Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(226,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.226");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.4 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.226 |
Dual form | 675.2.e.d.451.4 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | + | 1.67303i | 0.683013 | + | 1.18301i | 0.974057 | + | 0.226303i | \(0.0726640\pi\) |
−0.291044 | + | 0.956710i | \(0.594003\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.866025 | + | 1.50000i | −0.433013 | + | 0.750000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.448288 | − | 0.776457i | −0.169437 | − | 0.293473i | 0.768785 | − | 0.639507i | \(-0.220862\pi\) |
−0.938222 | + | 0.346034i | \(0.887528\pi\) | |||||||
\(8\) | 0.517638 | 0.183013 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.36603 | + | 4.09808i | 0.713384 | + | 1.23562i | 0.963580 | + | 0.267421i | \(0.0861715\pi\) |
−0.250196 | + | 0.968195i | \(0.580495\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.22474 | + | 2.12132i | −0.339683 | + | 0.588348i | −0.984373 | − | 0.176096i | \(-0.943653\pi\) |
0.644690 | + | 0.764444i | \(0.276986\pi\) | |||||||
\(14\) | 0.866025 | − | 1.50000i | 0.231455 | − | 0.400892i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.23205 | + | 3.86603i | 0.558013 | + | 0.966506i | ||||
\(17\) | −0.378937 | −0.0919058 | −0.0459529 | − | 0.998944i | \(-0.514632\pi\) | ||||
−0.0459529 | + | 0.998944i | \(0.514632\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.73205 | 0.626775 | 0.313388 | − | 0.949625i | \(-0.398536\pi\) | ||||
0.313388 | + | 0.949625i | \(0.398536\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.57081 | + | 7.91688i | −0.974500 | + | 1.68788i | ||||
\(23\) | −0.965926 | + | 1.67303i | −0.201409 | + | 0.348851i | −0.948983 | − | 0.315328i | \(-0.897886\pi\) |
0.747573 | + | 0.664179i | \(0.231219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.73205 | −0.928032 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.55291 | 0.293473 | ||||||||
\(29\) | 3.23205 | + | 5.59808i | 0.600177 | + | 1.03954i | 0.992794 | + | 0.119835i | \(0.0382364\pi\) |
−0.392617 | + | 0.919702i | \(0.628430\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.36603 | − | 2.36603i | 0.245345 | − | 0.424951i | −0.716883 | − | 0.697193i | \(-0.754432\pi\) |
0.962229 | + | 0.272243i | \(0.0877653\pi\) | |||||||
\(32\) | −3.79435 | + | 6.57201i | −0.670753 | + | 1.16178i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.366025 | − | 0.633975i | −0.0627728 | − | 0.108726i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.24264 | −0.697486 | −0.348743 | − | 0.937218i | \(-0.613391\pi\) | ||||
−0.348743 | + | 0.937218i | \(0.613391\pi\) | |||||||
\(38\) | 2.63896 | + | 4.57081i | 0.428096 | + | 0.741483i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.13397 | − | 3.69615i | 0.333271 | − | 0.577242i | −0.649880 | − | 0.760037i | \(-0.725181\pi\) |
0.983151 | + | 0.182795i | \(0.0585143\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.57081 | − | 7.91688i | −0.697042 | − | 1.20731i | −0.969487 | − | 0.245141i | \(-0.921166\pi\) |
0.272445 | − | 0.962171i | \(-0.412168\pi\) | |||||||
\(44\) | −8.19615 | −1.23562 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.73205 | −0.550261 | ||||||||
\(47\) | 2.19067 | + | 3.79435i | 0.319542 | + | 0.553463i | 0.980393 | − | 0.197054i | \(-0.0631376\pi\) |
−0.660850 | + | 0.750518i | \(0.729804\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.09808 | − | 5.36603i | 0.442582 | − | 0.766575i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.12132 | − | 3.67423i | −0.294174 | − | 0.509525i | ||||
\(53\) | −3.86370 | −0.530720 | −0.265360 | − | 0.964149i | \(-0.585491\pi\) | ||||
−0.265360 | + | 0.964149i | \(0.585491\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.232051 | − | 0.401924i | −0.0310091 | − | 0.0537093i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.24384 | + | 10.8147i | −0.819857 | + | 1.42003i | ||||
\(59\) | 1.26795 | − | 2.19615i | 0.165073 | − | 0.285915i | −0.771608 | − | 0.636098i | \(-0.780547\pi\) |
0.936681 | + | 0.350183i | \(0.113881\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.33013 | − | 9.23205i | −0.682453 | − | 1.18204i | −0.974230 | − | 0.225557i | \(-0.927580\pi\) |
0.291777 | − | 0.956486i | \(-0.405753\pi\) | |||||||
\(62\) | 5.27792 | 0.670296 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.73205 | −0.716506 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.56961 | − | 4.45069i | 0.313928 | − | 0.543739i | −0.665281 | − | 0.746593i | \(-0.731688\pi\) |
0.979209 | + | 0.202854i | \(0.0650217\pi\) | |||||||
\(68\) | 0.328169 | − | 0.568406i | 0.0397964 | − | 0.0689294i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.80385 | −0.451434 | −0.225717 | − | 0.974193i | \(-0.572472\pi\) | ||||
−0.225717 | + | 0.974193i | \(0.572472\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.48528 | 0.993127 | 0.496564 | − | 0.868000i | \(-0.334595\pi\) | ||||
0.496564 | + | 0.868000i | \(0.334595\pi\) | |||||||
\(74\) | −4.09808 | − | 7.09808i | −0.476392 | − | 0.825135i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.36603 | + | 4.09808i | −0.271402 | + | 0.470082i | ||||
\(77\) | 2.12132 | − | 3.67423i | 0.241747 | − | 0.418718i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.267949 | − | 0.464102i | −0.0301466 | − | 0.0522155i | 0.850558 | − | 0.525880i | \(-0.176264\pi\) |
−0.880705 | + | 0.473665i | \(0.842931\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.24504 | 0.910513 | ||||||||
\(83\) | −5.20857 | − | 9.02150i | −0.571714 | − | 0.990238i | −0.996390 | − | 0.0848929i | \(-0.972945\pi\) |
0.424676 | − | 0.905346i | \(-0.360388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.83013 | − | 15.2942i | 0.952177 | − | 1.64922i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.22474 | + | 2.12132i | 0.130558 | + | 0.226134i | ||||
\(89\) | 7.39230 | 0.783583 | 0.391791 | − | 0.920054i | \(-0.371856\pi\) | ||||
0.391791 | + | 0.920054i | \(0.371856\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.19615 | 0.230219 | ||||||||
\(92\) | −1.67303 | − | 2.89778i | −0.174426 | − | 0.302114i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.23205 | + | 7.33013i | −0.436503 | + | 0.756045i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.13922 | + | 8.90138i | 0.521808 | + | 0.903799i | 0.999678 | + | 0.0253679i | \(0.00807572\pi\) |
−0.477870 | + | 0.878431i | \(0.658591\pi\) | |||||||
\(98\) | 11.9700 | 1.20916 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.26795 | + | 2.19615i | 0.126166 | + | 0.218525i | 0.922188 | − | 0.386742i | \(-0.126400\pi\) |
−0.796022 | + | 0.605267i | \(0.793066\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.57081 | − | 7.91688i | 0.450375 | − | 0.780073i | −0.548034 | − | 0.836456i | \(-0.684624\pi\) |
0.998409 | + | 0.0563832i | \(0.0179569\pi\) | |||||||
\(104\) | −0.633975 | + | 1.09808i | −0.0621663 | + | 0.107675i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.73205 | − | 6.46410i | −0.362489 | − | 0.627849i | ||||
\(107\) | −11.7298 | −1.13396 | −0.566982 | − | 0.823730i | \(-0.691889\pi\) | ||||
