Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(17,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.bt (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.4 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.17 |
Dual form | 1008.2.bt.c.593.4 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.09077 | + | 3.62132i | 0.935021 | + | 1.61950i | 0.774597 | + | 0.632456i | \(0.217953\pi\) |
0.160424 | + | 0.987048i | \(0.448714\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.62132 | + | 2.09077i | 0.612801 | + | 0.790237i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.59808 | + | 1.50000i | 0.783349 | + | 0.452267i | 0.837616 | − | 0.546259i | \(-0.183949\pi\) |
−0.0542666 | + | 0.998526i | \(0.517282\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.44949i | − | 0.679366i | −0.940540 | − | 0.339683i | \(-0.889680\pi\) | ||
0.940540 | − | 0.339683i | \(-0.110320\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.507306 | + | 0.878680i | −0.123040 | + | 0.213111i | −0.920965 | − | 0.389645i | \(-0.872598\pi\) |
0.797925 | + | 0.602756i | \(0.205931\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.878680 | − | 0.507306i | 0.201583 | − | 0.116384i | −0.395811 | − | 0.918332i | \(-0.629536\pi\) |
0.597394 | + | 0.801948i | \(0.296203\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.67423 | − | 2.12132i | 0.766131 | − | 0.442326i | −0.0653618 | − | 0.997862i | \(-0.520820\pi\) |
0.831493 | + | 0.555536i | \(0.187487\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.24264 | + | 10.8126i | −1.24853 | + | 2.16251i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.24264i | − | 0.230753i | −0.993322 | − | 0.115376i | \(-0.963193\pi\) | ||
0.993322 | − | 0.115376i | \(-0.0368074\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.86396 | − | 2.80821i | −0.873593 | − | 0.504369i | −0.00505256 | − | 0.999987i | \(-0.501608\pi\) |
−0.868541 | + | 0.495618i | \(0.834942\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.18154 | + | 10.2426i | −0.706809 | + | 1.73132i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.12132 | − | 7.13834i | −0.677541 | − | 1.17354i | −0.975719 | − | 0.219025i | \(-0.929712\pi\) |
0.298178 | − | 0.954510i | \(-0.403621\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.02922 | 0.316912 | 0.158456 | − | 0.987366i | \(-0.449348\pi\) | ||||
0.158456 | + | 0.987366i | \(0.449348\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.24264 | −1.25699 | −0.628495 | − | 0.777813i | \(-0.716329\pi\) | ||||
−0.628495 | + | 0.777813i | \(0.716329\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.507306 | + | 0.878680i | 0.0739982 | + | 0.128169i | 0.900650 | − | 0.434545i | \(-0.143091\pi\) |
−0.826652 | + | 0.562713i | \(0.809757\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.74264 | + | 6.77962i | −0.248949 | + | 0.968517i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.07616 | + | 0.621320i | 0.147822 | + | 0.0853449i | 0.572087 | − | 0.820193i | \(-0.306134\pi\) |
−0.424265 | + | 0.905538i | \(0.639467\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.5446i | 1.69152i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.76500 | − | 9.98528i | 0.750540 | − | 1.29997i | −0.197022 | − | 0.980399i | \(-0.563127\pi\) |
0.947561 | − | 0.319574i | \(-0.103540\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.12132 | − | 2.95680i | 0.655718 | − | 0.378579i | −0.134926 | − | 0.990856i | \(-0.543080\pi\) |
0.790643 | + | 0.612277i | \(0.209746\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.87039 | − | 5.12132i | 1.10024 | − | 0.635222i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | + | 8.66025i | −0.610847 | + | 1.05802i | 0.380251 | + | 0.924883i | \(0.375838\pi\) |
−0.991098 | + | 0.133135i | \(0.957496\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.2426i | 1.21558i | 0.794099 | + | 0.607789i | \(0.207943\pi\) | ||||
−0.794099 | + | 0.607789i | \(0.792057\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.24264 | + | 4.18154i | 0.847687 | + | 0.489412i | 0.859870 | − | 0.510513i | \(-0.170545\pi\) |
−0.0121828 | + | 0.999926i | \(0.503878\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.07616 | + | 7.86396i | 0.122640 | + | 0.896182i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.62132 | − | 9.73641i | −0.632448 | − | 1.09543i | −0.987050 | − | 0.160415i | \(-0.948717\pi\) |
0.354602 | − | 0.935017i | \(-0.384616\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.16693 | 0.347616 | 0.173808 | − | 0.984780i | \(-0.444393\pi\) | ||||
0.173808 | + | 0.984780i | \(0.444393\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.24264 | −0.460179 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.19615 | + | 9.00000i | 0.550791 | + | 0.953998i | 0.998218 | + | 0.0596775i | \(0.0190072\pi\) |
−0.447427 | + | 0.894321i | \(0.647659\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.12132 | − | 3.97141i | 0.536860 | − | 0.416317i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.67423 | + | 2.12132i | 0.376969 | + | 0.217643i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.76127i | − | 0.381900i | −0.981600 | − | 0.190950i | \(-0.938843\pi\) | ||
0.981600 | − | 0.190950i | \(-0.0611568\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.2426 | − | 7.64564i | 1.30484 | − | 0.753348i | 0.323607 | − | 0.946192i | \(-0.395105\pi\) |
0.981229 | + | 0.192844i | \(0.0617712\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.75039 | + | 2.74264i | −0.459238 | + | 0.265141i | −0.711724 | − | 0.702459i | \(-0.752085\pi\) |
0.252486 | + | 0.967601i | \(0.418752\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.757359 | + | 1.31178i | −0.0725419 | + | 0.125646i | −0.900015 | − | 0.435860i | \(-0.856444\pi\) |
