − | 0.390016i | ||||
\(711\) | −5.46410 | −0.204920 | ||||||||
\(712\) | −34.6410 | + | 34.6410i | −1.29823 | + | 1.29823i | ||||
\(713\) | −26.9282 | −1.00847 | ||||||||
\(714\) | −18.9282 | − | 5.07180i | −0.708370 | − | 0.189807i | ||||
\(715\) | − | 16.3923i | − | 0.613037i | ||||||
\(716\) | 10.3923 | − | 18.0000i | 0.388379 | − | 0.672692i | ||||
\(717\) | − | 37.4641i | − | 1.39912i | ||||||
\(718\) | −11.5359 | + | 43.0526i | −0.430516 | + | 1.60671i | ||||
\(719\) | 30.9282 | 1.15343 | 0.576714 | − | 0.816946i | \(-0.304335\pi\) | ||||
0.576714 | + | 0.816946i | \(0.304335\pi\) | |||||||
\(720\) | −12.0000 | + | 6.92820i | −0.447214 | + | 0.258199i | ||||
\(721\) | −8.78461 | −0.327156 | ||||||||
\(722\) | −6.75833 | + | 25.2224i | −0.251519 | + | 0.938682i | ||||
\(723\) | 60.7846i | 2.26060i | ||||||||
\(724\) | 8.92820 | − | 15.4641i | 0.331814 | − | 0.574719i | ||||
\(725\) | 14.0000i | 0.519947i | ||||||||
\(726\) | −31.1244 | − | 8.33975i | −1.15513 | − | 0.309517i | ||||
\(727\) | −22.9282 | −0.850360 | −0.425180 | − | 0.905109i | \(-0.639789\pi\) | ||||
−0.425180 | + | 0.905109i | \(0.639789\pi\) | |||||||
\(728\) | 2.53590 | + | 2.53590i | 0.0939866 | + | 0.0939866i | ||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | −35.3205 | − | 9.46410i | −1.30727 | − | 0.350282i | ||||
\(731\) | 2.92820i | 0.108304i | ||||||||
\(732\) | 10.1436 | + | 5.85641i | 0.374918 | + | 0.216459i | ||||
\(733\) | − | 37.3205i | − | 1.37846i | −0.724541 | − | 0.689232i | \(-0.757948\pi\) | ||
0.724541 | − | 0.689232i | \(-0.242052\pi\) | |||||||
\(734\) | 8.14359 | − | 30.3923i | 0.300586 | − | 1.12180i | ||||
\(735\) | 37.3590 | 1.37801 | ||||||||
\(736\) | −21.8564 | + | 5.85641i | −0.805638 | + | 0.215870i | ||||
\(737\) | 3.46410 | 0.127602 | ||||||||
\(738\) | 3.26795 | − | 12.1962i | 0.120295 | − | 0.448947i | ||||
\(739\) | − | 39.7654i | − | 1.46279i | −0.681953 | − | 0.731396i | \(-0.738869\pi\) | ||
0.681953 | − | 0.731396i | \(-0.261131\pi\) | |||||||
\(740\) | −53.5692 | − | 30.9282i | −1.96924 | − | 1.13694i | ||||
\(741\) | 1.46410i | 0.0537851i | ||||||||
\(742\) | 5.07180 | + | 1.35898i | 0.186192 | + | 0.0498899i | ||||
\(743\) | −32.1962 | −1.18116 | −0.590581 | − | 0.806978i | \(-0.701101\pi\) | ||||
−0.590581 | + | 0.806978i | \(0.701101\pi\) | |||||||
\(744\) | 26.9282 | + | 26.9282i | 0.987236 | + | 0.987236i | ||||
\(745\) | 44.7846 | 1.64078 | ||||||||
\(746\) | −20.1962 | − | 5.41154i | −0.739434 | − | 0.198131i | ||||
\(747\) | 3.26795i | 0.119568i | ||||||||
\(748\) | 25.8564 | − | 44.7846i | 0.945404 | − | 1.63749i | ||||
\(749\) | 6.24871i | 0.228323i | ||||||||
\(750\) | −5.07180 | + | 18.9282i | −0.185196 | + | 0.691160i | ||||
\(751\) | 1.07180 | 0.0391104 | 0.0195552 | − | 0.999809i | \(-0.493775\pi\) | ||||
0.0195552 | + | 0.999809i | \(0.493775\pi\) | |||||||
\(752\) | 13.4641 | + | 23.3205i | 0.490985 | + | 0.850411i | ||||
\(753\) | −12.7846 | −0.465897 | ||||||||
\(754\) | 0.732051 | − | 2.73205i | 0.0266597 | − | 0.0994954i | ||||
\(755\) | 24.6795i | 0.898179i | ||||||||
\(756\) | 5.07180 | − | 8.78461i | 0.184459 | − | 0.319493i | ||||
\(757\) | − | 40.7846i | − | 1.48234i | −0.671316 | − | 0.741171i | \(-0.734271\pi\) | ||
0.671316 | − | 0.741171i | \(-0.265729\pi\) | |||||||
\(758\) | 19.9282 | + | 5.33975i | 0.723825 | + | 0.193948i | ||||
\(759\) | 37.8564 | 1.37410 | ||||||||
\(760\) | −5.07180 | + | 5.07180i | −0.183973 | + | 0.183973i | ||||
\(761\) | 18.7846 | 0.680942 | 0.340471 | − | 0.940255i | \(-0.389414\pi\) | ||||
0.340471 | + | 0.940255i | \(0.389414\pi\) | |||||||
\(762\) | −10.9282 | − | 2.92820i | −0.395887 | − | 0.106078i | ||||
\(763\) | − | 2.53590i | − | 0.0918057i | ||||||
\(764\) | 25.1769 | + | 14.5359i | 0.910869 | + | 0.525890i | ||||
\(765\) | 18.9282i | 0.684351i | ||||||||
\(766\) | 3.78461 | − | 14.1244i | 0.136744 | − | 0.510334i | ||||
\(767\) | 10.1962 | 0.368162 | ||||||||
\(768\) | 27.7128 | + | 16.0000i | 1.00000 | + | 0.577350i | ||||
\(769\) | 31.4641 | 1.13462 | 0.567312 | − | 0.823503i | \(-0.307983\pi\) | ||||
0.567312 | + | 0.823503i | \(0.307983\pi\) | |||||||
\(770\) | 7.60770 | − | 28.3923i | 0.274162 | − | 1.02319i | ||||
\(771\) | 47.7128i | 1.71833i | ||||||||
\(772\) | 2.78461 | + | 1.60770i | 0.100220 | + | 0.0578622i | ||||
\(773\) | − | 27.4641i | − | 0.987815i | −0.869514 | − |