−0.566982 | + | 0.823730i | \(0.691889\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.66025 | −0.446371 | −0.223186 | − | 0.974776i | \(-0.571646\pi\) | ||||
−0.223186 | + | 0.974776i | \(0.571646\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.00120 | − | 3.46618i | 0.189096 | − | 0.327524i | ||||
\(113\) | 1.27551 | − | 2.20925i | 0.119990 | − | 0.207829i | −0.799773 | − | 0.600302i | \(-0.795047\pi\) |
0.919764 | + | 0.392473i | \(0.128380\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −11.1962 | −1.03954 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.89898 | 0.450988 | ||||||||
\(119\) | 0.169873 | + | 0.294229i | 0.0155722 | + | 0.0269719i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.69615 | + | 9.86603i | −0.517832 | + | 0.896911i | ||||
\(122\) | 10.2970 | − | 17.8350i | 0.932248 | − | 1.61470i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.36603 | + | 4.09808i | 0.212475 | + | 0.368018i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.65874 | −0.413397 | −0.206698 | − | 0.978405i | \(-0.566272\pi\) | ||||
−0.206698 | + | 0.978405i | \(0.566272\pi\) | |||||||
\(128\) | 2.05197 | + | 3.55412i | 0.181370 | + | 0.314142i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.464102 | + | 0.803848i | −0.0405487 | + | 0.0702325i | −0.885588 | − | 0.464473i | \(-0.846244\pi\) |
0.845039 | + | 0.534705i | \(0.179577\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.22474 | − | 2.12132i | −0.106199 | − | 0.183942i | ||||
\(134\) | 9.92820 | 0.857666 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.196152 | −0.0168199 | ||||||||
\(137\) | −9.28032 | − | 16.0740i | −0.792871 | − | 1.37329i | −0.924182 | − | 0.381952i | \(-0.875252\pi\) |
0.131311 | − | 0.991341i | \(-0.458081\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | − | 6.92820i | 0.339276 | − | 0.587643i | −0.645021 | − | 0.764165i | \(-0.723151\pi\) |
0.984297 | + | 0.176522i | \(0.0564848\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.67423 | − | 6.36396i | −0.308335 | − | 0.534052i | ||||
\(143\) | −11.5911 | −0.969297 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.19615 | + | 14.1962i | 0.678318 | + | 1.17488i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.67423 | − | 6.36396i | 0.302020 | − | 0.523114i | ||||
\(149\) | 3.86603 | − | 6.69615i | 0.316717 | − | 0.548570i | −0.663084 | − | 0.748545i | \(-0.730753\pi\) |
0.979801 | + | 0.199975i | \(0.0640861\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.2942 | + | 19.5622i | 0.919111 | + | 1.59195i | 0.800768 | + | 0.598975i | \(0.204425\pi\) |
0.118343 | + | 0.992973i | \(0.462242\pi\) | |||||||
\(152\) | 1.41421 | 0.114708 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.19615 | 0.660465 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.6945 | − | 18.5235i | 0.853517 | − | 1.47833i | −0.0244975 | − | 0.999700i | \(-0.507799\pi\) |
0.878014 | − | 0.478635i | \(-0.158868\pi\) | |||||||
\(158\) | 0.517638 | − | 0.896575i | 0.0411811 | − | 0.0713277i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.73205 | 0.136505 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.9396 | −1.48346 | −0.741731 | − | 0.670697i | \(-0.765995\pi\) | ||||
−0.741731 | + | 0.670697i | \(0.765995\pi\) | |||||||
\(164\) | 3.69615 | + | 6.40192i | 0.288621 | + | 0.499906i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.0622 | − | 17.4282i | 0.780976 | − | 1.35269i | ||||
\(167\) | −8.50386 | + | 14.7291i | −0.658049 | + | 1.13977i | 0.323071 | + | 0.946375i | \(0.395285\pi\) |
−0.981120 | + | 0.193399i | \(0.938049\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.50000 | + | 6.06218i | 0.269231 | + | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15.8338 | 1.20731 | ||||||||
\(173\) | 0.378937 | + | 0.656339i | 0.0288101 | + | 0.0499005i | 0.880071 | − | 0.474842i | \(-0.157495\pi\) |
−0.851261 | + | 0.524743i | \(0.824162\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.5622 | + | 18.2942i | −0.796154 | + | 1.37898i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.14042 | + | 12.3676i | 0.535197 | + | 0.926988i | ||||
\(179\) | −24.5885 | −1.83783 | −0.918914 | − | 0.394458i | \(-0.870932\pi\) | ||||
−0.918914 | + | 0.394458i | \(0.870932\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.46410 | 0.629132 | 0.314566 | − | 0.949236i | \(-0.398141\pi\) | ||||
0.314566 | + | 0.949236i | \(0.398141\pi\) | |||||||
\(182\) | 2.12132 | + | 3.67423i | 0.157243 | + | 0.272352i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.500000 | + | 0.866025i | −0.0368605 | + | 0.0638442i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.896575 | − | 1.55291i | −0.0655641 | − | 0.113560i | ||||
\(188\) | −7.58871 | −0.553463 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.169873 | + | 0.294229i | 0.0122916 | + | 0.0212896i | 0.872106 | − | 0.489317i | \(-0.162754\pi\) |
−0.859814 | + | 0.510607i | \(0.829421\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.3664 | − | 17.9551i | 0.746187 | − | 1.29243i | −0.203451 | − | 0.979085i | \(-0.565216\pi\) |
0.949638 | − | 0.313349i | \(-0.101451\pi\) | |||||||
\(194\) | −9.92820 | + | 17.1962i | −0.712803 | + | 1.23461i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.36603 | + | 9.29423i | 0.383288 | + | 0.663873i | ||||
\(197\) | 20.8343 | 1.48438 | 0.742190 | − | 0.670190i | \(-0.233787\pi\) | ||||
0.742190 | + | 0.670190i | \(0.233787\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.58846 | 0.325267 | 0.162634 | − | 0.986687i | \(-0.448001\pi\) | ||||
0.162634 | + | 0.986687i | \(0.448001\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.44949 | + | 4.24264i | −0.172345 | + | 0.298511i | ||||
\(203\) | 2.89778 | − | 5.01910i | 0.203384 | − | 0.352272i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.6603 | 1.23045 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10.9348 | −0.758190 | ||||||||
\(209\) | 6.46410 | + | 11.1962i | 0.447131 | + | 0.774454i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.56218 | − | 11.3660i | 0.451759 | − | 0.782469i | −0.546736 | − | 0.837305i | \(-0.684130\pi\) |
0.998495 | + | 0.0548353i | \(0.0174634\pi\) | |||||||
\(212\) | 3.34607 | − | 5.79555i | 0.229809 | − | 0.398040i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.3301 | − | 19.6244i | −0.774512 | − | 1.34149i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.44949 | −0.166282 | ||||||||
\(218\) | −4.50146 | − | 7.79676i | −0.304877 | − | 0.528063i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.464102 | − | 0.803848i | 0.0312189 | − | 0.0540726i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.36516 | + | 14.4889i | 0.560173 | + | 0.970248i | 0.997481 | + | 0.0709359i | \(0.0225986\pi\) |
−0.437308 | + | 0.899312i | \(0.644068\pi\) | |||||||
\(224\) | 6.80385 | 0.454601 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.92820 | 0.327819 | ||||||||
\(227\) | −0.947343 | − | 1.64085i | −0.0628774 | − | 0.108907i | 0.832873 | − | 0.553464i | \(-0.186694\pi\) |
−0.895750 | + | 0.444557i | \(0.853361\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.96410 | + | 17.2583i | −0.658446 | + | 1.14046i | 0.322571 | + | 0.946545i | \(0.395453\pi\) |
−0.981018 | + | 0.193917i | \(0.937881\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.67303 | + | 2.89778i | 0.109840 | + | 0.190248i | ||||