0.827473 | + | 0.561506i | \(0.189778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.48528i | − | 0.798228i | −0.916901 | − | 0.399114i | \(-0.869318\pi\) | ||
0.916901 | − | 0.399114i | \(-0.130682\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.3640 | + | 8.87039i | 1.43270 | + | 0.827168i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.65962 | + | 0.363961i | −0.243807 | + | 0.0333643i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | − | 1.73205i | −0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −31.3000 | −2.79956 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.24264 | 0.465209 | 0.232605 | − | 0.972571i | \(-0.425275\pi\) | ||||
0.232605 | + | 0.972571i | \(0.425275\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.59808 | + | 4.50000i | 0.226995 | + | 0.393167i | 0.956916 | − | 0.290365i | \(-0.0937766\pi\) |
−0.729921 | + | 0.683531i | \(0.760443\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.48528 | + | 1.01461i | 0.215501 | + | 0.0879780i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.5446 | + | 7.24264i | 1.07176 | + | 0.618781i | 0.928662 | − | 0.370928i | \(-0.120960\pi\) |
0.143098 | + | 0.989709i | \(0.454294\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 20.1903i | − | 1.71252i | −0.516549 | − | 0.856258i | \(-0.672783\pi\) | ||
0.516549 | − | 0.856258i | \(-0.327217\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.67423 | − | 6.36396i | 0.307255 | − | 0.532181i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.50000 | − | 2.59808i | 0.373705 | − | 0.215758i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.7408 | + | 10.2426i | −1.45338 | + | 0.839110i | −0.998671 | − | 0.0515300i | \(-0.983590\pi\) |
−0.454709 | + | 0.890640i | \(0.650257\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.62132 | + | 2.80821i | −0.131941 | + | 0.228529i | −0.924425 | − | 0.381364i | \(-0.875454\pi\) |
0.792484 | + | 0.609893i | \(0.208788\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 23.4853i | − | 1.88638i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.7279 | − | 7.34847i | −1.01580 | − | 0.586472i | −0.102915 | − | 0.994690i | \(-0.532817\pi\) |
−0.912884 | + | 0.408219i | \(0.866150\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.3923 | + | 4.24264i | 0.819028 | + | 0.334367i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.12132 | + | 5.40629i | 0.244481 | + | 0.423453i | 0.961985 | − | 0.273101i | \(-0.0880492\pi\) |
−0.717505 | + | 0.696554i | \(0.754716\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.0600 | −1.78444 | −0.892219 | − | 0.451603i | \(-0.850852\pi\) | ||||
−0.892219 | + | 0.451603i | \(0.850852\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.3923 | − | 18.0000i | −0.790112 | − | 1.36851i | −0.925897 | − | 0.377776i | \(-0.876689\pi\) |
0.135785 | − | 0.990738i | \(-0.456644\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −32.7279 | + | 4.47871i | −2.47400 | + | 0.338559i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.23999 | − | 4.75736i | −0.615886 | − | 0.355582i | 0.159380 | − | 0.987217i | \(-0.449051\pi\) |
−0.775265 | + | 0.631636i | \(0.782384\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.02922i | − | 0.150831i | −0.997152 | − | 0.0754155i | \(-0.975972\pi\) | ||
0.997152 | − | 0.0754155i | \(-0.0240283\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.2335 | − | 29.8492i | 1.26703 | − | 2.19456i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.63604 | + | 1.52192i | −0.192766 | + | 0.111294i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.34847 | − | 4.24264i | 0.531717 | − | 0.306987i | −0.209999 | − | 0.977702i | \(-0.567346\pi\) |
0.741715 | + | 0.670715i | \(0.234013\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.74264 | − | 6.48244i | 0.269401 | − | 0.466617i | −0.699306 | − | 0.714822i | \(-0.746508\pi\) |
0.968707 | + | 0.248206i | \(0.0798409\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.51472i | − | 0.677896i | −0.940805 | − | 0.338948i | \(-0.889929\pi\) | ||
0.940805 | − | 0.338948i | \(-0.110071\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.9706 | + | 8.06591i | 0.990347 | + | 0.571777i | 0.905378 | − | 0.424607i | \(-0.139588\pi\) |
0.0849690 | + | 0.996384i | \(0.472921\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.59808 | − | 2.01472i | 0.182349 | − | 0.141406i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.24264 | + | 7.34847i | 0.296319 | + | 0.513239i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.04384 | 0.210547 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.24264 | −0.567447 | −0.283723 | − | 0.958906i | \(-0.591570\pi\) | ||||
−0.283723 | + | 0.958906i | \(0.591570\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.2335 | − | 29.8492i | −1.17531 | − | 2.03570i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.01472 | − | 14.7224i | −0.136768 | − | 0.999424i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.15232 | + | 1.24264i | 0.144780 | + | 0.0835891i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 12.5446i | − | 0.840050i | −0.907513 | − | 0.420025i | \(-0.862021\pi\) | ||
0.907513 | − | 0.420025i | \(-0.137979\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.79423 | + | 13.5000i | −0.517321 | + | 0.896026i | 0.482476 | + | 0.875909i | \(0.339737\pi\) |
−0.999798 | + | 0.0201176i | \(0.993596\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.0000 | + | 6.92820i | −0.792982 | + | 0.457829i | −0.841011 | − | 0.541017i | \(-0.818039\pi\) |