\(233\) | 7.07107 | 0.463241 | 0.231621 | − | 0.972806i | \(-0.425597\pi\) | ||||
0.231621 | + | 0.972806i | \(0.425597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.19615 | + | 3.80385i | 0.142957 | + | 0.247609i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.328169 | + | 0.568406i | −0.0212721 | + | 0.0368443i | ||||
\(239\) | 6.46410 | − | 11.1962i | 0.418128 | − | 0.724219i | −0.577623 | − | 0.816304i | \(-0.696020\pi\) |
0.995751 | + | 0.0920846i | \(0.0293530\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.13397 | − | 5.42820i | −0.201877 | − | 0.349661i | 0.747256 | − | 0.664536i | \(-0.231371\pi\) |
−0.949133 | + | 0.314875i | \(0.898037\pi\) | |||||||
\(242\) | −22.0082 | −1.41474 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 18.4641 | 1.18204 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.34607 | + | 5.79555i | −0.212905 | + | 0.368762i | ||||
\(248\) | 0.707107 | − | 1.22474i | 0.0449013 | − | 0.0777714i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.5885 | −1.17329 | −0.586647 | − | 0.809843i | \(-0.699552\pi\) | ||||
−0.586647 | + | 0.809843i | \(0.699552\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.14162 | −0.574729 | ||||||||
\(254\) | −4.50000 | − | 7.79423i | −0.282355 | − | 0.489053i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.69615 | + | 16.7942i | −0.606010 | + | 1.04964i | ||||
\(257\) | 11.2122 | − | 19.4201i | 0.699396 | − | 1.21139i | −0.269280 | − | 0.963062i | \(-0.586786\pi\) |
0.968676 | − | 0.248328i | \(-0.0798810\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.90192 | + | 3.29423i | 0.118180 | + | 0.204693i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.79315 | −0.110781 | ||||||||
\(263\) | 3.81294 | + | 6.60420i | 0.235116 | + | 0.407232i | 0.959306 | − | 0.282368i | \(-0.0911198\pi\) |
−0.724191 | + | 0.689600i | \(0.757786\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.36603 | − | 4.09808i | 0.145070 | − | 0.251269i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.45069 | + | 7.70882i | 0.271869 | + | 0.470891i | ||||
\(269\) | −17.1962 | −1.04847 | −0.524234 | − | 0.851574i | \(-0.675648\pi\) | ||||
−0.524234 | + | 0.851574i | \(0.675648\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.5167 | −1.42854 | −0.714268 | − | 0.699873i | \(-0.753240\pi\) | ||||
−0.714268 | + | 0.699873i | \(0.753240\pi\) | |||||||
\(272\) | −0.845807 | − | 1.46498i | −0.0512846 | − | 0.0888276i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.9282 | − | 31.0526i | 1.08308 | − | 1.87595i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.12372 | + | 10.6066i | 0.367939 | + | 0.637289i | 0.989243 | − | 0.146281i | \(-0.0467302\pi\) |
−0.621304 | + | 0.783569i | \(0.713397\pi\) | |||||||
\(278\) | 15.4548 | 0.926918 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.13397 | − | 14.0885i | −0.485232 | − | 0.840447i | 0.514624 | − | 0.857416i | \(-0.327932\pi\) |
−0.999856 | + | 0.0169692i | \(0.994598\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.24144 | − | 3.88229i | 0.133240 | − | 0.230778i | −0.791684 | − | 0.610931i | \(-0.790795\pi\) |
0.924924 | + | 0.380153i | \(0.124129\pi\) | |||||||
\(284\) | 3.29423 | − | 5.70577i | 0.195477 | − | 0.338575i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.1962 | − | 19.3923i | −0.662042 | − | 1.14669i | ||||
\(287\) | −3.82654 | −0.225873 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8564 | −0.991553 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.34847 | + | 12.7279i | −0.430037 | + | 0.744845i | ||||
\(293\) | −4.43211 | + | 7.67664i | −0.258927 | + | 0.448474i | −0.965955 | − | 0.258711i | \(-0.916702\pi\) |
0.707028 | + | 0.707186i | \(0.250035\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.19615 | −0.127649 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.9372 | 0.865287 | ||||||||
\(299\) | −2.36603 | − | 4.09808i | −0.136831 | − | 0.236998i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.09808 | + | 7.09808i | −0.236209 | + | 0.409126i | ||||
\(302\) | −21.8188 | + | 37.7912i | −1.25553 | + | 2.17464i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.09808 | + | 10.5622i | 0.349749 | + | 0.605782i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.8719 | −1.47659 | −0.738295 | − | 0.674478i | \(-0.764369\pi\) | ||||
−0.738295 | + | 0.674478i | \(0.764369\pi\) | |||||||
\(308\) | 3.67423 | + | 6.36396i | 0.209359 | + | 0.362620i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.0263 | − | 24.2942i | 0.795357 | − | 1.37760i | −0.127255 | − | 0.991870i | \(-0.540617\pi\) |
0.922612 | − | 0.385729i | \(-0.126050\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.77766 | + | 4.81105i | 0.157003 | + | 0.271936i | 0.933786 | − | 0.357831i | \(-0.116484\pi\) |
−0.776784 | + | 0.629767i | \(0.783150\pi\) | |||||||
\(314\) | 41.3205 | 2.33185 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.928203 | 0.0522155 | ||||||||
\(317\) | 17.5761 | + | 30.4428i | 0.987174 | + | 1.70984i | 0.631846 | + | 0.775094i | \(0.282297\pi\) |
0.355328 | + | 0.934742i | \(0.384369\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.2942 | + | 26.4904i | −0.856312 | + | 1.48318i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.67303 | + | 2.89778i | 0.0932345 | + | 0.161487i | ||||
\(323\) | −1.03528 | −0.0576043 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.2942 | − | 31.6865i | −1.01322 | − | 1.75495i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.10463 | − | 1.91327i | 0.0609928 | − | 0.105643i | ||||
\(329\) | 1.96410 | − | 3.40192i | 0.108284 | − | 0.187554i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.19615 | − | 10.7321i | −0.340571 | − | 0.589887i | 0.643968 | − | 0.765053i | \(-0.277287\pi\) |
−0.984539 | + | 0.175166i | \(0.943954\pi\) | |||||||
\(332\) | 18.0430 | 0.990238 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −32.8564 | −1.79782 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.896575 | + | 1.55291i | −0.0488396 | + | 0.0845926i | −0.889412 | − | 0.457107i | \(-0.848886\pi\) |
0.840572 | + | 0.541700i | \(0.182219\pi\) | |||||||
\(338\) | −6.76148 | + | 11.7112i | −0.367776 | + | 0.637007i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.9282 | 0.700101 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.8313 | −0.638833 | ||||||||
\(344\) | −2.36603 | − | 4.09808i | −0.127568 | − | 0.220953i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.732051 | + | 1.26795i | −0.0393553 | + | 0.0681654i | ||||
\(347\) | −4.94975 | + | 8.57321i | −0.265716 | + | 0.460234i | −0.967751 | − | 0.251909i | \(-0.918942\pi\) |
0.702035 | + | 0.712143i | \(0.252275\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.7679 | − | 18.6506i | −0.576395 | − | 0.998346i | −0.995889 | − | 0.0905872i | \(-0.971126\pi\) |
0.419493 | − | 0.907758i | \(-0.362208\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −35.9101 | −1.91402 | ||||||||
\(353\) | −4.52004 | − | 7.82894i | −0.240578 | − | 0.416693i | 0.720301 | − | 0.693661i | \(-0.244004\pi\) |
−0.960879 | + | 0.276969i | \(0.910670\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.40192 | + | 11.0885i | −0.339301 | + | 0.587687i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −23.7506 | − | 41.1373i | −1.25526 | − | 2.17417i | ||||
\(359\) | −9.80385 | −0.517427 | −0.258714 | − | 0.965954i | \(-0.583299\pi\) | ||||
−0.258714 | + | 0.965954i | \(0.583299\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.5359 | −0.607153 | ||||||||
\(362\) | 8.17569 | + | 14.1607i | 0.429705 | + | 0.744271i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.90192 | + | 3.29423i | −0.0996879 | + | 0.172664i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.3998 | − | 21.4770i | −0.647262 | − | 1.12109i | −0.983774 | − | 0.179411i | \(-0.942581\pi\) |
0.336512 | − | 0.941679i | \(-0.390753\pi\) | |||||||
\(368\) | −8.62398 | −0.449556 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.73205 | + | 3.00000i | 0.0899236 | + | 0.155752i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.0740 | + | 27.8410i | −0.832280 | + | 1.44155i | 0.0639468 | + | 0.997953i | \(0.479631\pi\) |
−0.896226 | + | 0.443597i | \(0.853702\pi\) | |||||||
\(374\) | 1.73205 | − | 3.00000i | 0.0895622 | − | 0.155126i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.13397 | + | 1.96410i | 0.0584803 | + | 0.101291i | ||||
\(377\) | −15.8338 | −0.815480 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.5359 | 0.643926 | 0.321963 | − | 0.946752i | \(-0.395657\pi\) | ||||
0.321963 | + | 0.946752i | \(0.395657\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.328169 | + | 0.568406i | −0.0167906 | + | 0.0290822i | ||||
\(383\) | −10.2277 | + | 17.7148i | −0.522609 | + | 0.905186i | 0.477045 | + | 0.878879i | \(0.341708\pi\) |
−0.999654 | + | 0.0263067i | \(0.991625\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 40.0526 | 2.03862 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −17.8028 | −0.903799 | ||||||||
\(389\) | −12.0622 | − | 20.8923i | −0.611577 | − | 1.05928i | −0.990975 | − | 0.134048i | \(-0.957202\pi\) |
0.379398 | − | 0.925234i | \(-0.376131\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.366025 | − | 0.633975i | 0.0185107 | − | 0.0320615i | ||||
\(392\) | 1.60368 | − | 2.77766i | 0.0809982 | − | 0.140293i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 20.1244 | + | 34.8564i | 1.01385 | + | 1.75604i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.3939 | 1.47524 | 0.737618 | − | 0.675218i | \(-0.235950\pi\) | ||||
0.737618 | + | 0.675218i | \(0.235950\pi\) | |||||||
\(398\) | 4.43211 | + | 7.67664i | 0.222162 | + | 0.384795i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.4641 | + | 26.7846i | −0.772240 | + | 1.33756i | 0.164092 | + | 0.986445i | \(0.447531\pi\) |
−0.936333 | + | 0.351115i | \(0.885803\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.34607 | + | 5.79555i | 0.166679 | + | 0.288697i | ||||
\(404\) | −4.39230 | −0.218525 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.1962 | 0.555656 | ||||||||
\(407\) | −10.0382 | − | 17.3867i | −0.497575 | − | 0.861825i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.7321 | − | 20.3205i | 0.580113 | − | 1.00478i | −0.415353 | − | 0.909660i | \(-0.636342\pi\) |
0.995465 | − | 0.0951241i | \(-0.0303248\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.91688 | + | 13.7124i | 0.390036 | + | 0.675563i | ||||
\(413\) | −2.27362 | −0.111878 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9.29423 | − | 16.0981i | −0.455687 | − | 0.789273i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −12.4877 | + | 21.6293i | −0.610793 | + | 1.05792i | ||||
\(419\) | −8.02628 | + | 13.9019i | −0.392109 | + | 0.679153i | −0.992728 | − | 0.120383i | \(-0.961588\pi\) |
0.600618 | + | 0.799536i | \(0.294921\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.26795 | + | 10.8564i | 0.305481 | + | 0.529109i | 0.977368 | − | 0.211545i | \(-0.0678494\pi\) |
−0.671887 | + | 0.740653i | \(0.734516\pi\) | |||||||
\(422\) | 25.3543 | 1.23423 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.00000 | −0.0971286 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.77886 | + | 8.27723i | −0.231265 | + | 0.400563i | ||||
\(428\) | 10.1583 | − | 17.5947i | 0.491021 | − | 0.850473i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.00000 | 0.289010 | 0.144505 | − | 0.989504i | \(-0.453841\pi\) | ||||
0.144505 | + | 0.989504i | \(0.453841\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.5307 | 1.46721 | 0.733606 | − | 0.679575i | \(-0.237836\pi\) | ||||
0.733606 | + | 0.679575i | \(0.237836\pi\) | |||||||
\(434\) | −2.36603 | − | 4.09808i | −0.113573 | − | 0.196714i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.03590 | − | 6.99038i | 0.193284 | − | 0.334779i | ||||
\(437\) | −2.63896 | + | 4.57081i | −0.126239 | + | 0.218651i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.66025 | − | 8.07180i | −0.222422 | − | 0.385246i | 0.733121 | − | 0.680098i | \(-0.238063\pi\) |
−0.955543 | + | 0.294852i | \(0.904730\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.79315 | 0.0852915 | ||||||||
\(443\) | 6.95095 | + | 12.0394i | 0.330250 | + | 0.572009i | 0.982561 | − | 0.185942i | \(-0.0595338\pi\) |
−0.652311 | + | 0.757951i | \(0.726200\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16.1603 | + | 27.9904i | −0.765210 | + | 1.32538i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.56961 | + | 4.45069i | 0.121403 | + | 0.210275i | ||||
\(449\) | 12.0000 | 0.566315 | 0.283158 | − | 0.959073i | \(-0.408618\pi\) | ||||
0.283158 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.1962 | 0.951000 | ||||||||
\(452\) | 2.20925 | + | 3.82654i | 0.103915 | + | 0.179985i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.83013 | − | 3.16987i | 0.0858921 | − | 0.148770i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.2987 | + | 29.9623i | 0.809201 | + | 1.40158i | 0.913418 | + | 0.407022i | \(0.133433\pi\) |
−0.104218 | + | 0.994554i | \(0.533234\pi\) | |||||||
\(458\) | −38.4983 | −1.79891 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.35641 | + | 16.2058i | 0.435771 | + | 0.754778i | 0.997358 | − | 0.0726397i | \(-0.0231423\pi\) |
−0.561587 | + | 0.827418i | \(0.689809\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.0879327 | + | 0.152304i | −0.00408658 | + | 0.00707816i | −0.868061 | − | 0.496457i | \(-0.834634\pi\) |
0.863975 | + | 0.503535i | \(0.167967\pi\) | |||||||
\(464\) | −14.4282 | + | 24.9904i | −0.669813 | + | 1.16015i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.83013 | + | 11.8301i | 0.316400 | + | 0.548020i | ||||
\(467\) | −5.75839 | −0.266467 | −0.133233 | − | 0.991085i | \(-0.542536\pi\) | ||||
−0.133233 | + | 0.991085i | \(0.542536\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.60770 | −0.212764 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.656339 | − | 1.13681i | 0.0302104 | − | 0.0523260i | ||||
\(473\) | 21.6293 | − | 37.4631i | 0.994517 | − | 1.72255i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.588457 | −0.0269719 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.9754 | 1.14235 | ||||||||
\(479\) | 15.9282 | + | 27.5885i | 0.727778 | + | 1.26055i | 0.957820 | + | 0.287368i | \(0.0927803\pi\) |
−0.230042 | + | 0.973181i | \(0.573886\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.19615 | − | 9.00000i | 0.236924 | − | 0.410365i | ||||