0.0480291 | + | 0.998846i | \(0.484706\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.82655 | + | 3.36396i | −0.381710 | + | 0.220380i | −0.678562 | − | 0.734543i | \(-0.737397\pi\) |
0.296852 | + | 0.954924i | \(0.404063\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.12132 | + | 3.67423i | −0.138380 | + | 0.239681i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.7279i | 0.823301i | 0.911342 | + | 0.411650i | \(0.135048\pi\) | ||||
−0.911342 | + | 0.411650i | \(0.864952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.7426 | + | 8.51167i | 0.949657 | + | 0.548285i | 0.892974 | − | 0.450108i | \(-0.148614\pi\) |
0.0566826 | + | 0.998392i | \(0.481948\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −28.1946 | + | 7.86396i | −1.80129 | + | 0.502410i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.24264 | − | 2.15232i | −0.0790673 | − | 0.136949i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.6177 | 1.11202 | 0.556009 | − | 0.831176i | \(-0.312332\pi\) | ||||
0.556009 | + | 0.831176i | \(0.312332\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.7279 | 0.800198 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.5446 | − | 21.7279i | −0.782512 | − | 1.35535i | −0.930474 | − | 0.366358i | \(-0.880605\pi\) |
0.147962 | − | 0.988993i | \(-0.452729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.24264 | − | 20.1903i | 0.512173 | − | 1.25456i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.5673 | + | 13.6066i | 1.45322 | + | 0.839019i | 0.998663 | − | 0.0516967i | \(-0.0164629\pi\) |
0.454561 | + | 0.890716i | \(0.349796\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.19615i | 0.319197i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.25770 | − | 9.10660i | 0.320568 | − | 0.555239i | −0.660038 | − | 0.751232i | \(-0.729460\pi\) |
0.980605 | + | 0.195993i | \(0.0627930\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.62132 | − | 5.55487i | 0.584454 | − | 0.337434i | −0.178448 | − | 0.983949i | \(-0.557108\pi\) |
0.762901 | + | 0.646515i | \(0.223774\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −32.4377 | + | 18.7279i | −1.95607 | + | 1.12934i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.4853 | − | 18.1610i | 0.630000 | − | 1.09119i | −0.357552 | − | 0.933893i | \(-0.616388\pi\) |
0.987551 | − | 0.157298i | \(-0.0502783\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000i | 0.357930i | 0.983855 | + | 0.178965i | \(0.0572749\pi\) | ||||
−0.983855 | + | 0.178965i | \(0.942725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.63604 | + | 3.25397i | 0.335028 | + | 0.193428i | 0.658071 | − | 0.752956i | \(-0.271373\pi\) |
−0.323043 | + | 0.946384i | \(0.604706\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.29002 | + | 4.24264i | 0.194204 | + | 0.250435i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.98528 | + | 13.8309i | 0.469722 | + | 0.813583i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.18154 | 0.244288 | 0.122144 | − | 0.992512i | \(-0.461023\pi\) | ||||
0.122144 | + | 0.992512i | \(0.461023\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 48.2132 | 2.80708 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.19615 | − | 9.00000i | −0.300501 | − | 0.520483i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.3640 | − | 17.2335i | −0.770286 | − | 0.993321i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.4150 | + | 12.3640i | 1.22622 | + | 0.707958i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.6690i | − | 1.40793i | −0.710233 | − | 0.703966i | \(-0.751411\pi\) | ||
0.710233 | − | 0.703966i | \(-0.248589\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.37769 | − | 16.2426i | 0.531760 | − | 0.921036i | −0.467552 | − | 0.883965i | \(-0.654864\pi\) |
0.999313 | − | 0.0370703i | \(-0.0118026\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.985281 | + | 0.568852i | −0.0556914 | + | 0.0321534i | −0.527587 | − | 0.849501i | \(-0.676903\pi\) |
0.471896 | + | 0.881654i | \(0.343570\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.27231 | + | 3.62132i | −0.352288 | + | 0.203394i | −0.665693 | − | 0.746226i | \(-0.731864\pi\) |
0.313404 | + | 0.949620i | \(0.398530\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.86396 | − | 3.22848i | 0.104362 | − | 0.180760i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.02944i | 0.0572794i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.4853 | + | 15.2913i | 1.46914 | + | 0.848208i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.01461 | + | 2.48528i | −0.0559374 | + | 0.137018i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.72792 | + | 15.1172i | 0.479730 | + | 0.830917i | 0.999730 | − | 0.0232497i | \(-0.00740129\pi\) |
−0.520000 | + | 0.854166i | \(0.674068\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −41.8154 | −2.28462 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.00000 | −0.272367 | −0.136184 | − | 0.990684i | \(-0.543484\pi\) | ||||
−0.136184 | + | 0.990684i | \(0.543484\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.42463 | − | 14.5919i | −0.456219 | − | 0.790195i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.5446 | + | 7.24264i | 0.673431 | + | 0.388805i | 0.797375 | − | 0.603484i | \(-0.206221\pi\) |
−0.123945 | + | 0.992289i | \(0.539555\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 36.9164i | − | 1.97609i | −0.154163 | − | 0.988045i | \(-0.549268\pi\) | ||
0.154163 | − | 0.988045i | \(-0.450732\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.37769 | + | 16.2426i | −0.499124 | + | 0.864509i | −0.999999 | − | 0.00101095i | \(-0.999678\pi\) |
0.500875 | + | 0.865519i | \(0.333012\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −37.0919 | + | 21.4150i | −1.96863 | + | 1.13659i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.5885 | − | 9.00000i | 0.822727 | − | 0.475002i | −0.0286287 | − | 0.999590i | \(-0.509114\pi\) |
0.851356 | + | 0.524588i | \(0.175781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.98528 | + | 15.5630i | −0.472910 | + | 0.819103i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.9706i | 1.83044i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.3492 | − | 9.43924i | −0.853424 | − | 0.492724i | 0.00838099 | − | 0.999965i | \(-0.497332\pi\) |
−0.861804 | + | 0.507241i | \(0.830666\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.445759 | + | 3.25736i | 0.0231427 | + | 0.169114i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.7279 | − | 18.5813i | −0.555471 | − | 0.962104i | −0.997867 | − | 0.0652837i | \(-0.979205\pi\) |
0.442396 | − | 0.896820i | \(-0.354129\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.04384 | −0.156766 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.48528 | 0.230393 | 0.115197 | − | 0.993343i | \(-0.463250\pi\) | ||||
0.115197 | + | 0.993343i | \(0.463250\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.21076 | + | 10.7574i | 0.317355 | + | 0.549675i | 0.979935 | − | 0.199316i | \(-0.0638719\pi\) |
−0.662580 | + | 0.748991i | \(0.730539\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.2279 | + | 20.3389i | −1.33670 | + | 1.03656i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.8493 | + | 9.72792i | 0.854291 | + | 0.493225i | 0.862096 | − | 0.506744i | \(-0.169151\pi\) |
−0.00780525 | + | 0.999970i | \(0.502485\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.30463i | 0.217695i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 23.5058 | − | 40.7132i | 1.18270 | − | 2.04850i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.0000 | − | 6.92820i | 0.602263 | − | 0.347717i | −0.167668 | − | 0.985843i | \(-0.553624\pi\) |
0.769931 | + | 0.638127i | \(0.220290\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.87868 | + | 11.9142i | −0.342651 | + | 0.593490i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 24.7279i | − | 1.22572i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.98528 | − | 2.30090i | −0.197059 | − | 0.113772i | 0.398224 | − | 0.917288i | \(-0.369627\pi\) |
−0.595283 | + | 0.803516i | \(0.702960\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 30.2238 | − | 4.13604i | 1.48722 | − | 0.203521i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.62132 | + | 11.4685i | 0.325028 | + | 0.562965i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.05845 | −0.198268 | −0.0991341 | − | 0.995074i | \(-0.531607\pi\) | ||||
−0.0991341 | + | 0.995074i | \(0.531607\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.75736 | −0.280597 | −0.140298 | − | 0.990109i | \(-0.544806\pi\) | ||||
−0.140298 | + | 0.990109i | \(0.544806\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.33386 | − | 10.9706i | −0.307237 | − | 0.532150i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.4853 | + | 5.91359i | 0.700992 | + | 0.286179i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.7408 | + | 10.2426i | 0.854543 | + | 0.493371i | 0.862181 | − | 0.506600i | \(-0.169098\pi\) |
−0.00763808 | + | 0.999971i | \(0.502431\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.46410i | 0.166474i | 0.996530 | + | 0.0832370i | \(0.0265259\pi\) | ||||
−0.996530 | + | 0.0832370i | \(0.973474\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.15232 | − | 3.72792i | 0.102959 | − | 0.178331i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.5919 | + | 13.6208i | −1.12598 | + | 0.650084i | −0.942921 | − | 0.333018i | \(-0.891933\pi\) |
−0.183059 | + | 0.983102i | \(0.558600\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.8396 | + | 17.2279i | −1.41772 | + | 0.818523i | −0.996099 | − | 0.0882469i | \(-0.971874\pi\) |
−0.421625 | + | 0.906770i | \(0.638540\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.7279 | + | 37.6339i | −1.03000 | + | 1.78402i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 10.2426i | − | 0.483380i | −0.970354 | − | 0.241690i | \(-0.922298\pi\) | ||
0.970354 | − | 0.241690i | \(-0.0777017\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.27208 | + | 3.04384i | 0.248252 | + | 0.143329i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25.0892 | + | 10.2426i | 1.17620 | + | 0.480182i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.5000 | + | 19.9186i | 0.537947 | + | 0.931752i | 0.999014 | + | 0.0443868i | \(0.0141334\pi\) |
−0.461067 | + | 0.887365i | \(0.652533\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.8138 | 1.06255 | 0.531273 | − | 0.847201i | \(-0.321714\pi\) | ||||
0.531273 | + | 0.847201i | \(0.321714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.4558 | −0.997138 | −0.498569 | − | 0.866850i | \(-0.666141\pi\) | ||||
−0.498569 | + | 0.866850i | \(0.666141\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.50079 | + | 16.4558i | 0.439644 | + | 0.761486i | 0.997662 | − | 0.0683432i | \(-0.0217713\pi\) |
−0.558018 | + | 0.829829i | \(0.688438\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.2132 | + | 3.58719i | −1.21041 | + | 0.165641i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.4150 | − | 12.3640i | −0.984663 | − | 0.568496i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.6677i | 0.581235i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.2481 | + | 31.6066i | −0.833776 | + | 1.44414i | 0.0612470 | + | 0.998123i | \(0.480492\pi\) |
−0.895023 | + | 0.446020i | \(0.852841\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.4853 | + | 10.0951i | −0.797260 | + | 0.460298i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.6208 | − | 7.86396i | 0.618488 | − | 0.357084i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.1066 | − | 24.4334i | 0.639231 | − | 1.10718i | −0.346371 | − | 0.938098i | \(-0.612586\pi\) |