\(482\) | 6.05437 | − | 10.4865i | 0.275769 | − | 0.477646i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.86603 | − | 17.0885i | −0.448456 | − | 0.776748i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.13681 | 0.0515139 | 0.0257569 | − | 0.999668i | \(-0.491800\pi\) | ||||
0.0257569 | + | 0.999668i | \(0.491800\pi\) | |||||||
\(488\) | −2.75908 | − | 4.77886i | −0.124898 | − | 0.216329i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.8564 | + | 18.8038i | −0.489943 | + | 0.848606i | −0.999933 | − | 0.0115744i | \(-0.996316\pi\) |
0.509990 | + | 0.860180i | \(0.329649\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.22474 | − | 2.12132i | −0.0551597 | − | 0.0955395i | ||||
\(494\) | −12.9282 | −0.581667 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.1962 | 0.547623 | ||||||||
\(497\) | 1.70522 | + | 2.95352i | 0.0764895 | + | 0.132484i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.92820 | − | 3.33975i | 0.0863182 | − | 0.149508i | −0.819634 | − | 0.572888i | \(-0.805823\pi\) |
0.905952 | + | 0.423380i | \(0.139156\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −17.9551 | − | 31.0991i | −0.801374 | − | 1.38802i | ||||
\(503\) | 29.3567 | 1.30895 | 0.654476 | − | 0.756083i | \(-0.272889\pi\) | ||||
0.654476 | + | 0.756083i | \(0.272889\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.83013 | − | 15.2942i | −0.392547 | − | 0.679911i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.03459 | − | 6.98811i | 0.179006 | − | 0.310047i | ||||
\(509\) | −5.42820 | + | 9.40192i | −0.240601 | + | 0.416733i | −0.960886 | − | 0.276946i | \(-0.910678\pi\) |
0.720285 | + | 0.693679i | \(0.244011\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.80385 | − | 6.58846i | −0.168272 | − | 0.291456i | ||||
\(512\) | −29.2552 | −1.29291 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 43.3205 | 1.91079 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.3664 | + | 17.9551i | −0.455912 | + | 0.789663i | ||||
\(518\) | −3.67423 | + | 6.36396i | −0.161437 | + | 0.279616i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.39230 | −0.0609980 | −0.0304990 | − | 0.999535i | \(-0.509710\pi\) | ||||
−0.0304990 | + | 0.999535i | \(0.509710\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.9468 | 1.35321 | 0.676604 | − | 0.736347i | \(-0.263451\pi\) | ||||
0.676604 | + | 0.736347i | \(0.263451\pi\) | |||||||
\(524\) | −0.803848 | − | 1.39230i | −0.0351162 | − | 0.0608231i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.36603 | + | 12.7583i | −0.321174 | + | 0.556290i | ||||
\(527\) | −0.517638 | + | 0.896575i | −0.0225487 | + | 0.0390554i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.63397 | + | 16.6865i | 0.418868 | + | 0.725501i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.24264 | 0.183942 | ||||||||
\(533\) | 5.22715 | + | 9.05369i | 0.226413 | + | 0.392159i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.33013 | − | 2.30385i | 0.0574527 | − | 0.0995111i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.6102 | − | 28.7697i | −0.716117 | − | 1.24035i | ||||
\(539\) | 29.3205 | 1.26292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.3923 | 0.919727 | 0.459864 | − | 0.887990i | \(-0.347898\pi\) | ||||
0.459864 | + | 0.887990i | \(0.347898\pi\) | |||||||
\(542\) | −22.7153 | − | 39.3441i | −0.975708 | − | 1.68998i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.43782 | − | 2.49038i | 0.0616461 | − | 0.106774i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.1452 | − | 26.2323i | −0.647563 | − | 1.12161i | −0.983703 | − | 0.179800i | \(-0.942455\pi\) |
0.336140 | − | 0.941812i | \(-0.390878\pi\) | |||||||
\(548\) | 32.1480 | 1.37329 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.83013 | + | 15.2942i | 0.376176 | + | 0.651556i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.240237 | + | 0.416102i | −0.0102159 | + | 0.0176945i | ||||
\(554\) | −11.8301 | + | 20.4904i | −0.502614 | + | 0.870553i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.92820 | + | 12.0000i | 0.293821 | + | 0.508913i | ||||
\(557\) | 31.1127 | 1.31829 | 0.659144 | − | 0.752017i | \(-0.270919\pi\) | ||||
0.659144 | + | 0.752017i | \(0.270919\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.3923 | 0.947094 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.7136 | − | 27.2168i | 0.662840 | − | 1.14807i | ||||
\(563\) | −13.7818 | + | 23.8707i | −0.580833 | + | 1.00603i | 0.414548 | + | 0.910027i | \(0.363940\pi\) |
−0.995381 | + | 0.0960045i | \(0.969394\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.66025 | 0.364018 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.96902 | −0.0826181 | ||||||||
\(569\) | −2.66025 | − | 4.60770i | −0.111524 | − | 0.193165i | 0.804861 | − | 0.593463i | \(-0.202240\pi\) |
−0.916385 | + | 0.400299i | \(0.868906\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.73205 | + | 4.73205i | −0.114333 | + | 0.198030i | −0.917513 | − | 0.397706i | \(-0.869806\pi\) |
0.803180 | + | 0.595736i | \(0.203140\pi\) | |||||||
\(572\) | 10.0382 | − | 17.3867i | 0.419718 | − | 0.726973i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.69615 | − | 6.40192i | −0.154274 | − | 0.267211i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.5617 | 1.18904 | 0.594519 | − | 0.804082i | \(-0.297343\pi\) | ||||
0.594519 | + | 0.804082i | \(0.297343\pi\) | |||||||
\(578\) | −16.2820 | − | 28.2013i | −0.677244 | − | 1.17302i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.66987 | + | 8.08846i | −0.193739 | + | 0.335566i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.14162 | − | 15.8338i | −0.378607 | − | 0.655767i | ||||
\(584\) | 4.39230 | 0.181755 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.1244 | −0.707401 | ||||||||
\(587\) | 11.0041 | + | 19.0597i | 0.454189 | + | 0.786678i | 0.998641 | − | 0.0521138i | \(-0.0165959\pi\) |
−0.544452 | + | 0.838792i | \(0.683263\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.73205 | − | 6.46410i | 0.153776 | − | 0.266349i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.46979 | − | 16.4022i | −0.389206 | − | 0.674124i | ||||
\(593\) | 28.9406 | 1.18845 | 0.594224 | − | 0.804299i | \(-0.297459\pi\) | ||||
0.594224 | + | 0.804299i | \(0.297459\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.69615 | + | 11.5981i | 0.274285 | + | 0.475076i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.57081 | − | 7.91688i | 0.186914 | − | 0.323745i | ||||
\(599\) | 16.8564 | − | 29.1962i | 0.688734 | − | 1.19292i | −0.283514 | − | 0.958968i | \(-0.591500\pi\) |
0.972248 | − | 0.233954i | \(-0.0751666\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.46410 | + | 14.6603i | 0.345258 | + | 0.598004i | 0.985401 | − | 0.170252i | \(-0.0544581\pi\) |
−0.640143 | + | 0.768256i | \(0.721125\pi\) | |||||||
\(602\) | −15.8338 | −0.645335 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −39.1244 | −1.59195 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.36276 | + | 7.55652i | −0.177079 | + | 0.306710i | −0.940879 | − | 0.338743i | \(-0.889998\pi\) |
0.763800 | + | 0.645453i | \(0.223331\pi\) | |||||||
\(608\) | −10.3664 | + | 17.9551i | −0.420412 | + | 0.728174i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.7321 | −0.434172 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.3190 | −0.982236 | −0.491118 | − | 0.871093i | \(-0.663412\pi\) | ||||