0.985602 | − | 0.169083i | \(-0.0540806\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19.9706i | − | 0.901259i | −0.892711 | − | 0.450629i | \(-0.851200\pi\) | ||
0.892711 | − | 0.450629i | \(-0.148800\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.09188 | + | 0.630399i | 0.0491759 | + | 0.0283917i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.4150 | + | 16.6066i | −0.960594 | + | 0.744908i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.9706 | − | 31.1259i | −0.804473 | − | 1.39339i | −0.916646 | − | 0.399699i | \(-0.869115\pi\) |
0.112173 | − | 0.993689i | \(-0.464219\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.29002 | −0.146695 | −0.0733474 | − | 0.997306i | \(-0.523368\pi\) | ||||
−0.0733474 | + | 0.997306i | \(0.523368\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.8462 | + | 36.1066i | 0.923990 | + | 1.60040i | 0.793178 | + | 0.608990i | \(0.208425\pi\) |
0.130812 | + | 0.991407i | \(0.458242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.00000 | + | 21.9223i | 0.132712 | + | 0.969786i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 55.3746 | + | 31.9706i | 2.44010 | + | 1.40879i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.04384i | 0.133868i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.0081 | − | 17.3345i | 0.438462 | − | 0.759439i | −0.559109 | − | 0.829094i | \(-0.688857\pi\) |
0.997571 | + | 0.0696551i | \(0.0221899\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.8492 | − | 13.7694i | 1.04285 | − | 0.602092i | 0.122214 | − | 0.992504i | \(-0.461001\pi\) |
0.920641 | + | 0.390411i | \(0.127667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.93503 | − | 2.84924i | 0.214973 | − | 0.124115i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.50000 | + | 4.33013i | −0.108696 | + | 0.188266i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4.97056i | − | 0.215299i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.8640 | − | 11.4685i | −0.858794 | − | 0.495825i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14.6969 | + | 15.0000i | −0.633042 | + | 0.646096i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.36396 | + | 9.29065i | 0.230615 | + | 0.399436i | 0.957989 | − | 0.286804i | \(-0.0925930\pi\) |
−0.727374 | + | 0.686241i | \(0.759260\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.33386 | −0.271313 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.6985 | −0.842246 | −0.421123 | − | 0.907003i | \(-0.638364\pi\) | ||||
−0.421123 | + | 0.907003i | \(0.638364\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.630399 | − | 1.09188i | −0.0268559 | − | 0.0465158i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.2426 | − | 27.5387i | 0.478086 | − | 1.17107i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.6208 | − | 7.86396i | −0.577131 | − | 0.333207i | 0.182861 | − | 0.983139i | \(-0.441464\pi\) |
−0.759992 | + | 0.649932i | \(0.774797\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.1903i | 0.853957i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.0989 | − | 20.9558i | 0.509906 | − | 0.883184i | −0.490028 | − | 0.871707i | \(-0.663013\pi\) |
0.999934 | − | 0.0114768i | \(-0.00365325\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.7279 | − | 17.7408i | 1.29273 | − | 0.746360i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.52192 | + | 0.878680i | −0.0638021 | + | 0.0368362i | −0.531562 | − | 0.847020i | \(-0.678395\pi\) |
0.467760 | + | 0.883856i | \(0.345061\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.36396 | + | 14.4868i | −0.350021 | + | 0.606254i | −0.986253 | − | 0.165244i | \(-0.947159\pi\) |
0.636232 | + | 0.771498i | \(0.280492\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 52.9706i | 2.20903i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.7426 | + | 10.2437i | 0.738636 | + | 0.426452i | 0.821573 | − | 0.570103i | \(-0.193097\pi\) |
−0.0829373 | + | 0.996555i | \(0.526430\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.13461 | + | 6.62132i | 0.213019 | + | 0.274699i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.86396 | + | 3.22848i | 0.0771974 | + | 0.133710i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.19615 | −0.214468 | −0.107234 | − | 0.994234i | \(-0.534199\pi\) | ||||
−0.107234 | + | 0.994234i | \(0.534199\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.69848 | −0.234802 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.2042 | + | 26.3345i | 0.624363 | + | 1.08143i | 0.988664 | + | 0.150148i | \(0.0479749\pi\) |
−0.364300 | + | 0.931282i | \(0.618692\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.87868 | − | 8.87039i | −0.281998 | − | 0.363650i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.6339 | − | 21.7279i | −1.53768 | − | 0.887779i | −0.998974 | − | 0.0452836i | \(-0.985581\pi\) |
−0.538704 | − | 0.842495i | \(-0.681086\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.03668i | 0.246241i | 0.992392 | + | 0.123121i | \(0.0392902\pi\) | ||||
−0.992392 | + | 0.123121i | \(0.960710\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.18154 | − | 7.24264i | 0.170004 | − | 0.294455i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.6213 | − | 12.4831i | 0.877582 | − | 0.506672i | 0.00772182 | − | 0.999970i | \(-0.497542\pi\) |
0.869860 | + | 0.493298i | \(0.164209\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.15232 | − | 1.24264i | 0.0870734 | − | 0.0502719i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.60660 | + | 4.51477i | −0.105280 | + | 0.182350i | −0.913852 | − | 0.406046i | \(-0.866907\pi\) |
0.808573 | + | 0.588396i | \(0.200240\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.6985i | 1.67872i | 0.543578 | + | 0.839359i | \(0.317069\pi\) | ||||
−0.543578 | + | 0.839359i | \(0.682931\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.3345 | + | 23.8645i | 1.66137 | + | 0.959195i | 0.972060 | + | 0.234733i | \(0.0754217\pi\) |
0.689315 | + | 0.724462i | \(0.257912\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.3923 | + | 25.4558i | −0.416359 | + | 1.01987i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −34.2279 | − | 59.2845i | −1.36912 | − | 2.37138i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.36308 | 0.333458 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.2426 | −1.32337 | −0.661684 | − | 0.749783i | \(-0.730158\pi\) | ||||
−0.661684 | + | 0.749783i | \(0.730158\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.9612 | + | 18.9853i | 0.434980 | + | 0.753408i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.6066 | + | 4.26858i | 0.657978 | + | 0.169127i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.1119 | + | 20.8492i | 1.42634 | + | 0.823496i | 0.996829 | − | 0.0795681i | \(-0.0253541\pi\) |
0.429507 | + | 0.903064i | \(0.358687\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.62357i | 0.103463i | 0.998661 | + | 0.0517317i | \(0.0164741\pi\) | ||||
−0.998661 | + | 0.0517317i | \(0.983526\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.82655 | + | 10.0919i | −0.229065 | + | 0.396753i | −0.957531 | − | 0.288329i | \(-0.906900\pi\) |
0.728466 | + | 0.685082i | \(0.240234\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.9558 | − | 17.2950i | 1.17587 | − | 0.678889i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.31615 | − | 5.37868i | 0.364569 | − | 0.210484i | −0.306514 | − | 0.951866i | \(-0.599163\pi\) |
0.671083 | + | 0.741382i | \(0.265829\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.8640 | + | 18.8169i | −0.424490 | + | 0.735238i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 6.00000i | − | 0.233727i | −0.993148 | − | 0.116863i | \(-0.962716\pi\) | ||
0.993148 | − | 0.116863i | \(-0.0372840\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.1213 | + | 20.2773i | 1.36606 | + | 0.788696i | 0.990422 | − | 0.138071i | \(-0.0440901\pi\) |
0.375639 | + | 0.926766i | \(0.377423\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.52192 | + | 11.1213i | 0.0590174 | + | 0.431266i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.63604 | − | 4.56575i | −0.102068 | − | 0.176787i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.7408 | 0.684875 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.9706 | −0.615620 | −0.307810 | − | 0.951448i | \(-0.599596\pi\) | ||||
−0.307810 | + | 0.951448i | \(0.599596\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.27231 | − | 10.8640i | −0.241064 | − | 0.417536i | 0.719953 | − | 0.694023i | \(-0.244163\pi\) |
−0.961018 | + | 0.276487i | \(0.910830\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.86396 | − | 6.09823i | 0.301791 | − | 0.234029i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.4912 | − | 12.9853i | −0.860601 | − | 0.496868i | 0.00361277 | − | 0.999993i | \(-0.498850\pi\) |
−0.864213 | + | 0.503125i | \(0.832183\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 60.5708i | 2.31429i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.52192 | − | 2.63604i | 0.0579805 | − | 0.100425i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.727922 | − | 0.420266i | 0.0276915 | − | 0.0159877i | −0.486090 | − | 0.873909i | \(-0.661577\pi\) |
0.513782 | + | 0.857921i | \(0.328244\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 73.1154 | − | 42.2132i | 2.77343 | − | 1.60124i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.02944 | + | 1.78304i | −0.0389927 | + | 0.0675374i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 38.6985i | − | 1.46162i | −0.682580 | − | 0.730811i | \(-0.739142\pi\) | ||
0.682580 | − | 0.730811i | \(-0.260858\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.24264 | − | 4.18154i | −0.273161 | − | 0.157710i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.48528 | + | 6.03668i | 0.130892 | + | 0.226712i | 0.924021 | − | 0.382342i | \(-0.124882\pi\) |
−0.793128 | + | 0.609055i | \(0.791549\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −23.8284 | −0.892382 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30.7279 | 1.14916 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.5300 | − | 19.9706i | −0.429997 | − | 0.744776i | 0.566876 | − | 0.823803i | \(-0.308152\pi\) |
−0.996872 | + | 0.0790270i | \(0.974819\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.4558 | + | 15.2913i | 1.39493 | + | 0.569477i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.4361 | + | 7.75736i | 0.499006 | + | 0.288101i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 26.4010i | − | 0.979160i | −0.871958 | − | 0.489580i | \(-0.837150\pi\) | ||
0.871958 | − | 0.489580i | \(-0.162850\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.18154 | − | 7.24264i | 0.154660 | − | 0.267879i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.0919 | + | 19.6830i | −1.25921 | + | 0.727007i | −0.972921 | − | 0.231136i | \(-0.925756\pi\) |
−0.286291 | + | 0.958143i | \(0.592422\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.9808 | + | 15.0000i | −0.957014 | + | 0.552532i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.7279 | + | 30.7057i | −0.652132 | + | 1.12953i | 0.330472 | + | 0.943816i | \(0.392792\pi\) |
−0.982605 | + | 0.185710i | \(0.940541\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 21.5147i | − | 0.789298i | −0.918832 | − | 0.394649i | \(-0.870866\pi\) | ||