−0.491118 | + | 0.871093i | \(0.663412\pi\) | |||||||
\(614\) | −24.9904 | − | 43.2846i | −1.00853 | − | 1.74682i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.09808 | − | 1.90192i | 0.0442428 | − | 0.0766307i | ||||
\(617\) | 6.55343 | − | 11.3509i | 0.263831 | − | 0.456969i | −0.703426 | − | 0.710769i | \(-0.748347\pi\) |
0.967257 | + | 0.253800i | \(0.0816805\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.90192 | − | 17.1506i | −0.397992 | − | 0.689342i | 0.595486 | − | 0.803366i | \(-0.296959\pi\) |
−0.993478 | + | 0.114023i | \(0.963626\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 54.1934 | 2.17296 | ||||||||
\(623\) | −3.31388 | − | 5.73981i | −0.132768 | − | 0.229961i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5.36603 | + | 9.29423i | −0.214470 | + | 0.371472i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.5235 | + | 32.0836i | 0.739167 | + | 1.28028i | ||||
\(629\) | 1.60770 | 0.0641030 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.3205 | −1.32647 | −0.663234 | − | 0.748412i | \(-0.730817\pi\) | ||||
−0.663234 | + | 0.748412i | \(0.730817\pi\) | |||||||
\(632\) | −0.138701 | − | 0.240237i | −0.00551722 | − | 0.00955610i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −33.9545 | + | 58.8109i | −1.34850 | + | 2.33568i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.58871 | + | 13.1440i | 0.300675 | + | 0.520785i | ||||
\(638\) | −59.0924 | −2.33949 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.5263 | − | 21.6962i | −0.494758 | − | 0.856946i | 0.505223 | − | 0.862989i | \(-0.331410\pi\) |
−0.999982 | + | 0.00604207i | \(0.998077\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.6078 | + | 21.8374i | −0.497203 | + | 0.861181i | −0.999995 | − | 0.00322641i | \(-0.998973\pi\) |
0.502792 | + | 0.864408i | \(0.332306\pi\) | |||||||
\(644\) | −1.50000 | + | 2.59808i | −0.0591083 | + | 0.102379i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.00000 | − | 1.73205i | −0.0393445 | − | 0.0681466i | ||||
\(647\) | −12.3861 | −0.486950 | −0.243475 | − | 0.969907i | \(-0.578287\pi\) | ||||
−0.243475 | + | 0.969907i | \(0.578287\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.0000 | 0.471041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.4022 | − | 28.4094i | 0.642358 | − | 1.11260i | ||||
\(653\) | 0.226633 | − | 0.392541i | 0.00886885 | − | 0.0153613i | −0.861557 | − | 0.507661i | \(-0.830510\pi\) |
0.870426 | + | 0.492300i | \(0.163844\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 19.0526 | 0.743877 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.58871 | 0.295839 | ||||||||
\(659\) | 18.1244 | + | 31.3923i | 0.706025 | + | 1.22287i | 0.966320 | + | 0.257342i | \(0.0828466\pi\) |
−0.260296 | + | 0.965529i | \(0.583820\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.3923 | − | 26.6603i | 0.598691 | − | 1.03696i | −0.394323 | − | 0.918972i | \(-0.629021\pi\) |
0.993015 | − | 0.117992i | \(-0.0376457\pi\) | |||||||
\(662\) | 11.9700 | − | 20.7327i | 0.465229 | − | 0.805800i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.69615 | − | 4.66987i | −0.104631 | − | 0.181226i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.4877 | −0.483525 | ||||||||
\(668\) | −14.7291 | − | 25.5116i | −0.569887 | − | 0.987073i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.2224 | − | 43.6865i | 0.973701 | − | 1.68650i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.808643 | + | 1.40061i | 0.0311709 | + | 0.0539896i | 0.881190 | − | 0.472762i | \(-0.156743\pi\) |
−0.850019 | + | 0.526752i | \(0.823410\pi\) | |||||||
\(674\) | −3.46410 | −0.133432 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.1244 | −0.466321 | ||||||||
\(677\) | −16.5409 | − | 28.6496i | −0.635717 | − | 1.10109i | −0.986363 | − | 0.164586i | \(-0.947371\pi\) |
0.350646 | − | 0.936508i | \(-0.385962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.60770 | − | 7.98076i | 0.176827 | − | 0.306274i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.4877 | + | 21.6293i | 0.478178 | + | 0.828229i | ||||
\(683\) | −19.6975 | −0.753702 | −0.376851 | − | 0.926274i | \(-0.622993\pi\) | ||||
−0.376851 | + | 0.926274i | \(0.622993\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.4282 | − | 19.7942i | −0.436331 | − | 0.755747i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20.4046 | − | 35.3417i | 0.777917 | − | 1.34739i | ||||
\(689\) | 4.73205 | − | 8.19615i | 0.180277 | − | 0.312249i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.1244 | − | 17.5359i | −0.385149 | − | 0.667097i | 0.606641 | − | 0.794976i | \(-0.292516\pi\) |
−0.991790 | + | 0.127879i | \(0.959183\pi\) | |||||||
\(692\) | −1.31268 | −0.0499005 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.1244 | −0.725951 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.808643 | + | 1.40061i | −0.0306295 | + | 0.0530519i | ||||
\(698\) | 20.8021 | − | 36.0303i | 0.787370 | − | 1.36377i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.1962 | 0.876107 | 0.438053 | − | 0.898949i | \(-0.355668\pi\) | ||||
0.438053 | + | 0.898949i | \(0.355668\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.5911 | −0.437167 | ||||||||
\(704\) | −13.5622 | − | 23.4904i | −0.511144 | − | 0.885327i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.73205 | − | 15.1244i | 0.328635 | − | 0.569213i | ||||
\(707\) | 1.13681 | − | 1.96902i | 0.0427542 | − | 0.0740525i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.8923 | + | 27.5263i | 0.596848 | + | 1.03377i | 0.993283 | + | 0.115708i | \(0.0369138\pi\) |
−0.396435 | + | 0.918063i | \(0.629753\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.82654 | 0.143406 | ||||||||
\(713\) | 2.63896 | + | 4.57081i | 0.0988298 | + | 0.171178i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 21.2942 | − | 36.8827i | 0.795803 | − | 1.37837i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.46979 | − | 16.4022i | −0.353409 | − | 0.612123i | ||||
\(719\) | −19.6077 | −0.731244 | −0.365622 | − | 0.930763i | \(-0.619144\pi\) | ||||
−0.365622 | + | 0.930763i | \(0.619144\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.19615 | −0.305241 | ||||||||
\(722\) | −11.1428 | − | 19.2999i | −0.414693 | − | 0.718269i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.33013 | + | 12.6962i | −0.272422 | + | 0.471849i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.1607 | − | 24.5271i | −0.525192 | − | 0.909659i | −0.999570 | − | 0.0293377i | \(-0.990660\pi\) |
0.474378 | − | 0.880321i | \(-0.342673\pi\) | |||||||
\(728\) | 1.13681 | 0.0421331 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.73205 | + | 3.00000i | 0.0640622 | + | 0.110959i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.7327 | + | 35.9101i | −0.765781 | + | 1.32637i | 0.174052 | + | 0.984736i | \(0.444314\pi\) |
−0.939833 | + | 0.341635i | \(0.889019\pi\) | |||||||
\(734\) | 23.9545 | − | 41.4904i | 0.884176 | − | 1.53144i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.33013 | − | 12.6962i | −0.270192 | − | 0.467986i | ||||
\(737\) | 24.3190 | 0.895803 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.8564 | −1.68686 | −0.843428 | − | 0.537243i | \(-0.819466\pi\) | ||||