0.918832 | − | 0.394649i | \(-0.129134\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −74.1838 | − | 42.8300i | −2.71788 | − | 1.56917i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.4361 | − | 5.48528i | −0.490946 | − | 0.200428i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.3787 | + | 23.1726i | 0.488195 | + | 0.845578i | 0.999908 | − | 0.0135781i | \(-0.00432217\pi\) |
−0.511713 | + | 0.859157i | \(0.670989\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.5592 | −0.493471 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.2426 | −1.53533 | −0.767667 | − | 0.640848i | \(-0.778583\pi\) | ||||
−0.767667 | + | 0.640848i | \(0.778583\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.53653 | − | 4.39340i | −0.0919491 | − | 0.159261i | 0.816382 | − | 0.577512i | \(-0.195976\pi\) |
−0.908331 | + | 0.418252i | \(0.862643\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.97056 | + | 0.543359i | −0.143744 | + | 0.0196709i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.4588 | − | 14.1213i | −0.883158 | − | 0.509891i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 49.0408i | − | 1.76846i | −0.467056 | − | 0.884228i | \(-0.654685\pi\) | ||
0.467056 | − | 0.884228i | \(-0.345315\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.5300 | + | 19.9706i | −0.414706 | + | 0.718291i | −0.995398 | − | 0.0958322i | \(-0.969449\pi\) |
0.580692 | + | 0.814123i | \(0.302782\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 60.7279 | − | 35.0613i | 2.18141 | − | 1.25944i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.78304 | − | 1.02944i | 0.0638840 | − | 0.0368834i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.3640 | + | 26.6112i | −0.549766 | + | 0.952222i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 61.4558i | − | 2.19345i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.1213 | − | 18.5453i | −1.14500 | − | 0.661067i | −0.197337 | − | 0.980336i | \(-0.563229\pi\) |
−0.947664 | + | 0.319269i | \(0.896563\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.7408 | − | 13.7574i | 0.630789 | − | 0.489155i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.24264 | − | 12.5446i | −0.257194 | − | 0.445473i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.6339 | −1.33306 | −0.666530 | − | 0.745478i | \(-0.732221\pi\) | ||||
−0.666530 | + | 0.745478i | \(0.732221\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.02944 | −0.0364189 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.5446 | + | 21.7279i | 0.442690 | + | 0.766762i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.36396 | + | 46.5043i | 0.224300 | + | 1.63906i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.4815 | − | 20.4853i | −1.24746 | − | 0.720224i | −0.276862 | − | 0.960910i | \(-0.589294\pi\) |
−0.970603 | + | 0.240686i | \(0.922628\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.1769i | 1.09477i | 0.836881 | + | 0.547385i | \(0.184377\pi\) | ||||
−0.836881 | + | 0.547385i | \(0.815623\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.0519 | + | 22.6066i | −0.457189 | + | 0.791875i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.24264 | + | 4.18154i | −0.253388 | + | 0.146294i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.6454 | − | 24.6213i | 1.48833 | − | 0.859290i | 0.488423 | − | 0.872607i | \(-0.337572\pi\) |
0.999911 | + | 0.0133172i | \(0.00423912\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.9706 | + | 32.8580i | −0.661272 | + | 1.14536i | 0.319009 | + | 0.947752i | \(0.396650\pi\) |
−0.980282 | + | 0.197606i | \(0.936683\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 4.02944i | − | 0.140117i | −0.997543 | − | 0.0700586i | \(-0.977681\pi\) | ||
0.997543 | − | 0.0700586i | \(-0.0223186\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.3345 | − | 20.4004i | −1.22722 | − | 0.708535i | −0.260772 | − | 0.965401i | \(-0.583977\pi\) |
−0.966447 | + | 0.256865i | \(0.917310\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.07306 | − | 4.97056i | −0.175771 | − | 0.172220i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −48.2132 | − | 83.5077i | −1.66849 | − | 2.88990i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.0746 | 0.831149 | 0.415574 | − | 0.909559i | \(-0.363581\pi\) | ||||
0.415574 | + | 0.909559i | \(0.363581\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.4558 | 0.946753 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.6354 | + | 25.3492i | 0.503473 | + | 0.872040i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00000 | − | 4.89898i | 0.0687208 | − | 0.168331i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.2854 | − | 17.4853i | −1.03817 | − | 0.599388i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.27541i | 0.0779085i | 0.999241 | + | 0.0389543i | \(0.0124027\pi\) | ||||
−0.999241 | + | 0.0389543i | \(0.987597\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.0081 | + | 17.3345i | −0.341870 | + | 0.592136i | −0.984780 | − | 0.173806i | \(-0.944394\pi\) |
0.642910 | + | 0.765942i | \(0.277727\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.87868 | + | 2.23936i | −0.132339 | + | 0.0764059i | −0.564708 | − | 0.825291i | \(-0.691011\pi\) |
0.432369 | + | 0.901697i | \(0.357678\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.7215 | + | 25.2426i | −1.48830 | + | 0.859269i | −0.999911 | − | 0.0133573i | \(-0.995748\pi\) |
−0.488388 | + | 0.872627i | \(0.662415\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 43.4558 | − | 75.2677i | 1.47754 | − | 2.55918i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 33.7279i | − | 1.14414i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.2132 | + | 12.2474i | 0.718782 | + | 0.414989i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −50.7473 | − | 65.4411i | −1.71557 | − | 2.21231i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.24264 | + | 10.8126i | 0.210799 | + | 0.365115i | 0.951965 | − | 0.306207i | \(-0.0990601\pi\) |
−0.741166 | + | 0.671322i | \(0.765727\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.7862 | −1.34043 | −0.670215 | − | 0.742167i | \(-0.733798\pi\) | ||||
−0.670215 | + | 0.742167i | \(0.733798\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.45584 | 0.318214 | 0.159107 | − | 0.987261i | \(-0.449138\pi\) | ||||
0.159107 | + | 0.987261i | \(0.449138\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.4296 | − | 38.8492i | −0.753113 | − | 1.30443i | −0.946307 | − | 0.323269i | \(-0.895218\pi\) |
0.193194 | − | 0.981161i | \(-0.438115\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.50000 | + | 10.9612i | 0.285081 | + | 0.367625i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.891519 | + | 0.514719i | 0.0298335 | + | 0.0172244i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 39.7862i | − | 1.32991i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.48960 | + | 6.04416i | −0.116385 | + | 0.201584i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.09188 | + | 0.630399i | −0.0363759 | + | 0.0210016i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.34847 | − | 4.24264i | 0.244271 | − | 0.141030i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.8492 | − | 23.9876i | 0.459857 | − | 0.796495i | −0.539096 | − | 0.842244i | \(-0.681234\pi\) |
0.998953 | + | 0.0457492i | \(0.0145675\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 18.7279i | − | 0.620484i | −0.950658 | − | 0.310242i | \(-0.899590\pi\) | ||
0.950658 | − | 0.310242i | \(-0.100410\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.22792 | + | 4.75039i | 0.272304 | + | 0.157215i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.19615 | + | 12.7279i | −0.171592 | + | 0.420313i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.75736 | + | 16.9002i | 0.321866 | + | 0.557488i | 0.980873 | − | 0.194649i | \(-0.0623567\pi\) |
−0.659007 | + | 0.752136i | \(0.729023\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.0892 | 0.825823 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 102.912 | 3.38372 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.64501 | + | 2.84924i | 0.0539711 | + | 0.0934806i | 0.891749 | − | 0.452531i | \(-0.149479\pi\) |
−0.837778 | + | 0.546012i | \(0.816145\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.90812 | + | 6.84116i | 0.0625360 | + | 0.224210i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.0227 | − | 6.36396i | −0.360481 | − | 0.208124i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 4.00746i | − | 0.130918i | −0.997855 | − | 0.0654590i | \(-0.979149\pi\) | ||
0.997855 | − | 0.0654590i | \(-0.0208512\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.0423 | − | 45.1066i | 0.848955 | − | 1.47043i | −0.0331867 | − | 0.999449i | \(-0.510566\pi\) |
0.882142 | − | 0.470984i | \(-0.156101\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.45584 | − | 4.30463i | 0.242796 | − | 0.140178i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.8931 | + | 11.4853i | −0.646439 | + | 0.373221i | −0.787090 | − | 0.616838i | \(-0.788414\pi\) |
0.140652 | + | 0.990059i | \(0.455080\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.2426 | − | 17.7408i | 0.332490 | − | 0.575890i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.6985i | 1.35075i | 0.737476 | + | 0.675373i | \(0.236017\pi\) | ||||
−0.737476 | + | 0.675373i | \(0.763983\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.7279 | + | 17.7408i | 0.994332 | + | 0.574078i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.19615 | + | 37.9706i | 0.167793 | + | 1.22613i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.272078 | + | 0.471253i | 0.00877671 | + | 0.0152017i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31.3000 | 1.00758 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.2721 | −0.716222 | −0.358111 | − | 0.933679i | \(-0.616579\pi\) | ||||
−0.358111 | + | 0.933679i | \(0.616579\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.6581 | + | 44.4411i | 0.823407 | + | 1.42618i | 0.903130 | + | 0.429367i | \(0.141263\pi\) |
−0.0797229 | + | 0.996817i | \(0.525404\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.2132 | − | 32.7349i | 1.35329 | − | 1.04943i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.5027 | − | 15.8787i | −0.879889 | − | 0.508004i | −0.00926698 | − | 0.999957i | \(-0.502950\pi\) |
−0.870622 | + | 0.491953i | \(0.836283\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.1769i | 0.996419i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.05845 | − | 7.02944i | 0.129444 | − | 0.224204i | −0.794017 | − | 0.607895i | \(-0.792014\pi\) |
0.923461 | + | 0.383691i | \(0.125347\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.4558 | − | 19.8931i | 1.09785 | − | 0.633847i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30.2854 | + | 17.4853i | −0.963020 | + | 0.556000i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.89340 | − | 8.47561i | 0.155444 | − | 0.269237i | −0.777777 | − | 0.628541i | \(-0.783653\pi\) |
0.933221 | + | 0.359304i | \(0.116986\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 67.4558i | 2.13849i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.27208 | − | 4.77589i | −0.261979 | − | 0.151254i | 0.363258 | − | 0.931689i | \(-0.381664\pi\) |
−0.625237 | + | 0.780435i | \(0.714998\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))