−0.843428 | + | 0.537243i | \(0.819466\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.34607 | + | 5.79555i | −0.122838 | + | 0.212762i | ||||
\(743\) | 12.6586 | − | 21.9253i | 0.464398 | − | 0.804361i | −0.534776 | − | 0.844994i | \(-0.679604\pi\) |
0.999174 | + | 0.0406329i | \(0.0129374\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −62.1051 | −2.27383 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.10583 | 0.113560 | ||||||||
\(749\) | 5.25833 | + | 9.10770i | 0.192135 | + | 0.332788i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.2224 | + | 29.8301i | −0.628455 | + | 1.08852i | 0.359406 | + | 0.933181i | \(0.382979\pi\) |
−0.987862 | + | 0.155336i | \(0.950354\pi\) | |||||||
\(752\) | −9.77938 | + | 16.9384i | −0.356617 | + | 0.617679i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15.2942 | − | 26.4904i | −0.556983 | − | 0.964723i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.34847 | 0.267085 | 0.133542 | − | 0.991043i | \(-0.457365\pi\) | ||||
0.133542 | + | 0.991043i | \(0.457365\pi\) | |||||||
\(758\) | 12.1087 | + | 20.9730i | 0.439810 | + | 0.761772i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.03590 | − | 1.79423i | 0.0375513 | − | 0.0650407i | −0.846639 | − | 0.532168i | \(-0.821378\pi\) |
0.884190 | + | 0.467127i | \(0.154711\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.08913 | + | 3.61849i | 0.0756318 | + | 0.130998i | ||||
\(764\) | −0.588457 | −0.0212896 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −39.5167 | −1.42779 | ||||||||
\(767\) | 3.10583 | + | 5.37945i | 0.112145 | + | 0.194241i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.8205 | − | 23.9378i | 0.498380 | − | 0.863220i | −0.501618 | − | 0.865089i | \(-0.667262\pi\) |
0.999998 | + | 0.00186930i | \(0.000595016\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.9551 | + | 31.0991i | 0.646217 | + | 1.11928i | ||||
\(773\) | 7.72741 | 0.277935 | 0.138968 | − | 0.990297i | \(-0.455622\pi\) | ||||
0.138968 | + | 0.990297i | \(0.455622\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.66025 | + | 4.60770i | 0.0954976 | + | 0.165407i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.3023 | − | 40.3608i | 0.835429 | − | 1.44701i | ||||
\(779\) | 5.83013 | − | 10.0981i | 0.208886 | − | 0.361801i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.00000 | − | 15.5885i | −0.322045 | − | 0.557799i | ||||
\(782\) | 1.41421 | 0.0505722 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 27.6603 | 0.987866 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.15711 | − | 14.1285i | 0.290770 | − | 0.503628i | −0.683222 | − | 0.730210i | \(-0.739422\pi\) |
0.973992 | + | 0.226583i | \(0.0727553\pi\) | |||||||
\(788\) | −18.0430 | + | 31.2514i | −0.642755 | + | 1.11328i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.28719 | −0.0813230 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.1122 | 0.927271 | ||||||||
\(794\) | 28.3923 | + | 49.1769i | 1.00761 | + | 1.74522i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.97372 | + | 6.88269i | −0.140845 | + | 0.243950i | ||||
\(797\) | 7.95404 | − | 13.7768i | 0.281747 | − | 0.487999i | −0.690068 | − | 0.723744i | \(-0.742420\pi\) |
0.971815 | + | 0.235745i | \(0.0757529\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.830127 | − | 1.43782i | −0.0293678 | − | 0.0508665i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −59.7487 | −2.10980 | ||||||||
\(803\) | 20.0764 | + | 34.7733i | 0.708480 | + | 1.22712i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.46410 | + | 11.1962i | −0.227688 | + | 0.394368i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.656339 | + | 1.13681i | 0.0230899 | + | 0.0399929i | ||||
\(809\) | −37.1769 | −1.30707 | −0.653535 | − | 0.756896i | \(-0.726715\pi\) | ||||
−0.653535 | + | 0.756896i | \(0.726715\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.5692 | 1.52992 | 0.764961 | − | 0.644076i | \(-0.222758\pi\) | ||||
0.764961 | + | 0.644076i | \(0.222758\pi\) | |||||||
\(812\) | 5.01910 | + | 8.69333i | 0.176136 | + | 0.305076i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 19.3923 | − | 33.5885i | 0.679700 | − | 1.17727i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.4877 | − | 21.6293i | −0.436889 | − | 0.756714i | ||||
\(818\) | 45.3292 | 1.58490 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.7224 | − | 25.5000i | −0.513816 | − | 0.889956i | −0.999872 | − | 0.0160280i | \(-0.994898\pi\) |
0.486055 | − | 0.873928i | \(-0.338435\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.01669 | + | 1.76097i | −0.0354397 | + | 0.0613834i | −0.883201 | − | 0.468994i | \(-0.844617\pi\) |
0.847762 | + | 0.530378i | \(0.177950\pi\) | |||||||
\(824\) | 2.36603 | − | 4.09808i | 0.0824244 | − | 0.142763i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.19615 | − | 3.80385i | −0.0764139 | − | 0.132353i | ||||
\(827\) | −11.5539 | −0.401770 | −0.200885 | − | 0.979615i | \(-0.564382\pi\) | ||||
−0.200885 | + | 0.979615i | \(0.564382\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.5885 | 1.09711 | 0.548556 | − | 0.836114i | \(-0.315178\pi\) | ||||
0.548556 | + | 0.836114i | \(0.315178\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7.02030 | − | 12.1595i | 0.243385 | − | 0.421555i | ||||
\(833\) | −1.17398 | + | 2.03339i | −0.0406759 | + | 0.0704527i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −22.3923 | −0.774454 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −31.0112 | −1.07126 | ||||||||
\(839\) | 0.633975 | + | 1.09808i | 0.0218872 | + | 0.0379098i | 0.876762 | − | 0.480925i | \(-0.159699\pi\) |
−0.854874 | + | 0.518835i | \(0.826366\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.39230 | + | 11.0718i | −0.220424 | + | 0.381786i | ||||
\(842\) | −12.1087 | + | 20.9730i | −0.417295 | + | 0.722776i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.3660 | + | 19.6865i | 0.391235 | + | 0.677638i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.2141 | 0.350959 | ||||||||
\(848\) | −8.62398 | − | 14.9372i | −0.296149 | − | 0.512945i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.09808 | − | 7.09808i | 0.140480 | − | 0.243319i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.4746 | + | 30.2669i | 0.598319 | + | 1.03632i | 0.993069 | + | 0.117530i | \(0.0374977\pi\) |
−0.394750 | + | 0.918788i | \(0.629169\pi\) | |||||||
\(854\) | −18.4641 | −0.631829 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.07180 | −0.207530 | ||||||||
\(857\) | 4.43211 | + | 7.67664i | 0.151398 | + | 0.262229i | 0.931742 | − | 0.363122i | \(-0.118289\pi\) |
−0.780344 | + | 0.625351i | \(0.784956\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.2224 | − | 19.4378i | 0.382904 | − | 0.663210i | −0.608572 | − | 0.793499i | \(-0.708257\pi\) |
0.991476 | + | 0.130289i | \(0.0415905\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.79555 | + | 10.0382i | 0.197397 | + | 0.341902i | ||||
\(863\) | −13.0697 | −0.444898 | −0.222449 | − | 0.974944i | \(-0.571405\pi\) | ||||
−0.222449 | + | 0.974944i | \(0.571405\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 29.4904 | + | 51.0788i | 1.00212 | + | 1.73573i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.12132 | − | 3.67423i | 0.0720023 | − | 0.124712i | ||||
\(869\) | 1.26795 | − | 2.19615i | 0.0430122 | − | 0.0744994i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.29423 | + | 10.9019i | 0.213272 | + | 0.369398i | ||||
\(872\) | −2.41233 | −0.0816916 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.1962 | −0.344890 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.36156 | − | 4.09034i | 0.0797441 | − | 0.138121i | −0.823395 | − | 0.567468i | \(-0.807923\pi\) |
0.903139 | + | 0.429347i | \(0.141256\pi\) | |||||||
\(878\) | 9.00292 | − | 15.5935i | 0.303834 | − | 0.526256i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.41154 | 0.283392 | 0.141696 | − | 0.989910i | \(-0.454744\pi\) | ||||
0.141696 | + | 0.989910i | \(0.454744\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.6913 | 0.595359 | 0.297679 | − | 0.954666i | \(-0.403787\pi\) | ||||
0.297679 | + | 0.954666i | \(0.403787\pi\) | |||||||
\(884\) | 0.803848 | + | 1.39230i | 0.0270363 | + | 0.0468283i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.4282 | + | 23.2583i | −0.451129 | + | 0.781379i | ||||
\(887\) | −14.0914 | + | 24.4070i | −0.473142 | + | 0.819506i | −0.999527 | − | 0.0307403i | \(-0.990214\pi\) |
0.526386 | + | 0.850246i | \(0.323547\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.08846 | + | 3.61731i | 0.0700446 | + | 0.121321i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −28.9778 | −0.970248 | ||||||||
\(893\) | 5.98502 | + | 10.3664i | 0.200281 | + | 0.346897i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.83975 | − | 3.18653i | 0.0614616 | − | 0.106455i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.5911 | + | 20.0764i | 0.386800 | + | 0.669958i | ||||
\(899\) | 17.6603 | 0.589002 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.46410 | 0.0487763 | ||||||||
\(902\) | 19.5080 | + | 33.7888i | 0.649545 | + | 1.12504i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.660254 | − | 1.14359i | 0.0219597 | − | 0.0380354i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.8553 | + | 43.0506i | 0.825305 | + | 1.42947i | 0.901686 | + | 0.432392i | \(0.142330\pi\) |
−0.0763808 | + | 0.997079i | \(0.524336\pi\) | |||||||
\(908\) | 3.28169 | 0.108907 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.0718 | + | 19.1769i | 0.366825 | + | 0.635360i | 0.989067 | − | 0.147465i | \(-0.0471114\pi\) |
−0.622242 | + | 0.782825i | \(0.713778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.6472 | − | 42.6902i | 0.815703 | − | 1.41284i | ||||
\(914\) | −33.4186 | + | 57.8827i | −1.10539 | + | 1.91459i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.2583 | − | 29.8923i | −0.570231 | − | 0.987670i | ||||
\(917\) | 0.832204 | 0.0274818 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.1769 | −0.500640 | −0.250320 | − | 0.968163i | \(-0.580536\pi\) | ||||
−0.250320 | + | 0.968163i | \(0.580536\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.0752 | + | 31.3071i | −0.595275 | + | 1.03105i | ||||
\(923\) | 4.65874 | − | 8.06918i | 0.153344 | − | 0.265600i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.339746 | −0.0111647 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −49.0542 | −1.61028 | ||||||||
\(929\) | 1.73205 | + | 3.00000i | 0.0568267 | + | 0.0984268i | 0.893039 | − | 0.449979i | \(-0.148568\pi\) |
−0.836213 | + | 0.548405i | \(0.815235\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.46410 | − | 14.6603i | 0.277400 | − | 0.480470i | ||||
\(932\) | −6.12372 | + | 10.6066i | −0.200589 | + | 0.347431i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.56218 | − | 9.63397i | −0.182000 | − | 0.315233i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.8647 | −0.452941 | −0.226471 | − | 0.974018i | \(-0.572719\pi\) | ||||
−0.226471 | + | 0.974018i | \(0.572719\pi\) | |||||||
\(938\) | −4.45069 | − | 7.70882i | −0.145320 | − | 0.251702i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.16025 | + | 7.20577i | −0.135620 | + | 0.234901i | −0.925834 | − | 0.377930i | \(-0.876636\pi\) |
0.790214 | + | 0.612831i | \(0.209969\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.12252 | + | 7.14042i | 0.134248 | + | 0.232524i | ||||
\(944\) | 11.3205 | 0.368451 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 83.5692 | 2.71707 | ||||||||
\(947\) | −1.15539 | − | 2.00120i | −0.0375453 | − | 0.0650303i | 0.846642 | − | 0.532163i | \(-0.178621\pi\) |
−0.884187 | + | 0.467132i | \(0.845287\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.3923 | + | 18.0000i | −0.337348 | + | 0.584305i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.0879327 | + | 0.152304i | 0.00284992 | + | 0.00493620i | ||||
\(953\) | −37.0197 | −1.19919 | −0.599594 | − | 0.800305i | \(-0.704671\pi\) | ||||
−0.599594 | + | 0.800305i | \(0.704671\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.1962 | + | 19.3923i | 0.362109 | + | 0.627192i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −30.7709 | + | 53.2968i | −0.994163 | + | 1.72194i | ||||
\(959\) | −8.32051 | + | 14.4115i | −0.268683 | + | 0.465373i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.7679 | + | 20.3827i | 0.379611 | + | 0.657506i | ||||
\(962\) | 20.0764 | 0.647289 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.8564 | 0.349661 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.3545 | + | 30.0588i | −0.558082 | + | 0.966627i | 0.439574 | + | 0.898206i | \(0.355129\pi\) |
−0.997657 | + | 0.0684208i | \(0.978204\pi\) | |||||||
\(968\) | −2.94855 | + | 5.10703i | −0.0947698 | + | 0.164146i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.8038 | −0.892268 | −0.446134 | − | 0.894966i | \(-0.647200\pi\) | ||||
−0.446134 | + | 0.894966i | \(0.647200\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.17260 | −0.229943 | ||||||||
\(974\) | 1.09808 | + | 1.90192i | 0.0351846 | + | 0.0609416i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 23.7942 | − | 41.2128i | 0.761635 | − | 1.31919i | ||||
\(977\) | 7.77817 | − | 13.4722i | 0.248846 | − | 0.431014i | −0.714360 | − | 0.699778i | \(-0.753282\pi\) |
0.963206 | + | 0.268765i | \(0.0866154\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.4904 | + | 30.2942i | 0.558995 | + | 0.968208i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −41.9459 | −1.33855 | ||||||||
\(983\) | −17.9365 | − | 31.0669i | −0.572085 | − | 0.990881i | −0.996352 | − | 0.0853431i | \(-0.972801\pi\) |
0.424266 | − | 0.905537i | \(-0.360532\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.36603 | − | 4.09808i | 0.0753496 | − | 0.130509i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.79555 | − | 10.0382i | −0.184381 | − | 0.319358i | ||||
\(989\) | 17.6603 | 0.561563 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.0718 | 0.796432 | 0.398216 | − | 0.917292i | \(-0.369629\pi\) | ||||
0.398216 | + | 0.917292i | \(0.369629\pi\) | |||||||
\(992\) | 10.3664 | + | 17.9551i | 0.329132 | + | 0.570074i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.29423 | + | 5.70577i | −0.104487 | + | 0.180976i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.58871 | − | 13.1440i | −0.240337 | − | 0.416275i | 0.720473 | − | 0.693483i | \(-0.243925\pi\) |
−0.960810 | + | 0.277207i | \(0.910591\pi\) | |||||||
\(998\) | 7.45001 | 0.235826 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))